Properties

Label 6040.2.a.l.1.2
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.2
Root \(2.02556\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.75822 q^{3}\) \(+1.00000 q^{5}\) \(+1.53187 q^{7}\) \(+0.0913304 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.75822 q^{3}\) \(+1.00000 q^{5}\) \(+1.53187 q^{7}\) \(+0.0913304 q^{9}\) \(-5.86599 q^{11}\) \(+0.896819 q^{13}\) \(-1.75822 q^{15}\) \(-5.84925 q^{17}\) \(+3.50732 q^{19}\) \(-2.69336 q^{21}\) \(+2.74263 q^{23}\) \(+1.00000 q^{25}\) \(+5.11408 q^{27}\) \(+2.53080 q^{29}\) \(+5.38052 q^{31}\) \(+10.3137 q^{33}\) \(+1.53187 q^{35}\) \(+1.58441 q^{37}\) \(-1.57680 q^{39}\) \(+1.42627 q^{41}\) \(+8.60118 q^{43}\) \(+0.0913304 q^{45}\) \(+1.37054 q^{47}\) \(-4.65338 q^{49}\) \(+10.2843 q^{51}\) \(-10.7071 q^{53}\) \(-5.86599 q^{55}\) \(-6.16663 q^{57}\) \(-0.677690 q^{59}\) \(+8.86107 q^{61}\) \(+0.139906 q^{63}\) \(+0.896819 q^{65}\) \(-9.39938 q^{67}\) \(-4.82215 q^{69}\) \(-4.08725 q^{71}\) \(-4.48639 q^{73}\) \(-1.75822 q^{75}\) \(-8.98591 q^{77}\) \(+6.93088 q^{79}\) \(-9.26565 q^{81}\) \(-5.69567 q^{83}\) \(-5.84925 q^{85}\) \(-4.44971 q^{87}\) \(-3.48085 q^{89}\) \(+1.37381 q^{91}\) \(-9.46012 q^{93}\) \(+3.50732 q^{95}\) \(-10.1605 q^{97}\) \(-0.535743 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.75822 −1.01511 −0.507554 0.861620i \(-0.669450\pi\)
−0.507554 + 0.861620i \(0.669450\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.53187 0.578991 0.289496 0.957179i \(-0.406512\pi\)
0.289496 + 0.957179i \(0.406512\pi\)
\(8\) 0 0
\(9\) 0.0913304 0.0304435
\(10\) 0 0
\(11\) −5.86599 −1.76866 −0.884331 0.466860i \(-0.845385\pi\)
−0.884331 + 0.466860i \(0.845385\pi\)
\(12\) 0 0
\(13\) 0.896819 0.248733 0.124366 0.992236i \(-0.460310\pi\)
0.124366 + 0.992236i \(0.460310\pi\)
\(14\) 0 0
\(15\) −1.75822 −0.453970
\(16\) 0 0
\(17\) −5.84925 −1.41865 −0.709326 0.704880i \(-0.751001\pi\)
−0.709326 + 0.704880i \(0.751001\pi\)
\(18\) 0 0
\(19\) 3.50732 0.804634 0.402317 0.915500i \(-0.368205\pi\)
0.402317 + 0.915500i \(0.368205\pi\)
\(20\) 0 0
\(21\) −2.69336 −0.587738
\(22\) 0 0
\(23\) 2.74263 0.571879 0.285939 0.958248i \(-0.407694\pi\)
0.285939 + 0.958248i \(0.407694\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.11408 0.984204
\(28\) 0 0
\(29\) 2.53080 0.469959 0.234979 0.972000i \(-0.424498\pi\)
0.234979 + 0.972000i \(0.424498\pi\)
\(30\) 0 0
\(31\) 5.38052 0.966369 0.483185 0.875519i \(-0.339480\pi\)
0.483185 + 0.875519i \(0.339480\pi\)
\(32\) 0 0
\(33\) 10.3137 1.79538
\(34\) 0 0
\(35\) 1.53187 0.258933
\(36\) 0 0
\(37\) 1.58441 0.260476 0.130238 0.991483i \(-0.458426\pi\)
0.130238 + 0.991483i \(0.458426\pi\)
\(38\) 0 0
\(39\) −1.57680 −0.252491
\(40\) 0 0
\(41\) 1.42627 0.222746 0.111373 0.993779i \(-0.464475\pi\)
0.111373 + 0.993779i \(0.464475\pi\)
\(42\) 0 0
\(43\) 8.60118 1.31167 0.655833 0.754906i \(-0.272317\pi\)
0.655833 + 0.754906i \(0.272317\pi\)
\(44\) 0 0
\(45\) 0.0913304 0.0136147
\(46\) 0 0
\(47\) 1.37054 0.199913 0.0999567 0.994992i \(-0.468130\pi\)
0.0999567 + 0.994992i \(0.468130\pi\)
\(48\) 0 0
\(49\) −4.65338 −0.664769
\(50\) 0 0
\(51\) 10.2843 1.44008
\(52\) 0 0
\(53\) −10.7071 −1.47074 −0.735369 0.677667i \(-0.762991\pi\)
−0.735369 + 0.677667i \(0.762991\pi\)
\(54\) 0 0
\(55\) −5.86599 −0.790970
\(56\) 0 0
\(57\) −6.16663 −0.816790
\(58\) 0 0
\(59\) −0.677690 −0.0882278 −0.0441139 0.999027i \(-0.514046\pi\)
−0.0441139 + 0.999027i \(0.514046\pi\)
\(60\) 0 0
\(61\) 8.86107 1.13454 0.567272 0.823531i \(-0.307999\pi\)
0.567272 + 0.823531i \(0.307999\pi\)
\(62\) 0 0
\(63\) 0.139906 0.0176265
\(64\) 0 0
\(65\) 0.896819 0.111237
\(66\) 0 0
\(67\) −9.39938 −1.14832 −0.574158 0.818744i \(-0.694671\pi\)
−0.574158 + 0.818744i \(0.694671\pi\)
\(68\) 0 0
\(69\) −4.82215 −0.580519
\(70\) 0 0
\(71\) −4.08725 −0.485067 −0.242533 0.970143i \(-0.577978\pi\)
−0.242533 + 0.970143i \(0.577978\pi\)
\(72\) 0 0
\(73\) −4.48639 −0.525093 −0.262546 0.964919i \(-0.584562\pi\)
−0.262546 + 0.964919i \(0.584562\pi\)
\(74\) 0 0
\(75\) −1.75822 −0.203022
\(76\) 0 0
\(77\) −8.98591 −1.02404
\(78\) 0 0
\(79\) 6.93088 0.779785 0.389892 0.920860i \(-0.372512\pi\)
0.389892 + 0.920860i \(0.372512\pi\)
\(80\) 0 0
\(81\) −9.26565 −1.02952
\(82\) 0 0
\(83\) −5.69567 −0.625181 −0.312590 0.949888i \(-0.601197\pi\)
−0.312590 + 0.949888i \(0.601197\pi\)
\(84\) 0 0
\(85\) −5.84925 −0.634441
\(86\) 0 0
\(87\) −4.44971 −0.477059
\(88\) 0 0
\(89\) −3.48085 −0.368969 −0.184485 0.982835i \(-0.559062\pi\)
−0.184485 + 0.982835i \(0.559062\pi\)
\(90\) 0 0
\(91\) 1.37381 0.144014
\(92\) 0 0
\(93\) −9.46012 −0.980969
\(94\) 0 0
\(95\) 3.50732 0.359843
\(96\) 0 0
\(97\) −10.1605 −1.03164 −0.515821 0.856696i \(-0.672513\pi\)
−0.515821 + 0.856696i \(0.672513\pi\)
\(98\) 0 0
\(99\) −0.535743 −0.0538442
\(100\) 0 0
\(101\) −4.31990 −0.429846 −0.214923 0.976631i \(-0.568950\pi\)
−0.214923 + 0.976631i \(0.568950\pi\)
\(102\) 0 0
\(103\) 1.60268 0.157916 0.0789581 0.996878i \(-0.474841\pi\)
0.0789581 + 0.996878i \(0.474841\pi\)
\(104\) 0 0
\(105\) −2.69336 −0.262845
\(106\) 0 0
\(107\) 3.00707 0.290704 0.145352 0.989380i \(-0.453568\pi\)
0.145352 + 0.989380i \(0.453568\pi\)
\(108\) 0 0
\(109\) −3.79992 −0.363967 −0.181983 0.983302i \(-0.558252\pi\)
−0.181983 + 0.983302i \(0.558252\pi\)
\(110\) 0 0
\(111\) −2.78574 −0.264411
\(112\) 0 0
\(113\) −9.81560 −0.923374 −0.461687 0.887043i \(-0.652756\pi\)
−0.461687 + 0.887043i \(0.652756\pi\)
\(114\) 0 0
\(115\) 2.74263 0.255752
\(116\) 0 0
\(117\) 0.0819068 0.00757229
\(118\) 0 0
\(119\) −8.96028 −0.821387
\(120\) 0 0
\(121\) 23.4098 2.12817
\(122\) 0 0
\(123\) −2.50770 −0.226111
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 13.8098 1.22542 0.612712 0.790306i \(-0.290079\pi\)
0.612712 + 0.790306i \(0.290079\pi\)
\(128\) 0 0
\(129\) −15.1227 −1.33148
\(130\) 0 0
\(131\) 4.30009 0.375700 0.187850 0.982198i \(-0.439848\pi\)
0.187850 + 0.982198i \(0.439848\pi\)
\(132\) 0 0
\(133\) 5.37275 0.465876
\(134\) 0 0
\(135\) 5.11408 0.440150
\(136\) 0 0
\(137\) −8.88971 −0.759499 −0.379750 0.925089i \(-0.623990\pi\)
−0.379750 + 0.925089i \(0.623990\pi\)
\(138\) 0 0
\(139\) −13.0154 −1.10395 −0.551974 0.833861i \(-0.686125\pi\)
−0.551974 + 0.833861i \(0.686125\pi\)
\(140\) 0 0
\(141\) −2.40970 −0.202934
\(142\) 0 0
\(143\) −5.26073 −0.439924
\(144\) 0 0
\(145\) 2.53080 0.210172
\(146\) 0 0
\(147\) 8.18166 0.674812
\(148\) 0 0
\(149\) −16.0145 −1.31196 −0.655979 0.754780i \(-0.727744\pi\)
−0.655979 + 0.754780i \(0.727744\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) −0.534214 −0.0431887
\(154\) 0 0
\(155\) 5.38052 0.432173
\(156\) 0 0
\(157\) −4.59585 −0.366789 −0.183395 0.983039i \(-0.558709\pi\)
−0.183395 + 0.983039i \(0.558709\pi\)
\(158\) 0 0
\(159\) 18.8255 1.49296
\(160\) 0 0
\(161\) 4.20135 0.331113
\(162\) 0 0
\(163\) 9.09815 0.712622 0.356311 0.934367i \(-0.384034\pi\)
0.356311 + 0.934367i \(0.384034\pi\)
\(164\) 0 0
\(165\) 10.3137 0.802919
\(166\) 0 0
\(167\) −0.796650 −0.0616466 −0.0308233 0.999525i \(-0.509813\pi\)
−0.0308233 + 0.999525i \(0.509813\pi\)
\(168\) 0 0
\(169\) −12.1957 −0.938132
\(170\) 0 0
\(171\) 0.320325 0.0244958
\(172\) 0 0
\(173\) 7.12220 0.541491 0.270745 0.962651i \(-0.412730\pi\)
0.270745 + 0.962651i \(0.412730\pi\)
\(174\) 0 0
\(175\) 1.53187 0.115798
\(176\) 0 0
\(177\) 1.19153 0.0895607
\(178\) 0 0
\(179\) 17.2246 1.28743 0.643714 0.765266i \(-0.277393\pi\)
0.643714 + 0.765266i \(0.277393\pi\)
\(180\) 0 0
\(181\) −14.0189 −1.04202 −0.521010 0.853551i \(-0.674445\pi\)
−0.521010 + 0.853551i \(0.674445\pi\)
\(182\) 0 0
\(183\) −15.5797 −1.15168
\(184\) 0 0
\(185\) 1.58441 0.116488
\(186\) 0 0
\(187\) 34.3117 2.50912
\(188\) 0 0
\(189\) 7.83408 0.569846
\(190\) 0 0
\(191\) −20.1365 −1.45703 −0.728515 0.685030i \(-0.759789\pi\)
−0.728515 + 0.685030i \(0.759789\pi\)
\(192\) 0 0
\(193\) 15.4161 1.10968 0.554839 0.831958i \(-0.312780\pi\)
0.554839 + 0.831958i \(0.312780\pi\)
\(194\) 0 0
\(195\) −1.57680 −0.112917
\(196\) 0 0
\(197\) −1.48952 −0.106124 −0.0530621 0.998591i \(-0.516898\pi\)
−0.0530621 + 0.998591i \(0.516898\pi\)
\(198\) 0 0
\(199\) −19.6758 −1.39478 −0.697389 0.716693i \(-0.745655\pi\)
−0.697389 + 0.716693i \(0.745655\pi\)
\(200\) 0 0
\(201\) 16.5262 1.16567
\(202\) 0 0
\(203\) 3.87686 0.272102
\(204\) 0 0
\(205\) 1.42627 0.0996151
\(206\) 0 0
\(207\) 0.250486 0.0174100
\(208\) 0 0
\(209\) −20.5739 −1.42313
\(210\) 0 0
\(211\) 7.42206 0.510956 0.255478 0.966815i \(-0.417767\pi\)
0.255478 + 0.966815i \(0.417767\pi\)
\(212\) 0 0
\(213\) 7.18627 0.492395
\(214\) 0 0
\(215\) 8.60118 0.586595
\(216\) 0 0
\(217\) 8.24223 0.559519
\(218\) 0 0
\(219\) 7.88806 0.533025
\(220\) 0 0
\(221\) −5.24572 −0.352865
\(222\) 0 0
\(223\) −16.3488 −1.09480 −0.547398 0.836873i \(-0.684381\pi\)
−0.547398 + 0.836873i \(0.684381\pi\)
\(224\) 0 0
\(225\) 0.0913304 0.00608869
\(226\) 0 0
\(227\) 17.1484 1.13818 0.569091 0.822275i \(-0.307295\pi\)
0.569091 + 0.822275i \(0.307295\pi\)
\(228\) 0 0
\(229\) −3.25018 −0.214778 −0.107389 0.994217i \(-0.534249\pi\)
−0.107389 + 0.994217i \(0.534249\pi\)
\(230\) 0 0
\(231\) 15.7992 1.03951
\(232\) 0 0
\(233\) 5.62635 0.368594 0.184297 0.982871i \(-0.440999\pi\)
0.184297 + 0.982871i \(0.440999\pi\)
\(234\) 0 0
\(235\) 1.37054 0.0894040
\(236\) 0 0
\(237\) −12.1860 −0.791565
\(238\) 0 0
\(239\) −24.2274 −1.56714 −0.783569 0.621305i \(-0.786603\pi\)
−0.783569 + 0.621305i \(0.786603\pi\)
\(240\) 0 0
\(241\) 6.52347 0.420214 0.210107 0.977678i \(-0.432619\pi\)
0.210107 + 0.977678i \(0.432619\pi\)
\(242\) 0 0
\(243\) 0.948806 0.0608660
\(244\) 0 0
\(245\) −4.65338 −0.297294
\(246\) 0 0
\(247\) 3.14543 0.200139
\(248\) 0 0
\(249\) 10.0142 0.634626
\(250\) 0 0
\(251\) −18.6179 −1.17515 −0.587575 0.809170i \(-0.699917\pi\)
−0.587575 + 0.809170i \(0.699917\pi\)
\(252\) 0 0
\(253\) −16.0883 −1.01146
\(254\) 0 0
\(255\) 10.2843 0.644025
\(256\) 0 0
\(257\) −8.21540 −0.512462 −0.256231 0.966616i \(-0.582481\pi\)
−0.256231 + 0.966616i \(0.582481\pi\)
\(258\) 0 0
\(259\) 2.42711 0.150813
\(260\) 0 0
\(261\) 0.231139 0.0143072
\(262\) 0 0
\(263\) −5.54055 −0.341645 −0.170822 0.985302i \(-0.554642\pi\)
−0.170822 + 0.985302i \(0.554642\pi\)
\(264\) 0 0
\(265\) −10.7071 −0.657734
\(266\) 0 0
\(267\) 6.12009 0.374543
\(268\) 0 0
\(269\) −11.4492 −0.698067 −0.349034 0.937110i \(-0.613490\pi\)
−0.349034 + 0.937110i \(0.613490\pi\)
\(270\) 0 0
\(271\) −27.4858 −1.66965 −0.834823 0.550519i \(-0.814430\pi\)
−0.834823 + 0.550519i \(0.814430\pi\)
\(272\) 0 0
\(273\) −2.41545 −0.146190
\(274\) 0 0
\(275\) −5.86599 −0.353732
\(276\) 0 0
\(277\) 16.8535 1.01263 0.506316 0.862348i \(-0.331007\pi\)
0.506316 + 0.862348i \(0.331007\pi\)
\(278\) 0 0
\(279\) 0.491404 0.0294196
\(280\) 0 0
\(281\) −21.7851 −1.29959 −0.649794 0.760110i \(-0.725145\pi\)
−0.649794 + 0.760110i \(0.725145\pi\)
\(282\) 0 0
\(283\) 0.920695 0.0547297 0.0273648 0.999626i \(-0.491288\pi\)
0.0273648 + 0.999626i \(0.491288\pi\)
\(284\) 0 0
\(285\) −6.16663 −0.365280
\(286\) 0 0
\(287\) 2.18486 0.128968
\(288\) 0 0
\(289\) 17.2138 1.01257
\(290\) 0 0
\(291\) 17.8644 1.04723
\(292\) 0 0
\(293\) −20.7956 −1.21489 −0.607446 0.794361i \(-0.707806\pi\)
−0.607446 + 0.794361i \(0.707806\pi\)
\(294\) 0 0
\(295\) −0.677690 −0.0394567
\(296\) 0 0
\(297\) −29.9991 −1.74072
\(298\) 0 0
\(299\) 2.45965 0.142245
\(300\) 0 0
\(301\) 13.1759 0.759444
\(302\) 0 0
\(303\) 7.59533 0.436340
\(304\) 0 0
\(305\) 8.86107 0.507383
\(306\) 0 0
\(307\) 28.2546 1.61257 0.806287 0.591524i \(-0.201474\pi\)
0.806287 + 0.591524i \(0.201474\pi\)
\(308\) 0 0
\(309\) −2.81785 −0.160302
\(310\) 0 0
\(311\) −29.4020 −1.66723 −0.833617 0.552343i \(-0.813734\pi\)
−0.833617 + 0.552343i \(0.813734\pi\)
\(312\) 0 0
\(313\) −10.4870 −0.592759 −0.296379 0.955070i \(-0.595779\pi\)
−0.296379 + 0.955070i \(0.595779\pi\)
\(314\) 0 0
\(315\) 0.139906 0.00788281
\(316\) 0 0
\(317\) 16.4809 0.925660 0.462830 0.886447i \(-0.346834\pi\)
0.462830 + 0.886447i \(0.346834\pi\)
\(318\) 0 0
\(319\) −14.8457 −0.831198
\(320\) 0 0
\(321\) −5.28708 −0.295096
\(322\) 0 0
\(323\) −20.5152 −1.14150
\(324\) 0 0
\(325\) 0.896819 0.0497466
\(326\) 0 0
\(327\) 6.68109 0.369465
\(328\) 0 0
\(329\) 2.09948 0.115748
\(330\) 0 0
\(331\) −21.4363 −1.17824 −0.589122 0.808044i \(-0.700526\pi\)
−0.589122 + 0.808044i \(0.700526\pi\)
\(332\) 0 0
\(333\) 0.144705 0.00792978
\(334\) 0 0
\(335\) −9.39938 −0.513543
\(336\) 0 0
\(337\) 12.3688 0.673769 0.336884 0.941546i \(-0.390627\pi\)
0.336884 + 0.941546i \(0.390627\pi\)
\(338\) 0 0
\(339\) 17.2580 0.937324
\(340\) 0 0
\(341\) −31.5620 −1.70918
\(342\) 0 0
\(343\) −17.8514 −0.963887
\(344\) 0 0
\(345\) −4.82215 −0.259616
\(346\) 0 0
\(347\) 18.5505 0.995844 0.497922 0.867222i \(-0.334097\pi\)
0.497922 + 0.867222i \(0.334097\pi\)
\(348\) 0 0
\(349\) 23.2080 1.24230 0.621148 0.783693i \(-0.286667\pi\)
0.621148 + 0.783693i \(0.286667\pi\)
\(350\) 0 0
\(351\) 4.58640 0.244804
\(352\) 0 0
\(353\) −0.625977 −0.0333174 −0.0166587 0.999861i \(-0.505303\pi\)
−0.0166587 + 0.999861i \(0.505303\pi\)
\(354\) 0 0
\(355\) −4.08725 −0.216929
\(356\) 0 0
\(357\) 15.7541 0.833796
\(358\) 0 0
\(359\) 14.0173 0.739804 0.369902 0.929071i \(-0.379391\pi\)
0.369902 + 0.929071i \(0.379391\pi\)
\(360\) 0 0
\(361\) −6.69872 −0.352564
\(362\) 0 0
\(363\) −41.1596 −2.16032
\(364\) 0 0
\(365\) −4.48639 −0.234829
\(366\) 0 0
\(367\) −5.42961 −0.283423 −0.141712 0.989908i \(-0.545261\pi\)
−0.141712 + 0.989908i \(0.545261\pi\)
\(368\) 0 0
\(369\) 0.130262 0.00678116
\(370\) 0 0
\(371\) −16.4019 −0.851544
\(372\) 0 0
\(373\) −10.6591 −0.551909 −0.275954 0.961171i \(-0.588994\pi\)
−0.275954 + 0.961171i \(0.588994\pi\)
\(374\) 0 0
\(375\) −1.75822 −0.0907940
\(376\) 0 0
\(377\) 2.26967 0.116894
\(378\) 0 0
\(379\) −26.0060 −1.33584 −0.667919 0.744234i \(-0.732815\pi\)
−0.667919 + 0.744234i \(0.732815\pi\)
\(380\) 0 0
\(381\) −24.2807 −1.24394
\(382\) 0 0
\(383\) −6.36092 −0.325028 −0.162514 0.986706i \(-0.551960\pi\)
−0.162514 + 0.986706i \(0.551960\pi\)
\(384\) 0 0
\(385\) −8.98591 −0.457965
\(386\) 0 0
\(387\) 0.785549 0.0399317
\(388\) 0 0
\(389\) 37.6073 1.90677 0.953384 0.301760i \(-0.0975741\pi\)
0.953384 + 0.301760i \(0.0975741\pi\)
\(390\) 0 0
\(391\) −16.0424 −0.811297
\(392\) 0 0
\(393\) −7.56049 −0.381376
\(394\) 0 0
\(395\) 6.93088 0.348730
\(396\) 0 0
\(397\) −33.8051 −1.69663 −0.848315 0.529491i \(-0.822383\pi\)
−0.848315 + 0.529491i \(0.822383\pi\)
\(398\) 0 0
\(399\) −9.44646 −0.472914
\(400\) 0 0
\(401\) 15.1960 0.758851 0.379425 0.925222i \(-0.376122\pi\)
0.379425 + 0.925222i \(0.376122\pi\)
\(402\) 0 0
\(403\) 4.82535 0.240368
\(404\) 0 0
\(405\) −9.26565 −0.460414
\(406\) 0 0
\(407\) −9.29415 −0.460694
\(408\) 0 0
\(409\) −8.30582 −0.410696 −0.205348 0.978689i \(-0.565833\pi\)
−0.205348 + 0.978689i \(0.565833\pi\)
\(410\) 0 0
\(411\) 15.6300 0.770973
\(412\) 0 0
\(413\) −1.03813 −0.0510831
\(414\) 0 0
\(415\) −5.69567 −0.279589
\(416\) 0 0
\(417\) 22.8838 1.12063
\(418\) 0 0
\(419\) 15.1450 0.739880 0.369940 0.929056i \(-0.379378\pi\)
0.369940 + 0.929056i \(0.379378\pi\)
\(420\) 0 0
\(421\) −9.05358 −0.441245 −0.220622 0.975359i \(-0.570809\pi\)
−0.220622 + 0.975359i \(0.570809\pi\)
\(422\) 0 0
\(423\) 0.125172 0.00608606
\(424\) 0 0
\(425\) −5.84925 −0.283730
\(426\) 0 0
\(427\) 13.5740 0.656891
\(428\) 0 0
\(429\) 9.24951 0.446571
\(430\) 0 0
\(431\) −7.77083 −0.374307 −0.187154 0.982331i \(-0.559926\pi\)
−0.187154 + 0.982331i \(0.559926\pi\)
\(432\) 0 0
\(433\) 13.7060 0.658669 0.329334 0.944213i \(-0.393176\pi\)
0.329334 + 0.944213i \(0.393176\pi\)
\(434\) 0 0
\(435\) −4.44971 −0.213347
\(436\) 0 0
\(437\) 9.61929 0.460153
\(438\) 0 0
\(439\) 13.1755 0.628834 0.314417 0.949285i \(-0.398191\pi\)
0.314417 + 0.949285i \(0.398191\pi\)
\(440\) 0 0
\(441\) −0.424995 −0.0202379
\(442\) 0 0
\(443\) −18.4434 −0.876271 −0.438136 0.898909i \(-0.644361\pi\)
−0.438136 + 0.898909i \(0.644361\pi\)
\(444\) 0 0
\(445\) −3.48085 −0.165008
\(446\) 0 0
\(447\) 28.1569 1.33178
\(448\) 0 0
\(449\) −36.2875 −1.71251 −0.856257 0.516550i \(-0.827216\pi\)
−0.856257 + 0.516550i \(0.827216\pi\)
\(450\) 0 0
\(451\) −8.36649 −0.393963
\(452\) 0 0
\(453\) 1.75822 0.0826083
\(454\) 0 0
\(455\) 1.37381 0.0644051
\(456\) 0 0
\(457\) −21.3689 −0.999594 −0.499797 0.866143i \(-0.666592\pi\)
−0.499797 + 0.866143i \(0.666592\pi\)
\(458\) 0 0
\(459\) −29.9135 −1.39624
\(460\) 0 0
\(461\) −30.9613 −1.44201 −0.721006 0.692929i \(-0.756320\pi\)
−0.721006 + 0.692929i \(0.756320\pi\)
\(462\) 0 0
\(463\) 1.32893 0.0617606 0.0308803 0.999523i \(-0.490169\pi\)
0.0308803 + 0.999523i \(0.490169\pi\)
\(464\) 0 0
\(465\) −9.46012 −0.438703
\(466\) 0 0
\(467\) 19.4495 0.900017 0.450009 0.893024i \(-0.351421\pi\)
0.450009 + 0.893024i \(0.351421\pi\)
\(468\) 0 0
\(469\) −14.3986 −0.664866
\(470\) 0 0
\(471\) 8.08051 0.372330
\(472\) 0 0
\(473\) −50.4544 −2.31990
\(474\) 0 0
\(475\) 3.50732 0.160927
\(476\) 0 0
\(477\) −0.977886 −0.0447743
\(478\) 0 0
\(479\) 29.0961 1.32944 0.664718 0.747095i \(-0.268552\pi\)
0.664718 + 0.747095i \(0.268552\pi\)
\(480\) 0 0
\(481\) 1.42093 0.0647889
\(482\) 0 0
\(483\) −7.38689 −0.336115
\(484\) 0 0
\(485\) −10.1605 −0.461365
\(486\) 0 0
\(487\) −6.13509 −0.278007 −0.139004 0.990292i \(-0.544390\pi\)
−0.139004 + 0.990292i \(0.544390\pi\)
\(488\) 0 0
\(489\) −15.9965 −0.723388
\(490\) 0 0
\(491\) 41.3118 1.86438 0.932188 0.361975i \(-0.117898\pi\)
0.932188 + 0.361975i \(0.117898\pi\)
\(492\) 0 0
\(493\) −14.8033 −0.666708
\(494\) 0 0
\(495\) −0.535743 −0.0240799
\(496\) 0 0
\(497\) −6.26112 −0.280850
\(498\) 0 0
\(499\) 1.53948 0.0689165 0.0344582 0.999406i \(-0.489029\pi\)
0.0344582 + 0.999406i \(0.489029\pi\)
\(500\) 0 0
\(501\) 1.40068 0.0625780
\(502\) 0 0
\(503\) −13.6651 −0.609296 −0.304648 0.952465i \(-0.598539\pi\)
−0.304648 + 0.952465i \(0.598539\pi\)
\(504\) 0 0
\(505\) −4.31990 −0.192233
\(506\) 0 0
\(507\) 21.4427 0.952305
\(508\) 0 0
\(509\) −31.6725 −1.40386 −0.701929 0.712247i \(-0.747678\pi\)
−0.701929 + 0.712247i \(0.747678\pi\)
\(510\) 0 0
\(511\) −6.87256 −0.304024
\(512\) 0 0
\(513\) 17.9367 0.791924
\(514\) 0 0
\(515\) 1.60268 0.0706223
\(516\) 0 0
\(517\) −8.03956 −0.353579
\(518\) 0 0
\(519\) −12.5224 −0.549671
\(520\) 0 0
\(521\) 16.7786 0.735084 0.367542 0.930007i \(-0.380199\pi\)
0.367542 + 0.930007i \(0.380199\pi\)
\(522\) 0 0
\(523\) 23.9418 1.04690 0.523452 0.852055i \(-0.324644\pi\)
0.523452 + 0.852055i \(0.324644\pi\)
\(524\) 0 0
\(525\) −2.69336 −0.117548
\(526\) 0 0
\(527\) −31.4720 −1.37094
\(528\) 0 0
\(529\) −15.4780 −0.672955
\(530\) 0 0
\(531\) −0.0618937 −0.00268596
\(532\) 0 0
\(533\) 1.27911 0.0554043
\(534\) 0 0
\(535\) 3.00707 0.130007
\(536\) 0 0
\(537\) −30.2846 −1.30688
\(538\) 0 0
\(539\) 27.2967 1.17575
\(540\) 0 0
\(541\) −20.2387 −0.870130 −0.435065 0.900399i \(-0.643275\pi\)
−0.435065 + 0.900399i \(0.643275\pi\)
\(542\) 0 0
\(543\) 24.6484 1.05776
\(544\) 0 0
\(545\) −3.79992 −0.162771
\(546\) 0 0
\(547\) 7.96450 0.340537 0.170269 0.985398i \(-0.445536\pi\)
0.170269 + 0.985398i \(0.445536\pi\)
\(548\) 0 0
\(549\) 0.809284 0.0345394
\(550\) 0 0
\(551\) 8.87634 0.378145
\(552\) 0 0
\(553\) 10.6172 0.451489
\(554\) 0 0
\(555\) −2.78574 −0.118248
\(556\) 0 0
\(557\) −17.1594 −0.727066 −0.363533 0.931581i \(-0.618430\pi\)
−0.363533 + 0.931581i \(0.618430\pi\)
\(558\) 0 0
\(559\) 7.71370 0.326255
\(560\) 0 0
\(561\) −60.3274 −2.54702
\(562\) 0 0
\(563\) −26.2028 −1.10431 −0.552157 0.833740i \(-0.686195\pi\)
−0.552157 + 0.833740i \(0.686195\pi\)
\(564\) 0 0
\(565\) −9.81560 −0.412945
\(566\) 0 0
\(567\) −14.1937 −0.596081
\(568\) 0 0
\(569\) 0.963737 0.0404020 0.0202010 0.999796i \(-0.493569\pi\)
0.0202010 + 0.999796i \(0.493569\pi\)
\(570\) 0 0
\(571\) 2.97981 0.124701 0.0623505 0.998054i \(-0.480140\pi\)
0.0623505 + 0.998054i \(0.480140\pi\)
\(572\) 0 0
\(573\) 35.4044 1.47904
\(574\) 0 0
\(575\) 2.74263 0.114376
\(576\) 0 0
\(577\) −2.20361 −0.0917376 −0.0458688 0.998947i \(-0.514606\pi\)
−0.0458688 + 0.998947i \(0.514606\pi\)
\(578\) 0 0
\(579\) −27.1049 −1.12644
\(580\) 0 0
\(581\) −8.72501 −0.361974
\(582\) 0 0
\(583\) 62.8079 2.60124
\(584\) 0 0
\(585\) 0.0819068 0.00338643
\(586\) 0 0
\(587\) 29.2899 1.20892 0.604462 0.796634i \(-0.293388\pi\)
0.604462 + 0.796634i \(0.293388\pi\)
\(588\) 0 0
\(589\) 18.8712 0.777573
\(590\) 0 0
\(591\) 2.61891 0.107727
\(592\) 0 0
\(593\) 16.2252 0.666291 0.333145 0.942875i \(-0.391890\pi\)
0.333145 + 0.942875i \(0.391890\pi\)
\(594\) 0 0
\(595\) −8.96028 −0.367336
\(596\) 0 0
\(597\) 34.5943 1.41585
\(598\) 0 0
\(599\) −47.2495 −1.93056 −0.965281 0.261215i \(-0.915877\pi\)
−0.965281 + 0.261215i \(0.915877\pi\)
\(600\) 0 0
\(601\) −22.0922 −0.901159 −0.450580 0.892736i \(-0.648783\pi\)
−0.450580 + 0.892736i \(0.648783\pi\)
\(602\) 0 0
\(603\) −0.858449 −0.0349587
\(604\) 0 0
\(605\) 23.4098 0.951745
\(606\) 0 0
\(607\) 4.45091 0.180657 0.0903285 0.995912i \(-0.471208\pi\)
0.0903285 + 0.995912i \(0.471208\pi\)
\(608\) 0 0
\(609\) −6.81636 −0.276213
\(610\) 0 0
\(611\) 1.22912 0.0497250
\(612\) 0 0
\(613\) −5.61033 −0.226599 −0.113299 0.993561i \(-0.536142\pi\)
−0.113299 + 0.993561i \(0.536142\pi\)
\(614\) 0 0
\(615\) −2.50770 −0.101120
\(616\) 0 0
\(617\) −9.51146 −0.382917 −0.191458 0.981501i \(-0.561322\pi\)
−0.191458 + 0.981501i \(0.561322\pi\)
\(618\) 0 0
\(619\) 0.189188 0.00760410 0.00380205 0.999993i \(-0.498790\pi\)
0.00380205 + 0.999993i \(0.498790\pi\)
\(620\) 0 0
\(621\) 14.0260 0.562846
\(622\) 0 0
\(623\) −5.33219 −0.213630
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 36.1734 1.44463
\(628\) 0 0
\(629\) −9.26763 −0.369525
\(630\) 0 0
\(631\) −9.21580 −0.366875 −0.183438 0.983031i \(-0.558723\pi\)
−0.183438 + 0.983031i \(0.558723\pi\)
\(632\) 0 0
\(633\) −13.0496 −0.518675
\(634\) 0 0
\(635\) 13.8098 0.548026
\(636\) 0 0
\(637\) −4.17324 −0.165350
\(638\) 0 0
\(639\) −0.373290 −0.0147671
\(640\) 0 0
\(641\) −34.7524 −1.37264 −0.686318 0.727301i \(-0.740774\pi\)
−0.686318 + 0.727301i \(0.740774\pi\)
\(642\) 0 0
\(643\) −43.7367 −1.72481 −0.862403 0.506223i \(-0.831041\pi\)
−0.862403 + 0.506223i \(0.831041\pi\)
\(644\) 0 0
\(645\) −15.1227 −0.595457
\(646\) 0 0
\(647\) 37.9083 1.49033 0.745165 0.666880i \(-0.232371\pi\)
0.745165 + 0.666880i \(0.232371\pi\)
\(648\) 0 0
\(649\) 3.97532 0.156045
\(650\) 0 0
\(651\) −14.4916 −0.567972
\(652\) 0 0
\(653\) −47.5355 −1.86021 −0.930104 0.367296i \(-0.880283\pi\)
−0.930104 + 0.367296i \(0.880283\pi\)
\(654\) 0 0
\(655\) 4.30009 0.168018
\(656\) 0 0
\(657\) −0.409744 −0.0159856
\(658\) 0 0
\(659\) 30.6495 1.19394 0.596968 0.802265i \(-0.296372\pi\)
0.596968 + 0.802265i \(0.296372\pi\)
\(660\) 0 0
\(661\) 3.88104 0.150955 0.0754775 0.997148i \(-0.475952\pi\)
0.0754775 + 0.997148i \(0.475952\pi\)
\(662\) 0 0
\(663\) 9.22312 0.358196
\(664\) 0 0
\(665\) 5.37275 0.208346
\(666\) 0 0
\(667\) 6.94107 0.268759
\(668\) 0 0
\(669\) 28.7447 1.11134
\(670\) 0 0
\(671\) −51.9789 −2.00662
\(672\) 0 0
\(673\) 7.29019 0.281016 0.140508 0.990080i \(-0.455126\pi\)
0.140508 + 0.990080i \(0.455126\pi\)
\(674\) 0 0
\(675\) 5.11408 0.196841
\(676\) 0 0
\(677\) 26.5940 1.02209 0.511045 0.859554i \(-0.329259\pi\)
0.511045 + 0.859554i \(0.329259\pi\)
\(678\) 0 0
\(679\) −15.5645 −0.597312
\(680\) 0 0
\(681\) −30.1507 −1.15538
\(682\) 0 0
\(683\) −10.4189 −0.398669 −0.199335 0.979931i \(-0.563878\pi\)
−0.199335 + 0.979931i \(0.563878\pi\)
\(684\) 0 0
\(685\) −8.88971 −0.339658
\(686\) 0 0
\(687\) 5.71453 0.218023
\(688\) 0 0
\(689\) −9.60236 −0.365821
\(690\) 0 0
\(691\) −12.3495 −0.469797 −0.234899 0.972020i \(-0.575476\pi\)
−0.234899 + 0.972020i \(0.575476\pi\)
\(692\) 0 0
\(693\) −0.820687 −0.0311753
\(694\) 0 0
\(695\) −13.0154 −0.493701
\(696\) 0 0
\(697\) −8.34262 −0.315999
\(698\) 0 0
\(699\) −9.89235 −0.374163
\(700\) 0 0
\(701\) 48.3114 1.82470 0.912348 0.409415i \(-0.134267\pi\)
0.912348 + 0.409415i \(0.134267\pi\)
\(702\) 0 0
\(703\) 5.55704 0.209588
\(704\) 0 0
\(705\) −2.40970 −0.0907547
\(706\) 0 0
\(707\) −6.61751 −0.248877
\(708\) 0 0
\(709\) 19.8506 0.745505 0.372752 0.927931i \(-0.378414\pi\)
0.372752 + 0.927931i \(0.378414\pi\)
\(710\) 0 0
\(711\) 0.633000 0.0237393
\(712\) 0 0
\(713\) 14.7568 0.552646
\(714\) 0 0
\(715\) −5.26073 −0.196740
\(716\) 0 0
\(717\) 42.5970 1.59081
\(718\) 0 0
\(719\) 14.8568 0.554066 0.277033 0.960860i \(-0.410649\pi\)
0.277033 + 0.960860i \(0.410649\pi\)
\(720\) 0 0
\(721\) 2.45509 0.0914321
\(722\) 0 0
\(723\) −11.4697 −0.426562
\(724\) 0 0
\(725\) 2.53080 0.0939917
\(726\) 0 0
\(727\) −13.7074 −0.508378 −0.254189 0.967155i \(-0.581809\pi\)
−0.254189 + 0.967155i \(0.581809\pi\)
\(728\) 0 0
\(729\) 26.1287 0.967731
\(730\) 0 0
\(731\) −50.3105 −1.86080
\(732\) 0 0
\(733\) 6.62488 0.244696 0.122348 0.992487i \(-0.460958\pi\)
0.122348 + 0.992487i \(0.460958\pi\)
\(734\) 0 0
\(735\) 8.18166 0.301785
\(736\) 0 0
\(737\) 55.1367 2.03098
\(738\) 0 0
\(739\) −6.95622 −0.255889 −0.127944 0.991781i \(-0.540838\pi\)
−0.127944 + 0.991781i \(0.540838\pi\)
\(740\) 0 0
\(741\) −5.53035 −0.203163
\(742\) 0 0
\(743\) 43.3827 1.59156 0.795778 0.605589i \(-0.207062\pi\)
0.795778 + 0.605589i \(0.207062\pi\)
\(744\) 0 0
\(745\) −16.0145 −0.586725
\(746\) 0 0
\(747\) −0.520188 −0.0190327
\(748\) 0 0
\(749\) 4.60643 0.168315
\(750\) 0 0
\(751\) −0.760362 −0.0277460 −0.0138730 0.999904i \(-0.504416\pi\)
−0.0138730 + 0.999904i \(0.504416\pi\)
\(752\) 0 0
\(753\) 32.7343 1.19290
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) 3.55688 0.129277 0.0646385 0.997909i \(-0.479411\pi\)
0.0646385 + 0.997909i \(0.479411\pi\)
\(758\) 0 0
\(759\) 28.2867 1.02674
\(760\) 0 0
\(761\) −18.5180 −0.671277 −0.335638 0.941991i \(-0.608952\pi\)
−0.335638 + 0.941991i \(0.608952\pi\)
\(762\) 0 0
\(763\) −5.82098 −0.210733
\(764\) 0 0
\(765\) −0.534214 −0.0193146
\(766\) 0 0
\(767\) −0.607766 −0.0219452
\(768\) 0 0
\(769\) 12.4366 0.448474 0.224237 0.974535i \(-0.428011\pi\)
0.224237 + 0.974535i \(0.428011\pi\)
\(770\) 0 0
\(771\) 14.4445 0.520205
\(772\) 0 0
\(773\) −17.0639 −0.613745 −0.306872 0.951751i \(-0.599283\pi\)
−0.306872 + 0.951751i \(0.599283\pi\)
\(774\) 0 0
\(775\) 5.38052 0.193274
\(776\) 0 0
\(777\) −4.26739 −0.153092
\(778\) 0 0
\(779\) 5.00239 0.179229
\(780\) 0 0
\(781\) 23.9757 0.857920
\(782\) 0 0
\(783\) 12.9427 0.462535
\(784\) 0 0
\(785\) −4.59585 −0.164033
\(786\) 0 0
\(787\) −29.9387 −1.06720 −0.533599 0.845737i \(-0.679161\pi\)
−0.533599 + 0.845737i \(0.679161\pi\)
\(788\) 0 0
\(789\) 9.74149 0.346806
\(790\) 0 0
\(791\) −15.0362 −0.534626
\(792\) 0 0
\(793\) 7.94677 0.282198
\(794\) 0 0
\(795\) 18.8255 0.667671
\(796\) 0 0
\(797\) 36.0516 1.27701 0.638506 0.769617i \(-0.279553\pi\)
0.638506 + 0.769617i \(0.279553\pi\)
\(798\) 0 0
\(799\) −8.01662 −0.283608
\(800\) 0 0
\(801\) −0.317907 −0.0112327
\(802\) 0 0
\(803\) 26.3171 0.928711
\(804\) 0 0
\(805\) 4.20135 0.148078
\(806\) 0 0
\(807\) 20.1301 0.708613
\(808\) 0 0
\(809\) −22.5150 −0.791585 −0.395793 0.918340i \(-0.629530\pi\)
−0.395793 + 0.918340i \(0.629530\pi\)
\(810\) 0 0
\(811\) −25.6944 −0.902252 −0.451126 0.892460i \(-0.648977\pi\)
−0.451126 + 0.892460i \(0.648977\pi\)
\(812\) 0 0
\(813\) 48.3261 1.69487
\(814\) 0 0
\(815\) 9.09815 0.318694
\(816\) 0 0
\(817\) 30.1671 1.05541
\(818\) 0 0
\(819\) 0.125470 0.00438429
\(820\) 0 0
\(821\) 35.0675 1.22387 0.611933 0.790910i \(-0.290392\pi\)
0.611933 + 0.790910i \(0.290392\pi\)
\(822\) 0 0
\(823\) −3.25821 −0.113574 −0.0567870 0.998386i \(-0.518086\pi\)
−0.0567870 + 0.998386i \(0.518086\pi\)
\(824\) 0 0
\(825\) 10.3137 0.359076
\(826\) 0 0
\(827\) 31.2078 1.08520 0.542601 0.839990i \(-0.317440\pi\)
0.542601 + 0.839990i \(0.317440\pi\)
\(828\) 0 0
\(829\) −17.1949 −0.597204 −0.298602 0.954378i \(-0.596520\pi\)
−0.298602 + 0.954378i \(0.596520\pi\)
\(830\) 0 0
\(831\) −29.6322 −1.02793
\(832\) 0 0
\(833\) 27.2188 0.943076
\(834\) 0 0
\(835\) −0.796650 −0.0275692
\(836\) 0 0
\(837\) 27.5164 0.951105
\(838\) 0 0
\(839\) −33.0184 −1.13992 −0.569960 0.821672i \(-0.693041\pi\)
−0.569960 + 0.821672i \(0.693041\pi\)
\(840\) 0 0
\(841\) −22.5950 −0.779139
\(842\) 0 0
\(843\) 38.3029 1.31922
\(844\) 0 0
\(845\) −12.1957 −0.419545
\(846\) 0 0
\(847\) 35.8607 1.23219
\(848\) 0 0
\(849\) −1.61878 −0.0555565
\(850\) 0 0
\(851\) 4.34546 0.148961
\(852\) 0 0
\(853\) −22.9546 −0.785950 −0.392975 0.919549i \(-0.628554\pi\)
−0.392975 + 0.919549i \(0.628554\pi\)
\(854\) 0 0
\(855\) 0.320325 0.0109549
\(856\) 0 0
\(857\) 30.0367 1.02603 0.513017 0.858379i \(-0.328528\pi\)
0.513017 + 0.858379i \(0.328528\pi\)
\(858\) 0 0
\(859\) −1.43708 −0.0490326 −0.0245163 0.999699i \(-0.507805\pi\)
−0.0245163 + 0.999699i \(0.507805\pi\)
\(860\) 0 0
\(861\) −3.84146 −0.130916
\(862\) 0 0
\(863\) −33.2010 −1.13017 −0.565087 0.825031i \(-0.691158\pi\)
−0.565087 + 0.825031i \(0.691158\pi\)
\(864\) 0 0
\(865\) 7.12220 0.242162
\(866\) 0 0
\(867\) −30.2655 −1.02787
\(868\) 0 0
\(869\) −40.6565 −1.37918
\(870\) 0 0
\(871\) −8.42954 −0.285624
\(872\) 0 0
\(873\) −0.927962 −0.0314068
\(874\) 0 0
\(875\) 1.53187 0.0517866
\(876\) 0 0
\(877\) 20.6050 0.695780 0.347890 0.937535i \(-0.386898\pi\)
0.347890 + 0.937535i \(0.386898\pi\)
\(878\) 0 0
\(879\) 36.5632 1.23325
\(880\) 0 0
\(881\) −7.46176 −0.251393 −0.125696 0.992069i \(-0.540117\pi\)
−0.125696 + 0.992069i \(0.540117\pi\)
\(882\) 0 0
\(883\) 21.2146 0.713927 0.356963 0.934118i \(-0.383812\pi\)
0.356963 + 0.934118i \(0.383812\pi\)
\(884\) 0 0
\(885\) 1.19153 0.0400528
\(886\) 0 0
\(887\) −20.6074 −0.691930 −0.345965 0.938247i \(-0.612448\pi\)
−0.345965 + 0.938247i \(0.612448\pi\)
\(888\) 0 0
\(889\) 21.1548 0.709510
\(890\) 0 0
\(891\) 54.3522 1.82087
\(892\) 0 0
\(893\) 4.80691 0.160857
\(894\) 0 0
\(895\) 17.2246 0.575755
\(896\) 0 0
\(897\) −4.32460 −0.144394
\(898\) 0 0
\(899\) 13.6170 0.454153
\(900\) 0 0
\(901\) 62.6287 2.08647
\(902\) 0 0
\(903\) −23.1660 −0.770917
\(904\) 0 0
\(905\) −14.0189 −0.466005
\(906\) 0 0
\(907\) 4.29099 0.142480 0.0712400 0.997459i \(-0.477304\pi\)
0.0712400 + 0.997459i \(0.477304\pi\)
\(908\) 0 0
\(909\) −0.394538 −0.0130860
\(910\) 0 0
\(911\) 1.41804 0.0469817 0.0234908 0.999724i \(-0.492522\pi\)
0.0234908 + 0.999724i \(0.492522\pi\)
\(912\) 0 0
\(913\) 33.4107 1.10573
\(914\) 0 0
\(915\) −15.5797 −0.515048
\(916\) 0 0
\(917\) 6.58716 0.217527
\(918\) 0 0
\(919\) −3.14868 −0.103865 −0.0519327 0.998651i \(-0.516538\pi\)
−0.0519327 + 0.998651i \(0.516538\pi\)
\(920\) 0 0
\(921\) −49.6777 −1.63694
\(922\) 0 0
\(923\) −3.66552 −0.120652
\(924\) 0 0
\(925\) 1.58441 0.0520952
\(926\) 0 0
\(927\) 0.146373 0.00480752
\(928\) 0 0
\(929\) −33.5346 −1.10023 −0.550117 0.835087i \(-0.685417\pi\)
−0.550117 + 0.835087i \(0.685417\pi\)
\(930\) 0 0
\(931\) −16.3209 −0.534896
\(932\) 0 0
\(933\) 51.6951 1.69242
\(934\) 0 0
\(935\) 34.3117 1.12211
\(936\) 0 0
\(937\) −55.8247 −1.82371 −0.911857 0.410508i \(-0.865351\pi\)
−0.911857 + 0.410508i \(0.865351\pi\)
\(938\) 0 0
\(939\) 18.4384 0.601714
\(940\) 0 0
\(941\) 15.2251 0.496323 0.248162 0.968719i \(-0.420174\pi\)
0.248162 + 0.968719i \(0.420174\pi\)
\(942\) 0 0
\(943\) 3.91174 0.127384
\(944\) 0 0
\(945\) 7.83408 0.254843
\(946\) 0 0
\(947\) 46.7913 1.52051 0.760256 0.649623i \(-0.225073\pi\)
0.760256 + 0.649623i \(0.225073\pi\)
\(948\) 0 0
\(949\) −4.02348 −0.130608
\(950\) 0 0
\(951\) −28.9770 −0.939645
\(952\) 0 0
\(953\) 47.7062 1.54536 0.772678 0.634798i \(-0.218917\pi\)
0.772678 + 0.634798i \(0.218917\pi\)
\(954\) 0 0
\(955\) −20.1365 −0.651603
\(956\) 0 0
\(957\) 26.1019 0.843755
\(958\) 0 0
\(959\) −13.6179 −0.439743
\(960\) 0 0
\(961\) −2.05005 −0.0661307
\(962\) 0 0
\(963\) 0.274637 0.00885004
\(964\) 0 0
\(965\) 15.4161 0.496263
\(966\) 0 0
\(967\) −15.6087 −0.501942 −0.250971 0.967995i \(-0.580750\pi\)
−0.250971 + 0.967995i \(0.580750\pi\)
\(968\) 0 0
\(969\) 36.0702 1.15874
\(970\) 0 0
\(971\) 30.2597 0.971081 0.485541 0.874214i \(-0.338623\pi\)
0.485541 + 0.874214i \(0.338623\pi\)
\(972\) 0 0
\(973\) −19.9378 −0.639176
\(974\) 0 0
\(975\) −1.57680 −0.0504981
\(976\) 0 0
\(977\) 26.0786 0.834330 0.417165 0.908831i \(-0.363024\pi\)
0.417165 + 0.908831i \(0.363024\pi\)
\(978\) 0 0
\(979\) 20.4186 0.652582
\(980\) 0 0
\(981\) −0.347048 −0.0110804
\(982\) 0 0
\(983\) −6.67475 −0.212891 −0.106446 0.994319i \(-0.533947\pi\)
−0.106446 + 0.994319i \(0.533947\pi\)
\(984\) 0 0
\(985\) −1.48952 −0.0474602
\(986\) 0 0
\(987\) −3.69134 −0.117497
\(988\) 0 0
\(989\) 23.5899 0.750115
\(990\) 0 0
\(991\) −39.8910 −1.26718 −0.633589 0.773669i \(-0.718419\pi\)
−0.633589 + 0.773669i \(0.718419\pi\)
\(992\) 0 0
\(993\) 37.6896 1.19604
\(994\) 0 0
\(995\) −19.6758 −0.623763
\(996\) 0 0
\(997\) 23.0871 0.731177 0.365588 0.930777i \(-0.380868\pi\)
0.365588 + 0.930777i \(0.380868\pi\)
\(998\) 0 0
\(999\) 8.10281 0.256361
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 \(a_p\))