Properties

Label 6040.2.a.l.1.9
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 1.9
Root \(-2.61675\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.50073 q^{3}\) \(+1.00000 q^{5}\) \(-2.23459 q^{7}\) \(+3.25367 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.50073 q^{3}\) \(+1.00000 q^{5}\) \(-2.23459 q^{7}\) \(+3.25367 q^{9}\) \(-0.595816 q^{11}\) \(-3.72317 q^{13}\) \(+2.50073 q^{15}\) \(-2.87712 q^{17}\) \(-4.54184 q^{19}\) \(-5.58812 q^{21}\) \(+6.52105 q^{23}\) \(+1.00000 q^{25}\) \(+0.634355 q^{27}\) \(-3.40521 q^{29}\) \(-4.46118 q^{31}\) \(-1.48998 q^{33}\) \(-2.23459 q^{35}\) \(-1.19972 q^{37}\) \(-9.31066 q^{39}\) \(+6.99016 q^{41}\) \(-6.50220 q^{43}\) \(+3.25367 q^{45}\) \(+1.73067 q^{47}\) \(-2.00660 q^{49}\) \(-7.19492 q^{51}\) \(+1.40445 q^{53}\) \(-0.595816 q^{55}\) \(-11.3579 q^{57}\) \(+4.59179 q^{59}\) \(-0.884262 q^{61}\) \(-7.27062 q^{63}\) \(-3.72317 q^{65}\) \(-7.08341 q^{67}\) \(+16.3074 q^{69}\) \(-4.77071 q^{71}\) \(-12.6755 q^{73}\) \(+2.50073 q^{75}\) \(+1.33141 q^{77}\) \(-5.17110 q^{79}\) \(-8.17465 q^{81}\) \(-1.25705 q^{83}\) \(-2.87712 q^{85}\) \(-8.51551 q^{87}\) \(-0.496952 q^{89}\) \(+8.31977 q^{91}\) \(-11.1562 q^{93}\) \(-4.54184 q^{95}\) \(-13.7580 q^{97}\) \(-1.93859 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.50073 1.44380 0.721900 0.691998i \(-0.243269\pi\)
0.721900 + 0.691998i \(0.243269\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.23459 −0.844597 −0.422298 0.906457i \(-0.638777\pi\)
−0.422298 + 0.906457i \(0.638777\pi\)
\(8\) 0 0
\(9\) 3.25367 1.08456
\(10\) 0 0
\(11\) −0.595816 −0.179645 −0.0898227 0.995958i \(-0.528630\pi\)
−0.0898227 + 0.995958i \(0.528630\pi\)
\(12\) 0 0
\(13\) −3.72317 −1.03262 −0.516311 0.856401i \(-0.672695\pi\)
−0.516311 + 0.856401i \(0.672695\pi\)
\(14\) 0 0
\(15\) 2.50073 0.645687
\(16\) 0 0
\(17\) −2.87712 −0.697805 −0.348903 0.937159i \(-0.613446\pi\)
−0.348903 + 0.937159i \(0.613446\pi\)
\(18\) 0 0
\(19\) −4.54184 −1.04197 −0.520985 0.853566i \(-0.674435\pi\)
−0.520985 + 0.853566i \(0.674435\pi\)
\(20\) 0 0
\(21\) −5.58812 −1.21943
\(22\) 0 0
\(23\) 6.52105 1.35973 0.679866 0.733336i \(-0.262038\pi\)
0.679866 + 0.733336i \(0.262038\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0.634355 0.122082
\(28\) 0 0
\(29\) −3.40521 −0.632331 −0.316165 0.948704i \(-0.602395\pi\)
−0.316165 + 0.948704i \(0.602395\pi\)
\(30\) 0 0
\(31\) −4.46118 −0.801251 −0.400625 0.916242i \(-0.631207\pi\)
−0.400625 + 0.916242i \(0.631207\pi\)
\(32\) 0 0
\(33\) −1.48998 −0.259372
\(34\) 0 0
\(35\) −2.23459 −0.377715
\(36\) 0 0
\(37\) −1.19972 −0.197232 −0.0986162 0.995126i \(-0.531442\pi\)
−0.0986162 + 0.995126i \(0.531442\pi\)
\(38\) 0 0
\(39\) −9.31066 −1.49090
\(40\) 0 0
\(41\) 6.99016 1.09168 0.545840 0.837890i \(-0.316211\pi\)
0.545840 + 0.837890i \(0.316211\pi\)
\(42\) 0 0
\(43\) −6.50220 −0.991576 −0.495788 0.868444i \(-0.665121\pi\)
−0.495788 + 0.868444i \(0.665121\pi\)
\(44\) 0 0
\(45\) 3.25367 0.485028
\(46\) 0 0
\(47\) 1.73067 0.252444 0.126222 0.992002i \(-0.459715\pi\)
0.126222 + 0.992002i \(0.459715\pi\)
\(48\) 0 0
\(49\) −2.00660 −0.286657
\(50\) 0 0
\(51\) −7.19492 −1.00749
\(52\) 0 0
\(53\) 1.40445 0.192916 0.0964578 0.995337i \(-0.469249\pi\)
0.0964578 + 0.995337i \(0.469249\pi\)
\(54\) 0 0
\(55\) −0.595816 −0.0803398
\(56\) 0 0
\(57\) −11.3579 −1.50439
\(58\) 0 0
\(59\) 4.59179 0.597801 0.298900 0.954284i \(-0.403380\pi\)
0.298900 + 0.954284i \(0.403380\pi\)
\(60\) 0 0
\(61\) −0.884262 −0.113218 −0.0566090 0.998396i \(-0.518029\pi\)
−0.0566090 + 0.998396i \(0.518029\pi\)
\(62\) 0 0
\(63\) −7.27062 −0.916012
\(64\) 0 0
\(65\) −3.72317 −0.461803
\(66\) 0 0
\(67\) −7.08341 −0.865377 −0.432688 0.901544i \(-0.642435\pi\)
−0.432688 + 0.901544i \(0.642435\pi\)
\(68\) 0 0
\(69\) 16.3074 1.96318
\(70\) 0 0
\(71\) −4.77071 −0.566179 −0.283089 0.959094i \(-0.591359\pi\)
−0.283089 + 0.959094i \(0.591359\pi\)
\(72\) 0 0
\(73\) −12.6755 −1.48355 −0.741776 0.670648i \(-0.766016\pi\)
−0.741776 + 0.670648i \(0.766016\pi\)
\(74\) 0 0
\(75\) 2.50073 0.288760
\(76\) 0 0
\(77\) 1.33141 0.151728
\(78\) 0 0
\(79\) −5.17110 −0.581794 −0.290897 0.956754i \(-0.593954\pi\)
−0.290897 + 0.956754i \(0.593954\pi\)
\(80\) 0 0
\(81\) −8.17465 −0.908295
\(82\) 0 0
\(83\) −1.25705 −0.137979 −0.0689897 0.997617i \(-0.521978\pi\)
−0.0689897 + 0.997617i \(0.521978\pi\)
\(84\) 0 0
\(85\) −2.87712 −0.312068
\(86\) 0 0
\(87\) −8.51551 −0.912959
\(88\) 0 0
\(89\) −0.496952 −0.0526769 −0.0263384 0.999653i \(-0.508385\pi\)
−0.0263384 + 0.999653i \(0.508385\pi\)
\(90\) 0 0
\(91\) 8.31977 0.872149
\(92\) 0 0
\(93\) −11.1562 −1.15685
\(94\) 0 0
\(95\) −4.54184 −0.465983
\(96\) 0 0
\(97\) −13.7580 −1.39691 −0.698457 0.715652i \(-0.746130\pi\)
−0.698457 + 0.715652i \(0.746130\pi\)
\(98\) 0 0
\(99\) −1.93859 −0.194835
\(100\) 0 0
\(101\) 6.72952 0.669613 0.334806 0.942287i \(-0.391329\pi\)
0.334806 + 0.942287i \(0.391329\pi\)
\(102\) 0 0
\(103\) 17.8215 1.75600 0.878002 0.478657i \(-0.158876\pi\)
0.878002 + 0.478657i \(0.158876\pi\)
\(104\) 0 0
\(105\) −5.58812 −0.545345
\(106\) 0 0
\(107\) 4.87081 0.470879 0.235440 0.971889i \(-0.424347\pi\)
0.235440 + 0.971889i \(0.424347\pi\)
\(108\) 0 0
\(109\) −8.56483 −0.820362 −0.410181 0.912004i \(-0.634534\pi\)
−0.410181 + 0.912004i \(0.634534\pi\)
\(110\) 0 0
\(111\) −3.00017 −0.284764
\(112\) 0 0
\(113\) −1.92152 −0.180762 −0.0903809 0.995907i \(-0.528808\pi\)
−0.0903809 + 0.995907i \(0.528808\pi\)
\(114\) 0 0
\(115\) 6.52105 0.608091
\(116\) 0 0
\(117\) −12.1140 −1.11994
\(118\) 0 0
\(119\) 6.42920 0.589364
\(120\) 0 0
\(121\) −10.6450 −0.967728
\(122\) 0 0
\(123\) 17.4805 1.57617
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −9.79230 −0.868926 −0.434463 0.900690i \(-0.643062\pi\)
−0.434463 + 0.900690i \(0.643062\pi\)
\(128\) 0 0
\(129\) −16.2603 −1.43164
\(130\) 0 0
\(131\) −13.0867 −1.14339 −0.571693 0.820467i \(-0.693713\pi\)
−0.571693 + 0.820467i \(0.693713\pi\)
\(132\) 0 0
\(133\) 10.1492 0.880044
\(134\) 0 0
\(135\) 0.634355 0.0545966
\(136\) 0 0
\(137\) −2.89866 −0.247650 −0.123825 0.992304i \(-0.539516\pi\)
−0.123825 + 0.992304i \(0.539516\pi\)
\(138\) 0 0
\(139\) −5.72145 −0.485287 −0.242644 0.970116i \(-0.578015\pi\)
−0.242644 + 0.970116i \(0.578015\pi\)
\(140\) 0 0
\(141\) 4.32794 0.364479
\(142\) 0 0
\(143\) 2.21833 0.185506
\(144\) 0 0
\(145\) −3.40521 −0.282787
\(146\) 0 0
\(147\) −5.01796 −0.413875
\(148\) 0 0
\(149\) 10.8717 0.890640 0.445320 0.895371i \(-0.353090\pi\)
0.445320 + 0.895371i \(0.353090\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) −9.36121 −0.756809
\(154\) 0 0
\(155\) −4.46118 −0.358330
\(156\) 0 0
\(157\) −1.54050 −0.122945 −0.0614727 0.998109i \(-0.519580\pi\)
−0.0614727 + 0.998109i \(0.519580\pi\)
\(158\) 0 0
\(159\) 3.51215 0.278531
\(160\) 0 0
\(161\) −14.5719 −1.14843
\(162\) 0 0
\(163\) 18.9269 1.48247 0.741235 0.671245i \(-0.234240\pi\)
0.741235 + 0.671245i \(0.234240\pi\)
\(164\) 0 0
\(165\) −1.48998 −0.115995
\(166\) 0 0
\(167\) −15.4690 −1.19702 −0.598512 0.801114i \(-0.704241\pi\)
−0.598512 + 0.801114i \(0.704241\pi\)
\(168\) 0 0
\(169\) 0.862007 0.0663082
\(170\) 0 0
\(171\) −14.7776 −1.13007
\(172\) 0 0
\(173\) 0.494021 0.0375597 0.0187799 0.999824i \(-0.494022\pi\)
0.0187799 + 0.999824i \(0.494022\pi\)
\(174\) 0 0
\(175\) −2.23459 −0.168919
\(176\) 0 0
\(177\) 11.4829 0.863104
\(178\) 0 0
\(179\) −2.14246 −0.160135 −0.0800675 0.996789i \(-0.525514\pi\)
−0.0800675 + 0.996789i \(0.525514\pi\)
\(180\) 0 0
\(181\) −5.26919 −0.391656 −0.195828 0.980638i \(-0.562739\pi\)
−0.195828 + 0.980638i \(0.562739\pi\)
\(182\) 0 0
\(183\) −2.21130 −0.163464
\(184\) 0 0
\(185\) −1.19972 −0.0882050
\(186\) 0 0
\(187\) 1.71424 0.125357
\(188\) 0 0
\(189\) −1.41752 −0.103110
\(190\) 0 0
\(191\) 18.4623 1.33588 0.667941 0.744214i \(-0.267176\pi\)
0.667941 + 0.744214i \(0.267176\pi\)
\(192\) 0 0
\(193\) −3.42365 −0.246440 −0.123220 0.992379i \(-0.539322\pi\)
−0.123220 + 0.992379i \(0.539322\pi\)
\(194\) 0 0
\(195\) −9.31066 −0.666750
\(196\) 0 0
\(197\) 11.3266 0.806987 0.403494 0.914983i \(-0.367796\pi\)
0.403494 + 0.914983i \(0.367796\pi\)
\(198\) 0 0
\(199\) −9.44925 −0.669840 −0.334920 0.942247i \(-0.608709\pi\)
−0.334920 + 0.942247i \(0.608709\pi\)
\(200\) 0 0
\(201\) −17.7137 −1.24943
\(202\) 0 0
\(203\) 7.60925 0.534064
\(204\) 0 0
\(205\) 6.99016 0.488214
\(206\) 0 0
\(207\) 21.2173 1.47471
\(208\) 0 0
\(209\) 2.70610 0.187185
\(210\) 0 0
\(211\) 1.83176 0.126103 0.0630517 0.998010i \(-0.479917\pi\)
0.0630517 + 0.998010i \(0.479917\pi\)
\(212\) 0 0
\(213\) −11.9303 −0.817449
\(214\) 0 0
\(215\) −6.50220 −0.443446
\(216\) 0 0
\(217\) 9.96891 0.676734
\(218\) 0 0
\(219\) −31.6980 −2.14195
\(220\) 0 0
\(221\) 10.7120 0.720569
\(222\) 0 0
\(223\) 14.9018 0.997899 0.498950 0.866631i \(-0.333719\pi\)
0.498950 + 0.866631i \(0.333719\pi\)
\(224\) 0 0
\(225\) 3.25367 0.216911
\(226\) 0 0
\(227\) 1.84861 0.122696 0.0613482 0.998116i \(-0.480460\pi\)
0.0613482 + 0.998116i \(0.480460\pi\)
\(228\) 0 0
\(229\) −0.282678 −0.0186799 −0.00933993 0.999956i \(-0.502973\pi\)
−0.00933993 + 0.999956i \(0.502973\pi\)
\(230\) 0 0
\(231\) 3.32949 0.219064
\(232\) 0 0
\(233\) 29.3691 1.92404 0.962018 0.272985i \(-0.0880109\pi\)
0.962018 + 0.272985i \(0.0880109\pi\)
\(234\) 0 0
\(235\) 1.73067 0.112896
\(236\) 0 0
\(237\) −12.9315 −0.839994
\(238\) 0 0
\(239\) −27.3417 −1.76859 −0.884295 0.466930i \(-0.845360\pi\)
−0.884295 + 0.466930i \(0.845360\pi\)
\(240\) 0 0
\(241\) −15.1842 −0.978099 −0.489050 0.872256i \(-0.662656\pi\)
−0.489050 + 0.872256i \(0.662656\pi\)
\(242\) 0 0
\(243\) −22.3457 −1.43348
\(244\) 0 0
\(245\) −2.00660 −0.128197
\(246\) 0 0
\(247\) 16.9100 1.07596
\(248\) 0 0
\(249\) −3.14355 −0.199215
\(250\) 0 0
\(251\) 16.0107 1.01059 0.505293 0.862948i \(-0.331384\pi\)
0.505293 + 0.862948i \(0.331384\pi\)
\(252\) 0 0
\(253\) −3.88534 −0.244269
\(254\) 0 0
\(255\) −7.19492 −0.450563
\(256\) 0 0
\(257\) −3.68137 −0.229638 −0.114819 0.993386i \(-0.536629\pi\)
−0.114819 + 0.993386i \(0.536629\pi\)
\(258\) 0 0
\(259\) 2.68088 0.166582
\(260\) 0 0
\(261\) −11.0794 −0.685798
\(262\) 0 0
\(263\) 8.37151 0.516210 0.258105 0.966117i \(-0.416902\pi\)
0.258105 + 0.966117i \(0.416902\pi\)
\(264\) 0 0
\(265\) 1.40445 0.0862745
\(266\) 0 0
\(267\) −1.24275 −0.0760548
\(268\) 0 0
\(269\) 25.5313 1.55667 0.778334 0.627850i \(-0.216065\pi\)
0.778334 + 0.627850i \(0.216065\pi\)
\(270\) 0 0
\(271\) 13.1676 0.799872 0.399936 0.916543i \(-0.369032\pi\)
0.399936 + 0.916543i \(0.369032\pi\)
\(272\) 0 0
\(273\) 20.8055 1.25921
\(274\) 0 0
\(275\) −0.595816 −0.0359291
\(276\) 0 0
\(277\) 15.6240 0.938758 0.469379 0.882997i \(-0.344478\pi\)
0.469379 + 0.882997i \(0.344478\pi\)
\(278\) 0 0
\(279\) −14.5152 −0.869001
\(280\) 0 0
\(281\) −10.3803 −0.619236 −0.309618 0.950861i \(-0.600201\pi\)
−0.309618 + 0.950861i \(0.600201\pi\)
\(282\) 0 0
\(283\) 14.6520 0.870969 0.435484 0.900196i \(-0.356577\pi\)
0.435484 + 0.900196i \(0.356577\pi\)
\(284\) 0 0
\(285\) −11.3579 −0.672786
\(286\) 0 0
\(287\) −15.6202 −0.922029
\(288\) 0 0
\(289\) −8.72216 −0.513068
\(290\) 0 0
\(291\) −34.4051 −2.01686
\(292\) 0 0
\(293\) −21.1456 −1.23534 −0.617669 0.786438i \(-0.711923\pi\)
−0.617669 + 0.786438i \(0.711923\pi\)
\(294\) 0 0
\(295\) 4.59179 0.267345
\(296\) 0 0
\(297\) −0.377959 −0.0219314
\(298\) 0 0
\(299\) −24.2790 −1.40409
\(300\) 0 0
\(301\) 14.5298 0.837482
\(302\) 0 0
\(303\) 16.8287 0.966786
\(304\) 0 0
\(305\) −0.884262 −0.0506327
\(306\) 0 0
\(307\) −29.7630 −1.69866 −0.849331 0.527860i \(-0.822994\pi\)
−0.849331 + 0.527860i \(0.822994\pi\)
\(308\) 0 0
\(309\) 44.5668 2.53532
\(310\) 0 0
\(311\) −4.35955 −0.247207 −0.123604 0.992332i \(-0.539445\pi\)
−0.123604 + 0.992332i \(0.539445\pi\)
\(312\) 0 0
\(313\) 9.57090 0.540979 0.270490 0.962723i \(-0.412814\pi\)
0.270490 + 0.962723i \(0.412814\pi\)
\(314\) 0 0
\(315\) −7.27062 −0.409653
\(316\) 0 0
\(317\) 2.73886 0.153829 0.0769147 0.997038i \(-0.475493\pi\)
0.0769147 + 0.997038i \(0.475493\pi\)
\(318\) 0 0
\(319\) 2.02888 0.113595
\(320\) 0 0
\(321\) 12.1806 0.679855
\(322\) 0 0
\(323\) 13.0674 0.727091
\(324\) 0 0
\(325\) −3.72317 −0.206524
\(326\) 0 0
\(327\) −21.4184 −1.18444
\(328\) 0 0
\(329\) −3.86734 −0.213213
\(330\) 0 0
\(331\) −22.3972 −1.23106 −0.615531 0.788112i \(-0.711059\pi\)
−0.615531 + 0.788112i \(0.711059\pi\)
\(332\) 0 0
\(333\) −3.90348 −0.213910
\(334\) 0 0
\(335\) −7.08341 −0.387008
\(336\) 0 0
\(337\) −14.5160 −0.790738 −0.395369 0.918522i \(-0.629383\pi\)
−0.395369 + 0.918522i \(0.629383\pi\)
\(338\) 0 0
\(339\) −4.80522 −0.260984
\(340\) 0 0
\(341\) 2.65804 0.143941
\(342\) 0 0
\(343\) 20.1261 1.08671
\(344\) 0 0
\(345\) 16.3074 0.877961
\(346\) 0 0
\(347\) 13.5090 0.725200 0.362600 0.931945i \(-0.381889\pi\)
0.362600 + 0.931945i \(0.381889\pi\)
\(348\) 0 0
\(349\) −1.19745 −0.0640981 −0.0320491 0.999486i \(-0.510203\pi\)
−0.0320491 + 0.999486i \(0.510203\pi\)
\(350\) 0 0
\(351\) −2.36181 −0.126064
\(352\) 0 0
\(353\) 13.3936 0.712869 0.356435 0.934320i \(-0.383992\pi\)
0.356435 + 0.934320i \(0.383992\pi\)
\(354\) 0 0
\(355\) −4.77071 −0.253203
\(356\) 0 0
\(357\) 16.0777 0.850923
\(358\) 0 0
\(359\) 30.1532 1.59142 0.795712 0.605675i \(-0.207097\pi\)
0.795712 + 0.605675i \(0.207097\pi\)
\(360\) 0 0
\(361\) 1.62830 0.0856998
\(362\) 0 0
\(363\) −26.6203 −1.39720
\(364\) 0 0
\(365\) −12.6755 −0.663465
\(366\) 0 0
\(367\) −3.47684 −0.181490 −0.0907449 0.995874i \(-0.528925\pi\)
−0.0907449 + 0.995874i \(0.528925\pi\)
\(368\) 0 0
\(369\) 22.7437 1.18399
\(370\) 0 0
\(371\) −3.13837 −0.162936
\(372\) 0 0
\(373\) −31.7637 −1.64466 −0.822332 0.569009i \(-0.807327\pi\)
−0.822332 + 0.569009i \(0.807327\pi\)
\(374\) 0 0
\(375\) 2.50073 0.129137
\(376\) 0 0
\(377\) 12.6782 0.652959
\(378\) 0 0
\(379\) 26.1043 1.34089 0.670444 0.741960i \(-0.266104\pi\)
0.670444 + 0.741960i \(0.266104\pi\)
\(380\) 0 0
\(381\) −24.4879 −1.25455
\(382\) 0 0
\(383\) −24.7126 −1.26275 −0.631377 0.775476i \(-0.717510\pi\)
−0.631377 + 0.775476i \(0.717510\pi\)
\(384\) 0 0
\(385\) 1.33141 0.0678547
\(386\) 0 0
\(387\) −21.1560 −1.07542
\(388\) 0 0
\(389\) 16.5502 0.839126 0.419563 0.907726i \(-0.362183\pi\)
0.419563 + 0.907726i \(0.362183\pi\)
\(390\) 0 0
\(391\) −18.7619 −0.948828
\(392\) 0 0
\(393\) −32.7263 −1.65082
\(394\) 0 0
\(395\) −5.17110 −0.260186
\(396\) 0 0
\(397\) 12.9094 0.647904 0.323952 0.946074i \(-0.394988\pi\)
0.323952 + 0.946074i \(0.394988\pi\)
\(398\) 0 0
\(399\) 25.3803 1.27061
\(400\) 0 0
\(401\) 2.96235 0.147933 0.0739663 0.997261i \(-0.476434\pi\)
0.0739663 + 0.997261i \(0.476434\pi\)
\(402\) 0 0
\(403\) 16.6097 0.827389
\(404\) 0 0
\(405\) −8.17465 −0.406202
\(406\) 0 0
\(407\) 0.714811 0.0354319
\(408\) 0 0
\(409\) 3.79317 0.187560 0.0937801 0.995593i \(-0.470105\pi\)
0.0937801 + 0.995593i \(0.470105\pi\)
\(410\) 0 0
\(411\) −7.24879 −0.357556
\(412\) 0 0
\(413\) −10.2608 −0.504900
\(414\) 0 0
\(415\) −1.25705 −0.0617063
\(416\) 0 0
\(417\) −14.3078 −0.700657
\(418\) 0 0
\(419\) 5.82390 0.284516 0.142258 0.989830i \(-0.454564\pi\)
0.142258 + 0.989830i \(0.454564\pi\)
\(420\) 0 0
\(421\) −32.2079 −1.56972 −0.784859 0.619675i \(-0.787265\pi\)
−0.784859 + 0.619675i \(0.787265\pi\)
\(422\) 0 0
\(423\) 5.63102 0.273790
\(424\) 0 0
\(425\) −2.87712 −0.139561
\(426\) 0 0
\(427\) 1.97596 0.0956236
\(428\) 0 0
\(429\) 5.54744 0.267833
\(430\) 0 0
\(431\) 31.8411 1.53373 0.766865 0.641808i \(-0.221815\pi\)
0.766865 + 0.641808i \(0.221815\pi\)
\(432\) 0 0
\(433\) 3.26192 0.156758 0.0783790 0.996924i \(-0.475026\pi\)
0.0783790 + 0.996924i \(0.475026\pi\)
\(434\) 0 0
\(435\) −8.51551 −0.408288
\(436\) 0 0
\(437\) −29.6175 −1.41680
\(438\) 0 0
\(439\) 11.2835 0.538531 0.269265 0.963066i \(-0.413219\pi\)
0.269265 + 0.963066i \(0.413219\pi\)
\(440\) 0 0
\(441\) −6.52880 −0.310895
\(442\) 0 0
\(443\) 1.59261 0.0756673 0.0378336 0.999284i \(-0.487954\pi\)
0.0378336 + 0.999284i \(0.487954\pi\)
\(444\) 0 0
\(445\) −0.496952 −0.0235578
\(446\) 0 0
\(447\) 27.1871 1.28591
\(448\) 0 0
\(449\) −5.41951 −0.255762 −0.127881 0.991789i \(-0.540818\pi\)
−0.127881 + 0.991789i \(0.540818\pi\)
\(450\) 0 0
\(451\) −4.16485 −0.196115
\(452\) 0 0
\(453\) −2.50073 −0.117495
\(454\) 0 0
\(455\) 8.31977 0.390037
\(456\) 0 0
\(457\) −0.152758 −0.00714572 −0.00357286 0.999994i \(-0.501137\pi\)
−0.00357286 + 0.999994i \(0.501137\pi\)
\(458\) 0 0
\(459\) −1.82512 −0.0851892
\(460\) 0 0
\(461\) 28.0000 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(462\) 0 0
\(463\) 36.5086 1.69670 0.848349 0.529438i \(-0.177597\pi\)
0.848349 + 0.529438i \(0.177597\pi\)
\(464\) 0 0
\(465\) −11.1562 −0.517357
\(466\) 0 0
\(467\) 22.8318 1.05653 0.528265 0.849079i \(-0.322843\pi\)
0.528265 + 0.849079i \(0.322843\pi\)
\(468\) 0 0
\(469\) 15.8285 0.730894
\(470\) 0 0
\(471\) −3.85238 −0.177509
\(472\) 0 0
\(473\) 3.87411 0.178132
\(474\) 0 0
\(475\) −4.54184 −0.208394
\(476\) 0 0
\(477\) 4.56960 0.209228
\(478\) 0 0
\(479\) 22.5769 1.03156 0.515782 0.856720i \(-0.327502\pi\)
0.515782 + 0.856720i \(0.327502\pi\)
\(480\) 0 0
\(481\) 4.46676 0.203667
\(482\) 0 0
\(483\) −36.4404 −1.65810
\(484\) 0 0
\(485\) −13.7580 −0.624719
\(486\) 0 0
\(487\) −18.6400 −0.844658 −0.422329 0.906443i \(-0.638787\pi\)
−0.422329 + 0.906443i \(0.638787\pi\)
\(488\) 0 0
\(489\) 47.3312 2.14039
\(490\) 0 0
\(491\) −7.74615 −0.349579 −0.174789 0.984606i \(-0.555924\pi\)
−0.174789 + 0.984606i \(0.555924\pi\)
\(492\) 0 0
\(493\) 9.79720 0.441244
\(494\) 0 0
\(495\) −1.93859 −0.0871330
\(496\) 0 0
\(497\) 10.6606 0.478193
\(498\) 0 0
\(499\) 17.8916 0.800936 0.400468 0.916311i \(-0.368847\pi\)
0.400468 + 0.916311i \(0.368847\pi\)
\(500\) 0 0
\(501\) −38.6837 −1.72826
\(502\) 0 0
\(503\) 3.65161 0.162817 0.0814087 0.996681i \(-0.474058\pi\)
0.0814087 + 0.996681i \(0.474058\pi\)
\(504\) 0 0
\(505\) 6.72952 0.299460
\(506\) 0 0
\(507\) 2.15565 0.0957357
\(508\) 0 0
\(509\) 17.2974 0.766695 0.383348 0.923604i \(-0.374771\pi\)
0.383348 + 0.923604i \(0.374771\pi\)
\(510\) 0 0
\(511\) 28.3245 1.25300
\(512\) 0 0
\(513\) −2.88114 −0.127205
\(514\) 0 0
\(515\) 17.8215 0.785309
\(516\) 0 0
\(517\) −1.03116 −0.0453504
\(518\) 0 0
\(519\) 1.23541 0.0542287
\(520\) 0 0
\(521\) −2.71324 −0.118869 −0.0594345 0.998232i \(-0.518930\pi\)
−0.0594345 + 0.998232i \(0.518930\pi\)
\(522\) 0 0
\(523\) 41.9196 1.83301 0.916507 0.400018i \(-0.130996\pi\)
0.916507 + 0.400018i \(0.130996\pi\)
\(524\) 0 0
\(525\) −5.58812 −0.243886
\(526\) 0 0
\(527\) 12.8354 0.559117
\(528\) 0 0
\(529\) 19.5240 0.848871
\(530\) 0 0
\(531\) 14.9402 0.648348
\(532\) 0 0
\(533\) −26.0256 −1.12729
\(534\) 0 0
\(535\) 4.87081 0.210584
\(536\) 0 0
\(537\) −5.35772 −0.231203
\(538\) 0 0
\(539\) 1.19556 0.0514965
\(540\) 0 0
\(541\) −1.78080 −0.0765628 −0.0382814 0.999267i \(-0.512188\pi\)
−0.0382814 + 0.999267i \(0.512188\pi\)
\(542\) 0 0
\(543\) −13.1768 −0.565472
\(544\) 0 0
\(545\) −8.56483 −0.366877
\(546\) 0 0
\(547\) −14.6949 −0.628309 −0.314154 0.949372i \(-0.601721\pi\)
−0.314154 + 0.949372i \(0.601721\pi\)
\(548\) 0 0
\(549\) −2.87709 −0.122791
\(550\) 0 0
\(551\) 15.4659 0.658869
\(552\) 0 0
\(553\) 11.5553 0.491381
\(554\) 0 0
\(555\) −3.00017 −0.127350
\(556\) 0 0
\(557\) 11.4666 0.485856 0.242928 0.970044i \(-0.421892\pi\)
0.242928 + 0.970044i \(0.421892\pi\)
\(558\) 0 0
\(559\) 24.2088 1.02392
\(560\) 0 0
\(561\) 4.28685 0.180991
\(562\) 0 0
\(563\) −2.83079 −0.119303 −0.0596517 0.998219i \(-0.518999\pi\)
−0.0596517 + 0.998219i \(0.518999\pi\)
\(564\) 0 0
\(565\) −1.92152 −0.0808391
\(566\) 0 0
\(567\) 18.2670 0.767142
\(568\) 0 0
\(569\) −37.8446 −1.58653 −0.793264 0.608878i \(-0.791620\pi\)
−0.793264 + 0.608878i \(0.791620\pi\)
\(570\) 0 0
\(571\) 11.0219 0.461251 0.230625 0.973043i \(-0.425923\pi\)
0.230625 + 0.973043i \(0.425923\pi\)
\(572\) 0 0
\(573\) 46.1692 1.92875
\(574\) 0 0
\(575\) 6.52105 0.271946
\(576\) 0 0
\(577\) −16.7739 −0.698305 −0.349153 0.937066i \(-0.613531\pi\)
−0.349153 + 0.937066i \(0.613531\pi\)
\(578\) 0 0
\(579\) −8.56164 −0.355810
\(580\) 0 0
\(581\) 2.80900 0.116537
\(582\) 0 0
\(583\) −0.836792 −0.0346564
\(584\) 0 0
\(585\) −12.1140 −0.500851
\(586\) 0 0
\(587\) −5.42080 −0.223741 −0.111870 0.993723i \(-0.535684\pi\)
−0.111870 + 0.993723i \(0.535684\pi\)
\(588\) 0 0
\(589\) 20.2619 0.834879
\(590\) 0 0
\(591\) 28.3248 1.16513
\(592\) 0 0
\(593\) −0.636921 −0.0261552 −0.0130776 0.999914i \(-0.504163\pi\)
−0.0130776 + 0.999914i \(0.504163\pi\)
\(594\) 0 0
\(595\) 6.42920 0.263572
\(596\) 0 0
\(597\) −23.6301 −0.967114
\(598\) 0 0
\(599\) −29.3506 −1.19923 −0.599616 0.800288i \(-0.704680\pi\)
−0.599616 + 0.800288i \(0.704680\pi\)
\(600\) 0 0
\(601\) −16.3740 −0.667910 −0.333955 0.942589i \(-0.608383\pi\)
−0.333955 + 0.942589i \(0.608383\pi\)
\(602\) 0 0
\(603\) −23.0471 −0.938549
\(604\) 0 0
\(605\) −10.6450 −0.432781
\(606\) 0 0
\(607\) 12.1263 0.492191 0.246095 0.969246i \(-0.420852\pi\)
0.246095 + 0.969246i \(0.420852\pi\)
\(608\) 0 0
\(609\) 19.0287 0.771082
\(610\) 0 0
\(611\) −6.44358 −0.260679
\(612\) 0 0
\(613\) 11.6390 0.470095 0.235047 0.971984i \(-0.424475\pi\)
0.235047 + 0.971984i \(0.424475\pi\)
\(614\) 0 0
\(615\) 17.4805 0.704883
\(616\) 0 0
\(617\) −21.0453 −0.847251 −0.423626 0.905837i \(-0.639243\pi\)
−0.423626 + 0.905837i \(0.639243\pi\)
\(618\) 0 0
\(619\) −48.3482 −1.94328 −0.971638 0.236472i \(-0.924009\pi\)
−0.971638 + 0.236472i \(0.924009\pi\)
\(620\) 0 0
\(621\) 4.13666 0.165998
\(622\) 0 0
\(623\) 1.11049 0.0444907
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 6.76724 0.270257
\(628\) 0 0
\(629\) 3.45174 0.137630
\(630\) 0 0
\(631\) −35.7760 −1.42422 −0.712111 0.702067i \(-0.752261\pi\)
−0.712111 + 0.702067i \(0.752261\pi\)
\(632\) 0 0
\(633\) 4.58074 0.182068
\(634\) 0 0
\(635\) −9.79230 −0.388596
\(636\) 0 0
\(637\) 7.47090 0.296008
\(638\) 0 0
\(639\) −15.5223 −0.614053
\(640\) 0 0
\(641\) −7.52766 −0.297325 −0.148662 0.988888i \(-0.547497\pi\)
−0.148662 + 0.988888i \(0.547497\pi\)
\(642\) 0 0
\(643\) −9.10077 −0.358899 −0.179450 0.983767i \(-0.557432\pi\)
−0.179450 + 0.983767i \(0.557432\pi\)
\(644\) 0 0
\(645\) −16.2603 −0.640247
\(646\) 0 0
\(647\) 45.0870 1.77255 0.886276 0.463158i \(-0.153284\pi\)
0.886276 + 0.463158i \(0.153284\pi\)
\(648\) 0 0
\(649\) −2.73586 −0.107392
\(650\) 0 0
\(651\) 24.9296 0.977068
\(652\) 0 0
\(653\) 10.5418 0.412534 0.206267 0.978496i \(-0.433868\pi\)
0.206267 + 0.978496i \(0.433868\pi\)
\(654\) 0 0
\(655\) −13.0867 −0.511338
\(656\) 0 0
\(657\) −41.2418 −1.60900
\(658\) 0 0
\(659\) 22.5415 0.878093 0.439047 0.898464i \(-0.355316\pi\)
0.439047 + 0.898464i \(0.355316\pi\)
\(660\) 0 0
\(661\) 21.7894 0.847510 0.423755 0.905777i \(-0.360712\pi\)
0.423755 + 0.905777i \(0.360712\pi\)
\(662\) 0 0
\(663\) 26.7879 1.04036
\(664\) 0 0
\(665\) 10.1492 0.393567
\(666\) 0 0
\(667\) −22.2055 −0.859801
\(668\) 0 0
\(669\) 37.2655 1.44077
\(670\) 0 0
\(671\) 0.526857 0.0203391
\(672\) 0 0
\(673\) −41.8986 −1.61507 −0.807536 0.589818i \(-0.799199\pi\)
−0.807536 + 0.589818i \(0.799199\pi\)
\(674\) 0 0
\(675\) 0.634355 0.0244163
\(676\) 0 0
\(677\) −28.4061 −1.09174 −0.545868 0.837871i \(-0.683800\pi\)
−0.545868 + 0.837871i \(0.683800\pi\)
\(678\) 0 0
\(679\) 30.7435 1.17983
\(680\) 0 0
\(681\) 4.62287 0.177149
\(682\) 0 0
\(683\) −22.2452 −0.851189 −0.425595 0.904914i \(-0.639935\pi\)
−0.425595 + 0.904914i \(0.639935\pi\)
\(684\) 0 0
\(685\) −2.89866 −0.110752
\(686\) 0 0
\(687\) −0.706902 −0.0269700
\(688\) 0 0
\(689\) −5.22900 −0.199209
\(690\) 0 0
\(691\) −17.1019 −0.650586 −0.325293 0.945613i \(-0.605463\pi\)
−0.325293 + 0.945613i \(0.605463\pi\)
\(692\) 0 0
\(693\) 4.33195 0.164557
\(694\) 0 0
\(695\) −5.72145 −0.217027
\(696\) 0 0
\(697\) −20.1116 −0.761780
\(698\) 0 0
\(699\) 73.4444 2.77792
\(700\) 0 0
\(701\) −14.1734 −0.535320 −0.267660 0.963513i \(-0.586250\pi\)
−0.267660 + 0.963513i \(0.586250\pi\)
\(702\) 0 0
\(703\) 5.44893 0.205510
\(704\) 0 0
\(705\) 4.32794 0.163000
\(706\) 0 0
\(707\) −15.0377 −0.565553
\(708\) 0 0
\(709\) 29.0166 1.08974 0.544872 0.838520i \(-0.316578\pi\)
0.544872 + 0.838520i \(0.316578\pi\)
\(710\) 0 0
\(711\) −16.8250 −0.630988
\(712\) 0 0
\(713\) −29.0915 −1.08949
\(714\) 0 0
\(715\) 2.21833 0.0829607
\(716\) 0 0
\(717\) −68.3744 −2.55349
\(718\) 0 0
\(719\) 32.8260 1.22420 0.612101 0.790780i \(-0.290325\pi\)
0.612101 + 0.790780i \(0.290325\pi\)
\(720\) 0 0
\(721\) −39.8238 −1.48311
\(722\) 0 0
\(723\) −37.9716 −1.41218
\(724\) 0 0
\(725\) −3.40521 −0.126466
\(726\) 0 0
\(727\) 19.6767 0.729768 0.364884 0.931053i \(-0.381109\pi\)
0.364884 + 0.931053i \(0.381109\pi\)
\(728\) 0 0
\(729\) −31.3566 −1.16136
\(730\) 0 0
\(731\) 18.7076 0.691927
\(732\) 0 0
\(733\) 23.8154 0.879643 0.439822 0.898085i \(-0.355042\pi\)
0.439822 + 0.898085i \(0.355042\pi\)
\(734\) 0 0
\(735\) −5.01796 −0.185090
\(736\) 0 0
\(737\) 4.22041 0.155461
\(738\) 0 0
\(739\) −6.24066 −0.229566 −0.114783 0.993391i \(-0.536617\pi\)
−0.114783 + 0.993391i \(0.536617\pi\)
\(740\) 0 0
\(741\) 42.2875 1.55347
\(742\) 0 0
\(743\) 9.18899 0.337111 0.168556 0.985692i \(-0.446090\pi\)
0.168556 + 0.985692i \(0.446090\pi\)
\(744\) 0 0
\(745\) 10.8717 0.398306
\(746\) 0 0
\(747\) −4.09003 −0.149646
\(748\) 0 0
\(749\) −10.8843 −0.397703
\(750\) 0 0
\(751\) −13.9511 −0.509084 −0.254542 0.967062i \(-0.581925\pi\)
−0.254542 + 0.967062i \(0.581925\pi\)
\(752\) 0 0
\(753\) 40.0385 1.45908
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) −37.2959 −1.35554 −0.677771 0.735273i \(-0.737054\pi\)
−0.677771 + 0.735273i \(0.737054\pi\)
\(758\) 0 0
\(759\) −9.71621 −0.352676
\(760\) 0 0
\(761\) −35.5858 −1.28999 −0.644993 0.764189i \(-0.723140\pi\)
−0.644993 + 0.764189i \(0.723140\pi\)
\(762\) 0 0
\(763\) 19.1389 0.692875
\(764\) 0 0
\(765\) −9.36121 −0.338455
\(766\) 0 0
\(767\) −17.0960 −0.617302
\(768\) 0 0
\(769\) −29.5041 −1.06395 −0.531973 0.846761i \(-0.678549\pi\)
−0.531973 + 0.846761i \(0.678549\pi\)
\(770\) 0 0
\(771\) −9.20612 −0.331550
\(772\) 0 0
\(773\) −22.3314 −0.803205 −0.401602 0.915814i \(-0.631547\pi\)
−0.401602 + 0.915814i \(0.631547\pi\)
\(774\) 0 0
\(775\) −4.46118 −0.160250
\(776\) 0 0
\(777\) 6.70417 0.240511
\(778\) 0 0
\(779\) −31.7482 −1.13750
\(780\) 0 0
\(781\) 2.84246 0.101711
\(782\) 0 0
\(783\) −2.16011 −0.0771960
\(784\) 0 0
\(785\) −1.54050 −0.0549829
\(786\) 0 0
\(787\) 3.07679 0.109676 0.0548379 0.998495i \(-0.482536\pi\)
0.0548379 + 0.998495i \(0.482536\pi\)
\(788\) 0 0
\(789\) 20.9349 0.745303
\(790\) 0 0
\(791\) 4.29382 0.152671
\(792\) 0 0
\(793\) 3.29226 0.116911
\(794\) 0 0
\(795\) 3.51215 0.124563
\(796\) 0 0
\(797\) −5.24635 −0.185835 −0.0929177 0.995674i \(-0.529619\pi\)
−0.0929177 + 0.995674i \(0.529619\pi\)
\(798\) 0 0
\(799\) −4.97935 −0.176157
\(800\) 0 0
\(801\) −1.61692 −0.0571310
\(802\) 0 0
\(803\) 7.55225 0.266513
\(804\) 0 0
\(805\) −14.5719 −0.513591
\(806\) 0 0
\(807\) 63.8469 2.24752
\(808\) 0 0
\(809\) −7.54397 −0.265232 −0.132616 0.991168i \(-0.542338\pi\)
−0.132616 + 0.991168i \(0.542338\pi\)
\(810\) 0 0
\(811\) 30.3175 1.06459 0.532295 0.846559i \(-0.321330\pi\)
0.532295 + 0.846559i \(0.321330\pi\)
\(812\) 0 0
\(813\) 32.9286 1.15486
\(814\) 0 0
\(815\) 18.9269 0.662981
\(816\) 0 0
\(817\) 29.5319 1.03319
\(818\) 0 0
\(819\) 27.0698 0.945894
\(820\) 0 0
\(821\) −8.68993 −0.303281 −0.151640 0.988436i \(-0.548456\pi\)
−0.151640 + 0.988436i \(0.548456\pi\)
\(822\) 0 0
\(823\) −2.16280 −0.0753903 −0.0376952 0.999289i \(-0.512002\pi\)
−0.0376952 + 0.999289i \(0.512002\pi\)
\(824\) 0 0
\(825\) −1.48998 −0.0518743
\(826\) 0 0
\(827\) 17.0630 0.593337 0.296669 0.954980i \(-0.404124\pi\)
0.296669 + 0.954980i \(0.404124\pi\)
\(828\) 0 0
\(829\) −34.8709 −1.21112 −0.605558 0.795801i \(-0.707050\pi\)
−0.605558 + 0.795801i \(0.707050\pi\)
\(830\) 0 0
\(831\) 39.0716 1.35538
\(832\) 0 0
\(833\) 5.77323 0.200030
\(834\) 0 0
\(835\) −15.4690 −0.535325
\(836\) 0 0
\(837\) −2.82997 −0.0978180
\(838\) 0 0
\(839\) 10.5512 0.364267 0.182133 0.983274i \(-0.441700\pi\)
0.182133 + 0.983274i \(0.441700\pi\)
\(840\) 0 0
\(841\) −17.4046 −0.600158
\(842\) 0 0
\(843\) −25.9583 −0.894053
\(844\) 0 0
\(845\) 0.862007 0.0296539
\(846\) 0 0
\(847\) 23.7872 0.817339
\(848\) 0 0
\(849\) 36.6406 1.25750
\(850\) 0 0
\(851\) −7.82342 −0.268183
\(852\) 0 0
\(853\) −36.3930 −1.24607 −0.623036 0.782193i \(-0.714101\pi\)
−0.623036 + 0.782193i \(0.714101\pi\)
\(854\) 0 0
\(855\) −14.7776 −0.505384
\(856\) 0 0
\(857\) −43.5153 −1.48646 −0.743228 0.669039i \(-0.766706\pi\)
−0.743228 + 0.669039i \(0.766706\pi\)
\(858\) 0 0
\(859\) 25.5083 0.870331 0.435165 0.900351i \(-0.356690\pi\)
0.435165 + 0.900351i \(0.356690\pi\)
\(860\) 0 0
\(861\) −39.0619 −1.33122
\(862\) 0 0
\(863\) 10.3708 0.353025 0.176513 0.984298i \(-0.443518\pi\)
0.176513 + 0.984298i \(0.443518\pi\)
\(864\) 0 0
\(865\) 0.494021 0.0167972
\(866\) 0 0
\(867\) −21.8118 −0.740767
\(868\) 0 0
\(869\) 3.08103 0.104517
\(870\) 0 0
\(871\) 26.3728 0.893607
\(872\) 0 0
\(873\) −44.7640 −1.51503
\(874\) 0 0
\(875\) −2.23459 −0.0755430
\(876\) 0 0
\(877\) −34.0213 −1.14882 −0.574408 0.818569i \(-0.694768\pi\)
−0.574408 + 0.818569i \(0.694768\pi\)
\(878\) 0 0
\(879\) −52.8795 −1.78358
\(880\) 0 0
\(881\) 14.9969 0.505259 0.252630 0.967563i \(-0.418705\pi\)
0.252630 + 0.967563i \(0.418705\pi\)
\(882\) 0 0
\(883\) −16.2566 −0.547079 −0.273540 0.961861i \(-0.588194\pi\)
−0.273540 + 0.961861i \(0.588194\pi\)
\(884\) 0 0
\(885\) 11.4829 0.385992
\(886\) 0 0
\(887\) 29.6093 0.994182 0.497091 0.867699i \(-0.334402\pi\)
0.497091 + 0.867699i \(0.334402\pi\)
\(888\) 0 0
\(889\) 21.8818 0.733892
\(890\) 0 0
\(891\) 4.87059 0.163171
\(892\) 0 0
\(893\) −7.86042 −0.263039
\(894\) 0 0
\(895\) −2.14246 −0.0716145
\(896\) 0 0
\(897\) −60.7152 −2.02722
\(898\) 0 0
\(899\) 15.1912 0.506656
\(900\) 0 0
\(901\) −4.04077 −0.134617
\(902\) 0 0
\(903\) 36.3351 1.20916
\(904\) 0 0
\(905\) −5.26919 −0.175154
\(906\) 0 0
\(907\) 14.8796 0.494070 0.247035 0.969007i \(-0.420544\pi\)
0.247035 + 0.969007i \(0.420544\pi\)
\(908\) 0 0
\(909\) 21.8956 0.726232
\(910\) 0 0
\(911\) −31.5430 −1.04507 −0.522534 0.852618i \(-0.675013\pi\)
−0.522534 + 0.852618i \(0.675013\pi\)
\(912\) 0 0
\(913\) 0.748972 0.0247874
\(914\) 0 0
\(915\) −2.21130 −0.0731034
\(916\) 0 0
\(917\) 29.2434 0.965701
\(918\) 0 0
\(919\) 8.19526 0.270337 0.135168 0.990823i \(-0.456842\pi\)
0.135168 + 0.990823i \(0.456842\pi\)
\(920\) 0 0
\(921\) −74.4292 −2.45253
\(922\) 0 0
\(923\) 17.7622 0.584649
\(924\) 0 0
\(925\) −1.19972 −0.0394465
\(926\) 0 0
\(927\) 57.9852 1.90448
\(928\) 0 0
\(929\) 9.76470 0.320369 0.160185 0.987087i \(-0.448791\pi\)
0.160185 + 0.987087i \(0.448791\pi\)
\(930\) 0 0
\(931\) 9.11364 0.298687
\(932\) 0 0
\(933\) −10.9021 −0.356917
\(934\) 0 0
\(935\) 1.71424 0.0560615
\(936\) 0 0
\(937\) 35.5725 1.16210 0.581052 0.813867i \(-0.302641\pi\)
0.581052 + 0.813867i \(0.302641\pi\)
\(938\) 0 0
\(939\) 23.9343 0.781065
\(940\) 0 0
\(941\) −51.8087 −1.68892 −0.844458 0.535622i \(-0.820077\pi\)
−0.844458 + 0.535622i \(0.820077\pi\)
\(942\) 0 0
\(943\) 45.5832 1.48439
\(944\) 0 0
\(945\) −1.41752 −0.0461121
\(946\) 0 0
\(947\) −28.2648 −0.918481 −0.459241 0.888312i \(-0.651878\pi\)
−0.459241 + 0.888312i \(0.651878\pi\)
\(948\) 0 0
\(949\) 47.1930 1.53195
\(950\) 0 0
\(951\) 6.84915 0.222099
\(952\) 0 0
\(953\) −12.4268 −0.402545 −0.201272 0.979535i \(-0.564508\pi\)
−0.201272 + 0.979535i \(0.564508\pi\)
\(954\) 0 0
\(955\) 18.4623 0.597425
\(956\) 0 0
\(957\) 5.07368 0.164009
\(958\) 0 0
\(959\) 6.47733 0.209164
\(960\) 0 0
\(961\) −11.0979 −0.357997
\(962\) 0 0
\(963\) 15.8480 0.510695
\(964\) 0 0
\(965\) −3.42365 −0.110211
\(966\) 0 0
\(967\) 53.2390 1.71205 0.856026 0.516934i \(-0.172927\pi\)
0.856026 + 0.516934i \(0.172927\pi\)
\(968\) 0 0
\(969\) 32.6782 1.04977
\(970\) 0 0
\(971\) −21.1474 −0.678652 −0.339326 0.940669i \(-0.610199\pi\)
−0.339326 + 0.940669i \(0.610199\pi\)
\(972\) 0 0
\(973\) 12.7851 0.409872
\(974\) 0 0
\(975\) −9.31066 −0.298180
\(976\) 0 0
\(977\) 37.2318 1.19115 0.595576 0.803299i \(-0.296924\pi\)
0.595576 + 0.803299i \(0.296924\pi\)
\(978\) 0 0
\(979\) 0.296092 0.00946315
\(980\) 0 0
\(981\) −27.8671 −0.889728
\(982\) 0 0
\(983\) 6.13633 0.195719 0.0978593 0.995200i \(-0.468800\pi\)
0.0978593 + 0.995200i \(0.468800\pi\)
\(984\) 0 0
\(985\) 11.3266 0.360896
\(986\) 0 0
\(987\) −9.67119 −0.307837
\(988\) 0 0
\(989\) −42.4011 −1.34828
\(990\) 0 0
\(991\) 4.68364 0.148781 0.0743903 0.997229i \(-0.476299\pi\)
0.0743903 + 0.997229i \(0.476299\pi\)
\(992\) 0 0
\(993\) −56.0095 −1.77741
\(994\) 0 0
\(995\) −9.44925 −0.299561
\(996\) 0 0
\(997\) −10.5068 −0.332753 −0.166376 0.986062i \(-0.553207\pi\)
−0.166376 + 0.986062i \(0.553207\pi\)
\(998\) 0 0
\(999\) −0.761047 −0.0240785
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 \(a_p\))