Properties

Label 8048.2.a.v.1.24
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.24
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.22675 q^{3}\) \(-3.90847 q^{5}\) \(+0.127234 q^{7}\) \(+1.95840 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.22675 q^{3}\) \(-3.90847 q^{5}\) \(+0.127234 q^{7}\) \(+1.95840 q^{9}\) \(-1.34859 q^{11}\) \(-1.48851 q^{13}\) \(-8.70316 q^{15}\) \(+1.12665 q^{17}\) \(+3.57046 q^{19}\) \(+0.283317 q^{21}\) \(+6.17751 q^{23}\) \(+10.2761 q^{25}\) \(-2.31939 q^{27}\) \(-0.0940486 q^{29}\) \(-1.35429 q^{31}\) \(-3.00297 q^{33}\) \(-0.497289 q^{35}\) \(+2.38774 q^{37}\) \(-3.31452 q^{39}\) \(+9.91105 q^{41}\) \(-2.37943 q^{43}\) \(-7.65433 q^{45}\) \(-12.8539 q^{47}\) \(-6.98381 q^{49}\) \(+2.50877 q^{51}\) \(+0.100296 q^{53}\) \(+5.27093 q^{55}\) \(+7.95051 q^{57}\) \(-10.4855 q^{59}\) \(-8.89059 q^{61}\) \(+0.249174 q^{63}\) \(+5.81778 q^{65}\) \(-5.58516 q^{67}\) \(+13.7557 q^{69}\) \(+9.40758 q^{71}\) \(+4.22594 q^{73}\) \(+22.8823 q^{75}\) \(-0.171587 q^{77}\) \(-12.2627 q^{79}\) \(-11.0399 q^{81}\) \(+0.492027 q^{83}\) \(-4.40349 q^{85}\) \(-0.209422 q^{87}\) \(+8.78902 q^{89}\) \(-0.189388 q^{91}\) \(-3.01567 q^{93}\) \(-13.9550 q^{95}\) \(+18.6955 q^{97}\) \(-2.64108 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.22675 1.28561 0.642806 0.766029i \(-0.277770\pi\)
0.642806 + 0.766029i \(0.277770\pi\)
\(4\) 0 0
\(5\) −3.90847 −1.74792 −0.873960 0.485998i \(-0.838456\pi\)
−0.873960 + 0.485998i \(0.838456\pi\)
\(6\) 0 0
\(7\) 0.127234 0.0480898 0.0240449 0.999711i \(-0.492346\pi\)
0.0240449 + 0.999711i \(0.492346\pi\)
\(8\) 0 0
\(9\) 1.95840 0.652799
\(10\) 0 0
\(11\) −1.34859 −0.406616 −0.203308 0.979115i \(-0.565169\pi\)
−0.203308 + 0.979115i \(0.565169\pi\)
\(12\) 0 0
\(13\) −1.48851 −0.412837 −0.206419 0.978464i \(-0.566181\pi\)
−0.206419 + 0.978464i \(0.566181\pi\)
\(14\) 0 0
\(15\) −8.70316 −2.24715
\(16\) 0 0
\(17\) 1.12665 0.273254 0.136627 0.990623i \(-0.456374\pi\)
0.136627 + 0.990623i \(0.456374\pi\)
\(18\) 0 0
\(19\) 3.57046 0.819120 0.409560 0.912283i \(-0.365682\pi\)
0.409560 + 0.912283i \(0.365682\pi\)
\(20\) 0 0
\(21\) 0.283317 0.0618249
\(22\) 0 0
\(23\) 6.17751 1.28810 0.644050 0.764983i \(-0.277253\pi\)
0.644050 + 0.764983i \(0.277253\pi\)
\(24\) 0 0
\(25\) 10.2761 2.05522
\(26\) 0 0
\(27\) −2.31939 −0.446366
\(28\) 0 0
\(29\) −0.0940486 −0.0174644 −0.00873220 0.999962i \(-0.502780\pi\)
−0.00873220 + 0.999962i \(0.502780\pi\)
\(30\) 0 0
\(31\) −1.35429 −0.243238 −0.121619 0.992577i \(-0.538809\pi\)
−0.121619 + 0.992577i \(0.538809\pi\)
\(32\) 0 0
\(33\) −3.00297 −0.522751
\(34\) 0 0
\(35\) −0.497289 −0.0840571
\(36\) 0 0
\(37\) 2.38774 0.392542 0.196271 0.980550i \(-0.437117\pi\)
0.196271 + 0.980550i \(0.437117\pi\)
\(38\) 0 0
\(39\) −3.31452 −0.530749
\(40\) 0 0
\(41\) 9.91105 1.54785 0.773923 0.633280i \(-0.218292\pi\)
0.773923 + 0.633280i \(0.218292\pi\)
\(42\) 0 0
\(43\) −2.37943 −0.362860 −0.181430 0.983404i \(-0.558073\pi\)
−0.181430 + 0.983404i \(0.558073\pi\)
\(44\) 0 0
\(45\) −7.65433 −1.14104
\(46\) 0 0
\(47\) −12.8539 −1.87493 −0.937467 0.348074i \(-0.886836\pi\)
−0.937467 + 0.348074i \(0.886836\pi\)
\(48\) 0 0
\(49\) −6.98381 −0.997687
\(50\) 0 0
\(51\) 2.50877 0.351298
\(52\) 0 0
\(53\) 0.100296 0.0137767 0.00688835 0.999976i \(-0.497807\pi\)
0.00688835 + 0.999976i \(0.497807\pi\)
\(54\) 0 0
\(55\) 5.27093 0.710732
\(56\) 0 0
\(57\) 7.95051 1.05307
\(58\) 0 0
\(59\) −10.4855 −1.36510 −0.682549 0.730840i \(-0.739129\pi\)
−0.682549 + 0.730840i \(0.739129\pi\)
\(60\) 0 0
\(61\) −8.89059 −1.13832 −0.569162 0.822226i \(-0.692732\pi\)
−0.569162 + 0.822226i \(0.692732\pi\)
\(62\) 0 0
\(63\) 0.249174 0.0313930
\(64\) 0 0
\(65\) 5.81778 0.721606
\(66\) 0 0
\(67\) −5.58516 −0.682336 −0.341168 0.940002i \(-0.610823\pi\)
−0.341168 + 0.940002i \(0.610823\pi\)
\(68\) 0 0
\(69\) 13.7557 1.65600
\(70\) 0 0
\(71\) 9.40758 1.11647 0.558237 0.829681i \(-0.311478\pi\)
0.558237 + 0.829681i \(0.311478\pi\)
\(72\) 0 0
\(73\) 4.22594 0.494609 0.247304 0.968938i \(-0.420455\pi\)
0.247304 + 0.968938i \(0.420455\pi\)
\(74\) 0 0
\(75\) 22.8823 2.64222
\(76\) 0 0
\(77\) −0.171587 −0.0195541
\(78\) 0 0
\(79\) −12.2627 −1.37967 −0.689833 0.723969i \(-0.742316\pi\)
−0.689833 + 0.723969i \(0.742316\pi\)
\(80\) 0 0
\(81\) −11.0399 −1.22665
\(82\) 0 0
\(83\) 0.492027 0.0540069 0.0270035 0.999635i \(-0.491403\pi\)
0.0270035 + 0.999635i \(0.491403\pi\)
\(84\) 0 0
\(85\) −4.40349 −0.477625
\(86\) 0 0
\(87\) −0.209422 −0.0224524
\(88\) 0 0
\(89\) 8.78902 0.931634 0.465817 0.884881i \(-0.345760\pi\)
0.465817 + 0.884881i \(0.345760\pi\)
\(90\) 0 0
\(91\) −0.189388 −0.0198533
\(92\) 0 0
\(93\) −3.01567 −0.312710
\(94\) 0 0
\(95\) −13.9550 −1.43176
\(96\) 0 0
\(97\) 18.6955 1.89824 0.949122 0.314908i \(-0.101974\pi\)
0.949122 + 0.314908i \(0.101974\pi\)
\(98\) 0 0
\(99\) −2.64108 −0.265439
\(100\) 0 0
\(101\) −3.41811 −0.340115 −0.170057 0.985434i \(-0.554395\pi\)
−0.170057 + 0.985434i \(0.554395\pi\)
\(102\) 0 0
\(103\) −0.0306739 −0.00302239 −0.00151119 0.999999i \(-0.500481\pi\)
−0.00151119 + 0.999999i \(0.500481\pi\)
\(104\) 0 0
\(105\) −1.10734 −0.108065
\(106\) 0 0
\(107\) 16.7393 1.61825 0.809126 0.587635i \(-0.199941\pi\)
0.809126 + 0.587635i \(0.199941\pi\)
\(108\) 0 0
\(109\) −6.73233 −0.644840 −0.322420 0.946597i \(-0.604496\pi\)
−0.322420 + 0.946597i \(0.604496\pi\)
\(110\) 0 0
\(111\) 5.31689 0.504657
\(112\) 0 0
\(113\) −11.0582 −1.04027 −0.520134 0.854085i \(-0.674118\pi\)
−0.520134 + 0.854085i \(0.674118\pi\)
\(114\) 0 0
\(115\) −24.1446 −2.25150
\(116\) 0 0
\(117\) −2.91508 −0.269500
\(118\) 0 0
\(119\) 0.143348 0.0131407
\(120\) 0 0
\(121\) −9.18130 −0.834663
\(122\) 0 0
\(123\) 22.0694 1.98993
\(124\) 0 0
\(125\) −20.6215 −1.84444
\(126\) 0 0
\(127\) −1.72214 −0.152815 −0.0764076 0.997077i \(-0.524345\pi\)
−0.0764076 + 0.997077i \(0.524345\pi\)
\(128\) 0 0
\(129\) −5.29839 −0.466497
\(130\) 0 0
\(131\) 14.9999 1.31055 0.655273 0.755393i \(-0.272554\pi\)
0.655273 + 0.755393i \(0.272554\pi\)
\(132\) 0 0
\(133\) 0.454283 0.0393913
\(134\) 0 0
\(135\) 9.06525 0.780212
\(136\) 0 0
\(137\) −4.23865 −0.362132 −0.181066 0.983471i \(-0.557955\pi\)
−0.181066 + 0.983471i \(0.557955\pi\)
\(138\) 0 0
\(139\) −20.2272 −1.71565 −0.857824 0.513944i \(-0.828184\pi\)
−0.857824 + 0.513944i \(0.828184\pi\)
\(140\) 0 0
\(141\) −28.6224 −2.41044
\(142\) 0 0
\(143\) 2.00739 0.167866
\(144\) 0 0
\(145\) 0.367586 0.0305264
\(146\) 0 0
\(147\) −15.5512 −1.28264
\(148\) 0 0
\(149\) −20.4272 −1.67346 −0.836732 0.547612i \(-0.815537\pi\)
−0.836732 + 0.547612i \(0.815537\pi\)
\(150\) 0 0
\(151\) −20.9022 −1.70100 −0.850500 0.525975i \(-0.823701\pi\)
−0.850500 + 0.525975i \(0.823701\pi\)
\(152\) 0 0
\(153\) 2.20643 0.178380
\(154\) 0 0
\(155\) 5.29321 0.425161
\(156\) 0 0
\(157\) −4.56927 −0.364667 −0.182334 0.983237i \(-0.558365\pi\)
−0.182334 + 0.983237i \(0.558365\pi\)
\(158\) 0 0
\(159\) 0.223333 0.0177115
\(160\) 0 0
\(161\) 0.785988 0.0619445
\(162\) 0 0
\(163\) −7.31476 −0.572936 −0.286468 0.958090i \(-0.592481\pi\)
−0.286468 + 0.958090i \(0.592481\pi\)
\(164\) 0 0
\(165\) 11.7370 0.913726
\(166\) 0 0
\(167\) 14.9467 1.15661 0.578303 0.815822i \(-0.303715\pi\)
0.578303 + 0.815822i \(0.303715\pi\)
\(168\) 0 0
\(169\) −10.7844 −0.829565
\(170\) 0 0
\(171\) 6.99238 0.534721
\(172\) 0 0
\(173\) −18.2864 −1.39029 −0.695145 0.718870i \(-0.744660\pi\)
−0.695145 + 0.718870i \(0.744660\pi\)
\(174\) 0 0
\(175\) 1.30747 0.0988353
\(176\) 0 0
\(177\) −23.3486 −1.75499
\(178\) 0 0
\(179\) 14.6387 1.09415 0.547075 0.837084i \(-0.315741\pi\)
0.547075 + 0.837084i \(0.315741\pi\)
\(180\) 0 0
\(181\) −18.6879 −1.38906 −0.694531 0.719463i \(-0.744388\pi\)
−0.694531 + 0.719463i \(0.744388\pi\)
\(182\) 0 0
\(183\) −19.7971 −1.46344
\(184\) 0 0
\(185\) −9.33240 −0.686132
\(186\) 0 0
\(187\) −1.51940 −0.111109
\(188\) 0 0
\(189\) −0.295104 −0.0214657
\(190\) 0 0
\(191\) −7.95144 −0.575346 −0.287673 0.957729i \(-0.592882\pi\)
−0.287673 + 0.957729i \(0.592882\pi\)
\(192\) 0 0
\(193\) −7.37180 −0.530634 −0.265317 0.964161i \(-0.585477\pi\)
−0.265317 + 0.964161i \(0.585477\pi\)
\(194\) 0 0
\(195\) 12.9547 0.927706
\(196\) 0 0
\(197\) −12.7159 −0.905969 −0.452984 0.891519i \(-0.649641\pi\)
−0.452984 + 0.891519i \(0.649641\pi\)
\(198\) 0 0
\(199\) −3.41792 −0.242290 −0.121145 0.992635i \(-0.538657\pi\)
−0.121145 + 0.992635i \(0.538657\pi\)
\(200\) 0 0
\(201\) −12.4367 −0.877220
\(202\) 0 0
\(203\) −0.0119662 −0.000839860 0
\(204\) 0 0
\(205\) −38.7370 −2.70551
\(206\) 0 0
\(207\) 12.0980 0.840870
\(208\) 0 0
\(209\) −4.81510 −0.333067
\(210\) 0 0
\(211\) 15.1230 1.04111 0.520555 0.853828i \(-0.325725\pi\)
0.520555 + 0.853828i \(0.325725\pi\)
\(212\) 0 0
\(213\) 20.9483 1.43535
\(214\) 0 0
\(215\) 9.29993 0.634250
\(216\) 0 0
\(217\) −0.172312 −0.0116973
\(218\) 0 0
\(219\) 9.41009 0.635875
\(220\) 0 0
\(221\) −1.67703 −0.112809
\(222\) 0 0
\(223\) −28.0583 −1.87892 −0.939461 0.342657i \(-0.888673\pi\)
−0.939461 + 0.342657i \(0.888673\pi\)
\(224\) 0 0
\(225\) 20.1247 1.34165
\(226\) 0 0
\(227\) −4.52803 −0.300536 −0.150268 0.988645i \(-0.548014\pi\)
−0.150268 + 0.988645i \(0.548014\pi\)
\(228\) 0 0
\(229\) 4.88767 0.322986 0.161493 0.986874i \(-0.448369\pi\)
0.161493 + 0.986874i \(0.448369\pi\)
\(230\) 0 0
\(231\) −0.382080 −0.0251390
\(232\) 0 0
\(233\) 10.8902 0.713442 0.356721 0.934211i \(-0.383895\pi\)
0.356721 + 0.934211i \(0.383895\pi\)
\(234\) 0 0
\(235\) 50.2390 3.27723
\(236\) 0 0
\(237\) −27.3060 −1.77371
\(238\) 0 0
\(239\) 0.468879 0.0303293 0.0151646 0.999885i \(-0.495173\pi\)
0.0151646 + 0.999885i \(0.495173\pi\)
\(240\) 0 0
\(241\) 7.11565 0.458359 0.229180 0.973384i \(-0.426396\pi\)
0.229180 + 0.973384i \(0.426396\pi\)
\(242\) 0 0
\(243\) −17.6248 −1.13063
\(244\) 0 0
\(245\) 27.2960 1.74388
\(246\) 0 0
\(247\) −5.31465 −0.338163
\(248\) 0 0
\(249\) 1.09562 0.0694320
\(250\) 0 0
\(251\) −16.4814 −1.04030 −0.520150 0.854075i \(-0.674124\pi\)
−0.520150 + 0.854075i \(0.674124\pi\)
\(252\) 0 0
\(253\) −8.33095 −0.523762
\(254\) 0 0
\(255\) −9.80545 −0.614041
\(256\) 0 0
\(257\) −18.7437 −1.16920 −0.584599 0.811322i \(-0.698748\pi\)
−0.584599 + 0.811322i \(0.698748\pi\)
\(258\) 0 0
\(259\) 0.303801 0.0188773
\(260\) 0 0
\(261\) −0.184185 −0.0114007
\(262\) 0 0
\(263\) 3.45247 0.212888 0.106444 0.994319i \(-0.466053\pi\)
0.106444 + 0.994319i \(0.466053\pi\)
\(264\) 0 0
\(265\) −0.392003 −0.0240806
\(266\) 0 0
\(267\) 19.5709 1.19772
\(268\) 0 0
\(269\) 8.54448 0.520966 0.260483 0.965478i \(-0.416118\pi\)
0.260483 + 0.965478i \(0.416118\pi\)
\(270\) 0 0
\(271\) 12.7868 0.776743 0.388372 0.921503i \(-0.373038\pi\)
0.388372 + 0.921503i \(0.373038\pi\)
\(272\) 0 0
\(273\) −0.421719 −0.0255236
\(274\) 0 0
\(275\) −13.8583 −0.835687
\(276\) 0 0
\(277\) 26.4273 1.58786 0.793932 0.608006i \(-0.208030\pi\)
0.793932 + 0.608006i \(0.208030\pi\)
\(278\) 0 0
\(279\) −2.65224 −0.158786
\(280\) 0 0
\(281\) −6.28222 −0.374766 −0.187383 0.982287i \(-0.560001\pi\)
−0.187383 + 0.982287i \(0.560001\pi\)
\(282\) 0 0
\(283\) −28.1857 −1.67547 −0.837734 0.546078i \(-0.816120\pi\)
−0.837734 + 0.546078i \(0.816120\pi\)
\(284\) 0 0
\(285\) −31.0743 −1.84068
\(286\) 0 0
\(287\) 1.26102 0.0744356
\(288\) 0 0
\(289\) −15.7307 −0.925332
\(290\) 0 0
\(291\) 41.6302 2.44041
\(292\) 0 0
\(293\) −25.2689 −1.47622 −0.738112 0.674678i \(-0.764282\pi\)
−0.738112 + 0.674678i \(0.764282\pi\)
\(294\) 0 0
\(295\) 40.9823 2.38608
\(296\) 0 0
\(297\) 3.12791 0.181500
\(298\) 0 0
\(299\) −9.19526 −0.531776
\(300\) 0 0
\(301\) −0.302744 −0.0174499
\(302\) 0 0
\(303\) −7.61126 −0.437255
\(304\) 0 0
\(305\) 34.7486 1.98970
\(306\) 0 0
\(307\) −6.65104 −0.379595 −0.189798 0.981823i \(-0.560783\pi\)
−0.189798 + 0.981823i \(0.560783\pi\)
\(308\) 0 0
\(309\) −0.0683029 −0.00388562
\(310\) 0 0
\(311\) 19.2914 1.09391 0.546957 0.837161i \(-0.315786\pi\)
0.546957 + 0.837161i \(0.315786\pi\)
\(312\) 0 0
\(313\) 11.9686 0.676507 0.338253 0.941055i \(-0.390164\pi\)
0.338253 + 0.941055i \(0.390164\pi\)
\(314\) 0 0
\(315\) −0.973888 −0.0548724
\(316\) 0 0
\(317\) −3.53040 −0.198287 −0.0991435 0.995073i \(-0.531610\pi\)
−0.0991435 + 0.995073i \(0.531610\pi\)
\(318\) 0 0
\(319\) 0.126833 0.00710131
\(320\) 0 0
\(321\) 37.2742 2.08045
\(322\) 0 0
\(323\) 4.02267 0.223827
\(324\) 0 0
\(325\) −15.2961 −0.848472
\(326\) 0 0
\(327\) −14.9912 −0.829014
\(328\) 0 0
\(329\) −1.63545 −0.0901652
\(330\) 0 0
\(331\) 3.15944 0.173659 0.0868293 0.996223i \(-0.472327\pi\)
0.0868293 + 0.996223i \(0.472327\pi\)
\(332\) 0 0
\(333\) 4.67614 0.256251
\(334\) 0 0
\(335\) 21.8294 1.19267
\(336\) 0 0
\(337\) −2.86571 −0.156105 −0.0780525 0.996949i \(-0.524870\pi\)
−0.0780525 + 0.996949i \(0.524870\pi\)
\(338\) 0 0
\(339\) −24.6238 −1.33738
\(340\) 0 0
\(341\) 1.82639 0.0989046
\(342\) 0 0
\(343\) −1.77921 −0.0960684
\(344\) 0 0
\(345\) −53.7639 −2.89455
\(346\) 0 0
\(347\) 1.87206 0.100497 0.0502486 0.998737i \(-0.483999\pi\)
0.0502486 + 0.998737i \(0.483999\pi\)
\(348\) 0 0
\(349\) −19.1333 −1.02418 −0.512091 0.858931i \(-0.671129\pi\)
−0.512091 + 0.858931i \(0.671129\pi\)
\(350\) 0 0
\(351\) 3.45242 0.184277
\(352\) 0 0
\(353\) 17.9121 0.953365 0.476683 0.879075i \(-0.341839\pi\)
0.476683 + 0.879075i \(0.341839\pi\)
\(354\) 0 0
\(355\) −36.7692 −1.95151
\(356\) 0 0
\(357\) 0.319200 0.0168939
\(358\) 0 0
\(359\) −18.6237 −0.982920 −0.491460 0.870900i \(-0.663537\pi\)
−0.491460 + 0.870900i \(0.663537\pi\)
\(360\) 0 0
\(361\) −6.25180 −0.329042
\(362\) 0 0
\(363\) −20.4444 −1.07305
\(364\) 0 0
\(365\) −16.5169 −0.864536
\(366\) 0 0
\(367\) −14.1199 −0.737051 −0.368526 0.929618i \(-0.620137\pi\)
−0.368526 + 0.929618i \(0.620137\pi\)
\(368\) 0 0
\(369\) 19.4098 1.01043
\(370\) 0 0
\(371\) 0.0127610 0.000662519 0
\(372\) 0 0
\(373\) −17.4991 −0.906071 −0.453035 0.891493i \(-0.649659\pi\)
−0.453035 + 0.891493i \(0.649659\pi\)
\(374\) 0 0
\(375\) −45.9189 −2.37124
\(376\) 0 0
\(377\) 0.139992 0.00720995
\(378\) 0 0
\(379\) −1.86167 −0.0956278 −0.0478139 0.998856i \(-0.515225\pi\)
−0.0478139 + 0.998856i \(0.515225\pi\)
\(380\) 0 0
\(381\) −3.83477 −0.196461
\(382\) 0 0
\(383\) 6.59670 0.337075 0.168538 0.985695i \(-0.446096\pi\)
0.168538 + 0.985695i \(0.446096\pi\)
\(384\) 0 0
\(385\) 0.670640 0.0341790
\(386\) 0 0
\(387\) −4.65987 −0.236875
\(388\) 0 0
\(389\) −1.58169 −0.0801950 −0.0400975 0.999196i \(-0.512767\pi\)
−0.0400975 + 0.999196i \(0.512767\pi\)
\(390\) 0 0
\(391\) 6.95992 0.351978
\(392\) 0 0
\(393\) 33.4009 1.68485
\(394\) 0 0
\(395\) 47.9285 2.41154
\(396\) 0 0
\(397\) 25.3966 1.27462 0.637309 0.770608i \(-0.280047\pi\)
0.637309 + 0.770608i \(0.280047\pi\)
\(398\) 0 0
\(399\) 1.01157 0.0506420
\(400\) 0 0
\(401\) −7.54246 −0.376652 −0.188326 0.982107i \(-0.560306\pi\)
−0.188326 + 0.982107i \(0.560306\pi\)
\(402\) 0 0
\(403\) 2.01587 0.100418
\(404\) 0 0
\(405\) 43.1490 2.14409
\(406\) 0 0
\(407\) −3.22009 −0.159614
\(408\) 0 0
\(409\) −4.76455 −0.235592 −0.117796 0.993038i \(-0.537583\pi\)
−0.117796 + 0.993038i \(0.537583\pi\)
\(410\) 0 0
\(411\) −9.43840 −0.465562
\(412\) 0 0
\(413\) −1.33411 −0.0656473
\(414\) 0 0
\(415\) −1.92307 −0.0943998
\(416\) 0 0
\(417\) −45.0408 −2.20566
\(418\) 0 0
\(419\) 13.6082 0.664806 0.332403 0.943137i \(-0.392141\pi\)
0.332403 + 0.943137i \(0.392141\pi\)
\(420\) 0 0
\(421\) −12.8645 −0.626978 −0.313489 0.949592i \(-0.601498\pi\)
−0.313489 + 0.949592i \(0.601498\pi\)
\(422\) 0 0
\(423\) −25.1730 −1.22395
\(424\) 0 0
\(425\) 11.5776 0.561597
\(426\) 0 0
\(427\) −1.13118 −0.0547418
\(428\) 0 0
\(429\) 4.46994 0.215811
\(430\) 0 0
\(431\) 30.4285 1.46569 0.732844 0.680397i \(-0.238193\pi\)
0.732844 + 0.680397i \(0.238193\pi\)
\(432\) 0 0
\(433\) 8.49495 0.408241 0.204121 0.978946i \(-0.434567\pi\)
0.204121 + 0.978946i \(0.434567\pi\)
\(434\) 0 0
\(435\) 0.818521 0.0392451
\(436\) 0 0
\(437\) 22.0566 1.05511
\(438\) 0 0
\(439\) 15.8520 0.756576 0.378288 0.925688i \(-0.376513\pi\)
0.378288 + 0.925688i \(0.376513\pi\)
\(440\) 0 0
\(441\) −13.6771 −0.651289
\(442\) 0 0
\(443\) 5.52175 0.262346 0.131173 0.991359i \(-0.458126\pi\)
0.131173 + 0.991359i \(0.458126\pi\)
\(444\) 0 0
\(445\) −34.3516 −1.62842
\(446\) 0 0
\(447\) −45.4863 −2.15143
\(448\) 0 0
\(449\) 31.5859 1.49063 0.745314 0.666713i \(-0.232299\pi\)
0.745314 + 0.666713i \(0.232299\pi\)
\(450\) 0 0
\(451\) −13.3660 −0.629379
\(452\) 0 0
\(453\) −46.5440 −2.18683
\(454\) 0 0
\(455\) 0.740217 0.0347019
\(456\) 0 0
\(457\) 8.14835 0.381164 0.190582 0.981671i \(-0.438963\pi\)
0.190582 + 0.981671i \(0.438963\pi\)
\(458\) 0 0
\(459\) −2.61314 −0.121971
\(460\) 0 0
\(461\) −20.2099 −0.941269 −0.470634 0.882328i \(-0.655975\pi\)
−0.470634 + 0.882328i \(0.655975\pi\)
\(462\) 0 0
\(463\) 1.03697 0.0481922 0.0240961 0.999710i \(-0.492329\pi\)
0.0240961 + 0.999710i \(0.492329\pi\)
\(464\) 0 0
\(465\) 11.7866 0.546592
\(466\) 0 0
\(467\) 0.734354 0.0339819 0.0169909 0.999856i \(-0.494591\pi\)
0.0169909 + 0.999856i \(0.494591\pi\)
\(468\) 0 0
\(469\) −0.710621 −0.0328134
\(470\) 0 0
\(471\) −10.1746 −0.468821
\(472\) 0 0
\(473\) 3.20889 0.147545
\(474\) 0 0
\(475\) 36.6905 1.68347
\(476\) 0 0
\(477\) 0.196419 0.00899341
\(478\) 0 0
\(479\) 29.1901 1.33373 0.666865 0.745179i \(-0.267636\pi\)
0.666865 + 0.745179i \(0.267636\pi\)
\(480\) 0 0
\(481\) −3.55416 −0.162056
\(482\) 0 0
\(483\) 1.75019 0.0796366
\(484\) 0 0
\(485\) −73.0709 −3.31798
\(486\) 0 0
\(487\) −30.1353 −1.36556 −0.682781 0.730623i \(-0.739230\pi\)
−0.682781 + 0.730623i \(0.739230\pi\)
\(488\) 0 0
\(489\) −16.2881 −0.736574
\(490\) 0 0
\(491\) −29.5021 −1.33141 −0.665706 0.746214i \(-0.731870\pi\)
−0.665706 + 0.746214i \(0.731870\pi\)
\(492\) 0 0
\(493\) −0.105960 −0.00477221
\(494\) 0 0
\(495\) 10.3226 0.463965
\(496\) 0 0
\(497\) 1.19696 0.0536910
\(498\) 0 0
\(499\) 5.49945 0.246189 0.123095 0.992395i \(-0.460718\pi\)
0.123095 + 0.992395i \(0.460718\pi\)
\(500\) 0 0
\(501\) 33.2824 1.48695
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 13.3596 0.594493
\(506\) 0 0
\(507\) −24.0140 −1.06650
\(508\) 0 0
\(509\) 34.6106 1.53409 0.767043 0.641595i \(-0.221727\pi\)
0.767043 + 0.641595i \(0.221727\pi\)
\(510\) 0 0
\(511\) 0.537682 0.0237856
\(512\) 0 0
\(513\) −8.28128 −0.365628
\(514\) 0 0
\(515\) 0.119888 0.00528289
\(516\) 0 0
\(517\) 17.3347 0.762379
\(518\) 0 0
\(519\) −40.7192 −1.78737
\(520\) 0 0
\(521\) −21.6347 −0.947834 −0.473917 0.880570i \(-0.657160\pi\)
−0.473917 + 0.880570i \(0.657160\pi\)
\(522\) 0 0
\(523\) −9.56540 −0.418266 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(524\) 0 0
\(525\) 2.91140 0.127064
\(526\) 0 0
\(527\) −1.52582 −0.0664657
\(528\) 0 0
\(529\) 15.1617 0.659203
\(530\) 0 0
\(531\) −20.5348 −0.891134
\(532\) 0 0
\(533\) −14.7527 −0.639009
\(534\) 0 0
\(535\) −65.4251 −2.82857
\(536\) 0 0
\(537\) 32.5967 1.40665
\(538\) 0 0
\(539\) 9.41832 0.405676
\(540\) 0 0
\(541\) −7.05411 −0.303280 −0.151640 0.988436i \(-0.548455\pi\)
−0.151640 + 0.988436i \(0.548455\pi\)
\(542\) 0 0
\(543\) −41.6132 −1.78579
\(544\) 0 0
\(545\) 26.3131 1.12713
\(546\) 0 0
\(547\) 4.00855 0.171393 0.0856966 0.996321i \(-0.472688\pi\)
0.0856966 + 0.996321i \(0.472688\pi\)
\(548\) 0 0
\(549\) −17.4113 −0.743096
\(550\) 0 0
\(551\) −0.335797 −0.0143054
\(552\) 0 0
\(553\) −1.56023 −0.0663479
\(554\) 0 0
\(555\) −20.7809 −0.882099
\(556\) 0 0
\(557\) 22.1913 0.940275 0.470137 0.882593i \(-0.344204\pi\)
0.470137 + 0.882593i \(0.344204\pi\)
\(558\) 0 0
\(559\) 3.54180 0.149802
\(560\) 0 0
\(561\) −3.38331 −0.142844
\(562\) 0 0
\(563\) −36.2816 −1.52909 −0.764545 0.644571i \(-0.777036\pi\)
−0.764545 + 0.644571i \(0.777036\pi\)
\(564\) 0 0
\(565\) 43.2206 1.81830
\(566\) 0 0
\(567\) −1.40464 −0.0589895
\(568\) 0 0
\(569\) −25.9315 −1.08710 −0.543552 0.839376i \(-0.682921\pi\)
−0.543552 + 0.839376i \(0.682921\pi\)
\(570\) 0 0
\(571\) 4.84904 0.202926 0.101463 0.994839i \(-0.467648\pi\)
0.101463 + 0.994839i \(0.467648\pi\)
\(572\) 0 0
\(573\) −17.7058 −0.739672
\(574\) 0 0
\(575\) 63.4808 2.64733
\(576\) 0 0
\(577\) −1.13047 −0.0470620 −0.0235310 0.999723i \(-0.507491\pi\)
−0.0235310 + 0.999723i \(0.507491\pi\)
\(578\) 0 0
\(579\) −16.4151 −0.682189
\(580\) 0 0
\(581\) 0.0626024 0.00259718
\(582\) 0 0
\(583\) −0.135258 −0.00560183
\(584\) 0 0
\(585\) 11.3935 0.471064
\(586\) 0 0
\(587\) −16.5250 −0.682060 −0.341030 0.940052i \(-0.610776\pi\)
−0.341030 + 0.940052i \(0.610776\pi\)
\(588\) 0 0
\(589\) −4.83545 −0.199241
\(590\) 0 0
\(591\) −28.3150 −1.16472
\(592\) 0 0
\(593\) −33.9678 −1.39489 −0.697445 0.716638i \(-0.745680\pi\)
−0.697445 + 0.716638i \(0.745680\pi\)
\(594\) 0 0
\(595\) −0.560272 −0.0229689
\(596\) 0 0
\(597\) −7.61083 −0.311491
\(598\) 0 0
\(599\) 27.4333 1.12089 0.560447 0.828190i \(-0.310629\pi\)
0.560447 + 0.828190i \(0.310629\pi\)
\(600\) 0 0
\(601\) 15.8279 0.645634 0.322817 0.946461i \(-0.395370\pi\)
0.322817 + 0.946461i \(0.395370\pi\)
\(602\) 0 0
\(603\) −10.9380 −0.445428
\(604\) 0 0
\(605\) 35.8848 1.45892
\(606\) 0 0
\(607\) 40.3952 1.63959 0.819794 0.572658i \(-0.194088\pi\)
0.819794 + 0.572658i \(0.194088\pi\)
\(608\) 0 0
\(609\) −0.0266456 −0.00107973
\(610\) 0 0
\(611\) 19.1331 0.774043
\(612\) 0 0
\(613\) 8.20436 0.331371 0.165686 0.986179i \(-0.447016\pi\)
0.165686 + 0.986179i \(0.447016\pi\)
\(614\) 0 0
\(615\) −86.2575 −3.47824
\(616\) 0 0
\(617\) 15.6643 0.630623 0.315311 0.948988i \(-0.397891\pi\)
0.315311 + 0.948988i \(0.397891\pi\)
\(618\) 0 0
\(619\) −11.8251 −0.475290 −0.237645 0.971352i \(-0.576375\pi\)
−0.237645 + 0.971352i \(0.576375\pi\)
\(620\) 0 0
\(621\) −14.3280 −0.574965
\(622\) 0 0
\(623\) 1.11826 0.0448021
\(624\) 0 0
\(625\) 29.2179 1.16872
\(626\) 0 0
\(627\) −10.7220 −0.428196
\(628\) 0 0
\(629\) 2.69015 0.107263
\(630\) 0 0
\(631\) −14.3728 −0.572170 −0.286085 0.958204i \(-0.592354\pi\)
−0.286085 + 0.958204i \(0.592354\pi\)
\(632\) 0 0
\(633\) 33.6751 1.33846
\(634\) 0 0
\(635\) 6.73093 0.267109
\(636\) 0 0
\(637\) 10.3954 0.411882
\(638\) 0 0
\(639\) 18.4238 0.728833
\(640\) 0 0
\(641\) −44.9593 −1.77579 −0.887893 0.460051i \(-0.847831\pi\)
−0.887893 + 0.460051i \(0.847831\pi\)
\(642\) 0 0
\(643\) 33.1775 1.30839 0.654196 0.756325i \(-0.273007\pi\)
0.654196 + 0.756325i \(0.273007\pi\)
\(644\) 0 0
\(645\) 20.7086 0.815400
\(646\) 0 0
\(647\) 3.17050 0.124645 0.0623226 0.998056i \(-0.480149\pi\)
0.0623226 + 0.998056i \(0.480149\pi\)
\(648\) 0 0
\(649\) 14.1407 0.555071
\(650\) 0 0
\(651\) −0.383694 −0.0150382
\(652\) 0 0
\(653\) 9.08500 0.355524 0.177762 0.984074i \(-0.443114\pi\)
0.177762 + 0.984074i \(0.443114\pi\)
\(654\) 0 0
\(655\) −58.6265 −2.29073
\(656\) 0 0
\(657\) 8.27606 0.322880
\(658\) 0 0
\(659\) 0.0644937 0.00251232 0.00125616 0.999999i \(-0.499600\pi\)
0.00125616 + 0.999999i \(0.499600\pi\)
\(660\) 0 0
\(661\) 22.7167 0.883576 0.441788 0.897120i \(-0.354344\pi\)
0.441788 + 0.897120i \(0.354344\pi\)
\(662\) 0 0
\(663\) −3.73432 −0.145029
\(664\) 0 0
\(665\) −1.77555 −0.0688529
\(666\) 0 0
\(667\) −0.580987 −0.0224959
\(668\) 0 0
\(669\) −62.4786 −2.41556
\(670\) 0 0
\(671\) 11.9898 0.462861
\(672\) 0 0
\(673\) −30.3698 −1.17067 −0.585335 0.810792i \(-0.699037\pi\)
−0.585335 + 0.810792i \(0.699037\pi\)
\(674\) 0 0
\(675\) −23.8343 −0.917382
\(676\) 0 0
\(677\) −10.1454 −0.389921 −0.194960 0.980811i \(-0.562458\pi\)
−0.194960 + 0.980811i \(0.562458\pi\)
\(678\) 0 0
\(679\) 2.37870 0.0912862
\(680\) 0 0
\(681\) −10.0828 −0.386372
\(682\) 0 0
\(683\) 15.3406 0.586993 0.293497 0.955960i \(-0.405181\pi\)
0.293497 + 0.955960i \(0.405181\pi\)
\(684\) 0 0
\(685\) 16.5666 0.632978
\(686\) 0 0
\(687\) 10.8836 0.415235
\(688\) 0 0
\(689\) −0.149291 −0.00568753
\(690\) 0 0
\(691\) −4.81419 −0.183140 −0.0915702 0.995799i \(-0.529189\pi\)
−0.0915702 + 0.995799i \(0.529189\pi\)
\(692\) 0 0
\(693\) −0.336034 −0.0127649
\(694\) 0 0
\(695\) 79.0573 2.99881
\(696\) 0 0
\(697\) 11.1663 0.422955
\(698\) 0 0
\(699\) 24.2498 0.917210
\(700\) 0 0
\(701\) −16.8248 −0.635465 −0.317733 0.948180i \(-0.602921\pi\)
−0.317733 + 0.948180i \(0.602921\pi\)
\(702\) 0 0
\(703\) 8.52533 0.321539
\(704\) 0 0
\(705\) 111.870 4.21325
\(706\) 0 0
\(707\) −0.434899 −0.0163560
\(708\) 0 0
\(709\) 25.8837 0.972084 0.486042 0.873936i \(-0.338440\pi\)
0.486042 + 0.873936i \(0.338440\pi\)
\(710\) 0 0
\(711\) −24.0153 −0.900644
\(712\) 0 0
\(713\) −8.36616 −0.313315
\(714\) 0 0
\(715\) −7.84581 −0.293417
\(716\) 0 0
\(717\) 1.04407 0.0389917
\(718\) 0 0
\(719\) 40.4115 1.50709 0.753547 0.657394i \(-0.228341\pi\)
0.753547 + 0.657394i \(0.228341\pi\)
\(720\) 0 0
\(721\) −0.00390275 −0.000145346 0
\(722\) 0 0
\(723\) 15.8447 0.589272
\(724\) 0 0
\(725\) −0.966455 −0.0358932
\(726\) 0 0
\(727\) 23.7913 0.882369 0.441185 0.897416i \(-0.354558\pi\)
0.441185 + 0.897416i \(0.354558\pi\)
\(728\) 0 0
\(729\) −6.12639 −0.226903
\(730\) 0 0
\(731\) −2.68080 −0.0991528
\(732\) 0 0
\(733\) 26.2965 0.971282 0.485641 0.874158i \(-0.338586\pi\)
0.485641 + 0.874158i \(0.338586\pi\)
\(734\) 0 0
\(735\) 60.7812 2.24195
\(736\) 0 0
\(737\) 7.53212 0.277449
\(738\) 0 0
\(739\) 27.1782 0.999766 0.499883 0.866093i \(-0.333376\pi\)
0.499883 + 0.866093i \(0.333376\pi\)
\(740\) 0 0
\(741\) −11.8344 −0.434747
\(742\) 0 0
\(743\) 35.3208 1.29580 0.647898 0.761727i \(-0.275648\pi\)
0.647898 + 0.761727i \(0.275648\pi\)
\(744\) 0 0
\(745\) 79.8392 2.92508
\(746\) 0 0
\(747\) 0.963583 0.0352557
\(748\) 0 0
\(749\) 2.12981 0.0778215
\(750\) 0 0
\(751\) 5.11785 0.186753 0.0933765 0.995631i \(-0.470234\pi\)
0.0933765 + 0.995631i \(0.470234\pi\)
\(752\) 0 0
\(753\) −36.7000 −1.33742
\(754\) 0 0
\(755\) 81.6957 2.97321
\(756\) 0 0
\(757\) −6.49682 −0.236131 −0.118065 0.993006i \(-0.537669\pi\)
−0.118065 + 0.993006i \(0.537669\pi\)
\(758\) 0 0
\(759\) −18.5509 −0.673355
\(760\) 0 0
\(761\) 35.0920 1.27208 0.636041 0.771655i \(-0.280571\pi\)
0.636041 + 0.771655i \(0.280571\pi\)
\(762\) 0 0
\(763\) −0.856579 −0.0310102
\(764\) 0 0
\(765\) −8.62377 −0.311793
\(766\) 0 0
\(767\) 15.6077 0.563563
\(768\) 0 0
\(769\) −29.6939 −1.07079 −0.535395 0.844602i \(-0.679837\pi\)
−0.535395 + 0.844602i \(0.679837\pi\)
\(770\) 0 0
\(771\) −41.7374 −1.50314
\(772\) 0 0
\(773\) −22.6109 −0.813258 −0.406629 0.913593i \(-0.633296\pi\)
−0.406629 + 0.913593i \(0.633296\pi\)
\(774\) 0 0
\(775\) −13.9169 −0.499909
\(776\) 0 0
\(777\) 0.676487 0.0242688
\(778\) 0 0
\(779\) 35.3870 1.26787
\(780\) 0 0
\(781\) −12.6870 −0.453977
\(782\) 0 0
\(783\) 0.218135 0.00779552
\(784\) 0 0
\(785\) 17.8588 0.637409
\(786\) 0 0
\(787\) 43.9375 1.56620 0.783101 0.621895i \(-0.213637\pi\)
0.783101 + 0.621895i \(0.213637\pi\)
\(788\) 0 0
\(789\) 7.68777 0.273692
\(790\) 0 0
\(791\) −1.40698 −0.0500263
\(792\) 0 0
\(793\) 13.2337 0.469942
\(794\) 0 0
\(795\) −0.872891 −0.0309583
\(796\) 0 0
\(797\) 46.7524 1.65605 0.828027 0.560688i \(-0.189463\pi\)
0.828027 + 0.560688i \(0.189463\pi\)
\(798\) 0 0
\(799\) −14.4819 −0.512332
\(800\) 0 0
\(801\) 17.2124 0.608170
\(802\) 0 0
\(803\) −5.69907 −0.201116
\(804\) 0 0
\(805\) −3.07201 −0.108274
\(806\) 0 0
\(807\) 19.0264 0.669760
\(808\) 0 0
\(809\) 13.3923 0.470848 0.235424 0.971893i \(-0.424352\pi\)
0.235424 + 0.971893i \(0.424352\pi\)
\(810\) 0 0
\(811\) 13.3858 0.470037 0.235019 0.971991i \(-0.424485\pi\)
0.235019 + 0.971991i \(0.424485\pi\)
\(812\) 0 0
\(813\) 28.4730 0.998591
\(814\) 0 0
\(815\) 28.5895 1.00145
\(816\) 0 0
\(817\) −8.49567 −0.297226
\(818\) 0 0
\(819\) −0.370897 −0.0129602
\(820\) 0 0
\(821\) 4.23562 0.147824 0.0739122 0.997265i \(-0.476452\pi\)
0.0739122 + 0.997265i \(0.476452\pi\)
\(822\) 0 0
\(823\) −13.3570 −0.465597 −0.232799 0.972525i \(-0.574788\pi\)
−0.232799 + 0.972525i \(0.574788\pi\)
\(824\) 0 0
\(825\) −30.8589 −1.07437
\(826\) 0 0
\(827\) −4.13307 −0.143721 −0.0718604 0.997415i \(-0.522894\pi\)
−0.0718604 + 0.997415i \(0.522894\pi\)
\(828\) 0 0
\(829\) −30.2050 −1.04906 −0.524532 0.851391i \(-0.675760\pi\)
−0.524532 + 0.851391i \(0.675760\pi\)
\(830\) 0 0
\(831\) 58.8469 2.04138
\(832\) 0 0
\(833\) −7.86834 −0.272622
\(834\) 0 0
\(835\) −58.4185 −2.02166
\(836\) 0 0
\(837\) 3.14113 0.108573
\(838\) 0 0
\(839\) −34.3993 −1.18760 −0.593798 0.804614i \(-0.702372\pi\)
−0.593798 + 0.804614i \(0.702372\pi\)
\(840\) 0 0
\(841\) −28.9912 −0.999695
\(842\) 0 0
\(843\) −13.9889 −0.481804
\(844\) 0 0
\(845\) 42.1503 1.45001
\(846\) 0 0
\(847\) −1.16817 −0.0401388
\(848\) 0 0
\(849\) −62.7625 −2.15400
\(850\) 0 0
\(851\) 14.7503 0.505633
\(852\) 0 0
\(853\) −9.70737 −0.332374 −0.166187 0.986094i \(-0.553146\pi\)
−0.166187 + 0.986094i \(0.553146\pi\)
\(854\) 0 0
\(855\) −27.3295 −0.934648
\(856\) 0 0
\(857\) −34.7710 −1.18775 −0.593877 0.804556i \(-0.702404\pi\)
−0.593877 + 0.804556i \(0.702404\pi\)
\(858\) 0 0
\(859\) 26.5064 0.904387 0.452194 0.891920i \(-0.350642\pi\)
0.452194 + 0.891920i \(0.350642\pi\)
\(860\) 0 0
\(861\) 2.80797 0.0956954
\(862\) 0 0
\(863\) 7.76135 0.264199 0.132100 0.991236i \(-0.457828\pi\)
0.132100 + 0.991236i \(0.457828\pi\)
\(864\) 0 0
\(865\) 71.4718 2.43011
\(866\) 0 0
\(867\) −35.0282 −1.18962
\(868\) 0 0
\(869\) 16.5374 0.560994
\(870\) 0 0
\(871\) 8.31355 0.281694
\(872\) 0 0
\(873\) 36.6133 1.23917
\(874\) 0 0
\(875\) −2.62375 −0.0886990
\(876\) 0 0
\(877\) 33.4061 1.12804 0.564021 0.825760i \(-0.309254\pi\)
0.564021 + 0.825760i \(0.309254\pi\)
\(878\) 0 0
\(879\) −56.2674 −1.89785
\(880\) 0 0
\(881\) 45.5473 1.53453 0.767263 0.641332i \(-0.221618\pi\)
0.767263 + 0.641332i \(0.221618\pi\)
\(882\) 0 0
\(883\) −8.05533 −0.271084 −0.135542 0.990772i \(-0.543278\pi\)
−0.135542 + 0.990772i \(0.543278\pi\)
\(884\) 0 0
\(885\) 91.2571 3.06757
\(886\) 0 0
\(887\) 37.8462 1.27075 0.635376 0.772203i \(-0.280845\pi\)
0.635376 + 0.772203i \(0.280845\pi\)
\(888\) 0 0
\(889\) −0.219114 −0.00734886
\(890\) 0 0
\(891\) 14.8883 0.498777
\(892\) 0 0
\(893\) −45.8944 −1.53580
\(894\) 0 0
\(895\) −57.2150 −1.91249
\(896\) 0 0
\(897\) −20.4755 −0.683657
\(898\) 0 0
\(899\) 0.127369 0.00424801
\(900\) 0 0
\(901\) 0.112999 0.00376453
\(902\) 0 0
\(903\) −0.674134 −0.0224338
\(904\) 0 0
\(905\) 73.0411 2.42797
\(906\) 0 0
\(907\) 0.311482 0.0103426 0.00517129 0.999987i \(-0.498354\pi\)
0.00517129 + 0.999987i \(0.498354\pi\)
\(908\) 0 0
\(909\) −6.69401 −0.222026
\(910\) 0 0
\(911\) −42.8928 −1.42110 −0.710551 0.703646i \(-0.751554\pi\)
−0.710551 + 0.703646i \(0.751554\pi\)
\(912\) 0 0
\(913\) −0.663544 −0.0219601
\(914\) 0 0
\(915\) 77.3762 2.55798
\(916\) 0 0
\(917\) 1.90849 0.0630239
\(918\) 0 0
\(919\) −40.2516 −1.32778 −0.663889 0.747831i \(-0.731095\pi\)
−0.663889 + 0.747831i \(0.731095\pi\)
\(920\) 0 0
\(921\) −14.8102 −0.488012
\(922\) 0 0
\(923\) −14.0032 −0.460922
\(924\) 0 0
\(925\) 24.5367 0.806761
\(926\) 0 0
\(927\) −0.0600716 −0.00197301
\(928\) 0 0
\(929\) 14.7060 0.482489 0.241244 0.970464i \(-0.422444\pi\)
0.241244 + 0.970464i \(0.422444\pi\)
\(930\) 0 0
\(931\) −24.9354 −0.817226
\(932\) 0 0
\(933\) 42.9570 1.40635
\(934\) 0 0
\(935\) 5.93851 0.194210
\(936\) 0 0
\(937\) 26.2273 0.856807 0.428404 0.903587i \(-0.359076\pi\)
0.428404 + 0.903587i \(0.359076\pi\)
\(938\) 0 0
\(939\) 26.6511 0.869725
\(940\) 0 0
\(941\) −51.2435 −1.67049 −0.835246 0.549877i \(-0.814675\pi\)
−0.835246 + 0.549877i \(0.814675\pi\)
\(942\) 0 0
\(943\) 61.2257 1.99378
\(944\) 0 0
\(945\) 1.15340 0.0375203
\(946\) 0 0
\(947\) −31.3479 −1.01867 −0.509334 0.860569i \(-0.670108\pi\)
−0.509334 + 0.860569i \(0.670108\pi\)
\(948\) 0 0
\(949\) −6.29034 −0.204193
\(950\) 0 0
\(951\) −7.86130 −0.254920
\(952\) 0 0
\(953\) −28.4399 −0.921260 −0.460630 0.887592i \(-0.652377\pi\)
−0.460630 + 0.887592i \(0.652377\pi\)
\(954\) 0 0
\(955\) 31.0779 1.00566
\(956\) 0 0
\(957\) 0.282426 0.00912953
\(958\) 0 0
\(959\) −0.539299 −0.0174149
\(960\) 0 0
\(961\) −29.1659 −0.940835
\(962\) 0 0
\(963\) 32.7822 1.05639
\(964\) 0 0
\(965\) 28.8124 0.927505
\(966\) 0 0
\(967\) −15.0183 −0.482956 −0.241478 0.970406i \(-0.577632\pi\)
−0.241478 + 0.970406i \(0.577632\pi\)
\(968\) 0 0
\(969\) 8.95747 0.287755
\(970\) 0 0
\(971\) 4.87993 0.156604 0.0783022 0.996930i \(-0.475050\pi\)
0.0783022 + 0.996930i \(0.475050\pi\)
\(972\) 0 0
\(973\) −2.57358 −0.0825052
\(974\) 0 0
\(975\) −34.0604 −1.09081
\(976\) 0 0
\(977\) 47.3517 1.51492 0.757458 0.652884i \(-0.226441\pi\)
0.757458 + 0.652884i \(0.226441\pi\)
\(978\) 0 0
\(979\) −11.8528 −0.378818
\(980\) 0 0
\(981\) −13.1846 −0.420951
\(982\) 0 0
\(983\) 16.7138 0.533087 0.266543 0.963823i \(-0.414118\pi\)
0.266543 + 0.963823i \(0.414118\pi\)
\(984\) 0 0
\(985\) 49.6996 1.58356
\(986\) 0 0
\(987\) −3.64173 −0.115918
\(988\) 0 0
\(989\) −14.6990 −0.467400
\(990\) 0 0
\(991\) 22.3986 0.711516 0.355758 0.934578i \(-0.384223\pi\)
0.355758 + 0.934578i \(0.384223\pi\)
\(992\) 0 0
\(993\) 7.03527 0.223258
\(994\) 0 0
\(995\) 13.3588 0.423503
\(996\) 0 0
\(997\) −52.8835 −1.67484 −0.837418 0.546563i \(-0.815936\pi\)
−0.837418 + 0.546563i \(0.815936\pi\)
\(998\) 0 0
\(999\) −5.53809 −0.175217
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 \(a_p\))