Properties

Label 6008.2.a.e.1.4
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.96484 q^{3}\) \(+2.30894 q^{5}\) \(-3.32968 q^{7}\) \(+5.79029 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.96484 q^{3}\) \(+2.30894 q^{5}\) \(-3.32968 q^{7}\) \(+5.79029 q^{9}\) \(+2.14673 q^{11}\) \(+7.10748 q^{13}\) \(-6.84566 q^{15}\) \(+1.94537 q^{17}\) \(-1.57430 q^{19}\) \(+9.87198 q^{21}\) \(+1.61890 q^{23}\) \(+0.331224 q^{25}\) \(-8.27278 q^{27}\) \(-0.641396 q^{29}\) \(+9.34979 q^{31}\) \(-6.36473 q^{33}\) \(-7.68805 q^{35}\) \(+3.74005 q^{37}\) \(-21.0726 q^{39}\) \(+6.15103 q^{41}\) \(+7.41503 q^{43}\) \(+13.3695 q^{45}\) \(+8.21995 q^{47}\) \(+4.08678 q^{49}\) \(-5.76772 q^{51}\) \(-3.90788 q^{53}\) \(+4.95669 q^{55}\) \(+4.66756 q^{57}\) \(-4.72476 q^{59}\) \(-3.28446 q^{61}\) \(-19.2798 q^{63}\) \(+16.4108 q^{65}\) \(-1.90142 q^{67}\) \(-4.79978 q^{69}\) \(-7.00941 q^{71}\) \(+5.45222 q^{73}\) \(-0.982028 q^{75}\) \(-7.14794 q^{77}\) \(+9.26342 q^{79}\) \(+7.15661 q^{81}\) \(-4.26867 q^{83}\) \(+4.49175 q^{85}\) \(+1.90164 q^{87}\) \(-5.75983 q^{89}\) \(-23.6657 q^{91}\) \(-27.7207 q^{93}\) \(-3.63498 q^{95}\) \(-3.83915 q^{97}\) \(+12.4302 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.96484 −1.71175 −0.855876 0.517180i \(-0.826982\pi\)
−0.855876 + 0.517180i \(0.826982\pi\)
\(4\) 0 0
\(5\) 2.30894 1.03259 0.516296 0.856410i \(-0.327311\pi\)
0.516296 + 0.856410i \(0.327311\pi\)
\(6\) 0 0
\(7\) −3.32968 −1.25850 −0.629251 0.777202i \(-0.716638\pi\)
−0.629251 + 0.777202i \(0.716638\pi\)
\(8\) 0 0
\(9\) 5.79029 1.93010
\(10\) 0 0
\(11\) 2.14673 0.647264 0.323632 0.946183i \(-0.395096\pi\)
0.323632 + 0.946183i \(0.395096\pi\)
\(12\) 0 0
\(13\) 7.10748 1.97126 0.985631 0.168915i \(-0.0540263\pi\)
0.985631 + 0.168915i \(0.0540263\pi\)
\(14\) 0 0
\(15\) −6.84566 −1.76754
\(16\) 0 0
\(17\) 1.94537 0.471822 0.235911 0.971775i \(-0.424193\pi\)
0.235911 + 0.971775i \(0.424193\pi\)
\(18\) 0 0
\(19\) −1.57430 −0.361170 −0.180585 0.983559i \(-0.557799\pi\)
−0.180585 + 0.983559i \(0.557799\pi\)
\(20\) 0 0
\(21\) 9.87198 2.15424
\(22\) 0 0
\(23\) 1.61890 0.337564 0.168782 0.985653i \(-0.446017\pi\)
0.168782 + 0.985653i \(0.446017\pi\)
\(24\) 0 0
\(25\) 0.331224 0.0662449
\(26\) 0 0
\(27\) −8.27278 −1.59210
\(28\) 0 0
\(29\) −0.641396 −0.119104 −0.0595521 0.998225i \(-0.518967\pi\)
−0.0595521 + 0.998225i \(0.518967\pi\)
\(30\) 0 0
\(31\) 9.34979 1.67927 0.839636 0.543149i \(-0.182768\pi\)
0.839636 + 0.543149i \(0.182768\pi\)
\(32\) 0 0
\(33\) −6.36473 −1.10796
\(34\) 0 0
\(35\) −7.68805 −1.29952
\(36\) 0 0
\(37\) 3.74005 0.614861 0.307431 0.951571i \(-0.400531\pi\)
0.307431 + 0.951571i \(0.400531\pi\)
\(38\) 0 0
\(39\) −21.0726 −3.37431
\(40\) 0 0
\(41\) 6.15103 0.960630 0.480315 0.877096i \(-0.340522\pi\)
0.480315 + 0.877096i \(0.340522\pi\)
\(42\) 0 0
\(43\) 7.41503 1.13078 0.565391 0.824823i \(-0.308725\pi\)
0.565391 + 0.824823i \(0.308725\pi\)
\(44\) 0 0
\(45\) 13.3695 1.99300
\(46\) 0 0
\(47\) 8.21995 1.19900 0.599502 0.800374i \(-0.295366\pi\)
0.599502 + 0.800374i \(0.295366\pi\)
\(48\) 0 0
\(49\) 4.08678 0.583825
\(50\) 0 0
\(51\) −5.76772 −0.807642
\(52\) 0 0
\(53\) −3.90788 −0.536788 −0.268394 0.963309i \(-0.586493\pi\)
−0.268394 + 0.963309i \(0.586493\pi\)
\(54\) 0 0
\(55\) 4.95669 0.668360
\(56\) 0 0
\(57\) 4.66756 0.618234
\(58\) 0 0
\(59\) −4.72476 −0.615112 −0.307556 0.951530i \(-0.599511\pi\)
−0.307556 + 0.951530i \(0.599511\pi\)
\(60\) 0 0
\(61\) −3.28446 −0.420532 −0.210266 0.977644i \(-0.567433\pi\)
−0.210266 + 0.977644i \(0.567433\pi\)
\(62\) 0 0
\(63\) −19.2798 −2.42903
\(64\) 0 0
\(65\) 16.4108 2.03551
\(66\) 0 0
\(67\) −1.90142 −0.232295 −0.116148 0.993232i \(-0.537055\pi\)
−0.116148 + 0.993232i \(0.537055\pi\)
\(68\) 0 0
\(69\) −4.79978 −0.577826
\(70\) 0 0
\(71\) −7.00941 −0.831864 −0.415932 0.909396i \(-0.636545\pi\)
−0.415932 + 0.909396i \(0.636545\pi\)
\(72\) 0 0
\(73\) 5.45222 0.638134 0.319067 0.947732i \(-0.396631\pi\)
0.319067 + 0.947732i \(0.396631\pi\)
\(74\) 0 0
\(75\) −0.982028 −0.113395
\(76\) 0 0
\(77\) −7.14794 −0.814583
\(78\) 0 0
\(79\) 9.26342 1.04222 0.521108 0.853491i \(-0.325519\pi\)
0.521108 + 0.853491i \(0.325519\pi\)
\(80\) 0 0
\(81\) 7.15661 0.795179
\(82\) 0 0
\(83\) −4.26867 −0.468548 −0.234274 0.972171i \(-0.575271\pi\)
−0.234274 + 0.972171i \(0.575271\pi\)
\(84\) 0 0
\(85\) 4.49175 0.487199
\(86\) 0 0
\(87\) 1.90164 0.203877
\(88\) 0 0
\(89\) −5.75983 −0.610541 −0.305270 0.952266i \(-0.598747\pi\)
−0.305270 + 0.952266i \(0.598747\pi\)
\(90\) 0 0
\(91\) −23.6657 −2.48083
\(92\) 0 0
\(93\) −27.7207 −2.87450
\(94\) 0 0
\(95\) −3.63498 −0.372941
\(96\) 0 0
\(97\) −3.83915 −0.389807 −0.194903 0.980822i \(-0.562439\pi\)
−0.194903 + 0.980822i \(0.562439\pi\)
\(98\) 0 0
\(99\) 12.4302 1.24928
\(100\) 0 0
\(101\) −9.18715 −0.914155 −0.457078 0.889427i \(-0.651104\pi\)
−0.457078 + 0.889427i \(0.651104\pi\)
\(102\) 0 0
\(103\) −16.4749 −1.62332 −0.811660 0.584130i \(-0.801436\pi\)
−0.811660 + 0.584130i \(0.801436\pi\)
\(104\) 0 0
\(105\) 22.7939 2.22445
\(106\) 0 0
\(107\) 3.87884 0.374982 0.187491 0.982266i \(-0.439964\pi\)
0.187491 + 0.982266i \(0.439964\pi\)
\(108\) 0 0
\(109\) −7.78957 −0.746106 −0.373053 0.927810i \(-0.621689\pi\)
−0.373053 + 0.927810i \(0.621689\pi\)
\(110\) 0 0
\(111\) −11.0887 −1.05249
\(112\) 0 0
\(113\) 14.4347 1.35791 0.678953 0.734181i \(-0.262434\pi\)
0.678953 + 0.734181i \(0.262434\pi\)
\(114\) 0 0
\(115\) 3.73795 0.348566
\(116\) 0 0
\(117\) 41.1544 3.80473
\(118\) 0 0
\(119\) −6.47747 −0.593788
\(120\) 0 0
\(121\) −6.39154 −0.581049
\(122\) 0 0
\(123\) −18.2368 −1.64436
\(124\) 0 0
\(125\) −10.7799 −0.964187
\(126\) 0 0
\(127\) 2.43815 0.216351 0.108175 0.994132i \(-0.465499\pi\)
0.108175 + 0.994132i \(0.465499\pi\)
\(128\) 0 0
\(129\) −21.9844 −1.93562
\(130\) 0 0
\(131\) −7.53690 −0.658502 −0.329251 0.944242i \(-0.606796\pi\)
−0.329251 + 0.944242i \(0.606796\pi\)
\(132\) 0 0
\(133\) 5.24193 0.454533
\(134\) 0 0
\(135\) −19.1014 −1.64399
\(136\) 0 0
\(137\) 6.28100 0.536622 0.268311 0.963332i \(-0.413535\pi\)
0.268311 + 0.963332i \(0.413535\pi\)
\(138\) 0 0
\(139\) 6.74449 0.572060 0.286030 0.958221i \(-0.407664\pi\)
0.286030 + 0.958221i \(0.407664\pi\)
\(140\) 0 0
\(141\) −24.3709 −2.05240
\(142\) 0 0
\(143\) 15.2579 1.27593
\(144\) 0 0
\(145\) −1.48095 −0.122986
\(146\) 0 0
\(147\) −12.1167 −0.999365
\(148\) 0 0
\(149\) 11.7319 0.961113 0.480556 0.876964i \(-0.340435\pi\)
0.480556 + 0.876964i \(0.340435\pi\)
\(150\) 0 0
\(151\) 0.710557 0.0578243 0.0289122 0.999582i \(-0.490796\pi\)
0.0289122 + 0.999582i \(0.490796\pi\)
\(152\) 0 0
\(153\) 11.2643 0.910662
\(154\) 0 0
\(155\) 21.5882 1.73400
\(156\) 0 0
\(157\) 18.0109 1.43743 0.718714 0.695306i \(-0.244731\pi\)
0.718714 + 0.695306i \(0.244731\pi\)
\(158\) 0 0
\(159\) 11.5862 0.918849
\(160\) 0 0
\(161\) −5.39042 −0.424825
\(162\) 0 0
\(163\) 6.53890 0.512166 0.256083 0.966655i \(-0.417568\pi\)
0.256083 + 0.966655i \(0.417568\pi\)
\(164\) 0 0
\(165\) −14.6958 −1.14407
\(166\) 0 0
\(167\) −3.76092 −0.291029 −0.145514 0.989356i \(-0.546484\pi\)
−0.145514 + 0.989356i \(0.546484\pi\)
\(168\) 0 0
\(169\) 37.5163 2.88587
\(170\) 0 0
\(171\) −9.11568 −0.697093
\(172\) 0 0
\(173\) −9.71597 −0.738691 −0.369346 0.929292i \(-0.620418\pi\)
−0.369346 + 0.929292i \(0.620418\pi\)
\(174\) 0 0
\(175\) −1.10287 −0.0833692
\(176\) 0 0
\(177\) 14.0082 1.05292
\(178\) 0 0
\(179\) 17.6447 1.31883 0.659414 0.751780i \(-0.270804\pi\)
0.659414 + 0.751780i \(0.270804\pi\)
\(180\) 0 0
\(181\) −18.2802 −1.35875 −0.679377 0.733789i \(-0.737750\pi\)
−0.679377 + 0.733789i \(0.737750\pi\)
\(182\) 0 0
\(183\) 9.73790 0.719846
\(184\) 0 0
\(185\) 8.63558 0.634900
\(186\) 0 0
\(187\) 4.17619 0.305393
\(188\) 0 0
\(189\) 27.5457 2.00366
\(190\) 0 0
\(191\) 16.4119 1.18752 0.593762 0.804641i \(-0.297642\pi\)
0.593762 + 0.804641i \(0.297642\pi\)
\(192\) 0 0
\(193\) −22.1718 −1.59596 −0.797981 0.602683i \(-0.794099\pi\)
−0.797981 + 0.602683i \(0.794099\pi\)
\(194\) 0 0
\(195\) −48.6554 −3.48429
\(196\) 0 0
\(197\) −17.1780 −1.22388 −0.611940 0.790904i \(-0.709611\pi\)
−0.611940 + 0.790904i \(0.709611\pi\)
\(198\) 0 0
\(199\) −1.79443 −0.127204 −0.0636018 0.997975i \(-0.520259\pi\)
−0.0636018 + 0.997975i \(0.520259\pi\)
\(200\) 0 0
\(201\) 5.63741 0.397632
\(202\) 0 0
\(203\) 2.13564 0.149893
\(204\) 0 0
\(205\) 14.2024 0.991938
\(206\) 0 0
\(207\) 9.37391 0.651531
\(208\) 0 0
\(209\) −3.37961 −0.233772
\(210\) 0 0
\(211\) 17.1733 1.18226 0.591131 0.806576i \(-0.298682\pi\)
0.591131 + 0.806576i \(0.298682\pi\)
\(212\) 0 0
\(213\) 20.7818 1.42394
\(214\) 0 0
\(215\) 17.1209 1.16764
\(216\) 0 0
\(217\) −31.1318 −2.11337
\(218\) 0 0
\(219\) −16.1650 −1.09233
\(220\) 0 0
\(221\) 13.8267 0.930084
\(222\) 0 0
\(223\) 12.4274 0.832200 0.416100 0.909319i \(-0.363397\pi\)
0.416100 + 0.909319i \(0.363397\pi\)
\(224\) 0 0
\(225\) 1.91789 0.127859
\(226\) 0 0
\(227\) 10.5705 0.701589 0.350794 0.936453i \(-0.385912\pi\)
0.350794 + 0.936453i \(0.385912\pi\)
\(228\) 0 0
\(229\) −0.689808 −0.0455838 −0.0227919 0.999740i \(-0.507256\pi\)
−0.0227919 + 0.999740i \(0.507256\pi\)
\(230\) 0 0
\(231\) 21.1925 1.39436
\(232\) 0 0
\(233\) −3.82540 −0.250610 −0.125305 0.992118i \(-0.539991\pi\)
−0.125305 + 0.992118i \(0.539991\pi\)
\(234\) 0 0
\(235\) 18.9794 1.23808
\(236\) 0 0
\(237\) −27.4646 −1.78402
\(238\) 0 0
\(239\) −11.9284 −0.771586 −0.385793 0.922585i \(-0.626072\pi\)
−0.385793 + 0.922585i \(0.626072\pi\)
\(240\) 0 0
\(241\) −25.6594 −1.65287 −0.826435 0.563032i \(-0.809635\pi\)
−0.826435 + 0.563032i \(0.809635\pi\)
\(242\) 0 0
\(243\) 3.60011 0.230947
\(244\) 0 0
\(245\) 9.43614 0.602853
\(246\) 0 0
\(247\) −11.1893 −0.711960
\(248\) 0 0
\(249\) 12.6559 0.802038
\(250\) 0 0
\(251\) −6.19074 −0.390756 −0.195378 0.980728i \(-0.562593\pi\)
−0.195378 + 0.980728i \(0.562593\pi\)
\(252\) 0 0
\(253\) 3.47535 0.218493
\(254\) 0 0
\(255\) −13.3173 −0.833964
\(256\) 0 0
\(257\) 17.7040 1.10434 0.552172 0.833730i \(-0.313799\pi\)
0.552172 + 0.833730i \(0.313799\pi\)
\(258\) 0 0
\(259\) −12.4532 −0.773804
\(260\) 0 0
\(261\) −3.71387 −0.229883
\(262\) 0 0
\(263\) −14.1052 −0.869764 −0.434882 0.900488i \(-0.643210\pi\)
−0.434882 + 0.900488i \(0.643210\pi\)
\(264\) 0 0
\(265\) −9.02307 −0.554283
\(266\) 0 0
\(267\) 17.0770 1.04509
\(268\) 0 0
\(269\) 13.5630 0.826948 0.413474 0.910516i \(-0.364315\pi\)
0.413474 + 0.910516i \(0.364315\pi\)
\(270\) 0 0
\(271\) −13.9666 −0.848412 −0.424206 0.905566i \(-0.639447\pi\)
−0.424206 + 0.905566i \(0.639447\pi\)
\(272\) 0 0
\(273\) 70.1649 4.24658
\(274\) 0 0
\(275\) 0.711050 0.0428779
\(276\) 0 0
\(277\) 9.91202 0.595556 0.297778 0.954635i \(-0.403755\pi\)
0.297778 + 0.954635i \(0.403755\pi\)
\(278\) 0 0
\(279\) 54.1380 3.24116
\(280\) 0 0
\(281\) −6.66988 −0.397892 −0.198946 0.980010i \(-0.563752\pi\)
−0.198946 + 0.980010i \(0.563752\pi\)
\(282\) 0 0
\(283\) −8.00761 −0.476003 −0.238002 0.971265i \(-0.576492\pi\)
−0.238002 + 0.971265i \(0.576492\pi\)
\(284\) 0 0
\(285\) 10.7771 0.638383
\(286\) 0 0
\(287\) −20.4810 −1.20895
\(288\) 0 0
\(289\) −13.2155 −0.777384
\(290\) 0 0
\(291\) 11.3825 0.667253
\(292\) 0 0
\(293\) 0.724694 0.0423371 0.0211685 0.999776i \(-0.493261\pi\)
0.0211685 + 0.999776i \(0.493261\pi\)
\(294\) 0 0
\(295\) −10.9092 −0.635159
\(296\) 0 0
\(297\) −17.7594 −1.03051
\(298\) 0 0
\(299\) 11.5063 0.665427
\(300\) 0 0
\(301\) −24.6897 −1.42309
\(302\) 0 0
\(303\) 27.2384 1.56481
\(304\) 0 0
\(305\) −7.58363 −0.434237
\(306\) 0 0
\(307\) 14.0225 0.800306 0.400153 0.916448i \(-0.368957\pi\)
0.400153 + 0.916448i \(0.368957\pi\)
\(308\) 0 0
\(309\) 48.8455 2.77872
\(310\) 0 0
\(311\) −23.4147 −1.32773 −0.663863 0.747854i \(-0.731084\pi\)
−0.663863 + 0.747854i \(0.731084\pi\)
\(312\) 0 0
\(313\) −32.4687 −1.83524 −0.917621 0.397457i \(-0.869893\pi\)
−0.917621 + 0.397457i \(0.869893\pi\)
\(314\) 0 0
\(315\) −44.5161 −2.50820
\(316\) 0 0
\(317\) 25.6751 1.44206 0.721028 0.692905i \(-0.243670\pi\)
0.721028 + 0.692905i \(0.243670\pi\)
\(318\) 0 0
\(319\) −1.37691 −0.0770919
\(320\) 0 0
\(321\) −11.5002 −0.641877
\(322\) 0 0
\(323\) −3.06260 −0.170408
\(324\) 0 0
\(325\) 2.35417 0.130586
\(326\) 0 0
\(327\) 23.0949 1.27715
\(328\) 0 0
\(329\) −27.3698 −1.50895
\(330\) 0 0
\(331\) −12.9087 −0.709526 −0.354763 0.934956i \(-0.615438\pi\)
−0.354763 + 0.934956i \(0.615438\pi\)
\(332\) 0 0
\(333\) 21.6560 1.18674
\(334\) 0 0
\(335\) −4.39027 −0.239866
\(336\) 0 0
\(337\) 32.5660 1.77398 0.886990 0.461788i \(-0.152792\pi\)
0.886990 + 0.461788i \(0.152792\pi\)
\(338\) 0 0
\(339\) −42.7968 −2.32440
\(340\) 0 0
\(341\) 20.0715 1.08693
\(342\) 0 0
\(343\) 9.70010 0.523756
\(344\) 0 0
\(345\) −11.0824 −0.596658
\(346\) 0 0
\(347\) 22.8921 1.22891 0.614455 0.788952i \(-0.289376\pi\)
0.614455 + 0.788952i \(0.289376\pi\)
\(348\) 0 0
\(349\) 22.8101 1.22100 0.610498 0.792018i \(-0.290969\pi\)
0.610498 + 0.792018i \(0.290969\pi\)
\(350\) 0 0
\(351\) −58.7986 −3.13844
\(352\) 0 0
\(353\) 34.5706 1.84001 0.920003 0.391911i \(-0.128186\pi\)
0.920003 + 0.391911i \(0.128186\pi\)
\(354\) 0 0
\(355\) −16.1843 −0.858975
\(356\) 0 0
\(357\) 19.2047 1.01642
\(358\) 0 0
\(359\) 29.5296 1.55851 0.779256 0.626706i \(-0.215597\pi\)
0.779256 + 0.626706i \(0.215597\pi\)
\(360\) 0 0
\(361\) −16.5216 −0.869556
\(362\) 0 0
\(363\) 18.9499 0.994612
\(364\) 0 0
\(365\) 12.5889 0.658931
\(366\) 0 0
\(367\) 36.9416 1.92833 0.964167 0.265296i \(-0.0854698\pi\)
0.964167 + 0.265296i \(0.0854698\pi\)
\(368\) 0 0
\(369\) 35.6163 1.85411
\(370\) 0 0
\(371\) 13.0120 0.675549
\(372\) 0 0
\(373\) 5.19099 0.268779 0.134390 0.990929i \(-0.457093\pi\)
0.134390 + 0.990929i \(0.457093\pi\)
\(374\) 0 0
\(375\) 31.9608 1.65045
\(376\) 0 0
\(377\) −4.55871 −0.234785
\(378\) 0 0
\(379\) 18.3266 0.941376 0.470688 0.882300i \(-0.344006\pi\)
0.470688 + 0.882300i \(0.344006\pi\)
\(380\) 0 0
\(381\) −7.22872 −0.370339
\(382\) 0 0
\(383\) 29.8558 1.52556 0.762779 0.646659i \(-0.223834\pi\)
0.762779 + 0.646659i \(0.223834\pi\)
\(384\) 0 0
\(385\) −16.5042 −0.841131
\(386\) 0 0
\(387\) 42.9352 2.18252
\(388\) 0 0
\(389\) 21.3831 1.08417 0.542084 0.840324i \(-0.317635\pi\)
0.542084 + 0.840324i \(0.317635\pi\)
\(390\) 0 0
\(391\) 3.14936 0.159270
\(392\) 0 0
\(393\) 22.3457 1.12719
\(394\) 0 0
\(395\) 21.3887 1.07618
\(396\) 0 0
\(397\) 18.1874 0.912799 0.456400 0.889775i \(-0.349139\pi\)
0.456400 + 0.889775i \(0.349139\pi\)
\(398\) 0 0
\(399\) −15.5415 −0.778048
\(400\) 0 0
\(401\) −8.76900 −0.437903 −0.218952 0.975736i \(-0.570264\pi\)
−0.218952 + 0.975736i \(0.570264\pi\)
\(402\) 0 0
\(403\) 66.4535 3.31028
\(404\) 0 0
\(405\) 16.5242 0.821095
\(406\) 0 0
\(407\) 8.02890 0.397978
\(408\) 0 0
\(409\) 14.3029 0.707231 0.353616 0.935391i \(-0.384952\pi\)
0.353616 + 0.935391i \(0.384952\pi\)
\(410\) 0 0
\(411\) −18.6222 −0.918564
\(412\) 0 0
\(413\) 15.7320 0.774119
\(414\) 0 0
\(415\) −9.85613 −0.483818
\(416\) 0 0
\(417\) −19.9963 −0.979225
\(418\) 0 0
\(419\) −16.0911 −0.786103 −0.393052 0.919516i \(-0.628581\pi\)
−0.393052 + 0.919516i \(0.628581\pi\)
\(420\) 0 0
\(421\) 6.01049 0.292934 0.146467 0.989216i \(-0.453210\pi\)
0.146467 + 0.989216i \(0.453210\pi\)
\(422\) 0 0
\(423\) 47.5959 2.31419
\(424\) 0 0
\(425\) 0.644354 0.0312558
\(426\) 0 0
\(427\) 10.9362 0.529240
\(428\) 0 0
\(429\) −45.2372 −2.18407
\(430\) 0 0
\(431\) −28.4861 −1.37213 −0.686064 0.727541i \(-0.740663\pi\)
−0.686064 + 0.727541i \(0.740663\pi\)
\(432\) 0 0
\(433\) −33.5031 −1.61006 −0.805028 0.593237i \(-0.797850\pi\)
−0.805028 + 0.593237i \(0.797850\pi\)
\(434\) 0 0
\(435\) 4.39077 0.210522
\(436\) 0 0
\(437\) −2.54864 −0.121918
\(438\) 0 0
\(439\) −19.3704 −0.924498 −0.462249 0.886750i \(-0.652957\pi\)
−0.462249 + 0.886750i \(0.652957\pi\)
\(440\) 0 0
\(441\) 23.6636 1.12684
\(442\) 0 0
\(443\) −13.6945 −0.650647 −0.325324 0.945603i \(-0.605473\pi\)
−0.325324 + 0.945603i \(0.605473\pi\)
\(444\) 0 0
\(445\) −13.2991 −0.630439
\(446\) 0 0
\(447\) −34.7832 −1.64519
\(448\) 0 0
\(449\) 40.0748 1.89125 0.945623 0.325265i \(-0.105454\pi\)
0.945623 + 0.325265i \(0.105454\pi\)
\(450\) 0 0
\(451\) 13.2046 0.621782
\(452\) 0 0
\(453\) −2.10669 −0.0989809
\(454\) 0 0
\(455\) −54.6427 −2.56169
\(456\) 0 0
\(457\) 5.56196 0.260178 0.130089 0.991502i \(-0.458474\pi\)
0.130089 + 0.991502i \(0.458474\pi\)
\(458\) 0 0
\(459\) −16.0936 −0.751186
\(460\) 0 0
\(461\) 22.3505 1.04097 0.520484 0.853872i \(-0.325752\pi\)
0.520484 + 0.853872i \(0.325752\pi\)
\(462\) 0 0
\(463\) 10.9988 0.511157 0.255578 0.966788i \(-0.417734\pi\)
0.255578 + 0.966788i \(0.417734\pi\)
\(464\) 0 0
\(465\) −64.0055 −2.96818
\(466\) 0 0
\(467\) 13.2253 0.611992 0.305996 0.952033i \(-0.401011\pi\)
0.305996 + 0.952033i \(0.401011\pi\)
\(468\) 0 0
\(469\) 6.33112 0.292344
\(470\) 0 0
\(471\) −53.3996 −2.46052
\(472\) 0 0
\(473\) 15.9181 0.731915
\(474\) 0 0
\(475\) −0.521448 −0.0239257
\(476\) 0 0
\(477\) −22.6277 −1.03605
\(478\) 0 0
\(479\) −17.2571 −0.788496 −0.394248 0.919004i \(-0.628995\pi\)
−0.394248 + 0.919004i \(0.628995\pi\)
\(480\) 0 0
\(481\) 26.5824 1.21205
\(482\) 0 0
\(483\) 15.9818 0.727195
\(484\) 0 0
\(485\) −8.86439 −0.402511
\(486\) 0 0
\(487\) −35.0380 −1.58772 −0.793861 0.608099i \(-0.791932\pi\)
−0.793861 + 0.608099i \(0.791932\pi\)
\(488\) 0 0
\(489\) −19.3868 −0.876702
\(490\) 0 0
\(491\) −17.1423 −0.773621 −0.386810 0.922159i \(-0.626423\pi\)
−0.386810 + 0.922159i \(0.626423\pi\)
\(492\) 0 0
\(493\) −1.24775 −0.0561959
\(494\) 0 0
\(495\) 28.7007 1.29000
\(496\) 0 0
\(497\) 23.3391 1.04690
\(498\) 0 0
\(499\) 9.99835 0.447588 0.223794 0.974637i \(-0.428156\pi\)
0.223794 + 0.974637i \(0.428156\pi\)
\(500\) 0 0
\(501\) 11.1505 0.498170
\(502\) 0 0
\(503\) 23.8412 1.06303 0.531514 0.847049i \(-0.321623\pi\)
0.531514 + 0.847049i \(0.321623\pi\)
\(504\) 0 0
\(505\) −21.2126 −0.943949
\(506\) 0 0
\(507\) −111.230 −4.93990
\(508\) 0 0
\(509\) 9.69965 0.429929 0.214965 0.976622i \(-0.431036\pi\)
0.214965 + 0.976622i \(0.431036\pi\)
\(510\) 0 0
\(511\) −18.1541 −0.803092
\(512\) 0 0
\(513\) 13.0239 0.575018
\(514\) 0 0
\(515\) −38.0396 −1.67623
\(516\) 0 0
\(517\) 17.6460 0.776072
\(518\) 0 0
\(519\) 28.8063 1.26446
\(520\) 0 0
\(521\) 36.3748 1.59361 0.796803 0.604239i \(-0.206523\pi\)
0.796803 + 0.604239i \(0.206523\pi\)
\(522\) 0 0
\(523\) −1.54998 −0.0677759 −0.0338879 0.999426i \(-0.510789\pi\)
−0.0338879 + 0.999426i \(0.510789\pi\)
\(524\) 0 0
\(525\) 3.26984 0.142708
\(526\) 0 0
\(527\) 18.1888 0.792317
\(528\) 0 0
\(529\) −20.3792 −0.886051
\(530\) 0 0
\(531\) −27.3578 −1.18723
\(532\) 0 0
\(533\) 43.7184 1.89365
\(534\) 0 0
\(535\) 8.95604 0.387203
\(536\) 0 0
\(537\) −52.3138 −2.25751
\(538\) 0 0
\(539\) 8.77322 0.377889
\(540\) 0 0
\(541\) 15.7180 0.675771 0.337885 0.941187i \(-0.390288\pi\)
0.337885 + 0.941187i \(0.390288\pi\)
\(542\) 0 0
\(543\) 54.1978 2.32585
\(544\) 0 0
\(545\) −17.9857 −0.770422
\(546\) 0 0
\(547\) 30.1450 1.28891 0.644454 0.764643i \(-0.277085\pi\)
0.644454 + 0.764643i \(0.277085\pi\)
\(548\) 0 0
\(549\) −19.0180 −0.811667
\(550\) 0 0
\(551\) 1.00975 0.0430169
\(552\) 0 0
\(553\) −30.8442 −1.31163
\(554\) 0 0
\(555\) −25.6031 −1.08679
\(556\) 0 0
\(557\) −33.5264 −1.42056 −0.710279 0.703921i \(-0.751431\pi\)
−0.710279 + 0.703921i \(0.751431\pi\)
\(558\) 0 0
\(559\) 52.7022 2.22907
\(560\) 0 0
\(561\) −12.3818 −0.522758
\(562\) 0 0
\(563\) −32.3019 −1.36136 −0.680681 0.732580i \(-0.738316\pi\)
−0.680681 + 0.732580i \(0.738316\pi\)
\(564\) 0 0
\(565\) 33.3290 1.40216
\(566\) 0 0
\(567\) −23.8292 −1.00073
\(568\) 0 0
\(569\) −43.7160 −1.83267 −0.916335 0.400412i \(-0.868867\pi\)
−0.916335 + 0.400412i \(0.868867\pi\)
\(570\) 0 0
\(571\) 36.1720 1.51375 0.756876 0.653558i \(-0.226725\pi\)
0.756876 + 0.653558i \(0.226725\pi\)
\(572\) 0 0
\(573\) −48.6587 −2.03275
\(574\) 0 0
\(575\) 0.536219 0.0223619
\(576\) 0 0
\(577\) 17.9014 0.745246 0.372623 0.927983i \(-0.378458\pi\)
0.372623 + 0.927983i \(0.378458\pi\)
\(578\) 0 0
\(579\) 65.7359 2.73189
\(580\) 0 0
\(581\) 14.2133 0.589668
\(582\) 0 0
\(583\) −8.38917 −0.347444
\(584\) 0 0
\(585\) 95.0232 3.92873
\(586\) 0 0
\(587\) 5.26648 0.217371 0.108686 0.994076i \(-0.465336\pi\)
0.108686 + 0.994076i \(0.465336\pi\)
\(588\) 0 0
\(589\) −14.7194 −0.606503
\(590\) 0 0
\(591\) 50.9300 2.09498
\(592\) 0 0
\(593\) 7.47905 0.307128 0.153564 0.988139i \(-0.450925\pi\)
0.153564 + 0.988139i \(0.450925\pi\)
\(594\) 0 0
\(595\) −14.9561 −0.613141
\(596\) 0 0
\(597\) 5.32020 0.217741
\(598\) 0 0
\(599\) −10.9421 −0.447081 −0.223541 0.974695i \(-0.571762\pi\)
−0.223541 + 0.974695i \(0.571762\pi\)
\(600\) 0 0
\(601\) 34.1253 1.39200 0.696000 0.718042i \(-0.254961\pi\)
0.696000 + 0.718042i \(0.254961\pi\)
\(602\) 0 0
\(603\) −11.0098 −0.448353
\(604\) 0 0
\(605\) −14.7577 −0.599986
\(606\) 0 0
\(607\) 8.43853 0.342510 0.171255 0.985227i \(-0.445218\pi\)
0.171255 + 0.985227i \(0.445218\pi\)
\(608\) 0 0
\(609\) −6.33185 −0.256579
\(610\) 0 0
\(611\) 58.4232 2.36355
\(612\) 0 0
\(613\) −18.9245 −0.764353 −0.382177 0.924089i \(-0.624825\pi\)
−0.382177 + 0.924089i \(0.624825\pi\)
\(614\) 0 0
\(615\) −42.1079 −1.69795
\(616\) 0 0
\(617\) 24.7639 0.996959 0.498479 0.866902i \(-0.333892\pi\)
0.498479 + 0.866902i \(0.333892\pi\)
\(618\) 0 0
\(619\) −37.7193 −1.51607 −0.758034 0.652215i \(-0.773840\pi\)
−0.758034 + 0.652215i \(0.773840\pi\)
\(620\) 0 0
\(621\) −13.3928 −0.537435
\(622\) 0 0
\(623\) 19.1784 0.768366
\(624\) 0 0
\(625\) −26.5464 −1.06186
\(626\) 0 0
\(627\) 10.0200 0.400161
\(628\) 0 0
\(629\) 7.27579 0.290105
\(630\) 0 0
\(631\) −45.2793 −1.80254 −0.901269 0.433259i \(-0.857363\pi\)
−0.901269 + 0.433259i \(0.857363\pi\)
\(632\) 0 0
\(633\) −50.9163 −2.02374
\(634\) 0 0
\(635\) 5.62954 0.223402
\(636\) 0 0
\(637\) 29.0467 1.15087
\(638\) 0 0
\(639\) −40.5865 −1.60558
\(640\) 0 0
\(641\) 14.6587 0.578984 0.289492 0.957180i \(-0.406514\pi\)
0.289492 + 0.957180i \(0.406514\pi\)
\(642\) 0 0
\(643\) 9.97165 0.393243 0.196622 0.980479i \(-0.437003\pi\)
0.196622 + 0.980479i \(0.437003\pi\)
\(644\) 0 0
\(645\) −50.7608 −1.99870
\(646\) 0 0
\(647\) −19.3158 −0.759383 −0.379692 0.925113i \(-0.623970\pi\)
−0.379692 + 0.925113i \(0.623970\pi\)
\(648\) 0 0
\(649\) −10.1428 −0.398140
\(650\) 0 0
\(651\) 92.3010 3.61756
\(652\) 0 0
\(653\) −31.6977 −1.24043 −0.620213 0.784433i \(-0.712954\pi\)
−0.620213 + 0.784433i \(0.712954\pi\)
\(654\) 0 0
\(655\) −17.4023 −0.679963
\(656\) 0 0
\(657\) 31.5699 1.23166
\(658\) 0 0
\(659\) 11.2622 0.438712 0.219356 0.975645i \(-0.429604\pi\)
0.219356 + 0.975645i \(0.429604\pi\)
\(660\) 0 0
\(661\) −18.0861 −0.703467 −0.351733 0.936100i \(-0.614408\pi\)
−0.351733 + 0.936100i \(0.614408\pi\)
\(662\) 0 0
\(663\) −40.9940 −1.59207
\(664\) 0 0
\(665\) 12.1033 0.469347
\(666\) 0 0
\(667\) −1.03836 −0.0402053
\(668\) 0 0
\(669\) −36.8453 −1.42452
\(670\) 0 0
\(671\) −7.05085 −0.272195
\(672\) 0 0
\(673\) 23.3041 0.898306 0.449153 0.893455i \(-0.351726\pi\)
0.449153 + 0.893455i \(0.351726\pi\)
\(674\) 0 0
\(675\) −2.74014 −0.105468
\(676\) 0 0
\(677\) 9.89149 0.380161 0.190080 0.981769i \(-0.439125\pi\)
0.190080 + 0.981769i \(0.439125\pi\)
\(678\) 0 0
\(679\) 12.7832 0.490572
\(680\) 0 0
\(681\) −31.3399 −1.20095
\(682\) 0 0
\(683\) 6.47860 0.247897 0.123948 0.992289i \(-0.460444\pi\)
0.123948 + 0.992289i \(0.460444\pi\)
\(684\) 0 0
\(685\) 14.5025 0.554111
\(686\) 0 0
\(687\) 2.04517 0.0780282
\(688\) 0 0
\(689\) −27.7752 −1.05815
\(690\) 0 0
\(691\) 22.6049 0.859932 0.429966 0.902845i \(-0.358525\pi\)
0.429966 + 0.902845i \(0.358525\pi\)
\(692\) 0 0
\(693\) −41.3886 −1.57222
\(694\) 0 0
\(695\) 15.5726 0.590704
\(696\) 0 0
\(697\) 11.9660 0.453246
\(698\) 0 0
\(699\) 11.3417 0.428983
\(700\) 0 0
\(701\) −5.85443 −0.221119 −0.110559 0.993870i \(-0.535264\pi\)
−0.110559 + 0.993870i \(0.535264\pi\)
\(702\) 0 0
\(703\) −5.88798 −0.222069
\(704\) 0 0
\(705\) −56.2710 −2.11929
\(706\) 0 0
\(707\) 30.5903 1.15047
\(708\) 0 0
\(709\) −39.5665 −1.48595 −0.742975 0.669319i \(-0.766586\pi\)
−0.742975 + 0.669319i \(0.766586\pi\)
\(710\) 0 0
\(711\) 53.6379 2.01158
\(712\) 0 0
\(713\) 15.1364 0.566862
\(714\) 0 0
\(715\) 35.2296 1.31751
\(716\) 0 0
\(717\) 35.3659 1.32077
\(718\) 0 0
\(719\) 25.1305 0.937211 0.468606 0.883407i \(-0.344757\pi\)
0.468606 + 0.883407i \(0.344757\pi\)
\(720\) 0 0
\(721\) 54.8562 2.04295
\(722\) 0 0
\(723\) 76.0762 2.82930
\(724\) 0 0
\(725\) −0.212446 −0.00789004
\(726\) 0 0
\(727\) −11.6844 −0.433351 −0.216675 0.976244i \(-0.569521\pi\)
−0.216675 + 0.976244i \(0.569521\pi\)
\(728\) 0 0
\(729\) −32.1436 −1.19050
\(730\) 0 0
\(731\) 14.4250 0.533528
\(732\) 0 0
\(733\) −8.64586 −0.319342 −0.159671 0.987170i \(-0.551043\pi\)
−0.159671 + 0.987170i \(0.551043\pi\)
\(734\) 0 0
\(735\) −27.9767 −1.03194
\(736\) 0 0
\(737\) −4.08184 −0.150357
\(738\) 0 0
\(739\) −13.1160 −0.482480 −0.241240 0.970466i \(-0.577554\pi\)
−0.241240 + 0.970466i \(0.577554\pi\)
\(740\) 0 0
\(741\) 33.1746 1.21870
\(742\) 0 0
\(743\) −35.5580 −1.30450 −0.652249 0.758005i \(-0.726174\pi\)
−0.652249 + 0.758005i \(0.726174\pi\)
\(744\) 0 0
\(745\) 27.0883 0.992437
\(746\) 0 0
\(747\) −24.7169 −0.904343
\(748\) 0 0
\(749\) −12.9153 −0.471915
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 18.3546 0.668878
\(754\) 0 0
\(755\) 1.64064 0.0597089
\(756\) 0 0
\(757\) 13.7047 0.498105 0.249053 0.968490i \(-0.419881\pi\)
0.249053 + 0.968490i \(0.419881\pi\)
\(758\) 0 0
\(759\) −10.3039 −0.374006
\(760\) 0 0
\(761\) −18.2910 −0.663047 −0.331524 0.943447i \(-0.607563\pi\)
−0.331524 + 0.943447i \(0.607563\pi\)
\(762\) 0 0
\(763\) 25.9368 0.938975
\(764\) 0 0
\(765\) 26.0086 0.940342
\(766\) 0 0
\(767\) −33.5812 −1.21255
\(768\) 0 0
\(769\) 7.69104 0.277346 0.138673 0.990338i \(-0.455716\pi\)
0.138673 + 0.990338i \(0.455716\pi\)
\(770\) 0 0
\(771\) −52.4896 −1.89037
\(772\) 0 0
\(773\) 18.4709 0.664353 0.332177 0.943217i \(-0.392217\pi\)
0.332177 + 0.943217i \(0.392217\pi\)
\(774\) 0 0
\(775\) 3.09688 0.111243
\(776\) 0 0
\(777\) 36.9218 1.32456
\(778\) 0 0
\(779\) −9.68360 −0.346951
\(780\) 0 0
\(781\) −15.0473 −0.538436
\(782\) 0 0
\(783\) 5.30612 0.189625
\(784\) 0 0
\(785\) 41.5862 1.48428
\(786\) 0 0
\(787\) 12.2391 0.436276 0.218138 0.975918i \(-0.430002\pi\)
0.218138 + 0.975918i \(0.430002\pi\)
\(788\) 0 0
\(789\) 41.8197 1.48882
\(790\) 0 0
\(791\) −48.0631 −1.70893
\(792\) 0 0
\(793\) −23.3442 −0.828978
\(794\) 0 0
\(795\) 26.7520 0.948795
\(796\) 0 0
\(797\) 41.6753 1.47621 0.738107 0.674683i \(-0.235720\pi\)
0.738107 + 0.674683i \(0.235720\pi\)
\(798\) 0 0
\(799\) 15.9909 0.565716
\(800\) 0 0
\(801\) −33.3511 −1.17840
\(802\) 0 0
\(803\) 11.7045 0.413041
\(804\) 0 0
\(805\) −12.4462 −0.438670
\(806\) 0 0
\(807\) −40.2120 −1.41553
\(808\) 0 0
\(809\) −38.9670 −1.37001 −0.685004 0.728539i \(-0.740200\pi\)
−0.685004 + 0.728539i \(0.740200\pi\)
\(810\) 0 0
\(811\) 12.1814 0.427748 0.213874 0.976861i \(-0.431392\pi\)
0.213874 + 0.976861i \(0.431392\pi\)
\(812\) 0 0
\(813\) 41.4089 1.45227
\(814\) 0 0
\(815\) 15.0980 0.528858
\(816\) 0 0
\(817\) −11.6735 −0.408405
\(818\) 0 0
\(819\) −137.031 −4.78825
\(820\) 0 0
\(821\) −1.29476 −0.0451876 −0.0225938 0.999745i \(-0.507192\pi\)
−0.0225938 + 0.999745i \(0.507192\pi\)
\(822\) 0 0
\(823\) −7.93827 −0.276711 −0.138355 0.990383i \(-0.544182\pi\)
−0.138355 + 0.990383i \(0.544182\pi\)
\(824\) 0 0
\(825\) −2.10815 −0.0733964
\(826\) 0 0
\(827\) 11.5139 0.400376 0.200188 0.979758i \(-0.435845\pi\)
0.200188 + 0.979758i \(0.435845\pi\)
\(828\) 0 0
\(829\) −32.2404 −1.11975 −0.559877 0.828576i \(-0.689152\pi\)
−0.559877 + 0.828576i \(0.689152\pi\)
\(830\) 0 0
\(831\) −29.3876 −1.01944
\(832\) 0 0
\(833\) 7.95030 0.275462
\(834\) 0 0
\(835\) −8.68376 −0.300514
\(836\) 0 0
\(837\) −77.3488 −2.67356
\(838\) 0 0
\(839\) −42.5398 −1.46864 −0.734318 0.678805i \(-0.762498\pi\)
−0.734318 + 0.678805i \(0.762498\pi\)
\(840\) 0 0
\(841\) −28.5886 −0.985814
\(842\) 0 0
\(843\) 19.7752 0.681092
\(844\) 0 0
\(845\) 86.6231 2.97993
\(846\) 0 0
\(847\) 21.2818 0.731251
\(848\) 0 0
\(849\) 23.7413 0.814800
\(850\) 0 0
\(851\) 6.05478 0.207555
\(852\) 0 0
\(853\) 41.2526 1.41246 0.706231 0.707981i \(-0.250394\pi\)
0.706231 + 0.707981i \(0.250394\pi\)
\(854\) 0 0
\(855\) −21.0476 −0.719813
\(856\) 0 0
\(857\) 12.3667 0.422437 0.211219 0.977439i \(-0.432257\pi\)
0.211219 + 0.977439i \(0.432257\pi\)
\(858\) 0 0
\(859\) 0.456325 0.0155696 0.00778480 0.999970i \(-0.497522\pi\)
0.00778480 + 0.999970i \(0.497522\pi\)
\(860\) 0 0
\(861\) 60.7229 2.06943
\(862\) 0 0
\(863\) −0.736221 −0.0250613 −0.0125306 0.999921i \(-0.503989\pi\)
−0.0125306 + 0.999921i \(0.503989\pi\)
\(864\) 0 0
\(865\) −22.4336 −0.762766
\(866\) 0 0
\(867\) 39.1820 1.33069
\(868\) 0 0
\(869\) 19.8861 0.674589
\(870\) 0 0
\(871\) −13.5143 −0.457915
\(872\) 0 0
\(873\) −22.2298 −0.752365
\(874\) 0 0
\(875\) 35.8938 1.21343
\(876\) 0 0
\(877\) 4.86767 0.164369 0.0821847 0.996617i \(-0.473810\pi\)
0.0821847 + 0.996617i \(0.473810\pi\)
\(878\) 0 0
\(879\) −2.14860 −0.0724706
\(880\) 0 0
\(881\) −5.61743 −0.189256 −0.0946279 0.995513i \(-0.530166\pi\)
−0.0946279 + 0.995513i \(0.530166\pi\)
\(882\) 0 0
\(883\) 25.3147 0.851906 0.425953 0.904745i \(-0.359939\pi\)
0.425953 + 0.904745i \(0.359939\pi\)
\(884\) 0 0
\(885\) 32.3441 1.08724
\(886\) 0 0
\(887\) −48.8485 −1.64017 −0.820086 0.572240i \(-0.806075\pi\)
−0.820086 + 0.572240i \(0.806075\pi\)
\(888\) 0 0
\(889\) −8.11825 −0.272277
\(890\) 0 0
\(891\) 15.3633 0.514691
\(892\) 0 0
\(893\) −12.9407 −0.433044
\(894\) 0 0
\(895\) 40.7407 1.36181
\(896\) 0 0
\(897\) −34.1144 −1.13905
\(898\) 0 0
\(899\) −5.99692 −0.200008
\(900\) 0 0
\(901\) −7.60227 −0.253268
\(902\) 0 0
\(903\) 73.2011 2.43598
\(904\) 0 0
\(905\) −42.2079 −1.40304
\(906\) 0 0
\(907\) −32.2393 −1.07049 −0.535244 0.844697i \(-0.679781\pi\)
−0.535244 + 0.844697i \(0.679781\pi\)
\(908\) 0 0
\(909\) −53.1963 −1.76441
\(910\) 0 0
\(911\) −11.6411 −0.385685 −0.192843 0.981230i \(-0.561771\pi\)
−0.192843 + 0.981230i \(0.561771\pi\)
\(912\) 0 0
\(913\) −9.16370 −0.303274
\(914\) 0 0
\(915\) 22.4843 0.743307
\(916\) 0 0
\(917\) 25.0955 0.828726
\(918\) 0 0
\(919\) −13.7608 −0.453928 −0.226964 0.973903i \(-0.572880\pi\)
−0.226964 + 0.973903i \(0.572880\pi\)
\(920\) 0 0
\(921\) −41.5745 −1.36993
\(922\) 0 0
\(923\) −49.8193 −1.63982
\(924\) 0 0
\(925\) 1.23880 0.0407314
\(926\) 0 0
\(927\) −95.3945 −3.13317
\(928\) 0 0
\(929\) −1.60249 −0.0525759 −0.0262880 0.999654i \(-0.508369\pi\)
−0.0262880 + 0.999654i \(0.508369\pi\)
\(930\) 0 0
\(931\) −6.43383 −0.210860
\(932\) 0 0
\(933\) 69.4209 2.27274
\(934\) 0 0
\(935\) 9.64260 0.315347
\(936\) 0 0
\(937\) 48.8298 1.59520 0.797599 0.603188i \(-0.206103\pi\)
0.797599 + 0.603188i \(0.206103\pi\)
\(938\) 0 0
\(939\) 96.2647 3.14148
\(940\) 0 0
\(941\) −46.4533 −1.51433 −0.757167 0.653221i \(-0.773417\pi\)
−0.757167 + 0.653221i \(0.773417\pi\)
\(942\) 0 0
\(943\) 9.95791 0.324274
\(944\) 0 0
\(945\) 63.6015 2.06896
\(946\) 0 0
\(947\) −44.3975 −1.44273 −0.721363 0.692557i \(-0.756484\pi\)
−0.721363 + 0.692557i \(0.756484\pi\)
\(948\) 0 0
\(949\) 38.7515 1.25793
\(950\) 0 0
\(951\) −76.1226 −2.46845
\(952\) 0 0
\(953\) 30.7460 0.995960 0.497980 0.867188i \(-0.334075\pi\)
0.497980 + 0.867188i \(0.334075\pi\)
\(954\) 0 0
\(955\) 37.8942 1.22623
\(956\) 0 0
\(957\) 4.08231 0.131962
\(958\) 0 0
\(959\) −20.9137 −0.675339
\(960\) 0 0
\(961\) 56.4186 1.81996
\(962\) 0 0
\(963\) 22.4596 0.723752
\(964\) 0 0
\(965\) −51.1935 −1.64798
\(966\) 0 0
\(967\) 9.03412 0.290518 0.145259 0.989394i \(-0.453599\pi\)
0.145259 + 0.989394i \(0.453599\pi\)
\(968\) 0 0
\(969\) 9.08014 0.291696
\(970\) 0 0
\(971\) 42.3739 1.35984 0.679922 0.733284i \(-0.262014\pi\)
0.679922 + 0.733284i \(0.262014\pi\)
\(972\) 0 0
\(973\) −22.4570 −0.719938
\(974\) 0 0
\(975\) −6.97975 −0.223531
\(976\) 0 0
\(977\) −20.2542 −0.647988 −0.323994 0.946059i \(-0.605026\pi\)
−0.323994 + 0.946059i \(0.605026\pi\)
\(978\) 0 0
\(979\) −12.3648 −0.395181
\(980\) 0 0
\(981\) −45.1039 −1.44006
\(982\) 0 0
\(983\) 8.87659 0.283119 0.141560 0.989930i \(-0.454788\pi\)
0.141560 + 0.989930i \(0.454788\pi\)
\(984\) 0 0
\(985\) −39.6630 −1.26377
\(986\) 0 0
\(987\) 81.1472 2.58294
\(988\) 0 0
\(989\) 12.0042 0.381711
\(990\) 0 0
\(991\) −47.2553 −1.50111 −0.750557 0.660806i \(-0.770215\pi\)
−0.750557 + 0.660806i \(0.770215\pi\)
\(992\) 0 0
\(993\) 38.2722 1.21453
\(994\) 0 0
\(995\) −4.14324 −0.131349
\(996\) 0 0
\(997\) 8.82304 0.279429 0.139714 0.990192i \(-0.455382\pi\)
0.139714 + 0.990192i \(0.455382\pi\)
\(998\) 0 0
\(999\) −30.9406 −0.978919
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 \(a_p\))