Properties

Label 8008.2.a.y.1.6
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.36889\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.36889 q^{3} -3.92349 q^{5} +1.00000 q^{7} -1.12615 q^{9} +O(q^{10})\) \(q-1.36889 q^{3} -3.92349 q^{5} +1.00000 q^{7} -1.12615 q^{9} -1.00000 q^{11} -1.00000 q^{13} +5.37081 q^{15} -2.95970 q^{17} -3.52044 q^{19} -1.36889 q^{21} +4.25065 q^{23} +10.3938 q^{25} +5.64823 q^{27} -9.21747 q^{29} +1.84881 q^{31} +1.36889 q^{33} -3.92349 q^{35} +0.471628 q^{37} +1.36889 q^{39} +6.70492 q^{41} +12.6251 q^{43} +4.41844 q^{45} +5.58340 q^{47} +1.00000 q^{49} +4.05149 q^{51} +12.0869 q^{53} +3.92349 q^{55} +4.81908 q^{57} -7.88278 q^{59} -11.8317 q^{61} -1.12615 q^{63} +3.92349 q^{65} -0.782757 q^{67} -5.81866 q^{69} -0.831881 q^{71} -7.35993 q^{73} -14.2279 q^{75} -1.00000 q^{77} +3.31354 q^{79} -4.35334 q^{81} +12.9354 q^{83} +11.6123 q^{85} +12.6177 q^{87} -9.73498 q^{89} -1.00000 q^{91} -2.53081 q^{93} +13.8124 q^{95} -0.699621 q^{97} +1.12615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.36889 −0.790327 −0.395163 0.918611i \(-0.629312\pi\)
−0.395163 + 0.918611i \(0.629312\pi\)
\(4\) 0 0
\(5\) −3.92349 −1.75464 −0.877318 0.479909i \(-0.840670\pi\)
−0.877318 + 0.479909i \(0.840670\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −1.12615 −0.375383
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 5.37081 1.38674
\(16\) 0 0
\(17\) −2.95970 −0.717832 −0.358916 0.933370i \(-0.616854\pi\)
−0.358916 + 0.933370i \(0.616854\pi\)
\(18\) 0 0
\(19\) −3.52044 −0.807644 −0.403822 0.914838i \(-0.632319\pi\)
−0.403822 + 0.914838i \(0.632319\pi\)
\(20\) 0 0
\(21\) −1.36889 −0.298715
\(22\) 0 0
\(23\) 4.25065 0.886322 0.443161 0.896442i \(-0.353857\pi\)
0.443161 + 0.896442i \(0.353857\pi\)
\(24\) 0 0
\(25\) 10.3938 2.07875
\(26\) 0 0
\(27\) 5.64823 1.08700
\(28\) 0 0
\(29\) −9.21747 −1.71164 −0.855821 0.517273i \(-0.826947\pi\)
−0.855821 + 0.517273i \(0.826947\pi\)
\(30\) 0 0
\(31\) 1.84881 0.332056 0.166028 0.986121i \(-0.446906\pi\)
0.166028 + 0.986121i \(0.446906\pi\)
\(32\) 0 0
\(33\) 1.36889 0.238293
\(34\) 0 0
\(35\) −3.92349 −0.663190
\(36\) 0 0
\(37\) 0.471628 0.0775352 0.0387676 0.999248i \(-0.487657\pi\)
0.0387676 + 0.999248i \(0.487657\pi\)
\(38\) 0 0
\(39\) 1.36889 0.219197
\(40\) 0 0
\(41\) 6.70492 1.04713 0.523567 0.851985i \(-0.324601\pi\)
0.523567 + 0.851985i \(0.324601\pi\)
\(42\) 0 0
\(43\) 12.6251 1.92531 0.962657 0.270725i \(-0.0872635\pi\)
0.962657 + 0.270725i \(0.0872635\pi\)
\(44\) 0 0
\(45\) 4.41844 0.658662
\(46\) 0 0
\(47\) 5.58340 0.814422 0.407211 0.913334i \(-0.366501\pi\)
0.407211 + 0.913334i \(0.366501\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 4.05149 0.567322
\(52\) 0 0
\(53\) 12.0869 1.66027 0.830134 0.557565i \(-0.188264\pi\)
0.830134 + 0.557565i \(0.188264\pi\)
\(54\) 0 0
\(55\) 3.92349 0.529043
\(56\) 0 0
\(57\) 4.81908 0.638303
\(58\) 0 0
\(59\) −7.88278 −1.02625 −0.513125 0.858314i \(-0.671512\pi\)
−0.513125 + 0.858314i \(0.671512\pi\)
\(60\) 0 0
\(61\) −11.8317 −1.51490 −0.757450 0.652893i \(-0.773555\pi\)
−0.757450 + 0.652893i \(0.773555\pi\)
\(62\) 0 0
\(63\) −1.12615 −0.141882
\(64\) 0 0
\(65\) 3.92349 0.486649
\(66\) 0 0
\(67\) −0.782757 −0.0956290 −0.0478145 0.998856i \(-0.515226\pi\)
−0.0478145 + 0.998856i \(0.515226\pi\)
\(68\) 0 0
\(69\) −5.81866 −0.700484
\(70\) 0 0
\(71\) −0.831881 −0.0987261 −0.0493630 0.998781i \(-0.515719\pi\)
−0.0493630 + 0.998781i \(0.515719\pi\)
\(72\) 0 0
\(73\) −7.35993 −0.861415 −0.430707 0.902492i \(-0.641736\pi\)
−0.430707 + 0.902492i \(0.641736\pi\)
\(74\) 0 0
\(75\) −14.2279 −1.64289
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 3.31354 0.372803 0.186401 0.982474i \(-0.440318\pi\)
0.186401 + 0.982474i \(0.440318\pi\)
\(80\) 0 0
\(81\) −4.35334 −0.483704
\(82\) 0 0
\(83\) 12.9354 1.41984 0.709920 0.704283i \(-0.248731\pi\)
0.709920 + 0.704283i \(0.248731\pi\)
\(84\) 0 0
\(85\) 11.6123 1.25954
\(86\) 0 0
\(87\) 12.6177 1.35276
\(88\) 0 0
\(89\) −9.73498 −1.03191 −0.515953 0.856617i \(-0.672562\pi\)
−0.515953 + 0.856617i \(0.672562\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −2.53081 −0.262433
\(94\) 0 0
\(95\) 13.8124 1.41712
\(96\) 0 0
\(97\) −0.699621 −0.0710357 −0.0355179 0.999369i \(-0.511308\pi\)
−0.0355179 + 0.999369i \(0.511308\pi\)
\(98\) 0 0
\(99\) 1.12615 0.113182
\(100\) 0 0
\(101\) −9.86753 −0.981856 −0.490928 0.871200i \(-0.663342\pi\)
−0.490928 + 0.871200i \(0.663342\pi\)
\(102\) 0 0
\(103\) 5.51293 0.543205 0.271603 0.962409i \(-0.412446\pi\)
0.271603 + 0.962409i \(0.412446\pi\)
\(104\) 0 0
\(105\) 5.37081 0.524137
\(106\) 0 0
\(107\) 1.72204 0.166476 0.0832382 0.996530i \(-0.473474\pi\)
0.0832382 + 0.996530i \(0.473474\pi\)
\(108\) 0 0
\(109\) 7.44416 0.713021 0.356511 0.934291i \(-0.383966\pi\)
0.356511 + 0.934291i \(0.383966\pi\)
\(110\) 0 0
\(111\) −0.645605 −0.0612782
\(112\) 0 0
\(113\) 6.99925 0.658434 0.329217 0.944254i \(-0.393215\pi\)
0.329217 + 0.944254i \(0.393215\pi\)
\(114\) 0 0
\(115\) −16.6774 −1.55517
\(116\) 0 0
\(117\) 1.12615 0.104113
\(118\) 0 0
\(119\) −2.95970 −0.271315
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −9.17828 −0.827578
\(124\) 0 0
\(125\) −21.1623 −1.89282
\(126\) 0 0
\(127\) −1.81379 −0.160947 −0.0804737 0.996757i \(-0.525643\pi\)
−0.0804737 + 0.996757i \(0.525643\pi\)
\(128\) 0 0
\(129\) −17.2824 −1.52163
\(130\) 0 0
\(131\) −4.48032 −0.391447 −0.195723 0.980659i \(-0.562706\pi\)
−0.195723 + 0.980659i \(0.562706\pi\)
\(132\) 0 0
\(133\) −3.52044 −0.305261
\(134\) 0 0
\(135\) −22.1608 −1.90729
\(136\) 0 0
\(137\) −7.35564 −0.628435 −0.314217 0.949351i \(-0.601742\pi\)
−0.314217 + 0.949351i \(0.601742\pi\)
\(138\) 0 0
\(139\) 4.79409 0.406629 0.203315 0.979113i \(-0.434829\pi\)
0.203315 + 0.979113i \(0.434829\pi\)
\(140\) 0 0
\(141\) −7.64304 −0.643660
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 36.1646 3.00331
\(146\) 0 0
\(147\) −1.36889 −0.112904
\(148\) 0 0
\(149\) 4.53609 0.371611 0.185805 0.982587i \(-0.440511\pi\)
0.185805 + 0.982587i \(0.440511\pi\)
\(150\) 0 0
\(151\) 11.5746 0.941924 0.470962 0.882153i \(-0.343907\pi\)
0.470962 + 0.882153i \(0.343907\pi\)
\(152\) 0 0
\(153\) 3.33307 0.269462
\(154\) 0 0
\(155\) −7.25379 −0.582638
\(156\) 0 0
\(157\) 23.1828 1.85019 0.925096 0.379734i \(-0.123984\pi\)
0.925096 + 0.379734i \(0.123984\pi\)
\(158\) 0 0
\(159\) −16.5456 −1.31215
\(160\) 0 0
\(161\) 4.25065 0.334998
\(162\) 0 0
\(163\) −9.86881 −0.772985 −0.386492 0.922293i \(-0.626313\pi\)
−0.386492 + 0.922293i \(0.626313\pi\)
\(164\) 0 0
\(165\) −5.37081 −0.418117
\(166\) 0 0
\(167\) 15.7798 1.22108 0.610541 0.791985i \(-0.290952\pi\)
0.610541 + 0.791985i \(0.290952\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.96454 0.303176
\(172\) 0 0
\(173\) 15.1450 1.15146 0.575728 0.817641i \(-0.304719\pi\)
0.575728 + 0.817641i \(0.304719\pi\)
\(174\) 0 0
\(175\) 10.3938 0.785694
\(176\) 0 0
\(177\) 10.7906 0.811073
\(178\) 0 0
\(179\) −19.7436 −1.47571 −0.737853 0.674961i \(-0.764160\pi\)
−0.737853 + 0.674961i \(0.764160\pi\)
\(180\) 0 0
\(181\) 5.07812 0.377454 0.188727 0.982030i \(-0.439564\pi\)
0.188727 + 0.982030i \(0.439564\pi\)
\(182\) 0 0
\(183\) 16.1963 1.19727
\(184\) 0 0
\(185\) −1.85043 −0.136046
\(186\) 0 0
\(187\) 2.95970 0.216435
\(188\) 0 0
\(189\) 5.64823 0.410848
\(190\) 0 0
\(191\) 14.5000 1.04918 0.524590 0.851355i \(-0.324219\pi\)
0.524590 + 0.851355i \(0.324219\pi\)
\(192\) 0 0
\(193\) 21.6987 1.56191 0.780954 0.624589i \(-0.214733\pi\)
0.780954 + 0.624589i \(0.214733\pi\)
\(194\) 0 0
\(195\) −5.37081 −0.384612
\(196\) 0 0
\(197\) −24.4856 −1.74453 −0.872265 0.489033i \(-0.837350\pi\)
−0.872265 + 0.489033i \(0.837350\pi\)
\(198\) 0 0
\(199\) 6.62802 0.469848 0.234924 0.972014i \(-0.424516\pi\)
0.234924 + 0.972014i \(0.424516\pi\)
\(200\) 0 0
\(201\) 1.07151 0.0755782
\(202\) 0 0
\(203\) −9.21747 −0.646940
\(204\) 0 0
\(205\) −26.3067 −1.83734
\(206\) 0 0
\(207\) −4.78687 −0.332711
\(208\) 0 0
\(209\) 3.52044 0.243514
\(210\) 0 0
\(211\) −1.48137 −0.101981 −0.0509907 0.998699i \(-0.516238\pi\)
−0.0509907 + 0.998699i \(0.516238\pi\)
\(212\) 0 0
\(213\) 1.13875 0.0780259
\(214\) 0 0
\(215\) −49.5345 −3.37823
\(216\) 0 0
\(217\) 1.84881 0.125506
\(218\) 0 0
\(219\) 10.0749 0.680799
\(220\) 0 0
\(221\) 2.95970 0.199091
\(222\) 0 0
\(223\) 9.88882 0.662204 0.331102 0.943595i \(-0.392580\pi\)
0.331102 + 0.943595i \(0.392580\pi\)
\(224\) 0 0
\(225\) −11.7049 −0.780329
\(226\) 0 0
\(227\) −3.28655 −0.218136 −0.109068 0.994034i \(-0.534787\pi\)
−0.109068 + 0.994034i \(0.534787\pi\)
\(228\) 0 0
\(229\) −24.3860 −1.61147 −0.805737 0.592274i \(-0.798230\pi\)
−0.805737 + 0.592274i \(0.798230\pi\)
\(230\) 0 0
\(231\) 1.36889 0.0900661
\(232\) 0 0
\(233\) −19.5317 −1.27956 −0.639782 0.768556i \(-0.720975\pi\)
−0.639782 + 0.768556i \(0.720975\pi\)
\(234\) 0 0
\(235\) −21.9064 −1.42902
\(236\) 0 0
\(237\) −4.53586 −0.294636
\(238\) 0 0
\(239\) 5.47876 0.354392 0.177196 0.984176i \(-0.443297\pi\)
0.177196 + 0.984176i \(0.443297\pi\)
\(240\) 0 0
\(241\) 14.7097 0.947536 0.473768 0.880650i \(-0.342893\pi\)
0.473768 + 0.880650i \(0.342893\pi\)
\(242\) 0 0
\(243\) −10.9855 −0.704718
\(244\) 0 0
\(245\) −3.92349 −0.250662
\(246\) 0 0
\(247\) 3.52044 0.224000
\(248\) 0 0
\(249\) −17.7070 −1.12214
\(250\) 0 0
\(251\) −31.0379 −1.95910 −0.979548 0.201209i \(-0.935513\pi\)
−0.979548 + 0.201209i \(0.935513\pi\)
\(252\) 0 0
\(253\) −4.25065 −0.267236
\(254\) 0 0
\(255\) −15.8960 −0.995445
\(256\) 0 0
\(257\) −2.89779 −0.180759 −0.0903797 0.995907i \(-0.528808\pi\)
−0.0903797 + 0.995907i \(0.528808\pi\)
\(258\) 0 0
\(259\) 0.471628 0.0293056
\(260\) 0 0
\(261\) 10.3803 0.642522
\(262\) 0 0
\(263\) −13.9612 −0.860887 −0.430444 0.902617i \(-0.641643\pi\)
−0.430444 + 0.902617i \(0.641643\pi\)
\(264\) 0 0
\(265\) −47.4229 −2.91317
\(266\) 0 0
\(267\) 13.3261 0.815543
\(268\) 0 0
\(269\) −6.34620 −0.386935 −0.193467 0.981107i \(-0.561973\pi\)
−0.193467 + 0.981107i \(0.561973\pi\)
\(270\) 0 0
\(271\) −23.6989 −1.43961 −0.719803 0.694178i \(-0.755768\pi\)
−0.719803 + 0.694178i \(0.755768\pi\)
\(272\) 0 0
\(273\) 1.36889 0.0828488
\(274\) 0 0
\(275\) −10.3938 −0.626767
\(276\) 0 0
\(277\) 26.7582 1.60775 0.803873 0.594802i \(-0.202769\pi\)
0.803873 + 0.594802i \(0.202769\pi\)
\(278\) 0 0
\(279\) −2.08204 −0.124648
\(280\) 0 0
\(281\) 12.4095 0.740290 0.370145 0.928974i \(-0.379308\pi\)
0.370145 + 0.928974i \(0.379308\pi\)
\(282\) 0 0
\(283\) 7.10729 0.422484 0.211242 0.977434i \(-0.432249\pi\)
0.211242 + 0.977434i \(0.432249\pi\)
\(284\) 0 0
\(285\) −18.9076 −1.11999
\(286\) 0 0
\(287\) 6.70492 0.395779
\(288\) 0 0
\(289\) −8.24018 −0.484717
\(290\) 0 0
\(291\) 0.957701 0.0561414
\(292\) 0 0
\(293\) −22.9499 −1.34075 −0.670374 0.742023i \(-0.733866\pi\)
−0.670374 + 0.742023i \(0.733866\pi\)
\(294\) 0 0
\(295\) 30.9280 1.80070
\(296\) 0 0
\(297\) −5.64823 −0.327744
\(298\) 0 0
\(299\) −4.25065 −0.245822
\(300\) 0 0
\(301\) 12.6251 0.727700
\(302\) 0 0
\(303\) 13.5075 0.775987
\(304\) 0 0
\(305\) 46.4217 2.65810
\(306\) 0 0
\(307\) −17.6540 −1.00757 −0.503785 0.863829i \(-0.668059\pi\)
−0.503785 + 0.863829i \(0.668059\pi\)
\(308\) 0 0
\(309\) −7.54658 −0.429310
\(310\) 0 0
\(311\) −26.3068 −1.49172 −0.745861 0.666102i \(-0.767962\pi\)
−0.745861 + 0.666102i \(0.767962\pi\)
\(312\) 0 0
\(313\) 33.5958 1.89895 0.949475 0.313844i \(-0.101617\pi\)
0.949475 + 0.313844i \(0.101617\pi\)
\(314\) 0 0
\(315\) 4.41844 0.248951
\(316\) 0 0
\(317\) −13.9822 −0.785317 −0.392659 0.919684i \(-0.628445\pi\)
−0.392659 + 0.919684i \(0.628445\pi\)
\(318\) 0 0
\(319\) 9.21747 0.516079
\(320\) 0 0
\(321\) −2.35728 −0.131571
\(322\) 0 0
\(323\) 10.4194 0.579753
\(324\) 0 0
\(325\) −10.3938 −0.576542
\(326\) 0 0
\(327\) −10.1902 −0.563520
\(328\) 0 0
\(329\) 5.58340 0.307823
\(330\) 0 0
\(331\) −6.93059 −0.380940 −0.190470 0.981693i \(-0.561001\pi\)
−0.190470 + 0.981693i \(0.561001\pi\)
\(332\) 0 0
\(333\) −0.531124 −0.0291054
\(334\) 0 0
\(335\) 3.07114 0.167794
\(336\) 0 0
\(337\) 26.6642 1.45249 0.726245 0.687436i \(-0.241264\pi\)
0.726245 + 0.687436i \(0.241264\pi\)
\(338\) 0 0
\(339\) −9.58118 −0.520378
\(340\) 0 0
\(341\) −1.84881 −0.100119
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 22.8294 1.22910
\(346\) 0 0
\(347\) −9.51291 −0.510680 −0.255340 0.966851i \(-0.582187\pi\)
−0.255340 + 0.966851i \(0.582187\pi\)
\(348\) 0 0
\(349\) 23.7941 1.27367 0.636835 0.771000i \(-0.280243\pi\)
0.636835 + 0.771000i \(0.280243\pi\)
\(350\) 0 0
\(351\) −5.64823 −0.301480
\(352\) 0 0
\(353\) −11.2681 −0.599740 −0.299870 0.953980i \(-0.596943\pi\)
−0.299870 + 0.953980i \(0.596943\pi\)
\(354\) 0 0
\(355\) 3.26387 0.173228
\(356\) 0 0
\(357\) 4.05149 0.214428
\(358\) 0 0
\(359\) −34.9300 −1.84353 −0.921767 0.387745i \(-0.873254\pi\)
−0.921767 + 0.387745i \(0.873254\pi\)
\(360\) 0 0
\(361\) −6.60650 −0.347711
\(362\) 0 0
\(363\) −1.36889 −0.0718479
\(364\) 0 0
\(365\) 28.8766 1.51147
\(366\) 0 0
\(367\) −27.2940 −1.42473 −0.712367 0.701807i \(-0.752377\pi\)
−0.712367 + 0.701807i \(0.752377\pi\)
\(368\) 0 0
\(369\) −7.55075 −0.393076
\(370\) 0 0
\(371\) 12.0869 0.627522
\(372\) 0 0
\(373\) −35.9483 −1.86133 −0.930665 0.365872i \(-0.880771\pi\)
−0.930665 + 0.365872i \(0.880771\pi\)
\(374\) 0 0
\(375\) 28.9688 1.49594
\(376\) 0 0
\(377\) 9.21747 0.474724
\(378\) 0 0
\(379\) 8.57316 0.440374 0.220187 0.975458i \(-0.429333\pi\)
0.220187 + 0.975458i \(0.429333\pi\)
\(380\) 0 0
\(381\) 2.48287 0.127201
\(382\) 0 0
\(383\) −11.7435 −0.600065 −0.300033 0.953929i \(-0.596998\pi\)
−0.300033 + 0.953929i \(0.596998\pi\)
\(384\) 0 0
\(385\) 3.92349 0.199959
\(386\) 0 0
\(387\) −14.2178 −0.722731
\(388\) 0 0
\(389\) −18.6387 −0.945021 −0.472510 0.881325i \(-0.656652\pi\)
−0.472510 + 0.881325i \(0.656652\pi\)
\(390\) 0 0
\(391\) −12.5806 −0.636231
\(392\) 0 0
\(393\) 6.13304 0.309371
\(394\) 0 0
\(395\) −13.0006 −0.654133
\(396\) 0 0
\(397\) −14.8418 −0.744890 −0.372445 0.928054i \(-0.621480\pi\)
−0.372445 + 0.928054i \(0.621480\pi\)
\(398\) 0 0
\(399\) 4.81908 0.241256
\(400\) 0 0
\(401\) −6.72889 −0.336024 −0.168012 0.985785i \(-0.553735\pi\)
−0.168012 + 0.985785i \(0.553735\pi\)
\(402\) 0 0
\(403\) −1.84881 −0.0920959
\(404\) 0 0
\(405\) 17.0803 0.848725
\(406\) 0 0
\(407\) −0.471628 −0.0233777
\(408\) 0 0
\(409\) −8.27349 −0.409098 −0.204549 0.978856i \(-0.565573\pi\)
−0.204549 + 0.978856i \(0.565573\pi\)
\(410\) 0 0
\(411\) 10.0690 0.496669
\(412\) 0 0
\(413\) −7.88278 −0.387886
\(414\) 0 0
\(415\) −50.7517 −2.49130
\(416\) 0 0
\(417\) −6.56256 −0.321370
\(418\) 0 0
\(419\) 1.11189 0.0543191 0.0271596 0.999631i \(-0.491354\pi\)
0.0271596 + 0.999631i \(0.491354\pi\)
\(420\) 0 0
\(421\) 15.0839 0.735146 0.367573 0.929995i \(-0.380189\pi\)
0.367573 + 0.929995i \(0.380189\pi\)
\(422\) 0 0
\(423\) −6.28774 −0.305721
\(424\) 0 0
\(425\) −30.7624 −1.49219
\(426\) 0 0
\(427\) −11.8317 −0.572578
\(428\) 0 0
\(429\) −1.36889 −0.0660905
\(430\) 0 0
\(431\) 38.2980 1.84475 0.922374 0.386298i \(-0.126246\pi\)
0.922374 + 0.386298i \(0.126246\pi\)
\(432\) 0 0
\(433\) 28.5031 1.36977 0.684885 0.728651i \(-0.259853\pi\)
0.684885 + 0.728651i \(0.259853\pi\)
\(434\) 0 0
\(435\) −49.5053 −2.37360
\(436\) 0 0
\(437\) −14.9642 −0.715833
\(438\) 0 0
\(439\) −32.1423 −1.53407 −0.767034 0.641607i \(-0.778268\pi\)
−0.767034 + 0.641607i \(0.778268\pi\)
\(440\) 0 0
\(441\) −1.12615 −0.0536262
\(442\) 0 0
\(443\) 29.7332 1.41267 0.706333 0.707880i \(-0.250348\pi\)
0.706333 + 0.707880i \(0.250348\pi\)
\(444\) 0 0
\(445\) 38.1951 1.81062
\(446\) 0 0
\(447\) −6.20939 −0.293694
\(448\) 0 0
\(449\) 8.20721 0.387322 0.193661 0.981068i \(-0.437964\pi\)
0.193661 + 0.981068i \(0.437964\pi\)
\(450\) 0 0
\(451\) −6.70492 −0.315723
\(452\) 0 0
\(453\) −15.8443 −0.744428
\(454\) 0 0
\(455\) 3.92349 0.183936
\(456\) 0 0
\(457\) −21.9390 −1.02626 −0.513132 0.858310i \(-0.671515\pi\)
−0.513132 + 0.858310i \(0.671515\pi\)
\(458\) 0 0
\(459\) −16.7171 −0.780286
\(460\) 0 0
\(461\) −33.0049 −1.53719 −0.768597 0.639734i \(-0.779045\pi\)
−0.768597 + 0.639734i \(0.779045\pi\)
\(462\) 0 0
\(463\) −28.0210 −1.30225 −0.651123 0.758973i \(-0.725702\pi\)
−0.651123 + 0.758973i \(0.725702\pi\)
\(464\) 0 0
\(465\) 9.92961 0.460475
\(466\) 0 0
\(467\) 1.92140 0.0889116 0.0444558 0.999011i \(-0.485845\pi\)
0.0444558 + 0.999011i \(0.485845\pi\)
\(468\) 0 0
\(469\) −0.782757 −0.0361444
\(470\) 0 0
\(471\) −31.7347 −1.46226
\(472\) 0 0
\(473\) −12.6251 −0.580504
\(474\) 0 0
\(475\) −36.5906 −1.67889
\(476\) 0 0
\(477\) −13.6117 −0.623237
\(478\) 0 0
\(479\) 14.8084 0.676613 0.338307 0.941036i \(-0.390146\pi\)
0.338307 + 0.941036i \(0.390146\pi\)
\(480\) 0 0
\(481\) −0.471628 −0.0215044
\(482\) 0 0
\(483\) −5.81866 −0.264758
\(484\) 0 0
\(485\) 2.74495 0.124642
\(486\) 0 0
\(487\) 10.2831 0.465972 0.232986 0.972480i \(-0.425150\pi\)
0.232986 + 0.972480i \(0.425150\pi\)
\(488\) 0 0
\(489\) 13.5093 0.610911
\(490\) 0 0
\(491\) 20.0218 0.903573 0.451787 0.892126i \(-0.350787\pi\)
0.451787 + 0.892126i \(0.350787\pi\)
\(492\) 0 0
\(493\) 27.2809 1.22867
\(494\) 0 0
\(495\) −4.41844 −0.198594
\(496\) 0 0
\(497\) −0.831881 −0.0373149
\(498\) 0 0
\(499\) −32.3216 −1.44691 −0.723456 0.690370i \(-0.757448\pi\)
−0.723456 + 0.690370i \(0.757448\pi\)
\(500\) 0 0
\(501\) −21.6008 −0.965053
\(502\) 0 0
\(503\) −12.8365 −0.572350 −0.286175 0.958177i \(-0.592384\pi\)
−0.286175 + 0.958177i \(0.592384\pi\)
\(504\) 0 0
\(505\) 38.7151 1.72280
\(506\) 0 0
\(507\) −1.36889 −0.0607944
\(508\) 0 0
\(509\) −35.4870 −1.57294 −0.786468 0.617632i \(-0.788092\pi\)
−0.786468 + 0.617632i \(0.788092\pi\)
\(510\) 0 0
\(511\) −7.35993 −0.325584
\(512\) 0 0
\(513\) −19.8843 −0.877911
\(514\) 0 0
\(515\) −21.6299 −0.953128
\(516\) 0 0
\(517\) −5.58340 −0.245558
\(518\) 0 0
\(519\) −20.7318 −0.910026
\(520\) 0 0
\(521\) −10.5604 −0.462658 −0.231329 0.972876i \(-0.574307\pi\)
−0.231329 + 0.972876i \(0.574307\pi\)
\(522\) 0 0
\(523\) 19.6286 0.858300 0.429150 0.903233i \(-0.358813\pi\)
0.429150 + 0.903233i \(0.358813\pi\)
\(524\) 0 0
\(525\) −14.2279 −0.620955
\(526\) 0 0
\(527\) −5.47193 −0.238361
\(528\) 0 0
\(529\) −4.93197 −0.214433
\(530\) 0 0
\(531\) 8.87719 0.385237
\(532\) 0 0
\(533\) −6.70492 −0.290422
\(534\) 0 0
\(535\) −6.75642 −0.292106
\(536\) 0 0
\(537\) 27.0268 1.16629
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 36.9553 1.58883 0.794416 0.607375i \(-0.207777\pi\)
0.794416 + 0.607375i \(0.207777\pi\)
\(542\) 0 0
\(543\) −6.95137 −0.298312
\(544\) 0 0
\(545\) −29.2071 −1.25109
\(546\) 0 0
\(547\) −14.6151 −0.624895 −0.312448 0.949935i \(-0.601149\pi\)
−0.312448 + 0.949935i \(0.601149\pi\)
\(548\) 0 0
\(549\) 13.3243 0.568668
\(550\) 0 0
\(551\) 32.4495 1.38240
\(552\) 0 0
\(553\) 3.31354 0.140906
\(554\) 0 0
\(555\) 2.53303 0.107521
\(556\) 0 0
\(557\) −11.1401 −0.472021 −0.236011 0.971750i \(-0.575840\pi\)
−0.236011 + 0.971750i \(0.575840\pi\)
\(558\) 0 0
\(559\) −12.6251 −0.533986
\(560\) 0 0
\(561\) −4.05149 −0.171054
\(562\) 0 0
\(563\) 2.07994 0.0876591 0.0438296 0.999039i \(-0.486044\pi\)
0.0438296 + 0.999039i \(0.486044\pi\)
\(564\) 0 0
\(565\) −27.4615 −1.15531
\(566\) 0 0
\(567\) −4.35334 −0.182823
\(568\) 0 0
\(569\) 47.3776 1.98617 0.993087 0.117383i \(-0.0374506\pi\)
0.993087 + 0.117383i \(0.0374506\pi\)
\(570\) 0 0
\(571\) −26.4238 −1.10580 −0.552900 0.833248i \(-0.686479\pi\)
−0.552900 + 0.833248i \(0.686479\pi\)
\(572\) 0 0
\(573\) −19.8488 −0.829195
\(574\) 0 0
\(575\) 44.1802 1.84244
\(576\) 0 0
\(577\) −16.0595 −0.668564 −0.334282 0.942473i \(-0.608494\pi\)
−0.334282 + 0.942473i \(0.608494\pi\)
\(578\) 0 0
\(579\) −29.7031 −1.23442
\(580\) 0 0
\(581\) 12.9354 0.536649
\(582\) 0 0
\(583\) −12.0869 −0.500589
\(584\) 0 0
\(585\) −4.41844 −0.182680
\(586\) 0 0
\(587\) −9.47574 −0.391106 −0.195553 0.980693i \(-0.562650\pi\)
−0.195553 + 0.980693i \(0.562650\pi\)
\(588\) 0 0
\(589\) −6.50863 −0.268183
\(590\) 0 0
\(591\) 33.5181 1.37875
\(592\) 0 0
\(593\) −33.6277 −1.38092 −0.690462 0.723368i \(-0.742593\pi\)
−0.690462 + 0.723368i \(0.742593\pi\)
\(594\) 0 0
\(595\) 11.6123 0.476060
\(596\) 0 0
\(597\) −9.07301 −0.371334
\(598\) 0 0
\(599\) −5.38046 −0.219840 −0.109920 0.993940i \(-0.535059\pi\)
−0.109920 + 0.993940i \(0.535059\pi\)
\(600\) 0 0
\(601\) −26.4364 −1.07836 −0.539182 0.842189i \(-0.681266\pi\)
−0.539182 + 0.842189i \(0.681266\pi\)
\(602\) 0 0
\(603\) 0.881502 0.0358976
\(604\) 0 0
\(605\) −3.92349 −0.159512
\(606\) 0 0
\(607\) 8.89838 0.361174 0.180587 0.983559i \(-0.442200\pi\)
0.180587 + 0.983559i \(0.442200\pi\)
\(608\) 0 0
\(609\) 12.6177 0.511294
\(610\) 0 0
\(611\) −5.58340 −0.225880
\(612\) 0 0
\(613\) 35.9224 1.45089 0.725446 0.688279i \(-0.241633\pi\)
0.725446 + 0.688279i \(0.241633\pi\)
\(614\) 0 0
\(615\) 36.0109 1.45210
\(616\) 0 0
\(617\) −25.4334 −1.02391 −0.511956 0.859012i \(-0.671079\pi\)
−0.511956 + 0.859012i \(0.671079\pi\)
\(618\) 0 0
\(619\) 9.83143 0.395158 0.197579 0.980287i \(-0.436692\pi\)
0.197579 + 0.980287i \(0.436692\pi\)
\(620\) 0 0
\(621\) 24.0087 0.963434
\(622\) 0 0
\(623\) −9.73498 −0.390024
\(624\) 0 0
\(625\) 31.0614 1.24245
\(626\) 0 0
\(627\) −4.81908 −0.192456
\(628\) 0 0
\(629\) −1.39588 −0.0556573
\(630\) 0 0
\(631\) −1.26016 −0.0501661 −0.0250831 0.999685i \(-0.507985\pi\)
−0.0250831 + 0.999685i \(0.507985\pi\)
\(632\) 0 0
\(633\) 2.02782 0.0805987
\(634\) 0 0
\(635\) 7.11637 0.282404
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 0.936822 0.0370601
\(640\) 0 0
\(641\) 19.1849 0.757760 0.378880 0.925446i \(-0.376309\pi\)
0.378880 + 0.925446i \(0.376309\pi\)
\(642\) 0 0
\(643\) −15.3088 −0.603720 −0.301860 0.953352i \(-0.597607\pi\)
−0.301860 + 0.953352i \(0.597607\pi\)
\(644\) 0 0
\(645\) 67.8071 2.66990
\(646\) 0 0
\(647\) −17.2197 −0.676976 −0.338488 0.940971i \(-0.609915\pi\)
−0.338488 + 0.940971i \(0.609915\pi\)
\(648\) 0 0
\(649\) 7.88278 0.309426
\(650\) 0 0
\(651\) −2.53081 −0.0991904
\(652\) 0 0
\(653\) 30.9933 1.21286 0.606431 0.795136i \(-0.292601\pi\)
0.606431 + 0.795136i \(0.292601\pi\)
\(654\) 0 0
\(655\) 17.5785 0.686847
\(656\) 0 0
\(657\) 8.28839 0.323361
\(658\) 0 0
\(659\) −30.2889 −1.17989 −0.589944 0.807444i \(-0.700850\pi\)
−0.589944 + 0.807444i \(0.700850\pi\)
\(660\) 0 0
\(661\) 18.7447 0.729086 0.364543 0.931187i \(-0.381225\pi\)
0.364543 + 0.931187i \(0.381225\pi\)
\(662\) 0 0
\(663\) −4.05149 −0.157347
\(664\) 0 0
\(665\) 13.8124 0.535622
\(666\) 0 0
\(667\) −39.1802 −1.51707
\(668\) 0 0
\(669\) −13.5367 −0.523358
\(670\) 0 0
\(671\) 11.8317 0.456759
\(672\) 0 0
\(673\) −3.31762 −0.127885 −0.0639423 0.997954i \(-0.520367\pi\)
−0.0639423 + 0.997954i \(0.520367\pi\)
\(674\) 0 0
\(675\) 58.7063 2.25961
\(676\) 0 0
\(677\) −5.10434 −0.196176 −0.0980878 0.995178i \(-0.531273\pi\)
−0.0980878 + 0.995178i \(0.531273\pi\)
\(678\) 0 0
\(679\) −0.699621 −0.0268490
\(680\) 0 0
\(681\) 4.49892 0.172399
\(682\) 0 0
\(683\) 49.7613 1.90406 0.952032 0.305999i \(-0.0989904\pi\)
0.952032 + 0.305999i \(0.0989904\pi\)
\(684\) 0 0
\(685\) 28.8598 1.10267
\(686\) 0 0
\(687\) 33.3817 1.27359
\(688\) 0 0
\(689\) −12.0869 −0.460475
\(690\) 0 0
\(691\) −41.3988 −1.57488 −0.787441 0.616390i \(-0.788595\pi\)
−0.787441 + 0.616390i \(0.788595\pi\)
\(692\) 0 0
\(693\) 1.12615 0.0427789
\(694\) 0 0
\(695\) −18.8095 −0.713487
\(696\) 0 0
\(697\) −19.8446 −0.751666
\(698\) 0 0
\(699\) 26.7367 1.01127
\(700\) 0 0
\(701\) 33.3662 1.26022 0.630111 0.776505i \(-0.283009\pi\)
0.630111 + 0.776505i \(0.283009\pi\)
\(702\) 0 0
\(703\) −1.66034 −0.0626209
\(704\) 0 0
\(705\) 29.9874 1.12939
\(706\) 0 0
\(707\) −9.86753 −0.371107
\(708\) 0 0
\(709\) 39.3320 1.47714 0.738572 0.674174i \(-0.235500\pi\)
0.738572 + 0.674174i \(0.235500\pi\)
\(710\) 0 0
\(711\) −3.73155 −0.139944
\(712\) 0 0
\(713\) 7.85865 0.294309
\(714\) 0 0
\(715\) −3.92349 −0.146730
\(716\) 0 0
\(717\) −7.49980 −0.280085
\(718\) 0 0
\(719\) −31.6552 −1.18054 −0.590270 0.807206i \(-0.700979\pi\)
−0.590270 + 0.807206i \(0.700979\pi\)
\(720\) 0 0
\(721\) 5.51293 0.205312
\(722\) 0 0
\(723\) −20.1359 −0.748864
\(724\) 0 0
\(725\) −95.8041 −3.55808
\(726\) 0 0
\(727\) 25.3027 0.938424 0.469212 0.883086i \(-0.344538\pi\)
0.469212 + 0.883086i \(0.344538\pi\)
\(728\) 0 0
\(729\) 28.0979 1.04066
\(730\) 0 0
\(731\) −37.3666 −1.38205
\(732\) 0 0
\(733\) 40.4044 1.49237 0.746185 0.665739i \(-0.231884\pi\)
0.746185 + 0.665739i \(0.231884\pi\)
\(734\) 0 0
\(735\) 5.37081 0.198105
\(736\) 0 0
\(737\) 0.782757 0.0288332
\(738\) 0 0
\(739\) 22.9622 0.844678 0.422339 0.906438i \(-0.361209\pi\)
0.422339 + 0.906438i \(0.361209\pi\)
\(740\) 0 0
\(741\) −4.81908 −0.177033
\(742\) 0 0
\(743\) −45.4301 −1.66667 −0.833335 0.552769i \(-0.813571\pi\)
−0.833335 + 0.552769i \(0.813571\pi\)
\(744\) 0 0
\(745\) −17.7973 −0.652042
\(746\) 0 0
\(747\) −14.5671 −0.532984
\(748\) 0 0
\(749\) 1.72204 0.0629222
\(750\) 0 0
\(751\) 2.04380 0.0745792 0.0372896 0.999305i \(-0.488128\pi\)
0.0372896 + 0.999305i \(0.488128\pi\)
\(752\) 0 0
\(753\) 42.4874 1.54833
\(754\) 0 0
\(755\) −45.4126 −1.65273
\(756\) 0 0
\(757\) −18.7041 −0.679813 −0.339906 0.940459i \(-0.610395\pi\)
−0.339906 + 0.940459i \(0.610395\pi\)
\(758\) 0 0
\(759\) 5.81866 0.211204
\(760\) 0 0
\(761\) −26.1854 −0.949221 −0.474611 0.880196i \(-0.657411\pi\)
−0.474611 + 0.880196i \(0.657411\pi\)
\(762\) 0 0
\(763\) 7.44416 0.269497
\(764\) 0 0
\(765\) −13.0772 −0.472809
\(766\) 0 0
\(767\) 7.88278 0.284631
\(768\) 0 0
\(769\) 5.11583 0.184481 0.0922407 0.995737i \(-0.470597\pi\)
0.0922407 + 0.995737i \(0.470597\pi\)
\(770\) 0 0
\(771\) 3.96675 0.142859
\(772\) 0 0
\(773\) 14.8675 0.534747 0.267373 0.963593i \(-0.413844\pi\)
0.267373 + 0.963593i \(0.413844\pi\)
\(774\) 0 0
\(775\) 19.2161 0.690263
\(776\) 0 0
\(777\) −0.645605 −0.0231610
\(778\) 0 0
\(779\) −23.6043 −0.845711
\(780\) 0 0
\(781\) 0.831881 0.0297670
\(782\) 0 0
\(783\) −52.0624 −1.86056
\(784\) 0 0
\(785\) −90.9576 −3.24641
\(786\) 0 0
\(787\) 17.1119 0.609972 0.304986 0.952357i \(-0.401348\pi\)
0.304986 + 0.952357i \(0.401348\pi\)
\(788\) 0 0
\(789\) 19.1114 0.680382
\(790\) 0 0
\(791\) 6.99925 0.248865
\(792\) 0 0
\(793\) 11.8317 0.420158
\(794\) 0 0
\(795\) 64.9166 2.30235
\(796\) 0 0
\(797\) 27.3720 0.969567 0.484783 0.874634i \(-0.338898\pi\)
0.484783 + 0.874634i \(0.338898\pi\)
\(798\) 0 0
\(799\) −16.5252 −0.584619
\(800\) 0 0
\(801\) 10.9630 0.387360
\(802\) 0 0
\(803\) 7.35993 0.259726
\(804\) 0 0
\(805\) −16.6774 −0.587800
\(806\) 0 0
\(807\) 8.68722 0.305805
\(808\) 0 0
\(809\) 15.6997 0.551971 0.275985 0.961162i \(-0.410996\pi\)
0.275985 + 0.961162i \(0.410996\pi\)
\(810\) 0 0
\(811\) −7.63057 −0.267946 −0.133973 0.990985i \(-0.542773\pi\)
−0.133973 + 0.990985i \(0.542773\pi\)
\(812\) 0 0
\(813\) 32.4411 1.13776
\(814\) 0 0
\(815\) 38.7202 1.35631
\(816\) 0 0
\(817\) −44.4460 −1.55497
\(818\) 0 0
\(819\) 1.12615 0.0393509
\(820\) 0 0
\(821\) 47.6814 1.66409 0.832045 0.554708i \(-0.187170\pi\)
0.832045 + 0.554708i \(0.187170\pi\)
\(822\) 0 0
\(823\) −39.0778 −1.36217 −0.681084 0.732205i \(-0.738491\pi\)
−0.681084 + 0.732205i \(0.738491\pi\)
\(824\) 0 0
\(825\) 14.2279 0.495351
\(826\) 0 0
\(827\) 20.5380 0.714176 0.357088 0.934071i \(-0.383770\pi\)
0.357088 + 0.934071i \(0.383770\pi\)
\(828\) 0 0
\(829\) 40.0917 1.39244 0.696221 0.717827i \(-0.254863\pi\)
0.696221 + 0.717827i \(0.254863\pi\)
\(830\) 0 0
\(831\) −36.6289 −1.27064
\(832\) 0 0
\(833\) −2.95970 −0.102547
\(834\) 0 0
\(835\) −61.9120 −2.14255
\(836\) 0 0
\(837\) 10.4425 0.360946
\(838\) 0 0
\(839\) 44.7619 1.54535 0.772676 0.634800i \(-0.218918\pi\)
0.772676 + 0.634800i \(0.218918\pi\)
\(840\) 0 0
\(841\) 55.9617 1.92972
\(842\) 0 0
\(843\) −16.9872 −0.585071
\(844\) 0 0
\(845\) −3.92349 −0.134972
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −9.72907 −0.333901
\(850\) 0 0
\(851\) 2.00473 0.0687212
\(852\) 0 0
\(853\) 20.6013 0.705376 0.352688 0.935741i \(-0.385268\pi\)
0.352688 + 0.935741i \(0.385268\pi\)
\(854\) 0 0
\(855\) −15.5548 −0.531964
\(856\) 0 0
\(857\) −8.76523 −0.299414 −0.149707 0.988730i \(-0.547833\pi\)
−0.149707 + 0.988730i \(0.547833\pi\)
\(858\) 0 0
\(859\) 34.7334 1.18509 0.592544 0.805538i \(-0.298124\pi\)
0.592544 + 0.805538i \(0.298124\pi\)
\(860\) 0 0
\(861\) −9.17828 −0.312795
\(862\) 0 0
\(863\) 43.5787 1.48344 0.741719 0.670711i \(-0.234011\pi\)
0.741719 + 0.670711i \(0.234011\pi\)
\(864\) 0 0
\(865\) −59.4213 −2.02039
\(866\) 0 0
\(867\) 11.2799 0.383085
\(868\) 0 0
\(869\) −3.31354 −0.112404
\(870\) 0 0
\(871\) 0.782757 0.0265227
\(872\) 0 0
\(873\) 0.787878 0.0266656
\(874\) 0 0
\(875\) −21.1623 −0.715417
\(876\) 0 0
\(877\) 32.4574 1.09601 0.548003 0.836476i \(-0.315388\pi\)
0.548003 + 0.836476i \(0.315388\pi\)
\(878\) 0 0
\(879\) 31.4158 1.05963
\(880\) 0 0
\(881\) 11.1530 0.375755 0.187877 0.982193i \(-0.439839\pi\)
0.187877 + 0.982193i \(0.439839\pi\)
\(882\) 0 0
\(883\) −34.6085 −1.16467 −0.582335 0.812949i \(-0.697861\pi\)
−0.582335 + 0.812949i \(0.697861\pi\)
\(884\) 0 0
\(885\) −42.3369 −1.42314
\(886\) 0 0
\(887\) 30.0443 1.00879 0.504394 0.863474i \(-0.331716\pi\)
0.504394 + 0.863474i \(0.331716\pi\)
\(888\) 0 0
\(889\) −1.81379 −0.0608324
\(890\) 0 0
\(891\) 4.35334 0.145842
\(892\) 0 0
\(893\) −19.6560 −0.657764
\(894\) 0 0
\(895\) 77.4638 2.58933
\(896\) 0 0
\(897\) 5.81866 0.194279
\(898\) 0 0
\(899\) −17.0414 −0.568361
\(900\) 0 0
\(901\) −35.7737 −1.19179
\(902\) 0 0
\(903\) −17.2824 −0.575121
\(904\) 0 0
\(905\) −19.9239 −0.662294
\(906\) 0 0
\(907\) 25.8933 0.859773 0.429886 0.902883i \(-0.358554\pi\)
0.429886 + 0.902883i \(0.358554\pi\)
\(908\) 0 0
\(909\) 11.1123 0.368573
\(910\) 0 0
\(911\) 52.5754 1.74190 0.870950 0.491372i \(-0.163504\pi\)
0.870950 + 0.491372i \(0.163504\pi\)
\(912\) 0 0
\(913\) −12.9354 −0.428098
\(914\) 0 0
\(915\) −63.5460 −2.10077
\(916\) 0 0
\(917\) −4.48032 −0.147953
\(918\) 0 0
\(919\) −16.9725 −0.559870 −0.279935 0.960019i \(-0.590313\pi\)
−0.279935 + 0.960019i \(0.590313\pi\)
\(920\) 0 0
\(921\) 24.1664 0.796309
\(922\) 0 0
\(923\) 0.831881 0.0273817
\(924\) 0 0
\(925\) 4.90199 0.161176
\(926\) 0 0
\(927\) −6.20839 −0.203910
\(928\) 0 0
\(929\) 26.7855 0.878803 0.439402 0.898291i \(-0.355191\pi\)
0.439402 + 0.898291i \(0.355191\pi\)
\(930\) 0 0
\(931\) −3.52044 −0.115378
\(932\) 0 0
\(933\) 36.0110 1.17895
\(934\) 0 0
\(935\) −11.6123 −0.379764
\(936\) 0 0
\(937\) −6.40506 −0.209244 −0.104622 0.994512i \(-0.533363\pi\)
−0.104622 + 0.994512i \(0.533363\pi\)
\(938\) 0 0
\(939\) −45.9889 −1.50079
\(940\) 0 0
\(941\) −35.5346 −1.15839 −0.579197 0.815187i \(-0.696634\pi\)
−0.579197 + 0.815187i \(0.696634\pi\)
\(942\) 0 0
\(943\) 28.5003 0.928097
\(944\) 0 0
\(945\) −22.1608 −0.720890
\(946\) 0 0
\(947\) −31.3711 −1.01943 −0.509713 0.860345i \(-0.670248\pi\)
−0.509713 + 0.860345i \(0.670248\pi\)
\(948\) 0 0
\(949\) 7.35993 0.238914
\(950\) 0 0
\(951\) 19.1400 0.620657
\(952\) 0 0
\(953\) −21.3368 −0.691167 −0.345584 0.938388i \(-0.612319\pi\)
−0.345584 + 0.938388i \(0.612319\pi\)
\(954\) 0 0
\(955\) −56.8904 −1.84093
\(956\) 0 0
\(957\) −12.6177 −0.407871
\(958\) 0 0
\(959\) −7.35564 −0.237526
\(960\) 0 0
\(961\) −27.5819 −0.889739
\(962\) 0 0
\(963\) −1.93928 −0.0624925
\(964\) 0 0
\(965\) −85.1346 −2.74058
\(966\) 0 0
\(967\) 23.4016 0.752544 0.376272 0.926509i \(-0.377206\pi\)
0.376272 + 0.926509i \(0.377206\pi\)
\(968\) 0 0
\(969\) −14.2630 −0.458195
\(970\) 0 0
\(971\) −18.2293 −0.585007 −0.292503 0.956265i \(-0.594488\pi\)
−0.292503 + 0.956265i \(0.594488\pi\)
\(972\) 0 0
\(973\) 4.79409 0.153691
\(974\) 0 0
\(975\) 14.2279 0.455656
\(976\) 0 0
\(977\) −42.0299 −1.34465 −0.672327 0.740254i \(-0.734705\pi\)
−0.672327 + 0.740254i \(0.734705\pi\)
\(978\) 0 0
\(979\) 9.73498 0.311131
\(980\) 0 0
\(981\) −8.38324 −0.267656
\(982\) 0 0
\(983\) −38.0019 −1.21207 −0.606037 0.795437i \(-0.707242\pi\)
−0.606037 + 0.795437i \(0.707242\pi\)
\(984\) 0 0
\(985\) 96.0691 3.06102
\(986\) 0 0
\(987\) −7.64304 −0.243281
\(988\) 0 0
\(989\) 53.6650 1.70645
\(990\) 0 0
\(991\) 12.1620 0.386338 0.193169 0.981165i \(-0.438123\pi\)
0.193169 + 0.981165i \(0.438123\pi\)
\(992\) 0 0
\(993\) 9.48720 0.301067
\(994\) 0 0
\(995\) −26.0050 −0.824413
\(996\) 0 0
\(997\) −12.7700 −0.404430 −0.202215 0.979341i \(-0.564814\pi\)
−0.202215 + 0.979341i \(0.564814\pi\)
\(998\) 0 0
\(999\) 2.66387 0.0842810
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 \(a_p\))