Properties

Label 8008.2.a.u.1.9
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.67231\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.67231 q^{3} +0.943895 q^{5} -1.00000 q^{7} +4.14126 q^{9} +O(q^{10})\) \(q+2.67231 q^{3} +0.943895 q^{5} -1.00000 q^{7} +4.14126 q^{9} -1.00000 q^{11} -1.00000 q^{13} +2.52238 q^{15} -0.622063 q^{17} -2.30010 q^{19} -2.67231 q^{21} -6.63973 q^{23} -4.10906 q^{25} +3.04980 q^{27} -9.44550 q^{29} -6.80361 q^{31} -2.67231 q^{33} -0.943895 q^{35} +3.75243 q^{37} -2.67231 q^{39} +0.0796215 q^{41} +6.71975 q^{43} +3.90891 q^{45} +4.55768 q^{47} +1.00000 q^{49} -1.66235 q^{51} -5.69712 q^{53} -0.943895 q^{55} -6.14659 q^{57} -5.42152 q^{59} -5.72339 q^{61} -4.14126 q^{63} -0.943895 q^{65} +0.881277 q^{67} -17.7434 q^{69} -14.0794 q^{71} +9.92776 q^{73} -10.9807 q^{75} +1.00000 q^{77} +12.9505 q^{79} -4.27376 q^{81} +5.11394 q^{83} -0.587162 q^{85} -25.2413 q^{87} -17.5642 q^{89} +1.00000 q^{91} -18.1814 q^{93} -2.17105 q^{95} -6.32556 q^{97} -4.14126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 2.67231 1.54286 0.771430 0.636314i \(-0.219542\pi\)
0.771430 + 0.636314i \(0.219542\pi\)
\(4\) 0 0
\(5\) 0.943895 0.422123 0.211061 0.977473i \(-0.432308\pi\)
0.211061 + 0.977473i \(0.432308\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 4.14126 1.38042
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.52238 0.651276
\(16\) 0 0
\(17\) −0.622063 −0.150873 −0.0754363 0.997151i \(-0.524035\pi\)
−0.0754363 + 0.997151i \(0.524035\pi\)
\(18\) 0 0
\(19\) −2.30010 −0.527679 −0.263840 0.964567i \(-0.584989\pi\)
−0.263840 + 0.964567i \(0.584989\pi\)
\(20\) 0 0
\(21\) −2.67231 −0.583147
\(22\) 0 0
\(23\) −6.63973 −1.38448 −0.692240 0.721668i \(-0.743376\pi\)
−0.692240 + 0.721668i \(0.743376\pi\)
\(24\) 0 0
\(25\) −4.10906 −0.821813
\(26\) 0 0
\(27\) 3.04980 0.586934
\(28\) 0 0
\(29\) −9.44550 −1.75398 −0.876992 0.480504i \(-0.840454\pi\)
−0.876992 + 0.480504i \(0.840454\pi\)
\(30\) 0 0
\(31\) −6.80361 −1.22196 −0.610982 0.791645i \(-0.709225\pi\)
−0.610982 + 0.791645i \(0.709225\pi\)
\(32\) 0 0
\(33\) −2.67231 −0.465190
\(34\) 0 0
\(35\) −0.943895 −0.159547
\(36\) 0 0
\(37\) 3.75243 0.616896 0.308448 0.951241i \(-0.400190\pi\)
0.308448 + 0.951241i \(0.400190\pi\)
\(38\) 0 0
\(39\) −2.67231 −0.427913
\(40\) 0 0
\(41\) 0.0796215 0.0124348 0.00621739 0.999981i \(-0.498021\pi\)
0.00621739 + 0.999981i \(0.498021\pi\)
\(42\) 0 0
\(43\) 6.71975 1.02475 0.512376 0.858761i \(-0.328765\pi\)
0.512376 + 0.858761i \(0.328765\pi\)
\(44\) 0 0
\(45\) 3.90891 0.582706
\(46\) 0 0
\(47\) 4.55768 0.664806 0.332403 0.943137i \(-0.392141\pi\)
0.332403 + 0.943137i \(0.392141\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.66235 −0.232775
\(52\) 0 0
\(53\) −5.69712 −0.782559 −0.391280 0.920272i \(-0.627968\pi\)
−0.391280 + 0.920272i \(0.627968\pi\)
\(54\) 0 0
\(55\) −0.943895 −0.127275
\(56\) 0 0
\(57\) −6.14659 −0.814135
\(58\) 0 0
\(59\) −5.42152 −0.705822 −0.352911 0.935657i \(-0.614808\pi\)
−0.352911 + 0.935657i \(0.614808\pi\)
\(60\) 0 0
\(61\) −5.72339 −0.732805 −0.366403 0.930456i \(-0.619411\pi\)
−0.366403 + 0.930456i \(0.619411\pi\)
\(62\) 0 0
\(63\) −4.14126 −0.521749
\(64\) 0 0
\(65\) −0.943895 −0.117076
\(66\) 0 0
\(67\) 0.881277 0.107665 0.0538326 0.998550i \(-0.482856\pi\)
0.0538326 + 0.998550i \(0.482856\pi\)
\(68\) 0 0
\(69\) −17.7434 −2.13606
\(70\) 0 0
\(71\) −14.0794 −1.67092 −0.835459 0.549553i \(-0.814798\pi\)
−0.835459 + 0.549553i \(0.814798\pi\)
\(72\) 0 0
\(73\) 9.92776 1.16196 0.580978 0.813919i \(-0.302670\pi\)
0.580978 + 0.813919i \(0.302670\pi\)
\(74\) 0 0
\(75\) −10.9807 −1.26794
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 12.9505 1.45705 0.728524 0.685020i \(-0.240207\pi\)
0.728524 + 0.685020i \(0.240207\pi\)
\(80\) 0 0
\(81\) −4.27376 −0.474862
\(82\) 0 0
\(83\) 5.11394 0.561327 0.280664 0.959806i \(-0.409445\pi\)
0.280664 + 0.959806i \(0.409445\pi\)
\(84\) 0 0
\(85\) −0.587162 −0.0636867
\(86\) 0 0
\(87\) −25.2413 −2.70615
\(88\) 0 0
\(89\) −17.5642 −1.86180 −0.930902 0.365269i \(-0.880977\pi\)
−0.930902 + 0.365269i \(0.880977\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −18.1814 −1.88532
\(94\) 0 0
\(95\) −2.17105 −0.222745
\(96\) 0 0
\(97\) −6.32556 −0.642263 −0.321131 0.947035i \(-0.604063\pi\)
−0.321131 + 0.947035i \(0.604063\pi\)
\(98\) 0 0
\(99\) −4.14126 −0.416212
\(100\) 0 0
\(101\) 0.252869 0.0251614 0.0125807 0.999921i \(-0.495995\pi\)
0.0125807 + 0.999921i \(0.495995\pi\)
\(102\) 0 0
\(103\) −2.98359 −0.293982 −0.146991 0.989138i \(-0.546959\pi\)
−0.146991 + 0.989138i \(0.546959\pi\)
\(104\) 0 0
\(105\) −2.52238 −0.246159
\(106\) 0 0
\(107\) −13.8680 −1.34067 −0.670337 0.742057i \(-0.733850\pi\)
−0.670337 + 0.742057i \(0.733850\pi\)
\(108\) 0 0
\(109\) −4.22019 −0.404220 −0.202110 0.979363i \(-0.564780\pi\)
−0.202110 + 0.979363i \(0.564780\pi\)
\(110\) 0 0
\(111\) 10.0277 0.951785
\(112\) 0 0
\(113\) 4.97460 0.467971 0.233986 0.972240i \(-0.424823\pi\)
0.233986 + 0.972240i \(0.424823\pi\)
\(114\) 0 0
\(115\) −6.26721 −0.584420
\(116\) 0 0
\(117\) −4.14126 −0.382859
\(118\) 0 0
\(119\) 0.622063 0.0570245
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.212774 0.0191851
\(124\) 0 0
\(125\) −8.59800 −0.769028
\(126\) 0 0
\(127\) 21.4344 1.90200 0.950999 0.309193i \(-0.100059\pi\)
0.950999 + 0.309193i \(0.100059\pi\)
\(128\) 0 0
\(129\) 17.9573 1.58105
\(130\) 0 0
\(131\) 19.9358 1.74180 0.870899 0.491462i \(-0.163537\pi\)
0.870899 + 0.491462i \(0.163537\pi\)
\(132\) 0 0
\(133\) 2.30010 0.199444
\(134\) 0 0
\(135\) 2.87869 0.247758
\(136\) 0 0
\(137\) 7.30422 0.624042 0.312021 0.950075i \(-0.398994\pi\)
0.312021 + 0.950075i \(0.398994\pi\)
\(138\) 0 0
\(139\) −4.24746 −0.360265 −0.180133 0.983642i \(-0.557653\pi\)
−0.180133 + 0.983642i \(0.557653\pi\)
\(140\) 0 0
\(141\) 12.1795 1.02570
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −8.91556 −0.740397
\(146\) 0 0
\(147\) 2.67231 0.220409
\(148\) 0 0
\(149\) 1.38025 0.113075 0.0565374 0.998400i \(-0.481994\pi\)
0.0565374 + 0.998400i \(0.481994\pi\)
\(150\) 0 0
\(151\) −20.9083 −1.70149 −0.850746 0.525577i \(-0.823849\pi\)
−0.850746 + 0.525577i \(0.823849\pi\)
\(152\) 0 0
\(153\) −2.57612 −0.208267
\(154\) 0 0
\(155\) −6.42189 −0.515818
\(156\) 0 0
\(157\) −6.86501 −0.547888 −0.273944 0.961746i \(-0.588328\pi\)
−0.273944 + 0.961746i \(0.588328\pi\)
\(158\) 0 0
\(159\) −15.2245 −1.20738
\(160\) 0 0
\(161\) 6.63973 0.523284
\(162\) 0 0
\(163\) 20.6584 1.61809 0.809046 0.587745i \(-0.199984\pi\)
0.809046 + 0.587745i \(0.199984\pi\)
\(164\) 0 0
\(165\) −2.52238 −0.196367
\(166\) 0 0
\(167\) 15.9293 1.23265 0.616323 0.787494i \(-0.288622\pi\)
0.616323 + 0.787494i \(0.288622\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −9.52530 −0.728418
\(172\) 0 0
\(173\) 6.27650 0.477193 0.238597 0.971119i \(-0.423313\pi\)
0.238597 + 0.971119i \(0.423313\pi\)
\(174\) 0 0
\(175\) 4.10906 0.310616
\(176\) 0 0
\(177\) −14.4880 −1.08899
\(178\) 0 0
\(179\) 13.1482 0.982741 0.491371 0.870951i \(-0.336496\pi\)
0.491371 + 0.870951i \(0.336496\pi\)
\(180\) 0 0
\(181\) 5.59416 0.415811 0.207905 0.978149i \(-0.433335\pi\)
0.207905 + 0.978149i \(0.433335\pi\)
\(182\) 0 0
\(183\) −15.2947 −1.13062
\(184\) 0 0
\(185\) 3.54190 0.260406
\(186\) 0 0
\(187\) 0.622063 0.0454898
\(188\) 0 0
\(189\) −3.04980 −0.221840
\(190\) 0 0
\(191\) 10.3362 0.747902 0.373951 0.927448i \(-0.378003\pi\)
0.373951 + 0.927448i \(0.378003\pi\)
\(192\) 0 0
\(193\) −1.56178 −0.112419 −0.0562096 0.998419i \(-0.517901\pi\)
−0.0562096 + 0.998419i \(0.517901\pi\)
\(194\) 0 0
\(195\) −2.52238 −0.180632
\(196\) 0 0
\(197\) 4.63858 0.330485 0.165243 0.986253i \(-0.447159\pi\)
0.165243 + 0.986253i \(0.447159\pi\)
\(198\) 0 0
\(199\) −2.04937 −0.145276 −0.0726380 0.997358i \(-0.523142\pi\)
−0.0726380 + 0.997358i \(0.523142\pi\)
\(200\) 0 0
\(201\) 2.35505 0.166112
\(202\) 0 0
\(203\) 9.44550 0.662944
\(204\) 0 0
\(205\) 0.0751543 0.00524900
\(206\) 0 0
\(207\) −27.4968 −1.91116
\(208\) 0 0
\(209\) 2.30010 0.159101
\(210\) 0 0
\(211\) −24.4861 −1.68569 −0.842847 0.538153i \(-0.819122\pi\)
−0.842847 + 0.538153i \(0.819122\pi\)
\(212\) 0 0
\(213\) −37.6246 −2.57799
\(214\) 0 0
\(215\) 6.34273 0.432571
\(216\) 0 0
\(217\) 6.80361 0.461859
\(218\) 0 0
\(219\) 26.5301 1.79274
\(220\) 0 0
\(221\) 0.622063 0.0418445
\(222\) 0 0
\(223\) −3.54602 −0.237459 −0.118729 0.992927i \(-0.537882\pi\)
−0.118729 + 0.992927i \(0.537882\pi\)
\(224\) 0 0
\(225\) −17.0167 −1.13445
\(226\) 0 0
\(227\) 17.4468 1.15798 0.578992 0.815334i \(-0.303446\pi\)
0.578992 + 0.815334i \(0.303446\pi\)
\(228\) 0 0
\(229\) −14.4112 −0.952318 −0.476159 0.879359i \(-0.657971\pi\)
−0.476159 + 0.879359i \(0.657971\pi\)
\(230\) 0 0
\(231\) 2.67231 0.175825
\(232\) 0 0
\(233\) 20.9702 1.37380 0.686902 0.726750i \(-0.258970\pi\)
0.686902 + 0.726750i \(0.258970\pi\)
\(234\) 0 0
\(235\) 4.30197 0.280630
\(236\) 0 0
\(237\) 34.6079 2.24802
\(238\) 0 0
\(239\) −18.5110 −1.19738 −0.598688 0.800983i \(-0.704311\pi\)
−0.598688 + 0.800983i \(0.704311\pi\)
\(240\) 0 0
\(241\) 3.19427 0.205761 0.102881 0.994694i \(-0.467194\pi\)
0.102881 + 0.994694i \(0.467194\pi\)
\(242\) 0 0
\(243\) −20.5702 −1.31958
\(244\) 0 0
\(245\) 0.943895 0.0603032
\(246\) 0 0
\(247\) 2.30010 0.146352
\(248\) 0 0
\(249\) 13.6660 0.866050
\(250\) 0 0
\(251\) −18.4037 −1.16163 −0.580816 0.814035i \(-0.697266\pi\)
−0.580816 + 0.814035i \(0.697266\pi\)
\(252\) 0 0
\(253\) 6.63973 0.417436
\(254\) 0 0
\(255\) −1.56908 −0.0982597
\(256\) 0 0
\(257\) 15.4668 0.964794 0.482397 0.875953i \(-0.339766\pi\)
0.482397 + 0.875953i \(0.339766\pi\)
\(258\) 0 0
\(259\) −3.75243 −0.233165
\(260\) 0 0
\(261\) −39.1162 −2.42123
\(262\) 0 0
\(263\) 10.6139 0.654479 0.327240 0.944941i \(-0.393882\pi\)
0.327240 + 0.944941i \(0.393882\pi\)
\(264\) 0 0
\(265\) −5.37748 −0.330336
\(266\) 0 0
\(267\) −46.9371 −2.87250
\(268\) 0 0
\(269\) −14.9925 −0.914110 −0.457055 0.889438i \(-0.651096\pi\)
−0.457055 + 0.889438i \(0.651096\pi\)
\(270\) 0 0
\(271\) 4.58603 0.278581 0.139291 0.990252i \(-0.455518\pi\)
0.139291 + 0.990252i \(0.455518\pi\)
\(272\) 0 0
\(273\) 2.67231 0.161736
\(274\) 0 0
\(275\) 4.10906 0.247786
\(276\) 0 0
\(277\) 14.5269 0.872836 0.436418 0.899744i \(-0.356247\pi\)
0.436418 + 0.899744i \(0.356247\pi\)
\(278\) 0 0
\(279\) −28.1755 −1.68682
\(280\) 0 0
\(281\) −18.1373 −1.08198 −0.540989 0.841030i \(-0.681950\pi\)
−0.540989 + 0.841030i \(0.681950\pi\)
\(282\) 0 0
\(283\) 0.331455 0.0197030 0.00985149 0.999951i \(-0.496864\pi\)
0.00985149 + 0.999951i \(0.496864\pi\)
\(284\) 0 0
\(285\) −5.80173 −0.343665
\(286\) 0 0
\(287\) −0.0796215 −0.00469991
\(288\) 0 0
\(289\) −16.6130 −0.977237
\(290\) 0 0
\(291\) −16.9039 −0.990922
\(292\) 0 0
\(293\) 17.1755 1.00340 0.501702 0.865040i \(-0.332707\pi\)
0.501702 + 0.865040i \(0.332707\pi\)
\(294\) 0 0
\(295\) −5.11735 −0.297944
\(296\) 0 0
\(297\) −3.04980 −0.176967
\(298\) 0 0
\(299\) 6.63973 0.383985
\(300\) 0 0
\(301\) −6.71975 −0.387320
\(302\) 0 0
\(303\) 0.675745 0.0388205
\(304\) 0 0
\(305\) −5.40228 −0.309334
\(306\) 0 0
\(307\) 15.7290 0.897701 0.448850 0.893607i \(-0.351834\pi\)
0.448850 + 0.893607i \(0.351834\pi\)
\(308\) 0 0
\(309\) −7.97309 −0.453573
\(310\) 0 0
\(311\) 9.20898 0.522193 0.261097 0.965313i \(-0.415916\pi\)
0.261097 + 0.965313i \(0.415916\pi\)
\(312\) 0 0
\(313\) −23.6431 −1.33639 −0.668194 0.743987i \(-0.732933\pi\)
−0.668194 + 0.743987i \(0.732933\pi\)
\(314\) 0 0
\(315\) −3.90891 −0.220242
\(316\) 0 0
\(317\) −21.7679 −1.22261 −0.611305 0.791395i \(-0.709355\pi\)
−0.611305 + 0.791395i \(0.709355\pi\)
\(318\) 0 0
\(319\) 9.44550 0.528846
\(320\) 0 0
\(321\) −37.0597 −2.06847
\(322\) 0 0
\(323\) 1.43081 0.0796123
\(324\) 0 0
\(325\) 4.10906 0.227930
\(326\) 0 0
\(327\) −11.2777 −0.623656
\(328\) 0 0
\(329\) −4.55768 −0.251273
\(330\) 0 0
\(331\) 3.00474 0.165155 0.0825776 0.996585i \(-0.473685\pi\)
0.0825776 + 0.996585i \(0.473685\pi\)
\(332\) 0 0
\(333\) 15.5398 0.851575
\(334\) 0 0
\(335\) 0.831833 0.0454479
\(336\) 0 0
\(337\) 27.2933 1.48676 0.743381 0.668868i \(-0.233221\pi\)
0.743381 + 0.668868i \(0.233221\pi\)
\(338\) 0 0
\(339\) 13.2937 0.722014
\(340\) 0 0
\(341\) 6.80361 0.368436
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −16.7479 −0.901679
\(346\) 0 0
\(347\) −23.4221 −1.25736 −0.628682 0.777662i \(-0.716405\pi\)
−0.628682 + 0.777662i \(0.716405\pi\)
\(348\) 0 0
\(349\) −0.119337 −0.00638799 −0.00319399 0.999995i \(-0.501017\pi\)
−0.00319399 + 0.999995i \(0.501017\pi\)
\(350\) 0 0
\(351\) −3.04980 −0.162786
\(352\) 0 0
\(353\) −10.8199 −0.575884 −0.287942 0.957648i \(-0.592971\pi\)
−0.287942 + 0.957648i \(0.592971\pi\)
\(354\) 0 0
\(355\) −13.2895 −0.705332
\(356\) 0 0
\(357\) 1.66235 0.0879808
\(358\) 0 0
\(359\) −34.2412 −1.80718 −0.903591 0.428395i \(-0.859079\pi\)
−0.903591 + 0.428395i \(0.859079\pi\)
\(360\) 0 0
\(361\) −13.7095 −0.721555
\(362\) 0 0
\(363\) 2.67231 0.140260
\(364\) 0 0
\(365\) 9.37076 0.490488
\(366\) 0 0
\(367\) −0.382253 −0.0199535 −0.00997673 0.999950i \(-0.503176\pi\)
−0.00997673 + 0.999950i \(0.503176\pi\)
\(368\) 0 0
\(369\) 0.329733 0.0171652
\(370\) 0 0
\(371\) 5.69712 0.295780
\(372\) 0 0
\(373\) 27.3857 1.41798 0.708989 0.705219i \(-0.249151\pi\)
0.708989 + 0.705219i \(0.249151\pi\)
\(374\) 0 0
\(375\) −22.9765 −1.18650
\(376\) 0 0
\(377\) 9.44550 0.486468
\(378\) 0 0
\(379\) 29.4156 1.51098 0.755489 0.655161i \(-0.227399\pi\)
0.755489 + 0.655161i \(0.227399\pi\)
\(380\) 0 0
\(381\) 57.2795 2.93452
\(382\) 0 0
\(383\) −16.7429 −0.855520 −0.427760 0.903892i \(-0.640697\pi\)
−0.427760 + 0.903892i \(0.640697\pi\)
\(384\) 0 0
\(385\) 0.943895 0.0481053
\(386\) 0 0
\(387\) 27.8282 1.41459
\(388\) 0 0
\(389\) 35.7424 1.81221 0.906105 0.423052i \(-0.139041\pi\)
0.906105 + 0.423052i \(0.139041\pi\)
\(390\) 0 0
\(391\) 4.13033 0.208880
\(392\) 0 0
\(393\) 53.2747 2.68735
\(394\) 0 0
\(395\) 12.2239 0.615053
\(396\) 0 0
\(397\) −29.2038 −1.46570 −0.732849 0.680391i \(-0.761810\pi\)
−0.732849 + 0.680391i \(0.761810\pi\)
\(398\) 0 0
\(399\) 6.14659 0.307714
\(400\) 0 0
\(401\) 27.4926 1.37292 0.686458 0.727170i \(-0.259165\pi\)
0.686458 + 0.727170i \(0.259165\pi\)
\(402\) 0 0
\(403\) 6.80361 0.338912
\(404\) 0 0
\(405\) −4.03398 −0.200450
\(406\) 0 0
\(407\) −3.75243 −0.186001
\(408\) 0 0
\(409\) 3.97056 0.196331 0.0981657 0.995170i \(-0.468702\pi\)
0.0981657 + 0.995170i \(0.468702\pi\)
\(410\) 0 0
\(411\) 19.5192 0.962809
\(412\) 0 0
\(413\) 5.42152 0.266776
\(414\) 0 0
\(415\) 4.82702 0.236949
\(416\) 0 0
\(417\) −11.3506 −0.555839
\(418\) 0 0
\(419\) 29.1363 1.42340 0.711701 0.702483i \(-0.247925\pi\)
0.711701 + 0.702483i \(0.247925\pi\)
\(420\) 0 0
\(421\) −20.2393 −0.986401 −0.493200 0.869916i \(-0.664173\pi\)
−0.493200 + 0.869916i \(0.664173\pi\)
\(422\) 0 0
\(423\) 18.8745 0.917711
\(424\) 0 0
\(425\) 2.55610 0.123989
\(426\) 0 0
\(427\) 5.72339 0.276974
\(428\) 0 0
\(429\) 2.67231 0.129020
\(430\) 0 0
\(431\) −26.8811 −1.29482 −0.647409 0.762143i \(-0.724147\pi\)
−0.647409 + 0.762143i \(0.724147\pi\)
\(432\) 0 0
\(433\) 27.4491 1.31912 0.659561 0.751651i \(-0.270742\pi\)
0.659561 + 0.751651i \(0.270742\pi\)
\(434\) 0 0
\(435\) −23.8252 −1.14233
\(436\) 0 0
\(437\) 15.2720 0.730561
\(438\) 0 0
\(439\) 10.8693 0.518764 0.259382 0.965775i \(-0.416481\pi\)
0.259382 + 0.965775i \(0.416481\pi\)
\(440\) 0 0
\(441\) 4.14126 0.197203
\(442\) 0 0
\(443\) −7.56409 −0.359381 −0.179690 0.983723i \(-0.557510\pi\)
−0.179690 + 0.983723i \(0.557510\pi\)
\(444\) 0 0
\(445\) −16.5788 −0.785910
\(446\) 0 0
\(447\) 3.68847 0.174459
\(448\) 0 0
\(449\) −23.9356 −1.12959 −0.564796 0.825230i \(-0.691045\pi\)
−0.564796 + 0.825230i \(0.691045\pi\)
\(450\) 0 0
\(451\) −0.0796215 −0.00374923
\(452\) 0 0
\(453\) −55.8735 −2.62517
\(454\) 0 0
\(455\) 0.943895 0.0442505
\(456\) 0 0
\(457\) 12.1799 0.569752 0.284876 0.958564i \(-0.408048\pi\)
0.284876 + 0.958564i \(0.408048\pi\)
\(458\) 0 0
\(459\) −1.89717 −0.0885522
\(460\) 0 0
\(461\) −28.5468 −1.32956 −0.664779 0.747040i \(-0.731474\pi\)
−0.664779 + 0.747040i \(0.731474\pi\)
\(462\) 0 0
\(463\) −20.0101 −0.929947 −0.464973 0.885325i \(-0.653936\pi\)
−0.464973 + 0.885325i \(0.653936\pi\)
\(464\) 0 0
\(465\) −17.1613 −0.795836
\(466\) 0 0
\(467\) 2.84287 0.131552 0.0657762 0.997834i \(-0.479048\pi\)
0.0657762 + 0.997834i \(0.479048\pi\)
\(468\) 0 0
\(469\) −0.881277 −0.0406936
\(470\) 0 0
\(471\) −18.3455 −0.845314
\(472\) 0 0
\(473\) −6.71975 −0.308974
\(474\) 0 0
\(475\) 9.45125 0.433653
\(476\) 0 0
\(477\) −23.5932 −1.08026
\(478\) 0 0
\(479\) −33.2946 −1.52127 −0.760635 0.649180i \(-0.775112\pi\)
−0.760635 + 0.649180i \(0.775112\pi\)
\(480\) 0 0
\(481\) −3.75243 −0.171096
\(482\) 0 0
\(483\) 17.7434 0.807354
\(484\) 0 0
\(485\) −5.97066 −0.271114
\(486\) 0 0
\(487\) 6.12895 0.277729 0.138865 0.990311i \(-0.455655\pi\)
0.138865 + 0.990311i \(0.455655\pi\)
\(488\) 0 0
\(489\) 55.2058 2.49649
\(490\) 0 0
\(491\) −31.3676 −1.41560 −0.707799 0.706413i \(-0.750312\pi\)
−0.707799 + 0.706413i \(0.750312\pi\)
\(492\) 0 0
\(493\) 5.87570 0.264628
\(494\) 0 0
\(495\) −3.90891 −0.175693
\(496\) 0 0
\(497\) 14.0794 0.631547
\(498\) 0 0
\(499\) 15.9022 0.711882 0.355941 0.934508i \(-0.384160\pi\)
0.355941 + 0.934508i \(0.384160\pi\)
\(500\) 0 0
\(501\) 42.5680 1.90180
\(502\) 0 0
\(503\) 39.8665 1.77756 0.888779 0.458336i \(-0.151554\pi\)
0.888779 + 0.458336i \(0.151554\pi\)
\(504\) 0 0
\(505\) 0.238682 0.0106212
\(506\) 0 0
\(507\) 2.67231 0.118682
\(508\) 0 0
\(509\) −34.8910 −1.54652 −0.773259 0.634090i \(-0.781375\pi\)
−0.773259 + 0.634090i \(0.781375\pi\)
\(510\) 0 0
\(511\) −9.92776 −0.439178
\(512\) 0 0
\(513\) −7.01484 −0.309713
\(514\) 0 0
\(515\) −2.81619 −0.124096
\(516\) 0 0
\(517\) −4.55768 −0.200446
\(518\) 0 0
\(519\) 16.7728 0.736243
\(520\) 0 0
\(521\) −15.5113 −0.679564 −0.339782 0.940504i \(-0.610353\pi\)
−0.339782 + 0.940504i \(0.610353\pi\)
\(522\) 0 0
\(523\) −39.1321 −1.71113 −0.855565 0.517696i \(-0.826790\pi\)
−0.855565 + 0.517696i \(0.826790\pi\)
\(524\) 0 0
\(525\) 10.9807 0.479237
\(526\) 0 0
\(527\) 4.23227 0.184361
\(528\) 0 0
\(529\) 21.0860 0.916783
\(530\) 0 0
\(531\) −22.4519 −0.974330
\(532\) 0 0
\(533\) −0.0796215 −0.00344879
\(534\) 0 0
\(535\) −13.0900 −0.565929
\(536\) 0 0
\(537\) 35.1361 1.51623
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −19.0457 −0.818839 −0.409419 0.912346i \(-0.634269\pi\)
−0.409419 + 0.912346i \(0.634269\pi\)
\(542\) 0 0
\(543\) 14.9493 0.641538
\(544\) 0 0
\(545\) −3.98341 −0.170631
\(546\) 0 0
\(547\) −26.4349 −1.13028 −0.565138 0.824996i \(-0.691177\pi\)
−0.565138 + 0.824996i \(0.691177\pi\)
\(548\) 0 0
\(549\) −23.7020 −1.01158
\(550\) 0 0
\(551\) 21.7256 0.925541
\(552\) 0 0
\(553\) −12.9505 −0.550712
\(554\) 0 0
\(555\) 9.46507 0.401770
\(556\) 0 0
\(557\) −5.44948 −0.230902 −0.115451 0.993313i \(-0.536831\pi\)
−0.115451 + 0.993313i \(0.536831\pi\)
\(558\) 0 0
\(559\) −6.71975 −0.284215
\(560\) 0 0
\(561\) 1.66235 0.0701844
\(562\) 0 0
\(563\) 35.5127 1.49668 0.748341 0.663314i \(-0.230851\pi\)
0.748341 + 0.663314i \(0.230851\pi\)
\(564\) 0 0
\(565\) 4.69550 0.197541
\(566\) 0 0
\(567\) 4.27376 0.179481
\(568\) 0 0
\(569\) 8.65028 0.362639 0.181319 0.983424i \(-0.441963\pi\)
0.181319 + 0.983424i \(0.441963\pi\)
\(570\) 0 0
\(571\) 3.05741 0.127949 0.0639744 0.997952i \(-0.479622\pi\)
0.0639744 + 0.997952i \(0.479622\pi\)
\(572\) 0 0
\(573\) 27.6216 1.15391
\(574\) 0 0
\(575\) 27.2831 1.13778
\(576\) 0 0
\(577\) 2.44179 0.101653 0.0508266 0.998707i \(-0.483814\pi\)
0.0508266 + 0.998707i \(0.483814\pi\)
\(578\) 0 0
\(579\) −4.17356 −0.173447
\(580\) 0 0
\(581\) −5.11394 −0.212162
\(582\) 0 0
\(583\) 5.69712 0.235951
\(584\) 0 0
\(585\) −3.90891 −0.161614
\(586\) 0 0
\(587\) −27.0088 −1.11477 −0.557386 0.830253i \(-0.688196\pi\)
−0.557386 + 0.830253i \(0.688196\pi\)
\(588\) 0 0
\(589\) 15.6490 0.644805
\(590\) 0 0
\(591\) 12.3957 0.509893
\(592\) 0 0
\(593\) −30.0961 −1.23590 −0.617950 0.786217i \(-0.712037\pi\)
−0.617950 + 0.786217i \(0.712037\pi\)
\(594\) 0 0
\(595\) 0.587162 0.0240713
\(596\) 0 0
\(597\) −5.47656 −0.224141
\(598\) 0 0
\(599\) 12.7143 0.519494 0.259747 0.965677i \(-0.416361\pi\)
0.259747 + 0.965677i \(0.416361\pi\)
\(600\) 0 0
\(601\) −28.4621 −1.16099 −0.580497 0.814262i \(-0.697142\pi\)
−0.580497 + 0.814262i \(0.697142\pi\)
\(602\) 0 0
\(603\) 3.64960 0.148623
\(604\) 0 0
\(605\) 0.943895 0.0383748
\(606\) 0 0
\(607\) −16.7279 −0.678963 −0.339482 0.940613i \(-0.610252\pi\)
−0.339482 + 0.940613i \(0.610252\pi\)
\(608\) 0 0
\(609\) 25.2413 1.02283
\(610\) 0 0
\(611\) −4.55768 −0.184384
\(612\) 0 0
\(613\) 1.26254 0.0509937 0.0254968 0.999675i \(-0.491883\pi\)
0.0254968 + 0.999675i \(0.491883\pi\)
\(614\) 0 0
\(615\) 0.200836 0.00809848
\(616\) 0 0
\(617\) −36.7618 −1.47997 −0.739987 0.672622i \(-0.765168\pi\)
−0.739987 + 0.672622i \(0.765168\pi\)
\(618\) 0 0
\(619\) 24.8761 0.999856 0.499928 0.866067i \(-0.333360\pi\)
0.499928 + 0.866067i \(0.333360\pi\)
\(620\) 0 0
\(621\) −20.2498 −0.812597
\(622\) 0 0
\(623\) 17.5642 0.703696
\(624\) 0 0
\(625\) 12.4297 0.497188
\(626\) 0 0
\(627\) 6.14659 0.245471
\(628\) 0 0
\(629\) −2.33425 −0.0930727
\(630\) 0 0
\(631\) 15.3940 0.612826 0.306413 0.951899i \(-0.400871\pi\)
0.306413 + 0.951899i \(0.400871\pi\)
\(632\) 0 0
\(633\) −65.4346 −2.60079
\(634\) 0 0
\(635\) 20.2319 0.802877
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −58.3064 −2.30657
\(640\) 0 0
\(641\) 0.890745 0.0351823 0.0175912 0.999845i \(-0.494400\pi\)
0.0175912 + 0.999845i \(0.494400\pi\)
\(642\) 0 0
\(643\) −20.2157 −0.797230 −0.398615 0.917118i \(-0.630509\pi\)
−0.398615 + 0.917118i \(0.630509\pi\)
\(644\) 0 0
\(645\) 16.9498 0.667397
\(646\) 0 0
\(647\) 23.7779 0.934805 0.467402 0.884045i \(-0.345190\pi\)
0.467402 + 0.884045i \(0.345190\pi\)
\(648\) 0 0
\(649\) 5.42152 0.212813
\(650\) 0 0
\(651\) 18.1814 0.712584
\(652\) 0 0
\(653\) 15.6339 0.611800 0.305900 0.952064i \(-0.401043\pi\)
0.305900 + 0.952064i \(0.401043\pi\)
\(654\) 0 0
\(655\) 18.8173 0.735252
\(656\) 0 0
\(657\) 41.1134 1.60399
\(658\) 0 0
\(659\) 4.22340 0.164520 0.0822602 0.996611i \(-0.473786\pi\)
0.0822602 + 0.996611i \(0.473786\pi\)
\(660\) 0 0
\(661\) 5.21814 0.202962 0.101481 0.994837i \(-0.467642\pi\)
0.101481 + 0.994837i \(0.467642\pi\)
\(662\) 0 0
\(663\) 1.66235 0.0645602
\(664\) 0 0
\(665\) 2.17105 0.0841898
\(666\) 0 0
\(667\) 62.7155 2.42836
\(668\) 0 0
\(669\) −9.47607 −0.366366
\(670\) 0 0
\(671\) 5.72339 0.220949
\(672\) 0 0
\(673\) −13.0488 −0.502993 −0.251497 0.967858i \(-0.580923\pi\)
−0.251497 + 0.967858i \(0.580923\pi\)
\(674\) 0 0
\(675\) −12.5318 −0.482349
\(676\) 0 0
\(677\) −47.4039 −1.82188 −0.910940 0.412540i \(-0.864642\pi\)
−0.910940 + 0.412540i \(0.864642\pi\)
\(678\) 0 0
\(679\) 6.32556 0.242753
\(680\) 0 0
\(681\) 46.6232 1.78661
\(682\) 0 0
\(683\) 8.29654 0.317458 0.158729 0.987322i \(-0.449260\pi\)
0.158729 + 0.987322i \(0.449260\pi\)
\(684\) 0 0
\(685\) 6.89441 0.263422
\(686\) 0 0
\(687\) −38.5112 −1.46929
\(688\) 0 0
\(689\) 5.69712 0.217043
\(690\) 0 0
\(691\) −11.1261 −0.423258 −0.211629 0.977350i \(-0.567877\pi\)
−0.211629 + 0.977350i \(0.567877\pi\)
\(692\) 0 0
\(693\) 4.14126 0.157313
\(694\) 0 0
\(695\) −4.00916 −0.152076
\(696\) 0 0
\(697\) −0.0495296 −0.00187607
\(698\) 0 0
\(699\) 56.0390 2.11959
\(700\) 0 0
\(701\) 5.96866 0.225433 0.112717 0.993627i \(-0.464045\pi\)
0.112717 + 0.993627i \(0.464045\pi\)
\(702\) 0 0
\(703\) −8.63097 −0.325523
\(704\) 0 0
\(705\) 11.4962 0.432972
\(706\) 0 0
\(707\) −0.252869 −0.00951011
\(708\) 0 0
\(709\) 1.04032 0.0390702 0.0195351 0.999809i \(-0.493781\pi\)
0.0195351 + 0.999809i \(0.493781\pi\)
\(710\) 0 0
\(711\) 53.6314 2.01134
\(712\) 0 0
\(713\) 45.1741 1.69178
\(714\) 0 0
\(715\) 0.943895 0.0352997
\(716\) 0 0
\(717\) −49.4671 −1.84738
\(718\) 0 0
\(719\) 1.67643 0.0625202 0.0312601 0.999511i \(-0.490048\pi\)
0.0312601 + 0.999511i \(0.490048\pi\)
\(720\) 0 0
\(721\) 2.98359 0.111115
\(722\) 0 0
\(723\) 8.53609 0.317461
\(724\) 0 0
\(725\) 38.8121 1.44145
\(726\) 0 0
\(727\) −6.49034 −0.240713 −0.120357 0.992731i \(-0.538404\pi\)
−0.120357 + 0.992731i \(0.538404\pi\)
\(728\) 0 0
\(729\) −42.1488 −1.56107
\(730\) 0 0
\(731\) −4.18011 −0.154607
\(732\) 0 0
\(733\) −22.8230 −0.842986 −0.421493 0.906832i \(-0.638494\pi\)
−0.421493 + 0.906832i \(0.638494\pi\)
\(734\) 0 0
\(735\) 2.52238 0.0930395
\(736\) 0 0
\(737\) −0.881277 −0.0324623
\(738\) 0 0
\(739\) −19.6535 −0.722967 −0.361483 0.932379i \(-0.617730\pi\)
−0.361483 + 0.932379i \(0.617730\pi\)
\(740\) 0 0
\(741\) 6.14659 0.225800
\(742\) 0 0
\(743\) −52.4646 −1.92474 −0.962371 0.271741i \(-0.912401\pi\)
−0.962371 + 0.271741i \(0.912401\pi\)
\(744\) 0 0
\(745\) 1.30281 0.0477314
\(746\) 0 0
\(747\) 21.1781 0.774867
\(748\) 0 0
\(749\) 13.8680 0.506727
\(750\) 0 0
\(751\) 22.7094 0.828677 0.414338 0.910123i \(-0.364013\pi\)
0.414338 + 0.910123i \(0.364013\pi\)
\(752\) 0 0
\(753\) −49.1805 −1.79224
\(754\) 0 0
\(755\) −19.7352 −0.718238
\(756\) 0 0
\(757\) −15.6724 −0.569623 −0.284812 0.958584i \(-0.591931\pi\)
−0.284812 + 0.958584i \(0.591931\pi\)
\(758\) 0 0
\(759\) 17.7434 0.644046
\(760\) 0 0
\(761\) 19.3546 0.701602 0.350801 0.936450i \(-0.385909\pi\)
0.350801 + 0.936450i \(0.385909\pi\)
\(762\) 0 0
\(763\) 4.22019 0.152781
\(764\) 0 0
\(765\) −2.43159 −0.0879143
\(766\) 0 0
\(767\) 5.42152 0.195760
\(768\) 0 0
\(769\) 5.32834 0.192145 0.0960725 0.995374i \(-0.469372\pi\)
0.0960725 + 0.995374i \(0.469372\pi\)
\(770\) 0 0
\(771\) 41.3322 1.48854
\(772\) 0 0
\(773\) −7.32303 −0.263391 −0.131696 0.991290i \(-0.542042\pi\)
−0.131696 + 0.991290i \(0.542042\pi\)
\(774\) 0 0
\(775\) 27.9564 1.00422
\(776\) 0 0
\(777\) −10.0277 −0.359741
\(778\) 0 0
\(779\) −0.183137 −0.00656158
\(780\) 0 0
\(781\) 14.0794 0.503801
\(782\) 0 0
\(783\) −28.8068 −1.02947
\(784\) 0 0
\(785\) −6.47985 −0.231276
\(786\) 0 0
\(787\) 36.0448 1.28486 0.642430 0.766345i \(-0.277927\pi\)
0.642430 + 0.766345i \(0.277927\pi\)
\(788\) 0 0
\(789\) 28.3636 1.00977
\(790\) 0 0
\(791\) −4.97460 −0.176876
\(792\) 0 0
\(793\) 5.72339 0.203244
\(794\) 0 0
\(795\) −14.3703 −0.509662
\(796\) 0 0
\(797\) −50.6311 −1.79345 −0.896723 0.442593i \(-0.854059\pi\)
−0.896723 + 0.442593i \(0.854059\pi\)
\(798\) 0 0
\(799\) −2.83517 −0.100301
\(800\) 0 0
\(801\) −72.7380 −2.57007
\(802\) 0 0
\(803\) −9.92776 −0.350343
\(804\) 0 0
\(805\) 6.26721 0.220890
\(806\) 0 0
\(807\) −40.0647 −1.41034
\(808\) 0 0
\(809\) −0.182728 −0.00642436 −0.00321218 0.999995i \(-0.501022\pi\)
−0.00321218 + 0.999995i \(0.501022\pi\)
\(810\) 0 0
\(811\) −19.2195 −0.674886 −0.337443 0.941346i \(-0.609562\pi\)
−0.337443 + 0.941346i \(0.609562\pi\)
\(812\) 0 0
\(813\) 12.2553 0.429812
\(814\) 0 0
\(815\) 19.4994 0.683033
\(816\) 0 0
\(817\) −15.4561 −0.540740
\(818\) 0 0
\(819\) 4.14126 0.144707
\(820\) 0 0
\(821\) 5.75003 0.200678 0.100339 0.994953i \(-0.468007\pi\)
0.100339 + 0.994953i \(0.468007\pi\)
\(822\) 0 0
\(823\) −0.184311 −0.00642468 −0.00321234 0.999995i \(-0.501023\pi\)
−0.00321234 + 0.999995i \(0.501023\pi\)
\(824\) 0 0
\(825\) 10.9807 0.382299
\(826\) 0 0
\(827\) 31.2284 1.08592 0.542959 0.839759i \(-0.317304\pi\)
0.542959 + 0.839759i \(0.317304\pi\)
\(828\) 0 0
\(829\) −33.0865 −1.14914 −0.574570 0.818455i \(-0.694831\pi\)
−0.574570 + 0.818455i \(0.694831\pi\)
\(830\) 0 0
\(831\) 38.8204 1.34666
\(832\) 0 0
\(833\) −0.622063 −0.0215532
\(834\) 0 0
\(835\) 15.0356 0.520327
\(836\) 0 0
\(837\) −20.7496 −0.717212
\(838\) 0 0
\(839\) −14.7184 −0.508134 −0.254067 0.967187i \(-0.581768\pi\)
−0.254067 + 0.967187i \(0.581768\pi\)
\(840\) 0 0
\(841\) 60.2174 2.07646
\(842\) 0 0
\(843\) −48.4684 −1.66934
\(844\) 0 0
\(845\) 0.943895 0.0324710
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 0.885753 0.0303990
\(850\) 0 0
\(851\) −24.9151 −0.854080
\(852\) 0 0
\(853\) −44.3126 −1.51723 −0.758617 0.651537i \(-0.774125\pi\)
−0.758617 + 0.651537i \(0.774125\pi\)
\(854\) 0 0
\(855\) −8.99089 −0.307482
\(856\) 0 0
\(857\) 57.0681 1.94941 0.974704 0.223499i \(-0.0717481\pi\)
0.974704 + 0.223499i \(0.0717481\pi\)
\(858\) 0 0
\(859\) 16.9776 0.579268 0.289634 0.957137i \(-0.406466\pi\)
0.289634 + 0.957137i \(0.406466\pi\)
\(860\) 0 0
\(861\) −0.212774 −0.00725130
\(862\) 0 0
\(863\) 31.6259 1.07656 0.538280 0.842766i \(-0.319074\pi\)
0.538280 + 0.842766i \(0.319074\pi\)
\(864\) 0 0
\(865\) 5.92435 0.201434
\(866\) 0 0
\(867\) −44.3952 −1.50774
\(868\) 0 0
\(869\) −12.9505 −0.439316
\(870\) 0 0
\(871\) −0.881277 −0.0298609
\(872\) 0 0
\(873\) −26.1958 −0.886592
\(874\) 0 0
\(875\) 8.59800 0.290665
\(876\) 0 0
\(877\) 15.8296 0.534528 0.267264 0.963623i \(-0.413880\pi\)
0.267264 + 0.963623i \(0.413880\pi\)
\(878\) 0 0
\(879\) 45.8984 1.54811
\(880\) 0 0
\(881\) −1.28259 −0.0432114 −0.0216057 0.999767i \(-0.506878\pi\)
−0.0216057 + 0.999767i \(0.506878\pi\)
\(882\) 0 0
\(883\) −8.17237 −0.275022 −0.137511 0.990500i \(-0.543910\pi\)
−0.137511 + 0.990500i \(0.543910\pi\)
\(884\) 0 0
\(885\) −13.6752 −0.459685
\(886\) 0 0
\(887\) 31.6676 1.06330 0.531648 0.846966i \(-0.321573\pi\)
0.531648 + 0.846966i \(0.321573\pi\)
\(888\) 0 0
\(889\) −21.4344 −0.718888
\(890\) 0 0
\(891\) 4.27376 0.143176
\(892\) 0 0
\(893\) −10.4831 −0.350804
\(894\) 0 0
\(895\) 12.4105 0.414837
\(896\) 0 0
\(897\) 17.7434 0.592436
\(898\) 0 0
\(899\) 64.2634 2.14331
\(900\) 0 0
\(901\) 3.54397 0.118067
\(902\) 0 0
\(903\) −17.9573 −0.597580
\(904\) 0 0
\(905\) 5.28030 0.175523
\(906\) 0 0
\(907\) 7.37750 0.244966 0.122483 0.992471i \(-0.460914\pi\)
0.122483 + 0.992471i \(0.460914\pi\)
\(908\) 0 0
\(909\) 1.04719 0.0347333
\(910\) 0 0
\(911\) 34.1627 1.13186 0.565931 0.824453i \(-0.308517\pi\)
0.565931 + 0.824453i \(0.308517\pi\)
\(912\) 0 0
\(913\) −5.11394 −0.169247
\(914\) 0 0
\(915\) −14.4366 −0.477259
\(916\) 0 0
\(917\) −19.9358 −0.658338
\(918\) 0 0
\(919\) −22.3652 −0.737759 −0.368880 0.929477i \(-0.620259\pi\)
−0.368880 + 0.929477i \(0.620259\pi\)
\(920\) 0 0
\(921\) 42.0328 1.38503
\(922\) 0 0
\(923\) 14.0794 0.463429
\(924\) 0 0
\(925\) −15.4190 −0.506973
\(926\) 0 0
\(927\) −12.3558 −0.405818
\(928\) 0 0
\(929\) −32.8077 −1.07638 −0.538192 0.842822i \(-0.680893\pi\)
−0.538192 + 0.842822i \(0.680893\pi\)
\(930\) 0 0
\(931\) −2.30010 −0.0753827
\(932\) 0 0
\(933\) 24.6093 0.805671
\(934\) 0 0
\(935\) 0.587162 0.0192023
\(936\) 0 0
\(937\) 29.7488 0.971850 0.485925 0.874001i \(-0.338483\pi\)
0.485925 + 0.874001i \(0.338483\pi\)
\(938\) 0 0
\(939\) −63.1818 −2.06186
\(940\) 0 0
\(941\) −21.9579 −0.715806 −0.357903 0.933759i \(-0.616508\pi\)
−0.357903 + 0.933759i \(0.616508\pi\)
\(942\) 0 0
\(943\) −0.528665 −0.0172157
\(944\) 0 0
\(945\) −2.87869 −0.0936437
\(946\) 0 0
\(947\) 11.7444 0.381642 0.190821 0.981625i \(-0.438885\pi\)
0.190821 + 0.981625i \(0.438885\pi\)
\(948\) 0 0
\(949\) −9.92776 −0.322269
\(950\) 0 0
\(951\) −58.1708 −1.88632
\(952\) 0 0
\(953\) 0.524312 0.0169841 0.00849206 0.999964i \(-0.497297\pi\)
0.00849206 + 0.999964i \(0.497297\pi\)
\(954\) 0 0
\(955\) 9.75629 0.315706
\(956\) 0 0
\(957\) 25.2413 0.815936
\(958\) 0 0
\(959\) −7.30422 −0.235866
\(960\) 0 0
\(961\) 15.2890 0.493195
\(962\) 0 0
\(963\) −57.4311 −1.85069
\(964\) 0 0
\(965\) −1.47415 −0.0474547
\(966\) 0 0
\(967\) 48.6593 1.56478 0.782389 0.622790i \(-0.214001\pi\)
0.782389 + 0.622790i \(0.214001\pi\)
\(968\) 0 0
\(969\) 3.82357 0.122831
\(970\) 0 0
\(971\) 59.2641 1.90187 0.950937 0.309385i \(-0.100123\pi\)
0.950937 + 0.309385i \(0.100123\pi\)
\(972\) 0 0
\(973\) 4.24746 0.136167
\(974\) 0 0
\(975\) 10.9807 0.351664
\(976\) 0 0
\(977\) 29.3365 0.938557 0.469279 0.883050i \(-0.344514\pi\)
0.469279 + 0.883050i \(0.344514\pi\)
\(978\) 0 0
\(979\) 17.5642 0.561355
\(980\) 0 0
\(981\) −17.4769 −0.557994
\(982\) 0 0
\(983\) 5.19772 0.165782 0.0828908 0.996559i \(-0.473585\pi\)
0.0828908 + 0.996559i \(0.473585\pi\)
\(984\) 0 0
\(985\) 4.37833 0.139505
\(986\) 0 0
\(987\) −12.1795 −0.387679
\(988\) 0 0
\(989\) −44.6173 −1.41875
\(990\) 0 0
\(991\) 43.5533 1.38352 0.691759 0.722129i \(-0.256836\pi\)
0.691759 + 0.722129i \(0.256836\pi\)
\(992\) 0 0
\(993\) 8.02959 0.254811
\(994\) 0 0
\(995\) −1.93439 −0.0613243
\(996\) 0 0
\(997\) −39.0598 −1.23704 −0.618518 0.785770i \(-0.712267\pi\)
−0.618518 + 0.785770i \(0.712267\pi\)
\(998\) 0 0
\(999\) 11.4442 0.362077
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 \(a_p\))