Properties

Label 8004.2.a.j.1.10
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(0.897331\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+0.897331 q^{5}\) \(+3.81467 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+0.897331 q^{5}\) \(+3.81467 q^{7}\) \(+1.00000 q^{9}\) \(+5.23385 q^{11}\) \(-3.43366 q^{13}\) \(+0.897331 q^{15}\) \(+1.92187 q^{17}\) \(-7.80360 q^{19}\) \(+3.81467 q^{21}\) \(+1.00000 q^{23}\) \(-4.19480 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+3.73130 q^{31}\) \(+5.23385 q^{33}\) \(+3.42302 q^{35}\) \(+0.939833 q^{37}\) \(-3.43366 q^{39}\) \(-5.90444 q^{41}\) \(-2.82368 q^{43}\) \(+0.897331 q^{45}\) \(+13.3375 q^{47}\) \(+7.55171 q^{49}\) \(+1.92187 q^{51}\) \(+12.4108 q^{53}\) \(+4.69649 q^{55}\) \(-7.80360 q^{57}\) \(-3.06388 q^{59}\) \(+9.88695 q^{61}\) \(+3.81467 q^{63}\) \(-3.08113 q^{65}\) \(+14.3222 q^{67}\) \(+1.00000 q^{69}\) \(+10.5787 q^{71}\) \(-9.23222 q^{73}\) \(-4.19480 q^{75}\) \(+19.9654 q^{77}\) \(+2.22128 q^{79}\) \(+1.00000 q^{81}\) \(+2.48600 q^{83}\) \(+1.72455 q^{85}\) \(-1.00000 q^{87}\) \(-13.2715 q^{89}\) \(-13.0983 q^{91}\) \(+3.73130 q^{93}\) \(-7.00241 q^{95}\) \(-7.70919 q^{97}\) \(+5.23385 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.897331 0.401299 0.200649 0.979663i \(-0.435695\pi\)
0.200649 + 0.979663i \(0.435695\pi\)
\(6\) 0 0
\(7\) 3.81467 1.44181 0.720905 0.693034i \(-0.243726\pi\)
0.720905 + 0.693034i \(0.243726\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.23385 1.57806 0.789032 0.614352i \(-0.210583\pi\)
0.789032 + 0.614352i \(0.210583\pi\)
\(12\) 0 0
\(13\) −3.43366 −0.952327 −0.476164 0.879357i \(-0.657973\pi\)
−0.476164 + 0.879357i \(0.657973\pi\)
\(14\) 0 0
\(15\) 0.897331 0.231690
\(16\) 0 0
\(17\) 1.92187 0.466122 0.233061 0.972462i \(-0.425126\pi\)
0.233061 + 0.972462i \(0.425126\pi\)
\(18\) 0 0
\(19\) −7.80360 −1.79027 −0.895134 0.445796i \(-0.852921\pi\)
−0.895134 + 0.445796i \(0.852921\pi\)
\(20\) 0 0
\(21\) 3.81467 0.832429
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.19480 −0.838959
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 3.73130 0.670162 0.335081 0.942189i \(-0.391236\pi\)
0.335081 + 0.942189i \(0.391236\pi\)
\(32\) 0 0
\(33\) 5.23385 0.911096
\(34\) 0 0
\(35\) 3.42302 0.578596
\(36\) 0 0
\(37\) 0.939833 0.154508 0.0772538 0.997011i \(-0.475385\pi\)
0.0772538 + 0.997011i \(0.475385\pi\)
\(38\) 0 0
\(39\) −3.43366 −0.549826
\(40\) 0 0
\(41\) −5.90444 −0.922119 −0.461060 0.887369i \(-0.652531\pi\)
−0.461060 + 0.887369i \(0.652531\pi\)
\(42\) 0 0
\(43\) −2.82368 −0.430607 −0.215303 0.976547i \(-0.569074\pi\)
−0.215303 + 0.976547i \(0.569074\pi\)
\(44\) 0 0
\(45\) 0.897331 0.133766
\(46\) 0 0
\(47\) 13.3375 1.94547 0.972734 0.231923i \(-0.0745019\pi\)
0.972734 + 0.231923i \(0.0745019\pi\)
\(48\) 0 0
\(49\) 7.55171 1.07882
\(50\) 0 0
\(51\) 1.92187 0.269116
\(52\) 0 0
\(53\) 12.4108 1.70475 0.852377 0.522928i \(-0.175160\pi\)
0.852377 + 0.522928i \(0.175160\pi\)
\(54\) 0 0
\(55\) 4.69649 0.633275
\(56\) 0 0
\(57\) −7.80360 −1.03361
\(58\) 0 0
\(59\) −3.06388 −0.398884 −0.199442 0.979910i \(-0.563913\pi\)
−0.199442 + 0.979910i \(0.563913\pi\)
\(60\) 0 0
\(61\) 9.88695 1.26589 0.632947 0.774195i \(-0.281845\pi\)
0.632947 + 0.774195i \(0.281845\pi\)
\(62\) 0 0
\(63\) 3.81467 0.480603
\(64\) 0 0
\(65\) −3.08113 −0.382168
\(66\) 0 0
\(67\) 14.3222 1.74973 0.874866 0.484365i \(-0.160949\pi\)
0.874866 + 0.484365i \(0.160949\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 10.5787 1.25547 0.627733 0.778429i \(-0.283983\pi\)
0.627733 + 0.778429i \(0.283983\pi\)
\(72\) 0 0
\(73\) −9.23222 −1.08055 −0.540275 0.841489i \(-0.681680\pi\)
−0.540275 + 0.841489i \(0.681680\pi\)
\(74\) 0 0
\(75\) −4.19480 −0.484373
\(76\) 0 0
\(77\) 19.9654 2.27527
\(78\) 0 0
\(79\) 2.22128 0.249914 0.124957 0.992162i \(-0.460121\pi\)
0.124957 + 0.992162i \(0.460121\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.48600 0.272874 0.136437 0.990649i \(-0.456435\pi\)
0.136437 + 0.990649i \(0.456435\pi\)
\(84\) 0 0
\(85\) 1.72455 0.187054
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −13.2715 −1.40678 −0.703390 0.710804i \(-0.748331\pi\)
−0.703390 + 0.710804i \(0.748331\pi\)
\(90\) 0 0
\(91\) −13.0983 −1.37307
\(92\) 0 0
\(93\) 3.73130 0.386918
\(94\) 0 0
\(95\) −7.00241 −0.718432
\(96\) 0 0
\(97\) −7.70919 −0.782750 −0.391375 0.920231i \(-0.628000\pi\)
−0.391375 + 0.920231i \(0.628000\pi\)
\(98\) 0 0
\(99\) 5.23385 0.526021
\(100\) 0 0
\(101\) 13.1086 1.30435 0.652176 0.758068i \(-0.273856\pi\)
0.652176 + 0.758068i \(0.273856\pi\)
\(102\) 0 0
\(103\) 18.5637 1.82913 0.914567 0.404435i \(-0.132532\pi\)
0.914567 + 0.404435i \(0.132532\pi\)
\(104\) 0 0
\(105\) 3.42302 0.334053
\(106\) 0 0
\(107\) 12.8057 1.23797 0.618987 0.785401i \(-0.287543\pi\)
0.618987 + 0.785401i \(0.287543\pi\)
\(108\) 0 0
\(109\) −1.08922 −0.104328 −0.0521640 0.998639i \(-0.516612\pi\)
−0.0521640 + 0.998639i \(0.516612\pi\)
\(110\) 0 0
\(111\) 0.939833 0.0892050
\(112\) 0 0
\(113\) 15.8228 1.48849 0.744244 0.667908i \(-0.232810\pi\)
0.744244 + 0.667908i \(0.232810\pi\)
\(114\) 0 0
\(115\) 0.897331 0.0836765
\(116\) 0 0
\(117\) −3.43366 −0.317442
\(118\) 0 0
\(119\) 7.33130 0.672059
\(120\) 0 0
\(121\) 16.3931 1.49029
\(122\) 0 0
\(123\) −5.90444 −0.532386
\(124\) 0 0
\(125\) −8.25078 −0.737972
\(126\) 0 0
\(127\) 20.9937 1.86289 0.931444 0.363885i \(-0.118550\pi\)
0.931444 + 0.363885i \(0.118550\pi\)
\(128\) 0 0
\(129\) −2.82368 −0.248611
\(130\) 0 0
\(131\) −11.8838 −1.03829 −0.519145 0.854686i \(-0.673749\pi\)
−0.519145 + 0.854686i \(0.673749\pi\)
\(132\) 0 0
\(133\) −29.7682 −2.58123
\(134\) 0 0
\(135\) 0.897331 0.0772299
\(136\) 0 0
\(137\) −9.74379 −0.832468 −0.416234 0.909258i \(-0.636650\pi\)
−0.416234 + 0.909258i \(0.636650\pi\)
\(138\) 0 0
\(139\) −21.7119 −1.84158 −0.920790 0.390060i \(-0.872454\pi\)
−0.920790 + 0.390060i \(0.872454\pi\)
\(140\) 0 0
\(141\) 13.3375 1.12322
\(142\) 0 0
\(143\) −17.9713 −1.50283
\(144\) 0 0
\(145\) −0.897331 −0.0745193
\(146\) 0 0
\(147\) 7.55171 0.622854
\(148\) 0 0
\(149\) −0.0539251 −0.00441771 −0.00220886 0.999998i \(-0.500703\pi\)
−0.00220886 + 0.999998i \(0.500703\pi\)
\(150\) 0 0
\(151\) −9.95429 −0.810069 −0.405034 0.914301i \(-0.632740\pi\)
−0.405034 + 0.914301i \(0.632740\pi\)
\(152\) 0 0
\(153\) 1.92187 0.155374
\(154\) 0 0
\(155\) 3.34821 0.268935
\(156\) 0 0
\(157\) −5.32590 −0.425053 −0.212527 0.977155i \(-0.568169\pi\)
−0.212527 + 0.977155i \(0.568169\pi\)
\(158\) 0 0
\(159\) 12.4108 0.984240
\(160\) 0 0
\(161\) 3.81467 0.300638
\(162\) 0 0
\(163\) 18.3644 1.43841 0.719206 0.694797i \(-0.244506\pi\)
0.719206 + 0.694797i \(0.244506\pi\)
\(164\) 0 0
\(165\) 4.69649 0.365621
\(166\) 0 0
\(167\) −16.8360 −1.30281 −0.651405 0.758730i \(-0.725820\pi\)
−0.651405 + 0.758730i \(0.725820\pi\)
\(168\) 0 0
\(169\) −1.20995 −0.0930729
\(170\) 0 0
\(171\) −7.80360 −0.596756
\(172\) 0 0
\(173\) −22.0282 −1.67478 −0.837388 0.546609i \(-0.815918\pi\)
−0.837388 + 0.546609i \(0.815918\pi\)
\(174\) 0 0
\(175\) −16.0018 −1.20962
\(176\) 0 0
\(177\) −3.06388 −0.230296
\(178\) 0 0
\(179\) 2.29809 0.171767 0.0858837 0.996305i \(-0.472629\pi\)
0.0858837 + 0.996305i \(0.472629\pi\)
\(180\) 0 0
\(181\) 1.94435 0.144522 0.0722611 0.997386i \(-0.476979\pi\)
0.0722611 + 0.997386i \(0.476979\pi\)
\(182\) 0 0
\(183\) 9.88695 0.730865
\(184\) 0 0
\(185\) 0.843341 0.0620037
\(186\) 0 0
\(187\) 10.0588 0.735570
\(188\) 0 0
\(189\) 3.81467 0.277476
\(190\) 0 0
\(191\) 13.7295 0.993430 0.496715 0.867914i \(-0.334539\pi\)
0.496715 + 0.867914i \(0.334539\pi\)
\(192\) 0 0
\(193\) 13.9644 1.00518 0.502591 0.864524i \(-0.332380\pi\)
0.502591 + 0.864524i \(0.332380\pi\)
\(194\) 0 0
\(195\) −3.08113 −0.220645
\(196\) 0 0
\(197\) 6.85157 0.488154 0.244077 0.969756i \(-0.421515\pi\)
0.244077 + 0.969756i \(0.421515\pi\)
\(198\) 0 0
\(199\) 14.0960 0.999240 0.499620 0.866245i \(-0.333473\pi\)
0.499620 + 0.866245i \(0.333473\pi\)
\(200\) 0 0
\(201\) 14.3222 1.01021
\(202\) 0 0
\(203\) −3.81467 −0.267737
\(204\) 0 0
\(205\) −5.29824 −0.370045
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −40.8428 −2.82516
\(210\) 0 0
\(211\) −1.38760 −0.0955265 −0.0477632 0.998859i \(-0.515209\pi\)
−0.0477632 + 0.998859i \(0.515209\pi\)
\(212\) 0 0
\(213\) 10.5787 0.724844
\(214\) 0 0
\(215\) −2.53377 −0.172802
\(216\) 0 0
\(217\) 14.2337 0.966246
\(218\) 0 0
\(219\) −9.23222 −0.623856
\(220\) 0 0
\(221\) −6.59905 −0.443900
\(222\) 0 0
\(223\) −8.82944 −0.591263 −0.295632 0.955302i \(-0.595530\pi\)
−0.295632 + 0.955302i \(0.595530\pi\)
\(224\) 0 0
\(225\) −4.19480 −0.279653
\(226\) 0 0
\(227\) 27.1801 1.80401 0.902004 0.431727i \(-0.142096\pi\)
0.902004 + 0.431727i \(0.142096\pi\)
\(228\) 0 0
\(229\) −3.21756 −0.212622 −0.106311 0.994333i \(-0.533904\pi\)
−0.106311 + 0.994333i \(0.533904\pi\)
\(230\) 0 0
\(231\) 19.9654 1.31363
\(232\) 0 0
\(233\) 2.82764 0.185245 0.0926225 0.995701i \(-0.470475\pi\)
0.0926225 + 0.995701i \(0.470475\pi\)
\(234\) 0 0
\(235\) 11.9681 0.780714
\(236\) 0 0
\(237\) 2.22128 0.144288
\(238\) 0 0
\(239\) −25.8036 −1.66909 −0.834547 0.550937i \(-0.814271\pi\)
−0.834547 + 0.550937i \(0.814271\pi\)
\(240\) 0 0
\(241\) −27.3656 −1.76277 −0.881387 0.472396i \(-0.843389\pi\)
−0.881387 + 0.472396i \(0.843389\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 6.77638 0.432927
\(246\) 0 0
\(247\) 26.7950 1.70492
\(248\) 0 0
\(249\) 2.48600 0.157544
\(250\) 0 0
\(251\) −2.14400 −0.135328 −0.0676639 0.997708i \(-0.521555\pi\)
−0.0676639 + 0.997708i \(0.521555\pi\)
\(252\) 0 0
\(253\) 5.23385 0.329049
\(254\) 0 0
\(255\) 1.72455 0.107996
\(256\) 0 0
\(257\) −18.0033 −1.12302 −0.561508 0.827471i \(-0.689779\pi\)
−0.561508 + 0.827471i \(0.689779\pi\)
\(258\) 0 0
\(259\) 3.58515 0.222771
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −10.5249 −0.648991 −0.324495 0.945887i \(-0.605194\pi\)
−0.324495 + 0.945887i \(0.605194\pi\)
\(264\) 0 0
\(265\) 11.1366 0.684115
\(266\) 0 0
\(267\) −13.2715 −0.812204
\(268\) 0 0
\(269\) 1.28161 0.0781413 0.0390706 0.999236i \(-0.487560\pi\)
0.0390706 + 0.999236i \(0.487560\pi\)
\(270\) 0 0
\(271\) −1.11624 −0.0678070 −0.0339035 0.999425i \(-0.510794\pi\)
−0.0339035 + 0.999425i \(0.510794\pi\)
\(272\) 0 0
\(273\) −13.0983 −0.792745
\(274\) 0 0
\(275\) −21.9549 −1.32393
\(276\) 0 0
\(277\) 4.29599 0.258121 0.129061 0.991637i \(-0.458804\pi\)
0.129061 + 0.991637i \(0.458804\pi\)
\(278\) 0 0
\(279\) 3.73130 0.223387
\(280\) 0 0
\(281\) −16.1931 −0.965999 −0.482999 0.875621i \(-0.660453\pi\)
−0.482999 + 0.875621i \(0.660453\pi\)
\(282\) 0 0
\(283\) 4.02545 0.239288 0.119644 0.992817i \(-0.461825\pi\)
0.119644 + 0.992817i \(0.461825\pi\)
\(284\) 0 0
\(285\) −7.00241 −0.414787
\(286\) 0 0
\(287\) −22.5235 −1.32952
\(288\) 0 0
\(289\) −13.3064 −0.782731
\(290\) 0 0
\(291\) −7.70919 −0.451921
\(292\) 0 0
\(293\) −21.5224 −1.25735 −0.628676 0.777667i \(-0.716403\pi\)
−0.628676 + 0.777667i \(0.716403\pi\)
\(294\) 0 0
\(295\) −2.74932 −0.160071
\(296\) 0 0
\(297\) 5.23385 0.303699
\(298\) 0 0
\(299\) −3.43366 −0.198574
\(300\) 0 0
\(301\) −10.7714 −0.620853
\(302\) 0 0
\(303\) 13.1086 0.753068
\(304\) 0 0
\(305\) 8.87187 0.508002
\(306\) 0 0
\(307\) 7.57632 0.432403 0.216202 0.976349i \(-0.430633\pi\)
0.216202 + 0.976349i \(0.430633\pi\)
\(308\) 0 0
\(309\) 18.5637 1.05605
\(310\) 0 0
\(311\) −13.2050 −0.748789 −0.374394 0.927270i \(-0.622149\pi\)
−0.374394 + 0.927270i \(0.622149\pi\)
\(312\) 0 0
\(313\) 23.9026 1.35105 0.675527 0.737336i \(-0.263916\pi\)
0.675527 + 0.737336i \(0.263916\pi\)
\(314\) 0 0
\(315\) 3.42302 0.192865
\(316\) 0 0
\(317\) −3.42802 −0.192537 −0.0962683 0.995355i \(-0.530691\pi\)
−0.0962683 + 0.995355i \(0.530691\pi\)
\(318\) 0 0
\(319\) −5.23385 −0.293039
\(320\) 0 0
\(321\) 12.8057 0.714744
\(322\) 0 0
\(323\) −14.9975 −0.834483
\(324\) 0 0
\(325\) 14.4035 0.798964
\(326\) 0 0
\(327\) −1.08922 −0.0602338
\(328\) 0 0
\(329\) 50.8780 2.80499
\(330\) 0 0
\(331\) 19.5447 1.07428 0.537138 0.843494i \(-0.319505\pi\)
0.537138 + 0.843494i \(0.319505\pi\)
\(332\) 0 0
\(333\) 0.939833 0.0515025
\(334\) 0 0
\(335\) 12.8517 0.702165
\(336\) 0 0
\(337\) −27.5463 −1.50054 −0.750272 0.661129i \(-0.770078\pi\)
−0.750272 + 0.661129i \(0.770078\pi\)
\(338\) 0 0
\(339\) 15.8228 0.859379
\(340\) 0 0
\(341\) 19.5291 1.05756
\(342\) 0 0
\(343\) 2.10458 0.113637
\(344\) 0 0
\(345\) 0.897331 0.0483107
\(346\) 0 0
\(347\) 17.9600 0.964141 0.482070 0.876132i \(-0.339885\pi\)
0.482070 + 0.876132i \(0.339885\pi\)
\(348\) 0 0
\(349\) −15.2215 −0.814790 −0.407395 0.913252i \(-0.633563\pi\)
−0.407395 + 0.913252i \(0.633563\pi\)
\(350\) 0 0
\(351\) −3.43366 −0.183275
\(352\) 0 0
\(353\) −30.5406 −1.62551 −0.812756 0.582604i \(-0.802034\pi\)
−0.812756 + 0.582604i \(0.802034\pi\)
\(354\) 0 0
\(355\) 9.49263 0.503817
\(356\) 0 0
\(357\) 7.33130 0.388013
\(358\) 0 0
\(359\) −29.2887 −1.54580 −0.772900 0.634528i \(-0.781195\pi\)
−0.772900 + 0.634528i \(0.781195\pi\)
\(360\) 0 0
\(361\) 41.8962 2.20506
\(362\) 0 0
\(363\) 16.3931 0.860417
\(364\) 0 0
\(365\) −8.28436 −0.433623
\(366\) 0 0
\(367\) 5.83369 0.304516 0.152258 0.988341i \(-0.451346\pi\)
0.152258 + 0.988341i \(0.451346\pi\)
\(368\) 0 0
\(369\) −5.90444 −0.307373
\(370\) 0 0
\(371\) 47.3431 2.45793
\(372\) 0 0
\(373\) 6.18034 0.320006 0.160003 0.987117i \(-0.448850\pi\)
0.160003 + 0.987117i \(0.448850\pi\)
\(374\) 0 0
\(375\) −8.25078 −0.426068
\(376\) 0 0
\(377\) 3.43366 0.176843
\(378\) 0 0
\(379\) 28.9038 1.48469 0.742344 0.670019i \(-0.233714\pi\)
0.742344 + 0.670019i \(0.233714\pi\)
\(380\) 0 0
\(381\) 20.9937 1.07554
\(382\) 0 0
\(383\) −3.03770 −0.155219 −0.0776096 0.996984i \(-0.524729\pi\)
−0.0776096 + 0.996984i \(0.524729\pi\)
\(384\) 0 0
\(385\) 17.9156 0.913062
\(386\) 0 0
\(387\) −2.82368 −0.143536
\(388\) 0 0
\(389\) −4.43947 −0.225090 −0.112545 0.993647i \(-0.535900\pi\)
−0.112545 + 0.993647i \(0.535900\pi\)
\(390\) 0 0
\(391\) 1.92187 0.0971931
\(392\) 0 0
\(393\) −11.8838 −0.599457
\(394\) 0 0
\(395\) 1.99322 0.100290
\(396\) 0 0
\(397\) −14.6535 −0.735436 −0.367718 0.929937i \(-0.619861\pi\)
−0.367718 + 0.929937i \(0.619861\pi\)
\(398\) 0 0
\(399\) −29.7682 −1.49027
\(400\) 0 0
\(401\) −5.70941 −0.285115 −0.142557 0.989787i \(-0.545533\pi\)
−0.142557 + 0.989787i \(0.545533\pi\)
\(402\) 0 0
\(403\) −12.8120 −0.638214
\(404\) 0 0
\(405\) 0.897331 0.0445887
\(406\) 0 0
\(407\) 4.91894 0.243823
\(408\) 0 0
\(409\) −10.1737 −0.503055 −0.251527 0.967850i \(-0.580933\pi\)
−0.251527 + 0.967850i \(0.580933\pi\)
\(410\) 0 0
\(411\) −9.74379 −0.480626
\(412\) 0 0
\(413\) −11.6877 −0.575115
\(414\) 0 0
\(415\) 2.23077 0.109504
\(416\) 0 0
\(417\) −21.7119 −1.06324
\(418\) 0 0
\(419\) 26.3758 1.28854 0.644272 0.764796i \(-0.277160\pi\)
0.644272 + 0.764796i \(0.277160\pi\)
\(420\) 0 0
\(421\) 38.1010 1.85693 0.928464 0.371422i \(-0.121130\pi\)
0.928464 + 0.371422i \(0.121130\pi\)
\(422\) 0 0
\(423\) 13.3375 0.648489
\(424\) 0 0
\(425\) −8.06185 −0.391057
\(426\) 0 0
\(427\) 37.7155 1.82518
\(428\) 0 0
\(429\) −17.9713 −0.867661
\(430\) 0 0
\(431\) 4.20187 0.202397 0.101199 0.994866i \(-0.467732\pi\)
0.101199 + 0.994866i \(0.467732\pi\)
\(432\) 0 0
\(433\) 27.2424 1.30918 0.654592 0.755982i \(-0.272840\pi\)
0.654592 + 0.755982i \(0.272840\pi\)
\(434\) 0 0
\(435\) −0.897331 −0.0430237
\(436\) 0 0
\(437\) −7.80360 −0.373297
\(438\) 0 0
\(439\) −21.4883 −1.02558 −0.512791 0.858513i \(-0.671389\pi\)
−0.512791 + 0.858513i \(0.671389\pi\)
\(440\) 0 0
\(441\) 7.55171 0.359605
\(442\) 0 0
\(443\) 12.1798 0.578681 0.289341 0.957226i \(-0.406564\pi\)
0.289341 + 0.957226i \(0.406564\pi\)
\(444\) 0 0
\(445\) −11.9090 −0.564539
\(446\) 0 0
\(447\) −0.0539251 −0.00255057
\(448\) 0 0
\(449\) −8.96580 −0.423122 −0.211561 0.977365i \(-0.567855\pi\)
−0.211561 + 0.977365i \(0.567855\pi\)
\(450\) 0 0
\(451\) −30.9029 −1.45516
\(452\) 0 0
\(453\) −9.95429 −0.467693
\(454\) 0 0
\(455\) −11.7535 −0.551013
\(456\) 0 0
\(457\) 28.6575 1.34054 0.670271 0.742117i \(-0.266178\pi\)
0.670271 + 0.742117i \(0.266178\pi\)
\(458\) 0 0
\(459\) 1.92187 0.0897052
\(460\) 0 0
\(461\) −14.1620 −0.659590 −0.329795 0.944053i \(-0.606980\pi\)
−0.329795 + 0.944053i \(0.606980\pi\)
\(462\) 0 0
\(463\) −29.2565 −1.35967 −0.679833 0.733367i \(-0.737948\pi\)
−0.679833 + 0.733367i \(0.737948\pi\)
\(464\) 0 0
\(465\) 3.34821 0.155270
\(466\) 0 0
\(467\) 31.1030 1.43927 0.719637 0.694351i \(-0.244308\pi\)
0.719637 + 0.694351i \(0.244308\pi\)
\(468\) 0 0
\(469\) 54.6344 2.52278
\(470\) 0 0
\(471\) −5.32590 −0.245405
\(472\) 0 0
\(473\) −14.7787 −0.679525
\(474\) 0 0
\(475\) 32.7345 1.50196
\(476\) 0 0
\(477\) 12.4108 0.568251
\(478\) 0 0
\(479\) 3.86249 0.176482 0.0882409 0.996099i \(-0.471875\pi\)
0.0882409 + 0.996099i \(0.471875\pi\)
\(480\) 0 0
\(481\) −3.22707 −0.147142
\(482\) 0 0
\(483\) 3.81467 0.173573
\(484\) 0 0
\(485\) −6.91770 −0.314116
\(486\) 0 0
\(487\) −16.7922 −0.760929 −0.380465 0.924795i \(-0.624236\pi\)
−0.380465 + 0.924795i \(0.624236\pi\)
\(488\) 0 0
\(489\) 18.3644 0.830468
\(490\) 0 0
\(491\) −15.8110 −0.713540 −0.356770 0.934192i \(-0.616122\pi\)
−0.356770 + 0.934192i \(0.616122\pi\)
\(492\) 0 0
\(493\) −1.92187 −0.0865566
\(494\) 0 0
\(495\) 4.69649 0.211092
\(496\) 0 0
\(497\) 40.3544 1.81014
\(498\) 0 0
\(499\) −34.0511 −1.52433 −0.762167 0.647380i \(-0.775865\pi\)
−0.762167 + 0.647380i \(0.775865\pi\)
\(500\) 0 0
\(501\) −16.8360 −0.752178
\(502\) 0 0
\(503\) 2.51408 0.112097 0.0560486 0.998428i \(-0.482150\pi\)
0.0560486 + 0.998428i \(0.482150\pi\)
\(504\) 0 0
\(505\) 11.7627 0.523434
\(506\) 0 0
\(507\) −1.20995 −0.0537356
\(508\) 0 0
\(509\) −17.5905 −0.779686 −0.389843 0.920881i \(-0.627471\pi\)
−0.389843 + 0.920881i \(0.627471\pi\)
\(510\) 0 0
\(511\) −35.2179 −1.55795
\(512\) 0 0
\(513\) −7.80360 −0.344537
\(514\) 0 0
\(515\) 16.6578 0.734029
\(516\) 0 0
\(517\) 69.8062 3.07007
\(518\) 0 0
\(519\) −22.0282 −0.966932
\(520\) 0 0
\(521\) 39.9368 1.74966 0.874832 0.484426i \(-0.160972\pi\)
0.874832 + 0.484426i \(0.160972\pi\)
\(522\) 0 0
\(523\) −6.76095 −0.295636 −0.147818 0.989015i \(-0.547225\pi\)
−0.147818 + 0.989015i \(0.547225\pi\)
\(524\) 0 0
\(525\) −16.0018 −0.698374
\(526\) 0 0
\(527\) 7.17108 0.312377
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −3.06388 −0.132961
\(532\) 0 0
\(533\) 20.2739 0.878159
\(534\) 0 0
\(535\) 11.4909 0.496797
\(536\) 0 0
\(537\) 2.29809 0.0991700
\(538\) 0 0
\(539\) 39.5245 1.70244
\(540\) 0 0
\(541\) −13.6532 −0.586997 −0.293498 0.955960i \(-0.594820\pi\)
−0.293498 + 0.955960i \(0.594820\pi\)
\(542\) 0 0
\(543\) 1.94435 0.0834399
\(544\) 0 0
\(545\) −0.977388 −0.0418667
\(546\) 0 0
\(547\) 27.3579 1.16974 0.584870 0.811127i \(-0.301146\pi\)
0.584870 + 0.811127i \(0.301146\pi\)
\(548\) 0 0
\(549\) 9.88695 0.421965
\(550\) 0 0
\(551\) 7.80360 0.332445
\(552\) 0 0
\(553\) 8.47345 0.360328
\(554\) 0 0
\(555\) 0.843341 0.0357978
\(556\) 0 0
\(557\) −21.0863 −0.893456 −0.446728 0.894670i \(-0.647411\pi\)
−0.446728 + 0.894670i \(0.647411\pi\)
\(558\) 0 0
\(559\) 9.69556 0.410078
\(560\) 0 0
\(561\) 10.0588 0.424681
\(562\) 0 0
\(563\) −17.2843 −0.728446 −0.364223 0.931312i \(-0.618665\pi\)
−0.364223 + 0.931312i \(0.618665\pi\)
\(564\) 0 0
\(565\) 14.1983 0.597328
\(566\) 0 0
\(567\) 3.81467 0.160201
\(568\) 0 0
\(569\) −14.4233 −0.604658 −0.302329 0.953204i \(-0.597764\pi\)
−0.302329 + 0.953204i \(0.597764\pi\)
\(570\) 0 0
\(571\) −8.58461 −0.359255 −0.179627 0.983735i \(-0.557489\pi\)
−0.179627 + 0.983735i \(0.557489\pi\)
\(572\) 0 0
\(573\) 13.7295 0.573557
\(574\) 0 0
\(575\) −4.19480 −0.174935
\(576\) 0 0
\(577\) −11.1434 −0.463907 −0.231953 0.972727i \(-0.574512\pi\)
−0.231953 + 0.972727i \(0.574512\pi\)
\(578\) 0 0
\(579\) 13.9644 0.580342
\(580\) 0 0
\(581\) 9.48328 0.393433
\(582\) 0 0
\(583\) 64.9562 2.69021
\(584\) 0 0
\(585\) −3.08113 −0.127389
\(586\) 0 0
\(587\) −28.2597 −1.16640 −0.583200 0.812328i \(-0.698200\pi\)
−0.583200 + 0.812328i \(0.698200\pi\)
\(588\) 0 0
\(589\) −29.1176 −1.19977
\(590\) 0 0
\(591\) 6.85157 0.281836
\(592\) 0 0
\(593\) 25.4794 1.04631 0.523157 0.852236i \(-0.324754\pi\)
0.523157 + 0.852236i \(0.324754\pi\)
\(594\) 0 0
\(595\) 6.57860 0.269696
\(596\) 0 0
\(597\) 14.0960 0.576911
\(598\) 0 0
\(599\) −39.7316 −1.62339 −0.811694 0.584082i \(-0.801454\pi\)
−0.811694 + 0.584082i \(0.801454\pi\)
\(600\) 0 0
\(601\) −12.5941 −0.513725 −0.256863 0.966448i \(-0.582689\pi\)
−0.256863 + 0.966448i \(0.582689\pi\)
\(602\) 0 0
\(603\) 14.3222 0.583244
\(604\) 0 0
\(605\) 14.7101 0.598049
\(606\) 0 0
\(607\) −35.7473 −1.45094 −0.725470 0.688254i \(-0.758378\pi\)
−0.725470 + 0.688254i \(0.758378\pi\)
\(608\) 0 0
\(609\) −3.81467 −0.154578
\(610\) 0 0
\(611\) −45.7964 −1.85272
\(612\) 0 0
\(613\) −24.5319 −0.990835 −0.495418 0.868655i \(-0.664985\pi\)
−0.495418 + 0.868655i \(0.664985\pi\)
\(614\) 0 0
\(615\) −5.29824 −0.213646
\(616\) 0 0
\(617\) −31.9825 −1.28757 −0.643784 0.765207i \(-0.722637\pi\)
−0.643784 + 0.765207i \(0.722637\pi\)
\(618\) 0 0
\(619\) −21.6271 −0.869266 −0.434633 0.900608i \(-0.643122\pi\)
−0.434633 + 0.900608i \(0.643122\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −50.6265 −2.02831
\(624\) 0 0
\(625\) 13.5703 0.542812
\(626\) 0 0
\(627\) −40.8428 −1.63111
\(628\) 0 0
\(629\) 1.80624 0.0720194
\(630\) 0 0
\(631\) −2.28377 −0.0909156 −0.0454578 0.998966i \(-0.514475\pi\)
−0.0454578 + 0.998966i \(0.514475\pi\)
\(632\) 0 0
\(633\) −1.38760 −0.0551522
\(634\) 0 0
\(635\) 18.8383 0.747574
\(636\) 0 0
\(637\) −25.9300 −1.02739
\(638\) 0 0
\(639\) 10.5787 0.418489
\(640\) 0 0
\(641\) 13.9618 0.551459 0.275730 0.961235i \(-0.411081\pi\)
0.275730 + 0.961235i \(0.411081\pi\)
\(642\) 0 0
\(643\) −15.5694 −0.613997 −0.306999 0.951710i \(-0.599325\pi\)
−0.306999 + 0.951710i \(0.599325\pi\)
\(644\) 0 0
\(645\) −2.53377 −0.0997672
\(646\) 0 0
\(647\) −49.3101 −1.93858 −0.969289 0.245924i \(-0.920909\pi\)
−0.969289 + 0.245924i \(0.920909\pi\)
\(648\) 0 0
\(649\) −16.0359 −0.629464
\(650\) 0 0
\(651\) 14.2337 0.557863
\(652\) 0 0
\(653\) 7.26719 0.284387 0.142194 0.989839i \(-0.454584\pi\)
0.142194 + 0.989839i \(0.454584\pi\)
\(654\) 0 0
\(655\) −10.6637 −0.416664
\(656\) 0 0
\(657\) −9.23222 −0.360183
\(658\) 0 0
\(659\) 8.90275 0.346802 0.173401 0.984851i \(-0.444524\pi\)
0.173401 + 0.984851i \(0.444524\pi\)
\(660\) 0 0
\(661\) 4.56464 0.177544 0.0887720 0.996052i \(-0.471706\pi\)
0.0887720 + 0.996052i \(0.471706\pi\)
\(662\) 0 0
\(663\) −6.59905 −0.256286
\(664\) 0 0
\(665\) −26.7119 −1.03584
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −8.82944 −0.341366
\(670\) 0 0
\(671\) 51.7468 1.99766
\(672\) 0 0
\(673\) −5.28579 −0.203752 −0.101876 0.994797i \(-0.532485\pi\)
−0.101876 + 0.994797i \(0.532485\pi\)
\(674\) 0 0
\(675\) −4.19480 −0.161458
\(676\) 0 0
\(677\) 26.6869 1.02566 0.512831 0.858490i \(-0.328597\pi\)
0.512831 + 0.858490i \(0.328597\pi\)
\(678\) 0 0
\(679\) −29.4080 −1.12858
\(680\) 0 0
\(681\) 27.1801 1.04154
\(682\) 0 0
\(683\) −7.20362 −0.275639 −0.137819 0.990457i \(-0.544009\pi\)
−0.137819 + 0.990457i \(0.544009\pi\)
\(684\) 0 0
\(685\) −8.74340 −0.334068
\(686\) 0 0
\(687\) −3.21756 −0.122758
\(688\) 0 0
\(689\) −42.6145 −1.62348
\(690\) 0 0
\(691\) 30.4661 1.15898 0.579492 0.814978i \(-0.303251\pi\)
0.579492 + 0.814978i \(0.303251\pi\)
\(692\) 0 0
\(693\) 19.9654 0.758423
\(694\) 0 0
\(695\) −19.4828 −0.739023
\(696\) 0 0
\(697\) −11.3476 −0.429820
\(698\) 0 0
\(699\) 2.82764 0.106951
\(700\) 0 0
\(701\) 20.7783 0.784784 0.392392 0.919798i \(-0.371648\pi\)
0.392392 + 0.919798i \(0.371648\pi\)
\(702\) 0 0
\(703\) −7.33408 −0.276610
\(704\) 0 0
\(705\) 11.9681 0.450745
\(706\) 0 0
\(707\) 50.0049 1.88063
\(708\) 0 0
\(709\) 19.4473 0.730359 0.365179 0.930937i \(-0.381008\pi\)
0.365179 + 0.930937i \(0.381008\pi\)
\(710\) 0 0
\(711\) 2.22128 0.0833046
\(712\) 0 0
\(713\) 3.73130 0.139738
\(714\) 0 0
\(715\) −16.1262 −0.603085
\(716\) 0 0
\(717\) −25.8036 −0.963652
\(718\) 0 0
\(719\) 26.2733 0.979827 0.489914 0.871771i \(-0.337028\pi\)
0.489914 + 0.871771i \(0.337028\pi\)
\(720\) 0 0
\(721\) 70.8143 2.63726
\(722\) 0 0
\(723\) −27.3656 −1.01774
\(724\) 0 0
\(725\) 4.19480 0.155791
\(726\) 0 0
\(727\) 28.3921 1.05300 0.526502 0.850174i \(-0.323503\pi\)
0.526502 + 0.850174i \(0.323503\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.42674 −0.200715
\(732\) 0 0
\(733\) 46.1551 1.70478 0.852389 0.522909i \(-0.175153\pi\)
0.852389 + 0.522909i \(0.175153\pi\)
\(734\) 0 0
\(735\) 6.77638 0.249951
\(736\) 0 0
\(737\) 74.9600 2.76119
\(738\) 0 0
\(739\) −4.13404 −0.152073 −0.0760365 0.997105i \(-0.524227\pi\)
−0.0760365 + 0.997105i \(0.524227\pi\)
\(740\) 0 0
\(741\) 26.7950 0.984337
\(742\) 0 0
\(743\) −31.3373 −1.14965 −0.574826 0.818276i \(-0.694930\pi\)
−0.574826 + 0.818276i \(0.694930\pi\)
\(744\) 0 0
\(745\) −0.0483886 −0.00177282
\(746\) 0 0
\(747\) 2.48600 0.0909581
\(748\) 0 0
\(749\) 48.8495 1.78492
\(750\) 0 0
\(751\) 15.2978 0.558226 0.279113 0.960258i \(-0.409960\pi\)
0.279113 + 0.960258i \(0.409960\pi\)
\(752\) 0 0
\(753\) −2.14400 −0.0781315
\(754\) 0 0
\(755\) −8.93229 −0.325079
\(756\) 0 0
\(757\) −38.9382 −1.41523 −0.707617 0.706596i \(-0.750230\pi\)
−0.707617 + 0.706596i \(0.750230\pi\)
\(758\) 0 0
\(759\) 5.23385 0.189977
\(760\) 0 0
\(761\) −16.3325 −0.592054 −0.296027 0.955180i \(-0.595662\pi\)
−0.296027 + 0.955180i \(0.595662\pi\)
\(762\) 0 0
\(763\) −4.15500 −0.150421
\(764\) 0 0
\(765\) 1.72455 0.0623513
\(766\) 0 0
\(767\) 10.5204 0.379868
\(768\) 0 0
\(769\) −52.3619 −1.88822 −0.944109 0.329634i \(-0.893075\pi\)
−0.944109 + 0.329634i \(0.893075\pi\)
\(770\) 0 0
\(771\) −18.0033 −0.648373
\(772\) 0 0
\(773\) −20.5849 −0.740388 −0.370194 0.928955i \(-0.620709\pi\)
−0.370194 + 0.928955i \(0.620709\pi\)
\(774\) 0 0
\(775\) −15.6521 −0.562239
\(776\) 0 0
\(777\) 3.58515 0.128617
\(778\) 0 0
\(779\) 46.0759 1.65084
\(780\) 0 0
\(781\) 55.3675 1.98121
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −4.77910 −0.170573
\(786\) 0 0
\(787\) −54.1435 −1.93001 −0.965003 0.262239i \(-0.915539\pi\)
−0.965003 + 0.262239i \(0.915539\pi\)
\(788\) 0 0
\(789\) −10.5249 −0.374695
\(790\) 0 0
\(791\) 60.3589 2.14612
\(792\) 0 0
\(793\) −33.9485 −1.20555
\(794\) 0 0
\(795\) 11.1366 0.394974
\(796\) 0 0
\(797\) 50.2674 1.78056 0.890281 0.455412i \(-0.150508\pi\)
0.890281 + 0.455412i \(0.150508\pi\)
\(798\) 0 0
\(799\) 25.6328 0.906825
\(800\) 0 0
\(801\) −13.2715 −0.468926
\(802\) 0 0
\(803\) −48.3200 −1.70518
\(804\) 0 0
\(805\) 3.42302 0.120646
\(806\) 0 0
\(807\) 1.28161 0.0451149
\(808\) 0 0
\(809\) 7.91149 0.278153 0.139077 0.990282i \(-0.455587\pi\)
0.139077 + 0.990282i \(0.455587\pi\)
\(810\) 0 0
\(811\) −8.86464 −0.311280 −0.155640 0.987814i \(-0.549744\pi\)
−0.155640 + 0.987814i \(0.549744\pi\)
\(812\) 0 0
\(813\) −1.11624 −0.0391484
\(814\) 0 0
\(815\) 16.4790 0.577233
\(816\) 0 0
\(817\) 22.0349 0.770902
\(818\) 0 0
\(819\) −13.0983 −0.457692
\(820\) 0 0
\(821\) −1.24346 −0.0433970 −0.0216985 0.999765i \(-0.506907\pi\)
−0.0216985 + 0.999765i \(0.506907\pi\)
\(822\) 0 0
\(823\) −17.8486 −0.622163 −0.311081 0.950383i \(-0.600691\pi\)
−0.311081 + 0.950383i \(0.600691\pi\)
\(824\) 0 0
\(825\) −21.9549 −0.764372
\(826\) 0 0
\(827\) −14.7403 −0.512570 −0.256285 0.966601i \(-0.582499\pi\)
−0.256285 + 0.966601i \(0.582499\pi\)
\(828\) 0 0
\(829\) −2.83338 −0.0984075 −0.0492038 0.998789i \(-0.515668\pi\)
−0.0492038 + 0.998789i \(0.515668\pi\)
\(830\) 0 0
\(831\) 4.29599 0.149026
\(832\) 0 0
\(833\) 14.5134 0.502859
\(834\) 0 0
\(835\) −15.1075 −0.522816
\(836\) 0 0
\(837\) 3.73130 0.128973
\(838\) 0 0
\(839\) −17.7053 −0.611255 −0.305627 0.952151i \(-0.598866\pi\)
−0.305627 + 0.952151i \(0.598866\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −16.1931 −0.557720
\(844\) 0 0
\(845\) −1.08572 −0.0373500
\(846\) 0 0
\(847\) 62.5344 2.14871
\(848\) 0 0
\(849\) 4.02545 0.138153
\(850\) 0 0
\(851\) 0.939833 0.0322171
\(852\) 0 0
\(853\) −9.48557 −0.324780 −0.162390 0.986727i \(-0.551920\pi\)
−0.162390 + 0.986727i \(0.551920\pi\)
\(854\) 0 0
\(855\) −7.00241 −0.239477
\(856\) 0 0
\(857\) 13.4094 0.458058 0.229029 0.973420i \(-0.426445\pi\)
0.229029 + 0.973420i \(0.426445\pi\)
\(858\) 0 0
\(859\) −34.9045 −1.19093 −0.595463 0.803382i \(-0.703031\pi\)
−0.595463 + 0.803382i \(0.703031\pi\)
\(860\) 0 0
\(861\) −22.5235 −0.767599
\(862\) 0 0
\(863\) 38.8001 1.32077 0.660386 0.750926i \(-0.270393\pi\)
0.660386 + 0.750926i \(0.270393\pi\)
\(864\) 0 0
\(865\) −19.7666 −0.672085
\(866\) 0 0
\(867\) −13.3064 −0.451910
\(868\) 0 0
\(869\) 11.6258 0.394380
\(870\) 0 0
\(871\) −49.1775 −1.66632
\(872\) 0 0
\(873\) −7.70919 −0.260917
\(874\) 0 0
\(875\) −31.4740 −1.06401
\(876\) 0 0
\(877\) −22.4583 −0.758365 −0.379182 0.925322i \(-0.623795\pi\)
−0.379182 + 0.925322i \(0.623795\pi\)
\(878\) 0 0
\(879\) −21.5224 −0.725932
\(880\) 0 0
\(881\) 24.8079 0.835799 0.417900 0.908493i \(-0.362766\pi\)
0.417900 + 0.908493i \(0.362766\pi\)
\(882\) 0 0
\(883\) 1.03936 0.0349773 0.0174886 0.999847i \(-0.494433\pi\)
0.0174886 + 0.999847i \(0.494433\pi\)
\(884\) 0 0
\(885\) −2.74932 −0.0924173
\(886\) 0 0
\(887\) −5.32456 −0.178781 −0.0893906 0.995997i \(-0.528492\pi\)
−0.0893906 + 0.995997i \(0.528492\pi\)
\(888\) 0 0
\(889\) 80.0840 2.68593
\(890\) 0 0
\(891\) 5.23385 0.175340
\(892\) 0 0
\(893\) −104.080 −3.48291
\(894\) 0 0
\(895\) 2.06215 0.0689300
\(896\) 0 0
\(897\) −3.43366 −0.114647
\(898\) 0 0
\(899\) −3.73130 −0.124446
\(900\) 0 0
\(901\) 23.8519 0.794623
\(902\) 0 0
\(903\) −10.7714 −0.358450
\(904\) 0 0
\(905\) 1.74472 0.0579965
\(906\) 0 0
\(907\) −25.7645 −0.855497 −0.427749 0.903898i \(-0.640693\pi\)
−0.427749 + 0.903898i \(0.640693\pi\)
\(908\) 0 0
\(909\) 13.1086 0.434784
\(910\) 0 0
\(911\) −36.3906 −1.20567 −0.602837 0.797864i \(-0.705963\pi\)
−0.602837 + 0.797864i \(0.705963\pi\)
\(912\) 0 0
\(913\) 13.0114 0.430613
\(914\) 0 0
\(915\) 8.87187 0.293295
\(916\) 0 0
\(917\) −45.3326 −1.49702
\(918\) 0 0
\(919\) 30.3593 1.00146 0.500731 0.865603i \(-0.333065\pi\)
0.500731 + 0.865603i \(0.333065\pi\)
\(920\) 0 0
\(921\) 7.57632 0.249648
\(922\) 0 0
\(923\) −36.3239 −1.19561
\(924\) 0 0
\(925\) −3.94241 −0.129626
\(926\) 0 0
\(927\) 18.5637 0.609711
\(928\) 0 0
\(929\) 8.91679 0.292550 0.146275 0.989244i \(-0.453271\pi\)
0.146275 + 0.989244i \(0.453271\pi\)
\(930\) 0 0
\(931\) −58.9305 −1.93137
\(932\) 0 0
\(933\) −13.2050 −0.432313
\(934\) 0 0
\(935\) 9.02604 0.295183
\(936\) 0 0
\(937\) 30.9839 1.01220 0.506099 0.862475i \(-0.331087\pi\)
0.506099 + 0.862475i \(0.331087\pi\)
\(938\) 0 0
\(939\) 23.9026 0.780031
\(940\) 0 0
\(941\) 53.3625 1.73957 0.869783 0.493434i \(-0.164259\pi\)
0.869783 + 0.493434i \(0.164259\pi\)
\(942\) 0 0
\(943\) −5.90444 −0.192275
\(944\) 0 0
\(945\) 3.42302 0.111351
\(946\) 0 0
\(947\) −45.6156 −1.48231 −0.741155 0.671334i \(-0.765722\pi\)
−0.741155 + 0.671334i \(0.765722\pi\)
\(948\) 0 0
\(949\) 31.7003 1.02904
\(950\) 0 0
\(951\) −3.42802 −0.111161
\(952\) 0 0
\(953\) 22.5093 0.729147 0.364574 0.931175i \(-0.381215\pi\)
0.364574 + 0.931175i \(0.381215\pi\)
\(954\) 0 0
\(955\) 12.3199 0.398662
\(956\) 0 0
\(957\) −5.23385 −0.169186
\(958\) 0 0
\(959\) −37.1693 −1.20026
\(960\) 0 0
\(961\) −17.0774 −0.550883
\(962\) 0 0
\(963\) 12.8057 0.412658
\(964\) 0 0
\(965\) 12.5307 0.403378
\(966\) 0 0
\(967\) −2.31451 −0.0744295 −0.0372147 0.999307i \(-0.511849\pi\)
−0.0372147 + 0.999307i \(0.511849\pi\)
\(968\) 0 0
\(969\) −14.9975 −0.481789
\(970\) 0 0
\(971\) 29.4829 0.946152 0.473076 0.881022i \(-0.343144\pi\)
0.473076 + 0.881022i \(0.343144\pi\)
\(972\) 0 0
\(973\) −82.8237 −2.65521
\(974\) 0 0
\(975\) 14.4035 0.461282
\(976\) 0 0
\(977\) 13.0559 0.417697 0.208848 0.977948i \(-0.433029\pi\)
0.208848 + 0.977948i \(0.433029\pi\)
\(978\) 0 0
\(979\) −69.4611 −2.21999
\(980\) 0 0
\(981\) −1.08922 −0.0347760
\(982\) 0 0
\(983\) −7.30342 −0.232943 −0.116471 0.993194i \(-0.537158\pi\)
−0.116471 + 0.993194i \(0.537158\pi\)
\(984\) 0 0
\(985\) 6.14812 0.195895
\(986\) 0 0
\(987\) 50.8780 1.61946
\(988\) 0 0
\(989\) −2.82368 −0.0897877
\(990\) 0 0
\(991\) 4.49027 0.142638 0.0713190 0.997454i \(-0.477279\pi\)
0.0713190 + 0.997454i \(0.477279\pi\)
\(992\) 0 0
\(993\) 19.5447 0.620234
\(994\) 0 0
\(995\) 12.6488 0.400993
\(996\) 0 0
\(997\) 14.3467 0.454365 0.227183 0.973852i \(-0.427049\pi\)
0.227183 + 0.973852i \(0.427049\pi\)
\(998\) 0 0
\(999\) 0.939833 0.0297350
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 \(a_p\))