Properties

Label 4008.2.a.i.1.5
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.141931\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.858069 q^{5}\) \(+2.33225 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.858069 q^{5}\) \(+2.33225 q^{7}\) \(+1.00000 q^{9}\) \(+0.664078 q^{11}\) \(-2.80424 q^{13}\) \(-0.858069 q^{15}\) \(-4.73771 q^{17}\) \(-7.58466 q^{19}\) \(+2.33225 q^{21}\) \(+6.58999 q^{23}\) \(-4.26372 q^{25}\) \(+1.00000 q^{27}\) \(-4.75833 q^{29}\) \(-2.96038 q^{31}\) \(+0.664078 q^{33}\) \(-2.00123 q^{35}\) \(+4.12480 q^{37}\) \(-2.80424 q^{39}\) \(-7.76756 q^{41}\) \(+4.13938 q^{43}\) \(-0.858069 q^{45}\) \(-1.39111 q^{47}\) \(-1.56060 q^{49}\) \(-4.73771 q^{51}\) \(-1.74469 q^{53}\) \(-0.569824 q^{55}\) \(-7.58466 q^{57}\) \(-10.2363 q^{59}\) \(-0.762183 q^{61}\) \(+2.33225 q^{63}\) \(+2.40623 q^{65}\) \(+0.00130165 q^{67}\) \(+6.58999 q^{69}\) \(-2.99630 q^{71}\) \(-16.6717 q^{73}\) \(-4.26372 q^{75}\) \(+1.54880 q^{77}\) \(-10.5928 q^{79}\) \(+1.00000 q^{81}\) \(+17.4041 q^{83}\) \(+4.06528 q^{85}\) \(-4.75833 q^{87}\) \(-4.94100 q^{89}\) \(-6.54021 q^{91}\) \(-2.96038 q^{93}\) \(+6.50816 q^{95}\) \(+17.4544 q^{97}\) \(+0.664078 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 13q^{85} \) \(\mathstrut -\mathstrut 9q^{87} \) \(\mathstrut +\mathstrut 13q^{89} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.858069 −0.383740 −0.191870 0.981420i \(-0.561455\pi\)
−0.191870 + 0.981420i \(0.561455\pi\)
\(6\) 0 0
\(7\) 2.33225 0.881509 0.440754 0.897628i \(-0.354711\pi\)
0.440754 + 0.897628i \(0.354711\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.664078 0.200227 0.100113 0.994976i \(-0.468079\pi\)
0.100113 + 0.994976i \(0.468079\pi\)
\(12\) 0 0
\(13\) −2.80424 −0.777757 −0.388879 0.921289i \(-0.627137\pi\)
−0.388879 + 0.921289i \(0.627137\pi\)
\(14\) 0 0
\(15\) −0.858069 −0.221552
\(16\) 0 0
\(17\) −4.73771 −1.14906 −0.574532 0.818482i \(-0.694816\pi\)
−0.574532 + 0.818482i \(0.694816\pi\)
\(18\) 0 0
\(19\) −7.58466 −1.74004 −0.870021 0.493015i \(-0.835895\pi\)
−0.870021 + 0.493015i \(0.835895\pi\)
\(20\) 0 0
\(21\) 2.33225 0.508939
\(22\) 0 0
\(23\) 6.58999 1.37411 0.687054 0.726606i \(-0.258903\pi\)
0.687054 + 0.726606i \(0.258903\pi\)
\(24\) 0 0
\(25\) −4.26372 −0.852744
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.75833 −0.883600 −0.441800 0.897114i \(-0.645660\pi\)
−0.441800 + 0.897114i \(0.645660\pi\)
\(30\) 0 0
\(31\) −2.96038 −0.531700 −0.265850 0.964014i \(-0.585653\pi\)
−0.265850 + 0.964014i \(0.585653\pi\)
\(32\) 0 0
\(33\) 0.664078 0.115601
\(34\) 0 0
\(35\) −2.00123 −0.338270
\(36\) 0 0
\(37\) 4.12480 0.678113 0.339056 0.940766i \(-0.389892\pi\)
0.339056 + 0.940766i \(0.389892\pi\)
\(38\) 0 0
\(39\) −2.80424 −0.449038
\(40\) 0 0
\(41\) −7.76756 −1.21309 −0.606544 0.795050i \(-0.707445\pi\)
−0.606544 + 0.795050i \(0.707445\pi\)
\(42\) 0 0
\(43\) 4.13938 0.631249 0.315624 0.948884i \(-0.397786\pi\)
0.315624 + 0.948884i \(0.397786\pi\)
\(44\) 0 0
\(45\) −0.858069 −0.127913
\(46\) 0 0
\(47\) −1.39111 −0.202914 −0.101457 0.994840i \(-0.532350\pi\)
−0.101457 + 0.994840i \(0.532350\pi\)
\(48\) 0 0
\(49\) −1.56060 −0.222942
\(50\) 0 0
\(51\) −4.73771 −0.663412
\(52\) 0 0
\(53\) −1.74469 −0.239651 −0.119826 0.992795i \(-0.538234\pi\)
−0.119826 + 0.992795i \(0.538234\pi\)
\(54\) 0 0
\(55\) −0.569824 −0.0768351
\(56\) 0 0
\(57\) −7.58466 −1.00461
\(58\) 0 0
\(59\) −10.2363 −1.33265 −0.666325 0.745661i \(-0.732134\pi\)
−0.666325 + 0.745661i \(0.732134\pi\)
\(60\) 0 0
\(61\) −0.762183 −0.0975875 −0.0487937 0.998809i \(-0.515538\pi\)
−0.0487937 + 0.998809i \(0.515538\pi\)
\(62\) 0 0
\(63\) 2.33225 0.293836
\(64\) 0 0
\(65\) 2.40623 0.298457
\(66\) 0 0
\(67\) 0.00130165 0.000159022 0 7.95109e−5 1.00000i \(-0.499975\pi\)
7.95109e−5 1.00000i \(0.499975\pi\)
\(68\) 0 0
\(69\) 6.58999 0.793342
\(70\) 0 0
\(71\) −2.99630 −0.355596 −0.177798 0.984067i \(-0.556897\pi\)
−0.177798 + 0.984067i \(0.556897\pi\)
\(72\) 0 0
\(73\) −16.6717 −1.95128 −0.975640 0.219379i \(-0.929597\pi\)
−0.975640 + 0.219379i \(0.929597\pi\)
\(74\) 0 0
\(75\) −4.26372 −0.492332
\(76\) 0 0
\(77\) 1.54880 0.176502
\(78\) 0 0
\(79\) −10.5928 −1.19178 −0.595891 0.803065i \(-0.703201\pi\)
−0.595891 + 0.803065i \(0.703201\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 17.4041 1.91035 0.955177 0.296037i \(-0.0956650\pi\)
0.955177 + 0.296037i \(0.0956650\pi\)
\(84\) 0 0
\(85\) 4.06528 0.440941
\(86\) 0 0
\(87\) −4.75833 −0.510147
\(88\) 0 0
\(89\) −4.94100 −0.523745 −0.261872 0.965103i \(-0.584340\pi\)
−0.261872 + 0.965103i \(0.584340\pi\)
\(90\) 0 0
\(91\) −6.54021 −0.685600
\(92\) 0 0
\(93\) −2.96038 −0.306977
\(94\) 0 0
\(95\) 6.50816 0.667723
\(96\) 0 0
\(97\) 17.4544 1.77222 0.886112 0.463471i \(-0.153396\pi\)
0.886112 + 0.463471i \(0.153396\pi\)
\(98\) 0 0
\(99\) 0.664078 0.0667423
\(100\) 0 0
\(101\) 2.83624 0.282216 0.141108 0.989994i \(-0.454933\pi\)
0.141108 + 0.989994i \(0.454933\pi\)
\(102\) 0 0
\(103\) 1.68361 0.165891 0.0829454 0.996554i \(-0.473567\pi\)
0.0829454 + 0.996554i \(0.473567\pi\)
\(104\) 0 0
\(105\) −2.00123 −0.195300
\(106\) 0 0
\(107\) 10.4960 1.01468 0.507341 0.861745i \(-0.330628\pi\)
0.507341 + 0.861745i \(0.330628\pi\)
\(108\) 0 0
\(109\) −3.61751 −0.346494 −0.173247 0.984878i \(-0.555426\pi\)
−0.173247 + 0.984878i \(0.555426\pi\)
\(110\) 0 0
\(111\) 4.12480 0.391509
\(112\) 0 0
\(113\) 2.15002 0.202257 0.101129 0.994873i \(-0.467755\pi\)
0.101129 + 0.994873i \(0.467755\pi\)
\(114\) 0 0
\(115\) −5.65467 −0.527300
\(116\) 0 0
\(117\) −2.80424 −0.259252
\(118\) 0 0
\(119\) −11.0495 −1.01291
\(120\) 0 0
\(121\) −10.5590 −0.959909
\(122\) 0 0
\(123\) −7.76756 −0.700377
\(124\) 0 0
\(125\) 7.94891 0.710972
\(126\) 0 0
\(127\) −12.3626 −1.09701 −0.548504 0.836148i \(-0.684802\pi\)
−0.548504 + 0.836148i \(0.684802\pi\)
\(128\) 0 0
\(129\) 4.13938 0.364452
\(130\) 0 0
\(131\) 20.5805 1.79812 0.899061 0.437822i \(-0.144250\pi\)
0.899061 + 0.437822i \(0.144250\pi\)
\(132\) 0 0
\(133\) −17.6894 −1.53386
\(134\) 0 0
\(135\) −0.858069 −0.0738508
\(136\) 0 0
\(137\) 10.1249 0.865031 0.432515 0.901627i \(-0.357626\pi\)
0.432515 + 0.901627i \(0.357626\pi\)
\(138\) 0 0
\(139\) 1.84695 0.156656 0.0783280 0.996928i \(-0.475042\pi\)
0.0783280 + 0.996928i \(0.475042\pi\)
\(140\) 0 0
\(141\) −1.39111 −0.117153
\(142\) 0 0
\(143\) −1.86224 −0.155728
\(144\) 0 0
\(145\) 4.08297 0.339073
\(146\) 0 0
\(147\) −1.56060 −0.128716
\(148\) 0 0
\(149\) 5.36994 0.439922 0.219961 0.975509i \(-0.429407\pi\)
0.219961 + 0.975509i \(0.429407\pi\)
\(150\) 0 0
\(151\) −13.0563 −1.06251 −0.531254 0.847213i \(-0.678279\pi\)
−0.531254 + 0.847213i \(0.678279\pi\)
\(152\) 0 0
\(153\) −4.73771 −0.383021
\(154\) 0 0
\(155\) 2.54021 0.204034
\(156\) 0 0
\(157\) 5.47662 0.437082 0.218541 0.975828i \(-0.429870\pi\)
0.218541 + 0.975828i \(0.429870\pi\)
\(158\) 0 0
\(159\) −1.74469 −0.138363
\(160\) 0 0
\(161\) 15.3695 1.21129
\(162\) 0 0
\(163\) 18.0321 1.41239 0.706193 0.708019i \(-0.250411\pi\)
0.706193 + 0.708019i \(0.250411\pi\)
\(164\) 0 0
\(165\) −0.569824 −0.0443607
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −5.13621 −0.395093
\(170\) 0 0
\(171\) −7.58466 −0.580014
\(172\) 0 0
\(173\) 11.9069 0.905266 0.452633 0.891697i \(-0.350485\pi\)
0.452633 + 0.891697i \(0.350485\pi\)
\(174\) 0 0
\(175\) −9.94407 −0.751701
\(176\) 0 0
\(177\) −10.2363 −0.769406
\(178\) 0 0
\(179\) −9.99610 −0.747144 −0.373572 0.927601i \(-0.621867\pi\)
−0.373572 + 0.927601i \(0.621867\pi\)
\(180\) 0 0
\(181\) −12.9764 −0.964526 −0.482263 0.876027i \(-0.660185\pi\)
−0.482263 + 0.876027i \(0.660185\pi\)
\(182\) 0 0
\(183\) −0.762183 −0.0563422
\(184\) 0 0
\(185\) −3.53936 −0.260219
\(186\) 0 0
\(187\) −3.14621 −0.230073
\(188\) 0 0
\(189\) 2.33225 0.169646
\(190\) 0 0
\(191\) −0.780931 −0.0565062 −0.0282531 0.999601i \(-0.508994\pi\)
−0.0282531 + 0.999601i \(0.508994\pi\)
\(192\) 0 0
\(193\) −3.18460 −0.229232 −0.114616 0.993410i \(-0.536564\pi\)
−0.114616 + 0.993410i \(0.536564\pi\)
\(194\) 0 0
\(195\) 2.40623 0.172314
\(196\) 0 0
\(197\) −7.29302 −0.519606 −0.259803 0.965662i \(-0.583658\pi\)
−0.259803 + 0.965662i \(0.583658\pi\)
\(198\) 0 0
\(199\) −20.4949 −1.45284 −0.726422 0.687249i \(-0.758818\pi\)
−0.726422 + 0.687249i \(0.758818\pi\)
\(200\) 0 0
\(201\) 0.00130165 9.18113e−5 0
\(202\) 0 0
\(203\) −11.0976 −0.778901
\(204\) 0 0
\(205\) 6.66510 0.465511
\(206\) 0 0
\(207\) 6.58999 0.458036
\(208\) 0 0
\(209\) −5.03681 −0.348403
\(210\) 0 0
\(211\) 2.79418 0.192359 0.0961795 0.995364i \(-0.469338\pi\)
0.0961795 + 0.995364i \(0.469338\pi\)
\(212\) 0 0
\(213\) −2.99630 −0.205303
\(214\) 0 0
\(215\) −3.55187 −0.242235
\(216\) 0 0
\(217\) −6.90435 −0.468698
\(218\) 0 0
\(219\) −16.6717 −1.12657
\(220\) 0 0
\(221\) 13.2857 0.893692
\(222\) 0 0
\(223\) −1.07046 −0.0716830 −0.0358415 0.999357i \(-0.511411\pi\)
−0.0358415 + 0.999357i \(0.511411\pi\)
\(224\) 0 0
\(225\) −4.26372 −0.284248
\(226\) 0 0
\(227\) −3.06628 −0.203516 −0.101758 0.994809i \(-0.532447\pi\)
−0.101758 + 0.994809i \(0.532447\pi\)
\(228\) 0 0
\(229\) −0.166978 −0.0110342 −0.00551710 0.999985i \(-0.501756\pi\)
−0.00551710 + 0.999985i \(0.501756\pi\)
\(230\) 0 0
\(231\) 1.54880 0.101903
\(232\) 0 0
\(233\) 9.75862 0.639309 0.319654 0.947534i \(-0.396433\pi\)
0.319654 + 0.947534i \(0.396433\pi\)
\(234\) 0 0
\(235\) 1.19367 0.0778663
\(236\) 0 0
\(237\) −10.5928 −0.688076
\(238\) 0 0
\(239\) −27.8243 −1.79980 −0.899902 0.436093i \(-0.856362\pi\)
−0.899902 + 0.436093i \(0.856362\pi\)
\(240\) 0 0
\(241\) −6.03419 −0.388696 −0.194348 0.980933i \(-0.562259\pi\)
−0.194348 + 0.980933i \(0.562259\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.33910 0.0855519
\(246\) 0 0
\(247\) 21.2693 1.35333
\(248\) 0 0
\(249\) 17.4041 1.10294
\(250\) 0 0
\(251\) −19.2169 −1.21296 −0.606481 0.795098i \(-0.707419\pi\)
−0.606481 + 0.795098i \(0.707419\pi\)
\(252\) 0 0
\(253\) 4.37627 0.275133
\(254\) 0 0
\(255\) 4.06528 0.254578
\(256\) 0 0
\(257\) −8.38942 −0.523318 −0.261659 0.965160i \(-0.584270\pi\)
−0.261659 + 0.965160i \(0.584270\pi\)
\(258\) 0 0
\(259\) 9.62007 0.597762
\(260\) 0 0
\(261\) −4.75833 −0.294533
\(262\) 0 0
\(263\) −16.9678 −1.04628 −0.523139 0.852247i \(-0.675239\pi\)
−0.523139 + 0.852247i \(0.675239\pi\)
\(264\) 0 0
\(265\) 1.49706 0.0919638
\(266\) 0 0
\(267\) −4.94100 −0.302384
\(268\) 0 0
\(269\) −13.6797 −0.834068 −0.417034 0.908891i \(-0.636930\pi\)
−0.417034 + 0.908891i \(0.636930\pi\)
\(270\) 0 0
\(271\) −16.2857 −0.989284 −0.494642 0.869097i \(-0.664701\pi\)
−0.494642 + 0.869097i \(0.664701\pi\)
\(272\) 0 0
\(273\) −6.54021 −0.395831
\(274\) 0 0
\(275\) −2.83144 −0.170742
\(276\) 0 0
\(277\) −4.11423 −0.247200 −0.123600 0.992332i \(-0.539444\pi\)
−0.123600 + 0.992332i \(0.539444\pi\)
\(278\) 0 0
\(279\) −2.96038 −0.177233
\(280\) 0 0
\(281\) 29.3388 1.75020 0.875102 0.483939i \(-0.160794\pi\)
0.875102 + 0.483939i \(0.160794\pi\)
\(282\) 0 0
\(283\) −16.5471 −0.983621 −0.491810 0.870702i \(-0.663665\pi\)
−0.491810 + 0.870702i \(0.663665\pi\)
\(284\) 0 0
\(285\) 6.50816 0.385510
\(286\) 0 0
\(287\) −18.1159 −1.06935
\(288\) 0 0
\(289\) 5.44589 0.320346
\(290\) 0 0
\(291\) 17.4544 1.02319
\(292\) 0 0
\(293\) −31.9181 −1.86468 −0.932338 0.361588i \(-0.882235\pi\)
−0.932338 + 0.361588i \(0.882235\pi\)
\(294\) 0 0
\(295\) 8.78344 0.511391
\(296\) 0 0
\(297\) 0.664078 0.0385337
\(298\) 0 0
\(299\) −18.4799 −1.06872
\(300\) 0 0
\(301\) 9.65407 0.556451
\(302\) 0 0
\(303\) 2.83624 0.162938
\(304\) 0 0
\(305\) 0.654005 0.0374482
\(306\) 0 0
\(307\) −12.7567 −0.728063 −0.364031 0.931387i \(-0.618600\pi\)
−0.364031 + 0.931387i \(0.618600\pi\)
\(308\) 0 0
\(309\) 1.68361 0.0957771
\(310\) 0 0
\(311\) −4.06532 −0.230523 −0.115262 0.993335i \(-0.536771\pi\)
−0.115262 + 0.993335i \(0.536771\pi\)
\(312\) 0 0
\(313\) −9.87994 −0.558447 −0.279224 0.960226i \(-0.590077\pi\)
−0.279224 + 0.960226i \(0.590077\pi\)
\(314\) 0 0
\(315\) −2.00123 −0.112757
\(316\) 0 0
\(317\) 11.2409 0.631353 0.315676 0.948867i \(-0.397769\pi\)
0.315676 + 0.948867i \(0.397769\pi\)
\(318\) 0 0
\(319\) −3.15990 −0.176920
\(320\) 0 0
\(321\) 10.4960 0.585827
\(322\) 0 0
\(323\) 35.9339 1.99942
\(324\) 0 0
\(325\) 11.9565 0.663228
\(326\) 0 0
\(327\) −3.61751 −0.200049
\(328\) 0 0
\(329\) −3.24442 −0.178871
\(330\) 0 0
\(331\) −14.6160 −0.803370 −0.401685 0.915778i \(-0.631575\pi\)
−0.401685 + 0.915778i \(0.631575\pi\)
\(332\) 0 0
\(333\) 4.12480 0.226038
\(334\) 0 0
\(335\) −0.00111690 −6.10230e−5 0
\(336\) 0 0
\(337\) 12.7052 0.692094 0.346047 0.938217i \(-0.387524\pi\)
0.346047 + 0.938217i \(0.387524\pi\)
\(338\) 0 0
\(339\) 2.15002 0.116773
\(340\) 0 0
\(341\) −1.96592 −0.106461
\(342\) 0 0
\(343\) −19.9655 −1.07803
\(344\) 0 0
\(345\) −5.65467 −0.304437
\(346\) 0 0
\(347\) 34.7085 1.86325 0.931625 0.363422i \(-0.118392\pi\)
0.931625 + 0.363422i \(0.118392\pi\)
\(348\) 0 0
\(349\) −0.432938 −0.0231746 −0.0115873 0.999933i \(-0.503688\pi\)
−0.0115873 + 0.999933i \(0.503688\pi\)
\(350\) 0 0
\(351\) −2.80424 −0.149679
\(352\) 0 0
\(353\) 15.5524 0.827769 0.413884 0.910329i \(-0.364172\pi\)
0.413884 + 0.910329i \(0.364172\pi\)
\(354\) 0 0
\(355\) 2.57103 0.136456
\(356\) 0 0
\(357\) −11.0495 −0.584803
\(358\) 0 0
\(359\) 12.9062 0.681163 0.340581 0.940215i \(-0.389376\pi\)
0.340581 + 0.940215i \(0.389376\pi\)
\(360\) 0 0
\(361\) 38.5271 2.02774
\(362\) 0 0
\(363\) −10.5590 −0.554204
\(364\) 0 0
\(365\) 14.3055 0.748784
\(366\) 0 0
\(367\) −24.5614 −1.28210 −0.641048 0.767501i \(-0.721500\pi\)
−0.641048 + 0.767501i \(0.721500\pi\)
\(368\) 0 0
\(369\) −7.76756 −0.404363
\(370\) 0 0
\(371\) −4.06905 −0.211255
\(372\) 0 0
\(373\) 25.7222 1.33184 0.665922 0.746021i \(-0.268038\pi\)
0.665922 + 0.746021i \(0.268038\pi\)
\(374\) 0 0
\(375\) 7.94891 0.410480
\(376\) 0 0
\(377\) 13.3435 0.687226
\(378\) 0 0
\(379\) 34.4480 1.76947 0.884737 0.466090i \(-0.154338\pi\)
0.884737 + 0.466090i \(0.154338\pi\)
\(380\) 0 0
\(381\) −12.3626 −0.633358
\(382\) 0 0
\(383\) 19.7939 1.01142 0.505711 0.862703i \(-0.331230\pi\)
0.505711 + 0.862703i \(0.331230\pi\)
\(384\) 0 0
\(385\) −1.32897 −0.0677308
\(386\) 0 0
\(387\) 4.13938 0.210416
\(388\) 0 0
\(389\) 18.5357 0.939798 0.469899 0.882720i \(-0.344290\pi\)
0.469899 + 0.882720i \(0.344290\pi\)
\(390\) 0 0
\(391\) −31.2215 −1.57894
\(392\) 0 0
\(393\) 20.5805 1.03815
\(394\) 0 0
\(395\) 9.08935 0.457335
\(396\) 0 0
\(397\) −5.39197 −0.270615 −0.135308 0.990804i \(-0.543202\pi\)
−0.135308 + 0.990804i \(0.543202\pi\)
\(398\) 0 0
\(399\) −17.6894 −0.885575
\(400\) 0 0
\(401\) −13.8183 −0.690055 −0.345027 0.938593i \(-0.612130\pi\)
−0.345027 + 0.938593i \(0.612130\pi\)
\(402\) 0 0
\(403\) 8.30163 0.413534
\(404\) 0 0
\(405\) −0.858069 −0.0426378
\(406\) 0 0
\(407\) 2.73919 0.135776
\(408\) 0 0
\(409\) 6.26519 0.309794 0.154897 0.987931i \(-0.450495\pi\)
0.154897 + 0.987931i \(0.450495\pi\)
\(410\) 0 0
\(411\) 10.1249 0.499426
\(412\) 0 0
\(413\) −23.8736 −1.17474
\(414\) 0 0
\(415\) −14.9340 −0.733079
\(416\) 0 0
\(417\) 1.84695 0.0904454
\(418\) 0 0
\(419\) 0.914237 0.0446634 0.0223317 0.999751i \(-0.492891\pi\)
0.0223317 + 0.999751i \(0.492891\pi\)
\(420\) 0 0
\(421\) 31.5414 1.53723 0.768617 0.639709i \(-0.220945\pi\)
0.768617 + 0.639709i \(0.220945\pi\)
\(422\) 0 0
\(423\) −1.39111 −0.0676381
\(424\) 0 0
\(425\) 20.2003 0.979856
\(426\) 0 0
\(427\) −1.77760 −0.0860242
\(428\) 0 0
\(429\) −1.86224 −0.0899096
\(430\) 0 0
\(431\) 38.5807 1.85837 0.929184 0.369619i \(-0.120512\pi\)
0.929184 + 0.369619i \(0.120512\pi\)
\(432\) 0 0
\(433\) 8.12866 0.390639 0.195319 0.980740i \(-0.437426\pi\)
0.195319 + 0.980740i \(0.437426\pi\)
\(434\) 0 0
\(435\) 4.08297 0.195764
\(436\) 0 0
\(437\) −49.9829 −2.39101
\(438\) 0 0
\(439\) −28.3001 −1.35069 −0.675344 0.737503i \(-0.736005\pi\)
−0.675344 + 0.737503i \(0.736005\pi\)
\(440\) 0 0
\(441\) −1.56060 −0.0743141
\(442\) 0 0
\(443\) −38.5945 −1.83368 −0.916841 0.399253i \(-0.869269\pi\)
−0.916841 + 0.399253i \(0.869269\pi\)
\(444\) 0 0
\(445\) 4.23971 0.200982
\(446\) 0 0
\(447\) 5.36994 0.253989
\(448\) 0 0
\(449\) 9.70687 0.458096 0.229048 0.973415i \(-0.426439\pi\)
0.229048 + 0.973415i \(0.426439\pi\)
\(450\) 0 0
\(451\) −5.15826 −0.242893
\(452\) 0 0
\(453\) −13.0563 −0.613439
\(454\) 0 0
\(455\) 5.61195 0.263092
\(456\) 0 0
\(457\) −25.1697 −1.17739 −0.588694 0.808356i \(-0.700358\pi\)
−0.588694 + 0.808356i \(0.700358\pi\)
\(458\) 0 0
\(459\) −4.73771 −0.221137
\(460\) 0 0
\(461\) 33.4704 1.55887 0.779435 0.626483i \(-0.215506\pi\)
0.779435 + 0.626483i \(0.215506\pi\)
\(462\) 0 0
\(463\) 23.8185 1.10694 0.553469 0.832870i \(-0.313304\pi\)
0.553469 + 0.832870i \(0.313304\pi\)
\(464\) 0 0
\(465\) 2.54021 0.117799
\(466\) 0 0
\(467\) 5.42414 0.250999 0.125500 0.992094i \(-0.459947\pi\)
0.125500 + 0.992094i \(0.459947\pi\)
\(468\) 0 0
\(469\) 0.00303578 0.000140179 0
\(470\) 0 0
\(471\) 5.47662 0.252349
\(472\) 0 0
\(473\) 2.74887 0.126393
\(474\) 0 0
\(475\) 32.3389 1.48381
\(476\) 0 0
\(477\) −1.74469 −0.0798838
\(478\) 0 0
\(479\) 12.8509 0.587172 0.293586 0.955933i \(-0.405151\pi\)
0.293586 + 0.955933i \(0.405151\pi\)
\(480\) 0 0
\(481\) −11.5669 −0.527407
\(482\) 0 0
\(483\) 15.3695 0.699338
\(484\) 0 0
\(485\) −14.9771 −0.680073
\(486\) 0 0
\(487\) −32.9193 −1.49171 −0.745857 0.666106i \(-0.767960\pi\)
−0.745857 + 0.666106i \(0.767960\pi\)
\(488\) 0 0
\(489\) 18.0321 0.815442
\(490\) 0 0
\(491\) −23.3929 −1.05571 −0.527854 0.849335i \(-0.677003\pi\)
−0.527854 + 0.849335i \(0.677003\pi\)
\(492\) 0 0
\(493\) 22.5436 1.01531
\(494\) 0 0
\(495\) −0.569824 −0.0256117
\(496\) 0 0
\(497\) −6.98813 −0.313461
\(498\) 0 0
\(499\) 7.77468 0.348042 0.174021 0.984742i \(-0.444324\pi\)
0.174021 + 0.984742i \(0.444324\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −11.5995 −0.517195 −0.258597 0.965985i \(-0.583260\pi\)
−0.258597 + 0.965985i \(0.583260\pi\)
\(504\) 0 0
\(505\) −2.43369 −0.108298
\(506\) 0 0
\(507\) −5.13621 −0.228107
\(508\) 0 0
\(509\) −14.3183 −0.634646 −0.317323 0.948317i \(-0.602784\pi\)
−0.317323 + 0.948317i \(0.602784\pi\)
\(510\) 0 0
\(511\) −38.8827 −1.72007
\(512\) 0 0
\(513\) −7.58466 −0.334871
\(514\) 0 0
\(515\) −1.44465 −0.0636590
\(516\) 0 0
\(517\) −0.923805 −0.0406289
\(518\) 0 0
\(519\) 11.9069 0.522656
\(520\) 0 0
\(521\) 24.7954 1.08631 0.543153 0.839633i \(-0.317230\pi\)
0.543153 + 0.839633i \(0.317230\pi\)
\(522\) 0 0
\(523\) 15.8863 0.694660 0.347330 0.937743i \(-0.387088\pi\)
0.347330 + 0.937743i \(0.387088\pi\)
\(524\) 0 0
\(525\) −9.94407 −0.433995
\(526\) 0 0
\(527\) 14.0254 0.610957
\(528\) 0 0
\(529\) 20.4280 0.888174
\(530\) 0 0
\(531\) −10.2363 −0.444217
\(532\) 0 0
\(533\) 21.7821 0.943489
\(534\) 0 0
\(535\) −9.00625 −0.389374
\(536\) 0 0
\(537\) −9.99610 −0.431364
\(538\) 0 0
\(539\) −1.03636 −0.0446391
\(540\) 0 0
\(541\) −34.8029 −1.49629 −0.748147 0.663532i \(-0.769056\pi\)
−0.748147 + 0.663532i \(0.769056\pi\)
\(542\) 0 0
\(543\) −12.9764 −0.556869
\(544\) 0 0
\(545\) 3.10407 0.132964
\(546\) 0 0
\(547\) −16.7384 −0.715682 −0.357841 0.933782i \(-0.616487\pi\)
−0.357841 + 0.933782i \(0.616487\pi\)
\(548\) 0 0
\(549\) −0.762183 −0.0325292
\(550\) 0 0
\(551\) 36.0903 1.53750
\(552\) 0 0
\(553\) −24.7051 −1.05057
\(554\) 0 0
\(555\) −3.53936 −0.150237
\(556\) 0 0
\(557\) −4.14278 −0.175535 −0.0877677 0.996141i \(-0.527973\pi\)
−0.0877677 + 0.996141i \(0.527973\pi\)
\(558\) 0 0
\(559\) −11.6078 −0.490959
\(560\) 0 0
\(561\) −3.14621 −0.132833
\(562\) 0 0
\(563\) 31.1358 1.31222 0.656109 0.754666i \(-0.272201\pi\)
0.656109 + 0.754666i \(0.272201\pi\)
\(564\) 0 0
\(565\) −1.84487 −0.0776142
\(566\) 0 0
\(567\) 2.33225 0.0979454
\(568\) 0 0
\(569\) −16.2278 −0.680305 −0.340153 0.940370i \(-0.610479\pi\)
−0.340153 + 0.940370i \(0.610479\pi\)
\(570\) 0 0
\(571\) −15.7948 −0.660991 −0.330495 0.943808i \(-0.607216\pi\)
−0.330495 + 0.943808i \(0.607216\pi\)
\(572\) 0 0
\(573\) −0.780931 −0.0326239
\(574\) 0 0
\(575\) −28.0979 −1.17176
\(576\) 0 0
\(577\) 29.3450 1.22165 0.610825 0.791766i \(-0.290838\pi\)
0.610825 + 0.791766i \(0.290838\pi\)
\(578\) 0 0
\(579\) −3.18460 −0.132347
\(580\) 0 0
\(581\) 40.5909 1.68399
\(582\) 0 0
\(583\) −1.15861 −0.0479847
\(584\) 0 0
\(585\) 2.40623 0.0994855
\(586\) 0 0
\(587\) 3.97172 0.163931 0.0819653 0.996635i \(-0.473880\pi\)
0.0819653 + 0.996635i \(0.473880\pi\)
\(588\) 0 0
\(589\) 22.4535 0.925180
\(590\) 0 0
\(591\) −7.29302 −0.299995
\(592\) 0 0
\(593\) 13.0664 0.536573 0.268286 0.963339i \(-0.413543\pi\)
0.268286 + 0.963339i \(0.413543\pi\)
\(594\) 0 0
\(595\) 9.48126 0.388694
\(596\) 0 0
\(597\) −20.4949 −0.838800
\(598\) 0 0
\(599\) 26.1897 1.07008 0.535042 0.844826i \(-0.320296\pi\)
0.535042 + 0.844826i \(0.320296\pi\)
\(600\) 0 0
\(601\) 31.0894 1.26816 0.634082 0.773266i \(-0.281378\pi\)
0.634082 + 0.773266i \(0.281378\pi\)
\(602\) 0 0
\(603\) 0.00130165 5.30073e−5 0
\(604\) 0 0
\(605\) 9.06035 0.368356
\(606\) 0 0
\(607\) 7.46967 0.303185 0.151592 0.988443i \(-0.451560\pi\)
0.151592 + 0.988443i \(0.451560\pi\)
\(608\) 0 0
\(609\) −11.0976 −0.449699
\(610\) 0 0
\(611\) 3.90101 0.157818
\(612\) 0 0
\(613\) −7.66230 −0.309477 −0.154739 0.987955i \(-0.549454\pi\)
−0.154739 + 0.987955i \(0.549454\pi\)
\(614\) 0 0
\(615\) 6.66510 0.268763
\(616\) 0 0
\(617\) 11.5871 0.466479 0.233239 0.972419i \(-0.425067\pi\)
0.233239 + 0.972419i \(0.425067\pi\)
\(618\) 0 0
\(619\) 4.39728 0.176741 0.0883707 0.996088i \(-0.471834\pi\)
0.0883707 + 0.996088i \(0.471834\pi\)
\(620\) 0 0
\(621\) 6.58999 0.264447
\(622\) 0 0
\(623\) −11.5237 −0.461685
\(624\) 0 0
\(625\) 14.4979 0.579915
\(626\) 0 0
\(627\) −5.03681 −0.201151
\(628\) 0 0
\(629\) −19.5421 −0.779194
\(630\) 0 0
\(631\) −25.3849 −1.01056 −0.505279 0.862956i \(-0.668610\pi\)
−0.505279 + 0.862956i \(0.668610\pi\)
\(632\) 0 0
\(633\) 2.79418 0.111059
\(634\) 0 0
\(635\) 10.6080 0.420966
\(636\) 0 0
\(637\) 4.37629 0.173395
\(638\) 0 0
\(639\) −2.99630 −0.118532
\(640\) 0 0
\(641\) 23.9833 0.947283 0.473642 0.880718i \(-0.342939\pi\)
0.473642 + 0.880718i \(0.342939\pi\)
\(642\) 0 0
\(643\) −27.3549 −1.07877 −0.539386 0.842059i \(-0.681344\pi\)
−0.539386 + 0.842059i \(0.681344\pi\)
\(644\) 0 0
\(645\) −3.55187 −0.139855
\(646\) 0 0
\(647\) −8.92955 −0.351057 −0.175528 0.984474i \(-0.556163\pi\)
−0.175528 + 0.984474i \(0.556163\pi\)
\(648\) 0 0
\(649\) −6.79769 −0.266833
\(650\) 0 0
\(651\) −6.90435 −0.270603
\(652\) 0 0
\(653\) 1.42815 0.0558877 0.0279438 0.999609i \(-0.491104\pi\)
0.0279438 + 0.999609i \(0.491104\pi\)
\(654\) 0 0
\(655\) −17.6594 −0.690012
\(656\) 0 0
\(657\) −16.6717 −0.650426
\(658\) 0 0
\(659\) −20.7009 −0.806394 −0.403197 0.915113i \(-0.632101\pi\)
−0.403197 + 0.915113i \(0.632101\pi\)
\(660\) 0 0
\(661\) 13.2990 0.517272 0.258636 0.965975i \(-0.416727\pi\)
0.258636 + 0.965975i \(0.416727\pi\)
\(662\) 0 0
\(663\) 13.2857 0.515974
\(664\) 0 0
\(665\) 15.1787 0.588604
\(666\) 0 0
\(667\) −31.3574 −1.21416
\(668\) 0 0
\(669\) −1.07046 −0.0413862
\(670\) 0 0
\(671\) −0.506148 −0.0195396
\(672\) 0 0
\(673\) 12.6827 0.488882 0.244441 0.969664i \(-0.421396\pi\)
0.244441 + 0.969664i \(0.421396\pi\)
\(674\) 0 0
\(675\) −4.26372 −0.164111
\(676\) 0 0
\(677\) 2.60520 0.100126 0.0500629 0.998746i \(-0.484058\pi\)
0.0500629 + 0.998746i \(0.484058\pi\)
\(678\) 0 0
\(679\) 40.7080 1.56223
\(680\) 0 0
\(681\) −3.06628 −0.117500
\(682\) 0 0
\(683\) 24.5138 0.937995 0.468998 0.883199i \(-0.344615\pi\)
0.468998 + 0.883199i \(0.344615\pi\)
\(684\) 0 0
\(685\) −8.68788 −0.331947
\(686\) 0 0
\(687\) −0.166978 −0.00637060
\(688\) 0 0
\(689\) 4.89253 0.186391
\(690\) 0 0
\(691\) 32.0143 1.21788 0.608941 0.793215i \(-0.291595\pi\)
0.608941 + 0.793215i \(0.291595\pi\)
\(692\) 0 0
\(693\) 1.54880 0.0588339
\(694\) 0 0
\(695\) −1.58481 −0.0601152
\(696\) 0 0
\(697\) 36.8004 1.39392
\(698\) 0 0
\(699\) 9.75862 0.369105
\(700\) 0 0
\(701\) −4.88152 −0.184372 −0.0921862 0.995742i \(-0.529386\pi\)
−0.0921862 + 0.995742i \(0.529386\pi\)
\(702\) 0 0
\(703\) −31.2852 −1.17994
\(704\) 0 0
\(705\) 1.19367 0.0449561
\(706\) 0 0
\(707\) 6.61482 0.248776
\(708\) 0 0
\(709\) 42.2523 1.58682 0.793408 0.608690i \(-0.208305\pi\)
0.793408 + 0.608690i \(0.208305\pi\)
\(710\) 0 0
\(711\) −10.5928 −0.397261
\(712\) 0 0
\(713\) −19.5089 −0.730613
\(714\) 0 0
\(715\) 1.59793 0.0597590
\(716\) 0 0
\(717\) −27.8243 −1.03912
\(718\) 0 0
\(719\) −42.4125 −1.58172 −0.790860 0.611997i \(-0.790366\pi\)
−0.790860 + 0.611997i \(0.790366\pi\)
\(720\) 0 0
\(721\) 3.92660 0.146234
\(722\) 0 0
\(723\) −6.03419 −0.224414
\(724\) 0 0
\(725\) 20.2882 0.753484
\(726\) 0 0
\(727\) 22.1250 0.820570 0.410285 0.911957i \(-0.365429\pi\)
0.410285 + 0.911957i \(0.365429\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −19.6112 −0.725345
\(732\) 0 0
\(733\) 35.9161 1.32659 0.663297 0.748357i \(-0.269157\pi\)
0.663297 + 0.748357i \(0.269157\pi\)
\(734\) 0 0
\(735\) 1.33910 0.0493934
\(736\) 0 0
\(737\) 0.000864396 0 3.18404e−5 0
\(738\) 0 0
\(739\) −20.3434 −0.748344 −0.374172 0.927359i \(-0.622073\pi\)
−0.374172 + 0.927359i \(0.622073\pi\)
\(740\) 0 0
\(741\) 21.2693 0.781345
\(742\) 0 0
\(743\) 47.9841 1.76036 0.880182 0.474636i \(-0.157420\pi\)
0.880182 + 0.474636i \(0.157420\pi\)
\(744\) 0 0
\(745\) −4.60778 −0.168816
\(746\) 0 0
\(747\) 17.4041 0.636784
\(748\) 0 0
\(749\) 24.4792 0.894451
\(750\) 0 0
\(751\) 40.8830 1.49184 0.745922 0.666034i \(-0.232009\pi\)
0.745922 + 0.666034i \(0.232009\pi\)
\(752\) 0 0
\(753\) −19.2169 −0.700304
\(754\) 0 0
\(755\) 11.2032 0.407727
\(756\) 0 0
\(757\) 52.4727 1.90715 0.953576 0.301151i \(-0.0973708\pi\)
0.953576 + 0.301151i \(0.0973708\pi\)
\(758\) 0 0
\(759\) 4.37627 0.158848
\(760\) 0 0
\(761\) −30.9663 −1.12253 −0.561264 0.827636i \(-0.689685\pi\)
−0.561264 + 0.827636i \(0.689685\pi\)
\(762\) 0 0
\(763\) −8.43694 −0.305438
\(764\) 0 0
\(765\) 4.06528 0.146980
\(766\) 0 0
\(767\) 28.7050 1.03648
\(768\) 0 0
\(769\) −24.2091 −0.873003 −0.436501 0.899704i \(-0.643783\pi\)
−0.436501 + 0.899704i \(0.643783\pi\)
\(770\) 0 0
\(771\) −8.38942 −0.302138
\(772\) 0 0
\(773\) −13.4368 −0.483289 −0.241644 0.970365i \(-0.577687\pi\)
−0.241644 + 0.970365i \(0.577687\pi\)
\(774\) 0 0
\(775\) 12.6222 0.453404
\(776\) 0 0
\(777\) 9.62007 0.345118
\(778\) 0 0
\(779\) 58.9143 2.11082
\(780\) 0 0
\(781\) −1.98978 −0.0711998
\(782\) 0 0
\(783\) −4.75833 −0.170049
\(784\) 0 0
\(785\) −4.69932 −0.167726
\(786\) 0 0
\(787\) −38.7500 −1.38129 −0.690644 0.723195i \(-0.742673\pi\)
−0.690644 + 0.723195i \(0.742673\pi\)
\(788\) 0 0
\(789\) −16.9678 −0.604069
\(790\) 0 0
\(791\) 5.01440 0.178292
\(792\) 0 0
\(793\) 2.13735 0.0758994
\(794\) 0 0
\(795\) 1.49706 0.0530953
\(796\) 0 0
\(797\) −4.12743 −0.146201 −0.0731006 0.997325i \(-0.523289\pi\)
−0.0731006 + 0.997325i \(0.523289\pi\)
\(798\) 0 0
\(799\) 6.59067 0.233161
\(800\) 0 0
\(801\) −4.94100 −0.174582
\(802\) 0 0
\(803\) −11.0713 −0.390699
\(804\) 0 0
\(805\) −13.1881 −0.464820
\(806\) 0 0
\(807\) −13.6797 −0.481549
\(808\) 0 0
\(809\) −43.5841 −1.53233 −0.766167 0.642641i \(-0.777839\pi\)
−0.766167 + 0.642641i \(0.777839\pi\)
\(810\) 0 0
\(811\) −6.11071 −0.214576 −0.107288 0.994228i \(-0.534217\pi\)
−0.107288 + 0.994228i \(0.534217\pi\)
\(812\) 0 0
\(813\) −16.2857 −0.571163
\(814\) 0 0
\(815\) −15.4728 −0.541989
\(816\) 0 0
\(817\) −31.3958 −1.09840
\(818\) 0 0
\(819\) −6.54021 −0.228533
\(820\) 0 0
\(821\) −44.6483 −1.55824 −0.779118 0.626878i \(-0.784333\pi\)
−0.779118 + 0.626878i \(0.784333\pi\)
\(822\) 0 0
\(823\) −52.0320 −1.81372 −0.906861 0.421429i \(-0.861529\pi\)
−0.906861 + 0.421429i \(0.861529\pi\)
\(824\) 0 0
\(825\) −2.83144 −0.0985781
\(826\) 0 0
\(827\) 0.434728 0.0151170 0.00755849 0.999971i \(-0.497594\pi\)
0.00755849 + 0.999971i \(0.497594\pi\)
\(828\) 0 0
\(829\) 45.0928 1.56614 0.783069 0.621935i \(-0.213653\pi\)
0.783069 + 0.621935i \(0.213653\pi\)
\(830\) 0 0
\(831\) −4.11423 −0.142721
\(832\) 0 0
\(833\) 7.39365 0.256175
\(834\) 0 0
\(835\) 0.858069 0.0296947
\(836\) 0 0
\(837\) −2.96038 −0.102326
\(838\) 0 0
\(839\) −28.8473 −0.995919 −0.497960 0.867200i \(-0.665917\pi\)
−0.497960 + 0.867200i \(0.665917\pi\)
\(840\) 0 0
\(841\) −6.35829 −0.219251
\(842\) 0 0
\(843\) 29.3388 1.01048
\(844\) 0 0
\(845\) 4.40722 0.151613
\(846\) 0 0
\(847\) −24.6263 −0.846168
\(848\) 0 0
\(849\) −16.5471 −0.567894
\(850\) 0 0
\(851\) 27.1824 0.931800
\(852\) 0 0
\(853\) −34.0205 −1.16484 −0.582420 0.812888i \(-0.697894\pi\)
−0.582420 + 0.812888i \(0.697894\pi\)
\(854\) 0 0
\(855\) 6.50816 0.222574
\(856\) 0 0
\(857\) −4.41103 −0.150678 −0.0753389 0.997158i \(-0.524004\pi\)
−0.0753389 + 0.997158i \(0.524004\pi\)
\(858\) 0 0
\(859\) 0.717858 0.0244930 0.0122465 0.999925i \(-0.496102\pi\)
0.0122465 + 0.999925i \(0.496102\pi\)
\(860\) 0 0
\(861\) −18.1159 −0.617388
\(862\) 0 0
\(863\) 37.7870 1.28628 0.643142 0.765747i \(-0.277630\pi\)
0.643142 + 0.765747i \(0.277630\pi\)
\(864\) 0 0
\(865\) −10.2170 −0.347387
\(866\) 0 0
\(867\) 5.44589 0.184952
\(868\) 0 0
\(869\) −7.03444 −0.238627
\(870\) 0 0
\(871\) −0.00365014 −0.000123680 0
\(872\) 0 0
\(873\) 17.4544 0.590741
\(874\) 0 0
\(875\) 18.5389 0.626728
\(876\) 0 0
\(877\) −33.0599 −1.11635 −0.558177 0.829722i \(-0.688499\pi\)
−0.558177 + 0.829722i \(0.688499\pi\)
\(878\) 0 0
\(879\) −31.9181 −1.07657
\(880\) 0 0
\(881\) −33.8792 −1.14142 −0.570710 0.821152i \(-0.693332\pi\)
−0.570710 + 0.821152i \(0.693332\pi\)
\(882\) 0 0
\(883\) −36.9683 −1.24408 −0.622041 0.782985i \(-0.713696\pi\)
−0.622041 + 0.782985i \(0.713696\pi\)
\(884\) 0 0
\(885\) 8.78344 0.295252
\(886\) 0 0
\(887\) 27.6020 0.926786 0.463393 0.886153i \(-0.346632\pi\)
0.463393 + 0.886153i \(0.346632\pi\)
\(888\) 0 0
\(889\) −28.8328 −0.967022
\(890\) 0 0
\(891\) 0.664078 0.0222474
\(892\) 0 0
\(893\) 10.5511 0.353079
\(894\) 0 0
\(895\) 8.57734 0.286709
\(896\) 0 0
\(897\) −18.4799 −0.617027
\(898\) 0 0
\(899\) 14.0865 0.469810
\(900\) 0 0
\(901\) 8.26583 0.275375
\(902\) 0 0
\(903\) 9.65407 0.321267
\(904\) 0 0
\(905\) 11.1346 0.370127
\(906\) 0 0
\(907\) 35.2051 1.16897 0.584484 0.811406i \(-0.301297\pi\)
0.584484 + 0.811406i \(0.301297\pi\)
\(908\) 0 0
\(909\) 2.83624 0.0940720
\(910\) 0 0
\(911\) 3.23223 0.107088 0.0535442 0.998565i \(-0.482948\pi\)
0.0535442 + 0.998565i \(0.482948\pi\)
\(912\) 0 0
\(913\) 11.5577 0.382504
\(914\) 0 0
\(915\) 0.654005 0.0216207
\(916\) 0 0
\(917\) 47.9988 1.58506
\(918\) 0 0
\(919\) 11.7314 0.386984 0.193492 0.981102i \(-0.438019\pi\)
0.193492 + 0.981102i \(0.438019\pi\)
\(920\) 0 0
\(921\) −12.7567 −0.420347
\(922\) 0 0
\(923\) 8.40236 0.276567
\(924\) 0 0
\(925\) −17.5870 −0.578256
\(926\) 0 0
\(927\) 1.68361 0.0552970
\(928\) 0 0
\(929\) 36.8679 1.20960 0.604798 0.796379i \(-0.293254\pi\)
0.604798 + 0.796379i \(0.293254\pi\)
\(930\) 0 0
\(931\) 11.8366 0.387929
\(932\) 0 0
\(933\) −4.06532 −0.133093
\(934\) 0 0
\(935\) 2.69966 0.0882884
\(936\) 0 0
\(937\) −10.7009 −0.349583 −0.174792 0.984605i \(-0.555925\pi\)
−0.174792 + 0.984605i \(0.555925\pi\)
\(938\) 0 0
\(939\) −9.87994 −0.322420
\(940\) 0 0
\(941\) −4.86481 −0.158588 −0.0792942 0.996851i \(-0.525267\pi\)
−0.0792942 + 0.996851i \(0.525267\pi\)
\(942\) 0 0
\(943\) −51.1881 −1.66692
\(944\) 0 0
\(945\) −2.00123 −0.0651001
\(946\) 0 0
\(947\) −4.67872 −0.152038 −0.0760190 0.997106i \(-0.524221\pi\)
−0.0760190 + 0.997106i \(0.524221\pi\)
\(948\) 0 0
\(949\) 46.7516 1.51762
\(950\) 0 0
\(951\) 11.2409 0.364512
\(952\) 0 0
\(953\) −38.4497 −1.24551 −0.622754 0.782418i \(-0.713986\pi\)
−0.622754 + 0.782418i \(0.713986\pi\)
\(954\) 0 0
\(955\) 0.670092 0.0216837
\(956\) 0 0
\(957\) −3.15990 −0.102145
\(958\) 0 0
\(959\) 23.6139 0.762532
\(960\) 0 0
\(961\) −22.2362 −0.717295
\(962\) 0 0
\(963\) 10.4960 0.338227
\(964\) 0 0
\(965\) 2.73260 0.0879656
\(966\) 0 0
\(967\) 30.5693 0.983044 0.491522 0.870865i \(-0.336441\pi\)
0.491522 + 0.870865i \(0.336441\pi\)
\(968\) 0 0
\(969\) 35.9339 1.15436
\(970\) 0 0
\(971\) 0.810886 0.0260226 0.0130113 0.999915i \(-0.495858\pi\)
0.0130113 + 0.999915i \(0.495858\pi\)
\(972\) 0 0
\(973\) 4.30755 0.138094
\(974\) 0 0
\(975\) 11.9565 0.382915
\(976\) 0 0
\(977\) 9.23855 0.295567 0.147784 0.989020i \(-0.452786\pi\)
0.147784 + 0.989020i \(0.452786\pi\)
\(978\) 0 0
\(979\) −3.28120 −0.104868
\(980\) 0 0
\(981\) −3.61751 −0.115498
\(982\) 0 0
\(983\) −1.30384 −0.0415861 −0.0207931 0.999784i \(-0.506619\pi\)
−0.0207931 + 0.999784i \(0.506619\pi\)
\(984\) 0 0
\(985\) 6.25791 0.199394
\(986\) 0 0
\(987\) −3.24442 −0.103271
\(988\) 0 0
\(989\) 27.2785 0.867405
\(990\) 0 0
\(991\) 53.9125 1.71259 0.856293 0.516490i \(-0.172762\pi\)
0.856293 + 0.516490i \(0.172762\pi\)
\(992\) 0 0
\(993\) −14.6160 −0.463826
\(994\) 0 0
\(995\) 17.5860 0.557515
\(996\) 0 0
\(997\) −47.6636 −1.50952 −0.754760 0.656001i \(-0.772247\pi\)
−0.754760 + 0.656001i \(0.772247\pi\)
\(998\) 0 0
\(999\) 4.12480 0.130503
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 \(a_p\))