Properties

Label 8004.2.a.d.1.6
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
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: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
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 1.6
Root \(1.24887\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+0.138622 q^{5}\) \(-3.33662 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+0.138622 q^{5}\) \(-3.33662 q^{7}\) \(+1.00000 q^{9}\) \(-2.06616 q^{11}\) \(-0.702105 q^{13}\) \(+0.138622 q^{15}\) \(+4.32538 q^{17}\) \(+2.44146 q^{19}\) \(-3.33662 q^{21}\) \(+1.00000 q^{23}\) \(-4.98078 q^{25}\) \(+1.00000 q^{27}\) \(+1.00000 q^{29}\) \(+7.41338 q^{31}\) \(-2.06616 q^{33}\) \(-0.462529 q^{35}\) \(-2.90399 q^{37}\) \(-0.702105 q^{39}\) \(-4.05761 q^{41}\) \(+0.235390 q^{43}\) \(+0.138622 q^{45}\) \(-2.05531 q^{47}\) \(+4.13301 q^{49}\) \(+4.32538 q^{51}\) \(-3.22303 q^{53}\) \(-0.286416 q^{55}\) \(+2.44146 q^{57}\) \(-10.7016 q^{59}\) \(-2.78827 q^{61}\) \(-3.33662 q^{63}\) \(-0.0973274 q^{65}\) \(-11.6076 q^{67}\) \(+1.00000 q^{69}\) \(+7.47417 q^{71}\) \(+9.16987 q^{73}\) \(-4.98078 q^{75}\) \(+6.89398 q^{77}\) \(+11.0456 q^{79}\) \(+1.00000 q^{81}\) \(-12.3394 q^{83}\) \(+0.599594 q^{85}\) \(+1.00000 q^{87}\) \(+3.05613 q^{89}\) \(+2.34265 q^{91}\) \(+7.41338 q^{93}\) \(+0.338441 q^{95}\) \(+2.74522 q^{97}\) \(-2.06616 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 11q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 5q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 0.138622 0.0619938 0.0309969 0.999519i \(-0.490132\pi\)
0.0309969 + 0.999519i \(0.490132\pi\)
\(6\) 0 0
\(7\) −3.33662 −1.26112 −0.630561 0.776139i \(-0.717175\pi\)
−0.630561 + 0.776139i \(0.717175\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.06616 −0.622971 −0.311485 0.950251i \(-0.600826\pi\)
−0.311485 + 0.950251i \(0.600826\pi\)
\(12\) 0 0
\(13\) −0.702105 −0.194729 −0.0973644 0.995249i \(-0.531041\pi\)
−0.0973644 + 0.995249i \(0.531041\pi\)
\(14\) 0 0
\(15\) 0.138622 0.0357921
\(16\) 0 0
\(17\) 4.32538 1.04906 0.524529 0.851392i \(-0.324241\pi\)
0.524529 + 0.851392i \(0.324241\pi\)
\(18\) 0 0
\(19\) 2.44146 0.560110 0.280055 0.959984i \(-0.409647\pi\)
0.280055 + 0.959984i \(0.409647\pi\)
\(20\) 0 0
\(21\) −3.33662 −0.728109
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.98078 −0.996157
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 7.41338 1.33148 0.665741 0.746183i \(-0.268116\pi\)
0.665741 + 0.746183i \(0.268116\pi\)
\(32\) 0 0
\(33\) −2.06616 −0.359672
\(34\) 0 0
\(35\) −0.462529 −0.0781817
\(36\) 0 0
\(37\) −2.90399 −0.477413 −0.238707 0.971092i \(-0.576723\pi\)
−0.238707 + 0.971092i \(0.576723\pi\)
\(38\) 0 0
\(39\) −0.702105 −0.112427
\(40\) 0 0
\(41\) −4.05761 −0.633692 −0.316846 0.948477i \(-0.602624\pi\)
−0.316846 + 0.948477i \(0.602624\pi\)
\(42\) 0 0
\(43\) 0.235390 0.0358966 0.0179483 0.999839i \(-0.494287\pi\)
0.0179483 + 0.999839i \(0.494287\pi\)
\(44\) 0 0
\(45\) 0.138622 0.0206646
\(46\) 0 0
\(47\) −2.05531 −0.299798 −0.149899 0.988701i \(-0.547895\pi\)
−0.149899 + 0.988701i \(0.547895\pi\)
\(48\) 0 0
\(49\) 4.13301 0.590430
\(50\) 0 0
\(51\) 4.32538 0.605674
\(52\) 0 0
\(53\) −3.22303 −0.442718 −0.221359 0.975192i \(-0.571049\pi\)
−0.221359 + 0.975192i \(0.571049\pi\)
\(54\) 0 0
\(55\) −0.286416 −0.0386203
\(56\) 0 0
\(57\) 2.44146 0.323379
\(58\) 0 0
\(59\) −10.7016 −1.39323 −0.696614 0.717446i \(-0.745311\pi\)
−0.696614 + 0.717446i \(0.745311\pi\)
\(60\) 0 0
\(61\) −2.78827 −0.357001 −0.178501 0.983940i \(-0.557125\pi\)
−0.178501 + 0.983940i \(0.557125\pi\)
\(62\) 0 0
\(63\) −3.33662 −0.420374
\(64\) 0 0
\(65\) −0.0973274 −0.0120720
\(66\) 0 0
\(67\) −11.6076 −1.41809 −0.709046 0.705163i \(-0.750874\pi\)
−0.709046 + 0.705163i \(0.750874\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 7.47417 0.887021 0.443510 0.896269i \(-0.353733\pi\)
0.443510 + 0.896269i \(0.353733\pi\)
\(72\) 0 0
\(73\) 9.16987 1.07325 0.536626 0.843820i \(-0.319699\pi\)
0.536626 + 0.843820i \(0.319699\pi\)
\(74\) 0 0
\(75\) −4.98078 −0.575131
\(76\) 0 0
\(77\) 6.89398 0.785642
\(78\) 0 0
\(79\) 11.0456 1.24273 0.621364 0.783522i \(-0.286579\pi\)
0.621364 + 0.783522i \(0.286579\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.3394 −1.35442 −0.677210 0.735790i \(-0.736811\pi\)
−0.677210 + 0.735790i \(0.736811\pi\)
\(84\) 0 0
\(85\) 0.599594 0.0650351
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) 3.05613 0.323950 0.161975 0.986795i \(-0.448214\pi\)
0.161975 + 0.986795i \(0.448214\pi\)
\(90\) 0 0
\(91\) 2.34265 0.245577
\(92\) 0 0
\(93\) 7.41338 0.768731
\(94\) 0 0
\(95\) 0.338441 0.0347233
\(96\) 0 0
\(97\) 2.74522 0.278735 0.139368 0.990241i \(-0.455493\pi\)
0.139368 + 0.990241i \(0.455493\pi\)
\(98\) 0 0
\(99\) −2.06616 −0.207657
\(100\) 0 0
\(101\) −13.4238 −1.33572 −0.667861 0.744286i \(-0.732790\pi\)
−0.667861 + 0.744286i \(0.732790\pi\)
\(102\) 0 0
\(103\) 5.32865 0.525047 0.262524 0.964926i \(-0.415445\pi\)
0.262524 + 0.964926i \(0.415445\pi\)
\(104\) 0 0
\(105\) −0.462529 −0.0451383
\(106\) 0 0
\(107\) 13.7453 1.32880 0.664402 0.747375i \(-0.268686\pi\)
0.664402 + 0.747375i \(0.268686\pi\)
\(108\) 0 0
\(109\) −6.22293 −0.596049 −0.298024 0.954558i \(-0.596328\pi\)
−0.298024 + 0.954558i \(0.596328\pi\)
\(110\) 0 0
\(111\) −2.90399 −0.275635
\(112\) 0 0
\(113\) 0.191841 0.0180468 0.00902342 0.999959i \(-0.497128\pi\)
0.00902342 + 0.999959i \(0.497128\pi\)
\(114\) 0 0
\(115\) 0.138622 0.0129266
\(116\) 0 0
\(117\) −0.702105 −0.0649096
\(118\) 0 0
\(119\) −14.4321 −1.32299
\(120\) 0 0
\(121\) −6.73099 −0.611908
\(122\) 0 0
\(123\) −4.05761 −0.365862
\(124\) 0 0
\(125\) −1.38356 −0.123749
\(126\) 0 0
\(127\) −19.8935 −1.76526 −0.882632 0.470065i \(-0.844231\pi\)
−0.882632 + 0.470065i \(0.844231\pi\)
\(128\) 0 0
\(129\) 0.235390 0.0207249
\(130\) 0 0
\(131\) −9.36944 −0.818611 −0.409306 0.912397i \(-0.634229\pi\)
−0.409306 + 0.912397i \(0.634229\pi\)
\(132\) 0 0
\(133\) −8.14622 −0.706367
\(134\) 0 0
\(135\) 0.138622 0.0119307
\(136\) 0 0
\(137\) −4.64779 −0.397088 −0.198544 0.980092i \(-0.563621\pi\)
−0.198544 + 0.980092i \(0.563621\pi\)
\(138\) 0 0
\(139\) 1.53574 0.130260 0.0651300 0.997877i \(-0.479254\pi\)
0.0651300 + 0.997877i \(0.479254\pi\)
\(140\) 0 0
\(141\) −2.05531 −0.173089
\(142\) 0 0
\(143\) 1.45066 0.121310
\(144\) 0 0
\(145\) 0.138622 0.0115120
\(146\) 0 0
\(147\) 4.13301 0.340885
\(148\) 0 0
\(149\) −15.6363 −1.28097 −0.640486 0.767970i \(-0.721267\pi\)
−0.640486 + 0.767970i \(0.721267\pi\)
\(150\) 0 0
\(151\) −0.131361 −0.0106900 −0.00534500 0.999986i \(-0.501701\pi\)
−0.00534500 + 0.999986i \(0.501701\pi\)
\(152\) 0 0
\(153\) 4.32538 0.349686
\(154\) 0 0
\(155\) 1.02766 0.0825436
\(156\) 0 0
\(157\) −22.4628 −1.79272 −0.896362 0.443324i \(-0.853799\pi\)
−0.896362 + 0.443324i \(0.853799\pi\)
\(158\) 0 0
\(159\) −3.22303 −0.255603
\(160\) 0 0
\(161\) −3.33662 −0.262962
\(162\) 0 0
\(163\) 16.0695 1.25866 0.629329 0.777139i \(-0.283330\pi\)
0.629329 + 0.777139i \(0.283330\pi\)
\(164\) 0 0
\(165\) −0.286416 −0.0222974
\(166\) 0 0
\(167\) 14.0563 1.08771 0.543856 0.839178i \(-0.316964\pi\)
0.543856 + 0.839178i \(0.316964\pi\)
\(168\) 0 0
\(169\) −12.5070 −0.962081
\(170\) 0 0
\(171\) 2.44146 0.186703
\(172\) 0 0
\(173\) −19.4446 −1.47835 −0.739174 0.673514i \(-0.764784\pi\)
−0.739174 + 0.673514i \(0.764784\pi\)
\(174\) 0 0
\(175\) 16.6190 1.25628
\(176\) 0 0
\(177\) −10.7016 −0.804380
\(178\) 0 0
\(179\) −6.84250 −0.511432 −0.255716 0.966752i \(-0.582311\pi\)
−0.255716 + 0.966752i \(0.582311\pi\)
\(180\) 0 0
\(181\) 17.2255 1.28036 0.640182 0.768223i \(-0.278859\pi\)
0.640182 + 0.768223i \(0.278859\pi\)
\(182\) 0 0
\(183\) −2.78827 −0.206115
\(184\) 0 0
\(185\) −0.402558 −0.0295966
\(186\) 0 0
\(187\) −8.93692 −0.653532
\(188\) 0 0
\(189\) −3.33662 −0.242703
\(190\) 0 0
\(191\) 6.76311 0.489361 0.244681 0.969604i \(-0.421317\pi\)
0.244681 + 0.969604i \(0.421317\pi\)
\(192\) 0 0
\(193\) −19.1555 −1.37884 −0.689420 0.724362i \(-0.742135\pi\)
−0.689420 + 0.724362i \(0.742135\pi\)
\(194\) 0 0
\(195\) −0.0973274 −0.00696976
\(196\) 0 0
\(197\) 22.7833 1.62324 0.811622 0.584183i \(-0.198585\pi\)
0.811622 + 0.584183i \(0.198585\pi\)
\(198\) 0 0
\(199\) 17.0668 1.20983 0.604916 0.796289i \(-0.293207\pi\)
0.604916 + 0.796289i \(0.293207\pi\)
\(200\) 0 0
\(201\) −11.6076 −0.818735
\(202\) 0 0
\(203\) −3.33662 −0.234185
\(204\) 0 0
\(205\) −0.562475 −0.0392849
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −5.04445 −0.348932
\(210\) 0 0
\(211\) −21.7265 −1.49572 −0.747858 0.663859i \(-0.768918\pi\)
−0.747858 + 0.663859i \(0.768918\pi\)
\(212\) 0 0
\(213\) 7.47417 0.512122
\(214\) 0 0
\(215\) 0.0326303 0.00222537
\(216\) 0 0
\(217\) −24.7356 −1.67916
\(218\) 0 0
\(219\) 9.16987 0.619643
\(220\) 0 0
\(221\) −3.03687 −0.204282
\(222\) 0 0
\(223\) 1.66917 0.111776 0.0558880 0.998437i \(-0.482201\pi\)
0.0558880 + 0.998437i \(0.482201\pi\)
\(224\) 0 0
\(225\) −4.98078 −0.332052
\(226\) 0 0
\(227\) 7.86528 0.522037 0.261019 0.965334i \(-0.415942\pi\)
0.261019 + 0.965334i \(0.415942\pi\)
\(228\) 0 0
\(229\) −25.6280 −1.69355 −0.846774 0.531954i \(-0.821458\pi\)
−0.846774 + 0.531954i \(0.821458\pi\)
\(230\) 0 0
\(231\) 6.89398 0.453591
\(232\) 0 0
\(233\) −11.8273 −0.774833 −0.387416 0.921905i \(-0.626632\pi\)
−0.387416 + 0.921905i \(0.626632\pi\)
\(234\) 0 0
\(235\) −0.284912 −0.0185856
\(236\) 0 0
\(237\) 11.0456 0.717489
\(238\) 0 0
\(239\) −15.0934 −0.976314 −0.488157 0.872756i \(-0.662331\pi\)
−0.488157 + 0.872756i \(0.662331\pi\)
\(240\) 0 0
\(241\) −4.05076 −0.260933 −0.130466 0.991453i \(-0.541647\pi\)
−0.130466 + 0.991453i \(0.541647\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.572928 0.0366030
\(246\) 0 0
\(247\) −1.71416 −0.109069
\(248\) 0 0
\(249\) −12.3394 −0.781975
\(250\) 0 0
\(251\) −12.3880 −0.781923 −0.390961 0.920407i \(-0.627857\pi\)
−0.390961 + 0.920407i \(0.627857\pi\)
\(252\) 0 0
\(253\) −2.06616 −0.129898
\(254\) 0 0
\(255\) 0.599594 0.0375480
\(256\) 0 0
\(257\) −3.36413 −0.209848 −0.104924 0.994480i \(-0.533460\pi\)
−0.104924 + 0.994480i \(0.533460\pi\)
\(258\) 0 0
\(259\) 9.68950 0.602076
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −2.66208 −0.164151 −0.0820754 0.996626i \(-0.526155\pi\)
−0.0820754 + 0.996626i \(0.526155\pi\)
\(264\) 0 0
\(265\) −0.446784 −0.0274457
\(266\) 0 0
\(267\) 3.05613 0.187032
\(268\) 0 0
\(269\) −27.7521 −1.69208 −0.846038 0.533122i \(-0.821019\pi\)
−0.846038 + 0.533122i \(0.821019\pi\)
\(270\) 0 0
\(271\) −14.0820 −0.855420 −0.427710 0.903916i \(-0.640679\pi\)
−0.427710 + 0.903916i \(0.640679\pi\)
\(272\) 0 0
\(273\) 2.34265 0.141784
\(274\) 0 0
\(275\) 10.2911 0.620576
\(276\) 0 0
\(277\) −21.3082 −1.28029 −0.640143 0.768256i \(-0.721125\pi\)
−0.640143 + 0.768256i \(0.721125\pi\)
\(278\) 0 0
\(279\) 7.41338 0.443827
\(280\) 0 0
\(281\) 6.82977 0.407430 0.203715 0.979030i \(-0.434698\pi\)
0.203715 + 0.979030i \(0.434698\pi\)
\(282\) 0 0
\(283\) −15.5966 −0.927123 −0.463562 0.886065i \(-0.653429\pi\)
−0.463562 + 0.886065i \(0.653429\pi\)
\(284\) 0 0
\(285\) 0.338441 0.0200475
\(286\) 0 0
\(287\) 13.5387 0.799163
\(288\) 0 0
\(289\) 1.70890 0.100524
\(290\) 0 0
\(291\) 2.74522 0.160928
\(292\) 0 0
\(293\) −4.78475 −0.279528 −0.139764 0.990185i \(-0.544634\pi\)
−0.139764 + 0.990185i \(0.544634\pi\)
\(294\) 0 0
\(295\) −1.48348 −0.0863714
\(296\) 0 0
\(297\) −2.06616 −0.119891
\(298\) 0 0
\(299\) −0.702105 −0.0406038
\(300\) 0 0
\(301\) −0.785406 −0.0452700
\(302\) 0 0
\(303\) −13.4238 −0.771179
\(304\) 0 0
\(305\) −0.386516 −0.0221318
\(306\) 0 0
\(307\) 1.56614 0.0893842 0.0446921 0.999001i \(-0.485769\pi\)
0.0446921 + 0.999001i \(0.485769\pi\)
\(308\) 0 0
\(309\) 5.32865 0.303136
\(310\) 0 0
\(311\) −23.2734 −1.31972 −0.659858 0.751390i \(-0.729384\pi\)
−0.659858 + 0.751390i \(0.729384\pi\)
\(312\) 0 0
\(313\) −9.54782 −0.539675 −0.269837 0.962906i \(-0.586970\pi\)
−0.269837 + 0.962906i \(0.586970\pi\)
\(314\) 0 0
\(315\) −0.462529 −0.0260606
\(316\) 0 0
\(317\) 4.20816 0.236354 0.118177 0.992993i \(-0.462295\pi\)
0.118177 + 0.992993i \(0.462295\pi\)
\(318\) 0 0
\(319\) −2.06616 −0.115683
\(320\) 0 0
\(321\) 13.7453 0.767186
\(322\) 0 0
\(323\) 10.5602 0.587588
\(324\) 0 0
\(325\) 3.49703 0.193980
\(326\) 0 0
\(327\) −6.22293 −0.344129
\(328\) 0 0
\(329\) 6.85779 0.378082
\(330\) 0 0
\(331\) −5.28355 −0.290410 −0.145205 0.989402i \(-0.546384\pi\)
−0.145205 + 0.989402i \(0.546384\pi\)
\(332\) 0 0
\(333\) −2.90399 −0.159138
\(334\) 0 0
\(335\) −1.60907 −0.0879128
\(336\) 0 0
\(337\) −11.0431 −0.601554 −0.300777 0.953695i \(-0.597246\pi\)
−0.300777 + 0.953695i \(0.597246\pi\)
\(338\) 0 0
\(339\) 0.191841 0.0104193
\(340\) 0 0
\(341\) −15.3172 −0.829474
\(342\) 0 0
\(343\) 9.56604 0.516518
\(344\) 0 0
\(345\) 0.138622 0.00746317
\(346\) 0 0
\(347\) 35.2662 1.89319 0.946595 0.322425i \(-0.104498\pi\)
0.946595 + 0.322425i \(0.104498\pi\)
\(348\) 0 0
\(349\) 28.9854 1.55155 0.775776 0.631008i \(-0.217359\pi\)
0.775776 + 0.631008i \(0.217359\pi\)
\(350\) 0 0
\(351\) −0.702105 −0.0374756
\(352\) 0 0
\(353\) −9.29498 −0.494722 −0.247361 0.968923i \(-0.579563\pi\)
−0.247361 + 0.968923i \(0.579563\pi\)
\(354\) 0 0
\(355\) 1.03609 0.0549898
\(356\) 0 0
\(357\) −14.4321 −0.763829
\(358\) 0 0
\(359\) −21.9567 −1.15883 −0.579416 0.815032i \(-0.696719\pi\)
−0.579416 + 0.815032i \(0.696719\pi\)
\(360\) 0 0
\(361\) −13.0393 −0.686277
\(362\) 0 0
\(363\) −6.73099 −0.353285
\(364\) 0 0
\(365\) 1.27115 0.0665350
\(366\) 0 0
\(367\) 21.2236 1.10786 0.553932 0.832562i \(-0.313127\pi\)
0.553932 + 0.832562i \(0.313127\pi\)
\(368\) 0 0
\(369\) −4.05761 −0.211231
\(370\) 0 0
\(371\) 10.7540 0.558322
\(372\) 0 0
\(373\) −4.56449 −0.236340 −0.118170 0.992993i \(-0.537703\pi\)
−0.118170 + 0.992993i \(0.537703\pi\)
\(374\) 0 0
\(375\) −1.38356 −0.0714467
\(376\) 0 0
\(377\) −0.702105 −0.0361602
\(378\) 0 0
\(379\) −24.0049 −1.23305 −0.616524 0.787336i \(-0.711460\pi\)
−0.616524 + 0.787336i \(0.711460\pi\)
\(380\) 0 0
\(381\) −19.8935 −1.01918
\(382\) 0 0
\(383\) 23.2380 1.18741 0.593704 0.804684i \(-0.297665\pi\)
0.593704 + 0.804684i \(0.297665\pi\)
\(384\) 0 0
\(385\) 0.955660 0.0487049
\(386\) 0 0
\(387\) 0.235390 0.0119655
\(388\) 0 0
\(389\) 27.5066 1.39464 0.697321 0.716759i \(-0.254375\pi\)
0.697321 + 0.716759i \(0.254375\pi\)
\(390\) 0 0
\(391\) 4.32538 0.218744
\(392\) 0 0
\(393\) −9.36944 −0.472626
\(394\) 0 0
\(395\) 1.53117 0.0770414
\(396\) 0 0
\(397\) −11.7160 −0.588008 −0.294004 0.955804i \(-0.594988\pi\)
−0.294004 + 0.955804i \(0.594988\pi\)
\(398\) 0 0
\(399\) −8.14622 −0.407821
\(400\) 0 0
\(401\) 23.4290 1.16999 0.584994 0.811037i \(-0.301097\pi\)
0.584994 + 0.811037i \(0.301097\pi\)
\(402\) 0 0
\(403\) −5.20497 −0.259278
\(404\) 0 0
\(405\) 0.138622 0.00688820
\(406\) 0 0
\(407\) 6.00011 0.297414
\(408\) 0 0
\(409\) 1.07003 0.0529096 0.0264548 0.999650i \(-0.491578\pi\)
0.0264548 + 0.999650i \(0.491578\pi\)
\(410\) 0 0
\(411\) −4.64779 −0.229259
\(412\) 0 0
\(413\) 35.7071 1.75703
\(414\) 0 0
\(415\) −1.71051 −0.0839656
\(416\) 0 0
\(417\) 1.53574 0.0752057
\(418\) 0 0
\(419\) −10.9312 −0.534024 −0.267012 0.963693i \(-0.586036\pi\)
−0.267012 + 0.963693i \(0.586036\pi\)
\(420\) 0 0
\(421\) 4.63235 0.225767 0.112883 0.993608i \(-0.463991\pi\)
0.112883 + 0.993608i \(0.463991\pi\)
\(422\) 0 0
\(423\) −2.05531 −0.0999327
\(424\) 0 0
\(425\) −21.5438 −1.04503
\(426\) 0 0
\(427\) 9.30338 0.450222
\(428\) 0 0
\(429\) 1.45066 0.0700385
\(430\) 0 0
\(431\) −0.537917 −0.0259106 −0.0129553 0.999916i \(-0.504124\pi\)
−0.0129553 + 0.999916i \(0.504124\pi\)
\(432\) 0 0
\(433\) 8.35692 0.401608 0.200804 0.979631i \(-0.435645\pi\)
0.200804 + 0.979631i \(0.435645\pi\)
\(434\) 0 0
\(435\) 0.138622 0.00664643
\(436\) 0 0
\(437\) 2.44146 0.116791
\(438\) 0 0
\(439\) −18.5296 −0.884372 −0.442186 0.896923i \(-0.645797\pi\)
−0.442186 + 0.896923i \(0.645797\pi\)
\(440\) 0 0
\(441\) 4.13301 0.196810
\(442\) 0 0
\(443\) −22.9601 −1.09087 −0.545435 0.838153i \(-0.683635\pi\)
−0.545435 + 0.838153i \(0.683635\pi\)
\(444\) 0 0
\(445\) 0.423648 0.0200829
\(446\) 0 0
\(447\) −15.6363 −0.739570
\(448\) 0 0
\(449\) −12.8847 −0.608069 −0.304034 0.952661i \(-0.598334\pi\)
−0.304034 + 0.952661i \(0.598334\pi\)
\(450\) 0 0
\(451\) 8.38366 0.394771
\(452\) 0 0
\(453\) −0.131361 −0.00617187
\(454\) 0 0
\(455\) 0.324744 0.0152242
\(456\) 0 0
\(457\) −6.25690 −0.292685 −0.146343 0.989234i \(-0.546750\pi\)
−0.146343 + 0.989234i \(0.546750\pi\)
\(458\) 0 0
\(459\) 4.32538 0.201891
\(460\) 0 0
\(461\) 33.5984 1.56483 0.782416 0.622756i \(-0.213987\pi\)
0.782416 + 0.622756i \(0.213987\pi\)
\(462\) 0 0
\(463\) −8.53294 −0.396559 −0.198280 0.980145i \(-0.563535\pi\)
−0.198280 + 0.980145i \(0.563535\pi\)
\(464\) 0 0
\(465\) 1.02766 0.0476565
\(466\) 0 0
\(467\) 16.5443 0.765579 0.382790 0.923836i \(-0.374963\pi\)
0.382790 + 0.923836i \(0.374963\pi\)
\(468\) 0 0
\(469\) 38.7300 1.78839
\(470\) 0 0
\(471\) −22.4628 −1.03503
\(472\) 0 0
\(473\) −0.486353 −0.0223625
\(474\) 0 0
\(475\) −12.1604 −0.557957
\(476\) 0 0
\(477\) −3.22303 −0.147573
\(478\) 0 0
\(479\) 32.6154 1.49024 0.745119 0.666932i \(-0.232393\pi\)
0.745119 + 0.666932i \(0.232393\pi\)
\(480\) 0 0
\(481\) 2.03891 0.0929661
\(482\) 0 0
\(483\) −3.33662 −0.151821
\(484\) 0 0
\(485\) 0.380549 0.0172799
\(486\) 0 0
\(487\) 26.8002 1.21443 0.607217 0.794536i \(-0.292286\pi\)
0.607217 + 0.794536i \(0.292286\pi\)
\(488\) 0 0
\(489\) 16.0695 0.726686
\(490\) 0 0
\(491\) −1.18043 −0.0532719 −0.0266359 0.999645i \(-0.508479\pi\)
−0.0266359 + 0.999645i \(0.508479\pi\)
\(492\) 0 0
\(493\) 4.32538 0.194805
\(494\) 0 0
\(495\) −0.286416 −0.0128734
\(496\) 0 0
\(497\) −24.9384 −1.11864
\(498\) 0 0
\(499\) −36.0023 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(500\) 0 0
\(501\) 14.0563 0.627991
\(502\) 0 0
\(503\) 21.0968 0.940661 0.470330 0.882490i \(-0.344135\pi\)
0.470330 + 0.882490i \(0.344135\pi\)
\(504\) 0 0
\(505\) −1.86084 −0.0828064
\(506\) 0 0
\(507\) −12.5070 −0.555458
\(508\) 0 0
\(509\) −20.3383 −0.901478 −0.450739 0.892656i \(-0.648839\pi\)
−0.450739 + 0.892656i \(0.648839\pi\)
\(510\) 0 0
\(511\) −30.5964 −1.35350
\(512\) 0 0
\(513\) 2.44146 0.107793
\(514\) 0 0
\(515\) 0.738669 0.0325496
\(516\) 0 0
\(517\) 4.24660 0.186765
\(518\) 0 0
\(519\) −19.4446 −0.853525
\(520\) 0 0
\(521\) −16.3917 −0.718135 −0.359067 0.933312i \(-0.616905\pi\)
−0.359067 + 0.933312i \(0.616905\pi\)
\(522\) 0 0
\(523\) 32.2893 1.41191 0.705956 0.708256i \(-0.250518\pi\)
0.705956 + 0.708256i \(0.250518\pi\)
\(524\) 0 0
\(525\) 16.6190 0.725311
\(526\) 0 0
\(527\) 32.0657 1.39680
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −10.7016 −0.464409
\(532\) 0 0
\(533\) 2.84887 0.123398
\(534\) 0 0
\(535\) 1.90540 0.0823776
\(536\) 0 0
\(537\) −6.84250 −0.295276
\(538\) 0 0
\(539\) −8.53946 −0.367821
\(540\) 0 0
\(541\) 38.2985 1.64658 0.823290 0.567622i \(-0.192136\pi\)
0.823290 + 0.567622i \(0.192136\pi\)
\(542\) 0 0
\(543\) 17.2255 0.739219
\(544\) 0 0
\(545\) −0.862637 −0.0369513
\(546\) 0 0
\(547\) −4.29502 −0.183642 −0.0918208 0.995776i \(-0.529269\pi\)
−0.0918208 + 0.995776i \(0.529269\pi\)
\(548\) 0 0
\(549\) −2.78827 −0.119000
\(550\) 0 0
\(551\) 2.44146 0.104010
\(552\) 0 0
\(553\) −36.8550 −1.56723
\(554\) 0 0
\(555\) −0.402558 −0.0170876
\(556\) 0 0
\(557\) −28.5287 −1.20880 −0.604400 0.796681i \(-0.706587\pi\)
−0.604400 + 0.796681i \(0.706587\pi\)
\(558\) 0 0
\(559\) −0.165268 −0.00699011
\(560\) 0 0
\(561\) −8.93692 −0.377317
\(562\) 0 0
\(563\) −30.7568 −1.29625 −0.648123 0.761536i \(-0.724446\pi\)
−0.648123 + 0.761536i \(0.724446\pi\)
\(564\) 0 0
\(565\) 0.0265934 0.00111879
\(566\) 0 0
\(567\) −3.33662 −0.140125
\(568\) 0 0
\(569\) 18.5814 0.778973 0.389486 0.921032i \(-0.372653\pi\)
0.389486 + 0.921032i \(0.372653\pi\)
\(570\) 0 0
\(571\) −14.3754 −0.601593 −0.300797 0.953688i \(-0.597253\pi\)
−0.300797 + 0.953688i \(0.597253\pi\)
\(572\) 0 0
\(573\) 6.76311 0.282533
\(574\) 0 0
\(575\) −4.98078 −0.207713
\(576\) 0 0
\(577\) 17.8952 0.744986 0.372493 0.928035i \(-0.378503\pi\)
0.372493 + 0.928035i \(0.378503\pi\)
\(578\) 0 0
\(579\) −19.1555 −0.796074
\(580\) 0 0
\(581\) 41.1717 1.70809
\(582\) 0 0
\(583\) 6.65930 0.275800
\(584\) 0 0
\(585\) −0.0973274 −0.00402399
\(586\) 0 0
\(587\) −9.83427 −0.405904 −0.202952 0.979189i \(-0.565053\pi\)
−0.202952 + 0.979189i \(0.565053\pi\)
\(588\) 0 0
\(589\) 18.0995 0.745776
\(590\) 0 0
\(591\) 22.7833 0.937180
\(592\) 0 0
\(593\) 18.1723 0.746247 0.373124 0.927782i \(-0.378287\pi\)
0.373124 + 0.927782i \(0.378287\pi\)
\(594\) 0 0
\(595\) −2.00062 −0.0820172
\(596\) 0 0
\(597\) 17.0668 0.698497
\(598\) 0 0
\(599\) 14.4396 0.589985 0.294992 0.955500i \(-0.404683\pi\)
0.294992 + 0.955500i \(0.404683\pi\)
\(600\) 0 0
\(601\) −22.5937 −0.921617 −0.460808 0.887500i \(-0.652440\pi\)
−0.460808 + 0.887500i \(0.652440\pi\)
\(602\) 0 0
\(603\) −11.6076 −0.472697
\(604\) 0 0
\(605\) −0.933064 −0.0379345
\(606\) 0 0
\(607\) 34.3011 1.39224 0.696120 0.717925i \(-0.254908\pi\)
0.696120 + 0.717925i \(0.254908\pi\)
\(608\) 0 0
\(609\) −3.33662 −0.135207
\(610\) 0 0
\(611\) 1.44305 0.0583794
\(612\) 0 0
\(613\) 41.0333 1.65732 0.828659 0.559753i \(-0.189104\pi\)
0.828659 + 0.559753i \(0.189104\pi\)
\(614\) 0 0
\(615\) −0.562475 −0.0226812
\(616\) 0 0
\(617\) −23.0204 −0.926767 −0.463384 0.886158i \(-0.653365\pi\)
−0.463384 + 0.886158i \(0.653365\pi\)
\(618\) 0 0
\(619\) −29.5961 −1.18957 −0.594785 0.803885i \(-0.702763\pi\)
−0.594785 + 0.803885i \(0.702763\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −10.1972 −0.408540
\(624\) 0 0
\(625\) 24.7121 0.988485
\(626\) 0 0
\(627\) −5.04445 −0.201456
\(628\) 0 0
\(629\) −12.5609 −0.500834
\(630\) 0 0
\(631\) 9.57230 0.381067 0.190534 0.981681i \(-0.438978\pi\)
0.190534 + 0.981681i \(0.438978\pi\)
\(632\) 0 0
\(633\) −21.7265 −0.863552
\(634\) 0 0
\(635\) −2.75768 −0.109435
\(636\) 0 0
\(637\) −2.90181 −0.114974
\(638\) 0 0
\(639\) 7.47417 0.295674
\(640\) 0 0
\(641\) 26.5793 1.04982 0.524909 0.851158i \(-0.324099\pi\)
0.524909 + 0.851158i \(0.324099\pi\)
\(642\) 0 0
\(643\) −12.8133 −0.505305 −0.252653 0.967557i \(-0.581303\pi\)
−0.252653 + 0.967557i \(0.581303\pi\)
\(644\) 0 0
\(645\) 0.0326303 0.00128482
\(646\) 0 0
\(647\) 15.3443 0.603246 0.301623 0.953427i \(-0.402472\pi\)
0.301623 + 0.953427i \(0.402472\pi\)
\(648\) 0 0
\(649\) 22.1112 0.867940
\(650\) 0 0
\(651\) −24.7356 −0.969464
\(652\) 0 0
\(653\) 30.6963 1.20124 0.600619 0.799535i \(-0.294921\pi\)
0.600619 + 0.799535i \(0.294921\pi\)
\(654\) 0 0
\(655\) −1.29881 −0.0507488
\(656\) 0 0
\(657\) 9.16987 0.357751
\(658\) 0 0
\(659\) 36.3908 1.41758 0.708792 0.705418i \(-0.249241\pi\)
0.708792 + 0.705418i \(0.249241\pi\)
\(660\) 0 0
\(661\) −14.8679 −0.578294 −0.289147 0.957285i \(-0.593372\pi\)
−0.289147 + 0.957285i \(0.593372\pi\)
\(662\) 0 0
\(663\) −3.03687 −0.117942
\(664\) 0 0
\(665\) −1.12925 −0.0437903
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 1.66917 0.0645338
\(670\) 0 0
\(671\) 5.76101 0.222401
\(672\) 0 0
\(673\) −12.0592 −0.464848 −0.232424 0.972615i \(-0.574666\pi\)
−0.232424 + 0.972615i \(0.574666\pi\)
\(674\) 0 0
\(675\) −4.98078 −0.191710
\(676\) 0 0
\(677\) −25.0028 −0.960937 −0.480469 0.877012i \(-0.659533\pi\)
−0.480469 + 0.877012i \(0.659533\pi\)
\(678\) 0 0
\(679\) −9.15976 −0.351519
\(680\) 0 0
\(681\) 7.86528 0.301398
\(682\) 0 0
\(683\) 11.6252 0.444826 0.222413 0.974953i \(-0.428607\pi\)
0.222413 + 0.974953i \(0.428607\pi\)
\(684\) 0 0
\(685\) −0.644288 −0.0246170
\(686\) 0 0
\(687\) −25.6280 −0.977770
\(688\) 0 0
\(689\) 2.26291 0.0862099
\(690\) 0 0
\(691\) 6.77933 0.257898 0.128949 0.991651i \(-0.458840\pi\)
0.128949 + 0.991651i \(0.458840\pi\)
\(692\) 0 0
\(693\) 6.89398 0.261881
\(694\) 0 0
\(695\) 0.212888 0.00807531
\(696\) 0 0
\(697\) −17.5507 −0.664780
\(698\) 0 0
\(699\) −11.8273 −0.447350
\(700\) 0 0
\(701\) 16.0754 0.607160 0.303580 0.952806i \(-0.401818\pi\)
0.303580 + 0.952806i \(0.401818\pi\)
\(702\) 0 0
\(703\) −7.08998 −0.267404
\(704\) 0 0
\(705\) −0.284912 −0.0107304
\(706\) 0 0
\(707\) 44.7902 1.68451
\(708\) 0 0
\(709\) −15.6323 −0.587083 −0.293542 0.955946i \(-0.594834\pi\)
−0.293542 + 0.955946i \(0.594834\pi\)
\(710\) 0 0
\(711\) 11.0456 0.414243
\(712\) 0 0
\(713\) 7.41338 0.277633
\(714\) 0 0
\(715\) 0.201094 0.00752048
\(716\) 0 0
\(717\) −15.0934 −0.563675
\(718\) 0 0
\(719\) 49.2658 1.83730 0.918652 0.395067i \(-0.129279\pi\)
0.918652 + 0.395067i \(0.129279\pi\)
\(720\) 0 0
\(721\) −17.7796 −0.662149
\(722\) 0 0
\(723\) −4.05076 −0.150649
\(724\) 0 0
\(725\) −4.98078 −0.184982
\(726\) 0 0
\(727\) −29.4731 −1.09310 −0.546549 0.837427i \(-0.684059\pi\)
−0.546549 + 0.837427i \(0.684059\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.01815 0.0376577
\(732\) 0 0
\(733\) −48.2391 −1.78175 −0.890875 0.454248i \(-0.849908\pi\)
−0.890875 + 0.454248i \(0.849908\pi\)
\(734\) 0 0
\(735\) 0.572928 0.0211328
\(736\) 0 0
\(737\) 23.9831 0.883429
\(738\) 0 0
\(739\) −12.6485 −0.465281 −0.232640 0.972563i \(-0.574737\pi\)
−0.232640 + 0.972563i \(0.574737\pi\)
\(740\) 0 0
\(741\) −1.71416 −0.0629713
\(742\) 0 0
\(743\) −24.9291 −0.914561 −0.457280 0.889323i \(-0.651176\pi\)
−0.457280 + 0.889323i \(0.651176\pi\)
\(744\) 0 0
\(745\) −2.16753 −0.0794123
\(746\) 0 0
\(747\) −12.3394 −0.451473
\(748\) 0 0
\(749\) −45.8627 −1.67579
\(750\) 0 0
\(751\) 31.5561 1.15150 0.575749 0.817626i \(-0.304711\pi\)
0.575749 + 0.817626i \(0.304711\pi\)
\(752\) 0 0
\(753\) −12.3880 −0.451443
\(754\) 0 0
\(755\) −0.0182095 −0.000662713 0
\(756\) 0 0
\(757\) −50.8340 −1.84759 −0.923797 0.382882i \(-0.874932\pi\)
−0.923797 + 0.382882i \(0.874932\pi\)
\(758\) 0 0
\(759\) −2.06616 −0.0749968
\(760\) 0 0
\(761\) −42.0280 −1.52351 −0.761757 0.647862i \(-0.775663\pi\)
−0.761757 + 0.647862i \(0.775663\pi\)
\(762\) 0 0
\(763\) 20.7635 0.751691
\(764\) 0 0
\(765\) 0.599594 0.0216784
\(766\) 0 0
\(767\) 7.51363 0.271302
\(768\) 0 0
\(769\) −23.7074 −0.854910 −0.427455 0.904037i \(-0.640590\pi\)
−0.427455 + 0.904037i \(0.640590\pi\)
\(770\) 0 0
\(771\) −3.36413 −0.121156
\(772\) 0 0
\(773\) 45.9892 1.65412 0.827058 0.562117i \(-0.190013\pi\)
0.827058 + 0.562117i \(0.190013\pi\)
\(774\) 0 0
\(775\) −36.9244 −1.32636
\(776\) 0 0
\(777\) 9.68950 0.347609
\(778\) 0 0
\(779\) −9.90649 −0.354937
\(780\) 0 0
\(781\) −15.4428 −0.552588
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) −3.11384 −0.111138
\(786\) 0 0
\(787\) −26.6405 −0.949633 −0.474817 0.880085i \(-0.657486\pi\)
−0.474817 + 0.880085i \(0.657486\pi\)
\(788\) 0 0
\(789\) −2.66208 −0.0947725
\(790\) 0 0
\(791\) −0.640098 −0.0227593
\(792\) 0 0
\(793\) 1.95766 0.0695184
\(794\) 0 0
\(795\) −0.446784 −0.0158458
\(796\) 0 0
\(797\) −13.0712 −0.463005 −0.231503 0.972834i \(-0.574364\pi\)
−0.231503 + 0.972834i \(0.574364\pi\)
\(798\) 0 0
\(799\) −8.89001 −0.314506
\(800\) 0 0
\(801\) 3.05613 0.107983
\(802\) 0 0
\(803\) −18.9464 −0.668605
\(804\) 0 0
\(805\) −0.462529 −0.0163020
\(806\) 0 0
\(807\) −27.7521 −0.976921
\(808\) 0 0
\(809\) −46.1007 −1.62081 −0.810407 0.585867i \(-0.800754\pi\)
−0.810407 + 0.585867i \(0.800754\pi\)
\(810\) 0 0
\(811\) 51.4502 1.80666 0.903331 0.428944i \(-0.141114\pi\)
0.903331 + 0.428944i \(0.141114\pi\)
\(812\) 0 0
\(813\) −14.0820 −0.493877
\(814\) 0 0
\(815\) 2.22759 0.0780289
\(816\) 0 0
\(817\) 0.574695 0.0201060
\(818\) 0 0
\(819\) 2.34265 0.0818590
\(820\) 0 0
\(821\) 18.8958 0.659468 0.329734 0.944074i \(-0.393041\pi\)
0.329734 + 0.944074i \(0.393041\pi\)
\(822\) 0 0
\(823\) −44.2997 −1.54419 −0.772095 0.635508i \(-0.780791\pi\)
−0.772095 + 0.635508i \(0.780791\pi\)
\(824\) 0 0
\(825\) 10.2911 0.358290
\(826\) 0 0
\(827\) 55.2164 1.92006 0.960031 0.279894i \(-0.0902994\pi\)
0.960031 + 0.279894i \(0.0902994\pi\)
\(828\) 0 0
\(829\) 20.0445 0.696173 0.348086 0.937462i \(-0.386832\pi\)
0.348086 + 0.937462i \(0.386832\pi\)
\(830\) 0 0
\(831\) −21.3082 −0.739173
\(832\) 0 0
\(833\) 17.8768 0.619396
\(834\) 0 0
\(835\) 1.94852 0.0674314
\(836\) 0 0
\(837\) 7.41338 0.256244
\(838\) 0 0
\(839\) 36.2113 1.25015 0.625077 0.780563i \(-0.285068\pi\)
0.625077 + 0.780563i \(0.285068\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 6.82977 0.235230
\(844\) 0 0
\(845\) −1.73376 −0.0596430
\(846\) 0 0
\(847\) 22.4587 0.771691
\(848\) 0 0
\(849\) −15.5966 −0.535275
\(850\) 0 0
\(851\) −2.90399 −0.0995475
\(852\) 0 0
\(853\) 10.3414 0.354083 0.177041 0.984203i \(-0.443347\pi\)
0.177041 + 0.984203i \(0.443347\pi\)
\(854\) 0 0
\(855\) 0.338441 0.0115744
\(856\) 0 0
\(857\) −39.0306 −1.33326 −0.666630 0.745389i \(-0.732264\pi\)
−0.666630 + 0.745389i \(0.732264\pi\)
\(858\) 0 0
\(859\) −30.8566 −1.05281 −0.526407 0.850232i \(-0.676461\pi\)
−0.526407 + 0.850232i \(0.676461\pi\)
\(860\) 0 0
\(861\) 13.5387 0.461397
\(862\) 0 0
\(863\) 26.4991 0.902041 0.451021 0.892514i \(-0.351060\pi\)
0.451021 + 0.892514i \(0.351060\pi\)
\(864\) 0 0
\(865\) −2.69546 −0.0916484
\(866\) 0 0
\(867\) 1.70890 0.0580373
\(868\) 0 0
\(869\) −22.8220 −0.774183
\(870\) 0 0
\(871\) 8.14973 0.276143
\(872\) 0 0
\(873\) 2.74522 0.0929118
\(874\) 0 0
\(875\) 4.61641 0.156063
\(876\) 0 0
\(877\) 48.2089 1.62790 0.813950 0.580935i \(-0.197313\pi\)
0.813950 + 0.580935i \(0.197313\pi\)
\(878\) 0 0
\(879\) −4.78475 −0.161385
\(880\) 0 0
\(881\) 1.44657 0.0487363 0.0243681 0.999703i \(-0.492243\pi\)
0.0243681 + 0.999703i \(0.492243\pi\)
\(882\) 0 0
\(883\) −53.2500 −1.79200 −0.896002 0.444049i \(-0.853541\pi\)
−0.896002 + 0.444049i \(0.853541\pi\)
\(884\) 0 0
\(885\) −1.48348 −0.0498666
\(886\) 0 0
\(887\) −16.8685 −0.566390 −0.283195 0.959062i \(-0.591394\pi\)
−0.283195 + 0.959062i \(0.591394\pi\)
\(888\) 0 0
\(889\) 66.3770 2.22621
\(890\) 0 0
\(891\) −2.06616 −0.0692189
\(892\) 0 0
\(893\) −5.01797 −0.167920
\(894\) 0 0
\(895\) −0.948523 −0.0317056
\(896\) 0 0
\(897\) −0.702105 −0.0234426
\(898\) 0 0
\(899\) 7.41338 0.247250
\(900\) 0 0
\(901\) −13.9408 −0.464437
\(902\) 0 0
\(903\) −0.785406 −0.0261367
\(904\) 0 0
\(905\) 2.38784 0.0793746
\(906\) 0 0
\(907\) −20.3282 −0.674988 −0.337494 0.941328i \(-0.609579\pi\)
−0.337494 + 0.941328i \(0.609579\pi\)
\(908\) 0 0
\(909\) −13.4238 −0.445240
\(910\) 0 0
\(911\) 18.6443 0.617713 0.308856 0.951109i \(-0.400054\pi\)
0.308856 + 0.951109i \(0.400054\pi\)
\(912\) 0 0
\(913\) 25.4951 0.843764
\(914\) 0 0
\(915\) −0.386516 −0.0127778
\(916\) 0 0
\(917\) 31.2622 1.03237
\(918\) 0 0
\(919\) −37.5774 −1.23956 −0.619782 0.784774i \(-0.712779\pi\)
−0.619782 + 0.784774i \(0.712779\pi\)
\(920\) 0 0
\(921\) 1.56614 0.0516060
\(922\) 0 0
\(923\) −5.24765 −0.172729
\(924\) 0 0
\(925\) 14.4641 0.475578
\(926\) 0 0
\(927\) 5.32865 0.175016
\(928\) 0 0
\(929\) 24.3674 0.799468 0.399734 0.916631i \(-0.369103\pi\)
0.399734 + 0.916631i \(0.369103\pi\)
\(930\) 0 0
\(931\) 10.0906 0.330706
\(932\) 0 0
\(933\) −23.2734 −0.761939
\(934\) 0 0
\(935\) −1.23886 −0.0405149
\(936\) 0 0
\(937\) 28.7809 0.940231 0.470116 0.882605i \(-0.344212\pi\)
0.470116 + 0.882605i \(0.344212\pi\)
\(938\) 0 0
\(939\) −9.54782 −0.311581
\(940\) 0 0
\(941\) 25.9181 0.844906 0.422453 0.906385i \(-0.361169\pi\)
0.422453 + 0.906385i \(0.361169\pi\)
\(942\) 0 0
\(943\) −4.05761 −0.132134
\(944\) 0 0
\(945\) −0.462529 −0.0150461
\(946\) 0 0
\(947\) 52.4650 1.70488 0.852442 0.522822i \(-0.175121\pi\)
0.852442 + 0.522822i \(0.175121\pi\)
\(948\) 0 0
\(949\) −6.43821 −0.208993
\(950\) 0 0
\(951\) 4.20816 0.136459
\(952\) 0 0
\(953\) 37.1505 1.20342 0.601711 0.798714i \(-0.294486\pi\)
0.601711 + 0.798714i \(0.294486\pi\)
\(954\) 0 0
\(955\) 0.937517 0.0303373
\(956\) 0 0
\(957\) −2.06616 −0.0667894
\(958\) 0 0
\(959\) 15.5079 0.500776
\(960\) 0 0
\(961\) 23.9581 0.772843
\(962\) 0 0
\(963\) 13.7453 0.442935
\(964\) 0 0
\(965\) −2.65537 −0.0854795
\(966\) 0 0
\(967\) 25.9982 0.836046 0.418023 0.908436i \(-0.362723\pi\)
0.418023 + 0.908436i \(0.362723\pi\)
\(968\) 0 0
\(969\) 10.5602 0.339244
\(970\) 0 0
\(971\) 22.7888 0.731327 0.365664 0.930747i \(-0.380842\pi\)
0.365664 + 0.930747i \(0.380842\pi\)
\(972\) 0 0
\(973\) −5.12419 −0.164274
\(974\) 0 0
\(975\) 3.49703 0.111995
\(976\) 0 0
\(977\) 36.4695 1.16676 0.583382 0.812198i \(-0.301729\pi\)
0.583382 + 0.812198i \(0.301729\pi\)
\(978\) 0 0
\(979\) −6.31446 −0.201811
\(980\) 0 0
\(981\) −6.22293 −0.198683
\(982\) 0 0
\(983\) −3.18723 −0.101657 −0.0508284 0.998707i \(-0.516186\pi\)
−0.0508284 + 0.998707i \(0.516186\pi\)
\(984\) 0 0
\(985\) 3.15827 0.100631
\(986\) 0 0
\(987\) 6.85779 0.218286
\(988\) 0 0
\(989\) 0.235390 0.00748496
\(990\) 0 0
\(991\) 53.1446 1.68819 0.844097 0.536191i \(-0.180137\pi\)
0.844097 + 0.536191i \(0.180137\pi\)
\(992\) 0 0
\(993\) −5.28355 −0.167668
\(994\) 0 0
\(995\) 2.36584 0.0750020
\(996\) 0 0
\(997\) −51.0173 −1.61573 −0.807867 0.589364i \(-0.799378\pi\)
−0.807867 + 0.589364i \(0.799378\pi\)
\(998\) 0 0
\(999\) −2.90399 −0.0918782
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 \(a_p\))