Properties

Label 8001.2.a.v.1.9
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.823573\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.823573 q^{2}\) \(-1.32173 q^{4}\) \(+2.87784 q^{5}\) \(+1.00000 q^{7}\) \(+2.73569 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.823573 q^{2}\) \(-1.32173 q^{4}\) \(+2.87784 q^{5}\) \(+1.00000 q^{7}\) \(+2.73569 q^{8}\) \(-2.37011 q^{10}\) \(+2.49735 q^{11}\) \(-3.14350 q^{13}\) \(-0.823573 q^{14}\) \(+0.390415 q^{16}\) \(+2.04099 q^{17}\) \(+3.80024 q^{19}\) \(-3.80372 q^{20}\) \(-2.05675 q^{22}\) \(+0.178746 q^{23}\) \(+3.28195 q^{25}\) \(+2.58890 q^{26}\) \(-1.32173 q^{28}\) \(-7.77822 q^{29}\) \(+8.24454 q^{31}\) \(-5.79291 q^{32}\) \(-1.68090 q^{34}\) \(+2.87784 q^{35}\) \(+0.0498363 q^{37}\) \(-3.12978 q^{38}\) \(+7.87286 q^{40}\) \(+2.14558 q^{41}\) \(+4.51117 q^{43}\) \(-3.30082 q^{44}\) \(-0.147210 q^{46}\) \(+0.391553 q^{47}\) \(+1.00000 q^{49}\) \(-2.70293 q^{50}\) \(+4.15485 q^{52}\) \(+8.31101 q^{53}\) \(+7.18698 q^{55}\) \(+2.73569 q^{56}\) \(+6.40593 q^{58}\) \(-14.3285 q^{59}\) \(+8.25276 q^{61}\) \(-6.78999 q^{62}\) \(+3.99005 q^{64}\) \(-9.04648 q^{65}\) \(-5.83463 q^{67}\) \(-2.69763 q^{68}\) \(-2.37011 q^{70}\) \(-8.03307 q^{71}\) \(+14.0099 q^{73}\) \(-0.0410438 q^{74}\) \(-5.02288 q^{76}\) \(+2.49735 q^{77}\) \(-5.72861 q^{79}\) \(+1.12355 q^{80}\) \(-1.76704 q^{82}\) \(+8.13150 q^{83}\) \(+5.87364 q^{85}\) \(-3.71528 q^{86}\) \(+6.83197 q^{88}\) \(+15.4810 q^{89}\) \(-3.14350 q^{91}\) \(-0.236253 q^{92}\) \(-0.322472 q^{94}\) \(+10.9365 q^{95}\) \(-1.62954 q^{97}\) \(-0.823573 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.823573 −0.582354 −0.291177 0.956669i \(-0.594047\pi\)
−0.291177 + 0.956669i \(0.594047\pi\)
\(3\) 0 0
\(4\) −1.32173 −0.660863
\(5\) 2.87784 1.28701 0.643504 0.765443i \(-0.277480\pi\)
0.643504 + 0.765443i \(0.277480\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.73569 0.967211
\(9\) 0 0
\(10\) −2.37011 −0.749495
\(11\) 2.49735 0.752980 0.376490 0.926421i \(-0.377131\pi\)
0.376490 + 0.926421i \(0.377131\pi\)
\(12\) 0 0
\(13\) −3.14350 −0.871850 −0.435925 0.899983i \(-0.643579\pi\)
−0.435925 + 0.899983i \(0.643579\pi\)
\(14\) −0.823573 −0.220109
\(15\) 0 0
\(16\) 0.390415 0.0976038
\(17\) 2.04099 0.495012 0.247506 0.968886i \(-0.420389\pi\)
0.247506 + 0.968886i \(0.420389\pi\)
\(18\) 0 0
\(19\) 3.80024 0.871836 0.435918 0.899987i \(-0.356424\pi\)
0.435918 + 0.899987i \(0.356424\pi\)
\(20\) −3.80372 −0.850537
\(21\) 0 0
\(22\) −2.05675 −0.438501
\(23\) 0.178746 0.0372711 0.0186355 0.999826i \(-0.494068\pi\)
0.0186355 + 0.999826i \(0.494068\pi\)
\(24\) 0 0
\(25\) 3.28195 0.656391
\(26\) 2.58890 0.507726
\(27\) 0 0
\(28\) −1.32173 −0.249783
\(29\) −7.77822 −1.44438 −0.722189 0.691695i \(-0.756864\pi\)
−0.722189 + 0.691695i \(0.756864\pi\)
\(30\) 0 0
\(31\) 8.24454 1.48076 0.740382 0.672187i \(-0.234645\pi\)
0.740382 + 0.672187i \(0.234645\pi\)
\(32\) −5.79291 −1.02405
\(33\) 0 0
\(34\) −1.68090 −0.288273
\(35\) 2.87784 0.486444
\(36\) 0 0
\(37\) 0.0498363 0.00819303 0.00409652 0.999992i \(-0.498696\pi\)
0.00409652 + 0.999992i \(0.498696\pi\)
\(38\) −3.12978 −0.507717
\(39\) 0 0
\(40\) 7.87286 1.24481
\(41\) 2.14558 0.335084 0.167542 0.985865i \(-0.446417\pi\)
0.167542 + 0.985865i \(0.446417\pi\)
\(42\) 0 0
\(43\) 4.51117 0.687946 0.343973 0.938979i \(-0.388227\pi\)
0.343973 + 0.938979i \(0.388227\pi\)
\(44\) −3.30082 −0.497617
\(45\) 0 0
\(46\) −0.147210 −0.0217050
\(47\) 0.391553 0.0571138 0.0285569 0.999592i \(-0.490909\pi\)
0.0285569 + 0.999592i \(0.490909\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −2.70293 −0.382252
\(51\) 0 0
\(52\) 4.15485 0.576174
\(53\) 8.31101 1.14160 0.570802 0.821088i \(-0.306632\pi\)
0.570802 + 0.821088i \(0.306632\pi\)
\(54\) 0 0
\(55\) 7.18698 0.969092
\(56\) 2.73569 0.365571
\(57\) 0 0
\(58\) 6.40593 0.841140
\(59\) −14.3285 −1.86542 −0.932709 0.360630i \(-0.882562\pi\)
−0.932709 + 0.360630i \(0.882562\pi\)
\(60\) 0 0
\(61\) 8.25276 1.05666 0.528329 0.849040i \(-0.322819\pi\)
0.528329 + 0.849040i \(0.322819\pi\)
\(62\) −6.78999 −0.862329
\(63\) 0 0
\(64\) 3.99005 0.498757
\(65\) −9.04648 −1.12208
\(66\) 0 0
\(67\) −5.83463 −0.712814 −0.356407 0.934331i \(-0.615998\pi\)
−0.356407 + 0.934331i \(0.615998\pi\)
\(68\) −2.69763 −0.327136
\(69\) 0 0
\(70\) −2.37011 −0.283283
\(71\) −8.03307 −0.953349 −0.476675 0.879080i \(-0.658158\pi\)
−0.476675 + 0.879080i \(0.658158\pi\)
\(72\) 0 0
\(73\) 14.0099 1.63973 0.819866 0.572556i \(-0.194048\pi\)
0.819866 + 0.572556i \(0.194048\pi\)
\(74\) −0.0410438 −0.00477125
\(75\) 0 0
\(76\) −5.02288 −0.576164
\(77\) 2.49735 0.284600
\(78\) 0 0
\(79\) −5.72861 −0.644520 −0.322260 0.946651i \(-0.604442\pi\)
−0.322260 + 0.946651i \(0.604442\pi\)
\(80\) 1.12355 0.125617
\(81\) 0 0
\(82\) −1.76704 −0.195137
\(83\) 8.13150 0.892548 0.446274 0.894896i \(-0.352751\pi\)
0.446274 + 0.894896i \(0.352751\pi\)
\(84\) 0 0
\(85\) 5.87364 0.637085
\(86\) −3.71528 −0.400629
\(87\) 0 0
\(88\) 6.83197 0.728291
\(89\) 15.4810 1.64098 0.820490 0.571660i \(-0.193701\pi\)
0.820490 + 0.571660i \(0.193701\pi\)
\(90\) 0 0
\(91\) −3.14350 −0.329528
\(92\) −0.236253 −0.0246311
\(93\) 0 0
\(94\) −0.322472 −0.0332605
\(95\) 10.9365 1.12206
\(96\) 0 0
\(97\) −1.62954 −0.165455 −0.0827275 0.996572i \(-0.526363\pi\)
−0.0827275 + 0.996572i \(0.526363\pi\)
\(98\) −0.823573 −0.0831935
\(99\) 0 0
\(100\) −4.33785 −0.433785
\(101\) 18.5531 1.84611 0.923054 0.384672i \(-0.125685\pi\)
0.923054 + 0.384672i \(0.125685\pi\)
\(102\) 0 0
\(103\) 13.8022 1.35997 0.679984 0.733227i \(-0.261987\pi\)
0.679984 + 0.733227i \(0.261987\pi\)
\(104\) −8.59963 −0.843263
\(105\) 0 0
\(106\) −6.84472 −0.664818
\(107\) −11.5898 −1.12043 −0.560216 0.828347i \(-0.689282\pi\)
−0.560216 + 0.828347i \(0.689282\pi\)
\(108\) 0 0
\(109\) 4.90568 0.469879 0.234939 0.972010i \(-0.424511\pi\)
0.234939 + 0.972010i \(0.424511\pi\)
\(110\) −5.91900 −0.564355
\(111\) 0 0
\(112\) 0.390415 0.0368908
\(113\) −11.4900 −1.08089 −0.540446 0.841379i \(-0.681744\pi\)
−0.540446 + 0.841379i \(0.681744\pi\)
\(114\) 0 0
\(115\) 0.514401 0.0479682
\(116\) 10.2807 0.954537
\(117\) 0 0
\(118\) 11.8006 1.08633
\(119\) 2.04099 0.187097
\(120\) 0 0
\(121\) −4.76323 −0.433021
\(122\) −6.79675 −0.615349
\(123\) 0 0
\(124\) −10.8970 −0.978582
\(125\) −4.94426 −0.442228
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 8.29971 0.733598
\(129\) 0 0
\(130\) 7.45044 0.653447
\(131\) −4.61325 −0.403062 −0.201531 0.979482i \(-0.564592\pi\)
−0.201531 + 0.979482i \(0.564592\pi\)
\(132\) 0 0
\(133\) 3.80024 0.329523
\(134\) 4.80525 0.415110
\(135\) 0 0
\(136\) 5.58350 0.478781
\(137\) 7.76252 0.663197 0.331599 0.943421i \(-0.392412\pi\)
0.331599 + 0.943421i \(0.392412\pi\)
\(138\) 0 0
\(139\) 13.1628 1.11646 0.558228 0.829688i \(-0.311481\pi\)
0.558228 + 0.829688i \(0.311481\pi\)
\(140\) −3.80372 −0.321473
\(141\) 0 0
\(142\) 6.61582 0.555187
\(143\) −7.85043 −0.656486
\(144\) 0 0
\(145\) −22.3845 −1.85893
\(146\) −11.5382 −0.954905
\(147\) 0 0
\(148\) −0.0658699 −0.00541447
\(149\) −14.6464 −1.19988 −0.599940 0.800045i \(-0.704809\pi\)
−0.599940 + 0.800045i \(0.704809\pi\)
\(150\) 0 0
\(151\) −5.84407 −0.475584 −0.237792 0.971316i \(-0.576424\pi\)
−0.237792 + 0.971316i \(0.576424\pi\)
\(152\) 10.3963 0.843249
\(153\) 0 0
\(154\) −2.05675 −0.165738
\(155\) 23.7265 1.90576
\(156\) 0 0
\(157\) 2.25235 0.179757 0.0898786 0.995953i \(-0.471352\pi\)
0.0898786 + 0.995953i \(0.471352\pi\)
\(158\) 4.71794 0.375339
\(159\) 0 0
\(160\) −16.6711 −1.31796
\(161\) 0.178746 0.0140871
\(162\) 0 0
\(163\) 17.9604 1.40677 0.703385 0.710809i \(-0.251671\pi\)
0.703385 + 0.710809i \(0.251671\pi\)
\(164\) −2.83587 −0.221445
\(165\) 0 0
\(166\) −6.69689 −0.519779
\(167\) −6.74574 −0.522001 −0.261000 0.965339i \(-0.584052\pi\)
−0.261000 + 0.965339i \(0.584052\pi\)
\(168\) 0 0
\(169\) −3.11841 −0.239878
\(170\) −4.83737 −0.371009
\(171\) 0 0
\(172\) −5.96253 −0.454639
\(173\) −13.0095 −0.989096 −0.494548 0.869150i \(-0.664666\pi\)
−0.494548 + 0.869150i \(0.664666\pi\)
\(174\) 0 0
\(175\) 3.28195 0.248092
\(176\) 0.975004 0.0734937
\(177\) 0 0
\(178\) −12.7497 −0.955632
\(179\) 13.0566 0.975894 0.487947 0.872873i \(-0.337746\pi\)
0.487947 + 0.872873i \(0.337746\pi\)
\(180\) 0 0
\(181\) −8.28417 −0.615758 −0.307879 0.951426i \(-0.599619\pi\)
−0.307879 + 0.951426i \(0.599619\pi\)
\(182\) 2.58890 0.191902
\(183\) 0 0
\(184\) 0.488992 0.0360490
\(185\) 0.143421 0.0105445
\(186\) 0 0
\(187\) 5.09707 0.372734
\(188\) −0.517526 −0.0377444
\(189\) 0 0
\(190\) −9.00700 −0.653436
\(191\) −1.47363 −0.106628 −0.0533140 0.998578i \(-0.516978\pi\)
−0.0533140 + 0.998578i \(0.516978\pi\)
\(192\) 0 0
\(193\) −3.64272 −0.262209 −0.131104 0.991369i \(-0.541852\pi\)
−0.131104 + 0.991369i \(0.541852\pi\)
\(194\) 1.34205 0.0963534
\(195\) 0 0
\(196\) −1.32173 −0.0944091
\(197\) −1.55636 −0.110886 −0.0554429 0.998462i \(-0.517657\pi\)
−0.0554429 + 0.998462i \(0.517657\pi\)
\(198\) 0 0
\(199\) −4.82683 −0.342165 −0.171083 0.985257i \(-0.554726\pi\)
−0.171083 + 0.985257i \(0.554726\pi\)
\(200\) 8.97840 0.634869
\(201\) 0 0
\(202\) −15.2799 −1.07509
\(203\) −7.77822 −0.545924
\(204\) 0 0
\(205\) 6.17464 0.431256
\(206\) −11.3671 −0.791984
\(207\) 0 0
\(208\) −1.22727 −0.0850959
\(209\) 9.49055 0.656475
\(210\) 0 0
\(211\) 13.2751 0.913893 0.456947 0.889494i \(-0.348943\pi\)
0.456947 + 0.889494i \(0.348943\pi\)
\(212\) −10.9849 −0.754445
\(213\) 0 0
\(214\) 9.54508 0.652488
\(215\) 12.9824 0.885393
\(216\) 0 0
\(217\) 8.24454 0.559676
\(218\) −4.04019 −0.273636
\(219\) 0 0
\(220\) −9.49922 −0.640437
\(221\) −6.41585 −0.431577
\(222\) 0 0
\(223\) 17.5530 1.17544 0.587718 0.809066i \(-0.300027\pi\)
0.587718 + 0.809066i \(0.300027\pi\)
\(224\) −5.79291 −0.387055
\(225\) 0 0
\(226\) 9.46288 0.629462
\(227\) −18.5774 −1.23303 −0.616514 0.787344i \(-0.711455\pi\)
−0.616514 + 0.787344i \(0.711455\pi\)
\(228\) 0 0
\(229\) 22.9178 1.51445 0.757226 0.653153i \(-0.226554\pi\)
0.757226 + 0.653153i \(0.226554\pi\)
\(230\) −0.423647 −0.0279345
\(231\) 0 0
\(232\) −21.2788 −1.39702
\(233\) 4.19204 0.274630 0.137315 0.990527i \(-0.456153\pi\)
0.137315 + 0.990527i \(0.456153\pi\)
\(234\) 0 0
\(235\) 1.12683 0.0735060
\(236\) 18.9384 1.23279
\(237\) 0 0
\(238\) −1.68090 −0.108957
\(239\) 16.4112 1.06155 0.530776 0.847512i \(-0.321901\pi\)
0.530776 + 0.847512i \(0.321901\pi\)
\(240\) 0 0
\(241\) −19.4130 −1.25050 −0.625252 0.780423i \(-0.715004\pi\)
−0.625252 + 0.780423i \(0.715004\pi\)
\(242\) 3.92287 0.252172
\(243\) 0 0
\(244\) −10.9079 −0.698306
\(245\) 2.87784 0.183858
\(246\) 0 0
\(247\) −11.9461 −0.760110
\(248\) 22.5545 1.43221
\(249\) 0 0
\(250\) 4.07196 0.257533
\(251\) −2.54869 −0.160872 −0.0804359 0.996760i \(-0.525631\pi\)
−0.0804359 + 0.996760i \(0.525631\pi\)
\(252\) 0 0
\(253\) 0.446391 0.0280644
\(254\) −0.823573 −0.0516756
\(255\) 0 0
\(256\) −14.8155 −0.925971
\(257\) −9.24122 −0.576451 −0.288226 0.957563i \(-0.593065\pi\)
−0.288226 + 0.957563i \(0.593065\pi\)
\(258\) 0 0
\(259\) 0.0498363 0.00309668
\(260\) 11.9570 0.741540
\(261\) 0 0
\(262\) 3.79935 0.234725
\(263\) −9.94843 −0.613447 −0.306723 0.951799i \(-0.599233\pi\)
−0.306723 + 0.951799i \(0.599233\pi\)
\(264\) 0 0
\(265\) 23.9177 1.46925
\(266\) −3.12978 −0.191899
\(267\) 0 0
\(268\) 7.71179 0.471072
\(269\) −3.68337 −0.224579 −0.112290 0.993676i \(-0.535818\pi\)
−0.112290 + 0.993676i \(0.535818\pi\)
\(270\) 0 0
\(271\) 8.76862 0.532656 0.266328 0.963883i \(-0.414190\pi\)
0.266328 + 0.963883i \(0.414190\pi\)
\(272\) 0.796833 0.0483151
\(273\) 0 0
\(274\) −6.39301 −0.386216
\(275\) 8.19620 0.494249
\(276\) 0 0
\(277\) 6.04083 0.362958 0.181479 0.983395i \(-0.441912\pi\)
0.181479 + 0.983395i \(0.441912\pi\)
\(278\) −10.8406 −0.650173
\(279\) 0 0
\(280\) 7.87286 0.470494
\(281\) 29.8481 1.78059 0.890293 0.455388i \(-0.150499\pi\)
0.890293 + 0.455388i \(0.150499\pi\)
\(282\) 0 0
\(283\) −0.479453 −0.0285005 −0.0142502 0.999898i \(-0.504536\pi\)
−0.0142502 + 0.999898i \(0.504536\pi\)
\(284\) 10.6175 0.630034
\(285\) 0 0
\(286\) 6.46540 0.382307
\(287\) 2.14558 0.126650
\(288\) 0 0
\(289\) −12.8344 −0.754963
\(290\) 18.4352 1.08255
\(291\) 0 0
\(292\) −18.5172 −1.08364
\(293\) 20.9011 1.22106 0.610528 0.791994i \(-0.290957\pi\)
0.610528 + 0.791994i \(0.290957\pi\)
\(294\) 0 0
\(295\) −41.2352 −2.40081
\(296\) 0.136336 0.00792439
\(297\) 0 0
\(298\) 12.0624 0.698755
\(299\) −0.561887 −0.0324948
\(300\) 0 0
\(301\) 4.51117 0.260019
\(302\) 4.81302 0.276958
\(303\) 0 0
\(304\) 1.48367 0.0850944
\(305\) 23.7501 1.35993
\(306\) 0 0
\(307\) −23.1940 −1.32375 −0.661876 0.749613i \(-0.730240\pi\)
−0.661876 + 0.749613i \(0.730240\pi\)
\(308\) −3.30082 −0.188082
\(309\) 0 0
\(310\) −19.5405 −1.10982
\(311\) −25.8909 −1.46814 −0.734069 0.679075i \(-0.762381\pi\)
−0.734069 + 0.679075i \(0.762381\pi\)
\(312\) 0 0
\(313\) 18.2780 1.03313 0.516566 0.856247i \(-0.327210\pi\)
0.516566 + 0.856247i \(0.327210\pi\)
\(314\) −1.85498 −0.104682
\(315\) 0 0
\(316\) 7.57166 0.425939
\(317\) −25.2643 −1.41898 −0.709491 0.704714i \(-0.751075\pi\)
−0.709491 + 0.704714i \(0.751075\pi\)
\(318\) 0 0
\(319\) −19.4249 −1.08759
\(320\) 11.4827 0.641904
\(321\) 0 0
\(322\) −0.147210 −0.00820370
\(323\) 7.75625 0.431569
\(324\) 0 0
\(325\) −10.3168 −0.572274
\(326\) −14.7917 −0.819239
\(327\) 0 0
\(328\) 5.86964 0.324097
\(329\) 0.391553 0.0215870
\(330\) 0 0
\(331\) −9.71108 −0.533769 −0.266885 0.963728i \(-0.585994\pi\)
−0.266885 + 0.963728i \(0.585994\pi\)
\(332\) −10.7476 −0.589852
\(333\) 0 0
\(334\) 5.55561 0.303989
\(335\) −16.7911 −0.917397
\(336\) 0 0
\(337\) −0.338072 −0.0184159 −0.00920797 0.999958i \(-0.502931\pi\)
−0.00920797 + 0.999958i \(0.502931\pi\)
\(338\) 2.56824 0.139694
\(339\) 0 0
\(340\) −7.76334 −0.421026
\(341\) 20.5895 1.11499
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 12.3411 0.665389
\(345\) 0 0
\(346\) 10.7143 0.576005
\(347\) −10.8081 −0.580211 −0.290106 0.956995i \(-0.593690\pi\)
−0.290106 + 0.956995i \(0.593690\pi\)
\(348\) 0 0
\(349\) −30.2039 −1.61678 −0.808388 0.588650i \(-0.799660\pi\)
−0.808388 + 0.588650i \(0.799660\pi\)
\(350\) −2.70293 −0.144478
\(351\) 0 0
\(352\) −14.4669 −0.771090
\(353\) 24.0686 1.28104 0.640521 0.767941i \(-0.278719\pi\)
0.640521 + 0.767941i \(0.278719\pi\)
\(354\) 0 0
\(355\) −23.1179 −1.22697
\(356\) −20.4616 −1.08446
\(357\) 0 0
\(358\) −10.7530 −0.568316
\(359\) −6.18593 −0.326481 −0.163240 0.986586i \(-0.552195\pi\)
−0.163240 + 0.986586i \(0.552195\pi\)
\(360\) 0 0
\(361\) −4.55815 −0.239903
\(362\) 6.82262 0.358589
\(363\) 0 0
\(364\) 4.15485 0.217773
\(365\) 40.3182 2.11035
\(366\) 0 0
\(367\) −11.5359 −0.602170 −0.301085 0.953597i \(-0.597349\pi\)
−0.301085 + 0.953597i \(0.597349\pi\)
\(368\) 0.0697850 0.00363780
\(369\) 0 0
\(370\) −0.118118 −0.00614064
\(371\) 8.31101 0.431486
\(372\) 0 0
\(373\) −19.8284 −1.02668 −0.513338 0.858186i \(-0.671591\pi\)
−0.513338 + 0.858186i \(0.671591\pi\)
\(374\) −4.19781 −0.217064
\(375\) 0 0
\(376\) 1.07116 0.0552411
\(377\) 24.4508 1.25928
\(378\) 0 0
\(379\) −9.80003 −0.503394 −0.251697 0.967806i \(-0.580989\pi\)
−0.251697 + 0.967806i \(0.580989\pi\)
\(380\) −14.4550 −0.741528
\(381\) 0 0
\(382\) 1.21364 0.0620953
\(383\) −8.47434 −0.433018 −0.216509 0.976281i \(-0.569467\pi\)
−0.216509 + 0.976281i \(0.569467\pi\)
\(384\) 0 0
\(385\) 7.18698 0.366282
\(386\) 3.00005 0.152698
\(387\) 0 0
\(388\) 2.15381 0.109343
\(389\) 38.7291 1.96365 0.981823 0.189800i \(-0.0607840\pi\)
0.981823 + 0.189800i \(0.0607840\pi\)
\(390\) 0 0
\(391\) 0.364818 0.0184496
\(392\) 2.73569 0.138173
\(393\) 0 0
\(394\) 1.28177 0.0645749
\(395\) −16.4860 −0.829502
\(396\) 0 0
\(397\) 15.0600 0.755838 0.377919 0.925839i \(-0.376640\pi\)
0.377919 + 0.925839i \(0.376640\pi\)
\(398\) 3.97525 0.199261
\(399\) 0 0
\(400\) 1.28132 0.0640662
\(401\) −7.21253 −0.360177 −0.180088 0.983650i \(-0.557638\pi\)
−0.180088 + 0.983650i \(0.557638\pi\)
\(402\) 0 0
\(403\) −25.9167 −1.29100
\(404\) −24.5222 −1.22002
\(405\) 0 0
\(406\) 6.40593 0.317921
\(407\) 0.124459 0.00616919
\(408\) 0 0
\(409\) 22.4241 1.10880 0.554400 0.832250i \(-0.312948\pi\)
0.554400 + 0.832250i \(0.312948\pi\)
\(410\) −5.08527 −0.251144
\(411\) 0 0
\(412\) −18.2427 −0.898753
\(413\) −14.3285 −0.705062
\(414\) 0 0
\(415\) 23.4011 1.14872
\(416\) 18.2100 0.892819
\(417\) 0 0
\(418\) −7.81616 −0.382301
\(419\) 35.0231 1.71099 0.855496 0.517809i \(-0.173252\pi\)
0.855496 + 0.517809i \(0.173252\pi\)
\(420\) 0 0
\(421\) 4.53382 0.220965 0.110483 0.993878i \(-0.464760\pi\)
0.110483 + 0.993878i \(0.464760\pi\)
\(422\) −10.9330 −0.532210
\(423\) 0 0
\(424\) 22.7363 1.10417
\(425\) 6.69843 0.324922
\(426\) 0 0
\(427\) 8.25276 0.399379
\(428\) 15.3186 0.740452
\(429\) 0 0
\(430\) −10.6920 −0.515612
\(431\) 7.51951 0.362202 0.181101 0.983464i \(-0.442034\pi\)
0.181101 + 0.983464i \(0.442034\pi\)
\(432\) 0 0
\(433\) 28.4018 1.36490 0.682452 0.730930i \(-0.260914\pi\)
0.682452 + 0.730930i \(0.260914\pi\)
\(434\) −6.78999 −0.325930
\(435\) 0 0
\(436\) −6.48397 −0.310526
\(437\) 0.679277 0.0324942
\(438\) 0 0
\(439\) 21.3607 1.01949 0.509745 0.860325i \(-0.329740\pi\)
0.509745 + 0.860325i \(0.329740\pi\)
\(440\) 19.6613 0.937316
\(441\) 0 0
\(442\) 5.28392 0.251330
\(443\) −14.5312 −0.690400 −0.345200 0.938529i \(-0.612189\pi\)
−0.345200 + 0.938529i \(0.612189\pi\)
\(444\) 0 0
\(445\) 44.5518 2.11196
\(446\) −14.4562 −0.684520
\(447\) 0 0
\(448\) 3.99005 0.188512
\(449\) 1.55717 0.0734876 0.0367438 0.999325i \(-0.488301\pi\)
0.0367438 + 0.999325i \(0.488301\pi\)
\(450\) 0 0
\(451\) 5.35827 0.252311
\(452\) 15.1867 0.714321
\(453\) 0 0
\(454\) 15.2999 0.718059
\(455\) −9.04648 −0.424106
\(456\) 0 0
\(457\) −1.20252 −0.0562515 −0.0281258 0.999604i \(-0.508954\pi\)
−0.0281258 + 0.999604i \(0.508954\pi\)
\(458\) −18.8745 −0.881948
\(459\) 0 0
\(460\) −0.679898 −0.0317004
\(461\) −32.4395 −1.51086 −0.755429 0.655231i \(-0.772571\pi\)
−0.755429 + 0.655231i \(0.772571\pi\)
\(462\) 0 0
\(463\) 24.1154 1.12074 0.560368 0.828244i \(-0.310660\pi\)
0.560368 + 0.828244i \(0.310660\pi\)
\(464\) −3.03673 −0.140977
\(465\) 0 0
\(466\) −3.45245 −0.159932
\(467\) −27.5828 −1.27638 −0.638191 0.769878i \(-0.720317\pi\)
−0.638191 + 0.769878i \(0.720317\pi\)
\(468\) 0 0
\(469\) −5.83463 −0.269418
\(470\) −0.928023 −0.0428065
\(471\) 0 0
\(472\) −39.1984 −1.80425
\(473\) 11.2660 0.518010
\(474\) 0 0
\(475\) 12.4722 0.572265
\(476\) −2.69763 −0.123646
\(477\) 0 0
\(478\) −13.5158 −0.618199
\(479\) 26.6971 1.21982 0.609910 0.792471i \(-0.291206\pi\)
0.609910 + 0.792471i \(0.291206\pi\)
\(480\) 0 0
\(481\) −0.156660 −0.00714309
\(482\) 15.9881 0.728237
\(483\) 0 0
\(484\) 6.29569 0.286168
\(485\) −4.68956 −0.212942
\(486\) 0 0
\(487\) 20.3423 0.921798 0.460899 0.887453i \(-0.347527\pi\)
0.460899 + 0.887453i \(0.347527\pi\)
\(488\) 22.5770 1.02201
\(489\) 0 0
\(490\) −2.37011 −0.107071
\(491\) 10.3444 0.466838 0.233419 0.972376i \(-0.425009\pi\)
0.233419 + 0.972376i \(0.425009\pi\)
\(492\) 0 0
\(493\) −15.8753 −0.714985
\(494\) 9.83846 0.442653
\(495\) 0 0
\(496\) 3.21879 0.144528
\(497\) −8.03307 −0.360332
\(498\) 0 0
\(499\) 8.63127 0.386389 0.193194 0.981161i \(-0.438115\pi\)
0.193194 + 0.981161i \(0.438115\pi\)
\(500\) 6.53496 0.292252
\(501\) 0 0
\(502\) 2.09903 0.0936844
\(503\) −3.53121 −0.157449 −0.0787245 0.996896i \(-0.525085\pi\)
−0.0787245 + 0.996896i \(0.525085\pi\)
\(504\) 0 0
\(505\) 53.3930 2.37596
\(506\) −0.367636 −0.0163434
\(507\) 0 0
\(508\) −1.32173 −0.0586421
\(509\) 14.8864 0.659830 0.329915 0.944011i \(-0.392980\pi\)
0.329915 + 0.944011i \(0.392980\pi\)
\(510\) 0 0
\(511\) 14.0099 0.619760
\(512\) −4.39775 −0.194355
\(513\) 0 0
\(514\) 7.61082 0.335699
\(515\) 39.7204 1.75029
\(516\) 0 0
\(517\) 0.977845 0.0430056
\(518\) −0.0410438 −0.00180336
\(519\) 0 0
\(520\) −24.7483 −1.08529
\(521\) 35.0975 1.53765 0.768826 0.639458i \(-0.220841\pi\)
0.768826 + 0.639458i \(0.220841\pi\)
\(522\) 0 0
\(523\) 31.8044 1.39071 0.695355 0.718667i \(-0.255247\pi\)
0.695355 + 0.718667i \(0.255247\pi\)
\(524\) 6.09746 0.266369
\(525\) 0 0
\(526\) 8.19326 0.357243
\(527\) 16.8270 0.732996
\(528\) 0 0
\(529\) −22.9680 −0.998611
\(530\) −19.6980 −0.855627
\(531\) 0 0
\(532\) −5.02288 −0.217770
\(533\) −6.74464 −0.292143
\(534\) 0 0
\(535\) −33.3537 −1.44201
\(536\) −15.9617 −0.689441
\(537\) 0 0
\(538\) 3.03353 0.130785
\(539\) 2.49735 0.107569
\(540\) 0 0
\(541\) 2.82729 0.121555 0.0607774 0.998151i \(-0.480642\pi\)
0.0607774 + 0.998151i \(0.480642\pi\)
\(542\) −7.22160 −0.310194
\(543\) 0 0
\(544\) −11.8233 −0.506918
\(545\) 14.1178 0.604738
\(546\) 0 0
\(547\) 30.1788 1.29035 0.645176 0.764034i \(-0.276784\pi\)
0.645176 + 0.764034i \(0.276784\pi\)
\(548\) −10.2599 −0.438283
\(549\) 0 0
\(550\) −6.75017 −0.287828
\(551\) −29.5591 −1.25926
\(552\) 0 0
\(553\) −5.72861 −0.243605
\(554\) −4.97507 −0.211370
\(555\) 0 0
\(556\) −17.3977 −0.737825
\(557\) 31.9667 1.35447 0.677236 0.735766i \(-0.263178\pi\)
0.677236 + 0.735766i \(0.263178\pi\)
\(558\) 0 0
\(559\) −14.1809 −0.599786
\(560\) 1.12355 0.0474787
\(561\) 0 0
\(562\) −24.5821 −1.03693
\(563\) −45.6546 −1.92411 −0.962057 0.272849i \(-0.912034\pi\)
−0.962057 + 0.272849i \(0.912034\pi\)
\(564\) 0 0
\(565\) −33.0665 −1.39112
\(566\) 0.394864 0.0165974
\(567\) 0 0
\(568\) −21.9759 −0.922090
\(569\) 18.7255 0.785012 0.392506 0.919749i \(-0.371608\pi\)
0.392506 + 0.919749i \(0.371608\pi\)
\(570\) 0 0
\(571\) −4.52907 −0.189536 −0.0947678 0.995499i \(-0.530211\pi\)
−0.0947678 + 0.995499i \(0.530211\pi\)
\(572\) 10.3761 0.433847
\(573\) 0 0
\(574\) −1.76704 −0.0737550
\(575\) 0.586635 0.0244644
\(576\) 0 0
\(577\) −8.47904 −0.352987 −0.176494 0.984302i \(-0.556475\pi\)
−0.176494 + 0.984302i \(0.556475\pi\)
\(578\) 10.5700 0.439656
\(579\) 0 0
\(580\) 29.5861 1.22850
\(581\) 8.13150 0.337352
\(582\) 0 0
\(583\) 20.7555 0.859605
\(584\) 38.3266 1.58597
\(585\) 0 0
\(586\) −17.2136 −0.711088
\(587\) 0.755169 0.0311691 0.0155846 0.999879i \(-0.495039\pi\)
0.0155846 + 0.999879i \(0.495039\pi\)
\(588\) 0 0
\(589\) 31.3313 1.29098
\(590\) 33.9603 1.39812
\(591\) 0 0
\(592\) 0.0194568 0.000799671 0
\(593\) −29.2749 −1.20218 −0.601088 0.799183i \(-0.705266\pi\)
−0.601088 + 0.799183i \(0.705266\pi\)
\(594\) 0 0
\(595\) 5.87364 0.240796
\(596\) 19.3585 0.792957
\(597\) 0 0
\(598\) 0.462755 0.0189235
\(599\) 1.60224 0.0654658 0.0327329 0.999464i \(-0.489579\pi\)
0.0327329 + 0.999464i \(0.489579\pi\)
\(600\) 0 0
\(601\) 28.8736 1.17778 0.588889 0.808214i \(-0.299566\pi\)
0.588889 + 0.808214i \(0.299566\pi\)
\(602\) −3.71528 −0.151423
\(603\) 0 0
\(604\) 7.72427 0.314296
\(605\) −13.7078 −0.557302
\(606\) 0 0
\(607\) 45.4619 1.84524 0.922621 0.385707i \(-0.126043\pi\)
0.922621 + 0.385707i \(0.126043\pi\)
\(608\) −22.0145 −0.892804
\(609\) 0 0
\(610\) −19.5600 −0.791959
\(611\) −1.23085 −0.0497947
\(612\) 0 0
\(613\) −2.01541 −0.0814015 −0.0407008 0.999171i \(-0.512959\pi\)
−0.0407008 + 0.999171i \(0.512959\pi\)
\(614\) 19.1020 0.770893
\(615\) 0 0
\(616\) 6.83197 0.275268
\(617\) 17.0285 0.685541 0.342771 0.939419i \(-0.388635\pi\)
0.342771 + 0.939419i \(0.388635\pi\)
\(618\) 0 0
\(619\) 34.6985 1.39465 0.697325 0.716755i \(-0.254374\pi\)
0.697325 + 0.716755i \(0.254374\pi\)
\(620\) −31.3599 −1.25944
\(621\) 0 0
\(622\) 21.3230 0.854976
\(623\) 15.4810 0.620232
\(624\) 0 0
\(625\) −30.6385 −1.22554
\(626\) −15.0533 −0.601649
\(627\) 0 0
\(628\) −2.97699 −0.118795
\(629\) 0.101715 0.00405565
\(630\) 0 0
\(631\) 45.6586 1.81764 0.908820 0.417187i \(-0.136984\pi\)
0.908820 + 0.417187i \(0.136984\pi\)
\(632\) −15.6717 −0.623386
\(633\) 0 0
\(634\) 20.8070 0.826350
\(635\) 2.87784 0.114204
\(636\) 0 0
\(637\) −3.14350 −0.124550
\(638\) 15.9979 0.633362
\(639\) 0 0
\(640\) 23.8852 0.944147
\(641\) −29.6589 −1.17146 −0.585728 0.810508i \(-0.699191\pi\)
−0.585728 + 0.810508i \(0.699191\pi\)
\(642\) 0 0
\(643\) 38.6046 1.52242 0.761209 0.648507i \(-0.224606\pi\)
0.761209 + 0.648507i \(0.224606\pi\)
\(644\) −0.236253 −0.00930967
\(645\) 0 0
\(646\) −6.38784 −0.251326
\(647\) 43.7708 1.72081 0.860404 0.509613i \(-0.170211\pi\)
0.860404 + 0.509613i \(0.170211\pi\)
\(648\) 0 0
\(649\) −35.7834 −1.40462
\(650\) 8.49666 0.333267
\(651\) 0 0
\(652\) −23.7388 −0.929683
\(653\) −29.4964 −1.15428 −0.577142 0.816644i \(-0.695832\pi\)
−0.577142 + 0.816644i \(0.695832\pi\)
\(654\) 0 0
\(655\) −13.2762 −0.518744
\(656\) 0.837668 0.0327054
\(657\) 0 0
\(658\) −0.322472 −0.0125713
\(659\) 19.0408 0.741724 0.370862 0.928688i \(-0.379062\pi\)
0.370862 + 0.928688i \(0.379062\pi\)
\(660\) 0 0
\(661\) 23.6329 0.919213 0.459607 0.888123i \(-0.347990\pi\)
0.459607 + 0.888123i \(0.347990\pi\)
\(662\) 7.99779 0.310843
\(663\) 0 0
\(664\) 22.2452 0.863282
\(665\) 10.9365 0.424099
\(666\) 0 0
\(667\) −1.39032 −0.0538335
\(668\) 8.91602 0.344971
\(669\) 0 0
\(670\) 13.8287 0.534250
\(671\) 20.6100 0.795642
\(672\) 0 0
\(673\) −10.4509 −0.402853 −0.201426 0.979504i \(-0.564558\pi\)
−0.201426 + 0.979504i \(0.564558\pi\)
\(674\) 0.278427 0.0107246
\(675\) 0 0
\(676\) 4.12169 0.158526
\(677\) −26.1735 −1.00593 −0.502965 0.864307i \(-0.667758\pi\)
−0.502965 + 0.864307i \(0.667758\pi\)
\(678\) 0 0
\(679\) −1.62954 −0.0625361
\(680\) 16.0684 0.616196
\(681\) 0 0
\(682\) −16.9570 −0.649317
\(683\) −40.9830 −1.56817 −0.784085 0.620653i \(-0.786867\pi\)
−0.784085 + 0.620653i \(0.786867\pi\)
\(684\) 0 0
\(685\) 22.3393 0.853540
\(686\) −0.823573 −0.0314442
\(687\) 0 0
\(688\) 1.76123 0.0671462
\(689\) −26.1256 −0.995308
\(690\) 0 0
\(691\) −26.1490 −0.994754 −0.497377 0.867534i \(-0.665703\pi\)
−0.497377 + 0.867534i \(0.665703\pi\)
\(692\) 17.1950 0.653658
\(693\) 0 0
\(694\) 8.90130 0.337889
\(695\) 37.8805 1.43689
\(696\) 0 0
\(697\) 4.37911 0.165871
\(698\) 24.8751 0.941537
\(699\) 0 0
\(700\) −4.33785 −0.163955
\(701\) −4.34759 −0.164206 −0.0821030 0.996624i \(-0.526164\pi\)
−0.0821030 + 0.996624i \(0.526164\pi\)
\(702\) 0 0
\(703\) 0.189390 0.00714298
\(704\) 9.96457 0.375554
\(705\) 0 0
\(706\) −19.8222 −0.746020
\(707\) 18.5531 0.697763
\(708\) 0 0
\(709\) 32.4246 1.21773 0.608865 0.793274i \(-0.291625\pi\)
0.608865 + 0.793274i \(0.291625\pi\)
\(710\) 19.0393 0.714531
\(711\) 0 0
\(712\) 42.3511 1.58717
\(713\) 1.47368 0.0551896
\(714\) 0 0
\(715\) −22.5923 −0.844903
\(716\) −17.2572 −0.644933
\(717\) 0 0
\(718\) 5.09457 0.190128
\(719\) 8.83585 0.329522 0.164761 0.986334i \(-0.447315\pi\)
0.164761 + 0.986334i \(0.447315\pi\)
\(720\) 0 0
\(721\) 13.8022 0.514020
\(722\) 3.75397 0.139708
\(723\) 0 0
\(724\) 10.9494 0.406932
\(725\) −25.5278 −0.948077
\(726\) 0 0
\(727\) 22.5666 0.836950 0.418475 0.908228i \(-0.362565\pi\)
0.418475 + 0.908228i \(0.362565\pi\)
\(728\) −8.59963 −0.318723
\(729\) 0 0
\(730\) −33.2050 −1.22897
\(731\) 9.20724 0.340542
\(732\) 0 0
\(733\) 18.1667 0.671001 0.335501 0.942040i \(-0.391095\pi\)
0.335501 + 0.942040i \(0.391095\pi\)
\(734\) 9.50068 0.350677
\(735\) 0 0
\(736\) −1.03546 −0.0381675
\(737\) −14.5711 −0.536734
\(738\) 0 0
\(739\) 15.3064 0.563055 0.281527 0.959553i \(-0.409159\pi\)
0.281527 + 0.959553i \(0.409159\pi\)
\(740\) −0.189563 −0.00696848
\(741\) 0 0
\(742\) −6.84472 −0.251278
\(743\) 12.1332 0.445125 0.222562 0.974918i \(-0.428558\pi\)
0.222562 + 0.974918i \(0.428558\pi\)
\(744\) 0 0
\(745\) −42.1500 −1.54426
\(746\) 16.3302 0.597889
\(747\) 0 0
\(748\) −6.73693 −0.246327
\(749\) −11.5898 −0.423483
\(750\) 0 0
\(751\) −41.2242 −1.50429 −0.752147 0.658996i \(-0.770981\pi\)
−0.752147 + 0.658996i \(0.770981\pi\)
\(752\) 0.152868 0.00557452
\(753\) 0 0
\(754\) −20.1371 −0.733348
\(755\) −16.8183 −0.612081
\(756\) 0 0
\(757\) −41.3673 −1.50352 −0.751759 0.659437i \(-0.770795\pi\)
−0.751759 + 0.659437i \(0.770795\pi\)
\(758\) 8.07105 0.293154
\(759\) 0 0
\(760\) 29.9188 1.08527
\(761\) 1.38604 0.0502440 0.0251220 0.999684i \(-0.492003\pi\)
0.0251220 + 0.999684i \(0.492003\pi\)
\(762\) 0 0
\(763\) 4.90568 0.177598
\(764\) 1.94773 0.0704666
\(765\) 0 0
\(766\) 6.97924 0.252170
\(767\) 45.0418 1.62636
\(768\) 0 0
\(769\) −30.4676 −1.09869 −0.549344 0.835596i \(-0.685122\pi\)
−0.549344 + 0.835596i \(0.685122\pi\)
\(770\) −5.91900 −0.213306
\(771\) 0 0
\(772\) 4.81468 0.173284
\(773\) 40.1159 1.44287 0.721435 0.692482i \(-0.243483\pi\)
0.721435 + 0.692482i \(0.243483\pi\)
\(774\) 0 0
\(775\) 27.0582 0.971960
\(776\) −4.45792 −0.160030
\(777\) 0 0
\(778\) −31.8963 −1.14354
\(779\) 8.15373 0.292138
\(780\) 0 0
\(781\) −20.0614 −0.717853
\(782\) −0.300454 −0.0107442
\(783\) 0 0
\(784\) 0.390415 0.0139434
\(785\) 6.48190 0.231349
\(786\) 0 0
\(787\) −31.5702 −1.12536 −0.562678 0.826676i \(-0.690229\pi\)
−0.562678 + 0.826676i \(0.690229\pi\)
\(788\) 2.05708 0.0732804
\(789\) 0 0
\(790\) 13.5775 0.483064
\(791\) −11.4900 −0.408538
\(792\) 0 0
\(793\) −25.9425 −0.921247
\(794\) −12.4030 −0.440166
\(795\) 0 0
\(796\) 6.37976 0.226124
\(797\) −46.5952 −1.65049 −0.825244 0.564777i \(-0.808962\pi\)
−0.825244 + 0.564777i \(0.808962\pi\)
\(798\) 0 0
\(799\) 0.799154 0.0282720
\(800\) −19.0121 −0.672178
\(801\) 0 0
\(802\) 5.94005 0.209750
\(803\) 34.9876 1.23469
\(804\) 0 0
\(805\) 0.514401 0.0181303
\(806\) 21.3443 0.751822
\(807\) 0 0
\(808\) 50.7556 1.78558
\(809\) 1.54408 0.0542868 0.0271434 0.999632i \(-0.491359\pi\)
0.0271434 + 0.999632i \(0.491359\pi\)
\(810\) 0 0
\(811\) 20.5329 0.721009 0.360505 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(812\) 10.2807 0.360781
\(813\) 0 0
\(814\) −0.102501 −0.00359265
\(815\) 51.6873 1.81053
\(816\) 0 0
\(817\) 17.1435 0.599776
\(818\) −18.4679 −0.645715
\(819\) 0 0
\(820\) −8.16119 −0.285001
\(821\) −15.0246 −0.524362 −0.262181 0.965019i \(-0.584442\pi\)
−0.262181 + 0.965019i \(0.584442\pi\)
\(822\) 0 0
\(823\) −19.6086 −0.683513 −0.341756 0.939789i \(-0.611022\pi\)
−0.341756 + 0.939789i \(0.611022\pi\)
\(824\) 37.7584 1.31538
\(825\) 0 0
\(826\) 11.8006 0.410596
\(827\) 21.4027 0.744246 0.372123 0.928183i \(-0.378630\pi\)
0.372123 + 0.928183i \(0.378630\pi\)
\(828\) 0 0
\(829\) −7.52819 −0.261465 −0.130732 0.991418i \(-0.541733\pi\)
−0.130732 + 0.991418i \(0.541733\pi\)
\(830\) −19.2726 −0.668960
\(831\) 0 0
\(832\) −12.5427 −0.434841
\(833\) 2.04099 0.0707161
\(834\) 0 0
\(835\) −19.4131 −0.671819
\(836\) −12.5439 −0.433840
\(837\) 0 0
\(838\) −28.8441 −0.996404
\(839\) −1.62392 −0.0560640 −0.0280320 0.999607i \(-0.508924\pi\)
−0.0280320 + 0.999607i \(0.508924\pi\)
\(840\) 0 0
\(841\) 31.5007 1.08623
\(842\) −3.73394 −0.128680
\(843\) 0 0
\(844\) −17.5460 −0.603959
\(845\) −8.97428 −0.308725
\(846\) 0 0
\(847\) −4.76323 −0.163667
\(848\) 3.24474 0.111425
\(849\) 0 0
\(850\) −5.51665 −0.189220
\(851\) 0.00890802 0.000305363 0
\(852\) 0 0
\(853\) 50.2026 1.71891 0.859453 0.511215i \(-0.170804\pi\)
0.859453 + 0.511215i \(0.170804\pi\)
\(854\) −6.79675 −0.232580
\(855\) 0 0
\(856\) −31.7062 −1.08369
\(857\) 14.6499 0.500430 0.250215 0.968190i \(-0.419499\pi\)
0.250215 + 0.968190i \(0.419499\pi\)
\(858\) 0 0
\(859\) 15.5012 0.528893 0.264447 0.964400i \(-0.414811\pi\)
0.264447 + 0.964400i \(0.414811\pi\)
\(860\) −17.1592 −0.585124
\(861\) 0 0
\(862\) −6.19287 −0.210930
\(863\) 4.15587 0.141468 0.0707338 0.997495i \(-0.477466\pi\)
0.0707338 + 0.997495i \(0.477466\pi\)
\(864\) 0 0
\(865\) −37.4393 −1.27298
\(866\) −23.3910 −0.794858
\(867\) 0 0
\(868\) −10.8970 −0.369869
\(869\) −14.3064 −0.485310
\(870\) 0 0
\(871\) 18.3412 0.621466
\(872\) 13.4204 0.454472
\(873\) 0 0
\(874\) −0.559435 −0.0189232
\(875\) −4.94426 −0.167146
\(876\) 0 0
\(877\) −29.3465 −0.990963 −0.495481 0.868619i \(-0.665008\pi\)
−0.495481 + 0.868619i \(0.665008\pi\)
\(878\) −17.5921 −0.593705
\(879\) 0 0
\(880\) 2.80590 0.0945870
\(881\) 43.6729 1.47138 0.735688 0.677320i \(-0.236859\pi\)
0.735688 + 0.677320i \(0.236859\pi\)
\(882\) 0 0
\(883\) −45.3693 −1.52680 −0.763399 0.645927i \(-0.776471\pi\)
−0.763399 + 0.645927i \(0.776471\pi\)
\(884\) 8.48000 0.285213
\(885\) 0 0
\(886\) 11.9675 0.402057
\(887\) 29.4945 0.990330 0.495165 0.868799i \(-0.335108\pi\)
0.495165 + 0.868799i \(0.335108\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −36.6916 −1.22991
\(891\) 0 0
\(892\) −23.2003 −0.776802
\(893\) 1.48799 0.0497939
\(894\) 0 0
\(895\) 37.5747 1.25598
\(896\) 8.29971 0.277274
\(897\) 0 0
\(898\) −1.28245 −0.0427958
\(899\) −64.1278 −2.13878
\(900\) 0 0
\(901\) 16.9627 0.565108
\(902\) −4.41293 −0.146935
\(903\) 0 0
\(904\) −31.4331 −1.04545
\(905\) −23.8405 −0.792485
\(906\) 0 0
\(907\) −39.5099 −1.31190 −0.655952 0.754802i \(-0.727733\pi\)
−0.655952 + 0.754802i \(0.727733\pi\)
\(908\) 24.5543 0.814863
\(909\) 0 0
\(910\) 7.45044 0.246980
\(911\) −14.6770 −0.486271 −0.243135 0.969992i \(-0.578176\pi\)
−0.243135 + 0.969992i \(0.578176\pi\)
\(912\) 0 0
\(913\) 20.3072 0.672071
\(914\) 0.990364 0.0327583
\(915\) 0 0
\(916\) −30.2911 −1.00085
\(917\) −4.61325 −0.152343
\(918\) 0 0
\(919\) 15.1107 0.498457 0.249229 0.968445i \(-0.419823\pi\)
0.249229 + 0.968445i \(0.419823\pi\)
\(920\) 1.40724 0.0463953
\(921\) 0 0
\(922\) 26.7163 0.879854
\(923\) 25.2519 0.831178
\(924\) 0 0
\(925\) 0.163560 0.00537783
\(926\) −19.8608 −0.652665
\(927\) 0 0
\(928\) 45.0585 1.47912
\(929\) 27.4154 0.899469 0.449735 0.893162i \(-0.351519\pi\)
0.449735 + 0.893162i \(0.351519\pi\)
\(930\) 0 0
\(931\) 3.80024 0.124548
\(932\) −5.54073 −0.181493
\(933\) 0 0
\(934\) 22.7165 0.743306
\(935\) 14.6685 0.479712
\(936\) 0 0
\(937\) 2.63753 0.0861644 0.0430822 0.999072i \(-0.486282\pi\)
0.0430822 + 0.999072i \(0.486282\pi\)
\(938\) 4.80525 0.156897
\(939\) 0 0
\(940\) −1.48935 −0.0485774
\(941\) −47.8351 −1.55938 −0.779690 0.626166i \(-0.784623\pi\)
−0.779690 + 0.626166i \(0.784623\pi\)
\(942\) 0 0
\(943\) 0.383514 0.0124889
\(944\) −5.59408 −0.182072
\(945\) 0 0
\(946\) −9.27836 −0.301665
\(947\) 59.9898 1.94941 0.974704 0.223500i \(-0.0717483\pi\)
0.974704 + 0.223500i \(0.0717483\pi\)
\(948\) 0 0
\(949\) −44.0400 −1.42960
\(950\) −10.2718 −0.333261
\(951\) 0 0
\(952\) 5.58350 0.180962
\(953\) 10.9525 0.354785 0.177393 0.984140i \(-0.443234\pi\)
0.177393 + 0.984140i \(0.443234\pi\)
\(954\) 0 0
\(955\) −4.24087 −0.137231
\(956\) −21.6911 −0.701541
\(957\) 0 0
\(958\) −21.9870 −0.710367
\(959\) 7.76252 0.250665
\(960\) 0 0
\(961\) 36.9725 1.19266
\(962\) 0.129021 0.00415981
\(963\) 0 0
\(964\) 25.6587 0.826412
\(965\) −10.4832 −0.337465
\(966\) 0 0
\(967\) 5.81937 0.187138 0.0935692 0.995613i \(-0.470172\pi\)
0.0935692 + 0.995613i \(0.470172\pi\)
\(968\) −13.0307 −0.418823
\(969\) 0 0
\(970\) 3.86220 0.124008
\(971\) −27.0322 −0.867505 −0.433752 0.901032i \(-0.642811\pi\)
−0.433752 + 0.901032i \(0.642811\pi\)
\(972\) 0 0
\(973\) 13.1628 0.421981
\(974\) −16.7534 −0.536813
\(975\) 0 0
\(976\) 3.22200 0.103134
\(977\) −18.5562 −0.593666 −0.296833 0.954929i \(-0.595930\pi\)
−0.296833 + 0.954929i \(0.595930\pi\)
\(978\) 0 0
\(979\) 38.6615 1.23563
\(980\) −3.80372 −0.121505
\(981\) 0 0
\(982\) −8.51941 −0.271865
\(983\) −0.886444 −0.0282732 −0.0141366 0.999900i \(-0.504500\pi\)
−0.0141366 + 0.999900i \(0.504500\pi\)
\(984\) 0 0
\(985\) −4.47895 −0.142711
\(986\) 13.0744 0.416375
\(987\) 0 0
\(988\) 15.7894 0.502329
\(989\) 0.806352 0.0256405
\(990\) 0 0
\(991\) 3.64119 0.115666 0.0578331 0.998326i \(-0.481581\pi\)
0.0578331 + 0.998326i \(0.481581\pi\)
\(992\) −47.7599 −1.51638
\(993\) 0 0
\(994\) 6.61582 0.209841
\(995\) −13.8908 −0.440370
\(996\) 0 0
\(997\) −34.8191 −1.10273 −0.551367 0.834263i \(-0.685893\pi\)
−0.551367 + 0.834263i \(0.685893\pi\)
\(998\) −7.10848 −0.225015
\(999\) 0 0
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 \(a_p\))