Properties

Label 8001.2.a.v.1.7
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 1.7
Root \(1.35771\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.35771 q^{2} -0.156613 q^{4} -4.06757 q^{5} +1.00000 q^{7} +2.92806 q^{8} +O(q^{10})\) \(q-1.35771 q^{2} -0.156613 q^{4} -4.06757 q^{5} +1.00000 q^{7} +2.92806 q^{8} +5.52260 q^{10} -4.14107 q^{11} +3.33246 q^{13} -1.35771 q^{14} -3.66225 q^{16} +1.50369 q^{17} +5.47517 q^{19} +0.637032 q^{20} +5.62239 q^{22} +6.86481 q^{23} +11.5451 q^{25} -4.52453 q^{26} -0.156613 q^{28} +9.24608 q^{29} -7.77701 q^{31} -0.883841 q^{32} -2.04158 q^{34} -4.06757 q^{35} +8.24505 q^{37} -7.43372 q^{38} -11.9101 q^{40} +4.27213 q^{41} -4.47938 q^{43} +0.648543 q^{44} -9.32046 q^{46} +8.84174 q^{47} +1.00000 q^{49} -15.6750 q^{50} -0.521905 q^{52} -4.29491 q^{53} +16.8441 q^{55} +2.92806 q^{56} -12.5535 q^{58} -3.63171 q^{59} -3.59520 q^{61} +10.5590 q^{62} +8.52450 q^{64} -13.5550 q^{65} -0.939878 q^{67} -0.235496 q^{68} +5.52260 q^{70} -4.09929 q^{71} +6.53569 q^{73} -11.1944 q^{74} -0.857480 q^{76} -4.14107 q^{77} -7.66941 q^{79} +14.8964 q^{80} -5.80033 q^{82} +0.904225 q^{83} -6.11635 q^{85} +6.08172 q^{86} -12.1253 q^{88} +0.889515 q^{89} +3.33246 q^{91} -1.07512 q^{92} -12.0046 q^{94} -22.2706 q^{95} -10.8632 q^{97} -1.35771 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + O(q^{10}) \) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + 9q^{11} + 24q^{13} - 4q^{14} + 20q^{16} - 17q^{17} + 23q^{19} - 5q^{20} - 3q^{22} + 17q^{23} + 38q^{25} - 28q^{26} + 22q^{28} - 2q^{29} + 16q^{31} - 17q^{32} + 29q^{34} - 5q^{35} + 56q^{37} - 2q^{38} - 13q^{40} + 7q^{41} + 19q^{43} + 29q^{44} + 10q^{46} - 25q^{47} + 19q^{49} + 9q^{50} + 16q^{52} - 18q^{53} + 10q^{55} - 9q^{56} + 31q^{58} - 11q^{59} + 26q^{61} - 26q^{62} + 45q^{64} - 27q^{65} + 24q^{67} - 14q^{68} + 32q^{71} + 51q^{73} + 12q^{76} + 9q^{77} + 30q^{79} + 30q^{80} - 52q^{82} - q^{83} + 44q^{85} + 24q^{86} - 30q^{88} - 5q^{89} + 24q^{91} + 88q^{92} + 7q^{94} + 24q^{95} + 5q^{97} - 4q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35771 −0.960049 −0.480024 0.877255i \(-0.659372\pi\)
−0.480024 + 0.877255i \(0.659372\pi\)
\(3\) 0 0
\(4\) −0.156613 −0.0783063
\(5\) −4.06757 −1.81907 −0.909536 0.415625i \(-0.863563\pi\)
−0.909536 + 0.415625i \(0.863563\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.92806 1.03523
\(9\) 0 0
\(10\) 5.52260 1.74640
\(11\) −4.14107 −1.24858 −0.624290 0.781193i \(-0.714612\pi\)
−0.624290 + 0.781193i \(0.714612\pi\)
\(12\) 0 0
\(13\) 3.33246 0.924258 0.462129 0.886813i \(-0.347086\pi\)
0.462129 + 0.886813i \(0.347086\pi\)
\(14\) −1.35771 −0.362864
\(15\) 0 0
\(16\) −3.66225 −0.915562
\(17\) 1.50369 0.364698 0.182349 0.983234i \(-0.441630\pi\)
0.182349 + 0.983234i \(0.441630\pi\)
\(18\) 0 0
\(19\) 5.47517 1.25609 0.628045 0.778177i \(-0.283855\pi\)
0.628045 + 0.778177i \(0.283855\pi\)
\(20\) 0.637032 0.142445
\(21\) 0 0
\(22\) 5.62239 1.19870
\(23\) 6.86481 1.43141 0.715706 0.698401i \(-0.246105\pi\)
0.715706 + 0.698401i \(0.246105\pi\)
\(24\) 0 0
\(25\) 11.5451 2.30902
\(26\) −4.52453 −0.887333
\(27\) 0 0
\(28\) −0.156613 −0.0295970
\(29\) 9.24608 1.71695 0.858477 0.512852i \(-0.171411\pi\)
0.858477 + 0.512852i \(0.171411\pi\)
\(30\) 0 0
\(31\) −7.77701 −1.39679 −0.698396 0.715711i \(-0.746103\pi\)
−0.698396 + 0.715711i \(0.746103\pi\)
\(32\) −0.883841 −0.156243
\(33\) 0 0
\(34\) −2.04158 −0.350128
\(35\) −4.06757 −0.687545
\(36\) 0 0
\(37\) 8.24505 1.35548 0.677739 0.735303i \(-0.262960\pi\)
0.677739 + 0.735303i \(0.262960\pi\)
\(38\) −7.43372 −1.20591
\(39\) 0 0
\(40\) −11.9101 −1.88315
\(41\) 4.27213 0.667194 0.333597 0.942716i \(-0.391737\pi\)
0.333597 + 0.942716i \(0.391737\pi\)
\(42\) 0 0
\(43\) −4.47938 −0.683099 −0.341550 0.939864i \(-0.610952\pi\)
−0.341550 + 0.939864i \(0.610952\pi\)
\(44\) 0.648543 0.0977716
\(45\) 0 0
\(46\) −9.32046 −1.37423
\(47\) 8.84174 1.28970 0.644850 0.764309i \(-0.276920\pi\)
0.644850 + 0.764309i \(0.276920\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −15.6750 −2.21677
\(51\) 0 0
\(52\) −0.521905 −0.0723752
\(53\) −4.29491 −0.589952 −0.294976 0.955505i \(-0.595312\pi\)
−0.294976 + 0.955505i \(0.595312\pi\)
\(54\) 0 0
\(55\) 16.8441 2.27126
\(56\) 2.92806 0.391279
\(57\) 0 0
\(58\) −12.5535 −1.64836
\(59\) −3.63171 −0.472808 −0.236404 0.971655i \(-0.575969\pi\)
−0.236404 + 0.971655i \(0.575969\pi\)
\(60\) 0 0
\(61\) −3.59520 −0.460318 −0.230159 0.973153i \(-0.573925\pi\)
−0.230159 + 0.973153i \(0.573925\pi\)
\(62\) 10.5590 1.34099
\(63\) 0 0
\(64\) 8.52450 1.06556
\(65\) −13.5550 −1.68129
\(66\) 0 0
\(67\) −0.939878 −0.114824 −0.0574122 0.998351i \(-0.518285\pi\)
−0.0574122 + 0.998351i \(0.518285\pi\)
\(68\) −0.235496 −0.0285581
\(69\) 0 0
\(70\) 5.52260 0.660076
\(71\) −4.09929 −0.486496 −0.243248 0.969964i \(-0.578213\pi\)
−0.243248 + 0.969964i \(0.578213\pi\)
\(72\) 0 0
\(73\) 6.53569 0.764945 0.382472 0.923967i \(-0.375073\pi\)
0.382472 + 0.923967i \(0.375073\pi\)
\(74\) −11.1944 −1.30132
\(75\) 0 0
\(76\) −0.857480 −0.0983597
\(77\) −4.14107 −0.471919
\(78\) 0 0
\(79\) −7.66941 −0.862876 −0.431438 0.902143i \(-0.641994\pi\)
−0.431438 + 0.902143i \(0.641994\pi\)
\(80\) 14.8964 1.66547
\(81\) 0 0
\(82\) −5.80033 −0.640539
\(83\) 0.904225 0.0992515 0.0496258 0.998768i \(-0.484197\pi\)
0.0496258 + 0.998768i \(0.484197\pi\)
\(84\) 0 0
\(85\) −6.11635 −0.663412
\(86\) 6.08172 0.655808
\(87\) 0 0
\(88\) −12.1253 −1.29256
\(89\) 0.889515 0.0942884 0.0471442 0.998888i \(-0.484988\pi\)
0.0471442 + 0.998888i \(0.484988\pi\)
\(90\) 0 0
\(91\) 3.33246 0.349337
\(92\) −1.07512 −0.112089
\(93\) 0 0
\(94\) −12.0046 −1.23818
\(95\) −22.2706 −2.28492
\(96\) 0 0
\(97\) −10.8632 −1.10299 −0.551497 0.834177i \(-0.685943\pi\)
−0.551497 + 0.834177i \(0.685943\pi\)
\(98\) −1.35771 −0.137150
\(99\) 0 0
\(100\) −1.80811 −0.180811
\(101\) −7.33839 −0.730197 −0.365098 0.930969i \(-0.618965\pi\)
−0.365098 + 0.930969i \(0.618965\pi\)
\(102\) 0 0
\(103\) 4.53321 0.446670 0.223335 0.974742i \(-0.428306\pi\)
0.223335 + 0.974742i \(0.428306\pi\)
\(104\) 9.75766 0.956817
\(105\) 0 0
\(106\) 5.83126 0.566382
\(107\) 3.67395 0.355175 0.177587 0.984105i \(-0.443171\pi\)
0.177587 + 0.984105i \(0.443171\pi\)
\(108\) 0 0
\(109\) 14.0170 1.34259 0.671293 0.741192i \(-0.265739\pi\)
0.671293 + 0.741192i \(0.265739\pi\)
\(110\) −22.8695 −2.18052
\(111\) 0 0
\(112\) −3.66225 −0.346050
\(113\) −10.5328 −0.990845 −0.495423 0.868652i \(-0.664987\pi\)
−0.495423 + 0.868652i \(0.664987\pi\)
\(114\) 0 0
\(115\) −27.9231 −2.60384
\(116\) −1.44805 −0.134448
\(117\) 0 0
\(118\) 4.93082 0.453919
\(119\) 1.50369 0.137843
\(120\) 0 0
\(121\) 6.14846 0.558951
\(122\) 4.88126 0.441928
\(123\) 0 0
\(124\) 1.21798 0.109378
\(125\) −26.6227 −2.38121
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −9.80615 −0.866749
\(129\) 0 0
\(130\) 18.4038 1.61412
\(131\) 13.5622 1.18493 0.592466 0.805595i \(-0.298154\pi\)
0.592466 + 0.805595i \(0.298154\pi\)
\(132\) 0 0
\(133\) 5.47517 0.474758
\(134\) 1.27609 0.110237
\(135\) 0 0
\(136\) 4.40289 0.377545
\(137\) 21.5286 1.83931 0.919656 0.392724i \(-0.128467\pi\)
0.919656 + 0.392724i \(0.128467\pi\)
\(138\) 0 0
\(139\) 6.20276 0.526111 0.263056 0.964781i \(-0.415270\pi\)
0.263056 + 0.964781i \(0.415270\pi\)
\(140\) 0.637032 0.0538390
\(141\) 0 0
\(142\) 5.56566 0.467060
\(143\) −13.8000 −1.15401
\(144\) 0 0
\(145\) −37.6091 −3.12326
\(146\) −8.87360 −0.734384
\(147\) 0 0
\(148\) −1.29128 −0.106142
\(149\) −20.7051 −1.69622 −0.848112 0.529817i \(-0.822261\pi\)
−0.848112 + 0.529817i \(0.822261\pi\)
\(150\) 0 0
\(151\) 4.24264 0.345261 0.172631 0.984987i \(-0.444773\pi\)
0.172631 + 0.984987i \(0.444773\pi\)
\(152\) 16.0316 1.30034
\(153\) 0 0
\(154\) 5.62239 0.453065
\(155\) 31.6335 2.54087
\(156\) 0 0
\(157\) −7.13470 −0.569411 −0.284705 0.958615i \(-0.591896\pi\)
−0.284705 + 0.958615i \(0.591896\pi\)
\(158\) 10.4129 0.828403
\(159\) 0 0
\(160\) 3.59509 0.284216
\(161\) 6.86481 0.541023
\(162\) 0 0
\(163\) 24.3942 1.91070 0.955349 0.295479i \(-0.0954793\pi\)
0.955349 + 0.295479i \(0.0954793\pi\)
\(164\) −0.669069 −0.0522455
\(165\) 0 0
\(166\) −1.22768 −0.0952863
\(167\) 15.1000 1.16847 0.584237 0.811583i \(-0.301394\pi\)
0.584237 + 0.811583i \(0.301394\pi\)
\(168\) 0 0
\(169\) −1.89470 −0.145746
\(170\) 8.30426 0.636908
\(171\) 0 0
\(172\) 0.701527 0.0534909
\(173\) 3.35769 0.255281 0.127640 0.991821i \(-0.459260\pi\)
0.127640 + 0.991821i \(0.459260\pi\)
\(174\) 0 0
\(175\) 11.5451 0.872729
\(176\) 15.1656 1.14315
\(177\) 0 0
\(178\) −1.20771 −0.0905215
\(179\) 2.72845 0.203934 0.101967 0.994788i \(-0.467486\pi\)
0.101967 + 0.994788i \(0.467486\pi\)
\(180\) 0 0
\(181\) −15.5927 −1.15899 −0.579497 0.814974i \(-0.696751\pi\)
−0.579497 + 0.814974i \(0.696751\pi\)
\(182\) −4.52453 −0.335380
\(183\) 0 0
\(184\) 20.1006 1.48184
\(185\) −33.5373 −2.46571
\(186\) 0 0
\(187\) −6.22688 −0.455354
\(188\) −1.38473 −0.100992
\(189\) 0 0
\(190\) 30.2372 2.19363
\(191\) 6.09888 0.441299 0.220650 0.975353i \(-0.429182\pi\)
0.220650 + 0.975353i \(0.429182\pi\)
\(192\) 0 0
\(193\) −11.7723 −0.847390 −0.423695 0.905805i \(-0.639267\pi\)
−0.423695 + 0.905805i \(0.639267\pi\)
\(194\) 14.7492 1.05893
\(195\) 0 0
\(196\) −0.156613 −0.0111866
\(197\) −9.06253 −0.645679 −0.322839 0.946454i \(-0.604637\pi\)
−0.322839 + 0.946454i \(0.604637\pi\)
\(198\) 0 0
\(199\) −14.7682 −1.04689 −0.523446 0.852059i \(-0.675354\pi\)
−0.523446 + 0.852059i \(0.675354\pi\)
\(200\) 33.8048 2.39036
\(201\) 0 0
\(202\) 9.96343 0.701024
\(203\) 9.24608 0.648948
\(204\) 0 0
\(205\) −17.3772 −1.21367
\(206\) −6.15480 −0.428825
\(207\) 0 0
\(208\) −12.2043 −0.846216
\(209\) −22.6731 −1.56833
\(210\) 0 0
\(211\) −8.40152 −0.578385 −0.289192 0.957271i \(-0.593387\pi\)
−0.289192 + 0.957271i \(0.593387\pi\)
\(212\) 0.672637 0.0461969
\(213\) 0 0
\(214\) −4.98818 −0.340985
\(215\) 18.2202 1.24261
\(216\) 0 0
\(217\) −7.77701 −0.527938
\(218\) −19.0311 −1.28895
\(219\) 0 0
\(220\) −2.63799 −0.177854
\(221\) 5.01098 0.337075
\(222\) 0 0
\(223\) 20.1977 1.35254 0.676268 0.736656i \(-0.263596\pi\)
0.676268 + 0.736656i \(0.263596\pi\)
\(224\) −0.883841 −0.0590541
\(225\) 0 0
\(226\) 14.3006 0.951260
\(227\) 6.19838 0.411401 0.205700 0.978615i \(-0.434053\pi\)
0.205700 + 0.978615i \(0.434053\pi\)
\(228\) 0 0
\(229\) −19.1653 −1.26648 −0.633240 0.773955i \(-0.718275\pi\)
−0.633240 + 0.773955i \(0.718275\pi\)
\(230\) 37.9116 2.49982
\(231\) 0 0
\(232\) 27.0731 1.77744
\(233\) 28.1199 1.84220 0.921098 0.389331i \(-0.127294\pi\)
0.921098 + 0.389331i \(0.127294\pi\)
\(234\) 0 0
\(235\) −35.9644 −2.34606
\(236\) 0.568771 0.0370238
\(237\) 0 0
\(238\) −2.04158 −0.132336
\(239\) 1.16086 0.0750897 0.0375448 0.999295i \(-0.488046\pi\)
0.0375448 + 0.999295i \(0.488046\pi\)
\(240\) 0 0
\(241\) −3.36538 −0.216783 −0.108391 0.994108i \(-0.534570\pi\)
−0.108391 + 0.994108i \(0.534570\pi\)
\(242\) −8.34785 −0.536620
\(243\) 0 0
\(244\) 0.563054 0.0360458
\(245\) −4.06757 −0.259867
\(246\) 0 0
\(247\) 18.2458 1.16095
\(248\) −22.7716 −1.44600
\(249\) 0 0
\(250\) 36.1460 2.28607
\(251\) −27.6043 −1.74237 −0.871185 0.490955i \(-0.836648\pi\)
−0.871185 + 0.490955i \(0.836648\pi\)
\(252\) 0 0
\(253\) −28.4277 −1.78723
\(254\) −1.35771 −0.0851906
\(255\) 0 0
\(256\) −3.73505 −0.233441
\(257\) 26.7692 1.66981 0.834907 0.550391i \(-0.185521\pi\)
0.834907 + 0.550391i \(0.185521\pi\)
\(258\) 0 0
\(259\) 8.24505 0.512322
\(260\) 2.12288 0.131656
\(261\) 0 0
\(262\) −18.4136 −1.13759
\(263\) −8.17676 −0.504201 −0.252100 0.967701i \(-0.581121\pi\)
−0.252100 + 0.967701i \(0.581121\pi\)
\(264\) 0 0
\(265\) 17.4698 1.07316
\(266\) −7.43372 −0.455790
\(267\) 0 0
\(268\) 0.147197 0.00899147
\(269\) −10.2343 −0.623994 −0.311997 0.950083i \(-0.600998\pi\)
−0.311997 + 0.950083i \(0.600998\pi\)
\(270\) 0 0
\(271\) 15.6853 0.952814 0.476407 0.879225i \(-0.341939\pi\)
0.476407 + 0.879225i \(0.341939\pi\)
\(272\) −5.50688 −0.333904
\(273\) 0 0
\(274\) −29.2297 −1.76583
\(275\) −47.8091 −2.88300
\(276\) 0 0
\(277\) 15.1536 0.910489 0.455244 0.890366i \(-0.349552\pi\)
0.455244 + 0.890366i \(0.349552\pi\)
\(278\) −8.42157 −0.505092
\(279\) 0 0
\(280\) −11.9101 −0.711764
\(281\) −19.6547 −1.17250 −0.586250 0.810130i \(-0.699396\pi\)
−0.586250 + 0.810130i \(0.699396\pi\)
\(282\) 0 0
\(283\) −29.3642 −1.74552 −0.872761 0.488148i \(-0.837672\pi\)
−0.872761 + 0.488148i \(0.837672\pi\)
\(284\) 0.642000 0.0380957
\(285\) 0 0
\(286\) 18.7364 1.10791
\(287\) 4.27213 0.252176
\(288\) 0 0
\(289\) −14.7389 −0.866995
\(290\) 51.0624 2.99849
\(291\) 0 0
\(292\) −1.02357 −0.0599000
\(293\) −4.40237 −0.257189 −0.128594 0.991697i \(-0.541047\pi\)
−0.128594 + 0.991697i \(0.541047\pi\)
\(294\) 0 0
\(295\) 14.7722 0.860072
\(296\) 24.1420 1.40323
\(297\) 0 0
\(298\) 28.1115 1.62846
\(299\) 22.8767 1.32300
\(300\) 0 0
\(301\) −4.47938 −0.258187
\(302\) −5.76030 −0.331468
\(303\) 0 0
\(304\) −20.0514 −1.15003
\(305\) 14.6237 0.837352
\(306\) 0 0
\(307\) 33.2964 1.90032 0.950162 0.311756i \(-0.100917\pi\)
0.950162 + 0.311756i \(0.100917\pi\)
\(308\) 0.648543 0.0369542
\(309\) 0 0
\(310\) −42.9493 −2.43936
\(311\) −30.8539 −1.74956 −0.874782 0.484517i \(-0.838995\pi\)
−0.874782 + 0.484517i \(0.838995\pi\)
\(312\) 0 0
\(313\) −9.70430 −0.548519 −0.274260 0.961656i \(-0.588433\pi\)
−0.274260 + 0.961656i \(0.588433\pi\)
\(314\) 9.68688 0.546662
\(315\) 0 0
\(316\) 1.20113 0.0675686
\(317\) 12.8962 0.724322 0.362161 0.932116i \(-0.382039\pi\)
0.362161 + 0.932116i \(0.382039\pi\)
\(318\) 0 0
\(319\) −38.2887 −2.14375
\(320\) −34.6740 −1.93833
\(321\) 0 0
\(322\) −9.32046 −0.519409
\(323\) 8.23295 0.458094
\(324\) 0 0
\(325\) 38.4736 2.13413
\(326\) −33.1203 −1.83436
\(327\) 0 0
\(328\) 12.5091 0.690697
\(329\) 8.84174 0.487461
\(330\) 0 0
\(331\) −33.3548 −1.83335 −0.916674 0.399636i \(-0.869137\pi\)
−0.916674 + 0.399636i \(0.869137\pi\)
\(332\) −0.141613 −0.00777202
\(333\) 0 0
\(334\) −20.5015 −1.12179
\(335\) 3.82302 0.208874
\(336\) 0 0
\(337\) 31.6811 1.72578 0.862891 0.505390i \(-0.168651\pi\)
0.862891 + 0.505390i \(0.168651\pi\)
\(338\) 2.57246 0.139924
\(339\) 0 0
\(340\) 0.957898 0.0519493
\(341\) 32.2052 1.74401
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −13.1159 −0.707162
\(345\) 0 0
\(346\) −4.55879 −0.245082
\(347\) 32.2561 1.73160 0.865800 0.500390i \(-0.166810\pi\)
0.865800 + 0.500390i \(0.166810\pi\)
\(348\) 0 0
\(349\) 21.2214 1.13596 0.567978 0.823044i \(-0.307726\pi\)
0.567978 + 0.823044i \(0.307726\pi\)
\(350\) −15.6750 −0.837862
\(351\) 0 0
\(352\) 3.66005 0.195081
\(353\) −21.6154 −1.15047 −0.575235 0.817988i \(-0.695089\pi\)
−0.575235 + 0.817988i \(0.695089\pi\)
\(354\) 0 0
\(355\) 16.6741 0.884971
\(356\) −0.139309 −0.00738337
\(357\) 0 0
\(358\) −3.70445 −0.195786
\(359\) 9.14005 0.482393 0.241197 0.970476i \(-0.422460\pi\)
0.241197 + 0.970476i \(0.422460\pi\)
\(360\) 0 0
\(361\) 10.9775 0.577763
\(362\) 21.1704 1.11269
\(363\) 0 0
\(364\) −0.521905 −0.0273553
\(365\) −26.5844 −1.39149
\(366\) 0 0
\(367\) 17.4322 0.909954 0.454977 0.890503i \(-0.349647\pi\)
0.454977 + 0.890503i \(0.349647\pi\)
\(368\) −25.1406 −1.31055
\(369\) 0 0
\(370\) 45.5341 2.36720
\(371\) −4.29491 −0.222981
\(372\) 0 0
\(373\) 23.2475 1.20371 0.601855 0.798606i \(-0.294429\pi\)
0.601855 + 0.798606i \(0.294429\pi\)
\(374\) 8.45432 0.437162
\(375\) 0 0
\(376\) 25.8892 1.33513
\(377\) 30.8122 1.58691
\(378\) 0 0
\(379\) −19.8749 −1.02090 −0.510452 0.859906i \(-0.670522\pi\)
−0.510452 + 0.859906i \(0.670522\pi\)
\(380\) 3.48786 0.178923
\(381\) 0 0
\(382\) −8.28053 −0.423669
\(383\) −29.4149 −1.50303 −0.751514 0.659717i \(-0.770676\pi\)
−0.751514 + 0.659717i \(0.770676\pi\)
\(384\) 0 0
\(385\) 16.8441 0.858454
\(386\) 15.9834 0.813536
\(387\) 0 0
\(388\) 1.70132 0.0863713
\(389\) 7.56699 0.383662 0.191831 0.981428i \(-0.438557\pi\)
0.191831 + 0.981428i \(0.438557\pi\)
\(390\) 0 0
\(391\) 10.3225 0.522033
\(392\) 2.92806 0.147890
\(393\) 0 0
\(394\) 12.3043 0.619883
\(395\) 31.1958 1.56963
\(396\) 0 0
\(397\) 12.8178 0.643305 0.321653 0.946858i \(-0.395762\pi\)
0.321653 + 0.946858i \(0.395762\pi\)
\(398\) 20.0510 1.00507
\(399\) 0 0
\(400\) −42.2811 −2.11405
\(401\) −33.4344 −1.66963 −0.834816 0.550528i \(-0.814426\pi\)
−0.834816 + 0.550528i \(0.814426\pi\)
\(402\) 0 0
\(403\) −25.9166 −1.29100
\(404\) 1.14928 0.0571790
\(405\) 0 0
\(406\) −12.5535 −0.623021
\(407\) −34.1433 −1.69242
\(408\) 0 0
\(409\) −17.1785 −0.849422 −0.424711 0.905329i \(-0.639624\pi\)
−0.424711 + 0.905329i \(0.639624\pi\)
\(410\) 23.5932 1.16519
\(411\) 0 0
\(412\) −0.709957 −0.0349771
\(413\) −3.63171 −0.178705
\(414\) 0 0
\(415\) −3.67800 −0.180546
\(416\) −2.94537 −0.144408
\(417\) 0 0
\(418\) 30.7835 1.50567
\(419\) 29.5133 1.44182 0.720910 0.693029i \(-0.243724\pi\)
0.720910 + 0.693029i \(0.243724\pi\)
\(420\) 0 0
\(421\) −20.9064 −1.01892 −0.509458 0.860495i \(-0.670154\pi\)
−0.509458 + 0.860495i \(0.670154\pi\)
\(422\) 11.4069 0.555278
\(423\) 0 0
\(424\) −12.5758 −0.610734
\(425\) 17.3603 0.842096
\(426\) 0 0
\(427\) −3.59520 −0.173984
\(428\) −0.575387 −0.0278124
\(429\) 0 0
\(430\) −24.7378 −1.19296
\(431\) 21.1316 1.01787 0.508937 0.860804i \(-0.330039\pi\)
0.508937 + 0.860804i \(0.330039\pi\)
\(432\) 0 0
\(433\) 4.15711 0.199778 0.0998890 0.994999i \(-0.468151\pi\)
0.0998890 + 0.994999i \(0.468151\pi\)
\(434\) 10.5590 0.506846
\(435\) 0 0
\(436\) −2.19524 −0.105133
\(437\) 37.5860 1.79798
\(438\) 0 0
\(439\) −6.72225 −0.320835 −0.160418 0.987049i \(-0.551284\pi\)
−0.160418 + 0.987049i \(0.551284\pi\)
\(440\) 49.3205 2.35126
\(441\) 0 0
\(442\) −6.80348 −0.323609
\(443\) 22.5903 1.07330 0.536649 0.843805i \(-0.319690\pi\)
0.536649 + 0.843805i \(0.319690\pi\)
\(444\) 0 0
\(445\) −3.61816 −0.171517
\(446\) −27.4227 −1.29850
\(447\) 0 0
\(448\) 8.52450 0.402745
\(449\) 40.0006 1.88775 0.943873 0.330308i \(-0.107153\pi\)
0.943873 + 0.330308i \(0.107153\pi\)
\(450\) 0 0
\(451\) −17.6912 −0.833045
\(452\) 1.64957 0.0775894
\(453\) 0 0
\(454\) −8.41563 −0.394965
\(455\) −13.5550 −0.635469
\(456\) 0 0
\(457\) 5.14695 0.240764 0.120382 0.992728i \(-0.461588\pi\)
0.120382 + 0.992728i \(0.461588\pi\)
\(458\) 26.0210 1.21588
\(459\) 0 0
\(460\) 4.37311 0.203897
\(461\) 1.65601 0.0771279 0.0385639 0.999256i \(-0.487722\pi\)
0.0385639 + 0.999256i \(0.487722\pi\)
\(462\) 0 0
\(463\) 29.8032 1.38507 0.692537 0.721383i \(-0.256493\pi\)
0.692537 + 0.721383i \(0.256493\pi\)
\(464\) −33.8614 −1.57198
\(465\) 0 0
\(466\) −38.1788 −1.76860
\(467\) 12.4102 0.574277 0.287139 0.957889i \(-0.407296\pi\)
0.287139 + 0.957889i \(0.407296\pi\)
\(468\) 0 0
\(469\) −0.939878 −0.0433995
\(470\) 48.8294 2.25233
\(471\) 0 0
\(472\) −10.6339 −0.489464
\(473\) 18.5494 0.852904
\(474\) 0 0
\(475\) 63.2115 2.90034
\(476\) −0.235496 −0.0107940
\(477\) 0 0
\(478\) −1.57611 −0.0720898
\(479\) 23.2909 1.06419 0.532095 0.846685i \(-0.321405\pi\)
0.532095 + 0.846685i \(0.321405\pi\)
\(480\) 0 0
\(481\) 27.4763 1.25281
\(482\) 4.56922 0.208122
\(483\) 0 0
\(484\) −0.962926 −0.0437694
\(485\) 44.1869 2.00642
\(486\) 0 0
\(487\) −11.8607 −0.537460 −0.268730 0.963216i \(-0.586604\pi\)
−0.268730 + 0.963216i \(0.586604\pi\)
\(488\) −10.5270 −0.476534
\(489\) 0 0
\(490\) 5.52260 0.249485
\(491\) 34.9281 1.57628 0.788142 0.615493i \(-0.211043\pi\)
0.788142 + 0.615493i \(0.211043\pi\)
\(492\) 0 0
\(493\) 13.9032 0.626170
\(494\) −24.7726 −1.11457
\(495\) 0 0
\(496\) 28.4813 1.27885
\(497\) −4.09929 −0.183878
\(498\) 0 0
\(499\) 13.9524 0.624597 0.312299 0.949984i \(-0.398901\pi\)
0.312299 + 0.949984i \(0.398901\pi\)
\(500\) 4.16945 0.186463
\(501\) 0 0
\(502\) 37.4788 1.67276
\(503\) 33.5301 1.49504 0.747518 0.664242i \(-0.231246\pi\)
0.747518 + 0.664242i \(0.231246\pi\)
\(504\) 0 0
\(505\) 29.8494 1.32828
\(506\) 38.5967 1.71583
\(507\) 0 0
\(508\) −0.156613 −0.00694856
\(509\) −8.96936 −0.397560 −0.198780 0.980044i \(-0.563698\pi\)
−0.198780 + 0.980044i \(0.563698\pi\)
\(510\) 0 0
\(511\) 6.53569 0.289122
\(512\) 24.6834 1.09086
\(513\) 0 0
\(514\) −36.3449 −1.60310
\(515\) −18.4391 −0.812525
\(516\) 0 0
\(517\) −36.6143 −1.61029
\(518\) −11.1944 −0.491855
\(519\) 0 0
\(520\) −39.6899 −1.74052
\(521\) −3.45790 −0.151493 −0.0757467 0.997127i \(-0.524134\pi\)
−0.0757467 + 0.997127i \(0.524134\pi\)
\(522\) 0 0
\(523\) 7.35603 0.321657 0.160828 0.986982i \(-0.448583\pi\)
0.160828 + 0.986982i \(0.448583\pi\)
\(524\) −2.12401 −0.0927877
\(525\) 0 0
\(526\) 11.1017 0.484057
\(527\) −11.6942 −0.509407
\(528\) 0 0
\(529\) 24.1257 1.04894
\(530\) −23.7191 −1.03029
\(531\) 0 0
\(532\) −0.857480 −0.0371765
\(533\) 14.2367 0.616660
\(534\) 0 0
\(535\) −14.9441 −0.646088
\(536\) −2.75202 −0.118869
\(537\) 0 0
\(538\) 13.8952 0.599065
\(539\) −4.14107 −0.178369
\(540\) 0 0
\(541\) 13.1595 0.565769 0.282884 0.959154i \(-0.408709\pi\)
0.282884 + 0.959154i \(0.408709\pi\)
\(542\) −21.2961 −0.914748
\(543\) 0 0
\(544\) −1.32902 −0.0569813
\(545\) −57.0151 −2.44226
\(546\) 0 0
\(547\) −41.0280 −1.75423 −0.877116 0.480279i \(-0.840535\pi\)
−0.877116 + 0.480279i \(0.840535\pi\)
\(548\) −3.37165 −0.144030
\(549\) 0 0
\(550\) 64.9111 2.76782
\(551\) 50.6239 2.15665
\(552\) 0 0
\(553\) −7.66941 −0.326136
\(554\) −20.5742 −0.874114
\(555\) 0 0
\(556\) −0.971430 −0.0411978
\(557\) −22.0235 −0.933165 −0.466582 0.884478i \(-0.654515\pi\)
−0.466582 + 0.884478i \(0.654515\pi\)
\(558\) 0 0
\(559\) −14.9274 −0.631360
\(560\) 14.8964 0.629490
\(561\) 0 0
\(562\) 26.6854 1.12566
\(563\) −25.8895 −1.09111 −0.545556 0.838074i \(-0.683682\pi\)
−0.545556 + 0.838074i \(0.683682\pi\)
\(564\) 0 0
\(565\) 42.8430 1.80242
\(566\) 39.8682 1.67579
\(567\) 0 0
\(568\) −12.0030 −0.503634
\(569\) −16.3568 −0.685713 −0.342856 0.939388i \(-0.611394\pi\)
−0.342856 + 0.939388i \(0.611394\pi\)
\(570\) 0 0
\(571\) −43.7952 −1.83277 −0.916385 0.400298i \(-0.868907\pi\)
−0.916385 + 0.400298i \(0.868907\pi\)
\(572\) 2.16125 0.0903662
\(573\) 0 0
\(574\) −5.80033 −0.242101
\(575\) 79.2551 3.30516
\(576\) 0 0
\(577\) 16.4323 0.684087 0.342043 0.939684i \(-0.388881\pi\)
0.342043 + 0.939684i \(0.388881\pi\)
\(578\) 20.0112 0.832358
\(579\) 0 0
\(580\) 5.89005 0.244571
\(581\) 0.904225 0.0375136
\(582\) 0 0
\(583\) 17.7855 0.736601
\(584\) 19.1369 0.791891
\(585\) 0 0
\(586\) 5.97715 0.246914
\(587\) 18.2183 0.751951 0.375976 0.926630i \(-0.377308\pi\)
0.375976 + 0.926630i \(0.377308\pi\)
\(588\) 0 0
\(589\) −42.5805 −1.75450
\(590\) −20.0565 −0.825711
\(591\) 0 0
\(592\) −30.1954 −1.24102
\(593\) −0.539852 −0.0221691 −0.0110845 0.999939i \(-0.503528\pi\)
−0.0110845 + 0.999939i \(0.503528\pi\)
\(594\) 0 0
\(595\) −6.11635 −0.250746
\(596\) 3.24267 0.132825
\(597\) 0 0
\(598\) −31.0601 −1.27014
\(599\) 28.9266 1.18191 0.590954 0.806705i \(-0.298752\pi\)
0.590954 + 0.806705i \(0.298752\pi\)
\(600\) 0 0
\(601\) 6.27630 0.256016 0.128008 0.991773i \(-0.459142\pi\)
0.128008 + 0.991773i \(0.459142\pi\)
\(602\) 6.08172 0.247872
\(603\) 0 0
\(604\) −0.664451 −0.0270361
\(605\) −25.0093 −1.01677
\(606\) 0 0
\(607\) −11.9901 −0.486664 −0.243332 0.969943i \(-0.578240\pi\)
−0.243332 + 0.969943i \(0.578240\pi\)
\(608\) −4.83918 −0.196255
\(609\) 0 0
\(610\) −19.8548 −0.803899
\(611\) 29.4648 1.19202
\(612\) 0 0
\(613\) −18.0885 −0.730588 −0.365294 0.930892i \(-0.619031\pi\)
−0.365294 + 0.930892i \(0.619031\pi\)
\(614\) −45.2069 −1.82440
\(615\) 0 0
\(616\) −12.1253 −0.488543
\(617\) 33.8316 1.36201 0.681004 0.732280i \(-0.261544\pi\)
0.681004 + 0.732280i \(0.261544\pi\)
\(618\) 0 0
\(619\) 17.0117 0.683759 0.341879 0.939744i \(-0.388937\pi\)
0.341879 + 0.939744i \(0.388937\pi\)
\(620\) −4.95421 −0.198966
\(621\) 0 0
\(622\) 41.8908 1.67967
\(623\) 0.889515 0.0356377
\(624\) 0 0
\(625\) 50.5641 2.02256
\(626\) 13.1757 0.526605
\(627\) 0 0
\(628\) 1.11738 0.0445884
\(629\) 12.3980 0.494340
\(630\) 0 0
\(631\) 40.9850 1.63159 0.815794 0.578342i \(-0.196300\pi\)
0.815794 + 0.578342i \(0.196300\pi\)
\(632\) −22.4565 −0.893272
\(633\) 0 0
\(634\) −17.5093 −0.695384
\(635\) −4.06757 −0.161417
\(636\) 0 0
\(637\) 3.33246 0.132037
\(638\) 51.9851 2.05811
\(639\) 0 0
\(640\) 39.8872 1.57668
\(641\) −18.3751 −0.725773 −0.362887 0.931833i \(-0.618209\pi\)
−0.362887 + 0.931833i \(0.618209\pi\)
\(642\) 0 0
\(643\) −40.6254 −1.60211 −0.801054 0.598592i \(-0.795727\pi\)
−0.801054 + 0.598592i \(0.795727\pi\)
\(644\) −1.07512 −0.0423655
\(645\) 0 0
\(646\) −11.1780 −0.439792
\(647\) 17.3245 0.681095 0.340548 0.940227i \(-0.389388\pi\)
0.340548 + 0.940227i \(0.389388\pi\)
\(648\) 0 0
\(649\) 15.0392 0.590339
\(650\) −52.2362 −2.04887
\(651\) 0 0
\(652\) −3.82043 −0.149620
\(653\) −3.87508 −0.151644 −0.0758219 0.997121i \(-0.524158\pi\)
−0.0758219 + 0.997121i \(0.524158\pi\)
\(654\) 0 0
\(655\) −55.1651 −2.15548
\(656\) −15.6456 −0.610858
\(657\) 0 0
\(658\) −12.0046 −0.467986
\(659\) −23.7917 −0.926795 −0.463397 0.886151i \(-0.653370\pi\)
−0.463397 + 0.886151i \(0.653370\pi\)
\(660\) 0 0
\(661\) 27.3539 1.06394 0.531972 0.846762i \(-0.321451\pi\)
0.531972 + 0.846762i \(0.321451\pi\)
\(662\) 45.2863 1.76010
\(663\) 0 0
\(664\) 2.64763 0.102748
\(665\) −22.2706 −0.863618
\(666\) 0 0
\(667\) 63.4726 2.45767
\(668\) −2.36485 −0.0914988
\(669\) 0 0
\(670\) −5.19057 −0.200529
\(671\) 14.8880 0.574744
\(672\) 0 0
\(673\) 26.3576 1.01601 0.508006 0.861354i \(-0.330383\pi\)
0.508006 + 0.861354i \(0.330383\pi\)
\(674\) −43.0139 −1.65684
\(675\) 0 0
\(676\) 0.296734 0.0114128
\(677\) −39.4511 −1.51623 −0.758115 0.652121i \(-0.773879\pi\)
−0.758115 + 0.652121i \(0.773879\pi\)
\(678\) 0 0
\(679\) −10.8632 −0.416892
\(680\) −17.9091 −0.686782
\(681\) 0 0
\(682\) −43.7254 −1.67433
\(683\) 8.64860 0.330930 0.165465 0.986216i \(-0.447088\pi\)
0.165465 + 0.986216i \(0.447088\pi\)
\(684\) 0 0
\(685\) −87.5691 −3.34584
\(686\) −1.35771 −0.0518378
\(687\) 0 0
\(688\) 16.4046 0.625419
\(689\) −14.3126 −0.545268
\(690\) 0 0
\(691\) −9.10919 −0.346530 −0.173265 0.984875i \(-0.555432\pi\)
−0.173265 + 0.984875i \(0.555432\pi\)
\(692\) −0.525857 −0.0199901
\(693\) 0 0
\(694\) −43.7946 −1.66242
\(695\) −25.2301 −0.957034
\(696\) 0 0
\(697\) 6.42395 0.243324
\(698\) −28.8126 −1.09057
\(699\) 0 0
\(700\) −1.80811 −0.0683401
\(701\) −9.44526 −0.356743 −0.178371 0.983963i \(-0.557083\pi\)
−0.178371 + 0.983963i \(0.557083\pi\)
\(702\) 0 0
\(703\) 45.1431 1.70260
\(704\) −35.3005 −1.33044
\(705\) 0 0
\(706\) 29.3475 1.10451
\(707\) −7.33839 −0.275988
\(708\) 0 0
\(709\) −4.58727 −0.172279 −0.0861393 0.996283i \(-0.527453\pi\)
−0.0861393 + 0.996283i \(0.527453\pi\)
\(710\) −22.6387 −0.849616
\(711\) 0 0
\(712\) 2.60456 0.0976099
\(713\) −53.3878 −1.99939
\(714\) 0 0
\(715\) 56.1323 2.09923
\(716\) −0.427309 −0.0159693
\(717\) 0 0
\(718\) −12.4096 −0.463121
\(719\) 2.72744 0.101716 0.0508581 0.998706i \(-0.483804\pi\)
0.0508581 + 0.998706i \(0.483804\pi\)
\(720\) 0 0
\(721\) 4.53321 0.168825
\(722\) −14.9043 −0.554681
\(723\) 0 0
\(724\) 2.44201 0.0907565
\(725\) 106.747 3.96449
\(726\) 0 0
\(727\) 18.5557 0.688194 0.344097 0.938934i \(-0.388185\pi\)
0.344097 + 0.938934i \(0.388185\pi\)
\(728\) 9.75766 0.361643
\(729\) 0 0
\(730\) 36.0940 1.33590
\(731\) −6.73559 −0.249125
\(732\) 0 0
\(733\) 28.8879 1.06700 0.533499 0.845801i \(-0.320877\pi\)
0.533499 + 0.845801i \(0.320877\pi\)
\(734\) −23.6680 −0.873600
\(735\) 0 0
\(736\) −6.06741 −0.223648
\(737\) 3.89210 0.143367
\(738\) 0 0
\(739\) 36.6965 1.34990 0.674951 0.737863i \(-0.264165\pi\)
0.674951 + 0.737863i \(0.264165\pi\)
\(740\) 5.25236 0.193081
\(741\) 0 0
\(742\) 5.83126 0.214072
\(743\) −23.9221 −0.877618 −0.438809 0.898580i \(-0.644600\pi\)
−0.438809 + 0.898580i \(0.644600\pi\)
\(744\) 0 0
\(745\) 84.2192 3.08555
\(746\) −31.5634 −1.15562
\(747\) 0 0
\(748\) 0.975207 0.0356571
\(749\) 3.67395 0.134243
\(750\) 0 0
\(751\) −35.6390 −1.30049 −0.650243 0.759727i \(-0.725333\pi\)
−0.650243 + 0.759727i \(0.725333\pi\)
\(752\) −32.3806 −1.18080
\(753\) 0 0
\(754\) −41.8342 −1.52351
\(755\) −17.2572 −0.628055
\(756\) 0 0
\(757\) −28.0965 −1.02118 −0.510592 0.859823i \(-0.670574\pi\)
−0.510592 + 0.859823i \(0.670574\pi\)
\(758\) 26.9844 0.980118
\(759\) 0 0
\(760\) −65.2098 −2.36541
\(761\) −22.6232 −0.820091 −0.410045 0.912065i \(-0.634487\pi\)
−0.410045 + 0.912065i \(0.634487\pi\)
\(762\) 0 0
\(763\) 14.0170 0.507450
\(764\) −0.955161 −0.0345565
\(765\) 0 0
\(766\) 39.9370 1.44298
\(767\) −12.1025 −0.436997
\(768\) 0 0
\(769\) 15.2047 0.548295 0.274148 0.961688i \(-0.411604\pi\)
0.274148 + 0.961688i \(0.411604\pi\)
\(770\) −22.8695 −0.824158
\(771\) 0 0
\(772\) 1.84369 0.0663559
\(773\) −7.25076 −0.260792 −0.130396 0.991462i \(-0.541625\pi\)
−0.130396 + 0.991462i \(0.541625\pi\)
\(774\) 0 0
\(775\) −89.7865 −3.22523
\(776\) −31.8082 −1.14185
\(777\) 0 0
\(778\) −10.2738 −0.368334
\(779\) 23.3906 0.838056
\(780\) 0 0
\(781\) 16.9754 0.607429
\(782\) −14.0151 −0.501177
\(783\) 0 0
\(784\) −3.66225 −0.130795
\(785\) 29.0209 1.03580
\(786\) 0 0
\(787\) −14.1413 −0.504083 −0.252041 0.967716i \(-0.581102\pi\)
−0.252041 + 0.967716i \(0.581102\pi\)
\(788\) 1.41931 0.0505607
\(789\) 0 0
\(790\) −42.3550 −1.50692
\(791\) −10.5328 −0.374504
\(792\) 0 0
\(793\) −11.9809 −0.425453
\(794\) −17.4029 −0.617604
\(795\) 0 0
\(796\) 2.31289 0.0819782
\(797\) −46.8079 −1.65802 −0.829010 0.559234i \(-0.811095\pi\)
−0.829010 + 0.559234i \(0.811095\pi\)
\(798\) 0 0
\(799\) 13.2952 0.470351
\(800\) −10.2040 −0.360768
\(801\) 0 0
\(802\) 45.3943 1.60293
\(803\) −27.0648 −0.955094
\(804\) 0 0
\(805\) −27.9231 −0.984160
\(806\) 35.1873 1.23942
\(807\) 0 0
\(808\) −21.4873 −0.755919
\(809\) −23.7428 −0.834753 −0.417377 0.908734i \(-0.637050\pi\)
−0.417377 + 0.908734i \(0.637050\pi\)
\(810\) 0 0
\(811\) 17.4329 0.612150 0.306075 0.952007i \(-0.400984\pi\)
0.306075 + 0.952007i \(0.400984\pi\)
\(812\) −1.44805 −0.0508167
\(813\) 0 0
\(814\) 46.3569 1.62481
\(815\) −99.2249 −3.47570
\(816\) 0 0
\(817\) −24.5254 −0.858034
\(818\) 23.3235 0.815486
\(819\) 0 0
\(820\) 2.72148 0.0950383
\(821\) 0.499582 0.0174355 0.00871777 0.999962i \(-0.497225\pi\)
0.00871777 + 0.999962i \(0.497225\pi\)
\(822\) 0 0
\(823\) 50.5433 1.76183 0.880915 0.473274i \(-0.156928\pi\)
0.880915 + 0.473274i \(0.156928\pi\)
\(824\) 13.2735 0.462405
\(825\) 0 0
\(826\) 4.93082 0.171565
\(827\) 5.11034 0.177704 0.0888520 0.996045i \(-0.471680\pi\)
0.0888520 + 0.996045i \(0.471680\pi\)
\(828\) 0 0
\(829\) −50.7911 −1.76405 −0.882025 0.471203i \(-0.843820\pi\)
−0.882025 + 0.471203i \(0.843820\pi\)
\(830\) 4.99367 0.173333
\(831\) 0 0
\(832\) 28.4076 0.984855
\(833\) 1.50369 0.0520997
\(834\) 0 0
\(835\) −61.4203 −2.12554
\(836\) 3.55089 0.122810
\(837\) 0 0
\(838\) −40.0706 −1.38422
\(839\) 12.1037 0.417865 0.208932 0.977930i \(-0.433001\pi\)
0.208932 + 0.977930i \(0.433001\pi\)
\(840\) 0 0
\(841\) 56.4900 1.94793
\(842\) 28.3849 0.978210
\(843\) 0 0
\(844\) 1.31578 0.0452911
\(845\) 7.70683 0.265123
\(846\) 0 0
\(847\) 6.14846 0.211264
\(848\) 15.7290 0.540137
\(849\) 0 0
\(850\) −23.5703 −0.808453
\(851\) 56.6007 1.94025
\(852\) 0 0
\(853\) 31.5795 1.08126 0.540631 0.841260i \(-0.318185\pi\)
0.540631 + 0.841260i \(0.318185\pi\)
\(854\) 4.88126 0.167033
\(855\) 0 0
\(856\) 10.7576 0.367686
\(857\) 36.7530 1.25546 0.627729 0.778432i \(-0.283985\pi\)
0.627729 + 0.778432i \(0.283985\pi\)
\(858\) 0 0
\(859\) 26.9999 0.921225 0.460613 0.887601i \(-0.347630\pi\)
0.460613 + 0.887601i \(0.347630\pi\)
\(860\) −2.85351 −0.0973038
\(861\) 0 0
\(862\) −28.6907 −0.977209
\(863\) −10.8508 −0.369365 −0.184682 0.982798i \(-0.559126\pi\)
−0.184682 + 0.982798i \(0.559126\pi\)
\(864\) 0 0
\(865\) −13.6576 −0.464374
\(866\) −5.64417 −0.191797
\(867\) 0 0
\(868\) 1.21798 0.0413408
\(869\) 31.7596 1.07737
\(870\) 0 0
\(871\) −3.13211 −0.106127
\(872\) 41.0427 1.38988
\(873\) 0 0
\(874\) −51.0311 −1.72615
\(875\) −26.6227 −0.900011
\(876\) 0 0
\(877\) −12.3835 −0.418162 −0.209081 0.977898i \(-0.567047\pi\)
−0.209081 + 0.977898i \(0.567047\pi\)
\(878\) 9.12689 0.308018
\(879\) 0 0
\(880\) −61.6872 −2.07948
\(881\) −32.1116 −1.08187 −0.540933 0.841066i \(-0.681929\pi\)
−0.540933 + 0.841066i \(0.681929\pi\)
\(882\) 0 0
\(883\) 13.1303 0.441870 0.220935 0.975289i \(-0.429089\pi\)
0.220935 + 0.975289i \(0.429089\pi\)
\(884\) −0.784783 −0.0263951
\(885\) 0 0
\(886\) −30.6712 −1.03042
\(887\) −16.1209 −0.541289 −0.270644 0.962679i \(-0.587237\pi\)
−0.270644 + 0.962679i \(0.587237\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 4.91243 0.164665
\(891\) 0 0
\(892\) −3.16321 −0.105912
\(893\) 48.4101 1.61998
\(894\) 0 0
\(895\) −11.0982 −0.370970
\(896\) −9.80615 −0.327600
\(897\) 0 0
\(898\) −54.3094 −1.81233
\(899\) −71.9069 −2.39823
\(900\) 0 0
\(901\) −6.45821 −0.215154
\(902\) 24.0196 0.799764
\(903\) 0 0
\(904\) −30.8408 −1.02575
\(905\) 63.4242 2.10829
\(906\) 0 0
\(907\) −7.43444 −0.246857 −0.123428 0.992353i \(-0.539389\pi\)
−0.123428 + 0.992353i \(0.539389\pi\)
\(908\) −0.970744 −0.0322153
\(909\) 0 0
\(910\) 18.4038 0.610081
\(911\) 18.7356 0.620740 0.310370 0.950616i \(-0.399547\pi\)
0.310370 + 0.950616i \(0.399547\pi\)
\(912\) 0 0
\(913\) −3.74446 −0.123923
\(914\) −6.98809 −0.231145
\(915\) 0 0
\(916\) 3.00153 0.0991733
\(917\) 13.5622 0.447863
\(918\) 0 0
\(919\) 59.5412 1.96408 0.982041 0.188666i \(-0.0604165\pi\)
0.982041 + 0.188666i \(0.0604165\pi\)
\(920\) −81.7606 −2.69557
\(921\) 0 0
\(922\) −2.24838 −0.0740465
\(923\) −13.6607 −0.449648
\(924\) 0 0
\(925\) 95.1900 3.12983
\(926\) −40.4643 −1.32974
\(927\) 0 0
\(928\) −8.17207 −0.268261
\(929\) −8.96931 −0.294274 −0.147137 0.989116i \(-0.547006\pi\)
−0.147137 + 0.989116i \(0.547006\pi\)
\(930\) 0 0
\(931\) 5.47517 0.179441
\(932\) −4.40393 −0.144255
\(933\) 0 0
\(934\) −16.8496 −0.551334
\(935\) 25.3283 0.828322
\(936\) 0 0
\(937\) 19.6061 0.640503 0.320252 0.947333i \(-0.396233\pi\)
0.320252 + 0.947333i \(0.396233\pi\)
\(938\) 1.27609 0.0416657
\(939\) 0 0
\(940\) 5.63247 0.183711
\(941\) −31.9202 −1.04057 −0.520285 0.853993i \(-0.674174\pi\)
−0.520285 + 0.853993i \(0.674174\pi\)
\(942\) 0 0
\(943\) 29.3274 0.955030
\(944\) 13.3002 0.432885
\(945\) 0 0
\(946\) −25.1848 −0.818829
\(947\) 1.95493 0.0635265 0.0317633 0.999495i \(-0.489888\pi\)
0.0317633 + 0.999495i \(0.489888\pi\)
\(948\) 0 0
\(949\) 21.7799 0.707007
\(950\) −85.8231 −2.78447
\(951\) 0 0
\(952\) 4.40289 0.142699
\(953\) 3.28363 0.106367 0.0531836 0.998585i \(-0.483063\pi\)
0.0531836 + 0.998585i \(0.483063\pi\)
\(954\) 0 0
\(955\) −24.8076 −0.802755
\(956\) −0.181805 −0.00587999
\(957\) 0 0
\(958\) −31.6224 −1.02167
\(959\) 21.5286 0.695195
\(960\) 0 0
\(961\) 29.4819 0.951030
\(962\) −37.3050 −1.20276
\(963\) 0 0
\(964\) 0.527060 0.0169755
\(965\) 47.8847 1.54146
\(966\) 0 0
\(967\) −58.3821 −1.87744 −0.938720 0.344680i \(-0.887987\pi\)
−0.938720 + 0.344680i \(0.887987\pi\)
\(968\) 18.0031 0.578641
\(969\) 0 0
\(970\) −59.9932 −1.92627
\(971\) 31.4550 1.00944 0.504719 0.863284i \(-0.331596\pi\)
0.504719 + 0.863284i \(0.331596\pi\)
\(972\) 0 0
\(973\) 6.20276 0.198851
\(974\) 16.1034 0.515988
\(975\) 0 0
\(976\) 13.1665 0.421450
\(977\) 13.3824 0.428141 0.214070 0.976818i \(-0.431328\pi\)
0.214070 + 0.976818i \(0.431328\pi\)
\(978\) 0 0
\(979\) −3.68354 −0.117727
\(980\) 0.637032 0.0203492
\(981\) 0 0
\(982\) −47.4224 −1.51331
\(983\) 59.8159 1.90783 0.953915 0.300077i \(-0.0970124\pi\)
0.953915 + 0.300077i \(0.0970124\pi\)
\(984\) 0 0
\(985\) 36.8625 1.17454
\(986\) −18.8766 −0.601153
\(987\) 0 0
\(988\) −2.85752 −0.0909098
\(989\) −30.7501 −0.977797
\(990\) 0 0
\(991\) 23.0477 0.732134 0.366067 0.930588i \(-0.380704\pi\)
0.366067 + 0.930588i \(0.380704\pi\)
\(992\) 6.87365 0.218238
\(993\) 0 0
\(994\) 5.56566 0.176532
\(995\) 60.0708 1.90437
\(996\) 0 0
\(997\) −11.0638 −0.350395 −0.175197 0.984533i \(-0.556056\pi\)
−0.175197 + 0.984533i \(0.556056\pi\)
\(998\) −18.9434 −0.599644
\(999\) 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 \(a_p\))