Properties

Label 8001.2.a.u.1.18
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
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: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(2.77035\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.77035 q^{2} +5.67483 q^{4} +3.69380 q^{5} +1.00000 q^{7} +10.1806 q^{8} +O(q^{10})\) \(q+2.77035 q^{2} +5.67483 q^{4} +3.69380 q^{5} +1.00000 q^{7} +10.1806 q^{8} +10.2331 q^{10} +5.84456 q^{11} -6.83862 q^{13} +2.77035 q^{14} +16.8540 q^{16} -2.91249 q^{17} -0.728183 q^{19} +20.9617 q^{20} +16.1915 q^{22} -8.42541 q^{23} +8.64414 q^{25} -18.9454 q^{26} +5.67483 q^{28} -5.16908 q^{29} -0.147299 q^{31} +26.3305 q^{32} -8.06861 q^{34} +3.69380 q^{35} +0.220660 q^{37} -2.01732 q^{38} +37.6049 q^{40} -6.63743 q^{41} +2.26302 q^{43} +33.1669 q^{44} -23.3413 q^{46} +2.62826 q^{47} +1.00000 q^{49} +23.9473 q^{50} -38.8080 q^{52} +12.8622 q^{53} +21.5886 q^{55} +10.1806 q^{56} -14.3202 q^{58} -5.14980 q^{59} +10.8107 q^{61} -0.408069 q^{62} +39.2364 q^{64} -25.2605 q^{65} +2.61979 q^{67} -16.5279 q^{68} +10.2331 q^{70} +3.60167 q^{71} -6.18425 q^{73} +0.611304 q^{74} -4.13231 q^{76} +5.84456 q^{77} +3.74021 q^{79} +62.2554 q^{80} -18.3880 q^{82} -5.02267 q^{83} -10.7582 q^{85} +6.26936 q^{86} +59.5009 q^{88} -9.91415 q^{89} -6.83862 q^{91} -47.8128 q^{92} +7.28119 q^{94} -2.68976 q^{95} -3.08019 q^{97} +2.77035 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} + O(q^{10}) \) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} - 4q^{10} + 9q^{11} - 25q^{13} + 6q^{14} + 34q^{16} + 17q^{17} - 5q^{19} + 21q^{20} + 5q^{22} + 14q^{23} + 28q^{25} + 8q^{26} + 22q^{28} + 17q^{29} + 5q^{31} + 53q^{32} - 19q^{34} + 10q^{35} - 15q^{37} + 22q^{38} - q^{40} + 17q^{41} + q^{43} + 33q^{44} + 10q^{46} + 31q^{47} + 18q^{49} + 35q^{50} - 70q^{52} + 35q^{53} + 4q^{55} + 21q^{56} + 3q^{58} + 46q^{59} - 5q^{61} + 10q^{62} + 63q^{64} + 12q^{65} + 6q^{67} + 56q^{68} - 4q^{70} + 22q^{71} - 16q^{73} - 18q^{74} + 32q^{76} + 9q^{77} + 46q^{79} + 30q^{80} - 12q^{82} + 46q^{83} + 4q^{85} - 18q^{86} + 30q^{88} + 42q^{89} - 25q^{91} + 48q^{92} + 3q^{94} + 2q^{95} - 35q^{97} + 6q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.77035 1.95893 0.979466 0.201609i \(-0.0646170\pi\)
0.979466 + 0.201609i \(0.0646170\pi\)
\(3\) 0 0
\(4\) 5.67483 2.83742
\(5\) 3.69380 1.65192 0.825958 0.563731i \(-0.190635\pi\)
0.825958 + 0.563731i \(0.190635\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 10.1806 3.59937
\(9\) 0 0
\(10\) 10.2331 3.23599
\(11\) 5.84456 1.76220 0.881101 0.472929i \(-0.156803\pi\)
0.881101 + 0.472929i \(0.156803\pi\)
\(12\) 0 0
\(13\) −6.83862 −1.89669 −0.948346 0.317238i \(-0.897244\pi\)
−0.948346 + 0.317238i \(0.897244\pi\)
\(14\) 2.77035 0.740407
\(15\) 0 0
\(16\) 16.8540 4.21351
\(17\) −2.91249 −0.706383 −0.353191 0.935551i \(-0.614904\pi\)
−0.353191 + 0.935551i \(0.614904\pi\)
\(18\) 0 0
\(19\) −0.728183 −0.167057 −0.0835283 0.996505i \(-0.526619\pi\)
−0.0835283 + 0.996505i \(0.526619\pi\)
\(20\) 20.9617 4.68717
\(21\) 0 0
\(22\) 16.1915 3.45203
\(23\) −8.42541 −1.75682 −0.878410 0.477908i \(-0.841395\pi\)
−0.878410 + 0.477908i \(0.841395\pi\)
\(24\) 0 0
\(25\) 8.64414 1.72883
\(26\) −18.9454 −3.71549
\(27\) 0 0
\(28\) 5.67483 1.07244
\(29\) −5.16908 −0.959874 −0.479937 0.877303i \(-0.659341\pi\)
−0.479937 + 0.877303i \(0.659341\pi\)
\(30\) 0 0
\(31\) −0.147299 −0.0264556 −0.0132278 0.999913i \(-0.504211\pi\)
−0.0132278 + 0.999913i \(0.504211\pi\)
\(32\) 26.3305 4.65461
\(33\) 0 0
\(34\) −8.06861 −1.38376
\(35\) 3.69380 0.624366
\(36\) 0 0
\(37\) 0.220660 0.0362762 0.0181381 0.999835i \(-0.494226\pi\)
0.0181381 + 0.999835i \(0.494226\pi\)
\(38\) −2.01732 −0.327253
\(39\) 0 0
\(40\) 37.6049 5.94586
\(41\) −6.63743 −1.03659 −0.518296 0.855201i \(-0.673433\pi\)
−0.518296 + 0.855201i \(0.673433\pi\)
\(42\) 0 0
\(43\) 2.26302 0.345107 0.172554 0.985000i \(-0.444798\pi\)
0.172554 + 0.985000i \(0.444798\pi\)
\(44\) 33.1669 5.00010
\(45\) 0 0
\(46\) −23.3413 −3.44149
\(47\) 2.62826 0.383371 0.191685 0.981456i \(-0.438605\pi\)
0.191685 + 0.981456i \(0.438605\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 23.9473 3.38666
\(51\) 0 0
\(52\) −38.8080 −5.38170
\(53\) 12.8622 1.76676 0.883379 0.468659i \(-0.155263\pi\)
0.883379 + 0.468659i \(0.155263\pi\)
\(54\) 0 0
\(55\) 21.5886 2.91101
\(56\) 10.1806 1.36043
\(57\) 0 0
\(58\) −14.3202 −1.88033
\(59\) −5.14980 −0.670447 −0.335223 0.942139i \(-0.608812\pi\)
−0.335223 + 0.942139i \(0.608812\pi\)
\(60\) 0 0
\(61\) 10.8107 1.38417 0.692086 0.721815i \(-0.256692\pi\)
0.692086 + 0.721815i \(0.256692\pi\)
\(62\) −0.408069 −0.0518248
\(63\) 0 0
\(64\) 39.2364 4.90456
\(65\) −25.2605 −3.13318
\(66\) 0 0
\(67\) 2.61979 0.320059 0.160029 0.987112i \(-0.448841\pi\)
0.160029 + 0.987112i \(0.448841\pi\)
\(68\) −16.5279 −2.00430
\(69\) 0 0
\(70\) 10.2331 1.22309
\(71\) 3.60167 0.427440 0.213720 0.976895i \(-0.431442\pi\)
0.213720 + 0.976895i \(0.431442\pi\)
\(72\) 0 0
\(73\) −6.18425 −0.723811 −0.361906 0.932215i \(-0.617874\pi\)
−0.361906 + 0.932215i \(0.617874\pi\)
\(74\) 0.611304 0.0710626
\(75\) 0 0
\(76\) −4.13231 −0.474009
\(77\) 5.84456 0.666050
\(78\) 0 0
\(79\) 3.74021 0.420807 0.210403 0.977615i \(-0.432522\pi\)
0.210403 + 0.977615i \(0.432522\pi\)
\(80\) 62.2554 6.96037
\(81\) 0 0
\(82\) −18.3880 −2.03061
\(83\) −5.02267 −0.551310 −0.275655 0.961257i \(-0.588895\pi\)
−0.275655 + 0.961257i \(0.588895\pi\)
\(84\) 0 0
\(85\) −10.7582 −1.16689
\(86\) 6.26936 0.676042
\(87\) 0 0
\(88\) 59.5009 6.34282
\(89\) −9.91415 −1.05090 −0.525449 0.850825i \(-0.676103\pi\)
−0.525449 + 0.850825i \(0.676103\pi\)
\(90\) 0 0
\(91\) −6.83862 −0.716882
\(92\) −47.8128 −4.98483
\(93\) 0 0
\(94\) 7.28119 0.750998
\(95\) −2.68976 −0.275964
\(96\) 0 0
\(97\) −3.08019 −0.312745 −0.156373 0.987698i \(-0.549980\pi\)
−0.156373 + 0.987698i \(0.549980\pi\)
\(98\) 2.77035 0.279847
\(99\) 0 0
\(100\) 49.0541 4.90541
\(101\) 6.71801 0.668467 0.334233 0.942490i \(-0.391523\pi\)
0.334233 + 0.942490i \(0.391523\pi\)
\(102\) 0 0
\(103\) −15.9532 −1.57192 −0.785958 0.618280i \(-0.787830\pi\)
−0.785958 + 0.618280i \(0.787830\pi\)
\(104\) −69.6210 −6.82690
\(105\) 0 0
\(106\) 35.6328 3.46096
\(107\) −17.3101 −1.67343 −0.836714 0.547640i \(-0.815526\pi\)
−0.836714 + 0.547640i \(0.815526\pi\)
\(108\) 0 0
\(109\) −3.73388 −0.357641 −0.178820 0.983882i \(-0.557228\pi\)
−0.178820 + 0.983882i \(0.557228\pi\)
\(110\) 59.8080 5.70247
\(111\) 0 0
\(112\) 16.8540 1.59256
\(113\) 5.36995 0.505162 0.252581 0.967576i \(-0.418721\pi\)
0.252581 + 0.967576i \(0.418721\pi\)
\(114\) 0 0
\(115\) −31.1218 −2.90212
\(116\) −29.3337 −2.72356
\(117\) 0 0
\(118\) −14.2667 −1.31336
\(119\) −2.91249 −0.266988
\(120\) 0 0
\(121\) 23.1589 2.10535
\(122\) 29.9495 2.71150
\(123\) 0 0
\(124\) −0.835896 −0.0750657
\(125\) 13.4607 1.20396
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 56.0377 4.95308
\(129\) 0 0
\(130\) −69.9803 −6.13768
\(131\) 18.6600 1.63033 0.815166 0.579227i \(-0.196646\pi\)
0.815166 + 0.579227i \(0.196646\pi\)
\(132\) 0 0
\(133\) −0.728183 −0.0631415
\(134\) 7.25774 0.626974
\(135\) 0 0
\(136\) −29.6508 −2.54253
\(137\) −10.2323 −0.874203 −0.437101 0.899412i \(-0.643995\pi\)
−0.437101 + 0.899412i \(0.643995\pi\)
\(138\) 0 0
\(139\) 6.06275 0.514236 0.257118 0.966380i \(-0.417227\pi\)
0.257118 + 0.966380i \(0.417227\pi\)
\(140\) 20.9617 1.77159
\(141\) 0 0
\(142\) 9.97789 0.837326
\(143\) −39.9687 −3.34235
\(144\) 0 0
\(145\) −19.0935 −1.58563
\(146\) −17.1325 −1.41790
\(147\) 0 0
\(148\) 1.25221 0.102931
\(149\) −3.78097 −0.309749 −0.154874 0.987934i \(-0.549497\pi\)
−0.154874 + 0.987934i \(0.549497\pi\)
\(150\) 0 0
\(151\) −8.80071 −0.716192 −0.358096 0.933685i \(-0.616574\pi\)
−0.358096 + 0.933685i \(0.616574\pi\)
\(152\) −7.41331 −0.601299
\(153\) 0 0
\(154\) 16.1915 1.30475
\(155\) −0.544092 −0.0437025
\(156\) 0 0
\(157\) −2.06816 −0.165057 −0.0825287 0.996589i \(-0.526300\pi\)
−0.0825287 + 0.996589i \(0.526300\pi\)
\(158\) 10.3617 0.824332
\(159\) 0 0
\(160\) 97.2594 7.68903
\(161\) −8.42541 −0.664016
\(162\) 0 0
\(163\) −5.55816 −0.435349 −0.217674 0.976021i \(-0.569847\pi\)
−0.217674 + 0.976021i \(0.569847\pi\)
\(164\) −37.6663 −2.94124
\(165\) 0 0
\(166\) −13.9145 −1.07998
\(167\) 4.47087 0.345966 0.172983 0.984925i \(-0.444659\pi\)
0.172983 + 0.984925i \(0.444659\pi\)
\(168\) 0 0
\(169\) 33.7667 2.59744
\(170\) −29.8038 −2.28585
\(171\) 0 0
\(172\) 12.8423 0.979213
\(173\) 6.66702 0.506884 0.253442 0.967351i \(-0.418437\pi\)
0.253442 + 0.967351i \(0.418437\pi\)
\(174\) 0 0
\(175\) 8.64414 0.653436
\(176\) 98.5045 7.42506
\(177\) 0 0
\(178\) −27.4657 −2.05864
\(179\) −23.8805 −1.78491 −0.892457 0.451132i \(-0.851020\pi\)
−0.892457 + 0.451132i \(0.851020\pi\)
\(180\) 0 0
\(181\) 4.67808 0.347719 0.173860 0.984770i \(-0.444376\pi\)
0.173860 + 0.984770i \(0.444376\pi\)
\(182\) −18.9454 −1.40432
\(183\) 0 0
\(184\) −85.7755 −6.32345
\(185\) 0.815072 0.0599253
\(186\) 0 0
\(187\) −17.0222 −1.24479
\(188\) 14.9149 1.08778
\(189\) 0 0
\(190\) −7.45157 −0.540594
\(191\) −20.6313 −1.49283 −0.746414 0.665482i \(-0.768226\pi\)
−0.746414 + 0.665482i \(0.768226\pi\)
\(192\) 0 0
\(193\) −0.649615 −0.0467603 −0.0233802 0.999727i \(-0.507443\pi\)
−0.0233802 + 0.999727i \(0.507443\pi\)
\(194\) −8.53319 −0.612647
\(195\) 0 0
\(196\) 5.67483 0.405345
\(197\) −10.5454 −0.751330 −0.375665 0.926755i \(-0.622586\pi\)
−0.375665 + 0.926755i \(0.622586\pi\)
\(198\) 0 0
\(199\) −19.2177 −1.36231 −0.681155 0.732139i \(-0.738522\pi\)
−0.681155 + 0.732139i \(0.738522\pi\)
\(200\) 88.0022 6.22270
\(201\) 0 0
\(202\) 18.6112 1.30948
\(203\) −5.16908 −0.362798
\(204\) 0 0
\(205\) −24.5173 −1.71236
\(206\) −44.1959 −3.07928
\(207\) 0 0
\(208\) −115.258 −7.99173
\(209\) −4.25591 −0.294387
\(210\) 0 0
\(211\) −0.801027 −0.0551450 −0.0275725 0.999620i \(-0.508778\pi\)
−0.0275725 + 0.999620i \(0.508778\pi\)
\(212\) 72.9908 5.01303
\(213\) 0 0
\(214\) −47.9549 −3.27813
\(215\) 8.35914 0.570089
\(216\) 0 0
\(217\) −0.147299 −0.00999929
\(218\) −10.3442 −0.700594
\(219\) 0 0
\(220\) 122.512 8.25975
\(221\) 19.9174 1.33979
\(222\) 0 0
\(223\) −26.6856 −1.78700 −0.893498 0.449066i \(-0.851757\pi\)
−0.893498 + 0.449066i \(0.851757\pi\)
\(224\) 26.3305 1.75928
\(225\) 0 0
\(226\) 14.8766 0.989579
\(227\) 5.62346 0.373242 0.186621 0.982432i \(-0.440246\pi\)
0.186621 + 0.982432i \(0.440246\pi\)
\(228\) 0 0
\(229\) 30.0812 1.98782 0.993912 0.110179i \(-0.0351426\pi\)
0.993912 + 0.110179i \(0.0351426\pi\)
\(230\) −86.2182 −5.68506
\(231\) 0 0
\(232\) −52.6242 −3.45495
\(233\) 25.0722 1.64254 0.821269 0.570542i \(-0.193267\pi\)
0.821269 + 0.570542i \(0.193267\pi\)
\(234\) 0 0
\(235\) 9.70826 0.633297
\(236\) −29.2243 −1.90234
\(237\) 0 0
\(238\) −8.06861 −0.523011
\(239\) 5.11449 0.330829 0.165414 0.986224i \(-0.447104\pi\)
0.165414 + 0.986224i \(0.447104\pi\)
\(240\) 0 0
\(241\) −17.2167 −1.10902 −0.554511 0.832176i \(-0.687095\pi\)
−0.554511 + 0.832176i \(0.687095\pi\)
\(242\) 64.1582 4.12425
\(243\) 0 0
\(244\) 61.3491 3.92747
\(245\) 3.69380 0.235988
\(246\) 0 0
\(247\) 4.97977 0.316855
\(248\) −1.49958 −0.0952237
\(249\) 0 0
\(250\) 37.2909 2.35848
\(251\) 6.60961 0.417195 0.208597 0.978002i \(-0.433110\pi\)
0.208597 + 0.978002i \(0.433110\pi\)
\(252\) 0 0
\(253\) −49.2428 −3.09587
\(254\) 2.77035 0.173827
\(255\) 0 0
\(256\) 76.7711 4.79820
\(257\) 8.00894 0.499584 0.249792 0.968299i \(-0.419638\pi\)
0.249792 + 0.968299i \(0.419638\pi\)
\(258\) 0 0
\(259\) 0.220660 0.0137111
\(260\) −143.349 −8.89012
\(261\) 0 0
\(262\) 51.6947 3.19371
\(263\) −2.81053 −0.173305 −0.0866523 0.996239i \(-0.527617\pi\)
−0.0866523 + 0.996239i \(0.527617\pi\)
\(264\) 0 0
\(265\) 47.5104 2.91854
\(266\) −2.01732 −0.123690
\(267\) 0 0
\(268\) 14.8669 0.908140
\(269\) 16.8965 1.03020 0.515099 0.857131i \(-0.327755\pi\)
0.515099 + 0.857131i \(0.327755\pi\)
\(270\) 0 0
\(271\) −4.61690 −0.280457 −0.140228 0.990119i \(-0.544784\pi\)
−0.140228 + 0.990119i \(0.544784\pi\)
\(272\) −49.0872 −2.97635
\(273\) 0 0
\(274\) −28.3470 −1.71250
\(275\) 50.5212 3.04654
\(276\) 0 0
\(277\) 8.56502 0.514622 0.257311 0.966329i \(-0.417163\pi\)
0.257311 + 0.966329i \(0.417163\pi\)
\(278\) 16.7959 1.00735
\(279\) 0 0
\(280\) 37.6049 2.24733
\(281\) 9.85734 0.588040 0.294020 0.955799i \(-0.405007\pi\)
0.294020 + 0.955799i \(0.405007\pi\)
\(282\) 0 0
\(283\) −14.8460 −0.882505 −0.441253 0.897383i \(-0.645466\pi\)
−0.441253 + 0.897383i \(0.645466\pi\)
\(284\) 20.4389 1.21282
\(285\) 0 0
\(286\) −110.727 −6.54744
\(287\) −6.63743 −0.391795
\(288\) 0 0
\(289\) −8.51740 −0.501023
\(290\) −52.8958 −3.10615
\(291\) 0 0
\(292\) −35.0946 −2.05375
\(293\) 22.3075 1.30322 0.651609 0.758555i \(-0.274094\pi\)
0.651609 + 0.758555i \(0.274094\pi\)
\(294\) 0 0
\(295\) −19.0223 −1.10752
\(296\) 2.24644 0.130572
\(297\) 0 0
\(298\) −10.4746 −0.606777
\(299\) 57.6182 3.33215
\(300\) 0 0
\(301\) 2.26302 0.130438
\(302\) −24.3810 −1.40297
\(303\) 0 0
\(304\) −12.2728 −0.703895
\(305\) 39.9327 2.28654
\(306\) 0 0
\(307\) 21.4884 1.22641 0.613205 0.789924i \(-0.289880\pi\)
0.613205 + 0.789924i \(0.289880\pi\)
\(308\) 33.1669 1.88986
\(309\) 0 0
\(310\) −1.50732 −0.0856103
\(311\) 2.66770 0.151272 0.0756358 0.997136i \(-0.475901\pi\)
0.0756358 + 0.997136i \(0.475901\pi\)
\(312\) 0 0
\(313\) −4.03542 −0.228095 −0.114048 0.993475i \(-0.536382\pi\)
−0.114048 + 0.993475i \(0.536382\pi\)
\(314\) −5.72953 −0.323336
\(315\) 0 0
\(316\) 21.2251 1.19400
\(317\) −27.9402 −1.56928 −0.784639 0.619953i \(-0.787152\pi\)
−0.784639 + 0.619953i \(0.787152\pi\)
\(318\) 0 0
\(319\) −30.2110 −1.69149
\(320\) 144.932 8.10192
\(321\) 0 0
\(322\) −23.3413 −1.30076
\(323\) 2.12083 0.118006
\(324\) 0 0
\(325\) −59.1140 −3.27905
\(326\) −15.3980 −0.852819
\(327\) 0 0
\(328\) −67.5727 −3.73108
\(329\) 2.62826 0.144901
\(330\) 0 0
\(331\) 27.9479 1.53616 0.768079 0.640355i \(-0.221213\pi\)
0.768079 + 0.640355i \(0.221213\pi\)
\(332\) −28.5028 −1.56429
\(333\) 0 0
\(334\) 12.3859 0.677724
\(335\) 9.67699 0.528711
\(336\) 0 0
\(337\) 11.7508 0.640108 0.320054 0.947399i \(-0.396299\pi\)
0.320054 + 0.947399i \(0.396299\pi\)
\(338\) 93.5456 5.08821
\(339\) 0 0
\(340\) −61.0507 −3.31094
\(341\) −0.860897 −0.0466202
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 23.0388 1.24217
\(345\) 0 0
\(346\) 18.4700 0.992952
\(347\) 32.9383 1.76822 0.884110 0.467279i \(-0.154766\pi\)
0.884110 + 0.467279i \(0.154766\pi\)
\(348\) 0 0
\(349\) 26.7484 1.43181 0.715903 0.698199i \(-0.246015\pi\)
0.715903 + 0.698199i \(0.246015\pi\)
\(350\) 23.9473 1.28004
\(351\) 0 0
\(352\) 153.890 8.20236
\(353\) −21.2637 −1.13175 −0.565875 0.824491i \(-0.691462\pi\)
−0.565875 + 0.824491i \(0.691462\pi\)
\(354\) 0 0
\(355\) 13.3039 0.706095
\(356\) −56.2611 −2.98183
\(357\) 0 0
\(358\) −66.1574 −3.49653
\(359\) 20.8707 1.10152 0.550758 0.834665i \(-0.314339\pi\)
0.550758 + 0.834665i \(0.314339\pi\)
\(360\) 0 0
\(361\) −18.4697 −0.972092
\(362\) 12.9599 0.681158
\(363\) 0 0
\(364\) −38.8080 −2.03409
\(365\) −22.8434 −1.19568
\(366\) 0 0
\(367\) 9.11925 0.476021 0.238010 0.971263i \(-0.423505\pi\)
0.238010 + 0.971263i \(0.423505\pi\)
\(368\) −142.002 −7.40238
\(369\) 0 0
\(370\) 2.25803 0.117390
\(371\) 12.8622 0.667772
\(372\) 0 0
\(373\) −18.2620 −0.945572 −0.472786 0.881177i \(-0.656752\pi\)
−0.472786 + 0.881177i \(0.656752\pi\)
\(374\) −47.1575 −2.43846
\(375\) 0 0
\(376\) 26.7572 1.37989
\(377\) 35.3494 1.82059
\(378\) 0 0
\(379\) −15.4251 −0.792332 −0.396166 0.918179i \(-0.629659\pi\)
−0.396166 + 0.918179i \(0.629659\pi\)
\(380\) −15.2639 −0.783023
\(381\) 0 0
\(382\) −57.1559 −2.92435
\(383\) 1.07843 0.0551054 0.0275527 0.999620i \(-0.491229\pi\)
0.0275527 + 0.999620i \(0.491229\pi\)
\(384\) 0 0
\(385\) 21.5886 1.10026
\(386\) −1.79966 −0.0916003
\(387\) 0 0
\(388\) −17.4795 −0.887389
\(389\) 9.69935 0.491776 0.245888 0.969298i \(-0.420920\pi\)
0.245888 + 0.969298i \(0.420920\pi\)
\(390\) 0 0
\(391\) 24.5389 1.24099
\(392\) 10.1806 0.514196
\(393\) 0 0
\(394\) −29.2145 −1.47181
\(395\) 13.8156 0.695138
\(396\) 0 0
\(397\) −13.4990 −0.677495 −0.338747 0.940877i \(-0.610003\pi\)
−0.338747 + 0.940877i \(0.610003\pi\)
\(398\) −53.2398 −2.66867
\(399\) 0 0
\(400\) 145.689 7.28444
\(401\) −12.9871 −0.648547 −0.324273 0.945963i \(-0.605120\pi\)
−0.324273 + 0.945963i \(0.605120\pi\)
\(402\) 0 0
\(403\) 1.00732 0.0501782
\(404\) 38.1236 1.89672
\(405\) 0 0
\(406\) −14.3202 −0.710698
\(407\) 1.28966 0.0639260
\(408\) 0 0
\(409\) −28.0022 −1.38462 −0.692310 0.721600i \(-0.743407\pi\)
−0.692310 + 0.721600i \(0.743407\pi\)
\(410\) −67.9215 −3.35440
\(411\) 0 0
\(412\) −90.5317 −4.46018
\(413\) −5.14980 −0.253405
\(414\) 0 0
\(415\) −18.5527 −0.910718
\(416\) −180.064 −8.82836
\(417\) 0 0
\(418\) −11.7904 −0.576685
\(419\) 17.9029 0.874612 0.437306 0.899313i \(-0.355933\pi\)
0.437306 + 0.899313i \(0.355933\pi\)
\(420\) 0 0
\(421\) −5.02171 −0.244743 −0.122372 0.992484i \(-0.539050\pi\)
−0.122372 + 0.992484i \(0.539050\pi\)
\(422\) −2.21912 −0.108025
\(423\) 0 0
\(424\) 130.944 6.35922
\(425\) −25.1760 −1.22121
\(426\) 0 0
\(427\) 10.8107 0.523168
\(428\) −98.2317 −4.74821
\(429\) 0 0
\(430\) 23.1577 1.11677
\(431\) 9.87050 0.475445 0.237723 0.971333i \(-0.423599\pi\)
0.237723 + 0.971333i \(0.423599\pi\)
\(432\) 0 0
\(433\) −20.6320 −0.991511 −0.495756 0.868462i \(-0.665109\pi\)
−0.495756 + 0.868462i \(0.665109\pi\)
\(434\) −0.408069 −0.0195879
\(435\) 0 0
\(436\) −21.1891 −1.01478
\(437\) 6.13524 0.293488
\(438\) 0 0
\(439\) 12.5226 0.597671 0.298836 0.954305i \(-0.403402\pi\)
0.298836 + 0.954305i \(0.403402\pi\)
\(440\) 219.784 10.4778
\(441\) 0 0
\(442\) 55.1782 2.62456
\(443\) −17.5570 −0.834157 −0.417079 0.908870i \(-0.636946\pi\)
−0.417079 + 0.908870i \(0.636946\pi\)
\(444\) 0 0
\(445\) −36.6209 −1.73600
\(446\) −73.9283 −3.50061
\(447\) 0 0
\(448\) 39.2364 1.85375
\(449\) −15.1729 −0.716052 −0.358026 0.933712i \(-0.616550\pi\)
−0.358026 + 0.933712i \(0.616550\pi\)
\(450\) 0 0
\(451\) −38.7928 −1.82668
\(452\) 30.4735 1.43336
\(453\) 0 0
\(454\) 15.5789 0.731156
\(455\) −25.2605 −1.18423
\(456\) 0 0
\(457\) 8.72959 0.408353 0.204176 0.978934i \(-0.434548\pi\)
0.204176 + 0.978934i \(0.434548\pi\)
\(458\) 83.3355 3.89401
\(459\) 0 0
\(460\) −176.611 −8.23452
\(461\) −39.0180 −1.81725 −0.908625 0.417613i \(-0.862867\pi\)
−0.908625 + 0.417613i \(0.862867\pi\)
\(462\) 0 0
\(463\) 23.1406 1.07544 0.537718 0.843125i \(-0.319287\pi\)
0.537718 + 0.843125i \(0.319287\pi\)
\(464\) −87.1199 −4.04444
\(465\) 0 0
\(466\) 69.4589 3.21762
\(467\) 5.76547 0.266794 0.133397 0.991063i \(-0.457411\pi\)
0.133397 + 0.991063i \(0.457411\pi\)
\(468\) 0 0
\(469\) 2.61979 0.120971
\(470\) 26.8953 1.24059
\(471\) 0 0
\(472\) −52.4279 −2.41319
\(473\) 13.2264 0.608149
\(474\) 0 0
\(475\) −6.29452 −0.288812
\(476\) −16.5279 −0.757555
\(477\) 0 0
\(478\) 14.1689 0.648071
\(479\) −18.8928 −0.863233 −0.431616 0.902057i \(-0.642057\pi\)
−0.431616 + 0.902057i \(0.642057\pi\)
\(480\) 0 0
\(481\) −1.50901 −0.0688048
\(482\) −47.6961 −2.17250
\(483\) 0 0
\(484\) 131.423 5.97377
\(485\) −11.3776 −0.516629
\(486\) 0 0
\(487\) −11.2365 −0.509174 −0.254587 0.967050i \(-0.581940\pi\)
−0.254587 + 0.967050i \(0.581940\pi\)
\(488\) 110.059 4.98215
\(489\) 0 0
\(490\) 10.2331 0.462285
\(491\) 28.7501 1.29747 0.648736 0.761014i \(-0.275298\pi\)
0.648736 + 0.761014i \(0.275298\pi\)
\(492\) 0 0
\(493\) 15.0549 0.678039
\(494\) 13.7957 0.620697
\(495\) 0 0
\(496\) −2.48258 −0.111471
\(497\) 3.60167 0.161557
\(498\) 0 0
\(499\) 5.34025 0.239063 0.119531 0.992830i \(-0.461861\pi\)
0.119531 + 0.992830i \(0.461861\pi\)
\(500\) 76.3874 3.41615
\(501\) 0 0
\(502\) 18.3109 0.817257
\(503\) 22.5608 1.00593 0.502967 0.864306i \(-0.332242\pi\)
0.502967 + 0.864306i \(0.332242\pi\)
\(504\) 0 0
\(505\) 24.8150 1.10425
\(506\) −136.420 −6.06460
\(507\) 0 0
\(508\) 5.67483 0.251780
\(509\) 6.47857 0.287158 0.143579 0.989639i \(-0.454139\pi\)
0.143579 + 0.989639i \(0.454139\pi\)
\(510\) 0 0
\(511\) −6.18425 −0.273575
\(512\) 100.607 4.44626
\(513\) 0 0
\(514\) 22.1876 0.978652
\(515\) −58.9279 −2.59667
\(516\) 0 0
\(517\) 15.3610 0.675577
\(518\) 0.611304 0.0268591
\(519\) 0 0
\(520\) −257.166 −11.2775
\(521\) 23.6416 1.03576 0.517878 0.855454i \(-0.326722\pi\)
0.517878 + 0.855454i \(0.326722\pi\)
\(522\) 0 0
\(523\) 21.6939 0.948609 0.474304 0.880361i \(-0.342700\pi\)
0.474304 + 0.880361i \(0.342700\pi\)
\(524\) 105.892 4.62593
\(525\) 0 0
\(526\) −7.78614 −0.339492
\(527\) 0.429006 0.0186878
\(528\) 0 0
\(529\) 47.9876 2.08642
\(530\) 131.620 5.71722
\(531\) 0 0
\(532\) −4.13231 −0.179159
\(533\) 45.3908 1.96610
\(534\) 0 0
\(535\) −63.9399 −2.76436
\(536\) 26.6710 1.15201
\(537\) 0 0
\(538\) 46.8092 2.01809
\(539\) 5.84456 0.251743
\(540\) 0 0
\(541\) −13.9628 −0.600306 −0.300153 0.953891i \(-0.597038\pi\)
−0.300153 + 0.953891i \(0.597038\pi\)
\(542\) −12.7904 −0.549396
\(543\) 0 0
\(544\) −76.6872 −3.28794
\(545\) −13.7922 −0.590793
\(546\) 0 0
\(547\) −27.1167 −1.15943 −0.579714 0.814820i \(-0.696836\pi\)
−0.579714 + 0.814820i \(0.696836\pi\)
\(548\) −58.0665 −2.48048
\(549\) 0 0
\(550\) 139.961 5.96797
\(551\) 3.76404 0.160353
\(552\) 0 0
\(553\) 3.74021 0.159050
\(554\) 23.7281 1.00811
\(555\) 0 0
\(556\) 34.4051 1.45910
\(557\) −9.65775 −0.409212 −0.204606 0.978844i \(-0.565591\pi\)
−0.204606 + 0.978844i \(0.565591\pi\)
\(558\) 0 0
\(559\) −15.4759 −0.654562
\(560\) 62.2554 2.63077
\(561\) 0 0
\(562\) 27.3083 1.15193
\(563\) 12.9538 0.545939 0.272970 0.962023i \(-0.411994\pi\)
0.272970 + 0.962023i \(0.411994\pi\)
\(564\) 0 0
\(565\) 19.8355 0.834486
\(566\) −41.1287 −1.72877
\(567\) 0 0
\(568\) 36.6671 1.53852
\(569\) 6.56268 0.275122 0.137561 0.990493i \(-0.456074\pi\)
0.137561 + 0.990493i \(0.456074\pi\)
\(570\) 0 0
\(571\) 42.3502 1.77230 0.886150 0.463398i \(-0.153370\pi\)
0.886150 + 0.463398i \(0.153370\pi\)
\(572\) −226.816 −9.48364
\(573\) 0 0
\(574\) −18.3880 −0.767500
\(575\) −72.8305 −3.03724
\(576\) 0 0
\(577\) 0.112165 0.00466947 0.00233474 0.999997i \(-0.499257\pi\)
0.00233474 + 0.999997i \(0.499257\pi\)
\(578\) −23.5962 −0.981471
\(579\) 0 0
\(580\) −108.353 −4.49910
\(581\) −5.02267 −0.208375
\(582\) 0 0
\(583\) 75.1739 3.11338
\(584\) −62.9591 −2.60527
\(585\) 0 0
\(586\) 61.7995 2.55292
\(587\) −7.07831 −0.292153 −0.146076 0.989273i \(-0.546665\pi\)
−0.146076 + 0.989273i \(0.546665\pi\)
\(588\) 0 0
\(589\) 0.107260 0.00441959
\(590\) −52.6985 −2.16956
\(591\) 0 0
\(592\) 3.71901 0.152850
\(593\) −20.3183 −0.834374 −0.417187 0.908821i \(-0.636984\pi\)
−0.417187 + 0.908821i \(0.636984\pi\)
\(594\) 0 0
\(595\) −10.7582 −0.441041
\(596\) −21.4563 −0.878886
\(597\) 0 0
\(598\) 159.622 6.52745
\(599\) −15.2665 −0.623772 −0.311886 0.950119i \(-0.600961\pi\)
−0.311886 + 0.950119i \(0.600961\pi\)
\(600\) 0 0
\(601\) −21.2328 −0.866104 −0.433052 0.901369i \(-0.642563\pi\)
−0.433052 + 0.901369i \(0.642563\pi\)
\(602\) 6.26936 0.255520
\(603\) 0 0
\(604\) −49.9426 −2.03213
\(605\) 85.5443 3.47787
\(606\) 0 0
\(607\) 35.3036 1.43293 0.716465 0.697623i \(-0.245759\pi\)
0.716465 + 0.697623i \(0.245759\pi\)
\(608\) −19.1734 −0.777583
\(609\) 0 0
\(610\) 110.627 4.47917
\(611\) −17.9737 −0.727136
\(612\) 0 0
\(613\) −39.9099 −1.61195 −0.805974 0.591951i \(-0.798358\pi\)
−0.805974 + 0.591951i \(0.798358\pi\)
\(614\) 59.5304 2.40245
\(615\) 0 0
\(616\) 59.5009 2.39736
\(617\) 32.7641 1.31903 0.659516 0.751690i \(-0.270761\pi\)
0.659516 + 0.751690i \(0.270761\pi\)
\(618\) 0 0
\(619\) −13.3437 −0.536327 −0.268164 0.963373i \(-0.586417\pi\)
−0.268164 + 0.963373i \(0.586417\pi\)
\(620\) −3.08763 −0.124002
\(621\) 0 0
\(622\) 7.39047 0.296331
\(623\) −9.91415 −0.397202
\(624\) 0 0
\(625\) 6.50050 0.260020
\(626\) −11.1795 −0.446823
\(627\) 0 0
\(628\) −11.7365 −0.468336
\(629\) −0.642669 −0.0256249
\(630\) 0 0
\(631\) 7.08019 0.281858 0.140929 0.990020i \(-0.454991\pi\)
0.140929 + 0.990020i \(0.454991\pi\)
\(632\) 38.0775 1.51464
\(633\) 0 0
\(634\) −77.4041 −3.07411
\(635\) 3.69380 0.146584
\(636\) 0 0
\(637\) −6.83862 −0.270956
\(638\) −83.6951 −3.31352
\(639\) 0 0
\(640\) 206.992 8.18208
\(641\) −3.09638 −0.122300 −0.0611499 0.998129i \(-0.519477\pi\)
−0.0611499 + 0.998129i \(0.519477\pi\)
\(642\) 0 0
\(643\) 11.9201 0.470083 0.235041 0.971985i \(-0.424477\pi\)
0.235041 + 0.971985i \(0.424477\pi\)
\(644\) −47.8128 −1.88409
\(645\) 0 0
\(646\) 5.87543 0.231166
\(647\) 3.56438 0.140130 0.0700652 0.997542i \(-0.477679\pi\)
0.0700652 + 0.997542i \(0.477679\pi\)
\(648\) 0 0
\(649\) −30.0983 −1.18146
\(650\) −163.766 −6.42345
\(651\) 0 0
\(652\) −31.5416 −1.23527
\(653\) 7.64872 0.299318 0.149659 0.988738i \(-0.452182\pi\)
0.149659 + 0.988738i \(0.452182\pi\)
\(654\) 0 0
\(655\) 68.9263 2.69317
\(656\) −111.867 −4.36769
\(657\) 0 0
\(658\) 7.28119 0.283850
\(659\) 13.2146 0.514768 0.257384 0.966309i \(-0.417140\pi\)
0.257384 + 0.966309i \(0.417140\pi\)
\(660\) 0 0
\(661\) −1.55692 −0.0605572 −0.0302786 0.999541i \(-0.509639\pi\)
−0.0302786 + 0.999541i \(0.509639\pi\)
\(662\) 77.4256 3.00923
\(663\) 0 0
\(664\) −51.1336 −1.98437
\(665\) −2.68976 −0.104304
\(666\) 0 0
\(667\) 43.5517 1.68633
\(668\) 25.3714 0.981649
\(669\) 0 0
\(670\) 26.8086 1.03571
\(671\) 63.1840 2.43919
\(672\) 0 0
\(673\) −37.3157 −1.43842 −0.719208 0.694795i \(-0.755495\pi\)
−0.719208 + 0.694795i \(0.755495\pi\)
\(674\) 32.5539 1.25393
\(675\) 0 0
\(676\) 191.620 7.37001
\(677\) 5.28980 0.203303 0.101652 0.994820i \(-0.467587\pi\)
0.101652 + 0.994820i \(0.467587\pi\)
\(678\) 0 0
\(679\) −3.08019 −0.118207
\(680\) −109.524 −4.20006
\(681\) 0 0
\(682\) −2.38498 −0.0913258
\(683\) 23.9694 0.917163 0.458581 0.888652i \(-0.348358\pi\)
0.458581 + 0.888652i \(0.348358\pi\)
\(684\) 0 0
\(685\) −37.7960 −1.44411
\(686\) 2.77035 0.105772
\(687\) 0 0
\(688\) 38.1411 1.45411
\(689\) −87.9597 −3.35100
\(690\) 0 0
\(691\) 41.7326 1.58758 0.793791 0.608191i \(-0.208104\pi\)
0.793791 + 0.608191i \(0.208104\pi\)
\(692\) 37.8342 1.43824
\(693\) 0 0
\(694\) 91.2505 3.46382
\(695\) 22.3946 0.849475
\(696\) 0 0
\(697\) 19.3314 0.732231
\(698\) 74.1023 2.80481
\(699\) 0 0
\(700\) 49.0541 1.85407
\(701\) 37.9876 1.43477 0.717385 0.696677i \(-0.245339\pi\)
0.717385 + 0.696677i \(0.245339\pi\)
\(702\) 0 0
\(703\) −0.160680 −0.00606018
\(704\) 229.320 8.64282
\(705\) 0 0
\(706\) −58.9078 −2.21702
\(707\) 6.71801 0.252657
\(708\) 0 0
\(709\) 31.4515 1.18118 0.590592 0.806970i \(-0.298894\pi\)
0.590592 + 0.806970i \(0.298894\pi\)
\(710\) 36.8563 1.38319
\(711\) 0 0
\(712\) −100.932 −3.78257
\(713\) 1.24105 0.0464778
\(714\) 0 0
\(715\) −147.636 −5.52129
\(716\) −135.518 −5.06455
\(717\) 0 0
\(718\) 57.8192 2.15779
\(719\) −41.6021 −1.55150 −0.775748 0.631043i \(-0.782627\pi\)
−0.775748 + 0.631043i \(0.782627\pi\)
\(720\) 0 0
\(721\) −15.9532 −0.594128
\(722\) −51.1676 −1.90426
\(723\) 0 0
\(724\) 26.5473 0.986624
\(725\) −44.6823 −1.65946
\(726\) 0 0
\(727\) 26.5582 0.984990 0.492495 0.870315i \(-0.336085\pi\)
0.492495 + 0.870315i \(0.336085\pi\)
\(728\) −69.6210 −2.58033
\(729\) 0 0
\(730\) −63.2841 −2.34225
\(731\) −6.59103 −0.243778
\(732\) 0 0
\(733\) −31.8971 −1.17815 −0.589073 0.808080i \(-0.700507\pi\)
−0.589073 + 0.808080i \(0.700507\pi\)
\(734\) 25.2635 0.932493
\(735\) 0 0
\(736\) −221.845 −8.17731
\(737\) 15.3116 0.564008
\(738\) 0 0
\(739\) 8.69965 0.320022 0.160011 0.987115i \(-0.448847\pi\)
0.160011 + 0.987115i \(0.448847\pi\)
\(740\) 4.62539 0.170033
\(741\) 0 0
\(742\) 35.6328 1.30812
\(743\) −12.8619 −0.471857 −0.235928 0.971770i \(-0.575813\pi\)
−0.235928 + 0.971770i \(0.575813\pi\)
\(744\) 0 0
\(745\) −13.9661 −0.511679
\(746\) −50.5922 −1.85231
\(747\) 0 0
\(748\) −96.5983 −3.53198
\(749\) −17.3101 −0.632496
\(750\) 0 0
\(751\) 34.2868 1.25114 0.625571 0.780167i \(-0.284866\pi\)
0.625571 + 0.780167i \(0.284866\pi\)
\(752\) 44.2968 1.61534
\(753\) 0 0
\(754\) 97.9301 3.56640
\(755\) −32.5080 −1.18309
\(756\) 0 0
\(757\) 48.4358 1.76043 0.880215 0.474576i \(-0.157399\pi\)
0.880215 + 0.474576i \(0.157399\pi\)
\(758\) −42.7328 −1.55212
\(759\) 0 0
\(760\) −27.3833 −0.993296
\(761\) 1.81753 0.0658853 0.0329427 0.999457i \(-0.489512\pi\)
0.0329427 + 0.999457i \(0.489512\pi\)
\(762\) 0 0
\(763\) −3.73388 −0.135176
\(764\) −117.079 −4.23577
\(765\) 0 0
\(766\) 2.98764 0.107948
\(767\) 35.2175 1.27163
\(768\) 0 0
\(769\) −13.2880 −0.479179 −0.239590 0.970874i \(-0.577013\pi\)
−0.239590 + 0.970874i \(0.577013\pi\)
\(770\) 59.8080 2.15533
\(771\) 0 0
\(772\) −3.68646 −0.132678
\(773\) 7.17442 0.258046 0.129023 0.991642i \(-0.458816\pi\)
0.129023 + 0.991642i \(0.458816\pi\)
\(774\) 0 0
\(775\) −1.27327 −0.0457373
\(776\) −31.3580 −1.12569
\(777\) 0 0
\(778\) 26.8706 0.963357
\(779\) 4.83326 0.173170
\(780\) 0 0
\(781\) 21.0502 0.753235
\(782\) 67.9814 2.43101
\(783\) 0 0
\(784\) 16.8540 0.601930
\(785\) −7.63938 −0.272661
\(786\) 0 0
\(787\) 24.0658 0.857852 0.428926 0.903340i \(-0.358892\pi\)
0.428926 + 0.903340i \(0.358892\pi\)
\(788\) −59.8435 −2.13184
\(789\) 0 0
\(790\) 38.2740 1.36173
\(791\) 5.36995 0.190933
\(792\) 0 0
\(793\) −73.9305 −2.62535
\(794\) −37.3969 −1.32717
\(795\) 0 0
\(796\) −109.057 −3.86544
\(797\) −22.2703 −0.788853 −0.394427 0.918927i \(-0.629057\pi\)
−0.394427 + 0.918927i \(0.629057\pi\)
\(798\) 0 0
\(799\) −7.65478 −0.270807
\(800\) 227.604 8.04702
\(801\) 0 0
\(802\) −35.9789 −1.27046
\(803\) −36.1442 −1.27550
\(804\) 0 0
\(805\) −31.1218 −1.09690
\(806\) 2.79063 0.0982957
\(807\) 0 0
\(808\) 68.3931 2.40606
\(809\) 14.4820 0.509159 0.254580 0.967052i \(-0.418063\pi\)
0.254580 + 0.967052i \(0.418063\pi\)
\(810\) 0 0
\(811\) −33.3208 −1.17005 −0.585026 0.811014i \(-0.698916\pi\)
−0.585026 + 0.811014i \(0.698916\pi\)
\(812\) −29.3337 −1.02941
\(813\) 0 0
\(814\) 3.57280 0.125227
\(815\) −20.5307 −0.719160
\(816\) 0 0
\(817\) −1.64789 −0.0576525
\(818\) −77.5758 −2.71238
\(819\) 0 0
\(820\) −139.132 −4.85869
\(821\) 29.5966 1.03293 0.516464 0.856309i \(-0.327248\pi\)
0.516464 + 0.856309i \(0.327248\pi\)
\(822\) 0 0
\(823\) −5.04541 −0.175872 −0.0879359 0.996126i \(-0.528027\pi\)
−0.0879359 + 0.996126i \(0.528027\pi\)
\(824\) −162.413 −5.65791
\(825\) 0 0
\(826\) −14.2667 −0.496404
\(827\) 4.98336 0.173289 0.0866443 0.996239i \(-0.472386\pi\)
0.0866443 + 0.996239i \(0.472386\pi\)
\(828\) 0 0
\(829\) −16.2886 −0.565728 −0.282864 0.959160i \(-0.591285\pi\)
−0.282864 + 0.959160i \(0.591285\pi\)
\(830\) −51.3975 −1.78403
\(831\) 0 0
\(832\) −268.323 −9.30243
\(833\) −2.91249 −0.100912
\(834\) 0 0
\(835\) 16.5145 0.571507
\(836\) −24.1516 −0.835299
\(837\) 0 0
\(838\) 49.5972 1.71331
\(839\) 17.4021 0.600787 0.300393 0.953815i \(-0.402882\pi\)
0.300393 + 0.953815i \(0.402882\pi\)
\(840\) 0 0
\(841\) −2.28059 −0.0786410
\(842\) −13.9119 −0.479435
\(843\) 0 0
\(844\) −4.54569 −0.156469
\(845\) 124.727 4.29075
\(846\) 0 0
\(847\) 23.1589 0.795749
\(848\) 216.780 7.44426
\(849\) 0 0
\(850\) −69.7463 −2.39228
\(851\) −1.85915 −0.0637308
\(852\) 0 0
\(853\) −12.2893 −0.420777 −0.210389 0.977618i \(-0.567473\pi\)
−0.210389 + 0.977618i \(0.567473\pi\)
\(854\) 29.9495 1.02485
\(855\) 0 0
\(856\) −176.226 −6.02329
\(857\) −6.88542 −0.235202 −0.117601 0.993061i \(-0.537520\pi\)
−0.117601 + 0.993061i \(0.537520\pi\)
\(858\) 0 0
\(859\) −26.4083 −0.901039 −0.450520 0.892767i \(-0.648761\pi\)
−0.450520 + 0.892767i \(0.648761\pi\)
\(860\) 47.4367 1.61758
\(861\) 0 0
\(862\) 27.3447 0.931365
\(863\) 15.6362 0.532261 0.266131 0.963937i \(-0.414255\pi\)
0.266131 + 0.963937i \(0.414255\pi\)
\(864\) 0 0
\(865\) 24.6266 0.837331
\(866\) −57.1579 −1.94230
\(867\) 0 0
\(868\) −0.835896 −0.0283722
\(869\) 21.8599 0.741546
\(870\) 0 0
\(871\) −17.9158 −0.607053
\(872\) −38.0130 −1.28728
\(873\) 0 0
\(874\) 16.9968 0.574924
\(875\) 13.4607 0.455056
\(876\) 0 0
\(877\) −4.24374 −0.143301 −0.0716504 0.997430i \(-0.522827\pi\)
−0.0716504 + 0.997430i \(0.522827\pi\)
\(878\) 34.6920 1.17080
\(879\) 0 0
\(880\) 363.856 12.2656
\(881\) −15.7838 −0.531768 −0.265884 0.964005i \(-0.585664\pi\)
−0.265884 + 0.964005i \(0.585664\pi\)
\(882\) 0 0
\(883\) 33.4214 1.12472 0.562360 0.826892i \(-0.309893\pi\)
0.562360 + 0.826892i \(0.309893\pi\)
\(884\) 113.028 3.80154
\(885\) 0 0
\(886\) −48.6390 −1.63406
\(887\) 7.62418 0.255995 0.127998 0.991774i \(-0.459145\pi\)
0.127998 + 0.991774i \(0.459145\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −101.453 −3.40070
\(891\) 0 0
\(892\) −151.436 −5.07045
\(893\) −1.91385 −0.0640447
\(894\) 0 0
\(895\) −88.2099 −2.94853
\(896\) 56.0377 1.87209
\(897\) 0 0
\(898\) −42.0342 −1.40270
\(899\) 0.761400 0.0253941
\(900\) 0 0
\(901\) −37.4610 −1.24801
\(902\) −107.470 −3.57835
\(903\) 0 0
\(904\) 54.6691 1.81827
\(905\) 17.2799 0.574403
\(906\) 0 0
\(907\) −22.2359 −0.738331 −0.369165 0.929364i \(-0.620356\pi\)
−0.369165 + 0.929364i \(0.620356\pi\)
\(908\) 31.9122 1.05904
\(909\) 0 0
\(910\) −69.9803 −2.31983
\(911\) −7.49497 −0.248319 −0.124160 0.992262i \(-0.539624\pi\)
−0.124160 + 0.992262i \(0.539624\pi\)
\(912\) 0 0
\(913\) −29.3553 −0.971519
\(914\) 24.1840 0.799936
\(915\) 0 0
\(916\) 170.706 5.64028
\(917\) 18.6600 0.616208
\(918\) 0 0
\(919\) −42.1185 −1.38936 −0.694680 0.719319i \(-0.744454\pi\)
−0.694680 + 0.719319i \(0.744454\pi\)
\(920\) −316.837 −10.4458
\(921\) 0 0
\(922\) −108.093 −3.55987
\(923\) −24.6305 −0.810722
\(924\) 0 0
\(925\) 1.90741 0.0627153
\(926\) 64.1076 2.10671
\(927\) 0 0
\(928\) −136.104 −4.46784
\(929\) −15.2870 −0.501549 −0.250775 0.968046i \(-0.580685\pi\)
−0.250775 + 0.968046i \(0.580685\pi\)
\(930\) 0 0
\(931\) −0.728183 −0.0238652
\(932\) 142.281 4.66056
\(933\) 0 0
\(934\) 15.9724 0.522632
\(935\) −62.8767 −2.05629
\(936\) 0 0
\(937\) 10.6073 0.346526 0.173263 0.984876i \(-0.444569\pi\)
0.173263 + 0.984876i \(0.444569\pi\)
\(938\) 7.25774 0.236974
\(939\) 0 0
\(940\) 55.0927 1.79693
\(941\) 40.6002 1.32353 0.661764 0.749713i \(-0.269808\pi\)
0.661764 + 0.749713i \(0.269808\pi\)
\(942\) 0 0
\(943\) 55.9231 1.82111
\(944\) −86.7950 −2.82494
\(945\) 0 0
\(946\) 36.6416 1.19132
\(947\) −42.6979 −1.38749 −0.693747 0.720219i \(-0.744041\pi\)
−0.693747 + 0.720219i \(0.744041\pi\)
\(948\) 0 0
\(949\) 42.2917 1.37285
\(950\) −17.4380 −0.565764
\(951\) 0 0
\(952\) −29.6508 −0.960988
\(953\) 29.4085 0.952636 0.476318 0.879273i \(-0.341971\pi\)
0.476318 + 0.879273i \(0.341971\pi\)
\(954\) 0 0
\(955\) −76.2078 −2.46603
\(956\) 29.0238 0.938698
\(957\) 0 0
\(958\) −52.3395 −1.69101
\(959\) −10.2323 −0.330418
\(960\) 0 0
\(961\) −30.9783 −0.999300
\(962\) −4.18047 −0.134784
\(963\) 0 0
\(964\) −97.7016 −3.14676
\(965\) −2.39955 −0.0772441
\(966\) 0 0
\(967\) −37.9006 −1.21880 −0.609400 0.792863i \(-0.708590\pi\)
−0.609400 + 0.792863i \(0.708590\pi\)
\(968\) 235.771 7.57795
\(969\) 0 0
\(970\) −31.5199 −1.01204
\(971\) 18.8576 0.605170 0.302585 0.953122i \(-0.402150\pi\)
0.302585 + 0.953122i \(0.402150\pi\)
\(972\) 0 0
\(973\) 6.06275 0.194363
\(974\) −31.1290 −0.997438
\(975\) 0 0
\(976\) 182.205 5.83223
\(977\) −1.39022 −0.0444772 −0.0222386 0.999753i \(-0.507079\pi\)
−0.0222386 + 0.999753i \(0.507079\pi\)
\(978\) 0 0
\(979\) −57.9439 −1.85189
\(980\) 20.9617 0.669596
\(981\) 0 0
\(982\) 79.6477 2.54166
\(983\) −8.63107 −0.275288 −0.137644 0.990482i \(-0.543953\pi\)
−0.137644 + 0.990482i \(0.543953\pi\)
\(984\) 0 0
\(985\) −38.9527 −1.24114
\(986\) 41.7073 1.32823
\(987\) 0 0
\(988\) 28.2593 0.899049
\(989\) −19.0669 −0.606292
\(990\) 0 0
\(991\) −44.1925 −1.40382 −0.701911 0.712264i \(-0.747670\pi\)
−0.701911 + 0.712264i \(0.747670\pi\)
\(992\) −3.87844 −0.123141
\(993\) 0 0
\(994\) 9.97789 0.316479
\(995\) −70.9865 −2.25042
\(996\) 0 0
\(997\) 31.2697 0.990320 0.495160 0.868802i \(-0.335109\pi\)
0.495160 + 0.868802i \(0.335109\pi\)
\(998\) 14.7944 0.468308
\(999\) 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 \(a_p\))