Properties

Label 4028.2.a.d.1.3
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.44269\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44269 q^{3} -3.59133 q^{5} +0.459217 q^{7} +2.96674 q^{9} +O(q^{10})\) \(q-2.44269 q^{3} -3.59133 q^{5} +0.459217 q^{7} +2.96674 q^{9} -3.29838 q^{11} -5.41041 q^{13} +8.77250 q^{15} +6.52731 q^{17} -1.00000 q^{19} -1.12173 q^{21} +0.522155 q^{23} +7.89763 q^{25} +0.0812467 q^{27} -0.139943 q^{29} +2.51077 q^{31} +8.05692 q^{33} -1.64920 q^{35} +5.52082 q^{37} +13.2160 q^{39} +0.693306 q^{41} -2.18127 q^{43} -10.6545 q^{45} +2.32738 q^{47} -6.78912 q^{49} -15.9442 q^{51} +1.00000 q^{53} +11.8456 q^{55} +2.44269 q^{57} +9.55995 q^{59} +6.77344 q^{61} +1.36238 q^{63} +19.4306 q^{65} -2.42099 q^{67} -1.27546 q^{69} -3.70484 q^{71} +0.506311 q^{73} -19.2915 q^{75} -1.51467 q^{77} +1.41051 q^{79} -9.09868 q^{81} +5.81322 q^{83} -23.4417 q^{85} +0.341839 q^{87} -0.997992 q^{89} -2.48455 q^{91} -6.13304 q^{93} +3.59133 q^{95} +0.119394 q^{97} -9.78542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.44269 −1.41029 −0.705144 0.709064i \(-0.749118\pi\)
−0.705144 + 0.709064i \(0.749118\pi\)
\(4\) 0 0
\(5\) −3.59133 −1.60609 −0.803045 0.595918i \(-0.796788\pi\)
−0.803045 + 0.595918i \(0.796788\pi\)
\(6\) 0 0
\(7\) 0.459217 0.173568 0.0867839 0.996227i \(-0.472341\pi\)
0.0867839 + 0.996227i \(0.472341\pi\)
\(8\) 0 0
\(9\) 2.96674 0.988913
\(10\) 0 0
\(11\) −3.29838 −0.994498 −0.497249 0.867608i \(-0.665656\pi\)
−0.497249 + 0.867608i \(0.665656\pi\)
\(12\) 0 0
\(13\) −5.41041 −1.50058 −0.750289 0.661110i \(-0.770086\pi\)
−0.750289 + 0.661110i \(0.770086\pi\)
\(14\) 0 0
\(15\) 8.77250 2.26505
\(16\) 0 0
\(17\) 6.52731 1.58311 0.791553 0.611100i \(-0.209273\pi\)
0.791553 + 0.611100i \(0.209273\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −1.12173 −0.244781
\(22\) 0 0
\(23\) 0.522155 0.108877 0.0544384 0.998517i \(-0.482663\pi\)
0.0544384 + 0.998517i \(0.482663\pi\)
\(24\) 0 0
\(25\) 7.89763 1.57953
\(26\) 0 0
\(27\) 0.0812467 0.0156359
\(28\) 0 0
\(29\) −0.139943 −0.0259869 −0.0129934 0.999916i \(-0.504136\pi\)
−0.0129934 + 0.999916i \(0.504136\pi\)
\(30\) 0 0
\(31\) 2.51077 0.450948 0.225474 0.974249i \(-0.427607\pi\)
0.225474 + 0.974249i \(0.427607\pi\)
\(32\) 0 0
\(33\) 8.05692 1.40253
\(34\) 0 0
\(35\) −1.64920 −0.278765
\(36\) 0 0
\(37\) 5.52082 0.907617 0.453809 0.891099i \(-0.350065\pi\)
0.453809 + 0.891099i \(0.350065\pi\)
\(38\) 0 0
\(39\) 13.2160 2.11625
\(40\) 0 0
\(41\) 0.693306 0.108276 0.0541381 0.998533i \(-0.482759\pi\)
0.0541381 + 0.998533i \(0.482759\pi\)
\(42\) 0 0
\(43\) −2.18127 −0.332641 −0.166321 0.986072i \(-0.553189\pi\)
−0.166321 + 0.986072i \(0.553189\pi\)
\(44\) 0 0
\(45\) −10.6545 −1.58828
\(46\) 0 0
\(47\) 2.32738 0.339484 0.169742 0.985489i \(-0.445707\pi\)
0.169742 + 0.985489i \(0.445707\pi\)
\(48\) 0 0
\(49\) −6.78912 −0.969874
\(50\) 0 0
\(51\) −15.9442 −2.23264
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 11.8456 1.59725
\(56\) 0 0
\(57\) 2.44269 0.323542
\(58\) 0 0
\(59\) 9.55995 1.24460 0.622300 0.782779i \(-0.286198\pi\)
0.622300 + 0.782779i \(0.286198\pi\)
\(60\) 0 0
\(61\) 6.77344 0.867250 0.433625 0.901093i \(-0.357234\pi\)
0.433625 + 0.901093i \(0.357234\pi\)
\(62\) 0 0
\(63\) 1.36238 0.171643
\(64\) 0 0
\(65\) 19.4306 2.41006
\(66\) 0 0
\(67\) −2.42099 −0.295771 −0.147885 0.989005i \(-0.547247\pi\)
−0.147885 + 0.989005i \(0.547247\pi\)
\(68\) 0 0
\(69\) −1.27546 −0.153548
\(70\) 0 0
\(71\) −3.70484 −0.439683 −0.219842 0.975536i \(-0.570554\pi\)
−0.219842 + 0.975536i \(0.570554\pi\)
\(72\) 0 0
\(73\) 0.506311 0.0592592 0.0296296 0.999561i \(-0.490567\pi\)
0.0296296 + 0.999561i \(0.490567\pi\)
\(74\) 0 0
\(75\) −19.2915 −2.22759
\(76\) 0 0
\(77\) −1.51467 −0.172613
\(78\) 0 0
\(79\) 1.41051 0.158695 0.0793476 0.996847i \(-0.474716\pi\)
0.0793476 + 0.996847i \(0.474716\pi\)
\(80\) 0 0
\(81\) −9.09868 −1.01096
\(82\) 0 0
\(83\) 5.81322 0.638084 0.319042 0.947741i \(-0.396639\pi\)
0.319042 + 0.947741i \(0.396639\pi\)
\(84\) 0 0
\(85\) −23.4417 −2.54261
\(86\) 0 0
\(87\) 0.341839 0.0366490
\(88\) 0 0
\(89\) −0.997992 −0.105787 −0.0528935 0.998600i \(-0.516844\pi\)
−0.0528935 + 0.998600i \(0.516844\pi\)
\(90\) 0 0
\(91\) −2.48455 −0.260452
\(92\) 0 0
\(93\) −6.13304 −0.635967
\(94\) 0 0
\(95\) 3.59133 0.368462
\(96\) 0 0
\(97\) 0.119394 0.0121226 0.00606131 0.999982i \(-0.498071\pi\)
0.00606131 + 0.999982i \(0.498071\pi\)
\(98\) 0 0
\(99\) −9.78542 −0.983472
\(100\) 0 0
\(101\) 14.7246 1.46515 0.732577 0.680684i \(-0.238317\pi\)
0.732577 + 0.680684i \(0.238317\pi\)
\(102\) 0 0
\(103\) 8.60036 0.847419 0.423709 0.905798i \(-0.360728\pi\)
0.423709 + 0.905798i \(0.360728\pi\)
\(104\) 0 0
\(105\) 4.02848 0.393140
\(106\) 0 0
\(107\) −8.84427 −0.855007 −0.427504 0.904014i \(-0.640607\pi\)
−0.427504 + 0.904014i \(0.640607\pi\)
\(108\) 0 0
\(109\) 5.17303 0.495486 0.247743 0.968826i \(-0.420311\pi\)
0.247743 + 0.968826i \(0.420311\pi\)
\(110\) 0 0
\(111\) −13.4857 −1.28000
\(112\) 0 0
\(113\) 2.27378 0.213899 0.106949 0.994264i \(-0.465892\pi\)
0.106949 + 0.994264i \(0.465892\pi\)
\(114\) 0 0
\(115\) −1.87523 −0.174866
\(116\) 0 0
\(117\) −16.0513 −1.48394
\(118\) 0 0
\(119\) 2.99745 0.274776
\(120\) 0 0
\(121\) −0.120708 −0.0109734
\(122\) 0 0
\(123\) −1.69353 −0.152701
\(124\) 0 0
\(125\) −10.4063 −0.930770
\(126\) 0 0
\(127\) 0.423104 0.0375444 0.0187722 0.999824i \(-0.494024\pi\)
0.0187722 + 0.999824i \(0.494024\pi\)
\(128\) 0 0
\(129\) 5.32818 0.469120
\(130\) 0 0
\(131\) −13.6472 −1.19236 −0.596181 0.802850i \(-0.703316\pi\)
−0.596181 + 0.802850i \(0.703316\pi\)
\(132\) 0 0
\(133\) −0.459217 −0.0398192
\(134\) 0 0
\(135\) −0.291784 −0.0251127
\(136\) 0 0
\(137\) 15.7066 1.34191 0.670953 0.741500i \(-0.265885\pi\)
0.670953 + 0.741500i \(0.265885\pi\)
\(138\) 0 0
\(139\) −1.85836 −0.157624 −0.0788120 0.996889i \(-0.525113\pi\)
−0.0788120 + 0.996889i \(0.525113\pi\)
\(140\) 0 0
\(141\) −5.68508 −0.478770
\(142\) 0 0
\(143\) 17.8456 1.49232
\(144\) 0 0
\(145\) 0.502583 0.0417372
\(146\) 0 0
\(147\) 16.5837 1.36780
\(148\) 0 0
\(149\) −11.3101 −0.926562 −0.463281 0.886211i \(-0.653328\pi\)
−0.463281 + 0.886211i \(0.653328\pi\)
\(150\) 0 0
\(151\) −6.98244 −0.568223 −0.284111 0.958791i \(-0.591699\pi\)
−0.284111 + 0.958791i \(0.591699\pi\)
\(152\) 0 0
\(153\) 19.3648 1.56555
\(154\) 0 0
\(155\) −9.01700 −0.724263
\(156\) 0 0
\(157\) −22.1303 −1.76619 −0.883097 0.469190i \(-0.844546\pi\)
−0.883097 + 0.469190i \(0.844546\pi\)
\(158\) 0 0
\(159\) −2.44269 −0.193718
\(160\) 0 0
\(161\) 0.239783 0.0188975
\(162\) 0 0
\(163\) −13.9225 −1.09049 −0.545246 0.838276i \(-0.683564\pi\)
−0.545246 + 0.838276i \(0.683564\pi\)
\(164\) 0 0
\(165\) −28.9350 −2.25259
\(166\) 0 0
\(167\) −12.6856 −0.981639 −0.490820 0.871261i \(-0.663303\pi\)
−0.490820 + 0.871261i \(0.663303\pi\)
\(168\) 0 0
\(169\) 16.2726 1.25174
\(170\) 0 0
\(171\) −2.96674 −0.226872
\(172\) 0 0
\(173\) 16.3626 1.24403 0.622014 0.783006i \(-0.286315\pi\)
0.622014 + 0.783006i \(0.286315\pi\)
\(174\) 0 0
\(175\) 3.62673 0.274155
\(176\) 0 0
\(177\) −23.3520 −1.75524
\(178\) 0 0
\(179\) 19.7991 1.47986 0.739928 0.672686i \(-0.234860\pi\)
0.739928 + 0.672686i \(0.234860\pi\)
\(180\) 0 0
\(181\) −0.832069 −0.0618472 −0.0309236 0.999522i \(-0.509845\pi\)
−0.0309236 + 0.999522i \(0.509845\pi\)
\(182\) 0 0
\(183\) −16.5454 −1.22307
\(184\) 0 0
\(185\) −19.8271 −1.45772
\(186\) 0 0
\(187\) −21.5295 −1.57440
\(188\) 0 0
\(189\) 0.0373099 0.00271390
\(190\) 0 0
\(191\) −20.6072 −1.49109 −0.745544 0.666457i \(-0.767810\pi\)
−0.745544 + 0.666457i \(0.767810\pi\)
\(192\) 0 0
\(193\) −14.5116 −1.04457 −0.522283 0.852772i \(-0.674920\pi\)
−0.522283 + 0.852772i \(0.674920\pi\)
\(194\) 0 0
\(195\) −47.4628 −3.39889
\(196\) 0 0
\(197\) −11.1698 −0.795816 −0.397908 0.917425i \(-0.630264\pi\)
−0.397908 + 0.917425i \(0.630264\pi\)
\(198\) 0 0
\(199\) 12.6912 0.899656 0.449828 0.893115i \(-0.351485\pi\)
0.449828 + 0.893115i \(0.351485\pi\)
\(200\) 0 0
\(201\) 5.91372 0.417122
\(202\) 0 0
\(203\) −0.0642644 −0.00451048
\(204\) 0 0
\(205\) −2.48989 −0.173901
\(206\) 0 0
\(207\) 1.54910 0.107670
\(208\) 0 0
\(209\) 3.29838 0.228154
\(210\) 0 0
\(211\) 14.0065 0.964250 0.482125 0.876103i \(-0.339865\pi\)
0.482125 + 0.876103i \(0.339865\pi\)
\(212\) 0 0
\(213\) 9.04977 0.620080
\(214\) 0 0
\(215\) 7.83367 0.534252
\(216\) 0 0
\(217\) 1.15299 0.0782700
\(218\) 0 0
\(219\) −1.23676 −0.0835726
\(220\) 0 0
\(221\) −35.3155 −2.37557
\(222\) 0 0
\(223\) −23.6750 −1.58539 −0.792697 0.609616i \(-0.791324\pi\)
−0.792697 + 0.609616i \(0.791324\pi\)
\(224\) 0 0
\(225\) 23.4302 1.56201
\(226\) 0 0
\(227\) −21.0646 −1.39810 −0.699052 0.715070i \(-0.746395\pi\)
−0.699052 + 0.715070i \(0.746395\pi\)
\(228\) 0 0
\(229\) 3.48274 0.230146 0.115073 0.993357i \(-0.463290\pi\)
0.115073 + 0.993357i \(0.463290\pi\)
\(230\) 0 0
\(231\) 3.69987 0.243434
\(232\) 0 0
\(233\) 26.4470 1.73260 0.866301 0.499522i \(-0.166491\pi\)
0.866301 + 0.499522i \(0.166491\pi\)
\(234\) 0 0
\(235\) −8.35840 −0.545242
\(236\) 0 0
\(237\) −3.44545 −0.223806
\(238\) 0 0
\(239\) −9.16490 −0.592828 −0.296414 0.955060i \(-0.595791\pi\)
−0.296414 + 0.955060i \(0.595791\pi\)
\(240\) 0 0
\(241\) 18.5407 1.19431 0.597156 0.802125i \(-0.296297\pi\)
0.597156 + 0.802125i \(0.296297\pi\)
\(242\) 0 0
\(243\) 21.9815 1.41011
\(244\) 0 0
\(245\) 24.3819 1.55771
\(246\) 0 0
\(247\) 5.41041 0.344256
\(248\) 0 0
\(249\) −14.1999 −0.899882
\(250\) 0 0
\(251\) 10.2376 0.646190 0.323095 0.946367i \(-0.395277\pi\)
0.323095 + 0.946367i \(0.395277\pi\)
\(252\) 0 0
\(253\) −1.72226 −0.108278
\(254\) 0 0
\(255\) 57.2609 3.58581
\(256\) 0 0
\(257\) 14.4460 0.901118 0.450559 0.892747i \(-0.351225\pi\)
0.450559 + 0.892747i \(0.351225\pi\)
\(258\) 0 0
\(259\) 2.53526 0.157533
\(260\) 0 0
\(261\) −0.415176 −0.0256987
\(262\) 0 0
\(263\) −12.2924 −0.757979 −0.378989 0.925401i \(-0.623728\pi\)
−0.378989 + 0.925401i \(0.623728\pi\)
\(264\) 0 0
\(265\) −3.59133 −0.220613
\(266\) 0 0
\(267\) 2.43779 0.149190
\(268\) 0 0
\(269\) −15.5365 −0.947276 −0.473638 0.880720i \(-0.657060\pi\)
−0.473638 + 0.880720i \(0.657060\pi\)
\(270\) 0 0
\(271\) −25.2889 −1.53619 −0.768094 0.640337i \(-0.778795\pi\)
−0.768094 + 0.640337i \(0.778795\pi\)
\(272\) 0 0
\(273\) 6.06900 0.367312
\(274\) 0 0
\(275\) −26.0494 −1.57084
\(276\) 0 0
\(277\) −22.6407 −1.36035 −0.680173 0.733052i \(-0.738095\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(278\) 0 0
\(279\) 7.44881 0.445948
\(280\) 0 0
\(281\) 11.2599 0.671709 0.335854 0.941914i \(-0.390975\pi\)
0.335854 + 0.941914i \(0.390975\pi\)
\(282\) 0 0
\(283\) −32.1904 −1.91352 −0.956760 0.290879i \(-0.906052\pi\)
−0.956760 + 0.290879i \(0.906052\pi\)
\(284\) 0 0
\(285\) −8.77250 −0.519638
\(286\) 0 0
\(287\) 0.318378 0.0187933
\(288\) 0 0
\(289\) 25.6058 1.50623
\(290\) 0 0
\(291\) −0.291642 −0.0170964
\(292\) 0 0
\(293\) −7.03529 −0.411006 −0.205503 0.978656i \(-0.565883\pi\)
−0.205503 + 0.978656i \(0.565883\pi\)
\(294\) 0 0
\(295\) −34.3329 −1.99894
\(296\) 0 0
\(297\) −0.267982 −0.0155499
\(298\) 0 0
\(299\) −2.82507 −0.163378
\(300\) 0 0
\(301\) −1.00168 −0.0577358
\(302\) 0 0
\(303\) −35.9677 −2.06629
\(304\) 0 0
\(305\) −24.3256 −1.39288
\(306\) 0 0
\(307\) −4.19538 −0.239443 −0.119721 0.992808i \(-0.538200\pi\)
−0.119721 + 0.992808i \(0.538200\pi\)
\(308\) 0 0
\(309\) −21.0080 −1.19510
\(310\) 0 0
\(311\) −15.1362 −0.858296 −0.429148 0.903234i \(-0.641186\pi\)
−0.429148 + 0.903234i \(0.641186\pi\)
\(312\) 0 0
\(313\) −2.26357 −0.127944 −0.0639722 0.997952i \(-0.520377\pi\)
−0.0639722 + 0.997952i \(0.520377\pi\)
\(314\) 0 0
\(315\) −4.89274 −0.275675
\(316\) 0 0
\(317\) 8.24703 0.463199 0.231600 0.972811i \(-0.425604\pi\)
0.231600 + 0.972811i \(0.425604\pi\)
\(318\) 0 0
\(319\) 0.461586 0.0258439
\(320\) 0 0
\(321\) 21.6038 1.20581
\(322\) 0 0
\(323\) −6.52731 −0.363189
\(324\) 0 0
\(325\) −42.7294 −2.37020
\(326\) 0 0
\(327\) −12.6361 −0.698778
\(328\) 0 0
\(329\) 1.06877 0.0589234
\(330\) 0 0
\(331\) −28.0021 −1.53913 −0.769567 0.638567i \(-0.779528\pi\)
−0.769567 + 0.638567i \(0.779528\pi\)
\(332\) 0 0
\(333\) 16.3788 0.897555
\(334\) 0 0
\(335\) 8.69455 0.475034
\(336\) 0 0
\(337\) −24.9915 −1.36137 −0.680686 0.732576i \(-0.738318\pi\)
−0.680686 + 0.732576i \(0.738318\pi\)
\(338\) 0 0
\(339\) −5.55413 −0.301659
\(340\) 0 0
\(341\) −8.28147 −0.448467
\(342\) 0 0
\(343\) −6.33220 −0.341907
\(344\) 0 0
\(345\) 4.58061 0.246612
\(346\) 0 0
\(347\) −2.47834 −0.133044 −0.0665222 0.997785i \(-0.521190\pi\)
−0.0665222 + 0.997785i \(0.521190\pi\)
\(348\) 0 0
\(349\) 30.3845 1.62645 0.813223 0.581952i \(-0.197711\pi\)
0.813223 + 0.581952i \(0.197711\pi\)
\(350\) 0 0
\(351\) −0.439578 −0.0234630
\(352\) 0 0
\(353\) −9.45770 −0.503382 −0.251691 0.967808i \(-0.580987\pi\)
−0.251691 + 0.967808i \(0.580987\pi\)
\(354\) 0 0
\(355\) 13.3053 0.706171
\(356\) 0 0
\(357\) −7.32185 −0.387514
\(358\) 0 0
\(359\) −6.37708 −0.336569 −0.168285 0.985738i \(-0.553823\pi\)
−0.168285 + 0.985738i \(0.553823\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0.294852 0.0154757
\(364\) 0 0
\(365\) −1.81833 −0.0951756
\(366\) 0 0
\(367\) −5.25534 −0.274327 −0.137163 0.990548i \(-0.543799\pi\)
−0.137163 + 0.990548i \(0.543799\pi\)
\(368\) 0 0
\(369\) 2.05686 0.107076
\(370\) 0 0
\(371\) 0.459217 0.0238414
\(372\) 0 0
\(373\) 15.2815 0.791248 0.395624 0.918413i \(-0.370528\pi\)
0.395624 + 0.918413i \(0.370528\pi\)
\(374\) 0 0
\(375\) 25.4194 1.31265
\(376\) 0 0
\(377\) 0.757152 0.0389953
\(378\) 0 0
\(379\) −15.9601 −0.819818 −0.409909 0.912127i \(-0.634439\pi\)
−0.409909 + 0.912127i \(0.634439\pi\)
\(380\) 0 0
\(381\) −1.03351 −0.0529485
\(382\) 0 0
\(383\) 2.18080 0.111434 0.0557169 0.998447i \(-0.482256\pi\)
0.0557169 + 0.998447i \(0.482256\pi\)
\(384\) 0 0
\(385\) 5.43968 0.277232
\(386\) 0 0
\(387\) −6.47127 −0.328953
\(388\) 0 0
\(389\) 21.8895 1.10984 0.554921 0.831903i \(-0.312749\pi\)
0.554921 + 0.831903i \(0.312749\pi\)
\(390\) 0 0
\(391\) 3.40827 0.172364
\(392\) 0 0
\(393\) 33.3359 1.68157
\(394\) 0 0
\(395\) −5.06562 −0.254879
\(396\) 0 0
\(397\) 27.0175 1.35597 0.677984 0.735076i \(-0.262854\pi\)
0.677984 + 0.735076i \(0.262854\pi\)
\(398\) 0 0
\(399\) 1.12173 0.0561565
\(400\) 0 0
\(401\) 24.2691 1.21194 0.605969 0.795488i \(-0.292785\pi\)
0.605969 + 0.795488i \(0.292785\pi\)
\(402\) 0 0
\(403\) −13.5843 −0.676683
\(404\) 0 0
\(405\) 32.6763 1.62370
\(406\) 0 0
\(407\) −18.2097 −0.902624
\(408\) 0 0
\(409\) 15.4805 0.765463 0.382731 0.923860i \(-0.374983\pi\)
0.382731 + 0.923860i \(0.374983\pi\)
\(410\) 0 0
\(411\) −38.3664 −1.89247
\(412\) 0 0
\(413\) 4.39009 0.216022
\(414\) 0 0
\(415\) −20.8772 −1.02482
\(416\) 0 0
\(417\) 4.53940 0.222295
\(418\) 0 0
\(419\) 21.6618 1.05825 0.529124 0.848545i \(-0.322521\pi\)
0.529124 + 0.848545i \(0.322521\pi\)
\(420\) 0 0
\(421\) −31.1808 −1.51966 −0.759830 0.650122i \(-0.774718\pi\)
−0.759830 + 0.650122i \(0.774718\pi\)
\(422\) 0 0
\(423\) 6.90474 0.335720
\(424\) 0 0
\(425\) 51.5503 2.50056
\(426\) 0 0
\(427\) 3.11048 0.150527
\(428\) 0 0
\(429\) −43.5912 −2.10460
\(430\) 0 0
\(431\) 14.4428 0.695683 0.347841 0.937553i \(-0.386915\pi\)
0.347841 + 0.937553i \(0.386915\pi\)
\(432\) 0 0
\(433\) 13.4118 0.644529 0.322264 0.946650i \(-0.395556\pi\)
0.322264 + 0.946650i \(0.395556\pi\)
\(434\) 0 0
\(435\) −1.22765 −0.0588615
\(436\) 0 0
\(437\) −0.522155 −0.0249781
\(438\) 0 0
\(439\) 10.6117 0.506469 0.253235 0.967405i \(-0.418506\pi\)
0.253235 + 0.967405i \(0.418506\pi\)
\(440\) 0 0
\(441\) −20.1415 −0.959121
\(442\) 0 0
\(443\) 31.0643 1.47591 0.737955 0.674850i \(-0.235792\pi\)
0.737955 + 0.674850i \(0.235792\pi\)
\(444\) 0 0
\(445\) 3.58411 0.169903
\(446\) 0 0
\(447\) 27.6272 1.30672
\(448\) 0 0
\(449\) 10.0955 0.476438 0.238219 0.971212i \(-0.423436\pi\)
0.238219 + 0.971212i \(0.423436\pi\)
\(450\) 0 0
\(451\) −2.28679 −0.107681
\(452\) 0 0
\(453\) 17.0559 0.801358
\(454\) 0 0
\(455\) 8.92285 0.418309
\(456\) 0 0
\(457\) −20.2946 −0.949341 −0.474671 0.880164i \(-0.657433\pi\)
−0.474671 + 0.880164i \(0.657433\pi\)
\(458\) 0 0
\(459\) 0.530323 0.0247534
\(460\) 0 0
\(461\) 7.08506 0.329984 0.164992 0.986295i \(-0.447240\pi\)
0.164992 + 0.986295i \(0.447240\pi\)
\(462\) 0 0
\(463\) −13.5240 −0.628512 −0.314256 0.949338i \(-0.601755\pi\)
−0.314256 + 0.949338i \(0.601755\pi\)
\(464\) 0 0
\(465\) 22.0258 1.02142
\(466\) 0 0
\(467\) 23.4060 1.08310 0.541550 0.840668i \(-0.317838\pi\)
0.541550 + 0.840668i \(0.317838\pi\)
\(468\) 0 0
\(469\) −1.11176 −0.0513362
\(470\) 0 0
\(471\) 54.0576 2.49084
\(472\) 0 0
\(473\) 7.19467 0.330811
\(474\) 0 0
\(475\) −7.89763 −0.362368
\(476\) 0 0
\(477\) 2.96674 0.135838
\(478\) 0 0
\(479\) −8.39605 −0.383625 −0.191813 0.981432i \(-0.561437\pi\)
−0.191813 + 0.981432i \(0.561437\pi\)
\(480\) 0 0
\(481\) −29.8699 −1.36195
\(482\) 0 0
\(483\) −0.585715 −0.0266509
\(484\) 0 0
\(485\) −0.428782 −0.0194700
\(486\) 0 0
\(487\) −16.8844 −0.765106 −0.382553 0.923934i \(-0.624955\pi\)
−0.382553 + 0.923934i \(0.624955\pi\)
\(488\) 0 0
\(489\) 34.0083 1.53791
\(490\) 0 0
\(491\) 18.2612 0.824115 0.412057 0.911158i \(-0.364810\pi\)
0.412057 + 0.911158i \(0.364810\pi\)
\(492\) 0 0
\(493\) −0.913455 −0.0411399
\(494\) 0 0
\(495\) 35.1427 1.57954
\(496\) 0 0
\(497\) −1.70132 −0.0763148
\(498\) 0 0
\(499\) 17.2036 0.770140 0.385070 0.922887i \(-0.374177\pi\)
0.385070 + 0.922887i \(0.374177\pi\)
\(500\) 0 0
\(501\) 30.9869 1.38439
\(502\) 0 0
\(503\) 29.7989 1.32867 0.664333 0.747436i \(-0.268715\pi\)
0.664333 + 0.747436i \(0.268715\pi\)
\(504\) 0 0
\(505\) −52.8809 −2.35317
\(506\) 0 0
\(507\) −39.7488 −1.76531
\(508\) 0 0
\(509\) 7.79995 0.345727 0.172863 0.984946i \(-0.444698\pi\)
0.172863 + 0.984946i \(0.444698\pi\)
\(510\) 0 0
\(511\) 0.232507 0.0102855
\(512\) 0 0
\(513\) −0.0812467 −0.00358713
\(514\) 0 0
\(515\) −30.8867 −1.36103
\(516\) 0 0
\(517\) −7.67659 −0.337616
\(518\) 0 0
\(519\) −39.9689 −1.75444
\(520\) 0 0
\(521\) 6.85304 0.300237 0.150119 0.988668i \(-0.452034\pi\)
0.150119 + 0.988668i \(0.452034\pi\)
\(522\) 0 0
\(523\) −15.0537 −0.658254 −0.329127 0.944286i \(-0.606755\pi\)
−0.329127 + 0.944286i \(0.606755\pi\)
\(524\) 0 0
\(525\) −8.85897 −0.386637
\(526\) 0 0
\(527\) 16.3886 0.713899
\(528\) 0 0
\(529\) −22.7274 −0.988146
\(530\) 0 0
\(531\) 28.3619 1.23080
\(532\) 0 0
\(533\) −3.75107 −0.162477
\(534\) 0 0
\(535\) 31.7626 1.37322
\(536\) 0 0
\(537\) −48.3631 −2.08702
\(538\) 0 0
\(539\) 22.3931 0.964538
\(540\) 0 0
\(541\) 28.6664 1.23246 0.616232 0.787564i \(-0.288658\pi\)
0.616232 + 0.787564i \(0.288658\pi\)
\(542\) 0 0
\(543\) 2.03249 0.0872223
\(544\) 0 0
\(545\) −18.5780 −0.795796
\(546\) 0 0
\(547\) −2.68722 −0.114897 −0.0574486 0.998348i \(-0.518297\pi\)
−0.0574486 + 0.998348i \(0.518297\pi\)
\(548\) 0 0
\(549\) 20.0950 0.857635
\(550\) 0 0
\(551\) 0.139943 0.00596179
\(552\) 0 0
\(553\) 0.647732 0.0275444
\(554\) 0 0
\(555\) 48.4314 2.05580
\(556\) 0 0
\(557\) −14.3606 −0.608476 −0.304238 0.952596i \(-0.598402\pi\)
−0.304238 + 0.952596i \(0.598402\pi\)
\(558\) 0 0
\(559\) 11.8016 0.499154
\(560\) 0 0
\(561\) 52.5900 2.22035
\(562\) 0 0
\(563\) 31.2562 1.31729 0.658646 0.752453i \(-0.271130\pi\)
0.658646 + 0.752453i \(0.271130\pi\)
\(564\) 0 0
\(565\) −8.16588 −0.343541
\(566\) 0 0
\(567\) −4.17827 −0.175471
\(568\) 0 0
\(569\) 42.7820 1.79351 0.896756 0.442525i \(-0.145917\pi\)
0.896756 + 0.442525i \(0.145917\pi\)
\(570\) 0 0
\(571\) −26.1120 −1.09275 −0.546377 0.837540i \(-0.683993\pi\)
−0.546377 + 0.837540i \(0.683993\pi\)
\(572\) 0 0
\(573\) 50.3371 2.10286
\(574\) 0 0
\(575\) 4.12379 0.171974
\(576\) 0 0
\(577\) 21.4036 0.891045 0.445522 0.895271i \(-0.353018\pi\)
0.445522 + 0.895271i \(0.353018\pi\)
\(578\) 0 0
\(579\) 35.4473 1.47314
\(580\) 0 0
\(581\) 2.66953 0.110751
\(582\) 0 0
\(583\) −3.29838 −0.136605
\(584\) 0 0
\(585\) 57.6454 2.38334
\(586\) 0 0
\(587\) 37.4229 1.54461 0.772304 0.635254i \(-0.219104\pi\)
0.772304 + 0.635254i \(0.219104\pi\)
\(588\) 0 0
\(589\) −2.51077 −0.103455
\(590\) 0 0
\(591\) 27.2844 1.12233
\(592\) 0 0
\(593\) 8.00459 0.328709 0.164355 0.986401i \(-0.447446\pi\)
0.164355 + 0.986401i \(0.447446\pi\)
\(594\) 0 0
\(595\) −10.7648 −0.441315
\(596\) 0 0
\(597\) −31.0007 −1.26877
\(598\) 0 0
\(599\) 0.810623 0.0331212 0.0165606 0.999863i \(-0.494728\pi\)
0.0165606 + 0.999863i \(0.494728\pi\)
\(600\) 0 0
\(601\) 32.5115 1.32617 0.663086 0.748544i \(-0.269247\pi\)
0.663086 + 0.748544i \(0.269247\pi\)
\(602\) 0 0
\(603\) −7.18243 −0.292491
\(604\) 0 0
\(605\) 0.433501 0.0176243
\(606\) 0 0
\(607\) −1.17275 −0.0476003 −0.0238002 0.999717i \(-0.507577\pi\)
−0.0238002 + 0.999717i \(0.507577\pi\)
\(608\) 0 0
\(609\) 0.156978 0.00636108
\(610\) 0 0
\(611\) −12.5921 −0.509422
\(612\) 0 0
\(613\) −35.1142 −1.41825 −0.709124 0.705084i \(-0.750909\pi\)
−0.709124 + 0.705084i \(0.750909\pi\)
\(614\) 0 0
\(615\) 6.08203 0.245251
\(616\) 0 0
\(617\) −39.2551 −1.58035 −0.790176 0.612880i \(-0.790011\pi\)
−0.790176 + 0.612880i \(0.790011\pi\)
\(618\) 0 0
\(619\) 14.4939 0.582557 0.291279 0.956638i \(-0.405919\pi\)
0.291279 + 0.956638i \(0.405919\pi\)
\(620\) 0 0
\(621\) 0.0424234 0.00170239
\(622\) 0 0
\(623\) −0.458295 −0.0183612
\(624\) 0 0
\(625\) −2.11562 −0.0846248
\(626\) 0 0
\(627\) −8.05692 −0.321762
\(628\) 0 0
\(629\) 36.0361 1.43685
\(630\) 0 0
\(631\) −35.0764 −1.39637 −0.698184 0.715918i \(-0.746008\pi\)
−0.698184 + 0.715918i \(0.746008\pi\)
\(632\) 0 0
\(633\) −34.2136 −1.35987
\(634\) 0 0
\(635\) −1.51951 −0.0602997
\(636\) 0 0
\(637\) 36.7319 1.45537
\(638\) 0 0
\(639\) −10.9913 −0.434808
\(640\) 0 0
\(641\) 8.53787 0.337225 0.168613 0.985682i \(-0.446071\pi\)
0.168613 + 0.985682i \(0.446071\pi\)
\(642\) 0 0
\(643\) 21.7819 0.858993 0.429496 0.903069i \(-0.358691\pi\)
0.429496 + 0.903069i \(0.358691\pi\)
\(644\) 0 0
\(645\) −19.1352 −0.753449
\(646\) 0 0
\(647\) −23.7341 −0.933085 −0.466543 0.884499i \(-0.654501\pi\)
−0.466543 + 0.884499i \(0.654501\pi\)
\(648\) 0 0
\(649\) −31.5323 −1.23775
\(650\) 0 0
\(651\) −2.81640 −0.110383
\(652\) 0 0
\(653\) −29.9648 −1.17261 −0.586306 0.810089i \(-0.699419\pi\)
−0.586306 + 0.810089i \(0.699419\pi\)
\(654\) 0 0
\(655\) 49.0115 1.91504
\(656\) 0 0
\(657\) 1.50209 0.0586022
\(658\) 0 0
\(659\) −27.3446 −1.06520 −0.532598 0.846368i \(-0.678784\pi\)
−0.532598 + 0.846368i \(0.678784\pi\)
\(660\) 0 0
\(661\) −30.3894 −1.18201 −0.591005 0.806668i \(-0.701269\pi\)
−0.591005 + 0.806668i \(0.701269\pi\)
\(662\) 0 0
\(663\) 86.2648 3.35025
\(664\) 0 0
\(665\) 1.64920 0.0639532
\(666\) 0 0
\(667\) −0.0730722 −0.00282937
\(668\) 0 0
\(669\) 57.8307 2.23586
\(670\) 0 0
\(671\) −22.3414 −0.862479
\(672\) 0 0
\(673\) 32.5992 1.25661 0.628303 0.777969i \(-0.283750\pi\)
0.628303 + 0.777969i \(0.283750\pi\)
\(674\) 0 0
\(675\) 0.641656 0.0246974
\(676\) 0 0
\(677\) −6.02569 −0.231586 −0.115793 0.993273i \(-0.536941\pi\)
−0.115793 + 0.993273i \(0.536941\pi\)
\(678\) 0 0
\(679\) 0.0548277 0.00210409
\(680\) 0 0
\(681\) 51.4542 1.97173
\(682\) 0 0
\(683\) −9.87214 −0.377747 −0.188874 0.982001i \(-0.560484\pi\)
−0.188874 + 0.982001i \(0.560484\pi\)
\(684\) 0 0
\(685\) −56.4075 −2.15522
\(686\) 0 0
\(687\) −8.50726 −0.324572
\(688\) 0 0
\(689\) −5.41041 −0.206120
\(690\) 0 0
\(691\) −33.1098 −1.25955 −0.629777 0.776776i \(-0.716854\pi\)
−0.629777 + 0.776776i \(0.716854\pi\)
\(692\) 0 0
\(693\) −4.49363 −0.170699
\(694\) 0 0
\(695\) 6.67397 0.253158
\(696\) 0 0
\(697\) 4.52543 0.171413
\(698\) 0 0
\(699\) −64.6019 −2.44347
\(700\) 0 0
\(701\) 37.5585 1.41857 0.709283 0.704924i \(-0.249019\pi\)
0.709283 + 0.704924i \(0.249019\pi\)
\(702\) 0 0
\(703\) −5.52082 −0.208222
\(704\) 0 0
\(705\) 20.4170 0.768948
\(706\) 0 0
\(707\) 6.76180 0.254303
\(708\) 0 0
\(709\) 19.3947 0.728385 0.364192 0.931324i \(-0.381345\pi\)
0.364192 + 0.931324i \(0.381345\pi\)
\(710\) 0 0
\(711\) 4.18463 0.156936
\(712\) 0 0
\(713\) 1.31101 0.0490978
\(714\) 0 0
\(715\) −64.0893 −2.39680
\(716\) 0 0
\(717\) 22.3870 0.836058
\(718\) 0 0
\(719\) −24.8440 −0.926525 −0.463263 0.886221i \(-0.653321\pi\)
−0.463263 + 0.886221i \(0.653321\pi\)
\(720\) 0 0
\(721\) 3.94943 0.147085
\(722\) 0 0
\(723\) −45.2892 −1.68432
\(724\) 0 0
\(725\) −1.10522 −0.0410469
\(726\) 0 0
\(727\) −24.2408 −0.899041 −0.449520 0.893270i \(-0.648405\pi\)
−0.449520 + 0.893270i \(0.648405\pi\)
\(728\) 0 0
\(729\) −26.3980 −0.977704
\(730\) 0 0
\(731\) −14.2379 −0.526606
\(732\) 0 0
\(733\) 10.4327 0.385340 0.192670 0.981264i \(-0.438285\pi\)
0.192670 + 0.981264i \(0.438285\pi\)
\(734\) 0 0
\(735\) −59.5576 −2.19681
\(736\) 0 0
\(737\) 7.98533 0.294143
\(738\) 0 0
\(739\) −7.54830 −0.277669 −0.138834 0.990316i \(-0.544336\pi\)
−0.138834 + 0.990316i \(0.544336\pi\)
\(740\) 0 0
\(741\) −13.2160 −0.485501
\(742\) 0 0
\(743\) −43.4918 −1.59556 −0.797779 0.602950i \(-0.793992\pi\)
−0.797779 + 0.602950i \(0.793992\pi\)
\(744\) 0 0
\(745\) 40.6184 1.48814
\(746\) 0 0
\(747\) 17.2463 0.631010
\(748\) 0 0
\(749\) −4.06144 −0.148402
\(750\) 0 0
\(751\) −38.7891 −1.41544 −0.707718 0.706495i \(-0.750275\pi\)
−0.707718 + 0.706495i \(0.750275\pi\)
\(752\) 0 0
\(753\) −25.0072 −0.911314
\(754\) 0 0
\(755\) 25.0762 0.912617
\(756\) 0 0
\(757\) −28.2065 −1.02518 −0.512592 0.858632i \(-0.671315\pi\)
−0.512592 + 0.858632i \(0.671315\pi\)
\(758\) 0 0
\(759\) 4.20696 0.152703
\(760\) 0 0
\(761\) 6.67415 0.241938 0.120969 0.992656i \(-0.461400\pi\)
0.120969 + 0.992656i \(0.461400\pi\)
\(762\) 0 0
\(763\) 2.37554 0.0860004
\(764\) 0 0
\(765\) −69.5455 −2.51442
\(766\) 0 0
\(767\) −51.7233 −1.86762
\(768\) 0 0
\(769\) −2.63193 −0.0949098 −0.0474549 0.998873i \(-0.515111\pi\)
−0.0474549 + 0.998873i \(0.515111\pi\)
\(770\) 0 0
\(771\) −35.2871 −1.27084
\(772\) 0 0
\(773\) 4.21113 0.151464 0.0757319 0.997128i \(-0.475871\pi\)
0.0757319 + 0.997128i \(0.475871\pi\)
\(774\) 0 0
\(775\) 19.8291 0.712284
\(776\) 0 0
\(777\) −6.19285 −0.222167
\(778\) 0 0
\(779\) −0.693306 −0.0248403
\(780\) 0 0
\(781\) 12.2199 0.437264
\(782\) 0 0
\(783\) −0.0113700 −0.000406329 0
\(784\) 0 0
\(785\) 79.4773 2.83667
\(786\) 0 0
\(787\) −3.68760 −0.131449 −0.0657245 0.997838i \(-0.520936\pi\)
−0.0657245 + 0.997838i \(0.520936\pi\)
\(788\) 0 0
\(789\) 30.0264 1.06897
\(790\) 0 0
\(791\) 1.04416 0.0371260
\(792\) 0 0
\(793\) −36.6471 −1.30138
\(794\) 0 0
\(795\) 8.77250 0.311129
\(796\) 0 0
\(797\) 12.8926 0.456680 0.228340 0.973581i \(-0.426670\pi\)
0.228340 + 0.973581i \(0.426670\pi\)
\(798\) 0 0
\(799\) 15.1916 0.537439
\(800\) 0 0
\(801\) −2.96078 −0.104614
\(802\) 0 0
\(803\) −1.67000 −0.0589332
\(804\) 0 0
\(805\) −0.861138 −0.0303511
\(806\) 0 0
\(807\) 37.9508 1.33593
\(808\) 0 0
\(809\) 14.9880 0.526950 0.263475 0.964666i \(-0.415131\pi\)
0.263475 + 0.964666i \(0.415131\pi\)
\(810\) 0 0
\(811\) −8.76181 −0.307669 −0.153834 0.988097i \(-0.549162\pi\)
−0.153834 + 0.988097i \(0.549162\pi\)
\(812\) 0 0
\(813\) 61.7729 2.16647
\(814\) 0 0
\(815\) 50.0002 1.75143
\(816\) 0 0
\(817\) 2.18127 0.0763131
\(818\) 0 0
\(819\) −7.37102 −0.257564
\(820\) 0 0
\(821\) −42.0284 −1.46680 −0.733401 0.679796i \(-0.762068\pi\)
−0.733401 + 0.679796i \(0.762068\pi\)
\(822\) 0 0
\(823\) −41.5337 −1.44777 −0.723886 0.689919i \(-0.757646\pi\)
−0.723886 + 0.689919i \(0.757646\pi\)
\(824\) 0 0
\(825\) 63.6305 2.21533
\(826\) 0 0
\(827\) −24.2613 −0.843648 −0.421824 0.906678i \(-0.638610\pi\)
−0.421824 + 0.906678i \(0.638610\pi\)
\(828\) 0 0
\(829\) −20.2229 −0.702371 −0.351185 0.936306i \(-0.614221\pi\)
−0.351185 + 0.936306i \(0.614221\pi\)
\(830\) 0 0
\(831\) 55.3041 1.91848
\(832\) 0 0
\(833\) −44.3147 −1.53541
\(834\) 0 0
\(835\) 45.5581 1.57660
\(836\) 0 0
\(837\) 0.203992 0.00705100
\(838\) 0 0
\(839\) 44.1482 1.52417 0.762083 0.647480i \(-0.224177\pi\)
0.762083 + 0.647480i \(0.224177\pi\)
\(840\) 0 0
\(841\) −28.9804 −0.999325
\(842\) 0 0
\(843\) −27.5044 −0.947303
\(844\) 0 0
\(845\) −58.4401 −2.01040
\(846\) 0 0
\(847\) −0.0554311 −0.00190464
\(848\) 0 0
\(849\) 78.6312 2.69861
\(850\) 0 0
\(851\) 2.88273 0.0988186
\(852\) 0 0
\(853\) 15.1577 0.518988 0.259494 0.965745i \(-0.416444\pi\)
0.259494 + 0.965745i \(0.416444\pi\)
\(854\) 0 0
\(855\) 10.6545 0.364377
\(856\) 0 0
\(857\) −56.4588 −1.92859 −0.964297 0.264822i \(-0.914687\pi\)
−0.964297 + 0.264822i \(0.914687\pi\)
\(858\) 0 0
\(859\) 57.1254 1.94909 0.974547 0.224182i \(-0.0719709\pi\)
0.974547 + 0.224182i \(0.0719709\pi\)
\(860\) 0 0
\(861\) −0.777699 −0.0265039
\(862\) 0 0
\(863\) −42.5571 −1.44866 −0.724330 0.689453i \(-0.757851\pi\)
−0.724330 + 0.689453i \(0.757851\pi\)
\(864\) 0 0
\(865\) −58.7636 −1.99802
\(866\) 0 0
\(867\) −62.5471 −2.12421
\(868\) 0 0
\(869\) −4.65241 −0.157822
\(870\) 0 0
\(871\) 13.0985 0.443827
\(872\) 0 0
\(873\) 0.354210 0.0119882
\(874\) 0 0
\(875\) −4.77876 −0.161552
\(876\) 0 0
\(877\) 35.6540 1.20395 0.601974 0.798515i \(-0.294381\pi\)
0.601974 + 0.798515i \(0.294381\pi\)
\(878\) 0 0
\(879\) 17.1850 0.579637
\(880\) 0 0
\(881\) 37.3422 1.25809 0.629045 0.777369i \(-0.283446\pi\)
0.629045 + 0.777369i \(0.283446\pi\)
\(882\) 0 0
\(883\) −45.0379 −1.51565 −0.757823 0.652460i \(-0.773737\pi\)
−0.757823 + 0.652460i \(0.773737\pi\)
\(884\) 0 0
\(885\) 83.8647 2.81908
\(886\) 0 0
\(887\) −14.1403 −0.474785 −0.237392 0.971414i \(-0.576293\pi\)
−0.237392 + 0.971414i \(0.576293\pi\)
\(888\) 0 0
\(889\) 0.194297 0.00651650
\(890\) 0 0
\(891\) 30.0109 1.00540
\(892\) 0 0
\(893\) −2.32738 −0.0778829
\(894\) 0 0
\(895\) −71.1051 −2.37678
\(896\) 0 0
\(897\) 6.90078 0.230410
\(898\) 0 0
\(899\) −0.351366 −0.0117187
\(900\) 0 0
\(901\) 6.52731 0.217456
\(902\) 0 0
\(903\) 2.44679 0.0814241
\(904\) 0 0
\(905\) 2.98823 0.0993321
\(906\) 0 0
\(907\) 24.6723 0.819231 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(908\) 0 0
\(909\) 43.6841 1.44891
\(910\) 0 0
\(911\) −11.1526 −0.369502 −0.184751 0.982785i \(-0.559148\pi\)
−0.184751 + 0.982785i \(0.559148\pi\)
\(912\) 0 0
\(913\) −19.1742 −0.634573
\(914\) 0 0
\(915\) 59.4200 1.96437
\(916\) 0 0
\(917\) −6.26703 −0.206955
\(918\) 0 0
\(919\) −9.65827 −0.318597 −0.159299 0.987230i \(-0.550923\pi\)
−0.159299 + 0.987230i \(0.550923\pi\)
\(920\) 0 0
\(921\) 10.2480 0.337684
\(922\) 0 0
\(923\) 20.0447 0.659779
\(924\) 0 0
\(925\) 43.6014 1.43360
\(926\) 0 0
\(927\) 25.5150 0.838023
\(928\) 0 0
\(929\) −18.7420 −0.614906 −0.307453 0.951563i \(-0.599477\pi\)
−0.307453 + 0.951563i \(0.599477\pi\)
\(930\) 0 0
\(931\) 6.78912 0.222504
\(932\) 0 0
\(933\) 36.9731 1.21044
\(934\) 0 0
\(935\) 77.3196 2.52862
\(936\) 0 0
\(937\) −53.7374 −1.75552 −0.877762 0.479096i \(-0.840965\pi\)
−0.877762 + 0.479096i \(0.840965\pi\)
\(938\) 0 0
\(939\) 5.52919 0.180438
\(940\) 0 0
\(941\) 51.6184 1.68271 0.841356 0.540481i \(-0.181758\pi\)
0.841356 + 0.540481i \(0.181758\pi\)
\(942\) 0 0
\(943\) 0.362014 0.0117888
\(944\) 0 0
\(945\) −0.133992 −0.00435876
\(946\) 0 0
\(947\) −10.9639 −0.356278 −0.178139 0.984005i \(-0.557008\pi\)
−0.178139 + 0.984005i \(0.557008\pi\)
\(948\) 0 0
\(949\) −2.73935 −0.0889231
\(950\) 0 0
\(951\) −20.1449 −0.653244
\(952\) 0 0
\(953\) −28.3189 −0.917340 −0.458670 0.888607i \(-0.651674\pi\)
−0.458670 + 0.888607i \(0.651674\pi\)
\(954\) 0 0
\(955\) 74.0073 2.39482
\(956\) 0 0
\(957\) −1.12751 −0.0364473
\(958\) 0 0
\(959\) 7.21274 0.232912
\(960\) 0 0
\(961\) −24.6960 −0.796646
\(962\) 0 0
\(963\) −26.2386 −0.845528
\(964\) 0 0
\(965\) 52.1158 1.67767
\(966\) 0 0
\(967\) −4.90853 −0.157848 −0.0789239 0.996881i \(-0.525148\pi\)
−0.0789239 + 0.996881i \(0.525148\pi\)
\(968\) 0 0
\(969\) 15.9442 0.512202
\(970\) 0 0
\(971\) −11.6759 −0.374698 −0.187349 0.982293i \(-0.559990\pi\)
−0.187349 + 0.982293i \(0.559990\pi\)
\(972\) 0 0
\(973\) −0.853390 −0.0273584
\(974\) 0 0
\(975\) 104.375 3.34267
\(976\) 0 0
\(977\) 14.9786 0.479208 0.239604 0.970871i \(-0.422982\pi\)
0.239604 + 0.970871i \(0.422982\pi\)
\(978\) 0 0
\(979\) 3.29175 0.105205
\(980\) 0 0
\(981\) 15.3470 0.489993
\(982\) 0 0
\(983\) 55.5582 1.77203 0.886016 0.463655i \(-0.153462\pi\)
0.886016 + 0.463655i \(0.153462\pi\)
\(984\) 0 0
\(985\) 40.1144 1.27815
\(986\) 0 0
\(987\) −2.61069 −0.0830990
\(988\) 0 0
\(989\) −1.13896 −0.0362169
\(990\) 0 0
\(991\) −25.8769 −0.822007 −0.411004 0.911634i \(-0.634822\pi\)
−0.411004 + 0.911634i \(0.634822\pi\)
\(992\) 0 0
\(993\) 68.4004 2.17062
\(994\) 0 0
\(995\) −45.5783 −1.44493
\(996\) 0 0
\(997\) 29.0385 0.919659 0.459830 0.888007i \(-0.347910\pi\)
0.459830 + 0.888007i \(0.347910\pi\)
\(998\) 0 0
\(999\) 0.448549 0.0141915
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 \(a_p\))