Properties

Label 8036.2.a.q.1.15
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(-3.24213\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.24213 q^{3} +1.49679 q^{5} +7.51143 q^{9} +O(q^{10})\) \(q+3.24213 q^{3} +1.49679 q^{5} +7.51143 q^{9} -2.60103 q^{11} +2.15963 q^{13} +4.85278 q^{15} +7.81895 q^{17} -4.98834 q^{19} -5.00028 q^{23} -2.75963 q^{25} +14.6267 q^{27} +0.404401 q^{29} +1.13325 q^{31} -8.43288 q^{33} -1.67690 q^{37} +7.00181 q^{39} -1.00000 q^{41} -0.0986445 q^{43} +11.2430 q^{45} +6.72337 q^{47} +25.3501 q^{51} +13.0309 q^{53} -3.89319 q^{55} -16.1729 q^{57} +15.1985 q^{59} -1.87235 q^{61} +3.23251 q^{65} -4.60485 q^{67} -16.2116 q^{69} -1.21035 q^{71} +3.16046 q^{73} -8.94708 q^{75} +12.5713 q^{79} +24.8873 q^{81} +12.0343 q^{83} +11.7033 q^{85} +1.31112 q^{87} +12.3299 q^{89} +3.67414 q^{93} -7.46649 q^{95} +16.3259 q^{97} -19.5374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) 3.24213 1.87185 0.935923 0.352204i \(-0.114568\pi\)
0.935923 + 0.352204i \(0.114568\pi\)
\(4\) 0 0
\(5\) 1.49679 0.669384 0.334692 0.942328i \(-0.391368\pi\)
0.334692 + 0.942328i \(0.391368\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 7.51143 2.50381
\(10\) 0 0
\(11\) −2.60103 −0.784240 −0.392120 0.919914i \(-0.628258\pi\)
−0.392120 + 0.919914i \(0.628258\pi\)
\(12\) 0 0
\(13\) 2.15963 0.598974 0.299487 0.954100i \(-0.403185\pi\)
0.299487 + 0.954100i \(0.403185\pi\)
\(14\) 0 0
\(15\) 4.85278 1.25298
\(16\) 0 0
\(17\) 7.81895 1.89637 0.948187 0.317712i \(-0.102915\pi\)
0.948187 + 0.317712i \(0.102915\pi\)
\(18\) 0 0
\(19\) −4.98834 −1.14440 −0.572202 0.820113i \(-0.693911\pi\)
−0.572202 + 0.820113i \(0.693911\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.00028 −1.04263 −0.521315 0.853364i \(-0.674558\pi\)
−0.521315 + 0.853364i \(0.674558\pi\)
\(24\) 0 0
\(25\) −2.75963 −0.551926
\(26\) 0 0
\(27\) 14.6267 2.81490
\(28\) 0 0
\(29\) 0.404401 0.0750953 0.0375476 0.999295i \(-0.488045\pi\)
0.0375476 + 0.999295i \(0.488045\pi\)
\(30\) 0 0
\(31\) 1.13325 0.203537 0.101769 0.994808i \(-0.467550\pi\)
0.101769 + 0.994808i \(0.467550\pi\)
\(32\) 0 0
\(33\) −8.43288 −1.46798
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.67690 −0.275680 −0.137840 0.990454i \(-0.544016\pi\)
−0.137840 + 0.990454i \(0.544016\pi\)
\(38\) 0 0
\(39\) 7.00181 1.12119
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −0.0986445 −0.0150431 −0.00752157 0.999972i \(-0.502394\pi\)
−0.00752157 + 0.999972i \(0.502394\pi\)
\(44\) 0 0
\(45\) 11.2430 1.67601
\(46\) 0 0
\(47\) 6.72337 0.980704 0.490352 0.871524i \(-0.336868\pi\)
0.490352 + 0.871524i \(0.336868\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 25.3501 3.54972
\(52\) 0 0
\(53\) 13.0309 1.78993 0.894964 0.446138i \(-0.147201\pi\)
0.894964 + 0.446138i \(0.147201\pi\)
\(54\) 0 0
\(55\) −3.89319 −0.524957
\(56\) 0 0
\(57\) −16.1729 −2.14215
\(58\) 0 0
\(59\) 15.1985 1.97868 0.989341 0.145618i \(-0.0465170\pi\)
0.989341 + 0.145618i \(0.0465170\pi\)
\(60\) 0 0
\(61\) −1.87235 −0.239730 −0.119865 0.992790i \(-0.538246\pi\)
−0.119865 + 0.992790i \(0.538246\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.23251 0.400943
\(66\) 0 0
\(67\) −4.60485 −0.562572 −0.281286 0.959624i \(-0.590761\pi\)
−0.281286 + 0.959624i \(0.590761\pi\)
\(68\) 0 0
\(69\) −16.2116 −1.95164
\(70\) 0 0
\(71\) −1.21035 −0.143642 −0.0718212 0.997418i \(-0.522881\pi\)
−0.0718212 + 0.997418i \(0.522881\pi\)
\(72\) 0 0
\(73\) 3.16046 0.369904 0.184952 0.982748i \(-0.440787\pi\)
0.184952 + 0.982748i \(0.440787\pi\)
\(74\) 0 0
\(75\) −8.94708 −1.03312
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 12.5713 1.41439 0.707193 0.707020i \(-0.249961\pi\)
0.707193 + 0.707020i \(0.249961\pi\)
\(80\) 0 0
\(81\) 24.8873 2.76525
\(82\) 0 0
\(83\) 12.0343 1.32094 0.660469 0.750853i \(-0.270357\pi\)
0.660469 + 0.750853i \(0.270357\pi\)
\(84\) 0 0
\(85\) 11.7033 1.26940
\(86\) 0 0
\(87\) 1.31112 0.140567
\(88\) 0 0
\(89\) 12.3299 1.30696 0.653481 0.756943i \(-0.273308\pi\)
0.653481 + 0.756943i \(0.273308\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 3.67414 0.380990
\(94\) 0 0
\(95\) −7.46649 −0.766045
\(96\) 0 0
\(97\) 16.3259 1.65764 0.828822 0.559512i \(-0.189012\pi\)
0.828822 + 0.559512i \(0.189012\pi\)
\(98\) 0 0
\(99\) −19.5374 −1.96359
\(100\) 0 0
\(101\) 13.1826 1.31172 0.655859 0.754883i \(-0.272306\pi\)
0.655859 + 0.754883i \(0.272306\pi\)
\(102\) 0 0
\(103\) −2.41497 −0.237954 −0.118977 0.992897i \(-0.537961\pi\)
−0.118977 + 0.992897i \(0.537961\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.9079 −1.73122 −0.865609 0.500721i \(-0.833068\pi\)
−0.865609 + 0.500721i \(0.833068\pi\)
\(108\) 0 0
\(109\) 11.0933 1.06255 0.531273 0.847201i \(-0.321714\pi\)
0.531273 + 0.847201i \(0.321714\pi\)
\(110\) 0 0
\(111\) −5.43673 −0.516031
\(112\) 0 0
\(113\) −4.48247 −0.421675 −0.210838 0.977521i \(-0.567619\pi\)
−0.210838 + 0.977521i \(0.567619\pi\)
\(114\) 0 0
\(115\) −7.48436 −0.697920
\(116\) 0 0
\(117\) 16.2219 1.49972
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.23465 −0.384968
\(122\) 0 0
\(123\) −3.24213 −0.292333
\(124\) 0 0
\(125\) −11.6145 −1.03883
\(126\) 0 0
\(127\) −13.7744 −1.22228 −0.611142 0.791521i \(-0.709290\pi\)
−0.611142 + 0.791521i \(0.709290\pi\)
\(128\) 0 0
\(129\) −0.319818 −0.0281584
\(130\) 0 0
\(131\) −3.79644 −0.331697 −0.165848 0.986151i \(-0.553036\pi\)
−0.165848 + 0.986151i \(0.553036\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 21.8930 1.88425
\(136\) 0 0
\(137\) −0.00898688 −0.000767801 0 −0.000383900 1.00000i \(-0.500122\pi\)
−0.000383900 1.00000i \(0.500122\pi\)
\(138\) 0 0
\(139\) −1.05225 −0.0892507 −0.0446254 0.999004i \(-0.514209\pi\)
−0.0446254 + 0.999004i \(0.514209\pi\)
\(140\) 0 0
\(141\) 21.7981 1.83573
\(142\) 0 0
\(143\) −5.61726 −0.469739
\(144\) 0 0
\(145\) 0.605302 0.0502676
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.58959 −0.457917 −0.228959 0.973436i \(-0.573532\pi\)
−0.228959 + 0.973436i \(0.573532\pi\)
\(150\) 0 0
\(151\) −20.8788 −1.69909 −0.849546 0.527515i \(-0.823124\pi\)
−0.849546 + 0.527515i \(0.823124\pi\)
\(152\) 0 0
\(153\) 58.7315 4.74816
\(154\) 0 0
\(155\) 1.69623 0.136244
\(156\) 0 0
\(157\) −13.7208 −1.09504 −0.547521 0.836792i \(-0.684428\pi\)
−0.547521 + 0.836792i \(0.684428\pi\)
\(158\) 0 0
\(159\) 42.2478 3.35047
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −24.0930 −1.88711 −0.943556 0.331214i \(-0.892542\pi\)
−0.943556 + 0.331214i \(0.892542\pi\)
\(164\) 0 0
\(165\) −12.6222 −0.982639
\(166\) 0 0
\(167\) 5.46141 0.422616 0.211308 0.977419i \(-0.432228\pi\)
0.211308 + 0.977419i \(0.432228\pi\)
\(168\) 0 0
\(169\) −8.33600 −0.641230
\(170\) 0 0
\(171\) −37.4696 −2.86537
\(172\) 0 0
\(173\) −16.9973 −1.29228 −0.646139 0.763220i \(-0.723617\pi\)
−0.646139 + 0.763220i \(0.723617\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 49.2757 3.70379
\(178\) 0 0
\(179\) −9.11221 −0.681078 −0.340539 0.940230i \(-0.610610\pi\)
−0.340539 + 0.940230i \(0.610610\pi\)
\(180\) 0 0
\(181\) −4.21950 −0.313633 −0.156816 0.987628i \(-0.550123\pi\)
−0.156816 + 0.987628i \(0.550123\pi\)
\(182\) 0 0
\(183\) −6.07040 −0.448737
\(184\) 0 0
\(185\) −2.50996 −0.184536
\(186\) 0 0
\(187\) −20.3373 −1.48721
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.16197 −0.518222 −0.259111 0.965848i \(-0.583430\pi\)
−0.259111 + 0.965848i \(0.583430\pi\)
\(192\) 0 0
\(193\) −1.15715 −0.0832934 −0.0416467 0.999132i \(-0.513260\pi\)
−0.0416467 + 0.999132i \(0.513260\pi\)
\(194\) 0 0
\(195\) 10.4802 0.750504
\(196\) 0 0
\(197\) −2.30106 −0.163944 −0.0819720 0.996635i \(-0.526122\pi\)
−0.0819720 + 0.996635i \(0.526122\pi\)
\(198\) 0 0
\(199\) 17.1511 1.21581 0.607905 0.794010i \(-0.292010\pi\)
0.607905 + 0.794010i \(0.292010\pi\)
\(200\) 0 0
\(201\) −14.9295 −1.05305
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.49679 −0.104540
\(206\) 0 0
\(207\) −37.5592 −2.61055
\(208\) 0 0
\(209\) 12.9748 0.897487
\(210\) 0 0
\(211\) 6.24067 0.429625 0.214813 0.976655i \(-0.431086\pi\)
0.214813 + 0.976655i \(0.431086\pi\)
\(212\) 0 0
\(213\) −3.92412 −0.268877
\(214\) 0 0
\(215\) −0.147650 −0.0100696
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.2466 0.692403
\(220\) 0 0
\(221\) 16.8860 1.13588
\(222\) 0 0
\(223\) −5.45026 −0.364976 −0.182488 0.983208i \(-0.558415\pi\)
−0.182488 + 0.983208i \(0.558415\pi\)
\(224\) 0 0
\(225\) −20.7287 −1.38192
\(226\) 0 0
\(227\) −11.3106 −0.750709 −0.375354 0.926881i \(-0.622479\pi\)
−0.375354 + 0.926881i \(0.622479\pi\)
\(228\) 0 0
\(229\) −6.96496 −0.460257 −0.230129 0.973160i \(-0.573915\pi\)
−0.230129 + 0.973160i \(0.573915\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.40261 0.550474 0.275237 0.961376i \(-0.411244\pi\)
0.275237 + 0.961376i \(0.411244\pi\)
\(234\) 0 0
\(235\) 10.0635 0.656467
\(236\) 0 0
\(237\) 40.7580 2.64751
\(238\) 0 0
\(239\) −8.49866 −0.549732 −0.274866 0.961482i \(-0.588634\pi\)
−0.274866 + 0.961482i \(0.588634\pi\)
\(240\) 0 0
\(241\) 2.87685 0.185314 0.0926572 0.995698i \(-0.470464\pi\)
0.0926572 + 0.995698i \(0.470464\pi\)
\(242\) 0 0
\(243\) 36.8079 2.36123
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −10.7730 −0.685468
\(248\) 0 0
\(249\) 39.0169 2.47259
\(250\) 0 0
\(251\) 10.3806 0.655217 0.327608 0.944814i \(-0.393757\pi\)
0.327608 + 0.944814i \(0.393757\pi\)
\(252\) 0 0
\(253\) 13.0059 0.817672
\(254\) 0 0
\(255\) 37.9437 2.37613
\(256\) 0 0
\(257\) 15.1372 0.944233 0.472117 0.881536i \(-0.343490\pi\)
0.472117 + 0.881536i \(0.343490\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.03763 0.188024
\(262\) 0 0
\(263\) −21.5130 −1.32655 −0.663276 0.748375i \(-0.730834\pi\)
−0.663276 + 0.748375i \(0.730834\pi\)
\(264\) 0 0
\(265\) 19.5044 1.19815
\(266\) 0 0
\(267\) 39.9750 2.44643
\(268\) 0 0
\(269\) −20.8515 −1.27134 −0.635668 0.771962i \(-0.719275\pi\)
−0.635668 + 0.771962i \(0.719275\pi\)
\(270\) 0 0
\(271\) −31.0705 −1.88740 −0.943700 0.330801i \(-0.892681\pi\)
−0.943700 + 0.330801i \(0.892681\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.17787 0.432842
\(276\) 0 0
\(277\) −15.1088 −0.907801 −0.453901 0.891052i \(-0.649968\pi\)
−0.453901 + 0.891052i \(0.649968\pi\)
\(278\) 0 0
\(279\) 8.51230 0.509618
\(280\) 0 0
\(281\) −2.60682 −0.155510 −0.0777548 0.996973i \(-0.524775\pi\)
−0.0777548 + 0.996973i \(0.524775\pi\)
\(282\) 0 0
\(283\) 9.81175 0.583248 0.291624 0.956533i \(-0.405804\pi\)
0.291624 + 0.956533i \(0.405804\pi\)
\(284\) 0 0
\(285\) −24.2073 −1.43392
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 44.1360 2.59624
\(290\) 0 0
\(291\) 52.9307 3.10286
\(292\) 0 0
\(293\) −13.7070 −0.800769 −0.400384 0.916347i \(-0.631123\pi\)
−0.400384 + 0.916347i \(0.631123\pi\)
\(294\) 0 0
\(295\) 22.7490 1.32450
\(296\) 0 0
\(297\) −38.0443 −2.20756
\(298\) 0 0
\(299\) −10.7988 −0.624508
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 42.7398 2.45534
\(304\) 0 0
\(305\) −2.80251 −0.160471
\(306\) 0 0
\(307\) 21.2774 1.21436 0.607182 0.794563i \(-0.292300\pi\)
0.607182 + 0.794563i \(0.292300\pi\)
\(308\) 0 0
\(309\) −7.82965 −0.445413
\(310\) 0 0
\(311\) −22.8754 −1.29714 −0.648571 0.761154i \(-0.724633\pi\)
−0.648571 + 0.761154i \(0.724633\pi\)
\(312\) 0 0
\(313\) −33.8192 −1.91157 −0.955787 0.294060i \(-0.904993\pi\)
−0.955787 + 0.294060i \(0.904993\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.8336 0.833138 0.416569 0.909104i \(-0.363232\pi\)
0.416569 + 0.909104i \(0.363232\pi\)
\(318\) 0 0
\(319\) −1.05186 −0.0588927
\(320\) 0 0
\(321\) −58.0597 −3.24057
\(322\) 0 0
\(323\) −39.0036 −2.17022
\(324\) 0 0
\(325\) −5.95978 −0.330589
\(326\) 0 0
\(327\) 35.9660 1.98892
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 29.3364 1.61247 0.806236 0.591594i \(-0.201501\pi\)
0.806236 + 0.591594i \(0.201501\pi\)
\(332\) 0 0
\(333\) −12.5959 −0.690251
\(334\) 0 0
\(335\) −6.89248 −0.376576
\(336\) 0 0
\(337\) −25.8091 −1.40591 −0.702957 0.711232i \(-0.748137\pi\)
−0.702957 + 0.711232i \(0.748137\pi\)
\(338\) 0 0
\(339\) −14.5328 −0.789311
\(340\) 0 0
\(341\) −2.94761 −0.159622
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −24.2653 −1.30640
\(346\) 0 0
\(347\) 3.80579 0.204305 0.102153 0.994769i \(-0.467427\pi\)
0.102153 + 0.994769i \(0.467427\pi\)
\(348\) 0 0
\(349\) 0.239149 0.0128013 0.00640067 0.999980i \(-0.497963\pi\)
0.00640067 + 0.999980i \(0.497963\pi\)
\(350\) 0 0
\(351\) 31.5882 1.68605
\(352\) 0 0
\(353\) 4.72219 0.251337 0.125668 0.992072i \(-0.459892\pi\)
0.125668 + 0.992072i \(0.459892\pi\)
\(354\) 0 0
\(355\) −1.81164 −0.0961519
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −31.2266 −1.64807 −0.824037 0.566535i \(-0.808283\pi\)
−0.824037 + 0.566535i \(0.808283\pi\)
\(360\) 0 0
\(361\) 5.88355 0.309660
\(362\) 0 0
\(363\) −13.7293 −0.720602
\(364\) 0 0
\(365\) 4.73053 0.247607
\(366\) 0 0
\(367\) −26.0787 −1.36130 −0.680649 0.732610i \(-0.738302\pi\)
−0.680649 + 0.732610i \(0.738302\pi\)
\(368\) 0 0
\(369\) −7.51143 −0.391029
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 8.91964 0.461841 0.230921 0.972973i \(-0.425826\pi\)
0.230921 + 0.972973i \(0.425826\pi\)
\(374\) 0 0
\(375\) −37.6558 −1.94454
\(376\) 0 0
\(377\) 0.873356 0.0449801
\(378\) 0 0
\(379\) 10.9678 0.563380 0.281690 0.959506i \(-0.409105\pi\)
0.281690 + 0.959506i \(0.409105\pi\)
\(380\) 0 0
\(381\) −44.6586 −2.28793
\(382\) 0 0
\(383\) 21.5001 1.09860 0.549302 0.835624i \(-0.314894\pi\)
0.549302 + 0.835624i \(0.314894\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.740961 −0.0376652
\(388\) 0 0
\(389\) −16.3029 −0.826589 −0.413295 0.910597i \(-0.635622\pi\)
−0.413295 + 0.910597i \(0.635622\pi\)
\(390\) 0 0
\(391\) −39.0969 −1.97722
\(392\) 0 0
\(393\) −12.3086 −0.620885
\(394\) 0 0
\(395\) 18.8166 0.946767
\(396\) 0 0
\(397\) 21.9023 1.09925 0.549623 0.835413i \(-0.314771\pi\)
0.549623 + 0.835413i \(0.314771\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.9606 0.597284 0.298642 0.954365i \(-0.403466\pi\)
0.298642 + 0.954365i \(0.403466\pi\)
\(402\) 0 0
\(403\) 2.44739 0.121913
\(404\) 0 0
\(405\) 37.2509 1.85101
\(406\) 0 0
\(407\) 4.36166 0.216199
\(408\) 0 0
\(409\) 30.0777 1.48725 0.743624 0.668598i \(-0.233105\pi\)
0.743624 + 0.668598i \(0.233105\pi\)
\(410\) 0 0
\(411\) −0.0291367 −0.00143721
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 18.0128 0.884215
\(416\) 0 0
\(417\) −3.41154 −0.167064
\(418\) 0 0
\(419\) −12.5534 −0.613273 −0.306636 0.951827i \(-0.599204\pi\)
−0.306636 + 0.951827i \(0.599204\pi\)
\(420\) 0 0
\(421\) 30.0470 1.46440 0.732200 0.681090i \(-0.238494\pi\)
0.732200 + 0.681090i \(0.238494\pi\)
\(422\) 0 0
\(423\) 50.5021 2.45550
\(424\) 0 0
\(425\) −21.5774 −1.04666
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −18.2119 −0.879279
\(430\) 0 0
\(431\) −24.3805 −1.17437 −0.587185 0.809453i \(-0.699764\pi\)
−0.587185 + 0.809453i \(0.699764\pi\)
\(432\) 0 0
\(433\) −11.9120 −0.572455 −0.286228 0.958162i \(-0.592401\pi\)
−0.286228 + 0.958162i \(0.592401\pi\)
\(434\) 0 0
\(435\) 1.96247 0.0940932
\(436\) 0 0
\(437\) 24.9431 1.19319
\(438\) 0 0
\(439\) 11.1595 0.532614 0.266307 0.963888i \(-0.414196\pi\)
0.266307 + 0.963888i \(0.414196\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −16.6578 −0.791434 −0.395717 0.918372i \(-0.629504\pi\)
−0.395717 + 0.918372i \(0.629504\pi\)
\(444\) 0 0
\(445\) 18.4552 0.874859
\(446\) 0 0
\(447\) −18.1222 −0.857151
\(448\) 0 0
\(449\) 32.0634 1.51317 0.756583 0.653897i \(-0.226867\pi\)
0.756583 + 0.653897i \(0.226867\pi\)
\(450\) 0 0
\(451\) 2.60103 0.122478
\(452\) 0 0
\(453\) −67.6918 −3.18044
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.51609 0.304810 0.152405 0.988318i \(-0.451298\pi\)
0.152405 + 0.988318i \(0.451298\pi\)
\(458\) 0 0
\(459\) 114.365 5.33810
\(460\) 0 0
\(461\) −11.0378 −0.514082 −0.257041 0.966400i \(-0.582748\pi\)
−0.257041 + 0.966400i \(0.582748\pi\)
\(462\) 0 0
\(463\) 25.7136 1.19501 0.597507 0.801864i \(-0.296158\pi\)
0.597507 + 0.801864i \(0.296158\pi\)
\(464\) 0 0
\(465\) 5.49940 0.255029
\(466\) 0 0
\(467\) 21.9608 1.01623 0.508113 0.861291i \(-0.330343\pi\)
0.508113 + 0.861291i \(0.330343\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −44.4848 −2.04975
\(472\) 0 0
\(473\) 0.256577 0.0117974
\(474\) 0 0
\(475\) 13.7660 0.631626
\(476\) 0 0
\(477\) 97.8805 4.48164
\(478\) 0 0
\(479\) −15.4932 −0.707901 −0.353951 0.935264i \(-0.615162\pi\)
−0.353951 + 0.935264i \(0.615162\pi\)
\(480\) 0 0
\(481\) −3.62148 −0.165125
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 24.4364 1.10960
\(486\) 0 0
\(487\) 34.0797 1.54430 0.772150 0.635440i \(-0.219181\pi\)
0.772150 + 0.635440i \(0.219181\pi\)
\(488\) 0 0
\(489\) −78.1128 −3.53238
\(490\) 0 0
\(491\) −0.00976244 −0.000440573 0 −0.000220286 1.00000i \(-0.500070\pi\)
−0.000220286 1.00000i \(0.500070\pi\)
\(492\) 0 0
\(493\) 3.16199 0.142409
\(494\) 0 0
\(495\) −29.2434 −1.31439
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −21.9496 −0.982599 −0.491300 0.870991i \(-0.663478\pi\)
−0.491300 + 0.870991i \(0.663478\pi\)
\(500\) 0 0
\(501\) 17.7066 0.791073
\(502\) 0 0
\(503\) 20.0786 0.895260 0.447630 0.894219i \(-0.352268\pi\)
0.447630 + 0.894219i \(0.352268\pi\)
\(504\) 0 0
\(505\) 19.7316 0.878043
\(506\) 0 0
\(507\) −27.0264 −1.20029
\(508\) 0 0
\(509\) −1.84080 −0.0815922 −0.0407961 0.999167i \(-0.512989\pi\)
−0.0407961 + 0.999167i \(0.512989\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −72.9627 −3.22138
\(514\) 0 0
\(515\) −3.61469 −0.159282
\(516\) 0 0
\(517\) −17.4877 −0.769107
\(518\) 0 0
\(519\) −55.1074 −2.41895
\(520\) 0 0
\(521\) 5.94737 0.260559 0.130279 0.991477i \(-0.458413\pi\)
0.130279 + 0.991477i \(0.458413\pi\)
\(522\) 0 0
\(523\) −9.87253 −0.431696 −0.215848 0.976427i \(-0.569252\pi\)
−0.215848 + 0.976427i \(0.569252\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.86080 0.385982
\(528\) 0 0
\(529\) 2.00280 0.0870785
\(530\) 0 0
\(531\) 114.163 4.95424
\(532\) 0 0
\(533\) −2.15963 −0.0935440
\(534\) 0 0
\(535\) −26.8043 −1.15885
\(536\) 0 0
\(537\) −29.5430 −1.27487
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −3.60499 −0.154991 −0.0774954 0.996993i \(-0.524692\pi\)
−0.0774954 + 0.996993i \(0.524692\pi\)
\(542\) 0 0
\(543\) −13.6802 −0.587072
\(544\) 0 0
\(545\) 16.6043 0.711251
\(546\) 0 0
\(547\) 38.4142 1.64247 0.821235 0.570590i \(-0.193285\pi\)
0.821235 + 0.570590i \(0.193285\pi\)
\(548\) 0 0
\(549\) −14.0640 −0.600237
\(550\) 0 0
\(551\) −2.01729 −0.0859394
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −8.13763 −0.345423
\(556\) 0 0
\(557\) 41.9327 1.77674 0.888372 0.459123i \(-0.151836\pi\)
0.888372 + 0.459123i \(0.151836\pi\)
\(558\) 0 0
\(559\) −0.213036 −0.00901044
\(560\) 0 0
\(561\) −65.9363 −2.78383
\(562\) 0 0
\(563\) 13.0546 0.550186 0.275093 0.961418i \(-0.411291\pi\)
0.275093 + 0.961418i \(0.411291\pi\)
\(564\) 0 0
\(565\) −6.70930 −0.282262
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.77130 0.409634 0.204817 0.978800i \(-0.434340\pi\)
0.204817 + 0.978800i \(0.434340\pi\)
\(570\) 0 0
\(571\) −30.9066 −1.29340 −0.646701 0.762744i \(-0.723852\pi\)
−0.646701 + 0.762744i \(0.723852\pi\)
\(572\) 0 0
\(573\) −23.2201 −0.970033
\(574\) 0 0
\(575\) 13.7989 0.575455
\(576\) 0 0
\(577\) −32.3793 −1.34797 −0.673983 0.738747i \(-0.735418\pi\)
−0.673983 + 0.738747i \(0.735418\pi\)
\(578\) 0 0
\(579\) −3.75163 −0.155912
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −33.8937 −1.40373
\(584\) 0 0
\(585\) 24.2807 1.00389
\(586\) 0 0
\(587\) −40.3400 −1.66501 −0.832506 0.554016i \(-0.813095\pi\)
−0.832506 + 0.554016i \(0.813095\pi\)
\(588\) 0 0
\(589\) −5.65302 −0.232929
\(590\) 0 0
\(591\) −7.46035 −0.306878
\(592\) 0 0
\(593\) −7.24357 −0.297458 −0.148729 0.988878i \(-0.547518\pi\)
−0.148729 + 0.988878i \(0.547518\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 55.6062 2.27581
\(598\) 0 0
\(599\) −32.0113 −1.30794 −0.653972 0.756519i \(-0.726899\pi\)
−0.653972 + 0.756519i \(0.726899\pi\)
\(600\) 0 0
\(601\) −30.6709 −1.25109 −0.625546 0.780187i \(-0.715124\pi\)
−0.625546 + 0.780187i \(0.715124\pi\)
\(602\) 0 0
\(603\) −34.5890 −1.40857
\(604\) 0 0
\(605\) −6.33837 −0.257692
\(606\) 0 0
\(607\) 40.0906 1.62723 0.813615 0.581405i \(-0.197497\pi\)
0.813615 + 0.581405i \(0.197497\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14.5200 0.587416
\(612\) 0 0
\(613\) −11.3707 −0.459258 −0.229629 0.973278i \(-0.573751\pi\)
−0.229629 + 0.973278i \(0.573751\pi\)
\(614\) 0 0
\(615\) −4.85278 −0.195683
\(616\) 0 0
\(617\) −5.51261 −0.221929 −0.110965 0.993824i \(-0.535394\pi\)
−0.110965 + 0.993824i \(0.535394\pi\)
\(618\) 0 0
\(619\) −21.2191 −0.852869 −0.426434 0.904519i \(-0.640230\pi\)
−0.426434 + 0.904519i \(0.640230\pi\)
\(620\) 0 0
\(621\) −73.1374 −2.93490
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −3.58631 −0.143453
\(626\) 0 0
\(627\) 42.0661 1.67996
\(628\) 0 0
\(629\) −13.1116 −0.522793
\(630\) 0 0
\(631\) −18.1401 −0.722147 −0.361073 0.932537i \(-0.617590\pi\)
−0.361073 + 0.932537i \(0.617590\pi\)
\(632\) 0 0
\(633\) 20.2331 0.804193
\(634\) 0 0
\(635\) −20.6174 −0.818177
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −9.09148 −0.359653
\(640\) 0 0
\(641\) −9.53870 −0.376756 −0.188378 0.982097i \(-0.560323\pi\)
−0.188378 + 0.982097i \(0.560323\pi\)
\(642\) 0 0
\(643\) −28.3896 −1.11958 −0.559788 0.828636i \(-0.689117\pi\)
−0.559788 + 0.828636i \(0.689117\pi\)
\(644\) 0 0
\(645\) −0.478700 −0.0188488
\(646\) 0 0
\(647\) −47.6272 −1.87242 −0.936208 0.351445i \(-0.885690\pi\)
−0.936208 + 0.351445i \(0.885690\pi\)
\(648\) 0 0
\(649\) −39.5318 −1.55176
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 28.5006 1.11532 0.557658 0.830071i \(-0.311700\pi\)
0.557658 + 0.830071i \(0.311700\pi\)
\(654\) 0 0
\(655\) −5.68246 −0.222032
\(656\) 0 0
\(657\) 23.7396 0.926168
\(658\) 0 0
\(659\) 42.8168 1.66791 0.833954 0.551835i \(-0.186072\pi\)
0.833954 + 0.551835i \(0.186072\pi\)
\(660\) 0 0
\(661\) −32.7509 −1.27386 −0.636931 0.770921i \(-0.719796\pi\)
−0.636931 + 0.770921i \(0.719796\pi\)
\(662\) 0 0
\(663\) 54.7468 2.12619
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.02212 −0.0782966
\(668\) 0 0
\(669\) −17.6705 −0.683180
\(670\) 0 0
\(671\) 4.87003 0.188005
\(672\) 0 0
\(673\) −12.7103 −0.489944 −0.244972 0.969530i \(-0.578779\pi\)
−0.244972 + 0.969530i \(0.578779\pi\)
\(674\) 0 0
\(675\) −40.3641 −1.55362
\(676\) 0 0
\(677\) 2.17361 0.0835388 0.0417694 0.999127i \(-0.486701\pi\)
0.0417694 + 0.999127i \(0.486701\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −36.6704 −1.40521
\(682\) 0 0
\(683\) −11.5806 −0.443119 −0.221559 0.975147i \(-0.571115\pi\)
−0.221559 + 0.975147i \(0.571115\pi\)
\(684\) 0 0
\(685\) −0.0134514 −0.000513953 0
\(686\) 0 0
\(687\) −22.5813 −0.861531
\(688\) 0 0
\(689\) 28.1419 1.07212
\(690\) 0 0
\(691\) 38.9363 1.48121 0.740603 0.671943i \(-0.234540\pi\)
0.740603 + 0.671943i \(0.234540\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.57500 −0.0597430
\(696\) 0 0
\(697\) −7.81895 −0.296164
\(698\) 0 0
\(699\) 27.2424 1.03040
\(700\) 0 0
\(701\) −28.2623 −1.06745 −0.533726 0.845658i \(-0.679209\pi\)
−0.533726 + 0.845658i \(0.679209\pi\)
\(702\) 0 0
\(703\) 8.36494 0.315490
\(704\) 0 0
\(705\) 32.6271 1.22881
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −10.6038 −0.398233 −0.199116 0.979976i \(-0.563807\pi\)
−0.199116 + 0.979976i \(0.563807\pi\)
\(710\) 0 0
\(711\) 94.4287 3.54135
\(712\) 0 0
\(713\) −5.66655 −0.212214
\(714\) 0 0
\(715\) −8.40784 −0.314435
\(716\) 0 0
\(717\) −27.5538 −1.02901
\(718\) 0 0
\(719\) −33.3423 −1.24346 −0.621729 0.783232i \(-0.713570\pi\)
−0.621729 + 0.783232i \(0.713570\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 9.32714 0.346880
\(724\) 0 0
\(725\) −1.11600 −0.0414470
\(726\) 0 0
\(727\) 53.5627 1.98653 0.993265 0.115861i \(-0.0369628\pi\)
0.993265 + 0.115861i \(0.0369628\pi\)
\(728\) 0 0
\(729\) 44.6743 1.65460
\(730\) 0 0
\(731\) −0.771296 −0.0285274
\(732\) 0 0
\(733\) 3.09276 0.114234 0.0571169 0.998367i \(-0.481809\pi\)
0.0571169 + 0.998367i \(0.481809\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11.9773 0.441191
\(738\) 0 0
\(739\) 7.80935 0.287271 0.143636 0.989631i \(-0.454121\pi\)
0.143636 + 0.989631i \(0.454121\pi\)
\(740\) 0 0
\(741\) −34.9274 −1.28309
\(742\) 0 0
\(743\) 16.2197 0.595042 0.297521 0.954715i \(-0.403840\pi\)
0.297521 + 0.954715i \(0.403840\pi\)
\(744\) 0 0
\(745\) −8.36643 −0.306522
\(746\) 0 0
\(747\) 90.3950 3.30738
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −20.5274 −0.749056 −0.374528 0.927216i \(-0.622195\pi\)
−0.374528 + 0.927216i \(0.622195\pi\)
\(752\) 0 0
\(753\) 33.6552 1.22646
\(754\) 0 0
\(755\) −31.2511 −1.13734
\(756\) 0 0
\(757\) −7.72214 −0.280666 −0.140333 0.990104i \(-0.544817\pi\)
−0.140333 + 0.990104i \(0.544817\pi\)
\(758\) 0 0
\(759\) 42.1668 1.53056
\(760\) 0 0
\(761\) 20.6779 0.749574 0.374787 0.927111i \(-0.377716\pi\)
0.374787 + 0.927111i \(0.377716\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 87.9085 3.17834
\(766\) 0 0
\(767\) 32.8232 1.18518
\(768\) 0 0
\(769\) −17.9006 −0.645511 −0.322756 0.946482i \(-0.604609\pi\)
−0.322756 + 0.946482i \(0.604609\pi\)
\(770\) 0 0
\(771\) 49.0769 1.76746
\(772\) 0 0
\(773\) −3.94378 −0.141848 −0.0709240 0.997482i \(-0.522595\pi\)
−0.0709240 + 0.997482i \(0.522595\pi\)
\(774\) 0 0
\(775\) −3.12734 −0.112337
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.98834 0.178726
\(780\) 0 0
\(781\) 3.14816 0.112650
\(782\) 0 0
\(783\) 5.91503 0.211386
\(784\) 0 0
\(785\) −20.5372 −0.733003
\(786\) 0 0
\(787\) 15.1175 0.538882 0.269441 0.963017i \(-0.413161\pi\)
0.269441 + 0.963017i \(0.413161\pi\)
\(788\) 0 0
\(789\) −69.7482 −2.48310
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −4.04358 −0.143592
\(794\) 0 0
\(795\) 63.2360 2.24275
\(796\) 0 0
\(797\) −51.2221 −1.81438 −0.907190 0.420721i \(-0.861777\pi\)
−0.907190 + 0.420721i \(0.861777\pi\)
\(798\) 0 0
\(799\) 52.5697 1.85978
\(800\) 0 0
\(801\) 92.6148 3.27238
\(802\) 0 0
\(803\) −8.22044 −0.290093
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −67.6033 −2.37975
\(808\) 0 0
\(809\) −29.2576 −1.02864 −0.514322 0.857597i \(-0.671956\pi\)
−0.514322 + 0.857597i \(0.671956\pi\)
\(810\) 0 0
\(811\) −42.6431 −1.49740 −0.748702 0.662907i \(-0.769322\pi\)
−0.748702 + 0.662907i \(0.769322\pi\)
\(812\) 0 0
\(813\) −100.735 −3.53292
\(814\) 0 0
\(815\) −36.0621 −1.26320
\(816\) 0 0
\(817\) 0.492072 0.0172154
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −14.3946 −0.502376 −0.251188 0.967938i \(-0.580821\pi\)
−0.251188 + 0.967938i \(0.580821\pi\)
\(822\) 0 0
\(823\) −49.0112 −1.70842 −0.854211 0.519927i \(-0.825959\pi\)
−0.854211 + 0.519927i \(0.825959\pi\)
\(824\) 0 0
\(825\) 23.2716 0.810214
\(826\) 0 0
\(827\) 18.0400 0.627312 0.313656 0.949537i \(-0.398446\pi\)
0.313656 + 0.949537i \(0.398446\pi\)
\(828\) 0 0
\(829\) −12.9888 −0.451120 −0.225560 0.974229i \(-0.572421\pi\)
−0.225560 + 0.974229i \(0.572421\pi\)
\(830\) 0 0
\(831\) −48.9848 −1.69926
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 8.17457 0.282892
\(836\) 0 0
\(837\) 16.5756 0.572937
\(838\) 0 0
\(839\) −20.9007 −0.721571 −0.360785 0.932649i \(-0.617491\pi\)
−0.360785 + 0.932649i \(0.617491\pi\)
\(840\) 0 0
\(841\) −28.8365 −0.994361
\(842\) 0 0
\(843\) −8.45164 −0.291090
\(844\) 0 0
\(845\) −12.4772 −0.429229
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 31.8110 1.09175
\(850\) 0 0
\(851\) 8.38496 0.287433
\(852\) 0 0
\(853\) 25.5850 0.876013 0.438006 0.898972i \(-0.355685\pi\)
0.438006 + 0.898972i \(0.355685\pi\)
\(854\) 0 0
\(855\) −56.0840 −1.91803
\(856\) 0 0
\(857\) −23.8589 −0.815005 −0.407503 0.913204i \(-0.633600\pi\)
−0.407503 + 0.913204i \(0.633600\pi\)
\(858\) 0 0
\(859\) −30.2417 −1.03183 −0.515917 0.856639i \(-0.672549\pi\)
−0.515917 + 0.856639i \(0.672549\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 33.1988 1.13010 0.565049 0.825057i \(-0.308857\pi\)
0.565049 + 0.825057i \(0.308857\pi\)
\(864\) 0 0
\(865\) −25.4413 −0.865030
\(866\) 0 0
\(867\) 143.095 4.85975
\(868\) 0 0
\(869\) −32.6984 −1.10922
\(870\) 0 0
\(871\) −9.94477 −0.336966
\(872\) 0 0
\(873\) 122.631 4.15042
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −22.9618 −0.775364 −0.387682 0.921793i \(-0.626724\pi\)
−0.387682 + 0.921793i \(0.626724\pi\)
\(878\) 0 0
\(879\) −44.4398 −1.49892
\(880\) 0 0
\(881\) −0.0996818 −0.00335837 −0.00167918 0.999999i \(-0.500535\pi\)
−0.00167918 + 0.999999i \(0.500535\pi\)
\(882\) 0 0
\(883\) 42.2637 1.42229 0.711143 0.703048i \(-0.248178\pi\)
0.711143 + 0.703048i \(0.248178\pi\)
\(884\) 0 0
\(885\) 73.7552 2.47926
\(886\) 0 0
\(887\) 43.0159 1.44433 0.722167 0.691719i \(-0.243146\pi\)
0.722167 + 0.691719i \(0.243146\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −64.7325 −2.16862
\(892\) 0 0
\(893\) −33.5385 −1.12232
\(894\) 0 0
\(895\) −13.6390 −0.455903
\(896\) 0 0
\(897\) −35.0110 −1.16898
\(898\) 0 0
\(899\) 0.458285 0.0152847
\(900\) 0 0
\(901\) 101.888 3.39437
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6.31569 −0.209941
\(906\) 0 0
\(907\) 12.7608 0.423715 0.211858 0.977301i \(-0.432049\pi\)
0.211858 + 0.977301i \(0.432049\pi\)
\(908\) 0 0
\(909\) 99.0202 3.28429
\(910\) 0 0
\(911\) −22.4015 −0.742196 −0.371098 0.928594i \(-0.621019\pi\)
−0.371098 + 0.928594i \(0.621019\pi\)
\(912\) 0 0
\(913\) −31.3016 −1.03593
\(914\) 0 0
\(915\) −9.08610 −0.300377
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −47.4888 −1.56651 −0.783256 0.621700i \(-0.786442\pi\)
−0.783256 + 0.621700i \(0.786442\pi\)
\(920\) 0 0
\(921\) 68.9841 2.27310
\(922\) 0 0
\(923\) −2.61391 −0.0860380
\(924\) 0 0
\(925\) 4.62762 0.152155
\(926\) 0 0
\(927\) −18.1399 −0.595791
\(928\) 0 0
\(929\) 19.9053 0.653072 0.326536 0.945185i \(-0.394119\pi\)
0.326536 + 0.945185i \(0.394119\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −74.1650 −2.42805
\(934\) 0 0
\(935\) −30.4406 −0.995515
\(936\) 0 0
\(937\) 25.0489 0.818310 0.409155 0.912465i \(-0.365823\pi\)
0.409155 + 0.912465i \(0.365823\pi\)
\(938\) 0 0
\(939\) −109.646 −3.57817
\(940\) 0 0
\(941\) 12.7460 0.415509 0.207755 0.978181i \(-0.433384\pi\)
0.207755 + 0.978181i \(0.433384\pi\)
\(942\) 0 0
\(943\) 5.00028 0.162832
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 29.6762 0.964347 0.482174 0.876076i \(-0.339847\pi\)
0.482174 + 0.876076i \(0.339847\pi\)
\(948\) 0 0
\(949\) 6.82542 0.221563
\(950\) 0 0
\(951\) 48.0925 1.55951
\(952\) 0 0
\(953\) 29.3545 0.950887 0.475443 0.879746i \(-0.342288\pi\)
0.475443 + 0.879746i \(0.342288\pi\)
\(954\) 0 0
\(955\) −10.7200 −0.346890
\(956\) 0 0
\(957\) −3.41026 −0.110238
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −29.7158 −0.958573
\(962\) 0 0
\(963\) −134.514 −4.33464
\(964\) 0 0
\(965\) −1.73201 −0.0557552
\(966\) 0 0
\(967\) −0.156677 −0.00503841 −0.00251920 0.999997i \(-0.500802\pi\)
−0.00251920 + 0.999997i \(0.500802\pi\)
\(968\) 0 0
\(969\) −126.455 −4.06232
\(970\) 0 0
\(971\) 28.8865 0.927011 0.463505 0.886094i \(-0.346591\pi\)
0.463505 + 0.886094i \(0.346591\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −19.3224 −0.618812
\(976\) 0 0
\(977\) −37.9126 −1.21293 −0.606466 0.795109i \(-0.707414\pi\)
−0.606466 + 0.795109i \(0.707414\pi\)
\(978\) 0 0
\(979\) −32.0703 −1.02497
\(980\) 0 0
\(981\) 83.3266 2.66041
\(982\) 0 0
\(983\) 15.8649 0.506012 0.253006 0.967465i \(-0.418581\pi\)
0.253006 + 0.967465i \(0.418581\pi\)
\(984\) 0 0
\(985\) −3.44420 −0.109741
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.493250 0.0156844
\(990\) 0 0
\(991\) 43.8398 1.39262 0.696308 0.717743i \(-0.254825\pi\)
0.696308 + 0.717743i \(0.254825\pi\)
\(992\) 0 0
\(993\) 95.1124 3.01830
\(994\) 0 0
\(995\) 25.6716 0.813843
\(996\) 0 0
\(997\) 21.9847 0.696262 0.348131 0.937446i \(-0.386816\pi\)
0.348131 + 0.937446i \(0.386816\pi\)
\(998\) 0 0
\(999\) −24.5274 −0.776013
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 \(a_p\))