Properties

Label 8036.2.a.t.1.20
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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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: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Root \(3.29362\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.29362 q^{3}\) \(+3.10165 q^{5}\) \(+7.84790 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.29362 q^{3}\) \(+3.10165 q^{5}\) \(+7.84790 q^{9}\) \(+3.57618 q^{11}\) \(-2.94081 q^{13}\) \(+10.2157 q^{15}\) \(+0.836188 q^{17}\) \(+1.07491 q^{19}\) \(-4.90605 q^{23}\) \(+4.62026 q^{25}\) \(+15.9671 q^{27}\) \(-3.82134 q^{29}\) \(+5.16536 q^{31}\) \(+11.7785 q^{33}\) \(-6.09614 q^{37}\) \(-9.68590 q^{39}\) \(-1.00000 q^{41}\) \(+7.59000 q^{43}\) \(+24.3415 q^{45}\) \(-13.2989 q^{47}\) \(+2.75408 q^{51}\) \(-3.67058 q^{53}\) \(+11.0921 q^{55}\) \(+3.54033 q^{57}\) \(+8.05522 q^{59}\) \(+6.21710 q^{61}\) \(-9.12138 q^{65}\) \(+10.9460 q^{67}\) \(-16.1586 q^{69}\) \(+10.9994 q^{71}\) \(+8.78244 q^{73}\) \(+15.2174 q^{75}\) \(-4.46561 q^{79}\) \(+29.0458 q^{81}\) \(-11.2702 q^{83}\) \(+2.59357 q^{85}\) \(-12.5860 q^{87}\) \(+1.02946 q^{89}\) \(+17.0127 q^{93}\) \(+3.33399 q^{95}\) \(-12.3000 q^{97}\) \(+28.0655 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.29362 1.90157 0.950785 0.309852i \(-0.100280\pi\)
0.950785 + 0.309852i \(0.100280\pi\)
\(4\) 0 0
\(5\) 3.10165 1.38710 0.693551 0.720408i \(-0.256045\pi\)
0.693551 + 0.720408i \(0.256045\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 7.84790 2.61597
\(10\) 0 0
\(11\) 3.57618 1.07826 0.539129 0.842223i \(-0.318754\pi\)
0.539129 + 0.842223i \(0.318754\pi\)
\(12\) 0 0
\(13\) −2.94081 −0.815634 −0.407817 0.913064i \(-0.633710\pi\)
−0.407817 + 0.913064i \(0.633710\pi\)
\(14\) 0 0
\(15\) 10.2157 2.63767
\(16\) 0 0
\(17\) 0.836188 0.202805 0.101403 0.994845i \(-0.467667\pi\)
0.101403 + 0.994845i \(0.467667\pi\)
\(18\) 0 0
\(19\) 1.07491 0.246600 0.123300 0.992369i \(-0.460652\pi\)
0.123300 + 0.992369i \(0.460652\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.90605 −1.02298 −0.511491 0.859288i \(-0.670907\pi\)
−0.511491 + 0.859288i \(0.670907\pi\)
\(24\) 0 0
\(25\) 4.62026 0.924052
\(26\) 0 0
\(27\) 15.9671 3.07287
\(28\) 0 0
\(29\) −3.82134 −0.709605 −0.354803 0.934941i \(-0.615452\pi\)
−0.354803 + 0.934941i \(0.615452\pi\)
\(30\) 0 0
\(31\) 5.16536 0.927726 0.463863 0.885907i \(-0.346463\pi\)
0.463863 + 0.885907i \(0.346463\pi\)
\(32\) 0 0
\(33\) 11.7785 2.05038
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.09614 −1.00220 −0.501100 0.865390i \(-0.667071\pi\)
−0.501100 + 0.865390i \(0.667071\pi\)
\(38\) 0 0
\(39\) −9.68590 −1.55099
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 7.59000 1.15746 0.578732 0.815518i \(-0.303548\pi\)
0.578732 + 0.815518i \(0.303548\pi\)
\(44\) 0 0
\(45\) 24.3415 3.62861
\(46\) 0 0
\(47\) −13.2989 −1.93984 −0.969920 0.243425i \(-0.921729\pi\)
−0.969920 + 0.243425i \(0.921729\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 2.75408 0.385648
\(52\) 0 0
\(53\) −3.67058 −0.504194 −0.252097 0.967702i \(-0.581120\pi\)
−0.252097 + 0.967702i \(0.581120\pi\)
\(54\) 0 0
\(55\) 11.0921 1.49565
\(56\) 0 0
\(57\) 3.54033 0.468928
\(58\) 0 0
\(59\) 8.05522 1.04870 0.524350 0.851503i \(-0.324308\pi\)
0.524350 + 0.851503i \(0.324308\pi\)
\(60\) 0 0
\(61\) 6.21710 0.796018 0.398009 0.917382i \(-0.369701\pi\)
0.398009 + 0.917382i \(0.369701\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9.12138 −1.13137
\(66\) 0 0
\(67\) 10.9460 1.33727 0.668634 0.743591i \(-0.266879\pi\)
0.668634 + 0.743591i \(0.266879\pi\)
\(68\) 0 0
\(69\) −16.1586 −1.94527
\(70\) 0 0
\(71\) 10.9994 1.30538 0.652692 0.757624i \(-0.273640\pi\)
0.652692 + 0.757624i \(0.273640\pi\)
\(72\) 0 0
\(73\) 8.78244 1.02791 0.513953 0.857818i \(-0.328180\pi\)
0.513953 + 0.857818i \(0.328180\pi\)
\(74\) 0 0
\(75\) 15.2174 1.75715
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −4.46561 −0.502420 −0.251210 0.967933i \(-0.580828\pi\)
−0.251210 + 0.967933i \(0.580828\pi\)
\(80\) 0 0
\(81\) 29.0458 3.22732
\(82\) 0 0
\(83\) −11.2702 −1.23706 −0.618531 0.785760i \(-0.712272\pi\)
−0.618531 + 0.785760i \(0.712272\pi\)
\(84\) 0 0
\(85\) 2.59357 0.281312
\(86\) 0 0
\(87\) −12.5860 −1.34936
\(88\) 0 0
\(89\) 1.02946 0.109122 0.0545611 0.998510i \(-0.482624\pi\)
0.0545611 + 0.998510i \(0.482624\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 17.0127 1.76414
\(94\) 0 0
\(95\) 3.33399 0.342060
\(96\) 0 0
\(97\) −12.3000 −1.24888 −0.624440 0.781073i \(-0.714673\pi\)
−0.624440 + 0.781073i \(0.714673\pi\)
\(98\) 0 0
\(99\) 28.0655 2.82069
\(100\) 0 0
\(101\) −9.02323 −0.897845 −0.448922 0.893571i \(-0.648192\pi\)
−0.448922 + 0.893571i \(0.648192\pi\)
\(102\) 0 0
\(103\) −0.663227 −0.0653497 −0.0326749 0.999466i \(-0.510403\pi\)
−0.0326749 + 0.999466i \(0.510403\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −14.4968 −1.40146 −0.700731 0.713425i \(-0.747143\pi\)
−0.700731 + 0.713425i \(0.747143\pi\)
\(108\) 0 0
\(109\) −13.4957 −1.29265 −0.646325 0.763063i \(-0.723695\pi\)
−0.646325 + 0.763063i \(0.723695\pi\)
\(110\) 0 0
\(111\) −20.0783 −1.90575
\(112\) 0 0
\(113\) 17.8171 1.67610 0.838048 0.545597i \(-0.183697\pi\)
0.838048 + 0.545597i \(0.183697\pi\)
\(114\) 0 0
\(115\) −15.2169 −1.41898
\(116\) 0 0
\(117\) −23.0792 −2.13367
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.78904 0.162640
\(122\) 0 0
\(123\) −3.29362 −0.296975
\(124\) 0 0
\(125\) −1.17782 −0.105348
\(126\) 0 0
\(127\) 2.27006 0.201435 0.100718 0.994915i \(-0.467886\pi\)
0.100718 + 0.994915i \(0.467886\pi\)
\(128\) 0 0
\(129\) 24.9985 2.20100
\(130\) 0 0
\(131\) 18.1096 1.58224 0.791122 0.611659i \(-0.209498\pi\)
0.791122 + 0.611659i \(0.209498\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 49.5245 4.26239
\(136\) 0 0
\(137\) −0.326566 −0.0279004 −0.0139502 0.999903i \(-0.504441\pi\)
−0.0139502 + 0.999903i \(0.504441\pi\)
\(138\) 0 0
\(139\) 11.3280 0.960825 0.480413 0.877043i \(-0.340487\pi\)
0.480413 + 0.877043i \(0.340487\pi\)
\(140\) 0 0
\(141\) −43.8014 −3.68874
\(142\) 0 0
\(143\) −10.5169 −0.879464
\(144\) 0 0
\(145\) −11.8525 −0.984295
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.35370 0.766285 0.383142 0.923689i \(-0.374842\pi\)
0.383142 + 0.923689i \(0.374842\pi\)
\(150\) 0 0
\(151\) 19.3212 1.57234 0.786169 0.618012i \(-0.212062\pi\)
0.786169 + 0.618012i \(0.212062\pi\)
\(152\) 0 0
\(153\) 6.56232 0.530532
\(154\) 0 0
\(155\) 16.0212 1.28685
\(156\) 0 0
\(157\) 7.85883 0.627203 0.313601 0.949555i \(-0.398464\pi\)
0.313601 + 0.949555i \(0.398464\pi\)
\(158\) 0 0
\(159\) −12.0895 −0.958759
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 6.46497 0.506375 0.253188 0.967417i \(-0.418521\pi\)
0.253188 + 0.967417i \(0.418521\pi\)
\(164\) 0 0
\(165\) 36.5330 2.84409
\(166\) 0 0
\(167\) −12.8889 −0.997370 −0.498685 0.866783i \(-0.666184\pi\)
−0.498685 + 0.866783i \(0.666184\pi\)
\(168\) 0 0
\(169\) −4.35163 −0.334741
\(170\) 0 0
\(171\) 8.43575 0.645098
\(172\) 0 0
\(173\) −15.9211 −1.21046 −0.605231 0.796050i \(-0.706919\pi\)
−0.605231 + 0.796050i \(0.706919\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 26.5308 1.99418
\(178\) 0 0
\(179\) −9.17161 −0.685518 −0.342759 0.939423i \(-0.611361\pi\)
−0.342759 + 0.939423i \(0.611361\pi\)
\(180\) 0 0
\(181\) −5.15105 −0.382875 −0.191437 0.981505i \(-0.561315\pi\)
−0.191437 + 0.981505i \(0.561315\pi\)
\(182\) 0 0
\(183\) 20.4767 1.51368
\(184\) 0 0
\(185\) −18.9081 −1.39015
\(186\) 0 0
\(187\) 2.99036 0.218676
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.35390 0.459752 0.229876 0.973220i \(-0.426168\pi\)
0.229876 + 0.973220i \(0.426168\pi\)
\(192\) 0 0
\(193\) −24.0051 −1.72793 −0.863964 0.503553i \(-0.832026\pi\)
−0.863964 + 0.503553i \(0.832026\pi\)
\(194\) 0 0
\(195\) −30.0423 −2.15138
\(196\) 0 0
\(197\) −4.82514 −0.343777 −0.171889 0.985116i \(-0.554987\pi\)
−0.171889 + 0.985116i \(0.554987\pi\)
\(198\) 0 0
\(199\) −19.9592 −1.41487 −0.707434 0.706779i \(-0.750147\pi\)
−0.707434 + 0.706779i \(0.750147\pi\)
\(200\) 0 0
\(201\) 36.0520 2.54291
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.10165 −0.216629
\(206\) 0 0
\(207\) −38.5022 −2.67609
\(208\) 0 0
\(209\) 3.84405 0.265899
\(210\) 0 0
\(211\) −24.8929 −1.71370 −0.856849 0.515568i \(-0.827581\pi\)
−0.856849 + 0.515568i \(0.827581\pi\)
\(212\) 0 0
\(213\) 36.2276 2.48228
\(214\) 0 0
\(215\) 23.5416 1.60552
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 28.9260 1.95464
\(220\) 0 0
\(221\) −2.45907 −0.165415
\(222\) 0 0
\(223\) −20.5603 −1.37682 −0.688410 0.725321i \(-0.741691\pi\)
−0.688410 + 0.725321i \(0.741691\pi\)
\(224\) 0 0
\(225\) 36.2593 2.41729
\(226\) 0 0
\(227\) −17.4532 −1.15841 −0.579205 0.815182i \(-0.696637\pi\)
−0.579205 + 0.815182i \(0.696637\pi\)
\(228\) 0 0
\(229\) 2.71799 0.179610 0.0898051 0.995959i \(-0.471376\pi\)
0.0898051 + 0.995959i \(0.471376\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.5594 −0.691770 −0.345885 0.938277i \(-0.612421\pi\)
−0.345885 + 0.938277i \(0.612421\pi\)
\(234\) 0 0
\(235\) −41.2485 −2.69076
\(236\) 0 0
\(237\) −14.7080 −0.955387
\(238\) 0 0
\(239\) −28.0324 −1.81326 −0.906632 0.421921i \(-0.861356\pi\)
−0.906632 + 0.421921i \(0.861356\pi\)
\(240\) 0 0
\(241\) 19.5604 1.25999 0.629997 0.776598i \(-0.283056\pi\)
0.629997 + 0.776598i \(0.283056\pi\)
\(242\) 0 0
\(243\) 47.7645 3.06409
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.16110 −0.201136
\(248\) 0 0
\(249\) −37.1196 −2.35236
\(250\) 0 0
\(251\) −17.9605 −1.13365 −0.566827 0.823837i \(-0.691829\pi\)
−0.566827 + 0.823837i \(0.691829\pi\)
\(252\) 0 0
\(253\) −17.5449 −1.10304
\(254\) 0 0
\(255\) 8.54221 0.534934
\(256\) 0 0
\(257\) 23.2256 1.44877 0.724387 0.689394i \(-0.242123\pi\)
0.724387 + 0.689394i \(0.242123\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −29.9895 −1.85630
\(262\) 0 0
\(263\) 23.2408 1.43309 0.716546 0.697540i \(-0.245722\pi\)
0.716546 + 0.697540i \(0.245722\pi\)
\(264\) 0 0
\(265\) −11.3849 −0.699368
\(266\) 0 0
\(267\) 3.39063 0.207503
\(268\) 0 0
\(269\) 12.7842 0.779468 0.389734 0.920927i \(-0.372567\pi\)
0.389734 + 0.920927i \(0.372567\pi\)
\(270\) 0 0
\(271\) −0.118816 −0.00721755 −0.00360877 0.999993i \(-0.501149\pi\)
−0.00360877 + 0.999993i \(0.501149\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.5229 0.996366
\(276\) 0 0
\(277\) 3.92104 0.235592 0.117796 0.993038i \(-0.462417\pi\)
0.117796 + 0.993038i \(0.462417\pi\)
\(278\) 0 0
\(279\) 40.5372 2.42690
\(280\) 0 0
\(281\) 15.3884 0.917995 0.458998 0.888437i \(-0.348209\pi\)
0.458998 + 0.888437i \(0.348209\pi\)
\(282\) 0 0
\(283\) 1.04168 0.0619212 0.0309606 0.999521i \(-0.490143\pi\)
0.0309606 + 0.999521i \(0.490143\pi\)
\(284\) 0 0
\(285\) 10.9809 0.650451
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.3008 −0.958870
\(290\) 0 0
\(291\) −40.5116 −2.37483
\(292\) 0 0
\(293\) 0.376897 0.0220185 0.0110093 0.999939i \(-0.496496\pi\)
0.0110093 + 0.999939i \(0.496496\pi\)
\(294\) 0 0
\(295\) 24.9845 1.45465
\(296\) 0 0
\(297\) 57.1012 3.31335
\(298\) 0 0
\(299\) 14.4278 0.834380
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −29.7190 −1.70731
\(304\) 0 0
\(305\) 19.2833 1.10416
\(306\) 0 0
\(307\) −1.62744 −0.0928830 −0.0464415 0.998921i \(-0.514788\pi\)
−0.0464415 + 0.998921i \(0.514788\pi\)
\(308\) 0 0
\(309\) −2.18442 −0.124267
\(310\) 0 0
\(311\) −7.17325 −0.406758 −0.203379 0.979100i \(-0.565192\pi\)
−0.203379 + 0.979100i \(0.565192\pi\)
\(312\) 0 0
\(313\) −5.50398 −0.311103 −0.155552 0.987828i \(-0.549716\pi\)
−0.155552 + 0.987828i \(0.549716\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 29.1090 1.63493 0.817464 0.575980i \(-0.195380\pi\)
0.817464 + 0.575980i \(0.195380\pi\)
\(318\) 0 0
\(319\) −13.6658 −0.765137
\(320\) 0 0
\(321\) −47.7470 −2.66498
\(322\) 0 0
\(323\) 0.898823 0.0500119
\(324\) 0 0
\(325\) −13.5873 −0.753689
\(326\) 0 0
\(327\) −44.4495 −2.45806
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 21.1759 1.16393 0.581967 0.813212i \(-0.302283\pi\)
0.581967 + 0.813212i \(0.302283\pi\)
\(332\) 0 0
\(333\) −47.8419 −2.62172
\(334\) 0 0
\(335\) 33.9508 1.85493
\(336\) 0 0
\(337\) −0.192702 −0.0104971 −0.00524856 0.999986i \(-0.501671\pi\)
−0.00524856 + 0.999986i \(0.501671\pi\)
\(338\) 0 0
\(339\) 58.6828 3.18721
\(340\) 0 0
\(341\) 18.4722 1.00033
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −50.1185 −2.69829
\(346\) 0 0
\(347\) −29.8981 −1.60501 −0.802507 0.596643i \(-0.796501\pi\)
−0.802507 + 0.596643i \(0.796501\pi\)
\(348\) 0 0
\(349\) 18.8946 1.01140 0.505701 0.862709i \(-0.331234\pi\)
0.505701 + 0.862709i \(0.331234\pi\)
\(350\) 0 0
\(351\) −46.9563 −2.50634
\(352\) 0 0
\(353\) −32.9608 −1.75433 −0.877164 0.480190i \(-0.840568\pi\)
−0.877164 + 0.480190i \(0.840568\pi\)
\(354\) 0 0
\(355\) 34.1162 1.81070
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.47853 −0.289146 −0.144573 0.989494i \(-0.546181\pi\)
−0.144573 + 0.989494i \(0.546181\pi\)
\(360\) 0 0
\(361\) −17.8446 −0.939188
\(362\) 0 0
\(363\) 5.89241 0.309271
\(364\) 0 0
\(365\) 27.2401 1.42581
\(366\) 0 0
\(367\) 21.1999 1.10663 0.553314 0.832973i \(-0.313363\pi\)
0.553314 + 0.832973i \(0.313363\pi\)
\(368\) 0 0
\(369\) −7.84790 −0.408545
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 11.5756 0.599361 0.299681 0.954040i \(-0.403120\pi\)
0.299681 + 0.954040i \(0.403120\pi\)
\(374\) 0 0
\(375\) −3.87929 −0.200326
\(376\) 0 0
\(377\) 11.2378 0.578778
\(378\) 0 0
\(379\) −31.2015 −1.60271 −0.801357 0.598186i \(-0.795888\pi\)
−0.801357 + 0.598186i \(0.795888\pi\)
\(380\) 0 0
\(381\) 7.47670 0.383043
\(382\) 0 0
\(383\) 16.4489 0.840498 0.420249 0.907409i \(-0.361943\pi\)
0.420249 + 0.907409i \(0.361943\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 59.5656 3.02789
\(388\) 0 0
\(389\) 31.5077 1.59751 0.798753 0.601659i \(-0.205494\pi\)
0.798753 + 0.601659i \(0.205494\pi\)
\(390\) 0 0
\(391\) −4.10238 −0.207466
\(392\) 0 0
\(393\) 59.6461 3.00875
\(394\) 0 0
\(395\) −13.8508 −0.696908
\(396\) 0 0
\(397\) 1.76668 0.0886671 0.0443335 0.999017i \(-0.485884\pi\)
0.0443335 + 0.999017i \(0.485884\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.0284 −0.650609 −0.325304 0.945609i \(-0.605467\pi\)
−0.325304 + 0.945609i \(0.605467\pi\)
\(402\) 0 0
\(403\) −15.1903 −0.756685
\(404\) 0 0
\(405\) 90.0902 4.47662
\(406\) 0 0
\(407\) −21.8009 −1.08063
\(408\) 0 0
\(409\) −19.2624 −0.952465 −0.476232 0.879320i \(-0.657998\pi\)
−0.476232 + 0.879320i \(0.657998\pi\)
\(410\) 0 0
\(411\) −1.07558 −0.0530545
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −34.9562 −1.71593
\(416\) 0 0
\(417\) 37.3100 1.82708
\(418\) 0 0
\(419\) 34.7472 1.69751 0.848757 0.528783i \(-0.177351\pi\)
0.848757 + 0.528783i \(0.177351\pi\)
\(420\) 0 0
\(421\) −35.8518 −1.74731 −0.873654 0.486548i \(-0.838256\pi\)
−0.873654 + 0.486548i \(0.838256\pi\)
\(422\) 0 0
\(423\) −104.368 −5.07456
\(424\) 0 0
\(425\) 3.86341 0.187403
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −34.6385 −1.67236
\(430\) 0 0
\(431\) 32.1395 1.54811 0.774053 0.633121i \(-0.218226\pi\)
0.774053 + 0.633121i \(0.218226\pi\)
\(432\) 0 0
\(433\) 16.3202 0.784300 0.392150 0.919901i \(-0.371731\pi\)
0.392150 + 0.919901i \(0.371731\pi\)
\(434\) 0 0
\(435\) −39.0375 −1.87170
\(436\) 0 0
\(437\) −5.27354 −0.252268
\(438\) 0 0
\(439\) −40.5846 −1.93700 −0.968498 0.249020i \(-0.919892\pi\)
−0.968498 + 0.249020i \(0.919892\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.64749 −0.315832 −0.157916 0.987453i \(-0.550477\pi\)
−0.157916 + 0.987453i \(0.550477\pi\)
\(444\) 0 0
\(445\) 3.19302 0.151364
\(446\) 0 0
\(447\) 30.8075 1.45714
\(448\) 0 0
\(449\) 38.8140 1.83175 0.915873 0.401469i \(-0.131500\pi\)
0.915873 + 0.401469i \(0.131500\pi\)
\(450\) 0 0
\(451\) −3.57618 −0.168396
\(452\) 0 0
\(453\) 63.6366 2.98991
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −31.2024 −1.45959 −0.729794 0.683667i \(-0.760384\pi\)
−0.729794 + 0.683667i \(0.760384\pi\)
\(458\) 0 0
\(459\) 13.3515 0.623195
\(460\) 0 0
\(461\) 27.0080 1.25789 0.628943 0.777451i \(-0.283488\pi\)
0.628943 + 0.777451i \(0.283488\pi\)
\(462\) 0 0
\(463\) 27.4666 1.27648 0.638242 0.769836i \(-0.279662\pi\)
0.638242 + 0.769836i \(0.279662\pi\)
\(464\) 0 0
\(465\) 52.7675 2.44704
\(466\) 0 0
\(467\) −1.74434 −0.0807186 −0.0403593 0.999185i \(-0.512850\pi\)
−0.0403593 + 0.999185i \(0.512850\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 25.8840 1.19267
\(472\) 0 0
\(473\) 27.1432 1.24805
\(474\) 0 0
\(475\) 4.96634 0.227872
\(476\) 0 0
\(477\) −28.8064 −1.31895
\(478\) 0 0
\(479\) −28.1747 −1.28733 −0.643667 0.765306i \(-0.722588\pi\)
−0.643667 + 0.765306i \(0.722588\pi\)
\(480\) 0 0
\(481\) 17.9276 0.817428
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −38.1505 −1.73232
\(486\) 0 0
\(487\) 17.4673 0.791521 0.395760 0.918354i \(-0.370481\pi\)
0.395760 + 0.918354i \(0.370481\pi\)
\(488\) 0 0
\(489\) 21.2931 0.962908
\(490\) 0 0
\(491\) −30.9428 −1.39643 −0.698215 0.715889i \(-0.746022\pi\)
−0.698215 + 0.715889i \(0.746022\pi\)
\(492\) 0 0
\(493\) −3.19536 −0.143912
\(494\) 0 0
\(495\) 87.0494 3.91258
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.3387 0.552357 0.276178 0.961106i \(-0.410932\pi\)
0.276178 + 0.961106i \(0.410932\pi\)
\(500\) 0 0
\(501\) −42.4509 −1.89657
\(502\) 0 0
\(503\) −23.9299 −1.06698 −0.533491 0.845806i \(-0.679120\pi\)
−0.533491 + 0.845806i \(0.679120\pi\)
\(504\) 0 0
\(505\) −27.9869 −1.24540
\(506\) 0 0
\(507\) −14.3326 −0.636533
\(508\) 0 0
\(509\) 5.19945 0.230461 0.115231 0.993339i \(-0.463239\pi\)
0.115231 + 0.993339i \(0.463239\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 17.1632 0.757772
\(514\) 0 0
\(515\) −2.05710 −0.0906467
\(516\) 0 0
\(517\) −47.5591 −2.09165
\(518\) 0 0
\(519\) −52.4381 −2.30178
\(520\) 0 0
\(521\) 10.2730 0.450069 0.225035 0.974351i \(-0.427751\pi\)
0.225035 + 0.974351i \(0.427751\pi\)
\(522\) 0 0
\(523\) −42.6012 −1.86282 −0.931411 0.363968i \(-0.881422\pi\)
−0.931411 + 0.363968i \(0.881422\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.31921 0.188148
\(528\) 0 0
\(529\) 1.06935 0.0464935
\(530\) 0 0
\(531\) 63.2166 2.74337
\(532\) 0 0
\(533\) 2.94081 0.127381
\(534\) 0 0
\(535\) −44.9642 −1.94397
\(536\) 0 0
\(537\) −30.2078 −1.30356
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 31.5742 1.35748 0.678740 0.734379i \(-0.262526\pi\)
0.678740 + 0.734379i \(0.262526\pi\)
\(542\) 0 0
\(543\) −16.9656 −0.728063
\(544\) 0 0
\(545\) −41.8589 −1.79304
\(546\) 0 0
\(547\) 25.7924 1.10280 0.551402 0.834239i \(-0.314093\pi\)
0.551402 + 0.834239i \(0.314093\pi\)
\(548\) 0 0
\(549\) 48.7911 2.08236
\(550\) 0 0
\(551\) −4.10758 −0.174989
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −62.2761 −2.64347
\(556\) 0 0
\(557\) −34.3941 −1.45732 −0.728662 0.684874i \(-0.759857\pi\)
−0.728662 + 0.684874i \(0.759857\pi\)
\(558\) 0 0
\(559\) −22.3208 −0.944068
\(560\) 0 0
\(561\) 9.84908 0.415828
\(562\) 0 0
\(563\) −14.1609 −0.596812 −0.298406 0.954439i \(-0.596455\pi\)
−0.298406 + 0.954439i \(0.596455\pi\)
\(564\) 0 0
\(565\) 55.2626 2.32492
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 17.0368 0.714221 0.357111 0.934062i \(-0.383762\pi\)
0.357111 + 0.934062i \(0.383762\pi\)
\(570\) 0 0
\(571\) −12.0827 −0.505646 −0.252823 0.967513i \(-0.581359\pi\)
−0.252823 + 0.967513i \(0.581359\pi\)
\(572\) 0 0
\(573\) 20.9273 0.874251
\(574\) 0 0
\(575\) −22.6672 −0.945289
\(576\) 0 0
\(577\) 24.1332 1.00468 0.502338 0.864671i \(-0.332473\pi\)
0.502338 + 0.864671i \(0.332473\pi\)
\(578\) 0 0
\(579\) −79.0637 −3.28578
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −13.1267 −0.543651
\(584\) 0 0
\(585\) −71.5837 −2.95962
\(586\) 0 0
\(587\) 10.4115 0.429728 0.214864 0.976644i \(-0.431069\pi\)
0.214864 + 0.976644i \(0.431069\pi\)
\(588\) 0 0
\(589\) 5.55228 0.228778
\(590\) 0 0
\(591\) −15.8922 −0.653716
\(592\) 0 0
\(593\) −13.2660 −0.544769 −0.272384 0.962189i \(-0.587812\pi\)
−0.272384 + 0.962189i \(0.587812\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −65.7379 −2.69047
\(598\) 0 0
\(599\) −18.2672 −0.746376 −0.373188 0.927756i \(-0.621735\pi\)
−0.373188 + 0.927756i \(0.621735\pi\)
\(600\) 0 0
\(601\) 16.0344 0.654055 0.327028 0.945015i \(-0.393953\pi\)
0.327028 + 0.945015i \(0.393953\pi\)
\(602\) 0 0
\(603\) 85.9033 3.49825
\(604\) 0 0
\(605\) 5.54898 0.225598
\(606\) 0 0
\(607\) −3.59212 −0.145800 −0.0728999 0.997339i \(-0.523225\pi\)
−0.0728999 + 0.997339i \(0.523225\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 39.1095 1.58220
\(612\) 0 0
\(613\) −15.2533 −0.616076 −0.308038 0.951374i \(-0.599672\pi\)
−0.308038 + 0.951374i \(0.599672\pi\)
\(614\) 0 0
\(615\) −10.2157 −0.411935
\(616\) 0 0
\(617\) −3.60446 −0.145110 −0.0725551 0.997364i \(-0.523115\pi\)
−0.0725551 + 0.997364i \(0.523115\pi\)
\(618\) 0 0
\(619\) 6.29819 0.253145 0.126573 0.991957i \(-0.459602\pi\)
0.126573 + 0.991957i \(0.459602\pi\)
\(620\) 0 0
\(621\) −78.3355 −3.14350
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −26.7545 −1.07018
\(626\) 0 0
\(627\) 12.6608 0.505625
\(628\) 0 0
\(629\) −5.09752 −0.203251
\(630\) 0 0
\(631\) −14.0810 −0.560556 −0.280278 0.959919i \(-0.590427\pi\)
−0.280278 + 0.959919i \(0.590427\pi\)
\(632\) 0 0
\(633\) −81.9876 −3.25871
\(634\) 0 0
\(635\) 7.04094 0.279411
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 86.3218 3.41484
\(640\) 0 0
\(641\) −45.4067 −1.79346 −0.896728 0.442582i \(-0.854063\pi\)
−0.896728 + 0.442582i \(0.854063\pi\)
\(642\) 0 0
\(643\) 23.1129 0.911482 0.455741 0.890112i \(-0.349374\pi\)
0.455741 + 0.890112i \(0.349374\pi\)
\(644\) 0 0
\(645\) 77.5369 3.05301
\(646\) 0 0
\(647\) 0.334277 0.0131418 0.00657090 0.999978i \(-0.497908\pi\)
0.00657090 + 0.999978i \(0.497908\pi\)
\(648\) 0 0
\(649\) 28.8069 1.13077
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.1516 −1.21905 −0.609527 0.792765i \(-0.708641\pi\)
−0.609527 + 0.792765i \(0.708641\pi\)
\(654\) 0 0
\(655\) 56.1697 2.19473
\(656\) 0 0
\(657\) 68.9237 2.68897
\(658\) 0 0
\(659\) −8.50658 −0.331369 −0.165685 0.986179i \(-0.552983\pi\)
−0.165685 + 0.986179i \(0.552983\pi\)
\(660\) 0 0
\(661\) 29.6835 1.15455 0.577277 0.816549i \(-0.304115\pi\)
0.577277 + 0.816549i \(0.304115\pi\)
\(662\) 0 0
\(663\) −8.09923 −0.314548
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 18.7477 0.725914
\(668\) 0 0
\(669\) −67.7178 −2.61812
\(670\) 0 0
\(671\) 22.2334 0.858312
\(672\) 0 0
\(673\) −24.7554 −0.954249 −0.477125 0.878836i \(-0.658321\pi\)
−0.477125 + 0.878836i \(0.658321\pi\)
\(674\) 0 0
\(675\) 73.7722 2.83950
\(676\) 0 0
\(677\) 32.8223 1.26146 0.630731 0.776002i \(-0.282755\pi\)
0.630731 + 0.776002i \(0.282755\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −57.4842 −2.20280
\(682\) 0 0
\(683\) −3.40083 −0.130129 −0.0650647 0.997881i \(-0.520725\pi\)
−0.0650647 + 0.997881i \(0.520725\pi\)
\(684\) 0 0
\(685\) −1.01289 −0.0387007
\(686\) 0 0
\(687\) 8.95203 0.341541
\(688\) 0 0
\(689\) 10.7945 0.411238
\(690\) 0 0
\(691\) 23.5148 0.894544 0.447272 0.894398i \(-0.352396\pi\)
0.447272 + 0.894398i \(0.352396\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 35.1354 1.33276
\(696\) 0 0
\(697\) −0.836188 −0.0316729
\(698\) 0 0
\(699\) −34.7786 −1.31545
\(700\) 0 0
\(701\) −8.44634 −0.319014 −0.159507 0.987197i \(-0.550990\pi\)
−0.159507 + 0.987197i \(0.550990\pi\)
\(702\) 0 0
\(703\) −6.55278 −0.247143
\(704\) 0 0
\(705\) −135.857 −5.11666
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 8.30596 0.311937 0.155969 0.987762i \(-0.450150\pi\)
0.155969 + 0.987762i \(0.450150\pi\)
\(710\) 0 0
\(711\) −35.0456 −1.31431
\(712\) 0 0
\(713\) −25.3415 −0.949048
\(714\) 0 0
\(715\) −32.6197 −1.21991
\(716\) 0 0
\(717\) −92.3279 −3.44805
\(718\) 0 0
\(719\) −39.5762 −1.47594 −0.737972 0.674832i \(-0.764216\pi\)
−0.737972 + 0.674832i \(0.764216\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 64.4243 2.39597
\(724\) 0 0
\(725\) −17.6556 −0.655712
\(726\) 0 0
\(727\) 32.3315 1.19911 0.599554 0.800334i \(-0.295345\pi\)
0.599554 + 0.800334i \(0.295345\pi\)
\(728\) 0 0
\(729\) 70.1803 2.59927
\(730\) 0 0
\(731\) 6.34667 0.234740
\(732\) 0 0
\(733\) −7.94991 −0.293637 −0.146818 0.989163i \(-0.546903\pi\)
−0.146818 + 0.989163i \(0.546903\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 39.1449 1.44192
\(738\) 0 0
\(739\) −0.926861 −0.0340951 −0.0170476 0.999855i \(-0.505427\pi\)
−0.0170476 + 0.999855i \(0.505427\pi\)
\(740\) 0 0
\(741\) −10.4114 −0.382473
\(742\) 0 0
\(743\) −46.3280 −1.69961 −0.849804 0.527098i \(-0.823280\pi\)
−0.849804 + 0.527098i \(0.823280\pi\)
\(744\) 0 0
\(745\) 29.0119 1.06291
\(746\) 0 0
\(747\) −88.4472 −3.23611
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 14.1445 0.516139 0.258070 0.966126i \(-0.416914\pi\)
0.258070 + 0.966126i \(0.416914\pi\)
\(752\) 0 0
\(753\) −59.1549 −2.15572
\(754\) 0 0
\(755\) 59.9277 2.18099
\(756\) 0 0
\(757\) −34.9749 −1.27118 −0.635592 0.772025i \(-0.719244\pi\)
−0.635592 + 0.772025i \(0.719244\pi\)
\(758\) 0 0
\(759\) −57.7862 −2.09751
\(760\) 0 0
\(761\) 32.5723 1.18075 0.590373 0.807131i \(-0.298981\pi\)
0.590373 + 0.807131i \(0.298981\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 20.3540 0.735902
\(766\) 0 0
\(767\) −23.6889 −0.855356
\(768\) 0 0
\(769\) 3.66978 0.132335 0.0661677 0.997809i \(-0.478923\pi\)
0.0661677 + 0.997809i \(0.478923\pi\)
\(770\) 0 0
\(771\) 76.4962 2.75494
\(772\) 0 0
\(773\) −42.3480 −1.52315 −0.761576 0.648076i \(-0.775574\pi\)
−0.761576 + 0.648076i \(0.775574\pi\)
\(774\) 0 0
\(775\) 23.8653 0.857267
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.07491 −0.0385125
\(780\) 0 0
\(781\) 39.3356 1.40754
\(782\) 0 0
\(783\) −61.0158 −2.18053
\(784\) 0 0
\(785\) 24.3754 0.869994
\(786\) 0 0
\(787\) 54.1762 1.93117 0.965587 0.260080i \(-0.0837491\pi\)
0.965587 + 0.260080i \(0.0837491\pi\)
\(788\) 0 0
\(789\) 76.5464 2.72512
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −18.2833 −0.649259
\(794\) 0 0
\(795\) −37.4974 −1.32990
\(796\) 0 0
\(797\) 23.4371 0.830186 0.415093 0.909779i \(-0.363749\pi\)
0.415093 + 0.909779i \(0.363749\pi\)
\(798\) 0 0
\(799\) −11.1204 −0.393410
\(800\) 0 0
\(801\) 8.07907 0.285460
\(802\) 0 0
\(803\) 31.4076 1.10835
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 42.1063 1.48221
\(808\) 0 0
\(809\) 9.01729 0.317031 0.158515 0.987356i \(-0.449329\pi\)
0.158515 + 0.987356i \(0.449329\pi\)
\(810\) 0 0
\(811\) −15.4811 −0.543614 −0.271807 0.962352i \(-0.587621\pi\)
−0.271807 + 0.962352i \(0.587621\pi\)
\(812\) 0 0
\(813\) −0.391334 −0.0137247
\(814\) 0 0
\(815\) 20.0521 0.702394
\(816\) 0 0
\(817\) 8.15854 0.285431
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −6.58546 −0.229834 −0.114917 0.993375i \(-0.536660\pi\)
−0.114917 + 0.993375i \(0.536660\pi\)
\(822\) 0 0
\(823\) 25.0408 0.872867 0.436433 0.899737i \(-0.356241\pi\)
0.436433 + 0.899737i \(0.356241\pi\)
\(824\) 0 0
\(825\) 54.4200 1.89466
\(826\) 0 0
\(827\) 16.6075 0.577499 0.288749 0.957405i \(-0.406761\pi\)
0.288749 + 0.957405i \(0.406761\pi\)
\(828\) 0 0
\(829\) 44.0905 1.53133 0.765664 0.643241i \(-0.222411\pi\)
0.765664 + 0.643241i \(0.222411\pi\)
\(830\) 0 0
\(831\) 12.9144 0.447995
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −39.9768 −1.38345
\(836\) 0 0
\(837\) 82.4759 2.85078
\(838\) 0 0
\(839\) −3.41164 −0.117783 −0.0588915 0.998264i \(-0.518757\pi\)
−0.0588915 + 0.998264i \(0.518757\pi\)
\(840\) 0 0
\(841\) −14.3974 −0.496461
\(842\) 0 0
\(843\) 50.6835 1.74563
\(844\) 0 0
\(845\) −13.4972 −0.464319
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 3.43088 0.117748
\(850\) 0 0
\(851\) 29.9080 1.02523
\(852\) 0 0
\(853\) −42.9233 −1.46967 −0.734833 0.678248i \(-0.762740\pi\)
−0.734833 + 0.678248i \(0.762740\pi\)
\(854\) 0 0
\(855\) 26.1648 0.894817
\(856\) 0 0
\(857\) −5.54303 −0.189346 −0.0946731 0.995508i \(-0.530181\pi\)
−0.0946731 + 0.995508i \(0.530181\pi\)
\(858\) 0 0
\(859\) −1.55350 −0.0530049 −0.0265024 0.999649i \(-0.508437\pi\)
−0.0265024 + 0.999649i \(0.508437\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 30.7310 1.04610 0.523048 0.852303i \(-0.324795\pi\)
0.523048 + 0.852303i \(0.324795\pi\)
\(864\) 0 0
\(865\) −49.3819 −1.67904
\(866\) 0 0
\(867\) −53.6885 −1.82336
\(868\) 0 0
\(869\) −15.9698 −0.541738
\(870\) 0 0
\(871\) −32.1902 −1.09072
\(872\) 0 0
\(873\) −96.5296 −3.26703
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 36.0669 1.21789 0.608946 0.793212i \(-0.291593\pi\)
0.608946 + 0.793212i \(0.291593\pi\)
\(878\) 0 0
\(879\) 1.24135 0.0418698
\(880\) 0 0
\(881\) 8.68973 0.292764 0.146382 0.989228i \(-0.453237\pi\)
0.146382 + 0.989228i \(0.453237\pi\)
\(882\) 0 0
\(883\) −35.7617 −1.20348 −0.601738 0.798694i \(-0.705525\pi\)
−0.601738 + 0.798694i \(0.705525\pi\)
\(884\) 0 0
\(885\) 82.2894 2.76613
\(886\) 0 0
\(887\) 50.8003 1.70571 0.852853 0.522150i \(-0.174870\pi\)
0.852853 + 0.522150i \(0.174870\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 103.873 3.47988
\(892\) 0 0
\(893\) −14.2950 −0.478365
\(894\) 0 0
\(895\) −28.4472 −0.950884
\(896\) 0 0
\(897\) 47.5195 1.58663
\(898\) 0 0
\(899\) −19.7386 −0.658319
\(900\) 0 0
\(901\) −3.06930 −0.102253
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −15.9768 −0.531086
\(906\) 0 0
\(907\) 25.0711 0.832471 0.416235 0.909257i \(-0.363349\pi\)
0.416235 + 0.909257i \(0.363349\pi\)
\(908\) 0 0
\(909\) −70.8134 −2.34873
\(910\) 0 0
\(911\) 26.2558 0.869894 0.434947 0.900456i \(-0.356767\pi\)
0.434947 + 0.900456i \(0.356767\pi\)
\(912\) 0 0
\(913\) −40.3041 −1.33387
\(914\) 0 0
\(915\) 63.5117 2.09963
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 42.3342 1.39647 0.698237 0.715866i \(-0.253968\pi\)
0.698237 + 0.715866i \(0.253968\pi\)
\(920\) 0 0
\(921\) −5.36017 −0.176624
\(922\) 0 0
\(923\) −32.3470 −1.06472
\(924\) 0 0
\(925\) −28.1658 −0.926084
\(926\) 0 0
\(927\) −5.20494 −0.170953
\(928\) 0 0
\(929\) 34.4915 1.13163 0.565814 0.824533i \(-0.308562\pi\)
0.565814 + 0.824533i \(0.308562\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −23.6259 −0.773478
\(934\) 0 0
\(935\) 9.27505 0.303327
\(936\) 0 0
\(937\) 26.1040 0.852782 0.426391 0.904539i \(-0.359785\pi\)
0.426391 + 0.904539i \(0.359785\pi\)
\(938\) 0 0
\(939\) −18.1280 −0.591585
\(940\) 0 0
\(941\) −12.9381 −0.421770 −0.210885 0.977511i \(-0.567634\pi\)
−0.210885 + 0.977511i \(0.567634\pi\)
\(942\) 0 0
\(943\) 4.90605 0.159763
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −31.6880 −1.02972 −0.514861 0.857274i \(-0.672157\pi\)
−0.514861 + 0.857274i \(0.672157\pi\)
\(948\) 0 0
\(949\) −25.8275 −0.838396
\(950\) 0 0
\(951\) 95.8740 3.10893
\(952\) 0 0
\(953\) −12.5326 −0.405971 −0.202986 0.979182i \(-0.565064\pi\)
−0.202986 + 0.979182i \(0.565064\pi\)
\(954\) 0 0
\(955\) 19.7076 0.637723
\(956\) 0 0
\(957\) −45.0098 −1.45496
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −4.31906 −0.139325
\(962\) 0 0
\(963\) −113.770 −3.66618
\(964\) 0 0
\(965\) −74.4557 −2.39681
\(966\) 0 0
\(967\) −55.5778 −1.78726 −0.893630 0.448804i \(-0.851850\pi\)
−0.893630 + 0.448804i \(0.851850\pi\)
\(968\) 0 0
\(969\) 2.96038 0.0951010
\(970\) 0 0
\(971\) 17.8504 0.572847 0.286424 0.958103i \(-0.407534\pi\)
0.286424 + 0.958103i \(0.407534\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −44.7514 −1.43319
\(976\) 0 0
\(977\) −8.93281 −0.285786 −0.142893 0.989738i \(-0.545640\pi\)
−0.142893 + 0.989738i \(0.545640\pi\)
\(978\) 0 0
\(979\) 3.68152 0.117662
\(980\) 0 0
\(981\) −105.913 −3.38153
\(982\) 0 0
\(983\) −33.1246 −1.05651 −0.528256 0.849085i \(-0.677154\pi\)
−0.528256 + 0.849085i \(0.677154\pi\)
\(984\) 0 0
\(985\) −14.9659 −0.476854
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −37.2369 −1.18407
\(990\) 0 0
\(991\) 19.7747 0.628164 0.314082 0.949396i \(-0.398303\pi\)
0.314082 + 0.949396i \(0.398303\pi\)
\(992\) 0 0
\(993\) 69.7453 2.21330
\(994\) 0 0
\(995\) −61.9065 −1.96257
\(996\) 0 0
\(997\) −0.706048 −0.0223608 −0.0111804 0.999937i \(-0.503559\pi\)
−0.0111804 + 0.999937i \(0.503559\pi\)
\(998\) 0 0
\(999\) −97.3378 −3.07963
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 \(a_p\))