Properties

Label 6036.2.a.g.1.5
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.01946\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-2.01946 q^{5}\) \(-2.53250 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-2.01946 q^{5}\) \(-2.53250 q^{7}\) \(+1.00000 q^{9}\) \(+4.24449 q^{11}\) \(-2.95131 q^{13}\) \(-2.01946 q^{15}\) \(+7.86103 q^{17}\) \(-7.02817 q^{19}\) \(-2.53250 q^{21}\) \(-2.38097 q^{23}\) \(-0.921780 q^{25}\) \(+1.00000 q^{27}\) \(-0.629927 q^{29}\) \(+4.91752 q^{31}\) \(+4.24449 q^{33}\) \(+5.11428 q^{35}\) \(+1.38091 q^{37}\) \(-2.95131 q^{39}\) \(+4.74319 q^{41}\) \(-1.92065 q^{43}\) \(-2.01946 q^{45}\) \(+4.57547 q^{47}\) \(-0.586439 q^{49}\) \(+7.86103 q^{51}\) \(-5.90347 q^{53}\) \(-8.57157 q^{55}\) \(-7.02817 q^{57}\) \(+7.09876 q^{59}\) \(-11.3443 q^{61}\) \(-2.53250 q^{63}\) \(+5.96004 q^{65}\) \(+5.20369 q^{67}\) \(-2.38097 q^{69}\) \(-15.1860 q^{71}\) \(+5.38038 q^{73}\) \(-0.921780 q^{75}\) \(-10.7492 q^{77}\) \(+8.24659 q^{79}\) \(+1.00000 q^{81}\) \(-3.55142 q^{83}\) \(-15.8750 q^{85}\) \(-0.629927 q^{87}\) \(-6.50278 q^{89}\) \(+7.47418 q^{91}\) \(+4.91752 q^{93}\) \(+14.1931 q^{95}\) \(-17.5190 q^{97}\) \(+4.24449 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −2.01946 −0.903130 −0.451565 0.892238i \(-0.649134\pi\)
−0.451565 + 0.892238i \(0.649134\pi\)
\(6\) 0 0
\(7\) −2.53250 −0.957195 −0.478598 0.878034i \(-0.658855\pi\)
−0.478598 + 0.878034i \(0.658855\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.24449 1.27976 0.639881 0.768474i \(-0.278984\pi\)
0.639881 + 0.768474i \(0.278984\pi\)
\(12\) 0 0
\(13\) −2.95131 −0.818545 −0.409272 0.912412i \(-0.634217\pi\)
−0.409272 + 0.912412i \(0.634217\pi\)
\(14\) 0 0
\(15\) −2.01946 −0.521422
\(16\) 0 0
\(17\) 7.86103 1.90658 0.953290 0.302057i \(-0.0976734\pi\)
0.953290 + 0.302057i \(0.0976734\pi\)
\(18\) 0 0
\(19\) −7.02817 −1.61237 −0.806186 0.591662i \(-0.798472\pi\)
−0.806186 + 0.591662i \(0.798472\pi\)
\(20\) 0 0
\(21\) −2.53250 −0.552637
\(22\) 0 0
\(23\) −2.38097 −0.496466 −0.248233 0.968700i \(-0.579850\pi\)
−0.248233 + 0.968700i \(0.579850\pi\)
\(24\) 0 0
\(25\) −0.921780 −0.184356
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.629927 −0.116974 −0.0584872 0.998288i \(-0.518628\pi\)
−0.0584872 + 0.998288i \(0.518628\pi\)
\(30\) 0 0
\(31\) 4.91752 0.883213 0.441606 0.897209i \(-0.354409\pi\)
0.441606 + 0.897209i \(0.354409\pi\)
\(32\) 0 0
\(33\) 4.24449 0.738870
\(34\) 0 0
\(35\) 5.11428 0.864472
\(36\) 0 0
\(37\) 1.38091 0.227020 0.113510 0.993537i \(-0.463791\pi\)
0.113510 + 0.993537i \(0.463791\pi\)
\(38\) 0 0
\(39\) −2.95131 −0.472587
\(40\) 0 0
\(41\) 4.74319 0.740762 0.370381 0.928880i \(-0.379227\pi\)
0.370381 + 0.928880i \(0.379227\pi\)
\(42\) 0 0
\(43\) −1.92065 −0.292897 −0.146448 0.989218i \(-0.546784\pi\)
−0.146448 + 0.989218i \(0.546784\pi\)
\(44\) 0 0
\(45\) −2.01946 −0.301043
\(46\) 0 0
\(47\) 4.57547 0.667401 0.333701 0.942679i \(-0.391703\pi\)
0.333701 + 0.942679i \(0.391703\pi\)
\(48\) 0 0
\(49\) −0.586439 −0.0837771
\(50\) 0 0
\(51\) 7.86103 1.10076
\(52\) 0 0
\(53\) −5.90347 −0.810904 −0.405452 0.914116i \(-0.632886\pi\)
−0.405452 + 0.914116i \(0.632886\pi\)
\(54\) 0 0
\(55\) −8.57157 −1.15579
\(56\) 0 0
\(57\) −7.02817 −0.930904
\(58\) 0 0
\(59\) 7.09876 0.924179 0.462090 0.886833i \(-0.347100\pi\)
0.462090 + 0.886833i \(0.347100\pi\)
\(60\) 0 0
\(61\) −11.3443 −1.45249 −0.726243 0.687438i \(-0.758735\pi\)
−0.726243 + 0.687438i \(0.758735\pi\)
\(62\) 0 0
\(63\) −2.53250 −0.319065
\(64\) 0 0
\(65\) 5.96004 0.739253
\(66\) 0 0
\(67\) 5.20369 0.635731 0.317866 0.948136i \(-0.397034\pi\)
0.317866 + 0.948136i \(0.397034\pi\)
\(68\) 0 0
\(69\) −2.38097 −0.286635
\(70\) 0 0
\(71\) −15.1860 −1.80225 −0.901125 0.433559i \(-0.857257\pi\)
−0.901125 + 0.433559i \(0.857257\pi\)
\(72\) 0 0
\(73\) 5.38038 0.629726 0.314863 0.949137i \(-0.398041\pi\)
0.314863 + 0.949137i \(0.398041\pi\)
\(74\) 0 0
\(75\) −0.921780 −0.106438
\(76\) 0 0
\(77\) −10.7492 −1.22498
\(78\) 0 0
\(79\) 8.24659 0.927814 0.463907 0.885884i \(-0.346447\pi\)
0.463907 + 0.885884i \(0.346447\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.55142 −0.389819 −0.194909 0.980821i \(-0.562441\pi\)
−0.194909 + 0.980821i \(0.562441\pi\)
\(84\) 0 0
\(85\) −15.8750 −1.72189
\(86\) 0 0
\(87\) −0.629927 −0.0675352
\(88\) 0 0
\(89\) −6.50278 −0.689293 −0.344647 0.938732i \(-0.612001\pi\)
−0.344647 + 0.938732i \(0.612001\pi\)
\(90\) 0 0
\(91\) 7.47418 0.783507
\(92\) 0 0
\(93\) 4.91752 0.509923
\(94\) 0 0
\(95\) 14.1931 1.45618
\(96\) 0 0
\(97\) −17.5190 −1.77879 −0.889394 0.457141i \(-0.848874\pi\)
−0.889394 + 0.457141i \(0.848874\pi\)
\(98\) 0 0
\(99\) 4.24449 0.426587
\(100\) 0 0
\(101\) 2.11356 0.210307 0.105153 0.994456i \(-0.466467\pi\)
0.105153 + 0.994456i \(0.466467\pi\)
\(102\) 0 0
\(103\) −16.2304 −1.59923 −0.799613 0.600515i \(-0.794962\pi\)
−0.799613 + 0.600515i \(0.794962\pi\)
\(104\) 0 0
\(105\) 5.11428 0.499103
\(106\) 0 0
\(107\) 8.13701 0.786634 0.393317 0.919403i \(-0.371327\pi\)
0.393317 + 0.919403i \(0.371327\pi\)
\(108\) 0 0
\(109\) −9.54930 −0.914657 −0.457329 0.889298i \(-0.651194\pi\)
−0.457329 + 0.889298i \(0.651194\pi\)
\(110\) 0 0
\(111\) 1.38091 0.131070
\(112\) 0 0
\(113\) −13.0671 −1.22925 −0.614627 0.788818i \(-0.710693\pi\)
−0.614627 + 0.788818i \(0.710693\pi\)
\(114\) 0 0
\(115\) 4.80827 0.448374
\(116\) 0 0
\(117\) −2.95131 −0.272848
\(118\) 0 0
\(119\) −19.9081 −1.82497
\(120\) 0 0
\(121\) 7.01567 0.637789
\(122\) 0 0
\(123\) 4.74319 0.427679
\(124\) 0 0
\(125\) 11.9588 1.06963
\(126\) 0 0
\(127\) −5.03653 −0.446920 −0.223460 0.974713i \(-0.571735\pi\)
−0.223460 + 0.974713i \(0.571735\pi\)
\(128\) 0 0
\(129\) −1.92065 −0.169104
\(130\) 0 0
\(131\) −5.79467 −0.506283 −0.253141 0.967429i \(-0.581464\pi\)
−0.253141 + 0.967429i \(0.581464\pi\)
\(132\) 0 0
\(133\) 17.7988 1.54336
\(134\) 0 0
\(135\) −2.01946 −0.173807
\(136\) 0 0
\(137\) 6.64234 0.567494 0.283747 0.958899i \(-0.408422\pi\)
0.283747 + 0.958899i \(0.408422\pi\)
\(138\) 0 0
\(139\) 11.6369 0.987026 0.493513 0.869738i \(-0.335713\pi\)
0.493513 + 0.869738i \(0.335713\pi\)
\(140\) 0 0
\(141\) 4.57547 0.385324
\(142\) 0 0
\(143\) −12.5268 −1.04754
\(144\) 0 0
\(145\) 1.27211 0.105643
\(146\) 0 0
\(147\) −0.586439 −0.0483687
\(148\) 0 0
\(149\) 1.73821 0.142400 0.0711999 0.997462i \(-0.477317\pi\)
0.0711999 + 0.997462i \(0.477317\pi\)
\(150\) 0 0
\(151\) −15.4779 −1.25957 −0.629786 0.776769i \(-0.716858\pi\)
−0.629786 + 0.776769i \(0.716858\pi\)
\(152\) 0 0
\(153\) 7.86103 0.635526
\(154\) 0 0
\(155\) −9.93074 −0.797656
\(156\) 0 0
\(157\) 12.9643 1.03467 0.517334 0.855784i \(-0.326925\pi\)
0.517334 + 0.855784i \(0.326925\pi\)
\(158\) 0 0
\(159\) −5.90347 −0.468175
\(160\) 0 0
\(161\) 6.02980 0.475215
\(162\) 0 0
\(163\) 2.07407 0.162454 0.0812268 0.996696i \(-0.474116\pi\)
0.0812268 + 0.996696i \(0.474116\pi\)
\(164\) 0 0
\(165\) −8.57157 −0.667296
\(166\) 0 0
\(167\) −17.0029 −1.31572 −0.657861 0.753140i \(-0.728538\pi\)
−0.657861 + 0.753140i \(0.728538\pi\)
\(168\) 0 0
\(169\) −4.28980 −0.329984
\(170\) 0 0
\(171\) −7.02817 −0.537457
\(172\) 0 0
\(173\) 4.09680 0.311474 0.155737 0.987799i \(-0.450225\pi\)
0.155737 + 0.987799i \(0.450225\pi\)
\(174\) 0 0
\(175\) 2.33441 0.176465
\(176\) 0 0
\(177\) 7.09876 0.533575
\(178\) 0 0
\(179\) −16.1857 −1.20978 −0.604888 0.796311i \(-0.706782\pi\)
−0.604888 + 0.796311i \(0.706782\pi\)
\(180\) 0 0
\(181\) 8.02017 0.596134 0.298067 0.954545i \(-0.403658\pi\)
0.298067 + 0.954545i \(0.403658\pi\)
\(182\) 0 0
\(183\) −11.3443 −0.838593
\(184\) 0 0
\(185\) −2.78869 −0.205029
\(186\) 0 0
\(187\) 33.3660 2.43997
\(188\) 0 0
\(189\) −2.53250 −0.184212
\(190\) 0 0
\(191\) −0.505177 −0.0365534 −0.0182767 0.999833i \(-0.505818\pi\)
−0.0182767 + 0.999833i \(0.505818\pi\)
\(192\) 0 0
\(193\) −5.10206 −0.367254 −0.183627 0.982996i \(-0.558784\pi\)
−0.183627 + 0.982996i \(0.558784\pi\)
\(194\) 0 0
\(195\) 5.96004 0.426808
\(196\) 0 0
\(197\) 11.6387 0.829224 0.414612 0.909998i \(-0.363917\pi\)
0.414612 + 0.909998i \(0.363917\pi\)
\(198\) 0 0
\(199\) −25.0047 −1.77254 −0.886269 0.463171i \(-0.846712\pi\)
−0.886269 + 0.463171i \(0.846712\pi\)
\(200\) 0 0
\(201\) 5.20369 0.367040
\(202\) 0 0
\(203\) 1.59529 0.111967
\(204\) 0 0
\(205\) −9.57868 −0.669004
\(206\) 0 0
\(207\) −2.38097 −0.165489
\(208\) 0 0
\(209\) −29.8310 −2.06345
\(210\) 0 0
\(211\) −0.649648 −0.0447236 −0.0223618 0.999750i \(-0.507119\pi\)
−0.0223618 + 0.999750i \(0.507119\pi\)
\(212\) 0 0
\(213\) −15.1860 −1.04053
\(214\) 0 0
\(215\) 3.87868 0.264524
\(216\) 0 0
\(217\) −12.4536 −0.845407
\(218\) 0 0
\(219\) 5.38038 0.363573
\(220\) 0 0
\(221\) −23.2003 −1.56062
\(222\) 0 0
\(223\) 7.21727 0.483304 0.241652 0.970363i \(-0.422311\pi\)
0.241652 + 0.970363i \(0.422311\pi\)
\(224\) 0 0
\(225\) −0.921780 −0.0614520
\(226\) 0 0
\(227\) −19.6905 −1.30690 −0.653451 0.756969i \(-0.726680\pi\)
−0.653451 + 0.756969i \(0.726680\pi\)
\(228\) 0 0
\(229\) −7.73068 −0.510858 −0.255429 0.966828i \(-0.582217\pi\)
−0.255429 + 0.966828i \(0.582217\pi\)
\(230\) 0 0
\(231\) −10.7492 −0.707243
\(232\) 0 0
\(233\) −13.4122 −0.878659 −0.439330 0.898326i \(-0.644784\pi\)
−0.439330 + 0.898326i \(0.644784\pi\)
\(234\) 0 0
\(235\) −9.23999 −0.602750
\(236\) 0 0
\(237\) 8.24659 0.535674
\(238\) 0 0
\(239\) −9.18032 −0.593826 −0.296913 0.954905i \(-0.595957\pi\)
−0.296913 + 0.954905i \(0.595957\pi\)
\(240\) 0 0
\(241\) −4.16316 −0.268173 −0.134086 0.990970i \(-0.542810\pi\)
−0.134086 + 0.990970i \(0.542810\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.18429 0.0756616
\(246\) 0 0
\(247\) 20.7423 1.31980
\(248\) 0 0
\(249\) −3.55142 −0.225062
\(250\) 0 0
\(251\) 2.70130 0.170505 0.0852524 0.996359i \(-0.472830\pi\)
0.0852524 + 0.996359i \(0.472830\pi\)
\(252\) 0 0
\(253\) −10.1060 −0.635358
\(254\) 0 0
\(255\) −15.8750 −0.994133
\(256\) 0 0
\(257\) −21.0351 −1.31213 −0.656067 0.754703i \(-0.727781\pi\)
−0.656067 + 0.754703i \(0.727781\pi\)
\(258\) 0 0
\(259\) −3.49716 −0.217303
\(260\) 0 0
\(261\) −0.629927 −0.0389915
\(262\) 0 0
\(263\) 8.02727 0.494983 0.247491 0.968890i \(-0.420394\pi\)
0.247491 + 0.968890i \(0.420394\pi\)
\(264\) 0 0
\(265\) 11.9218 0.732352
\(266\) 0 0
\(267\) −6.50278 −0.397964
\(268\) 0 0
\(269\) −11.5170 −0.702201 −0.351101 0.936338i \(-0.614193\pi\)
−0.351101 + 0.936338i \(0.614193\pi\)
\(270\) 0 0
\(271\) 1.05095 0.0638410 0.0319205 0.999490i \(-0.489838\pi\)
0.0319205 + 0.999490i \(0.489838\pi\)
\(272\) 0 0
\(273\) 7.47418 0.452358
\(274\) 0 0
\(275\) −3.91248 −0.235932
\(276\) 0 0
\(277\) −26.6531 −1.60143 −0.800716 0.599044i \(-0.795547\pi\)
−0.800716 + 0.599044i \(0.795547\pi\)
\(278\) 0 0
\(279\) 4.91752 0.294404
\(280\) 0 0
\(281\) −15.9460 −0.951257 −0.475629 0.879646i \(-0.657779\pi\)
−0.475629 + 0.879646i \(0.657779\pi\)
\(282\) 0 0
\(283\) 4.19913 0.249612 0.124806 0.992181i \(-0.460169\pi\)
0.124806 + 0.992181i \(0.460169\pi\)
\(284\) 0 0
\(285\) 14.1931 0.840727
\(286\) 0 0
\(287\) −12.0121 −0.709054
\(288\) 0 0
\(289\) 44.7958 2.63505
\(290\) 0 0
\(291\) −17.5190 −1.02698
\(292\) 0 0
\(293\) −22.2635 −1.30065 −0.650323 0.759657i \(-0.725367\pi\)
−0.650323 + 0.759657i \(0.725367\pi\)
\(294\) 0 0
\(295\) −14.3357 −0.834654
\(296\) 0 0
\(297\) 4.24449 0.246290
\(298\) 0 0
\(299\) 7.02696 0.406380
\(300\) 0 0
\(301\) 4.86405 0.280359
\(302\) 0 0
\(303\) 2.11356 0.121421
\(304\) 0 0
\(305\) 22.9093 1.31178
\(306\) 0 0
\(307\) −12.5229 −0.714718 −0.357359 0.933967i \(-0.616323\pi\)
−0.357359 + 0.933967i \(0.616323\pi\)
\(308\) 0 0
\(309\) −16.2304 −0.923314
\(310\) 0 0
\(311\) −8.00220 −0.453763 −0.226882 0.973922i \(-0.572853\pi\)
−0.226882 + 0.973922i \(0.572853\pi\)
\(312\) 0 0
\(313\) −15.7311 −0.889173 −0.444587 0.895736i \(-0.646649\pi\)
−0.444587 + 0.895736i \(0.646649\pi\)
\(314\) 0 0
\(315\) 5.11428 0.288157
\(316\) 0 0
\(317\) 17.7878 0.999063 0.499532 0.866296i \(-0.333505\pi\)
0.499532 + 0.866296i \(0.333505\pi\)
\(318\) 0 0
\(319\) −2.67372 −0.149699
\(320\) 0 0
\(321\) 8.13701 0.454164
\(322\) 0 0
\(323\) −55.2486 −3.07412
\(324\) 0 0
\(325\) 2.72045 0.150904
\(326\) 0 0
\(327\) −9.54930 −0.528078
\(328\) 0 0
\(329\) −11.5874 −0.638834
\(330\) 0 0
\(331\) 18.4270 1.01284 0.506419 0.862288i \(-0.330969\pi\)
0.506419 + 0.862288i \(0.330969\pi\)
\(332\) 0 0
\(333\) 1.38091 0.0756734
\(334\) 0 0
\(335\) −10.5086 −0.574148
\(336\) 0 0
\(337\) 14.5829 0.794381 0.397191 0.917736i \(-0.369985\pi\)
0.397191 + 0.917736i \(0.369985\pi\)
\(338\) 0 0
\(339\) −13.0671 −0.709710
\(340\) 0 0
\(341\) 20.8724 1.13030
\(342\) 0 0
\(343\) 19.2127 1.03739
\(344\) 0 0
\(345\) 4.80827 0.258869
\(346\) 0 0
\(347\) −28.1874 −1.51318 −0.756589 0.653890i \(-0.773136\pi\)
−0.756589 + 0.653890i \(0.773136\pi\)
\(348\) 0 0
\(349\) −20.1091 −1.07642 −0.538208 0.842812i \(-0.680899\pi\)
−0.538208 + 0.842812i \(0.680899\pi\)
\(350\) 0 0
\(351\) −2.95131 −0.157529
\(352\) 0 0
\(353\) −20.8412 −1.10927 −0.554634 0.832095i \(-0.687142\pi\)
−0.554634 + 0.832095i \(0.687142\pi\)
\(354\) 0 0
\(355\) 30.6676 1.62767
\(356\) 0 0
\(357\) −19.9081 −1.05365
\(358\) 0 0
\(359\) −20.7585 −1.09559 −0.547796 0.836612i \(-0.684533\pi\)
−0.547796 + 0.836612i \(0.684533\pi\)
\(360\) 0 0
\(361\) 30.3951 1.59974
\(362\) 0 0
\(363\) 7.01567 0.368227
\(364\) 0 0
\(365\) −10.8655 −0.568725
\(366\) 0 0
\(367\) 11.2571 0.587616 0.293808 0.955864i \(-0.405077\pi\)
0.293808 + 0.955864i \(0.405077\pi\)
\(368\) 0 0
\(369\) 4.74319 0.246921
\(370\) 0 0
\(371\) 14.9505 0.776193
\(372\) 0 0
\(373\) 32.8855 1.70275 0.851373 0.524561i \(-0.175770\pi\)
0.851373 + 0.524561i \(0.175770\pi\)
\(374\) 0 0
\(375\) 11.9588 0.617550
\(376\) 0 0
\(377\) 1.85911 0.0957488
\(378\) 0 0
\(379\) 32.4684 1.66779 0.833895 0.551923i \(-0.186106\pi\)
0.833895 + 0.551923i \(0.186106\pi\)
\(380\) 0 0
\(381\) −5.03653 −0.258029
\(382\) 0 0
\(383\) 10.0388 0.512958 0.256479 0.966550i \(-0.417438\pi\)
0.256479 + 0.966550i \(0.417438\pi\)
\(384\) 0 0
\(385\) 21.7075 1.10632
\(386\) 0 0
\(387\) −1.92065 −0.0976323
\(388\) 0 0
\(389\) −0.0747660 −0.00379079 −0.00189539 0.999998i \(-0.500603\pi\)
−0.00189539 + 0.999998i \(0.500603\pi\)
\(390\) 0 0
\(391\) −18.7169 −0.946552
\(392\) 0 0
\(393\) −5.79467 −0.292302
\(394\) 0 0
\(395\) −16.6537 −0.837937
\(396\) 0 0
\(397\) −8.22255 −0.412678 −0.206339 0.978481i \(-0.566155\pi\)
−0.206339 + 0.978481i \(0.566155\pi\)
\(398\) 0 0
\(399\) 17.7988 0.891057
\(400\) 0 0
\(401\) 30.3843 1.51732 0.758661 0.651486i \(-0.225854\pi\)
0.758661 + 0.651486i \(0.225854\pi\)
\(402\) 0 0
\(403\) −14.5131 −0.722949
\(404\) 0 0
\(405\) −2.01946 −0.100348
\(406\) 0 0
\(407\) 5.86126 0.290532
\(408\) 0 0
\(409\) 11.7817 0.582568 0.291284 0.956637i \(-0.405917\pi\)
0.291284 + 0.956637i \(0.405917\pi\)
\(410\) 0 0
\(411\) 6.64234 0.327643
\(412\) 0 0
\(413\) −17.9776 −0.884620
\(414\) 0 0
\(415\) 7.17194 0.352057
\(416\) 0 0
\(417\) 11.6369 0.569860
\(418\) 0 0
\(419\) 11.3422 0.554102 0.277051 0.960855i \(-0.410643\pi\)
0.277051 + 0.960855i \(0.410643\pi\)
\(420\) 0 0
\(421\) 9.49711 0.462861 0.231430 0.972851i \(-0.425659\pi\)
0.231430 + 0.972851i \(0.425659\pi\)
\(422\) 0 0
\(423\) 4.57547 0.222467
\(424\) 0 0
\(425\) −7.24614 −0.351489
\(426\) 0 0
\(427\) 28.7294 1.39031
\(428\) 0 0
\(429\) −12.5268 −0.604799
\(430\) 0 0
\(431\) 4.48878 0.216217 0.108108 0.994139i \(-0.465521\pi\)
0.108108 + 0.994139i \(0.465521\pi\)
\(432\) 0 0
\(433\) −24.5817 −1.18132 −0.590661 0.806920i \(-0.701133\pi\)
−0.590661 + 0.806920i \(0.701133\pi\)
\(434\) 0 0
\(435\) 1.27211 0.0609931
\(436\) 0 0
\(437\) 16.7338 0.800488
\(438\) 0 0
\(439\) −30.0677 −1.43505 −0.717526 0.696532i \(-0.754725\pi\)
−0.717526 + 0.696532i \(0.754725\pi\)
\(440\) 0 0
\(441\) −0.586439 −0.0279257
\(442\) 0 0
\(443\) −6.71285 −0.318937 −0.159468 0.987203i \(-0.550978\pi\)
−0.159468 + 0.987203i \(0.550978\pi\)
\(444\) 0 0
\(445\) 13.1321 0.622522
\(446\) 0 0
\(447\) 1.73821 0.0822146
\(448\) 0 0
\(449\) −23.0759 −1.08902 −0.544509 0.838755i \(-0.683284\pi\)
−0.544509 + 0.838755i \(0.683284\pi\)
\(450\) 0 0
\(451\) 20.1324 0.947998
\(452\) 0 0
\(453\) −15.4779 −0.727214
\(454\) 0 0
\(455\) −15.0938 −0.707609
\(456\) 0 0
\(457\) −37.4921 −1.75381 −0.876904 0.480665i \(-0.840395\pi\)
−0.876904 + 0.480665i \(0.840395\pi\)
\(458\) 0 0
\(459\) 7.86103 0.366921
\(460\) 0 0
\(461\) 29.0705 1.35395 0.676973 0.736008i \(-0.263291\pi\)
0.676973 + 0.736008i \(0.263291\pi\)
\(462\) 0 0
\(463\) −8.40645 −0.390681 −0.195340 0.980736i \(-0.562581\pi\)
−0.195340 + 0.980736i \(0.562581\pi\)
\(464\) 0 0
\(465\) −9.93074 −0.460527
\(466\) 0 0
\(467\) 13.4203 0.621018 0.310509 0.950570i \(-0.399501\pi\)
0.310509 + 0.950570i \(0.399501\pi\)
\(468\) 0 0
\(469\) −13.1783 −0.608519
\(470\) 0 0
\(471\) 12.9643 0.597366
\(472\) 0 0
\(473\) −8.15219 −0.374838
\(474\) 0 0
\(475\) 6.47843 0.297251
\(476\) 0 0
\(477\) −5.90347 −0.270301
\(478\) 0 0
\(479\) −5.25266 −0.240000 −0.120000 0.992774i \(-0.538289\pi\)
−0.120000 + 0.992774i \(0.538289\pi\)
\(480\) 0 0
\(481\) −4.07549 −0.185826
\(482\) 0 0
\(483\) 6.02980 0.274366
\(484\) 0 0
\(485\) 35.3790 1.60648
\(486\) 0 0
\(487\) 20.3929 0.924092 0.462046 0.886856i \(-0.347116\pi\)
0.462046 + 0.886856i \(0.347116\pi\)
\(488\) 0 0
\(489\) 2.07407 0.0937926
\(490\) 0 0
\(491\) 9.72205 0.438750 0.219375 0.975641i \(-0.429598\pi\)
0.219375 + 0.975641i \(0.429598\pi\)
\(492\) 0 0
\(493\) −4.95187 −0.223021
\(494\) 0 0
\(495\) −8.57157 −0.385264
\(496\) 0 0
\(497\) 38.4586 1.72511
\(498\) 0 0
\(499\) 15.7348 0.704387 0.352194 0.935927i \(-0.385436\pi\)
0.352194 + 0.935927i \(0.385436\pi\)
\(500\) 0 0
\(501\) −17.0029 −0.759632
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −4.26825 −0.189935
\(506\) 0 0
\(507\) −4.28980 −0.190517
\(508\) 0 0
\(509\) −12.4472 −0.551714 −0.275857 0.961199i \(-0.588962\pi\)
−0.275857 + 0.961199i \(0.588962\pi\)
\(510\) 0 0
\(511\) −13.6258 −0.602771
\(512\) 0 0
\(513\) −7.02817 −0.310301
\(514\) 0 0
\(515\) 32.7766 1.44431
\(516\) 0 0
\(517\) 19.4205 0.854114
\(518\) 0 0
\(519\) 4.09680 0.179830
\(520\) 0 0
\(521\) 27.3762 1.19937 0.599687 0.800235i \(-0.295292\pi\)
0.599687 + 0.800235i \(0.295292\pi\)
\(522\) 0 0
\(523\) 10.0862 0.441037 0.220519 0.975383i \(-0.429225\pi\)
0.220519 + 0.975383i \(0.429225\pi\)
\(524\) 0 0
\(525\) 2.33441 0.101882
\(526\) 0 0
\(527\) 38.6568 1.68392
\(528\) 0 0
\(529\) −17.3310 −0.753521
\(530\) 0 0
\(531\) 7.09876 0.308060
\(532\) 0 0
\(533\) −13.9986 −0.606347
\(534\) 0 0
\(535\) −16.4324 −0.710433
\(536\) 0 0
\(537\) −16.1857 −0.698464
\(538\) 0 0
\(539\) −2.48913 −0.107215
\(540\) 0 0
\(541\) −16.5271 −0.710555 −0.355277 0.934761i \(-0.615614\pi\)
−0.355277 + 0.934761i \(0.615614\pi\)
\(542\) 0 0
\(543\) 8.02017 0.344178
\(544\) 0 0
\(545\) 19.2844 0.826054
\(546\) 0 0
\(547\) 4.75516 0.203316 0.101658 0.994819i \(-0.467585\pi\)
0.101658 + 0.994819i \(0.467585\pi\)
\(548\) 0 0
\(549\) −11.3443 −0.484162
\(550\) 0 0
\(551\) 4.42723 0.188606
\(552\) 0 0
\(553\) −20.8845 −0.888099
\(554\) 0 0
\(555\) −2.78869 −0.118373
\(556\) 0 0
\(557\) −38.7255 −1.64085 −0.820426 0.571753i \(-0.806264\pi\)
−0.820426 + 0.571753i \(0.806264\pi\)
\(558\) 0 0
\(559\) 5.66843 0.239749
\(560\) 0 0
\(561\) 33.3660 1.40872
\(562\) 0 0
\(563\) −13.1048 −0.552301 −0.276151 0.961114i \(-0.589059\pi\)
−0.276151 + 0.961114i \(0.589059\pi\)
\(564\) 0 0
\(565\) 26.3886 1.11018
\(566\) 0 0
\(567\) −2.53250 −0.106355
\(568\) 0 0
\(569\) −5.96578 −0.250098 −0.125049 0.992151i \(-0.539909\pi\)
−0.125049 + 0.992151i \(0.539909\pi\)
\(570\) 0 0
\(571\) 9.60891 0.402120 0.201060 0.979579i \(-0.435561\pi\)
0.201060 + 0.979579i \(0.435561\pi\)
\(572\) 0 0
\(573\) −0.505177 −0.0211041
\(574\) 0 0
\(575\) 2.19473 0.0915265
\(576\) 0 0
\(577\) −2.67626 −0.111414 −0.0557071 0.998447i \(-0.517741\pi\)
−0.0557071 + 0.998447i \(0.517741\pi\)
\(578\) 0 0
\(579\) −5.10206 −0.212034
\(580\) 0 0
\(581\) 8.99396 0.373132
\(582\) 0 0
\(583\) −25.0572 −1.03776
\(584\) 0 0
\(585\) 5.96004 0.246418
\(586\) 0 0
\(587\) 17.3459 0.715942 0.357971 0.933733i \(-0.383469\pi\)
0.357971 + 0.933733i \(0.383469\pi\)
\(588\) 0 0
\(589\) −34.5612 −1.42407
\(590\) 0 0
\(591\) 11.6387 0.478753
\(592\) 0 0
\(593\) 43.9187 1.80352 0.901762 0.432234i \(-0.142275\pi\)
0.901762 + 0.432234i \(0.142275\pi\)
\(594\) 0 0
\(595\) 40.2035 1.64818
\(596\) 0 0
\(597\) −25.0047 −1.02338
\(598\) 0 0
\(599\) 19.2550 0.786737 0.393368 0.919381i \(-0.371310\pi\)
0.393368 + 0.919381i \(0.371310\pi\)
\(600\) 0 0
\(601\) −22.9669 −0.936838 −0.468419 0.883506i \(-0.655176\pi\)
−0.468419 + 0.883506i \(0.655176\pi\)
\(602\) 0 0
\(603\) 5.20369 0.211910
\(604\) 0 0
\(605\) −14.1679 −0.576006
\(606\) 0 0
\(607\) 7.69084 0.312161 0.156081 0.987744i \(-0.450114\pi\)
0.156081 + 0.987744i \(0.450114\pi\)
\(608\) 0 0
\(609\) 1.59529 0.0646444
\(610\) 0 0
\(611\) −13.5036 −0.546298
\(612\) 0 0
\(613\) 1.95217 0.0788473 0.0394237 0.999223i \(-0.487448\pi\)
0.0394237 + 0.999223i \(0.487448\pi\)
\(614\) 0 0
\(615\) −9.57868 −0.386250
\(616\) 0 0
\(617\) 21.1141 0.850023 0.425011 0.905188i \(-0.360270\pi\)
0.425011 + 0.905188i \(0.360270\pi\)
\(618\) 0 0
\(619\) −26.4155 −1.06173 −0.530865 0.847456i \(-0.678133\pi\)
−0.530865 + 0.847456i \(0.678133\pi\)
\(620\) 0 0
\(621\) −2.38097 −0.0955450
\(622\) 0 0
\(623\) 16.4683 0.659788
\(624\) 0 0
\(625\) −19.5414 −0.781657
\(626\) 0 0
\(627\) −29.8310 −1.19133
\(628\) 0 0
\(629\) 10.8554 0.432832
\(630\) 0 0
\(631\) −27.0893 −1.07841 −0.539204 0.842175i \(-0.681275\pi\)
−0.539204 + 0.842175i \(0.681275\pi\)
\(632\) 0 0
\(633\) −0.649648 −0.0258212
\(634\) 0 0
\(635\) 10.1711 0.403626
\(636\) 0 0
\(637\) 1.73076 0.0685753
\(638\) 0 0
\(639\) −15.1860 −0.600750
\(640\) 0 0
\(641\) −44.8094 −1.76987 −0.884933 0.465719i \(-0.845796\pi\)
−0.884933 + 0.465719i \(0.845796\pi\)
\(642\) 0 0
\(643\) 40.7483 1.60695 0.803477 0.595335i \(-0.202981\pi\)
0.803477 + 0.595335i \(0.202981\pi\)
\(644\) 0 0
\(645\) 3.87868 0.152723
\(646\) 0 0
\(647\) 39.4355 1.55037 0.775184 0.631736i \(-0.217657\pi\)
0.775184 + 0.631736i \(0.217657\pi\)
\(648\) 0 0
\(649\) 30.1306 1.18273
\(650\) 0 0
\(651\) −12.4536 −0.488096
\(652\) 0 0
\(653\) −17.2143 −0.673647 −0.336824 0.941568i \(-0.609353\pi\)
−0.336824 + 0.941568i \(0.609353\pi\)
\(654\) 0 0
\(655\) 11.7021 0.457239
\(656\) 0 0
\(657\) 5.38038 0.209909
\(658\) 0 0
\(659\) 13.6754 0.532717 0.266359 0.963874i \(-0.414179\pi\)
0.266359 + 0.963874i \(0.414179\pi\)
\(660\) 0 0
\(661\) 0.396413 0.0154187 0.00770934 0.999970i \(-0.497546\pi\)
0.00770934 + 0.999970i \(0.497546\pi\)
\(662\) 0 0
\(663\) −23.2003 −0.901025
\(664\) 0 0
\(665\) −35.9441 −1.39385
\(666\) 0 0
\(667\) 1.49984 0.0580738
\(668\) 0 0
\(669\) 7.21727 0.279036
\(670\) 0 0
\(671\) −48.1507 −1.85884
\(672\) 0 0
\(673\) 14.7027 0.566747 0.283373 0.959010i \(-0.408546\pi\)
0.283373 + 0.959010i \(0.408546\pi\)
\(674\) 0 0
\(675\) −0.921780 −0.0354793
\(676\) 0 0
\(677\) 42.9339 1.65009 0.825043 0.565071i \(-0.191151\pi\)
0.825043 + 0.565071i \(0.191151\pi\)
\(678\) 0 0
\(679\) 44.3670 1.70265
\(680\) 0 0
\(681\) −19.6905 −0.754541
\(682\) 0 0
\(683\) 15.9889 0.611797 0.305899 0.952064i \(-0.401043\pi\)
0.305899 + 0.952064i \(0.401043\pi\)
\(684\) 0 0
\(685\) −13.4139 −0.512521
\(686\) 0 0
\(687\) −7.73068 −0.294944
\(688\) 0 0
\(689\) 17.4229 0.663761
\(690\) 0 0
\(691\) 10.3477 0.393645 0.196823 0.980439i \(-0.436938\pi\)
0.196823 + 0.980439i \(0.436938\pi\)
\(692\) 0 0
\(693\) −10.7492 −0.408327
\(694\) 0 0
\(695\) −23.5002 −0.891413
\(696\) 0 0
\(697\) 37.2863 1.41232
\(698\) 0 0
\(699\) −13.4122 −0.507294
\(700\) 0 0
\(701\) 0.407304 0.0153837 0.00769183 0.999970i \(-0.497552\pi\)
0.00769183 + 0.999970i \(0.497552\pi\)
\(702\) 0 0
\(703\) −9.70527 −0.366041
\(704\) 0 0
\(705\) −9.23999 −0.347998
\(706\) 0 0
\(707\) −5.35259 −0.201305
\(708\) 0 0
\(709\) −15.7842 −0.592789 −0.296394 0.955066i \(-0.595784\pi\)
−0.296394 + 0.955066i \(0.595784\pi\)
\(710\) 0 0
\(711\) 8.24659 0.309271
\(712\) 0 0
\(713\) −11.7085 −0.438485
\(714\) 0 0
\(715\) 25.2973 0.946067
\(716\) 0 0
\(717\) −9.18032 −0.342845
\(718\) 0 0
\(719\) −32.6429 −1.21737 −0.608687 0.793410i \(-0.708303\pi\)
−0.608687 + 0.793410i \(0.708303\pi\)
\(720\) 0 0
\(721\) 41.1035 1.53077
\(722\) 0 0
\(723\) −4.16316 −0.154830
\(724\) 0 0
\(725\) 0.580654 0.0215649
\(726\) 0 0
\(727\) 17.9242 0.664770 0.332385 0.943144i \(-0.392147\pi\)
0.332385 + 0.943144i \(0.392147\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −15.0983 −0.558431
\(732\) 0 0
\(733\) 5.28982 0.195384 0.0976920 0.995217i \(-0.468854\pi\)
0.0976920 + 0.995217i \(0.468854\pi\)
\(734\) 0 0
\(735\) 1.18429 0.0436832
\(736\) 0 0
\(737\) 22.0870 0.813584
\(738\) 0 0
\(739\) 43.9774 1.61773 0.808867 0.587992i \(-0.200081\pi\)
0.808867 + 0.587992i \(0.200081\pi\)
\(740\) 0 0
\(741\) 20.7423 0.761986
\(742\) 0 0
\(743\) 35.0566 1.28610 0.643050 0.765824i \(-0.277669\pi\)
0.643050 + 0.765824i \(0.277669\pi\)
\(744\) 0 0
\(745\) −3.51025 −0.128606
\(746\) 0 0
\(747\) −3.55142 −0.129940
\(748\) 0 0
\(749\) −20.6070 −0.752963
\(750\) 0 0
\(751\) 39.6506 1.44687 0.723436 0.690392i \(-0.242562\pi\)
0.723436 + 0.690392i \(0.242562\pi\)
\(752\) 0 0
\(753\) 2.70130 0.0984410
\(754\) 0 0
\(755\) 31.2570 1.13756
\(756\) 0 0
\(757\) −15.5005 −0.563374 −0.281687 0.959506i \(-0.590894\pi\)
−0.281687 + 0.959506i \(0.590894\pi\)
\(758\) 0 0
\(759\) −10.1060 −0.366824
\(760\) 0 0
\(761\) −3.67337 −0.133159 −0.0665797 0.997781i \(-0.521209\pi\)
−0.0665797 + 0.997781i \(0.521209\pi\)
\(762\) 0 0
\(763\) 24.1836 0.875506
\(764\) 0 0
\(765\) −15.8750 −0.573963
\(766\) 0 0
\(767\) −20.9506 −0.756482
\(768\) 0 0
\(769\) 28.4920 1.02745 0.513723 0.857956i \(-0.328266\pi\)
0.513723 + 0.857956i \(0.328266\pi\)
\(770\) 0 0
\(771\) −21.0351 −0.757561
\(772\) 0 0
\(773\) 15.6900 0.564331 0.282165 0.959366i \(-0.408947\pi\)
0.282165 + 0.959366i \(0.408947\pi\)
\(774\) 0 0
\(775\) −4.53287 −0.162826
\(776\) 0 0
\(777\) −3.49716 −0.125460
\(778\) 0 0
\(779\) −33.3359 −1.19438
\(780\) 0 0
\(781\) −64.4569 −2.30645
\(782\) 0 0
\(783\) −0.629927 −0.0225117
\(784\) 0 0
\(785\) −26.1810 −0.934439
\(786\) 0 0
\(787\) 21.7844 0.776531 0.388265 0.921548i \(-0.373074\pi\)
0.388265 + 0.921548i \(0.373074\pi\)
\(788\) 0 0
\(789\) 8.02727 0.285779
\(790\) 0 0
\(791\) 33.0926 1.17664
\(792\) 0 0
\(793\) 33.4804 1.18893
\(794\) 0 0
\(795\) 11.9218 0.422823
\(796\) 0 0
\(797\) 48.2495 1.70908 0.854542 0.519382i \(-0.173838\pi\)
0.854542 + 0.519382i \(0.173838\pi\)
\(798\) 0 0
\(799\) 35.9679 1.27245
\(800\) 0 0
\(801\) −6.50278 −0.229764
\(802\) 0 0
\(803\) 22.8370 0.805899
\(804\) 0 0
\(805\) −12.1769 −0.429181
\(806\) 0 0
\(807\) −11.5170 −0.405416
\(808\) 0 0
\(809\) 38.6407 1.35854 0.679268 0.733891i \(-0.262298\pi\)
0.679268 + 0.733891i \(0.262298\pi\)
\(810\) 0 0
\(811\) −36.2377 −1.27248 −0.636239 0.771492i \(-0.719511\pi\)
−0.636239 + 0.771492i \(0.719511\pi\)
\(812\) 0 0
\(813\) 1.05095 0.0368586
\(814\) 0 0
\(815\) −4.18850 −0.146717
\(816\) 0 0
\(817\) 13.4987 0.472259
\(818\) 0 0
\(819\) 7.47418 0.261169
\(820\) 0 0
\(821\) −29.8347 −1.04124 −0.520618 0.853789i \(-0.674299\pi\)
−0.520618 + 0.853789i \(0.674299\pi\)
\(822\) 0 0
\(823\) −12.5527 −0.437560 −0.218780 0.975774i \(-0.570208\pi\)
−0.218780 + 0.975774i \(0.570208\pi\)
\(824\) 0 0
\(825\) −3.91248 −0.136215
\(826\) 0 0
\(827\) 16.4591 0.572340 0.286170 0.958179i \(-0.407618\pi\)
0.286170 + 0.958179i \(0.407618\pi\)
\(828\) 0 0
\(829\) −47.9337 −1.66481 −0.832404 0.554169i \(-0.813036\pi\)
−0.832404 + 0.554169i \(0.813036\pi\)
\(830\) 0 0
\(831\) −26.6531 −0.924587
\(832\) 0 0
\(833\) −4.61002 −0.159728
\(834\) 0 0
\(835\) 34.3366 1.18827
\(836\) 0 0
\(837\) 4.91752 0.169974
\(838\) 0 0
\(839\) −25.9577 −0.896159 −0.448079 0.893994i \(-0.647892\pi\)
−0.448079 + 0.893994i \(0.647892\pi\)
\(840\) 0 0
\(841\) −28.6032 −0.986317
\(842\) 0 0
\(843\) −15.9460 −0.549209
\(844\) 0 0
\(845\) 8.66307 0.298019
\(846\) 0 0
\(847\) −17.7672 −0.610488
\(848\) 0 0
\(849\) 4.19913 0.144114
\(850\) 0 0
\(851\) −3.28790 −0.112708
\(852\) 0 0
\(853\) −39.3407 −1.34700 −0.673500 0.739187i \(-0.735210\pi\)
−0.673500 + 0.739187i \(0.735210\pi\)
\(854\) 0 0
\(855\) 14.1931 0.485394
\(856\) 0 0
\(857\) −24.9662 −0.852830 −0.426415 0.904528i \(-0.640224\pi\)
−0.426415 + 0.904528i \(0.640224\pi\)
\(858\) 0 0
\(859\) 10.6182 0.362287 0.181144 0.983457i \(-0.442020\pi\)
0.181144 + 0.983457i \(0.442020\pi\)
\(860\) 0 0
\(861\) −12.0121 −0.409372
\(862\) 0 0
\(863\) −19.3732 −0.659470 −0.329735 0.944073i \(-0.606959\pi\)
−0.329735 + 0.944073i \(0.606959\pi\)
\(864\) 0 0
\(865\) −8.27333 −0.281302
\(866\) 0 0
\(867\) 44.7958 1.52134
\(868\) 0 0
\(869\) 35.0025 1.18738
\(870\) 0 0
\(871\) −15.3577 −0.520375
\(872\) 0 0
\(873\) −17.5190 −0.592930
\(874\) 0 0
\(875\) −30.2857 −1.02384
\(876\) 0 0
\(877\) −11.9970 −0.405110 −0.202555 0.979271i \(-0.564924\pi\)
−0.202555 + 0.979271i \(0.564924\pi\)
\(878\) 0 0
\(879\) −22.2635 −0.750929
\(880\) 0 0
\(881\) 8.86347 0.298618 0.149309 0.988791i \(-0.452295\pi\)
0.149309 + 0.988791i \(0.452295\pi\)
\(882\) 0 0
\(883\) 40.5950 1.36613 0.683065 0.730358i \(-0.260647\pi\)
0.683065 + 0.730358i \(0.260647\pi\)
\(884\) 0 0
\(885\) −14.3357 −0.481888
\(886\) 0 0
\(887\) 1.46229 0.0490988 0.0245494 0.999699i \(-0.492185\pi\)
0.0245494 + 0.999699i \(0.492185\pi\)
\(888\) 0 0
\(889\) 12.7550 0.427789
\(890\) 0 0
\(891\) 4.24449 0.142196
\(892\) 0 0
\(893\) −32.1572 −1.07610
\(894\) 0 0
\(895\) 32.6864 1.09258
\(896\) 0 0
\(897\) 7.02696 0.234624
\(898\) 0 0
\(899\) −3.09768 −0.103313
\(900\) 0 0
\(901\) −46.4073 −1.54605
\(902\) 0 0
\(903\) 4.86405 0.161866
\(904\) 0 0
\(905\) −16.1964 −0.538387
\(906\) 0 0
\(907\) −23.9893 −0.796551 −0.398276 0.917266i \(-0.630391\pi\)
−0.398276 + 0.917266i \(0.630391\pi\)
\(908\) 0 0
\(909\) 2.11356 0.0701023
\(910\) 0 0
\(911\) 9.33223 0.309191 0.154595 0.987978i \(-0.450593\pi\)
0.154595 + 0.987978i \(0.450593\pi\)
\(912\) 0 0
\(913\) −15.0739 −0.498875
\(914\) 0 0
\(915\) 22.9093 0.757359
\(916\) 0 0
\(917\) 14.6750 0.484611
\(918\) 0 0
\(919\) −16.3333 −0.538787 −0.269394 0.963030i \(-0.586823\pi\)
−0.269394 + 0.963030i \(0.586823\pi\)
\(920\) 0 0
\(921\) −12.5229 −0.412642
\(922\) 0 0
\(923\) 44.8186 1.47522
\(924\) 0 0
\(925\) −1.27290 −0.0418526
\(926\) 0 0
\(927\) −16.2304 −0.533076
\(928\) 0 0
\(929\) 48.1109 1.57847 0.789233 0.614093i \(-0.210478\pi\)
0.789233 + 0.614093i \(0.210478\pi\)
\(930\) 0 0
\(931\) 4.12159 0.135080
\(932\) 0 0
\(933\) −8.00220 −0.261980
\(934\) 0 0
\(935\) −67.3814 −2.20361
\(936\) 0 0
\(937\) 10.7224 0.350285 0.175142 0.984543i \(-0.443961\pi\)
0.175142 + 0.984543i \(0.443961\pi\)
\(938\) 0 0
\(939\) −15.7311 −0.513364
\(940\) 0 0
\(941\) 22.6505 0.738386 0.369193 0.929353i \(-0.379634\pi\)
0.369193 + 0.929353i \(0.379634\pi\)
\(942\) 0 0
\(943\) −11.2934 −0.367763
\(944\) 0 0
\(945\) 5.11428 0.166368
\(946\) 0 0
\(947\) −55.7265 −1.81087 −0.905434 0.424486i \(-0.860455\pi\)
−0.905434 + 0.424486i \(0.860455\pi\)
\(948\) 0 0
\(949\) −15.8792 −0.515459
\(950\) 0 0
\(951\) 17.7878 0.576809
\(952\) 0 0
\(953\) 4.80440 0.155630 0.0778150 0.996968i \(-0.475206\pi\)
0.0778150 + 0.996968i \(0.475206\pi\)
\(954\) 0 0
\(955\) 1.02019 0.0330124
\(956\) 0 0
\(957\) −2.67372 −0.0864289
\(958\) 0 0
\(959\) −16.8217 −0.543202
\(960\) 0 0
\(961\) −6.81800 −0.219935
\(962\) 0 0
\(963\) 8.13701 0.262211
\(964\) 0 0
\(965\) 10.3034 0.331678
\(966\) 0 0
\(967\) 8.55364 0.275067 0.137533 0.990497i \(-0.456083\pi\)
0.137533 + 0.990497i \(0.456083\pi\)
\(968\) 0 0
\(969\) −55.2486 −1.77484
\(970\) 0 0
\(971\) −24.0553 −0.771973 −0.385986 0.922504i \(-0.626139\pi\)
−0.385986 + 0.922504i \(0.626139\pi\)
\(972\) 0 0
\(973\) −29.4704 −0.944777
\(974\) 0 0
\(975\) 2.72045 0.0871243
\(976\) 0 0
\(977\) −18.4717 −0.590961 −0.295480 0.955349i \(-0.595480\pi\)
−0.295480 + 0.955349i \(0.595480\pi\)
\(978\) 0 0
\(979\) −27.6010 −0.882131
\(980\) 0 0
\(981\) −9.54930 −0.304886
\(982\) 0 0
\(983\) 9.68346 0.308855 0.154427 0.988004i \(-0.450647\pi\)
0.154427 + 0.988004i \(0.450647\pi\)
\(984\) 0 0
\(985\) −23.5039 −0.748897
\(986\) 0 0
\(987\) −11.5874 −0.368831
\(988\) 0 0
\(989\) 4.57301 0.145413
\(990\) 0 0
\(991\) 21.0292 0.668015 0.334007 0.942570i \(-0.391599\pi\)
0.334007 + 0.942570i \(0.391599\pi\)
\(992\) 0 0
\(993\) 18.4270 0.584762
\(994\) 0 0
\(995\) 50.4961 1.60083
\(996\) 0 0
\(997\) 16.5281 0.523452 0.261726 0.965142i \(-0.415708\pi\)
0.261726 + 0.965142i \(0.415708\pi\)
\(998\) 0 0
\(999\) 1.38091 0.0436901
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 \(a_p\))