Properties

Label 6004.2.a.d.1.4
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.654712\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.654712 q^{5}\) \(-2.24646 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.654712 q^{5}\) \(-2.24646 q^{7}\) \(-3.00000 q^{9}\) \(+4.24164 q^{11}\) \(-4.30857 q^{13}\) \(-4.04162 q^{17}\) \(+1.00000 q^{19}\) \(-2.93647 q^{23}\) \(-4.57135 q^{25}\) \(+1.01990 q^{29}\) \(+8.52340 q^{31}\) \(+1.47078 q^{35}\) \(-8.68866 q^{37}\) \(-9.95657 q^{41}\) \(+4.61782 q^{43}\) \(+1.96414 q^{45}\) \(+9.53741 q^{47}\) \(-1.95344 q^{49}\) \(+3.71778 q^{53}\) \(-2.77705 q^{55}\) \(+0.335151 q^{59}\) \(+7.24078 q^{61}\) \(+6.73937 q^{63}\) \(+2.82087 q^{65}\) \(+0.613087 q^{67}\) \(+7.70518 q^{71}\) \(+1.41742 q^{73}\) \(-9.52866 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(-11.5845 q^{83}\) \(+2.64610 q^{85}\) \(-2.60392 q^{89}\) \(+9.67900 q^{91}\) \(-0.654712 q^{95}\) \(+12.5210 q^{97}\) \(-12.7249 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −0.654712 −0.292796 −0.146398 0.989226i \(-0.546768\pi\)
−0.146398 + 0.989226i \(0.546768\pi\)
\(6\) 0 0
\(7\) −2.24646 −0.849081 −0.424540 0.905409i \(-0.639564\pi\)
−0.424540 + 0.905409i \(0.639564\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 4.24164 1.27890 0.639452 0.768831i \(-0.279161\pi\)
0.639452 + 0.768831i \(0.279161\pi\)
\(12\) 0 0
\(13\) −4.30857 −1.19498 −0.597491 0.801876i \(-0.703835\pi\)
−0.597491 + 0.801876i \(0.703835\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.04162 −0.980238 −0.490119 0.871656i \(-0.663047\pi\)
−0.490119 + 0.871656i \(0.663047\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.93647 −0.612295 −0.306148 0.951984i \(-0.599040\pi\)
−0.306148 + 0.951984i \(0.599040\pi\)
\(24\) 0 0
\(25\) −4.57135 −0.914270
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.01990 0.189390 0.0946952 0.995506i \(-0.469812\pi\)
0.0946952 + 0.995506i \(0.469812\pi\)
\(30\) 0 0
\(31\) 8.52340 1.53085 0.765423 0.643527i \(-0.222530\pi\)
0.765423 + 0.643527i \(0.222530\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.47078 0.248608
\(36\) 0 0
\(37\) −8.68866 −1.42841 −0.714203 0.699938i \(-0.753211\pi\)
−0.714203 + 0.699938i \(0.753211\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.95657 −1.55495 −0.777477 0.628911i \(-0.783501\pi\)
−0.777477 + 0.628911i \(0.783501\pi\)
\(42\) 0 0
\(43\) 4.61782 0.704212 0.352106 0.935960i \(-0.385466\pi\)
0.352106 + 0.935960i \(0.385466\pi\)
\(44\) 0 0
\(45\) 1.96414 0.292796
\(46\) 0 0
\(47\) 9.53741 1.39117 0.695587 0.718442i \(-0.255144\pi\)
0.695587 + 0.718442i \(0.255144\pi\)
\(48\) 0 0
\(49\) −1.95344 −0.279062
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.71778 0.510677 0.255338 0.966852i \(-0.417813\pi\)
0.255338 + 0.966852i \(0.417813\pi\)
\(54\) 0 0
\(55\) −2.77705 −0.374458
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.335151 0.0436329 0.0218164 0.999762i \(-0.493055\pi\)
0.0218164 + 0.999762i \(0.493055\pi\)
\(60\) 0 0
\(61\) 7.24078 0.927087 0.463544 0.886074i \(-0.346578\pi\)
0.463544 + 0.886074i \(0.346578\pi\)
\(62\) 0 0
\(63\) 6.73937 0.849081
\(64\) 0 0
\(65\) 2.82087 0.349886
\(66\) 0 0
\(67\) 0.613087 0.0749005 0.0374503 0.999298i \(-0.488076\pi\)
0.0374503 + 0.999298i \(0.488076\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.70518 0.914436 0.457218 0.889355i \(-0.348846\pi\)
0.457218 + 0.889355i \(0.348846\pi\)
\(72\) 0 0
\(73\) 1.41742 0.165897 0.0829483 0.996554i \(-0.473566\pi\)
0.0829483 + 0.996554i \(0.473566\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.52866 −1.08589
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −11.5845 −1.27157 −0.635784 0.771867i \(-0.719323\pi\)
−0.635784 + 0.771867i \(0.719323\pi\)
\(84\) 0 0
\(85\) 2.64610 0.287010
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.60392 −0.276015 −0.138007 0.990431i \(-0.544070\pi\)
−0.138007 + 0.990431i \(0.544070\pi\)
\(90\) 0 0
\(91\) 9.67900 1.01464
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.654712 −0.0671721
\(96\) 0 0
\(97\) 12.5210 1.27132 0.635658 0.771971i \(-0.280729\pi\)
0.635658 + 0.771971i \(0.280729\pi\)
\(98\) 0 0
\(99\) −12.7249 −1.27890
\(100\) 0 0
\(101\) −11.2322 −1.11765 −0.558823 0.829287i \(-0.688747\pi\)
−0.558823 + 0.829287i \(0.688747\pi\)
\(102\) 0 0
\(103\) −13.7998 −1.35974 −0.679869 0.733334i \(-0.737963\pi\)
−0.679869 + 0.733334i \(0.737963\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18.8460 1.82191 0.910957 0.412502i \(-0.135345\pi\)
0.910957 + 0.412502i \(0.135345\pi\)
\(108\) 0 0
\(109\) −3.40673 −0.326305 −0.163153 0.986601i \(-0.552166\pi\)
−0.163153 + 0.986601i \(0.552166\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.77958 −0.261481 −0.130741 0.991417i \(-0.541736\pi\)
−0.130741 + 0.991417i \(0.541736\pi\)
\(114\) 0 0
\(115\) 1.92254 0.179278
\(116\) 0 0
\(117\) 12.9257 1.19498
\(118\) 0 0
\(119\) 9.07933 0.832301
\(120\) 0 0
\(121\) 6.99153 0.635593
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.26648 0.560491
\(126\) 0 0
\(127\) 14.2202 1.26184 0.630919 0.775849i \(-0.282678\pi\)
0.630919 + 0.775849i \(0.282678\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.83012 −0.684120 −0.342060 0.939678i \(-0.611125\pi\)
−0.342060 + 0.939678i \(0.611125\pi\)
\(132\) 0 0
\(133\) −2.24646 −0.194792
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.8506 1.26877 0.634387 0.773015i \(-0.281253\pi\)
0.634387 + 0.773015i \(0.281253\pi\)
\(138\) 0 0
\(139\) 14.4740 1.22767 0.613835 0.789434i \(-0.289626\pi\)
0.613835 + 0.789434i \(0.289626\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −18.2754 −1.52827
\(144\) 0 0
\(145\) −0.667740 −0.0554528
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.65984 −0.217903 −0.108951 0.994047i \(-0.534749\pi\)
−0.108951 + 0.994047i \(0.534749\pi\)
\(150\) 0 0
\(151\) −0.0897947 −0.00730739 −0.00365369 0.999993i \(-0.501163\pi\)
−0.00365369 + 0.999993i \(0.501163\pi\)
\(152\) 0 0
\(153\) 12.1249 0.980238
\(154\) 0 0
\(155\) −5.58037 −0.448226
\(156\) 0 0
\(157\) 1.84399 0.147167 0.0735833 0.997289i \(-0.476557\pi\)
0.0735833 + 0.997289i \(0.476557\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.59664 0.519888
\(162\) 0 0
\(163\) 24.2171 1.89683 0.948416 0.317029i \(-0.102685\pi\)
0.948416 + 0.317029i \(0.102685\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.8406 −1.53531 −0.767656 0.640862i \(-0.778577\pi\)
−0.767656 + 0.640862i \(0.778577\pi\)
\(168\) 0 0
\(169\) 5.56374 0.427980
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) 0.939402 0.0714214 0.0357107 0.999362i \(-0.488631\pi\)
0.0357107 + 0.999362i \(0.488631\pi\)
\(174\) 0 0
\(175\) 10.2693 0.776289
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 25.9496 1.93957 0.969783 0.243967i \(-0.0784490\pi\)
0.969783 + 0.243967i \(0.0784490\pi\)
\(180\) 0 0
\(181\) 15.5410 1.15515 0.577577 0.816336i \(-0.303998\pi\)
0.577577 + 0.816336i \(0.303998\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.68857 0.418232
\(186\) 0 0
\(187\) −17.1431 −1.25363
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −21.9972 −1.59166 −0.795832 0.605518i \(-0.792966\pi\)
−0.795832 + 0.605518i \(0.792966\pi\)
\(192\) 0 0
\(193\) −25.9817 −1.87020 −0.935101 0.354380i \(-0.884692\pi\)
−0.935101 + 0.354380i \(0.884692\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.7465 1.05065 0.525323 0.850903i \(-0.323944\pi\)
0.525323 + 0.850903i \(0.323944\pi\)
\(198\) 0 0
\(199\) −18.1910 −1.28952 −0.644761 0.764384i \(-0.723043\pi\)
−0.644761 + 0.764384i \(0.723043\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.29116 −0.160808
\(204\) 0 0
\(205\) 6.51869 0.455285
\(206\) 0 0
\(207\) 8.80940 0.612295
\(208\) 0 0
\(209\) 4.24164 0.293401
\(210\) 0 0
\(211\) 8.74717 0.602180 0.301090 0.953596i \(-0.402650\pi\)
0.301090 + 0.953596i \(0.402650\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.02335 −0.206190
\(216\) 0 0
\(217\) −19.1474 −1.29981
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.4136 1.17137
\(222\) 0 0
\(223\) −13.3996 −0.897304 −0.448652 0.893707i \(-0.648096\pi\)
−0.448652 + 0.893707i \(0.648096\pi\)
\(224\) 0 0
\(225\) 13.7141 0.914270
\(226\) 0 0
\(227\) 9.52766 0.632373 0.316187 0.948697i \(-0.397597\pi\)
0.316187 + 0.948697i \(0.397597\pi\)
\(228\) 0 0
\(229\) 27.6995 1.83044 0.915219 0.402957i \(-0.132018\pi\)
0.915219 + 0.402957i \(0.132018\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −14.8803 −0.974843 −0.487422 0.873167i \(-0.662062\pi\)
−0.487422 + 0.873167i \(0.662062\pi\)
\(234\) 0 0
\(235\) −6.24426 −0.407331
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 25.4292 1.64488 0.822440 0.568851i \(-0.192612\pi\)
0.822440 + 0.568851i \(0.192612\pi\)
\(240\) 0 0
\(241\) 4.08684 0.263257 0.131628 0.991299i \(-0.457979\pi\)
0.131628 + 0.991299i \(0.457979\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.27894 0.0817084
\(246\) 0 0
\(247\) −4.30857 −0.274147
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.7598 0.742271 0.371135 0.928579i \(-0.378969\pi\)
0.371135 + 0.928579i \(0.378969\pi\)
\(252\) 0 0
\(253\) −12.4554 −0.783067
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.66944 −0.416028 −0.208014 0.978126i \(-0.566700\pi\)
−0.208014 + 0.978126i \(0.566700\pi\)
\(258\) 0 0
\(259\) 19.5187 1.21283
\(260\) 0 0
\(261\) −3.05970 −0.189390
\(262\) 0 0
\(263\) 6.90137 0.425557 0.212778 0.977100i \(-0.431749\pi\)
0.212778 + 0.977100i \(0.431749\pi\)
\(264\) 0 0
\(265\) −2.43408 −0.149524
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.2177 1.11075 0.555376 0.831599i \(-0.312574\pi\)
0.555376 + 0.831599i \(0.312574\pi\)
\(270\) 0 0
\(271\) 21.6723 1.31650 0.658249 0.752800i \(-0.271297\pi\)
0.658249 + 0.752800i \(0.271297\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −19.3900 −1.16926
\(276\) 0 0
\(277\) 28.5581 1.71589 0.857945 0.513741i \(-0.171741\pi\)
0.857945 + 0.513741i \(0.171741\pi\)
\(278\) 0 0
\(279\) −25.5702 −1.53085
\(280\) 0 0
\(281\) 11.2279 0.669802 0.334901 0.942253i \(-0.391297\pi\)
0.334901 + 0.942253i \(0.391297\pi\)
\(282\) 0 0
\(283\) −4.31615 −0.256569 −0.128284 0.991737i \(-0.540947\pi\)
−0.128284 + 0.991737i \(0.540947\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 22.3670 1.32028
\(288\) 0 0
\(289\) −0.665267 −0.0391334
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.1197 0.941722 0.470861 0.882207i \(-0.343943\pi\)
0.470861 + 0.882207i \(0.343943\pi\)
\(294\) 0 0
\(295\) −0.219427 −0.0127755
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.6520 0.731681
\(300\) 0 0
\(301\) −10.3737 −0.597932
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.74063 −0.271448
\(306\) 0 0
\(307\) 24.6540 1.40708 0.703540 0.710656i \(-0.251602\pi\)
0.703540 + 0.710656i \(0.251602\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.07763 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(312\) 0 0
\(313\) −25.4576 −1.43895 −0.719473 0.694520i \(-0.755617\pi\)
−0.719473 + 0.694520i \(0.755617\pi\)
\(314\) 0 0
\(315\) −4.41235 −0.248608
\(316\) 0 0
\(317\) −29.4618 −1.65474 −0.827368 0.561659i \(-0.810163\pi\)
−0.827368 + 0.561659i \(0.810163\pi\)
\(318\) 0 0
\(319\) 4.32605 0.242212
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.04162 −0.224882
\(324\) 0 0
\(325\) 19.6960 1.09254
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −21.4254 −1.18122
\(330\) 0 0
\(331\) −24.4189 −1.34218 −0.671091 0.741375i \(-0.734174\pi\)
−0.671091 + 0.741375i \(0.734174\pi\)
\(332\) 0 0
\(333\) 26.0660 1.42841
\(334\) 0 0
\(335\) −0.401396 −0.0219306
\(336\) 0 0
\(337\) 20.8581 1.13621 0.568106 0.822956i \(-0.307677\pi\)
0.568106 + 0.822956i \(0.307677\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 36.1532 1.95781
\(342\) 0 0
\(343\) 20.1135 1.08603
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −27.6997 −1.48700 −0.743498 0.668738i \(-0.766835\pi\)
−0.743498 + 0.668738i \(0.766835\pi\)
\(348\) 0 0
\(349\) 23.5168 1.25882 0.629412 0.777072i \(-0.283296\pi\)
0.629412 + 0.777072i \(0.283296\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −20.4581 −1.08888 −0.544438 0.838801i \(-0.683257\pi\)
−0.544438 + 0.838801i \(0.683257\pi\)
\(354\) 0 0
\(355\) −5.04467 −0.267743
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.37845 −0.0727516 −0.0363758 0.999338i \(-0.511581\pi\)
−0.0363758 + 0.999338i \(0.511581\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.928003 −0.0485739
\(366\) 0 0
\(367\) 21.1590 1.10449 0.552247 0.833681i \(-0.313771\pi\)
0.552247 + 0.833681i \(0.313771\pi\)
\(368\) 0 0
\(369\) 29.8697 1.55495
\(370\) 0 0
\(371\) −8.35183 −0.433606
\(372\) 0 0
\(373\) 7.83107 0.405478 0.202739 0.979233i \(-0.435016\pi\)
0.202739 + 0.979233i \(0.435016\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.39430 −0.226318
\(378\) 0 0
\(379\) 14.3241 0.735780 0.367890 0.929869i \(-0.380080\pi\)
0.367890 + 0.929869i \(0.380080\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.13902 0.211494 0.105747 0.994393i \(-0.466277\pi\)
0.105747 + 0.994393i \(0.466277\pi\)
\(384\) 0 0
\(385\) 6.23853 0.317945
\(386\) 0 0
\(387\) −13.8535 −0.704212
\(388\) 0 0
\(389\) 4.24401 0.215180 0.107590 0.994195i \(-0.465687\pi\)
0.107590 + 0.994195i \(0.465687\pi\)
\(390\) 0 0
\(391\) 11.8681 0.600195
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −0.654712 −0.0329421
\(396\) 0 0
\(397\) −7.15641 −0.359170 −0.179585 0.983742i \(-0.557475\pi\)
−0.179585 + 0.983742i \(0.557475\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.1289 −0.555750 −0.277875 0.960617i \(-0.589630\pi\)
−0.277875 + 0.960617i \(0.589630\pi\)
\(402\) 0 0
\(403\) −36.7236 −1.82933
\(404\) 0 0
\(405\) −5.89241 −0.292796
\(406\) 0 0
\(407\) −36.8542 −1.82679
\(408\) 0 0
\(409\) −6.43950 −0.318413 −0.159207 0.987245i \(-0.550894\pi\)
−0.159207 + 0.987245i \(0.550894\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.752901 −0.0370478
\(414\) 0 0
\(415\) 7.58454 0.372310
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 21.4052 1.04571 0.522857 0.852420i \(-0.324866\pi\)
0.522857 + 0.852420i \(0.324866\pi\)
\(420\) 0 0
\(421\) −32.7376 −1.59553 −0.797767 0.602966i \(-0.793985\pi\)
−0.797767 + 0.602966i \(0.793985\pi\)
\(422\) 0 0
\(423\) −28.6122 −1.39117
\(424\) 0 0
\(425\) 18.4757 0.896203
\(426\) 0 0
\(427\) −16.2661 −0.787172
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.5888 1.32891 0.664454 0.747329i \(-0.268664\pi\)
0.664454 + 0.747329i \(0.268664\pi\)
\(432\) 0 0
\(433\) −24.5252 −1.17861 −0.589304 0.807911i \(-0.700598\pi\)
−0.589304 + 0.807911i \(0.700598\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.93647 −0.140470
\(438\) 0 0
\(439\) 2.62412 0.125242 0.0626212 0.998037i \(-0.480054\pi\)
0.0626212 + 0.998037i \(0.480054\pi\)
\(440\) 0 0
\(441\) 5.86031 0.279062
\(442\) 0 0
\(443\) −24.6048 −1.16901 −0.584506 0.811390i \(-0.698712\pi\)
−0.584506 + 0.811390i \(0.698712\pi\)
\(444\) 0 0
\(445\) 1.70482 0.0808161
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −19.7548 −0.932286 −0.466143 0.884709i \(-0.654357\pi\)
−0.466143 + 0.884709i \(0.654357\pi\)
\(450\) 0 0
\(451\) −42.2322 −1.98864
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.33696 −0.297081
\(456\) 0 0
\(457\) 23.7733 1.11207 0.556035 0.831159i \(-0.312322\pi\)
0.556035 + 0.831159i \(0.312322\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 29.8445 1.39000 0.694998 0.719011i \(-0.255405\pi\)
0.694998 + 0.719011i \(0.255405\pi\)
\(462\) 0 0
\(463\) −4.38127 −0.203615 −0.101808 0.994804i \(-0.532463\pi\)
−0.101808 + 0.994804i \(0.532463\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.0911720 −0.00421894 −0.00210947 0.999998i \(-0.500671\pi\)
−0.00210947 + 0.999998i \(0.500671\pi\)
\(468\) 0 0
\(469\) −1.37727 −0.0635966
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 19.5872 0.900618
\(474\) 0 0
\(475\) −4.57135 −0.209748
\(476\) 0 0
\(477\) −11.1533 −0.510677
\(478\) 0 0
\(479\) 22.6605 1.03538 0.517692 0.855567i \(-0.326791\pi\)
0.517692 + 0.855567i \(0.326791\pi\)
\(480\) 0 0
\(481\) 37.4357 1.70692
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.19766 −0.372236
\(486\) 0 0
\(487\) 3.34863 0.151741 0.0758706 0.997118i \(-0.475826\pi\)
0.0758706 + 0.997118i \(0.475826\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 24.5521 1.10802 0.554010 0.832510i \(-0.313097\pi\)
0.554010 + 0.832510i \(0.313097\pi\)
\(492\) 0 0
\(493\) −4.12205 −0.185648
\(494\) 0 0
\(495\) 8.33116 0.374458
\(496\) 0 0
\(497\) −17.3093 −0.776430
\(498\) 0 0
\(499\) −23.1104 −1.03456 −0.517282 0.855815i \(-0.673056\pi\)
−0.517282 + 0.855815i \(0.673056\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −38.8628 −1.73280 −0.866402 0.499347i \(-0.833573\pi\)
−0.866402 + 0.499347i \(0.833573\pi\)
\(504\) 0 0
\(505\) 7.35386 0.327242
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.2610 0.499134 0.249567 0.968358i \(-0.419712\pi\)
0.249567 + 0.968358i \(0.419712\pi\)
\(510\) 0 0
\(511\) −3.18417 −0.140860
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9.03492 0.398126
\(516\) 0 0
\(517\) 40.4543 1.77918
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.8461 0.694232 0.347116 0.937822i \(-0.387161\pi\)
0.347116 + 0.937822i \(0.387161\pi\)
\(522\) 0 0
\(523\) −16.6662 −0.728761 −0.364381 0.931250i \(-0.618719\pi\)
−0.364381 + 0.931250i \(0.618719\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −34.4484 −1.50059
\(528\) 0 0
\(529\) −14.3772 −0.625094
\(530\) 0 0
\(531\) −1.00545 −0.0436329
\(532\) 0 0
\(533\) 42.8985 1.85814
\(534\) 0 0
\(535\) −12.3387 −0.533449
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8.28577 −0.356894
\(540\) 0 0
\(541\) −17.0423 −0.732707 −0.366354 0.930476i \(-0.619394\pi\)
−0.366354 + 0.930476i \(0.619394\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.23042 0.0955409
\(546\) 0 0
\(547\) 7.89279 0.337471 0.168736 0.985661i \(-0.446032\pi\)
0.168736 + 0.985661i \(0.446032\pi\)
\(548\) 0 0
\(549\) −21.7223 −0.927087
\(550\) 0 0
\(551\) 1.01990 0.0434491
\(552\) 0 0
\(553\) −2.24646 −0.0955290
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.8309 0.797893 0.398946 0.916974i \(-0.369376\pi\)
0.398946 + 0.916974i \(0.369376\pi\)
\(558\) 0 0
\(559\) −19.8962 −0.841520
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.22514 0.220213 0.110107 0.993920i \(-0.464881\pi\)
0.110107 + 0.993920i \(0.464881\pi\)
\(564\) 0 0
\(565\) 1.81983 0.0765607
\(566\) 0 0
\(567\) −20.2181 −0.849081
\(568\) 0 0
\(569\) −40.7608 −1.70878 −0.854390 0.519632i \(-0.826069\pi\)
−0.854390 + 0.519632i \(0.826069\pi\)
\(570\) 0 0
\(571\) 31.5947 1.32220 0.661098 0.750300i \(-0.270091\pi\)
0.661098 + 0.750300i \(0.270091\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.4236 0.559804
\(576\) 0 0
\(577\) 19.7485 0.822139 0.411070 0.911604i \(-0.365155\pi\)
0.411070 + 0.911604i \(0.365155\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 26.0242 1.07966
\(582\) 0 0
\(583\) 15.7695 0.653106
\(584\) 0 0
\(585\) −8.46261 −0.349886
\(586\) 0 0
\(587\) −39.8829 −1.64614 −0.823071 0.567939i \(-0.807741\pi\)
−0.823071 + 0.567939i \(0.807741\pi\)
\(588\) 0 0
\(589\) 8.52340 0.351200
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.8652 0.692569 0.346285 0.938129i \(-0.387443\pi\)
0.346285 + 0.938129i \(0.387443\pi\)
\(594\) 0 0
\(595\) −5.94435 −0.243695
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.8685 1.66984 0.834920 0.550371i \(-0.185514\pi\)
0.834920 + 0.550371i \(0.185514\pi\)
\(600\) 0 0
\(601\) −12.3527 −0.503877 −0.251938 0.967743i \(-0.581068\pi\)
−0.251938 + 0.967743i \(0.581068\pi\)
\(602\) 0 0
\(603\) −1.83926 −0.0749005
\(604\) 0 0
\(605\) −4.57744 −0.186099
\(606\) 0 0
\(607\) −10.0787 −0.409080 −0.204540 0.978858i \(-0.565570\pi\)
−0.204540 + 0.978858i \(0.565570\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −41.0926 −1.66243
\(612\) 0 0
\(613\) 8.27833 0.334359 0.167179 0.985927i \(-0.446534\pi\)
0.167179 + 0.985927i \(0.446534\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.6757 −1.19470 −0.597350 0.801981i \(-0.703780\pi\)
−0.597350 + 0.801981i \(0.703780\pi\)
\(618\) 0 0
\(619\) 43.2322 1.73765 0.868825 0.495119i \(-0.164875\pi\)
0.868825 + 0.495119i \(0.164875\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.84959 0.234359
\(624\) 0 0
\(625\) 18.7540 0.750161
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 35.1163 1.40018
\(630\) 0 0
\(631\) 14.5753 0.580234 0.290117 0.956991i \(-0.406306\pi\)
0.290117 + 0.956991i \(0.406306\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.31013 −0.369461
\(636\) 0 0
\(637\) 8.41651 0.333474
\(638\) 0 0
\(639\) −23.1155 −0.914436
\(640\) 0 0
\(641\) 13.4479 0.531161 0.265581 0.964089i \(-0.414436\pi\)
0.265581 + 0.964089i \(0.414436\pi\)
\(642\) 0 0
\(643\) −36.0946 −1.42343 −0.711717 0.702467i \(-0.752082\pi\)
−0.711717 + 0.702467i \(0.752082\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 48.3466 1.90070 0.950351 0.311181i \(-0.100724\pi\)
0.950351 + 0.311181i \(0.100724\pi\)
\(648\) 0 0
\(649\) 1.42159 0.0558022
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −16.2497 −0.635902 −0.317951 0.948107i \(-0.602995\pi\)
−0.317951 + 0.948107i \(0.602995\pi\)
\(654\) 0 0
\(655\) 5.12647 0.200308
\(656\) 0 0
\(657\) −4.25226 −0.165897
\(658\) 0 0
\(659\) −45.8058 −1.78434 −0.892170 0.451700i \(-0.850818\pi\)
−0.892170 + 0.451700i \(0.850818\pi\)
\(660\) 0 0
\(661\) 19.5919 0.762036 0.381018 0.924568i \(-0.375574\pi\)
0.381018 + 0.924568i \(0.375574\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.47078 0.0570345
\(666\) 0 0
\(667\) −2.99490 −0.115963
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 30.7128 1.18565
\(672\) 0 0
\(673\) 46.3225 1.78560 0.892801 0.450451i \(-0.148737\pi\)
0.892801 + 0.450451i \(0.148737\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.62999 −0.139512 −0.0697560 0.997564i \(-0.522222\pi\)
−0.0697560 + 0.997564i \(0.522222\pi\)
\(678\) 0 0
\(679\) −28.1279 −1.07945
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.7809 0.948215 0.474107 0.880467i \(-0.342771\pi\)
0.474107 + 0.880467i \(0.342771\pi\)
\(684\) 0 0
\(685\) −9.72288 −0.371492
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16.0183 −0.610249
\(690\) 0 0
\(691\) −49.6119 −1.88733 −0.943663 0.330907i \(-0.892645\pi\)
−0.943663 + 0.330907i \(0.892645\pi\)
\(692\) 0 0
\(693\) 28.5860 1.08589
\(694\) 0 0
\(695\) −9.47632 −0.359457
\(696\) 0 0
\(697\) 40.2407 1.52423
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.18305 0.0446834 0.0223417 0.999750i \(-0.492888\pi\)
0.0223417 + 0.999750i \(0.492888\pi\)
\(702\) 0 0
\(703\) −8.68866 −0.327699
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25.2326 0.948971
\(708\) 0 0
\(709\) −35.0883 −1.31777 −0.658885 0.752244i \(-0.728972\pi\)
−0.658885 + 0.752244i \(0.728972\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −25.0287 −0.937331
\(714\) 0 0
\(715\) 11.9651 0.447470
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 44.0944 1.64444 0.822222 0.569168i \(-0.192734\pi\)
0.822222 + 0.569168i \(0.192734\pi\)
\(720\) 0 0
\(721\) 31.0007 1.15453
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.66232 −0.173154
\(726\) 0 0
\(727\) −32.5684 −1.20790 −0.603948 0.797024i \(-0.706406\pi\)
−0.603948 + 0.797024i \(0.706406\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −18.6635 −0.690295
\(732\) 0 0
\(733\) −40.0263 −1.47841 −0.739203 0.673482i \(-0.764798\pi\)
−0.739203 + 0.673482i \(0.764798\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.60050 0.0957905
\(738\) 0 0
\(739\) 16.1669 0.594709 0.297354 0.954767i \(-0.403896\pi\)
0.297354 + 0.954767i \(0.403896\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.331677 −0.0121680 −0.00608402 0.999981i \(-0.501937\pi\)
−0.00608402 + 0.999981i \(0.501937\pi\)
\(744\) 0 0
\(745\) 1.74143 0.0638011
\(746\) 0 0
\(747\) 34.7536 1.27157
\(748\) 0 0
\(749\) −42.3367 −1.54695
\(750\) 0 0
\(751\) −5.31416 −0.193917 −0.0969583 0.995288i \(-0.530911\pi\)
−0.0969583 + 0.995288i \(0.530911\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.0587897 0.00213958
\(756\) 0 0
\(757\) 22.3297 0.811588 0.405794 0.913965i \(-0.366995\pi\)
0.405794 + 0.913965i \(0.366995\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10.2979 0.373298 0.186649 0.982427i \(-0.440237\pi\)
0.186649 + 0.982427i \(0.440237\pi\)
\(762\) 0 0
\(763\) 7.65306 0.277059
\(764\) 0 0
\(765\) −7.93830 −0.287010
\(766\) 0 0
\(767\) −1.44402 −0.0521405
\(768\) 0 0
\(769\) −35.5275 −1.28116 −0.640578 0.767893i \(-0.721305\pi\)
−0.640578 + 0.767893i \(0.721305\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −36.5918 −1.31612 −0.658058 0.752968i \(-0.728622\pi\)
−0.658058 + 0.752968i \(0.728622\pi\)
\(774\) 0 0
\(775\) −38.9634 −1.39961
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.95657 −0.356731
\(780\) 0 0
\(781\) 32.6826 1.16948
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.20728 −0.0430898
\(786\) 0 0
\(787\) −19.7961 −0.705655 −0.352827 0.935688i \(-0.614780\pi\)
−0.352827 + 0.935688i \(0.614780\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6.24421 0.222019
\(792\) 0 0
\(793\) −31.1974 −1.10785
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20.1443 0.713549 0.356775 0.934190i \(-0.383876\pi\)
0.356775 + 0.934190i \(0.383876\pi\)
\(798\) 0 0
\(799\) −38.5466 −1.36368
\(800\) 0 0
\(801\) 7.81176 0.276015
\(802\) 0 0
\(803\) 6.01219 0.212166
\(804\) 0 0
\(805\) −4.31890 −0.152221
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 21.8228 0.767247 0.383624 0.923490i \(-0.374676\pi\)
0.383624 + 0.923490i \(0.374676\pi\)
\(810\) 0 0
\(811\) 34.6656 1.21727 0.608637 0.793449i \(-0.291717\pi\)
0.608637 + 0.793449i \(0.291717\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −15.8553 −0.555385
\(816\) 0 0
\(817\) 4.61782 0.161557
\(818\) 0 0
\(819\) −29.0370 −1.01464
\(820\) 0 0
\(821\) 20.1315 0.702596 0.351298 0.936264i \(-0.385740\pi\)
0.351298 + 0.936264i \(0.385740\pi\)
\(822\) 0 0
\(823\) −12.6505 −0.440967 −0.220483 0.975391i \(-0.570764\pi\)
−0.220483 + 0.975391i \(0.570764\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −38.5829 −1.34166 −0.670830 0.741611i \(-0.734062\pi\)
−0.670830 + 0.741611i \(0.734062\pi\)
\(828\) 0 0
\(829\) −24.7962 −0.861207 −0.430603 0.902541i \(-0.641699\pi\)
−0.430603 + 0.902541i \(0.641699\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7.89505 0.273547
\(834\) 0 0
\(835\) 12.9899 0.449533
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 5.96886 0.206068 0.103034 0.994678i \(-0.467145\pi\)
0.103034 + 0.994678i \(0.467145\pi\)
\(840\) 0 0
\(841\) −27.9598 −0.964131
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.64265 −0.125311
\(846\) 0 0
\(847\) −15.7062 −0.539670
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 25.5139 0.874607
\(852\) 0 0
\(853\) −35.8056 −1.22596 −0.612981 0.790098i \(-0.710030\pi\)
−0.612981 + 0.790098i \(0.710030\pi\)
\(854\) 0 0
\(855\) 1.96414 0.0671721
\(856\) 0 0
\(857\) −1.25594 −0.0429021 −0.0214511 0.999770i \(-0.506829\pi\)
−0.0214511 + 0.999770i \(0.506829\pi\)
\(858\) 0 0
\(859\) 54.3420 1.85413 0.927063 0.374905i \(-0.122325\pi\)
0.927063 + 0.374905i \(0.122325\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 29.4058 1.00099 0.500493 0.865741i \(-0.333152\pi\)
0.500493 + 0.865741i \(0.333152\pi\)
\(864\) 0 0
\(865\) −0.615038 −0.0209119
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.24164 0.143888
\(870\) 0 0
\(871\) −2.64153 −0.0895047
\(872\) 0 0
\(873\) −37.5630 −1.27132
\(874\) 0 0
\(875\) −14.0774 −0.475902
\(876\) 0 0
\(877\) 48.2839 1.63043 0.815215 0.579158i \(-0.196619\pi\)
0.815215 + 0.579158i \(0.196619\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 37.5945 1.26659 0.633296 0.773910i \(-0.281702\pi\)
0.633296 + 0.773910i \(0.281702\pi\)
\(882\) 0 0
\(883\) −1.21467 −0.0408770 −0.0204385 0.999791i \(-0.506506\pi\)
−0.0204385 + 0.999791i \(0.506506\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 6.28546 0.211045 0.105523 0.994417i \(-0.466348\pi\)
0.105523 + 0.994417i \(0.466348\pi\)
\(888\) 0 0
\(889\) −31.9450 −1.07140
\(890\) 0 0
\(891\) 38.1748 1.27890
\(892\) 0 0
\(893\) 9.53741 0.319157
\(894\) 0 0
\(895\) −16.9895 −0.567898
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.69300 0.289928
\(900\) 0 0
\(901\) −15.0259 −0.500585
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.1749 −0.338225
\(906\) 0 0
\(907\) 20.1998 0.670724 0.335362 0.942089i \(-0.391141\pi\)
0.335362 + 0.942089i \(0.391141\pi\)
\(908\) 0 0
\(909\) 33.6966 1.11765
\(910\) 0 0
\(911\) 32.3731 1.07257 0.536284 0.844038i \(-0.319828\pi\)
0.536284 + 0.844038i \(0.319828\pi\)
\(912\) 0 0
\(913\) −49.1375 −1.62621
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 17.5900 0.580873
\(918\) 0 0
\(919\) 41.1700 1.35807 0.679036 0.734105i \(-0.262398\pi\)
0.679036 + 0.734105i \(0.262398\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −33.1983 −1.09273
\(924\) 0 0
\(925\) 39.7189 1.30595
\(926\) 0 0
\(927\) 41.3995 1.35974
\(928\) 0 0
\(929\) 45.2050 1.48313 0.741564 0.670882i \(-0.234084\pi\)
0.741564 + 0.670882i \(0.234084\pi\)
\(930\) 0 0
\(931\) −1.95344 −0.0640213
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 11.2238 0.367058
\(936\) 0 0
\(937\) −50.5610 −1.65176 −0.825878 0.563849i \(-0.809320\pi\)
−0.825878 + 0.563849i \(0.809320\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 51.2818 1.67174 0.835870 0.548927i \(-0.184964\pi\)
0.835870 + 0.548927i \(0.184964\pi\)
\(942\) 0 0
\(943\) 29.2371 0.952092
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 19.7081 0.640428 0.320214 0.947345i \(-0.396245\pi\)
0.320214 + 0.947345i \(0.396245\pi\)
\(948\) 0 0
\(949\) −6.10705 −0.198243
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 56.2773 1.82300 0.911500 0.411301i \(-0.134926\pi\)
0.911500 + 0.411301i \(0.134926\pi\)
\(954\) 0 0
\(955\) 14.4019 0.466033
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −33.3613 −1.07729
\(960\) 0 0
\(961\) 41.6483 1.34349
\(962\) 0 0
\(963\) −56.5380 −1.82191
\(964\) 0 0
\(965\) 17.0105 0.547588
\(966\) 0 0
\(967\) 27.6609 0.889515 0.444757 0.895651i \(-0.353290\pi\)
0.444757 + 0.895651i \(0.353290\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.00270 −0.128453 −0.0642264 0.997935i \(-0.520458\pi\)
−0.0642264 + 0.997935i \(0.520458\pi\)
\(972\) 0 0
\(973\) −32.5153 −1.04239
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −48.3862 −1.54801 −0.774006 0.633178i \(-0.781750\pi\)
−0.774006 + 0.633178i \(0.781750\pi\)
\(978\) 0 0
\(979\) −11.0449 −0.352996
\(980\) 0 0
\(981\) 10.2202 0.326305
\(982\) 0 0
\(983\) 56.7753 1.81085 0.905425 0.424506i \(-0.139552\pi\)
0.905425 + 0.424506i \(0.139552\pi\)
\(984\) 0 0
\(985\) −9.65473 −0.307625
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −13.5601 −0.431186
\(990\) 0 0
\(991\) −6.59162 −0.209390 −0.104695 0.994504i \(-0.533387\pi\)
−0.104695 + 0.994504i \(0.533387\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 11.9098 0.377567
\(996\) 0 0
\(997\) −41.9864 −1.32972 −0.664861 0.746967i \(-0.731509\pi\)
−0.664861 + 0.746967i \(0.731509\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))