Properties

Label 8036.2.a.p.1.9
Level $8036$
Weight $2$
Character 8036.1
Self dual yes
Analytic conductor $64.168$
Analytic rank $0$
Dimension $10$
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - 18 x^{8} + 32 x^{7} + 110 x^{6} - 154 x^{5} - 282 x^{4} + 256 x^{3} + 253 x^{2} - 126 x - 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.70664\) of defining polynomial
Character \(\chi\) \(=\) 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70664 q^{3} +0.469317 q^{5} +4.32591 q^{9} +O(q^{10})\) \(q+2.70664 q^{3} +0.469317 q^{5} +4.32591 q^{9} +4.72750 q^{11} +1.70239 q^{13} +1.27027 q^{15} -3.62142 q^{17} +0.482699 q^{19} -0.0771055 q^{23} -4.77974 q^{25} +3.58875 q^{27} +0.891222 q^{29} +9.17820 q^{31} +12.7957 q^{33} +2.10312 q^{37} +4.60775 q^{39} +1.00000 q^{41} +6.61340 q^{43} +2.03022 q^{45} +4.76867 q^{47} -9.80188 q^{51} -12.1209 q^{53} +2.21870 q^{55} +1.30649 q^{57} +8.46582 q^{59} +1.21796 q^{61} +0.798959 q^{65} -3.96167 q^{67} -0.208697 q^{69} +5.12294 q^{71} -10.6052 q^{73} -12.9370 q^{75} +14.6429 q^{79} -3.26426 q^{81} +1.02509 q^{83} -1.69960 q^{85} +2.41222 q^{87} -3.74768 q^{89} +24.8421 q^{93} +0.226539 q^{95} +11.0675 q^{97} +20.4507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.70664 1.56268 0.781340 0.624106i \(-0.214537\pi\)
0.781340 + 0.624106i \(0.214537\pi\)
\(4\) 0 0
\(5\) 0.469317 0.209885 0.104943 0.994478i \(-0.466534\pi\)
0.104943 + 0.994478i \(0.466534\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 4.32591 1.44197
\(10\) 0 0
\(11\) 4.72750 1.42540 0.712698 0.701471i \(-0.247473\pi\)
0.712698 + 0.701471i \(0.247473\pi\)
\(12\) 0 0
\(13\) 1.70239 0.472157 0.236078 0.971734i \(-0.424138\pi\)
0.236078 + 0.971734i \(0.424138\pi\)
\(14\) 0 0
\(15\) 1.27027 0.327983
\(16\) 0 0
\(17\) −3.62142 −0.878323 −0.439162 0.898408i \(-0.644724\pi\)
−0.439162 + 0.898408i \(0.644724\pi\)
\(18\) 0 0
\(19\) 0.482699 0.110739 0.0553694 0.998466i \(-0.482366\pi\)
0.0553694 + 0.998466i \(0.482366\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.0771055 −0.0160776 −0.00803881 0.999968i \(-0.502559\pi\)
−0.00803881 + 0.999968i \(0.502559\pi\)
\(24\) 0 0
\(25\) −4.77974 −0.955948
\(26\) 0 0
\(27\) 3.58875 0.690655
\(28\) 0 0
\(29\) 0.891222 0.165496 0.0827479 0.996571i \(-0.473630\pi\)
0.0827479 + 0.996571i \(0.473630\pi\)
\(30\) 0 0
\(31\) 9.17820 1.64845 0.824227 0.566259i \(-0.191610\pi\)
0.824227 + 0.566259i \(0.191610\pi\)
\(32\) 0 0
\(33\) 12.7957 2.22744
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.10312 0.345750 0.172875 0.984944i \(-0.444694\pi\)
0.172875 + 0.984944i \(0.444694\pi\)
\(38\) 0 0
\(39\) 4.60775 0.737830
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 6.61340 1.00853 0.504267 0.863548i \(-0.331763\pi\)
0.504267 + 0.863548i \(0.331763\pi\)
\(44\) 0 0
\(45\) 2.03022 0.302648
\(46\) 0 0
\(47\) 4.76867 0.695582 0.347791 0.937572i \(-0.386932\pi\)
0.347791 + 0.937572i \(0.386932\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −9.80188 −1.37254
\(52\) 0 0
\(53\) −12.1209 −1.66493 −0.832466 0.554076i \(-0.813072\pi\)
−0.832466 + 0.554076i \(0.813072\pi\)
\(54\) 0 0
\(55\) 2.21870 0.299169
\(56\) 0 0
\(57\) 1.30649 0.173049
\(58\) 0 0
\(59\) 8.46582 1.10216 0.551078 0.834454i \(-0.314217\pi\)
0.551078 + 0.834454i \(0.314217\pi\)
\(60\) 0 0
\(61\) 1.21796 0.155944 0.0779719 0.996956i \(-0.475156\pi\)
0.0779719 + 0.996956i \(0.475156\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.798959 0.0990987
\(66\) 0 0
\(67\) −3.96167 −0.483995 −0.241998 0.970277i \(-0.577803\pi\)
−0.241998 + 0.970277i \(0.577803\pi\)
\(68\) 0 0
\(69\) −0.208697 −0.0251242
\(70\) 0 0
\(71\) 5.12294 0.607981 0.303991 0.952675i \(-0.401681\pi\)
0.303991 + 0.952675i \(0.401681\pi\)
\(72\) 0 0
\(73\) −10.6052 −1.24124 −0.620622 0.784110i \(-0.713120\pi\)
−0.620622 + 0.784110i \(0.713120\pi\)
\(74\) 0 0
\(75\) −12.9370 −1.49384
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 14.6429 1.64745 0.823725 0.566989i \(-0.191892\pi\)
0.823725 + 0.566989i \(0.191892\pi\)
\(80\) 0 0
\(81\) −3.26426 −0.362695
\(82\) 0 0
\(83\) 1.02509 0.112519 0.0562594 0.998416i \(-0.482083\pi\)
0.0562594 + 0.998416i \(0.482083\pi\)
\(84\) 0 0
\(85\) −1.69960 −0.184347
\(86\) 0 0
\(87\) 2.41222 0.258617
\(88\) 0 0
\(89\) −3.74768 −0.397253 −0.198626 0.980075i \(-0.563648\pi\)
−0.198626 + 0.980075i \(0.563648\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 24.8421 2.57601
\(94\) 0 0
\(95\) 0.226539 0.0232424
\(96\) 0 0
\(97\) 11.0675 1.12373 0.561867 0.827228i \(-0.310083\pi\)
0.561867 + 0.827228i \(0.310083\pi\)
\(98\) 0 0
\(99\) 20.4507 2.05538
\(100\) 0 0
\(101\) 10.9512 1.08969 0.544844 0.838537i \(-0.316589\pi\)
0.544844 + 0.838537i \(0.316589\pi\)
\(102\) 0 0
\(103\) −12.2036 −1.20246 −0.601230 0.799076i \(-0.705323\pi\)
−0.601230 + 0.799076i \(0.705323\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.4055 1.10262 0.551308 0.834302i \(-0.314129\pi\)
0.551308 + 0.834302i \(0.314129\pi\)
\(108\) 0 0
\(109\) 6.49074 0.621700 0.310850 0.950459i \(-0.399386\pi\)
0.310850 + 0.950459i \(0.399386\pi\)
\(110\) 0 0
\(111\) 5.69238 0.540297
\(112\) 0 0
\(113\) 11.5427 1.08584 0.542922 0.839783i \(-0.317318\pi\)
0.542922 + 0.839783i \(0.317318\pi\)
\(114\) 0 0
\(115\) −0.0361870 −0.00337445
\(116\) 0 0
\(117\) 7.36436 0.680835
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.3493 1.03175
\(122\) 0 0
\(123\) 2.70664 0.244050
\(124\) 0 0
\(125\) −4.58980 −0.410524
\(126\) 0 0
\(127\) −1.91879 −0.170265 −0.0851326 0.996370i \(-0.527131\pi\)
−0.0851326 + 0.996370i \(0.527131\pi\)
\(128\) 0 0
\(129\) 17.9001 1.57602
\(130\) 0 0
\(131\) 9.65847 0.843864 0.421932 0.906627i \(-0.361352\pi\)
0.421932 + 0.906627i \(0.361352\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.68426 0.144958
\(136\) 0 0
\(137\) −20.8543 −1.78171 −0.890853 0.454291i \(-0.849893\pi\)
−0.890853 + 0.454291i \(0.849893\pi\)
\(138\) 0 0
\(139\) 6.00753 0.509552 0.254776 0.967000i \(-0.417998\pi\)
0.254776 + 0.967000i \(0.417998\pi\)
\(140\) 0 0
\(141\) 12.9071 1.08697
\(142\) 0 0
\(143\) 8.04803 0.673010
\(144\) 0 0
\(145\) 0.418266 0.0347351
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −18.5867 −1.52268 −0.761342 0.648350i \(-0.775459\pi\)
−0.761342 + 0.648350i \(0.775459\pi\)
\(150\) 0 0
\(151\) −2.37742 −0.193472 −0.0967360 0.995310i \(-0.530840\pi\)
−0.0967360 + 0.995310i \(0.530840\pi\)
\(152\) 0 0
\(153\) −15.6659 −1.26651
\(154\) 0 0
\(155\) 4.30749 0.345986
\(156\) 0 0
\(157\) −11.4328 −0.912434 −0.456217 0.889869i \(-0.650796\pi\)
−0.456217 + 0.889869i \(0.650796\pi\)
\(158\) 0 0
\(159\) −32.8069 −2.60176
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 6.28613 0.492368 0.246184 0.969223i \(-0.420823\pi\)
0.246184 + 0.969223i \(0.420823\pi\)
\(164\) 0 0
\(165\) 6.00522 0.467506
\(166\) 0 0
\(167\) −11.3925 −0.881577 −0.440788 0.897611i \(-0.645301\pi\)
−0.440788 + 0.897611i \(0.645301\pi\)
\(168\) 0 0
\(169\) −10.1019 −0.777068
\(170\) 0 0
\(171\) 2.08811 0.159682
\(172\) 0 0
\(173\) −21.5221 −1.63629 −0.818147 0.575009i \(-0.804998\pi\)
−0.818147 + 0.575009i \(0.804998\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 22.9139 1.72232
\(178\) 0 0
\(179\) −6.43044 −0.480633 −0.240317 0.970695i \(-0.577251\pi\)
−0.240317 + 0.970695i \(0.577251\pi\)
\(180\) 0 0
\(181\) 17.3408 1.28893 0.644465 0.764634i \(-0.277080\pi\)
0.644465 + 0.764634i \(0.277080\pi\)
\(182\) 0 0
\(183\) 3.29658 0.243690
\(184\) 0 0
\(185\) 0.987030 0.0725679
\(186\) 0 0
\(187\) −17.1203 −1.25196
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.106130 −0.00767931 −0.00383966 0.999993i \(-0.501222\pi\)
−0.00383966 + 0.999993i \(0.501222\pi\)
\(192\) 0 0
\(193\) 2.28602 0.164552 0.0822758 0.996610i \(-0.473781\pi\)
0.0822758 + 0.996610i \(0.473781\pi\)
\(194\) 0 0
\(195\) 2.16250 0.154860
\(196\) 0 0
\(197\) 1.89180 0.134785 0.0673924 0.997727i \(-0.478532\pi\)
0.0673924 + 0.997727i \(0.478532\pi\)
\(198\) 0 0
\(199\) −0.291932 −0.0206945 −0.0103472 0.999946i \(-0.503294\pi\)
−0.0103472 + 0.999946i \(0.503294\pi\)
\(200\) 0 0
\(201\) −10.7228 −0.756329
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.469317 0.0327786
\(206\) 0 0
\(207\) −0.333551 −0.0231834
\(208\) 0 0
\(209\) 2.28196 0.157847
\(210\) 0 0
\(211\) 23.3493 1.60743 0.803717 0.595012i \(-0.202853\pi\)
0.803717 + 0.595012i \(0.202853\pi\)
\(212\) 0 0
\(213\) 13.8660 0.950080
\(214\) 0 0
\(215\) 3.10378 0.211676
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −28.7044 −1.93967
\(220\) 0 0
\(221\) −6.16505 −0.414706
\(222\) 0 0
\(223\) −13.1824 −0.882757 −0.441379 0.897321i \(-0.645510\pi\)
−0.441379 + 0.897321i \(0.645510\pi\)
\(224\) 0 0
\(225\) −20.6767 −1.37845
\(226\) 0 0
\(227\) 10.7195 0.711479 0.355740 0.934585i \(-0.384229\pi\)
0.355740 + 0.934585i \(0.384229\pi\)
\(228\) 0 0
\(229\) −12.8550 −0.849482 −0.424741 0.905315i \(-0.639635\pi\)
−0.424741 + 0.905315i \(0.639635\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.1885 −0.798492 −0.399246 0.916844i \(-0.630728\pi\)
−0.399246 + 0.916844i \(0.630728\pi\)
\(234\) 0 0
\(235\) 2.23802 0.145992
\(236\) 0 0
\(237\) 39.6330 2.57444
\(238\) 0 0
\(239\) 4.28190 0.276973 0.138487 0.990364i \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(240\) 0 0
\(241\) −1.35442 −0.0872456 −0.0436228 0.999048i \(-0.513890\pi\)
−0.0436228 + 0.999048i \(0.513890\pi\)
\(242\) 0 0
\(243\) −19.6014 −1.25743
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.821740 0.0522861
\(248\) 0 0
\(249\) 2.77456 0.175831
\(250\) 0 0
\(251\) 11.0524 0.697620 0.348810 0.937193i \(-0.386586\pi\)
0.348810 + 0.937193i \(0.386586\pi\)
\(252\) 0 0
\(253\) −0.364517 −0.0229170
\(254\) 0 0
\(255\) −4.60019 −0.288075
\(256\) 0 0
\(257\) 13.7831 0.859766 0.429883 0.902884i \(-0.358555\pi\)
0.429883 + 0.902884i \(0.358555\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.85534 0.238640
\(262\) 0 0
\(263\) −5.36247 −0.330664 −0.165332 0.986238i \(-0.552870\pi\)
−0.165332 + 0.986238i \(0.552870\pi\)
\(264\) 0 0
\(265\) −5.68855 −0.349445
\(266\) 0 0
\(267\) −10.1436 −0.620779
\(268\) 0 0
\(269\) 9.47122 0.577471 0.288735 0.957409i \(-0.406765\pi\)
0.288735 + 0.957409i \(0.406765\pi\)
\(270\) 0 0
\(271\) −2.27313 −0.138083 −0.0690413 0.997614i \(-0.521994\pi\)
−0.0690413 + 0.997614i \(0.521994\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −22.5962 −1.36260
\(276\) 0 0
\(277\) −18.7734 −1.12798 −0.563991 0.825781i \(-0.690735\pi\)
−0.563991 + 0.825781i \(0.690735\pi\)
\(278\) 0 0
\(279\) 39.7040 2.37702
\(280\) 0 0
\(281\) −5.35062 −0.319192 −0.159596 0.987182i \(-0.551019\pi\)
−0.159596 + 0.987182i \(0.551019\pi\)
\(282\) 0 0
\(283\) 10.6731 0.634452 0.317226 0.948350i \(-0.397249\pi\)
0.317226 + 0.948350i \(0.397249\pi\)
\(284\) 0 0
\(285\) 0.613160 0.0363205
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −3.88533 −0.228549
\(290\) 0 0
\(291\) 29.9557 1.75604
\(292\) 0 0
\(293\) −11.9925 −0.700608 −0.350304 0.936636i \(-0.613922\pi\)
−0.350304 + 0.936636i \(0.613922\pi\)
\(294\) 0 0
\(295\) 3.97316 0.231326
\(296\) 0 0
\(297\) 16.9658 0.984457
\(298\) 0 0
\(299\) −0.131263 −0.00759115
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 29.6411 1.70283
\(304\) 0 0
\(305\) 0.571610 0.0327303
\(306\) 0 0
\(307\) 9.58847 0.547243 0.273622 0.961837i \(-0.411778\pi\)
0.273622 + 0.961837i \(0.411778\pi\)
\(308\) 0 0
\(309\) −33.0309 −1.87906
\(310\) 0 0
\(311\) −8.06040 −0.457063 −0.228532 0.973536i \(-0.573392\pi\)
−0.228532 + 0.973536i \(0.573392\pi\)
\(312\) 0 0
\(313\) 15.2940 0.864467 0.432233 0.901762i \(-0.357726\pi\)
0.432233 + 0.901762i \(0.357726\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.16644 −0.290176 −0.145088 0.989419i \(-0.546347\pi\)
−0.145088 + 0.989419i \(0.546347\pi\)
\(318\) 0 0
\(319\) 4.21325 0.235897
\(320\) 0 0
\(321\) 30.8707 1.72303
\(322\) 0 0
\(323\) −1.74806 −0.0972645
\(324\) 0 0
\(325\) −8.13696 −0.451357
\(326\) 0 0
\(327\) 17.5681 0.971518
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11.7547 −0.646097 −0.323049 0.946382i \(-0.604708\pi\)
−0.323049 + 0.946382i \(0.604708\pi\)
\(332\) 0 0
\(333\) 9.09789 0.498561
\(334\) 0 0
\(335\) −1.85928 −0.101583
\(336\) 0 0
\(337\) 13.0144 0.708941 0.354471 0.935067i \(-0.384661\pi\)
0.354471 + 0.935067i \(0.384661\pi\)
\(338\) 0 0
\(339\) 31.2419 1.69683
\(340\) 0 0
\(341\) 43.3900 2.34970
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.0979451 −0.00527319
\(346\) 0 0
\(347\) 16.1209 0.865418 0.432709 0.901534i \(-0.357558\pi\)
0.432709 + 0.901534i \(0.357558\pi\)
\(348\) 0 0
\(349\) 9.39124 0.502701 0.251351 0.967896i \(-0.419125\pi\)
0.251351 + 0.967896i \(0.419125\pi\)
\(350\) 0 0
\(351\) 6.10943 0.326097
\(352\) 0 0
\(353\) 25.6538 1.36542 0.682708 0.730691i \(-0.260802\pi\)
0.682708 + 0.730691i \(0.260802\pi\)
\(354\) 0 0
\(355\) 2.40429 0.127606
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.6006 −0.559476 −0.279738 0.960076i \(-0.590248\pi\)
−0.279738 + 0.960076i \(0.590248\pi\)
\(360\) 0 0
\(361\) −18.7670 −0.987737
\(362\) 0 0
\(363\) 30.7184 1.61230
\(364\) 0 0
\(365\) −4.97720 −0.260519
\(366\) 0 0
\(367\) −25.0989 −1.31015 −0.655077 0.755562i \(-0.727364\pi\)
−0.655077 + 0.755562i \(0.727364\pi\)
\(368\) 0 0
\(369\) 4.32591 0.225198
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −21.1194 −1.09352 −0.546760 0.837290i \(-0.684139\pi\)
−0.546760 + 0.837290i \(0.684139\pi\)
\(374\) 0 0
\(375\) −12.4229 −0.641518
\(376\) 0 0
\(377\) 1.51720 0.0781399
\(378\) 0 0
\(379\) −23.5309 −1.20870 −0.604352 0.796718i \(-0.706568\pi\)
−0.604352 + 0.796718i \(0.706568\pi\)
\(380\) 0 0
\(381\) −5.19348 −0.266070
\(382\) 0 0
\(383\) −2.96252 −0.151378 −0.0756890 0.997131i \(-0.524116\pi\)
−0.0756890 + 0.997131i \(0.524116\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 28.6089 1.45427
\(388\) 0 0
\(389\) −4.62441 −0.234467 −0.117233 0.993104i \(-0.537403\pi\)
−0.117233 + 0.993104i \(0.537403\pi\)
\(390\) 0 0
\(391\) 0.279231 0.0141213
\(392\) 0 0
\(393\) 26.1420 1.31869
\(394\) 0 0
\(395\) 6.87215 0.345775
\(396\) 0 0
\(397\) −9.06114 −0.454766 −0.227383 0.973805i \(-0.573017\pi\)
−0.227383 + 0.973805i \(0.573017\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 19.7406 0.985797 0.492898 0.870087i \(-0.335937\pi\)
0.492898 + 0.870087i \(0.335937\pi\)
\(402\) 0 0
\(403\) 15.6248 0.778329
\(404\) 0 0
\(405\) −1.53197 −0.0761244
\(406\) 0 0
\(407\) 9.94249 0.492831
\(408\) 0 0
\(409\) 35.6659 1.76356 0.881782 0.471658i \(-0.156344\pi\)
0.881782 + 0.471658i \(0.156344\pi\)
\(410\) 0 0
\(411\) −56.4452 −2.78424
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.481095 0.0236160
\(416\) 0 0
\(417\) 16.2602 0.796267
\(418\) 0 0
\(419\) 18.8381 0.920303 0.460151 0.887840i \(-0.347795\pi\)
0.460151 + 0.887840i \(0.347795\pi\)
\(420\) 0 0
\(421\) 10.1778 0.496034 0.248017 0.968756i \(-0.420221\pi\)
0.248017 + 0.968756i \(0.420221\pi\)
\(422\) 0 0
\(423\) 20.6288 1.00301
\(424\) 0 0
\(425\) 17.3094 0.839631
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 21.7831 1.05170
\(430\) 0 0
\(431\) 14.1486 0.681515 0.340757 0.940151i \(-0.389317\pi\)
0.340757 + 0.940151i \(0.389317\pi\)
\(432\) 0 0
\(433\) −0.0822900 −0.00395461 −0.00197730 0.999998i \(-0.500629\pi\)
−0.00197730 + 0.999998i \(0.500629\pi\)
\(434\) 0 0
\(435\) 1.13210 0.0542799
\(436\) 0 0
\(437\) −0.0372188 −0.00178042
\(438\) 0 0
\(439\) 33.2966 1.58916 0.794580 0.607159i \(-0.207691\pi\)
0.794580 + 0.607159i \(0.207691\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.3965 −0.684000 −0.342000 0.939700i \(-0.611104\pi\)
−0.342000 + 0.939700i \(0.611104\pi\)
\(444\) 0 0
\(445\) −1.75885 −0.0833775
\(446\) 0 0
\(447\) −50.3076 −2.37947
\(448\) 0 0
\(449\) −2.30585 −0.108820 −0.0544100 0.998519i \(-0.517328\pi\)
−0.0544100 + 0.998519i \(0.517328\pi\)
\(450\) 0 0
\(451\) 4.72750 0.222609
\(452\) 0 0
\(453\) −6.43483 −0.302335
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.7308 −0.876188 −0.438094 0.898929i \(-0.644346\pi\)
−0.438094 + 0.898929i \(0.644346\pi\)
\(458\) 0 0
\(459\) −12.9964 −0.606618
\(460\) 0 0
\(461\) −21.5879 −1.00545 −0.502725 0.864447i \(-0.667669\pi\)
−0.502725 + 0.864447i \(0.667669\pi\)
\(462\) 0 0
\(463\) 17.5466 0.815458 0.407729 0.913103i \(-0.366321\pi\)
0.407729 + 0.913103i \(0.366321\pi\)
\(464\) 0 0
\(465\) 11.6588 0.540665
\(466\) 0 0
\(467\) 3.70864 0.171615 0.0858076 0.996312i \(-0.472653\pi\)
0.0858076 + 0.996312i \(0.472653\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −30.9444 −1.42584
\(472\) 0 0
\(473\) 31.2649 1.43756
\(474\) 0 0
\(475\) −2.30718 −0.105861
\(476\) 0 0
\(477\) −52.4338 −2.40078
\(478\) 0 0
\(479\) 2.20086 0.100560 0.0502798 0.998735i \(-0.483989\pi\)
0.0502798 + 0.998735i \(0.483989\pi\)
\(480\) 0 0
\(481\) 3.58032 0.163248
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.19417 0.235855
\(486\) 0 0
\(487\) −5.11732 −0.231888 −0.115944 0.993256i \(-0.536989\pi\)
−0.115944 + 0.993256i \(0.536989\pi\)
\(488\) 0 0
\(489\) 17.0143 0.769413
\(490\) 0 0
\(491\) −1.26077 −0.0568976 −0.0284488 0.999595i \(-0.509057\pi\)
−0.0284488 + 0.999595i \(0.509057\pi\)
\(492\) 0 0
\(493\) −3.22749 −0.145359
\(494\) 0 0
\(495\) 9.59788 0.431393
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −25.1914 −1.12772 −0.563862 0.825869i \(-0.690685\pi\)
−0.563862 + 0.825869i \(0.690685\pi\)
\(500\) 0 0
\(501\) −30.8354 −1.37762
\(502\) 0 0
\(503\) −29.0850 −1.29684 −0.648418 0.761285i \(-0.724569\pi\)
−0.648418 + 0.761285i \(0.724569\pi\)
\(504\) 0 0
\(505\) 5.13960 0.228709
\(506\) 0 0
\(507\) −27.3422 −1.21431
\(508\) 0 0
\(509\) −16.5493 −0.733535 −0.366767 0.930313i \(-0.619536\pi\)
−0.366767 + 0.930313i \(0.619536\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.73229 0.0764823
\(514\) 0 0
\(515\) −5.72738 −0.252379
\(516\) 0 0
\(517\) 22.5439 0.991480
\(518\) 0 0
\(519\) −58.2526 −2.55700
\(520\) 0 0
\(521\) 43.9342 1.92479 0.962396 0.271649i \(-0.0875689\pi\)
0.962396 + 0.271649i \(0.0875689\pi\)
\(522\) 0 0
\(523\) −2.18798 −0.0956736 −0.0478368 0.998855i \(-0.515233\pi\)
−0.0478368 + 0.998855i \(0.515233\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −33.2381 −1.44788
\(528\) 0 0
\(529\) −22.9941 −0.999742
\(530\) 0 0
\(531\) 36.6223 1.58927
\(532\) 0 0
\(533\) 1.70239 0.0737385
\(534\) 0 0
\(535\) 5.35282 0.231423
\(536\) 0 0
\(537\) −17.4049 −0.751076
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −42.5895 −1.83107 −0.915533 0.402243i \(-0.868231\pi\)
−0.915533 + 0.402243i \(0.868231\pi\)
\(542\) 0 0
\(543\) 46.9353 2.01419
\(544\) 0 0
\(545\) 3.04622 0.130486
\(546\) 0 0
\(547\) −25.1538 −1.07550 −0.537749 0.843105i \(-0.680725\pi\)
−0.537749 + 0.843105i \(0.680725\pi\)
\(548\) 0 0
\(549\) 5.26878 0.224866
\(550\) 0 0
\(551\) 0.430192 0.0183268
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 2.67153 0.113400
\(556\) 0 0
\(557\) −40.6947 −1.72429 −0.862145 0.506662i \(-0.830879\pi\)
−0.862145 + 0.506662i \(0.830879\pi\)
\(558\) 0 0
\(559\) 11.2586 0.476186
\(560\) 0 0
\(561\) −46.3384 −1.95641
\(562\) 0 0
\(563\) 11.8745 0.500452 0.250226 0.968187i \(-0.419495\pi\)
0.250226 + 0.968187i \(0.419495\pi\)
\(564\) 0 0
\(565\) 5.41718 0.227902
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.3873 −0.435458 −0.217729 0.976009i \(-0.569865\pi\)
−0.217729 + 0.976009i \(0.569865\pi\)
\(570\) 0 0
\(571\) 27.4888 1.15037 0.575184 0.818024i \(-0.304930\pi\)
0.575184 + 0.818024i \(0.304930\pi\)
\(572\) 0 0
\(573\) −0.287256 −0.0120003
\(574\) 0 0
\(575\) 0.368544 0.0153694
\(576\) 0 0
\(577\) 31.5606 1.31388 0.656942 0.753941i \(-0.271849\pi\)
0.656942 + 0.753941i \(0.271849\pi\)
\(578\) 0 0
\(579\) 6.18745 0.257142
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −57.3015 −2.37319
\(584\) 0 0
\(585\) 3.45622 0.142897
\(586\) 0 0
\(587\) 23.0329 0.950670 0.475335 0.879805i \(-0.342327\pi\)
0.475335 + 0.879805i \(0.342327\pi\)
\(588\) 0 0
\(589\) 4.43031 0.182548
\(590\) 0 0
\(591\) 5.12041 0.210626
\(592\) 0 0
\(593\) −4.97167 −0.204162 −0.102081 0.994776i \(-0.532550\pi\)
−0.102081 + 0.994776i \(0.532550\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.790154 −0.0323389
\(598\) 0 0
\(599\) 39.7974 1.62608 0.813038 0.582211i \(-0.197812\pi\)
0.813038 + 0.582211i \(0.197812\pi\)
\(600\) 0 0
\(601\) −37.1297 −1.51455 −0.757276 0.653094i \(-0.773470\pi\)
−0.757276 + 0.653094i \(0.773470\pi\)
\(602\) 0 0
\(603\) −17.1378 −0.697906
\(604\) 0 0
\(605\) 5.32641 0.216549
\(606\) 0 0
\(607\) −3.52274 −0.142984 −0.0714918 0.997441i \(-0.522776\pi\)
−0.0714918 + 0.997441i \(0.522776\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.11811 0.328424
\(612\) 0 0
\(613\) −33.7942 −1.36493 −0.682467 0.730916i \(-0.739093\pi\)
−0.682467 + 0.730916i \(0.739093\pi\)
\(614\) 0 0
\(615\) 1.27027 0.0512224
\(616\) 0 0
\(617\) −14.1546 −0.569843 −0.284922 0.958551i \(-0.591968\pi\)
−0.284922 + 0.958551i \(0.591968\pi\)
\(618\) 0 0
\(619\) −24.0838 −0.968011 −0.484006 0.875065i \(-0.660819\pi\)
−0.484006 + 0.875065i \(0.660819\pi\)
\(620\) 0 0
\(621\) −0.276712 −0.0111041
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 21.7446 0.869785
\(626\) 0 0
\(627\) 6.17645 0.246664
\(628\) 0 0
\(629\) −7.61627 −0.303680
\(630\) 0 0
\(631\) 40.8465 1.62607 0.813037 0.582213i \(-0.197813\pi\)
0.813037 + 0.582213i \(0.197813\pi\)
\(632\) 0 0
\(633\) 63.1983 2.51191
\(634\) 0 0
\(635\) −0.900522 −0.0357361
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 22.1614 0.876690
\(640\) 0 0
\(641\) 31.7190 1.25283 0.626413 0.779491i \(-0.284522\pi\)
0.626413 + 0.779491i \(0.284522\pi\)
\(642\) 0 0
\(643\) 42.8966 1.69168 0.845838 0.533440i \(-0.179101\pi\)
0.845838 + 0.533440i \(0.179101\pi\)
\(644\) 0 0
\(645\) 8.40083 0.330782
\(646\) 0 0
\(647\) −41.1500 −1.61777 −0.808886 0.587966i \(-0.799929\pi\)
−0.808886 + 0.587966i \(0.799929\pi\)
\(648\) 0 0
\(649\) 40.0222 1.57101
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.7638 0.460351 0.230176 0.973149i \(-0.426070\pi\)
0.230176 + 0.973149i \(0.426070\pi\)
\(654\) 0 0
\(655\) 4.53289 0.177115
\(656\) 0 0
\(657\) −45.8770 −1.78983
\(658\) 0 0
\(659\) −31.1634 −1.21396 −0.606978 0.794719i \(-0.707618\pi\)
−0.606978 + 0.794719i \(0.707618\pi\)
\(660\) 0 0
\(661\) 9.04814 0.351932 0.175966 0.984396i \(-0.443695\pi\)
0.175966 + 0.984396i \(0.443695\pi\)
\(662\) 0 0
\(663\) −16.6866 −0.648053
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.0687182 −0.00266078
\(668\) 0 0
\(669\) −35.6800 −1.37947
\(670\) 0 0
\(671\) 5.75791 0.222281
\(672\) 0 0
\(673\) −30.4453 −1.17358 −0.586791 0.809739i \(-0.699609\pi\)
−0.586791 + 0.809739i \(0.699609\pi\)
\(674\) 0 0
\(675\) −17.1533 −0.660231
\(676\) 0 0
\(677\) −36.7599 −1.41280 −0.706399 0.707814i \(-0.749682\pi\)
−0.706399 + 0.707814i \(0.749682\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 29.0139 1.11181
\(682\) 0 0
\(683\) 2.06099 0.0788615 0.0394308 0.999222i \(-0.487446\pi\)
0.0394308 + 0.999222i \(0.487446\pi\)
\(684\) 0 0
\(685\) −9.78731 −0.373954
\(686\) 0 0
\(687\) −34.7938 −1.32747
\(688\) 0 0
\(689\) −20.6344 −0.786109
\(690\) 0 0
\(691\) 17.4256 0.662901 0.331451 0.943473i \(-0.392462\pi\)
0.331451 + 0.943473i \(0.392462\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.81944 0.106947
\(696\) 0 0
\(697\) −3.62142 −0.137171
\(698\) 0 0
\(699\) −32.9898 −1.24779
\(700\) 0 0
\(701\) −36.8136 −1.39043 −0.695216 0.718801i \(-0.744691\pi\)
−0.695216 + 0.718801i \(0.744691\pi\)
\(702\) 0 0
\(703\) 1.01517 0.0382880
\(704\) 0 0
\(705\) 6.05752 0.228139
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13.9160 −0.522628 −0.261314 0.965254i \(-0.584156\pi\)
−0.261314 + 0.965254i \(0.584156\pi\)
\(710\) 0 0
\(711\) 63.3436 2.37557
\(712\) 0 0
\(713\) −0.707690 −0.0265032
\(714\) 0 0
\(715\) 3.77708 0.141255
\(716\) 0 0
\(717\) 11.5896 0.432821
\(718\) 0 0
\(719\) −18.9441 −0.706497 −0.353248 0.935530i \(-0.614923\pi\)
−0.353248 + 0.935530i \(0.614923\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −3.66592 −0.136337
\(724\) 0 0
\(725\) −4.25981 −0.158205
\(726\) 0 0
\(727\) 24.0404 0.891608 0.445804 0.895131i \(-0.352918\pi\)
0.445804 + 0.895131i \(0.352918\pi\)
\(728\) 0 0
\(729\) −43.2612 −1.60227
\(730\) 0 0
\(731\) −23.9499 −0.885819
\(732\) 0 0
\(733\) −26.0115 −0.960755 −0.480378 0.877062i \(-0.659500\pi\)
−0.480378 + 0.877062i \(0.659500\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.7288 −0.689884
\(738\) 0 0
\(739\) −32.4689 −1.19439 −0.597193 0.802097i \(-0.703718\pi\)
−0.597193 + 0.802097i \(0.703718\pi\)
\(740\) 0 0
\(741\) 2.22416 0.0817064
\(742\) 0 0
\(743\) 33.3797 1.22458 0.612291 0.790633i \(-0.290248\pi\)
0.612291 + 0.790633i \(0.290248\pi\)
\(744\) 0 0
\(745\) −8.72308 −0.319589
\(746\) 0 0
\(747\) 4.43446 0.162249
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7.44890 0.271814 0.135907 0.990722i \(-0.456605\pi\)
0.135907 + 0.990722i \(0.456605\pi\)
\(752\) 0 0
\(753\) 29.9148 1.09016
\(754\) 0 0
\(755\) −1.11577 −0.0406069
\(756\) 0 0
\(757\) 23.2573 0.845301 0.422650 0.906293i \(-0.361100\pi\)
0.422650 + 0.906293i \(0.361100\pi\)
\(758\) 0 0
\(759\) −0.986615 −0.0358119
\(760\) 0 0
\(761\) −28.0263 −1.01595 −0.507976 0.861371i \(-0.669606\pi\)
−0.507976 + 0.861371i \(0.669606\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −7.35229 −0.265823
\(766\) 0 0
\(767\) 14.4121 0.520390
\(768\) 0 0
\(769\) 25.2387 0.910131 0.455065 0.890458i \(-0.349616\pi\)
0.455065 + 0.890458i \(0.349616\pi\)
\(770\) 0 0
\(771\) 37.3059 1.34354
\(772\) 0 0
\(773\) 12.3719 0.444988 0.222494 0.974934i \(-0.428580\pi\)
0.222494 + 0.974934i \(0.428580\pi\)
\(774\) 0 0
\(775\) −43.8694 −1.57584
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.482699 0.0172945
\(780\) 0 0
\(781\) 24.2187 0.866614
\(782\) 0 0
\(783\) 3.19837 0.114301
\(784\) 0 0
\(785\) −5.36560 −0.191506
\(786\) 0 0
\(787\) −17.7301 −0.632012 −0.316006 0.948757i \(-0.602342\pi\)
−0.316006 + 0.948757i \(0.602342\pi\)
\(788\) 0 0
\(789\) −14.5143 −0.516722
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2.07344 0.0736299
\(794\) 0 0
\(795\) −15.3969 −0.546070
\(796\) 0 0
\(797\) −27.8951 −0.988095 −0.494048 0.869435i \(-0.664483\pi\)
−0.494048 + 0.869435i \(0.664483\pi\)
\(798\) 0 0
\(799\) −17.2694 −0.610946
\(800\) 0 0
\(801\) −16.2121 −0.572826
\(802\) 0 0
\(803\) −50.1360 −1.76926
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 25.6352 0.902402
\(808\) 0 0
\(809\) −38.5032 −1.35370 −0.676850 0.736121i \(-0.736655\pi\)
−0.676850 + 0.736121i \(0.736655\pi\)
\(810\) 0 0
\(811\) 24.3236 0.854118 0.427059 0.904224i \(-0.359550\pi\)
0.427059 + 0.904224i \(0.359550\pi\)
\(812\) 0 0
\(813\) −6.15254 −0.215779
\(814\) 0 0
\(815\) 2.95019 0.103341
\(816\) 0 0
\(817\) 3.19228 0.111684
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −44.0376 −1.53692 −0.768462 0.639895i \(-0.778978\pi\)
−0.768462 + 0.639895i \(0.778978\pi\)
\(822\) 0 0
\(823\) 41.5903 1.44975 0.724873 0.688883i \(-0.241899\pi\)
0.724873 + 0.688883i \(0.241899\pi\)
\(824\) 0 0
\(825\) −61.1599 −2.12931
\(826\) 0 0
\(827\) 12.2346 0.425437 0.212719 0.977113i \(-0.431768\pi\)
0.212719 + 0.977113i \(0.431768\pi\)
\(828\) 0 0
\(829\) 33.6302 1.16803 0.584013 0.811744i \(-0.301482\pi\)
0.584013 + 0.811744i \(0.301482\pi\)
\(830\) 0 0
\(831\) −50.8128 −1.76268
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −5.34669 −0.185030
\(836\) 0 0
\(837\) 32.9383 1.13851
\(838\) 0 0
\(839\) 12.3839 0.427541 0.213771 0.976884i \(-0.431426\pi\)
0.213771 + 0.976884i \(0.431426\pi\)
\(840\) 0 0
\(841\) −28.2057 −0.972611
\(842\) 0 0
\(843\) −14.4822 −0.498794
\(844\) 0 0
\(845\) −4.74099 −0.163095
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 28.8883 0.991445
\(850\) 0 0
\(851\) −0.162162 −0.00555884
\(852\) 0 0
\(853\) 11.8119 0.404432 0.202216 0.979341i \(-0.435186\pi\)
0.202216 + 0.979341i \(0.435186\pi\)
\(854\) 0 0
\(855\) 0.979987 0.0335149
\(856\) 0 0
\(857\) −2.06114 −0.0704072 −0.0352036 0.999380i \(-0.511208\pi\)
−0.0352036 + 0.999380i \(0.511208\pi\)
\(858\) 0 0
\(859\) 39.0418 1.33209 0.666045 0.745911i \(-0.267986\pi\)
0.666045 + 0.745911i \(0.267986\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 27.5583 0.938095 0.469048 0.883173i \(-0.344597\pi\)
0.469048 + 0.883173i \(0.344597\pi\)
\(864\) 0 0
\(865\) −10.1007 −0.343434
\(866\) 0 0
\(867\) −10.5162 −0.357148
\(868\) 0 0
\(869\) 69.2242 2.34827
\(870\) 0 0
\(871\) −6.74429 −0.228521
\(872\) 0 0
\(873\) 47.8770 1.62039
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −54.7549 −1.84894 −0.924471 0.381253i \(-0.875493\pi\)
−0.924471 + 0.381253i \(0.875493\pi\)
\(878\) 0 0
\(879\) −32.4593 −1.09483
\(880\) 0 0
\(881\) 51.4637 1.73386 0.866929 0.498432i \(-0.166091\pi\)
0.866929 + 0.498432i \(0.166091\pi\)
\(882\) 0 0
\(883\) −28.5358 −0.960305 −0.480152 0.877185i \(-0.659419\pi\)
−0.480152 + 0.877185i \(0.659419\pi\)
\(884\) 0 0
\(885\) 10.7539 0.361489
\(886\) 0 0
\(887\) −21.7123 −0.729027 −0.364514 0.931198i \(-0.618765\pi\)
−0.364514 + 0.931198i \(0.618765\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −15.4318 −0.516984
\(892\) 0 0
\(893\) 2.30183 0.0770279
\(894\) 0 0
\(895\) −3.01792 −0.100878
\(896\) 0 0
\(897\) −0.355283 −0.0118625
\(898\) 0 0
\(899\) 8.17982 0.272812
\(900\) 0 0
\(901\) 43.8948 1.46235
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.13833 0.270527
\(906\) 0 0
\(907\) −41.4824 −1.37740 −0.688700 0.725046i \(-0.741818\pi\)
−0.688700 + 0.725046i \(0.741818\pi\)
\(908\) 0 0
\(909\) 47.3740 1.57130
\(910\) 0 0
\(911\) 34.7992 1.15295 0.576474 0.817115i \(-0.304428\pi\)
0.576474 + 0.817115i \(0.304428\pi\)
\(912\) 0 0
\(913\) 4.84614 0.160384
\(914\) 0 0
\(915\) 1.54714 0.0511469
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 15.9080 0.524755 0.262378 0.964965i \(-0.415493\pi\)
0.262378 + 0.964965i \(0.415493\pi\)
\(920\) 0 0
\(921\) 25.9526 0.855166
\(922\) 0 0
\(923\) 8.72122 0.287062
\(924\) 0 0
\(925\) −10.0524 −0.330519
\(926\) 0 0
\(927\) −52.7918 −1.73391
\(928\) 0 0
\(929\) −54.5601 −1.79006 −0.895029 0.446008i \(-0.852845\pi\)
−0.895029 + 0.446008i \(0.852845\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −21.8166 −0.714243
\(934\) 0 0
\(935\) −8.03484 −0.262767
\(936\) 0 0
\(937\) −3.49463 −0.114164 −0.0570822 0.998369i \(-0.518180\pi\)
−0.0570822 + 0.998369i \(0.518180\pi\)
\(938\) 0 0
\(939\) 41.3953 1.35088
\(940\) 0 0
\(941\) −18.2788 −0.595871 −0.297936 0.954586i \(-0.596298\pi\)
−0.297936 + 0.954586i \(0.596298\pi\)
\(942\) 0 0
\(943\) −0.0771055 −0.00251090
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −13.6963 −0.445069 −0.222534 0.974925i \(-0.571433\pi\)
−0.222534 + 0.974925i \(0.571433\pi\)
\(948\) 0 0
\(949\) −18.0541 −0.586061
\(950\) 0 0
\(951\) −13.9837 −0.453452
\(952\) 0 0
\(953\) −41.4865 −1.34388 −0.671940 0.740606i \(-0.734539\pi\)
−0.671940 + 0.740606i \(0.734539\pi\)
\(954\) 0 0
\(955\) −0.0498088 −0.00161177
\(956\) 0 0
\(957\) 11.4038 0.368631
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 53.2394 1.71740
\(962\) 0 0
\(963\) 49.3393 1.58994
\(964\) 0 0
\(965\) 1.07287 0.0345369
\(966\) 0 0
\(967\) −9.55841 −0.307378 −0.153689 0.988119i \(-0.549115\pi\)
−0.153689 + 0.988119i \(0.549115\pi\)
\(968\) 0 0
\(969\) −4.73136 −0.151993
\(970\) 0 0
\(971\) 38.0415 1.22081 0.610405 0.792090i \(-0.291007\pi\)
0.610405 + 0.792090i \(0.291007\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −22.0238 −0.705327
\(976\) 0 0
\(977\) 52.4259 1.67725 0.838626 0.544708i \(-0.183360\pi\)
0.838626 + 0.544708i \(0.183360\pi\)
\(978\) 0 0
\(979\) −17.7171 −0.566242
\(980\) 0 0
\(981\) 28.0783 0.896471
\(982\) 0 0
\(983\) −22.4487 −0.716002 −0.358001 0.933721i \(-0.616542\pi\)
−0.358001 + 0.933721i \(0.616542\pi\)
\(984\) 0 0
\(985\) 0.887853 0.0282893
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.509930 −0.0162148
\(990\) 0 0
\(991\) −38.6350 −1.22728 −0.613641 0.789585i \(-0.710296\pi\)
−0.613641 + 0.789585i \(0.710296\pi\)
\(992\) 0 0
\(993\) −31.8158 −1.00964
\(994\) 0 0
\(995\) −0.137009 −0.00434347
\(996\) 0 0
\(997\) −46.4862 −1.47223 −0.736116 0.676855i \(-0.763342\pi\)
−0.736116 + 0.676855i \(0.763342\pi\)
\(998\) 0 0
\(999\) 7.54756 0.238794
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8036.2.a.p.1.9 yes 10
7.6 odd 2 8036.2.a.o.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8036.2.a.o.1.2 10 7.6 odd 2
8036.2.a.p.1.9 yes 10 1.1 even 1 trivial