Properties

Label 8036.2.a.p.1.2
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 1.2
Root \(-1.91097\) of defining polynomial
Character \(\chi\) \(=\) 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.91097 q^{3} +1.95825 q^{5} +0.651806 q^{9} +O(q^{10})\) \(q-1.91097 q^{3} +1.95825 q^{5} +0.651806 q^{9} +0.643473 q^{11} -3.67505 q^{13} -3.74216 q^{15} -4.14775 q^{17} -0.715949 q^{19} -6.03491 q^{23} -1.16525 q^{25} +4.48733 q^{27} -8.58210 q^{29} +6.28884 q^{31} -1.22966 q^{33} +5.47767 q^{37} +7.02290 q^{39} +1.00000 q^{41} -10.5823 q^{43} +1.27640 q^{45} -9.33410 q^{47} +7.92622 q^{51} -0.928777 q^{53} +1.26008 q^{55} +1.36816 q^{57} +3.27970 q^{59} +3.37016 q^{61} -7.19667 q^{65} +13.9906 q^{67} +11.5325 q^{69} -0.555038 q^{71} +13.7022 q^{73} +2.22675 q^{75} +3.09679 q^{79} -10.5306 q^{81} -6.57829 q^{83} -8.12234 q^{85} +16.4001 q^{87} +16.3958 q^{89} -12.0178 q^{93} -1.40201 q^{95} +18.8641 q^{97} +0.419420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) −1.91097 −1.10330 −0.551649 0.834076i \(-0.686001\pi\)
−0.551649 + 0.834076i \(0.686001\pi\)
\(4\) 0 0
\(5\) 1.95825 0.875757 0.437879 0.899034i \(-0.355730\pi\)
0.437879 + 0.899034i \(0.355730\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.651806 0.217269
\(10\) 0 0
\(11\) 0.643473 0.194015 0.0970073 0.995284i \(-0.469073\pi\)
0.0970073 + 0.995284i \(0.469073\pi\)
\(12\) 0 0
\(13\) −3.67505 −1.01927 −0.509637 0.860389i \(-0.670220\pi\)
−0.509637 + 0.860389i \(0.670220\pi\)
\(14\) 0 0
\(15\) −3.74216 −0.966222
\(16\) 0 0
\(17\) −4.14775 −1.00598 −0.502988 0.864293i \(-0.667766\pi\)
−0.502988 + 0.864293i \(0.667766\pi\)
\(18\) 0 0
\(19\) −0.715949 −0.164250 −0.0821250 0.996622i \(-0.526171\pi\)
−0.0821250 + 0.996622i \(0.526171\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.03491 −1.25836 −0.629182 0.777258i \(-0.716610\pi\)
−0.629182 + 0.777258i \(0.716610\pi\)
\(24\) 0 0
\(25\) −1.16525 −0.233049
\(26\) 0 0
\(27\) 4.48733 0.863587
\(28\) 0 0
\(29\) −8.58210 −1.59366 −0.796828 0.604206i \(-0.793490\pi\)
−0.796828 + 0.604206i \(0.793490\pi\)
\(30\) 0 0
\(31\) 6.28884 1.12951 0.564754 0.825259i \(-0.308971\pi\)
0.564754 + 0.825259i \(0.308971\pi\)
\(32\) 0 0
\(33\) −1.22966 −0.214056
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.47767 0.900523 0.450261 0.892897i \(-0.351331\pi\)
0.450261 + 0.892897i \(0.351331\pi\)
\(38\) 0 0
\(39\) 7.02290 1.12456
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −10.5823 −1.61379 −0.806893 0.590698i \(-0.798853\pi\)
−0.806893 + 0.590698i \(0.798853\pi\)
\(44\) 0 0
\(45\) 1.27640 0.190275
\(46\) 0 0
\(47\) −9.33410 −1.36152 −0.680760 0.732507i \(-0.738350\pi\)
−0.680760 + 0.732507i \(0.738350\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 7.92622 1.10989
\(52\) 0 0
\(53\) −0.928777 −0.127577 −0.0637887 0.997963i \(-0.520318\pi\)
−0.0637887 + 0.997963i \(0.520318\pi\)
\(54\) 0 0
\(55\) 1.26008 0.169910
\(56\) 0 0
\(57\) 1.36816 0.181217
\(58\) 0 0
\(59\) 3.27970 0.426980 0.213490 0.976945i \(-0.431517\pi\)
0.213490 + 0.976945i \(0.431517\pi\)
\(60\) 0 0
\(61\) 3.37016 0.431504 0.215752 0.976448i \(-0.430780\pi\)
0.215752 + 0.976448i \(0.430780\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.19667 −0.892637
\(66\) 0 0
\(67\) 13.9906 1.70923 0.854614 0.519264i \(-0.173794\pi\)
0.854614 + 0.519264i \(0.173794\pi\)
\(68\) 0 0
\(69\) 11.5325 1.38835
\(70\) 0 0
\(71\) −0.555038 −0.0658709 −0.0329355 0.999457i \(-0.510486\pi\)
−0.0329355 + 0.999457i \(0.510486\pi\)
\(72\) 0 0
\(73\) 13.7022 1.60373 0.801863 0.597508i \(-0.203842\pi\)
0.801863 + 0.597508i \(0.203842\pi\)
\(74\) 0 0
\(75\) 2.22675 0.257123
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 3.09679 0.348416 0.174208 0.984709i \(-0.444264\pi\)
0.174208 + 0.984709i \(0.444264\pi\)
\(80\) 0 0
\(81\) −10.5306 −1.17006
\(82\) 0 0
\(83\) −6.57829 −0.722061 −0.361030 0.932554i \(-0.617575\pi\)
−0.361030 + 0.932554i \(0.617575\pi\)
\(84\) 0 0
\(85\) −8.12234 −0.880992
\(86\) 0 0
\(87\) 16.4001 1.75828
\(88\) 0 0
\(89\) 16.3958 1.73795 0.868974 0.494858i \(-0.164780\pi\)
0.868974 + 0.494858i \(0.164780\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −12.0178 −1.24619
\(94\) 0 0
\(95\) −1.40201 −0.143843
\(96\) 0 0
\(97\) 18.8641 1.91536 0.957678 0.287840i \(-0.0929372\pi\)
0.957678 + 0.287840i \(0.0929372\pi\)
\(98\) 0 0
\(99\) 0.419420 0.0421533
\(100\) 0 0
\(101\) −6.25842 −0.622736 −0.311368 0.950289i \(-0.600787\pi\)
−0.311368 + 0.950289i \(0.600787\pi\)
\(102\) 0 0
\(103\) −4.69885 −0.462991 −0.231496 0.972836i \(-0.574362\pi\)
−0.231496 + 0.972836i \(0.574362\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.02610 0.292544 0.146272 0.989244i \(-0.453273\pi\)
0.146272 + 0.989244i \(0.453273\pi\)
\(108\) 0 0
\(109\) 13.5508 1.29793 0.648967 0.760817i \(-0.275201\pi\)
0.648967 + 0.760817i \(0.275201\pi\)
\(110\) 0 0
\(111\) −10.4677 −0.993546
\(112\) 0 0
\(113\) 7.33757 0.690260 0.345130 0.938555i \(-0.387835\pi\)
0.345130 + 0.938555i \(0.387835\pi\)
\(114\) 0 0
\(115\) −11.8179 −1.10202
\(116\) 0 0
\(117\) −2.39542 −0.221456
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.5859 −0.962358
\(122\) 0 0
\(123\) −1.91097 −0.172306
\(124\) 0 0
\(125\) −12.0731 −1.07985
\(126\) 0 0
\(127\) −19.8301 −1.75963 −0.879817 0.475312i \(-0.842335\pi\)
−0.879817 + 0.475312i \(0.842335\pi\)
\(128\) 0 0
\(129\) 20.2225 1.78049
\(130\) 0 0
\(131\) −13.2327 −1.15614 −0.578072 0.815986i \(-0.696195\pi\)
−0.578072 + 0.815986i \(0.696195\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 8.78732 0.756292
\(136\) 0 0
\(137\) 13.4024 1.14505 0.572523 0.819889i \(-0.305965\pi\)
0.572523 + 0.819889i \(0.305965\pi\)
\(138\) 0 0
\(139\) 22.4485 1.90406 0.952030 0.306003i \(-0.0989918\pi\)
0.952030 + 0.306003i \(0.0989918\pi\)
\(140\) 0 0
\(141\) 17.8372 1.50216
\(142\) 0 0
\(143\) −2.36480 −0.197754
\(144\) 0 0
\(145\) −16.8059 −1.39566
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 19.9192 1.63185 0.815924 0.578159i \(-0.196229\pi\)
0.815924 + 0.578159i \(0.196229\pi\)
\(150\) 0 0
\(151\) 19.3734 1.57659 0.788294 0.615299i \(-0.210965\pi\)
0.788294 + 0.615299i \(0.210965\pi\)
\(152\) 0 0
\(153\) −2.70353 −0.218567
\(154\) 0 0
\(155\) 12.3151 0.989175
\(156\) 0 0
\(157\) 5.70389 0.455220 0.227610 0.973752i \(-0.426909\pi\)
0.227610 + 0.973752i \(0.426909\pi\)
\(158\) 0 0
\(159\) 1.77486 0.140756
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −11.3263 −0.887146 −0.443573 0.896238i \(-0.646289\pi\)
−0.443573 + 0.896238i \(0.646289\pi\)
\(164\) 0 0
\(165\) −2.40798 −0.187461
\(166\) 0 0
\(167\) 6.12840 0.474230 0.237115 0.971482i \(-0.423798\pi\)
0.237115 + 0.971482i \(0.423798\pi\)
\(168\) 0 0
\(169\) 0.505968 0.0389206
\(170\) 0 0
\(171\) −0.466660 −0.0356864
\(172\) 0 0
\(173\) −0.598647 −0.0455143 −0.0227571 0.999741i \(-0.507244\pi\)
−0.0227571 + 0.999741i \(0.507244\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.26741 −0.471087
\(178\) 0 0
\(179\) −10.8022 −0.807397 −0.403699 0.914892i \(-0.632276\pi\)
−0.403699 + 0.914892i \(0.632276\pi\)
\(180\) 0 0
\(181\) 13.8512 1.02955 0.514777 0.857324i \(-0.327875\pi\)
0.514777 + 0.857324i \(0.327875\pi\)
\(182\) 0 0
\(183\) −6.44027 −0.476078
\(184\) 0 0
\(185\) 10.7267 0.788639
\(186\) 0 0
\(187\) −2.66897 −0.195174
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.2949 −1.46849 −0.734243 0.678886i \(-0.762463\pi\)
−0.734243 + 0.678886i \(0.762463\pi\)
\(192\) 0 0
\(193\) 2.74477 0.197573 0.0987866 0.995109i \(-0.468504\pi\)
0.0987866 + 0.995109i \(0.468504\pi\)
\(194\) 0 0
\(195\) 13.7526 0.984846
\(196\) 0 0
\(197\) −14.7453 −1.05056 −0.525280 0.850929i \(-0.676039\pi\)
−0.525280 + 0.850929i \(0.676039\pi\)
\(198\) 0 0
\(199\) −9.53698 −0.676059 −0.338029 0.941136i \(-0.609760\pi\)
−0.338029 + 0.941136i \(0.609760\pi\)
\(200\) 0 0
\(201\) −26.7357 −1.88579
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1.95825 0.136770
\(206\) 0 0
\(207\) −3.93359 −0.273403
\(208\) 0 0
\(209\) −0.460694 −0.0318669
\(210\) 0 0
\(211\) −17.4826 −1.20355 −0.601775 0.798666i \(-0.705540\pi\)
−0.601775 + 0.798666i \(0.705540\pi\)
\(212\) 0 0
\(213\) 1.06066 0.0726754
\(214\) 0 0
\(215\) −20.7228 −1.41328
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −26.1846 −1.76939
\(220\) 0 0
\(221\) 15.2432 1.02537
\(222\) 0 0
\(223\) 1.69394 0.113435 0.0567174 0.998390i \(-0.481937\pi\)
0.0567174 + 0.998390i \(0.481937\pi\)
\(224\) 0 0
\(225\) −0.759515 −0.0506343
\(226\) 0 0
\(227\) 20.5800 1.36594 0.682970 0.730446i \(-0.260688\pi\)
0.682970 + 0.730446i \(0.260688\pi\)
\(228\) 0 0
\(229\) 13.1024 0.865830 0.432915 0.901435i \(-0.357485\pi\)
0.432915 + 0.901435i \(0.357485\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.60096 −0.432443 −0.216222 0.976344i \(-0.569373\pi\)
−0.216222 + 0.976344i \(0.569373\pi\)
\(234\) 0 0
\(235\) −18.2785 −1.19236
\(236\) 0 0
\(237\) −5.91787 −0.384407
\(238\) 0 0
\(239\) −8.80511 −0.569555 −0.284778 0.958594i \(-0.591920\pi\)
−0.284778 + 0.958594i \(0.591920\pi\)
\(240\) 0 0
\(241\) 3.09739 0.199520 0.0997602 0.995012i \(-0.468192\pi\)
0.0997602 + 0.995012i \(0.468192\pi\)
\(242\) 0 0
\(243\) 6.66161 0.427343
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.63115 0.167416
\(248\) 0 0
\(249\) 12.5709 0.796649
\(250\) 0 0
\(251\) 19.4178 1.22564 0.612819 0.790223i \(-0.290035\pi\)
0.612819 + 0.790223i \(0.290035\pi\)
\(252\) 0 0
\(253\) −3.88330 −0.244141
\(254\) 0 0
\(255\) 15.5215 0.971997
\(256\) 0 0
\(257\) 2.62884 0.163983 0.0819913 0.996633i \(-0.473872\pi\)
0.0819913 + 0.996633i \(0.473872\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −5.59386 −0.346252
\(262\) 0 0
\(263\) −3.36712 −0.207625 −0.103813 0.994597i \(-0.533104\pi\)
−0.103813 + 0.994597i \(0.533104\pi\)
\(264\) 0 0
\(265\) −1.81878 −0.111727
\(266\) 0 0
\(267\) −31.3318 −1.91748
\(268\) 0 0
\(269\) 11.7979 0.719332 0.359666 0.933081i \(-0.382891\pi\)
0.359666 + 0.933081i \(0.382891\pi\)
\(270\) 0 0
\(271\) −6.86899 −0.417261 −0.208631 0.977994i \(-0.566901\pi\)
−0.208631 + 0.977994i \(0.566901\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.749805 −0.0452150
\(276\) 0 0
\(277\) −25.4503 −1.52916 −0.764579 0.644530i \(-0.777053\pi\)
−0.764579 + 0.644530i \(0.777053\pi\)
\(278\) 0 0
\(279\) 4.09910 0.245407
\(280\) 0 0
\(281\) 30.1862 1.80076 0.900379 0.435106i \(-0.143289\pi\)
0.900379 + 0.435106i \(0.143289\pi\)
\(282\) 0 0
\(283\) 0.426937 0.0253788 0.0126894 0.999919i \(-0.495961\pi\)
0.0126894 + 0.999919i \(0.495961\pi\)
\(284\) 0 0
\(285\) 2.67920 0.158702
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.203821 0.0119895
\(290\) 0 0
\(291\) −36.0487 −2.11321
\(292\) 0 0
\(293\) −12.6014 −0.736184 −0.368092 0.929789i \(-0.619989\pi\)
−0.368092 + 0.929789i \(0.619989\pi\)
\(294\) 0 0
\(295\) 6.42248 0.373931
\(296\) 0 0
\(297\) 2.88748 0.167548
\(298\) 0 0
\(299\) 22.1786 1.28262
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 11.9596 0.687064
\(304\) 0 0
\(305\) 6.59962 0.377893
\(306\) 0 0
\(307\) −8.09076 −0.461764 −0.230882 0.972982i \(-0.574161\pi\)
−0.230882 + 0.972982i \(0.574161\pi\)
\(308\) 0 0
\(309\) 8.97936 0.510818
\(310\) 0 0
\(311\) 0.357500 0.0202720 0.0101360 0.999949i \(-0.496774\pi\)
0.0101360 + 0.999949i \(0.496774\pi\)
\(312\) 0 0
\(313\) 26.5989 1.50346 0.751729 0.659472i \(-0.229220\pi\)
0.751729 + 0.659472i \(0.229220\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −25.5545 −1.43528 −0.717642 0.696413i \(-0.754778\pi\)
−0.717642 + 0.696413i \(0.754778\pi\)
\(318\) 0 0
\(319\) −5.52235 −0.309192
\(320\) 0 0
\(321\) −5.78278 −0.322764
\(322\) 0 0
\(323\) 2.96958 0.165232
\(324\) 0 0
\(325\) 4.28234 0.237541
\(326\) 0 0
\(327\) −25.8952 −1.43201
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 16.0465 0.881998 0.440999 0.897508i \(-0.354624\pi\)
0.440999 + 0.897508i \(0.354624\pi\)
\(332\) 0 0
\(333\) 3.57038 0.195655
\(334\) 0 0
\(335\) 27.3972 1.49687
\(336\) 0 0
\(337\) −6.34485 −0.345626 −0.172813 0.984955i \(-0.555286\pi\)
−0.172813 + 0.984955i \(0.555286\pi\)
\(338\) 0 0
\(339\) −14.0219 −0.761564
\(340\) 0 0
\(341\) 4.04670 0.219141
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 22.5836 1.21586
\(346\) 0 0
\(347\) −25.4136 −1.36427 −0.682136 0.731225i \(-0.738949\pi\)
−0.682136 + 0.731225i \(0.738949\pi\)
\(348\) 0 0
\(349\) 5.87318 0.314384 0.157192 0.987568i \(-0.449756\pi\)
0.157192 + 0.987568i \(0.449756\pi\)
\(350\) 0 0
\(351\) −16.4911 −0.880232
\(352\) 0 0
\(353\) 18.3167 0.974901 0.487451 0.873151i \(-0.337927\pi\)
0.487451 + 0.873151i \(0.337927\pi\)
\(354\) 0 0
\(355\) −1.08691 −0.0576870
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.1404 0.587967 0.293983 0.955810i \(-0.405019\pi\)
0.293983 + 0.955810i \(0.405019\pi\)
\(360\) 0 0
\(361\) −18.4874 −0.973022
\(362\) 0 0
\(363\) 20.2294 1.06177
\(364\) 0 0
\(365\) 26.8324 1.40447
\(366\) 0 0
\(367\) −5.92956 −0.309520 −0.154760 0.987952i \(-0.549460\pi\)
−0.154760 + 0.987952i \(0.549460\pi\)
\(368\) 0 0
\(369\) 0.651806 0.0339317
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3.33117 0.172481 0.0862406 0.996274i \(-0.472515\pi\)
0.0862406 + 0.996274i \(0.472515\pi\)
\(374\) 0 0
\(375\) 23.0714 1.19140
\(376\) 0 0
\(377\) 31.5396 1.62437
\(378\) 0 0
\(379\) −5.80640 −0.298255 −0.149127 0.988818i \(-0.547646\pi\)
−0.149127 + 0.988818i \(0.547646\pi\)
\(380\) 0 0
\(381\) 37.8947 1.94140
\(382\) 0 0
\(383\) 0.396175 0.0202436 0.0101218 0.999949i \(-0.496778\pi\)
0.0101218 + 0.999949i \(0.496778\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.89761 −0.350625
\(388\) 0 0
\(389\) 37.1505 1.88361 0.941803 0.336166i \(-0.109130\pi\)
0.941803 + 0.336166i \(0.109130\pi\)
\(390\) 0 0
\(391\) 25.0313 1.26589
\(392\) 0 0
\(393\) 25.2872 1.27557
\(394\) 0 0
\(395\) 6.06429 0.305128
\(396\) 0 0
\(397\) 11.1069 0.557441 0.278720 0.960372i \(-0.410090\pi\)
0.278720 + 0.960372i \(0.410090\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14.3534 −0.716774 −0.358387 0.933573i \(-0.616673\pi\)
−0.358387 + 0.933573i \(0.616673\pi\)
\(402\) 0 0
\(403\) −23.1118 −1.15128
\(404\) 0 0
\(405\) −20.6215 −1.02469
\(406\) 0 0
\(407\) 3.52473 0.174715
\(408\) 0 0
\(409\) 21.8460 1.08021 0.540107 0.841597i \(-0.318384\pi\)
0.540107 + 0.841597i \(0.318384\pi\)
\(410\) 0 0
\(411\) −25.6116 −1.26333
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.8819 −0.632350
\(416\) 0 0
\(417\) −42.8985 −2.10075
\(418\) 0 0
\(419\) −11.2265 −0.548450 −0.274225 0.961666i \(-0.588421\pi\)
−0.274225 + 0.961666i \(0.588421\pi\)
\(420\) 0 0
\(421\) 22.0291 1.07363 0.536817 0.843699i \(-0.319627\pi\)
0.536817 + 0.843699i \(0.319627\pi\)
\(422\) 0 0
\(423\) −6.08403 −0.295815
\(424\) 0 0
\(425\) 4.83315 0.234442
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.51905 0.218182
\(430\) 0 0
\(431\) 20.5384 0.989300 0.494650 0.869092i \(-0.335296\pi\)
0.494650 + 0.869092i \(0.335296\pi\)
\(432\) 0 0
\(433\) 20.9277 1.00572 0.502862 0.864367i \(-0.332281\pi\)
0.502862 + 0.864367i \(0.332281\pi\)
\(434\) 0 0
\(435\) 32.1156 1.53983
\(436\) 0 0
\(437\) 4.32068 0.206686
\(438\) 0 0
\(439\) 8.02256 0.382896 0.191448 0.981503i \(-0.438682\pi\)
0.191448 + 0.981503i \(0.438682\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 23.3599 1.10986 0.554931 0.831897i \(-0.312745\pi\)
0.554931 + 0.831897i \(0.312745\pi\)
\(444\) 0 0
\(445\) 32.1070 1.52202
\(446\) 0 0
\(447\) −38.0651 −1.80042
\(448\) 0 0
\(449\) 26.8838 1.26872 0.634362 0.773036i \(-0.281263\pi\)
0.634362 + 0.773036i \(0.281263\pi\)
\(450\) 0 0
\(451\) 0.643473 0.0303000
\(452\) 0 0
\(453\) −37.0221 −1.73945
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 36.1981 1.69327 0.846637 0.532170i \(-0.178623\pi\)
0.846637 + 0.532170i \(0.178623\pi\)
\(458\) 0 0
\(459\) −18.6123 −0.868748
\(460\) 0 0
\(461\) −10.0948 −0.470163 −0.235081 0.971976i \(-0.575536\pi\)
−0.235081 + 0.971976i \(0.575536\pi\)
\(462\) 0 0
\(463\) 5.51652 0.256374 0.128187 0.991750i \(-0.459084\pi\)
0.128187 + 0.991750i \(0.459084\pi\)
\(464\) 0 0
\(465\) −23.5338 −1.09136
\(466\) 0 0
\(467\) −16.7658 −0.775830 −0.387915 0.921695i \(-0.626805\pi\)
−0.387915 + 0.921695i \(0.626805\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −10.9000 −0.502243
\(472\) 0 0
\(473\) −6.80943 −0.313098
\(474\) 0 0
\(475\) 0.834257 0.0382783
\(476\) 0 0
\(477\) −0.605382 −0.0277186
\(478\) 0 0
\(479\) 29.4210 1.34428 0.672141 0.740423i \(-0.265375\pi\)
0.672141 + 0.740423i \(0.265375\pi\)
\(480\) 0 0
\(481\) −20.1307 −0.917880
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 36.9406 1.67739
\(486\) 0 0
\(487\) −30.2436 −1.37047 −0.685234 0.728323i \(-0.740300\pi\)
−0.685234 + 0.728323i \(0.740300\pi\)
\(488\) 0 0
\(489\) 21.6443 0.978787
\(490\) 0 0
\(491\) 1.38354 0.0624383 0.0312192 0.999513i \(-0.490061\pi\)
0.0312192 + 0.999513i \(0.490061\pi\)
\(492\) 0 0
\(493\) 35.5964 1.60318
\(494\) 0 0
\(495\) 0.821330 0.0369160
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 5.03472 0.225385 0.112693 0.993630i \(-0.464052\pi\)
0.112693 + 0.993630i \(0.464052\pi\)
\(500\) 0 0
\(501\) −11.7112 −0.523218
\(502\) 0 0
\(503\) −15.9805 −0.712533 −0.356267 0.934384i \(-0.615951\pi\)
−0.356267 + 0.934384i \(0.615951\pi\)
\(504\) 0 0
\(505\) −12.2556 −0.545365
\(506\) 0 0
\(507\) −0.966889 −0.0429411
\(508\) 0 0
\(509\) −27.0090 −1.19715 −0.598576 0.801066i \(-0.704267\pi\)
−0.598576 + 0.801066i \(0.704267\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −3.21270 −0.141844
\(514\) 0 0
\(515\) −9.20153 −0.405468
\(516\) 0 0
\(517\) −6.00625 −0.264155
\(518\) 0 0
\(519\) 1.14400 0.0502159
\(520\) 0 0
\(521\) −15.9602 −0.699229 −0.349615 0.936894i \(-0.613687\pi\)
−0.349615 + 0.936894i \(0.613687\pi\)
\(522\) 0 0
\(523\) 1.19280 0.0521575 0.0260787 0.999660i \(-0.491698\pi\)
0.0260787 + 0.999660i \(0.491698\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26.0845 −1.13626
\(528\) 0 0
\(529\) 13.4201 0.583482
\(530\) 0 0
\(531\) 2.13773 0.0927695
\(532\) 0 0
\(533\) −3.67505 −0.159184
\(534\) 0 0
\(535\) 5.92587 0.256198
\(536\) 0 0
\(537\) 20.6428 0.890800
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −24.4332 −1.05047 −0.525233 0.850959i \(-0.676022\pi\)
−0.525233 + 0.850959i \(0.676022\pi\)
\(542\) 0 0
\(543\) −26.4693 −1.13591
\(544\) 0 0
\(545\) 26.5359 1.13667
\(546\) 0 0
\(547\) 36.7175 1.56993 0.784964 0.619541i \(-0.212681\pi\)
0.784964 + 0.619541i \(0.212681\pi\)
\(548\) 0 0
\(549\) 2.19669 0.0937523
\(550\) 0 0
\(551\) 6.14435 0.261758
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −20.4983 −0.870105
\(556\) 0 0
\(557\) 17.3858 0.736660 0.368330 0.929695i \(-0.379930\pi\)
0.368330 + 0.929695i \(0.379930\pi\)
\(558\) 0 0
\(559\) 38.8904 1.64489
\(560\) 0 0
\(561\) 5.10031 0.215335
\(562\) 0 0
\(563\) 36.0940 1.52118 0.760590 0.649232i \(-0.224910\pi\)
0.760590 + 0.649232i \(0.224910\pi\)
\(564\) 0 0
\(565\) 14.3688 0.604501
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.0482 −0.421245 −0.210622 0.977568i \(-0.567549\pi\)
−0.210622 + 0.977568i \(0.567549\pi\)
\(570\) 0 0
\(571\) 33.7668 1.41309 0.706547 0.707666i \(-0.250252\pi\)
0.706547 + 0.707666i \(0.250252\pi\)
\(572\) 0 0
\(573\) 38.7829 1.62018
\(574\) 0 0
\(575\) 7.03215 0.293261
\(576\) 0 0
\(577\) −38.3567 −1.59681 −0.798405 0.602120i \(-0.794323\pi\)
−0.798405 + 0.602120i \(0.794323\pi\)
\(578\) 0 0
\(579\) −5.24518 −0.217982
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.597643 −0.0247519
\(584\) 0 0
\(585\) −4.69083 −0.193942
\(586\) 0 0
\(587\) 46.0630 1.90122 0.950612 0.310382i \(-0.100457\pi\)
0.950612 + 0.310382i \(0.100457\pi\)
\(588\) 0 0
\(589\) −4.50248 −0.185522
\(590\) 0 0
\(591\) 28.1778 1.15908
\(592\) 0 0
\(593\) 18.4036 0.755743 0.377872 0.925858i \(-0.376656\pi\)
0.377872 + 0.925858i \(0.376656\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 18.2249 0.745895
\(598\) 0 0
\(599\) 41.2588 1.68579 0.842894 0.538080i \(-0.180850\pi\)
0.842894 + 0.538080i \(0.180850\pi\)
\(600\) 0 0
\(601\) 4.38098 0.178704 0.0893519 0.996000i \(-0.471520\pi\)
0.0893519 + 0.996000i \(0.471520\pi\)
\(602\) 0 0
\(603\) 9.11918 0.371362
\(604\) 0 0
\(605\) −20.7299 −0.842792
\(606\) 0 0
\(607\) 10.0526 0.408024 0.204012 0.978968i \(-0.434602\pi\)
0.204012 + 0.978968i \(0.434602\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 34.3033 1.38776
\(612\) 0 0
\(613\) 25.0095 1.01013 0.505063 0.863083i \(-0.331469\pi\)
0.505063 + 0.863083i \(0.331469\pi\)
\(614\) 0 0
\(615\) −3.74216 −0.150899
\(616\) 0 0
\(617\) 13.4390 0.541032 0.270516 0.962716i \(-0.412806\pi\)
0.270516 + 0.962716i \(0.412806\pi\)
\(618\) 0 0
\(619\) 31.2843 1.25742 0.628710 0.777639i \(-0.283583\pi\)
0.628710 + 0.777639i \(0.283583\pi\)
\(620\) 0 0
\(621\) −27.0806 −1.08671
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −17.8160 −0.712639
\(626\) 0 0
\(627\) 0.880373 0.0351587
\(628\) 0 0
\(629\) −22.7200 −0.905905
\(630\) 0 0
\(631\) −12.7490 −0.507530 −0.253765 0.967266i \(-0.581669\pi\)
−0.253765 + 0.967266i \(0.581669\pi\)
\(632\) 0 0
\(633\) 33.4087 1.32788
\(634\) 0 0
\(635\) −38.8323 −1.54101
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.361777 −0.0143117
\(640\) 0 0
\(641\) 12.9352 0.510909 0.255455 0.966821i \(-0.417775\pi\)
0.255455 + 0.966821i \(0.417775\pi\)
\(642\) 0 0
\(643\) −31.2875 −1.23386 −0.616929 0.787019i \(-0.711624\pi\)
−0.616929 + 0.787019i \(0.711624\pi\)
\(644\) 0 0
\(645\) 39.6007 1.55928
\(646\) 0 0
\(647\) −50.4938 −1.98512 −0.992558 0.121771i \(-0.961143\pi\)
−0.992558 + 0.121771i \(0.961143\pi\)
\(648\) 0 0
\(649\) 2.11040 0.0828404
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 37.3278 1.46075 0.730374 0.683047i \(-0.239346\pi\)
0.730374 + 0.683047i \(0.239346\pi\)
\(654\) 0 0
\(655\) −25.9129 −1.01250
\(656\) 0 0
\(657\) 8.93120 0.348439
\(658\) 0 0
\(659\) 3.19788 0.124572 0.0622859 0.998058i \(-0.480161\pi\)
0.0622859 + 0.998058i \(0.480161\pi\)
\(660\) 0 0
\(661\) −13.6505 −0.530942 −0.265471 0.964119i \(-0.585527\pi\)
−0.265471 + 0.964119i \(0.585527\pi\)
\(662\) 0 0
\(663\) −29.1292 −1.13129
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 51.7922 2.00540
\(668\) 0 0
\(669\) −3.23707 −0.125152
\(670\) 0 0
\(671\) 2.16861 0.0837181
\(672\) 0 0
\(673\) −27.9374 −1.07691 −0.538454 0.842655i \(-0.680991\pi\)
−0.538454 + 0.842655i \(0.680991\pi\)
\(674\) 0 0
\(675\) −5.22884 −0.201258
\(676\) 0 0
\(677\) 1.03395 0.0397380 0.0198690 0.999803i \(-0.493675\pi\)
0.0198690 + 0.999803i \(0.493675\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −39.3277 −1.50704
\(682\) 0 0
\(683\) −23.3348 −0.892880 −0.446440 0.894814i \(-0.647308\pi\)
−0.446440 + 0.894814i \(0.647308\pi\)
\(684\) 0 0
\(685\) 26.2453 1.00278
\(686\) 0 0
\(687\) −25.0383 −0.955269
\(688\) 0 0
\(689\) 3.41330 0.130036
\(690\) 0 0
\(691\) 42.5815 1.61988 0.809939 0.586514i \(-0.199500\pi\)
0.809939 + 0.586514i \(0.199500\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 43.9599 1.66750
\(696\) 0 0
\(697\) −4.14775 −0.157107
\(698\) 0 0
\(699\) 12.6142 0.477114
\(700\) 0 0
\(701\) −36.9932 −1.39721 −0.698606 0.715506i \(-0.746196\pi\)
−0.698606 + 0.715506i \(0.746196\pi\)
\(702\) 0 0
\(703\) −3.92173 −0.147911
\(704\) 0 0
\(705\) 34.9297 1.31553
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 23.1663 0.870030 0.435015 0.900423i \(-0.356743\pi\)
0.435015 + 0.900423i \(0.356743\pi\)
\(710\) 0 0
\(711\) 2.01850 0.0756998
\(712\) 0 0
\(713\) −37.9525 −1.42133
\(714\) 0 0
\(715\) −4.63087 −0.173185
\(716\) 0 0
\(717\) 16.8263 0.628390
\(718\) 0 0
\(719\) −10.5992 −0.395283 −0.197642 0.980274i \(-0.563328\pi\)
−0.197642 + 0.980274i \(0.563328\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −5.91902 −0.220131
\(724\) 0 0
\(725\) 10.0003 0.371400
\(726\) 0 0
\(727\) −52.8233 −1.95911 −0.979554 0.201182i \(-0.935522\pi\)
−0.979554 + 0.201182i \(0.935522\pi\)
\(728\) 0 0
\(729\) 18.8616 0.698576
\(730\) 0 0
\(731\) 43.8927 1.62343
\(732\) 0 0
\(733\) −13.0832 −0.483237 −0.241619 0.970371i \(-0.577678\pi\)
−0.241619 + 0.970371i \(0.577678\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.00260 0.331615
\(738\) 0 0
\(739\) 8.43697 0.310359 0.155180 0.987886i \(-0.450404\pi\)
0.155180 + 0.987886i \(0.450404\pi\)
\(740\) 0 0
\(741\) −5.02804 −0.184710
\(742\) 0 0
\(743\) −29.0216 −1.06470 −0.532350 0.846524i \(-0.678691\pi\)
−0.532350 + 0.846524i \(0.678691\pi\)
\(744\) 0 0
\(745\) 39.0069 1.42910
\(746\) 0 0
\(747\) −4.28777 −0.156881
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12.4098 0.452839 0.226419 0.974030i \(-0.427298\pi\)
0.226419 + 0.974030i \(0.427298\pi\)
\(752\) 0 0
\(753\) −37.1068 −1.35225
\(754\) 0 0
\(755\) 37.9381 1.38071
\(756\) 0 0
\(757\) −1.47607 −0.0536486 −0.0268243 0.999640i \(-0.508539\pi\)
−0.0268243 + 0.999640i \(0.508539\pi\)
\(758\) 0 0
\(759\) 7.42087 0.269361
\(760\) 0 0
\(761\) 28.3360 1.02718 0.513589 0.858036i \(-0.328316\pi\)
0.513589 + 0.858036i \(0.328316\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −5.29419 −0.191412
\(766\) 0 0
\(767\) −12.0530 −0.435210
\(768\) 0 0
\(769\) −45.3967 −1.63705 −0.818523 0.574473i \(-0.805207\pi\)
−0.818523 + 0.574473i \(0.805207\pi\)
\(770\) 0 0
\(771\) −5.02364 −0.180922
\(772\) 0 0
\(773\) 36.9475 1.32891 0.664455 0.747328i \(-0.268664\pi\)
0.664455 + 0.747328i \(0.268664\pi\)
\(774\) 0 0
\(775\) −7.32804 −0.263231
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.715949 −0.0256515
\(780\) 0 0
\(781\) −0.357153 −0.0127799
\(782\) 0 0
\(783\) −38.5107 −1.37626
\(784\) 0 0
\(785\) 11.1696 0.398662
\(786\) 0 0
\(787\) −43.0165 −1.53337 −0.766686 0.642023i \(-0.778096\pi\)
−0.766686 + 0.642023i \(0.778096\pi\)
\(788\) 0 0
\(789\) 6.43446 0.229073
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −12.3855 −0.439821
\(794\) 0 0
\(795\) 3.47563 0.123268
\(796\) 0 0
\(797\) 5.89036 0.208647 0.104324 0.994543i \(-0.466732\pi\)
0.104324 + 0.994543i \(0.466732\pi\)
\(798\) 0 0
\(799\) 38.7155 1.36966
\(800\) 0 0
\(801\) 10.6869 0.377601
\(802\) 0 0
\(803\) 8.81703 0.311146
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −22.5455 −0.793639
\(808\) 0 0
\(809\) 40.7584 1.43299 0.716495 0.697592i \(-0.245745\pi\)
0.716495 + 0.697592i \(0.245745\pi\)
\(810\) 0 0
\(811\) 17.1874 0.603530 0.301765 0.953382i \(-0.402424\pi\)
0.301765 + 0.953382i \(0.402424\pi\)
\(812\) 0 0
\(813\) 13.1264 0.460364
\(814\) 0 0
\(815\) −22.1798 −0.776924
\(816\) 0 0
\(817\) 7.57639 0.265064
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −17.3992 −0.607236 −0.303618 0.952794i \(-0.598195\pi\)
−0.303618 + 0.952794i \(0.598195\pi\)
\(822\) 0 0
\(823\) −10.6879 −0.372555 −0.186278 0.982497i \(-0.559642\pi\)
−0.186278 + 0.982497i \(0.559642\pi\)
\(824\) 0 0
\(825\) 1.43286 0.0498856
\(826\) 0 0
\(827\) 2.70437 0.0940401 0.0470200 0.998894i \(-0.485028\pi\)
0.0470200 + 0.998894i \(0.485028\pi\)
\(828\) 0 0
\(829\) −31.6178 −1.09813 −0.549067 0.835779i \(-0.685017\pi\)
−0.549067 + 0.835779i \(0.685017\pi\)
\(830\) 0 0
\(831\) 48.6347 1.68712
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 12.0010 0.415310
\(836\) 0 0
\(837\) 28.2201 0.975428
\(838\) 0 0
\(839\) 6.93740 0.239506 0.119753 0.992804i \(-0.461790\pi\)
0.119753 + 0.992804i \(0.461790\pi\)
\(840\) 0 0
\(841\) 44.6525 1.53974
\(842\) 0 0
\(843\) −57.6849 −1.98678
\(844\) 0 0
\(845\) 0.990813 0.0340850
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −0.815864 −0.0280004
\(850\) 0 0
\(851\) −33.0572 −1.13319
\(852\) 0 0
\(853\) −12.4961 −0.427859 −0.213929 0.976849i \(-0.568626\pi\)
−0.213929 + 0.976849i \(0.568626\pi\)
\(854\) 0 0
\(855\) −0.913838 −0.0312526
\(856\) 0 0
\(857\) 13.9355 0.476029 0.238014 0.971262i \(-0.423504\pi\)
0.238014 + 0.971262i \(0.423504\pi\)
\(858\) 0 0
\(859\) −48.7496 −1.66332 −0.831658 0.555289i \(-0.812608\pi\)
−0.831658 + 0.555289i \(0.812608\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17.4213 0.593029 0.296514 0.955028i \(-0.404176\pi\)
0.296514 + 0.955028i \(0.404176\pi\)
\(864\) 0 0
\(865\) −1.17230 −0.0398595
\(866\) 0 0
\(867\) −0.389496 −0.0132280
\(868\) 0 0
\(869\) 1.99270 0.0675977
\(870\) 0 0
\(871\) −51.4162 −1.74217
\(872\) 0 0
\(873\) 12.2957 0.416147
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 23.2166 0.783967 0.391984 0.919972i \(-0.371789\pi\)
0.391984 + 0.919972i \(0.371789\pi\)
\(878\) 0 0
\(879\) 24.0810 0.812231
\(880\) 0 0
\(881\) −55.2811 −1.86247 −0.931233 0.364424i \(-0.881266\pi\)
−0.931233 + 0.364424i \(0.881266\pi\)
\(882\) 0 0
\(883\) 1.01055 0.0340078 0.0170039 0.999855i \(-0.494587\pi\)
0.0170039 + 0.999855i \(0.494587\pi\)
\(884\) 0 0
\(885\) −12.2732 −0.412558
\(886\) 0 0
\(887\) −39.1254 −1.31370 −0.656852 0.754020i \(-0.728112\pi\)
−0.656852 + 0.754020i \(0.728112\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −6.77614 −0.227009
\(892\) 0 0
\(893\) 6.68274 0.223629
\(894\) 0 0
\(895\) −21.1535 −0.707084
\(896\) 0 0
\(897\) −42.3826 −1.41511
\(898\) 0 0
\(899\) −53.9714 −1.80005
\(900\) 0 0
\(901\) 3.85233 0.128340
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 27.1242 0.901639
\(906\) 0 0
\(907\) 14.6946 0.487926 0.243963 0.969785i \(-0.421553\pi\)
0.243963 + 0.969785i \(0.421553\pi\)
\(908\) 0 0
\(909\) −4.07927 −0.135301
\(910\) 0 0
\(911\) 11.2682 0.373331 0.186665 0.982424i \(-0.440232\pi\)
0.186665 + 0.982424i \(0.440232\pi\)
\(912\) 0 0
\(913\) −4.23295 −0.140090
\(914\) 0 0
\(915\) −12.6117 −0.416929
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −11.6108 −0.383004 −0.191502 0.981492i \(-0.561336\pi\)
−0.191502 + 0.981492i \(0.561336\pi\)
\(920\) 0 0
\(921\) 15.4612 0.509464
\(922\) 0 0
\(923\) 2.03979 0.0671406
\(924\) 0 0
\(925\) −6.38283 −0.209866
\(926\) 0 0
\(927\) −3.06274 −0.100594
\(928\) 0 0
\(929\) 23.8126 0.781265 0.390632 0.920547i \(-0.372256\pi\)
0.390632 + 0.920547i \(0.372256\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.683172 −0.0223661
\(934\) 0 0
\(935\) −5.22651 −0.170925
\(936\) 0 0
\(937\) 50.1180 1.63728 0.818641 0.574305i \(-0.194728\pi\)
0.818641 + 0.574305i \(0.194728\pi\)
\(938\) 0 0
\(939\) −50.8297 −1.65876
\(940\) 0 0
\(941\) −0.313120 −0.0102074 −0.00510371 0.999987i \(-0.501625\pi\)
−0.00510371 + 0.999987i \(0.501625\pi\)
\(942\) 0 0
\(943\) −6.03491 −0.196524
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 37.3034 1.21220 0.606100 0.795389i \(-0.292733\pi\)
0.606100 + 0.795389i \(0.292733\pi\)
\(948\) 0 0
\(949\) −50.3564 −1.63464
\(950\) 0 0
\(951\) 48.8339 1.58355
\(952\) 0 0
\(953\) −45.1980 −1.46411 −0.732053 0.681248i \(-0.761438\pi\)
−0.732053 + 0.681248i \(0.761438\pi\)
\(954\) 0 0
\(955\) −39.7425 −1.28604
\(956\) 0 0
\(957\) 10.5531 0.341132
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 8.54945 0.275789
\(962\) 0 0
\(963\) 1.97243 0.0635606
\(964\) 0 0
\(965\) 5.37496 0.173026
\(966\) 0 0
\(967\) 42.3517 1.36194 0.680969 0.732312i \(-0.261559\pi\)
0.680969 + 0.732312i \(0.261559\pi\)
\(968\) 0 0
\(969\) −5.67477 −0.182300
\(970\) 0 0
\(971\) −27.1336 −0.870758 −0.435379 0.900247i \(-0.643386\pi\)
−0.435379 + 0.900247i \(0.643386\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −8.18341 −0.262079
\(976\) 0 0
\(977\) 34.4694 1.10278 0.551388 0.834249i \(-0.314099\pi\)
0.551388 + 0.834249i \(0.314099\pi\)
\(978\) 0 0
\(979\) 10.5502 0.337187
\(980\) 0 0
\(981\) 8.83251 0.282000
\(982\) 0 0
\(983\) 13.3302 0.425168 0.212584 0.977143i \(-0.431812\pi\)
0.212584 + 0.977143i \(0.431812\pi\)
\(984\) 0 0
\(985\) −28.8750 −0.920035
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 63.8632 2.03073
\(990\) 0 0
\(991\) 36.2557 1.15170 0.575850 0.817555i \(-0.304671\pi\)
0.575850 + 0.817555i \(0.304671\pi\)
\(992\) 0 0
\(993\) −30.6645 −0.973107
\(994\) 0 0
\(995\) −18.6758 −0.592063
\(996\) 0 0
\(997\) 9.06746 0.287169 0.143585 0.989638i \(-0.454137\pi\)
0.143585 + 0.989638i \(0.454137\pi\)
\(998\) 0 0
\(999\) 24.5801 0.777679
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.1.2 yes 10
7.6 odd 2 8036.2.a.o.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8036.2.a.o.1.9 10 7.6 odd 2
8036.2.a.p.1.2 yes 10 1.1 even 1 trivial