Properties

Label 7800.2.a.bn.1.2
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.363328\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.36333 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.36333 q^{7} +1.00000 q^{9} -5.64600 q^{11} -1.00000 q^{13} +2.14134 q^{17} +2.41468 q^{19} -1.36333 q^{21} -2.72666 q^{23} +1.00000 q^{27} -5.28267 q^{29} -1.64600 q^{31} -5.64600 q^{33} +3.86799 q^{37} -1.00000 q^{39} +5.86799 q^{41} -9.00933 q^{43} +3.77801 q^{47} -5.14134 q^{49} +2.14134 q^{51} +12.0093 q^{53} +2.41468 q^{57} +6.19269 q^{59} +11.5946 q^{61} -1.36333 q^{63} -0.324695 q^{67} -2.72666 q^{69} +11.8680 q^{71} +8.28267 q^{73} +7.69735 q^{77} +2.31198 q^{79} +1.00000 q^{81} +10.3727 q^{83} -5.28267 q^{87} +3.73599 q^{89} +1.36333 q^{91} -1.64600 q^{93} -16.8480 q^{97} -5.64600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{3} - 2q^{7} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{3} - 2q^{7} + 3q^{9} + 2q^{11} - 3q^{13} - 2q^{17} + 3q^{19} - 2q^{21} - 4q^{23} + 3q^{27} + q^{29} + 14q^{31} + 2q^{33} - q^{37} - 3q^{39} + 5q^{41} - 6q^{43} + 5q^{47} - 7q^{49} - 2q^{51} + 15q^{53} + 3q^{57} + 8q^{59} + 18q^{61} - 2q^{63} - 3q^{67} - 4q^{69} + 23q^{71} + 8q^{73} + 2q^{77} + 7q^{79} + 3q^{81} + 8q^{83} + q^{87} - 14q^{89} + 2q^{91} + 14q^{93} + 2q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.36333 −0.515290 −0.257645 0.966240i \(-0.582946\pi\)
−0.257645 + 0.966240i \(0.582946\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.64600 −1.70233 −0.851167 0.524896i \(-0.824104\pi\)
−0.851167 + 0.524896i \(0.824104\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.14134 0.519350 0.259675 0.965696i \(-0.416385\pi\)
0.259675 + 0.965696i \(0.416385\pi\)
\(18\) 0 0
\(19\) 2.41468 0.553966 0.276983 0.960875i \(-0.410666\pi\)
0.276983 + 0.960875i \(0.410666\pi\)
\(20\) 0 0
\(21\) −1.36333 −0.297503
\(22\) 0 0
\(23\) −2.72666 −0.568547 −0.284274 0.958743i \(-0.591752\pi\)
−0.284274 + 0.958743i \(0.591752\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.28267 −0.980968 −0.490484 0.871450i \(-0.663180\pi\)
−0.490484 + 0.871450i \(0.663180\pi\)
\(30\) 0 0
\(31\) −1.64600 −0.295630 −0.147815 0.989015i \(-0.547224\pi\)
−0.147815 + 0.989015i \(0.547224\pi\)
\(32\) 0 0
\(33\) −5.64600 −0.982843
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.86799 0.635894 0.317947 0.948108i \(-0.397007\pi\)
0.317947 + 0.948108i \(0.397007\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 5.86799 0.916426 0.458213 0.888842i \(-0.348490\pi\)
0.458213 + 0.888842i \(0.348490\pi\)
\(42\) 0 0
\(43\) −9.00933 −1.37391 −0.686955 0.726700i \(-0.741053\pi\)
−0.686955 + 0.726700i \(0.741053\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.77801 0.551079 0.275540 0.961290i \(-0.411143\pi\)
0.275540 + 0.961290i \(0.411143\pi\)
\(48\) 0 0
\(49\) −5.14134 −0.734477
\(50\) 0 0
\(51\) 2.14134 0.299847
\(52\) 0 0
\(53\) 12.0093 1.64961 0.824804 0.565419i \(-0.191285\pi\)
0.824804 + 0.565419i \(0.191285\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.41468 0.319832
\(58\) 0 0
\(59\) 6.19269 0.806219 0.403110 0.915152i \(-0.367929\pi\)
0.403110 + 0.915152i \(0.367929\pi\)
\(60\) 0 0
\(61\) 11.5946 1.48454 0.742271 0.670099i \(-0.233749\pi\)
0.742271 + 0.670099i \(0.233749\pi\)
\(62\) 0 0
\(63\) −1.36333 −0.171763
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −0.324695 −0.0396678 −0.0198339 0.999803i \(-0.506314\pi\)
−0.0198339 + 0.999803i \(0.506314\pi\)
\(68\) 0 0
\(69\) −2.72666 −0.328251
\(70\) 0 0
\(71\) 11.8680 1.40847 0.704236 0.709966i \(-0.251290\pi\)
0.704236 + 0.709966i \(0.251290\pi\)
\(72\) 0 0
\(73\) 8.28267 0.969413 0.484707 0.874677i \(-0.338926\pi\)
0.484707 + 0.874677i \(0.338926\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.69735 0.877195
\(78\) 0 0
\(79\) 2.31198 0.260118 0.130059 0.991506i \(-0.458483\pi\)
0.130059 + 0.991506i \(0.458483\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 10.3727 1.13855 0.569274 0.822148i \(-0.307225\pi\)
0.569274 + 0.822148i \(0.307225\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.28267 −0.566362
\(88\) 0 0
\(89\) 3.73599 0.396014 0.198007 0.980201i \(-0.436553\pi\)
0.198007 + 0.980201i \(0.436553\pi\)
\(90\) 0 0
\(91\) 1.36333 0.142916
\(92\) 0 0
\(93\) −1.64600 −0.170682
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.8480 −1.71066 −0.855328 0.518086i \(-0.826645\pi\)
−0.855328 + 0.518086i \(0.826645\pi\)
\(98\) 0 0
\(99\) −5.64600 −0.567444
\(100\) 0 0
\(101\) −5.87732 −0.584815 −0.292408 0.956294i \(-0.594456\pi\)
−0.292408 + 0.956294i \(0.594456\pi\)
\(102\) 0 0
\(103\) −14.0187 −1.38130 −0.690650 0.723189i \(-0.742675\pi\)
−0.690650 + 0.723189i \(0.742675\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.8773 −1.05155 −0.525775 0.850624i \(-0.676225\pi\)
−0.525775 + 0.850624i \(0.676225\pi\)
\(108\) 0 0
\(109\) −3.58532 −0.343411 −0.171706 0.985148i \(-0.554928\pi\)
−0.171706 + 0.985148i \(0.554928\pi\)
\(110\) 0 0
\(111\) 3.86799 0.367134
\(112\) 0 0
\(113\) 18.5653 1.74648 0.873240 0.487290i \(-0.162014\pi\)
0.873240 + 0.487290i \(0.162014\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −2.91934 −0.267616
\(120\) 0 0
\(121\) 20.8773 1.89794
\(122\) 0 0
\(123\) 5.86799 0.529099
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.858664 −0.0761941 −0.0380970 0.999274i \(-0.512130\pi\)
−0.0380970 + 0.999274i \(0.512130\pi\)
\(128\) 0 0
\(129\) −9.00933 −0.793227
\(130\) 0 0
\(131\) −1.86799 −0.163207 −0.0816036 0.996665i \(-0.526004\pi\)
−0.0816036 + 0.996665i \(0.526004\pi\)
\(132\) 0 0
\(133\) −3.29200 −0.285453
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.24404 −0.448028 −0.224014 0.974586i \(-0.571916\pi\)
−0.224014 + 0.974586i \(0.571916\pi\)
\(138\) 0 0
\(139\) 8.17997 0.693816 0.346908 0.937899i \(-0.387232\pi\)
0.346908 + 0.937899i \(0.387232\pi\)
\(140\) 0 0
\(141\) 3.77801 0.318166
\(142\) 0 0
\(143\) 5.64600 0.472142
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −5.14134 −0.424050
\(148\) 0 0
\(149\) 9.73599 0.797603 0.398801 0.917037i \(-0.369426\pi\)
0.398801 + 0.917037i \(0.369426\pi\)
\(150\) 0 0
\(151\) 1.18336 0.0963004 0.0481502 0.998840i \(-0.484667\pi\)
0.0481502 + 0.998840i \(0.484667\pi\)
\(152\) 0 0
\(153\) 2.14134 0.173117
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 17.9800 1.43496 0.717481 0.696578i \(-0.245295\pi\)
0.717481 + 0.696578i \(0.245295\pi\)
\(158\) 0 0
\(159\) 12.0093 0.952402
\(160\) 0 0
\(161\) 3.71733 0.292966
\(162\) 0 0
\(163\) 4.28267 0.335445 0.167722 0.985834i \(-0.446359\pi\)
0.167722 + 0.985834i \(0.446359\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.41468 −0.496383 −0.248191 0.968711i \(-0.579836\pi\)
−0.248191 + 0.968711i \(0.579836\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 2.41468 0.184655
\(172\) 0 0
\(173\) 17.1800 1.30617 0.653084 0.757285i \(-0.273475\pi\)
0.653084 + 0.757285i \(0.273475\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.19269 0.465471
\(178\) 0 0
\(179\) 7.11203 0.531578 0.265789 0.964031i \(-0.414368\pi\)
0.265789 + 0.964031i \(0.414368\pi\)
\(180\) 0 0
\(181\) 25.4333 1.89045 0.945223 0.326427i \(-0.105845\pi\)
0.945223 + 0.326427i \(0.105845\pi\)
\(182\) 0 0
\(183\) 11.5946 0.857101
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.0900 −0.884107
\(188\) 0 0
\(189\) −1.36333 −0.0991675
\(190\) 0 0
\(191\) 16.1214 1.16650 0.583250 0.812292i \(-0.301781\pi\)
0.583250 + 0.812292i \(0.301781\pi\)
\(192\) 0 0
\(193\) 10.0187 0.721159 0.360579 0.932729i \(-0.382579\pi\)
0.360579 + 0.932729i \(0.382579\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.0187 −0.713800 −0.356900 0.934143i \(-0.616166\pi\)
−0.356900 + 0.934143i \(0.616166\pi\)
\(198\) 0 0
\(199\) −15.4427 −1.09470 −0.547351 0.836903i \(-0.684364\pi\)
−0.547351 + 0.836903i \(0.684364\pi\)
\(200\) 0 0
\(201\) −0.324695 −0.0229022
\(202\) 0 0
\(203\) 7.20202 0.505482
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.72666 −0.189516
\(208\) 0 0
\(209\) −13.6333 −0.943034
\(210\) 0 0
\(211\) 17.8387 1.22807 0.614033 0.789280i \(-0.289546\pi\)
0.614033 + 0.789280i \(0.289546\pi\)
\(212\) 0 0
\(213\) 11.8680 0.813181
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.24404 0.152335
\(218\) 0 0
\(219\) 8.28267 0.559691
\(220\) 0 0
\(221\) −2.14134 −0.144042
\(222\) 0 0
\(223\) −6.56534 −0.439648 −0.219824 0.975540i \(-0.570548\pi\)
−0.219824 + 0.975540i \(0.570548\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.3820 0.888194 0.444097 0.895979i \(-0.353525\pi\)
0.444097 + 0.895979i \(0.353525\pi\)
\(228\) 0 0
\(229\) 9.88665 0.653328 0.326664 0.945140i \(-0.394075\pi\)
0.326664 + 0.945140i \(0.394075\pi\)
\(230\) 0 0
\(231\) 7.69735 0.506449
\(232\) 0 0
\(233\) −26.8667 −1.76009 −0.880047 0.474886i \(-0.842489\pi\)
−0.880047 + 0.474886i \(0.842489\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.31198 0.150179
\(238\) 0 0
\(239\) 27.4847 1.77784 0.888918 0.458066i \(-0.151458\pi\)
0.888918 + 0.458066i \(0.151458\pi\)
\(240\) 0 0
\(241\) −10.0187 −0.645358 −0.322679 0.946508i \(-0.604584\pi\)
−0.322679 + 0.946508i \(0.604584\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.41468 −0.153642
\(248\) 0 0
\(249\) 10.3727 0.657340
\(250\) 0 0
\(251\) −24.1507 −1.52438 −0.762188 0.647355i \(-0.775875\pi\)
−0.762188 + 0.647355i \(0.775875\pi\)
\(252\) 0 0
\(253\) 15.3947 0.967857
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.15066 0.0717765 0.0358882 0.999356i \(-0.488574\pi\)
0.0358882 + 0.999356i \(0.488574\pi\)
\(258\) 0 0
\(259\) −5.27334 −0.327670
\(260\) 0 0
\(261\) −5.28267 −0.326989
\(262\) 0 0
\(263\) −2.28267 −0.140756 −0.0703778 0.997520i \(-0.522420\pi\)
−0.0703778 + 0.997520i \(0.522420\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.73599 0.228639
\(268\) 0 0
\(269\) 8.17064 0.498173 0.249086 0.968481i \(-0.419870\pi\)
0.249086 + 0.968481i \(0.419870\pi\)
\(270\) 0 0
\(271\) 21.5433 1.30866 0.654331 0.756208i \(-0.272950\pi\)
0.654331 + 0.756208i \(0.272950\pi\)
\(272\) 0 0
\(273\) 1.36333 0.0825124
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −23.1307 −1.38979 −0.694894 0.719112i \(-0.744549\pi\)
−0.694894 + 0.719112i \(0.744549\pi\)
\(278\) 0 0
\(279\) −1.64600 −0.0985435
\(280\) 0 0
\(281\) 4.96137 0.295970 0.147985 0.988990i \(-0.452721\pi\)
0.147985 + 0.988990i \(0.452721\pi\)
\(282\) 0 0
\(283\) 4.74531 0.282080 0.141040 0.990004i \(-0.454955\pi\)
0.141040 + 0.990004i \(0.454955\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) −12.4147 −0.730275
\(290\) 0 0
\(291\) −16.8480 −0.987648
\(292\) 0 0
\(293\) 29.7360 1.73719 0.868597 0.495518i \(-0.165022\pi\)
0.868597 + 0.495518i \(0.165022\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.64600 −0.327614
\(298\) 0 0
\(299\) 2.72666 0.157687
\(300\) 0 0
\(301\) 12.2827 0.707961
\(302\) 0 0
\(303\) −5.87732 −0.337643
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 18.4520 1.05311 0.526555 0.850141i \(-0.323483\pi\)
0.526555 + 0.850141i \(0.323483\pi\)
\(308\) 0 0
\(309\) −14.0187 −0.797494
\(310\) 0 0
\(311\) 15.9160 0.902511 0.451255 0.892395i \(-0.350976\pi\)
0.451255 + 0.892395i \(0.350976\pi\)
\(312\) 0 0
\(313\) −1.99067 −0.112519 −0.0562597 0.998416i \(-0.517917\pi\)
−0.0562597 + 0.998416i \(0.517917\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.26401 −0.127160 −0.0635799 0.997977i \(-0.520252\pi\)
−0.0635799 + 0.997977i \(0.520252\pi\)
\(318\) 0 0
\(319\) 29.8260 1.66993
\(320\) 0 0
\(321\) −10.8773 −0.607113
\(322\) 0 0
\(323\) 5.17064 0.287702
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3.58532 −0.198269
\(328\) 0 0
\(329\) −5.15066 −0.283965
\(330\) 0 0
\(331\) 1.69867 0.0933674 0.0466837 0.998910i \(-0.485135\pi\)
0.0466837 + 0.998910i \(0.485135\pi\)
\(332\) 0 0
\(333\) 3.86799 0.211965
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −20.7067 −1.12796 −0.563982 0.825787i \(-0.690731\pi\)
−0.563982 + 0.825787i \(0.690731\pi\)
\(338\) 0 0
\(339\) 18.5653 1.00833
\(340\) 0 0
\(341\) 9.29332 0.503261
\(342\) 0 0
\(343\) 16.5526 0.893758
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.97070 0.427889 0.213945 0.976846i \(-0.431369\pi\)
0.213945 + 0.976846i \(0.431369\pi\)
\(348\) 0 0
\(349\) 6.56534 0.351435 0.175717 0.984441i \(-0.443776\pi\)
0.175717 + 0.984441i \(0.443776\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −20.4520 −1.08855 −0.544275 0.838907i \(-0.683195\pi\)
−0.544275 + 0.838907i \(0.683195\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.91934 −0.154508
\(358\) 0 0
\(359\) −11.8994 −0.628025 −0.314012 0.949419i \(-0.601673\pi\)
−0.314012 + 0.949419i \(0.601673\pi\)
\(360\) 0 0
\(361\) −13.1693 −0.693122
\(362\) 0 0
\(363\) 20.8773 1.09578
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −23.5853 −1.23114 −0.615572 0.788081i \(-0.711075\pi\)
−0.615572 + 0.788081i \(0.711075\pi\)
\(368\) 0 0
\(369\) 5.86799 0.305475
\(370\) 0 0
\(371\) −16.3727 −0.850026
\(372\) 0 0
\(373\) −25.1693 −1.30322 −0.651609 0.758555i \(-0.725906\pi\)
−0.651609 + 0.758555i \(0.725906\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.28267 0.272071
\(378\) 0 0
\(379\) −8.83530 −0.453839 −0.226919 0.973914i \(-0.572865\pi\)
−0.226919 + 0.973914i \(0.572865\pi\)
\(380\) 0 0
\(381\) −0.858664 −0.0439907
\(382\) 0 0
\(383\) −27.9053 −1.42589 −0.712947 0.701218i \(-0.752640\pi\)
−0.712947 + 0.701218i \(0.752640\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −9.00933 −0.457970
\(388\) 0 0
\(389\) −0.697352 −0.0353571 −0.0176786 0.999844i \(-0.505628\pi\)
−0.0176786 + 0.999844i \(0.505628\pi\)
\(390\) 0 0
\(391\) −5.83869 −0.295275
\(392\) 0 0
\(393\) −1.86799 −0.0942278
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 17.8867 0.897705 0.448853 0.893606i \(-0.351833\pi\)
0.448853 + 0.893606i \(0.351833\pi\)
\(398\) 0 0
\(399\) −3.29200 −0.164806
\(400\) 0 0
\(401\) 25.1120 1.25404 0.627018 0.779005i \(-0.284275\pi\)
0.627018 + 0.779005i \(0.284275\pi\)
\(402\) 0 0
\(403\) 1.64600 0.0819931
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21.8387 −1.08250
\(408\) 0 0
\(409\) −23.6774 −1.17077 −0.585385 0.810755i \(-0.699057\pi\)
−0.585385 + 0.810755i \(0.699057\pi\)
\(410\) 0 0
\(411\) −5.24404 −0.258669
\(412\) 0 0
\(413\) −8.44267 −0.415436
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 8.17997 0.400575
\(418\) 0 0
\(419\) −18.7347 −0.915248 −0.457624 0.889146i \(-0.651299\pi\)
−0.457624 + 0.889146i \(0.651299\pi\)
\(420\) 0 0
\(421\) 4.26401 0.207815 0.103908 0.994587i \(-0.466865\pi\)
0.103908 + 0.994587i \(0.466865\pi\)
\(422\) 0 0
\(423\) 3.77801 0.183693
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −15.8073 −0.764969
\(428\) 0 0
\(429\) 5.64600 0.272591
\(430\) 0 0
\(431\) 20.1693 0.971522 0.485761 0.874092i \(-0.338543\pi\)
0.485761 + 0.874092i \(0.338543\pi\)
\(432\) 0 0
\(433\) −20.6974 −0.994651 −0.497326 0.867564i \(-0.665685\pi\)
−0.497326 + 0.867564i \(0.665685\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.58400 −0.314956
\(438\) 0 0
\(439\) −2.31198 −0.110345 −0.0551723 0.998477i \(-0.517571\pi\)
−0.0551723 + 0.998477i \(0.517571\pi\)
\(440\) 0 0
\(441\) −5.14134 −0.244826
\(442\) 0 0
\(443\) 2.25337 0.107061 0.0535304 0.998566i \(-0.482953\pi\)
0.0535304 + 0.998566i \(0.482953\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9.73599 0.460496
\(448\) 0 0
\(449\) 22.1693 1.04624 0.523118 0.852261i \(-0.324769\pi\)
0.523118 + 0.852261i \(0.324769\pi\)
\(450\) 0 0
\(451\) −33.1307 −1.56006
\(452\) 0 0
\(453\) 1.18336 0.0555990
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 31.4720 1.47220 0.736098 0.676875i \(-0.236666\pi\)
0.736098 + 0.676875i \(0.236666\pi\)
\(458\) 0 0
\(459\) 2.14134 0.0999490
\(460\) 0 0
\(461\) 17.7360 0.826047 0.413024 0.910720i \(-0.364473\pi\)
0.413024 + 0.910720i \(0.364473\pi\)
\(462\) 0 0
\(463\) −0.431266 −0.0200426 −0.0100213 0.999950i \(-0.503190\pi\)
−0.0100213 + 0.999950i \(0.503190\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.30265 −0.245377 −0.122689 0.992445i \(-0.539152\pi\)
−0.122689 + 0.992445i \(0.539152\pi\)
\(468\) 0 0
\(469\) 0.442666 0.0204404
\(470\) 0 0
\(471\) 17.9800 0.828476
\(472\) 0 0
\(473\) 50.8667 2.33885
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0093 0.549869
\(478\) 0 0
\(479\) −2.07934 −0.0950074 −0.0475037 0.998871i \(-0.515127\pi\)
−0.0475037 + 0.998871i \(0.515127\pi\)
\(480\) 0 0
\(481\) −3.86799 −0.176365
\(482\) 0 0
\(483\) 3.71733 0.169144
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −15.3633 −0.696179 −0.348089 0.937461i \(-0.613169\pi\)
−0.348089 + 0.937461i \(0.613169\pi\)
\(488\) 0 0
\(489\) 4.28267 0.193669
\(490\) 0 0
\(491\) 28.2173 1.27343 0.636714 0.771100i \(-0.280293\pi\)
0.636714 + 0.771100i \(0.280293\pi\)
\(492\) 0 0
\(493\) −11.3120 −0.509466
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.1800 −0.725771
\(498\) 0 0
\(499\) 7.15405 0.320259 0.160130 0.987096i \(-0.448809\pi\)
0.160130 + 0.987096i \(0.448809\pi\)
\(500\) 0 0
\(501\) −6.41468 −0.286587
\(502\) 0 0
\(503\) 5.09337 0.227102 0.113551 0.993532i \(-0.463777\pi\)
0.113551 + 0.993532i \(0.463777\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −21.4906 −0.952555 −0.476278 0.879295i \(-0.658014\pi\)
−0.476278 + 0.879295i \(0.658014\pi\)
\(510\) 0 0
\(511\) −11.2920 −0.499529
\(512\) 0 0
\(513\) 2.41468 0.106611
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −21.3306 −0.938120
\(518\) 0 0
\(519\) 17.1800 0.754117
\(520\) 0 0
\(521\) 25.7360 1.12751 0.563757 0.825941i \(-0.309355\pi\)
0.563757 + 0.825941i \(0.309355\pi\)
\(522\) 0 0
\(523\) −0.972014 −0.0425032 −0.0212516 0.999774i \(-0.506765\pi\)
−0.0212516 + 0.999774i \(0.506765\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.52464 −0.153536
\(528\) 0 0
\(529\) −15.5653 −0.676754
\(530\) 0 0
\(531\) 6.19269 0.268740
\(532\) 0 0
\(533\) −5.86799 −0.254171
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 7.11203 0.306907
\(538\) 0 0
\(539\) 29.0280 1.25032
\(540\) 0 0
\(541\) 13.6774 0.588036 0.294018 0.955800i \(-0.405007\pi\)
0.294018 + 0.955800i \(0.405007\pi\)
\(542\) 0 0
\(543\) 25.4333 1.09145
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −33.7546 −1.44324 −0.721622 0.692287i \(-0.756603\pi\)
−0.721622 + 0.692287i \(0.756603\pi\)
\(548\) 0 0
\(549\) 11.5946 0.494848
\(550\) 0 0
\(551\) −12.7560 −0.543422
\(552\) 0 0
\(553\) −3.15198 −0.134036
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10.2827 0.435691 0.217845 0.975983i \(-0.430097\pi\)
0.217845 + 0.975983i \(0.430097\pi\)
\(558\) 0 0
\(559\) 9.00933 0.381054
\(560\) 0 0
\(561\) −12.0900 −0.510440
\(562\) 0 0
\(563\) −35.3841 −1.49126 −0.745630 0.666360i \(-0.767851\pi\)
−0.745630 + 0.666360i \(0.767851\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1.36333 −0.0572544
\(568\) 0 0
\(569\) 21.7160 0.910382 0.455191 0.890394i \(-0.349571\pi\)
0.455191 + 0.890394i \(0.349571\pi\)
\(570\) 0 0
\(571\) 24.9507 1.04416 0.522078 0.852898i \(-0.325157\pi\)
0.522078 + 0.852898i \(0.325157\pi\)
\(572\) 0 0
\(573\) 16.1214 0.673479
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −27.1893 −1.13191 −0.565953 0.824438i \(-0.691492\pi\)
−0.565953 + 0.824438i \(0.691492\pi\)
\(578\) 0 0
\(579\) 10.0187 0.416361
\(580\) 0 0
\(581\) −14.1413 −0.586681
\(582\) 0 0
\(583\) −67.8047 −2.80818
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −47.5220 −1.96144 −0.980721 0.195411i \(-0.937396\pi\)
−0.980721 + 0.195411i \(0.937396\pi\)
\(588\) 0 0
\(589\) −3.97456 −0.163769
\(590\) 0 0
\(591\) −10.0187 −0.412112
\(592\) 0 0
\(593\) 17.9453 0.736923 0.368462 0.929643i \(-0.379885\pi\)
0.368462 + 0.929643i \(0.379885\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −15.4427 −0.632026
\(598\) 0 0
\(599\) 15.4720 0.632168 0.316084 0.948731i \(-0.397632\pi\)
0.316084 + 0.948731i \(0.397632\pi\)
\(600\) 0 0
\(601\) 45.7453 1.86599 0.932995 0.359889i \(-0.117185\pi\)
0.932995 + 0.359889i \(0.117185\pi\)
\(602\) 0 0
\(603\) −0.324695 −0.0132226
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −15.3467 −0.622905 −0.311453 0.950262i \(-0.600815\pi\)
−0.311453 + 0.950262i \(0.600815\pi\)
\(608\) 0 0
\(609\) 7.20202 0.291840
\(610\) 0 0
\(611\) −3.77801 −0.152842
\(612\) 0 0
\(613\) −5.67738 −0.229307 −0.114654 0.993406i \(-0.536576\pi\)
−0.114654 + 0.993406i \(0.536576\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.8867 0.881123 0.440562 0.897722i \(-0.354779\pi\)
0.440562 + 0.897722i \(0.354779\pi\)
\(618\) 0 0
\(619\) 21.4134 0.860676 0.430338 0.902668i \(-0.358394\pi\)
0.430338 + 0.902668i \(0.358394\pi\)
\(620\) 0 0
\(621\) −2.72666 −0.109417
\(622\) 0 0
\(623\) −5.09337 −0.204062
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −13.6333 −0.544461
\(628\) 0 0
\(629\) 8.28267 0.330252
\(630\) 0 0
\(631\) 35.1893 1.40086 0.700432 0.713719i \(-0.252991\pi\)
0.700432 + 0.713719i \(0.252991\pi\)
\(632\) 0 0
\(633\) 17.8387 0.709024
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.14134 0.203707
\(638\) 0 0
\(639\) 11.8680 0.469491
\(640\) 0 0
\(641\) 33.5547 1.32533 0.662665 0.748916i \(-0.269425\pi\)
0.662665 + 0.748916i \(0.269425\pi\)
\(642\) 0 0
\(643\) 18.7160 0.738087 0.369044 0.929412i \(-0.379685\pi\)
0.369044 + 0.929412i \(0.379685\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.5653 −0.651251 −0.325625 0.945499i \(-0.605575\pi\)
−0.325625 + 0.945499i \(0.605575\pi\)
\(648\) 0 0
\(649\) −34.9639 −1.37245
\(650\) 0 0
\(651\) 2.24404 0.0879508
\(652\) 0 0
\(653\) 26.5454 1.03880 0.519400 0.854531i \(-0.326155\pi\)
0.519400 + 0.854531i \(0.326155\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 8.28267 0.323138
\(658\) 0 0
\(659\) 36.3306 1.41524 0.707620 0.706593i \(-0.249769\pi\)
0.707620 + 0.706593i \(0.249769\pi\)
\(660\) 0 0
\(661\) 22.2279 0.864566 0.432283 0.901738i \(-0.357708\pi\)
0.432283 + 0.901738i \(0.357708\pi\)
\(662\) 0 0
\(663\) −2.14134 −0.0831626
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 14.4040 0.557726
\(668\) 0 0
\(669\) −6.56534 −0.253831
\(670\) 0 0
\(671\) −65.4634 −2.52719
\(672\) 0 0
\(673\) 1.46264 0.0563807 0.0281903 0.999603i \(-0.491026\pi\)
0.0281903 + 0.999603i \(0.491026\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.5653 0.713524 0.356762 0.934195i \(-0.383881\pi\)
0.356762 + 0.934195i \(0.383881\pi\)
\(678\) 0 0
\(679\) 22.9694 0.881484
\(680\) 0 0
\(681\) 13.3820 0.512799
\(682\) 0 0
\(683\) 6.03138 0.230784 0.115392 0.993320i \(-0.463188\pi\)
0.115392 + 0.993320i \(0.463188\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 9.88665 0.377199
\(688\) 0 0
\(689\) −12.0093 −0.457519
\(690\) 0 0
\(691\) 14.1566 0.538543 0.269271 0.963064i \(-0.413217\pi\)
0.269271 + 0.963064i \(0.413217\pi\)
\(692\) 0 0
\(693\) 7.69735 0.292398
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.5653 0.475946
\(698\) 0 0
\(699\) −26.8667 −1.01619
\(700\) 0 0
\(701\) 6.26270 0.236539 0.118269 0.992982i \(-0.462265\pi\)
0.118269 + 0.992982i \(0.462265\pi\)
\(702\) 0 0
\(703\) 9.33996 0.352263
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.01272 0.301349
\(708\) 0 0
\(709\) 6.28267 0.235951 0.117975 0.993017i \(-0.462360\pi\)
0.117975 + 0.993017i \(0.462360\pi\)
\(710\) 0 0
\(711\) 2.31198 0.0867059
\(712\) 0 0
\(713\) 4.48808 0.168080
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 27.4847 1.02643
\(718\) 0 0
\(719\) −28.9253 −1.07873 −0.539366 0.842072i \(-0.681336\pi\)
−0.539366 + 0.842072i \(0.681336\pi\)
\(720\) 0 0
\(721\) 19.1120 0.711769
\(722\) 0 0
\(723\) −10.0187 −0.372598
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −40.2427 −1.49252 −0.746260 0.665655i \(-0.768152\pi\)
−0.746260 + 0.665655i \(0.768152\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −19.2920 −0.713540
\(732\) 0 0
\(733\) 19.7907 0.730987 0.365494 0.930814i \(-0.380900\pi\)
0.365494 + 0.930814i \(0.380900\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.83323 0.0675278
\(738\) 0 0
\(739\) −18.1634 −0.668151 −0.334075 0.942546i \(-0.608424\pi\)
−0.334075 + 0.942546i \(0.608424\pi\)
\(740\) 0 0
\(741\) −2.41468 −0.0887055
\(742\) 0 0
\(743\) 24.2661 0.890236 0.445118 0.895472i \(-0.353162\pi\)
0.445118 + 0.895472i \(0.353162\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 10.3727 0.379516
\(748\) 0 0
\(749\) 14.8294 0.541853
\(750\) 0 0
\(751\) 28.2720 1.03166 0.515830 0.856691i \(-0.327483\pi\)
0.515830 + 0.856691i \(0.327483\pi\)
\(752\) 0 0
\(753\) −24.1507 −0.880099
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 37.0853 1.34789 0.673944 0.738783i \(-0.264599\pi\)
0.673944 + 0.738783i \(0.264599\pi\)
\(758\) 0 0
\(759\) 15.3947 0.558792
\(760\) 0 0
\(761\) 28.4919 1.03283 0.516416 0.856338i \(-0.327266\pi\)
0.516416 + 0.856338i \(0.327266\pi\)
\(762\) 0 0
\(763\) 4.88797 0.176956
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.19269 −0.223605
\(768\) 0 0
\(769\) −27.6774 −0.998072 −0.499036 0.866581i \(-0.666312\pi\)
−0.499036 + 0.866581i \(0.666312\pi\)
\(770\) 0 0
\(771\) 1.15066 0.0414402
\(772\) 0 0
\(773\) 32.6426 1.17407 0.587037 0.809560i \(-0.300294\pi\)
0.587037 + 0.809560i \(0.300294\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −5.27334 −0.189180
\(778\) 0 0
\(779\) 14.1693 0.507669
\(780\) 0 0
\(781\) −67.0067 −2.39769
\(782\) 0 0
\(783\) −5.28267 −0.188787
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −50.6740 −1.80633 −0.903166 0.429291i \(-0.858764\pi\)
−0.903166 + 0.429291i \(0.858764\pi\)
\(788\) 0 0
\(789\) −2.28267 −0.0812653
\(790\) 0 0
\(791\) −25.3107 −0.899943
\(792\) 0 0
\(793\) −11.5946 −0.411738
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24.3586 −0.862827 −0.431413 0.902154i \(-0.641985\pi\)
−0.431413 + 0.902154i \(0.641985\pi\)
\(798\) 0 0
\(799\) 8.08998 0.286203
\(800\) 0 0
\(801\) 3.73599 0.132005
\(802\) 0 0
\(803\) −46.7640 −1.65026
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 8.17064 0.287620
\(808\) 0 0
\(809\) −50.6027 −1.77909 −0.889547 0.456843i \(-0.848980\pi\)
−0.889547 + 0.456843i \(0.848980\pi\)
\(810\) 0 0
\(811\) 18.4168 0.646700 0.323350 0.946280i \(-0.395191\pi\)
0.323350 + 0.946280i \(0.395191\pi\)
\(812\) 0 0
\(813\) 21.5433 0.755556
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −21.7546 −0.761099
\(818\) 0 0
\(819\) 1.36333 0.0476385
\(820\) 0 0
\(821\) −31.4906 −1.09903 −0.549515 0.835484i \(-0.685188\pi\)
−0.549515 + 0.835484i \(0.685188\pi\)
\(822\) 0 0
\(823\) 18.7347 0.653049 0.326525 0.945189i \(-0.394122\pi\)
0.326525 + 0.945189i \(0.394122\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −16.7580 −0.582734 −0.291367 0.956611i \(-0.594110\pi\)
−0.291367 + 0.956611i \(0.594110\pi\)
\(828\) 0 0
\(829\) −20.1014 −0.698150 −0.349075 0.937095i \(-0.613504\pi\)
−0.349075 + 0.937095i \(0.613504\pi\)
\(830\) 0 0
\(831\) −23.1307 −0.802395
\(832\) 0 0
\(833\) −11.0093 −0.381451
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.64600 −0.0568941
\(838\) 0 0
\(839\) −6.82936 −0.235776 −0.117888 0.993027i \(-0.537612\pi\)
−0.117888 + 0.993027i \(0.537612\pi\)
\(840\) 0 0
\(841\) −1.09337 −0.0377026
\(842\) 0 0
\(843\) 4.96137 0.170879
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −28.4626 −0.977988
\(848\) 0 0
\(849\) 4.74531 0.162859
\(850\) 0 0
\(851\) −10.5467 −0.361536
\(852\) 0 0
\(853\) 10.2279 0.350198 0.175099 0.984551i \(-0.443975\pi\)
0.175099 + 0.984551i \(0.443975\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 31.1307 1.06340 0.531702 0.846931i \(-0.321553\pi\)
0.531702 + 0.846931i \(0.321553\pi\)
\(858\) 0 0
\(859\) −33.0093 −1.12626 −0.563132 0.826367i \(-0.690404\pi\)
−0.563132 + 0.826367i \(0.690404\pi\)
\(860\) 0 0
\(861\) −8.00000 −0.272639
\(862\) 0 0
\(863\) 44.4206 1.51210 0.756048 0.654516i \(-0.227128\pi\)
0.756048 + 0.654516i \(0.227128\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −12.4147 −0.421625
\(868\) 0 0
\(869\) −13.0534 −0.442807
\(870\) 0 0
\(871\) 0.324695 0.0110019
\(872\) 0 0
\(873\) −16.8480 −0.570219
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 15.8867 0.536454 0.268227 0.963356i \(-0.413562\pi\)
0.268227 + 0.963356i \(0.413562\pi\)
\(878\) 0 0
\(879\) 29.7360 1.00297
\(880\) 0 0
\(881\) 3.13201 0.105520 0.0527600 0.998607i \(-0.483198\pi\)
0.0527600 + 0.998607i \(0.483198\pi\)
\(882\) 0 0
\(883\) −33.1307 −1.11494 −0.557468 0.830198i \(-0.688227\pi\)
−0.557468 + 0.830198i \(0.688227\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −19.8200 −0.665491 −0.332746 0.943017i \(-0.607975\pi\)
−0.332746 + 0.943017i \(0.607975\pi\)
\(888\) 0 0
\(889\) 1.17064 0.0392620
\(890\) 0 0
\(891\) −5.64600 −0.189148
\(892\) 0 0
\(893\) 9.12268 0.305279
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.72666 0.0910404
\(898\) 0 0
\(899\) 8.69528 0.290004
\(900\) 0 0
\(901\) 25.7160 0.856724
\(902\) 0 0
\(903\) 12.2827 0.408742
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −14.6426 −0.486200 −0.243100 0.970001i \(-0.578164\pi\)
−0.243100 + 0.970001i \(0.578164\pi\)
\(908\) 0 0
\(909\) −5.87732 −0.194938
\(910\) 0 0
\(911\) −37.8973 −1.25559 −0.627797 0.778377i \(-0.716043\pi\)
−0.627797 + 0.778377i \(0.716043\pi\)
\(912\) 0 0
\(913\) −58.5640 −1.93819
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.54669 0.0840990
\(918\) 0 0
\(919\) 26.2534 0.866019 0.433009 0.901389i \(-0.357452\pi\)
0.433009 + 0.901389i \(0.357452\pi\)
\(920\) 0 0
\(921\) 18.4520 0.608014
\(922\) 0 0
\(923\) −11.8680 −0.390640
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −14.0187 −0.460433
\(928\) 0 0
\(929\) 52.2066 1.71284 0.856422 0.516276i \(-0.172682\pi\)
0.856422 + 0.516276i \(0.172682\pi\)
\(930\) 0 0
\(931\) −12.4147 −0.406875
\(932\) 0 0
\(933\) 15.9160 0.521065
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −16.3213 −0.533194 −0.266597 0.963808i \(-0.585899\pi\)
−0.266597 + 0.963808i \(0.585899\pi\)
\(938\) 0 0
\(939\) −1.99067 −0.0649631
\(940\) 0 0
\(941\) 35.7546 1.16557 0.582784 0.812627i \(-0.301963\pi\)
0.582784 + 0.812627i \(0.301963\pi\)
\(942\) 0 0
\(943\) −16.0000 −0.521032
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.73260 0.283771 0.141886 0.989883i \(-0.454683\pi\)
0.141886 + 0.989883i \(0.454683\pi\)
\(948\) 0 0
\(949\) −8.28267 −0.268867
\(950\) 0 0
\(951\) −2.26401 −0.0734157
\(952\) 0 0
\(953\) 28.8280 0.933832 0.466916 0.884302i \(-0.345365\pi\)
0.466916 + 0.884302i \(0.345365\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 29.8260 0.964137
\(958\) 0 0
\(959\) 7.14935 0.230864
\(960\) 0 0
\(961\) −28.2907 −0.912603
\(962\) 0 0
\(963\) −10.8773 −0.350517
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 38.0687 1.22421 0.612103 0.790778i \(-0.290324\pi\)
0.612103 + 0.790778i \(0.290324\pi\)
\(968\) 0 0
\(969\) 5.17064 0.166105
\(970\) 0 0
\(971\) 1.72534 0.0553687 0.0276844 0.999617i \(-0.491187\pi\)
0.0276844 + 0.999617i \(0.491187\pi\)
\(972\) 0 0
\(973\) −11.1520 −0.357516
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 21.7173 0.694799 0.347399 0.937717i \(-0.387065\pi\)
0.347399 + 0.937717i \(0.387065\pi\)
\(978\) 0 0
\(979\) −21.0934 −0.674147
\(980\) 0 0
\(981\) −3.58532 −0.114470
\(982\) 0 0
\(983\) 13.0153 0.415123 0.207561 0.978222i \(-0.433447\pi\)
0.207561 + 0.978222i \(0.433447\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −5.15066 −0.163947
\(988\) 0 0
\(989\) 24.5653 0.781133
\(990\) 0 0
\(991\) 23.1413 0.735109 0.367554 0.930002i \(-0.380195\pi\)
0.367554 + 0.930002i \(0.380195\pi\)
\(992\) 0 0
\(993\) 1.69867 0.0539057
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 34.9707 1.10753 0.553767 0.832672i \(-0.313190\pi\)
0.553767 + 0.832672i \(0.313190\pi\)
\(998\) 0 0
\(999\) 3.86799 0.122378
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 7800.2.a.bn.1.2 yes 3
5.4 even 2 7800.2.a.bm.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bm.1.2 3 5.4 even 2
7800.2.a.bn.1.2 yes 3 1.1 even 1 trivial