Properties

Label 7800.2.a.bp.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.12489\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{9} -4.64002 q^{11} +1.00000 q^{13} +4.24977 q^{17} -6.24977 q^{19} +2.24977 q^{23} +1.00000 q^{27} -9.21949 q^{29} +9.28005 q^{31} -4.64002 q^{33} +7.28005 q^{37} +1.00000 q^{39} -5.67030 q^{41} -4.24977 q^{43} +2.88979 q^{47} -7.00000 q^{49} +4.24977 q^{51} -9.21949 q^{53} -6.24977 q^{57} +5.92007 q^{59} +0.969724 q^{61} -1.93945 q^{67} +2.24977 q^{69} +5.60975 q^{71} -12.5601 q^{73} +12.2498 q^{79} +1.00000 q^{81} -3.67030 q^{83} -9.21949 q^{87} -9.67030 q^{89} +9.28005 q^{93} -6.00000 q^{97} -4.64002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{3} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{3} + 3q^{9} - 6q^{11} + 3q^{13} - 4q^{17} - 2q^{19} - 10q^{23} + 3q^{27} - 10q^{29} + 12q^{31} - 6q^{33} + 6q^{37} + 3q^{39} - 10q^{41} + 4q^{43} - 16q^{47} - 21q^{49} - 4q^{51} - 10q^{53} - 2q^{57} - 6q^{59} + 2q^{61} - 4q^{67} - 10q^{69} + 8q^{71} - 6q^{73} + 20q^{79} + 3q^{81} - 4q^{83} - 10q^{87} - 22q^{89} + 12q^{93} - 18q^{97} - 6q^{99} + O(q^{100}) \)

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
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.64002 −1.39902 −0.699510 0.714623i \(-0.746598\pi\)
−0.699510 + 0.714623i \(0.746598\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.24977 1.03072 0.515360 0.856974i \(-0.327658\pi\)
0.515360 + 0.856974i \(0.327658\pi\)
\(18\) 0 0
\(19\) −6.24977 −1.43380 −0.716898 0.697178i \(-0.754439\pi\)
−0.716898 + 0.697178i \(0.754439\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.24977 0.469110 0.234555 0.972103i \(-0.424637\pi\)
0.234555 + 0.972103i \(0.424637\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −9.21949 −1.71202 −0.856009 0.516962i \(-0.827063\pi\)
−0.856009 + 0.516962i \(0.827063\pi\)
\(30\) 0 0
\(31\) 9.28005 1.66675 0.833373 0.552711i \(-0.186407\pi\)
0.833373 + 0.552711i \(0.186407\pi\)
\(32\) 0 0
\(33\) −4.64002 −0.807724
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.28005 1.19683 0.598416 0.801185i \(-0.295797\pi\)
0.598416 + 0.801185i \(0.295797\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −5.67030 −0.885552 −0.442776 0.896632i \(-0.646006\pi\)
−0.442776 + 0.896632i \(0.646006\pi\)
\(42\) 0 0
\(43\) −4.24977 −0.648084 −0.324042 0.946043i \(-0.605042\pi\)
−0.324042 + 0.946043i \(0.605042\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.88979 0.421520 0.210760 0.977538i \(-0.432406\pi\)
0.210760 + 0.977538i \(0.432406\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 4.24977 0.595087
\(52\) 0 0
\(53\) −9.21949 −1.26639 −0.633197 0.773990i \(-0.718258\pi\)
−0.633197 + 0.773990i \(0.718258\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −6.24977 −0.827802
\(58\) 0 0
\(59\) 5.92007 0.770728 0.385364 0.922765i \(-0.374076\pi\)
0.385364 + 0.922765i \(0.374076\pi\)
\(60\) 0 0
\(61\) 0.969724 0.124160 0.0620802 0.998071i \(-0.480227\pi\)
0.0620802 + 0.998071i \(0.480227\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.93945 −0.236941 −0.118471 0.992958i \(-0.537799\pi\)
−0.118471 + 0.992958i \(0.537799\pi\)
\(68\) 0 0
\(69\) 2.24977 0.270841
\(70\) 0 0
\(71\) 5.60975 0.665755 0.332877 0.942970i \(-0.391981\pi\)
0.332877 + 0.942970i \(0.391981\pi\)
\(72\) 0 0
\(73\) −12.5601 −1.47005 −0.735024 0.678041i \(-0.762829\pi\)
−0.735024 + 0.678041i \(0.762829\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 12.2498 1.37821 0.689103 0.724663i \(-0.258005\pi\)
0.689103 + 0.724663i \(0.258005\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.67030 −0.402868 −0.201434 0.979502i \(-0.564560\pi\)
−0.201434 + 0.979502i \(0.564560\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.21949 −0.988434
\(88\) 0 0
\(89\) −9.67030 −1.02505 −0.512525 0.858672i \(-0.671290\pi\)
−0.512525 + 0.858672i \(0.671290\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 9.28005 0.962296
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) −4.64002 −0.466340
\(100\) 0 0
\(101\) −15.2800 −1.52042 −0.760211 0.649677i \(-0.774904\pi\)
−0.760211 + 0.649677i \(0.774904\pi\)
\(102\) 0 0
\(103\) 1.21949 0.120160 0.0600802 0.998194i \(-0.480864\pi\)
0.0600802 + 0.998194i \(0.480864\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.28005 −0.510441 −0.255221 0.966883i \(-0.582148\pi\)
−0.255221 + 0.966883i \(0.582148\pi\)
\(108\) 0 0
\(109\) −10.1892 −0.975950 −0.487975 0.872858i \(-0.662264\pi\)
−0.487975 + 0.872858i \(0.662264\pi\)
\(110\) 0 0
\(111\) 7.28005 0.690991
\(112\) 0 0
\(113\) 1.03028 0.0969202 0.0484601 0.998825i \(-0.484569\pi\)
0.0484601 + 0.998825i \(0.484569\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 10.5298 0.957256
\(122\) 0 0
\(123\) −5.67030 −0.511274
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.0303 −0.978779 −0.489389 0.872065i \(-0.662780\pi\)
−0.489389 + 0.872065i \(0.662780\pi\)
\(128\) 0 0
\(129\) −4.24977 −0.374171
\(130\) 0 0
\(131\) 7.21949 0.630770 0.315385 0.948964i \(-0.397866\pi\)
0.315385 + 0.948964i \(0.397866\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.10929 0.692823 0.346412 0.938083i \(-0.387400\pi\)
0.346412 + 0.938083i \(0.387400\pi\)
\(138\) 0 0
\(139\) −19.0596 −1.61662 −0.808309 0.588759i \(-0.799617\pi\)
−0.808309 + 0.588759i \(0.799617\pi\)
\(140\) 0 0
\(141\) 2.88979 0.243365
\(142\) 0 0
\(143\) −4.64002 −0.388018
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −7.00000 −0.577350
\(148\) 0 0
\(149\) 3.92007 0.321145 0.160572 0.987024i \(-0.448666\pi\)
0.160572 + 0.987024i \(0.448666\pi\)
\(150\) 0 0
\(151\) 21.7796 1.77240 0.886199 0.463305i \(-0.153337\pi\)
0.886199 + 0.463305i \(0.153337\pi\)
\(152\) 0 0
\(153\) 4.24977 0.343574
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −21.5904 −1.72310 −0.861550 0.507673i \(-0.830506\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(158\) 0 0
\(159\) −9.21949 −0.731153
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.28005 0.100261 0.0501305 0.998743i \(-0.484036\pi\)
0.0501305 + 0.998743i \(0.484036\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.8898 −1.46174 −0.730868 0.682519i \(-0.760885\pi\)
−0.730868 + 0.682519i \(0.760885\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −6.24977 −0.477932
\(172\) 0 0
\(173\) −22.9991 −1.74859 −0.874294 0.485397i \(-0.838675\pi\)
−0.874294 + 0.485397i \(0.838675\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.92007 0.444980
\(178\) 0 0
\(179\) −4.49954 −0.336312 −0.168156 0.985760i \(-0.553781\pi\)
−0.168156 + 0.985760i \(0.553781\pi\)
\(180\) 0 0
\(181\) −21.0596 −1.56535 −0.782675 0.622430i \(-0.786145\pi\)
−0.782675 + 0.622430i \(0.786145\pi\)
\(182\) 0 0
\(183\) 0.969724 0.0716841
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −19.7190 −1.44200
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −14.4390 −1.04477 −0.522384 0.852710i \(-0.674957\pi\)
−0.522384 + 0.852710i \(0.674957\pi\)
\(192\) 0 0
\(193\) 21.7190 1.56337 0.781685 0.623673i \(-0.214360\pi\)
0.781685 + 0.623673i \(0.214360\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.0109 −0.926988 −0.463494 0.886100i \(-0.653404\pi\)
−0.463494 + 0.886100i \(0.653404\pi\)
\(198\) 0 0
\(199\) 18.6888 1.32481 0.662406 0.749145i \(-0.269536\pi\)
0.662406 + 0.749145i \(0.269536\pi\)
\(200\) 0 0
\(201\) −1.93945 −0.136798
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.24977 0.156370
\(208\) 0 0
\(209\) 28.9991 2.00591
\(210\) 0 0
\(211\) −8.24977 −0.567938 −0.283969 0.958834i \(-0.591651\pi\)
−0.283969 + 0.958834i \(0.591651\pi\)
\(212\) 0 0
\(213\) 5.60975 0.384374
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −12.5601 −0.848732
\(220\) 0 0
\(221\) 4.24977 0.285871
\(222\) 0 0
\(223\) 9.77959 0.654890 0.327445 0.944870i \(-0.393812\pi\)
0.327445 + 0.944870i \(0.393812\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 25.4499 1.68917 0.844584 0.535423i \(-0.179848\pi\)
0.844584 + 0.535423i \(0.179848\pi\)
\(228\) 0 0
\(229\) −8.24977 −0.545160 −0.272580 0.962133i \(-0.587877\pi\)
−0.272580 + 0.962133i \(0.587877\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.5904 0.759310 0.379655 0.925128i \(-0.376043\pi\)
0.379655 + 0.925128i \(0.376043\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 12.2498 0.795708
\(238\) 0 0
\(239\) −6.88979 −0.445664 −0.222832 0.974857i \(-0.571530\pi\)
−0.222832 + 0.974857i \(0.571530\pi\)
\(240\) 0 0
\(241\) 21.2195 1.36687 0.683434 0.730012i \(-0.260486\pi\)
0.683434 + 0.730012i \(0.260486\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.24977 −0.397663
\(248\) 0 0
\(249\) −3.67030 −0.232596
\(250\) 0 0
\(251\) −24.3397 −1.53631 −0.768154 0.640266i \(-0.778824\pi\)
−0.768154 + 0.640266i \(0.778824\pi\)
\(252\) 0 0
\(253\) −10.4390 −0.656294
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −23.4693 −1.46397 −0.731986 0.681319i \(-0.761407\pi\)
−0.731986 + 0.681319i \(0.761407\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −9.21949 −0.570672
\(262\) 0 0
\(263\) −22.6282 −1.39532 −0.697658 0.716431i \(-0.745774\pi\)
−0.697658 + 0.716431i \(0.745774\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −9.67030 −0.591813
\(268\) 0 0
\(269\) 12.2791 0.748672 0.374336 0.927293i \(-0.377871\pi\)
0.374336 + 0.927293i \(0.377871\pi\)
\(270\) 0 0
\(271\) −22.9385 −1.39342 −0.696708 0.717355i \(-0.745353\pi\)
−0.696708 + 0.717355i \(0.745353\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 11.5298 0.692760 0.346380 0.938094i \(-0.387411\pi\)
0.346380 + 0.938094i \(0.387411\pi\)
\(278\) 0 0
\(279\) 9.28005 0.555582
\(280\) 0 0
\(281\) −11.3288 −0.675819 −0.337909 0.941179i \(-0.609720\pi\)
−0.337909 + 0.941179i \(0.609720\pi\)
\(282\) 0 0
\(283\) 20.9991 1.24827 0.624133 0.781318i \(-0.285452\pi\)
0.624133 + 0.781318i \(0.285452\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.06055 0.0623854
\(290\) 0 0
\(291\) −6.00000 −0.351726
\(292\) 0 0
\(293\) −4.26915 −0.249406 −0.124703 0.992194i \(-0.539798\pi\)
−0.124703 + 0.992194i \(0.539798\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.64002 −0.269241
\(298\) 0 0
\(299\) 2.24977 0.130108
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −15.2800 −0.877816
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 1.21949 0.0693746
\(310\) 0 0
\(311\) 3.71904 0.210887 0.105444 0.994425i \(-0.466374\pi\)
0.105444 + 0.994425i \(0.466374\pi\)
\(312\) 0 0
\(313\) 1.52982 0.0864704 0.0432352 0.999065i \(-0.486234\pi\)
0.0432352 + 0.999065i \(0.486234\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.1093 0.904788 0.452394 0.891818i \(-0.350570\pi\)
0.452394 + 0.891818i \(0.350570\pi\)
\(318\) 0 0
\(319\) 42.7787 2.39515
\(320\) 0 0
\(321\) −5.28005 −0.294703
\(322\) 0 0
\(323\) −26.5601 −1.47784
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −10.1892 −0.563465
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 15.5298 0.853596 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(332\) 0 0
\(333\) 7.28005 0.398944
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −21.4087 −1.16621 −0.583103 0.812398i \(-0.698162\pi\)
−0.583103 + 0.812398i \(0.698162\pi\)
\(338\) 0 0
\(339\) 1.03028 0.0559569
\(340\) 0 0
\(341\) −43.0596 −2.33181
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.62065 −0.248049 −0.124025 0.992279i \(-0.539580\pi\)
−0.124025 + 0.992279i \(0.539580\pi\)
\(348\) 0 0
\(349\) 23.9688 1.28302 0.641510 0.767114i \(-0.278308\pi\)
0.641510 + 0.767114i \(0.278308\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −0.511357 −0.0272168 −0.0136084 0.999907i \(-0.504332\pi\)
−0.0136084 + 0.999907i \(0.504332\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.6694 −0.668664 −0.334332 0.942455i \(-0.608511\pi\)
−0.334332 + 0.942455i \(0.608511\pi\)
\(360\) 0 0
\(361\) 20.0596 1.05577
\(362\) 0 0
\(363\) 10.5298 0.552672
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.841057 −0.0439028 −0.0219514 0.999759i \(-0.506988\pi\)
−0.0219514 + 0.999759i \(0.506988\pi\)
\(368\) 0 0
\(369\) −5.67030 −0.295184
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −29.0596 −1.50465 −0.752325 0.658792i \(-0.771068\pi\)
−0.752325 + 0.658792i \(0.771068\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.21949 −0.474828
\(378\) 0 0
\(379\) 9.75023 0.500836 0.250418 0.968138i \(-0.419432\pi\)
0.250418 + 0.968138i \(0.419432\pi\)
\(380\) 0 0
\(381\) −11.0303 −0.565098
\(382\) 0 0
\(383\) −7.38934 −0.377577 −0.188789 0.982018i \(-0.560456\pi\)
−0.188789 + 0.982018i \(0.560456\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.24977 −0.216028
\(388\) 0 0
\(389\) −14.0000 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) 0 0
\(391\) 9.56101 0.483521
\(392\) 0 0
\(393\) 7.21949 0.364175
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 26.2186 1.31587 0.657936 0.753074i \(-0.271430\pi\)
0.657936 + 0.753074i \(0.271430\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.2909 0.513905 0.256953 0.966424i \(-0.417282\pi\)
0.256953 + 0.966424i \(0.417282\pi\)
\(402\) 0 0
\(403\) 9.28005 0.462272
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −33.7796 −1.67439
\(408\) 0 0
\(409\) −11.9007 −0.588451 −0.294226 0.955736i \(-0.595062\pi\)
−0.294226 + 0.955736i \(0.595062\pi\)
\(410\) 0 0
\(411\) 8.10929 0.400002
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −19.0596 −0.933354
\(418\) 0 0
\(419\) 26.2791 1.28382 0.641910 0.766780i \(-0.278142\pi\)
0.641910 + 0.766780i \(0.278142\pi\)
\(420\) 0 0
\(421\) 22.3103 1.08734 0.543669 0.839300i \(-0.317035\pi\)
0.543669 + 0.839300i \(0.317035\pi\)
\(422\) 0 0
\(423\) 2.88979 0.140507
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −4.64002 −0.224022
\(430\) 0 0
\(431\) 12.0487 0.580367 0.290184 0.956971i \(-0.406284\pi\)
0.290184 + 0.956971i \(0.406284\pi\)
\(432\) 0 0
\(433\) 27.5904 1.32591 0.662954 0.748660i \(-0.269302\pi\)
0.662954 + 0.748660i \(0.269302\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −14.0606 −0.672607
\(438\) 0 0
\(439\) 19.8789 0.948768 0.474384 0.880318i \(-0.342671\pi\)
0.474384 + 0.880318i \(0.342671\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) 17.9007 0.850488 0.425244 0.905079i \(-0.360188\pi\)
0.425244 + 0.905079i \(0.360188\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 3.92007 0.185413
\(448\) 0 0
\(449\) −17.2682 −0.814938 −0.407469 0.913219i \(-0.633589\pi\)
−0.407469 + 0.913219i \(0.633589\pi\)
\(450\) 0 0
\(451\) 26.3103 1.23890
\(452\) 0 0
\(453\) 21.7796 1.02329
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −30.4995 −1.42671 −0.713354 0.700804i \(-0.752825\pi\)
−0.713354 + 0.700804i \(0.752825\pi\)
\(458\) 0 0
\(459\) 4.24977 0.198362
\(460\) 0 0
\(461\) −2.64002 −0.122958 −0.0614791 0.998108i \(-0.519582\pi\)
−0.0614791 + 0.998108i \(0.519582\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.78051 −0.221215 −0.110608 0.993864i \(-0.535280\pi\)
−0.110608 + 0.993864i \(0.535280\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −21.5904 −0.994832
\(472\) 0 0
\(473\) 19.7190 0.906682
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.21949 −0.422132
\(478\) 0 0
\(479\) 9.11021 0.416256 0.208128 0.978102i \(-0.433263\pi\)
0.208128 + 0.978102i \(0.433263\pi\)
\(480\) 0 0
\(481\) 7.28005 0.331942
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −26.2791 −1.19082 −0.595411 0.803422i \(-0.703011\pi\)
−0.595411 + 0.803422i \(0.703011\pi\)
\(488\) 0 0
\(489\) 1.28005 0.0578857
\(490\) 0 0
\(491\) 5.40115 0.243751 0.121875 0.992545i \(-0.461109\pi\)
0.121875 + 0.992545i \(0.461109\pi\)
\(492\) 0 0
\(493\) −39.1807 −1.76461
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 22.9092 1.02556 0.512778 0.858521i \(-0.328617\pi\)
0.512778 + 0.858521i \(0.328617\pi\)
\(500\) 0 0
\(501\) −18.8898 −0.843934
\(502\) 0 0
\(503\) 37.3094 1.66354 0.831772 0.555117i \(-0.187327\pi\)
0.831772 + 0.555117i \(0.187327\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −0.700576 −0.0310525 −0.0155262 0.999879i \(-0.504942\pi\)
−0.0155262 + 0.999879i \(0.504942\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −6.24977 −0.275934
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −13.4087 −0.589715
\(518\) 0 0
\(519\) −22.9991 −1.00955
\(520\) 0 0
\(521\) 13.8401 0.606348 0.303174 0.952935i \(-0.401954\pi\)
0.303174 + 0.952935i \(0.401954\pi\)
\(522\) 0 0
\(523\) −43.6878 −1.91034 −0.955168 0.296064i \(-0.904326\pi\)
−0.955168 + 0.296064i \(0.904326\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 39.4381 1.71795
\(528\) 0 0
\(529\) −17.9385 −0.779936
\(530\) 0 0
\(531\) 5.92007 0.256909
\(532\) 0 0
\(533\) −5.67030 −0.245608
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.49954 −0.194170
\(538\) 0 0
\(539\) 32.4802 1.39902
\(540\) 0 0
\(541\) 14.1892 0.610042 0.305021 0.952346i \(-0.401336\pi\)
0.305021 + 0.952346i \(0.401336\pi\)
\(542\) 0 0
\(543\) −21.0596 −0.903755
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 44.3085 1.89449 0.947247 0.320504i \(-0.103852\pi\)
0.947247 + 0.320504i \(0.103852\pi\)
\(548\) 0 0
\(549\) 0.969724 0.0413868
\(550\) 0 0
\(551\) 57.6197 2.45468
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −39.2077 −1.66128 −0.830641 0.556808i \(-0.812026\pi\)
−0.830641 + 0.556808i \(0.812026\pi\)
\(558\) 0 0
\(559\) −4.24977 −0.179746
\(560\) 0 0
\(561\) −19.7190 −0.832538
\(562\) 0 0
\(563\) −18.0606 −0.761162 −0.380581 0.924748i \(-0.624276\pi\)
−0.380581 + 0.924748i \(0.624276\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −42.3397 −1.77497 −0.887486 0.460835i \(-0.847550\pi\)
−0.887486 + 0.460835i \(0.847550\pi\)
\(570\) 0 0
\(571\) −39.9301 −1.67102 −0.835510 0.549475i \(-0.814828\pi\)
−0.835510 + 0.549475i \(0.814828\pi\)
\(572\) 0 0
\(573\) −14.4390 −0.603197
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 21.3406 0.888421 0.444210 0.895923i \(-0.353484\pi\)
0.444210 + 0.895923i \(0.353484\pi\)
\(578\) 0 0
\(579\) 21.7190 0.902612
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 42.7787 1.77171
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.7905 1.35341 0.676704 0.736255i \(-0.263408\pi\)
0.676704 + 0.736255i \(0.263408\pi\)
\(588\) 0 0
\(589\) −57.9982 −2.38977
\(590\) 0 0
\(591\) −13.0109 −0.535197
\(592\) 0 0
\(593\) 6.66938 0.273879 0.136939 0.990579i \(-0.456273\pi\)
0.136939 + 0.990579i \(0.456273\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 18.6888 0.764880
\(598\) 0 0
\(599\) 1.40115 0.0572495 0.0286247 0.999590i \(-0.490887\pi\)
0.0286247 + 0.999590i \(0.490887\pi\)
\(600\) 0 0
\(601\) 0.349078 0.0142392 0.00711959 0.999975i \(-0.497734\pi\)
0.00711959 + 0.999975i \(0.497734\pi\)
\(602\) 0 0
\(603\) −1.93945 −0.0789804
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −27.2800 −1.10726 −0.553631 0.832762i \(-0.686758\pi\)
−0.553631 + 0.832762i \(0.686758\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.88979 0.116909
\(612\) 0 0
\(613\) 9.34060 0.377263 0.188632 0.982048i \(-0.439595\pi\)
0.188632 + 0.982048i \(0.439595\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −34.6694 −1.39574 −0.697868 0.716226i \(-0.745868\pi\)
−0.697868 + 0.716226i \(0.745868\pi\)
\(618\) 0 0
\(619\) 19.6509 0.789837 0.394919 0.918716i \(-0.370773\pi\)
0.394919 + 0.918716i \(0.370773\pi\)
\(620\) 0 0
\(621\) 2.24977 0.0902802
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 28.9991 1.15811
\(628\) 0 0
\(629\) 30.9385 1.23360
\(630\) 0 0
\(631\) −43.3993 −1.72770 −0.863850 0.503749i \(-0.831953\pi\)
−0.863850 + 0.503749i \(0.831953\pi\)
\(632\) 0 0
\(633\) −8.24977 −0.327899
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −7.00000 −0.277350
\(638\) 0 0
\(639\) 5.60975 0.221918
\(640\) 0 0
\(641\) −4.56009 −0.180113 −0.0900564 0.995937i \(-0.528705\pi\)
−0.0900564 + 0.995937i \(0.528705\pi\)
\(642\) 0 0
\(643\) −8.62065 −0.339965 −0.169983 0.985447i \(-0.554371\pi\)
−0.169983 + 0.985447i \(0.554371\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.40871 −0.291267 −0.145633 0.989339i \(-0.546522\pi\)
−0.145633 + 0.989339i \(0.546522\pi\)
\(648\) 0 0
\(649\) −27.4693 −1.07826
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.00000 −0.0782660 −0.0391330 0.999234i \(-0.512460\pi\)
−0.0391330 + 0.999234i \(0.512460\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −12.5601 −0.490016
\(658\) 0 0
\(659\) 40.3784 1.57292 0.786460 0.617641i \(-0.211911\pi\)
0.786460 + 0.617641i \(0.211911\pi\)
\(660\) 0 0
\(661\) 39.0284 1.51803 0.759015 0.651073i \(-0.225681\pi\)
0.759015 + 0.651073i \(0.225681\pi\)
\(662\) 0 0
\(663\) 4.24977 0.165047
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −20.7418 −0.803124
\(668\) 0 0
\(669\) 9.77959 0.378101
\(670\) 0 0
\(671\) −4.49954 −0.173703
\(672\) 0 0
\(673\) −11.1807 −0.430986 −0.215493 0.976505i \(-0.569136\pi\)
−0.215493 + 0.976505i \(0.569136\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33.3406 −1.28138 −0.640692 0.767798i \(-0.721352\pi\)
−0.640692 + 0.767798i \(0.721352\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 25.4499 0.975242
\(682\) 0 0
\(683\) −31.8889 −1.22019 −0.610097 0.792327i \(-0.708870\pi\)
−0.610097 + 0.792327i \(0.708870\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −8.24977 −0.314748
\(688\) 0 0
\(689\) −9.21949 −0.351235
\(690\) 0 0
\(691\) 39.0303 1.48478 0.742391 0.669967i \(-0.233692\pi\)
0.742391 + 0.669967i \(0.233692\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −24.0975 −0.912757
\(698\) 0 0
\(699\) 11.5904 0.438388
\(700\) 0 0
\(701\) −44.5601 −1.68301 −0.841506 0.540248i \(-0.818330\pi\)
−0.841506 + 0.540248i \(0.818330\pi\)
\(702\) 0 0
\(703\) −45.4986 −1.71601
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 23.4305 0.879951 0.439976 0.898010i \(-0.354987\pi\)
0.439976 + 0.898010i \(0.354987\pi\)
\(710\) 0 0
\(711\) 12.2498 0.459402
\(712\) 0 0
\(713\) 20.8780 0.781886
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.88979 −0.257304
\(718\) 0 0
\(719\) −15.0984 −0.563075 −0.281537 0.959550i \(-0.590844\pi\)
−0.281537 + 0.959550i \(0.590844\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 21.2195 0.789162
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.40871 0.126422 0.0632111 0.998000i \(-0.479866\pi\)
0.0632111 + 0.998000i \(0.479866\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −18.0606 −0.667994
\(732\) 0 0
\(733\) 12.4390 0.459445 0.229722 0.973256i \(-0.426218\pi\)
0.229722 + 0.973256i \(0.426218\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.99908 0.331485
\(738\) 0 0
\(739\) −13.4693 −0.495475 −0.247737 0.968827i \(-0.579687\pi\)
−0.247737 + 0.968827i \(0.579687\pi\)
\(740\) 0 0
\(741\) −6.24977 −0.229591
\(742\) 0 0
\(743\) −45.4111 −1.66597 −0.832986 0.553293i \(-0.813371\pi\)
−0.832986 + 0.553293i \(0.813371\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.67030 −0.134289
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.56101 0.0569621 0.0284810 0.999594i \(-0.490933\pi\)
0.0284810 + 0.999594i \(0.490933\pi\)
\(752\) 0 0
\(753\) −24.3397 −0.886987
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 38.8780 1.41304 0.706522 0.707691i \(-0.250263\pi\)
0.706522 + 0.707691i \(0.250263\pi\)
\(758\) 0 0
\(759\) −10.4390 −0.378911
\(760\) 0 0
\(761\) 5.42809 0.196768 0.0983841 0.995149i \(-0.468633\pi\)
0.0983841 + 0.995149i \(0.468633\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.92007 0.213761
\(768\) 0 0
\(769\) 16.4390 0.592805 0.296403 0.955063i \(-0.404213\pi\)
0.296403 + 0.955063i \(0.404213\pi\)
\(770\) 0 0
\(771\) −23.4693 −0.845225
\(772\) 0 0
\(773\) 42.3884 1.52461 0.762303 0.647221i \(-0.224069\pi\)
0.762303 + 0.647221i \(0.224069\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 35.4381 1.26970
\(780\) 0 0
\(781\) −26.0294 −0.931404
\(782\) 0 0
\(783\) −9.21949 −0.329478
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −15.5592 −0.554625 −0.277312 0.960780i \(-0.589444\pi\)
−0.277312 + 0.960780i \(0.589444\pi\)
\(788\) 0 0
\(789\) −22.6282 −0.805586
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.969724 0.0344359
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 36.4002 1.28936 0.644681 0.764452i \(-0.276990\pi\)
0.644681 + 0.764452i \(0.276990\pi\)
\(798\) 0 0
\(799\) 12.2810 0.434469
\(800\) 0 0
\(801\) −9.67030 −0.341683
\(802\) 0 0
\(803\) 58.2791 2.05663
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12.2791 0.432246
\(808\) 0 0
\(809\) 5.59793 0.196813 0.0984064 0.995146i \(-0.468625\pi\)
0.0984064 + 0.995146i \(0.468625\pi\)
\(810\) 0 0
\(811\) 28.1892 0.989857 0.494929 0.868934i \(-0.335194\pi\)
0.494929 + 0.868934i \(0.335194\pi\)
\(812\) 0 0
\(813\) −22.9385 −0.804489
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 26.5601 0.929220
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 33.8208 1.18035 0.590176 0.807274i \(-0.299058\pi\)
0.590176 + 0.807274i \(0.299058\pi\)
\(822\) 0 0
\(823\) −2.53830 −0.0884795 −0.0442397 0.999021i \(-0.514087\pi\)
−0.0442397 + 0.999021i \(0.514087\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −12.6694 −0.440558 −0.220279 0.975437i \(-0.570697\pi\)
−0.220279 + 0.975437i \(0.570697\pi\)
\(828\) 0 0
\(829\) −37.4693 −1.30136 −0.650681 0.759351i \(-0.725516\pi\)
−0.650681 + 0.759351i \(0.725516\pi\)
\(830\) 0 0
\(831\) 11.5298 0.399965
\(832\) 0 0
\(833\) −29.7484 −1.03072
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.28005 0.320765
\(838\) 0 0
\(839\) −19.3893 −0.669394 −0.334697 0.942326i \(-0.608634\pi\)
−0.334697 + 0.942326i \(0.608634\pi\)
\(840\) 0 0
\(841\) 55.9991 1.93100
\(842\) 0 0
\(843\) −11.3288 −0.390184
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 20.9991 0.720687
\(850\) 0 0
\(851\) 16.3784 0.561446
\(852\) 0 0
\(853\) −7.77959 −0.266368 −0.133184 0.991091i \(-0.542520\pi\)
−0.133184 + 0.991091i \(0.542520\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −26.9697 −0.921268 −0.460634 0.887590i \(-0.652378\pi\)
−0.460634 + 0.887590i \(0.652378\pi\)
\(858\) 0 0
\(859\) 5.93189 0.202393 0.101197 0.994866i \(-0.467733\pi\)
0.101197 + 0.994866i \(0.467733\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 33.3288 1.13452 0.567262 0.823537i \(-0.308002\pi\)
0.567262 + 0.823537i \(0.308002\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.06055 0.0360182
\(868\) 0 0
\(869\) −56.8392 −1.92814
\(870\) 0 0
\(871\) −1.93945 −0.0657157
\(872\) 0 0
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 19.1589 0.646952 0.323476 0.946236i \(-0.395149\pi\)
0.323476 + 0.946236i \(0.395149\pi\)
\(878\) 0 0
\(879\) −4.26915 −0.143995
\(880\) 0 0
\(881\) 53.8989 1.81590 0.907949 0.419080i \(-0.137647\pi\)
0.907949 + 0.419080i \(0.137647\pi\)
\(882\) 0 0
\(883\) −22.9385 −0.771943 −0.385972 0.922511i \(-0.626134\pi\)
−0.385972 + 0.922511i \(0.626134\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 47.5298 1.59590 0.797948 0.602727i \(-0.205919\pi\)
0.797948 + 0.602727i \(0.205919\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4.64002 −0.155447
\(892\) 0 0
\(893\) −18.0606 −0.604373
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.24977 0.0751177
\(898\) 0 0
\(899\) −85.5573 −2.85350
\(900\) 0 0
\(901\) −39.1807 −1.30530
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 20.6206 0.684697 0.342349 0.939573i \(-0.388778\pi\)
0.342349 + 0.939573i \(0.388778\pi\)
\(908\) 0 0
\(909\) −15.2800 −0.506807
\(910\) 0 0
\(911\) −41.2413 −1.36638 −0.683192 0.730238i \(-0.739409\pi\)
−0.683192 + 0.730238i \(0.739409\pi\)
\(912\) 0 0
\(913\) 17.0303 0.563620
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 37.2489 1.22873 0.614363 0.789023i \(-0.289413\pi\)
0.614363 + 0.789023i \(0.289413\pi\)
\(920\) 0 0
\(921\) −20.0000 −0.659022
\(922\) 0 0
\(923\) 5.60975 0.184647
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.21949 0.0400535
\(928\) 0 0
\(929\) −59.0091 −1.93602 −0.968012 0.250903i \(-0.919273\pi\)
−0.968012 + 0.250903i \(0.919273\pi\)
\(930\) 0 0
\(931\) 43.7484 1.43380
\(932\) 0 0
\(933\) 3.71904 0.121756
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 56.9679 1.86106 0.930530 0.366216i \(-0.119347\pi\)
0.930530 + 0.366216i \(0.119347\pi\)
\(938\) 0 0
\(939\) 1.52982 0.0499237
\(940\) 0 0
\(941\) 2.35906 0.0769032 0.0384516 0.999260i \(-0.487757\pi\)
0.0384516 + 0.999260i \(0.487757\pi\)
\(942\) 0 0
\(943\) −12.7569 −0.415421
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −43.4481 −1.41187 −0.705936 0.708276i \(-0.749473\pi\)
−0.705936 + 0.708276i \(0.749473\pi\)
\(948\) 0 0
\(949\) −12.5601 −0.407718
\(950\) 0 0
\(951\) 16.1093 0.522379
\(952\) 0 0
\(953\) −23.5904 −0.764167 −0.382084 0.924128i \(-0.624793\pi\)
−0.382084 + 0.924128i \(0.624793\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 42.7787 1.38284
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 55.1193 1.77804
\(962\) 0 0
\(963\) −5.28005 −0.170147
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −31.5979 −1.01612 −0.508060 0.861321i \(-0.669637\pi\)
−0.508060 + 0.861321i \(0.669637\pi\)
\(968\) 0 0
\(969\) −26.5601 −0.853233
\(970\) 0 0
\(971\) −0.499542 −0.0160311 −0.00801553 0.999968i \(-0.502551\pi\)
−0.00801553 + 0.999968i \(0.502551\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −18.7081 −0.598526 −0.299263 0.954171i \(-0.596741\pi\)
−0.299263 + 0.954171i \(0.596741\pi\)
\(978\) 0 0
\(979\) 44.8704 1.43406
\(980\) 0 0
\(981\) −10.1892 −0.325317
\(982\) 0 0
\(983\) 3.83016 0.122163 0.0610815 0.998133i \(-0.480545\pi\)
0.0610815 + 0.998133i \(0.480545\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.56101 −0.304022
\(990\) 0 0
\(991\) 6.43899 0.204541 0.102271 0.994757i \(-0.467389\pi\)
0.102271 + 0.994757i \(0.467389\pi\)
\(992\) 0 0
\(993\) 15.5298 0.492824
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 12.1505 0.384809 0.192405 0.981316i \(-0.438371\pi\)
0.192405 + 0.981316i \(0.438371\pi\)
\(998\) 0 0
\(999\) 7.28005 0.230330
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.bp.1.1 3
5.2 odd 4 1560.2.l.c.1249.3 6
5.3 odd 4 1560.2.l.c.1249.6 yes 6
5.4 even 2 7800.2.a.bj.1.1 3
15.2 even 4 4680.2.l.e.2809.1 6
15.8 even 4 4680.2.l.e.2809.2 6
20.3 even 4 3120.2.l.m.1249.3 6
20.7 even 4 3120.2.l.m.1249.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.c.1249.3 6 5.2 odd 4
1560.2.l.c.1249.6 yes 6 5.3 odd 4
3120.2.l.m.1249.3 6 20.3 even 4
3120.2.l.m.1249.6 6 20.7 even 4
4680.2.l.e.2809.1 6 15.2 even 4
4680.2.l.e.2809.2 6 15.8 even 4
7800.2.a.bj.1.1 3 5.4 even 2
7800.2.a.bp.1.1 3 1.1 even 1 trivial