Properties

Label 2646.2.a.l.1.1
Level $2646$
Weight $2$
Character 2646.1
Self dual yes
Analytic conductor $21.128$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.1284163748\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2646.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{8} -2.00000 q^{10} +2.00000 q^{11} -1.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} -4.00000 q^{19} +2.00000 q^{20} -2.00000 q^{22} -3.00000 q^{23} -1.00000 q^{25} +1.00000 q^{26} -7.00000 q^{29} -11.0000 q^{31} -1.00000 q^{32} +3.00000 q^{34} -6.00000 q^{37} +4.00000 q^{38} -2.00000 q^{40} +6.00000 q^{41} +1.00000 q^{43} +2.00000 q^{44} +3.00000 q^{46} +8.00000 q^{47} +1.00000 q^{50} -1.00000 q^{52} -1.00000 q^{53} +4.00000 q^{55} +7.00000 q^{58} -7.00000 q^{59} -14.0000 q^{61} +11.0000 q^{62} +1.00000 q^{64} -2.00000 q^{65} -11.0000 q^{67} -3.00000 q^{68} +11.0000 q^{71} -8.00000 q^{73} +6.00000 q^{74} -4.00000 q^{76} +4.00000 q^{79} +2.00000 q^{80} -6.00000 q^{82} -6.00000 q^{85} -1.00000 q^{86} -2.00000 q^{88} +1.00000 q^{89} -3.00000 q^{92} -8.00000 q^{94} -8.00000 q^{95} +16.0000 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −2.00000 −0.632456
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) 0 0
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0 0
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) −2.00000 −0.316228
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 7.00000 0.919145
\(59\) −7.00000 −0.911322 −0.455661 0.890153i \(-0.650597\pi\)
−0.455661 + 0.890153i \(0.650597\pi\)
\(60\) 0 0
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 11.0000 1.39700
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −11.0000 −1.34386 −0.671932 0.740613i \(-0.734535\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 0 0
\(71\) 11.0000 1.30546 0.652730 0.757591i \(-0.273624\pi\)
0.652730 + 0.757591i \(0.273624\pi\)
\(72\) 0 0
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 2.00000 0.223607
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.00000 −0.312772
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −16.0000 −1.59206 −0.796030 0.605257i \(-0.793070\pi\)
−0.796030 + 0.605257i \(0.793070\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 16.0000 1.54678 0.773389 0.633932i \(-0.218560\pi\)
0.773389 + 0.633932i \(0.218560\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) −4.00000 −0.381385
\(111\) 0 0
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) −6.00000 −0.559503
\(116\) −7.00000 −0.649934
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 14.0000 1.26750
\(123\) 0 0
\(124\) −11.0000 −0.987829
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 2.00000 0.175412
\(131\) 15.0000 1.31056 0.655278 0.755388i \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 11.0000 0.950255
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) 8.00000 0.683486 0.341743 0.939793i \(-0.388983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) 0 0
\(139\) 6.00000 0.508913 0.254457 0.967084i \(-0.418103\pi\)
0.254457 + 0.967084i \(0.418103\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −11.0000 −0.923099
\(143\) −2.00000 −0.167248
\(144\) 0 0
\(145\) −14.0000 −1.16264
\(146\) 8.00000 0.662085
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) 0 0
\(155\) −22.0000 −1.76708
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) −4.00000 −0.318223
\(159\) 0 0
\(160\) −2.00000 −0.158114
\(161\) 0 0
\(162\) 0 0
\(163\) 9.00000 0.704934 0.352467 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 0 0
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) 1.00000 0.0762493
\(173\) −8.00000 −0.608229 −0.304114 0.952636i \(-0.598361\pi\)
−0.304114 + 0.952636i \(0.598361\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) −1.00000 −0.0749532
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) −12.0000 −0.882258
\(186\) 0 0
\(187\) −6.00000 −0.438763
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) −19.0000 −1.36765 −0.683825 0.729646i \(-0.739685\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(194\) −16.0000 −1.14873
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −5.00000 −0.354441 −0.177220 0.984171i \(-0.556711\pi\)
−0.177220 + 0.984171i \(0.556711\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) 16.0000 1.12576
\(203\) 0 0
\(204\) 0 0
\(205\) 12.0000 0.838116
\(206\) 13.0000 0.905753
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −1.00000 −0.0686803
\(213\) 0 0
\(214\) −16.0000 −1.09374
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) 0 0
\(220\) 4.00000 0.269680
\(221\) 3.00000 0.201802
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −10.0000 −0.665190
\(227\) 13.0000 0.862840 0.431420 0.902151i \(-0.358013\pi\)
0.431420 + 0.902151i \(0.358013\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 7.00000 0.459573
\(233\) 8.00000 0.524097 0.262049 0.965055i \(-0.415602\pi\)
0.262049 + 0.965055i \(0.415602\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) −7.00000 −0.455661
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −14.0000 −0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) 11.0000 0.698501
\(249\) 0 0
\(250\) 12.0000 0.758947
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) −15.0000 −0.926703
\(263\) 23.0000 1.41824 0.709120 0.705087i \(-0.249092\pi\)
0.709120 + 0.705087i \(0.249092\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) −11.0000 −0.671932
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) −7.00000 −0.425220 −0.212610 0.977137i \(-0.568196\pi\)
−0.212610 + 0.977137i \(0.568196\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −8.00000 −0.483298
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) 16.0000 0.961347 0.480673 0.876900i \(-0.340392\pi\)
0.480673 + 0.876900i \(0.340392\pi\)
\(278\) −6.00000 −0.359856
\(279\) 0 0
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) 16.0000 0.951101 0.475551 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 11.0000 0.652730
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 14.0000 0.822108
\(291\) 0 0
\(292\) −8.00000 −0.468165
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) −14.0000 −0.815112
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −5.00000 −0.289642
\(299\) 3.00000 0.173494
\(300\) 0 0
\(301\) 0 0
\(302\) −4.00000 −0.230174
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) −28.0000 −1.60328
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 22.0000 1.24952
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 0 0
\(313\) 24.0000 1.35656 0.678280 0.734803i \(-0.262726\pi\)
0.678280 + 0.734803i \(0.262726\pi\)
\(314\) 7.00000 0.395033
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 0 0
\(319\) −14.0000 −0.783850
\(320\) 2.00000 0.111803
\(321\) 0 0
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) −9.00000 −0.498464
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 11.0000 0.604615 0.302307 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 14.0000 0.766046
\(335\) −22.0000 −1.20199
\(336\) 0 0
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) −6.00000 −0.325396
\(341\) −22.0000 −1.19137
\(342\) 0 0
\(343\) 0 0
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) 8.00000 0.430083
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 0 0
\(349\) −27.0000 −1.44528 −0.722638 0.691226i \(-0.757071\pi\)
−0.722638 + 0.691226i \(0.757071\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −33.0000 −1.75641 −0.878206 0.478282i \(-0.841260\pi\)
−0.878206 + 0.478282i \(0.841260\pi\)
\(354\) 0 0
\(355\) 22.0000 1.16764
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) 6.00000 0.317110
\(359\) 19.0000 1.00278 0.501391 0.865221i \(-0.332822\pi\)
0.501391 + 0.865221i \(0.332822\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −7.00000 −0.367912
\(363\) 0 0
\(364\) 0 0
\(365\) −16.0000 −0.837478
\(366\) 0 0
\(367\) −11.0000 −0.574195 −0.287098 0.957901i \(-0.592690\pi\)
−0.287098 + 0.957901i \(0.592690\pi\)
\(368\) −3.00000 −0.156386
\(369\) 0 0
\(370\) 12.0000 0.623850
\(371\) 0 0
\(372\) 0 0
\(373\) −20.0000 −1.03556 −0.517780 0.855514i \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) 6.00000 0.310253
\(375\) 0 0
\(376\) −8.00000 −0.412568
\(377\) 7.00000 0.360518
\(378\) 0 0
\(379\) 24.0000 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) −8.00000 −0.410391
\(381\) 0 0
\(382\) 24.0000 1.22795
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) 16.0000 0.812277
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 38.0000 1.90717 0.953583 0.301131i \(-0.0973643\pi\)
0.953583 + 0.301131i \(0.0973643\pi\)
\(398\) 5.00000 0.250627
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) 11.0000 0.547949
\(404\) −16.0000 −0.796030
\(405\) 0 0
\(406\) 0 0
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) 18.0000 0.890043 0.445021 0.895520i \(-0.353196\pi\)
0.445021 + 0.895520i \(0.353196\pi\)
\(410\) −12.0000 −0.592638
\(411\) 0 0
\(412\) −13.0000 −0.640464
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) 8.00000 0.391293
\(419\) −19.0000 −0.928211 −0.464105 0.885780i \(-0.653624\pi\)
−0.464105 + 0.885780i \(0.653624\pi\)
\(420\) 0 0
\(421\) 24.0000 1.16969 0.584844 0.811146i \(-0.301156\pi\)
0.584844 + 0.811146i \(0.301156\pi\)
\(422\) −5.00000 −0.243396
\(423\) 0 0
\(424\) 1.00000 0.0485643
\(425\) 3.00000 0.145521
\(426\) 0 0
\(427\) 0 0
\(428\) 16.0000 0.773389
\(429\) 0 0
\(430\) −2.00000 −0.0964486
\(431\) 4.00000 0.192673 0.0963366 0.995349i \(-0.469287\pi\)
0.0963366 + 0.995349i \(0.469287\pi\)
\(432\) 0 0
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 16.0000 0.766261
\(437\) 12.0000 0.574038
\(438\) 0 0
\(439\) 3.00000 0.143182 0.0715911 0.997434i \(-0.477192\pi\)
0.0715911 + 0.997434i \(0.477192\pi\)
\(440\) −4.00000 −0.190693
\(441\) 0 0
\(442\) −3.00000 −0.142695
\(443\) −18.0000 −0.855206 −0.427603 0.903967i \(-0.640642\pi\)
−0.427603 + 0.903967i \(0.640642\pi\)
\(444\) 0 0
\(445\) 2.00000 0.0948091
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) 0 0
\(449\) 42.0000 1.98210 0.991051 0.133482i \(-0.0426157\pi\)
0.991051 + 0.133482i \(0.0426157\pi\)
\(450\) 0 0
\(451\) 12.0000 0.565058
\(452\) 10.0000 0.470360
\(453\) 0 0
\(454\) −13.0000 −0.610120
\(455\) 0 0
\(456\) 0 0
\(457\) 23.0000 1.07589 0.537947 0.842978i \(-0.319200\pi\)
0.537947 + 0.842978i \(0.319200\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) −6.00000 −0.279751
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −7.00000 −0.324967
\(465\) 0 0
\(466\) −8.00000 −0.370593
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −16.0000 −0.738025
\(471\) 0 0
\(472\) 7.00000 0.322201
\(473\) 2.00000 0.0919601
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) 8.00000 0.364390
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 32.0000 1.45305
\(486\) 0 0
\(487\) −20.0000 −0.906287 −0.453143 0.891438i \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 14.0000 0.633750
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 21.0000 0.945792
\(494\) −4.00000 −0.179969
\(495\) 0 0
\(496\) −11.0000 −0.493915
\(497\) 0 0
\(498\) 0 0
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) −12.0000 −0.536656
\(501\) 0 0
\(502\) 28.0000 1.24970
\(503\) 22.0000 0.980932 0.490466 0.871460i \(-0.336827\pi\)
0.490466 + 0.871460i \(0.336827\pi\)
\(504\) 0 0
\(505\) −32.0000 −1.42398
\(506\) 6.00000 0.266733
\(507\) 0 0
\(508\) 14.0000 0.621150
\(509\) −38.0000 −1.68432 −0.842160 0.539227i \(-0.818716\pi\)
−0.842160 + 0.539227i \(0.818716\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 14.0000 0.617514
\(515\) −26.0000 −1.14570
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) 0 0
\(520\) 2.00000 0.0877058
\(521\) −35.0000 −1.53338 −0.766689 0.642019i \(-0.778097\pi\)
−0.766689 + 0.642019i \(0.778097\pi\)
\(522\) 0 0
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 15.0000 0.655278
\(525\) 0 0
\(526\) −23.0000 −1.00285
\(527\) 33.0000 1.43750
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 2.00000 0.0868744
\(531\) 0 0
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) 32.0000 1.38348
\(536\) 11.0000 0.475128
\(537\) 0 0
\(538\) 10.0000 0.431131
\(539\) 0 0
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 7.00000 0.300676
\(543\) 0 0
\(544\) 3.00000 0.128624
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) 8.00000 0.341743
\(549\) 0 0
\(550\) 2.00000 0.0852803
\(551\) 28.0000 1.19284
\(552\) 0 0
\(553\) 0 0
\(554\) −16.0000 −0.679775
\(555\) 0 0
\(556\) 6.00000 0.254457
\(557\) −3.00000 −0.127114 −0.0635570 0.997978i \(-0.520244\pi\)
−0.0635570 + 0.997978i \(0.520244\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) 30.0000 1.26547
\(563\) 1.00000 0.0421450 0.0210725 0.999778i \(-0.493292\pi\)
0.0210725 + 0.999778i \(0.493292\pi\)
\(564\) 0 0
\(565\) 20.0000 0.841406
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) −11.0000 −0.461550
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 0 0
\(571\) −21.0000 −0.878823 −0.439411 0.898286i \(-0.644813\pi\)
−0.439411 + 0.898286i \(0.644813\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 0 0
\(574\) 0 0
\(575\) 3.00000 0.125109
\(576\) 0 0
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) −14.0000 −0.581318
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) 8.00000 0.331042
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) 29.0000 1.19696 0.598479 0.801138i \(-0.295772\pi\)
0.598479 + 0.801138i \(0.295772\pi\)
\(588\) 0 0
\(589\) 44.0000 1.81299
\(590\) 14.0000 0.576371
\(591\) 0 0
\(592\) −6.00000 −0.246598
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.00000 0.204808
\(597\) 0 0
\(598\) −3.00000 −0.122679
\(599\) −9.00000 −0.367730 −0.183865 0.982952i \(-0.558861\pi\)
−0.183865 + 0.982952i \(0.558861\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.00000 0.162758
\(605\) −14.0000 −0.569181
\(606\) 0 0
\(607\) 33.0000 1.33943 0.669714 0.742619i \(-0.266417\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 28.0000 1.13369
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) 2.00000 0.0807134
\(615\) 0 0
\(616\) 0 0
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 0 0
\(619\) 46.0000 1.84890 0.924448 0.381308i \(-0.124526\pi\)
0.924448 + 0.381308i \(0.124526\pi\)
\(620\) −22.0000 −0.883541
\(621\) 0 0
\(622\) 8.00000 0.320771
\(623\) 0 0
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −24.0000 −0.959233
\(627\) 0 0
\(628\) −7.00000 −0.279330
\(629\) 18.0000 0.717707
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) −4.00000 −0.159111
\(633\) 0 0
\(634\) 30.0000 1.19145
\(635\) 28.0000 1.11115
\(636\) 0 0
\(637\) 0 0
\(638\) 14.0000 0.554265
\(639\) 0 0
\(640\) −2.00000 −0.0790569
\(641\) 28.0000 1.10593 0.552967 0.833203i \(-0.313496\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(642\) 0 0
\(643\) −42.0000 −1.65632 −0.828159 0.560493i \(-0.810612\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 0 0
\(649\) −14.0000 −0.549548
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) 9.00000 0.352467
\(653\) −25.0000 −0.978326 −0.489163 0.872192i \(-0.662698\pi\)
−0.489163 + 0.872192i \(0.662698\pi\)
\(654\) 0 0
\(655\) 30.0000 1.17220
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) −11.0000 −0.427527
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 21.0000 0.813123
\(668\) −14.0000 −0.541676
\(669\) 0 0
\(670\) 22.0000 0.849934
\(671\) −28.0000 −1.08093
\(672\) 0 0
\(673\) 23.0000 0.886585 0.443292 0.896377i \(-0.353810\pi\)
0.443292 + 0.896377i \(0.353810\pi\)
\(674\) 13.0000 0.500741
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.00000 0.230089
\(681\) 0 0
\(682\) 22.0000 0.842424
\(683\) −14.0000 −0.535695 −0.267848 0.963461i \(-0.586312\pi\)
−0.267848 + 0.963461i \(0.586312\pi\)
\(684\) 0 0
\(685\) 16.0000 0.611329
\(686\) 0 0
\(687\) 0 0
\(688\) 1.00000 0.0381246
\(689\) 1.00000 0.0380970
\(690\) 0 0
\(691\) 22.0000 0.836919 0.418460 0.908235i \(-0.362570\pi\)
0.418460 + 0.908235i \(0.362570\pi\)
\(692\) −8.00000 −0.304114
\(693\) 0 0
\(694\) −6.00000 −0.227757
\(695\) 12.0000 0.455186
\(696\) 0 0
\(697\) −18.0000 −0.681799
\(698\) 27.0000 1.02197
\(699\) 0 0
\(700\) 0 0
\(701\) −14.0000 −0.528773 −0.264386 0.964417i \(-0.585169\pi\)
−0.264386 + 0.964417i \(0.585169\pi\)
\(702\) 0 0
\(703\) 24.0000 0.905177
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) 33.0000 1.24197
\(707\) 0 0
\(708\) 0 0
\(709\) 22.0000 0.826227 0.413114 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) −22.0000 −0.825645
\(711\) 0 0
\(712\) −1.00000 −0.0374766
\(713\) 33.0000 1.23586
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) −6.00000 −0.224231
\(717\) 0 0
\(718\) −19.0000 −0.709074
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) 7.00000 0.260153
\(725\) 7.00000 0.259973
\(726\) 0 0
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16.0000 0.592187
\(731\) −3.00000 −0.110959
\(732\) 0 0
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) 11.0000 0.406017
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) −22.0000 −0.810380
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −12.0000 −0.441129
\(741\) 0 0
\(742\) 0 0
\(743\) −15.0000 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) 20.0000 0.732252
\(747\) 0 0
\(748\) −6.00000 −0.219382
\(749\) 0 0
\(750\) 0 0
\(751\) −30.0000 −1.09472 −0.547358 0.836899i \(-0.684366\pi\)
−0.547358 + 0.836899i \(0.684366\pi\)
\(752\) 8.00000 0.291730
\(753\) 0 0
\(754\) −7.00000 −0.254925
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) −24.0000 −0.871719
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) −1.00000 −0.0362500 −0.0181250 0.999836i \(-0.505770\pi\)
−0.0181250 + 0.999836i \(0.505770\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) −18.0000 −0.650366
\(767\) 7.00000 0.252755
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −19.0000 −0.683825
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) 11.0000 0.395132
\(776\) −16.0000 −0.574367
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 22.0000 0.787222
\(782\) −9.00000 −0.321839
\(783\) 0 0
\(784\) 0 0
\(785\) −14.0000 −0.499681
\(786\) 0 0
\(787\) −38.0000 −1.35455 −0.677277 0.735728i \(-0.736840\pi\)
−0.677277 + 0.735728i \(0.736840\pi\)
\(788\) 18.0000 0.641223
\(789\) 0 0
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) 0 0
\(793\) 14.0000 0.497155
\(794\) −38.0000 −1.34857
\(795\) 0 0
\(796\) −5.00000 −0.177220
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) −18.0000 −0.635602
\(803\) −16.0000 −0.564628
\(804\) 0 0
\(805\) 0 0
\(806\) −11.0000 −0.387458
\(807\) 0 0
\(808\) 16.0000 0.562878
\(809\) 36.0000 1.26569 0.632846 0.774277i \(-0.281886\pi\)
0.632846 + 0.774277i \(0.281886\pi\)
\(810\) 0 0
\(811\) −22.0000 −0.772524 −0.386262 0.922389i \(-0.626234\pi\)
−0.386262 + 0.922389i \(0.626234\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 12.0000 0.420600
\(815\) 18.0000 0.630512
\(816\) 0 0
\(817\) −4.00000 −0.139942
\(818\) −18.0000 −0.629355
\(819\) 0 0
\(820\) 12.0000 0.419058
\(821\) 35.0000 1.22151 0.610754 0.791820i \(-0.290866\pi\)
0.610754 + 0.791820i \(0.290866\pi\)
\(822\) 0 0
\(823\) 34.0000 1.18517 0.592583 0.805510i \(-0.298108\pi\)
0.592583 + 0.805510i \(0.298108\pi\)
\(824\) 13.0000 0.452876
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 22.0000 0.764092 0.382046 0.924143i \(-0.375220\pi\)
0.382046 + 0.924143i \(0.375220\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) 0 0
\(834\) 0 0
\(835\) −28.0000 −0.968980
\(836\) −8.00000 −0.276686
\(837\) 0 0
\(838\) 19.0000 0.656344
\(839\) 18.0000 0.621429 0.310715 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) −24.0000 −0.827095
\(843\) 0 0
\(844\) 5.00000 0.172107
\(845\) −24.0000 −0.825625
\(846\) 0 0
\(847\) 0 0
\(848\) −1.00000 −0.0343401
\(849\) 0 0
\(850\) −3.00000 −0.102899
\(851\) 18.0000 0.617032
\(852\) 0 0
\(853\) 17.0000 0.582069 0.291034 0.956713i \(-0.406001\pi\)
0.291034 + 0.956713i \(0.406001\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −16.0000 −0.546869
\(857\) −9.00000 −0.307434 −0.153717 0.988115i \(-0.549124\pi\)
−0.153717 + 0.988115i \(0.549124\pi\)
\(858\) 0 0
\(859\) −30.0000 −1.02359 −0.511793 0.859109i \(-0.671019\pi\)
−0.511793 + 0.859109i \(0.671019\pi\)
\(860\) 2.00000 0.0681994
\(861\) 0 0
\(862\) −4.00000 −0.136241
\(863\) 3.00000 0.102121 0.0510606 0.998696i \(-0.483740\pi\)
0.0510606 + 0.998696i \(0.483740\pi\)
\(864\) 0 0
\(865\) −16.0000 −0.544016
\(866\) 28.0000 0.951479
\(867\) 0 0
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 0 0
\(871\) 11.0000 0.372721
\(872\) −16.0000 −0.541828
\(873\) 0 0
\(874\) −12.0000 −0.405906
\(875\) 0 0
\(876\) 0 0
\(877\) −36.0000 −1.21563 −0.607817 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(878\) −3.00000 −0.101245
\(879\) 0 0
\(880\) 4.00000 0.134840
\(881\) 47.0000 1.58347 0.791735 0.610865i \(-0.209178\pi\)
0.791735 + 0.610865i \(0.209178\pi\)
\(882\) 0 0
\(883\) −5.00000 −0.168263 −0.0841317 0.996455i \(-0.526812\pi\)
−0.0841317 + 0.996455i \(0.526812\pi\)
\(884\) 3.00000 0.100901
\(885\) 0 0
\(886\) 18.0000 0.604722
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −2.00000 −0.0670402
\(891\) 0 0
\(892\) −8.00000 −0.267860
\(893\) −32.0000 −1.07084
\(894\) 0 0
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) −42.0000 −1.40156
\(899\) 77.0000 2.56809
\(900\) 0 0
\(901\) 3.00000 0.0999445
\(902\) −12.0000 −0.399556
\(903\) 0 0
\(904\) −10.0000 −0.332595
\(905\) 14.0000 0.465376
\(906\) 0 0
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) 13.0000 0.431420
\(909\) 0 0
\(910\) 0 0
\(911\) −8.00000 −0.265052 −0.132526 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −23.0000 −0.760772
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 0 0
\(919\) 48.0000 1.58337 0.791687 0.610927i \(-0.209203\pi\)
0.791687 + 0.610927i \(0.209203\pi\)
\(920\) 6.00000 0.197814
\(921\) 0 0
\(922\) 12.0000 0.395199
\(923\) −11.0000 −0.362069
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) −20.0000 −0.657241
\(927\) 0 0
\(928\) 7.00000 0.229786
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 8.00000 0.262049
\(933\) 0 0
\(934\) −28.0000 −0.916188
\(935\) −12.0000 −0.392442
\(936\) 0 0
\(937\) 42.0000 1.37208 0.686040 0.727564i \(-0.259347\pi\)
0.686040 + 0.727564i \(0.259347\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 16.0000 0.521862
\(941\) −6.00000 −0.195594 −0.0977972 0.995206i \(-0.531180\pi\)
−0.0977972 + 0.995206i \(0.531180\pi\)
\(942\) 0 0
\(943\) −18.0000 −0.586161
\(944\) −7.00000 −0.227831
\(945\) 0 0
\(946\) −2.00000 −0.0650256
\(947\) −4.00000 −0.129983 −0.0649913 0.997886i \(-0.520702\pi\)
−0.0649913 + 0.997886i \(0.520702\pi\)
\(948\) 0 0
\(949\) 8.00000 0.259691
\(950\) −4.00000 −0.129777
\(951\) 0 0
\(952\) 0 0
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) 0 0
\(955\) −48.0000 −1.55324
\(956\) 0 0
\(957\) 0 0
\(958\) −30.0000 −0.969256
\(959\) 0 0
\(960\) 0 0
\(961\) 90.0000 2.90323
\(962\) −6.00000 −0.193448
\(963\) 0 0
\(964\) −8.00000 −0.257663
\(965\) −38.0000 −1.22326
\(966\) 0 0
\(967\) 22.0000 0.707472 0.353736 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) −32.0000 −1.02746
\(971\) 23.0000 0.738105 0.369053 0.929409i \(-0.379682\pi\)
0.369053 + 0.929409i \(0.379682\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 20.0000 0.640841
\(975\) 0 0
\(976\) −14.0000 −0.448129
\(977\) −52.0000 −1.66363 −0.831814 0.555055i \(-0.812697\pi\)
−0.831814 + 0.555055i \(0.812697\pi\)
\(978\) 0 0
\(979\) 2.00000 0.0639203
\(980\) 0 0
\(981\) 0 0
\(982\) −30.0000 −0.957338
\(983\) 62.0000 1.97749 0.988746 0.149601i \(-0.0477989\pi\)
0.988746 + 0.149601i \(0.0477989\pi\)
\(984\) 0 0
\(985\) 36.0000 1.14706
\(986\) −21.0000 −0.668776
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) −3.00000 −0.0953945
\(990\) 0 0
\(991\) −34.0000 −1.08005 −0.540023 0.841650i \(-0.681584\pi\)
−0.540023 + 0.841650i \(0.681584\pi\)
\(992\) 11.0000 0.349250
\(993\) 0 0
\(994\) 0 0
\(995\) −10.0000 −0.317021
\(996\) 0 0
\(997\) −37.0000 −1.17180 −0.585901 0.810383i \(-0.699259\pi\)
−0.585901 + 0.810383i \(0.699259\pi\)
\(998\) 36.0000 1.13956
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2646.2.a.l.1.1 yes 1
3.2 odd 2 2646.2.a.s.1.1 yes 1
7.6 odd 2 2646.2.a.d.1.1 1
21.20 even 2 2646.2.a.ba.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2646.2.a.d.1.1 1 7.6 odd 2
2646.2.a.l.1.1 yes 1 1.1 even 1 trivial
2646.2.a.s.1.1 yes 1 3.2 odd 2
2646.2.a.ba.1.1 yes 1 21.20 even 2