Properties

Label 6003.2.a.e.1.1
Level 6003
Weight 2
Character 6003.1
Self dual yes
Analytic conductor 47.934
Analytic rank 1
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
Defining polynomial: \(x^{2} - 6\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.44949\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{4} -2.44949 q^{5} -4.44949 q^{7} +O(q^{10})\) \(q-2.00000 q^{4} -2.44949 q^{5} -4.44949 q^{7} +1.00000 q^{13} +4.00000 q^{16} +1.44949 q^{17} -1.00000 q^{19} +4.89898 q^{20} +1.00000 q^{23} +1.00000 q^{25} +8.89898 q^{28} -1.00000 q^{29} -10.4495 q^{31} +10.8990 q^{35} +9.89898 q^{37} +9.34847 q^{41} -0.101021 q^{43} +12.4495 q^{47} +12.7980 q^{49} -2.00000 q^{52} +2.00000 q^{53} +0.550510 q^{59} -3.10102 q^{61} -8.00000 q^{64} -2.44949 q^{65} -8.89898 q^{67} -2.89898 q^{68} +12.3485 q^{71} -14.2474 q^{73} +2.00000 q^{76} +5.89898 q^{79} -9.79796 q^{80} +7.55051 q^{83} -3.55051 q^{85} -5.44949 q^{89} -4.44949 q^{91} -2.00000 q^{92} +2.44949 q^{95} +16.8990 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{4} - 4q^{7} + O(q^{10}) \) \( 2q - 4q^{4} - 4q^{7} + 2q^{13} + 8q^{16} - 2q^{17} - 2q^{19} + 2q^{23} + 2q^{25} + 8q^{28} - 2q^{29} - 16q^{31} + 12q^{35} + 10q^{37} + 4q^{41} - 10q^{43} + 20q^{47} + 6q^{49} - 4q^{52} + 4q^{53} + 6q^{59} - 16q^{61} - 16q^{64} - 8q^{67} + 4q^{68} + 10q^{71} - 4q^{73} + 4q^{76} + 2q^{79} + 20q^{83} - 12q^{85} - 6q^{89} - 4q^{91} - 4q^{92} + 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) −2.44949 −1.09545 −0.547723 0.836660i \(-0.684505\pi\)
−0.547723 + 0.836660i \(0.684505\pi\)
\(6\) 0 0
\(7\) −4.44949 −1.68175 −0.840875 0.541230i \(-0.817959\pi\)
−0.840875 + 0.541230i \(0.817959\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 1.44949 0.351553 0.175776 0.984430i \(-0.443756\pi\)
0.175776 + 0.984430i \(0.443756\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 4.89898 1.09545
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 8.89898 1.68175
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −10.4495 −1.87678 −0.938392 0.345573i \(-0.887685\pi\)
−0.938392 + 0.345573i \(0.887685\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 10.8990 1.84226
\(36\) 0 0
\(37\) 9.89898 1.62738 0.813691 0.581298i \(-0.197455\pi\)
0.813691 + 0.581298i \(0.197455\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.34847 1.45999 0.729993 0.683455i \(-0.239523\pi\)
0.729993 + 0.683455i \(0.239523\pi\)
\(42\) 0 0
\(43\) −0.101021 −0.0154055 −0.00770274 0.999970i \(-0.502452\pi\)
−0.00770274 + 0.999970i \(0.502452\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.4495 1.81594 0.907972 0.419030i \(-0.137630\pi\)
0.907972 + 0.419030i \(0.137630\pi\)
\(48\) 0 0
\(49\) 12.7980 1.82828
\(50\) 0 0
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.550510 0.0716703 0.0358352 0.999358i \(-0.488591\pi\)
0.0358352 + 0.999358i \(0.488591\pi\)
\(60\) 0 0
\(61\) −3.10102 −0.397045 −0.198522 0.980096i \(-0.563614\pi\)
−0.198522 + 0.980096i \(0.563614\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −2.44949 −0.303822
\(66\) 0 0
\(67\) −8.89898 −1.08718 −0.543592 0.839350i \(-0.682936\pi\)
−0.543592 + 0.839350i \(0.682936\pi\)
\(68\) −2.89898 −0.351553
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3485 1.46549 0.732747 0.680501i \(-0.238238\pi\)
0.732747 + 0.680501i \(0.238238\pi\)
\(72\) 0 0
\(73\) −14.2474 −1.66754 −0.833769 0.552114i \(-0.813821\pi\)
−0.833769 + 0.552114i \(0.813821\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) 5.89898 0.663687 0.331844 0.943334i \(-0.392329\pi\)
0.331844 + 0.943334i \(0.392329\pi\)
\(80\) −9.79796 −1.09545
\(81\) 0 0
\(82\) 0 0
\(83\) 7.55051 0.828776 0.414388 0.910100i \(-0.363996\pi\)
0.414388 + 0.910100i \(0.363996\pi\)
\(84\) 0 0
\(85\) −3.55051 −0.385107
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.44949 −0.577645 −0.288822 0.957383i \(-0.593264\pi\)
−0.288822 + 0.957383i \(0.593264\pi\)
\(90\) 0 0
\(91\) −4.44949 −0.466433
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) 0 0
\(95\) 2.44949 0.251312
\(96\) 0 0
\(97\) 16.8990 1.71583 0.857916 0.513790i \(-0.171759\pi\)
0.857916 + 0.513790i \(0.171759\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) −10.4495 −1.03976 −0.519882 0.854238i \(-0.674024\pi\)
−0.519882 + 0.854238i \(0.674024\pi\)
\(102\) 0 0
\(103\) 1.79796 0.177158 0.0885791 0.996069i \(-0.471767\pi\)
0.0885791 + 0.996069i \(0.471767\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.2474 1.37735 0.688676 0.725069i \(-0.258192\pi\)
0.688676 + 0.725069i \(0.258192\pi\)
\(108\) 0 0
\(109\) −6.44949 −0.617749 −0.308875 0.951103i \(-0.599952\pi\)
−0.308875 + 0.951103i \(0.599952\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −17.7980 −1.68175
\(113\) 16.8990 1.58972 0.794861 0.606791i \(-0.207544\pi\)
0.794861 + 0.606791i \(0.207544\pi\)
\(114\) 0 0
\(115\) −2.44949 −0.228416
\(116\) 2.00000 0.185695
\(117\) 0 0
\(118\) 0 0
\(119\) −6.44949 −0.591224
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 20.8990 1.87678
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 10.2474 0.909314 0.454657 0.890667i \(-0.349762\pi\)
0.454657 + 0.890667i \(0.349762\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −18.6969 −1.63356 −0.816780 0.576950i \(-0.804243\pi\)
−0.816780 + 0.576950i \(0.804243\pi\)
\(132\) 0 0
\(133\) 4.44949 0.385820
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −20.1464 −1.72123 −0.860613 0.509260i \(-0.829919\pi\)
−0.860613 + 0.509260i \(0.829919\pi\)
\(138\) 0 0
\(139\) 6.00000 0.508913 0.254457 0.967084i \(-0.418103\pi\)
0.254457 + 0.967084i \(0.418103\pi\)
\(140\) −21.7980 −1.84226
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 2.44949 0.203419
\(146\) 0 0
\(147\) 0 0
\(148\) −19.7980 −1.62738
\(149\) 0.898979 0.0736473 0.0368236 0.999322i \(-0.488276\pi\)
0.0368236 + 0.999322i \(0.488276\pi\)
\(150\) 0 0
\(151\) 18.5959 1.51331 0.756657 0.653812i \(-0.226831\pi\)
0.756657 + 0.653812i \(0.226831\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 25.5959 2.05591
\(156\) 0 0
\(157\) −20.5959 −1.64373 −0.821867 0.569680i \(-0.807067\pi\)
−0.821867 + 0.569680i \(0.807067\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.44949 −0.350669
\(162\) 0 0
\(163\) 12.8990 1.01033 0.505163 0.863024i \(-0.331432\pi\)
0.505163 + 0.863024i \(0.331432\pi\)
\(164\) −18.6969 −1.45999
\(165\) 0 0
\(166\) 0 0
\(167\) −6.34847 −0.491259 −0.245630 0.969364i \(-0.578995\pi\)
−0.245630 + 0.969364i \(0.578995\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0.202041 0.0154055
\(173\) −23.2474 −1.76747 −0.883735 0.467987i \(-0.844979\pi\)
−0.883735 + 0.467987i \(0.844979\pi\)
\(174\) 0 0
\(175\) −4.44949 −0.336350
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.65153 −0.123441 −0.0617206 0.998093i \(-0.519659\pi\)
−0.0617206 + 0.998093i \(0.519659\pi\)
\(180\) 0 0
\(181\) −15.7980 −1.17425 −0.587127 0.809495i \(-0.699741\pi\)
−0.587127 + 0.809495i \(0.699741\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −24.2474 −1.78271
\(186\) 0 0
\(187\) 0 0
\(188\) −24.8990 −1.81594
\(189\) 0 0
\(190\) 0 0
\(191\) 22.1464 1.60246 0.801230 0.598357i \(-0.204180\pi\)
0.801230 + 0.598357i \(0.204180\pi\)
\(192\) 0 0
\(193\) −15.7980 −1.13716 −0.568581 0.822627i \(-0.692507\pi\)
−0.568581 + 0.822627i \(0.692507\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −25.5959 −1.82828
\(197\) −24.1464 −1.72036 −0.860181 0.509989i \(-0.829649\pi\)
−0.860181 + 0.509989i \(0.829649\pi\)
\(198\) 0 0
\(199\) −20.2474 −1.43530 −0.717652 0.696402i \(-0.754783\pi\)
−0.717652 + 0.696402i \(0.754783\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.44949 0.312293
\(204\) 0 0
\(205\) −22.8990 −1.59933
\(206\) 0 0
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −18.0454 −1.24230 −0.621149 0.783693i \(-0.713334\pi\)
−0.621149 + 0.783693i \(0.713334\pi\)
\(212\) −4.00000 −0.274721
\(213\) 0 0
\(214\) 0 0
\(215\) 0.247449 0.0168759
\(216\) 0 0
\(217\) 46.4949 3.15628
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.44949 0.0975032
\(222\) 0 0
\(223\) −21.8990 −1.46646 −0.733232 0.679978i \(-0.761989\pi\)
−0.733232 + 0.679978i \(0.761989\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.0000 −0.929213 −0.464606 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(228\) 0 0
\(229\) −7.20204 −0.475924 −0.237962 0.971274i \(-0.576479\pi\)
−0.237962 + 0.971274i \(0.576479\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.1464 0.795739 0.397869 0.917442i \(-0.369750\pi\)
0.397869 + 0.917442i \(0.369750\pi\)
\(234\) 0 0
\(235\) −30.4949 −1.98927
\(236\) −1.10102 −0.0716703
\(237\) 0 0
\(238\) 0 0
\(239\) −8.55051 −0.553087 −0.276543 0.961001i \(-0.589189\pi\)
−0.276543 + 0.961001i \(0.589189\pi\)
\(240\) 0 0
\(241\) 20.6969 1.33321 0.666604 0.745412i \(-0.267747\pi\)
0.666604 + 0.745412i \(0.267747\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 6.20204 0.397045
\(245\) −31.3485 −2.00278
\(246\) 0 0
\(247\) −1.00000 −0.0636285
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.55051 0.539703 0.269852 0.962902i \(-0.413025\pi\)
0.269852 + 0.962902i \(0.413025\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −15.4495 −0.963713 −0.481856 0.876250i \(-0.660037\pi\)
−0.481856 + 0.876250i \(0.660037\pi\)
\(258\) 0 0
\(259\) −44.0454 −2.73685
\(260\) 4.89898 0.303822
\(261\) 0 0
\(262\) 0 0
\(263\) 16.8990 1.04204 0.521018 0.853546i \(-0.325552\pi\)
0.521018 + 0.853546i \(0.325552\pi\)
\(264\) 0 0
\(265\) −4.89898 −0.300942
\(266\) 0 0
\(267\) 0 0
\(268\) 17.7980 1.08718
\(269\) 23.5959 1.43867 0.719334 0.694664i \(-0.244447\pi\)
0.719334 + 0.694664i \(0.244447\pi\)
\(270\) 0 0
\(271\) 7.10102 0.431356 0.215678 0.976465i \(-0.430804\pi\)
0.215678 + 0.976465i \(0.430804\pi\)
\(272\) 5.79796 0.351553
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7.00000 −0.420589 −0.210295 0.977638i \(-0.567442\pi\)
−0.210295 + 0.977638i \(0.567442\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −24.4949 −1.46124 −0.730622 0.682783i \(-0.760770\pi\)
−0.730622 + 0.682783i \(0.760770\pi\)
\(282\) 0 0
\(283\) 22.0454 1.31046 0.655232 0.755428i \(-0.272571\pi\)
0.655232 + 0.755428i \(0.272571\pi\)
\(284\) −24.6969 −1.46549
\(285\) 0 0
\(286\) 0 0
\(287\) −41.5959 −2.45533
\(288\) 0 0
\(289\) −14.8990 −0.876411
\(290\) 0 0
\(291\) 0 0
\(292\) 28.4949 1.66754
\(293\) 2.75255 0.160806 0.0804029 0.996762i \(-0.474379\pi\)
0.0804029 + 0.996762i \(0.474379\pi\)
\(294\) 0 0
\(295\) −1.34847 −0.0785109
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.00000 0.0578315
\(300\) 0 0
\(301\) 0.449490 0.0259082
\(302\) 0 0
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 7.59592 0.434941
\(306\) 0 0
\(307\) 27.3485 1.56086 0.780430 0.625243i \(-0.215000\pi\)
0.780430 + 0.625243i \(0.215000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.79796 −0.555591 −0.277796 0.960640i \(-0.589604\pi\)
−0.277796 + 0.960640i \(0.589604\pi\)
\(312\) 0 0
\(313\) 15.3485 0.867547 0.433773 0.901022i \(-0.357182\pi\)
0.433773 + 0.901022i \(0.357182\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −11.7980 −0.663687
\(317\) 6.24745 0.350892 0.175446 0.984489i \(-0.443863\pi\)
0.175446 + 0.984489i \(0.443863\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 19.5959 1.09545
\(321\) 0 0
\(322\) 0 0
\(323\) −1.44949 −0.0806518
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −55.3939 −3.05396
\(330\) 0 0
\(331\) 33.5959 1.84660 0.923299 0.384081i \(-0.125482\pi\)
0.923299 + 0.384081i \(0.125482\pi\)
\(332\) −15.1010 −0.828776
\(333\) 0 0
\(334\) 0 0
\(335\) 21.7980 1.19095
\(336\) 0 0
\(337\) 6.79796 0.370308 0.185154 0.982709i \(-0.440722\pi\)
0.185154 + 0.982709i \(0.440722\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 7.10102 0.385107
\(341\) 0 0
\(342\) 0 0
\(343\) −25.7980 −1.39296
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.1464 0.652054 0.326027 0.945360i \(-0.394290\pi\)
0.326027 + 0.945360i \(0.394290\pi\)
\(348\) 0 0
\(349\) 17.6969 0.947295 0.473648 0.880714i \(-0.342937\pi\)
0.473648 + 0.880714i \(0.342937\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.89898 −0.473645 −0.236822 0.971553i \(-0.576106\pi\)
−0.236822 + 0.971553i \(0.576106\pi\)
\(354\) 0 0
\(355\) −30.2474 −1.60537
\(356\) 10.8990 0.577645
\(357\) 0 0
\(358\) 0 0
\(359\) −15.0454 −0.794066 −0.397033 0.917804i \(-0.629960\pi\)
−0.397033 + 0.917804i \(0.629960\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 8.89898 0.466433
\(365\) 34.8990 1.82670
\(366\) 0 0
\(367\) −14.0000 −0.730794 −0.365397 0.930852i \(-0.619067\pi\)
−0.365397 + 0.930852i \(0.619067\pi\)
\(368\) 4.00000 0.208514
\(369\) 0 0
\(370\) 0 0
\(371\) −8.89898 −0.462012
\(372\) 0 0
\(373\) −4.65153 −0.240847 −0.120424 0.992723i \(-0.538425\pi\)
−0.120424 + 0.992723i \(0.538425\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.00000 −0.0515026
\(378\) 0 0
\(379\) −5.00000 −0.256833 −0.128416 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) −4.89898 −0.251312
\(381\) 0 0
\(382\) 0 0
\(383\) −15.7980 −0.807238 −0.403619 0.914927i \(-0.632248\pi\)
−0.403619 + 0.914927i \(0.632248\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −33.7980 −1.71583
\(389\) −30.3485 −1.53873 −0.769364 0.638810i \(-0.779427\pi\)
−0.769364 + 0.638810i \(0.779427\pi\)
\(390\) 0 0
\(391\) 1.44949 0.0733038
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −14.4495 −0.727033
\(396\) 0 0
\(397\) 6.69694 0.336110 0.168055 0.985778i \(-0.446251\pi\)
0.168055 + 0.985778i \(0.446251\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 12.6969 0.634055 0.317027 0.948416i \(-0.397315\pi\)
0.317027 + 0.948416i \(0.397315\pi\)
\(402\) 0 0
\(403\) −10.4495 −0.520526
\(404\) 20.8990 1.03976
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 23.1464 1.14452 0.572259 0.820073i \(-0.306067\pi\)
0.572259 + 0.820073i \(0.306067\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −3.59592 −0.177158
\(413\) −2.44949 −0.120532
\(414\) 0 0
\(415\) −18.4949 −0.907879
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.59592 0.371085 0.185542 0.982636i \(-0.440596\pi\)
0.185542 + 0.982636i \(0.440596\pi\)
\(420\) 0 0
\(421\) −9.69694 −0.472600 −0.236300 0.971680i \(-0.575935\pi\)
−0.236300 + 0.971680i \(0.575935\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.44949 0.0703106
\(426\) 0 0
\(427\) 13.7980 0.667730
\(428\) −28.4949 −1.37735
\(429\) 0 0
\(430\) 0 0
\(431\) 34.4949 1.66156 0.830780 0.556600i \(-0.187895\pi\)
0.830780 + 0.556600i \(0.187895\pi\)
\(432\) 0 0
\(433\) −6.00000 −0.288342 −0.144171 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 12.8990 0.617749
\(437\) −1.00000 −0.0478365
\(438\) 0 0
\(439\) 8.30306 0.396284 0.198142 0.980173i \(-0.436509\pi\)
0.198142 + 0.980173i \(0.436509\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.1464 −0.529583 −0.264791 0.964306i \(-0.585303\pi\)
−0.264791 + 0.964306i \(0.585303\pi\)
\(444\) 0 0
\(445\) 13.3485 0.632778
\(446\) 0 0
\(447\) 0 0
\(448\) 35.5959 1.68175
\(449\) −14.2020 −0.670236 −0.335118 0.942176i \(-0.608776\pi\)
−0.335118 + 0.942176i \(0.608776\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −33.7980 −1.58972
\(453\) 0 0
\(454\) 0 0
\(455\) 10.8990 0.510952
\(456\) 0 0
\(457\) 16.4495 0.769475 0.384737 0.923026i \(-0.374292\pi\)
0.384737 + 0.923026i \(0.374292\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 4.89898 0.228416
\(461\) −4.00000 −0.186299 −0.0931493 0.995652i \(-0.529693\pi\)
−0.0931493 + 0.995652i \(0.529693\pi\)
\(462\) 0 0
\(463\) 4.10102 0.190591 0.0952953 0.995449i \(-0.469620\pi\)
0.0952953 + 0.995449i \(0.469620\pi\)
\(464\) −4.00000 −0.185695
\(465\) 0 0
\(466\) 0 0
\(467\) 30.1464 1.39501 0.697505 0.716580i \(-0.254293\pi\)
0.697505 + 0.716580i \(0.254293\pi\)
\(468\) 0 0
\(469\) 39.5959 1.82837
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 12.8990 0.591224
\(477\) 0 0
\(478\) 0 0
\(479\) −16.8990 −0.772134 −0.386067 0.922471i \(-0.626167\pi\)
−0.386067 + 0.922471i \(0.626167\pi\)
\(480\) 0 0
\(481\) 9.89898 0.451355
\(482\) 0 0
\(483\) 0 0
\(484\) 22.0000 1.00000
\(485\) −41.3939 −1.87960
\(486\) 0 0
\(487\) 24.6969 1.11913 0.559563 0.828788i \(-0.310969\pi\)
0.559563 + 0.828788i \(0.310969\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15.5505 0.701785 0.350892 0.936416i \(-0.385878\pi\)
0.350892 + 0.936416i \(0.385878\pi\)
\(492\) 0 0
\(493\) −1.44949 −0.0652817
\(494\) 0 0
\(495\) 0 0
\(496\) −41.7980 −1.87678
\(497\) −54.9444 −2.46459
\(498\) 0 0
\(499\) −28.1010 −1.25797 −0.628987 0.777416i \(-0.716530\pi\)
−0.628987 + 0.777416i \(0.716530\pi\)
\(500\) −19.5959 −0.876356
\(501\) 0 0
\(502\) 0 0
\(503\) 0.752551 0.0335546 0.0167773 0.999859i \(-0.494659\pi\)
0.0167773 + 0.999859i \(0.494659\pi\)
\(504\) 0 0
\(505\) 25.5959 1.13900
\(506\) 0 0
\(507\) 0 0
\(508\) −20.4949 −0.909314
\(509\) −1.85357 −0.0821581 −0.0410791 0.999156i \(-0.513080\pi\)
−0.0410791 + 0.999156i \(0.513080\pi\)
\(510\) 0 0
\(511\) 63.3939 2.80438
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.40408 −0.194067
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.0454 1.14107 0.570535 0.821273i \(-0.306736\pi\)
0.570535 + 0.821273i \(0.306736\pi\)
\(522\) 0 0
\(523\) −1.34847 −0.0589644 −0.0294822 0.999565i \(-0.509386\pi\)
−0.0294822 + 0.999565i \(0.509386\pi\)
\(524\) 37.3939 1.63356
\(525\) 0 0
\(526\) 0 0
\(527\) −15.1464 −0.659789
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) −8.89898 −0.385820
\(533\) 9.34847 0.404927
\(534\) 0 0
\(535\) −34.8990 −1.50881
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −16.8990 −0.726544 −0.363272 0.931683i \(-0.618340\pi\)
−0.363272 + 0.931683i \(0.618340\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 15.7980 0.676710
\(546\) 0 0
\(547\) −13.6969 −0.585639 −0.292819 0.956168i \(-0.594593\pi\)
−0.292819 + 0.956168i \(0.594593\pi\)
\(548\) 40.2929 1.72123
\(549\) 0 0
\(550\) 0 0
\(551\) 1.00000 0.0426014
\(552\) 0 0
\(553\) −26.2474 −1.11616
\(554\) 0 0
\(555\) 0 0
\(556\) −12.0000 −0.508913
\(557\) 35.1464 1.48920 0.744601 0.667510i \(-0.232640\pi\)
0.744601 + 0.667510i \(0.232640\pi\)
\(558\) 0 0
\(559\) −0.101021 −0.00427271
\(560\) 43.5959 1.84226
\(561\) 0 0
\(562\) 0 0
\(563\) 9.24745 0.389733 0.194867 0.980830i \(-0.437573\pi\)
0.194867 + 0.980830i \(0.437573\pi\)
\(564\) 0 0
\(565\) −41.3939 −1.74145
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16.2020 0.679225 0.339612 0.940565i \(-0.389704\pi\)
0.339612 + 0.940565i \(0.389704\pi\)
\(570\) 0 0
\(571\) 34.0454 1.42476 0.712378 0.701796i \(-0.247618\pi\)
0.712378 + 0.701796i \(0.247618\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 28.2474 1.17596 0.587978 0.808877i \(-0.299924\pi\)
0.587978 + 0.808877i \(0.299924\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) −4.89898 −0.203419
\(581\) −33.5959 −1.39379
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.0454 0.868637 0.434318 0.900759i \(-0.356989\pi\)
0.434318 + 0.900759i \(0.356989\pi\)
\(588\) 0 0
\(589\) 10.4495 0.430564
\(590\) 0 0
\(591\) 0 0
\(592\) 39.5959 1.62738
\(593\) −39.2474 −1.61170 −0.805850 0.592120i \(-0.798291\pi\)
−0.805850 + 0.592120i \(0.798291\pi\)
\(594\) 0 0
\(595\) 15.7980 0.647653
\(596\) −1.79796 −0.0736473
\(597\) 0 0
\(598\) 0 0
\(599\) −13.3485 −0.545404 −0.272702 0.962099i \(-0.587917\pi\)
−0.272702 + 0.962099i \(0.587917\pi\)
\(600\) 0 0
\(601\) 1.30306 0.0531530 0.0265765 0.999647i \(-0.491539\pi\)
0.0265765 + 0.999647i \(0.491539\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −37.1918 −1.51331
\(605\) 26.9444 1.09545
\(606\) 0 0
\(607\) 5.34847 0.217088 0.108544 0.994092i \(-0.465381\pi\)
0.108544 + 0.994092i \(0.465381\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.4495 0.503652
\(612\) 0 0
\(613\) 10.0000 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.20204 −0.330202 −0.165101 0.986277i \(-0.552795\pi\)
−0.165101 + 0.986277i \(0.552795\pi\)
\(618\) 0 0
\(619\) 10.7980 0.434007 0.217003 0.976171i \(-0.430372\pi\)
0.217003 + 0.976171i \(0.430372\pi\)
\(620\) −51.1918 −2.05591
\(621\) 0 0
\(622\) 0 0
\(623\) 24.2474 0.971454
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) 0 0
\(628\) 41.1918 1.64373
\(629\) 14.3485 0.572111
\(630\) 0 0
\(631\) −32.6969 −1.30164 −0.650822 0.759230i \(-0.725576\pi\)
−0.650822 + 0.759230i \(0.725576\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −25.1010 −0.996104
\(636\) 0 0
\(637\) 12.7980 0.507074
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 33.0454 1.30522 0.652608 0.757696i \(-0.273675\pi\)
0.652608 + 0.757696i \(0.273675\pi\)
\(642\) 0 0
\(643\) −3.10102 −0.122292 −0.0611462 0.998129i \(-0.519476\pi\)
−0.0611462 + 0.998129i \(0.519476\pi\)
\(644\) 8.89898 0.350669
\(645\) 0 0
\(646\) 0 0
\(647\) 1.24745 0.0490423 0.0245211 0.999699i \(-0.492194\pi\)
0.0245211 + 0.999699i \(0.492194\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −25.7980 −1.01033
\(653\) −42.7423 −1.67264 −0.836319 0.548244i \(-0.815297\pi\)
−0.836319 + 0.548244i \(0.815297\pi\)
\(654\) 0 0
\(655\) 45.7980 1.78947
\(656\) 37.3939 1.45999
\(657\) 0 0
\(658\) 0 0
\(659\) 9.44949 0.368100 0.184050 0.982917i \(-0.441079\pi\)
0.184050 + 0.982917i \(0.441079\pi\)
\(660\) 0 0
\(661\) −7.34847 −0.285822 −0.142911 0.989736i \(-0.545646\pi\)
−0.142911 + 0.989736i \(0.545646\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.8990 −0.422644
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 12.6969 0.491259
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.89898 0.0732003 0.0366001 0.999330i \(-0.488347\pi\)
0.0366001 + 0.999330i \(0.488347\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 24.0000 0.923077
\(677\) −23.7980 −0.914630 −0.457315 0.889305i \(-0.651189\pi\)
−0.457315 + 0.889305i \(0.651189\pi\)
\(678\) 0 0
\(679\) −75.1918 −2.88560
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −26.6969 −1.02153 −0.510765 0.859720i \(-0.670638\pi\)
−0.510765 + 0.859720i \(0.670638\pi\)
\(684\) 0 0
\(685\) 49.3485 1.88551
\(686\) 0 0
\(687\) 0 0
\(688\) −0.404082 −0.0154055
\(689\) 2.00000 0.0761939
\(690\) 0 0
\(691\) 29.1010 1.10705 0.553527 0.832831i \(-0.313281\pi\)
0.553527 + 0.832831i \(0.313281\pi\)
\(692\) 46.4949 1.76747
\(693\) 0 0
\(694\) 0 0
\(695\) −14.6969 −0.557487
\(696\) 0 0
\(697\) 13.5505 0.513262
\(698\) 0 0
\(699\) 0 0
\(700\) 8.89898 0.336350
\(701\) 17.7526 0.670505 0.335252 0.942128i \(-0.391178\pi\)
0.335252 + 0.942128i \(0.391178\pi\)
\(702\) 0 0
\(703\) −9.89898 −0.373347
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 46.4949 1.74862
\(708\) 0 0
\(709\) 15.3485 0.576424 0.288212 0.957567i \(-0.406939\pi\)
0.288212 + 0.957567i \(0.406939\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.4495 −0.391336
\(714\) 0 0
\(715\) 0 0
\(716\) 3.30306 0.123441
\(717\) 0 0
\(718\) 0 0
\(719\) −21.7423 −0.810853 −0.405426 0.914128i \(-0.632877\pi\)
−0.405426 + 0.914128i \(0.632877\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 0 0
\(723\) 0 0
\(724\) 31.5959 1.17425
\(725\) −1.00000 −0.0371391
\(726\) 0 0
\(727\) −35.5959 −1.32018 −0.660090 0.751187i \(-0.729482\pi\)
−0.660090 + 0.751187i \(0.729482\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.146428 −0.00541584
\(732\) 0 0
\(733\) −40.8990 −1.51064 −0.755319 0.655357i \(-0.772518\pi\)
−0.755319 + 0.655357i \(0.772518\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 35.7980 1.31685 0.658425 0.752647i \(-0.271223\pi\)
0.658425 + 0.752647i \(0.271223\pi\)
\(740\) 48.4949 1.78271
\(741\) 0 0
\(742\) 0 0
\(743\) −16.7526 −0.614591 −0.307296 0.951614i \(-0.599424\pi\)
−0.307296 + 0.951614i \(0.599424\pi\)
\(744\) 0 0
\(745\) −2.20204 −0.0806765
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −63.3939 −2.31636
\(750\) 0 0
\(751\) −11.4949 −0.419455 −0.209727 0.977760i \(-0.567258\pi\)
−0.209727 + 0.977760i \(0.567258\pi\)
\(752\) 49.7980 1.81594
\(753\) 0 0
\(754\) 0 0
\(755\) −45.5505 −1.65775
\(756\) 0 0
\(757\) 12.1010 0.439819 0.219910 0.975520i \(-0.429424\pi\)
0.219910 + 0.975520i \(0.429424\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3.24745 0.117720 0.0588600 0.998266i \(-0.481253\pi\)
0.0588600 + 0.998266i \(0.481253\pi\)
\(762\) 0 0
\(763\) 28.6969 1.03890
\(764\) −44.2929 −1.60246
\(765\) 0 0
\(766\) 0 0
\(767\) 0.550510 0.0198778
\(768\) 0 0
\(769\) −42.1010 −1.51820 −0.759101 0.650973i \(-0.774361\pi\)
−0.759101 + 0.650973i \(0.774361\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 31.5959 1.13716
\(773\) 36.6969 1.31990 0.659949 0.751311i \(-0.270578\pi\)
0.659949 + 0.751311i \(0.270578\pi\)
\(774\) 0 0
\(775\) −10.4495 −0.375357
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.34847 −0.334944
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 51.1918 1.82828
\(785\) 50.4495 1.80062
\(786\) 0 0
\(787\) −40.2929 −1.43629 −0.718143 0.695896i \(-0.755007\pi\)
−0.718143 + 0.695896i \(0.755007\pi\)
\(788\) 48.2929 1.72036
\(789\) 0 0
\(790\) 0 0
\(791\) −75.1918 −2.67351
\(792\) 0 0
\(793\) −3.10102 −0.110120
\(794\) 0 0
\(795\) 0 0
\(796\) 40.4949 1.43530
\(797\) −32.6969 −1.15818 −0.579092 0.815262i \(-0.696593\pi\)
−0.579092 + 0.815262i \(0.696593\pi\)
\(798\) 0 0
\(799\) 18.0454 0.638401
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 10.8990 0.384139
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −21.1010 −0.741872 −0.370936 0.928658i \(-0.620963\pi\)
−0.370936 + 0.928658i \(0.620963\pi\)
\(810\) 0 0
\(811\) 19.3031 0.677822 0.338911 0.940818i \(-0.389941\pi\)
0.338911 + 0.940818i \(0.389941\pi\)
\(812\) −8.89898 −0.312293
\(813\) 0 0
\(814\) 0 0
\(815\) −31.5959 −1.10676
\(816\) 0 0
\(817\) 0.101021 0.00353426
\(818\) 0 0
\(819\) 0 0
\(820\) 45.7980 1.59933
\(821\) 24.3485 0.849767 0.424884 0.905248i \(-0.360315\pi\)
0.424884 + 0.905248i \(0.360315\pi\)
\(822\) 0 0
\(823\) −16.8536 −0.587479 −0.293739 0.955886i \(-0.594900\pi\)
−0.293739 + 0.955886i \(0.594900\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.3485 0.777132 0.388566 0.921421i \(-0.372970\pi\)
0.388566 + 0.921421i \(0.372970\pi\)
\(828\) 0 0
\(829\) −50.2929 −1.74674 −0.873372 0.487055i \(-0.838071\pi\)
−0.873372 + 0.487055i \(0.838071\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −8.00000 −0.277350
\(833\) 18.5505 0.642737
\(834\) 0 0
\(835\) 15.5505 0.538148
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −51.3939 −1.77431 −0.887157 0.461468i \(-0.847323\pi\)
−0.887157 + 0.461468i \(0.847323\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 0 0
\(844\) 36.0908 1.24230
\(845\) 29.3939 1.01118
\(846\) 0 0
\(847\) 48.9444 1.68175
\(848\) 8.00000 0.274721
\(849\) 0 0
\(850\) 0 0
\(851\) 9.89898 0.339333
\(852\) 0 0
\(853\) −23.3939 −0.800991 −0.400496 0.916299i \(-0.631162\pi\)
−0.400496 + 0.916299i \(0.631162\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −40.2929 −1.37638 −0.688189 0.725532i \(-0.741594\pi\)
−0.688189 + 0.725532i \(0.741594\pi\)
\(858\) 0 0
\(859\) −12.6515 −0.431665 −0.215832 0.976430i \(-0.569246\pi\)
−0.215832 + 0.976430i \(0.569246\pi\)
\(860\) −0.494897 −0.0168759
\(861\) 0 0
\(862\) 0 0
\(863\) −30.2929 −1.03118 −0.515590 0.856835i \(-0.672427\pi\)
−0.515590 + 0.856835i \(0.672427\pi\)
\(864\) 0 0
\(865\) 56.9444 1.93617
\(866\) 0 0
\(867\) 0 0
\(868\) −92.9898 −3.15628
\(869\) 0 0
\(870\) 0 0
\(871\) −8.89898 −0.301530
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −43.5959 −1.47381
\(876\) 0 0
\(877\) −46.5959 −1.57343 −0.786716 0.617315i \(-0.788220\pi\)
−0.786716 + 0.617315i \(0.788220\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.348469 −0.0117402 −0.00587011 0.999983i \(-0.501869\pi\)
−0.00587011 + 0.999983i \(0.501869\pi\)
\(882\) 0 0
\(883\) −35.0908 −1.18090 −0.590450 0.807074i \(-0.701050\pi\)
−0.590450 + 0.807074i \(0.701050\pi\)
\(884\) −2.89898 −0.0975032
\(885\) 0 0
\(886\) 0 0
\(887\) −42.5403 −1.42836 −0.714182 0.699960i \(-0.753201\pi\)
−0.714182 + 0.699960i \(0.753201\pi\)
\(888\) 0 0
\(889\) −45.5959 −1.52924
\(890\) 0 0
\(891\) 0 0
\(892\) 43.7980 1.46646
\(893\) −12.4495 −0.416606
\(894\) 0 0
\(895\) 4.04541 0.135223
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 10.4495 0.348510
\(900\) 0 0
\(901\) 2.89898 0.0965790
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 38.6969 1.28633
\(906\) 0 0
\(907\) −26.5959 −0.883103 −0.441551 0.897236i \(-0.645572\pi\)
−0.441551 + 0.897236i \(0.645572\pi\)
\(908\) 28.0000 0.929213
\(909\) 0 0
\(910\) 0 0
\(911\) 47.4495 1.57207 0.786036 0.618181i \(-0.212130\pi\)
0.786036 + 0.618181i \(0.212130\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 14.4041 0.475924
\(917\) 83.1918 2.74724
\(918\) 0 0
\(919\) −28.6969 −0.946625 −0.473312 0.880895i \(-0.656942\pi\)
−0.473312 + 0.880895i \(0.656942\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 12.3485 0.406455
\(924\) 0 0
\(925\) 9.89898 0.325476
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.84337 0.158906 0.0794529 0.996839i \(-0.474683\pi\)
0.0794529 + 0.996839i \(0.474683\pi\)
\(930\) 0 0
\(931\) −12.7980 −0.419436
\(932\) −24.2929 −0.795739
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 29.1918 0.953656 0.476828 0.878997i \(-0.341787\pi\)
0.476828 + 0.878997i \(0.341787\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 60.9898 1.98927
\(941\) 32.4949 1.05930 0.529652 0.848215i \(-0.322323\pi\)
0.529652 + 0.848215i \(0.322323\pi\)
\(942\) 0 0
\(943\) 9.34847 0.304428
\(944\) 2.20204 0.0716703
\(945\) 0 0
\(946\) 0 0
\(947\) 6.69694 0.217621 0.108811 0.994062i \(-0.465296\pi\)
0.108811 + 0.994062i \(0.465296\pi\)
\(948\) 0 0
\(949\) −14.2474 −0.462492
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 26.6515 0.863328 0.431664 0.902035i \(-0.357927\pi\)
0.431664 + 0.902035i \(0.357927\pi\)
\(954\) 0 0
\(955\) −54.2474 −1.75541
\(956\) 17.1010 0.553087
\(957\) 0 0
\(958\) 0 0
\(959\) 89.6413 2.89467
\(960\) 0 0
\(961\) 78.1918 2.52232
\(962\) 0 0
\(963\) 0 0
\(964\) −41.3939 −1.33321
\(965\) 38.6969 1.24570
\(966\) 0 0
\(967\) −21.5505 −0.693018 −0.346509 0.938047i \(-0.612633\pi\)
−0.346509 + 0.938047i \(0.612633\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −22.2929 −0.715412 −0.357706 0.933834i \(-0.616441\pi\)
−0.357706 + 0.933834i \(0.616441\pi\)
\(972\) 0 0
\(973\) −26.6969 −0.855865
\(974\) 0 0
\(975\) 0 0
\(976\) −12.4041 −0.397045
\(977\) −26.4495 −0.846194 −0.423097 0.906084i \(-0.639057\pi\)
−0.423097 + 0.906084i \(0.639057\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 62.6969 2.00278
\(981\) 0 0
\(982\) 0 0
\(983\) −11.7423 −0.374523 −0.187261 0.982310i \(-0.559961\pi\)
−0.187261 + 0.982310i \(0.559961\pi\)
\(984\) 0 0
\(985\) 59.1464 1.88456
\(986\) 0 0
\(987\) 0 0
\(988\) 2.00000 0.0636285
\(989\) −0.101021 −0.00321227
\(990\) 0 0
\(991\) −51.5959 −1.63900 −0.819499 0.573080i \(-0.805748\pi\)
−0.819499 + 0.573080i \(0.805748\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 49.5959 1.57230
\(996\) 0 0
\(997\) −60.9898 −1.93157 −0.965783 0.259351i \(-0.916491\pi\)
−0.965783 + 0.259351i \(0.916491\pi\)
\(998\) 0 0
\(999\) 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 6003.2.a.e.1.1 2
3.2 odd 2 2001.2.a.e.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.e.1.2 2 3.2 odd 2
6003.2.a.e.1.1 2 1.1 even 1 trivial