Properties

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

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.3732.1
Defining polynomial: \(x^{3} - x^{2} - 13 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.77576\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.48059 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.48059 q^{7} +1.00000 q^{9} +5.77576 q^{11} -1.00000 q^{13} +3.00000 q^{17} +2.29517 q^{19} +1.48059 q^{21} -4.29517 q^{23} +1.00000 q^{27} +6.55152 q^{29} +5.77576 q^{31} +5.77576 q^{33} +3.25635 q^{37} -1.00000 q^{39} +5.25635 q^{41} +5.25635 q^{43} -5.03210 q^{47} -4.80786 q^{49} +3.00000 q^{51} -3.29517 q^{53} +2.29517 q^{57} -5.03210 q^{59} -4.55152 q^{61} +1.48059 q^{63} +4.22424 q^{67} -4.29517 q^{69} -12.8079 q^{71} -12.8079 q^{73} +8.55152 q^{77} -1.25635 q^{79} +1.00000 q^{81} -12.0709 q^{83} +6.55152 q^{87} +13.5515 q^{89} -1.48059 q^{91} +5.77576 q^{93} +6.96118 q^{97} +5.77576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} + q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{3} + q^{7} + 3 q^{9} + 5 q^{11} - 3 q^{13} + 9 q^{17} - 2 q^{19} + q^{21} - 4 q^{23} + 3 q^{27} - 5 q^{29} + 5 q^{31} + 5 q^{33} - 6 q^{37} - 3 q^{39} + 13 q^{47} + 26 q^{49} + 9 q^{51} - q^{53} - 2 q^{57} + 13 q^{59} + 11 q^{61} + q^{63} + 25 q^{67} - 4 q^{69} + 2 q^{71} + 2 q^{73} + q^{77} + 12 q^{79} + 3 q^{81} - 15 q^{83} - 5 q^{87} + 16 q^{89} - q^{91} + 5 q^{93} + 14 q^{97} + 5 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.48059 0.559610 0.279805 0.960057i \(-0.409730\pi\)
0.279805 + 0.960057i \(0.409730\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.77576 1.74146 0.870728 0.491765i \(-0.163648\pi\)
0.870728 + 0.491765i \(0.163648\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 2.29517 0.526548 0.263274 0.964721i \(-0.415198\pi\)
0.263274 + 0.964721i \(0.415198\pi\)
\(20\) 0 0
\(21\) 1.48059 0.323091
\(22\) 0 0
\(23\) −4.29517 −0.895605 −0.447802 0.894133i \(-0.647793\pi\)
−0.447802 + 0.894133i \(0.647793\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.55152 1.21659 0.608293 0.793713i \(-0.291855\pi\)
0.608293 + 0.793713i \(0.291855\pi\)
\(30\) 0 0
\(31\) 5.77576 1.03736 0.518678 0.854969i \(-0.326424\pi\)
0.518678 + 0.854969i \(0.326424\pi\)
\(32\) 0 0
\(33\) 5.77576 1.00543
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.25635 0.535340 0.267670 0.963511i \(-0.413746\pi\)
0.267670 + 0.963511i \(0.413746\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 5.25635 0.820903 0.410452 0.911882i \(-0.365371\pi\)
0.410452 + 0.911882i \(0.365371\pi\)
\(42\) 0 0
\(43\) 5.25635 0.801585 0.400793 0.916169i \(-0.368735\pi\)
0.400793 + 0.916169i \(0.368735\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.03210 −0.734008 −0.367004 0.930219i \(-0.619616\pi\)
−0.367004 + 0.930219i \(0.619616\pi\)
\(48\) 0 0
\(49\) −4.80786 −0.686837
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) −3.29517 −0.452626 −0.226313 0.974055i \(-0.572667\pi\)
−0.226313 + 0.974055i \(0.572667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.29517 0.304003
\(58\) 0 0
\(59\) −5.03210 −0.655124 −0.327562 0.944830i \(-0.606227\pi\)
−0.327562 + 0.944830i \(0.606227\pi\)
\(60\) 0 0
\(61\) −4.55152 −0.582762 −0.291381 0.956607i \(-0.594115\pi\)
−0.291381 + 0.956607i \(0.594115\pi\)
\(62\) 0 0
\(63\) 1.48059 0.186537
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.22424 0.516073 0.258037 0.966135i \(-0.416924\pi\)
0.258037 + 0.966135i \(0.416924\pi\)
\(68\) 0 0
\(69\) −4.29517 −0.517078
\(70\) 0 0
\(71\) −12.8079 −1.52001 −0.760007 0.649915i \(-0.774804\pi\)
−0.760007 + 0.649915i \(0.774804\pi\)
\(72\) 0 0
\(73\) −12.8079 −1.49905 −0.749523 0.661978i \(-0.769717\pi\)
−0.749523 + 0.661978i \(0.769717\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.55152 0.974536
\(78\) 0 0
\(79\) −1.25635 −0.141350 −0.0706749 0.997499i \(-0.522515\pi\)
−0.0706749 + 0.997499i \(0.522515\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.0709 −1.32496 −0.662478 0.749081i \(-0.730495\pi\)
−0.662478 + 0.749081i \(0.730495\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.55152 0.702396
\(88\) 0 0
\(89\) 13.5515 1.43646 0.718229 0.695807i \(-0.244953\pi\)
0.718229 + 0.695807i \(0.244953\pi\)
\(90\) 0 0
\(91\) −1.48059 −0.155208
\(92\) 0 0
\(93\) 5.77576 0.598918
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.96118 0.706800 0.353400 0.935472i \(-0.385025\pi\)
0.353400 + 0.935472i \(0.385025\pi\)
\(98\) 0 0
\(99\) 5.77576 0.580485
\(100\) 0 0
\(101\) −2.33399 −0.232241 −0.116121 0.993235i \(-0.537046\pi\)
−0.116121 + 0.993235i \(0.537046\pi\)
\(102\) 0 0
\(103\) 3.25635 0.320857 0.160429 0.987047i \(-0.448712\pi\)
0.160429 + 0.987047i \(0.448712\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20.1419 1.94719 0.973593 0.228289i \(-0.0733132\pi\)
0.973593 + 0.228289i \(0.0733132\pi\)
\(108\) 0 0
\(109\) 18.8079 1.80147 0.900733 0.434373i \(-0.143030\pi\)
0.900733 + 0.434373i \(0.143030\pi\)
\(110\) 0 0
\(111\) 3.25635 0.309079
\(112\) 0 0
\(113\) 7.55152 0.710387 0.355193 0.934793i \(-0.384415\pi\)
0.355193 + 0.934793i \(0.384415\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) 4.44176 0.407176
\(120\) 0 0
\(121\) 22.3594 2.03267
\(122\) 0 0
\(123\) 5.25635 0.473949
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2.80786 −0.249157 −0.124579 0.992210i \(-0.539758\pi\)
−0.124579 + 0.992210i \(0.539758\pi\)
\(128\) 0 0
\(129\) 5.25635 0.462795
\(130\) 0 0
\(131\) 2.29517 0.200530 0.100265 0.994961i \(-0.468031\pi\)
0.100265 + 0.994961i \(0.468031\pi\)
\(132\) 0 0
\(133\) 3.39820 0.294661
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.1419 −1.20822 −0.604110 0.796901i \(-0.706471\pi\)
−0.604110 + 0.796901i \(0.706471\pi\)
\(138\) 0 0
\(139\) −7.92235 −0.671965 −0.335982 0.941868i \(-0.609068\pi\)
−0.335982 + 0.941868i \(0.609068\pi\)
\(140\) 0 0
\(141\) −5.03210 −0.423779
\(142\) 0 0
\(143\) −5.77576 −0.482993
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.80786 −0.396546
\(148\) 0 0
\(149\) −18.0642 −1.47988 −0.739939 0.672674i \(-0.765146\pi\)
−0.739939 + 0.672674i \(0.765146\pi\)
\(150\) 0 0
\(151\) −23.0321 −1.87433 −0.937163 0.348892i \(-0.886558\pi\)
−0.937163 + 0.348892i \(0.886558\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3.29517 −0.262983 −0.131492 0.991317i \(-0.541977\pi\)
−0.131492 + 0.991317i \(0.541977\pi\)
\(158\) 0 0
\(159\) −3.29517 −0.261324
\(160\) 0 0
\(161\) −6.35938 −0.501189
\(162\) 0 0
\(163\) −8.21752 −0.643646 −0.321823 0.946800i \(-0.604296\pi\)
−0.321823 + 0.946800i \(0.604296\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.743655 0.0575457 0.0287729 0.999586i \(-0.490840\pi\)
0.0287729 + 0.999586i \(0.490840\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 2.29517 0.175516
\(172\) 0 0
\(173\) 4.25635 0.323604 0.161802 0.986823i \(-0.448269\pi\)
0.161802 + 0.986823i \(0.448269\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.03210 −0.378236
\(178\) 0 0
\(179\) 9.76904 0.730172 0.365086 0.930974i \(-0.381040\pi\)
0.365086 + 0.930974i \(0.381040\pi\)
\(180\) 0 0
\(181\) 18.8467 1.40086 0.700432 0.713720i \(-0.252991\pi\)
0.700432 + 0.713720i \(0.252991\pi\)
\(182\) 0 0
\(183\) −4.55152 −0.336458
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 17.3273 1.26710
\(188\) 0 0
\(189\) 1.48059 0.107697
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) −18.2175 −1.31133 −0.655663 0.755054i \(-0.727611\pi\)
−0.655663 + 0.755054i \(0.727611\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.84669 −0.701547 −0.350774 0.936460i \(-0.614081\pi\)
−0.350774 + 0.936460i \(0.614081\pi\)
\(198\) 0 0
\(199\) −6.59034 −0.467177 −0.233588 0.972336i \(-0.575047\pi\)
−0.233588 + 0.972336i \(0.575047\pi\)
\(200\) 0 0
\(201\) 4.22424 0.297955
\(202\) 0 0
\(203\) 9.70009 0.680813
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.29517 −0.298535
\(208\) 0 0
\(209\) 13.2563 0.916961
\(210\) 0 0
\(211\) −2.80786 −0.193301 −0.0966505 0.995318i \(-0.530813\pi\)
−0.0966505 + 0.995318i \(0.530813\pi\)
\(212\) 0 0
\(213\) −12.8079 −0.877580
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 8.55152 0.580515
\(218\) 0 0
\(219\) −12.8079 −0.865475
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 10.8855 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.7369 1.24361 0.621807 0.783171i \(-0.286399\pi\)
0.621807 + 0.783171i \(0.286399\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 8.55152 0.562648
\(232\) 0 0
\(233\) 0.448485 0.0293812 0.0146906 0.999892i \(-0.495324\pi\)
0.0146906 + 0.999892i \(0.495324\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.25635 −0.0816084
\(238\) 0 0
\(239\) 24.9545 1.61417 0.807085 0.590436i \(-0.201044\pi\)
0.807085 + 0.590436i \(0.201044\pi\)
\(240\) 0 0
\(241\) 5.78248 0.372482 0.186241 0.982504i \(-0.440369\pi\)
0.186241 + 0.982504i \(0.440369\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.29517 −0.146038
\(248\) 0 0
\(249\) −12.0709 −0.764964
\(250\) 0 0
\(251\) 9.33399 0.589157 0.294578 0.955627i \(-0.404821\pi\)
0.294578 + 0.955627i \(0.404821\pi\)
\(252\) 0 0
\(253\) −24.8079 −1.55966
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.192140 −0.0119853 −0.00599267 0.999982i \(-0.501908\pi\)
−0.00599267 + 0.999982i \(0.501908\pi\)
\(258\) 0 0
\(259\) 4.82130 0.299581
\(260\) 0 0
\(261\) 6.55152 0.405529
\(262\) 0 0
\(263\) −7.25635 −0.447445 −0.223723 0.974653i \(-0.571821\pi\)
−0.223723 + 0.974653i \(0.571821\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 13.5515 0.829339
\(268\) 0 0
\(269\) −12.9224 −0.787890 −0.393945 0.919134i \(-0.628890\pi\)
−0.393945 + 0.919134i \(0.628890\pi\)
\(270\) 0 0
\(271\) −23.6224 −1.43496 −0.717481 0.696578i \(-0.754705\pi\)
−0.717481 + 0.696578i \(0.754705\pi\)
\(272\) 0 0
\(273\) −1.48059 −0.0896092
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −6.96118 −0.418256 −0.209128 0.977888i \(-0.567063\pi\)
−0.209128 + 0.977888i \(0.567063\pi\)
\(278\) 0 0
\(279\) 5.77576 0.345786
\(280\) 0 0
\(281\) 13.4097 0.799953 0.399977 0.916525i \(-0.369018\pi\)
0.399977 + 0.916525i \(0.369018\pi\)
\(282\) 0 0
\(283\) −9.40966 −0.559346 −0.279673 0.960095i \(-0.590226\pi\)
−0.279673 + 0.960095i \(0.590226\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.78248 0.459385
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 6.96118 0.408071
\(292\) 0 0
\(293\) −17.1030 −0.999170 −0.499585 0.866265i \(-0.666514\pi\)
−0.499585 + 0.866265i \(0.666514\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 5.77576 0.335143
\(298\) 0 0
\(299\) 4.29517 0.248396
\(300\) 0 0
\(301\) 7.78248 0.448575
\(302\) 0 0
\(303\) −2.33399 −0.134084
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 18.3594 1.04782 0.523912 0.851772i \(-0.324472\pi\)
0.523912 + 0.851772i \(0.324472\pi\)
\(308\) 0 0
\(309\) 3.25635 0.185247
\(310\) 0 0
\(311\) 27.6157 1.56594 0.782972 0.622057i \(-0.213703\pi\)
0.782972 + 0.622057i \(0.213703\pi\)
\(312\) 0 0
\(313\) −21.2952 −1.20367 −0.601837 0.798619i \(-0.705564\pi\)
−0.601837 + 0.798619i \(0.705564\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.372819 0.0209396 0.0104698 0.999945i \(-0.496667\pi\)
0.0104698 + 0.999945i \(0.496667\pi\)
\(318\) 0 0
\(319\) 37.8400 2.11863
\(320\) 0 0
\(321\) 20.1419 1.12421
\(322\) 0 0
\(323\) 6.88551 0.383120
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 18.8079 1.04008
\(328\) 0 0
\(329\) −7.45047 −0.410758
\(330\) 0 0
\(331\) 9.39820 0.516572 0.258286 0.966069i \(-0.416842\pi\)
0.258286 + 0.966069i \(0.416842\pi\)
\(332\) 0 0
\(333\) 3.25635 0.178447
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5.58836 −0.304417 −0.152209 0.988348i \(-0.548639\pi\)
−0.152209 + 0.988348i \(0.548639\pi\)
\(338\) 0 0
\(339\) 7.55152 0.410142
\(340\) 0 0
\(341\) 33.3594 1.80651
\(342\) 0 0
\(343\) −17.4826 −0.943970
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.89697 0.370249 0.185124 0.982715i \(-0.440731\pi\)
0.185124 + 0.982715i \(0.440731\pi\)
\(348\) 0 0
\(349\) 13.3340 0.713752 0.356876 0.934152i \(-0.383842\pi\)
0.356876 + 0.934152i \(0.383842\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 36.3594 1.93521 0.967607 0.252461i \(-0.0812398\pi\)
0.967607 + 0.252461i \(0.0812398\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 4.44176 0.235083
\(358\) 0 0
\(359\) −3.03210 −0.160028 −0.0800141 0.996794i \(-0.525497\pi\)
−0.0800141 + 0.996794i \(0.525497\pi\)
\(360\) 0 0
\(361\) −13.7322 −0.722747
\(362\) 0 0
\(363\) 22.3594 1.17356
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 21.1807 1.10562 0.552811 0.833307i \(-0.313555\pi\)
0.552811 + 0.833307i \(0.313555\pi\)
\(368\) 0 0
\(369\) 5.25635 0.273634
\(370\) 0 0
\(371\) −4.87879 −0.253294
\(372\) 0 0
\(373\) −22.1787 −1.14837 −0.574185 0.818726i \(-0.694681\pi\)
−0.574185 + 0.818726i \(0.694681\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.55152 −0.337420
\(378\) 0 0
\(379\) −17.8400 −0.916377 −0.458189 0.888855i \(-0.651502\pi\)
−0.458189 + 0.888855i \(0.651502\pi\)
\(380\) 0 0
\(381\) −2.80786 −0.143851
\(382\) 0 0
\(383\) −20.2175 −1.03307 −0.516534 0.856267i \(-0.672778\pi\)
−0.516534 + 0.856267i \(0.672778\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.25635 0.267195
\(388\) 0 0
\(389\) −18.6545 −0.945823 −0.472911 0.881110i \(-0.656797\pi\)
−0.472911 + 0.881110i \(0.656797\pi\)
\(390\) 0 0
\(391\) −12.8855 −0.651648
\(392\) 0 0
\(393\) 2.29517 0.115776
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −21.6292 −1.08554 −0.542768 0.839882i \(-0.682624\pi\)
−0.542768 + 0.839882i \(0.682624\pi\)
\(398\) 0 0
\(399\) 3.39820 0.170123
\(400\) 0 0
\(401\) 33.0274 1.64931 0.824654 0.565638i \(-0.191370\pi\)
0.824654 + 0.565638i \(0.191370\pi\)
\(402\) 0 0
\(403\) −5.77576 −0.287711
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 18.8079 0.932271
\(408\) 0 0
\(409\) 31.0274 1.53420 0.767102 0.641525i \(-0.221698\pi\)
0.767102 + 0.641525i \(0.221698\pi\)
\(410\) 0 0
\(411\) −14.1419 −0.697566
\(412\) 0 0
\(413\) −7.45047 −0.366614
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.92235 −0.387959
\(418\) 0 0
\(419\) 16.7437 0.817981 0.408991 0.912539i \(-0.365881\pi\)
0.408991 + 0.912539i \(0.365881\pi\)
\(420\) 0 0
\(421\) 23.6934 1.15474 0.577372 0.816481i \(-0.304078\pi\)
0.577372 + 0.816481i \(0.304078\pi\)
\(422\) 0 0
\(423\) −5.03210 −0.244669
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6.73892 −0.326119
\(428\) 0 0
\(429\) −5.77576 −0.278856
\(430\) 0 0
\(431\) 30.8855 1.48770 0.743851 0.668345i \(-0.232997\pi\)
0.743851 + 0.668345i \(0.232997\pi\)
\(432\) 0 0
\(433\) −20.1419 −0.967956 −0.483978 0.875080i \(-0.660808\pi\)
−0.483978 + 0.875080i \(0.660808\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.85814 −0.471579
\(438\) 0 0
\(439\) 35.2429 1.68205 0.841026 0.540995i \(-0.181952\pi\)
0.841026 + 0.540995i \(0.181952\pi\)
\(440\) 0 0
\(441\) −4.80786 −0.228946
\(442\) 0 0
\(443\) −13.8467 −0.657876 −0.328938 0.944352i \(-0.606691\pi\)
−0.328938 + 0.944352i \(0.606691\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −18.0642 −0.854408
\(448\) 0 0
\(449\) −24.4350 −1.15316 −0.576580 0.817040i \(-0.695613\pi\)
−0.576580 + 0.817040i \(0.695613\pi\)
\(450\) 0 0
\(451\) 30.3594 1.42957
\(452\) 0 0
\(453\) −23.0321 −1.08214
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.4370 0.675336 0.337668 0.941265i \(-0.390362\pi\)
0.337668 + 0.941265i \(0.390362\pi\)
\(458\) 0 0
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) 39.6157 1.84509 0.922544 0.385892i \(-0.126106\pi\)
0.922544 + 0.385892i \(0.126106\pi\)
\(462\) 0 0
\(463\) −33.9176 −1.57629 −0.788143 0.615493i \(-0.788957\pi\)
−0.788143 + 0.615493i \(0.788957\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 27.4739 1.27134 0.635669 0.771961i \(-0.280724\pi\)
0.635669 + 0.771961i \(0.280724\pi\)
\(468\) 0 0
\(469\) 6.25436 0.288800
\(470\) 0 0
\(471\) −3.29517 −0.151833
\(472\) 0 0
\(473\) 30.3594 1.39593
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.29517 −0.150875
\(478\) 0 0
\(479\) 1.26307 0.0577110 0.0288555 0.999584i \(-0.490814\pi\)
0.0288555 + 0.999584i \(0.490814\pi\)
\(480\) 0 0
\(481\) −3.25635 −0.148477
\(482\) 0 0
\(483\) −6.35938 −0.289362
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −22.4303 −1.01641 −0.508207 0.861235i \(-0.669692\pi\)
−0.508207 + 0.861235i \(0.669692\pi\)
\(488\) 0 0
\(489\) −8.21752 −0.371609
\(490\) 0 0
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 0 0
\(493\) 19.6545 0.885196
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.9632 −0.850614
\(498\) 0 0
\(499\) −1.70009 −0.0761066 −0.0380533 0.999276i \(-0.512116\pi\)
−0.0380533 + 0.999276i \(0.512116\pi\)
\(500\) 0 0
\(501\) 0.743655 0.0332240
\(502\) 0 0
\(503\) 7.19214 0.320682 0.160341 0.987062i \(-0.448741\pi\)
0.160341 + 0.987062i \(0.448741\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −20.1399 −0.892684 −0.446342 0.894862i \(-0.647274\pi\)
−0.446342 + 0.894862i \(0.647274\pi\)
\(510\) 0 0
\(511\) −18.9632 −0.838881
\(512\) 0 0
\(513\) 2.29517 0.101334
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −29.0642 −1.27824
\(518\) 0 0
\(519\) 4.25635 0.186833
\(520\) 0 0
\(521\) −29.1030 −1.27503 −0.637513 0.770439i \(-0.720037\pi\)
−0.637513 + 0.770439i \(0.720037\pi\)
\(522\) 0 0
\(523\) −36.1419 −1.58037 −0.790186 0.612866i \(-0.790016\pi\)
−0.790186 + 0.612866i \(0.790016\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 17.3273 0.754788
\(528\) 0 0
\(529\) −4.55152 −0.197892
\(530\) 0 0
\(531\) −5.03210 −0.218375
\(532\) 0 0
\(533\) −5.25635 −0.227678
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.76904 0.421565
\(538\) 0 0
\(539\) −27.7690 −1.19610
\(540\) 0 0
\(541\) 8.80786 0.378679 0.189340 0.981912i \(-0.439365\pi\)
0.189340 + 0.981912i \(0.439365\pi\)
\(542\) 0 0
\(543\) 18.8467 0.808789
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.07567 0.0887490 0.0443745 0.999015i \(-0.485871\pi\)
0.0443745 + 0.999015i \(0.485871\pi\)
\(548\) 0 0
\(549\) −4.55152 −0.194254
\(550\) 0 0
\(551\) 15.0368 0.640591
\(552\) 0 0
\(553\) −1.86013 −0.0791007
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.2175 −0.602416 −0.301208 0.953559i \(-0.597390\pi\)
−0.301208 + 0.953559i \(0.597390\pi\)
\(558\) 0 0
\(559\) −5.25635 −0.222320
\(560\) 0 0
\(561\) 17.3273 0.731558
\(562\) 0 0
\(563\) 37.9109 1.59775 0.798877 0.601495i \(-0.205428\pi\)
0.798877 + 0.601495i \(0.205428\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.48059 0.0621788
\(568\) 0 0
\(569\) −34.2563 −1.43610 −0.718050 0.695991i \(-0.754965\pi\)
−0.718050 + 0.695991i \(0.754965\pi\)
\(570\) 0 0
\(571\) −6.37282 −0.266694 −0.133347 0.991069i \(-0.542573\pi\)
−0.133347 + 0.991069i \(0.542573\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −41.1672 −1.71381 −0.856907 0.515471i \(-0.827617\pi\)
−0.856907 + 0.515471i \(0.827617\pi\)
\(578\) 0 0
\(579\) −18.2175 −0.757094
\(580\) 0 0
\(581\) −17.8721 −0.741458
\(582\) 0 0
\(583\) −19.0321 −0.788229
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.6593 1.01780 0.508899 0.860826i \(-0.330053\pi\)
0.508899 + 0.860826i \(0.330053\pi\)
\(588\) 0 0
\(589\) 13.2563 0.546218
\(590\) 0 0
\(591\) −9.84669 −0.405039
\(592\) 0 0
\(593\) 22.4350 0.921297 0.460648 0.887583i \(-0.347617\pi\)
0.460648 + 0.887583i \(0.347617\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.59034 −0.269725
\(598\) 0 0
\(599\) 21.9885 0.898427 0.449214 0.893424i \(-0.351704\pi\)
0.449214 + 0.893424i \(0.351704\pi\)
\(600\) 0 0
\(601\) −10.3982 −0.424151 −0.212076 0.977253i \(-0.568022\pi\)
−0.212076 + 0.977253i \(0.568022\pi\)
\(602\) 0 0
\(603\) 4.22424 0.172024
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 9.47387 0.384532 0.192266 0.981343i \(-0.438416\pi\)
0.192266 + 0.981343i \(0.438416\pi\)
\(608\) 0 0
\(609\) 9.70009 0.393068
\(610\) 0 0
\(611\) 5.03210 0.203577
\(612\) 0 0
\(613\) 5.10303 0.206109 0.103055 0.994676i \(-0.467138\pi\)
0.103055 + 0.994676i \(0.467138\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 41.4739 1.66967 0.834837 0.550496i \(-0.185562\pi\)
0.834837 + 0.550496i \(0.185562\pi\)
\(618\) 0 0
\(619\) 28.8721 1.16047 0.580233 0.814450i \(-0.302961\pi\)
0.580233 + 0.814450i \(0.302961\pi\)
\(620\) 0 0
\(621\) −4.29517 −0.172359
\(622\) 0 0
\(623\) 20.0642 0.803855
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 13.2563 0.529407
\(628\) 0 0
\(629\) 9.76904 0.389517
\(630\) 0 0
\(631\) −18.6660 −0.743082 −0.371541 0.928417i \(-0.621170\pi\)
−0.371541 + 0.928417i \(0.621170\pi\)
\(632\) 0 0
\(633\) −2.80786 −0.111602
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.80786 0.190494
\(638\) 0 0
\(639\) −12.8079 −0.506671
\(640\) 0 0
\(641\) 26.0254 1.02794 0.513970 0.857808i \(-0.328174\pi\)
0.513970 + 0.857808i \(0.328174\pi\)
\(642\) 0 0
\(643\) 11.3206 0.446439 0.223219 0.974768i \(-0.428343\pi\)
0.223219 + 0.974768i \(0.428343\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.7322 0.421926 0.210963 0.977494i \(-0.432340\pi\)
0.210963 + 0.977494i \(0.432340\pi\)
\(648\) 0 0
\(649\) −29.0642 −1.14087
\(650\) 0 0
\(651\) 8.55152 0.335160
\(652\) 0 0
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −12.8079 −0.499682
\(658\) 0 0
\(659\) −25.6914 −1.00079 −0.500397 0.865796i \(-0.666813\pi\)
−0.500397 + 0.865796i \(0.666813\pi\)
\(660\) 0 0
\(661\) 12.6660 0.492651 0.246325 0.969187i \(-0.420777\pi\)
0.246325 + 0.969187i \(0.420777\pi\)
\(662\) 0 0
\(663\) −3.00000 −0.116510
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −28.1399 −1.08958
\(668\) 0 0
\(669\) 10.8855 0.420858
\(670\) 0 0
\(671\) −26.2884 −1.01485
\(672\) 0 0
\(673\) 27.2817 1.05163 0.525817 0.850598i \(-0.323760\pi\)
0.525817 + 0.850598i \(0.323760\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −25.4097 −0.976573 −0.488286 0.872684i \(-0.662378\pi\)
−0.488286 + 0.872684i \(0.662378\pi\)
\(678\) 0 0
\(679\) 10.3066 0.395532
\(680\) 0 0
\(681\) 18.7369 0.718001
\(682\) 0 0
\(683\) −9.55625 −0.365660 −0.182830 0.983145i \(-0.558526\pi\)
−0.182830 + 0.983145i \(0.558526\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.00000 0.0763048
\(688\) 0 0
\(689\) 3.29517 0.125536
\(690\) 0 0
\(691\) 26.0575 0.991273 0.495637 0.868530i \(-0.334935\pi\)
0.495637 + 0.868530i \(0.334935\pi\)
\(692\) 0 0
\(693\) 8.55152 0.324845
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 15.7690 0.597295
\(698\) 0 0
\(699\) 0.448485 0.0169633
\(700\) 0 0
\(701\) −49.4992 −1.86956 −0.934780 0.355226i \(-0.884404\pi\)
−0.934780 + 0.355226i \(0.884404\pi\)
\(702\) 0 0
\(703\) 7.47387 0.281882
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.45568 −0.129964
\(708\) 0 0
\(709\) 7.33399 0.275434 0.137717 0.990472i \(-0.456024\pi\)
0.137717 + 0.990472i \(0.456024\pi\)
\(710\) 0 0
\(711\) −1.25635 −0.0471166
\(712\) 0 0
\(713\) −24.8079 −0.929062
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 24.9545 0.931941
\(718\) 0 0
\(719\) −30.9497 −1.15423 −0.577115 0.816663i \(-0.695821\pi\)
−0.577115 + 0.816663i \(0.695821\pi\)
\(720\) 0 0
\(721\) 4.82130 0.179555
\(722\) 0 0
\(723\) 5.78248 0.215053
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −26.6660 −0.988987 −0.494494 0.869181i \(-0.664646\pi\)
−0.494494 + 0.869181i \(0.664646\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.7690 0.583239
\(732\) 0 0
\(733\) −27.6934 −1.02288 −0.511439 0.859320i \(-0.670887\pi\)
−0.511439 + 0.859320i \(0.670887\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.3982 0.898719
\(738\) 0 0
\(739\) −1.91761 −0.0705405 −0.0352703 0.999378i \(-0.511229\pi\)
−0.0352703 + 0.999378i \(0.511229\pi\)
\(740\) 0 0
\(741\) −2.29517 −0.0843152
\(742\) 0 0
\(743\) 50.2884 1.84490 0.922452 0.386112i \(-0.126182\pi\)
0.922452 + 0.386112i \(0.126182\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −12.0709 −0.441652
\(748\) 0 0
\(749\) 29.8218 1.08966
\(750\) 0 0
\(751\) 13.4758 0.491741 0.245870 0.969303i \(-0.420926\pi\)
0.245870 + 0.969303i \(0.420926\pi\)
\(752\) 0 0
\(753\) 9.33399 0.340150
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −24.1030 −0.876040 −0.438020 0.898965i \(-0.644320\pi\)
−0.438020 + 0.898965i \(0.644320\pi\)
\(758\) 0 0
\(759\) −24.8079 −0.900468
\(760\) 0 0
\(761\) 28.2175 1.02288 0.511442 0.859318i \(-0.329111\pi\)
0.511442 + 0.859318i \(0.329111\pi\)
\(762\) 0 0
\(763\) 27.8467 1.00812
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.03210 0.181699
\(768\) 0 0
\(769\) −32.9612 −1.18861 −0.594305 0.804240i \(-0.702573\pi\)
−0.594305 + 0.804240i \(0.702573\pi\)
\(770\) 0 0
\(771\) −0.192140 −0.00691974
\(772\) 0 0
\(773\) −8.88353 −0.319518 −0.159759 0.987156i \(-0.551072\pi\)
−0.159759 + 0.987156i \(0.551072\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 4.82130 0.172963
\(778\) 0 0
\(779\) 12.0642 0.432245
\(780\) 0 0
\(781\) −73.9751 −2.64704
\(782\) 0 0
\(783\) 6.55152 0.234132
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −12.8788 −0.459079 −0.229540 0.973299i \(-0.573722\pi\)
−0.229540 + 0.973299i \(0.573722\pi\)
\(788\) 0 0
\(789\) −7.25635 −0.258333
\(790\) 0 0
\(791\) 11.1807 0.397539
\(792\) 0 0
\(793\) 4.55152 0.161629
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.78050 −0.0984902 −0.0492451 0.998787i \(-0.515682\pi\)
−0.0492451 + 0.998787i \(0.515682\pi\)
\(798\) 0 0
\(799\) −15.0963 −0.534069
\(800\) 0 0
\(801\) 13.5515 0.478819
\(802\) 0 0
\(803\) −73.9751 −2.61052
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −12.9224 −0.454888
\(808\) 0 0
\(809\) 8.14186 0.286252 0.143126 0.989704i \(-0.454285\pi\)
0.143126 + 0.989704i \(0.454285\pi\)
\(810\) 0 0
\(811\) −18.7255 −0.657540 −0.328770 0.944410i \(-0.606634\pi\)
−0.328770 + 0.944410i \(0.606634\pi\)
\(812\) 0 0
\(813\) −23.6224 −0.828475
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 12.0642 0.422073
\(818\) 0 0
\(819\) −1.48059 −0.0517359
\(820\) 0 0
\(821\) −23.5401 −0.821554 −0.410777 0.911736i \(-0.634742\pi\)
−0.410777 + 0.911736i \(0.634742\pi\)
\(822\) 0 0
\(823\) 51.7576 1.80416 0.902078 0.431573i \(-0.142041\pi\)
0.902078 + 0.431573i \(0.142041\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −37.5333 −1.30516 −0.652581 0.757719i \(-0.726314\pi\)
−0.652581 + 0.757719i \(0.726314\pi\)
\(828\) 0 0
\(829\) 37.8835 1.31575 0.657875 0.753127i \(-0.271456\pi\)
0.657875 + 0.753127i \(0.271456\pi\)
\(830\) 0 0
\(831\) −6.96118 −0.241480
\(832\) 0 0
\(833\) −14.4236 −0.499747
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5.77576 0.199639
\(838\) 0 0
\(839\) −0.0891094 −0.00307640 −0.00153820 0.999999i \(-0.500490\pi\)
−0.00153820 + 0.999999i \(0.500490\pi\)
\(840\) 0 0
\(841\) 13.9224 0.480081
\(842\) 0 0
\(843\) 13.4097 0.461853
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 33.1050 1.13750
\(848\) 0 0
\(849\) −9.40966 −0.322939
\(850\) 0 0
\(851\) −13.9866 −0.479453
\(852\) 0 0
\(853\) −19.2583 −0.659393 −0.329696 0.944087i \(-0.606946\pi\)
−0.329696 + 0.944087i \(0.606946\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.84470 0.0630138 0.0315069 0.999504i \(-0.489969\pi\)
0.0315069 + 0.999504i \(0.489969\pi\)
\(858\) 0 0
\(859\) 49.3848 1.68499 0.842493 0.538707i \(-0.181087\pi\)
0.842493 + 0.538707i \(0.181087\pi\)
\(860\) 0 0
\(861\) 7.78248 0.265226
\(862\) 0 0
\(863\) 29.1720 0.993026 0.496513 0.868029i \(-0.334614\pi\)
0.496513 + 0.868029i \(0.334614\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) −7.25635 −0.246155
\(870\) 0 0
\(871\) −4.22424 −0.143133
\(872\) 0 0
\(873\) 6.96118 0.235600
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 22.1419 0.747677 0.373839 0.927494i \(-0.378041\pi\)
0.373839 + 0.927494i \(0.378041\pi\)
\(878\) 0 0
\(879\) −17.1030 −0.576871
\(880\) 0 0
\(881\) −16.1145 −0.542911 −0.271455 0.962451i \(-0.587505\pi\)
−0.271455 + 0.962451i \(0.587505\pi\)
\(882\) 0 0
\(883\) −59.1672 −1.99114 −0.995568 0.0940444i \(-0.970020\pi\)
−0.995568 + 0.0940444i \(0.970020\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −34.5654 −1.16059 −0.580297 0.814405i \(-0.697063\pi\)
−0.580297 + 0.814405i \(0.697063\pi\)
\(888\) 0 0
\(889\) −4.15728 −0.139431
\(890\) 0 0
\(891\) 5.77576 0.193495
\(892\) 0 0
\(893\) −11.5495 −0.386490
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.29517 0.143412
\(898\) 0 0
\(899\) 37.8400 1.26203
\(900\) 0 0
\(901\) −9.88551 −0.329334
\(902\) 0 0
\(903\) 7.78248 0.258985
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −4.74167 −0.157445 −0.0787223 0.996897i \(-0.525084\pi\)
−0.0787223 + 0.996897i \(0.525084\pi\)
\(908\) 0 0
\(909\) −2.33399 −0.0774137
\(910\) 0 0
\(911\) −0.450469 −0.0149247 −0.00746235 0.999972i \(-0.502375\pi\)
−0.00746235 + 0.999972i \(0.502375\pi\)
\(912\) 0 0
\(913\) −69.7188 −2.30735
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.39820 0.112218
\(918\) 0 0
\(919\) −19.5515 −0.644945 −0.322472 0.946579i \(-0.604514\pi\)
−0.322472 + 0.946579i \(0.604514\pi\)
\(920\) 0 0
\(921\) 18.3594 0.604962
\(922\) 0 0
\(923\) 12.8079 0.421576
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 3.25635 0.106952
\(928\) 0 0
\(929\) −25.6934 −0.842972 −0.421486 0.906835i \(-0.638491\pi\)
−0.421486 + 0.906835i \(0.638491\pi\)
\(930\) 0 0
\(931\) −11.0349 −0.361653
\(932\) 0 0
\(933\) 27.6157 0.904098
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −35.6545 −1.16478 −0.582392 0.812908i \(-0.697883\pi\)
−0.582392 + 0.812908i \(0.697883\pi\)
\(938\) 0 0
\(939\) −21.2952 −0.694942
\(940\) 0 0
\(941\) −5.26979 −0.171790 −0.0858951 0.996304i \(-0.527375\pi\)
−0.0858951 + 0.996304i \(0.527375\pi\)
\(942\) 0 0
\(943\) −22.5769 −0.735205
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 39.9042 1.29671 0.648356 0.761338i \(-0.275457\pi\)
0.648356 + 0.761338i \(0.275457\pi\)
\(948\) 0 0
\(949\) 12.8079 0.415761
\(950\) 0 0
\(951\) 0.372819 0.0120895
\(952\) 0 0
\(953\) 30.2563 0.980099 0.490050 0.871695i \(-0.336979\pi\)
0.490050 + 0.871695i \(0.336979\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 37.8400 1.22319
\(958\) 0 0
\(959\) −20.9383 −0.676132
\(960\) 0 0
\(961\) 2.35938 0.0761089
\(962\) 0 0
\(963\) 20.1419 0.649062
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 29.3915 0.945166 0.472583 0.881286i \(-0.343322\pi\)
0.472583 + 0.881286i \(0.343322\pi\)
\(968\) 0 0
\(969\) 6.88551 0.221194
\(970\) 0 0
\(971\) −13.4739 −0.432397 −0.216198 0.976349i \(-0.569366\pi\)
−0.216198 + 0.976349i \(0.569366\pi\)
\(972\) 0 0
\(973\) −11.7297 −0.376038
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −31.6934 −1.01396 −0.506980 0.861958i \(-0.669238\pi\)
−0.506980 + 0.861958i \(0.669238\pi\)
\(978\) 0 0
\(979\) 78.2703 2.50153
\(980\) 0 0
\(981\) 18.8079 0.600489
\(982\) 0 0
\(983\) 13.9311 0.444332 0.222166 0.975009i \(-0.428687\pi\)
0.222166 + 0.975009i \(0.428687\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −7.45047 −0.237151
\(988\) 0 0
\(989\) −22.5769 −0.717904
\(990\) 0 0
\(991\) 50.6296 1.60830 0.804152 0.594424i \(-0.202620\pi\)
0.804152 + 0.594424i \(0.202620\pi\)
\(992\) 0 0
\(993\) 9.39820 0.298243
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −38.4002 −1.21615 −0.608073 0.793881i \(-0.708057\pi\)
−0.608073 + 0.793881i \(0.708057\pi\)
\(998\) 0 0
\(999\) 3.25635 0.103026
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.bs.1.2 yes 3
5.4 even 2 7800.2.a.bh.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bh.1.2 3 5.4 even 2
7800.2.a.bs.1.2 yes 3 1.1 even 1 trivial