Properties

Label 7800.2.a.bu.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $4$
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: \(4\)
Coefficient field: 4.4.461844.1
Defining polynomial: \(x^{4} - x^{3} - 14 x^{2} - 12 x + 6\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.32424\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -3.32424 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -3.32424 q^{7} +1.00000 q^{9} +4.84395 q^{11} -1.00000 q^{13} +1.11760 q^{17} +4.05060 q^{19} +3.32424 q^{21} +4.16820 q^{23} -1.00000 q^{27} +5.64849 q^{29} -7.49244 q^{31} -4.84395 q^{33} +8.69908 q^{37} +1.00000 q^{39} +5.63731 q^{41} -12.8167 q^{43} +6.89455 q^{47} +4.05060 q^{49} -1.11760 q^{51} -12.2300 q^{53} -4.05060 q^{57} +0.910956 q^{59} +2.46911 q^{61} -3.32424 q^{63} -10.0233 q^{67} -4.16820 q^{69} +8.05060 q^{71} -10.4034 q^{73} -16.1025 q^{77} -10.6991 q^{79} +1.00000 q^{81} -2.67576 q^{83} -5.64849 q^{87} -3.68791 q^{89} +3.32424 q^{91} +7.49244 q^{93} +6.64849 q^{97} +4.84395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 3q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 3q^{7} + 4q^{9} + 5q^{11} - 4q^{13} - 7q^{17} + 3q^{19} + 3q^{21} - 8q^{23} - 4q^{27} + 2q^{29} + 5q^{31} - 5q^{33} + q^{37} + 4q^{39} + 7q^{41} - 6q^{43} + 3q^{49} + 7q^{51} - 6q^{53} - 3q^{57} - 9q^{59} + 19q^{61} - 3q^{63} + 4q^{67} + 8q^{69} + 19q^{71} + 6q^{73} + 17q^{77} - 9q^{79} + 4q^{81} - 21q^{83} - 2q^{87} + 14q^{89} + 3q^{91} - 5q^{93} + 6q^{97} + 5q^{99} + O(q^{100}) \)

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
\(7\) −3.32424 −1.25645 −0.628223 0.778033i \(-0.716217\pi\)
−0.628223 + 0.778033i \(0.716217\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.84395 1.46051 0.730253 0.683176i \(-0.239402\pi\)
0.730253 + 0.683176i \(0.239402\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.11760 0.271058 0.135529 0.990773i \(-0.456727\pi\)
0.135529 + 0.990773i \(0.456727\pi\)
\(18\) 0 0
\(19\) 4.05060 0.929271 0.464635 0.885502i \(-0.346185\pi\)
0.464635 + 0.885502i \(0.346185\pi\)
\(20\) 0 0
\(21\) 3.32424 0.725409
\(22\) 0 0
\(23\) 4.16820 0.869129 0.434565 0.900641i \(-0.356902\pi\)
0.434565 + 0.900641i \(0.356902\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.64849 1.04890 0.524449 0.851442i \(-0.324271\pi\)
0.524449 + 0.851442i \(0.324271\pi\)
\(30\) 0 0
\(31\) −7.49244 −1.34568 −0.672841 0.739787i \(-0.734926\pi\)
−0.672841 + 0.739787i \(0.734926\pi\)
\(32\) 0 0
\(33\) −4.84395 −0.843224
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.69908 1.43012 0.715060 0.699063i \(-0.246399\pi\)
0.715060 + 0.699063i \(0.246399\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 5.63731 0.880400 0.440200 0.897900i \(-0.354908\pi\)
0.440200 + 0.897900i \(0.354908\pi\)
\(42\) 0 0
\(43\) −12.8167 −1.95453 −0.977263 0.212030i \(-0.931992\pi\)
−0.977263 + 0.212030i \(0.931992\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.89455 1.00567 0.502837 0.864381i \(-0.332290\pi\)
0.502837 + 0.864381i \(0.332290\pi\)
\(48\) 0 0
\(49\) 4.05060 0.578657
\(50\) 0 0
\(51\) −1.11760 −0.156495
\(52\) 0 0
\(53\) −12.2300 −1.67992 −0.839958 0.542651i \(-0.817420\pi\)
−0.839958 + 0.542651i \(0.817420\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.05060 −0.536515
\(58\) 0 0
\(59\) 0.910956 0.118596 0.0592982 0.998240i \(-0.481114\pi\)
0.0592982 + 0.998240i \(0.481114\pi\)
\(60\) 0 0
\(61\) 2.46911 0.316137 0.158069 0.987428i \(-0.449473\pi\)
0.158069 + 0.987428i \(0.449473\pi\)
\(62\) 0 0
\(63\) −3.32424 −0.418815
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −10.0233 −1.22454 −0.612272 0.790647i \(-0.709744\pi\)
−0.612272 + 0.790647i \(0.709744\pi\)
\(68\) 0 0
\(69\) −4.16820 −0.501792
\(70\) 0 0
\(71\) 8.05060 0.955430 0.477715 0.878515i \(-0.341465\pi\)
0.477715 + 0.878515i \(0.341465\pi\)
\(72\) 0 0
\(73\) −10.4034 −1.21763 −0.608813 0.793314i \(-0.708354\pi\)
−0.608813 + 0.793314i \(0.708354\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16.1025 −1.83505
\(78\) 0 0
\(79\) −10.6991 −1.20374 −0.601871 0.798594i \(-0.705578\pi\)
−0.601871 + 0.798594i \(0.705578\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −2.67576 −0.293702 −0.146851 0.989159i \(-0.546914\pi\)
−0.146851 + 0.989159i \(0.546914\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.64849 −0.605581
\(88\) 0 0
\(89\) −3.68791 −0.390917 −0.195459 0.980712i \(-0.562620\pi\)
−0.195459 + 0.980712i \(0.562620\pi\)
\(90\) 0 0
\(91\) 3.32424 0.348475
\(92\) 0 0
\(93\) 7.49244 0.776930
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.64849 0.675052 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(98\) 0 0
\(99\) 4.84395 0.486836
\(100\) 0 0
\(101\) 11.6991 1.16410 0.582051 0.813152i \(-0.302250\pi\)
0.582051 + 0.813152i \(0.302250\pi\)
\(102\) 0 0
\(103\) 19.1531 1.88721 0.943604 0.331075i \(-0.107411\pi\)
0.943604 + 0.331075i \(0.107411\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.8673 1.24393 0.621964 0.783046i \(-0.286335\pi\)
0.621964 + 0.783046i \(0.286335\pi\)
\(108\) 0 0
\(109\) −11.1124 −1.06437 −0.532186 0.846627i \(-0.678629\pi\)
−0.532186 + 0.846627i \(0.678629\pi\)
\(110\) 0 0
\(111\) −8.69908 −0.825681
\(112\) 0 0
\(113\) 10.7497 1.01125 0.505623 0.862755i \(-0.331263\pi\)
0.505623 + 0.862755i \(0.331263\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −3.71518 −0.340570
\(120\) 0 0
\(121\) 12.4639 1.13308
\(122\) 0 0
\(123\) −5.63731 −0.508299
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 11.3476 1.00693 0.503467 0.864014i \(-0.332058\pi\)
0.503467 + 0.864014i \(0.332058\pi\)
\(128\) 0 0
\(129\) 12.8167 1.12845
\(130\) 0 0
\(131\) −8.38699 −0.732775 −0.366387 0.930462i \(-0.619406\pi\)
−0.366387 + 0.930462i \(0.619406\pi\)
\(132\) 0 0
\(133\) −13.4652 −1.16758
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.80551 −0.837741 −0.418870 0.908046i \(-0.637574\pi\)
−0.418870 + 0.908046i \(0.637574\pi\)
\(138\) 0 0
\(139\) −10.2352 −0.868138 −0.434069 0.900880i \(-0.642923\pi\)
−0.434069 + 0.900880i \(0.642923\pi\)
\(140\) 0 0
\(141\) −6.89455 −0.580626
\(142\) 0 0
\(143\) −4.84395 −0.405072
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.05060 −0.334088
\(148\) 0 0
\(149\) 10.6485 0.872358 0.436179 0.899860i \(-0.356331\pi\)
0.436179 + 0.899860i \(0.356331\pi\)
\(150\) 0 0
\(151\) −5.42544 −0.441516 −0.220758 0.975329i \(-0.570853\pi\)
−0.220758 + 0.975329i \(0.570853\pi\)
\(152\) 0 0
\(153\) 1.11760 0.0903526
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.94940 0.554623 0.277311 0.960780i \(-0.410557\pi\)
0.277311 + 0.960780i \(0.410557\pi\)
\(158\) 0 0
\(159\) 12.2300 0.969900
\(160\) 0 0
\(161\) −13.8561 −1.09201
\(162\) 0 0
\(163\) −18.2694 −1.43097 −0.715485 0.698629i \(-0.753794\pi\)
−0.715485 + 0.698629i \(0.753794\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −17.9961 −1.39258 −0.696288 0.717762i \(-0.745167\pi\)
−0.696288 + 0.717762i \(0.745167\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 4.05060 0.309757
\(172\) 0 0
\(173\) 18.9573 1.44130 0.720648 0.693301i \(-0.243844\pi\)
0.720648 + 0.693301i \(0.243844\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.910956 −0.0684717
\(178\) 0 0
\(179\) −11.7773 −0.880274 −0.440137 0.897931i \(-0.645070\pi\)
−0.440137 + 0.897931i \(0.645070\pi\)
\(180\) 0 0
\(181\) 11.5979 0.862064 0.431032 0.902337i \(-0.358150\pi\)
0.431032 + 0.902337i \(0.358150\pi\)
\(182\) 0 0
\(183\) −2.46911 −0.182522
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.41360 0.395882
\(188\) 0 0
\(189\) 3.32424 0.241803
\(190\) 0 0
\(191\) 23.2970 1.68571 0.842855 0.538141i \(-0.180873\pi\)
0.842855 + 0.538141i \(0.180873\pi\)
\(192\) 0 0
\(193\) 12.6386 0.909746 0.454873 0.890556i \(-0.349685\pi\)
0.454873 + 0.890556i \(0.349685\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 24.0913 1.71643 0.858217 0.513287i \(-0.171572\pi\)
0.858217 + 0.513287i \(0.171572\pi\)
\(198\) 0 0
\(199\) −12.1176 −0.858994 −0.429497 0.903068i \(-0.641309\pi\)
−0.429497 + 0.903068i \(0.641309\pi\)
\(200\) 0 0
\(201\) 10.0233 0.706991
\(202\) 0 0
\(203\) −18.7770 −1.31788
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.16820 0.289710
\(208\) 0 0
\(209\) 19.6209 1.35721
\(210\) 0 0
\(211\) −0.168197 −0.0115792 −0.00578959 0.999983i \(-0.501843\pi\)
−0.00578959 + 0.999983i \(0.501843\pi\)
\(212\) 0 0
\(213\) −8.05060 −0.551618
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 24.9067 1.69078
\(218\) 0 0
\(219\) 10.4034 0.702996
\(220\) 0 0
\(221\) −1.11760 −0.0751779
\(222\) 0 0
\(223\) 25.5440 1.71055 0.855277 0.518171i \(-0.173387\pi\)
0.855277 + 0.518171i \(0.173387\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.70995 −0.445355 −0.222677 0.974892i \(-0.571480\pi\)
−0.222677 + 0.974892i \(0.571480\pi\)
\(228\) 0 0
\(229\) 2.92182 0.193079 0.0965396 0.995329i \(-0.469223\pi\)
0.0965396 + 0.995329i \(0.469223\pi\)
\(230\) 0 0
\(231\) 16.1025 1.05947
\(232\) 0 0
\(233\) 1.68791 0.110578 0.0552892 0.998470i \(-0.482392\pi\)
0.0552892 + 0.998470i \(0.482392\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.6991 0.694980
\(238\) 0 0
\(239\) −16.2079 −1.04840 −0.524202 0.851594i \(-0.675636\pi\)
−0.524202 + 0.851594i \(0.675636\pi\)
\(240\) 0 0
\(241\) 12.1682 0.783822 0.391911 0.920003i \(-0.371814\pi\)
0.391911 + 0.920003i \(0.371814\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.05060 −0.257733
\(248\) 0 0
\(249\) 2.67576 0.169569
\(250\) 0 0
\(251\) 15.6373 0.987018 0.493509 0.869741i \(-0.335714\pi\)
0.493509 + 0.869741i \(0.335714\pi\)
\(252\) 0 0
\(253\) 20.1906 1.26937
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.5210 0.718660 0.359330 0.933211i \(-0.383005\pi\)
0.359330 + 0.933211i \(0.383005\pi\)
\(258\) 0 0
\(259\) −28.9179 −1.79687
\(260\) 0 0
\(261\) 5.64849 0.349633
\(262\) 0 0
\(263\) −1.41852 −0.0874694 −0.0437347 0.999043i \(-0.513926\pi\)
−0.0437347 + 0.999043i \(0.513926\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.68791 0.225696
\(268\) 0 0
\(269\) 26.3982 1.60952 0.804762 0.593597i \(-0.202293\pi\)
0.804762 + 0.593597i \(0.202293\pi\)
\(270\) 0 0
\(271\) 27.1133 1.64702 0.823509 0.567303i \(-0.192013\pi\)
0.823509 + 0.567303i \(0.192013\pi\)
\(272\) 0 0
\(273\) −3.32424 −0.201192
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.0861 −0.666098 −0.333049 0.942910i \(-0.608077\pi\)
−0.333049 + 0.942910i \(0.608077\pi\)
\(278\) 0 0
\(279\) −7.49244 −0.448561
\(280\) 0 0
\(281\) 9.17938 0.547596 0.273798 0.961787i \(-0.411720\pi\)
0.273798 + 0.961787i \(0.411720\pi\)
\(282\) 0 0
\(283\) −31.8686 −1.89439 −0.947195 0.320658i \(-0.896096\pi\)
−0.947195 + 0.320658i \(0.896096\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.7398 −1.10617
\(288\) 0 0
\(289\) −15.7510 −0.926528
\(290\) 0 0
\(291\) −6.64849 −0.389741
\(292\) 0 0
\(293\) −9.14061 −0.534000 −0.267000 0.963696i \(-0.586032\pi\)
−0.267000 + 0.963696i \(0.586032\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.84395 −0.281075
\(298\) 0 0
\(299\) −4.16820 −0.241053
\(300\) 0 0
\(301\) 42.6058 2.45576
\(302\) 0 0
\(303\) −11.6991 −0.672095
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.40211 0.422461 0.211230 0.977436i \(-0.432253\pi\)
0.211230 + 0.977436i \(0.432253\pi\)
\(308\) 0 0
\(309\) −19.1531 −1.08958
\(310\) 0 0
\(311\) 21.5098 1.21971 0.609855 0.792513i \(-0.291228\pi\)
0.609855 + 0.792513i \(0.291228\pi\)
\(312\) 0 0
\(313\) −11.1458 −0.630000 −0.315000 0.949092i \(-0.602005\pi\)
−0.315000 + 0.949092i \(0.602005\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 27.0960 1.52186 0.760931 0.648833i \(-0.224743\pi\)
0.760931 + 0.648833i \(0.224743\pi\)
\(318\) 0 0
\(319\) 27.3610 1.53192
\(320\) 0 0
\(321\) −12.8673 −0.718182
\(322\) 0 0
\(323\) 4.52695 0.251886
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 11.1124 0.614516
\(328\) 0 0
\(329\) −22.9192 −1.26357
\(330\) 0 0
\(331\) 10.0670 0.553333 0.276666 0.960966i \(-0.410770\pi\)
0.276666 + 0.960966i \(0.410770\pi\)
\(332\) 0 0
\(333\) 8.69908 0.476707
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 35.0749 1.91065 0.955326 0.295555i \(-0.0955046\pi\)
0.955326 + 0.295555i \(0.0955046\pi\)
\(338\) 0 0
\(339\) −10.7497 −0.583843
\(340\) 0 0
\(341\) −36.2930 −1.96538
\(342\) 0 0
\(343\) 9.80453 0.529395
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.15702 −0.169478 −0.0847388 0.996403i \(-0.527006\pi\)
−0.0847388 + 0.996403i \(0.527006\pi\)
\(348\) 0 0
\(349\) 31.3883 1.68018 0.840088 0.542450i \(-0.182503\pi\)
0.840088 + 0.542450i \(0.182503\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −24.3325 −1.29509 −0.647543 0.762029i \(-0.724203\pi\)
−0.647543 + 0.762029i \(0.724203\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 3.71518 0.196628
\(358\) 0 0
\(359\) 26.1915 1.38234 0.691168 0.722694i \(-0.257096\pi\)
0.691168 + 0.722694i \(0.257096\pi\)
\(360\) 0 0
\(361\) −2.59266 −0.136456
\(362\) 0 0
\(363\) −12.4639 −0.654184
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −19.2806 −1.00644 −0.503219 0.864159i \(-0.667851\pi\)
−0.503219 + 0.864159i \(0.667851\pi\)
\(368\) 0 0
\(369\) 5.63731 0.293467
\(370\) 0 0
\(371\) 40.6554 2.11072
\(372\) 0 0
\(373\) 19.8331 1.02692 0.513459 0.858114i \(-0.328364\pi\)
0.513459 + 0.858114i \(0.328364\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.64849 −0.290912
\(378\) 0 0
\(379\) −21.5936 −1.10919 −0.554595 0.832120i \(-0.687127\pi\)
−0.554595 + 0.832120i \(0.687127\pi\)
\(380\) 0 0
\(381\) −11.3476 −0.581354
\(382\) 0 0
\(383\) −7.81540 −0.399348 −0.199674 0.979862i \(-0.563988\pi\)
−0.199674 + 0.979862i \(0.563988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.8167 −0.651509
\(388\) 0 0
\(389\) 19.7043 0.999048 0.499524 0.866300i \(-0.333508\pi\)
0.499524 + 0.866300i \(0.333508\pi\)
\(390\) 0 0
\(391\) 4.65838 0.235584
\(392\) 0 0
\(393\) 8.38699 0.423068
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.96848 −0.249361 −0.124680 0.992197i \(-0.539791\pi\)
−0.124680 + 0.992197i \(0.539791\pi\)
\(398\) 0 0
\(399\) 13.4652 0.674102
\(400\) 0 0
\(401\) −25.6209 −1.27945 −0.639723 0.768605i \(-0.720951\pi\)
−0.639723 + 0.768605i \(0.720951\pi\)
\(402\) 0 0
\(403\) 7.49244 0.373225
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 42.1380 2.08870
\(408\) 0 0
\(409\) 13.6761 0.676238 0.338119 0.941103i \(-0.390209\pi\)
0.338119 + 0.941103i \(0.390209\pi\)
\(410\) 0 0
\(411\) 9.80551 0.483670
\(412\) 0 0
\(413\) −3.02824 −0.149010
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 10.2352 0.501220
\(418\) 0 0
\(419\) 7.50330 0.366560 0.183280 0.983061i \(-0.441328\pi\)
0.183280 + 0.983061i \(0.441328\pi\)
\(420\) 0 0
\(421\) −9.39817 −0.458039 −0.229019 0.973422i \(-0.573552\pi\)
−0.229019 + 0.973422i \(0.573552\pi\)
\(422\) 0 0
\(423\) 6.89455 0.335225
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −8.20793 −0.397210
\(428\) 0 0
\(429\) 4.84395 0.233868
\(430\) 0 0
\(431\) 4.77598 0.230051 0.115025 0.993363i \(-0.463305\pi\)
0.115025 + 0.993363i \(0.463305\pi\)
\(432\) 0 0
\(433\) 2.50853 0.120552 0.0602762 0.998182i \(-0.480802\pi\)
0.0602762 + 0.998182i \(0.480802\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 16.8837 0.807656
\(438\) 0 0
\(439\) −13.0900 −0.624752 −0.312376 0.949958i \(-0.601125\pi\)
−0.312376 + 0.949958i \(0.601125\pi\)
\(440\) 0 0
\(441\) 4.05060 0.192886
\(442\) 0 0
\(443\) −38.2089 −1.81536 −0.907680 0.419663i \(-0.862148\pi\)
−0.907680 + 0.419663i \(0.862148\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −10.6485 −0.503656
\(448\) 0 0
\(449\) 9.29103 0.438471 0.219235 0.975672i \(-0.429644\pi\)
0.219235 + 0.975672i \(0.429644\pi\)
\(450\) 0 0
\(451\) 27.3069 1.28583
\(452\) 0 0
\(453\) 5.42544 0.254909
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.05189 −0.236317 −0.118159 0.992995i \(-0.537699\pi\)
−0.118159 + 0.992995i \(0.537699\pi\)
\(458\) 0 0
\(459\) −1.11760 −0.0521651
\(460\) 0 0
\(461\) −9.89881 −0.461033 −0.230517 0.973068i \(-0.574042\pi\)
−0.230517 + 0.973068i \(0.574042\pi\)
\(462\) 0 0
\(463\) −24.8906 −1.15676 −0.578382 0.815766i \(-0.696316\pi\)
−0.578382 + 0.815766i \(0.696316\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 26.7333 1.23707 0.618534 0.785758i \(-0.287727\pi\)
0.618534 + 0.785758i \(0.287727\pi\)
\(468\) 0 0
\(469\) 33.3200 1.53857
\(470\) 0 0
\(471\) −6.94940 −0.320212
\(472\) 0 0
\(473\) −62.0834 −2.85460
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −12.2300 −0.559972
\(478\) 0 0
\(479\) 10.8827 0.497244 0.248622 0.968601i \(-0.420022\pi\)
0.248622 + 0.968601i \(0.420022\pi\)
\(480\) 0 0
\(481\) −8.69908 −0.396644
\(482\) 0 0
\(483\) 13.8561 0.630475
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.88337 0.0853438 0.0426719 0.999089i \(-0.486413\pi\)
0.0426719 + 0.999089i \(0.486413\pi\)
\(488\) 0 0
\(489\) 18.2694 0.826170
\(490\) 0 0
\(491\) −32.2050 −1.45339 −0.726695 0.686960i \(-0.758945\pi\)
−0.726695 + 0.686960i \(0.758945\pi\)
\(492\) 0 0
\(493\) 6.31275 0.284312
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −26.7621 −1.20045
\(498\) 0 0
\(499\) 8.03516 0.359703 0.179852 0.983694i \(-0.442438\pi\)
0.179852 + 0.983694i \(0.442438\pi\)
\(500\) 0 0
\(501\) 17.9961 0.804005
\(502\) 0 0
\(503\) −2.40340 −0.107162 −0.0535811 0.998564i \(-0.517064\pi\)
−0.0535811 + 0.998564i \(0.517064\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −1.91064 −0.0846877 −0.0423438 0.999103i \(-0.513482\pi\)
−0.0423438 + 0.999103i \(0.513482\pi\)
\(510\) 0 0
\(511\) 34.5834 1.52988
\(512\) 0 0
\(513\) −4.05060 −0.178838
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 33.3969 1.46879
\(518\) 0 0
\(519\) −18.9573 −0.832133
\(520\) 0 0
\(521\) −15.0618 −0.659868 −0.329934 0.944004i \(-0.607027\pi\)
−0.329934 + 0.944004i \(0.607027\pi\)
\(522\) 0 0
\(523\) 33.1649 1.45020 0.725100 0.688643i \(-0.241793\pi\)
0.725100 + 0.688643i \(0.241793\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.37355 −0.364758
\(528\) 0 0
\(529\) −5.62613 −0.244614
\(530\) 0 0
\(531\) 0.910956 0.0395321
\(532\) 0 0
\(533\) −5.63731 −0.244179
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 11.7773 0.508227
\(538\) 0 0
\(539\) 19.6209 0.845132
\(540\) 0 0
\(541\) −6.50459 −0.279654 −0.139827 0.990176i \(-0.544655\pi\)
−0.139827 + 0.990176i \(0.544655\pi\)
\(542\) 0 0
\(543\) −11.5979 −0.497713
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 41.5118 1.77492 0.887459 0.460887i \(-0.152469\pi\)
0.887459 + 0.460887i \(0.152469\pi\)
\(548\) 0 0
\(549\) 2.46911 0.105379
\(550\) 0 0
\(551\) 22.8797 0.974710
\(552\) 0 0
\(553\) 35.5664 1.51244
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13.7004 0.580503 0.290252 0.956950i \(-0.406261\pi\)
0.290252 + 0.956950i \(0.406261\pi\)
\(558\) 0 0
\(559\) 12.8167 0.542088
\(560\) 0 0
\(561\) −5.41360 −0.228562
\(562\) 0 0
\(563\) −35.3476 −1.48972 −0.744861 0.667219i \(-0.767484\pi\)
−0.744861 + 0.667219i \(0.767484\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −3.32424 −0.139605
\(568\) 0 0
\(569\) 36.2483 1.51961 0.759804 0.650152i \(-0.225295\pi\)
0.759804 + 0.650152i \(0.225295\pi\)
\(570\) 0 0
\(571\) 7.96581 0.333359 0.166679 0.986011i \(-0.446696\pi\)
0.166679 + 0.986011i \(0.446696\pi\)
\(572\) 0 0
\(573\) −23.2970 −0.973245
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 21.8219 0.908458 0.454229 0.890885i \(-0.349915\pi\)
0.454229 + 0.890885i \(0.349915\pi\)
\(578\) 0 0
\(579\) −12.6386 −0.525242
\(580\) 0 0
\(581\) 8.89487 0.369021
\(582\) 0 0
\(583\) −59.2414 −2.45353
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 26.3518 1.08766 0.543828 0.839197i \(-0.316974\pi\)
0.543828 + 0.839197i \(0.316974\pi\)
\(588\) 0 0
\(589\) −30.3489 −1.25050
\(590\) 0 0
\(591\) −24.0913 −0.990984
\(592\) 0 0
\(593\) 21.8522 0.897361 0.448680 0.893692i \(-0.351894\pi\)
0.448680 + 0.893692i \(0.351894\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 12.1176 0.495940
\(598\) 0 0
\(599\) 20.4822 0.836881 0.418441 0.908244i \(-0.362577\pi\)
0.418441 + 0.908244i \(0.362577\pi\)
\(600\) 0 0
\(601\) 31.1380 1.27014 0.635072 0.772453i \(-0.280970\pi\)
0.635072 + 0.772453i \(0.280970\pi\)
\(602\) 0 0
\(603\) −10.0233 −0.408181
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11.6715 0.473732 0.236866 0.971542i \(-0.423880\pi\)
0.236866 + 0.971542i \(0.423880\pi\)
\(608\) 0 0
\(609\) 18.7770 0.760880
\(610\) 0 0
\(611\) −6.89455 −0.278924
\(612\) 0 0
\(613\) 41.3758 1.67115 0.835577 0.549374i \(-0.185134\pi\)
0.835577 + 0.549374i \(0.185134\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −42.7359 −1.72048 −0.860240 0.509889i \(-0.829687\pi\)
−0.860240 + 0.509889i \(0.829687\pi\)
\(618\) 0 0
\(619\) 7.44087 0.299074 0.149537 0.988756i \(-0.452222\pi\)
0.149537 + 0.988756i \(0.452222\pi\)
\(620\) 0 0
\(621\) −4.16820 −0.167264
\(622\) 0 0
\(623\) 12.2595 0.491167
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −19.6209 −0.783583
\(628\) 0 0
\(629\) 9.72210 0.387645
\(630\) 0 0
\(631\) −17.7221 −0.705506 −0.352753 0.935717i \(-0.614754\pi\)
−0.352753 + 0.935717i \(0.614754\pi\)
\(632\) 0 0
\(633\) 0.168197 0.00668524
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −4.05060 −0.160491
\(638\) 0 0
\(639\) 8.05060 0.318477
\(640\) 0 0
\(641\) −31.4764 −1.24324 −0.621621 0.783319i \(-0.713525\pi\)
−0.621621 + 0.783319i \(0.713525\pi\)
\(642\) 0 0
\(643\) 40.7234 1.60597 0.802987 0.595997i \(-0.203243\pi\)
0.802987 + 0.595997i \(0.203243\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −44.1255 −1.73475 −0.867376 0.497653i \(-0.834195\pi\)
−0.867376 + 0.497653i \(0.834195\pi\)
\(648\) 0 0
\(649\) 4.41263 0.173211
\(650\) 0 0
\(651\) −24.9067 −0.976171
\(652\) 0 0
\(653\) −6.02301 −0.235699 −0.117849 0.993031i \(-0.537600\pi\)
−0.117849 + 0.993031i \(0.537600\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −10.4034 −0.405875
\(658\) 0 0
\(659\) −5.26810 −0.205216 −0.102608 0.994722i \(-0.532719\pi\)
−0.102608 + 0.994722i \(0.532719\pi\)
\(660\) 0 0
\(661\) 8.72144 0.339225 0.169612 0.985511i \(-0.445748\pi\)
0.169612 + 0.985511i \(0.445748\pi\)
\(662\) 0 0
\(663\) 1.11760 0.0434040
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 23.5440 0.911628
\(668\) 0 0
\(669\) −25.5440 −0.987589
\(670\) 0 0
\(671\) 11.9603 0.461721
\(672\) 0 0
\(673\) −6.04931 −0.233184 −0.116592 0.993180i \(-0.537197\pi\)
−0.116592 + 0.993180i \(0.537197\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13.6636 0.525135 0.262568 0.964914i \(-0.415431\pi\)
0.262568 + 0.964914i \(0.415431\pi\)
\(678\) 0 0
\(679\) −22.1012 −0.848166
\(680\) 0 0
\(681\) 6.70995 0.257126
\(682\) 0 0
\(683\) 3.41555 0.130692 0.0653462 0.997863i \(-0.479185\pi\)
0.0653462 + 0.997863i \(0.479185\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.92182 −0.111474
\(688\) 0 0
\(689\) 12.2300 0.465925
\(690\) 0 0
\(691\) 20.6153 0.784242 0.392121 0.919914i \(-0.371741\pi\)
0.392121 + 0.919914i \(0.371741\pi\)
\(692\) 0 0
\(693\) −16.1025 −0.611683
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 6.30026 0.238639
\(698\) 0 0
\(699\) −1.68791 −0.0638425
\(700\) 0 0
\(701\) −13.5861 −0.513138 −0.256569 0.966526i \(-0.582592\pi\)
−0.256569 + 0.966526i \(0.582592\pi\)
\(702\) 0 0
\(703\) 35.2365 1.32897
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −38.8906 −1.46263
\(708\) 0 0
\(709\) −1.39616 −0.0524339 −0.0262169 0.999656i \(-0.508346\pi\)
−0.0262169 + 0.999656i \(0.508346\pi\)
\(710\) 0 0
\(711\) −10.6991 −0.401247
\(712\) 0 0
\(713\) −31.2300 −1.16957
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 16.2079 0.605296
\(718\) 0 0
\(719\) −37.6130 −1.40273 −0.701365 0.712803i \(-0.747425\pi\)
−0.701365 + 0.712803i \(0.747425\pi\)
\(720\) 0 0
\(721\) −63.6695 −2.37118
\(722\) 0 0
\(723\) −12.1682 −0.452540
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −35.0191 −1.29879 −0.649393 0.760453i \(-0.724977\pi\)
−0.649393 + 0.760453i \(0.724977\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −14.3239 −0.529790
\(732\) 0 0
\(733\) 17.8824 0.660502 0.330251 0.943893i \(-0.392867\pi\)
0.330251 + 0.943893i \(0.392867\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −48.5525 −1.78846
\(738\) 0 0
\(739\) 34.2034 1.25819 0.629095 0.777328i \(-0.283425\pi\)
0.629095 + 0.777328i \(0.283425\pi\)
\(740\) 0 0
\(741\) 4.05060 0.148802
\(742\) 0 0
\(743\) 4.96155 0.182022 0.0910109 0.995850i \(-0.470990\pi\)
0.0910109 + 0.995850i \(0.470990\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.67576 −0.0979008
\(748\) 0 0
\(749\) −42.7740 −1.56293
\(750\) 0 0
\(751\) −30.8574 −1.12600 −0.563001 0.826456i \(-0.690353\pi\)
−0.563001 + 0.826456i \(0.690353\pi\)
\(752\) 0 0
\(753\) −15.6373 −0.569855
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 34.9534 1.27040 0.635201 0.772347i \(-0.280917\pi\)
0.635201 + 0.772347i \(0.280917\pi\)
\(758\) 0 0
\(759\) −20.1906 −0.732871
\(760\) 0 0
\(761\) −9.79304 −0.354997 −0.177499 0.984121i \(-0.556801\pi\)
−0.177499 + 0.984121i \(0.556801\pi\)
\(762\) 0 0
\(763\) 36.9402 1.33733
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.910956 −0.0328927
\(768\) 0 0
\(769\) 1.66555 0.0600613 0.0300306 0.999549i \(-0.490440\pi\)
0.0300306 + 0.999549i \(0.490440\pi\)
\(770\) 0 0
\(771\) −11.5210 −0.414919
\(772\) 0 0
\(773\) 32.7273 1.17712 0.588560 0.808454i \(-0.299695\pi\)
0.588560 + 0.808454i \(0.299695\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 28.9179 1.03742
\(778\) 0 0
\(779\) 22.8345 0.818130
\(780\) 0 0
\(781\) 38.9967 1.39541
\(782\) 0 0
\(783\) −5.64849 −0.201860
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −13.4484 −0.479382 −0.239691 0.970849i \(-0.577046\pi\)
−0.239691 + 0.970849i \(0.577046\pi\)
\(788\) 0 0
\(789\) 1.41852 0.0505005
\(790\) 0 0
\(791\) −35.7346 −1.27057
\(792\) 0 0
\(793\) −2.46911 −0.0876808
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 25.6544 0.908727 0.454363 0.890816i \(-0.349867\pi\)
0.454363 + 0.890816i \(0.349867\pi\)
\(798\) 0 0
\(799\) 7.70535 0.272596
\(800\) 0 0
\(801\) −3.68791 −0.130306
\(802\) 0 0
\(803\) −50.3936 −1.77835
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −26.3982 −0.929260
\(808\) 0 0
\(809\) −29.9915 −1.05444 −0.527222 0.849727i \(-0.676766\pi\)
−0.527222 + 0.849727i \(0.676766\pi\)
\(810\) 0 0
\(811\) 11.1133 0.390242 0.195121 0.980779i \(-0.437490\pi\)
0.195121 + 0.980779i \(0.437490\pi\)
\(812\) 0 0
\(813\) −27.1133 −0.950907
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −51.9152 −1.81628
\(818\) 0 0
\(819\) 3.32424 0.116158
\(820\) 0 0
\(821\) −1.62090 −0.0565699 −0.0282850 0.999600i \(-0.509005\pi\)
−0.0282850 + 0.999600i \(0.509005\pi\)
\(822\) 0 0
\(823\) 40.5007 1.41176 0.705882 0.708329i \(-0.250551\pi\)
0.705882 + 0.708329i \(0.250551\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 4.95560 0.172323 0.0861616 0.996281i \(-0.472540\pi\)
0.0861616 + 0.996281i \(0.472540\pi\)
\(828\) 0 0
\(829\) −26.2588 −0.912007 −0.456004 0.889978i \(-0.650720\pi\)
−0.456004 + 0.889978i \(0.650720\pi\)
\(830\) 0 0
\(831\) 11.0861 0.384572
\(832\) 0 0
\(833\) 4.52695 0.156849
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 7.49244 0.258977
\(838\) 0 0
\(839\) 32.0565 1.10671 0.553357 0.832944i \(-0.313346\pi\)
0.553357 + 0.832944i \(0.313346\pi\)
\(840\) 0 0
\(841\) 2.90541 0.100187
\(842\) 0 0
\(843\) −9.17938 −0.316154
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −41.4330 −1.42365
\(848\) 0 0
\(849\) 31.8686 1.09373
\(850\) 0 0
\(851\) 36.2595 1.24296
\(852\) 0 0
\(853\) 52.5775 1.80022 0.900110 0.435662i \(-0.143486\pi\)
0.900110 + 0.435662i \(0.143486\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.5940 0.566839 0.283419 0.958996i \(-0.408531\pi\)
0.283419 + 0.958996i \(0.408531\pi\)
\(858\) 0 0
\(859\) 27.0742 0.923761 0.461881 0.886942i \(-0.347175\pi\)
0.461881 + 0.886942i \(0.347175\pi\)
\(860\) 0 0
\(861\) 18.7398 0.638650
\(862\) 0 0
\(863\) 9.99903 0.340371 0.170185 0.985412i \(-0.445563\pi\)
0.170185 + 0.985412i \(0.445563\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 15.7510 0.534931
\(868\) 0 0
\(869\) −51.8259 −1.75807
\(870\) 0 0
\(871\) 10.0233 0.339628
\(872\) 0 0
\(873\) 6.64849 0.225017
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −3.10248 −0.104763 −0.0523817 0.998627i \(-0.516681\pi\)
−0.0523817 + 0.998627i \(0.516681\pi\)
\(878\) 0 0
\(879\) 9.14061 0.308305
\(880\) 0 0
\(881\) 8.19121 0.275969 0.137984 0.990434i \(-0.455938\pi\)
0.137984 + 0.990434i \(0.455938\pi\)
\(882\) 0 0
\(883\) −39.1649 −1.31800 −0.659002 0.752141i \(-0.729021\pi\)
−0.659002 + 0.752141i \(0.729021\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 21.2543 0.713649 0.356824 0.934172i \(-0.383859\pi\)
0.356824 + 0.934172i \(0.383859\pi\)
\(888\) 0 0
\(889\) −37.7221 −1.26516
\(890\) 0 0
\(891\) 4.84395 0.162279
\(892\) 0 0
\(893\) 27.9270 0.934543
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.16820 0.139172
\(898\) 0 0
\(899\) −42.3210 −1.41148
\(900\) 0 0
\(901\) −13.6682 −0.455354
\(902\) 0 0
\(903\) −42.6058 −1.41783
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −25.0618 −0.832163 −0.416081 0.909327i \(-0.636597\pi\)
−0.416081 + 0.909327i \(0.636597\pi\)
\(908\) 0 0
\(909\) 11.6991 0.388034
\(910\) 0 0
\(911\) 10.3246 0.342068 0.171034 0.985265i \(-0.445289\pi\)
0.171034 + 0.985265i \(0.445289\pi\)
\(912\) 0 0
\(913\) −12.9612 −0.428954
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 27.8804 0.920692
\(918\) 0 0
\(919\) −20.0605 −0.661734 −0.330867 0.943677i \(-0.607341\pi\)
−0.330867 + 0.943677i \(0.607341\pi\)
\(920\) 0 0
\(921\) −7.40211 −0.243908
\(922\) 0 0
\(923\) −8.05060 −0.264989
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 19.1531 0.629070
\(928\) 0 0
\(929\) 38.8692 1.27526 0.637629 0.770344i \(-0.279915\pi\)
0.637629 + 0.770344i \(0.279915\pi\)
\(930\) 0 0
\(931\) 16.4073 0.537729
\(932\) 0 0
\(933\) −21.5098 −0.704200
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 53.5007 1.74779 0.873895 0.486115i \(-0.161586\pi\)
0.873895 + 0.486115i \(0.161586\pi\)
\(938\) 0 0
\(939\) 11.1458 0.363731
\(940\) 0 0
\(941\) −20.1906 −0.658193 −0.329097 0.944296i \(-0.606744\pi\)
−0.329097 + 0.944296i \(0.606744\pi\)
\(942\) 0 0
\(943\) 23.4974 0.765181
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35.4839 1.15307 0.576536 0.817071i \(-0.304404\pi\)
0.576536 + 0.817071i \(0.304404\pi\)
\(948\) 0 0
\(949\) 10.4034 0.337709
\(950\) 0 0
\(951\) −27.0960 −0.878647
\(952\) 0 0
\(953\) −1.02630 −0.0332450 −0.0166225 0.999862i \(-0.505291\pi\)
−0.0166225 + 0.999862i \(0.505291\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −27.3610 −0.884456
\(958\) 0 0
\(959\) 32.5959 1.05258
\(960\) 0 0
\(961\) 25.1367 0.810860
\(962\) 0 0
\(963\) 12.8673 0.414642
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 16.8465 0.541748 0.270874 0.962615i \(-0.412687\pi\)
0.270874 + 0.962615i \(0.412687\pi\)
\(968\) 0 0
\(969\) −4.52695 −0.145427
\(970\) 0 0
\(971\) 51.3153 1.64679 0.823394 0.567471i \(-0.192078\pi\)
0.823394 + 0.567471i \(0.192078\pi\)
\(972\) 0 0
\(973\) 34.0243 1.09077
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 50.2733 1.60839 0.804193 0.594368i \(-0.202598\pi\)
0.804193 + 0.594368i \(0.202598\pi\)
\(978\) 0 0
\(979\) −17.8640 −0.570937
\(980\) 0 0
\(981\) −11.1124 −0.354791
\(982\) 0 0
\(983\) −30.5319 −0.973815 −0.486908 0.873454i \(-0.661875\pi\)
−0.486908 + 0.873454i \(0.661875\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 22.9192 0.729525
\(988\) 0 0
\(989\) −53.4225 −1.69874
\(990\) 0 0
\(991\) −20.8876 −0.663517 −0.331759 0.943364i \(-0.607642\pi\)
−0.331759 + 0.943364i \(0.607642\pi\)
\(992\) 0 0
\(993\) −10.0670 −0.319467
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −14.7727 −0.467856 −0.233928 0.972254i \(-0.575158\pi\)
−0.233928 + 0.972254i \(0.575158\pi\)
\(998\) 0 0
\(999\) −8.69908 −0.275227
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.bu.1.1 4
5.4 even 2 7800.2.a.bx.1.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bu.1.1 4 1.1 even 1 trivial
7800.2.a.bx.1.4 yes 4 5.4 even 2