Properties

Label 9576.2.a.bi.1.2
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(76.4647449756\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.23607 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+1.23607 q^{5} +1.00000 q^{7} -2.00000 q^{11} -4.47214 q^{13} -1.23607 q^{17} -1.00000 q^{19} +2.00000 q^{23} -3.47214 q^{25} +5.70820 q^{29} -1.52786 q^{31} +1.23607 q^{35} +8.47214 q^{37} -8.47214 q^{41} +8.00000 q^{43} +1.70820 q^{47} +1.00000 q^{49} +11.2361 q^{53} -2.47214 q^{55} -8.94427 q^{59} -13.4164 q^{61} -5.52786 q^{65} -1.52786 q^{67} +7.70820 q^{71} +12.4721 q^{73} -2.00000 q^{77} +4.00000 q^{79} -13.7082 q^{83} -1.52786 q^{85} +4.47214 q^{89} -4.47214 q^{91} -1.23607 q^{95} -17.4164 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} + 2 q^{7} - 4 q^{11} + 2 q^{17} - 2 q^{19} + 4 q^{23} + 2 q^{25} - 2 q^{29} - 12 q^{31} - 2 q^{35} + 8 q^{37} - 8 q^{41} + 16 q^{43} - 10 q^{47} + 2 q^{49} + 18 q^{53} + 4 q^{55} - 20 q^{65} - 12 q^{67} + 2 q^{71} + 16 q^{73} - 4 q^{77} + 8 q^{79} - 14 q^{83} - 12 q^{85} + 2 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.23607 0.552786 0.276393 0.961045i \(-0.410861\pi\)
0.276393 + 0.961045i \(0.410861\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −4.47214 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.23607 −0.299791 −0.149895 0.988702i \(-0.547894\pi\)
−0.149895 + 0.988702i \(0.547894\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 0 0
\(25\) −3.47214 −0.694427
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.70820 1.05999 0.529993 0.848002i \(-0.322194\pi\)
0.529993 + 0.848002i \(0.322194\pi\)
\(30\) 0 0
\(31\) −1.52786 −0.274412 −0.137206 0.990543i \(-0.543812\pi\)
−0.137206 + 0.990543i \(0.543812\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.23607 0.208934
\(36\) 0 0
\(37\) 8.47214 1.39281 0.696405 0.717649i \(-0.254782\pi\)
0.696405 + 0.717649i \(0.254782\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.47214 −1.32313 −0.661563 0.749890i \(-0.730106\pi\)
−0.661563 + 0.749890i \(0.730106\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.70820 0.249167 0.124584 0.992209i \(-0.460241\pi\)
0.124584 + 0.992209i \(0.460241\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.2361 1.54339 0.771696 0.635991i \(-0.219409\pi\)
0.771696 + 0.635991i \(0.219409\pi\)
\(54\) 0 0
\(55\) −2.47214 −0.333343
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.94427 −1.16445 −0.582223 0.813029i \(-0.697817\pi\)
−0.582223 + 0.813029i \(0.697817\pi\)
\(60\) 0 0
\(61\) −13.4164 −1.71780 −0.858898 0.512148i \(-0.828850\pi\)
−0.858898 + 0.512148i \(0.828850\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.52786 −0.685647
\(66\) 0 0
\(67\) −1.52786 −0.186658 −0.0933292 0.995635i \(-0.529751\pi\)
−0.0933292 + 0.995635i \(0.529751\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.70820 0.914796 0.457398 0.889262i \(-0.348782\pi\)
0.457398 + 0.889262i \(0.348782\pi\)
\(72\) 0 0
\(73\) 12.4721 1.45975 0.729877 0.683579i \(-0.239578\pi\)
0.729877 + 0.683579i \(0.239578\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −13.7082 −1.50467 −0.752335 0.658780i \(-0.771073\pi\)
−0.752335 + 0.658780i \(0.771073\pi\)
\(84\) 0 0
\(85\) −1.52786 −0.165720
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.47214 0.474045 0.237023 0.971504i \(-0.423828\pi\)
0.237023 + 0.971504i \(0.423828\pi\)
\(90\) 0 0
\(91\) −4.47214 −0.468807
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.23607 −0.126818
\(96\) 0 0
\(97\) −17.4164 −1.76837 −0.884184 0.467139i \(-0.845285\pi\)
−0.884184 + 0.467139i \(0.845285\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.7639 −1.07105 −0.535526 0.844519i \(-0.679886\pi\)
−0.535526 + 0.844519i \(0.679886\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −18.1803 −1.75756 −0.878780 0.477227i \(-0.841642\pi\)
−0.878780 + 0.477227i \(0.841642\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.23607 −0.680712 −0.340356 0.940297i \(-0.610548\pi\)
−0.340356 + 0.940297i \(0.610548\pi\)
\(114\) 0 0
\(115\) 2.47214 0.230528
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.23607 −0.113310
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) −15.4164 −1.36798 −0.683992 0.729489i \(-0.739758\pi\)
−0.683992 + 0.729489i \(0.739758\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −15.2361 −1.33118 −0.665591 0.746317i \(-0.731820\pi\)
−0.665591 + 0.746317i \(0.731820\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.00000 −0.341743 −0.170872 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) 0 0
\(139\) 9.52786 0.808143 0.404071 0.914727i \(-0.367595\pi\)
0.404071 + 0.914727i \(0.367595\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.94427 0.747958
\(144\) 0 0
\(145\) 7.05573 0.585946
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.5279 1.10825 0.554123 0.832435i \(-0.313054\pi\)
0.554123 + 0.832435i \(0.313054\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.88854 −0.151691
\(156\) 0 0
\(157\) −3.52786 −0.281554 −0.140777 0.990041i \(-0.544960\pi\)
−0.140777 + 0.990041i \(0.544960\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.00000 0.157622
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −23.4164 −1.81202 −0.906008 0.423261i \(-0.860886\pi\)
−0.906008 + 0.423261i \(0.860886\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −20.4721 −1.55647 −0.778234 0.627975i \(-0.783884\pi\)
−0.778234 + 0.627975i \(0.783884\pi\)
\(174\) 0 0
\(175\) −3.47214 −0.262469
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.70820 −0.576138 −0.288069 0.957610i \(-0.593013\pi\)
−0.288069 + 0.957610i \(0.593013\pi\)
\(180\) 0 0
\(181\) −3.52786 −0.262224 −0.131112 0.991368i \(-0.541855\pi\)
−0.131112 + 0.991368i \(0.541855\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.4721 0.769927
\(186\) 0 0
\(187\) 2.47214 0.180780
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) 0 0
\(193\) −8.47214 −0.609838 −0.304919 0.952378i \(-0.598629\pi\)
−0.304919 + 0.952378i \(0.598629\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −20.9443 −1.48470 −0.742350 0.670012i \(-0.766289\pi\)
−0.742350 + 0.670012i \(0.766289\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.70820 0.400637
\(204\) 0 0
\(205\) −10.4721 −0.731406
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −6.47214 −0.445560 −0.222780 0.974869i \(-0.571513\pi\)
−0.222780 + 0.974869i \(0.571513\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.88854 0.674393
\(216\) 0 0
\(217\) −1.52786 −0.103718
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.52786 0.371844
\(222\) 0 0
\(223\) −13.5279 −0.905893 −0.452946 0.891538i \(-0.649627\pi\)
−0.452946 + 0.891538i \(0.649627\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.52786 0.366897 0.183449 0.983029i \(-0.441274\pi\)
0.183449 + 0.983029i \(0.441274\pi\)
\(228\) 0 0
\(229\) 14.9443 0.987545 0.493773 0.869591i \(-0.335618\pi\)
0.493773 + 0.869591i \(0.335618\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.41641 0.485865 0.242933 0.970043i \(-0.421891\pi\)
0.242933 + 0.970043i \(0.421891\pi\)
\(234\) 0 0
\(235\) 2.11146 0.137736
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 13.4164 0.867835 0.433918 0.900953i \(-0.357131\pi\)
0.433918 + 0.900953i \(0.357131\pi\)
\(240\) 0 0
\(241\) 21.4164 1.37955 0.689776 0.724023i \(-0.257709\pi\)
0.689776 + 0.724023i \(0.257709\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.23607 0.0789695
\(246\) 0 0
\(247\) 4.47214 0.284555
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.7639 0.805652 0.402826 0.915277i \(-0.368028\pi\)
0.402826 + 0.915277i \(0.368028\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.94427 0.183659 0.0918293 0.995775i \(-0.470729\pi\)
0.0918293 + 0.995775i \(0.470729\pi\)
\(258\) 0 0
\(259\) 8.47214 0.526433
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −20.4721 −1.26237 −0.631183 0.775634i \(-0.717430\pi\)
−0.631183 + 0.775634i \(0.717430\pi\)
\(264\) 0 0
\(265\) 13.8885 0.853166
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.00000 −0.121942 −0.0609711 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 0 0
\(271\) 7.41641 0.450515 0.225257 0.974299i \(-0.427678\pi\)
0.225257 + 0.974299i \(0.427678\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.94427 0.418755
\(276\) 0 0
\(277\) 21.4164 1.28679 0.643394 0.765536i \(-0.277526\pi\)
0.643394 + 0.765536i \(0.277526\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.2361 −0.670288 −0.335144 0.942167i \(-0.608785\pi\)
−0.335144 + 0.942167i \(0.608785\pi\)
\(282\) 0 0
\(283\) 0.944272 0.0561311 0.0280656 0.999606i \(-0.491065\pi\)
0.0280656 + 0.999606i \(0.491065\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.47214 −0.500094
\(288\) 0 0
\(289\) −15.4721 −0.910126
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.52786 −0.439783 −0.219891 0.975524i \(-0.570570\pi\)
−0.219891 + 0.975524i \(0.570570\pi\)
\(294\) 0 0
\(295\) −11.0557 −0.643689
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.94427 −0.517261
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −16.5836 −0.949574
\(306\) 0 0
\(307\) −17.5279 −1.00037 −0.500184 0.865919i \(-0.666734\pi\)
−0.500184 + 0.865919i \(0.666734\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.34752 −0.0764111 −0.0382055 0.999270i \(-0.512164\pi\)
−0.0382055 + 0.999270i \(0.512164\pi\)
\(312\) 0 0
\(313\) 5.41641 0.306153 0.153077 0.988214i \(-0.451082\pi\)
0.153077 + 0.988214i \(0.451082\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.6525 0.822965 0.411483 0.911418i \(-0.365011\pi\)
0.411483 + 0.911418i \(0.365011\pi\)
\(318\) 0 0
\(319\) −11.4164 −0.639196
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.23607 0.0687767
\(324\) 0 0
\(325\) 15.5279 0.861331
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.70820 0.0941763
\(330\) 0 0
\(331\) −11.0557 −0.607678 −0.303839 0.952723i \(-0.598268\pi\)
−0.303839 + 0.952723i \(0.598268\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.88854 −0.103182
\(336\) 0 0
\(337\) −6.94427 −0.378279 −0.189139 0.981950i \(-0.560570\pi\)
−0.189139 + 0.981950i \(0.560570\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.05573 0.165477
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −30.3607 −1.62985 −0.814923 0.579569i \(-0.803221\pi\)
−0.814923 + 0.579569i \(0.803221\pi\)
\(348\) 0 0
\(349\) 34.9443 1.87052 0.935262 0.353956i \(-0.115164\pi\)
0.935262 + 0.353956i \(0.115164\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −30.1803 −1.60634 −0.803169 0.595752i \(-0.796854\pi\)
−0.803169 + 0.595752i \(0.796854\pi\)
\(354\) 0 0
\(355\) 9.52786 0.505687
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.9443 −0.788729 −0.394364 0.918954i \(-0.629035\pi\)
−0.394364 + 0.918954i \(0.629035\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15.4164 0.806932
\(366\) 0 0
\(367\) 20.9443 1.09328 0.546641 0.837367i \(-0.315906\pi\)
0.546641 + 0.837367i \(0.315906\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 11.2361 0.583348
\(372\) 0 0
\(373\) 31.8885 1.65113 0.825563 0.564310i \(-0.190858\pi\)
0.825563 + 0.564310i \(0.190858\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −25.5279 −1.31475
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.52786 −0.0780702 −0.0390351 0.999238i \(-0.512428\pi\)
−0.0390351 + 0.999238i \(0.512428\pi\)
\(384\) 0 0
\(385\) −2.47214 −0.125992
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −24.3607 −1.23514 −0.617568 0.786518i \(-0.711882\pi\)
−0.617568 + 0.786518i \(0.711882\pi\)
\(390\) 0 0
\(391\) −2.47214 −0.125021
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.94427 0.248773
\(396\) 0 0
\(397\) −19.8885 −0.998177 −0.499089 0.866551i \(-0.666332\pi\)
−0.499089 + 0.866551i \(0.666332\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.76393 −0.237899 −0.118950 0.992900i \(-0.537953\pi\)
−0.118950 + 0.992900i \(0.537953\pi\)
\(402\) 0 0
\(403\) 6.83282 0.340367
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −16.9443 −0.839896
\(408\) 0 0
\(409\) 35.3050 1.74572 0.872859 0.487973i \(-0.162264\pi\)
0.872859 + 0.487973i \(0.162264\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.94427 −0.440119
\(414\) 0 0
\(415\) −16.9443 −0.831762
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −27.5967 −1.34819 −0.674095 0.738645i \(-0.735466\pi\)
−0.674095 + 0.738645i \(0.735466\pi\)
\(420\) 0 0
\(421\) 15.5279 0.756782 0.378391 0.925646i \(-0.376478\pi\)
0.378391 + 0.925646i \(0.376478\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.29180 0.208183
\(426\) 0 0
\(427\) −13.4164 −0.649265
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 28.6525 1.38014 0.690071 0.723742i \(-0.257579\pi\)
0.690071 + 0.723742i \(0.257579\pi\)
\(432\) 0 0
\(433\) 10.5836 0.508615 0.254307 0.967123i \(-0.418152\pi\)
0.254307 + 0.967123i \(0.418152\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) 12.3607 0.589943 0.294972 0.955506i \(-0.404690\pi\)
0.294972 + 0.955506i \(0.404690\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.4164 0.637433 0.318716 0.947850i \(-0.396748\pi\)
0.318716 + 0.947850i \(0.396748\pi\)
\(444\) 0 0
\(445\) 5.52786 0.262046
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 23.2361 1.09658 0.548289 0.836289i \(-0.315279\pi\)
0.548289 + 0.836289i \(0.315279\pi\)
\(450\) 0 0
\(451\) 16.9443 0.797875
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.52786 −0.259150
\(456\) 0 0
\(457\) 21.4164 1.00182 0.500909 0.865500i \(-0.332999\pi\)
0.500909 + 0.865500i \(0.332999\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 28.0689 1.30730 0.653649 0.756798i \(-0.273237\pi\)
0.653649 + 0.756798i \(0.273237\pi\)
\(462\) 0 0
\(463\) −41.8885 −1.94673 −0.973363 0.229270i \(-0.926366\pi\)
−0.973363 + 0.229270i \(0.926366\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.7639 0.960840 0.480420 0.877039i \(-0.340484\pi\)
0.480420 + 0.877039i \(0.340484\pi\)
\(468\) 0 0
\(469\) −1.52786 −0.0705502
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16.0000 −0.735681
\(474\) 0 0
\(475\) 3.47214 0.159313
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −25.7082 −1.17464 −0.587319 0.809356i \(-0.699817\pi\)
−0.587319 + 0.809356i \(0.699817\pi\)
\(480\) 0 0
\(481\) −37.8885 −1.72757
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −21.5279 −0.977530
\(486\) 0 0
\(487\) −39.4164 −1.78613 −0.893064 0.449930i \(-0.851449\pi\)
−0.893064 + 0.449930i \(0.851449\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 31.3050 1.41277 0.706386 0.707826i \(-0.250324\pi\)
0.706386 + 0.707826i \(0.250324\pi\)
\(492\) 0 0
\(493\) −7.05573 −0.317774
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.70820 0.345760
\(498\) 0 0
\(499\) 5.88854 0.263607 0.131804 0.991276i \(-0.457923\pi\)
0.131804 + 0.991276i \(0.457923\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.29180 −0.102186 −0.0510931 0.998694i \(-0.516271\pi\)
−0.0510931 + 0.998694i \(0.516271\pi\)
\(504\) 0 0
\(505\) −13.3050 −0.592063
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −27.8885 −1.23614 −0.618069 0.786124i \(-0.712085\pi\)
−0.618069 + 0.786124i \(0.712085\pi\)
\(510\) 0 0
\(511\) 12.4721 0.551735
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.94427 0.217871
\(516\) 0 0
\(517\) −3.41641 −0.150253
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.11146 0.355369 0.177685 0.984087i \(-0.443139\pi\)
0.177685 + 0.984087i \(0.443139\pi\)
\(522\) 0 0
\(523\) 41.3050 1.80614 0.903070 0.429494i \(-0.141308\pi\)
0.903070 + 0.429494i \(0.141308\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.88854 0.0822663
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 37.8885 1.64114
\(534\) 0 0
\(535\) −22.4721 −0.971555
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.3607 0.529473
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.70820 −0.243178
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 33.3050 1.41118 0.705588 0.708622i \(-0.250683\pi\)
0.705588 + 0.708622i \(0.250683\pi\)
\(558\) 0 0
\(559\) −35.7771 −1.51321
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.4721 0.778508 0.389254 0.921131i \(-0.372733\pi\)
0.389254 + 0.921131i \(0.372733\pi\)
\(564\) 0 0
\(565\) −8.94427 −0.376288
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −45.1246 −1.89172 −0.945861 0.324572i \(-0.894780\pi\)
−0.945861 + 0.324572i \(0.894780\pi\)
\(570\) 0 0
\(571\) −13.8885 −0.581217 −0.290609 0.956842i \(-0.593858\pi\)
−0.290609 + 0.956842i \(0.593858\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.94427 −0.289596
\(576\) 0 0
\(577\) −23.5279 −0.979478 −0.489739 0.871869i \(-0.662908\pi\)
−0.489739 + 0.871869i \(0.662908\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −13.7082 −0.568712
\(582\) 0 0
\(583\) −22.4721 −0.930701
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −45.1246 −1.86249 −0.931246 0.364391i \(-0.881277\pi\)
−0.931246 + 0.364391i \(0.881277\pi\)
\(588\) 0 0
\(589\) 1.52786 0.0629545
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −46.5410 −1.91121 −0.955605 0.294650i \(-0.904797\pi\)
−0.955605 + 0.294650i \(0.904797\pi\)
\(594\) 0 0
\(595\) −1.52786 −0.0626363
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −37.5967 −1.53616 −0.768081 0.640353i \(-0.778788\pi\)
−0.768081 + 0.640353i \(0.778788\pi\)
\(600\) 0 0
\(601\) 27.3050 1.11379 0.556896 0.830582i \(-0.311992\pi\)
0.556896 + 0.830582i \(0.311992\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −8.65248 −0.351773
\(606\) 0 0
\(607\) −11.0557 −0.448738 −0.224369 0.974504i \(-0.572032\pi\)
−0.224369 + 0.974504i \(0.572032\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.63932 −0.309054
\(612\) 0 0
\(613\) 42.3607 1.71093 0.855466 0.517859i \(-0.173271\pi\)
0.855466 + 0.517859i \(0.173271\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.88854 −0.237064 −0.118532 0.992950i \(-0.537819\pi\)
−0.118532 + 0.992950i \(0.537819\pi\)
\(618\) 0 0
\(619\) 35.4164 1.42351 0.711753 0.702430i \(-0.247902\pi\)
0.711753 + 0.702430i \(0.247902\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.47214 0.179172
\(624\) 0 0
\(625\) 4.41641 0.176656
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10.4721 −0.417551
\(630\) 0 0
\(631\) 8.94427 0.356066 0.178033 0.984025i \(-0.443027\pi\)
0.178033 + 0.984025i \(0.443027\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −19.0557 −0.756204
\(636\) 0 0
\(637\) −4.47214 −0.177192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 27.2361 1.07576 0.537880 0.843021i \(-0.319225\pi\)
0.537880 + 0.843021i \(0.319225\pi\)
\(642\) 0 0
\(643\) −15.0557 −0.593740 −0.296870 0.954918i \(-0.595943\pi\)
−0.296870 + 0.954918i \(0.595943\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.7082 0.696181 0.348091 0.937461i \(-0.386830\pi\)
0.348091 + 0.937461i \(0.386830\pi\)
\(648\) 0 0
\(649\) 17.8885 0.702187
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −48.7214 −1.90661 −0.953307 0.302003i \(-0.902345\pi\)
−0.953307 + 0.302003i \(0.902345\pi\)
\(654\) 0 0
\(655\) −18.8328 −0.735859
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −30.7639 −1.19839 −0.599196 0.800602i \(-0.704513\pi\)
−0.599196 + 0.800602i \(0.704513\pi\)
\(660\) 0 0
\(661\) −36.2492 −1.40993 −0.704966 0.709241i \(-0.749038\pi\)
−0.704966 + 0.709241i \(0.749038\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.23607 −0.0479327
\(666\) 0 0
\(667\) 11.4164 0.442045
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 26.8328 1.03587
\(672\) 0 0
\(673\) −18.3607 −0.707752 −0.353876 0.935292i \(-0.615137\pi\)
−0.353876 + 0.935292i \(0.615137\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 0 0
\(679\) −17.4164 −0.668380
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.7639 −0.717982 −0.358991 0.933341i \(-0.616879\pi\)
−0.358991 + 0.933341i \(0.616879\pi\)
\(684\) 0 0
\(685\) −4.94427 −0.188911
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −50.2492 −1.91434
\(690\) 0 0
\(691\) −24.3607 −0.926724 −0.463362 0.886169i \(-0.653357\pi\)
−0.463362 + 0.886169i \(0.653357\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 11.7771 0.446730
\(696\) 0 0
\(697\) 10.4721 0.396660
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27.7771 −1.04913 −0.524563 0.851372i \(-0.675771\pi\)
−0.524563 + 0.851372i \(0.675771\pi\)
\(702\) 0 0
\(703\) −8.47214 −0.319533
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.7639 −0.404819
\(708\) 0 0
\(709\) 35.3050 1.32591 0.662953 0.748661i \(-0.269303\pi\)
0.662953 + 0.748661i \(0.269303\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.05573 −0.114438
\(714\) 0 0
\(715\) 11.0557 0.413461
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −32.7639 −1.22189 −0.610944 0.791674i \(-0.709210\pi\)
−0.610944 + 0.791674i \(0.709210\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19.8197 −0.736084
\(726\) 0 0
\(727\) 23.4164 0.868466 0.434233 0.900800i \(-0.357019\pi\)
0.434233 + 0.900800i \(0.357019\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −9.88854 −0.365741
\(732\) 0 0
\(733\) 37.4164 1.38201 0.691003 0.722852i \(-0.257169\pi\)
0.691003 + 0.722852i \(0.257169\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.05573 0.112559
\(738\) 0 0
\(739\) 24.0000 0.882854 0.441427 0.897297i \(-0.354472\pi\)
0.441427 + 0.897297i \(0.354472\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 49.5967 1.81953 0.909764 0.415126i \(-0.136262\pi\)
0.909764 + 0.415126i \(0.136262\pi\)
\(744\) 0 0
\(745\) 16.7214 0.612623
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.1803 −0.664295
\(750\) 0 0
\(751\) −32.9443 −1.20215 −0.601077 0.799191i \(-0.705261\pi\)
−0.601077 + 0.799191i \(0.705261\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.94427 0.179940
\(756\) 0 0
\(757\) −15.8885 −0.577479 −0.288739 0.957408i \(-0.593236\pi\)
−0.288739 + 0.957408i \(0.593236\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 25.2361 0.914807 0.457403 0.889259i \(-0.348780\pi\)
0.457403 + 0.889259i \(0.348780\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 40.0000 1.44432
\(768\) 0 0
\(769\) 19.5279 0.704193 0.352096 0.935964i \(-0.385469\pi\)
0.352096 + 0.935964i \(0.385469\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 44.2492 1.59153 0.795767 0.605603i \(-0.207068\pi\)
0.795767 + 0.605603i \(0.207068\pi\)
\(774\) 0 0
\(775\) 5.30495 0.190559
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.47214 0.303546
\(780\) 0 0
\(781\) −15.4164 −0.551642
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.36068 −0.155639
\(786\) 0 0
\(787\) −21.5279 −0.767385 −0.383693 0.923461i \(-0.625348\pi\)
−0.383693 + 0.923461i \(0.625348\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.23607 −0.257285
\(792\) 0 0
\(793\) 60.0000 2.13066
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.4164 0.758608 0.379304 0.925272i \(-0.376163\pi\)
0.379304 + 0.925272i \(0.376163\pi\)
\(798\) 0 0
\(799\) −2.11146 −0.0746979
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −24.9443 −0.880264
\(804\) 0 0
\(805\) 2.47214 0.0871313
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.88854 −0.0663977 −0.0331988 0.999449i \(-0.510569\pi\)
−0.0331988 + 0.999449i \(0.510569\pi\)
\(810\) 0 0
\(811\) −3.05573 −0.107301 −0.0536506 0.998560i \(-0.517086\pi\)
−0.0536506 + 0.998560i \(0.517086\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −19.7771 −0.692761
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30.2492 −1.05571 −0.527853 0.849336i \(-0.677003\pi\)
−0.527853 + 0.849336i \(0.677003\pi\)
\(822\) 0 0
\(823\) −42.8328 −1.49306 −0.746529 0.665353i \(-0.768281\pi\)
−0.746529 + 0.665353i \(0.768281\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26.7639 0.930673 0.465337 0.885134i \(-0.345933\pi\)
0.465337 + 0.885134i \(0.345933\pi\)
\(828\) 0 0
\(829\) 1.41641 0.0491939 0.0245969 0.999697i \(-0.492170\pi\)
0.0245969 + 0.999697i \(0.492170\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.23607 −0.0428272
\(834\) 0 0
\(835\) −28.9443 −1.00166
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −8.94427 −0.308791 −0.154395 0.988009i \(-0.549343\pi\)
−0.154395 + 0.988009i \(0.549343\pi\)
\(840\) 0 0
\(841\) 3.58359 0.123572
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.65248 0.297654
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 16.9443 0.580842
\(852\) 0 0
\(853\) −29.7771 −1.01955 −0.509774 0.860308i \(-0.670271\pi\)
−0.509774 + 0.860308i \(0.670271\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 32.2492 1.10161 0.550806 0.834633i \(-0.314320\pi\)
0.550806 + 0.834633i \(0.314320\pi\)
\(858\) 0 0
\(859\) −7.05573 −0.240738 −0.120369 0.992729i \(-0.538408\pi\)
−0.120369 + 0.992729i \(0.538408\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 47.1246 1.60414 0.802070 0.597230i \(-0.203732\pi\)
0.802070 + 0.597230i \(0.203732\pi\)
\(864\) 0 0
\(865\) −25.3050 −0.860394
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −8.00000 −0.271381
\(870\) 0 0
\(871\) 6.83282 0.231521
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10.4721 −0.354023
\(876\) 0 0
\(877\) 28.8328 0.973615 0.486808 0.873509i \(-0.338161\pi\)
0.486808 + 0.873509i \(0.338161\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −46.1803 −1.55586 −0.777928 0.628354i \(-0.783729\pi\)
−0.777928 + 0.628354i \(0.783729\pi\)
\(882\) 0 0
\(883\) 5.88854 0.198165 0.0990826 0.995079i \(-0.468409\pi\)
0.0990826 + 0.995079i \(0.468409\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −24.5836 −0.825436 −0.412718 0.910859i \(-0.635421\pi\)
−0.412718 + 0.910859i \(0.635421\pi\)
\(888\) 0 0
\(889\) −15.4164 −0.517050
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.70820 −0.0571629
\(894\) 0 0
\(895\) −9.52786 −0.318481
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −8.72136 −0.290874
\(900\) 0 0
\(901\) −13.8885 −0.462694
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.36068 −0.144954
\(906\) 0 0
\(907\) −25.5279 −0.847639 −0.423819 0.905747i \(-0.639311\pi\)
−0.423819 + 0.905747i \(0.639311\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −26.5410 −0.879343 −0.439672 0.898159i \(-0.644905\pi\)
−0.439672 + 0.898159i \(0.644905\pi\)
\(912\) 0 0
\(913\) 27.4164 0.907351
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15.2361 −0.503139
\(918\) 0 0
\(919\) −35.7771 −1.18018 −0.590089 0.807338i \(-0.700907\pi\)
−0.590089 + 0.807338i \(0.700907\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −34.4721 −1.13466
\(924\) 0 0
\(925\) −29.4164 −0.967206
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −6.40325 −0.210084 −0.105042 0.994468i \(-0.533498\pi\)
−0.105042 + 0.994468i \(0.533498\pi\)
\(930\) 0 0
\(931\) −1.00000 −0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 3.05573 0.0999330
\(936\) 0 0
\(937\) 16.1115 0.526338 0.263169 0.964750i \(-0.415232\pi\)
0.263169 + 0.964750i \(0.415232\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 12.8328 0.418338 0.209169 0.977880i \(-0.432924\pi\)
0.209169 + 0.977880i \(0.432924\pi\)
\(942\) 0 0
\(943\) −16.9443 −0.551781
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −26.0000 −0.844886 −0.422443 0.906389i \(-0.638827\pi\)
−0.422443 + 0.906389i \(0.638827\pi\)
\(948\) 0 0
\(949\) −55.7771 −1.81060
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 13.3475 0.432369 0.216184 0.976353i \(-0.430639\pi\)
0.216184 + 0.976353i \(0.430639\pi\)
\(954\) 0 0
\(955\) −12.3607 −0.399982
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.00000 −0.129167
\(960\) 0 0
\(961\) −28.6656 −0.924698
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −10.4721 −0.337110
\(966\) 0 0
\(967\) 18.8328 0.605623 0.302811 0.953051i \(-0.402075\pi\)
0.302811 + 0.953051i \(0.402075\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −46.8328 −1.50294 −0.751468 0.659769i \(-0.770654\pi\)
−0.751468 + 0.659769i \(0.770654\pi\)
\(972\) 0 0
\(973\) 9.52786 0.305449
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 50.0689 1.60185 0.800923 0.598768i \(-0.204343\pi\)
0.800923 + 0.598768i \(0.204343\pi\)
\(978\) 0 0
\(979\) −8.94427 −0.285860
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 48.7214 1.55397 0.776985 0.629519i \(-0.216748\pi\)
0.776985 + 0.629519i \(0.216748\pi\)
\(984\) 0 0
\(985\) −14.8328 −0.472613
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) 52.3607 1.66329 0.831646 0.555306i \(-0.187399\pi\)
0.831646 + 0.555306i \(0.187399\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −25.8885 −0.820722
\(996\) 0 0
\(997\) −16.4721 −0.521678 −0.260839 0.965382i \(-0.583999\pi\)
−0.260839 + 0.965382i \(0.583999\pi\)
\(998\) 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 9576.2.a.bi.1.2 2
3.2 odd 2 9576.2.a.bv.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bi.1.2 2 1.1 even 1 trivial
9576.2.a.bv.1.1 yes 2 3.2 odd 2