Properties

Label 9200.2.a.bu.1.1
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.618034 q^{3} +1.61803 q^{7} -2.61803 q^{9} +O(q^{10})\) \(q-0.618034 q^{3} +1.61803 q^{7} -2.61803 q^{9} -3.85410 q^{11} -4.09017 q^{13} +5.09017 q^{17} +4.85410 q^{19} -1.00000 q^{21} +1.00000 q^{23} +3.47214 q^{27} -4.76393 q^{29} +2.09017 q^{31} +2.38197 q^{33} +2.47214 q^{37} +2.52786 q^{39} -12.3262 q^{41} +9.70820 q^{47} -4.38197 q^{49} -3.14590 q^{51} +8.47214 q^{53} -3.00000 q^{57} +11.7082 q^{59} +6.32624 q^{61} -4.23607 q^{63} +5.52786 q^{67} -0.618034 q^{69} -7.09017 q^{71} +1.23607 q^{73} -6.23607 q^{77} -10.4721 q^{79} +5.70820 q^{81} +10.9443 q^{83} +2.94427 q^{87} -1.52786 q^{89} -6.61803 q^{91} -1.29180 q^{93} -14.6180 q^{97} +10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + q^{7} - 3 q^{9} + O(q^{10}) \) \( 2 q + q^{3} + q^{7} - 3 q^{9} - q^{11} + 3 q^{13} - q^{17} + 3 q^{19} - 2 q^{21} + 2 q^{23} - 2 q^{27} - 14 q^{29} - 7 q^{31} + 7 q^{33} - 4 q^{37} + 14 q^{39} - 9 q^{41} + 6 q^{47} - 11 q^{49} - 13 q^{51} + 8 q^{53} - 6 q^{57} + 10 q^{59} - 3 q^{61} - 4 q^{63} + 20 q^{67} + q^{69} - 3 q^{71} - 2 q^{73} - 8 q^{77} - 12 q^{79} - 2 q^{81} + 4 q^{83} - 12 q^{87} - 12 q^{89} - 11 q^{91} - 16 q^{93} - 27 q^{97} + 9 q^{99} + O(q^{100}) \)

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
\(3\) −0.618034 −0.356822 −0.178411 0.983956i \(-0.557096\pi\)
−0.178411 + 0.983956i \(0.557096\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.61803 0.611559 0.305780 0.952102i \(-0.401083\pi\)
0.305780 + 0.952102i \(0.401083\pi\)
\(8\) 0 0
\(9\) −2.61803 −0.872678
\(10\) 0 0
\(11\) −3.85410 −1.16206 −0.581028 0.813884i \(-0.697349\pi\)
−0.581028 + 0.813884i \(0.697349\pi\)
\(12\) 0 0
\(13\) −4.09017 −1.13441 −0.567205 0.823577i \(-0.691975\pi\)
−0.567205 + 0.823577i \(0.691975\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.09017 1.23455 0.617274 0.786748i \(-0.288237\pi\)
0.617274 + 0.786748i \(0.288237\pi\)
\(18\) 0 0
\(19\) 4.85410 1.11361 0.556804 0.830644i \(-0.312028\pi\)
0.556804 + 0.830644i \(0.312028\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.47214 0.668213
\(28\) 0 0
\(29\) −4.76393 −0.884640 −0.442320 0.896857i \(-0.645844\pi\)
−0.442320 + 0.896857i \(0.645844\pi\)
\(30\) 0 0
\(31\) 2.09017 0.375406 0.187703 0.982226i \(-0.439896\pi\)
0.187703 + 0.982226i \(0.439896\pi\)
\(32\) 0 0
\(33\) 2.38197 0.414647
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.47214 0.406417 0.203208 0.979136i \(-0.434863\pi\)
0.203208 + 0.979136i \(0.434863\pi\)
\(38\) 0 0
\(39\) 2.52786 0.404782
\(40\) 0 0
\(41\) −12.3262 −1.92503 −0.962517 0.271220i \(-0.912573\pi\)
−0.962517 + 0.271220i \(0.912573\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.70820 1.41609 0.708044 0.706169i \(-0.249578\pi\)
0.708044 + 0.706169i \(0.249578\pi\)
\(48\) 0 0
\(49\) −4.38197 −0.625995
\(50\) 0 0
\(51\) −3.14590 −0.440514
\(52\) 0 0
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.00000 −0.397360
\(58\) 0 0
\(59\) 11.7082 1.52428 0.762139 0.647413i \(-0.224149\pi\)
0.762139 + 0.647413i \(0.224149\pi\)
\(60\) 0 0
\(61\) 6.32624 0.809992 0.404996 0.914319i \(-0.367273\pi\)
0.404996 + 0.914319i \(0.367273\pi\)
\(62\) 0 0
\(63\) −4.23607 −0.533694
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.52786 0.675336 0.337668 0.941265i \(-0.390362\pi\)
0.337668 + 0.941265i \(0.390362\pi\)
\(68\) 0 0
\(69\) −0.618034 −0.0744025
\(70\) 0 0
\(71\) −7.09017 −0.841448 −0.420724 0.907189i \(-0.638224\pi\)
−0.420724 + 0.907189i \(0.638224\pi\)
\(72\) 0 0
\(73\) 1.23607 0.144671 0.0723354 0.997380i \(-0.476955\pi\)
0.0723354 + 0.997380i \(0.476955\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.23607 −0.710666
\(78\) 0 0
\(79\) −10.4721 −1.17821 −0.589104 0.808057i \(-0.700519\pi\)
−0.589104 + 0.808057i \(0.700519\pi\)
\(80\) 0 0
\(81\) 5.70820 0.634245
\(82\) 0 0
\(83\) 10.9443 1.20129 0.600645 0.799516i \(-0.294911\pi\)
0.600645 + 0.799516i \(0.294911\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.94427 0.315659
\(88\) 0 0
\(89\) −1.52786 −0.161953 −0.0809766 0.996716i \(-0.525804\pi\)
−0.0809766 + 0.996716i \(0.525804\pi\)
\(90\) 0 0
\(91\) −6.61803 −0.693758
\(92\) 0 0
\(93\) −1.29180 −0.133953
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.6180 −1.48424 −0.742118 0.670269i \(-0.766179\pi\)
−0.742118 + 0.670269i \(0.766179\pi\)
\(98\) 0 0
\(99\) 10.0902 1.01410
\(100\) 0 0
\(101\) −13.7082 −1.36402 −0.682009 0.731344i \(-0.738893\pi\)
−0.682009 + 0.731344i \(0.738893\pi\)
\(102\) 0 0
\(103\) −3.56231 −0.351004 −0.175502 0.984479i \(-0.556155\pi\)
−0.175502 + 0.984479i \(0.556155\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.18034 −0.404129 −0.202064 0.979372i \(-0.564765\pi\)
−0.202064 + 0.979372i \(0.564765\pi\)
\(108\) 0 0
\(109\) 8.56231 0.820120 0.410060 0.912059i \(-0.365508\pi\)
0.410060 + 0.912059i \(0.365508\pi\)
\(110\) 0 0
\(111\) −1.52786 −0.145018
\(112\) 0 0
\(113\) −18.9443 −1.78213 −0.891064 0.453878i \(-0.850040\pi\)
−0.891064 + 0.453878i \(0.850040\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 10.7082 0.989974
\(118\) 0 0
\(119\) 8.23607 0.754999
\(120\) 0 0
\(121\) 3.85410 0.350373
\(122\) 0 0
\(123\) 7.61803 0.686895
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −6.18034 −0.548416 −0.274208 0.961670i \(-0.588416\pi\)
−0.274208 + 0.961670i \(0.588416\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 14.9443 1.30569 0.652844 0.757493i \(-0.273576\pi\)
0.652844 + 0.757493i \(0.273576\pi\)
\(132\) 0 0
\(133\) 7.85410 0.681037
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.32624 −0.455051 −0.227526 0.973772i \(-0.573064\pi\)
−0.227526 + 0.973772i \(0.573064\pi\)
\(138\) 0 0
\(139\) −17.2361 −1.46194 −0.730972 0.682407i \(-0.760933\pi\)
−0.730972 + 0.682407i \(0.760933\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 15.7639 1.31825
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2.70820 0.223369
\(148\) 0 0
\(149\) −1.14590 −0.0938756 −0.0469378 0.998898i \(-0.514946\pi\)
−0.0469378 + 0.998898i \(0.514946\pi\)
\(150\) 0 0
\(151\) −17.5623 −1.42920 −0.714600 0.699533i \(-0.753391\pi\)
−0.714600 + 0.699533i \(0.753391\pi\)
\(152\) 0 0
\(153\) −13.3262 −1.07736
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.70820 −0.774799 −0.387400 0.921912i \(-0.626627\pi\)
−0.387400 + 0.921912i \(0.626627\pi\)
\(158\) 0 0
\(159\) −5.23607 −0.415247
\(160\) 0 0
\(161\) 1.61803 0.127519
\(162\) 0 0
\(163\) 3.61803 0.283386 0.141693 0.989911i \(-0.454745\pi\)
0.141693 + 0.989911i \(0.454745\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 3.72949 0.286884
\(170\) 0 0
\(171\) −12.7082 −0.971821
\(172\) 0 0
\(173\) 21.5623 1.63935 0.819676 0.572828i \(-0.194154\pi\)
0.819676 + 0.572828i \(0.194154\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.23607 −0.543896
\(178\) 0 0
\(179\) 20.1803 1.50835 0.754175 0.656674i \(-0.228037\pi\)
0.754175 + 0.656674i \(0.228037\pi\)
\(180\) 0 0
\(181\) −18.8541 −1.40141 −0.700707 0.713449i \(-0.747132\pi\)
−0.700707 + 0.713449i \(0.747132\pi\)
\(182\) 0 0
\(183\) −3.90983 −0.289023
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −19.6180 −1.43461
\(188\) 0 0
\(189\) 5.61803 0.408652
\(190\) 0 0
\(191\) 0.291796 0.0211136 0.0105568 0.999944i \(-0.496640\pi\)
0.0105568 + 0.999944i \(0.496640\pi\)
\(192\) 0 0
\(193\) −5.23607 −0.376900 −0.188450 0.982083i \(-0.560346\pi\)
−0.188450 + 0.982083i \(0.560346\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.43769 0.173679 0.0868393 0.996222i \(-0.472323\pi\)
0.0868393 + 0.996222i \(0.472323\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) −3.41641 −0.240975
\(202\) 0 0
\(203\) −7.70820 −0.541010
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.61803 −0.181966
\(208\) 0 0
\(209\) −18.7082 −1.29407
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 0 0
\(213\) 4.38197 0.300247
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.38197 0.229583
\(218\) 0 0
\(219\) −0.763932 −0.0516217
\(220\) 0 0
\(221\) −20.8197 −1.40048
\(222\) 0 0
\(223\) −3.05573 −0.204627 −0.102313 0.994752i \(-0.532624\pi\)
−0.102313 + 0.994752i \(0.532624\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.2361 −1.54223 −0.771116 0.636695i \(-0.780301\pi\)
−0.771116 + 0.636695i \(0.780301\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 3.85410 0.253581
\(232\) 0 0
\(233\) −19.7082 −1.29113 −0.645564 0.763706i \(-0.723378\pi\)
−0.645564 + 0.763706i \(0.723378\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 6.47214 0.420410
\(238\) 0 0
\(239\) −24.3607 −1.57576 −0.787881 0.615828i \(-0.788822\pi\)
−0.787881 + 0.615828i \(0.788822\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −13.9443 −0.894525
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −19.8541 −1.26329
\(248\) 0 0
\(249\) −6.76393 −0.428647
\(250\) 0 0
\(251\) −12.8541 −0.811344 −0.405672 0.914019i \(-0.632962\pi\)
−0.405672 + 0.914019i \(0.632962\pi\)
\(252\) 0 0
\(253\) −3.85410 −0.242305
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 30.1803 1.88260 0.941299 0.337574i \(-0.109606\pi\)
0.941299 + 0.337574i \(0.109606\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 12.4721 0.772006
\(262\) 0 0
\(263\) −21.7426 −1.34071 −0.670354 0.742041i \(-0.733858\pi\)
−0.670354 + 0.742041i \(0.733858\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.944272 0.0577885
\(268\) 0 0
\(269\) 8.18034 0.498764 0.249382 0.968405i \(-0.419773\pi\)
0.249382 + 0.968405i \(0.419773\pi\)
\(270\) 0 0
\(271\) 14.6738 0.891368 0.445684 0.895190i \(-0.352961\pi\)
0.445684 + 0.895190i \(0.352961\pi\)
\(272\) 0 0
\(273\) 4.09017 0.247548
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2.58359 −0.155233 −0.0776165 0.996983i \(-0.524731\pi\)
−0.0776165 + 0.996983i \(0.524731\pi\)
\(278\) 0 0
\(279\) −5.47214 −0.327608
\(280\) 0 0
\(281\) 27.2361 1.62477 0.812384 0.583123i \(-0.198169\pi\)
0.812384 + 0.583123i \(0.198169\pi\)
\(282\) 0 0
\(283\) −9.05573 −0.538307 −0.269154 0.963097i \(-0.586744\pi\)
−0.269154 + 0.963097i \(0.586744\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −19.9443 −1.17727
\(288\) 0 0
\(289\) 8.90983 0.524108
\(290\) 0 0
\(291\) 9.03444 0.529608
\(292\) 0 0
\(293\) −15.8885 −0.928219 −0.464109 0.885778i \(-0.653626\pi\)
−0.464109 + 0.885778i \(0.653626\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −13.3820 −0.776500
\(298\) 0 0
\(299\) −4.09017 −0.236541
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 8.47214 0.486711
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 27.4508 1.56670 0.783351 0.621579i \(-0.213509\pi\)
0.783351 + 0.621579i \(0.213509\pi\)
\(308\) 0 0
\(309\) 2.20163 0.125246
\(310\) 0 0
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 11.7984 0.666884 0.333442 0.942771i \(-0.391790\pi\)
0.333442 + 0.942771i \(0.391790\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.0901699 −0.00506445 −0.00253222 0.999997i \(-0.500806\pi\)
−0.00253222 + 0.999997i \(0.500806\pi\)
\(318\) 0 0
\(319\) 18.3607 1.02800
\(320\) 0 0
\(321\) 2.58359 0.144202
\(322\) 0 0
\(323\) 24.7082 1.37480
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −5.29180 −0.292637
\(328\) 0 0
\(329\) 15.7082 0.866021
\(330\) 0 0
\(331\) −14.7639 −0.811499 −0.405750 0.913984i \(-0.632989\pi\)
−0.405750 + 0.913984i \(0.632989\pi\)
\(332\) 0 0
\(333\) −6.47214 −0.354671
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −29.3262 −1.59750 −0.798751 0.601662i \(-0.794506\pi\)
−0.798751 + 0.601662i \(0.794506\pi\)
\(338\) 0 0
\(339\) 11.7082 0.635902
\(340\) 0 0
\(341\) −8.05573 −0.436242
\(342\) 0 0
\(343\) −18.4164 −0.994393
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.61803 −0.462640 −0.231320 0.972878i \(-0.574304\pi\)
−0.231320 + 0.972878i \(0.574304\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −14.2016 −0.758027
\(352\) 0 0
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −5.09017 −0.269400
\(358\) 0 0
\(359\) 18.3607 0.969040 0.484520 0.874780i \(-0.338994\pi\)
0.484520 + 0.874780i \(0.338994\pi\)
\(360\) 0 0
\(361\) 4.56231 0.240121
\(362\) 0 0
\(363\) −2.38197 −0.125021
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −2.47214 −0.129044 −0.0645222 0.997916i \(-0.520552\pi\)
−0.0645222 + 0.997916i \(0.520552\pi\)
\(368\) 0 0
\(369\) 32.2705 1.67994
\(370\) 0 0
\(371\) 13.7082 0.711694
\(372\) 0 0
\(373\) 2.18034 0.112894 0.0564469 0.998406i \(-0.482023\pi\)
0.0564469 + 0.998406i \(0.482023\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 19.4853 1.00354
\(378\) 0 0
\(379\) −33.4508 −1.71825 −0.859127 0.511762i \(-0.828993\pi\)
−0.859127 + 0.511762i \(0.828993\pi\)
\(380\) 0 0
\(381\) 3.81966 0.195687
\(382\) 0 0
\(383\) 17.8885 0.914062 0.457031 0.889451i \(-0.348913\pi\)
0.457031 + 0.889451i \(0.348913\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.67376 0.287671 0.143836 0.989602i \(-0.454056\pi\)
0.143836 + 0.989602i \(0.454056\pi\)
\(390\) 0 0
\(391\) 5.09017 0.257421
\(392\) 0 0
\(393\) −9.23607 −0.465898
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.32624 0.417882 0.208941 0.977928i \(-0.432998\pi\)
0.208941 + 0.977928i \(0.432998\pi\)
\(398\) 0 0
\(399\) −4.85410 −0.243009
\(400\) 0 0
\(401\) 11.7082 0.584680 0.292340 0.956314i \(-0.405566\pi\)
0.292340 + 0.956314i \(0.405566\pi\)
\(402\) 0 0
\(403\) −8.54915 −0.425864
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.52786 −0.472279
\(408\) 0 0
\(409\) 21.2148 1.04900 0.524502 0.851409i \(-0.324252\pi\)
0.524502 + 0.851409i \(0.324252\pi\)
\(410\) 0 0
\(411\) 3.29180 0.162372
\(412\) 0 0
\(413\) 18.9443 0.932187
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 10.6525 0.521654
\(418\) 0 0
\(419\) −5.52786 −0.270054 −0.135027 0.990842i \(-0.543112\pi\)
−0.135027 + 0.990842i \(0.543112\pi\)
\(420\) 0 0
\(421\) −28.7426 −1.40083 −0.700415 0.713735i \(-0.747002\pi\)
−0.700415 + 0.713735i \(0.747002\pi\)
\(422\) 0 0
\(423\) −25.4164 −1.23579
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 10.2361 0.495358
\(428\) 0 0
\(429\) −9.74265 −0.470379
\(430\) 0 0
\(431\) −34.6525 −1.66915 −0.834576 0.550894i \(-0.814287\pi\)
−0.834576 + 0.550894i \(0.814287\pi\)
\(432\) 0 0
\(433\) 29.5066 1.41800 0.708998 0.705211i \(-0.249148\pi\)
0.708998 + 0.705211i \(0.249148\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.85410 0.232203
\(438\) 0 0
\(439\) 15.6180 0.745408 0.372704 0.927950i \(-0.378431\pi\)
0.372704 + 0.927950i \(0.378431\pi\)
\(440\) 0 0
\(441\) 11.4721 0.546292
\(442\) 0 0
\(443\) 13.9098 0.660876 0.330438 0.943828i \(-0.392804\pi\)
0.330438 + 0.943828i \(0.392804\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.708204 0.0334969
\(448\) 0 0
\(449\) 18.5623 0.876009 0.438005 0.898973i \(-0.355685\pi\)
0.438005 + 0.898973i \(0.355685\pi\)
\(450\) 0 0
\(451\) 47.5066 2.23700
\(452\) 0 0
\(453\) 10.8541 0.509970
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −33.7771 −1.58003 −0.790013 0.613090i \(-0.789926\pi\)
−0.790013 + 0.613090i \(0.789926\pi\)
\(458\) 0 0
\(459\) 17.6738 0.824941
\(460\) 0 0
\(461\) −34.7639 −1.61912 −0.809559 0.587039i \(-0.800294\pi\)
−0.809559 + 0.587039i \(0.800294\pi\)
\(462\) 0 0
\(463\) 2.00000 0.0929479 0.0464739 0.998920i \(-0.485202\pi\)
0.0464739 + 0.998920i \(0.485202\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 23.1246 1.07008 0.535040 0.844827i \(-0.320297\pi\)
0.535040 + 0.844827i \(0.320297\pi\)
\(468\) 0 0
\(469\) 8.94427 0.413008
\(470\) 0 0
\(471\) 6.00000 0.276465
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −22.1803 −1.01557
\(478\) 0 0
\(479\) −3.88854 −0.177672 −0.0888361 0.996046i \(-0.528315\pi\)
−0.0888361 + 0.996046i \(0.528315\pi\)
\(480\) 0 0
\(481\) −10.1115 −0.461043
\(482\) 0 0
\(483\) −1.00000 −0.0455016
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −42.1803 −1.91137 −0.955687 0.294385i \(-0.904885\pi\)
−0.955687 + 0.294385i \(0.904885\pi\)
\(488\) 0 0
\(489\) −2.23607 −0.101118
\(490\) 0 0
\(491\) 16.1803 0.730209 0.365104 0.930967i \(-0.381033\pi\)
0.365104 + 0.930967i \(0.381033\pi\)
\(492\) 0 0
\(493\) −24.2492 −1.09213
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −11.4721 −0.514596
\(498\) 0 0
\(499\) 32.3607 1.44866 0.724331 0.689452i \(-0.242149\pi\)
0.724331 + 0.689452i \(0.242149\pi\)
\(500\) 0 0
\(501\) 4.94427 0.220894
\(502\) 0 0
\(503\) 20.6738 0.921797 0.460899 0.887453i \(-0.347527\pi\)
0.460899 + 0.887453i \(0.347527\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.30495 −0.102366
\(508\) 0 0
\(509\) 5.34752 0.237025 0.118512 0.992953i \(-0.462187\pi\)
0.118512 + 0.992953i \(0.462187\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) 16.8541 0.744127
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −37.4164 −1.64557
\(518\) 0 0
\(519\) −13.3262 −0.584957
\(520\) 0 0
\(521\) −24.4721 −1.07214 −0.536072 0.844172i \(-0.680092\pi\)
−0.536072 + 0.844172i \(0.680092\pi\)
\(522\) 0 0
\(523\) −26.0000 −1.13690 −0.568450 0.822718i \(-0.692457\pi\)
−0.568450 + 0.822718i \(0.692457\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.6393 0.463456
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −30.6525 −1.33020
\(532\) 0 0
\(533\) 50.4164 2.18378
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −12.4721 −0.538212
\(538\) 0 0
\(539\) 16.8885 0.727441
\(540\) 0 0
\(541\) −30.8328 −1.32561 −0.662803 0.748794i \(-0.730633\pi\)
−0.662803 + 0.748794i \(0.730633\pi\)
\(542\) 0 0
\(543\) 11.6525 0.500056
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −36.9230 −1.57871 −0.789356 0.613935i \(-0.789586\pi\)
−0.789356 + 0.613935i \(0.789586\pi\)
\(548\) 0 0
\(549\) −16.5623 −0.706862
\(550\) 0 0
\(551\) −23.1246 −0.985142
\(552\) 0 0
\(553\) −16.9443 −0.720544
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −30.8328 −1.30643 −0.653214 0.757173i \(-0.726580\pi\)
−0.653214 + 0.757173i \(0.726580\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 12.1246 0.511902
\(562\) 0 0
\(563\) 21.8885 0.922492 0.461246 0.887272i \(-0.347403\pi\)
0.461246 + 0.887272i \(0.347403\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 9.23607 0.387878
\(568\) 0 0
\(569\) −2.00000 −0.0838444 −0.0419222 0.999121i \(-0.513348\pi\)
−0.0419222 + 0.999121i \(0.513348\pi\)
\(570\) 0 0
\(571\) 30.9787 1.29642 0.648209 0.761462i \(-0.275518\pi\)
0.648209 + 0.761462i \(0.275518\pi\)
\(572\) 0 0
\(573\) −0.180340 −0.00753381
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 12.4721 0.519222 0.259611 0.965713i \(-0.416406\pi\)
0.259611 + 0.965713i \(0.416406\pi\)
\(578\) 0 0
\(579\) 3.23607 0.134486
\(580\) 0 0
\(581\) 17.7082 0.734660
\(582\) 0 0
\(583\) −32.6525 −1.35233
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.3820 0.469784 0.234892 0.972021i \(-0.424526\pi\)
0.234892 + 0.972021i \(0.424526\pi\)
\(588\) 0 0
\(589\) 10.1459 0.418054
\(590\) 0 0
\(591\) −1.50658 −0.0619723
\(592\) 0 0
\(593\) −34.7639 −1.42758 −0.713792 0.700358i \(-0.753024\pi\)
−0.713792 + 0.700358i \(0.753024\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.23607 0.0505889
\(598\) 0 0
\(599\) 20.6180 0.842430 0.421215 0.906961i \(-0.361604\pi\)
0.421215 + 0.906961i \(0.361604\pi\)
\(600\) 0 0
\(601\) 0.270510 0.0110343 0.00551716 0.999985i \(-0.498244\pi\)
0.00551716 + 0.999985i \(0.498244\pi\)
\(602\) 0 0
\(603\) −14.4721 −0.589351
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 17.5279 0.711434 0.355717 0.934594i \(-0.384237\pi\)
0.355717 + 0.934594i \(0.384237\pi\)
\(608\) 0 0
\(609\) 4.76393 0.193044
\(610\) 0 0
\(611\) −39.7082 −1.60642
\(612\) 0 0
\(613\) 43.3050 1.74907 0.874535 0.484962i \(-0.161167\pi\)
0.874535 + 0.484962i \(0.161167\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.9098 −0.922315 −0.461158 0.887318i \(-0.652566\pi\)
−0.461158 + 0.887318i \(0.652566\pi\)
\(618\) 0 0
\(619\) −21.7984 −0.876151 −0.438075 0.898938i \(-0.644340\pi\)
−0.438075 + 0.898938i \(0.644340\pi\)
\(620\) 0 0
\(621\) 3.47214 0.139332
\(622\) 0 0
\(623\) −2.47214 −0.0990440
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 11.5623 0.461754
\(628\) 0 0
\(629\) 12.5836 0.501741
\(630\) 0 0
\(631\) 16.0689 0.639692 0.319846 0.947470i \(-0.396369\pi\)
0.319846 + 0.947470i \(0.396369\pi\)
\(632\) 0 0
\(633\) 8.65248 0.343905
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 17.9230 0.710135
\(638\) 0 0
\(639\) 18.5623 0.734313
\(640\) 0 0
\(641\) −44.3607 −1.75214 −0.876071 0.482183i \(-0.839844\pi\)
−0.876071 + 0.482183i \(0.839844\pi\)
\(642\) 0 0
\(643\) −21.7082 −0.856088 −0.428044 0.903758i \(-0.640797\pi\)
−0.428044 + 0.903758i \(0.640797\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 44.2492 1.73962 0.869808 0.493390i \(-0.164242\pi\)
0.869808 + 0.493390i \(0.164242\pi\)
\(648\) 0 0
\(649\) −45.1246 −1.77130
\(650\) 0 0
\(651\) −2.09017 −0.0819202
\(652\) 0 0
\(653\) −21.0344 −0.823141 −0.411571 0.911378i \(-0.635020\pi\)
−0.411571 + 0.911378i \(0.635020\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.23607 −0.126251
\(658\) 0 0
\(659\) −34.2492 −1.33416 −0.667080 0.744986i \(-0.732456\pi\)
−0.667080 + 0.744986i \(0.732456\pi\)
\(660\) 0 0
\(661\) 34.3262 1.33514 0.667568 0.744549i \(-0.267335\pi\)
0.667568 + 0.744549i \(0.267335\pi\)
\(662\) 0 0
\(663\) 12.8673 0.499723
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.76393 −0.184460
\(668\) 0 0
\(669\) 1.88854 0.0730153
\(670\) 0 0
\(671\) −24.3820 −0.941255
\(672\) 0 0
\(673\) −6.94427 −0.267682 −0.133841 0.991003i \(-0.542731\pi\)
−0.133841 + 0.991003i \(0.542731\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.0557 1.27043 0.635217 0.772333i \(-0.280910\pi\)
0.635217 + 0.772333i \(0.280910\pi\)
\(678\) 0 0
\(679\) −23.6525 −0.907699
\(680\) 0 0
\(681\) 14.3607 0.550302
\(682\) 0 0
\(683\) −11.4377 −0.437651 −0.218826 0.975764i \(-0.570223\pi\)
−0.218826 + 0.975764i \(0.570223\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −6.18034 −0.235795
\(688\) 0 0
\(689\) −34.6525 −1.32015
\(690\) 0 0
\(691\) 24.7639 0.942064 0.471032 0.882116i \(-0.343882\pi\)
0.471032 + 0.882116i \(0.343882\pi\)
\(692\) 0 0
\(693\) 16.3262 0.620182
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −62.7426 −2.37655
\(698\) 0 0
\(699\) 12.1803 0.460703
\(700\) 0 0
\(701\) −48.3394 −1.82575 −0.912877 0.408235i \(-0.866144\pi\)
−0.912877 + 0.408235i \(0.866144\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −22.1803 −0.834178
\(708\) 0 0
\(709\) −14.9098 −0.559950 −0.279975 0.960007i \(-0.590326\pi\)
−0.279975 + 0.960007i \(0.590326\pi\)
\(710\) 0 0
\(711\) 27.4164 1.02820
\(712\) 0 0
\(713\) 2.09017 0.0782775
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 15.0557 0.562266
\(718\) 0 0
\(719\) −1.72949 −0.0644991 −0.0322495 0.999480i \(-0.510267\pi\)
−0.0322495 + 0.999480i \(0.510267\pi\)
\(720\) 0 0
\(721\) −5.76393 −0.214660
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 52.7984 1.95818 0.979092 0.203420i \(-0.0652056\pi\)
0.979092 + 0.203420i \(0.0652056\pi\)
\(728\) 0 0
\(729\) −8.50658 −0.315058
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 2.58359 0.0954272 0.0477136 0.998861i \(-0.484807\pi\)
0.0477136 + 0.998861i \(0.484807\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.3050 −0.784778
\(738\) 0 0
\(739\) −21.8885 −0.805183 −0.402592 0.915380i \(-0.631890\pi\)
−0.402592 + 0.915380i \(0.631890\pi\)
\(740\) 0 0
\(741\) 12.2705 0.450768
\(742\) 0 0
\(743\) −44.6312 −1.63736 −0.818680 0.574250i \(-0.805294\pi\)
−0.818680 + 0.574250i \(0.805294\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −28.6525 −1.04834
\(748\) 0 0
\(749\) −6.76393 −0.247149
\(750\) 0 0
\(751\) −29.0132 −1.05871 −0.529353 0.848402i \(-0.677565\pi\)
−0.529353 + 0.848402i \(0.677565\pi\)
\(752\) 0 0
\(753\) 7.94427 0.289505
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −17.8885 −0.650170 −0.325085 0.945685i \(-0.605393\pi\)
−0.325085 + 0.945685i \(0.605393\pi\)
\(758\) 0 0
\(759\) 2.38197 0.0864599
\(760\) 0 0
\(761\) −35.8673 −1.30019 −0.650094 0.759854i \(-0.725270\pi\)
−0.650094 + 0.759854i \(0.725270\pi\)
\(762\) 0 0
\(763\) 13.8541 0.501552
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −47.8885 −1.72916
\(768\) 0 0
\(769\) −33.4164 −1.20503 −0.602513 0.798109i \(-0.705834\pi\)
−0.602513 + 0.798109i \(0.705834\pi\)
\(770\) 0 0
\(771\) −18.6525 −0.671753
\(772\) 0 0
\(773\) −11.0557 −0.397647 −0.198823 0.980035i \(-0.563712\pi\)
−0.198823 + 0.980035i \(0.563712\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −2.47214 −0.0886874
\(778\) 0 0
\(779\) −59.8328 −2.14373
\(780\) 0 0
\(781\) 27.3262 0.977810
\(782\) 0 0
\(783\) −16.5410 −0.591128
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −43.1246 −1.53723 −0.768613 0.639714i \(-0.779053\pi\)
−0.768613 + 0.639714i \(0.779053\pi\)
\(788\) 0 0
\(789\) 13.4377 0.478395
\(790\) 0 0
\(791\) −30.6525 −1.08988
\(792\) 0 0
\(793\) −25.8754 −0.918862
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −0.291796 −0.0103359 −0.00516797 0.999987i \(-0.501645\pi\)
−0.00516797 + 0.999987i \(0.501645\pi\)
\(798\) 0 0
\(799\) 49.4164 1.74823
\(800\) 0 0
\(801\) 4.00000 0.141333
\(802\) 0 0
\(803\) −4.76393 −0.168116
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −5.05573 −0.177970
\(808\) 0 0
\(809\) −4.25735 −0.149681 −0.0748403 0.997196i \(-0.523845\pi\)
−0.0748403 + 0.997196i \(0.523845\pi\)
\(810\) 0 0
\(811\) −44.1803 −1.55138 −0.775691 0.631113i \(-0.782598\pi\)
−0.775691 + 0.631113i \(0.782598\pi\)
\(812\) 0 0
\(813\) −9.06888 −0.318060
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 17.3262 0.605428
\(820\) 0 0
\(821\) −50.9443 −1.77797 −0.888984 0.457939i \(-0.848588\pi\)
−0.888984 + 0.457939i \(0.848588\pi\)
\(822\) 0 0
\(823\) −1.41641 −0.0493729 −0.0246864 0.999695i \(-0.507859\pi\)
−0.0246864 + 0.999695i \(0.507859\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 8.29180 0.288334 0.144167 0.989553i \(-0.453950\pi\)
0.144167 + 0.989553i \(0.453950\pi\)
\(828\) 0 0
\(829\) 1.05573 0.0366670 0.0183335 0.999832i \(-0.494164\pi\)
0.0183335 + 0.999832i \(0.494164\pi\)
\(830\) 0 0
\(831\) 1.59675 0.0553906
\(832\) 0 0
\(833\) −22.3050 −0.772821
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 7.25735 0.250851
\(838\) 0 0
\(839\) 43.0132 1.48498 0.742490 0.669858i \(-0.233645\pi\)
0.742490 + 0.669858i \(0.233645\pi\)
\(840\) 0 0
\(841\) −6.30495 −0.217412
\(842\) 0 0
\(843\) −16.8328 −0.579753
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 6.23607 0.214274
\(848\) 0 0
\(849\) 5.59675 0.192080
\(850\) 0 0
\(851\) 2.47214 0.0847437
\(852\) 0 0
\(853\) −13.7984 −0.472447 −0.236224 0.971699i \(-0.575910\pi\)
−0.236224 + 0.971699i \(0.575910\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 33.4164 1.14148 0.570741 0.821130i \(-0.306656\pi\)
0.570741 + 0.821130i \(0.306656\pi\)
\(858\) 0 0
\(859\) −34.0689 −1.16242 −0.581208 0.813755i \(-0.697420\pi\)
−0.581208 + 0.813755i \(0.697420\pi\)
\(860\) 0 0
\(861\) 12.3262 0.420077
\(862\) 0 0
\(863\) 37.2361 1.26753 0.633765 0.773525i \(-0.281509\pi\)
0.633765 + 0.773525i \(0.281509\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −5.50658 −0.187013
\(868\) 0 0
\(869\) 40.3607 1.36914
\(870\) 0 0
\(871\) −22.6099 −0.766107
\(872\) 0 0
\(873\) 38.2705 1.29526
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 23.7426 0.801732 0.400866 0.916137i \(-0.368709\pi\)
0.400866 + 0.916137i \(0.368709\pi\)
\(878\) 0 0
\(879\) 9.81966 0.331209
\(880\) 0 0
\(881\) 35.4164 1.19321 0.596605 0.802535i \(-0.296516\pi\)
0.596605 + 0.802535i \(0.296516\pi\)
\(882\) 0 0
\(883\) −4.56231 −0.153534 −0.0767669 0.997049i \(-0.524460\pi\)
−0.0767669 + 0.997049i \(0.524460\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −58.8328 −1.97541 −0.987706 0.156321i \(-0.950037\pi\)
−0.987706 + 0.156321i \(0.950037\pi\)
\(888\) 0 0
\(889\) −10.0000 −0.335389
\(890\) 0 0
\(891\) −22.0000 −0.737028
\(892\) 0 0
\(893\) 47.1246 1.57697
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.52786 0.0844029
\(898\) 0 0
\(899\) −9.95743 −0.332099
\(900\) 0 0
\(901\) 43.1246 1.43669
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −33.1246 −1.09988 −0.549942 0.835203i \(-0.685350\pi\)
−0.549942 + 0.835203i \(0.685350\pi\)
\(908\) 0 0
\(909\) 35.8885 1.19035
\(910\) 0 0
\(911\) 22.0689 0.731175 0.365587 0.930777i \(-0.380868\pi\)
0.365587 + 0.930777i \(0.380868\pi\)
\(912\) 0 0
\(913\) −42.1803 −1.39597
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 24.1803 0.798505
\(918\) 0 0
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) −16.9656 −0.559034
\(922\) 0 0
\(923\) 29.0000 0.954547
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 9.32624 0.306314
\(928\) 0 0
\(929\) −12.4721 −0.409198 −0.204599 0.978846i \(-0.565589\pi\)
−0.204599 + 0.978846i \(0.565589\pi\)
\(930\) 0 0
\(931\) −21.2705 −0.697113
\(932\) 0 0
\(933\) 2.47214 0.0809341
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 12.2016 0.398610 0.199305 0.979938i \(-0.436132\pi\)
0.199305 + 0.979938i \(0.436132\pi\)
\(938\) 0 0
\(939\) −7.29180 −0.237959
\(940\) 0 0
\(941\) −60.5066 −1.97246 −0.986229 0.165385i \(-0.947113\pi\)
−0.986229 + 0.165385i \(0.947113\pi\)
\(942\) 0 0
\(943\) −12.3262 −0.401398
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.68692 0.184800 0.0924000 0.995722i \(-0.470546\pi\)
0.0924000 + 0.995722i \(0.470546\pi\)
\(948\) 0 0
\(949\) −5.05573 −0.164116
\(950\) 0 0
\(951\) 0.0557281 0.00180711
\(952\) 0 0
\(953\) 20.7984 0.673725 0.336863 0.941554i \(-0.390634\pi\)
0.336863 + 0.941554i \(0.390634\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −11.3475 −0.366813
\(958\) 0 0
\(959\) −8.61803 −0.278291
\(960\) 0 0
\(961\) −26.6312 −0.859071
\(962\) 0 0
\(963\) 10.9443 0.352674
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 50.5410 1.62529 0.812645 0.582759i \(-0.198027\pi\)
0.812645 + 0.582759i \(0.198027\pi\)
\(968\) 0 0
\(969\) −15.2705 −0.490559
\(970\) 0 0
\(971\) −0.729490 −0.0234105 −0.0117052 0.999931i \(-0.503726\pi\)
−0.0117052 + 0.999931i \(0.503726\pi\)
\(972\) 0 0
\(973\) −27.8885 −0.894066
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.43769 0.109982 0.0549908 0.998487i \(-0.482487\pi\)
0.0549908 + 0.998487i \(0.482487\pi\)
\(978\) 0 0
\(979\) 5.88854 0.188199
\(980\) 0 0
\(981\) −22.4164 −0.715701
\(982\) 0 0
\(983\) 19.2705 0.614634 0.307317 0.951607i \(-0.400569\pi\)
0.307317 + 0.951607i \(0.400569\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −9.70820 −0.309016
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 10.5066 0.333752 0.166876 0.985978i \(-0.446632\pi\)
0.166876 + 0.985978i \(0.446632\pi\)
\(992\) 0 0
\(993\) 9.12461 0.289561
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 41.1935 1.30461 0.652306 0.757956i \(-0.273802\pi\)
0.652306 + 0.757956i \(0.273802\pi\)
\(998\) 0 0
\(999\) 8.58359 0.271573
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 9200.2.a.bu.1.1 2
4.3 odd 2 1150.2.a.j.1.2 2
5.4 even 2 1840.2.a.l.1.2 2
20.3 even 4 1150.2.b.i.599.4 4
20.7 even 4 1150.2.b.i.599.1 4
20.19 odd 2 230.2.a.c.1.1 2
40.19 odd 2 7360.2.a.bh.1.2 2
40.29 even 2 7360.2.a.bn.1.1 2
60.59 even 2 2070.2.a.u.1.2 2
460.459 even 2 5290.2.a.o.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.c.1.1 2 20.19 odd 2
1150.2.a.j.1.2 2 4.3 odd 2
1150.2.b.i.599.1 4 20.7 even 4
1150.2.b.i.599.4 4 20.3 even 4
1840.2.a.l.1.2 2 5.4 even 2
2070.2.a.u.1.2 2 60.59 even 2
5290.2.a.o.1.1 2 460.459 even 2
7360.2.a.bh.1.2 2 40.19 odd 2
7360.2.a.bn.1.1 2 40.29 even 2
9200.2.a.bu.1.1 2 1.1 even 1 trivial