Properties

Label 7360.2.a.bn.1.1
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.7698958877\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.618034 q^{3} -1.00000 q^{5} -1.61803 q^{7} -2.61803 q^{9} +O(q^{10})\) \(q-0.618034 q^{3} -1.00000 q^{5} -1.61803 q^{7} -2.61803 q^{9} +3.85410 q^{11} -4.09017 q^{13} +0.618034 q^{15} -5.09017 q^{17} -4.85410 q^{19} +1.00000 q^{21} -1.00000 q^{23} +1.00000 q^{25} +3.47214 q^{27} +4.76393 q^{29} +2.09017 q^{31} -2.38197 q^{33} +1.61803 q^{35} +2.47214 q^{37} +2.52786 q^{39} -12.3262 q^{41} +2.61803 q^{45} -9.70820 q^{47} -4.38197 q^{49} +3.14590 q^{51} +8.47214 q^{53} -3.85410 q^{55} +3.00000 q^{57} -11.7082 q^{59} -6.32624 q^{61} +4.23607 q^{63} +4.09017 q^{65} +5.52786 q^{67} +0.618034 q^{69} -7.09017 q^{71} -1.23607 q^{73} -0.618034 q^{75} -6.23607 q^{77} -10.4721 q^{79} +5.70820 q^{81} +10.9443 q^{83} +5.09017 q^{85} -2.94427 q^{87} -1.52786 q^{89} +6.61803 q^{91} -1.29180 q^{93} +4.85410 q^{95} +14.6180 q^{97} -10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 2 q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( 2 q + q^{3} - 2 q^{5} - q^{7} - 3 q^{9} + q^{11} + 3 q^{13} - q^{15} + q^{17} - 3 q^{19} + 2 q^{21} - 2 q^{23} + 2 q^{25} - 2 q^{27} + 14 q^{29} - 7 q^{31} - 7 q^{33} + q^{35} - 4 q^{37} + 14 q^{39} - 9 q^{41} + 3 q^{45} - 6 q^{47} - 11 q^{49} + 13 q^{51} + 8 q^{53} - q^{55} + 6 q^{57} - 10 q^{59} + 3 q^{61} + 4 q^{63} - 3 q^{65} + 20 q^{67} - q^{69} - 3 q^{71} + 2 q^{73} + q^{75} - 8 q^{77} - 12 q^{79} - 2 q^{81} + 4 q^{83} - q^{85} + 12 q^{87} - 12 q^{89} + 11 q^{91} - 16 q^{93} + 3 q^{95} + 27 q^{97} - 9 q^{99} + O(q^{100}) \)

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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.61803 −0.611559 −0.305780 0.952102i \(-0.598917\pi\)
−0.305780 + 0.952102i \(0.598917\pi\)
\(8\) 0 0
\(9\) −2.61803 −0.872678
\(10\) 0 0
\(11\) 3.85410 1.16206 0.581028 0.813884i \(-0.302651\pi\)
0.581028 + 0.813884i \(0.302651\pi\)
\(12\) 0 0
\(13\) −4.09017 −1.13441 −0.567205 0.823577i \(-0.691975\pi\)
−0.567205 + 0.823577i \(0.691975\pi\)
\(14\) 0 0
\(15\) 0.618034 0.159576
\(16\) 0 0
\(17\) −5.09017 −1.23455 −0.617274 0.786748i \(-0.711763\pi\)
−0.617274 + 0.786748i \(0.711763\pi\)
\(18\) 0 0
\(19\) −4.85410 −1.11361 −0.556804 0.830644i \(-0.687972\pi\)
−0.556804 + 0.830644i \(0.687972\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 3.47214 0.668213
\(28\) 0 0
\(29\) 4.76393 0.884640 0.442320 0.896857i \(-0.354156\pi\)
0.442320 + 0.896857i \(0.354156\pi\)
\(30\) 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
\(35\) 1.61803 0.273498
\(36\) 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
\(45\) 2.61803 0.390273
\(46\) 0 0
\(47\) −9.70820 −1.41609 −0.708044 0.706169i \(-0.750422\pi\)
−0.708044 + 0.706169i \(0.750422\pi\)
\(48\) 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
\(55\) −3.85410 −0.519687
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) −11.7082 −1.52428 −0.762139 0.647413i \(-0.775851\pi\)
−0.762139 + 0.647413i \(0.775851\pi\)
\(60\) 0 0
\(61\) −6.32624 −0.809992 −0.404996 0.914319i \(-0.632727\pi\)
−0.404996 + 0.914319i \(0.632727\pi\)
\(62\) 0 0
\(63\) 4.23607 0.533694
\(64\) 0 0
\(65\) 4.09017 0.507323
\(66\) 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 \(-0.523045\pi\)
−0.0723354 + 0.997380i \(0.523045\pi\)
\(74\) 0 0
\(75\) −0.618034 −0.0713644
\(76\) 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
\(85\) 5.09017 0.552106
\(86\) 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
\(95\) 4.85410 0.498020
\(96\) 0 0
\(97\) 14.6180 1.48424 0.742118 0.670269i \(-0.233821\pi\)
0.742118 + 0.670269i \(0.233821\pi\)
\(98\) 0 0
\(99\) −10.0902 −1.01410
\(100\) 0 0
\(101\) 13.7082 1.36402 0.682009 0.731344i \(-0.261107\pi\)
0.682009 + 0.731344i \(0.261107\pi\)
\(102\) 0 0
\(103\) 3.56231 0.351004 0.175502 0.984479i \(-0.443845\pi\)
0.175502 + 0.984479i \(0.443845\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) 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 \(-0.634492\pi\)
−0.410060 + 0.912059i \(0.634492\pi\)
\(110\) 0 0
\(111\) −1.52786 −0.145018
\(112\) 0 0
\(113\) 18.9443 1.78213 0.891064 0.453878i \(-0.149960\pi\)
0.891064 + 0.453878i \(0.149960\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 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
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.18034 0.548416 0.274208 0.961670i \(-0.411584\pi\)
0.274208 + 0.961670i \(0.411584\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −14.9443 −1.30569 −0.652844 0.757493i \(-0.726424\pi\)
−0.652844 + 0.757493i \(0.726424\pi\)
\(132\) 0 0
\(133\) 7.85410 0.681037
\(134\) 0 0
\(135\) −3.47214 −0.298834
\(136\) 0 0
\(137\) 5.32624 0.455051 0.227526 0.973772i \(-0.426936\pi\)
0.227526 + 0.973772i \(0.426936\pi\)
\(138\) 0 0
\(139\) 17.2361 1.46194 0.730972 0.682407i \(-0.239067\pi\)
0.730972 + 0.682407i \(0.239067\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −15.7639 −1.31825
\(144\) 0 0
\(145\) −4.76393 −0.395623
\(146\) 0 0
\(147\) 2.70820 0.223369
\(148\) 0 0
\(149\) 1.14590 0.0938756 0.0469378 0.998898i \(-0.485054\pi\)
0.0469378 + 0.998898i \(0.485054\pi\)
\(150\) 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
\(155\) −2.09017 −0.167886
\(156\) 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
\(165\) 2.38197 0.185436
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 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
\(175\) −1.61803 −0.122312
\(176\) 0 0
\(177\) 7.23607 0.543896
\(178\) 0 0
\(179\) −20.1803 −1.50835 −0.754175 0.656674i \(-0.771963\pi\)
−0.754175 + 0.656674i \(0.771963\pi\)
\(180\) 0 0
\(181\) 18.8541 1.40141 0.700707 0.713449i \(-0.252868\pi\)
0.700707 + 0.713449i \(0.252868\pi\)
\(182\) 0 0
\(183\) 3.90983 0.289023
\(184\) 0 0
\(185\) −2.47214 −0.181755
\(186\) 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 \(-0.439654\pi\)
0.188450 + 0.982083i \(0.439654\pi\)
\(194\) 0 0
\(195\) −2.52786 −0.181024
\(196\) 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
\(205\) 12.3262 0.860902
\(206\) 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 \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 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 \(-0.467376\pi\)
0.102313 + 0.994752i \(0.467376\pi\)
\(224\) 0 0
\(225\) −2.61803 −0.174536
\(226\) 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 \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 3.85410 0.253581
\(232\) 0 0
\(233\) 19.7082 1.29113 0.645564 0.763706i \(-0.276622\pi\)
0.645564 + 0.763706i \(0.276622\pi\)
\(234\) 0 0
\(235\) 9.70820 0.633293
\(236\) 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
\(245\) 4.38197 0.279954
\(246\) 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 \(-0.367038\pi\)
0.405672 + 0.914019i \(0.367038\pi\)
\(252\) 0 0
\(253\) −3.85410 −0.242305
\(254\) 0 0
\(255\) −3.14590 −0.197004
\(256\) 0 0
\(257\) −30.1803 −1.88260 −0.941299 0.337574i \(-0.890394\pi\)
−0.941299 + 0.337574i \(0.890394\pi\)
\(258\) 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 \(-0.266142\pi\)
0.670354 + 0.742041i \(0.266142\pi\)
\(264\) 0 0
\(265\) −8.47214 −0.520439
\(266\) 0 0
\(267\) 0.944272 0.0577885
\(268\) 0 0
\(269\) −8.18034 −0.498764 −0.249382 0.968405i \(-0.580227\pi\)
−0.249382 + 0.968405i \(0.580227\pi\)
\(270\) 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
\(275\) 3.85410 0.232411
\(276\) 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
\(285\) −3.00000 −0.177705
\(286\) 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
\(295\) 11.7082 0.681678
\(296\) 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
\(305\) 6.32624 0.362239
\(306\) 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 \(-0.608210\pi\)
−0.333442 + 0.942771i \(0.608210\pi\)
\(314\) 0 0
\(315\) −4.23607 −0.238675
\(316\) 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
\(325\) −4.09017 −0.226882
\(326\) 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 \(-0.367011\pi\)
0.405750 + 0.913984i \(0.367011\pi\)
\(332\) 0 0
\(333\) −6.47214 −0.354671
\(334\) 0 0
\(335\) −5.52786 −0.302019
\(336\) 0 0
\(337\) 29.3262 1.59750 0.798751 0.601662i \(-0.205494\pi\)
0.798751 + 0.601662i \(0.205494\pi\)
\(338\) 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
\(345\) −0.618034 −0.0332738
\(346\) 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 \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) −14.2016 −0.758027
\(352\) 0 0
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 0 0
\(355\) 7.09017 0.376307
\(356\) 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
\(365\) 1.23607 0.0646988
\(366\) 0 0
\(367\) 2.47214 0.129044 0.0645222 0.997916i \(-0.479448\pi\)
0.0645222 + 0.997916i \(0.479448\pi\)
\(368\) 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
\(375\) 0.618034 0.0319151
\(376\) 0 0
\(377\) −19.4853 −1.00354
\(378\) 0 0
\(379\) 33.4508 1.71825 0.859127 0.511762i \(-0.171007\pi\)
0.859127 + 0.511762i \(0.171007\pi\)
\(380\) 0 0
\(381\) −3.81966 −0.195687
\(382\) 0 0
\(383\) −17.8885 −0.914062 −0.457031 0.889451i \(-0.651087\pi\)
−0.457031 + 0.889451i \(0.651087\pi\)
\(384\) 0 0
\(385\) 6.23607 0.317819
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.67376 −0.287671 −0.143836 0.989602i \(-0.545944\pi\)
−0.143836 + 0.989602i \(0.545944\pi\)
\(390\) 0 0
\(391\) 5.09017 0.257421
\(392\) 0 0
\(393\) 9.23607 0.465898
\(394\) 0 0
\(395\) 10.4721 0.526910
\(396\) 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
\(405\) −5.70820 −0.283643
\(406\) 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
\(415\) −10.9443 −0.537233
\(416\) 0 0
\(417\) −10.6525 −0.521654
\(418\) 0 0
\(419\) 5.52786 0.270054 0.135027 0.990842i \(-0.456888\pi\)
0.135027 + 0.990842i \(0.456888\pi\)
\(420\) 0 0
\(421\) 28.7426 1.40083 0.700415 0.713735i \(-0.252998\pi\)
0.700415 + 0.713735i \(0.252998\pi\)
\(422\) 0 0
\(423\) 25.4164 1.23579
\(424\) 0 0
\(425\) −5.09017 −0.246910
\(426\) 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 \(-0.750852\pi\)
−0.708998 + 0.705211i \(0.750852\pi\)
\(434\) 0 0
\(435\) 2.94427 0.141167
\(436\) 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
\(445\) 1.52786 0.0724277
\(446\) 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
\(455\) −6.61803 −0.310258
\(456\) 0 0
\(457\) 33.7771 1.58003 0.790013 0.613090i \(-0.210074\pi\)
0.790013 + 0.613090i \(0.210074\pi\)
\(458\) 0 0
\(459\) −17.6738 −0.824941
\(460\) 0 0
\(461\) 34.7639 1.61912 0.809559 0.587039i \(-0.199706\pi\)
0.809559 + 0.587039i \(0.199706\pi\)
\(462\) 0 0
\(463\) −2.00000 −0.0929479 −0.0464739 0.998920i \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) 0 0
\(465\) 1.29180 0.0599056
\(466\) 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
\(475\) −4.85410 −0.222721
\(476\) 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
\(485\) −14.6180 −0.663771
\(486\) 0 0
\(487\) 42.1803 1.91137 0.955687 0.294385i \(-0.0951149\pi\)
0.955687 + 0.294385i \(0.0951149\pi\)
\(488\) 0 0
\(489\) −2.23607 −0.101118
\(490\) 0 0
\(491\) −16.1803 −0.730209 −0.365104 0.930967i \(-0.618967\pi\)
−0.365104 + 0.930967i \(0.618967\pi\)
\(492\) 0 0
\(493\) −24.2492 −1.09213
\(494\) 0 0
\(495\) 10.0902 0.453519
\(496\) 0 0
\(497\) 11.4721 0.514596
\(498\) 0 0
\(499\) −32.3607 −1.44866 −0.724331 0.689452i \(-0.757851\pi\)
−0.724331 + 0.689452i \(0.757851\pi\)
\(500\) 0 0
\(501\) −4.94427 −0.220894
\(502\) 0 0
\(503\) −20.6738 −0.921797 −0.460899 0.887453i \(-0.652473\pi\)
−0.460899 + 0.887453i \(0.652473\pi\)
\(504\) 0 0
\(505\) −13.7082 −0.610007
\(506\) 0 0
\(507\) −2.30495 −0.102366
\(508\) 0 0
\(509\) −5.34752 −0.237025 −0.118512 0.992953i \(-0.537813\pi\)
−0.118512 + 0.992953i \(0.537813\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) −16.8541 −0.744127
\(514\) 0 0
\(515\) −3.56231 −0.156974
\(516\) 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
\(525\) 1.00000 0.0436436
\(526\) 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
\(535\) 4.18034 0.180732
\(536\) 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 \(-0.269367\pi\)
0.662803 + 0.748794i \(0.269367\pi\)
\(542\) 0 0
\(543\) −11.6525 −0.500056
\(544\) 0 0
\(545\) 8.56231 0.366769
\(546\) 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
\(555\) 1.52786 0.0648542
\(556\) 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
\(565\) −18.9443 −0.796992
\(566\) 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 \(-0.724482\pi\)
−0.648209 + 0.761462i \(0.724482\pi\)
\(572\) 0 0
\(573\) −0.180340 −0.00753381
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −12.4721 −0.519222 −0.259611 0.965713i \(-0.583594\pi\)
−0.259611 + 0.965713i \(0.583594\pi\)
\(578\) 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
\(585\) −10.7082 −0.442730
\(586\) 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 \(-0.246976\pi\)
0.713792 + 0.700358i \(0.246976\pi\)
\(594\) 0 0
\(595\) −8.23607 −0.337646
\(596\) 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
\(605\) −3.85410 −0.156692
\(606\) 0 0
\(607\) −17.5279 −0.711434 −0.355717 0.934594i \(-0.615763\pi\)
−0.355717 + 0.934594i \(0.615763\pi\)
\(608\) 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
\(615\) −7.61803 −0.307189
\(616\) 0 0
\(617\) 22.9098 0.922315 0.461158 0.887318i \(-0.347434\pi\)
0.461158 + 0.887318i \(0.347434\pi\)
\(618\) 0 0
\(619\) 21.7984 0.876151 0.438075 0.898938i \(-0.355660\pi\)
0.438075 + 0.898938i \(0.355660\pi\)
\(620\) 0 0
\(621\) −3.47214 −0.139332
\(622\) 0 0
\(623\) 2.47214 0.0990440
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 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
\(635\) −6.18034 −0.245259
\(636\) 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 \(-0.835758\pi\)
−0.869808 + 0.493390i \(0.835758\pi\)
\(648\) 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
\(655\) 14.9443 0.583921
\(656\) 0 0
\(657\) 3.23607 0.126251
\(658\) 0 0
\(659\) 34.2492 1.33416 0.667080 0.744986i \(-0.267544\pi\)
0.667080 + 0.744986i \(0.267544\pi\)
\(660\) 0 0
\(661\) −34.3262 −1.33514 −0.667568 0.744549i \(-0.732665\pi\)
−0.667568 + 0.744549i \(0.732665\pi\)
\(662\) 0 0
\(663\) −12.8673 −0.499723
\(664\) 0 0
\(665\) −7.85410 −0.304569
\(666\) 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 \(-0.457269\pi\)
0.133841 + 0.991003i \(0.457269\pi\)
\(674\) 0 0
\(675\) 3.47214 0.133643
\(676\) 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
\(685\) −5.32624 −0.203505
\(686\) 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 \(-0.656118\pi\)
−0.471032 + 0.882116i \(0.656118\pi\)
\(692\) 0 0
\(693\) 16.3262 0.620182
\(694\) 0 0
\(695\) −17.2361 −0.653801
\(696\) 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 \(-0.133856\pi\)
0.912877 + 0.408235i \(0.133856\pi\)
\(702\) 0 0
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) −6.00000 −0.225973
\(706\) 0 0
\(707\) −22.1803 −0.834178
\(708\) 0 0
\(709\) 14.9098 0.559950 0.279975 0.960007i \(-0.409674\pi\)
0.279975 + 0.960007i \(0.409674\pi\)
\(710\) 0 0
\(711\) 27.4164 1.02820
\(712\) 0 0
\(713\) −2.09017 −0.0782775
\(714\) 0 0
\(715\) 15.7639 0.589538
\(716\) 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
\(725\) 4.76393 0.176928
\(726\) 0 0
\(727\) −52.7984 −1.95818 −0.979092 0.203420i \(-0.934794\pi\)
−0.979092 + 0.203420i \(0.934794\pi\)
\(728\) 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
\(735\) −2.70820 −0.0998936
\(736\) 0 0
\(737\) 21.3050 0.784778
\(738\) 0 0
\(739\) 21.8885 0.805183 0.402592 0.915380i \(-0.368110\pi\)
0.402592 + 0.915380i \(0.368110\pi\)
\(740\) 0 0
\(741\) −12.2705 −0.450768
\(742\) 0 0
\(743\) 44.6312 1.63736 0.818680 0.574250i \(-0.194706\pi\)
0.818680 + 0.574250i \(0.194706\pi\)
\(744\) 0 0
\(745\) −1.14590 −0.0419825
\(746\) 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
\(755\) 17.5623 0.639158
\(756\) 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
\(765\) −13.3262 −0.481811
\(766\) 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
\(775\) 2.09017 0.0750811
\(776\) 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
\(785\) 9.70820 0.346501
\(786\) 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
\(795\) 5.23607 0.185704
\(796\) 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
\(805\) −1.61803 −0.0570282
\(806\) 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 \(-0.217402\pi\)
0.775691 + 0.631113i \(0.217402\pi\)
\(812\) 0 0
\(813\) −9.06888 −0.318060
\(814\) 0 0
\(815\) −3.61803 −0.126734
\(816\) 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 \(-0.151412\pi\)
0.888984 + 0.457939i \(0.151412\pi\)
\(822\) 0 0
\(823\) 1.41641 0.0493729 0.0246864 0.999695i \(-0.492141\pi\)
0.0246864 + 0.999695i \(0.492141\pi\)
\(824\) 0 0
\(825\) −2.38197 −0.0829294
\(826\) 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 \(-0.505836\pi\)
−0.0183335 + 0.999832i \(0.505836\pi\)
\(830\) 0 0
\(831\) 1.59675 0.0553906
\(832\) 0 0
\(833\) 22.3050 0.772821
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) 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
\(845\) −3.72949 −0.128298
\(846\) 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
\(855\) −12.7082 −0.434611
\(856\) 0 0
\(857\) −33.4164 −1.14148 −0.570741 0.821130i \(-0.693344\pi\)
−0.570741 + 0.821130i \(0.693344\pi\)
\(858\) 0 0
\(859\) 34.0689 1.16242 0.581208 0.813755i \(-0.302580\pi\)
0.581208 + 0.813755i \(0.302580\pi\)
\(860\) 0 0
\(861\) −12.3262 −0.420077
\(862\) 0 0
\(863\) −37.2361 −1.26753 −0.633765 0.773525i \(-0.718491\pi\)
−0.633765 + 0.773525i \(0.718491\pi\)
\(864\) 0 0
\(865\) −21.5623 −0.733140
\(866\) 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
\(875\) 1.61803 0.0546995
\(876\) 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
\(885\) −7.23607 −0.243238
\(886\) 0 0
\(887\) 58.8328 1.97541 0.987706 0.156321i \(-0.0499634\pi\)
0.987706 + 0.156321i \(0.0499634\pi\)
\(888\) 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
\(895\) 20.1803 0.674554
\(896\) 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
\(905\) −18.8541 −0.626732
\(906\) 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
\(915\) −3.90983 −0.129255
\(916\) 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
\(925\) 2.47214 0.0812833
\(926\) 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
\(935\) 19.6180 0.641578
\(936\) 0 0
\(937\) −12.2016 −0.398610 −0.199305 0.979938i \(-0.563868\pi\)
−0.199305 + 0.979938i \(0.563868\pi\)
\(938\) 0 0
\(939\) 7.29180 0.237959
\(940\) 0 0
\(941\) 60.5066 1.97246 0.986229 0.165385i \(-0.0528868\pi\)
0.986229 + 0.165385i \(0.0528868\pi\)
\(942\) 0 0
\(943\) 12.3262 0.401398
\(944\) 0 0
\(945\) 5.61803 0.182755
\(946\) 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 \(-0.609366\pi\)
−0.336863 + 0.941554i \(0.609366\pi\)
\(954\) 0 0
\(955\) −0.291796 −0.00944230
\(956\) 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
\(965\) −5.23607 −0.168555
\(966\) 0 0
\(967\) −50.5410 −1.62529 −0.812645 0.582759i \(-0.801973\pi\)
−0.812645 + 0.582759i \(0.801973\pi\)
\(968\) 0 0
\(969\) −15.2705 −0.490559
\(970\) 0 0
\(971\) 0.729490 0.0234105 0.0117052 0.999931i \(-0.496274\pi\)
0.0117052 + 0.999931i \(0.496274\pi\)
\(972\) 0 0
\(973\) −27.8885 −0.894066
\(974\) 0 0
\(975\) 2.52786 0.0809564
\(976\) 0 0
\(977\) −3.43769 −0.109982 −0.0549908 0.998487i \(-0.517513\pi\)
−0.0549908 + 0.998487i \(0.517513\pi\)
\(978\) 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 \(-0.599431\pi\)
−0.307317 + 0.951607i \(0.599431\pi\)
\(984\) 0 0
\(985\) −2.43769 −0.0776714
\(986\) 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
\(995\) 2.00000 0.0634043
\(996\) 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 7360.2.a.bn.1.1 2
4.3 odd 2 7360.2.a.bh.1.2 2
8.3 odd 2 230.2.a.c.1.1 2
8.5 even 2 1840.2.a.l.1.2 2
24.11 even 2 2070.2.a.u.1.2 2
40.3 even 4 1150.2.b.i.599.1 4
40.19 odd 2 1150.2.a.j.1.2 2
40.27 even 4 1150.2.b.i.599.4 4
40.29 even 2 9200.2.a.bu.1.1 2
184.91 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 8.3 odd 2
1150.2.a.j.1.2 2 40.19 odd 2
1150.2.b.i.599.1 4 40.3 even 4
1150.2.b.i.599.4 4 40.27 even 4
1840.2.a.l.1.2 2 8.5 even 2
2070.2.a.u.1.2 2 24.11 even 2
5290.2.a.o.1.1 2 184.91 even 2
7360.2.a.bh.1.2 2 4.3 odd 2
7360.2.a.bn.1.1 2 1.1 even 1 trivial
9200.2.a.bu.1.1 2 40.29 even 2