Properties

Label 1840.2.a.t.1.2
Level $1840$
Weight $2$
Character 1840.1
Self dual yes
Analytic conductor $14.692$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.6924739719\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.621.1
Defining polynomial: \(x^{3} - 6 x - 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.523976\) of defining polynomial
Character \(\chi\) \(=\) 1840.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.523976 q^{3} -1.00000 q^{5} -0.476024 q^{7} -2.72545 q^{9} +O(q^{10})\) \(q+0.523976 q^{3} -1.00000 q^{5} -0.476024 q^{7} -2.72545 q^{9} +1.67750 q^{11} +2.67750 q^{13} -0.523976 q^{15} +1.67750 q^{17} -7.92692 q^{19} -0.249425 q^{21} -1.00000 q^{23} +1.00000 q^{25} -3.00000 q^{27} -2.20147 q^{29} -6.77340 q^{31} +0.878968 q^{33} +0.476024 q^{35} +4.00000 q^{37} +1.40294 q^{39} +5.97487 q^{41} +0.402945 q^{43} +2.72545 q^{45} -1.79853 q^{47} -6.77340 q^{49} +0.878968 q^{51} -10.8059 q^{53} -1.67750 q^{55} -4.15352 q^{57} -9.45090 q^{59} +6.32250 q^{61} +1.29738 q^{63} -2.67750 q^{65} -14.7100 q^{67} -0.523976 q^{69} -9.97487 q^{71} -6.10557 q^{73} +0.523976 q^{75} -0.798528 q^{77} +6.60442 q^{81} -4.49885 q^{83} -1.67750 q^{85} -1.15352 q^{87} -3.59706 q^{89} -1.27455 q^{91} -3.54910 q^{93} +7.92692 q^{95} -6.08044 q^{97} -4.57193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{5} - 3 q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q - 3 q^{5} - 3 q^{7} + 3 q^{9} - 3 q^{11} - 3 q^{17} - 3 q^{19} + 12 q^{21} - 3 q^{23} + 3 q^{25} - 9 q^{27} + 3 q^{29} - 6 q^{31} - 15 q^{33} + 3 q^{35} + 12 q^{37} - 15 q^{39} - 6 q^{41} - 18 q^{43} - 3 q^{45} - 15 q^{47} - 6 q^{49} - 15 q^{51} + 6 q^{53} + 3 q^{55} - 6 q^{57} - 6 q^{59} + 27 q^{61} - 12 q^{63} - 12 q^{67} - 6 q^{71} - 15 q^{73} - 12 q^{77} - 9 q^{81} + 12 q^{83} + 3 q^{85} + 3 q^{87} - 30 q^{89} - 15 q^{91} - 33 q^{93} + 3 q^{95} + 9 q^{97} - 9 q^{99} + O(q^{100}) \)

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
\(3\) 0.523976 0.302518 0.151259 0.988494i \(-0.451667\pi\)
0.151259 + 0.988494i \(0.451667\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.476024 −0.179920 −0.0899600 0.995945i \(-0.528674\pi\)
−0.0899600 + 0.995945i \(0.528674\pi\)
\(8\) 0 0
\(9\) −2.72545 −0.908483
\(10\) 0 0
\(11\) 1.67750 0.505784 0.252892 0.967495i \(-0.418618\pi\)
0.252892 + 0.967495i \(0.418618\pi\)
\(12\) 0 0
\(13\) 2.67750 0.742604 0.371302 0.928512i \(-0.378911\pi\)
0.371302 + 0.928512i \(0.378911\pi\)
\(14\) 0 0
\(15\) −0.523976 −0.135290
\(16\) 0 0
\(17\) 1.67750 0.406853 0.203426 0.979090i \(-0.434792\pi\)
0.203426 + 0.979090i \(0.434792\pi\)
\(18\) 0 0
\(19\) −7.92692 −1.81856 −0.909280 0.416184i \(-0.863367\pi\)
−0.909280 + 0.416184i \(0.863367\pi\)
\(20\) 0 0
\(21\) −0.249425 −0.0544290
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −3.00000 −0.577350
\(28\) 0 0
\(29\) −2.20147 −0.408803 −0.204402 0.978887i \(-0.565525\pi\)
−0.204402 + 0.978887i \(0.565525\pi\)
\(30\) 0 0
\(31\) −6.77340 −1.21654 −0.608269 0.793731i \(-0.708136\pi\)
−0.608269 + 0.793731i \(0.708136\pi\)
\(32\) 0 0
\(33\) 0.878968 0.153009
\(34\) 0 0
\(35\) 0.476024 0.0804627
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 1.40294 0.224651
\(40\) 0 0
\(41\) 5.97487 0.933119 0.466559 0.884490i \(-0.345493\pi\)
0.466559 + 0.884490i \(0.345493\pi\)
\(42\) 0 0
\(43\) 0.402945 0.0614485 0.0307242 0.999528i \(-0.490219\pi\)
0.0307242 + 0.999528i \(0.490219\pi\)
\(44\) 0 0
\(45\) 2.72545 0.406286
\(46\) 0 0
\(47\) −1.79853 −0.262342 −0.131171 0.991360i \(-0.541874\pi\)
−0.131171 + 0.991360i \(0.541874\pi\)
\(48\) 0 0
\(49\) −6.77340 −0.967629
\(50\) 0 0
\(51\) 0.878968 0.123080
\(52\) 0 0
\(53\) −10.8059 −1.48430 −0.742152 0.670232i \(-0.766195\pi\)
−0.742152 + 0.670232i \(0.766195\pi\)
\(54\) 0 0
\(55\) −1.67750 −0.226194
\(56\) 0 0
\(57\) −4.15352 −0.550147
\(58\) 0 0
\(59\) −9.45090 −1.23040 −0.615201 0.788370i \(-0.710925\pi\)
−0.615201 + 0.788370i \(0.710925\pi\)
\(60\) 0 0
\(61\) 6.32250 0.809514 0.404757 0.914424i \(-0.367356\pi\)
0.404757 + 0.914424i \(0.367356\pi\)
\(62\) 0 0
\(63\) 1.29738 0.163454
\(64\) 0 0
\(65\) −2.67750 −0.332102
\(66\) 0 0
\(67\) −14.7100 −1.79711 −0.898555 0.438860i \(-0.855382\pi\)
−0.898555 + 0.438860i \(0.855382\pi\)
\(68\) 0 0
\(69\) −0.523976 −0.0630793
\(70\) 0 0
\(71\) −9.97487 −1.18380 −0.591900 0.806012i \(-0.701622\pi\)
−0.591900 + 0.806012i \(0.701622\pi\)
\(72\) 0 0
\(73\) −6.10557 −0.714603 −0.357301 0.933989i \(-0.616303\pi\)
−0.357301 + 0.933989i \(0.616303\pi\)
\(74\) 0 0
\(75\) 0.523976 0.0605036
\(76\) 0 0
\(77\) −0.798528 −0.0910007
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 6.60442 0.733824
\(82\) 0 0
\(83\) −4.49885 −0.493813 −0.246906 0.969039i \(-0.579414\pi\)
−0.246906 + 0.969039i \(0.579414\pi\)
\(84\) 0 0
\(85\) −1.67750 −0.181950
\(86\) 0 0
\(87\) −1.15352 −0.123670
\(88\) 0 0
\(89\) −3.59706 −0.381287 −0.190644 0.981659i \(-0.561057\pi\)
−0.190644 + 0.981659i \(0.561057\pi\)
\(90\) 0 0
\(91\) −1.27455 −0.133609
\(92\) 0 0
\(93\) −3.54910 −0.368025
\(94\) 0 0
\(95\) 7.92692 0.813285
\(96\) 0 0
\(97\) −6.08044 −0.617375 −0.308688 0.951163i \(-0.599890\pi\)
−0.308688 + 0.951163i \(0.599890\pi\)
\(98\) 0 0
\(99\) −4.57193 −0.459496
\(100\) 0 0
\(101\) 11.4509 1.13941 0.569703 0.821850i \(-0.307058\pi\)
0.569703 + 0.821850i \(0.307058\pi\)
\(102\) 0 0
\(103\) 2.32250 0.228843 0.114422 0.993432i \(-0.463499\pi\)
0.114422 + 0.993432i \(0.463499\pi\)
\(104\) 0 0
\(105\) 0.249425 0.0243414
\(106\) 0 0
\(107\) 7.85384 0.759260 0.379630 0.925138i \(-0.376051\pi\)
0.379630 + 0.925138i \(0.376051\pi\)
\(108\) 0 0
\(109\) 13.9269 1.33396 0.666979 0.745077i \(-0.267587\pi\)
0.666979 + 0.745077i \(0.267587\pi\)
\(110\) 0 0
\(111\) 2.09591 0.198935
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) −7.29738 −0.674643
\(118\) 0 0
\(119\) −0.798528 −0.0732009
\(120\) 0 0
\(121\) −8.18601 −0.744182
\(122\) 0 0
\(123\) 3.13069 0.282285
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 11.1033 0.985256 0.492628 0.870240i \(-0.336036\pi\)
0.492628 + 0.870240i \(0.336036\pi\)
\(128\) 0 0
\(129\) 0.211133 0.0185893
\(130\) 0 0
\(131\) −7.65237 −0.668591 −0.334295 0.942468i \(-0.608498\pi\)
−0.334295 + 0.942468i \(0.608498\pi\)
\(132\) 0 0
\(133\) 3.77340 0.327195
\(134\) 0 0
\(135\) 3.00000 0.258199
\(136\) 0 0
\(137\) −21.3778 −1.82643 −0.913215 0.407478i \(-0.866408\pi\)
−0.913215 + 0.407478i \(0.866408\pi\)
\(138\) 0 0
\(139\) 8.60442 0.729817 0.364909 0.931043i \(-0.381100\pi\)
0.364909 + 0.931043i \(0.381100\pi\)
\(140\) 0 0
\(141\) −0.942386 −0.0793632
\(142\) 0 0
\(143\) 4.49149 0.375597
\(144\) 0 0
\(145\) 2.20147 0.182822
\(146\) 0 0
\(147\) −3.54910 −0.292725
\(148\) 0 0
\(149\) 4.97487 0.407558 0.203779 0.979017i \(-0.434678\pi\)
0.203779 + 0.979017i \(0.434678\pi\)
\(150\) 0 0
\(151\) 0.926921 0.0754318 0.0377159 0.999289i \(-0.487992\pi\)
0.0377159 + 0.999289i \(0.487992\pi\)
\(152\) 0 0
\(153\) −4.57193 −0.369619
\(154\) 0 0
\(155\) 6.77340 0.544053
\(156\) 0 0
\(157\) 22.3527 1.78394 0.891970 0.452096i \(-0.149323\pi\)
0.891970 + 0.452096i \(0.149323\pi\)
\(158\) 0 0
\(159\) −5.66203 −0.449028
\(160\) 0 0
\(161\) 0.476024 0.0375159
\(162\) 0 0
\(163\) 7.93658 0.621641 0.310821 0.950469i \(-0.399396\pi\)
0.310821 + 0.950469i \(0.399396\pi\)
\(164\) 0 0
\(165\) −0.878968 −0.0684276
\(166\) 0 0
\(167\) −12.8059 −0.990949 −0.495475 0.868622i \(-0.665006\pi\)
−0.495475 + 0.868622i \(0.665006\pi\)
\(168\) 0 0
\(169\) −5.83102 −0.448540
\(170\) 0 0
\(171\) 21.6044 1.65213
\(172\) 0 0
\(173\) −24.6752 −1.87602 −0.938010 0.346608i \(-0.887334\pi\)
−0.938010 + 0.346608i \(0.887334\pi\)
\(174\) 0 0
\(175\) −0.476024 −0.0359840
\(176\) 0 0
\(177\) −4.95205 −0.372219
\(178\) 0 0
\(179\) 13.1033 0.979384 0.489692 0.871895i \(-0.337109\pi\)
0.489692 + 0.871895i \(0.337109\pi\)
\(180\) 0 0
\(181\) 9.52398 0.707912 0.353956 0.935262i \(-0.384836\pi\)
0.353956 + 0.935262i \(0.384836\pi\)
\(182\) 0 0
\(183\) 3.31284 0.244892
\(184\) 0 0
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) 2.81399 0.205780
\(188\) 0 0
\(189\) 1.42807 0.103877
\(190\) 0 0
\(191\) −5.85384 −0.423569 −0.211785 0.977316i \(-0.567928\pi\)
−0.211785 + 0.977316i \(0.567928\pi\)
\(192\) 0 0
\(193\) 4.41261 0.317626 0.158813 0.987309i \(-0.449233\pi\)
0.158813 + 0.987309i \(0.449233\pi\)
\(194\) 0 0
\(195\) −1.40294 −0.100467
\(196\) 0 0
\(197\) 11.4258 0.814053 0.407026 0.913416i \(-0.366566\pi\)
0.407026 + 0.913416i \(0.366566\pi\)
\(198\) 0 0
\(199\) 0.307039 0.0217654 0.0108827 0.999941i \(-0.496536\pi\)
0.0108827 + 0.999941i \(0.496536\pi\)
\(200\) 0 0
\(201\) −7.70768 −0.543658
\(202\) 0 0
\(203\) 1.04795 0.0735519
\(204\) 0 0
\(205\) −5.97487 −0.417303
\(206\) 0 0
\(207\) 2.72545 0.189432
\(208\) 0 0
\(209\) −13.2974 −0.919799
\(210\) 0 0
\(211\) −17.3047 −1.19131 −0.595654 0.803241i \(-0.703107\pi\)
−0.595654 + 0.803241i \(0.703107\pi\)
\(212\) 0 0
\(213\) −5.22660 −0.358121
\(214\) 0 0
\(215\) −0.402945 −0.0274806
\(216\) 0 0
\(217\) 3.22430 0.218880
\(218\) 0 0
\(219\) −3.19917 −0.216180
\(220\) 0 0
\(221\) 4.49149 0.302130
\(222\) 0 0
\(223\) 1.90409 0.127508 0.0637538 0.997966i \(-0.479693\pi\)
0.0637538 + 0.997966i \(0.479693\pi\)
\(224\) 0 0
\(225\) −2.72545 −0.181697
\(226\) 0 0
\(227\) −17.3550 −1.15189 −0.575946 0.817488i \(-0.695366\pi\)
−0.575946 + 0.817488i \(0.695366\pi\)
\(228\) 0 0
\(229\) −6.19181 −0.409166 −0.204583 0.978849i \(-0.565584\pi\)
−0.204583 + 0.978849i \(0.565584\pi\)
\(230\) 0 0
\(231\) −0.418410 −0.0275293
\(232\) 0 0
\(233\) −15.7985 −1.03500 −0.517498 0.855684i \(-0.673137\pi\)
−0.517498 + 0.855684i \(0.673137\pi\)
\(234\) 0 0
\(235\) 1.79853 0.117323
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.34763 −0.410594 −0.205297 0.978700i \(-0.565816\pi\)
−0.205297 + 0.978700i \(0.565816\pi\)
\(240\) 0 0
\(241\) 5.69296 0.366716 0.183358 0.983046i \(-0.441303\pi\)
0.183358 + 0.983046i \(0.441303\pi\)
\(242\) 0 0
\(243\) 12.4606 0.799345
\(244\) 0 0
\(245\) 6.77340 0.432737
\(246\) 0 0
\(247\) −21.2243 −1.35047
\(248\) 0 0
\(249\) −2.35729 −0.149387
\(250\) 0 0
\(251\) 28.9246 1.82571 0.912853 0.408288i \(-0.133874\pi\)
0.912853 + 0.408288i \(0.133874\pi\)
\(252\) 0 0
\(253\) −1.67750 −0.105463
\(254\) 0 0
\(255\) −0.878968 −0.0550431
\(256\) 0 0
\(257\) −14.5085 −0.905016 −0.452508 0.891760i \(-0.649471\pi\)
−0.452508 + 0.891760i \(0.649471\pi\)
\(258\) 0 0
\(259\) −1.90409 −0.118315
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 15.7734 0.972630 0.486315 0.873784i \(-0.338341\pi\)
0.486315 + 0.873784i \(0.338341\pi\)
\(264\) 0 0
\(265\) 10.8059 0.663801
\(266\) 0 0
\(267\) −1.88477 −0.115346
\(268\) 0 0
\(269\) −6.20147 −0.378110 −0.189055 0.981966i \(-0.560543\pi\)
−0.189055 + 0.981966i \(0.560543\pi\)
\(270\) 0 0
\(271\) 25.5696 1.55324 0.776622 0.629967i \(-0.216931\pi\)
0.776622 + 0.629967i \(0.216931\pi\)
\(272\) 0 0
\(273\) −0.667835 −0.0404192
\(274\) 0 0
\(275\) 1.67750 0.101157
\(276\) 0 0
\(277\) 7.03829 0.422890 0.211445 0.977390i \(-0.432183\pi\)
0.211445 + 0.977390i \(0.432183\pi\)
\(278\) 0 0
\(279\) 18.4606 1.10520
\(280\) 0 0
\(281\) 29.0627 1.73373 0.866867 0.498540i \(-0.166130\pi\)
0.866867 + 0.498540i \(0.166130\pi\)
\(282\) 0 0
\(283\) 18.6141 1.10649 0.553246 0.833018i \(-0.313389\pi\)
0.553246 + 0.833018i \(0.313389\pi\)
\(284\) 0 0
\(285\) 4.15352 0.246033
\(286\) 0 0
\(287\) −2.84418 −0.167887
\(288\) 0 0
\(289\) −14.1860 −0.834471
\(290\) 0 0
\(291\) −3.18601 −0.186767
\(292\) 0 0
\(293\) 23.4006 1.36708 0.683540 0.729913i \(-0.260439\pi\)
0.683540 + 0.729913i \(0.260439\pi\)
\(294\) 0 0
\(295\) 9.45090 0.550253
\(296\) 0 0
\(297\) −5.03249 −0.292015
\(298\) 0 0
\(299\) −2.67750 −0.154844
\(300\) 0 0
\(301\) −0.191811 −0.0110558
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) −6.32250 −0.362026
\(306\) 0 0
\(307\) 1.53134 0.0873981 0.0436990 0.999045i \(-0.486086\pi\)
0.0436990 + 0.999045i \(0.486086\pi\)
\(308\) 0 0
\(309\) 1.21694 0.0692291
\(310\) 0 0
\(311\) 7.55646 0.428488 0.214244 0.976780i \(-0.431271\pi\)
0.214244 + 0.976780i \(0.431271\pi\)
\(312\) 0 0
\(313\) −2.32987 −0.131692 −0.0658459 0.997830i \(-0.520975\pi\)
−0.0658459 + 0.997830i \(0.520975\pi\)
\(314\) 0 0
\(315\) −1.29738 −0.0730990
\(316\) 0 0
\(317\) −15.3778 −0.863704 −0.431852 0.901944i \(-0.642140\pi\)
−0.431852 + 0.901944i \(0.642140\pi\)
\(318\) 0 0
\(319\) −3.69296 −0.206766
\(320\) 0 0
\(321\) 4.11523 0.229690
\(322\) 0 0
\(323\) −13.2974 −0.739886
\(324\) 0 0
\(325\) 2.67750 0.148521
\(326\) 0 0
\(327\) 7.29738 0.403546
\(328\) 0 0
\(329\) 0.856142 0.0472006
\(330\) 0 0
\(331\) −22.9115 −1.25933 −0.629664 0.776868i \(-0.716807\pi\)
−0.629664 + 0.776868i \(0.716807\pi\)
\(332\) 0 0
\(333\) −10.9018 −0.597415
\(334\) 0 0
\(335\) 14.7100 0.803692
\(336\) 0 0
\(337\) 26.5410 1.44578 0.722890 0.690963i \(-0.242813\pi\)
0.722890 + 0.690963i \(0.242813\pi\)
\(338\) 0 0
\(339\) −5.23976 −0.284585
\(340\) 0 0
\(341\) −11.3624 −0.615306
\(342\) 0 0
\(343\) 6.55646 0.354016
\(344\) 0 0
\(345\) 0.523976 0.0282099
\(346\) 0 0
\(347\) 3.27455 0.175787 0.0878936 0.996130i \(-0.471986\pi\)
0.0878936 + 0.996130i \(0.471986\pi\)
\(348\) 0 0
\(349\) 32.0553 1.71588 0.857941 0.513749i \(-0.171744\pi\)
0.857941 + 0.513749i \(0.171744\pi\)
\(350\) 0 0
\(351\) −8.03249 −0.428742
\(352\) 0 0
\(353\) 11.1535 0.593642 0.296821 0.954933i \(-0.404074\pi\)
0.296821 + 0.954933i \(0.404074\pi\)
\(354\) 0 0
\(355\) 9.97487 0.529411
\(356\) 0 0
\(357\) −0.418410 −0.0221446
\(358\) 0 0
\(359\) −22.4029 −1.18238 −0.591191 0.806532i \(-0.701342\pi\)
−0.591191 + 0.806532i \(0.701342\pi\)
\(360\) 0 0
\(361\) 43.8361 2.30716
\(362\) 0 0
\(363\) −4.28927 −0.225129
\(364\) 0 0
\(365\) 6.10557 0.319580
\(366\) 0 0
\(367\) −14.2877 −0.745813 −0.372906 0.927869i \(-0.621639\pi\)
−0.372906 + 0.927869i \(0.621639\pi\)
\(368\) 0 0
\(369\) −16.2842 −0.847722
\(370\) 0 0
\(371\) 5.14386 0.267056
\(372\) 0 0
\(373\) −1.23976 −0.0641925 −0.0320963 0.999485i \(-0.510218\pi\)
−0.0320963 + 0.999485i \(0.510218\pi\)
\(374\) 0 0
\(375\) −0.523976 −0.0270580
\(376\) 0 0
\(377\) −5.89443 −0.303579
\(378\) 0 0
\(379\) −4.38748 −0.225370 −0.112685 0.993631i \(-0.535945\pi\)
−0.112685 + 0.993631i \(0.535945\pi\)
\(380\) 0 0
\(381\) 5.81785 0.298057
\(382\) 0 0
\(383\) −18.4989 −0.945247 −0.472624 0.881264i \(-0.656693\pi\)
−0.472624 + 0.881264i \(0.656693\pi\)
\(384\) 0 0
\(385\) 0.798528 0.0406967
\(386\) 0 0
\(387\) −1.09821 −0.0558249
\(388\) 0 0
\(389\) 21.6775 1.09909 0.549546 0.835463i \(-0.314801\pi\)
0.549546 + 0.835463i \(0.314801\pi\)
\(390\) 0 0
\(391\) −1.67750 −0.0848346
\(392\) 0 0
\(393\) −4.00966 −0.202261
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −20.6849 −1.03814 −0.519072 0.854731i \(-0.673722\pi\)
−0.519072 + 0.854731i \(0.673722\pi\)
\(398\) 0 0
\(399\) 1.97717 0.0989825
\(400\) 0 0
\(401\) −28.5638 −1.42641 −0.713205 0.700956i \(-0.752757\pi\)
−0.713205 + 0.700956i \(0.752757\pi\)
\(402\) 0 0
\(403\) −18.1358 −0.903406
\(404\) 0 0
\(405\) −6.60442 −0.328176
\(406\) 0 0
\(407\) 6.70998 0.332602
\(408\) 0 0
\(409\) 16.7734 0.829391 0.414696 0.909960i \(-0.363888\pi\)
0.414696 + 0.909960i \(0.363888\pi\)
\(410\) 0 0
\(411\) −11.2015 −0.552528
\(412\) 0 0
\(413\) 4.49885 0.221374
\(414\) 0 0
\(415\) 4.49885 0.220840
\(416\) 0 0
\(417\) 4.50851 0.220783
\(418\) 0 0
\(419\) 4.59476 0.224469 0.112234 0.993682i \(-0.464199\pi\)
0.112234 + 0.993682i \(0.464199\pi\)
\(420\) 0 0
\(421\) 31.8310 1.55135 0.775674 0.631133i \(-0.217410\pi\)
0.775674 + 0.631133i \(0.217410\pi\)
\(422\) 0 0
\(423\) 4.90179 0.238333
\(424\) 0 0
\(425\) 1.67750 0.0813705
\(426\) 0 0
\(427\) −3.00966 −0.145648
\(428\) 0 0
\(429\) 2.35343 0.113625
\(430\) 0 0
\(431\) 16.0650 0.773823 0.386911 0.922117i \(-0.373542\pi\)
0.386911 + 0.922117i \(0.373542\pi\)
\(432\) 0 0
\(433\) −7.68486 −0.369311 −0.184655 0.982803i \(-0.559117\pi\)
−0.184655 + 0.982803i \(0.559117\pi\)
\(434\) 0 0
\(435\) 1.15352 0.0553070
\(436\) 0 0
\(437\) 7.92692 0.379196
\(438\) 0 0
\(439\) −15.9822 −0.762790 −0.381395 0.924412i \(-0.624556\pi\)
−0.381395 + 0.924412i \(0.624556\pi\)
\(440\) 0 0
\(441\) 18.4606 0.879074
\(442\) 0 0
\(443\) 3.57929 0.170057 0.0850286 0.996379i \(-0.472902\pi\)
0.0850286 + 0.996379i \(0.472902\pi\)
\(444\) 0 0
\(445\) 3.59706 0.170517
\(446\) 0 0
\(447\) 2.60672 0.123293
\(448\) 0 0
\(449\) −28.5217 −1.34602 −0.673011 0.739633i \(-0.734999\pi\)
−0.673011 + 0.739633i \(0.734999\pi\)
\(450\) 0 0
\(451\) 10.0228 0.471956
\(452\) 0 0
\(453\) 0.485685 0.0228195
\(454\) 0 0
\(455\) 1.27455 0.0597519
\(456\) 0 0
\(457\) −4.49885 −0.210447 −0.105224 0.994449i \(-0.533556\pi\)
−0.105224 + 0.994449i \(0.533556\pi\)
\(458\) 0 0
\(459\) −5.03249 −0.234896
\(460\) 0 0
\(461\) 2.29738 0.107000 0.0534998 0.998568i \(-0.482962\pi\)
0.0534998 + 0.998568i \(0.482962\pi\)
\(462\) 0 0
\(463\) 33.4966 1.55672 0.778358 0.627820i \(-0.216053\pi\)
0.778358 + 0.627820i \(0.216053\pi\)
\(464\) 0 0
\(465\) 3.54910 0.164586
\(466\) 0 0
\(467\) 5.23976 0.242467 0.121234 0.992624i \(-0.461315\pi\)
0.121234 + 0.992624i \(0.461315\pi\)
\(468\) 0 0
\(469\) 7.00230 0.323336
\(470\) 0 0
\(471\) 11.7123 0.539674
\(472\) 0 0
\(473\) 0.675938 0.0310797
\(474\) 0 0
\(475\) −7.92692 −0.363712
\(476\) 0 0
\(477\) 29.4509 1.34846
\(478\) 0 0
\(479\) 2.40294 0.109793 0.0548967 0.998492i \(-0.482517\pi\)
0.0548967 + 0.998492i \(0.482517\pi\)
\(480\) 0 0
\(481\) 10.7100 0.488333
\(482\) 0 0
\(483\) 0.249425 0.0113492
\(484\) 0 0
\(485\) 6.08044 0.276099
\(486\) 0 0
\(487\) −25.8944 −1.17339 −0.586694 0.809808i \(-0.699571\pi\)
−0.586694 + 0.809808i \(0.699571\pi\)
\(488\) 0 0
\(489\) 4.15858 0.188058
\(490\) 0 0
\(491\) 0.489189 0.0220768 0.0110384 0.999939i \(-0.496486\pi\)
0.0110384 + 0.999939i \(0.496486\pi\)
\(492\) 0 0
\(493\) −3.69296 −0.166323
\(494\) 0 0
\(495\) 4.57193 0.205493
\(496\) 0 0
\(497\) 4.74828 0.212989
\(498\) 0 0
\(499\) 38.4583 1.72163 0.860814 0.508920i \(-0.169955\pi\)
0.860814 + 0.508920i \(0.169955\pi\)
\(500\) 0 0
\(501\) −6.70998 −0.299780
\(502\) 0 0
\(503\) −37.8960 −1.68970 −0.844849 0.535004i \(-0.820310\pi\)
−0.844849 + 0.535004i \(0.820310\pi\)
\(504\) 0 0
\(505\) −11.4509 −0.509558
\(506\) 0 0
\(507\) −3.05531 −0.135691
\(508\) 0 0
\(509\) 8.70032 0.385635 0.192818 0.981235i \(-0.438237\pi\)
0.192818 + 0.981235i \(0.438237\pi\)
\(510\) 0 0
\(511\) 2.90639 0.128571
\(512\) 0 0
\(513\) 23.7808 1.04995
\(514\) 0 0
\(515\) −2.32250 −0.102342
\(516\) 0 0
\(517\) −3.01702 −0.132689
\(518\) 0 0
\(519\) −12.9292 −0.567530
\(520\) 0 0
\(521\) 25.1129 1.10022 0.550109 0.835093i \(-0.314586\pi\)
0.550109 + 0.835093i \(0.314586\pi\)
\(522\) 0 0
\(523\) −12.7100 −0.555769 −0.277884 0.960615i \(-0.589633\pi\)
−0.277884 + 0.960615i \(0.589633\pi\)
\(524\) 0 0
\(525\) −0.249425 −0.0108858
\(526\) 0 0
\(527\) −11.3624 −0.494952
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 25.7579 1.11780
\(532\) 0 0
\(533\) 15.9977 0.692937
\(534\) 0 0
\(535\) −7.85384 −0.339551
\(536\) 0 0
\(537\) 6.86580 0.296281
\(538\) 0 0
\(539\) −11.3624 −0.489411
\(540\) 0 0
\(541\) −0.251725 −0.0108225 −0.00541124 0.999985i \(-0.501722\pi\)
−0.00541124 + 0.999985i \(0.501722\pi\)
\(542\) 0 0
\(543\) 4.99034 0.214156
\(544\) 0 0
\(545\) −13.9269 −0.596564
\(546\) 0 0
\(547\) −24.3395 −1.04068 −0.520342 0.853958i \(-0.674195\pi\)
−0.520342 + 0.853958i \(0.674195\pi\)
\(548\) 0 0
\(549\) −17.2317 −0.735429
\(550\) 0 0
\(551\) 17.4509 0.743433
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.09591 −0.0889662
\(556\) 0 0
\(557\) −23.4966 −0.995581 −0.497790 0.867297i \(-0.665855\pi\)
−0.497790 + 0.867297i \(0.665855\pi\)
\(558\) 0 0
\(559\) 1.07888 0.0456319
\(560\) 0 0
\(561\) 1.47447 0.0622520
\(562\) 0 0
\(563\) 19.5159 0.822496 0.411248 0.911523i \(-0.365093\pi\)
0.411248 + 0.911523i \(0.365093\pi\)
\(564\) 0 0
\(565\) 10.0000 0.420703
\(566\) 0 0
\(567\) −3.14386 −0.132030
\(568\) 0 0
\(569\) −8.51817 −0.357100 −0.178550 0.983931i \(-0.557141\pi\)
−0.178550 + 0.983931i \(0.557141\pi\)
\(570\) 0 0
\(571\) 27.4811 1.15005 0.575024 0.818137i \(-0.304993\pi\)
0.575024 + 0.818137i \(0.304993\pi\)
\(572\) 0 0
\(573\) −3.06728 −0.128137
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −26.1512 −1.08869 −0.544345 0.838862i \(-0.683222\pi\)
−0.544345 + 0.838862i \(0.683222\pi\)
\(578\) 0 0
\(579\) 2.31210 0.0960877
\(580\) 0 0
\(581\) 2.14156 0.0888468
\(582\) 0 0
\(583\) −18.1268 −0.750737
\(584\) 0 0
\(585\) 7.29738 0.301709
\(586\) 0 0
\(587\) 34.3276 1.41685 0.708425 0.705786i \(-0.249406\pi\)
0.708425 + 0.705786i \(0.249406\pi\)
\(588\) 0 0
\(589\) 53.6922 2.21235
\(590\) 0 0
\(591\) 5.98683 0.246265
\(592\) 0 0
\(593\) 15.9497 0.654978 0.327489 0.944855i \(-0.393798\pi\)
0.327489 + 0.944855i \(0.393798\pi\)
\(594\) 0 0
\(595\) 0.798528 0.0327364
\(596\) 0 0
\(597\) 0.160881 0.00658443
\(598\) 0 0
\(599\) −40.5940 −1.65863 −0.829313 0.558784i \(-0.811268\pi\)
−0.829313 + 0.558784i \(0.811268\pi\)
\(600\) 0 0
\(601\) −29.0302 −1.18417 −0.592083 0.805877i \(-0.701694\pi\)
−0.592083 + 0.805877i \(0.701694\pi\)
\(602\) 0 0
\(603\) 40.0913 1.63264
\(604\) 0 0
\(605\) 8.18601 0.332809
\(606\) 0 0
\(607\) −16.9977 −0.689915 −0.344958 0.938618i \(-0.612107\pi\)
−0.344958 + 0.938618i \(0.612107\pi\)
\(608\) 0 0
\(609\) 0.549103 0.0222508
\(610\) 0 0
\(611\) −4.81555 −0.194816
\(612\) 0 0
\(613\) 30.3024 1.22390 0.611952 0.790895i \(-0.290385\pi\)
0.611952 + 0.790895i \(0.290385\pi\)
\(614\) 0 0
\(615\) −3.13069 −0.126242
\(616\) 0 0
\(617\) −6.13069 −0.246812 −0.123406 0.992356i \(-0.539382\pi\)
−0.123406 + 0.992356i \(0.539382\pi\)
\(618\) 0 0
\(619\) 33.7305 1.35574 0.677872 0.735180i \(-0.262902\pi\)
0.677872 + 0.735180i \(0.262902\pi\)
\(620\) 0 0
\(621\) 3.00000 0.120386
\(622\) 0 0
\(623\) 1.71228 0.0686012
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −6.96751 −0.278256
\(628\) 0 0
\(629\) 6.70998 0.267545
\(630\) 0 0
\(631\) −4.85614 −0.193320 −0.0966600 0.995317i \(-0.530816\pi\)
−0.0966600 + 0.995317i \(0.530816\pi\)
\(632\) 0 0
\(633\) −9.06728 −0.360392
\(634\) 0 0
\(635\) −11.1033 −0.440620
\(636\) 0 0
\(637\) −18.1358 −0.718565
\(638\) 0 0
\(639\) 27.1860 1.07546
\(640\) 0 0
\(641\) 7.78887 0.307642 0.153821 0.988099i \(-0.450842\pi\)
0.153821 + 0.988099i \(0.450842\pi\)
\(642\) 0 0
\(643\) −43.6427 −1.72110 −0.860550 0.509366i \(-0.829880\pi\)
−0.860550 + 0.509366i \(0.829880\pi\)
\(644\) 0 0
\(645\) −0.211133 −0.00831337
\(646\) 0 0
\(647\) 15.4606 0.607817 0.303909 0.952701i \(-0.401708\pi\)
0.303909 + 0.952701i \(0.401708\pi\)
\(648\) 0 0
\(649\) −15.8538 −0.622318
\(650\) 0 0
\(651\) 1.68946 0.0662150
\(652\) 0 0
\(653\) −9.70613 −0.379830 −0.189915 0.981801i \(-0.560821\pi\)
−0.189915 + 0.981801i \(0.560821\pi\)
\(654\) 0 0
\(655\) 7.65237 0.299003
\(656\) 0 0
\(657\) 16.6404 0.649204
\(658\) 0 0
\(659\) −50.7100 −1.97538 −0.987690 0.156422i \(-0.950004\pi\)
−0.987690 + 0.156422i \(0.950004\pi\)
\(660\) 0 0
\(661\) 33.0132 1.28406 0.642032 0.766678i \(-0.278092\pi\)
0.642032 + 0.766678i \(0.278092\pi\)
\(662\) 0 0
\(663\) 2.35343 0.0913998
\(664\) 0 0
\(665\) −3.77340 −0.146326
\(666\) 0 0
\(667\) 2.20147 0.0852413
\(668\) 0 0
\(669\) 0.997701 0.0385733
\(670\) 0 0
\(671\) 10.6060 0.409439
\(672\) 0 0
\(673\) 19.2494 0.742011 0.371005 0.928631i \(-0.379013\pi\)
0.371005 + 0.928631i \(0.379013\pi\)
\(674\) 0 0
\(675\) −3.00000 −0.115470
\(676\) 0 0
\(677\) −25.1941 −0.968288 −0.484144 0.874988i \(-0.660869\pi\)
−0.484144 + 0.874988i \(0.660869\pi\)
\(678\) 0 0
\(679\) 2.89443 0.111078
\(680\) 0 0
\(681\) −9.09361 −0.348468
\(682\) 0 0
\(683\) −9.48339 −0.362872 −0.181436 0.983403i \(-0.558074\pi\)
−0.181436 + 0.983403i \(0.558074\pi\)
\(684\) 0 0
\(685\) 21.3778 0.816804
\(686\) 0 0
\(687\) −3.24436 −0.123780
\(688\) 0 0
\(689\) −28.9327 −1.10225
\(690\) 0 0
\(691\) 23.8538 0.907443 0.453721 0.891144i \(-0.350096\pi\)
0.453721 + 0.891144i \(0.350096\pi\)
\(692\) 0 0
\(693\) 2.17635 0.0826726
\(694\) 0 0
\(695\) −8.60442 −0.326384
\(696\) 0 0
\(697\) 10.0228 0.379642
\(698\) 0 0
\(699\) −8.27806 −0.313105
\(700\) 0 0
\(701\) 19.8767 0.750731 0.375366 0.926877i \(-0.377517\pi\)
0.375366 + 0.926877i \(0.377517\pi\)
\(702\) 0 0
\(703\) −31.7077 −1.19588
\(704\) 0 0
\(705\) 0.942386 0.0354923
\(706\) 0 0
\(707\) −5.45090 −0.205002
\(708\) 0 0
\(709\) −6.72545 −0.252580 −0.126290 0.991993i \(-0.540307\pi\)
−0.126290 + 0.991993i \(0.540307\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.77340 0.253666
\(714\) 0 0
\(715\) −4.49149 −0.167972
\(716\) 0 0
\(717\) −3.32601 −0.124212
\(718\) 0 0
\(719\) 38.2294 1.42571 0.712857 0.701309i \(-0.247401\pi\)
0.712857 + 0.701309i \(0.247401\pi\)
\(720\) 0 0
\(721\) −1.10557 −0.0411735
\(722\) 0 0
\(723\) 2.98298 0.110938
\(724\) 0 0
\(725\) −2.20147 −0.0817606
\(726\) 0 0
\(727\) 3.72315 0.138084 0.0690420 0.997614i \(-0.478006\pi\)
0.0690420 + 0.997614i \(0.478006\pi\)
\(728\) 0 0
\(729\) −13.2842 −0.492008
\(730\) 0 0
\(731\) 0.675938 0.0250005
\(732\) 0 0
\(733\) −8.49885 −0.313912 −0.156956 0.987606i \(-0.550168\pi\)
−0.156956 + 0.987606i \(0.550168\pi\)
\(734\) 0 0
\(735\) 3.54910 0.130911
\(736\) 0 0
\(737\) −24.6759 −0.908950
\(738\) 0 0
\(739\) 0.251725 0.00925984 0.00462992 0.999989i \(-0.498526\pi\)
0.00462992 + 0.999989i \(0.498526\pi\)
\(740\) 0 0
\(741\) −11.1210 −0.408541
\(742\) 0 0
\(743\) 29.7305 1.09071 0.545353 0.838206i \(-0.316395\pi\)
0.545353 + 0.838206i \(0.316395\pi\)
\(744\) 0 0
\(745\) −4.97487 −0.182265
\(746\) 0 0
\(747\) 12.2614 0.448621
\(748\) 0 0
\(749\) −3.73861 −0.136606
\(750\) 0 0
\(751\) −10.6597 −0.388979 −0.194490 0.980905i \(-0.562305\pi\)
−0.194490 + 0.980905i \(0.562305\pi\)
\(752\) 0 0
\(753\) 15.1558 0.552309
\(754\) 0 0
\(755\) −0.926921 −0.0337341
\(756\) 0 0
\(757\) −16.1918 −0.588501 −0.294251 0.955728i \(-0.595070\pi\)
−0.294251 + 0.955728i \(0.595070\pi\)
\(758\) 0 0
\(759\) −0.878968 −0.0319045
\(760\) 0 0
\(761\) −46.9343 −1.70137 −0.850683 0.525679i \(-0.823811\pi\)
−0.850683 + 0.525679i \(0.823811\pi\)
\(762\) 0 0
\(763\) −6.62954 −0.240006
\(764\) 0 0
\(765\) 4.57193 0.165298
\(766\) 0 0
\(767\) −25.3047 −0.913701
\(768\) 0 0
\(769\) −35.9954 −1.29803 −0.649014 0.760777i \(-0.724818\pi\)
−0.649014 + 0.760777i \(0.724818\pi\)
\(770\) 0 0
\(771\) −7.60212 −0.273784
\(772\) 0 0
\(773\) −21.8229 −0.784916 −0.392458 0.919770i \(-0.628375\pi\)
−0.392458 + 0.919770i \(0.628375\pi\)
\(774\) 0 0
\(775\) −6.77340 −0.243308
\(776\) 0 0
\(777\) −0.997701 −0.0357923
\(778\) 0 0
\(779\) −47.3624 −1.69693
\(780\) 0 0
\(781\) −16.7328 −0.598747
\(782\) 0 0
\(783\) 6.60442 0.236023
\(784\) 0 0
\(785\) −22.3527 −0.797802
\(786\) 0 0
\(787\) 7.16318 0.255340 0.127670 0.991817i \(-0.459250\pi\)
0.127670 + 0.991817i \(0.459250\pi\)
\(788\) 0 0
\(789\) 8.26489 0.294238
\(790\) 0 0
\(791\) 4.76024 0.169255
\(792\) 0 0
\(793\) 16.9285 0.601148
\(794\) 0 0
\(795\) 5.66203 0.200812
\(796\) 0 0
\(797\) −48.0604 −1.70239 −0.851193 0.524853i \(-0.824120\pi\)
−0.851193 + 0.524853i \(0.824120\pi\)
\(798\) 0 0
\(799\) −3.01702 −0.106735
\(800\) 0 0
\(801\) 9.80359 0.346393
\(802\) 0 0
\(803\) −10.2421 −0.361435
\(804\) 0 0
\(805\) −0.476024 −0.0167776
\(806\) 0 0
\(807\) −3.24943 −0.114385
\(808\) 0 0
\(809\) 0.0611183 0.00214880 0.00107440 0.999999i \(-0.499658\pi\)
0.00107440 + 0.999999i \(0.499658\pi\)
\(810\) 0 0
\(811\) −25.9092 −0.909794 −0.454897 0.890544i \(-0.650324\pi\)
−0.454897 + 0.890544i \(0.650324\pi\)
\(812\) 0 0
\(813\) 13.3979 0.469884
\(814\) 0 0
\(815\) −7.93658 −0.278006
\(816\) 0 0
\(817\) −3.19411 −0.111748
\(818\) 0 0
\(819\) 3.47372 0.121382
\(820\) 0 0
\(821\) −21.0936 −0.736172 −0.368086 0.929792i \(-0.619987\pi\)
−0.368086 + 0.929792i \(0.619987\pi\)
\(822\) 0 0
\(823\) 37.2641 1.29895 0.649473 0.760384i \(-0.274989\pi\)
0.649473 + 0.760384i \(0.274989\pi\)
\(824\) 0 0
\(825\) 0.878968 0.0306017
\(826\) 0 0
\(827\) 4.45320 0.154853 0.0774264 0.996998i \(-0.475330\pi\)
0.0774264 + 0.996998i \(0.475330\pi\)
\(828\) 0 0
\(829\) −38.1300 −1.32431 −0.662154 0.749368i \(-0.730358\pi\)
−0.662154 + 0.749368i \(0.730358\pi\)
\(830\) 0 0
\(831\) 3.68790 0.127932
\(832\) 0 0
\(833\) −11.3624 −0.393682
\(834\) 0 0
\(835\) 12.8059 0.443166
\(836\) 0 0
\(837\) 20.3202 0.702369
\(838\) 0 0
\(839\) 7.15858 0.247142 0.123571 0.992336i \(-0.460565\pi\)
0.123571 + 0.992336i \(0.460565\pi\)
\(840\) 0 0
\(841\) −24.1535 −0.832880
\(842\) 0 0
\(843\) 15.2282 0.524486
\(844\) 0 0
\(845\) 5.83102 0.200593
\(846\) 0 0
\(847\) 3.89673 0.133893
\(848\) 0 0
\(849\) 9.75334 0.334734
\(850\) 0 0
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −49.6199 −1.69895 −0.849476 0.527627i \(-0.823082\pi\)
−0.849476 + 0.527627i \(0.823082\pi\)
\(854\) 0 0
\(855\) −21.6044 −0.738855
\(856\) 0 0
\(857\) −44.0360 −1.50424 −0.752120 0.659026i \(-0.770969\pi\)
−0.752120 + 0.659026i \(0.770969\pi\)
\(858\) 0 0
\(859\) 49.5062 1.68913 0.844565 0.535453i \(-0.179859\pi\)
0.844565 + 0.535453i \(0.179859\pi\)
\(860\) 0 0
\(861\) −1.49028 −0.0507887
\(862\) 0 0
\(863\) −20.7962 −0.707912 −0.353956 0.935262i \(-0.615164\pi\)
−0.353956 + 0.935262i \(0.615164\pi\)
\(864\) 0 0
\(865\) 24.6752 0.838982
\(866\) 0 0
\(867\) −7.43313 −0.252442
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −39.3859 −1.33454
\(872\) 0 0
\(873\) 16.5719 0.560875
\(874\) 0 0
\(875\) 0.476024 0.0160925
\(876\) 0 0
\(877\) −5.42071 −0.183044 −0.0915222 0.995803i \(-0.529173\pi\)
−0.0915222 + 0.995803i \(0.529173\pi\)
\(878\) 0 0
\(879\) 12.2614 0.413566
\(880\) 0 0
\(881\) −45.8036 −1.54316 −0.771581 0.636131i \(-0.780534\pi\)
−0.771581 + 0.636131i \(0.780534\pi\)
\(882\) 0 0
\(883\) −57.1860 −1.92446 −0.962231 0.272234i \(-0.912238\pi\)
−0.962231 + 0.272234i \(0.912238\pi\)
\(884\) 0 0
\(885\) 4.95205 0.166461
\(886\) 0 0
\(887\) 15.5371 0.521686 0.260843 0.965381i \(-0.415999\pi\)
0.260843 + 0.965381i \(0.415999\pi\)
\(888\) 0 0
\(889\) −5.28542 −0.177267
\(890\) 0 0
\(891\) 11.0789 0.371157
\(892\) 0 0
\(893\) 14.2568 0.477085
\(894\) 0 0
\(895\) −13.1033 −0.437994
\(896\) 0 0
\(897\) −1.40294 −0.0468430
\(898\) 0 0
\(899\) 14.9115 0.497325
\(900\) 0 0
\(901\) −18.1268 −0.603892
\(902\) 0 0
\(903\) −0.100505 −0.00334458
\(904\) 0 0
\(905\) −9.52398 −0.316588
\(906\) 0 0
\(907\) 32.8515 1.09082 0.545409 0.838170i \(-0.316374\pi\)
0.545409 + 0.838170i \(0.316374\pi\)
\(908\) 0 0
\(909\) −31.2088 −1.03513
\(910\) 0 0
\(911\) −8.95205 −0.296595 −0.148297 0.988943i \(-0.547379\pi\)
−0.148297 + 0.988943i \(0.547379\pi\)
\(912\) 0 0
\(913\) −7.54680 −0.249763
\(914\) 0 0
\(915\) −3.31284 −0.109519
\(916\) 0 0
\(917\) 3.64271 0.120293
\(918\) 0 0
\(919\) 49.8229 1.64351 0.821753 0.569844i \(-0.192996\pi\)
0.821753 + 0.569844i \(0.192996\pi\)
\(920\) 0 0
\(921\) 0.802385 0.0264395
\(922\) 0 0
\(923\) −26.7077 −0.879094
\(924\) 0 0
\(925\) 4.00000 0.131519
\(926\) 0 0
\(927\) −6.32987 −0.207900
\(928\) 0 0
\(929\) 25.0723 0.822597 0.411298 0.911501i \(-0.365075\pi\)
0.411298 + 0.911501i \(0.365075\pi\)
\(930\) 0 0
\(931\) 53.6922 1.75969
\(932\) 0 0
\(933\) 3.95941 0.129625
\(934\) 0 0
\(935\) −2.81399 −0.0920274
\(936\) 0 0
\(937\) 21.3322 0.696891 0.348446 0.937329i \(-0.386710\pi\)
0.348446 + 0.937329i \(0.386710\pi\)
\(938\) 0 0
\(939\) −1.22079 −0.0398391
\(940\) 0 0
\(941\) 3.93428 0.128254 0.0641270 0.997942i \(-0.479574\pi\)
0.0641270 + 0.997942i \(0.479574\pi\)
\(942\) 0 0
\(943\) −5.97487 −0.194569
\(944\) 0 0
\(945\) −1.42807 −0.0464551
\(946\) 0 0
\(947\) −48.6420 −1.58065 −0.790326 0.612687i \(-0.790089\pi\)
−0.790326 + 0.612687i \(0.790089\pi\)
\(948\) 0 0
\(949\) −16.3476 −0.530667
\(950\) 0 0
\(951\) −8.05761 −0.261286
\(952\) 0 0
\(953\) −15.5623 −0.504111 −0.252056 0.967713i \(-0.581107\pi\)
−0.252056 + 0.967713i \(0.581107\pi\)
\(954\) 0 0
\(955\) 5.85384 0.189426
\(956\) 0 0
\(957\) −1.93502 −0.0625505
\(958\) 0 0
\(959\) 10.1763 0.328611
\(960\) 0 0
\(961\) 14.8790 0.479967
\(962\) 0 0
\(963\) −21.4052 −0.689774
\(964\) 0 0
\(965\) −4.41261 −0.142047
\(966\) 0 0
\(967\) −6.80083 −0.218700 −0.109350 0.994003i \(-0.534877\pi\)
−0.109350 + 0.994003i \(0.534877\pi\)
\(968\) 0 0
\(969\) −6.96751 −0.223829
\(970\) 0 0
\(971\) −6.46406 −0.207442 −0.103721 0.994606i \(-0.533075\pi\)
−0.103721 + 0.994606i \(0.533075\pi\)
\(972\) 0 0
\(973\) −4.09591 −0.131309
\(974\) 0 0
\(975\) 1.40294 0.0449302
\(976\) 0 0
\(977\) 9.18601 0.293886 0.146943 0.989145i \(-0.453057\pi\)
0.146943 + 0.989145i \(0.453057\pi\)
\(978\) 0 0
\(979\) −6.03405 −0.192849
\(980\) 0 0
\(981\) −37.9571 −1.21188
\(982\) 0 0
\(983\) −15.3705 −0.490241 −0.245121 0.969493i \(-0.578828\pi\)
−0.245121 + 0.969493i \(0.578828\pi\)
\(984\) 0 0
\(985\) −11.4258 −0.364055
\(986\) 0 0
\(987\) 0.448598 0.0142790
\(988\) 0 0
\(989\) −0.402945 −0.0128129
\(990\) 0 0
\(991\) 52.0109 1.65218 0.826090 0.563538i \(-0.190560\pi\)
0.826090 + 0.563538i \(0.190560\pi\)
\(992\) 0 0
\(993\) −12.0051 −0.380969
\(994\) 0 0
\(995\) −0.307039 −0.00973379
\(996\) 0 0
\(997\) 15.7123 0.497613 0.248807 0.968553i \(-0.419962\pi\)
0.248807 + 0.968553i \(0.419962\pi\)
\(998\) 0 0
\(999\) −12.0000 −0.379663
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 1840.2.a.t.1.2 3
4.3 odd 2 920.2.a.g.1.2 3
5.4 even 2 9200.2.a.cd.1.2 3
8.3 odd 2 7360.2.a.cb.1.2 3
8.5 even 2 7360.2.a.ca.1.2 3
12.11 even 2 8280.2.a.bo.1.2 3
20.3 even 4 4600.2.e.r.4049.3 6
20.7 even 4 4600.2.e.r.4049.4 6
20.19 odd 2 4600.2.a.y.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.g.1.2 3 4.3 odd 2
1840.2.a.t.1.2 3 1.1 even 1 trivial
4600.2.a.y.1.2 3 20.19 odd 2
4600.2.e.r.4049.3 6 20.3 even 4
4600.2.e.r.4049.4 6 20.7 even 4
7360.2.a.ca.1.2 3 8.5 even 2
7360.2.a.cb.1.2 3 8.3 odd 2
8280.2.a.bo.1.2 3 12.11 even 2
9200.2.a.cd.1.2 3 5.4 even 2