Properties

Label 3640.2.a.o.1.2
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.0655463357\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.86081\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.46260 q^{3} -1.00000 q^{5} -1.00000 q^{7} -0.860806 q^{9} +O(q^{10})\) \(q-1.46260 q^{3} -1.00000 q^{5} -1.00000 q^{7} -0.860806 q^{9} -1.39821 q^{11} +1.00000 q^{13} +1.46260 q^{15} +1.25901 q^{17} -0.462598 q^{19} +1.46260 q^{21} +8.04502 q^{23} +1.00000 q^{25} +5.64681 q^{27} -5.65722 q^{29} +5.46260 q^{31} +2.04502 q^{33} +1.00000 q^{35} -0.815790 q^{37} -1.46260 q^{39} +7.58242 q^{41} -1.07480 q^{43} +0.860806 q^{45} -8.69182 q^{47} +1.00000 q^{49} -1.84143 q^{51} -4.79641 q^{53} +1.39821 q^{55} +0.676596 q^{57} +6.43281 q^{59} -4.60179 q^{61} +0.860806 q^{63} -1.00000 q^{65} +2.13919 q^{67} -11.7666 q^{69} +0.128782 q^{71} -13.4882 q^{73} -1.46260 q^{75} +1.39821 q^{77} +3.06439 q^{79} -5.67660 q^{81} +1.44322 q^{83} -1.25901 q^{85} +8.27424 q^{87} -11.5076 q^{89} -1.00000 q^{91} -7.98959 q^{93} +0.462598 q^{95} -8.17380 q^{97} +1.20359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{9} - q^{11} + 3 q^{13} + 2 q^{15} - 5 q^{17} + q^{19} + 2 q^{21} + 5 q^{23} + 3 q^{25} + q^{27} - 5 q^{29} + 14 q^{31} - 13 q^{33} + 3 q^{35} - 16 q^{37} - 2 q^{39} + 6 q^{41} - 8 q^{43} - 3 q^{45} + 9 q^{47} + 3 q^{49} + 20 q^{51} - 8 q^{53} + q^{55} + 10 q^{57} - 7 q^{59} - 17 q^{61} - 3 q^{63} - 3 q^{65} + 12 q^{67} - 5 q^{69} + 2 q^{71} + q^{73} - 2 q^{75} + q^{77} + 10 q^{79} - 25 q^{81} - 18 q^{83} + 5 q^{85} - 27 q^{87} - 13 q^{89} - 3 q^{91} - 20 q^{93} - q^{95} - 7 q^{97} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.46260 −0.844432 −0.422216 0.906495i \(-0.638748\pi\)
−0.422216 + 0.906495i \(0.638748\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.860806 −0.286935
\(10\) 0 0
\(11\) −1.39821 −0.421575 −0.210788 0.977532i \(-0.567603\pi\)
−0.210788 + 0.977532i \(0.567603\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.46260 0.377641
\(16\) 0 0
\(17\) 1.25901 0.305356 0.152678 0.988276i \(-0.451210\pi\)
0.152678 + 0.988276i \(0.451210\pi\)
\(18\) 0 0
\(19\) −0.462598 −0.106127 −0.0530637 0.998591i \(-0.516899\pi\)
−0.0530637 + 0.998591i \(0.516899\pi\)
\(20\) 0 0
\(21\) 1.46260 0.319165
\(22\) 0 0
\(23\) 8.04502 1.67750 0.838751 0.544515i \(-0.183286\pi\)
0.838751 + 0.544515i \(0.183286\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.64681 1.08673
\(28\) 0 0
\(29\) −5.65722 −1.05052 −0.525260 0.850942i \(-0.676032\pi\)
−0.525260 + 0.850942i \(0.676032\pi\)
\(30\) 0 0
\(31\) 5.46260 0.981112 0.490556 0.871410i \(-0.336794\pi\)
0.490556 + 0.871410i \(0.336794\pi\)
\(32\) 0 0
\(33\) 2.04502 0.355992
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −0.815790 −0.134115 −0.0670575 0.997749i \(-0.521361\pi\)
−0.0670575 + 0.997749i \(0.521361\pi\)
\(38\) 0 0
\(39\) −1.46260 −0.234203
\(40\) 0 0
\(41\) 7.58242 1.18417 0.592087 0.805874i \(-0.298304\pi\)
0.592087 + 0.805874i \(0.298304\pi\)
\(42\) 0 0
\(43\) −1.07480 −0.163906 −0.0819530 0.996636i \(-0.526116\pi\)
−0.0819530 + 0.996636i \(0.526116\pi\)
\(44\) 0 0
\(45\) 0.860806 0.128321
\(46\) 0 0
\(47\) −8.69182 −1.26783 −0.633916 0.773402i \(-0.718554\pi\)
−0.633916 + 0.773402i \(0.718554\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.84143 −0.257852
\(52\) 0 0
\(53\) −4.79641 −0.658838 −0.329419 0.944184i \(-0.606853\pi\)
−0.329419 + 0.944184i \(0.606853\pi\)
\(54\) 0 0
\(55\) 1.39821 0.188534
\(56\) 0 0
\(57\) 0.676596 0.0896173
\(58\) 0 0
\(59\) 6.43281 0.837481 0.418740 0.908106i \(-0.362472\pi\)
0.418740 + 0.908106i \(0.362472\pi\)
\(60\) 0 0
\(61\) −4.60179 −0.589199 −0.294600 0.955621i \(-0.595186\pi\)
−0.294600 + 0.955621i \(0.595186\pi\)
\(62\) 0 0
\(63\) 0.860806 0.108451
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 2.13919 0.261344 0.130672 0.991426i \(-0.458286\pi\)
0.130672 + 0.991426i \(0.458286\pi\)
\(68\) 0 0
\(69\) −11.7666 −1.41654
\(70\) 0 0
\(71\) 0.128782 0.0152836 0.00764180 0.999971i \(-0.497568\pi\)
0.00764180 + 0.999971i \(0.497568\pi\)
\(72\) 0 0
\(73\) −13.4882 −1.57868 −0.789340 0.613957i \(-0.789577\pi\)
−0.789340 + 0.613957i \(0.789577\pi\)
\(74\) 0 0
\(75\) −1.46260 −0.168886
\(76\) 0 0
\(77\) 1.39821 0.159341
\(78\) 0 0
\(79\) 3.06439 0.344771 0.172385 0.985030i \(-0.444853\pi\)
0.172385 + 0.985030i \(0.444853\pi\)
\(80\) 0 0
\(81\) −5.67660 −0.630733
\(82\) 0 0
\(83\) 1.44322 0.158414 0.0792072 0.996858i \(-0.474761\pi\)
0.0792072 + 0.996858i \(0.474761\pi\)
\(84\) 0 0
\(85\) −1.25901 −0.136559
\(86\) 0 0
\(87\) 8.27424 0.887092
\(88\) 0 0
\(89\) −11.5076 −1.21980 −0.609902 0.792477i \(-0.708791\pi\)
−0.609902 + 0.792477i \(0.708791\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −7.98959 −0.828482
\(94\) 0 0
\(95\) 0.462598 0.0474616
\(96\) 0 0
\(97\) −8.17380 −0.829923 −0.414962 0.909839i \(-0.636205\pi\)
−0.414962 + 0.909839i \(0.636205\pi\)
\(98\) 0 0
\(99\) 1.20359 0.120965
\(100\) 0 0
\(101\) −13.4882 −1.34213 −0.671065 0.741399i \(-0.734163\pi\)
−0.671065 + 0.741399i \(0.734163\pi\)
\(102\) 0 0
\(103\) 9.75622 0.961308 0.480654 0.876910i \(-0.340399\pi\)
0.480654 + 0.876910i \(0.340399\pi\)
\(104\) 0 0
\(105\) −1.46260 −0.142735
\(106\) 0 0
\(107\) −13.5720 −1.31206 −0.656028 0.754737i \(-0.727765\pi\)
−0.656028 + 0.754737i \(0.727765\pi\)
\(108\) 0 0
\(109\) 14.7368 1.41153 0.705767 0.708444i \(-0.250603\pi\)
0.705767 + 0.708444i \(0.250603\pi\)
\(110\) 0 0
\(111\) 1.19317 0.113251
\(112\) 0 0
\(113\) 16.2638 1.52997 0.764986 0.644047i \(-0.222746\pi\)
0.764986 + 0.644047i \(0.222746\pi\)
\(114\) 0 0
\(115\) −8.04502 −0.750202
\(116\) 0 0
\(117\) −0.860806 −0.0795815
\(118\) 0 0
\(119\) −1.25901 −0.115414
\(120\) 0 0
\(121\) −9.04502 −0.822274
\(122\) 0 0
\(123\) −11.0900 −0.999955
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.99104 −0.442883 −0.221441 0.975174i \(-0.571076\pi\)
−0.221441 + 0.975174i \(0.571076\pi\)
\(128\) 0 0
\(129\) 1.57201 0.138407
\(130\) 0 0
\(131\) −9.35319 −0.817192 −0.408596 0.912715i \(-0.633982\pi\)
−0.408596 + 0.912715i \(0.633982\pi\)
\(132\) 0 0
\(133\) 0.462598 0.0401124
\(134\) 0 0
\(135\) −5.64681 −0.486000
\(136\) 0 0
\(137\) −3.63640 −0.310678 −0.155339 0.987861i \(-0.549647\pi\)
−0.155339 + 0.987861i \(0.549647\pi\)
\(138\) 0 0
\(139\) −6.21881 −0.527473 −0.263736 0.964595i \(-0.584955\pi\)
−0.263736 + 0.964595i \(0.584955\pi\)
\(140\) 0 0
\(141\) 12.7126 1.07060
\(142\) 0 0
\(143\) −1.39821 −0.116924
\(144\) 0 0
\(145\) 5.65722 0.469807
\(146\) 0 0
\(147\) −1.46260 −0.120633
\(148\) 0 0
\(149\) 16.7819 1.37482 0.687412 0.726268i \(-0.258747\pi\)
0.687412 + 0.726268i \(0.258747\pi\)
\(150\) 0 0
\(151\) 21.8116 1.77501 0.887503 0.460802i \(-0.152438\pi\)
0.887503 + 0.460802i \(0.152438\pi\)
\(152\) 0 0
\(153\) −1.08377 −0.0876173
\(154\) 0 0
\(155\) −5.46260 −0.438766
\(156\) 0 0
\(157\) −22.7562 −1.81614 −0.908072 0.418814i \(-0.862446\pi\)
−0.908072 + 0.418814i \(0.862446\pi\)
\(158\) 0 0
\(159\) 7.01523 0.556344
\(160\) 0 0
\(161\) −8.04502 −0.634036
\(162\) 0 0
\(163\) −9.87603 −0.773551 −0.386775 0.922174i \(-0.626411\pi\)
−0.386775 + 0.922174i \(0.626411\pi\)
\(164\) 0 0
\(165\) −2.04502 −0.159204
\(166\) 0 0
\(167\) −17.4224 −1.34819 −0.674093 0.738647i \(-0.735465\pi\)
−0.674093 + 0.738647i \(0.735465\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.398207 0.0304517
\(172\) 0 0
\(173\) −23.0796 −1.75471 −0.877356 0.479841i \(-0.840694\pi\)
−0.877356 + 0.479841i \(0.840694\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) −9.40862 −0.707195
\(178\) 0 0
\(179\) 12.1842 0.910691 0.455345 0.890315i \(-0.349516\pi\)
0.455345 + 0.890315i \(0.349516\pi\)
\(180\) 0 0
\(181\) 15.3595 1.14166 0.570830 0.821068i \(-0.306622\pi\)
0.570830 + 0.821068i \(0.306622\pi\)
\(182\) 0 0
\(183\) 6.73057 0.497538
\(184\) 0 0
\(185\) 0.815790 0.0599781
\(186\) 0 0
\(187\) −1.76036 −0.128730
\(188\) 0 0
\(189\) −5.64681 −0.410745
\(190\) 0 0
\(191\) −3.41758 −0.247288 −0.123644 0.992327i \(-0.539458\pi\)
−0.123644 + 0.992327i \(0.539458\pi\)
\(192\) 0 0
\(193\) −14.5526 −1.04752 −0.523761 0.851865i \(-0.675471\pi\)
−0.523761 + 0.851865i \(0.675471\pi\)
\(194\) 0 0
\(195\) 1.46260 0.104739
\(196\) 0 0
\(197\) −3.09418 −0.220451 −0.110226 0.993907i \(-0.535157\pi\)
−0.110226 + 0.993907i \(0.535157\pi\)
\(198\) 0 0
\(199\) −18.3684 −1.30210 −0.651051 0.759034i \(-0.725672\pi\)
−0.651051 + 0.759034i \(0.725672\pi\)
\(200\) 0 0
\(201\) −3.12878 −0.220687
\(202\) 0 0
\(203\) 5.65722 0.397059
\(204\) 0 0
\(205\) −7.58242 −0.529579
\(206\) 0 0
\(207\) −6.92520 −0.481334
\(208\) 0 0
\(209\) 0.646809 0.0447407
\(210\) 0 0
\(211\) 22.0554 1.51836 0.759179 0.650882i \(-0.225601\pi\)
0.759179 + 0.650882i \(0.225601\pi\)
\(212\) 0 0
\(213\) −0.188356 −0.0129060
\(214\) 0 0
\(215\) 1.07480 0.0733010
\(216\) 0 0
\(217\) −5.46260 −0.370825
\(218\) 0 0
\(219\) 19.7279 1.33309
\(220\) 0 0
\(221\) 1.25901 0.0846904
\(222\) 0 0
\(223\) 9.11982 0.610708 0.305354 0.952239i \(-0.401225\pi\)
0.305354 + 0.952239i \(0.401225\pi\)
\(224\) 0 0
\(225\) −0.860806 −0.0573871
\(226\) 0 0
\(227\) −6.00000 −0.398234 −0.199117 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) 0 0
\(229\) −11.6662 −0.770923 −0.385462 0.922724i \(-0.625958\pi\)
−0.385462 + 0.922724i \(0.625958\pi\)
\(230\) 0 0
\(231\) −2.04502 −0.134552
\(232\) 0 0
\(233\) −18.7819 −1.23044 −0.615220 0.788355i \(-0.710933\pi\)
−0.615220 + 0.788355i \(0.710933\pi\)
\(234\) 0 0
\(235\) 8.69182 0.566992
\(236\) 0 0
\(237\) −4.48197 −0.291135
\(238\) 0 0
\(239\) −0.407170 −0.0263377 −0.0131688 0.999913i \(-0.504192\pi\)
−0.0131688 + 0.999913i \(0.504192\pi\)
\(240\) 0 0
\(241\) −7.77704 −0.500963 −0.250482 0.968121i \(-0.580589\pi\)
−0.250482 + 0.968121i \(0.580589\pi\)
\(242\) 0 0
\(243\) −8.63785 −0.554118
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −0.462598 −0.0294344
\(248\) 0 0
\(249\) −2.11086 −0.133770
\(250\) 0 0
\(251\) −14.8206 −0.935468 −0.467734 0.883869i \(-0.654930\pi\)
−0.467734 + 0.883869i \(0.654930\pi\)
\(252\) 0 0
\(253\) −11.2486 −0.707193
\(254\) 0 0
\(255\) 1.84143 0.115315
\(256\) 0 0
\(257\) 2.09003 0.130373 0.0651863 0.997873i \(-0.479236\pi\)
0.0651863 + 0.997873i \(0.479236\pi\)
\(258\) 0 0
\(259\) 0.815790 0.0506907
\(260\) 0 0
\(261\) 4.86977 0.301431
\(262\) 0 0
\(263\) 0.497202 0.0306588 0.0153294 0.999882i \(-0.495120\pi\)
0.0153294 + 0.999882i \(0.495120\pi\)
\(264\) 0 0
\(265\) 4.79641 0.294641
\(266\) 0 0
\(267\) 16.8310 1.03004
\(268\) 0 0
\(269\) −23.7279 −1.44671 −0.723357 0.690474i \(-0.757402\pi\)
−0.723357 + 0.690474i \(0.757402\pi\)
\(270\) 0 0
\(271\) 11.5478 0.701480 0.350740 0.936473i \(-0.385930\pi\)
0.350740 + 0.936473i \(0.385930\pi\)
\(272\) 0 0
\(273\) 1.46260 0.0885205
\(274\) 0 0
\(275\) −1.39821 −0.0843151
\(276\) 0 0
\(277\) −25.8504 −1.55320 −0.776600 0.629994i \(-0.783057\pi\)
−0.776600 + 0.629994i \(0.783057\pi\)
\(278\) 0 0
\(279\) −4.70224 −0.281516
\(280\) 0 0
\(281\) 14.3684 0.857148 0.428574 0.903507i \(-0.359016\pi\)
0.428574 + 0.903507i \(0.359016\pi\)
\(282\) 0 0
\(283\) 15.1336 0.899599 0.449800 0.893130i \(-0.351495\pi\)
0.449800 + 0.893130i \(0.351495\pi\)
\(284\) 0 0
\(285\) −0.676596 −0.0400781
\(286\) 0 0
\(287\) −7.58242 −0.447576
\(288\) 0 0
\(289\) −15.4149 −0.906758
\(290\) 0 0
\(291\) 11.9550 0.700814
\(292\) 0 0
\(293\) −3.31444 −0.193632 −0.0968159 0.995302i \(-0.530866\pi\)
−0.0968159 + 0.995302i \(0.530866\pi\)
\(294\) 0 0
\(295\) −6.43281 −0.374533
\(296\) 0 0
\(297\) −7.89541 −0.458138
\(298\) 0 0
\(299\) 8.04502 0.465255
\(300\) 0 0
\(301\) 1.07480 0.0619506
\(302\) 0 0
\(303\) 19.7279 1.13334
\(304\) 0 0
\(305\) 4.60179 0.263498
\(306\) 0 0
\(307\) −8.49720 −0.484961 −0.242480 0.970156i \(-0.577961\pi\)
−0.242480 + 0.970156i \(0.577961\pi\)
\(308\) 0 0
\(309\) −14.2694 −0.811759
\(310\) 0 0
\(311\) 15.0748 0.854814 0.427407 0.904059i \(-0.359427\pi\)
0.427407 + 0.904059i \(0.359427\pi\)
\(312\) 0 0
\(313\) −1.91478 −0.108230 −0.0541150 0.998535i \(-0.517234\pi\)
−0.0541150 + 0.998535i \(0.517234\pi\)
\(314\) 0 0
\(315\) −0.860806 −0.0485009
\(316\) 0 0
\(317\) −27.1890 −1.52709 −0.763544 0.645756i \(-0.776542\pi\)
−0.763544 + 0.645756i \(0.776542\pi\)
\(318\) 0 0
\(319\) 7.90997 0.442873
\(320\) 0 0
\(321\) 19.8504 1.10794
\(322\) 0 0
\(323\) −0.582418 −0.0324066
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) −21.5541 −1.19194
\(328\) 0 0
\(329\) 8.69182 0.479196
\(330\) 0 0
\(331\) −18.9494 −1.04155 −0.520776 0.853693i \(-0.674357\pi\)
−0.520776 + 0.853693i \(0.674357\pi\)
\(332\) 0 0
\(333\) 0.702237 0.0384823
\(334\) 0 0
\(335\) −2.13919 −0.116877
\(336\) 0 0
\(337\) 25.2486 1.37538 0.687689 0.726005i \(-0.258625\pi\)
0.687689 + 0.726005i \(0.258625\pi\)
\(338\) 0 0
\(339\) −23.7875 −1.29196
\(340\) 0 0
\(341\) −7.63785 −0.413613
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 11.7666 0.633494
\(346\) 0 0
\(347\) −18.3476 −0.984951 −0.492475 0.870326i \(-0.663908\pi\)
−0.492475 + 0.870326i \(0.663908\pi\)
\(348\) 0 0
\(349\) 17.2292 0.922259 0.461130 0.887333i \(-0.347444\pi\)
0.461130 + 0.887333i \(0.347444\pi\)
\(350\) 0 0
\(351\) 5.64681 0.301404
\(352\) 0 0
\(353\) 2.19462 0.116808 0.0584040 0.998293i \(-0.481399\pi\)
0.0584040 + 0.998293i \(0.481399\pi\)
\(354\) 0 0
\(355\) −0.128782 −0.00683504
\(356\) 0 0
\(357\) 1.84143 0.0974589
\(358\) 0 0
\(359\) −30.5664 −1.61323 −0.806617 0.591075i \(-0.798704\pi\)
−0.806617 + 0.591075i \(0.798704\pi\)
\(360\) 0 0
\(361\) −18.7860 −0.988737
\(362\) 0 0
\(363\) 13.2292 0.694354
\(364\) 0 0
\(365\) 13.4882 0.706007
\(366\) 0 0
\(367\) −10.4072 −0.543250 −0.271625 0.962403i \(-0.587561\pi\)
−0.271625 + 0.962403i \(0.587561\pi\)
\(368\) 0 0
\(369\) −6.52699 −0.339781
\(370\) 0 0
\(371\) 4.79641 0.249017
\(372\) 0 0
\(373\) 16.4585 0.852186 0.426093 0.904679i \(-0.359890\pi\)
0.426093 + 0.904679i \(0.359890\pi\)
\(374\) 0 0
\(375\) 1.46260 0.0755283
\(376\) 0 0
\(377\) −5.65722 −0.291362
\(378\) 0 0
\(379\) 31.3836 1.61207 0.806035 0.591868i \(-0.201609\pi\)
0.806035 + 0.591868i \(0.201609\pi\)
\(380\) 0 0
\(381\) 7.29988 0.373984
\(382\) 0 0
\(383\) 27.5270 1.40656 0.703282 0.710911i \(-0.251717\pi\)
0.703282 + 0.710911i \(0.251717\pi\)
\(384\) 0 0
\(385\) −1.39821 −0.0712592
\(386\) 0 0
\(387\) 0.925197 0.0470304
\(388\) 0 0
\(389\) −8.07625 −0.409482 −0.204741 0.978816i \(-0.565635\pi\)
−0.204741 + 0.978816i \(0.565635\pi\)
\(390\) 0 0
\(391\) 10.1288 0.512235
\(392\) 0 0
\(393\) 13.6800 0.690063
\(394\) 0 0
\(395\) −3.06439 −0.154186
\(396\) 0 0
\(397\) −9.33237 −0.468378 −0.234189 0.972191i \(-0.575243\pi\)
−0.234189 + 0.972191i \(0.575243\pi\)
\(398\) 0 0
\(399\) −0.676596 −0.0338722
\(400\) 0 0
\(401\) 20.9073 1.04406 0.522030 0.852927i \(-0.325175\pi\)
0.522030 + 0.852927i \(0.325175\pi\)
\(402\) 0 0
\(403\) 5.46260 0.272111
\(404\) 0 0
\(405\) 5.67660 0.282072
\(406\) 0 0
\(407\) 1.14064 0.0565396
\(408\) 0 0
\(409\) 34.9169 1.72653 0.863265 0.504751i \(-0.168416\pi\)
0.863265 + 0.504751i \(0.168416\pi\)
\(410\) 0 0
\(411\) 5.31859 0.262347
\(412\) 0 0
\(413\) −6.43281 −0.316538
\(414\) 0 0
\(415\) −1.44322 −0.0708451
\(416\) 0 0
\(417\) 9.09563 0.445415
\(418\) 0 0
\(419\) −29.4674 −1.43958 −0.719789 0.694193i \(-0.755761\pi\)
−0.719789 + 0.694193i \(0.755761\pi\)
\(420\) 0 0
\(421\) −19.4882 −0.949799 −0.474899 0.880040i \(-0.657516\pi\)
−0.474899 + 0.880040i \(0.657516\pi\)
\(422\) 0 0
\(423\) 7.48197 0.363786
\(424\) 0 0
\(425\) 1.25901 0.0610711
\(426\) 0 0
\(427\) 4.60179 0.222696
\(428\) 0 0
\(429\) 2.04502 0.0987343
\(430\) 0 0
\(431\) −10.2605 −0.494229 −0.247115 0.968986i \(-0.579482\pi\)
−0.247115 + 0.968986i \(0.579482\pi\)
\(432\) 0 0
\(433\) −10.9211 −0.524832 −0.262416 0.964955i \(-0.584519\pi\)
−0.262416 + 0.964955i \(0.584519\pi\)
\(434\) 0 0
\(435\) −8.27424 −0.396720
\(436\) 0 0
\(437\) −3.72161 −0.178029
\(438\) 0 0
\(439\) −9.38365 −0.447857 −0.223929 0.974606i \(-0.571888\pi\)
−0.223929 + 0.974606i \(0.571888\pi\)
\(440\) 0 0
\(441\) −0.860806 −0.0409908
\(442\) 0 0
\(443\) −20.5872 −0.978129 −0.489065 0.872248i \(-0.662662\pi\)
−0.489065 + 0.872248i \(0.662662\pi\)
\(444\) 0 0
\(445\) 11.5076 0.545513
\(446\) 0 0
\(447\) −24.5451 −1.16094
\(448\) 0 0
\(449\) −25.9612 −1.22519 −0.612594 0.790398i \(-0.709874\pi\)
−0.612594 + 0.790398i \(0.709874\pi\)
\(450\) 0 0
\(451\) −10.6018 −0.499219
\(452\) 0 0
\(453\) −31.9017 −1.49887
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) −13.5284 −0.632834 −0.316417 0.948620i \(-0.602480\pi\)
−0.316417 + 0.948620i \(0.602480\pi\)
\(458\) 0 0
\(459\) 7.10941 0.331839
\(460\) 0 0
\(461\) −34.6129 −1.61208 −0.806041 0.591859i \(-0.798394\pi\)
−0.806041 + 0.591859i \(0.798394\pi\)
\(462\) 0 0
\(463\) −8.55263 −0.397474 −0.198737 0.980053i \(-0.563684\pi\)
−0.198737 + 0.980053i \(0.563684\pi\)
\(464\) 0 0
\(465\) 7.98959 0.370508
\(466\) 0 0
\(467\) 15.6274 0.723151 0.361576 0.932343i \(-0.382239\pi\)
0.361576 + 0.932343i \(0.382239\pi\)
\(468\) 0 0
\(469\) −2.13919 −0.0987788
\(470\) 0 0
\(471\) 33.2832 1.53361
\(472\) 0 0
\(473\) 1.50280 0.0690987
\(474\) 0 0
\(475\) −0.462598 −0.0212255
\(476\) 0 0
\(477\) 4.12878 0.189044
\(478\) 0 0
\(479\) −12.5824 −0.574905 −0.287453 0.957795i \(-0.592808\pi\)
−0.287453 + 0.957795i \(0.592808\pi\)
\(480\) 0 0
\(481\) −0.815790 −0.0371968
\(482\) 0 0
\(483\) 11.7666 0.535400
\(484\) 0 0
\(485\) 8.17380 0.371153
\(486\) 0 0
\(487\) 34.1849 1.54906 0.774532 0.632534i \(-0.217985\pi\)
0.774532 + 0.632534i \(0.217985\pi\)
\(488\) 0 0
\(489\) 14.4447 0.653211
\(490\) 0 0
\(491\) 10.1496 0.458045 0.229023 0.973421i \(-0.426447\pi\)
0.229023 + 0.973421i \(0.426447\pi\)
\(492\) 0 0
\(493\) −7.12252 −0.320782
\(494\) 0 0
\(495\) −1.20359 −0.0540971
\(496\) 0 0
\(497\) −0.128782 −0.00577666
\(498\) 0 0
\(499\) 18.9910 0.850156 0.425078 0.905157i \(-0.360247\pi\)
0.425078 + 0.905157i \(0.360247\pi\)
\(500\) 0 0
\(501\) 25.4820 1.13845
\(502\) 0 0
\(503\) 21.7729 0.970805 0.485403 0.874291i \(-0.338673\pi\)
0.485403 + 0.874291i \(0.338673\pi\)
\(504\) 0 0
\(505\) 13.4882 0.600219
\(506\) 0 0
\(507\) −1.46260 −0.0649563
\(508\) 0 0
\(509\) −16.0554 −0.711644 −0.355822 0.934554i \(-0.615799\pi\)
−0.355822 + 0.934554i \(0.615799\pi\)
\(510\) 0 0
\(511\) 13.4882 0.596685
\(512\) 0 0
\(513\) −2.61220 −0.115332
\(514\) 0 0
\(515\) −9.75622 −0.429910
\(516\) 0 0
\(517\) 12.1530 0.534487
\(518\) 0 0
\(519\) 33.7562 1.48173
\(520\) 0 0
\(521\) 27.4916 1.20443 0.602215 0.798334i \(-0.294285\pi\)
0.602215 + 0.798334i \(0.294285\pi\)
\(522\) 0 0
\(523\) −2.34423 −0.102506 −0.0512530 0.998686i \(-0.516321\pi\)
−0.0512530 + 0.998686i \(0.516321\pi\)
\(524\) 0 0
\(525\) 1.46260 0.0638330
\(526\) 0 0
\(527\) 6.87748 0.299588
\(528\) 0 0
\(529\) 41.7223 1.81401
\(530\) 0 0
\(531\) −5.53740 −0.240303
\(532\) 0 0
\(533\) 7.58242 0.328431
\(534\) 0 0
\(535\) 13.5720 0.586769
\(536\) 0 0
\(537\) −17.8206 −0.769016
\(538\) 0 0
\(539\) −1.39821 −0.0602251
\(540\) 0 0
\(541\) −21.8116 −0.937756 −0.468878 0.883263i \(-0.655342\pi\)
−0.468878 + 0.883263i \(0.655342\pi\)
\(542\) 0 0
\(543\) −22.4647 −0.964053
\(544\) 0 0
\(545\) −14.7368 −0.631257
\(546\) 0 0
\(547\) 0.796415 0.0340522 0.0170261 0.999855i \(-0.494580\pi\)
0.0170261 + 0.999855i \(0.494580\pi\)
\(548\) 0 0
\(549\) 3.96125 0.169062
\(550\) 0 0
\(551\) 2.61702 0.111489
\(552\) 0 0
\(553\) −3.06439 −0.130311
\(554\) 0 0
\(555\) −1.19317 −0.0506474
\(556\) 0 0
\(557\) 15.7625 0.667878 0.333939 0.942595i \(-0.391622\pi\)
0.333939 + 0.942595i \(0.391622\pi\)
\(558\) 0 0
\(559\) −1.07480 −0.0454593
\(560\) 0 0
\(561\) 2.57470 0.108704
\(562\) 0 0
\(563\) −9.49239 −0.400056 −0.200028 0.979790i \(-0.564103\pi\)
−0.200028 + 0.979790i \(0.564103\pi\)
\(564\) 0 0
\(565\) −16.2638 −0.684224
\(566\) 0 0
\(567\) 5.67660 0.238395
\(568\) 0 0
\(569\) 29.7327 1.24646 0.623230 0.782039i \(-0.285820\pi\)
0.623230 + 0.782039i \(0.285820\pi\)
\(570\) 0 0
\(571\) 26.6032 1.11331 0.556656 0.830743i \(-0.312084\pi\)
0.556656 + 0.830743i \(0.312084\pi\)
\(572\) 0 0
\(573\) 4.99855 0.208817
\(574\) 0 0
\(575\) 8.04502 0.335500
\(576\) 0 0
\(577\) 3.05398 0.127139 0.0635694 0.997977i \(-0.479752\pi\)
0.0635694 + 0.997977i \(0.479752\pi\)
\(578\) 0 0
\(579\) 21.2847 0.884560
\(580\) 0 0
\(581\) −1.44322 −0.0598750
\(582\) 0 0
\(583\) 6.70638 0.277750
\(584\) 0 0
\(585\) 0.860806 0.0355899
\(586\) 0 0
\(587\) −21.3144 −0.879741 −0.439871 0.898061i \(-0.644976\pi\)
−0.439871 + 0.898061i \(0.644976\pi\)
\(588\) 0 0
\(589\) −2.52699 −0.104123
\(590\) 0 0
\(591\) 4.52554 0.186156
\(592\) 0 0
\(593\) 4.64681 0.190822 0.0954108 0.995438i \(-0.469584\pi\)
0.0954108 + 0.995438i \(0.469584\pi\)
\(594\) 0 0
\(595\) 1.25901 0.0516145
\(596\) 0 0
\(597\) 26.8656 1.09954
\(598\) 0 0
\(599\) 21.0215 0.858915 0.429457 0.903087i \(-0.358705\pi\)
0.429457 + 0.903087i \(0.358705\pi\)
\(600\) 0 0
\(601\) 34.2188 1.39581 0.697907 0.716188i \(-0.254115\pi\)
0.697907 + 0.716188i \(0.254115\pi\)
\(602\) 0 0
\(603\) −1.84143 −0.0749889
\(604\) 0 0
\(605\) 9.04502 0.367732
\(606\) 0 0
\(607\) −42.4841 −1.72438 −0.862188 0.506588i \(-0.830906\pi\)
−0.862188 + 0.506588i \(0.830906\pi\)
\(608\) 0 0
\(609\) −8.27424 −0.335289
\(610\) 0 0
\(611\) −8.69182 −0.351634
\(612\) 0 0
\(613\) 12.6018 0.508982 0.254491 0.967075i \(-0.418092\pi\)
0.254491 + 0.967075i \(0.418092\pi\)
\(614\) 0 0
\(615\) 11.0900 0.447193
\(616\) 0 0
\(617\) −9.71747 −0.391210 −0.195605 0.980683i \(-0.562667\pi\)
−0.195605 + 0.980683i \(0.562667\pi\)
\(618\) 0 0
\(619\) −13.7473 −0.552549 −0.276274 0.961079i \(-0.589100\pi\)
−0.276274 + 0.961079i \(0.589100\pi\)
\(620\) 0 0
\(621\) 45.4287 1.82299
\(622\) 0 0
\(623\) 11.5076 0.461043
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.946021 −0.0377804
\(628\) 0 0
\(629\) −1.02709 −0.0409528
\(630\) 0 0
\(631\) 42.5664 1.69454 0.847271 0.531161i \(-0.178244\pi\)
0.847271 + 0.531161i \(0.178244\pi\)
\(632\) 0 0
\(633\) −32.2582 −1.28215
\(634\) 0 0
\(635\) 4.99104 0.198063
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −0.110856 −0.00438541
\(640\) 0 0
\(641\) −2.49575 −0.0985763 −0.0492882 0.998785i \(-0.515695\pi\)
−0.0492882 + 0.998785i \(0.515695\pi\)
\(642\) 0 0
\(643\) −0.963947 −0.0380144 −0.0190072 0.999819i \(-0.506051\pi\)
−0.0190072 + 0.999819i \(0.506051\pi\)
\(644\) 0 0
\(645\) −1.57201 −0.0618977
\(646\) 0 0
\(647\) −7.32755 −0.288076 −0.144038 0.989572i \(-0.546009\pi\)
−0.144038 + 0.989572i \(0.546009\pi\)
\(648\) 0 0
\(649\) −8.99440 −0.353061
\(650\) 0 0
\(651\) 7.98959 0.313137
\(652\) 0 0
\(653\) −11.7812 −0.461033 −0.230517 0.973068i \(-0.574042\pi\)
−0.230517 + 0.973068i \(0.574042\pi\)
\(654\) 0 0
\(655\) 9.35319 0.365459
\(656\) 0 0
\(657\) 11.6108 0.452979
\(658\) 0 0
\(659\) −38.2147 −1.48863 −0.744316 0.667828i \(-0.767224\pi\)
−0.744316 + 0.667828i \(0.767224\pi\)
\(660\) 0 0
\(661\) −23.5679 −0.916683 −0.458342 0.888776i \(-0.651556\pi\)
−0.458342 + 0.888776i \(0.651556\pi\)
\(662\) 0 0
\(663\) −1.84143 −0.0715152
\(664\) 0 0
\(665\) −0.462598 −0.0179388
\(666\) 0 0
\(667\) −45.5124 −1.76225
\(668\) 0 0
\(669\) −13.3386 −0.515701
\(670\) 0 0
\(671\) 6.43426 0.248392
\(672\) 0 0
\(673\) 43.3870 1.67245 0.836223 0.548389i \(-0.184759\pi\)
0.836223 + 0.548389i \(0.184759\pi\)
\(674\) 0 0
\(675\) 5.64681 0.217346
\(676\) 0 0
\(677\) 0.691825 0.0265890 0.0132945 0.999912i \(-0.495768\pi\)
0.0132945 + 0.999912i \(0.495768\pi\)
\(678\) 0 0
\(679\) 8.17380 0.313682
\(680\) 0 0
\(681\) 8.77559 0.336281
\(682\) 0 0
\(683\) 35.8704 1.37254 0.686272 0.727345i \(-0.259246\pi\)
0.686272 + 0.727345i \(0.259246\pi\)
\(684\) 0 0
\(685\) 3.63640 0.138940
\(686\) 0 0
\(687\) 17.0629 0.650992
\(688\) 0 0
\(689\) −4.79641 −0.182729
\(690\) 0 0
\(691\) 32.6337 1.24144 0.620722 0.784031i \(-0.286839\pi\)
0.620722 + 0.784031i \(0.286839\pi\)
\(692\) 0 0
\(693\) −1.20359 −0.0457204
\(694\) 0 0
\(695\) 6.21881 0.235893
\(696\) 0 0
\(697\) 9.54636 0.361594
\(698\) 0 0
\(699\) 27.4703 1.03902
\(700\) 0 0
\(701\) 6.83102 0.258004 0.129002 0.991644i \(-0.458823\pi\)
0.129002 + 0.991644i \(0.458823\pi\)
\(702\) 0 0
\(703\) 0.377383 0.0142333
\(704\) 0 0
\(705\) −12.7126 −0.478786
\(706\) 0 0
\(707\) 13.4882 0.507277
\(708\) 0 0
\(709\) −22.1350 −0.831299 −0.415650 0.909525i \(-0.636446\pi\)
−0.415650 + 0.909525i \(0.636446\pi\)
\(710\) 0 0
\(711\) −2.63785 −0.0989269
\(712\) 0 0
\(713\) 43.9467 1.64582
\(714\) 0 0
\(715\) 1.39821 0.0522900
\(716\) 0 0
\(717\) 0.595527 0.0222403
\(718\) 0 0
\(719\) −43.2549 −1.61313 −0.806567 0.591142i \(-0.798677\pi\)
−0.806567 + 0.591142i \(0.798677\pi\)
\(720\) 0 0
\(721\) −9.75622 −0.363340
\(722\) 0 0
\(723\) 11.3747 0.423029
\(724\) 0 0
\(725\) −5.65722 −0.210104
\(726\) 0 0
\(727\) −48.8109 −1.81029 −0.905147 0.425098i \(-0.860240\pi\)
−0.905147 + 0.425098i \(0.860240\pi\)
\(728\) 0 0
\(729\) 29.6635 1.09865
\(730\) 0 0
\(731\) −1.35319 −0.0500496
\(732\) 0 0
\(733\) 3.20359 0.118327 0.0591636 0.998248i \(-0.481157\pi\)
0.0591636 + 0.998248i \(0.481157\pi\)
\(734\) 0 0
\(735\) 1.46260 0.0539488
\(736\) 0 0
\(737\) −2.99104 −0.110176
\(738\) 0 0
\(739\) 8.18836 0.301214 0.150607 0.988594i \(-0.451877\pi\)
0.150607 + 0.988594i \(0.451877\pi\)
\(740\) 0 0
\(741\) 0.676596 0.0248554
\(742\) 0 0
\(743\) 35.7175 1.31035 0.655173 0.755479i \(-0.272596\pi\)
0.655173 + 0.755479i \(0.272596\pi\)
\(744\) 0 0
\(745\) −16.7819 −0.614840
\(746\) 0 0
\(747\) −1.24234 −0.0454547
\(748\) 0 0
\(749\) 13.5720 0.495910
\(750\) 0 0
\(751\) −14.5374 −0.530477 −0.265239 0.964183i \(-0.585451\pi\)
−0.265239 + 0.964183i \(0.585451\pi\)
\(752\) 0 0
\(753\) 21.6766 0.789939
\(754\) 0 0
\(755\) −21.8116 −0.793807
\(756\) 0 0
\(757\) 19.2036 0.697966 0.348983 0.937129i \(-0.386527\pi\)
0.348983 + 0.937129i \(0.386527\pi\)
\(758\) 0 0
\(759\) 16.4522 0.597177
\(760\) 0 0
\(761\) 0.0401993 0.00145722 0.000728612 1.00000i \(-0.499768\pi\)
0.000728612 1.00000i \(0.499768\pi\)
\(762\) 0 0
\(763\) −14.7368 −0.533509
\(764\) 0 0
\(765\) 1.08377 0.0391836
\(766\) 0 0
\(767\) 6.43281 0.232275
\(768\) 0 0
\(769\) 39.5783 1.42723 0.713614 0.700539i \(-0.247057\pi\)
0.713614 + 0.700539i \(0.247057\pi\)
\(770\) 0 0
\(771\) −3.05688 −0.110091
\(772\) 0 0
\(773\) −39.8504 −1.43332 −0.716660 0.697423i \(-0.754330\pi\)
−0.716660 + 0.697423i \(0.754330\pi\)
\(774\) 0 0
\(775\) 5.46260 0.196222
\(776\) 0 0
\(777\) −1.19317 −0.0428048
\(778\) 0 0
\(779\) −3.50761 −0.125673
\(780\) 0 0
\(781\) −0.180064 −0.00644319
\(782\) 0 0
\(783\) −31.9452 −1.14163
\(784\) 0 0
\(785\) 22.7562 0.812204
\(786\) 0 0
\(787\) −39.4141 −1.40496 −0.702481 0.711703i \(-0.747924\pi\)
−0.702481 + 0.711703i \(0.747924\pi\)
\(788\) 0 0
\(789\) −0.727207 −0.0258893
\(790\) 0 0
\(791\) −16.2638 −0.578275
\(792\) 0 0
\(793\) −4.60179 −0.163414
\(794\) 0 0
\(795\) −7.01523 −0.248805
\(796\) 0 0
\(797\) −22.1094 −0.783155 −0.391578 0.920145i \(-0.628071\pi\)
−0.391578 + 0.920145i \(0.628071\pi\)
\(798\) 0 0
\(799\) −10.9431 −0.387140
\(800\) 0 0
\(801\) 9.90582 0.350005
\(802\) 0 0
\(803\) 18.8594 0.665532
\(804\) 0 0
\(805\) 8.04502 0.283550
\(806\) 0 0
\(807\) 34.7044 1.22165
\(808\) 0 0
\(809\) −26.2951 −0.924485 −0.462243 0.886753i \(-0.652955\pi\)
−0.462243 + 0.886753i \(0.652955\pi\)
\(810\) 0 0
\(811\) 2.70638 0.0950340 0.0475170 0.998870i \(-0.484869\pi\)
0.0475170 + 0.998870i \(0.484869\pi\)
\(812\) 0 0
\(813\) −16.8898 −0.592352
\(814\) 0 0
\(815\) 9.87603 0.345942
\(816\) 0 0
\(817\) 0.497202 0.0173949
\(818\) 0 0
\(819\) 0.860806 0.0300790
\(820\) 0 0
\(821\) 47.5845 1.66071 0.830356 0.557233i \(-0.188137\pi\)
0.830356 + 0.557233i \(0.188137\pi\)
\(822\) 0 0
\(823\) −24.6323 −0.858626 −0.429313 0.903156i \(-0.641244\pi\)
−0.429313 + 0.903156i \(0.641244\pi\)
\(824\) 0 0
\(825\) 2.04502 0.0711983
\(826\) 0 0
\(827\) −16.7785 −0.583445 −0.291723 0.956503i \(-0.594228\pi\)
−0.291723 + 0.956503i \(0.594228\pi\)
\(828\) 0 0
\(829\) −21.9821 −0.763469 −0.381734 0.924272i \(-0.624673\pi\)
−0.381734 + 0.924272i \(0.624673\pi\)
\(830\) 0 0
\(831\) 37.8087 1.31157
\(832\) 0 0
\(833\) 1.25901 0.0436222
\(834\) 0 0
\(835\) 17.4224 0.602927
\(836\) 0 0
\(837\) 30.8462 1.06620
\(838\) 0 0
\(839\) 50.6143 1.74740 0.873700 0.486465i \(-0.161714\pi\)
0.873700 + 0.486465i \(0.161714\pi\)
\(840\) 0 0
\(841\) 3.00415 0.103591
\(842\) 0 0
\(843\) −21.0152 −0.723803
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 9.04502 0.310790
\(848\) 0 0
\(849\) −22.1344 −0.759650
\(850\) 0 0
\(851\) −6.56304 −0.224978
\(852\) 0 0
\(853\) 9.55118 0.327026 0.163513 0.986541i \(-0.447717\pi\)
0.163513 + 0.986541i \(0.447717\pi\)
\(854\) 0 0
\(855\) −0.398207 −0.0136184
\(856\) 0 0
\(857\) 41.3193 1.41144 0.705719 0.708491i \(-0.250624\pi\)
0.705719 + 0.708491i \(0.250624\pi\)
\(858\) 0 0
\(859\) −40.7015 −1.38872 −0.694358 0.719630i \(-0.744312\pi\)
−0.694358 + 0.719630i \(0.744312\pi\)
\(860\) 0 0
\(861\) 11.0900 0.377947
\(862\) 0 0
\(863\) −38.6039 −1.31409 −0.657046 0.753850i \(-0.728194\pi\)
−0.657046 + 0.753850i \(0.728194\pi\)
\(864\) 0 0
\(865\) 23.0796 0.784731
\(866\) 0 0
\(867\) 22.5458 0.765695
\(868\) 0 0
\(869\) −4.28465 −0.145347
\(870\) 0 0
\(871\) 2.13919 0.0724838
\(872\) 0 0
\(873\) 7.03605 0.238134
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −35.0256 −1.18273 −0.591366 0.806403i \(-0.701411\pi\)
−0.591366 + 0.806403i \(0.701411\pi\)
\(878\) 0 0
\(879\) 4.84770 0.163509
\(880\) 0 0
\(881\) −7.60246 −0.256133 −0.128067 0.991766i \(-0.540877\pi\)
−0.128067 + 0.991766i \(0.540877\pi\)
\(882\) 0 0
\(883\) 38.2396 1.28687 0.643433 0.765502i \(-0.277509\pi\)
0.643433 + 0.765502i \(0.277509\pi\)
\(884\) 0 0
\(885\) 9.40862 0.316267
\(886\) 0 0
\(887\) −15.2084 −0.510648 −0.255324 0.966856i \(-0.582182\pi\)
−0.255324 + 0.966856i \(0.582182\pi\)
\(888\) 0 0
\(889\) 4.99104 0.167394
\(890\) 0 0
\(891\) 7.93706 0.265901
\(892\) 0 0
\(893\) 4.02082 0.134552
\(894\) 0 0
\(895\) −12.1842 −0.407273
\(896\) 0 0
\(897\) −11.7666 −0.392876
\(898\) 0 0
\(899\) −30.9031 −1.03068
\(900\) 0 0
\(901\) −6.03875 −0.201180
\(902\) 0 0
\(903\) −1.57201 −0.0523131
\(904\) 0 0
\(905\) −15.3595 −0.510566
\(906\) 0 0
\(907\) 43.1440 1.43257 0.716287 0.697806i \(-0.245840\pi\)
0.716287 + 0.697806i \(0.245840\pi\)
\(908\) 0 0
\(909\) 11.6108 0.385104
\(910\) 0 0
\(911\) 1.59698 0.0529102 0.0264551 0.999650i \(-0.491578\pi\)
0.0264551 + 0.999650i \(0.491578\pi\)
\(912\) 0 0
\(913\) −2.01793 −0.0667836
\(914\) 0 0
\(915\) −6.73057 −0.222506
\(916\) 0 0
\(917\) 9.35319 0.308870
\(918\) 0 0
\(919\) 19.8310 0.654165 0.327082 0.944996i \(-0.393935\pi\)
0.327082 + 0.944996i \(0.393935\pi\)
\(920\) 0 0
\(921\) 12.4280 0.409516
\(922\) 0 0
\(923\) 0.128782 0.00423891
\(924\) 0 0
\(925\) −0.815790 −0.0268230
\(926\) 0 0
\(927\) −8.39821 −0.275833
\(928\) 0 0
\(929\) −41.4335 −1.35939 −0.679694 0.733496i \(-0.737888\pi\)
−0.679694 + 0.733496i \(0.737888\pi\)
\(930\) 0 0
\(931\) −0.462598 −0.0151611
\(932\) 0 0
\(933\) −22.0484 −0.721832
\(934\) 0 0
\(935\) 1.76036 0.0575700
\(936\) 0 0
\(937\) 36.7923 1.20195 0.600976 0.799267i \(-0.294779\pi\)
0.600976 + 0.799267i \(0.294779\pi\)
\(938\) 0 0
\(939\) 2.80056 0.0913929
\(940\) 0 0
\(941\) −13.2174 −0.430874 −0.215437 0.976518i \(-0.569118\pi\)
−0.215437 + 0.976518i \(0.569118\pi\)
\(942\) 0 0
\(943\) 61.0007 1.98646
\(944\) 0 0
\(945\) 5.64681 0.183691
\(946\) 0 0
\(947\) −32.4834 −1.05557 −0.527785 0.849378i \(-0.676977\pi\)
−0.527785 + 0.849378i \(0.676977\pi\)
\(948\) 0 0
\(949\) −13.4882 −0.437847
\(950\) 0 0
\(951\) 39.7666 1.28952
\(952\) 0 0
\(953\) 23.8325 0.772009 0.386005 0.922497i \(-0.373855\pi\)
0.386005 + 0.922497i \(0.373855\pi\)
\(954\) 0 0
\(955\) 3.41758 0.110590
\(956\) 0 0
\(957\) −11.5691 −0.373976
\(958\) 0 0
\(959\) 3.63640 0.117425
\(960\) 0 0
\(961\) −1.16002 −0.0374200
\(962\) 0 0
\(963\) 11.6829 0.376475
\(964\) 0 0
\(965\) 14.5526 0.468466
\(966\) 0 0
\(967\) 12.0256 0.386719 0.193359 0.981128i \(-0.438062\pi\)
0.193359 + 0.981128i \(0.438062\pi\)
\(968\) 0 0
\(969\) 0.851843 0.0273651
\(970\) 0 0
\(971\) −4.75140 −0.152480 −0.0762398 0.997090i \(-0.524291\pi\)
−0.0762398 + 0.997090i \(0.524291\pi\)
\(972\) 0 0
\(973\) 6.21881 0.199366
\(974\) 0 0
\(975\) −1.46260 −0.0468406
\(976\) 0 0
\(977\) 20.5139 0.656297 0.328149 0.944626i \(-0.393575\pi\)
0.328149 + 0.944626i \(0.393575\pi\)
\(978\) 0 0
\(979\) 16.0900 0.514240
\(980\) 0 0
\(981\) −12.6856 −0.405019
\(982\) 0 0
\(983\) −5.35319 −0.170740 −0.0853701 0.996349i \(-0.527207\pi\)
−0.0853701 + 0.996349i \(0.527207\pi\)
\(984\) 0 0
\(985\) 3.09418 0.0985887
\(986\) 0 0
\(987\) −12.7126 −0.404648
\(988\) 0 0
\(989\) −8.64681 −0.274953
\(990\) 0 0
\(991\) 13.9508 0.443163 0.221581 0.975142i \(-0.428878\pi\)
0.221581 + 0.975142i \(0.428878\pi\)
\(992\) 0 0
\(993\) 27.7153 0.879520
\(994\) 0 0
\(995\) 18.3684 0.582318
\(996\) 0 0
\(997\) 29.4120 0.931487 0.465743 0.884920i \(-0.345787\pi\)
0.465743 + 0.884920i \(0.345787\pi\)
\(998\) 0 0
\(999\) −4.60661 −0.145747
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 3640.2.a.o.1.2 3
4.3 odd 2 7280.2.a.bp.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.o.1.2 3 1.1 even 1 trivial
7280.2.a.bp.1.2 3 4.3 odd 2