Properties

Label 4600.2.a.y.1.3
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.621.1
Defining polynomial: \( x^{3} - 6x - 3 \) Copy content Toggle raw display
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 1.3
Root \(-2.14510\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.14510 q^{3} +1.14510 q^{7} +1.60147 q^{9} +O(q^{10})\) \(q+2.14510 q^{3} +1.14510 q^{7} +1.60147 q^{9} +5.89167 q^{11} +4.89167 q^{13} +5.89167 q^{17} -2.34803 q^{19} +2.45636 q^{21} -1.00000 q^{23} -3.00000 q^{27} +3.74657 q^{29} +5.68874 q^{31} +12.6382 q^{33} -4.00000 q^{37} +10.4931 q^{39} -1.05783 q^{41} -11.4931 q^{43} -7.74657 q^{47} -5.68874 q^{49} +12.6382 q^{51} -12.9863 q^{53} -5.03677 q^{57} +0.797069 q^{59} +13.8917 q^{61} +1.83384 q^{63} +15.5667 q^{67} -2.14510 q^{69} +2.94217 q^{71} -6.32698 q^{73} +6.74657 q^{77} -11.2397 q^{81} +0.912726 q^{83} +8.03677 q^{87} -15.4931 q^{89} +5.60147 q^{91} +12.2029 q^{93} -13.3848 q^{97} +9.43531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{7} + 3 q^{9} + 3 q^{11} + 3 q^{17} + 3 q^{19} + 12 q^{21} - 3 q^{23} - 9 q^{27} + 3 q^{29} + 6 q^{31} + 15 q^{33} - 12 q^{37} + 15 q^{39} - 6 q^{41} - 18 q^{43} - 15 q^{47} - 6 q^{49} + 15 q^{51} - 6 q^{53} + 6 q^{57} + 6 q^{59} + 27 q^{61} - 12 q^{63} - 12 q^{67} + 6 q^{71} + 15 q^{73} + 12 q^{77} - 9 q^{81} + 12 q^{83} + 3 q^{87} - 30 q^{89} + 15 q^{91} + 33 q^{93} - 9 q^{97} + 9 q^{99}+O(q^{100}) \) 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
\(3\) 2.14510 1.23848 0.619238 0.785204i \(-0.287442\pi\)
0.619238 + 0.785204i \(0.287442\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.14510 0.432808 0.216404 0.976304i \(-0.430567\pi\)
0.216404 + 0.976304i \(0.430567\pi\)
\(8\) 0 0
\(9\) 1.60147 0.533822
\(10\) 0 0
\(11\) 5.89167 1.77641 0.888203 0.459452i \(-0.151954\pi\)
0.888203 + 0.459452i \(0.151954\pi\)
\(12\) 0 0
\(13\) 4.89167 1.35671 0.678353 0.734736i \(-0.262694\pi\)
0.678353 + 0.734736i \(0.262694\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.89167 1.42894 0.714470 0.699666i \(-0.246668\pi\)
0.714470 + 0.699666i \(0.246668\pi\)
\(18\) 0 0
\(19\) −2.34803 −0.538676 −0.269338 0.963046i \(-0.586805\pi\)
−0.269338 + 0.963046i \(0.586805\pi\)
\(20\) 0 0
\(21\) 2.45636 0.536022
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.00000 −0.577350
\(28\) 0 0
\(29\) 3.74657 0.695720 0.347860 0.937546i \(-0.386908\pi\)
0.347860 + 0.937546i \(0.386908\pi\)
\(30\) 0 0
\(31\) 5.68874 1.02173 0.510864 0.859662i \(-0.329326\pi\)
0.510864 + 0.859662i \(0.329326\pi\)
\(32\) 0 0
\(33\) 12.6382 2.20004
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 10.4931 1.68025
\(40\) 0 0
\(41\) −1.05783 −0.165205 −0.0826025 0.996583i \(-0.526323\pi\)
−0.0826025 + 0.996583i \(0.526323\pi\)
\(42\) 0 0
\(43\) −11.4931 −1.75269 −0.876343 0.481687i \(-0.840024\pi\)
−0.876343 + 0.481687i \(0.840024\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.74657 −1.12995 −0.564977 0.825107i \(-0.691115\pi\)
−0.564977 + 0.825107i \(0.691115\pi\)
\(48\) 0 0
\(49\) −5.68874 −0.812677
\(50\) 0 0
\(51\) 12.6382 1.76971
\(52\) 0 0
\(53\) −12.9863 −1.78380 −0.891901 0.452231i \(-0.850628\pi\)
−0.891901 + 0.452231i \(0.850628\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5.03677 −0.667137
\(58\) 0 0
\(59\) 0.797069 0.103770 0.0518848 0.998653i \(-0.483477\pi\)
0.0518848 + 0.998653i \(0.483477\pi\)
\(60\) 0 0
\(61\) 13.8917 1.77865 0.889323 0.457279i \(-0.151176\pi\)
0.889323 + 0.457279i \(0.151176\pi\)
\(62\) 0 0
\(63\) 1.83384 0.231042
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 15.5667 1.90177 0.950887 0.309540i \(-0.100175\pi\)
0.950887 + 0.309540i \(0.100175\pi\)
\(68\) 0 0
\(69\) −2.14510 −0.258240
\(70\) 0 0
\(71\) 2.94217 0.349172 0.174586 0.984642i \(-0.444141\pi\)
0.174586 + 0.984642i \(0.444141\pi\)
\(72\) 0 0
\(73\) −6.32698 −0.740517 −0.370258 0.928929i \(-0.620731\pi\)
−0.370258 + 0.928929i \(0.620731\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.74657 0.768843
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −11.2397 −1.24886
\(82\) 0 0
\(83\) 0.912726 0.100185 0.0500923 0.998745i \(-0.484048\pi\)
0.0500923 + 0.998745i \(0.484048\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 8.03677 0.861633
\(88\) 0 0
\(89\) −15.4931 −1.64227 −0.821135 0.570735i \(-0.806659\pi\)
−0.821135 + 0.570735i \(0.806659\pi\)
\(90\) 0 0
\(91\) 5.60147 0.587193
\(92\) 0 0
\(93\) 12.2029 1.26539
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −13.3848 −1.35902 −0.679511 0.733666i \(-0.737808\pi\)
−0.679511 + 0.733666i \(0.737808\pi\)
\(98\) 0 0
\(99\) 9.43531 0.948284
\(100\) 0 0
\(101\) 2.79707 0.278319 0.139159 0.990270i \(-0.455560\pi\)
0.139159 + 0.990270i \(0.455560\pi\)
\(102\) 0 0
\(103\) 9.89167 0.974655 0.487328 0.873219i \(-0.337972\pi\)
0.487328 + 0.873219i \(0.337972\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.6961 −1.22738 −0.613688 0.789549i \(-0.710315\pi\)
−0.613688 + 0.789549i \(0.710315\pi\)
\(108\) 0 0
\(109\) 3.65197 0.349795 0.174897 0.984587i \(-0.444041\pi\)
0.174897 + 0.984587i \(0.444041\pi\)
\(110\) 0 0
\(111\) −8.58041 −0.814417
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 7.83384 0.724239
\(118\) 0 0
\(119\) 6.74657 0.618457
\(120\) 0 0
\(121\) 23.7118 2.15562
\(122\) 0 0
\(123\) −2.26915 −0.204602
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −12.1524 −1.07835 −0.539177 0.842193i \(-0.681265\pi\)
−0.539177 + 0.842193i \(0.681265\pi\)
\(128\) 0 0
\(129\) −24.6540 −2.17066
\(130\) 0 0
\(131\) −6.94950 −0.607181 −0.303590 0.952803i \(-0.598185\pi\)
−0.303590 + 0.952803i \(0.598185\pi\)
\(132\) 0 0
\(133\) −2.68874 −0.233143
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.44904 0.209235 0.104618 0.994513i \(-0.466638\pi\)
0.104618 + 0.994513i \(0.466638\pi\)
\(138\) 0 0
\(139\) 9.23970 0.783702 0.391851 0.920029i \(-0.371835\pi\)
0.391851 + 0.920029i \(0.371835\pi\)
\(140\) 0 0
\(141\) −16.6172 −1.39942
\(142\) 0 0
\(143\) 28.8201 2.41006
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −12.2029 −1.00648
\(148\) 0 0
\(149\) −2.05783 −0.168584 −0.0842919 0.996441i \(-0.526863\pi\)
−0.0842919 + 0.996441i \(0.526863\pi\)
\(150\) 0 0
\(151\) 9.34803 0.760732 0.380366 0.924836i \(-0.375798\pi\)
0.380366 + 0.924836i \(0.375798\pi\)
\(152\) 0 0
\(153\) 9.43531 0.762799
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3.60879 0.288013 0.144007 0.989577i \(-0.454001\pi\)
0.144007 + 0.989577i \(0.454001\pi\)
\(158\) 0 0
\(159\) −27.8569 −2.20920
\(160\) 0 0
\(161\) −1.14510 −0.0902467
\(162\) 0 0
\(163\) −21.2554 −1.66485 −0.832427 0.554135i \(-0.813049\pi\)
−0.832427 + 0.554135i \(0.813049\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.9863 0.850143 0.425072 0.905160i \(-0.360249\pi\)
0.425072 + 0.905160i \(0.360249\pi\)
\(168\) 0 0
\(169\) 10.9284 0.840650
\(170\) 0 0
\(171\) −3.76030 −0.287557
\(172\) 0 0
\(173\) 6.28288 0.477678 0.238839 0.971059i \(-0.423233\pi\)
0.238839 + 0.971059i \(0.423233\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.70979 0.128516
\(178\) 0 0
\(179\) 10.1524 0.758828 0.379414 0.925227i \(-0.376126\pi\)
0.379414 + 0.925227i \(0.376126\pi\)
\(180\) 0 0
\(181\) 11.1451 0.828409 0.414204 0.910184i \(-0.364060\pi\)
0.414204 + 0.910184i \(0.364060\pi\)
\(182\) 0 0
\(183\) 29.7991 2.20281
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 34.7118 2.53838
\(188\) 0 0
\(189\) −3.43531 −0.249882
\(190\) 0 0
\(191\) −14.6961 −1.06337 −0.531685 0.846942i \(-0.678441\pi\)
−0.531685 + 0.846942i \(0.678441\pi\)
\(192\) 0 0
\(193\) 26.4005 1.90035 0.950176 0.311715i \(-0.100903\pi\)
0.950176 + 0.311715i \(0.100903\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.26076 0.303567 0.151783 0.988414i \(-0.451498\pi\)
0.151783 + 0.988414i \(0.451498\pi\)
\(198\) 0 0
\(199\) 18.0735 1.28120 0.640600 0.767875i \(-0.278686\pi\)
0.640600 + 0.767875i \(0.278686\pi\)
\(200\) 0 0
\(201\) 33.3921 2.35530
\(202\) 0 0
\(203\) 4.29021 0.301113
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.60147 −0.111310
\(208\) 0 0
\(209\) −13.8338 −0.956907
\(210\) 0 0
\(211\) −11.8990 −0.819161 −0.409580 0.912274i \(-0.634325\pi\)
−0.409580 + 0.912274i \(0.634325\pi\)
\(212\) 0 0
\(213\) 6.31126 0.432440
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.51419 0.442212
\(218\) 0 0
\(219\) −13.5720 −0.917112
\(220\) 0 0
\(221\) 28.8201 1.93865
\(222\) 0 0
\(223\) −4.58041 −0.306727 −0.153363 0.988170i \(-0.549011\pi\)
−0.153363 + 0.988170i \(0.549011\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.21666 −0.147125 −0.0735624 0.997291i \(-0.523437\pi\)
−0.0735624 + 0.997291i \(0.523437\pi\)
\(228\) 0 0
\(229\) −19.1608 −1.26618 −0.633091 0.774077i \(-0.718214\pi\)
−0.633091 + 0.774077i \(0.718214\pi\)
\(230\) 0 0
\(231\) 14.4721 0.952193
\(232\) 0 0
\(233\) 21.7466 1.42467 0.712333 0.701842i \(-0.247639\pi\)
0.712333 + 0.701842i \(0.247639\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 20.9495 1.35511 0.677555 0.735472i \(-0.263039\pi\)
0.677555 + 0.735472i \(0.263039\pi\)
\(240\) 0 0
\(241\) 24.0735 1.55071 0.775357 0.631523i \(-0.217570\pi\)
0.775357 + 0.631523i \(0.217570\pi\)
\(242\) 0 0
\(243\) −15.1103 −0.969328
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −11.4858 −0.730825
\(248\) 0 0
\(249\) 1.95789 0.124076
\(250\) 0 0
\(251\) −7.82651 −0.494005 −0.247003 0.969015i \(-0.579446\pi\)
−0.247003 + 0.969015i \(0.579446\pi\)
\(252\) 0 0
\(253\) −5.89167 −0.370406
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.82012 −0.612562 −0.306281 0.951941i \(-0.599085\pi\)
−0.306281 + 0.951941i \(0.599085\pi\)
\(258\) 0 0
\(259\) −4.58041 −0.284613
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 14.6887 0.905746 0.452873 0.891575i \(-0.350399\pi\)
0.452873 + 0.891575i \(0.350399\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −33.2344 −2.03391
\(268\) 0 0
\(269\) −0.253432 −0.0154520 −0.00772600 0.999970i \(-0.502459\pi\)
−0.00772600 + 0.999970i \(0.502459\pi\)
\(270\) 0 0
\(271\) −19.6099 −1.19121 −0.595607 0.803276i \(-0.703088\pi\)
−0.595607 + 0.803276i \(0.703088\pi\)
\(272\) 0 0
\(273\) 12.0157 0.727224
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −29.1976 −1.75431 −0.877157 0.480204i \(-0.840563\pi\)
−0.877157 + 0.480204i \(0.840563\pi\)
\(278\) 0 0
\(279\) 9.11032 0.545421
\(280\) 0 0
\(281\) −27.1755 −1.62115 −0.810577 0.585633i \(-0.800846\pi\)
−0.810577 + 0.585633i \(0.800846\pi\)
\(282\) 0 0
\(283\) −18.1471 −1.07873 −0.539366 0.842071i \(-0.681336\pi\)
−0.539366 + 0.842071i \(0.681336\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.21132 −0.0715021
\(288\) 0 0
\(289\) 17.7118 1.04187
\(290\) 0 0
\(291\) −28.7118 −1.68311
\(292\) 0 0
\(293\) −0.681412 −0.0398085 −0.0199043 0.999802i \(-0.506336\pi\)
−0.0199043 + 0.999802i \(0.506336\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −17.6750 −1.02561
\(298\) 0 0
\(299\) −4.89167 −0.282893
\(300\) 0 0
\(301\) −13.1608 −0.758577
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −26.5877 −1.51744 −0.758721 0.651415i \(-0.774176\pi\)
−0.758721 + 0.651415i \(0.774176\pi\)
\(308\) 0 0
\(309\) 21.2186 1.20709
\(310\) 0 0
\(311\) 13.5299 0.767211 0.383605 0.923497i \(-0.374682\pi\)
0.383605 + 0.923497i \(0.374682\pi\)
\(312\) 0 0
\(313\) −19.8412 −1.12149 −0.560745 0.827989i \(-0.689485\pi\)
−0.560745 + 0.827989i \(0.689485\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.55096 −0.199442 −0.0997210 0.995015i \(-0.531795\pi\)
−0.0997210 + 0.995015i \(0.531795\pi\)
\(318\) 0 0
\(319\) 22.0735 1.23588
\(320\) 0 0
\(321\) −27.2344 −1.52007
\(322\) 0 0
\(323\) −13.8338 −0.769736
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 7.83384 0.433212
\(328\) 0 0
\(329\) −8.87062 −0.489053
\(330\) 0 0
\(331\) −13.3133 −0.731763 −0.365881 0.930662i \(-0.619232\pi\)
−0.365881 + 0.930662i \(0.619232\pi\)
\(332\) 0 0
\(333\) −6.40586 −0.351039
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 20.4951 1.11644 0.558220 0.829693i \(-0.311484\pi\)
0.558220 + 0.829693i \(0.311484\pi\)
\(338\) 0 0
\(339\) 21.4510 1.16506
\(340\) 0 0
\(341\) 33.5162 1.81500
\(342\) 0 0
\(343\) −14.5299 −0.784541
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.60147 0.408068 0.204034 0.978964i \(-0.434595\pi\)
0.204034 + 0.978964i \(0.434595\pi\)
\(348\) 0 0
\(349\) 5.55736 0.297479 0.148739 0.988876i \(-0.452478\pi\)
0.148739 + 0.988876i \(0.452478\pi\)
\(350\) 0 0
\(351\) −14.6750 −0.783294
\(352\) 0 0
\(353\) −1.96323 −0.104492 −0.0522460 0.998634i \(-0.516638\pi\)
−0.0522460 + 0.998634i \(0.516638\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 14.4721 0.765944
\(358\) 0 0
\(359\) 10.5069 0.554531 0.277266 0.960793i \(-0.410572\pi\)
0.277266 + 0.960793i \(0.410572\pi\)
\(360\) 0 0
\(361\) −13.4867 −0.709828
\(362\) 0 0
\(363\) 50.8642 2.66968
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −33.7412 −1.76128 −0.880639 0.473788i \(-0.842886\pi\)
−0.880639 + 0.473788i \(0.842886\pi\)
\(368\) 0 0
\(369\) −1.69408 −0.0881901
\(370\) 0 0
\(371\) −14.8706 −0.772044
\(372\) 0 0
\(373\) 17.4510 0.903580 0.451790 0.892124i \(-0.350786\pi\)
0.451790 + 0.892124i \(0.350786\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 18.3270 0.943887
\(378\) 0 0
\(379\) −33.4584 −1.71864 −0.859320 0.511438i \(-0.829113\pi\)
−0.859320 + 0.511438i \(0.829113\pi\)
\(380\) 0 0
\(381\) −26.0682 −1.33551
\(382\) 0 0
\(383\) −13.0873 −0.668728 −0.334364 0.942444i \(-0.608522\pi\)
−0.334364 + 0.942444i \(0.608522\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −18.4059 −0.935623
\(388\) 0 0
\(389\) 14.1083 0.715321 0.357660 0.933852i \(-0.383575\pi\)
0.357660 + 0.933852i \(0.383575\pi\)
\(390\) 0 0
\(391\) −5.89167 −0.297955
\(392\) 0 0
\(393\) −14.9074 −0.751978
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.6245 −0.834360 −0.417180 0.908824i \(-0.636982\pi\)
−0.417180 + 0.908824i \(0.636982\pi\)
\(398\) 0 0
\(399\) −5.76762 −0.288742
\(400\) 0 0
\(401\) 22.2628 1.11175 0.555874 0.831266i \(-0.312384\pi\)
0.555874 + 0.831266i \(0.312384\pi\)
\(402\) 0 0
\(403\) 27.8274 1.38618
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −23.5667 −1.16816
\(408\) 0 0
\(409\) 15.6887 0.775758 0.387879 0.921710i \(-0.373208\pi\)
0.387879 + 0.921710i \(0.373208\pi\)
\(410\) 0 0
\(411\) 5.25343 0.259133
\(412\) 0 0
\(413\) 0.912726 0.0449123
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 19.8201 0.970595
\(418\) 0 0
\(419\) −5.66769 −0.276885 −0.138442 0.990371i \(-0.544210\pi\)
−0.138442 + 0.990371i \(0.544210\pi\)
\(420\) 0 0
\(421\) 15.0716 0.734543 0.367271 0.930114i \(-0.380292\pi\)
0.367271 + 0.930114i \(0.380292\pi\)
\(422\) 0 0
\(423\) −12.4059 −0.603194
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 15.9074 0.769813
\(428\) 0 0
\(429\) 61.8221 2.98480
\(430\) 0 0
\(431\) 29.3500 1.41374 0.706870 0.707343i \(-0.250106\pi\)
0.706870 + 0.707343i \(0.250106\pi\)
\(432\) 0 0
\(433\) −29.6245 −1.42366 −0.711832 0.702350i \(-0.752134\pi\)
−0.711832 + 0.702350i \(0.752134\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.34803 0.112322
\(438\) 0 0
\(439\) −20.7907 −0.992285 −0.496142 0.868241i \(-0.665251\pi\)
−0.496142 + 0.868241i \(0.665251\pi\)
\(440\) 0 0
\(441\) −9.11032 −0.433825
\(442\) 0 0
\(443\) −21.2975 −1.01188 −0.505938 0.862570i \(-0.668854\pi\)
−0.505938 + 0.862570i \(0.668854\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.41425 −0.208787
\(448\) 0 0
\(449\) −19.3197 −0.911751 −0.455875 0.890044i \(-0.650674\pi\)
−0.455875 + 0.890044i \(0.650674\pi\)
\(450\) 0 0
\(451\) −6.23238 −0.293471
\(452\) 0 0
\(453\) 20.0525 0.942148
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.912726 −0.0426955 −0.0213478 0.999772i \(-0.506796\pi\)
−0.0213478 + 0.999772i \(0.506796\pi\)
\(458\) 0 0
\(459\) −17.6750 −0.824999
\(460\) 0 0
\(461\) 2.83384 0.131985 0.0659926 0.997820i \(-0.478979\pi\)
0.0659926 + 0.997820i \(0.478979\pi\)
\(462\) 0 0
\(463\) 17.2618 0.802225 0.401112 0.916029i \(-0.368624\pi\)
0.401112 + 0.916029i \(0.368624\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.4510 0.992635 0.496318 0.868141i \(-0.334685\pi\)
0.496318 + 0.868141i \(0.334685\pi\)
\(468\) 0 0
\(469\) 17.8255 0.823103
\(470\) 0 0
\(471\) 7.74123 0.356697
\(472\) 0 0
\(473\) −67.7138 −3.11348
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −20.7971 −0.952232
\(478\) 0 0
\(479\) 9.49314 0.433752 0.216876 0.976199i \(-0.430413\pi\)
0.216876 + 0.976199i \(0.430413\pi\)
\(480\) 0 0
\(481\) −19.5667 −0.892164
\(482\) 0 0
\(483\) −2.45636 −0.111768
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −38.3270 −1.73676 −0.868381 0.495898i \(-0.834839\pi\)
−0.868381 + 0.495898i \(0.834839\pi\)
\(488\) 0 0
\(489\) −45.5951 −2.06188
\(490\) 0 0
\(491\) −13.9947 −0.631570 −0.315785 0.948831i \(-0.602268\pi\)
−0.315785 + 0.948831i \(0.602268\pi\)
\(492\) 0 0
\(493\) 22.0735 0.994143
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.36909 0.151124
\(498\) 0 0
\(499\) −0.0642277 −0.00287522 −0.00143761 0.999999i \(-0.500458\pi\)
−0.00143761 + 0.999999i \(0.500458\pi\)
\(500\) 0 0
\(501\) 23.5667 1.05288
\(502\) 0 0
\(503\) 24.2785 1.08252 0.541262 0.840854i \(-0.317947\pi\)
0.541262 + 0.840854i \(0.317947\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.4426 1.04112
\(508\) 0 0
\(509\) −2.65929 −0.117871 −0.0589356 0.998262i \(-0.518771\pi\)
−0.0589356 + 0.998262i \(0.518771\pi\)
\(510\) 0 0
\(511\) −7.24504 −0.320502
\(512\) 0 0
\(513\) 7.04410 0.311005
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −45.6402 −2.00726
\(518\) 0 0
\(519\) 13.4774 0.591593
\(520\) 0 0
\(521\) −17.0598 −0.747404 −0.373702 0.927549i \(-0.621912\pi\)
−0.373702 + 0.927549i \(0.621912\pi\)
\(522\) 0 0
\(523\) 17.5667 0.768137 0.384069 0.923305i \(-0.374523\pi\)
0.384069 + 0.923305i \(0.374523\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 33.5162 1.45999
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 1.27648 0.0553944
\(532\) 0 0
\(533\) −5.17455 −0.224135
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 21.7780 0.939790
\(538\) 0 0
\(539\) −33.5162 −1.44364
\(540\) 0 0
\(541\) −8.36909 −0.359815 −0.179908 0.983684i \(-0.557580\pi\)
−0.179908 + 0.983684i \(0.557580\pi\)
\(542\) 0 0
\(543\) 23.9074 1.02596
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 16.7486 0.716117 0.358058 0.933699i \(-0.383439\pi\)
0.358058 + 0.933699i \(0.383439\pi\)
\(548\) 0 0
\(549\) 22.2470 0.949480
\(550\) 0 0
\(551\) −8.79707 −0.374768
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.26182 0.307693 0.153847 0.988095i \(-0.450834\pi\)
0.153847 + 0.988095i \(0.450834\pi\)
\(558\) 0 0
\(559\) −56.2206 −2.37788
\(560\) 0 0
\(561\) 74.4603 3.14372
\(562\) 0 0
\(563\) −34.5530 −1.45623 −0.728117 0.685453i \(-0.759604\pi\)
−0.728117 + 0.685453i \(0.759604\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −12.8706 −0.540515
\(568\) 0 0
\(569\) 34.7275 1.45585 0.727926 0.685655i \(-0.240484\pi\)
0.727926 + 0.685655i \(0.240484\pi\)
\(570\) 0 0
\(571\) 14.7034 0.615318 0.307659 0.951497i \(-0.400454\pi\)
0.307659 + 0.951497i \(0.400454\pi\)
\(572\) 0 0
\(573\) −31.5246 −1.31696
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 6.13777 0.255519 0.127759 0.991805i \(-0.459221\pi\)
0.127759 + 0.991805i \(0.459221\pi\)
\(578\) 0 0
\(579\) 56.6318 2.35354
\(580\) 0 0
\(581\) 1.04516 0.0433607
\(582\) 0 0
\(583\) −76.5108 −3.16876
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.33338 0.0550344 0.0275172 0.999621i \(-0.491240\pi\)
0.0275172 + 0.999621i \(0.491240\pi\)
\(588\) 0 0
\(589\) −13.3574 −0.550380
\(590\) 0 0
\(591\) 9.13977 0.375960
\(592\) 0 0
\(593\) −1.88434 −0.0773807 −0.0386903 0.999251i \(-0.512319\pi\)
−0.0386903 + 0.999251i \(0.512319\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 38.7696 1.58673
\(598\) 0 0
\(599\) −43.7632 −1.78812 −0.894058 0.447951i \(-0.852154\pi\)
−0.894058 + 0.447951i \(0.852154\pi\)
\(600\) 0 0
\(601\) 4.50046 0.183578 0.0917889 0.995778i \(-0.470742\pi\)
0.0917889 + 0.995778i \(0.470742\pi\)
\(602\) 0 0
\(603\) 24.9295 1.01521
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −6.17455 −0.250617 −0.125309 0.992118i \(-0.539992\pi\)
−0.125309 + 0.992118i \(0.539992\pi\)
\(608\) 0 0
\(609\) 9.20293 0.372922
\(610\) 0 0
\(611\) −37.8937 −1.53301
\(612\) 0 0
\(613\) 9.72445 0.392767 0.196383 0.980527i \(-0.437080\pi\)
0.196383 + 0.980527i \(0.437080\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.730849 0.0294229 0.0147114 0.999892i \(-0.495317\pi\)
0.0147114 + 0.999892i \(0.495317\pi\)
\(618\) 0 0
\(619\) 11.1598 0.448549 0.224274 0.974526i \(-0.427999\pi\)
0.224274 + 0.974526i \(0.427999\pi\)
\(620\) 0 0
\(621\) 3.00000 0.120386
\(622\) 0 0
\(623\) −17.7412 −0.710787
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −29.6750 −1.18511
\(628\) 0 0
\(629\) −23.5667 −0.939665
\(630\) 0 0
\(631\) −4.87062 −0.193896 −0.0969481 0.995289i \(-0.530908\pi\)
−0.0969481 + 0.995289i \(0.530908\pi\)
\(632\) 0 0
\(633\) −25.5246 −1.01451
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −27.8274 −1.10256
\(638\) 0 0
\(639\) 4.71179 0.186395
\(640\) 0 0
\(641\) 32.6540 1.28975 0.644877 0.764286i \(-0.276909\pi\)
0.644877 + 0.764286i \(0.276909\pi\)
\(642\) 0 0
\(643\) −47.9579 −1.89127 −0.945637 0.325223i \(-0.894561\pi\)
−0.945637 + 0.325223i \(0.894561\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12.1103 −0.476106 −0.238053 0.971252i \(-0.576509\pi\)
−0.238053 + 0.971252i \(0.576509\pi\)
\(648\) 0 0
\(649\) 4.69607 0.184337
\(650\) 0 0
\(651\) 13.9736 0.547669
\(652\) 0 0
\(653\) 43.2133 1.69107 0.845534 0.533922i \(-0.179282\pi\)
0.845534 + 0.533922i \(0.179282\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −10.1324 −0.395304
\(658\) 0 0
\(659\) 20.4333 0.795969 0.397984 0.917392i \(-0.369710\pi\)
0.397984 + 0.917392i \(0.369710\pi\)
\(660\) 0 0
\(661\) 48.1398 1.87242 0.936210 0.351441i \(-0.114308\pi\)
0.936210 + 0.351441i \(0.114308\pi\)
\(662\) 0 0
\(663\) 61.8221 2.40097
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.74657 −0.145068
\(668\) 0 0
\(669\) −9.82545 −0.379874
\(670\) 0 0
\(671\) 81.8452 3.15960
\(672\) 0 0
\(673\) −16.5436 −0.637710 −0.318855 0.947803i \(-0.603298\pi\)
−0.318855 + 0.947803i \(0.603298\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 48.9863 1.88270 0.941348 0.337438i \(-0.109560\pi\)
0.941348 + 0.337438i \(0.109560\pi\)
\(678\) 0 0
\(679\) −15.3270 −0.588195
\(680\) 0 0
\(681\) −4.75496 −0.182210
\(682\) 0 0
\(683\) 21.8779 0.837136 0.418568 0.908185i \(-0.362532\pi\)
0.418568 + 0.908185i \(0.362532\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −41.1019 −1.56814
\(688\) 0 0
\(689\) −63.5246 −2.42009
\(690\) 0 0
\(691\) −3.30393 −0.125688 −0.0628438 0.998023i \(-0.520017\pi\)
−0.0628438 + 0.998023i \(0.520017\pi\)
\(692\) 0 0
\(693\) 10.8044 0.410425
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.23238 −0.236068
\(698\) 0 0
\(699\) 46.6486 1.76441
\(700\) 0 0
\(701\) −4.46369 −0.168591 −0.0842956 0.996441i \(-0.526864\pi\)
−0.0842956 + 0.996441i \(0.526864\pi\)
\(702\) 0 0
\(703\) 9.39214 0.354231
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.20293 0.120459
\(708\) 0 0
\(709\) −2.39853 −0.0900789 −0.0450394 0.998985i \(-0.514341\pi\)
−0.0450394 + 0.998985i \(0.514341\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.68874 −0.213045
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 44.9388 1.67827
\(718\) 0 0
\(719\) 12.0725 0.450228 0.225114 0.974332i \(-0.427725\pi\)
0.225114 + 0.974332i \(0.427725\pi\)
\(720\) 0 0
\(721\) 11.3270 0.421839
\(722\) 0 0
\(723\) 51.6402 1.92052
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −11.4269 −0.423801 −0.211900 0.977291i \(-0.567965\pi\)
−0.211900 + 0.977291i \(0.567965\pi\)
\(728\) 0 0
\(729\) 1.30592 0.0483676
\(730\) 0 0
\(731\) −67.7138 −2.50448
\(732\) 0 0
\(733\) 3.08727 0.114031 0.0570155 0.998373i \(-0.481842\pi\)
0.0570155 + 0.998373i \(0.481842\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 91.7138 3.37832
\(738\) 0 0
\(739\) −8.36909 −0.307862 −0.153931 0.988082i \(-0.549193\pi\)
−0.153931 + 0.988082i \(0.549193\pi\)
\(740\) 0 0
\(741\) −24.6382 −0.905108
\(742\) 0 0
\(743\) −15.1598 −0.556158 −0.278079 0.960558i \(-0.589698\pi\)
−0.278079 + 0.960558i \(0.589698\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.46170 0.0534808
\(748\) 0 0
\(749\) −14.5383 −0.531218
\(750\) 0 0
\(751\) −33.6823 −1.22909 −0.614543 0.788883i \(-0.710660\pi\)
−0.614543 + 0.788883i \(0.710660\pi\)
\(752\) 0 0
\(753\) −16.7887 −0.611813
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 29.1608 1.05987 0.529934 0.848039i \(-0.322217\pi\)
0.529934 + 0.848039i \(0.322217\pi\)
\(758\) 0 0
\(759\) −12.6382 −0.458739
\(760\) 0 0
\(761\) −6.91912 −0.250818 −0.125409 0.992105i \(-0.540024\pi\)
−0.125409 + 0.992105i \(0.540024\pi\)
\(762\) 0 0
\(763\) 4.18188 0.151394
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.89900 0.140785
\(768\) 0 0
\(769\) −14.3491 −0.517442 −0.258721 0.965952i \(-0.583301\pi\)
−0.258721 + 0.965952i \(0.583301\pi\)
\(770\) 0 0
\(771\) −21.0652 −0.758643
\(772\) 0 0
\(773\) −50.6265 −1.82091 −0.910454 0.413609i \(-0.864268\pi\)
−0.910454 + 0.413609i \(0.864268\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −9.82545 −0.352486
\(778\) 0 0
\(779\) 2.48382 0.0889920
\(780\) 0 0
\(781\) 17.3343 0.620270
\(782\) 0 0
\(783\) −11.2397 −0.401674
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20.9442 −0.746579 −0.373289 0.927715i \(-0.621770\pi\)
−0.373289 + 0.927715i \(0.621770\pi\)
\(788\) 0 0
\(789\) 31.5089 1.12174
\(790\) 0 0
\(791\) 11.4510 0.407152
\(792\) 0 0
\(793\) 67.9535 2.41310
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19.0009 −0.673047 −0.336524 0.941675i \(-0.609251\pi\)
−0.336524 + 0.941675i \(0.609251\pi\)
\(798\) 0 0
\(799\) −45.6402 −1.61464
\(800\) 0 0
\(801\) −24.8117 −0.876679
\(802\) 0 0
\(803\) −37.2765 −1.31546
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.543637 −0.0191369
\(808\) 0 0
\(809\) 18.4300 0.647963 0.323982 0.946063i \(-0.394978\pi\)
0.323982 + 0.946063i \(0.394978\pi\)
\(810\) 0 0
\(811\) −21.1387 −0.742280 −0.371140 0.928577i \(-0.621033\pi\)
−0.371140 + 0.928577i \(0.621033\pi\)
\(812\) 0 0
\(813\) −42.0652 −1.47529
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 26.9863 0.944130
\(818\) 0 0
\(819\) 8.97055 0.313457
\(820\) 0 0
\(821\) −16.7550 −0.584752 −0.292376 0.956303i \(-0.594446\pi\)
−0.292376 + 0.956303i \(0.594446\pi\)
\(822\) 0 0
\(823\) −24.9220 −0.868728 −0.434364 0.900737i \(-0.643027\pi\)
−0.434364 + 0.900737i \(0.643027\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 6.62252 0.230288 0.115144 0.993349i \(-0.463267\pi\)
0.115144 + 0.993349i \(0.463267\pi\)
\(828\) 0 0
\(829\) 52.7001 1.83035 0.915174 0.403058i \(-0.132053\pi\)
0.915174 + 0.403058i \(0.132053\pi\)
\(830\) 0 0
\(831\) −62.6318 −2.17267
\(832\) 0 0
\(833\) −33.5162 −1.16127
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −17.0662 −0.589895
\(838\) 0 0
\(839\) 42.5951 1.47054 0.735272 0.677772i \(-0.237054\pi\)
0.735272 + 0.677772i \(0.237054\pi\)
\(840\) 0 0
\(841\) −14.9632 −0.515973
\(842\) 0 0
\(843\) −58.2942 −2.00776
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 27.1524 0.932969
\(848\) 0 0
\(849\) −38.9274 −1.33598
\(850\) 0 0
\(851\) 4.00000 0.137118
\(852\) 0 0
\(853\) 57.7255 1.97648 0.988242 0.152898i \(-0.0488606\pi\)
0.988242 + 0.152898i \(0.0488606\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 55.3721 1.89148 0.945738 0.324930i \(-0.105341\pi\)
0.945738 + 0.324930i \(0.105341\pi\)
\(858\) 0 0
\(859\) −14.3544 −0.489767 −0.244883 0.969553i \(-0.578750\pi\)
−0.244883 + 0.969553i \(0.578750\pi\)
\(860\) 0 0
\(861\) −2.59841 −0.0885536
\(862\) 0 0
\(863\) −15.9211 −0.541961 −0.270981 0.962585i \(-0.587348\pi\)
−0.270981 + 0.962585i \(0.587348\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 37.9936 1.29033
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 76.1471 2.58015
\(872\) 0 0
\(873\) −21.4353 −0.725475
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 30.2975 1.02308 0.511538 0.859261i \(-0.329076\pi\)
0.511538 + 0.859261i \(0.329076\pi\)
\(878\) 0 0
\(879\) −1.46170 −0.0493019
\(880\) 0 0
\(881\) −11.1883 −0.376943 −0.188471 0.982079i \(-0.560353\pi\)
−0.188471 + 0.982079i \(0.560353\pi\)
\(882\) 0 0
\(883\) −25.2882 −0.851016 −0.425508 0.904955i \(-0.639905\pi\)
−0.425508 + 0.904955i \(0.639905\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32.2849 1.08402 0.542010 0.840372i \(-0.317664\pi\)
0.542010 + 0.840372i \(0.317664\pi\)
\(888\) 0 0
\(889\) −13.9158 −0.466720
\(890\) 0 0
\(891\) −66.2206 −2.21847
\(892\) 0 0
\(893\) 18.1892 0.608679
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −10.4931 −0.350356
\(898\) 0 0
\(899\) 21.3133 0.710837
\(900\) 0 0
\(901\) −76.5108 −2.54895
\(902\) 0 0
\(903\) −28.2313 −0.939479
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.47848 0.0490922 0.0245461 0.999699i \(-0.492186\pi\)
0.0245461 + 0.999699i \(0.492186\pi\)
\(908\) 0 0
\(909\) 4.47941 0.148573
\(910\) 0 0
\(911\) 5.70979 0.189174 0.0945870 0.995517i \(-0.469847\pi\)
0.0945870 + 0.995517i \(0.469847\pi\)
\(912\) 0 0
\(913\) 5.37748 0.177969
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.95789 −0.262793
\(918\) 0 0
\(919\) 22.6265 0.746379 0.373190 0.927755i \(-0.378264\pi\)
0.373190 + 0.927755i \(0.378264\pi\)
\(920\) 0 0
\(921\) −57.0334 −1.87932
\(922\) 0 0
\(923\) 14.3921 0.473723
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 15.8412 0.520292
\(928\) 0 0
\(929\) −50.0829 −1.64317 −0.821583 0.570089i \(-0.806909\pi\)
−0.821583 + 0.570089i \(0.806909\pi\)
\(930\) 0 0
\(931\) 13.3574 0.437770
\(932\) 0 0
\(933\) 29.0230 0.950172
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −9.98428 −0.326172 −0.163086 0.986612i \(-0.552145\pi\)
−0.163086 + 0.986612i \(0.552145\pi\)
\(938\) 0 0
\(939\) −42.5613 −1.38894
\(940\) 0 0
\(941\) −36.0809 −1.17620 −0.588101 0.808787i \(-0.700124\pi\)
−0.588101 + 0.808787i \(0.700124\pi\)
\(942\) 0 0
\(943\) 1.05783 0.0344476
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 32.4730 1.05523 0.527616 0.849483i \(-0.323086\pi\)
0.527616 + 0.849483i \(0.323086\pi\)
\(948\) 0 0
\(949\) −30.9495 −1.00466
\(950\) 0 0
\(951\) −7.61718 −0.247004
\(952\) 0 0
\(953\) 39.3427 1.27443 0.637217 0.770684i \(-0.280085\pi\)
0.637217 + 0.770684i \(0.280085\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 47.3500 1.53061
\(958\) 0 0
\(959\) 2.80440 0.0905587
\(960\) 0 0
\(961\) 1.36176 0.0439278
\(962\) 0 0
\(963\) −20.3323 −0.655200
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −23.5720 −0.758025 −0.379013 0.925392i \(-0.623736\pi\)
−0.379013 + 0.925392i \(0.623736\pi\)
\(968\) 0 0
\(969\) −29.6750 −0.953299
\(970\) 0 0
\(971\) 12.9368 0.415163 0.207581 0.978218i \(-0.433441\pi\)
0.207581 + 0.978218i \(0.433441\pi\)
\(972\) 0 0
\(973\) 10.5804 0.339192
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22.7118 0.726614 0.363307 0.931669i \(-0.381648\pi\)
0.363307 + 0.931669i \(0.381648\pi\)
\(978\) 0 0
\(979\) −91.2805 −2.91734
\(980\) 0 0
\(981\) 5.84850 0.186728
\(982\) 0 0
\(983\) −26.1819 −0.835072 −0.417536 0.908660i \(-0.637106\pi\)
−0.417536 + 0.908660i \(0.637106\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −19.0284 −0.605680
\(988\) 0 0
\(989\) 11.4931 0.365460
\(990\) 0 0
\(991\) −56.3143 −1.78888 −0.894442 0.447185i \(-0.852427\pi\)
−0.894442 + 0.447185i \(0.852427\pi\)
\(992\) 0 0
\(993\) −28.5583 −0.906270
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 3.74123 0.118486 0.0592430 0.998244i \(-0.481131\pi\)
0.0592430 + 0.998244i \(0.481131\pi\)
\(998\) 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 4600.2.a.y.1.3 3
4.3 odd 2 9200.2.a.cd.1.1 3
5.2 odd 4 4600.2.e.r.4049.2 6
5.3 odd 4 4600.2.e.r.4049.5 6
5.4 even 2 920.2.a.g.1.1 3
15.14 odd 2 8280.2.a.bo.1.1 3
20.19 odd 2 1840.2.a.t.1.3 3
40.19 odd 2 7360.2.a.ca.1.1 3
40.29 even 2 7360.2.a.cb.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.g.1.1 3 5.4 even 2
1840.2.a.t.1.3 3 20.19 odd 2
4600.2.a.y.1.3 3 1.1 even 1 trivial
4600.2.e.r.4049.2 6 5.2 odd 4
4600.2.e.r.4049.5 6 5.3 odd 4
7360.2.a.ca.1.1 3 40.19 odd 2
7360.2.a.cb.1.3 3 40.29 even 2
8280.2.a.bo.1.1 3 15.14 odd 2
9200.2.a.cd.1.1 3 4.3 odd 2