Properties

Label 2352.4.a.cg.1.1
Level $2352$
Weight $4$
Character 2352.1
Self dual yes
Analytic conductor $138.772$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(138.772492334\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.57516.1
Defining polynomial: \(x^{3} - x^{2} - 24 x + 6\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.55637\) of defining polynomial
Character \(\chi\) \(=\) 2352.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{3} -17.8732 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -17.8732 q^{5} +9.00000 q^{9} +11.3942 q^{11} +13.0987 q^{13} +53.6196 q^{15} -53.2674 q^{17} -42.4223 q^{19} -152.085 q^{23} +194.451 q^{25} -27.0000 q^{27} +186.493 q^{29} -157.874 q^{31} -34.1825 q^{33} +3.74588 q^{37} -39.2960 q^{39} +39.3230 q^{41} -429.439 q^{43} -160.859 q^{45} +21.1869 q^{47} +159.802 q^{51} +365.904 q^{53} -203.650 q^{55} +127.267 q^{57} -226.578 q^{59} -651.973 q^{61} -234.115 q^{65} -145.433 q^{67} +456.256 q^{69} +368.962 q^{71} -608.906 q^{73} -583.354 q^{75} -910.237 q^{79} +81.0000 q^{81} -327.929 q^{83} +952.058 q^{85} -559.480 q^{87} +37.6118 q^{89} +473.621 q^{93} +758.222 q^{95} -722.013 q^{97} +102.547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 9q^{3} - 11q^{5} + 27q^{9} + O(q^{10}) \) \( 3q - 9q^{3} - 11q^{5} + 27q^{9} - 35q^{11} - 62q^{13} + 33q^{15} - 48q^{17} - 202q^{19} - 216q^{23} + 130q^{25} - 81q^{27} + 53q^{29} - 95q^{31} + 105q^{33} + 262q^{37} + 186q^{39} - 244q^{41} - 360q^{43} - 99q^{45} - 210q^{47} + 144q^{51} + 393q^{53} - 1031q^{55} + 606q^{57} + 1143q^{59} + 70q^{61} - 472q^{65} + 628q^{67} + 648q^{69} - 318q^{71} - 988q^{73} - 390q^{75} - 861q^{79} + 243q^{81} + 519q^{83} + 1800q^{85} - 159q^{87} - 1766q^{89} + 285q^{93} + 736q^{95} - 19q^{97} - 315q^{99} + O(q^{100}) \)

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
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) −17.8732 −1.59863 −0.799314 0.600914i \(-0.794804\pi\)
−0.799314 + 0.600914i \(0.794804\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 11.3942 0.312315 0.156158 0.987732i \(-0.450089\pi\)
0.156158 + 0.987732i \(0.450089\pi\)
\(12\) 0 0
\(13\) 13.0987 0.279455 0.139728 0.990190i \(-0.455377\pi\)
0.139728 + 0.990190i \(0.455377\pi\)
\(14\) 0 0
\(15\) 53.6196 0.922968
\(16\) 0 0
\(17\) −53.2674 −0.759955 −0.379977 0.924996i \(-0.624068\pi\)
−0.379977 + 0.924996i \(0.624068\pi\)
\(18\) 0 0
\(19\) −42.4223 −0.512228 −0.256114 0.966647i \(-0.582442\pi\)
−0.256114 + 0.966647i \(0.582442\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −152.085 −1.37878 −0.689391 0.724389i \(-0.742122\pi\)
−0.689391 + 0.724389i \(0.742122\pi\)
\(24\) 0 0
\(25\) 194.451 1.55561
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 186.493 1.19417 0.597085 0.802178i \(-0.296325\pi\)
0.597085 + 0.802178i \(0.296325\pi\)
\(30\) 0 0
\(31\) −157.874 −0.914676 −0.457338 0.889293i \(-0.651197\pi\)
−0.457338 + 0.889293i \(0.651197\pi\)
\(32\) 0 0
\(33\) −34.1825 −0.180315
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.74588 0.0166438 0.00832188 0.999965i \(-0.497351\pi\)
0.00832188 + 0.999965i \(0.497351\pi\)
\(38\) 0 0
\(39\) −39.2960 −0.161344
\(40\) 0 0
\(41\) 39.3230 0.149786 0.0748930 0.997192i \(-0.476138\pi\)
0.0748930 + 0.997192i \(0.476138\pi\)
\(42\) 0 0
\(43\) −429.439 −1.52300 −0.761498 0.648168i \(-0.775536\pi\)
−0.761498 + 0.648168i \(0.775536\pi\)
\(44\) 0 0
\(45\) −160.859 −0.532876
\(46\) 0 0
\(47\) 21.1869 0.0657537 0.0328768 0.999459i \(-0.489533\pi\)
0.0328768 + 0.999459i \(0.489533\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 159.802 0.438760
\(52\) 0 0
\(53\) 365.904 0.948317 0.474158 0.880440i \(-0.342752\pi\)
0.474158 + 0.880440i \(0.342752\pi\)
\(54\) 0 0
\(55\) −203.650 −0.499276
\(56\) 0 0
\(57\) 127.267 0.295735
\(58\) 0 0
\(59\) −226.578 −0.499964 −0.249982 0.968250i \(-0.580425\pi\)
−0.249982 + 0.968250i \(0.580425\pi\)
\(60\) 0 0
\(61\) −651.973 −1.36847 −0.684235 0.729262i \(-0.739864\pi\)
−0.684235 + 0.729262i \(0.739864\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −234.115 −0.446745
\(66\) 0 0
\(67\) −145.433 −0.265186 −0.132593 0.991171i \(-0.542330\pi\)
−0.132593 + 0.991171i \(0.542330\pi\)
\(68\) 0 0
\(69\) 456.256 0.796041
\(70\) 0 0
\(71\) 368.962 0.616728 0.308364 0.951268i \(-0.400218\pi\)
0.308364 + 0.951268i \(0.400218\pi\)
\(72\) 0 0
\(73\) −608.906 −0.976261 −0.488130 0.872771i \(-0.662321\pi\)
−0.488130 + 0.872771i \(0.662321\pi\)
\(74\) 0 0
\(75\) −583.354 −0.898133
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −910.237 −1.29633 −0.648163 0.761502i \(-0.724462\pi\)
−0.648163 + 0.761502i \(0.724462\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −327.929 −0.433674 −0.216837 0.976208i \(-0.569574\pi\)
−0.216837 + 0.976208i \(0.569574\pi\)
\(84\) 0 0
\(85\) 952.058 1.21489
\(86\) 0 0
\(87\) −559.480 −0.689455
\(88\) 0 0
\(89\) 37.6118 0.0447960 0.0223980 0.999749i \(-0.492870\pi\)
0.0223980 + 0.999749i \(0.492870\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 473.621 0.528089
\(94\) 0 0
\(95\) 758.222 0.818863
\(96\) 0 0
\(97\) −722.013 −0.755766 −0.377883 0.925853i \(-0.623348\pi\)
−0.377883 + 0.925853i \(0.623348\pi\)
\(98\) 0 0
\(99\) 102.547 0.104105
\(100\) 0 0
\(101\) −1518.67 −1.49617 −0.748087 0.663601i \(-0.769027\pi\)
−0.748087 + 0.663601i \(0.769027\pi\)
\(102\) 0 0
\(103\) −1051.88 −1.00626 −0.503132 0.864210i \(-0.667819\pi\)
−0.503132 + 0.864210i \(0.667819\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −766.520 −0.692545 −0.346273 0.938134i \(-0.612553\pi\)
−0.346273 + 0.938134i \(0.612553\pi\)
\(108\) 0 0
\(109\) −1427.05 −1.25400 −0.627002 0.779018i \(-0.715718\pi\)
−0.627002 + 0.779018i \(0.715718\pi\)
\(110\) 0 0
\(111\) −11.2376 −0.00960928
\(112\) 0 0
\(113\) 362.564 0.301833 0.150917 0.988546i \(-0.451778\pi\)
0.150917 + 0.988546i \(0.451778\pi\)
\(114\) 0 0
\(115\) 2718.25 2.20416
\(116\) 0 0
\(117\) 117.888 0.0931517
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1201.17 −0.902459
\(122\) 0 0
\(123\) −117.969 −0.0864789
\(124\) 0 0
\(125\) −1241.32 −0.888216
\(126\) 0 0
\(127\) −974.777 −0.681082 −0.340541 0.940230i \(-0.610610\pi\)
−0.340541 + 0.940230i \(0.610610\pi\)
\(128\) 0 0
\(129\) 1288.32 0.879302
\(130\) 0 0
\(131\) −1792.70 −1.19564 −0.597821 0.801629i \(-0.703967\pi\)
−0.597821 + 0.801629i \(0.703967\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 482.577 0.307656
\(136\) 0 0
\(137\) 1684.42 1.05043 0.525217 0.850969i \(-0.323984\pi\)
0.525217 + 0.850969i \(0.323984\pi\)
\(138\) 0 0
\(139\) 315.089 0.192270 0.0961350 0.995368i \(-0.469352\pi\)
0.0961350 + 0.995368i \(0.469352\pi\)
\(140\) 0 0
\(141\) −63.5606 −0.0379629
\(142\) 0 0
\(143\) 149.248 0.0872781
\(144\) 0 0
\(145\) −3333.23 −1.90903
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1893.77 1.04123 0.520617 0.853790i \(-0.325702\pi\)
0.520617 + 0.853790i \(0.325702\pi\)
\(150\) 0 0
\(151\) 2011.84 1.08425 0.542124 0.840299i \(-0.317620\pi\)
0.542124 + 0.840299i \(0.317620\pi\)
\(152\) 0 0
\(153\) −479.406 −0.253318
\(154\) 0 0
\(155\) 2821.71 1.46223
\(156\) 0 0
\(157\) 3828.50 1.94616 0.973082 0.230460i \(-0.0740232\pi\)
0.973082 + 0.230460i \(0.0740232\pi\)
\(158\) 0 0
\(159\) −1097.71 −0.547511
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3509.26 1.68630 0.843148 0.537682i \(-0.180700\pi\)
0.843148 + 0.537682i \(0.180700\pi\)
\(164\) 0 0
\(165\) 610.950 0.288257
\(166\) 0 0
\(167\) −343.008 −0.158939 −0.0794694 0.996837i \(-0.525323\pi\)
−0.0794694 + 0.996837i \(0.525323\pi\)
\(168\) 0 0
\(169\) −2025.42 −0.921905
\(170\) 0 0
\(171\) −381.800 −0.170743
\(172\) 0 0
\(173\) 4187.21 1.84016 0.920081 0.391729i \(-0.128123\pi\)
0.920081 + 0.391729i \(0.128123\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 679.733 0.288654
\(178\) 0 0
\(179\) 1970.29 0.822716 0.411358 0.911474i \(-0.365055\pi\)
0.411358 + 0.911474i \(0.365055\pi\)
\(180\) 0 0
\(181\) 3613.10 1.48376 0.741878 0.670535i \(-0.233935\pi\)
0.741878 + 0.670535i \(0.233935\pi\)
\(182\) 0 0
\(183\) 1955.92 0.790086
\(184\) 0 0
\(185\) −66.9509 −0.0266072
\(186\) 0 0
\(187\) −606.936 −0.237345
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1907.77 −0.722729 −0.361365 0.932425i \(-0.617689\pi\)
−0.361365 + 0.932425i \(0.617689\pi\)
\(192\) 0 0
\(193\) 2399.93 0.895080 0.447540 0.894264i \(-0.352300\pi\)
0.447540 + 0.894264i \(0.352300\pi\)
\(194\) 0 0
\(195\) 702.346 0.257928
\(196\) 0 0
\(197\) 1514.32 0.547668 0.273834 0.961777i \(-0.411708\pi\)
0.273834 + 0.961777i \(0.411708\pi\)
\(198\) 0 0
\(199\) 1367.78 0.487232 0.243616 0.969872i \(-0.421666\pi\)
0.243616 + 0.969872i \(0.421666\pi\)
\(200\) 0 0
\(201\) 436.300 0.153105
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −702.828 −0.239452
\(206\) 0 0
\(207\) −1368.77 −0.459594
\(208\) 0 0
\(209\) −483.366 −0.159977
\(210\) 0 0
\(211\) −4302.52 −1.40378 −0.701891 0.712285i \(-0.747661\pi\)
−0.701891 + 0.712285i \(0.747661\pi\)
\(212\) 0 0
\(213\) −1106.89 −0.356068
\(214\) 0 0
\(215\) 7675.45 2.43470
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1826.72 0.563644
\(220\) 0 0
\(221\) −697.731 −0.212373
\(222\) 0 0
\(223\) −1497.19 −0.449592 −0.224796 0.974406i \(-0.572172\pi\)
−0.224796 + 0.974406i \(0.572172\pi\)
\(224\) 0 0
\(225\) 1750.06 0.518537
\(226\) 0 0
\(227\) 1603.32 0.468795 0.234397 0.972141i \(-0.424688\pi\)
0.234397 + 0.972141i \(0.424688\pi\)
\(228\) 0 0
\(229\) −1010.52 −0.291603 −0.145802 0.989314i \(-0.546576\pi\)
−0.145802 + 0.989314i \(0.546576\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 198.217 0.0557323 0.0278661 0.999612i \(-0.491129\pi\)
0.0278661 + 0.999612i \(0.491129\pi\)
\(234\) 0 0
\(235\) −378.677 −0.105116
\(236\) 0 0
\(237\) 2730.71 0.748434
\(238\) 0 0
\(239\) 1201.19 0.325098 0.162549 0.986700i \(-0.448028\pi\)
0.162549 + 0.986700i \(0.448028\pi\)
\(240\) 0 0
\(241\) 2732.69 0.730407 0.365204 0.930928i \(-0.380999\pi\)
0.365204 + 0.930928i \(0.380999\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −555.675 −0.143145
\(248\) 0 0
\(249\) 983.788 0.250382
\(250\) 0 0
\(251\) 7565.82 1.90259 0.951295 0.308281i \(-0.0997537\pi\)
0.951295 + 0.308281i \(0.0997537\pi\)
\(252\) 0 0
\(253\) −1732.88 −0.430615
\(254\) 0 0
\(255\) −2856.18 −0.701414
\(256\) 0 0
\(257\) −5008.68 −1.21569 −0.607846 0.794055i \(-0.707966\pi\)
−0.607846 + 0.794055i \(0.707966\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1678.44 0.398057
\(262\) 0 0
\(263\) 6248.81 1.46509 0.732544 0.680720i \(-0.238333\pi\)
0.732544 + 0.680720i \(0.238333\pi\)
\(264\) 0 0
\(265\) −6539.88 −1.51601
\(266\) 0 0
\(267\) −112.835 −0.0258630
\(268\) 0 0
\(269\) 3588.45 0.813351 0.406676 0.913573i \(-0.366688\pi\)
0.406676 + 0.913573i \(0.366688\pi\)
\(270\) 0 0
\(271\) −1983.14 −0.444529 −0.222264 0.974986i \(-0.571345\pi\)
−0.222264 + 0.974986i \(0.571345\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2215.61 0.485841
\(276\) 0 0
\(277\) 7363.91 1.59731 0.798654 0.601790i \(-0.205546\pi\)
0.798654 + 0.601790i \(0.205546\pi\)
\(278\) 0 0
\(279\) −1420.86 −0.304892
\(280\) 0 0
\(281\) −5312.05 −1.12772 −0.563861 0.825869i \(-0.690685\pi\)
−0.563861 + 0.825869i \(0.690685\pi\)
\(282\) 0 0
\(283\) −1091.76 −0.229324 −0.114662 0.993405i \(-0.536578\pi\)
−0.114662 + 0.993405i \(0.536578\pi\)
\(284\) 0 0
\(285\) −2274.67 −0.472770
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2075.59 −0.422469
\(290\) 0 0
\(291\) 2166.04 0.436341
\(292\) 0 0
\(293\) 7191.86 1.43397 0.716985 0.697089i \(-0.245522\pi\)
0.716985 + 0.697089i \(0.245522\pi\)
\(294\) 0 0
\(295\) 4049.67 0.799257
\(296\) 0 0
\(297\) −307.642 −0.0601051
\(298\) 0 0
\(299\) −1992.12 −0.385308
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 4556.02 0.863816
\(304\) 0 0
\(305\) 11652.9 2.18767
\(306\) 0 0
\(307\) 541.355 0.100641 0.0503204 0.998733i \(-0.483976\pi\)
0.0503204 + 0.998733i \(0.483976\pi\)
\(308\) 0 0
\(309\) 3155.65 0.580966
\(310\) 0 0
\(311\) 54.0168 0.00984892 0.00492446 0.999988i \(-0.498432\pi\)
0.00492446 + 0.999988i \(0.498432\pi\)
\(312\) 0 0
\(313\) −3772.94 −0.681340 −0.340670 0.940183i \(-0.610654\pi\)
−0.340670 + 0.940183i \(0.610654\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1719.24 0.304612 0.152306 0.988333i \(-0.451330\pi\)
0.152306 + 0.988333i \(0.451330\pi\)
\(318\) 0 0
\(319\) 2124.93 0.372957
\(320\) 0 0
\(321\) 2299.56 0.399841
\(322\) 0 0
\(323\) 2259.72 0.389270
\(324\) 0 0
\(325\) 2547.06 0.434724
\(326\) 0 0
\(327\) 4281.15 0.724000
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −8408.21 −1.39625 −0.698123 0.715978i \(-0.745981\pi\)
−0.698123 + 0.715978i \(0.745981\pi\)
\(332\) 0 0
\(333\) 33.7129 0.00554792
\(334\) 0 0
\(335\) 2599.36 0.423935
\(336\) 0 0
\(337\) 2789.46 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(338\) 0 0
\(339\) −1087.69 −0.174263
\(340\) 0 0
\(341\) −1798.84 −0.285667
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −8154.76 −1.27257
\(346\) 0 0
\(347\) 3471.96 0.537132 0.268566 0.963261i \(-0.413450\pi\)
0.268566 + 0.963261i \(0.413450\pi\)
\(348\) 0 0
\(349\) 6626.12 1.01630 0.508149 0.861269i \(-0.330330\pi\)
0.508149 + 0.861269i \(0.330330\pi\)
\(350\) 0 0
\(351\) −353.664 −0.0537812
\(352\) 0 0
\(353\) −9468.40 −1.42763 −0.713813 0.700337i \(-0.753033\pi\)
−0.713813 + 0.700337i \(0.753033\pi\)
\(354\) 0 0
\(355\) −6594.53 −0.985919
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6279.55 0.923182 0.461591 0.887093i \(-0.347279\pi\)
0.461591 + 0.887093i \(0.347279\pi\)
\(360\) 0 0
\(361\) −5059.35 −0.737622
\(362\) 0 0
\(363\) 3603.52 0.521035
\(364\) 0 0
\(365\) 10883.1 1.56068
\(366\) 0 0
\(367\) −10827.8 −1.54008 −0.770038 0.637998i \(-0.779763\pi\)
−0.770038 + 0.637998i \(0.779763\pi\)
\(368\) 0 0
\(369\) 353.907 0.0499286
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5239.23 0.727284 0.363642 0.931539i \(-0.381533\pi\)
0.363642 + 0.931539i \(0.381533\pi\)
\(374\) 0 0
\(375\) 3723.96 0.512812
\(376\) 0 0
\(377\) 2442.81 0.333717
\(378\) 0 0
\(379\) 11050.4 1.49768 0.748839 0.662751i \(-0.230611\pi\)
0.748839 + 0.662751i \(0.230611\pi\)
\(380\) 0 0
\(381\) 2924.33 0.393223
\(382\) 0 0
\(383\) −10468.0 −1.39658 −0.698292 0.715813i \(-0.746056\pi\)
−0.698292 + 0.715813i \(0.746056\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3864.95 −0.507665
\(388\) 0 0
\(389\) −11614.0 −1.51377 −0.756884 0.653550i \(-0.773279\pi\)
−0.756884 + 0.653550i \(0.773279\pi\)
\(390\) 0 0
\(391\) 8101.19 1.04781
\(392\) 0 0
\(393\) 5378.11 0.690304
\(394\) 0 0
\(395\) 16268.9 2.07234
\(396\) 0 0
\(397\) 6707.30 0.847934 0.423967 0.905678i \(-0.360637\pi\)
0.423967 + 0.905678i \(0.360637\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5526.38 0.688215 0.344107 0.938930i \(-0.388182\pi\)
0.344107 + 0.938930i \(0.388182\pi\)
\(402\) 0 0
\(403\) −2067.94 −0.255611
\(404\) 0 0
\(405\) −1447.73 −0.177625
\(406\) 0 0
\(407\) 42.6811 0.00519810
\(408\) 0 0
\(409\) 1318.91 0.159452 0.0797258 0.996817i \(-0.474596\pi\)
0.0797258 + 0.996817i \(0.474596\pi\)
\(410\) 0 0
\(411\) −5053.25 −0.606468
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 5861.15 0.693283
\(416\) 0 0
\(417\) −945.268 −0.111007
\(418\) 0 0
\(419\) 3656.13 0.426286 0.213143 0.977021i \(-0.431630\pi\)
0.213143 + 0.977021i \(0.431630\pi\)
\(420\) 0 0
\(421\) −135.389 −0.0156733 −0.00783663 0.999969i \(-0.502495\pi\)
−0.00783663 + 0.999969i \(0.502495\pi\)
\(422\) 0 0
\(423\) 190.682 0.0219179
\(424\) 0 0
\(425\) −10357.9 −1.18219
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −447.745 −0.0503900
\(430\) 0 0
\(431\) −8389.16 −0.937568 −0.468784 0.883313i \(-0.655308\pi\)
−0.468784 + 0.883313i \(0.655308\pi\)
\(432\) 0 0
\(433\) 8243.02 0.914859 0.457430 0.889246i \(-0.348770\pi\)
0.457430 + 0.889246i \(0.348770\pi\)
\(434\) 0 0
\(435\) 9999.70 1.10218
\(436\) 0 0
\(437\) 6451.81 0.706252
\(438\) 0 0
\(439\) −18283.2 −1.98772 −0.993859 0.110649i \(-0.964707\pi\)
−0.993859 + 0.110649i \(0.964707\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1210.44 −0.129818 −0.0649092 0.997891i \(-0.520676\pi\)
−0.0649092 + 0.997891i \(0.520676\pi\)
\(444\) 0 0
\(445\) −672.243 −0.0716121
\(446\) 0 0
\(447\) −5681.32 −0.601157
\(448\) 0 0
\(449\) −8301.16 −0.872508 −0.436254 0.899824i \(-0.643695\pi\)
−0.436254 + 0.899824i \(0.643695\pi\)
\(450\) 0 0
\(451\) 448.052 0.0467804
\(452\) 0 0
\(453\) −6035.52 −0.625990
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12293.8 −1.25838 −0.629188 0.777253i \(-0.716612\pi\)
−0.629188 + 0.777253i \(0.716612\pi\)
\(458\) 0 0
\(459\) 1438.22 0.146253
\(460\) 0 0
\(461\) −19434.2 −1.96343 −0.981717 0.190346i \(-0.939039\pi\)
−0.981717 + 0.190346i \(0.939039\pi\)
\(462\) 0 0
\(463\) 12491.1 1.25380 0.626902 0.779098i \(-0.284322\pi\)
0.626902 + 0.779098i \(0.284322\pi\)
\(464\) 0 0
\(465\) −8465.13 −0.844217
\(466\) 0 0
\(467\) 3385.17 0.335433 0.167716 0.985835i \(-0.446361\pi\)
0.167716 + 0.985835i \(0.446361\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −11485.5 −1.12362
\(472\) 0 0
\(473\) −4893.09 −0.475654
\(474\) 0 0
\(475\) −8249.07 −0.796828
\(476\) 0 0
\(477\) 3293.14 0.316106
\(478\) 0 0
\(479\) 5979.41 0.570368 0.285184 0.958473i \(-0.407945\pi\)
0.285184 + 0.958473i \(0.407945\pi\)
\(480\) 0 0
\(481\) 49.0661 0.00465119
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12904.7 1.20819
\(486\) 0 0
\(487\) 1114.96 0.103745 0.0518725 0.998654i \(-0.483481\pi\)
0.0518725 + 0.998654i \(0.483481\pi\)
\(488\) 0 0
\(489\) −10527.8 −0.973583
\(490\) 0 0
\(491\) −1086.23 −0.0998387 −0.0499194 0.998753i \(-0.515896\pi\)
−0.0499194 + 0.998753i \(0.515896\pi\)
\(492\) 0 0
\(493\) −9934.01 −0.907516
\(494\) 0 0
\(495\) −1832.85 −0.166425
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2213.50 0.198577 0.0992884 0.995059i \(-0.468343\pi\)
0.0992884 + 0.995059i \(0.468343\pi\)
\(500\) 0 0
\(501\) 1029.02 0.0917634
\(502\) 0 0
\(503\) −2643.32 −0.234314 −0.117157 0.993113i \(-0.537378\pi\)
−0.117157 + 0.993113i \(0.537378\pi\)
\(504\) 0 0
\(505\) 27143.5 2.39183
\(506\) 0 0
\(507\) 6076.27 0.532262
\(508\) 0 0
\(509\) 665.169 0.0579236 0.0289618 0.999581i \(-0.490780\pi\)
0.0289618 + 0.999581i \(0.490780\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1145.40 0.0985784
\(514\) 0 0
\(515\) 18800.5 1.60864
\(516\) 0 0
\(517\) 241.406 0.0205359
\(518\) 0 0
\(519\) −12561.6 −1.06242
\(520\) 0 0
\(521\) 11762.0 0.989063 0.494531 0.869160i \(-0.335340\pi\)
0.494531 + 0.869160i \(0.335340\pi\)
\(522\) 0 0
\(523\) 10122.6 0.846330 0.423165 0.906053i \(-0.360919\pi\)
0.423165 + 0.906053i \(0.360919\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8409.52 0.695112
\(528\) 0 0
\(529\) 10963.0 0.901042
\(530\) 0 0
\(531\) −2039.20 −0.166655
\(532\) 0 0
\(533\) 515.079 0.0418585
\(534\) 0 0
\(535\) 13700.2 1.10712
\(536\) 0 0
\(537\) −5910.86 −0.474995
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 16118.0 1.28090 0.640449 0.768001i \(-0.278748\pi\)
0.640449 + 0.768001i \(0.278748\pi\)
\(542\) 0 0
\(543\) −10839.3 −0.856647
\(544\) 0 0
\(545\) 25505.9 2.00469
\(546\) 0 0
\(547\) 626.100 0.0489399 0.0244699 0.999701i \(-0.492210\pi\)
0.0244699 + 0.999701i \(0.492210\pi\)
\(548\) 0 0
\(549\) −5867.76 −0.456156
\(550\) 0 0
\(551\) −7911.47 −0.611688
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 200.853 0.0153617
\(556\) 0 0
\(557\) 20771.2 1.58008 0.790039 0.613057i \(-0.210060\pi\)
0.790039 + 0.613057i \(0.210060\pi\)
\(558\) 0 0
\(559\) −5625.08 −0.425609
\(560\) 0 0
\(561\) 1820.81 0.137031
\(562\) 0 0
\(563\) −5521.72 −0.413344 −0.206672 0.978410i \(-0.566263\pi\)
−0.206672 + 0.978410i \(0.566263\pi\)
\(564\) 0 0
\(565\) −6480.18 −0.482519
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7574.81 0.558089 0.279044 0.960278i \(-0.409982\pi\)
0.279044 + 0.960278i \(0.409982\pi\)
\(570\) 0 0
\(571\) 331.248 0.0242772 0.0121386 0.999926i \(-0.496136\pi\)
0.0121386 + 0.999926i \(0.496136\pi\)
\(572\) 0 0
\(573\) 5723.31 0.417268
\(574\) 0 0
\(575\) −29573.2 −2.14485
\(576\) 0 0
\(577\) −2038.11 −0.147050 −0.0735248 0.997293i \(-0.523425\pi\)
−0.0735248 + 0.997293i \(0.523425\pi\)
\(578\) 0 0
\(579\) −7199.78 −0.516775
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4169.17 0.296174
\(584\) 0 0
\(585\) −2107.04 −0.148915
\(586\) 0 0
\(587\) 5232.90 0.367947 0.183973 0.982931i \(-0.441104\pi\)
0.183973 + 0.982931i \(0.441104\pi\)
\(588\) 0 0
\(589\) 6697.36 0.468523
\(590\) 0 0
\(591\) −4542.95 −0.316196
\(592\) 0 0
\(593\) 5720.24 0.396125 0.198062 0.980189i \(-0.436535\pi\)
0.198062 + 0.980189i \(0.436535\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4103.33 −0.281304
\(598\) 0 0
\(599\) −18088.4 −1.23384 −0.616922 0.787024i \(-0.711621\pi\)
−0.616922 + 0.787024i \(0.711621\pi\)
\(600\) 0 0
\(601\) 1821.43 0.123623 0.0618117 0.998088i \(-0.480312\pi\)
0.0618117 + 0.998088i \(0.480312\pi\)
\(602\) 0 0
\(603\) −1308.90 −0.0883955
\(604\) 0 0
\(605\) 21468.8 1.44270
\(606\) 0 0
\(607\) 2372.20 0.158624 0.0793120 0.996850i \(-0.474728\pi\)
0.0793120 + 0.996850i \(0.474728\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 277.520 0.0183752
\(612\) 0 0
\(613\) 9725.08 0.640770 0.320385 0.947287i \(-0.396188\pi\)
0.320385 + 0.947287i \(0.396188\pi\)
\(614\) 0 0
\(615\) 2108.48 0.138248
\(616\) 0 0
\(617\) −5329.51 −0.347744 −0.173872 0.984768i \(-0.555628\pi\)
−0.173872 + 0.984768i \(0.555628\pi\)
\(618\) 0 0
\(619\) −15976.6 −1.03740 −0.518702 0.854955i \(-0.673585\pi\)
−0.518702 + 0.854955i \(0.673585\pi\)
\(620\) 0 0
\(621\) 4106.31 0.265347
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −2120.06 −0.135684
\(626\) 0 0
\(627\) 1450.10 0.0923625
\(628\) 0 0
\(629\) −199.533 −0.0126485
\(630\) 0 0
\(631\) 4199.98 0.264974 0.132487 0.991185i \(-0.457704\pi\)
0.132487 + 0.991185i \(0.457704\pi\)
\(632\) 0 0
\(633\) 12907.6 0.810474
\(634\) 0 0
\(635\) 17422.4 1.08880
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3320.66 0.205576
\(640\) 0 0
\(641\) 2648.51 0.163198 0.0815988 0.996665i \(-0.473997\pi\)
0.0815988 + 0.996665i \(0.473997\pi\)
\(642\) 0 0
\(643\) 13.4305 0.000823715 0 0.000411857 1.00000i \(-0.499869\pi\)
0.000411857 1.00000i \(0.499869\pi\)
\(644\) 0 0
\(645\) −23026.3 −1.40568
\(646\) 0 0
\(647\) 11624.1 0.706324 0.353162 0.935562i \(-0.385106\pi\)
0.353162 + 0.935562i \(0.385106\pi\)
\(648\) 0 0
\(649\) −2581.66 −0.156146
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28516.6 −1.70894 −0.854471 0.519499i \(-0.826119\pi\)
−0.854471 + 0.519499i \(0.826119\pi\)
\(654\) 0 0
\(655\) 32041.3 1.91139
\(656\) 0 0
\(657\) −5480.15 −0.325420
\(658\) 0 0
\(659\) −18048.6 −1.06688 −0.533440 0.845838i \(-0.679101\pi\)
−0.533440 + 0.845838i \(0.679101\pi\)
\(660\) 0 0
\(661\) −17841.4 −1.04985 −0.524926 0.851148i \(-0.675907\pi\)
−0.524926 + 0.851148i \(0.675907\pi\)
\(662\) 0 0
\(663\) 2093.19 0.122614
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −28362.9 −1.64650
\(668\) 0 0
\(669\) 4491.56 0.259572
\(670\) 0 0
\(671\) −7428.68 −0.427394
\(672\) 0 0
\(673\) −6826.13 −0.390978 −0.195489 0.980706i \(-0.562629\pi\)
−0.195489 + 0.980706i \(0.562629\pi\)
\(674\) 0 0
\(675\) −5250.19 −0.299378
\(676\) 0 0
\(677\) 21286.9 1.20845 0.604225 0.796814i \(-0.293483\pi\)
0.604225 + 0.796814i \(0.293483\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −4809.97 −0.270659
\(682\) 0 0
\(683\) 20696.8 1.15951 0.579753 0.814793i \(-0.303149\pi\)
0.579753 + 0.814793i \(0.303149\pi\)
\(684\) 0 0
\(685\) −30105.9 −1.67925
\(686\) 0 0
\(687\) 3031.56 0.168357
\(688\) 0 0
\(689\) 4792.86 0.265012
\(690\) 0 0
\(691\) 31341.9 1.72548 0.862738 0.505652i \(-0.168748\pi\)
0.862738 + 0.505652i \(0.168748\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5631.66 −0.307368
\(696\) 0 0
\(697\) −2094.63 −0.113831
\(698\) 0 0
\(699\) −594.651 −0.0321770
\(700\) 0 0
\(701\) −9213.32 −0.496408 −0.248204 0.968708i \(-0.579840\pi\)
−0.248204 + 0.968708i \(0.579840\pi\)
\(702\) 0 0
\(703\) −158.909 −0.00852541
\(704\) 0 0
\(705\) 1136.03 0.0606886
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 14516.5 0.768942 0.384471 0.923137i \(-0.374384\pi\)
0.384471 + 0.923137i \(0.374384\pi\)
\(710\) 0 0
\(711\) −8192.14 −0.432108
\(712\) 0 0
\(713\) 24010.3 1.26114
\(714\) 0 0
\(715\) −2667.54 −0.139525
\(716\) 0 0
\(717\) −3603.56 −0.187695
\(718\) 0 0
\(719\) 25882.4 1.34249 0.671246 0.741235i \(-0.265760\pi\)
0.671246 + 0.741235i \(0.265760\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −8198.08 −0.421701
\(724\) 0 0
\(725\) 36263.9 1.85767
\(726\) 0 0
\(727\) 32181.2 1.64172 0.820862 0.571127i \(-0.193494\pi\)
0.820862 + 0.571127i \(0.193494\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 22875.1 1.15741
\(732\) 0 0
\(733\) −20836.1 −1.04993 −0.524966 0.851123i \(-0.675922\pi\)
−0.524966 + 0.851123i \(0.675922\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1657.09 −0.0828217
\(738\) 0 0
\(739\) −26434.9 −1.31586 −0.657931 0.753078i \(-0.728568\pi\)
−0.657931 + 0.753078i \(0.728568\pi\)
\(740\) 0 0
\(741\) 1667.03 0.0826447
\(742\) 0 0
\(743\) −9954.69 −0.491524 −0.245762 0.969330i \(-0.579038\pi\)
−0.245762 + 0.969330i \(0.579038\pi\)
\(744\) 0 0
\(745\) −33847.8 −1.66455
\(746\) 0 0
\(747\) −2951.36 −0.144558
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 33204.5 1.61338 0.806692 0.590973i \(-0.201256\pi\)
0.806692 + 0.590973i \(0.201256\pi\)
\(752\) 0 0
\(753\) −22697.5 −1.09846
\(754\) 0 0
\(755\) −35958.1 −1.73331
\(756\) 0 0
\(757\) 1964.06 0.0942998 0.0471499 0.998888i \(-0.484986\pi\)
0.0471499 + 0.998888i \(0.484986\pi\)
\(758\) 0 0
\(759\) 5198.65 0.248615
\(760\) 0 0
\(761\) 38553.8 1.83650 0.918248 0.396005i \(-0.129604\pi\)
0.918248 + 0.396005i \(0.129604\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 8568.53 0.404962
\(766\) 0 0
\(767\) −2967.87 −0.139718
\(768\) 0 0
\(769\) 19715.0 0.924501 0.462251 0.886749i \(-0.347042\pi\)
0.462251 + 0.886749i \(0.347042\pi\)
\(770\) 0 0
\(771\) 15026.0 0.701880
\(772\) 0 0
\(773\) 14700.7 0.684019 0.342010 0.939696i \(-0.388892\pi\)
0.342010 + 0.939696i \(0.388892\pi\)
\(774\) 0 0
\(775\) −30698.8 −1.42288
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1668.17 −0.0767246
\(780\) 0 0
\(781\) 4204.01 0.192614
\(782\) 0 0
\(783\) −5035.32 −0.229818
\(784\) 0 0
\(785\) −68427.6 −3.11119
\(786\) 0 0
\(787\) −23918.6 −1.08336 −0.541681 0.840584i \(-0.682212\pi\)
−0.541681 + 0.840584i \(0.682212\pi\)
\(788\) 0 0
\(789\) −18746.4 −0.845869
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −8539.98 −0.382426
\(794\) 0 0
\(795\) 19619.6 0.875266
\(796\) 0 0
\(797\) −38252.7 −1.70010 −0.850051 0.526700i \(-0.823429\pi\)
−0.850051 + 0.526700i \(0.823429\pi\)
\(798\) 0 0
\(799\) −1128.57 −0.0499698
\(800\) 0 0
\(801\) 338.506 0.0149320
\(802\) 0 0
\(803\) −6937.96 −0.304901
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −10765.3 −0.469589
\(808\) 0 0
\(809\) −31435.6 −1.36615 −0.683075 0.730348i \(-0.739358\pi\)
−0.683075 + 0.730348i \(0.739358\pi\)
\(810\) 0 0
\(811\) 11467.0 0.496501 0.248250 0.968696i \(-0.420144\pi\)
0.248250 + 0.968696i \(0.420144\pi\)
\(812\) 0 0
\(813\) 5949.43 0.256649
\(814\) 0 0
\(815\) −62721.7 −2.69576
\(816\) 0 0
\(817\) 18217.8 0.780121
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −5030.57 −0.213847 −0.106923 0.994267i \(-0.534100\pi\)
−0.106923 + 0.994267i \(0.534100\pi\)
\(822\) 0 0
\(823\) 13985.2 0.592336 0.296168 0.955136i \(-0.404291\pi\)
0.296168 + 0.955136i \(0.404291\pi\)
\(824\) 0 0
\(825\) −6646.83 −0.280500
\(826\) 0 0
\(827\) 13939.5 0.586125 0.293063 0.956093i \(-0.405326\pi\)
0.293063 + 0.956093i \(0.405326\pi\)
\(828\) 0 0
\(829\) 20104.4 0.842286 0.421143 0.906994i \(-0.361629\pi\)
0.421143 + 0.906994i \(0.361629\pi\)
\(830\) 0 0
\(831\) −22091.7 −0.922207
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 6130.66 0.254084
\(836\) 0 0
\(837\) 4262.59 0.176030
\(838\) 0 0
\(839\) 15949.5 0.656302 0.328151 0.944625i \(-0.393575\pi\)
0.328151 + 0.944625i \(0.393575\pi\)
\(840\) 0 0
\(841\) 10390.8 0.426043
\(842\) 0 0
\(843\) 15936.1 0.651091
\(844\) 0 0
\(845\) 36200.8 1.47378
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 3275.29 0.132400
\(850\) 0 0
\(851\) −569.694 −0.0229481
\(852\) 0 0
\(853\) −11802.0 −0.473730 −0.236865 0.971543i \(-0.576120\pi\)
−0.236865 + 0.971543i \(0.576120\pi\)
\(854\) 0 0
\(855\) 6824.00 0.272954
\(856\) 0 0
\(857\) −9595.28 −0.382460 −0.191230 0.981545i \(-0.561248\pi\)
−0.191230 + 0.981545i \(0.561248\pi\)
\(858\) 0 0
\(859\) 21840.9 0.867521 0.433760 0.901028i \(-0.357186\pi\)
0.433760 + 0.901028i \(0.357186\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26531.6 1.04652 0.523260 0.852173i \(-0.324716\pi\)
0.523260 + 0.852173i \(0.324716\pi\)
\(864\) 0 0
\(865\) −74838.9 −2.94173
\(866\) 0 0
\(867\) 6226.77 0.243912
\(868\) 0 0
\(869\) −10371.4 −0.404862
\(870\) 0 0
\(871\) −1904.98 −0.0741077
\(872\) 0 0
\(873\) −6498.11 −0.251922
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6832.46 −0.263074 −0.131537 0.991311i \(-0.541991\pi\)
−0.131537 + 0.991311i \(0.541991\pi\)
\(878\) 0 0
\(879\) −21575.6 −0.827903
\(880\) 0 0
\(881\) 3994.77 0.152766 0.0763832 0.997079i \(-0.475663\pi\)
0.0763832 + 0.997079i \(0.475663\pi\)
\(882\) 0 0
\(883\) −13727.0 −0.523161 −0.261580 0.965182i \(-0.584244\pi\)
−0.261580 + 0.965182i \(0.584244\pi\)
\(884\) 0 0
\(885\) −12149.0 −0.461451
\(886\) 0 0
\(887\) 44119.4 1.67011 0.835054 0.550169i \(-0.185437\pi\)
0.835054 + 0.550169i \(0.185437\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 922.926 0.0347017
\(892\) 0 0
\(893\) −898.796 −0.0336809
\(894\) 0 0
\(895\) −35215.3 −1.31522
\(896\) 0 0
\(897\) 5976.35 0.222458
\(898\) 0 0
\(899\) −29442.4 −1.09228
\(900\) 0 0
\(901\) −19490.7 −0.720678
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −64577.7 −2.37197
\(906\) 0 0
\(907\) −36905.8 −1.35109 −0.675545 0.737319i \(-0.736092\pi\)
−0.675545 + 0.737319i \(0.736092\pi\)
\(908\) 0 0
\(909\) −13668.1 −0.498725
\(910\) 0 0
\(911\) 3169.56 0.115271 0.0576356 0.998338i \(-0.481644\pi\)
0.0576356 + 0.998338i \(0.481644\pi\)
\(912\) 0 0
\(913\) −3736.48 −0.135443
\(914\) 0 0
\(915\) −34958.6 −1.26305
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −8727.00 −0.313250 −0.156625 0.987658i \(-0.550061\pi\)
−0.156625 + 0.987658i \(0.550061\pi\)
\(920\) 0 0
\(921\) −1624.06 −0.0581050
\(922\) 0 0
\(923\) 4832.91 0.172348
\(924\) 0 0
\(925\) 728.392 0.0258912
\(926\) 0 0
\(927\) −9466.95 −0.335421
\(928\) 0 0
\(929\) −19405.1 −0.685317 −0.342659 0.939460i \(-0.611327\pi\)
−0.342659 + 0.939460i \(0.611327\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −162.050 −0.00568628
\(934\) 0 0
\(935\) 10847.9 0.379427
\(936\) 0 0
\(937\) 615.692 0.0214662 0.0107331 0.999942i \(-0.496583\pi\)
0.0107331 + 0.999942i \(0.496583\pi\)
\(938\) 0 0
\(939\) 11318.8 0.393372
\(940\) 0 0
\(941\) 29602.0 1.02550 0.512751 0.858537i \(-0.328626\pi\)
0.512751 + 0.858537i \(0.328626\pi\)
\(942\) 0 0
\(943\) −5980.46 −0.206522
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −13537.4 −0.464527 −0.232264 0.972653i \(-0.574613\pi\)
−0.232264 + 0.972653i \(0.574613\pi\)
\(948\) 0 0
\(949\) −7975.85 −0.272821
\(950\) 0 0
\(951\) −5157.71 −0.175868
\(952\) 0 0
\(953\) 33468.5 1.13762 0.568810 0.822469i \(-0.307404\pi\)
0.568810 + 0.822469i \(0.307404\pi\)
\(954\) 0 0
\(955\) 34097.9 1.15538
\(956\) 0 0
\(957\) −6374.80 −0.215327
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −4866.88 −0.163368
\(962\) 0 0
\(963\) −6898.68 −0.230848
\(964\) 0 0
\(965\) −42894.4 −1.43090
\(966\) 0 0
\(967\) 55733.5 1.85343 0.926715 0.375764i \(-0.122620\pi\)
0.926715 + 0.375764i \(0.122620\pi\)
\(968\) 0 0
\(969\) −6779.17 −0.224745
\(970\) 0 0
\(971\) −19491.3 −0.644187 −0.322094 0.946708i \(-0.604387\pi\)
−0.322094 + 0.946708i \(0.604387\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −7641.17 −0.250988
\(976\) 0 0
\(977\) −6241.56 −0.204386 −0.102193 0.994765i \(-0.532586\pi\)
−0.102193 + 0.994765i \(0.532586\pi\)
\(978\) 0 0
\(979\) 428.554 0.0139905
\(980\) 0 0
\(981\) −12843.4 −0.418001
\(982\) 0 0
\(983\) 59694.6 1.93689 0.968444 0.249231i \(-0.0801778\pi\)
0.968444 + 0.249231i \(0.0801778\pi\)
\(984\) 0 0
\(985\) −27065.7 −0.875517
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 65311.4 2.09988
\(990\) 0 0
\(991\) −15561.6 −0.498821 −0.249411 0.968398i \(-0.580237\pi\)
−0.249411 + 0.968398i \(0.580237\pi\)
\(992\) 0 0
\(993\) 25224.6 0.806123
\(994\) 0 0
\(995\) −24446.6 −0.778903
\(996\) 0 0
\(997\) −19884.9 −0.631657 −0.315829 0.948816i \(-0.602282\pi\)
−0.315829 + 0.948816i \(0.602282\pi\)
\(998\) 0 0
\(999\) −101.139 −0.00320309
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 2352.4.a.cg.1.1 3
4.3 odd 2 147.4.a.m.1.1 3
7.3 odd 6 336.4.q.k.289.1 6
7.5 odd 6 336.4.q.k.193.1 6
7.6 odd 2 2352.4.a.ci.1.3 3
12.11 even 2 441.4.a.t.1.3 3
28.3 even 6 21.4.e.b.16.3 yes 6
28.11 odd 6 147.4.e.n.79.3 6
28.19 even 6 21.4.e.b.4.3 6
28.23 odd 6 147.4.e.n.67.3 6
28.27 even 2 147.4.a.l.1.1 3
84.11 even 6 441.4.e.w.226.1 6
84.23 even 6 441.4.e.w.361.1 6
84.47 odd 6 63.4.e.c.46.1 6
84.59 odd 6 63.4.e.c.37.1 6
84.83 odd 2 441.4.a.s.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.e.b.4.3 6 28.19 even 6
21.4.e.b.16.3 yes 6 28.3 even 6
63.4.e.c.37.1 6 84.59 odd 6
63.4.e.c.46.1 6 84.47 odd 6
147.4.a.l.1.1 3 28.27 even 2
147.4.a.m.1.1 3 4.3 odd 2
147.4.e.n.67.3 6 28.23 odd 6
147.4.e.n.79.3 6 28.11 odd 6
336.4.q.k.193.1 6 7.5 odd 6
336.4.q.k.289.1 6 7.3 odd 6
441.4.a.s.1.3 3 84.83 odd 2
441.4.a.t.1.3 3 12.11 even 2
441.4.e.w.226.1 6 84.11 even 6
441.4.e.w.361.1 6 84.23 even 6
2352.4.a.cg.1.1 3 1.1 even 1 trivial
2352.4.a.ci.1.3 3 7.6 odd 2