Properties

Label 2160.4.a.x.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2160,4,Mod(1,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(127.444125612\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{21}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 540)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.79129\) of defining polynomial
Character \(\chi\) \(=\) 2160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -12.7477 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -12.7477 q^{7} -34.7477 q^{11} -75.7386 q^{13} -84.2341 q^{17} +83.7477 q^{19} -172.982 q^{23} +25.0000 q^{25} +88.2250 q^{29} -205.711 q^{31} +63.7386 q^{35} -286.000 q^{37} -321.702 q^{41} +168.766 q^{43} +390.468 q^{47} -180.495 q^{49} +91.6932 q^{53} +173.739 q^{55} -122.766 q^{59} -878.405 q^{61} +378.693 q^{65} +1037.40 q^{67} -605.216 q^{71} -13.8114 q^{73} +442.955 q^{77} +573.298 q^{79} +627.936 q^{83} +421.170 q^{85} -1013.11 q^{89} +965.495 q^{91} -418.739 q^{95} +1155.82 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 10 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 10 q^{5} + 2 q^{7} - 42 q^{11} - 14 q^{13} + 24 q^{17} + 140 q^{19} - 126 q^{23} + 50 q^{25} - 126 q^{29} + 56 q^{31} - 10 q^{35} - 572 q^{37} - 66 q^{41} + 530 q^{43} + 396 q^{47} - 306 q^{49} - 504 q^{53} + 210 q^{55} - 438 q^{59} - 602 q^{61} + 70 q^{65} + 920 q^{67} - 798 q^{71} - 770 q^{73} + 336 q^{77} + 1724 q^{79} + 486 q^{83} - 120 q^{85} - 294 q^{89} + 1876 q^{91} - 700 q^{95} + 112 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −12.7477 −0.688313 −0.344156 0.938912i \(-0.611835\pi\)
−0.344156 + 0.938912i \(0.611835\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −34.7477 −0.952439 −0.476220 0.879326i \(-0.657993\pi\)
−0.476220 + 0.879326i \(0.657993\pi\)
\(12\) 0 0
\(13\) −75.7386 −1.61586 −0.807928 0.589282i \(-0.799411\pi\)
−0.807928 + 0.589282i \(0.799411\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −84.2341 −1.20175 −0.600876 0.799343i \(-0.705181\pi\)
−0.600876 + 0.799343i \(0.705181\pi\)
\(18\) 0 0
\(19\) 83.7477 1.01121 0.505606 0.862764i \(-0.331269\pi\)
0.505606 + 0.862764i \(0.331269\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −172.982 −1.56823 −0.784113 0.620618i \(-0.786882\pi\)
−0.784113 + 0.620618i \(0.786882\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 88.2250 0.564930 0.282465 0.959278i \(-0.408848\pi\)
0.282465 + 0.959278i \(0.408848\pi\)
\(30\) 0 0
\(31\) −205.711 −1.19183 −0.595917 0.803046i \(-0.703211\pi\)
−0.595917 + 0.803046i \(0.703211\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 63.7386 0.307823
\(36\) 0 0
\(37\) −286.000 −1.27076 −0.635380 0.772200i \(-0.719156\pi\)
−0.635380 + 0.772200i \(0.719156\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −321.702 −1.22540 −0.612701 0.790315i \(-0.709917\pi\)
−0.612701 + 0.790315i \(0.709917\pi\)
\(42\) 0 0
\(43\) 168.766 0.598525 0.299262 0.954171i \(-0.403259\pi\)
0.299262 + 0.954171i \(0.403259\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 390.468 1.21182 0.605911 0.795532i \(-0.292809\pi\)
0.605911 + 0.795532i \(0.292809\pi\)
\(48\) 0 0
\(49\) −180.495 −0.526226
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 91.6932 0.237642 0.118821 0.992916i \(-0.462089\pi\)
0.118821 + 0.992916i \(0.462089\pi\)
\(54\) 0 0
\(55\) 173.739 0.425944
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −122.766 −0.270894 −0.135447 0.990785i \(-0.543247\pi\)
−0.135447 + 0.990785i \(0.543247\pi\)
\(60\) 0 0
\(61\) −878.405 −1.84374 −0.921870 0.387499i \(-0.873339\pi\)
−0.921870 + 0.387499i \(0.873339\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 378.693 0.722632
\(66\) 0 0
\(67\) 1037.40 1.89163 0.945814 0.324708i \(-0.105266\pi\)
0.945814 + 0.324708i \(0.105266\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −605.216 −1.01163 −0.505816 0.862641i \(-0.668809\pi\)
−0.505816 + 0.862641i \(0.668809\pi\)
\(72\) 0 0
\(73\) −13.8114 −0.0221438 −0.0110719 0.999939i \(-0.503524\pi\)
−0.0110719 + 0.999939i \(0.503524\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 442.955 0.655576
\(78\) 0 0
\(79\) 573.298 0.816469 0.408234 0.912877i \(-0.366145\pi\)
0.408234 + 0.912877i \(0.366145\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 627.936 0.830421 0.415211 0.909725i \(-0.363708\pi\)
0.415211 + 0.909725i \(0.363708\pi\)
\(84\) 0 0
\(85\) 421.170 0.537439
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1013.11 −1.20662 −0.603310 0.797507i \(-0.706152\pi\)
−0.603310 + 0.797507i \(0.706152\pi\)
\(90\) 0 0
\(91\) 965.495 1.11221
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −418.739 −0.452228
\(96\) 0 0
\(97\) 1155.82 1.20985 0.604926 0.796282i \(-0.293203\pi\)
0.604926 + 0.796282i \(0.293203\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −853.873 −0.841223 −0.420611 0.907241i \(-0.638184\pi\)
−0.420611 + 0.907241i \(0.638184\pi\)
\(102\) 0 0
\(103\) 1029.95 0.985277 0.492639 0.870234i \(-0.336032\pi\)
0.492639 + 0.870234i \(0.336032\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −514.845 −0.465159 −0.232579 0.972577i \(-0.574717\pi\)
−0.232579 + 0.972577i \(0.574717\pi\)
\(108\) 0 0
\(109\) −656.873 −0.577220 −0.288610 0.957447i \(-0.593193\pi\)
−0.288610 + 0.957447i \(0.593193\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1701.44 1.41644 0.708222 0.705990i \(-0.249498\pi\)
0.708222 + 0.705990i \(0.249498\pi\)
\(114\) 0 0
\(115\) 864.909 0.701332
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1073.79 0.827180
\(120\) 0 0
\(121\) −123.595 −0.0928591
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −345.405 −0.241336 −0.120668 0.992693i \(-0.538504\pi\)
−0.120668 + 0.992693i \(0.538504\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2827.87 −1.88605 −0.943024 0.332724i \(-0.892032\pi\)
−0.943024 + 0.332724i \(0.892032\pi\)
\(132\) 0 0
\(133\) −1067.59 −0.696031
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1227.84 −0.765703 −0.382852 0.923810i \(-0.625058\pi\)
−0.382852 + 0.923810i \(0.625058\pi\)
\(138\) 0 0
\(139\) 40.1091 0.0244749 0.0122374 0.999925i \(-0.496105\pi\)
0.0122374 + 0.999925i \(0.496105\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2631.75 1.53900
\(144\) 0 0
\(145\) −441.125 −0.252644
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 480.730 0.264315 0.132157 0.991229i \(-0.457810\pi\)
0.132157 + 0.991229i \(0.457810\pi\)
\(150\) 0 0
\(151\) 76.0000 0.0409589 0.0204794 0.999790i \(-0.493481\pi\)
0.0204794 + 0.999790i \(0.493481\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1028.56 0.533004
\(156\) 0 0
\(157\) −438.602 −0.222957 −0.111479 0.993767i \(-0.535559\pi\)
−0.111479 + 0.993767i \(0.535559\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2205.12 1.07943
\(162\) 0 0
\(163\) −1755.87 −0.843746 −0.421873 0.906655i \(-0.638627\pi\)
−0.421873 + 0.906655i \(0.638627\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2787.55 1.29166 0.645831 0.763481i \(-0.276511\pi\)
0.645831 + 0.763481i \(0.276511\pi\)
\(168\) 0 0
\(169\) 3539.34 1.61099
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1216.36 −0.534556 −0.267278 0.963619i \(-0.586124\pi\)
−0.267278 + 0.963619i \(0.586124\pi\)
\(174\) 0 0
\(175\) −318.693 −0.137663
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2531.98 −1.05726 −0.528628 0.848854i \(-0.677293\pi\)
−0.528628 + 0.848854i \(0.677293\pi\)
\(180\) 0 0
\(181\) 3444.82 1.41465 0.707324 0.706889i \(-0.249902\pi\)
0.707324 + 0.706889i \(0.249902\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1430.00 0.568301
\(186\) 0 0
\(187\) 2926.94 1.14460
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1702.57 −0.644994 −0.322497 0.946571i \(-0.604522\pi\)
−0.322497 + 0.946571i \(0.604522\pi\)
\(192\) 0 0
\(193\) 685.489 0.255661 0.127830 0.991796i \(-0.459199\pi\)
0.127830 + 0.991796i \(0.459199\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4362.95 −1.57791 −0.788953 0.614454i \(-0.789377\pi\)
−0.788953 + 0.614454i \(0.789377\pi\)
\(198\) 0 0
\(199\) 2920.20 1.04024 0.520119 0.854094i \(-0.325888\pi\)
0.520119 + 0.854094i \(0.325888\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1124.67 −0.388848
\(204\) 0 0
\(205\) 1608.51 0.548016
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2910.04 −0.963119
\(210\) 0 0
\(211\) 213.384 0.0696207 0.0348103 0.999394i \(-0.488917\pi\)
0.0348103 + 0.999394i \(0.488917\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −843.830 −0.267668
\(216\) 0 0
\(217\) 2622.35 0.820354
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6379.78 1.94186
\(222\) 0 0
\(223\) −2091.55 −0.628073 −0.314036 0.949411i \(-0.601681\pi\)
−0.314036 + 0.949411i \(0.601681\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4483.60 1.31095 0.655477 0.755215i \(-0.272468\pi\)
0.655477 + 0.755215i \(0.272468\pi\)
\(228\) 0 0
\(229\) 4931.09 1.42295 0.711475 0.702712i \(-0.248028\pi\)
0.711475 + 0.702712i \(0.248028\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −773.782 −0.217563 −0.108781 0.994066i \(-0.534695\pi\)
−0.108781 + 0.994066i \(0.534695\pi\)
\(234\) 0 0
\(235\) −1952.34 −0.541943
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4412.40 −1.19420 −0.597101 0.802166i \(-0.703681\pi\)
−0.597101 + 0.802166i \(0.703681\pi\)
\(240\) 0 0
\(241\) 6143.41 1.64204 0.821021 0.570898i \(-0.193405\pi\)
0.821021 + 0.570898i \(0.193405\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 902.477 0.235335
\(246\) 0 0
\(247\) −6342.94 −1.63397
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 746.895 0.187823 0.0939116 0.995581i \(-0.470063\pi\)
0.0939116 + 0.995581i \(0.470063\pi\)
\(252\) 0 0
\(253\) 6010.72 1.49364
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7546.62 1.83169 0.915847 0.401528i \(-0.131521\pi\)
0.915847 + 0.401528i \(0.131521\pi\)
\(258\) 0 0
\(259\) 3645.85 0.874680
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1383.99 0.324488 0.162244 0.986751i \(-0.448127\pi\)
0.162244 + 0.986751i \(0.448127\pi\)
\(264\) 0 0
\(265\) −458.466 −0.106277
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6987.28 −1.58372 −0.791862 0.610700i \(-0.790888\pi\)
−0.791862 + 0.610700i \(0.790888\pi\)
\(270\) 0 0
\(271\) 3600.27 0.807014 0.403507 0.914977i \(-0.367791\pi\)
0.403507 + 0.914977i \(0.367791\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −868.693 −0.190488
\(276\) 0 0
\(277\) 1803.74 0.391251 0.195625 0.980679i \(-0.437326\pi\)
0.195625 + 0.980679i \(0.437326\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3712.97 0.788245 0.394123 0.919058i \(-0.371048\pi\)
0.394123 + 0.919058i \(0.371048\pi\)
\(282\) 0 0
\(283\) 828.961 0.174122 0.0870612 0.996203i \(-0.472252\pi\)
0.0870612 + 0.996203i \(0.472252\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4100.97 0.843459
\(288\) 0 0
\(289\) 2182.38 0.444206
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1686.32 −0.336232 −0.168116 0.985767i \(-0.553768\pi\)
−0.168116 + 0.985767i \(0.553768\pi\)
\(294\) 0 0
\(295\) 613.830 0.121148
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 13101.4 2.53403
\(300\) 0 0
\(301\) −2151.38 −0.411972
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4392.02 0.824546
\(306\) 0 0
\(307\) 5760.81 1.07097 0.535483 0.844546i \(-0.320129\pi\)
0.535483 + 0.844546i \(0.320129\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6887.96 −1.25588 −0.627942 0.778260i \(-0.716103\pi\)
−0.627942 + 0.778260i \(0.716103\pi\)
\(312\) 0 0
\(313\) −3056.66 −0.551989 −0.275995 0.961159i \(-0.589007\pi\)
−0.275995 + 0.961159i \(0.589007\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9656.47 −1.71092 −0.855459 0.517870i \(-0.826725\pi\)
−0.855459 + 0.517870i \(0.826725\pi\)
\(318\) 0 0
\(319\) −3065.62 −0.538062
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7054.41 −1.21523
\(324\) 0 0
\(325\) −1893.47 −0.323171
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4977.58 −0.834112
\(330\) 0 0
\(331\) −8879.07 −1.47443 −0.737217 0.675656i \(-0.763861\pi\)
−0.737217 + 0.675656i \(0.763861\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5187.02 −0.845962
\(336\) 0 0
\(337\) 2610.17 0.421914 0.210957 0.977495i \(-0.432342\pi\)
0.210957 + 0.977495i \(0.432342\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7148.00 1.13515
\(342\) 0 0
\(343\) 6673.38 1.05052
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3806.48 0.588884 0.294442 0.955669i \(-0.404866\pi\)
0.294442 + 0.955669i \(0.404866\pi\)
\(348\) 0 0
\(349\) 4080.99 0.625932 0.312966 0.949764i \(-0.398677\pi\)
0.312966 + 0.949764i \(0.398677\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5016.64 −0.756399 −0.378200 0.925724i \(-0.623457\pi\)
−0.378200 + 0.925724i \(0.623457\pi\)
\(354\) 0 0
\(355\) 3026.08 0.452416
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −515.859 −0.0758384 −0.0379192 0.999281i \(-0.512073\pi\)
−0.0379192 + 0.999281i \(0.512073\pi\)
\(360\) 0 0
\(361\) 154.682 0.0225517
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 69.0568 0.00990301
\(366\) 0 0
\(367\) −4562.29 −0.648909 −0.324455 0.945901i \(-0.605181\pi\)
−0.324455 + 0.945901i \(0.605181\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1168.88 −0.163572
\(372\) 0 0
\(373\) 10438.1 1.44897 0.724485 0.689290i \(-0.242078\pi\)
0.724485 + 0.689290i \(0.242078\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6682.04 −0.912845
\(378\) 0 0
\(379\) −7375.64 −0.999634 −0.499817 0.866131i \(-0.666599\pi\)
−0.499817 + 0.866131i \(0.666599\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7277.13 −0.970872 −0.485436 0.874272i \(-0.661339\pi\)
−0.485436 + 0.874272i \(0.661339\pi\)
\(384\) 0 0
\(385\) −2214.77 −0.293183
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11099.4 1.44669 0.723344 0.690488i \(-0.242604\pi\)
0.723344 + 0.690488i \(0.242604\pi\)
\(390\) 0 0
\(391\) 14571.0 1.88462
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2866.49 −0.365136
\(396\) 0 0
\(397\) 5.73405 0.000724896 0 0.000362448 1.00000i \(-0.499885\pi\)
0.000362448 1.00000i \(0.499885\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6078.65 0.756991 0.378496 0.925603i \(-0.376441\pi\)
0.378496 + 0.925603i \(0.376441\pi\)
\(402\) 0 0
\(403\) 15580.3 1.92583
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9937.85 1.21032
\(408\) 0 0
\(409\) −11154.5 −1.34855 −0.674273 0.738482i \(-0.735543\pi\)
−0.674273 + 0.738482i \(0.735543\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1564.99 0.186460
\(414\) 0 0
\(415\) −3139.68 −0.371376
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6718.81 −0.783378 −0.391689 0.920098i \(-0.628109\pi\)
−0.391689 + 0.920098i \(0.628109\pi\)
\(420\) 0 0
\(421\) −9299.47 −1.07655 −0.538276 0.842768i \(-0.680924\pi\)
−0.538276 + 0.842768i \(0.680924\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2105.85 −0.240350
\(426\) 0 0
\(427\) 11197.7 1.26907
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2338.96 −0.261400 −0.130700 0.991422i \(-0.541723\pi\)
−0.130700 + 0.991422i \(0.541723\pi\)
\(432\) 0 0
\(433\) 11685.4 1.29691 0.648457 0.761251i \(-0.275414\pi\)
0.648457 + 0.761251i \(0.275414\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −14486.8 −1.58581
\(438\) 0 0
\(439\) 16103.8 1.75078 0.875388 0.483421i \(-0.160606\pi\)
0.875388 + 0.483421i \(0.160606\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11263.9 1.20804 0.604021 0.796968i \(-0.293564\pi\)
0.604021 + 0.796968i \(0.293564\pi\)
\(444\) 0 0
\(445\) 5065.53 0.539617
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10612.8 −1.11548 −0.557739 0.830016i \(-0.688331\pi\)
−0.557739 + 0.830016i \(0.688331\pi\)
\(450\) 0 0
\(451\) 11178.4 1.16712
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4827.48 −0.497397
\(456\) 0 0
\(457\) 2493.02 0.255183 0.127592 0.991827i \(-0.459275\pi\)
0.127592 + 0.991827i \(0.459275\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15411.4 1.55701 0.778506 0.627637i \(-0.215978\pi\)
0.778506 + 0.627637i \(0.215978\pi\)
\(462\) 0 0
\(463\) 8831.79 0.886497 0.443248 0.896399i \(-0.353826\pi\)
0.443248 + 0.896399i \(0.353826\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8430.83 0.835401 0.417701 0.908585i \(-0.362836\pi\)
0.417701 + 0.908585i \(0.362836\pi\)
\(468\) 0 0
\(469\) −13224.5 −1.30203
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5864.23 −0.570058
\(474\) 0 0
\(475\) 2093.69 0.202243
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8626.05 −0.822827 −0.411414 0.911449i \(-0.634965\pi\)
−0.411414 + 0.911449i \(0.634965\pi\)
\(480\) 0 0
\(481\) 21661.2 2.05336
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5779.09 −0.541062
\(486\) 0 0
\(487\) 12182.8 1.13358 0.566792 0.823861i \(-0.308184\pi\)
0.566792 + 0.823861i \(0.308184\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −21020.9 −1.93210 −0.966049 0.258357i \(-0.916819\pi\)
−0.966049 + 0.258357i \(0.916819\pi\)
\(492\) 0 0
\(493\) −7431.55 −0.678905
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7715.13 0.696319
\(498\) 0 0
\(499\) 8890.70 0.797600 0.398800 0.917038i \(-0.369427\pi\)
0.398800 + 0.917038i \(0.369427\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2433.17 0.215686 0.107843 0.994168i \(-0.465606\pi\)
0.107843 + 0.994168i \(0.465606\pi\)
\(504\) 0 0
\(505\) 4269.36 0.376206
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15257.6 −1.32865 −0.664324 0.747445i \(-0.731281\pi\)
−0.664324 + 0.747445i \(0.731281\pi\)
\(510\) 0 0
\(511\) 176.064 0.0152419
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5149.73 −0.440629
\(516\) 0 0
\(517\) −13567.9 −1.15419
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12991.2 1.09242 0.546212 0.837647i \(-0.316069\pi\)
0.546212 + 0.837647i \(0.316069\pi\)
\(522\) 0 0
\(523\) −1501.60 −0.125545 −0.0627727 0.998028i \(-0.519994\pi\)
−0.0627727 + 0.998028i \(0.519994\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 17327.9 1.43229
\(528\) 0 0
\(529\) 17755.7 1.45933
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24365.3 1.98007
\(534\) 0 0
\(535\) 2574.23 0.208025
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6271.81 0.501198
\(540\) 0 0
\(541\) −18683.1 −1.48475 −0.742375 0.669985i \(-0.766301\pi\)
−0.742375 + 0.669985i \(0.766301\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3284.36 0.258141
\(546\) 0 0
\(547\) 2830.89 0.221280 0.110640 0.993861i \(-0.464710\pi\)
0.110640 + 0.993861i \(0.464710\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7388.64 0.571265
\(552\) 0 0
\(553\) −7308.24 −0.561986
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2065.19 −0.157100 −0.0785500 0.996910i \(-0.525029\pi\)
−0.0785500 + 0.996910i \(0.525029\pi\)
\(558\) 0 0
\(559\) −12782.1 −0.967129
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20528.0 1.53668 0.768341 0.640040i \(-0.221082\pi\)
0.768341 + 0.640040i \(0.221082\pi\)
\(564\) 0 0
\(565\) −8507.20 −0.633453
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17758.5 −1.30839 −0.654195 0.756326i \(-0.726992\pi\)
−0.654195 + 0.756326i \(0.726992\pi\)
\(570\) 0 0
\(571\) −12609.1 −0.924126 −0.462063 0.886847i \(-0.652891\pi\)
−0.462063 + 0.886847i \(0.652891\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4324.55 −0.313645
\(576\) 0 0
\(577\) 1266.62 0.0913863 0.0456932 0.998956i \(-0.485450\pi\)
0.0456932 + 0.998956i \(0.485450\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8004.76 −0.571589
\(582\) 0 0
\(583\) −3186.13 −0.226340
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8943.52 −0.628856 −0.314428 0.949281i \(-0.601813\pi\)
−0.314428 + 0.949281i \(0.601813\pi\)
\(588\) 0 0
\(589\) −17227.9 −1.20520
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16200.0 −1.12185 −0.560924 0.827868i \(-0.689554\pi\)
−0.560924 + 0.827868i \(0.689554\pi\)
\(594\) 0 0
\(595\) −5368.97 −0.369926
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19630.1 1.33900 0.669501 0.742811i \(-0.266508\pi\)
0.669501 + 0.742811i \(0.266508\pi\)
\(600\) 0 0
\(601\) 11537.5 0.783066 0.391533 0.920164i \(-0.371945\pi\)
0.391533 + 0.920164i \(0.371945\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 617.977 0.0415279
\(606\) 0 0
\(607\) 6346.35 0.424366 0.212183 0.977230i \(-0.431943\pi\)
0.212183 + 0.977230i \(0.431943\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −29573.5 −1.95813
\(612\) 0 0
\(613\) −12007.3 −0.791144 −0.395572 0.918435i \(-0.629454\pi\)
−0.395572 + 0.918435i \(0.629454\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8650.85 0.564457 0.282229 0.959347i \(-0.408926\pi\)
0.282229 + 0.959347i \(0.408926\pi\)
\(618\) 0 0
\(619\) −11528.8 −0.748597 −0.374299 0.927308i \(-0.622117\pi\)
−0.374299 + 0.927308i \(0.622117\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12914.8 0.830531
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 24090.9 1.52714
\(630\) 0 0
\(631\) 4739.76 0.299028 0.149514 0.988760i \(-0.452229\pi\)
0.149514 + 0.988760i \(0.452229\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1727.02 0.107929
\(636\) 0 0
\(637\) 13670.5 0.850305
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 29213.8 1.80012 0.900060 0.435766i \(-0.143522\pi\)
0.900060 + 0.435766i \(0.143522\pi\)
\(642\) 0 0
\(643\) −23444.5 −1.43789 −0.718943 0.695069i \(-0.755374\pi\)
−0.718943 + 0.695069i \(0.755374\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −27783.6 −1.68823 −0.844116 0.536160i \(-0.819874\pi\)
−0.844116 + 0.536160i \(0.819874\pi\)
\(648\) 0 0
\(649\) 4265.84 0.258010
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8533.05 0.511369 0.255684 0.966760i \(-0.417699\pi\)
0.255684 + 0.966760i \(0.417699\pi\)
\(654\) 0 0
\(655\) 14139.4 0.843467
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1085.28 −0.0641522 −0.0320761 0.999485i \(-0.510212\pi\)
−0.0320761 + 0.999485i \(0.510212\pi\)
\(660\) 0 0
\(661\) −403.736 −0.0237572 −0.0118786 0.999929i \(-0.503781\pi\)
−0.0118786 + 0.999929i \(0.503781\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5337.97 0.311274
\(666\) 0 0
\(667\) −15261.3 −0.885938
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 30522.6 1.75605
\(672\) 0 0
\(673\) −25125.0 −1.43907 −0.719537 0.694454i \(-0.755646\pi\)
−0.719537 + 0.694454i \(0.755646\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4361.67 −0.247611 −0.123805 0.992307i \(-0.539510\pi\)
−0.123805 + 0.992307i \(0.539510\pi\)
\(678\) 0 0
\(679\) −14734.1 −0.832756
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14945.1 0.837275 0.418637 0.908153i \(-0.362508\pi\)
0.418637 + 0.908153i \(0.362508\pi\)
\(684\) 0 0
\(685\) 6139.19 0.342433
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6944.72 −0.383995
\(690\) 0 0
\(691\) −21499.1 −1.18359 −0.591797 0.806087i \(-0.701581\pi\)
−0.591797 + 0.806087i \(0.701581\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −200.545 −0.0109455
\(696\) 0 0
\(697\) 27098.3 1.47263
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −28878.4 −1.55595 −0.777977 0.628293i \(-0.783754\pi\)
−0.777977 + 0.628293i \(0.783754\pi\)
\(702\) 0 0
\(703\) −23951.8 −1.28501
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10884.9 0.579024
\(708\) 0 0
\(709\) −19945.5 −1.05651 −0.528257 0.849084i \(-0.677154\pi\)
−0.528257 + 0.849084i \(0.677154\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 35584.3 1.86907
\(714\) 0 0
\(715\) −13158.7 −0.688264
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18280.0 −0.948160 −0.474080 0.880482i \(-0.657219\pi\)
−0.474080 + 0.880482i \(0.657219\pi\)
\(720\) 0 0
\(721\) −13129.5 −0.678179
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2205.62 0.112986
\(726\) 0 0
\(727\) −17999.1 −0.918225 −0.459112 0.888378i \(-0.651833\pi\)
−0.459112 + 0.888378i \(0.651833\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −14215.8 −0.719278
\(732\) 0 0
\(733\) 9899.87 0.498854 0.249427 0.968394i \(-0.419758\pi\)
0.249427 + 0.968394i \(0.419758\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −36047.4 −1.80166
\(738\) 0 0
\(739\) 16358.7 0.814294 0.407147 0.913363i \(-0.366524\pi\)
0.407147 + 0.913363i \(0.366524\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 756.028 0.0373297 0.0186648 0.999826i \(-0.494058\pi\)
0.0186648 + 0.999826i \(0.494058\pi\)
\(744\) 0 0
\(745\) −2403.65 −0.118205
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6563.11 0.320175
\(750\) 0 0
\(751\) 31368.4 1.52417 0.762083 0.647480i \(-0.224177\pi\)
0.762083 + 0.647480i \(0.224177\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −380.000 −0.0183174
\(756\) 0 0
\(757\) −17559.4 −0.843072 −0.421536 0.906812i \(-0.638509\pi\)
−0.421536 + 0.906812i \(0.638509\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −23502.4 −1.11953 −0.559765 0.828651i \(-0.689109\pi\)
−0.559765 + 0.828651i \(0.689109\pi\)
\(762\) 0 0
\(763\) 8373.63 0.397308
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9298.12 0.437726
\(768\) 0 0
\(769\) 32276.0 1.51352 0.756762 0.653690i \(-0.226780\pi\)
0.756762 + 0.653690i \(0.226780\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8693.38 0.404501 0.202251 0.979334i \(-0.435174\pi\)
0.202251 + 0.979334i \(0.435174\pi\)
\(774\) 0 0
\(775\) −5142.78 −0.238367
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −26941.8 −1.23914
\(780\) 0 0
\(781\) 21029.9 0.963519
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2193.01 0.0997095
\(786\) 0 0
\(787\) −20817.0 −0.942881 −0.471440 0.881898i \(-0.656266\pi\)
−0.471440 + 0.881898i \(0.656266\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −21689.5 −0.974956
\(792\) 0 0
\(793\) 66529.2 2.97922
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42466.0 −1.88736 −0.943678 0.330865i \(-0.892659\pi\)
−0.943678 + 0.330865i \(0.892659\pi\)
\(798\) 0 0
\(799\) −32890.7 −1.45631
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 479.914 0.0210906
\(804\) 0 0
\(805\) −11025.6 −0.482736
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −32955.4 −1.43220 −0.716101 0.697997i \(-0.754075\pi\)
−0.716101 + 0.697997i \(0.754075\pi\)
\(810\) 0 0
\(811\) 3396.82 0.147076 0.0735379 0.997292i \(-0.476571\pi\)
0.0735379 + 0.997292i \(0.476571\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8779.36 0.377335
\(816\) 0 0
\(817\) 14133.8 0.605236
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 13138.9 0.558529 0.279265 0.960214i \(-0.409909\pi\)
0.279265 + 0.960214i \(0.409909\pi\)
\(822\) 0 0
\(823\) −24645.2 −1.04384 −0.521918 0.852996i \(-0.674783\pi\)
−0.521918 + 0.852996i \(0.674783\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −14508.9 −0.610064 −0.305032 0.952342i \(-0.598667\pi\)
−0.305032 + 0.952342i \(0.598667\pi\)
\(828\) 0 0
\(829\) 28408.6 1.19019 0.595097 0.803654i \(-0.297113\pi\)
0.595097 + 0.803654i \(0.297113\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 15203.9 0.632392
\(834\) 0 0
\(835\) −13937.8 −0.577649
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −14950.0 −0.615173 −0.307587 0.951520i \(-0.599521\pi\)
−0.307587 + 0.951520i \(0.599521\pi\)
\(840\) 0 0
\(841\) −16605.3 −0.680854
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −17696.7 −0.720456
\(846\) 0 0
\(847\) 1575.56 0.0639161
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 49472.8 1.99284
\(852\) 0 0
\(853\) −47855.4 −1.92091 −0.960456 0.278432i \(-0.910185\pi\)
−0.960456 + 0.278432i \(0.910185\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 25938.2 1.03388 0.516939 0.856022i \(-0.327071\pi\)
0.516939 + 0.856022i \(0.327071\pi\)
\(858\) 0 0
\(859\) 7594.80 0.301666 0.150833 0.988559i \(-0.451804\pi\)
0.150833 + 0.988559i \(0.451804\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −20686.0 −0.815943 −0.407972 0.912995i \(-0.633764\pi\)
−0.407972 + 0.912995i \(0.633764\pi\)
\(864\) 0 0
\(865\) 6081.81 0.239061
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −19920.8 −0.777637
\(870\) 0 0
\(871\) −78571.6 −3.05660
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1593.47 0.0615645
\(876\) 0 0
\(877\) −40023.1 −1.54103 −0.770515 0.637422i \(-0.780001\pi\)
−0.770515 + 0.637422i \(0.780001\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −21863.6 −0.836100 −0.418050 0.908424i \(-0.637286\pi\)
−0.418050 + 0.908424i \(0.637286\pi\)
\(882\) 0 0
\(883\) −25239.1 −0.961906 −0.480953 0.876746i \(-0.659709\pi\)
−0.480953 + 0.876746i \(0.659709\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −42160.4 −1.59595 −0.797974 0.602691i \(-0.794095\pi\)
−0.797974 + 0.602691i \(0.794095\pi\)
\(888\) 0 0
\(889\) 4403.12 0.166115
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 32700.8 1.22541
\(894\) 0 0
\(895\) 12659.9 0.472819
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −18148.9 −0.673303
\(900\) 0 0
\(901\) −7723.69 −0.285587
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17224.1 −0.632650
\(906\) 0 0
\(907\) 9290.99 0.340135 0.170067 0.985432i \(-0.445601\pi\)
0.170067 + 0.985432i \(0.445601\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 48448.8 1.76200 0.881000 0.473116i \(-0.156871\pi\)
0.881000 + 0.473116i \(0.156871\pi\)
\(912\) 0 0
\(913\) −21819.4 −0.790926
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 36048.9 1.29819
\(918\) 0 0
\(919\) 39905.6 1.43239 0.716193 0.697902i \(-0.245883\pi\)
0.716193 + 0.697902i \(0.245883\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 45838.2 1.63465
\(924\) 0 0
\(925\) −7150.00 −0.254152
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 34488.4 1.21800 0.609002 0.793169i \(-0.291570\pi\)
0.609002 + 0.793169i \(0.291570\pi\)
\(930\) 0 0
\(931\) −15116.1 −0.532126
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −14634.7 −0.511878
\(936\) 0 0
\(937\) −57056.3 −1.98927 −0.994635 0.103443i \(-0.967014\pi\)
−0.994635 + 0.103443i \(0.967014\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 52473.4 1.81784 0.908919 0.416974i \(-0.136909\pi\)
0.908919 + 0.416974i \(0.136909\pi\)
\(942\) 0 0
\(943\) 55648.6 1.92171
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −19062.2 −0.654107 −0.327053 0.945006i \(-0.606056\pi\)
−0.327053 + 0.945006i \(0.606056\pi\)
\(948\) 0 0
\(949\) 1046.05 0.0357812
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36107.0 1.22730 0.613652 0.789577i \(-0.289700\pi\)
0.613652 + 0.789577i \(0.289700\pi\)
\(954\) 0 0
\(955\) 8512.86 0.288450
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 15652.2 0.527043
\(960\) 0 0
\(961\) 12526.2 0.420468
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3427.44 −0.114335
\(966\) 0 0
\(967\) −42749.6 −1.42165 −0.710824 0.703369i \(-0.751678\pi\)
−0.710824 + 0.703369i \(0.751678\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 42208.9 1.39500 0.697501 0.716583i \(-0.254295\pi\)
0.697501 + 0.716583i \(0.254295\pi\)
\(972\) 0 0
\(973\) −511.300 −0.0168464
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6217.51 −0.203599 −0.101799 0.994805i \(-0.532460\pi\)
−0.101799 + 0.994805i \(0.532460\pi\)
\(978\) 0 0
\(979\) 35203.2 1.14923
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 40932.0 1.32811 0.664053 0.747686i \(-0.268835\pi\)
0.664053 + 0.747686i \(0.268835\pi\)
\(984\) 0 0
\(985\) 21814.8 0.705661
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −29193.4 −0.938622
\(990\) 0 0
\(991\) −13878.5 −0.444870 −0.222435 0.974947i \(-0.571401\pi\)
−0.222435 + 0.974947i \(0.571401\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −14601.0 −0.465208
\(996\) 0 0
\(997\) 6733.80 0.213903 0.106952 0.994264i \(-0.465891\pi\)
0.106952 + 0.994264i \(0.465891\pi\)
\(998\) 0 0
\(999\) 0 0
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 2160.4.a.x.1.1 2
3.2 odd 2 2160.4.a.bc.1.1 2
4.3 odd 2 540.4.a.e.1.2 2
12.11 even 2 540.4.a.h.1.2 yes 2
36.7 odd 6 1620.4.i.r.1081.1 4
36.11 even 6 1620.4.i.o.1081.1 4
36.23 even 6 1620.4.i.o.541.1 4
36.31 odd 6 1620.4.i.r.541.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
540.4.a.e.1.2 2 4.3 odd 2
540.4.a.h.1.2 yes 2 12.11 even 2
1620.4.i.o.541.1 4 36.23 even 6
1620.4.i.o.1081.1 4 36.11 even 6
1620.4.i.r.541.1 4 36.31 odd 6
1620.4.i.r.1081.1 4 36.7 odd 6
2160.4.a.x.1.1 2 1.1 even 1 trivial
2160.4.a.bc.1.1 2 3.2 odd 2