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Properties

Label 2400.4.a.l.1.1
Level $2400$
Weight $4$
Character 2400.1
Self dual yes
Analytic conductor $141.605$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2400,4,Mod(1,2400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2400, 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("2400.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2400.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: \(141.604584014\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 96)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2400.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -36.0000 q^{7} +9.00000 q^{9} +36.0000 q^{11} -54.0000 q^{13} +22.0000 q^{17} -36.0000 q^{19} -108.000 q^{21} -144.000 q^{23} +27.0000 q^{27} +50.0000 q^{29} +108.000 q^{31} +108.000 q^{33} -214.000 q^{37} -162.000 q^{39} -446.000 q^{41} +252.000 q^{43} +72.0000 q^{47} +953.000 q^{49} +66.0000 q^{51} +22.0000 q^{53} -108.000 q^{57} +684.000 q^{59} -466.000 q^{61} -324.000 q^{63} -180.000 q^{67} -432.000 q^{69} -576.000 q^{71} +54.0000 q^{73} -1296.00 q^{77} +972.000 q^{79} +81.0000 q^{81} -684.000 q^{83} +150.000 q^{87} +346.000 q^{89} +1944.00 q^{91} +324.000 q^{93} +1134.00 q^{97} +324.000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −36.0000 −1.94382 −0.971909 − 0.235358i \(-0.924374\pi\)
−0.971909 + 0.235358i \(0.924374\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 36.0000 0.986764 0.493382 − 0.869813i \(-0.335760\pi\)
0.493382 + 0.869813i \(0.335760\pi\)
\(12\) 0 0
\(13\) −54.0000 −1.15207 −0.576035 − 0.817425i \(-0.695401\pi\)
−0.576035 + 0.817425i \(0.695401\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 22.0000 0.313870 0.156935 − 0.987609i \(-0.449839\pi\)
0.156935 + 0.987609i \(0.449839\pi\)
\(18\) 0 0
\(19\) −36.0000 −0.434682 −0.217341 − 0.976096i \(-0.569738\pi\)
−0.217341 + 0.976096i \(0.569738\pi\)
\(20\) 0 0
\(21\) −108.000 −1.12226
\(22\) 0 0
\(23\) −144.000 −1.30548 −0.652741 − 0.757581i \(-0.726381\pi\)
−0.652741 + 0.757581i \(0.726381\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 50.0000 0.320164 0.160082 − 0.987104i \(-0.448824\pi\)
0.160082 + 0.987104i \(0.448824\pi\)
\(30\) 0 0
\(31\) 108.000 0.625722 0.312861 − 0.949799i \(-0.398713\pi\)
0.312861 + 0.949799i \(0.398713\pi\)
\(32\) 0 0
\(33\) 108.000 0.569709
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −214.000 −0.950848 −0.475424 − 0.879757i \(-0.657705\pi\)
−0.475424 + 0.879757i \(0.657705\pi\)
\(38\) 0 0
\(39\) −162.000 −0.665148
\(40\) 0 0
\(41\) −446.000 −1.69887 −0.849433 − 0.527697i \(-0.823056\pi\)
−0.849433 + 0.527697i \(0.823056\pi\)
\(42\) 0 0
\(43\) 252.000 0.893713 0.446856 − 0.894606i \(-0.352544\pi\)
0.446856 + 0.894606i \(0.352544\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 72.0000 0.223453 0.111726 − 0.993739i \(-0.464362\pi\)
0.111726 + 0.993739i \(0.464362\pi\)
\(48\) 0 0
\(49\) 953.000 2.77843
\(50\) 0 0
\(51\) 66.0000 0.181213
\(52\) 0 0
\(53\) 22.0000 0.0570176 0.0285088 − 0.999594i \(-0.490924\pi\)
0.0285088 + 0.999594i \(0.490924\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −108.000 −0.250964
\(58\) 0 0
\(59\) 684.000 1.50931 0.754654 − 0.656123i \(-0.227805\pi\)
0.754654 + 0.656123i \(0.227805\pi\)
\(60\) 0 0
\(61\) −466.000 −0.978118 −0.489059 − 0.872251i \(-0.662660\pi\)
−0.489059 + 0.872251i \(0.662660\pi\)
\(62\) 0 0
\(63\) −324.000 −0.647939
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −180.000 −0.328216 −0.164108 − 0.986442i \(-0.552475\pi\)
−0.164108 + 0.986442i \(0.552475\pi\)
\(68\) 0 0
\(69\) −432.000 −0.753720
\(70\) 0 0
\(71\) −576.000 −0.962798 −0.481399 − 0.876502i \(-0.659871\pi\)
−0.481399 + 0.876502i \(0.659871\pi\)
\(72\) 0 0
\(73\) 54.0000 0.0865784 0.0432892 − 0.999063i \(-0.486216\pi\)
0.0432892 + 0.999063i \(0.486216\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1296.00 −1.91809
\(78\) 0 0
\(79\) 972.000 1.38429 0.692143 − 0.721761i \(-0.256667\pi\)
0.692143 + 0.721761i \(0.256667\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −684.000 −0.904563 −0.452282 − 0.891875i \(-0.649390\pi\)
−0.452282 + 0.891875i \(0.649390\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 150.000 0.184847
\(88\) 0 0
\(89\) 346.000 0.412089 0.206045 − 0.978543i \(-0.433941\pi\)
0.206045 + 0.978543i \(0.433941\pi\)
\(90\) 0 0
\(91\) 1944.00 2.23941
\(92\) 0 0
\(93\) 324.000 0.361261
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1134.00 1.18701 0.593506 − 0.804829i \(-0.297743\pi\)
0.593506 + 0.804829i \(0.297743\pi\)
\(98\) 0 0
\(99\) 324.000 0.328921
\(100\) 0 0
\(101\) 58.0000 0.0571407 0.0285704 − 0.999592i \(-0.490905\pi\)
0.0285704 + 0.999592i \(0.490905\pi\)
\(102\) 0 0
\(103\) 1332.00 1.27423 0.637116 − 0.770768i \(-0.280127\pi\)
0.637116 + 0.770768i \(0.280127\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −396.000 −0.357783 −0.178891 − 0.983869i \(-0.557251\pi\)
−0.178891 + 0.983869i \(0.557251\pi\)
\(108\) 0 0
\(109\) −1242.00 −1.09139 −0.545697 − 0.837982i \(-0.683735\pi\)
−0.545697 + 0.837982i \(0.683735\pi\)
\(110\) 0 0
\(111\) −642.000 −0.548972
\(112\) 0 0
\(113\) 446.000 0.371293 0.185647 − 0.982617i \(-0.440562\pi\)
0.185647 + 0.982617i \(0.440562\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −486.000 −0.384023
\(118\) 0 0
\(119\) −792.000 −0.610105
\(120\) 0 0
\(121\) −35.0000 −0.0262960
\(122\) 0 0
\(123\) −1338.00 −0.980841
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1116.00 0.779756 0.389878 − 0.920867i \(-0.372517\pi\)
0.389878 + 0.920867i \(0.372517\pi\)
\(128\) 0 0
\(129\) 756.000 0.515985
\(130\) 0 0
\(131\) −2700.00 −1.80076 −0.900382 − 0.435100i \(-0.856713\pi\)
−0.900382 + 0.435100i \(0.856713\pi\)
\(132\) 0 0
\(133\) 1296.00 0.844943
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1678.00 1.04643 0.523216 − 0.852200i \(-0.324732\pi\)
0.523216 + 0.852200i \(0.324732\pi\)
\(138\) 0 0
\(139\) −36.0000 −0.0219675 −0.0109837 − 0.999940i \(-0.503496\pi\)
−0.0109837 + 0.999940i \(0.503496\pi\)
\(140\) 0 0
\(141\) 216.000 0.129011
\(142\) 0 0
\(143\) −1944.00 −1.13682
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2859.00 1.60412
\(148\) 0 0
\(149\) 1634.00 0.898406 0.449203 − 0.893430i \(-0.351708\pi\)
0.449203 + 0.893430i \(0.351708\pi\)
\(150\) 0 0
\(151\) 1908.00 1.02828 0.514142 − 0.857705i \(-0.328110\pi\)
0.514142 + 0.857705i \(0.328110\pi\)
\(152\) 0 0
\(153\) 198.000 0.104623
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2306.00 1.17222 0.586111 − 0.810231i \(-0.300658\pi\)
0.586111 + 0.810231i \(0.300658\pi\)
\(158\) 0 0
\(159\) 66.0000 0.0329191
\(160\) 0 0
\(161\) 5184.00 2.53762
\(162\) 0 0
\(163\) 1476.00 0.709259 0.354630 − 0.935007i \(-0.384607\pi\)
0.354630 + 0.935007i \(0.384607\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2808.00 1.30114 0.650568 − 0.759448i \(-0.274531\pi\)
0.650568 + 0.759448i \(0.274531\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) 0 0
\(171\) −324.000 −0.144894
\(172\) 0 0
\(173\) −58.0000 −0.0254894 −0.0127447 − 0.999919i \(-0.504057\pi\)
−0.0127447 + 0.999919i \(0.504057\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2052.00 0.871400
\(178\) 0 0
\(179\) 3492.00 1.45812 0.729062 − 0.684447i \(-0.239956\pi\)
0.729062 + 0.684447i \(0.239956\pi\)
\(180\) 0 0
\(181\) −162.000 −0.0665269 −0.0332634 − 0.999447i \(-0.510590\pi\)
−0.0332634 + 0.999447i \(0.510590\pi\)
\(182\) 0 0
\(183\) −1398.00 −0.564717
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 792.000 0.309715
\(188\) 0 0
\(189\) −972.000 −0.374088
\(190\) 0 0
\(191\) 2880.00 1.09104 0.545522 − 0.838096i \(-0.316331\pi\)
0.545522 + 0.838096i \(0.316331\pi\)
\(192\) 0 0
\(193\) 2414.00 0.900329 0.450165 − 0.892946i \(-0.351365\pi\)
0.450165 + 0.892946i \(0.351365\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2678.00 0.968526 0.484263 − 0.874923i \(-0.339088\pi\)
0.484263 + 0.874923i \(0.339088\pi\)
\(198\) 0 0
\(199\) 828.000 0.294952 0.147476 − 0.989066i \(-0.452885\pi\)
0.147476 + 0.989066i \(0.452885\pi\)
\(200\) 0 0
\(201\) −540.000 −0.189496
\(202\) 0 0
\(203\) −1800.00 −0.622341
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1296.00 −0.435161
\(208\) 0 0
\(209\) −1296.00 −0.428929
\(210\) 0 0
\(211\) 1476.00 0.481574 0.240787 − 0.970578i \(-0.422595\pi\)
0.240787 + 0.970578i \(0.422595\pi\)
\(212\) 0 0
\(213\) −1728.00 −0.555871
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −3888.00 −1.21629
\(218\) 0 0
\(219\) 162.000 0.0499861
\(220\) 0 0
\(221\) −1188.00 −0.361600
\(222\) 0 0
\(223\) 1260.00 0.378367 0.189183 − 0.981942i \(-0.439416\pi\)
0.189183 + 0.981942i \(0.439416\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3060.00 0.894711 0.447355 − 0.894356i \(-0.352366\pi\)
0.447355 + 0.894356i \(0.352366\pi\)
\(228\) 0 0
\(229\) 1566.00 0.451896 0.225948 − 0.974139i \(-0.427452\pi\)
0.225948 + 0.974139i \(0.427452\pi\)
\(230\) 0 0
\(231\) −3888.00 −1.10741
\(232\) 0 0
\(233\) −3434.00 −0.965531 −0.482766 − 0.875750i \(-0.660368\pi\)
−0.482766 + 0.875750i \(0.660368\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2916.00 0.799218
\(238\) 0 0
\(239\) −1440.00 −0.389732 −0.194866 − 0.980830i \(-0.562427\pi\)
−0.194866 + 0.980830i \(0.562427\pi\)
\(240\) 0 0
\(241\) −270.000 −0.0721669 −0.0360835 − 0.999349i \(-0.511488\pi\)
−0.0360835 + 0.999349i \(0.511488\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1944.00 0.500784
\(248\) 0 0
\(249\) −2052.00 −0.522250
\(250\) 0 0
\(251\) −3564.00 −0.896246 −0.448123 − 0.893972i \(-0.647907\pi\)
−0.448123 + 0.893972i \(0.647907\pi\)
\(252\) 0 0
\(253\) −5184.00 −1.28820
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7682.00 −1.86455 −0.932276 − 0.361747i \(-0.882180\pi\)
−0.932276 + 0.361747i \(0.882180\pi\)
\(258\) 0 0
\(259\) 7704.00 1.84828
\(260\) 0 0
\(261\) 450.000 0.106721
\(262\) 0 0
\(263\) 1368.00 0.320740 0.160370 − 0.987057i \(-0.448731\pi\)
0.160370 + 0.987057i \(0.448731\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1038.00 0.237920
\(268\) 0 0
\(269\) 4450.00 1.00863 0.504315 − 0.863520i \(-0.331745\pi\)
0.504315 + 0.863520i \(0.331745\pi\)
\(270\) 0 0
\(271\) −3420.00 −0.766606 −0.383303 − 0.923623i \(-0.625213\pi\)
−0.383303 + 0.923623i \(0.625213\pi\)
\(272\) 0 0
\(273\) 5832.00 1.29293
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7614.00 −1.65156 −0.825778 − 0.563996i \(-0.809264\pi\)
−0.825778 + 0.563996i \(0.809264\pi\)
\(278\) 0 0
\(279\) 972.000 0.208574
\(280\) 0 0
\(281\) −6422.00 −1.36336 −0.681680 − 0.731650i \(-0.738751\pi\)
−0.681680 + 0.731650i \(0.738751\pi\)
\(282\) 0 0
\(283\) 5364.00 1.12670 0.563351 − 0.826218i \(-0.309512\pi\)
0.563351 + 0.826218i \(0.309512\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 16056.0 3.30228
\(288\) 0 0
\(289\) −4429.00 −0.901486
\(290\) 0 0
\(291\) 3402.00 0.685322
\(292\) 0 0
\(293\) −122.000 −0.0243253 −0.0121627 − 0.999926i \(-0.503872\pi\)
−0.0121627 + 0.999926i \(0.503872\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 972.000 0.189903
\(298\) 0 0
\(299\) 7776.00 1.50401
\(300\) 0 0
\(301\) −9072.00 −1.73721
\(302\) 0 0
\(303\) 174.000 0.0329902
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 6876.00 1.27829 0.639143 − 0.769088i \(-0.279289\pi\)
0.639143 + 0.769088i \(0.279289\pi\)
\(308\) 0 0
\(309\) 3996.00 0.735678
\(310\) 0 0
\(311\) 9288.00 1.69349 0.846743 − 0.532002i \(-0.178560\pi\)
0.846743 + 0.532002i \(0.178560\pi\)
\(312\) 0 0
\(313\) −2234.00 −0.403429 −0.201714 − 0.979444i \(-0.564651\pi\)
−0.201714 + 0.979444i \(0.564651\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3614.00 0.640323 0.320162 − 0.947363i \(-0.396263\pi\)
0.320162 + 0.947363i \(0.396263\pi\)
\(318\) 0 0
\(319\) 1800.00 0.315927
\(320\) 0 0
\(321\) −1188.00 −0.206566
\(322\) 0 0
\(323\) −792.000 −0.136434
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3726.00 −0.630117
\(328\) 0 0
\(329\) −2592.00 −0.434351
\(330\) 0 0
\(331\) 684.000 0.113583 0.0567916 − 0.998386i \(-0.481913\pi\)
0.0567916 + 0.998386i \(0.481913\pi\)
\(332\) 0 0
\(333\) −1926.00 −0.316949
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −10530.0 −1.70209 −0.851047 − 0.525090i \(-0.824032\pi\)
−0.851047 + 0.525090i \(0.824032\pi\)
\(338\) 0 0
\(339\) 1338.00 0.214366
\(340\) 0 0
\(341\) 3888.00 0.617440
\(342\) 0 0
\(343\) −21960.0 −3.45693
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1548.00 0.239484 0.119742 − 0.992805i \(-0.461793\pi\)
0.119742 + 0.992805i \(0.461793\pi\)
\(348\) 0 0
\(349\) −4786.00 −0.734065 −0.367033 − 0.930208i \(-0.619626\pi\)
−0.367033 + 0.930208i \(0.619626\pi\)
\(350\) 0 0
\(351\) −1458.00 −0.221716
\(352\) 0 0
\(353\) 6638.00 1.00086 0.500432 − 0.865776i \(-0.333174\pi\)
0.500432 + 0.865776i \(0.333174\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2376.00 −0.352244
\(358\) 0 0
\(359\) 4320.00 0.635100 0.317550 − 0.948242i \(-0.397140\pi\)
0.317550 + 0.948242i \(0.397140\pi\)
\(360\) 0 0
\(361\) −5563.00 −0.811051
\(362\) 0 0
\(363\) −105.000 −0.0151820
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 2340.00 0.332826 0.166413 − 0.986056i \(-0.446782\pi\)
0.166413 + 0.986056i \(0.446782\pi\)
\(368\) 0 0
\(369\) −4014.00 −0.566289
\(370\) 0 0
\(371\) −792.000 −0.110832
\(372\) 0 0
\(373\) 3850.00 0.534438 0.267219 − 0.963636i \(-0.413895\pi\)
0.267219 + 0.963636i \(0.413895\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2700.00 −0.368852
\(378\) 0 0
\(379\) 2052.00 0.278111 0.139056 − 0.990285i \(-0.455593\pi\)
0.139056 + 0.990285i \(0.455593\pi\)
\(380\) 0 0
\(381\) 3348.00 0.450192
\(382\) 0 0
\(383\) −9504.00 −1.26797 −0.633984 − 0.773346i \(-0.718581\pi\)
−0.633984 + 0.773346i \(0.718581\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2268.00 0.297904
\(388\) 0 0
\(389\) −7726.00 −1.00700 −0.503501 − 0.863995i \(-0.667955\pi\)
−0.503501 + 0.863995i \(0.667955\pi\)
\(390\) 0 0
\(391\) −3168.00 −0.409751
\(392\) 0 0
\(393\) −8100.00 −1.03967
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 9826.00 1.24220 0.621099 − 0.783732i \(-0.286686\pi\)
0.621099 + 0.783732i \(0.286686\pi\)
\(398\) 0 0
\(399\) 3888.00 0.487828
\(400\) 0 0
\(401\) 13082.0 1.62914 0.814568 − 0.580067i \(-0.196974\pi\)
0.814568 + 0.580067i \(0.196974\pi\)
\(402\) 0 0
\(403\) −5832.00 −0.720875
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7704.00 −0.938263
\(408\) 0 0
\(409\) 6426.00 0.776883 0.388442 − 0.921473i \(-0.373014\pi\)
0.388442 + 0.921473i \(0.373014\pi\)
\(410\) 0 0
\(411\) 5034.00 0.604158
\(412\) 0 0
\(413\) −24624.0 −2.93382
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −108.000 −0.0126829
\(418\) 0 0
\(419\) 6444.00 0.751337 0.375668 − 0.926754i \(-0.377413\pi\)
0.375668 + 0.926754i \(0.377413\pi\)
\(420\) 0 0
\(421\) −2322.00 −0.268806 −0.134403 − 0.990927i \(-0.542912\pi\)
−0.134403 + 0.990927i \(0.542912\pi\)
\(422\) 0 0
\(423\) 648.000 0.0744843
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 16776.0 1.90128
\(428\) 0 0
\(429\) −5832.00 −0.656344
\(430\) 0 0
\(431\) 16488.0 1.84269 0.921345 − 0.388747i \(-0.127092\pi\)
0.921345 + 0.388747i \(0.127092\pi\)
\(432\) 0 0
\(433\) 3566.00 0.395776 0.197888 − 0.980225i \(-0.436592\pi\)
0.197888 + 0.980225i \(0.436592\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5184.00 0.567470
\(438\) 0 0
\(439\) 6588.00 0.716237 0.358119 − 0.933676i \(-0.383418\pi\)
0.358119 + 0.933676i \(0.383418\pi\)
\(440\) 0 0
\(441\) 8577.00 0.926142
\(442\) 0 0
\(443\) 9900.00 1.06177 0.530884 − 0.847445i \(-0.321860\pi\)
0.530884 + 0.847445i \(0.321860\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4902.00 0.518695
\(448\) 0 0
\(449\) −1382.00 −0.145257 −0.0726287 − 0.997359i \(-0.523139\pi\)
−0.0726287 + 0.997359i \(0.523139\pi\)
\(450\) 0 0
\(451\) −16056.0 −1.67638
\(452\) 0 0
\(453\) 5724.00 0.593680
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 13878.0 1.42054 0.710269 − 0.703931i \(-0.248574\pi\)
0.710269 + 0.703931i \(0.248574\pi\)
\(458\) 0 0
\(459\) 594.000 0.0604042
\(460\) 0 0
\(461\) 7610.00 0.768835 0.384418 − 0.923159i \(-0.374402\pi\)
0.384418 + 0.923159i \(0.374402\pi\)
\(462\) 0 0
\(463\) −8388.00 −0.841951 −0.420976 − 0.907072i \(-0.638312\pi\)
−0.420976 + 0.907072i \(0.638312\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1116.00 −0.110583 −0.0552916 − 0.998470i \(-0.517609\pi\)
−0.0552916 + 0.998470i \(0.517609\pi\)
\(468\) 0 0
\(469\) 6480.00 0.637993
\(470\) 0 0
\(471\) 6918.00 0.676783
\(472\) 0 0
\(473\) 9072.00 0.881884
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 198.000 0.0190059
\(478\) 0 0
\(479\) −15048.0 −1.43541 −0.717704 − 0.696348i \(-0.754807\pi\)
−0.717704 + 0.696348i \(0.754807\pi\)
\(480\) 0 0
\(481\) 11556.0 1.09544
\(482\) 0 0
\(483\) 15552.0 1.46509
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6300.00 0.586202 0.293101 − 0.956082i \(-0.405313\pi\)
0.293101 + 0.956082i \(0.405313\pi\)
\(488\) 0 0
\(489\) 4428.00 0.409491
\(490\) 0 0
\(491\) −9684.00 −0.890087 −0.445044 − 0.895509i \(-0.646812\pi\)
−0.445044 + 0.895509i \(0.646812\pi\)
\(492\) 0 0
\(493\) 1100.00 0.100490
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20736.0 1.87150
\(498\) 0 0
\(499\) 14436.0 1.29508 0.647539 − 0.762032i \(-0.275798\pi\)
0.647539 + 0.762032i \(0.275798\pi\)
\(500\) 0 0
\(501\) 8424.00 0.751211
\(502\) 0 0
\(503\) 1008.00 0.0893529 0.0446764 − 0.999002i \(-0.485774\pi\)
0.0446764 + 0.999002i \(0.485774\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2157.00 0.188946
\(508\) 0 0
\(509\) −3550.00 −0.309137 −0.154569 − 0.987982i \(-0.549399\pi\)
−0.154569 + 0.987982i \(0.549399\pi\)
\(510\) 0 0
\(511\) −1944.00 −0.168293
\(512\) 0 0
\(513\) −972.000 −0.0836547
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2592.00 0.220495
\(518\) 0 0
\(519\) −174.000 −0.0147163
\(520\) 0 0
\(521\) −12766.0 −1.07349 −0.536745 − 0.843744i \(-0.680346\pi\)
−0.536745 + 0.843744i \(0.680346\pi\)
\(522\) 0 0
\(523\) −20628.0 −1.72466 −0.862332 − 0.506343i \(-0.830997\pi\)
−0.862332 + 0.506343i \(0.830997\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2376.00 0.196395
\(528\) 0 0
\(529\) 8569.00 0.704282
\(530\) 0 0
\(531\) 6156.00 0.503103
\(532\) 0 0
\(533\) 24084.0 1.95721
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10476.0 0.841849
\(538\) 0 0
\(539\) 34308.0 2.74165
\(540\) 0 0
\(541\) −6858.00 −0.545006 −0.272503 − 0.962155i \(-0.587852\pi\)
−0.272503 + 0.962155i \(0.587852\pi\)
\(542\) 0 0
\(543\) −486.000 −0.0384093
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15444.0 1.20720 0.603599 − 0.797288i \(-0.293733\pi\)
0.603599 + 0.797288i \(0.293733\pi\)
\(548\) 0 0
\(549\) −4194.00 −0.326039
\(550\) 0 0
\(551\) −1800.00 −0.139170
\(552\) 0 0
\(553\) −34992.0 −2.69080
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12938.0 −0.984202 −0.492101 − 0.870538i \(-0.663771\pi\)
−0.492101 + 0.870538i \(0.663771\pi\)
\(558\) 0 0
\(559\) −13608.0 −1.02962
\(560\) 0 0
\(561\) 2376.00 0.178814
\(562\) 0 0
\(563\) 17748.0 1.32858 0.664289 − 0.747476i \(-0.268735\pi\)
0.664289 + 0.747476i \(0.268735\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2916.00 −0.215980
\(568\) 0 0
\(569\) −10318.0 −0.760199 −0.380099 − 0.924946i \(-0.624110\pi\)
−0.380099 + 0.924946i \(0.624110\pi\)
\(570\) 0 0
\(571\) 14652.0 1.07385 0.536924 − 0.843631i \(-0.319586\pi\)
0.536924 + 0.843631i \(0.319586\pi\)
\(572\) 0 0
\(573\) 8640.00 0.629915
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −18578.0 −1.34040 −0.670201 − 0.742179i \(-0.733792\pi\)
−0.670201 + 0.742179i \(0.733792\pi\)
\(578\) 0 0
\(579\) 7242.00 0.519805
\(580\) 0 0
\(581\) 24624.0 1.75831
\(582\) 0 0
\(583\) 792.000 0.0562629
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1620.00 0.113909 0.0569545 − 0.998377i \(-0.481861\pi\)
0.0569545 + 0.998377i \(0.481861\pi\)
\(588\) 0 0
\(589\) −3888.00 −0.271990
\(590\) 0 0
\(591\) 8034.00 0.559179
\(592\) 0 0
\(593\) 4126.00 0.285724 0.142862 − 0.989743i \(-0.454369\pi\)
0.142862 + 0.989743i \(0.454369\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2484.00 0.170290
\(598\) 0 0
\(599\) 16992.0 1.15906 0.579528 − 0.814952i \(-0.303237\pi\)
0.579528 + 0.814952i \(0.303237\pi\)
\(600\) 0 0
\(601\) −11846.0 −0.804007 −0.402004 − 0.915638i \(-0.631686\pi\)
−0.402004 + 0.915638i \(0.631686\pi\)
\(602\) 0 0
\(603\) −1620.00 −0.109405
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −8676.00 −0.580145 −0.290072 − 0.957005i \(-0.593679\pi\)
−0.290072 + 0.957005i \(0.593679\pi\)
\(608\) 0 0
\(609\) −5400.00 −0.359309
\(610\) 0 0
\(611\) −3888.00 −0.257433
\(612\) 0 0
\(613\) 9178.00 0.604724 0.302362 − 0.953193i \(-0.402225\pi\)
0.302362 + 0.953193i \(0.402225\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16646.0 1.08613 0.543065 − 0.839690i \(-0.317264\pi\)
0.543065 + 0.839690i \(0.317264\pi\)
\(618\) 0 0
\(619\) 10044.0 0.652185 0.326092 − 0.945338i \(-0.394268\pi\)
0.326092 + 0.945338i \(0.394268\pi\)
\(620\) 0 0
\(621\) −3888.00 −0.251240
\(622\) 0 0
\(623\) −12456.0 −0.801026
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −3888.00 −0.247642
\(628\) 0 0
\(629\) −4708.00 −0.298442
\(630\) 0 0
\(631\) 1620.00 0.102205 0.0511024 − 0.998693i \(-0.483727\pi\)
0.0511024 + 0.998693i \(0.483727\pi\)
\(632\) 0 0
\(633\) 4428.00 0.278037
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −51462.0 −3.20094
\(638\) 0 0
\(639\) −5184.00 −0.320933
\(640\) 0 0
\(641\) −7078.00 −0.436138 −0.218069 − 0.975933i \(-0.569976\pi\)
−0.218069 + 0.975933i \(0.569976\pi\)
\(642\) 0 0
\(643\) 13716.0 0.841223 0.420611 − 0.907241i \(-0.361816\pi\)
0.420611 + 0.907241i \(0.361816\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16704.0 1.01500 0.507498 − 0.861653i \(-0.330571\pi\)
0.507498 + 0.861653i \(0.330571\pi\)
\(648\) 0 0
\(649\) 24624.0 1.48933
\(650\) 0 0
\(651\) −11664.0 −0.702225
\(652\) 0 0
\(653\) 19670.0 1.17878 0.589392 − 0.807847i \(-0.299367\pi\)
0.589392 + 0.807847i \(0.299367\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 486.000 0.0288595
\(658\) 0 0
\(659\) −31500.0 −1.86201 −0.931006 − 0.365004i \(-0.881068\pi\)
−0.931006 + 0.365004i \(0.881068\pi\)
\(660\) 0 0
\(661\) −20666.0 −1.21606 −0.608029 − 0.793915i \(-0.708040\pi\)
−0.608029 + 0.793915i \(0.708040\pi\)
\(662\) 0 0
\(663\) −3564.00 −0.208770
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7200.00 −0.417969
\(668\) 0 0
\(669\) 3780.00 0.218450
\(670\) 0 0
\(671\) −16776.0 −0.965172
\(672\) 0 0
\(673\) 574.000 0.0328768 0.0164384 − 0.999865i \(-0.494767\pi\)
0.0164384 + 0.999865i \(0.494767\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7934.00 0.450411 0.225206 − 0.974311i \(-0.427695\pi\)
0.225206 + 0.974311i \(0.427695\pi\)
\(678\) 0 0
\(679\) −40824.0 −2.30734
\(680\) 0 0
\(681\) 9180.00 0.516561
\(682\) 0 0
\(683\) 1548.00 0.0867241 0.0433621 − 0.999059i \(-0.486193\pi\)
0.0433621 + 0.999059i \(0.486193\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4698.00 0.260902
\(688\) 0 0
\(689\) −1188.00 −0.0656882
\(690\) 0 0
\(691\) −26100.0 −1.43689 −0.718445 − 0.695584i \(-0.755146\pi\)
−0.718445 + 0.695584i \(0.755146\pi\)
\(692\) 0 0
\(693\) −11664.0 −0.639363
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9812.00 −0.533222
\(698\) 0 0
\(699\) −10302.0 −0.557450
\(700\) 0 0
\(701\) −35230.0 −1.89817 −0.949086 − 0.315017i \(-0.897990\pi\)
−0.949086 + 0.315017i \(0.897990\pi\)
\(702\) 0 0
\(703\) 7704.00 0.413317
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2088.00 −0.111071
\(708\) 0 0
\(709\) 19710.0 1.04404 0.522020 − 0.852933i \(-0.325179\pi\)
0.522020 + 0.852933i \(0.325179\pi\)
\(710\) 0 0
\(711\) 8748.00 0.461428
\(712\) 0 0
\(713\) −15552.0 −0.816868
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −4320.00 −0.225012
\(718\) 0 0
\(719\) −23112.0 −1.19879 −0.599396 − 0.800452i \(-0.704593\pi\)
−0.599396 + 0.800452i \(0.704593\pi\)
\(720\) 0 0
\(721\) −47952.0 −2.47687
\(722\) 0 0
\(723\) −810.000 −0.0416656
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1548.00 0.0789713 0.0394857 − 0.999220i \(-0.487428\pi\)
0.0394857 + 0.999220i \(0.487428\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 5544.00 0.280509
\(732\) 0 0
\(733\) 25434.0 1.28162 0.640809 − 0.767700i \(-0.278599\pi\)
0.640809 + 0.767700i \(0.278599\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6480.00 −0.323872
\(738\) 0 0
\(739\) 2340.00 0.116479 0.0582397 − 0.998303i \(-0.481451\pi\)
0.0582397 + 0.998303i \(0.481451\pi\)
\(740\) 0 0
\(741\) 5832.00 0.289128
\(742\) 0 0
\(743\) −20664.0 −1.02031 −0.510154 − 0.860083i \(-0.670412\pi\)
−0.510154 + 0.860083i \(0.670412\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −6156.00 −0.301521
\(748\) 0 0
\(749\) 14256.0 0.695464
\(750\) 0 0
\(751\) 26892.0 1.30666 0.653331 − 0.757072i \(-0.273371\pi\)
0.653331 + 0.757072i \(0.273371\pi\)
\(752\) 0 0
\(753\) −10692.0 −0.517448
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −29646.0 −1.42338 −0.711692 − 0.702491i \(-0.752071\pi\)
−0.711692 + 0.702491i \(0.752071\pi\)
\(758\) 0 0
\(759\) −15552.0 −0.743744
\(760\) 0 0
\(761\) 14242.0 0.678413 0.339206 − 0.940712i \(-0.389842\pi\)
0.339206 + 0.940712i \(0.389842\pi\)
\(762\) 0 0
\(763\) 44712.0 2.12147
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −36936.0 −1.73883
\(768\) 0 0
\(769\) 20018.0 0.938709 0.469355 − 0.883010i \(-0.344487\pi\)
0.469355 + 0.883010i \(0.344487\pi\)
\(770\) 0 0
\(771\) −23046.0 −1.07650
\(772\) 0 0
\(773\) −12938.0 −0.602002 −0.301001 − 0.953624i \(-0.597321\pi\)
−0.301001 + 0.953624i \(0.597321\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 23112.0 1.06710
\(778\) 0 0
\(779\) 16056.0 0.738467
\(780\) 0 0
\(781\) −20736.0 −0.950054
\(782\) 0 0
\(783\) 1350.00 0.0616157
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −21708.0 −0.983236 −0.491618 − 0.870811i \(-0.663594\pi\)
−0.491618 + 0.870811i \(0.663594\pi\)
\(788\) 0 0
\(789\) 4104.00 0.185179
\(790\) 0 0
\(791\) −16056.0 −0.721726
\(792\) 0 0
\(793\) 25164.0 1.12686
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30470.0 1.35421 0.677103 − 0.735888i \(-0.263235\pi\)
0.677103 + 0.735888i \(0.263235\pi\)
\(798\) 0 0
\(799\) 1584.00 0.0701350
\(800\) 0 0
\(801\) 3114.00 0.137363
\(802\) 0 0
\(803\) 1944.00 0.0854325
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 13350.0 0.582332
\(808\) 0 0
\(809\) 18706.0 0.812939 0.406470 − 0.913664i \(-0.366760\pi\)
0.406470 + 0.913664i \(0.366760\pi\)
\(810\) 0 0
\(811\) 20196.0 0.874448 0.437224 − 0.899353i \(-0.355962\pi\)
0.437224 + 0.899353i \(0.355962\pi\)
\(812\) 0 0
\(813\) −10260.0 −0.442600
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −9072.00 −0.388481
\(818\) 0 0
\(819\) 17496.0 0.746471
\(820\) 0 0
\(821\) 14746.0 0.626844 0.313422 − 0.949614i \(-0.398525\pi\)
0.313422 + 0.949614i \(0.398525\pi\)
\(822\) 0 0
\(823\) −26244.0 −1.11155 −0.555777 − 0.831332i \(-0.687579\pi\)
−0.555777 + 0.831332i \(0.687579\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29124.0 1.22460 0.612298 − 0.790627i \(-0.290245\pi\)
0.612298 + 0.790627i \(0.290245\pi\)
\(828\) 0 0
\(829\) −16362.0 −0.685495 −0.342748 − 0.939427i \(-0.611358\pi\)
−0.342748 + 0.939427i \(0.611358\pi\)
\(830\) 0 0
\(831\) −22842.0 −0.953526
\(832\) 0 0
\(833\) 20966.0 0.872063
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2916.00 0.120420
\(838\) 0 0
\(839\) −21168.0 −0.871038 −0.435519 − 0.900180i \(-0.643435\pi\)
−0.435519 + 0.900180i \(0.643435\pi\)
\(840\) 0 0
\(841\) −21889.0 −0.897495
\(842\) 0 0
\(843\) −19266.0 −0.787137
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1260.00 0.0511147
\(848\) 0 0
\(849\) 16092.0 0.650502
\(850\) 0 0
\(851\) 30816.0 1.24131
\(852\) 0 0
\(853\) −31462.0 −1.26288 −0.631441 − 0.775424i \(-0.717536\pi\)
−0.631441 + 0.775424i \(0.717536\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −41746.0 −1.66396 −0.831981 − 0.554803i \(-0.812793\pi\)
−0.831981 + 0.554803i \(0.812793\pi\)
\(858\) 0 0
\(859\) 44388.0 1.76310 0.881548 − 0.472095i \(-0.156502\pi\)
0.881548 + 0.472095i \(0.156502\pi\)
\(860\) 0 0
\(861\) 48168.0 1.90657
\(862\) 0 0
\(863\) −22752.0 −0.897436 −0.448718 − 0.893673i \(-0.648119\pi\)
−0.448718 + 0.893673i \(0.648119\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −13287.0 −0.520473
\(868\) 0 0
\(869\) 34992.0 1.36596
\(870\) 0 0
\(871\) 9720.00 0.378128
\(872\) 0 0
\(873\) 10206.0 0.395671
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −8030.00 −0.309183 −0.154592 − 0.987978i \(-0.549406\pi\)
−0.154592 + 0.987978i \(0.549406\pi\)
\(878\) 0 0
\(879\) −366.000 −0.0140442
\(880\) 0 0
\(881\) 2354.00 0.0900207 0.0450104 − 0.998987i \(-0.485668\pi\)
0.0450104 + 0.998987i \(0.485668\pi\)
\(882\) 0 0
\(883\) 41364.0 1.57645 0.788227 − 0.615384i \(-0.210999\pi\)
0.788227 + 0.615384i \(0.210999\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −17496.0 −0.662298 −0.331149 − 0.943579i \(-0.607436\pi\)
−0.331149 + 0.943579i \(0.607436\pi\)
\(888\) 0 0
\(889\) −40176.0 −1.51570
\(890\) 0 0
\(891\) 2916.00 0.109640
\(892\) 0 0
\(893\) −2592.00 −0.0971310
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 23328.0 0.868338
\(898\) 0 0
\(899\) 5400.00 0.200334
\(900\) 0 0
\(901\) 484.000 0.0178961
\(902\) 0 0
\(903\) −27216.0 −1.00298
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −45108.0 −1.65136 −0.825682 − 0.564136i \(-0.809209\pi\)
−0.825682 + 0.564136i \(0.809209\pi\)
\(908\) 0 0
\(909\) 522.000 0.0190469
\(910\) 0 0
\(911\) −20448.0 −0.743658 −0.371829 − 0.928301i \(-0.621269\pi\)
−0.371829 + 0.928301i \(0.621269\pi\)
\(912\) 0 0
\(913\) −24624.0 −0.892591
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 97200.0 3.50036
\(918\) 0 0
\(919\) −33948.0 −1.21854 −0.609272 − 0.792962i \(-0.708538\pi\)
−0.609272 + 0.792962i \(0.708538\pi\)
\(920\) 0 0
\(921\) 20628.0 0.738019
\(922\) 0 0
\(923\) 31104.0 1.10921
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 11988.0 0.424744
\(928\) 0 0
\(929\) −54166.0 −1.91295 −0.956474 − 0.291817i \(-0.905740\pi\)
−0.956474 + 0.291817i \(0.905740\pi\)
\(930\) 0 0
\(931\) −34308.0 −1.20773
\(932\) 0 0
\(933\) 27864.0 0.977735
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 8966.00 0.312600 0.156300 − 0.987710i \(-0.450043\pi\)
0.156300 + 0.987710i \(0.450043\pi\)
\(938\) 0 0
\(939\) −6702.00 −0.232920
\(940\) 0 0
\(941\) 27770.0 0.962036 0.481018 − 0.876711i \(-0.340267\pi\)
0.481018 + 0.876711i \(0.340267\pi\)
\(942\) 0 0
\(943\) 64224.0 2.21784
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −42660.0 −1.46385 −0.731924 − 0.681386i \(-0.761377\pi\)
−0.731924 + 0.681386i \(0.761377\pi\)
\(948\) 0 0
\(949\) −2916.00 −0.0997443
\(950\) 0 0
\(951\) 10842.0 0.369691
\(952\) 0 0
\(953\) −16178.0 −0.549902 −0.274951 − 0.961458i \(-0.588662\pi\)
−0.274951 + 0.961458i \(0.588662\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 5400.00 0.182400
\(958\) 0 0
\(959\) −60408.0 −2.03407
\(960\) 0 0
\(961\) −18127.0 −0.608472
\(962\) 0 0
\(963\) −3564.00 −0.119261
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −52236.0 −1.73712 −0.868561 − 0.495583i \(-0.834955\pi\)
−0.868561 + 0.495583i \(0.834955\pi\)
\(968\) 0 0
\(969\) −2376.00 −0.0787700
\(970\) 0 0
\(971\) 12276.0 0.405722 0.202861 − 0.979208i \(-0.434976\pi\)
0.202861 + 0.979208i \(0.434976\pi\)
\(972\) 0 0
\(973\) 1296.00 0.0427008
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −12730.0 −0.416856 −0.208428 − 0.978038i \(-0.566835\pi\)
−0.208428 + 0.978038i \(0.566835\pi\)
\(978\) 0 0
\(979\) 12456.0 0.406635
\(980\) 0 0
\(981\) −11178.0 −0.363798
\(982\) 0 0
\(983\) 48744.0 1.58158 0.790789 − 0.612088i \(-0.209670\pi\)
0.790789 + 0.612088i \(0.209670\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −7776.00 −0.250773
\(988\) 0 0
\(989\) −36288.0 −1.16673
\(990\) 0 0
\(991\) 57852.0 1.85442 0.927210 − 0.374543i \(-0.122200\pi\)
0.927210 + 0.374543i \(0.122200\pi\)
\(992\) 0 0
\(993\) 2052.00 0.0655773
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 13210.0 0.419624 0.209812 − 0.977742i \(-0.432715\pi\)
0.209812 + 0.977742i \(0.432715\pi\)
\(998\) 0 0
\(999\) −5778.00 −0.182991
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 2400.4.a.l.1.1 1
4.3 odd 2 2400.4.a.k.1.1 1
5.4 even 2 96.4.a.a.1.1 ✓ 1
15.14 odd 2 288.4.a.k.1.1 1
20.19 odd 2 96.4.a.d.1.1 yes 1
40.19 odd 2 192.4.a.e.1.1 1
40.29 even 2 192.4.a.k.1.1 1
60.59 even 2 288.4.a.j.1.1 1
80.19 odd 4 768.4.d.p.385.2 2
80.29 even 4 768.4.d.a.385.1 2
80.59 odd 4 768.4.d.p.385.1 2
80.69 even 4 768.4.d.a.385.2 2
120.29 odd 2 576.4.a.f.1.1 1
120.59 even 2 576.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.4.a.a.1.1 ✓ 1 5.4 even 2
96.4.a.d.1.1 yes 1 20.19 odd 2
192.4.a.e.1.1 1 40.19 odd 2
192.4.a.k.1.1 1 40.29 even 2
288.4.a.j.1.1 1 60.59 even 2
288.4.a.k.1.1 1 15.14 odd 2
576.4.a.e.1.1 1 120.59 even 2
576.4.a.f.1.1 1 120.29 odd 2
768.4.d.a.385.1 2 80.29 even 4
768.4.d.a.385.2 2 80.69 even 4
768.4.d.p.385.1 2 80.59 odd 4
768.4.d.p.385.2 2 80.19 odd 4
2400.4.a.k.1.1 1 4.3 odd 2
2400.4.a.l.1.1 1 1.1 even 1 trivial