Properties

Label 1200.4.a.d.1.1
Level $1200$
Weight $4$
Character 1200.1
Self dual yes
Analytic conductor $70.802$
Analytic rank $1$
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] = [1200,4,Mod(1,1200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1200, 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("1200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.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: \(70.8022920069\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 300)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} -13.0000 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -13.0000 q^{7} +9.00000 q^{9} -6.00000 q^{11} -5.00000 q^{13} +78.0000 q^{17} -65.0000 q^{19} +39.0000 q^{21} +138.000 q^{23} -27.0000 q^{27} +66.0000 q^{29} -299.000 q^{31} +18.0000 q^{33} +214.000 q^{37} +15.0000 q^{39} +360.000 q^{41} +203.000 q^{43} +78.0000 q^{47} -174.000 q^{49} -234.000 q^{51} -636.000 q^{53} +195.000 q^{57} -786.000 q^{59} +467.000 q^{61} -117.000 q^{63} -217.000 q^{67} -414.000 q^{69} +360.000 q^{71} +286.000 q^{73} +78.0000 q^{77} -272.000 q^{79} +81.0000 q^{81} +498.000 q^{83} -198.000 q^{87} +65.0000 q^{91} +897.000 q^{93} +511.000 q^{97} -54.0000 q^{99} +O(q^{100})\)

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
\(7\) −13.0000 −0.701934 −0.350967 0.936388i \(-0.614147\pi\)
−0.350967 + 0.936388i \(0.614147\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −6.00000 −0.164461 −0.0822304 0.996613i \(-0.526204\pi\)
−0.0822304 + 0.996613i \(0.526204\pi\)
\(12\) 0 0
\(13\) −5.00000 −0.106673 −0.0533366 0.998577i \(-0.516986\pi\)
−0.0533366 + 0.998577i \(0.516986\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 78.0000 1.11281 0.556405 0.830911i \(-0.312180\pi\)
0.556405 + 0.830911i \(0.312180\pi\)
\(18\) 0 0
\(19\) −65.0000 −0.784843 −0.392422 0.919785i \(-0.628363\pi\)
−0.392422 + 0.919785i \(0.628363\pi\)
\(20\) 0 0
\(21\) 39.0000 0.405262
\(22\) 0 0
\(23\) 138.000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 66.0000 0.422617 0.211308 0.977419i \(-0.432228\pi\)
0.211308 + 0.977419i \(0.432228\pi\)
\(30\) 0 0
\(31\) −299.000 −1.73232 −0.866161 0.499765i \(-0.833420\pi\)
−0.866161 + 0.499765i \(0.833420\pi\)
\(32\) 0 0
\(33\) 18.0000 0.0949514
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 214.000 0.950848 0.475424 0.879757i \(-0.342295\pi\)
0.475424 + 0.879757i \(0.342295\pi\)
\(38\) 0 0
\(39\) 15.0000 0.0615878
\(40\) 0 0
\(41\) 360.000 1.37128 0.685641 0.727940i \(-0.259522\pi\)
0.685641 + 0.727940i \(0.259522\pi\)
\(42\) 0 0
\(43\) 203.000 0.719935 0.359968 0.932965i \(-0.382788\pi\)
0.359968 + 0.932965i \(0.382788\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 78.0000 0.242074 0.121037 0.992648i \(-0.461378\pi\)
0.121037 + 0.992648i \(0.461378\pi\)
\(48\) 0 0
\(49\) −174.000 −0.507289
\(50\) 0 0
\(51\) −234.000 −0.642481
\(52\) 0 0
\(53\) −636.000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 195.000 0.453129
\(58\) 0 0
\(59\) −786.000 −1.73438 −0.867191 0.497976i \(-0.834077\pi\)
−0.867191 + 0.497976i \(0.834077\pi\)
\(60\) 0 0
\(61\) 467.000 0.980217 0.490108 0.871662i \(-0.336957\pi\)
0.490108 + 0.871662i \(0.336957\pi\)
\(62\) 0 0
\(63\) −117.000 −0.233978
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −217.000 −0.395683 −0.197842 0.980234i \(-0.563393\pi\)
−0.197842 + 0.980234i \(0.563393\pi\)
\(68\) 0 0
\(69\) −414.000 −0.722315
\(70\) 0 0
\(71\) 360.000 0.601748 0.300874 0.953664i \(-0.402722\pi\)
0.300874 + 0.953664i \(0.402722\pi\)
\(72\) 0 0
\(73\) 286.000 0.458545 0.229272 0.973362i \(-0.426365\pi\)
0.229272 + 0.973362i \(0.426365\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 78.0000 0.115441
\(78\) 0 0
\(79\) −272.000 −0.387372 −0.193686 0.981064i \(-0.562044\pi\)
−0.193686 + 0.981064i \(0.562044\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 498.000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −198.000 −0.243998
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 65.0000 0.0748775
\(92\) 0 0
\(93\) 897.000 1.00016
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 511.000 0.534889 0.267444 0.963573i \(-0.413821\pi\)
0.267444 + 0.963573i \(0.413821\pi\)
\(98\) 0 0
\(99\) −54.0000 −0.0548202
\(100\) 0 0
\(101\) −1812.00 −1.78516 −0.892578 0.450893i \(-0.851106\pi\)
−0.892578 + 0.450893i \(0.851106\pi\)
\(102\) 0 0
\(103\) −1708.00 −1.63392 −0.816962 0.576691i \(-0.804344\pi\)
−0.816962 + 0.576691i \(0.804344\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1236.00 1.11672 0.558358 0.829600i \(-0.311432\pi\)
0.558358 + 0.829600i \(0.311432\pi\)
\(108\) 0 0
\(109\) −1543.00 −1.35590 −0.677948 0.735110i \(-0.737130\pi\)
−0.677948 + 0.735110i \(0.737130\pi\)
\(110\) 0 0
\(111\) −642.000 −0.548972
\(112\) 0 0
\(113\) −1884.00 −1.56842 −0.784212 0.620494i \(-0.786932\pi\)
−0.784212 + 0.620494i \(0.786932\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −45.0000 −0.0355577
\(118\) 0 0
\(119\) −1014.00 −0.781120
\(120\) 0 0
\(121\) −1295.00 −0.972953
\(122\) 0 0
\(123\) −1080.00 −0.791710
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2072.00 1.44772 0.723859 0.689948i \(-0.242366\pi\)
0.723859 + 0.689948i \(0.242366\pi\)
\(128\) 0 0
\(129\) −609.000 −0.415655
\(130\) 0 0
\(131\) 2508.00 1.67271 0.836355 0.548188i \(-0.184682\pi\)
0.836355 + 0.548188i \(0.184682\pi\)
\(132\) 0 0
\(133\) 845.000 0.550908
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1566.00 −0.976587 −0.488293 0.872679i \(-0.662380\pi\)
−0.488293 + 0.872679i \(0.662380\pi\)
\(138\) 0 0
\(139\) 196.000 0.119601 0.0598004 0.998210i \(-0.480954\pi\)
0.0598004 + 0.998210i \(0.480954\pi\)
\(140\) 0 0
\(141\) −234.000 −0.139761
\(142\) 0 0
\(143\) 30.0000 0.0175435
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 522.000 0.292883
\(148\) 0 0
\(149\) −1278.00 −0.702670 −0.351335 0.936250i \(-0.614272\pi\)
−0.351335 + 0.936250i \(0.614272\pi\)
\(150\) 0 0
\(151\) −1385.00 −0.746422 −0.373211 0.927747i \(-0.621743\pi\)
−0.373211 + 0.927747i \(0.621743\pi\)
\(152\) 0 0
\(153\) 702.000 0.370937
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 481.000 0.244509 0.122255 0.992499i \(-0.460988\pi\)
0.122255 + 0.992499i \(0.460988\pi\)
\(158\) 0 0
\(159\) 1908.00 0.951662
\(160\) 0 0
\(161\) −1794.00 −0.878180
\(162\) 0 0
\(163\) −2815.00 −1.35269 −0.676343 0.736587i \(-0.736436\pi\)
−0.676343 + 0.736587i \(0.736436\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1956.00 0.906346 0.453173 0.891423i \(-0.350292\pi\)
0.453173 + 0.891423i \(0.350292\pi\)
\(168\) 0 0
\(169\) −2172.00 −0.988621
\(170\) 0 0
\(171\) −585.000 −0.261614
\(172\) 0 0
\(173\) −2382.00 −1.04682 −0.523411 0.852081i \(-0.675341\pi\)
−0.523411 + 0.852081i \(0.675341\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2358.00 1.00135
\(178\) 0 0
\(179\) −4386.00 −1.83142 −0.915712 0.401834i \(-0.868373\pi\)
−0.915712 + 0.401834i \(0.868373\pi\)
\(180\) 0 0
\(181\) −2275.00 −0.934251 −0.467125 0.884191i \(-0.654710\pi\)
−0.467125 + 0.884191i \(0.654710\pi\)
\(182\) 0 0
\(183\) −1401.00 −0.565928
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −468.000 −0.183014
\(188\) 0 0
\(189\) 351.000 0.135087
\(190\) 0 0
\(191\) −714.000 −0.270488 −0.135244 0.990812i \(-0.543182\pi\)
−0.135244 + 0.990812i \(0.543182\pi\)
\(192\) 0 0
\(193\) −1547.00 −0.576971 −0.288486 0.957484i \(-0.593152\pi\)
−0.288486 + 0.957484i \(0.593152\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −438.000 −0.158407 −0.0792036 0.996858i \(-0.525238\pi\)
−0.0792036 + 0.996858i \(0.525238\pi\)
\(198\) 0 0
\(199\) −437.000 −0.155669 −0.0778344 0.996966i \(-0.524801\pi\)
−0.0778344 + 0.996966i \(0.524801\pi\)
\(200\) 0 0
\(201\) 651.000 0.228448
\(202\) 0 0
\(203\) −858.000 −0.296649
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1242.00 0.417029
\(208\) 0 0
\(209\) 390.000 0.129076
\(210\) 0 0
\(211\) −1625.00 −0.530188 −0.265094 0.964223i \(-0.585403\pi\)
−0.265094 + 0.964223i \(0.585403\pi\)
\(212\) 0 0
\(213\) −1080.00 −0.347420
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3887.00 1.21598
\(218\) 0 0
\(219\) −858.000 −0.264741
\(220\) 0 0
\(221\) −390.000 −0.118707
\(222\) 0 0
\(223\) 875.000 0.262755 0.131377 0.991332i \(-0.458060\pi\)
0.131377 + 0.991332i \(0.458060\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4680.00 −1.36838 −0.684191 0.729303i \(-0.739844\pi\)
−0.684191 + 0.729303i \(0.739844\pi\)
\(228\) 0 0
\(229\) 1469.00 0.423905 0.211953 0.977280i \(-0.432018\pi\)
0.211953 + 0.977280i \(0.432018\pi\)
\(230\) 0 0
\(231\) −234.000 −0.0666497
\(232\) 0 0
\(233\) −3960.00 −1.11343 −0.556713 0.830705i \(-0.687938\pi\)
−0.556713 + 0.830705i \(0.687938\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 816.000 0.223649
\(238\) 0 0
\(239\) −2652.00 −0.717756 −0.358878 0.933385i \(-0.616841\pi\)
−0.358878 + 0.933385i \(0.616841\pi\)
\(240\) 0 0
\(241\) 5753.00 1.53769 0.768845 0.639435i \(-0.220832\pi\)
0.768845 + 0.639435i \(0.220832\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 325.000 0.0837217
\(248\) 0 0
\(249\) −1494.00 −0.380235
\(250\) 0 0
\(251\) −3588.00 −0.902281 −0.451141 0.892453i \(-0.648983\pi\)
−0.451141 + 0.892453i \(0.648983\pi\)
\(252\) 0 0
\(253\) −828.000 −0.205755
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 564.000 0.136892 0.0684462 0.997655i \(-0.478196\pi\)
0.0684462 + 0.997655i \(0.478196\pi\)
\(258\) 0 0
\(259\) −2782.00 −0.667433
\(260\) 0 0
\(261\) 594.000 0.140872
\(262\) 0 0
\(263\) 1248.00 0.292604 0.146302 0.989240i \(-0.453263\pi\)
0.146302 + 0.989240i \(0.453263\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7266.00 −1.64690 −0.823450 0.567390i \(-0.807953\pi\)
−0.823450 + 0.567390i \(0.807953\pi\)
\(270\) 0 0
\(271\) −3224.00 −0.722672 −0.361336 0.932436i \(-0.617679\pi\)
−0.361336 + 0.932436i \(0.617679\pi\)
\(272\) 0 0
\(273\) −195.000 −0.0432305
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 151.000 0.0327535 0.0163767 0.999866i \(-0.494787\pi\)
0.0163767 + 0.999866i \(0.494787\pi\)
\(278\) 0 0
\(279\) −2691.00 −0.577441
\(280\) 0 0
\(281\) 7566.00 1.60623 0.803113 0.595826i \(-0.203175\pi\)
0.803113 + 0.595826i \(0.203175\pi\)
\(282\) 0 0
\(283\) 1469.00 0.308562 0.154281 0.988027i \(-0.450694\pi\)
0.154281 + 0.988027i \(0.450694\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4680.00 −0.962549
\(288\) 0 0
\(289\) 1171.00 0.238347
\(290\) 0 0
\(291\) −1533.00 −0.308818
\(292\) 0 0
\(293\) 306.000 0.0610127 0.0305063 0.999535i \(-0.490288\pi\)
0.0305063 + 0.999535i \(0.490288\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 162.000 0.0316505
\(298\) 0 0
\(299\) −690.000 −0.133457
\(300\) 0 0
\(301\) −2639.00 −0.505347
\(302\) 0 0
\(303\) 5436.00 1.03066
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4661.00 0.866506 0.433253 0.901272i \(-0.357366\pi\)
0.433253 + 0.901272i \(0.357366\pi\)
\(308\) 0 0
\(309\) 5124.00 0.943347
\(310\) 0 0
\(311\) −2514.00 −0.458379 −0.229189 0.973382i \(-0.573608\pi\)
−0.229189 + 0.973382i \(0.573608\pi\)
\(312\) 0 0
\(313\) −6707.00 −1.21119 −0.605594 0.795774i \(-0.707065\pi\)
−0.605594 + 0.795774i \(0.707065\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4632.00 −0.820691 −0.410345 0.911930i \(-0.634592\pi\)
−0.410345 + 0.911930i \(0.634592\pi\)
\(318\) 0 0
\(319\) −396.000 −0.0695039
\(320\) 0 0
\(321\) −3708.00 −0.644736
\(322\) 0 0
\(323\) −5070.00 −0.873382
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4629.00 0.782827
\(328\) 0 0
\(329\) −1014.00 −0.169920
\(330\) 0 0
\(331\) 988.000 0.164065 0.0820323 0.996630i \(-0.473859\pi\)
0.0820323 + 0.996630i \(0.473859\pi\)
\(332\) 0 0
\(333\) 1926.00 0.316949
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 9079.00 1.46755 0.733775 0.679392i \(-0.237756\pi\)
0.733775 + 0.679392i \(0.237756\pi\)
\(338\) 0 0
\(339\) 5652.00 0.905530
\(340\) 0 0
\(341\) 1794.00 0.284899
\(342\) 0 0
\(343\) 6721.00 1.05802
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5994.00 −0.927305 −0.463652 0.886017i \(-0.653461\pi\)
−0.463652 + 0.886017i \(0.653461\pi\)
\(348\) 0 0
\(349\) −286.000 −0.0438660 −0.0219330 0.999759i \(-0.506982\pi\)
−0.0219330 + 0.999759i \(0.506982\pi\)
\(350\) 0 0
\(351\) 135.000 0.0205293
\(352\) 0 0
\(353\) 11466.0 1.72882 0.864410 0.502787i \(-0.167692\pi\)
0.864410 + 0.502787i \(0.167692\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 3042.00 0.450980
\(358\) 0 0
\(359\) 624.000 0.0917367 0.0458683 0.998947i \(-0.485395\pi\)
0.0458683 + 0.998947i \(0.485395\pi\)
\(360\) 0 0
\(361\) −2634.00 −0.384021
\(362\) 0 0
\(363\) 3885.00 0.561734
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8477.00 1.20571 0.602855 0.797851i \(-0.294030\pi\)
0.602855 + 0.797851i \(0.294030\pi\)
\(368\) 0 0
\(369\) 3240.00 0.457094
\(370\) 0 0
\(371\) 8268.00 1.15702
\(372\) 0 0
\(373\) 11257.0 1.56264 0.781321 0.624130i \(-0.214546\pi\)
0.781321 + 0.624130i \(0.214546\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −330.000 −0.0450819
\(378\) 0 0
\(379\) 1213.00 0.164400 0.0822000 0.996616i \(-0.473805\pi\)
0.0822000 + 0.996616i \(0.473805\pi\)
\(380\) 0 0
\(381\) −6216.00 −0.835841
\(382\) 0 0
\(383\) −11076.0 −1.47769 −0.738847 0.673873i \(-0.764630\pi\)
−0.738847 + 0.673873i \(0.764630\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1827.00 0.239978
\(388\) 0 0
\(389\) −8016.00 −1.04480 −0.522400 0.852700i \(-0.674963\pi\)
−0.522400 + 0.852700i \(0.674963\pi\)
\(390\) 0 0
\(391\) 10764.0 1.39222
\(392\) 0 0
\(393\) −7524.00 −0.965739
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −6851.00 −0.866100 −0.433050 0.901370i \(-0.642563\pi\)
−0.433050 + 0.901370i \(0.642563\pi\)
\(398\) 0 0
\(399\) −2535.00 −0.318067
\(400\) 0 0
\(401\) 12636.0 1.57360 0.786798 0.617211i \(-0.211738\pi\)
0.786798 + 0.617211i \(0.211738\pi\)
\(402\) 0 0
\(403\) 1495.00 0.184792
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1284.00 −0.156377
\(408\) 0 0
\(409\) 10829.0 1.30919 0.654596 0.755979i \(-0.272839\pi\)
0.654596 + 0.755979i \(0.272839\pi\)
\(410\) 0 0
\(411\) 4698.00 0.563833
\(412\) 0 0
\(413\) 10218.0 1.21742
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −588.000 −0.0690515
\(418\) 0 0
\(419\) 6252.00 0.728950 0.364475 0.931213i \(-0.381248\pi\)
0.364475 + 0.931213i \(0.381248\pi\)
\(420\) 0 0
\(421\) −15730.0 −1.82098 −0.910491 0.413529i \(-0.864296\pi\)
−0.910491 + 0.413529i \(0.864296\pi\)
\(422\) 0 0
\(423\) 702.000 0.0806913
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6071.00 −0.688047
\(428\) 0 0
\(429\) −90.0000 −0.0101288
\(430\) 0 0
\(431\) 10062.0 1.12452 0.562262 0.826959i \(-0.309931\pi\)
0.562262 + 0.826959i \(0.309931\pi\)
\(432\) 0 0
\(433\) −707.000 −0.0784671 −0.0392335 0.999230i \(-0.512492\pi\)
−0.0392335 + 0.999230i \(0.512492\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8970.00 −0.981907
\(438\) 0 0
\(439\) 12493.0 1.35822 0.679110 0.734037i \(-0.262366\pi\)
0.679110 + 0.734037i \(0.262366\pi\)
\(440\) 0 0
\(441\) −1566.00 −0.169096
\(442\) 0 0
\(443\) −5928.00 −0.635774 −0.317887 0.948129i \(-0.602973\pi\)
−0.317887 + 0.948129i \(0.602973\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 3834.00 0.405687
\(448\) 0 0
\(449\) −2028.00 −0.213156 −0.106578 0.994304i \(-0.533989\pi\)
−0.106578 + 0.994304i \(0.533989\pi\)
\(450\) 0 0
\(451\) −2160.00 −0.225522
\(452\) 0 0
\(453\) 4155.00 0.430947
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17030.0 −1.74317 −0.871586 0.490242i \(-0.836908\pi\)
−0.871586 + 0.490242i \(0.836908\pi\)
\(458\) 0 0
\(459\) −2106.00 −0.214160
\(460\) 0 0
\(461\) −1044.00 −0.105475 −0.0527374 0.998608i \(-0.516795\pi\)
−0.0527374 + 0.998608i \(0.516795\pi\)
\(462\) 0 0
\(463\) 9704.00 0.974046 0.487023 0.873389i \(-0.338083\pi\)
0.487023 + 0.873389i \(0.338083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4194.00 −0.415579 −0.207789 0.978174i \(-0.566627\pi\)
−0.207789 + 0.978174i \(0.566627\pi\)
\(468\) 0 0
\(469\) 2821.00 0.277743
\(470\) 0 0
\(471\) −1443.00 −0.141168
\(472\) 0 0
\(473\) −1218.00 −0.118401
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −5724.00 −0.549442
\(478\) 0 0
\(479\) 12174.0 1.16126 0.580631 0.814167i \(-0.302806\pi\)
0.580631 + 0.814167i \(0.302806\pi\)
\(480\) 0 0
\(481\) −1070.00 −0.101430
\(482\) 0 0
\(483\) 5382.00 0.507018
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1651.00 −0.153622 −0.0768110 0.997046i \(-0.524474\pi\)
−0.0768110 + 0.997046i \(0.524474\pi\)
\(488\) 0 0
\(489\) 8445.00 0.780974
\(490\) 0 0
\(491\) 6456.00 0.593391 0.296696 0.954972i \(-0.404115\pi\)
0.296696 + 0.954972i \(0.404115\pi\)
\(492\) 0 0
\(493\) 5148.00 0.470293
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4680.00 −0.422388
\(498\) 0 0
\(499\) 559.000 0.0501489 0.0250744 0.999686i \(-0.492018\pi\)
0.0250744 + 0.999686i \(0.492018\pi\)
\(500\) 0 0
\(501\) −5868.00 −0.523279
\(502\) 0 0
\(503\) −14208.0 −1.25945 −0.629725 0.776818i \(-0.716832\pi\)
−0.629725 + 0.776818i \(0.716832\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6516.00 0.570781
\(508\) 0 0
\(509\) −8082.00 −0.703789 −0.351894 0.936040i \(-0.614462\pi\)
−0.351894 + 0.936040i \(0.614462\pi\)
\(510\) 0 0
\(511\) −3718.00 −0.321868
\(512\) 0 0
\(513\) 1755.00 0.151043
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −468.000 −0.0398116
\(518\) 0 0
\(519\) 7146.00 0.604383
\(520\) 0 0
\(521\) 20502.0 1.72401 0.862005 0.506900i \(-0.169209\pi\)
0.862005 + 0.506900i \(0.169209\pi\)
\(522\) 0 0
\(523\) 2069.00 0.172985 0.0864924 0.996253i \(-0.472434\pi\)
0.0864924 + 0.996253i \(0.472434\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23322.0 −1.92775
\(528\) 0 0
\(529\) 6877.00 0.565217
\(530\) 0 0
\(531\) −7074.00 −0.578127
\(532\) 0 0
\(533\) −1800.00 −0.146279
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 13158.0 1.05737
\(538\) 0 0
\(539\) 1044.00 0.0834291
\(540\) 0 0
\(541\) 1553.00 0.123417 0.0617086 0.998094i \(-0.480345\pi\)
0.0617086 + 0.998094i \(0.480345\pi\)
\(542\) 0 0
\(543\) 6825.00 0.539390
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12584.0 0.983643 0.491822 0.870696i \(-0.336331\pi\)
0.491822 + 0.870696i \(0.336331\pi\)
\(548\) 0 0
\(549\) 4203.00 0.326739
\(550\) 0 0
\(551\) −4290.00 −0.331688
\(552\) 0 0
\(553\) 3536.00 0.271910
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20754.0 −1.57877 −0.789385 0.613898i \(-0.789601\pi\)
−0.789385 + 0.613898i \(0.789601\pi\)
\(558\) 0 0
\(559\) −1015.00 −0.0767977
\(560\) 0 0
\(561\) 1404.00 0.105663
\(562\) 0 0
\(563\) 14370.0 1.07571 0.537854 0.843038i \(-0.319235\pi\)
0.537854 + 0.843038i \(0.319235\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1053.00 −0.0779927
\(568\) 0 0
\(569\) 15774.0 1.16218 0.581090 0.813839i \(-0.302626\pi\)
0.581090 + 0.813839i \(0.302626\pi\)
\(570\) 0 0
\(571\) 3055.00 0.223902 0.111951 0.993714i \(-0.464290\pi\)
0.111951 + 0.993714i \(0.464290\pi\)
\(572\) 0 0
\(573\) 2142.00 0.156166
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 25021.0 1.80526 0.902632 0.430412i \(-0.141632\pi\)
0.902632 + 0.430412i \(0.141632\pi\)
\(578\) 0 0
\(579\) 4641.00 0.333115
\(580\) 0 0
\(581\) −6474.00 −0.462284
\(582\) 0 0
\(583\) 3816.00 0.271085
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18828.0 −1.32388 −0.661938 0.749559i \(-0.730266\pi\)
−0.661938 + 0.749559i \(0.730266\pi\)
\(588\) 0 0
\(589\) 19435.0 1.35960
\(590\) 0 0
\(591\) 1314.00 0.0914564
\(592\) 0 0
\(593\) −19968.0 −1.38278 −0.691389 0.722483i \(-0.743001\pi\)
−0.691389 + 0.722483i \(0.743001\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1311.00 0.0898755
\(598\) 0 0
\(599\) −9684.00 −0.660563 −0.330282 0.943882i \(-0.607144\pi\)
−0.330282 + 0.943882i \(0.607144\pi\)
\(600\) 0 0
\(601\) 23243.0 1.57754 0.788770 0.614688i \(-0.210718\pi\)
0.788770 + 0.614688i \(0.210718\pi\)
\(602\) 0 0
\(603\) −1953.00 −0.131894
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −22984.0 −1.53689 −0.768445 0.639916i \(-0.778969\pi\)
−0.768445 + 0.639916i \(0.778969\pi\)
\(608\) 0 0
\(609\) 2574.00 0.171271
\(610\) 0 0
\(611\) −390.000 −0.0258228
\(612\) 0 0
\(613\) −13754.0 −0.906230 −0.453115 0.891452i \(-0.649687\pi\)
−0.453115 + 0.891452i \(0.649687\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9468.00 −0.617775 −0.308888 0.951099i \(-0.599957\pi\)
−0.308888 + 0.951099i \(0.599957\pi\)
\(618\) 0 0
\(619\) 28099.0 1.82455 0.912273 0.409582i \(-0.134326\pi\)
0.912273 + 0.409582i \(0.134326\pi\)
\(620\) 0 0
\(621\) −3726.00 −0.240772
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1170.00 −0.0745220
\(628\) 0 0
\(629\) 16692.0 1.05811
\(630\) 0 0
\(631\) −14807.0 −0.934164 −0.467082 0.884214i \(-0.654695\pi\)
−0.467082 + 0.884214i \(0.654695\pi\)
\(632\) 0 0
\(633\) 4875.00 0.306104
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 870.000 0.0541141
\(638\) 0 0
\(639\) 3240.00 0.200583
\(640\) 0 0
\(641\) 20844.0 1.28438 0.642191 0.766545i \(-0.278026\pi\)
0.642191 + 0.766545i \(0.278026\pi\)
\(642\) 0 0
\(643\) 3692.00 0.226436 0.113218 0.993570i \(-0.463884\pi\)
0.113218 + 0.993570i \(0.463884\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20004.0 −1.21552 −0.607758 0.794123i \(-0.707931\pi\)
−0.607758 + 0.794123i \(0.707931\pi\)
\(648\) 0 0
\(649\) 4716.00 0.285238
\(650\) 0 0
\(651\) −11661.0 −0.702044
\(652\) 0 0
\(653\) 17862.0 1.07044 0.535218 0.844714i \(-0.320230\pi\)
0.535218 + 0.844714i \(0.320230\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2574.00 0.152848
\(658\) 0 0
\(659\) −18552.0 −1.09664 −0.548318 0.836270i \(-0.684732\pi\)
−0.548318 + 0.836270i \(0.684732\pi\)
\(660\) 0 0
\(661\) −12382.0 −0.728599 −0.364300 0.931282i \(-0.618692\pi\)
−0.364300 + 0.931282i \(0.618692\pi\)
\(662\) 0 0
\(663\) 1170.00 0.0685355
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 9108.00 0.528730
\(668\) 0 0
\(669\) −2625.00 −0.151702
\(670\) 0 0
\(671\) −2802.00 −0.161207
\(672\) 0 0
\(673\) 1690.00 0.0967975 0.0483987 0.998828i \(-0.484588\pi\)
0.0483987 + 0.998828i \(0.484588\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5682.00 −0.322566 −0.161283 0.986908i \(-0.551563\pi\)
−0.161283 + 0.986908i \(0.551563\pi\)
\(678\) 0 0
\(679\) −6643.00 −0.375456
\(680\) 0 0
\(681\) 14040.0 0.790035
\(682\) 0 0
\(683\) 31512.0 1.76541 0.882704 0.469930i \(-0.155721\pi\)
0.882704 + 0.469930i \(0.155721\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −4407.00 −0.244742
\(688\) 0 0
\(689\) 3180.00 0.175832
\(690\) 0 0
\(691\) −20648.0 −1.13674 −0.568370 0.822773i \(-0.692426\pi\)
−0.568370 + 0.822773i \(0.692426\pi\)
\(692\) 0 0
\(693\) 702.000 0.0384802
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 28080.0 1.52598
\(698\) 0 0
\(699\) 11880.0 0.642837
\(700\) 0 0
\(701\) −11874.0 −0.639764 −0.319882 0.947457i \(-0.603643\pi\)
−0.319882 + 0.947457i \(0.603643\pi\)
\(702\) 0 0
\(703\) −13910.0 −0.746267
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 23556.0 1.25306
\(708\) 0 0
\(709\) −10699.0 −0.566727 −0.283363 0.959013i \(-0.591450\pi\)
−0.283363 + 0.959013i \(0.591450\pi\)
\(710\) 0 0
\(711\) −2448.00 −0.129124
\(712\) 0 0
\(713\) −41262.0 −2.16728
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 7956.00 0.414396
\(718\) 0 0
\(719\) 5598.00 0.290362 0.145181 0.989405i \(-0.453624\pi\)
0.145181 + 0.989405i \(0.453624\pi\)
\(720\) 0 0
\(721\) 22204.0 1.14691
\(722\) 0 0
\(723\) −17259.0 −0.887786
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 22859.0 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 15834.0 0.801151
\(732\) 0 0
\(733\) 31642.0 1.59444 0.797220 0.603689i \(-0.206303\pi\)
0.797220 + 0.603689i \(0.206303\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1302.00 0.0650743
\(738\) 0 0
\(739\) 12220.0 0.608281 0.304141 0.952627i \(-0.401631\pi\)
0.304141 + 0.952627i \(0.401631\pi\)
\(740\) 0 0
\(741\) −975.000 −0.0483367
\(742\) 0 0
\(743\) 17892.0 0.883437 0.441719 0.897154i \(-0.354369\pi\)
0.441719 + 0.897154i \(0.354369\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 4482.00 0.219529
\(748\) 0 0
\(749\) −16068.0 −0.783861
\(750\) 0 0
\(751\) 16648.0 0.808914 0.404457 0.914557i \(-0.367461\pi\)
0.404457 + 0.914557i \(0.367461\pi\)
\(752\) 0 0
\(753\) 10764.0 0.520932
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −31733.0 −1.52359 −0.761794 0.647820i \(-0.775681\pi\)
−0.761794 + 0.647820i \(0.775681\pi\)
\(758\) 0 0
\(759\) 2484.00 0.118792
\(760\) 0 0
\(761\) −10068.0 −0.479586 −0.239793 0.970824i \(-0.577080\pi\)
−0.239793 + 0.970824i \(0.577080\pi\)
\(762\) 0 0
\(763\) 20059.0 0.951749
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3930.00 0.185012
\(768\) 0 0
\(769\) 24323.0 1.14058 0.570292 0.821442i \(-0.306830\pi\)
0.570292 + 0.821442i \(0.306830\pi\)
\(770\) 0 0
\(771\) −1692.00 −0.0790349
\(772\) 0 0
\(773\) 2184.00 0.101621 0.0508105 0.998708i \(-0.483820\pi\)
0.0508105 + 0.998708i \(0.483820\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 8346.00 0.385342
\(778\) 0 0
\(779\) −23400.0 −1.07624
\(780\) 0 0
\(781\) −2160.00 −0.0989640
\(782\) 0 0
\(783\) −1782.00 −0.0813327
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −37531.0 −1.69992 −0.849959 0.526849i \(-0.823373\pi\)
−0.849959 + 0.526849i \(0.823373\pi\)
\(788\) 0 0
\(789\) −3744.00 −0.168935
\(790\) 0 0
\(791\) 24492.0 1.10093
\(792\) 0 0
\(793\) −2335.00 −0.104563
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −28644.0 −1.27305 −0.636526 0.771255i \(-0.719629\pi\)
−0.636526 + 0.771255i \(0.719629\pi\)
\(798\) 0 0
\(799\) 6084.00 0.269382
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1716.00 −0.0754126
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 21798.0 0.950838
\(808\) 0 0
\(809\) −17316.0 −0.752532 −0.376266 0.926512i \(-0.622792\pi\)
−0.376266 + 0.926512i \(0.622792\pi\)
\(810\) 0 0
\(811\) −425.000 −0.0184017 −0.00920084 0.999958i \(-0.502929\pi\)
−0.00920084 + 0.999958i \(0.502929\pi\)
\(812\) 0 0
\(813\) 9672.00 0.417235
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −13195.0 −0.565036
\(818\) 0 0
\(819\) 585.000 0.0249592
\(820\) 0 0
\(821\) −25194.0 −1.07098 −0.535491 0.844541i \(-0.679874\pi\)
−0.535491 + 0.844541i \(0.679874\pi\)
\(822\) 0 0
\(823\) −33961.0 −1.43840 −0.719202 0.694801i \(-0.755492\pi\)
−0.719202 + 0.694801i \(0.755492\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1956.00 −0.0822452 −0.0411226 0.999154i \(-0.513093\pi\)
−0.0411226 + 0.999154i \(0.513093\pi\)
\(828\) 0 0
\(829\) −47302.0 −1.98174 −0.990872 0.134803i \(-0.956960\pi\)
−0.990872 + 0.134803i \(0.956960\pi\)
\(830\) 0 0
\(831\) −453.000 −0.0189102
\(832\) 0 0
\(833\) −13572.0 −0.564516
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 8073.00 0.333386
\(838\) 0 0
\(839\) −30726.0 −1.26434 −0.632169 0.774831i \(-0.717835\pi\)
−0.632169 + 0.774831i \(0.717835\pi\)
\(840\) 0 0
\(841\) −20033.0 −0.821395
\(842\) 0 0
\(843\) −22698.0 −0.927355
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 16835.0 0.682949
\(848\) 0 0
\(849\) −4407.00 −0.178148
\(850\) 0 0
\(851\) 29532.0 1.18959
\(852\) 0 0
\(853\) 34489.0 1.38439 0.692193 0.721713i \(-0.256645\pi\)
0.692193 + 0.721713i \(0.256645\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −8484.00 −0.338166 −0.169083 0.985602i \(-0.554081\pi\)
−0.169083 + 0.985602i \(0.554081\pi\)
\(858\) 0 0
\(859\) 520.000 0.0206544 0.0103272 0.999947i \(-0.496713\pi\)
0.0103272 + 0.999947i \(0.496713\pi\)
\(860\) 0 0
\(861\) 14040.0 0.555728
\(862\) 0 0
\(863\) −6864.00 −0.270745 −0.135373 0.990795i \(-0.543223\pi\)
−0.135373 + 0.990795i \(0.543223\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −3513.00 −0.137610
\(868\) 0 0
\(869\) 1632.00 0.0637075
\(870\) 0 0
\(871\) 1085.00 0.0422088
\(872\) 0 0
\(873\) 4599.00 0.178296
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 38857.0 1.49613 0.748066 0.663624i \(-0.230983\pi\)
0.748066 + 0.663624i \(0.230983\pi\)
\(878\) 0 0
\(879\) −918.000 −0.0352257
\(880\) 0 0
\(881\) −10080.0 −0.385475 −0.192738 0.981250i \(-0.561737\pi\)
−0.192738 + 0.981250i \(0.561737\pi\)
\(882\) 0 0
\(883\) −34549.0 −1.31672 −0.658362 0.752702i \(-0.728750\pi\)
−0.658362 + 0.752702i \(0.728750\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −18798.0 −0.711584 −0.355792 0.934565i \(-0.615789\pi\)
−0.355792 + 0.934565i \(0.615789\pi\)
\(888\) 0 0
\(889\) −26936.0 −1.01620
\(890\) 0 0
\(891\) −486.000 −0.0182734
\(892\) 0 0
\(893\) −5070.00 −0.189990
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2070.00 0.0770516
\(898\) 0 0
\(899\) −19734.0 −0.732109
\(900\) 0 0
\(901\) −49608.0 −1.83428
\(902\) 0 0
\(903\) 7917.00 0.291762
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 50276.0 1.84056 0.920280 0.391261i \(-0.127961\pi\)
0.920280 + 0.391261i \(0.127961\pi\)
\(908\) 0 0
\(909\) −16308.0 −0.595052
\(910\) 0 0
\(911\) 20502.0 0.745622 0.372811 0.927907i \(-0.378394\pi\)
0.372811 + 0.927907i \(0.378394\pi\)
\(912\) 0 0
\(913\) −2988.00 −0.108311
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −32604.0 −1.17413
\(918\) 0 0
\(919\) −37817.0 −1.35742 −0.678709 0.734407i \(-0.737460\pi\)
−0.678709 + 0.734407i \(0.737460\pi\)
\(920\) 0 0
\(921\) −13983.0 −0.500277
\(922\) 0 0
\(923\) −1800.00 −0.0641904
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −15372.0 −0.544642
\(928\) 0 0
\(929\) −11778.0 −0.415957 −0.207978 0.978133i \(-0.566688\pi\)
−0.207978 + 0.978133i \(0.566688\pi\)
\(930\) 0 0
\(931\) 11310.0 0.398142
\(932\) 0 0
\(933\) 7542.00 0.264645
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 18409.0 0.641831 0.320916 0.947108i \(-0.396009\pi\)
0.320916 + 0.947108i \(0.396009\pi\)
\(938\) 0 0
\(939\) 20121.0 0.699280
\(940\) 0 0
\(941\) −9330.00 −0.323219 −0.161610 0.986855i \(-0.551669\pi\)
−0.161610 + 0.986855i \(0.551669\pi\)
\(942\) 0 0
\(943\) 49680.0 1.71559
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 49146.0 1.68641 0.843205 0.537592i \(-0.180666\pi\)
0.843205 + 0.537592i \(0.180666\pi\)
\(948\) 0 0
\(949\) −1430.00 −0.0489144
\(950\) 0 0
\(951\) 13896.0 0.473826
\(952\) 0 0
\(953\) 5928.00 0.201497 0.100749 0.994912i \(-0.467876\pi\)
0.100749 + 0.994912i \(0.467876\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1188.00 0.0401281
\(958\) 0 0
\(959\) 20358.0 0.685500
\(960\) 0 0
\(961\) 59610.0 2.00094
\(962\) 0 0
\(963\) 11124.0 0.372239
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −9520.00 −0.316590 −0.158295 0.987392i \(-0.550600\pi\)
−0.158295 + 0.987392i \(0.550600\pi\)
\(968\) 0 0
\(969\) 15210.0 0.504247
\(970\) 0 0
\(971\) −12558.0 −0.415042 −0.207521 0.978231i \(-0.566539\pi\)
−0.207521 + 0.978231i \(0.566539\pi\)
\(972\) 0 0
\(973\) −2548.00 −0.0839518
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 46206.0 1.51306 0.756531 0.653958i \(-0.226893\pi\)
0.756531 + 0.653958i \(0.226893\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −13887.0 −0.451965
\(982\) 0 0
\(983\) −32676.0 −1.06023 −0.530113 0.847927i \(-0.677851\pi\)
−0.530113 + 0.847927i \(0.677851\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3042.00 0.0981033
\(988\) 0 0
\(989\) 28014.0 0.900701
\(990\) 0 0
\(991\) 8137.00 0.260828 0.130414 0.991460i \(-0.458369\pi\)
0.130414 + 0.991460i \(0.458369\pi\)
\(992\) 0 0
\(993\) −2964.00 −0.0947228
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −18578.0 −0.590142 −0.295071 0.955475i \(-0.595343\pi\)
−0.295071 + 0.955475i \(0.595343\pi\)
\(998\) 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 1200.4.a.d.1.1 1
4.3 odd 2 300.4.a.h.1.1 yes 1
5.2 odd 4 1200.4.f.k.49.2 2
5.3 odd 4 1200.4.f.k.49.1 2
5.4 even 2 1200.4.a.bi.1.1 1
12.11 even 2 900.4.a.l.1.1 1
20.3 even 4 300.4.d.c.49.2 2
20.7 even 4 300.4.d.c.49.1 2
20.19 odd 2 300.4.a.a.1.1 1
60.23 odd 4 900.4.d.e.649.1 2
60.47 odd 4 900.4.d.e.649.2 2
60.59 even 2 900.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.4.a.a.1.1 1 20.19 odd 2
300.4.a.h.1.1 yes 1 4.3 odd 2
300.4.d.c.49.1 2 20.7 even 4
300.4.d.c.49.2 2 20.3 even 4
900.4.a.f.1.1 1 60.59 even 2
900.4.a.l.1.1 1 12.11 even 2
900.4.d.e.649.1 2 60.23 odd 4
900.4.d.e.649.2 2 60.47 odd 4
1200.4.a.d.1.1 1 1.1 even 1 trivial
1200.4.a.bi.1.1 1 5.4 even 2
1200.4.f.k.49.1 2 5.3 odd 4
1200.4.f.k.49.2 2 5.2 odd 4