Properties

Label 396.4.a.h.1.2
Level $396$
Weight $4$
Character 396.1
Self dual yes
Analytic conductor $23.365$
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] = [396,4,Mod(1,396)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(396, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("396.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 396.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: \(23.3647563623\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{31}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 31 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(5.56776\) of defining polynomial
Character \(\chi\) \(=\) 396.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.13553 q^{5} -0.864471 q^{7} +O(q^{10})\) \(q+5.13553 q^{5} -0.864471 q^{7} +11.0000 q^{11} +51.6776 q^{13} -52.8132 q^{17} -56.2711 q^{19} +211.949 q^{23} -98.6263 q^{25} +174.542 q^{29} +211.897 q^{31} -4.43952 q^{35} -86.9816 q^{37} +151.084 q^{41} -74.0000 q^{43} +163.509 q^{47} -342.253 q^{49} +539.099 q^{53} +56.4908 q^{55} +365.187 q^{59} +499.912 q^{61} +265.392 q^{65} +189.421 q^{67} +751.744 q^{71} +352.374 q^{73} -9.50918 q^{77} -319.678 q^{79} +811.018 q^{83} -271.224 q^{85} -1103.18 q^{89} -44.6738 q^{91} -288.982 q^{95} -551.758 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 12 q^{5} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 12 q^{5} - 24 q^{7} + 22 q^{11} - 8 q^{13} + 28 q^{17} - 68 q^{19} + 268 q^{23} + 70 q^{25} + 260 q^{29} + 112 q^{31} + 392 q^{35} + 316 q^{37} + 124 q^{41} - 148 q^{43} + 572 q^{47} - 150 q^{49} + 76 q^{53} - 132 q^{55} + 864 q^{59} - 136 q^{61} + 1288 q^{65} - 512 q^{67} + 724 q^{71} + 972 q^{73} - 264 q^{77} - 528 q^{79} + 2112 q^{83} - 1656 q^{85} + 288 q^{89} + 1336 q^{91} - 88 q^{95} + 500 q^{97}+O(q^{100}) \) 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
\(5\) 5.13553 0.459336 0.229668 0.973269i \(-0.426236\pi\)
0.229668 + 0.973269i \(0.426236\pi\)
\(6\) 0 0
\(7\) −0.864471 −0.0466771 −0.0233385 0.999728i \(-0.507430\pi\)
−0.0233385 + 0.999728i \(0.507430\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) 51.6776 1.10252 0.551262 0.834333i \(-0.314147\pi\)
0.551262 + 0.834333i \(0.314147\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −52.8132 −0.753475 −0.376738 0.926320i \(-0.622954\pi\)
−0.376738 + 0.926320i \(0.622954\pi\)
\(18\) 0 0
\(19\) −56.2711 −0.679446 −0.339723 0.940526i \(-0.610333\pi\)
−0.339723 + 0.940526i \(0.610333\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 211.949 1.92149 0.960747 0.277426i \(-0.0894814\pi\)
0.960747 + 0.277426i \(0.0894814\pi\)
\(24\) 0 0
\(25\) −98.6263 −0.789011
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 174.542 1.11764 0.558822 0.829288i \(-0.311254\pi\)
0.558822 + 0.829288i \(0.311254\pi\)
\(30\) 0 0
\(31\) 211.897 1.22767 0.613837 0.789433i \(-0.289625\pi\)
0.613837 + 0.789433i \(0.289625\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.43952 −0.0214404
\(36\) 0 0
\(37\) −86.9816 −0.386478 −0.193239 0.981152i \(-0.561899\pi\)
−0.193239 + 0.981152i \(0.561899\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 151.084 0.575497 0.287749 0.957706i \(-0.407093\pi\)
0.287749 + 0.957706i \(0.407093\pi\)
\(42\) 0 0
\(43\) −74.0000 −0.262439 −0.131220 0.991353i \(-0.541889\pi\)
−0.131220 + 0.991353i \(0.541889\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 163.509 0.507452 0.253726 0.967276i \(-0.418344\pi\)
0.253726 + 0.967276i \(0.418344\pi\)
\(48\) 0 0
\(49\) −342.253 −0.997821
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 539.099 1.39719 0.698594 0.715519i \(-0.253810\pi\)
0.698594 + 0.715519i \(0.253810\pi\)
\(54\) 0 0
\(55\) 56.4908 0.138495
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 365.187 0.805818 0.402909 0.915240i \(-0.367999\pi\)
0.402909 + 0.915240i \(0.367999\pi\)
\(60\) 0 0
\(61\) 499.912 1.04930 0.524649 0.851319i \(-0.324197\pi\)
0.524649 + 0.851319i \(0.324197\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 265.392 0.506428
\(66\) 0 0
\(67\) 189.421 0.345395 0.172698 0.984975i \(-0.444752\pi\)
0.172698 + 0.984975i \(0.444752\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 751.744 1.25656 0.628278 0.777989i \(-0.283760\pi\)
0.628278 + 0.777989i \(0.283760\pi\)
\(72\) 0 0
\(73\) 352.374 0.564962 0.282481 0.959273i \(-0.408843\pi\)
0.282481 + 0.959273i \(0.408843\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.50918 −0.0140737
\(78\) 0 0
\(79\) −319.678 −0.455273 −0.227636 0.973746i \(-0.573100\pi\)
−0.227636 + 0.973746i \(0.573100\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 811.018 1.07254 0.536270 0.844046i \(-0.319833\pi\)
0.536270 + 0.844046i \(0.319833\pi\)
\(84\) 0 0
\(85\) −271.224 −0.346098
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1103.18 −1.31390 −0.656948 0.753936i \(-0.728153\pi\)
−0.656948 + 0.753936i \(0.728153\pi\)
\(90\) 0 0
\(91\) −44.6738 −0.0514625
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −288.982 −0.312094
\(96\) 0 0
\(97\) −551.758 −0.577552 −0.288776 0.957397i \(-0.593248\pi\)
−0.288776 + 0.957397i \(0.593248\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 196.476 0.193566 0.0967828 0.995306i \(-0.469145\pi\)
0.0967828 + 0.995306i \(0.469145\pi\)
\(102\) 0 0
\(103\) 261.832 0.250476 0.125238 0.992127i \(-0.460031\pi\)
0.125238 + 0.992127i \(0.460031\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1393.68 1.25918 0.629591 0.776926i \(-0.283222\pi\)
0.629591 + 0.776926i \(0.283222\pi\)
\(108\) 0 0
\(109\) −190.491 −0.167392 −0.0836959 0.996491i \(-0.526672\pi\)
−0.0836959 + 0.996491i \(0.526672\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 226.095 0.188223 0.0941116 0.995562i \(-0.469999\pi\)
0.0941116 + 0.995562i \(0.469999\pi\)
\(114\) 0 0
\(115\) 1088.47 0.882611
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 45.6555 0.0351700
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1148.44 −0.821756
\(126\) 0 0
\(127\) −2585.70 −1.80664 −0.903322 0.428964i \(-0.858879\pi\)
−0.903322 + 0.428964i \(0.858879\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1867.55 −1.24556 −0.622779 0.782398i \(-0.713997\pi\)
−0.622779 + 0.782398i \(0.713997\pi\)
\(132\) 0 0
\(133\) 48.6447 0.0317145
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1447.56 −0.902726 −0.451363 0.892340i \(-0.649062\pi\)
−0.451363 + 0.892340i \(0.649062\pi\)
\(138\) 0 0
\(139\) 298.513 0.182155 0.0910775 0.995844i \(-0.470969\pi\)
0.0910775 + 0.995844i \(0.470969\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 568.454 0.332423
\(144\) 0 0
\(145\) 896.366 0.513373
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3240.09 −1.78147 −0.890735 0.454524i \(-0.849809\pi\)
−0.890735 + 0.454524i \(0.849809\pi\)
\(150\) 0 0
\(151\) 169.875 0.0915513 0.0457757 0.998952i \(-0.485424\pi\)
0.0457757 + 0.998952i \(0.485424\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1088.21 0.563914
\(156\) 0 0
\(157\) 2622.42 1.33307 0.666536 0.745473i \(-0.267776\pi\)
0.666536 + 0.745473i \(0.267776\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −183.224 −0.0896897
\(162\) 0 0
\(163\) −684.879 −0.329103 −0.164552 0.986368i \(-0.552618\pi\)
−0.164552 + 0.986368i \(0.552618\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1302.51 −0.603538 −0.301769 0.953381i \(-0.597577\pi\)
−0.301769 + 0.953381i \(0.597577\pi\)
\(168\) 0 0
\(169\) 473.579 0.215557
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3157.79 −1.38776 −0.693881 0.720090i \(-0.744100\pi\)
−0.693881 + 0.720090i \(0.744100\pi\)
\(174\) 0 0
\(175\) 85.2596 0.0368287
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −843.619 −0.352263 −0.176131 0.984367i \(-0.556358\pi\)
−0.176131 + 0.984367i \(0.556358\pi\)
\(180\) 0 0
\(181\) −2539.42 −1.04284 −0.521419 0.853301i \(-0.674597\pi\)
−0.521419 + 0.853301i \(0.674597\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −446.697 −0.177523
\(186\) 0 0
\(187\) −580.945 −0.227181
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 365.883 0.138609 0.0693046 0.997596i \(-0.477922\pi\)
0.0693046 + 0.997596i \(0.477922\pi\)
\(192\) 0 0
\(193\) −1566.10 −0.584096 −0.292048 0.956404i \(-0.594337\pi\)
−0.292048 + 0.956404i \(0.594337\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2487.39 −0.899591 −0.449795 0.893132i \(-0.648503\pi\)
−0.449795 + 0.893132i \(0.648503\pi\)
\(198\) 0 0
\(199\) 4288.44 1.52764 0.763818 0.645432i \(-0.223323\pi\)
0.763818 + 0.645432i \(0.223323\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −150.887 −0.0521683
\(204\) 0 0
\(205\) 775.897 0.264346
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −618.982 −0.204861
\(210\) 0 0
\(211\) −1667.95 −0.544200 −0.272100 0.962269i \(-0.587718\pi\)
−0.272100 + 0.962269i \(0.587718\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −380.029 −0.120548
\(216\) 0 0
\(217\) −183.179 −0.0573042
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2729.26 −0.830724
\(222\) 0 0
\(223\) −301.479 −0.0905316 −0.0452658 0.998975i \(-0.514413\pi\)
−0.0452658 + 0.998975i \(0.514413\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1153.01 0.337128 0.168564 0.985691i \(-0.446087\pi\)
0.168564 + 0.985691i \(0.446087\pi\)
\(228\) 0 0
\(229\) 495.861 0.143089 0.0715445 0.997437i \(-0.477207\pi\)
0.0715445 + 0.997437i \(0.477207\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5009.50 −1.40851 −0.704256 0.709946i \(-0.748719\pi\)
−0.704256 + 0.709946i \(0.748719\pi\)
\(234\) 0 0
\(235\) 839.706 0.233091
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1971.52 0.533585 0.266792 0.963754i \(-0.414036\pi\)
0.266792 + 0.963754i \(0.414036\pi\)
\(240\) 0 0
\(241\) −5622.20 −1.50273 −0.751365 0.659887i \(-0.770604\pi\)
−0.751365 + 0.659887i \(0.770604\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1757.65 −0.458335
\(246\) 0 0
\(247\) −2907.96 −0.749104
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2142.29 0.538725 0.269362 0.963039i \(-0.413187\pi\)
0.269362 + 0.963039i \(0.413187\pi\)
\(252\) 0 0
\(253\) 2331.44 0.579352
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1393.29 −0.338175 −0.169088 0.985601i \(-0.554082\pi\)
−0.169088 + 0.985601i \(0.554082\pi\)
\(258\) 0 0
\(259\) 75.1931 0.0180397
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7244.29 1.69849 0.849244 0.528001i \(-0.177058\pi\)
0.849244 + 0.528001i \(0.177058\pi\)
\(264\) 0 0
\(265\) 2768.56 0.641778
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3082.48 0.698670 0.349335 0.936998i \(-0.386407\pi\)
0.349335 + 0.936998i \(0.386407\pi\)
\(270\) 0 0
\(271\) 5463.79 1.22473 0.612365 0.790575i \(-0.290218\pi\)
0.612365 + 0.790575i \(0.290218\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1084.89 −0.237896
\(276\) 0 0
\(277\) 2395.43 0.519593 0.259797 0.965663i \(-0.416344\pi\)
0.259797 + 0.965663i \(0.416344\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6345.21 1.34706 0.673529 0.739161i \(-0.264778\pi\)
0.673529 + 0.739161i \(0.264778\pi\)
\(282\) 0 0
\(283\) −6903.80 −1.45014 −0.725068 0.688677i \(-0.758192\pi\)
−0.725068 + 0.688677i \(0.758192\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −130.608 −0.0268625
\(288\) 0 0
\(289\) −2123.77 −0.432275
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7349.12 −1.46532 −0.732662 0.680592i \(-0.761723\pi\)
−0.732662 + 0.680592i \(0.761723\pi\)
\(294\) 0 0
\(295\) 1875.43 0.370141
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 10953.0 2.11849
\(300\) 0 0
\(301\) 63.9709 0.0122499
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2567.31 0.481980
\(306\) 0 0
\(307\) 621.325 0.115508 0.0577539 0.998331i \(-0.481606\pi\)
0.0577539 + 0.998331i \(0.481606\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 674.748 0.123027 0.0615136 0.998106i \(-0.480407\pi\)
0.0615136 + 0.998106i \(0.480407\pi\)
\(312\) 0 0
\(313\) −367.510 −0.0663670 −0.0331835 0.999449i \(-0.510565\pi\)
−0.0331835 + 0.999449i \(0.510565\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3027.35 −0.536381 −0.268190 0.963366i \(-0.586426\pi\)
−0.268190 + 0.963366i \(0.586426\pi\)
\(318\) 0 0
\(319\) 1919.96 0.336982
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2971.85 0.511945
\(324\) 0 0
\(325\) −5096.78 −0.869903
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −141.349 −0.0236864
\(330\) 0 0
\(331\) 8180.62 1.35845 0.679226 0.733930i \(-0.262316\pi\)
0.679226 + 0.733930i \(0.262316\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 972.778 0.158652
\(336\) 0 0
\(337\) 8582.67 1.38732 0.693662 0.720301i \(-0.255996\pi\)
0.693662 + 0.720301i \(0.255996\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2330.87 0.370158
\(342\) 0 0
\(343\) 592.381 0.0932524
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 169.435 0.0262125 0.0131063 0.999914i \(-0.495828\pi\)
0.0131063 + 0.999914i \(0.495828\pi\)
\(348\) 0 0
\(349\) −6107.13 −0.936697 −0.468349 0.883544i \(-0.655151\pi\)
−0.468349 + 0.883544i \(0.655151\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10191.0 1.53658 0.768292 0.640100i \(-0.221107\pi\)
0.768292 + 0.640100i \(0.221107\pi\)
\(354\) 0 0
\(355\) 3860.60 0.577181
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13015.3 1.91343 0.956716 0.291025i \(-0.0939962\pi\)
0.956716 + 0.291025i \(0.0939962\pi\)
\(360\) 0 0
\(361\) −3692.57 −0.538354
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1809.63 0.259507
\(366\) 0 0
\(367\) −7541.19 −1.07261 −0.536303 0.844025i \(-0.680180\pi\)
−0.536303 + 0.844025i \(0.680180\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −466.035 −0.0652166
\(372\) 0 0
\(373\) −3186.02 −0.442268 −0.221134 0.975243i \(-0.570976\pi\)
−0.221134 + 0.975243i \(0.570976\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9019.93 1.23223
\(378\) 0 0
\(379\) −10641.9 −1.44232 −0.721159 0.692769i \(-0.756390\pi\)
−0.721159 + 0.692769i \(0.756390\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1845.84 −0.246261 −0.123130 0.992391i \(-0.539293\pi\)
−0.123130 + 0.992391i \(0.539293\pi\)
\(384\) 0 0
\(385\) −48.8347 −0.00646454
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4615.33 0.601560 0.300780 0.953694i \(-0.402753\pi\)
0.300780 + 0.953694i \(0.402753\pi\)
\(390\) 0 0
\(391\) −11193.7 −1.44780
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1641.71 −0.209123
\(396\) 0 0
\(397\) 10168.0 1.28544 0.642719 0.766102i \(-0.277806\pi\)
0.642719 + 0.766102i \(0.277806\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9577.61 −1.19273 −0.596363 0.802715i \(-0.703388\pi\)
−0.596363 + 0.802715i \(0.703388\pi\)
\(402\) 0 0
\(403\) 10950.4 1.35354
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −956.798 −0.116528
\(408\) 0 0
\(409\) −3895.73 −0.470981 −0.235491 0.971877i \(-0.575670\pi\)
−0.235491 + 0.971877i \(0.575670\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −315.694 −0.0376132
\(414\) 0 0
\(415\) 4165.01 0.492656
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 163.208 0.0190292 0.00951462 0.999955i \(-0.496971\pi\)
0.00951462 + 0.999955i \(0.496971\pi\)
\(420\) 0 0
\(421\) 13611.6 1.57574 0.787871 0.615841i \(-0.211183\pi\)
0.787871 + 0.615841i \(0.211183\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5208.77 0.594500
\(426\) 0 0
\(427\) −432.160 −0.0489781
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 309.524 0.0345922 0.0172961 0.999850i \(-0.494494\pi\)
0.0172961 + 0.999850i \(0.494494\pi\)
\(432\) 0 0
\(433\) 11406.1 1.26592 0.632960 0.774185i \(-0.281840\pi\)
0.632960 + 0.774185i \(0.281840\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −11926.6 −1.30555
\(438\) 0 0
\(439\) −16541.7 −1.79838 −0.899192 0.437554i \(-0.855845\pi\)
−0.899192 + 0.437554i \(0.855845\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3728.94 0.399926 0.199963 0.979803i \(-0.435918\pi\)
0.199963 + 0.979803i \(0.435918\pi\)
\(444\) 0 0
\(445\) −5665.41 −0.603519
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3344.45 −0.351524 −0.175762 0.984433i \(-0.556239\pi\)
−0.175762 + 0.984433i \(0.556239\pi\)
\(450\) 0 0
\(451\) 1661.93 0.173519
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −229.424 −0.0236386
\(456\) 0 0
\(457\) −16692.1 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8755.78 0.884593 0.442297 0.896869i \(-0.354164\pi\)
0.442297 + 0.896869i \(0.354164\pi\)
\(462\) 0 0
\(463\) 11017.1 1.10585 0.552924 0.833232i \(-0.313512\pi\)
0.552924 + 0.833232i \(0.313512\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3146.12 0.311746 0.155873 0.987777i \(-0.450181\pi\)
0.155873 + 0.987777i \(0.450181\pi\)
\(468\) 0 0
\(469\) −163.749 −0.0161220
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −814.000 −0.0791285
\(474\) 0 0
\(475\) 5549.81 0.536090
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1789.35 −0.170683 −0.0853417 0.996352i \(-0.527198\pi\)
−0.0853417 + 0.996352i \(0.527198\pi\)
\(480\) 0 0
\(481\) −4495.01 −0.426101
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2833.57 −0.265290
\(486\) 0 0
\(487\) 7891.84 0.734319 0.367160 0.930158i \(-0.380330\pi\)
0.367160 + 0.930158i \(0.380330\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12340.1 −1.13422 −0.567111 0.823641i \(-0.691939\pi\)
−0.567111 + 0.823641i \(0.691939\pi\)
\(492\) 0 0
\(493\) −9218.12 −0.842116
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −649.861 −0.0586524
\(498\) 0 0
\(499\) 13615.4 1.22146 0.610732 0.791837i \(-0.290875\pi\)
0.610732 + 0.791837i \(0.290875\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4092.13 −0.362742 −0.181371 0.983415i \(-0.558053\pi\)
−0.181371 + 0.983415i \(0.558053\pi\)
\(504\) 0 0
\(505\) 1009.01 0.0889115
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −18821.2 −1.63897 −0.819483 0.573104i \(-0.805739\pi\)
−0.819483 + 0.573104i \(0.805739\pi\)
\(510\) 0 0
\(511\) −304.617 −0.0263708
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1344.64 0.115053
\(516\) 0 0
\(517\) 1798.60 0.153003
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6851.87 −0.576172 −0.288086 0.957605i \(-0.593019\pi\)
−0.288086 + 0.957605i \(0.593019\pi\)
\(522\) 0 0
\(523\) −20338.2 −1.70043 −0.850216 0.526433i \(-0.823529\pi\)
−0.850216 + 0.526433i \(0.823529\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11191.0 −0.925022
\(528\) 0 0
\(529\) 32755.3 2.69214
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7807.68 0.634499
\(534\) 0 0
\(535\) 7157.31 0.578388
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3764.78 −0.300854
\(540\) 0 0
\(541\) −6446.58 −0.512311 −0.256155 0.966636i \(-0.582456\pi\)
−0.256155 + 0.966636i \(0.582456\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −978.271 −0.0768890
\(546\) 0 0
\(547\) −20285.9 −1.58567 −0.792834 0.609438i \(-0.791395\pi\)
−0.792834 + 0.609438i \(0.791395\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9821.67 −0.759378
\(552\) 0 0
\(553\) 276.352 0.0212508
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18441.2 −1.40284 −0.701418 0.712750i \(-0.747449\pi\)
−0.701418 + 0.712750i \(0.747449\pi\)
\(558\) 0 0
\(559\) −3824.15 −0.289345
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20335.0 −1.52224 −0.761118 0.648614i \(-0.775349\pi\)
−0.761118 + 0.648614i \(0.775349\pi\)
\(564\) 0 0
\(565\) 1161.12 0.0864576
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22960.4 1.69165 0.845825 0.533460i \(-0.179109\pi\)
0.845825 + 0.533460i \(0.179109\pi\)
\(570\) 0 0
\(571\) −13239.5 −0.970323 −0.485161 0.874425i \(-0.661239\pi\)
−0.485161 + 0.874425i \(0.661239\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −20903.7 −1.51608
\(576\) 0 0
\(577\) −11439.5 −0.825361 −0.412681 0.910876i \(-0.635407\pi\)
−0.412681 + 0.910876i \(0.635407\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −701.102 −0.0500630
\(582\) 0 0
\(583\) 5930.09 0.421268
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8474.43 −0.595873 −0.297936 0.954586i \(-0.596298\pi\)
−0.297936 + 0.954586i \(0.596298\pi\)
\(588\) 0 0
\(589\) −11923.7 −0.834138
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16321.7 1.13027 0.565136 0.824998i \(-0.308824\pi\)
0.565136 + 0.824998i \(0.308824\pi\)
\(594\) 0 0
\(595\) 234.465 0.0161548
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11407.4 −0.778117 −0.389059 0.921213i \(-0.627200\pi\)
−0.389059 + 0.921213i \(0.627200\pi\)
\(600\) 0 0
\(601\) 22493.8 1.52669 0.763347 0.645989i \(-0.223555\pi\)
0.763347 + 0.645989i \(0.223555\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 621.399 0.0417578
\(606\) 0 0
\(607\) 14720.9 0.984354 0.492177 0.870495i \(-0.336201\pi\)
0.492177 + 0.870495i \(0.336201\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8449.77 0.559478
\(612\) 0 0
\(613\) −10291.2 −0.678068 −0.339034 0.940774i \(-0.610100\pi\)
−0.339034 + 0.940774i \(0.610100\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5682.09 −0.370750 −0.185375 0.982668i \(-0.559350\pi\)
−0.185375 + 0.982668i \(0.559350\pi\)
\(618\) 0 0
\(619\) 19433.1 1.26184 0.630922 0.775847i \(-0.282677\pi\)
0.630922 + 0.775847i \(0.282677\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 953.667 0.0613288
\(624\) 0 0
\(625\) 6430.45 0.411549
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4593.78 0.291202
\(630\) 0 0
\(631\) −15008.3 −0.946863 −0.473432 0.880831i \(-0.656985\pi\)
−0.473432 + 0.880831i \(0.656985\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −13278.9 −0.829856
\(636\) 0 0
\(637\) −17686.8 −1.10012
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 26697.2 1.64505 0.822524 0.568731i \(-0.192565\pi\)
0.822524 + 0.568731i \(0.192565\pi\)
\(642\) 0 0
\(643\) −17052.5 −1.04586 −0.522928 0.852377i \(-0.675161\pi\)
−0.522928 + 0.852377i \(0.675161\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −19430.9 −1.18069 −0.590345 0.807151i \(-0.701008\pi\)
−0.590345 + 0.807151i \(0.701008\pi\)
\(648\) 0 0
\(649\) 4017.06 0.242963
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13484.8 −0.808116 −0.404058 0.914733i \(-0.632401\pi\)
−0.404058 + 0.914733i \(0.632401\pi\)
\(654\) 0 0
\(655\) −9590.83 −0.572130
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −23752.4 −1.40404 −0.702020 0.712157i \(-0.747718\pi\)
−0.702020 + 0.712157i \(0.747718\pi\)
\(660\) 0 0
\(661\) 22078.0 1.29914 0.649571 0.760301i \(-0.274949\pi\)
0.649571 + 0.760301i \(0.274949\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 249.816 0.0145676
\(666\) 0 0
\(667\) 36994.0 2.14754
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5499.03 0.316375
\(672\) 0 0
\(673\) −20273.4 −1.16119 −0.580595 0.814192i \(-0.697180\pi\)
−0.580595 + 0.814192i \(0.697180\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −25947.6 −1.47304 −0.736519 0.676417i \(-0.763532\pi\)
−0.736519 + 0.676417i \(0.763532\pi\)
\(678\) 0 0
\(679\) 476.979 0.0269584
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9293.09 0.520630 0.260315 0.965524i \(-0.416174\pi\)
0.260315 + 0.965524i \(0.416174\pi\)
\(684\) 0 0
\(685\) −7433.99 −0.414654
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 27859.4 1.54043
\(690\) 0 0
\(691\) 2879.37 0.158518 0.0792592 0.996854i \(-0.474745\pi\)
0.0792592 + 0.996854i \(0.474745\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1533.02 0.0836703
\(696\) 0 0
\(697\) −7979.24 −0.433623
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14194.6 −0.764795 −0.382398 0.923998i \(-0.624902\pi\)
−0.382398 + 0.923998i \(0.624902\pi\)
\(702\) 0 0
\(703\) 4894.55 0.262591
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −169.848 −0.00903507
\(708\) 0 0
\(709\) −19233.2 −1.01879 −0.509393 0.860534i \(-0.670130\pi\)
−0.509393 + 0.860534i \(0.670130\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 44911.4 2.35897
\(714\) 0 0
\(715\) 2919.31 0.152694
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32319.6 1.67638 0.838190 0.545378i \(-0.183614\pi\)
0.838190 + 0.545378i \(0.183614\pi\)
\(720\) 0 0
\(721\) −226.346 −0.0116915
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −17214.5 −0.881833
\(726\) 0 0
\(727\) 26551.7 1.35454 0.677268 0.735737i \(-0.263164\pi\)
0.677268 + 0.735737i \(0.263164\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3908.17 0.197742
\(732\) 0 0
\(733\) 31494.5 1.58701 0.793504 0.608565i \(-0.208255\pi\)
0.793504 + 0.608565i \(0.208255\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2083.63 0.104141
\(738\) 0 0
\(739\) 14450.0 0.719283 0.359642 0.933091i \(-0.382899\pi\)
0.359642 + 0.933091i \(0.382899\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −11693.6 −0.577383 −0.288692 0.957422i \(-0.593220\pi\)
−0.288692 + 0.957422i \(0.593220\pi\)
\(744\) 0 0
\(745\) −16639.6 −0.818292
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1204.80 −0.0587750
\(750\) 0 0
\(751\) −1082.31 −0.0525888 −0.0262944 0.999654i \(-0.508371\pi\)
−0.0262944 + 0.999654i \(0.508371\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 872.399 0.0420528
\(756\) 0 0
\(757\) 3150.38 0.151258 0.0756291 0.997136i \(-0.475904\pi\)
0.0756291 + 0.997136i \(0.475904\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16026.3 0.763406 0.381703 0.924285i \(-0.375338\pi\)
0.381703 + 0.924285i \(0.375338\pi\)
\(762\) 0 0
\(763\) 164.674 0.00781336
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18872.0 0.888433
\(768\) 0 0
\(769\) −24674.3 −1.15706 −0.578528 0.815662i \(-0.696373\pi\)
−0.578528 + 0.815662i \(0.696373\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 28881.8 1.34386 0.671932 0.740613i \(-0.265465\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(774\) 0 0
\(775\) −20898.7 −0.968648
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8501.67 −0.391019
\(780\) 0 0
\(781\) 8269.18 0.378866
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 13467.5 0.612327
\(786\) 0 0
\(787\) −24240.9 −1.09796 −0.548981 0.835835i \(-0.684984\pi\)
−0.548981 + 0.835835i \(0.684984\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −195.453 −0.00878571
\(792\) 0 0
\(793\) 25834.3 1.15688
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1476.34 0.0656145 0.0328072 0.999462i \(-0.489555\pi\)
0.0328072 + 0.999462i \(0.489555\pi\)
\(798\) 0 0
\(799\) −8635.44 −0.382353
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3876.11 0.170342
\(804\) 0 0
\(805\) −940.950 −0.0411977
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 36215.0 1.57386 0.786930 0.617042i \(-0.211669\pi\)
0.786930 + 0.617042i \(0.211669\pi\)
\(810\) 0 0
\(811\) −36279.6 −1.57084 −0.785419 0.618964i \(-0.787553\pi\)
−0.785419 + 0.618964i \(0.787553\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3517.22 −0.151169
\(816\) 0 0
\(817\) 4164.06 0.178313
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 15206.6 0.646422 0.323211 0.946327i \(-0.395238\pi\)
0.323211 + 0.946327i \(0.395238\pi\)
\(822\) 0 0
\(823\) −15023.1 −0.636296 −0.318148 0.948041i \(-0.603061\pi\)
−0.318148 + 0.948041i \(0.603061\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1108.16 0.0465957 0.0232978 0.999729i \(-0.492583\pi\)
0.0232978 + 0.999729i \(0.492583\pi\)
\(828\) 0 0
\(829\) 37519.7 1.57191 0.785955 0.618283i \(-0.212172\pi\)
0.785955 + 0.618283i \(0.212172\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 18075.5 0.751833
\(834\) 0 0
\(835\) −6689.05 −0.277227
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −112.813 −0.00464210 −0.00232105 0.999997i \(-0.500739\pi\)
−0.00232105 + 0.999997i \(0.500739\pi\)
\(840\) 0 0
\(841\) 6075.95 0.249127
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2432.08 0.0990130
\(846\) 0 0
\(847\) −104.601 −0.00424337
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −18435.6 −0.742615
\(852\) 0 0
\(853\) −15005.7 −0.602326 −0.301163 0.953573i \(-0.597375\pi\)
−0.301163 + 0.953573i \(0.597375\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16517.0 0.658353 0.329177 0.944268i \(-0.393229\pi\)
0.329177 + 0.944268i \(0.393229\pi\)
\(858\) 0 0
\(859\) 21272.5 0.844945 0.422473 0.906376i \(-0.361162\pi\)
0.422473 + 0.906376i \(0.361162\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1173.70 −0.0462959 −0.0231479 0.999732i \(-0.507369\pi\)
−0.0231479 + 0.999732i \(0.507369\pi\)
\(864\) 0 0
\(865\) −16216.9 −0.637448
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −3516.45 −0.137270
\(870\) 0 0
\(871\) 9788.84 0.380806
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 992.793 0.0383572
\(876\) 0 0
\(877\) 5338.75 0.205561 0.102780 0.994704i \(-0.467226\pi\)
0.102780 + 0.994704i \(0.467226\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 21936.8 0.838898 0.419449 0.907779i \(-0.362223\pi\)
0.419449 + 0.907779i \(0.362223\pi\)
\(882\) 0 0
\(883\) 30167.4 1.14973 0.574866 0.818247i \(-0.305054\pi\)
0.574866 + 0.818247i \(0.305054\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22302.6 −0.844250 −0.422125 0.906538i \(-0.638716\pi\)
−0.422125 + 0.906538i \(0.638716\pi\)
\(888\) 0 0
\(889\) 2235.26 0.0843288
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −9200.83 −0.344786
\(894\) 0 0
\(895\) −4332.43 −0.161807
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 36985.0 1.37210
\(900\) 0 0
\(901\) −28471.5 −1.05275
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −13041.3 −0.479013
\(906\) 0 0
\(907\) −1261.17 −0.0461704 −0.0230852 0.999734i \(-0.507349\pi\)
−0.0230852 + 0.999734i \(0.507349\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 33089.3 1.20340 0.601700 0.798722i \(-0.294490\pi\)
0.601700 + 0.798722i \(0.294490\pi\)
\(912\) 0 0
\(913\) 8921.20 0.323383
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1614.44 0.0581390
\(918\) 0 0
\(919\) −43973.8 −1.57841 −0.789207 0.614128i \(-0.789508\pi\)
−0.789207 + 0.614128i \(0.789508\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 38848.3 1.38538
\(924\) 0 0
\(925\) 8578.68 0.304935
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 51539.4 1.82019 0.910093 0.414403i \(-0.136010\pi\)
0.910093 + 0.414403i \(0.136010\pi\)
\(930\) 0 0
\(931\) 19258.9 0.677965
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2983.46 −0.104352
\(936\) 0 0
\(937\) −4384.73 −0.152874 −0.0764369 0.997074i \(-0.524354\pi\)
−0.0764369 + 0.997074i \(0.524354\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 23862.3 0.826663 0.413332 0.910581i \(-0.364365\pi\)
0.413332 + 0.910581i \(0.364365\pi\)
\(942\) 0 0
\(943\) 32022.1 1.10581
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −33377.7 −1.14533 −0.572666 0.819789i \(-0.694091\pi\)
−0.572666 + 0.819789i \(0.694091\pi\)
\(948\) 0 0
\(949\) 18209.8 0.622883
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −25097.9 −0.853095 −0.426547 0.904465i \(-0.640270\pi\)
−0.426547 + 0.904465i \(0.640270\pi\)
\(954\) 0 0
\(955\) 1879.00 0.0636681
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1251.37 0.0421366
\(960\) 0 0
\(961\) 15109.5 0.507184
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −8042.76 −0.268296
\(966\) 0 0
\(967\) 963.547 0.0320430 0.0160215 0.999872i \(-0.494900\pi\)
0.0160215 + 0.999872i \(0.494900\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −28702.2 −0.948607 −0.474304 0.880361i \(-0.657300\pi\)
−0.474304 + 0.880361i \(0.657300\pi\)
\(972\) 0 0
\(973\) −258.056 −0.00850246
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −18696.2 −0.612226 −0.306113 0.951995i \(-0.599028\pi\)
−0.306113 + 0.951995i \(0.599028\pi\)
\(978\) 0 0
\(979\) −12135.0 −0.396155
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −35820.2 −1.16224 −0.581122 0.813817i \(-0.697386\pi\)
−0.581122 + 0.813817i \(0.697386\pi\)
\(984\) 0 0
\(985\) −12774.1 −0.413214
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −15684.2 −0.504276
\(990\) 0 0
\(991\) 32090.3 1.02864 0.514320 0.857598i \(-0.328044\pi\)
0.514320 + 0.857598i \(0.328044\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 22023.4 0.701697
\(996\) 0 0
\(997\) 3963.89 0.125915 0.0629577 0.998016i \(-0.479947\pi\)
0.0629577 + 0.998016i \(0.479947\pi\)
\(998\) 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 396.4.a.h.1.2 2
3.2 odd 2 396.4.a.j.1.1 yes 2
4.3 odd 2 1584.4.a.y.1.2 2
12.11 even 2 1584.4.a.bi.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
396.4.a.h.1.2 2 1.1 even 1 trivial
396.4.a.j.1.1 yes 2 3.2 odd 2
1584.4.a.y.1.2 2 4.3 odd 2
1584.4.a.bi.1.1 2 12.11 even 2