Properties

Label 6012.2.a.j.1.3
Level $6012$
Weight $2$
Character 6012.1
Self dual yes
Analytic conductor $48.006$
Analytic rank $1$
Dimension $10$
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] = [6012,2,Mod(1,6012)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6012.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.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: \(48.0060616952\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 26x^{8} + 82x^{7} + 211x^{6} - 340x^{5} - 593x^{4} + 192x^{3} + 423x^{2} + 126x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.20804\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.55061 q^{5} -2.20804 q^{7} +O(q^{10})\) \(q-3.55061 q^{5} -2.20804 q^{7} -4.03191 q^{11} +0.294662 q^{13} +7.93181 q^{17} +1.66885 q^{19} +4.24235 q^{23} +7.60685 q^{25} -5.37239 q^{29} -5.91837 q^{31} +7.83988 q^{35} +6.66478 q^{37} +6.87811 q^{41} +11.6835 q^{43} -11.6994 q^{47} -2.12457 q^{49} -1.71086 q^{53} +14.3157 q^{55} -7.53719 q^{59} +2.37266 q^{61} -1.04623 q^{65} +8.92029 q^{67} -14.2771 q^{71} +11.0170 q^{73} +8.90260 q^{77} +8.32039 q^{79} +0.974422 q^{83} -28.1628 q^{85} +13.4831 q^{89} -0.650624 q^{91} -5.92546 q^{95} +12.4003 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 6 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 6 q^{5} + 4 q^{7} - 8 q^{11} - 2 q^{13} - 6 q^{17} - 20 q^{23} + 24 q^{25} - 8 q^{29} - 4 q^{31} - 4 q^{37} + 14 q^{41} + 20 q^{43} - 48 q^{47} - 2 q^{49} - 22 q^{53} - 6 q^{55} - 2 q^{59} - 8 q^{61} - 28 q^{65} - 6 q^{67} - 20 q^{71} + 20 q^{73} - 24 q^{77} - 4 q^{79} - 46 q^{83} - 18 q^{85} + 8 q^{89} + 28 q^{91} - 36 q^{95} - 34 q^{97}+O(q^{100}) \) 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
\(5\) −3.55061 −1.58788 −0.793941 0.607995i \(-0.791974\pi\)
−0.793941 + 0.607995i \(0.791974\pi\)
\(6\) 0 0
\(7\) −2.20804 −0.834559 −0.417280 0.908778i \(-0.637016\pi\)
−0.417280 + 0.908778i \(0.637016\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.03191 −1.21567 −0.607833 0.794065i \(-0.707961\pi\)
−0.607833 + 0.794065i \(0.707961\pi\)
\(12\) 0 0
\(13\) 0.294662 0.0817245 0.0408623 0.999165i \(-0.486990\pi\)
0.0408623 + 0.999165i \(0.486990\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.93181 1.92375 0.961874 0.273494i \(-0.0881793\pi\)
0.961874 + 0.273494i \(0.0881793\pi\)
\(18\) 0 0
\(19\) 1.66885 0.382862 0.191431 0.981506i \(-0.438687\pi\)
0.191431 + 0.981506i \(0.438687\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.24235 0.884591 0.442295 0.896869i \(-0.354164\pi\)
0.442295 + 0.896869i \(0.354164\pi\)
\(24\) 0 0
\(25\) 7.60685 1.52137
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.37239 −0.997628 −0.498814 0.866709i \(-0.666231\pi\)
−0.498814 + 0.866709i \(0.666231\pi\)
\(30\) 0 0
\(31\) −5.91837 −1.06297 −0.531486 0.847067i \(-0.678366\pi\)
−0.531486 + 0.847067i \(0.678366\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.83988 1.32518
\(36\) 0 0
\(37\) 6.66478 1.09568 0.547841 0.836582i \(-0.315450\pi\)
0.547841 + 0.836582i \(0.315450\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.87811 1.07418 0.537090 0.843525i \(-0.319524\pi\)
0.537090 + 0.843525i \(0.319524\pi\)
\(42\) 0 0
\(43\) 11.6835 1.78171 0.890857 0.454285i \(-0.150105\pi\)
0.890857 + 0.454285i \(0.150105\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.6994 −1.70654 −0.853270 0.521470i \(-0.825384\pi\)
−0.853270 + 0.521470i \(0.825384\pi\)
\(48\) 0 0
\(49\) −2.12457 −0.303511
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.71086 −0.235005 −0.117502 0.993073i \(-0.537489\pi\)
−0.117502 + 0.993073i \(0.537489\pi\)
\(54\) 0 0
\(55\) 14.3157 1.93033
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.53719 −0.981258 −0.490629 0.871369i \(-0.663233\pi\)
−0.490629 + 0.871369i \(0.663233\pi\)
\(60\) 0 0
\(61\) 2.37266 0.303788 0.151894 0.988397i \(-0.451463\pi\)
0.151894 + 0.988397i \(0.451463\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.04623 −0.129769
\(66\) 0 0
\(67\) 8.92029 1.08979 0.544893 0.838505i \(-0.316570\pi\)
0.544893 + 0.838505i \(0.316570\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14.2771 −1.69438 −0.847191 0.531289i \(-0.821708\pi\)
−0.847191 + 0.531289i \(0.821708\pi\)
\(72\) 0 0
\(73\) 11.0170 1.28944 0.644719 0.764419i \(-0.276974\pi\)
0.644719 + 0.764419i \(0.276974\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 8.90260 1.01454
\(78\) 0 0
\(79\) 8.32039 0.936117 0.468058 0.883698i \(-0.344954\pi\)
0.468058 + 0.883698i \(0.344954\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.974422 0.106957 0.0534784 0.998569i \(-0.482969\pi\)
0.0534784 + 0.998569i \(0.482969\pi\)
\(84\) 0 0
\(85\) −28.1628 −3.05468
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.4831 1.42920 0.714602 0.699531i \(-0.246608\pi\)
0.714602 + 0.699531i \(0.246608\pi\)
\(90\) 0 0
\(91\) −0.650624 −0.0682040
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.92546 −0.607939
\(96\) 0 0
\(97\) 12.4003 1.25906 0.629532 0.776974i \(-0.283247\pi\)
0.629532 + 0.776974i \(0.283247\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.93174 0.590230 0.295115 0.955462i \(-0.404642\pi\)
0.295115 + 0.955462i \(0.404642\pi\)
\(102\) 0 0
\(103\) −14.1541 −1.39465 −0.697324 0.716756i \(-0.745626\pi\)
−0.697324 + 0.716756i \(0.745626\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.93955 0.187503 0.0937517 0.995596i \(-0.470114\pi\)
0.0937517 + 0.995596i \(0.470114\pi\)
\(108\) 0 0
\(109\) −10.8243 −1.03678 −0.518391 0.855144i \(-0.673469\pi\)
−0.518391 + 0.855144i \(0.673469\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.4515 −1.07727 −0.538635 0.842539i \(-0.681060\pi\)
−0.538635 + 0.842539i \(0.681060\pi\)
\(114\) 0 0
\(115\) −15.0629 −1.40463
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −17.5137 −1.60548
\(120\) 0 0
\(121\) 5.25626 0.477842
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.25591 −0.827874
\(126\) 0 0
\(127\) 2.28212 0.202506 0.101253 0.994861i \(-0.467715\pi\)
0.101253 + 0.994861i \(0.467715\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −22.0903 −1.93004 −0.965020 0.262177i \(-0.915559\pi\)
−0.965020 + 0.262177i \(0.915559\pi\)
\(132\) 0 0
\(133\) −3.68489 −0.319521
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.3823 −0.972452 −0.486226 0.873833i \(-0.661627\pi\)
−0.486226 + 0.873833i \(0.661627\pi\)
\(138\) 0 0
\(139\) −2.21711 −0.188053 −0.0940266 0.995570i \(-0.529974\pi\)
−0.0940266 + 0.995570i \(0.529974\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.18805 −0.0993497
\(144\) 0 0
\(145\) 19.0753 1.58412
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.96062 −0.734083 −0.367041 0.930205i \(-0.619629\pi\)
−0.367041 + 0.930205i \(0.619629\pi\)
\(150\) 0 0
\(151\) 6.29768 0.512498 0.256249 0.966611i \(-0.417513\pi\)
0.256249 + 0.966611i \(0.417513\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 21.0139 1.68787
\(156\) 0 0
\(157\) 3.25805 0.260021 0.130010 0.991513i \(-0.458499\pi\)
0.130010 + 0.991513i \(0.458499\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −9.36726 −0.738243
\(162\) 0 0
\(163\) −4.09781 −0.320965 −0.160483 0.987039i \(-0.551305\pi\)
−0.160483 + 0.987039i \(0.551305\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −12.9132 −0.993321
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.21336 −0.168279 −0.0841394 0.996454i \(-0.526814\pi\)
−0.0841394 + 0.996454i \(0.526814\pi\)
\(174\) 0 0
\(175\) −16.7962 −1.26967
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.1599 −0.908871 −0.454436 0.890780i \(-0.650159\pi\)
−0.454436 + 0.890780i \(0.650159\pi\)
\(180\) 0 0
\(181\) −11.7837 −0.875874 −0.437937 0.899006i \(-0.644291\pi\)
−0.437937 + 0.899006i \(0.644291\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −23.6640 −1.73982
\(186\) 0 0
\(187\) −31.9803 −2.33863
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.28053 0.382086 0.191043 0.981582i \(-0.438813\pi\)
0.191043 + 0.981582i \(0.438813\pi\)
\(192\) 0 0
\(193\) −2.96897 −0.213711 −0.106855 0.994275i \(-0.534078\pi\)
−0.106855 + 0.994275i \(0.534078\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.6973 −1.04714 −0.523571 0.851982i \(-0.675400\pi\)
−0.523571 + 0.851982i \(0.675400\pi\)
\(198\) 0 0
\(199\) −8.70190 −0.616861 −0.308431 0.951247i \(-0.599804\pi\)
−0.308431 + 0.951247i \(0.599804\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 11.8624 0.832579
\(204\) 0 0
\(205\) −24.4215 −1.70567
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6.72866 −0.465431
\(210\) 0 0
\(211\) −3.97823 −0.273873 −0.136936 0.990580i \(-0.543726\pi\)
−0.136936 + 0.990580i \(0.543726\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −41.4835 −2.82915
\(216\) 0 0
\(217\) 13.0680 0.887113
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.33720 0.157217
\(222\) 0 0
\(223\) 22.0052 1.47358 0.736790 0.676121i \(-0.236341\pi\)
0.736790 + 0.676121i \(0.236341\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.76931 −0.250178 −0.125089 0.992146i \(-0.539922\pi\)
−0.125089 + 0.992146i \(0.539922\pi\)
\(228\) 0 0
\(229\) −17.1199 −1.13132 −0.565658 0.824640i \(-0.691378\pi\)
−0.565658 + 0.824640i \(0.691378\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.0631 1.31438 0.657190 0.753725i \(-0.271745\pi\)
0.657190 + 0.753725i \(0.271745\pi\)
\(234\) 0 0
\(235\) 41.5402 2.70978
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.7343 −0.759029 −0.379515 0.925186i \(-0.623909\pi\)
−0.379515 + 0.925186i \(0.623909\pi\)
\(240\) 0 0
\(241\) −29.8701 −1.92410 −0.962051 0.272871i \(-0.912027\pi\)
−0.962051 + 0.272871i \(0.912027\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.54354 0.481939
\(246\) 0 0
\(247\) 0.491748 0.0312892
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.6006 0.984703 0.492351 0.870397i \(-0.336138\pi\)
0.492351 + 0.870397i \(0.336138\pi\)
\(252\) 0 0
\(253\) −17.1047 −1.07537
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.26641 −0.203753 −0.101876 0.994797i \(-0.532485\pi\)
−0.101876 + 0.994797i \(0.532485\pi\)
\(258\) 0 0
\(259\) −14.7161 −0.914413
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.86610 0.608370 0.304185 0.952613i \(-0.401616\pi\)
0.304185 + 0.952613i \(0.401616\pi\)
\(264\) 0 0
\(265\) 6.07460 0.373160
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.55598 0.338754 0.169377 0.985551i \(-0.445824\pi\)
0.169377 + 0.985551i \(0.445824\pi\)
\(270\) 0 0
\(271\) 3.07130 0.186568 0.0932841 0.995640i \(-0.470264\pi\)
0.0932841 + 0.995640i \(0.470264\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −30.6701 −1.84948
\(276\) 0 0
\(277\) 6.76698 0.406588 0.203294 0.979118i \(-0.434835\pi\)
0.203294 + 0.979118i \(0.434835\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −22.0634 −1.31619 −0.658095 0.752935i \(-0.728638\pi\)
−0.658095 + 0.752935i \(0.728638\pi\)
\(282\) 0 0
\(283\) −3.83028 −0.227687 −0.113843 0.993499i \(-0.536316\pi\)
−0.113843 + 0.993499i \(0.536316\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −15.1871 −0.896467
\(288\) 0 0
\(289\) 45.9137 2.70080
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.96214 −0.406733 −0.203366 0.979103i \(-0.565188\pi\)
−0.203366 + 0.979103i \(0.565188\pi\)
\(294\) 0 0
\(295\) 26.7616 1.55812
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.25006 0.0722927
\(300\) 0 0
\(301\) −25.7975 −1.48695
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −8.42441 −0.482380
\(306\) 0 0
\(307\) −18.7402 −1.06956 −0.534779 0.844992i \(-0.679605\pi\)
−0.534779 + 0.844992i \(0.679605\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.4427 0.762263 0.381132 0.924521i \(-0.375534\pi\)
0.381132 + 0.924521i \(0.375534\pi\)
\(312\) 0 0
\(313\) −10.4741 −0.592033 −0.296016 0.955183i \(-0.595658\pi\)
−0.296016 + 0.955183i \(0.595658\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.28731 0.409296 0.204648 0.978836i \(-0.434395\pi\)
0.204648 + 0.978836i \(0.434395\pi\)
\(318\) 0 0
\(319\) 21.6610 1.21278
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 13.2370 0.736529
\(324\) 0 0
\(325\) 2.24145 0.124333
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 25.8328 1.42421
\(330\) 0 0
\(331\) −11.5439 −0.634508 −0.317254 0.948341i \(-0.602761\pi\)
−0.317254 + 0.948341i \(0.602761\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −31.6725 −1.73045
\(336\) 0 0
\(337\) 21.9308 1.19465 0.597324 0.802000i \(-0.296231\pi\)
0.597324 + 0.802000i \(0.296231\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 23.8623 1.29222
\(342\) 0 0
\(343\) 20.1474 1.08786
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.2498 −0.764967 −0.382484 0.923962i \(-0.624931\pi\)
−0.382484 + 0.923962i \(0.624931\pi\)
\(348\) 0 0
\(349\) −23.7841 −1.27313 −0.636566 0.771222i \(-0.719646\pi\)
−0.636566 + 0.771222i \(0.719646\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 20.2344 1.07697 0.538483 0.842636i \(-0.318998\pi\)
0.538483 + 0.842636i \(0.318998\pi\)
\(354\) 0 0
\(355\) 50.6925 2.69048
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.2426 0.593360 0.296680 0.954977i \(-0.404121\pi\)
0.296680 + 0.954977i \(0.404121\pi\)
\(360\) 0 0
\(361\) −16.2149 −0.853417
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −39.1170 −2.04748
\(366\) 0 0
\(367\) 22.4318 1.17093 0.585466 0.810697i \(-0.300912\pi\)
0.585466 + 0.810697i \(0.300912\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.77764 0.196125
\(372\) 0 0
\(373\) 14.7002 0.761148 0.380574 0.924751i \(-0.375726\pi\)
0.380574 + 0.924751i \(0.375726\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.58304 −0.0815306
\(378\) 0 0
\(379\) −10.8018 −0.554852 −0.277426 0.960747i \(-0.589481\pi\)
−0.277426 + 0.960747i \(0.589481\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −22.4252 −1.14587 −0.572936 0.819600i \(-0.694196\pi\)
−0.572936 + 0.819600i \(0.694196\pi\)
\(384\) 0 0
\(385\) −31.6097 −1.61098
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7.31218 0.370742 0.185371 0.982669i \(-0.440651\pi\)
0.185371 + 0.982669i \(0.440651\pi\)
\(390\) 0 0
\(391\) 33.6495 1.70173
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −29.5425 −1.48644
\(396\) 0 0
\(397\) −21.1341 −1.06069 −0.530345 0.847782i \(-0.677938\pi\)
−0.530345 + 0.847782i \(0.677938\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.71434 −0.135548 −0.0677738 0.997701i \(-0.521590\pi\)
−0.0677738 + 0.997701i \(0.521590\pi\)
\(402\) 0 0
\(403\) −1.74392 −0.0868708
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −26.8718 −1.33198
\(408\) 0 0
\(409\) −37.0922 −1.83409 −0.917047 0.398780i \(-0.869434\pi\)
−0.917047 + 0.398780i \(0.869434\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.6424 0.818918
\(414\) 0 0
\(415\) −3.45980 −0.169835
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −33.2791 −1.62579 −0.812895 0.582411i \(-0.802110\pi\)
−0.812895 + 0.582411i \(0.802110\pi\)
\(420\) 0 0
\(421\) 13.9871 0.681689 0.340845 0.940120i \(-0.389287\pi\)
0.340845 + 0.940120i \(0.389287\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 60.3361 2.92673
\(426\) 0 0
\(427\) −5.23893 −0.253530
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.1646 −0.585950 −0.292975 0.956120i \(-0.594645\pi\)
−0.292975 + 0.956120i \(0.594645\pi\)
\(432\) 0 0
\(433\) 21.2617 1.02177 0.510886 0.859649i \(-0.329318\pi\)
0.510886 + 0.859649i \(0.329318\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.07986 0.338676
\(438\) 0 0
\(439\) −30.9982 −1.47946 −0.739731 0.672902i \(-0.765047\pi\)
−0.739731 + 0.672902i \(0.765047\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −24.2547 −1.15238 −0.576189 0.817317i \(-0.695461\pi\)
−0.576189 + 0.817317i \(0.695461\pi\)
\(444\) 0 0
\(445\) −47.8732 −2.26941
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.27291 0.154458 0.0772291 0.997013i \(-0.475393\pi\)
0.0772291 + 0.997013i \(0.475393\pi\)
\(450\) 0 0
\(451\) −27.7319 −1.30584
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.31012 0.108300
\(456\) 0 0
\(457\) 12.8794 0.602471 0.301235 0.953550i \(-0.402601\pi\)
0.301235 + 0.953550i \(0.402601\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −35.5766 −1.65697 −0.828483 0.560014i \(-0.810796\pi\)
−0.828483 + 0.560014i \(0.810796\pi\)
\(462\) 0 0
\(463\) 30.4976 1.41734 0.708671 0.705539i \(-0.249295\pi\)
0.708671 + 0.705539i \(0.249295\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.09517 0.235776 0.117888 0.993027i \(-0.462388\pi\)
0.117888 + 0.993027i \(0.462388\pi\)
\(468\) 0 0
\(469\) −19.6963 −0.909492
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −47.1067 −2.16597
\(474\) 0 0
\(475\) 12.6947 0.582474
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 33.0421 1.50973 0.754865 0.655880i \(-0.227702\pi\)
0.754865 + 0.655880i \(0.227702\pi\)
\(480\) 0 0
\(481\) 1.96386 0.0895442
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −44.0288 −1.99925
\(486\) 0 0
\(487\) 24.5450 1.11224 0.556120 0.831102i \(-0.312289\pi\)
0.556120 + 0.831102i \(0.312289\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.313854 0.0141641 0.00708203 0.999975i \(-0.497746\pi\)
0.00708203 + 0.999975i \(0.497746\pi\)
\(492\) 0 0
\(493\) −42.6128 −1.91918
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 31.5244 1.41406
\(498\) 0 0
\(499\) 9.37644 0.419747 0.209874 0.977729i \(-0.432695\pi\)
0.209874 + 0.977729i \(0.432695\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 36.3288 1.61982 0.809910 0.586554i \(-0.199516\pi\)
0.809910 + 0.586554i \(0.199516\pi\)
\(504\) 0 0
\(505\) −21.0613 −0.937216
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 27.7895 1.23175 0.615874 0.787844i \(-0.288803\pi\)
0.615874 + 0.787844i \(0.288803\pi\)
\(510\) 0 0
\(511\) −24.3259 −1.07611
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 50.2558 2.21454
\(516\) 0 0
\(517\) 47.1711 2.07458
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 31.6428 1.38630 0.693149 0.720795i \(-0.256223\pi\)
0.693149 + 0.720795i \(0.256223\pi\)
\(522\) 0 0
\(523\) −28.9004 −1.26372 −0.631862 0.775081i \(-0.717709\pi\)
−0.631862 + 0.775081i \(0.717709\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −46.9434 −2.04489
\(528\) 0 0
\(529\) −5.00249 −0.217499
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.02672 0.0877868
\(534\) 0 0
\(535\) −6.88659 −0.297733
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8.56608 0.368967
\(540\) 0 0
\(541\) −22.9331 −0.985970 −0.492985 0.870038i \(-0.664094\pi\)
−0.492985 + 0.870038i \(0.664094\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 38.4330 1.64629
\(546\) 0 0
\(547\) −39.8027 −1.70184 −0.850920 0.525295i \(-0.823955\pi\)
−0.850920 + 0.525295i \(0.823955\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8.96574 −0.381953
\(552\) 0 0
\(553\) −18.3717 −0.781245
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.4714 −0.655545 −0.327772 0.944757i \(-0.606298\pi\)
−0.327772 + 0.944757i \(0.606298\pi\)
\(558\) 0 0
\(559\) 3.44268 0.145610
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.4599 −0.525120 −0.262560 0.964916i \(-0.584567\pi\)
−0.262560 + 0.964916i \(0.584567\pi\)
\(564\) 0 0
\(565\) 40.6600 1.71058
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.9960 1.38326 0.691632 0.722250i \(-0.256892\pi\)
0.691632 + 0.722250i \(0.256892\pi\)
\(570\) 0 0
\(571\) 29.0059 1.21386 0.606929 0.794756i \(-0.292401\pi\)
0.606929 + 0.794756i \(0.292401\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 32.2709 1.34579
\(576\) 0 0
\(577\) 44.3082 1.84458 0.922288 0.386505i \(-0.126318\pi\)
0.922288 + 0.386505i \(0.126318\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.15156 −0.0892618
\(582\) 0 0
\(583\) 6.89803 0.285687
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0664 −0.498035 −0.249018 0.968499i \(-0.580108\pi\)
−0.249018 + 0.968499i \(0.580108\pi\)
\(588\) 0 0
\(589\) −9.87691 −0.406971
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −13.1853 −0.541457 −0.270728 0.962656i \(-0.587264\pi\)
−0.270728 + 0.962656i \(0.587264\pi\)
\(594\) 0 0
\(595\) 62.1845 2.54932
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −21.1252 −0.863151 −0.431575 0.902077i \(-0.642042\pi\)
−0.431575 + 0.902077i \(0.642042\pi\)
\(600\) 0 0
\(601\) 30.6746 1.25124 0.625621 0.780127i \(-0.284846\pi\)
0.625621 + 0.780127i \(0.284846\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −18.6629 −0.758757
\(606\) 0 0
\(607\) −15.8394 −0.642903 −0.321451 0.946926i \(-0.604171\pi\)
−0.321451 + 0.946926i \(0.604171\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.44738 −0.139466
\(612\) 0 0
\(613\) 49.1558 1.98538 0.992692 0.120672i \(-0.0385050\pi\)
0.992692 + 0.120672i \(0.0385050\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.9563 1.40729 0.703644 0.710552i \(-0.251555\pi\)
0.703644 + 0.710552i \(0.251555\pi\)
\(618\) 0 0
\(619\) −28.5675 −1.14823 −0.574113 0.818776i \(-0.694653\pi\)
−0.574113 + 0.818776i \(0.694653\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −29.7712 −1.19276
\(624\) 0 0
\(625\) −5.17008 −0.206803
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 52.8638 2.10782
\(630\) 0 0
\(631\) −13.4630 −0.535955 −0.267977 0.963425i \(-0.586355\pi\)
−0.267977 + 0.963425i \(0.586355\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.10293 −0.321555
\(636\) 0 0
\(637\) −0.626031 −0.0248043
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −25.7483 −1.01700 −0.508498 0.861063i \(-0.669799\pi\)
−0.508498 + 0.861063i \(0.669799\pi\)
\(642\) 0 0
\(643\) 29.7685 1.17396 0.586978 0.809603i \(-0.300318\pi\)
0.586978 + 0.809603i \(0.300318\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.7282 0.696966 0.348483 0.937315i \(-0.386697\pi\)
0.348483 + 0.937315i \(0.386697\pi\)
\(648\) 0 0
\(649\) 30.3892 1.19288
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −26.5359 −1.03843 −0.519216 0.854643i \(-0.673776\pi\)
−0.519216 + 0.854643i \(0.673776\pi\)
\(654\) 0 0
\(655\) 78.4341 3.06468
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.886549 0.0345350 0.0172675 0.999851i \(-0.494503\pi\)
0.0172675 + 0.999851i \(0.494503\pi\)
\(660\) 0 0
\(661\) 23.1798 0.901588 0.450794 0.892628i \(-0.351141\pi\)
0.450794 + 0.892628i \(0.351141\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 13.0836 0.507361
\(666\) 0 0
\(667\) −22.7915 −0.882492
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.56636 −0.369305
\(672\) 0 0
\(673\) −32.8011 −1.26439 −0.632195 0.774809i \(-0.717846\pi\)
−0.632195 + 0.774809i \(0.717846\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31.9458 −1.22778 −0.613888 0.789393i \(-0.710395\pi\)
−0.613888 + 0.789393i \(0.710395\pi\)
\(678\) 0 0
\(679\) −27.3804 −1.05076
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −31.4310 −1.20267 −0.601336 0.798996i \(-0.705365\pi\)
−0.601336 + 0.798996i \(0.705365\pi\)
\(684\) 0 0
\(685\) 40.4140 1.54414
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.504126 −0.0192057
\(690\) 0 0
\(691\) 16.6651 0.633972 0.316986 0.948430i \(-0.397329\pi\)
0.316986 + 0.948430i \(0.397329\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.87211 0.298606
\(696\) 0 0
\(697\) 54.5559 2.06645
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.20372 0.309850 0.154925 0.987926i \(-0.450486\pi\)
0.154925 + 0.987926i \(0.450486\pi\)
\(702\) 0 0
\(703\) 11.1225 0.419495
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −13.0975 −0.492582
\(708\) 0 0
\(709\) −46.1822 −1.73441 −0.867204 0.497953i \(-0.834085\pi\)
−0.867204 + 0.497953i \(0.834085\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −25.1078 −0.940295
\(714\) 0 0
\(715\) 4.21830 0.157756
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.24550 −0.0837430 −0.0418715 0.999123i \(-0.513332\pi\)
−0.0418715 + 0.999123i \(0.513332\pi\)
\(720\) 0 0
\(721\) 31.2528 1.16392
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −40.8670 −1.51776
\(726\) 0 0
\(727\) −16.4556 −0.610306 −0.305153 0.952303i \(-0.598708\pi\)
−0.305153 + 0.952303i \(0.598708\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 92.6711 3.42757
\(732\) 0 0
\(733\) −45.4200 −1.67763 −0.838813 0.544420i \(-0.816750\pi\)
−0.838813 + 0.544420i \(0.816750\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −35.9658 −1.32482
\(738\) 0 0
\(739\) −47.7343 −1.75594 −0.877968 0.478720i \(-0.841101\pi\)
−0.877968 + 0.478720i \(0.841101\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 27.1583 0.996341 0.498170 0.867079i \(-0.334005\pi\)
0.498170 + 0.867079i \(0.334005\pi\)
\(744\) 0 0
\(745\) 31.8157 1.16564
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.28260 −0.156483
\(750\) 0 0
\(751\) 21.1521 0.771851 0.385925 0.922530i \(-0.373882\pi\)
0.385925 + 0.922530i \(0.373882\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −22.3606 −0.813786
\(756\) 0 0
\(757\) 38.7840 1.40963 0.704815 0.709391i \(-0.251030\pi\)
0.704815 + 0.709391i \(0.251030\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.21024 0.0438710 0.0219355 0.999759i \(-0.493017\pi\)
0.0219355 + 0.999759i \(0.493017\pi\)
\(762\) 0 0
\(763\) 23.9005 0.865257
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.22092 −0.0801928
\(768\) 0 0
\(769\) 10.0314 0.361740 0.180870 0.983507i \(-0.442109\pi\)
0.180870 + 0.983507i \(0.442109\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.0328 0.720529 0.360265 0.932850i \(-0.382686\pi\)
0.360265 + 0.932850i \(0.382686\pi\)
\(774\) 0 0
\(775\) −45.0202 −1.61717
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.4786 0.411262
\(780\) 0 0
\(781\) 57.5640 2.05980
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11.5681 −0.412882
\(786\) 0 0
\(787\) −29.8024 −1.06234 −0.531171 0.847265i \(-0.678248\pi\)
−0.531171 + 0.847265i \(0.678248\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 25.2854 0.899046
\(792\) 0 0
\(793\) 0.699134 0.0248270
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.3543 0.614720 0.307360 0.951593i \(-0.400554\pi\)
0.307360 + 0.951593i \(0.400554\pi\)
\(798\) 0 0
\(799\) −92.7978 −3.28295
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −44.4194 −1.56753
\(804\) 0 0
\(805\) 33.2595 1.17224
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −29.8720 −1.05024 −0.525121 0.851027i \(-0.675980\pi\)
−0.525121 + 0.851027i \(0.675980\pi\)
\(810\) 0 0
\(811\) −42.8357 −1.50416 −0.752082 0.659069i \(-0.770950\pi\)
−0.752082 + 0.659069i \(0.770950\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 14.5497 0.509655
\(816\) 0 0
\(817\) 19.4980 0.682149
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6.61185 0.230755 0.115378 0.993322i \(-0.463192\pi\)
0.115378 + 0.993322i \(0.463192\pi\)
\(822\) 0 0
\(823\) −6.03393 −0.210330 −0.105165 0.994455i \(-0.533537\pi\)
−0.105165 + 0.994455i \(0.533537\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20.4064 −0.709599 −0.354800 0.934942i \(-0.615451\pi\)
−0.354800 + 0.934942i \(0.615451\pi\)
\(828\) 0 0
\(829\) 45.6242 1.58459 0.792297 0.610136i \(-0.208885\pi\)
0.792297 + 0.610136i \(0.208885\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −16.8517 −0.583878
\(834\) 0 0
\(835\) −3.55061 −0.122874
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −36.8866 −1.27347 −0.636733 0.771084i \(-0.719715\pi\)
−0.636733 + 0.771084i \(0.719715\pi\)
\(840\) 0 0
\(841\) −0.137440 −0.00473933
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 45.8497 1.57728
\(846\) 0 0
\(847\) −11.6060 −0.398787
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 28.2743 0.969231
\(852\) 0 0
\(853\) −1.36938 −0.0468867 −0.0234433 0.999725i \(-0.507463\pi\)
−0.0234433 + 0.999725i \(0.507463\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −57.7831 −1.97383 −0.986916 0.161237i \(-0.948452\pi\)
−0.986916 + 0.161237i \(0.948452\pi\)
\(858\) 0 0
\(859\) 29.3215 1.00044 0.500219 0.865899i \(-0.333253\pi\)
0.500219 + 0.865899i \(0.333253\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.25132 −0.314919 −0.157459 0.987525i \(-0.550330\pi\)
−0.157459 + 0.987525i \(0.550330\pi\)
\(864\) 0 0
\(865\) 7.85879 0.267207
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −33.5470 −1.13800
\(870\) 0 0
\(871\) 2.62847 0.0890623
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 20.4374 0.690910
\(876\) 0 0
\(877\) −45.8933 −1.54971 −0.774853 0.632141i \(-0.782176\pi\)
−0.774853 + 0.632141i \(0.782176\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.88681 −0.0635683 −0.0317842 0.999495i \(-0.510119\pi\)
−0.0317842 + 0.999495i \(0.510119\pi\)
\(882\) 0 0
\(883\) 16.7750 0.564523 0.282261 0.959338i \(-0.408915\pi\)
0.282261 + 0.959338i \(0.408915\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 22.6974 0.762103 0.381051 0.924554i \(-0.375562\pi\)
0.381051 + 0.924554i \(0.375562\pi\)
\(888\) 0 0
\(889\) −5.03901 −0.169003
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −19.5247 −0.653368
\(894\) 0 0
\(895\) 43.1750 1.44318
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 31.7958 1.06045
\(900\) 0 0
\(901\) −13.5702 −0.452090
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 41.8393 1.39078
\(906\) 0 0
\(907\) 9.54330 0.316880 0.158440 0.987369i \(-0.449354\pi\)
0.158440 + 0.987369i \(0.449354\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −38.9918 −1.29186 −0.645928 0.763398i \(-0.723529\pi\)
−0.645928 + 0.763398i \(0.723529\pi\)
\(912\) 0 0
\(913\) −3.92878 −0.130024
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 48.7762 1.61073
\(918\) 0 0
\(919\) −39.8168 −1.31344 −0.656718 0.754136i \(-0.728056\pi\)
−0.656718 + 0.754136i \(0.728056\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4.20692 −0.138473
\(924\) 0 0
\(925\) 50.6980 1.66694
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 43.5575 1.42907 0.714537 0.699598i \(-0.246637\pi\)
0.714537 + 0.699598i \(0.246637\pi\)
\(930\) 0 0
\(931\) −3.54560 −0.116202
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 113.550 3.71347
\(936\) 0 0
\(937\) 10.9873 0.358938 0.179469 0.983764i \(-0.442562\pi\)
0.179469 + 0.983764i \(0.442562\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 34.6826 1.13062 0.565310 0.824878i \(-0.308756\pi\)
0.565310 + 0.824878i \(0.308756\pi\)
\(942\) 0 0
\(943\) 29.1793 0.950209
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −33.5561 −1.09043 −0.545213 0.838298i \(-0.683551\pi\)
−0.545213 + 0.838298i \(0.683551\pi\)
\(948\) 0 0
\(949\) 3.24628 0.105379
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 32.5724 1.05512 0.527562 0.849516i \(-0.323106\pi\)
0.527562 + 0.849516i \(0.323106\pi\)
\(954\) 0 0
\(955\) −18.7491 −0.606707
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 25.1325 0.811569
\(960\) 0 0
\(961\) 4.02715 0.129908
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10.5416 0.339348
\(966\) 0 0
\(967\) −1.25726 −0.0404308 −0.0202154 0.999796i \(-0.506435\pi\)
−0.0202154 + 0.999796i \(0.506435\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −46.4861 −1.49181 −0.745905 0.666053i \(-0.767983\pi\)
−0.745905 + 0.666053i \(0.767983\pi\)
\(972\) 0 0
\(973\) 4.89547 0.156942
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 52.2762 1.67246 0.836232 0.548376i \(-0.184754\pi\)
0.836232 + 0.548376i \(0.184754\pi\)
\(978\) 0 0
\(979\) −54.3625 −1.73743
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −32.9641 −1.05139 −0.525696 0.850673i \(-0.676195\pi\)
−0.525696 + 0.850673i \(0.676195\pi\)
\(984\) 0 0
\(985\) 52.1845 1.66274
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 49.5654 1.57609
\(990\) 0 0
\(991\) −38.7317 −1.23035 −0.615177 0.788389i \(-0.710915\pi\)
−0.615177 + 0.788389i \(0.710915\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 30.8971 0.979503
\(996\) 0 0
\(997\) −51.9696 −1.64589 −0.822947 0.568119i \(-0.807671\pi\)
−0.822947 + 0.568119i \(0.807671\pi\)
\(998\) 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 6012.2.a.j.1.3 10
3.2 odd 2 6012.2.a.k.1.8 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6012.2.a.j.1.3 10 1.1 even 1 trivial
6012.2.a.k.1.8 yes 10 3.2 odd 2