Properties

Label 7524.2.a.r.1.6
Level $7524$
Weight $2$
Character 7524.1
Self dual yes
Analytic conductor $60.079$
Analytic rank $0$
Dimension $6$
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] = [7524,2,Mod(1,7524)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7524, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("7524.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7524.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: \(60.0794424808\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 12x^{4} + 28x^{3} + 16x^{2} - 60x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 836)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.18868\) of defining polynomial
Character \(\chi\) \(=\) 7524.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.62873 q^{5} -4.31127 q^{7} +O(q^{10})\) \(q+3.62873 q^{5} -4.31127 q^{7} -1.00000 q^{11} -6.10370 q^{13} +0.694815 q^{17} +1.00000 q^{19} +7.79640 q^{23} +8.16767 q^{25} -6.02709 q^{29} -6.26529 q^{31} -15.6444 q^{35} +10.1139 q^{37} +2.04380 q^{41} -2.16767 q^{43} +10.2074 q^{47} +11.5870 q^{49} +1.95798 q^{53} -3.62873 q^{55} -5.89831 q^{59} +6.84803 q^{61} -22.1487 q^{65} -8.35725 q^{67} -0.566034 q^{71} +7.29948 q^{73} +4.31127 q^{77} -13.9103 q^{79} +7.05772 q^{83} +2.52129 q^{85} +14.3590 q^{89} +26.3147 q^{91} +3.62873 q^{95} -2.89842 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{7} - 6 q^{11} + 2 q^{13} - 12 q^{17} + 6 q^{19} + 2 q^{23} + 26 q^{25} - 4 q^{29} - 20 q^{31} - 20 q^{35} + 22 q^{37} + 2 q^{41} + 10 q^{43} - 16 q^{47} + 48 q^{49} - 12 q^{53} + 14 q^{59} + 12 q^{61} - 10 q^{65} - 12 q^{67} + 30 q^{71} + 24 q^{73} - 2 q^{77} + 14 q^{83} + 12 q^{85} + 14 q^{89} + 20 q^{91} - 46 q^{97}+O(q^{100}) \) 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
\(5\) 3.62873 1.62282 0.811408 0.584480i \(-0.198701\pi\)
0.811408 + 0.584480i \(0.198701\pi\)
\(6\) 0 0
\(7\) −4.31127 −1.62951 −0.814753 0.579808i \(-0.803128\pi\)
−0.814753 + 0.579808i \(0.803128\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −6.10370 −1.69286 −0.846431 0.532498i \(-0.821253\pi\)
−0.846431 + 0.532498i \(0.821253\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.694815 0.168517 0.0842587 0.996444i \(-0.473148\pi\)
0.0842587 + 0.996444i \(0.473148\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.79640 1.62566 0.812830 0.582500i \(-0.197926\pi\)
0.812830 + 0.582500i \(0.197926\pi\)
\(24\) 0 0
\(25\) 8.16767 1.63353
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.02709 −1.11920 −0.559602 0.828762i \(-0.689046\pi\)
−0.559602 + 0.828762i \(0.689046\pi\)
\(30\) 0 0
\(31\) −6.26529 −1.12528 −0.562639 0.826703i \(-0.690214\pi\)
−0.562639 + 0.826703i \(0.690214\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −15.6444 −2.64439
\(36\) 0 0
\(37\) 10.1139 1.66271 0.831354 0.555744i \(-0.187566\pi\)
0.831354 + 0.555744i \(0.187566\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.04380 0.319189 0.159594 0.987183i \(-0.448981\pi\)
0.159594 + 0.987183i \(0.448981\pi\)
\(42\) 0 0
\(43\) −2.16767 −0.330566 −0.165283 0.986246i \(-0.552854\pi\)
−0.165283 + 0.986246i \(0.552854\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.2074 1.48890 0.744451 0.667677i \(-0.232711\pi\)
0.744451 + 0.667677i \(0.232711\pi\)
\(48\) 0 0
\(49\) 11.5870 1.65529
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.95798 0.268949 0.134475 0.990917i \(-0.457065\pi\)
0.134475 + 0.990917i \(0.457065\pi\)
\(54\) 0 0
\(55\) −3.62873 −0.489298
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.89831 −0.767895 −0.383948 0.923355i \(-0.625436\pi\)
−0.383948 + 0.923355i \(0.625436\pi\)
\(60\) 0 0
\(61\) 6.84803 0.876800 0.438400 0.898780i \(-0.355545\pi\)
0.438400 + 0.898780i \(0.355545\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −22.1487 −2.74720
\(66\) 0 0
\(67\) −8.35725 −1.02100 −0.510501 0.859877i \(-0.670540\pi\)
−0.510501 + 0.859877i \(0.670540\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.566034 −0.0671759 −0.0335880 0.999436i \(-0.510693\pi\)
−0.0335880 + 0.999436i \(0.510693\pi\)
\(72\) 0 0
\(73\) 7.29948 0.854339 0.427170 0.904172i \(-0.359511\pi\)
0.427170 + 0.904172i \(0.359511\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.31127 0.491315
\(78\) 0 0
\(79\) −13.9103 −1.56503 −0.782513 0.622635i \(-0.786062\pi\)
−0.782513 + 0.622635i \(0.786062\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.05772 0.774685 0.387343 0.921936i \(-0.373393\pi\)
0.387343 + 0.921936i \(0.373393\pi\)
\(84\) 0 0
\(85\) 2.52129 0.273473
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.3590 1.52205 0.761027 0.648720i \(-0.224695\pi\)
0.761027 + 0.648720i \(0.224695\pi\)
\(90\) 0 0
\(91\) 26.3147 2.75853
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.62873 0.372300
\(96\) 0 0
\(97\) −2.89842 −0.294290 −0.147145 0.989115i \(-0.547008\pi\)
−0.147145 + 0.989115i \(0.547008\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.57491 0.753732 0.376866 0.926268i \(-0.377002\pi\)
0.376866 + 0.926268i \(0.377002\pi\)
\(102\) 0 0
\(103\) 3.29026 0.324199 0.162099 0.986774i \(-0.448173\pi\)
0.162099 + 0.986774i \(0.448173\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.9079 −1.05451 −0.527255 0.849707i \(-0.676779\pi\)
−0.527255 + 0.849707i \(0.676779\pi\)
\(108\) 0 0
\(109\) 5.42741 0.519852 0.259926 0.965629i \(-0.416302\pi\)
0.259926 + 0.965629i \(0.416302\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.9439 −1.12359 −0.561794 0.827277i \(-0.689889\pi\)
−0.561794 + 0.827277i \(0.689889\pi\)
\(114\) 0 0
\(115\) 28.2910 2.63815
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.99553 −0.274600
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.4946 1.02811
\(126\) 0 0
\(127\) 7.72813 0.685761 0.342880 0.939379i \(-0.388597\pi\)
0.342880 + 0.939379i \(0.388597\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.5909 0.925335 0.462668 0.886532i \(-0.346892\pi\)
0.462668 + 0.886532i \(0.346892\pi\)
\(132\) 0 0
\(133\) −4.31127 −0.373834
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.74829 0.747417 0.373708 0.927546i \(-0.378086\pi\)
0.373708 + 0.927546i \(0.378086\pi\)
\(138\) 0 0
\(139\) 10.2696 0.871055 0.435527 0.900175i \(-0.356562\pi\)
0.435527 + 0.900175i \(0.356562\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.10370 0.510417
\(144\) 0 0
\(145\) −21.8707 −1.81626
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 21.5725 1.76729 0.883643 0.468161i \(-0.155083\pi\)
0.883643 + 0.468161i \(0.155083\pi\)
\(150\) 0 0
\(151\) −0.461397 −0.0375479 −0.0187740 0.999824i \(-0.505976\pi\)
−0.0187740 + 0.999824i \(0.505976\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −22.7350 −1.82612
\(156\) 0 0
\(157\) −4.52449 −0.361093 −0.180547 0.983566i \(-0.557787\pi\)
−0.180547 + 0.983566i \(0.557787\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −33.6124 −2.64903
\(162\) 0 0
\(163\) 11.9622 0.936953 0.468477 0.883476i \(-0.344803\pi\)
0.468477 + 0.883476i \(0.344803\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.83576 0.761114 0.380557 0.924758i \(-0.375732\pi\)
0.380557 + 0.924758i \(0.375732\pi\)
\(168\) 0 0
\(169\) 24.2552 1.86578
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.7818 0.971783 0.485891 0.874019i \(-0.338495\pi\)
0.485891 + 0.874019i \(0.338495\pi\)
\(174\) 0 0
\(175\) −35.2130 −2.66185
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.13311 0.607897 0.303949 0.952688i \(-0.401695\pi\)
0.303949 + 0.952688i \(0.401695\pi\)
\(180\) 0 0
\(181\) 18.5543 1.37913 0.689564 0.724225i \(-0.257802\pi\)
0.689564 + 0.724225i \(0.257802\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 36.7004 2.69827
\(186\) 0 0
\(187\) −0.694815 −0.0508099
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.6265 0.768910 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(192\) 0 0
\(193\) −0.759689 −0.0546836 −0.0273418 0.999626i \(-0.508704\pi\)
−0.0273418 + 0.999626i \(0.508704\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.68678 −0.120178 −0.0600891 0.998193i \(-0.519138\pi\)
−0.0600891 + 0.998193i \(0.519138\pi\)
\(198\) 0 0
\(199\) 24.2153 1.71658 0.858290 0.513166i \(-0.171527\pi\)
0.858290 + 0.513166i \(0.171527\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 25.9844 1.82375
\(204\) 0 0
\(205\) 7.41641 0.517984
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −28.4049 −1.95547 −0.977735 0.209841i \(-0.932705\pi\)
−0.977735 + 0.209841i \(0.932705\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.86588 −0.536448
\(216\) 0 0
\(217\) 27.0113 1.83365
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.24094 −0.285277
\(222\) 0 0
\(223\) −8.82043 −0.590660 −0.295330 0.955395i \(-0.595430\pi\)
−0.295330 + 0.955395i \(0.595430\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.2796 1.14689 0.573443 0.819246i \(-0.305607\pi\)
0.573443 + 0.819246i \(0.305607\pi\)
\(228\) 0 0
\(229\) 2.15539 0.142432 0.0712162 0.997461i \(-0.477312\pi\)
0.0712162 + 0.997461i \(0.477312\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.9733 −0.784398 −0.392199 0.919880i \(-0.628285\pi\)
−0.392199 + 0.919880i \(0.628285\pi\)
\(234\) 0 0
\(235\) 37.0399 2.41622
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.7692 −1.21408 −0.607038 0.794673i \(-0.707643\pi\)
−0.607038 + 0.794673i \(0.707643\pi\)
\(240\) 0 0
\(241\) 14.9468 0.962807 0.481404 0.876499i \(-0.340127\pi\)
0.481404 + 0.876499i \(0.340127\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 42.0462 2.68624
\(246\) 0 0
\(247\) −6.10370 −0.388369
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.1955 0.769771 0.384885 0.922964i \(-0.374241\pi\)
0.384885 + 0.922964i \(0.374241\pi\)
\(252\) 0 0
\(253\) −7.79640 −0.490155
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.96669 0.434570 0.217285 0.976108i \(-0.430280\pi\)
0.217285 + 0.976108i \(0.430280\pi\)
\(258\) 0 0
\(259\) −43.6036 −2.70939
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −25.0396 −1.54401 −0.772005 0.635617i \(-0.780746\pi\)
−0.772005 + 0.635617i \(0.780746\pi\)
\(264\) 0 0
\(265\) 7.10498 0.436455
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.58130 −0.0964134 −0.0482067 0.998837i \(-0.515351\pi\)
−0.0482067 + 0.998837i \(0.515351\pi\)
\(270\) 0 0
\(271\) 5.57867 0.338880 0.169440 0.985540i \(-0.445804\pi\)
0.169440 + 0.985540i \(0.445804\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.16767 −0.492529
\(276\) 0 0
\(277\) 30.5385 1.83488 0.917440 0.397874i \(-0.130252\pi\)
0.917440 + 0.397874i \(0.130252\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 15.0369 0.897029 0.448514 0.893776i \(-0.351953\pi\)
0.448514 + 0.893776i \(0.351953\pi\)
\(282\) 0 0
\(283\) 29.1158 1.73076 0.865378 0.501120i \(-0.167079\pi\)
0.865378 + 0.501120i \(0.167079\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.81139 −0.520120
\(288\) 0 0
\(289\) −16.5172 −0.971602
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.88816 −0.343990 −0.171995 0.985098i \(-0.555021\pi\)
−0.171995 + 0.985098i \(0.555021\pi\)
\(294\) 0 0
\(295\) −21.4034 −1.24615
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −47.5869 −2.75202
\(300\) 0 0
\(301\) 9.34540 0.538660
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 24.8496 1.42289
\(306\) 0 0
\(307\) 19.2140 1.09660 0.548300 0.836282i \(-0.315275\pi\)
0.548300 + 0.836282i \(0.315275\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −26.7459 −1.51662 −0.758310 0.651894i \(-0.773975\pi\)
−0.758310 + 0.651894i \(0.773975\pi\)
\(312\) 0 0
\(313\) −16.0435 −0.906834 −0.453417 0.891298i \(-0.649795\pi\)
−0.453417 + 0.891298i \(0.649795\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.5664 −1.04280 −0.521398 0.853314i \(-0.674589\pi\)
−0.521398 + 0.853314i \(0.674589\pi\)
\(318\) 0 0
\(319\) 6.02709 0.337453
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.694815 0.0386605
\(324\) 0 0
\(325\) −49.8530 −2.76535
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −44.0069 −2.42618
\(330\) 0 0
\(331\) −34.6196 −1.90286 −0.951431 0.307861i \(-0.900387\pi\)
−0.951431 + 0.307861i \(0.900387\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −30.3262 −1.65690
\(336\) 0 0
\(337\) 2.84625 0.155045 0.0775224 0.996991i \(-0.475299\pi\)
0.0775224 + 0.996991i \(0.475299\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.26529 0.339284
\(342\) 0 0
\(343\) −19.7760 −1.06780
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.0153 −0.537651 −0.268826 0.963189i \(-0.586636\pi\)
−0.268826 + 0.963189i \(0.586636\pi\)
\(348\) 0 0
\(349\) −0.712288 −0.0381279 −0.0190640 0.999818i \(-0.506069\pi\)
−0.0190640 + 0.999818i \(0.506069\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −32.4528 −1.72729 −0.863645 0.504101i \(-0.831824\pi\)
−0.863645 + 0.504101i \(0.831824\pi\)
\(354\) 0 0
\(355\) −2.05398 −0.109014
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −19.6749 −1.03840 −0.519200 0.854653i \(-0.673770\pi\)
−0.519200 + 0.854653i \(0.673770\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 26.4878 1.38644
\(366\) 0 0
\(367\) −31.5887 −1.64891 −0.824457 0.565924i \(-0.808520\pi\)
−0.824457 + 0.565924i \(0.808520\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.44138 −0.438255
\(372\) 0 0
\(373\) 20.4557 1.05916 0.529579 0.848260i \(-0.322350\pi\)
0.529579 + 0.848260i \(0.322350\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 36.7876 1.89466
\(378\) 0 0
\(379\) 6.22508 0.319761 0.159880 0.987136i \(-0.448889\pi\)
0.159880 + 0.987136i \(0.448889\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.592813 0.0302913 0.0151457 0.999885i \(-0.495179\pi\)
0.0151457 + 0.999885i \(0.495179\pi\)
\(384\) 0 0
\(385\) 15.6444 0.797314
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −32.2424 −1.63475 −0.817377 0.576103i \(-0.804573\pi\)
−0.817377 + 0.576103i \(0.804573\pi\)
\(390\) 0 0
\(391\) 5.41705 0.273952
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −50.4765 −2.53975
\(396\) 0 0
\(397\) −25.1889 −1.26420 −0.632098 0.774888i \(-0.717806\pi\)
−0.632098 + 0.774888i \(0.717806\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.3272 1.11497 0.557484 0.830188i \(-0.311767\pi\)
0.557484 + 0.830188i \(0.311767\pi\)
\(402\) 0 0
\(403\) 38.2414 1.90494
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.1139 −0.501325
\(408\) 0 0
\(409\) 24.1005 1.19169 0.595847 0.803098i \(-0.296817\pi\)
0.595847 + 0.803098i \(0.296817\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 25.4292 1.25129
\(414\) 0 0
\(415\) 25.6105 1.25717
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 17.0480 0.832851 0.416425 0.909170i \(-0.363283\pi\)
0.416425 + 0.909170i \(0.363283\pi\)
\(420\) 0 0
\(421\) 4.12963 0.201266 0.100633 0.994924i \(-0.467913\pi\)
0.100633 + 0.994924i \(0.467913\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.67502 0.275279
\(426\) 0 0
\(427\) −29.5237 −1.42875
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.86783 0.282643 0.141322 0.989964i \(-0.454865\pi\)
0.141322 + 0.989964i \(0.454865\pi\)
\(432\) 0 0
\(433\) 15.5840 0.748920 0.374460 0.927243i \(-0.377828\pi\)
0.374460 + 0.927243i \(0.377828\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.79640 0.372952
\(438\) 0 0
\(439\) 13.1937 0.629699 0.314850 0.949142i \(-0.398046\pi\)
0.314850 + 0.949142i \(0.398046\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.14411 0.196893 0.0984463 0.995142i \(-0.468613\pi\)
0.0984463 + 0.995142i \(0.468613\pi\)
\(444\) 0 0
\(445\) 52.1050 2.47002
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 35.9971 1.69881 0.849405 0.527742i \(-0.176961\pi\)
0.849405 + 0.527742i \(0.176961\pi\)
\(450\) 0 0
\(451\) −2.04380 −0.0962390
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 95.4889 4.47659
\(456\) 0 0
\(457\) 7.94870 0.371825 0.185912 0.982566i \(-0.440476\pi\)
0.185912 + 0.982566i \(0.440476\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.33968 0.434992 0.217496 0.976061i \(-0.430211\pi\)
0.217496 + 0.976061i \(0.430211\pi\)
\(462\) 0 0
\(463\) 13.0328 0.605686 0.302843 0.953040i \(-0.402064\pi\)
0.302843 + 0.953040i \(0.402064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.1169 −0.792076 −0.396038 0.918234i \(-0.629615\pi\)
−0.396038 + 0.918234i \(0.629615\pi\)
\(468\) 0 0
\(469\) 36.0304 1.66373
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.16767 0.0996695
\(474\) 0 0
\(475\) 8.16767 0.374758
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −39.8917 −1.82270 −0.911349 0.411635i \(-0.864958\pi\)
−0.911349 + 0.411635i \(0.864958\pi\)
\(480\) 0 0
\(481\) −61.7319 −2.81473
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.5176 −0.477578
\(486\) 0 0
\(487\) −21.3504 −0.967478 −0.483739 0.875212i \(-0.660722\pi\)
−0.483739 + 0.875212i \(0.660722\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.0293 0.768524 0.384262 0.923224i \(-0.374456\pi\)
0.384262 + 0.923224i \(0.374456\pi\)
\(492\) 0 0
\(493\) −4.18771 −0.188605
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.44033 0.109464
\(498\) 0 0
\(499\) −4.94667 −0.221443 −0.110722 0.993851i \(-0.535316\pi\)
−0.110722 + 0.993851i \(0.535316\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.22196 0.143660 0.0718301 0.997417i \(-0.477116\pi\)
0.0718301 + 0.997417i \(0.477116\pi\)
\(504\) 0 0
\(505\) 27.4873 1.22317
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.1751 −0.451003 −0.225502 0.974243i \(-0.572402\pi\)
−0.225502 + 0.974243i \(0.572402\pi\)
\(510\) 0 0
\(511\) −31.4700 −1.39215
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11.9395 0.526115
\(516\) 0 0
\(517\) −10.2074 −0.448921
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 33.3792 1.46237 0.731186 0.682179i \(-0.238967\pi\)
0.731186 + 0.682179i \(0.238967\pi\)
\(522\) 0 0
\(523\) −2.17534 −0.0951208 −0.0475604 0.998868i \(-0.515145\pi\)
−0.0475604 + 0.998868i \(0.515145\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.35321 −0.189629
\(528\) 0 0
\(529\) 37.7838 1.64277
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.4748 −0.540342
\(534\) 0 0
\(535\) −39.5819 −1.71127
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.5870 −0.499089
\(540\) 0 0
\(541\) 24.6958 1.06176 0.530878 0.847448i \(-0.321862\pi\)
0.530878 + 0.847448i \(0.321862\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 19.6946 0.843624
\(546\) 0 0
\(547\) −9.80330 −0.419159 −0.209579 0.977792i \(-0.567209\pi\)
−0.209579 + 0.977792i \(0.567209\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.02709 −0.256763
\(552\) 0 0
\(553\) 59.9708 2.55022
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.1796 0.516065 0.258033 0.966136i \(-0.416926\pi\)
0.258033 + 0.966136i \(0.416926\pi\)
\(558\) 0 0
\(559\) 13.2308 0.559603
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −10.6703 −0.449698 −0.224849 0.974394i \(-0.572189\pi\)
−0.224849 + 0.974394i \(0.572189\pi\)
\(564\) 0 0
\(565\) −43.3412 −1.82338
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20.8260 0.873072 0.436536 0.899687i \(-0.356205\pi\)
0.436536 + 0.899687i \(0.356205\pi\)
\(570\) 0 0
\(571\) 21.5755 0.902907 0.451454 0.892295i \(-0.350906\pi\)
0.451454 + 0.892295i \(0.350906\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 63.6784 2.65557
\(576\) 0 0
\(577\) 15.5212 0.646157 0.323079 0.946372i \(-0.395282\pi\)
0.323079 + 0.946372i \(0.395282\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −30.4277 −1.26235
\(582\) 0 0
\(583\) −1.95798 −0.0810912
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.08383 −0.168558 −0.0842789 0.996442i \(-0.526859\pi\)
−0.0842789 + 0.996442i \(0.526859\pi\)
\(588\) 0 0
\(589\) −6.26529 −0.258157
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 45.1039 1.85220 0.926098 0.377283i \(-0.123142\pi\)
0.926098 + 0.377283i \(0.123142\pi\)
\(594\) 0 0
\(595\) −10.8700 −0.445626
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.29026 0.0527186 0.0263593 0.999653i \(-0.491609\pi\)
0.0263593 + 0.999653i \(0.491609\pi\)
\(600\) 0 0
\(601\) −29.0011 −1.18298 −0.591489 0.806313i \(-0.701460\pi\)
−0.591489 + 0.806313i \(0.701460\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.62873 0.147529
\(606\) 0 0
\(607\) −11.0119 −0.446958 −0.223479 0.974709i \(-0.571741\pi\)
−0.223479 + 0.974709i \(0.571741\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −62.3029 −2.52051
\(612\) 0 0
\(613\) 1.94010 0.0783600 0.0391800 0.999232i \(-0.487525\pi\)
0.0391800 + 0.999232i \(0.487525\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.1760 −0.610964 −0.305482 0.952198i \(-0.598818\pi\)
−0.305482 + 0.952198i \(0.598818\pi\)
\(618\) 0 0
\(619\) 35.8548 1.44113 0.720564 0.693389i \(-0.243883\pi\)
0.720564 + 0.693389i \(0.243883\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −61.9057 −2.48020
\(624\) 0 0
\(625\) 0.872460 0.0348984
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.02726 0.280195
\(630\) 0 0
\(631\) −1.43092 −0.0569640 −0.0284820 0.999594i \(-0.509067\pi\)
−0.0284820 + 0.999594i \(0.509067\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 28.0433 1.11286
\(636\) 0 0
\(637\) −70.7239 −2.80218
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 27.8685 1.10074 0.550369 0.834922i \(-0.314487\pi\)
0.550369 + 0.834922i \(0.314487\pi\)
\(642\) 0 0
\(643\) −1.90753 −0.0752256 −0.0376128 0.999292i \(-0.511975\pi\)
−0.0376128 + 0.999292i \(0.511975\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 44.9164 1.76584 0.882922 0.469519i \(-0.155573\pi\)
0.882922 + 0.469519i \(0.155573\pi\)
\(648\) 0 0
\(649\) 5.89831 0.231529
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −23.6282 −0.924642 −0.462321 0.886713i \(-0.652983\pi\)
−0.462321 + 0.886713i \(0.652983\pi\)
\(654\) 0 0
\(655\) 38.4317 1.50165
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.7391 0.418334 0.209167 0.977880i \(-0.432925\pi\)
0.209167 + 0.977880i \(0.432925\pi\)
\(660\) 0 0
\(661\) −46.0837 −1.79245 −0.896224 0.443603i \(-0.853700\pi\)
−0.896224 + 0.443603i \(0.853700\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −15.6444 −0.606665
\(666\) 0 0
\(667\) −46.9896 −1.81945
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.84803 −0.264365
\(672\) 0 0
\(673\) −22.6538 −0.873242 −0.436621 0.899646i \(-0.643825\pi\)
−0.436621 + 0.899646i \(0.643825\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −24.3654 −0.936438 −0.468219 0.883613i \(-0.655104\pi\)
−0.468219 + 0.883613i \(0.655104\pi\)
\(678\) 0 0
\(679\) 12.4959 0.479547
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26.6471 1.01962 0.509811 0.860286i \(-0.329715\pi\)
0.509811 + 0.860286i \(0.329715\pi\)
\(684\) 0 0
\(685\) 31.7452 1.21292
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −11.9509 −0.455294
\(690\) 0 0
\(691\) 39.6176 1.50713 0.753563 0.657376i \(-0.228334\pi\)
0.753563 + 0.657376i \(0.228334\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 37.2655 1.41356
\(696\) 0 0
\(697\) 1.42007 0.0537888
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.92410 −0.0726722 −0.0363361 0.999340i \(-0.511569\pi\)
−0.0363361 + 0.999340i \(0.511569\pi\)
\(702\) 0 0
\(703\) 10.1139 0.381451
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −32.6575 −1.22821
\(708\) 0 0
\(709\) −6.91616 −0.259742 −0.129871 0.991531i \(-0.541456\pi\)
−0.129871 + 0.991531i \(0.541456\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −48.8466 −1.82932
\(714\) 0 0
\(715\) 22.1487 0.828313
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12.3035 0.458843 0.229422 0.973327i \(-0.426317\pi\)
0.229422 + 0.973327i \(0.426317\pi\)
\(720\) 0 0
\(721\) −14.1852 −0.528284
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −49.2273 −1.82826
\(726\) 0 0
\(727\) −27.6098 −1.02399 −0.511995 0.858989i \(-0.671093\pi\)
−0.511995 + 0.858989i \(0.671093\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.50613 −0.0557062
\(732\) 0 0
\(733\) −45.0293 −1.66319 −0.831597 0.555380i \(-0.812573\pi\)
−0.831597 + 0.555380i \(0.812573\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.35725 0.307843
\(738\) 0 0
\(739\) 37.8963 1.39404 0.697018 0.717053i \(-0.254510\pi\)
0.697018 + 0.717053i \(0.254510\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −23.3103 −0.855172 −0.427586 0.903975i \(-0.640636\pi\)
−0.427586 + 0.903975i \(0.640636\pi\)
\(744\) 0 0
\(745\) 78.2807 2.86798
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 47.0270 1.71833
\(750\) 0 0
\(751\) −14.9643 −0.546056 −0.273028 0.962006i \(-0.588025\pi\)
−0.273028 + 0.962006i \(0.588025\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.67428 −0.0609334
\(756\) 0 0
\(757\) −13.3436 −0.484980 −0.242490 0.970154i \(-0.577964\pi\)
−0.242490 + 0.970154i \(0.577964\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.6962 0.423986 0.211993 0.977271i \(-0.432005\pi\)
0.211993 + 0.977271i \(0.432005\pi\)
\(762\) 0 0
\(763\) −23.3990 −0.847102
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 36.0015 1.29994
\(768\) 0 0
\(769\) 41.2234 1.48655 0.743276 0.668985i \(-0.233271\pi\)
0.743276 + 0.668985i \(0.233271\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12.9999 0.467574 0.233787 0.972288i \(-0.424888\pi\)
0.233787 + 0.972288i \(0.424888\pi\)
\(774\) 0 0
\(775\) −51.1728 −1.83818
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.04380 0.0732269
\(780\) 0 0
\(781\) 0.566034 0.0202543
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −16.4181 −0.585988
\(786\) 0 0
\(787\) 4.63820 0.165334 0.0826669 0.996577i \(-0.473656\pi\)
0.0826669 + 0.996577i \(0.473656\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 51.4934 1.83089
\(792\) 0 0
\(793\) −41.7983 −1.48430
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.0271 0.390600 0.195300 0.980744i \(-0.437432\pi\)
0.195300 + 0.980744i \(0.437432\pi\)
\(798\) 0 0
\(799\) 7.09226 0.250906
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −7.29948 −0.257593
\(804\) 0 0
\(805\) −121.970 −4.29888
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 18.8659 0.663290 0.331645 0.943404i \(-0.392396\pi\)
0.331645 + 0.943404i \(0.392396\pi\)
\(810\) 0 0
\(811\) −13.9642 −0.490348 −0.245174 0.969479i \(-0.578845\pi\)
−0.245174 + 0.969479i \(0.578845\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 43.4076 1.52050
\(816\) 0 0
\(817\) −2.16767 −0.0758371
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 30.8485 1.07662 0.538310 0.842747i \(-0.319063\pi\)
0.538310 + 0.842747i \(0.319063\pi\)
\(822\) 0 0
\(823\) −9.48137 −0.330500 −0.165250 0.986252i \(-0.552843\pi\)
−0.165250 + 0.986252i \(0.552843\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −16.7454 −0.582296 −0.291148 0.956678i \(-0.594037\pi\)
−0.291148 + 0.956678i \(0.594037\pi\)
\(828\) 0 0
\(829\) 1.59130 0.0552682 0.0276341 0.999618i \(-0.491203\pi\)
0.0276341 + 0.999618i \(0.491203\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 8.05085 0.278945
\(834\) 0 0
\(835\) 35.6913 1.23515
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 5.12222 0.176839 0.0884193 0.996083i \(-0.471818\pi\)
0.0884193 + 0.996083i \(0.471818\pi\)
\(840\) 0 0
\(841\) 7.32587 0.252616
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 88.0154 3.02782
\(846\) 0 0
\(847\) −4.31127 −0.148137
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 78.8516 2.70300
\(852\) 0 0
\(853\) −51.2020 −1.75312 −0.876561 0.481290i \(-0.840168\pi\)
−0.876561 + 0.481290i \(0.840168\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 7.92412 0.270683 0.135341 0.990799i \(-0.456787\pi\)
0.135341 + 0.990799i \(0.456787\pi\)
\(858\) 0 0
\(859\) −39.4668 −1.34659 −0.673296 0.739373i \(-0.735122\pi\)
−0.673296 + 0.739373i \(0.735122\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 52.1231 1.77429 0.887145 0.461491i \(-0.152685\pi\)
0.887145 + 0.461491i \(0.152685\pi\)
\(864\) 0 0
\(865\) 46.3817 1.57703
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 13.9103 0.471873
\(870\) 0 0
\(871\) 51.0102 1.72841
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −49.5563 −1.67531
\(876\) 0 0
\(877\) 20.6344 0.696773 0.348386 0.937351i \(-0.386730\pi\)
0.348386 + 0.937351i \(0.386730\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −42.3008 −1.42515 −0.712574 0.701597i \(-0.752471\pi\)
−0.712574 + 0.701597i \(0.752471\pi\)
\(882\) 0 0
\(883\) −47.1397 −1.58638 −0.793188 0.608977i \(-0.791580\pi\)
−0.793188 + 0.608977i \(0.791580\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −5.41860 −0.181939 −0.0909694 0.995854i \(-0.528997\pi\)
−0.0909694 + 0.995854i \(0.528997\pi\)
\(888\) 0 0
\(889\) −33.3180 −1.11745
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 10.2074 0.341578
\(894\) 0 0
\(895\) 29.5129 0.986506
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 37.7615 1.25942
\(900\) 0 0
\(901\) 1.36043 0.0453226
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 67.3284 2.23807
\(906\) 0 0
\(907\) 22.1148 0.734309 0.367154 0.930160i \(-0.380332\pi\)
0.367154 + 0.930160i \(0.380332\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −18.0321 −0.597429 −0.298715 0.954343i \(-0.596558\pi\)
−0.298715 + 0.954343i \(0.596558\pi\)
\(912\) 0 0
\(913\) −7.05772 −0.233576
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −45.6604 −1.50784
\(918\) 0 0
\(919\) −36.9395 −1.21852 −0.609261 0.792970i \(-0.708534\pi\)
−0.609261 + 0.792970i \(0.708534\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 3.45490 0.113720
\(924\) 0 0
\(925\) 82.6066 2.71609
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −10.2792 −0.337250 −0.168625 0.985680i \(-0.553933\pi\)
−0.168625 + 0.985680i \(0.553933\pi\)
\(930\) 0 0
\(931\) 11.5870 0.379750
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.52129 −0.0824551
\(936\) 0 0
\(937\) 1.42527 0.0465615 0.0232807 0.999729i \(-0.492589\pi\)
0.0232807 + 0.999729i \(0.492589\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −32.0967 −1.04632 −0.523161 0.852234i \(-0.675247\pi\)
−0.523161 + 0.852234i \(0.675247\pi\)
\(942\) 0 0
\(943\) 15.9343 0.518892
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.61405 0.279919 0.139959 0.990157i \(-0.455303\pi\)
0.139959 + 0.990157i \(0.455303\pi\)
\(948\) 0 0
\(949\) −44.5538 −1.44628
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −6.48103 −0.209941 −0.104971 0.994475i \(-0.533475\pi\)
−0.104971 + 0.994475i \(0.533475\pi\)
\(954\) 0 0
\(955\) 38.5609 1.24780
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −37.7162 −1.21792
\(960\) 0 0
\(961\) 8.25380 0.266252
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.75671 −0.0887415
\(966\) 0 0
\(967\) 55.2454 1.77657 0.888286 0.459292i \(-0.151897\pi\)
0.888286 + 0.459292i \(0.151897\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −30.1518 −0.967618 −0.483809 0.875174i \(-0.660747\pi\)
−0.483809 + 0.875174i \(0.660747\pi\)
\(972\) 0 0
\(973\) −44.2750 −1.41939
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −22.6608 −0.724984 −0.362492 0.931987i \(-0.618074\pi\)
−0.362492 + 0.931987i \(0.618074\pi\)
\(978\) 0 0
\(979\) −14.3590 −0.458917
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −17.3274 −0.552658 −0.276329 0.961063i \(-0.589118\pi\)
−0.276329 + 0.961063i \(0.589118\pi\)
\(984\) 0 0
\(985\) −6.12087 −0.195027
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −16.9000 −0.537389
\(990\) 0 0
\(991\) 27.1931 0.863818 0.431909 0.901917i \(-0.357840\pi\)
0.431909 + 0.901917i \(0.357840\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 87.8709 2.78569
\(996\) 0 0
\(997\) 21.0570 0.666881 0.333441 0.942771i \(-0.391790\pi\)
0.333441 + 0.942771i \(0.391790\pi\)
\(998\) 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 7524.2.a.r.1.6 6
3.2 odd 2 836.2.a.d.1.2 6
12.11 even 2 3344.2.a.x.1.5 6
33.32 even 2 9196.2.a.k.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.a.d.1.2 6 3.2 odd 2
3344.2.a.x.1.5 6 12.11 even 2
7524.2.a.r.1.6 6 1.1 even 1 trivial
9196.2.a.k.1.2 6 33.32 even 2