Properties

Label 9800.2.a.da.1.5
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9800,2,Mod(1,9800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9800, 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("9800.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.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: \(78.2533939809\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 18x^{6} + 85x^{4} - 38x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.402377\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.402377 q^{3} -2.83809 q^{9} +O(q^{10})\) \(q+0.402377 q^{3} -2.83809 q^{9} -5.46025 q^{11} +4.97046 q^{13} +6.78705 q^{17} +0.859799 q^{19} +5.40714 q^{23} -2.34912 q^{27} -9.29834 q^{29} -6.99413 q^{31} -2.19708 q^{33} +2.76025 q^{37} +2.00000 q^{39} +9.53854 q^{41} -4.76025 q^{43} +11.1262 q^{47} +2.73095 q^{51} -1.89120 q^{53} +0.345964 q^{57} -11.2031 q^{59} +5.50482 q^{61} -3.86191 q^{67} +2.17571 q^{69} -10.4364 q^{71} +0.173406 q^{73} +5.13095 q^{79} +7.56905 q^{81} +6.43972 q^{83} -3.74144 q^{87} +6.51482 q^{89} -2.81428 q^{93} -8.94270 q^{97} +15.4967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{9} + 4 q^{11} + 4 q^{23} + 8 q^{29} + 16 q^{39} - 16 q^{43} + 52 q^{51} + 28 q^{53} + 8 q^{57} - 40 q^{67} + 8 q^{71} + 20 q^{79} + 56 q^{81} + 56 q^{93} + 36 q^{99}+O(q^{100}) \) 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
\(3\) 0.402377 0.232313 0.116156 0.993231i \(-0.462943\pi\)
0.116156 + 0.993231i \(0.462943\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.83809 −0.946031
\(10\) 0 0
\(11\) −5.46025 −1.64633 −0.823163 0.567805i \(-0.807793\pi\)
−0.823163 + 0.567805i \(0.807793\pi\)
\(12\) 0 0
\(13\) 4.97046 1.37856 0.689279 0.724496i \(-0.257927\pi\)
0.689279 + 0.724496i \(0.257927\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.78705 1.64610 0.823051 0.567968i \(-0.192270\pi\)
0.823051 + 0.567968i \(0.192270\pi\)
\(18\) 0 0
\(19\) 0.859799 0.197251 0.0986257 0.995125i \(-0.468555\pi\)
0.0986257 + 0.995125i \(0.468555\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.40714 1.12747 0.563733 0.825957i \(-0.309365\pi\)
0.563733 + 0.825957i \(0.309365\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.34912 −0.452087
\(28\) 0 0
\(29\) −9.29834 −1.72666 −0.863329 0.504641i \(-0.831625\pi\)
−0.863329 + 0.504641i \(0.831625\pi\)
\(30\) 0 0
\(31\) −6.99413 −1.25618 −0.628092 0.778139i \(-0.716164\pi\)
−0.628092 + 0.778139i \(0.716164\pi\)
\(32\) 0 0
\(33\) −2.19708 −0.382462
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.76025 0.453782 0.226891 0.973920i \(-0.427144\pi\)
0.226891 + 0.973920i \(0.427144\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 9.53854 1.48967 0.744835 0.667249i \(-0.232528\pi\)
0.744835 + 0.667249i \(0.232528\pi\)
\(42\) 0 0
\(43\) −4.76025 −0.725931 −0.362965 0.931803i \(-0.618236\pi\)
−0.362965 + 0.931803i \(0.618236\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.1262 1.62292 0.811459 0.584410i \(-0.198674\pi\)
0.811459 + 0.584410i \(0.198674\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 2.73095 0.382410
\(52\) 0 0
\(53\) −1.89120 −0.259776 −0.129888 0.991529i \(-0.541462\pi\)
−0.129888 + 0.991529i \(0.541462\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.345964 0.0458240
\(58\) 0 0
\(59\) −11.2031 −1.45852 −0.729260 0.684237i \(-0.760135\pi\)
−0.729260 + 0.684237i \(0.760135\pi\)
\(60\) 0 0
\(61\) 5.50482 0.704820 0.352410 0.935846i \(-0.385362\pi\)
0.352410 + 0.935846i \(0.385362\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.86191 −0.471807 −0.235903 0.971777i \(-0.575805\pi\)
−0.235903 + 0.971777i \(0.575805\pi\)
\(68\) 0 0
\(69\) 2.17571 0.261925
\(70\) 0 0
\(71\) −10.4364 −1.23858 −0.619288 0.785164i \(-0.712579\pi\)
−0.619288 + 0.785164i \(0.712579\pi\)
\(72\) 0 0
\(73\) 0.173406 0.0202956 0.0101478 0.999949i \(-0.496770\pi\)
0.0101478 + 0.999949i \(0.496770\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.13095 0.577277 0.288639 0.957438i \(-0.406797\pi\)
0.288639 + 0.957438i \(0.406797\pi\)
\(80\) 0 0
\(81\) 7.56905 0.841005
\(82\) 0 0
\(83\) 6.43972 0.706851 0.353425 0.935463i \(-0.385017\pi\)
0.353425 + 0.935463i \(0.385017\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.74144 −0.401124
\(88\) 0 0
\(89\) 6.51482 0.690570 0.345285 0.938498i \(-0.387782\pi\)
0.345285 + 0.938498i \(0.387782\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.81428 −0.291827
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.94270 −0.907994 −0.453997 0.891003i \(-0.650002\pi\)
−0.453997 + 0.891003i \(0.650002\pi\)
\(98\) 0 0
\(99\) 15.4967 1.55748
\(100\) 0 0
\(101\) −5.91898 −0.588961 −0.294480 0.955658i \(-0.595147\pi\)
−0.294480 + 0.955658i \(0.595147\pi\)
\(102\) 0 0
\(103\) 6.03734 0.594877 0.297438 0.954741i \(-0.403868\pi\)
0.297438 + 0.954741i \(0.403868\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.6514 −1.70643 −0.853215 0.521560i \(-0.825350\pi\)
−0.853215 + 0.521560i \(0.825350\pi\)
\(108\) 0 0
\(109\) −4.54523 −0.435355 −0.217677 0.976021i \(-0.569848\pi\)
−0.217677 + 0.976021i \(0.569848\pi\)
\(110\) 0 0
\(111\) 1.11066 0.105419
\(112\) 0 0
\(113\) 16.4895 1.55121 0.775603 0.631221i \(-0.217446\pi\)
0.775603 + 0.631221i \(0.217446\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −14.1066 −1.30416
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 18.8143 1.71039
\(122\) 0 0
\(123\) 3.83809 0.346069
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −15.5745 −1.38202 −0.691008 0.722847i \(-0.742833\pi\)
−0.691008 + 0.722847i \(0.742833\pi\)
\(128\) 0 0
\(129\) −1.91542 −0.168643
\(130\) 0 0
\(131\) 10.1699 0.888548 0.444274 0.895891i \(-0.353462\pi\)
0.444274 + 0.895891i \(0.353462\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.32929 0.540748 0.270374 0.962755i \(-0.412853\pi\)
0.270374 + 0.962755i \(0.412853\pi\)
\(138\) 0 0
\(139\) −5.25448 −0.445679 −0.222839 0.974855i \(-0.571533\pi\)
−0.222839 + 0.974855i \(0.571533\pi\)
\(140\) 0 0
\(141\) 4.47691 0.377024
\(142\) 0 0
\(143\) −27.1399 −2.26956
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.65404 0.381274 0.190637 0.981661i \(-0.438945\pi\)
0.190637 + 0.981661i \(0.438945\pi\)
\(150\) 0 0
\(151\) 20.8188 1.69421 0.847106 0.531423i \(-0.178343\pi\)
0.847106 + 0.531423i \(0.178343\pi\)
\(152\) 0 0
\(153\) −19.2623 −1.55726
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 14.7949 1.18076 0.590379 0.807126i \(-0.298978\pi\)
0.590379 + 0.807126i \(0.298978\pi\)
\(158\) 0 0
\(159\) −0.760975 −0.0603492
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.1143 0.792212 0.396106 0.918205i \(-0.370361\pi\)
0.396106 + 0.918205i \(0.370361\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.0416 1.00919 0.504594 0.863357i \(-0.331642\pi\)
0.504594 + 0.863357i \(0.331642\pi\)
\(168\) 0 0
\(169\) 11.7055 0.900421
\(170\) 0 0
\(171\) −2.44019 −0.186606
\(172\) 0 0
\(173\) 4.16754 0.316852 0.158426 0.987371i \(-0.449358\pi\)
0.158426 + 0.987371i \(0.449358\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.50787 −0.338832
\(178\) 0 0
\(179\) 0.239753 0.0179200 0.00895998 0.999960i \(-0.497148\pi\)
0.00895998 + 0.999960i \(0.497148\pi\)
\(180\) 0 0
\(181\) −15.5959 −1.15924 −0.579619 0.814888i \(-0.696798\pi\)
−0.579619 + 0.814888i \(0.696798\pi\)
\(182\) 0 0
\(183\) 2.21501 0.163738
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −37.0590 −2.71002
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.83261 0.132603 0.0663016 0.997800i \(-0.478880\pi\)
0.0663016 + 0.997800i \(0.478880\pi\)
\(192\) 0 0
\(193\) 23.7338 1.70840 0.854200 0.519945i \(-0.174048\pi\)
0.854200 + 0.519945i \(0.174048\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.88665 0.134418 0.0672089 0.997739i \(-0.478591\pi\)
0.0672089 + 0.997739i \(0.478591\pi\)
\(198\) 0 0
\(199\) 15.2919 1.08401 0.542006 0.840375i \(-0.317665\pi\)
0.542006 + 0.840375i \(0.317665\pi\)
\(200\) 0 0
\(201\) −1.55394 −0.109607
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −15.3460 −1.06662
\(208\) 0 0
\(209\) −4.69471 −0.324740
\(210\) 0 0
\(211\) 23.0038 1.58365 0.791824 0.610749i \(-0.209132\pi\)
0.791824 + 0.610749i \(0.209132\pi\)
\(212\) 0 0
\(213\) −4.19938 −0.287737
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0.0697744 0.00471492
\(220\) 0 0
\(221\) 33.7348 2.26925
\(222\) 0 0
\(223\) 4.35325 0.291515 0.145758 0.989320i \(-0.453438\pi\)
0.145758 + 0.989320i \(0.453438\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.57175 0.502555 0.251277 0.967915i \(-0.419149\pi\)
0.251277 + 0.967915i \(0.419149\pi\)
\(228\) 0 0
\(229\) −8.29774 −0.548330 −0.274165 0.961683i \(-0.588401\pi\)
−0.274165 + 0.961683i \(0.588401\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.2690 1.06582 0.532910 0.846172i \(-0.321098\pi\)
0.532910 + 0.846172i \(0.321098\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.06458 0.134109
\(238\) 0 0
\(239\) −3.45932 −0.223765 −0.111882 0.993721i \(-0.535688\pi\)
−0.111882 + 0.993721i \(0.535688\pi\)
\(240\) 0 0
\(241\) −20.3197 −1.30891 −0.654454 0.756102i \(-0.727102\pi\)
−0.654454 + 0.756102i \(0.727102\pi\)
\(242\) 0 0
\(243\) 10.0930 0.647464
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.27360 0.271923
\(248\) 0 0
\(249\) 2.59120 0.164210
\(250\) 0 0
\(251\) 27.0867 1.70970 0.854849 0.518876i \(-0.173649\pi\)
0.854849 + 0.518876i \(0.173649\pi\)
\(252\) 0 0
\(253\) −29.5243 −1.85618
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.87399 0.491166 0.245583 0.969376i \(-0.421021\pi\)
0.245583 + 0.969376i \(0.421021\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 26.3895 1.63347
\(262\) 0 0
\(263\) 17.2983 1.06666 0.533331 0.845907i \(-0.320940\pi\)
0.533331 + 0.845907i \(0.320940\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.62142 0.160428
\(268\) 0 0
\(269\) −26.2251 −1.59897 −0.799486 0.600685i \(-0.794895\pi\)
−0.799486 + 0.600685i \(0.794895\pi\)
\(270\) 0 0
\(271\) 3.21075 0.195039 0.0975195 0.995234i \(-0.468909\pi\)
0.0975195 + 0.995234i \(0.468909\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.61760 0.0971922 0.0485961 0.998819i \(-0.484525\pi\)
0.0485961 + 0.998819i \(0.484525\pi\)
\(278\) 0 0
\(279\) 19.8500 1.18839
\(280\) 0 0
\(281\) 8.65404 0.516257 0.258128 0.966111i \(-0.416894\pi\)
0.258128 + 0.966111i \(0.416894\pi\)
\(282\) 0 0
\(283\) 15.9646 0.949000 0.474500 0.880256i \(-0.342629\pi\)
0.474500 + 0.880256i \(0.342629\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 29.0641 1.70965
\(290\) 0 0
\(291\) −3.59834 −0.210938
\(292\) 0 0
\(293\) 22.0239 1.28665 0.643324 0.765594i \(-0.277555\pi\)
0.643324 + 0.765594i \(0.277555\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 12.8267 0.744283
\(298\) 0 0
\(299\) 26.8760 1.55428
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −2.38166 −0.136823
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 14.8144 0.845502 0.422751 0.906246i \(-0.361065\pi\)
0.422751 + 0.906246i \(0.361065\pi\)
\(308\) 0 0
\(309\) 2.42929 0.138197
\(310\) 0 0
\(311\) −27.0216 −1.53225 −0.766126 0.642690i \(-0.777818\pi\)
−0.766126 + 0.642690i \(0.777818\pi\)
\(312\) 0 0
\(313\) 30.5423 1.72635 0.863177 0.504902i \(-0.168471\pi\)
0.863177 + 0.504902i \(0.168471\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −25.1895 −1.41479 −0.707393 0.706821i \(-0.750129\pi\)
−0.707393 + 0.706821i \(0.750129\pi\)
\(318\) 0 0
\(319\) 50.7712 2.84264
\(320\) 0 0
\(321\) −7.10254 −0.396425
\(322\) 0 0
\(323\) 5.83550 0.324696
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.82890 −0.101138
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 34.5364 1.89829 0.949147 0.314834i \(-0.101949\pi\)
0.949147 + 0.314834i \(0.101949\pi\)
\(332\) 0 0
\(333\) −7.83384 −0.429292
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.34596 0.454634 0.227317 0.973821i \(-0.427005\pi\)
0.227317 + 0.973821i \(0.427005\pi\)
\(338\) 0 0
\(339\) 6.63501 0.360365
\(340\) 0 0
\(341\) 38.1897 2.06809
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.5398 −0.995266 −0.497633 0.867388i \(-0.665797\pi\)
−0.497633 + 0.867388i \(0.665797\pi\)
\(348\) 0 0
\(349\) 32.6411 1.74724 0.873619 0.486611i \(-0.161767\pi\)
0.873619 + 0.486611i \(0.161767\pi\)
\(350\) 0 0
\(351\) −11.6762 −0.623229
\(352\) 0 0
\(353\) −0.307217 −0.0163515 −0.00817576 0.999967i \(-0.502602\pi\)
−0.00817576 + 0.999967i \(0.502602\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.3778 0.653278 0.326639 0.945149i \(-0.394084\pi\)
0.326639 + 0.945149i \(0.394084\pi\)
\(360\) 0 0
\(361\) −18.2607 −0.961092
\(362\) 0 0
\(363\) 7.57044 0.397345
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 34.6730 1.80992 0.904959 0.425499i \(-0.139902\pi\)
0.904959 + 0.425499i \(0.139902\pi\)
\(368\) 0 0
\(369\) −27.0713 −1.40927
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 26.1126 1.35206 0.676030 0.736874i \(-0.263699\pi\)
0.676030 + 0.736874i \(0.263699\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −46.2170 −2.38030
\(378\) 0 0
\(379\) −6.16572 −0.316712 −0.158356 0.987382i \(-0.550619\pi\)
−0.158356 + 0.987382i \(0.550619\pi\)
\(380\) 0 0
\(381\) −6.26683 −0.321060
\(382\) 0 0
\(383\) −10.7102 −0.547264 −0.273632 0.961834i \(-0.588225\pi\)
−0.273632 + 0.961834i \(0.588225\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 13.5100 0.686753
\(388\) 0 0
\(389\) −22.5426 −1.14296 −0.571479 0.820617i \(-0.693630\pi\)
−0.571479 + 0.820617i \(0.693630\pi\)
\(390\) 0 0
\(391\) 36.6985 1.85592
\(392\) 0 0
\(393\) 4.09213 0.206421
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 33.4458 1.67860 0.839299 0.543670i \(-0.182966\pi\)
0.839299 + 0.543670i \(0.182966\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.22597 −0.260973 −0.130486 0.991450i \(-0.541654\pi\)
−0.130486 + 0.991450i \(0.541654\pi\)
\(402\) 0 0
\(403\) −34.7641 −1.73172
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15.0716 −0.747073
\(408\) 0 0
\(409\) −11.9445 −0.590619 −0.295310 0.955402i \(-0.595423\pi\)
−0.295310 + 0.955402i \(0.595423\pi\)
\(410\) 0 0
\(411\) 2.54676 0.125623
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.11428 −0.103537
\(418\) 0 0
\(419\) −28.4553 −1.39013 −0.695067 0.718945i \(-0.744625\pi\)
−0.695067 + 0.718945i \(0.744625\pi\)
\(420\) 0 0
\(421\) 3.56357 0.173678 0.0868388 0.996222i \(-0.472323\pi\)
0.0868388 + 0.996222i \(0.472323\pi\)
\(422\) 0 0
\(423\) −31.5771 −1.53533
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −10.9205 −0.527246
\(430\) 0 0
\(431\) −11.9974 −0.577895 −0.288947 0.957345i \(-0.593305\pi\)
−0.288947 + 0.957345i \(0.593305\pi\)
\(432\) 0 0
\(433\) 11.5203 0.553629 0.276814 0.960923i \(-0.410721\pi\)
0.276814 + 0.960923i \(0.410721\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.64905 0.222394
\(438\) 0 0
\(439\) 2.86394 0.136688 0.0683441 0.997662i \(-0.478228\pi\)
0.0683441 + 0.997662i \(0.478228\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.8188 0.561530 0.280765 0.959777i \(-0.409412\pi\)
0.280765 + 0.959777i \(0.409412\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.87268 0.0885746
\(448\) 0 0
\(449\) −10.4612 −0.493693 −0.246847 0.969055i \(-0.579394\pi\)
−0.246847 + 0.969055i \(0.579394\pi\)
\(450\) 0 0
\(451\) −52.0828 −2.45248
\(452\) 0 0
\(453\) 8.37702 0.393587
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.29286 −0.154033 −0.0770167 0.997030i \(-0.524539\pi\)
−0.0770167 + 0.997030i \(0.524539\pi\)
\(458\) 0 0
\(459\) −15.9436 −0.744182
\(460\) 0 0
\(461\) 5.66513 0.263851 0.131926 0.991260i \(-0.457884\pi\)
0.131926 + 0.991260i \(0.457884\pi\)
\(462\) 0 0
\(463\) −3.24431 −0.150776 −0.0753878 0.997154i \(-0.524019\pi\)
−0.0753878 + 0.997154i \(0.524019\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10.0096 −0.463188 −0.231594 0.972812i \(-0.574394\pi\)
−0.231594 + 0.972812i \(0.574394\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 5.95311 0.274305
\(472\) 0 0
\(473\) 25.9921 1.19512
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.36740 0.245756
\(478\) 0 0
\(479\) −32.9470 −1.50539 −0.752693 0.658371i \(-0.771246\pi\)
−0.752693 + 0.658371i \(0.771246\pi\)
\(480\) 0 0
\(481\) 13.7197 0.625565
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −20.1152 −0.911507 −0.455754 0.890106i \(-0.650630\pi\)
−0.455754 + 0.890106i \(0.650630\pi\)
\(488\) 0 0
\(489\) 4.06976 0.184041
\(490\) 0 0
\(491\) −10.1602 −0.458525 −0.229263 0.973365i \(-0.573631\pi\)
−0.229263 + 0.973365i \(0.573631\pi\)
\(492\) 0 0
\(493\) −63.1083 −2.84225
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −22.3791 −1.00182 −0.500912 0.865498i \(-0.667002\pi\)
−0.500912 + 0.865498i \(0.667002\pi\)
\(500\) 0 0
\(501\) 5.24763 0.234447
\(502\) 0 0
\(503\) 7.67042 0.342007 0.171004 0.985270i \(-0.445299\pi\)
0.171004 + 0.985270i \(0.445299\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.71002 0.209179
\(508\) 0 0
\(509\) 0.0745813 0.00330576 0.00165288 0.999999i \(-0.499474\pi\)
0.00165288 + 0.999999i \(0.499474\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.01977 −0.0891749
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −60.7516 −2.67185
\(518\) 0 0
\(519\) 1.67692 0.0736087
\(520\) 0 0
\(521\) −25.4085 −1.11317 −0.556584 0.830791i \(-0.687888\pi\)
−0.556584 + 0.830791i \(0.687888\pi\)
\(522\) 0 0
\(523\) −26.7790 −1.17096 −0.585482 0.810686i \(-0.699095\pi\)
−0.585482 + 0.810686i \(0.699095\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −47.4695 −2.06781
\(528\) 0 0
\(529\) 6.23716 0.271181
\(530\) 0 0
\(531\) 31.7954 1.37980
\(532\) 0 0
\(533\) 47.4110 2.05360
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.0964710 0.00416303
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.31926 0.0997129 0.0498564 0.998756i \(-0.484124\pi\)
0.0498564 + 0.998756i \(0.484124\pi\)
\(542\) 0 0
\(543\) −6.27545 −0.269305
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.5800 0.666153 0.333076 0.942900i \(-0.391913\pi\)
0.333076 + 0.942900i \(0.391913\pi\)
\(548\) 0 0
\(549\) −15.6232 −0.666781
\(550\) 0 0
\(551\) −7.99470 −0.340586
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.71262 −0.284423 −0.142211 0.989836i \(-0.545421\pi\)
−0.142211 + 0.989836i \(0.545421\pi\)
\(558\) 0 0
\(559\) −23.6606 −1.00074
\(560\) 0 0
\(561\) −14.9117 −0.629572
\(562\) 0 0
\(563\) −10.3302 −0.435366 −0.217683 0.976020i \(-0.569850\pi\)
−0.217683 + 0.976020i \(0.569850\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.8410 −0.957544 −0.478772 0.877939i \(-0.658918\pi\)
−0.478772 + 0.877939i \(0.658918\pi\)
\(570\) 0 0
\(571\) 14.0540 0.588143 0.294071 0.955783i \(-0.404990\pi\)
0.294071 + 0.955783i \(0.404990\pi\)
\(572\) 0 0
\(573\) 0.737402 0.0308054
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 31.8186 1.32463 0.662313 0.749227i \(-0.269575\pi\)
0.662313 + 0.749227i \(0.269575\pi\)
\(578\) 0 0
\(579\) 9.54996 0.396883
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 10.3264 0.427676
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 31.2423 1.28951 0.644754 0.764390i \(-0.276960\pi\)
0.644754 + 0.764390i \(0.276960\pi\)
\(588\) 0 0
\(589\) −6.01355 −0.247784
\(590\) 0 0
\(591\) 0.759143 0.0312270
\(592\) 0 0
\(593\) 2.80706 0.115272 0.0576360 0.998338i \(-0.481644\pi\)
0.0576360 + 0.998338i \(0.481644\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.15310 0.251830
\(598\) 0 0
\(599\) −12.6038 −0.514978 −0.257489 0.966281i \(-0.582895\pi\)
−0.257489 + 0.966281i \(0.582895\pi\)
\(600\) 0 0
\(601\) 11.2563 0.459154 0.229577 0.973290i \(-0.426266\pi\)
0.229577 + 0.973290i \(0.426266\pi\)
\(602\) 0 0
\(603\) 10.9604 0.446344
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −20.4581 −0.830371 −0.415185 0.909737i \(-0.636283\pi\)
−0.415185 + 0.909737i \(0.636283\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 55.3022 2.23729
\(612\) 0 0
\(613\) 23.2976 0.940981 0.470491 0.882405i \(-0.344077\pi\)
0.470491 + 0.882405i \(0.344077\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.75766 −0.191536 −0.0957680 0.995404i \(-0.530531\pi\)
−0.0957680 + 0.995404i \(0.530531\pi\)
\(618\) 0 0
\(619\) 18.5368 0.745057 0.372529 0.928021i \(-0.378491\pi\)
0.372529 + 0.928021i \(0.378491\pi\)
\(620\) 0 0
\(621\) −12.7020 −0.509714
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.88905 −0.0754412
\(628\) 0 0
\(629\) 18.7339 0.746971
\(630\) 0 0
\(631\) −5.99286 −0.238572 −0.119286 0.992860i \(-0.538061\pi\)
−0.119286 + 0.992860i \(0.538061\pi\)
\(632\) 0 0
\(633\) 9.25621 0.367901
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 29.6196 1.17173
\(640\) 0 0
\(641\) 44.1100 1.74224 0.871121 0.491069i \(-0.163394\pi\)
0.871121 + 0.491069i \(0.163394\pi\)
\(642\) 0 0
\(643\) 21.5499 0.849846 0.424923 0.905230i \(-0.360301\pi\)
0.424923 + 0.905230i \(0.360301\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −50.5430 −1.98705 −0.993526 0.113606i \(-0.963760\pi\)
−0.993526 + 0.113606i \(0.963760\pi\)
\(648\) 0 0
\(649\) 61.1717 2.40120
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.88861 −0.230439 −0.115220 0.993340i \(-0.536757\pi\)
−0.115220 + 0.993340i \(0.536757\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.492141 −0.0192002
\(658\) 0 0
\(659\) −18.8198 −0.733114 −0.366557 0.930396i \(-0.619463\pi\)
−0.366557 + 0.930396i \(0.619463\pi\)
\(660\) 0 0
\(661\) 21.9156 0.852419 0.426209 0.904625i \(-0.359849\pi\)
0.426209 + 0.904625i \(0.359849\pi\)
\(662\) 0 0
\(663\) 13.5741 0.527174
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −50.2774 −1.94675
\(668\) 0 0
\(669\) 1.75165 0.0677227
\(670\) 0 0
\(671\) −30.0577 −1.16036
\(672\) 0 0
\(673\) 6.22597 0.239994 0.119997 0.992774i \(-0.461712\pi\)
0.119997 + 0.992774i \(0.461712\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33.8802 −1.30212 −0.651061 0.759025i \(-0.725676\pi\)
−0.651061 + 0.759025i \(0.725676\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 3.04670 0.116750
\(682\) 0 0
\(683\) −4.89379 −0.187256 −0.0936278 0.995607i \(-0.529846\pi\)
−0.0936278 + 0.995607i \(0.529846\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −3.33882 −0.127384
\(688\) 0 0
\(689\) −9.40013 −0.358116
\(690\) 0 0
\(691\) 18.5131 0.704271 0.352136 0.935949i \(-0.385456\pi\)
0.352136 + 0.935949i \(0.385456\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 64.7386 2.45215
\(698\) 0 0
\(699\) 6.54629 0.247604
\(700\) 0 0
\(701\) 23.1348 0.873788 0.436894 0.899513i \(-0.356078\pi\)
0.436894 + 0.899513i \(0.356078\pi\)
\(702\) 0 0
\(703\) 2.37326 0.0895091
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 47.6963 1.79127 0.895635 0.444789i \(-0.146722\pi\)
0.895635 + 0.444789i \(0.146722\pi\)
\(710\) 0 0
\(711\) −14.5621 −0.546122
\(712\) 0 0
\(713\) −37.8183 −1.41630
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.39195 −0.0519834
\(718\) 0 0
\(719\) 25.4102 0.947642 0.473821 0.880621i \(-0.342874\pi\)
0.473821 + 0.880621i \(0.342874\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −8.17620 −0.304076
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.78695 0.0662744 0.0331372 0.999451i \(-0.489450\pi\)
0.0331372 + 0.999451i \(0.489450\pi\)
\(728\) 0 0
\(729\) −18.6460 −0.690591
\(730\) 0 0
\(731\) −32.3080 −1.19496
\(732\) 0 0
\(733\) −14.0748 −0.519864 −0.259932 0.965627i \(-0.583700\pi\)
−0.259932 + 0.965627i \(0.583700\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.0870 0.776748
\(738\) 0 0
\(739\) 24.1628 0.888844 0.444422 0.895817i \(-0.353409\pi\)
0.444422 + 0.895817i \(0.353409\pi\)
\(740\) 0 0
\(741\) 1.71960 0.0631710
\(742\) 0 0
\(743\) −32.6579 −1.19810 −0.599050 0.800711i \(-0.704455\pi\)
−0.599050 + 0.800711i \(0.704455\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −18.2765 −0.668703
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −34.2871 −1.25116 −0.625578 0.780162i \(-0.715137\pi\)
−0.625578 + 0.780162i \(0.715137\pi\)
\(752\) 0 0
\(753\) 10.8991 0.397185
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 13.1452 0.477772 0.238886 0.971048i \(-0.423218\pi\)
0.238886 + 0.971048i \(0.423218\pi\)
\(758\) 0 0
\(759\) −11.8799 −0.431213
\(760\) 0 0
\(761\) 39.2129 1.42147 0.710734 0.703461i \(-0.248363\pi\)
0.710734 + 0.703461i \(0.248363\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −55.6846 −2.01065
\(768\) 0 0
\(769\) 11.8339 0.426742 0.213371 0.976971i \(-0.431556\pi\)
0.213371 + 0.976971i \(0.431556\pi\)
\(770\) 0 0
\(771\) 3.16831 0.114104
\(772\) 0 0
\(773\) 51.8065 1.86335 0.931676 0.363291i \(-0.118347\pi\)
0.931676 + 0.363291i \(0.118347\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.20123 0.293840
\(780\) 0 0
\(781\) 56.9855 2.03910
\(782\) 0 0
\(783\) 21.8429 0.780600
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −24.7399 −0.881881 −0.440940 0.897536i \(-0.645355\pi\)
−0.440940 + 0.897536i \(0.645355\pi\)
\(788\) 0 0
\(789\) 6.96046 0.247799
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 27.3615 0.971635
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.33277 −0.118053 −0.0590264 0.998256i \(-0.518800\pi\)
−0.0590264 + 0.998256i \(0.518800\pi\)
\(798\) 0 0
\(799\) 75.5138 2.67149
\(800\) 0 0
\(801\) −18.4897 −0.653300
\(802\) 0 0
\(803\) −0.946837 −0.0334131
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −10.5524 −0.371461
\(808\) 0 0
\(809\) 4.21883 0.148326 0.0741631 0.997246i \(-0.476371\pi\)
0.0741631 + 0.997246i \(0.476371\pi\)
\(810\) 0 0
\(811\) −13.7657 −0.483380 −0.241690 0.970353i \(-0.577702\pi\)
−0.241690 + 0.970353i \(0.577702\pi\)
\(812\) 0 0
\(813\) 1.29193 0.0453100
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −4.09286 −0.143191
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 36.2252 1.26427 0.632135 0.774859i \(-0.282179\pi\)
0.632135 + 0.774859i \(0.282179\pi\)
\(822\) 0 0
\(823\) 26.7119 0.931118 0.465559 0.885017i \(-0.345853\pi\)
0.465559 + 0.885017i \(0.345853\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −55.8703 −1.94280 −0.971400 0.237449i \(-0.923689\pi\)
−0.971400 + 0.237449i \(0.923689\pi\)
\(828\) 0 0
\(829\) 17.5979 0.611199 0.305600 0.952160i \(-0.401143\pi\)
0.305600 + 0.952160i \(0.401143\pi\)
\(830\) 0 0
\(831\) 0.650885 0.0225790
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 16.4300 0.567905
\(838\) 0 0
\(839\) −9.56870 −0.330348 −0.165174 0.986264i \(-0.552819\pi\)
−0.165174 + 0.986264i \(0.552819\pi\)
\(840\) 0 0
\(841\) 57.4591 1.98135
\(842\) 0 0
\(843\) 3.48219 0.119933
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 6.42381 0.220465
\(850\) 0 0
\(851\) 14.9250 0.511624
\(852\) 0 0
\(853\) −11.2026 −0.383569 −0.191784 0.981437i \(-0.561427\pi\)
−0.191784 + 0.981437i \(0.561427\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 30.4891 1.04149 0.520744 0.853713i \(-0.325655\pi\)
0.520744 + 0.853713i \(0.325655\pi\)
\(858\) 0 0
\(859\) −34.4774 −1.17635 −0.588176 0.808733i \(-0.700154\pi\)
−0.588176 + 0.808733i \(0.700154\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 55.4155 1.88637 0.943183 0.332274i \(-0.107816\pi\)
0.943183 + 0.332274i \(0.107816\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 11.6947 0.397173
\(868\) 0 0
\(869\) −28.0162 −0.950386
\(870\) 0 0
\(871\) −19.1954 −0.650413
\(872\) 0 0
\(873\) 25.3802 0.858990
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.908794 0.0306878 0.0153439 0.999882i \(-0.495116\pi\)
0.0153439 + 0.999882i \(0.495116\pi\)
\(878\) 0 0
\(879\) 8.86191 0.298905
\(880\) 0 0
\(881\) −51.5348 −1.73625 −0.868126 0.496344i \(-0.834676\pi\)
−0.868126 + 0.496344i \(0.834676\pi\)
\(882\) 0 0
\(883\) −28.3047 −0.952530 −0.476265 0.879302i \(-0.658010\pi\)
−0.476265 + 0.879302i \(0.658010\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.36739 0.113066 0.0565330 0.998401i \(-0.481995\pi\)
0.0565330 + 0.998401i \(0.481995\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −41.3289 −1.38457
\(892\) 0 0
\(893\) 9.56627 0.320123
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 10.8143 0.361078
\(898\) 0 0
\(899\) 65.0338 2.16900
\(900\) 0 0
\(901\) −12.8357 −0.427618
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −43.4695 −1.44338 −0.721691 0.692215i \(-0.756635\pi\)
−0.721691 + 0.692215i \(0.756635\pi\)
\(908\) 0 0
\(909\) 16.7986 0.557175
\(910\) 0 0
\(911\) 10.9276 0.362049 0.181024 0.983479i \(-0.442059\pi\)
0.181024 + 0.983479i \(0.442059\pi\)
\(912\) 0 0
\(913\) −35.1624 −1.16371
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.165425 0.00545687 0.00272844 0.999996i \(-0.499132\pi\)
0.00272844 + 0.999996i \(0.499132\pi\)
\(920\) 0 0
\(921\) 5.96097 0.196421
\(922\) 0 0
\(923\) −51.8739 −1.70745
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −17.1345 −0.562772
\(928\) 0 0
\(929\) −50.6798 −1.66275 −0.831376 0.555711i \(-0.812446\pi\)
−0.831376 + 0.555711i \(0.812446\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −10.8729 −0.355962
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 35.5069 1.15996 0.579980 0.814631i \(-0.303060\pi\)
0.579980 + 0.814631i \(0.303060\pi\)
\(938\) 0 0
\(939\) 12.2895 0.401054
\(940\) 0 0
\(941\) 0.813025 0.0265039 0.0132519 0.999912i \(-0.495782\pi\)
0.0132519 + 0.999912i \(0.495782\pi\)
\(942\) 0 0
\(943\) 51.5762 1.67955
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 40.1281 1.30399 0.651995 0.758224i \(-0.273933\pi\)
0.651995 + 0.758224i \(0.273933\pi\)
\(948\) 0 0
\(949\) 0.861905 0.0279786
\(950\) 0 0
\(951\) −10.1357 −0.328672
\(952\) 0 0
\(953\) −0.949783 −0.0307665 −0.0153833 0.999882i \(-0.504897\pi\)
−0.0153833 + 0.999882i \(0.504897\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 20.4292 0.660381
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 17.9179 0.577997
\(962\) 0 0
\(963\) 50.0964 1.61434
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −22.1648 −0.712772 −0.356386 0.934339i \(-0.615991\pi\)
−0.356386 + 0.934339i \(0.615991\pi\)
\(968\) 0 0
\(969\) 2.34807 0.0754310
\(970\) 0 0
\(971\) −24.6789 −0.791983 −0.395992 0.918254i \(-0.629599\pi\)
−0.395992 + 0.918254i \(0.629599\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19.5162 −0.624380 −0.312190 0.950020i \(-0.601063\pi\)
−0.312190 + 0.950020i \(0.601063\pi\)
\(978\) 0 0
\(979\) −35.5725 −1.13690
\(980\) 0 0
\(981\) 12.8998 0.411859
\(982\) 0 0
\(983\) −25.6405 −0.817805 −0.408903 0.912578i \(-0.634088\pi\)
−0.408903 + 0.912578i \(0.634088\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −25.7393 −0.818463
\(990\) 0 0
\(991\) −36.2045 −1.15008 −0.575038 0.818127i \(-0.695013\pi\)
−0.575038 + 0.818127i \(0.695013\pi\)
\(992\) 0 0
\(993\) 13.8967 0.440998
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 29.5358 0.935409 0.467704 0.883885i \(-0.345081\pi\)
0.467704 + 0.883885i \(0.345081\pi\)
\(998\) 0 0
\(999\) −6.48414 −0.205149
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 9800.2.a.da.1.5 yes 8
5.4 even 2 9800.2.a.cz.1.4 8
7.6 odd 2 inner 9800.2.a.da.1.4 yes 8
35.34 odd 2 9800.2.a.cz.1.5 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9800.2.a.cz.1.4 8 5.4 even 2
9800.2.a.cz.1.5 yes 8 35.34 odd 2
9800.2.a.da.1.4 yes 8 7.6 odd 2 inner
9800.2.a.da.1.5 yes 8 1.1 even 1 trivial