Properties

Label 6400.2.a.bz.1.2
Level $6400$
Weight $2$
Character 6400.1
Self dual yes
Analytic conductor $51.104$
Analytic rank $1$
Dimension $2$
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] = [6400,2,Mod(1,6400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6400, 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("6400.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6400 = 2^{8} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6400.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: \(51.1042572936\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{10}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 640)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.16228\) of defining polynomial
Character \(\chi\) \(=\) 6400.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.16228 q^{3} -3.16228 q^{7} +7.00000 q^{9} +O(q^{10})\) \(q+3.16228 q^{3} -3.16228 q^{7} +7.00000 q^{9} -6.00000 q^{13} +2.00000 q^{17} -6.32456 q^{19} -10.0000 q^{21} -3.16228 q^{23} +12.6491 q^{27} -4.00000 q^{29} +6.32456 q^{31} -2.00000 q^{37} -18.9737 q^{39} -3.16228 q^{43} +9.48683 q^{47} +3.00000 q^{49} +6.32456 q^{51} -6.00000 q^{53} -20.0000 q^{57} +6.32456 q^{59} +2.00000 q^{61} -22.1359 q^{63} -9.48683 q^{67} -10.0000 q^{69} +6.32456 q^{71} -14.0000 q^{73} -12.6491 q^{79} +19.0000 q^{81} -3.16228 q^{83} -12.6491 q^{87} -10.0000 q^{89} +18.9737 q^{91} +20.0000 q^{93} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 14 q^{9} - 12 q^{13} + 4 q^{17} - 20 q^{21} - 8 q^{29} - 4 q^{37} + 6 q^{49} - 12 q^{53} - 40 q^{57} + 4 q^{61} - 20 q^{69} - 28 q^{73} + 38 q^{81} - 20 q^{89} + 40 q^{93} - 4 q^{97}+O(q^{100}) \) 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
\(3\) 3.16228 1.82574 0.912871 0.408248i \(-0.133860\pi\)
0.912871 + 0.408248i \(0.133860\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.16228 −1.19523 −0.597614 0.801784i \(-0.703885\pi\)
−0.597614 + 0.801784i \(0.703885\pi\)
\(8\) 0 0
\(9\) 7.00000 2.33333
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −6.32456 −1.45095 −0.725476 0.688247i \(-0.758380\pi\)
−0.725476 + 0.688247i \(0.758380\pi\)
\(20\) 0 0
\(21\) −10.0000 −2.18218
\(22\) 0 0
\(23\) −3.16228 −0.659380 −0.329690 0.944089i \(-0.606944\pi\)
−0.329690 + 0.944089i \(0.606944\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 12.6491 2.43432
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 6.32456 1.13592 0.567962 0.823055i \(-0.307732\pi\)
0.567962 + 0.823055i \(0.307732\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) −18.9737 −3.03822
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −3.16228 −0.482243 −0.241121 0.970495i \(-0.577515\pi\)
−0.241121 + 0.970495i \(0.577515\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.48683 1.38380 0.691898 0.721995i \(-0.256775\pi\)
0.691898 + 0.721995i \(0.256775\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) 6.32456 0.885615
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −20.0000 −2.64906
\(58\) 0 0
\(59\) 6.32456 0.823387 0.411693 0.911322i \(-0.364937\pi\)
0.411693 + 0.911322i \(0.364937\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) −22.1359 −2.78887
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −9.48683 −1.15900 −0.579501 0.814972i \(-0.696752\pi\)
−0.579501 + 0.814972i \(0.696752\pi\)
\(68\) 0 0
\(69\) −10.0000 −1.20386
\(70\) 0 0
\(71\) 6.32456 0.750587 0.375293 0.926906i \(-0.377542\pi\)
0.375293 + 0.926906i \(0.377542\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −12.6491 −1.42314 −0.711568 0.702617i \(-0.752015\pi\)
−0.711568 + 0.702617i \(0.752015\pi\)
\(80\) 0 0
\(81\) 19.0000 2.11111
\(82\) 0 0
\(83\) −3.16228 −0.347105 −0.173553 0.984825i \(-0.555525\pi\)
−0.173553 + 0.984825i \(0.555525\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −12.6491 −1.35613
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 18.9737 1.98898
\(92\) 0 0
\(93\) 20.0000 2.07390
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −15.8114 −1.55794 −0.778971 0.627060i \(-0.784258\pi\)
−0.778971 + 0.627060i \(0.784258\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.8114 −1.52854 −0.764272 0.644894i \(-0.776902\pi\)
−0.764272 + 0.644894i \(0.776902\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −6.32456 −0.600300
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −42.0000 −3.88290
\(118\) 0 0
\(119\) −6.32456 −0.579771
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.48683 −0.841820 −0.420910 0.907102i \(-0.638289\pi\)
−0.420910 + 0.907102i \(0.638289\pi\)
\(128\) 0 0
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) −12.6491 −1.10516 −0.552579 0.833461i \(-0.686356\pi\)
−0.552579 + 0.833461i \(0.686356\pi\)
\(132\) 0 0
\(133\) 20.0000 1.73422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) 6.32456 0.536442 0.268221 0.963357i \(-0.413564\pi\)
0.268221 + 0.963357i \(0.413564\pi\)
\(140\) 0 0
\(141\) 30.0000 2.52646
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.48683 0.782461
\(148\) 0 0
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 6.32456 0.514685 0.257343 0.966320i \(-0.417153\pi\)
0.257343 + 0.966320i \(0.417153\pi\)
\(152\) 0 0
\(153\) 14.0000 1.13183
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) −18.9737 −1.50471
\(160\) 0 0
\(161\) 10.0000 0.788110
\(162\) 0 0
\(163\) −9.48683 −0.743066 −0.371533 0.928420i \(-0.621168\pi\)
−0.371533 + 0.928420i \(0.621168\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.8114 1.22352 0.611761 0.791043i \(-0.290461\pi\)
0.611761 + 0.791043i \(0.290461\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) −44.2719 −3.38556
\(172\) 0 0
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 20.0000 1.50329
\(178\) 0 0
\(179\) 18.9737 1.41816 0.709079 0.705129i \(-0.249111\pi\)
0.709079 + 0.705129i \(0.249111\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 6.32456 0.467525
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −40.0000 −2.90957
\(190\) 0 0
\(191\) 18.9737 1.37289 0.686443 0.727183i \(-0.259171\pi\)
0.686443 + 0.727183i \(0.259171\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −30.0000 −2.11604
\(202\) 0 0
\(203\) 12.6491 0.887794
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −22.1359 −1.53855
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 20.0000 1.37038
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −20.0000 −1.35769
\(218\) 0 0
\(219\) −44.2719 −2.99162
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 22.1359 1.48233 0.741166 0.671322i \(-0.234273\pi\)
0.741166 + 0.671322i \(0.234273\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.48683 0.629663 0.314832 0.949148i \(-0.398052\pi\)
0.314832 + 0.949148i \(0.398052\pi\)
\(228\) 0 0
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −40.0000 −2.59828
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 22.1359 1.42002
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 37.9473 2.41453
\(248\) 0 0
\(249\) −10.0000 −0.633724
\(250\) 0 0
\(251\) 12.6491 0.798405 0.399202 0.916863i \(-0.369287\pi\)
0.399202 + 0.916863i \(0.369287\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) 6.32456 0.392989
\(260\) 0 0
\(261\) −28.0000 −1.73316
\(262\) 0 0
\(263\) −22.1359 −1.36496 −0.682480 0.730904i \(-0.739099\pi\)
−0.682480 + 0.730904i \(0.739099\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −31.6228 −1.93528
\(268\) 0 0
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) 6.32456 0.384189 0.192095 0.981376i \(-0.438472\pi\)
0.192095 + 0.981376i \(0.438472\pi\)
\(272\) 0 0
\(273\) 60.0000 3.63137
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 0 0
\(279\) 44.2719 2.65049
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 3.16228 0.187978 0.0939889 0.995573i \(-0.470038\pi\)
0.0939889 + 0.995573i \(0.470038\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −6.32456 −0.370752
\(292\) 0 0
\(293\) −26.0000 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 18.9737 1.09728
\(300\) 0 0
\(301\) 10.0000 0.576390
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 15.8114 0.902404 0.451202 0.892422i \(-0.350995\pi\)
0.451202 + 0.892422i \(0.350995\pi\)
\(308\) 0 0
\(309\) −50.0000 −2.84440
\(310\) 0 0
\(311\) −18.9737 −1.07590 −0.537949 0.842977i \(-0.680801\pi\)
−0.537949 + 0.842977i \(0.680801\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.0000 1.23564 0.617822 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −50.0000 −2.79073
\(322\) 0 0
\(323\) −12.6491 −0.703815
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −31.6228 −1.74874
\(328\) 0 0
\(329\) −30.0000 −1.65395
\(330\) 0 0
\(331\) −12.6491 −0.695258 −0.347629 0.937632i \(-0.613013\pi\)
−0.347629 + 0.937632i \(0.613013\pi\)
\(332\) 0 0
\(333\) −14.0000 −0.767195
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) −18.9737 −1.03051
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 12.6491 0.682988
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.8114 0.848800 0.424400 0.905475i \(-0.360485\pi\)
0.424400 + 0.905475i \(0.360485\pi\)
\(348\) 0 0
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 0 0
\(351\) −75.8947 −4.05096
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −20.0000 −1.05851
\(358\) 0 0
\(359\) 12.6491 0.667595 0.333797 0.942645i \(-0.391670\pi\)
0.333797 + 0.942645i \(0.391670\pi\)
\(360\) 0 0
\(361\) 21.0000 1.10526
\(362\) 0 0
\(363\) −34.7851 −1.82574
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3.16228 0.165070 0.0825348 0.996588i \(-0.473698\pi\)
0.0825348 + 0.996588i \(0.473698\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 18.9737 0.985064
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 6.32456 0.324871 0.162435 0.986719i \(-0.448065\pi\)
0.162435 + 0.986719i \(0.448065\pi\)
\(380\) 0 0
\(381\) −30.0000 −1.53695
\(382\) 0 0
\(383\) 22.1359 1.13109 0.565547 0.824716i \(-0.308665\pi\)
0.565547 + 0.824716i \(0.308665\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −22.1359 −1.12523
\(388\) 0 0
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −6.32456 −0.319847
\(392\) 0 0
\(393\) −40.0000 −2.01773
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) 63.2456 3.16624
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) −37.9473 −1.89029
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 36.0000 1.78009 0.890043 0.455877i \(-0.150674\pi\)
0.890043 + 0.455877i \(0.150674\pi\)
\(410\) 0 0
\(411\) 56.9210 2.80771
\(412\) 0 0
\(413\) −20.0000 −0.984136
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) 31.6228 1.54487 0.772437 0.635092i \(-0.219038\pi\)
0.772437 + 0.635092i \(0.219038\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 66.4078 3.22886
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6.32456 −0.306067
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 31.6228 1.52322 0.761608 0.648038i \(-0.224410\pi\)
0.761608 + 0.648038i \(0.224410\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 20.0000 0.956730
\(438\) 0 0
\(439\) −12.6491 −0.603709 −0.301855 0.953354i \(-0.597606\pi\)
−0.301855 + 0.953354i \(0.597606\pi\)
\(440\) 0 0
\(441\) 21.0000 1.00000
\(442\) 0 0
\(443\) 41.1096 1.95318 0.976588 0.215117i \(-0.0690133\pi\)
0.976588 + 0.215117i \(0.0690133\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 31.6228 1.49571
\(448\) 0 0
\(449\) 4.00000 0.188772 0.0943858 0.995536i \(-0.469911\pi\)
0.0943858 + 0.995536i \(0.469911\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 20.0000 0.939682
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 0 0
\(459\) 25.2982 1.18082
\(460\) 0 0
\(461\) −40.0000 −1.86299 −0.931493 0.363760i \(-0.881493\pi\)
−0.931493 + 0.363760i \(0.881493\pi\)
\(462\) 0 0
\(463\) 3.16228 0.146964 0.0734818 0.997297i \(-0.476589\pi\)
0.0734818 + 0.997297i \(0.476589\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.16228 −0.146333 −0.0731664 0.997320i \(-0.523310\pi\)
−0.0731664 + 0.997320i \(0.523310\pi\)
\(468\) 0 0
\(469\) 30.0000 1.38527
\(470\) 0 0
\(471\) −6.32456 −0.291420
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −42.0000 −1.92305
\(478\) 0 0
\(479\) 25.2982 1.15591 0.577953 0.816070i \(-0.303852\pi\)
0.577953 + 0.816070i \(0.303852\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) 0 0
\(483\) 31.6228 1.43889
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 9.48683 0.429889 0.214945 0.976626i \(-0.431043\pi\)
0.214945 + 0.976626i \(0.431043\pi\)
\(488\) 0 0
\(489\) −30.0000 −1.35665
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −20.0000 −0.897123
\(498\) 0 0
\(499\) −31.6228 −1.41563 −0.707815 0.706398i \(-0.750319\pi\)
−0.707815 + 0.706398i \(0.750319\pi\)
\(500\) 0 0
\(501\) 50.0000 2.23384
\(502\) 0 0
\(503\) 34.7851 1.55099 0.775494 0.631354i \(-0.217501\pi\)
0.775494 + 0.631354i \(0.217501\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 72.7324 3.23016
\(508\) 0 0
\(509\) −36.0000 −1.59567 −0.797836 0.602875i \(-0.794022\pi\)
−0.797836 + 0.602875i \(0.794022\pi\)
\(510\) 0 0
\(511\) 44.2719 1.95847
\(512\) 0 0
\(513\) −80.0000 −3.53209
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 44.2719 1.94332
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 3.16228 0.138277 0.0691384 0.997607i \(-0.477975\pi\)
0.0691384 + 0.997607i \(0.477975\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.6491 0.551004
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) 44.2719 1.92124
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 60.0000 2.58919
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 40.0000 1.71973 0.859867 0.510518i \(-0.170546\pi\)
0.859867 + 0.510518i \(0.170546\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −15.8114 −0.676046 −0.338023 0.941138i \(-0.609758\pi\)
−0.338023 + 0.941138i \(0.609758\pi\)
\(548\) 0 0
\(549\) 14.0000 0.597505
\(550\) 0 0
\(551\) 25.2982 1.07774
\(552\) 0 0
\(553\) 40.0000 1.70097
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) 18.9737 0.802501
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 28.4605 1.19947 0.599734 0.800200i \(-0.295273\pi\)
0.599734 + 0.800200i \(0.295273\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −60.0833 −2.52326
\(568\) 0 0
\(569\) 4.00000 0.167689 0.0838444 0.996479i \(-0.473280\pi\)
0.0838444 + 0.996479i \(0.473280\pi\)
\(570\) 0 0
\(571\) 12.6491 0.529349 0.264674 0.964338i \(-0.414736\pi\)
0.264674 + 0.964338i \(0.414736\pi\)
\(572\) 0 0
\(573\) 60.0000 2.50654
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 0 0
\(579\) −44.2719 −1.83988
\(580\) 0 0
\(581\) 10.0000 0.414870
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.16228 0.130521 0.0652606 0.997868i \(-0.479212\pi\)
0.0652606 + 0.997868i \(0.479212\pi\)
\(588\) 0 0
\(589\) −40.0000 −1.64817
\(590\) 0 0
\(591\) −56.9210 −2.34142
\(592\) 0 0
\(593\) 46.0000 1.88899 0.944497 0.328521i \(-0.106550\pi\)
0.944497 + 0.328521i \(0.106550\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −37.9473 −1.55049 −0.775243 0.631663i \(-0.782373\pi\)
−0.775243 + 0.631663i \(0.782373\pi\)
\(600\) 0 0
\(601\) 40.0000 1.63163 0.815817 0.578310i \(-0.196288\pi\)
0.815817 + 0.578310i \(0.196288\pi\)
\(602\) 0 0
\(603\) −66.4078 −2.70434
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 34.7851 1.41188 0.705941 0.708271i \(-0.250524\pi\)
0.705941 + 0.708271i \(0.250524\pi\)
\(608\) 0 0
\(609\) 40.0000 1.62088
\(610\) 0 0
\(611\) −56.9210 −2.30278
\(612\) 0 0
\(613\) 46.0000 1.85792 0.928961 0.370177i \(-0.120703\pi\)
0.928961 + 0.370177i \(0.120703\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −31.6228 −1.27103 −0.635513 0.772090i \(-0.719211\pi\)
−0.635513 + 0.772090i \(0.719211\pi\)
\(620\) 0 0
\(621\) −40.0000 −1.60514
\(622\) 0 0
\(623\) 31.6228 1.26694
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) −6.32456 −0.251777 −0.125888 0.992044i \(-0.540178\pi\)
−0.125888 + 0.992044i \(0.540178\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) 44.2719 1.75137
\(640\) 0 0
\(641\) −40.0000 −1.57991 −0.789953 0.613168i \(-0.789895\pi\)
−0.789953 + 0.613168i \(0.789895\pi\)
\(642\) 0 0
\(643\) 9.48683 0.374124 0.187062 0.982348i \(-0.440103\pi\)
0.187062 + 0.982348i \(0.440103\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.48683 0.372966 0.186483 0.982458i \(-0.440291\pi\)
0.186483 + 0.982458i \(0.440291\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −63.2456 −2.47879
\(652\) 0 0
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −98.0000 −3.82334
\(658\) 0 0
\(659\) −44.2719 −1.72459 −0.862294 0.506408i \(-0.830973\pi\)
−0.862294 + 0.506408i \(0.830973\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 0 0
\(663\) −37.9473 −1.47375
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.6491 0.489776
\(668\) 0 0
\(669\) 70.0000 2.70636
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) 6.32456 0.242714
\(680\) 0 0
\(681\) 30.0000 1.14960
\(682\) 0 0
\(683\) 22.1359 0.847008 0.423504 0.905894i \(-0.360800\pi\)
0.423504 + 0.905894i \(0.360800\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −12.6491 −0.482594
\(688\) 0 0
\(689\) 36.0000 1.37149
\(690\) 0 0
\(691\) −37.9473 −1.44358 −0.721792 0.692110i \(-0.756681\pi\)
−0.721792 + 0.692110i \(0.756681\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 44.2719 1.67452
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) 12.6491 0.477070
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.00000 0.150223 0.0751116 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 0 0
\(711\) −88.5438 −3.32065
\(712\) 0 0
\(713\) −20.0000 −0.749006
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −50.5964 −1.88693 −0.943464 0.331474i \(-0.892454\pi\)
−0.943464 + 0.331474i \(0.892454\pi\)
\(720\) 0 0
\(721\) 50.0000 1.86210
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −3.16228 −0.117282 −0.0586412 0.998279i \(-0.518677\pi\)
−0.0586412 + 0.998279i \(0.518677\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −6.32456 −0.233922
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 18.9737 0.697958 0.348979 0.937131i \(-0.386529\pi\)
0.348979 + 0.937131i \(0.386529\pi\)
\(740\) 0 0
\(741\) 120.000 4.40831
\(742\) 0 0
\(743\) −9.48683 −0.348038 −0.174019 0.984742i \(-0.555675\pi\)
−0.174019 + 0.984742i \(0.555675\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −22.1359 −0.809912
\(748\) 0 0
\(749\) 50.0000 1.82696
\(750\) 0 0
\(751\) 6.32456 0.230786 0.115393 0.993320i \(-0.463187\pi\)
0.115393 + 0.993320i \(0.463187\pi\)
\(752\) 0 0
\(753\) 40.0000 1.45768
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) 0 0
\(763\) 31.6228 1.14482
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −37.9473 −1.37020
\(768\) 0 0
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 56.9210 2.04996
\(772\) 0 0
\(773\) −34.0000 −1.22290 −0.611448 0.791285i \(-0.709412\pi\)
−0.611448 + 0.791285i \(0.709412\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 20.0000 0.717496
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −50.5964 −1.80817
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 3.16228 0.112723 0.0563615 0.998410i \(-0.482050\pi\)
0.0563615 + 0.998410i \(0.482050\pi\)
\(788\) 0 0
\(789\) −70.0000 −2.49207
\(790\) 0 0
\(791\) 18.9737 0.674626
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) 18.9737 0.671240
\(800\) 0 0
\(801\) −70.0000 −2.47333
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 31.6228 1.11317
\(808\) 0 0
\(809\) −10.0000 −0.351581 −0.175791 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) 0 0
\(811\) 12.6491 0.444170 0.222085 0.975027i \(-0.428714\pi\)
0.222085 + 0.975027i \(0.428714\pi\)
\(812\) 0 0
\(813\) 20.0000 0.701431
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 20.0000 0.699711
\(818\) 0 0
\(819\) 132.816 4.64095
\(820\) 0 0
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) −28.4605 −0.992071 −0.496035 0.868302i \(-0.665211\pi\)
−0.496035 + 0.868302i \(0.665211\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.48683 −0.329890 −0.164945 0.986303i \(-0.552745\pi\)
−0.164945 + 0.986303i \(0.552745\pi\)
\(828\) 0 0
\(829\) 10.0000 0.347314 0.173657 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) 6.32456 0.219396
\(832\) 0 0
\(833\) 6.00000 0.207888
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 80.0000 2.76520
\(838\) 0 0
\(839\) −12.6491 −0.436696 −0.218348 0.975871i \(-0.570067\pi\)
−0.218348 + 0.975871i \(0.570067\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 34.7851 1.19523
\(848\) 0 0
\(849\) 10.0000 0.343199
\(850\) 0 0
\(851\) 6.32456 0.216803
\(852\) 0 0
\(853\) 46.0000 1.57501 0.787505 0.616308i \(-0.211372\pi\)
0.787505 + 0.616308i \(0.211372\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −44.2719 −1.51054 −0.755269 0.655415i \(-0.772494\pi\)
−0.755269 + 0.655415i \(0.772494\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −34.7851 −1.18410 −0.592049 0.805902i \(-0.701681\pi\)
−0.592049 + 0.805902i \(0.701681\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −41.1096 −1.39616
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 56.9210 1.92869
\(872\) 0 0
\(873\) −14.0000 −0.473828
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 38.0000 1.28317 0.641584 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) 0 0
\(879\) −82.2192 −2.77319
\(880\) 0 0
\(881\) −40.0000 −1.34763 −0.673817 0.738898i \(-0.735346\pi\)
−0.673817 + 0.738898i \(0.735346\pi\)
\(882\) 0 0
\(883\) 3.16228 0.106419 0.0532096 0.998583i \(-0.483055\pi\)
0.0532096 + 0.998583i \(0.483055\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 47.4342 1.59268 0.796342 0.604847i \(-0.206766\pi\)
0.796342 + 0.604847i \(0.206766\pi\)
\(888\) 0 0
\(889\) 30.0000 1.00617
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −60.0000 −2.00782
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 60.0000 2.00334
\(898\) 0 0
\(899\) −25.2982 −0.843743
\(900\) 0 0
\(901\) −12.0000 −0.399778
\(902\) 0 0
\(903\) 31.6228 1.05234
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −53.7587 −1.78503 −0.892515 0.451019i \(-0.851061\pi\)
−0.892515 + 0.451019i \(0.851061\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 31.6228 1.04771 0.523855 0.851808i \(-0.324493\pi\)
0.523855 + 0.851808i \(0.324493\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 40.0000 1.32092
\(918\) 0 0
\(919\) −12.6491 −0.417256 −0.208628 0.977995i \(-0.566900\pi\)
−0.208628 + 0.977995i \(0.566900\pi\)
\(920\) 0 0
\(921\) 50.0000 1.64756
\(922\) 0 0
\(923\) −37.9473 −1.24905
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −110.680 −3.63520
\(928\) 0 0
\(929\) −4.00000 −0.131236 −0.0656179 0.997845i \(-0.520902\pi\)
−0.0656179 + 0.997845i \(0.520902\pi\)
\(930\) 0 0
\(931\) −18.9737 −0.621837
\(932\) 0 0
\(933\) −60.0000 −1.96431
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 38.0000 1.24141 0.620703 0.784046i \(-0.286847\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(938\) 0 0
\(939\) 18.9737 0.619182
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 15.8114 0.513801 0.256901 0.966438i \(-0.417299\pi\)
0.256901 + 0.966438i \(0.417299\pi\)
\(948\) 0 0
\(949\) 84.0000 2.72676
\(950\) 0 0
\(951\) 69.5701 2.25597
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −56.9210 −1.83807
\(960\) 0 0
\(961\) 9.00000 0.290323
\(962\) 0 0
\(963\) −110.680 −3.56660
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −22.1359 −0.711844 −0.355922 0.934516i \(-0.615833\pi\)
−0.355922 + 0.934516i \(0.615833\pi\)
\(968\) 0 0
\(969\) −40.0000 −1.28499
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) −20.0000 −0.641171
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.00000 −0.0639857 −0.0319928 0.999488i \(-0.510185\pi\)
−0.0319928 + 0.999488i \(0.510185\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −70.0000 −2.23493
\(982\) 0 0
\(983\) −47.4342 −1.51291 −0.756457 0.654043i \(-0.773072\pi\)
−0.756457 + 0.654043i \(0.773072\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −94.8683 −3.01969
\(988\) 0 0
\(989\) 10.0000 0.317982
\(990\) 0 0
\(991\) 44.2719 1.40634 0.703171 0.711020i \(-0.251767\pi\)
0.703171 + 0.711020i \(0.251767\pi\)
\(992\) 0 0
\(993\) −40.0000 −1.26936
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 18.0000 0.570066 0.285033 0.958518i \(-0.407995\pi\)
0.285033 + 0.958518i \(0.407995\pi\)
\(998\) 0 0
\(999\) −25.2982 −0.800400
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 6400.2.a.bz.1.2 2
4.3 odd 2 inner 6400.2.a.bz.1.1 2
5.4 even 2 1280.2.a.l.1.1 2
8.3 odd 2 6400.2.a.ca.1.2 2
8.5 even 2 6400.2.a.ca.1.1 2
16.3 odd 4 3200.2.d.j.1601.1 4
16.5 even 4 3200.2.d.j.1601.2 4
16.11 odd 4 3200.2.d.j.1601.3 4
16.13 even 4 3200.2.d.j.1601.4 4
20.19 odd 2 1280.2.a.l.1.2 2
40.19 odd 2 1280.2.a.h.1.1 2
40.29 even 2 1280.2.a.h.1.2 2
80.3 even 4 3200.2.f.q.449.4 4
80.13 odd 4 3200.2.f.q.449.1 4
80.19 odd 4 640.2.d.a.321.3 yes 4
80.27 even 4 3200.2.f.q.449.3 4
80.29 even 4 640.2.d.a.321.1 4
80.37 odd 4 3200.2.f.q.449.2 4
80.43 even 4 3200.2.f.p.449.2 4
80.53 odd 4 3200.2.f.p.449.3 4
80.59 odd 4 640.2.d.a.321.2 yes 4
80.67 even 4 3200.2.f.p.449.1 4
80.69 even 4 640.2.d.a.321.4 yes 4
80.77 odd 4 3200.2.f.p.449.4 4
240.29 odd 4 5760.2.k.t.2881.3 4
240.59 even 4 5760.2.k.t.2881.2 4
240.149 odd 4 5760.2.k.t.2881.1 4
240.179 even 4 5760.2.k.t.2881.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.d.a.321.1 4 80.29 even 4
640.2.d.a.321.2 yes 4 80.59 odd 4
640.2.d.a.321.3 yes 4 80.19 odd 4
640.2.d.a.321.4 yes 4 80.69 even 4
1280.2.a.h.1.1 2 40.19 odd 2
1280.2.a.h.1.2 2 40.29 even 2
1280.2.a.l.1.1 2 5.4 even 2
1280.2.a.l.1.2 2 20.19 odd 2
3200.2.d.j.1601.1 4 16.3 odd 4
3200.2.d.j.1601.2 4 16.5 even 4
3200.2.d.j.1601.3 4 16.11 odd 4
3200.2.d.j.1601.4 4 16.13 even 4
3200.2.f.p.449.1 4 80.67 even 4
3200.2.f.p.449.2 4 80.43 even 4
3200.2.f.p.449.3 4 80.53 odd 4
3200.2.f.p.449.4 4 80.77 odd 4
3200.2.f.q.449.1 4 80.13 odd 4
3200.2.f.q.449.2 4 80.37 odd 4
3200.2.f.q.449.3 4 80.27 even 4
3200.2.f.q.449.4 4 80.3 even 4
5760.2.k.t.2881.1 4 240.149 odd 4
5760.2.k.t.2881.2 4 240.59 even 4
5760.2.k.t.2881.3 4 240.29 odd 4
5760.2.k.t.2881.4 4 240.179 even 4
6400.2.a.bz.1.1 2 4.3 odd 2 inner
6400.2.a.bz.1.2 2 1.1 even 1 trivial
6400.2.a.ca.1.1 2 8.5 even 2
6400.2.a.ca.1.2 2 8.3 odd 2