Properties

Label 8280.2.a.bw.1.3
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $7$
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] = [8280,2,Mod(1,8280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8280.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.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: \(66.1161328736\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 3x^{6} - 18x^{5} + 46x^{4} + 60x^{3} - 76x^{2} - 51x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.22540\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} -2.82985 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -2.82985 q^{7} -4.94410 q^{11} +4.65799 q^{13} -2.16509 q^{17} -0.347949 q^{19} +1.00000 q^{23} +1.00000 q^{25} +1.32315 q^{29} +10.0343 q^{31} -2.82985 q^{35} -5.95454 q^{37} -4.98690 q^{41} +1.57815 q^{43} +13.0205 q^{47} +1.00804 q^{49} +5.12429 q^{53} -4.94410 q^{55} -12.4243 q^{59} +10.4630 q^{61} +4.65799 q^{65} -12.2600 q^{67} +4.84614 q^{71} +12.3742 q^{73} +13.9910 q^{77} -8.81099 q^{79} -14.0533 q^{83} -2.16509 q^{85} -13.2819 q^{89} -13.1814 q^{91} -0.347949 q^{95} -9.56802 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 7 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 7 q^{5} - 6 q^{7} - 2 q^{11} - 6 q^{13} - 4 q^{17} - 8 q^{19} + 7 q^{23} + 7 q^{25} + 2 q^{29} - 8 q^{31} - 6 q^{35} - 16 q^{37} + 2 q^{41} - 10 q^{43} - 8 q^{47} + 19 q^{49} - 10 q^{53} - 2 q^{55} - 24 q^{59} + 8 q^{61} - 6 q^{65} - 20 q^{67} - 8 q^{71} + 2 q^{73} - 12 q^{77} - 2 q^{79} - 22 q^{83} - 4 q^{85} - 16 q^{89} - 20 q^{91} - 8 q^{95} + 4 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.82985 −1.06958 −0.534791 0.844984i \(-0.679610\pi\)
−0.534791 + 0.844984i \(0.679610\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.94410 −1.49070 −0.745350 0.666673i \(-0.767718\pi\)
−0.745350 + 0.666673i \(0.767718\pi\)
\(12\) 0 0
\(13\) 4.65799 1.29189 0.645947 0.763382i \(-0.276463\pi\)
0.645947 + 0.763382i \(0.276463\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.16509 −0.525111 −0.262556 0.964917i \(-0.584565\pi\)
−0.262556 + 0.964917i \(0.584565\pi\)
\(18\) 0 0
\(19\) −0.347949 −0.0798249 −0.0399125 0.999203i \(-0.512708\pi\)
−0.0399125 + 0.999203i \(0.512708\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.32315 0.245702 0.122851 0.992425i \(-0.460796\pi\)
0.122851 + 0.992425i \(0.460796\pi\)
\(30\) 0 0
\(31\) 10.0343 1.80222 0.901109 0.433593i \(-0.142755\pi\)
0.901109 + 0.433593i \(0.142755\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.82985 −0.478332
\(36\) 0 0
\(37\) −5.95454 −0.978920 −0.489460 0.872026i \(-0.662806\pi\)
−0.489460 + 0.872026i \(0.662806\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.98690 −0.778822 −0.389411 0.921064i \(-0.627322\pi\)
−0.389411 + 0.921064i \(0.627322\pi\)
\(42\) 0 0
\(43\) 1.57815 0.240665 0.120333 0.992734i \(-0.461604\pi\)
0.120333 + 0.992734i \(0.461604\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 13.0205 1.89924 0.949619 0.313406i \(-0.101470\pi\)
0.949619 + 0.313406i \(0.101470\pi\)
\(48\) 0 0
\(49\) 1.00804 0.144006
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.12429 0.703876 0.351938 0.936023i \(-0.385523\pi\)
0.351938 + 0.936023i \(0.385523\pi\)
\(54\) 0 0
\(55\) −4.94410 −0.666662
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −12.4243 −1.61750 −0.808752 0.588149i \(-0.799857\pi\)
−0.808752 + 0.588149i \(0.799857\pi\)
\(60\) 0 0
\(61\) 10.4630 1.33965 0.669827 0.742517i \(-0.266368\pi\)
0.669827 + 0.742517i \(0.266368\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.65799 0.577753
\(66\) 0 0
\(67\) −12.2600 −1.49780 −0.748898 0.662686i \(-0.769417\pi\)
−0.748898 + 0.662686i \(0.769417\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.84614 0.575131 0.287566 0.957761i \(-0.407154\pi\)
0.287566 + 0.957761i \(0.407154\pi\)
\(72\) 0 0
\(73\) 12.3742 1.44829 0.724147 0.689646i \(-0.242234\pi\)
0.724147 + 0.689646i \(0.242234\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.9910 1.59443
\(78\) 0 0
\(79\) −8.81099 −0.991313 −0.495657 0.868519i \(-0.665073\pi\)
−0.495657 + 0.868519i \(0.665073\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −14.0533 −1.54255 −0.771274 0.636503i \(-0.780380\pi\)
−0.771274 + 0.636503i \(0.780380\pi\)
\(84\) 0 0
\(85\) −2.16509 −0.234837
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −13.2819 −1.40788 −0.703940 0.710259i \(-0.748578\pi\)
−0.703940 + 0.710259i \(0.748578\pi\)
\(90\) 0 0
\(91\) −13.1814 −1.38179
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.347949 −0.0356988
\(96\) 0 0
\(97\) −9.56802 −0.971485 −0.485743 0.874102i \(-0.661451\pi\)
−0.485743 + 0.874102i \(0.661451\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.1041 1.00540 0.502699 0.864462i \(-0.332340\pi\)
0.502699 + 0.864462i \(0.332340\pi\)
\(102\) 0 0
\(103\) −11.5213 −1.13523 −0.567613 0.823296i \(-0.692133\pi\)
−0.567613 + 0.823296i \(0.692133\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.1192 −1.65497 −0.827486 0.561486i \(-0.810230\pi\)
−0.827486 + 0.561486i \(0.810230\pi\)
\(108\) 0 0
\(109\) 10.6603 1.02107 0.510537 0.859856i \(-0.329447\pi\)
0.510537 + 0.859856i \(0.329447\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.61589 0.246082 0.123041 0.992402i \(-0.460735\pi\)
0.123041 + 0.992402i \(0.460735\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 6.12687 0.561650
\(120\) 0 0
\(121\) 13.4441 1.22219
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 4.23348 0.375660 0.187830 0.982202i \(-0.439855\pi\)
0.187830 + 0.982202i \(0.439855\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.87807 0.863051 0.431525 0.902101i \(-0.357976\pi\)
0.431525 + 0.902101i \(0.357976\pi\)
\(132\) 0 0
\(133\) 0.984642 0.0853793
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 11.2618 0.962159 0.481080 0.876677i \(-0.340245\pi\)
0.481080 + 0.876677i \(0.340245\pi\)
\(138\) 0 0
\(139\) −22.5163 −1.90981 −0.954905 0.296913i \(-0.904043\pi\)
−0.954905 + 0.296913i \(0.904043\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −23.0296 −1.92583
\(144\) 0 0
\(145\) 1.32315 0.109881
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −20.0435 −1.64203 −0.821015 0.570907i \(-0.806592\pi\)
−0.821015 + 0.570907i \(0.806592\pi\)
\(150\) 0 0
\(151\) −17.7448 −1.44405 −0.722025 0.691867i \(-0.756788\pi\)
−0.722025 + 0.691867i \(0.756788\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.0343 0.805976
\(156\) 0 0
\(157\) 3.47753 0.277537 0.138769 0.990325i \(-0.455686\pi\)
0.138769 + 0.990325i \(0.455686\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.82985 −0.223023
\(162\) 0 0
\(163\) 7.93108 0.621210 0.310605 0.950539i \(-0.399468\pi\)
0.310605 + 0.950539i \(0.399468\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.59285 −0.587552 −0.293776 0.955874i \(-0.594912\pi\)
−0.293776 + 0.955874i \(0.594912\pi\)
\(168\) 0 0
\(169\) 8.69689 0.668992
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −7.24531 −0.550850 −0.275425 0.961323i \(-0.588819\pi\)
−0.275425 + 0.961323i \(0.588819\pi\)
\(174\) 0 0
\(175\) −2.82985 −0.213916
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.54920 −0.115793 −0.0578964 0.998323i \(-0.518439\pi\)
−0.0578964 + 0.998323i \(0.518439\pi\)
\(180\) 0 0
\(181\) −1.41079 −0.104863 −0.0524316 0.998625i \(-0.516697\pi\)
−0.0524316 + 0.998625i \(0.516697\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.95454 −0.437786
\(186\) 0 0
\(187\) 10.7044 0.782784
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.5973 −0.766795 −0.383398 0.923583i \(-0.625246\pi\)
−0.383398 + 0.923583i \(0.625246\pi\)
\(192\) 0 0
\(193\) −20.7209 −1.49152 −0.745760 0.666215i \(-0.767914\pi\)
−0.745760 + 0.666215i \(0.767914\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −20.8915 −1.48846 −0.744228 0.667926i \(-0.767182\pi\)
−0.744228 + 0.667926i \(0.767182\pi\)
\(198\) 0 0
\(199\) −25.0562 −1.77618 −0.888092 0.459665i \(-0.847969\pi\)
−0.888092 + 0.459665i \(0.847969\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.74430 −0.262799
\(204\) 0 0
\(205\) −4.98690 −0.348300
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.72029 0.118995
\(210\) 0 0
\(211\) 11.6415 0.801436 0.400718 0.916201i \(-0.368761\pi\)
0.400718 + 0.916201i \(0.368761\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.57815 0.107629
\(216\) 0 0
\(217\) −28.3956 −1.92762
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −10.0850 −0.678388
\(222\) 0 0
\(223\) 19.4037 1.29937 0.649685 0.760204i \(-0.274901\pi\)
0.649685 + 0.760204i \(0.274901\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.44027 −0.427456 −0.213728 0.976893i \(-0.568561\pi\)
−0.213728 + 0.976893i \(0.568561\pi\)
\(228\) 0 0
\(229\) −1.42608 −0.0942380 −0.0471190 0.998889i \(-0.515004\pi\)
−0.0471190 + 0.998889i \(0.515004\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.9705 −0.718702 −0.359351 0.933202i \(-0.617002\pi\)
−0.359351 + 0.933202i \(0.617002\pi\)
\(234\) 0 0
\(235\) 13.0205 0.849365
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −14.7873 −0.956514 −0.478257 0.878220i \(-0.658731\pi\)
−0.478257 + 0.878220i \(0.658731\pi\)
\(240\) 0 0
\(241\) 10.0504 0.647401 0.323700 0.946160i \(-0.395073\pi\)
0.323700 + 0.946160i \(0.395073\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00804 0.0644013
\(246\) 0 0
\(247\) −1.62074 −0.103125
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.54142 0.223532 0.111766 0.993735i \(-0.464349\pi\)
0.111766 + 0.993735i \(0.464349\pi\)
\(252\) 0 0
\(253\) −4.94410 −0.310833
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.8020 −1.23522 −0.617608 0.786486i \(-0.711898\pi\)
−0.617608 + 0.786486i \(0.711898\pi\)
\(258\) 0 0
\(259\) 16.8504 1.04703
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.13769 0.378466 0.189233 0.981932i \(-0.439400\pi\)
0.189233 + 0.981932i \(0.439400\pi\)
\(264\) 0 0
\(265\) 5.12429 0.314783
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.27775 −0.138877 −0.0694385 0.997586i \(-0.522121\pi\)
−0.0694385 + 0.997586i \(0.522121\pi\)
\(270\) 0 0
\(271\) 30.8457 1.87374 0.936872 0.349674i \(-0.113707\pi\)
0.936872 + 0.349674i \(0.113707\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.94410 −0.298140
\(276\) 0 0
\(277\) 8.69943 0.522698 0.261349 0.965244i \(-0.415833\pi\)
0.261349 + 0.965244i \(0.415833\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.86657 0.349970 0.174985 0.984571i \(-0.444012\pi\)
0.174985 + 0.984571i \(0.444012\pi\)
\(282\) 0 0
\(283\) −5.30578 −0.315396 −0.157698 0.987487i \(-0.550407\pi\)
−0.157698 + 0.987487i \(0.550407\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.1122 0.833015
\(288\) 0 0
\(289\) −12.3124 −0.724258
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.61142 −0.0941401 −0.0470701 0.998892i \(-0.514988\pi\)
−0.0470701 + 0.998892i \(0.514988\pi\)
\(294\) 0 0
\(295\) −12.4243 −0.723370
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.65799 0.269379
\(300\) 0 0
\(301\) −4.46592 −0.257411
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 10.4630 0.599112
\(306\) 0 0
\(307\) −19.0852 −1.08925 −0.544626 0.838679i \(-0.683328\pi\)
−0.544626 + 0.838679i \(0.683328\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −33.9003 −1.92231 −0.961155 0.276011i \(-0.910988\pi\)
−0.961155 + 0.276011i \(0.910988\pi\)
\(312\) 0 0
\(313\) 23.8734 1.34940 0.674702 0.738090i \(-0.264272\pi\)
0.674702 + 0.738090i \(0.264272\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.3541 0.750041 0.375021 0.927016i \(-0.377636\pi\)
0.375021 + 0.927016i \(0.377636\pi\)
\(318\) 0 0
\(319\) −6.54176 −0.366268
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.753340 0.0419170
\(324\) 0 0
\(325\) 4.65799 0.258379
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −36.8461 −2.03139
\(330\) 0 0
\(331\) 23.5923 1.29675 0.648376 0.761320i \(-0.275449\pi\)
0.648376 + 0.761320i \(0.275449\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.2600 −0.669834
\(336\) 0 0
\(337\) 26.1866 1.42647 0.713237 0.700923i \(-0.247228\pi\)
0.713237 + 0.700923i \(0.247228\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −49.6106 −2.68657
\(342\) 0 0
\(343\) 16.9563 0.915556
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −33.4133 −1.79372 −0.896859 0.442316i \(-0.854157\pi\)
−0.896859 + 0.442316i \(0.854157\pi\)
\(348\) 0 0
\(349\) 13.7105 0.733904 0.366952 0.930240i \(-0.380401\pi\)
0.366952 + 0.930240i \(0.380401\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −32.6135 −1.73584 −0.867920 0.496704i \(-0.834544\pi\)
−0.867920 + 0.496704i \(0.834544\pi\)
\(354\) 0 0
\(355\) 4.84614 0.257207
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.30182 −0.227042 −0.113521 0.993536i \(-0.536213\pi\)
−0.113521 + 0.993536i \(0.536213\pi\)
\(360\) 0 0
\(361\) −18.8789 −0.993628
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 12.3742 0.647697
\(366\) 0 0
\(367\) −25.5453 −1.33345 −0.666727 0.745302i \(-0.732305\pi\)
−0.666727 + 0.745302i \(0.732305\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −14.5010 −0.752853
\(372\) 0 0
\(373\) −1.08868 −0.0563697 −0.0281848 0.999603i \(-0.508973\pi\)
−0.0281848 + 0.999603i \(0.508973\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.16321 0.317421
\(378\) 0 0
\(379\) −21.5620 −1.10756 −0.553782 0.832662i \(-0.686816\pi\)
−0.553782 + 0.832662i \(0.686816\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.31231 −0.322544 −0.161272 0.986910i \(-0.551560\pi\)
−0.161272 + 0.986910i \(0.551560\pi\)
\(384\) 0 0
\(385\) 13.9910 0.713049
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7.52936 0.381754 0.190877 0.981614i \(-0.438867\pi\)
0.190877 + 0.981614i \(0.438867\pi\)
\(390\) 0 0
\(391\) −2.16509 −0.109493
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.81099 −0.443329
\(396\) 0 0
\(397\) 24.5533 1.23229 0.616147 0.787631i \(-0.288693\pi\)
0.616147 + 0.787631i \(0.288693\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −30.4811 −1.52215 −0.761077 0.648662i \(-0.775329\pi\)
−0.761077 + 0.648662i \(0.775329\pi\)
\(402\) 0 0
\(403\) 46.7398 2.32827
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 29.4398 1.45928
\(408\) 0 0
\(409\) 37.8239 1.87027 0.935136 0.354290i \(-0.115277\pi\)
0.935136 + 0.354290i \(0.115277\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 35.1589 1.73005
\(414\) 0 0
\(415\) −14.0533 −0.689848
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.9254 −1.07112 −0.535562 0.844496i \(-0.679900\pi\)
−0.535562 + 0.844496i \(0.679900\pi\)
\(420\) 0 0
\(421\) 36.1125 1.76002 0.880008 0.474960i \(-0.157537\pi\)
0.880008 + 0.474960i \(0.157537\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.16509 −0.105022
\(426\) 0 0
\(427\) −29.6088 −1.43287
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.4074 1.60918 0.804590 0.593831i \(-0.202385\pi\)
0.804590 + 0.593831i \(0.202385\pi\)
\(432\) 0 0
\(433\) −24.9892 −1.20090 −0.600451 0.799661i \(-0.705012\pi\)
−0.600451 + 0.799661i \(0.705012\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.347949 −0.0166446
\(438\) 0 0
\(439\) 20.5951 0.982950 0.491475 0.870892i \(-0.336458\pi\)
0.491475 + 0.870892i \(0.336458\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.4349 −0.638312 −0.319156 0.947702i \(-0.603399\pi\)
−0.319156 + 0.947702i \(0.603399\pi\)
\(444\) 0 0
\(445\) −13.2819 −0.629623
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.0435 0.473980 0.236990 0.971512i \(-0.423839\pi\)
0.236990 + 0.971512i \(0.423839\pi\)
\(450\) 0 0
\(451\) 24.6557 1.16099
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13.1814 −0.617954
\(456\) 0 0
\(457\) 5.60889 0.262373 0.131186 0.991358i \(-0.458121\pi\)
0.131186 + 0.991358i \(0.458121\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −37.8370 −1.76224 −0.881121 0.472890i \(-0.843211\pi\)
−0.881121 + 0.472890i \(0.843211\pi\)
\(462\) 0 0
\(463\) −39.0326 −1.81400 −0.907000 0.421131i \(-0.861633\pi\)
−0.907000 + 0.421131i \(0.861633\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.70089 −0.217531 −0.108766 0.994067i \(-0.534690\pi\)
−0.108766 + 0.994067i \(0.534690\pi\)
\(468\) 0 0
\(469\) 34.6939 1.60201
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7.80251 −0.358760
\(474\) 0 0
\(475\) −0.347949 −0.0159650
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.8361 0.723570 0.361785 0.932262i \(-0.382167\pi\)
0.361785 + 0.932262i \(0.382167\pi\)
\(480\) 0 0
\(481\) −27.7362 −1.26466
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9.56802 −0.434461
\(486\) 0 0
\(487\) −16.6167 −0.752973 −0.376487 0.926422i \(-0.622868\pi\)
−0.376487 + 0.926422i \(0.622868\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 26.9471 1.21611 0.608054 0.793896i \(-0.291951\pi\)
0.608054 + 0.793896i \(0.291951\pi\)
\(492\) 0 0
\(493\) −2.86473 −0.129021
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −13.7139 −0.615150
\(498\) 0 0
\(499\) 15.5034 0.694029 0.347015 0.937860i \(-0.387195\pi\)
0.347015 + 0.937860i \(0.387195\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.4518 1.40236 0.701182 0.712982i \(-0.252656\pi\)
0.701182 + 0.712982i \(0.252656\pi\)
\(504\) 0 0
\(505\) 10.1041 0.449628
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.46634 0.0649943 0.0324971 0.999472i \(-0.489654\pi\)
0.0324971 + 0.999472i \(0.489654\pi\)
\(510\) 0 0
\(511\) −35.0172 −1.54907
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.5213 −0.507688
\(516\) 0 0
\(517\) −64.3747 −2.83120
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.58182 −0.244544 −0.122272 0.992497i \(-0.539018\pi\)
−0.122272 + 0.992497i \(0.539018\pi\)
\(522\) 0 0
\(523\) −11.2870 −0.493548 −0.246774 0.969073i \(-0.579371\pi\)
−0.246774 + 0.969073i \(0.579371\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.7252 −0.946365
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −23.2289 −1.00616
\(534\) 0 0
\(535\) −17.1192 −0.740126
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.98385 −0.214670
\(540\) 0 0
\(541\) 17.9045 0.769773 0.384887 0.922964i \(-0.374241\pi\)
0.384887 + 0.922964i \(0.374241\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.6603 0.456638
\(546\) 0 0
\(547\) −16.1535 −0.690673 −0.345336 0.938479i \(-0.612235\pi\)
−0.345336 + 0.938479i \(0.612235\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.460387 −0.0196132
\(552\) 0 0
\(553\) 24.9338 1.06029
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.90248 0.334839 0.167419 0.985886i \(-0.446457\pi\)
0.167419 + 0.985886i \(0.446457\pi\)
\(558\) 0 0
\(559\) 7.35100 0.310914
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.36386 0.310350 0.155175 0.987887i \(-0.450406\pi\)
0.155175 + 0.987887i \(0.450406\pi\)
\(564\) 0 0
\(565\) 2.61589 0.110051
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.18004 −0.0494698 −0.0247349 0.999694i \(-0.507874\pi\)
−0.0247349 + 0.999694i \(0.507874\pi\)
\(570\) 0 0
\(571\) 9.59220 0.401421 0.200711 0.979651i \(-0.435675\pi\)
0.200711 + 0.979651i \(0.435675\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −21.2966 −0.886589 −0.443294 0.896376i \(-0.646190\pi\)
−0.443294 + 0.896376i \(0.646190\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 39.7686 1.64988
\(582\) 0 0
\(583\) −25.3350 −1.04927
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 27.2149 1.12328 0.561640 0.827382i \(-0.310171\pi\)
0.561640 + 0.827382i \(0.310171\pi\)
\(588\) 0 0
\(589\) −3.49143 −0.143862
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24.6044 −1.01038 −0.505191 0.863008i \(-0.668578\pi\)
−0.505191 + 0.863008i \(0.668578\pi\)
\(594\) 0 0
\(595\) 6.12687 0.251177
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20.9286 0.855120 0.427560 0.903987i \(-0.359373\pi\)
0.427560 + 0.903987i \(0.359373\pi\)
\(600\) 0 0
\(601\) 28.1317 1.14752 0.573758 0.819025i \(-0.305485\pi\)
0.573758 + 0.819025i \(0.305485\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 13.4441 0.546580
\(606\) 0 0
\(607\) 4.02339 0.163304 0.0816522 0.996661i \(-0.473980\pi\)
0.0816522 + 0.996661i \(0.473980\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 60.6495 2.45362
\(612\) 0 0
\(613\) −30.9604 −1.25048 −0.625240 0.780432i \(-0.714999\pi\)
−0.625240 + 0.780432i \(0.714999\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 35.4413 1.42681 0.713407 0.700750i \(-0.247151\pi\)
0.713407 + 0.700750i \(0.247151\pi\)
\(618\) 0 0
\(619\) 7.61916 0.306240 0.153120 0.988208i \(-0.451068\pi\)
0.153120 + 0.988208i \(0.451068\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 37.5858 1.50584
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.8921 0.514042
\(630\) 0 0
\(631\) −21.6842 −0.863235 −0.431618 0.902057i \(-0.642057\pi\)
−0.431618 + 0.902057i \(0.642057\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.23348 0.168000
\(636\) 0 0
\(637\) 4.69544 0.186040
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 39.4616 1.55864 0.779320 0.626626i \(-0.215565\pi\)
0.779320 + 0.626626i \(0.215565\pi\)
\(642\) 0 0
\(643\) 3.18996 0.125800 0.0628999 0.998020i \(-0.479965\pi\)
0.0628999 + 0.998020i \(0.479965\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.2970 −0.719330 −0.359665 0.933081i \(-0.617109\pi\)
−0.359665 + 0.933081i \(0.617109\pi\)
\(648\) 0 0
\(649\) 61.4269 2.41122
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −33.0406 −1.29298 −0.646490 0.762923i \(-0.723764\pi\)
−0.646490 + 0.762923i \(0.723764\pi\)
\(654\) 0 0
\(655\) 9.87807 0.385968
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −27.7651 −1.08157 −0.540787 0.841160i \(-0.681873\pi\)
−0.540787 + 0.841160i \(0.681873\pi\)
\(660\) 0 0
\(661\) −30.2032 −1.17477 −0.587384 0.809308i \(-0.699842\pi\)
−0.587384 + 0.809308i \(0.699842\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.984642 0.0381828
\(666\) 0 0
\(667\) 1.32315 0.0512324
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −51.7303 −1.99702
\(672\) 0 0
\(673\) −23.3010 −0.898187 −0.449093 0.893485i \(-0.648253\pi\)
−0.449093 + 0.893485i \(0.648253\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −43.2511 −1.66228 −0.831138 0.556066i \(-0.812310\pi\)
−0.831138 + 0.556066i \(0.812310\pi\)
\(678\) 0 0
\(679\) 27.0760 1.03908
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.0271 0.919372 0.459686 0.888082i \(-0.347962\pi\)
0.459686 + 0.888082i \(0.347962\pi\)
\(684\) 0 0
\(685\) 11.2618 0.430291
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 23.8689 0.909333
\(690\) 0 0
\(691\) −18.0742 −0.687574 −0.343787 0.939048i \(-0.611710\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −22.5163 −0.854093
\(696\) 0 0
\(697\) 10.7971 0.408968
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.35858 −0.164621 −0.0823107 0.996607i \(-0.526230\pi\)
−0.0823107 + 0.996607i \(0.526230\pi\)
\(702\) 0 0
\(703\) 2.07187 0.0781422
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −28.5931 −1.07536
\(708\) 0 0
\(709\) 6.28641 0.236091 0.118045 0.993008i \(-0.462337\pi\)
0.118045 + 0.993008i \(0.462337\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.0343 0.375788
\(714\) 0 0
\(715\) −23.0296 −0.861257
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 44.9514 1.67640 0.838202 0.545360i \(-0.183607\pi\)
0.838202 + 0.545360i \(0.183607\pi\)
\(720\) 0 0
\(721\) 32.6035 1.21422
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.32315 0.0491404
\(726\) 0 0
\(727\) −22.6212 −0.838972 −0.419486 0.907762i \(-0.637790\pi\)
−0.419486 + 0.907762i \(0.637790\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.41683 −0.126376
\(732\) 0 0
\(733\) 45.9519 1.69727 0.848636 0.528977i \(-0.177424\pi\)
0.848636 + 0.528977i \(0.177424\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 60.6145 2.23276
\(738\) 0 0
\(739\) 12.1925 0.448509 0.224255 0.974531i \(-0.428005\pi\)
0.224255 + 0.974531i \(0.428005\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.03362 0.0746063 0.0373032 0.999304i \(-0.488123\pi\)
0.0373032 + 0.999304i \(0.488123\pi\)
\(744\) 0 0
\(745\) −20.0435 −0.734338
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 48.4447 1.77013
\(750\) 0 0
\(751\) −0.935597 −0.0341404 −0.0170702 0.999854i \(-0.505434\pi\)
−0.0170702 + 0.999854i \(0.505434\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −17.7448 −0.645798
\(756\) 0 0
\(757\) −28.4242 −1.03310 −0.516548 0.856258i \(-0.672783\pi\)
−0.516548 + 0.856258i \(0.672783\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −45.5123 −1.64982 −0.824909 0.565265i \(-0.808774\pi\)
−0.824909 + 0.565265i \(0.808774\pi\)
\(762\) 0 0
\(763\) −30.1671 −1.09212
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −57.8723 −2.08965
\(768\) 0 0
\(769\) 4.93028 0.177790 0.0888952 0.996041i \(-0.471666\pi\)
0.0888952 + 0.996041i \(0.471666\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.2800 0.477648 0.238824 0.971063i \(-0.423238\pi\)
0.238824 + 0.971063i \(0.423238\pi\)
\(774\) 0 0
\(775\) 10.0343 0.360443
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.73518 0.0621694
\(780\) 0 0
\(781\) −23.9598 −0.857349
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.47753 0.124118
\(786\) 0 0
\(787\) −9.94763 −0.354595 −0.177297 0.984157i \(-0.556735\pi\)
−0.177297 + 0.984157i \(0.556735\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.40256 −0.263205
\(792\) 0 0
\(793\) 48.7368 1.73069
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30.1642 −1.06847 −0.534236 0.845335i \(-0.679401\pi\)
−0.534236 + 0.845335i \(0.679401\pi\)
\(798\) 0 0
\(799\) −28.1906 −0.997312
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −61.1794 −2.15897
\(804\) 0 0
\(805\) −2.82985 −0.0997390
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −21.2734 −0.747935 −0.373967 0.927442i \(-0.622003\pi\)
−0.373967 + 0.927442i \(0.622003\pi\)
\(810\) 0 0
\(811\) −0.697841 −0.0245045 −0.0122523 0.999925i \(-0.503900\pi\)
−0.0122523 + 0.999925i \(0.503900\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 7.93108 0.277814
\(816\) 0 0
\(817\) −0.549114 −0.0192111
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 30.8586 1.07697 0.538486 0.842635i \(-0.318997\pi\)
0.538486 + 0.842635i \(0.318997\pi\)
\(822\) 0 0
\(823\) 19.6298 0.684253 0.342127 0.939654i \(-0.388853\pi\)
0.342127 + 0.939654i \(0.388853\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.73006 −0.338347 −0.169174 0.985586i \(-0.554110\pi\)
−0.169174 + 0.985586i \(0.554110\pi\)
\(828\) 0 0
\(829\) −19.6529 −0.682573 −0.341287 0.939959i \(-0.610863\pi\)
−0.341287 + 0.939959i \(0.610863\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.18250 −0.0756191
\(834\) 0 0
\(835\) −7.59285 −0.262761
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −32.1900 −1.11132 −0.555661 0.831409i \(-0.687535\pi\)
−0.555661 + 0.831409i \(0.687535\pi\)
\(840\) 0 0
\(841\) −27.2493 −0.939630
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.69689 0.299182
\(846\) 0 0
\(847\) −38.0447 −1.30723
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.95454 −0.204119
\(852\) 0 0
\(853\) −55.8766 −1.91318 −0.956590 0.291438i \(-0.905866\pi\)
−0.956590 + 0.291438i \(0.905866\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.15146 −0.210130 −0.105065 0.994465i \(-0.533505\pi\)
−0.105065 + 0.994465i \(0.533505\pi\)
\(858\) 0 0
\(859\) −30.7220 −1.04822 −0.524111 0.851650i \(-0.675602\pi\)
−0.524111 + 0.851650i \(0.675602\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 30.2001 1.02802 0.514012 0.857783i \(-0.328159\pi\)
0.514012 + 0.857783i \(0.328159\pi\)
\(864\) 0 0
\(865\) −7.24531 −0.246348
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 43.5624 1.47775
\(870\) 0 0
\(871\) −57.1069 −1.93499
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.82985 −0.0956663
\(876\) 0 0
\(877\) −19.8280 −0.669546 −0.334773 0.942299i \(-0.608660\pi\)
−0.334773 + 0.942299i \(0.608660\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −55.1069 −1.85660 −0.928300 0.371833i \(-0.878729\pi\)
−0.928300 + 0.371833i \(0.878729\pi\)
\(882\) 0 0
\(883\) −26.8178 −0.902490 −0.451245 0.892400i \(-0.649020\pi\)
−0.451245 + 0.892400i \(0.649020\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40.8503 −1.37162 −0.685810 0.727781i \(-0.740552\pi\)
−0.685810 + 0.727781i \(0.740552\pi\)
\(888\) 0 0
\(889\) −11.9801 −0.401799
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −4.53047 −0.151607
\(894\) 0 0
\(895\) −1.54920 −0.0517841
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 13.2769 0.442809
\(900\) 0 0
\(901\) −11.0945 −0.369613
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.41079 −0.0468962
\(906\) 0 0
\(907\) −9.16440 −0.304299 −0.152150 0.988357i \(-0.548620\pi\)
−0.152150 + 0.988357i \(0.548620\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 7.72553 0.255958 0.127979 0.991777i \(-0.459151\pi\)
0.127979 + 0.991777i \(0.459151\pi\)
\(912\) 0 0
\(913\) 69.4808 2.29948
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −27.9534 −0.923103
\(918\) 0 0
\(919\) 23.8924 0.788139 0.394069 0.919081i \(-0.371067\pi\)
0.394069 + 0.919081i \(0.371067\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 22.5733 0.743009
\(924\) 0 0
\(925\) −5.95454 −0.195784
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 19.6787 0.645636 0.322818 0.946461i \(-0.395370\pi\)
0.322818 + 0.946461i \(0.395370\pi\)
\(930\) 0 0
\(931\) −0.350746 −0.0114952
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 10.7044 0.350072
\(936\) 0 0
\(937\) −52.6536 −1.72012 −0.860058 0.510196i \(-0.829573\pi\)
−0.860058 + 0.510196i \(0.829573\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.34001 0.141480 0.0707401 0.997495i \(-0.477464\pi\)
0.0707401 + 0.997495i \(0.477464\pi\)
\(942\) 0 0
\(943\) −4.98690 −0.162396
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.0278 −0.585825 −0.292912 0.956139i \(-0.594624\pi\)
−0.292912 + 0.956139i \(0.594624\pi\)
\(948\) 0 0
\(949\) 57.6391 1.87104
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −43.3464 −1.40413 −0.702064 0.712113i \(-0.747738\pi\)
−0.702064 + 0.712113i \(0.747738\pi\)
\(954\) 0 0
\(955\) −10.5973 −0.342921
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −31.8691 −1.02911
\(960\) 0 0
\(961\) 69.6876 2.24799
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −20.7209 −0.667028
\(966\) 0 0
\(967\) 32.5215 1.04582 0.522911 0.852387i \(-0.324846\pi\)
0.522911 + 0.852387i \(0.324846\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −34.0432 −1.09250 −0.546249 0.837623i \(-0.683945\pi\)
−0.546249 + 0.837623i \(0.683945\pi\)
\(972\) 0 0
\(973\) 63.7178 2.04270
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 31.8626 1.01937 0.509687 0.860360i \(-0.329761\pi\)
0.509687 + 0.860360i \(0.329761\pi\)
\(978\) 0 0
\(979\) 65.6671 2.09873
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 17.9450 0.572357 0.286178 0.958176i \(-0.407615\pi\)
0.286178 + 0.958176i \(0.407615\pi\)
\(984\) 0 0
\(985\) −20.8915 −0.665658
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.57815 0.0501822
\(990\) 0 0
\(991\) −42.1482 −1.33888 −0.669441 0.742865i \(-0.733466\pi\)
−0.669441 + 0.742865i \(0.733466\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −25.0562 −0.794334
\(996\) 0 0
\(997\) −50.0852 −1.58622 −0.793108 0.609082i \(-0.791538\pi\)
−0.793108 + 0.609082i \(0.791538\pi\)
\(998\) 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 8280.2.a.bw.1.3 yes 7
3.2 odd 2 8280.2.a.bv.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bv.1.3 7 3.2 odd 2
8280.2.a.bw.1.3 yes 7 1.1 even 1 trivial