Properties

Label 8280.2.a.bi.1.2
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.568.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2760)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.76156\) 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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{5} +1.89692 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +1.89692 q^{7} +2.38776 q^{11} -4.38776 q^{13} -0.761557 q^{17} +0.864641 q^{19} +1.00000 q^{23} +1.00000 q^{25} -8.76156 q^{29} +9.35548 q^{31} -1.89692 q^{35} -0.103084 q^{37} -9.53707 q^{41} +3.25240 q^{43} -3.13536 q^{47} -3.40171 q^{49} -8.01395 q^{53} -2.38776 q^{55} -10.2201 q^{59} +3.64015 q^{61} +4.38776 q^{65} +12.6079 q^{67} +6.55539 q^{71} -4.92919 q^{73} +4.52937 q^{77} -7.04623 q^{79} -5.23844 q^{83} +0.761557 q^{85} +10.9817 q^{89} -8.32320 q^{91} -0.864641 q^{95} -0.0645508 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{5} + 2 q^{7} - 8 q^{11} + 2 q^{13} + 4 q^{17} + 3 q^{23} + 3 q^{25} - 20 q^{29} + 14 q^{31} - 2 q^{35} - 4 q^{37} + 8 q^{41} - 8 q^{43} - 12 q^{47} + 29 q^{49} + 8 q^{55} - 14 q^{59} - 22 q^{61} - 2 q^{65} + 6 q^{67} + 6 q^{71} - 10 q^{73} + 8 q^{77} + 4 q^{79} - 22 q^{83} - 4 q^{85} + 10 q^{89} - 12 q^{91} + 2 q^{97}+O(q^{100}) \) 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
\(7\) 1.89692 0.716967 0.358483 0.933536i \(-0.383294\pi\)
0.358483 + 0.933536i \(0.383294\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.38776 0.719935 0.359968 0.932965i \(-0.382788\pi\)
0.359968 + 0.932965i \(0.382788\pi\)
\(12\) 0 0
\(13\) −4.38776 −1.21694 −0.608472 0.793575i \(-0.708217\pi\)
−0.608472 + 0.793575i \(0.708217\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.761557 −0.184705 −0.0923524 0.995726i \(-0.529439\pi\)
−0.0923524 + 0.995726i \(0.529439\pi\)
\(18\) 0 0
\(19\) 0.864641 0.198362 0.0991811 0.995069i \(-0.468378\pi\)
0.0991811 + 0.995069i \(0.468378\pi\)
\(20\) 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
\(29\) −8.76156 −1.62698 −0.813490 0.581579i \(-0.802435\pi\)
−0.813490 + 0.581579i \(0.802435\pi\)
\(30\) 0 0
\(31\) 9.35548 1.68029 0.840147 0.542359i \(-0.182469\pi\)
0.840147 + 0.542359i \(0.182469\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.89692 −0.320637
\(36\) 0 0
\(37\) −0.103084 −0.0169469 −0.00847343 0.999964i \(-0.502697\pi\)
−0.00847343 + 0.999964i \(0.502697\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.53707 −1.48944 −0.744720 0.667377i \(-0.767417\pi\)
−0.744720 + 0.667377i \(0.767417\pi\)
\(42\) 0 0
\(43\) 3.25240 0.495986 0.247993 0.968762i \(-0.420229\pi\)
0.247993 + 0.968762i \(0.420229\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.13536 −0.457339 −0.228670 0.973504i \(-0.573438\pi\)
−0.228670 + 0.973504i \(0.573438\pi\)
\(48\) 0 0
\(49\) −3.40171 −0.485958
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.01395 −1.10080 −0.550401 0.834901i \(-0.685525\pi\)
−0.550401 + 0.834901i \(0.685525\pi\)
\(54\) 0 0
\(55\) −2.38776 −0.321965
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.2201 −1.33055 −0.665273 0.746600i \(-0.731685\pi\)
−0.665273 + 0.746600i \(0.731685\pi\)
\(60\) 0 0
\(61\) 3.64015 0.466074 0.233037 0.972468i \(-0.425134\pi\)
0.233037 + 0.972468i \(0.425134\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.38776 0.544234
\(66\) 0 0
\(67\) 12.6079 1.54030 0.770149 0.637865i \(-0.220182\pi\)
0.770149 + 0.637865i \(0.220182\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.55539 0.777982 0.388991 0.921242i \(-0.372824\pi\)
0.388991 + 0.921242i \(0.372824\pi\)
\(72\) 0 0
\(73\) −4.92919 −0.576918 −0.288459 0.957492i \(-0.593143\pi\)
−0.288459 + 0.957492i \(0.593143\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.52937 0.516170
\(78\) 0 0
\(79\) −7.04623 −0.792763 −0.396381 0.918086i \(-0.629734\pi\)
−0.396381 + 0.918086i \(0.629734\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.23844 −0.574994 −0.287497 0.957782i \(-0.592823\pi\)
−0.287497 + 0.957782i \(0.592823\pi\)
\(84\) 0 0
\(85\) 0.761557 0.0826025
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.9817 1.16406 0.582028 0.813169i \(-0.302259\pi\)
0.582028 + 0.813169i \(0.302259\pi\)
\(90\) 0 0
\(91\) −8.32320 −0.872509
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.864641 −0.0887103
\(96\) 0 0
\(97\) −0.0645508 −0.00655414 −0.00327707 0.999995i \(-0.501043\pi\)
−0.00327707 + 0.999995i \(0.501043\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.30299 0.129653 0.0648264 0.997897i \(-0.479351\pi\)
0.0648264 + 0.997897i \(0.479351\pi\)
\(102\) 0 0
\(103\) −4.98168 −0.490859 −0.245430 0.969414i \(-0.578929\pi\)
−0.245430 + 0.969414i \(0.578929\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.697006 0.0673821 0.0336911 0.999432i \(-0.489274\pi\)
0.0336911 + 0.999432i \(0.489274\pi\)
\(108\) 0 0
\(109\) −4.92919 −0.472131 −0.236065 0.971737i \(-0.575858\pi\)
−0.236065 + 0.971737i \(0.575858\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.53707 0.897172 0.448586 0.893740i \(-0.351928\pi\)
0.448586 + 0.893740i \(0.351928\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.44461 −0.132427
\(120\) 0 0
\(121\) −5.29862 −0.481693
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.38776 0.211879 0.105940 0.994373i \(-0.466215\pi\)
0.105940 + 0.994373i \(0.466215\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.953771 −0.0833314 −0.0416657 0.999132i \(-0.513266\pi\)
−0.0416657 + 0.999132i \(0.513266\pi\)
\(132\) 0 0
\(133\) 1.64015 0.142219
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.93545 −0.336228 −0.168114 0.985768i \(-0.553768\pi\)
−0.168114 + 0.985768i \(0.553768\pi\)
\(138\) 0 0
\(139\) −2.87859 −0.244159 −0.122080 0.992520i \(-0.538956\pi\)
−0.122080 + 0.992520i \(0.538956\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −10.4769 −0.876121
\(144\) 0 0
\(145\) 8.76156 0.727608
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −19.4340 −1.59209 −0.796047 0.605235i \(-0.793079\pi\)
−0.796047 + 0.605235i \(0.793079\pi\)
\(150\) 0 0
\(151\) −10.7110 −0.871646 −0.435823 0.900033i \(-0.643543\pi\)
−0.435823 + 0.900033i \(0.643543\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.35548 −0.751450
\(156\) 0 0
\(157\) −16.3372 −1.30385 −0.651924 0.758285i \(-0.726038\pi\)
−0.651924 + 0.758285i \(0.726038\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.89692 0.149498
\(162\) 0 0
\(163\) 11.2524 0.881356 0.440678 0.897665i \(-0.354738\pi\)
0.440678 + 0.897665i \(0.354738\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.59392 0.510253 0.255127 0.966908i \(-0.417883\pi\)
0.255127 + 0.966908i \(0.417883\pi\)
\(168\) 0 0
\(169\) 6.25240 0.480954
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 20.7110 1.57463 0.787313 0.616554i \(-0.211472\pi\)
0.787313 + 0.616554i \(0.211472\pi\)
\(174\) 0 0
\(175\) 1.89692 0.143393
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −22.2986 −1.66668 −0.833339 0.552763i \(-0.813574\pi\)
−0.833339 + 0.552763i \(0.813574\pi\)
\(180\) 0 0
\(181\) −21.4865 −1.59708 −0.798538 0.601944i \(-0.794393\pi\)
−0.798538 + 0.601944i \(0.794393\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.103084 0.00757886
\(186\) 0 0
\(187\) −1.81841 −0.132975
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.8646 0.930853 0.465426 0.885087i \(-0.345901\pi\)
0.465426 + 0.885087i \(0.345901\pi\)
\(192\) 0 0
\(193\) −18.0279 −1.29768 −0.648839 0.760926i \(-0.724745\pi\)
−0.648839 + 0.760926i \(0.724745\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.2341 −1.01414 −0.507068 0.861906i \(-0.669271\pi\)
−0.507068 + 0.861906i \(0.669271\pi\)
\(198\) 0 0
\(199\) 12.5693 0.891017 0.445509 0.895278i \(-0.353023\pi\)
0.445509 + 0.895278i \(0.353023\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −16.6199 −1.16649
\(204\) 0 0
\(205\) 9.53707 0.666098
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.06455 0.142808
\(210\) 0 0
\(211\) −5.12141 −0.352572 −0.176286 0.984339i \(-0.556408\pi\)
−0.176286 + 0.984339i \(0.556408\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.25240 −0.221812
\(216\) 0 0
\(217\) 17.7466 1.20472
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.34153 0.224775
\(222\) 0 0
\(223\) −0.747604 −0.0500633 −0.0250316 0.999687i \(-0.507969\pi\)
−0.0250316 + 0.999687i \(0.507969\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.49521 −0.0992404 −0.0496202 0.998768i \(-0.515801\pi\)
−0.0496202 + 0.998768i \(0.515801\pi\)
\(228\) 0 0
\(229\) 2.56934 0.169787 0.0848935 0.996390i \(-0.472945\pi\)
0.0848935 + 0.996390i \(0.472945\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.25240 −0.606145 −0.303072 0.952968i \(-0.598012\pi\)
−0.303072 + 0.952968i \(0.598012\pi\)
\(234\) 0 0
\(235\) 3.13536 0.204528
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −21.0602 −1.36227 −0.681135 0.732158i \(-0.738513\pi\)
−0.681135 + 0.732158i \(0.738513\pi\)
\(240\) 0 0
\(241\) 15.4340 0.994190 0.497095 0.867696i \(-0.334400\pi\)
0.497095 + 0.867696i \(0.334400\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.40171 0.217327
\(246\) 0 0
\(247\) −3.79383 −0.241396
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.747604 −0.0471883 −0.0235942 0.999722i \(-0.507511\pi\)
−0.0235942 + 0.999722i \(0.507511\pi\)
\(252\) 0 0
\(253\) 2.38776 0.150117
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 25.9388 1.61802 0.809008 0.587797i \(-0.200005\pi\)
0.809008 + 0.587797i \(0.200005\pi\)
\(258\) 0 0
\(259\) −0.195541 −0.0121503
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.8540 1.03926 0.519632 0.854390i \(-0.326069\pi\)
0.519632 + 0.854390i \(0.326069\pi\)
\(264\) 0 0
\(265\) 8.01395 0.492293
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −31.6016 −1.92678 −0.963392 0.268095i \(-0.913606\pi\)
−0.963392 + 0.268095i \(0.913606\pi\)
\(270\) 0 0
\(271\) −3.59829 −0.218581 −0.109290 0.994010i \(-0.534858\pi\)
−0.109290 + 0.994010i \(0.534858\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.38776 0.143987
\(276\) 0 0
\(277\) −19.9634 −1.19948 −0.599741 0.800194i \(-0.704730\pi\)
−0.599741 + 0.800194i \(0.704730\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.4157 1.45652 0.728258 0.685303i \(-0.240330\pi\)
0.728258 + 0.685303i \(0.240330\pi\)
\(282\) 0 0
\(283\) 29.9248 1.77885 0.889423 0.457085i \(-0.151106\pi\)
0.889423 + 0.457085i \(0.151106\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0910 −1.06788
\(288\) 0 0
\(289\) −16.4200 −0.965884
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 25.1247 1.46780 0.733901 0.679256i \(-0.237697\pi\)
0.733901 + 0.679256i \(0.237697\pi\)
\(294\) 0 0
\(295\) 10.2201 0.595038
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.38776 −0.253750
\(300\) 0 0
\(301\) 6.16952 0.355605
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.64015 −0.208434
\(306\) 0 0
\(307\) −5.64015 −0.321900 −0.160950 0.986963i \(-0.551456\pi\)
−0.160950 + 0.986963i \(0.551456\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −11.0462 −0.626374 −0.313187 0.949691i \(-0.601397\pi\)
−0.313187 + 0.949691i \(0.601397\pi\)
\(312\) 0 0
\(313\) −4.30925 −0.243573 −0.121787 0.992556i \(-0.538862\pi\)
−0.121787 + 0.992556i \(0.538862\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.62183 −0.484250 −0.242125 0.970245i \(-0.577844\pi\)
−0.242125 + 0.970245i \(0.577844\pi\)
\(318\) 0 0
\(319\) −20.9205 −1.17132
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.658473 −0.0366384
\(324\) 0 0
\(325\) −4.38776 −0.243389
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.94751 −0.327897
\(330\) 0 0
\(331\) −10.8786 −0.597942 −0.298971 0.954262i \(-0.596643\pi\)
−0.298971 + 0.954262i \(0.596643\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.6079 −0.688842
\(336\) 0 0
\(337\) 3.55102 0.193436 0.0967182 0.995312i \(-0.469165\pi\)
0.0967182 + 0.995312i \(0.469165\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 22.3386 1.20970
\(342\) 0 0
\(343\) −19.7312 −1.06538
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.31695 −0.285429 −0.142714 0.989764i \(-0.545583\pi\)
−0.142714 + 0.989764i \(0.545583\pi\)
\(348\) 0 0
\(349\) −6.57997 −0.352218 −0.176109 0.984371i \(-0.556351\pi\)
−0.176109 + 0.984371i \(0.556351\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.88296 0.526017 0.263009 0.964794i \(-0.415285\pi\)
0.263009 + 0.964794i \(0.415285\pi\)
\(354\) 0 0
\(355\) −6.55539 −0.347924
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −15.9109 −0.839744 −0.419872 0.907583i \(-0.637925\pi\)
−0.419872 + 0.907583i \(0.637925\pi\)
\(360\) 0 0
\(361\) −18.2524 −0.960652
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.92919 0.258006
\(366\) 0 0
\(367\) −21.5125 −1.12294 −0.561471 0.827496i \(-0.689765\pi\)
−0.561471 + 0.827496i \(0.689765\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −15.2018 −0.789238
\(372\) 0 0
\(373\) −24.2986 −1.25814 −0.629068 0.777351i \(-0.716563\pi\)
−0.629068 + 0.777351i \(0.716563\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 38.4436 1.97994
\(378\) 0 0
\(379\) 21.5510 1.10700 0.553501 0.832849i \(-0.313292\pi\)
0.553501 + 0.832849i \(0.313292\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −23.5371 −1.20269 −0.601344 0.798990i \(-0.705368\pi\)
−0.601344 + 0.798990i \(0.705368\pi\)
\(384\) 0 0
\(385\) −4.52937 −0.230838
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 21.6926 1.09986 0.549930 0.835211i \(-0.314654\pi\)
0.549930 + 0.835211i \(0.314654\pi\)
\(390\) 0 0
\(391\) −0.761557 −0.0385136
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.04623 0.354534
\(396\) 0 0
\(397\) −19.8863 −0.998064 −0.499032 0.866583i \(-0.666311\pi\)
−0.499032 + 0.866583i \(0.666311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.7755 −0.538103 −0.269052 0.963126i \(-0.586710\pi\)
−0.269052 + 0.963126i \(0.586710\pi\)
\(402\) 0 0
\(403\) −41.0496 −2.04482
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.246139 −0.0122006
\(408\) 0 0
\(409\) −11.3834 −0.562872 −0.281436 0.959580i \(-0.590811\pi\)
−0.281436 + 0.959580i \(0.590811\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −19.3867 −0.953958
\(414\) 0 0
\(415\) 5.23844 0.257145
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.6218 0.518910 0.259455 0.965755i \(-0.416457\pi\)
0.259455 + 0.965755i \(0.416457\pi\)
\(420\) 0 0
\(421\) −3.43398 −0.167362 −0.0836811 0.996493i \(-0.526668\pi\)
−0.0836811 + 0.996493i \(0.526668\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.761557 −0.0369409
\(426\) 0 0
\(427\) 6.90506 0.334159
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 23.8217 1.14745 0.573726 0.819047i \(-0.305497\pi\)
0.573726 + 0.819047i \(0.305497\pi\)
\(432\) 0 0
\(433\) 23.7957 1.14355 0.571775 0.820411i \(-0.306255\pi\)
0.571775 + 0.820411i \(0.306255\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.864641 0.0413614
\(438\) 0 0
\(439\) 38.6618 1.84523 0.922614 0.385726i \(-0.126049\pi\)
0.922614 + 0.385726i \(0.126049\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −28.3232 −1.34568 −0.672838 0.739790i \(-0.734925\pi\)
−0.672838 + 0.739790i \(0.734925\pi\)
\(444\) 0 0
\(445\) −10.9817 −0.520581
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −23.8078 −1.12356 −0.561779 0.827287i \(-0.689883\pi\)
−0.561779 + 0.827287i \(0.689883\pi\)
\(450\) 0 0
\(451\) −22.7722 −1.07230
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.32320 0.390198
\(456\) 0 0
\(457\) 32.7003 1.52966 0.764829 0.644234i \(-0.222824\pi\)
0.764829 + 0.644234i \(0.222824\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.7755 1.06076 0.530381 0.847760i \(-0.322049\pi\)
0.530381 + 0.847760i \(0.322049\pi\)
\(462\) 0 0
\(463\) −17.4061 −0.808929 −0.404465 0.914554i \(-0.632542\pi\)
−0.404465 + 0.914554i \(0.632542\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −24.8540 −1.15011 −0.575053 0.818116i \(-0.695019\pi\)
−0.575053 + 0.818116i \(0.695019\pi\)
\(468\) 0 0
\(469\) 23.9161 1.10434
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.76593 0.357078
\(474\) 0 0
\(475\) 0.864641 0.0396724
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.6402 −0.805999 −0.403000 0.915200i \(-0.632032\pi\)
−0.403000 + 0.915200i \(0.632032\pi\)
\(480\) 0 0
\(481\) 0.452306 0.0206234
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.0645508 0.00293110
\(486\) 0 0
\(487\) −14.7509 −0.668428 −0.334214 0.942497i \(-0.608471\pi\)
−0.334214 + 0.942497i \(0.608471\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.80779 −0.442619 −0.221310 0.975204i \(-0.571033\pi\)
−0.221310 + 0.975204i \(0.571033\pi\)
\(492\) 0 0
\(493\) 6.67243 0.300511
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.4350 0.557787
\(498\) 0 0
\(499\) −21.1772 −0.948023 −0.474011 0.880519i \(-0.657194\pi\)
−0.474011 + 0.880519i \(0.657194\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.4542 −1.00118 −0.500592 0.865684i \(-0.666884\pi\)
−0.500592 + 0.865684i \(0.666884\pi\)
\(504\) 0 0
\(505\) −1.30299 −0.0579825
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −22.9817 −1.01864 −0.509322 0.860576i \(-0.670104\pi\)
−0.509322 + 0.860576i \(0.670104\pi\)
\(510\) 0 0
\(511\) −9.35026 −0.413631
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.98168 0.219519
\(516\) 0 0
\(517\) −7.48647 −0.329255
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −21.4985 −0.941868 −0.470934 0.882168i \(-0.656083\pi\)
−0.470934 + 0.882168i \(0.656083\pi\)
\(522\) 0 0
\(523\) −15.4586 −0.675956 −0.337978 0.941154i \(-0.609743\pi\)
−0.337978 + 0.941154i \(0.609743\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7.12473 −0.310358
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 41.8463 1.81257
\(534\) 0 0
\(535\) −0.697006 −0.0301342
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8.12245 −0.349859
\(540\) 0 0
\(541\) −14.0279 −0.603107 −0.301553 0.953449i \(-0.597505\pi\)
−0.301553 + 0.953449i \(0.597505\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.92919 0.211143
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.57560 −0.322731
\(552\) 0 0
\(553\) −13.3661 −0.568385
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 23.9860 1.01632 0.508161 0.861262i \(-0.330326\pi\)
0.508161 + 0.861262i \(0.330326\pi\)
\(558\) 0 0
\(559\) −14.2707 −0.603587
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.2297 1.14760 0.573798 0.818997i \(-0.305470\pi\)
0.573798 + 0.818997i \(0.305470\pi\)
\(564\) 0 0
\(565\) −9.53707 −0.401227
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.9046 0.457145 0.228573 0.973527i \(-0.426594\pi\)
0.228573 + 0.973527i \(0.426594\pi\)
\(570\) 0 0
\(571\) −2.02458 −0.0847260 −0.0423630 0.999102i \(-0.513489\pi\)
−0.0423630 + 0.999102i \(0.513489\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −22.8034 −0.949319 −0.474659 0.880170i \(-0.657429\pi\)
−0.474659 + 0.880170i \(0.657429\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9.93689 −0.412252
\(582\) 0 0
\(583\) −19.1354 −0.792506
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.38150 −0.304667 −0.152334 0.988329i \(-0.548679\pi\)
−0.152334 + 0.988329i \(0.548679\pi\)
\(588\) 0 0
\(589\) 8.08913 0.333307
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.05829 −0.207719 −0.103860 0.994592i \(-0.533119\pi\)
−0.103860 + 0.994592i \(0.533119\pi\)
\(594\) 0 0
\(595\) 1.44461 0.0592232
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −14.2707 −0.583086 −0.291543 0.956558i \(-0.594169\pi\)
−0.291543 + 0.956558i \(0.594169\pi\)
\(600\) 0 0
\(601\) 20.4384 0.833698 0.416849 0.908976i \(-0.363134\pi\)
0.416849 + 0.908976i \(0.363134\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.29862 0.215420
\(606\) 0 0
\(607\) −32.8925 −1.33507 −0.667534 0.744580i \(-0.732650\pi\)
−0.667534 + 0.744580i \(0.732650\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 13.7572 0.556556
\(612\) 0 0
\(613\) −38.0000 −1.53481 −0.767403 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.56497 −0.0630035 −0.0315017 0.999504i \(-0.510029\pi\)
−0.0315017 + 0.999504i \(0.510029\pi\)
\(618\) 0 0
\(619\) 34.0925 1.37029 0.685146 0.728406i \(-0.259738\pi\)
0.685146 + 0.728406i \(0.259738\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 20.8313 0.834589
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.0785041 0.00313016
\(630\) 0 0
\(631\) −23.2924 −0.927255 −0.463627 0.886030i \(-0.653452\pi\)
−0.463627 + 0.886030i \(0.653452\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.38776 −0.0947552
\(636\) 0 0
\(637\) 14.9259 0.591384
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −41.4252 −1.63620 −0.818099 0.575077i \(-0.804972\pi\)
−0.818099 + 0.575077i \(0.804972\pi\)
\(642\) 0 0
\(643\) −35.6820 −1.40716 −0.703581 0.710615i \(-0.748417\pi\)
−0.703581 + 0.710615i \(0.748417\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.4436 1.03960 0.519802 0.854287i \(-0.326006\pi\)
0.519802 + 0.854287i \(0.326006\pi\)
\(648\) 0 0
\(649\) −24.4031 −0.957907
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.64015 0.142450 0.0712251 0.997460i \(-0.477309\pi\)
0.0712251 + 0.997460i \(0.477309\pi\)
\(654\) 0 0
\(655\) 0.953771 0.0372669
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13.1999 −0.514195 −0.257098 0.966385i \(-0.582766\pi\)
−0.257098 + 0.966385i \(0.582766\pi\)
\(660\) 0 0
\(661\) −28.2707 −1.09960 −0.549802 0.835295i \(-0.685297\pi\)
−0.549802 + 0.835295i \(0.685297\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.64015 −0.0636023
\(666\) 0 0
\(667\) −8.76156 −0.339249
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.69179 0.335543
\(672\) 0 0
\(673\) −7.22782 −0.278612 −0.139306 0.990249i \(-0.544487\pi\)
−0.139306 + 0.990249i \(0.544487\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 26.1064 1.00335 0.501675 0.865056i \(-0.332717\pi\)
0.501675 + 0.865056i \(0.332717\pi\)
\(678\) 0 0
\(679\) −0.122447 −0.00469910
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −35.3203 −1.35149 −0.675746 0.737134i \(-0.736179\pi\)
−0.675746 + 0.737134i \(0.736179\pi\)
\(684\) 0 0
\(685\) 3.93545 0.150366
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 35.1633 1.33961
\(690\) 0 0
\(691\) 39.8496 1.51595 0.757976 0.652282i \(-0.226188\pi\)
0.757976 + 0.652282i \(0.226188\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.87859 0.109191
\(696\) 0 0
\(697\) 7.26302 0.275107
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −50.1170 −1.89289 −0.946447 0.322859i \(-0.895356\pi\)
−0.946447 + 0.322859i \(0.895356\pi\)
\(702\) 0 0
\(703\) −0.0891304 −0.00336162
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.47167 0.0929567
\(708\) 0 0
\(709\) −31.8742 −1.19706 −0.598531 0.801100i \(-0.704249\pi\)
−0.598531 + 0.801100i \(0.704249\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.35548 0.350365
\(714\) 0 0
\(715\) 10.4769 0.391813
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 19.1526 0.714273 0.357136 0.934052i \(-0.383753\pi\)
0.357136 + 0.934052i \(0.383753\pi\)
\(720\) 0 0
\(721\) −9.44983 −0.351930
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.76156 −0.325396
\(726\) 0 0
\(727\) −23.7553 −0.881035 −0.440518 0.897744i \(-0.645205\pi\)
−0.440518 + 0.897744i \(0.645205\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.47689 −0.0916109
\(732\) 0 0
\(733\) −18.9152 −0.698650 −0.349325 0.937002i \(-0.613589\pi\)
−0.349325 + 0.937002i \(0.613589\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 30.1045 1.10891
\(738\) 0 0
\(739\) 42.1310 1.54981 0.774907 0.632076i \(-0.217797\pi\)
0.774907 + 0.632076i \(0.217797\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.41233 0.308619 0.154309 0.988023i \(-0.450685\pi\)
0.154309 + 0.988023i \(0.450685\pi\)
\(744\) 0 0
\(745\) 19.4340 0.712006
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.32216 0.0483108
\(750\) 0 0
\(751\) −25.5110 −0.930911 −0.465456 0.885071i \(-0.654110\pi\)
−0.465456 + 0.885071i \(0.654110\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10.7110 0.389812
\(756\) 0 0
\(757\) 46.0452 1.67354 0.836770 0.547554i \(-0.184441\pi\)
0.836770 + 0.547554i \(0.184441\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 37.5929 1.36274 0.681370 0.731939i \(-0.261384\pi\)
0.681370 + 0.731939i \(0.261384\pi\)
\(762\) 0 0
\(763\) −9.35026 −0.338502
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 44.8434 1.61920
\(768\) 0 0
\(769\) −0.230747 −0.00832095 −0.00416047 0.999991i \(-0.501324\pi\)
−0.00416047 + 0.999991i \(0.501324\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12.3998 0.445991 0.222995 0.974820i \(-0.428417\pi\)
0.222995 + 0.974820i \(0.428417\pi\)
\(774\) 0 0
\(775\) 9.35548 0.336059
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.24614 −0.295449
\(780\) 0 0
\(781\) 15.6527 0.560096
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 16.3372 0.583098
\(786\) 0 0
\(787\) −28.0943 −1.00146 −0.500728 0.865605i \(-0.666934\pi\)
−0.500728 + 0.865605i \(0.666934\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 18.0910 0.643243
\(792\) 0 0
\(793\) −15.9721 −0.567186
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 10.5187 0.372593 0.186297 0.982494i \(-0.440351\pi\)
0.186297 + 0.982494i \(0.440351\pi\)
\(798\) 0 0
\(799\) 2.38776 0.0844727
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −11.7697 −0.415344
\(804\) 0 0
\(805\) −1.89692 −0.0668575
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.527483 0.0185453 0.00927266 0.999957i \(-0.497048\pi\)
0.00927266 + 0.999957i \(0.497048\pi\)
\(810\) 0 0
\(811\) 31.4200 1.10331 0.551653 0.834074i \(-0.313997\pi\)
0.551653 + 0.834074i \(0.313997\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −11.2524 −0.394154
\(816\) 0 0
\(817\) 2.81215 0.0983848
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 24.6060 0.858755 0.429377 0.903125i \(-0.358733\pi\)
0.429377 + 0.903125i \(0.358733\pi\)
\(822\) 0 0
\(823\) −22.0925 −0.770095 −0.385047 0.922897i \(-0.625815\pi\)
−0.385047 + 0.922897i \(0.625815\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 30.0419 1.04466 0.522329 0.852744i \(-0.325063\pi\)
0.522329 + 0.852744i \(0.325063\pi\)
\(828\) 0 0
\(829\) −30.6358 −1.06402 −0.532012 0.846737i \(-0.678564\pi\)
−0.532012 + 0.846737i \(0.678564\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.59060 0.0897588
\(834\) 0 0
\(835\) −6.59392 −0.228192
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 37.3449 1.28929 0.644644 0.764483i \(-0.277006\pi\)
0.644644 + 0.764483i \(0.277006\pi\)
\(840\) 0 0
\(841\) 47.7649 1.64706
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −6.25240 −0.215089
\(846\) 0 0
\(847\) −10.0510 −0.345358
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −0.103084 −0.00353366
\(852\) 0 0
\(853\) 7.78510 0.266557 0.133278 0.991079i \(-0.457450\pi\)
0.133278 + 0.991079i \(0.457450\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −56.1483 −1.91799 −0.958994 0.283426i \(-0.908529\pi\)
−0.958994 + 0.283426i \(0.908529\pi\)
\(858\) 0 0
\(859\) −1.25051 −0.0426668 −0.0213334 0.999772i \(-0.506791\pi\)
−0.0213334 + 0.999772i \(0.506791\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −15.4865 −0.527166 −0.263583 0.964637i \(-0.584904\pi\)
−0.263583 + 0.964637i \(0.584904\pi\)
\(864\) 0 0
\(865\) −20.7110 −0.704194
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −16.8247 −0.570738
\(870\) 0 0
\(871\) −55.3203 −1.87446
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.89692 −0.0641275
\(876\) 0 0
\(877\) 26.7755 0.904145 0.452072 0.891981i \(-0.350685\pi\)
0.452072 + 0.891981i \(0.350685\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −5.75386 −0.193853 −0.0969263 0.995292i \(-0.530901\pi\)
−0.0969263 + 0.995292i \(0.530901\pi\)
\(882\) 0 0
\(883\) 22.8559 0.769162 0.384581 0.923091i \(-0.374346\pi\)
0.384581 + 0.923091i \(0.374346\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 39.0741 1.31198 0.655991 0.754769i \(-0.272251\pi\)
0.655991 + 0.754769i \(0.272251\pi\)
\(888\) 0 0
\(889\) 4.52937 0.151910
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.71096 −0.0907188
\(894\) 0 0
\(895\) 22.2986 0.745361
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −81.9686 −2.73380
\(900\) 0 0
\(901\) 6.10308 0.203323
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 21.4865 0.714234
\(906\) 0 0
\(907\) 29.2784 0.972174 0.486087 0.873910i \(-0.338424\pi\)
0.486087 + 0.873910i \(0.338424\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 25.9634 0.860204 0.430102 0.902780i \(-0.358478\pi\)
0.430102 + 0.902780i \(0.358478\pi\)
\(912\) 0 0
\(913\) −12.5081 −0.413958
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.80922 −0.0597458
\(918\) 0 0
\(919\) −26.9171 −0.887914 −0.443957 0.896048i \(-0.646426\pi\)
−0.443957 + 0.896048i \(0.646426\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −28.7634 −0.946760
\(924\) 0 0
\(925\) −0.103084 −0.00338937
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −41.9494 −1.37632 −0.688158 0.725561i \(-0.741580\pi\)
−0.688158 + 0.725561i \(0.741580\pi\)
\(930\) 0 0
\(931\) −2.94126 −0.0963958
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.81841 0.0594684
\(936\) 0 0
\(937\) 34.9817 1.14280 0.571401 0.820671i \(-0.306400\pi\)
0.571401 + 0.820671i \(0.306400\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.38776 0.143037 0.0715184 0.997439i \(-0.477216\pi\)
0.0715184 + 0.997439i \(0.477216\pi\)
\(942\) 0 0
\(943\) −9.53707 −0.310570
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −10.3265 −0.335567 −0.167784 0.985824i \(-0.553661\pi\)
−0.167784 + 0.985824i \(0.553661\pi\)
\(948\) 0 0
\(949\) 21.6281 0.702077
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 48.5048 1.57122 0.785612 0.618719i \(-0.212348\pi\)
0.785612 + 0.618719i \(0.212348\pi\)
\(954\) 0 0
\(955\) −12.8646 −0.416290
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.46522 −0.241064
\(960\) 0 0
\(961\) 56.5250 1.82339
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 18.0279 0.580339
\(966\) 0 0
\(967\) 29.9021 0.961588 0.480794 0.876834i \(-0.340349\pi\)
0.480794 + 0.876834i \(0.340349\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 7.15120 0.229493 0.114746 0.993395i \(-0.463394\pi\)
0.114746 + 0.993395i \(0.463394\pi\)
\(972\) 0 0
\(973\) −5.46045 −0.175054
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.7249 0.982977 0.491489 0.870884i \(-0.336453\pi\)
0.491489 + 0.870884i \(0.336453\pi\)
\(978\) 0 0
\(979\) 26.2216 0.838045
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 31.3588 1.00019 0.500095 0.865970i \(-0.333298\pi\)
0.500095 + 0.865970i \(0.333298\pi\)
\(984\) 0 0
\(985\) 14.2341 0.453535
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.25240 0.103420
\(990\) 0 0
\(991\) −54.1868 −1.72130 −0.860650 0.509197i \(-0.829943\pi\)
−0.860650 + 0.509197i \(0.829943\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12.5693 −0.398475
\(996\) 0 0
\(997\) 27.9354 0.884725 0.442362 0.896836i \(-0.354141\pi\)
0.442362 + 0.896836i \(0.354141\pi\)
\(998\) 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.bi.1.2 3
3.2 odd 2 2760.2.a.u.1.2 3
12.11 even 2 5520.2.a.bz.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.u.1.2 3 3.2 odd 2
5520.2.a.bz.1.2 3 12.11 even 2
8280.2.a.bi.1.2 3 1.1 even 1 trivial