Properties

Label 8036.2.a.o.1.8
Level $8036$
Weight $2$
Character 8036.1
Self dual yes
Analytic conductor $64.168$
Analytic rank $1$
Dimension $10$
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] = [8036,2,Mod(1,8036)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8036, 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("8036.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8036.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: \(64.1677830643\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 110x^{6} - 154x^{5} - 282x^{4} + 256x^{3} + 253x^{2} - 126x - 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-1.73395\) of defining polynomial
Character \(\chi\) \(=\) 8036.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.73395 q^{3} +3.41343 q^{5} +0.00658743 q^{9} +O(q^{10})\) \(q+1.73395 q^{3} +3.41343 q^{5} +0.00658743 q^{9} +1.67665 q^{11} -6.13889 q^{13} +5.91872 q^{15} -3.78979 q^{17} -3.86873 q^{19} -5.49935 q^{23} +6.65149 q^{25} -5.19043 q^{27} -0.172699 q^{29} -7.15470 q^{31} +2.90724 q^{33} -4.80199 q^{37} -10.6445 q^{39} -1.00000 q^{41} +0.845176 q^{43} +0.0224857 q^{45} -4.65792 q^{47} -6.57131 q^{51} +4.46567 q^{53} +5.72314 q^{55} -6.70819 q^{57} +3.38395 q^{59} -0.643064 q^{61} -20.9547 q^{65} -2.25183 q^{67} -9.53561 q^{69} -4.77826 q^{71} -9.42378 q^{73} +11.5334 q^{75} +3.64751 q^{79} -9.01972 q^{81} +12.7027 q^{83} -12.9362 q^{85} -0.299452 q^{87} -6.83667 q^{89} -12.4059 q^{93} -13.2056 q^{95} +0.615292 q^{97} +0.0110448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{3} - 4 q^{5} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{3} - 4 q^{5} + 10 q^{9} - 6 q^{13} - 4 q^{15} - 12 q^{17} - 8 q^{19} + 4 q^{23} + 16 q^{25} - 8 q^{27} + 2 q^{29} - 8 q^{31} + 6 q^{33} - 2 q^{37} - 2 q^{39} - 10 q^{41} - 2 q^{43} - 44 q^{45} + 14 q^{47} + 14 q^{51} + 8 q^{53} - 8 q^{55} - 10 q^{57} - 24 q^{59} - 14 q^{61} + 2 q^{65} - 8 q^{67} - 16 q^{69} + 10 q^{71} - 44 q^{73} + 50 q^{75} + 10 q^{79} - 14 q^{81} - 20 q^{83} + 8 q^{85} - 20 q^{87} - 6 q^{89} + 8 q^{93} + 4 q^{95} - 46 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.73395 1.00110 0.500549 0.865708i \(-0.333132\pi\)
0.500549 + 0.865708i \(0.333132\pi\)
\(4\) 0 0
\(5\) 3.41343 1.52653 0.763266 0.646085i \(-0.223595\pi\)
0.763266 + 0.646085i \(0.223595\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.00658743 0.00219581
\(10\) 0 0
\(11\) 1.67665 0.505530 0.252765 0.967528i \(-0.418660\pi\)
0.252765 + 0.967528i \(0.418660\pi\)
\(12\) 0 0
\(13\) −6.13889 −1.70262 −0.851311 0.524661i \(-0.824192\pi\)
−0.851311 + 0.524661i \(0.824192\pi\)
\(14\) 0 0
\(15\) 5.91872 1.52821
\(16\) 0 0
\(17\) −3.78979 −0.919159 −0.459580 0.888137i \(-0.652000\pi\)
−0.459580 + 0.888137i \(0.652000\pi\)
\(18\) 0 0
\(19\) −3.86873 −0.887547 −0.443774 0.896139i \(-0.646361\pi\)
−0.443774 + 0.896139i \(0.646361\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.49935 −1.14669 −0.573347 0.819312i \(-0.694355\pi\)
−0.573347 + 0.819312i \(0.694355\pi\)
\(24\) 0 0
\(25\) 6.65149 1.33030
\(26\) 0 0
\(27\) −5.19043 −0.998899
\(28\) 0 0
\(29\) −0.172699 −0.0320695 −0.0160347 0.999871i \(-0.505104\pi\)
−0.0160347 + 0.999871i \(0.505104\pi\)
\(30\) 0 0
\(31\) −7.15470 −1.28502 −0.642511 0.766276i \(-0.722107\pi\)
−0.642511 + 0.766276i \(0.722107\pi\)
\(32\) 0 0
\(33\) 2.90724 0.506085
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.80199 −0.789443 −0.394721 0.918801i \(-0.629159\pi\)
−0.394721 + 0.918801i \(0.629159\pi\)
\(38\) 0 0
\(39\) −10.6445 −1.70449
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 0.845176 0.128888 0.0644441 0.997921i \(-0.479473\pi\)
0.0644441 + 0.997921i \(0.479473\pi\)
\(44\) 0 0
\(45\) 0.0224857 0.00335197
\(46\) 0 0
\(47\) −4.65792 −0.679428 −0.339714 0.940529i \(-0.610330\pi\)
−0.339714 + 0.940529i \(0.610330\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −6.57131 −0.920168
\(52\) 0 0
\(53\) 4.46567 0.613407 0.306703 0.951805i \(-0.400774\pi\)
0.306703 + 0.951805i \(0.400774\pi\)
\(54\) 0 0
\(55\) 5.72314 0.771708
\(56\) 0 0
\(57\) −6.70819 −0.888521
\(58\) 0 0
\(59\) 3.38395 0.440553 0.220276 0.975437i \(-0.429304\pi\)
0.220276 + 0.975437i \(0.429304\pi\)
\(60\) 0 0
\(61\) −0.643064 −0.0823359 −0.0411679 0.999152i \(-0.513108\pi\)
−0.0411679 + 0.999152i \(0.513108\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −20.9547 −2.59911
\(66\) 0 0
\(67\) −2.25183 −0.275105 −0.137553 0.990494i \(-0.543924\pi\)
−0.137553 + 0.990494i \(0.543924\pi\)
\(68\) 0 0
\(69\) −9.53561 −1.14795
\(70\) 0 0
\(71\) −4.77826 −0.567076 −0.283538 0.958961i \(-0.591508\pi\)
−0.283538 + 0.958961i \(0.591508\pi\)
\(72\) 0 0
\(73\) −9.42378 −1.10297 −0.551485 0.834185i \(-0.685939\pi\)
−0.551485 + 0.834185i \(0.685939\pi\)
\(74\) 0 0
\(75\) 11.5334 1.33176
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 3.64751 0.410377 0.205189 0.978722i \(-0.434219\pi\)
0.205189 + 0.978722i \(0.434219\pi\)
\(80\) 0 0
\(81\) −9.01972 −1.00219
\(82\) 0 0
\(83\) 12.7027 1.39430 0.697149 0.716926i \(-0.254452\pi\)
0.697149 + 0.716926i \(0.254452\pi\)
\(84\) 0 0
\(85\) −12.9362 −1.40313
\(86\) 0 0
\(87\) −0.299452 −0.0321046
\(88\) 0 0
\(89\) −6.83667 −0.724685 −0.362343 0.932045i \(-0.618023\pi\)
−0.362343 + 0.932045i \(0.618023\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −12.4059 −1.28643
\(94\) 0 0
\(95\) −13.2056 −1.35487
\(96\) 0 0
\(97\) 0.615292 0.0624734 0.0312367 0.999512i \(-0.490055\pi\)
0.0312367 + 0.999512i \(0.490055\pi\)
\(98\) 0 0
\(99\) 0.0110448 0.00111005
\(100\) 0 0
\(101\) 6.55350 0.652098 0.326049 0.945353i \(-0.394283\pi\)
0.326049 + 0.945353i \(0.394283\pi\)
\(102\) 0 0
\(103\) 9.40980 0.927175 0.463588 0.886051i \(-0.346562\pi\)
0.463588 + 0.886051i \(0.346562\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.66303 0.354119 0.177059 0.984200i \(-0.443342\pi\)
0.177059 + 0.984200i \(0.443342\pi\)
\(108\) 0 0
\(109\) 10.1194 0.969263 0.484632 0.874718i \(-0.338954\pi\)
0.484632 + 0.874718i \(0.338954\pi\)
\(110\) 0 0
\(111\) −8.32642 −0.790309
\(112\) 0 0
\(113\) −11.0216 −1.03683 −0.518413 0.855131i \(-0.673477\pi\)
−0.518413 + 0.855131i \(0.673477\pi\)
\(114\) 0 0
\(115\) −18.7717 −1.75047
\(116\) 0 0
\(117\) −0.0404395 −0.00373863
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.18883 −0.744439
\(122\) 0 0
\(123\) −1.73395 −0.156345
\(124\) 0 0
\(125\) 5.63724 0.504210
\(126\) 0 0
\(127\) 15.1077 1.34059 0.670296 0.742094i \(-0.266167\pi\)
0.670296 + 0.742094i \(0.266167\pi\)
\(128\) 0 0
\(129\) 1.46549 0.129030
\(130\) 0 0
\(131\) −5.99133 −0.523465 −0.261732 0.965140i \(-0.584294\pi\)
−0.261732 + 0.965140i \(0.584294\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −17.7172 −1.52485
\(136\) 0 0
\(137\) −12.1656 −1.03938 −0.519688 0.854356i \(-0.673952\pi\)
−0.519688 + 0.854356i \(0.673952\pi\)
\(138\) 0 0
\(139\) 5.02141 0.425910 0.212955 0.977062i \(-0.431691\pi\)
0.212955 + 0.977062i \(0.431691\pi\)
\(140\) 0 0
\(141\) −8.07661 −0.680173
\(142\) 0 0
\(143\) −10.2928 −0.860728
\(144\) 0 0
\(145\) −0.589497 −0.0489550
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.7546 0.881055 0.440528 0.897739i \(-0.354791\pi\)
0.440528 + 0.897739i \(0.354791\pi\)
\(150\) 0 0
\(151\) −14.3236 −1.16564 −0.582818 0.812602i \(-0.698050\pi\)
−0.582818 + 0.812602i \(0.698050\pi\)
\(152\) 0 0
\(153\) −0.0249650 −0.00201830
\(154\) 0 0
\(155\) −24.4221 −1.96163
\(156\) 0 0
\(157\) 16.9304 1.35119 0.675596 0.737272i \(-0.263886\pi\)
0.675596 + 0.737272i \(0.263886\pi\)
\(158\) 0 0
\(159\) 7.74325 0.614080
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −5.72220 −0.448197 −0.224099 0.974566i \(-0.571944\pi\)
−0.224099 + 0.974566i \(0.571944\pi\)
\(164\) 0 0
\(165\) 9.92365 0.772555
\(166\) 0 0
\(167\) −11.3051 −0.874812 −0.437406 0.899264i \(-0.644103\pi\)
−0.437406 + 0.899264i \(0.644103\pi\)
\(168\) 0 0
\(169\) 24.6860 1.89892
\(170\) 0 0
\(171\) −0.0254850 −0.00194888
\(172\) 0 0
\(173\) 19.4786 1.48093 0.740465 0.672095i \(-0.234605\pi\)
0.740465 + 0.672095i \(0.234605\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.86761 0.441036
\(178\) 0 0
\(179\) 1.59474 0.119197 0.0595983 0.998222i \(-0.481018\pi\)
0.0595983 + 0.998222i \(0.481018\pi\)
\(180\) 0 0
\(181\) −7.25966 −0.539607 −0.269803 0.962915i \(-0.586959\pi\)
−0.269803 + 0.962915i \(0.586959\pi\)
\(182\) 0 0
\(183\) −1.11504 −0.0824262
\(184\) 0 0
\(185\) −16.3913 −1.20511
\(186\) 0 0
\(187\) −6.35417 −0.464663
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 23.7348 1.71739 0.858694 0.512488i \(-0.171276\pi\)
0.858694 + 0.512488i \(0.171276\pi\)
\(192\) 0 0
\(193\) 20.2501 1.45763 0.728817 0.684709i \(-0.240071\pi\)
0.728817 + 0.684709i \(0.240071\pi\)
\(194\) 0 0
\(195\) −36.3344 −2.60196
\(196\) 0 0
\(197\) −16.4401 −1.17131 −0.585654 0.810561i \(-0.699162\pi\)
−0.585654 + 0.810561i \(0.699162\pi\)
\(198\) 0 0
\(199\) 13.2785 0.941291 0.470646 0.882322i \(-0.344021\pi\)
0.470646 + 0.882322i \(0.344021\pi\)
\(200\) 0 0
\(201\) −3.90457 −0.275407
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.41343 −0.238404
\(206\) 0 0
\(207\) −0.0362266 −0.00251792
\(208\) 0 0
\(209\) −6.48652 −0.448682
\(210\) 0 0
\(211\) 1.73436 0.119398 0.0596991 0.998216i \(-0.480986\pi\)
0.0596991 + 0.998216i \(0.480986\pi\)
\(212\) 0 0
\(213\) −8.28528 −0.567698
\(214\) 0 0
\(215\) 2.88495 0.196752
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −16.3404 −1.10418
\(220\) 0 0
\(221\) 23.2651 1.56498
\(222\) 0 0
\(223\) −26.4764 −1.77299 −0.886496 0.462737i \(-0.846868\pi\)
−0.886496 + 0.462737i \(0.846868\pi\)
\(224\) 0 0
\(225\) 0.0438162 0.00292108
\(226\) 0 0
\(227\) −16.7320 −1.11054 −0.555271 0.831669i \(-0.687386\pi\)
−0.555271 + 0.831669i \(0.687386\pi\)
\(228\) 0 0
\(229\) −6.74483 −0.445711 −0.222855 0.974852i \(-0.571538\pi\)
−0.222855 + 0.974852i \(0.571538\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.7713 0.967697 0.483849 0.875152i \(-0.339239\pi\)
0.483849 + 0.875152i \(0.339239\pi\)
\(234\) 0 0
\(235\) −15.8995 −1.03717
\(236\) 0 0
\(237\) 6.32461 0.410828
\(238\) 0 0
\(239\) −16.2994 −1.05432 −0.527161 0.849766i \(-0.676743\pi\)
−0.527161 + 0.849766i \(0.676743\pi\)
\(240\) 0 0
\(241\) −8.34464 −0.537526 −0.268763 0.963206i \(-0.586615\pi\)
−0.268763 + 0.963206i \(0.586615\pi\)
\(242\) 0 0
\(243\) −0.0684584 −0.00439161
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 23.7497 1.51116
\(248\) 0 0
\(249\) 22.0258 1.39583
\(250\) 0 0
\(251\) 2.21866 0.140041 0.0700204 0.997546i \(-0.477694\pi\)
0.0700204 + 0.997546i \(0.477694\pi\)
\(252\) 0 0
\(253\) −9.22052 −0.579689
\(254\) 0 0
\(255\) −22.4307 −1.40467
\(256\) 0 0
\(257\) 24.4944 1.52792 0.763961 0.645263i \(-0.223252\pi\)
0.763961 + 0.645263i \(0.223252\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.00113764 −7.04184e−5 0
\(262\) 0 0
\(263\) −7.53312 −0.464512 −0.232256 0.972655i \(-0.574611\pi\)
−0.232256 + 0.972655i \(0.574611\pi\)
\(264\) 0 0
\(265\) 15.2432 0.936385
\(266\) 0 0
\(267\) −11.8544 −0.725480
\(268\) 0 0
\(269\) −22.0410 −1.34386 −0.671931 0.740614i \(-0.734535\pi\)
−0.671931 + 0.740614i \(0.734535\pi\)
\(270\) 0 0
\(271\) 21.4621 1.30373 0.651864 0.758336i \(-0.273987\pi\)
0.651864 + 0.758336i \(0.273987\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.1523 0.672506
\(276\) 0 0
\(277\) 31.7745 1.90915 0.954573 0.297977i \(-0.0963119\pi\)
0.954573 + 0.297977i \(0.0963119\pi\)
\(278\) 0 0
\(279\) −0.0471311 −0.00282166
\(280\) 0 0
\(281\) −5.66405 −0.337889 −0.168944 0.985626i \(-0.554036\pi\)
−0.168944 + 0.985626i \(0.554036\pi\)
\(282\) 0 0
\(283\) −22.1824 −1.31860 −0.659302 0.751878i \(-0.729148\pi\)
−0.659302 + 0.751878i \(0.729148\pi\)
\(284\) 0 0
\(285\) −22.8979 −1.35636
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2.63748 −0.155146
\(290\) 0 0
\(291\) 1.06689 0.0625419
\(292\) 0 0
\(293\) 0.662844 0.0387238 0.0193619 0.999813i \(-0.493837\pi\)
0.0193619 + 0.999813i \(0.493837\pi\)
\(294\) 0 0
\(295\) 11.5509 0.672518
\(296\) 0 0
\(297\) −8.70256 −0.504974
\(298\) 0 0
\(299\) 33.7599 1.95239
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 11.3635 0.652813
\(304\) 0 0
\(305\) −2.19505 −0.125688
\(306\) 0 0
\(307\) −11.6945 −0.667438 −0.333719 0.942673i \(-0.608304\pi\)
−0.333719 + 0.942673i \(0.608304\pi\)
\(308\) 0 0
\(309\) 16.3161 0.928193
\(310\) 0 0
\(311\) 10.1939 0.578044 0.289022 0.957322i \(-0.406670\pi\)
0.289022 + 0.957322i \(0.406670\pi\)
\(312\) 0 0
\(313\) −3.90892 −0.220945 −0.110473 0.993879i \(-0.535236\pi\)
−0.110473 + 0.993879i \(0.535236\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 19.2084 1.07885 0.539427 0.842033i \(-0.318641\pi\)
0.539427 + 0.842033i \(0.318641\pi\)
\(318\) 0 0
\(319\) −0.289557 −0.0162121
\(320\) 0 0
\(321\) 6.35152 0.354507
\(322\) 0 0
\(323\) 14.6617 0.815798
\(324\) 0 0
\(325\) −40.8328 −2.26500
\(326\) 0 0
\(327\) 17.5466 0.970327
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 25.3104 1.39119 0.695594 0.718435i \(-0.255141\pi\)
0.695594 + 0.718435i \(0.255141\pi\)
\(332\) 0 0
\(333\) −0.0316328 −0.00173346
\(334\) 0 0
\(335\) −7.68647 −0.419957
\(336\) 0 0
\(337\) 34.5103 1.87990 0.939948 0.341319i \(-0.110873\pi\)
0.939948 + 0.341319i \(0.110873\pi\)
\(338\) 0 0
\(339\) −19.1109 −1.03796
\(340\) 0 0
\(341\) −11.9960 −0.649618
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −32.5491 −1.75239
\(346\) 0 0
\(347\) 19.5932 1.05182 0.525910 0.850540i \(-0.323725\pi\)
0.525910 + 0.850540i \(0.323725\pi\)
\(348\) 0 0
\(349\) −27.0415 −1.44750 −0.723750 0.690063i \(-0.757583\pi\)
−0.723750 + 0.690063i \(0.757583\pi\)
\(350\) 0 0
\(351\) 31.8635 1.70075
\(352\) 0 0
\(353\) −28.6917 −1.52711 −0.763553 0.645745i \(-0.776547\pi\)
−0.763553 + 0.645745i \(0.776547\pi\)
\(354\) 0 0
\(355\) −16.3103 −0.865659
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −28.4429 −1.50116 −0.750578 0.660782i \(-0.770225\pi\)
−0.750578 + 0.660782i \(0.770225\pi\)
\(360\) 0 0
\(361\) −4.03293 −0.212260
\(362\) 0 0
\(363\) −14.1990 −0.745256
\(364\) 0 0
\(365\) −32.1674 −1.68372
\(366\) 0 0
\(367\) 27.2393 1.42188 0.710939 0.703254i \(-0.248270\pi\)
0.710939 + 0.703254i \(0.248270\pi\)
\(368\) 0 0
\(369\) −0.00658743 −0.000342928 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 12.0603 0.624461 0.312230 0.950006i \(-0.398924\pi\)
0.312230 + 0.950006i \(0.398924\pi\)
\(374\) 0 0
\(375\) 9.77471 0.504764
\(376\) 0 0
\(377\) 1.06018 0.0546022
\(378\) 0 0
\(379\) 28.8577 1.48232 0.741160 0.671329i \(-0.234276\pi\)
0.741160 + 0.671329i \(0.234276\pi\)
\(380\) 0 0
\(381\) 26.1960 1.34206
\(382\) 0 0
\(383\) 13.6206 0.695982 0.347991 0.937498i \(-0.386864\pi\)
0.347991 + 0.937498i \(0.386864\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.00556753 0.000283014 0
\(388\) 0 0
\(389\) −12.1436 −0.615704 −0.307852 0.951434i \(-0.599610\pi\)
−0.307852 + 0.951434i \(0.599610\pi\)
\(390\) 0 0
\(391\) 20.8414 1.05400
\(392\) 0 0
\(393\) −10.3887 −0.524039
\(394\) 0 0
\(395\) 12.4505 0.626454
\(396\) 0 0
\(397\) 24.1841 1.21376 0.606882 0.794792i \(-0.292420\pi\)
0.606882 + 0.794792i \(0.292420\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.87866 −0.343504 −0.171752 0.985140i \(-0.554943\pi\)
−0.171752 + 0.985140i \(0.554943\pi\)
\(402\) 0 0
\(403\) 43.9220 2.18791
\(404\) 0 0
\(405\) −30.7882 −1.52988
\(406\) 0 0
\(407\) −8.05128 −0.399087
\(408\) 0 0
\(409\) −8.83930 −0.437075 −0.218538 0.975829i \(-0.570129\pi\)
−0.218538 + 0.975829i \(0.570129\pi\)
\(410\) 0 0
\(411\) −21.0945 −1.04052
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 43.3596 2.12844
\(416\) 0 0
\(417\) 8.70687 0.426377
\(418\) 0 0
\(419\) −18.1974 −0.889000 −0.444500 0.895779i \(-0.646619\pi\)
−0.444500 + 0.895779i \(0.646619\pi\)
\(420\) 0 0
\(421\) −13.7003 −0.667711 −0.333856 0.942624i \(-0.608350\pi\)
−0.333856 + 0.942624i \(0.608350\pi\)
\(422\) 0 0
\(423\) −0.0306837 −0.00149189
\(424\) 0 0
\(425\) −25.2078 −1.22276
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −17.8472 −0.861672
\(430\) 0 0
\(431\) −29.1190 −1.40261 −0.701307 0.712859i \(-0.747400\pi\)
−0.701307 + 0.712859i \(0.747400\pi\)
\(432\) 0 0
\(433\) −5.49135 −0.263897 −0.131949 0.991257i \(-0.542123\pi\)
−0.131949 + 0.991257i \(0.542123\pi\)
\(434\) 0 0
\(435\) −1.02216 −0.0490087
\(436\) 0 0
\(437\) 21.2755 1.01775
\(438\) 0 0
\(439\) 8.58453 0.409717 0.204859 0.978792i \(-0.434327\pi\)
0.204859 + 0.978792i \(0.434327\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 33.1993 1.57734 0.788672 0.614814i \(-0.210769\pi\)
0.788672 + 0.614814i \(0.210769\pi\)
\(444\) 0 0
\(445\) −23.3365 −1.10625
\(446\) 0 0
\(447\) 18.6480 0.882022
\(448\) 0 0
\(449\) 17.3746 0.819960 0.409980 0.912094i \(-0.365536\pi\)
0.409980 + 0.912094i \(0.365536\pi\)
\(450\) 0 0
\(451\) −1.67665 −0.0789506
\(452\) 0 0
\(453\) −24.8364 −1.16692
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.33864 −0.343287 −0.171644 0.985159i \(-0.554908\pi\)
−0.171644 + 0.985159i \(0.554908\pi\)
\(458\) 0 0
\(459\) 19.6707 0.918148
\(460\) 0 0
\(461\) −2.46073 −0.114608 −0.0573038 0.998357i \(-0.518250\pi\)
−0.0573038 + 0.998357i \(0.518250\pi\)
\(462\) 0 0
\(463\) −35.1206 −1.63219 −0.816097 0.577915i \(-0.803866\pi\)
−0.816097 + 0.577915i \(0.803866\pi\)
\(464\) 0 0
\(465\) −42.3467 −1.96378
\(466\) 0 0
\(467\) −11.4411 −0.529433 −0.264716 0.964326i \(-0.585278\pi\)
−0.264716 + 0.964326i \(0.585278\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 29.3565 1.35268
\(472\) 0 0
\(473\) 1.41707 0.0651569
\(474\) 0 0
\(475\) −25.7328 −1.18070
\(476\) 0 0
\(477\) 0.0294173 0.00134692
\(478\) 0 0
\(479\) 12.8860 0.588778 0.294389 0.955686i \(-0.404884\pi\)
0.294389 + 0.955686i \(0.404884\pi\)
\(480\) 0 0
\(481\) 29.4789 1.34412
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.10025 0.0953676
\(486\) 0 0
\(487\) −29.5691 −1.33990 −0.669952 0.742405i \(-0.733685\pi\)
−0.669952 + 0.742405i \(0.733685\pi\)
\(488\) 0 0
\(489\) −9.92201 −0.448689
\(490\) 0 0
\(491\) −28.3180 −1.27797 −0.638986 0.769218i \(-0.720646\pi\)
−0.638986 + 0.769218i \(0.720646\pi\)
\(492\) 0 0
\(493\) 0.654494 0.0294769
\(494\) 0 0
\(495\) 0.0377008 0.00169452
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −9.71814 −0.435044 −0.217522 0.976055i \(-0.569797\pi\)
−0.217522 + 0.976055i \(0.569797\pi\)
\(500\) 0 0
\(501\) −19.6024 −0.875772
\(502\) 0 0
\(503\) −27.2237 −1.21385 −0.606923 0.794760i \(-0.707597\pi\)
−0.606923 + 0.794760i \(0.707597\pi\)
\(504\) 0 0
\(505\) 22.3699 0.995448
\(506\) 0 0
\(507\) 42.8043 1.90101
\(508\) 0 0
\(509\) −34.2038 −1.51606 −0.758028 0.652222i \(-0.773837\pi\)
−0.758028 + 0.652222i \(0.773837\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 20.0804 0.886570
\(514\) 0 0
\(515\) 32.1197 1.41536
\(516\) 0 0
\(517\) −7.80973 −0.343471
\(518\) 0 0
\(519\) 33.7749 1.48255
\(520\) 0 0
\(521\) −37.2153 −1.63043 −0.815216 0.579157i \(-0.803382\pi\)
−0.815216 + 0.579157i \(0.803382\pi\)
\(522\) 0 0
\(523\) 10.9891 0.480519 0.240259 0.970709i \(-0.422767\pi\)
0.240259 + 0.970709i \(0.422767\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 27.1148 1.18114
\(528\) 0 0
\(529\) 7.24290 0.314909
\(530\) 0 0
\(531\) 0.0222915 0.000967370 0
\(532\) 0 0
\(533\) 6.13889 0.265905
\(534\) 0 0
\(535\) 12.5035 0.540573
\(536\) 0 0
\(537\) 2.76520 0.119327
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −12.7378 −0.547643 −0.273821 0.961781i \(-0.588288\pi\)
−0.273821 + 0.961781i \(0.588288\pi\)
\(542\) 0 0
\(543\) −12.5879 −0.540199
\(544\) 0 0
\(545\) 34.5419 1.47961
\(546\) 0 0
\(547\) 16.0176 0.684865 0.342432 0.939542i \(-0.388749\pi\)
0.342432 + 0.939542i \(0.388749\pi\)
\(548\) 0 0
\(549\) −0.00423614 −0.000180794 0
\(550\) 0 0
\(551\) 0.668127 0.0284632
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −28.4216 −1.20643
\(556\) 0 0
\(557\) −39.0799 −1.65587 −0.827935 0.560824i \(-0.810484\pi\)
−0.827935 + 0.560824i \(0.810484\pi\)
\(558\) 0 0
\(559\) −5.18845 −0.219448
\(560\) 0 0
\(561\) −11.0178 −0.465173
\(562\) 0 0
\(563\) 29.1641 1.22912 0.614561 0.788869i \(-0.289333\pi\)
0.614561 + 0.788869i \(0.289333\pi\)
\(564\) 0 0
\(565\) −37.6215 −1.58275
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.6973 −0.448453 −0.224226 0.974537i \(-0.571986\pi\)
−0.224226 + 0.974537i \(0.571986\pi\)
\(570\) 0 0
\(571\) −6.67889 −0.279503 −0.139751 0.990187i \(-0.544630\pi\)
−0.139751 + 0.990187i \(0.544630\pi\)
\(572\) 0 0
\(573\) 41.1550 1.71927
\(574\) 0 0
\(575\) −36.5789 −1.52545
\(576\) 0 0
\(577\) −21.7440 −0.905213 −0.452607 0.891710i \(-0.649506\pi\)
−0.452607 + 0.891710i \(0.649506\pi\)
\(578\) 0 0
\(579\) 35.1127 1.45923
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 7.48739 0.310096
\(584\) 0 0
\(585\) −0.138037 −0.00570714
\(586\) 0 0
\(587\) 30.7691 1.26998 0.634988 0.772522i \(-0.281005\pi\)
0.634988 + 0.772522i \(0.281005\pi\)
\(588\) 0 0
\(589\) 27.6796 1.14052
\(590\) 0 0
\(591\) −28.5063 −1.17259
\(592\) 0 0
\(593\) 27.2968 1.12095 0.560473 0.828173i \(-0.310619\pi\)
0.560473 + 0.828173i \(0.310619\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 23.0244 0.942324
\(598\) 0 0
\(599\) −3.15083 −0.128739 −0.0643697 0.997926i \(-0.520504\pi\)
−0.0643697 + 0.997926i \(0.520504\pi\)
\(600\) 0 0
\(601\) −42.4377 −1.73107 −0.865534 0.500850i \(-0.833021\pi\)
−0.865534 + 0.500850i \(0.833021\pi\)
\(602\) 0 0
\(603\) −0.0148338 −0.000604079 0
\(604\) 0 0
\(605\) −27.9520 −1.13641
\(606\) 0 0
\(607\) 31.1857 1.26579 0.632894 0.774239i \(-0.281867\pi\)
0.632894 + 0.774239i \(0.281867\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 28.5945 1.15681
\(612\) 0 0
\(613\) 36.9343 1.49176 0.745880 0.666080i \(-0.232029\pi\)
0.745880 + 0.666080i \(0.232029\pi\)
\(614\) 0 0
\(615\) −5.91872 −0.238666
\(616\) 0 0
\(617\) −15.8487 −0.638045 −0.319023 0.947747i \(-0.603355\pi\)
−0.319023 + 0.947747i \(0.603355\pi\)
\(618\) 0 0
\(619\) 23.2914 0.936159 0.468080 0.883686i \(-0.344946\pi\)
0.468080 + 0.883686i \(0.344946\pi\)
\(620\) 0 0
\(621\) 28.5440 1.14543
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −14.0151 −0.560605
\(626\) 0 0
\(627\) −11.2473 −0.449175
\(628\) 0 0
\(629\) 18.1985 0.725624
\(630\) 0 0
\(631\) 17.4445 0.694453 0.347227 0.937781i \(-0.387123\pi\)
0.347227 + 0.937781i \(0.387123\pi\)
\(632\) 0 0
\(633\) 3.00730 0.119529
\(634\) 0 0
\(635\) 51.5690 2.04646
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.0314765 −0.00124519
\(640\) 0 0
\(641\) −28.8551 −1.13971 −0.569855 0.821746i \(-0.693000\pi\)
−0.569855 + 0.821746i \(0.693000\pi\)
\(642\) 0 0
\(643\) −17.4989 −0.690090 −0.345045 0.938586i \(-0.612136\pi\)
−0.345045 + 0.938586i \(0.612136\pi\)
\(644\) 0 0
\(645\) 5.00236 0.196968
\(646\) 0 0
\(647\) −22.7880 −0.895887 −0.447944 0.894062i \(-0.647843\pi\)
−0.447944 + 0.894062i \(0.647843\pi\)
\(648\) 0 0
\(649\) 5.67372 0.222713
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 43.1360 1.68804 0.844021 0.536311i \(-0.180182\pi\)
0.844021 + 0.536311i \(0.180182\pi\)
\(654\) 0 0
\(655\) −20.4510 −0.799086
\(656\) 0 0
\(657\) −0.0620785 −0.00242191
\(658\) 0 0
\(659\) 10.9211 0.425424 0.212712 0.977115i \(-0.431770\pi\)
0.212712 + 0.977115i \(0.431770\pi\)
\(660\) 0 0
\(661\) 28.4575 1.10687 0.553434 0.832893i \(-0.313317\pi\)
0.553434 + 0.832893i \(0.313317\pi\)
\(662\) 0 0
\(663\) 40.3406 1.56670
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.949735 0.0367739
\(668\) 0 0
\(669\) −45.9088 −1.77494
\(670\) 0 0
\(671\) −1.07820 −0.0416233
\(672\) 0 0
\(673\) −37.3470 −1.43962 −0.719810 0.694171i \(-0.755771\pi\)
−0.719810 + 0.694171i \(0.755771\pi\)
\(674\) 0 0
\(675\) −34.5241 −1.32883
\(676\) 0 0
\(677\) −19.5079 −0.749748 −0.374874 0.927076i \(-0.622314\pi\)
−0.374874 + 0.927076i \(0.622314\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −29.0125 −1.11176
\(682\) 0 0
\(683\) −46.3804 −1.77469 −0.887347 0.461101i \(-0.847454\pi\)
−0.887347 + 0.461101i \(0.847454\pi\)
\(684\) 0 0
\(685\) −41.5264 −1.58664
\(686\) 0 0
\(687\) −11.6952 −0.446200
\(688\) 0 0
\(689\) −27.4143 −1.04440
\(690\) 0 0
\(691\) 4.07303 0.154945 0.0774726 0.996994i \(-0.475315\pi\)
0.0774726 + 0.996994i \(0.475315\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17.1402 0.650165
\(696\) 0 0
\(697\) 3.78979 0.143549
\(698\) 0 0
\(699\) 25.6126 0.968759
\(700\) 0 0
\(701\) 47.2407 1.78426 0.892128 0.451783i \(-0.149212\pi\)
0.892128 + 0.451783i \(0.149212\pi\)
\(702\) 0 0
\(703\) 18.5776 0.700668
\(704\) 0 0
\(705\) −27.5689 −1.03831
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −15.8445 −0.595053 −0.297526 0.954714i \(-0.596162\pi\)
−0.297526 + 0.954714i \(0.596162\pi\)
\(710\) 0 0
\(711\) 0.0240277 0.000901110 0
\(712\) 0 0
\(713\) 39.3462 1.47353
\(714\) 0 0
\(715\) −35.1337 −1.31393
\(716\) 0 0
\(717\) −28.2624 −1.05548
\(718\) 0 0
\(719\) −46.2097 −1.72333 −0.861665 0.507478i \(-0.830578\pi\)
−0.861665 + 0.507478i \(0.830578\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −14.4692 −0.538115
\(724\) 0 0
\(725\) −1.14871 −0.0426619
\(726\) 0 0
\(727\) 46.2962 1.71703 0.858515 0.512788i \(-0.171387\pi\)
0.858515 + 0.512788i \(0.171387\pi\)
\(728\) 0 0
\(729\) 26.9405 0.997795
\(730\) 0 0
\(731\) −3.20304 −0.118469
\(732\) 0 0
\(733\) −14.3823 −0.531222 −0.265611 0.964080i \(-0.585574\pi\)
−0.265611 + 0.964080i \(0.585574\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.77555 −0.139074
\(738\) 0 0
\(739\) −23.1656 −0.852161 −0.426080 0.904685i \(-0.640106\pi\)
−0.426080 + 0.904685i \(0.640106\pi\)
\(740\) 0 0
\(741\) 41.1808 1.51282
\(742\) 0 0
\(743\) 8.59555 0.315340 0.157670 0.987492i \(-0.449602\pi\)
0.157670 + 0.987492i \(0.449602\pi\)
\(744\) 0 0
\(745\) 36.7102 1.34496
\(746\) 0 0
\(747\) 0.0836778 0.00306161
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 34.6291 1.26363 0.631817 0.775118i \(-0.282310\pi\)
0.631817 + 0.775118i \(0.282310\pi\)
\(752\) 0 0
\(753\) 3.84706 0.140194
\(754\) 0 0
\(755\) −48.8925 −1.77938
\(756\) 0 0
\(757\) 35.3458 1.28467 0.642333 0.766426i \(-0.277967\pi\)
0.642333 + 0.766426i \(0.277967\pi\)
\(758\) 0 0
\(759\) −15.9879 −0.580325
\(760\) 0 0
\(761\) −22.9971 −0.833645 −0.416823 0.908988i \(-0.636856\pi\)
−0.416823 + 0.908988i \(0.636856\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.0852161 −0.00308100
\(766\) 0 0
\(767\) −20.7737 −0.750095
\(768\) 0 0
\(769\) −15.5231 −0.559776 −0.279888 0.960033i \(-0.590297\pi\)
−0.279888 + 0.960033i \(0.590297\pi\)
\(770\) 0 0
\(771\) 42.4722 1.52960
\(772\) 0 0
\(773\) −40.7953 −1.46731 −0.733653 0.679524i \(-0.762186\pi\)
−0.733653 + 0.679524i \(0.762186\pi\)
\(774\) 0 0
\(775\) −47.5894 −1.70946
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.86873 0.138612
\(780\) 0 0
\(781\) −8.01150 −0.286674
\(782\) 0 0
\(783\) 0.896384 0.0320341
\(784\) 0 0
\(785\) 57.7907 2.06264
\(786\) 0 0
\(787\) −14.2880 −0.509313 −0.254656 0.967032i \(-0.581962\pi\)
−0.254656 + 0.967032i \(0.581962\pi\)
\(788\) 0 0
\(789\) −13.0621 −0.465022
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 3.94770 0.140187
\(794\) 0 0
\(795\) 26.4310 0.937412
\(796\) 0 0
\(797\) −44.9428 −1.59196 −0.795978 0.605326i \(-0.793043\pi\)
−0.795978 + 0.605326i \(0.793043\pi\)
\(798\) 0 0
\(799\) 17.6526 0.624502
\(800\) 0 0
\(801\) −0.0450360 −0.00159127
\(802\) 0 0
\(803\) −15.8004 −0.557585
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −38.2180 −1.34534
\(808\) 0 0
\(809\) −50.8169 −1.78663 −0.893314 0.449432i \(-0.851626\pi\)
−0.893314 + 0.449432i \(0.851626\pi\)
\(810\) 0 0
\(811\) −23.6587 −0.830769 −0.415385 0.909646i \(-0.636353\pi\)
−0.415385 + 0.909646i \(0.636353\pi\)
\(812\) 0 0
\(813\) 37.2142 1.30516
\(814\) 0 0
\(815\) −19.5323 −0.684187
\(816\) 0 0
\(817\) −3.26976 −0.114394
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29.0297 −1.01314 −0.506572 0.862198i \(-0.669087\pi\)
−0.506572 + 0.862198i \(0.669087\pi\)
\(822\) 0 0
\(823\) −53.7149 −1.87238 −0.936192 0.351488i \(-0.885676\pi\)
−0.936192 + 0.351488i \(0.885676\pi\)
\(824\) 0 0
\(825\) 19.3375 0.673244
\(826\) 0 0
\(827\) 6.55779 0.228037 0.114018 0.993479i \(-0.463628\pi\)
0.114018 + 0.993479i \(0.463628\pi\)
\(828\) 0 0
\(829\) −53.1994 −1.84769 −0.923847 0.382763i \(-0.874973\pi\)
−0.923847 + 0.382763i \(0.874973\pi\)
\(830\) 0 0
\(831\) 55.0955 1.91124
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −38.5890 −1.33543
\(836\) 0 0
\(837\) 37.1360 1.28361
\(838\) 0 0
\(839\) −22.3780 −0.772574 −0.386287 0.922379i \(-0.626242\pi\)
−0.386287 + 0.922379i \(0.626242\pi\)
\(840\) 0 0
\(841\) −28.9702 −0.998972
\(842\) 0 0
\(843\) −9.82119 −0.338260
\(844\) 0 0
\(845\) 84.2639 2.89877
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −38.4631 −1.32005
\(850\) 0 0
\(851\) 26.4079 0.905250
\(852\) 0 0
\(853\) −30.5227 −1.04508 −0.522539 0.852615i \(-0.675015\pi\)
−0.522539 + 0.852615i \(0.675015\pi\)
\(854\) 0 0
\(855\) −0.0869911 −0.00297503
\(856\) 0 0
\(857\) 41.8325 1.42897 0.714485 0.699651i \(-0.246661\pi\)
0.714485 + 0.699651i \(0.246661\pi\)
\(858\) 0 0
\(859\) −19.8918 −0.678699 −0.339349 0.940660i \(-0.610207\pi\)
−0.339349 + 0.940660i \(0.610207\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.48686 0.0506134 0.0253067 0.999680i \(-0.491944\pi\)
0.0253067 + 0.999680i \(0.491944\pi\)
\(864\) 0 0
\(865\) 66.4888 2.26069
\(866\) 0 0
\(867\) −4.57326 −0.155316
\(868\) 0 0
\(869\) 6.11562 0.207458
\(870\) 0 0
\(871\) 13.8238 0.468400
\(872\) 0 0
\(873\) 0.00405319 0.000137180 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −44.8377 −1.51406 −0.757032 0.653378i \(-0.773351\pi\)
−0.757032 + 0.653378i \(0.773351\pi\)
\(878\) 0 0
\(879\) 1.14934 0.0387663
\(880\) 0 0
\(881\) −43.5372 −1.46681 −0.733404 0.679794i \(-0.762069\pi\)
−0.733404 + 0.679794i \(0.762069\pi\)
\(882\) 0 0
\(883\) 0.769970 0.0259116 0.0129558 0.999916i \(-0.495876\pi\)
0.0129558 + 0.999916i \(0.495876\pi\)
\(884\) 0 0
\(885\) 20.0287 0.673256
\(886\) 0 0
\(887\) 16.9096 0.567770 0.283885 0.958858i \(-0.408377\pi\)
0.283885 + 0.958858i \(0.408377\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −15.1230 −0.506638
\(892\) 0 0
\(893\) 18.0202 0.603024
\(894\) 0 0
\(895\) 5.44354 0.181957
\(896\) 0 0
\(897\) 58.5381 1.95453
\(898\) 0 0
\(899\) 1.23561 0.0412100
\(900\) 0 0
\(901\) −16.9240 −0.563819
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −24.7803 −0.823726
\(906\) 0 0
\(907\) 55.6035 1.84628 0.923142 0.384459i \(-0.125612\pi\)
0.923142 + 0.384459i \(0.125612\pi\)
\(908\) 0 0
\(909\) 0.0431707 0.00143188
\(910\) 0 0
\(911\) 16.1374 0.534655 0.267327 0.963606i \(-0.413859\pi\)
0.267327 + 0.963606i \(0.413859\pi\)
\(912\) 0 0
\(913\) 21.2980 0.704860
\(914\) 0 0
\(915\) −3.80611 −0.125826
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 27.8317 0.918082 0.459041 0.888415i \(-0.348193\pi\)
0.459041 + 0.888415i \(0.348193\pi\)
\(920\) 0 0
\(921\) −20.2776 −0.668171
\(922\) 0 0
\(923\) 29.3333 0.965516
\(924\) 0 0
\(925\) −31.9404 −1.05019
\(926\) 0 0
\(927\) 0.0619864 0.00203590
\(928\) 0 0
\(929\) −28.1727 −0.924315 −0.462157 0.886798i \(-0.652925\pi\)
−0.462157 + 0.886798i \(0.652925\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 17.6757 0.578678
\(934\) 0 0
\(935\) −21.6895 −0.709323
\(936\) 0 0
\(937\) −31.3030 −1.02262 −0.511312 0.859395i \(-0.670840\pi\)
−0.511312 + 0.859395i \(0.670840\pi\)
\(938\) 0 0
\(939\) −6.77787 −0.221187
\(940\) 0 0
\(941\) −55.2328 −1.80054 −0.900270 0.435333i \(-0.856631\pi\)
−0.900270 + 0.435333i \(0.856631\pi\)
\(942\) 0 0
\(943\) 5.49935 0.179084
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.7591 −0.512101 −0.256050 0.966663i \(-0.582421\pi\)
−0.256050 + 0.966663i \(0.582421\pi\)
\(948\) 0 0
\(949\) 57.8516 1.87794
\(950\) 0 0
\(951\) 33.3065 1.08004
\(952\) 0 0
\(953\) −49.2694 −1.59599 −0.797996 0.602662i \(-0.794107\pi\)
−0.797996 + 0.602662i \(0.794107\pi\)
\(954\) 0 0
\(955\) 81.0170 2.62165
\(956\) 0 0
\(957\) −0.502078 −0.0162299
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 20.1898 0.651283
\(962\) 0 0
\(963\) 0.0241299 0.000777576 0
\(964\) 0 0
\(965\) 69.1223 2.22512
\(966\) 0 0
\(967\) −25.6867 −0.826030 −0.413015 0.910724i \(-0.635524\pi\)
−0.413015 + 0.910724i \(0.635524\pi\)
\(968\) 0 0
\(969\) 25.4226 0.816693
\(970\) 0 0
\(971\) 29.0629 0.932672 0.466336 0.884608i \(-0.345574\pi\)
0.466336 + 0.884608i \(0.345574\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −70.8021 −2.26748
\(976\) 0 0
\(977\) 13.0637 0.417946 0.208973 0.977921i \(-0.432988\pi\)
0.208973 + 0.977921i \(0.432988\pi\)
\(978\) 0 0
\(979\) −11.4627 −0.366350
\(980\) 0 0
\(981\) 0.0666608 0.00212832
\(982\) 0 0
\(983\) 29.4830 0.940361 0.470180 0.882570i \(-0.344189\pi\)
0.470180 + 0.882570i \(0.344189\pi\)
\(984\) 0 0
\(985\) −56.1171 −1.78804
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.64792 −0.147795
\(990\) 0 0
\(991\) −36.9953 −1.17520 −0.587598 0.809153i \(-0.699926\pi\)
−0.587598 + 0.809153i \(0.699926\pi\)
\(992\) 0 0
\(993\) 43.8871 1.39271
\(994\) 0 0
\(995\) 45.3254 1.43691
\(996\) 0 0
\(997\) −21.6514 −0.685707 −0.342854 0.939389i \(-0.611394\pi\)
−0.342854 + 0.939389i \(0.611394\pi\)
\(998\) 0 0
\(999\) 24.9244 0.788573
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 8036.2.a.o.1.8 10
7.6 odd 2 8036.2.a.p.1.3 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8036.2.a.o.1.8 10 1.1 even 1 trivial
8036.2.a.p.1.3 yes 10 7.6 odd 2