Properties

Label 504.6.a.o.1.1
Level $504$
Weight $6$
Character 504.1
Self dual yes
Analytic conductor $80.833$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,6,Mod(1,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 504.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: \(80.8334451857\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{1129}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 282 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 168)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(17.3003\) of defining polynomial
Character \(\chi\) \(=\) 504.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-67.2012 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-67.2012 q^{5} -49.0000 q^{7} +17.2012 q^{11} +807.610 q^{13} -777.604 q^{17} +262.379 q^{19} +1950.86 q^{23} +1391.00 q^{25} +1518.04 q^{29} +5474.47 q^{31} +3292.86 q^{35} +6586.95 q^{37} -2930.30 q^{41} -975.338 q^{43} -22985.1 q^{47} +2401.00 q^{49} -2645.71 q^{53} -1155.94 q^{55} -22510.9 q^{59} +9533.02 q^{61} -54272.3 q^{65} -67852.2 q^{67} +10158.5 q^{71} +60184.1 q^{73} -842.858 q^{77} -27760.3 q^{79} +13431.4 q^{83} +52255.9 q^{85} -120473. q^{89} -39572.9 q^{91} -17632.2 q^{95} -28652.0 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 98 q^{7} - 100 q^{11} + 540 q^{13} - 1152 q^{17} + 2944 q^{19} - 2684 q^{23} + 2782 q^{25} - 996 q^{29} + 2616 q^{31} - 3492 q^{37} - 17016 q^{41} + 13640 q^{43} - 11832 q^{47} + 4802 q^{49} - 37548 q^{53} - 9032 q^{55} + 6320 q^{59} + 39764 q^{61} - 72256 q^{65} - 27376 q^{67} - 35460 q^{71} + 64188 q^{73} + 4900 q^{77} - 110088 q^{79} + 5896 q^{83} + 27096 q^{85} - 167160 q^{89} - 26460 q^{91} + 162576 q^{95} - 11876 q^{97}+O(q^{100}) \) 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
\(5\) −67.2012 −1.20213 −0.601066 0.799200i \(-0.705257\pi\)
−0.601066 + 0.799200i \(0.705257\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 17.2012 0.0428624 0.0214312 0.999770i \(-0.493178\pi\)
0.0214312 + 0.999770i \(0.493178\pi\)
\(12\) 0 0
\(13\) 807.610 1.32539 0.662694 0.748890i \(-0.269413\pi\)
0.662694 + 0.748890i \(0.269413\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −777.604 −0.652583 −0.326292 0.945269i \(-0.605799\pi\)
−0.326292 + 0.945269i \(0.605799\pi\)
\(18\) 0 0
\(19\) 262.379 0.166742 0.0833709 0.996519i \(-0.473431\pi\)
0.0833709 + 0.996519i \(0.473431\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1950.86 0.768964 0.384482 0.923132i \(-0.374380\pi\)
0.384482 + 0.923132i \(0.374380\pi\)
\(24\) 0 0
\(25\) 1391.00 0.445120
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1518.04 0.335187 0.167593 0.985856i \(-0.446400\pi\)
0.167593 + 0.985856i \(0.446400\pi\)
\(30\) 0 0
\(31\) 5474.47 1.02315 0.511574 0.859239i \(-0.329063\pi\)
0.511574 + 0.859239i \(0.329063\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3292.86 0.454363
\(36\) 0 0
\(37\) 6586.95 0.791006 0.395503 0.918465i \(-0.370570\pi\)
0.395503 + 0.918465i \(0.370570\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2930.30 −0.272240 −0.136120 0.990692i \(-0.543463\pi\)
−0.136120 + 0.990692i \(0.543463\pi\)
\(42\) 0 0
\(43\) −975.338 −0.0804422 −0.0402211 0.999191i \(-0.512806\pi\)
−0.0402211 + 0.999191i \(0.512806\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −22985.1 −1.51776 −0.758878 0.651233i \(-0.774252\pi\)
−0.758878 + 0.651233i \(0.774252\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2645.71 −0.129376 −0.0646879 0.997906i \(-0.520605\pi\)
−0.0646879 + 0.997906i \(0.520605\pi\)
\(54\) 0 0
\(55\) −1155.94 −0.0515263
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −22510.9 −0.841903 −0.420951 0.907083i \(-0.638304\pi\)
−0.420951 + 0.907083i \(0.638304\pi\)
\(60\) 0 0
\(61\) 9533.02 0.328024 0.164012 0.986458i \(-0.447556\pi\)
0.164012 + 0.986458i \(0.447556\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −54272.3 −1.59329
\(66\) 0 0
\(67\) −67852.2 −1.84662 −0.923308 0.384060i \(-0.874526\pi\)
−0.923308 + 0.384060i \(0.874526\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10158.5 0.239157 0.119579 0.992825i \(-0.461846\pi\)
0.119579 + 0.992825i \(0.461846\pi\)
\(72\) 0 0
\(73\) 60184.1 1.32183 0.660913 0.750462i \(-0.270169\pi\)
0.660913 + 0.750462i \(0.270169\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −842.858 −0.0162005
\(78\) 0 0
\(79\) −27760.3 −0.500445 −0.250223 0.968188i \(-0.580504\pi\)
−0.250223 + 0.968188i \(0.580504\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13431.4 0.214006 0.107003 0.994259i \(-0.465875\pi\)
0.107003 + 0.994259i \(0.465875\pi\)
\(84\) 0 0
\(85\) 52255.9 0.784491
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −120473. −1.61219 −0.806095 0.591786i \(-0.798423\pi\)
−0.806095 + 0.591786i \(0.798423\pi\)
\(90\) 0 0
\(91\) −39572.9 −0.500950
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −17632.2 −0.200446
\(96\) 0 0
\(97\) −28652.0 −0.309190 −0.154595 0.987978i \(-0.549407\pi\)
−0.154595 + 0.987978i \(0.549407\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −70761.8 −0.690233 −0.345117 0.938560i \(-0.612161\pi\)
−0.345117 + 0.938560i \(0.612161\pi\)
\(102\) 0 0
\(103\) −127139. −1.18082 −0.590411 0.807103i \(-0.701034\pi\)
−0.590411 + 0.807103i \(0.701034\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 230347. 1.94501 0.972507 0.232872i \(-0.0748123\pi\)
0.972507 + 0.232872i \(0.0748123\pi\)
\(108\) 0 0
\(109\) −210266. −1.69513 −0.847563 0.530695i \(-0.821931\pi\)
−0.847563 + 0.530695i \(0.821931\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13935.4 0.102665 0.0513327 0.998682i \(-0.483653\pi\)
0.0513327 + 0.998682i \(0.483653\pi\)
\(114\) 0 0
\(115\) −131100. −0.924396
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 38102.6 0.246653
\(120\) 0 0
\(121\) −160755. −0.998163
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 116527. 0.667039
\(126\) 0 0
\(127\) −171345. −0.942675 −0.471337 0.881953i \(-0.656229\pi\)
−0.471337 + 0.881953i \(0.656229\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 237204. 1.20766 0.603828 0.797115i \(-0.293641\pi\)
0.603828 + 0.797115i \(0.293641\pi\)
\(132\) 0 0
\(133\) −12856.6 −0.0630225
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −53519.0 −0.243617 −0.121808 0.992554i \(-0.538869\pi\)
−0.121808 + 0.992554i \(0.538869\pi\)
\(138\) 0 0
\(139\) 118543. 0.520400 0.260200 0.965555i \(-0.416211\pi\)
0.260200 + 0.965555i \(0.416211\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 13891.8 0.0568094
\(144\) 0 0
\(145\) −102014. −0.402939
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 106643. 0.393519 0.196759 0.980452i \(-0.436958\pi\)
0.196759 + 0.980452i \(0.436958\pi\)
\(150\) 0 0
\(151\) 73169.2 0.261148 0.130574 0.991439i \(-0.458318\pi\)
0.130574 + 0.991439i \(0.458318\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −367891. −1.22996
\(156\) 0 0
\(157\) −496125. −1.60636 −0.803179 0.595738i \(-0.796860\pi\)
−0.803179 + 0.595738i \(0.796860\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −95592.1 −0.290641
\(162\) 0 0
\(163\) −59360.9 −0.174997 −0.0874986 0.996165i \(-0.527887\pi\)
−0.0874986 + 0.996165i \(0.527887\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 92468.0 0.256567 0.128283 0.991738i \(-0.459053\pi\)
0.128283 + 0.991738i \(0.459053\pi\)
\(168\) 0 0
\(169\) 280940. 0.756653
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −656493. −1.66769 −0.833844 0.552000i \(-0.813865\pi\)
−0.833844 + 0.552000i \(0.813865\pi\)
\(174\) 0 0
\(175\) −68159.0 −0.168240
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −347739. −0.811186 −0.405593 0.914054i \(-0.632935\pi\)
−0.405593 + 0.914054i \(0.632935\pi\)
\(180\) 0 0
\(181\) −829484. −1.88197 −0.940983 0.338454i \(-0.890096\pi\)
−0.940983 + 0.338454i \(0.890096\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −442651. −0.950893
\(186\) 0 0
\(187\) −13375.7 −0.0279713
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 820119. 1.62665 0.813324 0.581811i \(-0.197656\pi\)
0.813324 + 0.581811i \(0.197656\pi\)
\(192\) 0 0
\(193\) 4163.11 0.00804497 0.00402249 0.999992i \(-0.498720\pi\)
0.00402249 + 0.999992i \(0.498720\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −786994. −1.44479 −0.722397 0.691479i \(-0.756960\pi\)
−0.722397 + 0.691479i \(0.756960\pi\)
\(198\) 0 0
\(199\) −872156. −1.56121 −0.780605 0.625025i \(-0.785089\pi\)
−0.780605 + 0.625025i \(0.785089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −74383.7 −0.126689
\(204\) 0 0
\(205\) 196920. 0.327269
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4513.22 0.00714696
\(210\) 0 0
\(211\) 894531. 1.38321 0.691607 0.722274i \(-0.256903\pi\)
0.691607 + 0.722274i \(0.256903\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 65543.9 0.0967021
\(216\) 0 0
\(217\) −268249. −0.386713
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −628000. −0.864926
\(222\) 0 0
\(223\) 232594. 0.313211 0.156605 0.987661i \(-0.449945\pi\)
0.156605 + 0.987661i \(0.449945\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −981411. −1.26411 −0.632057 0.774922i \(-0.717789\pi\)
−0.632057 + 0.774922i \(0.717789\pi\)
\(228\) 0 0
\(229\) −1.31461e6 −1.65656 −0.828280 0.560315i \(-0.810680\pi\)
−0.828280 + 0.560315i \(0.810680\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 458394. 0.553158 0.276579 0.960991i \(-0.410799\pi\)
0.276579 + 0.960991i \(0.410799\pi\)
\(234\) 0 0
\(235\) 1.54463e6 1.82454
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −643863. −0.729119 −0.364559 0.931180i \(-0.618780\pi\)
−0.364559 + 0.931180i \(0.618780\pi\)
\(240\) 0 0
\(241\) 1.56858e6 1.73966 0.869829 0.493353i \(-0.164229\pi\)
0.869829 + 0.493353i \(0.164229\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −161350. −0.171733
\(246\) 0 0
\(247\) 211899. 0.220998
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 58945.2 0.0590560 0.0295280 0.999564i \(-0.490600\pi\)
0.0295280 + 0.999564i \(0.490600\pi\)
\(252\) 0 0
\(253\) 33557.1 0.0329597
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 602342. 0.568866 0.284433 0.958696i \(-0.408195\pi\)
0.284433 + 0.958696i \(0.408195\pi\)
\(258\) 0 0
\(259\) −322760. −0.298972
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 334651. 0.298334 0.149167 0.988812i \(-0.452341\pi\)
0.149167 + 0.988812i \(0.452341\pi\)
\(264\) 0 0
\(265\) 177795. 0.155527
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.45538e6 −1.22630 −0.613149 0.789967i \(-0.710097\pi\)
−0.613149 + 0.789967i \(0.710097\pi\)
\(270\) 0 0
\(271\) −612560. −0.506670 −0.253335 0.967379i \(-0.581528\pi\)
−0.253335 + 0.967379i \(0.581528\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 23926.9 0.0190789
\(276\) 0 0
\(277\) −724917. −0.567661 −0.283830 0.958875i \(-0.591605\pi\)
−0.283830 + 0.958875i \(0.591605\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.81846e6 1.37385 0.686924 0.726729i \(-0.258960\pi\)
0.686924 + 0.726729i \(0.258960\pi\)
\(282\) 0 0
\(283\) 708354. 0.525756 0.262878 0.964829i \(-0.415328\pi\)
0.262878 + 0.964829i \(0.415328\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 143585. 0.102897
\(288\) 0 0
\(289\) −815190. −0.574135
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.21719e6 1.50881 0.754404 0.656410i \(-0.227926\pi\)
0.754404 + 0.656410i \(0.227926\pi\)
\(294\) 0 0
\(295\) 1.51276e6 1.01208
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.57553e6 1.01918
\(300\) 0 0
\(301\) 47791.6 0.0304043
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −640630. −0.394328
\(306\) 0 0
\(307\) −1.76619e6 −1.06952 −0.534762 0.845003i \(-0.679599\pi\)
−0.534762 + 0.845003i \(0.679599\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 377794. 0.221490 0.110745 0.993849i \(-0.464676\pi\)
0.110745 + 0.993849i \(0.464676\pi\)
\(312\) 0 0
\(313\) −971758. −0.560657 −0.280328 0.959904i \(-0.590443\pi\)
−0.280328 + 0.959904i \(0.590443\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.01468e6 0.567127 0.283564 0.958953i \(-0.408483\pi\)
0.283564 + 0.958953i \(0.408483\pi\)
\(318\) 0 0
\(319\) 26112.0 0.0143669
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −204027. −0.108813
\(324\) 0 0
\(325\) 1.12338e6 0.589957
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.12627e6 0.573658
\(330\) 0 0
\(331\) 2.95015e6 1.48004 0.740021 0.672583i \(-0.234815\pi\)
0.740021 + 0.672583i \(0.234815\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.55975e6 2.21988
\(336\) 0 0
\(337\) 1.41135e6 0.676954 0.338477 0.940975i \(-0.390088\pi\)
0.338477 + 0.940975i \(0.390088\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 94167.5 0.0438546
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.47510e6 0.657656 0.328828 0.944390i \(-0.393346\pi\)
0.328828 + 0.944390i \(0.393346\pi\)
\(348\) 0 0
\(349\) 1.65202e6 0.726023 0.363012 0.931785i \(-0.381749\pi\)
0.363012 + 0.931785i \(0.381749\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.91161e6 −1.67078 −0.835390 0.549658i \(-0.814758\pi\)
−0.835390 + 0.549658i \(0.814758\pi\)
\(354\) 0 0
\(355\) −682663. −0.287498
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 576419. 0.236049 0.118025 0.993011i \(-0.462344\pi\)
0.118025 + 0.993011i \(0.462344\pi\)
\(360\) 0 0
\(361\) −2.40726e6 −0.972197
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.04444e6 −1.58901
\(366\) 0 0
\(367\) 459296. 0.178003 0.0890016 0.996031i \(-0.471632\pi\)
0.0890016 + 0.996031i \(0.471632\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 129640. 0.0488995
\(372\) 0 0
\(373\) −3.90270e6 −1.45242 −0.726211 0.687472i \(-0.758720\pi\)
−0.726211 + 0.687472i \(0.758720\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.22598e6 0.444253
\(378\) 0 0
\(379\) 4.80734e6 1.71912 0.859561 0.511032i \(-0.170737\pi\)
0.859561 + 0.511032i \(0.170737\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.36779e6 1.52148 0.760738 0.649059i \(-0.224837\pi\)
0.760738 + 0.649059i \(0.224837\pi\)
\(384\) 0 0
\(385\) 56641.1 0.0194751
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.18272e6 −1.73653 −0.868267 0.496097i \(-0.834766\pi\)
−0.868267 + 0.496097i \(0.834766\pi\)
\(390\) 0 0
\(391\) −1.51699e6 −0.501813
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.86553e6 0.601601
\(396\) 0 0
\(397\) −2.42731e6 −0.772945 −0.386472 0.922301i \(-0.626307\pi\)
−0.386472 + 0.922301i \(0.626307\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.07557e6 0.334024 0.167012 0.985955i \(-0.446588\pi\)
0.167012 + 0.985955i \(0.446588\pi\)
\(402\) 0 0
\(403\) 4.42124e6 1.35607
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 113303. 0.0339044
\(408\) 0 0
\(409\) 2.07931e6 0.614626 0.307313 0.951609i \(-0.400570\pi\)
0.307313 + 0.951609i \(0.400570\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.10303e6 0.318209
\(414\) 0 0
\(415\) −902605. −0.257263
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.35878e6 −0.934645 −0.467323 0.884087i \(-0.654781\pi\)
−0.467323 + 0.884087i \(0.654781\pi\)
\(420\) 0 0
\(421\) 5.07754e6 1.39620 0.698101 0.715999i \(-0.254029\pi\)
0.698101 + 0.715999i \(0.254029\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.08165e6 −0.290478
\(426\) 0 0
\(427\) −467118. −0.123981
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.98269e6 1.03272 0.516361 0.856371i \(-0.327286\pi\)
0.516361 + 0.856371i \(0.327286\pi\)
\(432\) 0 0
\(433\) 2.40905e6 0.617486 0.308743 0.951146i \(-0.400092\pi\)
0.308743 + 0.951146i \(0.400092\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 511863. 0.128218
\(438\) 0 0
\(439\) −964726. −0.238915 −0.119457 0.992839i \(-0.538115\pi\)
−0.119457 + 0.992839i \(0.538115\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.07046e6 −0.501253 −0.250627 0.968084i \(-0.580637\pi\)
−0.250627 + 0.968084i \(0.580637\pi\)
\(444\) 0 0
\(445\) 8.09596e6 1.93806
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.52864e6 −1.29420 −0.647101 0.762404i \(-0.724019\pi\)
−0.647101 + 0.762404i \(0.724019\pi\)
\(450\) 0 0
\(451\) −50404.7 −0.0116689
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.65934e6 0.602207
\(456\) 0 0
\(457\) −2.10358e6 −0.471161 −0.235580 0.971855i \(-0.575699\pi\)
−0.235580 + 0.971855i \(0.575699\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.89612e6 −0.634693 −0.317346 0.948310i \(-0.602792\pi\)
−0.317346 + 0.948310i \(0.602792\pi\)
\(462\) 0 0
\(463\) 3.84498e6 0.833569 0.416785 0.909005i \(-0.363157\pi\)
0.416785 + 0.909005i \(0.363157\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.59340e6 0.338090 0.169045 0.985608i \(-0.445932\pi\)
0.169045 + 0.985608i \(0.445932\pi\)
\(468\) 0 0
\(469\) 3.32476e6 0.697955
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16777.0 −0.00344795
\(474\) 0 0
\(475\) 364969. 0.0742201
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7.01607e6 1.39719 0.698595 0.715517i \(-0.253809\pi\)
0.698595 + 0.715517i \(0.253809\pi\)
\(480\) 0 0
\(481\) 5.31968e6 1.04839
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.92545e6 0.371687
\(486\) 0 0
\(487\) 2.51835e6 0.481164 0.240582 0.970629i \(-0.422662\pi\)
0.240582 + 0.970629i \(0.422662\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.01534e6 −1.31324 −0.656621 0.754220i \(-0.728015\pi\)
−0.656621 + 0.754220i \(0.728015\pi\)
\(492\) 0 0
\(493\) −1.18043e6 −0.218737
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −497766. −0.0903929
\(498\) 0 0
\(499\) −576968. −0.103729 −0.0518646 0.998654i \(-0.516516\pi\)
−0.0518646 + 0.998654i \(0.516516\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.65556e6 −0.467989 −0.233995 0.972238i \(-0.575180\pi\)
−0.233995 + 0.972238i \(0.575180\pi\)
\(504\) 0 0
\(505\) 4.75528e6 0.829751
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.69798e6 0.632660 0.316330 0.948649i \(-0.397549\pi\)
0.316330 + 0.948649i \(0.397549\pi\)
\(510\) 0 0
\(511\) −2.94902e6 −0.499604
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.54387e6 1.41950
\(516\) 0 0
\(517\) −395371. −0.0650547
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.29058e6 −0.369702 −0.184851 0.982767i \(-0.559180\pi\)
−0.184851 + 0.982767i \(0.559180\pi\)
\(522\) 0 0
\(523\) 3.31070e6 0.529256 0.264628 0.964351i \(-0.414751\pi\)
0.264628 + 0.964351i \(0.414751\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.25697e6 −0.667689
\(528\) 0 0
\(529\) −2.63049e6 −0.408694
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.36654e6 −0.360824
\(534\) 0 0
\(535\) −1.54796e7 −2.33816
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 41300.1 0.00612320
\(540\) 0 0
\(541\) −1.28977e7 −1.89461 −0.947306 0.320329i \(-0.896207\pi\)
−0.947306 + 0.320329i \(0.896207\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.41301e7 2.03776
\(546\) 0 0
\(547\) −658312. −0.0940727 −0.0470364 0.998893i \(-0.514978\pi\)
−0.0470364 + 0.998893i \(0.514978\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 398300. 0.0558896
\(552\) 0 0
\(553\) 1.36026e6 0.189151
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.28168e6 −0.175042 −0.0875211 0.996163i \(-0.527895\pi\)
−0.0875211 + 0.996163i \(0.527895\pi\)
\(558\) 0 0
\(559\) −787692. −0.106617
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.36647e7 −1.81690 −0.908448 0.417997i \(-0.862732\pi\)
−0.908448 + 0.417997i \(0.862732\pi\)
\(564\) 0 0
\(565\) −936477. −0.123417
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.49965e6 −0.841607 −0.420804 0.907152i \(-0.638252\pi\)
−0.420804 + 0.907152i \(0.638252\pi\)
\(570\) 0 0
\(571\) 7.67214e6 0.984750 0.492375 0.870383i \(-0.336129\pi\)
0.492375 + 0.870383i \(0.336129\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.71364e6 0.342281
\(576\) 0 0
\(577\) 4.80020e6 0.600233 0.300117 0.953903i \(-0.402974\pi\)
0.300117 + 0.953903i \(0.402974\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −658138. −0.0808866
\(582\) 0 0
\(583\) −45509.4 −0.00554536
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.44629e7 −1.73244 −0.866222 0.499660i \(-0.833458\pi\)
−0.866222 + 0.499660i \(0.833458\pi\)
\(588\) 0 0
\(589\) 1.43638e6 0.170601
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.27217e6 −0.615677 −0.307838 0.951439i \(-0.599606\pi\)
−0.307838 + 0.951439i \(0.599606\pi\)
\(594\) 0 0
\(595\) −2.56054e6 −0.296510
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.87792e6 −0.441603 −0.220801 0.975319i \(-0.570867\pi\)
−0.220801 + 0.975319i \(0.570867\pi\)
\(600\) 0 0
\(601\) −1.54530e7 −1.74512 −0.872560 0.488506i \(-0.837542\pi\)
−0.872560 + 0.488506i \(0.837542\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.08029e7 1.19992
\(606\) 0 0
\(607\) −5.55130e6 −0.611537 −0.305769 0.952106i \(-0.598913\pi\)
−0.305769 + 0.952106i \(0.598913\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.85630e7 −2.01161
\(612\) 0 0
\(613\) −240556. −0.0258562 −0.0129281 0.999916i \(-0.504115\pi\)
−0.0129281 + 0.999916i \(0.504115\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.00113e7 1.05871 0.529353 0.848402i \(-0.322435\pi\)
0.529353 + 0.848402i \(0.322435\pi\)
\(618\) 0 0
\(619\) −9.97498e6 −1.04637 −0.523185 0.852219i \(-0.675256\pi\)
−0.523185 + 0.852219i \(0.675256\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.90320e6 0.609351
\(624\) 0 0
\(625\) −1.21776e7 −1.24699
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5.12203e6 −0.516197
\(630\) 0 0
\(631\) −1.10575e7 −1.10557 −0.552783 0.833325i \(-0.686434\pi\)
−0.552783 + 0.833325i \(0.686434\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.15146e7 1.13322
\(636\) 0 0
\(637\) 1.93907e6 0.189341
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.64372e7 1.58009 0.790045 0.613049i \(-0.210057\pi\)
0.790045 + 0.613049i \(0.210057\pi\)
\(642\) 0 0
\(643\) −1.85762e6 −0.177186 −0.0885931 0.996068i \(-0.528237\pi\)
−0.0885931 + 0.996068i \(0.528237\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.09418e7 −1.02761 −0.513805 0.857907i \(-0.671764\pi\)
−0.513805 + 0.857907i \(0.671764\pi\)
\(648\) 0 0
\(649\) −387214. −0.0360860
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.28230e6 0.760095 0.380048 0.924967i \(-0.375908\pi\)
0.380048 + 0.924967i \(0.375908\pi\)
\(654\) 0 0
\(655\) −1.59404e7 −1.45176
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.11810e7 1.00293 0.501463 0.865179i \(-0.332795\pi\)
0.501463 + 0.865179i \(0.332795\pi\)
\(660\) 0 0
\(661\) −1.03445e7 −0.920882 −0.460441 0.887690i \(-0.652309\pi\)
−0.460441 + 0.887690i \(0.652309\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 863975. 0.0757613
\(666\) 0 0
\(667\) 2.96147e6 0.257747
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 163979. 0.0140599
\(672\) 0 0
\(673\) −1.19137e7 −1.01393 −0.506966 0.861966i \(-0.669233\pi\)
−0.506966 + 0.861966i \(0.669233\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.53559e7 −1.28766 −0.643832 0.765167i \(-0.722657\pi\)
−0.643832 + 0.765167i \(0.722657\pi\)
\(678\) 0 0
\(679\) 1.40395e6 0.116863
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.08388e6 0.0889054 0.0444527 0.999011i \(-0.485846\pi\)
0.0444527 + 0.999011i \(0.485846\pi\)
\(684\) 0 0
\(685\) 3.59654e6 0.292859
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.13670e6 −0.171473
\(690\) 0 0
\(691\) −1.89348e7 −1.50857 −0.754285 0.656547i \(-0.772016\pi\)
−0.754285 + 0.656547i \(0.772016\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.96620e6 −0.625589
\(696\) 0 0
\(697\) 2.27861e6 0.177660
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.25756e7 0.966569 0.483285 0.875463i \(-0.339444\pi\)
0.483285 + 0.875463i \(0.339444\pi\)
\(702\) 0 0
\(703\) 1.72827e6 0.131894
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.46733e6 0.260884
\(708\) 0 0
\(709\) −1.24208e7 −0.927969 −0.463985 0.885843i \(-0.653581\pi\)
−0.463985 + 0.885843i \(0.653581\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.06799e7 0.786764
\(714\) 0 0
\(715\) −933549. −0.0682923
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.53700e7 −1.10880 −0.554399 0.832251i \(-0.687052\pi\)
−0.554399 + 0.832251i \(0.687052\pi\)
\(720\) 0 0
\(721\) 6.22980e6 0.446309
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.11159e6 0.149198
\(726\) 0 0
\(727\) 2.70136e7 1.89560 0.947800 0.318866i \(-0.103302\pi\)
0.947800 + 0.318866i \(0.103302\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 758426. 0.0524952
\(732\) 0 0
\(733\) −397706. −0.0273403 −0.0136701 0.999907i \(-0.504351\pi\)
−0.0136701 + 0.999907i \(0.504351\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.16714e6 −0.0791505
\(738\) 0 0
\(739\) 6.30043e6 0.424384 0.212192 0.977228i \(-0.431940\pi\)
0.212192 + 0.977228i \(0.431940\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.23368e7 −0.819839 −0.409920 0.912122i \(-0.634443\pi\)
−0.409920 + 0.912122i \(0.634443\pi\)
\(744\) 0 0
\(745\) −7.16651e6 −0.473061
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.12870e7 −0.735146
\(750\) 0 0
\(751\) 2.14846e7 1.39004 0.695021 0.718990i \(-0.255395\pi\)
0.695021 + 0.718990i \(0.255395\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4.91706e6 −0.313934
\(756\) 0 0
\(757\) 1.23188e7 0.781317 0.390659 0.920536i \(-0.372247\pi\)
0.390659 + 0.920536i \(0.372247\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 592021. 0.0370575 0.0185287 0.999828i \(-0.494102\pi\)
0.0185287 + 0.999828i \(0.494102\pi\)
\(762\) 0 0
\(763\) 1.03030e7 0.640697
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.81800e7 −1.11585
\(768\) 0 0
\(769\) 1.02609e7 0.625704 0.312852 0.949802i \(-0.398716\pi\)
0.312852 + 0.949802i \(0.398716\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.00066e7 −1.20427 −0.602136 0.798393i \(-0.705684\pi\)
−0.602136 + 0.798393i \(0.705684\pi\)
\(774\) 0 0
\(775\) 7.61499e6 0.455423
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −768848. −0.0453938
\(780\) 0 0
\(781\) 174738. 0.0102509
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.33402e7 1.93105
\(786\) 0 0
\(787\) −1.57761e7 −0.907950 −0.453975 0.891014i \(-0.649995\pi\)
−0.453975 + 0.891014i \(0.649995\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −682836. −0.0388039
\(792\) 0 0
\(793\) 7.69896e6 0.434759
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.22357e7 1.23995 0.619977 0.784620i \(-0.287142\pi\)
0.619977 + 0.784620i \(0.287142\pi\)
\(798\) 0 0
\(799\) 1.78733e7 0.990462
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.03524e6 0.0566567
\(804\) 0 0
\(805\) 6.42390e6 0.349389
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.20194e7 −0.645669 −0.322834 0.946455i \(-0.604636\pi\)
−0.322834 + 0.946455i \(0.604636\pi\)
\(810\) 0 0
\(811\) 521352. 0.0278342 0.0139171 0.999903i \(-0.495570\pi\)
0.0139171 + 0.999903i \(0.495570\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3.98912e6 0.210370
\(816\) 0 0
\(817\) −255908. −0.0134131
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.42268e6 −0.125441 −0.0627203 0.998031i \(-0.519978\pi\)
−0.0627203 + 0.998031i \(0.519978\pi\)
\(822\) 0 0
\(823\) −1.65869e7 −0.853620 −0.426810 0.904341i \(-0.640363\pi\)
−0.426810 + 0.904341i \(0.640363\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.11159e6 −0.463266 −0.231633 0.972803i \(-0.574407\pi\)
−0.231633 + 0.972803i \(0.574407\pi\)
\(828\) 0 0
\(829\) −2.89737e7 −1.46426 −0.732130 0.681165i \(-0.761474\pi\)
−0.732130 + 0.681165i \(0.761474\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.86703e6 −0.0932262
\(834\) 0 0
\(835\) −6.21396e6 −0.308427
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2.06856e7 −1.01452 −0.507262 0.861792i \(-0.669342\pi\)
−0.507262 + 0.861792i \(0.669342\pi\)
\(840\) 0 0
\(841\) −1.82067e7 −0.887650
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.88795e7 −0.909597
\(846\) 0 0
\(847\) 7.87700e6 0.377270
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.28502e7 0.608255
\(852\) 0 0
\(853\) 3.02453e7 1.42326 0.711632 0.702552i \(-0.247956\pi\)
0.711632 + 0.702552i \(0.247956\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.17972e7 −0.548689 −0.274345 0.961631i \(-0.588461\pi\)
−0.274345 + 0.961631i \(0.588461\pi\)
\(858\) 0 0
\(859\) −1.87297e6 −0.0866060 −0.0433030 0.999062i \(-0.513788\pi\)
−0.0433030 + 0.999062i \(0.513788\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.65653e7 −1.21420 −0.607098 0.794627i \(-0.707666\pi\)
−0.607098 + 0.794627i \(0.707666\pi\)
\(864\) 0 0
\(865\) 4.41171e7 2.00478
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −477510. −0.0214503
\(870\) 0 0
\(871\) −5.47981e7 −2.44748
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −5.70982e6 −0.252117
\(876\) 0 0
\(877\) −7.56578e6 −0.332166 −0.166083 0.986112i \(-0.553112\pi\)
−0.166083 + 0.986112i \(0.553112\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.37674e7 −0.597603 −0.298801 0.954315i \(-0.596587\pi\)
−0.298801 + 0.954315i \(0.596587\pi\)
\(882\) 0 0
\(883\) −1.41355e7 −0.610110 −0.305055 0.952335i \(-0.598675\pi\)
−0.305055 + 0.952335i \(0.598675\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.46644e7 −0.625828 −0.312914 0.949782i \(-0.601305\pi\)
−0.312914 + 0.949782i \(0.601305\pi\)
\(888\) 0 0
\(889\) 8.39590e6 0.356298
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −6.03080e6 −0.253073
\(894\) 0 0
\(895\) 2.33685e7 0.975153
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.31045e6 0.342946
\(900\) 0 0
\(901\) 2.05732e6 0.0844285
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.57423e7 2.26237
\(906\) 0 0
\(907\) 687707. 0.0277578 0.0138789 0.999904i \(-0.495582\pi\)
0.0138789 + 0.999904i \(0.495582\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.91732e7 1.96305 0.981527 0.191323i \(-0.0612778\pi\)
0.981527 + 0.191323i \(0.0612778\pi\)
\(912\) 0 0
\(913\) 231036. 0.00917281
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.16230e7 −0.456451
\(918\) 0 0
\(919\) −5.17193e6 −0.202006 −0.101003 0.994886i \(-0.532205\pi\)
−0.101003 + 0.994886i \(0.532205\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 8.20410e6 0.316976
\(924\) 0 0
\(925\) 9.16244e6 0.352093
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4.83580e6 −0.183835 −0.0919177 0.995767i \(-0.529300\pi\)
−0.0919177 + 0.995767i \(0.529300\pi\)
\(930\) 0 0
\(931\) 629971. 0.0238203
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 898863. 0.0336252
\(936\) 0 0
\(937\) 4.88196e7 1.81654 0.908270 0.418385i \(-0.137404\pi\)
0.908270 + 0.418385i \(0.137404\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.83528e7 −0.675661 −0.337831 0.941207i \(-0.609693\pi\)
−0.337831 + 0.941207i \(0.609693\pi\)
\(942\) 0 0
\(943\) −5.71660e6 −0.209343
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.66145e7 −0.602020 −0.301010 0.953621i \(-0.597324\pi\)
−0.301010 + 0.953621i \(0.597324\pi\)
\(948\) 0 0
\(949\) 4.86053e7 1.75193
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.55298e7 1.62391 0.811957 0.583717i \(-0.198402\pi\)
0.811957 + 0.583717i \(0.198402\pi\)
\(954\) 0 0
\(955\) −5.51130e7 −1.95544
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.62243e6 0.0920784
\(960\) 0 0
\(961\) 1.34071e6 0.0468303
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −279766. −0.00967111
\(966\) 0 0
\(967\) 3.67650e7 1.26435 0.632176 0.774825i \(-0.282162\pi\)
0.632176 + 0.774825i \(0.282162\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.33403e7 0.454065 0.227033 0.973887i \(-0.427098\pi\)
0.227033 + 0.973887i \(0.427098\pi\)
\(972\) 0 0
\(973\) −5.80859e6 −0.196693
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.81112e7 1.27737 0.638685 0.769468i \(-0.279479\pi\)
0.638685 + 0.769468i \(0.279479\pi\)
\(978\) 0 0
\(979\) −2.07229e6 −0.0691024
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.42760e7 0.801296 0.400648 0.916232i \(-0.368785\pi\)
0.400648 + 0.916232i \(0.368785\pi\)
\(984\) 0 0
\(985\) 5.28869e7 1.73683
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.90275e6 −0.0618572
\(990\) 0 0
\(991\) −5.99075e6 −0.193775 −0.0968874 0.995295i \(-0.530889\pi\)
−0.0968874 + 0.995295i \(0.530889\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 5.86099e7 1.87678
\(996\) 0 0
\(997\) −1.10752e7 −0.352868 −0.176434 0.984312i \(-0.556456\pi\)
−0.176434 + 0.984312i \(0.556456\pi\)
\(998\) 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 504.6.a.o.1.1 2
3.2 odd 2 168.6.a.j.1.2 2
4.3 odd 2 1008.6.a.bn.1.1 2
12.11 even 2 336.6.a.t.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.j.1.2 2 3.2 odd 2
336.6.a.t.1.2 2 12.11 even 2
504.6.a.o.1.1 2 1.1 even 1 trivial
1008.6.a.bn.1.1 2 4.3 odd 2