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Properties

Label 576.6.a.u.1.1
Level $576$
Weight $6$
Character 576.1
Self dual yes
Analytic conductor $92.381$
Analytic rank $0$
Dimension $1$
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] = [576,6,Mod(1,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("576.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(92.3810802123\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 32)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+14.0000 q^{5} -208.000 q^{7} +O(q^{10})\) \(q+14.0000 q^{5} -208.000 q^{7} -536.000 q^{11} -694.000 q^{13} +1278.00 q^{17} -1112.00 q^{19} -3216.00 q^{23} -2929.00 q^{25} +2918.00 q^{29} -2624.00 q^{31} -2912.00 q^{35} +9458.00 q^{37} -170.000 q^{41} +19928.0 q^{43} -32.0000 q^{47} +26457.0 q^{49} -22178.0 q^{53} -7504.00 q^{55} +41480.0 q^{59} -15462.0 q^{61} -9716.00 q^{65} +20744.0 q^{67} -28592.0 q^{71} -53670.0 q^{73} +111488. q^{77} -69152.0 q^{79} -37800.0 q^{83} +17892.0 q^{85} +126806. q^{89} +144352. q^{91} -15568.0 q^{95} +62290.0 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) 14.0000 0.250440 0.125220 − 0.992129i \(-0.460036\pi\)
0.125220 + 0.992129i \(0.460036\pi\)
\(6\) 0 0
\(7\) −208.000 −1.60442 −0.802210 − 0.597042i \(-0.796343\pi\)
−0.802210 + 0.597042i \(0.796343\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −536.000 −1.33562 −0.667810 − 0.744332i \(-0.732768\pi\)
−0.667810 + 0.744332i \(0.732768\pi\)
\(12\) 0 0
\(13\) −694.000 −1.13894 −0.569470 − 0.822012i \(-0.692852\pi\)
−0.569470 + 0.822012i \(0.692852\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1278.00 1.07253 0.536264 − 0.844050i \(-0.319835\pi\)
0.536264 + 0.844050i \(0.319835\pi\)
\(18\) 0 0
\(19\) −1112.00 −0.706677 −0.353338 − 0.935496i \(-0.614954\pi\)
−0.353338 + 0.935496i \(0.614954\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3216.00 −1.26764 −0.633821 − 0.773480i \(-0.718514\pi\)
−0.633821 + 0.773480i \(0.718514\pi\)
\(24\) 0 0
\(25\) −2929.00 −0.937280
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2918.00 0.644303 0.322152 − 0.946688i \(-0.395594\pi\)
0.322152 + 0.946688i \(0.395594\pi\)
\(30\) 0 0
\(31\) −2624.00 −0.490410 −0.245205 − 0.969471i \(-0.578855\pi\)
−0.245205 + 0.969471i \(0.578855\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2912.00 −0.401810
\(36\) 0 0
\(37\) 9458.00 1.13578 0.567891 − 0.823104i \(-0.307759\pi\)
0.567891 + 0.823104i \(0.307759\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −170.000 −0.0157939 −0.00789695 − 0.999969i \(-0.502514\pi\)
−0.00789695 + 0.999969i \(0.502514\pi\)
\(42\) 0 0
\(43\) 19928.0 1.64359 0.821793 − 0.569786i \(-0.192974\pi\)
0.821793 + 0.569786i \(0.192974\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −32.0000 −0.00211303 −0.00105651 − 0.999999i \(-0.500336\pi\)
−0.00105651 + 0.999999i \(0.500336\pi\)
\(48\) 0 0
\(49\) 26457.0 1.57417
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −22178.0 −1.08451 −0.542254 − 0.840215i \(-0.682429\pi\)
−0.542254 + 0.840215i \(0.682429\pi\)
\(54\) 0 0
\(55\) −7504.00 −0.334492
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 41480.0 1.55135 0.775673 − 0.631135i \(-0.217411\pi\)
0.775673 + 0.631135i \(0.217411\pi\)
\(60\) 0 0
\(61\) −15462.0 −0.532036 −0.266018 − 0.963968i \(-0.585708\pi\)
−0.266018 + 0.963968i \(0.585708\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9716.00 −0.285236
\(66\) 0 0
\(67\) 20744.0 0.564554 0.282277 − 0.959333i \(-0.408910\pi\)
0.282277 + 0.959333i \(0.408910\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −28592.0 −0.673130 −0.336565 − 0.941660i \(-0.609265\pi\)
−0.336565 + 0.941660i \(0.609265\pi\)
\(72\) 0 0
\(73\) −53670.0 −1.17876 −0.589379 − 0.807857i \(-0.700627\pi\)
−0.589379 + 0.807857i \(0.700627\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 111488. 2.14290
\(78\) 0 0
\(79\) −69152.0 −1.24663 −0.623314 − 0.781971i \(-0.714214\pi\)
−0.623314 + 0.781971i \(0.714214\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −37800.0 −0.602277 −0.301139 − 0.953580i \(-0.597367\pi\)
−0.301139 + 0.953580i \(0.597367\pi\)
\(84\) 0 0
\(85\) 17892.0 0.268603
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 126806. 1.69693 0.848467 − 0.529249i \(-0.177526\pi\)
0.848467 + 0.529249i \(0.177526\pi\)
\(90\) 0 0
\(91\) 144352. 1.82734
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15568.0 −0.176980
\(96\) 0 0
\(97\) 62290.0 0.672185 0.336093 − 0.941829i \(-0.390894\pi\)
0.336093 + 0.941829i \(0.390894\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6414.00 0.0625641 0.0312821 − 0.999511i \(-0.490041\pi\)
0.0312821 + 0.999511i \(0.490041\pi\)
\(102\) 0 0
\(103\) −108432. −1.00708 −0.503541 − 0.863972i \(-0.667970\pi\)
−0.503541 + 0.863972i \(0.667970\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 103976. 0.877958 0.438979 − 0.898497i \(-0.355340\pi\)
0.438979 + 0.898497i \(0.355340\pi\)
\(108\) 0 0
\(109\) −2486.00 −0.0200417 −0.0100209 − 0.999950i \(-0.503190\pi\)
−0.0100209 + 0.999950i \(0.503190\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15794.0 −0.116358 −0.0581790 − 0.998306i \(-0.518529\pi\)
−0.0581790 + 0.998306i \(0.518529\pi\)
\(114\) 0 0
\(115\) −45024.0 −0.317468
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −265824. −1.72079
\(120\) 0 0
\(121\) 126245. 0.783882
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −84756.0 −0.485172
\(126\) 0 0
\(127\) 1024.00 0.00563366 0.00281683 − 0.999996i \(-0.499103\pi\)
0.00281683 + 0.999996i \(0.499103\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −22664.0 −0.115387 −0.0576937 − 0.998334i \(-0.518375\pi\)
−0.0576937 + 0.998334i \(0.518375\pi\)
\(132\) 0 0
\(133\) 231296. 1.13381
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 53238.0 0.242337 0.121169 − 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(138\) 0 0
\(139\) −19816.0 −0.0869919 −0.0434960 − 0.999054i \(-0.513850\pi\)
−0.0434960 + 0.999054i \(0.513850\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 371984. 1.52119
\(144\) 0 0
\(145\) 40852.0 0.161359
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 452190. 1.66861 0.834306 − 0.551302i \(-0.185869\pi\)
0.834306 + 0.551302i \(0.185869\pi\)
\(150\) 0 0
\(151\) −263280. −0.939670 −0.469835 − 0.882754i \(-0.655687\pi\)
−0.469835 + 0.882754i \(0.655687\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −36736.0 −0.122818
\(156\) 0 0
\(157\) 353530. 1.14466 0.572331 − 0.820023i \(-0.306039\pi\)
0.572331 + 0.820023i \(0.306039\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 668928. 2.03383
\(162\) 0 0
\(163\) 100936. 0.297562 0.148781 − 0.988870i \(-0.452465\pi\)
0.148781 + 0.988870i \(0.452465\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 284944. 0.790621 0.395310 − 0.918548i \(-0.370637\pi\)
0.395310 + 0.918548i \(0.370637\pi\)
\(168\) 0 0
\(169\) 110343. 0.297186
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 484374. 1.23045 0.615227 − 0.788350i \(-0.289064\pi\)
0.615227 + 0.788350i \(0.289064\pi\)
\(174\) 0 0
\(175\) 609232. 1.50379
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 406680. 0.948681 0.474341 − 0.880341i \(-0.342687\pi\)
0.474341 + 0.880341i \(0.342687\pi\)
\(180\) 0 0
\(181\) −570302. −1.29392 −0.646962 − 0.762523i \(-0.723961\pi\)
−0.646962 + 0.762523i \(0.723961\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 132412. 0.284445
\(186\) 0 0
\(187\) −685008. −1.43249
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −138624. −0.274951 −0.137475 − 0.990505i \(-0.543899\pi\)
−0.137475 + 0.990505i \(0.543899\pi\)
\(192\) 0 0
\(193\) 34482.0 0.0666345 0.0333173 − 0.999445i \(-0.489393\pi\)
0.0333173 + 0.999445i \(0.489393\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 643598. 1.18154 0.590771 − 0.806839i \(-0.298824\pi\)
0.590771 + 0.806839i \(0.298824\pi\)
\(198\) 0 0
\(199\) 1.10738e6 1.98227 0.991134 − 0.132865i \(-0.0424178\pi\)
0.991134 + 0.132865i \(0.0424178\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −606944. −1.03373
\(204\) 0 0
\(205\) −2380.00 −0.00395542
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 596032. 0.943852
\(210\) 0 0
\(211\) −229976. −0.355612 −0.177806 − 0.984066i \(-0.556900\pi\)
−0.177806 + 0.984066i \(0.556900\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 278992. 0.411619
\(216\) 0 0
\(217\) 545792. 0.786824
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −886932. −1.22155
\(222\) 0 0
\(223\) −1.08947e6 −1.46708 −0.733540 − 0.679646i \(-0.762133\pi\)
−0.733540 + 0.679646i \(0.762133\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −687048. −0.884958 −0.442479 − 0.896779i \(-0.645901\pi\)
−0.442479 + 0.896779i \(0.645901\pi\)
\(228\) 0 0
\(229\) 699730. 0.881743 0.440871 − 0.897570i \(-0.354670\pi\)
0.440871 + 0.897570i \(0.354670\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −937722. −1.13158 −0.565789 − 0.824550i \(-0.691428\pi\)
−0.565789 + 0.824550i \(0.691428\pi\)
\(234\) 0 0
\(235\) −448.000 −0.000529186 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −643488. −0.728695 −0.364347 − 0.931263i \(-0.618708\pi\)
−0.364347 + 0.931263i \(0.618708\pi\)
\(240\) 0 0
\(241\) 157282. 0.174436 0.0872181 − 0.996189i \(-0.472202\pi\)
0.0872181 + 0.996189i \(0.472202\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 370398. 0.394233
\(246\) 0 0
\(247\) 771728. 0.804863
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.58604e6 −1.58902 −0.794511 − 0.607250i \(-0.792273\pi\)
−0.794511 + 0.607250i \(0.792273\pi\)
\(252\) 0 0
\(253\) 1.72378e6 1.69309
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 654334. 0.617969 0.308984 − 0.951067i \(-0.400011\pi\)
0.308984 + 0.951067i \(0.400011\pi\)
\(258\) 0 0
\(259\) −1.96726e6 −1.82227
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 330192. 0.294359 0.147179 − 0.989110i \(-0.452981\pi\)
0.147179 + 0.989110i \(0.452981\pi\)
\(264\) 0 0
\(265\) −310492. −0.271604
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.56956e6 1.32250 0.661252 − 0.750164i \(-0.270026\pi\)
0.661252 + 0.750164i \(0.270026\pi\)
\(270\) 0 0
\(271\) 957792. 0.792224 0.396112 − 0.918202i \(-0.370359\pi\)
0.396112 + 0.918202i \(0.370359\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.56994e6 1.25185
\(276\) 0 0
\(277\) −565438. −0.442778 −0.221389 − 0.975186i \(-0.571059\pi\)
−0.221389 + 0.975186i \(0.571059\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.34127e6 1.01333 0.506664 − 0.862143i \(-0.330878\pi\)
0.506664 + 0.862143i \(0.330878\pi\)
\(282\) 0 0
\(283\) 734264. 0.544987 0.272494 − 0.962158i \(-0.412152\pi\)
0.272494 + 0.962158i \(0.412152\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 35360.0 0.0253401
\(288\) 0 0
\(289\) 213427. 0.150316
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.13320e6 −0.771149 −0.385574 − 0.922677i \(-0.625997\pi\)
−0.385574 + 0.922677i \(0.625997\pi\)
\(294\) 0 0
\(295\) 580720. 0.388519
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.23190e6 1.44377
\(300\) 0 0
\(301\) −4.14502e6 −2.63700
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −216468. −0.133243
\(306\) 0 0
\(307\) 2.91377e6 1.76445 0.882224 − 0.470829i \(-0.156045\pi\)
0.882224 + 0.470829i \(0.156045\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.43813e6 0.843134 0.421567 − 0.906797i \(-0.361480\pi\)
0.421567 + 0.906797i \(0.361480\pi\)
\(312\) 0 0
\(313\) −1.37601e6 −0.793888 −0.396944 − 0.917843i \(-0.629929\pi\)
−0.396944 + 0.917843i \(0.629929\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.23494e6 −0.690235 −0.345118 − 0.938559i \(-0.612161\pi\)
−0.345118 + 0.938559i \(0.612161\pi\)
\(318\) 0 0
\(319\) −1.56405e6 −0.860545
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.42114e6 −0.757930
\(324\) 0 0
\(325\) 2.03273e6 1.06751
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6656.00 0.00339019
\(330\) 0 0
\(331\) 1.48930e6 0.747160 0.373580 − 0.927598i \(-0.378130\pi\)
0.373580 + 0.927598i \(0.378130\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 290416. 0.141387
\(336\) 0 0
\(337\) 838226. 0.402056 0.201028 − 0.979586i \(-0.435572\pi\)
0.201028 + 0.979586i \(0.435572\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.40646e6 0.655002
\(342\) 0 0
\(343\) −2.00720e6 −0.921203
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −350008. −0.156047 −0.0780233 − 0.996952i \(-0.524861\pi\)
−0.0780233 + 0.996952i \(0.524861\pi\)
\(348\) 0 0
\(349\) 383642. 0.168602 0.0843010 − 0.996440i \(-0.473134\pi\)
0.0843010 + 0.996440i \(0.473134\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.09309e6 −1.74829 −0.874147 − 0.485661i \(-0.838579\pi\)
−0.874147 + 0.485661i \(0.838579\pi\)
\(354\) 0 0
\(355\) −400288. −0.168578
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.14430e6 −1.28762 −0.643811 − 0.765185i \(-0.722648\pi\)
−0.643811 + 0.765185i \(0.722648\pi\)
\(360\) 0 0
\(361\) −1.23955e6 −0.500608
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −751380. −0.295208
\(366\) 0 0
\(367\) −1.47619e6 −0.572108 −0.286054 − 0.958214i \(-0.592344\pi\)
−0.286054 + 0.958214i \(0.592344\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.61302e6 1.74001
\(372\) 0 0
\(373\) 3.73981e6 1.39180 0.695901 − 0.718138i \(-0.255005\pi\)
0.695901 + 0.718138i \(0.255005\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.02509e6 −0.733823
\(378\) 0 0
\(379\) −1.89966e6 −0.679324 −0.339662 − 0.940548i \(-0.610313\pi\)
−0.339662 + 0.940548i \(0.610313\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.74310e6 −0.607192 −0.303596 − 0.952801i \(-0.598187\pi\)
−0.303596 + 0.952801i \(0.598187\pi\)
\(384\) 0 0
\(385\) 1.56083e6 0.536666
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.69147e6 −0.901812 −0.450906 − 0.892571i \(-0.648899\pi\)
−0.450906 + 0.892571i \(0.648899\pi\)
\(390\) 0 0
\(391\) −4.11005e6 −1.35958
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −968128. −0.312205
\(396\) 0 0
\(397\) −5.37353e6 −1.71113 −0.855565 − 0.517695i \(-0.826790\pi\)
−0.855565 + 0.517695i \(0.826790\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −156418. −0.0485765 −0.0242882 − 0.999705i \(-0.507732\pi\)
−0.0242882 + 0.999705i \(0.507732\pi\)
\(402\) 0 0
\(403\) 1.82106e6 0.558548
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.06949e6 −1.51697
\(408\) 0 0
\(409\) −306086. −0.0904764 −0.0452382 − 0.998976i \(-0.514405\pi\)
−0.0452382 + 0.998976i \(0.514405\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.62784e6 −2.48901
\(414\) 0 0
\(415\) −529200. −0.150834
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.70868e6 −1.86682 −0.933409 − 0.358814i \(-0.883181\pi\)
−0.933409 + 0.358814i \(0.883181\pi\)
\(420\) 0 0
\(421\) −4.02347e6 −1.10636 −0.553179 − 0.833063i \(-0.686585\pi\)
−0.553179 + 0.833063i \(0.686585\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.74326e6 −1.00526
\(426\) 0 0
\(427\) 3.21610e6 0.853610
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.04304e6 1.82628 0.913139 − 0.407648i \(-0.133651\pi\)
0.913139 + 0.407648i \(0.133651\pi\)
\(432\) 0 0
\(433\) −1.25142e6 −0.320763 −0.160381 − 0.987055i \(-0.551272\pi\)
−0.160381 + 0.987055i \(0.551272\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.57619e6 0.895813
\(438\) 0 0
\(439\) −1.25406e6 −0.310569 −0.155285 − 0.987870i \(-0.549629\pi\)
−0.155285 + 0.987870i \(0.549629\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.18081e6 1.25426 0.627131 − 0.778914i \(-0.284229\pi\)
0.627131 + 0.778914i \(0.284229\pi\)
\(444\) 0 0
\(445\) 1.77528e6 0.424979
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.73064e6 1.34149 0.670745 − 0.741688i \(-0.265975\pi\)
0.670745 + 0.741688i \(0.265975\pi\)
\(450\) 0 0
\(451\) 91120.0 0.0210947
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.02093e6 0.457638
\(456\) 0 0
\(457\) −5.24153e6 −1.17400 −0.586999 − 0.809588i \(-0.699691\pi\)
−0.586999 + 0.809588i \(0.699691\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −173994. −0.0381313 −0.0190657 − 0.999818i \(-0.506069\pi\)
−0.0190657 + 0.999818i \(0.506069\pi\)
\(462\) 0 0
\(463\) 4.01277e6 0.869945 0.434972 − 0.900444i \(-0.356758\pi\)
0.434972 + 0.900444i \(0.356758\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 774616. 0.164359 0.0821796 − 0.996618i \(-0.473812\pi\)
0.0821796 + 0.996618i \(0.473812\pi\)
\(468\) 0 0
\(469\) −4.31475e6 −0.905782
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.06814e7 −2.19521
\(474\) 0 0
\(475\) 3.25705e6 0.662354
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.33530e6 −0.465054 −0.232527 − 0.972590i \(-0.574699\pi\)
−0.232527 + 0.972590i \(0.574699\pi\)
\(480\) 0 0
\(481\) −6.56385e6 −1.29359
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 872060. 0.168342
\(486\) 0 0
\(487\) 1.03947e6 0.198605 0.0993025 − 0.995057i \(-0.468339\pi\)
0.0993025 + 0.995057i \(0.468339\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.85092e6 1.46966 0.734830 − 0.678251i \(-0.237262\pi\)
0.734830 + 0.678251i \(0.237262\pi\)
\(492\) 0 0
\(493\) 3.72920e6 0.691033
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.94714e6 1.07998
\(498\) 0 0
\(499\) −2.71644e6 −0.488370 −0.244185 − 0.969729i \(-0.578520\pi\)
−0.244185 + 0.969729i \(0.578520\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.62034e6 0.814242 0.407121 − 0.913374i \(-0.366533\pi\)
0.407121 + 0.913374i \(0.366533\pi\)
\(504\) 0 0
\(505\) 89796.0 0.0156685
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.46198e6 −0.763366 −0.381683 − 0.924293i \(-0.624655\pi\)
−0.381683 + 0.924293i \(0.624655\pi\)
\(510\) 0 0
\(511\) 1.11634e7 1.89122
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.51805e6 −0.252213
\(516\) 0 0
\(517\) 17152.0 0.00282220
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.74375e6 −0.604245 −0.302122 − 0.953269i \(-0.597695\pi\)
−0.302122 + 0.953269i \(0.597695\pi\)
\(522\) 0 0
\(523\) −9.28433e6 −1.48421 −0.742107 − 0.670282i \(-0.766173\pi\)
−0.742107 + 0.670282i \(0.766173\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.35347e6 −0.525979
\(528\) 0 0
\(529\) 3.90631e6 0.606915
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 117980. 0.0179883
\(534\) 0 0
\(535\) 1.45566e6 0.219875
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.41810e7 −2.10249
\(540\) 0 0
\(541\) −862150. −0.126645 −0.0633227 − 0.997993i \(-0.520170\pi\)
−0.0633227 + 0.997993i \(0.520170\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −34804.0 −0.00501924
\(546\) 0 0
\(547\) −1.75442e6 −0.250707 −0.125353 − 0.992112i \(-0.540006\pi\)
−0.125353 + 0.992112i \(0.540006\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.24482e6 −0.455314
\(552\) 0 0
\(553\) 1.43836e7 2.00012
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.00292e7 −1.36971 −0.684856 − 0.728678i \(-0.740135\pi\)
−0.684856 + 0.728678i \(0.740135\pi\)
\(558\) 0 0
\(559\) −1.38300e7 −1.87195
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.27460e6 −0.701324 −0.350662 − 0.936502i \(-0.614043\pi\)
−0.350662 + 0.936502i \(0.614043\pi\)
\(564\) 0 0
\(565\) −221116. −0.0291406
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.36940e6 −1.08371 −0.541856 − 0.840471i \(-0.682278\pi\)
−0.541856 + 0.840471i \(0.682278\pi\)
\(570\) 0 0
\(571\) −4.02702e6 −0.516884 −0.258442 − 0.966027i \(-0.583209\pi\)
−0.258442 + 0.966027i \(0.583209\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.41966e6 1.18814
\(576\) 0 0
\(577\) 2.37568e6 0.297063 0.148532 − 0.988908i \(-0.452545\pi\)
0.148532 + 0.988908i \(0.452545\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.86240e6 0.966306
\(582\) 0 0
\(583\) 1.18874e7 1.44849
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.44028e6 −0.412096 −0.206048 − 0.978542i \(-0.566060\pi\)
−0.206048 + 0.978542i \(0.566060\pi\)
\(588\) 0 0
\(589\) 2.91789e6 0.346562
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.22942e6 0.377127 0.188564 − 0.982061i \(-0.439617\pi\)
0.188564 + 0.982061i \(0.439617\pi\)
\(594\) 0 0
\(595\) −3.72154e6 −0.430953
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.29714e6 1.05872 0.529361 − 0.848397i \(-0.322432\pi\)
0.529361 + 0.848397i \(0.322432\pi\)
\(600\) 0 0
\(601\) −1.12782e7 −1.27366 −0.636828 − 0.771006i \(-0.719754\pi\)
−0.636828 + 0.771006i \(0.719754\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.76743e6 0.196315
\(606\) 0 0
\(607\) 7.00115e6 0.771255 0.385627 − 0.922655i \(-0.373985\pi\)
0.385627 + 0.922655i \(0.373985\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 22208.0 0.00240661
\(612\) 0 0
\(613\) 6.19432e6 0.665798 0.332899 − 0.942962i \(-0.391973\pi\)
0.332899 + 0.942962i \(0.391973\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.62407e6 0.277500 0.138750 − 0.990327i \(-0.455692\pi\)
0.138750 + 0.990327i \(0.455692\pi\)
\(618\) 0 0
\(619\) 2.83721e6 0.297622 0.148811 − 0.988866i \(-0.452455\pi\)
0.148811 + 0.988866i \(0.452455\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.63756e7 −2.72259
\(624\) 0 0
\(625\) 7.96654e6 0.815774
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.20873e7 1.21816
\(630\) 0 0
\(631\) 1.29656e7 1.29634 0.648170 − 0.761496i \(-0.275535\pi\)
0.648170 + 0.761496i \(0.275535\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14336.0 0.00141089
\(636\) 0 0
\(637\) −1.83612e7 −1.79288
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.16798e7 1.12276 0.561382 − 0.827557i \(-0.310270\pi\)
0.561382 + 0.827557i \(0.310270\pi\)
\(642\) 0 0
\(643\) −7.02732e6 −0.670289 −0.335145 − 0.942167i \(-0.608785\pi\)
−0.335145 + 0.942167i \(0.608785\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.72821e6 0.913634 0.456817 − 0.889561i \(-0.348989\pi\)
0.456817 + 0.889561i \(0.348989\pi\)
\(648\) 0 0
\(649\) −2.22333e7 −2.07201
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.81425e6 −0.900688 −0.450344 − 0.892855i \(-0.648699\pi\)
−0.450344 + 0.892855i \(0.648699\pi\)
\(654\) 0 0
\(655\) −317296. −0.0288976
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.46652e7 1.31545 0.657724 − 0.753259i \(-0.271519\pi\)
0.657724 + 0.753259i \(0.271519\pi\)
\(660\) 0 0
\(661\) 1.41836e7 1.26265 0.631327 − 0.775517i \(-0.282511\pi\)
0.631327 + 0.775517i \(0.282511\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.23814e6 0.283950
\(666\) 0 0
\(667\) −9.38429e6 −0.816745
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.28763e6 0.710598
\(672\) 0 0
\(673\) 5.49941e6 0.468035 0.234018 − 0.972232i \(-0.424813\pi\)
0.234018 + 0.972232i \(0.424813\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.77375e7 1.48737 0.743687 − 0.668528i \(-0.233075\pi\)
0.743687 + 0.668528i \(0.233075\pi\)
\(678\) 0 0
\(679\) −1.29563e7 −1.07847
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.39670e6 −0.770768 −0.385384 − 0.922756i \(-0.625931\pi\)
−0.385384 + 0.922756i \(0.625931\pi\)
\(684\) 0 0
\(685\) 745332. 0.0606909
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.53915e7 1.23519
\(690\) 0 0
\(691\) 1.34767e7 1.07371 0.536857 − 0.843673i \(-0.319611\pi\)
0.536857 + 0.843673i \(0.319611\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −277424. −0.0217862
\(696\) 0 0
\(697\) −217260. −0.0169394
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.15594e7 1.65707 0.828536 − 0.559935i \(-0.189174\pi\)
0.828536 + 0.559935i \(0.189174\pi\)
\(702\) 0 0
\(703\) −1.05173e7 −0.802631
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.33411e6 −0.100379
\(708\) 0 0
\(709\) 6.38165e6 0.476779 0.238390 − 0.971170i \(-0.423380\pi\)
0.238390 + 0.971170i \(0.423380\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.43878e6 0.621664
\(714\) 0 0
\(715\) 5.20778e6 0.380967
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.63566e7 1.17997 0.589986 − 0.807413i \(-0.299133\pi\)
0.589986 + 0.807413i \(0.299133\pi\)
\(720\) 0 0
\(721\) 2.25539e7 1.61578
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.54682e6 −0.603893
\(726\) 0 0
\(727\) −2.13130e7 −1.49558 −0.747788 − 0.663937i \(-0.768884\pi\)
−0.747788 + 0.663937i \(0.768884\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.54680e7 1.76279
\(732\) 0 0
\(733\) −1.21571e7 −0.835737 −0.417869 − 0.908507i \(-0.637223\pi\)
−0.417869 + 0.908507i \(0.637223\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.11188e7 −0.754030
\(738\) 0 0
\(739\) 1.92337e7 1.29555 0.647773 − 0.761834i \(-0.275701\pi\)
0.647773 + 0.761834i \(0.275701\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.66565e6 −0.110691 −0.0553454 − 0.998467i \(-0.517626\pi\)
−0.0553454 + 0.998467i \(0.517626\pi\)
\(744\) 0 0
\(745\) 6.33066e6 0.417886
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.16270e7 −1.40861
\(750\) 0 0
\(751\) 9.81290e6 0.634888 0.317444 − 0.948277i \(-0.397175\pi\)
0.317444 + 0.948277i \(0.397175\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.68592e6 −0.235331
\(756\) 0 0
\(757\) 1.92753e7 1.22254 0.611269 − 0.791423i \(-0.290659\pi\)
0.611269 + 0.791423i \(0.290659\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.17863e7 0.737762 0.368881 − 0.929477i \(-0.379741\pi\)
0.368881 + 0.929477i \(0.379741\pi\)
\(762\) 0 0
\(763\) 517088. 0.0321553
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.87871e7 −1.76689
\(768\) 0 0
\(769\) 1.22941e7 0.749690 0.374845 − 0.927087i \(-0.377696\pi\)
0.374845 + 0.927087i \(0.377696\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.57086e6 0.154750 0.0773749 − 0.997002i \(-0.475346\pi\)
0.0773749 + 0.997002i \(0.475346\pi\)
\(774\) 0 0
\(775\) 7.68570e6 0.459652
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 189040. 0.0111612
\(780\) 0 0
\(781\) 1.53253e7 0.899046
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.94942e6 0.286669
\(786\) 0 0
\(787\) −5.54594e6 −0.319182 −0.159591 − 0.987183i \(-0.551018\pi\)
−0.159591 + 0.987183i \(0.551018\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.28515e6 0.186687
\(792\) 0 0
\(793\) 1.07306e7 0.605958
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.09610e7 1.16887 0.584436 − 0.811440i \(-0.301316\pi\)
0.584436 + 0.811440i \(0.301316\pi\)
\(798\) 0 0
\(799\) −40896.0 −0.00226628
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.87671e7 1.57437
\(804\) 0 0
\(805\) 9.36499e6 0.509352
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.70297e7 −1.45201 −0.726005 − 0.687690i \(-0.758625\pi\)
−0.726005 + 0.687690i \(0.758625\pi\)
\(810\) 0 0
\(811\) 2.13052e6 0.113745 0.0568727 − 0.998381i \(-0.481887\pi\)
0.0568727 + 0.998381i \(0.481887\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.41310e6 0.0745212
\(816\) 0 0
\(817\) −2.21599e7 −1.16148
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.58060e7 0.818396 0.409198 − 0.912446i \(-0.365809\pi\)
0.409198 + 0.912446i \(0.365809\pi\)
\(822\) 0 0
\(823\) −2.28848e7 −1.17773 −0.588867 − 0.808230i \(-0.700426\pi\)
−0.588867 + 0.808230i \(0.700426\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.55336e7 −1.29822 −0.649109 − 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(828\) 0 0
\(829\) −8.31786e6 −0.420364 −0.210182 − 0.977662i \(-0.567406\pi\)
−0.210182 + 0.977662i \(0.567406\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.38120e7 1.68834
\(834\) 0 0
\(835\) 3.98922e6 0.198003
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.66261e7 −1.79633 −0.898164 − 0.439660i \(-0.855099\pi\)
−0.898164 + 0.439660i \(0.855099\pi\)
\(840\) 0 0
\(841\) −1.19964e7 −0.584873
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.54480e6 0.0744271
\(846\) 0 0
\(847\) −2.62590e7 −1.25768
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.04169e7 −1.43976
\(852\) 0 0
\(853\) −1.74802e7 −0.822571 −0.411286 − 0.911507i \(-0.634920\pi\)
−0.411286 + 0.911507i \(0.634920\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.31062e6 −0.433038 −0.216519 − 0.976278i \(-0.569470\pi\)
−0.216519 + 0.976278i \(0.569470\pi\)
\(858\) 0 0
\(859\) 3.49525e7 1.61620 0.808101 − 0.589045i \(-0.200496\pi\)
0.808101 + 0.589045i \(0.200496\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.02349e7 0.924858 0.462429 − 0.886656i \(-0.346978\pi\)
0.462429 + 0.886656i \(0.346978\pi\)
\(864\) 0 0
\(865\) 6.78124e6 0.308155
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.70655e7 1.66502
\(870\) 0 0
\(871\) −1.43963e7 −0.642994
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.76292e7 0.778419
\(876\) 0 0
\(877\) 1.98342e7 0.870797 0.435398 − 0.900238i \(-0.356608\pi\)
0.435398 + 0.900238i \(0.356608\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.81023e7 1.65391 0.826954 − 0.562270i \(-0.190072\pi\)
0.826954 + 0.562270i \(0.190072\pi\)
\(882\) 0 0
\(883\) 2.41560e7 1.04261 0.521307 − 0.853369i \(-0.325445\pi\)
0.521307 + 0.853369i \(0.325445\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.02368e7 −0.863638 −0.431819 − 0.901960i \(-0.642128\pi\)
−0.431819 + 0.901960i \(0.642128\pi\)
\(888\) 0 0
\(889\) −212992. −0.00903876
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 35584.0 0.00149323
\(894\) 0 0
\(895\) 5.69352e6 0.237587
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.65683e6 −0.315973
\(900\) 0 0
\(901\) −2.83435e7 −1.16316
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.98423e6 −0.324050
\(906\) 0 0
\(907\) −1.97976e7 −0.799088 −0.399544 − 0.916714i \(-0.630831\pi\)
−0.399544 + 0.916714i \(0.630831\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.13242e7 0.851288 0.425644 − 0.904891i \(-0.360048\pi\)
0.425644 + 0.904891i \(0.360048\pi\)
\(912\) 0 0
\(913\) 2.02608e7 0.804414
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4.71411e6 0.185130
\(918\) 0 0
\(919\) 3.49941e7 1.36680 0.683401 − 0.730043i \(-0.260500\pi\)
0.683401 + 0.730043i \(0.260500\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.98428e7 0.766655
\(924\) 0 0
\(925\) −2.77025e7 −1.06455
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.88107e7 1.09525 0.547627 − 0.836722i \(-0.315531\pi\)
0.547627 + 0.836722i \(0.315531\pi\)
\(930\) 0 0
\(931\) −2.94202e7 −1.11243
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9.59011e6 −0.358752
\(936\) 0 0
\(937\) 1.28854e7 0.479457 0.239729 − 0.970840i \(-0.422941\pi\)
0.239729 + 0.970840i \(0.422941\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.27615e7 −1.94242 −0.971210 − 0.238227i \(-0.923434\pi\)
−0.971210 + 0.238227i \(0.923434\pi\)
\(942\) 0 0
\(943\) 546720. 0.0200210
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.53961e6 0.200726 0.100363 − 0.994951i \(-0.468000\pi\)
0.100363 + 0.994951i \(0.468000\pi\)
\(948\) 0 0
\(949\) 3.72470e7 1.34253
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 228102. 0.00813574 0.00406787 − 0.999992i \(-0.498705\pi\)
0.00406787 + 0.999992i \(0.498705\pi\)
\(954\) 0 0
\(955\) −1.94074e6 −0.0688586
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.10735e7 −0.388811
\(960\) 0 0
\(961\) −2.17438e7 −0.759498
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 482748. 0.0166879
\(966\) 0 0
\(967\) 7.36709e6 0.253355 0.126678 − 0.991944i \(-0.459569\pi\)
0.126678 + 0.991944i \(0.459569\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.91161e7 −0.650654 −0.325327 − 0.945602i \(-0.605474\pi\)
−0.325327 + 0.945602i \(0.605474\pi\)
\(972\) 0 0
\(973\) 4.12173e6 0.139572
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −5.57040e7 −1.86702 −0.933512 − 0.358546i \(-0.883273\pi\)
−0.933512 + 0.358546i \(0.883273\pi\)
\(978\) 0 0
\(979\) −6.79680e7 −2.26646
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.55469e7 0.513167 0.256584 − 0.966522i \(-0.417403\pi\)
0.256584 + 0.966522i \(0.417403\pi\)
\(984\) 0 0
\(985\) 9.01037e6 0.295905
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6.40884e7 −2.08348
\(990\) 0 0
\(991\) 2.36890e7 0.766237 0.383118 − 0.923699i \(-0.374850\pi\)
0.383118 + 0.923699i \(0.374850\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.55033e7 0.496438
\(996\) 0 0
\(997\) −3.71720e6 −0.118434 −0.0592172 − 0.998245i \(-0.518860\pi\)
−0.0592172 + 0.998245i \(0.518860\pi\)
\(998\) 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 576.6.a.u.1.1 1
3.2 odd 2 64.6.a.e.1.1 1
4.3 odd 2 576.6.a.v.1.1 1
8.3 odd 2 288.6.a.e.1.1 1
8.5 even 2 288.6.a.d.1.1 1
12.11 even 2 64.6.a.c.1.1 1
24.5 odd 2 32.6.a.a.1.1 ✓ 1
24.11 even 2 32.6.a.c.1.1 yes 1
48.5 odd 4 256.6.b.h.129.1 2
48.11 even 4 256.6.b.b.129.2 2
48.29 odd 4 256.6.b.h.129.2 2
48.35 even 4 256.6.b.b.129.1 2
120.29 odd 2 800.6.a.e.1.1 1
120.53 even 4 800.6.c.a.449.1 2
120.59 even 2 800.6.a.a.1.1 1
120.77 even 4 800.6.c.a.449.2 2
120.83 odd 4 800.6.c.b.449.2 2
120.107 odd 4 800.6.c.b.449.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.6.a.a.1.1 ✓ 1 24.5 odd 2
32.6.a.c.1.1 yes 1 24.11 even 2
64.6.a.c.1.1 1 12.11 even 2
64.6.a.e.1.1 1 3.2 odd 2
256.6.b.b.129.1 2 48.35 even 4
256.6.b.b.129.2 2 48.11 even 4
256.6.b.h.129.1 2 48.5 odd 4
256.6.b.h.129.2 2 48.29 odd 4
288.6.a.d.1.1 1 8.5 even 2
288.6.a.e.1.1 1 8.3 odd 2
576.6.a.u.1.1 1 1.1 even 1 trivial
576.6.a.v.1.1 1 4.3 odd 2
800.6.a.a.1.1 1 120.59 even 2
800.6.a.e.1.1 1 120.29 odd 2
800.6.c.a.449.1 2 120.53 even 4
800.6.c.a.449.2 2 120.77 even 4
800.6.c.b.449.1 2 120.107 odd 4
800.6.c.b.449.2 2 120.83 odd 4