↑

Properties

Label 432.6.a.a.1.1
Level $432$
Weight $6$
Character 432.1
Self dual yes
Analytic conductor $69.286$
Analytic rank $0$
Dimension $1$
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] = [432,6,Mod(1,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, 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("432.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 432.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: \(69.2858101592\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 432.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-84.0000 q^{5} +193.000 q^{7} +O(q^{10})\) \(q-84.0000 q^{5} +193.000 q^{7} +348.000 q^{11} +845.000 q^{13} -1692.00 q^{17} +79.0000 q^{19} -564.000 q^{23} +3931.00 q^{25} -6432.00 q^{29} -4940.00 q^{31} -16212.0 q^{35} -3805.00 q^{37} +12480.0 q^{41} +4936.00 q^{43} +8124.00 q^{47} +20442.0 q^{49} +33192.0 q^{53} -29232.0 q^{55} +42492.0 q^{59} -17833.0 q^{61} -70980.0 q^{65} +67699.0 q^{67} +28152.0 q^{71} -13975.0 q^{73} +67164.0 q^{77} +83983.0 q^{79} -33384.0 q^{83} +142128. q^{85} -77868.0 q^{89} +163085. q^{91} -6636.00 q^{95} -2083.00 q^{97} +O(q^{100})\)

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
\(5\) −84.0000 −1.50264 −0.751319 − 0.659939i \(-0.770582\pi\)
−0.751319 + 0.659939i \(0.770582\pi\)
\(6\) 0 0
\(7\) 193.000 1.48872 0.744359 − 0.667780i \(-0.232755\pi\)
0.744359 + 0.667780i \(0.232755\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 348.000 0.867157 0.433578 − 0.901116i \(-0.357251\pi\)
0.433578 + 0.901116i \(0.357251\pi\)
\(12\) 0 0
\(13\) 845.000 1.38675 0.693375 − 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1692.00 −1.41997 −0.709983 − 0.704219i \(-0.751297\pi\)
−0.709983 + 0.704219i \(0.751297\pi\)
\(18\) 0 0
\(19\) 79.0000 0.0502046 0.0251023 − 0.999685i \(-0.492009\pi\)
0.0251023 + 0.999685i \(0.492009\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −564.000 −0.222310 −0.111155 − 0.993803i \(-0.535455\pi\)
−0.111155 + 0.993803i \(0.535455\pi\)
\(24\) 0 0
\(25\) 3931.00 1.25792
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6432.00 −1.42021 −0.710103 − 0.704098i \(-0.751351\pi\)
−0.710103 + 0.704098i \(0.751351\pi\)
\(30\) 0 0
\(31\) −4940.00 −0.923257 −0.461629 − 0.887073i \(-0.652735\pi\)
−0.461629 + 0.887073i \(0.652735\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −16212.0 −2.23700
\(36\) 0 0
\(37\) −3805.00 −0.456931 −0.228465 − 0.973552i \(-0.573371\pi\)
−0.228465 + 0.973552i \(0.573371\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 12480.0 1.15946 0.579729 − 0.814809i \(-0.303158\pi\)
0.579729 + 0.814809i \(0.303158\pi\)
\(42\) 0 0
\(43\) 4936.00 0.407103 0.203551 − 0.979064i \(-0.434752\pi\)
0.203551 + 0.979064i \(0.434752\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8124.00 0.536445 0.268223 − 0.963357i \(-0.413564\pi\)
0.268223 + 0.963357i \(0.413564\pi\)
\(48\) 0 0
\(49\) 20442.0 1.21628
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 33192.0 1.62309 0.811547 − 0.584287i \(-0.198626\pi\)
0.811547 + 0.584287i \(0.198626\pi\)
\(54\) 0 0
\(55\) −29232.0 −1.30302
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 42492.0 1.58919 0.794597 − 0.607137i \(-0.207682\pi\)
0.794597 + 0.607137i \(0.207682\pi\)
\(60\) 0 0
\(61\) −17833.0 −0.613620 −0.306810 − 0.951771i \(-0.599262\pi\)
−0.306810 + 0.951771i \(0.599262\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −70980.0 −2.08378
\(66\) 0 0
\(67\) 67699.0 1.84245 0.921224 − 0.389033i \(-0.127191\pi\)
0.921224 + 0.389033i \(0.127191\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 28152.0 0.662771 0.331385 − 0.943495i \(-0.392484\pi\)
0.331385 + 0.943495i \(0.392484\pi\)
\(72\) 0 0
\(73\) −13975.0 −0.306934 −0.153467 − 0.988154i \(-0.549044\pi\)
−0.153467 + 0.988154i \(0.549044\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 67164.0 1.29095
\(78\) 0 0
\(79\) 83983.0 1.51399 0.756996 − 0.653419i \(-0.226666\pi\)
0.756996 + 0.653419i \(0.226666\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −33384.0 −0.531916 −0.265958 − 0.963985i \(-0.585688\pi\)
−0.265958 + 0.963985i \(0.585688\pi\)
\(84\) 0 0
\(85\) 142128. 2.13369
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −77868.0 −1.04204 −0.521020 − 0.853545i \(-0.674448\pi\)
−0.521020 + 0.853545i \(0.674448\pi\)
\(90\) 0 0
\(91\) 163085. 2.06448
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6636.00 −0.0754393
\(96\) 0 0
\(97\) −2083.00 −0.0224781 −0.0112391 − 0.999937i \(-0.503578\pi\)
−0.0112391 + 0.999937i \(0.503578\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 121440. 1.18456 0.592282 − 0.805731i \(-0.298227\pi\)
0.592282 + 0.805731i \(0.298227\pi\)
\(102\) 0 0
\(103\) −104147. −0.967283 −0.483642 − 0.875266i \(-0.660686\pi\)
−0.483642 + 0.875266i \(0.660686\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −61164.0 −0.516460 −0.258230 − 0.966084i \(-0.583139\pi\)
−0.258230 + 0.966084i \(0.583139\pi\)
\(108\) 0 0
\(109\) 101090. 0.814971 0.407485 − 0.913212i \(-0.366406\pi\)
0.407485 + 0.913212i \(0.366406\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −66540.0 −0.490215 −0.245108 − 0.969496i \(-0.578823\pi\)
−0.245108 + 0.969496i \(0.578823\pi\)
\(114\) 0 0
\(115\) 47376.0 0.334052
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −326556. −2.11393
\(120\) 0 0
\(121\) −39947.0 −0.248039
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −67704.0 −0.387560
\(126\) 0 0
\(127\) 128428. 0.706562 0.353281 − 0.935517i \(-0.385066\pi\)
0.353281 + 0.935517i \(0.385066\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 77232.0 0.393205 0.196603 − 0.980483i \(-0.437009\pi\)
0.196603 + 0.980483i \(0.437009\pi\)
\(132\) 0 0
\(133\) 15247.0 0.0747404
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −92724.0 −0.422076 −0.211038 − 0.977478i \(-0.567684\pi\)
−0.211038 + 0.977478i \(0.567684\pi\)
\(138\) 0 0
\(139\) −217007. −0.952657 −0.476329 − 0.879267i \(-0.658033\pi\)
−0.476329 + 0.879267i \(0.658033\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 294060. 1.20253
\(144\) 0 0
\(145\) 540288. 2.13405
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −87816.0 −0.324047 −0.162023 − 0.986787i \(-0.551802\pi\)
−0.162023 + 0.986787i \(0.551802\pi\)
\(150\) 0 0
\(151\) 233059. 0.831809 0.415904 − 0.909408i \(-0.363465\pi\)
0.415904 + 0.909408i \(0.363465\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 414960. 1.38732
\(156\) 0 0
\(157\) 343502. 1.11219 0.556096 − 0.831118i \(-0.312298\pi\)
0.556096 + 0.831118i \(0.312298\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −108852. −0.330957
\(162\) 0 0
\(163\) 367729. 1.08407 0.542037 − 0.840355i \(-0.317653\pi\)
0.542037 + 0.840355i \(0.317653\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 79068.0 0.219386 0.109693 − 0.993965i \(-0.465013\pi\)
0.109693 + 0.993965i \(0.465013\pi\)
\(168\) 0 0
\(169\) 342732. 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 460992. 1.17106 0.585529 − 0.810652i \(-0.300887\pi\)
0.585529 + 0.810652i \(0.300887\pi\)
\(174\) 0 0
\(175\) 758683. 1.87269
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −210168. −0.490269 −0.245134 − 0.969489i \(-0.578832\pi\)
−0.245134 + 0.969489i \(0.578832\pi\)
\(180\) 0 0
\(181\) 427025. 0.968851 0.484425 − 0.874833i \(-0.339029\pi\)
0.484425 + 0.874833i \(0.339029\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 319620. 0.686601
\(186\) 0 0
\(187\) −588816. −1.23133
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 476196. 0.944501 0.472250 − 0.881464i \(-0.343442\pi\)
0.472250 + 0.881464i \(0.343442\pi\)
\(192\) 0 0
\(193\) −468505. −0.905359 −0.452680 − 0.891673i \(-0.649532\pi\)
−0.452680 + 0.891673i \(0.649532\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 713340. 1.30958 0.654788 − 0.755812i \(-0.272758\pi\)
0.654788 + 0.755812i \(0.272758\pi\)
\(198\) 0 0
\(199\) 381877. 0.683582 0.341791 − 0.939776i \(-0.388966\pi\)
0.341791 + 0.939776i \(0.388966\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.24138e6 −2.11428
\(204\) 0 0
\(205\) −1.04832e6 −1.74224
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 27492.0 0.0435352
\(210\) 0 0
\(211\) 521317. 0.806113 0.403056 − 0.915175i \(-0.367948\pi\)
0.403056 + 0.915175i \(0.367948\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −414624. −0.611728
\(216\) 0 0
\(217\) −953420. −1.37447
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.42974e6 −1.96914
\(222\) 0 0
\(223\) −511988. −0.689442 −0.344721 − 0.938705i \(-0.612026\pi\)
−0.344721 + 0.938705i \(0.612026\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.01580e6 1.30841 0.654205 − 0.756318i \(-0.273004\pi\)
0.654205 + 0.756318i \(0.273004\pi\)
\(228\) 0 0
\(229\) 1.26435e6 1.59323 0.796613 − 0.604490i \(-0.206623\pi\)
0.796613 + 0.604490i \(0.206623\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 676944. 0.816889 0.408444 − 0.912783i \(-0.366071\pi\)
0.408444 + 0.912783i \(0.366071\pi\)
\(234\) 0 0
\(235\) −682416. −0.806083
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −174696. −0.197828 −0.0989141 − 0.995096i \(-0.531537\pi\)
−0.0989141 + 0.995096i \(0.531537\pi\)
\(240\) 0 0
\(241\) 73121.0 0.0810960 0.0405480 − 0.999178i \(-0.487090\pi\)
0.0405480 + 0.999178i \(0.487090\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.71713e6 −1.82763
\(246\) 0 0
\(247\) 66755.0 0.0696212
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −701424. −0.702743 −0.351371 − 0.936236i \(-0.614285\pi\)
−0.351371 + 0.936236i \(0.614285\pi\)
\(252\) 0 0
\(253\) −196272. −0.192778
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −260040. −0.245588 −0.122794 − 0.992432i \(-0.539185\pi\)
−0.122794 + 0.992432i \(0.539185\pi\)
\(258\) 0 0
\(259\) −734365. −0.680241
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.29065e6 −1.15058 −0.575292 − 0.817948i \(-0.695112\pi\)
−0.575292 + 0.817948i \(0.695112\pi\)
\(264\) 0 0
\(265\) −2.78813e6 −2.43892
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.03944e6 −1.71842 −0.859210 − 0.511623i \(-0.829045\pi\)
−0.859210 + 0.511623i \(0.829045\pi\)
\(270\) 0 0
\(271\) 91987.0 0.0760857 0.0380429 − 0.999276i \(-0.487888\pi\)
0.0380429 + 0.999276i \(0.487888\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.36799e6 1.09081
\(276\) 0 0
\(277\) 533210. 0.417541 0.208770 − 0.977965i \(-0.433054\pi\)
0.208770 + 0.977965i \(0.433054\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.45344e6 1.09807 0.549037 − 0.835798i \(-0.314995\pi\)
0.549037 + 0.835798i \(0.314995\pi\)
\(282\) 0 0
\(283\) 776368. 0.576238 0.288119 − 0.957595i \(-0.406970\pi\)
0.288119 + 0.957595i \(0.406970\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.40864e6 1.72610
\(288\) 0 0
\(289\) 1.44301e6 1.01630
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.34589e6 1.59639 0.798195 − 0.602399i \(-0.205788\pi\)
0.798195 + 0.602399i \(0.205788\pi\)
\(294\) 0 0
\(295\) −3.56933e6 −2.38798
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −476580. −0.308289
\(300\) 0 0
\(301\) 952648. 0.606061
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.49797e6 0.922049
\(306\) 0 0
\(307\) −40736.0 −0.0246679 −0.0123340 − 0.999924i \(-0.503926\pi\)
−0.0123340 + 0.999924i \(0.503926\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.13524e6 0.665557 0.332778 − 0.943005i \(-0.392014\pi\)
0.332778 + 0.943005i \(0.392014\pi\)
\(312\) 0 0
\(313\) −3.01840e6 −1.74147 −0.870734 − 0.491754i \(-0.836356\pi\)
−0.870734 + 0.491754i \(0.836356\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 874200. 0.488610 0.244305 − 0.969698i \(-0.421440\pi\)
0.244305 + 0.969698i \(0.421440\pi\)
\(318\) 0 0
\(319\) −2.23834e6 −1.23154
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −133668. −0.0712888
\(324\) 0 0
\(325\) 3.32170e6 1.74442
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.56793e6 0.798615
\(330\) 0 0
\(331\) 336361. 0.168747 0.0843734 − 0.996434i \(-0.473111\pi\)
0.0843734 + 0.996434i \(0.473111\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.68672e6 −2.76853
\(336\) 0 0
\(337\) −1.10932e6 −0.532088 −0.266044 − 0.963961i \(-0.585717\pi\)
−0.266044 + 0.963961i \(0.585717\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.71912e6 −0.800609
\(342\) 0 0
\(343\) 701555. 0.321978
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10200.0 0.00454754 0.00227377 − 0.999997i \(-0.499276\pi\)
0.00227377 + 0.999997i \(0.499276\pi\)
\(348\) 0 0
\(349\) −4.09206e6 −1.79837 −0.899184 − 0.437571i \(-0.855839\pi\)
−0.899184 + 0.437571i \(0.855839\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 643512. 0.274865 0.137433 − 0.990511i \(-0.456115\pi\)
0.137433 + 0.990511i \(0.456115\pi\)
\(354\) 0 0
\(355\) −2.36477e6 −0.995904
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 665892. 0.272689 0.136345 − 0.990661i \(-0.456465\pi\)
0.136345 + 0.990661i \(0.456465\pi\)
\(360\) 0 0
\(361\) −2.46986e6 −0.997480
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.17390e6 0.461210
\(366\) 0 0
\(367\) −4.91773e6 −1.90590 −0.952949 − 0.303131i \(-0.901968\pi\)
−0.952949 + 0.303131i \(0.901968\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.40606e6 2.41633
\(372\) 0 0
\(373\) −593461. −0.220862 −0.110431 − 0.993884i \(-0.535223\pi\)
−0.110431 + 0.993884i \(0.535223\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.43504e6 −1.96947
\(378\) 0 0
\(379\) 4.60257e6 1.64590 0.822948 − 0.568116i \(-0.192328\pi\)
0.822948 + 0.568116i \(0.192328\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.43338e6 1.54432 0.772161 − 0.635427i \(-0.219176\pi\)
0.772161 + 0.635427i \(0.219176\pi\)
\(384\) 0 0
\(385\) −5.64178e6 −1.93983
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.89560e6 −0.635146 −0.317573 − 0.948234i \(-0.602868\pi\)
−0.317573 + 0.948234i \(0.602868\pi\)
\(390\) 0 0
\(391\) 954288. 0.315673
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.05457e6 −2.27498
\(396\) 0 0
\(397\) −577762. −0.183981 −0.0919904 − 0.995760i \(-0.529323\pi\)
−0.0919904 + 0.995760i \(0.529323\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.44022e6 −1.37893 −0.689467 − 0.724318i \(-0.742155\pi\)
−0.689467 + 0.724318i \(0.742155\pi\)
\(402\) 0 0
\(403\) −4.17430e6 −1.28033
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.32414e6 −0.396230
\(408\) 0 0
\(409\) 1.04099e6 0.307709 0.153854 − 0.988094i \(-0.450831\pi\)
0.153854 + 0.988094i \(0.450831\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.20096e6 2.36586
\(414\) 0 0
\(415\) 2.80426e6 0.799277
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.28447e6 −0.357428 −0.178714 − 0.983901i \(-0.557194\pi\)
−0.178714 + 0.983901i \(0.557194\pi\)
\(420\) 0 0
\(421\) −105259. −0.0289437 −0.0144718 − 0.999895i \(-0.504607\pi\)
−0.0144718 + 0.999895i \(0.504607\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.65125e6 −1.78620
\(426\) 0 0
\(427\) −3.44177e6 −0.913507
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.39774e6 1.65895 0.829475 − 0.558544i \(-0.188640\pi\)
0.829475 + 0.558544i \(0.188640\pi\)
\(432\) 0 0
\(433\) 3.34584e6 0.857602 0.428801 − 0.903399i \(-0.358936\pi\)
0.428801 + 0.903399i \(0.358936\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −44556.0 −0.0111610
\(438\) 0 0
\(439\) 7.33745e6 1.81712 0.908561 − 0.417753i \(-0.137182\pi\)
0.908561 + 0.417753i \(0.137182\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.33063e6 −1.04844 −0.524218 − 0.851584i \(-0.675642\pi\)
−0.524218 + 0.851584i \(0.675642\pi\)
\(444\) 0 0
\(445\) 6.54091e6 1.56581
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.06544e6 0.717590 0.358795 − 0.933416i \(-0.383188\pi\)
0.358795 + 0.933416i \(0.383188\pi\)
\(450\) 0 0
\(451\) 4.34304e6 1.00543
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.36991e7 −3.10216
\(456\) 0 0
\(457\) −7.45638e6 −1.67008 −0.835040 − 0.550189i \(-0.814556\pi\)
−0.835040 + 0.550189i \(0.814556\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 613812. 0.134519 0.0672594 − 0.997736i \(-0.478574\pi\)
0.0672594 + 0.997736i \(0.478574\pi\)
\(462\) 0 0
\(463\) 3.49870e6 0.758497 0.379248 − 0.925295i \(-0.376183\pi\)
0.379248 + 0.925295i \(0.376183\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −714708. −0.151648 −0.0758240 − 0.997121i \(-0.524159\pi\)
−0.0758240 + 0.997121i \(0.524159\pi\)
\(468\) 0 0
\(469\) 1.30659e7 2.74288
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.71773e6 0.353022
\(474\) 0 0
\(475\) 310549. 0.0631533
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.56494e6 1.90477 0.952387 − 0.304893i \(-0.0986207\pi\)
0.952387 + 0.304893i \(0.0986207\pi\)
\(480\) 0 0
\(481\) −3.21522e6 −0.633649
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 174972. 0.0337765
\(486\) 0 0
\(487\) −2.06566e6 −0.394671 −0.197336 − 0.980336i \(-0.563229\pi\)
−0.197336 + 0.980336i \(0.563229\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.41871e6 0.452772 0.226386 − 0.974038i \(-0.427309\pi\)
0.226386 + 0.974038i \(0.427309\pi\)
\(492\) 0 0
\(493\) 1.08829e7 2.01664
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.43334e6 0.986678
\(498\) 0 0
\(499\) 1.24422e6 0.223690 0.111845 − 0.993726i \(-0.464324\pi\)
0.111845 + 0.993726i \(0.464324\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5.29304e6 −0.932794 −0.466397 − 0.884576i \(-0.654448\pi\)
−0.466397 + 0.884576i \(0.654448\pi\)
\(504\) 0 0
\(505\) −1.02010e7 −1.77997
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 817116. 0.139794 0.0698971 − 0.997554i \(-0.477733\pi\)
0.0698971 + 0.997554i \(0.477733\pi\)
\(510\) 0 0
\(511\) −2.69718e6 −0.456938
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.74835e6 1.45348
\(516\) 0 0
\(517\) 2.82715e6 0.465182
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.46777e6 0.559701 0.279851 − 0.960044i \(-0.409715\pi\)
0.279851 + 0.960044i \(0.409715\pi\)
\(522\) 0 0
\(523\) −7.79187e6 −1.24563 −0.622813 − 0.782371i \(-0.714010\pi\)
−0.622813 + 0.782371i \(0.714010\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.35848e6 1.31099
\(528\) 0 0
\(529\) −6.11825e6 −0.950578
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.05456e7 1.60788
\(534\) 0 0
\(535\) 5.13778e6 0.776052
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.11382e6 1.05470
\(540\) 0 0
\(541\) 5.77061e6 0.847674 0.423837 − 0.905739i \(-0.360683\pi\)
0.423837 + 0.905739i \(0.360683\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.49156e6 −1.22461
\(546\) 0 0
\(547\) −1.31754e7 −1.88277 −0.941385 − 0.337335i \(-0.890474\pi\)
−0.941385 + 0.337335i \(0.890474\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −508128. −0.0713008
\(552\) 0 0
\(553\) 1.62087e7 2.25391
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.10933e7 −1.51503 −0.757517 − 0.652815i \(-0.773588\pi\)
−0.757517 + 0.652815i \(0.773588\pi\)
\(558\) 0 0
\(559\) 4.17092e6 0.564550
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.66166e6 −0.619826 −0.309913 − 0.950765i \(-0.600300\pi\)
−0.309913 + 0.950765i \(0.600300\pi\)
\(564\) 0 0
\(565\) 5.58936e6 0.736616
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.40486e6 −0.311393 −0.155697 − 0.987805i \(-0.549762\pi\)
−0.155697 + 0.987805i \(0.549762\pi\)
\(570\) 0 0
\(571\) 7.90422e6 1.01454 0.507269 − 0.861788i \(-0.330655\pi\)
0.507269 + 0.861788i \(0.330655\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.21708e6 −0.279649
\(576\) 0 0
\(577\) −491893. −0.0615079 −0.0307540 − 0.999527i \(-0.509791\pi\)
−0.0307540 + 0.999527i \(0.509791\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.44311e6 −0.791873
\(582\) 0 0
\(583\) 1.15508e7 1.40748
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.66643e6 −0.918328 −0.459164 − 0.888352i \(-0.651851\pi\)
−0.459164 + 0.888352i \(0.651851\pi\)
\(588\) 0 0
\(589\) −390260. −0.0463517
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.44769e6 −0.986509 −0.493255 − 0.869885i \(-0.664193\pi\)
−0.493255 + 0.869885i \(0.664193\pi\)
\(594\) 0 0
\(595\) 2.74307e7 3.17647
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.40688e6 0.501839 0.250919 − 0.968008i \(-0.419267\pi\)
0.250919 + 0.968008i \(0.419267\pi\)
\(600\) 0 0
\(601\) −7.15509e6 −0.808033 −0.404017 − 0.914752i \(-0.632386\pi\)
−0.404017 + 0.914752i \(0.632386\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.35555e6 0.372713
\(606\) 0 0
\(607\) 3.84653e6 0.423738 0.211869 − 0.977298i \(-0.432045\pi\)
0.211869 + 0.977298i \(0.432045\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.86478e6 0.743915
\(612\) 0 0
\(613\) 3.91447e6 0.420748 0.210374 − 0.977621i \(-0.432532\pi\)
0.210374 + 0.977621i \(0.432532\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.55753e6 0.693470 0.346735 − 0.937963i \(-0.387290\pi\)
0.346735 + 0.937963i \(0.387290\pi\)
\(618\) 0 0
\(619\) −1.31044e6 −0.137465 −0.0687323 − 0.997635i \(-0.521895\pi\)
−0.0687323 + 0.997635i \(0.521895\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.50285e7 −1.55130
\(624\) 0 0
\(625\) −6.59724e6 −0.675557
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.43806e6 0.648826
\(630\) 0 0
\(631\) −9.61959e6 −0.961796 −0.480898 − 0.876776i \(-0.659689\pi\)
−0.480898 + 0.876776i \(0.659689\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.07880e7 −1.06171
\(636\) 0 0
\(637\) 1.72735e7 1.68668
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.13228e6 0.493362 0.246681 − 0.969097i \(-0.420660\pi\)
0.246681 + 0.969097i \(0.420660\pi\)
\(642\) 0 0
\(643\) 1.22386e7 1.16735 0.583677 − 0.811986i \(-0.301613\pi\)
0.583677 + 0.811986i \(0.301613\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.25686e7 −1.18039 −0.590196 − 0.807260i \(-0.700950\pi\)
−0.590196 + 0.807260i \(0.700950\pi\)
\(648\) 0 0
\(649\) 1.47872e7 1.37808
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −221016. −0.0202834 −0.0101417 − 0.999949i \(-0.503228\pi\)
−0.0101417 + 0.999949i \(0.503228\pi\)
\(654\) 0 0
\(655\) −6.48749e6 −0.590845
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.60623e7 −1.44077 −0.720385 − 0.693575i \(-0.756035\pi\)
−0.720385 + 0.693575i \(0.756035\pi\)
\(660\) 0 0
\(661\) −1.38939e7 −1.23686 −0.618431 − 0.785839i \(-0.712231\pi\)
−0.618431 + 0.785839i \(0.712231\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.28075e6 −0.112308
\(666\) 0 0
\(667\) 3.62765e6 0.315726
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.20588e6 −0.532105
\(672\) 0 0
\(673\) −5.74108e6 −0.488603 −0.244301 − 0.969699i \(-0.578559\pi\)
−0.244301 + 0.969699i \(0.578559\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.07448e7 −1.73955 −0.869775 − 0.493448i \(-0.835736\pi\)
−0.869775 + 0.493448i \(0.835736\pi\)
\(678\) 0 0
\(679\) −402019. −0.0334636
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.96982e7 1.61575 0.807876 − 0.589353i \(-0.200617\pi\)
0.807876 + 0.589353i \(0.200617\pi\)
\(684\) 0 0
\(685\) 7.78882e6 0.634227
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.80472e7 2.25083
\(690\) 0 0
\(691\) 1.60244e7 1.27669 0.638345 − 0.769750i \(-0.279619\pi\)
0.638345 + 0.769750i \(0.279619\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.82286e7 1.43150
\(696\) 0 0
\(697\) −2.11162e7 −1.64639
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8.68792e6 −0.667760 −0.333880 − 0.942616i \(-0.608358\pi\)
−0.333880 + 0.942616i \(0.608358\pi\)
\(702\) 0 0
\(703\) −300595. −0.0229400
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.34379e7 1.76348
\(708\) 0 0
\(709\) 1.67076e6 0.124824 0.0624122 − 0.998050i \(-0.480121\pi\)
0.0624122 + 0.998050i \(0.480121\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.78616e6 0.205250
\(714\) 0 0
\(715\) −2.47010e7 −1.80697
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.04148e6 0.0751327 0.0375663 − 0.999294i \(-0.488039\pi\)
0.0375663 + 0.999294i \(0.488039\pi\)
\(720\) 0 0
\(721\) −2.01004e7 −1.44001
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.52842e7 −1.78650
\(726\) 0 0
\(727\) −2.14851e7 −1.50765 −0.753826 − 0.657074i \(-0.771794\pi\)
−0.753826 + 0.657074i \(0.771794\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.35171e6 −0.578072
\(732\) 0 0
\(733\) 8.51410e6 0.585300 0.292650 − 0.956220i \(-0.405463\pi\)
0.292650 + 0.956220i \(0.405463\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.35593e7 1.59769
\(738\) 0 0
\(739\) −6.84992e6 −0.461397 −0.230698 − 0.973025i \(-0.574101\pi\)
−0.230698 + 0.973025i \(0.574101\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.39175e7 1.58944 0.794721 − 0.606975i \(-0.207617\pi\)
0.794721 + 0.606975i \(0.207617\pi\)
\(744\) 0 0
\(745\) 7.37654e6 0.486925
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.18047e7 −0.768862
\(750\) 0 0
\(751\) 4.23726e6 0.274148 0.137074 − 0.990561i \(-0.456230\pi\)
0.137074 + 0.990561i \(0.456230\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.95770e7 −1.24991
\(756\) 0 0
\(757\) 4.65548e6 0.295274 0.147637 − 0.989042i \(-0.452833\pi\)
0.147637 + 0.989042i \(0.452833\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.28282e7 0.802981 0.401490 − 0.915863i \(-0.368492\pi\)
0.401490 + 0.915863i \(0.368492\pi\)
\(762\) 0 0
\(763\) 1.95104e7 1.21326
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.59057e7 2.20382
\(768\) 0 0
\(769\) −1.61739e7 −0.986279 −0.493140 − 0.869950i \(-0.664151\pi\)
−0.493140 + 0.869950i \(0.664151\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.87208e7 1.12687 0.563437 − 0.826159i \(-0.309479\pi\)
0.563437 + 0.826159i \(0.309479\pi\)
\(774\) 0 0
\(775\) −1.94191e7 −1.16138
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 985920. 0.0582101
\(780\) 0 0
\(781\) 9.79690e6 0.574726
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.88542e7 −1.67122
\(786\) 0 0
\(787\) −2.43159e7 −1.39944 −0.699720 − 0.714418i \(-0.746692\pi\)
−0.699720 + 0.714418i \(0.746692\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.28422e7 −0.729792
\(792\) 0 0
\(793\) −1.50689e7 −0.850938
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.02221e7 1.68531 0.842653 − 0.538457i \(-0.180993\pi\)
0.842653 + 0.538457i \(0.180993\pi\)
\(798\) 0 0
\(799\) −1.37458e7 −0.761734
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.86330e6 −0.266160
\(804\) 0 0
\(805\) 9.14357e6 0.497309
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.56338e6 −0.406298 −0.203149 − 0.979148i \(-0.565118\pi\)
−0.203149 + 0.979148i \(0.565118\pi\)
\(810\) 0 0
\(811\) −2.05032e7 −1.09464 −0.547318 − 0.836925i \(-0.684351\pi\)
−0.547318 + 0.836925i \(0.684351\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3.08892e7 −1.62897
\(816\) 0 0
\(817\) 389944. 0.0204384
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.04436e7 0.540745 0.270373 − 0.962756i \(-0.412853\pi\)
0.270373 + 0.962756i \(0.412853\pi\)
\(822\) 0 0
\(823\) −230021. −0.0118377 −0.00591886 − 0.999982i \(-0.501884\pi\)
−0.00591886 + 0.999982i \(0.501884\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5.06437e6 −0.257491 −0.128745 − 0.991678i \(-0.541095\pi\)
−0.128745 + 0.991678i \(0.541095\pi\)
\(828\) 0 0
\(829\) −1.10835e7 −0.560131 −0.280065 − 0.959981i \(-0.590356\pi\)
−0.280065 + 0.959981i \(0.590356\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.45879e7 −1.72708
\(834\) 0 0
\(835\) −6.64171e6 −0.329658
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −480504. −0.0235663 −0.0117832 − 0.999931i \(-0.503751\pi\)
−0.0117832 + 0.999931i \(0.503751\pi\)
\(840\) 0 0
\(841\) 2.08595e7 1.01698
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.87895e7 −1.38705
\(846\) 0 0
\(847\) −7.70977e6 −0.369261
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.14602e6 0.101580
\(852\) 0 0
\(853\) −2.97168e7 −1.39839 −0.699197 − 0.714929i \(-0.746459\pi\)
−0.699197 + 0.714929i \(0.746459\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.79771e7 1.76632 0.883161 − 0.469071i \(-0.155411\pi\)
0.883161 + 0.469071i \(0.155411\pi\)
\(858\) 0 0
\(859\) −1.69655e7 −0.784482 −0.392241 − 0.919863i \(-0.628300\pi\)
−0.392241 + 0.919863i \(0.628300\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.59102e7 −1.18425 −0.592127 − 0.805845i \(-0.701711\pi\)
−0.592127 + 0.805845i \(0.701711\pi\)
\(864\) 0 0
\(865\) −3.87233e7 −1.75967
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.92261e7 1.31287
\(870\) 0 0
\(871\) 5.72057e7 2.55502
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.30669e7 −0.576968
\(876\) 0 0
\(877\) 3.31231e7 1.45422 0.727112 − 0.686519i \(-0.240862\pi\)
0.727112 + 0.686519i \(0.240862\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4.10627e6 0.178241 0.0891205 − 0.996021i \(-0.471594\pi\)
0.0891205 + 0.996021i \(0.471594\pi\)
\(882\) 0 0
\(883\) −763751. −0.0329648 −0.0164824 − 0.999864i \(-0.505247\pi\)
−0.0164824 + 0.999864i \(0.505247\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.90550e7 −0.813203 −0.406602 − 0.913606i \(-0.633286\pi\)
−0.406602 + 0.913606i \(0.633286\pi\)
\(888\) 0 0
\(889\) 2.47866e7 1.05187
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 641796. 0.0269320
\(894\) 0 0
\(895\) 1.76541e7 0.736696
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.17741e7 1.31121
\(900\) 0 0
\(901\) −5.61609e7 −2.30474
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.58701e7 −1.45583
\(906\) 0 0
\(907\) 8.30145e6 0.335070 0.167535 − 0.985866i \(-0.446419\pi\)
0.167535 + 0.985866i \(0.446419\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.08394e7 −0.831936 −0.415968 − 0.909379i \(-0.636557\pi\)
−0.415968 + 0.909379i \(0.636557\pi\)
\(912\) 0 0
\(913\) −1.16176e7 −0.461255
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.49058e7 0.585371
\(918\) 0 0
\(919\) −3.91396e7 −1.52872 −0.764359 − 0.644791i \(-0.776944\pi\)
−0.764359 + 0.644791i \(0.776944\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.37884e7 0.919098
\(924\) 0 0
\(925\) −1.49575e7 −0.574782
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.78645e7 −1.43944 −0.719720 − 0.694265i \(-0.755730\pi\)
−0.719720 + 0.694265i \(0.755730\pi\)
\(930\) 0 0
\(931\) 1.61492e6 0.0610627
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.94605e7 1.85025
\(936\) 0 0
\(937\) 1.60352e6 0.0596659 0.0298330 − 0.999555i \(-0.490502\pi\)
0.0298330 + 0.999555i \(0.490502\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.65683e6 −0.171442 −0.0857208 − 0.996319i \(-0.527319\pi\)
−0.0857208 + 0.996319i \(0.527319\pi\)
\(942\) 0 0
\(943\) −7.03872e6 −0.257759
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.85315e7 −1.03383 −0.516915 − 0.856037i \(-0.672920\pi\)
−0.516915 + 0.856037i \(0.672920\pi\)
\(948\) 0 0
\(949\) −1.18089e7 −0.425641
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.38479e7 −1.92060 −0.960299 − 0.278972i \(-0.910006\pi\)
−0.960299 + 0.278972i \(0.910006\pi\)
\(954\) 0 0
\(955\) −4.00005e7 −1.41924
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.78957e7 −0.628352
\(960\) 0 0
\(961\) −4.22555e6 −0.147596
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3.93544e7 1.36043
\(966\) 0 0
\(967\) 2.03972e7 0.701463 0.350732 − 0.936476i \(-0.385933\pi\)
0.350732 + 0.936476i \(0.385933\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.12267e7 0.382124 0.191062 − 0.981578i \(-0.438807\pi\)
0.191062 + 0.981578i \(0.438807\pi\)
\(972\) 0 0
\(973\) −4.18824e7 −1.41824
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.41594e7 −1.14492 −0.572458 − 0.819934i \(-0.694010\pi\)
−0.572458 + 0.819934i \(0.694010\pi\)
\(978\) 0 0
\(979\) −2.70981e7 −0.903611
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.80138e7 1.58483 0.792414 − 0.609984i \(-0.208824\pi\)
0.792414 + 0.609984i \(0.208824\pi\)
\(984\) 0 0
\(985\) −5.99206e7 −1.96782
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.78390e6 −0.0905031
\(990\) 0 0
\(991\) −3.73224e7 −1.20722 −0.603609 − 0.797280i \(-0.706271\pi\)
−0.603609 + 0.797280i \(0.706271\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3.20777e7 −1.02718
\(996\) 0 0
\(997\) 1.81971e7 0.579781 0.289890 − 0.957060i \(-0.406381\pi\)
0.289890 + 0.957060i \(0.406381\pi\)
\(998\) 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 432.6.a.a.1.1 1
3.2 odd 2 432.6.a.j.1.1 1
4.3 odd 2 54.6.a.d.1.1 yes 1
12.11 even 2 54.6.a.c.1.1 ✓ 1
36.7 odd 6 162.6.c.f.109.1 2
36.11 even 6 162.6.c.g.109.1 2
36.23 even 6 162.6.c.g.55.1 2
36.31 odd 6 162.6.c.f.55.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.6.a.c.1.1 ✓ 1 12.11 even 2
54.6.a.d.1.1 yes 1 4.3 odd 2
162.6.c.f.55.1 2 36.31 odd 6
162.6.c.f.109.1 2 36.7 odd 6
162.6.c.g.55.1 2 36.23 even 6
162.6.c.g.109.1 2 36.11 even 6
432.6.a.a.1.1 1 1.1 even 1 trivial
432.6.a.j.1.1 1 3.2 odd 2