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Properties

Label 720.6.a.x.1.1
Level $720$
Weight $6$
Character 720.1
Self dual yes
Analytic conductor $115.476$
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] = [720,6,Mod(1,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, 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("720.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.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: \(115.476350265\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+25.0000 q^{5} +244.000 q^{7} +O(q^{10})\) \(q+25.0000 q^{5} +244.000 q^{7} -144.000 q^{11} +50.0000 q^{13} +1914.00 q^{17} -140.000 q^{19} -624.000 q^{23} +625.000 q^{25} +3126.00 q^{29} +5176.00 q^{31} +6100.00 q^{35} +15698.0 q^{37} -12570.0 q^{41} -11516.0 q^{43} -26736.0 q^{47} +42729.0 q^{49} +19158.0 q^{53} -3600.00 q^{55} +27984.0 q^{59} +22022.0 q^{61} +1250.00 q^{65} +12676.0 q^{67} -59520.0 q^{71} -67102.0 q^{73} -35136.0 q^{77} -11048.0 q^{79} -115284. q^{83} +47850.0 q^{85} -73650.0 q^{89} +12200.0 q^{91} -3500.00 q^{95} +35522.0 q^{97} +O(q^{100})\)

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
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 244.000 1.88211 0.941054 − 0.338255i \(-0.109837\pi\)
0.941054 + 0.338255i \(0.109837\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −144.000 −0.358823 −0.179412 − 0.983774i \(-0.557419\pi\)
−0.179412 + 0.983774i \(0.557419\pi\)
\(12\) 0 0
\(13\) 50.0000 0.0820562 0.0410281 − 0.999158i \(-0.486937\pi\)
0.0410281 + 0.999158i \(0.486937\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1914.00 1.60627 0.803137 − 0.595794i \(-0.203163\pi\)
0.803137 + 0.595794i \(0.203163\pi\)
\(18\) 0 0
\(19\) −140.000 −0.0889701 −0.0444850 − 0.999010i \(-0.514165\pi\)
−0.0444850 + 0.999010i \(0.514165\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −624.000 −0.245960 −0.122980 − 0.992409i \(-0.539245\pi\)
−0.122980 + 0.992409i \(0.539245\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3126.00 0.690230 0.345115 − 0.938560i \(-0.387840\pi\)
0.345115 + 0.938560i \(0.387840\pi\)
\(30\) 0 0
\(31\) 5176.00 0.967364 0.483682 − 0.875244i \(-0.339299\pi\)
0.483682 + 0.875244i \(0.339299\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6100.00 0.841705
\(36\) 0 0
\(37\) 15698.0 1.88512 0.942562 − 0.334031i \(-0.108409\pi\)
0.942562 + 0.334031i \(0.108409\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12570.0 −1.16782 −0.583910 − 0.811819i \(-0.698478\pi\)
−0.583910 + 0.811819i \(0.698478\pi\)
\(42\) 0 0
\(43\) −11516.0 −0.949796 −0.474898 − 0.880041i \(-0.657515\pi\)
−0.474898 + 0.880041i \(0.657515\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −26736.0 −1.76544 −0.882718 − 0.469904i \(-0.844289\pi\)
−0.882718 + 0.469904i \(0.844289\pi\)
\(48\) 0 0
\(49\) 42729.0 2.54233
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 19158.0 0.936829 0.468415 − 0.883509i \(-0.344825\pi\)
0.468415 + 0.883509i \(0.344825\pi\)
\(54\) 0 0
\(55\) −3600.00 −0.160471
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 27984.0 1.04660 0.523299 − 0.852149i \(-0.324701\pi\)
0.523299 + 0.852149i \(0.324701\pi\)
\(60\) 0 0
\(61\) 22022.0 0.757761 0.378880 − 0.925446i \(-0.376309\pi\)
0.378880 + 0.925446i \(0.376309\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1250.00 0.0366967
\(66\) 0 0
\(67\) 12676.0 0.344981 0.172491 − 0.985011i \(-0.444819\pi\)
0.172491 + 0.985011i \(0.444819\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −59520.0 −1.40125 −0.700627 − 0.713527i \(-0.747096\pi\)
−0.700627 + 0.713527i \(0.747096\pi\)
\(72\) 0 0
\(73\) −67102.0 −1.47377 −0.736883 − 0.676021i \(-0.763703\pi\)
−0.736883 + 0.676021i \(0.763703\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −35136.0 −0.675345
\(78\) 0 0
\(79\) −11048.0 −0.199166 −0.0995832 − 0.995029i \(-0.531751\pi\)
−0.0995832 + 0.995029i \(0.531751\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −115284. −1.83685 −0.918425 − 0.395595i \(-0.870539\pi\)
−0.918425 + 0.395595i \(0.870539\pi\)
\(84\) 0 0
\(85\) 47850.0 0.718348
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −73650.0 −0.985593 −0.492797 − 0.870145i \(-0.664025\pi\)
−0.492797 + 0.870145i \(0.664025\pi\)
\(90\) 0 0
\(91\) 12200.0 0.154439
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3500.00 −0.0397886
\(96\) 0 0
\(97\) 35522.0 0.383326 0.191663 − 0.981461i \(-0.438612\pi\)
0.191663 + 0.981461i \(0.438612\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 112062. 1.09309 0.546544 − 0.837431i \(-0.315943\pi\)
0.546544 + 0.837431i \(0.315943\pi\)
\(102\) 0 0
\(103\) 106516. 0.989286 0.494643 − 0.869096i \(-0.335299\pi\)
0.494643 + 0.869096i \(0.335299\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −29292.0 −0.247337 −0.123669 − 0.992324i \(-0.539466\pi\)
−0.123669 + 0.992324i \(0.539466\pi\)
\(108\) 0 0
\(109\) 125318. 1.01029 0.505146 − 0.863034i \(-0.331439\pi\)
0.505146 + 0.863034i \(0.331439\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −166638. −1.22766 −0.613830 − 0.789438i \(-0.710372\pi\)
−0.613830 + 0.789438i \(0.710372\pi\)
\(114\) 0 0
\(115\) −15600.0 −0.109997
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 467016. 3.02318
\(120\) 0 0
\(121\) −140315. −0.871246
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 201724. 1.10981 0.554905 − 0.831914i \(-0.312755\pi\)
0.554905 + 0.831914i \(0.312755\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 131472. 0.669353 0.334676 − 0.942333i \(-0.391373\pi\)
0.334676 + 0.942333i \(0.391373\pi\)
\(132\) 0 0
\(133\) −34160.0 −0.167451
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 102042. 0.464491 0.232246 − 0.972657i \(-0.425393\pi\)
0.232246 + 0.972657i \(0.425393\pi\)
\(138\) 0 0
\(139\) 243604. 1.06942 0.534709 − 0.845036i \(-0.320421\pi\)
0.534709 + 0.845036i \(0.320421\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7200.00 −0.0294437
\(144\) 0 0
\(145\) 78150.0 0.308680
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 309462. 1.14194 0.570968 − 0.820972i \(-0.306568\pi\)
0.570968 + 0.820972i \(0.306568\pi\)
\(150\) 0 0
\(151\) 147160. 0.525227 0.262614 − 0.964901i \(-0.415416\pi\)
0.262614 + 0.964901i \(0.415416\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 129400. 0.432618
\(156\) 0 0
\(157\) 268082. 0.867998 0.433999 − 0.900913i \(-0.357102\pi\)
0.433999 + 0.900913i \(0.357102\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −152256. −0.462924
\(162\) 0 0
\(163\) 276580. 0.815364 0.407682 − 0.913124i \(-0.366337\pi\)
0.407682 + 0.913124i \(0.366337\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −592272. −1.64335 −0.821675 − 0.569956i \(-0.806960\pi\)
−0.821675 + 0.569956i \(0.806960\pi\)
\(168\) 0 0
\(169\) −368793. −0.993267
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −29154.0 −0.0740599 −0.0370299 − 0.999314i \(-0.511790\pi\)
−0.0370299 + 0.999314i \(0.511790\pi\)
\(174\) 0 0
\(175\) 152500. 0.376422
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 131784. 0.307419 0.153709 − 0.988116i \(-0.450878\pi\)
0.153709 + 0.988116i \(0.450878\pi\)
\(180\) 0 0
\(181\) −297730. −0.675501 −0.337751 − 0.941236i \(-0.609666\pi\)
−0.337751 + 0.941236i \(0.609666\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 392450. 0.843053
\(186\) 0 0
\(187\) −275616. −0.576369
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 851784. 1.68945 0.844726 − 0.535198i \(-0.179763\pi\)
0.844726 + 0.535198i \(0.179763\pi\)
\(192\) 0 0
\(193\) 292394. 0.565035 0.282517 − 0.959262i \(-0.408831\pi\)
0.282517 + 0.959262i \(0.408831\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 869526. 1.59631 0.798155 − 0.602453i \(-0.205810\pi\)
0.798155 + 0.602453i \(0.205810\pi\)
\(198\) 0 0
\(199\) 143992. 0.257754 0.128877 − 0.991661i \(-0.458863\pi\)
0.128877 + 0.991661i \(0.458863\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 762744. 1.29909
\(204\) 0 0
\(205\) −314250. −0.522265
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 20160.0 0.0319246
\(210\) 0 0
\(211\) −836420. −1.29336 −0.646678 − 0.762763i \(-0.723842\pi\)
−0.646678 + 0.762763i \(0.723842\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −287900. −0.424762
\(216\) 0 0
\(217\) 1.26294e6 1.82068
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 95700.0 0.131805
\(222\) 0 0
\(223\) −1.22090e6 −1.64406 −0.822031 − 0.569443i \(-0.807159\pi\)
−0.822031 + 0.569443i \(0.807159\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −173580. −0.223581 −0.111791 − 0.993732i \(-0.535659\pi\)
−0.111791 + 0.993732i \(0.535659\pi\)
\(228\) 0 0
\(229\) 120806. 0.152230 0.0761149 − 0.997099i \(-0.475748\pi\)
0.0761149 + 0.997099i \(0.475748\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −592590. −0.715096 −0.357548 − 0.933895i \(-0.616387\pi\)
−0.357548 + 0.933895i \(0.616387\pi\)
\(234\) 0 0
\(235\) −668400. −0.789527
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 706008. 0.799493 0.399747 − 0.916626i \(-0.369098\pi\)
0.399747 + 0.916626i \(0.369098\pi\)
\(240\) 0 0
\(241\) 1.56154e6 1.73185 0.865924 − 0.500175i \(-0.166731\pi\)
0.865924 + 0.500175i \(0.166731\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.06822e6 1.13697
\(246\) 0 0
\(247\) −7000.00 −0.00730055
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.48471e6 −1.48750 −0.743752 − 0.668456i \(-0.766955\pi\)
−0.743752 + 0.668456i \(0.766955\pi\)
\(252\) 0 0
\(253\) 89856.0 0.0882563
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −624558. −0.589848 −0.294924 − 0.955521i \(-0.595294\pi\)
−0.294924 + 0.955521i \(0.595294\pi\)
\(258\) 0 0
\(259\) 3.83031e6 3.54801
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 778896. 0.694369 0.347184 − 0.937797i \(-0.387138\pi\)
0.347184 + 0.937797i \(0.387138\pi\)
\(264\) 0 0
\(265\) 478950. 0.418963
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 11574.0 0.00975220 0.00487610 − 0.999988i \(-0.498448\pi\)
0.00487610 + 0.999988i \(0.498448\pi\)
\(270\) 0 0
\(271\) −118064. −0.0976550 −0.0488275 − 0.998807i \(-0.515548\pi\)
−0.0488275 + 0.998807i \(0.515548\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −90000.0 −0.0717647
\(276\) 0 0
\(277\) 659282. 0.516264 0.258132 − 0.966110i \(-0.416893\pi\)
0.258132 + 0.966110i \(0.416893\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.49057e6 1.12613 0.563064 − 0.826413i \(-0.309622\pi\)
0.563064 + 0.826413i \(0.309622\pi\)
\(282\) 0 0
\(283\) 1.13129e6 0.839670 0.419835 − 0.907600i \(-0.362088\pi\)
0.419835 + 0.907600i \(0.362088\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.06708e6 −2.19796
\(288\) 0 0
\(289\) 2.24354e6 1.58012
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −896298. −0.609935 −0.304967 − 0.952363i \(-0.598646\pi\)
−0.304967 + 0.952363i \(0.598646\pi\)
\(294\) 0 0
\(295\) 699600. 0.468053
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −31200.0 −0.0201826
\(300\) 0 0
\(301\) −2.80990e6 −1.78762
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 550550. 0.338881
\(306\) 0 0
\(307\) 1.38641e6 0.839550 0.419775 − 0.907628i \(-0.362109\pi\)
0.419775 + 0.907628i \(0.362109\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.19238e6 1.87160 0.935802 − 0.352525i \(-0.114677\pi\)
0.935802 + 0.352525i \(0.114677\pi\)
\(312\) 0 0
\(313\) 2.51683e6 1.45209 0.726045 − 0.687647i \(-0.241356\pi\)
0.726045 + 0.687647i \(0.241356\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.21897e6 1.24024 0.620118 − 0.784509i \(-0.287085\pi\)
0.620118 + 0.784509i \(0.287085\pi\)
\(318\) 0 0
\(319\) −450144. −0.247671
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −267960. −0.142910
\(324\) 0 0
\(325\) 31250.0 0.0164112
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.52358e6 −3.32274
\(330\) 0 0
\(331\) 27148.0 0.0136197 0.00680985 − 0.999977i \(-0.497832\pi\)
0.00680985 + 0.999977i \(0.497832\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 316900. 0.154280
\(336\) 0 0
\(337\) 2.19670e6 1.05365 0.526824 − 0.849974i \(-0.323383\pi\)
0.526824 + 0.849974i \(0.323383\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −745344. −0.347113
\(342\) 0 0
\(343\) 6.32497e6 2.90284
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −989652. −0.441224 −0.220612 − 0.975362i \(-0.570805\pi\)
−0.220612 + 0.975362i \(0.570805\pi\)
\(348\) 0 0
\(349\) −3.05055e6 −1.34065 −0.670325 − 0.742068i \(-0.733845\pi\)
−0.670325 + 0.742068i \(0.733845\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 339642. 0.145072 0.0725362 − 0.997366i \(-0.476891\pi\)
0.0725362 + 0.997366i \(0.476891\pi\)
\(354\) 0 0
\(355\) −1.48800e6 −0.626660
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.20678e6 −0.903696 −0.451848 − 0.892095i \(-0.649235\pi\)
−0.451848 + 0.892095i \(0.649235\pi\)
\(360\) 0 0
\(361\) −2.45650e6 −0.992084
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.67755e6 −0.659088
\(366\) 0 0
\(367\) −2.07132e6 −0.802752 −0.401376 − 0.915913i \(-0.631468\pi\)
−0.401376 + 0.915913i \(0.631468\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.67455e6 1.76321
\(372\) 0 0
\(373\) −1.94997e6 −0.725699 −0.362850 − 0.931848i \(-0.618196\pi\)
−0.362850 + 0.931848i \(0.618196\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 156300. 0.0566377
\(378\) 0 0
\(379\) −3.85003e6 −1.37678 −0.688392 − 0.725339i \(-0.741683\pi\)
−0.688392 + 0.725339i \(0.741683\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −67152.0 −0.0233917 −0.0116959 − 0.999932i \(-0.503723\pi\)
−0.0116959 + 0.999932i \(0.503723\pi\)
\(384\) 0 0
\(385\) −878400. −0.302023
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.32331e6 −1.44858 −0.724289 − 0.689496i \(-0.757832\pi\)
−0.724289 + 0.689496i \(0.757832\pi\)
\(390\) 0 0
\(391\) −1.19434e6 −0.395080
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −276200. −0.0890699
\(396\) 0 0
\(397\) 118298. 0.0376705 0.0188352 − 0.999823i \(-0.494004\pi\)
0.0188352 + 0.999823i \(0.494004\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.13901e6 0.974838 0.487419 − 0.873168i \(-0.337938\pi\)
0.487419 + 0.873168i \(0.337938\pi\)
\(402\) 0 0
\(403\) 258800. 0.0793783
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.26051e6 −0.676427
\(408\) 0 0
\(409\) −452614. −0.133789 −0.0668944 − 0.997760i \(-0.521309\pi\)
−0.0668944 + 0.997760i \(0.521309\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.82810e6 1.96981
\(414\) 0 0
\(415\) −2.88210e6 −0.821465
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.73579e6 1.03956 0.519778 − 0.854302i \(-0.326015\pi\)
0.519778 + 0.854302i \(0.326015\pi\)
\(420\) 0 0
\(421\) −1.87465e6 −0.515484 −0.257742 − 0.966214i \(-0.582978\pi\)
−0.257742 + 0.966214i \(0.582978\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.19625e6 0.321255
\(426\) 0 0
\(427\) 5.37337e6 1.42619
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.74019e6 −1.22914 −0.614572 − 0.788861i \(-0.710671\pi\)
−0.614572 + 0.788861i \(0.710671\pi\)
\(432\) 0 0
\(433\) −4.35377e6 −1.11595 −0.557976 − 0.829857i \(-0.688422\pi\)
−0.557976 + 0.829857i \(0.688422\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 87360.0 0.0218831
\(438\) 0 0
\(439\) −1.04929e6 −0.259856 −0.129928 − 0.991523i \(-0.541475\pi\)
−0.129928 + 0.991523i \(0.541475\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.00788e6 1.45449 0.727247 − 0.686375i \(-0.240799\pi\)
0.727247 + 0.686375i \(0.240799\pi\)
\(444\) 0 0
\(445\) −1.84125e6 −0.440771
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.37222e6 −0.321223 −0.160612 − 0.987018i \(-0.551347\pi\)
−0.160612 + 0.987018i \(0.551347\pi\)
\(450\) 0 0
\(451\) 1.81008e6 0.419041
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 305000. 0.0690671
\(456\) 0 0
\(457\) −389830. −0.0873142 −0.0436571 − 0.999047i \(-0.513901\pi\)
−0.0436571 + 0.999047i \(0.513901\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.15137e6 0.690633 0.345317 − 0.938486i \(-0.387771\pi\)
0.345317 + 0.938486i \(0.387771\pi\)
\(462\) 0 0
\(463\) −4.66939e6 −1.01230 −0.506148 − 0.862447i \(-0.668931\pi\)
−0.506148 + 0.862447i \(0.668931\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.92445e6 −1.04488 −0.522439 − 0.852677i \(-0.674978\pi\)
−0.522439 + 0.852677i \(0.674978\pi\)
\(468\) 0 0
\(469\) 3.09294e6 0.649292
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.65830e6 0.340809
\(474\) 0 0
\(475\) −87500.0 −0.0177940
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.03030e6 −0.802598 −0.401299 − 0.915947i \(-0.631441\pi\)
−0.401299 + 0.915947i \(0.631441\pi\)
\(480\) 0 0
\(481\) 784900. 0.154686
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 888050. 0.171429
\(486\) 0 0
\(487\) −4.14213e6 −0.791410 −0.395705 − 0.918378i \(-0.629500\pi\)
−0.395705 + 0.918378i \(0.629500\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.22854e6 −0.229977 −0.114988 − 0.993367i \(-0.536683\pi\)
−0.114988 + 0.993367i \(0.536683\pi\)
\(492\) 0 0
\(493\) 5.98316e6 1.10870
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.45229e7 −2.63731
\(498\) 0 0
\(499\) −3.64756e6 −0.655770 −0.327885 − 0.944718i \(-0.606336\pi\)
−0.327885 + 0.944718i \(0.606336\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.98454e6 −0.349735 −0.174867 − 0.984592i \(-0.555950\pi\)
−0.174867 + 0.984592i \(0.555950\pi\)
\(504\) 0 0
\(505\) 2.80155e6 0.488844
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.75852e6 0.985182 0.492591 − 0.870261i \(-0.336050\pi\)
0.492591 + 0.870261i \(0.336050\pi\)
\(510\) 0 0
\(511\) −1.63729e7 −2.77379
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.66290e6 0.442422
\(516\) 0 0
\(517\) 3.84998e6 0.633480
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.84008e6 1.10399 0.551997 − 0.833846i \(-0.313866\pi\)
0.551997 + 0.833846i \(0.313866\pi\)
\(522\) 0 0
\(523\) −7.26991e6 −1.16218 −0.581092 − 0.813838i \(-0.697374\pi\)
−0.581092 + 0.813838i \(0.697374\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.90686e6 1.55385
\(528\) 0 0
\(529\) −6.04697e6 −0.939504
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −628500. −0.0958269
\(534\) 0 0
\(535\) −732300. −0.110613
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.15298e6 −0.912249
\(540\) 0 0
\(541\) −1.88876e6 −0.277450 −0.138725 − 0.990331i \(-0.544300\pi\)
−0.138725 + 0.990331i \(0.544300\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.13295e6 0.451817
\(546\) 0 0
\(547\) 2.64867e6 0.378494 0.189247 − 0.981929i \(-0.439395\pi\)
0.189247 + 0.981929i \(0.439395\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −437640. −0.0614098
\(552\) 0 0
\(553\) −2.69571e6 −0.374853
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.82704e6 0.386095 0.193047 − 0.981189i \(-0.438163\pi\)
0.193047 + 0.981189i \(0.438163\pi\)
\(558\) 0 0
\(559\) −575800. −0.0779367
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.22050e6 1.22598 0.612990 − 0.790091i \(-0.289967\pi\)
0.612990 + 0.790091i \(0.289967\pi\)
\(564\) 0 0
\(565\) −4.16595e6 −0.549026
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.96705e6 0.384189 0.192094 − 0.981376i \(-0.438472\pi\)
0.192094 + 0.981376i \(0.438472\pi\)
\(570\) 0 0
\(571\) −1.56746e6 −0.201190 −0.100595 − 0.994927i \(-0.532075\pi\)
−0.100595 + 0.994927i \(0.532075\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −390000. −0.0491921
\(576\) 0 0
\(577\) −1.07923e7 −1.34951 −0.674754 − 0.738043i \(-0.735750\pi\)
−0.674754 + 0.738043i \(0.735750\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.81293e7 −3.45715
\(582\) 0 0
\(583\) −2.75875e6 −0.336156
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.34368e7 −1.60954 −0.804770 − 0.593586i \(-0.797712\pi\)
−0.804770 + 0.593586i \(0.797712\pi\)
\(588\) 0 0
\(589\) −724640. −0.0860665
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.53507e6 0.412821 0.206410 − 0.978465i \(-0.433822\pi\)
0.206410 + 0.978465i \(0.433822\pi\)
\(594\) 0 0
\(595\) 1.16754e7 1.35201
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.56850e6 −0.975749 −0.487874 − 0.872914i \(-0.662228\pi\)
−0.487874 + 0.872914i \(0.662228\pi\)
\(600\) 0 0
\(601\) −1.15733e7 −1.30699 −0.653493 − 0.756932i \(-0.726697\pi\)
−0.653493 + 0.756932i \(0.726697\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.50787e6 −0.389633
\(606\) 0 0
\(607\) −3.76651e6 −0.414923 −0.207461 − 0.978243i \(-0.566520\pi\)
−0.207461 + 0.978243i \(0.566520\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.33680e6 −0.144865
\(612\) 0 0
\(613\) 5.55106e6 0.596657 0.298328 − 0.954463i \(-0.403571\pi\)
0.298328 + 0.954463i \(0.403571\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.66393e6 −0.916225 −0.458113 − 0.888894i \(-0.651474\pi\)
−0.458113 + 0.888894i \(0.651474\pi\)
\(618\) 0 0
\(619\) 6.11780e6 0.641754 0.320877 − 0.947121i \(-0.396022\pi\)
0.320877 + 0.947121i \(0.396022\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.79706e7 −1.85499
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.00460e7 3.02803
\(630\) 0 0
\(631\) −4.11315e6 −0.411246 −0.205623 − 0.978631i \(-0.565922\pi\)
−0.205623 + 0.978631i \(0.565922\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.04310e6 0.496322
\(636\) 0 0
\(637\) 2.13645e6 0.208614
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −64674.0 −0.00621705 −0.00310853 − 0.999995i \(-0.500989\pi\)
−0.00310853 + 0.999995i \(0.500989\pi\)
\(642\) 0 0
\(643\) 2.42852e6 0.231640 0.115820 − 0.993270i \(-0.463050\pi\)
0.115820 + 0.993270i \(0.463050\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.43777e6 0.698525 0.349262 − 0.937025i \(-0.386432\pi\)
0.349262 + 0.937025i \(0.386432\pi\)
\(648\) 0 0
\(649\) −4.02970e6 −0.375544
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.99762e7 −1.83329 −0.916644 − 0.399706i \(-0.869112\pi\)
−0.916644 + 0.399706i \(0.869112\pi\)
\(654\) 0 0
\(655\) 3.28680e6 0.299344
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −742752. −0.0666239 −0.0333120 − 0.999445i \(-0.510605\pi\)
−0.0333120 + 0.999445i \(0.510605\pi\)
\(660\) 0 0
\(661\) −1.20838e7 −1.07573 −0.537863 − 0.843032i \(-0.680768\pi\)
−0.537863 + 0.843032i \(0.680768\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −854000. −0.0748865
\(666\) 0 0
\(667\) −1.95062e6 −0.169769
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.17117e6 −0.271902
\(672\) 0 0
\(673\) −7.14487e6 −0.608074 −0.304037 − 0.952660i \(-0.598335\pi\)
−0.304037 + 0.952660i \(0.598335\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.03255e7 −1.70440 −0.852198 − 0.523219i \(-0.824731\pi\)
−0.852198 + 0.523219i \(0.824731\pi\)
\(678\) 0 0
\(679\) 8.66737e6 0.721461
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6.65416e6 −0.545810 −0.272905 − 0.962041i \(-0.587984\pi\)
−0.272905 + 0.962041i \(0.587984\pi\)
\(684\) 0 0
\(685\) 2.55105e6 0.207727
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 957900. 0.0768727
\(690\) 0 0
\(691\) 1.11430e7 0.887784 0.443892 − 0.896080i \(-0.353597\pi\)
0.443892 + 0.896080i \(0.353597\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.09010e6 0.478258
\(696\) 0 0
\(697\) −2.40590e7 −1.87584
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.47407e7 −1.13299 −0.566493 − 0.824067i \(-0.691700\pi\)
−0.566493 + 0.824067i \(0.691700\pi\)
\(702\) 0 0
\(703\) −2.19772e6 −0.167720
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.73431e7 2.05731
\(708\) 0 0
\(709\) 2.01119e7 1.50258 0.751290 − 0.659973i \(-0.229432\pi\)
0.751290 + 0.659973i \(0.229432\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.22982e6 −0.237933
\(714\) 0 0
\(715\) −180000. −0.0131676
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 9.17933e6 0.662199 0.331100 − 0.943596i \(-0.392580\pi\)
0.331100 + 0.943596i \(0.392580\pi\)
\(720\) 0 0
\(721\) 2.59899e7 1.86194
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.95375e6 0.138046
\(726\) 0 0
\(727\) 1.72524e7 1.21064 0.605319 − 0.795983i \(-0.293046\pi\)
0.605319 + 0.795983i \(0.293046\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.20416e7 −1.52563
\(732\) 0 0
\(733\) 2.79936e7 1.92442 0.962209 − 0.272314i \(-0.0877888\pi\)
0.962209 + 0.272314i \(0.0877888\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.82534e6 −0.123787
\(738\) 0 0
\(739\) 6.96778e6 0.469335 0.234668 − 0.972076i \(-0.424600\pi\)
0.234668 + 0.972076i \(0.424600\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.35720e7 0.901929 0.450965 − 0.892542i \(-0.351080\pi\)
0.450965 + 0.892542i \(0.351080\pi\)
\(744\) 0 0
\(745\) 7.73655e6 0.510689
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7.14725e6 −0.465516
\(750\) 0 0
\(751\) −8.17647e6 −0.529013 −0.264506 − 0.964384i \(-0.585209\pi\)
−0.264506 + 0.964384i \(0.585209\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.67900e6 0.234889
\(756\) 0 0
\(757\) −8.60741e6 −0.545925 −0.272962 − 0.962025i \(-0.588003\pi\)
−0.272962 + 0.962025i \(0.588003\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.28596e7 1.43089 0.715446 − 0.698668i \(-0.246223\pi\)
0.715446 + 0.698668i \(0.246223\pi\)
\(762\) 0 0
\(763\) 3.05776e7 1.90148
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.39920e6 0.0858799
\(768\) 0 0
\(769\) 1.54790e7 0.943905 0.471952 − 0.881624i \(-0.343549\pi\)
0.471952 + 0.881624i \(0.343549\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.99671e7 1.80383 0.901915 − 0.431913i \(-0.142161\pi\)
0.901915 + 0.431913i \(0.142161\pi\)
\(774\) 0 0
\(775\) 3.23500e6 0.193473
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.75980e6 0.103901
\(780\) 0 0
\(781\) 8.57088e6 0.502803
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.70205e6 0.388180
\(786\) 0 0
\(787\) 1.06695e6 0.0614054 0.0307027 − 0.999529i \(-0.490225\pi\)
0.0307027 + 0.999529i \(0.490225\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.06597e7 −2.31059
\(792\) 0 0
\(793\) 1.10110e6 0.0621790
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.28008e6 0.294438 0.147219 − 0.989104i \(-0.452968\pi\)
0.147219 + 0.989104i \(0.452968\pi\)
\(798\) 0 0
\(799\) −5.11727e7 −2.83577
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.66269e6 0.528821
\(804\) 0 0
\(805\) −3.80640e6 −0.207026
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −5.68555e6 −0.305422 −0.152711 − 0.988271i \(-0.548800\pi\)
−0.152711 + 0.988271i \(0.548800\pi\)
\(810\) 0 0
\(811\) 2.71746e7 1.45081 0.725405 − 0.688322i \(-0.241652\pi\)
0.725405 + 0.688322i \(0.241652\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 6.91450e6 0.364642
\(816\) 0 0
\(817\) 1.61224e6 0.0845035
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.30951e7 −1.71359 −0.856793 − 0.515661i \(-0.827547\pi\)
−0.856793 + 0.515661i \(0.827547\pi\)
\(822\) 0 0
\(823\) −6.90631e6 −0.355424 −0.177712 − 0.984083i \(-0.556869\pi\)
−0.177712 + 0.984083i \(0.556869\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.37490e7 1.20748 0.603742 − 0.797180i \(-0.293676\pi\)
0.603742 + 0.797180i \(0.293676\pi\)
\(828\) 0 0
\(829\) −3.22011e7 −1.62736 −0.813681 − 0.581311i \(-0.802540\pi\)
−0.813681 + 0.581311i \(0.802540\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 8.17833e7 4.08368
\(834\) 0 0
\(835\) −1.48068e7 −0.734928
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.62821e7 −0.798554 −0.399277 − 0.916830i \(-0.630739\pi\)
−0.399277 + 0.916830i \(0.630739\pi\)
\(840\) 0 0
\(841\) −1.07393e7 −0.523582
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.21982e6 −0.444202
\(846\) 0 0
\(847\) −3.42369e7 −1.63978
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.79555e6 −0.463666
\(852\) 0 0
\(853\) −4.06728e7 −1.91395 −0.956977 − 0.290164i \(-0.906290\pi\)
−0.956977 + 0.290164i \(0.906290\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.99154e6 0.0926268 0.0463134 − 0.998927i \(-0.485253\pi\)
0.0463134 + 0.998927i \(0.485253\pi\)
\(858\) 0 0
\(859\) 3.62242e6 0.167500 0.0837502 − 0.996487i \(-0.473310\pi\)
0.0837502 + 0.996487i \(0.473310\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.38014e7 1.08786 0.543932 − 0.839129i \(-0.316935\pi\)
0.543932 + 0.839129i \(0.316935\pi\)
\(864\) 0 0
\(865\) −728850. −0.0331206
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.59091e6 0.0714655
\(870\) 0 0
\(871\) 633800. 0.0283078
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.81250e6 0.168341
\(876\) 0 0
\(877\) 1.08955e7 0.478352 0.239176 − 0.970976i \(-0.423123\pi\)
0.239176 + 0.970976i \(0.423123\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.79389e7 −0.778674 −0.389337 − 0.921095i \(-0.627296\pi\)
−0.389337 + 0.921095i \(0.627296\pi\)
\(882\) 0 0
\(883\) −7.70601e6 −0.332604 −0.166302 − 0.986075i \(-0.553183\pi\)
−0.166302 + 0.986075i \(0.553183\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.56776e7 −1.52260 −0.761301 − 0.648399i \(-0.775439\pi\)
−0.761301 + 0.648399i \(0.775439\pi\)
\(888\) 0 0
\(889\) 4.92207e7 2.08878
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.74304e6 0.157071
\(894\) 0 0
\(895\) 3.29460e6 0.137482
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.61802e7 0.667704
\(900\) 0 0
\(901\) 3.66684e7 1.50480
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.44325e6 −0.302093
\(906\) 0 0
\(907\) −1.90905e7 −0.770547 −0.385274 − 0.922802i \(-0.625893\pi\)
−0.385274 + 0.922802i \(0.625893\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 7.40453e6 0.295598 0.147799 − 0.989017i \(-0.452781\pi\)
0.147799 + 0.989017i \(0.452781\pi\)
\(912\) 0 0
\(913\) 1.66009e7 0.659105
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.20792e7 1.25979
\(918\) 0 0
\(919\) −2.47415e7 −0.966356 −0.483178 − 0.875522i \(-0.660518\pi\)
−0.483178 + 0.875522i \(0.660518\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.97600e6 −0.114982
\(924\) 0 0
\(925\) 9.81125e6 0.377025
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −8.85830e6 −0.336753 −0.168376 − 0.985723i \(-0.553852\pi\)
−0.168376 + 0.985723i \(0.553852\pi\)
\(930\) 0 0
\(931\) −5.98206e6 −0.226192
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −6.89040e6 −0.257760
\(936\) 0 0
\(937\) −3.06569e7 −1.14072 −0.570360 − 0.821395i \(-0.693196\pi\)
−0.570360 + 0.821395i \(0.693196\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.29302e7 −0.476027 −0.238013 − 0.971262i \(-0.576496\pi\)
−0.238013 + 0.971262i \(0.576496\pi\)
\(942\) 0 0
\(943\) 7.84368e6 0.287237
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.05701e7 0.745354 0.372677 − 0.927961i \(-0.378440\pi\)
0.372677 + 0.927961i \(0.378440\pi\)
\(948\) 0 0
\(949\) −3.35510e6 −0.120932
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.00489e7 −0.715087 −0.357544 − 0.933896i \(-0.616386\pi\)
−0.357544 + 0.933896i \(0.616386\pi\)
\(954\) 0 0
\(955\) 2.12946e7 0.755546
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.48982e7 0.874223
\(960\) 0 0
\(961\) −1.83818e6 −0.0642064
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 7.30985e6 0.252691
\(966\) 0 0
\(967\) 4.37266e6 0.150376 0.0751882 − 0.997169i \(-0.476044\pi\)
0.0751882 + 0.997169i \(0.476044\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.61184e7 0.888994 0.444497 − 0.895780i \(-0.353383\pi\)
0.444497 + 0.895780i \(0.353383\pi\)
\(972\) 0 0
\(973\) 5.94394e7 2.01276
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.61443e7 0.876275 0.438138 − 0.898908i \(-0.355638\pi\)
0.438138 + 0.898908i \(0.355638\pi\)
\(978\) 0 0
\(979\) 1.06056e7 0.353654
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.52466e7 0.503258 0.251629 − 0.967824i \(-0.419034\pi\)
0.251629 + 0.967824i \(0.419034\pi\)
\(984\) 0 0
\(985\) 2.17382e7 0.713891
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7.18598e6 0.233612
\(990\) 0 0
\(991\) 2.90665e7 0.940175 0.470088 − 0.882620i \(-0.344222\pi\)
0.470088 + 0.882620i \(0.344222\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.59980e6 0.115271
\(996\) 0 0
\(997\) 2.92663e6 0.0932461 0.0466230 − 0.998913i \(-0.485154\pi\)
0.0466230 + 0.998913i \(0.485154\pi\)
\(998\) 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 720.6.a.x.1.1 1
3.2 odd 2 240.6.a.d.1.1 1
4.3 odd 2 180.6.a.c.1.1 1
12.11 even 2 60.6.a.c.1.1 ✓ 1
20.3 even 4 900.6.d.f.649.2 2
20.7 even 4 900.6.d.f.649.1 2
20.19 odd 2 900.6.a.k.1.1 1
24.5 odd 2 960.6.a.bb.1.1 1
24.11 even 2 960.6.a.g.1.1 1
60.23 odd 4 300.6.d.c.49.2 2
60.47 odd 4 300.6.d.c.49.1 2
60.59 even 2 300.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.6.a.c.1.1 ✓ 1 12.11 even 2
180.6.a.c.1.1 1 4.3 odd 2
240.6.a.d.1.1 1 3.2 odd 2
300.6.a.c.1.1 1 60.59 even 2
300.6.d.c.49.1 2 60.47 odd 4
300.6.d.c.49.2 2 60.23 odd 4
720.6.a.x.1.1 1 1.1 even 1 trivial
900.6.a.k.1.1 1 20.19 odd 2
900.6.d.f.649.1 2 20.7 even 4
900.6.d.f.649.2 2 20.3 even 4
960.6.a.g.1.1 1 24.11 even 2
960.6.a.bb.1.1 1 24.5 odd 2