Properties

Label 900.6.a.u.1.1
Level $900$
Weight $6$
Character 900.1
Self dual yes
Analytic conductor $144.345$
Analytic rank $0$
Dimension $2$
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] = [900,6,Mod(1,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, 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("900.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.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: \(144.345437832\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{241}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 60 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 180)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(8.26209\) of defining polynomial
Character \(\chi\) \(=\) 900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-53.1450 q^{7} +O(q^{10})\) \(q-53.1450 q^{7} +585.725 q^{11} +1085.16 q^{13} +1592.90 q^{17} +2410.90 q^{19} -2671.45 q^{23} +8435.80 q^{29} -5024.15 q^{31} -1828.70 q^{37} +7971.30 q^{41} -10556.8 q^{43} -29386.0 q^{47} -13982.6 q^{49} -23064.2 q^{53} -2214.89 q^{59} +21931.4 q^{61} +410.167 q^{67} +53657.9 q^{71} +17564.8 q^{73} -31128.4 q^{77} +59507.8 q^{79} +22914.7 q^{83} +56700.9 q^{89} -57670.9 q^{91} +151477. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 80 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 80 q^{7} + 240 q^{11} + 680 q^{13} - 540 q^{17} + 1096 q^{19} - 3480 q^{23} + 9420 q^{29} + 2992 q^{31} + 7520 q^{37} + 27120 q^{41} - 4720 q^{43} - 38280 q^{47} - 13062 q^{49} - 53580 q^{53} + 46800 q^{59} + 21508 q^{61} + 10880 q^{67} + 45840 q^{71} - 9580 q^{73} - 77160 q^{77} + 91072 q^{79} + 14160 q^{83} + 35160 q^{89} - 111616 q^{91} + 98780 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −53.1450 −0.409938 −0.204969 0.978769i \(-0.565709\pi\)
−0.204969 + 0.978769i \(0.565709\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 585.725 1.45953 0.729764 0.683699i \(-0.239630\pi\)
0.729764 + 0.683699i \(0.239630\pi\)
\(12\) 0 0
\(13\) 1085.16 1.78088 0.890442 0.455097i \(-0.150395\pi\)
0.890442 + 0.455097i \(0.150395\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1592.90 1.33680 0.668400 0.743802i \(-0.266979\pi\)
0.668400 + 0.743802i \(0.266979\pi\)
\(18\) 0 0
\(19\) 2410.90 1.53213 0.766065 0.642764i \(-0.222212\pi\)
0.766065 + 0.642764i \(0.222212\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2671.45 −1.05300 −0.526499 0.850176i \(-0.676496\pi\)
−0.526499 + 0.850176i \(0.676496\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8435.80 1.86265 0.931325 0.364188i \(-0.118654\pi\)
0.931325 + 0.364188i \(0.118654\pi\)
\(30\) 0 0
\(31\) −5024.15 −0.938985 −0.469492 0.882936i \(-0.655563\pi\)
−0.469492 + 0.882936i \(0.655563\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1828.70 −0.219603 −0.109802 0.993954i \(-0.535022\pi\)
−0.109802 + 0.993954i \(0.535022\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7971.30 0.740576 0.370288 0.928917i \(-0.379259\pi\)
0.370288 + 0.928917i \(0.379259\pi\)
\(42\) 0 0
\(43\) −10556.8 −0.870682 −0.435341 0.900266i \(-0.643372\pi\)
−0.435341 + 0.900266i \(0.643372\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −29386.0 −1.94042 −0.970209 0.242271i \(-0.922108\pi\)
−0.970209 + 0.242271i \(0.922108\pi\)
\(48\) 0 0
\(49\) −13982.6 −0.831951
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −23064.2 −1.12784 −0.563922 0.825828i \(-0.690708\pi\)
−0.563922 + 0.825828i \(0.690708\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2214.89 −0.0828365 −0.0414183 0.999142i \(-0.513188\pi\)
−0.0414183 + 0.999142i \(0.513188\pi\)
\(60\) 0 0
\(61\) 21931.4 0.754644 0.377322 0.926082i \(-0.376845\pi\)
0.377322 + 0.926082i \(0.376845\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 410.167 0.0111628 0.00558141 0.999984i \(-0.498223\pi\)
0.00558141 + 0.999984i \(0.498223\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 53657.9 1.26324 0.631622 0.775276i \(-0.282389\pi\)
0.631622 + 0.775276i \(0.282389\pi\)
\(72\) 0 0
\(73\) 17564.8 0.385777 0.192889 0.981221i \(-0.438214\pi\)
0.192889 + 0.981221i \(0.438214\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −31128.4 −0.598315
\(78\) 0 0
\(79\) 59507.8 1.07277 0.536384 0.843974i \(-0.319790\pi\)
0.536384 + 0.843974i \(0.319790\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 22914.7 0.365105 0.182553 0.983196i \(-0.441564\pi\)
0.182553 + 0.983196i \(0.441564\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 56700.9 0.758779 0.379389 0.925237i \(-0.376134\pi\)
0.379389 + 0.925237i \(0.376134\pi\)
\(90\) 0 0
\(91\) −57670.9 −0.730051
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 151477. 1.63462 0.817311 0.576197i \(-0.195464\pi\)
0.817311 + 0.576197i \(0.195464\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −113395. −1.10609 −0.553045 0.833151i \(-0.686534\pi\)
−0.553045 + 0.833151i \(0.686534\pi\)
\(102\) 0 0
\(103\) −16700.2 −0.155106 −0.0775531 0.996988i \(-0.524711\pi\)
−0.0775531 + 0.996988i \(0.524711\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 174972. 1.47744 0.738719 0.674014i \(-0.235431\pi\)
0.738719 + 0.674014i \(0.235431\pi\)
\(108\) 0 0
\(109\) 93282.6 0.752029 0.376014 0.926614i \(-0.377294\pi\)
0.376014 + 0.926614i \(0.377294\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −103539. −0.762792 −0.381396 0.924412i \(-0.624557\pi\)
−0.381396 + 0.924412i \(0.624557\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −84654.8 −0.548005
\(120\) 0 0
\(121\) 182023. 1.13022
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 10725.7 0.0590088 0.0295044 0.999565i \(-0.490607\pi\)
0.0295044 + 0.999565i \(0.490607\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −115954. −0.590349 −0.295174 0.955443i \(-0.595378\pi\)
−0.295174 + 0.955443i \(0.595378\pi\)
\(132\) 0 0
\(133\) −128127. −0.628077
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 120066. 0.546535 0.273267 0.961938i \(-0.411896\pi\)
0.273267 + 0.961938i \(0.411896\pi\)
\(138\) 0 0
\(139\) −136471. −0.599106 −0.299553 0.954080i \(-0.596838\pi\)
−0.299553 + 0.954080i \(0.596838\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 635606. 2.59925
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −307357. −1.13417 −0.567085 0.823659i \(-0.691929\pi\)
−0.567085 + 0.823659i \(0.691929\pi\)
\(150\) 0 0
\(151\) 41402.9 0.147771 0.0738853 0.997267i \(-0.476460\pi\)
0.0738853 + 0.997267i \(0.476460\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 363308. 1.17632 0.588161 0.808744i \(-0.299852\pi\)
0.588161 + 0.808744i \(0.299852\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 141974. 0.431663
\(162\) 0 0
\(163\) −361620. −1.06606 −0.533032 0.846095i \(-0.678947\pi\)
−0.533032 + 0.846095i \(0.678947\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −127049. −0.352518 −0.176259 0.984344i \(-0.556400\pi\)
−0.176259 + 0.984344i \(0.556400\pi\)
\(168\) 0 0
\(169\) 806280. 2.17155
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −388638. −0.987257 −0.493629 0.869673i \(-0.664330\pi\)
−0.493629 + 0.869673i \(0.664330\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −365985. −0.853751 −0.426875 0.904310i \(-0.640386\pi\)
−0.426875 + 0.904310i \(0.640386\pi\)
\(180\) 0 0
\(181\) −747391. −1.69571 −0.847855 0.530228i \(-0.822106\pi\)
−0.847855 + 0.530228i \(0.822106\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 933002. 1.95110
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −726043. −1.44006 −0.720028 0.693946i \(-0.755871\pi\)
−0.720028 + 0.693946i \(0.755871\pi\)
\(192\) 0 0
\(193\) 215930. 0.417273 0.208636 0.977993i \(-0.433097\pi\)
0.208636 + 0.977993i \(0.433097\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −707885. −1.29956 −0.649781 0.760122i \(-0.725139\pi\)
−0.649781 + 0.760122i \(0.725139\pi\)
\(198\) 0 0
\(199\) 1.04820e6 1.87635 0.938174 0.346164i \(-0.112516\pi\)
0.938174 + 0.346164i \(0.112516\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −448321. −0.763570
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.41213e6 2.23618
\(210\) 0 0
\(211\) 975085. 1.50777 0.753887 0.657004i \(-0.228177\pi\)
0.753887 + 0.657004i \(0.228177\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 267009. 0.384925
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.72855e6 2.38069
\(222\) 0 0
\(223\) −129078. −0.173816 −0.0869079 0.996216i \(-0.527699\pi\)
−0.0869079 + 0.996216i \(0.527699\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.10942e6 1.42900 0.714502 0.699634i \(-0.246653\pi\)
0.714502 + 0.699634i \(0.246653\pi\)
\(228\) 0 0
\(229\) 555967. 0.700585 0.350292 0.936640i \(-0.386082\pi\)
0.350292 + 0.936640i \(0.386082\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 107780. 0.130062 0.0650310 0.997883i \(-0.479285\pi\)
0.0650310 + 0.997883i \(0.479285\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 691144. 0.782661 0.391331 0.920250i \(-0.372015\pi\)
0.391331 + 0.920250i \(0.372015\pi\)
\(240\) 0 0
\(241\) 601871. 0.667515 0.333758 0.942659i \(-0.391683\pi\)
0.333758 + 0.942659i \(0.391683\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.61621e6 2.72854
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 114860. 0.115076 0.0575380 0.998343i \(-0.481675\pi\)
0.0575380 + 0.998343i \(0.481675\pi\)
\(252\) 0 0
\(253\) −1.56474e6 −1.53688
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −924496. −0.873117 −0.436558 0.899676i \(-0.643803\pi\)
−0.436558 + 0.899676i \(0.643803\pi\)
\(258\) 0 0
\(259\) 97186.5 0.0900236
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.73745e6 −1.54890 −0.774448 0.632638i \(-0.781972\pi\)
−0.774448 + 0.632638i \(0.781972\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −108682. −0.0915751 −0.0457875 0.998951i \(-0.514580\pi\)
−0.0457875 + 0.998951i \(0.514580\pi\)
\(270\) 0 0
\(271\) −193643. −0.160169 −0.0800847 0.996788i \(-0.525519\pi\)
−0.0800847 + 0.996788i \(0.525519\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.70076e6 1.33182 0.665909 0.746033i \(-0.268044\pi\)
0.665909 + 0.746033i \(0.268044\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 131461. 0.0993184 0.0496592 0.998766i \(-0.484186\pi\)
0.0496592 + 0.998766i \(0.484186\pi\)
\(282\) 0 0
\(283\) −2.11575e6 −1.57036 −0.785178 0.619271i \(-0.787428\pi\)
−0.785178 + 0.619271i \(0.787428\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −423635. −0.303590
\(288\) 0 0
\(289\) 1.11748e6 0.787035
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 874729. 0.595257 0.297629 0.954682i \(-0.403804\pi\)
0.297629 + 0.954682i \(0.403804\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.89895e6 −1.87527
\(300\) 0 0
\(301\) 561040. 0.356925
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.26331e6 0.765002 0.382501 0.923955i \(-0.375063\pi\)
0.382501 + 0.923955i \(0.375063\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.33506e6 −0.782709 −0.391355 0.920240i \(-0.627993\pi\)
−0.391355 + 0.920240i \(0.627993\pi\)
\(312\) 0 0
\(313\) 1.61091e6 0.929414 0.464707 0.885465i \(-0.346160\pi\)
0.464707 + 0.885465i \(0.346160\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.94530e6 −1.08727 −0.543636 0.839321i \(-0.682953\pi\)
−0.543636 + 0.839321i \(0.682953\pi\)
\(318\) 0 0
\(319\) 4.94106e6 2.71859
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.84033e6 2.04815
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.56172e6 0.795450
\(330\) 0 0
\(331\) −1.89097e6 −0.948670 −0.474335 0.880344i \(-0.657311\pi\)
−0.474335 + 0.880344i \(0.657311\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.25968e6 1.56351 0.781754 0.623587i \(-0.214325\pi\)
0.781754 + 0.623587i \(0.214325\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.94277e6 −1.37047
\(342\) 0 0
\(343\) 1.63631e6 0.750986
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.70076e6 0.758264 0.379132 0.925343i \(-0.376223\pi\)
0.379132 + 0.925343i \(0.376223\pi\)
\(348\) 0 0
\(349\) 3.20230e6 1.40734 0.703669 0.710528i \(-0.251544\pi\)
0.703669 + 0.710528i \(0.251544\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.41449e6 −0.604175 −0.302088 0.953280i \(-0.597684\pi\)
−0.302088 + 0.953280i \(0.597684\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.37669e6 −0.563768 −0.281884 0.959448i \(-0.590959\pi\)
−0.281884 + 0.959448i \(0.590959\pi\)
\(360\) 0 0
\(361\) 3.33634e6 1.34742
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.04063e6 −0.403303 −0.201652 0.979457i \(-0.564631\pi\)
−0.201652 + 0.979457i \(0.564631\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.22575e6 0.462345
\(372\) 0 0
\(373\) −2.17929e6 −0.811040 −0.405520 0.914086i \(-0.632909\pi\)
−0.405520 + 0.914086i \(0.632909\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.15420e6 3.31716
\(378\) 0 0
\(379\) −1.98879e6 −0.711197 −0.355599 0.934639i \(-0.615723\pi\)
−0.355599 + 0.934639i \(0.615723\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −312912. −0.109000 −0.0544999 0.998514i \(-0.517356\pi\)
−0.0544999 + 0.998514i \(0.517356\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.07497e6 −1.03031 −0.515154 0.857098i \(-0.672265\pi\)
−0.515154 + 0.857098i \(0.672265\pi\)
\(390\) 0 0
\(391\) −4.25536e6 −1.40765
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4.03308e6 1.28428 0.642141 0.766586i \(-0.278046\pi\)
0.642141 + 0.766586i \(0.278046\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.60232e6 0.497608 0.248804 0.968554i \(-0.419962\pi\)
0.248804 + 0.968554i \(0.419962\pi\)
\(402\) 0 0
\(403\) −5.45201e6 −1.67222
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.07112e6 −0.320517
\(408\) 0 0
\(409\) −2.89467e6 −0.855640 −0.427820 0.903864i \(-0.640718\pi\)
−0.427820 + 0.903864i \(0.640718\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 117710. 0.0339578
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.70270e6 1.86515 0.932577 0.360970i \(-0.117554\pi\)
0.932577 + 0.360970i \(0.117554\pi\)
\(420\) 0 0
\(421\) 1.76525e6 0.485401 0.242701 0.970101i \(-0.421967\pi\)
0.242701 + 0.970101i \(0.421967\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.16555e6 −0.309357
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −374860. −0.0972022 −0.0486011 0.998818i \(-0.515476\pi\)
−0.0486011 + 0.998818i \(0.515476\pi\)
\(432\) 0 0
\(433\) −2.42835e6 −0.622430 −0.311215 0.950339i \(-0.600736\pi\)
−0.311215 + 0.950339i \(0.600736\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.44060e6 −1.61333
\(438\) 0 0
\(439\) 2.03256e6 0.503363 0.251682 0.967810i \(-0.419016\pi\)
0.251682 + 0.967810i \(0.419016\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.85613e6 0.691462 0.345731 0.938334i \(-0.387631\pi\)
0.345731 + 0.938334i \(0.387631\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.95580e6 −1.16011 −0.580053 0.814579i \(-0.696968\pi\)
−0.580053 + 0.814579i \(0.696968\pi\)
\(450\) 0 0
\(451\) 4.66899e6 1.08089
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.09688e6 −0.245679 −0.122840 0.992427i \(-0.539200\pi\)
−0.122840 + 0.992427i \(0.539200\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.76958e6 −0.606962 −0.303481 0.952837i \(-0.598149\pi\)
−0.303481 + 0.952837i \(0.598149\pi\)
\(462\) 0 0
\(463\) 4.28413e6 0.928773 0.464387 0.885633i \(-0.346275\pi\)
0.464387 + 0.885633i \(0.346275\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.94130e6 −1.04845 −0.524226 0.851579i \(-0.675645\pi\)
−0.524226 + 0.851579i \(0.675645\pi\)
\(468\) 0 0
\(469\) −21798.4 −0.00457606
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.18336e6 −1.27078
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7.29605e6 1.45294 0.726472 0.687196i \(-0.241159\pi\)
0.726472 + 0.687196i \(0.241159\pi\)
\(480\) 0 0
\(481\) −1.98444e6 −0.391088
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.28904e6 1.20161 0.600803 0.799397i \(-0.294848\pi\)
0.600803 + 0.799397i \(0.294848\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.01098e6 0.938035 0.469018 0.883189i \(-0.344608\pi\)
0.469018 + 0.883189i \(0.344608\pi\)
\(492\) 0 0
\(493\) 1.34374e7 2.48999
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.85165e6 −0.517851
\(498\) 0 0
\(499\) 796409. 0.143181 0.0715904 0.997434i \(-0.477193\pi\)
0.0715904 + 0.997434i \(0.477193\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5.08033e6 −0.895306 −0.447653 0.894207i \(-0.647740\pi\)
−0.447653 + 0.894207i \(0.647740\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.77725e6 −0.304056 −0.152028 0.988376i \(-0.548580\pi\)
−0.152028 + 0.988376i \(0.548580\pi\)
\(510\) 0 0
\(511\) −933483. −0.158144
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.72121e7 −2.83209
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.17893e6 −0.351681 −0.175840 0.984419i \(-0.556264\pi\)
−0.175840 + 0.984419i \(0.556264\pi\)
\(522\) 0 0
\(523\) −1.87227e6 −0.299305 −0.149652 0.988739i \(-0.547815\pi\)
−0.149652 + 0.988739i \(0.547815\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.00298e6 −1.25524
\(528\) 0 0
\(529\) 700305. 0.108805
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.65014e6 1.31888
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8.18996e6 −1.21426
\(540\) 0 0
\(541\) −1.45286e6 −0.213417 −0.106709 0.994290i \(-0.534031\pi\)
−0.106709 + 0.994290i \(0.534031\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 4.82156e6 0.689001 0.344500 0.938786i \(-0.388048\pi\)
0.344500 + 0.938786i \(0.388048\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.03379e7 2.85382
\(552\) 0 0
\(553\) −3.16254e6 −0.439768
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.26764e7 1.73125 0.865624 0.500695i \(-0.166922\pi\)
0.865624 + 0.500695i \(0.166922\pi\)
\(558\) 0 0
\(559\) −1.14558e7 −1.55058
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.29998e7 −1.72848 −0.864240 0.503080i \(-0.832200\pi\)
−0.864240 + 0.503080i \(0.832200\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.42964e7 1.85117 0.925587 0.378535i \(-0.123572\pi\)
0.925587 + 0.378535i \(0.123572\pi\)
\(570\) 0 0
\(571\) −5.40555e6 −0.693824 −0.346912 0.937898i \(-0.612770\pi\)
−0.346912 + 0.937898i \(0.612770\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.04395e7 −1.30539 −0.652694 0.757621i \(-0.726361\pi\)
−0.652694 + 0.757621i \(0.726361\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.21780e6 −0.149670
\(582\) 0 0
\(583\) −1.35093e7 −1.64612
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.61958e6 0.792931 0.396465 0.918050i \(-0.370237\pi\)
0.396465 + 0.918050i \(0.370237\pi\)
\(588\) 0 0
\(589\) −1.21127e7 −1.43865
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.50905e6 0.993675 0.496838 0.867843i \(-0.334494\pi\)
0.496838 + 0.867843i \(0.334494\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.67122e6 0.531940 0.265970 0.963981i \(-0.414308\pi\)
0.265970 + 0.963981i \(0.414308\pi\)
\(600\) 0 0
\(601\) 1.77737e6 0.200721 0.100360 0.994951i \(-0.468000\pi\)
0.100360 + 0.994951i \(0.468000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.29679e7 −1.42855 −0.714277 0.699863i \(-0.753244\pi\)
−0.714277 + 0.699863i \(0.753244\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.18885e7 −3.45566
\(612\) 0 0
\(613\) 1.21367e7 1.30451 0.652257 0.757998i \(-0.273822\pi\)
0.652257 + 0.757998i \(0.273822\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.42427e6 0.362122 0.181061 0.983472i \(-0.442047\pi\)
0.181061 + 0.983472i \(0.442047\pi\)
\(618\) 0 0
\(619\) −1.52375e7 −1.59841 −0.799203 0.601061i \(-0.794745\pi\)
−0.799203 + 0.601061i \(0.794745\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.01337e6 −0.311052
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.91294e6 −0.293566
\(630\) 0 0
\(631\) 215301. 0.0215265 0.0107632 0.999942i \(-0.496574\pi\)
0.0107632 + 0.999942i \(0.496574\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.51734e7 −1.48161
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.80128e6 −0.557671 −0.278836 0.960339i \(-0.589949\pi\)
−0.278836 + 0.960339i \(0.589949\pi\)
\(642\) 0 0
\(643\) 9.02804e6 0.861125 0.430562 0.902561i \(-0.358315\pi\)
0.430562 + 0.902561i \(0.358315\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.95365e6 0.183478 0.0917392 0.995783i \(-0.470757\pi\)
0.0917392 + 0.995783i \(0.470757\pi\)
\(648\) 0 0
\(649\) −1.29732e6 −0.120902
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.67419e6 0.796060 0.398030 0.917372i \(-0.369694\pi\)
0.398030 + 0.917372i \(0.369694\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.18122e7 −1.05954 −0.529768 0.848143i \(-0.677721\pi\)
−0.529768 + 0.848143i \(0.677721\pi\)
\(660\) 0 0
\(661\) 4.24221e6 0.377649 0.188824 0.982011i \(-0.439532\pi\)
0.188824 + 0.982011i \(0.439532\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.25358e7 −1.96137
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.28458e7 1.10142
\(672\) 0 0
\(673\) 2.05653e7 1.75024 0.875119 0.483907i \(-0.160783\pi\)
0.875119 + 0.483907i \(0.160783\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.36927e6 −0.701804 −0.350902 0.936412i \(-0.614125\pi\)
−0.350902 + 0.936412i \(0.614125\pi\)
\(678\) 0 0
\(679\) −8.05025e6 −0.670093
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.11826e7 0.917256 0.458628 0.888628i \(-0.348341\pi\)
0.458628 + 0.888628i \(0.348341\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.50284e7 −2.00856
\(690\) 0 0
\(691\) −1.27525e7 −1.01601 −0.508007 0.861353i \(-0.669618\pi\)
−0.508007 + 0.861353i \(0.669618\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.26975e7 0.990001
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.25558e6 0.634530 0.317265 0.948337i \(-0.397235\pi\)
0.317265 + 0.948337i \(0.397235\pi\)
\(702\) 0 0
\(703\) −4.40882e6 −0.336461
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.02639e6 0.453428
\(708\) 0 0
\(709\) 4.88990e6 0.365329 0.182665 0.983175i \(-0.441528\pi\)
0.182665 + 0.983175i \(0.441528\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.34218e7 0.988749
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.13547e6 0.154053 0.0770267 0.997029i \(-0.475457\pi\)
0.0770267 + 0.997029i \(0.475457\pi\)
\(720\) 0 0
\(721\) 887535. 0.0635839
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.58055e7 −1.10911 −0.554554 0.832148i \(-0.687111\pi\)
−0.554554 + 0.832148i \(0.687111\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.68159e7 −1.16393
\(732\) 0 0
\(733\) 2.28769e6 0.157267 0.0786335 0.996904i \(-0.474944\pi\)
0.0786335 + 0.996904i \(0.474944\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 240245. 0.0162924
\(738\) 0 0
\(739\) 4.49661e6 0.302883 0.151441 0.988466i \(-0.451609\pi\)
0.151441 + 0.988466i \(0.451609\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.69385e6 −0.644205 −0.322103 0.946705i \(-0.604390\pi\)
−0.322103 + 0.946705i \(0.604390\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9.29890e6 −0.605657
\(750\) 0 0
\(751\) −1.50258e7 −0.972163 −0.486082 0.873913i \(-0.661574\pi\)
−0.486082 + 0.873913i \(0.661574\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.42039e7 −0.900884 −0.450442 0.892806i \(-0.648734\pi\)
−0.450442 + 0.892806i \(0.648734\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.32337e6 0.0828358 0.0414179 0.999142i \(-0.486812\pi\)
0.0414179 + 0.999142i \(0.486812\pi\)
\(762\) 0 0
\(763\) −4.95751e6 −0.308285
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.40351e6 −0.147522
\(768\) 0 0
\(769\) −2.33698e7 −1.42508 −0.712540 0.701632i \(-0.752455\pi\)
−0.712540 + 0.701632i \(0.752455\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.74390e7 −1.04972 −0.524860 0.851188i \(-0.675882\pi\)
−0.524860 + 0.851188i \(0.675882\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.92180e7 1.13466
\(780\) 0 0
\(781\) 3.14288e7 1.84374
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 7.58390e6 0.436472 0.218236 0.975896i \(-0.429970\pi\)
0.218236 + 0.975896i \(0.429970\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.50256e6 0.312697
\(792\) 0 0
\(793\) 2.37991e7 1.34393
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 368007. 0.0205216 0.0102608 0.999947i \(-0.496734\pi\)
0.0102608 + 0.999947i \(0.496734\pi\)
\(798\) 0 0
\(799\) −4.68089e7 −2.59395
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.02882e7 0.563052
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.68278e7 1.44116 0.720582 0.693370i \(-0.243875\pi\)
0.720582 + 0.693370i \(0.243875\pi\)
\(810\) 0 0
\(811\) −3.07164e7 −1.63991 −0.819953 0.572431i \(-0.806000\pi\)
−0.819953 + 0.572431i \(0.806000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.54513e7 −1.33400
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 9.59084e6 0.496591 0.248295 0.968684i \(-0.420130\pi\)
0.248295 + 0.968684i \(0.420130\pi\)
\(822\) 0 0
\(823\) −3.42513e7 −1.76270 −0.881349 0.472466i \(-0.843364\pi\)
−0.881349 + 0.472466i \(0.843364\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.36507e6 −0.120249 −0.0601243 0.998191i \(-0.519150\pi\)
−0.0601243 + 0.998191i \(0.519150\pi\)
\(828\) 0 0
\(829\) −8.63277e6 −0.436279 −0.218139 0.975918i \(-0.569999\pi\)
−0.218139 + 0.975918i \(0.569999\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.22729e7 −1.11215
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.58597e7 0.777842 0.388921 0.921271i \(-0.372848\pi\)
0.388921 + 0.921271i \(0.372848\pi\)
\(840\) 0 0
\(841\) 5.06516e7 2.46947
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −9.67362e6 −0.463320
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.88529e6 0.231242
\(852\) 0 0
\(853\) 2.27282e7 1.06953 0.534764 0.845001i \(-0.320400\pi\)
0.534764 + 0.845001i \(0.320400\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.71180e7 −0.796163 −0.398081 0.917350i \(-0.630324\pi\)
−0.398081 + 0.917350i \(0.630324\pi\)
\(858\) 0 0
\(859\) 3.00031e7 1.38734 0.693669 0.720293i \(-0.255993\pi\)
0.693669 + 0.720293i \(0.255993\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.61288e6 0.119424 0.0597122 0.998216i \(-0.480982\pi\)
0.0597122 + 0.998216i \(0.480982\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.48552e7 1.56573
\(870\) 0 0
\(871\) 445097. 0.0198797
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 9.15655e6 0.402006 0.201003 0.979591i \(-0.435580\pi\)
0.201003 + 0.979591i \(0.435580\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.61189e7 1.13375 0.566873 0.823805i \(-0.308153\pi\)
0.566873 + 0.823805i \(0.308153\pi\)
\(882\) 0 0
\(883\) −9.12268e6 −0.393750 −0.196875 0.980429i \(-0.563079\pi\)
−0.196875 + 0.980429i \(0.563079\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8.28277e6 −0.353482 −0.176741 0.984257i \(-0.556555\pi\)
−0.176741 + 0.984257i \(0.556555\pi\)
\(888\) 0 0
\(889\) −570018. −0.0241899
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −7.08466e7 −2.97297
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.23828e7 −1.74900
\(900\) 0 0
\(901\) −3.67390e7 −1.50770
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 2.09147e7 0.844176 0.422088 0.906555i \(-0.361297\pi\)
0.422088 + 0.906555i \(0.361297\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.29585e6 0.171496 0.0857479 0.996317i \(-0.472672\pi\)
0.0857479 + 0.996317i \(0.472672\pi\)
\(912\) 0 0
\(913\) 1.34217e7 0.532881
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 6.16239e6 0.242006
\(918\) 0 0
\(919\) 1.79222e7 0.700007 0.350004 0.936748i \(-0.386180\pi\)
0.350004 + 0.936748i \(0.386180\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5.82274e7 2.24969
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.18638e7 −0.451009 −0.225505 0.974242i \(-0.572403\pi\)
−0.225505 + 0.974242i \(0.572403\pi\)
\(930\) 0 0
\(931\) −3.37107e7 −1.27466
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −3.19444e7 −1.18863 −0.594313 0.804234i \(-0.702576\pi\)
−0.594313 + 0.804234i \(0.702576\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.48231e7 −0.913866 −0.456933 0.889501i \(-0.651052\pi\)
−0.456933 + 0.889501i \(0.651052\pi\)
\(942\) 0 0
\(943\) −2.12949e7 −0.779825
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.38376e7 1.22610 0.613049 0.790045i \(-0.289943\pi\)
0.613049 + 0.790045i \(0.289943\pi\)
\(948\) 0 0
\(949\) 1.90606e7 0.687024
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.02206e7 0.721211 0.360605 0.932718i \(-0.382570\pi\)
0.360605 + 0.932718i \(0.382570\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.38090e6 −0.224045
\(960\) 0 0
\(961\) −3.38703e6 −0.118307
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 5.30981e7 1.82605 0.913025 0.407904i \(-0.133740\pi\)
0.913025 + 0.407904i \(0.133740\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.52073e7 1.19835 0.599176 0.800617i \(-0.295495\pi\)
0.599176 + 0.800617i \(0.295495\pi\)
\(972\) 0 0
\(973\) 7.25277e6 0.245596
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −4.08861e7 −1.37037 −0.685187 0.728368i \(-0.740279\pi\)
−0.685187 + 0.728368i \(0.740279\pi\)
\(978\) 0 0
\(979\) 3.32112e7 1.10746
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.29571e7 −0.757762 −0.378881 0.925445i \(-0.623691\pi\)
−0.378881 + 0.925445i \(0.623691\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.82019e7 0.916827
\(990\) 0 0
\(991\) 1.09601e7 0.354511 0.177256 0.984165i \(-0.443278\pi\)
0.177256 + 0.984165i \(0.443278\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.29419e6 −0.0412346 −0.0206173 0.999787i \(-0.506563\pi\)
−0.0206173 + 0.999787i \(0.506563\pi\)
\(998\) 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 900.6.a.u.1.1 2
3.2 odd 2 900.6.a.t.1.1 2
5.2 odd 4 900.6.d.n.649.2 4
5.3 odd 4 900.6.d.n.649.3 4
5.4 even 2 180.6.a.f.1.2 2
15.2 even 4 900.6.d.k.649.2 4
15.8 even 4 900.6.d.k.649.3 4
15.14 odd 2 180.6.a.g.1.2 yes 2
20.19 odd 2 720.6.a.bc.1.1 2
60.59 even 2 720.6.a.bg.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.6.a.f.1.2 2 5.4 even 2
180.6.a.g.1.2 yes 2 15.14 odd 2
720.6.a.bc.1.1 2 20.19 odd 2
720.6.a.bg.1.1 2 60.59 even 2
900.6.a.t.1.1 2 3.2 odd 2
900.6.a.u.1.1 2 1.1 even 1 trivial
900.6.d.k.649.2 4 15.2 even 4
900.6.d.k.649.3 4 15.8 even 4
900.6.d.n.649.2 4 5.2 odd 4
900.6.d.n.649.3 4 5.3 odd 4