Properties

Label 1008.6.a.bf.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
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] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{505}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 126 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-10.7361\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+28.4166 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+28.4166 q^{5} -49.0000 q^{7} +424.083 q^{11} +508.500 q^{13} +539.916 q^{17} -2603.00 q^{19} +261.251 q^{23} -2317.50 q^{25} -6879.66 q^{29} -5687.00 q^{31} -1392.41 q^{35} +4909.50 q^{37} +5723.42 q^{41} +1733.99 q^{43} -10147.8 q^{47} +2401.00 q^{49} +31181.5 q^{53} +12051.0 q^{55} -38845.5 q^{59} +13651.0 q^{61} +14449.8 q^{65} +30741.5 q^{67} -45627.9 q^{71} +21753.5 q^{73} -20780.1 q^{77} -32295.5 q^{79} -46637.3 q^{83} +15342.6 q^{85} +63757.4 q^{89} -24916.5 q^{91} -73968.4 q^{95} +115122. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 78 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 78 q^{5} - 98 q^{7} + 174 q^{11} + 208 q^{13} - 1482 q^{17} - 352 q^{19} + 3354 q^{23} + 5882 q^{25} - 276 q^{29} - 6520 q^{31} + 3822 q^{35} + 13864 q^{37} + 12930 q^{41} - 12712 q^{43} - 28116 q^{47} + 4802 q^{49} + 46992 q^{53} + 38664 q^{55} - 65556 q^{59} - 13148 q^{61} + 46428 q^{65} + 75236 q^{67} - 66042 q^{71} + 60496 q^{73} - 8526 q^{77} + 34916 q^{79} - 82488 q^{83} + 230508 q^{85} - 42510 q^{89} - 10192 q^{91} - 313512 q^{95} + 213256 q^{97}+O(q^{100}) \) 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
\(5\) 28.4166 0.508332 0.254166 0.967161i \(-0.418199\pi\)
0.254166 + 0.967161i \(0.418199\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 424.083 1.05674 0.528371 0.849013i \(-0.322803\pi\)
0.528371 + 0.849013i \(0.322803\pi\)
\(12\) 0 0
\(13\) 508.500 0.834511 0.417256 0.908789i \(-0.362992\pi\)
0.417256 + 0.908789i \(0.362992\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 539.916 0.453110 0.226555 0.973998i \(-0.427254\pi\)
0.226555 + 0.973998i \(0.427254\pi\)
\(18\) 0 0
\(19\) −2603.00 −1.65421 −0.827104 0.562050i \(-0.810013\pi\)
−0.827104 + 0.562050i \(0.810013\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 261.251 0.102977 0.0514883 0.998674i \(-0.483604\pi\)
0.0514883 + 0.998674i \(0.483604\pi\)
\(24\) 0 0
\(25\) −2317.50 −0.741599
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6879.66 −1.51905 −0.759525 0.650478i \(-0.774569\pi\)
−0.759525 + 0.650478i \(0.774569\pi\)
\(30\) 0 0
\(31\) −5687.00 −1.06287 −0.531433 0.847100i \(-0.678346\pi\)
−0.531433 + 0.847100i \(0.678346\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1392.41 −0.192131
\(36\) 0 0
\(37\) 4909.50 0.589567 0.294783 0.955564i \(-0.404752\pi\)
0.294783 + 0.955564i \(0.404752\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5723.42 0.531736 0.265868 0.964009i \(-0.414342\pi\)
0.265868 + 0.964009i \(0.414342\pi\)
\(42\) 0 0
\(43\) 1733.99 0.143013 0.0715066 0.997440i \(-0.477219\pi\)
0.0715066 + 0.997440i \(0.477219\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10147.8 −0.670083 −0.335042 0.942203i \(-0.608750\pi\)
−0.335042 + 0.942203i \(0.608750\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 31181.5 1.52478 0.762390 0.647118i \(-0.224026\pi\)
0.762390 + 0.647118i \(0.224026\pi\)
\(54\) 0 0
\(55\) 12051.0 0.537176
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −38845.5 −1.45282 −0.726408 0.687264i \(-0.758812\pi\)
−0.726408 + 0.687264i \(0.758812\pi\)
\(60\) 0 0
\(61\) 13651.0 0.469720 0.234860 0.972029i \(-0.424537\pi\)
0.234860 + 0.972029i \(0.424537\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 14449.8 0.424209
\(66\) 0 0
\(67\) 30741.5 0.836639 0.418320 0.908300i \(-0.362619\pi\)
0.418320 + 0.908300i \(0.362619\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −45627.9 −1.07420 −0.537099 0.843519i \(-0.680480\pi\)
−0.537099 + 0.843519i \(0.680480\pi\)
\(72\) 0 0
\(73\) 21753.5 0.477774 0.238887 0.971047i \(-0.423218\pi\)
0.238887 + 0.971047i \(0.423218\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −20780.1 −0.399411
\(78\) 0 0
\(79\) −32295.5 −0.582202 −0.291101 0.956692i \(-0.594022\pi\)
−0.291101 + 0.956692i \(0.594022\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −46637.3 −0.743085 −0.371542 0.928416i \(-0.621171\pi\)
−0.371542 + 0.928416i \(0.621171\pi\)
\(84\) 0 0
\(85\) 15342.6 0.230330
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 63757.4 0.853209 0.426604 0.904438i \(-0.359710\pi\)
0.426604 + 0.904438i \(0.359710\pi\)
\(90\) 0 0
\(91\) −24916.5 −0.315416
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −73968.4 −0.840886
\(96\) 0 0
\(97\) 115122. 1.24231 0.621156 0.783687i \(-0.286663\pi\)
0.621156 + 0.783687i \(0.286663\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −136803. −1.33442 −0.667208 0.744872i \(-0.732511\pi\)
−0.667208 + 0.744872i \(0.732511\pi\)
\(102\) 0 0
\(103\) 30426.0 0.282587 0.141293 0.989968i \(-0.454874\pi\)
0.141293 + 0.989968i \(0.454874\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −134612. −1.13664 −0.568321 0.822807i \(-0.692407\pi\)
−0.568321 + 0.822807i \(0.692407\pi\)
\(108\) 0 0
\(109\) 7722.00 0.0622535 0.0311267 0.999515i \(-0.490090\pi\)
0.0311267 + 0.999515i \(0.490090\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −214596. −1.58098 −0.790489 0.612476i \(-0.790174\pi\)
−0.790489 + 0.612476i \(0.790174\pi\)
\(114\) 0 0
\(115\) 7423.87 0.0523463
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −26455.9 −0.171259
\(120\) 0 0
\(121\) 18795.5 0.116705
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −154657. −0.885310
\(126\) 0 0
\(127\) −19445.6 −0.106982 −0.0534911 0.998568i \(-0.517035\pi\)
−0.0534911 + 0.998568i \(0.517035\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −63451.1 −0.323043 −0.161522 0.986869i \(-0.551640\pi\)
−0.161522 + 0.986869i \(0.551640\pi\)
\(132\) 0 0
\(133\) 127547. 0.625231
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 231176. 1.05231 0.526153 0.850390i \(-0.323634\pi\)
0.526153 + 0.850390i \(0.323634\pi\)
\(138\) 0 0
\(139\) −419126. −1.83996 −0.919978 0.391971i \(-0.871793\pi\)
−0.919978 + 0.391971i \(0.871793\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 215646. 0.881864
\(144\) 0 0
\(145\) −195497. −0.772182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 19393.6 0.0715635 0.0357818 0.999360i \(-0.488608\pi\)
0.0357818 + 0.999360i \(0.488608\pi\)
\(150\) 0 0
\(151\) 545294. 1.94620 0.973102 0.230376i \(-0.0739956\pi\)
0.973102 + 0.230376i \(0.0739956\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −161605. −0.540289
\(156\) 0 0
\(157\) 9538.03 0.0308823 0.0154411 0.999881i \(-0.495085\pi\)
0.0154411 + 0.999881i \(0.495085\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −12801.3 −0.0389215
\(162\) 0 0
\(163\) 566744. 1.67078 0.835388 0.549661i \(-0.185243\pi\)
0.835388 + 0.549661i \(0.185243\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 501555. 1.39164 0.695821 0.718215i \(-0.255041\pi\)
0.695821 + 0.718215i \(0.255041\pi\)
\(168\) 0 0
\(169\) −112721. −0.303591
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −111671. −0.283677 −0.141839 0.989890i \(-0.545301\pi\)
−0.141839 + 0.989890i \(0.545301\pi\)
\(174\) 0 0
\(175\) 113557. 0.280298
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −528436. −1.23271 −0.616354 0.787470i \(-0.711391\pi\)
−0.616354 + 0.787470i \(0.711391\pi\)
\(180\) 0 0
\(181\) −290808. −0.659797 −0.329898 0.944016i \(-0.607014\pi\)
−0.329898 + 0.944016i \(0.607014\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 139511. 0.299696
\(186\) 0 0
\(187\) 228969. 0.478821
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 51989.0 0.103116 0.0515582 0.998670i \(-0.483581\pi\)
0.0515582 + 0.998670i \(0.483581\pi\)
\(192\) 0 0
\(193\) −526004. −1.01647 −0.508236 0.861218i \(-0.669702\pi\)
−0.508236 + 0.861218i \(0.669702\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −977503. −1.79454 −0.897269 0.441485i \(-0.854452\pi\)
−0.897269 + 0.441485i \(0.854452\pi\)
\(198\) 0 0
\(199\) −1.01780e6 −1.82192 −0.910962 0.412491i \(-0.864659\pi\)
−0.910962 + 0.412491i \(0.864659\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 337103. 0.574147
\(204\) 0 0
\(205\) 162640. 0.270298
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.10389e6 −1.74807
\(210\) 0 0
\(211\) −248461. −0.384195 −0.192098 0.981376i \(-0.561529\pi\)
−0.192098 + 0.981376i \(0.561529\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 49274.2 0.0726982
\(216\) 0 0
\(217\) 278663. 0.401726
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 274547. 0.378125
\(222\) 0 0
\(223\) 118450. 0.159505 0.0797525 0.996815i \(-0.474587\pi\)
0.0797525 + 0.996815i \(0.474587\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 717556. 0.924254 0.462127 0.886814i \(-0.347086\pi\)
0.462127 + 0.886814i \(0.347086\pi\)
\(228\) 0 0
\(229\) −1.33467e6 −1.68184 −0.840918 0.541162i \(-0.817984\pi\)
−0.840918 + 0.541162i \(0.817984\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 68576.4 0.0827532 0.0413766 0.999144i \(-0.486826\pi\)
0.0413766 + 0.999144i \(0.486826\pi\)
\(234\) 0 0
\(235\) −288367. −0.340625
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 461972. 0.523144 0.261572 0.965184i \(-0.415759\pi\)
0.261572 + 0.965184i \(0.415759\pi\)
\(240\) 0 0
\(241\) 142028. 0.157518 0.0787592 0.996894i \(-0.474904\pi\)
0.0787592 + 0.996894i \(0.474904\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 68228.3 0.0726188
\(246\) 0 0
\(247\) −1.32362e6 −1.38045
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −672493. −0.673757 −0.336879 0.941548i \(-0.609371\pi\)
−0.336879 + 0.941548i \(0.609371\pi\)
\(252\) 0 0
\(253\) 110792. 0.108820
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.16584e6 −1.10104 −0.550522 0.834821i \(-0.685571\pi\)
−0.550522 + 0.834821i \(0.685571\pi\)
\(258\) 0 0
\(259\) −240566. −0.222835
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.23336e6 −1.09952 −0.549758 0.835324i \(-0.685280\pi\)
−0.549758 + 0.835324i \(0.685280\pi\)
\(264\) 0 0
\(265\) 886073. 0.775094
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 71305.8 0.0600819 0.0300410 0.999549i \(-0.490436\pi\)
0.0300410 + 0.999549i \(0.490436\pi\)
\(270\) 0 0
\(271\) −1.20152e6 −0.993821 −0.496911 0.867802i \(-0.665532\pi\)
−0.496911 + 0.867802i \(0.665532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −982811. −0.783679
\(276\) 0 0
\(277\) −1.64304e6 −1.28661 −0.643307 0.765608i \(-0.722438\pi\)
−0.643307 + 0.765608i \(0.722438\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 37163.4 0.0280770 0.0140385 0.999901i \(-0.495531\pi\)
0.0140385 + 0.999901i \(0.495531\pi\)
\(282\) 0 0
\(283\) 19110.2 0.0141841 0.00709203 0.999975i \(-0.497743\pi\)
0.00709203 + 0.999975i \(0.497743\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −280447. −0.200977
\(288\) 0 0
\(289\) −1.12835e6 −0.794691
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.49662e6 1.01846 0.509230 0.860631i \(-0.329930\pi\)
0.509230 + 0.860631i \(0.329930\pi\)
\(294\) 0 0
\(295\) −1.10386e6 −0.738513
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 132846. 0.0859351
\(300\) 0 0
\(301\) −84965.7 −0.0540539
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 387915. 0.238774
\(306\) 0 0
\(307\) 1.82699e6 1.10634 0.553172 0.833067i \(-0.313417\pi\)
0.553172 + 0.833067i \(0.313417\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.65586e6 −0.970784 −0.485392 0.874297i \(-0.661323\pi\)
−0.485392 + 0.874297i \(0.661323\pi\)
\(312\) 0 0
\(313\) −3.03384e6 −1.75038 −0.875189 0.483781i \(-0.839263\pi\)
−0.875189 + 0.483781i \(0.839263\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.40939e6 0.787741 0.393871 0.919166i \(-0.371136\pi\)
0.393871 + 0.919166i \(0.371136\pi\)
\(318\) 0 0
\(319\) −2.91755e6 −1.60524
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.40540e6 −0.749538
\(324\) 0 0
\(325\) −1.17845e6 −0.618873
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 497244. 0.253268
\(330\) 0 0
\(331\) 942703. 0.472939 0.236469 0.971639i \(-0.424010\pi\)
0.236469 + 0.971639i \(0.424010\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 873570. 0.425290
\(336\) 0 0
\(337\) 1.23769e6 0.593658 0.296829 0.954931i \(-0.404071\pi\)
0.296829 + 0.954931i \(0.404071\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.41176e6 −1.12318
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.10799e6 −1.83150 −0.915748 0.401754i \(-0.868401\pi\)
−0.915748 + 0.401754i \(0.868401\pi\)
\(348\) 0 0
\(349\) 705558. 0.310076 0.155038 0.987908i \(-0.450450\pi\)
0.155038 + 0.987908i \(0.450450\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.72785e6 1.59229 0.796143 0.605108i \(-0.206870\pi\)
0.796143 + 0.605108i \(0.206870\pi\)
\(354\) 0 0
\(355\) −1.29659e6 −0.546049
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.87917e6 −1.17905 −0.589524 0.807751i \(-0.700685\pi\)
−0.589524 + 0.807751i \(0.700685\pi\)
\(360\) 0 0
\(361\) 4.29950e6 1.73640
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 618161. 0.242868
\(366\) 0 0
\(367\) −1.31628e6 −0.510132 −0.255066 0.966924i \(-0.582097\pi\)
−0.255066 + 0.966924i \(0.582097\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.52789e6 −0.576313
\(372\) 0 0
\(373\) 4.05141e6 1.50777 0.753884 0.657008i \(-0.228178\pi\)
0.753884 + 0.657008i \(0.228178\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.49831e6 −1.26766
\(378\) 0 0
\(379\) 4.92472e6 1.76110 0.880549 0.473954i \(-0.157174\pi\)
0.880549 + 0.473954i \(0.157174\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4.55593e6 1.58701 0.793506 0.608562i \(-0.208253\pi\)
0.793506 + 0.608562i \(0.208253\pi\)
\(384\) 0 0
\(385\) −590499. −0.203033
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.68937e6 −1.23617 −0.618085 0.786112i \(-0.712091\pi\)
−0.618085 + 0.786112i \(0.712091\pi\)
\(390\) 0 0
\(391\) 141054. 0.0466597
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −917728. −0.295952
\(396\) 0 0
\(397\) 1.54578e6 0.492233 0.246117 0.969240i \(-0.420845\pi\)
0.246117 + 0.969240i \(0.420845\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.66295e6 −1.75866 −0.879331 0.476212i \(-0.842010\pi\)
−0.879331 + 0.476212i \(0.842010\pi\)
\(402\) 0 0
\(403\) −2.89184e6 −0.886975
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.08204e6 0.623020
\(408\) 0 0
\(409\) 727819. 0.215137 0.107568 0.994198i \(-0.465694\pi\)
0.107568 + 0.994198i \(0.465694\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.90343e6 0.549113
\(414\) 0 0
\(415\) −1.32528e6 −0.377734
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.46306e6 −1.79847 −0.899235 0.437465i \(-0.855876\pi\)
−0.899235 + 0.437465i \(0.855876\pi\)
\(420\) 0 0
\(421\) −3.50166e6 −0.962874 −0.481437 0.876481i \(-0.659885\pi\)
−0.481437 + 0.876481i \(0.659885\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.25125e6 −0.336026
\(426\) 0 0
\(427\) −668898. −0.177538
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.35407e6 1.38832 0.694162 0.719819i \(-0.255775\pi\)
0.694162 + 0.719819i \(0.255775\pi\)
\(432\) 0 0
\(433\) −1.54042e6 −0.394839 −0.197420 0.980319i \(-0.563256\pi\)
−0.197420 + 0.980319i \(0.563256\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −680036. −0.170345
\(438\) 0 0
\(439\) 3.00831e6 0.745009 0.372505 0.928030i \(-0.378499\pi\)
0.372505 + 0.928030i \(0.378499\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.93545e6 −1.67906 −0.839528 0.543317i \(-0.817168\pi\)
−0.839528 + 0.543317i \(0.817168\pi\)
\(444\) 0 0
\(445\) 1.81177e6 0.433713
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.41345e6 −1.26724 −0.633619 0.773646i \(-0.718431\pi\)
−0.633619 + 0.773646i \(0.718431\pi\)
\(450\) 0 0
\(451\) 2.42720e6 0.561908
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −708042. −0.160336
\(456\) 0 0
\(457\) 551975. 0.123632 0.0618158 0.998088i \(-0.480311\pi\)
0.0618158 + 0.998088i \(0.480311\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.44254e6 −0.973597 −0.486799 0.873514i \(-0.661835\pi\)
−0.486799 + 0.873514i \(0.661835\pi\)
\(462\) 0 0
\(463\) 4.62590e6 1.00287 0.501434 0.865196i \(-0.332806\pi\)
0.501434 + 0.865196i \(0.332806\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.50087e6 1.16718 0.583592 0.812047i \(-0.301647\pi\)
0.583592 + 0.812047i \(0.301647\pi\)
\(468\) 0 0
\(469\) −1.50633e6 −0.316220
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 735357. 0.151128
\(474\) 0 0
\(475\) 6.03244e6 1.22676
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.56375e6 −0.709690 −0.354845 0.934925i \(-0.615466\pi\)
−0.354845 + 0.934925i \(0.615466\pi\)
\(480\) 0 0
\(481\) 2.49648e6 0.492000
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.27139e6 0.631507
\(486\) 0 0
\(487\) −3.74040e6 −0.714653 −0.357327 0.933979i \(-0.616312\pi\)
−0.357327 + 0.933979i \(0.616312\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5.00459e6 0.936838 0.468419 0.883506i \(-0.344824\pi\)
0.468419 + 0.883506i \(0.344824\pi\)
\(492\) 0 0
\(493\) −3.71444e6 −0.688297
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.23577e6 0.406009
\(498\) 0 0
\(499\) −2.58167e6 −0.464141 −0.232070 0.972699i \(-0.574550\pi\)
−0.232070 + 0.972699i \(0.574550\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.02089e6 −0.708601 −0.354301 0.935132i \(-0.615281\pi\)
−0.354301 + 0.935132i \(0.615281\pi\)
\(504\) 0 0
\(505\) −3.88747e6 −0.678326
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.13802e7 −1.94696 −0.973479 0.228776i \(-0.926528\pi\)
−0.973479 + 0.228776i \(0.926528\pi\)
\(510\) 0 0
\(511\) −1.06592e6 −0.180581
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 864604. 0.143648
\(516\) 0 0
\(517\) −4.30353e6 −0.708106
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.72031e6 0.761862 0.380931 0.924603i \(-0.375604\pi\)
0.380931 + 0.924603i \(0.375604\pi\)
\(522\) 0 0
\(523\) 8.46281e6 1.35288 0.676441 0.736496i \(-0.263521\pi\)
0.676441 + 0.736496i \(0.263521\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.07050e6 −0.481596
\(528\) 0 0
\(529\) −6.36809e6 −0.989396
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.91036e6 0.443739
\(534\) 0 0
\(535\) −3.82521e6 −0.577792
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.01822e6 0.150963
\(540\) 0 0
\(541\) 1.09051e7 1.60190 0.800952 0.598728i \(-0.204327\pi\)
0.800952 + 0.598728i \(0.204327\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 219433. 0.0316454
\(546\) 0 0
\(547\) 5.04856e6 0.721438 0.360719 0.932675i \(-0.382531\pi\)
0.360719 + 0.932675i \(0.382531\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.79077e7 2.51282
\(552\) 0 0
\(553\) 1.58248e6 0.220052
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.09175e7 1.49103 0.745516 0.666488i \(-0.232203\pi\)
0.745516 + 0.666488i \(0.232203\pi\)
\(558\) 0 0
\(559\) 881735. 0.119346
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.16432e6 −0.287774 −0.143887 0.989594i \(-0.545960\pi\)
−0.143887 + 0.989594i \(0.545960\pi\)
\(564\) 0 0
\(565\) −6.09810e6 −0.803662
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.80819e6 −1.27001 −0.635007 0.772507i \(-0.719003\pi\)
−0.635007 + 0.772507i \(0.719003\pi\)
\(570\) 0 0
\(571\) −1.54139e7 −1.97844 −0.989221 0.146430i \(-0.953222\pi\)
−0.989221 + 0.146430i \(0.953222\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −605448. −0.0763673
\(576\) 0 0
\(577\) −7.40379e6 −0.925794 −0.462897 0.886412i \(-0.653190\pi\)
−0.462897 + 0.886412i \(0.653190\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.28523e6 0.280860
\(582\) 0 0
\(583\) 1.32235e7 1.61130
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.83732e6 1.17837 0.589185 0.807998i \(-0.299449\pi\)
0.589185 + 0.807998i \(0.299449\pi\)
\(588\) 0 0
\(589\) 1.48032e7 1.75820
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6.01144e6 −0.702007 −0.351004 0.936374i \(-0.614160\pi\)
−0.351004 + 0.936374i \(0.614160\pi\)
\(594\) 0 0
\(595\) −751786. −0.0870567
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −604201. −0.0688041 −0.0344020 0.999408i \(-0.510953\pi\)
−0.0344020 + 0.999408i \(0.510953\pi\)
\(600\) 0 0
\(601\) 2.52672e6 0.285346 0.142673 0.989770i \(-0.454430\pi\)
0.142673 + 0.989770i \(0.454430\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 534103. 0.0593249
\(606\) 0 0
\(607\) −1.29052e7 −1.42165 −0.710823 0.703371i \(-0.751677\pi\)
−0.710823 + 0.703371i \(0.751677\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.16017e6 −0.559192
\(612\) 0 0
\(613\) −3.27264e6 −0.351760 −0.175880 0.984412i \(-0.556277\pi\)
−0.175880 + 0.984412i \(0.556277\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.31134e7 −1.38676 −0.693381 0.720571i \(-0.743880\pi\)
−0.693381 + 0.720571i \(0.743880\pi\)
\(618\) 0 0
\(619\) 2.56630e6 0.269203 0.134602 0.990900i \(-0.457025\pi\)
0.134602 + 0.990900i \(0.457025\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.12411e6 −0.322483
\(624\) 0 0
\(625\) 2.84734e6 0.291567
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.65072e6 0.267139
\(630\) 0 0
\(631\) −1.08637e7 −1.08618 −0.543092 0.839673i \(-0.682747\pi\)
−0.543092 + 0.839673i \(0.682747\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −552577. −0.0543824
\(636\) 0 0
\(637\) 1.22091e6 0.119216
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.55104e7 1.49100 0.745500 0.666506i \(-0.232211\pi\)
0.745500 + 0.666506i \(0.232211\pi\)
\(642\) 0 0
\(643\) −3.47784e6 −0.331728 −0.165864 0.986149i \(-0.553041\pi\)
−0.165864 + 0.986149i \(0.553041\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.45505e6 0.887980 0.443990 0.896032i \(-0.353563\pi\)
0.443990 + 0.896032i \(0.353563\pi\)
\(648\) 0 0
\(649\) −1.64737e7 −1.53525
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.27403e7 1.16922 0.584610 0.811315i \(-0.301248\pi\)
0.584610 + 0.811315i \(0.301248\pi\)
\(654\) 0 0
\(655\) −1.80306e6 −0.164213
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.02252e6 0.719610 0.359805 0.933027i \(-0.382843\pi\)
0.359805 + 0.933027i \(0.382843\pi\)
\(660\) 0 0
\(661\) 2.12008e7 1.88734 0.943669 0.330892i \(-0.107350\pi\)
0.943669 + 0.330892i \(0.107350\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.62445e6 0.317825
\(666\) 0 0
\(667\) −1.79732e6 −0.156427
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.78915e6 0.496374
\(672\) 0 0
\(673\) −1.73938e7 −1.48032 −0.740162 0.672428i \(-0.765251\pi\)
−0.740162 + 0.672428i \(0.765251\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.35417e7 1.97408 0.987042 0.160464i \(-0.0512991\pi\)
0.987042 + 0.160464i \(0.0512991\pi\)
\(678\) 0 0
\(679\) −5.64100e6 −0.469550
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.31970e7 −1.08249 −0.541243 0.840866i \(-0.682046\pi\)
−0.541243 + 0.840866i \(0.682046\pi\)
\(684\) 0 0
\(685\) 6.56925e6 0.534921
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.58558e7 1.27245
\(690\) 0 0
\(691\) 9.74172e6 0.776140 0.388070 0.921630i \(-0.373142\pi\)
0.388070 + 0.921630i \(0.373142\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.19101e7 −0.935308
\(696\) 0 0
\(697\) 3.09016e6 0.240935
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.23931e7 0.952542 0.476271 0.879299i \(-0.341988\pi\)
0.476271 + 0.879299i \(0.341988\pi\)
\(702\) 0 0
\(703\) −1.27794e7 −0.975266
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.70333e6 0.504362
\(708\) 0 0
\(709\) 1.18843e7 0.887884 0.443942 0.896055i \(-0.353580\pi\)
0.443942 + 0.896055i \(0.353580\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.48573e6 −0.109450
\(714\) 0 0
\(715\) 6.12793e6 0.448279
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.57469e7 1.13599 0.567993 0.823034i \(-0.307720\pi\)
0.567993 + 0.823034i \(0.307720\pi\)
\(720\) 0 0
\(721\) −1.49087e6 −0.106808
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.59436e7 1.12653
\(726\) 0 0
\(727\) 9.34544e6 0.655788 0.327894 0.944714i \(-0.393661\pi\)
0.327894 + 0.944714i \(0.393661\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 936210. 0.0648008
\(732\) 0 0
\(733\) −1.42667e7 −0.980763 −0.490381 0.871508i \(-0.663143\pi\)
−0.490381 + 0.871508i \(0.663143\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.30370e7 0.884112
\(738\) 0 0
\(739\) 1.75852e7 1.18451 0.592253 0.805752i \(-0.298239\pi\)
0.592253 + 0.805752i \(0.298239\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36857.8 0.00244939 0.00122469 0.999999i \(-0.499610\pi\)
0.00122469 + 0.999999i \(0.499610\pi\)
\(744\) 0 0
\(745\) 551099. 0.0363780
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.59598e6 0.429610
\(750\) 0 0
\(751\) 1.73284e7 1.12114 0.560570 0.828107i \(-0.310582\pi\)
0.560570 + 0.828107i \(0.310582\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.54954e7 0.989317
\(756\) 0 0
\(757\) 1.04739e7 0.664308 0.332154 0.943225i \(-0.392225\pi\)
0.332154 + 0.943225i \(0.392225\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 615867. 0.0385501 0.0192751 0.999814i \(-0.493864\pi\)
0.0192751 + 0.999814i \(0.493864\pi\)
\(762\) 0 0
\(763\) −378378. −0.0235296
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.97529e7 −1.21239
\(768\) 0 0
\(769\) 2.82564e7 1.72306 0.861531 0.507705i \(-0.169506\pi\)
0.861531 + 0.507705i \(0.169506\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.80327e7 1.08546 0.542729 0.839908i \(-0.317391\pi\)
0.542729 + 0.839908i \(0.317391\pi\)
\(774\) 0 0
\(775\) 1.31796e7 0.788221
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.48980e7 −0.879601
\(780\) 0 0
\(781\) −1.93500e7 −1.13515
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 271038. 0.0156984
\(786\) 0 0
\(787\) −3.13051e7 −1.80168 −0.900841 0.434149i \(-0.857049\pi\)
−0.900841 + 0.434149i \(0.857049\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.05152e7 0.597554
\(792\) 0 0
\(793\) 6.94152e6 0.391987
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.38176e7 −0.770525 −0.385262 0.922807i \(-0.625889\pi\)
−0.385262 + 0.922807i \(0.625889\pi\)
\(798\) 0 0
\(799\) −5.47898e6 −0.303621
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.22529e6 0.504884
\(804\) 0 0
\(805\) −363770. −0.0197850
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8.02702e6 −0.431204 −0.215602 0.976481i \(-0.569171\pi\)
−0.215602 + 0.976481i \(0.569171\pi\)
\(810\) 0 0
\(811\) −5.68487e6 −0.303507 −0.151753 0.988418i \(-0.548492\pi\)
−0.151753 + 0.988418i \(0.548492\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.61050e7 0.849308
\(816\) 0 0
\(817\) −4.51358e6 −0.236574
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.26582e7 −0.655412 −0.327706 0.944780i \(-0.606276\pi\)
−0.327706 + 0.944780i \(0.606276\pi\)
\(822\) 0 0
\(823\) 6.69435e6 0.344516 0.172258 0.985052i \(-0.444894\pi\)
0.172258 + 0.985052i \(0.444894\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 6.41484e6 0.326153 0.163077 0.986613i \(-0.447858\pi\)
0.163077 + 0.986613i \(0.447858\pi\)
\(828\) 0 0
\(829\) −4.66483e6 −0.235749 −0.117874 0.993029i \(-0.537608\pi\)
−0.117874 + 0.993029i \(0.537608\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.29634e6 0.0647300
\(834\) 0 0
\(835\) 1.42525e7 0.707416
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −7.16720e6 −0.351516 −0.175758 0.984433i \(-0.556238\pi\)
−0.175758 + 0.984433i \(0.556238\pi\)
\(840\) 0 0
\(841\) 2.68186e7 1.30751
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.20315e6 −0.154325
\(846\) 0 0
\(847\) −920977. −0.0441103
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.28261e6 0.0607116
\(852\) 0 0
\(853\) −2.18869e7 −1.02994 −0.514970 0.857208i \(-0.672197\pi\)
−0.514970 + 0.857208i \(0.672197\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.15656e7 −1.00302 −0.501509 0.865152i \(-0.667222\pi\)
−0.501509 + 0.865152i \(0.667222\pi\)
\(858\) 0 0
\(859\) −1.68364e7 −0.778514 −0.389257 0.921129i \(-0.627268\pi\)
−0.389257 + 0.921129i \(0.627268\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −5.28356e6 −0.241490 −0.120745 0.992684i \(-0.538528\pi\)
−0.120745 + 0.992684i \(0.538528\pi\)
\(864\) 0 0
\(865\) −3.17331e6 −0.144202
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.36960e7 −0.615238
\(870\) 0 0
\(871\) 1.56320e7 0.698185
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 7.57821e6 0.334616
\(876\) 0 0
\(877\) 3.77000e7 1.65517 0.827584 0.561342i \(-0.189715\pi\)
0.827584 + 0.561342i \(0.189715\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.59165e7 −1.12496 −0.562480 0.826811i \(-0.690153\pi\)
−0.562480 + 0.826811i \(0.690153\pi\)
\(882\) 0 0
\(883\) 8.24975e6 0.356073 0.178036 0.984024i \(-0.443026\pi\)
0.178036 + 0.984024i \(0.443026\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.84834e6 0.377618 0.188809 0.982014i \(-0.439537\pi\)
0.188809 + 0.982014i \(0.439537\pi\)
\(888\) 0 0
\(889\) 952833. 0.0404355
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.64148e7 1.10846
\(894\) 0 0
\(895\) −1.50164e7 −0.626624
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.91246e7 1.61455
\(900\) 0 0
\(901\) 1.68354e7 0.690893
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8.26378e6 −0.335396
\(906\) 0 0
\(907\) −3.52189e6 −0.142153 −0.0710767 0.997471i \(-0.522644\pi\)
−0.0710767 + 0.997471i \(0.522644\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.67890e7 1.06945 0.534726 0.845026i \(-0.320415\pi\)
0.534726 + 0.845026i \(0.320415\pi\)
\(912\) 0 0
\(913\) −1.97781e7 −0.785250
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.10910e6 0.122099
\(918\) 0 0
\(919\) 4.21717e7 1.64715 0.823574 0.567209i \(-0.191977\pi\)
0.823574 + 0.567209i \(0.191977\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.32018e7 −0.896431
\(924\) 0 0
\(925\) −1.13778e7 −0.437222
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −4.24746e6 −0.161469 −0.0807347 0.996736i \(-0.525727\pi\)
−0.0807347 + 0.996736i \(0.525727\pi\)
\(930\) 0 0
\(931\) −6.24980e6 −0.236315
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6.50653e6 0.243400
\(936\) 0 0
\(937\) 4.39330e6 0.163471 0.0817357 0.996654i \(-0.473954\pi\)
0.0817357 + 0.996654i \(0.473954\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 924321. 0.0340290 0.0170145 0.999855i \(-0.494584\pi\)
0.0170145 + 0.999855i \(0.494584\pi\)
\(942\) 0 0
\(943\) 1.49525e6 0.0547563
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.87692e7 1.40479 0.702395 0.711787i \(-0.252114\pi\)
0.702395 + 0.711787i \(0.252114\pi\)
\(948\) 0 0
\(949\) 1.10617e7 0.398708
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.28022e7 −0.813289 −0.406644 0.913587i \(-0.633301\pi\)
−0.406644 + 0.913587i \(0.633301\pi\)
\(954\) 0 0
\(955\) 1.47735e6 0.0524174
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.13276e7 −0.397734
\(960\) 0 0
\(961\) 3.71280e6 0.129686
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.49472e7 −0.516705
\(966\) 0 0
\(967\) 3.66797e7 1.26142 0.630709 0.776019i \(-0.282764\pi\)
0.630709 + 0.776019i \(0.282764\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.38200e7 −0.470391 −0.235195 0.971948i \(-0.575573\pi\)
−0.235195 + 0.971948i \(0.575573\pi\)
\(972\) 0 0
\(973\) 2.05372e7 0.695438
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.05752e7 −0.689616 −0.344808 0.938673i \(-0.612056\pi\)
−0.344808 + 0.938673i \(0.612056\pi\)
\(978\) 0 0
\(979\) 2.70384e7 0.901622
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −5.77676e7 −1.90678 −0.953390 0.301742i \(-0.902432\pi\)
−0.953390 + 0.301742i \(0.902432\pi\)
\(984\) 0 0
\(985\) −2.77773e7 −0.912221
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 453008. 0.0147270
\(990\) 0 0
\(991\) 3.65391e7 1.18188 0.590940 0.806715i \(-0.298757\pi\)
0.590940 + 0.806715i \(0.298757\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.89224e7 −0.926142
\(996\) 0 0
\(997\) −3.57190e7 −1.13805 −0.569024 0.822321i \(-0.692679\pi\)
−0.569024 + 0.822321i \(0.692679\pi\)
\(998\) 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 1008.6.a.bf.1.2 2
3.2 odd 2 336.6.a.u.1.1 2
4.3 odd 2 252.6.a.e.1.2 2
12.11 even 2 84.6.a.d.1.1 2
84.11 even 6 588.6.i.h.373.2 4
84.23 even 6 588.6.i.h.361.2 4
84.47 odd 6 588.6.i.n.361.1 4
84.59 odd 6 588.6.i.n.373.1 4
84.83 odd 2 588.6.a.g.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.d.1.1 2 12.11 even 2
252.6.a.e.1.2 2 4.3 odd 2
336.6.a.u.1.1 2 3.2 odd 2
588.6.a.g.1.2 2 84.83 odd 2
588.6.i.h.361.2 4 84.23 even 6
588.6.i.h.373.2 4 84.11 even 6
588.6.i.n.361.1 4 84.47 odd 6
588.6.i.n.373.1 4 84.59 odd 6
1008.6.a.bf.1.2 2 1.1 even 1 trivial