Properties

Label 1008.6.a.b.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
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] = [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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
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)
 
\(f(q)\) \(=\) \(q-84.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-84.0000 q^{5} -49.0000 q^{7} -336.000 q^{11} +584.000 q^{13} +1458.00 q^{17} -470.000 q^{19} -4200.00 q^{23} +3931.00 q^{25} -4866.00 q^{29} +7372.00 q^{31} +4116.00 q^{35} +14330.0 q^{37} -6222.00 q^{41} -3704.00 q^{43} -1812.00 q^{47} +2401.00 q^{49} +37242.0 q^{53} +28224.0 q^{55} +34302.0 q^{59} +24476.0 q^{61} -49056.0 q^{65} +17452.0 q^{67} +28224.0 q^{71} +3602.00 q^{73} +16464.0 q^{77} -42872.0 q^{79} -35202.0 q^{83} -122472. q^{85} -26730.0 q^{89} -28616.0 q^{91} +39480.0 q^{95} -16978.0 q^{97} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −84.0000 −1.50264 −0.751319 0.659939i \(-0.770582\pi\)
−0.751319 + 0.659939i \(0.770582\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −336.000 −0.837255 −0.418627 0.908158i \(-0.637489\pi\)
−0.418627 + 0.908158i \(0.637489\pi\)
\(12\) 0 0
\(13\) 584.000 0.958417 0.479208 0.877701i \(-0.340924\pi\)
0.479208 + 0.877701i \(0.340924\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1458.00 1.22359 0.611794 0.791017i \(-0.290448\pi\)
0.611794 + 0.791017i \(0.290448\pi\)
\(18\) 0 0
\(19\) −470.000 −0.298685 −0.149343 0.988786i \(-0.547716\pi\)
−0.149343 + 0.988786i \(0.547716\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4200.00 −1.65550 −0.827751 0.561096i \(-0.810380\pi\)
−0.827751 + 0.561096i \(0.810380\pi\)
\(24\) 0 0
\(25\) 3931.00 1.25792
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4866.00 −1.07443 −0.537214 0.843446i \(-0.680523\pi\)
−0.537214 + 0.843446i \(0.680523\pi\)
\(30\) 0 0
\(31\) 7372.00 1.37778 0.688892 0.724864i \(-0.258097\pi\)
0.688892 + 0.724864i \(0.258097\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4116.00 0.567944
\(36\) 0 0
\(37\) 14330.0 1.72085 0.860423 0.509581i \(-0.170200\pi\)
0.860423 + 0.509581i \(0.170200\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6222.00 −0.578057 −0.289028 0.957321i \(-0.593332\pi\)
−0.289028 + 0.957321i \(0.593332\pi\)
\(42\) 0 0
\(43\) −3704.00 −0.305492 −0.152746 0.988265i \(-0.548812\pi\)
−0.152746 + 0.988265i \(0.548812\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1812.00 −0.119650 −0.0598251 0.998209i \(-0.519054\pi\)
−0.0598251 + 0.998209i \(0.519054\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 37242.0 1.82114 0.910570 0.413355i \(-0.135643\pi\)
0.910570 + 0.413355i \(0.135643\pi\)
\(54\) 0 0
\(55\) 28224.0 1.25809
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 34302.0 1.28289 0.641445 0.767169i \(-0.278335\pi\)
0.641445 + 0.767169i \(0.278335\pi\)
\(60\) 0 0
\(61\) 24476.0 0.842201 0.421101 0.907014i \(-0.361644\pi\)
0.421101 + 0.907014i \(0.361644\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −49056.0 −1.44015
\(66\) 0 0
\(67\) 17452.0 0.474961 0.237481 0.971392i \(-0.423678\pi\)
0.237481 + 0.971392i \(0.423678\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 28224.0 0.664466 0.332233 0.943197i \(-0.392198\pi\)
0.332233 + 0.943197i \(0.392198\pi\)
\(72\) 0 0
\(73\) 3602.00 0.0791109 0.0395555 0.999217i \(-0.487406\pi\)
0.0395555 + 0.999217i \(0.487406\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 16464.0 0.316453
\(78\) 0 0
\(79\) −42872.0 −0.772869 −0.386435 0.922317i \(-0.626294\pi\)
−0.386435 + 0.922317i \(0.626294\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −35202.0 −0.560883 −0.280441 0.959871i \(-0.590481\pi\)
−0.280441 + 0.959871i \(0.590481\pi\)
\(84\) 0 0
\(85\) −122472. −1.83861
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −26730.0 −0.357704 −0.178852 0.983876i \(-0.557238\pi\)
−0.178852 + 0.983876i \(0.557238\pi\)
\(90\) 0 0
\(91\) −28616.0 −0.362248
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 39480.0 0.448816
\(96\) 0 0
\(97\) −16978.0 −0.183213 −0.0916067 0.995795i \(-0.529200\pi\)
−0.0916067 + 0.995795i \(0.529200\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −99204.0 −0.967667 −0.483833 0.875160i \(-0.660756\pi\)
−0.483833 + 0.875160i \(0.660756\pi\)
\(102\) 0 0
\(103\) 131644. 1.22267 0.611333 0.791373i \(-0.290634\pi\)
0.611333 + 0.791373i \(0.290634\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 48852.0 0.412499 0.206250 0.978499i \(-0.433874\pi\)
0.206250 + 0.978499i \(0.433874\pi\)
\(108\) 0 0
\(109\) −56374.0 −0.454478 −0.227239 0.973839i \(-0.572970\pi\)
−0.227239 + 0.973839i \(0.572970\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8742.00 −0.0644043 −0.0322021 0.999481i \(-0.510252\pi\)
−0.0322021 + 0.999481i \(0.510252\pi\)
\(114\) 0 0
\(115\) 352800. 2.48762
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −71442.0 −0.462473
\(120\) 0 0
\(121\) −48155.0 −0.299005
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −67704.0 −0.387560
\(126\) 0 0
\(127\) −315992. −1.73847 −0.869234 0.494401i \(-0.835388\pi\)
−0.869234 + 0.494401i \(0.835388\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −24666.0 −0.125580 −0.0627900 0.998027i \(-0.520000\pi\)
−0.0627900 + 0.998027i \(0.520000\pi\)
\(132\) 0 0
\(133\) 23030.0 0.112892
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −303234. −1.38031 −0.690155 0.723662i \(-0.742458\pi\)
−0.690155 + 0.723662i \(0.742458\pi\)
\(138\) 0 0
\(139\) −250586. −1.10007 −0.550034 0.835142i \(-0.685385\pi\)
−0.550034 + 0.835142i \(0.685385\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −196224. −0.802439
\(144\) 0 0
\(145\) 408744. 1.61448
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 60594.0 0.223596 0.111798 0.993731i \(-0.464339\pi\)
0.111798 + 0.993731i \(0.464339\pi\)
\(150\) 0 0
\(151\) −124448. −0.444166 −0.222083 0.975028i \(-0.571286\pi\)
−0.222083 + 0.975028i \(0.571286\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −619248. −2.07031
\(156\) 0 0
\(157\) 76040.0 0.246203 0.123101 0.992394i \(-0.460716\pi\)
0.123101 + 0.992394i \(0.460716\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 205800. 0.625721
\(162\) 0 0
\(163\) −124256. −0.366310 −0.183155 0.983084i \(-0.558631\pi\)
−0.183155 + 0.983084i \(0.558631\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −72420.0 −0.200940 −0.100470 0.994940i \(-0.532035\pi\)
−0.100470 + 0.994940i \(0.532035\pi\)
\(168\) 0 0
\(169\) −30237.0 −0.0814370
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 441552. 1.12167 0.560837 0.827926i \(-0.310479\pi\)
0.560837 + 0.827926i \(0.310479\pi\)
\(174\) 0 0
\(175\) −192619. −0.475449
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10692.0 −0.0249417 −0.0124709 0.999922i \(-0.503970\pi\)
−0.0124709 + 0.999922i \(0.503970\pi\)
\(180\) 0 0
\(181\) −546064. −1.23893 −0.619465 0.785024i \(-0.712651\pi\)
−0.619465 + 0.785024i \(0.712651\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.20372e6 −2.58581
\(186\) 0 0
\(187\) −489888. −1.02445
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −575976. −1.14241 −0.571204 0.820808i \(-0.693523\pi\)
−0.571204 + 0.820808i \(0.693523\pi\)
\(192\) 0 0
\(193\) −413938. −0.799912 −0.399956 0.916534i \(-0.630975\pi\)
−0.399956 + 0.916534i \(0.630975\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 494946. 0.908641 0.454320 0.890838i \(-0.349882\pi\)
0.454320 + 0.890838i \(0.349882\pi\)
\(198\) 0 0
\(199\) −520364. −0.931482 −0.465741 0.884921i \(-0.654212\pi\)
−0.465741 + 0.884921i \(0.654212\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 238434. 0.406095
\(204\) 0 0
\(205\) 522648. 0.868610
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 157920. 0.250076
\(210\) 0 0
\(211\) −183284. −0.283412 −0.141706 0.989909i \(-0.545259\pi\)
−0.141706 + 0.989909i \(0.545259\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 311136. 0.459044
\(216\) 0 0
\(217\) −361228. −0.520753
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 851472. 1.17271
\(222\) 0 0
\(223\) 1.27746e6 1.72023 0.860115 0.510100i \(-0.170392\pi\)
0.860115 + 0.510100i \(0.170392\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.28764e6 −1.65856 −0.829279 0.558835i \(-0.811248\pi\)
−0.829279 + 0.558835i \(0.811248\pi\)
\(228\) 0 0
\(229\) 350936. 0.442221 0.221110 0.975249i \(-0.429032\pi\)
0.221110 + 0.975249i \(0.429032\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −836154. −1.00901 −0.504506 0.863408i \(-0.668325\pi\)
−0.504506 + 0.863408i \(0.668325\pi\)
\(234\) 0 0
\(235\) 152208. 0.179791
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 774336. 0.876869 0.438434 0.898763i \(-0.355533\pi\)
0.438434 + 0.898763i \(0.355533\pi\)
\(240\) 0 0
\(241\) −1.15285e6 −1.27859 −0.639293 0.768963i \(-0.720773\pi\)
−0.639293 + 0.768963i \(0.720773\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −201684. −0.214663
\(246\) 0 0
\(247\) −274480. −0.286265
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.35801e6 1.36056 0.680282 0.732951i \(-0.261858\pi\)
0.680282 + 0.732951i \(0.261858\pi\)
\(252\) 0 0
\(253\) 1.41120e6 1.38608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 317742. 0.300083 0.150042 0.988680i \(-0.452059\pi\)
0.150042 + 0.988680i \(0.452059\pi\)
\(258\) 0 0
\(259\) −702170. −0.650418
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.05101e6 0.936951 0.468475 0.883477i \(-0.344804\pi\)
0.468475 + 0.883477i \(0.344804\pi\)
\(264\) 0 0
\(265\) −3.12833e6 −2.73651
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.18958e6 −1.00234 −0.501169 0.865349i \(-0.667097\pi\)
−0.501169 + 0.865349i \(0.667097\pi\)
\(270\) 0 0
\(271\) 1.43008e6 1.18287 0.591435 0.806353i \(-0.298562\pi\)
0.591435 + 0.806353i \(0.298562\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.32082e6 −1.05320
\(276\) 0 0
\(277\) 63302.0 0.0495699 0.0247849 0.999693i \(-0.492110\pi\)
0.0247849 + 0.999693i \(0.492110\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 496614. 0.375192 0.187596 0.982246i \(-0.439930\pi\)
0.187596 + 0.982246i \(0.439930\pi\)
\(282\) 0 0
\(283\) 1.15842e6 0.859803 0.429902 0.902876i \(-0.358548\pi\)
0.429902 + 0.902876i \(0.358548\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 304878. 0.218485
\(288\) 0 0
\(289\) 705907. 0.497168
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.43886e6 −0.979151 −0.489575 0.871961i \(-0.662848\pi\)
−0.489575 + 0.871961i \(0.662848\pi\)
\(294\) 0 0
\(295\) −2.88137e6 −1.92772
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.45280e6 −1.58666
\(300\) 0 0
\(301\) 181496. 0.115465
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.05598e6 −1.26552
\(306\) 0 0
\(307\) 989098. 0.598954 0.299477 0.954104i \(-0.403188\pi\)
0.299477 + 0.954104i \(0.403188\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.22050e6 −1.30182 −0.650909 0.759155i \(-0.725612\pi\)
−0.650909 + 0.759155i \(0.725612\pi\)
\(312\) 0 0
\(313\) 2.33008e6 1.34434 0.672171 0.740396i \(-0.265362\pi\)
0.672171 + 0.740396i \(0.265362\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −427542. −0.238963 −0.119481 0.992836i \(-0.538123\pi\)
−0.119481 + 0.992836i \(0.538123\pi\)
\(318\) 0 0
\(319\) 1.63498e6 0.899569
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −685260. −0.365468
\(324\) 0 0
\(325\) 2.29570e6 1.20561
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 88788.0 0.0452235
\(330\) 0 0
\(331\) 396616. 0.198976 0.0994879 0.995039i \(-0.468280\pi\)
0.0994879 + 0.995039i \(0.468280\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.46597e6 −0.713695
\(336\) 0 0
\(337\) −3.21819e6 −1.54361 −0.771805 0.635860i \(-0.780646\pi\)
−0.771805 + 0.635860i \(0.780646\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.47699e6 −1.15356
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.78018e6 1.23951 0.619755 0.784796i \(-0.287232\pi\)
0.619755 + 0.784796i \(0.287232\pi\)
\(348\) 0 0
\(349\) −338800. −0.148895 −0.0744475 0.997225i \(-0.523719\pi\)
−0.0744475 + 0.997225i \(0.523719\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 362046. 0.154642 0.0773209 0.997006i \(-0.475363\pi\)
0.0773209 + 0.997006i \(0.475363\pi\)
\(354\) 0 0
\(355\) −2.37082e6 −0.998451
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 876528. 0.358946 0.179473 0.983763i \(-0.442561\pi\)
0.179473 + 0.983763i \(0.442561\pi\)
\(360\) 0 0
\(361\) −2.25520e6 −0.910787
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −302568. −0.118875
\(366\) 0 0
\(367\) −2.98062e6 −1.15516 −0.577578 0.816335i \(-0.696002\pi\)
−0.577578 + 0.816335i \(0.696002\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.82486e6 −0.688326
\(372\) 0 0
\(373\) 3.91441e6 1.45678 0.728391 0.685162i \(-0.240268\pi\)
0.728391 + 0.685162i \(0.240268\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.84174e6 −1.02975
\(378\) 0 0
\(379\) −3.60661e6 −1.28974 −0.644868 0.764294i \(-0.723088\pi\)
−0.644868 + 0.764294i \(0.723088\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.66644e6 −0.928826 −0.464413 0.885619i \(-0.653735\pi\)
−0.464413 + 0.885619i \(0.653735\pi\)
\(384\) 0 0
\(385\) −1.38298e6 −0.475513
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 213366. 0.0714910 0.0357455 0.999361i \(-0.488619\pi\)
0.0357455 + 0.999361i \(0.488619\pi\)
\(390\) 0 0
\(391\) −6.12360e6 −2.02565
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.60125e6 1.16134
\(396\) 0 0
\(397\) −4.09408e6 −1.30371 −0.651854 0.758345i \(-0.726008\pi\)
−0.651854 + 0.758345i \(0.726008\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −942366. −0.292657 −0.146328 0.989236i \(-0.546746\pi\)
−0.146328 + 0.989236i \(0.546746\pi\)
\(402\) 0 0
\(403\) 4.30525e6 1.32049
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.81488e6 −1.44079
\(408\) 0 0
\(409\) −4.84561e6 −1.43232 −0.716160 0.697936i \(-0.754102\pi\)
−0.716160 + 0.697936i \(0.754102\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.68080e6 −0.484887
\(414\) 0 0
\(415\) 2.95697e6 0.842804
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.73485e6 −0.482754 −0.241377 0.970431i \(-0.577599\pi\)
−0.241377 + 0.970431i \(0.577599\pi\)
\(420\) 0 0
\(421\) −1.65145e6 −0.454109 −0.227055 0.973882i \(-0.572910\pi\)
−0.227055 + 0.973882i \(0.572910\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.73140e6 1.53918
\(426\) 0 0
\(427\) −1.19932e6 −0.318322
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.14360e6 1.07445 0.537223 0.843440i \(-0.319473\pi\)
0.537223 + 0.843440i \(0.319473\pi\)
\(432\) 0 0
\(433\) −3.03966e6 −0.779121 −0.389561 0.921001i \(-0.627373\pi\)
−0.389561 + 0.921001i \(0.627373\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.97400e6 0.494474
\(438\) 0 0
\(439\) −2.54271e6 −0.629703 −0.314852 0.949141i \(-0.601955\pi\)
−0.314852 + 0.949141i \(0.601955\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.43210e6 −0.588806 −0.294403 0.955681i \(-0.595121\pi\)
−0.294403 + 0.955681i \(0.595121\pi\)
\(444\) 0 0
\(445\) 2.24532e6 0.537500
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.82853e6 −0.428042 −0.214021 0.976829i \(-0.568656\pi\)
−0.214021 + 0.976829i \(0.568656\pi\)
\(450\) 0 0
\(451\) 2.09059e6 0.483981
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.40374e6 0.544327
\(456\) 0 0
\(457\) 1.58063e6 0.354030 0.177015 0.984208i \(-0.443356\pi\)
0.177015 + 0.984208i \(0.443356\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.09604e6 −1.11681 −0.558407 0.829567i \(-0.688587\pi\)
−0.558407 + 0.829567i \(0.688587\pi\)
\(462\) 0 0
\(463\) 7.02338e6 1.52263 0.761313 0.648384i \(-0.224555\pi\)
0.761313 + 0.648384i \(0.224555\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.24845e6 −0.901443 −0.450722 0.892665i \(-0.648833\pi\)
−0.450722 + 0.892665i \(0.648833\pi\)
\(468\) 0 0
\(469\) −855148. −0.179518
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.24454e6 0.255775
\(474\) 0 0
\(475\) −1.84757e6 −0.375722
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 559284. 0.111377 0.0556883 0.998448i \(-0.482265\pi\)
0.0556883 + 0.998448i \(0.482265\pi\)
\(480\) 0 0
\(481\) 8.36872e6 1.64929
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.42615e6 0.275303
\(486\) 0 0
\(487\) 1.32057e6 0.252312 0.126156 0.992010i \(-0.459736\pi\)
0.126156 + 0.992010i \(0.459736\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.27193e6 1.17408 0.587040 0.809558i \(-0.300293\pi\)
0.587040 + 0.809558i \(0.300293\pi\)
\(492\) 0 0
\(493\) −7.09463e6 −1.31466
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.38298e6 −0.251144
\(498\) 0 0
\(499\) 3.93785e6 0.707959 0.353979 0.935253i \(-0.384828\pi\)
0.353979 + 0.935253i \(0.384828\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.59830e6 −1.33905 −0.669525 0.742790i \(-0.733502\pi\)
−0.669525 + 0.742790i \(0.733502\pi\)
\(504\) 0 0
\(505\) 8.33314e6 1.45405
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.82664e6 1.33900 0.669501 0.742812i \(-0.266508\pi\)
0.669501 + 0.742812i \(0.266508\pi\)
\(510\) 0 0
\(511\) −176498. −0.0299011
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.10581e7 −1.83722
\(516\) 0 0
\(517\) 608832. 0.100178
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.94454e6 −1.44366 −0.721828 0.692072i \(-0.756698\pi\)
−0.721828 + 0.692072i \(0.756698\pi\)
\(522\) 0 0
\(523\) −4.07481e6 −0.651407 −0.325704 0.945472i \(-0.605601\pi\)
−0.325704 + 0.945472i \(0.605601\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.07484e7 1.68584
\(528\) 0 0
\(529\) 1.12037e7 1.74069
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.63365e6 −0.554019
\(534\) 0 0
\(535\) −4.10357e6 −0.619837
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −806736. −0.119608
\(540\) 0 0
\(541\) −1.18676e7 −1.74329 −0.871644 0.490140i \(-0.836946\pi\)
−0.871644 + 0.490140i \(0.836946\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.73542e6 0.682915
\(546\) 0 0
\(547\) 5.37801e6 0.768516 0.384258 0.923226i \(-0.374457\pi\)
0.384258 + 0.923226i \(0.374457\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.28702e6 0.320916
\(552\) 0 0
\(553\) 2.10073e6 0.292117
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.64878e6 0.771466 0.385733 0.922611i \(-0.373949\pi\)
0.385733 + 0.922611i \(0.373949\pi\)
\(558\) 0 0
\(559\) −2.16314e6 −0.292789
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.56407e6 0.606850 0.303425 0.952855i \(-0.401870\pi\)
0.303425 + 0.952855i \(0.401870\pi\)
\(564\) 0 0
\(565\) 734328. 0.0967763
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.00165e6 −1.03609 −0.518047 0.855352i \(-0.673341\pi\)
−0.518047 + 0.855352i \(0.673341\pi\)
\(570\) 0 0
\(571\) 1.37164e7 1.76055 0.880275 0.474464i \(-0.157358\pi\)
0.880275 + 0.474464i \(0.157358\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.65102e7 −2.08249
\(576\) 0 0
\(577\) 6.09797e6 0.762510 0.381255 0.924470i \(-0.375492\pi\)
0.381255 + 0.924470i \(0.375492\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.72490e6 0.211994
\(582\) 0 0
\(583\) −1.25133e7 −1.52476
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.08462e6 −0.968422 −0.484211 0.874951i \(-0.660893\pi\)
−0.484211 + 0.874951i \(0.660893\pi\)
\(588\) 0 0
\(589\) −3.46484e6 −0.411524
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.41575e6 −0.165330 −0.0826649 0.996577i \(-0.526343\pi\)
−0.0826649 + 0.996577i \(0.526343\pi\)
\(594\) 0 0
\(595\) 6.00113e6 0.694929
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.75460e6 0.996941 0.498470 0.866907i \(-0.333895\pi\)
0.498470 + 0.866907i \(0.333895\pi\)
\(600\) 0 0
\(601\) 8.70276e6 0.982813 0.491407 0.870930i \(-0.336483\pi\)
0.491407 + 0.870930i \(0.336483\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.04502e6 0.449296
\(606\) 0 0
\(607\) 1.69578e7 1.86809 0.934045 0.357157i \(-0.116254\pi\)
0.934045 + 0.357157i \(0.116254\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.05821e6 −0.114675
\(612\) 0 0
\(613\) 1.76743e7 1.89973 0.949866 0.312658i \(-0.101220\pi\)
0.949866 + 0.312658i \(0.101220\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.70636e6 1.02646 0.513232 0.858250i \(-0.328448\pi\)
0.513232 + 0.858250i \(0.328448\pi\)
\(618\) 0 0
\(619\) −1.48739e7 −1.56027 −0.780133 0.625613i \(-0.784849\pi\)
−0.780133 + 0.625613i \(0.784849\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.30977e6 0.135199
\(624\) 0 0
\(625\) −6.59724e6 −0.675557
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.08931e7 2.10561
\(630\) 0 0
\(631\) −1.26353e7 −1.26331 −0.631656 0.775248i \(-0.717625\pi\)
−0.631656 + 0.775248i \(0.717625\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.65433e7 2.61229
\(636\) 0 0
\(637\) 1.40218e6 0.136917
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.23398e6 −0.599267 −0.299634 0.954054i \(-0.596864\pi\)
−0.299634 + 0.954054i \(0.596864\pi\)
\(642\) 0 0
\(643\) −1.06874e7 −1.01940 −0.509701 0.860352i \(-0.670244\pi\)
−0.509701 + 0.860352i \(0.670244\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.83258e7 1.72109 0.860544 0.509376i \(-0.170124\pi\)
0.860544 + 0.509376i \(0.170124\pi\)
\(648\) 0 0
\(649\) −1.15255e7 −1.07411
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.28857e6 0.668897 0.334448 0.942414i \(-0.391450\pi\)
0.334448 + 0.942414i \(0.391450\pi\)
\(654\) 0 0
\(655\) 2.07194e6 0.188701
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.54337e6 0.407534 0.203767 0.979019i \(-0.434681\pi\)
0.203767 + 0.979019i \(0.434681\pi\)
\(660\) 0 0
\(661\) −2.10021e7 −1.86964 −0.934821 0.355120i \(-0.884440\pi\)
−0.934821 + 0.355120i \(0.884440\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.93452e6 −0.169636
\(666\) 0 0
\(667\) 2.04372e7 1.77872
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.22394e6 −0.705137
\(672\) 0 0
\(673\) 3.46923e6 0.295253 0.147627 0.989043i \(-0.452837\pi\)
0.147627 + 0.989043i \(0.452837\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.80916e7 1.51707 0.758536 0.651631i \(-0.225915\pi\)
0.758536 + 0.651631i \(0.225915\pi\)
\(678\) 0 0
\(679\) 831922. 0.0692481
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.67752e6 0.383675 0.191838 0.981427i \(-0.438555\pi\)
0.191838 + 0.981427i \(0.438555\pi\)
\(684\) 0 0
\(685\) 2.54717e7 2.07411
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.17493e7 1.74541
\(690\) 0 0
\(691\) −1.68960e7 −1.34614 −0.673069 0.739579i \(-0.735024\pi\)
−0.673069 + 0.739579i \(0.735024\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.10492e7 1.65300
\(696\) 0 0
\(697\) −9.07168e6 −0.707303
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.40964e6 −0.185207 −0.0926035 0.995703i \(-0.529519\pi\)
−0.0926035 + 0.995703i \(0.529519\pi\)
\(702\) 0 0
\(703\) −6.73510e6 −0.513991
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.86100e6 0.365744
\(708\) 0 0
\(709\) −5.77010e6 −0.431090 −0.215545 0.976494i \(-0.569153\pi\)
−0.215545 + 0.976494i \(0.569153\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.09624e7 −2.28092
\(714\) 0 0
\(715\) 1.64828e7 1.20578
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.43716e7 −1.03677 −0.518385 0.855147i \(-0.673467\pi\)
−0.518385 + 0.855147i \(0.673467\pi\)
\(720\) 0 0
\(721\) −6.45056e6 −0.462124
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.91282e7 −1.35154
\(726\) 0 0
\(727\) 1.40705e7 0.987353 0.493676 0.869646i \(-0.335653\pi\)
0.493676 + 0.869646i \(0.335653\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.40043e6 −0.373796
\(732\) 0 0
\(733\) −3.75000e6 −0.257793 −0.128897 0.991658i \(-0.541144\pi\)
−0.128897 + 0.991658i \(0.541144\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.86387e6 −0.397664
\(738\) 0 0
\(739\) −2.61318e7 −1.76019 −0.880093 0.474802i \(-0.842520\pi\)
−0.880093 + 0.474802i \(0.842520\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −159072. −0.0105711 −0.00528557 0.999986i \(-0.501682\pi\)
−0.00528557 + 0.999986i \(0.501682\pi\)
\(744\) 0 0
\(745\) −5.08990e6 −0.335984
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.39375e6 −0.155910
\(750\) 0 0
\(751\) 2.65311e7 1.71654 0.858272 0.513196i \(-0.171539\pi\)
0.858272 + 0.513196i \(0.171539\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.04536e7 0.667421
\(756\) 0 0
\(757\) −1.52032e7 −0.964260 −0.482130 0.876100i \(-0.660137\pi\)
−0.482130 + 0.876100i \(0.660137\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4.71380e6 −0.295059 −0.147530 0.989058i \(-0.547132\pi\)
−0.147530 + 0.989058i \(0.547132\pi\)
\(762\) 0 0
\(763\) 2.76233e6 0.171776
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.00324e7 1.22954
\(768\) 0 0
\(769\) −1.58977e6 −0.0969434 −0.0484717 0.998825i \(-0.515435\pi\)
−0.0484717 + 0.998825i \(0.515435\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.69095e6 0.583334 0.291667 0.956520i \(-0.405790\pi\)
0.291667 + 0.956520i \(0.405790\pi\)
\(774\) 0 0
\(775\) 2.89793e7 1.73314
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.92434e6 0.172657
\(780\) 0 0
\(781\) −9.48326e6 −0.556327
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.38736e6 −0.369954
\(786\) 0 0
\(787\) 1.57170e6 0.0904549 0.0452275 0.998977i \(-0.485599\pi\)
0.0452275 + 0.998977i \(0.485599\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 428358. 0.0243425
\(792\) 0 0
\(793\) 1.42940e7 0.807180
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.25298e6 0.125635 0.0628175 0.998025i \(-0.479991\pi\)
0.0628175 + 0.998025i \(0.479991\pi\)
\(798\) 0 0
\(799\) −2.64190e6 −0.146403
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.21027e6 −0.0662360
\(804\) 0 0
\(805\) −1.72872e7 −0.940232
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.37938e7 1.27818 0.639090 0.769132i \(-0.279311\pi\)
0.639090 + 0.769132i \(0.279311\pi\)
\(810\) 0 0
\(811\) −5.32300e6 −0.284187 −0.142093 0.989853i \(-0.545383\pi\)
−0.142093 + 0.989853i \(0.545383\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.04375e7 0.550431
\(816\) 0 0
\(817\) 1.74088e6 0.0912460
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.48802e7 −0.770464 −0.385232 0.922820i \(-0.625879\pi\)
−0.385232 + 0.922820i \(0.625879\pi\)
\(822\) 0 0
\(823\) −2.00601e7 −1.03236 −0.516182 0.856479i \(-0.672647\pi\)
−0.516182 + 0.856479i \(0.672647\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.21539e7 0.617949 0.308975 0.951070i \(-0.400014\pi\)
0.308975 + 0.951070i \(0.400014\pi\)
\(828\) 0 0
\(829\) 3.21197e7 1.62325 0.811625 0.584179i \(-0.198583\pi\)
0.811625 + 0.584179i \(0.198583\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.50066e6 0.174798
\(834\) 0 0
\(835\) 6.08328e6 0.301941
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.01320e6 −0.0496922 −0.0248461 0.999691i \(-0.507910\pi\)
−0.0248461 + 0.999691i \(0.507910\pi\)
\(840\) 0 0
\(841\) 3.16681e6 0.154394
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.53991e6 0.122370
\(846\) 0 0
\(847\) 2.35960e6 0.113013
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −6.01860e7 −2.84886
\(852\) 0 0
\(853\) 234824. 0.0110502 0.00552510 0.999985i \(-0.498241\pi\)
0.00552510 + 0.999985i \(0.498241\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.83802e7 −1.31997 −0.659985 0.751279i \(-0.729437\pi\)
−0.659985 + 0.751279i \(0.729437\pi\)
\(858\) 0 0
\(859\) −4.00081e7 −1.84997 −0.924986 0.380001i \(-0.875924\pi\)
−0.924986 + 0.380001i \(0.875924\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.08030e7 −0.950823 −0.475411 0.879764i \(-0.657701\pi\)
−0.475411 + 0.879764i \(0.657701\pi\)
\(864\) 0 0
\(865\) −3.70904e7 −1.68547
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.44050e7 0.647088
\(870\) 0 0
\(871\) 1.01920e7 0.455211
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.31750e6 0.146484
\(876\) 0 0
\(877\) 3.03559e7 1.33273 0.666367 0.745624i \(-0.267848\pi\)
0.666367 + 0.745624i \(0.267848\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.58936e7 1.12396 0.561981 0.827150i \(-0.310039\pi\)
0.561981 + 0.827150i \(0.310039\pi\)
\(882\) 0 0
\(883\) 1.88813e7 0.814950 0.407475 0.913216i \(-0.366409\pi\)
0.407475 + 0.913216i \(0.366409\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.34431e7 −1.00048 −0.500238 0.865888i \(-0.666754\pi\)
−0.500238 + 0.865888i \(0.666754\pi\)
\(888\) 0 0
\(889\) 1.54836e7 0.657079
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 851640. 0.0357378
\(894\) 0 0
\(895\) 898128. 0.0374784
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.58722e7 −1.48033
\(900\) 0 0
\(901\) 5.42988e7 2.22833
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.58694e7 1.86166
\(906\) 0 0
\(907\) 5.60873e6 0.226384 0.113192 0.993573i \(-0.463892\pi\)
0.113192 + 0.993573i \(0.463892\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.16215e7 0.863156 0.431578 0.902076i \(-0.357957\pi\)
0.431578 + 0.902076i \(0.357957\pi\)
\(912\) 0 0
\(913\) 1.18279e7 0.469602
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.20863e6 0.0474648
\(918\) 0 0
\(919\) −4.51695e7 −1.76424 −0.882119 0.471028i \(-0.843883\pi\)
−0.882119 + 0.471028i \(0.843883\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.64828e7 0.636835
\(924\) 0 0
\(925\) 5.63312e7 2.16469
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.28729e7 0.869524 0.434762 0.900545i \(-0.356832\pi\)
0.434762 + 0.900545i \(0.356832\pi\)
\(930\) 0 0
\(931\) −1.12847e6 −0.0426693
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.11506e7 1.53938
\(936\) 0 0
\(937\) −1.79616e7 −0.668336 −0.334168 0.942514i \(-0.608455\pi\)
−0.334168 + 0.942514i \(0.608455\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.79697e7 0.661558 0.330779 0.943708i \(-0.392689\pi\)
0.330779 + 0.943708i \(0.392689\pi\)
\(942\) 0 0
\(943\) 2.61324e7 0.956974
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.32115e7 1.56576 0.782879 0.622174i \(-0.213750\pi\)
0.782879 + 0.622174i \(0.213750\pi\)
\(948\) 0 0
\(949\) 2.10357e6 0.0758213
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 7.50965e6 0.267848 0.133924 0.990992i \(-0.457242\pi\)
0.133924 + 0.990992i \(0.457242\pi\)
\(954\) 0 0
\(955\) 4.83820e7 1.71662
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.48585e7 0.521708
\(960\) 0 0
\(961\) 2.57172e7 0.898288
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3.47708e7 1.20198
\(966\) 0 0
\(967\) 1.69305e7 0.582242 0.291121 0.956686i \(-0.405972\pi\)
0.291121 + 0.956686i \(0.405972\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.86144e7 0.973949 0.486974 0.873416i \(-0.338101\pi\)
0.486974 + 0.873416i \(0.338101\pi\)
\(972\) 0 0
\(973\) 1.22787e7 0.415787
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.69445e7 −1.23826 −0.619132 0.785287i \(-0.712515\pi\)
−0.619132 + 0.785287i \(0.712515\pi\)
\(978\) 0 0
\(979\) 8.98128e6 0.299489
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −3.88787e7 −1.28330 −0.641650 0.766998i \(-0.721750\pi\)
−0.641650 + 0.766998i \(0.721750\pi\)
\(984\) 0 0
\(985\) −4.15755e7 −1.36536
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.55568e7 0.505743
\(990\) 0 0
\(991\) −2.49212e7 −0.806092 −0.403046 0.915180i \(-0.632049\pi\)
−0.403046 + 0.915180i \(0.632049\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.37106e7 1.39968
\(996\) 0 0
\(997\) 1.01956e7 0.324845 0.162422 0.986721i \(-0.448069\pi\)
0.162422 + 0.986721i \(0.448069\pi\)
\(998\) 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.b.1.1 1
3.2 odd 2 112.6.a.c.1.1 1
4.3 odd 2 126.6.a.f.1.1 1
12.11 even 2 14.6.a.a.1.1 1
21.20 even 2 784.6.a.i.1.1 1
24.5 odd 2 448.6.a.l.1.1 1
24.11 even 2 448.6.a.e.1.1 1
28.27 even 2 882.6.a.x.1.1 1
60.23 odd 4 350.6.c.d.99.2 2
60.47 odd 4 350.6.c.d.99.1 2
60.59 even 2 350.6.a.i.1.1 1
84.11 even 6 98.6.c.c.79.1 2
84.23 even 6 98.6.c.c.67.1 2
84.47 odd 6 98.6.c.d.67.1 2
84.59 odd 6 98.6.c.d.79.1 2
84.83 odd 2 98.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.a.a.1.1 1 12.11 even 2
98.6.a.a.1.1 1 84.83 odd 2
98.6.c.c.67.1 2 84.23 even 6
98.6.c.c.79.1 2 84.11 even 6
98.6.c.d.67.1 2 84.47 odd 6
98.6.c.d.79.1 2 84.59 odd 6
112.6.a.c.1.1 1 3.2 odd 2
126.6.a.f.1.1 1 4.3 odd 2
350.6.a.i.1.1 1 60.59 even 2
350.6.c.d.99.1 2 60.47 odd 4
350.6.c.d.99.2 2 60.23 odd 4
448.6.a.e.1.1 1 24.11 even 2
448.6.a.l.1.1 1 24.5 odd 2
784.6.a.i.1.1 1 21.20 even 2
882.6.a.x.1.1 1 28.27 even 2
1008.6.a.b.1.1 1 1.1 even 1 trivial