Properties

Label 1008.6.a.c.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 21)
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)
 
\(f(q)\) \(=\) \(q-78.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-78.0000 q^{5} -49.0000 q^{7} +444.000 q^{11} -442.000 q^{13} +126.000 q^{17} -2684.00 q^{19} +4200.00 q^{23} +2959.00 q^{25} +5442.00 q^{29} -80.0000 q^{31} +3822.00 q^{35} -5434.00 q^{37} -7962.00 q^{41} +11524.0 q^{43} -13920.0 q^{47} +2401.00 q^{49} +9594.00 q^{53} -34632.0 q^{55} +27492.0 q^{59} +49478.0 q^{61} +34476.0 q^{65} +59356.0 q^{67} +32040.0 q^{71} -61846.0 q^{73} -21756.0 q^{77} +65776.0 q^{79} +40188.0 q^{83} -9828.00 q^{85} +7974.00 q^{89} +21658.0 q^{91} +209352. q^{95} -143662. q^{97} +O(q^{100})\)

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
\(5\) −78.0000 −1.39531 −0.697653 0.716436i \(-0.745772\pi\)
−0.697653 + 0.716436i \(0.745772\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 444.000 1.10637 0.553186 0.833058i \(-0.313412\pi\)
0.553186 + 0.833058i \(0.313412\pi\)
\(12\) 0 0
\(13\) −442.000 −0.725377 −0.362689 0.931910i \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 126.000 0.105742 0.0528711 0.998601i \(-0.483163\pi\)
0.0528711 + 0.998601i \(0.483163\pi\)
\(18\) 0 0
\(19\) −2684.00 −1.70568 −0.852842 0.522169i \(-0.825123\pi\)
−0.852842 + 0.522169i \(0.825123\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4200.00 1.65550 0.827751 0.561096i \(-0.189620\pi\)
0.827751 + 0.561096i \(0.189620\pi\)
\(24\) 0 0
\(25\) 2959.00 0.946880
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5442.00 1.20161 0.600805 0.799396i \(-0.294847\pi\)
0.600805 + 0.799396i \(0.294847\pi\)
\(30\) 0 0
\(31\) −80.0000 −0.0149515 −0.00747577 0.999972i \(-0.502380\pi\)
−0.00747577 + 0.999972i \(0.502380\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3822.00 0.527376
\(36\) 0 0
\(37\) −5434.00 −0.652552 −0.326276 0.945274i \(-0.605794\pi\)
−0.326276 + 0.945274i \(0.605794\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7962.00 −0.739712 −0.369856 0.929089i \(-0.620593\pi\)
−0.369856 + 0.929089i \(0.620593\pi\)
\(42\) 0 0
\(43\) 11524.0 0.950456 0.475228 0.879863i \(-0.342366\pi\)
0.475228 + 0.879863i \(0.342366\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −13920.0 −0.919167 −0.459584 0.888134i \(-0.652001\pi\)
−0.459584 + 0.888134i \(0.652001\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9594.00 0.469148 0.234574 0.972098i \(-0.424630\pi\)
0.234574 + 0.972098i \(0.424630\pi\)
\(54\) 0 0
\(55\) −34632.0 −1.54373
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 27492.0 1.02820 0.514098 0.857731i \(-0.328127\pi\)
0.514098 + 0.857731i \(0.328127\pi\)
\(60\) 0 0
\(61\) 49478.0 1.70250 0.851251 0.524759i \(-0.175845\pi\)
0.851251 + 0.524759i \(0.175845\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 34476.0 1.01212
\(66\) 0 0
\(67\) 59356.0 1.61539 0.807695 0.589600i \(-0.200715\pi\)
0.807695 + 0.589600i \(0.200715\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 32040.0 0.754304 0.377152 0.926151i \(-0.376903\pi\)
0.377152 + 0.926151i \(0.376903\pi\)
\(72\) 0 0
\(73\) −61846.0 −1.35833 −0.679164 0.733987i \(-0.737657\pi\)
−0.679164 + 0.733987i \(0.737657\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −21756.0 −0.418169
\(78\) 0 0
\(79\) 65776.0 1.18577 0.592884 0.805288i \(-0.297989\pi\)
0.592884 + 0.805288i \(0.297989\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 40188.0 0.640326 0.320163 0.947362i \(-0.396262\pi\)
0.320163 + 0.947362i \(0.396262\pi\)
\(84\) 0 0
\(85\) −9828.00 −0.147543
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7974.00 0.106709 0.0533545 0.998576i \(-0.483009\pi\)
0.0533545 + 0.998576i \(0.483009\pi\)
\(90\) 0 0
\(91\) 21658.0 0.274167
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 209352. 2.37995
\(96\) 0 0
\(97\) −143662. −1.55029 −0.775144 0.631784i \(-0.782323\pi\)
−0.775144 + 0.631784i \(0.782323\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2706.00 0.0263952 0.0131976 0.999913i \(-0.495799\pi\)
0.0131976 + 0.999913i \(0.495799\pi\)
\(102\) 0 0
\(103\) −131768. −1.22382 −0.611909 0.790928i \(-0.709598\pi\)
−0.611909 + 0.790928i \(0.709598\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −128916. −1.08855 −0.544274 0.838908i \(-0.683195\pi\)
−0.544274 + 0.838908i \(0.683195\pi\)
\(108\) 0 0
\(109\) −100978. −0.814068 −0.407034 0.913413i \(-0.633437\pi\)
−0.407034 + 0.913413i \(0.633437\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −220146. −1.62186 −0.810932 0.585140i \(-0.801040\pi\)
−0.810932 + 0.585140i \(0.801040\pi\)
\(114\) 0 0
\(115\) −327600. −2.30993
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6174.00 −0.0399668
\(120\) 0 0
\(121\) 36085.0 0.224059
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12948.0 0.0741187
\(126\) 0 0
\(127\) 74320.0 0.408880 0.204440 0.978879i \(-0.434463\pi\)
0.204440 + 0.978879i \(0.434463\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −155316. −0.790748 −0.395374 0.918520i \(-0.629385\pi\)
−0.395374 + 0.918520i \(0.629385\pi\)
\(132\) 0 0
\(133\) 131516. 0.644688
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 264246. 1.20284 0.601419 0.798934i \(-0.294602\pi\)
0.601419 + 0.798934i \(0.294602\pi\)
\(138\) 0 0
\(139\) −224612. −0.986043 −0.493022 0.870017i \(-0.664108\pi\)
−0.493022 + 0.870017i \(0.664108\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −196248. −0.802537
\(144\) 0 0
\(145\) −424476. −1.67661
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 82074.0 0.302859 0.151429 0.988468i \(-0.451612\pi\)
0.151429 + 0.988468i \(0.451612\pi\)
\(150\) 0 0
\(151\) 287032. 1.02444 0.512222 0.858853i \(-0.328823\pi\)
0.512222 + 0.858853i \(0.328823\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6240.00 0.0208620
\(156\) 0 0
\(157\) 129878. 0.420520 0.210260 0.977646i \(-0.432569\pi\)
0.210260 + 0.977646i \(0.432569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −205800. −0.625721
\(162\) 0 0
\(163\) −555284. −1.63699 −0.818495 0.574513i \(-0.805191\pi\)
−0.818495 + 0.574513i \(0.805191\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 43512.0 0.120731 0.0603654 0.998176i \(-0.480773\pi\)
0.0603654 + 0.998176i \(0.480773\pi\)
\(168\) 0 0
\(169\) −175929. −0.473828
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18330.0 0.0465637 0.0232818 0.999729i \(-0.492588\pi\)
0.0232818 + 0.999729i \(0.492588\pi\)
\(174\) 0 0
\(175\) −144991. −0.357887
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −153324. −0.357666 −0.178833 0.983879i \(-0.557232\pi\)
−0.178833 + 0.983879i \(0.557232\pi\)
\(180\) 0 0
\(181\) −382066. −0.866846 −0.433423 0.901191i \(-0.642694\pi\)
−0.433423 + 0.901191i \(0.642694\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 423852. 0.910510
\(186\) 0 0
\(187\) 55944.0 0.116990
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −273408. −0.542285 −0.271143 0.962539i \(-0.587402\pi\)
−0.271143 + 0.962539i \(0.587402\pi\)
\(192\) 0 0
\(193\) 153602. 0.296827 0.148414 0.988925i \(-0.452583\pi\)
0.148414 + 0.988925i \(0.452583\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −154422. −0.283494 −0.141747 0.989903i \(-0.545272\pi\)
−0.141747 + 0.989903i \(0.545272\pi\)
\(198\) 0 0
\(199\) 366856. 0.656694 0.328347 0.944557i \(-0.393508\pi\)
0.328347 + 0.944557i \(0.393508\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −266658. −0.454166
\(204\) 0 0
\(205\) 621036. 1.03212
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.19170e6 −1.88712
\(210\) 0 0
\(211\) −520244. −0.804453 −0.402227 0.915540i \(-0.631764\pi\)
−0.402227 + 0.915540i \(0.631764\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −898872. −1.32618
\(216\) 0 0
\(217\) 3920.00 0.00565115
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −55692.0 −0.0767030
\(222\) 0 0
\(223\) −304736. −0.410357 −0.205178 0.978725i \(-0.565777\pi\)
−0.205178 + 0.978725i \(0.565777\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 288588. 0.371718 0.185859 0.982576i \(-0.440493\pi\)
0.185859 + 0.982576i \(0.440493\pi\)
\(228\) 0 0
\(229\) 772190. 0.973051 0.486525 0.873666i \(-0.338264\pi\)
0.486525 + 0.873666i \(0.338264\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −252234. −0.304378 −0.152189 0.988351i \(-0.548632\pi\)
−0.152189 + 0.988351i \(0.548632\pi\)
\(234\) 0 0
\(235\) 1.08576e6 1.28252
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.45114e6 −1.64329 −0.821643 0.570002i \(-0.806942\pi\)
−0.821643 + 0.570002i \(0.806942\pi\)
\(240\) 0 0
\(241\) −146398. −0.162365 −0.0811825 0.996699i \(-0.525870\pi\)
−0.0811825 + 0.996699i \(0.525870\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −187278. −0.199329
\(246\) 0 0
\(247\) 1.18633e6 1.23726
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 607860. 0.609003 0.304501 0.952512i \(-0.401510\pi\)
0.304501 + 0.952512i \(0.401510\pi\)
\(252\) 0 0
\(253\) 1.86480e6 1.83160
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −95586.0 −0.0902737 −0.0451369 0.998981i \(-0.514372\pi\)
−0.0451369 + 0.998981i \(0.514372\pi\)
\(258\) 0 0
\(259\) 266266. 0.246642
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.20034e6 −1.96156 −0.980779 0.195121i \(-0.937490\pi\)
−0.980779 + 0.195121i \(0.937490\pi\)
\(264\) 0 0
\(265\) −748332. −0.654605
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.77025e6 −1.49160 −0.745801 0.666169i \(-0.767933\pi\)
−0.745801 + 0.666169i \(0.767933\pi\)
\(270\) 0 0
\(271\) 223504. 0.184868 0.0924341 0.995719i \(-0.470535\pi\)
0.0924341 + 0.995719i \(0.470535\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.31380e6 1.04760
\(276\) 0 0
\(277\) −342778. −0.268419 −0.134210 0.990953i \(-0.542850\pi\)
−0.134210 + 0.990953i \(0.542850\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −480378. −0.362925 −0.181463 0.983398i \(-0.558083\pi\)
−0.181463 + 0.983398i \(0.558083\pi\)
\(282\) 0 0
\(283\) 29980.0 0.0222518 0.0111259 0.999938i \(-0.496458\pi\)
0.0111259 + 0.999938i \(0.496458\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 390138. 0.279585
\(288\) 0 0
\(289\) −1.40398e6 −0.988819
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 198066. 0.134785 0.0673924 0.997727i \(-0.478532\pi\)
0.0673924 + 0.997727i \(0.478532\pi\)
\(294\) 0 0
\(295\) −2.14438e6 −1.43465
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.85640e6 −1.20086
\(300\) 0 0
\(301\) −564676. −0.359239
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.85928e6 −2.37551
\(306\) 0 0
\(307\) 1.04564e6 0.633191 0.316595 0.948561i \(-0.397460\pi\)
0.316595 + 0.948561i \(0.397460\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.83718e6 1.07708 0.538542 0.842598i \(-0.318975\pi\)
0.538542 + 0.842598i \(0.318975\pi\)
\(312\) 0 0
\(313\) −365494. −0.210872 −0.105436 0.994426i \(-0.533624\pi\)
−0.105436 + 0.994426i \(0.533624\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 28338.0 0.0158388 0.00791938 0.999969i \(-0.497479\pi\)
0.00791938 + 0.999969i \(0.497479\pi\)
\(318\) 0 0
\(319\) 2.41625e6 1.32943
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −338184. −0.180363
\(324\) 0 0
\(325\) −1.30788e6 −0.686845
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 682080. 0.347413
\(330\) 0 0
\(331\) −1.93392e6 −0.970214 −0.485107 0.874455i \(-0.661219\pi\)
−0.485107 + 0.874455i \(0.661219\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.62977e6 −2.25397
\(336\) 0 0
\(337\) −1.88817e6 −0.905664 −0.452832 0.891596i \(-0.649586\pi\)
−0.452832 + 0.891596i \(0.649586\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −35520.0 −0.0165420
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.91937e6 1.30156 0.650782 0.759264i \(-0.274441\pi\)
0.650782 + 0.759264i \(0.274441\pi\)
\(348\) 0 0
\(349\) −780682. −0.343092 −0.171546 0.985176i \(-0.554876\pi\)
−0.171546 + 0.985176i \(0.554876\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.33437e6 −0.569954 −0.284977 0.958534i \(-0.591986\pi\)
−0.284977 + 0.958534i \(0.591986\pi\)
\(354\) 0 0
\(355\) −2.49912e6 −1.05249
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.01743e6 0.416648 0.208324 0.978060i \(-0.433199\pi\)
0.208324 + 0.978060i \(0.433199\pi\)
\(360\) 0 0
\(361\) 4.72776e6 1.90936
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.82399e6 1.89528
\(366\) 0 0
\(367\) −837680. −0.324648 −0.162324 0.986737i \(-0.551899\pi\)
−0.162324 + 0.986737i \(0.551899\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −470106. −0.177321
\(372\) 0 0
\(373\) −1.51993e6 −0.565655 −0.282827 0.959171i \(-0.591272\pi\)
−0.282827 + 0.959171i \(0.591272\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.40536e6 −0.871620
\(378\) 0 0
\(379\) −2.64465e6 −0.945737 −0.472869 0.881133i \(-0.656781\pi\)
−0.472869 + 0.881133i \(0.656781\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.01336e6 0.701333 0.350667 0.936500i \(-0.385955\pi\)
0.350667 + 0.936500i \(0.385955\pi\)
\(384\) 0 0
\(385\) 1.69697e6 0.583474
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 726234. 0.243334 0.121667 0.992571i \(-0.461176\pi\)
0.121667 + 0.992571i \(0.461176\pi\)
\(390\) 0 0
\(391\) 529200. 0.175056
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.13053e6 −1.65451
\(396\) 0 0
\(397\) 4.57578e6 1.45710 0.728549 0.684993i \(-0.240195\pi\)
0.728549 + 0.684993i \(0.240195\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 33870.0 0.0105185 0.00525926 0.999986i \(-0.498326\pi\)
0.00525926 + 0.999986i \(0.498326\pi\)
\(402\) 0 0
\(403\) 35360.0 0.0108455
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.41270e6 −0.721966
\(408\) 0 0
\(409\) −5.86178e6 −1.73269 −0.866346 0.499444i \(-0.833538\pi\)
−0.866346 + 0.499444i \(0.833538\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.34711e6 −0.388622
\(414\) 0 0
\(415\) −3.13466e6 −0.893451
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 302748. 0.0842454 0.0421227 0.999112i \(-0.486588\pi\)
0.0421227 + 0.999112i \(0.486588\pi\)
\(420\) 0 0
\(421\) −5.36708e6 −1.47582 −0.737909 0.674900i \(-0.764187\pi\)
−0.737909 + 0.674900i \(0.764187\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 372834. 0.100125
\(426\) 0 0
\(427\) −2.42442e6 −0.643485
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.17706e6 0.305214 0.152607 0.988287i \(-0.451233\pi\)
0.152607 + 0.988287i \(0.451233\pi\)
\(432\) 0 0
\(433\) −3.66249e6 −0.938766 −0.469383 0.882995i \(-0.655524\pi\)
−0.469383 + 0.882995i \(0.655524\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.12728e7 −2.82376
\(438\) 0 0
\(439\) 2.53674e6 0.628225 0.314113 0.949386i \(-0.398293\pi\)
0.314113 + 0.949386i \(0.398293\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.01504e6 1.45623 0.728113 0.685457i \(-0.240397\pi\)
0.728113 + 0.685457i \(0.240397\pi\)
\(444\) 0 0
\(445\) −621972. −0.148892
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.65965e6 −1.32487 −0.662436 0.749119i \(-0.730477\pi\)
−0.662436 + 0.749119i \(0.730477\pi\)
\(450\) 0 0
\(451\) −3.53513e6 −0.818397
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.68932e6 −0.382547
\(456\) 0 0
\(457\) −6.46159e6 −1.44727 −0.723634 0.690184i \(-0.757530\pi\)
−0.723634 + 0.690184i \(0.757530\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.37353e6 0.739320 0.369660 0.929167i \(-0.379474\pi\)
0.369660 + 0.929167i \(0.379474\pi\)
\(462\) 0 0
\(463\) 4.54974e6 0.986358 0.493179 0.869928i \(-0.335835\pi\)
0.493179 + 0.869928i \(0.335835\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.01136e6 0.426773 0.213386 0.976968i \(-0.431551\pi\)
0.213386 + 0.976968i \(0.431551\pi\)
\(468\) 0 0
\(469\) −2.90844e6 −0.610560
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.11666e6 1.05156
\(474\) 0 0
\(475\) −7.94196e6 −1.61508
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.60402e6 −1.51427 −0.757137 0.653257i \(-0.773402\pi\)
−0.757137 + 0.653257i \(0.773402\pi\)
\(480\) 0 0
\(481\) 2.40183e6 0.473347
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.12056e7 2.16313
\(486\) 0 0
\(487\) −673112. −0.128607 −0.0643035 0.997930i \(-0.520483\pi\)
−0.0643035 + 0.997930i \(0.520483\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.47170e6 −0.462692 −0.231346 0.972872i \(-0.574313\pi\)
−0.231346 + 0.972872i \(0.574313\pi\)
\(492\) 0 0
\(493\) 685692. 0.127061
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.56996e6 −0.285100
\(498\) 0 0
\(499\) −6.08152e6 −1.09335 −0.546677 0.837343i \(-0.684108\pi\)
−0.546677 + 0.837343i \(0.684108\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −846216. −0.149129 −0.0745644 0.997216i \(-0.523757\pi\)
−0.0745644 + 0.997216i \(0.523757\pi\)
\(504\) 0 0
\(505\) −211068. −0.0368293
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.66785e6 1.31183 0.655917 0.754833i \(-0.272282\pi\)
0.655917 + 0.754833i \(0.272282\pi\)
\(510\) 0 0
\(511\) 3.03045e6 0.513400
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.02779e7 1.70760
\(516\) 0 0
\(517\) −6.18048e6 −1.01694
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.68938e6 1.56387 0.781937 0.623357i \(-0.214232\pi\)
0.781937 + 0.623357i \(0.214232\pi\)
\(522\) 0 0
\(523\) 7.51678e6 1.20165 0.600824 0.799381i \(-0.294839\pi\)
0.600824 + 0.799381i \(0.294839\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10080.0 −0.00158101
\(528\) 0 0
\(529\) 1.12037e7 1.74069
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.51920e6 0.536570
\(534\) 0 0
\(535\) 1.00554e7 1.51886
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.06604e6 0.158053
\(540\) 0 0
\(541\) 7.34325e6 1.07869 0.539343 0.842086i \(-0.318673\pi\)
0.539343 + 0.842086i \(0.318673\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.87628e6 1.13587
\(546\) 0 0
\(547\) −2.18296e6 −0.311945 −0.155973 0.987761i \(-0.549851\pi\)
−0.155973 + 0.987761i \(0.549851\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.46063e7 −2.04957
\(552\) 0 0
\(553\) −3.22302e6 −0.448178
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.25466e7 −1.71351 −0.856755 0.515724i \(-0.827523\pi\)
−0.856755 + 0.515724i \(0.827523\pi\)
\(558\) 0 0
\(559\) −5.09361e6 −0.689439
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.15972e6 0.686050 0.343025 0.939326i \(-0.388549\pi\)
0.343025 + 0.939326i \(0.388549\pi\)
\(564\) 0 0
\(565\) 1.71714e7 2.26300
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.17452e7 −1.52083 −0.760414 0.649439i \(-0.775004\pi\)
−0.760414 + 0.649439i \(0.775004\pi\)
\(570\) 0 0
\(571\) 7.54728e6 0.968725 0.484362 0.874867i \(-0.339052\pi\)
0.484362 + 0.874867i \(0.339052\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.24278e7 1.56756
\(576\) 0 0
\(577\) 9.28483e6 1.16101 0.580503 0.814258i \(-0.302856\pi\)
0.580503 + 0.814258i \(0.302856\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.96921e6 −0.242020
\(582\) 0 0
\(583\) 4.25974e6 0.519053
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.47623e6 0.176831 0.0884155 0.996084i \(-0.471820\pi\)
0.0884155 + 0.996084i \(0.471820\pi\)
\(588\) 0 0
\(589\) 214720. 0.0255026
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.24007e7 1.44813 0.724067 0.689729i \(-0.242270\pi\)
0.724067 + 0.689729i \(0.242270\pi\)
\(594\) 0 0
\(595\) 481572. 0.0557659
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.69127e6 −0.420348 −0.210174 0.977664i \(-0.567403\pi\)
−0.210174 + 0.977664i \(0.567403\pi\)
\(600\) 0 0
\(601\) 9.12223e6 1.03018 0.515092 0.857135i \(-0.327758\pi\)
0.515092 + 0.857135i \(0.327758\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.81463e6 −0.312632
\(606\) 0 0
\(607\) 5.67914e6 0.625620 0.312810 0.949816i \(-0.398730\pi\)
0.312810 + 0.949816i \(0.398730\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.15264e6 0.666743
\(612\) 0 0
\(613\) −1.40106e7 −1.50593 −0.752966 0.658060i \(-0.771377\pi\)
−0.752966 + 0.658060i \(0.771377\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 253686. 0.0268277 0.0134139 0.999910i \(-0.495730\pi\)
0.0134139 + 0.999910i \(0.495730\pi\)
\(618\) 0 0
\(619\) −4.30034e6 −0.451103 −0.225552 0.974231i \(-0.572418\pi\)
−0.225552 + 0.974231i \(0.572418\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −390726. −0.0403322
\(624\) 0 0
\(625\) −1.02568e7 −1.05030
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −684684. −0.0690023
\(630\) 0 0
\(631\) −1.04150e7 −1.04132 −0.520662 0.853763i \(-0.674315\pi\)
−0.520662 + 0.853763i \(0.674315\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.79696e6 −0.570514
\(636\) 0 0
\(637\) −1.06124e6 −0.103625
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.52714e6 −0.435190 −0.217595 0.976039i \(-0.569821\pi\)
−0.217595 + 0.976039i \(0.569821\pi\)
\(642\) 0 0
\(643\) −1.49687e7 −1.42776 −0.713882 0.700266i \(-0.753065\pi\)
−0.713882 + 0.700266i \(0.753065\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.73020e7 −1.62493 −0.812465 0.583010i \(-0.801875\pi\)
−0.812465 + 0.583010i \(0.801875\pi\)
\(648\) 0 0
\(649\) 1.22064e7 1.13757
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.07470e6 −0.373949 −0.186975 0.982365i \(-0.559868\pi\)
−0.186975 + 0.982365i \(0.559868\pi\)
\(654\) 0 0
\(655\) 1.21146e7 1.10334
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3.79475e6 −0.340384 −0.170192 0.985411i \(-0.554439\pi\)
−0.170192 + 0.985411i \(0.554439\pi\)
\(660\) 0 0
\(661\) 1.64261e7 1.46228 0.731142 0.682225i \(-0.238988\pi\)
0.731142 + 0.682225i \(0.238988\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.02582e7 −0.899537
\(666\) 0 0
\(667\) 2.28564e7 1.98927
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.19682e7 1.88360
\(672\) 0 0
\(673\) 5.50675e6 0.468660 0.234330 0.972157i \(-0.424710\pi\)
0.234330 + 0.972157i \(0.424710\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.83957e7 −1.54257 −0.771286 0.636488i \(-0.780386\pi\)
−0.771286 + 0.636488i \(0.780386\pi\)
\(678\) 0 0
\(679\) 7.03944e6 0.585954
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.75835e6 0.144229 0.0721146 0.997396i \(-0.477025\pi\)
0.0721146 + 0.997396i \(0.477025\pi\)
\(684\) 0 0
\(685\) −2.06112e7 −1.67833
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.24055e6 −0.340309
\(690\) 0 0
\(691\) 5.36314e6 0.427291 0.213646 0.976911i \(-0.431466\pi\)
0.213646 + 0.976911i \(0.431466\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.75197e7 1.37583
\(696\) 0 0
\(697\) −1.00321e6 −0.0782187
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.12606e7 1.63411 0.817054 0.576561i \(-0.195606\pi\)
0.817054 + 0.576561i \(0.195606\pi\)
\(702\) 0 0
\(703\) 1.45849e7 1.11305
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −132594. −0.00997643
\(708\) 0 0
\(709\) 2.07729e6 0.155196 0.0775980 0.996985i \(-0.475275\pi\)
0.0775980 + 0.996985i \(0.475275\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −336000. −0.0247523
\(714\) 0 0
\(715\) 1.53073e7 1.11979
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.23619e6 0.305600 0.152800 0.988257i \(-0.451171\pi\)
0.152800 + 0.988257i \(0.451171\pi\)
\(720\) 0 0
\(721\) 6.45663e6 0.462560
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.61029e7 1.13778
\(726\) 0 0
\(727\) −2.14524e7 −1.50536 −0.752678 0.658389i \(-0.771238\pi\)
−0.752678 + 0.658389i \(0.771238\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.45202e6 0.100503
\(732\) 0 0
\(733\) −1.48892e7 −1.02355 −0.511777 0.859118i \(-0.671013\pi\)
−0.511777 + 0.859118i \(0.671013\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.63541e7 1.78722
\(738\) 0 0
\(739\) −6.99324e6 −0.471050 −0.235525 0.971868i \(-0.575681\pi\)
−0.235525 + 0.971868i \(0.575681\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.90428e6 0.126549 0.0632745 0.997996i \(-0.479846\pi\)
0.0632745 + 0.997996i \(0.479846\pi\)
\(744\) 0 0
\(745\) −6.40177e6 −0.422581
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.31688e6 0.411432
\(750\) 0 0
\(751\) −1.95361e7 −1.26398 −0.631988 0.774978i \(-0.717761\pi\)
−0.631988 + 0.774978i \(0.717761\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.23885e7 −1.42941
\(756\) 0 0
\(757\) 1.25183e6 0.0793973 0.0396986 0.999212i \(-0.487360\pi\)
0.0396986 + 0.999212i \(0.487360\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.04472e7 −1.27989 −0.639944 0.768422i \(-0.721042\pi\)
−0.639944 + 0.768422i \(0.721042\pi\)
\(762\) 0 0
\(763\) 4.94792e6 0.307689
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.21515e7 −0.745831
\(768\) 0 0
\(769\) 2.21064e6 0.134804 0.0674020 0.997726i \(-0.478529\pi\)
0.0674020 + 0.997726i \(0.478529\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.29151e7 −0.777405 −0.388703 0.921363i \(-0.627077\pi\)
−0.388703 + 0.921363i \(0.627077\pi\)
\(774\) 0 0
\(775\) −236720. −0.0141573
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.13700e7 1.26171
\(780\) 0 0
\(781\) 1.42258e7 0.834541
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.01305e7 −0.586754
\(786\) 0 0
\(787\) 1.35499e7 0.779830 0.389915 0.920851i \(-0.372504\pi\)
0.389915 + 0.920851i \(0.372504\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.07872e7 0.613007
\(792\) 0 0
\(793\) −2.18693e7 −1.23496
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.45956e7 1.37155 0.685776 0.727813i \(-0.259463\pi\)
0.685776 + 0.727813i \(0.259463\pi\)
\(798\) 0 0
\(799\) −1.75392e6 −0.0971948
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.74596e7 −1.50282
\(804\) 0 0
\(805\) 1.60524e7 0.873072
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.55237e7 −0.833920 −0.416960 0.908925i \(-0.636905\pi\)
−0.416960 + 0.908925i \(0.636905\pi\)
\(810\) 0 0
\(811\) 2.66262e7 1.42153 0.710766 0.703429i \(-0.248349\pi\)
0.710766 + 0.703429i \(0.248349\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.33122e7 2.28410
\(816\) 0 0
\(817\) −3.09304e7 −1.62118
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.23891e7 0.641477 0.320739 0.947168i \(-0.396069\pi\)
0.320739 + 0.947168i \(0.396069\pi\)
\(822\) 0 0
\(823\) 3.65630e6 0.188166 0.0940831 0.995564i \(-0.470008\pi\)
0.0940831 + 0.995564i \(0.470008\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.80463e7 1.42597 0.712987 0.701178i \(-0.247342\pi\)
0.712987 + 0.701178i \(0.247342\pi\)
\(828\) 0 0
\(829\) 2.11153e7 1.06712 0.533558 0.845763i \(-0.320855\pi\)
0.533558 + 0.845763i \(0.320855\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 302526. 0.0151060
\(834\) 0 0
\(835\) −3.39394e6 −0.168456
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.33947e7 0.656944 0.328472 0.944514i \(-0.393466\pi\)
0.328472 + 0.944514i \(0.393466\pi\)
\(840\) 0 0
\(841\) 9.10422e6 0.443867
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.37225e7 0.661135
\(846\) 0 0
\(847\) −1.76816e6 −0.0846865
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.28228e7 −1.08030
\(852\) 0 0
\(853\) 3.01513e7 1.41884 0.709420 0.704786i \(-0.248957\pi\)
0.709420 + 0.704786i \(0.248957\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.39894e7 −1.11575 −0.557875 0.829925i \(-0.688383\pi\)
−0.557875 + 0.829925i \(0.688383\pi\)
\(858\) 0 0
\(859\) 8.87576e6 0.410414 0.205207 0.978719i \(-0.434213\pi\)
0.205207 + 0.978719i \(0.434213\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8.71286e6 −0.398230 −0.199115 0.979976i \(-0.563807\pi\)
−0.199115 + 0.979976i \(0.563807\pi\)
\(864\) 0 0
\(865\) −1.42974e6 −0.0649706
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.92045e7 1.31190
\(870\) 0 0
\(871\) −2.62354e7 −1.17177
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −634452. −0.0280142
\(876\) 0 0
\(877\) −2.95788e7 −1.29862 −0.649310 0.760524i \(-0.724942\pi\)
−0.649310 + 0.760524i \(0.724942\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.45670e7 −1.06638 −0.533190 0.845995i \(-0.679007\pi\)
−0.533190 + 0.845995i \(0.679007\pi\)
\(882\) 0 0
\(883\) −1.45682e7 −0.628788 −0.314394 0.949293i \(-0.601801\pi\)
−0.314394 + 0.949293i \(0.601801\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.61714e7 0.690141 0.345070 0.938577i \(-0.387855\pi\)
0.345070 + 0.938577i \(0.387855\pi\)
\(888\) 0 0
\(889\) −3.64168e6 −0.154542
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.73613e7 1.56781
\(894\) 0 0
\(895\) 1.19593e7 0.499054
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −435360. −0.0179659
\(900\) 0 0
\(901\) 1.20884e6 0.0496087
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.98011e7 1.20952
\(906\) 0 0
\(907\) −3.14446e7 −1.26919 −0.634596 0.772844i \(-0.718833\pi\)
−0.634596 + 0.772844i \(0.718833\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.51427e7 0.604514 0.302257 0.953227i \(-0.402260\pi\)
0.302257 + 0.953227i \(0.402260\pi\)
\(912\) 0 0
\(913\) 1.78435e7 0.708439
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 7.61048e6 0.298875
\(918\) 0 0
\(919\) −4.14876e7 −1.62043 −0.810214 0.586134i \(-0.800649\pi\)
−0.810214 + 0.586134i \(0.800649\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.41617e7 −0.547155
\(924\) 0 0
\(925\) −1.60792e7 −0.617889
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.78495e7 0.678556 0.339278 0.940686i \(-0.389817\pi\)
0.339278 + 0.940686i \(0.389817\pi\)
\(930\) 0 0
\(931\) −6.44428e6 −0.243669
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4.36363e6 −0.163237
\(936\) 0 0
\(937\) 2.96399e7 1.10288 0.551439 0.834215i \(-0.314079\pi\)
0.551439 + 0.834215i \(0.314079\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.22282e7 1.18648 0.593242 0.805024i \(-0.297848\pi\)
0.593242 + 0.805024i \(0.297848\pi\)
\(942\) 0 0
\(943\) −3.34404e7 −1.22459
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.84885e7 1.75697 0.878484 0.477772i \(-0.158556\pi\)
0.878484 + 0.477772i \(0.158556\pi\)
\(948\) 0 0
\(949\) 2.73359e7 0.985300
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.03264e7 0.724983 0.362491 0.931987i \(-0.381926\pi\)
0.362491 + 0.931987i \(0.381926\pi\)
\(954\) 0 0
\(955\) 2.13258e7 0.756654
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.29481e7 −0.454630
\(960\) 0 0
\(961\) −2.86228e7 −0.999776
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.19810e7 −0.414165
\(966\) 0 0
\(967\) 3.66292e6 0.125968 0.0629841 0.998015i \(-0.479938\pi\)
0.0629841 + 0.998015i \(0.479938\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.48741e6 0.0506271 0.0253136 0.999680i \(-0.491942\pi\)
0.0253136 + 0.999680i \(0.491942\pi\)
\(972\) 0 0
\(973\) 1.10060e7 0.372689
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −4.07930e7 −1.36725 −0.683627 0.729831i \(-0.739599\pi\)
−0.683627 + 0.729831i \(0.739599\pi\)
\(978\) 0 0
\(979\) 3.54046e6 0.118060
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −9.26326e6 −0.305759 −0.152880 0.988245i \(-0.548855\pi\)
−0.152880 + 0.988245i \(0.548855\pi\)
\(984\) 0 0
\(985\) 1.20449e7 0.395561
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.84008e7 1.57348
\(990\) 0 0
\(991\) 5.22051e7 1.68861 0.844303 0.535866i \(-0.180015\pi\)
0.844303 + 0.535866i \(0.180015\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.86148e7 −0.916289
\(996\) 0 0
\(997\) −1.86609e7 −0.594560 −0.297280 0.954790i \(-0.596079\pi\)
−0.297280 + 0.954790i \(0.596079\pi\)
\(998\) 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.c.1.1 1
3.2 odd 2 336.6.a.r.1.1 1
4.3 odd 2 63.6.a.d.1.1 1
12.11 even 2 21.6.a.a.1.1 1
28.27 even 2 441.6.a.j.1.1 1
60.23 odd 4 525.6.d.b.274.2 2
60.47 odd 4 525.6.d.b.274.1 2
60.59 even 2 525.6.a.d.1.1 1
84.11 even 6 147.6.e.j.79.1 2
84.23 even 6 147.6.e.j.67.1 2
84.47 odd 6 147.6.e.i.67.1 2
84.59 odd 6 147.6.e.i.79.1 2
84.83 odd 2 147.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.a.a.1.1 1 12.11 even 2
63.6.a.d.1.1 1 4.3 odd 2
147.6.a.b.1.1 1 84.83 odd 2
147.6.e.i.67.1 2 84.47 odd 6
147.6.e.i.79.1 2 84.59 odd 6
147.6.e.j.67.1 2 84.23 even 6
147.6.e.j.79.1 2 84.11 even 6
336.6.a.r.1.1 1 3.2 odd 2
441.6.a.j.1.1 1 28.27 even 2
525.6.a.d.1.1 1 60.59 even 2
525.6.d.b.274.1 2 60.47 odd 4
525.6.d.b.274.2 2 60.23 odd 4
1008.6.a.c.1.1 1 1.1 even 1 trivial