Properties

Label 1008.6.a.n.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(0\)
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)
 
\(f(q)\) \(=\) \(q-10.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-10.0000 q^{5} +49.0000 q^{7} -340.000 q^{11} -294.000 q^{13} -1226.00 q^{17} -2432.00 q^{19} +2000.00 q^{23} -3025.00 q^{25} +6746.00 q^{29} -8856.00 q^{31} -490.000 q^{35} +9182.00 q^{37} +14574.0 q^{41} -8108.00 q^{43} -312.000 q^{47} +2401.00 q^{49} +14634.0 q^{53} +3400.00 q^{55} -27656.0 q^{59} +34338.0 q^{61} +2940.00 q^{65} -12316.0 q^{67} +36920.0 q^{71} -61718.0 q^{73} -16660.0 q^{77} +64752.0 q^{79} -77056.0 q^{83} +12260.0 q^{85} +8166.00 q^{89} -14406.0 q^{91} +24320.0 q^{95} +20650.0 q^{97} +O(q^{100})\)

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
\(5\) −10.0000 −0.178885 −0.0894427 0.995992i \(-0.528509\pi\)
−0.0894427 + 0.995992i \(0.528509\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −340.000 −0.847222 −0.423611 0.905844i \(-0.639238\pi\)
−0.423611 + 0.905844i \(0.639238\pi\)
\(12\) 0 0
\(13\) −294.000 −0.482491 −0.241245 0.970464i \(-0.577556\pi\)
−0.241245 + 0.970464i \(0.577556\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1226.00 −1.02889 −0.514444 0.857524i \(-0.672002\pi\)
−0.514444 + 0.857524i \(0.672002\pi\)
\(18\) 0 0
\(19\) −2432.00 −1.54554 −0.772769 0.634688i \(-0.781129\pi\)
−0.772769 + 0.634688i \(0.781129\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2000.00 0.788334 0.394167 0.919039i \(-0.371033\pi\)
0.394167 + 0.919039i \(0.371033\pi\)
\(24\) 0 0
\(25\) −3025.00 −0.968000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6746.00 1.48954 0.744769 0.667323i \(-0.232560\pi\)
0.744769 + 0.667323i \(0.232560\pi\)
\(30\) 0 0
\(31\) −8856.00 −1.65513 −0.827567 0.561366i \(-0.810276\pi\)
−0.827567 + 0.561366i \(0.810276\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −490.000 −0.0676123
\(36\) 0 0
\(37\) 9182.00 1.10264 0.551319 0.834295i \(-0.314125\pi\)
0.551319 + 0.834295i \(0.314125\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 14574.0 1.35400 0.677001 0.735982i \(-0.263279\pi\)
0.677001 + 0.735982i \(0.263279\pi\)
\(42\) 0 0
\(43\) −8108.00 −0.668717 −0.334359 0.942446i \(-0.608520\pi\)
−0.334359 + 0.942446i \(0.608520\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −312.000 −0.0206020 −0.0103010 0.999947i \(-0.503279\pi\)
−0.0103010 + 0.999947i \(0.503279\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 14634.0 0.715605 0.357803 0.933797i \(-0.383526\pi\)
0.357803 + 0.933797i \(0.383526\pi\)
\(54\) 0 0
\(55\) 3400.00 0.151556
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −27656.0 −1.03433 −0.517165 0.855886i \(-0.673013\pi\)
−0.517165 + 0.855886i \(0.673013\pi\)
\(60\) 0 0
\(61\) 34338.0 1.18155 0.590773 0.806838i \(-0.298823\pi\)
0.590773 + 0.806838i \(0.298823\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2940.00 0.0863106
\(66\) 0 0
\(67\) −12316.0 −0.335184 −0.167592 0.985856i \(-0.553599\pi\)
−0.167592 + 0.985856i \(0.553599\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 36920.0 0.869192 0.434596 0.900625i \(-0.356891\pi\)
0.434596 + 0.900625i \(0.356891\pi\)
\(72\) 0 0
\(73\) −61718.0 −1.35552 −0.677758 0.735285i \(-0.737048\pi\)
−0.677758 + 0.735285i \(0.737048\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16660.0 −0.320220
\(78\) 0 0
\(79\) 64752.0 1.16731 0.583654 0.812002i \(-0.301622\pi\)
0.583654 + 0.812002i \(0.301622\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −77056.0 −1.22775 −0.613877 0.789402i \(-0.710391\pi\)
−0.613877 + 0.789402i \(0.710391\pi\)
\(84\) 0 0
\(85\) 12260.0 0.184053
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8166.00 0.109278 0.0546392 0.998506i \(-0.482599\pi\)
0.0546392 + 0.998506i \(0.482599\pi\)
\(90\) 0 0
\(91\) −14406.0 −0.182364
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 24320.0 0.276474
\(96\) 0 0
\(97\) 20650.0 0.222839 0.111419 0.993773i \(-0.464460\pi\)
0.111419 + 0.993773i \(0.464460\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −186250. −1.81674 −0.908370 0.418167i \(-0.862673\pi\)
−0.908370 + 0.418167i \(0.862673\pi\)
\(102\) 0 0
\(103\) 60064.0 0.557855 0.278927 0.960312i \(-0.410021\pi\)
0.278927 + 0.960312i \(0.410021\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 47892.0 0.404393 0.202196 0.979345i \(-0.435192\pi\)
0.202196 + 0.979345i \(0.435192\pi\)
\(108\) 0 0
\(109\) 22102.0 0.178183 0.0890913 0.996023i \(-0.471604\pi\)
0.0890913 + 0.996023i \(0.471604\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 245054. 1.80537 0.902684 0.430304i \(-0.141594\pi\)
0.902684 + 0.430304i \(0.141594\pi\)
\(114\) 0 0
\(115\) −20000.0 −0.141022
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −60074.0 −0.388883
\(120\) 0 0
\(121\) −45451.0 −0.282215
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 61500.0 0.352047
\(126\) 0 0
\(127\) 96696.0 0.531985 0.265992 0.963975i \(-0.414300\pi\)
0.265992 + 0.963975i \(0.414300\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 134368. 0.684097 0.342048 0.939682i \(-0.388879\pi\)
0.342048 + 0.939682i \(0.388879\pi\)
\(132\) 0 0
\(133\) −119168. −0.584158
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 294662. 1.34129 0.670645 0.741778i \(-0.266017\pi\)
0.670645 + 0.741778i \(0.266017\pi\)
\(138\) 0 0
\(139\) −314944. −1.38260 −0.691300 0.722568i \(-0.742962\pi\)
−0.691300 + 0.722568i \(0.742962\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 99960.0 0.408777
\(144\) 0 0
\(145\) −67460.0 −0.266457
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −113622. −0.419273 −0.209636 0.977779i \(-0.567228\pi\)
−0.209636 + 0.977779i \(0.567228\pi\)
\(150\) 0 0
\(151\) −408208. −1.45693 −0.728466 0.685082i \(-0.759766\pi\)
−0.728466 + 0.685082i \(0.759766\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 88560.0 0.296080
\(156\) 0 0
\(157\) 293546. 0.950445 0.475223 0.879866i \(-0.342368\pi\)
0.475223 + 0.879866i \(0.342368\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 98000.0 0.297962
\(162\) 0 0
\(163\) 317116. 0.934866 0.467433 0.884029i \(-0.345179\pi\)
0.467433 + 0.884029i \(0.345179\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 141568. 0.392802 0.196401 0.980524i \(-0.437075\pi\)
0.196401 + 0.980524i \(0.437075\pi\)
\(168\) 0 0
\(169\) −284857. −0.767203
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 71222.0 0.180925 0.0904626 0.995900i \(-0.471165\pi\)
0.0904626 + 0.995900i \(0.471165\pi\)
\(174\) 0 0
\(175\) −148225. −0.365870
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 485628. 1.13285 0.566423 0.824114i \(-0.308327\pi\)
0.566423 + 0.824114i \(0.308327\pi\)
\(180\) 0 0
\(181\) 657090. 1.49083 0.745416 0.666600i \(-0.232251\pi\)
0.745416 + 0.666600i \(0.232251\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −91820.0 −0.197246
\(186\) 0 0
\(187\) 416840. 0.871697
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 68304.0 0.135476 0.0677381 0.997703i \(-0.478422\pi\)
0.0677381 + 0.997703i \(0.478422\pi\)
\(192\) 0 0
\(193\) 352754. 0.681677 0.340839 0.940122i \(-0.389289\pi\)
0.340839 + 0.940122i \(0.389289\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −196982. −0.361627 −0.180814 0.983517i \(-0.557873\pi\)
−0.180814 + 0.983517i \(0.557873\pi\)
\(198\) 0 0
\(199\) 1.10392e6 1.97608 0.988041 0.154192i \(-0.0492775\pi\)
0.988041 + 0.154192i \(0.0492775\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 330554. 0.562992
\(204\) 0 0
\(205\) −145740. −0.242211
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 826880. 1.30941
\(210\) 0 0
\(211\) 103444. 0.159955 0.0799777 0.996797i \(-0.474515\pi\)
0.0799777 + 0.996797i \(0.474515\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 81080.0 0.119624
\(216\) 0 0
\(217\) −433944. −0.625582
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 360444. 0.496429
\(222\) 0 0
\(223\) −307328. −0.413847 −0.206924 0.978357i \(-0.566345\pi\)
−0.206924 + 0.978357i \(0.566345\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −891792. −1.14868 −0.574340 0.818617i \(-0.694741\pi\)
−0.574340 + 0.818617i \(0.694741\pi\)
\(228\) 0 0
\(229\) 276706. 0.348682 0.174341 0.984685i \(-0.444220\pi\)
0.174341 + 0.984685i \(0.444220\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.47943e6 −1.78528 −0.892639 0.450772i \(-0.851149\pi\)
−0.892639 + 0.450772i \(0.851149\pi\)
\(234\) 0 0
\(235\) 3120.00 0.00368540
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.00034e6 1.13280 0.566402 0.824129i \(-0.308335\pi\)
0.566402 + 0.824129i \(0.308335\pi\)
\(240\) 0 0
\(241\) 1.35833e6 1.50648 0.753239 0.657747i \(-0.228490\pi\)
0.753239 + 0.657747i \(0.228490\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −24010.0 −0.0255551
\(246\) 0 0
\(247\) 715008. 0.745708
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −177408. −0.177742 −0.0888708 0.996043i \(-0.528326\pi\)
−0.0888708 + 0.996043i \(0.528326\pi\)
\(252\) 0 0
\(253\) −680000. −0.667894
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −326658. −0.308504 −0.154252 0.988032i \(-0.549297\pi\)
−0.154252 + 0.988032i \(0.549297\pi\)
\(258\) 0 0
\(259\) 449918. 0.416758
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −34920.0 −0.0311304 −0.0155652 0.999879i \(-0.504955\pi\)
−0.0155652 + 0.999879i \(0.504955\pi\)
\(264\) 0 0
\(265\) −146340. −0.128011
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −716458. −0.603685 −0.301842 0.953358i \(-0.597602\pi\)
−0.301842 + 0.953358i \(0.597602\pi\)
\(270\) 0 0
\(271\) 953376. 0.788571 0.394286 0.918988i \(-0.370992\pi\)
0.394286 + 0.918988i \(0.370992\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.02850e6 0.820111
\(276\) 0 0
\(277\) −1.84729e6 −1.44656 −0.723279 0.690556i \(-0.757366\pi\)
−0.723279 + 0.690556i \(0.757366\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.99601e6 1.50798 0.753991 0.656885i \(-0.228126\pi\)
0.753991 + 0.656885i \(0.228126\pi\)
\(282\) 0 0
\(283\) −234088. −0.173745 −0.0868726 0.996219i \(-0.527687\pi\)
−0.0868726 + 0.996219i \(0.527687\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 714126. 0.511764
\(288\) 0 0
\(289\) 83219.0 0.0586108
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.50081e6 1.70181 0.850905 0.525320i \(-0.176054\pi\)
0.850905 + 0.525320i \(0.176054\pi\)
\(294\) 0 0
\(295\) 276560. 0.185027
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −588000. −0.380364
\(300\) 0 0
\(301\) −397292. −0.252751
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −343380. −0.211361
\(306\) 0 0
\(307\) −2.34203e6 −1.41823 −0.709115 0.705092i \(-0.750905\pi\)
−0.709115 + 0.705092i \(0.750905\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −163064. −0.0955998 −0.0477999 0.998857i \(-0.515221\pi\)
−0.0477999 + 0.998857i \(0.515221\pi\)
\(312\) 0 0
\(313\) 1.73965e6 1.00369 0.501847 0.864957i \(-0.332654\pi\)
0.501847 + 0.864957i \(0.332654\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.79771e6 1.00478 0.502392 0.864640i \(-0.332454\pi\)
0.502392 + 0.864640i \(0.332454\pi\)
\(318\) 0 0
\(319\) −2.29364e6 −1.26197
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.98163e6 1.59019
\(324\) 0 0
\(325\) 889350. 0.467051
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −15288.0 −0.00778683
\(330\) 0 0
\(331\) 2.47541e6 1.24187 0.620937 0.783861i \(-0.286752\pi\)
0.620937 + 0.783861i \(0.286752\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 123160. 0.0599595
\(336\) 0 0
\(337\) 89154.0 0.0427628 0.0213814 0.999771i \(-0.493194\pi\)
0.0213814 + 0.999771i \(0.493194\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.01104e6 1.40227
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 938556. 0.418443 0.209222 0.977868i \(-0.432907\pi\)
0.209222 + 0.977868i \(0.432907\pi\)
\(348\) 0 0
\(349\) 3.34268e6 1.46903 0.734516 0.678591i \(-0.237409\pi\)
0.734516 + 0.678591i \(0.237409\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.76606e6 1.60861 0.804305 0.594217i \(-0.202538\pi\)
0.804305 + 0.594217i \(0.202538\pi\)
\(354\) 0 0
\(355\) −369200. −0.155486
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.53934e6 −0.630376 −0.315188 0.949029i \(-0.602068\pi\)
−0.315188 + 0.949029i \(0.602068\pi\)
\(360\) 0 0
\(361\) 3.43852e6 1.38869
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 617180. 0.242482
\(366\) 0 0
\(367\) 859312. 0.333032 0.166516 0.986039i \(-0.446748\pi\)
0.166516 + 0.986039i \(0.446748\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 717066. 0.270473
\(372\) 0 0
\(373\) −976586. −0.363445 −0.181722 0.983350i \(-0.558167\pi\)
−0.181722 + 0.983350i \(0.558167\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.98332e6 −0.718688
\(378\) 0 0
\(379\) −106444. −0.0380648 −0.0190324 0.999819i \(-0.506059\pi\)
−0.0190324 + 0.999819i \(0.506059\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.00634e6 −0.698889 −0.349445 0.936957i \(-0.613630\pi\)
−0.349445 + 0.936957i \(0.613630\pi\)
\(384\) 0 0
\(385\) 166600. 0.0572827
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 684002. 0.229184 0.114592 0.993413i \(-0.463444\pi\)
0.114592 + 0.993413i \(0.463444\pi\)
\(390\) 0 0
\(391\) −2.45200e6 −0.811108
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −647520. −0.208814
\(396\) 0 0
\(397\) −222870. −0.0709701 −0.0354850 0.999370i \(-0.511298\pi\)
−0.0354850 + 0.999370i \(0.511298\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.90072e6 −0.590279 −0.295140 0.955454i \(-0.595366\pi\)
−0.295140 + 0.955454i \(0.595366\pi\)
\(402\) 0 0
\(403\) 2.60366e6 0.798587
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.12188e6 −0.934179
\(408\) 0 0
\(409\) 1.77715e6 0.525311 0.262656 0.964890i \(-0.415402\pi\)
0.262656 + 0.964890i \(0.415402\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.35514e6 −0.390940
\(414\) 0 0
\(415\) 770560. 0.219627
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 28056.0 0.00780712 0.00390356 0.999992i \(-0.498757\pi\)
0.00390356 + 0.999992i \(0.498757\pi\)
\(420\) 0 0
\(421\) −2.70897e6 −0.744902 −0.372451 0.928052i \(-0.621482\pi\)
−0.372451 + 0.928052i \(0.621482\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.70865e6 0.995964
\(426\) 0 0
\(427\) 1.68256e6 0.446582
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.53898e6 1.43627 0.718136 0.695902i \(-0.244995\pi\)
0.718136 + 0.695902i \(0.244995\pi\)
\(432\) 0 0
\(433\) −868294. −0.222560 −0.111280 0.993789i \(-0.535495\pi\)
−0.111280 + 0.993789i \(0.535495\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.86400e6 −1.21840
\(438\) 0 0
\(439\) 1.13767e6 0.281745 0.140872 0.990028i \(-0.455009\pi\)
0.140872 + 0.990028i \(0.455009\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.75399e6 0.424636 0.212318 0.977201i \(-0.431899\pi\)
0.212318 + 0.977201i \(0.431899\pi\)
\(444\) 0 0
\(445\) −81660.0 −0.0195483
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.41674e6 −0.565736 −0.282868 0.959159i \(-0.591286\pi\)
−0.282868 + 0.959159i \(0.591286\pi\)
\(450\) 0 0
\(451\) −4.95516e6 −1.14714
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 144060. 0.0326223
\(456\) 0 0
\(457\) −127430. −0.0285418 −0.0142709 0.999898i \(-0.504543\pi\)
−0.0142709 + 0.999898i \(0.504543\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 128198. 0.0280950 0.0140475 0.999901i \(-0.495528\pi\)
0.0140475 + 0.999901i \(0.495528\pi\)
\(462\) 0 0
\(463\) 4.01653e6 0.870760 0.435380 0.900247i \(-0.356614\pi\)
0.435380 + 0.900247i \(0.356614\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.67246e6 1.84014 0.920069 0.391757i \(-0.128133\pi\)
0.920069 + 0.391757i \(0.128133\pi\)
\(468\) 0 0
\(469\) −603484. −0.126687
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.75672e6 0.566552
\(474\) 0 0
\(475\) 7.35680e6 1.49608
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.28946e6 1.65077 0.825387 0.564567i \(-0.190957\pi\)
0.825387 + 0.564567i \(0.190957\pi\)
\(480\) 0 0
\(481\) −2.69951e6 −0.532013
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −206500. −0.0398626
\(486\) 0 0
\(487\) 8.91770e6 1.70385 0.851923 0.523667i \(-0.175437\pi\)
0.851923 + 0.523667i \(0.175437\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.71537e6 −1.06989 −0.534947 0.844886i \(-0.679668\pi\)
−0.534947 + 0.844886i \(0.679668\pi\)
\(492\) 0 0
\(493\) −8.27060e6 −1.53257
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.80908e6 0.328524
\(498\) 0 0
\(499\) −125116. −0.0224937 −0.0112469 0.999937i \(-0.503580\pi\)
−0.0112469 + 0.999937i \(0.503580\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.77116e6 −0.488362 −0.244181 0.969730i \(-0.578519\pi\)
−0.244181 + 0.969730i \(0.578519\pi\)
\(504\) 0 0
\(505\) 1.86250e6 0.324988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 138534. 0.0237007 0.0118504 0.999930i \(-0.496228\pi\)
0.0118504 + 0.999930i \(0.496228\pi\)
\(510\) 0 0
\(511\) −3.02418e6 −0.512337
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −600640. −0.0997921
\(516\) 0 0
\(517\) 106080. 0.0174545
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.80281e6 0.290976 0.145488 0.989360i \(-0.453525\pi\)
0.145488 + 0.989360i \(0.453525\pi\)
\(522\) 0 0
\(523\) −9.77247e6 −1.56225 −0.781124 0.624375i \(-0.785354\pi\)
−0.781124 + 0.624375i \(0.785354\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.08575e7 1.70295
\(528\) 0 0
\(529\) −2.43634e6 −0.378529
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.28476e6 −0.653293
\(534\) 0 0
\(535\) −478920. −0.0723400
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −816340. −0.121032
\(540\) 0 0
\(541\) 2.45504e6 0.360633 0.180316 0.983609i \(-0.442288\pi\)
0.180316 + 0.983609i \(0.442288\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −221020. −0.0318743
\(546\) 0 0
\(547\) −1.32081e7 −1.88744 −0.943721 0.330743i \(-0.892701\pi\)
−0.943721 + 0.330743i \(0.892701\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.64063e7 −2.30214
\(552\) 0 0
\(553\) 3.17285e6 0.441201
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.83293e6 −1.06976 −0.534880 0.844928i \(-0.679643\pi\)
−0.534880 + 0.844928i \(0.679643\pi\)
\(558\) 0 0
\(559\) 2.38375e6 0.322650
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.57908e6 0.475883 0.237942 0.971279i \(-0.423527\pi\)
0.237942 + 0.971279i \(0.423527\pi\)
\(564\) 0 0
\(565\) −2.45054e6 −0.322954
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.39581e6 0.439707 0.219853 0.975533i \(-0.429442\pi\)
0.219853 + 0.975533i \(0.429442\pi\)
\(570\) 0 0
\(571\) 1.47695e6 0.189572 0.0947862 0.995498i \(-0.469783\pi\)
0.0947862 + 0.995498i \(0.469783\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.05000e6 −0.763108
\(576\) 0 0
\(577\) −1.49961e7 −1.87516 −0.937580 0.347771i \(-0.886939\pi\)
−0.937580 + 0.347771i \(0.886939\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.77574e6 −0.464047
\(582\) 0 0
\(583\) −4.97556e6 −0.606276
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.29291e6 −0.394444 −0.197222 0.980359i \(-0.563192\pi\)
−0.197222 + 0.980359i \(0.563192\pi\)
\(588\) 0 0
\(589\) 2.15378e7 2.55807
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.17908e7 1.37692 0.688459 0.725275i \(-0.258287\pi\)
0.688459 + 0.725275i \(0.258287\pi\)
\(594\) 0 0
\(595\) 600740. 0.0695655
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.52642e6 −0.173823 −0.0869117 0.996216i \(-0.527700\pi\)
−0.0869117 + 0.996216i \(0.527700\pi\)
\(600\) 0 0
\(601\) −1.00142e7 −1.13092 −0.565458 0.824777i \(-0.691301\pi\)
−0.565458 + 0.824777i \(0.691301\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 454510. 0.0504841
\(606\) 0 0
\(607\) −1.20660e7 −1.32920 −0.664599 0.747200i \(-0.731398\pi\)
−0.664599 + 0.747200i \(0.731398\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 91728.0 0.00994029
\(612\) 0 0
\(613\) 5.81950e6 0.625511 0.312755 0.949834i \(-0.398748\pi\)
0.312755 + 0.949834i \(0.398748\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.16589e6 0.440550 0.220275 0.975438i \(-0.429305\pi\)
0.220275 + 0.975438i \(0.429305\pi\)
\(618\) 0 0
\(619\) 8.08090e6 0.847683 0.423841 0.905736i \(-0.360681\pi\)
0.423841 + 0.905736i \(0.360681\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 400134. 0.0413034
\(624\) 0 0
\(625\) 8.83812e6 0.905024
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.12571e7 −1.13449
\(630\) 0 0
\(631\) 8.40878e6 0.840735 0.420368 0.907354i \(-0.361901\pi\)
0.420368 + 0.907354i \(0.361901\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −966960. −0.0951643
\(636\) 0 0
\(637\) −705894. −0.0689272
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.29760e6 −0.605383 −0.302691 0.953089i \(-0.597885\pi\)
−0.302691 + 0.953089i \(0.597885\pi\)
\(642\) 0 0
\(643\) −4.39762e6 −0.419460 −0.209730 0.977759i \(-0.567259\pi\)
−0.209730 + 0.977759i \(0.567259\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.55397e6 0.615522 0.307761 0.951464i \(-0.400420\pi\)
0.307761 + 0.951464i \(0.400420\pi\)
\(648\) 0 0
\(649\) 9.40304e6 0.876308
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.79652e6 −0.348420 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(654\) 0 0
\(655\) −1.34368e6 −0.122375
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8.82684e6 −0.791757 −0.395879 0.918303i \(-0.629560\pi\)
−0.395879 + 0.918303i \(0.629560\pi\)
\(660\) 0 0
\(661\) −341270. −0.0303805 −0.0151902 0.999885i \(-0.504835\pi\)
−0.0151902 + 0.999885i \(0.504835\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.19168e6 0.104497
\(666\) 0 0
\(667\) 1.34920e7 1.17425
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.16749e7 −1.00103
\(672\) 0 0
\(673\) 4.41807e6 0.376006 0.188003 0.982168i \(-0.439799\pi\)
0.188003 + 0.982168i \(0.439799\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.63858e7 −1.37403 −0.687014 0.726644i \(-0.741079\pi\)
−0.687014 + 0.726644i \(0.741079\pi\)
\(678\) 0 0
\(679\) 1.01185e6 0.0842251
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.75399e7 −1.43872 −0.719360 0.694638i \(-0.755565\pi\)
−0.719360 + 0.694638i \(0.755565\pi\)
\(684\) 0 0
\(685\) −2.94662e6 −0.239937
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.30240e6 −0.345273
\(690\) 0 0
\(691\) −3.14638e6 −0.250678 −0.125339 0.992114i \(-0.540002\pi\)
−0.125339 + 0.992114i \(0.540002\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.14944e6 0.247327
\(696\) 0 0
\(697\) −1.78677e7 −1.39312
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.90919e7 1.46742 0.733709 0.679464i \(-0.237788\pi\)
0.733709 + 0.679464i \(0.237788\pi\)
\(702\) 0 0
\(703\) −2.23306e7 −1.70417
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.12625e6 −0.686663
\(708\) 0 0
\(709\) 990974. 0.0740366 0.0370183 0.999315i \(-0.488214\pi\)
0.0370183 + 0.999315i \(0.488214\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.77120e7 −1.30480
\(714\) 0 0
\(715\) −999600. −0.0731242
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.69014e7 −1.21928 −0.609638 0.792680i \(-0.708685\pi\)
−0.609638 + 0.792680i \(0.708685\pi\)
\(720\) 0 0
\(721\) 2.94314e6 0.210849
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.04066e7 −1.44187
\(726\) 0 0
\(727\) 2.34302e7 1.64414 0.822071 0.569384i \(-0.192818\pi\)
0.822071 + 0.569384i \(0.192818\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.94041e6 0.688035
\(732\) 0 0
\(733\) 975810. 0.0670819 0.0335409 0.999437i \(-0.489322\pi\)
0.0335409 + 0.999437i \(0.489322\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.18744e6 0.283975
\(738\) 0 0
\(739\) 6.30208e6 0.424495 0.212247 0.977216i \(-0.431922\pi\)
0.212247 + 0.977216i \(0.431922\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −6.95698e6 −0.462326 −0.231163 0.972915i \(-0.574253\pi\)
−0.231163 + 0.972915i \(0.574253\pi\)
\(744\) 0 0
\(745\) 1.13622e6 0.0750018
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.34671e6 0.152846
\(750\) 0 0
\(751\) −2.74535e7 −1.77622 −0.888112 0.459628i \(-0.847983\pi\)
−0.888112 + 0.459628i \(0.847983\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.08208e6 0.260624
\(756\) 0 0
\(757\) −1.96889e7 −1.24877 −0.624384 0.781118i \(-0.714650\pi\)
−0.624384 + 0.781118i \(0.714650\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.82079e7 1.76567 0.882835 0.469684i \(-0.155632\pi\)
0.882835 + 0.469684i \(0.155632\pi\)
\(762\) 0 0
\(763\) 1.08300e6 0.0673467
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.13086e6 0.499055
\(768\) 0 0
\(769\) −1.38081e6 −0.0842009 −0.0421005 0.999113i \(-0.513405\pi\)
−0.0421005 + 0.999113i \(0.513405\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.54347e7 0.929074 0.464537 0.885554i \(-0.346221\pi\)
0.464537 + 0.885554i \(0.346221\pi\)
\(774\) 0 0
\(775\) 2.67894e7 1.60217
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.54440e7 −2.09266
\(780\) 0 0
\(781\) −1.25528e7 −0.736399
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.93546e6 −0.170021
\(786\) 0 0
\(787\) 7.10107e6 0.408683 0.204342 0.978900i \(-0.434495\pi\)
0.204342 + 0.978900i \(0.434495\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.20076e7 0.682365
\(792\) 0 0
\(793\) −1.00954e7 −0.570085
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.48182e6 −0.361452 −0.180726 0.983533i \(-0.557845\pi\)
−0.180726 + 0.983533i \(0.557845\pi\)
\(798\) 0 0
\(799\) 382512. 0.0211972
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.09841e7 1.14842
\(804\) 0 0
\(805\) −980000. −0.0533011
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.60578e7 −0.862610 −0.431305 0.902206i \(-0.641947\pi\)
−0.431305 + 0.902206i \(0.641947\pi\)
\(810\) 0 0
\(811\) −4.84775e6 −0.258814 −0.129407 0.991592i \(-0.541307\pi\)
−0.129407 + 0.991592i \(0.541307\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3.17116e6 −0.167234
\(816\) 0 0
\(817\) 1.97187e7 1.03353
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.17976e7 −1.12863 −0.564314 0.825560i \(-0.690859\pi\)
−0.564314 + 0.825560i \(0.690859\pi\)
\(822\) 0 0
\(823\) −3.20206e7 −1.64790 −0.823948 0.566665i \(-0.808233\pi\)
−0.823948 + 0.566665i \(0.808233\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.19008e7 1.11352 0.556758 0.830675i \(-0.312045\pi\)
0.556758 + 0.830675i \(0.312045\pi\)
\(828\) 0 0
\(829\) −1.45999e7 −0.737844 −0.368922 0.929460i \(-0.620273\pi\)
−0.368922 + 0.929460i \(0.620273\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.94363e6 −0.146984
\(834\) 0 0
\(835\) −1.41568e6 −0.0702666
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 4.60947e6 0.226072 0.113036 0.993591i \(-0.463942\pi\)
0.113036 + 0.993591i \(0.463942\pi\)
\(840\) 0 0
\(841\) 2.49974e7 1.21872
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.84857e6 0.137241
\(846\) 0 0
\(847\) −2.22710e6 −0.106667
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.83640e7 0.869247
\(852\) 0 0
\(853\) −1.98437e7 −0.933793 −0.466897 0.884312i \(-0.654628\pi\)
−0.466897 + 0.884312i \(0.654628\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.22960e6 0.0571888 0.0285944 0.999591i \(-0.490897\pi\)
0.0285944 + 0.999591i \(0.490897\pi\)
\(858\) 0 0
\(859\) −3.33041e7 −1.53998 −0.769989 0.638058i \(-0.779738\pi\)
−0.769989 + 0.638058i \(0.779738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.36616e7 −1.08148 −0.540738 0.841191i \(-0.681855\pi\)
−0.540738 + 0.841191i \(0.681855\pi\)
\(864\) 0 0
\(865\) −712220. −0.0323649
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.20157e7 −0.988969
\(870\) 0 0
\(871\) 3.62090e6 0.161723
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.01350e6 0.133061
\(876\) 0 0
\(877\) −2.37812e7 −1.04408 −0.522042 0.852920i \(-0.674830\pi\)
−0.522042 + 0.852920i \(0.674830\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.41871e7 0.615818 0.307909 0.951416i \(-0.400371\pi\)
0.307909 + 0.951416i \(0.400371\pi\)
\(882\) 0 0
\(883\) −2.09281e7 −0.903293 −0.451647 0.892197i \(-0.649163\pi\)
−0.451647 + 0.892197i \(0.649163\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −7.98586e6 −0.340810 −0.170405 0.985374i \(-0.554508\pi\)
−0.170405 + 0.985374i \(0.554508\pi\)
\(888\) 0 0
\(889\) 4.73810e6 0.201071
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 758784. 0.0318412
\(894\) 0 0
\(895\) −4.85628e6 −0.202650
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.97426e7 −2.46538
\(900\) 0 0
\(901\) −1.79413e7 −0.736278
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −6.57090e6 −0.266688
\(906\) 0 0
\(907\) 2.31861e7 0.935856 0.467928 0.883767i \(-0.345001\pi\)
0.467928 + 0.883767i \(0.345001\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.65299e7 0.659895 0.329948 0.943999i \(-0.392969\pi\)
0.329948 + 0.943999i \(0.392969\pi\)
\(912\) 0 0
\(913\) 2.61990e7 1.04018
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 6.58403e6 0.258564
\(918\) 0 0
\(919\) −1.28087e7 −0.500283 −0.250142 0.968209i \(-0.580477\pi\)
−0.250142 + 0.968209i \(0.580477\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.08545e7 −0.419377
\(924\) 0 0
\(925\) −2.77756e7 −1.06735
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.97319e7 −1.13027 −0.565136 0.824998i \(-0.691176\pi\)
−0.565136 + 0.824998i \(0.691176\pi\)
\(930\) 0 0
\(931\) −5.83923e6 −0.220791
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4.16840e6 −0.155934
\(936\) 0 0
\(937\) 1.10970e7 0.412911 0.206456 0.978456i \(-0.433807\pi\)
0.206456 + 0.978456i \(0.433807\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.74313e7 −1.37804 −0.689019 0.724743i \(-0.741958\pi\)
−0.689019 + 0.724743i \(0.741958\pi\)
\(942\) 0 0
\(943\) 2.91480e7 1.06741
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.50907e7 0.546808 0.273404 0.961899i \(-0.411850\pi\)
0.273404 + 0.961899i \(0.411850\pi\)
\(948\) 0 0
\(949\) 1.81451e7 0.654024
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.15741e7 0.769484 0.384742 0.923024i \(-0.374290\pi\)
0.384742 + 0.923024i \(0.374290\pi\)
\(954\) 0 0
\(955\) −683040. −0.0242347
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.44384e7 0.506960
\(960\) 0 0
\(961\) 4.97996e7 1.73947
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.52754e6 −0.121942
\(966\) 0 0
\(967\) 3.29467e7 1.13304 0.566520 0.824048i \(-0.308289\pi\)
0.566520 + 0.824048i \(0.308289\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.24599e7 0.764470 0.382235 0.924065i \(-0.375154\pi\)
0.382235 + 0.924065i \(0.375154\pi\)
\(972\) 0 0
\(973\) −1.54323e7 −0.522573
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.16236e7 1.73026 0.865132 0.501545i \(-0.167235\pi\)
0.865132 + 0.501545i \(0.167235\pi\)
\(978\) 0 0
\(979\) −2.77644e6 −0.0925831
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.10202e7 −0.363751 −0.181876 0.983322i \(-0.558217\pi\)
−0.181876 + 0.983322i \(0.558217\pi\)
\(984\) 0 0
\(985\) 1.96982e6 0.0646898
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.62160e7 −0.527173
\(990\) 0 0
\(991\) −3.21029e7 −1.03839 −0.519194 0.854656i \(-0.673768\pi\)
−0.519194 + 0.854656i \(0.673768\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.10392e7 −0.353492
\(996\) 0 0
\(997\) 2.81772e7 0.897759 0.448879 0.893592i \(-0.351823\pi\)
0.448879 + 0.893592i \(0.351823\pi\)
\(998\) 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.n.1.1 1
3.2 odd 2 112.6.a.d.1.1 1
4.3 odd 2 126.6.a.c.1.1 1
12.11 even 2 14.6.a.b.1.1 1
21.20 even 2 784.6.a.h.1.1 1
24.5 odd 2 448.6.a.k.1.1 1
24.11 even 2 448.6.a.f.1.1 1
28.27 even 2 882.6.a.g.1.1 1
60.23 odd 4 350.6.c.f.99.1 2
60.47 odd 4 350.6.c.f.99.2 2
60.59 even 2 350.6.a.b.1.1 1
84.11 even 6 98.6.c.a.79.1 2
84.23 even 6 98.6.c.a.67.1 2
84.47 odd 6 98.6.c.b.67.1 2
84.59 odd 6 98.6.c.b.79.1 2
84.83 odd 2 98.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.a.b.1.1 1 12.11 even 2
98.6.a.b.1.1 1 84.83 odd 2
98.6.c.a.67.1 2 84.23 even 6
98.6.c.a.79.1 2 84.11 even 6
98.6.c.b.67.1 2 84.47 odd 6
98.6.c.b.79.1 2 84.59 odd 6
112.6.a.d.1.1 1 3.2 odd 2
126.6.a.c.1.1 1 4.3 odd 2
350.6.a.b.1.1 1 60.59 even 2
350.6.c.f.99.1 2 60.23 odd 4
350.6.c.f.99.2 2 60.47 odd 4
448.6.a.f.1.1 1 24.11 even 2
448.6.a.k.1.1 1 24.5 odd 2
784.6.a.h.1.1 1 21.20 even 2
882.6.a.g.1.1 1 28.27 even 2
1008.6.a.n.1.1 1 1.1 even 1 trivial