Properties

Label 1008.6.a.bv.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{106}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 106 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-10.2956\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-23.7738 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-23.7738 q^{5} -49.0000 q^{7} -590.869 q^{11} +505.095 q^{13} +517.964 q^{17} -932.905 q^{19} +3550.73 q^{23} -2559.81 q^{25} +5395.48 q^{29} +8329.00 q^{31} +1164.92 q^{35} -4936.43 q^{37} +5880.27 q^{41} -13540.8 q^{43} +7357.78 q^{47} +2401.00 q^{49} -3341.88 q^{53} +14047.2 q^{55} -42675.2 q^{59} +51327.6 q^{61} -12008.0 q^{65} +33755.0 q^{67} +17848.0 q^{71} -20628.2 q^{73} +28952.6 q^{77} -99202.0 q^{79} -61202.1 q^{83} -12314.0 q^{85} +90153.0 q^{89} -24749.7 q^{91} +22178.7 q^{95} -155739. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 76 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 76 q^{5} - 98 q^{7} - 564 q^{11} + 516 q^{13} - 76 q^{17} - 2360 q^{19} + 2036 q^{23} + 4270 q^{25} + 8320 q^{29} + 6280 q^{31} - 3724 q^{35} - 2460 q^{37} - 14308 q^{41} - 23128 q^{43} - 12712 q^{47} + 4802 q^{49} - 9896 q^{53} + 16728 q^{55} - 60888 q^{59} + 16172 q^{61} - 10920 q^{65} + 62568 q^{67} + 732 q^{71} + 1244 q^{73} + 27636 q^{77} - 11600 q^{79} - 132288 q^{83} - 71576 q^{85} + 93452 q^{89} - 25284 q^{91} - 120208 q^{95} - 272932 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −23.7738 −0.425278 −0.212639 0.977131i \(-0.568206\pi\)
−0.212639 + 0.977131i \(0.568206\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −590.869 −1.47234 −0.736172 0.676794i \(-0.763369\pi\)
−0.736172 + 0.676794i \(0.763369\pi\)
\(12\) 0 0
\(13\) 505.095 0.828924 0.414462 0.910067i \(-0.363970\pi\)
0.414462 + 0.910067i \(0.363970\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 517.964 0.434688 0.217344 0.976095i \(-0.430261\pi\)
0.217344 + 0.976095i \(0.430261\pi\)
\(18\) 0 0
\(19\) −932.905 −0.592862 −0.296431 0.955054i \(-0.595796\pi\)
−0.296431 + 0.955054i \(0.595796\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3550.73 1.39958 0.699790 0.714349i \(-0.253277\pi\)
0.699790 + 0.714349i \(0.253277\pi\)
\(24\) 0 0
\(25\) −2559.81 −0.819138
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5395.48 1.19134 0.595669 0.803230i \(-0.296887\pi\)
0.595669 + 0.803230i \(0.296887\pi\)
\(30\) 0 0
\(31\) 8329.00 1.55664 0.778321 0.627867i \(-0.216072\pi\)
0.778321 + 0.627867i \(0.216072\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1164.92 0.160740
\(36\) 0 0
\(37\) −4936.43 −0.592800 −0.296400 0.955064i \(-0.595786\pi\)
−0.296400 + 0.955064i \(0.595786\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5880.27 0.546308 0.273154 0.961970i \(-0.411933\pi\)
0.273154 + 0.961970i \(0.411933\pi\)
\(42\) 0 0
\(43\) −13540.8 −1.11679 −0.558396 0.829575i \(-0.688583\pi\)
−0.558396 + 0.829575i \(0.688583\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7357.78 0.485850 0.242925 0.970045i \(-0.421893\pi\)
0.242925 + 0.970045i \(0.421893\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3341.88 −0.163419 −0.0817093 0.996656i \(-0.526038\pi\)
−0.0817093 + 0.996656i \(0.526038\pi\)
\(54\) 0 0
\(55\) 14047.2 0.626156
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −42675.2 −1.59605 −0.798023 0.602626i \(-0.794121\pi\)
−0.798023 + 0.602626i \(0.794121\pi\)
\(60\) 0 0
\(61\) 51327.6 1.76615 0.883073 0.469235i \(-0.155470\pi\)
0.883073 + 0.469235i \(0.155470\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12008.0 −0.352523
\(66\) 0 0
\(67\) 33755.0 0.918651 0.459325 0.888268i \(-0.348091\pi\)
0.459325 + 0.888268i \(0.348091\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 17848.0 0.420188 0.210094 0.977681i \(-0.432623\pi\)
0.210094 + 0.977681i \(0.432623\pi\)
\(72\) 0 0
\(73\) −20628.2 −0.453058 −0.226529 0.974004i \(-0.572738\pi\)
−0.226529 + 0.974004i \(0.572738\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 28952.6 0.556494
\(78\) 0 0
\(79\) −99202.0 −1.78835 −0.894175 0.447718i \(-0.852237\pi\)
−0.894175 + 0.447718i \(0.852237\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −61202.1 −0.975149 −0.487575 0.873081i \(-0.662118\pi\)
−0.487575 + 0.873081i \(0.662118\pi\)
\(84\) 0 0
\(85\) −12314.0 −0.184863
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 90153.0 1.20644 0.603219 0.797576i \(-0.293884\pi\)
0.603219 + 0.797576i \(0.293884\pi\)
\(90\) 0 0
\(91\) −24749.7 −0.313304
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 22178.7 0.252131
\(96\) 0 0
\(97\) −155739. −1.68062 −0.840309 0.542107i \(-0.817627\pi\)
−0.840309 + 0.542107i \(0.817627\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −19635.0 −0.191526 −0.0957628 0.995404i \(-0.530529\pi\)
−0.0957628 + 0.995404i \(0.530529\pi\)
\(102\) 0 0
\(103\) 88981.8 0.826434 0.413217 0.910633i \(-0.364405\pi\)
0.413217 + 0.910633i \(0.364405\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −185903. −1.56973 −0.784867 0.619664i \(-0.787269\pi\)
−0.784867 + 0.619664i \(0.787269\pi\)
\(108\) 0 0
\(109\) −77652.7 −0.626023 −0.313012 0.949749i \(-0.601338\pi\)
−0.313012 + 0.949749i \(0.601338\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 246859. 1.81867 0.909334 0.416068i \(-0.136592\pi\)
0.909334 + 0.416068i \(0.136592\pi\)
\(114\) 0 0
\(115\) −84414.2 −0.595211
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −25380.2 −0.164296
\(120\) 0 0
\(121\) 188075. 1.16780
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 135149. 0.773640
\(126\) 0 0
\(127\) −210563. −1.15844 −0.579220 0.815171i \(-0.696643\pi\)
−0.579220 + 0.815171i \(0.696643\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 85398.9 0.434784 0.217392 0.976084i \(-0.430245\pi\)
0.217392 + 0.976084i \(0.430245\pi\)
\(132\) 0 0
\(133\) 45712.3 0.224081
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 86716.9 0.394732 0.197366 0.980330i \(-0.436761\pi\)
0.197366 + 0.980330i \(0.436761\pi\)
\(138\) 0 0
\(139\) 131720. 0.578247 0.289124 0.957292i \(-0.406636\pi\)
0.289124 + 0.957292i \(0.406636\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −298445. −1.22046
\(144\) 0 0
\(145\) −128271. −0.506650
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −30659.9 −0.113137 −0.0565685 0.998399i \(-0.518016\pi\)
−0.0565685 + 0.998399i \(0.518016\pi\)
\(150\) 0 0
\(151\) −125626. −0.448372 −0.224186 0.974546i \(-0.571972\pi\)
−0.224186 + 0.974546i \(0.571972\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −198012. −0.662006
\(156\) 0 0
\(157\) −516272. −1.67159 −0.835794 0.549043i \(-0.814992\pi\)
−0.835794 + 0.549043i \(0.814992\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −173986. −0.528991
\(162\) 0 0
\(163\) 119172. 0.351321 0.175660 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −39035.0 −0.108309 −0.0541543 0.998533i \(-0.517246\pi\)
−0.0541543 + 0.998533i \(0.517246\pi\)
\(168\) 0 0
\(169\) −116172. −0.312885
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 571616. 1.45207 0.726037 0.687655i \(-0.241360\pi\)
0.726037 + 0.687655i \(0.241360\pi\)
\(174\) 0 0
\(175\) 125431. 0.309605
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −846291. −1.97418 −0.987091 0.160160i \(-0.948799\pi\)
−0.987091 + 0.160160i \(0.948799\pi\)
\(180\) 0 0
\(181\) 491766. 1.11574 0.557868 0.829930i \(-0.311619\pi\)
0.557868 + 0.829930i \(0.311619\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 117358. 0.252105
\(186\) 0 0
\(187\) −306049. −0.640010
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −648886. −1.28702 −0.643509 0.765438i \(-0.722522\pi\)
−0.643509 + 0.765438i \(0.722522\pi\)
\(192\) 0 0
\(193\) −216436. −0.418251 −0.209125 0.977889i \(-0.567062\pi\)
−0.209125 + 0.977889i \(0.567062\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −178935. −0.328497 −0.164248 0.986419i \(-0.552520\pi\)
−0.164248 + 0.986419i \(0.552520\pi\)
\(198\) 0 0
\(199\) −303836. −0.543885 −0.271942 0.962314i \(-0.587666\pi\)
−0.271942 + 0.962314i \(0.587666\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −264378. −0.450283
\(204\) 0 0
\(205\) −139796. −0.232333
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 551224. 0.872897
\(210\) 0 0
\(211\) −634974. −0.981860 −0.490930 0.871199i \(-0.663343\pi\)
−0.490930 + 0.871199i \(0.663343\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 321915. 0.474947
\(216\) 0 0
\(217\) −408121. −0.588355
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 261621. 0.360323
\(222\) 0 0
\(223\) −1.20650e6 −1.62467 −0.812337 0.583188i \(-0.801805\pi\)
−0.812337 + 0.583188i \(0.801805\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 686964. 0.884849 0.442425 0.896806i \(-0.354118\pi\)
0.442425 + 0.896806i \(0.354118\pi\)
\(228\) 0 0
\(229\) −602459. −0.759170 −0.379585 0.925157i \(-0.623933\pi\)
−0.379585 + 0.925157i \(0.623933\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −262764. −0.317085 −0.158543 0.987352i \(-0.550680\pi\)
−0.158543 + 0.987352i \(0.550680\pi\)
\(234\) 0 0
\(235\) −174922. −0.206621
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 194880. 0.220685 0.110342 0.993894i \(-0.464805\pi\)
0.110342 + 0.993894i \(0.464805\pi\)
\(240\) 0 0
\(241\) 352082. 0.390482 0.195241 0.980755i \(-0.437451\pi\)
0.195241 + 0.980755i \(0.437451\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −57080.8 −0.0607540
\(246\) 0 0
\(247\) −471206. −0.491437
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 114343. 0.114558 0.0572791 0.998358i \(-0.481758\pi\)
0.0572791 + 0.998358i \(0.481758\pi\)
\(252\) 0 0
\(253\) −2.09801e6 −2.06066
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.78421e6 1.68505 0.842525 0.538657i \(-0.181068\pi\)
0.842525 + 0.538657i \(0.181068\pi\)
\(258\) 0 0
\(259\) 241885. 0.224057
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 46232.1 0.0412149 0.0206074 0.999788i \(-0.493440\pi\)
0.0206074 + 0.999788i \(0.493440\pi\)
\(264\) 0 0
\(265\) 79449.2 0.0694984
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −273850. −0.230745 −0.115372 0.993322i \(-0.536806\pi\)
−0.115372 + 0.993322i \(0.536806\pi\)
\(270\) 0 0
\(271\) 165105. 0.136564 0.0682821 0.997666i \(-0.478248\pi\)
0.0682821 + 0.997666i \(0.478248\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.51251e6 1.20605
\(276\) 0 0
\(277\) −605103. −0.473838 −0.236919 0.971529i \(-0.576138\pi\)
−0.236919 + 0.971529i \(0.576138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 618011. 0.466907 0.233454 0.972368i \(-0.424997\pi\)
0.233454 + 0.972368i \(0.424997\pi\)
\(282\) 0 0
\(283\) 218928. 0.162494 0.0812468 0.996694i \(-0.474110\pi\)
0.0812468 + 0.996694i \(0.474110\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −288133. −0.206485
\(288\) 0 0
\(289\) −1.15157e6 −0.811047
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.30928e6 −1.57147 −0.785736 0.618562i \(-0.787716\pi\)
−0.785736 + 0.618562i \(0.787716\pi\)
\(294\) 0 0
\(295\) 1.01455e6 0.678764
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.79345e6 1.16014
\(300\) 0 0
\(301\) 663497. 0.422107
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.22025e6 −0.751104
\(306\) 0 0
\(307\) −1.61363e6 −0.977145 −0.488572 0.872523i \(-0.662482\pi\)
−0.488572 + 0.872523i \(0.662482\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.11596e6 −0.654257 −0.327128 0.944980i \(-0.606081\pi\)
−0.327128 + 0.944980i \(0.606081\pi\)
\(312\) 0 0
\(313\) −2.02307e6 −1.16722 −0.583608 0.812036i \(-0.698359\pi\)
−0.583608 + 0.812036i \(0.698359\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.04841e6 0.585982 0.292991 0.956115i \(-0.405349\pi\)
0.292991 + 0.956115i \(0.405349\pi\)
\(318\) 0 0
\(319\) −3.18802e6 −1.75406
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −483211. −0.257710
\(324\) 0 0
\(325\) −1.29295e6 −0.679004
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −360531. −0.183634
\(330\) 0 0
\(331\) −3.29848e6 −1.65480 −0.827398 0.561617i \(-0.810180\pi\)
−0.827398 + 0.561617i \(0.810180\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −802483. −0.390682
\(336\) 0 0
\(337\) 2.64485e6 1.26861 0.634303 0.773084i \(-0.281287\pi\)
0.634303 + 0.773084i \(0.281287\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.92135e6 −2.29191
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.09974e6 0.936140 0.468070 0.883691i \(-0.344949\pi\)
0.468070 + 0.883691i \(0.344949\pi\)
\(348\) 0 0
\(349\) −2.91574e6 −1.28140 −0.640701 0.767790i \(-0.721356\pi\)
−0.640701 + 0.767790i \(0.721356\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.03901e6 −1.72520 −0.862598 0.505891i \(-0.831164\pi\)
−0.862598 + 0.505891i \(0.831164\pi\)
\(354\) 0 0
\(355\) −424314. −0.178697
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.68420e6 0.689696 0.344848 0.938658i \(-0.387930\pi\)
0.344848 + 0.938658i \(0.387930\pi\)
\(360\) 0 0
\(361\) −1.60579e6 −0.648515
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 490410. 0.192676
\(366\) 0 0
\(367\) −901845. −0.349516 −0.174758 0.984611i \(-0.555914\pi\)
−0.174758 + 0.984611i \(0.555914\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 163752. 0.0617664
\(372\) 0 0
\(373\) −1.48555e6 −0.552861 −0.276431 0.961034i \(-0.589152\pi\)
−0.276431 + 0.961034i \(0.589152\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.72523e6 0.987528
\(378\) 0 0
\(379\) −2.44302e6 −0.873633 −0.436817 0.899551i \(-0.643894\pi\)
−0.436817 + 0.899551i \(0.643894\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −457836. −0.159482 −0.0797412 0.996816i \(-0.525409\pi\)
−0.0797412 + 0.996816i \(0.525409\pi\)
\(384\) 0 0
\(385\) −688312. −0.236665
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.35458e6 0.453868 0.226934 0.973910i \(-0.427130\pi\)
0.226934 + 0.973910i \(0.427130\pi\)
\(390\) 0 0
\(391\) 1.83915e6 0.608380
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.35841e6 0.760546
\(396\) 0 0
\(397\) 3.25028e6 1.03501 0.517506 0.855680i \(-0.326861\pi\)
0.517506 + 0.855680i \(0.326861\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.99082e6 −1.54993 −0.774963 0.632006i \(-0.782232\pi\)
−0.774963 + 0.632006i \(0.782232\pi\)
\(402\) 0 0
\(403\) 4.20694e6 1.29034
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.91678e6 0.872806
\(408\) 0 0
\(409\) −2.16290e6 −0.639334 −0.319667 0.947530i \(-0.603571\pi\)
−0.319667 + 0.947530i \(0.603571\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.09109e6 0.603249
\(414\) 0 0
\(415\) 1.45501e6 0.414710
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.31464e6 −0.365823 −0.182912 0.983129i \(-0.558552\pi\)
−0.182912 + 0.983129i \(0.558552\pi\)
\(420\) 0 0
\(421\) 1.14615e6 0.315163 0.157581 0.987506i \(-0.449630\pi\)
0.157581 + 0.987506i \(0.449630\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.32589e6 −0.356069
\(426\) 0 0
\(427\) −2.51505e6 −0.667541
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.53987e6 1.43650 0.718251 0.695784i \(-0.244943\pi\)
0.718251 + 0.695784i \(0.244943\pi\)
\(432\) 0 0
\(433\) −3.52567e6 −0.903696 −0.451848 0.892095i \(-0.649235\pi\)
−0.451848 + 0.892095i \(0.649235\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.31249e6 −0.829757
\(438\) 0 0
\(439\) −5.93446e6 −1.46967 −0.734835 0.678246i \(-0.762740\pi\)
−0.734835 + 0.678246i \(0.762740\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.19294e6 0.288808 0.144404 0.989519i \(-0.453873\pi\)
0.144404 + 0.989519i \(0.453873\pi\)
\(444\) 0 0
\(445\) −2.14328e6 −0.513072
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.13944e6 −1.20310 −0.601548 0.798837i \(-0.705449\pi\)
−0.601548 + 0.798837i \(0.705449\pi\)
\(450\) 0 0
\(451\) −3.47447e6 −0.804353
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 588393. 0.133241
\(456\) 0 0
\(457\) 3.93737e6 0.881894 0.440947 0.897533i \(-0.354643\pi\)
0.440947 + 0.897533i \(0.354643\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.31710e6 −0.946105 −0.473053 0.881034i \(-0.656848\pi\)
−0.473053 + 0.881034i \(0.656848\pi\)
\(462\) 0 0
\(463\) 863360. 0.187171 0.0935857 0.995611i \(-0.470167\pi\)
0.0935857 + 0.995611i \(0.470167\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.84879e6 −0.392280 −0.196140 0.980576i \(-0.562841\pi\)
−0.196140 + 0.980576i \(0.562841\pi\)
\(468\) 0 0
\(469\) −1.65399e6 −0.347217
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.00081e6 1.64430
\(474\) 0 0
\(475\) 2.38806e6 0.485636
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.45491e6 1.08630 0.543149 0.839637i \(-0.317232\pi\)
0.543149 + 0.839637i \(0.317232\pi\)
\(480\) 0 0
\(481\) −2.49337e6 −0.491386
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.70251e6 0.714731
\(486\) 0 0
\(487\) −344795. −0.0658777 −0.0329388 0.999457i \(-0.510487\pi\)
−0.0329388 + 0.999457i \(0.510487\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.06521e7 −1.99404 −0.997018 0.0771721i \(-0.975411\pi\)
−0.997018 + 0.0771721i \(0.975411\pi\)
\(492\) 0 0
\(493\) 2.79466e6 0.517860
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −874551. −0.158816
\(498\) 0 0
\(499\) 2.85842e6 0.513895 0.256948 0.966425i \(-0.417283\pi\)
0.256948 + 0.966425i \(0.417283\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3.14241e6 0.553786 0.276893 0.960901i \(-0.410695\pi\)
0.276893 + 0.960901i \(0.410695\pi\)
\(504\) 0 0
\(505\) 466797. 0.0814517
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.66192e6 −0.284325 −0.142163 0.989843i \(-0.545406\pi\)
−0.142163 + 0.989843i \(0.545406\pi\)
\(510\) 0 0
\(511\) 1.01078e6 0.171240
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.11543e6 −0.351464
\(516\) 0 0
\(517\) −4.34748e6 −0.715338
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.18324e6 0.190976 0.0954881 0.995431i \(-0.469559\pi\)
0.0954881 + 0.995431i \(0.469559\pi\)
\(522\) 0 0
\(523\) −479133. −0.0765953 −0.0382976 0.999266i \(-0.512194\pi\)
−0.0382976 + 0.999266i \(0.512194\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.31412e6 0.676653
\(528\) 0 0
\(529\) 6.17131e6 0.958822
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.97009e6 0.452848
\(534\) 0 0
\(535\) 4.41961e6 0.667574
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.41868e6 −0.210335
\(540\) 0 0
\(541\) −5.40143e6 −0.793442 −0.396721 0.917939i \(-0.629852\pi\)
−0.396721 + 0.917939i \(0.629852\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.84610e6 0.266234
\(546\) 0 0
\(547\) 3.61094e6 0.516003 0.258001 0.966145i \(-0.416936\pi\)
0.258001 + 0.966145i \(0.416936\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.03347e6 −0.706298
\(552\) 0 0
\(553\) 4.86090e6 0.675933
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.04321e6 1.23505 0.617525 0.786551i \(-0.288135\pi\)
0.617525 + 0.786551i \(0.288135\pi\)
\(558\) 0 0
\(559\) −6.83937e6 −0.925735
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.40826e6 0.453170 0.226585 0.973991i \(-0.427244\pi\)
0.226585 + 0.973991i \(0.427244\pi\)
\(564\) 0 0
\(565\) −5.86878e6 −0.773440
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.29430e6 −0.426562 −0.213281 0.976991i \(-0.568415\pi\)
−0.213281 + 0.976991i \(0.568415\pi\)
\(570\) 0 0
\(571\) −5.86813e6 −0.753199 −0.376599 0.926376i \(-0.622907\pi\)
−0.376599 + 0.926376i \(0.622907\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −9.08917e6 −1.14645
\(576\) 0 0
\(577\) 1.23173e6 0.154019 0.0770096 0.997030i \(-0.475463\pi\)
0.0770096 + 0.997030i \(0.475463\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.99890e6 0.368572
\(582\) 0 0
\(583\) 1.97461e6 0.240608
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.58196e6 −0.788424 −0.394212 0.919020i \(-0.628982\pi\)
−0.394212 + 0.919020i \(0.628982\pi\)
\(588\) 0 0
\(589\) −7.77016e6 −0.922873
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.93053e6 −0.459002 −0.229501 0.973308i \(-0.573709\pi\)
−0.229501 + 0.973308i \(0.573709\pi\)
\(594\) 0 0
\(595\) 603384. 0.0698717
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.32868e7 −1.51305 −0.756524 0.653966i \(-0.773104\pi\)
−0.756524 + 0.653966i \(0.773104\pi\)
\(600\) 0 0
\(601\) 1.25036e7 1.41205 0.706025 0.708187i \(-0.250487\pi\)
0.706025 + 0.708187i \(0.250487\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.47126e6 −0.496639
\(606\) 0 0
\(607\) 1.24254e7 1.36880 0.684400 0.729107i \(-0.260064\pi\)
0.684400 + 0.729107i \(0.260064\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.71638e6 0.402733
\(612\) 0 0
\(613\) 3.63638e6 0.390857 0.195429 0.980718i \(-0.437390\pi\)
0.195429 + 0.980718i \(0.437390\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.50994e6 0.794188 0.397094 0.917778i \(-0.370019\pi\)
0.397094 + 0.917778i \(0.370019\pi\)
\(618\) 0 0
\(619\) −3.35237e6 −0.351662 −0.175831 0.984420i \(-0.556261\pi\)
−0.175831 + 0.984420i \(0.556261\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.41750e6 −0.455991
\(624\) 0 0
\(625\) 4.78639e6 0.490126
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.55689e6 −0.257683
\(630\) 0 0
\(631\) 2.66773e6 0.266728 0.133364 0.991067i \(-0.457422\pi\)
0.133364 + 0.991067i \(0.457422\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.00589e6 0.492659
\(636\) 0 0
\(637\) 1.21273e6 0.118418
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.30265e6 0.798126 0.399063 0.916923i \(-0.369335\pi\)
0.399063 + 0.916923i \(0.369335\pi\)
\(642\) 0 0
\(643\) −1.16120e7 −1.10759 −0.553796 0.832652i \(-0.686821\pi\)
−0.553796 + 0.832652i \(0.686821\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.91709e7 1.80045 0.900227 0.435421i \(-0.143400\pi\)
0.900227 + 0.435421i \(0.143400\pi\)
\(648\) 0 0
\(649\) 2.52155e7 2.34993
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.36350e7 1.25133 0.625665 0.780092i \(-0.284828\pi\)
0.625665 + 0.780092i \(0.284828\pi\)
\(654\) 0 0
\(655\) −2.03025e6 −0.184904
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3.71937e6 0.333623 0.166812 0.985989i \(-0.446653\pi\)
0.166812 + 0.985989i \(0.446653\pi\)
\(660\) 0 0
\(661\) 9.69481e6 0.863050 0.431525 0.902101i \(-0.357976\pi\)
0.431525 + 0.902101i \(0.357976\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.08676e6 −0.0952966
\(666\) 0 0
\(667\) 1.91579e7 1.66737
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.03279e7 −2.60038
\(672\) 0 0
\(673\) −1.51973e6 −0.129339 −0.0646695 0.997907i \(-0.520599\pi\)
−0.0646695 + 0.997907i \(0.520599\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.26234e7 1.89709 0.948543 0.316648i \(-0.102557\pi\)
0.948543 + 0.316648i \(0.102557\pi\)
\(678\) 0 0
\(679\) 7.63123e6 0.635214
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.21373e6 −0.0995567 −0.0497784 0.998760i \(-0.515851\pi\)
−0.0497784 + 0.998760i \(0.515851\pi\)
\(684\) 0 0
\(685\) −2.06159e6 −0.167871
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.68797e6 −0.135462
\(690\) 0 0
\(691\) 1.40481e7 1.11924 0.559619 0.828750i \(-0.310947\pi\)
0.559619 + 0.828750i \(0.310947\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.13147e6 −0.245916
\(696\) 0 0
\(697\) 3.04577e6 0.237473
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.42260e7 1.09342 0.546711 0.837321i \(-0.315880\pi\)
0.546711 + 0.837321i \(0.315880\pi\)
\(702\) 0 0
\(703\) 4.60522e6 0.351449
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 962113. 0.0723898
\(708\) 0 0
\(709\) −8.49859e6 −0.634938 −0.317469 0.948269i \(-0.602833\pi\)
−0.317469 + 0.948269i \(0.602833\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.95740e7 2.17864
\(714\) 0 0
\(715\) 7.09517e6 0.519036
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.77769e6 0.561085 0.280542 0.959842i \(-0.409486\pi\)
0.280542 + 0.959842i \(0.409486\pi\)
\(720\) 0 0
\(721\) −4.36011e6 −0.312363
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.38114e7 −0.975870
\(726\) 0 0
\(727\) 2.03361e7 1.42703 0.713513 0.700642i \(-0.247103\pi\)
0.713513 + 0.700642i \(0.247103\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7.01363e6 −0.485455
\(732\) 0 0
\(733\) −6.91670e6 −0.475488 −0.237744 0.971328i \(-0.576408\pi\)
−0.237744 + 0.971328i \(0.576408\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.99448e7 −1.35257
\(738\) 0 0
\(739\) 2.12775e7 1.43321 0.716605 0.697479i \(-0.245695\pi\)
0.716605 + 0.697479i \(0.245695\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.99548e7 −1.32610 −0.663049 0.748576i \(-0.730738\pi\)
−0.663049 + 0.748576i \(0.730738\pi\)
\(744\) 0 0
\(745\) 728902. 0.0481148
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 9.10923e6 0.593304
\(750\) 0 0
\(751\) −5.84360e6 −0.378077 −0.189039 0.981970i \(-0.560537\pi\)
−0.189039 + 0.981970i \(0.560537\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.98661e6 0.190683
\(756\) 0 0
\(757\) 2.32278e7 1.47322 0.736612 0.676315i \(-0.236424\pi\)
0.736612 + 0.676315i \(0.236424\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.93636e7 −1.21206 −0.606030 0.795441i \(-0.707239\pi\)
−0.606030 + 0.795441i \(0.707239\pi\)
\(762\) 0 0
\(763\) 3.80498e6 0.236614
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.15550e7 −1.32300
\(768\) 0 0
\(769\) 1.83678e7 1.12006 0.560031 0.828472i \(-0.310789\pi\)
0.560031 + 0.828472i \(0.310789\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.91439e7 −1.75428 −0.877140 0.480234i \(-0.840552\pi\)
−0.877140 + 0.480234i \(0.840552\pi\)
\(774\) 0 0
\(775\) −2.13206e7 −1.27510
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.48573e6 −0.323885
\(780\) 0 0
\(781\) −1.05458e7 −0.618661
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.22737e7 0.710890
\(786\) 0 0
\(787\) −4.53087e6 −0.260762 −0.130381 0.991464i \(-0.541620\pi\)
−0.130381 + 0.991464i \(0.541620\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.20961e7 −0.687392
\(792\) 0 0
\(793\) 2.59253e7 1.46400
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.19253e7 −0.665005 −0.332503 0.943102i \(-0.607893\pi\)
−0.332503 + 0.943102i \(0.607893\pi\)
\(798\) 0 0
\(799\) 3.81107e6 0.211193
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.21886e7 0.667057
\(804\) 0 0
\(805\) 4.13629e6 0.224968
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.25486e7 0.674099 0.337049 0.941487i \(-0.390571\pi\)
0.337049 + 0.941487i \(0.390571\pi\)
\(810\) 0 0
\(811\) 5.87349e6 0.313577 0.156788 0.987632i \(-0.449886\pi\)
0.156788 + 0.987632i \(0.449886\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.83316e6 −0.149409
\(816\) 0 0
\(817\) 1.26322e7 0.662103
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.44021e7 −1.26348 −0.631742 0.775178i \(-0.717660\pi\)
−0.631742 + 0.775178i \(0.717660\pi\)
\(822\) 0 0
\(823\) −2.45208e7 −1.26193 −0.630965 0.775812i \(-0.717341\pi\)
−0.630965 + 0.775812i \(0.717341\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.15215e7 −0.585792 −0.292896 0.956144i \(-0.594619\pi\)
−0.292896 + 0.956144i \(0.594619\pi\)
\(828\) 0 0
\(829\) −2.67057e7 −1.34964 −0.674820 0.737982i \(-0.735779\pi\)
−0.674820 + 0.737982i \(0.735779\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.24363e6 0.0620982
\(834\) 0 0
\(835\) 928009. 0.0460613
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.76624e7 1.35671 0.678353 0.734737i \(-0.262694\pi\)
0.678353 + 0.734737i \(0.262694\pi\)
\(840\) 0 0
\(841\) 8.60001e6 0.419285
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.76185e6 0.133063
\(846\) 0 0
\(847\) −9.21568e6 −0.441386
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.75279e7 −0.829671
\(852\) 0 0
\(853\) −1.46417e7 −0.688999 −0.344499 0.938787i \(-0.611951\pi\)
−0.344499 + 0.938787i \(0.611951\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.18815e7 −1.94792 −0.973959 0.226725i \(-0.927198\pi\)
−0.973959 + 0.226725i \(0.927198\pi\)
\(858\) 0 0
\(859\) 3.52752e7 1.63112 0.815562 0.578670i \(-0.196428\pi\)
0.815562 + 0.578670i \(0.196428\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.07135e7 1.40379 0.701895 0.712280i \(-0.252337\pi\)
0.701895 + 0.712280i \(0.252337\pi\)
\(864\) 0 0
\(865\) −1.35895e7 −0.617536
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.86154e7 2.63307
\(870\) 0 0
\(871\) 1.70495e7 0.761492
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.62232e6 −0.292408
\(876\) 0 0
\(877\) 2.97875e7 1.30778 0.653891 0.756588i \(-0.273135\pi\)
0.653891 + 0.756588i \(0.273135\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.74145e7 1.62405 0.812026 0.583621i \(-0.198365\pi\)
0.812026 + 0.583621i \(0.198365\pi\)
\(882\) 0 0
\(883\) −1.30401e7 −0.562832 −0.281416 0.959586i \(-0.590804\pi\)
−0.281416 + 0.959586i \(0.590804\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.76838e7 0.754687 0.377343 0.926073i \(-0.376838\pi\)
0.377343 + 0.926073i \(0.376838\pi\)
\(888\) 0 0
\(889\) 1.03176e7 0.437849
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −6.86411e6 −0.288042
\(894\) 0 0
\(895\) 2.01195e7 0.839577
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 4.49389e7 1.85448
\(900\) 0 0
\(901\) −1.73097e6 −0.0710360
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.16911e7 −0.474499
\(906\) 0 0
\(907\) −4.31052e6 −0.173985 −0.0869925 0.996209i \(-0.527726\pi\)
−0.0869925 + 0.996209i \(0.527726\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.16954e7 0.866106 0.433053 0.901368i \(-0.357436\pi\)
0.433053 + 0.901368i \(0.357436\pi\)
\(912\) 0 0
\(913\) 3.61624e7 1.43576
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.18454e6 −0.164333
\(918\) 0 0
\(919\) 1.38075e7 0.539296 0.269648 0.962959i \(-0.413093\pi\)
0.269648 + 0.962959i \(0.413093\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9.01493e6 0.348304
\(924\) 0 0
\(925\) 1.26363e7 0.485585
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −8.28005e6 −0.314770 −0.157385 0.987537i \(-0.550306\pi\)
−0.157385 + 0.987537i \(0.550306\pi\)
\(930\) 0 0
\(931\) −2.23990e6 −0.0846945
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7.27594e6 0.272182
\(936\) 0 0
\(937\) −3.03112e7 −1.12786 −0.563928 0.825824i \(-0.690711\pi\)
−0.563928 + 0.825824i \(0.690711\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.15564e7 −1.52990 −0.764952 0.644087i \(-0.777237\pi\)
−0.764952 + 0.644087i \(0.777237\pi\)
\(942\) 0 0
\(943\) 2.08792e7 0.764601
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.94364e6 −0.179132 −0.0895658 0.995981i \(-0.528548\pi\)
−0.0895658 + 0.995981i \(0.528548\pi\)
\(948\) 0 0
\(949\) −1.04192e7 −0.375551
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.18359e7 −1.84884 −0.924418 0.381380i \(-0.875449\pi\)
−0.924418 + 0.381380i \(0.875449\pi\)
\(954\) 0 0
\(955\) 1.54265e7 0.547341
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.24913e6 −0.149195
\(960\) 0 0
\(961\) 4.07430e7 1.42313
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5.14551e6 0.177873
\(966\) 0 0
\(967\) 1.92627e7 0.662446 0.331223 0.943553i \(-0.392539\pi\)
0.331223 + 0.943553i \(0.392539\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 6.97229e6 0.237316 0.118658 0.992935i \(-0.462141\pi\)
0.118658 + 0.992935i \(0.462141\pi\)
\(972\) 0 0
\(973\) −6.45426e6 −0.218557
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.65588e7 1.56051 0.780253 0.625465i \(-0.215090\pi\)
0.780253 + 0.625465i \(0.215090\pi\)
\(978\) 0 0
\(979\) −5.32686e7 −1.77629
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.10229e7 1.35408 0.677038 0.735948i \(-0.263263\pi\)
0.677038 + 0.735948i \(0.263263\pi\)
\(984\) 0 0
\(985\) 4.25397e6 0.139702
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.80795e7 −1.56304
\(990\) 0 0
\(991\) 3.31717e7 1.07296 0.536480 0.843913i \(-0.319753\pi\)
0.536480 + 0.843913i \(0.319753\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 7.22334e6 0.231302
\(996\) 0 0
\(997\) −5.20233e7 −1.65753 −0.828763 0.559600i \(-0.810955\pi\)
−0.828763 + 0.559600i \(0.810955\pi\)
\(998\) 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.bv.1.1 2
3.2 odd 2 1008.6.a.bg.1.2 2
4.3 odd 2 504.6.a.u.1.1 yes 2
12.11 even 2 504.6.a.k.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.k.1.2 2 12.11 even 2
504.6.a.u.1.1 yes 2 4.3 odd 2
1008.6.a.bg.1.2 2 3.2 odd 2
1008.6.a.bv.1.1 2 1.1 even 1 trivial