Properties

Label 1008.6.a.br.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{114}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 114 \) 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 1.2
Root \(10.6771\) 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)
 
\(f(q)\) \(=\) \(q+78.0625 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+78.0625 q^{5} +49.0000 q^{7} +746.437 q^{11} +9.75012 q^{13} +1754.69 q^{17} +603.250 q^{19} +3175.31 q^{23} +2968.75 q^{25} +3227.50 q^{29} -7881.75 q^{31} +3825.06 q^{35} +12362.7 q^{37} +3699.56 q^{41} -16915.0 q^{43} -658.130 q^{47} +2401.00 q^{49} +27891.1 q^{53} +58268.7 q^{55} -7456.38 q^{59} -43705.7 q^{61} +761.119 q^{65} +28643.5 q^{67} +9244.93 q^{71} -29816.5 q^{73} +36575.4 q^{77} -32928.5 q^{79} -40524.5 q^{83} +136975. q^{85} +41351.3 q^{89} +477.756 q^{91} +47091.2 q^{95} -110780. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 28 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 28 q^{5} + 98 q^{7} + 596 q^{11} + 532 q^{13} + 2100 q^{17} + 2744 q^{19} + 3660 q^{23} + 2350 q^{25} - 720 q^{29} - 3976 q^{31} + 1372 q^{35} + 6788 q^{37} - 4004 q^{41} - 19480 q^{43} - 21560 q^{47} + 4802 q^{49} + 57576 q^{53} + 65800 q^{55} - 22344 q^{59} - 38724 q^{61} - 25384 q^{65} - 7288 q^{67} - 3932 q^{71} + 19292 q^{73} + 29204 q^{77} - 15632 q^{79} - 22624 q^{83} + 119688 q^{85} + 112812 q^{89} + 26068 q^{91} - 60080 q^{95} - 36036 q^{97}+O(q^{100}) \) 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
\(5\) 78.0625 1.39642 0.698212 0.715891i \(-0.253979\pi\)
0.698212 + 0.715891i \(0.253979\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 746.437 1.85999 0.929997 0.367567i \(-0.119809\pi\)
0.929997 + 0.367567i \(0.119809\pi\)
\(12\) 0 0
\(13\) 9.75012 0.0160012 0.00800058 0.999968i \(-0.497453\pi\)
0.00800058 + 0.999968i \(0.497453\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1754.69 1.47257 0.736287 0.676669i \(-0.236577\pi\)
0.736287 + 0.676669i \(0.236577\pi\)
\(18\) 0 0
\(19\) 603.250 0.383366 0.191683 0.981457i \(-0.438605\pi\)
0.191683 + 0.981457i \(0.438605\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3175.31 1.25160 0.625802 0.779982i \(-0.284772\pi\)
0.625802 + 0.779982i \(0.284772\pi\)
\(24\) 0 0
\(25\) 2968.75 0.950000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3227.50 0.712641 0.356321 0.934364i \(-0.384031\pi\)
0.356321 + 0.934364i \(0.384031\pi\)
\(30\) 0 0
\(31\) −7881.75 −1.47305 −0.736526 0.676409i \(-0.763535\pi\)
−0.736526 + 0.676409i \(0.763535\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3825.06 0.527799
\(36\) 0 0
\(37\) 12362.7 1.48460 0.742302 0.670065i \(-0.233734\pi\)
0.742302 + 0.670065i \(0.233734\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3699.56 0.343709 0.171854 0.985122i \(-0.445024\pi\)
0.171854 + 0.985122i \(0.445024\pi\)
\(42\) 0 0
\(43\) −16915.0 −1.39509 −0.697543 0.716543i \(-0.745723\pi\)
−0.697543 + 0.716543i \(0.745723\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −658.130 −0.0434577 −0.0217289 0.999764i \(-0.506917\pi\)
−0.0217289 + 0.999764i \(0.506917\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 27891.1 1.36388 0.681940 0.731408i \(-0.261136\pi\)
0.681940 + 0.731408i \(0.261136\pi\)
\(54\) 0 0
\(55\) 58268.7 2.59734
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7456.38 −0.278867 −0.139434 0.990231i \(-0.544528\pi\)
−0.139434 + 0.990231i \(0.544528\pi\)
\(60\) 0 0
\(61\) −43705.7 −1.50388 −0.751941 0.659230i \(-0.770882\pi\)
−0.751941 + 0.659230i \(0.770882\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 761.119 0.0223444
\(66\) 0 0
\(67\) 28643.5 0.779541 0.389770 0.920912i \(-0.372554\pi\)
0.389770 + 0.920912i \(0.372554\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 9244.93 0.217650 0.108825 0.994061i \(-0.465291\pi\)
0.108825 + 0.994061i \(0.465291\pi\)
\(72\) 0 0
\(73\) −29816.5 −0.654861 −0.327431 0.944875i \(-0.606183\pi\)
−0.327431 + 0.944875i \(0.606183\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 36575.4 0.703012
\(78\) 0 0
\(79\) −32928.5 −0.593614 −0.296807 0.954938i \(-0.595922\pi\)
−0.296807 + 0.954938i \(0.595922\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −40524.5 −0.645687 −0.322844 0.946452i \(-0.604639\pi\)
−0.322844 + 0.946452i \(0.604639\pi\)
\(84\) 0 0
\(85\) 136975. 2.05634
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 41351.3 0.553368 0.276684 0.960961i \(-0.410764\pi\)
0.276684 + 0.960961i \(0.410764\pi\)
\(90\) 0 0
\(91\) 477.756 0.00604787
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 47091.2 0.535341
\(96\) 0 0
\(97\) −110780. −1.19546 −0.597728 0.801699i \(-0.703930\pi\)
−0.597728 + 0.801699i \(0.703930\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 80973.4 0.789840 0.394920 0.918716i \(-0.370772\pi\)
0.394920 + 0.918716i \(0.370772\pi\)
\(102\) 0 0
\(103\) −104902. −0.974298 −0.487149 0.873319i \(-0.661963\pi\)
−0.487149 + 0.873319i \(0.661963\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −193878. −1.63708 −0.818540 0.574450i \(-0.805216\pi\)
−0.818540 + 0.574450i \(0.805216\pi\)
\(108\) 0 0
\(109\) −154948. −1.24917 −0.624584 0.780957i \(-0.714732\pi\)
−0.624584 + 0.780957i \(0.714732\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 91578.5 0.674679 0.337340 0.941383i \(-0.390473\pi\)
0.337340 + 0.941383i \(0.390473\pi\)
\(114\) 0 0
\(115\) 247873. 1.74777
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 85979.7 0.556581
\(120\) 0 0
\(121\) 396118. 2.45958
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12197.3 −0.0698216
\(126\) 0 0
\(127\) −110234. −0.606465 −0.303233 0.952917i \(-0.598066\pi\)
−0.303233 + 0.952917i \(0.598066\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −361365. −1.83979 −0.919895 0.392166i \(-0.871726\pi\)
−0.919895 + 0.392166i \(0.871726\pi\)
\(132\) 0 0
\(133\) 29559.3 0.144899
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 293644. 1.33665 0.668327 0.743867i \(-0.267011\pi\)
0.668327 + 0.743867i \(0.267011\pi\)
\(138\) 0 0
\(139\) −92541.4 −0.406255 −0.203128 0.979152i \(-0.565111\pi\)
−0.203128 + 0.979152i \(0.565111\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7277.85 0.0297621
\(144\) 0 0
\(145\) 251946. 0.995149
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13179.0 0.0486313 0.0243157 0.999704i \(-0.492259\pi\)
0.0243157 + 0.999704i \(0.492259\pi\)
\(150\) 0 0
\(151\) 304869. 1.08811 0.544053 0.839051i \(-0.316889\pi\)
0.544053 + 0.839051i \(0.316889\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −615269. −2.05701
\(156\) 0 0
\(157\) −64050.2 −0.207382 −0.103691 0.994610i \(-0.533065\pi\)
−0.103691 + 0.994610i \(0.533065\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 155590. 0.473062
\(162\) 0 0
\(163\) −617219. −1.81958 −0.909788 0.415072i \(-0.863756\pi\)
−0.909788 + 0.415072i \(0.863756\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −494693. −1.37260 −0.686301 0.727318i \(-0.740767\pi\)
−0.686301 + 0.727318i \(0.740767\pi\)
\(168\) 0 0
\(169\) −371198. −0.999744
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −701459. −1.78191 −0.890957 0.454088i \(-0.849965\pi\)
−0.890957 + 0.454088i \(0.849965\pi\)
\(174\) 0 0
\(175\) 145469. 0.359066
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −197449. −0.460598 −0.230299 0.973120i \(-0.573971\pi\)
−0.230299 + 0.973120i \(0.573971\pi\)
\(180\) 0 0
\(181\) 869311. 1.97233 0.986163 0.165777i \(-0.0530133\pi\)
0.986163 + 0.165777i \(0.0530133\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 965066. 2.07314
\(186\) 0 0
\(187\) 1.30976e6 2.73898
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −119524. −0.237068 −0.118534 0.992950i \(-0.537819\pi\)
−0.118534 + 0.992950i \(0.537819\pi\)
\(192\) 0 0
\(193\) 170916. 0.330285 0.165143 0.986270i \(-0.447192\pi\)
0.165143 + 0.986270i \(0.447192\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −715090. −1.31279 −0.656394 0.754418i \(-0.727919\pi\)
−0.656394 + 0.754418i \(0.727919\pi\)
\(198\) 0 0
\(199\) 715708. 1.28116 0.640580 0.767892i \(-0.278694\pi\)
0.640580 + 0.767892i \(0.278694\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 158147. 0.269353
\(204\) 0 0
\(205\) 288797. 0.479963
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 450289. 0.713059
\(210\) 0 0
\(211\) 880061. 1.36084 0.680420 0.732823i \(-0.261798\pi\)
0.680420 + 0.732823i \(0.261798\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.32043e6 −1.94813
\(216\) 0 0
\(217\) −386206. −0.556762
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17108.4 0.0235629
\(222\) 0 0
\(223\) −514501. −0.692826 −0.346413 0.938082i \(-0.612600\pi\)
−0.346413 + 0.938082i \(0.612600\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 873242. 1.12479 0.562393 0.826870i \(-0.309881\pi\)
0.562393 + 0.826870i \(0.309881\pi\)
\(228\) 0 0
\(229\) −1.11239e6 −1.40174 −0.700869 0.713290i \(-0.747204\pi\)
−0.700869 + 0.713290i \(0.747204\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.21568e6 1.46700 0.733499 0.679691i \(-0.237886\pi\)
0.733499 + 0.679691i \(0.237886\pi\)
\(234\) 0 0
\(235\) −51375.2 −0.0606854
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 462246. 0.523454 0.261727 0.965142i \(-0.415708\pi\)
0.261727 + 0.965142i \(0.415708\pi\)
\(240\) 0 0
\(241\) −247817. −0.274845 −0.137423 0.990513i \(-0.543882\pi\)
−0.137423 + 0.990513i \(0.543882\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 187428. 0.199489
\(246\) 0 0
\(247\) 5881.76 0.00613430
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.25628e6 1.25864 0.629322 0.777145i \(-0.283333\pi\)
0.629322 + 0.777145i \(0.283333\pi\)
\(252\) 0 0
\(253\) 2.37017e6 2.32798
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 330237. 0.311884 0.155942 0.987766i \(-0.450159\pi\)
0.155942 + 0.987766i \(0.450159\pi\)
\(258\) 0 0
\(259\) 605775. 0.561128
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −187729. −0.167356 −0.0836781 0.996493i \(-0.526667\pi\)
−0.0836781 + 0.996493i \(0.526667\pi\)
\(264\) 0 0
\(265\) 2.17725e6 1.90456
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.02334e6 0.862264 0.431132 0.902289i \(-0.358114\pi\)
0.431132 + 0.902289i \(0.358114\pi\)
\(270\) 0 0
\(271\) 649145. 0.536931 0.268466 0.963289i \(-0.413483\pi\)
0.268466 + 0.963289i \(0.413483\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.21599e6 1.76699
\(276\) 0 0
\(277\) 1.40211e6 1.09795 0.548973 0.835840i \(-0.315019\pi\)
0.548973 + 0.835840i \(0.315019\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.63255e6 1.23339 0.616697 0.787201i \(-0.288470\pi\)
0.616697 + 0.787201i \(0.288470\pi\)
\(282\) 0 0
\(283\) −621056. −0.460962 −0.230481 0.973077i \(-0.574030\pi\)
−0.230481 + 0.973077i \(0.574030\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 181278. 0.129910
\(288\) 0 0
\(289\) 1.65907e6 1.16848
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 115908. 0.0788759 0.0394380 0.999222i \(-0.487443\pi\)
0.0394380 + 0.999222i \(0.487443\pi\)
\(294\) 0 0
\(295\) −582063. −0.389417
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 30959.7 0.0200271
\(300\) 0 0
\(301\) −828835. −0.527293
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.41178e6 −2.10006
\(306\) 0 0
\(307\) −765157. −0.463345 −0.231673 0.972794i \(-0.574420\pi\)
−0.231673 + 0.972794i \(0.574420\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 179636. 0.105315 0.0526576 0.998613i \(-0.483231\pi\)
0.0526576 + 0.998613i \(0.483231\pi\)
\(312\) 0 0
\(313\) 895716. 0.516785 0.258392 0.966040i \(-0.416807\pi\)
0.258392 + 0.966040i \(0.416807\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 228258. 0.127579 0.0637893 0.997963i \(-0.479681\pi\)
0.0637893 + 0.997963i \(0.479681\pi\)
\(318\) 0 0
\(319\) 2.40913e6 1.32551
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.05852e6 0.564535
\(324\) 0 0
\(325\) 28945.7 0.0152011
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −32248.4 −0.0164255
\(330\) 0 0
\(331\) 3.01591e6 1.51303 0.756516 0.653975i \(-0.226900\pi\)
0.756516 + 0.653975i \(0.226900\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.23598e6 1.08857
\(336\) 0 0
\(337\) −1.10209e6 −0.528619 −0.264310 0.964438i \(-0.585144\pi\)
−0.264310 + 0.964438i \(0.585144\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.88323e6 −2.73987
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.90191e6 −1.29378 −0.646891 0.762583i \(-0.723931\pi\)
−0.646891 + 0.762583i \(0.723931\pi\)
\(348\) 0 0
\(349\) −2.23892e6 −0.983954 −0.491977 0.870608i \(-0.663726\pi\)
−0.491977 + 0.870608i \(0.663726\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.05842e6 −0.879217 −0.439609 0.898189i \(-0.644883\pi\)
−0.439609 + 0.898189i \(0.644883\pi\)
\(354\) 0 0
\(355\) 721682. 0.303931
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.96387e6 −0.804222 −0.402111 0.915591i \(-0.631723\pi\)
−0.402111 + 0.915591i \(0.631723\pi\)
\(360\) 0 0
\(361\) −2.11219e6 −0.853031
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.32755e6 −0.914464
\(366\) 0 0
\(367\) 3.55132e6 1.37634 0.688169 0.725550i \(-0.258415\pi\)
0.688169 + 0.725550i \(0.258415\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.36667e6 0.515498
\(372\) 0 0
\(373\) 4.69562e6 1.74751 0.873757 0.486363i \(-0.161677\pi\)
0.873757 + 0.486363i \(0.161677\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 31468.5 0.0114031
\(378\) 0 0
\(379\) 957580. 0.342434 0.171217 0.985233i \(-0.445230\pi\)
0.171217 + 0.985233i \(0.445230\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.79644e6 −0.625772 −0.312886 0.949791i \(-0.601296\pi\)
−0.312886 + 0.949791i \(0.601296\pi\)
\(384\) 0 0
\(385\) 2.85517e6 0.981702
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.36239e6 −1.46167 −0.730836 0.682553i \(-0.760870\pi\)
−0.730836 + 0.682553i \(0.760870\pi\)
\(390\) 0 0
\(391\) 5.57168e6 1.84308
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.57048e6 −0.828937
\(396\) 0 0
\(397\) 3.84239e6 1.22356 0.611780 0.791028i \(-0.290454\pi\)
0.611780 + 0.791028i \(0.290454\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.66668e6 −1.13871 −0.569354 0.822093i \(-0.692806\pi\)
−0.569354 + 0.822093i \(0.692806\pi\)
\(402\) 0 0
\(403\) −76848.0 −0.0235706
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.22801e6 2.76135
\(408\) 0 0
\(409\) 2.90345e6 0.858236 0.429118 0.903248i \(-0.358824\pi\)
0.429118 + 0.903248i \(0.358824\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −365362. −0.105402
\(414\) 0 0
\(415\) −3.16344e6 −0.901653
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.94202e6 1.09694 0.548470 0.836170i \(-0.315210\pi\)
0.548470 + 0.836170i \(0.315210\pi\)
\(420\) 0 0
\(421\) −526504. −0.144776 −0.0723880 0.997377i \(-0.523062\pi\)
−0.0723880 + 0.997377i \(0.523062\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.20923e6 1.39895
\(426\) 0 0
\(427\) −2.14158e6 −0.568414
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −387004. −0.100351 −0.0501756 0.998740i \(-0.515978\pi\)
−0.0501756 + 0.998740i \(0.515978\pi\)
\(432\) 0 0
\(433\) −2.77123e6 −0.710318 −0.355159 0.934806i \(-0.615573\pi\)
−0.355159 + 0.934806i \(0.615573\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.91551e6 0.479822
\(438\) 0 0
\(439\) −3.01147e6 −0.745791 −0.372895 0.927873i \(-0.621635\pi\)
−0.372895 + 0.927873i \(0.621635\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.30598e6 −0.800370 −0.400185 0.916434i \(-0.631054\pi\)
−0.400185 + 0.916434i \(0.631054\pi\)
\(444\) 0 0
\(445\) 3.22799e6 0.772737
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.93077e6 0.686066 0.343033 0.939323i \(-0.388546\pi\)
0.343033 + 0.939323i \(0.388546\pi\)
\(450\) 0 0
\(451\) 2.76149e6 0.639296
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 37294.8 0.00844539
\(456\) 0 0
\(457\) −7.55328e6 −1.69178 −0.845892 0.533354i \(-0.820931\pi\)
−0.845892 + 0.533354i \(0.820931\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7.54017e6 1.65245 0.826226 0.563339i \(-0.190483\pi\)
0.826226 + 0.563339i \(0.190483\pi\)
\(462\) 0 0
\(463\) 2.69250e6 0.583719 0.291859 0.956461i \(-0.405726\pi\)
0.291859 + 0.956461i \(0.405726\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.28377e6 1.33330 0.666651 0.745370i \(-0.267727\pi\)
0.666651 + 0.745370i \(0.267727\pi\)
\(468\) 0 0
\(469\) 1.40353e6 0.294639
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.26260e7 −2.59485
\(474\) 0 0
\(475\) 1.79090e6 0.364198
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.63273e6 0.723426 0.361713 0.932290i \(-0.382192\pi\)
0.361713 + 0.932290i \(0.382192\pi\)
\(480\) 0 0
\(481\) 120538. 0.0237554
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.64780e6 −1.66936
\(486\) 0 0
\(487\) −626847. −0.119767 −0.0598837 0.998205i \(-0.519073\pi\)
−0.0598837 + 0.998205i \(0.519073\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3.21381e6 −0.601612 −0.300806 0.953685i \(-0.597256\pi\)
−0.300806 + 0.953685i \(0.597256\pi\)
\(492\) 0 0
\(493\) 5.66325e6 1.04942
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 453002. 0.0822638
\(498\) 0 0
\(499\) 1.64079e6 0.294987 0.147494 0.989063i \(-0.452879\pi\)
0.147494 + 0.989063i \(0.452879\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.47878e6 1.14176 0.570878 0.821035i \(-0.306603\pi\)
0.570878 + 0.821035i \(0.306603\pi\)
\(504\) 0 0
\(505\) 6.32099e6 1.10295
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.55190e6 0.949833 0.474916 0.880031i \(-0.342478\pi\)
0.474916 + 0.880031i \(0.342478\pi\)
\(510\) 0 0
\(511\) −1.46101e6 −0.247514
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.18893e6 −1.36053
\(516\) 0 0
\(517\) −491253. −0.0808311
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.57348e6 1.22237 0.611183 0.791490i \(-0.290694\pi\)
0.611183 + 0.791490i \(0.290694\pi\)
\(522\) 0 0
\(523\) −6.16189e6 −0.985053 −0.492526 0.870298i \(-0.663926\pi\)
−0.492526 + 0.870298i \(0.663926\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.38300e7 −2.16918
\(528\) 0 0
\(529\) 3.64626e6 0.566512
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 36071.2 0.00549974
\(534\) 0 0
\(535\) −1.51346e7 −2.28606
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.79220e6 0.265713
\(540\) 0 0
\(541\) −9.51400e6 −1.39756 −0.698779 0.715338i \(-0.746273\pi\)
−0.698779 + 0.715338i \(0.746273\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.20957e7 −1.74437
\(546\) 0 0
\(547\) −590098. −0.0843249 −0.0421624 0.999111i \(-0.513425\pi\)
−0.0421624 + 0.999111i \(0.513425\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.94699e6 0.273202
\(552\) 0 0
\(553\) −1.61350e6 −0.224365
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.71272e6 0.507054 0.253527 0.967328i \(-0.418409\pi\)
0.253527 + 0.967328i \(0.418409\pi\)
\(558\) 0 0
\(559\) −164923. −0.0223230
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.24074e6 −1.22867 −0.614336 0.789045i \(-0.710576\pi\)
−0.614336 + 0.789045i \(0.710576\pi\)
\(564\) 0 0
\(565\) 7.14884e6 0.942138
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.73509e6 0.872093 0.436047 0.899924i \(-0.356378\pi\)
0.436047 + 0.899924i \(0.356378\pi\)
\(570\) 0 0
\(571\) −3.66513e6 −0.470435 −0.235217 0.971943i \(-0.575580\pi\)
−0.235217 + 0.971943i \(0.575580\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.42670e6 1.18902
\(576\) 0 0
\(577\) −8.73504e6 −1.09226 −0.546129 0.837701i \(-0.683899\pi\)
−0.546129 + 0.837701i \(0.683899\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.98570e6 −0.244047
\(582\) 0 0
\(583\) 2.08190e7 2.53681
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.06478e6 0.966045 0.483022 0.875608i \(-0.339539\pi\)
0.483022 + 0.875608i \(0.339539\pi\)
\(588\) 0 0
\(589\) −4.75467e6 −0.564718
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.19273e6 0.723178 0.361589 0.932338i \(-0.382234\pi\)
0.361589 + 0.932338i \(0.382234\pi\)
\(594\) 0 0
\(595\) 6.71179e6 0.777223
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.30764e6 −0.262786 −0.131393 0.991330i \(-0.541945\pi\)
−0.131393 + 0.991330i \(0.541945\pi\)
\(600\) 0 0
\(601\) −1.09721e7 −1.23909 −0.619545 0.784961i \(-0.712683\pi\)
−0.619545 + 0.784961i \(0.712683\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.09219e7 3.43461
\(606\) 0 0
\(607\) 1.32918e7 1.46424 0.732121 0.681175i \(-0.238531\pi\)
0.732121 + 0.681175i \(0.238531\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6416.85 −0.000695374 0
\(612\) 0 0
\(613\) −1.17502e7 −1.26298 −0.631488 0.775385i \(-0.717556\pi\)
−0.631488 + 0.775385i \(0.717556\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.26344e6 0.239362 0.119681 0.992812i \(-0.461813\pi\)
0.119681 + 0.992812i \(0.461813\pi\)
\(618\) 0 0
\(619\) −1.23588e7 −1.29643 −0.648215 0.761457i \(-0.724484\pi\)
−0.648215 + 0.761457i \(0.724484\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.02621e6 0.209154
\(624\) 0 0
\(625\) −1.02295e7 −1.04750
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.16928e7 2.18619
\(630\) 0 0
\(631\) 2.74069e6 0.274023 0.137012 0.990569i \(-0.456250\pi\)
0.137012 + 0.990569i \(0.456250\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.60513e6 −0.846883
\(636\) 0 0
\(637\) 23410.0 0.00228588
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.49344e7 −1.43563 −0.717816 0.696232i \(-0.754858\pi\)
−0.717816 + 0.696232i \(0.754858\pi\)
\(642\) 0 0
\(643\) −1.12339e7 −1.07153 −0.535764 0.844368i \(-0.679976\pi\)
−0.535764 + 0.844368i \(0.679976\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.29688e6 0.497461 0.248731 0.968573i \(-0.419987\pi\)
0.248731 + 0.968573i \(0.419987\pi\)
\(648\) 0 0
\(649\) −5.56572e6 −0.518692
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.08138e7 0.992418 0.496209 0.868203i \(-0.334725\pi\)
0.496209 + 0.868203i \(0.334725\pi\)
\(654\) 0 0
\(655\) −2.82091e7 −2.56913
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −417354. −0.0374362 −0.0187181 0.999825i \(-0.505958\pi\)
−0.0187181 + 0.999825i \(0.505958\pi\)
\(660\) 0 0
\(661\) 6.80352e6 0.605661 0.302831 0.953044i \(-0.402068\pi\)
0.302831 + 0.953044i \(0.402068\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.30747e6 0.202340
\(666\) 0 0
\(667\) 1.02483e7 0.891944
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.26236e7 −2.79721
\(672\) 0 0
\(673\) −1.43365e7 −1.22013 −0.610066 0.792351i \(-0.708857\pi\)
−0.610066 + 0.792351i \(0.708857\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.09804e6 0.343641 0.171820 0.985128i \(-0.445035\pi\)
0.171820 + 0.985128i \(0.445035\pi\)
\(678\) 0 0
\(679\) −5.42824e6 −0.451840
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 8.16379e6 0.669638 0.334819 0.942282i \(-0.391325\pi\)
0.334819 + 0.942282i \(0.391325\pi\)
\(684\) 0 0
\(685\) 2.29225e7 1.86654
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 271942. 0.0218237
\(690\) 0 0
\(691\) −9.40335e6 −0.749182 −0.374591 0.927190i \(-0.622217\pi\)
−0.374591 + 0.927190i \(0.622217\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.22401e6 −0.567305
\(696\) 0 0
\(697\) 6.49157e6 0.506137
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.76733e7 −1.35838 −0.679192 0.733961i \(-0.737670\pi\)
−0.679192 + 0.733961i \(0.737670\pi\)
\(702\) 0 0
\(703\) 7.45783e6 0.569147
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.96770e6 0.298531
\(708\) 0 0
\(709\) 1.61349e7 1.20546 0.602728 0.797947i \(-0.294080\pi\)
0.602728 + 0.797947i \(0.294080\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.50270e7 −1.84368
\(714\) 0 0
\(715\) 568127. 0.0415605
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.10160e7 −1.51610 −0.758051 0.652195i \(-0.773848\pi\)
−0.758051 + 0.652195i \(0.773848\pi\)
\(720\) 0 0
\(721\) −5.14021e6 −0.368250
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.58163e6 0.677009
\(726\) 0 0
\(727\) −2.51729e7 −1.76643 −0.883217 0.468964i \(-0.844627\pi\)
−0.883217 + 0.468964i \(0.844627\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.96805e7 −2.05437
\(732\) 0 0
\(733\) −1.80996e7 −1.24425 −0.622127 0.782916i \(-0.713731\pi\)
−0.622127 + 0.782916i \(0.713731\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.13806e7 1.44994
\(738\) 0 0
\(739\) 9.69580e6 0.653089 0.326545 0.945182i \(-0.394116\pi\)
0.326545 + 0.945182i \(0.394116\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.72447e6 −0.313965 −0.156982 0.987601i \(-0.550177\pi\)
−0.156982 + 0.987601i \(0.550177\pi\)
\(744\) 0 0
\(745\) 1.02878e6 0.0679099
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9.50004e6 −0.618758
\(750\) 0 0
\(751\) −3.00055e7 −1.94134 −0.970668 0.240422i \(-0.922714\pi\)
−0.970668 + 0.240422i \(0.922714\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.37989e7 1.51946
\(756\) 0 0
\(757\) 907379. 0.0575505 0.0287752 0.999586i \(-0.490839\pi\)
0.0287752 + 0.999586i \(0.490839\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.22057e7 −0.764014 −0.382007 0.924159i \(-0.624767\pi\)
−0.382007 + 0.924159i \(0.624767\pi\)
\(762\) 0 0
\(763\) −7.59248e6 −0.472141
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −72700.6 −0.00446220
\(768\) 0 0
\(769\) −2.85670e7 −1.74200 −0.871000 0.491283i \(-0.836528\pi\)
−0.871000 + 0.491283i \(0.836528\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 905880. 0.0545283 0.0272642 0.999628i \(-0.491320\pi\)
0.0272642 + 0.999628i \(0.491320\pi\)
\(774\) 0 0
\(775\) −2.33989e7 −1.39940
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.23176e6 0.131766
\(780\) 0 0
\(781\) 6.90076e6 0.404827
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.99992e6 −0.289593
\(786\) 0 0
\(787\) 1.25311e7 0.721192 0.360596 0.932722i \(-0.382573\pi\)
0.360596 + 0.932722i \(0.382573\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.48735e6 0.255005
\(792\) 0 0
\(793\) −426136. −0.0240639
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.14513e6 0.175385 0.0876924 0.996148i \(-0.472051\pi\)
0.0876924 + 0.996148i \(0.472051\pi\)
\(798\) 0 0
\(799\) −1.15481e6 −0.0639947
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.22561e7 −1.21804
\(804\) 0 0
\(805\) 1.21458e7 0.660595
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −3.26907e6 −0.175611 −0.0878057 0.996138i \(-0.527985\pi\)
−0.0878057 + 0.996138i \(0.527985\pi\)
\(810\) 0 0
\(811\) −566320. −0.0302350 −0.0151175 0.999886i \(-0.504812\pi\)
−0.0151175 + 0.999886i \(0.504812\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4.81817e7 −2.54090
\(816\) 0 0
\(817\) −1.02040e7 −0.534828
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.98337e6 0.102694 0.0513471 0.998681i \(-0.483649\pi\)
0.0513471 + 0.998681i \(0.483649\pi\)
\(822\) 0 0
\(823\) 3.14336e7 1.61769 0.808844 0.588024i \(-0.200094\pi\)
0.808844 + 0.588024i \(0.200094\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.44099e7 0.732651 0.366325 0.930487i \(-0.380616\pi\)
0.366325 + 0.930487i \(0.380616\pi\)
\(828\) 0 0
\(829\) −3.60154e7 −1.82013 −0.910063 0.414469i \(-0.863967\pi\)
−0.910063 + 0.414469i \(0.863967\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.21300e6 0.210368
\(834\) 0 0
\(835\) −3.86170e7 −1.91673
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.05418e7 1.00747 0.503737 0.863857i \(-0.331958\pi\)
0.503737 + 0.863857i \(0.331958\pi\)
\(840\) 0 0
\(841\) −1.00944e7 −0.492142
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.89766e7 −1.39607
\(846\) 0 0
\(847\) 1.94098e7 0.929633
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.92556e7 1.85814
\(852\) 0 0
\(853\) −3.21606e7 −1.51339 −0.756695 0.653768i \(-0.773187\pi\)
−0.756695 + 0.653768i \(0.773187\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.87973e7 1.33937 0.669683 0.742647i \(-0.266430\pi\)
0.669683 + 0.742647i \(0.266430\pi\)
\(858\) 0 0
\(859\) 2.72233e7 1.25880 0.629401 0.777081i \(-0.283301\pi\)
0.629401 + 0.777081i \(0.283301\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 56328.3 0.00257454 0.00128727 0.999999i \(-0.499590\pi\)
0.00128727 + 0.999999i \(0.499590\pi\)
\(864\) 0 0
\(865\) −5.47576e7 −2.48831
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.45791e7 −1.10412
\(870\) 0 0
\(871\) 279277. 0.0124736
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −597669. −0.0263901
\(876\) 0 0
\(877\) 2.32650e7 1.02142 0.510710 0.859753i \(-0.329383\pi\)
0.510710 + 0.859753i \(0.329383\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.92252e7 −1.70265 −0.851326 0.524638i \(-0.824201\pi\)
−0.851326 + 0.524638i \(0.824201\pi\)
\(882\) 0 0
\(883\) −2.86152e7 −1.23508 −0.617540 0.786540i \(-0.711870\pi\)
−0.617540 + 0.786540i \(0.711870\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5.81794e6 0.248290 0.124145 0.992264i \(-0.460381\pi\)
0.124145 + 0.992264i \(0.460381\pi\)
\(888\) 0 0
\(889\) −5.40146e6 −0.229222
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −397017. −0.0166602
\(894\) 0 0
\(895\) −1.54134e7 −0.643191
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.54383e7 −1.04976
\(900\) 0 0
\(901\) 4.89402e7 2.00842
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.78606e7 2.75420
\(906\) 0 0
\(907\) −9.55467e6 −0.385654 −0.192827 0.981233i \(-0.561766\pi\)
−0.192827 + 0.981233i \(0.561766\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 5.36257e6 0.214081 0.107040 0.994255i \(-0.465863\pi\)
0.107040 + 0.994255i \(0.465863\pi\)
\(912\) 0 0
\(913\) −3.02490e7 −1.20097
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.77069e7 −0.695375
\(918\) 0 0
\(919\) −1.97667e6 −0.0772050 −0.0386025 0.999255i \(-0.512291\pi\)
−0.0386025 + 0.999255i \(0.512291\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 90139.2 0.00348265
\(924\) 0 0
\(925\) 3.67019e7 1.41037
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.09537e7 0.416412 0.208206 0.978085i \(-0.433238\pi\)
0.208206 + 0.978085i \(0.433238\pi\)
\(930\) 0 0
\(931\) 1.44840e6 0.0547666
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.02243e8 3.82478
\(936\) 0 0
\(937\) −6.80229e6 −0.253108 −0.126554 0.991960i \(-0.540392\pi\)
−0.126554 + 0.991960i \(0.540392\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.00214e6 0.110524 0.0552620 0.998472i \(-0.482401\pi\)
0.0552620 + 0.998472i \(0.482401\pi\)
\(942\) 0 0
\(943\) 1.17473e7 0.430187
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.85814e7 1.76033 0.880166 0.474665i \(-0.157431\pi\)
0.880166 + 0.474665i \(0.157431\pi\)
\(948\) 0 0
\(949\) −290714. −0.0104785
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −3.24058e7 −1.15582 −0.577911 0.816100i \(-0.696132\pi\)
−0.577911 + 0.816100i \(0.696132\pi\)
\(954\) 0 0
\(955\) −9.33036e6 −0.331047
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.43885e7 0.505208
\(960\) 0 0
\(961\) 3.34928e7 1.16988
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.33421e7 0.461218
\(966\) 0 0
\(967\) −2.37554e7 −0.816950 −0.408475 0.912769i \(-0.633939\pi\)
−0.408475 + 0.912769i \(0.633939\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.27649e7 −1.11522 −0.557610 0.830103i \(-0.688282\pi\)
−0.557610 + 0.830103i \(0.688282\pi\)
\(972\) 0 0
\(973\) −4.53453e6 −0.153550
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.09726e7 1.70844 0.854222 0.519908i \(-0.174034\pi\)
0.854222 + 0.519908i \(0.174034\pi\)
\(978\) 0 0
\(979\) 3.08662e7 1.02926
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.63735e7 1.20061 0.600304 0.799772i \(-0.295046\pi\)
0.600304 + 0.799772i \(0.295046\pi\)
\(984\) 0 0
\(985\) −5.58217e7 −1.83321
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.37104e7 −1.74609
\(990\) 0 0
\(991\) −7.46245e6 −0.241378 −0.120689 0.992690i \(-0.538510\pi\)
−0.120689 + 0.992690i \(0.538510\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 5.58699e7 1.78904
\(996\) 0 0
\(997\) −373648. −0.0119049 −0.00595243 0.999982i \(-0.501895\pi\)
−0.00595243 + 0.999982i \(0.501895\pi\)
\(998\) 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.br.1.2 2
3.2 odd 2 1008.6.a.bj.1.1 2
4.3 odd 2 504.6.a.q.1.2 yes 2
12.11 even 2 504.6.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.n.1.1 2 12.11 even 2
504.6.a.q.1.2 yes 2 4.3 odd 2
1008.6.a.bj.1.1 2 3.2 odd 2
1008.6.a.br.1.2 2 1.1 even 1 trivial