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Properties

Label 600.6.a.g.1.1
Level $600$
Weight $6$
Character 600.1
Self dual yes
Analytic conductor $96.230$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [600,6,Mod(1,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, 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("600.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 600.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: \(96.2302918878\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.00000 q^{3} +80.0000 q^{7} +81.0000 q^{9} +684.000 q^{11} +978.000 q^{13} +862.000 q^{17} +916.000 q^{19} +720.000 q^{21} +1552.00 q^{23} +729.000 q^{27} -7314.00 q^{29} -9312.00 q^{31} +6156.00 q^{33} +8826.00 q^{37} +8802.00 q^{39} -3286.00 q^{41} -7556.00 q^{43} +5960.00 q^{47} -10407.0 q^{49} +7758.00 q^{51} +8698.00 q^{53} +8244.00 q^{57} -42036.0 q^{59} +37518.0 q^{61} +6480.00 q^{63} -29324.0 q^{67} +13968.0 q^{69} +84408.0 q^{71} +46550.0 q^{73} +54720.0 q^{77} +26752.0 q^{79} +6561.00 q^{81} +7956.00 q^{83} -65826.0 q^{87} +59674.0 q^{89} +78240.0 q^{91} -83808.0 q^{93} -136898. q^{97} +55404.0 q^{99} +O(q^{100})\)

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
\(3\) 9.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 80.0000 0.617085 0.308542 − 0.951211i \(-0.400159\pi\)
0.308542 + 0.951211i \(0.400159\pi\)
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) 684.000 1.70441 0.852206 − 0.523207i \(-0.175265\pi\)
0.852206 + 0.523207i \(0.175265\pi\)
\(12\) 0 0
\(13\) 978.000 1.60502 0.802510 − 0.596639i \(-0.203497\pi\)
0.802510 + 0.596639i \(0.203497\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 862.000 0.723411 0.361705 − 0.932292i \(-0.382195\pi\)
0.361705 + 0.932292i \(0.382195\pi\)
\(18\) 0 0
\(19\) 916.000 0.582119 0.291059 − 0.956705i \(-0.405992\pi\)
0.291059 + 0.956705i \(0.405992\pi\)
\(20\) 0 0
\(21\) 720.000 0.356274
\(22\) 0 0
\(23\) 1552.00 0.611747 0.305874 − 0.952072i \(-0.401051\pi\)
0.305874 + 0.952072i \(0.401051\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −7314.00 −1.61495 −0.807477 − 0.589900i \(-0.799167\pi\)
−0.807477 + 0.589900i \(0.799167\pi\)
\(30\) 0 0
\(31\) −9312.00 −1.74036 −0.870179 − 0.492735i \(-0.835997\pi\)
−0.870179 + 0.492735i \(0.835997\pi\)
\(32\) 0 0
\(33\) 6156.00 0.984042
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8826.00 1.05989 0.529944 − 0.848033i \(-0.322213\pi\)
0.529944 + 0.848033i \(0.322213\pi\)
\(38\) 0 0
\(39\) 8802.00 0.926659
\(40\) 0 0
\(41\) −3286.00 −0.305287 −0.152643 − 0.988281i \(-0.548779\pi\)
−0.152643 + 0.988281i \(0.548779\pi\)
\(42\) 0 0
\(43\) −7556.00 −0.623190 −0.311595 − 0.950215i \(-0.600863\pi\)
−0.311595 + 0.950215i \(0.600863\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5960.00 0.393552 0.196776 − 0.980449i \(-0.436953\pi\)
0.196776 + 0.980449i \(0.436953\pi\)
\(48\) 0 0
\(49\) −10407.0 −0.619206
\(50\) 0 0
\(51\) 7758.00 0.417661
\(52\) 0 0
\(53\) 8698.00 0.425334 0.212667 − 0.977125i \(-0.431785\pi\)
0.212667 + 0.977125i \(0.431785\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8244.00 0.336086
\(58\) 0 0
\(59\) −42036.0 −1.57214 −0.786070 − 0.618137i \(-0.787888\pi\)
−0.786070 + 0.618137i \(0.787888\pi\)
\(60\) 0 0
\(61\) 37518.0 1.29097 0.645483 − 0.763774i \(-0.276656\pi\)
0.645483 + 0.763774i \(0.276656\pi\)
\(62\) 0 0
\(63\) 6480.00 0.205695
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −29324.0 −0.798061 −0.399031 − 0.916938i \(-0.630653\pi\)
−0.399031 + 0.916938i \(0.630653\pi\)
\(68\) 0 0
\(69\) 13968.0 0.353193
\(70\) 0 0
\(71\) 84408.0 1.98718 0.993591 − 0.113033i \(-0.0360566\pi\)
0.993591 + 0.113033i \(0.0360566\pi\)
\(72\) 0 0
\(73\) 46550.0 1.02238 0.511190 − 0.859468i \(-0.329205\pi\)
0.511190 + 0.859468i \(0.329205\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 54720.0 1.05177
\(78\) 0 0
\(79\) 26752.0 0.482268 0.241134 − 0.970492i \(-0.422481\pi\)
0.241134 + 0.970492i \(0.422481\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) 7956.00 0.126765 0.0633825 − 0.997989i \(-0.479811\pi\)
0.0633825 + 0.997989i \(0.479811\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −65826.0 −0.932394
\(88\) 0 0
\(89\) 59674.0 0.798565 0.399282 − 0.916828i \(-0.369259\pi\)
0.399282 + 0.916828i \(0.369259\pi\)
\(90\) 0 0
\(91\) 78240.0 0.990434
\(92\) 0 0
\(93\) −83808.0 −1.00480
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −136898. −1.47730 −0.738648 − 0.674091i \(-0.764536\pi\)
−0.738648 + 0.674091i \(0.764536\pi\)
\(98\) 0 0
\(99\) 55404.0 0.568137
\(100\) 0 0
\(101\) −202858. −1.97874 −0.989370 − 0.145421i \(-0.953546\pi\)
−0.989370 + 0.145421i \(0.953546\pi\)
\(102\) 0 0
\(103\) 8576.00 0.0796511 0.0398255 − 0.999207i \(-0.487320\pi\)
0.0398255 + 0.999207i \(0.487320\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 19948.0 0.168438 0.0842190 − 0.996447i \(-0.473160\pi\)
0.0842190 + 0.996447i \(0.473160\pi\)
\(108\) 0 0
\(109\) 37598.0 0.303109 0.151554 − 0.988449i \(-0.451572\pi\)
0.151554 + 0.988449i \(0.451572\pi\)
\(110\) 0 0
\(111\) 79434.0 0.611926
\(112\) 0 0
\(113\) 191838. 1.41331 0.706657 − 0.707556i \(-0.250203\pi\)
0.706657 + 0.707556i \(0.250203\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 79218.0 0.535007
\(118\) 0 0
\(119\) 68960.0 0.446406
\(120\) 0 0
\(121\) 306805. 1.90502
\(122\) 0 0
\(123\) −29574.0 −0.176257
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −98888.0 −0.544044 −0.272022 − 0.962291i \(-0.587692\pi\)
−0.272022 + 0.962291i \(0.587692\pi\)
\(128\) 0 0
\(129\) −68004.0 −0.359799
\(130\) 0 0
\(131\) 29636.0 0.150883 0.0754417 − 0.997150i \(-0.475963\pi\)
0.0754417 + 0.997150i \(0.475963\pi\)
\(132\) 0 0
\(133\) 73280.0 0.359217
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4614.00 0.0210028 0.0105014 − 0.999945i \(-0.496657\pi\)
0.0105014 + 0.999945i \(0.496657\pi\)
\(138\) 0 0
\(139\) −254292. −1.11634 −0.558169 − 0.829727i \(-0.688496\pi\)
−0.558169 + 0.829727i \(0.688496\pi\)
\(140\) 0 0
\(141\) 53640.0 0.227217
\(142\) 0 0
\(143\) 668952. 2.73561
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −93663.0 −0.357499
\(148\) 0 0
\(149\) −83226.0 −0.307110 −0.153555 − 0.988140i \(-0.549072\pi\)
−0.153555 + 0.988140i \(0.549072\pi\)
\(150\) 0 0
\(151\) −212616. −0.758846 −0.379423 − 0.925223i \(-0.623877\pi\)
−0.379423 + 0.925223i \(0.623877\pi\)
\(152\) 0 0
\(153\) 69822.0 0.241137
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −112702. −0.364907 −0.182454 − 0.983214i \(-0.558404\pi\)
−0.182454 + 0.983214i \(0.558404\pi\)
\(158\) 0 0
\(159\) 78282.0 0.245566
\(160\) 0 0
\(161\) 124160. 0.377500
\(162\) 0 0
\(163\) 411172. 1.21214 0.606072 − 0.795409i \(-0.292744\pi\)
0.606072 + 0.795409i \(0.292744\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −258896. −0.718347 −0.359173 − 0.933271i \(-0.616941\pi\)
−0.359173 + 0.933271i \(0.616941\pi\)
\(168\) 0 0
\(169\) 585191. 1.57609
\(170\) 0 0
\(171\) 74196.0 0.194040
\(172\) 0 0
\(173\) 397026. 1.00856 0.504282 − 0.863539i \(-0.331757\pi\)
0.504282 + 0.863539i \(0.331757\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −378324. −0.907676
\(178\) 0 0
\(179\) −473468. −1.10448 −0.552240 − 0.833685i \(-0.686227\pi\)
−0.552240 + 0.833685i \(0.686227\pi\)
\(180\) 0 0
\(181\) −79834.0 −0.181130 −0.0905652 − 0.995891i \(-0.528867\pi\)
−0.0905652 + 0.995891i \(0.528867\pi\)
\(182\) 0 0
\(183\) 337662. 0.745340
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 589608. 1.23299
\(188\) 0 0
\(189\) 58320.0 0.118758
\(190\) 0 0
\(191\) 397360. 0.788135 0.394068 − 0.919081i \(-0.371068\pi\)
0.394068 + 0.919081i \(0.371068\pi\)
\(192\) 0 0
\(193\) −777858. −1.50317 −0.751583 − 0.659638i \(-0.770709\pi\)
−0.751583 + 0.659638i \(0.770709\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −254678. −0.467548 −0.233774 − 0.972291i \(-0.575108\pi\)
−0.233774 + 0.972291i \(0.575108\pi\)
\(198\) 0 0
\(199\) −540264. −0.967104 −0.483552 − 0.875316i \(-0.660654\pi\)
−0.483552 + 0.875316i \(0.660654\pi\)
\(200\) 0 0
\(201\) −263916. −0.460761
\(202\) 0 0
\(203\) −585120. −0.996563
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 125712. 0.203916
\(208\) 0 0
\(209\) 626544. 0.992169
\(210\) 0 0
\(211\) 1.05690e6 1.63428 0.817142 − 0.576436i \(-0.195557\pi\)
0.817142 + 0.576436i \(0.195557\pi\)
\(212\) 0 0
\(213\) 759672. 1.14730
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −744960. −1.07395
\(218\) 0 0
\(219\) 418950. 0.590272
\(220\) 0 0
\(221\) 843036. 1.16109
\(222\) 0 0
\(223\) 1.09063e6 1.46864 0.734321 − 0.678802i \(-0.237501\pi\)
0.734321 + 0.678802i \(0.237501\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2772.00 0.00357050 0.00178525 − 0.999998i \(-0.499432\pi\)
0.00178525 + 0.999998i \(0.499432\pi\)
\(228\) 0 0
\(229\) −304458. −0.383653 −0.191827 − 0.981429i \(-0.561441\pi\)
−0.191827 + 0.981429i \(0.561441\pi\)
\(230\) 0 0
\(231\) 492480. 0.607238
\(232\) 0 0
\(233\) 329990. 0.398209 0.199104 − 0.979978i \(-0.436197\pi\)
0.199104 + 0.979978i \(0.436197\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 240768. 0.278438
\(238\) 0 0
\(239\) 721584. 0.817132 0.408566 − 0.912729i \(-0.366029\pi\)
0.408566 + 0.912729i \(0.366029\pi\)
\(240\) 0 0
\(241\) 271538. 0.301154 0.150577 − 0.988598i \(-0.451887\pi\)
0.150577 + 0.988598i \(0.451887\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 895848. 0.934312
\(248\) 0 0
\(249\) 71604.0 0.0731878
\(250\) 0 0
\(251\) 1.34534e6 1.34787 0.673935 − 0.738791i \(-0.264603\pi\)
0.673935 + 0.738791i \(0.264603\pi\)
\(252\) 0 0
\(253\) 1.06157e6 1.04267
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.62290e6 −1.53270 −0.766352 − 0.642421i \(-0.777930\pi\)
−0.766352 + 0.642421i \(0.777930\pi\)
\(258\) 0 0
\(259\) 706080. 0.654040
\(260\) 0 0
\(261\) −592434. −0.538318
\(262\) 0 0
\(263\) −472128. −0.420892 −0.210446 − 0.977606i \(-0.567492\pi\)
−0.210446 + 0.977606i \(0.567492\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 537066. 0.461052
\(268\) 0 0
\(269\) 2430.00 0.00204751 0.00102375 − 0.999999i \(-0.499674\pi\)
0.00102375 + 0.999999i \(0.499674\pi\)
\(270\) 0 0
\(271\) 1.65157e6 1.36607 0.683035 − 0.730385i \(-0.260659\pi\)
0.683035 + 0.730385i \(0.260659\pi\)
\(272\) 0 0
\(273\) 704160. 0.571827
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2.21129e6 −1.73159 −0.865796 − 0.500397i \(-0.833187\pi\)
−0.865796 + 0.500397i \(0.833187\pi\)
\(278\) 0 0
\(279\) −754272. −0.580120
\(280\) 0 0
\(281\) −423014. −0.319587 −0.159793 − 0.987150i \(-0.551083\pi\)
−0.159793 + 0.987150i \(0.551083\pi\)
\(282\) 0 0
\(283\) 487052. 0.361501 0.180750 − 0.983529i \(-0.442147\pi\)
0.180750 + 0.983529i \(0.442147\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −262880. −0.188388
\(288\) 0 0
\(289\) −676813. −0.476677
\(290\) 0 0
\(291\) −1.23208e6 −0.852918
\(292\) 0 0
\(293\) 1.02692e6 0.698825 0.349412 − 0.936969i \(-0.386381\pi\)
0.349412 + 0.936969i \(0.386381\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 498636. 0.328014
\(298\) 0 0
\(299\) 1.51786e6 0.981867
\(300\) 0 0
\(301\) −604480. −0.384561
\(302\) 0 0
\(303\) −1.82572e6 −1.14243
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.07133e6 0.648751 0.324376 − 0.945928i \(-0.394846\pi\)
0.324376 + 0.945928i \(0.394846\pi\)
\(308\) 0 0
\(309\) 77184.0 0.0459866
\(310\) 0 0
\(311\) 1.87422e6 1.09880 0.549400 − 0.835559i \(-0.314856\pi\)
0.549400 + 0.835559i \(0.314856\pi\)
\(312\) 0 0
\(313\) −2.92883e6 −1.68979 −0.844895 − 0.534932i \(-0.820337\pi\)
−0.844895 + 0.534932i \(0.820337\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.94831e6 1.64788 0.823938 − 0.566680i \(-0.191773\pi\)
0.823938 + 0.566680i \(0.191773\pi\)
\(318\) 0 0
\(319\) −5.00278e6 −2.75254
\(320\) 0 0
\(321\) 179532. 0.0972477
\(322\) 0 0
\(323\) 789592. 0.421111
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 338382. 0.175000
\(328\) 0 0
\(329\) 476800. 0.242855
\(330\) 0 0
\(331\) −856100. −0.429491 −0.214746 − 0.976670i \(-0.568892\pi\)
−0.214746 + 0.976670i \(0.568892\pi\)
\(332\) 0 0
\(333\) 714906. 0.353296
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.11272e6 1.49302 0.746509 − 0.665375i \(-0.231728\pi\)
0.746509 + 0.665375i \(0.231728\pi\)
\(338\) 0 0
\(339\) 1.72654e6 0.815977
\(340\) 0 0
\(341\) −6.36941e6 −2.96629
\(342\) 0 0
\(343\) −2.17712e6 −0.999188
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.09651e6 0.934701 0.467351 − 0.884072i \(-0.345209\pi\)
0.467351 + 0.884072i \(0.345209\pi\)
\(348\) 0 0
\(349\) −4.44677e6 −1.95425 −0.977127 − 0.212656i \(-0.931789\pi\)
−0.977127 + 0.212656i \(0.931789\pi\)
\(350\) 0 0
\(351\) 712962. 0.308886
\(352\) 0 0
\(353\) −1.80434e6 −0.770692 −0.385346 − 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 620640. 0.257733
\(358\) 0 0
\(359\) 2.84270e6 1.16411 0.582055 − 0.813149i \(-0.302249\pi\)
0.582055 + 0.813149i \(0.302249\pi\)
\(360\) 0 0
\(361\) −1.63704e6 −0.661138
\(362\) 0 0
\(363\) 2.76124e6 1.09986
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.65561e6 −0.641641 −0.320821 − 0.947140i \(-0.603959\pi\)
−0.320821 + 0.947140i \(0.603959\pi\)
\(368\) 0 0
\(369\) −266166. −0.101762
\(370\) 0 0
\(371\) 695840. 0.262467
\(372\) 0 0
\(373\) 199690. 0.0743163 0.0371582 − 0.999309i \(-0.488169\pi\)
0.0371582 + 0.999309i \(0.488169\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.15309e6 −2.59203
\(378\) 0 0
\(379\) −1.45610e6 −0.520707 −0.260353 − 0.965513i \(-0.583839\pi\)
−0.260353 + 0.965513i \(0.583839\pi\)
\(380\) 0 0
\(381\) −889992. −0.314104
\(382\) 0 0
\(383\) 4.62548e6 1.61124 0.805619 − 0.592434i \(-0.201833\pi\)
0.805619 + 0.592434i \(0.201833\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −612036. −0.207730
\(388\) 0 0
\(389\) 3.51068e6 1.17630 0.588149 − 0.808753i \(-0.299857\pi\)
0.588149 + 0.808753i \(0.299857\pi\)
\(390\) 0 0
\(391\) 1.33782e6 0.442545
\(392\) 0 0
\(393\) 266724. 0.0871125
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.84773e6 −1.54370 −0.771848 − 0.635807i \(-0.780667\pi\)
−0.771848 + 0.635807i \(0.780667\pi\)
\(398\) 0 0
\(399\) 659520. 0.207394
\(400\) 0 0
\(401\) −4.21515e6 −1.30904 −0.654519 − 0.756046i \(-0.727129\pi\)
−0.654519 + 0.756046i \(0.727129\pi\)
\(402\) 0 0
\(403\) −9.10714e6 −2.79331
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.03698e6 1.80648
\(408\) 0 0
\(409\) 4.49535e6 1.32879 0.664394 − 0.747383i \(-0.268690\pi\)
0.664394 + 0.747383i \(0.268690\pi\)
\(410\) 0 0
\(411\) 41526.0 0.0121259
\(412\) 0 0
\(413\) −3.36288e6 −0.970144
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.28863e6 −0.644518
\(418\) 0 0
\(419\) −4.44571e6 −1.23710 −0.618552 − 0.785744i \(-0.712280\pi\)
−0.618552 + 0.785744i \(0.712280\pi\)
\(420\) 0 0
\(421\) −4.87185e6 −1.33964 −0.669821 − 0.742523i \(-0.733629\pi\)
−0.669821 + 0.742523i \(0.733629\pi\)
\(422\) 0 0
\(423\) 482760. 0.131184
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.00144e6 0.796636
\(428\) 0 0
\(429\) 6.02057e6 1.57941
\(430\) 0 0
\(431\) 549152. 0.142397 0.0711983 − 0.997462i \(-0.477318\pi\)
0.0711983 + 0.997462i \(0.477318\pi\)
\(432\) 0 0
\(433\) −2.37675e6 −0.609206 −0.304603 − 0.952479i \(-0.598524\pi\)
−0.304603 + 0.952479i \(0.598524\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.42163e6 0.356110
\(438\) 0 0
\(439\) 1.31188e6 0.324887 0.162444 − 0.986718i \(-0.448062\pi\)
0.162444 + 0.986718i \(0.448062\pi\)
\(440\) 0 0
\(441\) −842967. −0.206402
\(442\) 0 0
\(443\) −2.92914e6 −0.709138 −0.354569 − 0.935030i \(-0.615372\pi\)
−0.354569 + 0.935030i \(0.615372\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −749034. −0.177310
\(448\) 0 0
\(449\) −4.30777e6 −1.00841 −0.504205 − 0.863584i \(-0.668214\pi\)
−0.504205 + 0.863584i \(0.668214\pi\)
\(450\) 0 0
\(451\) −2.24762e6 −0.520334
\(452\) 0 0
\(453\) −1.91354e6 −0.438120
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −4.48196e6 −1.00387 −0.501935 − 0.864905i \(-0.667378\pi\)
−0.501935 + 0.864905i \(0.667378\pi\)
\(458\) 0 0
\(459\) 628398. 0.139220
\(460\) 0 0
\(461\) −95906.0 −0.0210181 −0.0105091 − 0.999945i \(-0.503345\pi\)
−0.0105091 + 0.999945i \(0.503345\pi\)
\(462\) 0 0
\(463\) −7.24487e6 −1.57065 −0.785323 − 0.619086i \(-0.787503\pi\)
−0.785323 + 0.619086i \(0.787503\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.80528e6 0.383048 0.191524 − 0.981488i \(-0.438657\pi\)
0.191524 + 0.981488i \(0.438657\pi\)
\(468\) 0 0
\(469\) −2.34592e6 −0.492471
\(470\) 0 0
\(471\) −1.01432e6 −0.210679
\(472\) 0 0
\(473\) −5.16830e6 −1.06217
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 704538. 0.141778
\(478\) 0 0
\(479\) −1.02682e6 −0.204481 −0.102241 − 0.994760i \(-0.532601\pi\)
−0.102241 + 0.994760i \(0.532601\pi\)
\(480\) 0 0
\(481\) 8.63183e6 1.70114
\(482\) 0 0
\(483\) 1.11744e6 0.217950
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.43013e6 1.22856 0.614281 − 0.789087i \(-0.289446\pi\)
0.614281 + 0.789087i \(0.289446\pi\)
\(488\) 0 0
\(489\) 3.70055e6 0.699832
\(490\) 0 0
\(491\) −6.89637e6 −1.29097 −0.645486 − 0.763772i \(-0.723345\pi\)
−0.645486 + 0.763772i \(0.723345\pi\)
\(492\) 0 0
\(493\) −6.30467e6 −1.16827
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.75264e6 1.22626
\(498\) 0 0
\(499\) −8.27403e6 −1.48753 −0.743765 − 0.668441i \(-0.766962\pi\)
−0.743765 + 0.668441i \(0.766962\pi\)
\(500\) 0 0
\(501\) −2.33006e6 −0.414738
\(502\) 0 0
\(503\) 5.83070e6 1.02755 0.513773 − 0.857926i \(-0.328247\pi\)
0.513773 + 0.857926i \(0.328247\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 5.26672e6 0.909956
\(508\) 0 0
\(509\) 3.66421e6 0.626881 0.313441 − 0.949608i \(-0.398518\pi\)
0.313441 + 0.949608i \(0.398518\pi\)
\(510\) 0 0
\(511\) 3.72400e6 0.630895
\(512\) 0 0
\(513\) 667764. 0.112029
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 4.07664e6 0.670774
\(518\) 0 0
\(519\) 3.57323e6 0.582295
\(520\) 0 0
\(521\) −5.79381e6 −0.935126 −0.467563 − 0.883960i \(-0.654868\pi\)
−0.467563 + 0.883960i \(0.654868\pi\)
\(522\) 0 0
\(523\) −6.06676e6 −0.969845 −0.484922 − 0.874557i \(-0.661152\pi\)
−0.484922 + 0.874557i \(0.661152\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.02694e6 −1.25899
\(528\) 0 0
\(529\) −4.02764e6 −0.625765
\(530\) 0 0
\(531\) −3.40492e6 −0.524047
\(532\) 0 0
\(533\) −3.21371e6 −0.489991
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.26121e6 −0.637672
\(538\) 0 0
\(539\) −7.11839e6 −1.05538
\(540\) 0 0
\(541\) −2.19330e6 −0.322184 −0.161092 − 0.986939i \(-0.551502\pi\)
−0.161092 + 0.986939i \(0.551502\pi\)
\(542\) 0 0
\(543\) −718506. −0.104576
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.03263e7 −1.47563 −0.737814 − 0.675004i \(-0.764142\pi\)
−0.737814 + 0.675004i \(0.764142\pi\)
\(548\) 0 0
\(549\) 3.03896e6 0.430322
\(550\) 0 0
\(551\) −6.69962e6 −0.940094
\(552\) 0 0
\(553\) 2.14016e6 0.297600
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.01187e6 0.547910 0.273955 − 0.961742i \(-0.411668\pi\)
0.273955 + 0.961742i \(0.411668\pi\)
\(558\) 0 0
\(559\) −7.38977e6 −1.00023
\(560\) 0 0
\(561\) 5.30647e6 0.711867
\(562\) 0 0
\(563\) 9.59663e6 1.27599 0.637996 − 0.770040i \(-0.279764\pi\)
0.637996 + 0.770040i \(0.279764\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 524880. 0.0685650
\(568\) 0 0
\(569\) 6.76649e6 0.876159 0.438079 − 0.898936i \(-0.355659\pi\)
0.438079 + 0.898936i \(0.355659\pi\)
\(570\) 0 0
\(571\) 1.42954e7 1.83488 0.917439 − 0.397877i \(-0.130253\pi\)
0.917439 + 0.397877i \(0.130253\pi\)
\(572\) 0 0
\(573\) 3.57624e6 0.455030
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.38116e7 1.72705 0.863523 − 0.504309i \(-0.168253\pi\)
0.863523 + 0.504309i \(0.168253\pi\)
\(578\) 0 0
\(579\) −7.00072e6 −0.867854
\(580\) 0 0
\(581\) 636480. 0.0782248
\(582\) 0 0
\(583\) 5.94943e6 0.724943
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.82424e6 0.338303 0.169151 − 0.985590i \(-0.445897\pi\)
0.169151 + 0.985590i \(0.445897\pi\)
\(588\) 0 0
\(589\) −8.52979e6 −1.01310
\(590\) 0 0
\(591\) −2.29210e6 −0.269939
\(592\) 0 0
\(593\) 6.72749e6 0.785626 0.392813 − 0.919618i \(-0.371502\pi\)
0.392813 + 0.919618i \(0.371502\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.86238e6 −0.558358
\(598\) 0 0
\(599\) 1.02563e7 1.16795 0.583977 − 0.811770i \(-0.301496\pi\)
0.583977 + 0.811770i \(0.301496\pi\)
\(600\) 0 0
\(601\) −6.93684e6 −0.783385 −0.391693 − 0.920096i \(-0.628110\pi\)
−0.391693 + 0.920096i \(0.628110\pi\)
\(602\) 0 0
\(603\) −2.37524e6 −0.266020
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.04044e6 0.665422 0.332711 − 0.943029i \(-0.392037\pi\)
0.332711 + 0.943029i \(0.392037\pi\)
\(608\) 0 0
\(609\) −5.26608e6 −0.575366
\(610\) 0 0
\(611\) 5.82888e6 0.631658
\(612\) 0 0
\(613\) −5.65002e6 −0.607294 −0.303647 − 0.952785i \(-0.598204\pi\)
−0.303647 + 0.952785i \(0.598204\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.77818e6 0.822555 0.411278 − 0.911510i \(-0.365083\pi\)
0.411278 + 0.911510i \(0.365083\pi\)
\(618\) 0 0
\(619\) 5.86584e6 0.615323 0.307662 − 0.951496i \(-0.400454\pi\)
0.307662 + 0.951496i \(0.400454\pi\)
\(620\) 0 0
\(621\) 1.13141e6 0.117731
\(622\) 0 0
\(623\) 4.77392e6 0.492782
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 5.63890e6 0.572829
\(628\) 0 0
\(629\) 7.60801e6 0.766734
\(630\) 0 0
\(631\) −4.14394e6 −0.414324 −0.207162 − 0.978307i \(-0.566423\pi\)
−0.207162 + 0.978307i \(0.566423\pi\)
\(632\) 0 0
\(633\) 9.51210e6 0.943555
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.01780e7 −0.993839
\(638\) 0 0
\(639\) 6.83705e6 0.662394
\(640\) 0 0
\(641\) −8.41769e6 −0.809185 −0.404593 − 0.914497i \(-0.632587\pi\)
−0.404593 + 0.914497i \(0.632587\pi\)
\(642\) 0 0
\(643\) −1.79931e7 −1.71625 −0.858123 − 0.513444i \(-0.828370\pi\)
−0.858123 + 0.513444i \(0.828370\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.92533e6 0.744315 0.372157 − 0.928170i \(-0.378618\pi\)
0.372157 + 0.928170i \(0.378618\pi\)
\(648\) 0 0
\(649\) −2.87526e7 −2.67957
\(650\) 0 0
\(651\) −6.70464e6 −0.620045
\(652\) 0 0
\(653\) 1.53749e7 1.41101 0.705506 − 0.708704i \(-0.250720\pi\)
0.705506 + 0.708704i \(0.250720\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.77055e6 0.340793
\(658\) 0 0
\(659\) 1.46609e7 1.31507 0.657534 − 0.753425i \(-0.271600\pi\)
0.657534 + 0.753425i \(0.271600\pi\)
\(660\) 0 0
\(661\) −3.32825e6 −0.296287 −0.148143 − 0.988966i \(-0.547330\pi\)
−0.148143 + 0.988966i \(0.547330\pi\)
\(662\) 0 0
\(663\) 7.58732e6 0.670355
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.13513e7 −0.987943
\(668\) 0 0
\(669\) 9.81569e6 0.847921
\(670\) 0 0
\(671\) 2.56623e7 2.20034
\(672\) 0 0
\(673\) −2.08463e7 −1.77415 −0.887077 − 0.461621i \(-0.847268\pi\)
−0.887077 + 0.461621i \(0.847268\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.60880e7 −1.34906 −0.674530 − 0.738248i \(-0.735653\pi\)
−0.674530 + 0.738248i \(0.735653\pi\)
\(678\) 0 0
\(679\) −1.09518e7 −0.911618
\(680\) 0 0
\(681\) 24948.0 0.00206143
\(682\) 0 0
\(683\) −3.93124e6 −0.322461 −0.161231 − 0.986917i \(-0.551546\pi\)
−0.161231 + 0.986917i \(0.551546\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.74012e6 −0.221502
\(688\) 0 0
\(689\) 8.50664e6 0.682669
\(690\) 0 0
\(691\) 9.05300e6 0.721269 0.360634 − 0.932707i \(-0.382560\pi\)
0.360634 + 0.932707i \(0.382560\pi\)
\(692\) 0 0
\(693\) 4.43232e6 0.350589
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.83253e6 −0.220848
\(698\) 0 0
\(699\) 2.96991e6 0.229906
\(700\) 0 0
\(701\) 1.82887e7 1.40568 0.702842 − 0.711346i \(-0.251914\pi\)
0.702842 + 0.711346i \(0.251914\pi\)
\(702\) 0 0
\(703\) 8.08462e6 0.616980
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.62286e7 −1.22105
\(708\) 0 0
\(709\) 1.05416e7 0.787572 0.393786 − 0.919202i \(-0.371165\pi\)
0.393786 + 0.919202i \(0.371165\pi\)
\(710\) 0 0
\(711\) 2.16691e6 0.160756
\(712\) 0 0
\(713\) −1.44522e7 −1.06466
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6.49426e6 0.471771
\(718\) 0 0
\(719\) 1.34280e7 0.968703 0.484352 − 0.874873i \(-0.339056\pi\)
0.484352 + 0.874873i \(0.339056\pi\)
\(720\) 0 0
\(721\) 686080. 0.0491515
\(722\) 0 0
\(723\) 2.44384e6 0.173871
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −9.97059e6 −0.699657 −0.349828 − 0.936814i \(-0.613760\pi\)
−0.349828 + 0.936814i \(0.613760\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −6.51327e6 −0.450823
\(732\) 0 0
\(733\) 2.70572e7 1.86004 0.930020 − 0.367509i \(-0.119789\pi\)
0.930020 + 0.367509i \(0.119789\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.00576e7 −1.36022
\(738\) 0 0
\(739\) 4.87076e6 0.328084 0.164042 − 0.986453i \(-0.447547\pi\)
0.164042 + 0.986453i \(0.447547\pi\)
\(740\) 0 0
\(741\) 8.06263e6 0.539425
\(742\) 0 0
\(743\) −144288. −0.00958867 −0.00479433 − 0.999989i \(-0.501526\pi\)
−0.00479433 + 0.999989i \(0.501526\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 644436. 0.0422550
\(748\) 0 0
\(749\) 1.59584e6 0.103941
\(750\) 0 0
\(751\) −8.74882e6 −0.566043 −0.283022 − 0.959114i \(-0.591337\pi\)
−0.283022 + 0.959114i \(0.591337\pi\)
\(752\) 0 0
\(753\) 1.21081e7 0.778193
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 5.58062e6 0.353951 0.176975 − 0.984215i \(-0.443369\pi\)
0.176975 + 0.984215i \(0.443369\pi\)
\(758\) 0 0
\(759\) 9.55411e6 0.601985
\(760\) 0 0
\(761\) 273178. 0.0170995 0.00854976 − 0.999963i \(-0.497278\pi\)
0.00854976 + 0.999963i \(0.497278\pi\)
\(762\) 0 0
\(763\) 3.00784e6 0.187044
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.11112e7 −2.52332
\(768\) 0 0
\(769\) −2.16358e7 −1.31934 −0.659672 − 0.751554i \(-0.729305\pi\)
−0.659672 + 0.751554i \(0.729305\pi\)
\(770\) 0 0
\(771\) −1.46061e7 −0.884907
\(772\) 0 0
\(773\) −5.39836e6 −0.324947 −0.162474 − 0.986713i \(-0.551947\pi\)
−0.162474 + 0.986713i \(0.551947\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.35472e6 0.377610
\(778\) 0 0
\(779\) −3.00998e6 −0.177713
\(780\) 0 0
\(781\) 5.77351e7 3.38698
\(782\) 0 0
\(783\) −5.33191e6 −0.310798
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.56497e7 −0.900677 −0.450338 − 0.892858i \(-0.648697\pi\)
−0.450338 + 0.892858i \(0.648697\pi\)
\(788\) 0 0
\(789\) −4.24915e6 −0.243002
\(790\) 0 0
\(791\) 1.53470e7 0.872134
\(792\) 0 0
\(793\) 3.66926e7 2.07203
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.43553e7 1.35815 0.679074 − 0.734069i \(-0.262381\pi\)
0.679074 + 0.734069i \(0.262381\pi\)
\(798\) 0 0
\(799\) 5.13752e6 0.284699
\(800\) 0 0
\(801\) 4.83359e6 0.266188
\(802\) 0 0
\(803\) 3.18402e7 1.74256
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 21870.0 0.00118213
\(808\) 0 0
\(809\) −2.60329e7 −1.39846 −0.699231 − 0.714896i \(-0.746474\pi\)
−0.699231 + 0.714896i \(0.746474\pi\)
\(810\) 0 0
\(811\) −2.63808e7 −1.40843 −0.704217 − 0.709985i \(-0.748702\pi\)
−0.704217 + 0.709985i \(0.748702\pi\)
\(812\) 0 0
\(813\) 1.48641e7 0.788701
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −6.92130e6 −0.362771
\(818\) 0 0
\(819\) 6.33744e6 0.330145
\(820\) 0 0
\(821\) −7.46105e6 −0.386315 −0.193158 − 0.981168i \(-0.561873\pi\)
−0.193158 + 0.981168i \(0.561873\pi\)
\(822\) 0 0
\(823\) 3.34734e6 0.172266 0.0861332 − 0.996284i \(-0.472549\pi\)
0.0861332 + 0.996284i \(0.472549\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.70089e7 1.88167 0.940833 − 0.338872i \(-0.110045\pi\)
0.940833 + 0.338872i \(0.110045\pi\)
\(828\) 0 0
\(829\) 2.35921e7 1.19229 0.596143 − 0.802878i \(-0.296699\pi\)
0.596143 + 0.802878i \(0.296699\pi\)
\(830\) 0 0
\(831\) −1.99016e7 −0.999735
\(832\) 0 0
\(833\) −8.97083e6 −0.447940
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −6.78845e6 −0.334932
\(838\) 0 0
\(839\) −3.54805e7 −1.74014 −0.870071 − 0.492926i \(-0.835927\pi\)
−0.870071 + 0.492926i \(0.835927\pi\)
\(840\) 0 0
\(841\) 3.29834e7 1.60807
\(842\) 0 0
\(843\) −3.80713e6 −0.184514
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 2.45444e7 1.17556
\(848\) 0 0
\(849\) 4.38347e6 0.208713
\(850\) 0 0
\(851\) 1.36980e7 0.648383
\(852\) 0 0
\(853\) 5.54993e6 0.261165 0.130582 − 0.991437i \(-0.458315\pi\)
0.130582 + 0.991437i \(0.458315\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.21344e7 1.02948 0.514738 − 0.857348i \(-0.327889\pi\)
0.514738 + 0.857348i \(0.327889\pi\)
\(858\) 0 0
\(859\) −9.65533e6 −0.446462 −0.223231 − 0.974766i \(-0.571660\pi\)
−0.223231 + 0.974766i \(0.571660\pi\)
\(860\) 0 0
\(861\) −2.36592e6 −0.108766
\(862\) 0 0
\(863\) −1.43771e7 −0.657120 −0.328560 − 0.944483i \(-0.606563\pi\)
−0.328560 + 0.944483i \(0.606563\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −6.09132e6 −0.275210
\(868\) 0 0
\(869\) 1.82984e7 0.821983
\(870\) 0 0
\(871\) −2.86789e7 −1.28090
\(872\) 0 0
\(873\) −1.10887e7 −0.492432
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −9.01032e6 −0.395586 −0.197793 − 0.980244i \(-0.563377\pi\)
−0.197793 + 0.980244i \(0.563377\pi\)
\(878\) 0 0
\(879\) 9.24230e6 0.403467
\(880\) 0 0
\(881\) −1.64420e7 −0.713700 −0.356850 − 0.934162i \(-0.616149\pi\)
−0.356850 + 0.934162i \(0.616149\pi\)
\(882\) 0 0
\(883\) −6.06516e6 −0.261783 −0.130891 − 0.991397i \(-0.541784\pi\)
−0.130891 + 0.991397i \(0.541784\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.85746e7 −1.21947 −0.609735 − 0.792605i \(-0.708724\pi\)
−0.609735 + 0.792605i \(0.708724\pi\)
\(888\) 0 0
\(889\) −7.91104e6 −0.335722
\(890\) 0 0
\(891\) 4.48772e6 0.189379
\(892\) 0 0
\(893\) 5.45936e6 0.229094
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.36607e7 0.566881
\(898\) 0 0
\(899\) 6.81080e7 2.81060
\(900\) 0 0
\(901\) 7.49768e6 0.307691
\(902\) 0 0
\(903\) −5.44032e6 −0.222027
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.47466e7 0.595215 0.297607 − 0.954688i \(-0.403811\pi\)
0.297607 + 0.954688i \(0.403811\pi\)
\(908\) 0 0
\(909\) −1.64315e7 −0.659580
\(910\) 0 0
\(911\) −2.61222e6 −0.104283 −0.0521416 − 0.998640i \(-0.516605\pi\)
−0.0521416 + 0.998640i \(0.516605\pi\)
\(912\) 0 0
\(913\) 5.44190e6 0.216060
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.37088e6 0.0931078
\(918\) 0 0
\(919\) −4.66079e7 −1.82042 −0.910208 − 0.414152i \(-0.864078\pi\)
−0.910208 + 0.414152i \(0.864078\pi\)
\(920\) 0 0
\(921\) 9.64199e6 0.374557
\(922\) 0 0
\(923\) 8.25510e7 3.18947
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 694656. 0.0265504
\(928\) 0 0
\(929\) −3.16320e7 −1.20251 −0.601254 − 0.799058i \(-0.705332\pi\)
−0.601254 + 0.799058i \(0.705332\pi\)
\(930\) 0 0
\(931\) −9.53281e6 −0.360451
\(932\) 0 0
\(933\) 1.68679e7 0.634393
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.57021e7 −0.956355 −0.478177 − 0.878263i \(-0.658702\pi\)
−0.478177 + 0.878263i \(0.658702\pi\)
\(938\) 0 0
\(939\) −2.63594e7 −0.975601
\(940\) 0 0
\(941\) −7.01907e6 −0.258408 −0.129204 − 0.991618i \(-0.541242\pi\)
−0.129204 + 0.991618i \(0.541242\pi\)
\(942\) 0 0
\(943\) −5.09987e6 −0.186758
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.38467e6 −0.122643 −0.0613213 − 0.998118i \(-0.519531\pi\)
−0.0613213 + 0.998118i \(0.519531\pi\)
\(948\) 0 0
\(949\) 4.55259e7 1.64094
\(950\) 0 0
\(951\) 2.65348e7 0.951401
\(952\) 0 0
\(953\) 9.74473e6 0.347566 0.173783 − 0.984784i \(-0.444401\pi\)
0.173783 + 0.984784i \(0.444401\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −4.50250e7 −1.58918
\(958\) 0 0
\(959\) 369120. 0.0129605
\(960\) 0 0
\(961\) 5.80842e7 2.02885
\(962\) 0 0
\(963\) 1.61579e6 0.0561460
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.09405e7 0.376244 0.188122 − 0.982146i \(-0.439760\pi\)
0.188122 + 0.982146i \(0.439760\pi\)
\(968\) 0 0
\(969\) 7.10633e6 0.243128
\(970\) 0 0
\(971\) −2.25329e7 −0.766953 −0.383476 − 0.923551i \(-0.625273\pi\)
−0.383476 + 0.923551i \(0.625273\pi\)
\(972\) 0 0
\(973\) −2.03434e7 −0.688875
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.79146e7 0.935610 0.467805 − 0.883832i \(-0.345045\pi\)
0.467805 + 0.883832i \(0.345045\pi\)
\(978\) 0 0
\(979\) 4.08170e7 1.36108
\(980\) 0 0
\(981\) 3.04544e6 0.101036
\(982\) 0 0
\(983\) 3.07607e7 1.01534 0.507670 − 0.861551i \(-0.330507\pi\)
0.507670 + 0.861551i \(0.330507\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 4.29120e6 0.140212
\(988\) 0 0
\(989\) −1.17269e7 −0.381235
\(990\) 0 0
\(991\) −4.31296e6 −0.139505 −0.0697527 − 0.997564i \(-0.522221\pi\)
−0.0697527 + 0.997564i \(0.522221\pi\)
\(992\) 0 0
\(993\) −7.70490e6 −0.247967
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2.85667e7 0.910170 0.455085 − 0.890448i \(-0.349609\pi\)
0.455085 + 0.890448i \(0.349609\pi\)
\(998\) 0 0
\(999\) 6.43415e6 0.203975
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 600.6.a.g.1.1 1
5.2 odd 4 600.6.f.i.49.1 2
5.3 odd 4 600.6.f.i.49.2 2
5.4 even 2 120.6.a.c.1.1 ✓ 1
15.14 odd 2 360.6.a.c.1.1 1
20.19 odd 2 240.6.a.n.1.1 1
40.19 odd 2 960.6.a.f.1.1 1
40.29 even 2 960.6.a.o.1.1 1
60.59 even 2 720.6.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.6.a.c.1.1 ✓ 1 5.4 even 2
240.6.a.n.1.1 1 20.19 odd 2
360.6.a.c.1.1 1 15.14 odd 2
600.6.a.g.1.1 1 1.1 even 1 trivial
600.6.f.i.49.1 2 5.2 odd 4
600.6.f.i.49.2 2 5.3 odd 4
720.6.a.g.1.1 1 60.59 even 2
960.6.a.f.1.1 1 40.19 odd 2
960.6.a.o.1.1 1 40.29 even 2