Properties

Label 300.6.a.f.1.1
Level $300$
Weight $6$
Character 300.1
Self dual yes
Analytic conductor $48.115$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [300,6,Mod(1,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("300.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 300.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: \(48.1151459439\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 300.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.00000 q^{3} +91.0000 q^{7} +81.0000 q^{9} +O(q^{10})\) \(q+9.00000 q^{3} +91.0000 q^{7} +81.0000 q^{9} -174.000 q^{11} -785.000 q^{13} -1794.00 q^{17} -925.000 q^{19} +819.000 q^{21} +2346.00 q^{23} +729.000 q^{27} -726.000 q^{29} -811.000 q^{31} -1566.00 q^{33} -7922.00 q^{37} -7065.00 q^{39} -360.000 q^{41} +4951.00 q^{43} -9906.00 q^{47} -8526.00 q^{49} -16146.0 q^{51} +8292.00 q^{53} -8325.00 q^{57} +7014.00 q^{59} -51433.0 q^{61} +7371.00 q^{63} -581.000 q^{67} +21114.0 q^{69} -56520.0 q^{71} +42478.0 q^{73} -15834.0 q^{77} -28912.0 q^{79} +6561.00 q^{81} +104586. q^{83} -6534.00 q^{87} -118080. q^{89} -71435.0 q^{91} -7299.00 q^{93} -110273. q^{97} -14094.0 q^{99} +O(q^{100})\)

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
\(7\) 91.0000 0.701934 0.350967 0.936388i \(-0.385853\pi\)
0.350967 + 0.936388i \(0.385853\pi\)
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) −174.000 −0.433578 −0.216789 0.976218i \(-0.569558\pi\)
−0.216789 + 0.976218i \(0.569558\pi\)
\(12\) 0 0
\(13\) −785.000 −1.28828 −0.644142 0.764906i \(-0.722785\pi\)
−0.644142 + 0.764906i \(0.722785\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1794.00 −1.50557 −0.752784 0.658268i \(-0.771289\pi\)
−0.752784 + 0.658268i \(0.771289\pi\)
\(18\) 0 0
\(19\) −925.000 −0.587838 −0.293919 0.955830i \(-0.594960\pi\)
−0.293919 + 0.955830i \(0.594960\pi\)
\(20\) 0 0
\(21\) 819.000 0.405262
\(22\) 0 0
\(23\) 2346.00 0.924716 0.462358 0.886693i \(-0.347003\pi\)
0.462358 + 0.886693i \(0.347003\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −726.000 −0.160303 −0.0801515 0.996783i \(-0.525540\pi\)
−0.0801515 + 0.996783i \(0.525540\pi\)
\(30\) 0 0
\(31\) −811.000 −0.151571 −0.0757856 0.997124i \(-0.524146\pi\)
−0.0757856 + 0.997124i \(0.524146\pi\)
\(32\) 0 0
\(33\) −1566.00 −0.250327
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7922.00 −0.951329 −0.475664 0.879627i \(-0.657792\pi\)
−0.475664 + 0.879627i \(0.657792\pi\)
\(38\) 0 0
\(39\) −7065.00 −0.743791
\(40\) 0 0
\(41\) −360.000 −0.0334459 −0.0167229 0.999860i \(-0.505323\pi\)
−0.0167229 + 0.999860i \(0.505323\pi\)
\(42\) 0 0
\(43\) 4951.00 0.408340 0.204170 0.978935i \(-0.434550\pi\)
0.204170 + 0.978935i \(0.434550\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9906.00 −0.654114 −0.327057 0.945005i \(-0.606057\pi\)
−0.327057 + 0.945005i \(0.606057\pi\)
\(48\) 0 0
\(49\) −8526.00 −0.507289
\(50\) 0 0
\(51\) −16146.0 −0.869240
\(52\) 0 0
\(53\) 8292.00 0.405480 0.202740 0.979233i \(-0.435015\pi\)
0.202740 + 0.979233i \(0.435015\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −8325.00 −0.339388
\(58\) 0 0
\(59\) 7014.00 0.262323 0.131161 0.991361i \(-0.458129\pi\)
0.131161 + 0.991361i \(0.458129\pi\)
\(60\) 0 0
\(61\) −51433.0 −1.76977 −0.884886 0.465808i \(-0.845764\pi\)
−0.884886 + 0.465808i \(0.845764\pi\)
\(62\) 0 0
\(63\) 7371.00 0.233978
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −581.000 −0.0158121 −0.00790604 0.999969i \(-0.502517\pi\)
−0.00790604 + 0.999969i \(0.502517\pi\)
\(68\) 0 0
\(69\) 21114.0 0.533885
\(70\) 0 0
\(71\) −56520.0 −1.33063 −0.665313 0.746564i \(-0.731702\pi\)
−0.665313 + 0.746564i \(0.731702\pi\)
\(72\) 0 0
\(73\) 42478.0 0.932947 0.466473 0.884535i \(-0.345524\pi\)
0.466473 + 0.884535i \(0.345524\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −15834.0 −0.304343
\(78\) 0 0
\(79\) −28912.0 −0.521207 −0.260604 0.965446i \(-0.583922\pi\)
−0.260604 + 0.965446i \(0.583922\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) 104586. 1.66640 0.833198 0.552974i \(-0.186507\pi\)
0.833198 + 0.552974i \(0.186507\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6534.00 −0.0925510
\(88\) 0 0
\(89\) −118080. −1.58016 −0.790080 0.613003i \(-0.789961\pi\)
−0.790080 + 0.613003i \(0.789961\pi\)
\(90\) 0 0
\(91\) −71435.0 −0.904290
\(92\) 0 0
\(93\) −7299.00 −0.0875097
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −110273. −1.18998 −0.594990 0.803733i \(-0.702844\pi\)
−0.594990 + 0.803733i \(0.702844\pi\)
\(98\) 0 0
\(99\) −14094.0 −0.144526
\(100\) 0 0
\(101\) −193332. −1.88582 −0.942910 0.333047i \(-0.891923\pi\)
−0.942910 + 0.333047i \(0.891923\pi\)
\(102\) 0 0
\(103\) 37684.0 0.349997 0.174998 0.984569i \(-0.444008\pi\)
0.174998 + 0.984569i \(0.444008\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17292.0 −0.146011 −0.0730055 0.997332i \(-0.523259\pi\)
−0.0730055 + 0.997332i \(0.523259\pi\)
\(108\) 0 0
\(109\) 142133. 1.14585 0.572926 0.819607i \(-0.305808\pi\)
0.572926 + 0.819607i \(0.305808\pi\)
\(110\) 0 0
\(111\) −71298.0 −0.549250
\(112\) 0 0
\(113\) 68388.0 0.503830 0.251915 0.967749i \(-0.418940\pi\)
0.251915 + 0.967749i \(0.418940\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −63585.0 −0.429428
\(118\) 0 0
\(119\) −163254. −1.05681
\(120\) 0 0
\(121\) −130775. −0.812010
\(122\) 0 0
\(123\) −3240.00 −0.0193100
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −185384. −1.01991 −0.509956 0.860200i \(-0.670338\pi\)
−0.509956 + 0.860200i \(0.670338\pi\)
\(128\) 0 0
\(129\) 44559.0 0.235755
\(130\) 0 0
\(131\) 329772. 1.67894 0.839471 0.543405i \(-0.182865\pi\)
0.839471 + 0.543405i \(0.182865\pi\)
\(132\) 0 0
\(133\) −84175.0 −0.412624
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −143982. −0.655401 −0.327700 0.944782i \(-0.606274\pi\)
−0.327700 + 0.944782i \(0.606274\pi\)
\(138\) 0 0
\(139\) −365644. −1.60517 −0.802586 0.596537i \(-0.796543\pi\)
−0.802586 + 0.596537i \(0.796543\pi\)
\(140\) 0 0
\(141\) −89154.0 −0.377653
\(142\) 0 0
\(143\) 136590. 0.558572
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −76734.0 −0.292883
\(148\) 0 0
\(149\) 155178. 0.572617 0.286309 0.958137i \(-0.407572\pi\)
0.286309 + 0.958137i \(0.407572\pi\)
\(150\) 0 0
\(151\) −227185. −0.810844 −0.405422 0.914130i \(-0.632875\pi\)
−0.405422 + 0.914130i \(0.632875\pi\)
\(152\) 0 0
\(153\) −145314. −0.501856
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 171277. 0.554562 0.277281 0.960789i \(-0.410567\pi\)
0.277281 + 0.960789i \(0.410567\pi\)
\(158\) 0 0
\(159\) 74628.0 0.234104
\(160\) 0 0
\(161\) 213486. 0.649090
\(162\) 0 0
\(163\) −110675. −0.326273 −0.163136 0.986604i \(-0.552161\pi\)
−0.163136 + 0.986604i \(0.552161\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 440628. 1.22259 0.611295 0.791403i \(-0.290649\pi\)
0.611295 + 0.791403i \(0.290649\pi\)
\(168\) 0 0
\(169\) 244932. 0.659673
\(170\) 0 0
\(171\) −74925.0 −0.195946
\(172\) 0 0
\(173\) 699834. 1.77779 0.888894 0.458114i \(-0.151475\pi\)
0.888894 + 0.458114i \(0.151475\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 63126.0 0.151452
\(178\) 0 0
\(179\) −309786. −0.722652 −0.361326 0.932440i \(-0.617676\pi\)
−0.361326 + 0.932440i \(0.617676\pi\)
\(180\) 0 0
\(181\) 628625. 1.42625 0.713124 0.701038i \(-0.247280\pi\)
0.713124 + 0.701038i \(0.247280\pi\)
\(182\) 0 0
\(183\) −462897. −1.02178
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 312156. 0.652781
\(188\) 0 0
\(189\) 66339.0 0.135087
\(190\) 0 0
\(191\) 192774. 0.382353 0.191177 0.981556i \(-0.438770\pi\)
0.191177 + 0.981556i \(0.438770\pi\)
\(192\) 0 0
\(193\) −708971. −1.37005 −0.685023 0.728521i \(-0.740208\pi\)
−0.685023 + 0.728521i \(0.740208\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 119154. 0.218747 0.109374 0.994001i \(-0.465115\pi\)
0.109374 + 0.994001i \(0.465115\pi\)
\(198\) 0 0
\(199\) 1.01864e6 1.82343 0.911715 0.410822i \(-0.134758\pi\)
0.911715 + 0.410822i \(0.134758\pi\)
\(200\) 0 0
\(201\) −5229.00 −0.00912911
\(202\) 0 0
\(203\) −66066.0 −0.112522
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 190026. 0.308239
\(208\) 0 0
\(209\) 160950. 0.254874
\(210\) 0 0
\(211\) −32245.0 −0.0498605 −0.0249302 0.999689i \(-0.507936\pi\)
−0.0249302 + 0.999689i \(0.507936\pi\)
\(212\) 0 0
\(213\) −508680. −0.768238
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −73801.0 −0.106393
\(218\) 0 0
\(219\) 382302. 0.538637
\(220\) 0 0
\(221\) 1.40829e6 1.93960
\(222\) 0 0
\(223\) −815765. −1.09851 −0.549254 0.835656i \(-0.685088\pi\)
−0.549254 + 0.835656i \(0.685088\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.45908e6 1.87938 0.939690 0.342028i \(-0.111114\pi\)
0.939690 + 0.342028i \(0.111114\pi\)
\(228\) 0 0
\(229\) 406241. 0.511912 0.255956 0.966688i \(-0.417610\pi\)
0.255956 + 0.966688i \(0.417610\pi\)
\(230\) 0 0
\(231\) −142506. −0.175713
\(232\) 0 0
\(233\) 901080. 1.08736 0.543680 0.839292i \(-0.317030\pi\)
0.543680 + 0.839292i \(0.317030\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −260208. −0.300919
\(238\) 0 0
\(239\) −1.36513e6 −1.54589 −0.772947 0.634470i \(-0.781218\pi\)
−0.772947 + 0.634470i \(0.781218\pi\)
\(240\) 0 0
\(241\) −180247. −0.199906 −0.0999529 0.994992i \(-0.531869\pi\)
−0.0999529 + 0.994992i \(0.531869\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 726125. 0.757302
\(248\) 0 0
\(249\) 941274. 0.962094
\(250\) 0 0
\(251\) 1.87739e6 1.88092 0.940459 0.339908i \(-0.110396\pi\)
0.940459 + 0.339908i \(0.110396\pi\)
\(252\) 0 0
\(253\) −408204. −0.400937
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 825108. 0.779252 0.389626 0.920973i \(-0.372604\pi\)
0.389626 + 0.920973i \(0.372604\pi\)
\(258\) 0 0
\(259\) −720902. −0.667770
\(260\) 0 0
\(261\) −58806.0 −0.0534343
\(262\) 0 0
\(263\) −196944. −0.175571 −0.0877856 0.996139i \(-0.527979\pi\)
−0.0877856 + 0.996139i \(0.527979\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.06272e6 −0.912306
\(268\) 0 0
\(269\) −20874.0 −0.0175883 −0.00879417 0.999961i \(-0.502799\pi\)
−0.00879417 + 0.999961i \(0.502799\pi\)
\(270\) 0 0
\(271\) 770024. 0.636914 0.318457 0.947937i \(-0.396835\pi\)
0.318457 + 0.947937i \(0.396835\pi\)
\(272\) 0 0
\(273\) −642915. −0.522092
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.75169e6 −1.37170 −0.685849 0.727744i \(-0.740569\pi\)
−0.685849 + 0.727744i \(0.740569\pi\)
\(278\) 0 0
\(279\) −65691.0 −0.0505237
\(280\) 0 0
\(281\) 1.72693e6 1.30469 0.652346 0.757921i \(-0.273785\pi\)
0.652346 + 0.757921i \(0.273785\pi\)
\(282\) 0 0
\(283\) −2.20061e6 −1.63334 −0.816670 0.577105i \(-0.804182\pi\)
−0.816670 + 0.577105i \(0.804182\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −32760.0 −0.0234768
\(288\) 0 0
\(289\) 1.79858e6 1.26673
\(290\) 0 0
\(291\) −992457. −0.687036
\(292\) 0 0
\(293\) 2.04086e6 1.38881 0.694406 0.719583i \(-0.255667\pi\)
0.694406 + 0.719583i \(0.255667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −126846. −0.0834422
\(298\) 0 0
\(299\) −1.84161e6 −1.19130
\(300\) 0 0
\(301\) 450541. 0.286628
\(302\) 0 0
\(303\) −1.73999e6 −1.08878
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 433153. 0.262298 0.131149 0.991363i \(-0.458133\pi\)
0.131149 + 0.991363i \(0.458133\pi\)
\(308\) 0 0
\(309\) 339156. 0.202071
\(310\) 0 0
\(311\) −2.20663e6 −1.29368 −0.646841 0.762625i \(-0.723910\pi\)
−0.646841 + 0.762625i \(0.723910\pi\)
\(312\) 0 0
\(313\) 2.17607e6 1.25549 0.627743 0.778421i \(-0.283979\pi\)
0.627743 + 0.778421i \(0.283979\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 380136. 0.212467 0.106233 0.994341i \(-0.466121\pi\)
0.106233 + 0.994341i \(0.466121\pi\)
\(318\) 0 0
\(319\) 126324. 0.0695039
\(320\) 0 0
\(321\) −155628. −0.0842995
\(322\) 0 0
\(323\) 1.65945e6 0.885030
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.27920e6 0.661558
\(328\) 0 0
\(329\) −901446. −0.459145
\(330\) 0 0
\(331\) −3.43599e6 −1.72378 −0.861890 0.507096i \(-0.830719\pi\)
−0.861890 + 0.507096i \(0.830719\pi\)
\(332\) 0 0
\(333\) −641682. −0.317110
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.57718e6 −0.756494 −0.378247 0.925705i \(-0.623473\pi\)
−0.378247 + 0.925705i \(0.623473\pi\)
\(338\) 0 0
\(339\) 615492. 0.290886
\(340\) 0 0
\(341\) 141114. 0.0657180
\(342\) 0 0
\(343\) −2.30530e6 −1.05802
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.08744e6 −0.930659 −0.465330 0.885137i \(-0.654064\pi\)
−0.465330 + 0.885137i \(0.654064\pi\)
\(348\) 0 0
\(349\) 542426. 0.238384 0.119192 0.992871i \(-0.461970\pi\)
0.119192 + 0.992871i \(0.461970\pi\)
\(350\) 0 0
\(351\) −572265. −0.247930
\(352\) 0 0
\(353\) 4.16054e6 1.77710 0.888552 0.458776i \(-0.151712\pi\)
0.888552 + 0.458776i \(0.151712\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.46929e6 −0.610149
\(358\) 0 0
\(359\) −1.69018e6 −0.692143 −0.346071 0.938208i \(-0.612485\pi\)
−0.346071 + 0.938208i \(0.612485\pi\)
\(360\) 0 0
\(361\) −1.62047e6 −0.654446
\(362\) 0 0
\(363\) −1.17698e6 −0.468814
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 846061. 0.327896 0.163948 0.986469i \(-0.447577\pi\)
0.163948 + 0.986469i \(0.447577\pi\)
\(368\) 0 0
\(369\) −29160.0 −0.0111486
\(370\) 0 0
\(371\) 754572. 0.284620
\(372\) 0 0
\(373\) 1.25910e6 0.468585 0.234293 0.972166i \(-0.424723\pi\)
0.234293 + 0.972166i \(0.424723\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 569910. 0.206516
\(378\) 0 0
\(379\) −4.37437e6 −1.56429 −0.782145 0.623097i \(-0.785874\pi\)
−0.782145 + 0.623097i \(0.785874\pi\)
\(380\) 0 0
\(381\) −1.66846e6 −0.588847
\(382\) 0 0
\(383\) 4.77827e6 1.66446 0.832230 0.554430i \(-0.187064\pi\)
0.832230 + 0.554430i \(0.187064\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 401031. 0.136113
\(388\) 0 0
\(389\) 2.98618e6 1.00056 0.500278 0.865865i \(-0.333231\pi\)
0.500278 + 0.865865i \(0.333231\pi\)
\(390\) 0 0
\(391\) −4.20872e6 −1.39222
\(392\) 0 0
\(393\) 2.96795e6 0.969337
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 238633. 0.0759896 0.0379948 0.999278i \(-0.487903\pi\)
0.0379948 + 0.999278i \(0.487903\pi\)
\(398\) 0 0
\(399\) −757575. −0.238228
\(400\) 0 0
\(401\) −1.66856e6 −0.518182 −0.259091 0.965853i \(-0.583423\pi\)
−0.259091 + 0.965853i \(0.583423\pi\)
\(402\) 0 0
\(403\) 636635. 0.195267
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.37843e6 0.412475
\(408\) 0 0
\(409\) 3.05242e6 0.902269 0.451135 0.892456i \(-0.351019\pi\)
0.451135 + 0.892456i \(0.351019\pi\)
\(410\) 0 0
\(411\) −1.29584e6 −0.378396
\(412\) 0 0
\(413\) 638274. 0.184133
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.29080e6 −0.926746
\(418\) 0 0
\(419\) −3.16223e6 −0.879950 −0.439975 0.898010i \(-0.645013\pi\)
−0.439975 + 0.898010i \(0.645013\pi\)
\(420\) 0 0
\(421\) −2.76169e6 −0.759398 −0.379699 0.925110i \(-0.623973\pi\)
−0.379699 + 0.925110i \(0.623973\pi\)
\(422\) 0 0
\(423\) −802386. −0.218038
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −4.68040e6 −1.24226
\(428\) 0 0
\(429\) 1.22931e6 0.322491
\(430\) 0 0
\(431\) −2.46832e6 −0.640042 −0.320021 0.947410i \(-0.603690\pi\)
−0.320021 + 0.947410i \(0.603690\pi\)
\(432\) 0 0
\(433\) −838931. −0.215034 −0.107517 0.994203i \(-0.534290\pi\)
−0.107517 + 0.994203i \(0.534290\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.17005e6 −0.543583
\(438\) 0 0
\(439\) −481867. −0.119334 −0.0596672 0.998218i \(-0.519004\pi\)
−0.0596672 + 0.998218i \(0.519004\pi\)
\(440\) 0 0
\(441\) −690606. −0.169096
\(442\) 0 0
\(443\) −4.83550e6 −1.17066 −0.585331 0.810794i \(-0.699036\pi\)
−0.585331 + 0.810794i \(0.699036\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.39660e6 0.330601
\(448\) 0 0
\(449\) −1.64449e6 −0.384960 −0.192480 0.981301i \(-0.561653\pi\)
−0.192480 + 0.981301i \(0.561653\pi\)
\(450\) 0 0
\(451\) 62640.0 0.0145014
\(452\) 0 0
\(453\) −2.04466e6 −0.468141
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6.59903e6 −1.47805 −0.739026 0.673677i \(-0.764714\pi\)
−0.739026 + 0.673677i \(0.764714\pi\)
\(458\) 0 0
\(459\) −1.30783e6 −0.289747
\(460\) 0 0
\(461\) 253836. 0.0556290 0.0278145 0.999613i \(-0.491145\pi\)
0.0278145 + 0.999613i \(0.491145\pi\)
\(462\) 0 0
\(463\) 5.03985e6 1.09261 0.546305 0.837586i \(-0.316034\pi\)
0.546305 + 0.837586i \(0.316034\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 419958. 0.0891074 0.0445537 0.999007i \(-0.485813\pi\)
0.0445537 + 0.999007i \(0.485813\pi\)
\(468\) 0 0
\(469\) −52871.0 −0.0110990
\(470\) 0 0
\(471\) 1.54149e6 0.320176
\(472\) 0 0
\(473\) −861474. −0.177047
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 671652. 0.135160
\(478\) 0 0
\(479\) −7.28623e6 −1.45099 −0.725494 0.688228i \(-0.758389\pi\)
−0.725494 + 0.688228i \(0.758389\pi\)
\(480\) 0 0
\(481\) 6.21877e6 1.22558
\(482\) 0 0
\(483\) 1.92137e6 0.374752
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7.48420e6 1.42996 0.714978 0.699147i \(-0.246437\pi\)
0.714978 + 0.699147i \(0.246437\pi\)
\(488\) 0 0
\(489\) −996075. −0.188374
\(490\) 0 0
\(491\) −339816. −0.0636122 −0.0318061 0.999494i \(-0.510126\pi\)
−0.0318061 + 0.999494i \(0.510126\pi\)
\(492\) 0 0
\(493\) 1.30244e6 0.241347
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.14332e6 −0.934012
\(498\) 0 0
\(499\) 280499. 0.0504290 0.0252145 0.999682i \(-0.491973\pi\)
0.0252145 + 0.999682i \(0.491973\pi\)
\(500\) 0 0
\(501\) 3.96565e6 0.705863
\(502\) 0 0
\(503\) −2.41522e6 −0.425634 −0.212817 0.977092i \(-0.568264\pi\)
−0.212817 + 0.977092i \(0.568264\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.20439e6 0.380862
\(508\) 0 0
\(509\) 8.09746e6 1.38533 0.692667 0.721258i \(-0.256436\pi\)
0.692667 + 0.721258i \(0.256436\pi\)
\(510\) 0 0
\(511\) 3.86550e6 0.654867
\(512\) 0 0
\(513\) −674325. −0.113129
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.72364e6 0.283610
\(518\) 0 0
\(519\) 6.29851e6 1.02641
\(520\) 0 0
\(521\) −3.52334e6 −0.568670 −0.284335 0.958725i \(-0.591773\pi\)
−0.284335 + 0.958725i \(0.591773\pi\)
\(522\) 0 0
\(523\) −4.27241e6 −0.682996 −0.341498 0.939882i \(-0.610934\pi\)
−0.341498 + 0.939882i \(0.610934\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.45493e6 0.228201
\(528\) 0 0
\(529\) −932627. −0.144900
\(530\) 0 0
\(531\) 568134. 0.0874409
\(532\) 0 0
\(533\) 282600. 0.0430878
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.78807e6 −0.417223
\(538\) 0 0
\(539\) 1.48352e6 0.219949
\(540\) 0 0
\(541\) 3.80585e6 0.559061 0.279530 0.960137i \(-0.409821\pi\)
0.279530 + 0.960137i \(0.409821\pi\)
\(542\) 0 0
\(543\) 5.65762e6 0.823445
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.46327e6 1.06650 0.533250 0.845958i \(-0.320970\pi\)
0.533250 + 0.845958i \(0.320970\pi\)
\(548\) 0 0
\(549\) −4.16607e6 −0.589924
\(550\) 0 0
\(551\) 671550. 0.0942322
\(552\) 0 0
\(553\) −2.63099e6 −0.365853
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.26290e6 0.855338 0.427669 0.903935i \(-0.359335\pi\)
0.427669 + 0.903935i \(0.359335\pi\)
\(558\) 0 0
\(559\) −3.88654e6 −0.526057
\(560\) 0 0
\(561\) 2.80940e6 0.376883
\(562\) 0 0
\(563\) −1.34426e7 −1.78735 −0.893677 0.448710i \(-0.851883\pi\)
−0.893677 + 0.448710i \(0.851883\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 597051. 0.0779927
\(568\) 0 0
\(569\) 1.25046e7 1.61916 0.809579 0.587011i \(-0.199695\pi\)
0.809579 + 0.587011i \(0.199695\pi\)
\(570\) 0 0
\(571\) 6.80272e6 0.873156 0.436578 0.899666i \(-0.356190\pi\)
0.436578 + 0.899666i \(0.356190\pi\)
\(572\) 0 0
\(573\) 1.73497e6 0.220752
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 375517. 0.0469559 0.0234779 0.999724i \(-0.492526\pi\)
0.0234779 + 0.999724i \(0.492526\pi\)
\(578\) 0 0
\(579\) −6.38074e6 −0.790997
\(580\) 0 0
\(581\) 9.51733e6 1.16970
\(582\) 0 0
\(583\) −1.44281e6 −0.175807
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.36164e6 −0.402677 −0.201338 0.979522i \(-0.564529\pi\)
−0.201338 + 0.979522i \(0.564529\pi\)
\(588\) 0 0
\(589\) 750175. 0.0890993
\(590\) 0 0
\(591\) 1.07239e6 0.126294
\(592\) 0 0
\(593\) −9.31214e6 −1.08746 −0.543730 0.839260i \(-0.682988\pi\)
−0.543730 + 0.839260i \(0.682988\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9.16779e6 1.05276
\(598\) 0 0
\(599\) 1.03007e7 1.17301 0.586503 0.809947i \(-0.300504\pi\)
0.586503 + 0.809947i \(0.300504\pi\)
\(600\) 0 0
\(601\) −4.14328e6 −0.467905 −0.233953 0.972248i \(-0.575166\pi\)
−0.233953 + 0.972248i \(0.575166\pi\)
\(602\) 0 0
\(603\) −47061.0 −0.00527069
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.42729e6 0.708037 0.354019 0.935238i \(-0.384815\pi\)
0.354019 + 0.935238i \(0.384815\pi\)
\(608\) 0 0
\(609\) −594594. −0.0649647
\(610\) 0 0
\(611\) 7.77621e6 0.842684
\(612\) 0 0
\(613\) 2.11824e6 0.227679 0.113840 0.993499i \(-0.463685\pi\)
0.113840 + 0.993499i \(0.463685\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.53399e7 1.62222 0.811111 0.584892i \(-0.198863\pi\)
0.811111 + 0.584892i \(0.198863\pi\)
\(618\) 0 0
\(619\) 1.04124e7 1.09226 0.546128 0.837702i \(-0.316101\pi\)
0.546128 + 0.837702i \(0.316101\pi\)
\(620\) 0 0
\(621\) 1.71023e6 0.177962
\(622\) 0 0
\(623\) −1.07453e7 −1.10917
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.44855e6 0.147151
\(628\) 0 0
\(629\) 1.42121e7 1.43229
\(630\) 0 0
\(631\) 2.88626e6 0.288577 0.144288 0.989536i \(-0.453911\pi\)
0.144288 + 0.989536i \(0.453911\pi\)
\(632\) 0 0
\(633\) −290205. −0.0287869
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.69291e6 0.653531
\(638\) 0 0
\(639\) −4.57812e6 −0.443542
\(640\) 0 0
\(641\) −1.48587e7 −1.42835 −0.714176 0.699967i \(-0.753198\pi\)
−0.714176 + 0.699967i \(0.753198\pi\)
\(642\) 0 0
\(643\) 9.59676e6 0.915371 0.457686 0.889114i \(-0.348678\pi\)
0.457686 + 0.889114i \(0.348678\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.08529e7 −1.01926 −0.509632 0.860393i \(-0.670218\pi\)
−0.509632 + 0.860393i \(0.670218\pi\)
\(648\) 0 0
\(649\) −1.22044e6 −0.113737
\(650\) 0 0
\(651\) −664209. −0.0614260
\(652\) 0 0
\(653\) −1.20352e7 −1.10451 −0.552254 0.833676i \(-0.686232\pi\)
−0.552254 + 0.833676i \(0.686232\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.44072e6 0.310982
\(658\) 0 0
\(659\) −5.80711e6 −0.520891 −0.260445 0.965489i \(-0.583869\pi\)
−0.260445 + 0.965489i \(0.583869\pi\)
\(660\) 0 0
\(661\) 1.91093e7 1.70114 0.850570 0.525861i \(-0.176257\pi\)
0.850570 + 0.525861i \(0.176257\pi\)
\(662\) 0 0
\(663\) 1.26746e7 1.11983
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.70320e6 −0.148235
\(668\) 0 0
\(669\) −7.34189e6 −0.634223
\(670\) 0 0
\(671\) 8.94934e6 0.767335
\(672\) 0 0
\(673\) 2.15545e6 0.183443 0.0917213 0.995785i \(-0.470763\pi\)
0.0917213 + 0.995785i \(0.470763\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.69543e6 −0.729155 −0.364577 0.931173i \(-0.618786\pi\)
−0.364577 + 0.931173i \(0.618786\pi\)
\(678\) 0 0
\(679\) −1.00348e7 −0.835288
\(680\) 0 0
\(681\) 1.31317e7 1.08506
\(682\) 0 0
\(683\) −781896. −0.0641353 −0.0320677 0.999486i \(-0.510209\pi\)
−0.0320677 + 0.999486i \(0.510209\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 3.65617e6 0.295552
\(688\) 0 0
\(689\) −6.50922e6 −0.522373
\(690\) 0 0
\(691\) 1.13518e7 0.904416 0.452208 0.891912i \(-0.350636\pi\)
0.452208 + 0.891912i \(0.350636\pi\)
\(692\) 0 0
\(693\) −1.28255e6 −0.101448
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 645840. 0.0503550
\(698\) 0 0
\(699\) 8.10972e6 0.627788
\(700\) 0 0
\(701\) −1.99404e7 −1.53263 −0.766317 0.642462i \(-0.777913\pi\)
−0.766317 + 0.642462i \(0.777913\pi\)
\(702\) 0 0
\(703\) 7.32785e6 0.559227
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.75932e7 −1.32372
\(708\) 0 0
\(709\) −1.75367e7 −1.31018 −0.655092 0.755549i \(-0.727370\pi\)
−0.655092 + 0.755549i \(0.727370\pi\)
\(710\) 0 0
\(711\) −2.34187e6 −0.173736
\(712\) 0 0
\(713\) −1.90261e6 −0.140160
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.22862e7 −0.892523
\(718\) 0 0
\(719\) 1.78220e7 1.28568 0.642842 0.765999i \(-0.277755\pi\)
0.642842 + 0.765999i \(0.277755\pi\)
\(720\) 0 0
\(721\) 3.42924e6 0.245675
\(722\) 0 0
\(723\) −1.62222e6 −0.115416
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 8.29063e6 0.581770 0.290885 0.956758i \(-0.406050\pi\)
0.290885 + 0.956758i \(0.406050\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −8.88209e6 −0.614783
\(732\) 0 0
\(733\) −1.69219e7 −1.16330 −0.581648 0.813441i \(-0.697592\pi\)
−0.581648 + 0.813441i \(0.697592\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 101094. 0.00685578
\(738\) 0 0
\(739\) 9.40718e6 0.633648 0.316824 0.948484i \(-0.397383\pi\)
0.316824 + 0.948484i \(0.397383\pi\)
\(740\) 0 0
\(741\) 6.53512e6 0.437228
\(742\) 0 0
\(743\) −1.81581e7 −1.20670 −0.603348 0.797478i \(-0.706167\pi\)
−0.603348 + 0.797478i \(0.706167\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 8.47147e6 0.555465
\(748\) 0 0
\(749\) −1.57357e6 −0.102490
\(750\) 0 0
\(751\) −2.81468e7 −1.82108 −0.910541 0.413420i \(-0.864334\pi\)
−0.910541 + 0.413420i \(0.864334\pi\)
\(752\) 0 0
\(753\) 1.68965e7 1.08595
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −7.50436e6 −0.475964 −0.237982 0.971270i \(-0.576486\pi\)
−0.237982 + 0.971270i \(0.576486\pi\)
\(758\) 0 0
\(759\) −3.67384e6 −0.231481
\(760\) 0 0
\(761\) −3.18499e7 −1.99364 −0.996820 0.0796919i \(-0.974606\pi\)
−0.996820 + 0.0796919i \(0.974606\pi\)
\(762\) 0 0
\(763\) 1.29341e7 0.804313
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.50599e6 −0.337946
\(768\) 0 0
\(769\) −2.38750e7 −1.45588 −0.727942 0.685638i \(-0.759523\pi\)
−0.727942 + 0.685638i \(0.759523\pi\)
\(770\) 0 0
\(771\) 7.42597e6 0.449901
\(772\) 0 0
\(773\) −8.43665e6 −0.507833 −0.253917 0.967226i \(-0.581719\pi\)
−0.253917 + 0.967226i \(0.581719\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −6.48812e6 −0.385537
\(778\) 0 0
\(779\) 333000. 0.0196608
\(780\) 0 0
\(781\) 9.83448e6 0.576931
\(782\) 0 0
\(783\) −529254. −0.0308503
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.55971e7 −1.47317 −0.736587 0.676343i \(-0.763564\pi\)
−0.736587 + 0.676343i \(0.763564\pi\)
\(788\) 0 0
\(789\) −1.77250e6 −0.101366
\(790\) 0 0
\(791\) 6.22331e6 0.353655
\(792\) 0 0
\(793\) 4.03749e7 2.27997
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.22343e7 0.682231 0.341116 0.940021i \(-0.389195\pi\)
0.341116 + 0.940021i \(0.389195\pi\)
\(798\) 0 0
\(799\) 1.77714e7 0.984813
\(800\) 0 0
\(801\) −9.56448e6 −0.526720
\(802\) 0 0
\(803\) −7.39117e6 −0.404506
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −187866. −0.0101546
\(808\) 0 0
\(809\) −2.82538e7 −1.51777 −0.758885 0.651224i \(-0.774256\pi\)
−0.758885 + 0.651224i \(0.774256\pi\)
\(810\) 0 0
\(811\) −2.02221e7 −1.07963 −0.539815 0.841784i \(-0.681506\pi\)
−0.539815 + 0.841784i \(0.681506\pi\)
\(812\) 0 0
\(813\) 6.93022e6 0.367723
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −4.57968e6 −0.240038
\(818\) 0 0
\(819\) −5.78624e6 −0.301430
\(820\) 0 0
\(821\) 2.92645e6 0.151524 0.0757622 0.997126i \(-0.475861\pi\)
0.0757622 + 0.997126i \(0.475861\pi\)
\(822\) 0 0
\(823\) 1.19976e7 0.617439 0.308720 0.951153i \(-0.400100\pi\)
0.308720 + 0.951153i \(0.400100\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.87877e7 −1.46367 −0.731836 0.681481i \(-0.761336\pi\)
−0.731836 + 0.681481i \(0.761336\pi\)
\(828\) 0 0
\(829\) 6.76584e6 0.341929 0.170964 0.985277i \(-0.445312\pi\)
0.170964 + 0.985277i \(0.445312\pi\)
\(830\) 0 0
\(831\) −1.57652e7 −0.791950
\(832\) 0 0
\(833\) 1.52956e7 0.763757
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −591219. −0.0291699
\(838\) 0 0
\(839\) 1.64443e7 0.806512 0.403256 0.915087i \(-0.367878\pi\)
0.403256 + 0.915087i \(0.367878\pi\)
\(840\) 0 0
\(841\) −1.99841e7 −0.974303
\(842\) 0 0
\(843\) 1.55423e7 0.753264
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.19005e7 −0.569977
\(848\) 0 0
\(849\) −1.98055e7 −0.943009
\(850\) 0 0
\(851\) −1.85850e7 −0.879709
\(852\) 0 0
\(853\) −1.17440e7 −0.552642 −0.276321 0.961065i \(-0.589115\pi\)
−0.276321 + 0.961065i \(0.589115\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.59380e7 1.20638 0.603191 0.797597i \(-0.293896\pi\)
0.603191 + 0.797597i \(0.293896\pi\)
\(858\) 0 0
\(859\) −4.81132e6 −0.222475 −0.111238 0.993794i \(-0.535481\pi\)
−0.111238 + 0.993794i \(0.535481\pi\)
\(860\) 0 0
\(861\) −294840. −0.0135543
\(862\) 0 0
\(863\) 8.80123e6 0.402269 0.201134 0.979564i \(-0.435537\pi\)
0.201134 + 0.979564i \(0.435537\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.61872e7 0.731348
\(868\) 0 0
\(869\) 5.03069e6 0.225984
\(870\) 0 0
\(871\) 456085. 0.0203704
\(872\) 0 0
\(873\) −8.93211e6 −0.396660
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.47823e7 0.648998 0.324499 0.945886i \(-0.394804\pi\)
0.324499 + 0.945886i \(0.394804\pi\)
\(878\) 0 0
\(879\) 1.83677e7 0.801831
\(880\) 0 0
\(881\) −2.47219e7 −1.07311 −0.536553 0.843867i \(-0.680274\pi\)
−0.536553 + 0.843867i \(0.680274\pi\)
\(882\) 0 0
\(883\) 1.63912e7 0.707470 0.353735 0.935346i \(-0.384911\pi\)
0.353735 + 0.935346i \(0.384911\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.47481e7 −1.48293 −0.741467 0.670989i \(-0.765870\pi\)
−0.741467 + 0.670989i \(0.765870\pi\)
\(888\) 0 0
\(889\) −1.68699e7 −0.715911
\(890\) 0 0
\(891\) −1.14161e6 −0.0481754
\(892\) 0 0
\(893\) 9.16305e6 0.384513
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.65745e7 −0.687795
\(898\) 0 0
\(899\) 588786. 0.0242973
\(900\) 0 0
\(901\) −1.48758e7 −0.610478
\(902\) 0 0
\(903\) 4.05487e6 0.165485
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 4.42672e7 1.78675 0.893375 0.449312i \(-0.148331\pi\)
0.893375 + 0.449312i \(0.148331\pi\)
\(908\) 0 0
\(909\) −1.56599e7 −0.628607
\(910\) 0 0
\(911\) 5.78972e6 0.231133 0.115566 0.993300i \(-0.463132\pi\)
0.115566 + 0.993300i \(0.463132\pi\)
\(912\) 0 0
\(913\) −1.81980e7 −0.722513
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.00093e7 1.17851
\(918\) 0 0
\(919\) 6.95894e6 0.271803 0.135902 0.990722i \(-0.456607\pi\)
0.135902 + 0.990722i \(0.456607\pi\)
\(920\) 0 0
\(921\) 3.89838e6 0.151438
\(922\) 0 0
\(923\) 4.43682e7 1.71422
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 3.05240e6 0.116666
\(928\) 0 0
\(929\) 1.13281e7 0.430643 0.215321 0.976543i \(-0.430920\pi\)
0.215321 + 0.976543i \(0.430920\pi\)
\(930\) 0 0
\(931\) 7.88655e6 0.298204
\(932\) 0 0
\(933\) −1.98596e7 −0.746908
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −3.38002e7 −1.25768 −0.628840 0.777534i \(-0.716470\pi\)
−0.628840 + 0.777534i \(0.716470\pi\)
\(938\) 0 0
\(939\) 1.95846e7 0.724855
\(940\) 0 0
\(941\) −1.01912e7 −0.375190 −0.187595 0.982246i \(-0.560069\pi\)
−0.187595 + 0.982246i \(0.560069\pi\)
\(942\) 0 0
\(943\) −844560. −0.0309280
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.78585e7 −1.00944 −0.504722 0.863282i \(-0.668405\pi\)
−0.504722 + 0.863282i \(0.668405\pi\)
\(948\) 0 0
\(949\) −3.33452e7 −1.20190
\(950\) 0 0
\(951\) 3.42122e6 0.122668
\(952\) 0 0
\(953\) −1.26828e7 −0.452358 −0.226179 0.974086i \(-0.572623\pi\)
−0.226179 + 0.974086i \(0.572623\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.13692e6 0.0401281
\(958\) 0 0
\(959\) −1.31024e7 −0.460048
\(960\) 0 0
\(961\) −2.79714e7 −0.977026
\(962\) 0 0
\(963\) −1.40065e6 −0.0486704
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −3.17434e7 −1.09166 −0.545831 0.837896i \(-0.683786\pi\)
−0.545831 + 0.837896i \(0.683786\pi\)
\(968\) 0 0
\(969\) 1.49350e7 0.510972
\(970\) 0 0
\(971\) 1.81895e7 0.619117 0.309558 0.950880i \(-0.399819\pi\)
0.309558 + 0.950880i \(0.399819\pi\)
\(972\) 0 0
\(973\) −3.32736e7 −1.12672
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.61267e7 −0.875684 −0.437842 0.899052i \(-0.644257\pi\)
−0.437842 + 0.899052i \(0.644257\pi\)
\(978\) 0 0
\(979\) 2.05459e7 0.685123
\(980\) 0 0
\(981\) 1.15128e7 0.381951
\(982\) 0 0
\(983\) −6.44653e6 −0.212786 −0.106393 0.994324i \(-0.533930\pi\)
−0.106393 + 0.994324i \(0.533930\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −8.11301e6 −0.265088
\(988\) 0 0
\(989\) 1.16150e7 0.377598
\(990\) 0 0
\(991\) 2.16146e7 0.699139 0.349570 0.936910i \(-0.386328\pi\)
0.349570 + 0.936910i \(0.386328\pi\)
\(992\) 0 0
\(993\) −3.09239e7 −0.995224
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2.16105e7 0.688538 0.344269 0.938871i \(-0.388127\pi\)
0.344269 + 0.938871i \(0.388127\pi\)
\(998\) 0 0
\(999\) −5.77514e6 −0.183083
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 300.6.a.f.1.1 yes 1
3.2 odd 2 900.6.a.i.1.1 1
5.2 odd 4 300.6.d.b.49.1 2
5.3 odd 4 300.6.d.b.49.2 2
5.4 even 2 300.6.a.a.1.1 1
15.2 even 4 900.6.d.g.649.2 2
15.8 even 4 900.6.d.g.649.1 2
15.14 odd 2 900.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.6.a.a.1.1 1 5.4 even 2
300.6.a.f.1.1 yes 1 1.1 even 1 trivial
300.6.d.b.49.1 2 5.2 odd 4
300.6.d.b.49.2 2 5.3 odd 4
900.6.a.d.1.1 1 15.14 odd 2
900.6.a.i.1.1 1 3.2 odd 2
900.6.d.g.649.1 2 15.8 even 4
900.6.d.g.649.2 2 15.2 even 4