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Properties

Label 360.6.a.d.1.1
Level $360$
Weight $6$
Character 360.1
Self dual yes
Analytic conductor $57.738$
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] = [360,6,Mod(1,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, 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("360.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 360.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: \(57.7381751327\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 360.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-25.0000 q^{5} +128.000 q^{7} +O(q^{10})\) \(q-25.0000 q^{5} +128.000 q^{7} +308.000 q^{11} -1058.00 q^{13} -1586.00 q^{17} +2308.00 q^{19} -2656.00 q^{23} +625.000 q^{25} -1198.00 q^{29} +9520.00 q^{31} -3200.00 q^{35} +4470.00 q^{37} +6198.00 q^{41} -6332.00 q^{43} -14920.0 q^{47} -423.000 q^{49} -38310.0 q^{53} -7700.00 q^{55} -11564.0 q^{59} -48338.0 q^{61} +26450.0 q^{65} +56972.0 q^{67} -44856.0 q^{71} -19446.0 q^{73} +39424.0 q^{77} -77328.0 q^{79} -40364.0 q^{83} +39650.0 q^{85} -35706.0 q^{89} -135424. q^{91} -57700.0 q^{95} -97022.0 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 128.000 0.987336 0.493668 − 0.869651i \(-0.335656\pi\)
0.493668 + 0.869651i \(0.335656\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 308.000 0.767483 0.383742 − 0.923440i \(-0.374635\pi\)
0.383742 + 0.923440i \(0.374635\pi\)
\(12\) 0 0
\(13\) −1058.00 −1.73631 −0.868155 − 0.496293i \(-0.834694\pi\)
−0.868155 + 0.496293i \(0.834694\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1586.00 −1.33101 −0.665504 − 0.746394i \(-0.731783\pi\)
−0.665504 + 0.746394i \(0.731783\pi\)
\(18\) 0 0
\(19\) 2308.00 1.46674 0.733368 − 0.679832i \(-0.237947\pi\)
0.733368 + 0.679832i \(0.237947\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2656.00 −1.04691 −0.523454 − 0.852054i \(-0.675357\pi\)
−0.523454 + 0.852054i \(0.675357\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1198.00 −0.264522 −0.132261 − 0.991215i \(-0.542224\pi\)
−0.132261 + 0.991215i \(0.542224\pi\)
\(30\) 0 0
\(31\) 9520.00 1.77923 0.889616 − 0.456709i \(-0.150972\pi\)
0.889616 + 0.456709i \(0.150972\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3200.00 −0.441550
\(36\) 0 0
\(37\) 4470.00 0.536789 0.268394 − 0.963309i \(-0.413507\pi\)
0.268394 + 0.963309i \(0.413507\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6198.00 0.575827 0.287913 − 0.957656i \(-0.407038\pi\)
0.287913 + 0.957656i \(0.407038\pi\)
\(42\) 0 0
\(43\) −6332.00 −0.522240 −0.261120 − 0.965306i \(-0.584092\pi\)
−0.261120 + 0.965306i \(0.584092\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −14920.0 −0.985199 −0.492600 − 0.870256i \(-0.663953\pi\)
−0.492600 + 0.870256i \(0.663953\pi\)
\(48\) 0 0
\(49\) −423.000 −0.0251681
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −38310.0 −1.87337 −0.936683 − 0.350179i \(-0.886121\pi\)
−0.936683 + 0.350179i \(0.886121\pi\)
\(54\) 0 0
\(55\) −7700.00 −0.343229
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11564.0 −0.432492 −0.216246 − 0.976339i \(-0.569381\pi\)
−0.216246 + 0.976339i \(0.569381\pi\)
\(60\) 0 0
\(61\) −48338.0 −1.66328 −0.831638 − 0.555319i \(-0.812596\pi\)
−0.831638 + 0.555319i \(0.812596\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 26450.0 0.776501
\(66\) 0 0
\(67\) 56972.0 1.55051 0.775255 − 0.631649i \(-0.217621\pi\)
0.775255 + 0.631649i \(0.217621\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −44856.0 −1.05603 −0.528013 − 0.849236i \(-0.677063\pi\)
−0.528013 + 0.849236i \(0.677063\pi\)
\(72\) 0 0
\(73\) −19446.0 −0.427094 −0.213547 − 0.976933i \(-0.568502\pi\)
−0.213547 + 0.976933i \(0.568502\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 39424.0 0.757764
\(78\) 0 0
\(79\) −77328.0 −1.39402 −0.697010 − 0.717061i \(-0.745487\pi\)
−0.697010 + 0.717061i \(0.745487\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −40364.0 −0.643130 −0.321565 − 0.946887i \(-0.604209\pi\)
−0.321565 + 0.946887i \(0.604209\pi\)
\(84\) 0 0
\(85\) 39650.0 0.595245
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −35706.0 −0.477822 −0.238911 − 0.971041i \(-0.576790\pi\)
−0.238911 + 0.971041i \(0.576790\pi\)
\(90\) 0 0
\(91\) −135424. −1.71432
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −57700.0 −0.655944
\(96\) 0 0
\(97\) −97022.0 −1.04699 −0.523493 − 0.852030i \(-0.675371\pi\)
−0.523493 + 0.852030i \(0.675371\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 123690. 1.20651 0.603255 − 0.797548i \(-0.293870\pi\)
0.603255 + 0.797548i \(0.293870\pi\)
\(102\) 0 0
\(103\) 60688.0 0.563650 0.281825 − 0.959466i \(-0.409060\pi\)
0.281825 + 0.959466i \(0.409060\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 34956.0 0.295163 0.147582 − 0.989050i \(-0.452851\pi\)
0.147582 + 0.989050i \(0.452851\pi\)
\(108\) 0 0
\(109\) −51106.0 −0.412008 −0.206004 − 0.978551i \(-0.566046\pi\)
−0.206004 + 0.978551i \(0.566046\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −46962.0 −0.345980 −0.172990 − 0.984924i \(-0.555343\pi\)
−0.172990 + 0.984924i \(0.555343\pi\)
\(114\) 0 0
\(115\) 66400.0 0.468191
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −203008. −1.31415
\(120\) 0 0
\(121\) −66187.0 −0.410969
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −225768. −1.24209 −0.621045 − 0.783775i \(-0.713292\pi\)
−0.621045 + 0.783775i \(0.713292\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −47172.0 −0.240163 −0.120081 − 0.992764i \(-0.538316\pi\)
−0.120081 + 0.992764i \(0.538316\pi\)
\(132\) 0 0
\(133\) 295424. 1.44816
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −348970. −1.58850 −0.794249 − 0.607592i \(-0.792135\pi\)
−0.794249 + 0.607592i \(0.792135\pi\)
\(138\) 0 0
\(139\) −152196. −0.668138 −0.334069 − 0.942549i \(-0.608422\pi\)
−0.334069 + 0.942549i \(0.608422\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −325864. −1.33259
\(144\) 0 0
\(145\) 29950.0 0.118298
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 46042.0 0.169898 0.0849490 − 0.996385i \(-0.472927\pi\)
0.0849490 + 0.996385i \(0.472927\pi\)
\(150\) 0 0
\(151\) 1736.00 0.00619594 0.00309797 − 0.999995i \(-0.499014\pi\)
0.00309797 + 0.999995i \(0.499014\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −238000. −0.795697
\(156\) 0 0
\(157\) −59954.0 −0.194119 −0.0970597 − 0.995279i \(-0.530944\pi\)
−0.0970597 + 0.995279i \(0.530944\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −339968. −1.03365
\(162\) 0 0
\(163\) −187364. −0.552354 −0.276177 − 0.961107i \(-0.589068\pi\)
−0.276177 + 0.961107i \(0.589068\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 109248. 0.303125 0.151563 − 0.988448i \(-0.451569\pi\)
0.151563 + 0.988448i \(0.451569\pi\)
\(168\) 0 0
\(169\) 748071. 2.01477
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −734942. −1.86697 −0.933486 − 0.358614i \(-0.883249\pi\)
−0.933486 + 0.358614i \(0.883249\pi\)
\(174\) 0 0
\(175\) 80000.0 0.197467
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 500092. 1.16659 0.583294 − 0.812261i \(-0.301764\pi\)
0.583294 + 0.812261i \(0.301764\pi\)
\(180\) 0 0
\(181\) 20006.0 0.0453904 0.0226952 − 0.999742i \(-0.492775\pi\)
0.0226952 + 0.999742i \(0.492775\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −111750. −0.240059
\(186\) 0 0
\(187\) −488488. −1.02153
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 589648. 1.16952 0.584762 − 0.811205i \(-0.301188\pi\)
0.584762 + 0.811205i \(0.301188\pi\)
\(192\) 0 0
\(193\) 701794. 1.35618 0.678089 − 0.734980i \(-0.262809\pi\)
0.678089 + 0.734980i \(0.262809\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 965066. 1.77171 0.885853 − 0.463967i \(-0.153574\pi\)
0.885853 + 0.463967i \(0.153574\pi\)
\(198\) 0 0
\(199\) −298648. −0.534597 −0.267299 − 0.963614i \(-0.586131\pi\)
−0.267299 + 0.963614i \(0.586131\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −153344. −0.261172
\(204\) 0 0
\(205\) −154950. −0.257518
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 710864. 1.12570
\(210\) 0 0
\(211\) −664876. −1.02810 −0.514049 − 0.857761i \(-0.671855\pi\)
−0.514049 + 0.857761i \(0.671855\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 158300. 0.233553
\(216\) 0 0
\(217\) 1.21856e6 1.75670
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.67799e6 2.31104
\(222\) 0 0
\(223\) −66904.0 −0.0900928 −0.0450464 − 0.998985i \(-0.514344\pi\)
−0.0450464 + 0.998985i \(0.514344\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −170796. −0.219995 −0.109998 − 0.993932i \(-0.535084\pi\)
−0.109998 + 0.993932i \(0.535084\pi\)
\(228\) 0 0
\(229\) 790486. 0.996106 0.498053 − 0.867147i \(-0.334049\pi\)
0.498053 + 0.867147i \(0.334049\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −850026. −1.02575 −0.512876 − 0.858463i \(-0.671420\pi\)
−0.512876 + 0.858463i \(0.671420\pi\)
\(234\) 0 0
\(235\) 373000. 0.440595
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −717840. −0.812892 −0.406446 − 0.913675i \(-0.633232\pi\)
−0.406446 + 0.913675i \(0.633232\pi\)
\(240\) 0 0
\(241\) −1.48987e6 −1.65236 −0.826182 − 0.563403i \(-0.809492\pi\)
−0.826182 + 0.563403i \(0.809492\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 10575.0 0.0112555
\(246\) 0 0
\(247\) −2.44186e6 −2.54671
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −214908. −0.215312 −0.107656 − 0.994188i \(-0.534335\pi\)
−0.107656 + 0.994188i \(0.534335\pi\)
\(252\) 0 0
\(253\) −818048. −0.803484
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 218046. 0.205928 0.102964 − 0.994685i \(-0.467167\pi\)
0.102964 + 0.994685i \(0.467167\pi\)
\(258\) 0 0
\(259\) 572160. 0.529990
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.35077e6 1.20418 0.602090 − 0.798428i \(-0.294335\pi\)
0.602090 + 0.798428i \(0.294335\pi\)
\(264\) 0 0
\(265\) 957750. 0.837794
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.27367e6 1.07319 0.536593 − 0.843841i \(-0.319711\pi\)
0.536593 + 0.843841i \(0.319711\pi\)
\(270\) 0 0
\(271\) 582144. 0.481512 0.240756 − 0.970586i \(-0.422605\pi\)
0.240756 + 0.970586i \(0.422605\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 192500. 0.153497
\(276\) 0 0
\(277\) −88474.0 −0.0692813 −0.0346407 − 0.999400i \(-0.511029\pi\)
−0.0346407 + 0.999400i \(0.511029\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.28212e6 0.968640 0.484320 − 0.874891i \(-0.339067\pi\)
0.484320 + 0.874891i \(0.339067\pi\)
\(282\) 0 0
\(283\) 1.80434e6 1.33922 0.669611 − 0.742712i \(-0.266461\pi\)
0.669611 + 0.742712i \(0.266461\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 793344. 0.568534
\(288\) 0 0
\(289\) 1.09554e6 0.771584
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.25972e6 1.53775 0.768875 − 0.639399i \(-0.220817\pi\)
0.768875 + 0.639399i \(0.220817\pi\)
\(294\) 0 0
\(295\) 289100. 0.193416
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.81005e6 1.81776
\(300\) 0 0
\(301\) −810496. −0.515626
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.20845e6 0.743839
\(306\) 0 0
\(307\) 1.89190e6 1.14565 0.572825 − 0.819677i \(-0.305847\pi\)
0.572825 + 0.819677i \(0.305847\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.69799e6 −1.58176 −0.790878 − 0.611973i \(-0.790376\pi\)
−0.790878 + 0.611973i \(0.790376\pi\)
\(312\) 0 0
\(313\) 858074. 0.495067 0.247533 − 0.968879i \(-0.420380\pi\)
0.247533 + 0.968879i \(0.420380\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.12622e6 −1.74732 −0.873658 − 0.486540i \(-0.838259\pi\)
−0.873658 + 0.486540i \(0.838259\pi\)
\(318\) 0 0
\(319\) −368984. −0.203016
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.66049e6 −1.95224
\(324\) 0 0
\(325\) −661250. −0.347262
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.90976e6 −0.972723
\(330\) 0 0
\(331\) −544404. −0.273119 −0.136559 − 0.990632i \(-0.543604\pi\)
−0.136559 + 0.990632i \(0.543604\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.42430e6 −0.693409
\(336\) 0 0
\(337\) 3.87426e6 1.85829 0.929146 − 0.369714i \(-0.120544\pi\)
0.929146 + 0.369714i \(0.120544\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.93216e6 1.36553
\(342\) 0 0
\(343\) −2.20544e6 −1.01219
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.24771e6 1.44795 0.723975 − 0.689827i \(-0.242313\pi\)
0.723975 + 0.689827i \(0.242313\pi\)
\(348\) 0 0
\(349\) 296238. 0.130190 0.0650949 − 0.997879i \(-0.479265\pi\)
0.0650949 + 0.997879i \(0.479265\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −333026. −0.142246 −0.0711232 − 0.997468i \(-0.522658\pi\)
−0.0711232 + 0.997468i \(0.522658\pi\)
\(354\) 0 0
\(355\) 1.12140e6 0.472269
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.59054e6 −1.06085 −0.530424 − 0.847732i \(-0.677967\pi\)
−0.530424 + 0.847732i \(0.677967\pi\)
\(360\) 0 0
\(361\) 2.85076e6 1.15131
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 486150. 0.191002
\(366\) 0 0
\(367\) 1.21738e6 0.471805 0.235902 − 0.971777i \(-0.424195\pi\)
0.235902 + 0.971777i \(0.424195\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.90368e6 −1.84964
\(372\) 0 0
\(373\) −5.29030e6 −1.96883 −0.984415 − 0.175863i \(-0.943728\pi\)
−0.984415 + 0.175863i \(0.943728\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.26748e6 0.459292
\(378\) 0 0
\(379\) 4.66184e6 1.66709 0.833545 − 0.552452i \(-0.186308\pi\)
0.833545 + 0.552452i \(0.186308\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.69106e6 0.589065 0.294532 − 0.955641i \(-0.404836\pi\)
0.294532 + 0.955641i \(0.404836\pi\)
\(384\) 0 0
\(385\) −985600. −0.338882
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 453738. 0.152031 0.0760153 − 0.997107i \(-0.475780\pi\)
0.0760153 + 0.997107i \(0.475780\pi\)
\(390\) 0 0
\(391\) 4.21242e6 1.39344
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.93320e6 0.623425
\(396\) 0 0
\(397\) −1.39075e6 −0.442868 −0.221434 − 0.975175i \(-0.571074\pi\)
−0.221434 + 0.975175i \(0.571074\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.05224e6 −0.947890 −0.473945 − 0.880554i \(-0.657170\pi\)
−0.473945 + 0.880554i \(0.657170\pi\)
\(402\) 0 0
\(403\) −1.00722e7 −3.08930
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.37676e6 0.411976
\(408\) 0 0
\(409\) 196090. 0.0579625 0.0289813 − 0.999580i \(-0.490774\pi\)
0.0289813 + 0.999580i \(0.490774\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.48019e6 −0.427015
\(414\) 0 0
\(415\) 1.00910e6 0.287617
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.05076e6 1.40547 0.702736 − 0.711451i \(-0.251962\pi\)
0.702736 + 0.711451i \(0.251962\pi\)
\(420\) 0 0
\(421\) −3.95035e6 −1.08625 −0.543125 − 0.839652i \(-0.682759\pi\)
−0.543125 + 0.839652i \(0.682759\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −991250. −0.266202
\(426\) 0 0
\(427\) −6.18726e6 −1.64221
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.43178e6 −1.14917 −0.574585 − 0.818445i \(-0.694837\pi\)
−0.574585 + 0.818445i \(0.694837\pi\)
\(432\) 0 0
\(433\) −5.28638e6 −1.35500 −0.677499 − 0.735523i \(-0.736936\pi\)
−0.677499 + 0.735523i \(0.736936\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.13005e6 −1.53554
\(438\) 0 0
\(439\) 736024. 0.182276 0.0911382 − 0.995838i \(-0.470949\pi\)
0.0911382 + 0.995838i \(0.470949\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 998796. 0.241806 0.120903 − 0.992664i \(-0.461421\pi\)
0.120903 + 0.992664i \(0.461421\pi\)
\(444\) 0 0
\(445\) 892650. 0.213689
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.97088e6 −0.695456 −0.347728 − 0.937595i \(-0.613047\pi\)
−0.347728 + 0.937595i \(0.613047\pi\)
\(450\) 0 0
\(451\) 1.90898e6 0.441938
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.38560e6 0.766668
\(456\) 0 0
\(457\) −252950. −0.0566558 −0.0283279 − 0.999599i \(-0.509018\pi\)
−0.0283279 + 0.999599i \(0.509018\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.37328e6 0.520112 0.260056 − 0.965594i \(-0.416259\pi\)
0.260056 + 0.965594i \(0.416259\pi\)
\(462\) 0 0
\(463\) −5.89783e6 −1.27862 −0.639308 − 0.768951i \(-0.720779\pi\)
−0.639308 + 0.768951i \(0.720779\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.27136e6 −0.481940 −0.240970 − 0.970533i \(-0.577466\pi\)
−0.240970 + 0.970533i \(0.577466\pi\)
\(468\) 0 0
\(469\) 7.29242e6 1.53087
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.95026e6 −0.400810
\(474\) 0 0
\(475\) 1.44250e6 0.293347
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.30637e6 1.85328 0.926641 − 0.375948i \(-0.122683\pi\)
0.926641 + 0.375948i \(0.122683\pi\)
\(480\) 0 0
\(481\) −4.72926e6 −0.932031
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.42555e6 0.468226
\(486\) 0 0
\(487\) −2.09274e6 −0.399845 −0.199923 − 0.979812i \(-0.564069\pi\)
−0.199923 + 0.979812i \(0.564069\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.92088e6 −0.921168 −0.460584 − 0.887616i \(-0.652360\pi\)
−0.460584 + 0.887616i \(0.652360\pi\)
\(492\) 0 0
\(493\) 1.90003e6 0.352081
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.74157e6 −1.04265
\(498\) 0 0
\(499\) 3.84266e6 0.690845 0.345422 − 0.938447i \(-0.387736\pi\)
0.345422 + 0.938447i \(0.387736\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.89398e6 1.39116 0.695579 − 0.718450i \(-0.255148\pi\)
0.695579 + 0.718450i \(0.255148\pi\)
\(504\) 0 0
\(505\) −3.09225e6 −0.539568
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.46862e6 −0.593420 −0.296710 − 0.954968i \(-0.595890\pi\)
−0.296710 + 0.954968i \(0.595890\pi\)
\(510\) 0 0
\(511\) −2.48909e6 −0.421685
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.51720e6 −0.252072
\(516\) 0 0
\(517\) −4.59536e6 −0.756124
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.01356e7 −1.63589 −0.817947 − 0.575294i \(-0.804888\pi\)
−0.817947 + 0.575294i \(0.804888\pi\)
\(522\) 0 0
\(523\) 9.47760e6 1.51511 0.757555 − 0.652771i \(-0.226394\pi\)
0.757555 + 0.652771i \(0.226394\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.50987e7 −2.36817
\(528\) 0 0
\(529\) 617993. 0.0960162
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.55748e6 −0.999814
\(534\) 0 0
\(535\) −873900. −0.132001
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −130284. −0.0193161
\(540\) 0 0
\(541\) −3.44117e6 −0.505490 −0.252745 − 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.27765e6 0.184256
\(546\) 0 0
\(547\) 1.53950e6 0.219994 0.109997 − 0.993932i \(-0.464916\pi\)
0.109997 + 0.993932i \(0.464916\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.76498e6 −0.387984
\(552\) 0 0
\(553\) −9.89798e6 −1.37637
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.61360e6 0.630089 0.315045 − 0.949077i \(-0.397980\pi\)
0.315045 + 0.949077i \(0.397980\pi\)
\(558\) 0 0
\(559\) 6.69926e6 0.906770
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 723956. 0.0962590 0.0481295 − 0.998841i \(-0.484674\pi\)
0.0481295 + 0.998841i \(0.484674\pi\)
\(564\) 0 0
\(565\) 1.17405e6 0.154727
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.12650e6 1.18174 0.590872 − 0.806765i \(-0.298784\pi\)
0.590872 + 0.806765i \(0.298784\pi\)
\(570\) 0 0
\(571\) 8.25008e6 1.05893 0.529466 − 0.848331i \(-0.322393\pi\)
0.529466 + 0.848331i \(0.322393\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.66000e6 −0.209382
\(576\) 0 0
\(577\) 4.72551e6 0.590893 0.295446 − 0.955359i \(-0.404532\pi\)
0.295446 + 0.955359i \(0.404532\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.16659e6 −0.634986
\(582\) 0 0
\(583\) −1.17995e7 −1.43778
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.49064e6 0.298342 0.149171 − 0.988811i \(-0.452339\pi\)
0.149171 + 0.988811i \(0.452339\pi\)
\(588\) 0 0
\(589\) 2.19722e7 2.60966
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.03398e7 −1.20747 −0.603733 − 0.797186i \(-0.706321\pi\)
−0.603733 + 0.797186i \(0.706321\pi\)
\(594\) 0 0
\(595\) 5.07520e6 0.587707
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.93142e6 −0.789323 −0.394662 − 0.918827i \(-0.629138\pi\)
−0.394662 + 0.918827i \(0.629138\pi\)
\(600\) 0 0
\(601\) −9.82823e6 −1.10991 −0.554957 − 0.831879i \(-0.687265\pi\)
−0.554957 + 0.831879i \(0.687265\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.65468e6 0.183791
\(606\) 0 0
\(607\) 9.05273e6 0.997258 0.498629 − 0.866815i \(-0.333837\pi\)
0.498629 + 0.866815i \(0.333837\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.57854e7 1.71061
\(612\) 0 0
\(613\) −1.49035e7 −1.60190 −0.800951 − 0.598730i \(-0.795672\pi\)
−0.800951 + 0.598730i \(0.795672\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.23669e7 1.30782 0.653908 − 0.756574i \(-0.273128\pi\)
0.653908 + 0.756574i \(0.273128\pi\)
\(618\) 0 0
\(619\) 1.09991e7 1.15380 0.576900 − 0.816815i \(-0.304262\pi\)
0.576900 + 0.816815i \(0.304262\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.57037e6 −0.471771
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.08942e6 −0.714470
\(630\) 0 0
\(631\) −1.45420e7 −1.45396 −0.726979 − 0.686660i \(-0.759076\pi\)
−0.726979 + 0.686660i \(0.759076\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.64420e6 0.555480
\(636\) 0 0
\(637\) 447534. 0.0436996
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.98756e7 1.91062 0.955311 − 0.295603i \(-0.0955204\pi\)
0.955311 + 0.295603i \(0.0955204\pi\)
\(642\) 0 0
\(643\) 1.90161e7 1.81382 0.906911 − 0.421323i \(-0.138434\pi\)
0.906911 + 0.421323i \(0.138434\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.40701e6 0.507804 0.253902 − 0.967230i \(-0.418286\pi\)
0.253902 + 0.967230i \(0.418286\pi\)
\(648\) 0 0
\(649\) −3.56171e6 −0.331930
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.43171e6 0.223167 0.111583 − 0.993755i \(-0.464408\pi\)
0.111583 + 0.993755i \(0.464408\pi\)
\(654\) 0 0
\(655\) 1.17930e6 0.107404
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.26119e7 −1.13128 −0.565638 − 0.824654i \(-0.691370\pi\)
−0.565638 + 0.824654i \(0.691370\pi\)
\(660\) 0 0
\(661\) 1.78619e7 1.59010 0.795048 − 0.606547i \(-0.207446\pi\)
0.795048 + 0.606547i \(0.207446\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.38560e6 −0.647637
\(666\) 0 0
\(667\) 3.18189e6 0.276930
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.48881e7 −1.27654
\(672\) 0 0
\(673\) −1.96383e7 −1.67134 −0.835671 − 0.549230i \(-0.814921\pi\)
−0.835671 + 0.549230i \(0.814921\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4.87663e6 −0.408929 −0.204465 − 0.978874i \(-0.565545\pi\)
−0.204465 + 0.978874i \(0.565545\pi\)
\(678\) 0 0
\(679\) −1.24188e7 −1.03373
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.58065e7 1.29653 0.648265 − 0.761414i \(-0.275495\pi\)
0.648265 + 0.761414i \(0.275495\pi\)
\(684\) 0 0
\(685\) 8.72425e6 0.710398
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.05320e7 3.25274
\(690\) 0 0
\(691\) −3.23057e6 −0.257386 −0.128693 − 0.991685i \(-0.541078\pi\)
−0.128693 + 0.991685i \(0.541078\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.80490e6 0.298800
\(696\) 0 0
\(697\) −9.83003e6 −0.766431
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.04128e7 0.800338 0.400169 − 0.916441i \(-0.368951\pi\)
0.400169 + 0.916441i \(0.368951\pi\)
\(702\) 0 0
\(703\) 1.03168e7 0.787327
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.58323e7 1.19123
\(708\) 0 0
\(709\) −2.52484e7 −1.88633 −0.943166 − 0.332322i \(-0.892168\pi\)
−0.943166 + 0.332322i \(0.892168\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.52851e7 −1.86269
\(714\) 0 0
\(715\) 8.14660e6 0.595952
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.81508e7 1.30940 0.654702 − 0.755887i \(-0.272794\pi\)
0.654702 + 0.755887i \(0.272794\pi\)
\(720\) 0 0
\(721\) 7.76806e6 0.556512
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −748750. −0.0529044
\(726\) 0 0
\(727\) −1.51391e7 −1.06234 −0.531171 − 0.847264i \(-0.678248\pi\)
−0.531171 + 0.847264i \(0.678248\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.00426e7 0.695105
\(732\) 0 0
\(733\) −1.14297e7 −0.785732 −0.392866 − 0.919596i \(-0.628516\pi\)
−0.392866 + 0.919596i \(0.628516\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.75474e7 1.18999
\(738\) 0 0
\(739\) 1.69375e7 1.14087 0.570436 − 0.821342i \(-0.306774\pi\)
0.570436 + 0.821342i \(0.306774\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.03496e6 −0.334599 −0.167299 − 0.985906i \(-0.553505\pi\)
−0.167299 + 0.985906i \(0.553505\pi\)
\(744\) 0 0
\(745\) −1.15105e6 −0.0759807
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.47437e6 0.291425
\(750\) 0 0
\(751\) −1.21298e7 −0.784790 −0.392395 − 0.919797i \(-0.628353\pi\)
−0.392395 + 0.919797i \(0.628353\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −43400.0 −0.00277091
\(756\) 0 0
\(757\) 175238. 0.0111145 0.00555723 − 0.999985i \(-0.498231\pi\)
0.00555723 + 0.999985i \(0.498231\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.95274e6 0.310016 0.155008 − 0.987913i \(-0.450460\pi\)
0.155008 + 0.987913i \(0.450460\pi\)
\(762\) 0 0
\(763\) −6.54157e6 −0.406790
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.22347e7 0.750940
\(768\) 0 0
\(769\) 2.10466e7 1.28341 0.641706 − 0.766951i \(-0.278227\pi\)
0.641706 + 0.766951i \(0.278227\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.06401e7 −0.640468 −0.320234 − 0.947338i \(-0.603762\pi\)
−0.320234 + 0.947338i \(0.603762\pi\)
\(774\) 0 0
\(775\) 5.95000e6 0.355847
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.43050e7 0.844586
\(780\) 0 0
\(781\) −1.38156e7 −0.810483
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.49885e6 0.0868129
\(786\) 0 0
\(787\) 1.96691e7 1.13200 0.566000 − 0.824405i \(-0.308490\pi\)
0.566000 + 0.824405i \(0.308490\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.01114e6 −0.341598
\(792\) 0 0
\(793\) 5.11416e7 2.88796
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.13227e6 −0.174668 −0.0873340 − 0.996179i \(-0.527835\pi\)
−0.0873340 + 0.996179i \(0.527835\pi\)
\(798\) 0 0
\(799\) 2.36631e7 1.31131
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.98937e6 −0.327787
\(804\) 0 0
\(805\) 8.49920e6 0.462262
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.24482e7 0.668705 0.334353 − 0.942448i \(-0.391482\pi\)
0.334353 + 0.942448i \(0.391482\pi\)
\(810\) 0 0
\(811\) −1.85080e7 −0.988114 −0.494057 − 0.869430i \(-0.664487\pi\)
−0.494057 + 0.869430i \(0.664487\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.68410e6 0.247020
\(816\) 0 0
\(817\) −1.46143e7 −0.765987
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.69574e7 0.878012 0.439006 − 0.898484i \(-0.355331\pi\)
0.439006 + 0.898484i \(0.355331\pi\)
\(822\) 0 0
\(823\) −7.58470e6 −0.390336 −0.195168 − 0.980770i \(-0.562525\pi\)
−0.195168 + 0.980770i \(0.562525\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.55414e7 −1.80705 −0.903527 − 0.428530i \(-0.859031\pi\)
−0.903527 + 0.428530i \(0.859031\pi\)
\(828\) 0 0
\(829\) 2.32685e7 1.17593 0.587966 − 0.808885i \(-0.299929\pi\)
0.587966 + 0.808885i \(0.299929\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 670878. 0.0334989
\(834\) 0 0
\(835\) −2.73120e6 −0.135562
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −9.86074e6 −0.483621 −0.241810 − 0.970324i \(-0.577741\pi\)
−0.241810 + 0.970324i \(0.577741\pi\)
\(840\) 0 0
\(841\) −1.90759e7 −0.930028
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.87018e7 −0.901034
\(846\) 0 0
\(847\) −8.47194e6 −0.405765
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.18723e7 −0.561968
\(852\) 0 0
\(853\) 1.68084e7 0.790958 0.395479 − 0.918475i \(-0.370579\pi\)
0.395479 + 0.918475i \(0.370579\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.23125e7 1.50286 0.751429 − 0.659814i \(-0.229365\pi\)
0.751429 + 0.659814i \(0.229365\pi\)
\(858\) 0 0
\(859\) −2.62964e7 −1.21594 −0.607971 − 0.793959i \(-0.708016\pi\)
−0.607971 + 0.793959i \(0.708016\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.76512e7 −0.806766 −0.403383 − 0.915031i \(-0.632166\pi\)
−0.403383 + 0.915031i \(0.632166\pi\)
\(864\) 0 0
\(865\) 1.83736e7 0.834935
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.38170e7 −1.06989
\(870\) 0 0
\(871\) −6.02764e7 −2.69217
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.00000e6 −0.0883100
\(876\) 0 0
\(877\) 2.18595e7 0.959712 0.479856 − 0.877347i \(-0.340689\pi\)
0.479856 + 0.877347i \(0.340689\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.51282e7 −0.656670 −0.328335 − 0.944561i \(-0.606487\pi\)
−0.328335 + 0.944561i \(0.606487\pi\)
\(882\) 0 0
\(883\) 2.55738e7 1.10381 0.551903 − 0.833908i \(-0.313902\pi\)
0.551903 + 0.833908i \(0.313902\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.08945e7 −0.891709 −0.445855 − 0.895105i \(-0.647100\pi\)
−0.445855 + 0.895105i \(0.647100\pi\)
\(888\) 0 0
\(889\) −2.88983e7 −1.22636
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.44354e7 −1.44503
\(894\) 0 0
\(895\) −1.25023e7 −0.521714
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.14050e7 −0.470646
\(900\) 0 0
\(901\) 6.07597e7 2.49347
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −500150. −0.0202992
\(906\) 0 0
\(907\) −2.74921e7 −1.10966 −0.554830 − 0.831964i \(-0.687217\pi\)
−0.554830 + 0.831964i \(0.687217\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 893792. 0.0356813 0.0178406 − 0.999841i \(-0.494321\pi\)
0.0178406 + 0.999841i \(0.494321\pi\)
\(912\) 0 0
\(913\) −1.24321e7 −0.493592
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −6.03802e6 −0.237121
\(918\) 0 0
\(919\) 1.48402e7 0.579631 0.289815 − 0.957083i \(-0.406406\pi\)
0.289815 + 0.957083i \(0.406406\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.74576e7 1.83359
\(924\) 0 0
\(925\) 2.79375e6 0.107358
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.62858e7 −0.999268 −0.499634 − 0.866237i \(-0.666532\pi\)
−0.499634 + 0.866237i \(0.666532\pi\)
\(930\) 0 0
\(931\) −976284. −0.0369149
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.22122e7 0.456841
\(936\) 0 0
\(937\) 1.40620e7 0.523236 0.261618 − 0.965171i \(-0.415744\pi\)
0.261618 + 0.965171i \(0.415744\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.08818e7 0.400614 0.200307 − 0.979733i \(-0.435806\pi\)
0.200307 + 0.979733i \(0.435806\pi\)
\(942\) 0 0
\(943\) −1.64619e7 −0.602838
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.18288e7 0.428614 0.214307 − 0.976766i \(-0.431251\pi\)
0.214307 + 0.976766i \(0.431251\pi\)
\(948\) 0 0
\(949\) 2.05739e7 0.741567
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.19494e7 −0.426200 −0.213100 − 0.977030i \(-0.568356\pi\)
−0.213100 + 0.977030i \(0.568356\pi\)
\(954\) 0 0
\(955\) −1.47412e7 −0.523027
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.46682e7 −1.56838
\(960\) 0 0
\(961\) 6.20012e7 2.16567
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.75448e7 −0.606501
\(966\) 0 0
\(967\) −3.82902e7 −1.31680 −0.658402 − 0.752666i \(-0.728767\pi\)
−0.658402 + 0.752666i \(0.728767\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 3.26221e7 1.11036 0.555180 − 0.831730i \(-0.312649\pi\)
0.555180 + 0.831730i \(0.312649\pi\)
\(972\) 0 0
\(973\) −1.94811e7 −0.659677
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.44271e7 −0.818719 −0.409359 − 0.912373i \(-0.634248\pi\)
−0.409359 + 0.912373i \(0.634248\pi\)
\(978\) 0 0
\(979\) −1.09974e7 −0.366720
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.94363e7 −0.641547 −0.320774 − 0.947156i \(-0.603943\pi\)
−0.320774 + 0.947156i \(0.603943\pi\)
\(984\) 0 0
\(985\) −2.41266e7 −0.792331
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.68178e7 0.546737
\(990\) 0 0
\(991\) −1.69849e7 −0.549388 −0.274694 − 0.961532i \(-0.588577\pi\)
−0.274694 + 0.961532i \(0.588577\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 7.46620e6 0.239079
\(996\) 0 0
\(997\) −3.71296e7 −1.18299 −0.591496 − 0.806308i \(-0.701463\pi\)
−0.591496 + 0.806308i \(0.701463\pi\)
\(998\) 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 360.6.a.d.1.1 1
3.2 odd 2 120.6.a.d.1.1 ✓ 1
4.3 odd 2 720.6.a.b.1.1 1
12.11 even 2 240.6.a.l.1.1 1
15.2 even 4 600.6.f.c.49.2 2
15.8 even 4 600.6.f.c.49.1 2
15.14 odd 2 600.6.a.e.1.1 1
24.5 odd 2 960.6.a.s.1.1 1
24.11 even 2 960.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.6.a.d.1.1 ✓ 1 3.2 odd 2
240.6.a.l.1.1 1 12.11 even 2
360.6.a.d.1.1 1 1.1 even 1 trivial
600.6.a.e.1.1 1 15.14 odd 2
600.6.f.c.49.1 2 15.8 even 4
600.6.f.c.49.2 2 15.2 even 4
720.6.a.b.1.1 1 4.3 odd 2
960.6.a.b.1.1 1 24.11 even 2
960.6.a.s.1.1 1 24.5 odd 2