Properties

Label 392.6.a.m.1.6
Level $392$
Weight $6$
Character 392.1
Self dual yes
Analytic conductor $62.870$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,6,Mod(1,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, 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("392.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.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: \(62.8704573667\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 328x^{4} - 1328x^{3} + 25933x^{2} + 205840x + 390334 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(15.8064\) of defining polynomial
Character \(\chi\) \(=\) 392.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+17.5252 q^{3} -11.0064 q^{5} +64.1343 q^{9} +O(q^{10})\) \(q+17.5252 q^{3} -11.0064 q^{5} +64.1343 q^{9} -95.0461 q^{11} -157.485 q^{13} -192.890 q^{15} +100.530 q^{17} -664.804 q^{19} +2141.54 q^{23} -3003.86 q^{25} -3134.67 q^{27} -3050.77 q^{29} -3084.25 q^{31} -1665.71 q^{33} +11872.7 q^{37} -2759.96 q^{39} -4013.50 q^{41} -10366.6 q^{43} -705.888 q^{45} -22647.4 q^{47} +1761.81 q^{51} -27712.6 q^{53} +1046.12 q^{55} -11650.9 q^{57} -23383.9 q^{59} +10242.6 q^{61} +1733.34 q^{65} +6555.18 q^{67} +37531.0 q^{69} -21269.5 q^{71} -313.509 q^{73} -52643.4 q^{75} -59231.2 q^{79} -70520.4 q^{81} +107561. q^{83} -1106.47 q^{85} -53465.4 q^{87} +88357.3 q^{89} -54052.3 q^{93} +7317.11 q^{95} +164187. q^{97} -6095.71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 122 q^{9} + 248 q^{11} - 376 q^{15} - 2904 q^{23} + 1510 q^{25} - 408 q^{29} - 18648 q^{37} - 15240 q^{39} - 10584 q^{43} + 3016 q^{51} - 66772 q^{53} - 56264 q^{57} - 55316 q^{65} - 169632 q^{67} - 54880 q^{71} + 50576 q^{79} - 270194 q^{81} - 406076 q^{85} - 164944 q^{93} - 551912 q^{95} - 173512 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 17.5252 1.12425 0.562123 0.827054i \(-0.309985\pi\)
0.562123 + 0.827054i \(0.309985\pi\)
\(4\) 0 0
\(5\) −11.0064 −0.196889 −0.0984443 0.995143i \(-0.531387\pi\)
−0.0984443 + 0.995143i \(0.531387\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 64.1343 0.263927
\(10\) 0 0
\(11\) −95.0461 −0.236839 −0.118419 0.992964i \(-0.537783\pi\)
−0.118419 + 0.992964i \(0.537783\pi\)
\(12\) 0 0
\(13\) −157.485 −0.258452 −0.129226 0.991615i \(-0.541249\pi\)
−0.129226 + 0.991615i \(0.541249\pi\)
\(14\) 0 0
\(15\) −192.890 −0.221351
\(16\) 0 0
\(17\) 100.530 0.0843669 0.0421834 0.999110i \(-0.486569\pi\)
0.0421834 + 0.999110i \(0.486569\pi\)
\(18\) 0 0
\(19\) −664.804 −0.422483 −0.211242 0.977434i \(-0.567751\pi\)
−0.211242 + 0.977434i \(0.567751\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2141.54 0.844125 0.422062 0.906567i \(-0.361306\pi\)
0.422062 + 0.906567i \(0.361306\pi\)
\(24\) 0 0
\(25\) −3003.86 −0.961235
\(26\) 0 0
\(27\) −3134.67 −0.827526
\(28\) 0 0
\(29\) −3050.77 −0.673619 −0.336809 0.941573i \(-0.609348\pi\)
−0.336809 + 0.941573i \(0.609348\pi\)
\(30\) 0 0
\(31\) −3084.25 −0.576429 −0.288215 0.957566i \(-0.593062\pi\)
−0.288215 + 0.957566i \(0.593062\pi\)
\(32\) 0 0
\(33\) −1665.71 −0.266265
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11872.7 1.42576 0.712879 0.701287i \(-0.247391\pi\)
0.712879 + 0.701287i \(0.247391\pi\)
\(38\) 0 0
\(39\) −2759.96 −0.290564
\(40\) 0 0
\(41\) −4013.50 −0.372875 −0.186438 0.982467i \(-0.559694\pi\)
−0.186438 + 0.982467i \(0.559694\pi\)
\(42\) 0 0
\(43\) −10366.6 −0.854995 −0.427497 0.904017i \(-0.640605\pi\)
−0.427497 + 0.904017i \(0.640605\pi\)
\(44\) 0 0
\(45\) −705.888 −0.0519642
\(46\) 0 0
\(47\) −22647.4 −1.49546 −0.747729 0.664004i \(-0.768856\pi\)
−0.747729 + 0.664004i \(0.768856\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1761.81 0.0948491
\(52\) 0 0
\(53\) −27712.6 −1.35515 −0.677576 0.735453i \(-0.736969\pi\)
−0.677576 + 0.735453i \(0.736969\pi\)
\(54\) 0 0
\(55\) 1046.12 0.0466308
\(56\) 0 0
\(57\) −11650.9 −0.474975
\(58\) 0 0
\(59\) −23383.9 −0.874553 −0.437276 0.899327i \(-0.644057\pi\)
−0.437276 + 0.899327i \(0.644057\pi\)
\(60\) 0 0
\(61\) 10242.6 0.352440 0.176220 0.984351i \(-0.443613\pi\)
0.176220 + 0.984351i \(0.443613\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1733.34 0.0508863
\(66\) 0 0
\(67\) 6555.18 0.178401 0.0892006 0.996014i \(-0.471569\pi\)
0.0892006 + 0.996014i \(0.471569\pi\)
\(68\) 0 0
\(69\) 37531.0 0.949003
\(70\) 0 0
\(71\) −21269.5 −0.500739 −0.250370 0.968150i \(-0.580552\pi\)
−0.250370 + 0.968150i \(0.580552\pi\)
\(72\) 0 0
\(73\) −313.509 −0.00688562 −0.00344281 0.999994i \(-0.501096\pi\)
−0.00344281 + 0.999994i \(0.501096\pi\)
\(74\) 0 0
\(75\) −52643.4 −1.08066
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −59231.2 −1.06778 −0.533891 0.845553i \(-0.679271\pi\)
−0.533891 + 0.845553i \(0.679271\pi\)
\(80\) 0 0
\(81\) −70520.4 −1.19427
\(82\) 0 0
\(83\) 107561. 1.71380 0.856901 0.515481i \(-0.172387\pi\)
0.856901 + 0.515481i \(0.172387\pi\)
\(84\) 0 0
\(85\) −1106.47 −0.0166109
\(86\) 0 0
\(87\) −53465.4 −0.757312
\(88\) 0 0
\(89\) 88357.3 1.18241 0.591204 0.806522i \(-0.298653\pi\)
0.591204 + 0.806522i \(0.298653\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −54052.3 −0.648048
\(94\) 0 0
\(95\) 7317.11 0.0831822
\(96\) 0 0
\(97\) 164187. 1.77178 0.885891 0.463894i \(-0.153548\pi\)
0.885891 + 0.463894i \(0.153548\pi\)
\(98\) 0 0
\(99\) −6095.71 −0.0625081
\(100\) 0 0
\(101\) −29974.5 −0.292381 −0.146190 0.989256i \(-0.546701\pi\)
−0.146190 + 0.989256i \(0.546701\pi\)
\(102\) 0 0
\(103\) −81692.8 −0.758736 −0.379368 0.925246i \(-0.623859\pi\)
−0.379368 + 0.925246i \(0.623859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −56710.6 −0.478856 −0.239428 0.970914i \(-0.576960\pi\)
−0.239428 + 0.970914i \(0.576960\pi\)
\(108\) 0 0
\(109\) −185773. −1.49767 −0.748837 0.662754i \(-0.769387\pi\)
−0.748837 + 0.662754i \(0.769387\pi\)
\(110\) 0 0
\(111\) 208072. 1.60290
\(112\) 0 0
\(113\) −47906.7 −0.352940 −0.176470 0.984306i \(-0.556468\pi\)
−0.176470 + 0.984306i \(0.556468\pi\)
\(114\) 0 0
\(115\) −23570.7 −0.166199
\(116\) 0 0
\(117\) −10100.2 −0.0682125
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −152017. −0.943907
\(122\) 0 0
\(123\) −70337.5 −0.419203
\(124\) 0 0
\(125\) 67456.7 0.386145
\(126\) 0 0
\(127\) −30596.7 −0.168331 −0.0841656 0.996452i \(-0.526822\pi\)
−0.0841656 + 0.996452i \(0.526822\pi\)
\(128\) 0 0
\(129\) −181676. −0.961224
\(130\) 0 0
\(131\) −138321. −0.704223 −0.352111 0.935958i \(-0.614536\pi\)
−0.352111 + 0.935958i \(0.614536\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 34501.4 0.162931
\(136\) 0 0
\(137\) −147583. −0.671793 −0.335897 0.941899i \(-0.609039\pi\)
−0.335897 + 0.941899i \(0.609039\pi\)
\(138\) 0 0
\(139\) 167389. 0.734834 0.367417 0.930056i \(-0.380242\pi\)
0.367417 + 0.930056i \(0.380242\pi\)
\(140\) 0 0
\(141\) −396902. −1.68126
\(142\) 0 0
\(143\) 14968.3 0.0612115
\(144\) 0 0
\(145\) 33578.0 0.132628
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 149761. 0.552627 0.276314 0.961068i \(-0.410887\pi\)
0.276314 + 0.961068i \(0.410887\pi\)
\(150\) 0 0
\(151\) −320225. −1.14291 −0.571456 0.820633i \(-0.693621\pi\)
−0.571456 + 0.820633i \(0.693621\pi\)
\(152\) 0 0
\(153\) 6447.40 0.0222667
\(154\) 0 0
\(155\) 33946.6 0.113492
\(156\) 0 0
\(157\) −335799. −1.08725 −0.543626 0.839328i \(-0.682949\pi\)
−0.543626 + 0.839328i \(0.682949\pi\)
\(158\) 0 0
\(159\) −485670. −1.52352
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 494956. 1.45914 0.729571 0.683905i \(-0.239720\pi\)
0.729571 + 0.683905i \(0.239720\pi\)
\(164\) 0 0
\(165\) 18333.4 0.0524245
\(166\) 0 0
\(167\) 162081. 0.449717 0.224859 0.974391i \(-0.427808\pi\)
0.224859 + 0.974391i \(0.427808\pi\)
\(168\) 0 0
\(169\) −346492. −0.933202
\(170\) 0 0
\(171\) −42636.7 −0.111505
\(172\) 0 0
\(173\) −162681. −0.413257 −0.206629 0.978419i \(-0.566249\pi\)
−0.206629 + 0.978419i \(0.566249\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −409808. −0.983212
\(178\) 0 0
\(179\) −461348. −1.07621 −0.538104 0.842879i \(-0.680859\pi\)
−0.538104 + 0.842879i \(0.680859\pi\)
\(180\) 0 0
\(181\) −603891. −1.37013 −0.685065 0.728482i \(-0.740226\pi\)
−0.685065 + 0.728482i \(0.740226\pi\)
\(182\) 0 0
\(183\) 179504. 0.396229
\(184\) 0 0
\(185\) −130676. −0.280716
\(186\) 0 0
\(187\) −9554.95 −0.0199813
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 560655. 1.11202 0.556010 0.831176i \(-0.312332\pi\)
0.556010 + 0.831176i \(0.312332\pi\)
\(192\) 0 0
\(193\) 165122. 0.319089 0.159544 0.987191i \(-0.448997\pi\)
0.159544 + 0.987191i \(0.448997\pi\)
\(194\) 0 0
\(195\) 30377.2 0.0572087
\(196\) 0 0
\(197\) −678116. −1.24491 −0.622456 0.782655i \(-0.713865\pi\)
−0.622456 + 0.782655i \(0.713865\pi\)
\(198\) 0 0
\(199\) 370360. 0.662965 0.331483 0.943461i \(-0.392451\pi\)
0.331483 + 0.943461i \(0.392451\pi\)
\(200\) 0 0
\(201\) 114881. 0.200567
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 44174.2 0.0734148
\(206\) 0 0
\(207\) 137346. 0.222787
\(208\) 0 0
\(209\) 63187.0 0.100060
\(210\) 0 0
\(211\) 884876. 1.36828 0.684142 0.729349i \(-0.260177\pi\)
0.684142 + 0.729349i \(0.260177\pi\)
\(212\) 0 0
\(213\) −372754. −0.562954
\(214\) 0 0
\(215\) 114099. 0.168339
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5494.32 −0.00774112
\(220\) 0 0
\(221\) −15831.9 −0.0218048
\(222\) 0 0
\(223\) 307029. 0.413444 0.206722 0.978400i \(-0.433720\pi\)
0.206722 + 0.978400i \(0.433720\pi\)
\(224\) 0 0
\(225\) −192650. −0.253696
\(226\) 0 0
\(227\) 1.05427e6 1.35797 0.678983 0.734154i \(-0.262421\pi\)
0.678983 + 0.734154i \(0.262421\pi\)
\(228\) 0 0
\(229\) 768119. 0.967921 0.483960 0.875090i \(-0.339198\pi\)
0.483960 + 0.875090i \(0.339198\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.16012e6 −1.39995 −0.699976 0.714166i \(-0.746806\pi\)
−0.699976 + 0.714166i \(0.746806\pi\)
\(234\) 0 0
\(235\) 249267. 0.294439
\(236\) 0 0
\(237\) −1.03804e6 −1.20045
\(238\) 0 0
\(239\) 1.14943e6 1.30163 0.650816 0.759235i \(-0.274427\pi\)
0.650816 + 0.759235i \(0.274427\pi\)
\(240\) 0 0
\(241\) 112291. 0.124538 0.0622691 0.998059i \(-0.480166\pi\)
0.0622691 + 0.998059i \(0.480166\pi\)
\(242\) 0 0
\(243\) −474164. −0.515125
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 104697. 0.109192
\(248\) 0 0
\(249\) 1.88504e6 1.92673
\(250\) 0 0
\(251\) 214195. 0.214598 0.107299 0.994227i \(-0.465780\pi\)
0.107299 + 0.994227i \(0.465780\pi\)
\(252\) 0 0
\(253\) −203545. −0.199921
\(254\) 0 0
\(255\) −19391.2 −0.0186747
\(256\) 0 0
\(257\) 2.03227e6 1.91932 0.959662 0.281156i \(-0.0907177\pi\)
0.959662 + 0.281156i \(0.0907177\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −195659. −0.177786
\(262\) 0 0
\(263\) 1.09547e6 0.976584 0.488292 0.872680i \(-0.337620\pi\)
0.488292 + 0.872680i \(0.337620\pi\)
\(264\) 0 0
\(265\) 305016. 0.266814
\(266\) 0 0
\(267\) 1.54848e6 1.32932
\(268\) 0 0
\(269\) 311944. 0.262843 0.131421 0.991327i \(-0.458046\pi\)
0.131421 + 0.991327i \(0.458046\pi\)
\(270\) 0 0
\(271\) 67932.4 0.0561893 0.0280947 0.999605i \(-0.491056\pi\)
0.0280947 + 0.999605i \(0.491056\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 285505. 0.227658
\(276\) 0 0
\(277\) −498271. −0.390181 −0.195090 0.980785i \(-0.562500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(278\) 0 0
\(279\) −197807. −0.152135
\(280\) 0 0
\(281\) 1.47068e6 1.11110 0.555549 0.831484i \(-0.312508\pi\)
0.555549 + 0.831484i \(0.312508\pi\)
\(282\) 0 0
\(283\) 1.34284e6 0.996682 0.498341 0.866981i \(-0.333943\pi\)
0.498341 + 0.866981i \(0.333943\pi\)
\(284\) 0 0
\(285\) 128234. 0.0935172
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.40975e6 −0.992882
\(290\) 0 0
\(291\) 2.87742e6 1.99192
\(292\) 0 0
\(293\) −2.20931e6 −1.50345 −0.751724 0.659478i \(-0.770777\pi\)
−0.751724 + 0.659478i \(0.770777\pi\)
\(294\) 0 0
\(295\) 257372. 0.172189
\(296\) 0 0
\(297\) 297938. 0.195990
\(298\) 0 0
\(299\) −337260. −0.218166
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −525311. −0.328708
\(304\) 0 0
\(305\) −112734. −0.0693914
\(306\) 0 0
\(307\) −1.47223e6 −0.891516 −0.445758 0.895153i \(-0.647066\pi\)
−0.445758 + 0.895153i \(0.647066\pi\)
\(308\) 0 0
\(309\) −1.43169e6 −0.853005
\(310\) 0 0
\(311\) 687625. 0.403135 0.201568 0.979475i \(-0.435396\pi\)
0.201568 + 0.979475i \(0.435396\pi\)
\(312\) 0 0
\(313\) 3.27656e6 1.89041 0.945206 0.326473i \(-0.105860\pi\)
0.945206 + 0.326473i \(0.105860\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.35932e6 1.31868 0.659338 0.751847i \(-0.270837\pi\)
0.659338 + 0.751847i \(0.270837\pi\)
\(318\) 0 0
\(319\) 289963. 0.159539
\(320\) 0 0
\(321\) −993867. −0.538351
\(322\) 0 0
\(323\) −66832.6 −0.0356436
\(324\) 0 0
\(325\) 473062. 0.248433
\(326\) 0 0
\(327\) −3.25572e6 −1.68375
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.14714e6 0.575502 0.287751 0.957705i \(-0.407092\pi\)
0.287751 + 0.957705i \(0.407092\pi\)
\(332\) 0 0
\(333\) 761449. 0.376296
\(334\) 0 0
\(335\) −72149.0 −0.0351251
\(336\) 0 0
\(337\) 1.34477e6 0.645020 0.322510 0.946566i \(-0.395473\pi\)
0.322510 + 0.946566i \(0.395473\pi\)
\(338\) 0 0
\(339\) −839578. −0.396791
\(340\) 0 0
\(341\) 293146. 0.136521
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −413082. −0.186848
\(346\) 0 0
\(347\) 769358. 0.343008 0.171504 0.985183i \(-0.445137\pi\)
0.171504 + 0.985183i \(0.445137\pi\)
\(348\) 0 0
\(349\) −3.34745e6 −1.47113 −0.735564 0.677455i \(-0.763083\pi\)
−0.735564 + 0.677455i \(0.763083\pi\)
\(350\) 0 0
\(351\) 493662. 0.213876
\(352\) 0 0
\(353\) 1.72600e6 0.737231 0.368615 0.929582i \(-0.379832\pi\)
0.368615 + 0.929582i \(0.379832\pi\)
\(354\) 0 0
\(355\) 234101. 0.0985899
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.25940e6 0.925245 0.462623 0.886555i \(-0.346909\pi\)
0.462623 + 0.886555i \(0.346909\pi\)
\(360\) 0 0
\(361\) −2.03413e6 −0.821508
\(362\) 0 0
\(363\) −2.66414e6 −1.06118
\(364\) 0 0
\(365\) 3450.61 0.00135570
\(366\) 0 0
\(367\) −837273. −0.324490 −0.162245 0.986750i \(-0.551874\pi\)
−0.162245 + 0.986750i \(0.551874\pi\)
\(368\) 0 0
\(369\) −257403. −0.0984118
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3.69908e6 1.37665 0.688323 0.725405i \(-0.258347\pi\)
0.688323 + 0.725405i \(0.258347\pi\)
\(374\) 0 0
\(375\) 1.18220e6 0.434121
\(376\) 0 0
\(377\) 480449. 0.174098
\(378\) 0 0
\(379\) −752171. −0.268979 −0.134490 0.990915i \(-0.542939\pi\)
−0.134490 + 0.990915i \(0.542939\pi\)
\(380\) 0 0
\(381\) −536214. −0.189246
\(382\) 0 0
\(383\) −396510. −0.138120 −0.0690601 0.997613i \(-0.522000\pi\)
−0.0690601 + 0.997613i \(0.522000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −664852. −0.225656
\(388\) 0 0
\(389\) −3.46111e6 −1.15969 −0.579844 0.814727i \(-0.696887\pi\)
−0.579844 + 0.814727i \(0.696887\pi\)
\(390\) 0 0
\(391\) 215288. 0.0712162
\(392\) 0 0
\(393\) −2.42411e6 −0.791719
\(394\) 0 0
\(395\) 651923. 0.210234
\(396\) 0 0
\(397\) 424548. 0.135192 0.0675959 0.997713i \(-0.478467\pi\)
0.0675959 + 0.997713i \(0.478467\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −520438. −0.161625 −0.0808124 0.996729i \(-0.525751\pi\)
−0.0808124 + 0.996729i \(0.525751\pi\)
\(402\) 0 0
\(403\) 485723. 0.148979
\(404\) 0 0
\(405\) 776177. 0.235138
\(406\) 0 0
\(407\) −1.12846e6 −0.337675
\(408\) 0 0
\(409\) −964439. −0.285080 −0.142540 0.989789i \(-0.545527\pi\)
−0.142540 + 0.989789i \(0.545527\pi\)
\(410\) 0 0
\(411\) −2.58643e6 −0.755260
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.18386e6 −0.337428
\(416\) 0 0
\(417\) 2.93353e6 0.826134
\(418\) 0 0
\(419\) 588781. 0.163840 0.0819198 0.996639i \(-0.473895\pi\)
0.0819198 + 0.996639i \(0.473895\pi\)
\(420\) 0 0
\(421\) 29013.6 0.00797804 0.00398902 0.999992i \(-0.498730\pi\)
0.00398902 + 0.999992i \(0.498730\pi\)
\(422\) 0 0
\(423\) −1.45248e6 −0.394692
\(424\) 0 0
\(425\) −301977. −0.0810964
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 262323. 0.0688167
\(430\) 0 0
\(431\) −5.08256e6 −1.31792 −0.658960 0.752178i \(-0.729004\pi\)
−0.658960 + 0.752178i \(0.729004\pi\)
\(432\) 0 0
\(433\) 4.61686e6 1.18339 0.591694 0.806163i \(-0.298460\pi\)
0.591694 + 0.806163i \(0.298460\pi\)
\(434\) 0 0
\(435\) 588462. 0.149106
\(436\) 0 0
\(437\) −1.42370e6 −0.356629
\(438\) 0 0
\(439\) 3.42017e6 0.847005 0.423503 0.905895i \(-0.360800\pi\)
0.423503 + 0.905895i \(0.360800\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −549597. −0.133056 −0.0665281 0.997785i \(-0.521192\pi\)
−0.0665281 + 0.997785i \(0.521192\pi\)
\(444\) 0 0
\(445\) −972496. −0.232803
\(446\) 0 0
\(447\) 2.62459e6 0.621289
\(448\) 0 0
\(449\) 2.98225e6 0.698116 0.349058 0.937101i \(-0.386502\pi\)
0.349058 + 0.937101i \(0.386502\pi\)
\(450\) 0 0
\(451\) 381467. 0.0883112
\(452\) 0 0
\(453\) −5.61202e6 −1.28491
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.65175e6 −1.26588 −0.632939 0.774201i \(-0.718152\pi\)
−0.632939 + 0.774201i \(0.718152\pi\)
\(458\) 0 0
\(459\) −315127. −0.0698158
\(460\) 0 0
\(461\) 3.17668e6 0.696179 0.348089 0.937461i \(-0.386831\pi\)
0.348089 + 0.937461i \(0.386831\pi\)
\(462\) 0 0
\(463\) −5.69966e6 −1.23565 −0.617826 0.786315i \(-0.711987\pi\)
−0.617826 + 0.786315i \(0.711987\pi\)
\(464\) 0 0
\(465\) 594922. 0.127593
\(466\) 0 0
\(467\) 4.63943e6 0.984402 0.492201 0.870481i \(-0.336192\pi\)
0.492201 + 0.870481i \(0.336192\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.88496e6 −1.22234
\(472\) 0 0
\(473\) 985301. 0.202496
\(474\) 0 0
\(475\) 1.99698e6 0.406106
\(476\) 0 0
\(477\) −1.77733e6 −0.357661
\(478\) 0 0
\(479\) −2.20916e6 −0.439934 −0.219967 0.975507i \(-0.570595\pi\)
−0.219967 + 0.975507i \(0.570595\pi\)
\(480\) 0 0
\(481\) −1.86977e6 −0.368490
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.80711e6 −0.348844
\(486\) 0 0
\(487\) −7.82289e6 −1.49467 −0.747334 0.664449i \(-0.768666\pi\)
−0.747334 + 0.664449i \(0.768666\pi\)
\(488\) 0 0
\(489\) 8.67422e6 1.64043
\(490\) 0 0
\(491\) 4.08903e6 0.765449 0.382724 0.923863i \(-0.374986\pi\)
0.382724 + 0.923863i \(0.374986\pi\)
\(492\) 0 0
\(493\) −306693. −0.0568311
\(494\) 0 0
\(495\) 67091.9 0.0123071
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −911248. −0.163827 −0.0819135 0.996639i \(-0.526103\pi\)
−0.0819135 + 0.996639i \(0.526103\pi\)
\(500\) 0 0
\(501\) 2.84050e6 0.505593
\(502\) 0 0
\(503\) 1.10725e7 1.95130 0.975649 0.219336i \(-0.0703890\pi\)
0.975649 + 0.219336i \(0.0703890\pi\)
\(504\) 0 0
\(505\) 329912. 0.0575664
\(506\) 0 0
\(507\) −6.07235e6 −1.04915
\(508\) 0 0
\(509\) −6.80487e6 −1.16419 −0.582097 0.813119i \(-0.697768\pi\)
−0.582097 + 0.813119i \(0.697768\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 2.08394e6 0.349616
\(514\) 0 0
\(515\) 899144. 0.149386
\(516\) 0 0
\(517\) 2.15255e6 0.354182
\(518\) 0 0
\(519\) −2.85102e6 −0.464603
\(520\) 0 0
\(521\) −4.44538e6 −0.717487 −0.358744 0.933436i \(-0.616795\pi\)
−0.358744 + 0.933436i \(0.616795\pi\)
\(522\) 0 0
\(523\) 8.72959e6 1.39553 0.697766 0.716326i \(-0.254178\pi\)
0.697766 + 0.716326i \(0.254178\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −310059. −0.0486315
\(528\) 0 0
\(529\) −1.85015e6 −0.287453
\(530\) 0 0
\(531\) −1.49971e6 −0.230818
\(532\) 0 0
\(533\) 632065. 0.0963703
\(534\) 0 0
\(535\) 624180. 0.0942813
\(536\) 0 0
\(537\) −8.08524e6 −1.20992
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −3.73878e6 −0.549208 −0.274604 0.961557i \(-0.588547\pi\)
−0.274604 + 0.961557i \(0.588547\pi\)
\(542\) 0 0
\(543\) −1.05833e7 −1.54036
\(544\) 0 0
\(545\) 2.04470e6 0.294875
\(546\) 0 0
\(547\) −8.95708e6 −1.27996 −0.639982 0.768390i \(-0.721058\pi\)
−0.639982 + 0.768390i \(0.721058\pi\)
\(548\) 0 0
\(549\) 656901. 0.0930184
\(550\) 0 0
\(551\) 2.02816e6 0.284593
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.29013e6 −0.315593
\(556\) 0 0
\(557\) −3.40749e6 −0.465368 −0.232684 0.972552i \(-0.574751\pi\)
−0.232684 + 0.972552i \(0.574751\pi\)
\(558\) 0 0
\(559\) 1.63257e6 0.220975
\(560\) 0 0
\(561\) −167453. −0.0224639
\(562\) 0 0
\(563\) 7.39433e6 0.983169 0.491584 0.870830i \(-0.336418\pi\)
0.491584 + 0.870830i \(0.336418\pi\)
\(564\) 0 0
\(565\) 527281. 0.0694898
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.39745e6 0.569404 0.284702 0.958616i \(-0.408105\pi\)
0.284702 + 0.958616i \(0.408105\pi\)
\(570\) 0 0
\(571\) −4.11677e6 −0.528405 −0.264202 0.964467i \(-0.585109\pi\)
−0.264202 + 0.964467i \(0.585109\pi\)
\(572\) 0 0
\(573\) 9.82562e6 1.25018
\(574\) 0 0
\(575\) −6.43289e6 −0.811402
\(576\) 0 0
\(577\) −5.12253e6 −0.640538 −0.320269 0.947327i \(-0.603773\pi\)
−0.320269 + 0.947327i \(0.603773\pi\)
\(578\) 0 0
\(579\) 2.89380e6 0.358734
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.63398e6 0.320952
\(584\) 0 0
\(585\) 111167. 0.0134303
\(586\) 0 0
\(587\) −1.04610e7 −1.25308 −0.626538 0.779391i \(-0.715529\pi\)
−0.626538 + 0.779391i \(0.715529\pi\)
\(588\) 0 0
\(589\) 2.05043e6 0.243532
\(590\) 0 0
\(591\) −1.18842e7 −1.39959
\(592\) 0 0
\(593\) −1.38124e7 −1.61300 −0.806498 0.591237i \(-0.798640\pi\)
−0.806498 + 0.591237i \(0.798640\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.49064e6 0.745336
\(598\) 0 0
\(599\) −3.74704e6 −0.426699 −0.213349 0.976976i \(-0.568437\pi\)
−0.213349 + 0.976976i \(0.568437\pi\)
\(600\) 0 0
\(601\) −9.77914e6 −1.10437 −0.552185 0.833722i \(-0.686206\pi\)
−0.552185 + 0.833722i \(0.686206\pi\)
\(602\) 0 0
\(603\) 420412. 0.0470849
\(604\) 0 0
\(605\) 1.67316e6 0.185845
\(606\) 0 0
\(607\) −334361. −0.0368336 −0.0184168 0.999830i \(-0.505863\pi\)
−0.0184168 + 0.999830i \(0.505863\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.56662e6 0.386504
\(612\) 0 0
\(613\) 1.08435e6 0.116551 0.0582756 0.998301i \(-0.481440\pi\)
0.0582756 + 0.998301i \(0.481440\pi\)
\(614\) 0 0
\(615\) 774164. 0.0825363
\(616\) 0 0
\(617\) 7.42021e6 0.784699 0.392350 0.919816i \(-0.371662\pi\)
0.392350 + 0.919816i \(0.371662\pi\)
\(618\) 0 0
\(619\) −2.44590e6 −0.256574 −0.128287 0.991737i \(-0.540948\pi\)
−0.128287 + 0.991737i \(0.540948\pi\)
\(620\) 0 0
\(621\) −6.71301e6 −0.698536
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 8.64460e6 0.885207
\(626\) 0 0
\(627\) 1.10737e6 0.112492
\(628\) 0 0
\(629\) 1.19356e6 0.120287
\(630\) 0 0
\(631\) −1.54761e7 −1.54735 −0.773673 0.633585i \(-0.781583\pi\)
−0.773673 + 0.633585i \(0.781583\pi\)
\(632\) 0 0
\(633\) 1.55077e7 1.53829
\(634\) 0 0
\(635\) 336759. 0.0331425
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.36411e6 −0.132159
\(640\) 0 0
\(641\) −8.75649e6 −0.841753 −0.420877 0.907118i \(-0.638277\pi\)
−0.420877 + 0.907118i \(0.638277\pi\)
\(642\) 0 0
\(643\) −1.29737e7 −1.23747 −0.618736 0.785599i \(-0.712355\pi\)
−0.618736 + 0.785599i \(0.712355\pi\)
\(644\) 0 0
\(645\) 1.99961e6 0.189254
\(646\) 0 0
\(647\) −4.82476e6 −0.453121 −0.226561 0.973997i \(-0.572748\pi\)
−0.226561 + 0.973997i \(0.572748\pi\)
\(648\) 0 0
\(649\) 2.22254e6 0.207128
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 781133. 0.0716873 0.0358436 0.999357i \(-0.488588\pi\)
0.0358436 + 0.999357i \(0.488588\pi\)
\(654\) 0 0
\(655\) 1.52242e6 0.138653
\(656\) 0 0
\(657\) −20106.7 −0.00181730
\(658\) 0 0
\(659\) −3.55442e6 −0.318827 −0.159414 0.987212i \(-0.550960\pi\)
−0.159414 + 0.987212i \(0.550960\pi\)
\(660\) 0 0
\(661\) −9.88767e6 −0.880219 −0.440109 0.897944i \(-0.645060\pi\)
−0.440109 + 0.897944i \(0.645060\pi\)
\(662\) 0 0
\(663\) −277458. −0.0245139
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.53334e6 −0.568618
\(668\) 0 0
\(669\) 5.38075e6 0.464813
\(670\) 0 0
\(671\) −973517. −0.0834713
\(672\) 0 0
\(673\) −9.64825e6 −0.821128 −0.410564 0.911832i \(-0.634668\pi\)
−0.410564 + 0.911832i \(0.634668\pi\)
\(674\) 0 0
\(675\) 9.41609e6 0.795447
\(676\) 0 0
\(677\) 434057. 0.0363978 0.0181989 0.999834i \(-0.494207\pi\)
0.0181989 + 0.999834i \(0.494207\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.84764e7 1.52669
\(682\) 0 0
\(683\) 2.20366e7 1.80756 0.903778 0.428001i \(-0.140782\pi\)
0.903778 + 0.428001i \(0.140782\pi\)
\(684\) 0 0
\(685\) 1.62436e6 0.132268
\(686\) 0 0
\(687\) 1.34615e7 1.08818
\(688\) 0 0
\(689\) 4.36431e6 0.350242
\(690\) 0 0
\(691\) 1.00504e7 0.800737 0.400369 0.916354i \(-0.368882\pi\)
0.400369 + 0.916354i \(0.368882\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.84235e6 −0.144680
\(696\) 0 0
\(697\) −403476. −0.0314583
\(698\) 0 0
\(699\) −2.03314e7 −1.57389
\(700\) 0 0
\(701\) 2.39421e7 1.84021 0.920106 0.391668i \(-0.128102\pi\)
0.920106 + 0.391668i \(0.128102\pi\)
\(702\) 0 0
\(703\) −7.89303e6 −0.602359
\(704\) 0 0
\(705\) 4.36846e6 0.331021
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.05493e7 −0.788148 −0.394074 0.919079i \(-0.628935\pi\)
−0.394074 + 0.919079i \(0.628935\pi\)
\(710\) 0 0
\(711\) −3.79875e6 −0.281817
\(712\) 0 0
\(713\) −6.60506e6 −0.486578
\(714\) 0 0
\(715\) −164747. −0.0120518
\(716\) 0 0
\(717\) 2.01441e7 1.46335
\(718\) 0 0
\(719\) −9.30506e6 −0.671270 −0.335635 0.941992i \(-0.608951\pi\)
−0.335635 + 0.941992i \(0.608951\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.96793e6 0.140012
\(724\) 0 0
\(725\) 9.16407e6 0.647506
\(726\) 0 0
\(727\) 3.88455e6 0.272587 0.136294 0.990668i \(-0.456481\pi\)
0.136294 + 0.990668i \(0.456481\pi\)
\(728\) 0 0
\(729\) 8.82662e6 0.615142
\(730\) 0 0
\(731\) −1.04215e6 −0.0721332
\(732\) 0 0
\(733\) 2.15755e7 1.48320 0.741602 0.670840i \(-0.234066\pi\)
0.741602 + 0.670840i \(0.234066\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −623044. −0.0422523
\(738\) 0 0
\(739\) 2.79027e7 1.87947 0.939733 0.341909i \(-0.111074\pi\)
0.939733 + 0.341909i \(0.111074\pi\)
\(740\) 0 0
\(741\) 1.83483e6 0.122758
\(742\) 0 0
\(743\) −2.11208e7 −1.40358 −0.701790 0.712384i \(-0.747616\pi\)
−0.701790 + 0.712384i \(0.747616\pi\)
\(744\) 0 0
\(745\) −1.64833e6 −0.108806
\(746\) 0 0
\(747\) 6.89837e6 0.452319
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.86917e7 −1.85634 −0.928168 0.372161i \(-0.878617\pi\)
−0.928168 + 0.372161i \(0.878617\pi\)
\(752\) 0 0
\(753\) 3.75382e6 0.241261
\(754\) 0 0
\(755\) 3.52452e6 0.225026
\(756\) 0 0
\(757\) 1.39601e7 0.885421 0.442710 0.896665i \(-0.354017\pi\)
0.442710 + 0.896665i \(0.354017\pi\)
\(758\) 0 0
\(759\) −3.56718e6 −0.224761
\(760\) 0 0
\(761\) −2.41380e6 −0.151091 −0.0755456 0.997142i \(-0.524070\pi\)
−0.0755456 + 0.997142i \(0.524070\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −70962.7 −0.00438406
\(766\) 0 0
\(767\) 3.68260e6 0.226030
\(768\) 0 0
\(769\) −2.00276e7 −1.22128 −0.610638 0.791910i \(-0.709087\pi\)
−0.610638 + 0.791910i \(0.709087\pi\)
\(770\) 0 0
\(771\) 3.56160e7 2.15779
\(772\) 0 0
\(773\) 2.75771e7 1.65997 0.829983 0.557789i \(-0.188350\pi\)
0.829983 + 0.557789i \(0.188350\pi\)
\(774\) 0 0
\(775\) 9.26467e6 0.554084
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.66819e6 0.157534
\(780\) 0 0
\(781\) 2.02158e6 0.118594
\(782\) 0 0
\(783\) 9.56313e6 0.557437
\(784\) 0 0
\(785\) 3.69594e6 0.214068
\(786\) 0 0
\(787\) 1.74369e7 1.00354 0.501769 0.865002i \(-0.332683\pi\)
0.501769 + 0.865002i \(0.332683\pi\)
\(788\) 0 0
\(789\) 1.91983e7 1.09792
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.61305e6 −0.0910888
\(794\) 0 0
\(795\) 5.34549e6 0.299964
\(796\) 0 0
\(797\) 6.96631e6 0.388469 0.194235 0.980955i \(-0.437778\pi\)
0.194235 + 0.980955i \(0.437778\pi\)
\(798\) 0 0
\(799\) −2.27674e6 −0.126167
\(800\) 0 0
\(801\) 5.66673e6 0.312069
\(802\) 0 0
\(803\) 29797.8 0.00163078
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 5.46690e6 0.295500
\(808\) 0 0
\(809\) 9.66666e6 0.519285 0.259642 0.965705i \(-0.416395\pi\)
0.259642 + 0.965705i \(0.416395\pi\)
\(810\) 0 0
\(811\) −3.47649e7 −1.85604 −0.928022 0.372525i \(-0.878492\pi\)
−0.928022 + 0.372525i \(0.878492\pi\)
\(812\) 0 0
\(813\) 1.19053e6 0.0631706
\(814\) 0 0
\(815\) −5.44768e6 −0.287288
\(816\) 0 0
\(817\) 6.89173e6 0.361221
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.42770e7 −0.739231 −0.369616 0.929185i \(-0.620511\pi\)
−0.369616 + 0.929185i \(0.620511\pi\)
\(822\) 0 0
\(823\) 9.54227e6 0.491080 0.245540 0.969386i \(-0.421035\pi\)
0.245540 + 0.969386i \(0.421035\pi\)
\(824\) 0 0
\(825\) 5.00355e6 0.255943
\(826\) 0 0
\(827\) 3.08484e7 1.56844 0.784222 0.620480i \(-0.213062\pi\)
0.784222 + 0.620480i \(0.213062\pi\)
\(828\) 0 0
\(829\) −1.18676e7 −0.599757 −0.299878 0.953977i \(-0.596946\pi\)
−0.299878 + 0.953977i \(0.596946\pi\)
\(830\) 0 0
\(831\) −8.73232e6 −0.438659
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.78392e6 −0.0885442
\(836\) 0 0
\(837\) 9.66811e6 0.477010
\(838\) 0 0
\(839\) 2.05321e7 1.00700 0.503499 0.863996i \(-0.332046\pi\)
0.503499 + 0.863996i \(0.332046\pi\)
\(840\) 0 0
\(841\) −1.12040e7 −0.546238
\(842\) 0 0
\(843\) 2.57740e7 1.24915
\(844\) 0 0
\(845\) 3.81363e6 0.183737
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.35335e7 1.12052
\(850\) 0 0
\(851\) 2.54259e7 1.20352
\(852\) 0 0
\(853\) 543335. 0.0255679 0.0127840 0.999918i \(-0.495931\pi\)
0.0127840 + 0.999918i \(0.495931\pi\)
\(854\) 0 0
\(855\) 469277. 0.0219540
\(856\) 0 0
\(857\) −1.85917e7 −0.864704 −0.432352 0.901705i \(-0.642316\pi\)
−0.432352 + 0.901705i \(0.642316\pi\)
\(858\) 0 0
\(859\) 2.15483e7 0.996394 0.498197 0.867064i \(-0.333996\pi\)
0.498197 + 0.867064i \(0.333996\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.80274e7 0.823958 0.411979 0.911193i \(-0.364838\pi\)
0.411979 + 0.911193i \(0.364838\pi\)
\(864\) 0 0
\(865\) 1.79053e6 0.0813657
\(866\) 0 0
\(867\) −2.47062e7 −1.11624
\(868\) 0 0
\(869\) 5.62969e6 0.252892
\(870\) 0 0
\(871\) −1.03234e6 −0.0461082
\(872\) 0 0
\(873\) 1.05300e7 0.467621
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.98502e7 −1.31053 −0.655267 0.755397i \(-0.727444\pi\)
−0.655267 + 0.755397i \(0.727444\pi\)
\(878\) 0 0
\(879\) −3.87188e7 −1.69024
\(880\) 0 0
\(881\) −3.90709e7 −1.69595 −0.847975 0.530036i \(-0.822178\pi\)
−0.847975 + 0.530036i \(0.822178\pi\)
\(882\) 0 0
\(883\) −3.74333e7 −1.61568 −0.807842 0.589399i \(-0.799365\pi\)
−0.807842 + 0.589399i \(0.799365\pi\)
\(884\) 0 0
\(885\) 4.51051e6 0.193583
\(886\) 0 0
\(887\) −3.25735e7 −1.39013 −0.695064 0.718948i \(-0.744624\pi\)
−0.695064 + 0.718948i \(0.744624\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 6.70269e6 0.282849
\(892\) 0 0
\(893\) 1.50561e7 0.631806
\(894\) 0 0
\(895\) 5.07779e6 0.211893
\(896\) 0 0
\(897\) −5.91056e6 −0.245272
\(898\) 0 0
\(899\) 9.40934e6 0.388293
\(900\) 0 0
\(901\) −2.78594e6 −0.114330
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.64667e6 0.269763
\(906\) 0 0
\(907\) −3.29342e6 −0.132932 −0.0664659 0.997789i \(-0.521172\pi\)
−0.0664659 + 0.997789i \(0.521172\pi\)
\(908\) 0 0
\(909\) −1.92239e6 −0.0771672
\(910\) 0 0
\(911\) 2.47725e7 0.988950 0.494475 0.869192i \(-0.335360\pi\)
0.494475 + 0.869192i \(0.335360\pi\)
\(912\) 0 0
\(913\) −1.02233e7 −0.405895
\(914\) 0 0
\(915\) −1.97569e6 −0.0780129
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.50473e7 0.587718 0.293859 0.955849i \(-0.405060\pi\)
0.293859 + 0.955849i \(0.405060\pi\)
\(920\) 0 0
\(921\) −2.58012e7 −1.00228
\(922\) 0 0
\(923\) 3.34962e6 0.129417
\(924\) 0 0
\(925\) −3.56640e7 −1.37049
\(926\) 0 0
\(927\) −5.23931e6 −0.200251
\(928\) 0 0
\(929\) −3.20341e7 −1.21779 −0.608897 0.793250i \(-0.708388\pi\)
−0.608897 + 0.793250i \(0.708388\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.20508e7 0.453223
\(934\) 0 0
\(935\) 105166. 0.00393410
\(936\) 0 0
\(937\) −3.28148e7 −1.22101 −0.610507 0.792011i \(-0.709034\pi\)
−0.610507 + 0.792011i \(0.709034\pi\)
\(938\) 0 0
\(939\) 5.74224e7 2.12529
\(940\) 0 0
\(941\) −2.23532e7 −0.822935 −0.411467 0.911424i \(-0.634984\pi\)
−0.411467 + 0.911424i \(0.634984\pi\)
\(942\) 0 0
\(943\) −8.59507e6 −0.314753
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.84264e7 1.75472 0.877360 0.479834i \(-0.159303\pi\)
0.877360 + 0.479834i \(0.159303\pi\)
\(948\) 0 0
\(949\) 49372.9 0.00177960
\(950\) 0 0
\(951\) 4.13476e7 1.48251
\(952\) 0 0
\(953\) −3.85648e7 −1.37549 −0.687747 0.725951i \(-0.741400\pi\)
−0.687747 + 0.725951i \(0.741400\pi\)
\(954\) 0 0
\(955\) −6.17080e6 −0.218944
\(956\) 0 0
\(957\) 5.08168e6 0.179361
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −1.91165e7 −0.667729
\(962\) 0 0
\(963\) −3.63709e6 −0.126383
\(964\) 0 0
\(965\) −1.81740e6 −0.0628249
\(966\) 0 0
\(967\) −4.03667e7 −1.38821 −0.694107 0.719871i \(-0.744201\pi\)
−0.694107 + 0.719871i \(0.744201\pi\)
\(968\) 0 0
\(969\) −1.17126e6 −0.0400722
\(970\) 0 0
\(971\) −7.51470e6 −0.255778 −0.127889 0.991788i \(-0.540820\pi\)
−0.127889 + 0.991788i \(0.540820\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 8.29053e6 0.279300
\(976\) 0 0
\(977\) −4.57026e6 −0.153181 −0.0765904 0.997063i \(-0.524403\pi\)
−0.0765904 + 0.997063i \(0.524403\pi\)
\(978\) 0 0
\(979\) −8.39801e6 −0.280040
\(980\) 0 0
\(981\) −1.19144e7 −0.395277
\(982\) 0 0
\(983\) 3.62539e7 1.19666 0.598330 0.801250i \(-0.295831\pi\)
0.598330 + 0.801250i \(0.295831\pi\)
\(984\) 0 0
\(985\) 7.46362e6 0.245109
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.22004e7 −0.721722
\(990\) 0 0
\(991\) −5.45804e7 −1.76544 −0.882719 0.469901i \(-0.844289\pi\)
−0.882719 + 0.469901i \(0.844289\pi\)
\(992\) 0 0
\(993\) 2.01039e7 0.647006
\(994\) 0 0
\(995\) −4.07633e6 −0.130530
\(996\) 0 0
\(997\) −5.72786e7 −1.82496 −0.912482 0.409116i \(-0.865837\pi\)
−0.912482 + 0.409116i \(0.865837\pi\)
\(998\) 0 0
\(999\) −3.72170e7 −1.17985
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 392.6.a.m.1.6 yes 6
4.3 odd 2 784.6.a.bn.1.1 6
7.2 even 3 392.6.i.q.361.1 12
7.3 odd 6 392.6.i.q.177.6 12
7.4 even 3 392.6.i.q.177.1 12
7.5 odd 6 392.6.i.q.361.6 12
7.6 odd 2 inner 392.6.a.m.1.1 6
28.27 even 2 784.6.a.bn.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.6.a.m.1.1 6 7.6 odd 2 inner
392.6.a.m.1.6 yes 6 1.1 even 1 trivial
392.6.i.q.177.1 12 7.4 even 3
392.6.i.q.177.6 12 7.3 odd 6
392.6.i.q.361.1 12 7.2 even 3
392.6.i.q.361.6 12 7.5 odd 6
784.6.a.bn.1.1 6 4.3 odd 2
784.6.a.bn.1.6 6 28.27 even 2