Properties

Label 800.6.a.i.1.1
Level $800$
Weight $6$
Character 800.1
Self dual yes
Analytic conductor $128.307$
Analytic rank $1$
Dimension $2$
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] = [800,6,Mod(1,800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(800, 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("800.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.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: \(128.307055850\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-13.4164 q^{3} -138.636 q^{7} -63.0000 q^{9} +O(q^{10})\) \(q-13.4164 q^{3} -138.636 q^{7} -63.0000 q^{9} +259.384 q^{11} -154.000 q^{13} -178.000 q^{17} +965.981 q^{19} +1860.00 q^{21} -2634.09 q^{23} +4105.42 q^{27} +4110.00 q^{29} +3157.33 q^{31} -3480.00 q^{33} -7442.00 q^{37} +2066.13 q^{39} +7270.00 q^{41} +17910.9 q^{43} +7410.33 q^{47} +2413.00 q^{49} +2388.12 q^{51} -32226.0 q^{53} -12960.0 q^{57} +34041.9 q^{59} +26770.0 q^{61} +8734.08 q^{63} -49806.2 q^{67} +35340.0 q^{69} +54103.9 q^{71} +18534.0 q^{73} -35960.0 q^{77} -86741.5 q^{79} -39771.0 q^{81} +78642.5 q^{83} -55141.4 q^{87} -107590. q^{89} +21350.0 q^{91} -42360.0 q^{93} +108838. q^{97} -16341.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 126 q^{9} - 308 q^{13} - 356 q^{17} + 3720 q^{21} + 8220 q^{29} - 6960 q^{33} - 14884 q^{37} + 14540 q^{41} + 4826 q^{49} - 64452 q^{53} - 25920 q^{57} + 53540 q^{61} + 70680 q^{69} + 37068 q^{73} - 71920 q^{77} - 79542 q^{81} - 215180 q^{89} - 84720 q^{93} + 217676 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −13.4164 −0.860663 −0.430331 0.902671i \(-0.641603\pi\)
−0.430331 + 0.902671i \(0.641603\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −138.636 −1.06938 −0.534689 0.845049i \(-0.679571\pi\)
−0.534689 + 0.845049i \(0.679571\pi\)
\(8\) 0 0
\(9\) −63.0000 −0.259259
\(10\) 0 0
\(11\) 259.384 0.646340 0.323170 0.946341i \(-0.395251\pi\)
0.323170 + 0.946341i \(0.395251\pi\)
\(12\) 0 0
\(13\) −154.000 −0.252733 −0.126367 0.991984i \(-0.540332\pi\)
−0.126367 + 0.991984i \(0.540332\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −178.000 −0.149382 −0.0746909 0.997207i \(-0.523797\pi\)
−0.0746909 + 0.997207i \(0.523797\pi\)
\(18\) 0 0
\(19\) 965.981 0.613882 0.306941 0.951729i \(-0.400695\pi\)
0.306941 + 0.951729i \(0.400695\pi\)
\(20\) 0 0
\(21\) 1860.00 0.920375
\(22\) 0 0
\(23\) −2634.09 −1.03827 −0.519135 0.854692i \(-0.673746\pi\)
−0.519135 + 0.854692i \(0.673746\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4105.42 1.08380
\(28\) 0 0
\(29\) 4110.00 0.907500 0.453750 0.891129i \(-0.350086\pi\)
0.453750 + 0.891129i \(0.350086\pi\)
\(30\) 0 0
\(31\) 3157.33 0.590086 0.295043 0.955484i \(-0.404666\pi\)
0.295043 + 0.955484i \(0.404666\pi\)
\(32\) 0 0
\(33\) −3480.00 −0.556281
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7442.00 −0.893687 −0.446843 0.894612i \(-0.647452\pi\)
−0.446843 + 0.894612i \(0.647452\pi\)
\(38\) 0 0
\(39\) 2066.13 0.217518
\(40\) 0 0
\(41\) 7270.00 0.675421 0.337711 0.941250i \(-0.390347\pi\)
0.337711 + 0.941250i \(0.390347\pi\)
\(42\) 0 0
\(43\) 17910.9 1.47722 0.738612 0.674131i \(-0.235482\pi\)
0.738612 + 0.674131i \(0.235482\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7410.33 0.489320 0.244660 0.969609i \(-0.421324\pi\)
0.244660 + 0.969609i \(0.421324\pi\)
\(48\) 0 0
\(49\) 2413.00 0.143571
\(50\) 0 0
\(51\) 2388.12 0.128567
\(52\) 0 0
\(53\) −32226.0 −1.57586 −0.787928 0.615767i \(-0.788846\pi\)
−0.787928 + 0.615767i \(0.788846\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −12960.0 −0.528345
\(58\) 0 0
\(59\) 34041.9 1.27316 0.636581 0.771210i \(-0.280348\pi\)
0.636581 + 0.771210i \(0.280348\pi\)
\(60\) 0 0
\(61\) 26770.0 0.921136 0.460568 0.887624i \(-0.347646\pi\)
0.460568 + 0.887624i \(0.347646\pi\)
\(62\) 0 0
\(63\) 8734.08 0.277246
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −49806.2 −1.35549 −0.677745 0.735297i \(-0.737043\pi\)
−0.677745 + 0.735297i \(0.737043\pi\)
\(68\) 0 0
\(69\) 35340.0 0.893601
\(70\) 0 0
\(71\) 54103.9 1.27375 0.636873 0.770969i \(-0.280228\pi\)
0.636873 + 0.770969i \(0.280228\pi\)
\(72\) 0 0
\(73\) 18534.0 0.407063 0.203532 0.979068i \(-0.434758\pi\)
0.203532 + 0.979068i \(0.434758\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −35960.0 −0.691183
\(78\) 0 0
\(79\) −86741.5 −1.56372 −0.781861 0.623453i \(-0.785729\pi\)
−0.781861 + 0.623453i \(0.785729\pi\)
\(80\) 0 0
\(81\) −39771.0 −0.673525
\(82\) 0 0
\(83\) 78642.5 1.25303 0.626516 0.779409i \(-0.284480\pi\)
0.626516 + 0.779409i \(0.284480\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −55141.4 −0.781052
\(88\) 0 0
\(89\) −107590. −1.43978 −0.719891 0.694087i \(-0.755808\pi\)
−0.719891 + 0.694087i \(0.755808\pi\)
\(90\) 0 0
\(91\) 21350.0 0.270268
\(92\) 0 0
\(93\) −42360.0 −0.507865
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 108838. 1.17450 0.587248 0.809407i \(-0.300212\pi\)
0.587248 + 0.809407i \(0.300212\pi\)
\(98\) 0 0
\(99\) −16341.2 −0.167570
\(100\) 0 0
\(101\) 59198.0 0.577436 0.288718 0.957414i \(-0.406771\pi\)
0.288718 + 0.957414i \(0.406771\pi\)
\(102\) 0 0
\(103\) 112908. 1.04865 0.524326 0.851517i \(-0.324317\pi\)
0.524326 + 0.851517i \(0.324317\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −40039.0 −0.338084 −0.169042 0.985609i \(-0.554067\pi\)
−0.169042 + 0.985609i \(0.554067\pi\)
\(108\) 0 0
\(109\) −139614. −1.12554 −0.562772 0.826612i \(-0.690265\pi\)
−0.562772 + 0.826612i \(0.690265\pi\)
\(110\) 0 0
\(111\) 99844.9 0.769163
\(112\) 0 0
\(113\) 43046.0 0.317130 0.158565 0.987349i \(-0.449313\pi\)
0.158565 + 0.987349i \(0.449313\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 9702.00 0.0655234
\(118\) 0 0
\(119\) 24677.2 0.159746
\(120\) 0 0
\(121\) −93771.0 −0.582244
\(122\) 0 0
\(123\) −97537.3 −0.581310
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 157370. 0.865790 0.432895 0.901444i \(-0.357492\pi\)
0.432895 + 0.901444i \(0.357492\pi\)
\(128\) 0 0
\(129\) −240300. −1.27139
\(130\) 0 0
\(131\) −267729. −1.36307 −0.681533 0.731787i \(-0.738686\pi\)
−0.681533 + 0.731787i \(0.738686\pi\)
\(132\) 0 0
\(133\) −133920. −0.656472
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 112158. 0.510539 0.255269 0.966870i \(-0.417836\pi\)
0.255269 + 0.966870i \(0.417836\pi\)
\(138\) 0 0
\(139\) 147348. 0.646855 0.323428 0.946253i \(-0.395165\pi\)
0.323428 + 0.946253i \(0.395165\pi\)
\(140\) 0 0
\(141\) −99420.0 −0.421139
\(142\) 0 0
\(143\) −39945.1 −0.163352
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −32373.8 −0.123566
\(148\) 0 0
\(149\) −174566. −0.644160 −0.322080 0.946712i \(-0.604382\pi\)
−0.322080 + 0.946712i \(0.604382\pi\)
\(150\) 0 0
\(151\) 345258. 1.23226 0.616128 0.787646i \(-0.288700\pi\)
0.616128 + 0.787646i \(0.288700\pi\)
\(152\) 0 0
\(153\) 11214.0 0.0387286
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 26502.0 0.0858083 0.0429042 0.999079i \(-0.486339\pi\)
0.0429042 + 0.999079i \(0.486339\pi\)
\(158\) 0 0
\(159\) 432357. 1.35628
\(160\) 0 0
\(161\) 365180. 1.11030
\(162\) 0 0
\(163\) −141709. −0.417760 −0.208880 0.977941i \(-0.566982\pi\)
−0.208880 + 0.977941i \(0.566982\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 411047. 1.14051 0.570257 0.821466i \(-0.306844\pi\)
0.570257 + 0.821466i \(0.306844\pi\)
\(168\) 0 0
\(169\) −347577. −0.936126
\(170\) 0 0
\(171\) −60856.8 −0.159155
\(172\) 0 0
\(173\) −595946. −1.51388 −0.756940 0.653484i \(-0.773307\pi\)
−0.756940 + 0.653484i \(0.773307\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −456720. −1.09576
\(178\) 0 0
\(179\) −300939. −0.702014 −0.351007 0.936373i \(-0.614161\pi\)
−0.351007 + 0.936373i \(0.614161\pi\)
\(180\) 0 0
\(181\) 217022. 0.492388 0.246194 0.969221i \(-0.420820\pi\)
0.246194 + 0.969221i \(0.420820\pi\)
\(182\) 0 0
\(183\) −359157. −0.792788
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −46170.3 −0.0965515
\(188\) 0 0
\(189\) −569160. −1.15899
\(190\) 0 0
\(191\) −916260. −1.81734 −0.908668 0.417519i \(-0.862900\pi\)
−0.908668 + 0.417519i \(0.862900\pi\)
\(192\) 0 0
\(193\) −864114. −1.66985 −0.834926 0.550363i \(-0.814489\pi\)
−0.834926 + 0.550363i \(0.814489\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −432522. −0.794040 −0.397020 0.917810i \(-0.629956\pi\)
−0.397020 + 0.917810i \(0.629956\pi\)
\(198\) 0 0
\(199\) −795182. −1.42342 −0.711711 0.702473i \(-0.752079\pi\)
−0.711711 + 0.702473i \(0.752079\pi\)
\(200\) 0 0
\(201\) 668220. 1.16662
\(202\) 0 0
\(203\) −569795. −0.970462
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 165948. 0.269181
\(208\) 0 0
\(209\) 250560. 0.396777
\(210\) 0 0
\(211\) −453126. −0.700669 −0.350334 0.936625i \(-0.613932\pi\)
−0.350334 + 0.936625i \(0.613932\pi\)
\(212\) 0 0
\(213\) −725880. −1.09627
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −437720. −0.631026
\(218\) 0 0
\(219\) −248660. −0.350344
\(220\) 0 0
\(221\) 27412.0 0.0377537
\(222\) 0 0
\(223\) 430358. 0.579519 0.289760 0.957099i \(-0.406425\pi\)
0.289760 + 0.957099i \(0.406425\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.12403e6 −1.44782 −0.723909 0.689896i \(-0.757656\pi\)
−0.723909 + 0.689896i \(0.757656\pi\)
\(228\) 0 0
\(229\) −812410. −1.02373 −0.511866 0.859065i \(-0.671046\pi\)
−0.511866 + 0.859065i \(0.671046\pi\)
\(230\) 0 0
\(231\) 482454. 0.594875
\(232\) 0 0
\(233\) −846194. −1.02113 −0.510564 0.859840i \(-0.670563\pi\)
−0.510564 + 0.859840i \(0.670563\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.16376e6 1.34584
\(238\) 0 0
\(239\) −56688.8 −0.0641952 −0.0320976 0.999485i \(-0.510219\pi\)
−0.0320976 + 0.999485i \(0.510219\pi\)
\(240\) 0 0
\(241\) 1.27571e6 1.41485 0.707423 0.706790i \(-0.249857\pi\)
0.707423 + 0.706790i \(0.249857\pi\)
\(242\) 0 0
\(243\) −464033. −0.504119
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −148761. −0.155148
\(248\) 0 0
\(249\) −1.05510e6 −1.07844
\(250\) 0 0
\(251\) −50937.6 −0.0510334 −0.0255167 0.999674i \(-0.508123\pi\)
−0.0255167 + 0.999674i \(0.508123\pi\)
\(252\) 0 0
\(253\) −683240. −0.671076
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.64806e6 −1.55647 −0.778233 0.627976i \(-0.783884\pi\)
−0.778233 + 0.627976i \(0.783884\pi\)
\(258\) 0 0
\(259\) 1.03173e6 0.955690
\(260\) 0 0
\(261\) −258930. −0.235278
\(262\) 0 0
\(263\) −522994. −0.466238 −0.233119 0.972448i \(-0.574893\pi\)
−0.233119 + 0.972448i \(0.574893\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.44347e6 1.23917
\(268\) 0 0
\(269\) −1.93789e6 −1.63285 −0.816427 0.577448i \(-0.804049\pi\)
−0.816427 + 0.577448i \(0.804049\pi\)
\(270\) 0 0
\(271\) 1.00132e6 0.828228 0.414114 0.910225i \(-0.364092\pi\)
0.414114 + 0.910225i \(0.364092\pi\)
\(272\) 0 0
\(273\) −286440. −0.232609
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 445702. 0.349016 0.174508 0.984656i \(-0.444167\pi\)
0.174508 + 0.984656i \(0.444167\pi\)
\(278\) 0 0
\(279\) −198912. −0.152985
\(280\) 0 0
\(281\) 1.24647e6 0.941708 0.470854 0.882211i \(-0.343946\pi\)
0.470854 + 0.882211i \(0.343946\pi\)
\(282\) 0 0
\(283\) 2.27900e6 1.69153 0.845764 0.533557i \(-0.179145\pi\)
0.845764 + 0.533557i \(0.179145\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00789e6 −0.722281
\(288\) 0 0
\(289\) −1.38817e6 −0.977685
\(290\) 0 0
\(291\) −1.46021e6 −1.01084
\(292\) 0 0
\(293\) −2.45427e6 −1.67014 −0.835072 0.550140i \(-0.814574\pi\)
−0.835072 + 0.550140i \(0.814574\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.06488e6 0.700502
\(298\) 0 0
\(299\) 405650. 0.262406
\(300\) 0 0
\(301\) −2.48310e6 −1.57971
\(302\) 0 0
\(303\) −794225. −0.496977
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 20710.5 0.0125413 0.00627067 0.999980i \(-0.498004\pi\)
0.00627067 + 0.999980i \(0.498004\pi\)
\(308\) 0 0
\(309\) −1.51482e6 −0.902537
\(310\) 0 0
\(311\) −47270.5 −0.0277133 −0.0138567 0.999904i \(-0.504411\pi\)
−0.0138567 + 0.999904i \(0.504411\pi\)
\(312\) 0 0
\(313\) 2.79169e6 1.61067 0.805333 0.592822i \(-0.201986\pi\)
0.805333 + 0.592822i \(0.201986\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 471582. 0.263578 0.131789 0.991278i \(-0.457928\pi\)
0.131789 + 0.991278i \(0.457928\pi\)
\(318\) 0 0
\(319\) 1.06607e6 0.586554
\(320\) 0 0
\(321\) 537180. 0.290976
\(322\) 0 0
\(323\) −171945. −0.0917028
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.87312e6 0.968715
\(328\) 0 0
\(329\) −1.02734e6 −0.523268
\(330\) 0 0
\(331\) 3.09092e6 1.55066 0.775331 0.631555i \(-0.217583\pi\)
0.775331 + 0.631555i \(0.217583\pi\)
\(332\) 0 0
\(333\) 468846. 0.231697
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 665838. 0.319370 0.159685 0.987168i \(-0.448952\pi\)
0.159685 + 0.987168i \(0.448952\pi\)
\(338\) 0 0
\(339\) −577523. −0.272942
\(340\) 0 0
\(341\) 818960. 0.381397
\(342\) 0 0
\(343\) 1.99553e6 0.915847
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.80908e6 0.806556 0.403278 0.915078i \(-0.367871\pi\)
0.403278 + 0.915078i \(0.367871\pi\)
\(348\) 0 0
\(349\) −2.36181e6 −1.03796 −0.518981 0.854786i \(-0.673688\pi\)
−0.518981 + 0.854786i \(0.673688\pi\)
\(350\) 0 0
\(351\) −632235. −0.273912
\(352\) 0 0
\(353\) −1.14535e6 −0.489215 −0.244608 0.969622i \(-0.578659\pi\)
−0.244608 + 0.969622i \(0.578659\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −331080. −0.137487
\(358\) 0 0
\(359\) −767275. −0.314206 −0.157103 0.987582i \(-0.550216\pi\)
−0.157103 + 0.987582i \(0.550216\pi\)
\(360\) 0 0
\(361\) −1.54298e6 −0.623149
\(362\) 0 0
\(363\) 1.25807e6 0.501116
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.99537e6 −1.54843 −0.774215 0.632923i \(-0.781855\pi\)
−0.774215 + 0.632923i \(0.781855\pi\)
\(368\) 0 0
\(369\) −458010. −0.175109
\(370\) 0 0
\(371\) 4.46769e6 1.68519
\(372\) 0 0
\(373\) −4.68131e6 −1.74219 −0.871094 0.491117i \(-0.836589\pi\)
−0.871094 + 0.491117i \(0.836589\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −632940. −0.229356
\(378\) 0 0
\(379\) 337271. 0.120609 0.0603046 0.998180i \(-0.480793\pi\)
0.0603046 + 0.998180i \(0.480793\pi\)
\(380\) 0 0
\(381\) −2.11134e6 −0.745153
\(382\) 0 0
\(383\) 598689. 0.208547 0.104274 0.994549i \(-0.466748\pi\)
0.104274 + 0.994549i \(0.466748\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.12839e6 −0.382984
\(388\) 0 0
\(389\) 3.97243e6 1.33101 0.665506 0.746393i \(-0.268216\pi\)
0.665506 + 0.746393i \(0.268216\pi\)
\(390\) 0 0
\(391\) 468868. 0.155099
\(392\) 0 0
\(393\) 3.59196e6 1.17314
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 179398. 0.0571270 0.0285635 0.999592i \(-0.490907\pi\)
0.0285635 + 0.999592i \(0.490907\pi\)
\(398\) 0 0
\(399\) 1.79673e6 0.565001
\(400\) 0 0
\(401\) 6.14504e6 1.90838 0.954188 0.299208i \(-0.0967224\pi\)
0.954188 + 0.299208i \(0.0967224\pi\)
\(402\) 0 0
\(403\) −486229. −0.149134
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.93033e6 −0.577626
\(408\) 0 0
\(409\) −2.64503e6 −0.781847 −0.390923 0.920423i \(-0.627844\pi\)
−0.390923 + 0.920423i \(0.627844\pi\)
\(410\) 0 0
\(411\) −1.50476e6 −0.439402
\(412\) 0 0
\(413\) −4.71944e6 −1.36149
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.97688e6 −0.556724
\(418\) 0 0
\(419\) −2.15984e6 −0.601018 −0.300509 0.953779i \(-0.597157\pi\)
−0.300509 + 0.953779i \(0.597157\pi\)
\(420\) 0 0
\(421\) 1.47209e6 0.404789 0.202395 0.979304i \(-0.435128\pi\)
0.202395 + 0.979304i \(0.435128\pi\)
\(422\) 0 0
\(423\) −466851. −0.126861
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.71129e6 −0.985043
\(428\) 0 0
\(429\) 535920. 0.140591
\(430\) 0 0
\(431\) −6.63748e6 −1.72112 −0.860558 0.509352i \(-0.829885\pi\)
−0.860558 + 0.509352i \(0.829885\pi\)
\(432\) 0 0
\(433\) 6.27853e6 1.60931 0.804653 0.593746i \(-0.202351\pi\)
0.804653 + 0.593746i \(0.202351\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.54448e6 −0.637376
\(438\) 0 0
\(439\) −2.44021e6 −0.604319 −0.302160 0.953257i \(-0.597708\pi\)
−0.302160 + 0.953257i \(0.597708\pi\)
\(440\) 0 0
\(441\) −152019. −0.0372221
\(442\) 0 0
\(443\) 2.30646e6 0.558390 0.279195 0.960234i \(-0.409932\pi\)
0.279195 + 0.960234i \(0.409932\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.34205e6 0.554405
\(448\) 0 0
\(449\) 7.60241e6 1.77965 0.889826 0.456300i \(-0.150825\pi\)
0.889826 + 0.456300i \(0.150825\pi\)
\(450\) 0 0
\(451\) 1.88572e6 0.436552
\(452\) 0 0
\(453\) −4.63212e6 −1.06056
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.56938e6 0.351510 0.175755 0.984434i \(-0.443763\pi\)
0.175755 + 0.984434i \(0.443763\pi\)
\(458\) 0 0
\(459\) −730765. −0.161900
\(460\) 0 0
\(461\) −562602. −0.123296 −0.0616480 0.998098i \(-0.519636\pi\)
−0.0616480 + 0.998098i \(0.519636\pi\)
\(462\) 0 0
\(463\) 4.87382e6 1.05662 0.528308 0.849053i \(-0.322827\pi\)
0.528308 + 0.849053i \(0.322827\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.11862e6 1.08608 0.543039 0.839708i \(-0.317274\pi\)
0.543039 + 0.839708i \(0.317274\pi\)
\(468\) 0 0
\(469\) 6.90494e6 1.44953
\(470\) 0 0
\(471\) −355562. −0.0738521
\(472\) 0 0
\(473\) 4.64580e6 0.954790
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 2.03024e6 0.408555
\(478\) 0 0
\(479\) 4.00179e6 0.796922 0.398461 0.917185i \(-0.369544\pi\)
0.398461 + 0.917185i \(0.369544\pi\)
\(480\) 0 0
\(481\) 1.14607e6 0.225864
\(482\) 0 0
\(483\) −4.89940e6 −0.955598
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.68175e6 −0.321321 −0.160661 0.987010i \(-0.551362\pi\)
−0.160661 + 0.987010i \(0.551362\pi\)
\(488\) 0 0
\(489\) 1.90122e6 0.359551
\(490\) 0 0
\(491\) 115927. 0.0217010 0.0108505 0.999941i \(-0.496546\pi\)
0.0108505 + 0.999941i \(0.496546\pi\)
\(492\) 0 0
\(493\) −731580. −0.135564
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.50076e6 −1.36212
\(498\) 0 0
\(499\) −7.98867e6 −1.43623 −0.718113 0.695926i \(-0.754994\pi\)
−0.718113 + 0.695926i \(0.754994\pi\)
\(500\) 0 0
\(501\) −5.51478e6 −0.981598
\(502\) 0 0
\(503\) −8.07650e6 −1.42332 −0.711661 0.702523i \(-0.752057\pi\)
−0.711661 + 0.702523i \(0.752057\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.66323e6 0.805689
\(508\) 0 0
\(509\) 2.83427e6 0.484894 0.242447 0.970165i \(-0.422050\pi\)
0.242447 + 0.970165i \(0.422050\pi\)
\(510\) 0 0
\(511\) −2.56948e6 −0.435305
\(512\) 0 0
\(513\) 3.96576e6 0.665324
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.92212e6 0.316267
\(518\) 0 0
\(519\) 7.99545e6 1.30294
\(520\) 0 0
\(521\) 2.97526e6 0.480209 0.240105 0.970747i \(-0.422818\pi\)
0.240105 + 0.970747i \(0.422818\pi\)
\(522\) 0 0
\(523\) −7.72888e6 −1.23556 −0.617778 0.786352i \(-0.711967\pi\)
−0.617778 + 0.786352i \(0.711967\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −562004. −0.0881481
\(528\) 0 0
\(529\) 502077. 0.0780066
\(530\) 0 0
\(531\) −2.14464e6 −0.330079
\(532\) 0 0
\(533\) −1.11958e6 −0.170701
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.03752e6 0.604198
\(538\) 0 0
\(539\) 625893. 0.0927958
\(540\) 0 0
\(541\) −9.83660e6 −1.44495 −0.722474 0.691399i \(-0.756995\pi\)
−0.722474 + 0.691399i \(0.756995\pi\)
\(542\) 0 0
\(543\) −2.91166e6 −0.423780
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 3.45608e6 0.493873 0.246937 0.969032i \(-0.420576\pi\)
0.246937 + 0.969032i \(0.420576\pi\)
\(548\) 0 0
\(549\) −1.68651e6 −0.238813
\(550\) 0 0
\(551\) 3.97018e6 0.557098
\(552\) 0 0
\(553\) 1.20255e7 1.67221
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.05760e6 0.963871 0.481936 0.876207i \(-0.339934\pi\)
0.481936 + 0.876207i \(0.339934\pi\)
\(558\) 0 0
\(559\) −2.75828e6 −0.373344
\(560\) 0 0
\(561\) 619440. 0.0830983
\(562\) 0 0
\(563\) −2.32495e6 −0.309131 −0.154566 0.987983i \(-0.549398\pi\)
−0.154566 + 0.987983i \(0.549398\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 5.51370e6 0.720254
\(568\) 0 0
\(569\) 1.01947e7 1.32006 0.660029 0.751240i \(-0.270544\pi\)
0.660029 + 0.751240i \(0.270544\pi\)
\(570\) 0 0
\(571\) −1.21297e7 −1.55689 −0.778446 0.627712i \(-0.783992\pi\)
−0.778446 + 0.627712i \(0.783992\pi\)
\(572\) 0 0
\(573\) 1.22929e7 1.56411
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.46358e6 −0.183011 −0.0915053 0.995805i \(-0.529168\pi\)
−0.0915053 + 0.995805i \(0.529168\pi\)
\(578\) 0 0
\(579\) 1.15933e7 1.43718
\(580\) 0 0
\(581\) −1.09027e7 −1.33997
\(582\) 0 0
\(583\) −8.35891e6 −1.01854
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.18425e6 −0.620998 −0.310499 0.950574i \(-0.600496\pi\)
−0.310499 + 0.950574i \(0.600496\pi\)
\(588\) 0 0
\(589\) 3.04992e6 0.362243
\(590\) 0 0
\(591\) 5.80289e6 0.683401
\(592\) 0 0
\(593\) 1.02722e7 1.19957 0.599785 0.800161i \(-0.295253\pi\)
0.599785 + 0.800161i \(0.295253\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.06685e7 1.22509
\(598\) 0 0
\(599\) −1.39289e7 −1.58617 −0.793085 0.609111i \(-0.791526\pi\)
−0.793085 + 0.609111i \(0.791526\pi\)
\(600\) 0 0
\(601\) −4.81441e6 −0.543697 −0.271848 0.962340i \(-0.587635\pi\)
−0.271848 + 0.962340i \(0.587635\pi\)
\(602\) 0 0
\(603\) 3.13779e6 0.351423
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 1.04800e7 1.15449 0.577245 0.816571i \(-0.304128\pi\)
0.577245 + 0.816571i \(0.304128\pi\)
\(608\) 0 0
\(609\) 7.64460e6 0.835240
\(610\) 0 0
\(611\) −1.14119e6 −0.123667
\(612\) 0 0
\(613\) 3.07977e6 0.331029 0.165515 0.986207i \(-0.447071\pi\)
0.165515 + 0.986207i \(0.447071\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.15522e6 −0.122166 −0.0610831 0.998133i \(-0.519455\pi\)
−0.0610831 + 0.998133i \(0.519455\pi\)
\(618\) 0 0
\(619\) 1.76853e7 1.85517 0.927587 0.373606i \(-0.121879\pi\)
0.927587 + 0.373606i \(0.121879\pi\)
\(620\) 0 0
\(621\) −1.08140e7 −1.12528
\(622\) 0 0
\(623\) 1.49159e7 1.53967
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −3.36162e6 −0.341491
\(628\) 0 0
\(629\) 1.32468e6 0.133501
\(630\) 0 0
\(631\) −5.42541e6 −0.542449 −0.271225 0.962516i \(-0.587429\pi\)
−0.271225 + 0.962516i \(0.587429\pi\)
\(632\) 0 0
\(633\) 6.07932e6 0.603039
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −371602. −0.0362852
\(638\) 0 0
\(639\) −3.40855e6 −0.330230
\(640\) 0 0
\(641\) 1.16005e7 1.11515 0.557573 0.830128i \(-0.311733\pi\)
0.557573 + 0.830128i \(0.311733\pi\)
\(642\) 0 0
\(643\) 9.57873e6 0.913651 0.456826 0.889556i \(-0.348986\pi\)
0.456826 + 0.889556i \(0.348986\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.28130e7 −1.20334 −0.601671 0.798744i \(-0.705498\pi\)
−0.601671 + 0.798744i \(0.705498\pi\)
\(648\) 0 0
\(649\) 8.82992e6 0.822896
\(650\) 0 0
\(651\) 5.87263e6 0.543100
\(652\) 0 0
\(653\) 1.58665e6 0.145613 0.0728064 0.997346i \(-0.476804\pi\)
0.0728064 + 0.997346i \(0.476804\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.16764e6 −0.105535
\(658\) 0 0
\(659\) −1.95559e7 −1.75414 −0.877071 0.480361i \(-0.840506\pi\)
−0.877071 + 0.480361i \(0.840506\pi\)
\(660\) 0 0
\(661\) −7.46471e6 −0.664522 −0.332261 0.943188i \(-0.607811\pi\)
−0.332261 + 0.943188i \(0.607811\pi\)
\(662\) 0 0
\(663\) −367771. −0.0324933
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.08261e7 −0.942231
\(668\) 0 0
\(669\) −5.77386e6 −0.498771
\(670\) 0 0
\(671\) 6.94371e6 0.595367
\(672\) 0 0
\(673\) 1.09694e7 0.933568 0.466784 0.884371i \(-0.345413\pi\)
0.466784 + 0.884371i \(0.345413\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.52708e6 0.547327 0.273664 0.961825i \(-0.411764\pi\)
0.273664 + 0.961825i \(0.411764\pi\)
\(678\) 0 0
\(679\) −1.50889e7 −1.25598
\(680\) 0 0
\(681\) 1.50805e7 1.24608
\(682\) 0 0
\(683\) 1.54389e7 1.26638 0.633191 0.773995i \(-0.281745\pi\)
0.633191 + 0.773995i \(0.281745\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.08996e7 0.881089
\(688\) 0 0
\(689\) 4.96280e6 0.398271
\(690\) 0 0
\(691\) −4.78757e6 −0.381435 −0.190717 0.981645i \(-0.561081\pi\)
−0.190717 + 0.981645i \(0.561081\pi\)
\(692\) 0 0
\(693\) 2.26548e6 0.179196
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.29406e6 −0.100896
\(698\) 0 0
\(699\) 1.13529e7 0.878847
\(700\) 0 0
\(701\) −3.31891e6 −0.255094 −0.127547 0.991833i \(-0.540710\pi\)
−0.127547 + 0.991833i \(0.540710\pi\)
\(702\) 0 0
\(703\) −7.18883e6 −0.548618
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.20699e6 −0.617497
\(708\) 0 0
\(709\) 1.60044e7 1.19570 0.597852 0.801607i \(-0.296021\pi\)
0.597852 + 0.801607i \(0.296021\pi\)
\(710\) 0 0
\(711\) 5.46472e6 0.405409
\(712\) 0 0
\(713\) −8.31668e6 −0.612669
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 760560. 0.0552504
\(718\) 0 0
\(719\) 1.56006e7 1.12543 0.562715 0.826651i \(-0.309757\pi\)
0.562715 + 0.826651i \(0.309757\pi\)
\(720\) 0 0
\(721\) −1.56531e7 −1.12141
\(722\) 0 0
\(723\) −1.71154e7 −1.21771
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.14545e7 −0.803783 −0.401891 0.915687i \(-0.631647\pi\)
−0.401891 + 0.915687i \(0.631647\pi\)
\(728\) 0 0
\(729\) 1.58900e7 1.10740
\(730\) 0 0
\(731\) −3.18814e6 −0.220670
\(732\) 0 0
\(733\) −1.13267e7 −0.778650 −0.389325 0.921101i \(-0.627292\pi\)
−0.389325 + 0.921101i \(0.627292\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.29189e7 −0.876108
\(738\) 0 0
\(739\) −1.31055e7 −0.882756 −0.441378 0.897321i \(-0.645510\pi\)
−0.441378 + 0.897321i \(0.645510\pi\)
\(740\) 0 0
\(741\) 1.99584e6 0.133530
\(742\) 0 0
\(743\) 4.16787e6 0.276976 0.138488 0.990364i \(-0.455776\pi\)
0.138488 + 0.990364i \(0.455776\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −4.95448e6 −0.324860
\(748\) 0 0
\(749\) 5.55086e6 0.361539
\(750\) 0 0
\(751\) 2.89308e7 1.87180 0.935902 0.352260i \(-0.114587\pi\)
0.935902 + 0.352260i \(0.114587\pi\)
\(752\) 0 0
\(753\) 683400. 0.0439225
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −8.32870e6 −0.528247 −0.264124 0.964489i \(-0.585083\pi\)
−0.264124 + 0.964489i \(0.585083\pi\)
\(758\) 0 0
\(759\) 9.16663e6 0.577571
\(760\) 0 0
\(761\) 4.48292e6 0.280608 0.140304 0.990108i \(-0.455192\pi\)
0.140304 + 0.990108i \(0.455192\pi\)
\(762\) 0 0
\(763\) 1.93556e7 1.20363
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.24245e6 −0.321770
\(768\) 0 0
\(769\) 1.32141e6 0.0805790 0.0402895 0.999188i \(-0.487172\pi\)
0.0402895 + 0.999188i \(0.487172\pi\)
\(770\) 0 0
\(771\) 2.21110e7 1.33959
\(772\) 0 0
\(773\) 7.24897e6 0.436342 0.218171 0.975911i \(-0.429991\pi\)
0.218171 + 0.975911i \(0.429991\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.38421e7 −0.822527
\(778\) 0 0
\(779\) 7.02268e6 0.414629
\(780\) 0 0
\(781\) 1.40337e7 0.823273
\(782\) 0 0
\(783\) 1.68733e7 0.983547
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −4.98037e6 −0.286632 −0.143316 0.989677i \(-0.545777\pi\)
−0.143316 + 0.989677i \(0.545777\pi\)
\(788\) 0 0
\(789\) 7.01670e6 0.401273
\(790\) 0 0
\(791\) −5.96773e6 −0.339132
\(792\) 0 0
\(793\) −4.12258e6 −0.232802
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.48673e7 −0.829061 −0.414530 0.910036i \(-0.636054\pi\)
−0.414530 + 0.910036i \(0.636054\pi\)
\(798\) 0 0
\(799\) −1.31904e6 −0.0730955
\(800\) 0 0
\(801\) 6.77817e6 0.373277
\(802\) 0 0
\(803\) 4.80742e6 0.263101
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.59995e7 1.40534
\(808\) 0 0
\(809\) −684390. −0.0367648 −0.0183824 0.999831i \(-0.505852\pi\)
−0.0183824 + 0.999831i \(0.505852\pi\)
\(810\) 0 0
\(811\) −3.27890e7 −1.75056 −0.875279 0.483618i \(-0.839323\pi\)
−0.875279 + 0.483618i \(0.839323\pi\)
\(812\) 0 0
\(813\) −1.34341e7 −0.712825
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.73016e7 0.906841
\(818\) 0 0
\(819\) −1.34505e6 −0.0700694
\(820\) 0 0
\(821\) 7.17265e6 0.371383 0.185691 0.982608i \(-0.440548\pi\)
0.185691 + 0.982608i \(0.440548\pi\)
\(822\) 0 0
\(823\) −1.32939e6 −0.0684153 −0.0342077 0.999415i \(-0.510891\pi\)
−0.0342077 + 0.999415i \(0.510891\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.92964e7 0.981099 0.490550 0.871413i \(-0.336796\pi\)
0.490550 + 0.871413i \(0.336796\pi\)
\(828\) 0 0
\(829\) 7.10811e6 0.359226 0.179613 0.983737i \(-0.442515\pi\)
0.179613 + 0.983737i \(0.442515\pi\)
\(830\) 0 0
\(831\) −5.97972e6 −0.300385
\(832\) 0 0
\(833\) −429514. −0.0214469
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.29622e7 0.639534
\(838\) 0 0
\(839\) −8.24538e6 −0.404395 −0.202198 0.979345i \(-0.564808\pi\)
−0.202198 + 0.979345i \(0.564808\pi\)
\(840\) 0 0
\(841\) −3.61905e6 −0.176443
\(842\) 0 0
\(843\) −1.67231e7 −0.810493
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1.30001e7 0.622640
\(848\) 0 0
\(849\) −3.05761e7 −1.45584
\(850\) 0 0
\(851\) 1.96029e7 0.927889
\(852\) 0 0
\(853\) −1.86921e7 −0.879599 −0.439800 0.898096i \(-0.644951\pi\)
−0.439800 + 0.898096i \(0.644951\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.24473e7 1.04403 0.522013 0.852937i \(-0.325181\pi\)
0.522013 + 0.852937i \(0.325181\pi\)
\(858\) 0 0
\(859\) 3.24436e6 0.150019 0.0750094 0.997183i \(-0.476101\pi\)
0.0750094 + 0.997183i \(0.476101\pi\)
\(860\) 0 0
\(861\) 1.35222e7 0.621641
\(862\) 0 0
\(863\) 1.01542e6 0.0464108 0.0232054 0.999731i \(-0.492613\pi\)
0.0232054 + 0.999731i \(0.492613\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.86243e7 0.841457
\(868\) 0 0
\(869\) −2.24994e7 −1.01070
\(870\) 0 0
\(871\) 7.67015e6 0.342577
\(872\) 0 0
\(873\) −6.85679e6 −0.304499
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −3.96764e7 −1.74194 −0.870970 0.491337i \(-0.836508\pi\)
−0.870970 + 0.491337i \(0.836508\pi\)
\(878\) 0 0
\(879\) 3.29275e7 1.43743
\(880\) 0 0
\(881\) −2.44584e7 −1.06167 −0.530833 0.847477i \(-0.678121\pi\)
−0.530833 + 0.847477i \(0.678121\pi\)
\(882\) 0 0
\(883\) −3.11179e7 −1.34310 −0.671549 0.740960i \(-0.734371\pi\)
−0.671549 + 0.740960i \(0.734371\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.87514e7 −0.800249 −0.400124 0.916461i \(-0.631033\pi\)
−0.400124 + 0.916461i \(0.631033\pi\)
\(888\) 0 0
\(889\) −2.18172e7 −0.925858
\(890\) 0 0
\(891\) −1.03160e7 −0.435327
\(892\) 0 0
\(893\) 7.15824e6 0.300385
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −5.44236e6 −0.225843
\(898\) 0 0
\(899\) 1.29766e7 0.535503
\(900\) 0 0
\(901\) 5.73623e6 0.235404
\(902\) 0 0
\(903\) 3.33143e7 1.35960
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −5.07504e6 −0.204843 −0.102421 0.994741i \(-0.532659\pi\)
−0.102421 + 0.994741i \(0.532659\pi\)
\(908\) 0 0
\(909\) −3.72947e6 −0.149706
\(910\) 0 0
\(911\) −2.83599e7 −1.13216 −0.566082 0.824349i \(-0.691541\pi\)
−0.566082 + 0.824349i \(0.691541\pi\)
\(912\) 0 0
\(913\) 2.03986e7 0.809885
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.71169e7 1.45763
\(918\) 0 0
\(919\) 9.58570e6 0.374399 0.187200 0.982322i \(-0.440059\pi\)
0.187200 + 0.982322i \(0.440059\pi\)
\(920\) 0 0
\(921\) −277860. −0.0107939
\(922\) 0 0
\(923\) −8.33200e6 −0.321918
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −7.11321e6 −0.271873
\(928\) 0 0
\(929\) −3.82212e7 −1.45300 −0.726500 0.687167i \(-0.758854\pi\)
−0.726500 + 0.687167i \(0.758854\pi\)
\(930\) 0 0
\(931\) 2.33091e6 0.0881357
\(932\) 0 0
\(933\) 634200. 0.0238519
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 9.37422e6 0.348808 0.174404 0.984674i \(-0.444200\pi\)
0.174404 + 0.984674i \(0.444200\pi\)
\(938\) 0 0
\(939\) −3.74544e7 −1.38624
\(940\) 0 0
\(941\) 3.04898e6 0.112249 0.0561243 0.998424i \(-0.482126\pi\)
0.0561243 + 0.998424i \(0.482126\pi\)
\(942\) 0 0
\(943\) −1.91498e7 −0.701270
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.95948e7 −1.07236 −0.536180 0.844104i \(-0.680133\pi\)
−0.536180 + 0.844104i \(0.680133\pi\)
\(948\) 0 0
\(949\) −2.85424e6 −0.102878
\(950\) 0 0
\(951\) −6.32694e6 −0.226852
\(952\) 0 0
\(953\) −1.58338e7 −0.564744 −0.282372 0.959305i \(-0.591121\pi\)
−0.282372 + 0.959305i \(0.591121\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −1.43028e7 −0.504825
\(958\) 0 0
\(959\) −1.55492e7 −0.545960
\(960\) 0 0
\(961\) −1.86604e7 −0.651798
\(962\) 0 0
\(963\) 2.52246e6 0.0876513
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −8.69009e6 −0.298853 −0.149427 0.988773i \(-0.547743\pi\)
−0.149427 + 0.988773i \(0.547743\pi\)
\(968\) 0 0
\(969\) 2.30688e6 0.0789252
\(970\) 0 0
\(971\) 2.81474e7 0.958054 0.479027 0.877800i \(-0.340990\pi\)
0.479027 + 0.877800i \(0.340990\pi\)
\(972\) 0 0
\(973\) −2.04278e7 −0.691733
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.34090e7 1.45493 0.727467 0.686143i \(-0.240697\pi\)
0.727467 + 0.686143i \(0.240697\pi\)
\(978\) 0 0
\(979\) −2.79071e7 −0.930590
\(980\) 0 0
\(981\) 8.79568e6 0.291808
\(982\) 0 0
\(983\) −4.64172e7 −1.53213 −0.766065 0.642763i \(-0.777788\pi\)
−0.766065 + 0.642763i \(0.777788\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 1.37832e7 0.450358
\(988\) 0 0
\(989\) −4.71789e7 −1.53376
\(990\) 0 0
\(991\) −4.64577e7 −1.50271 −0.751353 0.659901i \(-0.770598\pi\)
−0.751353 + 0.659901i \(0.770598\pi\)
\(992\) 0 0
\(993\) −4.14690e7 −1.33460
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.35968e7 −0.433211 −0.216605 0.976259i \(-0.569499\pi\)
−0.216605 + 0.976259i \(0.569499\pi\)
\(998\) 0 0
\(999\) −3.05525e7 −0.968576
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 800.6.a.i.1.1 2
4.3 odd 2 inner 800.6.a.i.1.2 2
5.2 odd 4 800.6.c.h.449.4 4
5.3 odd 4 800.6.c.h.449.2 4
5.4 even 2 160.6.a.b.1.2 yes 2
20.3 even 4 800.6.c.h.449.3 4
20.7 even 4 800.6.c.h.449.1 4
20.19 odd 2 160.6.a.b.1.1 2
40.19 odd 2 320.6.a.t.1.2 2
40.29 even 2 320.6.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.b.1.1 2 20.19 odd 2
160.6.a.b.1.2 yes 2 5.4 even 2
320.6.a.t.1.1 2 40.29 even 2
320.6.a.t.1.2 2 40.19 odd 2
800.6.a.i.1.1 2 1.1 even 1 trivial
800.6.a.i.1.2 2 4.3 odd 2 inner
800.6.c.h.449.1 4 20.7 even 4
800.6.c.h.449.2 4 5.3 odd 4
800.6.c.h.449.3 4 20.3 even 4
800.6.c.h.449.4 4 5.2 odd 4