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Properties

Label 200.6.a.d.1.1
Level $200$
Weight $6$
Character 200.1
Self dual yes
Analytic conductor $32.077$
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] = [200,6,Mod(1,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, 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("200.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 200.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: \(32.0767639626\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+18.0000 q^{3} -242.000 q^{7} +81.0000 q^{9} +656.000 q^{11} +206.000 q^{13} -1690.00 q^{17} -1364.00 q^{19} -4356.00 q^{21} -2198.00 q^{23} -2916.00 q^{27} -2218.00 q^{29} -1700.00 q^{31} +11808.0 q^{33} +846.000 q^{37} +3708.00 q^{39} -1818.00 q^{41} -10534.0 q^{43} -12074.0 q^{47} +41757.0 q^{49} -30420.0 q^{51} -32586.0 q^{53} -24552.0 q^{57} +8668.00 q^{59} -34670.0 q^{61} -19602.0 q^{63} +47566.0 q^{67} -39564.0 q^{69} +948.000 q^{71} +63102.0 q^{73} -158752. q^{77} +46536.0 q^{79} -72171.0 q^{81} +88778.0 q^{83} -39924.0 q^{87} -104934. q^{89} -49852.0 q^{91} -30600.0 q^{93} +36254.0 q^{97} +53136.0 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 18.0000 1.15470 0.577350 − 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −242.000 −1.86668 −0.933341 − 0.358991i \(-0.883121\pi\)
−0.933341 + 0.358991i \(0.883121\pi\)
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) 656.000 1.63464 0.817320 − 0.576184i \(-0.195459\pi\)
0.817320 + 0.576184i \(0.195459\pi\)
\(12\) 0 0
\(13\) 206.000 0.338072 0.169036 − 0.985610i \(-0.445935\pi\)
0.169036 + 0.985610i \(0.445935\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1690.00 −1.41829 −0.709144 − 0.705064i \(-0.750918\pi\)
−0.709144 + 0.705064i \(0.750918\pi\)
\(18\) 0 0
\(19\) −1364.00 −0.866823 −0.433411 − 0.901196i \(-0.642690\pi\)
−0.433411 + 0.901196i \(0.642690\pi\)
\(20\) 0 0
\(21\) −4356.00 −2.15546
\(22\) 0 0
\(23\) −2198.00 −0.866379 −0.433190 − 0.901303i \(-0.642612\pi\)
−0.433190 + 0.901303i \(0.642612\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2916.00 −0.769800
\(28\) 0 0
\(29\) −2218.00 −0.489741 −0.244871 − 0.969556i \(-0.578745\pi\)
−0.244871 + 0.969556i \(0.578745\pi\)
\(30\) 0 0
\(31\) −1700.00 −0.317720 −0.158860 − 0.987301i \(-0.550782\pi\)
−0.158860 + 0.987301i \(0.550782\pi\)
\(32\) 0 0
\(33\) 11808.0 1.88752
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 846.000 0.101594 0.0507968 − 0.998709i \(-0.483824\pi\)
0.0507968 + 0.998709i \(0.483824\pi\)
\(38\) 0 0
\(39\) 3708.00 0.390372
\(40\) 0 0
\(41\) −1818.00 −0.168902 −0.0844509 − 0.996428i \(-0.526914\pi\)
−0.0844509 + 0.996428i \(0.526914\pi\)
\(42\) 0 0
\(43\) −10534.0 −0.868805 −0.434402 − 0.900719i \(-0.643040\pi\)
−0.434402 + 0.900719i \(0.643040\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12074.0 −0.797272 −0.398636 − 0.917109i \(-0.630516\pi\)
−0.398636 + 0.917109i \(0.630516\pi\)
\(48\) 0 0
\(49\) 41757.0 2.48450
\(50\) 0 0
\(51\) −30420.0 −1.63770
\(52\) 0 0
\(53\) −32586.0 −1.59346 −0.796730 − 0.604335i \(-0.793439\pi\)
−0.796730 + 0.604335i \(0.793439\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −24552.0 −1.00092
\(58\) 0 0
\(59\) 8668.00 0.324182 0.162091 − 0.986776i \(-0.448176\pi\)
0.162091 + 0.986776i \(0.448176\pi\)
\(60\) 0 0
\(61\) −34670.0 −1.19297 −0.596485 − 0.802624i \(-0.703436\pi\)
−0.596485 + 0.802624i \(0.703436\pi\)
\(62\) 0 0
\(63\) −19602.0 −0.622227
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 47566.0 1.29452 0.647261 − 0.762268i \(-0.275914\pi\)
0.647261 + 0.762268i \(0.275914\pi\)
\(68\) 0 0
\(69\) −39564.0 −1.00041
\(70\) 0 0
\(71\) 948.000 0.0223184 0.0111592 − 0.999938i \(-0.496448\pi\)
0.0111592 + 0.999938i \(0.496448\pi\)
\(72\) 0 0
\(73\) 63102.0 1.38591 0.692957 − 0.720979i \(-0.256308\pi\)
0.692957 + 0.720979i \(0.256308\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −158752. −3.05135
\(78\) 0 0
\(79\) 46536.0 0.838921 0.419461 − 0.907773i \(-0.362219\pi\)
0.419461 + 0.907773i \(0.362219\pi\)
\(80\) 0 0
\(81\) −72171.0 −1.22222
\(82\) 0 0
\(83\) 88778.0 1.41452 0.707262 − 0.706952i \(-0.249930\pi\)
0.707262 + 0.706952i \(0.249930\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −39924.0 −0.565504
\(88\) 0 0
\(89\) −104934. −1.40424 −0.702120 − 0.712059i \(-0.747763\pi\)
−0.702120 + 0.712059i \(0.747763\pi\)
\(90\) 0 0
\(91\) −49852.0 −0.631072
\(92\) 0 0
\(93\) −30600.0 −0.366872
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 36254.0 0.391225 0.195612 − 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(98\) 0 0
\(99\) 53136.0 0.544880
\(100\) 0 0
\(101\) 42486.0 0.414422 0.207211 − 0.978296i \(-0.433561\pi\)
0.207211 + 0.978296i \(0.433561\pi\)
\(102\) 0 0
\(103\) −147934. −1.37396 −0.686981 − 0.726675i \(-0.741065\pi\)
−0.686981 + 0.726675i \(0.741065\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18390.0 0.155282 0.0776412 − 0.996981i \(-0.475261\pi\)
0.0776412 + 0.996981i \(0.475261\pi\)
\(108\) 0 0
\(109\) −145006. −1.16901 −0.584507 − 0.811389i \(-0.698712\pi\)
−0.584507 + 0.811389i \(0.698712\pi\)
\(110\) 0 0
\(111\) 15228.0 0.117310
\(112\) 0 0
\(113\) −82746.0 −0.609608 −0.304804 − 0.952415i \(-0.598591\pi\)
−0.304804 + 0.952415i \(0.598591\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 16686.0 0.112691
\(118\) 0 0
\(119\) 408980. 2.64749
\(120\) 0 0
\(121\) 269285. 1.67205
\(122\) 0 0
\(123\) −32724.0 −0.195031
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 274446. 1.50990 0.754949 − 0.655784i \(-0.227662\pi\)
0.754949 + 0.655784i \(0.227662\pi\)
\(128\) 0 0
\(129\) −189612. −1.00321
\(130\) 0 0
\(131\) 202608. 1.03152 0.515761 − 0.856733i \(-0.327509\pi\)
0.515761 + 0.856733i \(0.327509\pi\)
\(132\) 0 0
\(133\) 330088. 1.61808
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 48142.0 0.219141 0.109570 − 0.993979i \(-0.465053\pi\)
0.109570 + 0.993979i \(0.465053\pi\)
\(138\) 0 0
\(139\) −111156. −0.487973 −0.243987 − 0.969779i \(-0.578455\pi\)
−0.243987 + 0.969779i \(0.578455\pi\)
\(140\) 0 0
\(141\) −217332. −0.920610
\(142\) 0 0
\(143\) 135136. 0.552626
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 751626. 2.86885
\(148\) 0 0
\(149\) 243178. 0.897343 0.448672 − 0.893697i \(-0.351897\pi\)
0.448672 + 0.893697i \(0.351897\pi\)
\(150\) 0 0
\(151\) 368852. 1.31647 0.658233 − 0.752814i \(-0.271304\pi\)
0.658233 + 0.752814i \(0.271304\pi\)
\(152\) 0 0
\(153\) −136890. −0.472763
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −319546. −1.03463 −0.517314 − 0.855796i \(-0.673068\pi\)
−0.517314 + 0.855796i \(0.673068\pi\)
\(158\) 0 0
\(159\) −586548. −1.83997
\(160\) 0 0
\(161\) 531916. 1.61725
\(162\) 0 0
\(163\) −69862.0 −0.205955 −0.102977 − 0.994684i \(-0.532837\pi\)
−0.102977 + 0.994684i \(0.532837\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 343422. 0.952877 0.476439 − 0.879208i \(-0.341927\pi\)
0.476439 + 0.879208i \(0.341927\pi\)
\(168\) 0 0
\(169\) −328857. −0.885708
\(170\) 0 0
\(171\) −110484. −0.288941
\(172\) 0 0
\(173\) 1142.00 0.00290102 0.00145051 − 0.999999i \(-0.499538\pi\)
0.00145051 + 0.999999i \(0.499538\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 156024. 0.374333
\(178\) 0 0
\(179\) −86684.0 −0.202212 −0.101106 − 0.994876i \(-0.532238\pi\)
−0.101106 + 0.994876i \(0.532238\pi\)
\(180\) 0 0
\(181\) −651418. −1.47796 −0.738981 − 0.673726i \(-0.764693\pi\)
−0.738981 + 0.673726i \(0.764693\pi\)
\(182\) 0 0
\(183\) −624060. −1.37752
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.10864e6 −2.31839
\(188\) 0 0
\(189\) 705672. 1.43697
\(190\) 0 0
\(191\) 29140.0 0.0577971 0.0288986 − 0.999582i \(-0.490800\pi\)
0.0288986 + 0.999582i \(0.490800\pi\)
\(192\) 0 0
\(193\) 646406. 1.24914 0.624571 − 0.780968i \(-0.285274\pi\)
0.624571 + 0.780968i \(0.285274\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −431138. −0.791500 −0.395750 − 0.918358i \(-0.629515\pi\)
−0.395750 + 0.918358i \(0.629515\pi\)
\(198\) 0 0
\(199\) −131608. −0.235586 −0.117793 − 0.993038i \(-0.537582\pi\)
−0.117793 + 0.993038i \(0.537582\pi\)
\(200\) 0 0
\(201\) 856188. 1.49479
\(202\) 0 0
\(203\) 536756. 0.914191
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −178038. −0.288793
\(208\) 0 0
\(209\) −894784. −1.41694
\(210\) 0 0
\(211\) 1.21078e6 1.87224 0.936118 − 0.351686i \(-0.114392\pi\)
0.936118 + 0.351686i \(0.114392\pi\)
\(212\) 0 0
\(213\) 17064.0 0.0257710
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 411400. 0.593082
\(218\) 0 0
\(219\) 1.13584e6 1.60031
\(220\) 0 0
\(221\) −348140. −0.479483
\(222\) 0 0
\(223\) −34886.0 −0.0469774 −0.0234887 − 0.999724i \(-0.507477\pi\)
−0.0234887 + 0.999724i \(0.507477\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 124182. 0.159954 0.0799768 − 0.996797i \(-0.474515\pi\)
0.0799768 + 0.996797i \(0.474515\pi\)
\(228\) 0 0
\(229\) −456386. −0.575100 −0.287550 − 0.957766i \(-0.592841\pi\)
−0.287550 + 0.957766i \(0.592841\pi\)
\(230\) 0 0
\(231\) −2.85754e6 −3.52340
\(232\) 0 0
\(233\) −252666. −0.304900 −0.152450 − 0.988311i \(-0.548716\pi\)
−0.152450 + 0.988311i \(0.548716\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 837648. 0.968703
\(238\) 0 0
\(239\) 65064.0 0.0736794 0.0368397 − 0.999321i \(-0.488271\pi\)
0.0368397 + 0.999321i \(0.488271\pi\)
\(240\) 0 0
\(241\) −1.40600e6 −1.55935 −0.779675 − 0.626185i \(-0.784615\pi\)
−0.779675 + 0.626185i \(0.784615\pi\)
\(242\) 0 0
\(243\) −590490. −0.641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −280984. −0.293048
\(248\) 0 0
\(249\) 1.59800e6 1.63335
\(250\) 0 0
\(251\) −548400. −0.549431 −0.274715 − 0.961526i \(-0.588584\pi\)
−0.274715 + 0.961526i \(0.588584\pi\)
\(252\) 0 0
\(253\) −1.44189e6 −1.41622
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 493830. 0.466385 0.233193 − 0.972431i \(-0.425083\pi\)
0.233193 + 0.972431i \(0.425083\pi\)
\(258\) 0 0
\(259\) −204732. −0.189643
\(260\) 0 0
\(261\) −179658. −0.163247
\(262\) 0 0
\(263\) 1.07181e6 0.955495 0.477748 − 0.878497i \(-0.341453\pi\)
0.477748 + 0.878497i \(0.341453\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.88881e6 −1.62148
\(268\) 0 0
\(269\) 999394. 0.842085 0.421043 − 0.907041i \(-0.361664\pi\)
0.421043 + 0.907041i \(0.361664\pi\)
\(270\) 0 0
\(271\) 1.00760e6 0.833425 0.416713 − 0.909038i \(-0.363182\pi\)
0.416713 + 0.909038i \(0.363182\pi\)
\(272\) 0 0
\(273\) −897336. −0.728700
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.02286e6 −0.800969 −0.400485 − 0.916303i \(-0.631158\pi\)
−0.400485 + 0.916303i \(0.631158\pi\)
\(278\) 0 0
\(279\) −137700. −0.105907
\(280\) 0 0
\(281\) −1.18172e6 −0.892790 −0.446395 − 0.894836i \(-0.647292\pi\)
−0.446395 + 0.894836i \(0.647292\pi\)
\(282\) 0 0
\(283\) 917506. 0.680993 0.340497 − 0.940246i \(-0.389405\pi\)
0.340497 + 0.940246i \(0.389405\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 439956. 0.315286
\(288\) 0 0
\(289\) 1.43624e6 1.01154
\(290\) 0 0
\(291\) 652572. 0.451748
\(292\) 0 0
\(293\) 512302. 0.348624 0.174312 − 0.984690i \(-0.444230\pi\)
0.174312 + 0.984690i \(0.444230\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.91290e6 −1.25835
\(298\) 0 0
\(299\) −452788. −0.292898
\(300\) 0 0
\(301\) 2.54923e6 1.62178
\(302\) 0 0
\(303\) 764748. 0.478533
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.40946e6 −0.853505 −0.426753 − 0.904368i \(-0.640342\pi\)
−0.426753 + 0.904368i \(0.640342\pi\)
\(308\) 0 0
\(309\) −2.66281e6 −1.58652
\(310\) 0 0
\(311\) −2.78604e6 −1.63337 −0.816687 − 0.577081i \(-0.804192\pi\)
−0.816687 + 0.577081i \(0.804192\pi\)
\(312\) 0 0
\(313\) −1.55086e6 −0.894770 −0.447385 − 0.894342i \(-0.647645\pi\)
−0.447385 + 0.894342i \(0.647645\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −377322. −0.210894 −0.105447 − 0.994425i \(-0.533627\pi\)
−0.105447 + 0.994425i \(0.533627\pi\)
\(318\) 0 0
\(319\) −1.45501e6 −0.800550
\(320\) 0 0
\(321\) 331020. 0.179305
\(322\) 0 0
\(323\) 2.30516e6 1.22940
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.61011e6 −1.34986
\(328\) 0 0
\(329\) 2.92191e6 1.48825
\(330\) 0 0
\(331\) −1.63063e6 −0.818062 −0.409031 − 0.912521i \(-0.634133\pi\)
−0.409031 + 0.912521i \(0.634133\pi\)
\(332\) 0 0
\(333\) 68526.0 0.0338645
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.36717e6 1.61506 0.807532 − 0.589824i \(-0.200803\pi\)
0.807532 + 0.589824i \(0.200803\pi\)
\(338\) 0 0
\(339\) −1.48943e6 −0.703915
\(340\) 0 0
\(341\) −1.11520e6 −0.519358
\(342\) 0 0
\(343\) −6.03790e6 −2.77109
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −837202. −0.373256 −0.186628 − 0.982431i \(-0.559756\pi\)
−0.186628 + 0.982431i \(0.559756\pi\)
\(348\) 0 0
\(349\) −1.51910e6 −0.667609 −0.333805 − 0.942642i \(-0.608333\pi\)
−0.333805 + 0.942642i \(0.608333\pi\)
\(350\) 0 0
\(351\) −600696. −0.260248
\(352\) 0 0
\(353\) 3.51851e6 1.50287 0.751436 − 0.659806i \(-0.229362\pi\)
0.751436 + 0.659806i \(0.229362\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.36164e6 3.05706
\(358\) 0 0
\(359\) −3.57089e6 −1.46231 −0.731156 − 0.682210i \(-0.761019\pi\)
−0.731156 + 0.682210i \(0.761019\pi\)
\(360\) 0 0
\(361\) −615603. −0.248618
\(362\) 0 0
\(363\) 4.84713e6 1.93071
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3.58231e6 1.38835 0.694173 − 0.719808i \(-0.255770\pi\)
0.694173 + 0.719808i \(0.255770\pi\)
\(368\) 0 0
\(369\) −147258. −0.0563006
\(370\) 0 0
\(371\) 7.88581e6 2.97448
\(372\) 0 0
\(373\) −635530. −0.236518 −0.118259 − 0.992983i \(-0.537731\pi\)
−0.118259 + 0.992983i \(0.537731\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −456908. −0.165568
\(378\) 0 0
\(379\) 67060.0 0.0239809 0.0119905 − 0.999928i \(-0.496183\pi\)
0.0119905 + 0.999928i \(0.496183\pi\)
\(380\) 0 0
\(381\) 4.94003e6 1.74348
\(382\) 0 0
\(383\) −4.45129e6 −1.55056 −0.775280 − 0.631618i \(-0.782391\pi\)
−0.775280 + 0.631618i \(0.782391\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −853254. −0.289602
\(388\) 0 0
\(389\) 5.79825e6 1.94278 0.971388 − 0.237496i \(-0.0763267\pi\)
0.971388 + 0.237496i \(0.0763267\pi\)
\(390\) 0 0
\(391\) 3.71462e6 1.22878
\(392\) 0 0
\(393\) 3.64694e6 1.19110
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −333874. −0.106318 −0.0531589 − 0.998586i \(-0.516929\pi\)
−0.0531589 + 0.998586i \(0.516929\pi\)
\(398\) 0 0
\(399\) 5.94158e6 1.86840
\(400\) 0 0
\(401\) −2.55689e6 −0.794057 −0.397029 − 0.917806i \(-0.629959\pi\)
−0.397029 + 0.917806i \(0.629959\pi\)
\(402\) 0 0
\(403\) −350200. −0.107412
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 554976. 0.166069
\(408\) 0 0
\(409\) −3.05511e6 −0.903063 −0.451531 − 0.892255i \(-0.649122\pi\)
−0.451531 + 0.892255i \(0.649122\pi\)
\(410\) 0 0
\(411\) 866556. 0.253042
\(412\) 0 0
\(413\) −2.09766e6 −0.605145
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.00081e6 −0.563463
\(418\) 0 0
\(419\) −3.54347e6 −0.986038 −0.493019 − 0.870019i \(-0.664107\pi\)
−0.493019 + 0.870019i \(0.664107\pi\)
\(420\) 0 0
\(421\) 1.97294e6 0.542511 0.271255 − 0.962507i \(-0.412561\pi\)
0.271255 + 0.962507i \(0.412561\pi\)
\(422\) 0 0
\(423\) −977994. −0.265757
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 8.39014e6 2.22689
\(428\) 0 0
\(429\) 2.43245e6 0.638117
\(430\) 0 0
\(431\) 1.37396e6 0.356270 0.178135 − 0.984006i \(-0.442994\pi\)
0.178135 + 0.984006i \(0.442994\pi\)
\(432\) 0 0
\(433\) −5.18813e6 −1.32981 −0.664907 − 0.746926i \(-0.731529\pi\)
−0.664907 + 0.746926i \(0.731529\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.99807e6 0.750997
\(438\) 0 0
\(439\) −2.94082e6 −0.728296 −0.364148 − 0.931341i \(-0.618640\pi\)
−0.364148 + 0.931341i \(0.618640\pi\)
\(440\) 0 0
\(441\) 3.38232e6 0.828167
\(442\) 0 0
\(443\) 1.28347e6 0.310724 0.155362 − 0.987858i \(-0.450346\pi\)
0.155362 + 0.987858i \(0.450346\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4.37720e6 1.03616
\(448\) 0 0
\(449\) −4.95263e6 −1.15937 −0.579683 − 0.814842i \(-0.696824\pi\)
−0.579683 + 0.814842i \(0.696824\pi\)
\(450\) 0 0
\(451\) −1.19261e6 −0.276094
\(452\) 0 0
\(453\) 6.63934e6 1.52012
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.91315e6 −1.77239 −0.886194 − 0.463315i \(-0.846660\pi\)
−0.886194 + 0.463315i \(0.846660\pi\)
\(458\) 0 0
\(459\) 4.92804e6 1.09180
\(460\) 0 0
\(461\) −6.18530e6 −1.35553 −0.677764 − 0.735280i \(-0.737051\pi\)
−0.677764 + 0.735280i \(0.737051\pi\)
\(462\) 0 0
\(463\) −491934. −0.106648 −0.0533242 − 0.998577i \(-0.516982\pi\)
−0.0533242 + 0.998577i \(0.516982\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −447442. −0.0949390 −0.0474695 − 0.998873i \(-0.515116\pi\)
−0.0474695 + 0.998873i \(0.515116\pi\)
\(468\) 0 0
\(469\) −1.15110e7 −2.41646
\(470\) 0 0
\(471\) −5.75183e6 −1.19469
\(472\) 0 0
\(473\) −6.91030e6 −1.42018
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −2.63947e6 −0.531154
\(478\) 0 0
\(479\) 8.18487e6 1.62995 0.814973 − 0.579499i \(-0.196752\pi\)
0.814973 + 0.579499i \(0.196752\pi\)
\(480\) 0 0
\(481\) 174276. 0.0343459
\(482\) 0 0
\(483\) 9.57449e6 1.86744
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6.21524e6 −1.18751 −0.593753 − 0.804648i \(-0.702354\pi\)
−0.593753 + 0.804648i \(0.702354\pi\)
\(488\) 0 0
\(489\) −1.25752e6 −0.237816
\(490\) 0 0
\(491\) 827856. 0.154971 0.0774856 − 0.996993i \(-0.475311\pi\)
0.0774856 + 0.996993i \(0.475311\pi\)
\(492\) 0 0
\(493\) 3.74842e6 0.694594
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −229416. −0.0416613
\(498\) 0 0
\(499\) −1.04004e7 −1.86982 −0.934908 − 0.354890i \(-0.884518\pi\)
−0.934908 + 0.354890i \(0.884518\pi\)
\(500\) 0 0
\(501\) 6.18160e6 1.10029
\(502\) 0 0
\(503\) −2.03821e6 −0.359193 −0.179597 − 0.983740i \(-0.557479\pi\)
−0.179597 + 0.983740i \(0.557479\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −5.91943e6 −1.02273
\(508\) 0 0
\(509\) 3.66133e6 0.626390 0.313195 − 0.949689i \(-0.398601\pi\)
0.313195 + 0.949689i \(0.398601\pi\)
\(510\) 0 0
\(511\) −1.52707e7 −2.58706
\(512\) 0 0
\(513\) 3.97742e6 0.667281
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −7.92054e6 −1.30325
\(518\) 0 0
\(519\) 20556.0 0.00334981
\(520\) 0 0
\(521\) 3.24713e6 0.524089 0.262045 − 0.965056i \(-0.415603\pi\)
0.262045 + 0.965056i \(0.415603\pi\)
\(522\) 0 0
\(523\) 4.97357e6 0.795086 0.397543 − 0.917584i \(-0.369863\pi\)
0.397543 + 0.917584i \(0.369863\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.87300e6 0.450619
\(528\) 0 0
\(529\) −1.60514e6 −0.249387
\(530\) 0 0
\(531\) 702108. 0.108061
\(532\) 0 0
\(533\) −374508. −0.0571009
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.56031e6 −0.233494
\(538\) 0 0
\(539\) 2.73926e7 4.06126
\(540\) 0 0
\(541\) 2.42544e6 0.356285 0.178142 − 0.984005i \(-0.442991\pi\)
0.178142 + 0.984005i \(0.442991\pi\)
\(542\) 0 0
\(543\) −1.17255e7 −1.70660
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 731254. 0.104496 0.0522480 − 0.998634i \(-0.483361\pi\)
0.0522480 + 0.998634i \(0.483361\pi\)
\(548\) 0 0
\(549\) −2.80827e6 −0.397656
\(550\) 0 0
\(551\) 3.02535e6 0.424519
\(552\) 0 0
\(553\) −1.12617e7 −1.56600
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.71992e6 −1.05433 −0.527163 − 0.849764i \(-0.676744\pi\)
−0.527163 + 0.849764i \(0.676744\pi\)
\(558\) 0 0
\(559\) −2.17000e6 −0.293718
\(560\) 0 0
\(561\) −1.99555e7 −2.67705
\(562\) 0 0
\(563\) −3.10576e6 −0.412949 −0.206475 − 0.978452i \(-0.566199\pi\)
−0.206475 + 0.978452i \(0.566199\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.74654e7 2.28150
\(568\) 0 0
\(569\) −482498. −0.0624762 −0.0312381 − 0.999512i \(-0.509945\pi\)
−0.0312381 + 0.999512i \(0.509945\pi\)
\(570\) 0 0
\(571\) 1.38502e7 1.77773 0.888865 − 0.458169i \(-0.151495\pi\)
0.888865 + 0.458169i \(0.151495\pi\)
\(572\) 0 0
\(573\) 524520. 0.0667384
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −7.09764e6 −0.887513 −0.443756 − 0.896147i \(-0.646354\pi\)
−0.443756 + 0.896147i \(0.646354\pi\)
\(578\) 0 0
\(579\) 1.16353e7 1.44239
\(580\) 0 0
\(581\) −2.14843e7 −2.64046
\(582\) 0 0
\(583\) −2.13764e7 −2.60473
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.56926e6 −0.187975 −0.0939873 − 0.995573i \(-0.529961\pi\)
−0.0939873 + 0.995573i \(0.529961\pi\)
\(588\) 0 0
\(589\) 2.31880e6 0.275407
\(590\) 0 0
\(591\) −7.76048e6 −0.913945
\(592\) 0 0
\(593\) 1.30477e7 1.52370 0.761848 − 0.647756i \(-0.224293\pi\)
0.761848 + 0.647756i \(0.224293\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.36894e6 −0.272031
\(598\) 0 0
\(599\) −5.24688e6 −0.597495 −0.298747 − 0.954332i \(-0.596569\pi\)
−0.298747 + 0.954332i \(0.596569\pi\)
\(600\) 0 0
\(601\) −5.57316e6 −0.629384 −0.314692 − 0.949194i \(-0.601901\pi\)
−0.314692 + 0.949194i \(0.601901\pi\)
\(602\) 0 0
\(603\) 3.85285e6 0.431508
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.98249e6 −0.218393 −0.109197 − 0.994020i \(-0.534828\pi\)
−0.109197 + 0.994020i \(0.534828\pi\)
\(608\) 0 0
\(609\) 9.66161e6 1.05562
\(610\) 0 0
\(611\) −2.48724e6 −0.269535
\(612\) 0 0
\(613\) −969810. −0.104240 −0.0521201 − 0.998641i \(-0.516598\pi\)
−0.0521201 + 0.998641i \(0.516598\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.12946e7 1.19442 0.597211 − 0.802084i \(-0.296275\pi\)
0.597211 + 0.802084i \(0.296275\pi\)
\(618\) 0 0
\(619\) −1.80728e7 −1.89583 −0.947914 − 0.318528i \(-0.896812\pi\)
−0.947914 + 0.318528i \(0.896812\pi\)
\(620\) 0 0
\(621\) 6.40937e6 0.666939
\(622\) 0 0
\(623\) 2.53940e7 2.62127
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.61061e7 −1.63615
\(628\) 0 0
\(629\) −1.42974e6 −0.144089
\(630\) 0 0
\(631\) 4.62634e6 0.462556 0.231278 − 0.972888i \(-0.425709\pi\)
0.231278 + 0.972888i \(0.425709\pi\)
\(632\) 0 0
\(633\) 2.17941e7 2.16187
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 8.60194e6 0.839939
\(638\) 0 0
\(639\) 76788.0 0.00743946
\(640\) 0 0
\(641\) 1.99058e7 1.91352 0.956762 − 0.290871i \(-0.0939452\pi\)
0.956762 + 0.290871i \(0.0939452\pi\)
\(642\) 0 0
\(643\) −1.21078e7 −1.15489 −0.577443 − 0.816431i \(-0.695949\pi\)
−0.577443 + 0.816431i \(0.695949\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.53124e6 0.237724 0.118862 − 0.992911i \(-0.462075\pi\)
0.118862 + 0.992911i \(0.462075\pi\)
\(648\) 0 0
\(649\) 5.68621e6 0.529921
\(650\) 0 0
\(651\) 7.40520e6 0.684832
\(652\) 0 0
\(653\) −1.37043e7 −1.25770 −0.628848 − 0.777529i \(-0.716473\pi\)
−0.628848 + 0.777529i \(0.716473\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.11126e6 0.461971
\(658\) 0 0
\(659\) −9.83320e6 −0.882026 −0.441013 − 0.897501i \(-0.645381\pi\)
−0.441013 + 0.897501i \(0.645381\pi\)
\(660\) 0 0
\(661\) 6.68687e6 0.595278 0.297639 − 0.954679i \(-0.403801\pi\)
0.297639 + 0.954679i \(0.403801\pi\)
\(662\) 0 0
\(663\) −6.26652e6 −0.553659
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4.87516e6 0.424302
\(668\) 0 0
\(669\) −627948. −0.0542448
\(670\) 0 0
\(671\) −2.27435e7 −1.95008
\(672\) 0 0
\(673\) 727566. 0.0619205 0.0309603 − 0.999521i \(-0.490143\pi\)
0.0309603 + 0.999521i \(0.490143\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.86951e7 −1.56768 −0.783839 − 0.620964i \(-0.786741\pi\)
−0.783839 + 0.620964i \(0.786741\pi\)
\(678\) 0 0
\(679\) −8.77347e6 −0.730293
\(680\) 0 0
\(681\) 2.23528e6 0.184699
\(682\) 0 0
\(683\) 1.79850e7 1.47523 0.737614 − 0.675223i \(-0.235952\pi\)
0.737614 + 0.675223i \(0.235952\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −8.21495e6 −0.664069
\(688\) 0 0
\(689\) −6.71272e6 −0.538704
\(690\) 0 0
\(691\) 1.20006e6 0.0956107 0.0478053 − 0.998857i \(-0.484777\pi\)
0.0478053 + 0.998857i \(0.484777\pi\)
\(692\) 0 0
\(693\) −1.28589e7 −1.01712
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3.07242e6 0.239551
\(698\) 0 0
\(699\) −4.54799e6 −0.352068
\(700\) 0 0
\(701\) −1.15194e7 −0.885393 −0.442697 − 0.896671i \(-0.645978\pi\)
−0.442697 + 0.896671i \(0.645978\pi\)
\(702\) 0 0
\(703\) −1.15394e6 −0.0880636
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.02816e7 −0.773593
\(708\) 0 0
\(709\) −610738. −0.0456288 −0.0228144 − 0.999740i \(-0.507263\pi\)
−0.0228144 + 0.999740i \(0.507263\pi\)
\(710\) 0 0
\(711\) 3.76942e6 0.279640
\(712\) 0 0
\(713\) 3.73660e6 0.275266
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.17115e6 0.0850776
\(718\) 0 0
\(719\) 3.97278e6 0.286597 0.143299 − 0.989680i \(-0.454229\pi\)
0.143299 + 0.989680i \(0.454229\pi\)
\(720\) 0 0
\(721\) 3.58000e7 2.56475
\(722\) 0 0
\(723\) −2.53080e7 −1.80058
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.23220e7 0.864658 0.432329 − 0.901716i \(-0.357692\pi\)
0.432329 + 0.901716i \(0.357692\pi\)
\(728\) 0 0
\(729\) 6.90873e6 0.481481
\(730\) 0 0
\(731\) 1.78025e7 1.23222
\(732\) 0 0
\(733\) −8.14579e6 −0.559981 −0.279990 − 0.960003i \(-0.590331\pi\)
−0.279990 + 0.960003i \(0.590331\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.12033e7 2.11608
\(738\) 0 0
\(739\) 7.16653e6 0.482723 0.241361 − 0.970435i \(-0.422406\pi\)
0.241361 + 0.970435i \(0.422406\pi\)
\(740\) 0 0
\(741\) −5.05771e6 −0.338383
\(742\) 0 0
\(743\) 5.65041e6 0.375498 0.187749 − 0.982217i \(-0.439881\pi\)
0.187749 + 0.982217i \(0.439881\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7.19102e6 0.471508
\(748\) 0 0
\(749\) −4.45038e6 −0.289863
\(750\) 0 0
\(751\) 9.09500e6 0.588441 0.294221 − 0.955738i \(-0.404940\pi\)
0.294221 + 0.955738i \(0.404940\pi\)
\(752\) 0 0
\(753\) −9.87120e6 −0.634428
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.12880e7 0.715944 0.357972 − 0.933732i \(-0.383468\pi\)
0.357972 + 0.933732i \(0.383468\pi\)
\(758\) 0 0
\(759\) −2.59540e7 −1.63531
\(760\) 0 0
\(761\) 1.52933e7 0.957283 0.478641 − 0.878011i \(-0.341129\pi\)
0.478641 + 0.878011i \(0.341129\pi\)
\(762\) 0 0
\(763\) 3.50915e7 2.18218
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.78561e6 0.109597
\(768\) 0 0
\(769\) 1.77402e6 0.108179 0.0540894 − 0.998536i \(-0.482774\pi\)
0.0540894 + 0.998536i \(0.482774\pi\)
\(770\) 0 0
\(771\) 8.88894e6 0.538535
\(772\) 0 0
\(773\) 1.46441e7 0.881484 0.440742 − 0.897634i \(-0.354715\pi\)
0.440742 + 0.897634i \(0.354715\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −3.68518e6 −0.218981
\(778\) 0 0
\(779\) 2.47975e6 0.146408
\(780\) 0 0
\(781\) 621888. 0.0364825
\(782\) 0 0
\(783\) 6.46769e6 0.377003
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 5.97074e6 0.343630 0.171815 − 0.985129i \(-0.445037\pi\)
0.171815 + 0.985129i \(0.445037\pi\)
\(788\) 0 0
\(789\) 1.92926e7 1.10331
\(790\) 0 0
\(791\) 2.00245e7 1.13794
\(792\) 0 0
\(793\) −7.14202e6 −0.403309
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.40500e7 1.89876 0.949382 − 0.314125i \(-0.101711\pi\)
0.949382 + 0.314125i \(0.101711\pi\)
\(798\) 0 0
\(799\) 2.04051e7 1.13076
\(800\) 0 0
\(801\) −8.49965e6 −0.468080
\(802\) 0 0
\(803\) 4.13949e7 2.26547
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.79891e7 0.972356
\(808\) 0 0
\(809\) −2.63540e7 −1.41571 −0.707857 − 0.706356i \(-0.750338\pi\)
−0.707857 + 0.706356i \(0.750338\pi\)
\(810\) 0 0
\(811\) −9.49658e6 −0.507008 −0.253504 − 0.967334i \(-0.581583\pi\)
−0.253504 + 0.967334i \(0.581583\pi\)
\(812\) 0 0
\(813\) 1.81369e7 0.962357
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.43684e7 0.753100
\(818\) 0 0
\(819\) −4.03801e6 −0.210357
\(820\) 0 0
\(821\) −1.59887e7 −0.827856 −0.413928 − 0.910310i \(-0.635843\pi\)
−0.413928 + 0.910310i \(0.635843\pi\)
\(822\) 0 0
\(823\) −3.18347e7 −1.63833 −0.819164 − 0.573559i \(-0.805562\pi\)
−0.819164 + 0.573559i \(0.805562\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.27575e7 −0.648635 −0.324317 − 0.945948i \(-0.605135\pi\)
−0.324317 + 0.945948i \(0.605135\pi\)
\(828\) 0 0
\(829\) 6.18613e6 0.312631 0.156316 − 0.987707i \(-0.450038\pi\)
0.156316 + 0.987707i \(0.450038\pi\)
\(830\) 0 0
\(831\) −1.84114e7 −0.924880
\(832\) 0 0
\(833\) −7.05693e7 −3.52374
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 4.95720e6 0.244581
\(838\) 0 0
\(839\) −5.66754e6 −0.277965 −0.138982 − 0.990295i \(-0.544383\pi\)
−0.138982 + 0.990295i \(0.544383\pi\)
\(840\) 0 0
\(841\) −1.55916e7 −0.760154
\(842\) 0 0
\(843\) −2.12710e7 −1.03091
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −6.51670e7 −3.12118
\(848\) 0 0
\(849\) 1.65151e7 0.786343
\(850\) 0 0
\(851\) −1.85951e6 −0.0880185
\(852\) 0 0
\(853\) 1.76010e7 0.828257 0.414129 − 0.910218i \(-0.364086\pi\)
0.414129 + 0.910218i \(0.364086\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −162162. −0.00754218 −0.00377109 − 0.999993i \(-0.501200\pi\)
−0.00377109 + 0.999993i \(0.501200\pi\)
\(858\) 0 0
\(859\) −7.10520e6 −0.328544 −0.164272 − 0.986415i \(-0.552527\pi\)
−0.164272 + 0.986415i \(0.552527\pi\)
\(860\) 0 0
\(861\) 7.91921e6 0.364061
\(862\) 0 0
\(863\) −4.08956e6 −0.186917 −0.0934586 − 0.995623i \(-0.529792\pi\)
−0.0934586 + 0.995623i \(0.529792\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 2.58524e7 1.16803
\(868\) 0 0
\(869\) 3.05276e7 1.37133
\(870\) 0 0
\(871\) 9.79860e6 0.437641
\(872\) 0 0
\(873\) 2.93657e6 0.130408
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −809194. −0.0355266 −0.0177633 − 0.999842i \(-0.505655\pi\)
−0.0177633 + 0.999842i \(0.505655\pi\)
\(878\) 0 0
\(879\) 9.22144e6 0.402556
\(880\) 0 0
\(881\) 3.90411e6 0.169466 0.0847329 − 0.996404i \(-0.472996\pi\)
0.0847329 + 0.996404i \(0.472996\pi\)
\(882\) 0 0
\(883\) −3.58290e7 −1.54644 −0.773220 − 0.634138i \(-0.781355\pi\)
−0.773220 + 0.634138i \(0.781355\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.77571e7 −1.18458 −0.592290 − 0.805725i \(-0.701776\pi\)
−0.592290 + 0.805725i \(0.701776\pi\)
\(888\) 0 0
\(889\) −6.64159e7 −2.81850
\(890\) 0 0
\(891\) −4.73442e7 −1.99789
\(892\) 0 0
\(893\) 1.64689e7 0.691094
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −8.15018e6 −0.338210
\(898\) 0 0
\(899\) 3.77060e6 0.155601
\(900\) 0 0
\(901\) 5.50703e7 2.25999
\(902\) 0 0
\(903\) 4.58861e7 1.87267
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.01914e7 −0.814981 −0.407490 − 0.913209i \(-0.633596\pi\)
−0.407490 + 0.913209i \(0.633596\pi\)
\(908\) 0 0
\(909\) 3.44137e6 0.138141
\(910\) 0 0
\(911\) 2.75179e7 1.09855 0.549274 − 0.835642i \(-0.314904\pi\)
0.549274 + 0.835642i \(0.314904\pi\)
\(912\) 0 0
\(913\) 5.82384e7 2.31224
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.90311e7 −1.92552
\(918\) 0 0
\(919\) 1.31786e7 0.514730 0.257365 − 0.966314i \(-0.417146\pi\)
0.257365 + 0.966314i \(0.417146\pi\)
\(920\) 0 0
\(921\) −2.53702e7 −0.985543
\(922\) 0 0
\(923\) 195288. 0.00754521
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.19827e7 −0.457988
\(928\) 0 0
\(929\) 4.00688e7 1.52323 0.761617 − 0.648027i \(-0.224406\pi\)
0.761617 + 0.648027i \(0.224406\pi\)
\(930\) 0 0
\(931\) −5.69565e7 −2.15362
\(932\) 0 0
\(933\) −5.01486e7 −1.88606
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −3.04258e7 −1.13212 −0.566060 − 0.824364i \(-0.691533\pi\)
−0.566060 + 0.824364i \(0.691533\pi\)
\(938\) 0 0
\(939\) −2.79154e7 −1.03319
\(940\) 0 0
\(941\) −3.26349e7 −1.20146 −0.600729 − 0.799452i \(-0.705123\pi\)
−0.600729 + 0.799452i \(0.705123\pi\)
\(942\) 0 0
\(943\) 3.99596e6 0.146333
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.01534e7 −1.09260 −0.546300 − 0.837589i \(-0.683964\pi\)
−0.546300 + 0.837589i \(0.683964\pi\)
\(948\) 0 0
\(949\) 1.29990e7 0.468538
\(950\) 0 0
\(951\) −6.79180e6 −0.243519
\(952\) 0 0
\(953\) −303066. −0.0108095 −0.00540474 − 0.999985i \(-0.501720\pi\)
−0.00540474 + 0.999985i \(0.501720\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −2.61901e7 −0.924396
\(958\) 0 0
\(959\) −1.16504e7 −0.409066
\(960\) 0 0
\(961\) −2.57392e7 −0.899054
\(962\) 0 0
\(963\) 1.48959e6 0.0517608
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 7.39863e6 0.254440 0.127220 − 0.991875i \(-0.459395\pi\)
0.127220 + 0.991875i \(0.459395\pi\)
\(968\) 0 0
\(969\) 4.14929e7 1.41959
\(970\) 0 0
\(971\) −6.18414e6 −0.210490 −0.105245 − 0.994446i \(-0.533563\pi\)
−0.105245 + 0.994446i \(0.533563\pi\)
\(972\) 0 0
\(973\) 2.68998e7 0.910891
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.63928e6 −0.0549436 −0.0274718 − 0.999623i \(-0.508746\pi\)
−0.0274718 + 0.999623i \(0.508746\pi\)
\(978\) 0 0
\(979\) −6.88367e7 −2.29543
\(980\) 0 0
\(981\) −1.17455e7 −0.389671
\(982\) 0 0
\(983\) 1.13020e7 0.373052 0.186526 − 0.982450i \(-0.440277\pi\)
0.186526 + 0.982450i \(0.440277\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 5.25943e7 1.71849
\(988\) 0 0
\(989\) 2.31537e7 0.752714
\(990\) 0 0
\(991\) 3.12643e6 0.101126 0.0505632 − 0.998721i \(-0.483898\pi\)
0.0505632 + 0.998721i \(0.483898\pi\)
\(992\) 0 0
\(993\) −2.93514e7 −0.944616
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 3.55827e7 1.13371 0.566854 − 0.823818i \(-0.308160\pi\)
0.566854 + 0.823818i \(0.308160\pi\)
\(998\) 0 0
\(999\) −2.46694e6 −0.0782067
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 200.6.a.d.1.1 1
4.3 odd 2 400.6.a.b.1.1 1
5.2 odd 4 200.6.c.b.49.1 2
5.3 odd 4 200.6.c.b.49.2 2
5.4 even 2 40.6.a.a.1.1 ✓ 1
15.14 odd 2 360.6.a.i.1.1 1
20.3 even 4 400.6.c.e.49.1 2
20.7 even 4 400.6.c.e.49.2 2
20.19 odd 2 80.6.a.g.1.1 1
40.19 odd 2 320.6.a.d.1.1 1
40.29 even 2 320.6.a.m.1.1 1
60.59 even 2 720.6.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.a.1.1 ✓ 1 5.4 even 2
80.6.a.g.1.1 1 20.19 odd 2
200.6.a.d.1.1 1 1.1 even 1 trivial
200.6.c.b.49.1 2 5.2 odd 4
200.6.c.b.49.2 2 5.3 odd 4
320.6.a.d.1.1 1 40.19 odd 2
320.6.a.m.1.1 1 40.29 even 2
360.6.a.i.1.1 1 15.14 odd 2
400.6.a.b.1.1 1 4.3 odd 2
400.6.c.e.49.1 2 20.3 even 4
400.6.c.e.49.2 2 20.7 even 4
720.6.a.k.1.1 1 60.59 even 2