Properties

Label 200.6.a.g.1.1
Level 200
Weight 6
Character 200.1
Self dual yes
Analytic conductor 32.077
Analytic rank 0
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0767639626\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{129}) \)
Defining polynomial: \(x^{2} - x - 32\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-5.17891\) of defining polynomial
Character \(\chi\) \(=\) 200.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.7156 q^{3} -94.1469 q^{7} +36.4124 q^{9} +O(q^{10})\) \(q-16.7156 q^{3} -94.1469 q^{7} +36.4124 q^{9} +143.706 q^{11} -421.412 q^{13} -1982.11 q^{17} -1317.76 q^{19} +1573.73 q^{21} +4020.02 q^{23} +3453.24 q^{27} -6417.28 q^{29} -2350.64 q^{31} -2402.14 q^{33} +7876.58 q^{37} +7044.18 q^{39} +15081.6 q^{41} -1141.40 q^{43} +21557.3 q^{47} -7943.36 q^{49} +33132.3 q^{51} -9560.44 q^{53} +22027.2 q^{57} +42740.7 q^{59} +32132.1 q^{61} -3428.11 q^{63} +30371.4 q^{67} -67197.2 q^{69} +36006.7 q^{71} +63438.0 q^{73} -13529.5 q^{77} -89922.8 q^{79} -66571.4 q^{81} -38211.2 q^{83} +107269. q^{87} +5745.69 q^{89} +39674.7 q^{91} +39292.5 q^{93} -178780. q^{97} +5232.69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 12q^{3} - 52q^{7} + 618q^{9} + O(q^{10}) \) \( 2q + 12q^{3} - 52q^{7} + 618q^{9} + 560q^{11} - 1388q^{13} - 148q^{17} - 1000q^{19} + 2784q^{21} + 2452q^{23} + 13176q^{27} + 1340q^{29} - 2248q^{31} + 9552q^{33} + 5940q^{37} - 20712q^{39} + 23076q^{41} - 17684q^{43} + 2908q^{47} - 22974q^{49} + 85800q^{51} + 5412q^{53} + 31152q^{57} + 62584q^{59} + 14108q^{61} + 21084q^{63} + 85412q^{67} - 112224q^{69} + 47208q^{71} + 67452q^{73} + 4016q^{77} - 65904q^{79} + 71298q^{81} - 108724q^{83} + 330024q^{87} - 55020q^{89} - 1064q^{91} + 42240q^{93} - 147668q^{97} + 247344q^{99} + O(q^{100}) \)

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
\(3\) −16.7156 −1.07231 −0.536154 0.844120i \(-0.680123\pi\)
−0.536154 + 0.844120i \(0.680123\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −94.1469 −0.726208 −0.363104 0.931749i \(-0.618283\pi\)
−0.363104 + 0.931749i \(0.618283\pi\)
\(8\) 0 0
\(9\) 36.4124 0.149845
\(10\) 0 0
\(11\) 143.706 0.358091 0.179046 0.983841i \(-0.442699\pi\)
0.179046 + 0.983841i \(0.442699\pi\)
\(12\) 0 0
\(13\) −421.412 −0.691590 −0.345795 0.938310i \(-0.612391\pi\)
−0.345795 + 0.938310i \(0.612391\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1982.11 −1.66344 −0.831718 0.555198i \(-0.812642\pi\)
−0.831718 + 0.555198i \(0.812642\pi\)
\(18\) 0 0
\(19\) −1317.76 −0.837439 −0.418720 0.908116i \(-0.637521\pi\)
−0.418720 + 0.908116i \(0.637521\pi\)
\(20\) 0 0
\(21\) 1573.73 0.778719
\(22\) 0 0
\(23\) 4020.02 1.58456 0.792280 0.610157i \(-0.208894\pi\)
0.792280 + 0.610157i \(0.208894\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3453.24 0.911628
\(28\) 0 0
\(29\) −6417.28 −1.41695 −0.708477 0.705734i \(-0.750617\pi\)
−0.708477 + 0.705734i \(0.750617\pi\)
\(30\) 0 0
\(31\) −2350.64 −0.439322 −0.219661 0.975576i \(-0.570495\pi\)
−0.219661 + 0.975576i \(0.570495\pi\)
\(32\) 0 0
\(33\) −2402.14 −0.383984
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7876.58 0.945874 0.472937 0.881096i \(-0.343194\pi\)
0.472937 + 0.881096i \(0.343194\pi\)
\(38\) 0 0
\(39\) 7044.18 0.741598
\(40\) 0 0
\(41\) 15081.6 1.40116 0.700582 0.713572i \(-0.252924\pi\)
0.700582 + 0.713572i \(0.252924\pi\)
\(42\) 0 0
\(43\) −1141.40 −0.0941384 −0.0470692 0.998892i \(-0.514988\pi\)
−0.0470692 + 0.998892i \(0.514988\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 21557.3 1.42348 0.711738 0.702445i \(-0.247908\pi\)
0.711738 + 0.702445i \(0.247908\pi\)
\(48\) 0 0
\(49\) −7943.36 −0.472622
\(50\) 0 0
\(51\) 33132.3 1.78372
\(52\) 0 0
\(53\) −9560.44 −0.467507 −0.233754 0.972296i \(-0.575101\pi\)
−0.233754 + 0.972296i \(0.575101\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 22027.2 0.897993
\(58\) 0 0
\(59\) 42740.7 1.59850 0.799248 0.601002i \(-0.205232\pi\)
0.799248 + 0.601002i \(0.205232\pi\)
\(60\) 0 0
\(61\) 32132.1 1.10564 0.552820 0.833301i \(-0.313552\pi\)
0.552820 + 0.833301i \(0.313552\pi\)
\(62\) 0 0
\(63\) −3428.11 −0.108819
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 30371.4 0.826567 0.413283 0.910602i \(-0.364382\pi\)
0.413283 + 0.910602i \(0.364382\pi\)
\(68\) 0 0
\(69\) −67197.2 −1.69914
\(70\) 0 0
\(71\) 36006.7 0.847692 0.423846 0.905734i \(-0.360680\pi\)
0.423846 + 0.905734i \(0.360680\pi\)
\(72\) 0 0
\(73\) 63438.0 1.39329 0.696647 0.717414i \(-0.254674\pi\)
0.696647 + 0.717414i \(0.254674\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13529.5 −0.260049
\(78\) 0 0
\(79\) −89922.8 −1.62107 −0.810536 0.585689i \(-0.800824\pi\)
−0.810536 + 0.585689i \(0.800824\pi\)
\(80\) 0 0
\(81\) −66571.4 −1.12739
\(82\) 0 0
\(83\) −38211.2 −0.608829 −0.304414 0.952540i \(-0.598461\pi\)
−0.304414 + 0.952540i \(0.598461\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 107269. 1.51941
\(88\) 0 0
\(89\) 5745.69 0.0768895 0.0384447 0.999261i \(-0.487760\pi\)
0.0384447 + 0.999261i \(0.487760\pi\)
\(90\) 0 0
\(91\) 39674.7 0.502238
\(92\) 0 0
\(93\) 39292.5 0.471088
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −178780. −1.92926 −0.964629 0.263613i \(-0.915086\pi\)
−0.964629 + 0.263613i \(0.915086\pi\)
\(98\) 0 0
\(99\) 5232.69 0.0536583
\(100\) 0 0
\(101\) 152223. 1.48483 0.742417 0.669938i \(-0.233679\pi\)
0.742417 + 0.669938i \(0.233679\pi\)
\(102\) 0 0
\(103\) 35830.1 0.332778 0.166389 0.986060i \(-0.446789\pi\)
0.166389 + 0.986060i \(0.446789\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −70030.2 −0.591324 −0.295662 0.955293i \(-0.595540\pi\)
−0.295662 + 0.955293i \(0.595540\pi\)
\(108\) 0 0
\(109\) 38466.9 0.310114 0.155057 0.987906i \(-0.450444\pi\)
0.155057 + 0.987906i \(0.450444\pi\)
\(110\) 0 0
\(111\) −131662. −1.01427
\(112\) 0 0
\(113\) −39951.6 −0.294333 −0.147166 0.989112i \(-0.547015\pi\)
−0.147166 + 0.989112i \(0.547015\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −15344.6 −0.103632
\(118\) 0 0
\(119\) 186610. 1.20800
\(120\) 0 0
\(121\) −140400. −0.871771
\(122\) 0 0
\(123\) −252099. −1.50248
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 233239. 1.28319 0.641596 0.767043i \(-0.278273\pi\)
0.641596 + 0.767043i \(0.278273\pi\)
\(128\) 0 0
\(129\) 19079.2 0.100945
\(130\) 0 0
\(131\) 55237.0 0.281224 0.140612 0.990065i \(-0.455093\pi\)
0.140612 + 0.990065i \(0.455093\pi\)
\(132\) 0 0
\(133\) 124063. 0.608155
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −261520. −1.19043 −0.595215 0.803566i \(-0.702933\pi\)
−0.595215 + 0.803566i \(0.702933\pi\)
\(138\) 0 0
\(139\) 293366. 1.28787 0.643935 0.765080i \(-0.277301\pi\)
0.643935 + 0.765080i \(0.277301\pi\)
\(140\) 0 0
\(141\) −360345. −1.52641
\(142\) 0 0
\(143\) −60559.6 −0.247653
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 132778. 0.506797
\(148\) 0 0
\(149\) −304505. −1.12364 −0.561822 0.827258i \(-0.689899\pi\)
−0.561822 + 0.827258i \(0.689899\pi\)
\(150\) 0 0
\(151\) −337909. −1.20603 −0.603015 0.797730i \(-0.706034\pi\)
−0.603015 + 0.797730i \(0.706034\pi\)
\(152\) 0 0
\(153\) −72173.5 −0.249258
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −68385.9 −0.221420 −0.110710 0.993853i \(-0.535313\pi\)
−0.110710 + 0.993853i \(0.535313\pi\)
\(158\) 0 0
\(159\) 159809. 0.501312
\(160\) 0 0
\(161\) −378473. −1.15072
\(162\) 0 0
\(163\) 404471. 1.19239 0.596195 0.802840i \(-0.296678\pi\)
0.596195 + 0.802840i \(0.296678\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −411733. −1.14242 −0.571209 0.820805i \(-0.693525\pi\)
−0.571209 + 0.820805i \(0.693525\pi\)
\(168\) 0 0
\(169\) −193705. −0.521703
\(170\) 0 0
\(171\) −47982.9 −0.125486
\(172\) 0 0
\(173\) 162247. 0.412155 0.206077 0.978536i \(-0.433930\pi\)
0.206077 + 0.978536i \(0.433930\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −714438. −1.71408
\(178\) 0 0
\(179\) 384396. 0.896698 0.448349 0.893859i \(-0.352012\pi\)
0.448349 + 0.893859i \(0.352012\pi\)
\(180\) 0 0
\(181\) 579219. 1.31415 0.657077 0.753823i \(-0.271792\pi\)
0.657077 + 0.753823i \(0.271792\pi\)
\(182\) 0 0
\(183\) −537108. −1.18559
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −284842. −0.595662
\(188\) 0 0
\(189\) −325112. −0.662031
\(190\) 0 0
\(191\) 142455. 0.282550 0.141275 0.989970i \(-0.454880\pi\)
0.141275 + 0.989970i \(0.454880\pi\)
\(192\) 0 0
\(193\) −267272. −0.516487 −0.258244 0.966080i \(-0.583144\pi\)
−0.258244 + 0.966080i \(0.583144\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14189.5 −0.0260496 −0.0130248 0.999915i \(-0.504146\pi\)
−0.0130248 + 0.999915i \(0.504146\pi\)
\(198\) 0 0
\(199\) 169198. 0.302875 0.151437 0.988467i \(-0.451610\pi\)
0.151437 + 0.988467i \(0.451610\pi\)
\(200\) 0 0
\(201\) −507677. −0.886335
\(202\) 0 0
\(203\) 604167. 1.02900
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 146379. 0.237439
\(208\) 0 0
\(209\) −189371. −0.299880
\(210\) 0 0
\(211\) −407591. −0.630259 −0.315129 0.949049i \(-0.602048\pi\)
−0.315129 + 0.949049i \(0.602048\pi\)
\(212\) 0 0
\(213\) −601875. −0.908987
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 221306. 0.319039
\(218\) 0 0
\(219\) −1.06041e6 −1.49404
\(220\) 0 0
\(221\) 835287. 1.15042
\(222\) 0 0
\(223\) 103743. 0.139700 0.0698500 0.997558i \(-0.477748\pi\)
0.0698500 + 0.997558i \(0.477748\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 803726. 1.03524 0.517622 0.855609i \(-0.326817\pi\)
0.517622 + 0.855609i \(0.326817\pi\)
\(228\) 0 0
\(229\) 1.35955e6 1.71319 0.856596 0.515988i \(-0.172575\pi\)
0.856596 + 0.515988i \(0.172575\pi\)
\(230\) 0 0
\(231\) 226154. 0.278852
\(232\) 0 0
\(233\) 622827. 0.751584 0.375792 0.926704i \(-0.377371\pi\)
0.375792 + 0.926704i \(0.377371\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.50312e6 1.73829
\(238\) 0 0
\(239\) −642843. −0.727964 −0.363982 0.931406i \(-0.618583\pi\)
−0.363982 + 0.931406i \(0.618583\pi\)
\(240\) 0 0
\(241\) 1.11814e6 1.24009 0.620046 0.784566i \(-0.287114\pi\)
0.620046 + 0.784566i \(0.287114\pi\)
\(242\) 0 0
\(243\) 273644. 0.297283
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 555322. 0.579165
\(248\) 0 0
\(249\) 638724. 0.652852
\(250\) 0 0
\(251\) 731067. 0.732442 0.366221 0.930528i \(-0.380651\pi\)
0.366221 + 0.930528i \(0.380651\pi\)
\(252\) 0 0
\(253\) 577702. 0.567418
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.76622e6 1.66806 0.834030 0.551720i \(-0.186028\pi\)
0.834030 + 0.551720i \(0.186028\pi\)
\(258\) 0 0
\(259\) −741555. −0.686901
\(260\) 0 0
\(261\) −233668. −0.212324
\(262\) 0 0
\(263\) −1.00926e6 −0.899735 −0.449868 0.893095i \(-0.648529\pi\)
−0.449868 + 0.893095i \(0.648529\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −96042.8 −0.0824492
\(268\) 0 0
\(269\) −775681. −0.653585 −0.326793 0.945096i \(-0.605968\pi\)
−0.326793 + 0.945096i \(0.605968\pi\)
\(270\) 0 0
\(271\) 1.21395e6 1.00410 0.502052 0.864837i \(-0.332578\pi\)
0.502052 + 0.864837i \(0.332578\pi\)
\(272\) 0 0
\(273\) −663187. −0.538554
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 218505. 0.171104 0.0855522 0.996334i \(-0.472735\pi\)
0.0855522 + 0.996334i \(0.472735\pi\)
\(278\) 0 0
\(279\) −85592.6 −0.0658303
\(280\) 0 0
\(281\) −316219. −0.238903 −0.119452 0.992840i \(-0.538114\pi\)
−0.119452 + 0.992840i \(0.538114\pi\)
\(282\) 0 0
\(283\) 927934. 0.688733 0.344366 0.938835i \(-0.388094\pi\)
0.344366 + 0.938835i \(0.388094\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.41989e6 −1.01754
\(288\) 0 0
\(289\) 2.50892e6 1.76702
\(290\) 0 0
\(291\) 2.98842e6 2.06876
\(292\) 0 0
\(293\) −262992. −0.178967 −0.0894835 0.995988i \(-0.528522\pi\)
−0.0894835 + 0.995988i \(0.528522\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 496252. 0.326446
\(298\) 0 0
\(299\) −1.69409e6 −1.09587
\(300\) 0 0
\(301\) 107459. 0.0683640
\(302\) 0 0
\(303\) −2.54451e6 −1.59220
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2.15704e6 −1.30621 −0.653104 0.757269i \(-0.726533\pi\)
−0.653104 + 0.757269i \(0.726533\pi\)
\(308\) 0 0
\(309\) −598923. −0.356841
\(310\) 0 0
\(311\) −2.33078e6 −1.36647 −0.683235 0.730199i \(-0.739427\pi\)
−0.683235 + 0.730199i \(0.739427\pi\)
\(312\) 0 0
\(313\) 1.12235e6 0.647539 0.323769 0.946136i \(-0.395050\pi\)
0.323769 + 0.946136i \(0.395050\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.27955e6 0.715169 0.357584 0.933881i \(-0.383600\pi\)
0.357584 + 0.933881i \(0.383600\pi\)
\(318\) 0 0
\(319\) −922203. −0.507399
\(320\) 0 0
\(321\) 1.17060e6 0.634082
\(322\) 0 0
\(323\) 2.61196e6 1.39303
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −642998. −0.332537
\(328\) 0 0
\(329\) −2.02956e6 −1.03374
\(330\) 0 0
\(331\) −2.09571e6 −1.05138 −0.525691 0.850675i \(-0.676193\pi\)
−0.525691 + 0.850675i \(0.676193\pi\)
\(332\) 0 0
\(333\) 286805. 0.141735
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 571289. 0.274019 0.137010 0.990570i \(-0.456251\pi\)
0.137010 + 0.990570i \(0.456251\pi\)
\(338\) 0 0
\(339\) 667817. 0.315615
\(340\) 0 0
\(341\) −337802. −0.157317
\(342\) 0 0
\(343\) 2.33017e6 1.06943
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.24067e6 −0.998973 −0.499486 0.866322i \(-0.666478\pi\)
−0.499486 + 0.866322i \(0.666478\pi\)
\(348\) 0 0
\(349\) 130448. 0.0573290 0.0286645 0.999589i \(-0.490875\pi\)
0.0286645 + 0.999589i \(0.490875\pi\)
\(350\) 0 0
\(351\) −1.45524e6 −0.630473
\(352\) 0 0
\(353\) −1.95452e6 −0.834839 −0.417420 0.908714i \(-0.637065\pi\)
−0.417420 + 0.908714i \(0.637065\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.11930e6 −1.29535
\(358\) 0 0
\(359\) −850543. −0.348305 −0.174153 0.984719i \(-0.555719\pi\)
−0.174153 + 0.984719i \(0.555719\pi\)
\(360\) 0 0
\(361\) −739600. −0.298696
\(362\) 0 0
\(363\) 2.34687e6 0.934807
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.50673e6 0.583941 0.291970 0.956427i \(-0.405689\pi\)
0.291970 + 0.956427i \(0.405689\pi\)
\(368\) 0 0
\(369\) 549159. 0.209958
\(370\) 0 0
\(371\) 900086. 0.339507
\(372\) 0 0
\(373\) −2.90602e6 −1.08150 −0.540749 0.841184i \(-0.681859\pi\)
−0.540749 + 0.841184i \(0.681859\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.70432e6 0.979952
\(378\) 0 0
\(379\) 5.16710e6 1.84777 0.923887 0.382665i \(-0.124994\pi\)
0.923887 + 0.382665i \(0.124994\pi\)
\(380\) 0 0
\(381\) −3.89874e6 −1.37598
\(382\) 0 0
\(383\) −3.85088e6 −1.34142 −0.670708 0.741721i \(-0.734010\pi\)
−0.670708 + 0.741721i \(0.734010\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −41561.1 −0.0141062
\(388\) 0 0
\(389\) 5.49855e6 1.84236 0.921179 0.389138i \(-0.127227\pi\)
0.921179 + 0.389138i \(0.127227\pi\)
\(390\) 0 0
\(391\) −7.96814e6 −2.63582
\(392\) 0 0
\(393\) −923321. −0.301558
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.71425e6 −0.545881 −0.272941 0.962031i \(-0.587996\pi\)
−0.272941 + 0.962031i \(0.587996\pi\)
\(398\) 0 0
\(399\) −2.07380e6 −0.652130
\(400\) 0 0
\(401\) 3.63329e6 1.12834 0.564169 0.825660i \(-0.309197\pi\)
0.564169 + 0.825660i \(0.309197\pi\)
\(402\) 0 0
\(403\) 990591. 0.303831
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.13191e6 0.338709
\(408\) 0 0
\(409\) −1.38246e6 −0.408642 −0.204321 0.978904i \(-0.565499\pi\)
−0.204321 + 0.978904i \(0.565499\pi\)
\(410\) 0 0
\(411\) 4.37148e6 1.27651
\(412\) 0 0
\(413\) −4.02390e6 −1.16084
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.90379e6 −1.38099
\(418\) 0 0
\(419\) 2.55435e6 0.710795 0.355398 0.934715i \(-0.384345\pi\)
0.355398 + 0.934715i \(0.384345\pi\)
\(420\) 0 0
\(421\) −1.68110e6 −0.462263 −0.231132 0.972923i \(-0.574243\pi\)
−0.231132 + 0.972923i \(0.574243\pi\)
\(422\) 0 0
\(423\) 784954. 0.213301
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.02513e6 −0.802925
\(428\) 0 0
\(429\) 1.01229e6 0.265560
\(430\) 0 0
\(431\) −2.32369e6 −0.602539 −0.301269 0.953539i \(-0.597410\pi\)
−0.301269 + 0.953539i \(0.597410\pi\)
\(432\) 0 0
\(433\) 4.06439e6 1.04178 0.520890 0.853624i \(-0.325600\pi\)
0.520890 + 0.853624i \(0.325600\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.29744e6 −1.32697
\(438\) 0 0
\(439\) 6.39272e6 1.58316 0.791579 0.611066i \(-0.209259\pi\)
0.791579 + 0.611066i \(0.209259\pi\)
\(440\) 0 0
\(441\) −289237. −0.0708202
\(442\) 0 0
\(443\) −3.23515e6 −0.783222 −0.391611 0.920131i \(-0.628082\pi\)
−0.391611 + 0.920131i \(0.628082\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5.08999e6 1.20489
\(448\) 0 0
\(449\) −2.74812e6 −0.643310 −0.321655 0.946857i \(-0.604239\pi\)
−0.321655 + 0.946857i \(0.604239\pi\)
\(450\) 0 0
\(451\) 2.16732e6 0.501745
\(452\) 0 0
\(453\) 5.64837e6 1.29324
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.37326e6 1.20350 0.601751 0.798684i \(-0.294470\pi\)
0.601751 + 0.798684i \(0.294470\pi\)
\(458\) 0 0
\(459\) −6.84472e6 −1.51644
\(460\) 0 0
\(461\) −8.19928e6 −1.79690 −0.898449 0.439078i \(-0.855305\pi\)
−0.898449 + 0.439078i \(0.855305\pi\)
\(462\) 0 0
\(463\) −3.76963e6 −0.817233 −0.408617 0.912706i \(-0.633989\pi\)
−0.408617 + 0.912706i \(0.633989\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.03412e6 −1.28033 −0.640165 0.768237i \(-0.721134\pi\)
−0.640165 + 0.768237i \(0.721134\pi\)
\(468\) 0 0
\(469\) −2.85937e6 −0.600259
\(470\) 0 0
\(471\) 1.14311e6 0.237431
\(472\) 0 0
\(473\) −164026. −0.0337101
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −348119. −0.0700537
\(478\) 0 0
\(479\) −5.26406e6 −1.04829 −0.524146 0.851629i \(-0.675615\pi\)
−0.524146 + 0.851629i \(0.675615\pi\)
\(480\) 0 0
\(481\) −3.31929e6 −0.654157
\(482\) 0 0
\(483\) 6.32641e6 1.23393
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 2.19979e6 0.420300 0.210150 0.977669i \(-0.432605\pi\)
0.210150 + 0.977669i \(0.432605\pi\)
\(488\) 0 0
\(489\) −6.76099e6 −1.27861
\(490\) 0 0
\(491\) 6.47314e6 1.21174 0.605872 0.795562i \(-0.292824\pi\)
0.605872 + 0.795562i \(0.292824\pi\)
\(492\) 0 0
\(493\) 1.27198e7 2.35701
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.38992e6 −0.615600
\(498\) 0 0
\(499\) 8.62090e6 1.54989 0.774946 0.632028i \(-0.217777\pi\)
0.774946 + 0.632028i \(0.217777\pi\)
\(500\) 0 0
\(501\) 6.88238e6 1.22502
\(502\) 0 0
\(503\) −8.10557e6 −1.42845 −0.714223 0.699918i \(-0.753220\pi\)
−0.714223 + 0.699918i \(0.753220\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.23789e6 0.559426
\(508\) 0 0
\(509\) −6.39610e6 −1.09426 −0.547131 0.837047i \(-0.684280\pi\)
−0.547131 + 0.837047i \(0.684280\pi\)
\(510\) 0 0
\(511\) −5.97250e6 −1.01182
\(512\) 0 0
\(513\) −4.55055e6 −0.763433
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 3.09792e6 0.509735
\(518\) 0 0
\(519\) −2.71205e6 −0.441957
\(520\) 0 0
\(521\) 7.53647e6 1.21639 0.608197 0.793786i \(-0.291893\pi\)
0.608197 + 0.793786i \(0.291893\pi\)
\(522\) 0 0
\(523\) −1.87780e6 −0.300189 −0.150095 0.988672i \(-0.547958\pi\)
−0.150095 + 0.988672i \(0.547958\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.65924e6 0.730784
\(528\) 0 0
\(529\) 9.72424e6 1.51083
\(530\) 0 0
\(531\) 1.55629e6 0.239527
\(532\) 0 0
\(533\) −6.35559e6 −0.969031
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.42542e6 −0.961537
\(538\) 0 0
\(539\) −1.14151e6 −0.169242
\(540\) 0 0
\(541\) 2.44482e6 0.359131 0.179566 0.983746i \(-0.442531\pi\)
0.179566 + 0.983746i \(0.442531\pi\)
\(542\) 0 0
\(543\) −9.68202e6 −1.40918
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.09485e7 1.56453 0.782266 0.622944i \(-0.214064\pi\)
0.782266 + 0.622944i \(0.214064\pi\)
\(548\) 0 0
\(549\) 1.17001e6 0.165675
\(550\) 0 0
\(551\) 8.45645e6 1.18661
\(552\) 0 0
\(553\) 8.46595e6 1.17723
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 768938. 0.105015 0.0525077 0.998621i \(-0.483279\pi\)
0.0525077 + 0.998621i \(0.483279\pi\)
\(558\) 0 0
\(559\) 481000. 0.0651052
\(560\) 0 0
\(561\) 4.76131e6 0.638733
\(562\) 0 0
\(563\) 1.47386e7 1.95968 0.979838 0.199792i \(-0.0640265\pi\)
0.979838 + 0.199792i \(0.0640265\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.26749e6 0.818721
\(568\) 0 0
\(569\) −3.33696e6 −0.432086 −0.216043 0.976384i \(-0.569315\pi\)
−0.216043 + 0.976384i \(0.569315\pi\)
\(570\) 0 0
\(571\) 1.54413e7 1.98195 0.990974 0.134051i \(-0.0427986\pi\)
0.990974 + 0.134051i \(0.0427986\pi\)
\(572\) 0 0
\(573\) −2.38123e6 −0.302981
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 4.05636e6 0.507221 0.253610 0.967306i \(-0.418382\pi\)
0.253610 + 0.967306i \(0.418382\pi\)
\(578\) 0 0
\(579\) 4.46762e6 0.553834
\(580\) 0 0
\(581\) 3.59746e6 0.442136
\(582\) 0 0
\(583\) −1.37389e6 −0.167410
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.22567e7 1.46818 0.734090 0.679052i \(-0.237609\pi\)
0.734090 + 0.679052i \(0.237609\pi\)
\(588\) 0 0
\(589\) 3.09759e6 0.367905
\(590\) 0 0
\(591\) 237186. 0.0279332
\(592\) 0 0
\(593\) −8.58993e6 −1.00312 −0.501560 0.865123i \(-0.667240\pi\)
−0.501560 + 0.865123i \(0.667240\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.82825e6 −0.324775
\(598\) 0 0
\(599\) 8.85849e6 1.00877 0.504386 0.863479i \(-0.331719\pi\)
0.504386 + 0.863479i \(0.331719\pi\)
\(600\) 0 0
\(601\) −8.50579e6 −0.960569 −0.480284 0.877113i \(-0.659467\pi\)
−0.480284 + 0.877113i \(0.659467\pi\)
\(602\) 0 0
\(603\) 1.10590e6 0.123857
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 3.15481e6 0.347537 0.173768 0.984787i \(-0.444406\pi\)
0.173768 + 0.984787i \(0.444406\pi\)
\(608\) 0 0
\(609\) −1.00990e7 −1.10341
\(610\) 0 0
\(611\) −9.08453e6 −0.984463
\(612\) 0 0
\(613\) −3.20689e6 −0.344694 −0.172347 0.985036i \(-0.555135\pi\)
−0.172347 + 0.985036i \(0.555135\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.31916e6 0.139504 0.0697519 0.997564i \(-0.477779\pi\)
0.0697519 + 0.997564i \(0.477779\pi\)
\(618\) 0 0
\(619\) −3.36061e6 −0.352526 −0.176263 0.984343i \(-0.556401\pi\)
−0.176263 + 0.984343i \(0.556401\pi\)
\(620\) 0 0
\(621\) 1.38821e7 1.44453
\(622\) 0 0
\(623\) −540939. −0.0558377
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.16545e6 0.321563
\(628\) 0 0
\(629\) −1.56123e7 −1.57340
\(630\) 0 0
\(631\) −1.46547e7 −1.46522 −0.732610 0.680648i \(-0.761698\pi\)
−0.732610 + 0.680648i \(0.761698\pi\)
\(632\) 0 0
\(633\) 6.81315e6 0.675832
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.34743e6 0.326861
\(638\) 0 0
\(639\) 1.31109e6 0.127023
\(640\) 0 0
\(641\) −5.67545e6 −0.545576 −0.272788 0.962074i \(-0.587946\pi\)
−0.272788 + 0.962074i \(0.587946\pi\)
\(642\) 0 0
\(643\) 1.81422e7 1.73047 0.865233 0.501370i \(-0.167170\pi\)
0.865233 + 0.501370i \(0.167170\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −472390. −0.0443649 −0.0221825 0.999754i \(-0.507061\pi\)
−0.0221825 + 0.999754i \(0.507061\pi\)
\(648\) 0 0
\(649\) 6.14210e6 0.572407
\(650\) 0 0
\(651\) −3.69927e6 −0.342108
\(652\) 0 0
\(653\) −9.79442e6 −0.898867 −0.449434 0.893314i \(-0.648374\pi\)
−0.449434 + 0.893314i \(0.648374\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.30993e6 0.208778
\(658\) 0 0
\(659\) −9.83251e6 −0.881964 −0.440982 0.897516i \(-0.645370\pi\)
−0.440982 + 0.897516i \(0.645370\pi\)
\(660\) 0 0
\(661\) 1.84120e6 0.163907 0.0819535 0.996636i \(-0.473884\pi\)
0.0819535 + 0.996636i \(0.473884\pi\)
\(662\) 0 0
\(663\) −1.39624e7 −1.23360
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.57976e7 −2.24525
\(668\) 0 0
\(669\) −1.73413e6 −0.149802
\(670\) 0 0
\(671\) 4.61758e6 0.395920
\(672\) 0 0
\(673\) 1.02990e7 0.876510 0.438255 0.898851i \(-0.355597\pi\)
0.438255 + 0.898851i \(0.355597\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.63461e6 0.304779 0.152390 0.988320i \(-0.451303\pi\)
0.152390 + 0.988320i \(0.451303\pi\)
\(678\) 0 0
\(679\) 1.68316e7 1.40104
\(680\) 0 0
\(681\) −1.34348e7 −1.11010
\(682\) 0 0
\(683\) 9.78443e6 0.802571 0.401286 0.915953i \(-0.368563\pi\)
0.401286 + 0.915953i \(0.368563\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.27257e7 −1.83707
\(688\) 0 0
\(689\) 4.02889e6 0.323323
\(690\) 0 0
\(691\) 4.67949e6 0.372824 0.186412 0.982472i \(-0.440314\pi\)
0.186412 + 0.982472i \(0.440314\pi\)
\(692\) 0 0
\(693\) −492641. −0.0389671
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.98935e7 −2.33075
\(698\) 0 0
\(699\) −1.04110e7 −0.805930
\(700\) 0 0
\(701\) −565147. −0.0434376 −0.0217188 0.999764i \(-0.506914\pi\)
−0.0217188 + 0.999764i \(0.506914\pi\)
\(702\) 0 0
\(703\) −1.03795e7 −0.792112
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.43314e7 −1.07830
\(708\) 0 0
\(709\) −1.00907e6 −0.0753889 −0.0376944 0.999289i \(-0.512001\pi\)
−0.0376944 + 0.999289i \(0.512001\pi\)
\(710\) 0 0
\(711\) −3.27431e6 −0.242910
\(712\) 0 0
\(713\) −9.44964e6 −0.696132
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.07455e7 0.780602
\(718\) 0 0
\(719\) −6.02329e6 −0.434522 −0.217261 0.976114i \(-0.569712\pi\)
−0.217261 + 0.976114i \(0.569712\pi\)
\(720\) 0 0
\(721\) −3.37329e6 −0.241666
\(722\) 0 0
\(723\) −1.86904e7 −1.32976
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.30828e6 0.161977 0.0809883 0.996715i \(-0.474192\pi\)
0.0809883 + 0.996715i \(0.474192\pi\)
\(728\) 0 0
\(729\) 1.16027e7 0.808612
\(730\) 0 0
\(731\) 2.26238e6 0.156593
\(732\) 0 0
\(733\) 1.65224e7 1.13583 0.567914 0.823088i \(-0.307751\pi\)
0.567914 + 0.823088i \(0.307751\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.36456e6 0.295986
\(738\) 0 0
\(739\) 2.41051e7 1.62367 0.811834 0.583888i \(-0.198469\pi\)
0.811834 + 0.583888i \(0.198469\pi\)
\(740\) 0 0
\(741\) −9.28255e6 −0.621043
\(742\) 0 0
\(743\) 2.54593e7 1.69190 0.845950 0.533262i \(-0.179034\pi\)
0.845950 + 0.533262i \(0.179034\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.39136e6 −0.0912301
\(748\) 0 0
\(749\) 6.59312e6 0.429424
\(750\) 0 0
\(751\) −1.25073e7 −0.809215 −0.404608 0.914490i \(-0.632592\pi\)
−0.404608 + 0.914490i \(0.632592\pi\)
\(752\) 0 0
\(753\) −1.22203e7 −0.785404
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 5.34914e6 0.339269 0.169635 0.985507i \(-0.445741\pi\)
0.169635 + 0.985507i \(0.445741\pi\)
\(758\) 0 0
\(759\) −9.65666e6 −0.608447
\(760\) 0 0
\(761\) −1.80369e7 −1.12901 −0.564507 0.825428i \(-0.690934\pi\)
−0.564507 + 0.825428i \(0.690934\pi\)
\(762\) 0 0
\(763\) −3.62154e6 −0.225207
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.80115e7 −1.10550
\(768\) 0 0
\(769\) 2.41928e7 1.47526 0.737632 0.675203i \(-0.235944\pi\)
0.737632 + 0.675203i \(0.235944\pi\)
\(770\) 0 0
\(771\) −2.95234e7 −1.78867
\(772\) 0 0
\(773\) 3.22531e6 0.194143 0.0970716 0.995277i \(-0.469052\pi\)
0.0970716 + 0.995277i \(0.469052\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.23956e7 0.736570
\(778\) 0 0
\(779\) −1.98740e7 −1.17339
\(780\) 0 0
\(781\) 5.17439e6 0.303551
\(782\) 0 0
\(783\) −2.21604e7 −1.29174
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.12227e6 0.0645896 0.0322948 0.999478i \(-0.489718\pi\)
0.0322948 + 0.999478i \(0.489718\pi\)
\(788\) 0 0
\(789\) 1.68705e7 0.964793
\(790\) 0 0
\(791\) 3.76132e6 0.213747
\(792\) 0 0
\(793\) −1.35408e7 −0.764650
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.48763e7 0.829560 0.414780 0.909922i \(-0.363859\pi\)
0.414780 + 0.909922i \(0.363859\pi\)
\(798\) 0 0
\(799\) −4.27291e7 −2.36786
\(800\) 0 0
\(801\) 209214. 0.0115215
\(802\) 0 0
\(803\) 9.11644e6 0.498926
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.29660e7 0.700845
\(808\) 0 0
\(809\) 1.86436e7 1.00152 0.500759 0.865587i \(-0.333054\pi\)
0.500759 + 0.865587i \(0.333054\pi\)
\(810\) 0 0
\(811\) 4.50701e6 0.240623 0.120311 0.992736i \(-0.461611\pi\)
0.120311 + 0.992736i \(0.461611\pi\)
\(812\) 0 0
\(813\) −2.02920e7 −1.07671
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.50409e6 0.0788352
\(818\) 0 0
\(819\) 1.44465e6 0.0752580
\(820\) 0 0
\(821\) −2.26560e7 −1.17307 −0.586537 0.809922i \(-0.699509\pi\)
−0.586537 + 0.809922i \(0.699509\pi\)
\(822\) 0 0
\(823\) 2.76806e7 1.42454 0.712272 0.701903i \(-0.247666\pi\)
0.712272 + 0.701903i \(0.247666\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7.42673e6 0.377602 0.188801 0.982015i \(-0.439540\pi\)
0.188801 + 0.982015i \(0.439540\pi\)
\(828\) 0 0
\(829\) 3.41770e7 1.72722 0.863610 0.504160i \(-0.168198\pi\)
0.863610 + 0.504160i \(0.168198\pi\)
\(830\) 0 0
\(831\) −3.65244e6 −0.183477
\(832\) 0 0
\(833\) 1.57446e7 0.786177
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −8.11734e6 −0.400498
\(838\) 0 0
\(839\) 155990. 0.00765051 0.00382526 0.999993i \(-0.498782\pi\)
0.00382526 + 0.999993i \(0.498782\pi\)
\(840\) 0 0
\(841\) 2.06703e7 1.00776
\(842\) 0 0
\(843\) 5.28580e6 0.256178
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1.32182e7 0.633087
\(848\) 0 0
\(849\) −1.55110e7 −0.738534
\(850\) 0 0
\(851\) 3.16640e7 1.49879
\(852\) 0 0
\(853\) 2.52778e7 1.18951 0.594754 0.803908i \(-0.297250\pi\)
0.594754 + 0.803908i \(0.297250\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.40854e6 −0.0655112 −0.0327556 0.999463i \(-0.510428\pi\)
−0.0327556 + 0.999463i \(0.510428\pi\)
\(858\) 0 0
\(859\) −246158. −0.0113823 −0.00569116 0.999984i \(-0.501812\pi\)
−0.00569116 + 0.999984i \(0.501812\pi\)
\(860\) 0 0
\(861\) 2.37344e7 1.09111
\(862\) 0 0
\(863\) −1.17019e7 −0.534849 −0.267424 0.963579i \(-0.586173\pi\)
−0.267424 + 0.963579i \(0.586173\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −4.19381e7 −1.89479
\(868\) 0 0
\(869\) −1.29225e7 −0.580492
\(870\) 0 0
\(871\) −1.27989e7 −0.571646
\(872\) 0 0
\(873\) −6.50982e6 −0.289090
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 7.85174e6 0.344720 0.172360 0.985034i \(-0.444861\pi\)
0.172360 + 0.985034i \(0.444861\pi\)
\(878\) 0 0
\(879\) 4.39607e6 0.191908
\(880\) 0 0
\(881\) 105461. 0.00457777 0.00228888 0.999997i \(-0.499271\pi\)
0.00228888 + 0.999997i \(0.499271\pi\)
\(882\) 0 0
\(883\) −1.43760e7 −0.620491 −0.310245 0.950656i \(-0.600411\pi\)
−0.310245 + 0.950656i \(0.600411\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.71725e7 −1.15963 −0.579816 0.814748i \(-0.696875\pi\)
−0.579816 + 0.814748i \(0.696875\pi\)
\(888\) 0 0
\(889\) −2.19587e7 −0.931864
\(890\) 0 0
\(891\) −9.56672e6 −0.403709
\(892\) 0 0
\(893\) −2.84075e7 −1.19208
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.83177e7 1.17511
\(898\) 0 0
\(899\) 1.50847e7 0.622499
\(900\) 0 0
\(901\) 1.89499e7 0.777668
\(902\) 0 0
\(903\) −1.79625e6 −0.0733073
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 5.25290e6 0.212022 0.106011 0.994365i \(-0.466192\pi\)
0.106011 + 0.994365i \(0.466192\pi\)
\(908\) 0 0
\(909\) 5.54282e6 0.222495
\(910\) 0 0
\(911\) 2.68057e7 1.07012 0.535059 0.844815i \(-0.320289\pi\)
0.535059 + 0.844815i \(0.320289\pi\)
\(912\) 0 0
\(913\) −5.49118e6 −0.218016
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −5.20039e6 −0.204227
\(918\) 0 0
\(919\) −1.25954e7 −0.491951 −0.245976 0.969276i \(-0.579108\pi\)
−0.245976 + 0.969276i \(0.579108\pi\)
\(920\) 0 0
\(921\) 3.60563e7 1.40066
\(922\) 0 0
\(923\) −1.51737e7 −0.586255
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.30466e6 0.0498652
\(928\) 0 0
\(929\) −3.23322e7 −1.22912 −0.614562 0.788868i \(-0.710667\pi\)
−0.614562 + 0.788868i \(0.710667\pi\)
\(930\) 0 0
\(931\) 1.04675e7 0.395792
\(932\) 0 0
\(933\) 3.89604e7 1.46528
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.04882e7 −0.762350 −0.381175 0.924503i \(-0.624481\pi\)
−0.381175 + 0.924503i \(0.624481\pi\)
\(938\) 0 0
\(939\) −1.87607e7 −0.694361
\(940\) 0 0
\(941\) −5.87135e6 −0.216154 −0.108077 0.994143i \(-0.534469\pi\)
−0.108077 + 0.994143i \(0.534469\pi\)
\(942\) 0 0
\(943\) 6.06285e7 2.22023
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.86718e7 0.676567 0.338284 0.941044i \(-0.390154\pi\)
0.338284 + 0.941044i \(0.390154\pi\)
\(948\) 0 0
\(949\) −2.67336e7 −0.963588
\(950\) 0 0
\(951\) −2.13885e7 −0.766882
\(952\) 0 0
\(953\) −1.55896e7 −0.556037 −0.278018 0.960576i \(-0.589678\pi\)
−0.278018 + 0.960576i \(0.589678\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.54152e7 0.544088
\(958\) 0 0
\(959\) 2.46213e7 0.864500
\(960\) 0 0
\(961\) −2.31036e7 −0.806996
\(962\) 0 0
\(963\) −2.54997e6 −0.0886071
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 3.24491e7 1.11593 0.557964 0.829865i \(-0.311583\pi\)
0.557964 + 0.829865i \(0.311583\pi\)
\(968\) 0 0
\(969\) −4.36605e7 −1.49375
\(970\) 0 0
\(971\) 3.73661e7 1.27183 0.635916 0.771758i \(-0.280622\pi\)
0.635916 + 0.771758i \(0.280622\pi\)
\(972\) 0 0
\(973\) −2.76195e7 −0.935261
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.23874e7 1.75586 0.877931 0.478787i \(-0.158923\pi\)
0.877931 + 0.478787i \(0.158923\pi\)
\(978\) 0 0
\(979\) 825691. 0.0275335
\(980\) 0 0
\(981\) 1.40067e6 0.0464690
\(982\) 0 0
\(983\) 4.75140e7 1.56833 0.784166 0.620551i \(-0.213091\pi\)
0.784166 + 0.620551i \(0.213091\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3.39253e7 1.10849
\(988\) 0 0
\(989\) −4.58846e6 −0.149168
\(990\) 0 0
\(991\) 2.47278e7 0.799835 0.399918 0.916551i \(-0.369039\pi\)
0.399918 + 0.916551i \(0.369039\pi\)
\(992\) 0 0
\(993\) 3.50311e7 1.12741
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.25139e7 −0.398709 −0.199355 0.979927i \(-0.563885\pi\)
−0.199355 + 0.979927i \(0.563885\pi\)
\(998\) 0 0
\(999\) 2.71997e7 0.862285
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.g.1.1 2
4.3 odd 2 400.6.a.q.1.2 2
5.2 odd 4 200.6.c.e.49.3 4
5.3 odd 4 200.6.c.e.49.2 4
5.4 even 2 40.6.a.d.1.2 2
15.14 odd 2 360.6.a.l.1.2 2
20.3 even 4 400.6.c.l.49.3 4
20.7 even 4 400.6.c.l.49.2 4
20.19 odd 2 80.6.a.i.1.1 2
40.19 odd 2 320.6.a.q.1.2 2
40.29 even 2 320.6.a.w.1.1 2
60.59 even 2 720.6.a.z.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.d.1.2 2 5.4 even 2
80.6.a.i.1.1 2 20.19 odd 2
200.6.a.g.1.1 2 1.1 even 1 trivial
200.6.c.e.49.2 4 5.3 odd 4
200.6.c.e.49.3 4 5.2 odd 4
320.6.a.q.1.2 2 40.19 odd 2
320.6.a.w.1.1 2 40.29 even 2
360.6.a.l.1.2 2 15.14 odd 2
400.6.a.q.1.2 2 4.3 odd 2
400.6.c.l.49.2 4 20.7 even 4
400.6.c.l.49.3 4 20.3 even 4
720.6.a.z.1.1 2 60.59 even 2