Properties

Label 400.6.a.q.1.2
Level 400
Weight 6
Character 400.1
Self dual yes
Analytic conductor 64.154
Analytic rank 1
Dimension 2
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1535279252\)
Analytic rank: \(1\)
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 1.2
Root \(-5.17891\) of defining polynomial
Character \(\chi\) \(=\) 400.1

$q$-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 \(-0.319877\pi\)
0.536154 + 0.844120i \(0.319877\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 94.1469 0.726208 0.363104 0.931749i \(-0.381717\pi\)
0.363104 + 0.931749i \(0.381717\pi\)
\(8\) 0 0
\(9\) 36.4124 0.149845
\(10\) 0 0
\(11\) −143.706 −0.358091 −0.179046 0.983841i \(-0.557301\pi\)
−0.179046 + 0.983841i \(0.557301\pi\)
\(12\) 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 \(-0.362479\pi\)
0.418720 + 0.908116i \(0.362479\pi\)
\(20\) 0 0
\(21\) 1573.73 0.778719
\(22\) 0 0
\(23\) −4020.02 −1.58456 −0.792280 0.610157i \(-0.791106\pi\)
−0.792280 + 0.610157i \(0.791106\pi\)
\(24\) 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 \(-0.429505\pi\)
0.219661 + 0.975576i \(0.429505\pi\)
\(32\) 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 \(-0.485012\pi\)
0.0470692 + 0.998892i \(0.485012\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −21557.3 −1.42348 −0.711738 0.702445i \(-0.752092\pi\)
−0.711738 + 0.702445i \(0.752092\pi\)
\(48\) 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 \(-0.794768\pi\)
−0.799248 + 0.601002i \(0.794768\pi\)
\(60\) 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 \(-0.635618\pi\)
−0.413283 + 0.910602i \(0.635618\pi\)
\(68\) 0 0
\(69\) −67197.2 −1.69914
\(70\) 0 0
\(71\) −36006.7 −0.847692 −0.423846 0.905734i \(-0.639320\pi\)
−0.423846 + 0.905734i \(0.639320\pi\)
\(72\) 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 \(-0.199176\pi\)
0.810536 + 0.585689i \(0.199176\pi\)
\(80\) 0 0
\(81\) −66571.4 −1.12739
\(82\) 0 0
\(83\) 38211.2 0.608829 0.304414 0.952540i \(-0.401539\pi\)
0.304414 + 0.952540i \(0.401539\pi\)
\(84\) 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 \(-0.553211\pi\)
−0.166389 + 0.986060i \(0.553211\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 70030.2 0.591324 0.295662 0.955293i \(-0.404460\pi\)
0.295662 + 0.955293i \(0.404460\pi\)
\(108\) 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 \(-0.721727\pi\)
−0.641596 + 0.767043i \(0.721727\pi\)
\(128\) 0 0
\(129\) 19079.2 0.100945
\(130\) 0 0
\(131\) −55237.0 −0.281224 −0.140612 0.990065i \(-0.544907\pi\)
−0.140612 + 0.990065i \(0.544907\pi\)
\(132\) 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 \(-0.722699\pi\)
−0.643935 + 0.765080i \(0.722699\pi\)
\(140\) 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 \(-0.293966\pi\)
0.603015 + 0.797730i \(0.293966\pi\)
\(152\) 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 \(-0.703322\pi\)
−0.596195 + 0.802840i \(0.703322\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 411733. 1.14242 0.571209 0.820805i \(-0.306475\pi\)
0.571209 + 0.820805i \(0.306475\pi\)
\(168\) 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 \(-0.647988\pi\)
−0.448349 + 0.893859i \(0.647988\pi\)
\(180\) 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 \(-0.545120\pi\)
−0.141275 + 0.989970i \(0.545120\pi\)
\(192\) 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 \(-0.548390\pi\)
−0.151437 + 0.988467i \(0.548390\pi\)
\(200\) 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 \(-0.397952\pi\)
0.315129 + 0.949049i \(0.397952\pi\)
\(212\) 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 \(-0.522252\pi\)
−0.0698500 + 0.997558i \(0.522252\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −803726. −1.03524 −0.517622 0.855609i \(-0.673183\pi\)
−0.517622 + 0.855609i \(0.673183\pi\)
\(228\) 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 \(-0.381417\pi\)
0.363982 + 0.931406i \(0.381417\pi\)
\(240\) 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 \(-0.619349\pi\)
−0.366221 + 0.930528i \(0.619349\pi\)
\(252\) 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 \(-0.351471\pi\)
0.449868 + 0.893095i \(0.351471\pi\)
\(264\) 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 \(-0.667422\pi\)
−0.502052 + 0.864837i \(0.667422\pi\)
\(272\) 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 \(-0.611906\pi\)
−0.344366 + 0.938835i \(0.611906\pi\)
\(284\) 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 \(-0.273467\pi\)
0.653104 + 0.757269i \(0.273467\pi\)
\(308\) 0 0
\(309\) −598923. −0.356841
\(310\) 0 0
\(311\) 2.33078e6 1.36647 0.683235 0.730199i \(-0.260573\pi\)
0.683235 + 0.730199i \(0.260573\pi\)
\(312\) 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 \(-0.323807\pi\)
0.525691 + 0.850675i \(0.323807\pi\)
\(332\) 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 \(-0.333522\pi\)
0.499486 + 0.866322i \(0.333522\pi\)
\(348\) 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 \(-0.444281\pi\)
0.174153 + 0.984719i \(0.444281\pi\)
\(360\) 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 \(-0.594311\pi\)
−0.291970 + 0.956427i \(0.594311\pi\)
\(368\) 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 \(-0.875006\pi\)
−0.923887 + 0.382665i \(0.875006\pi\)
\(380\) 0 0
\(381\) −3.89874e6 −1.37598
\(382\) 0 0
\(383\) 3.85088e6 1.34142 0.670708 0.741721i \(-0.265990\pi\)
0.670708 + 0.741721i \(0.265990\pi\)
\(384\) 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 \(-0.615655\pi\)
−0.355398 + 0.934715i \(0.615655\pi\)
\(420\) 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 \(-0.402590\pi\)
0.301269 + 0.953539i \(0.402590\pi\)
\(432\) 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 \(-0.790741\pi\)
−0.791579 + 0.611066i \(0.790741\pi\)
\(440\) 0 0
\(441\) −289237. −0.0708202
\(442\) 0 0
\(443\) 3.23515e6 0.783222 0.391611 0.920131i \(-0.371918\pi\)
0.391611 + 0.920131i \(0.371918\pi\)
\(444\) 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 \(-0.366011\pi\)
0.408617 + 0.912706i \(0.366011\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.03412e6 1.28033 0.640165 0.768237i \(-0.278866\pi\)
0.640165 + 0.768237i \(0.278866\pi\)
\(468\) 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 \(-0.324385\pi\)
0.524146 + 0.851629i \(0.324385\pi\)
\(480\) 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 \(-0.567395\pi\)
−0.210150 + 0.977669i \(0.567395\pi\)
\(488\) 0 0
\(489\) −6.76099e6 −1.27861
\(490\) 0 0
\(491\) −6.47314e6 −1.21174 −0.605872 0.795562i \(-0.707176\pi\)
−0.605872 + 0.795562i \(0.707176\pi\)
\(492\) 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 \(-0.782223\pi\)
−0.774946 + 0.632028i \(0.782223\pi\)
\(500\) 0 0
\(501\) 6.88238e6 1.22502
\(502\) 0 0
\(503\) 8.10557e6 1.42845 0.714223 0.699918i \(-0.246780\pi\)
0.714223 + 0.699918i \(0.246780\pi\)
\(504\) 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 \(-0.452042\pi\)
0.150095 + 0.988672i \(0.452042\pi\)
\(524\) 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 \(-0.785936\pi\)
−0.782266 + 0.622944i \(0.785936\pi\)
\(548\) 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 \(-0.935974\pi\)
−0.979838 + 0.199792i \(0.935974\pi\)
\(564\) 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 \(-0.957201\pi\)
−0.990974 + 0.134051i \(0.957201\pi\)
\(572\) 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 \(-0.762391\pi\)
−0.734090 + 0.679052i \(0.762391\pi\)
\(588\) 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 \(-0.668281\pi\)
−0.504386 + 0.863479i \(0.668281\pi\)
\(600\) 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 \(-0.555594\pi\)
−0.173768 + 0.984787i \(0.555594\pi\)
\(608\) 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 \(-0.443599\pi\)
0.176263 + 0.984343i \(0.443599\pi\)
\(620\) 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 \(-0.238302\pi\)
0.732610 + 0.680648i \(0.238302\pi\)
\(632\) 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 \(-0.832830\pi\)
−0.865233 + 0.501370i \(0.832830\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 472390. 0.0443649 0.0221825 0.999754i \(-0.492939\pi\)
0.0221825 + 0.999754i \(0.492939\pi\)
\(648\) 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 \(-0.354630\pi\)
0.440982 + 0.897516i \(0.354630\pi\)
\(660\) 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 \(-0.631437\pi\)
−0.401286 + 0.915953i \(0.631437\pi\)
\(684\) 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 \(-0.559686\pi\)
−0.186412 + 0.982472i \(0.559686\pi\)
\(692\) 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 \(-0.430288\pi\)
0.217261 + 0.976114i \(0.430288\pi\)
\(720\) 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 \(-0.525808\pi\)
−0.0809883 + 0.996715i \(0.525808\pi\)
\(728\) 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 \(-0.801531\pi\)
−0.811834 + 0.583888i \(0.801531\pi\)
\(740\) 0 0
\(741\) −9.28255e6 −0.621043
\(742\) 0 0
\(743\) −2.54593e7 −1.69190 −0.845950 0.533262i \(-0.820966\pi\)
−0.845950 + 0.533262i \(0.820966\pi\)
\(744\) 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 \(-0.367408\pi\)
0.404608 + 0.914490i \(0.367408\pi\)
\(752\) 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 \(-0.510282\pi\)
−0.0322948 + 0.999478i \(0.510282\pi\)
\(788\) 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 \(-0.538389\pi\)
−0.120311 + 0.992736i \(0.538389\pi\)
\(812\) 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 \(-0.752334\pi\)
−0.712272 + 0.701903i \(0.752334\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −7.42673e6 −0.377602 −0.188801 0.982015i \(-0.560460\pi\)
−0.188801 + 0.982015i \(0.560460\pi\)
\(828\) 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 \(-0.501218\pi\)
−0.00382526 + 0.999993i \(0.501218\pi\)
\(840\) 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 \(-0.498188\pi\)
0.00569116 + 0.999984i \(0.498188\pi\)
\(860\) 0 0
\(861\) 2.37344e7 1.09111
\(862\) 0 0
\(863\) 1.17019e7 0.534849 0.267424 0.963579i \(-0.413827\pi\)
0.267424 + 0.963579i \(0.413827\pi\)
\(864\) 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 \(-0.399589\pi\)
0.310245 + 0.950656i \(0.399589\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.71725e7 1.15963 0.579816 0.814748i \(-0.303125\pi\)
0.579816 + 0.814748i \(0.303125\pi\)
\(888\) 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 \(-0.533808\pi\)
−0.106011 + 0.994365i \(0.533808\pi\)
\(908\) 0 0
\(909\) 5.54282e6 0.222495
\(910\) 0 0
\(911\) −2.68057e7 −1.07012 −0.535059 0.844815i \(-0.679711\pi\)
−0.535059 + 0.844815i \(0.679711\pi\)
\(912\) 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 \(-0.420892\pi\)
0.245976 + 0.969276i \(0.420892\pi\)
\(920\) 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 \(-0.609846\pi\)
−0.338284 + 0.941044i \(0.609846\pi\)
\(948\) 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 \(-0.688417\pi\)
−0.557964 + 0.829865i \(0.688417\pi\)
\(968\) 0 0
\(969\) −4.36605e7 −1.49375
\(970\) 0 0
\(971\) −3.73661e7 −1.27183 −0.635916 0.771758i \(-0.719378\pi\)
−0.635916 + 0.771758i \(0.719378\pi\)
\(972\) 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 \(-0.786909\pi\)
−0.784166 + 0.620551i \(0.786909\pi\)
\(984\) 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 \(-0.630961\pi\)
−0.399918 + 0.916551i \(0.630961\pi\)
\(992\) 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 400.6.a.q.1.2 2
4.3 odd 2 200.6.a.g.1.1 2
5.2 odd 4 400.6.c.l.49.2 4
5.3 odd 4 400.6.c.l.49.3 4
5.4 even 2 80.6.a.i.1.1 2
15.14 odd 2 720.6.a.z.1.1 2
20.3 even 4 200.6.c.e.49.2 4
20.7 even 4 200.6.c.e.49.3 4
20.19 odd 2 40.6.a.d.1.2 2
40.19 odd 2 320.6.a.w.1.1 2
40.29 even 2 320.6.a.q.1.2 2
60.59 even 2 360.6.a.l.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.d.1.2 2 20.19 odd 2
80.6.a.i.1.1 2 5.4 even 2
200.6.a.g.1.1 2 4.3 odd 2
200.6.c.e.49.2 4 20.3 even 4
200.6.c.e.49.3 4 20.7 even 4
320.6.a.q.1.2 2 40.29 even 2
320.6.a.w.1.1 2 40.19 odd 2
360.6.a.l.1.2 2 60.59 even 2
400.6.a.q.1.2 2 1.1 even 1 trivial
400.6.c.l.49.2 4 5.2 odd 4
400.6.c.l.49.3 4 5.3 odd 4
720.6.a.z.1.1 2 15.14 odd 2