Properties

Label 320.6.a.d.1.1
Level 320
Weight 6
Character 320.1
Self dual yes
Analytic conductor 51.323
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.3228223402\)
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 \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q-18.0000 q^{3} +25.0000 q^{5} -242.000 q^{7} +81.0000 q^{9} +O(q^{10})\) \(q-18.0000 q^{3} +25.0000 q^{5} -242.000 q^{7} +81.0000 q^{9} +656.000 q^{11} +206.000 q^{13} -450.000 q^{15} +1690.00 q^{17} -1364.00 q^{19} +4356.00 q^{21} -2198.00 q^{23} +625.000 q^{25} +2916.00 q^{27} +2218.00 q^{29} +1700.00 q^{31} -11808.0 q^{33} -6050.00 q^{35} +846.000 q^{37} -3708.00 q^{39} -1818.00 q^{41} +10534.0 q^{43} +2025.00 q^{45} -12074.0 q^{47} +41757.0 q^{49} -30420.0 q^{51} -32586.0 q^{53} +16400.0 q^{55} +24552.0 q^{57} +8668.00 q^{59} +34670.0 q^{61} -19602.0 q^{63} +5150.00 q^{65} -47566.0 q^{67} +39564.0 q^{69} -948.000 q^{71} -63102.0 q^{73} -11250.0 q^{75} -158752. q^{77} -46536.0 q^{79} -72171.0 q^{81} -88778.0 q^{83} +42250.0 q^{85} -39924.0 q^{87} -104934. q^{89} -49852.0 q^{91} -30600.0 q^{93} -34100.0 q^{95} -36254.0 q^{97} +53136.0 q^{99} +O(q^{100})\)

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 \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 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
\(15\) −450.000 −0.516398
\(16\) 0 0
\(17\) 1690.00 1.41829 0.709144 0.705064i \(-0.249082\pi\)
0.709144 + 0.705064i \(0.249082\pi\)
\(18\) 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
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 2916.00 0.769800
\(28\) 0 0
\(29\) 2218.00 0.489741 0.244871 0.969556i \(-0.421255\pi\)
0.244871 + 0.969556i \(0.421255\pi\)
\(30\) 0 0
\(31\) 1700.00 0.317720 0.158860 0.987301i \(-0.449218\pi\)
0.158860 + 0.987301i \(0.449218\pi\)
\(32\) 0 0
\(33\) −11808.0 −1.88752
\(34\) 0 0
\(35\) −6050.00 −0.834805
\(36\) 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 \(-0.356960\pi\)
0.434402 + 0.900719i \(0.356960\pi\)
\(44\) 0 0
\(45\) 2025.00 0.149071
\(46\) 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
\(55\) 16400.0 0.731033
\(56\) 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 \(-0.296564\pi\)
0.596485 + 0.802624i \(0.296564\pi\)
\(62\) 0 0
\(63\) −19602.0 −0.622227
\(64\) 0 0
\(65\) 5150.00 0.151190
\(66\) 0 0
\(67\) −47566.0 −1.29452 −0.647261 0.762268i \(-0.724086\pi\)
−0.647261 + 0.762268i \(0.724086\pi\)
\(68\) 0 0
\(69\) 39564.0 1.00041
\(70\) 0 0
\(71\) −948.000 −0.0223184 −0.0111592 0.999938i \(-0.503552\pi\)
−0.0111592 + 0.999938i \(0.503552\pi\)
\(72\) 0 0
\(73\) −63102.0 −1.38591 −0.692957 0.720979i \(-0.743692\pi\)
−0.692957 + 0.720979i \(0.743692\pi\)
\(74\) 0 0
\(75\) −11250.0 −0.230940
\(76\) 0 0
\(77\) −158752. −3.05135
\(78\) 0 0
\(79\) −46536.0 −0.838921 −0.419461 0.907773i \(-0.637781\pi\)
−0.419461 + 0.907773i \(0.637781\pi\)
\(80\) 0 0
\(81\) −72171.0 −1.22222
\(82\) 0 0
\(83\) −88778.0 −1.41452 −0.707262 0.706952i \(-0.750070\pi\)
−0.707262 + 0.706952i \(0.750070\pi\)
\(84\) 0 0
\(85\) 42250.0 0.634278
\(86\) 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
\(95\) −34100.0 −0.387655
\(96\) 0 0
\(97\) −36254.0 −0.391225 −0.195612 0.980681i \(-0.562669\pi\)
−0.195612 + 0.980681i \(0.562669\pi\)
\(98\) 0 0
\(99\) 53136.0 0.544880
\(100\) 0 0
\(101\) −42486.0 −0.414422 −0.207211 0.978296i \(-0.566439\pi\)
−0.207211 + 0.978296i \(0.566439\pi\)
\(102\) 0 0
\(103\) −147934. −1.37396 −0.686981 0.726675i \(-0.741065\pi\)
−0.686981 + 0.726675i \(0.741065\pi\)
\(104\) 0 0
\(105\) 108900. 0.963950
\(106\) 0 0
\(107\) −18390.0 −0.155282 −0.0776412 0.996981i \(-0.524739\pi\)
−0.0776412 + 0.996981i \(0.524739\pi\)
\(108\) 0 0
\(109\) 145006. 1.16901 0.584507 0.811389i \(-0.301288\pi\)
0.584507 + 0.811389i \(0.301288\pi\)
\(110\) 0 0
\(111\) −15228.0 −0.117310
\(112\) 0 0
\(113\) 82746.0 0.609608 0.304804 0.952415i \(-0.401409\pi\)
0.304804 + 0.952415i \(0.401409\pi\)
\(114\) 0 0
\(115\) −54950.0 −0.387457
\(116\) 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
\(125\) 15625.0 0.0894427
\(126\) 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
\(135\) 72900.0 0.344265
\(136\) 0 0
\(137\) −48142.0 −0.219141 −0.109570 0.993979i \(-0.534947\pi\)
−0.109570 + 0.993979i \(0.534947\pi\)
\(138\) 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
\(145\) 55450.0 0.219019
\(146\) 0 0
\(147\) −751626. −2.86885
\(148\) 0 0
\(149\) −243178. −0.897343 −0.448672 0.893697i \(-0.648103\pi\)
−0.448672 + 0.893697i \(0.648103\pi\)
\(150\) 0 0
\(151\) −368852. −1.31647 −0.658233 0.752814i \(-0.728696\pi\)
−0.658233 + 0.752814i \(0.728696\pi\)
\(152\) 0 0
\(153\) 136890. 0.472763
\(154\) 0 0
\(155\) 42500.0 0.142089
\(156\) 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 \(-0.467163\pi\)
0.102977 + 0.994684i \(0.467163\pi\)
\(164\) 0 0
\(165\) −295200. −0.844124
\(166\) 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
\(175\) −151250. −0.373336
\(176\) 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 \(-0.235307\pi\)
0.738981 + 0.673726i \(0.235307\pi\)
\(182\) 0 0
\(183\) −624060. −1.37752
\(184\) 0 0
\(185\) 21150.0 0.0454340
\(186\) 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 \(-0.509200\pi\)
−0.0288986 + 0.999582i \(0.509200\pi\)
\(192\) 0 0
\(193\) −646406. −1.24914 −0.624571 0.780968i \(-0.714726\pi\)
−0.624571 + 0.780968i \(0.714726\pi\)
\(194\) 0 0
\(195\) −92700.0 −0.174579
\(196\) 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 \(-0.462418\pi\)
0.117793 + 0.993038i \(0.462418\pi\)
\(200\) 0 0
\(201\) 856188. 1.49479
\(202\) 0 0
\(203\) −536756. −0.914191
\(204\) 0 0
\(205\) −45450.0 −0.0755352
\(206\) 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
\(215\) 263350. 0.388541
\(216\) 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
\(225\) 50625.0 0.0666667
\(226\) 0 0
\(227\) −124182. −0.159954 −0.0799768 0.996797i \(-0.525485\pi\)
−0.0799768 + 0.996797i \(0.525485\pi\)
\(228\) 0 0
\(229\) 456386. 0.575100 0.287550 0.957766i \(-0.407159\pi\)
0.287550 + 0.957766i \(0.407159\pi\)
\(230\) 0 0
\(231\) 2.85754e6 3.52340
\(232\) 0 0
\(233\) 252666. 0.304900 0.152450 0.988311i \(-0.451284\pi\)
0.152450 + 0.988311i \(0.451284\pi\)
\(234\) 0 0
\(235\) −301850. −0.356551
\(236\) 0 0
\(237\) 837648. 0.968703
\(238\) 0 0
\(239\) −65064.0 −0.0736794 −0.0368397 0.999321i \(-0.511729\pi\)
−0.0368397 + 0.999321i \(0.511729\pi\)
\(240\) 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
\(245\) 1.04393e6 1.11110
\(246\) 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
\(255\) −760500. −0.732401
\(256\) 0 0
\(257\) −493830. −0.466385 −0.233193 0.972431i \(-0.574917\pi\)
−0.233193 + 0.972431i \(0.574917\pi\)
\(258\) 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
\(265\) −814650. −0.712617
\(266\) 0 0
\(267\) 1.88881e6 1.62148
\(268\) 0 0
\(269\) −999394. −0.842085 −0.421043 0.907041i \(-0.638336\pi\)
−0.421043 + 0.907041i \(0.638336\pi\)
\(270\) 0 0
\(271\) −1.00760e6 −0.833425 −0.416713 0.909038i \(-0.636818\pi\)
−0.416713 + 0.909038i \(0.636818\pi\)
\(272\) 0 0
\(273\) 897336. 0.728700
\(274\) 0 0
\(275\) 410000. 0.326928
\(276\) 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 \(-0.610595\pi\)
−0.340497 + 0.940246i \(0.610595\pi\)
\(284\) 0 0
\(285\) 613800. 0.447625
\(286\) 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
\(295\) 216700. 0.144979
\(296\) 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
\(305\) 866750. 0.533512
\(306\) 0 0
\(307\) 1.40946e6 0.853505 0.426753 0.904368i \(-0.359658\pi\)
0.426753 + 0.904368i \(0.359658\pi\)
\(308\) 0 0
\(309\) 2.66281e6 1.58652
\(310\) 0 0
\(311\) 2.78604e6 1.63337 0.816687 0.577081i \(-0.195808\pi\)
0.816687 + 0.577081i \(0.195808\pi\)
\(312\) 0 0
\(313\) 1.55086e6 0.894770 0.447385 0.894342i \(-0.352355\pi\)
0.447385 + 0.894342i \(0.352355\pi\)
\(314\) 0 0
\(315\) −490050. −0.278268
\(316\) 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
\(325\) 128750. 0.0676143
\(326\) 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
\(335\) −1.18915e6 −0.578928
\(336\) 0 0
\(337\) −3.36717e6 −1.61506 −0.807532 0.589824i \(-0.799197\pi\)
−0.807532 + 0.589824i \(0.799197\pi\)
\(338\) 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
\(345\) 989100. 0.447396
\(346\) 0 0
\(347\) 837202. 0.373256 0.186628 0.982431i \(-0.440244\pi\)
0.186628 + 0.982431i \(0.440244\pi\)
\(348\) 0 0
\(349\) 1.51910e6 0.667609 0.333805 0.942642i \(-0.391667\pi\)
0.333805 + 0.942642i \(0.391667\pi\)
\(350\) 0 0
\(351\) 600696. 0.260248
\(352\) 0 0
\(353\) −3.51851e6 −1.50287 −0.751436 0.659806i \(-0.770638\pi\)
−0.751436 + 0.659806i \(0.770638\pi\)
\(354\) 0 0
\(355\) −23700.0 −0.00998108
\(356\) 0 0
\(357\) 7.36164e6 3.05706
\(358\) 0 0
\(359\) 3.57089e6 1.46231 0.731156 0.682210i \(-0.238981\pi\)
0.731156 + 0.682210i \(0.238981\pi\)
\(360\) 0 0
\(361\) −615603. −0.248618
\(362\) 0 0
\(363\) −4.84713e6 −1.93071
\(364\) 0 0
\(365\) −1.57755e6 −0.619799
\(366\) 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
\(375\) −281250. −0.103280
\(376\) 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
\(385\) −3.96880e6 −1.36461
\(386\) 0 0
\(387\) 853254. 0.289602
\(388\) 0 0
\(389\) −5.79825e6 −1.94278 −0.971388 0.237496i \(-0.923673\pi\)
−0.971388 + 0.237496i \(0.923673\pi\)
\(390\) 0 0
\(391\) −3.71462e6 −1.22878
\(392\) 0 0
\(393\) −3.64694e6 −1.19110
\(394\) 0 0
\(395\) −1.16340e6 −0.375177
\(396\) 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
\(405\) −1.80428e6 −0.546594
\(406\) 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
\(415\) −2.21945e6 −0.632594
\(416\) 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 \(-0.587439\pi\)
−0.271255 + 0.962507i \(0.587439\pi\)
\(422\) 0 0
\(423\) −977994. −0.265757
\(424\) 0 0
\(425\) 1.05625e6 0.283658
\(426\) 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 \(-0.557006\pi\)
−0.178135 + 0.984006i \(0.557006\pi\)
\(432\) 0 0
\(433\) 5.18813e6 1.32981 0.664907 0.746926i \(-0.268471\pi\)
0.664907 + 0.746926i \(0.268471\pi\)
\(434\) 0 0
\(435\) −998100. −0.252901
\(436\) 0 0
\(437\) 2.99807e6 0.750997
\(438\) 0 0
\(439\) 2.94082e6 0.728296 0.364148 0.931341i \(-0.381360\pi\)
0.364148 + 0.931341i \(0.381360\pi\)
\(440\) 0 0
\(441\) 3.38232e6 0.828167
\(442\) 0 0
\(443\) −1.28347e6 −0.310724 −0.155362 0.987858i \(-0.549654\pi\)
−0.155362 + 0.987858i \(0.549654\pi\)
\(444\) 0 0
\(445\) −2.62335e6 −0.627995
\(446\) 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
\(455\) −1.24630e6 −0.282224
\(456\) 0 0
\(457\) 7.91315e6 1.77239 0.886194 0.463315i \(-0.153340\pi\)
0.886194 + 0.463315i \(0.153340\pi\)
\(458\) 0 0
\(459\) 4.92804e6 1.09180
\(460\) 0 0
\(461\) 6.18530e6 1.35553 0.677764 0.735280i \(-0.262949\pi\)
0.677764 + 0.735280i \(0.262949\pi\)
\(462\) 0 0
\(463\) −491934. −0.106648 −0.0533242 0.998577i \(-0.516982\pi\)
−0.0533242 + 0.998577i \(0.516982\pi\)
\(464\) 0 0
\(465\) −765000. −0.164070
\(466\) 0 0
\(467\) 447442. 0.0949390 0.0474695 0.998873i \(-0.484884\pi\)
0.0474695 + 0.998873i \(0.484884\pi\)
\(468\) 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
\(475\) −852500. −0.173365
\(476\) 0 0
\(477\) −2.63947e6 −0.531154
\(478\) 0 0
\(479\) −8.18487e6 −1.62995 −0.814973 0.579499i \(-0.803248\pi\)
−0.814973 + 0.579499i \(0.803248\pi\)
\(480\) 0 0
\(481\) 174276. 0.0343459
\(482\) 0 0
\(483\) −9.57449e6 −1.86744
\(484\) 0 0
\(485\) −906350. −0.174961
\(486\) 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
\(495\) 1.32840e6 0.243678
\(496\) 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
\(505\) −1.06215e6 −0.185335
\(506\) 0 0
\(507\) 5.91943e6 1.02273
\(508\) 0 0
\(509\) −3.66133e6 −0.626390 −0.313195 0.949689i \(-0.601399\pi\)
−0.313195 + 0.949689i \(0.601399\pi\)
\(510\) 0 0
\(511\) 1.52707e7 2.58706
\(512\) 0 0
\(513\) −3.97742e6 −0.667281
\(514\) 0 0
\(515\) −3.69835e6 −0.614455
\(516\) 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 \(-0.630137\pi\)
−0.397543 + 0.917584i \(0.630137\pi\)
\(524\) 0 0
\(525\) 2.72250e6 0.431092
\(526\) 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
\(535\) −459750. −0.0694444
\(536\) 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 \(-0.557009\pi\)
−0.178142 + 0.984005i \(0.557009\pi\)
\(542\) 0 0
\(543\) −1.17255e7 −1.70660
\(544\) 0 0
\(545\) 3.62515e6 0.522799
\(546\) 0 0
\(547\) −731254. −0.104496 −0.0522480 0.998634i \(-0.516639\pi\)
−0.0522480 + 0.998634i \(0.516639\pi\)
\(548\) 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
\(555\) −380700. −0.0524627
\(556\) 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 \(-0.433801\pi\)
0.206475 + 0.978452i \(0.433801\pi\)
\(564\) 0 0
\(565\) 2.06865e6 0.272625
\(566\) 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
\(575\) −1.37375e6 −0.173276
\(576\) 0 0
\(577\) 7.09764e6 0.887513 0.443756 0.896147i \(-0.353646\pi\)
0.443756 + 0.896147i \(0.353646\pi\)
\(578\) 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
\(585\) 417150. 0.0503968
\(586\) 0 0
\(587\) 1.56926e6 0.187975 0.0939873 0.995573i \(-0.470039\pi\)
0.0939873 + 0.995573i \(0.470039\pi\)
\(588\) 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 \(-0.775707\pi\)
−0.761848 + 0.647756i \(0.775707\pi\)
\(594\) 0 0
\(595\) −1.02245e7 −1.18399
\(596\) 0 0
\(597\) −2.36894e6 −0.272031
\(598\) 0 0
\(599\) 5.24688e6 0.597495 0.298747 0.954332i \(-0.403431\pi\)
0.298747 + 0.954332i \(0.403431\pi\)
\(600\) 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
\(605\) 6.73212e6 0.747763
\(606\) 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
\(615\) 818100. 0.0872205
\(616\) 0 0
\(617\) −1.12946e7 −1.19442 −0.597211 0.802084i \(-0.703725\pi\)
−0.597211 + 0.802084i \(0.703725\pi\)
\(618\) 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
\(625\) 390625. 0.0400000
\(626\) 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 \(-0.574291\pi\)
−0.231278 + 0.972888i \(0.574291\pi\)
\(632\) 0 0
\(633\) −2.17941e7 −2.16187
\(634\) 0 0
\(635\) 6.86115e6 0.675247
\(636\) 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 \(-0.304051\pi\)
0.577443 + 0.816431i \(0.304051\pi\)
\(644\) 0 0
\(645\) −4.74030e6 −0.448649
\(646\) 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
\(655\) 5.06520e6 0.461311
\(656\) 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 \(-0.596199\pi\)
−0.297639 + 0.954679i \(0.596199\pi\)
\(662\) 0 0
\(663\) −6.26652e6 −0.553659
\(664\) 0 0
\(665\) 8.25220e6 0.723628
\(666\) 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 \(-0.509857\pi\)
−0.0309603 + 0.999521i \(0.509857\pi\)
\(674\) 0 0
\(675\) 1.82250e6 0.153960
\(676\) 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 \(-0.764048\pi\)
−0.737614 + 0.675223i \(0.764048\pi\)
\(684\) 0 0
\(685\) −1.20355e6 −0.0980026
\(686\) 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
\(695\) −2.77890e6 −0.218228
\(696\) 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 \(-0.354022\pi\)
0.442697 + 0.896671i \(0.354022\pi\)
\(702\) 0 0
\(703\) −1.15394e6 −0.0880636
\(704\) 0 0
\(705\) 5.43330e6 0.411710
\(706\) 0 0
\(707\) 1.02816e7 0.773593
\(708\) 0 0
\(709\) 610738. 0.0456288 0.0228144 0.999740i \(-0.492737\pi\)
0.0228144 + 0.999740i \(0.492737\pi\)
\(710\) 0 0
\(711\) −3.76942e6 −0.279640
\(712\) 0 0
\(713\) −3.73660e6 −0.275266
\(714\) 0 0
\(715\) 3.37840e6 0.247142
\(716\) 0 0
\(717\) 1.17115e6 0.0850776
\(718\) 0 0
\(719\) −3.97278e6 −0.286597 −0.143299 0.989680i \(-0.545771\pi\)
−0.143299 + 0.989680i \(0.545771\pi\)
\(720\) 0 0
\(721\) 3.58000e7 2.56475
\(722\) 0 0
\(723\) 2.53080e7 1.80058
\(724\) 0 0
\(725\) 1.38625e6 0.0979482
\(726\) 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
\(735\) −1.87906e7 −1.28299
\(736\) 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
\(745\) −6.07945e6 −0.401304
\(746\) 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 \(-0.595060\pi\)
−0.294221 + 0.955738i \(0.595060\pi\)
\(752\) 0 0
\(753\) 9.87120e6 0.634428
\(754\) 0 0
\(755\) −9.22130e6 −0.588742
\(756\) 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
\(765\) 3.42225e6 0.211426
\(766\) 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
\(775\) 1.06250e6 0.0635440
\(776\) 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
\(785\) −7.98865e6 −0.462700
\(786\) 0 0
\(787\) −5.97074e6 −0.343630 −0.171815 0.985129i \(-0.554963\pi\)
−0.171815 + 0.985129i \(0.554963\pi\)
\(788\) 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
\(795\) 1.46637e7 0.822860
\(796\) 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
\(805\) 1.32979e7 0.723258
\(806\) 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
\(815\) 1.74655e6 0.0921058
\(816\) 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 \(-0.364157\pi\)
0.413928 + 0.910310i \(0.364157\pi\)
\(822\) 0 0
\(823\) −3.18347e7 −1.63833 −0.819164 0.573559i \(-0.805562\pi\)
−0.819164 + 0.573559i \(0.805562\pi\)
\(824\) 0 0
\(825\) −7.38000e6 −0.377504
\(826\) 0 0
\(827\) 1.27575e7 0.648635 0.324317 0.945948i \(-0.394865\pi\)
0.324317 + 0.945948i \(0.394865\pi\)
\(828\) 0 0
\(829\) −6.18613e6 −0.312631 −0.156316 0.987707i \(-0.549962\pi\)
−0.156316 + 0.987707i \(0.549962\pi\)
\(830\) 0 0
\(831\) 1.84114e7 0.924880
\(832\) 0 0
\(833\) 7.05693e7 3.52374
\(834\) 0 0
\(835\) 8.58555e6 0.426140
\(836\) 0 0
\(837\) 4.95720e6 0.244581
\(838\) 0 0
\(839\) 5.66754e6 0.277965 0.138982 0.990295i \(-0.455617\pi\)
0.138982 + 0.990295i \(0.455617\pi\)
\(840\) 0 0
\(841\) −1.55916e7 −0.760154
\(842\) 0 0
\(843\) 2.12710e7 1.03091
\(844\) 0 0
\(845\) −8.22143e6 −0.396100
\(846\) 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
\(855\) −2.76210e6 −0.129218
\(856\) 0 0
\(857\) 162162. 0.00754218 0.00377109 0.999993i \(-0.498800\pi\)
0.00377109 + 0.999993i \(0.498800\pi\)
\(858\) 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
\(865\) 28550.0 0.00129738
\(866\) 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
\(875\) −3.78125e6 −0.166961
\(876\) 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 \(-0.218645\pi\)
0.773220 + 0.634138i \(0.218645\pi\)
\(884\) 0 0
\(885\) −3.90060e6 −0.167407
\(886\) 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
\(895\) −2.16710e6 −0.0904318
\(896\) 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
\(905\) 1.62855e7 0.660965
\(906\) 0 0
\(907\) 2.01914e7 0.814981 0.407490 0.913209i \(-0.366404\pi\)
0.407490 + 0.913209i \(0.366404\pi\)
\(908\) 0 0
\(909\) −3.44137e6 −0.138141
\(910\) 0 0
\(911\) −2.75179e7 −1.09855 −0.549274 0.835642i \(-0.685096\pi\)
−0.549274 + 0.835642i \(0.685096\pi\)
\(912\) 0 0
\(913\) −5.82384e7 −2.31224
\(914\) 0 0
\(915\) −1.56015e7 −0.616047
\(916\) 0 0
\(917\) −4.90311e7 −1.92552
\(918\) 0 0
\(919\) −1.31786e7 −0.514730 −0.257365 0.966314i \(-0.582854\pi\)
−0.257365 + 0.966314i \(0.582854\pi\)
\(920\) 0 0
\(921\) −2.53702e7 −0.985543
\(922\) 0 0
\(923\) −195288. −0.00754521
\(924\) 0 0
\(925\) 528750. 0.0203187
\(926\) 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
\(935\) 2.77160e7 1.03682
\(936\) 0 0
\(937\) 3.04258e7 1.13212 0.566060 0.824364i \(-0.308467\pi\)
0.566060 + 0.824364i \(0.308467\pi\)
\(938\) 0 0
\(939\) −2.79154e7 −1.03319
\(940\) 0 0
\(941\) 3.26349e7 1.20146 0.600729 0.799452i \(-0.294877\pi\)
0.600729 + 0.799452i \(0.294877\pi\)
\(942\) 0 0
\(943\) 3.99596e6 0.146333
\(944\) 0 0
\(945\) −1.76418e7 −0.642634
\(946\) 0 0
\(947\) 3.01534e7 1.09260 0.546300 0.837589i \(-0.316036\pi\)
0.546300 + 0.837589i \(0.316036\pi\)
\(948\) 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 \(-0.498280\pi\)
0.00540474 + 0.999985i \(0.498280\pi\)
\(954\) 0 0
\(955\) −728500. −0.0258477
\(956\) 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
\(965\) −1.61601e7 −0.558634
\(966\) 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
\(975\) −2.31750e6 −0.0780743
\(976\) 0 0
\(977\) 1.63928e6 0.0549436 0.0274718 0.999623i \(-0.491254\pi\)
0.0274718 + 0.999623i \(0.491254\pi\)
\(978\) 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
\(985\) −1.07784e7 −0.353969
\(986\) 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 \(-0.516102\pi\)
−0.0505632 + 0.998721i \(0.516102\pi\)
\(992\) 0 0
\(993\) 2.93514e7 0.944616
\(994\) 0 0
\(995\) 3.29020e6 0.105357
\(996\) 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 320.6.a.d.1.1 1
4.3 odd 2 320.6.a.m.1.1 1
8.3 odd 2 40.6.a.a.1.1 1
8.5 even 2 80.6.a.g.1.1 1
24.5 odd 2 720.6.a.k.1.1 1
24.11 even 2 360.6.a.i.1.1 1
40.3 even 4 200.6.c.b.49.1 2
40.13 odd 4 400.6.c.e.49.2 2
40.19 odd 2 200.6.a.d.1.1 1
40.27 even 4 200.6.c.b.49.2 2
40.29 even 2 400.6.a.b.1.1 1
40.37 odd 4 400.6.c.e.49.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.a.1.1 1 8.3 odd 2
80.6.a.g.1.1 1 8.5 even 2
200.6.a.d.1.1 1 40.19 odd 2
200.6.c.b.49.1 2 40.3 even 4
200.6.c.b.49.2 2 40.27 even 4
320.6.a.d.1.1 1 1.1 even 1 trivial
320.6.a.m.1.1 1 4.3 odd 2
360.6.a.i.1.1 1 24.11 even 2
400.6.a.b.1.1 1 40.29 even 2
400.6.c.e.49.1 2 40.37 odd 4
400.6.c.e.49.2 2 40.13 odd 4
720.6.a.k.1.1 1 24.5 odd 2