Properties

Label 320.6.a.k.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 10)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.00000 q^{3} +25.0000 q^{5} +118.000 q^{7} -207.000 q^{9} +O(q^{10})\) \(q+6.00000 q^{3} +25.0000 q^{5} +118.000 q^{7} -207.000 q^{9} +192.000 q^{11} -1106.00 q^{13} +150.000 q^{15} +762.000 q^{17} -2740.00 q^{19} +708.000 q^{21} -1566.00 q^{23} +625.000 q^{25} -2700.00 q^{27} -5910.00 q^{29} +6868.00 q^{31} +1152.00 q^{33} +2950.00 q^{35} +5518.00 q^{37} -6636.00 q^{39} -378.000 q^{41} -2434.00 q^{43} -5175.00 q^{45} -13122.0 q^{47} -2883.00 q^{49} +4572.00 q^{51} +9174.00 q^{53} +4800.00 q^{55} -16440.0 q^{57} -34980.0 q^{59} +9838.00 q^{61} -24426.0 q^{63} -27650.0 q^{65} +33722.0 q^{67} -9396.00 q^{69} -70212.0 q^{71} +21986.0 q^{73} +3750.00 q^{75} +22656.0 q^{77} -4520.00 q^{79} +34101.0 q^{81} -109074. q^{83} +19050.0 q^{85} -35460.0 q^{87} +38490.0 q^{89} -130508. q^{91} +41208.0 q^{93} -68500.0 q^{95} -1918.00 q^{97} -39744.0 q^{99} +O(q^{100})\)

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
\(3\) 6.00000 0.384900 0.192450 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 118.000 0.910200 0.455100 0.890440i \(-0.349603\pi\)
0.455100 + 0.890440i \(0.349603\pi\)
\(8\) 0 0
\(9\) −207.000 −0.851852
\(10\) 0 0
\(11\) 192.000 0.478431 0.239216 0.970966i \(-0.423110\pi\)
0.239216 + 0.970966i \(0.423110\pi\)
\(12\) 0 0
\(13\) −1106.00 −1.81508 −0.907542 0.419961i \(-0.862044\pi\)
−0.907542 + 0.419961i \(0.862044\pi\)
\(14\) 0 0
\(15\) 150.000 0.172133
\(16\) 0 0
\(17\) 762.000 0.639488 0.319744 0.947504i \(-0.396403\pi\)
0.319744 + 0.947504i \(0.396403\pi\)
\(18\) 0 0
\(19\) −2740.00 −1.74127 −0.870636 0.491928i \(-0.836292\pi\)
−0.870636 + 0.491928i \(0.836292\pi\)
\(20\) 0 0
\(21\) 708.000 0.350336
\(22\) 0 0
\(23\) −1566.00 −0.617266 −0.308633 0.951181i \(-0.599871\pi\)
−0.308633 + 0.951181i \(0.599871\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −2700.00 −0.712778
\(28\) 0 0
\(29\) −5910.00 −1.30495 −0.652473 0.757812i \(-0.726268\pi\)
−0.652473 + 0.757812i \(0.726268\pi\)
\(30\) 0 0
\(31\) 6868.00 1.28359 0.641795 0.766877i \(-0.278190\pi\)
0.641795 + 0.766877i \(0.278190\pi\)
\(32\) 0 0
\(33\) 1152.00 0.184148
\(34\) 0 0
\(35\) 2950.00 0.407054
\(36\) 0 0
\(37\) 5518.00 0.662640 0.331320 0.943519i \(-0.392506\pi\)
0.331320 + 0.943519i \(0.392506\pi\)
\(38\) 0 0
\(39\) −6636.00 −0.698626
\(40\) 0 0
\(41\) −378.000 −0.0351182 −0.0175591 0.999846i \(-0.505590\pi\)
−0.0175591 + 0.999846i \(0.505590\pi\)
\(42\) 0 0
\(43\) −2434.00 −0.200747 −0.100374 0.994950i \(-0.532004\pi\)
−0.100374 + 0.994950i \(0.532004\pi\)
\(44\) 0 0
\(45\) −5175.00 −0.380960
\(46\) 0 0
\(47\) −13122.0 −0.866474 −0.433237 0.901280i \(-0.642629\pi\)
−0.433237 + 0.901280i \(0.642629\pi\)
\(48\) 0 0
\(49\) −2883.00 −0.171536
\(50\) 0 0
\(51\) 4572.00 0.246139
\(52\) 0 0
\(53\) 9174.00 0.448610 0.224305 0.974519i \(-0.427989\pi\)
0.224305 + 0.974519i \(0.427989\pi\)
\(54\) 0 0
\(55\) 4800.00 0.213961
\(56\) 0 0
\(57\) −16440.0 −0.670216
\(58\) 0 0
\(59\) −34980.0 −1.30825 −0.654124 0.756388i \(-0.726962\pi\)
−0.654124 + 0.756388i \(0.726962\pi\)
\(60\) 0 0
\(61\) 9838.00 0.338518 0.169259 0.985572i \(-0.445863\pi\)
0.169259 + 0.985572i \(0.445863\pi\)
\(62\) 0 0
\(63\) −24426.0 −0.775356
\(64\) 0 0
\(65\) −27650.0 −0.811730
\(66\) 0 0
\(67\) 33722.0 0.917754 0.458877 0.888500i \(-0.348252\pi\)
0.458877 + 0.888500i \(0.348252\pi\)
\(68\) 0 0
\(69\) −9396.00 −0.237586
\(70\) 0 0
\(71\) −70212.0 −1.65297 −0.826486 0.562957i \(-0.809664\pi\)
−0.826486 + 0.562957i \(0.809664\pi\)
\(72\) 0 0
\(73\) 21986.0 0.482880 0.241440 0.970416i \(-0.422380\pi\)
0.241440 + 0.970416i \(0.422380\pi\)
\(74\) 0 0
\(75\) 3750.00 0.0769800
\(76\) 0 0
\(77\) 22656.0 0.435468
\(78\) 0 0
\(79\) −4520.00 −0.0814837 −0.0407418 0.999170i \(-0.512972\pi\)
−0.0407418 + 0.999170i \(0.512972\pi\)
\(80\) 0 0
\(81\) 34101.0 0.577503
\(82\) 0 0
\(83\) −109074. −1.73790 −0.868952 0.494896i \(-0.835206\pi\)
−0.868952 + 0.494896i \(0.835206\pi\)
\(84\) 0 0
\(85\) 19050.0 0.285988
\(86\) 0 0
\(87\) −35460.0 −0.502274
\(88\) 0 0
\(89\) 38490.0 0.515078 0.257539 0.966268i \(-0.417088\pi\)
0.257539 + 0.966268i \(0.417088\pi\)
\(90\) 0 0
\(91\) −130508. −1.65209
\(92\) 0 0
\(93\) 41208.0 0.494054
\(94\) 0 0
\(95\) −68500.0 −0.778720
\(96\) 0 0
\(97\) −1918.00 −0.0206976 −0.0103488 0.999946i \(-0.503294\pi\)
−0.0103488 + 0.999946i \(0.503294\pi\)
\(98\) 0 0
\(99\) −39744.0 −0.407553
\(100\) 0 0
\(101\) −77622.0 −0.757149 −0.378575 0.925571i \(-0.623586\pi\)
−0.378575 + 0.925571i \(0.623586\pi\)
\(102\) 0 0
\(103\) 46714.0 0.433864 0.216932 0.976187i \(-0.430395\pi\)
0.216932 + 0.976187i \(0.430395\pi\)
\(104\) 0 0
\(105\) 17700.0 0.156675
\(106\) 0 0
\(107\) −1038.00 −0.00876472 −0.00438236 0.999990i \(-0.501395\pi\)
−0.00438236 + 0.999990i \(0.501395\pi\)
\(108\) 0 0
\(109\) −206930. −1.66823 −0.834117 0.551587i \(-0.814023\pi\)
−0.834117 + 0.551587i \(0.814023\pi\)
\(110\) 0 0
\(111\) 33108.0 0.255050
\(112\) 0 0
\(113\) 139386. 1.02689 0.513444 0.858123i \(-0.328369\pi\)
0.513444 + 0.858123i \(0.328369\pi\)
\(114\) 0 0
\(115\) −39150.0 −0.276050
\(116\) 0 0
\(117\) 228942. 1.54618
\(118\) 0 0
\(119\) 89916.0 0.582062
\(120\) 0 0
\(121\) −124187. −0.771104
\(122\) 0 0
\(123\) −2268.00 −0.0135170
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −299882. −1.64984 −0.824919 0.565252i \(-0.808779\pi\)
−0.824919 + 0.565252i \(0.808779\pi\)
\(128\) 0 0
\(129\) −14604.0 −0.0772676
\(130\) 0 0
\(131\) 7872.00 0.0400781 0.0200390 0.999799i \(-0.493621\pi\)
0.0200390 + 0.999799i \(0.493621\pi\)
\(132\) 0 0
\(133\) −323320. −1.58491
\(134\) 0 0
\(135\) −67500.0 −0.318764
\(136\) 0 0
\(137\) −164238. −0.747605 −0.373803 0.927508i \(-0.621946\pi\)
−0.373803 + 0.927508i \(0.621946\pi\)
\(138\) 0 0
\(139\) −282100. −1.23841 −0.619207 0.785228i \(-0.712546\pi\)
−0.619207 + 0.785228i \(0.712546\pi\)
\(140\) 0 0
\(141\) −78732.0 −0.333506
\(142\) 0 0
\(143\) −212352. −0.868393
\(144\) 0 0
\(145\) −147750. −0.583590
\(146\) 0 0
\(147\) −17298.0 −0.0660241
\(148\) 0 0
\(149\) 388950. 1.43525 0.717626 0.696429i \(-0.245229\pi\)
0.717626 + 0.696429i \(0.245229\pi\)
\(150\) 0 0
\(151\) 97948.0 0.349585 0.174793 0.984605i \(-0.444074\pi\)
0.174793 + 0.984605i \(0.444074\pi\)
\(152\) 0 0
\(153\) −157734. −0.544749
\(154\) 0 0
\(155\) 171700. 0.574039
\(156\) 0 0
\(157\) 3718.00 0.0120382 0.00601908 0.999982i \(-0.498084\pi\)
0.00601908 + 0.999982i \(0.498084\pi\)
\(158\) 0 0
\(159\) 55044.0 0.172670
\(160\) 0 0
\(161\) −184788. −0.561835
\(162\) 0 0
\(163\) −43234.0 −0.127455 −0.0637274 0.997967i \(-0.520299\pi\)
−0.0637274 + 0.997967i \(0.520299\pi\)
\(164\) 0 0
\(165\) 28800.0 0.0823536
\(166\) 0 0
\(167\) −186522. −0.517534 −0.258767 0.965940i \(-0.583316\pi\)
−0.258767 + 0.965940i \(0.583316\pi\)
\(168\) 0 0
\(169\) 851943. 2.29453
\(170\) 0 0
\(171\) 567180. 1.48331
\(172\) 0 0
\(173\) 374454. 0.951225 0.475612 0.879655i \(-0.342226\pi\)
0.475612 + 0.879655i \(0.342226\pi\)
\(174\) 0 0
\(175\) 73750.0 0.182040
\(176\) 0 0
\(177\) −209880. −0.503545
\(178\) 0 0
\(179\) 272100. 0.634740 0.317370 0.948302i \(-0.397200\pi\)
0.317370 + 0.948302i \(0.397200\pi\)
\(180\) 0 0
\(181\) 75418.0 0.171111 0.0855556 0.996333i \(-0.472733\pi\)
0.0855556 + 0.996333i \(0.472733\pi\)
\(182\) 0 0
\(183\) 59028.0 0.130296
\(184\) 0 0
\(185\) 137950. 0.296341
\(186\) 0 0
\(187\) 146304. 0.305951
\(188\) 0 0
\(189\) −318600. −0.648771
\(190\) 0 0
\(191\) 356988. 0.708060 0.354030 0.935234i \(-0.384811\pi\)
0.354030 + 0.935234i \(0.384811\pi\)
\(192\) 0 0
\(193\) −438694. −0.847751 −0.423876 0.905720i \(-0.639331\pi\)
−0.423876 + 0.905720i \(0.639331\pi\)
\(194\) 0 0
\(195\) −165900. −0.312435
\(196\) 0 0
\(197\) 156798. 0.287856 0.143928 0.989588i \(-0.454027\pi\)
0.143928 + 0.989588i \(0.454027\pi\)
\(198\) 0 0
\(199\) 162520. 0.290920 0.145460 0.989364i \(-0.453534\pi\)
0.145460 + 0.989364i \(0.453534\pi\)
\(200\) 0 0
\(201\) 202332. 0.353244
\(202\) 0 0
\(203\) −697380. −1.18776
\(204\) 0 0
\(205\) −9450.00 −0.0157053
\(206\) 0 0
\(207\) 324162. 0.525819
\(208\) 0 0
\(209\) −526080. −0.833079
\(210\) 0 0
\(211\) −181648. −0.280882 −0.140441 0.990089i \(-0.544852\pi\)
−0.140441 + 0.990089i \(0.544852\pi\)
\(212\) 0 0
\(213\) −421272. −0.636229
\(214\) 0 0
\(215\) −60850.0 −0.0897769
\(216\) 0 0
\(217\) 810424. 1.16832
\(218\) 0 0
\(219\) 131916. 0.185861
\(220\) 0 0
\(221\) −842772. −1.16073
\(222\) 0 0
\(223\) 288274. 0.388189 0.194095 0.980983i \(-0.437823\pi\)
0.194095 + 0.980983i \(0.437823\pi\)
\(224\) 0 0
\(225\) −129375. −0.170370
\(226\) 0 0
\(227\) 1.12552e6 1.44974 0.724869 0.688887i \(-0.241900\pi\)
0.724869 + 0.688887i \(0.241900\pi\)
\(228\) 0 0
\(229\) 415810. 0.523970 0.261985 0.965072i \(-0.415623\pi\)
0.261985 + 0.965072i \(0.415623\pi\)
\(230\) 0 0
\(231\) 135936. 0.167612
\(232\) 0 0
\(233\) 770586. 0.929889 0.464945 0.885340i \(-0.346074\pi\)
0.464945 + 0.885340i \(0.346074\pi\)
\(234\) 0 0
\(235\) −328050. −0.387499
\(236\) 0 0
\(237\) −27120.0 −0.0313631
\(238\) 0 0
\(239\) 595320. 0.674149 0.337074 0.941478i \(-0.390563\pi\)
0.337074 + 0.941478i \(0.390563\pi\)
\(240\) 0 0
\(241\) 273902. 0.303775 0.151888 0.988398i \(-0.451465\pi\)
0.151888 + 0.988398i \(0.451465\pi\)
\(242\) 0 0
\(243\) 860706. 0.935059
\(244\) 0 0
\(245\) −72075.0 −0.0767131
\(246\) 0 0
\(247\) 3.03044e6 3.16055
\(248\) 0 0
\(249\) −654444. −0.668920
\(250\) 0 0
\(251\) 850752. 0.852351 0.426176 0.904640i \(-0.359861\pi\)
0.426176 + 0.904640i \(0.359861\pi\)
\(252\) 0 0
\(253\) −300672. −0.295319
\(254\) 0 0
\(255\) 114300. 0.110077
\(256\) 0 0
\(257\) 825402. 0.779530 0.389765 0.920914i \(-0.372556\pi\)
0.389765 + 0.920914i \(0.372556\pi\)
\(258\) 0 0
\(259\) 651124. 0.603135
\(260\) 0 0
\(261\) 1.22337e6 1.11162
\(262\) 0 0
\(263\) −1.36465e6 −1.21655 −0.608276 0.793726i \(-0.708139\pi\)
−0.608276 + 0.793726i \(0.708139\pi\)
\(264\) 0 0
\(265\) 229350. 0.200625
\(266\) 0 0
\(267\) 230940. 0.198254
\(268\) 0 0
\(269\) 113310. 0.0954745 0.0477373 0.998860i \(-0.484799\pi\)
0.0477373 + 0.998860i \(0.484799\pi\)
\(270\) 0 0
\(271\) 849628. 0.702758 0.351379 0.936233i \(-0.385713\pi\)
0.351379 + 0.936233i \(0.385713\pi\)
\(272\) 0 0
\(273\) −783048. −0.635890
\(274\) 0 0
\(275\) 120000. 0.0956862
\(276\) 0 0
\(277\) −438602. −0.343456 −0.171728 0.985144i \(-0.554935\pi\)
−0.171728 + 0.985144i \(0.554935\pi\)
\(278\) 0 0
\(279\) −1.42168e6 −1.09343
\(280\) 0 0
\(281\) −1.45670e6 −1.10053 −0.550267 0.834989i \(-0.685474\pi\)
−0.550267 + 0.834989i \(0.685474\pi\)
\(282\) 0 0
\(283\) −120394. −0.0893591 −0.0446795 0.999001i \(-0.514227\pi\)
−0.0446795 + 0.999001i \(0.514227\pi\)
\(284\) 0 0
\(285\) −411000. −0.299730
\(286\) 0 0
\(287\) −44604.0 −0.0319646
\(288\) 0 0
\(289\) −839213. −0.591055
\(290\) 0 0
\(291\) −11508.0 −0.00796650
\(292\) 0 0
\(293\) 2.64209e6 1.79796 0.898978 0.437993i \(-0.144311\pi\)
0.898978 + 0.437993i \(0.144311\pi\)
\(294\) 0 0
\(295\) −874500. −0.585066
\(296\) 0 0
\(297\) −518400. −0.341015
\(298\) 0 0
\(299\) 1.73200e6 1.12039
\(300\) 0 0
\(301\) −287212. −0.182720
\(302\) 0 0
\(303\) −465732. −0.291427
\(304\) 0 0
\(305\) 245950. 0.151390
\(306\) 0 0
\(307\) −1.44756e6 −0.876577 −0.438288 0.898834i \(-0.644415\pi\)
−0.438288 + 0.898834i \(0.644415\pi\)
\(308\) 0 0
\(309\) 280284. 0.166994
\(310\) 0 0
\(311\) 928068. 0.544100 0.272050 0.962283i \(-0.412298\pi\)
0.272050 + 0.962283i \(0.412298\pi\)
\(312\) 0 0
\(313\) 2.29563e6 1.32446 0.662232 0.749299i \(-0.269609\pi\)
0.662232 + 0.749299i \(0.269609\pi\)
\(314\) 0 0
\(315\) −610650. −0.346750
\(316\) 0 0
\(317\) −2.73652e6 −1.52950 −0.764752 0.644324i \(-0.777139\pi\)
−0.764752 + 0.644324i \(0.777139\pi\)
\(318\) 0 0
\(319\) −1.13472e6 −0.624327
\(320\) 0 0
\(321\) −6228.00 −0.00337354
\(322\) 0 0
\(323\) −2.08788e6 −1.11352
\(324\) 0 0
\(325\) −691250. −0.363017
\(326\) 0 0
\(327\) −1.24158e6 −0.642104
\(328\) 0 0
\(329\) −1.54840e6 −0.788665
\(330\) 0 0
\(331\) 3.81879e6 1.91583 0.957913 0.287059i \(-0.0926776\pi\)
0.957913 + 0.287059i \(0.0926776\pi\)
\(332\) 0 0
\(333\) −1.14223e6 −0.564471
\(334\) 0 0
\(335\) 843050. 0.410432
\(336\) 0 0
\(337\) −2.21088e6 −1.06045 −0.530225 0.847857i \(-0.677892\pi\)
−0.530225 + 0.847857i \(0.677892\pi\)
\(338\) 0 0
\(339\) 836316. 0.395249
\(340\) 0 0
\(341\) 1.31866e6 0.614109
\(342\) 0 0
\(343\) −2.32342e6 −1.06633
\(344\) 0 0
\(345\) −234900. −0.106252
\(346\) 0 0
\(347\) −2.32724e6 −1.03757 −0.518785 0.854905i \(-0.673615\pi\)
−0.518785 + 0.854905i \(0.673615\pi\)
\(348\) 0 0
\(349\) 311290. 0.136805 0.0684024 0.997658i \(-0.478210\pi\)
0.0684024 + 0.997658i \(0.478210\pi\)
\(350\) 0 0
\(351\) 2.98620e6 1.29375
\(352\) 0 0
\(353\) −3.08657e6 −1.31838 −0.659189 0.751977i \(-0.729100\pi\)
−0.659189 + 0.751977i \(0.729100\pi\)
\(354\) 0 0
\(355\) −1.75530e6 −0.739232
\(356\) 0 0
\(357\) 539496. 0.224036
\(358\) 0 0
\(359\) 3.53076e6 1.44588 0.722940 0.690911i \(-0.242790\pi\)
0.722940 + 0.690911i \(0.242790\pi\)
\(360\) 0 0
\(361\) 5.03150e6 2.03203
\(362\) 0 0
\(363\) −745122. −0.296798
\(364\) 0 0
\(365\) 549650. 0.215950
\(366\) 0 0
\(367\) −35762.0 −0.0138598 −0.00692989 0.999976i \(-0.502206\pi\)
−0.00692989 + 0.999976i \(0.502206\pi\)
\(368\) 0 0
\(369\) 78246.0 0.0299155
\(370\) 0 0
\(371\) 1.08253e6 0.408325
\(372\) 0 0
\(373\) 1.71525e6 0.638346 0.319173 0.947696i \(-0.396595\pi\)
0.319173 + 0.947696i \(0.396595\pi\)
\(374\) 0 0
\(375\) 93750.0 0.0344265
\(376\) 0 0
\(377\) 6.53646e6 2.36859
\(378\) 0 0
\(379\) −3.10174e6 −1.10919 −0.554597 0.832119i \(-0.687127\pi\)
−0.554597 + 0.832119i \(0.687127\pi\)
\(380\) 0 0
\(381\) −1.79929e6 −0.635023
\(382\) 0 0
\(383\) −5.31949e6 −1.85299 −0.926494 0.376309i \(-0.877193\pi\)
−0.926494 + 0.376309i \(0.877193\pi\)
\(384\) 0 0
\(385\) 566400. 0.194747
\(386\) 0 0
\(387\) 503838. 0.171007
\(388\) 0 0
\(389\) −1.16145e6 −0.389158 −0.194579 0.980887i \(-0.562334\pi\)
−0.194579 + 0.980887i \(0.562334\pi\)
\(390\) 0 0
\(391\) −1.19329e6 −0.394734
\(392\) 0 0
\(393\) 47232.0 0.0154261
\(394\) 0 0
\(395\) −113000. −0.0364406
\(396\) 0 0
\(397\) −628562. −0.200157 −0.100079 0.994980i \(-0.531909\pi\)
−0.100079 + 0.994980i \(0.531909\pi\)
\(398\) 0 0
\(399\) −1.93992e6 −0.610031
\(400\) 0 0
\(401\) −2.72432e6 −0.846052 −0.423026 0.906118i \(-0.639032\pi\)
−0.423026 + 0.906118i \(0.639032\pi\)
\(402\) 0 0
\(403\) −7.59601e6 −2.32982
\(404\) 0 0
\(405\) 852525. 0.258267
\(406\) 0 0
\(407\) 1.05946e6 0.317027
\(408\) 0 0
\(409\) 1.78019e6 0.526209 0.263104 0.964767i \(-0.415254\pi\)
0.263104 + 0.964767i \(0.415254\pi\)
\(410\) 0 0
\(411\) −985428. −0.287753
\(412\) 0 0
\(413\) −4.12764e6 −1.19077
\(414\) 0 0
\(415\) −2.72685e6 −0.777215
\(416\) 0 0
\(417\) −1.69260e6 −0.476666
\(418\) 0 0
\(419\) 650580. 0.181036 0.0905181 0.995895i \(-0.471148\pi\)
0.0905181 + 0.995895i \(0.471148\pi\)
\(420\) 0 0
\(421\) 3.54060e6 0.973579 0.486790 0.873519i \(-0.338168\pi\)
0.486790 + 0.873519i \(0.338168\pi\)
\(422\) 0 0
\(423\) 2.71625e6 0.738107
\(424\) 0 0
\(425\) 476250. 0.127898
\(426\) 0 0
\(427\) 1.16088e6 0.308119
\(428\) 0 0
\(429\) −1.27411e6 −0.334245
\(430\) 0 0
\(431\) 548748. 0.142292 0.0711459 0.997466i \(-0.477334\pi\)
0.0711459 + 0.997466i \(0.477334\pi\)
\(432\) 0 0
\(433\) −1.49241e6 −0.382534 −0.191267 0.981538i \(-0.561260\pi\)
−0.191267 + 0.981538i \(0.561260\pi\)
\(434\) 0 0
\(435\) −886500. −0.224624
\(436\) 0 0
\(437\) 4.29084e6 1.07483
\(438\) 0 0
\(439\) −4.86212e6 −1.20411 −0.602053 0.798456i \(-0.705650\pi\)
−0.602053 + 0.798456i \(0.705650\pi\)
\(440\) 0 0
\(441\) 596781. 0.146123
\(442\) 0 0
\(443\) −1.86155e6 −0.450678 −0.225339 0.974280i \(-0.572349\pi\)
−0.225339 + 0.974280i \(0.572349\pi\)
\(444\) 0 0
\(445\) 962250. 0.230350
\(446\) 0 0
\(447\) 2.33370e6 0.552429
\(448\) 0 0
\(449\) 3.73719e6 0.874841 0.437421 0.899257i \(-0.355892\pi\)
0.437421 + 0.899257i \(0.355892\pi\)
\(450\) 0 0
\(451\) −72576.0 −0.0168016
\(452\) 0 0
\(453\) 587688. 0.134555
\(454\) 0 0
\(455\) −3.26270e6 −0.738837
\(456\) 0 0
\(457\) −6.48276e6 −1.45201 −0.726005 0.687690i \(-0.758625\pi\)
−0.726005 + 0.687690i \(0.758625\pi\)
\(458\) 0 0
\(459\) −2.05740e6 −0.455813
\(460\) 0 0
\(461\) −1.50910e6 −0.330724 −0.165362 0.986233i \(-0.552879\pi\)
−0.165362 + 0.986233i \(0.552879\pi\)
\(462\) 0 0
\(463\) −8.68401e6 −1.88264 −0.941321 0.337513i \(-0.890414\pi\)
−0.941321 + 0.337513i \(0.890414\pi\)
\(464\) 0 0
\(465\) 1.03020e6 0.220948
\(466\) 0 0
\(467\) 6.96412e6 1.47766 0.738829 0.673893i \(-0.235379\pi\)
0.738829 + 0.673893i \(0.235379\pi\)
\(468\) 0 0
\(469\) 3.97920e6 0.835340
\(470\) 0 0
\(471\) 22308.0 0.00463349
\(472\) 0 0
\(473\) −467328. −0.0960437
\(474\) 0 0
\(475\) −1.71250e6 −0.348254
\(476\) 0 0
\(477\) −1.89902e6 −0.382149
\(478\) 0 0
\(479\) 5.51052e6 1.09737 0.548686 0.836029i \(-0.315128\pi\)
0.548686 + 0.836029i \(0.315128\pi\)
\(480\) 0 0
\(481\) −6.10291e6 −1.20275
\(482\) 0 0
\(483\) −1.10873e6 −0.216251
\(484\) 0 0
\(485\) −47950.0 −0.00925623
\(486\) 0 0
\(487\) −5.51808e6 −1.05430 −0.527152 0.849771i \(-0.676740\pi\)
−0.527152 + 0.849771i \(0.676740\pi\)
\(488\) 0 0
\(489\) −259404. −0.0490574
\(490\) 0 0
\(491\) −1.51277e6 −0.283184 −0.141592 0.989925i \(-0.545222\pi\)
−0.141592 + 0.989925i \(0.545222\pi\)
\(492\) 0 0
\(493\) −4.50342e6 −0.834498
\(494\) 0 0
\(495\) −993600. −0.182263
\(496\) 0 0
\(497\) −8.28502e6 −1.50454
\(498\) 0 0
\(499\) −1.93042e6 −0.347057 −0.173528 0.984829i \(-0.555517\pi\)
−0.173528 + 0.984829i \(0.555517\pi\)
\(500\) 0 0
\(501\) −1.11913e6 −0.199199
\(502\) 0 0
\(503\) −6.73105e6 −1.18621 −0.593106 0.805124i \(-0.702099\pi\)
−0.593106 + 0.805124i \(0.702099\pi\)
\(504\) 0 0
\(505\) −1.94055e6 −0.338607
\(506\) 0 0
\(507\) 5.11166e6 0.883165
\(508\) 0 0
\(509\) 556650. 0.0952331 0.0476165 0.998866i \(-0.484837\pi\)
0.0476165 + 0.998866i \(0.484837\pi\)
\(510\) 0 0
\(511\) 2.59435e6 0.439517
\(512\) 0 0
\(513\) 7.39800e6 1.24114
\(514\) 0 0
\(515\) 1.16785e6 0.194030
\(516\) 0 0
\(517\) −2.51942e6 −0.414548
\(518\) 0 0
\(519\) 2.24672e6 0.366127
\(520\) 0 0
\(521\) 1.01110e7 1.63192 0.815962 0.578106i \(-0.196208\pi\)
0.815962 + 0.578106i \(0.196208\pi\)
\(522\) 0 0
\(523\) −7.03719e6 −1.12498 −0.562491 0.826804i \(-0.690157\pi\)
−0.562491 + 0.826804i \(0.690157\pi\)
\(524\) 0 0
\(525\) 442500. 0.0700672
\(526\) 0 0
\(527\) 5.23342e6 0.820840
\(528\) 0 0
\(529\) −3.98399e6 −0.618983
\(530\) 0 0
\(531\) 7.24086e6 1.11443
\(532\) 0 0
\(533\) 418068. 0.0637425
\(534\) 0 0
\(535\) −25950.0 −0.00391970
\(536\) 0 0
\(537\) 1.63260e6 0.244312
\(538\) 0 0
\(539\) −553536. −0.0820680
\(540\) 0 0
\(541\) 4.23114e6 0.621533 0.310766 0.950486i \(-0.399414\pi\)
0.310766 + 0.950486i \(0.399414\pi\)
\(542\) 0 0
\(543\) 452508. 0.0658608
\(544\) 0 0
\(545\) −5.17325e6 −0.746057
\(546\) 0 0
\(547\) 4.44024e6 0.634510 0.317255 0.948340i \(-0.397239\pi\)
0.317255 + 0.948340i \(0.397239\pi\)
\(548\) 0 0
\(549\) −2.03647e6 −0.288367
\(550\) 0 0
\(551\) 1.61934e7 2.27227
\(552\) 0 0
\(553\) −533360. −0.0741665
\(554\) 0 0
\(555\) 827700. 0.114062
\(556\) 0 0
\(557\) 9.01448e6 1.23113 0.615563 0.788088i \(-0.288929\pi\)
0.615563 + 0.788088i \(0.288929\pi\)
\(558\) 0 0
\(559\) 2.69200e6 0.364373
\(560\) 0 0
\(561\) 877824. 0.117761
\(562\) 0 0
\(563\) −9.81287e6 −1.30474 −0.652372 0.757899i \(-0.726226\pi\)
−0.652372 + 0.757899i \(0.726226\pi\)
\(564\) 0 0
\(565\) 3.48465e6 0.459238
\(566\) 0 0
\(567\) 4.02392e6 0.525644
\(568\) 0 0
\(569\) 1.33152e7 1.72412 0.862061 0.506804i \(-0.169173\pi\)
0.862061 + 0.506804i \(0.169173\pi\)
\(570\) 0 0
\(571\) 9.95895e6 1.27827 0.639136 0.769094i \(-0.279292\pi\)
0.639136 + 0.769094i \(0.279292\pi\)
\(572\) 0 0
\(573\) 2.14193e6 0.272533
\(574\) 0 0
\(575\) −978750. −0.123453
\(576\) 0 0
\(577\) 4.50372e6 0.563160 0.281580 0.959538i \(-0.409141\pi\)
0.281580 + 0.959538i \(0.409141\pi\)
\(578\) 0 0
\(579\) −2.63216e6 −0.326300
\(580\) 0 0
\(581\) −1.28707e7 −1.58184
\(582\) 0 0
\(583\) 1.76141e6 0.214629
\(584\) 0 0
\(585\) 5.72355e6 0.691474
\(586\) 0 0
\(587\) 625842. 0.0749669 0.0374834 0.999297i \(-0.488066\pi\)
0.0374834 + 0.999297i \(0.488066\pi\)
\(588\) 0 0
\(589\) −1.88183e7 −2.23508
\(590\) 0 0
\(591\) 940788. 0.110796
\(592\) 0 0
\(593\) −2.50385e6 −0.292397 −0.146198 0.989255i \(-0.546704\pi\)
−0.146198 + 0.989255i \(0.546704\pi\)
\(594\) 0 0
\(595\) 2.24790e6 0.260306
\(596\) 0 0
\(597\) 975120. 0.111975
\(598\) 0 0
\(599\) 756480. 0.0861451 0.0430725 0.999072i \(-0.486285\pi\)
0.0430725 + 0.999072i \(0.486285\pi\)
\(600\) 0 0
\(601\) −1.38565e7 −1.56483 −0.782413 0.622760i \(-0.786011\pi\)
−0.782413 + 0.622760i \(0.786011\pi\)
\(602\) 0 0
\(603\) −6.98045e6 −0.781791
\(604\) 0 0
\(605\) −3.10468e6 −0.344848
\(606\) 0 0
\(607\) −1.13772e7 −1.25333 −0.626663 0.779291i \(-0.715580\pi\)
−0.626663 + 0.779291i \(0.715580\pi\)
\(608\) 0 0
\(609\) −4.18428e6 −0.457170
\(610\) 0 0
\(611\) 1.45129e7 1.57272
\(612\) 0 0
\(613\) 7.00161e6 0.752570 0.376285 0.926504i \(-0.377201\pi\)
0.376285 + 0.926504i \(0.377201\pi\)
\(614\) 0 0
\(615\) −56700.0 −0.00604499
\(616\) 0 0
\(617\) 7.90300e6 0.835755 0.417878 0.908503i \(-0.362774\pi\)
0.417878 + 0.908503i \(0.362774\pi\)
\(618\) 0 0
\(619\) 4.02362e6 0.422076 0.211038 0.977478i \(-0.432316\pi\)
0.211038 + 0.977478i \(0.432316\pi\)
\(620\) 0 0
\(621\) 4.22820e6 0.439974
\(622\) 0 0
\(623\) 4.54182e6 0.468824
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −3.15648e6 −0.320652
\(628\) 0 0
\(629\) 4.20472e6 0.423750
\(630\) 0 0
\(631\) 1.00227e7 1.00210 0.501049 0.865419i \(-0.332948\pi\)
0.501049 + 0.865419i \(0.332948\pi\)
\(632\) 0 0
\(633\) −1.08989e6 −0.108112
\(634\) 0 0
\(635\) −7.49705e6 −0.737830
\(636\) 0 0
\(637\) 3.18860e6 0.311352
\(638\) 0 0
\(639\) 1.45339e7 1.40809
\(640\) 0 0
\(641\) 6.37390e6 0.612718 0.306359 0.951916i \(-0.400889\pi\)
0.306359 + 0.951916i \(0.400889\pi\)
\(642\) 0 0
\(643\) 5.00457e6 0.477352 0.238676 0.971099i \(-0.423287\pi\)
0.238676 + 0.971099i \(0.423287\pi\)
\(644\) 0 0
\(645\) −365100. −0.0345551
\(646\) 0 0
\(647\) 8.71928e6 0.818879 0.409440 0.912337i \(-0.365724\pi\)
0.409440 + 0.912337i \(0.365724\pi\)
\(648\) 0 0
\(649\) −6.71616e6 −0.625906
\(650\) 0 0
\(651\) 4.86254e6 0.449688
\(652\) 0 0
\(653\) 1.58477e6 0.145440 0.0727201 0.997352i \(-0.476832\pi\)
0.0727201 + 0.997352i \(0.476832\pi\)
\(654\) 0 0
\(655\) 196800. 0.0179235
\(656\) 0 0
\(657\) −4.55110e6 −0.411342
\(658\) 0 0
\(659\) 1.26410e7 1.13388 0.566940 0.823759i \(-0.308127\pi\)
0.566940 + 0.823759i \(0.308127\pi\)
\(660\) 0 0
\(661\) 3.61572e6 0.321878 0.160939 0.986964i \(-0.448548\pi\)
0.160939 + 0.986964i \(0.448548\pi\)
\(662\) 0 0
\(663\) −5.05663e6 −0.446763
\(664\) 0 0
\(665\) −8.08300e6 −0.708791
\(666\) 0 0
\(667\) 9.25506e6 0.805498
\(668\) 0 0
\(669\) 1.72964e6 0.149414
\(670\) 0 0
\(671\) 1.88890e6 0.161958
\(672\) 0 0
\(673\) 1.11313e7 0.947349 0.473675 0.880700i \(-0.342927\pi\)
0.473675 + 0.880700i \(0.342927\pi\)
\(674\) 0 0
\(675\) −1.68750e6 −0.142556
\(676\) 0 0
\(677\) 235518. 0.0197493 0.00987467 0.999951i \(-0.496857\pi\)
0.00987467 + 0.999951i \(0.496857\pi\)
\(678\) 0 0
\(679\) −226324. −0.0188389
\(680\) 0 0
\(681\) 6.75313e6 0.558004
\(682\) 0 0
\(683\) 2.05830e7 1.68833 0.844164 0.536084i \(-0.180097\pi\)
0.844164 + 0.536084i \(0.180097\pi\)
\(684\) 0 0
\(685\) −4.10595e6 −0.334339
\(686\) 0 0
\(687\) 2.49486e6 0.201676
\(688\) 0 0
\(689\) −1.01464e7 −0.814265
\(690\) 0 0
\(691\) −9.54825e6 −0.760727 −0.380363 0.924837i \(-0.624201\pi\)
−0.380363 + 0.924837i \(0.624201\pi\)
\(692\) 0 0
\(693\) −4.68979e6 −0.370954
\(694\) 0 0
\(695\) −7.05250e6 −0.553836
\(696\) 0 0
\(697\) −288036. −0.0224577
\(698\) 0 0
\(699\) 4.62352e6 0.357915
\(700\) 0 0
\(701\) −1.29304e6 −0.0993843 −0.0496921 0.998765i \(-0.515824\pi\)
−0.0496921 + 0.998765i \(0.515824\pi\)
\(702\) 0 0
\(703\) −1.51193e7 −1.15384
\(704\) 0 0
\(705\) −1.96830e6 −0.149148
\(706\) 0 0
\(707\) −9.15940e6 −0.689157
\(708\) 0 0
\(709\) 2.12720e7 1.58926 0.794628 0.607097i \(-0.207666\pi\)
0.794628 + 0.607097i \(0.207666\pi\)
\(710\) 0 0
\(711\) 935640. 0.0694120
\(712\) 0 0
\(713\) −1.07553e7 −0.792316
\(714\) 0 0
\(715\) −5.30880e6 −0.388357
\(716\) 0 0
\(717\) 3.57192e6 0.259480
\(718\) 0 0
\(719\) −8.31732e6 −0.600014 −0.300007 0.953937i \(-0.596989\pi\)
−0.300007 + 0.953937i \(0.596989\pi\)
\(720\) 0 0
\(721\) 5.51225e6 0.394903
\(722\) 0 0
\(723\) 1.64341e6 0.116923
\(724\) 0 0
\(725\) −3.69375e6 −0.260989
\(726\) 0 0
\(727\) 4.36740e6 0.306469 0.153235 0.988190i \(-0.451031\pi\)
0.153235 + 0.988190i \(0.451031\pi\)
\(728\) 0 0
\(729\) −3.12231e6 −0.217599
\(730\) 0 0
\(731\) −1.85471e6 −0.128375
\(732\) 0 0
\(733\) 4.05645e6 0.278860 0.139430 0.990232i \(-0.455473\pi\)
0.139430 + 0.990232i \(0.455473\pi\)
\(734\) 0 0
\(735\) −432450. −0.0295269
\(736\) 0 0
\(737\) 6.47462e6 0.439082
\(738\) 0 0
\(739\) 768260. 0.0517484 0.0258742 0.999665i \(-0.491763\pi\)
0.0258742 + 0.999665i \(0.491763\pi\)
\(740\) 0 0
\(741\) 1.81826e7 1.21650
\(742\) 0 0
\(743\) −6.18781e6 −0.411211 −0.205605 0.978635i \(-0.565916\pi\)
−0.205605 + 0.978635i \(0.565916\pi\)
\(744\) 0 0
\(745\) 9.72375e6 0.641864
\(746\) 0 0
\(747\) 2.25783e7 1.48044
\(748\) 0 0
\(749\) −122484. −0.00797765
\(750\) 0 0
\(751\) −1.81698e7 −1.17557 −0.587787 0.809016i \(-0.700001\pi\)
−0.587787 + 0.809016i \(0.700001\pi\)
\(752\) 0 0
\(753\) 5.10451e6 0.328070
\(754\) 0 0
\(755\) 2.44870e6 0.156339
\(756\) 0 0
\(757\) −1.93494e7 −1.22724 −0.613618 0.789603i \(-0.710286\pi\)
−0.613618 + 0.789603i \(0.710286\pi\)
\(758\) 0 0
\(759\) −1.80403e6 −0.113668
\(760\) 0 0
\(761\) −3.01992e7 −1.89031 −0.945155 0.326621i \(-0.894090\pi\)
−0.945155 + 0.326621i \(0.894090\pi\)
\(762\) 0 0
\(763\) −2.44177e7 −1.51843
\(764\) 0 0
\(765\) −3.94335e6 −0.243619
\(766\) 0 0
\(767\) 3.86879e7 2.37458
\(768\) 0 0
\(769\) 2.15854e7 1.31627 0.658134 0.752901i \(-0.271346\pi\)
0.658134 + 0.752901i \(0.271346\pi\)
\(770\) 0 0
\(771\) 4.95241e6 0.300041
\(772\) 0 0
\(773\) −3.90895e6 −0.235294 −0.117647 0.993055i \(-0.537535\pi\)
−0.117647 + 0.993055i \(0.537535\pi\)
\(774\) 0 0
\(775\) 4.29250e6 0.256718
\(776\) 0 0
\(777\) 3.90674e6 0.232147
\(778\) 0 0
\(779\) 1.03572e6 0.0611503
\(780\) 0 0
\(781\) −1.34807e7 −0.790833
\(782\) 0 0
\(783\) 1.59570e7 0.930137
\(784\) 0 0
\(785\) 92950.0 0.00538363
\(786\) 0 0
\(787\) −2.65082e7 −1.52561 −0.762806 0.646628i \(-0.776179\pi\)
−0.762806 + 0.646628i \(0.776179\pi\)
\(788\) 0 0
\(789\) −8.18788e6 −0.468251
\(790\) 0 0
\(791\) 1.64475e7 0.934674
\(792\) 0 0
\(793\) −1.08808e7 −0.614439
\(794\) 0 0
\(795\) 1.37610e6 0.0772204
\(796\) 0 0
\(797\) −1.07940e7 −0.601919 −0.300960 0.953637i \(-0.597307\pi\)
−0.300960 + 0.953637i \(0.597307\pi\)
\(798\) 0 0
\(799\) −9.99896e6 −0.554100
\(800\) 0 0
\(801\) −7.96743e6 −0.438770
\(802\) 0 0
\(803\) 4.22131e6 0.231025
\(804\) 0 0
\(805\) −4.61970e6 −0.251260
\(806\) 0 0
\(807\) 679860. 0.0367482
\(808\) 0 0
\(809\) −1.11446e7 −0.598675 −0.299338 0.954147i \(-0.596766\pi\)
−0.299338 + 0.954147i \(0.596766\pi\)
\(810\) 0 0
\(811\) −1.14866e7 −0.613253 −0.306626 0.951830i \(-0.599200\pi\)
−0.306626 + 0.951830i \(0.599200\pi\)
\(812\) 0 0
\(813\) 5.09777e6 0.270492
\(814\) 0 0
\(815\) −1.08085e6 −0.0569995
\(816\) 0 0
\(817\) 6.66916e6 0.349555
\(818\) 0 0
\(819\) 2.70152e7 1.40734
\(820\) 0 0
\(821\) −3.04347e7 −1.57584 −0.787918 0.615781i \(-0.788841\pi\)
−0.787918 + 0.615781i \(0.788841\pi\)
\(822\) 0 0
\(823\) −4.09773e6 −0.210884 −0.105442 0.994425i \(-0.533626\pi\)
−0.105442 + 0.994425i \(0.533626\pi\)
\(824\) 0 0
\(825\) 720000. 0.0368297
\(826\) 0 0
\(827\) −1.70652e7 −0.867654 −0.433827 0.900996i \(-0.642837\pi\)
−0.433827 + 0.900996i \(0.642837\pi\)
\(828\) 0 0
\(829\) 2.47617e7 1.25139 0.625697 0.780066i \(-0.284815\pi\)
0.625697 + 0.780066i \(0.284815\pi\)
\(830\) 0 0
\(831\) −2.63161e6 −0.132196
\(832\) 0 0
\(833\) −2.19685e6 −0.109695
\(834\) 0 0
\(835\) −4.66305e6 −0.231448
\(836\) 0 0
\(837\) −1.85436e7 −0.914914
\(838\) 0 0
\(839\) −3.16529e7 −1.55242 −0.776208 0.630476i \(-0.782860\pi\)
−0.776208 + 0.630476i \(0.782860\pi\)
\(840\) 0 0
\(841\) 1.44170e7 0.702884
\(842\) 0 0
\(843\) −8.74019e6 −0.423596
\(844\) 0 0
\(845\) 2.12986e7 1.02615
\(846\) 0 0
\(847\) −1.46541e7 −0.701859
\(848\) 0 0
\(849\) −722364. −0.0343943
\(850\) 0 0
\(851\) −8.64119e6 −0.409025
\(852\) 0 0
\(853\) −2.82671e7 −1.33017 −0.665087 0.746765i \(-0.731606\pi\)
−0.665087 + 0.746765i \(0.731606\pi\)
\(854\) 0 0
\(855\) 1.41795e7 0.663354
\(856\) 0 0
\(857\) 2.60870e7 1.21331 0.606655 0.794966i \(-0.292511\pi\)
0.606655 + 0.794966i \(0.292511\pi\)
\(858\) 0 0
\(859\) −3.38111e7 −1.56342 −0.781710 0.623642i \(-0.785652\pi\)
−0.781710 + 0.623642i \(0.785652\pi\)
\(860\) 0 0
\(861\) −267624. −0.0123032
\(862\) 0 0
\(863\) −2.22817e7 −1.01841 −0.509204 0.860646i \(-0.670060\pi\)
−0.509204 + 0.860646i \(0.670060\pi\)
\(864\) 0 0
\(865\) 9.36135e6 0.425401
\(866\) 0 0
\(867\) −5.03528e6 −0.227497
\(868\) 0 0
\(869\) −867840. −0.0389843
\(870\) 0 0
\(871\) −3.72965e7 −1.66580
\(872\) 0 0
\(873\) 397026. 0.0176313
\(874\) 0 0
\(875\) 1.84375e6 0.0814108
\(876\) 0 0
\(877\) 3.46748e7 1.52235 0.761177 0.648545i \(-0.224622\pi\)
0.761177 + 0.648545i \(0.224622\pi\)
\(878\) 0 0
\(879\) 1.58526e7 0.692034
\(880\) 0 0
\(881\) 1.42603e7 0.618998 0.309499 0.950900i \(-0.399839\pi\)
0.309499 + 0.950900i \(0.399839\pi\)
\(882\) 0 0
\(883\) −3.75177e7 −1.61933 −0.809663 0.586895i \(-0.800350\pi\)
−0.809663 + 0.586895i \(0.800350\pi\)
\(884\) 0 0
\(885\) −5.24700e6 −0.225192
\(886\) 0 0
\(887\) −4.07657e7 −1.73975 −0.869873 0.493275i \(-0.835800\pi\)
−0.869873 + 0.493275i \(0.835800\pi\)
\(888\) 0 0
\(889\) −3.53861e7 −1.50168
\(890\) 0 0
\(891\) 6.54739e6 0.276296
\(892\) 0 0
\(893\) 3.59543e7 1.50877
\(894\) 0 0
\(895\) 6.80250e6 0.283864
\(896\) 0 0
\(897\) 1.03920e7 0.431238
\(898\) 0 0
\(899\) −4.05899e7 −1.67501
\(900\) 0 0
\(901\) 6.99059e6 0.286881
\(902\) 0 0
\(903\) −1.72327e6 −0.0703290
\(904\) 0 0
\(905\) 1.88545e6 0.0765233
\(906\) 0 0
\(907\) −3.57116e7 −1.44142 −0.720712 0.693235i \(-0.756185\pi\)
−0.720712 + 0.693235i \(0.756185\pi\)
\(908\) 0 0
\(909\) 1.60678e7 0.644979
\(910\) 0 0
\(911\) 2.11389e7 0.843893 0.421947 0.906621i \(-0.361347\pi\)
0.421947 + 0.906621i \(0.361347\pi\)
\(912\) 0 0
\(913\) −2.09422e7 −0.831468
\(914\) 0 0
\(915\) 1.47570e6 0.0582700
\(916\) 0 0
\(917\) 928896. 0.0364791
\(918\) 0 0
\(919\) −1.85996e7 −0.726465 −0.363233 0.931698i \(-0.618327\pi\)
−0.363233 + 0.931698i \(0.618327\pi\)
\(920\) 0 0
\(921\) −8.68535e6 −0.337395
\(922\) 0 0
\(923\) 7.76545e7 3.00028
\(924\) 0 0
\(925\) 3.44875e6 0.132528
\(926\) 0 0
\(927\) −9.66980e6 −0.369588
\(928\) 0 0
\(929\) 4.45110e7 1.69211 0.846055 0.533096i \(-0.178972\pi\)
0.846055 + 0.533096i \(0.178972\pi\)
\(930\) 0 0
\(931\) 7.89942e6 0.298690
\(932\) 0 0
\(933\) 5.56841e6 0.209424
\(934\) 0 0
\(935\) 3.65760e6 0.136826
\(936\) 0 0
\(937\) −2.19419e7 −0.816441 −0.408221 0.912883i \(-0.633851\pi\)
−0.408221 + 0.912883i \(0.633851\pi\)
\(938\) 0 0
\(939\) 1.37738e7 0.509787
\(940\) 0 0
\(941\) 7.77722e6 0.286319 0.143160 0.989700i \(-0.454274\pi\)
0.143160 + 0.989700i \(0.454274\pi\)
\(942\) 0 0
\(943\) 591948. 0.0216773
\(944\) 0 0
\(945\) −7.96500e6 −0.290139
\(946\) 0 0
\(947\) 3.17199e7 1.14936 0.574681 0.818378i \(-0.305126\pi\)
0.574681 + 0.818378i \(0.305126\pi\)
\(948\) 0 0
\(949\) −2.43165e7 −0.876468
\(950\) 0 0
\(951\) −1.64191e7 −0.588707
\(952\) 0 0
\(953\) −5.60285e6 −0.199838 −0.0999188 0.994996i \(-0.531858\pi\)
−0.0999188 + 0.994996i \(0.531858\pi\)
\(954\) 0 0
\(955\) 8.92470e6 0.316654
\(956\) 0 0
\(957\) −6.80832e6 −0.240304
\(958\) 0 0
\(959\) −1.93801e7 −0.680470
\(960\) 0 0
\(961\) 1.85403e7 0.647601
\(962\) 0 0
\(963\) 214866. 0.00746624
\(964\) 0 0
\(965\) −1.09673e7 −0.379126
\(966\) 0 0
\(967\) 2.03532e7 0.699949 0.349975 0.936759i \(-0.386190\pi\)
0.349975 + 0.936759i \(0.386190\pi\)
\(968\) 0 0
\(969\) −1.25273e7 −0.428595
\(970\) 0 0
\(971\) −2.34306e7 −0.797510 −0.398755 0.917057i \(-0.630558\pi\)
−0.398755 + 0.917057i \(0.630558\pi\)
\(972\) 0 0
\(973\) −3.32878e7 −1.12721
\(974\) 0 0
\(975\) −4.14750e6 −0.139725
\(976\) 0 0
\(977\) −4.30412e7 −1.44261 −0.721303 0.692619i \(-0.756457\pi\)
−0.721303 + 0.692619i \(0.756457\pi\)
\(978\) 0 0
\(979\) 7.39008e6 0.246429
\(980\) 0 0
\(981\) 4.28345e7 1.42109
\(982\) 0 0
\(983\) 4.75003e7 1.56788 0.783940 0.620837i \(-0.213207\pi\)
0.783940 + 0.620837i \(0.213207\pi\)
\(984\) 0 0
\(985\) 3.91995e6 0.128733
\(986\) 0 0
\(987\) −9.29038e6 −0.303557
\(988\) 0 0
\(989\) 3.81164e6 0.123914
\(990\) 0 0
\(991\) −2.09231e7 −0.676770 −0.338385 0.941008i \(-0.609881\pi\)
−0.338385 + 0.941008i \(0.609881\pi\)
\(992\) 0 0
\(993\) 2.29128e7 0.737402
\(994\) 0 0
\(995\) 4.06300e6 0.130104
\(996\) 0 0
\(997\) −2.96332e7 −0.944148 −0.472074 0.881559i \(-0.656495\pi\)
−0.472074 + 0.881559i \(0.656495\pi\)
\(998\) 0 0
\(999\) −1.48986e7 −0.472315
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.k.1.1 1
4.3 odd 2 320.6.a.f.1.1 1
8.3 odd 2 10.6.a.c.1.1 1
8.5 even 2 80.6.a.c.1.1 1
24.5 odd 2 720.6.a.v.1.1 1
24.11 even 2 90.6.a.b.1.1 1
40.3 even 4 50.6.b.b.49.1 2
40.13 odd 4 400.6.c.i.49.1 2
40.19 odd 2 50.6.a.b.1.1 1
40.27 even 4 50.6.b.b.49.2 2
40.29 even 2 400.6.a.i.1.1 1
40.37 odd 4 400.6.c.i.49.2 2
56.27 even 2 490.6.a.k.1.1 1
120.59 even 2 450.6.a.u.1.1 1
120.83 odd 4 450.6.c.f.199.2 2
120.107 odd 4 450.6.c.f.199.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.c.1.1 1 8.3 odd 2
50.6.a.b.1.1 1 40.19 odd 2
50.6.b.b.49.1 2 40.3 even 4
50.6.b.b.49.2 2 40.27 even 4
80.6.a.c.1.1 1 8.5 even 2
90.6.a.b.1.1 1 24.11 even 2
320.6.a.f.1.1 1 4.3 odd 2
320.6.a.k.1.1 1 1.1 even 1 trivial
400.6.a.i.1.1 1 40.29 even 2
400.6.c.i.49.1 2 40.13 odd 4
400.6.c.i.49.2 2 40.37 odd 4
450.6.a.u.1.1 1 120.59 even 2
450.6.c.f.199.1 2 120.107 odd 4
450.6.c.f.199.2 2 120.83 odd 4
490.6.a.k.1.1 1 56.27 even 2
720.6.a.v.1.1 1 24.5 odd 2