Properties

Label 400.6.a.k.1.1
Level 400
Weight 6
Character 400.1
Self dual yes
Analytic conductor 64.154
Analytic rank 1
Dimension 1
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: \(1\)
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 \(\chi\) \(=\) 400.1

$q$-expansion

\(f(q)\) \(=\) \(q+14.0000 q^{3} +158.000 q^{7} -47.0000 q^{9} +O(q^{10})\) \(q+14.0000 q^{3} +158.000 q^{7} -47.0000 q^{9} +148.000 q^{11} -684.000 q^{13} -2048.00 q^{17} -2220.00 q^{19} +2212.00 q^{21} -1246.00 q^{23} -4060.00 q^{27} -270.000 q^{29} +2048.00 q^{31} +2072.00 q^{33} +4372.00 q^{37} -9576.00 q^{39} -2398.00 q^{41} +2294.00 q^{43} -10682.0 q^{47} +8157.00 q^{49} -28672.0 q^{51} -2964.00 q^{53} -31080.0 q^{57} +39740.0 q^{59} -42298.0 q^{61} -7426.00 q^{63} +32098.0 q^{67} -17444.0 q^{69} +4248.00 q^{71} -30104.0 q^{73} +23384.0 q^{77} -35280.0 q^{79} -45419.0 q^{81} -27826.0 q^{83} -3780.00 q^{87} -85210.0 q^{89} -108072. q^{91} +28672.0 q^{93} +97232.0 q^{97} -6956.00 q^{99} +O(q^{100})\)

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
\(3\) 14.0000 0.898100 0.449050 0.893507i \(-0.351762\pi\)
0.449050 + 0.893507i \(0.351762\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 158.000 1.21874 0.609371 0.792885i \(-0.291422\pi\)
0.609371 + 0.792885i \(0.291422\pi\)
\(8\) 0 0
\(9\) −47.0000 −0.193416
\(10\) 0 0
\(11\) 148.000 0.368791 0.184395 0.982852i \(-0.440967\pi\)
0.184395 + 0.982852i \(0.440967\pi\)
\(12\) 0 0
\(13\) −684.000 −1.12253 −0.561265 0.827636i \(-0.689685\pi\)
−0.561265 + 0.827636i \(0.689685\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2048.00 −1.71873 −0.859365 0.511363i \(-0.829141\pi\)
−0.859365 + 0.511363i \(0.829141\pi\)
\(18\) 0 0
\(19\) −2220.00 −1.41081 −0.705406 0.708804i \(-0.749235\pi\)
−0.705406 + 0.708804i \(0.749235\pi\)
\(20\) 0 0
\(21\) 2212.00 1.09455
\(22\) 0 0
\(23\) −1246.00 −0.491132 −0.245566 0.969380i \(-0.578974\pi\)
−0.245566 + 0.969380i \(0.578974\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4060.00 −1.07181
\(28\) 0 0
\(29\) −270.000 −0.0596168 −0.0298084 0.999556i \(-0.509490\pi\)
−0.0298084 + 0.999556i \(0.509490\pi\)
\(30\) 0 0
\(31\) 2048.00 0.382759 0.191380 0.981516i \(-0.438704\pi\)
0.191380 + 0.981516i \(0.438704\pi\)
\(32\) 0 0
\(33\) 2072.00 0.331211
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4372.00 0.525020 0.262510 0.964929i \(-0.415450\pi\)
0.262510 + 0.964929i \(0.415450\pi\)
\(38\) 0 0
\(39\) −9576.00 −1.00814
\(40\) 0 0
\(41\) −2398.00 −0.222787 −0.111393 0.993776i \(-0.535531\pi\)
−0.111393 + 0.993776i \(0.535531\pi\)
\(42\) 0 0
\(43\) 2294.00 0.189200 0.0946002 0.995515i \(-0.469843\pi\)
0.0946002 + 0.995515i \(0.469843\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10682.0 −0.705355 −0.352678 0.935745i \(-0.614729\pi\)
−0.352678 + 0.935745i \(0.614729\pi\)
\(48\) 0 0
\(49\) 8157.00 0.485333
\(50\) 0 0
\(51\) −28672.0 −1.54359
\(52\) 0 0
\(53\) −2964.00 −0.144940 −0.0724700 0.997371i \(-0.523088\pi\)
−0.0724700 + 0.997371i \(0.523088\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −31080.0 −1.26705
\(58\) 0 0
\(59\) 39740.0 1.48627 0.743135 0.669141i \(-0.233338\pi\)
0.743135 + 0.669141i \(0.233338\pi\)
\(60\) 0 0
\(61\) −42298.0 −1.45544 −0.727722 0.685873i \(-0.759421\pi\)
−0.727722 + 0.685873i \(0.759421\pi\)
\(62\) 0 0
\(63\) −7426.00 −0.235724
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 32098.0 0.873556 0.436778 0.899569i \(-0.356119\pi\)
0.436778 + 0.899569i \(0.356119\pi\)
\(68\) 0 0
\(69\) −17444.0 −0.441086
\(70\) 0 0
\(71\) 4248.00 0.100009 0.0500044 0.998749i \(-0.484076\pi\)
0.0500044 + 0.998749i \(0.484076\pi\)
\(72\) 0 0
\(73\) −30104.0 −0.661176 −0.330588 0.943775i \(-0.607247\pi\)
−0.330588 + 0.943775i \(0.607247\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 23384.0 0.449461
\(78\) 0 0
\(79\) −35280.0 −0.636005 −0.318003 0.948090i \(-0.603012\pi\)
−0.318003 + 0.948090i \(0.603012\pi\)
\(80\) 0 0
\(81\) −45419.0 −0.769175
\(82\) 0 0
\(83\) −27826.0 −0.443359 −0.221680 0.975120i \(-0.571154\pi\)
−0.221680 + 0.975120i \(0.571154\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3780.00 −0.0535419
\(88\) 0 0
\(89\) −85210.0 −1.14029 −0.570145 0.821544i \(-0.693113\pi\)
−0.570145 + 0.821544i \(0.693113\pi\)
\(90\) 0 0
\(91\) −108072. −1.36807
\(92\) 0 0
\(93\) 28672.0 0.343756
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 97232.0 1.04925 0.524626 0.851333i \(-0.324205\pi\)
0.524626 + 0.851333i \(0.324205\pi\)
\(98\) 0 0
\(99\) −6956.00 −0.0713299
\(100\) 0 0
\(101\) −4298.00 −0.0419240 −0.0209620 0.999780i \(-0.506673\pi\)
−0.0209620 + 0.999780i \(0.506673\pi\)
\(102\) 0 0
\(103\) 124114. 1.15273 0.576365 0.817192i \(-0.304471\pi\)
0.576365 + 0.817192i \(0.304471\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −42342.0 −0.357530 −0.178765 0.983892i \(-0.557210\pi\)
−0.178765 + 0.983892i \(0.557210\pi\)
\(108\) 0 0
\(109\) −35990.0 −0.290145 −0.145073 0.989421i \(-0.546342\pi\)
−0.145073 + 0.989421i \(0.546342\pi\)
\(110\) 0 0
\(111\) 61208.0 0.471521
\(112\) 0 0
\(113\) 228816. 1.68574 0.842869 0.538118i \(-0.180865\pi\)
0.842869 + 0.538118i \(0.180865\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 32148.0 0.217115
\(118\) 0 0
\(119\) −323584. −2.09469
\(120\) 0 0
\(121\) −139147. −0.863993
\(122\) 0 0
\(123\) −33572.0 −0.200085
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 175238. 0.964093 0.482047 0.876146i \(-0.339894\pi\)
0.482047 + 0.876146i \(0.339894\pi\)
\(128\) 0 0
\(129\) 32116.0 0.169921
\(130\) 0 0
\(131\) −299652. −1.52559 −0.762797 0.646638i \(-0.776174\pi\)
−0.762797 + 0.646638i \(0.776174\pi\)
\(132\) 0 0
\(133\) −350760. −1.71942
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −107928. −0.491284 −0.245642 0.969361i \(-0.578999\pi\)
−0.245642 + 0.969361i \(0.578999\pi\)
\(138\) 0 0
\(139\) 196460. 0.862456 0.431228 0.902243i \(-0.358080\pi\)
0.431228 + 0.902243i \(0.358080\pi\)
\(140\) 0 0
\(141\) −149548. −0.633480
\(142\) 0 0
\(143\) −101232. −0.413978
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 114198. 0.435878
\(148\) 0 0
\(149\) 138850. 0.512366 0.256183 0.966628i \(-0.417535\pi\)
0.256183 + 0.966628i \(0.417535\pi\)
\(150\) 0 0
\(151\) −416152. −1.48528 −0.742642 0.669688i \(-0.766428\pi\)
−0.742642 + 0.669688i \(0.766428\pi\)
\(152\) 0 0
\(153\) 96256.0 0.332429
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −433108. −1.40232 −0.701160 0.713004i \(-0.747334\pi\)
−0.701160 + 0.713004i \(0.747334\pi\)
\(158\) 0 0
\(159\) −41496.0 −0.130171
\(160\) 0 0
\(161\) −196868. −0.598564
\(162\) 0 0
\(163\) 149134. 0.439651 0.219825 0.975539i \(-0.429451\pi\)
0.219825 + 0.975539i \(0.429451\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −559602. −1.55270 −0.776351 0.630301i \(-0.782932\pi\)
−0.776351 + 0.630301i \(0.782932\pi\)
\(168\) 0 0
\(169\) 96563.0 0.260072
\(170\) 0 0
\(171\) 104340. 0.272873
\(172\) 0 0
\(173\) −343804. −0.873365 −0.436682 0.899616i \(-0.643847\pi\)
−0.436682 + 0.899616i \(0.643847\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 556360. 1.33482
\(178\) 0 0
\(179\) −23980.0 −0.0559392 −0.0279696 0.999609i \(-0.508904\pi\)
−0.0279696 + 0.999609i \(0.508904\pi\)
\(180\) 0 0
\(181\) −651898. −1.47905 −0.739526 0.673128i \(-0.764950\pi\)
−0.739526 + 0.673128i \(0.764950\pi\)
\(182\) 0 0
\(183\) −592172. −1.30713
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −303104. −0.633852
\(188\) 0 0
\(189\) −641480. −1.30626
\(190\) 0 0
\(191\) −202752. −0.402144 −0.201072 0.979576i \(-0.564443\pi\)
−0.201072 + 0.979576i \(0.564443\pi\)
\(192\) 0 0
\(193\) 452656. 0.874732 0.437366 0.899284i \(-0.355911\pi\)
0.437366 + 0.899284i \(0.355911\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −337468. −0.619537 −0.309768 0.950812i \(-0.600252\pi\)
−0.309768 + 0.950812i \(0.600252\pi\)
\(198\) 0 0
\(199\) 561000. 1.00422 0.502112 0.864803i \(-0.332557\pi\)
0.502112 + 0.864803i \(0.332557\pi\)
\(200\) 0 0
\(201\) 449372. 0.784541
\(202\) 0 0
\(203\) −42660.0 −0.0726576
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 58562.0 0.0949927
\(208\) 0 0
\(209\) −328560. −0.520294
\(210\) 0 0
\(211\) 805548. 1.24562 0.622810 0.782373i \(-0.285991\pi\)
0.622810 + 0.782373i \(0.285991\pi\)
\(212\) 0 0
\(213\) 59472.0 0.0898180
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 323584. 0.466485
\(218\) 0 0
\(219\) −421456. −0.593802
\(220\) 0 0
\(221\) 1.40083e6 1.92932
\(222\) 0 0
\(223\) 1.21855e6 1.64090 0.820451 0.571717i \(-0.193722\pi\)
0.820451 + 0.571717i \(0.193722\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 564338. 0.726900 0.363450 0.931614i \(-0.381599\pi\)
0.363450 + 0.931614i \(0.381599\pi\)
\(228\) 0 0
\(229\) 560330. 0.706082 0.353041 0.935608i \(-0.385148\pi\)
0.353041 + 0.935608i \(0.385148\pi\)
\(230\) 0 0
\(231\) 327376. 0.403661
\(232\) 0 0
\(233\) 293576. 0.354267 0.177134 0.984187i \(-0.443318\pi\)
0.177134 + 0.984187i \(0.443318\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −493920. −0.571197
\(238\) 0 0
\(239\) −584240. −0.661602 −0.330801 0.943701i \(-0.607319\pi\)
−0.330801 + 0.943701i \(0.607319\pi\)
\(240\) 0 0
\(241\) −563798. −0.625289 −0.312645 0.949870i \(-0.601215\pi\)
−0.312645 + 0.949870i \(0.601215\pi\)
\(242\) 0 0
\(243\) 350714. 0.381011
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.51848e6 1.58368
\(248\) 0 0
\(249\) −389564. −0.398181
\(250\) 0 0
\(251\) 1.01975e6 1.02167 0.510833 0.859680i \(-0.329337\pi\)
0.510833 + 0.859680i \(0.329337\pi\)
\(252\) 0 0
\(253\) −184408. −0.181125
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −657408. −0.620872 −0.310436 0.950594i \(-0.600475\pi\)
−0.310436 + 0.950594i \(0.600475\pi\)
\(258\) 0 0
\(259\) 690776. 0.639864
\(260\) 0 0
\(261\) 12690.0 0.0115308
\(262\) 0 0
\(263\) −562366. −0.501337 −0.250668 0.968073i \(-0.580650\pi\)
−0.250668 + 0.968073i \(0.580650\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.19294e6 −1.02410
\(268\) 0 0
\(269\) 366570. 0.308870 0.154435 0.988003i \(-0.450644\pi\)
0.154435 + 0.988003i \(0.450644\pi\)
\(270\) 0 0
\(271\) −1.16075e6 −0.960099 −0.480050 0.877241i \(-0.659381\pi\)
−0.480050 + 0.877241i \(0.659381\pi\)
\(272\) 0 0
\(273\) −1.51301e6 −1.22867
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.51501e6 1.96943 0.984715 0.174172i \(-0.0557250\pi\)
0.984715 + 0.174172i \(0.0557250\pi\)
\(278\) 0 0
\(279\) −96256.0 −0.0740316
\(280\) 0 0
\(281\) 2.08600e6 1.57597 0.787987 0.615692i \(-0.211124\pi\)
0.787987 + 0.615692i \(0.211124\pi\)
\(282\) 0 0
\(283\) −2.23803e6 −1.66111 −0.830556 0.556935i \(-0.811977\pi\)
−0.830556 + 0.556935i \(0.811977\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −378884. −0.271520
\(288\) 0 0
\(289\) 2.77445e6 1.95403
\(290\) 0 0
\(291\) 1.36125e6 0.942334
\(292\) 0 0
\(293\) 975756. 0.664006 0.332003 0.943278i \(-0.392276\pi\)
0.332003 + 0.943278i \(0.392276\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −600880. −0.395273
\(298\) 0 0
\(299\) 852264. 0.551310
\(300\) 0 0
\(301\) 362452. 0.230587
\(302\) 0 0
\(303\) −60172.0 −0.0376520
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 87858.0 0.0532029 0.0266015 0.999646i \(-0.491531\pi\)
0.0266015 + 0.999646i \(0.491531\pi\)
\(308\) 0 0
\(309\) 1.73760e6 1.03527
\(310\) 0 0
\(311\) −599352. −0.351383 −0.175692 0.984445i \(-0.556216\pi\)
−0.175692 + 0.984445i \(0.556216\pi\)
\(312\) 0 0
\(313\) 2.09342e6 1.20780 0.603900 0.797060i \(-0.293613\pi\)
0.603900 + 0.797060i \(0.293613\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.41625e6 1.35050 0.675249 0.737590i \(-0.264036\pi\)
0.675249 + 0.737590i \(0.264036\pi\)
\(318\) 0 0
\(319\) −39960.0 −0.0219861
\(320\) 0 0
\(321\) −592788. −0.321097
\(322\) 0 0
\(323\) 4.54656e6 2.42480
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −503860. −0.260580
\(328\) 0 0
\(329\) −1.68776e6 −0.859647
\(330\) 0 0
\(331\) 1.64095e6 0.823237 0.411618 0.911356i \(-0.364964\pi\)
0.411618 + 0.911356i \(0.364964\pi\)
\(332\) 0 0
\(333\) −205484. −0.101547
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2.18773e6 −1.04935 −0.524673 0.851304i \(-0.675812\pi\)
−0.524673 + 0.851304i \(0.675812\pi\)
\(338\) 0 0
\(339\) 3.20342e6 1.51396
\(340\) 0 0
\(341\) 303104. 0.141158
\(342\) 0 0
\(343\) −1.36670e6 −0.627246
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.74502e6 1.22383 0.611916 0.790923i \(-0.290399\pi\)
0.611916 + 0.790923i \(0.290399\pi\)
\(348\) 0 0
\(349\) −2.65115e6 −1.16512 −0.582560 0.812788i \(-0.697949\pi\)
−0.582560 + 0.812788i \(0.697949\pi\)
\(350\) 0 0
\(351\) 2.77704e6 1.20313
\(352\) 0 0
\(353\) −3.05766e6 −1.30603 −0.653015 0.757345i \(-0.726496\pi\)
−0.653015 + 0.757345i \(0.726496\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −4.53018e6 −1.88124
\(358\) 0 0
\(359\) −3.79356e6 −1.55350 −0.776749 0.629810i \(-0.783133\pi\)
−0.776749 + 0.629810i \(0.783133\pi\)
\(360\) 0 0
\(361\) 2.45230e6 0.990389
\(362\) 0 0
\(363\) −1.94806e6 −0.775953
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.11060e6 −1.20553 −0.602767 0.797917i \(-0.705935\pi\)
−0.602767 + 0.797917i \(0.705935\pi\)
\(368\) 0 0
\(369\) 112706. 0.0430905
\(370\) 0 0
\(371\) −468312. −0.176645
\(372\) 0 0
\(373\) 1.41520e6 0.526677 0.263339 0.964703i \(-0.415176\pi\)
0.263339 + 0.964703i \(0.415176\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 184680. 0.0669216
\(378\) 0 0
\(379\) 3.90262e6 1.39559 0.697796 0.716297i \(-0.254164\pi\)
0.697796 + 0.716297i \(0.254164\pi\)
\(380\) 0 0
\(381\) 2.45333e6 0.865852
\(382\) 0 0
\(383\) 695674. 0.242331 0.121165 0.992632i \(-0.461337\pi\)
0.121165 + 0.992632i \(0.461337\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −107818. −0.0365943
\(388\) 0 0
\(389\) 498290. 0.166958 0.0834792 0.996510i \(-0.473397\pi\)
0.0834792 + 0.996510i \(0.473397\pi\)
\(390\) 0 0
\(391\) 2.55181e6 0.844124
\(392\) 0 0
\(393\) −4.19513e6 −1.37014
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.09567e6 −0.348901 −0.174451 0.984666i \(-0.555815\pi\)
−0.174451 + 0.984666i \(0.555815\pi\)
\(398\) 0 0
\(399\) −4.91064e6 −1.54421
\(400\) 0 0
\(401\) −2.49160e6 −0.773779 −0.386890 0.922126i \(-0.626451\pi\)
−0.386890 + 0.922126i \(0.626451\pi\)
\(402\) 0 0
\(403\) −1.40083e6 −0.429659
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 647056. 0.193623
\(408\) 0 0
\(409\) −3.63349e6 −1.07403 −0.537014 0.843573i \(-0.680448\pi\)
−0.537014 + 0.843573i \(0.680448\pi\)
\(410\) 0 0
\(411\) −1.51099e6 −0.441222
\(412\) 0 0
\(413\) 6.27892e6 1.81138
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.75044e6 0.774572
\(418\) 0 0
\(419\) 3.64378e6 1.01395 0.506976 0.861960i \(-0.330763\pi\)
0.506976 + 0.861960i \(0.330763\pi\)
\(420\) 0 0
\(421\) −1.82530e6 −0.501913 −0.250957 0.967998i \(-0.580745\pi\)
−0.250957 + 0.967998i \(0.580745\pi\)
\(422\) 0 0
\(423\) 502054. 0.136427
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6.68308e6 −1.77381
\(428\) 0 0
\(429\) −1.41725e6 −0.371794
\(430\) 0 0
\(431\) −2.85435e6 −0.740141 −0.370070 0.929004i \(-0.620666\pi\)
−0.370070 + 0.929004i \(0.620666\pi\)
\(432\) 0 0
\(433\) 587776. 0.150658 0.0753290 0.997159i \(-0.475999\pi\)
0.0753290 + 0.997159i \(0.475999\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.76612e6 0.692895
\(438\) 0 0
\(439\) −6.11604e6 −1.51464 −0.757319 0.653045i \(-0.773491\pi\)
−0.757319 + 0.653045i \(0.773491\pi\)
\(440\) 0 0
\(441\) −383379. −0.0938711
\(442\) 0 0
\(443\) −2.35771e6 −0.570795 −0.285398 0.958409i \(-0.592126\pi\)
−0.285398 + 0.958409i \(0.592126\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.94390e6 0.460156
\(448\) 0 0
\(449\) 5.49735e6 1.28688 0.643439 0.765497i \(-0.277507\pi\)
0.643439 + 0.765497i \(0.277507\pi\)
\(450\) 0 0
\(451\) −354904. −0.0821617
\(452\) 0 0
\(453\) −5.82613e6 −1.33393
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.16039e6 0.259905 0.129952 0.991520i \(-0.458518\pi\)
0.129952 + 0.991520i \(0.458518\pi\)
\(458\) 0 0
\(459\) 8.31488e6 1.84215
\(460\) 0 0
\(461\) −2.30330e6 −0.504775 −0.252387 0.967626i \(-0.581216\pi\)
−0.252387 + 0.967626i \(0.581216\pi\)
\(462\) 0 0
\(463\) 2.71343e6 0.588257 0.294128 0.955766i \(-0.404971\pi\)
0.294128 + 0.955766i \(0.404971\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.05050e6 0.859441 0.429721 0.902962i \(-0.358612\pi\)
0.429721 + 0.902962i \(0.358612\pi\)
\(468\) 0 0
\(469\) 5.07148e6 1.06464
\(470\) 0 0
\(471\) −6.06351e6 −1.25942
\(472\) 0 0
\(473\) 339512. 0.0697754
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 139308. 0.0280337
\(478\) 0 0
\(479\) −5.60528e6 −1.11624 −0.558121 0.829759i \(-0.688478\pi\)
−0.558121 + 0.829759i \(0.688478\pi\)
\(480\) 0 0
\(481\) −2.99045e6 −0.589350
\(482\) 0 0
\(483\) −2.75615e6 −0.537570
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7.13168e6 1.36260 0.681301 0.732003i \(-0.261414\pi\)
0.681301 + 0.732003i \(0.261414\pi\)
\(488\) 0 0
\(489\) 2.08788e6 0.394850
\(490\) 0 0
\(491\) −5.88145e6 −1.10098 −0.550492 0.834841i \(-0.685560\pi\)
−0.550492 + 0.834841i \(0.685560\pi\)
\(492\) 0 0
\(493\) 552960. 0.102465
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 671184. 0.121885
\(498\) 0 0
\(499\) −1.75710e6 −0.315897 −0.157948 0.987447i \(-0.550488\pi\)
−0.157948 + 0.987447i \(0.550488\pi\)
\(500\) 0 0
\(501\) −7.83443e6 −1.39448
\(502\) 0 0
\(503\) 4.91411e6 0.866015 0.433007 0.901390i \(-0.357452\pi\)
0.433007 + 0.901390i \(0.357452\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.35188e6 0.233571
\(508\) 0 0
\(509\) −5.75499e6 −0.984578 −0.492289 0.870432i \(-0.663840\pi\)
−0.492289 + 0.870432i \(0.663840\pi\)
\(510\) 0 0
\(511\) −4.75643e6 −0.805803
\(512\) 0 0
\(513\) 9.01320e6 1.51212
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.58094e6 −0.260128
\(518\) 0 0
\(519\) −4.81326e6 −0.784369
\(520\) 0 0
\(521\) −1.61980e6 −0.261437 −0.130718 0.991420i \(-0.541728\pi\)
−0.130718 + 0.991420i \(0.541728\pi\)
\(522\) 0 0
\(523\) 1.19117e7 1.90422 0.952112 0.305751i \(-0.0989074\pi\)
0.952112 + 0.305751i \(0.0989074\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.19430e6 −0.657860
\(528\) 0 0
\(529\) −4.88383e6 −0.758789
\(530\) 0 0
\(531\) −1.86778e6 −0.287468
\(532\) 0 0
\(533\) 1.64023e6 0.250085
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −335720. −0.0502391
\(538\) 0 0
\(539\) 1.20724e6 0.178986
\(540\) 0 0
\(541\) 4.07630e6 0.598788 0.299394 0.954130i \(-0.403215\pi\)
0.299394 + 0.954130i \(0.403215\pi\)
\(542\) 0 0
\(543\) −9.12657e6 −1.32834
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.23680e7 1.76739 0.883694 0.468065i \(-0.155049\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(548\) 0 0
\(549\) 1.98801e6 0.281505
\(550\) 0 0
\(551\) 599400. 0.0841081
\(552\) 0 0
\(553\) −5.57424e6 −0.775127
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −130308. −0.0177964 −0.00889822 0.999960i \(-0.502832\pi\)
−0.00889822 + 0.999960i \(0.502832\pi\)
\(558\) 0 0
\(559\) −1.56910e6 −0.212383
\(560\) 0 0
\(561\) −4.24346e6 −0.569262
\(562\) 0 0
\(563\) −5.91687e6 −0.786721 −0.393361 0.919384i \(-0.628688\pi\)
−0.393361 + 0.919384i \(0.628688\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −7.17620e6 −0.937426
\(568\) 0 0
\(569\) −9.03013e6 −1.16927 −0.584633 0.811298i \(-0.698761\pi\)
−0.584633 + 0.811298i \(0.698761\pi\)
\(570\) 0 0
\(571\) 1.07093e7 1.37459 0.687294 0.726379i \(-0.258798\pi\)
0.687294 + 0.726379i \(0.258798\pi\)
\(572\) 0 0
\(573\) −2.83853e6 −0.361166
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.22051e6 0.152617 0.0763084 0.997084i \(-0.475687\pi\)
0.0763084 + 0.997084i \(0.475687\pi\)
\(578\) 0 0
\(579\) 6.33718e6 0.785597
\(580\) 0 0
\(581\) −4.39651e6 −0.540341
\(582\) 0 0
\(583\) −438672. −0.0534526
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.47104e7 −1.76210 −0.881049 0.473026i \(-0.843162\pi\)
−0.881049 + 0.473026i \(0.843162\pi\)
\(588\) 0 0
\(589\) −4.54656e6 −0.540001
\(590\) 0 0
\(591\) −4.72455e6 −0.556406
\(592\) 0 0
\(593\) −8.52014e6 −0.994970 −0.497485 0.867472i \(-0.665743\pi\)
−0.497485 + 0.867472i \(0.665743\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.85400e6 0.901893
\(598\) 0 0
\(599\) −2.90100e6 −0.330355 −0.165177 0.986264i \(-0.552820\pi\)
−0.165177 + 0.986264i \(0.552820\pi\)
\(600\) 0 0
\(601\) 5.72760e6 0.646825 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(602\) 0 0
\(603\) −1.50861e6 −0.168959
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −8.79924e6 −0.969334 −0.484667 0.874699i \(-0.661059\pi\)
−0.484667 + 0.874699i \(0.661059\pi\)
\(608\) 0 0
\(609\) −597240. −0.0652538
\(610\) 0 0
\(611\) 7.30649e6 0.791782
\(612\) 0 0
\(613\) −1.03408e6 −0.111149 −0.0555744 0.998455i \(-0.517699\pi\)
−0.0555744 + 0.998455i \(0.517699\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.29854e7 −1.37323 −0.686616 0.727020i \(-0.740905\pi\)
−0.686616 + 0.727020i \(0.740905\pi\)
\(618\) 0 0
\(619\) −7.92002e6 −0.830806 −0.415403 0.909637i \(-0.636359\pi\)
−0.415403 + 0.909637i \(0.636359\pi\)
\(620\) 0 0
\(621\) 5.05876e6 0.526399
\(622\) 0 0
\(623\) −1.34632e7 −1.38972
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −4.59984e6 −0.467276
\(628\) 0 0
\(629\) −8.95386e6 −0.902368
\(630\) 0 0
\(631\) −1.68218e7 −1.68189 −0.840945 0.541120i \(-0.818001\pi\)
−0.840945 + 0.541120i \(0.818001\pi\)
\(632\) 0 0
\(633\) 1.12777e7 1.11869
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.57939e6 −0.544801
\(638\) 0 0
\(639\) −199656. −0.0193433
\(640\) 0 0
\(641\) −1.55154e7 −1.49148 −0.745741 0.666236i \(-0.767904\pi\)
−0.745741 + 0.666236i \(0.767904\pi\)
\(642\) 0 0
\(643\) 1.05801e7 1.00916 0.504582 0.863364i \(-0.331646\pi\)
0.504582 + 0.863364i \(0.331646\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.37883e7 1.29494 0.647471 0.762090i \(-0.275827\pi\)
0.647471 + 0.762090i \(0.275827\pi\)
\(648\) 0 0
\(649\) 5.88152e6 0.548123
\(650\) 0 0
\(651\) 4.53018e6 0.418950
\(652\) 0 0
\(653\) 1.58924e6 0.145850 0.0729248 0.997337i \(-0.476767\pi\)
0.0729248 + 0.997337i \(0.476767\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.41489e6 0.127882
\(658\) 0 0
\(659\) 9.12434e6 0.818442 0.409221 0.912435i \(-0.365801\pi\)
0.409221 + 0.912435i \(0.365801\pi\)
\(660\) 0 0
\(661\) 6.50310e6 0.578918 0.289459 0.957190i \(-0.406525\pi\)
0.289459 + 0.957190i \(0.406525\pi\)
\(662\) 0 0
\(663\) 1.96116e7 1.73273
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 336420. 0.0292797
\(668\) 0 0
\(669\) 1.70598e7 1.47369
\(670\) 0 0
\(671\) −6.26010e6 −0.536754
\(672\) 0 0
\(673\) 2.17810e6 0.185370 0.0926850 0.995695i \(-0.470455\pi\)
0.0926850 + 0.995695i \(0.470455\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.98419e6 −0.334094 −0.167047 0.985949i \(-0.553423\pi\)
−0.167047 + 0.985949i \(0.553423\pi\)
\(678\) 0 0
\(679\) 1.53627e7 1.27877
\(680\) 0 0
\(681\) 7.90073e6 0.652829
\(682\) 0 0
\(683\) −5.91563e6 −0.485231 −0.242616 0.970122i \(-0.578005\pi\)
−0.242616 + 0.970122i \(0.578005\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.84462e6 0.634133
\(688\) 0 0
\(689\) 2.02738e6 0.162700
\(690\) 0 0
\(691\) 1.55471e7 1.23867 0.619335 0.785127i \(-0.287402\pi\)
0.619335 + 0.785127i \(0.287402\pi\)
\(692\) 0 0
\(693\) −1.09905e6 −0.0869328
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 4.91110e6 0.382910
\(698\) 0 0
\(699\) 4.11006e6 0.318167
\(700\) 0 0
\(701\) −2.27103e7 −1.74553 −0.872766 0.488139i \(-0.837676\pi\)
−0.872766 + 0.488139i \(0.837676\pi\)
\(702\) 0 0
\(703\) −9.70584e6 −0.740704
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −679084. −0.0510946
\(708\) 0 0
\(709\) 6.29841e6 0.470560 0.235280 0.971928i \(-0.424399\pi\)
0.235280 + 0.971928i \(0.424399\pi\)
\(710\) 0 0
\(711\) 1.65816e6 0.123013
\(712\) 0 0
\(713\) −2.55181e6 −0.187985
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8.17936e6 −0.594185
\(718\) 0 0
\(719\) −2.11911e7 −1.52873 −0.764367 0.644782i \(-0.776948\pi\)
−0.764367 + 0.644782i \(0.776948\pi\)
\(720\) 0 0
\(721\) 1.96100e7 1.40488
\(722\) 0 0
\(723\) −7.89317e6 −0.561572
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.35610e7 0.951605 0.475803 0.879552i \(-0.342158\pi\)
0.475803 + 0.879552i \(0.342158\pi\)
\(728\) 0 0
\(729\) 1.59468e7 1.11136
\(730\) 0 0
\(731\) −4.69811e6 −0.325185
\(732\) 0 0
\(733\) −2.69413e7 −1.85208 −0.926038 0.377429i \(-0.876808\pi\)
−0.926038 + 0.377429i \(0.876808\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.75050e6 0.322160
\(738\) 0 0
\(739\) −2.77414e6 −0.186860 −0.0934302 0.995626i \(-0.529783\pi\)
−0.0934302 + 0.995626i \(0.529783\pi\)
\(740\) 0 0
\(741\) 2.12587e7 1.42230
\(742\) 0 0
\(743\) 1.85538e7 1.23299 0.616497 0.787358i \(-0.288551\pi\)
0.616497 + 0.787358i \(0.288551\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.30782e6 0.0857526
\(748\) 0 0
\(749\) −6.69004e6 −0.435736
\(750\) 0 0
\(751\) 2.19285e6 0.141876 0.0709380 0.997481i \(-0.477401\pi\)
0.0709380 + 0.997481i \(0.477401\pi\)
\(752\) 0 0
\(753\) 1.42765e7 0.917558
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 9.48749e6 0.601744 0.300872 0.953665i \(-0.402722\pi\)
0.300872 + 0.953665i \(0.402722\pi\)
\(758\) 0 0
\(759\) −2.58171e6 −0.162668
\(760\) 0 0
\(761\) 9.69580e6 0.606907 0.303453 0.952846i \(-0.401860\pi\)
0.303453 + 0.952846i \(0.401860\pi\)
\(762\) 0 0
\(763\) −5.68642e6 −0.353612
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.71822e7 −1.66838
\(768\) 0 0
\(769\) 9.32787e6 0.568809 0.284405 0.958704i \(-0.408204\pi\)
0.284405 + 0.958704i \(0.408204\pi\)
\(770\) 0 0
\(771\) −9.20371e6 −0.557606
\(772\) 0 0
\(773\) 9.68080e6 0.582723 0.291362 0.956613i \(-0.405892\pi\)
0.291362 + 0.956613i \(0.405892\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 9.67086e6 0.574662
\(778\) 0 0
\(779\) 5.32356e6 0.314310
\(780\) 0 0
\(781\) 628704. 0.0368824
\(782\) 0 0
\(783\) 1.09620e6 0.0638977
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −5.52302e6 −0.317863 −0.158931 0.987290i \(-0.550805\pi\)
−0.158931 + 0.987290i \(0.550805\pi\)
\(788\) 0 0
\(789\) −7.87312e6 −0.450251
\(790\) 0 0
\(791\) 3.61529e7 2.05448
\(792\) 0 0
\(793\) 2.89318e7 1.63378
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.71119e7 0.954230 0.477115 0.878841i \(-0.341682\pi\)
0.477115 + 0.878841i \(0.341682\pi\)
\(798\) 0 0
\(799\) 2.18767e7 1.21232
\(800\) 0 0
\(801\) 4.00487e6 0.220550
\(802\) 0 0
\(803\) −4.45539e6 −0.243836
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 5.13198e6 0.277397
\(808\) 0 0
\(809\) −1.45309e7 −0.780586 −0.390293 0.920691i \(-0.627626\pi\)
−0.390293 + 0.920691i \(0.627626\pi\)
\(810\) 0 0
\(811\) 2.13545e7 1.14009 0.570044 0.821614i \(-0.306926\pi\)
0.570044 + 0.821614i \(0.306926\pi\)
\(812\) 0 0
\(813\) −1.62505e7 −0.862266
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −5.09268e6 −0.266926
\(818\) 0 0
\(819\) 5.07938e6 0.264607
\(820\) 0 0
\(821\) 3.67967e7 1.90525 0.952623 0.304154i \(-0.0983737\pi\)
0.952623 + 0.304154i \(0.0983737\pi\)
\(822\) 0 0
\(823\) −3.30668e7 −1.70174 −0.850870 0.525376i \(-0.823925\pi\)
−0.850870 + 0.525376i \(0.823925\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.77309e7 0.901505 0.450752 0.892649i \(-0.351156\pi\)
0.450752 + 0.892649i \(0.351156\pi\)
\(828\) 0 0
\(829\) 1.29375e7 0.653830 0.326915 0.945054i \(-0.393991\pi\)
0.326915 + 0.945054i \(0.393991\pi\)
\(830\) 0 0
\(831\) 3.52102e7 1.76875
\(832\) 0 0
\(833\) −1.67055e7 −0.834157
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −8.31488e6 −0.410244
\(838\) 0 0
\(839\) −3.31812e7 −1.62738 −0.813688 0.581302i \(-0.802543\pi\)
−0.813688 + 0.581302i \(0.802543\pi\)
\(840\) 0 0
\(841\) −2.04382e7 −0.996446
\(842\) 0 0
\(843\) 2.92040e7 1.41538
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.19852e7 −1.05299
\(848\) 0 0
\(849\) −3.13324e7 −1.49185
\(850\) 0 0
\(851\) −5.44751e6 −0.257854
\(852\) 0 0
\(853\) 5.17224e6 0.243392 0.121696 0.992567i \(-0.461167\pi\)
0.121696 + 0.992567i \(0.461167\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.05320e7 0.489845 0.244922 0.969543i \(-0.421238\pi\)
0.244922 + 0.969543i \(0.421238\pi\)
\(858\) 0 0
\(859\) 1.14741e7 0.530563 0.265282 0.964171i \(-0.414535\pi\)
0.265282 + 0.964171i \(0.414535\pi\)
\(860\) 0 0
\(861\) −5.30438e6 −0.243852
\(862\) 0 0
\(863\) 1.92722e7 0.880856 0.440428 0.897788i \(-0.354827\pi\)
0.440428 + 0.897788i \(0.354827\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 3.88423e7 1.75492
\(868\) 0 0
\(869\) −5.22144e6 −0.234553
\(870\) 0 0
\(871\) −2.19550e7 −0.980593
\(872\) 0 0
\(873\) −4.56990e6 −0.202942
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −2.30524e7 −1.01208 −0.506042 0.862509i \(-0.668892\pi\)
−0.506042 + 0.862509i \(0.668892\pi\)
\(878\) 0 0
\(879\) 1.36606e7 0.596344
\(880\) 0 0
\(881\) 2.26690e7 0.983994 0.491997 0.870597i \(-0.336267\pi\)
0.491997 + 0.870597i \(0.336267\pi\)
\(882\) 0 0
\(883\) 3.67337e6 0.158549 0.0792745 0.996853i \(-0.474740\pi\)
0.0792745 + 0.996853i \(0.474740\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.39649e7 1.44951 0.724755 0.689007i \(-0.241953\pi\)
0.724755 + 0.689007i \(0.241953\pi\)
\(888\) 0 0
\(889\) 2.76876e7 1.17498
\(890\) 0 0
\(891\) −6.72201e6 −0.283665
\(892\) 0 0
\(893\) 2.37140e7 0.995123
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.19317e7 0.495132
\(898\) 0 0
\(899\) −552960. −0.0228189
\(900\) 0 0
\(901\) 6.07027e6 0.249113
\(902\) 0 0
\(903\) 5.07433e6 0.207090
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.13327e7 −0.861050 −0.430525 0.902579i \(-0.641672\pi\)
−0.430525 + 0.902579i \(0.641672\pi\)
\(908\) 0 0
\(909\) 202006. 0.00810876
\(910\) 0 0
\(911\) 1.03512e7 0.413235 0.206617 0.978422i \(-0.433754\pi\)
0.206617 + 0.978422i \(0.433754\pi\)
\(912\) 0 0
\(913\) −4.11825e6 −0.163507
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.73450e7 −1.85931
\(918\) 0 0
\(919\) 2.59019e7 1.01168 0.505839 0.862628i \(-0.331183\pi\)
0.505839 + 0.862628i \(0.331183\pi\)
\(920\) 0 0
\(921\) 1.23001e6 0.0477816
\(922\) 0 0
\(923\) −2.90563e6 −0.112263
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −5.83336e6 −0.222956
\(928\) 0 0
\(929\) −3.13230e7 −1.19076 −0.595379 0.803445i \(-0.702998\pi\)
−0.595379 + 0.803445i \(0.702998\pi\)
\(930\) 0 0
\(931\) −1.81085e7 −0.684714
\(932\) 0 0
\(933\) −8.39093e6 −0.315577
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 2.08461e7 0.775667 0.387833 0.921729i \(-0.373224\pi\)
0.387833 + 0.921729i \(0.373224\pi\)
\(938\) 0 0
\(939\) 2.93078e7 1.08472
\(940\) 0 0
\(941\) −3.82929e7 −1.40976 −0.704878 0.709328i \(-0.748998\pi\)
−0.704878 + 0.709328i \(0.748998\pi\)
\(942\) 0 0
\(943\) 2.98791e6 0.109418
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.25088e7 −1.54029 −0.770147 0.637866i \(-0.779817\pi\)
−0.770147 + 0.637866i \(0.779817\pi\)
\(948\) 0 0
\(949\) 2.05911e7 0.742189
\(950\) 0 0
\(951\) 3.38275e7 1.21288
\(952\) 0 0
\(953\) −3.91855e7 −1.39763 −0.698816 0.715302i \(-0.746289\pi\)
−0.698816 + 0.715302i \(0.746289\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −559440. −0.0197458
\(958\) 0 0
\(959\) −1.70526e7 −0.598749
\(960\) 0 0
\(961\) −2.44348e7 −0.853495
\(962\) 0 0
\(963\) 1.99007e6 0.0691518
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −1.84836e7 −0.635653 −0.317827 0.948149i \(-0.602953\pi\)
−0.317827 + 0.948149i \(0.602953\pi\)
\(968\) 0 0
\(969\) 6.36518e7 2.17772
\(970\) 0 0
\(971\) −3.95031e7 −1.34457 −0.672284 0.740294i \(-0.734686\pi\)
−0.672284 + 0.740294i \(0.734686\pi\)
\(972\) 0 0
\(973\) 3.10407e7 1.05111
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.29043e7 −1.10285 −0.551425 0.834225i \(-0.685916\pi\)
−0.551425 + 0.834225i \(0.685916\pi\)
\(978\) 0 0
\(979\) −1.26111e7 −0.420529
\(980\) 0 0
\(981\) 1.69153e6 0.0561186
\(982\) 0 0
\(983\) −2.65797e7 −0.877338 −0.438669 0.898649i \(-0.644550\pi\)
−0.438669 + 0.898649i \(0.644550\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2.36286e7 −0.772049
\(988\) 0 0
\(989\) −2.85832e6 −0.0929225
\(990\) 0 0
\(991\) −1.92964e7 −0.624153 −0.312077 0.950057i \(-0.601025\pi\)
−0.312077 + 0.950057i \(0.601025\pi\)
\(992\) 0 0
\(993\) 2.29733e7 0.739349
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 5.12017e7 1.63135 0.815674 0.578511i \(-0.196366\pi\)
0.815674 + 0.578511i \(0.196366\pi\)
\(998\) 0 0
\(999\) −1.77503e7 −0.562720
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.k.1.1 1
4.3 odd 2 50.6.a.e.1.1 1
5.2 odd 4 80.6.c.c.49.1 2
5.3 odd 4 80.6.c.c.49.2 2
5.4 even 2 400.6.a.c.1.1 1
12.11 even 2 450.6.a.c.1.1 1
15.2 even 4 720.6.f.a.289.1 2
15.8 even 4 720.6.f.a.289.2 2
20.3 even 4 10.6.b.a.9.1 2
20.7 even 4 10.6.b.a.9.2 yes 2
20.19 odd 2 50.6.a.c.1.1 1
40.3 even 4 320.6.c.b.129.2 2
40.13 odd 4 320.6.c.a.129.1 2
40.27 even 4 320.6.c.b.129.1 2
40.37 odd 4 320.6.c.a.129.2 2
60.23 odd 4 90.6.c.a.19.2 2
60.47 odd 4 90.6.c.a.19.1 2
60.59 even 2 450.6.a.w.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.b.a.9.1 2 20.3 even 4
10.6.b.a.9.2 yes 2 20.7 even 4
50.6.a.c.1.1 1 20.19 odd 2
50.6.a.e.1.1 1 4.3 odd 2
80.6.c.c.49.1 2 5.2 odd 4
80.6.c.c.49.2 2 5.3 odd 4
90.6.c.a.19.1 2 60.47 odd 4
90.6.c.a.19.2 2 60.23 odd 4
320.6.c.a.129.1 2 40.13 odd 4
320.6.c.a.129.2 2 40.37 odd 4
320.6.c.b.129.1 2 40.27 even 4
320.6.c.b.129.2 2 40.3 even 4
400.6.a.c.1.1 1 5.4 even 2
400.6.a.k.1.1 1 1.1 even 1 trivial
450.6.a.c.1.1 1 12.11 even 2
450.6.a.w.1.1 1 60.59 even 2
720.6.f.a.289.1 2 15.2 even 4
720.6.f.a.289.2 2 15.8 even 4