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Properties

Label 1568.4.a.e.1.1
Level $1568$
Weight $4$
Character 1568.1
Self dual yes
Analytic conductor $92.515$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1568,4,Mod(1,1568)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1568.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1568.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(92.5149948890\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 224)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1568.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{3} -23.0000 q^{9} +O(q^{10})\) \(q-2.00000 q^{3} -23.0000 q^{9} -20.0000 q^{11} +20.0000 q^{13} +50.0000 q^{17} +10.0000 q^{19} +72.0000 q^{23} -125.000 q^{25} +100.000 q^{27} -134.000 q^{29} -180.000 q^{31} +40.0000 q^{33} -270.000 q^{37} -40.0000 q^{39} +250.000 q^{41} -92.0000 q^{43} -236.000 q^{47} -100.000 q^{51} +150.000 q^{53} -20.0000 q^{57} +570.000 q^{59} +200.000 q^{61} -176.000 q^{67} -144.000 q^{69} +640.000 q^{71} -250.000 q^{73} +250.000 q^{75} +640.000 q^{79} +421.000 q^{81} +882.000 q^{83} +268.000 q^{87} -1074.00 q^{89} +360.000 q^{93} -270.000 q^{97} +460.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) −2.00000 −0.384900 −0.192450 − 0.981307i \(-0.561643\pi\)
−0.192450 + 0.981307i \(0.561643\pi\)
\(4\) 0 0
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −23.0000 −0.851852
\(10\) 0 0
\(11\) −20.0000 −0.548202 −0.274101 − 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 0 0
\(13\) 20.0000 0.426692 0.213346 − 0.976977i \(-0.431564\pi\)
0.213346 + 0.976977i \(0.431564\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 50.0000 0.713340 0.356670 − 0.934230i \(-0.383912\pi\)
0.356670 + 0.934230i \(0.383912\pi\)
\(18\) 0 0
\(19\) 10.0000 0.120745 0.0603726 − 0.998176i \(-0.480771\pi\)
0.0603726 + 0.998176i \(0.480771\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 72.0000 0.652741 0.326370 − 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) −125.000 −1.00000
\(26\) 0 0
\(27\) 100.000 0.712778
\(28\) 0 0
\(29\) −134.000 −0.858041 −0.429020 − 0.903295i \(-0.641141\pi\)
−0.429020 + 0.903295i \(0.641141\pi\)
\(30\) 0 0
\(31\) −180.000 −1.04287 −0.521435 − 0.853291i \(-0.674603\pi\)
−0.521435 + 0.853291i \(0.674603\pi\)
\(32\) 0 0
\(33\) 40.0000 0.211003
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −270.000 −1.19967 −0.599834 − 0.800124i \(-0.704767\pi\)
−0.599834 + 0.800124i \(0.704767\pi\)
\(38\) 0 0
\(39\) −40.0000 −0.164234
\(40\) 0 0
\(41\) 250.000 0.952279 0.476140 − 0.879370i \(-0.342036\pi\)
0.476140 + 0.879370i \(0.342036\pi\)
\(42\) 0 0
\(43\) −92.0000 −0.326276 −0.163138 − 0.986603i \(-0.552162\pi\)
−0.163138 + 0.986603i \(0.552162\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −236.000 −0.732428 −0.366214 − 0.930531i \(-0.619346\pi\)
−0.366214 + 0.930531i \(0.619346\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −100.000 −0.274565
\(52\) 0 0
\(53\) 150.000 0.388756 0.194378 − 0.980927i \(-0.437731\pi\)
0.194378 + 0.980927i \(0.437731\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −20.0000 −0.0464748
\(58\) 0 0
\(59\) 570.000 1.25776 0.628879 − 0.777503i \(-0.283514\pi\)
0.628879 + 0.777503i \(0.283514\pi\)
\(60\) 0 0
\(61\) 200.000 0.419793 0.209897 − 0.977724i \(-0.432687\pi\)
0.209897 + 0.977724i \(0.432687\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −176.000 −0.320923 −0.160461 − 0.987042i \(-0.551298\pi\)
−0.160461 + 0.987042i \(0.551298\pi\)
\(68\) 0 0
\(69\) −144.000 −0.251240
\(70\) 0 0
\(71\) 640.000 1.06978 0.534888 − 0.844923i \(-0.320354\pi\)
0.534888 + 0.844923i \(0.320354\pi\)
\(72\) 0 0
\(73\) −250.000 −0.400826 −0.200413 − 0.979712i \(-0.564228\pi\)
−0.200413 + 0.979712i \(0.564228\pi\)
\(74\) 0 0
\(75\) 250.000 0.384900
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 640.000 0.911464 0.455732 − 0.890117i \(-0.349378\pi\)
0.455732 + 0.890117i \(0.349378\pi\)
\(80\) 0 0
\(81\) 421.000 0.577503
\(82\) 0 0
\(83\) 882.000 1.16641 0.583205 − 0.812325i \(-0.301798\pi\)
0.583205 + 0.812325i \(0.301798\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 268.000 0.330260
\(88\) 0 0
\(89\) −1074.00 −1.27914 −0.639572 − 0.768731i \(-0.720888\pi\)
−0.639572 + 0.768731i \(0.720888\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 360.000 0.401401
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −270.000 −0.282622 −0.141311 − 0.989965i \(-0.545132\pi\)
−0.141311 + 0.989965i \(0.545132\pi\)
\(98\) 0 0
\(99\) 460.000 0.466987
\(100\) 0 0
\(101\) −1152.00 −1.13493 −0.567467 − 0.823396i \(-0.692076\pi\)
−0.567467 + 0.823396i \(0.692076\pi\)
\(102\) 0 0
\(103\) −148.000 −0.141581 −0.0707906 − 0.997491i \(-0.522552\pi\)
−0.0707906 + 0.997491i \(0.522552\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 456.000 0.411992 0.205996 − 0.978553i \(-0.433957\pi\)
0.205996 + 0.978553i \(0.433957\pi\)
\(108\) 0 0
\(109\) 450.000 0.395433 0.197716 − 0.980259i \(-0.436647\pi\)
0.197716 + 0.980259i \(0.436647\pi\)
\(110\) 0 0
\(111\) 540.000 0.461753
\(112\) 0 0
\(113\) 870.000 0.724272 0.362136 − 0.932125i \(-0.382048\pi\)
0.362136 + 0.932125i \(0.382048\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −460.000 −0.363479
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) −500.000 −0.366532
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1104.00 0.771371 0.385686 − 0.922630i \(-0.373965\pi\)
0.385686 + 0.922630i \(0.373965\pi\)
\(128\) 0 0
\(129\) 184.000 0.125584
\(130\) 0 0
\(131\) −1910.00 −1.27387 −0.636937 − 0.770916i \(-0.719799\pi\)
−0.636937 + 0.770916i \(0.719799\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −510.000 −0.318046 −0.159023 − 0.987275i \(-0.550834\pi\)
−0.159023 + 0.987275i \(0.550834\pi\)
\(138\) 0 0
\(139\) 3030.00 1.84893 0.924465 − 0.381267i \(-0.124512\pi\)
0.924465 + 0.381267i \(0.124512\pi\)
\(140\) 0 0
\(141\) 472.000 0.281912
\(142\) 0 0
\(143\) −400.000 −0.233914
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1150.00 0.632293 0.316147 − 0.948710i \(-0.397611\pi\)
0.316147 + 0.948710i \(0.397611\pi\)
\(150\) 0 0
\(151\) −3200.00 −1.72458 −0.862292 − 0.506411i \(-0.830972\pi\)
−0.862292 + 0.506411i \(0.830972\pi\)
\(152\) 0 0
\(153\) −1150.00 −0.607660
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2020.00 1.02684 0.513419 − 0.858138i \(-0.328379\pi\)
0.513419 + 0.858138i \(0.328379\pi\)
\(158\) 0 0
\(159\) −300.000 −0.149632
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3988.00 1.91635 0.958173 − 0.286191i \(-0.0923892\pi\)
0.958173 + 0.286191i \(0.0923892\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3876.00 1.79601 0.898006 − 0.439984i \(-0.145016\pi\)
0.898006 + 0.439984i \(0.145016\pi\)
\(168\) 0 0
\(169\) −1797.00 −0.817934
\(170\) 0 0
\(171\) −230.000 −0.102857
\(172\) 0 0
\(173\) 1980.00 0.870154 0.435077 − 0.900393i \(-0.356721\pi\)
0.435077 + 0.900393i \(0.356721\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1140.00 −0.484111
\(178\) 0 0
\(179\) 40.0000 0.0167025 0.00835123 − 0.999965i \(-0.497342\pi\)
0.00835123 + 0.999965i \(0.497342\pi\)
\(180\) 0 0
\(181\) 3292.00 1.35189 0.675946 − 0.736951i \(-0.263735\pi\)
0.675946 + 0.736951i \(0.263735\pi\)
\(182\) 0 0
\(183\) −400.000 −0.161578
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1000.00 −0.391055
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2480.00 0.939510 0.469755 − 0.882797i \(-0.344342\pi\)
0.469755 + 0.882797i \(0.344342\pi\)
\(192\) 0 0
\(193\) −2450.00 −0.913756 −0.456878 − 0.889529i \(-0.651032\pi\)
−0.456878 + 0.889529i \(0.651032\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2530.00 −0.915000 −0.457500 − 0.889210i \(-0.651255\pi\)
−0.457500 + 0.889210i \(0.651255\pi\)
\(198\) 0 0
\(199\) 3060.00 1.09004 0.545019 − 0.838424i \(-0.316522\pi\)
0.545019 + 0.838424i \(0.316522\pi\)
\(200\) 0 0
\(201\) 352.000 0.123523
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1656.00 −0.556038
\(208\) 0 0
\(209\) −200.000 −0.0661928
\(210\) 0 0
\(211\) 5280.00 1.72270 0.861351 − 0.508010i \(-0.169619\pi\)
0.861351 + 0.508010i \(0.169619\pi\)
\(212\) 0 0
\(213\) −1280.00 −0.411757
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 500.000 0.154278
\(220\) 0 0
\(221\) 1000.00 0.304377
\(222\) 0 0
\(223\) 3928.00 1.17954 0.589772 − 0.807570i \(-0.299218\pi\)
0.589772 + 0.807570i \(0.299218\pi\)
\(224\) 0 0
\(225\) 2875.00 0.851852
\(226\) 0 0
\(227\) 1754.00 0.512851 0.256425 − 0.966564i \(-0.417455\pi\)
0.256425 + 0.966564i \(0.417455\pi\)
\(228\) 0 0
\(229\) 6116.00 1.76488 0.882438 − 0.470429i \(-0.155901\pi\)
0.882438 + 0.470429i \(0.155901\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1450.00 0.407694 0.203847 − 0.979003i \(-0.434656\pi\)
0.203847 + 0.979003i \(0.434656\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1280.00 −0.350823
\(238\) 0 0
\(239\) 4040.00 1.09341 0.546707 − 0.837324i \(-0.315881\pi\)
0.546707 + 0.837324i \(0.315881\pi\)
\(240\) 0 0
\(241\) 6050.00 1.61707 0.808537 − 0.588446i \(-0.200260\pi\)
0.808537 + 0.588446i \(0.200260\pi\)
\(242\) 0 0
\(243\) −3542.00 −0.935059
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 200.000 0.0515210
\(248\) 0 0
\(249\) −1764.00 −0.448952
\(250\) 0 0
\(251\) 6390.00 1.60691 0.803453 − 0.595369i \(-0.202994\pi\)
0.803453 + 0.595369i \(0.202994\pi\)
\(252\) 0 0
\(253\) −1440.00 −0.357834
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5410.00 −1.31310 −0.656550 − 0.754283i \(-0.727985\pi\)
−0.656550 + 0.754283i \(0.727985\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3082.00 0.730923
\(262\) 0 0
\(263\) −4112.00 −0.964094 −0.482047 − 0.876145i \(-0.660107\pi\)
−0.482047 + 0.876145i \(0.660107\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2148.00 0.492343
\(268\) 0 0
\(269\) −2500.00 −0.566646 −0.283323 − 0.959025i \(-0.591437\pi\)
−0.283323 + 0.959025i \(0.591437\pi\)
\(270\) 0 0
\(271\) −1360.00 −0.304849 −0.152425 − 0.988315i \(-0.548708\pi\)
−0.152425 + 0.988315i \(0.548708\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2500.00 0.548202
\(276\) 0 0
\(277\) 1510.00 0.327535 0.163767 − 0.986499i \(-0.447635\pi\)
0.163767 + 0.986499i \(0.447635\pi\)
\(278\) 0 0
\(279\) 4140.00 0.888370
\(280\) 0 0
\(281\) 3850.00 0.817337 0.408669 − 0.912683i \(-0.365993\pi\)
0.408669 + 0.912683i \(0.365993\pi\)
\(282\) 0 0
\(283\) 3418.00 0.717947 0.358974 − 0.933348i \(-0.383127\pi\)
0.358974 + 0.933348i \(0.383127\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2413.00 −0.491146
\(290\) 0 0
\(291\) 540.000 0.108781
\(292\) 0 0
\(293\) −5320.00 −1.06074 −0.530372 − 0.847765i \(-0.677948\pi\)
−0.530372 + 0.847765i \(0.677948\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2000.00 −0.390747
\(298\) 0 0
\(299\) 1440.00 0.278520
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 2304.00 0.436836
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3706.00 0.688966 0.344483 − 0.938793i \(-0.388054\pi\)
0.344483 + 0.938793i \(0.388054\pi\)
\(308\) 0 0
\(309\) 296.000 0.0544947
\(310\) 0 0
\(311\) 520.000 0.0948119 0.0474059 − 0.998876i \(-0.484905\pi\)
0.0474059 + 0.998876i \(0.484905\pi\)
\(312\) 0 0
\(313\) −7510.00 −1.35620 −0.678100 − 0.734970i \(-0.737196\pi\)
−0.678100 + 0.734970i \(0.737196\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4390.00 0.777814 0.388907 − 0.921277i \(-0.372853\pi\)
0.388907 + 0.921277i \(0.372853\pi\)
\(318\) 0 0
\(319\) 2680.00 0.470380
\(320\) 0 0
\(321\) −912.000 −0.158576
\(322\) 0 0
\(323\) 500.000 0.0861323
\(324\) 0 0
\(325\) −2500.00 −0.426692
\(326\) 0 0
\(327\) −900.000 −0.152202
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2260.00 0.375290 0.187645 − 0.982237i \(-0.439915\pi\)
0.187645 + 0.982237i \(0.439915\pi\)
\(332\) 0 0
\(333\) 6210.00 1.02194
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2510.00 0.405722 0.202861 − 0.979208i \(-0.434976\pi\)
0.202861 + 0.979208i \(0.434976\pi\)
\(338\) 0 0
\(339\) −1740.00 −0.278772
\(340\) 0 0
\(341\) 3600.00 0.571704
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11436.0 −1.76921 −0.884606 − 0.466339i \(-0.845573\pi\)
−0.884606 + 0.466339i \(0.845573\pi\)
\(348\) 0 0
\(349\) 3836.00 0.588356 0.294178 − 0.955751i \(-0.404954\pi\)
0.294178 + 0.955751i \(0.404954\pi\)
\(350\) 0 0
\(351\) 2000.00 0.304137
\(352\) 0 0
\(353\) −2130.00 −0.321157 −0.160579 − 0.987023i \(-0.551336\pi\)
−0.160579 + 0.987023i \(0.551336\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8000.00 1.17611 0.588056 − 0.808821i \(-0.299894\pi\)
0.588056 + 0.808821i \(0.299894\pi\)
\(360\) 0 0
\(361\) −6759.00 −0.985421
\(362\) 0 0
\(363\) 1862.00 0.269228
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4376.00 −0.622412 −0.311206 − 0.950342i \(-0.600733\pi\)
−0.311206 + 0.950342i \(0.600733\pi\)
\(368\) 0 0
\(369\) −5750.00 −0.811201
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1790.00 0.248479 0.124240 − 0.992252i \(-0.460351\pi\)
0.124240 + 0.992252i \(0.460351\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2680.00 −0.366119
\(378\) 0 0
\(379\) −6100.00 −0.826744 −0.413372 − 0.910562i \(-0.635649\pi\)
−0.413372 + 0.910562i \(0.635649\pi\)
\(380\) 0 0
\(381\) −2208.00 −0.296901
\(382\) 0 0
\(383\) −11932.0 −1.59190 −0.795949 − 0.605364i \(-0.793028\pi\)
−0.795949 + 0.605364i \(0.793028\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2116.00 0.277939
\(388\) 0 0
\(389\) 9250.00 1.20564 0.602820 − 0.797878i \(-0.294044\pi\)
0.602820 + 0.797878i \(0.294044\pi\)
\(390\) 0 0
\(391\) 3600.00 0.465626
\(392\) 0 0
\(393\) 3820.00 0.490314
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 12780.0 1.61564 0.807821 − 0.589428i \(-0.200647\pi\)
0.807821 + 0.589428i \(0.200647\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5602.00 −0.697632 −0.348816 − 0.937191i \(-0.613416\pi\)
−0.348816 + 0.937191i \(0.613416\pi\)
\(402\) 0 0
\(403\) −3600.00 −0.444985
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5400.00 0.657661
\(408\) 0 0
\(409\) 5650.00 0.683067 0.341534 − 0.939870i \(-0.389054\pi\)
0.341534 + 0.939870i \(0.389054\pi\)
\(410\) 0 0
\(411\) 1020.00 0.122416
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −6060.00 −0.711653
\(418\) 0 0
\(419\) 1030.00 0.120093 0.0600463 − 0.998196i \(-0.480875\pi\)
0.0600463 + 0.998196i \(0.480875\pi\)
\(420\) 0 0
\(421\) −13850.0 −1.60334 −0.801672 − 0.597764i \(-0.796056\pi\)
−0.801672 + 0.597764i \(0.796056\pi\)
\(422\) 0 0
\(423\) 5428.00 0.623921
\(424\) 0 0
\(425\) −6250.00 −0.713340
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 800.000 0.0900335
\(430\) 0 0
\(431\) 6840.00 0.764434 0.382217 − 0.924073i \(-0.375161\pi\)
0.382217 + 0.924073i \(0.375161\pi\)
\(432\) 0 0
\(433\) 2650.00 0.294113 0.147056 − 0.989128i \(-0.453020\pi\)
0.147056 + 0.989128i \(0.453020\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 720.000 0.0788153
\(438\) 0 0
\(439\) 9240.00 1.00456 0.502279 − 0.864706i \(-0.332495\pi\)
0.502279 + 0.864706i \(0.332495\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14992.0 −1.60788 −0.803941 − 0.594710i \(-0.797267\pi\)
−0.803941 + 0.594710i \(0.797267\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2300.00 −0.243370
\(448\) 0 0
\(449\) −1950.00 −0.204958 −0.102479 − 0.994735i \(-0.532677\pi\)
−0.102479 + 0.994735i \(0.532677\pi\)
\(450\) 0 0
\(451\) −5000.00 −0.522042
\(452\) 0 0
\(453\) 6400.00 0.663793
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18170.0 −1.85986 −0.929931 − 0.367735i \(-0.880134\pi\)
−0.929931 + 0.367735i \(0.880134\pi\)
\(458\) 0 0
\(459\) 5000.00 0.508453
\(460\) 0 0
\(461\) 18132.0 1.83187 0.915934 − 0.401328i \(-0.131451\pi\)
0.915934 + 0.401328i \(0.131451\pi\)
\(462\) 0 0
\(463\) −3112.00 −0.312369 −0.156185 − 0.987728i \(-0.549919\pi\)
−0.156185 + 0.987728i \(0.549919\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9826.00 0.973647 0.486823 − 0.873500i \(-0.338156\pi\)
0.486823 + 0.873500i \(0.338156\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −4040.00 −0.395230
\(472\) 0 0
\(473\) 1840.00 0.178865
\(474\) 0 0
\(475\) −1250.00 −0.120745
\(476\) 0 0
\(477\) −3450.00 −0.331163
\(478\) 0 0
\(479\) −900.000 −0.0858498 −0.0429249 − 0.999078i \(-0.513668\pi\)
−0.0429249 + 0.999078i \(0.513668\pi\)
\(480\) 0 0
\(481\) −5400.00 −0.511889
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 9016.00 0.838920 0.419460 − 0.907774i \(-0.362219\pi\)
0.419460 + 0.907774i \(0.362219\pi\)
\(488\) 0 0
\(489\) −7976.00 −0.737602
\(490\) 0 0
\(491\) 1680.00 0.154414 0.0772071 − 0.997015i \(-0.475400\pi\)
0.0772071 + 0.997015i \(0.475400\pi\)
\(492\) 0 0
\(493\) −6700.00 −0.612075
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3280.00 0.294254 0.147127 − 0.989118i \(-0.452997\pi\)
0.147127 + 0.989118i \(0.452997\pi\)
\(500\) 0 0
\(501\) −7752.00 −0.691285
\(502\) 0 0
\(503\) −14448.0 −1.28072 −0.640362 − 0.768073i \(-0.721216\pi\)
−0.640362 + 0.768073i \(0.721216\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3594.00 0.314823
\(508\) 0 0
\(509\) 4604.00 0.400921 0.200460 − 0.979702i \(-0.435756\pi\)
0.200460 + 0.979702i \(0.435756\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1000.00 0.0860645
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 4720.00 0.401519
\(518\) 0 0
\(519\) −3960.00 −0.334922
\(520\) 0 0
\(521\) 12138.0 1.02068 0.510341 − 0.859972i \(-0.329519\pi\)
0.510341 + 0.859972i \(0.329519\pi\)
\(522\) 0 0
\(523\) −5822.00 −0.486765 −0.243383 − 0.969930i \(-0.578257\pi\)
−0.243383 + 0.969930i \(0.578257\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9000.00 −0.743921
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) 0 0
\(531\) −13110.0 −1.07142
\(532\) 0 0
\(533\) 5000.00 0.406330
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −80.0000 −0.00642878
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7078.00 0.562490 0.281245 − 0.959636i \(-0.409253\pi\)
0.281245 + 0.959636i \(0.409253\pi\)
\(542\) 0 0
\(543\) −6584.00 −0.520343
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1036.00 0.0809802 0.0404901 − 0.999180i \(-0.487108\pi\)
0.0404901 + 0.999180i \(0.487108\pi\)
\(548\) 0 0
\(549\) −4600.00 −0.357601
\(550\) 0 0
\(551\) −1340.00 −0.103604
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3590.00 0.273094 0.136547 − 0.990634i \(-0.456400\pi\)
0.136547 + 0.990634i \(0.456400\pi\)
\(558\) 0 0
\(559\) −1840.00 −0.139220
\(560\) 0 0
\(561\) 2000.00 0.150517
\(562\) 0 0
\(563\) 9838.00 0.736452 0.368226 − 0.929736i \(-0.379965\pi\)
0.368226 + 0.929736i \(0.379965\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11050.0 −0.814130 −0.407065 − 0.913399i \(-0.633448\pi\)
−0.407065 + 0.913399i \(0.633448\pi\)
\(570\) 0 0
\(571\) 10220.0 0.749026 0.374513 − 0.927222i \(-0.377810\pi\)
0.374513 + 0.927222i \(0.377810\pi\)
\(572\) 0 0
\(573\) −4960.00 −0.361618
\(574\) 0 0
\(575\) −9000.00 −0.652741
\(576\) 0 0
\(577\) 110.000 0.00793650 0.00396825 − 0.999992i \(-0.498737\pi\)
0.00396825 + 0.999992i \(0.498737\pi\)
\(578\) 0 0
\(579\) 4900.00 0.351705
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3000.00 −0.213117
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22866.0 −1.60780 −0.803902 − 0.594762i \(-0.797246\pi\)
−0.803902 + 0.594762i \(0.797246\pi\)
\(588\) 0 0
\(589\) −1800.00 −0.125921
\(590\) 0 0
\(591\) 5060.00 0.352184
\(592\) 0 0
\(593\) −23450.0 −1.62391 −0.811953 − 0.583723i \(-0.801595\pi\)
−0.811953 + 0.583723i \(0.801595\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6120.00 −0.419556
\(598\) 0 0
\(599\) 10280.0 0.701218 0.350609 − 0.936522i \(-0.385975\pi\)
0.350609 + 0.936522i \(0.385975\pi\)
\(600\) 0 0
\(601\) −6450.00 −0.437772 −0.218886 − 0.975750i \(-0.570242\pi\)
−0.218886 + 0.975750i \(0.570242\pi\)
\(602\) 0 0
\(603\) 4048.00 0.273379
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 16144.0 1.07951 0.539757 − 0.841821i \(-0.318516\pi\)
0.539757 + 0.841821i \(0.318516\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4720.00 −0.312522
\(612\) 0 0
\(613\) 29650.0 1.95359 0.976796 − 0.214171i \(-0.0687049\pi\)
0.976796 + 0.214171i \(0.0687049\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5830.00 0.380400 0.190200 − 0.981745i \(-0.439086\pi\)
0.190200 + 0.981745i \(0.439086\pi\)
\(618\) 0 0
\(619\) −25990.0 −1.68760 −0.843802 − 0.536655i \(-0.819688\pi\)
−0.843802 + 0.536655i \(0.819688\pi\)
\(620\) 0 0
\(621\) 7200.00 0.465259
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15625.0 1.00000
\(626\) 0 0
\(627\) 400.000 0.0254776
\(628\) 0 0
\(629\) −13500.0 −0.855771
\(630\) 0 0
\(631\) −24880.0 −1.56966 −0.784831 − 0.619709i \(-0.787250\pi\)
−0.784831 + 0.619709i \(0.787250\pi\)
\(632\) 0 0
\(633\) −10560.0 −0.663068
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −14720.0 −0.911290
\(640\) 0 0
\(641\) −15650.0 −0.964334 −0.482167 − 0.876079i \(-0.660150\pi\)
−0.482167 + 0.876079i \(0.660150\pi\)
\(642\) 0 0
\(643\) −21442.0 −1.31507 −0.657535 − 0.753424i \(-0.728401\pi\)
−0.657535 + 0.753424i \(0.728401\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15036.0 −0.913642 −0.456821 − 0.889559i \(-0.651012\pi\)
−0.456821 + 0.889559i \(0.651012\pi\)
\(648\) 0 0
\(649\) −11400.0 −0.689506
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 25810.0 1.54674 0.773372 − 0.633953i \(-0.218569\pi\)
0.773372 + 0.633953i \(0.218569\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5750.00 0.341444
\(658\) 0 0
\(659\) −26580.0 −1.57118 −0.785592 − 0.618745i \(-0.787641\pi\)
−0.785592 + 0.618745i \(0.787641\pi\)
\(660\) 0 0
\(661\) −3000.00 −0.176530 −0.0882651 − 0.996097i \(-0.528132\pi\)
−0.0882651 + 0.996097i \(0.528132\pi\)
\(662\) 0 0
\(663\) −2000.00 −0.117155
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −9648.00 −0.560078
\(668\) 0 0
\(669\) −7856.00 −0.454007
\(670\) 0 0
\(671\) −4000.00 −0.230132
\(672\) 0 0
\(673\) 23450.0 1.34314 0.671568 − 0.740943i \(-0.265621\pi\)
0.671568 + 0.740943i \(0.265621\pi\)
\(674\) 0 0
\(675\) −12500.0 −0.712778
\(676\) 0 0
\(677\) 29580.0 1.67925 0.839625 − 0.543167i \(-0.182775\pi\)
0.839625 + 0.543167i \(0.182775\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −3508.00 −0.197396
\(682\) 0 0
\(683\) 16368.0 0.916990 0.458495 − 0.888697i \(-0.348389\pi\)
0.458495 + 0.888697i \(0.348389\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −12232.0 −0.679301
\(688\) 0 0
\(689\) 3000.00 0.165879
\(690\) 0 0
\(691\) 11450.0 0.630360 0.315180 − 0.949032i \(-0.397935\pi\)
0.315180 + 0.949032i \(0.397935\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12500.0 0.679299
\(698\) 0 0
\(699\) −2900.00 −0.156921
\(700\) 0 0
\(701\) −8750.00 −0.471445 −0.235722 − 0.971820i \(-0.575746\pi\)
−0.235722 + 0.971820i \(0.575746\pi\)
\(702\) 0 0
\(703\) −2700.00 −0.144854
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 14146.0 0.749315 0.374657 − 0.927163i \(-0.377760\pi\)
0.374657 + 0.927163i \(0.377760\pi\)
\(710\) 0 0
\(711\) −14720.0 −0.776432
\(712\) 0 0
\(713\) −12960.0 −0.680723
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8080.00 −0.420855
\(718\) 0 0
\(719\) 8460.00 0.438811 0.219405 − 0.975634i \(-0.429588\pi\)
0.219405 + 0.975634i \(0.429588\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −12100.0 −0.622412
\(724\) 0 0
\(725\) 16750.0 0.858041
\(726\) 0 0
\(727\) −27604.0 −1.40822 −0.704110 − 0.710091i \(-0.748654\pi\)
−0.704110 + 0.710091i \(0.748654\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) −4600.00 −0.232746
\(732\) 0 0
\(733\) −13320.0 −0.671194 −0.335597 − 0.942006i \(-0.608938\pi\)
−0.335597 + 0.942006i \(0.608938\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3520.00 0.175931
\(738\) 0 0
\(739\) 19860.0 0.988582 0.494291 − 0.869297i \(-0.335428\pi\)
0.494291 + 0.869297i \(0.335428\pi\)
\(740\) 0 0
\(741\) −400.000 −0.0198305
\(742\) 0 0
\(743\) 19392.0 0.957501 0.478751 − 0.877951i \(-0.341090\pi\)
0.478751 + 0.877951i \(0.341090\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −20286.0 −0.993609
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −24760.0 −1.20307 −0.601535 − 0.798847i \(-0.705444\pi\)
−0.601535 + 0.798847i \(0.705444\pi\)
\(752\) 0 0
\(753\) −12780.0 −0.618498
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −8110.00 −0.389383 −0.194692 − 0.980865i \(-0.562371\pi\)
−0.194692 + 0.980865i \(0.562371\pi\)
\(758\) 0 0
\(759\) 2880.00 0.137730
\(760\) 0 0
\(761\) 10418.0 0.496258 0.248129 − 0.968727i \(-0.420184\pi\)
0.248129 + 0.968727i \(0.420184\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 11400.0 0.536676
\(768\) 0 0
\(769\) 9994.00 0.468651 0.234326 − 0.972158i \(-0.424712\pi\)
0.234326 + 0.972158i \(0.424712\pi\)
\(770\) 0 0
\(771\) 10820.0 0.505412
\(772\) 0 0
\(773\) 9240.00 0.429935 0.214967 − 0.976621i \(-0.431035\pi\)
0.214967 + 0.976621i \(0.431035\pi\)
\(774\) 0 0
\(775\) 22500.0 1.04287
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2500.00 0.114983
\(780\) 0 0
\(781\) −12800.0 −0.586453
\(782\) 0 0
\(783\) −13400.0 −0.611593
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 18434.0 0.834944 0.417472 − 0.908690i \(-0.362916\pi\)
0.417472 + 0.908690i \(0.362916\pi\)
\(788\) 0 0
\(789\) 8224.00 0.371080
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 4000.00 0.179123
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13980.0 0.621326 0.310663 − 0.950520i \(-0.399449\pi\)
0.310663 + 0.950520i \(0.399449\pi\)
\(798\) 0 0
\(799\) −11800.0 −0.522471
\(800\) 0 0
\(801\) 24702.0 1.08964
\(802\) 0 0
\(803\) 5000.00 0.219734
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 5000.00 0.218102
\(808\) 0 0
\(809\) −8554.00 −0.371746 −0.185873 − 0.982574i \(-0.559511\pi\)
−0.185873 + 0.982574i \(0.559511\pi\)
\(810\) 0 0
\(811\) −28910.0 −1.25175 −0.625874 − 0.779924i \(-0.715258\pi\)
−0.625874 + 0.779924i \(0.715258\pi\)
\(812\) 0 0
\(813\) 2720.00 0.117336
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −920.000 −0.0393962
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −38250.0 −1.62599 −0.812993 − 0.582274i \(-0.802163\pi\)
−0.812993 + 0.582274i \(0.802163\pi\)
\(822\) 0 0
\(823\) 23672.0 1.00262 0.501309 − 0.865269i \(-0.332852\pi\)
0.501309 + 0.865269i \(0.332852\pi\)
\(824\) 0 0
\(825\) −5000.00 −0.211003
\(826\) 0 0
\(827\) −23496.0 −0.987952 −0.493976 − 0.869476i \(-0.664457\pi\)
−0.493976 + 0.869476i \(0.664457\pi\)
\(828\) 0 0
\(829\) 9800.00 0.410577 0.205288 − 0.978702i \(-0.434187\pi\)
0.205288 + 0.978702i \(0.434187\pi\)
\(830\) 0 0
\(831\) −3020.00 −0.126068
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −18000.0 −0.743335
\(838\) 0 0
\(839\) −36740.0 −1.51181 −0.755903 − 0.654683i \(-0.772802\pi\)
−0.755903 + 0.654683i \(0.772802\pi\)
\(840\) 0 0
\(841\) −6433.00 −0.263766
\(842\) 0 0
\(843\) −7700.00 −0.314593
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −6836.00 −0.276338
\(850\) 0 0
\(851\) −19440.0 −0.783072
\(852\) 0 0
\(853\) −31500.0 −1.26441 −0.632204 − 0.774802i \(-0.717849\pi\)
−0.632204 + 0.774802i \(0.717849\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 12610.0 0.502625 0.251312 − 0.967906i \(-0.419138\pi\)
0.251312 + 0.967906i \(0.419138\pi\)
\(858\) 0 0
\(859\) 44230.0 1.75682 0.878410 − 0.477908i \(-0.158605\pi\)
0.878410 + 0.477908i \(0.158605\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −21888.0 −0.863356 −0.431678 − 0.902028i \(-0.642078\pi\)
−0.431678 + 0.902028i \(0.642078\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 4826.00 0.189042
\(868\) 0 0
\(869\) −12800.0 −0.499667
\(870\) 0 0
\(871\) −3520.00 −0.136935
\(872\) 0 0
\(873\) 6210.00 0.240752
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 9610.00 0.370019 0.185009 − 0.982737i \(-0.440768\pi\)
0.185009 + 0.982737i \(0.440768\pi\)
\(878\) 0 0
\(879\) 10640.0 0.408280
\(880\) 0 0
\(881\) 37350.0 1.42832 0.714162 − 0.699980i \(-0.246808\pi\)
0.714162 + 0.699980i \(0.246808\pi\)
\(882\) 0 0
\(883\) −27368.0 −1.04304 −0.521521 − 0.853238i \(-0.674635\pi\)
−0.521521 + 0.853238i \(0.674635\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −21684.0 −0.820831 −0.410416 − 0.911899i \(-0.634616\pi\)
−0.410416 + 0.911899i \(0.634616\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −8420.00 −0.316589
\(892\) 0 0
\(893\) −2360.00 −0.0884372
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −2880.00 −0.107202
\(898\) 0 0
\(899\) 24120.0 0.894824
\(900\) 0 0
\(901\) 7500.00 0.277315
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 26744.0 0.979074 0.489537 − 0.871983i \(-0.337166\pi\)
0.489537 + 0.871983i \(0.337166\pi\)
\(908\) 0 0
\(909\) 26496.0 0.966795
\(910\) 0 0
\(911\) 1520.00 0.0552797 0.0276399 − 0.999618i \(-0.491201\pi\)
0.0276399 + 0.999618i \(0.491201\pi\)
\(912\) 0 0
\(913\) −17640.0 −0.639429
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 16520.0 0.592976 0.296488 − 0.955037i \(-0.404185\pi\)
0.296488 + 0.955037i \(0.404185\pi\)
\(920\) 0 0
\(921\) −7412.00 −0.265183
\(922\) 0 0
\(923\) 12800.0 0.456465
\(924\) 0 0
\(925\) 33750.0 1.19967
\(926\) 0 0
\(927\) 3404.00 0.120606
\(928\) 0 0
\(929\) 6850.00 0.241917 0.120959 − 0.992658i \(-0.461403\pi\)
0.120959 + 0.992658i \(0.461403\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −1040.00 −0.0364931
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −21450.0 −0.747856 −0.373928 − 0.927458i \(-0.621989\pi\)
−0.373928 + 0.927458i \(0.621989\pi\)
\(938\) 0 0
\(939\) 15020.0 0.522001
\(940\) 0 0
\(941\) 13672.0 0.473639 0.236820 − 0.971554i \(-0.423895\pi\)
0.236820 + 0.971554i \(0.423895\pi\)
\(942\) 0 0
\(943\) 18000.0 0.621591
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −42436.0 −1.45616 −0.728081 − 0.685492i \(-0.759587\pi\)
−0.728081 + 0.685492i \(0.759587\pi\)
\(948\) 0 0
\(949\) −5000.00 −0.171029
\(950\) 0 0
\(951\) −8780.00 −0.299381
\(952\) 0 0
\(953\) −30310.0 −1.03026 −0.515130 − 0.857112i \(-0.672256\pi\)
−0.515130 + 0.857112i \(0.672256\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −5360.00 −0.181049
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 2609.00 0.0875768
\(962\) 0 0
\(963\) −10488.0 −0.350956
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 25976.0 0.863839 0.431919 − 0.901912i \(-0.357837\pi\)
0.431919 + 0.901912i \(0.357837\pi\)
\(968\) 0 0
\(969\) −1000.00 −0.0331524
\(970\) 0 0
\(971\) −41990.0 −1.38777 −0.693884 − 0.720087i \(-0.744102\pi\)
−0.693884 + 0.720087i \(0.744102\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 5000.00 0.164234
\(976\) 0 0
\(977\) 8730.00 0.285873 0.142936 − 0.989732i \(-0.454346\pi\)
0.142936 + 0.989732i \(0.454346\pi\)
\(978\) 0 0
\(979\) 21480.0 0.701230
\(980\) 0 0
\(981\) −10350.0 −0.336850
\(982\) 0 0
\(983\) −23668.0 −0.767947 −0.383974 − 0.923344i \(-0.625445\pi\)
−0.383974 + 0.923344i \(0.625445\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6624.00 −0.212974
\(990\) 0 0
\(991\) −22600.0 −0.724433 −0.362216 − 0.932094i \(-0.617980\pi\)
−0.362216 + 0.932094i \(0.617980\pi\)
\(992\) 0 0
\(993\) −4520.00 −0.144449
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −25960.0 −0.824635 −0.412318 − 0.911040i \(-0.635281\pi\)
−0.412318 + 0.911040i \(0.635281\pi\)
\(998\) 0 0
\(999\) −27000.0 −0.855097
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 1568.4.a.e.1.1 1
4.3 odd 2 1568.4.a.k.1.1 1
7.6 odd 2 224.4.a.b.1.1 yes 1
21.20 even 2 2016.4.a.c.1.1 1
28.27 even 2 224.4.a.a.1.1 ✓ 1
56.13 odd 2 448.4.a.f.1.1 1
56.27 even 2 448.4.a.j.1.1 1
84.83 odd 2 2016.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.4.a.a.1.1 ✓ 1 28.27 even 2
224.4.a.b.1.1 yes 1 7.6 odd 2
448.4.a.f.1.1 1 56.13 odd 2
448.4.a.j.1.1 1 56.27 even 2
1568.4.a.e.1.1 1 1.1 even 1 trivial
1568.4.a.k.1.1 1 4.3 odd 2
2016.4.a.c.1.1 1 21.20 even 2
2016.4.a.d.1.1 1 84.83 odd 2