↑

Properties

Label 1600.4.a.k.1.1
Level $1600$
Weight $4$
Character 1600.1
Self dual yes
Analytic conductor $94.403$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1600,4,Mod(1,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, 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("1600.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1600.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: \(94.4030560092\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 800)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{3} -10.0000 q^{7} -2.00000 q^{9} -15.0000 q^{11} -8.00000 q^{13} -21.0000 q^{17} +105.000 q^{19} +50.0000 q^{21} -10.0000 q^{23} +145.000 q^{27} +20.0000 q^{29} +230.000 q^{31} +75.0000 q^{33} +54.0000 q^{37} +40.0000 q^{39} -195.000 q^{41} +300.000 q^{43} -480.000 q^{47} -243.000 q^{49} +105.000 q^{51} -322.000 q^{53} -525.000 q^{57} +560.000 q^{59} +730.000 q^{61} +20.0000 q^{63} -255.000 q^{67} +50.0000 q^{69} +40.0000 q^{71} +317.000 q^{73} +150.000 q^{77} +830.000 q^{79} -671.000 q^{81} -75.0000 q^{83} -100.000 q^{87} -705.000 q^{89} +80.0000 q^{91} -1150.00 q^{93} -1434.00 q^{97} +30.0000 q^{99} +O(q^{100})\)

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
\(3\) −5.00000 −0.962250 −0.481125 − 0.876652i \(-0.659772\pi\)
−0.481125 + 0.876652i \(0.659772\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −10.0000 −0.539949 −0.269975 − 0.962867i \(-0.587015\pi\)
−0.269975 + 0.962867i \(0.587015\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.0740741
\(10\) 0 0
\(11\) −15.0000 −0.411152 −0.205576 − 0.978641i \(-0.565907\pi\)
−0.205576 + 0.978641i \(0.565907\pi\)
\(12\) 0 0
\(13\) −8.00000 −0.170677 −0.0853385 − 0.996352i \(-0.527197\pi\)
−0.0853385 + 0.996352i \(0.527197\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −21.0000 −0.299603 −0.149801 − 0.988716i \(-0.547863\pi\)
−0.149801 + 0.988716i \(0.547863\pi\)
\(18\) 0 0
\(19\) 105.000 1.26782 0.633912 − 0.773405i \(-0.281448\pi\)
0.633912 + 0.773405i \(0.281448\pi\)
\(20\) 0 0
\(21\) 50.0000 0.519566
\(22\) 0 0
\(23\) −10.0000 −0.0906584 −0.0453292 − 0.998972i \(-0.514434\pi\)
−0.0453292 + 0.998972i \(0.514434\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 145.000 1.03353
\(28\) 0 0
\(29\) 20.0000 0.128066 0.0640329 − 0.997948i \(-0.479604\pi\)
0.0640329 + 0.997948i \(0.479604\pi\)
\(30\) 0 0
\(31\) 230.000 1.33256 0.666278 − 0.745704i \(-0.267887\pi\)
0.666278 + 0.745704i \(0.267887\pi\)
\(32\) 0 0
\(33\) 75.0000 0.395631
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 54.0000 0.239934 0.119967 − 0.992778i \(-0.461721\pi\)
0.119967 + 0.992778i \(0.461721\pi\)
\(38\) 0 0
\(39\) 40.0000 0.164234
\(40\) 0 0
\(41\) −195.000 −0.742778 −0.371389 − 0.928477i \(-0.621118\pi\)
−0.371389 + 0.928477i \(0.621118\pi\)
\(42\) 0 0
\(43\) 300.000 1.06394 0.531972 − 0.846762i \(-0.321451\pi\)
0.531972 + 0.846762i \(0.321451\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −480.000 −1.48969 −0.744843 − 0.667240i \(-0.767475\pi\)
−0.744843 + 0.667240i \(0.767475\pi\)
\(48\) 0 0
\(49\) −243.000 −0.708455
\(50\) 0 0
\(51\) 105.000 0.288293
\(52\) 0 0
\(53\) −322.000 −0.834530 −0.417265 − 0.908785i \(-0.637011\pi\)
−0.417265 + 0.908785i \(0.637011\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −525.000 −1.21996
\(58\) 0 0
\(59\) 560.000 1.23569 0.617846 − 0.786299i \(-0.288006\pi\)
0.617846 + 0.786299i \(0.288006\pi\)
\(60\) 0 0
\(61\) 730.000 1.53224 0.766122 − 0.642695i \(-0.222184\pi\)
0.766122 + 0.642695i \(0.222184\pi\)
\(62\) 0 0
\(63\) 20.0000 0.0399962
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −255.000 −0.464973 −0.232487 − 0.972600i \(-0.574686\pi\)
−0.232487 + 0.972600i \(0.574686\pi\)
\(68\) 0 0
\(69\) 50.0000 0.0872361
\(70\) 0 0
\(71\) 40.0000 0.0668609 0.0334305 − 0.999441i \(-0.489357\pi\)
0.0334305 + 0.999441i \(0.489357\pi\)
\(72\) 0 0
\(73\) 317.000 0.508247 0.254124 − 0.967172i \(-0.418213\pi\)
0.254124 + 0.967172i \(0.418213\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 150.000 0.222001
\(78\) 0 0
\(79\) 830.000 1.18205 0.591027 − 0.806652i \(-0.298723\pi\)
0.591027 + 0.806652i \(0.298723\pi\)
\(80\) 0 0
\(81\) −671.000 −0.920439
\(82\) 0 0
\(83\) −75.0000 −0.0991846 −0.0495923 − 0.998770i \(-0.515792\pi\)
−0.0495923 + 0.998770i \(0.515792\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −100.000 −0.123231
\(88\) 0 0
\(89\) −705.000 −0.839661 −0.419831 − 0.907602i \(-0.637911\pi\)
−0.419831 + 0.907602i \(0.637911\pi\)
\(90\) 0 0
\(91\) 80.0000 0.0921569
\(92\) 0 0
\(93\) −1150.00 −1.28225
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1434.00 −1.50104 −0.750519 − 0.660849i \(-0.770196\pi\)
−0.750519 + 0.660849i \(0.770196\pi\)
\(98\) 0 0
\(99\) 30.0000 0.0304557
\(100\) 0 0
\(101\) 1902.00 1.87382 0.936911 − 0.349567i \(-0.113671\pi\)
0.936911 + 0.349567i \(0.113671\pi\)
\(102\) 0 0
\(103\) 1480.00 1.41581 0.707906 − 0.706306i \(-0.249640\pi\)
0.707906 + 0.706306i \(0.249640\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1945.00 −1.75729 −0.878646 − 0.477474i \(-0.841553\pi\)
−0.878646 + 0.477474i \(0.841553\pi\)
\(108\) 0 0
\(109\) 246.000 0.216170 0.108085 − 0.994142i \(-0.465528\pi\)
0.108085 + 0.994142i \(0.465528\pi\)
\(110\) 0 0
\(111\) −270.000 −0.230876
\(112\) 0 0
\(113\) 753.000 0.626870 0.313435 − 0.949610i \(-0.398520\pi\)
0.313435 + 0.949610i \(0.398520\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 16.0000 0.0126427
\(118\) 0 0
\(119\) 210.000 0.161770
\(120\) 0 0
\(121\) −1106.00 −0.830954
\(122\) 0 0
\(123\) 975.000 0.714738
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1490.00 1.04107 0.520536 − 0.853840i \(-0.325732\pi\)
0.520536 + 0.853840i \(0.325732\pi\)
\(128\) 0 0
\(129\) −1500.00 −1.02378
\(130\) 0 0
\(131\) 780.000 0.520221 0.260110 − 0.965579i \(-0.416241\pi\)
0.260110 + 0.965579i \(0.416241\pi\)
\(132\) 0 0
\(133\) −1050.00 −0.684561
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2749.00 −1.71433 −0.857164 − 0.515044i \(-0.827776\pi\)
−0.857164 + 0.515044i \(0.827776\pi\)
\(138\) 0 0
\(139\) −735.000 −0.448503 −0.224251 − 0.974531i \(-0.571994\pi\)
−0.224251 + 0.974531i \(0.571994\pi\)
\(140\) 0 0
\(141\) 2400.00 1.43345
\(142\) 0 0
\(143\) 120.000 0.0701742
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 1215.00 0.681711
\(148\) 0 0
\(149\) −836.000 −0.459650 −0.229825 − 0.973232i \(-0.573815\pi\)
−0.229825 + 0.973232i \(0.573815\pi\)
\(150\) 0 0
\(151\) −1790.00 −0.964690 −0.482345 − 0.875981i \(-0.660215\pi\)
−0.482345 + 0.875981i \(0.660215\pi\)
\(152\) 0 0
\(153\) 42.0000 0.0221928
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1374.00 −0.698453 −0.349227 − 0.937038i \(-0.613556\pi\)
−0.349227 + 0.937038i \(0.613556\pi\)
\(158\) 0 0
\(159\) 1610.00 0.803027
\(160\) 0 0
\(161\) 100.000 0.0489510
\(162\) 0 0
\(163\) −1895.00 −0.910600 −0.455300 − 0.890338i \(-0.650468\pi\)
−0.455300 + 0.890338i \(0.650468\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −720.000 −0.333624 −0.166812 − 0.985989i \(-0.553347\pi\)
−0.166812 + 0.985989i \(0.553347\pi\)
\(168\) 0 0
\(169\) −2133.00 −0.970869
\(170\) 0 0
\(171\) −210.000 −0.0939129
\(172\) 0 0
\(173\) −2512.00 −1.10395 −0.551976 − 0.833860i \(-0.686126\pi\)
−0.551976 + 0.833860i \(0.686126\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2800.00 −1.18904
\(178\) 0 0
\(179\) 165.000 0.0688976 0.0344488 − 0.999406i \(-0.489032\pi\)
0.0344488 + 0.999406i \(0.489032\pi\)
\(180\) 0 0
\(181\) 3158.00 1.29686 0.648432 − 0.761273i \(-0.275425\pi\)
0.648432 + 0.761273i \(0.275425\pi\)
\(182\) 0 0
\(183\) −3650.00 −1.47440
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 315.000 0.123182
\(188\) 0 0
\(189\) −1450.00 −0.558053
\(190\) 0 0
\(191\) 3290.00 1.24637 0.623183 − 0.782076i \(-0.285839\pi\)
0.623183 + 0.782076i \(0.285839\pi\)
\(192\) 0 0
\(193\) −197.000 −0.0734734 −0.0367367 − 0.999325i \(-0.511696\pi\)
−0.0367367 + 0.999325i \(0.511696\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1746.00 −0.631459 −0.315729 − 0.948849i \(-0.602249\pi\)
−0.315729 + 0.948849i \(0.602249\pi\)
\(198\) 0 0
\(199\) −4660.00 −1.65999 −0.829997 − 0.557768i \(-0.811658\pi\)
−0.829997 + 0.557768i \(0.811658\pi\)
\(200\) 0 0
\(201\) 1275.00 0.447421
\(202\) 0 0
\(203\) −200.000 −0.0691490
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 20.0000 0.00671544
\(208\) 0 0
\(209\) −1575.00 −0.521268
\(210\) 0 0
\(211\) −265.000 −0.0864614 −0.0432307 − 0.999065i \(-0.513765\pi\)
−0.0432307 + 0.999065i \(0.513765\pi\)
\(212\) 0 0
\(213\) −200.000 −0.0643370
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2300.00 −0.719512
\(218\) 0 0
\(219\) −1585.00 −0.489061
\(220\) 0 0
\(221\) 168.000 0.0511353
\(222\) 0 0
\(223\) −1060.00 −0.318309 −0.159154 − 0.987254i \(-0.550877\pi\)
−0.159154 + 0.987254i \(0.550877\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4660.00 1.36253 0.681267 − 0.732035i \(-0.261429\pi\)
0.681267 + 0.732035i \(0.261429\pi\)
\(228\) 0 0
\(229\) −1660.00 −0.479021 −0.239511 − 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(230\) 0 0
\(231\) −750.000 −0.213621
\(232\) 0 0
\(233\) −3462.00 −0.973404 −0.486702 − 0.873568i \(-0.661800\pi\)
−0.486702 + 0.873568i \(0.661800\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4150.00 −1.13743
\(238\) 0 0
\(239\) −4020.00 −1.08800 −0.544000 − 0.839085i \(-0.683091\pi\)
−0.544000 + 0.839085i \(0.683091\pi\)
\(240\) 0 0
\(241\) 3985.00 1.06513 0.532565 − 0.846389i \(-0.321228\pi\)
0.532565 + 0.846389i \(0.321228\pi\)
\(242\) 0 0
\(243\) −560.000 −0.147835
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −840.000 −0.216388
\(248\) 0 0
\(249\) 375.000 0.0954404
\(250\) 0 0
\(251\) −6625.00 −1.66600 −0.833001 − 0.553272i \(-0.813379\pi\)
−0.833001 + 0.553272i \(0.813379\pi\)
\(252\) 0 0
\(253\) 150.000 0.0372744
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2246.00 −0.545143 −0.272571 − 0.962136i \(-0.587874\pi\)
−0.272571 + 0.962136i \(0.587874\pi\)
\(258\) 0 0
\(259\) −540.000 −0.129552
\(260\) 0 0
\(261\) −40.0000 −0.00948635
\(262\) 0 0
\(263\) 3950.00 0.926112 0.463056 − 0.886329i \(-0.346753\pi\)
0.463056 + 0.886329i \(0.346753\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3525.00 0.807964
\(268\) 0 0
\(269\) −2656.00 −0.602004 −0.301002 − 0.953623i \(-0.597321\pi\)
−0.301002 + 0.953623i \(0.597321\pi\)
\(270\) 0 0
\(271\) 3110.00 0.697118 0.348559 − 0.937287i \(-0.386671\pi\)
0.348559 + 0.937287i \(0.386671\pi\)
\(272\) 0 0
\(273\) −400.000 −0.0886780
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −6884.00 −1.49321 −0.746606 − 0.665267i \(-0.768318\pi\)
−0.746606 + 0.665267i \(0.768318\pi\)
\(278\) 0 0
\(279\) −460.000 −0.0987078
\(280\) 0 0
\(281\) 4630.00 0.982928 0.491464 − 0.870898i \(-0.336462\pi\)
0.491464 + 0.870898i \(0.336462\pi\)
\(282\) 0 0
\(283\) −215.000 −0.0451605 −0.0225803 − 0.999745i \(-0.507188\pi\)
−0.0225803 + 0.999745i \(0.507188\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1950.00 0.401062
\(288\) 0 0
\(289\) −4472.00 −0.910238
\(290\) 0 0
\(291\) 7170.00 1.44437
\(292\) 0 0
\(293\) 1602.00 0.319419 0.159710 − 0.987164i \(-0.448944\pi\)
0.159710 + 0.987164i \(0.448944\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2175.00 −0.424937
\(298\) 0 0
\(299\) 80.0000 0.0154733
\(300\) 0 0
\(301\) −3000.00 −0.574475
\(302\) 0 0
\(303\) −9510.00 −1.80309
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1885.00 −0.350432 −0.175216 − 0.984530i \(-0.556062\pi\)
−0.175216 + 0.984530i \(0.556062\pi\)
\(308\) 0 0
\(309\) −7400.00 −1.36237
\(310\) 0 0
\(311\) −9250.00 −1.68656 −0.843279 − 0.537476i \(-0.819378\pi\)
−0.843279 + 0.537476i \(0.819378\pi\)
\(312\) 0 0
\(313\) −8162.00 −1.47394 −0.736970 − 0.675925i \(-0.763744\pi\)
−0.736970 + 0.675925i \(0.763744\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6924.00 −1.22678 −0.613392 − 0.789779i \(-0.710195\pi\)
−0.613392 + 0.789779i \(0.710195\pi\)
\(318\) 0 0
\(319\) −300.000 −0.0526545
\(320\) 0 0
\(321\) 9725.00 1.69096
\(322\) 0 0
\(323\) −2205.00 −0.379844
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1230.00 −0.208010
\(328\) 0 0
\(329\) 4800.00 0.804354
\(330\) 0 0
\(331\) −8075.00 −1.34091 −0.670456 − 0.741949i \(-0.733902\pi\)
−0.670456 + 0.741949i \(0.733902\pi\)
\(332\) 0 0
\(333\) −108.000 −0.0177729
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 4741.00 0.766346 0.383173 − 0.923677i \(-0.374831\pi\)
0.383173 + 0.923677i \(0.374831\pi\)
\(338\) 0 0
\(339\) −3765.00 −0.603206
\(340\) 0 0
\(341\) −3450.00 −0.547883
\(342\) 0 0
\(343\) 5860.00 0.922479
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8705.00 −1.34671 −0.673356 − 0.739319i \(-0.735148\pi\)
−0.673356 + 0.739319i \(0.735148\pi\)
\(348\) 0 0
\(349\) 1470.00 0.225465 0.112733 − 0.993625i \(-0.464040\pi\)
0.112733 + 0.993625i \(0.464040\pi\)
\(350\) 0 0
\(351\) −1160.00 −0.176399
\(352\) 0 0
\(353\) −1998.00 −0.301254 −0.150627 − 0.988591i \(-0.548129\pi\)
−0.150627 + 0.988591i \(0.548129\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1050.00 −0.155664
\(358\) 0 0
\(359\) 8190.00 1.20404 0.602022 − 0.798480i \(-0.294362\pi\)
0.602022 + 0.798480i \(0.294362\pi\)
\(360\) 0 0
\(361\) 4166.00 0.607377
\(362\) 0 0
\(363\) 5530.00 0.799586
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 5340.00 0.759525 0.379763 − 0.925084i \(-0.376006\pi\)
0.379763 + 0.925084i \(0.376006\pi\)
\(368\) 0 0
\(369\) 390.000 0.0550206
\(370\) 0 0
\(371\) 3220.00 0.450604
\(372\) 0 0
\(373\) 9378.00 1.30181 0.650904 − 0.759160i \(-0.274390\pi\)
0.650904 + 0.759160i \(0.274390\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −160.000 −0.0218579
\(378\) 0 0
\(379\) −4045.00 −0.548226 −0.274113 − 0.961697i \(-0.588384\pi\)
−0.274113 + 0.961697i \(0.588384\pi\)
\(380\) 0 0
\(381\) −7450.00 −1.00177
\(382\) 0 0
\(383\) 8090.00 1.07932 0.539660 − 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −600.000 −0.0788106
\(388\) 0 0
\(389\) −6574.00 −0.856851 −0.428425 − 0.903577i \(-0.640932\pi\)
−0.428425 + 0.903577i \(0.640932\pi\)
\(390\) 0 0
\(391\) 210.000 0.0271615
\(392\) 0 0
\(393\) −3900.00 −0.500583
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7036.00 −0.889488 −0.444744 − 0.895658i \(-0.646705\pi\)
−0.444744 + 0.895658i \(0.646705\pi\)
\(398\) 0 0
\(399\) 5250.00 0.658719
\(400\) 0 0
\(401\) 8277.00 1.03076 0.515379 − 0.856963i \(-0.327651\pi\)
0.515379 + 0.856963i \(0.327651\pi\)
\(402\) 0 0
\(403\) −1840.00 −0.227437
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −810.000 −0.0986492
\(408\) 0 0
\(409\) −2179.00 −0.263434 −0.131717 − 0.991287i \(-0.542049\pi\)
−0.131717 + 0.991287i \(0.542049\pi\)
\(410\) 0 0
\(411\) 13745.0 1.64961
\(412\) 0 0
\(413\) −5600.00 −0.667211
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 3675.00 0.431572
\(418\) 0 0
\(419\) 12245.0 1.42770 0.713851 − 0.700297i \(-0.246949\pi\)
0.713851 + 0.700297i \(0.246949\pi\)
\(420\) 0 0
\(421\) 660.000 0.0764048 0.0382024 − 0.999270i \(-0.487837\pi\)
0.0382024 + 0.999270i \(0.487837\pi\)
\(422\) 0 0
\(423\) 960.000 0.110347
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −7300.00 −0.827334
\(428\) 0 0
\(429\) −600.000 −0.0675251
\(430\) 0 0
\(431\) 7470.00 0.834843 0.417421 − 0.908713i \(-0.362934\pi\)
0.417421 + 0.908713i \(0.362934\pi\)
\(432\) 0 0
\(433\) −1173.00 −0.130187 −0.0650933 − 0.997879i \(-0.520734\pi\)
−0.0650933 + 0.997879i \(0.520734\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1050.00 −0.114939
\(438\) 0 0
\(439\) −5660.00 −0.615346 −0.307673 − 0.951492i \(-0.599550\pi\)
−0.307673 + 0.951492i \(0.599550\pi\)
\(440\) 0 0
\(441\) 486.000 0.0524781
\(442\) 0 0
\(443\) −1115.00 −0.119583 −0.0597915 − 0.998211i \(-0.519044\pi\)
−0.0597915 + 0.998211i \(0.519044\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4180.00 0.442298
\(448\) 0 0
\(449\) 4089.00 0.429781 0.214891 − 0.976638i \(-0.431060\pi\)
0.214891 + 0.976638i \(0.431060\pi\)
\(450\) 0 0
\(451\) 2925.00 0.305394
\(452\) 0 0
\(453\) 8950.00 0.928273
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4519.00 0.462560 0.231280 − 0.972887i \(-0.425709\pi\)
0.231280 + 0.972887i \(0.425709\pi\)
\(458\) 0 0
\(459\) −3045.00 −0.309648
\(460\) 0 0
\(461\) −10068.0 −1.01717 −0.508583 − 0.861013i \(-0.669830\pi\)
−0.508583 + 0.861013i \(0.669830\pi\)
\(462\) 0 0
\(463\) 1460.00 0.146548 0.0732742 − 0.997312i \(-0.476655\pi\)
0.0732742 + 0.997312i \(0.476655\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4740.00 −0.469681 −0.234841 − 0.972034i \(-0.575457\pi\)
−0.234841 + 0.972034i \(0.575457\pi\)
\(468\) 0 0
\(469\) 2550.00 0.251062
\(470\) 0 0
\(471\) 6870.00 0.672087
\(472\) 0 0
\(473\) −4500.00 −0.437442
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 644.000 0.0618171
\(478\) 0 0
\(479\) 8610.00 0.821296 0.410648 − 0.911794i \(-0.365302\pi\)
0.410648 + 0.911794i \(0.365302\pi\)
\(480\) 0 0
\(481\) −432.000 −0.0409512
\(482\) 0 0
\(483\) −500.000 −0.0471031
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −17710.0 −1.64788 −0.823939 − 0.566678i \(-0.808228\pi\)
−0.823939 + 0.566678i \(0.808228\pi\)
\(488\) 0 0
\(489\) 9475.00 0.876226
\(490\) 0 0
\(491\) −8660.00 −0.795968 −0.397984 − 0.917392i \(-0.630290\pi\)
−0.397984 + 0.917392i \(0.630290\pi\)
\(492\) 0 0
\(493\) −420.000 −0.0383689
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −400.000 −0.0361015
\(498\) 0 0
\(499\) 17300.0 1.55201 0.776006 − 0.630725i \(-0.217242\pi\)
0.776006 + 0.630725i \(0.217242\pi\)
\(500\) 0 0
\(501\) 3600.00 0.321030
\(502\) 0 0
\(503\) 1860.00 0.164877 0.0824387 − 0.996596i \(-0.473729\pi\)
0.0824387 + 0.996596i \(0.473729\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 10665.0 0.934219
\(508\) 0 0
\(509\) 5870.00 0.511165 0.255583 − 0.966787i \(-0.417733\pi\)
0.255583 + 0.966787i \(0.417733\pi\)
\(510\) 0 0
\(511\) −3170.00 −0.274428
\(512\) 0 0
\(513\) 15225.0 1.31033
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7200.00 0.612487
\(518\) 0 0
\(519\) 12560.0 1.06228
\(520\) 0 0
\(521\) −12187.0 −1.02480 −0.512401 − 0.858746i \(-0.671244\pi\)
−0.512401 + 0.858746i \(0.671244\pi\)
\(522\) 0 0
\(523\) 5315.00 0.444376 0.222188 − 0.975004i \(-0.428680\pi\)
0.222188 + 0.975004i \(0.428680\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4830.00 −0.399237
\(528\) 0 0
\(529\) −12067.0 −0.991781
\(530\) 0 0
\(531\) −1120.00 −0.0915327
\(532\) 0 0
\(533\) 1560.00 0.126775
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −825.000 −0.0662968
\(538\) 0 0
\(539\) 3645.00 0.291282
\(540\) 0 0
\(541\) 1672.00 0.132874 0.0664371 − 0.997791i \(-0.478837\pi\)
0.0664371 + 0.997791i \(0.478837\pi\)
\(542\) 0 0
\(543\) −15790.0 −1.24791
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 10595.0 0.828171 0.414085 − 0.910238i \(-0.364101\pi\)
0.414085 + 0.910238i \(0.364101\pi\)
\(548\) 0 0
\(549\) −1460.00 −0.113500
\(550\) 0 0
\(551\) 2100.00 0.162365
\(552\) 0 0
\(553\) −8300.00 −0.638249
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15264.0 1.16114 0.580571 − 0.814209i \(-0.302829\pi\)
0.580571 + 0.814209i \(0.302829\pi\)
\(558\) 0 0
\(559\) −2400.00 −0.181591
\(560\) 0 0
\(561\) −1575.00 −0.118532
\(562\) 0 0
\(563\) 15400.0 1.15281 0.576406 − 0.817164i \(-0.304455\pi\)
0.576406 + 0.817164i \(0.304455\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6710.00 0.496990
\(568\) 0 0
\(569\) 14569.0 1.07340 0.536700 − 0.843773i \(-0.319671\pi\)
0.536700 + 0.843773i \(0.319671\pi\)
\(570\) 0 0
\(571\) −7780.00 −0.570198 −0.285099 − 0.958498i \(-0.592026\pi\)
−0.285099 + 0.958498i \(0.592026\pi\)
\(572\) 0 0
\(573\) −16450.0 −1.19932
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19829.0 1.43066 0.715331 − 0.698786i \(-0.246276\pi\)
0.715331 + 0.698786i \(0.246276\pi\)
\(578\) 0 0
\(579\) 985.000 0.0706998
\(580\) 0 0
\(581\) 750.000 0.0535546
\(582\) 0 0
\(583\) 4830.00 0.343119
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −795.000 −0.0558998 −0.0279499 − 0.999609i \(-0.508898\pi\)
−0.0279499 + 0.999609i \(0.508898\pi\)
\(588\) 0 0
\(589\) 24150.0 1.68945
\(590\) 0 0
\(591\) 8730.00 0.607621
\(592\) 0 0
\(593\) 21457.0 1.48589 0.742946 − 0.669352i \(-0.233428\pi\)
0.742946 + 0.669352i \(0.233428\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 23300.0 1.59733
\(598\) 0 0
\(599\) −26570.0 −1.81239 −0.906194 − 0.422862i \(-0.861026\pi\)
−0.906194 + 0.422862i \(0.861026\pi\)
\(600\) 0 0
\(601\) −25245.0 −1.71342 −0.856710 − 0.515799i \(-0.827495\pi\)
−0.856710 + 0.515799i \(0.827495\pi\)
\(602\) 0 0
\(603\) 510.000 0.0344425
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −14040.0 −0.938824 −0.469412 − 0.882979i \(-0.655534\pi\)
−0.469412 + 0.882979i \(0.655534\pi\)
\(608\) 0 0
\(609\) 1000.00 0.0665387
\(610\) 0 0
\(611\) 3840.00 0.254255
\(612\) 0 0
\(613\) 19502.0 1.28496 0.642478 − 0.766304i \(-0.277906\pi\)
0.642478 + 0.766304i \(0.277906\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6286.00 −0.410154 −0.205077 − 0.978746i \(-0.565744\pi\)
−0.205077 + 0.978746i \(0.565744\pi\)
\(618\) 0 0
\(619\) 2420.00 0.157137 0.0785687 − 0.996909i \(-0.474965\pi\)
0.0785687 + 0.996909i \(0.474965\pi\)
\(620\) 0 0
\(621\) −1450.00 −0.0936981
\(622\) 0 0
\(623\) 7050.00 0.453374
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 7875.00 0.501590
\(628\) 0 0
\(629\) −1134.00 −0.0718848
\(630\) 0 0
\(631\) −2290.00 −0.144475 −0.0722373 − 0.997387i \(-0.523014\pi\)
−0.0722373 + 0.997387i \(0.523014\pi\)
\(632\) 0 0
\(633\) 1325.00 0.0831975
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1944.00 0.120917
\(638\) 0 0
\(639\) −80.0000 −0.00495266
\(640\) 0 0
\(641\) −15150.0 −0.933524 −0.466762 − 0.884383i \(-0.654580\pi\)
−0.466762 + 0.884383i \(0.654580\pi\)
\(642\) 0 0
\(643\) −7860.00 −0.482066 −0.241033 − 0.970517i \(-0.577486\pi\)
−0.241033 + 0.970517i \(0.577486\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2420.00 −0.147048 −0.0735240 − 0.997293i \(-0.523425\pi\)
−0.0735240 + 0.997293i \(0.523425\pi\)
\(648\) 0 0
\(649\) −8400.00 −0.508057
\(650\) 0 0
\(651\) 11500.0 0.692351
\(652\) 0 0
\(653\) −20462.0 −1.22625 −0.613124 − 0.789987i \(-0.710087\pi\)
−0.613124 + 0.789987i \(0.710087\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −634.000 −0.0376479
\(658\) 0 0
\(659\) −32205.0 −1.90369 −0.951843 − 0.306587i \(-0.900813\pi\)
−0.951843 + 0.306587i \(0.900813\pi\)
\(660\) 0 0
\(661\) 27100.0 1.59466 0.797328 − 0.603546i \(-0.206246\pi\)
0.797328 + 0.603546i \(0.206246\pi\)
\(662\) 0 0
\(663\) −840.000 −0.0492050
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −200.000 −0.0116102
\(668\) 0 0
\(669\) 5300.00 0.306293
\(670\) 0 0
\(671\) −10950.0 −0.629985
\(672\) 0 0
\(673\) 24182.0 1.38506 0.692532 − 0.721387i \(-0.256495\pi\)
0.692532 + 0.721387i \(0.256495\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 25704.0 1.45921 0.729605 − 0.683869i \(-0.239704\pi\)
0.729605 + 0.683869i \(0.239704\pi\)
\(678\) 0 0
\(679\) 14340.0 0.810484
\(680\) 0 0
\(681\) −23300.0 −1.31110
\(682\) 0 0
\(683\) −6525.00 −0.365552 −0.182776 − 0.983155i \(-0.558508\pi\)
−0.182776 + 0.983155i \(0.558508\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 8300.00 0.460939
\(688\) 0 0
\(689\) 2576.00 0.142435
\(690\) 0 0
\(691\) −28955.0 −1.59407 −0.797033 − 0.603935i \(-0.793599\pi\)
−0.797033 + 0.603935i \(0.793599\pi\)
\(692\) 0 0
\(693\) −300.000 −0.0164445
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 4095.00 0.222538
\(698\) 0 0
\(699\) 17310.0 0.936659
\(700\) 0 0
\(701\) −9720.00 −0.523708 −0.261854 − 0.965107i \(-0.584334\pi\)
−0.261854 + 0.965107i \(0.584334\pi\)
\(702\) 0 0
\(703\) 5670.00 0.304194
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −19020.0 −1.01177
\(708\) 0 0
\(709\) 25140.0 1.33167 0.665834 − 0.746100i \(-0.268076\pi\)
0.665834 + 0.746100i \(0.268076\pi\)
\(710\) 0 0
\(711\) −1660.00 −0.0875596
\(712\) 0 0
\(713\) −2300.00 −0.120807
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 20100.0 1.04693
\(718\) 0 0
\(719\) −30030.0 −1.55762 −0.778811 − 0.627259i \(-0.784177\pi\)
−0.778811 + 0.627259i \(0.784177\pi\)
\(720\) 0 0
\(721\) −14800.0 −0.764467
\(722\) 0 0
\(723\) −19925.0 −1.02492
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 36100.0 1.84164 0.920822 − 0.389984i \(-0.127519\pi\)
0.920822 + 0.389984i \(0.127519\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 0 0
\(731\) −6300.00 −0.318760
\(732\) 0 0
\(733\) 5368.00 0.270493 0.135247 − 0.990812i \(-0.456817\pi\)
0.135247 + 0.990812i \(0.456817\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3825.00 0.191175
\(738\) 0 0
\(739\) −25540.0 −1.27132 −0.635659 − 0.771970i \(-0.719272\pi\)
−0.635659 + 0.771970i \(0.719272\pi\)
\(740\) 0 0
\(741\) 4200.00 0.208220
\(742\) 0 0
\(743\) −18730.0 −0.924814 −0.462407 − 0.886668i \(-0.653014\pi\)
−0.462407 + 0.886668i \(0.653014\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 150.000 0.00734701
\(748\) 0 0
\(749\) 19450.0 0.948849
\(750\) 0 0
\(751\) −29940.0 −1.45476 −0.727381 − 0.686234i \(-0.759263\pi\)
−0.727381 + 0.686234i \(0.759263\pi\)
\(752\) 0 0
\(753\) 33125.0 1.60311
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 16216.0 0.778574 0.389287 − 0.921117i \(-0.372721\pi\)
0.389287 + 0.921117i \(0.372721\pi\)
\(758\) 0 0
\(759\) −750.000 −0.0358673
\(760\) 0 0
\(761\) −25843.0 −1.23102 −0.615511 − 0.788128i \(-0.711050\pi\)
−0.615511 + 0.788128i \(0.711050\pi\)
\(762\) 0 0
\(763\) −2460.00 −0.116721
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4480.00 −0.210904
\(768\) 0 0
\(769\) −27475.0 −1.28839 −0.644196 − 0.764860i \(-0.722808\pi\)
−0.644196 + 0.764860i \(0.722808\pi\)
\(770\) 0 0
\(771\) 11230.0 0.524564
\(772\) 0 0
\(773\) −3948.00 −0.183699 −0.0918497 − 0.995773i \(-0.529278\pi\)
−0.0918497 + 0.995773i \(0.529278\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2700.00 0.124661
\(778\) 0 0
\(779\) −20475.0 −0.941711
\(780\) 0 0
\(781\) −600.000 −0.0274900
\(782\) 0 0
\(783\) 2900.00 0.132360
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −22100.0 −1.00099 −0.500496 − 0.865739i \(-0.666849\pi\)
−0.500496 + 0.865739i \(0.666849\pi\)
\(788\) 0 0
\(789\) −19750.0 −0.891152
\(790\) 0 0
\(791\) −7530.00 −0.338478
\(792\) 0 0
\(793\) −5840.00 −0.261519
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16026.0 0.712259 0.356129 − 0.934437i \(-0.384096\pi\)
0.356129 + 0.934437i \(0.384096\pi\)
\(798\) 0 0
\(799\) 10080.0 0.446314
\(800\) 0 0
\(801\) 1410.00 0.0621971
\(802\) 0 0
\(803\) −4755.00 −0.208967
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 13280.0 0.579279
\(808\) 0 0
\(809\) 35770.0 1.55452 0.777260 − 0.629180i \(-0.216609\pi\)
0.777260 + 0.629180i \(0.216609\pi\)
\(810\) 0 0
\(811\) 30620.0 1.32579 0.662894 − 0.748714i \(-0.269328\pi\)
0.662894 + 0.748714i \(0.269328\pi\)
\(812\) 0 0
\(813\) −15550.0 −0.670802
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 31500.0 1.34889
\(818\) 0 0
\(819\) −160.000 −0.00682644
\(820\) 0 0
\(821\) 9150.00 0.388961 0.194481 − 0.980906i \(-0.437698\pi\)
0.194481 + 0.980906i \(0.437698\pi\)
\(822\) 0 0
\(823\) −28940.0 −1.22574 −0.612871 − 0.790183i \(-0.709985\pi\)
−0.612871 + 0.790183i \(0.709985\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25765.0 1.08336 0.541679 − 0.840586i \(-0.317789\pi\)
0.541679 + 0.840586i \(0.317789\pi\)
\(828\) 0 0
\(829\) 41584.0 1.74219 0.871093 − 0.491118i \(-0.163412\pi\)
0.871093 + 0.491118i \(0.163412\pi\)
\(830\) 0 0
\(831\) 34420.0 1.43684
\(832\) 0 0
\(833\) 5103.00 0.212255
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 33350.0 1.37723
\(838\) 0 0
\(839\) 20320.0 0.836143 0.418072 − 0.908414i \(-0.362706\pi\)
0.418072 + 0.908414i \(0.362706\pi\)
\(840\) 0 0
\(841\) −23989.0 −0.983599
\(842\) 0 0
\(843\) −23150.0 −0.945822
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 11060.0 0.448673
\(848\) 0 0
\(849\) 1075.00 0.0434557
\(850\) 0 0
\(851\) −540.000 −0.0217520
\(852\) 0 0
\(853\) 38882.0 1.56072 0.780360 − 0.625330i \(-0.215036\pi\)
0.780360 + 0.625330i \(0.215036\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −15269.0 −0.608610 −0.304305 − 0.952575i \(-0.598424\pi\)
−0.304305 + 0.952575i \(0.598424\pi\)
\(858\) 0 0
\(859\) −19375.0 −0.769577 −0.384788 − 0.923005i \(-0.625726\pi\)
−0.384788 + 0.923005i \(0.625726\pi\)
\(860\) 0 0
\(861\) −9750.00 −0.385922
\(862\) 0 0
\(863\) 22900.0 0.903274 0.451637 − 0.892202i \(-0.350840\pi\)
0.451637 + 0.892202i \(0.350840\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 22360.0 0.875877
\(868\) 0 0
\(869\) −12450.0 −0.486004
\(870\) 0 0
\(871\) 2040.00 0.0793602
\(872\) 0 0
\(873\) 2868.00 0.111188
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −23444.0 −0.902677 −0.451338 − 0.892353i \(-0.649053\pi\)
−0.451338 + 0.892353i \(0.649053\pi\)
\(878\) 0 0
\(879\) −8010.00 −0.307361
\(880\) 0 0
\(881\) 3750.00 0.143406 0.0717030 − 0.997426i \(-0.477157\pi\)
0.0717030 + 0.997426i \(0.477157\pi\)
\(882\) 0 0
\(883\) 37595.0 1.43281 0.716406 − 0.697684i \(-0.245786\pi\)
0.716406 + 0.697684i \(0.245786\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11420.0 0.432295 0.216148 − 0.976361i \(-0.430651\pi\)
0.216148 + 0.976361i \(0.430651\pi\)
\(888\) 0 0
\(889\) −14900.0 −0.562126
\(890\) 0 0
\(891\) 10065.0 0.378440
\(892\) 0 0
\(893\) −50400.0 −1.88866
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −400.000 −0.0148892
\(898\) 0 0
\(899\) 4600.00 0.170655
\(900\) 0 0
\(901\) 6762.00 0.250028
\(902\) 0 0
\(903\) 15000.0 0.552789
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2620.00 −0.0959158 −0.0479579 − 0.998849i \(-0.515271\pi\)
−0.0479579 + 0.998849i \(0.515271\pi\)
\(908\) 0 0
\(909\) −3804.00 −0.138802
\(910\) 0 0
\(911\) −46500.0 −1.69112 −0.845562 − 0.533877i \(-0.820734\pi\)
−0.845562 + 0.533877i \(0.820734\pi\)
\(912\) 0 0
\(913\) 1125.00 0.0407799
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7800.00 −0.280893
\(918\) 0 0
\(919\) −45190.0 −1.62207 −0.811034 − 0.584999i \(-0.801095\pi\)
−0.811034 + 0.584999i \(0.801095\pi\)
\(920\) 0 0
\(921\) 9425.00 0.337203
\(922\) 0 0
\(923\) −320.000 −0.0114116
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −2960.00 −0.104875
\(928\) 0 0
\(929\) 15166.0 0.535609 0.267804 − 0.963473i \(-0.413702\pi\)
0.267804 + 0.963473i \(0.413702\pi\)
\(930\) 0 0
\(931\) −25515.0 −0.898196
\(932\) 0 0
\(933\) 46250.0 1.62289
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 23789.0 0.829405 0.414703 − 0.909957i \(-0.363886\pi\)
0.414703 + 0.909957i \(0.363886\pi\)
\(938\) 0 0
\(939\) 40810.0 1.41830
\(940\) 0 0
\(941\) −47472.0 −1.64457 −0.822286 − 0.569074i \(-0.807302\pi\)
−0.822286 + 0.569074i \(0.807302\pi\)
\(942\) 0 0
\(943\) 1950.00 0.0673391
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 19760.0 0.678050 0.339025 − 0.940777i \(-0.389903\pi\)
0.339025 + 0.940777i \(0.389903\pi\)
\(948\) 0 0
\(949\) −2536.00 −0.0867461
\(950\) 0 0
\(951\) 34620.0 1.18047
\(952\) 0 0
\(953\) −36337.0 −1.23512 −0.617561 − 0.786523i \(-0.711879\pi\)
−0.617561 + 0.786523i \(0.711879\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1500.00 0.0506668
\(958\) 0 0
\(959\) 27490.0 0.925650
\(960\) 0 0
\(961\) 23109.0 0.775704
\(962\) 0 0
\(963\) 3890.00 0.130170
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −33880.0 −1.12669 −0.563344 − 0.826222i \(-0.690485\pi\)
−0.563344 + 0.826222i \(0.690485\pi\)
\(968\) 0 0
\(969\) 11025.0 0.365505
\(970\) 0 0
\(971\) −17175.0 −0.567633 −0.283817 − 0.958879i \(-0.591601\pi\)
−0.283817 + 0.958879i \(0.591601\pi\)
\(972\) 0 0
\(973\) 7350.00 0.242169
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 13311.0 0.435882 0.217941 − 0.975962i \(-0.430066\pi\)
0.217941 + 0.975962i \(0.430066\pi\)
\(978\) 0 0
\(979\) 10575.0 0.345228
\(980\) 0 0
\(981\) −492.000 −0.0160126
\(982\) 0 0
\(983\) −53110.0 −1.72324 −0.861621 − 0.507553i \(-0.830550\pi\)
−0.861621 + 0.507553i \(0.830550\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −24000.0 −0.773990
\(988\) 0 0
\(989\) −3000.00 −0.0964555
\(990\) 0 0
\(991\) 8990.00 0.288170 0.144085 − 0.989565i \(-0.453976\pi\)
0.144085 + 0.989565i \(0.453976\pi\)
\(992\) 0 0
\(993\) 40375.0 1.29029
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1236.00 0.0392623 0.0196311 − 0.999807i \(-0.493751\pi\)
0.0196311 + 0.999807i \(0.493751\pi\)
\(998\) 0 0
\(999\) 7830.00 0.247978
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 1600.4.a.k.1.1 1
4.3 odd 2 1600.4.a.bq.1.1 1
5.4 even 2 1600.4.a.bp.1.1 1
8.3 odd 2 800.4.a.b.1.1 ✓ 1
8.5 even 2 800.4.a.j.1.1 yes 1
20.19 odd 2 1600.4.a.l.1.1 1
40.3 even 4 800.4.c.c.449.1 2
40.13 odd 4 800.4.c.d.449.2 2
40.19 odd 2 800.4.a.i.1.1 yes 1
40.27 even 4 800.4.c.c.449.2 2
40.29 even 2 800.4.a.c.1.1 yes 1
40.37 odd 4 800.4.c.d.449.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
800.4.a.b.1.1 ✓ 1 8.3 odd 2
800.4.a.c.1.1 yes 1 40.29 even 2
800.4.a.i.1.1 yes 1 40.19 odd 2
800.4.a.j.1.1 yes 1 8.5 even 2
800.4.c.c.449.1 2 40.3 even 4
800.4.c.c.449.2 2 40.27 even 4
800.4.c.d.449.1 2 40.37 odd 4
800.4.c.d.449.2 2 40.13 odd 4
1600.4.a.k.1.1 1 1.1 even 1 trivial
1600.4.a.l.1.1 1 20.19 odd 2
1600.4.a.bp.1.1 1 5.4 even 2
1600.4.a.bq.1.1 1 4.3 odd 2