Properties

Label 2240.4.a.p.1.1
Level $2240$
Weight $4$
Character 2240.1
Self dual yes
Analytic conductor $132.164$
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] = [2240,4,Mod(1,2240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2240.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2240.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: \(132.164278413\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2240.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} -5.00000 q^{5} +7.00000 q^{7} -18.0000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -5.00000 q^{5} +7.00000 q^{7} -18.0000 q^{9} -17.0000 q^{11} +81.0000 q^{13} +15.0000 q^{15} -91.0000 q^{17} +102.000 q^{19} -21.0000 q^{21} +90.0000 q^{23} +25.0000 q^{25} +135.000 q^{27} +129.000 q^{29} -116.000 q^{31} +51.0000 q^{33} -35.0000 q^{35} -314.000 q^{37} -243.000 q^{39} -124.000 q^{41} -434.000 q^{43} +90.0000 q^{45} -497.000 q^{47} +49.0000 q^{49} +273.000 q^{51} +584.000 q^{53} +85.0000 q^{55} -306.000 q^{57} -332.000 q^{59} -220.000 q^{61} -126.000 q^{63} -405.000 q^{65} +384.000 q^{67} -270.000 q^{69} +664.000 q^{71} +230.000 q^{73} -75.0000 q^{75} -119.000 q^{77} -361.000 q^{79} +81.0000 q^{81} +1172.00 q^{83} +455.000 q^{85} -387.000 q^{87} +40.0000 q^{89} +567.000 q^{91} +348.000 q^{93} -510.000 q^{95} -175.000 q^{97} +306.000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) −18.0000 −0.666667
\(10\) 0 0
\(11\) −17.0000 −0.465972 −0.232986 0.972480i \(-0.574850\pi\)
−0.232986 + 0.972480i \(0.574850\pi\)
\(12\) 0 0
\(13\) 81.0000 1.72810 0.864052 0.503402i \(-0.167919\pi\)
0.864052 + 0.503402i \(0.167919\pi\)
\(14\) 0 0
\(15\) 15.0000 0.258199
\(16\) 0 0
\(17\) −91.0000 −1.29828 −0.649139 0.760669i \(-0.724871\pi\)
−0.649139 + 0.760669i \(0.724871\pi\)
\(18\) 0 0
\(19\) 102.000 1.23160 0.615800 0.787902i \(-0.288833\pi\)
0.615800 + 0.787902i \(0.288833\pi\)
\(20\) 0 0
\(21\) −21.0000 −0.218218
\(22\) 0 0
\(23\) 90.0000 0.815926 0.407963 0.912998i \(-0.366239\pi\)
0.407963 + 0.912998i \(0.366239\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 135.000 0.962250
\(28\) 0 0
\(29\) 129.000 0.826024 0.413012 0.910726i \(-0.364477\pi\)
0.413012 + 0.910726i \(0.364477\pi\)
\(30\) 0 0
\(31\) −116.000 −0.672071 −0.336036 0.941849i \(-0.609086\pi\)
−0.336036 + 0.941849i \(0.609086\pi\)
\(32\) 0 0
\(33\) 51.0000 0.269029
\(34\) 0 0
\(35\) −35.0000 −0.169031
\(36\) 0 0
\(37\) −314.000 −1.39517 −0.697585 0.716502i \(-0.745742\pi\)
−0.697585 + 0.716502i \(0.745742\pi\)
\(38\) 0 0
\(39\) −243.000 −0.997722
\(40\) 0 0
\(41\) −124.000 −0.472330 −0.236165 0.971713i \(-0.575891\pi\)
−0.236165 + 0.971713i \(0.575891\pi\)
\(42\) 0 0
\(43\) −434.000 −1.53917 −0.769586 0.638543i \(-0.779537\pi\)
−0.769586 + 0.638543i \(0.779537\pi\)
\(44\) 0 0
\(45\) 90.0000 0.298142
\(46\) 0 0
\(47\) −497.000 −1.54244 −0.771222 0.636566i \(-0.780354\pi\)
−0.771222 + 0.636566i \(0.780354\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 273.000 0.749562
\(52\) 0 0
\(53\) 584.000 1.51356 0.756779 0.653671i \(-0.226772\pi\)
0.756779 + 0.653671i \(0.226772\pi\)
\(54\) 0 0
\(55\) 85.0000 0.208389
\(56\) 0 0
\(57\) −306.000 −0.711065
\(58\) 0 0
\(59\) −332.000 −0.732588 −0.366294 0.930499i \(-0.619374\pi\)
−0.366294 + 0.930499i \(0.619374\pi\)
\(60\) 0 0
\(61\) −220.000 −0.461772 −0.230886 0.972981i \(-0.574163\pi\)
−0.230886 + 0.972981i \(0.574163\pi\)
\(62\) 0 0
\(63\) −126.000 −0.251976
\(64\) 0 0
\(65\) −405.000 −0.772832
\(66\) 0 0
\(67\) 384.000 0.700195 0.350098 0.936713i \(-0.386148\pi\)
0.350098 + 0.936713i \(0.386148\pi\)
\(68\) 0 0
\(69\) −270.000 −0.471075
\(70\) 0 0
\(71\) 664.000 1.10989 0.554946 0.831887i \(-0.312739\pi\)
0.554946 + 0.831887i \(0.312739\pi\)
\(72\) 0 0
\(73\) 230.000 0.368760 0.184380 0.982855i \(-0.440972\pi\)
0.184380 + 0.982855i \(0.440972\pi\)
\(74\) 0 0
\(75\) −75.0000 −0.115470
\(76\) 0 0
\(77\) −119.000 −0.176121
\(78\) 0 0
\(79\) −361.000 −0.514122 −0.257061 0.966395i \(-0.582754\pi\)
−0.257061 + 0.966395i \(0.582754\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 1172.00 1.54992 0.774962 0.632008i \(-0.217769\pi\)
0.774962 + 0.632008i \(0.217769\pi\)
\(84\) 0 0
\(85\) 455.000 0.580608
\(86\) 0 0
\(87\) −387.000 −0.476905
\(88\) 0 0
\(89\) 40.0000 0.0476404 0.0238202 0.999716i \(-0.492417\pi\)
0.0238202 + 0.999716i \(0.492417\pi\)
\(90\) 0 0
\(91\) 567.000 0.653162
\(92\) 0 0
\(93\) 348.000 0.388021
\(94\) 0 0
\(95\) −510.000 −0.550788
\(96\) 0 0
\(97\) −175.000 −0.183181 −0.0915905 0.995797i \(-0.529195\pi\)
−0.0915905 + 0.995797i \(0.529195\pi\)
\(98\) 0 0
\(99\) 306.000 0.310648
\(100\) 0 0
\(101\) −270.000 −0.266000 −0.133000 0.991116i \(-0.542461\pi\)
−0.133000 + 0.991116i \(0.542461\pi\)
\(102\) 0 0
\(103\) −565.000 −0.540496 −0.270248 0.962791i \(-0.587106\pi\)
−0.270248 + 0.962791i \(0.587106\pi\)
\(104\) 0 0
\(105\) 105.000 0.0975900
\(106\) 0 0
\(107\) −1206.00 −1.08961 −0.544806 0.838562i \(-0.683397\pi\)
−0.544806 + 0.838562i \(0.683397\pi\)
\(108\) 0 0
\(109\) 1419.00 1.24693 0.623466 0.781851i \(-0.285724\pi\)
0.623466 + 0.781851i \(0.285724\pi\)
\(110\) 0 0
\(111\) 942.000 0.805502
\(112\) 0 0
\(113\) −778.000 −0.647682 −0.323841 0.946111i \(-0.604974\pi\)
−0.323841 + 0.946111i \(0.604974\pi\)
\(114\) 0 0
\(115\) −450.000 −0.364893
\(116\) 0 0
\(117\) −1458.00 −1.15207
\(118\) 0 0
\(119\) −637.000 −0.490703
\(120\) 0 0
\(121\) −1042.00 −0.782870
\(122\) 0 0
\(123\) 372.000 0.272700
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −316.000 −0.220791 −0.110396 0.993888i \(-0.535212\pi\)
−0.110396 + 0.993888i \(0.535212\pi\)
\(128\) 0 0
\(129\) 1302.00 0.888641
\(130\) 0 0
\(131\) −1750.00 −1.16716 −0.583581 0.812055i \(-0.698349\pi\)
−0.583581 + 0.812055i \(0.698349\pi\)
\(132\) 0 0
\(133\) 714.000 0.465501
\(134\) 0 0
\(135\) −675.000 −0.430331
\(136\) 0 0
\(137\) 48.0000 0.0299337 0.0149668 0.999888i \(-0.495236\pi\)
0.0149668 + 0.999888i \(0.495236\pi\)
\(138\) 0 0
\(139\) −38.0000 −0.0231879 −0.0115939 0.999933i \(-0.503691\pi\)
−0.0115939 + 0.999933i \(0.503691\pi\)
\(140\) 0 0
\(141\) 1491.00 0.890531
\(142\) 0 0
\(143\) −1377.00 −0.805248
\(144\) 0 0
\(145\) −645.000 −0.369409
\(146\) 0 0
\(147\) −147.000 −0.0824786
\(148\) 0 0
\(149\) 3582.00 1.96946 0.984728 0.174101i \(-0.0557020\pi\)
0.984728 + 0.174101i \(0.0557020\pi\)
\(150\) 0 0
\(151\) 1927.00 1.03852 0.519262 0.854615i \(-0.326207\pi\)
0.519262 + 0.854615i \(0.326207\pi\)
\(152\) 0 0
\(153\) 1638.00 0.865519
\(154\) 0 0
\(155\) 580.000 0.300559
\(156\) 0 0
\(157\) 2510.00 1.27592 0.637961 0.770069i \(-0.279778\pi\)
0.637961 + 0.770069i \(0.279778\pi\)
\(158\) 0 0
\(159\) −1752.00 −0.873853
\(160\) 0 0
\(161\) 630.000 0.308391
\(162\) 0 0
\(163\) −1870.00 −0.898587 −0.449294 0.893384i \(-0.648324\pi\)
−0.449294 + 0.893384i \(0.648324\pi\)
\(164\) 0 0
\(165\) −255.000 −0.120313
\(166\) 0 0
\(167\) 2019.00 0.935538 0.467769 0.883851i \(-0.345058\pi\)
0.467769 + 0.883851i \(0.345058\pi\)
\(168\) 0 0
\(169\) 4364.00 1.98635
\(170\) 0 0
\(171\) −1836.00 −0.821067
\(172\) 0 0
\(173\) −1253.00 −0.550658 −0.275329 0.961350i \(-0.588787\pi\)
−0.275329 + 0.961350i \(0.588787\pi\)
\(174\) 0 0
\(175\) 175.000 0.0755929
\(176\) 0 0
\(177\) 996.000 0.422960
\(178\) 0 0
\(179\) 492.000 0.205440 0.102720 0.994710i \(-0.467245\pi\)
0.102720 + 0.994710i \(0.467245\pi\)
\(180\) 0 0
\(181\) 4448.00 1.82661 0.913307 0.407271i \(-0.133520\pi\)
0.913307 + 0.407271i \(0.133520\pi\)
\(182\) 0 0
\(183\) 660.000 0.266604
\(184\) 0 0
\(185\) 1570.00 0.623939
\(186\) 0 0
\(187\) 1547.00 0.604962
\(188\) 0 0
\(189\) 945.000 0.363696
\(190\) 0 0
\(191\) −3999.00 −1.51496 −0.757480 0.652858i \(-0.773570\pi\)
−0.757480 + 0.652858i \(0.773570\pi\)
\(192\) 0 0
\(193\) 4880.00 1.82005 0.910026 0.414551i \(-0.136061\pi\)
0.910026 + 0.414551i \(0.136061\pi\)
\(194\) 0 0
\(195\) 1215.00 0.446195
\(196\) 0 0
\(197\) −4712.00 −1.70414 −0.852071 0.523426i \(-0.824654\pi\)
−0.852071 + 0.523426i \(0.824654\pi\)
\(198\) 0 0
\(199\) −2756.00 −0.981747 −0.490874 0.871231i \(-0.663322\pi\)
−0.490874 + 0.871231i \(0.663322\pi\)
\(200\) 0 0
\(201\) −1152.00 −0.404258
\(202\) 0 0
\(203\) 903.000 0.312208
\(204\) 0 0
\(205\) 620.000 0.211233
\(206\) 0 0
\(207\) −1620.00 −0.543951
\(208\) 0 0
\(209\) −1734.00 −0.573891
\(210\) 0 0
\(211\) 697.000 0.227410 0.113705 0.993515i \(-0.463728\pi\)
0.113705 + 0.993515i \(0.463728\pi\)
\(212\) 0 0
\(213\) −1992.00 −0.640796
\(214\) 0 0
\(215\) 2170.00 0.688338
\(216\) 0 0
\(217\) −812.000 −0.254019
\(218\) 0 0
\(219\) −690.000 −0.212904
\(220\) 0 0
\(221\) −7371.00 −2.24356
\(222\) 0 0
\(223\) 707.000 0.212306 0.106153 0.994350i \(-0.466147\pi\)
0.106153 + 0.994350i \(0.466147\pi\)
\(224\) 0 0
\(225\) −450.000 −0.133333
\(226\) 0 0
\(227\) −559.000 −0.163446 −0.0817228 0.996655i \(-0.526042\pi\)
−0.0817228 + 0.996655i \(0.526042\pi\)
\(228\) 0 0
\(229\) 3836.00 1.10694 0.553472 0.832868i \(-0.313303\pi\)
0.553472 + 0.832868i \(0.313303\pi\)
\(230\) 0 0
\(231\) 357.000 0.101683
\(232\) 0 0
\(233\) −1368.00 −0.384638 −0.192319 0.981332i \(-0.561601\pi\)
−0.192319 + 0.981332i \(0.561601\pi\)
\(234\) 0 0
\(235\) 2485.00 0.689802
\(236\) 0 0
\(237\) 1083.00 0.296829
\(238\) 0 0
\(239\) 3803.00 1.02927 0.514635 0.857409i \(-0.327927\pi\)
0.514635 + 0.857409i \(0.327927\pi\)
\(240\) 0 0
\(241\) 5650.00 1.51016 0.755080 0.655633i \(-0.227598\pi\)
0.755080 + 0.655633i \(0.227598\pi\)
\(242\) 0 0
\(243\) −3888.00 −1.02640
\(244\) 0 0
\(245\) −245.000 −0.0638877
\(246\) 0 0
\(247\) 8262.00 2.12833
\(248\) 0 0
\(249\) −3516.00 −0.894849
\(250\) 0 0
\(251\) −1650.00 −0.414929 −0.207464 0.978243i \(-0.566521\pi\)
−0.207464 + 0.978243i \(0.566521\pi\)
\(252\) 0 0
\(253\) −1530.00 −0.380199
\(254\) 0 0
\(255\) −1365.00 −0.335214
\(256\) 0 0
\(257\) 5810.00 1.41019 0.705093 0.709115i \(-0.250905\pi\)
0.705093 + 0.709115i \(0.250905\pi\)
\(258\) 0 0
\(259\) −2198.00 −0.527325
\(260\) 0 0
\(261\) −2322.00 −0.550683
\(262\) 0 0
\(263\) 2758.00 0.646637 0.323319 0.946290i \(-0.395201\pi\)
0.323319 + 0.946290i \(0.395201\pi\)
\(264\) 0 0
\(265\) −2920.00 −0.676884
\(266\) 0 0
\(267\) −120.000 −0.0275052
\(268\) 0 0
\(269\) −186.000 −0.0421584 −0.0210792 0.999778i \(-0.506710\pi\)
−0.0210792 + 0.999778i \(0.506710\pi\)
\(270\) 0 0
\(271\) 6828.00 1.53052 0.765261 0.643720i \(-0.222610\pi\)
0.765261 + 0.643720i \(0.222610\pi\)
\(272\) 0 0
\(273\) −1701.00 −0.377103
\(274\) 0 0
\(275\) −425.000 −0.0931944
\(276\) 0 0
\(277\) 8214.00 1.78170 0.890851 0.454296i \(-0.150109\pi\)
0.890851 + 0.454296i \(0.150109\pi\)
\(278\) 0 0
\(279\) 2088.00 0.448048
\(280\) 0 0
\(281\) 6707.00 1.42387 0.711933 0.702248i \(-0.247820\pi\)
0.711933 + 0.702248i \(0.247820\pi\)
\(282\) 0 0
\(283\) −5497.00 −1.15464 −0.577319 0.816518i \(-0.695901\pi\)
−0.577319 + 0.816518i \(0.695901\pi\)
\(284\) 0 0
\(285\) 1530.00 0.317998
\(286\) 0 0
\(287\) −868.000 −0.178524
\(288\) 0 0
\(289\) 3368.00 0.685528
\(290\) 0 0
\(291\) 525.000 0.105760
\(292\) 0 0
\(293\) −313.000 −0.0624084 −0.0312042 0.999513i \(-0.509934\pi\)
−0.0312042 + 0.999513i \(0.509934\pi\)
\(294\) 0 0
\(295\) 1660.00 0.327624
\(296\) 0 0
\(297\) −2295.00 −0.448382
\(298\) 0 0
\(299\) 7290.00 1.41001
\(300\) 0 0
\(301\) −3038.00 −0.581752
\(302\) 0 0
\(303\) 810.000 0.153575
\(304\) 0 0
\(305\) 1100.00 0.206511
\(306\) 0 0
\(307\) 5479.00 1.01858 0.509288 0.860596i \(-0.329909\pi\)
0.509288 + 0.860596i \(0.329909\pi\)
\(308\) 0 0
\(309\) 1695.00 0.312056
\(310\) 0 0
\(311\) −4422.00 −0.806266 −0.403133 0.915141i \(-0.632079\pi\)
−0.403133 + 0.915141i \(0.632079\pi\)
\(312\) 0 0
\(313\) 275.000 0.0496611 0.0248305 0.999692i \(-0.492095\pi\)
0.0248305 + 0.999692i \(0.492095\pi\)
\(314\) 0 0
\(315\) 630.000 0.112687
\(316\) 0 0
\(317\) 4106.00 0.727495 0.363748 0.931498i \(-0.381497\pi\)
0.363748 + 0.931498i \(0.381497\pi\)
\(318\) 0 0
\(319\) −2193.00 −0.384904
\(320\) 0 0
\(321\) 3618.00 0.629087
\(322\) 0 0
\(323\) −9282.00 −1.59896
\(324\) 0 0
\(325\) 2025.00 0.345621
\(326\) 0 0
\(327\) −4257.00 −0.719916
\(328\) 0 0
\(329\) −3479.00 −0.582989
\(330\) 0 0
\(331\) 8260.00 1.37163 0.685817 0.727774i \(-0.259445\pi\)
0.685817 + 0.727774i \(0.259445\pi\)
\(332\) 0 0
\(333\) 5652.00 0.930113
\(334\) 0 0
\(335\) −1920.00 −0.313137
\(336\) 0 0
\(337\) 9946.00 1.60769 0.803847 0.594836i \(-0.202783\pi\)
0.803847 + 0.594836i \(0.202783\pi\)
\(338\) 0 0
\(339\) 2334.00 0.373939
\(340\) 0 0
\(341\) 1972.00 0.313167
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) 1350.00 0.210671
\(346\) 0 0
\(347\) −8798.00 −1.36110 −0.680550 0.732702i \(-0.738259\pi\)
−0.680550 + 0.732702i \(0.738259\pi\)
\(348\) 0 0
\(349\) 1838.00 0.281908 0.140954 0.990016i \(-0.454983\pi\)
0.140954 + 0.990016i \(0.454983\pi\)
\(350\) 0 0
\(351\) 10935.0 1.66287
\(352\) 0 0
\(353\) 2265.00 0.341512 0.170756 0.985313i \(-0.445379\pi\)
0.170756 + 0.985313i \(0.445379\pi\)
\(354\) 0 0
\(355\) −3320.00 −0.496359
\(356\) 0 0
\(357\) 1911.00 0.283308
\(358\) 0 0
\(359\) −4136.00 −0.608049 −0.304025 0.952664i \(-0.598331\pi\)
−0.304025 + 0.952664i \(0.598331\pi\)
\(360\) 0 0
\(361\) 3545.00 0.516839
\(362\) 0 0
\(363\) 3126.00 0.451990
\(364\) 0 0
\(365\) −1150.00 −0.164914
\(366\) 0 0
\(367\) 10031.0 1.42674 0.713370 0.700787i \(-0.247168\pi\)
0.713370 + 0.700787i \(0.247168\pi\)
\(368\) 0 0
\(369\) 2232.00 0.314887
\(370\) 0 0
\(371\) 4088.00 0.572071
\(372\) 0 0
\(373\) −2792.00 −0.387572 −0.193786 0.981044i \(-0.562077\pi\)
−0.193786 + 0.981044i \(0.562077\pi\)
\(374\) 0 0
\(375\) 375.000 0.0516398
\(376\) 0 0
\(377\) 10449.0 1.42746
\(378\) 0 0
\(379\) 9948.00 1.34827 0.674135 0.738608i \(-0.264517\pi\)
0.674135 + 0.738608i \(0.264517\pi\)
\(380\) 0 0
\(381\) 948.000 0.127474
\(382\) 0 0
\(383\) −2700.00 −0.360218 −0.180109 0.983647i \(-0.557645\pi\)
−0.180109 + 0.983647i \(0.557645\pi\)
\(384\) 0 0
\(385\) 595.000 0.0787637
\(386\) 0 0
\(387\) 7812.00 1.02611
\(388\) 0 0
\(389\) 631.000 0.0822441 0.0411221 0.999154i \(-0.486907\pi\)
0.0411221 + 0.999154i \(0.486907\pi\)
\(390\) 0 0
\(391\) −8190.00 −1.05930
\(392\) 0 0
\(393\) 5250.00 0.673861
\(394\) 0 0
\(395\) 1805.00 0.229923
\(396\) 0 0
\(397\) 13139.0 1.66103 0.830513 0.556999i \(-0.188047\pi\)
0.830513 + 0.556999i \(0.188047\pi\)
\(398\) 0 0
\(399\) −2142.00 −0.268757
\(400\) 0 0
\(401\) −887.000 −0.110461 −0.0552303 0.998474i \(-0.517589\pi\)
−0.0552303 + 0.998474i \(0.517589\pi\)
\(402\) 0 0
\(403\) −9396.00 −1.16141
\(404\) 0 0
\(405\) −405.000 −0.0496904
\(406\) 0 0
\(407\) 5338.00 0.650110
\(408\) 0 0
\(409\) −5190.00 −0.627455 −0.313727 0.949513i \(-0.601578\pi\)
−0.313727 + 0.949513i \(0.601578\pi\)
\(410\) 0 0
\(411\) −144.000 −0.0172822
\(412\) 0 0
\(413\) −2324.00 −0.276892
\(414\) 0 0
\(415\) −5860.00 −0.693147
\(416\) 0 0
\(417\) 114.000 0.0133875
\(418\) 0 0
\(419\) −5712.00 −0.665989 −0.332995 0.942929i \(-0.608059\pi\)
−0.332995 + 0.942929i \(0.608059\pi\)
\(420\) 0 0
\(421\) 11155.0 1.29136 0.645679 0.763609i \(-0.276575\pi\)
0.645679 + 0.763609i \(0.276575\pi\)
\(422\) 0 0
\(423\) 8946.00 1.02830
\(424\) 0 0
\(425\) −2275.00 −0.259656
\(426\) 0 0
\(427\) −1540.00 −0.174534
\(428\) 0 0
\(429\) 4131.00 0.464910
\(430\) 0 0
\(431\) −8499.00 −0.949843 −0.474922 0.880028i \(-0.657524\pi\)
−0.474922 + 0.880028i \(0.657524\pi\)
\(432\) 0 0
\(433\) 5102.00 0.566251 0.283125 0.959083i \(-0.408629\pi\)
0.283125 + 0.959083i \(0.408629\pi\)
\(434\) 0 0
\(435\) 1935.00 0.213279
\(436\) 0 0
\(437\) 9180.00 1.00489
\(438\) 0 0
\(439\) −15694.0 −1.70623 −0.853114 0.521725i \(-0.825289\pi\)
−0.853114 + 0.521725i \(0.825289\pi\)
\(440\) 0 0
\(441\) −882.000 −0.0952381
\(442\) 0 0
\(443\) 9142.00 0.980473 0.490236 0.871589i \(-0.336910\pi\)
0.490236 + 0.871589i \(0.336910\pi\)
\(444\) 0 0
\(445\) −200.000 −0.0213054
\(446\) 0 0
\(447\) −10746.0 −1.13707
\(448\) 0 0
\(449\) −17145.0 −1.80205 −0.901027 0.433762i \(-0.857186\pi\)
−0.901027 + 0.433762i \(0.857186\pi\)
\(450\) 0 0
\(451\) 2108.00 0.220093
\(452\) 0 0
\(453\) −5781.00 −0.599592
\(454\) 0 0
\(455\) −2835.00 −0.292103
\(456\) 0 0
\(457\) −10184.0 −1.04242 −0.521212 0.853427i \(-0.674520\pi\)
−0.521212 + 0.853427i \(0.674520\pi\)
\(458\) 0 0
\(459\) −12285.0 −1.24927
\(460\) 0 0
\(461\) 9152.00 0.924623 0.462311 0.886718i \(-0.347020\pi\)
0.462311 + 0.886718i \(0.347020\pi\)
\(462\) 0 0
\(463\) 1084.00 0.108807 0.0544036 0.998519i \(-0.482674\pi\)
0.0544036 + 0.998519i \(0.482674\pi\)
\(464\) 0 0
\(465\) −1740.00 −0.173528
\(466\) 0 0
\(467\) 19283.0 1.91073 0.955365 0.295428i \(-0.0954624\pi\)
0.955365 + 0.295428i \(0.0954624\pi\)
\(468\) 0 0
\(469\) 2688.00 0.264649
\(470\) 0 0
\(471\) −7530.00 −0.736654
\(472\) 0 0
\(473\) 7378.00 0.717211
\(474\) 0 0
\(475\) 2550.00 0.246320
\(476\) 0 0
\(477\) −10512.0 −1.00904
\(478\) 0 0
\(479\) 5118.00 0.488199 0.244100 0.969750i \(-0.421508\pi\)
0.244100 + 0.969750i \(0.421508\pi\)
\(480\) 0 0
\(481\) −25434.0 −2.41100
\(482\) 0 0
\(483\) −1890.00 −0.178050
\(484\) 0 0
\(485\) 875.000 0.0819210
\(486\) 0 0
\(487\) −2918.00 −0.271514 −0.135757 0.990742i \(-0.543347\pi\)
−0.135757 + 0.990742i \(0.543347\pi\)
\(488\) 0 0
\(489\) 5610.00 0.518800
\(490\) 0 0
\(491\) −18627.0 −1.71207 −0.856033 0.516921i \(-0.827078\pi\)
−0.856033 + 0.516921i \(0.827078\pi\)
\(492\) 0 0
\(493\) −11739.0 −1.07241
\(494\) 0 0
\(495\) −1530.00 −0.138926
\(496\) 0 0
\(497\) 4648.00 0.419500
\(498\) 0 0
\(499\) 12843.0 1.15217 0.576084 0.817391i \(-0.304580\pi\)
0.576084 + 0.817391i \(0.304580\pi\)
\(500\) 0 0
\(501\) −6057.00 −0.540133
\(502\) 0 0
\(503\) 18837.0 1.66978 0.834891 0.550415i \(-0.185531\pi\)
0.834891 + 0.550415i \(0.185531\pi\)
\(504\) 0 0
\(505\) 1350.00 0.118959
\(506\) 0 0
\(507\) −13092.0 −1.14682
\(508\) 0 0
\(509\) 7742.00 0.674181 0.337090 0.941472i \(-0.390557\pi\)
0.337090 + 0.941472i \(0.390557\pi\)
\(510\) 0 0
\(511\) 1610.00 0.139378
\(512\) 0 0
\(513\) 13770.0 1.18511
\(514\) 0 0
\(515\) 2825.00 0.241717
\(516\) 0 0
\(517\) 8449.00 0.718736
\(518\) 0 0
\(519\) 3759.00 0.317923
\(520\) 0 0
\(521\) 614.000 0.0516311 0.0258156 0.999667i \(-0.491782\pi\)
0.0258156 + 0.999667i \(0.491782\pi\)
\(522\) 0 0
\(523\) 17836.0 1.49123 0.745616 0.666376i \(-0.232156\pi\)
0.745616 + 0.666376i \(0.232156\pi\)
\(524\) 0 0
\(525\) −525.000 −0.0436436
\(526\) 0 0
\(527\) 10556.0 0.872536
\(528\) 0 0
\(529\) −4067.00 −0.334265
\(530\) 0 0
\(531\) 5976.00 0.488392
\(532\) 0 0
\(533\) −10044.0 −0.816236
\(534\) 0 0
\(535\) 6030.00 0.487289
\(536\) 0 0
\(537\) −1476.00 −0.118611
\(538\) 0 0
\(539\) −833.000 −0.0665674
\(540\) 0 0
\(541\) −23463.0 −1.86461 −0.932304 0.361675i \(-0.882205\pi\)
−0.932304 + 0.361675i \(0.882205\pi\)
\(542\) 0 0
\(543\) −13344.0 −1.05460
\(544\) 0 0
\(545\) −7095.00 −0.557645
\(546\) 0 0
\(547\) −1860.00 −0.145389 −0.0726946 0.997354i \(-0.523160\pi\)
−0.0726946 + 0.997354i \(0.523160\pi\)
\(548\) 0 0
\(549\) 3960.00 0.307848
\(550\) 0 0
\(551\) 13158.0 1.01733
\(552\) 0 0
\(553\) −2527.00 −0.194320
\(554\) 0 0
\(555\) −4710.00 −0.360231
\(556\) 0 0
\(557\) −10288.0 −0.782615 −0.391307 0.920260i \(-0.627977\pi\)
−0.391307 + 0.920260i \(0.627977\pi\)
\(558\) 0 0
\(559\) −35154.0 −2.65985
\(560\) 0 0
\(561\) −4641.00 −0.349275
\(562\) 0 0
\(563\) −2356.00 −0.176365 −0.0881826 0.996104i \(-0.528106\pi\)
−0.0881826 + 0.996104i \(0.528106\pi\)
\(564\) 0 0
\(565\) 3890.00 0.289652
\(566\) 0 0
\(567\) 567.000 0.0419961
\(568\) 0 0
\(569\) −15318.0 −1.12858 −0.564292 0.825575i \(-0.690851\pi\)
−0.564292 + 0.825575i \(0.690851\pi\)
\(570\) 0 0
\(571\) −13164.0 −0.964792 −0.482396 0.875953i \(-0.660233\pi\)
−0.482396 + 0.875953i \(0.660233\pi\)
\(572\) 0 0
\(573\) 11997.0 0.874663
\(574\) 0 0
\(575\) 2250.00 0.163185
\(576\) 0 0
\(577\) 8959.00 0.646392 0.323196 0.946332i \(-0.395243\pi\)
0.323196 + 0.946332i \(0.395243\pi\)
\(578\) 0 0
\(579\) −14640.0 −1.05081
\(580\) 0 0
\(581\) 8204.00 0.585816
\(582\) 0 0
\(583\) −9928.00 −0.705276
\(584\) 0 0
\(585\) 7290.00 0.515221
\(586\) 0 0
\(587\) 16952.0 1.19197 0.595983 0.802997i \(-0.296763\pi\)
0.595983 + 0.802997i \(0.296763\pi\)
\(588\) 0 0
\(589\) −11832.0 −0.827723
\(590\) 0 0
\(591\) 14136.0 0.983887
\(592\) 0 0
\(593\) 10071.0 0.697414 0.348707 0.937232i \(-0.386621\pi\)
0.348707 + 0.937232i \(0.386621\pi\)
\(594\) 0 0
\(595\) 3185.00 0.219449
\(596\) 0 0
\(597\) 8268.00 0.566812
\(598\) 0 0
\(599\) 2829.00 0.192971 0.0964856 0.995334i \(-0.469240\pi\)
0.0964856 + 0.995334i \(0.469240\pi\)
\(600\) 0 0
\(601\) −7662.00 −0.520032 −0.260016 0.965604i \(-0.583728\pi\)
−0.260016 + 0.965604i \(0.583728\pi\)
\(602\) 0 0
\(603\) −6912.00 −0.466797
\(604\) 0 0
\(605\) 5210.00 0.350110
\(606\) 0 0
\(607\) −907.000 −0.0606491 −0.0303245 0.999540i \(-0.509654\pi\)
−0.0303245 + 0.999540i \(0.509654\pi\)
\(608\) 0 0
\(609\) −2709.00 −0.180253
\(610\) 0 0
\(611\) −40257.0 −2.66551
\(612\) 0 0
\(613\) 29646.0 1.95333 0.976664 0.214771i \(-0.0689004\pi\)
0.976664 + 0.214771i \(0.0689004\pi\)
\(614\) 0 0
\(615\) −1860.00 −0.121955
\(616\) 0 0
\(617\) 11006.0 0.718128 0.359064 0.933313i \(-0.383096\pi\)
0.359064 + 0.933313i \(0.383096\pi\)
\(618\) 0 0
\(619\) 21098.0 1.36995 0.684976 0.728566i \(-0.259813\pi\)
0.684976 + 0.728566i \(0.259813\pi\)
\(620\) 0 0
\(621\) 12150.0 0.785125
\(622\) 0 0
\(623\) 280.000 0.0180064
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 5202.00 0.331336
\(628\) 0 0
\(629\) 28574.0 1.81132
\(630\) 0 0
\(631\) −21707.0 −1.36948 −0.684740 0.728787i \(-0.740084\pi\)
−0.684740 + 0.728787i \(0.740084\pi\)
\(632\) 0 0
\(633\) −2091.00 −0.131295
\(634\) 0 0
\(635\) 1580.00 0.0987408
\(636\) 0 0
\(637\) 3969.00 0.246872
\(638\) 0 0
\(639\) −11952.0 −0.739928
\(640\) 0 0
\(641\) 11090.0 0.683352 0.341676 0.939818i \(-0.389005\pi\)
0.341676 + 0.939818i \(0.389005\pi\)
\(642\) 0 0
\(643\) −995.000 −0.0610248 −0.0305124 0.999534i \(-0.509714\pi\)
−0.0305124 + 0.999534i \(0.509714\pi\)
\(644\) 0 0
\(645\) −6510.00 −0.397412
\(646\) 0 0
\(647\) 20792.0 1.26340 0.631699 0.775214i \(-0.282358\pi\)
0.631699 + 0.775214i \(0.282358\pi\)
\(648\) 0 0
\(649\) 5644.00 0.341366
\(650\) 0 0
\(651\) 2436.00 0.146658
\(652\) 0 0
\(653\) 10498.0 0.629125 0.314562 0.949237i \(-0.398142\pi\)
0.314562 + 0.949237i \(0.398142\pi\)
\(654\) 0 0
\(655\) 8750.00 0.521971
\(656\) 0 0
\(657\) −4140.00 −0.245840
\(658\) 0 0
\(659\) −6749.00 −0.398943 −0.199472 0.979904i \(-0.563923\pi\)
−0.199472 + 0.979904i \(0.563923\pi\)
\(660\) 0 0
\(661\) −12400.0 −0.729658 −0.364829 0.931074i \(-0.618873\pi\)
−0.364829 + 0.931074i \(0.618873\pi\)
\(662\) 0 0
\(663\) 22113.0 1.29532
\(664\) 0 0
\(665\) −3570.00 −0.208178
\(666\) 0 0
\(667\) 11610.0 0.673975
\(668\) 0 0
\(669\) −2121.00 −0.122575
\(670\) 0 0
\(671\) 3740.00 0.215173
\(672\) 0 0
\(673\) 16024.0 0.917801 0.458900 0.888488i \(-0.348244\pi\)
0.458900 + 0.888488i \(0.348244\pi\)
\(674\) 0 0
\(675\) 3375.00 0.192450
\(676\) 0 0
\(677\) −18735.0 −1.06358 −0.531791 0.846876i \(-0.678481\pi\)
−0.531791 + 0.846876i \(0.678481\pi\)
\(678\) 0 0
\(679\) −1225.00 −0.0692359
\(680\) 0 0
\(681\) 1677.00 0.0943653
\(682\) 0 0
\(683\) −12844.0 −0.719564 −0.359782 0.933036i \(-0.617149\pi\)
−0.359782 + 0.933036i \(0.617149\pi\)
\(684\) 0 0
\(685\) −240.000 −0.0133868
\(686\) 0 0
\(687\) −11508.0 −0.639094
\(688\) 0 0
\(689\) 47304.0 2.61559
\(690\) 0 0
\(691\) 25996.0 1.43116 0.715582 0.698529i \(-0.246162\pi\)
0.715582 + 0.698529i \(0.246162\pi\)
\(692\) 0 0
\(693\) 2142.00 0.117414
\(694\) 0 0
\(695\) 190.000 0.0103699
\(696\) 0 0
\(697\) 11284.0 0.613217
\(698\) 0 0
\(699\) 4104.00 0.222071
\(700\) 0 0
\(701\) −25435.0 −1.37042 −0.685212 0.728344i \(-0.740290\pi\)
−0.685212 + 0.728344i \(0.740290\pi\)
\(702\) 0 0
\(703\) −32028.0 −1.71829
\(704\) 0 0
\(705\) −7455.00 −0.398258
\(706\) 0 0
\(707\) −1890.00 −0.100539
\(708\) 0 0
\(709\) −3823.00 −0.202505 −0.101252 0.994861i \(-0.532285\pi\)
−0.101252 + 0.994861i \(0.532285\pi\)
\(710\) 0 0
\(711\) 6498.00 0.342748
\(712\) 0 0
\(713\) −10440.0 −0.548361
\(714\) 0 0
\(715\) 6885.00 0.360118
\(716\) 0 0
\(717\) −11409.0 −0.594250
\(718\) 0 0
\(719\) −21090.0 −1.09391 −0.546957 0.837161i \(-0.684214\pi\)
−0.546957 + 0.837161i \(0.684214\pi\)
\(720\) 0 0
\(721\) −3955.00 −0.204288
\(722\) 0 0
\(723\) −16950.0 −0.871891
\(724\) 0 0
\(725\) 3225.00 0.165205
\(726\) 0 0
\(727\) 7992.00 0.407712 0.203856 0.979001i \(-0.434653\pi\)
0.203856 + 0.979001i \(0.434653\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) 0 0
\(731\) 39494.0 1.99827
\(732\) 0 0
\(733\) 36965.0 1.86266 0.931332 0.364170i \(-0.118647\pi\)
0.931332 + 0.364170i \(0.118647\pi\)
\(734\) 0 0
\(735\) 735.000 0.0368856
\(736\) 0 0
\(737\) −6528.00 −0.326271
\(738\) 0 0
\(739\) −3305.00 −0.164515 −0.0822574 0.996611i \(-0.526213\pi\)
−0.0822574 + 0.996611i \(0.526213\pi\)
\(740\) 0 0
\(741\) −24786.0 −1.22879
\(742\) 0 0
\(743\) 2208.00 0.109022 0.0545112 0.998513i \(-0.482640\pi\)
0.0545112 + 0.998513i \(0.482640\pi\)
\(744\) 0 0
\(745\) −17910.0 −0.880767
\(746\) 0 0
\(747\) −21096.0 −1.03328
\(748\) 0 0
\(749\) −8442.00 −0.411834
\(750\) 0 0
\(751\) 11551.0 0.561254 0.280627 0.959817i \(-0.409458\pi\)
0.280627 + 0.959817i \(0.409458\pi\)
\(752\) 0 0
\(753\) 4950.00 0.239559
\(754\) 0 0
\(755\) −9635.00 −0.464442
\(756\) 0 0
\(757\) −9688.00 −0.465147 −0.232574 0.972579i \(-0.574715\pi\)
−0.232574 + 0.972579i \(0.574715\pi\)
\(758\) 0 0
\(759\) 4590.00 0.219508
\(760\) 0 0
\(761\) −7014.00 −0.334109 −0.167055 0.985948i \(-0.553426\pi\)
−0.167055 + 0.985948i \(0.553426\pi\)
\(762\) 0 0
\(763\) 9933.00 0.471296
\(764\) 0 0
\(765\) −8190.00 −0.387072
\(766\) 0 0
\(767\) −26892.0 −1.26599
\(768\) 0 0
\(769\) −6278.00 −0.294396 −0.147198 0.989107i \(-0.547025\pi\)
−0.147198 + 0.989107i \(0.547025\pi\)
\(770\) 0 0
\(771\) −17430.0 −0.814171
\(772\) 0 0
\(773\) −21351.0 −0.993457 −0.496728 0.867906i \(-0.665465\pi\)
−0.496728 + 0.867906i \(0.665465\pi\)
\(774\) 0 0
\(775\) −2900.00 −0.134414
\(776\) 0 0
\(777\) 6594.00 0.304451
\(778\) 0 0
\(779\) −12648.0 −0.581722
\(780\) 0 0
\(781\) −11288.0 −0.517178
\(782\) 0 0
\(783\) 17415.0 0.794842
\(784\) 0 0
\(785\) −12550.0 −0.570610
\(786\) 0 0
\(787\) −25967.0 −1.17614 −0.588071 0.808809i \(-0.700112\pi\)
−0.588071 + 0.808809i \(0.700112\pi\)
\(788\) 0 0
\(789\) −8274.00 −0.373336
\(790\) 0 0
\(791\) −5446.00 −0.244801
\(792\) 0 0
\(793\) −17820.0 −0.797991
\(794\) 0 0
\(795\) 8760.00 0.390799
\(796\) 0 0
\(797\) 8595.00 0.381996 0.190998 0.981590i \(-0.438828\pi\)
0.190998 + 0.981590i \(0.438828\pi\)
\(798\) 0 0
\(799\) 45227.0 2.00252
\(800\) 0 0
\(801\) −720.000 −0.0317602
\(802\) 0 0
\(803\) −3910.00 −0.171832
\(804\) 0 0
\(805\) −3150.00 −0.137917
\(806\) 0 0
\(807\) 558.000 0.0243402
\(808\) 0 0
\(809\) −13671.0 −0.594125 −0.297062 0.954858i \(-0.596007\pi\)
−0.297062 + 0.954858i \(0.596007\pi\)
\(810\) 0 0
\(811\) −11986.0 −0.518971 −0.259485 0.965747i \(-0.583553\pi\)
−0.259485 + 0.965747i \(0.583553\pi\)
\(812\) 0 0
\(813\) −20484.0 −0.883647
\(814\) 0 0
\(815\) 9350.00 0.401860
\(816\) 0 0
\(817\) −44268.0 −1.89564
\(818\) 0 0
\(819\) −10206.0 −0.435441
\(820\) 0 0
\(821\) 12951.0 0.550540 0.275270 0.961367i \(-0.411233\pi\)
0.275270 + 0.961367i \(0.411233\pi\)
\(822\) 0 0
\(823\) 12788.0 0.541630 0.270815 0.962631i \(-0.412707\pi\)
0.270815 + 0.962631i \(0.412707\pi\)
\(824\) 0 0
\(825\) 1275.00 0.0538058
\(826\) 0 0
\(827\) 24662.0 1.03698 0.518490 0.855084i \(-0.326495\pi\)
0.518490 + 0.855084i \(0.326495\pi\)
\(828\) 0 0
\(829\) −4124.00 −0.172777 −0.0863887 0.996262i \(-0.527533\pi\)
−0.0863887 + 0.996262i \(0.527533\pi\)
\(830\) 0 0
\(831\) −24642.0 −1.02867
\(832\) 0 0
\(833\) −4459.00 −0.185468
\(834\) 0 0
\(835\) −10095.0 −0.418385
\(836\) 0 0
\(837\) −15660.0 −0.646701
\(838\) 0 0
\(839\) 33154.0 1.36425 0.682123 0.731237i \(-0.261057\pi\)
0.682123 + 0.731237i \(0.261057\pi\)
\(840\) 0 0
\(841\) −7748.00 −0.317684
\(842\) 0 0
\(843\) −20121.0 −0.822069
\(844\) 0 0
\(845\) −21820.0 −0.888320
\(846\) 0 0
\(847\) −7294.00 −0.295897
\(848\) 0 0
\(849\) 16491.0 0.666631
\(850\) 0 0
\(851\) −28260.0 −1.13836
\(852\) 0 0
\(853\) −12050.0 −0.483686 −0.241843 0.970315i \(-0.577752\pi\)
−0.241843 + 0.970315i \(0.577752\pi\)
\(854\) 0 0
\(855\) 9180.00 0.367192
\(856\) 0 0
\(857\) 15270.0 0.608650 0.304325 0.952568i \(-0.401569\pi\)
0.304325 + 0.952568i \(0.401569\pi\)
\(858\) 0 0
\(859\) −12564.0 −0.499043 −0.249522 0.968369i \(-0.580273\pi\)
−0.249522 + 0.968369i \(0.580273\pi\)
\(860\) 0 0
\(861\) 2604.00 0.103071
\(862\) 0 0
\(863\) −12976.0 −0.511829 −0.255914 0.966699i \(-0.582377\pi\)
−0.255914 + 0.966699i \(0.582377\pi\)
\(864\) 0 0
\(865\) 6265.00 0.246262
\(866\) 0 0
\(867\) −10104.0 −0.395790
\(868\) 0 0
\(869\) 6137.00 0.239567
\(870\) 0 0
\(871\) 31104.0 1.21001
\(872\) 0 0
\(873\) 3150.00 0.122121
\(874\) 0 0
\(875\) −875.000 −0.0338062
\(876\) 0 0
\(877\) 15634.0 0.601964 0.300982 0.953630i \(-0.402686\pi\)
0.300982 + 0.953630i \(0.402686\pi\)
\(878\) 0 0
\(879\) 939.000 0.0360315
\(880\) 0 0
\(881\) −8896.00 −0.340197 −0.170099 0.985427i \(-0.554409\pi\)
−0.170099 + 0.985427i \(0.554409\pi\)
\(882\) 0 0
\(883\) −33456.0 −1.27507 −0.637533 0.770423i \(-0.720045\pi\)
−0.637533 + 0.770423i \(0.720045\pi\)
\(884\) 0 0
\(885\) −4980.00 −0.189154
\(886\) 0 0
\(887\) −8288.00 −0.313736 −0.156868 0.987620i \(-0.550140\pi\)
−0.156868 + 0.987620i \(0.550140\pi\)
\(888\) 0 0
\(889\) −2212.00 −0.0834512
\(890\) 0 0
\(891\) −1377.00 −0.0517747
\(892\) 0 0
\(893\) −50694.0 −1.89968
\(894\) 0 0
\(895\) −2460.00 −0.0918757
\(896\) 0 0
\(897\) −21870.0 −0.814067
\(898\) 0 0
\(899\) −14964.0 −0.555147
\(900\) 0 0
\(901\) −53144.0 −1.96502
\(902\) 0 0
\(903\) 9114.00 0.335875
\(904\) 0 0
\(905\) −22240.0 −0.816887
\(906\) 0 0
\(907\) 15398.0 0.563707 0.281853 0.959457i \(-0.409051\pi\)
0.281853 + 0.959457i \(0.409051\pi\)
\(908\) 0 0
\(909\) 4860.00 0.177333
\(910\) 0 0
\(911\) −22656.0 −0.823959 −0.411980 0.911193i \(-0.635162\pi\)
−0.411980 + 0.911193i \(0.635162\pi\)
\(912\) 0 0
\(913\) −19924.0 −0.722221
\(914\) 0 0
\(915\) −3300.00 −0.119229
\(916\) 0 0
\(917\) −12250.0 −0.441146
\(918\) 0 0
\(919\) −9149.00 −0.328398 −0.164199 0.986427i \(-0.552504\pi\)
−0.164199 + 0.986427i \(0.552504\pi\)
\(920\) 0 0
\(921\) −16437.0 −0.588076
\(922\) 0 0
\(923\) 53784.0 1.91801
\(924\) 0 0
\(925\) −7850.00 −0.279034
\(926\) 0 0
\(927\) 10170.0 0.360331
\(928\) 0 0
\(929\) −27272.0 −0.963149 −0.481574 0.876405i \(-0.659935\pi\)
−0.481574 + 0.876405i \(0.659935\pi\)
\(930\) 0 0
\(931\) 4998.00 0.175943
\(932\) 0 0
\(933\) 13266.0 0.465498
\(934\) 0 0
\(935\) −7735.00 −0.270547
\(936\) 0 0
\(937\) 44177.0 1.54023 0.770117 0.637902i \(-0.220198\pi\)
0.770117 + 0.637902i \(0.220198\pi\)
\(938\) 0 0
\(939\) −825.000 −0.0286718
\(940\) 0 0
\(941\) 2236.00 0.0774618 0.0387309 0.999250i \(-0.487668\pi\)
0.0387309 + 0.999250i \(0.487668\pi\)
\(942\) 0 0
\(943\) −11160.0 −0.385387
\(944\) 0 0
\(945\) −4725.00 −0.162650
\(946\) 0 0
\(947\) −17464.0 −0.599265 −0.299632 0.954055i \(-0.596864\pi\)
−0.299632 + 0.954055i \(0.596864\pi\)
\(948\) 0 0
\(949\) 18630.0 0.637255
\(950\) 0 0
\(951\) −12318.0 −0.420019
\(952\) 0 0
\(953\) −18336.0 −0.623254 −0.311627 0.950204i \(-0.600874\pi\)
−0.311627 + 0.950204i \(0.600874\pi\)
\(954\) 0 0
\(955\) 19995.0 0.677511
\(956\) 0 0
\(957\) 6579.00 0.222225
\(958\) 0 0
\(959\) 336.000 0.0113139
\(960\) 0 0
\(961\) −16335.0 −0.548320
\(962\) 0 0
\(963\) 21708.0 0.726408
\(964\) 0 0
\(965\) −24400.0 −0.813952
\(966\) 0 0
\(967\) 46802.0 1.55641 0.778206 0.628009i \(-0.216130\pi\)
0.778206 + 0.628009i \(0.216130\pi\)
\(968\) 0 0
\(969\) 27846.0 0.923160
\(970\) 0 0
\(971\) 45024.0 1.48804 0.744021 0.668156i \(-0.232916\pi\)
0.744021 + 0.668156i \(0.232916\pi\)
\(972\) 0 0
\(973\) −266.000 −0.00876420
\(974\) 0 0
\(975\) −6075.00 −0.199544
\(976\) 0 0
\(977\) 12786.0 0.418690 0.209345 0.977842i \(-0.432867\pi\)
0.209345 + 0.977842i \(0.432867\pi\)
\(978\) 0 0
\(979\) −680.000 −0.0221991
\(980\) 0 0
\(981\) −25542.0 −0.831288
\(982\) 0 0
\(983\) −33539.0 −1.08823 −0.544114 0.839011i \(-0.683134\pi\)
−0.544114 + 0.839011i \(0.683134\pi\)
\(984\) 0 0
\(985\) 23560.0 0.762116
\(986\) 0 0
\(987\) 10437.0 0.336589
\(988\) 0 0
\(989\) −39060.0 −1.25585
\(990\) 0 0
\(991\) 18200.0 0.583393 0.291696 0.956511i \(-0.405780\pi\)
0.291696 + 0.956511i \(0.405780\pi\)
\(992\) 0 0
\(993\) −24780.0 −0.791913
\(994\) 0 0
\(995\) 13780.0 0.439051
\(996\) 0 0
\(997\) 32599.0 1.03553 0.517764 0.855524i \(-0.326765\pi\)
0.517764 + 0.855524i \(0.326765\pi\)
\(998\) 0 0
\(999\) −42390.0 −1.34250
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 2240.4.a.p.1.1 1
4.3 odd 2 2240.4.a.w.1.1 1
8.3 odd 2 70.4.a.b.1.1 1
8.5 even 2 560.4.a.k.1.1 1
24.11 even 2 630.4.a.m.1.1 1
40.3 even 4 350.4.c.j.99.2 2
40.19 odd 2 350.4.a.t.1.1 1
40.27 even 4 350.4.c.j.99.1 2
56.3 even 6 490.4.e.l.471.1 2
56.11 odd 6 490.4.e.p.471.1 2
56.19 even 6 490.4.e.l.361.1 2
56.27 even 2 490.4.a.f.1.1 1
56.51 odd 6 490.4.e.p.361.1 2
280.139 even 2 2450.4.a.ba.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.4.a.b.1.1 1 8.3 odd 2
350.4.a.t.1.1 1 40.19 odd 2
350.4.c.j.99.1 2 40.27 even 4
350.4.c.j.99.2 2 40.3 even 4
490.4.a.f.1.1 1 56.27 even 2
490.4.e.l.361.1 2 56.19 even 6
490.4.e.l.471.1 2 56.3 even 6
490.4.e.p.361.1 2 56.51 odd 6
490.4.e.p.471.1 2 56.11 odd 6
560.4.a.k.1.1 1 8.5 even 2
630.4.a.m.1.1 1 24.11 even 2
2240.4.a.p.1.1 1 1.1 even 1 trivial
2240.4.a.w.1.1 1 4.3 odd 2
2450.4.a.ba.1.1 1 280.139 even 2