Properties

Label 1840.4.a.d.1.1
Level $1840$
Weight $4$
Character 1840.1
Self dual yes
Analytic conductor $108.564$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1840,4,Mod(1,1840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1840, 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("1840.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.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: \(108.563514411\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -5.00000 q^{5} +18.0000 q^{7} -26.0000 q^{9} +32.0000 q^{11} -47.0000 q^{13} +5.00000 q^{15} +20.0000 q^{17} -36.0000 q^{19} -18.0000 q^{21} +23.0000 q^{23} +25.0000 q^{25} +53.0000 q^{27} -27.0000 q^{29} +33.0000 q^{31} -32.0000 q^{33} -90.0000 q^{35} +56.0000 q^{37} +47.0000 q^{39} -157.000 q^{41} -18.0000 q^{43} +130.000 q^{45} -65.0000 q^{47} -19.0000 q^{49} -20.0000 q^{51} -14.0000 q^{53} -160.000 q^{55} +36.0000 q^{57} +744.000 q^{59} +552.000 q^{61} -468.000 q^{63} +235.000 q^{65} +156.000 q^{67} -23.0000 q^{69} -699.000 q^{71} -609.000 q^{73} -25.0000 q^{75} +576.000 q^{77} +644.000 q^{79} +649.000 q^{81} -512.000 q^{83} -100.000 q^{85} +27.0000 q^{87} -102.000 q^{89} -846.000 q^{91} -33.0000 q^{93} +180.000 q^{95} +578.000 q^{97} -832.000 q^{99} +O(q^{100})\)

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
\(3\) −1.00000 −0.192450 −0.0962250 0.995360i \(-0.530677\pi\)
−0.0962250 + 0.995360i \(0.530677\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 18.0000 0.971909 0.485954 0.873984i \(-0.338472\pi\)
0.485954 + 0.873984i \(0.338472\pi\)
\(8\) 0 0
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) 32.0000 0.877124 0.438562 0.898701i \(-0.355488\pi\)
0.438562 + 0.898701i \(0.355488\pi\)
\(12\) 0 0
\(13\) −47.0000 −1.00273 −0.501364 0.865237i \(-0.667168\pi\)
−0.501364 + 0.865237i \(0.667168\pi\)
\(14\) 0 0
\(15\) 5.00000 0.0860663
\(16\) 0 0
\(17\) 20.0000 0.285336 0.142668 0.989771i \(-0.454432\pi\)
0.142668 + 0.989771i \(0.454432\pi\)
\(18\) 0 0
\(19\) −36.0000 −0.434682 −0.217341 0.976096i \(-0.569738\pi\)
−0.217341 + 0.976096i \(0.569738\pi\)
\(20\) 0 0
\(21\) −18.0000 −0.187044
\(22\) 0 0
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 53.0000 0.377772
\(28\) 0 0
\(29\) −27.0000 −0.172889 −0.0864444 0.996257i \(-0.527550\pi\)
−0.0864444 + 0.996257i \(0.527550\pi\)
\(30\) 0 0
\(31\) 33.0000 0.191193 0.0955964 0.995420i \(-0.469524\pi\)
0.0955964 + 0.995420i \(0.469524\pi\)
\(32\) 0 0
\(33\) −32.0000 −0.168803
\(34\) 0 0
\(35\) −90.0000 −0.434651
\(36\) 0 0
\(37\) 56.0000 0.248820 0.124410 0.992231i \(-0.460296\pi\)
0.124410 + 0.992231i \(0.460296\pi\)
\(38\) 0 0
\(39\) 47.0000 0.192975
\(40\) 0 0
\(41\) −157.000 −0.598031 −0.299016 0.954248i \(-0.596658\pi\)
−0.299016 + 0.954248i \(0.596658\pi\)
\(42\) 0 0
\(43\) −18.0000 −0.0638366 −0.0319183 0.999490i \(-0.510162\pi\)
−0.0319183 + 0.999490i \(0.510162\pi\)
\(44\) 0 0
\(45\) 130.000 0.430650
\(46\) 0 0
\(47\) −65.0000 −0.201728 −0.100864 0.994900i \(-0.532161\pi\)
−0.100864 + 0.994900i \(0.532161\pi\)
\(48\) 0 0
\(49\) −19.0000 −0.0553936
\(50\) 0 0
\(51\) −20.0000 −0.0549129
\(52\) 0 0
\(53\) −14.0000 −0.0362839 −0.0181420 0.999835i \(-0.505775\pi\)
−0.0181420 + 0.999835i \(0.505775\pi\)
\(54\) 0 0
\(55\) −160.000 −0.392262
\(56\) 0 0
\(57\) 36.0000 0.0836547
\(58\) 0 0
\(59\) 744.000 1.64170 0.820852 0.571141i \(-0.193499\pi\)
0.820852 + 0.571141i \(0.193499\pi\)
\(60\) 0 0
\(61\) 552.000 1.15863 0.579314 0.815104i \(-0.303320\pi\)
0.579314 + 0.815104i \(0.303320\pi\)
\(62\) 0 0
\(63\) −468.000 −0.935912
\(64\) 0 0
\(65\) 235.000 0.448433
\(66\) 0 0
\(67\) 156.000 0.284454 0.142227 0.989834i \(-0.454574\pi\)
0.142227 + 0.989834i \(0.454574\pi\)
\(68\) 0 0
\(69\) −23.0000 −0.0401286
\(70\) 0 0
\(71\) −699.000 −1.16839 −0.584197 0.811612i \(-0.698591\pi\)
−0.584197 + 0.811612i \(0.698591\pi\)
\(72\) 0 0
\(73\) −609.000 −0.976412 −0.488206 0.872728i \(-0.662348\pi\)
−0.488206 + 0.872728i \(0.662348\pi\)
\(74\) 0 0
\(75\) −25.0000 −0.0384900
\(76\) 0 0
\(77\) 576.000 0.852484
\(78\) 0 0
\(79\) 644.000 0.917160 0.458580 0.888653i \(-0.348358\pi\)
0.458580 + 0.888653i \(0.348358\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 0 0
\(83\) −512.000 −0.677100 −0.338550 0.940948i \(-0.609936\pi\)
−0.338550 + 0.940948i \(0.609936\pi\)
\(84\) 0 0
\(85\) −100.000 −0.127606
\(86\) 0 0
\(87\) 27.0000 0.0332725
\(88\) 0 0
\(89\) −102.000 −0.121483 −0.0607415 0.998154i \(-0.519347\pi\)
−0.0607415 + 0.998154i \(0.519347\pi\)
\(90\) 0 0
\(91\) −846.000 −0.974559
\(92\) 0 0
\(93\) −33.0000 −0.0367951
\(94\) 0 0
\(95\) 180.000 0.194396
\(96\) 0 0
\(97\) 578.000 0.605021 0.302510 0.953146i \(-0.402175\pi\)
0.302510 + 0.953146i \(0.402175\pi\)
\(98\) 0 0
\(99\) −832.000 −0.844638
\(100\) 0 0
\(101\) −6.00000 −0.00591111 −0.00295556 0.999996i \(-0.500941\pi\)
−0.00295556 + 0.999996i \(0.500941\pi\)
\(102\) 0 0
\(103\) 160.000 0.153061 0.0765304 0.997067i \(-0.475616\pi\)
0.0765304 + 0.997067i \(0.475616\pi\)
\(104\) 0 0
\(105\) 90.0000 0.0836486
\(106\) 0 0
\(107\) −380.000 −0.343327 −0.171663 0.985156i \(-0.554914\pi\)
−0.171663 + 0.985156i \(0.554914\pi\)
\(108\) 0 0
\(109\) 250.000 0.219685 0.109842 0.993949i \(-0.464965\pi\)
0.109842 + 0.993949i \(0.464965\pi\)
\(110\) 0 0
\(111\) −56.0000 −0.0478854
\(112\) 0 0
\(113\) −390.000 −0.324674 −0.162337 0.986735i \(-0.551903\pi\)
−0.162337 + 0.986735i \(0.551903\pi\)
\(114\) 0 0
\(115\) −115.000 −0.0932505
\(116\) 0 0
\(117\) 1222.00 0.965589
\(118\) 0 0
\(119\) 360.000 0.277321
\(120\) 0 0
\(121\) −307.000 −0.230654
\(122\) 0 0
\(123\) 157.000 0.115091
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 769.000 0.537305 0.268652 0.963237i \(-0.413422\pi\)
0.268652 + 0.963237i \(0.413422\pi\)
\(128\) 0 0
\(129\) 18.0000 0.0122854
\(130\) 0 0
\(131\) 213.000 0.142060 0.0710301 0.997474i \(-0.477371\pi\)
0.0710301 + 0.997474i \(0.477371\pi\)
\(132\) 0 0
\(133\) −648.000 −0.422472
\(134\) 0 0
\(135\) −265.000 −0.168945
\(136\) 0 0
\(137\) 2836.00 1.76858 0.884291 0.466936i \(-0.154642\pi\)
0.884291 + 0.466936i \(0.154642\pi\)
\(138\) 0 0
\(139\) 1631.00 0.995249 0.497625 0.867393i \(-0.334206\pi\)
0.497625 + 0.867393i \(0.334206\pi\)
\(140\) 0 0
\(141\) 65.0000 0.0388226
\(142\) 0 0
\(143\) −1504.00 −0.879516
\(144\) 0 0
\(145\) 135.000 0.0773182
\(146\) 0 0
\(147\) 19.0000 0.0106605
\(148\) 0 0
\(149\) −1966.00 −1.08095 −0.540473 0.841361i \(-0.681755\pi\)
−0.540473 + 0.841361i \(0.681755\pi\)
\(150\) 0 0
\(151\) −35.0000 −0.0188626 −0.00943132 0.999956i \(-0.503002\pi\)
−0.00943132 + 0.999956i \(0.503002\pi\)
\(152\) 0 0
\(153\) −520.000 −0.274768
\(154\) 0 0
\(155\) −165.000 −0.0855040
\(156\) 0 0
\(157\) 1702.00 0.865187 0.432594 0.901589i \(-0.357599\pi\)
0.432594 + 0.901589i \(0.357599\pi\)
\(158\) 0 0
\(159\) 14.0000 0.00698284
\(160\) 0 0
\(161\) 414.000 0.202657
\(162\) 0 0
\(163\) 2045.00 0.982680 0.491340 0.870968i \(-0.336507\pi\)
0.491340 + 0.870968i \(0.336507\pi\)
\(164\) 0 0
\(165\) 160.000 0.0754908
\(166\) 0 0
\(167\) −1016.00 −0.470781 −0.235391 0.971901i \(-0.575637\pi\)
−0.235391 + 0.971901i \(0.575637\pi\)
\(168\) 0 0
\(169\) 12.0000 0.00546199
\(170\) 0 0
\(171\) 936.000 0.418583
\(172\) 0 0
\(173\) 598.000 0.262804 0.131402 0.991329i \(-0.458052\pi\)
0.131402 + 0.991329i \(0.458052\pi\)
\(174\) 0 0
\(175\) 450.000 0.194382
\(176\) 0 0
\(177\) −744.000 −0.315946
\(178\) 0 0
\(179\) 4607.00 1.92371 0.961853 0.273567i \(-0.0882036\pi\)
0.961853 + 0.273567i \(0.0882036\pi\)
\(180\) 0 0
\(181\) −1212.00 −0.497720 −0.248860 0.968540i \(-0.580056\pi\)
−0.248860 + 0.968540i \(0.580056\pi\)
\(182\) 0 0
\(183\) −552.000 −0.222978
\(184\) 0 0
\(185\) −280.000 −0.111276
\(186\) 0 0
\(187\) 640.000 0.250275
\(188\) 0 0
\(189\) 954.000 0.367160
\(190\) 0 0
\(191\) 1058.00 0.400807 0.200404 0.979713i \(-0.435775\pi\)
0.200404 + 0.979713i \(0.435775\pi\)
\(192\) 0 0
\(193\) 1047.00 0.390491 0.195245 0.980754i \(-0.437450\pi\)
0.195245 + 0.980754i \(0.437450\pi\)
\(194\) 0 0
\(195\) −235.000 −0.0863010
\(196\) 0 0
\(197\) 251.000 0.0907767 0.0453883 0.998969i \(-0.485547\pi\)
0.0453883 + 0.998969i \(0.485547\pi\)
\(198\) 0 0
\(199\) 3508.00 1.24963 0.624813 0.780775i \(-0.285175\pi\)
0.624813 + 0.780775i \(0.285175\pi\)
\(200\) 0 0
\(201\) −156.000 −0.0547432
\(202\) 0 0
\(203\) −486.000 −0.168032
\(204\) 0 0
\(205\) 785.000 0.267448
\(206\) 0 0
\(207\) −598.000 −0.200792
\(208\) 0 0
\(209\) −1152.00 −0.381270
\(210\) 0 0
\(211\) 3296.00 1.07538 0.537692 0.843141i \(-0.319296\pi\)
0.537692 + 0.843141i \(0.319296\pi\)
\(212\) 0 0
\(213\) 699.000 0.224858
\(214\) 0 0
\(215\) 90.0000 0.0285486
\(216\) 0 0
\(217\) 594.000 0.185822
\(218\) 0 0
\(219\) 609.000 0.187911
\(220\) 0 0
\(221\) −940.000 −0.286114
\(222\) 0 0
\(223\) 2720.00 0.816792 0.408396 0.912805i \(-0.366088\pi\)
0.408396 + 0.912805i \(0.366088\pi\)
\(224\) 0 0
\(225\) −650.000 −0.192593
\(226\) 0 0
\(227\) 4134.00 1.20874 0.604368 0.796705i \(-0.293426\pi\)
0.604368 + 0.796705i \(0.293426\pi\)
\(228\) 0 0
\(229\) −4510.00 −1.30144 −0.650719 0.759319i \(-0.725532\pi\)
−0.650719 + 0.759319i \(0.725532\pi\)
\(230\) 0 0
\(231\) −576.000 −0.164061
\(232\) 0 0
\(233\) −5003.00 −1.40668 −0.703342 0.710852i \(-0.748310\pi\)
−0.703342 + 0.710852i \(0.748310\pi\)
\(234\) 0 0
\(235\) 325.000 0.0902156
\(236\) 0 0
\(237\) −644.000 −0.176508
\(238\) 0 0
\(239\) 6309.00 1.70751 0.853756 0.520674i \(-0.174319\pi\)
0.853756 + 0.520674i \(0.174319\pi\)
\(240\) 0 0
\(241\) 3038.00 0.812012 0.406006 0.913871i \(-0.366921\pi\)
0.406006 + 0.913871i \(0.366921\pi\)
\(242\) 0 0
\(243\) −2080.00 −0.549103
\(244\) 0 0
\(245\) 95.0000 0.0247728
\(246\) 0 0
\(247\) 1692.00 0.435868
\(248\) 0 0
\(249\) 512.000 0.130308
\(250\) 0 0
\(251\) 1332.00 0.334961 0.167480 0.985875i \(-0.446437\pi\)
0.167480 + 0.985875i \(0.446437\pi\)
\(252\) 0 0
\(253\) 736.000 0.182893
\(254\) 0 0
\(255\) 100.000 0.0245578
\(256\) 0 0
\(257\) 3301.00 0.801209 0.400605 0.916251i \(-0.368800\pi\)
0.400605 + 0.916251i \(0.368800\pi\)
\(258\) 0 0
\(259\) 1008.00 0.241830
\(260\) 0 0
\(261\) 702.000 0.166485
\(262\) 0 0
\(263\) −2072.00 −0.485798 −0.242899 0.970052i \(-0.578098\pi\)
−0.242899 + 0.970052i \(0.578098\pi\)
\(264\) 0 0
\(265\) 70.0000 0.0162267
\(266\) 0 0
\(267\) 102.000 0.0233794
\(268\) 0 0
\(269\) 5721.00 1.29671 0.648356 0.761337i \(-0.275457\pi\)
0.648356 + 0.761337i \(0.275457\pi\)
\(270\) 0 0
\(271\) 5900.00 1.32251 0.661254 0.750162i \(-0.270025\pi\)
0.661254 + 0.750162i \(0.270025\pi\)
\(272\) 0 0
\(273\) 846.000 0.187554
\(274\) 0 0
\(275\) 800.000 0.175425
\(276\) 0 0
\(277\) 6371.00 1.38194 0.690968 0.722885i \(-0.257185\pi\)
0.690968 + 0.722885i \(0.257185\pi\)
\(278\) 0 0
\(279\) −858.000 −0.184112
\(280\) 0 0
\(281\) 3190.00 0.677222 0.338611 0.940926i \(-0.390043\pi\)
0.338611 + 0.940926i \(0.390043\pi\)
\(282\) 0 0
\(283\) 4226.00 0.887667 0.443833 0.896109i \(-0.353618\pi\)
0.443833 + 0.896109i \(0.353618\pi\)
\(284\) 0 0
\(285\) −180.000 −0.0374115
\(286\) 0 0
\(287\) −2826.00 −0.581232
\(288\) 0 0
\(289\) −4513.00 −0.918583
\(290\) 0 0
\(291\) −578.000 −0.116436
\(292\) 0 0
\(293\) 6048.00 1.20590 0.602949 0.797780i \(-0.293992\pi\)
0.602949 + 0.797780i \(0.293992\pi\)
\(294\) 0 0
\(295\) −3720.00 −0.734192
\(296\) 0 0
\(297\) 1696.00 0.331353
\(298\) 0 0
\(299\) −1081.00 −0.209083
\(300\) 0 0
\(301\) −324.000 −0.0620434
\(302\) 0 0
\(303\) 6.00000 0.00113759
\(304\) 0 0
\(305\) −2760.00 −0.518155
\(306\) 0 0
\(307\) −8628.00 −1.60399 −0.801997 0.597328i \(-0.796229\pi\)
−0.801997 + 0.597328i \(0.796229\pi\)
\(308\) 0 0
\(309\) −160.000 −0.0294566
\(310\) 0 0
\(311\) −8247.00 −1.50368 −0.751840 0.659346i \(-0.770833\pi\)
−0.751840 + 0.659346i \(0.770833\pi\)
\(312\) 0 0
\(313\) 2620.00 0.473135 0.236567 0.971615i \(-0.423978\pi\)
0.236567 + 0.971615i \(0.423978\pi\)
\(314\) 0 0
\(315\) 2340.00 0.418553
\(316\) 0 0
\(317\) 9906.00 1.75513 0.877565 0.479457i \(-0.159166\pi\)
0.877565 + 0.479457i \(0.159166\pi\)
\(318\) 0 0
\(319\) −864.000 −0.151645
\(320\) 0 0
\(321\) 380.000 0.0660733
\(322\) 0 0
\(323\) −720.000 −0.124031
\(324\) 0 0
\(325\) −1175.00 −0.200545
\(326\) 0 0
\(327\) −250.000 −0.0422784
\(328\) 0 0
\(329\) −1170.00 −0.196061
\(330\) 0 0
\(331\) 8115.00 1.34756 0.673778 0.738934i \(-0.264671\pi\)
0.673778 + 0.738934i \(0.264671\pi\)
\(332\) 0 0
\(333\) −1456.00 −0.239605
\(334\) 0 0
\(335\) −780.000 −0.127212
\(336\) 0 0
\(337\) −7586.00 −1.22622 −0.613109 0.789998i \(-0.710082\pi\)
−0.613109 + 0.789998i \(0.710082\pi\)
\(338\) 0 0
\(339\) 390.000 0.0624835
\(340\) 0 0
\(341\) 1056.00 0.167700
\(342\) 0 0
\(343\) −6516.00 −1.02575
\(344\) 0 0
\(345\) 115.000 0.0179461
\(346\) 0 0
\(347\) −1356.00 −0.209781 −0.104890 0.994484i \(-0.533449\pi\)
−0.104890 + 0.994484i \(0.533449\pi\)
\(348\) 0 0
\(349\) 6649.00 1.01981 0.509904 0.860231i \(-0.329681\pi\)
0.509904 + 0.860231i \(0.329681\pi\)
\(350\) 0 0
\(351\) −2491.00 −0.378803
\(352\) 0 0
\(353\) 10691.0 1.61197 0.805984 0.591938i \(-0.201637\pi\)
0.805984 + 0.591938i \(0.201637\pi\)
\(354\) 0 0
\(355\) 3495.00 0.522522
\(356\) 0 0
\(357\) −360.000 −0.0533704
\(358\) 0 0
\(359\) 6420.00 0.943829 0.471915 0.881644i \(-0.343563\pi\)
0.471915 + 0.881644i \(0.343563\pi\)
\(360\) 0 0
\(361\) −5563.00 −0.811051
\(362\) 0 0
\(363\) 307.000 0.0443893
\(364\) 0 0
\(365\) 3045.00 0.436665
\(366\) 0 0
\(367\) 524.000 0.0745302 0.0372651 0.999305i \(-0.488135\pi\)
0.0372651 + 0.999305i \(0.488135\pi\)
\(368\) 0 0
\(369\) 4082.00 0.575882
\(370\) 0 0
\(371\) −252.000 −0.0352647
\(372\) 0 0
\(373\) 5566.00 0.772645 0.386322 0.922364i \(-0.373745\pi\)
0.386322 + 0.922364i \(0.373745\pi\)
\(374\) 0 0
\(375\) 125.000 0.0172133
\(376\) 0 0
\(377\) 1269.00 0.173360
\(378\) 0 0
\(379\) −2240.00 −0.303591 −0.151796 0.988412i \(-0.548506\pi\)
−0.151796 + 0.988412i \(0.548506\pi\)
\(380\) 0 0
\(381\) −769.000 −0.103404
\(382\) 0 0
\(383\) −8778.00 −1.17111 −0.585555 0.810633i \(-0.699123\pi\)
−0.585555 + 0.810633i \(0.699123\pi\)
\(384\) 0 0
\(385\) −2880.00 −0.381243
\(386\) 0 0
\(387\) 468.000 0.0614723
\(388\) 0 0
\(389\) 4056.00 0.528656 0.264328 0.964433i \(-0.414850\pi\)
0.264328 + 0.964433i \(0.414850\pi\)
\(390\) 0 0
\(391\) 460.000 0.0594967
\(392\) 0 0
\(393\) −213.000 −0.0273395
\(394\) 0 0
\(395\) −3220.00 −0.410167
\(396\) 0 0
\(397\) −9151.00 −1.15687 −0.578433 0.815730i \(-0.696335\pi\)
−0.578433 + 0.815730i \(0.696335\pi\)
\(398\) 0 0
\(399\) 648.000 0.0813047
\(400\) 0 0
\(401\) 15930.0 1.98381 0.991903 0.126997i \(-0.0405340\pi\)
0.991903 + 0.126997i \(0.0405340\pi\)
\(402\) 0 0
\(403\) −1551.00 −0.191714
\(404\) 0 0
\(405\) −3245.00 −0.398137
\(406\) 0 0
\(407\) 1792.00 0.218246
\(408\) 0 0
\(409\) −5891.00 −0.712203 −0.356102 0.934447i \(-0.615894\pi\)
−0.356102 + 0.934447i \(0.615894\pi\)
\(410\) 0 0
\(411\) −2836.00 −0.340364
\(412\) 0 0
\(413\) 13392.0 1.59559
\(414\) 0 0
\(415\) 2560.00 0.302808
\(416\) 0 0
\(417\) −1631.00 −0.191536
\(418\) 0 0
\(419\) −15282.0 −1.78180 −0.890900 0.454199i \(-0.849926\pi\)
−0.890900 + 0.454199i \(0.849926\pi\)
\(420\) 0 0
\(421\) −10934.0 −1.26577 −0.632887 0.774244i \(-0.718130\pi\)
−0.632887 + 0.774244i \(0.718130\pi\)
\(422\) 0 0
\(423\) 1690.00 0.194257
\(424\) 0 0
\(425\) 500.000 0.0570672
\(426\) 0 0
\(427\) 9936.00 1.12608
\(428\) 0 0
\(429\) 1504.00 0.169263
\(430\) 0 0
\(431\) 2794.00 0.312256 0.156128 0.987737i \(-0.450099\pi\)
0.156128 + 0.987737i \(0.450099\pi\)
\(432\) 0 0
\(433\) −15062.0 −1.67167 −0.835835 0.548980i \(-0.815016\pi\)
−0.835835 + 0.548980i \(0.815016\pi\)
\(434\) 0 0
\(435\) −135.000 −0.0148799
\(436\) 0 0
\(437\) −828.000 −0.0906376
\(438\) 0 0
\(439\) −261.000 −0.0283755 −0.0141878 0.999899i \(-0.504516\pi\)
−0.0141878 + 0.999899i \(0.504516\pi\)
\(440\) 0 0
\(441\) 494.000 0.0533420
\(442\) 0 0
\(443\) 7083.00 0.759647 0.379823 0.925059i \(-0.375985\pi\)
0.379823 + 0.925059i \(0.375985\pi\)
\(444\) 0 0
\(445\) 510.000 0.0543288
\(446\) 0 0
\(447\) 1966.00 0.208028
\(448\) 0 0
\(449\) −10370.0 −1.08996 −0.544978 0.838450i \(-0.683462\pi\)
−0.544978 + 0.838450i \(0.683462\pi\)
\(450\) 0 0
\(451\) −5024.00 −0.524547
\(452\) 0 0
\(453\) 35.0000 0.00363012
\(454\) 0 0
\(455\) 4230.00 0.435836
\(456\) 0 0
\(457\) −10496.0 −1.07436 −0.537180 0.843468i \(-0.680510\pi\)
−0.537180 + 0.843468i \(0.680510\pi\)
\(458\) 0 0
\(459\) 1060.00 0.107792
\(460\) 0 0
\(461\) 18021.0 1.82065 0.910327 0.413889i \(-0.135830\pi\)
0.910327 + 0.413889i \(0.135830\pi\)
\(462\) 0 0
\(463\) 17188.0 1.72526 0.862629 0.505838i \(-0.168817\pi\)
0.862629 + 0.505838i \(0.168817\pi\)
\(464\) 0 0
\(465\) 165.000 0.0164553
\(466\) 0 0
\(467\) 15246.0 1.51071 0.755354 0.655317i \(-0.227465\pi\)
0.755354 + 0.655317i \(0.227465\pi\)
\(468\) 0 0
\(469\) 2808.00 0.276464
\(470\) 0 0
\(471\) −1702.00 −0.166505
\(472\) 0 0
\(473\) −576.000 −0.0559926
\(474\) 0 0
\(475\) −900.000 −0.0869365
\(476\) 0 0
\(477\) 364.000 0.0349401
\(478\) 0 0
\(479\) 8556.00 0.816145 0.408073 0.912949i \(-0.366201\pi\)
0.408073 + 0.912949i \(0.366201\pi\)
\(480\) 0 0
\(481\) −2632.00 −0.249499
\(482\) 0 0
\(483\) −414.000 −0.0390014
\(484\) 0 0
\(485\) −2890.00 −0.270573
\(486\) 0 0
\(487\) 1805.00 0.167951 0.0839757 0.996468i \(-0.473238\pi\)
0.0839757 + 0.996468i \(0.473238\pi\)
\(488\) 0 0
\(489\) −2045.00 −0.189117
\(490\) 0 0
\(491\) −5245.00 −0.482085 −0.241042 0.970515i \(-0.577489\pi\)
−0.241042 + 0.970515i \(0.577489\pi\)
\(492\) 0 0
\(493\) −540.000 −0.0493314
\(494\) 0 0
\(495\) 4160.00 0.377734
\(496\) 0 0
\(497\) −12582.0 −1.13557
\(498\) 0 0
\(499\) −9027.00 −0.809828 −0.404914 0.914355i \(-0.632698\pi\)
−0.404914 + 0.914355i \(0.632698\pi\)
\(500\) 0 0
\(501\) 1016.00 0.0906019
\(502\) 0 0
\(503\) −3522.00 −0.312203 −0.156102 0.987741i \(-0.549893\pi\)
−0.156102 + 0.987741i \(0.549893\pi\)
\(504\) 0 0
\(505\) 30.0000 0.00264353
\(506\) 0 0
\(507\) −12.0000 −0.00105116
\(508\) 0 0
\(509\) 3949.00 0.343883 0.171941 0.985107i \(-0.444996\pi\)
0.171941 + 0.985107i \(0.444996\pi\)
\(510\) 0 0
\(511\) −10962.0 −0.948983
\(512\) 0 0
\(513\) −1908.00 −0.164211
\(514\) 0 0
\(515\) −800.000 −0.0684509
\(516\) 0 0
\(517\) −2080.00 −0.176941
\(518\) 0 0
\(519\) −598.000 −0.0505767
\(520\) 0 0
\(521\) 3236.00 0.272115 0.136057 0.990701i \(-0.456557\pi\)
0.136057 + 0.990701i \(0.456557\pi\)
\(522\) 0 0
\(523\) −12394.0 −1.03624 −0.518118 0.855309i \(-0.673367\pi\)
−0.518118 + 0.855309i \(0.673367\pi\)
\(524\) 0 0
\(525\) −450.000 −0.0374088
\(526\) 0 0
\(527\) 660.000 0.0545542
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) −19344.0 −1.58090
\(532\) 0 0
\(533\) 7379.00 0.599662
\(534\) 0 0
\(535\) 1900.00 0.153540
\(536\) 0 0
\(537\) −4607.00 −0.370217
\(538\) 0 0
\(539\) −608.000 −0.0485870
\(540\) 0 0
\(541\) −7159.00 −0.568927 −0.284463 0.958687i \(-0.591815\pi\)
−0.284463 + 0.958687i \(0.591815\pi\)
\(542\) 0 0
\(543\) 1212.00 0.0957862
\(544\) 0 0
\(545\) −1250.00 −0.0982461
\(546\) 0 0
\(547\) 19761.0 1.54464 0.772321 0.635232i \(-0.219096\pi\)
0.772321 + 0.635232i \(0.219096\pi\)
\(548\) 0 0
\(549\) −14352.0 −1.11572
\(550\) 0 0
\(551\) 972.000 0.0751517
\(552\) 0 0
\(553\) 11592.0 0.891396
\(554\) 0 0
\(555\) 280.000 0.0214150
\(556\) 0 0
\(557\) 18010.0 1.37003 0.685016 0.728528i \(-0.259795\pi\)
0.685016 + 0.728528i \(0.259795\pi\)
\(558\) 0 0
\(559\) 846.000 0.0640107
\(560\) 0 0
\(561\) −640.000 −0.0481655
\(562\) 0 0
\(563\) 2648.00 0.198224 0.0991118 0.995076i \(-0.468400\pi\)
0.0991118 + 0.995076i \(0.468400\pi\)
\(564\) 0 0
\(565\) 1950.00 0.145198
\(566\) 0 0
\(567\) 11682.0 0.865252
\(568\) 0 0
\(569\) −1566.00 −0.115378 −0.0576890 0.998335i \(-0.518373\pi\)
−0.0576890 + 0.998335i \(0.518373\pi\)
\(570\) 0 0
\(571\) −2864.00 −0.209903 −0.104952 0.994477i \(-0.533469\pi\)
−0.104952 + 0.994477i \(0.533469\pi\)
\(572\) 0 0
\(573\) −1058.00 −0.0771354
\(574\) 0 0
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) −929.000 −0.0670273 −0.0335137 0.999438i \(-0.510670\pi\)
−0.0335137 + 0.999438i \(0.510670\pi\)
\(578\) 0 0
\(579\) −1047.00 −0.0751500
\(580\) 0 0
\(581\) −9216.00 −0.658079
\(582\) 0 0
\(583\) −448.000 −0.0318255
\(584\) 0 0
\(585\) −6110.00 −0.431825
\(586\) 0 0
\(587\) 19499.0 1.37106 0.685528 0.728046i \(-0.259571\pi\)
0.685528 + 0.728046i \(0.259571\pi\)
\(588\) 0 0
\(589\) −1188.00 −0.0831081
\(590\) 0 0
\(591\) −251.000 −0.0174700
\(592\) 0 0
\(593\) 6570.00 0.454971 0.227485 0.973782i \(-0.426950\pi\)
0.227485 + 0.973782i \(0.426950\pi\)
\(594\) 0 0
\(595\) −1800.00 −0.124022
\(596\) 0 0
\(597\) −3508.00 −0.240491
\(598\) 0 0
\(599\) −1880.00 −0.128238 −0.0641191 0.997942i \(-0.520424\pi\)
−0.0641191 + 0.997942i \(0.520424\pi\)
\(600\) 0 0
\(601\) 3701.00 0.251193 0.125596 0.992081i \(-0.459916\pi\)
0.125596 + 0.992081i \(0.459916\pi\)
\(602\) 0 0
\(603\) −4056.00 −0.273919
\(604\) 0 0
\(605\) 1535.00 0.103151
\(606\) 0 0
\(607\) 3080.00 0.205953 0.102976 0.994684i \(-0.467163\pi\)
0.102976 + 0.994684i \(0.467163\pi\)
\(608\) 0 0
\(609\) 486.000 0.0323378
\(610\) 0 0
\(611\) 3055.00 0.202278
\(612\) 0 0
\(613\) 24004.0 1.58159 0.790793 0.612083i \(-0.209668\pi\)
0.790793 + 0.612083i \(0.209668\pi\)
\(614\) 0 0
\(615\) −785.000 −0.0514703
\(616\) 0 0
\(617\) 780.000 0.0508940 0.0254470 0.999676i \(-0.491899\pi\)
0.0254470 + 0.999676i \(0.491899\pi\)
\(618\) 0 0
\(619\) −21892.0 −1.42151 −0.710754 0.703440i \(-0.751646\pi\)
−0.710754 + 0.703440i \(0.751646\pi\)
\(620\) 0 0
\(621\) 1219.00 0.0787710
\(622\) 0 0
\(623\) −1836.00 −0.118070
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 1152.00 0.0733755
\(628\) 0 0
\(629\) 1120.00 0.0709973
\(630\) 0 0
\(631\) −8050.00 −0.507869 −0.253935 0.967221i \(-0.581725\pi\)
−0.253935 + 0.967221i \(0.581725\pi\)
\(632\) 0 0
\(633\) −3296.00 −0.206958
\(634\) 0 0
\(635\) −3845.00 −0.240290
\(636\) 0 0
\(637\) 893.000 0.0555447
\(638\) 0 0
\(639\) 18174.0 1.12512
\(640\) 0 0
\(641\) −25890.0 −1.59531 −0.797655 0.603114i \(-0.793926\pi\)
−0.797655 + 0.603114i \(0.793926\pi\)
\(642\) 0 0
\(643\) −4774.00 −0.292797 −0.146398 0.989226i \(-0.546768\pi\)
−0.146398 + 0.989226i \(0.546768\pi\)
\(644\) 0 0
\(645\) −90.0000 −0.00549418
\(646\) 0 0
\(647\) −3349.00 −0.203497 −0.101749 0.994810i \(-0.532444\pi\)
−0.101749 + 0.994810i \(0.532444\pi\)
\(648\) 0 0
\(649\) 23808.0 1.43998
\(650\) 0 0
\(651\) −594.000 −0.0357614
\(652\) 0 0
\(653\) 24813.0 1.48699 0.743497 0.668739i \(-0.233166\pi\)
0.743497 + 0.668739i \(0.233166\pi\)
\(654\) 0 0
\(655\) −1065.00 −0.0635313
\(656\) 0 0
\(657\) 15834.0 0.940248
\(658\) 0 0
\(659\) −18180.0 −1.07465 −0.537323 0.843376i \(-0.680565\pi\)
−0.537323 + 0.843376i \(0.680565\pi\)
\(660\) 0 0
\(661\) −29250.0 −1.72117 −0.860585 0.509307i \(-0.829902\pi\)
−0.860585 + 0.509307i \(0.829902\pi\)
\(662\) 0 0
\(663\) 940.000 0.0550627
\(664\) 0 0
\(665\) 3240.00 0.188935
\(666\) 0 0
\(667\) −621.000 −0.0360498
\(668\) 0 0
\(669\) −2720.00 −0.157192
\(670\) 0 0
\(671\) 17664.0 1.01626
\(672\) 0 0
\(673\) −23027.0 −1.31891 −0.659454 0.751745i \(-0.729213\pi\)
−0.659454 + 0.751745i \(0.729213\pi\)
\(674\) 0 0
\(675\) 1325.00 0.0755545
\(676\) 0 0
\(677\) 20106.0 1.14141 0.570706 0.821154i \(-0.306669\pi\)
0.570706 + 0.821154i \(0.306669\pi\)
\(678\) 0 0
\(679\) 10404.0 0.588025
\(680\) 0 0
\(681\) −4134.00 −0.232621
\(682\) 0 0
\(683\) 18745.0 1.05016 0.525079 0.851054i \(-0.324036\pi\)
0.525079 + 0.851054i \(0.324036\pi\)
\(684\) 0 0
\(685\) −14180.0 −0.790934
\(686\) 0 0
\(687\) 4510.00 0.250462
\(688\) 0 0
\(689\) 658.000 0.0363829
\(690\) 0 0
\(691\) −24424.0 −1.34462 −0.672310 0.740270i \(-0.734698\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(692\) 0 0
\(693\) −14976.0 −0.820911
\(694\) 0 0
\(695\) −8155.00 −0.445089
\(696\) 0 0
\(697\) −3140.00 −0.170640
\(698\) 0 0
\(699\) 5003.00 0.270717
\(700\) 0 0
\(701\) −27278.0 −1.46972 −0.734862 0.678217i \(-0.762753\pi\)
−0.734862 + 0.678217i \(0.762753\pi\)
\(702\) 0 0
\(703\) −2016.00 −0.108158
\(704\) 0 0
\(705\) −325.000 −0.0173620
\(706\) 0 0
\(707\) −108.000 −0.00574506
\(708\) 0 0
\(709\) 12214.0 0.646977 0.323488 0.946232i \(-0.395144\pi\)
0.323488 + 0.946232i \(0.395144\pi\)
\(710\) 0 0
\(711\) −16744.0 −0.883191
\(712\) 0 0
\(713\) 759.000 0.0398664
\(714\) 0 0
\(715\) 7520.00 0.393332
\(716\) 0 0
\(717\) −6309.00 −0.328611
\(718\) 0 0
\(719\) −12932.0 −0.670768 −0.335384 0.942082i \(-0.608866\pi\)
−0.335384 + 0.942082i \(0.608866\pi\)
\(720\) 0 0
\(721\) 2880.00 0.148761
\(722\) 0 0
\(723\) −3038.00 −0.156272
\(724\) 0 0
\(725\) −675.000 −0.0345778
\(726\) 0 0
\(727\) −10046.0 −0.512497 −0.256249 0.966611i \(-0.582487\pi\)
−0.256249 + 0.966611i \(0.582487\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) −360.000 −0.0182149
\(732\) 0 0
\(733\) −5924.00 −0.298510 −0.149255 0.988799i \(-0.547688\pi\)
−0.149255 + 0.988799i \(0.547688\pi\)
\(734\) 0 0
\(735\) −95.0000 −0.00476752
\(736\) 0 0
\(737\) 4992.00 0.249502
\(738\) 0 0
\(739\) −829.000 −0.0412656 −0.0206328 0.999787i \(-0.506568\pi\)
−0.0206328 + 0.999787i \(0.506568\pi\)
\(740\) 0 0
\(741\) −1692.00 −0.0838828
\(742\) 0 0
\(743\) −7072.00 −0.349188 −0.174594 0.984641i \(-0.555861\pi\)
−0.174594 + 0.984641i \(0.555861\pi\)
\(744\) 0 0
\(745\) 9830.00 0.483414
\(746\) 0 0
\(747\) 13312.0 0.652022
\(748\) 0 0
\(749\) −6840.00 −0.333682
\(750\) 0 0
\(751\) −16234.0 −0.788798 −0.394399 0.918939i \(-0.629047\pi\)
−0.394399 + 0.918939i \(0.629047\pi\)
\(752\) 0 0
\(753\) −1332.00 −0.0644632
\(754\) 0 0
\(755\) 175.000 0.00843563
\(756\) 0 0
\(757\) 9128.00 0.438260 0.219130 0.975696i \(-0.429678\pi\)
0.219130 + 0.975696i \(0.429678\pi\)
\(758\) 0 0
\(759\) −736.000 −0.0351978
\(760\) 0 0
\(761\) 165.000 0.00785972 0.00392986 0.999992i \(-0.498749\pi\)
0.00392986 + 0.999992i \(0.498749\pi\)
\(762\) 0 0
\(763\) 4500.00 0.213514
\(764\) 0 0
\(765\) 2600.00 0.122880
\(766\) 0 0
\(767\) −34968.0 −1.64618
\(768\) 0 0
\(769\) −20834.0 −0.976974 −0.488487 0.872571i \(-0.662451\pi\)
−0.488487 + 0.872571i \(0.662451\pi\)
\(770\) 0 0
\(771\) −3301.00 −0.154193
\(772\) 0 0
\(773\) −31782.0 −1.47881 −0.739404 0.673262i \(-0.764893\pi\)
−0.739404 + 0.673262i \(0.764893\pi\)
\(774\) 0 0
\(775\) 825.000 0.0382385
\(776\) 0 0
\(777\) −1008.00 −0.0465403
\(778\) 0 0
\(779\) 5652.00 0.259954
\(780\) 0 0
\(781\) −22368.0 −1.02483
\(782\) 0 0
\(783\) −1431.00 −0.0653126
\(784\) 0 0
\(785\) −8510.00 −0.386923
\(786\) 0 0
\(787\) −33104.0 −1.49940 −0.749701 0.661776i \(-0.769803\pi\)
−0.749701 + 0.661776i \(0.769803\pi\)
\(788\) 0 0
\(789\) 2072.00 0.0934920
\(790\) 0 0
\(791\) −7020.00 −0.315553
\(792\) 0 0
\(793\) −25944.0 −1.16179
\(794\) 0 0
\(795\) −70.0000 −0.00312282
\(796\) 0 0
\(797\) 4736.00 0.210486 0.105243 0.994447i \(-0.466438\pi\)
0.105243 + 0.994447i \(0.466438\pi\)
\(798\) 0 0
\(799\) −1300.00 −0.0575603
\(800\) 0 0
\(801\) 2652.00 0.116984
\(802\) 0 0
\(803\) −19488.0 −0.856434
\(804\) 0 0
\(805\) −2070.00 −0.0906309
\(806\) 0 0
\(807\) −5721.00 −0.249552
\(808\) 0 0
\(809\) −7470.00 −0.324637 −0.162318 0.986738i \(-0.551897\pi\)
−0.162318 + 0.986738i \(0.551897\pi\)
\(810\) 0 0
\(811\) −19919.0 −0.862455 −0.431227 0.902243i \(-0.641919\pi\)
−0.431227 + 0.902243i \(0.641919\pi\)
\(812\) 0 0
\(813\) −5900.00 −0.254517
\(814\) 0 0
\(815\) −10225.0 −0.439468
\(816\) 0 0
\(817\) 648.000 0.0277487
\(818\) 0 0
\(819\) 21996.0 0.938465
\(820\) 0 0
\(821\) −22694.0 −0.964709 −0.482354 0.875976i \(-0.660218\pi\)
−0.482354 + 0.875976i \(0.660218\pi\)
\(822\) 0 0
\(823\) 31907.0 1.35141 0.675704 0.737173i \(-0.263840\pi\)
0.675704 + 0.737173i \(0.263840\pi\)
\(824\) 0 0
\(825\) −800.000 −0.0337605
\(826\) 0 0
\(827\) 15236.0 0.640638 0.320319 0.947310i \(-0.396210\pi\)
0.320319 + 0.947310i \(0.396210\pi\)
\(828\) 0 0
\(829\) 27286.0 1.14316 0.571581 0.820545i \(-0.306330\pi\)
0.571581 + 0.820545i \(0.306330\pi\)
\(830\) 0 0
\(831\) −6371.00 −0.265954
\(832\) 0 0
\(833\) −380.000 −0.0158058
\(834\) 0 0
\(835\) 5080.00 0.210540
\(836\) 0 0
\(837\) 1749.00 0.0722273
\(838\) 0 0
\(839\) −23054.0 −0.948644 −0.474322 0.880351i \(-0.657307\pi\)
−0.474322 + 0.880351i \(0.657307\pi\)
\(840\) 0 0
\(841\) −23660.0 −0.970109
\(842\) 0 0
\(843\) −3190.00 −0.130331
\(844\) 0 0
\(845\) −60.0000 −0.00244268
\(846\) 0 0
\(847\) −5526.00 −0.224174
\(848\) 0 0
\(849\) −4226.00 −0.170832
\(850\) 0 0
\(851\) 1288.00 0.0518826
\(852\) 0 0
\(853\) −34506.0 −1.38507 −0.692534 0.721385i \(-0.743506\pi\)
−0.692534 + 0.721385i \(0.743506\pi\)
\(854\) 0 0
\(855\) −4680.00 −0.187196
\(856\) 0 0
\(857\) −22263.0 −0.887386 −0.443693 0.896179i \(-0.646332\pi\)
−0.443693 + 0.896179i \(0.646332\pi\)
\(858\) 0 0
\(859\) −12851.0 −0.510443 −0.255221 0.966883i \(-0.582148\pi\)
−0.255221 + 0.966883i \(0.582148\pi\)
\(860\) 0 0
\(861\) 2826.00 0.111858
\(862\) 0 0
\(863\) −15723.0 −0.620182 −0.310091 0.950707i \(-0.600360\pi\)
−0.310091 + 0.950707i \(0.600360\pi\)
\(864\) 0 0
\(865\) −2990.00 −0.117530
\(866\) 0 0
\(867\) 4513.00 0.176781
\(868\) 0 0
\(869\) 20608.0 0.804463
\(870\) 0 0
\(871\) −7332.00 −0.285230
\(872\) 0 0
\(873\) −15028.0 −0.582613
\(874\) 0 0
\(875\) −2250.00 −0.0869302
\(876\) 0 0
\(877\) −886.000 −0.0341141 −0.0170571 0.999855i \(-0.505430\pi\)
−0.0170571 + 0.999855i \(0.505430\pi\)
\(878\) 0 0
\(879\) −6048.00 −0.232075
\(880\) 0 0
\(881\) −37120.0 −1.41953 −0.709764 0.704439i \(-0.751199\pi\)
−0.709764 + 0.704439i \(0.751199\pi\)
\(882\) 0 0
\(883\) 7524.00 0.286753 0.143376 0.989668i \(-0.454204\pi\)
0.143376 + 0.989668i \(0.454204\pi\)
\(884\) 0 0
\(885\) 3720.00 0.141295
\(886\) 0 0
\(887\) −9221.00 −0.349054 −0.174527 0.984652i \(-0.555840\pi\)
−0.174527 + 0.984652i \(0.555840\pi\)
\(888\) 0 0
\(889\) 13842.0 0.522211
\(890\) 0 0
\(891\) 20768.0 0.780869
\(892\) 0 0
\(893\) 2340.00 0.0876877
\(894\) 0 0
\(895\) −23035.0 −0.860307
\(896\) 0 0
\(897\) 1081.00 0.0402381
\(898\) 0 0
\(899\) −891.000 −0.0330551
\(900\) 0 0
\(901\) −280.000 −0.0103531
\(902\) 0 0
\(903\) 324.000 0.0119402
\(904\) 0 0
\(905\) 6060.00 0.222587
\(906\) 0 0
\(907\) −29116.0 −1.06591 −0.532955 0.846143i \(-0.678919\pi\)
−0.532955 + 0.846143i \(0.678919\pi\)
\(908\) 0 0
\(909\) 156.000 0.00569218
\(910\) 0 0
\(911\) −11440.0 −0.416053 −0.208026 0.978123i \(-0.566704\pi\)
−0.208026 + 0.978123i \(0.566704\pi\)
\(912\) 0 0
\(913\) −16384.0 −0.593901
\(914\) 0 0
\(915\) 2760.00 0.0997189
\(916\) 0 0
\(917\) 3834.00 0.138070
\(918\) 0 0
\(919\) −2958.00 −0.106176 −0.0530878 0.998590i \(-0.516906\pi\)
−0.0530878 + 0.998590i \(0.516906\pi\)
\(920\) 0 0
\(921\) 8628.00 0.308689
\(922\) 0 0
\(923\) 32853.0 1.17158
\(924\) 0 0
\(925\) 1400.00 0.0497640
\(926\) 0 0
\(927\) −4160.00 −0.147392
\(928\) 0 0
\(929\) 20907.0 0.738360 0.369180 0.929358i \(-0.379639\pi\)
0.369180 + 0.929358i \(0.379639\pi\)
\(930\) 0 0
\(931\) 684.000 0.0240786
\(932\) 0 0
\(933\) 8247.00 0.289383
\(934\) 0 0
\(935\) −3200.00 −0.111926
\(936\) 0 0
\(937\) 9748.00 0.339865 0.169932 0.985456i \(-0.445645\pi\)
0.169932 + 0.985456i \(0.445645\pi\)
\(938\) 0 0
\(939\) −2620.00 −0.0910548
\(940\) 0 0
\(941\) 19624.0 0.679834 0.339917 0.940455i \(-0.389601\pi\)
0.339917 + 0.940455i \(0.389601\pi\)
\(942\) 0 0
\(943\) −3611.00 −0.124698
\(944\) 0 0
\(945\) −4770.00 −0.164199
\(946\) 0 0
\(947\) 41859.0 1.43636 0.718181 0.695856i \(-0.244975\pi\)
0.718181 + 0.695856i \(0.244975\pi\)
\(948\) 0 0
\(949\) 28623.0 0.979075
\(950\) 0 0
\(951\) −9906.00 −0.337775
\(952\) 0 0
\(953\) 29226.0 0.993413 0.496707 0.867918i \(-0.334542\pi\)
0.496707 + 0.867918i \(0.334542\pi\)
\(954\) 0 0
\(955\) −5290.00 −0.179246
\(956\) 0 0
\(957\) 864.000 0.0291841
\(958\) 0 0
\(959\) 51048.0 1.71890
\(960\) 0 0
\(961\) −28702.0 −0.963445
\(962\) 0 0
\(963\) 9880.00 0.330611
\(964\) 0 0
\(965\) −5235.00 −0.174633
\(966\) 0 0
\(967\) 29849.0 0.992636 0.496318 0.868141i \(-0.334685\pi\)
0.496318 + 0.868141i \(0.334685\pi\)
\(968\) 0 0
\(969\) 720.000 0.0238697
\(970\) 0 0
\(971\) 9390.00 0.310339 0.155170 0.987888i \(-0.450408\pi\)
0.155170 + 0.987888i \(0.450408\pi\)
\(972\) 0 0
\(973\) 29358.0 0.967291
\(974\) 0 0
\(975\) 1175.00 0.0385950
\(976\) 0 0
\(977\) 33536.0 1.09817 0.549085 0.835767i \(-0.314976\pi\)
0.549085 + 0.835767i \(0.314976\pi\)
\(978\) 0 0
\(979\) −3264.00 −0.106556
\(980\) 0 0
\(981\) −6500.00 −0.211548
\(982\) 0 0
\(983\) −28994.0 −0.940758 −0.470379 0.882465i \(-0.655883\pi\)
−0.470379 + 0.882465i \(0.655883\pi\)
\(984\) 0 0
\(985\) −1255.00 −0.0405966
\(986\) 0 0
\(987\) 1170.00 0.0377320
\(988\) 0 0
\(989\) −414.000 −0.0133109
\(990\) 0 0
\(991\) −11272.0 −0.361319 −0.180659 0.983546i \(-0.557823\pi\)
−0.180659 + 0.983546i \(0.557823\pi\)
\(992\) 0 0
\(993\) −8115.00 −0.259337
\(994\) 0 0
\(995\) −17540.0 −0.558850
\(996\) 0 0
\(997\) 61186.0 1.94361 0.971805 0.235784i \(-0.0757658\pi\)
0.971805 + 0.235784i \(0.0757658\pi\)
\(998\) 0 0
\(999\) 2968.00 0.0939974
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 1840.4.a.d.1.1 1
4.3 odd 2 230.4.a.e.1.1 1
12.11 even 2 2070.4.a.e.1.1 1
20.3 even 4 1150.4.b.f.599.1 2
20.7 even 4 1150.4.b.f.599.2 2
20.19 odd 2 1150.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.e.1.1 1 4.3 odd 2
1150.4.a.b.1.1 1 20.19 odd 2
1150.4.b.f.599.1 2 20.3 even 4
1150.4.b.f.599.2 2 20.7 even 4
1840.4.a.d.1.1 1 1.1 even 1 trivial
2070.4.a.e.1.1 1 12.11 even 2