Properties

Label 1150.4.a.a.1.1
Level $1150$
Weight $4$
Character 1150.1
Self dual yes
Analytic conductor $67.852$
Analytic rank $1$
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] = [1150,4,Mod(1,1150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1150.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.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: \(67.8521965066\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1150.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +4.00000 q^{6} -21.0000 q^{7} -8.00000 q^{8} -23.0000 q^{9} +47.0000 q^{11} -8.00000 q^{12} -57.0000 q^{13} +42.0000 q^{14} +16.0000 q^{16} +84.0000 q^{17} +46.0000 q^{18} -5.00000 q^{19} +42.0000 q^{21} -94.0000 q^{22} -23.0000 q^{23} +16.0000 q^{24} +114.000 q^{26} +100.000 q^{27} -84.0000 q^{28} +285.000 q^{29} +82.0000 q^{31} -32.0000 q^{32} -94.0000 q^{33} -168.000 q^{34} -92.0000 q^{36} +54.0000 q^{37} +10.0000 q^{38} +114.000 q^{39} -53.0000 q^{41} -84.0000 q^{42} -197.000 q^{43} +188.000 q^{44} +46.0000 q^{46} +124.000 q^{47} -32.0000 q^{48} +98.0000 q^{49} -168.000 q^{51} -228.000 q^{52} +148.000 q^{53} -200.000 q^{54} +168.000 q^{56} +10.0000 q^{57} -570.000 q^{58} +30.0000 q^{59} -578.000 q^{61} -164.000 q^{62} +483.000 q^{63} +64.0000 q^{64} +188.000 q^{66} -296.000 q^{67} +336.000 q^{68} +46.0000 q^{69} +422.000 q^{71} +184.000 q^{72} -487.000 q^{73} -108.000 q^{74} -20.0000 q^{76} -987.000 q^{77} -228.000 q^{78} -405.000 q^{79} +421.000 q^{81} +106.000 q^{82} -397.000 q^{83} +168.000 q^{84} +394.000 q^{86} -570.000 q^{87} -376.000 q^{88} +730.000 q^{89} +1197.00 q^{91} -92.0000 q^{92} -164.000 q^{93} -248.000 q^{94} +64.0000 q^{96} +64.0000 q^{97} -196.000 q^{98} -1081.00 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −2.00000 −0.384900 −0.192450 0.981307i \(-0.561643\pi\)
−0.192450 + 0.981307i \(0.561643\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) 4.00000 0.272166
\(7\) −21.0000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −8.00000 −0.353553
\(9\) −23.0000 −0.851852
\(10\) 0 0
\(11\) 47.0000 1.28828 0.644138 0.764909i \(-0.277216\pi\)
0.644138 + 0.764909i \(0.277216\pi\)
\(12\) −8.00000 −0.192450
\(13\) −57.0000 −1.21607 −0.608037 0.793909i \(-0.708043\pi\)
−0.608037 + 0.793909i \(0.708043\pi\)
\(14\) 42.0000 0.801784
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 84.0000 1.19841 0.599206 0.800595i \(-0.295483\pi\)
0.599206 + 0.800595i \(0.295483\pi\)
\(18\) 46.0000 0.602350
\(19\) −5.00000 −0.0603726 −0.0301863 0.999544i \(-0.509610\pi\)
−0.0301863 + 0.999544i \(0.509610\pi\)
\(20\) 0 0
\(21\) 42.0000 0.436436
\(22\) −94.0000 −0.910949
\(23\) −23.0000 −0.208514
\(24\) 16.0000 0.136083
\(25\) 0 0
\(26\) 114.000 0.859894
\(27\) 100.000 0.712778
\(28\) −84.0000 −0.566947
\(29\) 285.000 1.82494 0.912468 0.409147i \(-0.134174\pi\)
0.912468 + 0.409147i \(0.134174\pi\)
\(30\) 0 0
\(31\) 82.0000 0.475085 0.237542 0.971377i \(-0.423658\pi\)
0.237542 + 0.971377i \(0.423658\pi\)
\(32\) −32.0000 −0.176777
\(33\) −94.0000 −0.495858
\(34\) −168.000 −0.847405
\(35\) 0 0
\(36\) −92.0000 −0.425926
\(37\) 54.0000 0.239934 0.119967 0.992778i \(-0.461721\pi\)
0.119967 + 0.992778i \(0.461721\pi\)
\(38\) 10.0000 0.0426898
\(39\) 114.000 0.468067
\(40\) 0 0
\(41\) −53.0000 −0.201883 −0.100942 0.994892i \(-0.532186\pi\)
−0.100942 + 0.994892i \(0.532186\pi\)
\(42\) −84.0000 −0.308607
\(43\) −197.000 −0.698656 −0.349328 0.937000i \(-0.613590\pi\)
−0.349328 + 0.937000i \(0.613590\pi\)
\(44\) 188.000 0.644138
\(45\) 0 0
\(46\) 46.0000 0.147442
\(47\) 124.000 0.384835 0.192418 0.981313i \(-0.438367\pi\)
0.192418 + 0.981313i \(0.438367\pi\)
\(48\) −32.0000 −0.0962250
\(49\) 98.0000 0.285714
\(50\) 0 0
\(51\) −168.000 −0.461269
\(52\) −228.000 −0.608037
\(53\) 148.000 0.383573 0.191786 0.981437i \(-0.438572\pi\)
0.191786 + 0.981437i \(0.438572\pi\)
\(54\) −200.000 −0.504010
\(55\) 0 0
\(56\) 168.000 0.400892
\(57\) 10.0000 0.0232374
\(58\) −570.000 −1.29043
\(59\) 30.0000 0.0661978 0.0330989 0.999452i \(-0.489462\pi\)
0.0330989 + 0.999452i \(0.489462\pi\)
\(60\) 0 0
\(61\) −578.000 −1.21320 −0.606601 0.795006i \(-0.707467\pi\)
−0.606601 + 0.795006i \(0.707467\pi\)
\(62\) −164.000 −0.335936
\(63\) 483.000 0.965909
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 188.000 0.350624
\(67\) −296.000 −0.539734 −0.269867 0.962898i \(-0.586980\pi\)
−0.269867 + 0.962898i \(0.586980\pi\)
\(68\) 336.000 0.599206
\(69\) 46.0000 0.0802572
\(70\) 0 0
\(71\) 422.000 0.705383 0.352691 0.935740i \(-0.385267\pi\)
0.352691 + 0.935740i \(0.385267\pi\)
\(72\) 184.000 0.301175
\(73\) −487.000 −0.780809 −0.390404 0.920643i \(-0.627665\pi\)
−0.390404 + 0.920643i \(0.627665\pi\)
\(74\) −108.000 −0.169659
\(75\) 0 0
\(76\) −20.0000 −0.0301863
\(77\) −987.000 −1.46077
\(78\) −228.000 −0.330973
\(79\) −405.000 −0.576786 −0.288393 0.957512i \(-0.593121\pi\)
−0.288393 + 0.957512i \(0.593121\pi\)
\(80\) 0 0
\(81\) 421.000 0.577503
\(82\) 106.000 0.142753
\(83\) −397.000 −0.525017 −0.262509 0.964930i \(-0.584550\pi\)
−0.262509 + 0.964930i \(0.584550\pi\)
\(84\) 168.000 0.218218
\(85\) 0 0
\(86\) 394.000 0.494025
\(87\) −570.000 −0.702419
\(88\) −376.000 −0.455474
\(89\) 730.000 0.869436 0.434718 0.900567i \(-0.356848\pi\)
0.434718 + 0.900567i \(0.356848\pi\)
\(90\) 0 0
\(91\) 1197.00 1.37890
\(92\) −92.0000 −0.104257
\(93\) −164.000 −0.182860
\(94\) −248.000 −0.272120
\(95\) 0 0
\(96\) 64.0000 0.0680414
\(97\) 64.0000 0.0669919 0.0334960 0.999439i \(-0.489336\pi\)
0.0334960 + 0.999439i \(0.489336\pi\)
\(98\) −196.000 −0.202031
\(99\) −1081.00 −1.09742
\(100\) 0 0
\(101\) 1002.00 0.987156 0.493578 0.869702i \(-0.335689\pi\)
0.493578 + 0.869702i \(0.335689\pi\)
\(102\) 336.000 0.326166
\(103\) −1807.00 −1.72863 −0.864316 0.502950i \(-0.832248\pi\)
−0.864316 + 0.502950i \(0.832248\pi\)
\(104\) 456.000 0.429947
\(105\) 0 0
\(106\) −296.000 −0.271227
\(107\) 1664.00 1.50341 0.751705 0.659499i \(-0.229232\pi\)
0.751705 + 0.659499i \(0.229232\pi\)
\(108\) 400.000 0.356389
\(109\) 470.000 0.413008 0.206504 0.978446i \(-0.433791\pi\)
0.206504 + 0.978446i \(0.433791\pi\)
\(110\) 0 0
\(111\) −108.000 −0.0923505
\(112\) −336.000 −0.283473
\(113\) −992.000 −0.825836 −0.412918 0.910768i \(-0.635490\pi\)
−0.412918 + 0.910768i \(0.635490\pi\)
\(114\) −20.0000 −0.0164313
\(115\) 0 0
\(116\) 1140.00 0.912468
\(117\) 1311.00 1.03591
\(118\) −60.0000 −0.0468089
\(119\) −1764.00 −1.35887
\(120\) 0 0
\(121\) 878.000 0.659654
\(122\) 1156.00 0.857863
\(123\) 106.000 0.0777049
\(124\) 328.000 0.237542
\(125\) 0 0
\(126\) −966.000 −0.683001
\(127\) 2274.00 1.58886 0.794429 0.607358i \(-0.207770\pi\)
0.794429 + 0.607358i \(0.207770\pi\)
\(128\) −128.000 −0.0883883
\(129\) 394.000 0.268913
\(130\) 0 0
\(131\) 1802.00 1.20184 0.600922 0.799308i \(-0.294800\pi\)
0.600922 + 0.799308i \(0.294800\pi\)
\(132\) −376.000 −0.247929
\(133\) 105.000 0.0684561
\(134\) 592.000 0.381649
\(135\) 0 0
\(136\) −672.000 −0.423702
\(137\) −106.000 −0.0661036 −0.0330518 0.999454i \(-0.510523\pi\)
−0.0330518 + 0.999454i \(0.510523\pi\)
\(138\) −92.0000 −0.0567504
\(139\) −2700.00 −1.64756 −0.823781 0.566909i \(-0.808139\pi\)
−0.823781 + 0.566909i \(0.808139\pi\)
\(140\) 0 0
\(141\) −248.000 −0.148123
\(142\) −844.000 −0.498781
\(143\) −2679.00 −1.56664
\(144\) −368.000 −0.212963
\(145\) 0 0
\(146\) 974.000 0.552115
\(147\) −196.000 −0.109971
\(148\) 216.000 0.119967
\(149\) −890.000 −0.489340 −0.244670 0.969606i \(-0.578680\pi\)
−0.244670 + 0.969606i \(0.578680\pi\)
\(150\) 0 0
\(151\) −3398.00 −1.83129 −0.915647 0.401984i \(-0.868321\pi\)
−0.915647 + 0.401984i \(0.868321\pi\)
\(152\) 40.0000 0.0213449
\(153\) −1932.00 −1.02087
\(154\) 1974.00 1.03292
\(155\) 0 0
\(156\) 456.000 0.234033
\(157\) −2976.00 −1.51281 −0.756403 0.654105i \(-0.773045\pi\)
−0.756403 + 0.654105i \(0.773045\pi\)
\(158\) 810.000 0.407849
\(159\) −296.000 −0.147637
\(160\) 0 0
\(161\) 483.000 0.236433
\(162\) −842.000 −0.408357
\(163\) −512.000 −0.246030 −0.123015 0.992405i \(-0.539256\pi\)
−0.123015 + 0.992405i \(0.539256\pi\)
\(164\) −212.000 −0.100942
\(165\) 0 0
\(166\) 794.000 0.371243
\(167\) −1426.00 −0.660762 −0.330381 0.943848i \(-0.607177\pi\)
−0.330381 + 0.943848i \(0.607177\pi\)
\(168\) −336.000 −0.154303
\(169\) 1052.00 0.478835
\(170\) 0 0
\(171\) 115.000 0.0514285
\(172\) −788.000 −0.349328
\(173\) −1047.00 −0.460127 −0.230063 0.973176i \(-0.573893\pi\)
−0.230063 + 0.973176i \(0.573893\pi\)
\(174\) 1140.00 0.496685
\(175\) 0 0
\(176\) 752.000 0.322069
\(177\) −60.0000 −0.0254795
\(178\) −1460.00 −0.614784
\(179\) −1380.00 −0.576235 −0.288117 0.957595i \(-0.593029\pi\)
−0.288117 + 0.957595i \(0.593029\pi\)
\(180\) 0 0
\(181\) 1332.00 0.546999 0.273499 0.961872i \(-0.411819\pi\)
0.273499 + 0.961872i \(0.411819\pi\)
\(182\) −2394.00 −0.975028
\(183\) 1156.00 0.466962
\(184\) 184.000 0.0737210
\(185\) 0 0
\(186\) 328.000 0.129302
\(187\) 3948.00 1.54388
\(188\) 496.000 0.192418
\(189\) −2100.00 −0.808214
\(190\) 0 0
\(191\) 1297.00 0.491349 0.245674 0.969352i \(-0.420991\pi\)
0.245674 + 0.969352i \(0.420991\pi\)
\(192\) −128.000 −0.0481125
\(193\) −3902.00 −1.45530 −0.727648 0.685951i \(-0.759387\pi\)
−0.727648 + 0.685951i \(0.759387\pi\)
\(194\) −128.000 −0.0473704
\(195\) 0 0
\(196\) 392.000 0.142857
\(197\) 149.000 0.0538874 0.0269437 0.999637i \(-0.491423\pi\)
0.0269437 + 0.999637i \(0.491423\pi\)
\(198\) 2162.00 0.775993
\(199\) −525.000 −0.187016 −0.0935082 0.995619i \(-0.529808\pi\)
−0.0935082 + 0.995619i \(0.529808\pi\)
\(200\) 0 0
\(201\) 592.000 0.207744
\(202\) −2004.00 −0.698024
\(203\) −5985.00 −2.06928
\(204\) −672.000 −0.230634
\(205\) 0 0
\(206\) 3614.00 1.22233
\(207\) 529.000 0.177623
\(208\) −912.000 −0.304018
\(209\) −235.000 −0.0777765
\(210\) 0 0
\(211\) −3518.00 −1.14782 −0.573908 0.818920i \(-0.694573\pi\)
−0.573908 + 0.818920i \(0.694573\pi\)
\(212\) 592.000 0.191786
\(213\) −844.000 −0.271502
\(214\) −3328.00 −1.06307
\(215\) 0 0
\(216\) −800.000 −0.252005
\(217\) −1722.00 −0.538696
\(218\) −940.000 −0.292041
\(219\) 974.000 0.300533
\(220\) 0 0
\(221\) −4788.00 −1.45736
\(222\) 216.000 0.0653017
\(223\) 2968.00 0.891264 0.445632 0.895216i \(-0.352979\pi\)
0.445632 + 0.895216i \(0.352979\pi\)
\(224\) 672.000 0.200446
\(225\) 0 0
\(226\) 1984.00 0.583954
\(227\) −4036.00 −1.18008 −0.590041 0.807373i \(-0.700889\pi\)
−0.590041 + 0.807373i \(0.700889\pi\)
\(228\) 40.0000 0.0116187
\(229\) −4190.00 −1.20910 −0.604548 0.796569i \(-0.706646\pi\)
−0.604548 + 0.796569i \(0.706646\pi\)
\(230\) 0 0
\(231\) 1974.00 0.562250
\(232\) −2280.00 −0.645213
\(233\) −977.000 −0.274701 −0.137351 0.990522i \(-0.543859\pi\)
−0.137351 + 0.990522i \(0.543859\pi\)
\(234\) −2622.00 −0.732502
\(235\) 0 0
\(236\) 120.000 0.0330989
\(237\) 810.000 0.222005
\(238\) 3528.00 0.960867
\(239\) −3740.00 −1.01222 −0.506110 0.862469i \(-0.668917\pi\)
−0.506110 + 0.862469i \(0.668917\pi\)
\(240\) 0 0
\(241\) 3692.00 0.986816 0.493408 0.869798i \(-0.335751\pi\)
0.493408 + 0.869798i \(0.335751\pi\)
\(242\) −1756.00 −0.466446
\(243\) −3542.00 −0.935059
\(244\) −2312.00 −0.606601
\(245\) 0 0
\(246\) −212.000 −0.0549456
\(247\) 285.000 0.0734175
\(248\) −656.000 −0.167968
\(249\) 794.000 0.202079
\(250\) 0 0
\(251\) −6468.00 −1.62652 −0.813260 0.581900i \(-0.802309\pi\)
−0.813260 + 0.581900i \(0.802309\pi\)
\(252\) 1932.00 0.482955
\(253\) −1081.00 −0.268624
\(254\) −4548.00 −1.12349
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −5586.00 −1.35582 −0.677909 0.735146i \(-0.737114\pi\)
−0.677909 + 0.735146i \(0.737114\pi\)
\(258\) −788.000 −0.190150
\(259\) −1134.00 −0.272059
\(260\) 0 0
\(261\) −6555.00 −1.55458
\(262\) −3604.00 −0.849832
\(263\) 6208.00 1.45552 0.727760 0.685832i \(-0.240562\pi\)
0.727760 + 0.685832i \(0.240562\pi\)
\(264\) 752.000 0.175312
\(265\) 0 0
\(266\) −210.000 −0.0484057
\(267\) −1460.00 −0.334646
\(268\) −1184.00 −0.269867
\(269\) −7895.00 −1.78947 −0.894734 0.446600i \(-0.852635\pi\)
−0.894734 + 0.446600i \(0.852635\pi\)
\(270\) 0 0
\(271\) −68.0000 −0.0152425 −0.00762123 0.999971i \(-0.502426\pi\)
−0.00762123 + 0.999971i \(0.502426\pi\)
\(272\) 1344.00 0.299603
\(273\) −2394.00 −0.530738
\(274\) 212.000 0.0467423
\(275\) 0 0
\(276\) 184.000 0.0401286
\(277\) 5289.00 1.14724 0.573620 0.819122i \(-0.305539\pi\)
0.573620 + 0.819122i \(0.305539\pi\)
\(278\) 5400.00 1.16500
\(279\) −1886.00 −0.404702
\(280\) 0 0
\(281\) −3408.00 −0.723503 −0.361751 0.932275i \(-0.617821\pi\)
−0.361751 + 0.932275i \(0.617821\pi\)
\(282\) 496.000 0.104739
\(283\) 1828.00 0.383969 0.191985 0.981398i \(-0.438508\pi\)
0.191985 + 0.981398i \(0.438508\pi\)
\(284\) 1688.00 0.352691
\(285\) 0 0
\(286\) 5358.00 1.10778
\(287\) 1113.00 0.228914
\(288\) 736.000 0.150588
\(289\) 2143.00 0.436190
\(290\) 0 0
\(291\) −128.000 −0.0257852
\(292\) −1948.00 −0.390404
\(293\) 6388.00 1.27369 0.636845 0.770992i \(-0.280239\pi\)
0.636845 + 0.770992i \(0.280239\pi\)
\(294\) 392.000 0.0777616
\(295\) 0 0
\(296\) −432.000 −0.0848294
\(297\) 4700.00 0.918255
\(298\) 1780.00 0.346016
\(299\) 1311.00 0.253569
\(300\) 0 0
\(301\) 4137.00 0.792202
\(302\) 6796.00 1.29492
\(303\) −2004.00 −0.379956
\(304\) −80.0000 −0.0150931
\(305\) 0 0
\(306\) 3864.00 0.721863
\(307\) −5016.00 −0.932502 −0.466251 0.884652i \(-0.654396\pi\)
−0.466251 + 0.884652i \(0.654396\pi\)
\(308\) −3948.00 −0.730384
\(309\) 3614.00 0.665350
\(310\) 0 0
\(311\) 5542.00 1.01048 0.505238 0.862980i \(-0.331405\pi\)
0.505238 + 0.862980i \(0.331405\pi\)
\(312\) −912.000 −0.165487
\(313\) 3838.00 0.693088 0.346544 0.938034i \(-0.387355\pi\)
0.346544 + 0.938034i \(0.387355\pi\)
\(314\) 5952.00 1.06972
\(315\) 0 0
\(316\) −1620.00 −0.288393
\(317\) −9771.00 −1.73121 −0.865606 0.500726i \(-0.833066\pi\)
−0.865606 + 0.500726i \(0.833066\pi\)
\(318\) 592.000 0.104395
\(319\) 13395.0 2.35102
\(320\) 0 0
\(321\) −3328.00 −0.578663
\(322\) −966.000 −0.167183
\(323\) −420.000 −0.0723512
\(324\) 1684.00 0.288752
\(325\) 0 0
\(326\) 1024.00 0.173970
\(327\) −940.000 −0.158967
\(328\) 424.000 0.0713765
\(329\) −2604.00 −0.436362
\(330\) 0 0
\(331\) 3982.00 0.661240 0.330620 0.943764i \(-0.392742\pi\)
0.330620 + 0.943764i \(0.392742\pi\)
\(332\) −1588.00 −0.262509
\(333\) −1242.00 −0.204388
\(334\) 2852.00 0.467229
\(335\) 0 0
\(336\) 672.000 0.109109
\(337\) −536.000 −0.0866403 −0.0433201 0.999061i \(-0.513794\pi\)
−0.0433201 + 0.999061i \(0.513794\pi\)
\(338\) −2104.00 −0.338587
\(339\) 1984.00 0.317865
\(340\) 0 0
\(341\) 3854.00 0.612040
\(342\) −230.000 −0.0363654
\(343\) 5145.00 0.809924
\(344\) 1576.00 0.247012
\(345\) 0 0
\(346\) 2094.00 0.325359
\(347\) 8024.00 1.24136 0.620679 0.784065i \(-0.286857\pi\)
0.620679 + 0.784065i \(0.286857\pi\)
\(348\) −2280.00 −0.351209
\(349\) −4675.00 −0.717040 −0.358520 0.933522i \(-0.616719\pi\)
−0.358520 + 0.933522i \(0.616719\pi\)
\(350\) 0 0
\(351\) −5700.00 −0.866791
\(352\) −1504.00 −0.227737
\(353\) −10347.0 −1.56010 −0.780050 0.625717i \(-0.784806\pi\)
−0.780050 + 0.625717i \(0.784806\pi\)
\(354\) 120.000 0.0180167
\(355\) 0 0
\(356\) 2920.00 0.434718
\(357\) 3528.00 0.523030
\(358\) 2760.00 0.407460
\(359\) 12715.0 1.86928 0.934641 0.355593i \(-0.115721\pi\)
0.934641 + 0.355593i \(0.115721\pi\)
\(360\) 0 0
\(361\) −6834.00 −0.996355
\(362\) −2664.00 −0.386787
\(363\) −1756.00 −0.253901
\(364\) 4788.00 0.689449
\(365\) 0 0
\(366\) −2312.00 −0.330192
\(367\) 7999.00 1.13772 0.568862 0.822433i \(-0.307384\pi\)
0.568862 + 0.822433i \(0.307384\pi\)
\(368\) −368.000 −0.0521286
\(369\) 1219.00 0.171975
\(370\) 0 0
\(371\) −3108.00 −0.434931
\(372\) −656.000 −0.0914301
\(373\) 3588.00 0.498069 0.249034 0.968495i \(-0.419887\pi\)
0.249034 + 0.968495i \(0.419887\pi\)
\(374\) −7896.00 −1.09169
\(375\) 0 0
\(376\) −992.000 −0.136060
\(377\) −16245.0 −2.21926
\(378\) 4200.00 0.571494
\(379\) −2060.00 −0.279195 −0.139598 0.990208i \(-0.544581\pi\)
−0.139598 + 0.990208i \(0.544581\pi\)
\(380\) 0 0
\(381\) −4548.00 −0.611551
\(382\) −2594.00 −0.347436
\(383\) 9943.00 1.32654 0.663268 0.748382i \(-0.269169\pi\)
0.663268 + 0.748382i \(0.269169\pi\)
\(384\) 256.000 0.0340207
\(385\) 0 0
\(386\) 7804.00 1.02905
\(387\) 4531.00 0.595152
\(388\) 256.000 0.0334960
\(389\) −14580.0 −1.90035 −0.950174 0.311720i \(-0.899095\pi\)
−0.950174 + 0.311720i \(0.899095\pi\)
\(390\) 0 0
\(391\) −1932.00 −0.249886
\(392\) −784.000 −0.101015
\(393\) −3604.00 −0.462590
\(394\) −298.000 −0.0381041
\(395\) 0 0
\(396\) −4324.00 −0.548710
\(397\) 14594.0 1.84497 0.922483 0.386037i \(-0.126156\pi\)
0.922483 + 0.386037i \(0.126156\pi\)
\(398\) 1050.00 0.132241
\(399\) −210.000 −0.0263487
\(400\) 0 0
\(401\) 9702.00 1.20822 0.604108 0.796902i \(-0.293529\pi\)
0.604108 + 0.796902i \(0.293529\pi\)
\(402\) −1184.00 −0.146897
\(403\) −4674.00 −0.577738
\(404\) 4008.00 0.493578
\(405\) 0 0
\(406\) 11970.0 1.46320
\(407\) 2538.00 0.309101
\(408\) 1344.00 0.163083
\(409\) −14315.0 −1.73064 −0.865319 0.501221i \(-0.832884\pi\)
−0.865319 + 0.501221i \(0.832884\pi\)
\(410\) 0 0
\(411\) 212.000 0.0254433
\(412\) −7228.00 −0.864316
\(413\) −630.000 −0.0750612
\(414\) −1058.00 −0.125599
\(415\) 0 0
\(416\) 1824.00 0.214973
\(417\) 5400.00 0.634147
\(418\) 470.000 0.0549963
\(419\) −975.000 −0.113680 −0.0568399 0.998383i \(-0.518102\pi\)
−0.0568399 + 0.998383i \(0.518102\pi\)
\(420\) 0 0
\(421\) −11138.0 −1.28939 −0.644695 0.764440i \(-0.723015\pi\)
−0.644695 + 0.764440i \(0.723015\pi\)
\(422\) 7036.00 0.811628
\(423\) −2852.00 −0.327823
\(424\) −1184.00 −0.135613
\(425\) 0 0
\(426\) 1688.00 0.191981
\(427\) 12138.0 1.37564
\(428\) 6656.00 0.751705
\(429\) 5358.00 0.602999
\(430\) 0 0
\(431\) −9568.00 −1.06931 −0.534657 0.845069i \(-0.679559\pi\)
−0.534657 + 0.845069i \(0.679559\pi\)
\(432\) 1600.00 0.178195
\(433\) −1762.00 −0.195557 −0.0977787 0.995208i \(-0.531174\pi\)
−0.0977787 + 0.995208i \(0.531174\pi\)
\(434\) 3444.00 0.380915
\(435\) 0 0
\(436\) 1880.00 0.206504
\(437\) 115.000 0.0125885
\(438\) −1948.00 −0.212509
\(439\) 4080.00 0.443571 0.221786 0.975095i \(-0.428811\pi\)
0.221786 + 0.975095i \(0.428811\pi\)
\(440\) 0 0
\(441\) −2254.00 −0.243386
\(442\) 9576.00 1.03051
\(443\) −9582.00 −1.02766 −0.513831 0.857891i \(-0.671774\pi\)
−0.513831 + 0.857891i \(0.671774\pi\)
\(444\) −432.000 −0.0461753
\(445\) 0 0
\(446\) −5936.00 −0.630219
\(447\) 1780.00 0.188347
\(448\) −1344.00 −0.141737
\(449\) −3290.00 −0.345801 −0.172901 0.984939i \(-0.555314\pi\)
−0.172901 + 0.984939i \(0.555314\pi\)
\(450\) 0 0
\(451\) −2491.00 −0.260081
\(452\) −3968.00 −0.412918
\(453\) 6796.00 0.704865
\(454\) 8072.00 0.834444
\(455\) 0 0
\(456\) −80.0000 −0.00821567
\(457\) 484.000 0.0495417 0.0247709 0.999693i \(-0.492114\pi\)
0.0247709 + 0.999693i \(0.492114\pi\)
\(458\) 8380.00 0.854960
\(459\) 8400.00 0.854201
\(460\) 0 0
\(461\) −10243.0 −1.03485 −0.517423 0.855730i \(-0.673109\pi\)
−0.517423 + 0.855730i \(0.673109\pi\)
\(462\) −3948.00 −0.397571
\(463\) 6208.00 0.623132 0.311566 0.950224i \(-0.399146\pi\)
0.311566 + 0.950224i \(0.399146\pi\)
\(464\) 4560.00 0.456234
\(465\) 0 0
\(466\) 1954.00 0.194243
\(467\) 6089.00 0.603352 0.301676 0.953411i \(-0.402454\pi\)
0.301676 + 0.953411i \(0.402454\pi\)
\(468\) 5244.00 0.517957
\(469\) 6216.00 0.612000
\(470\) 0 0
\(471\) 5952.00 0.582280
\(472\) −240.000 −0.0234044
\(473\) −9259.00 −0.900062
\(474\) −1620.00 −0.156981
\(475\) 0 0
\(476\) −7056.00 −0.679435
\(477\) −3404.00 −0.326747
\(478\) 7480.00 0.715747
\(479\) 8145.00 0.776941 0.388470 0.921461i \(-0.373004\pi\)
0.388470 + 0.921461i \(0.373004\pi\)
\(480\) 0 0
\(481\) −3078.00 −0.291777
\(482\) −7384.00 −0.697784
\(483\) −966.000 −0.0910032
\(484\) 3512.00 0.329827
\(485\) 0 0
\(486\) 7084.00 0.661187
\(487\) −1096.00 −0.101980 −0.0509902 0.998699i \(-0.516238\pi\)
−0.0509902 + 0.998699i \(0.516238\pi\)
\(488\) 4624.00 0.428932
\(489\) 1024.00 0.0946971
\(490\) 0 0
\(491\) −15318.0 −1.40793 −0.703963 0.710237i \(-0.748588\pi\)
−0.703963 + 0.710237i \(0.748588\pi\)
\(492\) 424.000 0.0388524
\(493\) 23940.0 2.18703
\(494\) −570.000 −0.0519140
\(495\) 0 0
\(496\) 1312.00 0.118771
\(497\) −8862.00 −0.799829
\(498\) −1588.00 −0.142892
\(499\) −7440.00 −0.667455 −0.333728 0.942670i \(-0.608307\pi\)
−0.333728 + 0.942670i \(0.608307\pi\)
\(500\) 0 0
\(501\) 2852.00 0.254327
\(502\) 12936.0 1.15012
\(503\) −6147.00 −0.544893 −0.272447 0.962171i \(-0.587833\pi\)
−0.272447 + 0.962171i \(0.587833\pi\)
\(504\) −3864.00 −0.341500
\(505\) 0 0
\(506\) 2162.00 0.189946
\(507\) −2104.00 −0.184304
\(508\) 9096.00 0.794429
\(509\) 1590.00 0.138459 0.0692294 0.997601i \(-0.477946\pi\)
0.0692294 + 0.997601i \(0.477946\pi\)
\(510\) 0 0
\(511\) 10227.0 0.885354
\(512\) −512.000 −0.0441942
\(513\) −500.000 −0.0430322
\(514\) 11172.0 0.958708
\(515\) 0 0
\(516\) 1576.00 0.134456
\(517\) 5828.00 0.495774
\(518\) 2268.00 0.192375
\(519\) 2094.00 0.177103
\(520\) 0 0
\(521\) −16638.0 −1.39909 −0.699543 0.714590i \(-0.746613\pi\)
−0.699543 + 0.714590i \(0.746613\pi\)
\(522\) 13110.0 1.09925
\(523\) 4453.00 0.372306 0.186153 0.982521i \(-0.440398\pi\)
0.186153 + 0.982521i \(0.440398\pi\)
\(524\) 7208.00 0.600922
\(525\) 0 0
\(526\) −12416.0 −1.02921
\(527\) 6888.00 0.569347
\(528\) −1504.00 −0.123964
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) −690.000 −0.0563907
\(532\) 420.000 0.0342280
\(533\) 3021.00 0.245505
\(534\) 2920.00 0.236631
\(535\) 0 0
\(536\) 2368.00 0.190825
\(537\) 2760.00 0.221793
\(538\) 15790.0 1.26534
\(539\) 4606.00 0.368079
\(540\) 0 0
\(541\) 18077.0 1.43658 0.718291 0.695743i \(-0.244925\pi\)
0.718291 + 0.695743i \(0.244925\pi\)
\(542\) 136.000 0.0107780
\(543\) −2664.00 −0.210540
\(544\) −2688.00 −0.211851
\(545\) 0 0
\(546\) 4788.00 0.375288
\(547\) 6644.00 0.519336 0.259668 0.965698i \(-0.416387\pi\)
0.259668 + 0.965698i \(0.416387\pi\)
\(548\) −424.000 −0.0330518
\(549\) 13294.0 1.03347
\(550\) 0 0
\(551\) −1425.00 −0.110176
\(552\) −368.000 −0.0283752
\(553\) 8505.00 0.654013
\(554\) −10578.0 −0.811220
\(555\) 0 0
\(556\) −10800.0 −0.823781
\(557\) 6954.00 0.528995 0.264498 0.964386i \(-0.414794\pi\)
0.264498 + 0.964386i \(0.414794\pi\)
\(558\) 3772.00 0.286168
\(559\) 11229.0 0.849617
\(560\) 0 0
\(561\) −7896.00 −0.594241
\(562\) 6816.00 0.511594
\(563\) −77.0000 −0.00576406 −0.00288203 0.999996i \(-0.500917\pi\)
−0.00288203 + 0.999996i \(0.500917\pi\)
\(564\) −992.000 −0.0740616
\(565\) 0 0
\(566\) −3656.00 −0.271507
\(567\) −8841.00 −0.654827
\(568\) −3376.00 −0.249391
\(569\) 14820.0 1.09189 0.545946 0.837820i \(-0.316170\pi\)
0.545946 + 0.837820i \(0.316170\pi\)
\(570\) 0 0
\(571\) 2492.00 0.182639 0.0913196 0.995822i \(-0.470892\pi\)
0.0913196 + 0.995822i \(0.470892\pi\)
\(572\) −10716.0 −0.783319
\(573\) −2594.00 −0.189120
\(574\) −2226.00 −0.161867
\(575\) 0 0
\(576\) −1472.00 −0.106481
\(577\) 5929.00 0.427777 0.213889 0.976858i \(-0.431387\pi\)
0.213889 + 0.976858i \(0.431387\pi\)
\(578\) −4286.00 −0.308433
\(579\) 7804.00 0.560144
\(580\) 0 0
\(581\) 8337.00 0.595313
\(582\) 256.000 0.0182329
\(583\) 6956.00 0.494148
\(584\) 3896.00 0.276058
\(585\) 0 0
\(586\) −12776.0 −0.900634
\(587\) 7274.00 0.511465 0.255733 0.966748i \(-0.417683\pi\)
0.255733 + 0.966748i \(0.417683\pi\)
\(588\) −784.000 −0.0549857
\(589\) −410.000 −0.0286821
\(590\) 0 0
\(591\) −298.000 −0.0207413
\(592\) 864.000 0.0599834
\(593\) 5823.00 0.403241 0.201621 0.979464i \(-0.435379\pi\)
0.201621 + 0.979464i \(0.435379\pi\)
\(594\) −9400.00 −0.649304
\(595\) 0 0
\(596\) −3560.00 −0.244670
\(597\) 1050.00 0.0719826
\(598\) −2622.00 −0.179300
\(599\) 10430.0 0.711449 0.355725 0.934591i \(-0.384234\pi\)
0.355725 + 0.934591i \(0.384234\pi\)
\(600\) 0 0
\(601\) −18998.0 −1.28943 −0.644713 0.764425i \(-0.723023\pi\)
−0.644713 + 0.764425i \(0.723023\pi\)
\(602\) −8274.00 −0.560171
\(603\) 6808.00 0.459773
\(604\) −13592.0 −0.915647
\(605\) 0 0
\(606\) 4008.00 0.268670
\(607\) −26416.0 −1.76638 −0.883190 0.469016i \(-0.844609\pi\)
−0.883190 + 0.469016i \(0.844609\pi\)
\(608\) 160.000 0.0106725
\(609\) 11970.0 0.796468
\(610\) 0 0
\(611\) −7068.00 −0.467988
\(612\) −7728.00 −0.510434
\(613\) −27262.0 −1.79625 −0.898125 0.439739i \(-0.855071\pi\)
−0.898125 + 0.439739i \(0.855071\pi\)
\(614\) 10032.0 0.659379
\(615\) 0 0
\(616\) 7896.00 0.516459
\(617\) 25584.0 1.66932 0.834662 0.550762i \(-0.185663\pi\)
0.834662 + 0.550762i \(0.185663\pi\)
\(618\) −7228.00 −0.470474
\(619\) −3640.00 −0.236355 −0.118178 0.992992i \(-0.537705\pi\)
−0.118178 + 0.992992i \(0.537705\pi\)
\(620\) 0 0
\(621\) −2300.00 −0.148625
\(622\) −11084.0 −0.714514
\(623\) −15330.0 −0.985848
\(624\) 1824.00 0.117017
\(625\) 0 0
\(626\) −7676.00 −0.490087
\(627\) 470.000 0.0299362
\(628\) −11904.0 −0.756403
\(629\) 4536.00 0.287539
\(630\) 0 0
\(631\) 19937.0 1.25781 0.628906 0.777481i \(-0.283503\pi\)
0.628906 + 0.777481i \(0.283503\pi\)
\(632\) 3240.00 0.203924
\(633\) 7036.00 0.441794
\(634\) 19542.0 1.22415
\(635\) 0 0
\(636\) −1184.00 −0.0738186
\(637\) −5586.00 −0.347450
\(638\) −26790.0 −1.66242
\(639\) −9706.00 −0.600882
\(640\) 0 0
\(641\) −14048.0 −0.865620 −0.432810 0.901485i \(-0.642478\pi\)
−0.432810 + 0.901485i \(0.642478\pi\)
\(642\) 6656.00 0.409177
\(643\) 13423.0 0.823253 0.411626 0.911353i \(-0.364961\pi\)
0.411626 + 0.911353i \(0.364961\pi\)
\(644\) 1932.00 0.118217
\(645\) 0 0
\(646\) 840.000 0.0511600
\(647\) 9024.00 0.548331 0.274165 0.961683i \(-0.411598\pi\)
0.274165 + 0.961683i \(0.411598\pi\)
\(648\) −3368.00 −0.204178
\(649\) 1410.00 0.0852810
\(650\) 0 0
\(651\) 3444.00 0.207344
\(652\) −2048.00 −0.123015
\(653\) 11263.0 0.674970 0.337485 0.941331i \(-0.390424\pi\)
0.337485 + 0.941331i \(0.390424\pi\)
\(654\) 1880.00 0.112406
\(655\) 0 0
\(656\) −848.000 −0.0504708
\(657\) 11201.0 0.665133
\(658\) 5208.00 0.308555
\(659\) 7425.00 0.438903 0.219451 0.975623i \(-0.429573\pi\)
0.219451 + 0.975623i \(0.429573\pi\)
\(660\) 0 0
\(661\) 2032.00 0.119570 0.0597849 0.998211i \(-0.480959\pi\)
0.0597849 + 0.998211i \(0.480959\pi\)
\(662\) −7964.00 −0.467567
\(663\) 9576.00 0.560937
\(664\) 3176.00 0.185622
\(665\) 0 0
\(666\) 2484.00 0.144524
\(667\) −6555.00 −0.380526
\(668\) −5704.00 −0.330381
\(669\) −5936.00 −0.343048
\(670\) 0 0
\(671\) −27166.0 −1.56294
\(672\) −1344.00 −0.0771517
\(673\) 11903.0 0.681764 0.340882 0.940106i \(-0.389274\pi\)
0.340882 + 0.940106i \(0.389274\pi\)
\(674\) 1072.00 0.0612639
\(675\) 0 0
\(676\) 4208.00 0.239417
\(677\) 18654.0 1.05898 0.529491 0.848315i \(-0.322383\pi\)
0.529491 + 0.848315i \(0.322383\pi\)
\(678\) −3968.00 −0.224764
\(679\) −1344.00 −0.0759617
\(680\) 0 0
\(681\) 8072.00 0.454214
\(682\) −7708.00 −0.432778
\(683\) −23302.0 −1.30546 −0.652728 0.757592i \(-0.726375\pi\)
−0.652728 + 0.757592i \(0.726375\pi\)
\(684\) 460.000 0.0257142
\(685\) 0 0
\(686\) −10290.0 −0.572703
\(687\) 8380.00 0.465381
\(688\) −3152.00 −0.174664
\(689\) −8436.00 −0.466453
\(690\) 0 0
\(691\) 16472.0 0.906837 0.453419 0.891298i \(-0.350204\pi\)
0.453419 + 0.891298i \(0.350204\pi\)
\(692\) −4188.00 −0.230063
\(693\) 22701.0 1.24436
\(694\) −16048.0 −0.877772
\(695\) 0 0
\(696\) 4560.00 0.248342
\(697\) −4452.00 −0.241939
\(698\) 9350.00 0.507024
\(699\) 1954.00 0.105733
\(700\) 0 0
\(701\) −19008.0 −1.02414 −0.512070 0.858944i \(-0.671121\pi\)
−0.512070 + 0.858944i \(0.671121\pi\)
\(702\) 11400.0 0.612913
\(703\) −270.000 −0.0144854
\(704\) 3008.00 0.161034
\(705\) 0 0
\(706\) 20694.0 1.10316
\(707\) −21042.0 −1.11933
\(708\) −240.000 −0.0127398
\(709\) −35870.0 −1.90004 −0.950018 0.312194i \(-0.898936\pi\)
−0.950018 + 0.312194i \(0.898936\pi\)
\(710\) 0 0
\(711\) 9315.00 0.491336
\(712\) −5840.00 −0.307392
\(713\) −1886.00 −0.0990621
\(714\) −7056.00 −0.369838
\(715\) 0 0
\(716\) −5520.00 −0.288117
\(717\) 7480.00 0.389604
\(718\) −25430.0 −1.32178
\(719\) 37610.0 1.95079 0.975394 0.220470i \(-0.0707590\pi\)
0.975394 + 0.220470i \(0.0707590\pi\)
\(720\) 0 0
\(721\) 37947.0 1.96008
\(722\) 13668.0 0.704529
\(723\) −7384.00 −0.379826
\(724\) 5328.00 0.273499
\(725\) 0 0
\(726\) 3512.00 0.179535
\(727\) −26176.0 −1.33537 −0.667685 0.744444i \(-0.732715\pi\)
−0.667685 + 0.744444i \(0.732715\pi\)
\(728\) −9576.00 −0.487514
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) −16548.0 −0.837278
\(732\) 4624.00 0.233481
\(733\) 17238.0 0.868622 0.434311 0.900763i \(-0.356992\pi\)
0.434311 + 0.900763i \(0.356992\pi\)
\(734\) −15998.0 −0.804492
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) −13912.0 −0.695326
\(738\) −2438.00 −0.121604
\(739\) −5910.00 −0.294185 −0.147093 0.989123i \(-0.546992\pi\)
−0.147093 + 0.989123i \(0.546992\pi\)
\(740\) 0 0
\(741\) −570.000 −0.0282584
\(742\) 6216.00 0.307543
\(743\) 31203.0 1.54068 0.770341 0.637632i \(-0.220086\pi\)
0.770341 + 0.637632i \(0.220086\pi\)
\(744\) 1312.00 0.0646509
\(745\) 0 0
\(746\) −7176.00 −0.352188
\(747\) 9131.00 0.447237
\(748\) 15792.0 0.771942
\(749\) −34944.0 −1.70471
\(750\) 0 0
\(751\) −36643.0 −1.78046 −0.890228 0.455516i \(-0.849455\pi\)
−0.890228 + 0.455516i \(0.849455\pi\)
\(752\) 1984.00 0.0962088
\(753\) 12936.0 0.626048
\(754\) 32490.0 1.56925
\(755\) 0 0
\(756\) −8400.00 −0.404107
\(757\) −846.000 −0.0406187 −0.0203094 0.999794i \(-0.506465\pi\)
−0.0203094 + 0.999794i \(0.506465\pi\)
\(758\) 4120.00 0.197421
\(759\) 2162.00 0.103393
\(760\) 0 0
\(761\) −11303.0 −0.538414 −0.269207 0.963082i \(-0.586762\pi\)
−0.269207 + 0.963082i \(0.586762\pi\)
\(762\) 9096.00 0.432432
\(763\) −9870.00 −0.468307
\(764\) 5188.00 0.245674
\(765\) 0 0
\(766\) −19886.0 −0.938003
\(767\) −1710.00 −0.0805013
\(768\) −512.000 −0.0240563
\(769\) −31830.0 −1.49261 −0.746306 0.665603i \(-0.768175\pi\)
−0.746306 + 0.665603i \(0.768175\pi\)
\(770\) 0 0
\(771\) 11172.0 0.521854
\(772\) −15608.0 −0.727648
\(773\) −15562.0 −0.724096 −0.362048 0.932159i \(-0.617922\pi\)
−0.362048 + 0.932159i \(0.617922\pi\)
\(774\) −9062.00 −0.420836
\(775\) 0 0
\(776\) −512.000 −0.0236852
\(777\) 2268.00 0.104716
\(778\) 29160.0 1.34375
\(779\) 265.000 0.0121882
\(780\) 0 0
\(781\) 19834.0 0.908728
\(782\) 3864.00 0.176696
\(783\) 28500.0 1.30078
\(784\) 1568.00 0.0714286
\(785\) 0 0
\(786\) 7208.00 0.327100
\(787\) −24771.0 −1.12197 −0.560985 0.827826i \(-0.689578\pi\)
−0.560985 + 0.827826i \(0.689578\pi\)
\(788\) 596.000 0.0269437
\(789\) −12416.0 −0.560230
\(790\) 0 0
\(791\) 20832.0 0.936410
\(792\) 8648.00 0.387997
\(793\) 32946.0 1.47534
\(794\) −29188.0 −1.30459
\(795\) 0 0
\(796\) −2100.00 −0.0935082
\(797\) −24486.0 −1.08825 −0.544127 0.839003i \(-0.683139\pi\)
−0.544127 + 0.839003i \(0.683139\pi\)
\(798\) 420.000 0.0186314
\(799\) 10416.0 0.461191
\(800\) 0 0
\(801\) −16790.0 −0.740631
\(802\) −19404.0 −0.854338
\(803\) −22889.0 −1.00590
\(804\) 2368.00 0.103872
\(805\) 0 0
\(806\) 9348.00 0.408523
\(807\) 15790.0 0.688766
\(808\) −8016.00 −0.349012
\(809\) 24705.0 1.07365 0.536824 0.843694i \(-0.319624\pi\)
0.536824 + 0.843694i \(0.319624\pi\)
\(810\) 0 0
\(811\) 6392.00 0.276761 0.138381 0.990379i \(-0.455810\pi\)
0.138381 + 0.990379i \(0.455810\pi\)
\(812\) −23940.0 −1.03464
\(813\) 136.000 0.00586682
\(814\) −5076.00 −0.218567
\(815\) 0 0
\(816\) −2688.00 −0.115317
\(817\) 985.000 0.0421797
\(818\) 28630.0 1.22375
\(819\) −27531.0 −1.17462
\(820\) 0 0
\(821\) 39047.0 1.65987 0.829933 0.557863i \(-0.188379\pi\)
0.829933 + 0.557863i \(0.188379\pi\)
\(822\) −424.000 −0.0179911
\(823\) 14348.0 0.607703 0.303852 0.952719i \(-0.401727\pi\)
0.303852 + 0.952719i \(0.401727\pi\)
\(824\) 14456.0 0.611163
\(825\) 0 0
\(826\) 1260.00 0.0530763
\(827\) 23749.0 0.998590 0.499295 0.866432i \(-0.333592\pi\)
0.499295 + 0.866432i \(0.333592\pi\)
\(828\) 2116.00 0.0888117
\(829\) 25125.0 1.05263 0.526313 0.850291i \(-0.323574\pi\)
0.526313 + 0.850291i \(0.323574\pi\)
\(830\) 0 0
\(831\) −10578.0 −0.441573
\(832\) −3648.00 −0.152009
\(833\) 8232.00 0.342403
\(834\) −10800.0 −0.448409
\(835\) 0 0
\(836\) −940.000 −0.0388883
\(837\) 8200.00 0.338630
\(838\) 1950.00 0.0803838
\(839\) −32295.0 −1.32890 −0.664450 0.747333i \(-0.731334\pi\)
−0.664450 + 0.747333i \(0.731334\pi\)
\(840\) 0 0
\(841\) 56836.0 2.33039
\(842\) 22276.0 0.911736
\(843\) 6816.00 0.278476
\(844\) −14072.0 −0.573908
\(845\) 0 0
\(846\) 5704.00 0.231806
\(847\) −18438.0 −0.747978
\(848\) 2368.00 0.0958932
\(849\) −3656.00 −0.147790
\(850\) 0 0
\(851\) −1242.00 −0.0500296
\(852\) −3376.00 −0.135751
\(853\) −29257.0 −1.17437 −0.587187 0.809451i \(-0.699765\pi\)
−0.587187 + 0.809451i \(0.699765\pi\)
\(854\) −24276.0 −0.972726
\(855\) 0 0
\(856\) −13312.0 −0.531536
\(857\) −11766.0 −0.468984 −0.234492 0.972118i \(-0.575343\pi\)
−0.234492 + 0.972118i \(0.575343\pi\)
\(858\) −10716.0 −0.426385
\(859\) −32390.0 −1.28653 −0.643267 0.765642i \(-0.722421\pi\)
−0.643267 + 0.765642i \(0.722421\pi\)
\(860\) 0 0
\(861\) −2226.00 −0.0881090
\(862\) 19136.0 0.756119
\(863\) −16332.0 −0.644204 −0.322102 0.946705i \(-0.604389\pi\)
−0.322102 + 0.946705i \(0.604389\pi\)
\(864\) −3200.00 −0.126003
\(865\) 0 0
\(866\) 3524.00 0.138280
\(867\) −4286.00 −0.167889
\(868\) −6888.00 −0.269348
\(869\) −19035.0 −0.743059
\(870\) 0 0
\(871\) 16872.0 0.656356
\(872\) −3760.00 −0.146020
\(873\) −1472.00 −0.0570672
\(874\) −230.000 −0.00890145
\(875\) 0 0
\(876\) 3896.00 0.150267
\(877\) −42226.0 −1.62585 −0.812925 0.582368i \(-0.802126\pi\)
−0.812925 + 0.582368i \(0.802126\pi\)
\(878\) −8160.00 −0.313652
\(879\) −12776.0 −0.490243
\(880\) 0 0
\(881\) −7158.00 −0.273733 −0.136867 0.990589i \(-0.543703\pi\)
−0.136867 + 0.990589i \(0.543703\pi\)
\(882\) 4508.00 0.172100
\(883\) −28672.0 −1.09274 −0.546370 0.837544i \(-0.683991\pi\)
−0.546370 + 0.837544i \(0.683991\pi\)
\(884\) −19152.0 −0.728678
\(885\) 0 0
\(886\) 19164.0 0.726667
\(887\) −5536.00 −0.209561 −0.104781 0.994495i \(-0.533414\pi\)
−0.104781 + 0.994495i \(0.533414\pi\)
\(888\) 864.000 0.0326508
\(889\) −47754.0 −1.80159
\(890\) 0 0
\(891\) 19787.0 0.743984
\(892\) 11872.0 0.445632
\(893\) −620.000 −0.0232335
\(894\) −3560.00 −0.133181
\(895\) 0 0
\(896\) 2688.00 0.100223
\(897\) −2622.00 −0.0975987
\(898\) 6580.00 0.244518
\(899\) 23370.0 0.867000
\(900\) 0 0
\(901\) 12432.0 0.459678
\(902\) 4982.00 0.183905
\(903\) −8274.00 −0.304919
\(904\) 7936.00 0.291977
\(905\) 0 0
\(906\) −13592.0 −0.498415
\(907\) −451.000 −0.0165107 −0.00825535 0.999966i \(-0.502628\pi\)
−0.00825535 + 0.999966i \(0.502628\pi\)
\(908\) −16144.0 −0.590041
\(909\) −23046.0 −0.840910
\(910\) 0 0
\(911\) −21013.0 −0.764206 −0.382103 0.924120i \(-0.624800\pi\)
−0.382103 + 0.924120i \(0.624800\pi\)
\(912\) 160.000 0.00580935
\(913\) −18659.0 −0.676367
\(914\) −968.000 −0.0350313
\(915\) 0 0
\(916\) −16760.0 −0.604548
\(917\) −37842.0 −1.36276
\(918\) −16800.0 −0.604012
\(919\) 28800.0 1.03376 0.516879 0.856058i \(-0.327094\pi\)
0.516879 + 0.856058i \(0.327094\pi\)
\(920\) 0 0
\(921\) 10032.0 0.358920
\(922\) 20486.0 0.731747
\(923\) −24054.0 −0.857797
\(924\) 7896.00 0.281125
\(925\) 0 0
\(926\) −12416.0 −0.440621
\(927\) 41561.0 1.47254
\(928\) −9120.00 −0.322606
\(929\) 39555.0 1.39694 0.698470 0.715639i \(-0.253865\pi\)
0.698470 + 0.715639i \(0.253865\pi\)
\(930\) 0 0
\(931\) −490.000 −0.0172493
\(932\) −3908.00 −0.137351
\(933\) −11084.0 −0.388932
\(934\) −12178.0 −0.426634
\(935\) 0 0
\(936\) −10488.0 −0.366251
\(937\) −38756.0 −1.35123 −0.675615 0.737254i \(-0.736122\pi\)
−0.675615 + 0.737254i \(0.736122\pi\)
\(938\) −12432.0 −0.432750
\(939\) −7676.00 −0.266770
\(940\) 0 0
\(941\) −3968.00 −0.137463 −0.0687317 0.997635i \(-0.521895\pi\)
−0.0687317 + 0.997635i \(0.521895\pi\)
\(942\) −11904.0 −0.411734
\(943\) 1219.00 0.0420955
\(944\) 480.000 0.0165494
\(945\) 0 0
\(946\) 18518.0 0.636440
\(947\) 32374.0 1.11089 0.555445 0.831553i \(-0.312548\pi\)
0.555445 + 0.831553i \(0.312548\pi\)
\(948\) 3240.00 0.111002
\(949\) 27759.0 0.949521
\(950\) 0 0
\(951\) 19542.0 0.666344
\(952\) 14112.0 0.480433
\(953\) −23122.0 −0.785934 −0.392967 0.919553i \(-0.628551\pi\)
−0.392967 + 0.919553i \(0.628551\pi\)
\(954\) 6808.00 0.231045
\(955\) 0 0
\(956\) −14960.0 −0.506110
\(957\) −26790.0 −0.904909
\(958\) −16290.0 −0.549380
\(959\) 2226.00 0.0749544
\(960\) 0 0
\(961\) −23067.0 −0.774294
\(962\) 6156.00 0.206317
\(963\) −38272.0 −1.28068
\(964\) 14768.0 0.493408
\(965\) 0 0
\(966\) 1932.00 0.0643489
\(967\) −16916.0 −0.562546 −0.281273 0.959628i \(-0.590757\pi\)
−0.281273 + 0.959628i \(0.590757\pi\)
\(968\) −7024.00 −0.233223
\(969\) 840.000 0.0278480
\(970\) 0 0
\(971\) 32277.0 1.06675 0.533377 0.845878i \(-0.320923\pi\)
0.533377 + 0.845878i \(0.320923\pi\)
\(972\) −14168.0 −0.467530
\(973\) 56700.0 1.86816
\(974\) 2192.00 0.0721111
\(975\) 0 0
\(976\) −9248.00 −0.303300
\(977\) −48076.0 −1.57430 −0.787148 0.616764i \(-0.788443\pi\)
−0.787148 + 0.616764i \(0.788443\pi\)
\(978\) −2048.00 −0.0669610
\(979\) 34310.0 1.12007
\(980\) 0 0
\(981\) −10810.0 −0.351821
\(982\) 30636.0 0.995554
\(983\) −37287.0 −1.20984 −0.604919 0.796287i \(-0.706794\pi\)
−0.604919 + 0.796287i \(0.706794\pi\)
\(984\) −848.000 −0.0274728
\(985\) 0 0
\(986\) −47880.0 −1.54646
\(987\) 5208.00 0.167956
\(988\) 1140.00 0.0367087
\(989\) 4531.00 0.145680
\(990\) 0 0
\(991\) 4872.00 0.156170 0.0780849 0.996947i \(-0.475119\pi\)
0.0780849 + 0.996947i \(0.475119\pi\)
\(992\) −2624.00 −0.0839840
\(993\) −7964.00 −0.254511
\(994\) 17724.0 0.565565
\(995\) 0 0
\(996\) 3176.00 0.101040
\(997\) −24751.0 −0.786231 −0.393115 0.919489i \(-0.628603\pi\)
−0.393115 + 0.919489i \(0.628603\pi\)
\(998\) 14880.0 0.471962
\(999\) 5400.00 0.171019
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 1150.4.a.a.1.1 1
5.2 odd 4 1150.4.b.g.599.1 2
5.3 odd 4 1150.4.b.g.599.2 2
5.4 even 2 1150.4.a.h.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.4.a.a.1.1 1 1.1 even 1 trivial
1150.4.a.h.1.1 yes 1 5.4 even 2
1150.4.b.g.599.1 2 5.2 odd 4
1150.4.b.g.599.2 2 5.3 odd 4