Properties

Label 98.4.a.f.1.1
Level $98$
Weight $4$
Character 98.1
Self dual yes
Analytic conductor $5.782$
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] = [98,4,Mod(1,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.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: \(5.78218718056\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 98.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +5.00000 q^{3} +4.00000 q^{4} +9.00000 q^{5} +10.0000 q^{6} +8.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +5.00000 q^{3} +4.00000 q^{4} +9.00000 q^{5} +10.0000 q^{6} +8.00000 q^{8} -2.00000 q^{9} +18.0000 q^{10} -57.0000 q^{11} +20.0000 q^{12} +70.0000 q^{13} +45.0000 q^{15} +16.0000 q^{16} -51.0000 q^{17} -4.00000 q^{18} -5.00000 q^{19} +36.0000 q^{20} -114.000 q^{22} +69.0000 q^{23} +40.0000 q^{24} -44.0000 q^{25} +140.000 q^{26} -145.000 q^{27} +114.000 q^{29} +90.0000 q^{30} -23.0000 q^{31} +32.0000 q^{32} -285.000 q^{33} -102.000 q^{34} -8.00000 q^{36} -253.000 q^{37} -10.0000 q^{38} +350.000 q^{39} +72.0000 q^{40} +42.0000 q^{41} -124.000 q^{43} -228.000 q^{44} -18.0000 q^{45} +138.000 q^{46} -201.000 q^{47} +80.0000 q^{48} -88.0000 q^{50} -255.000 q^{51} +280.000 q^{52} -393.000 q^{53} -290.000 q^{54} -513.000 q^{55} -25.0000 q^{57} +228.000 q^{58} -219.000 q^{59} +180.000 q^{60} +709.000 q^{61} -46.0000 q^{62} +64.0000 q^{64} +630.000 q^{65} -570.000 q^{66} +419.000 q^{67} -204.000 q^{68} +345.000 q^{69} -96.0000 q^{71} -16.0000 q^{72} +313.000 q^{73} -506.000 q^{74} -220.000 q^{75} -20.0000 q^{76} +700.000 q^{78} +461.000 q^{79} +144.000 q^{80} -671.000 q^{81} +84.0000 q^{82} +588.000 q^{83} -459.000 q^{85} -248.000 q^{86} +570.000 q^{87} -456.000 q^{88} +1017.00 q^{89} -36.0000 q^{90} +276.000 q^{92} -115.000 q^{93} -402.000 q^{94} -45.0000 q^{95} +160.000 q^{96} +1834.00 q^{97} +114.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 5.00000 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(4\) 4.00000 0.500000
\(5\) 9.00000 0.804984 0.402492 0.915423i \(-0.368144\pi\)
0.402492 + 0.915423i \(0.368144\pi\)
\(6\) 10.0000 0.680414
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −2.00000 −0.0740741
\(10\) 18.0000 0.569210
\(11\) −57.0000 −1.56238 −0.781188 0.624295i \(-0.785386\pi\)
−0.781188 + 0.624295i \(0.785386\pi\)
\(12\) 20.0000 0.481125
\(13\) 70.0000 1.49342 0.746712 0.665148i \(-0.231631\pi\)
0.746712 + 0.665148i \(0.231631\pi\)
\(14\) 0 0
\(15\) 45.0000 0.774597
\(16\) 16.0000 0.250000
\(17\) −51.0000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −4.00000 −0.0523783
\(19\) −5.00000 −0.0603726 −0.0301863 0.999544i \(-0.509610\pi\)
−0.0301863 + 0.999544i \(0.509610\pi\)
\(20\) 36.0000 0.402492
\(21\) 0 0
\(22\) −114.000 −1.10477
\(23\) 69.0000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 40.0000 0.340207
\(25\) −44.0000 −0.352000
\(26\) 140.000 1.05601
\(27\) −145.000 −1.03353
\(28\) 0 0
\(29\) 114.000 0.729975 0.364987 0.931012i \(-0.381073\pi\)
0.364987 + 0.931012i \(0.381073\pi\)
\(30\) 90.0000 0.547723
\(31\) −23.0000 −0.133256 −0.0666278 0.997778i \(-0.521224\pi\)
−0.0666278 + 0.997778i \(0.521224\pi\)
\(32\) 32.0000 0.176777
\(33\) −285.000 −1.50340
\(34\) −102.000 −0.514496
\(35\) 0 0
\(36\) −8.00000 −0.0370370
\(37\) −253.000 −1.12413 −0.562067 0.827092i \(-0.689994\pi\)
−0.562067 + 0.827092i \(0.689994\pi\)
\(38\) −10.0000 −0.0426898
\(39\) 350.000 1.43705
\(40\) 72.0000 0.284605
\(41\) 42.0000 0.159983 0.0799914 0.996796i \(-0.474511\pi\)
0.0799914 + 0.996796i \(0.474511\pi\)
\(42\) 0 0
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) −228.000 −0.781188
\(45\) −18.0000 −0.0596285
\(46\) 138.000 0.442326
\(47\) −201.000 −0.623806 −0.311903 0.950114i \(-0.600966\pi\)
−0.311903 + 0.950114i \(0.600966\pi\)
\(48\) 80.0000 0.240563
\(49\) 0 0
\(50\) −88.0000 −0.248902
\(51\) −255.000 −0.700140
\(52\) 280.000 0.746712
\(53\) −393.000 −1.01854 −0.509271 0.860606i \(-0.670085\pi\)
−0.509271 + 0.860606i \(0.670085\pi\)
\(54\) −290.000 −0.730815
\(55\) −513.000 −1.25769
\(56\) 0 0
\(57\) −25.0000 −0.0580935
\(58\) 228.000 0.516170
\(59\) −219.000 −0.483244 −0.241622 0.970371i \(-0.577679\pi\)
−0.241622 + 0.970371i \(0.577679\pi\)
\(60\) 180.000 0.387298
\(61\) 709.000 1.48817 0.744083 0.668087i \(-0.232887\pi\)
0.744083 + 0.668087i \(0.232887\pi\)
\(62\) −46.0000 −0.0942259
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 630.000 1.20218
\(66\) −570.000 −1.06306
\(67\) 419.000 0.764015 0.382007 0.924159i \(-0.375233\pi\)
0.382007 + 0.924159i \(0.375233\pi\)
\(68\) −204.000 −0.363803
\(69\) 345.000 0.601929
\(70\) 0 0
\(71\) −96.0000 −0.160466 −0.0802331 0.996776i \(-0.525566\pi\)
−0.0802331 + 0.996776i \(0.525566\pi\)
\(72\) −16.0000 −0.0261891
\(73\) 313.000 0.501834 0.250917 0.968009i \(-0.419268\pi\)
0.250917 + 0.968009i \(0.419268\pi\)
\(74\) −506.000 −0.794883
\(75\) −220.000 −0.338712
\(76\) −20.0000 −0.0301863
\(77\) 0 0
\(78\) 700.000 1.01615
\(79\) 461.000 0.656539 0.328269 0.944584i \(-0.393535\pi\)
0.328269 + 0.944584i \(0.393535\pi\)
\(80\) 144.000 0.201246
\(81\) −671.000 −0.920439
\(82\) 84.0000 0.113125
\(83\) 588.000 0.777607 0.388804 0.921321i \(-0.372888\pi\)
0.388804 + 0.921321i \(0.372888\pi\)
\(84\) 0 0
\(85\) −459.000 −0.585712
\(86\) −248.000 −0.310960
\(87\) 570.000 0.702419
\(88\) −456.000 −0.552384
\(89\) 1017.00 1.21126 0.605628 0.795748i \(-0.292922\pi\)
0.605628 + 0.795748i \(0.292922\pi\)
\(90\) −36.0000 −0.0421637
\(91\) 0 0
\(92\) 276.000 0.312772
\(93\) −115.000 −0.128225
\(94\) −402.000 −0.441097
\(95\) −45.0000 −0.0485990
\(96\) 160.000 0.170103
\(97\) 1834.00 1.91974 0.959868 0.280451i \(-0.0904839\pi\)
0.959868 + 0.280451i \(0.0904839\pi\)
\(98\) 0 0
\(99\) 114.000 0.115732
\(100\) −176.000 −0.176000
\(101\) 285.000 0.280778 0.140389 0.990096i \(-0.455165\pi\)
0.140389 + 0.990096i \(0.455165\pi\)
\(102\) −510.000 −0.495074
\(103\) 499.000 0.477359 0.238679 0.971098i \(-0.423286\pi\)
0.238679 + 0.971098i \(0.423286\pi\)
\(104\) 560.000 0.528005
\(105\) 0 0
\(106\) −786.000 −0.720218
\(107\) −1107.00 −1.00017 −0.500083 0.865978i \(-0.666697\pi\)
−0.500083 + 0.865978i \(0.666697\pi\)
\(108\) −580.000 −0.516764
\(109\) 923.000 0.811077 0.405538 0.914078i \(-0.367084\pi\)
0.405538 + 0.914078i \(0.367084\pi\)
\(110\) −1026.00 −0.889321
\(111\) −1265.00 −1.08170
\(112\) 0 0
\(113\) 1542.00 1.28371 0.641855 0.766826i \(-0.278165\pi\)
0.641855 + 0.766826i \(0.278165\pi\)
\(114\) −50.0000 −0.0410783
\(115\) 621.000 0.503553
\(116\) 456.000 0.364987
\(117\) −140.000 −0.110624
\(118\) −438.000 −0.341705
\(119\) 0 0
\(120\) 360.000 0.273861
\(121\) 1918.00 1.44102
\(122\) 1418.00 1.05229
\(123\) 210.000 0.153944
\(124\) −92.0000 −0.0666278
\(125\) −1521.00 −1.08834
\(126\) 0 0
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) 128.000 0.0883883
\(129\) −620.000 −0.423162
\(130\) 1260.00 0.850072
\(131\) −2049.00 −1.36658 −0.683290 0.730147i \(-0.739451\pi\)
−0.683290 + 0.730147i \(0.739451\pi\)
\(132\) −1140.00 −0.751699
\(133\) 0 0
\(134\) 838.000 0.540240
\(135\) −1305.00 −0.831974
\(136\) −408.000 −0.257248
\(137\) −141.000 −0.0879302 −0.0439651 0.999033i \(-0.513999\pi\)
−0.0439651 + 0.999033i \(0.513999\pi\)
\(138\) 690.000 0.425628
\(139\) −1484.00 −0.905548 −0.452774 0.891625i \(-0.649566\pi\)
−0.452774 + 0.891625i \(0.649566\pi\)
\(140\) 0 0
\(141\) −1005.00 −0.600257
\(142\) −192.000 −0.113467
\(143\) −3990.00 −2.33329
\(144\) −32.0000 −0.0185185
\(145\) 1026.00 0.587618
\(146\) 626.000 0.354850
\(147\) 0 0
\(148\) −1012.00 −0.562067
\(149\) −57.0000 −0.0313397 −0.0156699 0.999877i \(-0.504988\pi\)
−0.0156699 + 0.999877i \(0.504988\pi\)
\(150\) −440.000 −0.239506
\(151\) 839.000 0.452165 0.226082 0.974108i \(-0.427408\pi\)
0.226082 + 0.974108i \(0.427408\pi\)
\(152\) −40.0000 −0.0213449
\(153\) 102.000 0.0538968
\(154\) 0 0
\(155\) −207.000 −0.107269
\(156\) 1400.00 0.718524
\(157\) 2833.00 1.44011 0.720057 0.693915i \(-0.244115\pi\)
0.720057 + 0.693915i \(0.244115\pi\)
\(158\) 922.000 0.464243
\(159\) −1965.00 −0.980092
\(160\) 288.000 0.142302
\(161\) 0 0
\(162\) −1342.00 −0.650849
\(163\) −2311.00 −1.11050 −0.555250 0.831684i \(-0.687377\pi\)
−0.555250 + 0.831684i \(0.687377\pi\)
\(164\) 168.000 0.0799914
\(165\) −2565.00 −1.21021
\(166\) 1176.00 0.549851
\(167\) −1260.00 −0.583843 −0.291921 0.956442i \(-0.594295\pi\)
−0.291921 + 0.956442i \(0.594295\pi\)
\(168\) 0 0
\(169\) 2703.00 1.23031
\(170\) −918.000 −0.414161
\(171\) 10.0000 0.00447204
\(172\) −496.000 −0.219882
\(173\) −3267.00 −1.43575 −0.717877 0.696170i \(-0.754886\pi\)
−0.717877 + 0.696170i \(0.754886\pi\)
\(174\) 1140.00 0.496685
\(175\) 0 0
\(176\) −912.000 −0.390594
\(177\) −1095.00 −0.465001
\(178\) 2034.00 0.856487
\(179\) 1287.00 0.537402 0.268701 0.963224i \(-0.413406\pi\)
0.268701 + 0.963224i \(0.413406\pi\)
\(180\) −72.0000 −0.0298142
\(181\) 2674.00 1.09810 0.549052 0.835788i \(-0.314989\pi\)
0.549052 + 0.835788i \(0.314989\pi\)
\(182\) 0 0
\(183\) 3545.00 1.43199
\(184\) 552.000 0.221163
\(185\) −2277.00 −0.904910
\(186\) −230.000 −0.0906689
\(187\) 2907.00 1.13680
\(188\) −804.000 −0.311903
\(189\) 0 0
\(190\) −90.0000 −0.0343647
\(191\) 4185.00 1.58542 0.792712 0.609596i \(-0.208668\pi\)
0.792712 + 0.609596i \(0.208668\pi\)
\(192\) 320.000 0.120281
\(193\) −85.0000 −0.0317017 −0.0158509 0.999874i \(-0.505046\pi\)
−0.0158509 + 0.999874i \(0.505046\pi\)
\(194\) 3668.00 1.35746
\(195\) 3150.00 1.15680
\(196\) 0 0
\(197\) −390.000 −0.141047 −0.0705237 0.997510i \(-0.522467\pi\)
−0.0705237 + 0.997510i \(0.522467\pi\)
\(198\) 228.000 0.0818346
\(199\) 2833.00 1.00918 0.504588 0.863360i \(-0.331644\pi\)
0.504588 + 0.863360i \(0.331644\pi\)
\(200\) −352.000 −0.124451
\(201\) 2095.00 0.735174
\(202\) 570.000 0.198540
\(203\) 0 0
\(204\) −1020.00 −0.350070
\(205\) 378.000 0.128784
\(206\) 998.000 0.337543
\(207\) −138.000 −0.0463365
\(208\) 1120.00 0.373356
\(209\) 285.000 0.0943247
\(210\) 0 0
\(211\) −124.000 −0.0404574 −0.0202287 0.999795i \(-0.506439\pi\)
−0.0202287 + 0.999795i \(0.506439\pi\)
\(212\) −1572.00 −0.509271
\(213\) −480.000 −0.154409
\(214\) −2214.00 −0.707224
\(215\) −1116.00 −0.354003
\(216\) −1160.00 −0.365407
\(217\) 0 0
\(218\) 1846.00 0.573518
\(219\) 1565.00 0.482890
\(220\) −2052.00 −0.628845
\(221\) −3570.00 −1.08663
\(222\) −2530.00 −0.764876
\(223\) −56.0000 −0.0168163 −0.00840816 0.999965i \(-0.502676\pi\)
−0.00840816 + 0.999965i \(0.502676\pi\)
\(224\) 0 0
\(225\) 88.0000 0.0260741
\(226\) 3084.00 0.907720
\(227\) 3057.00 0.893834 0.446917 0.894576i \(-0.352522\pi\)
0.446917 + 0.894576i \(0.352522\pi\)
\(228\) −100.000 −0.0290468
\(229\) 961.000 0.277313 0.138656 0.990341i \(-0.455722\pi\)
0.138656 + 0.990341i \(0.455722\pi\)
\(230\) 1242.00 0.356065
\(231\) 0 0
\(232\) 912.000 0.258085
\(233\) −2829.00 −0.795425 −0.397712 0.917510i \(-0.630196\pi\)
−0.397712 + 0.917510i \(0.630196\pi\)
\(234\) −280.000 −0.0782230
\(235\) −1809.00 −0.502154
\(236\) −876.000 −0.241622
\(237\) 2305.00 0.631755
\(238\) 0 0
\(239\) −3540.00 −0.958090 −0.479045 0.877790i \(-0.659017\pi\)
−0.479045 + 0.877790i \(0.659017\pi\)
\(240\) 720.000 0.193649
\(241\) −5231.00 −1.39817 −0.699084 0.715040i \(-0.746409\pi\)
−0.699084 + 0.715040i \(0.746409\pi\)
\(242\) 3836.00 1.01896
\(243\) 560.000 0.147835
\(244\) 2836.00 0.744083
\(245\) 0 0
\(246\) 420.000 0.108855
\(247\) −350.000 −0.0901618
\(248\) −184.000 −0.0471130
\(249\) 2940.00 0.748253
\(250\) −3042.00 −0.769572
\(251\) −5040.00 −1.26742 −0.633709 0.773571i \(-0.718468\pi\)
−0.633709 + 0.773571i \(0.718468\pi\)
\(252\) 0 0
\(253\) −3933.00 −0.977334
\(254\) −4112.00 −1.01579
\(255\) −2295.00 −0.563602
\(256\) 256.000 0.0625000
\(257\) 1437.00 0.348784 0.174392 0.984676i \(-0.444204\pi\)
0.174392 + 0.984676i \(0.444204\pi\)
\(258\) −1240.00 −0.299221
\(259\) 0 0
\(260\) 2520.00 0.601091
\(261\) −228.000 −0.0540722
\(262\) −4098.00 −0.966318
\(263\) −2325.00 −0.545117 −0.272558 0.962139i \(-0.587870\pi\)
−0.272558 + 0.962139i \(0.587870\pi\)
\(264\) −2280.00 −0.531531
\(265\) −3537.00 −0.819910
\(266\) 0 0
\(267\) 5085.00 1.16553
\(268\) 1676.00 0.382007
\(269\) 2385.00 0.540580 0.270290 0.962779i \(-0.412880\pi\)
0.270290 + 0.962779i \(0.412880\pi\)
\(270\) −2610.00 −0.588295
\(271\) 331.000 0.0741949 0.0370975 0.999312i \(-0.488189\pi\)
0.0370975 + 0.999312i \(0.488189\pi\)
\(272\) −816.000 −0.181902
\(273\) 0 0
\(274\) −282.000 −0.0621761
\(275\) 2508.00 0.549957
\(276\) 1380.00 0.300965
\(277\) 4871.00 1.05657 0.528285 0.849067i \(-0.322835\pi\)
0.528285 + 0.849067i \(0.322835\pi\)
\(278\) −2968.00 −0.640319
\(279\) 46.0000 0.00987078
\(280\) 0 0
\(281\) −7026.00 −1.49159 −0.745794 0.666177i \(-0.767930\pi\)
−0.745794 + 0.666177i \(0.767930\pi\)
\(282\) −2010.00 −0.424446
\(283\) 5353.00 1.12439 0.562196 0.827004i \(-0.309957\pi\)
0.562196 + 0.827004i \(0.309957\pi\)
\(284\) −384.000 −0.0802331
\(285\) −225.000 −0.0467644
\(286\) −7980.00 −1.64989
\(287\) 0 0
\(288\) −64.0000 −0.0130946
\(289\) −2312.00 −0.470588
\(290\) 2052.00 0.415509
\(291\) 9170.00 1.84727
\(292\) 1252.00 0.250917
\(293\) −4158.00 −0.829054 −0.414527 0.910037i \(-0.636053\pi\)
−0.414527 + 0.910037i \(0.636053\pi\)
\(294\) 0 0
\(295\) −1971.00 −0.389004
\(296\) −2024.00 −0.397441
\(297\) 8265.00 1.61476
\(298\) −114.000 −0.0221605
\(299\) 4830.00 0.934201
\(300\) −880.000 −0.169356
\(301\) 0 0
\(302\) 1678.00 0.319729
\(303\) 1425.00 0.270179
\(304\) −80.0000 −0.0150931
\(305\) 6381.00 1.19795
\(306\) 204.000 0.0381108
\(307\) 9604.00 1.78544 0.892719 0.450615i \(-0.148795\pi\)
0.892719 + 0.450615i \(0.148795\pi\)
\(308\) 0 0
\(309\) 2495.00 0.459338
\(310\) −414.000 −0.0758504
\(311\) −10131.0 −1.84719 −0.923595 0.383369i \(-0.874764\pi\)
−0.923595 + 0.383369i \(0.874764\pi\)
\(312\) 2800.00 0.508073
\(313\) −10799.0 −1.95015 −0.975073 0.221885i \(-0.928779\pi\)
−0.975073 + 0.221885i \(0.928779\pi\)
\(314\) 5666.00 1.01831
\(315\) 0 0
\(316\) 1844.00 0.328269
\(317\) 531.000 0.0940818 0.0470409 0.998893i \(-0.485021\pi\)
0.0470409 + 0.998893i \(0.485021\pi\)
\(318\) −3930.00 −0.693030
\(319\) −6498.00 −1.14050
\(320\) 576.000 0.100623
\(321\) −5535.00 −0.962410
\(322\) 0 0
\(323\) 255.000 0.0439275
\(324\) −2684.00 −0.460219
\(325\) −3080.00 −0.525685
\(326\) −4622.00 −0.785242
\(327\) 4615.00 0.780459
\(328\) 336.000 0.0565625
\(329\) 0 0
\(330\) −5130.00 −0.855749
\(331\) −7015.00 −1.16489 −0.582446 0.812869i \(-0.697904\pi\)
−0.582446 + 0.812869i \(0.697904\pi\)
\(332\) 2352.00 0.388804
\(333\) 506.000 0.0832692
\(334\) −2520.00 −0.412839
\(335\) 3771.00 0.615020
\(336\) 0 0
\(337\) 8990.00 1.45316 0.726582 0.687079i \(-0.241108\pi\)
0.726582 + 0.687079i \(0.241108\pi\)
\(338\) 5406.00 0.869963
\(339\) 7710.00 1.23525
\(340\) −1836.00 −0.292856
\(341\) 1311.00 0.208195
\(342\) 20.0000 0.00316221
\(343\) 0 0
\(344\) −992.000 −0.155480
\(345\) 3105.00 0.484544
\(346\) −6534.00 −1.01523
\(347\) −8709.00 −1.34733 −0.673665 0.739037i \(-0.735281\pi\)
−0.673665 + 0.739037i \(0.735281\pi\)
\(348\) 2280.00 0.351209
\(349\) −6482.00 −0.994193 −0.497097 0.867695i \(-0.665601\pi\)
−0.497097 + 0.867695i \(0.665601\pi\)
\(350\) 0 0
\(351\) −10150.0 −1.54350
\(352\) −1824.00 −0.276192
\(353\) 2133.00 0.321609 0.160805 0.986986i \(-0.448591\pi\)
0.160805 + 0.986986i \(0.448591\pi\)
\(354\) −2190.00 −0.328806
\(355\) −864.000 −0.129173
\(356\) 4068.00 0.605628
\(357\) 0 0
\(358\) 2574.00 0.380000
\(359\) 3849.00 0.565856 0.282928 0.959141i \(-0.408694\pi\)
0.282928 + 0.959141i \(0.408694\pi\)
\(360\) −144.000 −0.0210819
\(361\) −6834.00 −0.996355
\(362\) 5348.00 0.776477
\(363\) 9590.00 1.38662
\(364\) 0 0
\(365\) 2817.00 0.403969
\(366\) 7090.00 1.01257
\(367\) −6491.00 −0.923236 −0.461618 0.887079i \(-0.652731\pi\)
−0.461618 + 0.887079i \(0.652731\pi\)
\(368\) 1104.00 0.156386
\(369\) −84.0000 −0.0118506
\(370\) −4554.00 −0.639868
\(371\) 0 0
\(372\) −460.000 −0.0641126
\(373\) 923.000 0.128126 0.0640632 0.997946i \(-0.479594\pi\)
0.0640632 + 0.997946i \(0.479594\pi\)
\(374\) 5814.00 0.803836
\(375\) −7605.00 −1.04725
\(376\) −1608.00 −0.220549
\(377\) 7980.00 1.09016
\(378\) 0 0
\(379\) 6344.00 0.859814 0.429907 0.902873i \(-0.358546\pi\)
0.429907 + 0.902873i \(0.358546\pi\)
\(380\) −180.000 −0.0242995
\(381\) −10280.0 −1.38231
\(382\) 8370.00 1.12106
\(383\) 5007.00 0.668005 0.334002 0.942572i \(-0.391601\pi\)
0.334002 + 0.942572i \(0.391601\pi\)
\(384\) 640.000 0.0850517
\(385\) 0 0
\(386\) −170.000 −0.0224165
\(387\) 248.000 0.0325751
\(388\) 7336.00 0.959868
\(389\) 12291.0 1.60200 0.801001 0.598664i \(-0.204301\pi\)
0.801001 + 0.598664i \(0.204301\pi\)
\(390\) 6300.00 0.817982
\(391\) −3519.00 −0.455150
\(392\) 0 0
\(393\) −10245.0 −1.31499
\(394\) −780.000 −0.0997356
\(395\) 4149.00 0.528503
\(396\) 456.000 0.0578658
\(397\) −887.000 −0.112134 −0.0560671 0.998427i \(-0.517856\pi\)
−0.0560671 + 0.998427i \(0.517856\pi\)
\(398\) 5666.00 0.713595
\(399\) 0 0
\(400\) −704.000 −0.0880000
\(401\) 11955.0 1.48879 0.744394 0.667740i \(-0.232738\pi\)
0.744394 + 0.667740i \(0.232738\pi\)
\(402\) 4190.00 0.519846
\(403\) −1610.00 −0.199007
\(404\) 1140.00 0.140389
\(405\) −6039.00 −0.740939
\(406\) 0 0
\(407\) 14421.0 1.75632
\(408\) −2040.00 −0.247537
\(409\) 3421.00 0.413588 0.206794 0.978384i \(-0.433697\pi\)
0.206794 + 0.978384i \(0.433697\pi\)
\(410\) 756.000 0.0910639
\(411\) −705.000 −0.0846109
\(412\) 1996.00 0.238679
\(413\) 0 0
\(414\) −276.000 −0.0327649
\(415\) 5292.00 0.625962
\(416\) 2240.00 0.264002
\(417\) −7420.00 −0.871364
\(418\) 570.000 0.0666976
\(419\) 5460.00 0.636607 0.318304 0.947989i \(-0.396887\pi\)
0.318304 + 0.947989i \(0.396887\pi\)
\(420\) 0 0
\(421\) 7730.00 0.894863 0.447431 0.894318i \(-0.352339\pi\)
0.447431 + 0.894318i \(0.352339\pi\)
\(422\) −248.000 −0.0286077
\(423\) 402.000 0.0462078
\(424\) −3144.00 −0.360109
\(425\) 2244.00 0.256118
\(426\) −960.000 −0.109183
\(427\) 0 0
\(428\) −4428.00 −0.500083
\(429\) −19950.0 −2.24521
\(430\) −2232.00 −0.250318
\(431\) −11313.0 −1.26433 −0.632167 0.774832i \(-0.717834\pi\)
−0.632167 + 0.774832i \(0.717834\pi\)
\(432\) −2320.00 −0.258382
\(433\) −4214.00 −0.467695 −0.233847 0.972273i \(-0.575132\pi\)
−0.233847 + 0.972273i \(0.575132\pi\)
\(434\) 0 0
\(435\) 5130.00 0.565436
\(436\) 3692.00 0.405538
\(437\) −345.000 −0.0377656
\(438\) 3130.00 0.341455
\(439\) −16553.0 −1.79962 −0.899808 0.436286i \(-0.856294\pi\)
−0.899808 + 0.436286i \(0.856294\pi\)
\(440\) −4104.00 −0.444660
\(441\) 0 0
\(442\) −7140.00 −0.768360
\(443\) −16395.0 −1.75835 −0.879176 0.476497i \(-0.841906\pi\)
−0.879176 + 0.476497i \(0.841906\pi\)
\(444\) −5060.00 −0.540849
\(445\) 9153.00 0.975042
\(446\) −112.000 −0.0118909
\(447\) −285.000 −0.0301567
\(448\) 0 0
\(449\) −15090.0 −1.58606 −0.793030 0.609182i \(-0.791498\pi\)
−0.793030 + 0.609182i \(0.791498\pi\)
\(450\) 176.000 0.0184372
\(451\) −2394.00 −0.249954
\(452\) 6168.00 0.641855
\(453\) 4195.00 0.435096
\(454\) 6114.00 0.632036
\(455\) 0 0
\(456\) −200.000 −0.0205392
\(457\) −14785.0 −1.51338 −0.756688 0.653776i \(-0.773184\pi\)
−0.756688 + 0.653776i \(0.773184\pi\)
\(458\) 1922.00 0.196090
\(459\) 7395.00 0.752002
\(460\) 2484.00 0.251776
\(461\) −2898.00 −0.292784 −0.146392 0.989227i \(-0.546766\pi\)
−0.146392 + 0.989227i \(0.546766\pi\)
\(462\) 0 0
\(463\) 464.000 0.0465743 0.0232872 0.999729i \(-0.492587\pi\)
0.0232872 + 0.999729i \(0.492587\pi\)
\(464\) 1824.00 0.182494
\(465\) −1035.00 −0.103219
\(466\) −5658.00 −0.562450
\(467\) −4233.00 −0.419443 −0.209721 0.977761i \(-0.567256\pi\)
−0.209721 + 0.977761i \(0.567256\pi\)
\(468\) −560.000 −0.0553120
\(469\) 0 0
\(470\) −3618.00 −0.355076
\(471\) 14165.0 1.38575
\(472\) −1752.00 −0.170852
\(473\) 7068.00 0.687076
\(474\) 4610.00 0.446718
\(475\) 220.000 0.0212511
\(476\) 0 0
\(477\) 786.000 0.0754475
\(478\) −7080.00 −0.677472
\(479\) −2739.00 −0.261270 −0.130635 0.991431i \(-0.541702\pi\)
−0.130635 + 0.991431i \(0.541702\pi\)
\(480\) 1440.00 0.136931
\(481\) −17710.0 −1.67881
\(482\) −10462.0 −0.988654
\(483\) 0 0
\(484\) 7672.00 0.720511
\(485\) 16506.0 1.54536
\(486\) 1120.00 0.104535
\(487\) 17051.0 1.58656 0.793280 0.608857i \(-0.208372\pi\)
0.793280 + 0.608857i \(0.208372\pi\)
\(488\) 5672.00 0.526146
\(489\) −11555.0 −1.06858
\(490\) 0 0
\(491\) −4296.00 −0.394859 −0.197429 0.980317i \(-0.563259\pi\)
−0.197429 + 0.980317i \(0.563259\pi\)
\(492\) 840.000 0.0769718
\(493\) −5814.00 −0.531135
\(494\) −700.000 −0.0637540
\(495\) 1026.00 0.0931622
\(496\) −368.000 −0.0333139
\(497\) 0 0
\(498\) 5880.00 0.529095
\(499\) 3401.00 0.305110 0.152555 0.988295i \(-0.451250\pi\)
0.152555 + 0.988295i \(0.451250\pi\)
\(500\) −6084.00 −0.544170
\(501\) −6300.00 −0.561803
\(502\) −10080.0 −0.896200
\(503\) −16800.0 −1.48921 −0.744607 0.667503i \(-0.767363\pi\)
−0.744607 + 0.667503i \(0.767363\pi\)
\(504\) 0 0
\(505\) 2565.00 0.226022
\(506\) −7866.00 −0.691080
\(507\) 13515.0 1.18387
\(508\) −8224.00 −0.718270
\(509\) −1839.00 −0.160142 −0.0800710 0.996789i \(-0.525515\pi\)
−0.0800710 + 0.996789i \(0.525515\pi\)
\(510\) −4590.00 −0.398527
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 725.000 0.0623967
\(514\) 2874.00 0.246628
\(515\) 4491.00 0.384266
\(516\) −2480.00 −0.211581
\(517\) 11457.0 0.974620
\(518\) 0 0
\(519\) −16335.0 −1.38155
\(520\) 5040.00 0.425036
\(521\) −303.000 −0.0254792 −0.0127396 0.999919i \(-0.504055\pi\)
−0.0127396 + 0.999919i \(0.504055\pi\)
\(522\) −456.000 −0.0382348
\(523\) 21667.0 1.81153 0.905767 0.423777i \(-0.139296\pi\)
0.905767 + 0.423777i \(0.139296\pi\)
\(524\) −8196.00 −0.683290
\(525\) 0 0
\(526\) −4650.00 −0.385456
\(527\) 1173.00 0.0969577
\(528\) −4560.00 −0.375849
\(529\) −7406.00 −0.608696
\(530\) −7074.00 −0.579764
\(531\) 438.000 0.0357958
\(532\) 0 0
\(533\) 2940.00 0.238922
\(534\) 10170.0 0.824155
\(535\) −9963.00 −0.805118
\(536\) 3352.00 0.270120
\(537\) 6435.00 0.517115
\(538\) 4770.00 0.382248
\(539\) 0 0
\(540\) −5220.00 −0.415987
\(541\) 5039.00 0.400450 0.200225 0.979750i \(-0.435833\pi\)
0.200225 + 0.979750i \(0.435833\pi\)
\(542\) 662.000 0.0524637
\(543\) 13370.0 1.05665
\(544\) −1632.00 −0.128624
\(545\) 8307.00 0.652904
\(546\) 0 0
\(547\) −2392.00 −0.186974 −0.0934868 0.995621i \(-0.529801\pi\)
−0.0934868 + 0.995621i \(0.529801\pi\)
\(548\) −564.000 −0.0439651
\(549\) −1418.00 −0.110235
\(550\) 5016.00 0.388878
\(551\) −570.000 −0.0440704
\(552\) 2760.00 0.212814
\(553\) 0 0
\(554\) 9742.00 0.747108
\(555\) −11385.0 −0.870750
\(556\) −5936.00 −0.452774
\(557\) −22149.0 −1.68489 −0.842445 0.538783i \(-0.818884\pi\)
−0.842445 + 0.538783i \(0.818884\pi\)
\(558\) 92.0000 0.00697970
\(559\) −8680.00 −0.656753
\(560\) 0 0
\(561\) 14535.0 1.09388
\(562\) −14052.0 −1.05471
\(563\) 8349.00 0.624988 0.312494 0.949920i \(-0.398836\pi\)
0.312494 + 0.949920i \(0.398836\pi\)
\(564\) −4020.00 −0.300129
\(565\) 13878.0 1.03337
\(566\) 10706.0 0.795065
\(567\) 0 0
\(568\) −768.000 −0.0567334
\(569\) −15345.0 −1.13057 −0.565286 0.824895i \(-0.691234\pi\)
−0.565286 + 0.824895i \(0.691234\pi\)
\(570\) −450.000 −0.0330674
\(571\) −11593.0 −0.849653 −0.424827 0.905275i \(-0.639665\pi\)
−0.424827 + 0.905275i \(0.639665\pi\)
\(572\) −15960.0 −1.16665
\(573\) 20925.0 1.52557
\(574\) 0 0
\(575\) −3036.00 −0.220191
\(576\) −128.000 −0.00925926
\(577\) 14593.0 1.05288 0.526442 0.850211i \(-0.323526\pi\)
0.526442 + 0.850211i \(0.323526\pi\)
\(578\) −4624.00 −0.332756
\(579\) −425.000 −0.0305050
\(580\) 4104.00 0.293809
\(581\) 0 0
\(582\) 18340.0 1.30622
\(583\) 22401.0 1.59135
\(584\) 2504.00 0.177425
\(585\) −1260.00 −0.0890506
\(586\) −8316.00 −0.586230
\(587\) 15372.0 1.08087 0.540435 0.841386i \(-0.318260\pi\)
0.540435 + 0.841386i \(0.318260\pi\)
\(588\) 0 0
\(589\) 115.000 0.00804498
\(590\) −3942.00 −0.275067
\(591\) −1950.00 −0.135723
\(592\) −4048.00 −0.281033
\(593\) 14373.0 0.995326 0.497663 0.867370i \(-0.334192\pi\)
0.497663 + 0.867370i \(0.334192\pi\)
\(594\) 16530.0 1.14181
\(595\) 0 0
\(596\) −228.000 −0.0156699
\(597\) 14165.0 0.971080
\(598\) 9660.00 0.660580
\(599\) 2547.00 0.173736 0.0868678 0.996220i \(-0.472314\pi\)
0.0868678 + 0.996220i \(0.472314\pi\)
\(600\) −1760.00 −0.119753
\(601\) 7042.00 0.477952 0.238976 0.971025i \(-0.423188\pi\)
0.238976 + 0.971025i \(0.423188\pi\)
\(602\) 0 0
\(603\) −838.000 −0.0565937
\(604\) 3356.00 0.226082
\(605\) 17262.0 1.16000
\(606\) 2850.00 0.191045
\(607\) 22591.0 1.51061 0.755305 0.655373i \(-0.227489\pi\)
0.755305 + 0.655373i \(0.227489\pi\)
\(608\) −160.000 −0.0106725
\(609\) 0 0
\(610\) 12762.0 0.847079
\(611\) −14070.0 −0.931606
\(612\) 408.000 0.0269484
\(613\) −8485.00 −0.559063 −0.279532 0.960136i \(-0.590179\pi\)
−0.279532 + 0.960136i \(0.590179\pi\)
\(614\) 19208.0 1.26249
\(615\) 1890.00 0.123922
\(616\) 0 0
\(617\) −18282.0 −1.19288 −0.596439 0.802658i \(-0.703418\pi\)
−0.596439 + 0.802658i \(0.703418\pi\)
\(618\) 4990.00 0.324801
\(619\) −2291.00 −0.148761 −0.0743805 0.997230i \(-0.523698\pi\)
−0.0743805 + 0.997230i \(0.523698\pi\)
\(620\) −828.000 −0.0536343
\(621\) −10005.0 −0.646517
\(622\) −20262.0 −1.30616
\(623\) 0 0
\(624\) 5600.00 0.359262
\(625\) −8189.00 −0.524096
\(626\) −21598.0 −1.37896
\(627\) 1425.00 0.0907640
\(628\) 11332.0 0.720057
\(629\) 12903.0 0.817927
\(630\) 0 0
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) 3688.00 0.232121
\(633\) −620.000 −0.0389302
\(634\) 1062.00 0.0665259
\(635\) −18504.0 −1.15639
\(636\) −7860.00 −0.490046
\(637\) 0 0
\(638\) −12996.0 −0.806452
\(639\) 192.000 0.0118864
\(640\) 1152.00 0.0711512
\(641\) 24975.0 1.53893 0.769464 0.638690i \(-0.220523\pi\)
0.769464 + 0.638690i \(0.220523\pi\)
\(642\) −11070.0 −0.680527
\(643\) −9548.00 −0.585593 −0.292797 0.956175i \(-0.594586\pi\)
−0.292797 + 0.956175i \(0.594586\pi\)
\(644\) 0 0
\(645\) −5580.00 −0.340639
\(646\) 510.000 0.0310614
\(647\) −10131.0 −0.615596 −0.307798 0.951452i \(-0.599592\pi\)
−0.307798 + 0.951452i \(0.599592\pi\)
\(648\) −5368.00 −0.325424
\(649\) 12483.0 0.755009
\(650\) −6160.00 −0.371716
\(651\) 0 0
\(652\) −9244.00 −0.555250
\(653\) 16659.0 0.998342 0.499171 0.866504i \(-0.333638\pi\)
0.499171 + 0.866504i \(0.333638\pi\)
\(654\) 9230.00 0.551868
\(655\) −18441.0 −1.10008
\(656\) 672.000 0.0399957
\(657\) −626.000 −0.0371729
\(658\) 0 0
\(659\) 29556.0 1.74710 0.873550 0.486735i \(-0.161812\pi\)
0.873550 + 0.486735i \(0.161812\pi\)
\(660\) −10260.0 −0.605106
\(661\) −191.000 −0.0112391 −0.00561955 0.999984i \(-0.501789\pi\)
−0.00561955 + 0.999984i \(0.501789\pi\)
\(662\) −14030.0 −0.823703
\(663\) −17850.0 −1.04561
\(664\) 4704.00 0.274926
\(665\) 0 0
\(666\) 1012.00 0.0588802
\(667\) 7866.00 0.456631
\(668\) −5040.00 −0.291921
\(669\) −280.000 −0.0161815
\(670\) 7542.00 0.434885
\(671\) −40413.0 −2.32508
\(672\) 0 0
\(673\) 2606.00 0.149263 0.0746314 0.997211i \(-0.476222\pi\)
0.0746314 + 0.997211i \(0.476222\pi\)
\(674\) 17980.0 1.02754
\(675\) 6380.00 0.363802
\(676\) 10812.0 0.615157
\(677\) 4209.00 0.238944 0.119472 0.992838i \(-0.461880\pi\)
0.119472 + 0.992838i \(0.461880\pi\)
\(678\) 15420.0 0.873454
\(679\) 0 0
\(680\) −3672.00 −0.207081
\(681\) 15285.0 0.860092
\(682\) 2622.00 0.147216
\(683\) 24303.0 1.36154 0.680768 0.732500i \(-0.261646\pi\)
0.680768 + 0.732500i \(0.261646\pi\)
\(684\) 40.0000 0.00223602
\(685\) −1269.00 −0.0707825
\(686\) 0 0
\(687\) 4805.00 0.266845
\(688\) −1984.00 −0.109941
\(689\) −27510.0 −1.52111
\(690\) 6210.00 0.342624
\(691\) −15041.0 −0.828056 −0.414028 0.910264i \(-0.635878\pi\)
−0.414028 + 0.910264i \(0.635878\pi\)
\(692\) −13068.0 −0.717877
\(693\) 0 0
\(694\) −17418.0 −0.952706
\(695\) −13356.0 −0.728952
\(696\) 4560.00 0.248342
\(697\) −2142.00 −0.116405
\(698\) −12964.0 −0.703001
\(699\) −14145.0 −0.765398
\(700\) 0 0
\(701\) 24726.0 1.33222 0.666111 0.745852i \(-0.267958\pi\)
0.666111 + 0.745852i \(0.267958\pi\)
\(702\) −20300.0 −1.09142
\(703\) 1265.00 0.0678668
\(704\) −3648.00 −0.195297
\(705\) −9045.00 −0.483198
\(706\) 4266.00 0.227412
\(707\) 0 0
\(708\) −4380.00 −0.232501
\(709\) −4957.00 −0.262573 −0.131286 0.991344i \(-0.541911\pi\)
−0.131286 + 0.991344i \(0.541911\pi\)
\(710\) −1728.00 −0.0913390
\(711\) −922.000 −0.0486325
\(712\) 8136.00 0.428244
\(713\) −1587.00 −0.0833571
\(714\) 0 0
\(715\) −35910.0 −1.87826
\(716\) 5148.00 0.268701
\(717\) −17700.0 −0.921923
\(718\) 7698.00 0.400121
\(719\) −27669.0 −1.43516 −0.717580 0.696476i \(-0.754750\pi\)
−0.717580 + 0.696476i \(0.754750\pi\)
\(720\) −288.000 −0.0149071
\(721\) 0 0
\(722\) −13668.0 −0.704529
\(723\) −26155.0 −1.34539
\(724\) 10696.0 0.549052
\(725\) −5016.00 −0.256951
\(726\) 19180.0 0.980491
\(727\) 13888.0 0.708497 0.354249 0.935151i \(-0.384737\pi\)
0.354249 + 0.935151i \(0.384737\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 5634.00 0.285649
\(731\) 6324.00 0.319975
\(732\) 14180.0 0.715994
\(733\) −14243.0 −0.717704 −0.358852 0.933394i \(-0.616832\pi\)
−0.358852 + 0.933394i \(0.616832\pi\)
\(734\) −12982.0 −0.652826
\(735\) 0 0
\(736\) 2208.00 0.110581
\(737\) −23883.0 −1.19368
\(738\) −168.000 −0.00837963
\(739\) 36959.0 1.83973 0.919864 0.392238i \(-0.128299\pi\)
0.919864 + 0.392238i \(0.128299\pi\)
\(740\) −9108.00 −0.452455
\(741\) −1750.00 −0.0867582
\(742\) 0 0
\(743\) −12528.0 −0.618584 −0.309292 0.950967i \(-0.600092\pi\)
−0.309292 + 0.950967i \(0.600092\pi\)
\(744\) −920.000 −0.0453345
\(745\) −513.000 −0.0252280
\(746\) 1846.00 0.0905990
\(747\) −1176.00 −0.0576005
\(748\) 11628.0 0.568398
\(749\) 0 0
\(750\) −15210.0 −0.740521
\(751\) −17767.0 −0.863285 −0.431643 0.902045i \(-0.642066\pi\)
−0.431643 + 0.902045i \(0.642066\pi\)
\(752\) −3216.00 −0.155951
\(753\) −25200.0 −1.21957
\(754\) 15960.0 0.770861
\(755\) 7551.00 0.363985
\(756\) 0 0
\(757\) −28726.0 −1.37921 −0.689606 0.724184i \(-0.742216\pi\)
−0.689606 + 0.724184i \(0.742216\pi\)
\(758\) 12688.0 0.607980
\(759\) −19665.0 −0.940440
\(760\) −360.000 −0.0171823
\(761\) 26469.0 1.26084 0.630421 0.776254i \(-0.282882\pi\)
0.630421 + 0.776254i \(0.282882\pi\)
\(762\) −20560.0 −0.977441
\(763\) 0 0
\(764\) 16740.0 0.792712
\(765\) 918.000 0.0433861
\(766\) 10014.0 0.472351
\(767\) −15330.0 −0.721687
\(768\) 1280.00 0.0601407
\(769\) −5054.00 −0.236999 −0.118499 0.992954i \(-0.537808\pi\)
−0.118499 + 0.992954i \(0.537808\pi\)
\(770\) 0 0
\(771\) 7185.00 0.335618
\(772\) −340.000 −0.0158509
\(773\) 35565.0 1.65483 0.827415 0.561590i \(-0.189810\pi\)
0.827415 + 0.561590i \(0.189810\pi\)
\(774\) 496.000 0.0230340
\(775\) 1012.00 0.0469060
\(776\) 14672.0 0.678730
\(777\) 0 0
\(778\) 24582.0 1.13279
\(779\) −210.000 −0.00965858
\(780\) 12600.0 0.578400
\(781\) 5472.00 0.250709
\(782\) −7038.00 −0.321839
\(783\) −16530.0 −0.754450
\(784\) 0 0
\(785\) 25497.0 1.15927
\(786\) −20490.0 −0.929840
\(787\) 8629.00 0.390839 0.195420 0.980720i \(-0.437393\pi\)
0.195420 + 0.980720i \(0.437393\pi\)
\(788\) −1560.00 −0.0705237
\(789\) −11625.0 −0.524539
\(790\) 8298.00 0.373708
\(791\) 0 0
\(792\) 912.000 0.0409173
\(793\) 49630.0 2.22246
\(794\) −1774.00 −0.0792908
\(795\) −17685.0 −0.788959
\(796\) 11332.0 0.504588
\(797\) −20706.0 −0.920256 −0.460128 0.887853i \(-0.652197\pi\)
−0.460128 + 0.887853i \(0.652197\pi\)
\(798\) 0 0
\(799\) 10251.0 0.453885
\(800\) −1408.00 −0.0622254
\(801\) −2034.00 −0.0897227
\(802\) 23910.0 1.05273
\(803\) −17841.0 −0.784054
\(804\) 8380.00 0.367587
\(805\) 0 0
\(806\) −3220.00 −0.140719
\(807\) 11925.0 0.520173
\(808\) 2280.00 0.0992700
\(809\) −16185.0 −0.703380 −0.351690 0.936117i \(-0.614393\pi\)
−0.351690 + 0.936117i \(0.614393\pi\)
\(810\) −12078.0 −0.523923
\(811\) 11788.0 0.510398 0.255199 0.966889i \(-0.417859\pi\)
0.255199 + 0.966889i \(0.417859\pi\)
\(812\) 0 0
\(813\) 1655.00 0.0713941
\(814\) 28842.0 1.24191
\(815\) −20799.0 −0.893935
\(816\) −4080.00 −0.175035
\(817\) 620.000 0.0265496
\(818\) 6842.00 0.292451
\(819\) 0 0
\(820\) 1512.00 0.0643919
\(821\) −29793.0 −1.26648 −0.633242 0.773954i \(-0.718276\pi\)
−0.633242 + 0.773954i \(0.718276\pi\)
\(822\) −1410.00 −0.0598290
\(823\) 30323.0 1.28432 0.642159 0.766572i \(-0.278039\pi\)
0.642159 + 0.766572i \(0.278039\pi\)
\(824\) 3992.00 0.168772
\(825\) 12540.0 0.529196
\(826\) 0 0
\(827\) 21156.0 0.889560 0.444780 0.895640i \(-0.353282\pi\)
0.444780 + 0.895640i \(0.353282\pi\)
\(828\) −552.000 −0.0231683
\(829\) 5269.00 0.220748 0.110374 0.993890i \(-0.464795\pi\)
0.110374 + 0.993890i \(0.464795\pi\)
\(830\) 10584.0 0.442622
\(831\) 24355.0 1.01669
\(832\) 4480.00 0.186678
\(833\) 0 0
\(834\) −14840.0 −0.616148
\(835\) −11340.0 −0.469984
\(836\) 1140.00 0.0471623
\(837\) 3335.00 0.137723
\(838\) 10920.0 0.450149
\(839\) 39816.0 1.63838 0.819190 0.573522i \(-0.194423\pi\)
0.819190 + 0.573522i \(0.194423\pi\)
\(840\) 0 0
\(841\) −11393.0 −0.467137
\(842\) 15460.0 0.632763
\(843\) −35130.0 −1.43528
\(844\) −496.000 −0.0202287
\(845\) 24327.0 0.990384
\(846\) 804.000 0.0326739
\(847\) 0 0
\(848\) −6288.00 −0.254635
\(849\) 26765.0 1.08195
\(850\) 4488.00 0.181103
\(851\) −17457.0 −0.703194
\(852\) −1920.00 −0.0772044
\(853\) −14546.0 −0.583875 −0.291938 0.956437i \(-0.594300\pi\)
−0.291938 + 0.956437i \(0.594300\pi\)
\(854\) 0 0
\(855\) 90.0000 0.00359992
\(856\) −8856.00 −0.353612
\(857\) 31449.0 1.25353 0.626766 0.779207i \(-0.284378\pi\)
0.626766 + 0.779207i \(0.284378\pi\)
\(858\) −39900.0 −1.58760
\(859\) 24523.0 0.974056 0.487028 0.873386i \(-0.338081\pi\)
0.487028 + 0.873386i \(0.338081\pi\)
\(860\) −4464.00 −0.177001
\(861\) 0 0
\(862\) −22626.0 −0.894019
\(863\) −8163.00 −0.321983 −0.160992 0.986956i \(-0.551469\pi\)
−0.160992 + 0.986956i \(0.551469\pi\)
\(864\) −4640.00 −0.182704
\(865\) −29403.0 −1.15576
\(866\) −8428.00 −0.330710
\(867\) −11560.0 −0.452824
\(868\) 0 0
\(869\) −26277.0 −1.02576
\(870\) 10260.0 0.399824
\(871\) 29330.0 1.14100
\(872\) 7384.00 0.286759
\(873\) −3668.00 −0.142203
\(874\) −690.000 −0.0267043
\(875\) 0 0
\(876\) 6260.00 0.241445
\(877\) 4367.00 0.168145 0.0840725 0.996460i \(-0.473207\pi\)
0.0840725 + 0.996460i \(0.473207\pi\)
\(878\) −33106.0 −1.27252
\(879\) −20790.0 −0.797758
\(880\) −8208.00 −0.314422
\(881\) 50190.0 1.91935 0.959673 0.281118i \(-0.0907053\pi\)
0.959673 + 0.281118i \(0.0907053\pi\)
\(882\) 0 0
\(883\) 12308.0 0.469079 0.234540 0.972107i \(-0.424642\pi\)
0.234540 + 0.972107i \(0.424642\pi\)
\(884\) −14280.0 −0.543313
\(885\) −9855.00 −0.374319
\(886\) −32790.0 −1.24334
\(887\) −31617.0 −1.19684 −0.598419 0.801183i \(-0.704204\pi\)
−0.598419 + 0.801183i \(0.704204\pi\)
\(888\) −10120.0 −0.382438
\(889\) 0 0
\(890\) 18306.0 0.689459
\(891\) 38247.0 1.43807
\(892\) −224.000 −0.00840816
\(893\) 1005.00 0.0376607
\(894\) −570.000 −0.0213240
\(895\) 11583.0 0.432600
\(896\) 0 0
\(897\) 24150.0 0.898935
\(898\) −30180.0 −1.12151
\(899\) −2622.00 −0.0972732
\(900\) 352.000 0.0130370
\(901\) 20043.0 0.741098
\(902\) −4788.00 −0.176744
\(903\) 0 0
\(904\) 12336.0 0.453860
\(905\) 24066.0 0.883957
\(906\) 8390.00 0.307659
\(907\) −13525.0 −0.495138 −0.247569 0.968870i \(-0.579632\pi\)
−0.247569 + 0.968870i \(0.579632\pi\)
\(908\) 12228.0 0.446917
\(909\) −570.000 −0.0207984
\(910\) 0 0
\(911\) −19248.0 −0.700016 −0.350008 0.936747i \(-0.613821\pi\)
−0.350008 + 0.936747i \(0.613821\pi\)
\(912\) −400.000 −0.0145234
\(913\) −33516.0 −1.21492
\(914\) −29570.0 −1.07012
\(915\) 31905.0 1.15273
\(916\) 3844.00 0.138656
\(917\) 0 0
\(918\) 14790.0 0.531746
\(919\) −8695.00 −0.312102 −0.156051 0.987749i \(-0.549876\pi\)
−0.156051 + 0.987749i \(0.549876\pi\)
\(920\) 4968.00 0.178033
\(921\) 48020.0 1.71804
\(922\) −5796.00 −0.207029
\(923\) −6720.00 −0.239644
\(924\) 0 0
\(925\) 11132.0 0.395695
\(926\) 928.000 0.0329330
\(927\) −998.000 −0.0353599
\(928\) 3648.00 0.129043
\(929\) −19479.0 −0.687928 −0.343964 0.938983i \(-0.611770\pi\)
−0.343964 + 0.938983i \(0.611770\pi\)
\(930\) −2070.00 −0.0729871
\(931\) 0 0
\(932\) −11316.0 −0.397712
\(933\) −50655.0 −1.77746
\(934\) −8466.00 −0.296591
\(935\) 26163.0 0.915103
\(936\) −1120.00 −0.0391115
\(937\) 12502.0 0.435883 0.217942 0.975962i \(-0.430066\pi\)
0.217942 + 0.975962i \(0.430066\pi\)
\(938\) 0 0
\(939\) −53995.0 −1.87653
\(940\) −7236.00 −0.251077
\(941\) 15993.0 0.554046 0.277023 0.960863i \(-0.410652\pi\)
0.277023 + 0.960863i \(0.410652\pi\)
\(942\) 28330.0 0.979874
\(943\) 2898.00 0.100076
\(944\) −3504.00 −0.120811
\(945\) 0 0
\(946\) 14136.0 0.485836
\(947\) 44001.0 1.50986 0.754932 0.655804i \(-0.227670\pi\)
0.754932 + 0.655804i \(0.227670\pi\)
\(948\) 9220.00 0.315877
\(949\) 21910.0 0.749451
\(950\) 440.000 0.0150268
\(951\) 2655.00 0.0905303
\(952\) 0 0
\(953\) −4002.00 −0.136031 −0.0680155 0.997684i \(-0.521667\pi\)
−0.0680155 + 0.997684i \(0.521667\pi\)
\(954\) 1572.00 0.0533495
\(955\) 37665.0 1.27624
\(956\) −14160.0 −0.479045
\(957\) −32490.0 −1.09744
\(958\) −5478.00 −0.184745
\(959\) 0 0
\(960\) 2880.00 0.0968246
\(961\) −29262.0 −0.982243
\(962\) −35420.0 −1.18710
\(963\) 2214.00 0.0740863
\(964\) −20924.0 −0.699084
\(965\) −765.000 −0.0255194
\(966\) 0 0
\(967\) 10544.0 0.350643 0.175322 0.984511i \(-0.443903\pi\)
0.175322 + 0.984511i \(0.443903\pi\)
\(968\) 15344.0 0.509478
\(969\) 1275.00 0.0422692
\(970\) 33012.0 1.09273
\(971\) 6183.00 0.204348 0.102174 0.994767i \(-0.467420\pi\)
0.102174 + 0.994767i \(0.467420\pi\)
\(972\) 2240.00 0.0739177
\(973\) 0 0
\(974\) 34102.0 1.12187
\(975\) −15400.0 −0.505841
\(976\) 11344.0 0.372042
\(977\) 3723.00 0.121913 0.0609567 0.998140i \(-0.480585\pi\)
0.0609567 + 0.998140i \(0.480585\pi\)
\(978\) −23110.0 −0.755600
\(979\) −57969.0 −1.89244
\(980\) 0 0
\(981\) −1846.00 −0.0600798
\(982\) −8592.00 −0.279207
\(983\) 45897.0 1.48920 0.744602 0.667509i \(-0.232639\pi\)
0.744602 + 0.667509i \(0.232639\pi\)
\(984\) 1680.00 0.0544273
\(985\) −3510.00 −0.113541
\(986\) −11628.0 −0.375569
\(987\) 0 0
\(988\) −1400.00 −0.0450809
\(989\) −8556.00 −0.275091
\(990\) 2052.00 0.0658756
\(991\) 6467.00 0.207297 0.103648 0.994614i \(-0.466948\pi\)
0.103648 + 0.994614i \(0.466948\pi\)
\(992\) −736.000 −0.0235565
\(993\) −35075.0 −1.12092
\(994\) 0 0
\(995\) 25497.0 0.812371
\(996\) 11760.0 0.374126
\(997\) −23039.0 −0.731848 −0.365924 0.930645i \(-0.619247\pi\)
−0.365924 + 0.930645i \(0.619247\pi\)
\(998\) 6802.00 0.215745
\(999\) 36685.0 1.16182
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 98.4.a.f.1.1 1
3.2 odd 2 882.4.a.c.1.1 1
4.3 odd 2 784.4.a.c.1.1 1
5.4 even 2 2450.4.a.d.1.1 1
7.2 even 3 98.4.c.a.67.1 2
7.3 odd 6 14.4.c.a.9.1 2
7.4 even 3 98.4.c.a.79.1 2
7.5 odd 6 14.4.c.a.11.1 yes 2
7.6 odd 2 98.4.a.d.1.1 1
21.2 odd 6 882.4.g.u.361.1 2
21.5 even 6 126.4.g.d.109.1 2
21.11 odd 6 882.4.g.u.667.1 2
21.17 even 6 126.4.g.d.37.1 2
21.20 even 2 882.4.a.f.1.1 1
28.3 even 6 112.4.i.a.65.1 2
28.19 even 6 112.4.i.a.81.1 2
28.27 even 2 784.4.a.p.1.1 1
35.3 even 12 350.4.j.b.149.2 4
35.12 even 12 350.4.j.b.249.2 4
35.17 even 12 350.4.j.b.149.1 4
35.19 odd 6 350.4.e.e.151.1 2
35.24 odd 6 350.4.e.e.51.1 2
35.33 even 12 350.4.j.b.249.1 4
35.34 odd 2 2450.4.a.q.1.1 1
56.3 even 6 448.4.i.e.65.1 2
56.5 odd 6 448.4.i.b.193.1 2
56.19 even 6 448.4.i.e.193.1 2
56.45 odd 6 448.4.i.b.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.a.9.1 2 7.3 odd 6
14.4.c.a.11.1 yes 2 7.5 odd 6
98.4.a.d.1.1 1 7.6 odd 2
98.4.a.f.1.1 1 1.1 even 1 trivial
98.4.c.a.67.1 2 7.2 even 3
98.4.c.a.79.1 2 7.4 even 3
112.4.i.a.65.1 2 28.3 even 6
112.4.i.a.81.1 2 28.19 even 6
126.4.g.d.37.1 2 21.17 even 6
126.4.g.d.109.1 2 21.5 even 6
350.4.e.e.51.1 2 35.24 odd 6
350.4.e.e.151.1 2 35.19 odd 6
350.4.j.b.149.1 4 35.17 even 12
350.4.j.b.149.2 4 35.3 even 12
350.4.j.b.249.1 4 35.33 even 12
350.4.j.b.249.2 4 35.12 even 12
448.4.i.b.65.1 2 56.45 odd 6
448.4.i.b.193.1 2 56.5 odd 6
448.4.i.e.65.1 2 56.3 even 6
448.4.i.e.193.1 2 56.19 even 6
784.4.a.c.1.1 1 4.3 odd 2
784.4.a.p.1.1 1 28.27 even 2
882.4.a.c.1.1 1 3.2 odd 2
882.4.a.f.1.1 1 21.20 even 2
882.4.g.u.361.1 2 21.2 odd 6
882.4.g.u.667.1 2 21.11 odd 6
2450.4.a.d.1.1 1 5.4 even 2
2450.4.a.q.1.1 1 35.34 odd 2