Properties

Label 350.4.a.k.1.1
Level $350$
Weight $4$
Character 350.1
Self dual yes
Analytic conductor $20.651$
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] = [350,4,Mod(1,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, 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("350.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 350.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: \(20.6506685020\)
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 \(\chi\) \(=\) 350.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -10.0000 q^{3} +4.00000 q^{4} -20.0000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +73.0000 q^{9} +9.00000 q^{11} -40.0000 q^{12} +52.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -96.0000 q^{17} +146.000 q^{18} -10.0000 q^{19} +70.0000 q^{21} +18.0000 q^{22} -75.0000 q^{23} -80.0000 q^{24} +104.000 q^{26} -460.000 q^{27} -28.0000 q^{28} +189.000 q^{29} -232.000 q^{31} +32.0000 q^{32} -90.0000 q^{33} -192.000 q^{34} +292.000 q^{36} -305.000 q^{37} -20.0000 q^{38} -520.000 q^{39} -438.000 q^{41} +140.000 q^{42} -353.000 q^{43} +36.0000 q^{44} -150.000 q^{46} +486.000 q^{47} -160.000 q^{48} +49.0000 q^{49} +960.000 q^{51} +208.000 q^{52} +354.000 q^{53} -920.000 q^{54} -56.0000 q^{56} +100.000 q^{57} +378.000 q^{58} -672.000 q^{59} +206.000 q^{61} -464.000 q^{62} -511.000 q^{63} +64.0000 q^{64} -180.000 q^{66} -599.000 q^{67} -384.000 q^{68} +750.000 q^{69} -471.000 q^{71} +584.000 q^{72} -614.000 q^{73} -610.000 q^{74} -40.0000 q^{76} -63.0000 q^{77} -1040.00 q^{78} +743.000 q^{79} +2629.00 q^{81} -876.000 q^{82} -996.000 q^{83} +280.000 q^{84} -706.000 q^{86} -1890.00 q^{87} +72.0000 q^{88} +180.000 q^{89} -364.000 q^{91} -300.000 q^{92} +2320.00 q^{93} +972.000 q^{94} -320.000 q^{96} +184.000 q^{97} +98.0000 q^{98} +657.000 q^{99} +O(q^{100})\)

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
\(3\) −10.0000 −1.92450 −0.962250 0.272166i \(-0.912260\pi\)
−0.962250 + 0.272166i \(0.912260\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −20.0000 −1.36083
\(7\) −7.00000 −0.377964
\(8\) 8.00000 0.353553
\(9\) 73.0000 2.70370
\(10\) 0 0
\(11\) 9.00000 0.246691 0.123346 0.992364i \(-0.460638\pi\)
0.123346 + 0.992364i \(0.460638\pi\)
\(12\) −40.0000 −0.962250
\(13\) 52.0000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −96.0000 −1.36961 −0.684806 0.728725i \(-0.740113\pi\)
−0.684806 + 0.728725i \(0.740113\pi\)
\(18\) 146.000 1.91181
\(19\) −10.0000 −0.120745 −0.0603726 0.998176i \(-0.519229\pi\)
−0.0603726 + 0.998176i \(0.519229\pi\)
\(20\) 0 0
\(21\) 70.0000 0.727393
\(22\) 18.0000 0.174437
\(23\) −75.0000 −0.679938 −0.339969 0.940437i \(-0.610417\pi\)
−0.339969 + 0.940437i \(0.610417\pi\)
\(24\) −80.0000 −0.680414
\(25\) 0 0
\(26\) 104.000 0.784465
\(27\) −460.000 −3.27878
\(28\) −28.0000 −0.188982
\(29\) 189.000 1.21022 0.605111 0.796141i \(-0.293129\pi\)
0.605111 + 0.796141i \(0.293129\pi\)
\(30\) 0 0
\(31\) −232.000 −1.34414 −0.672071 0.740486i \(-0.734595\pi\)
−0.672071 + 0.740486i \(0.734595\pi\)
\(32\) 32.0000 0.176777
\(33\) −90.0000 −0.474757
\(34\) −192.000 −0.968463
\(35\) 0 0
\(36\) 292.000 1.35185
\(37\) −305.000 −1.35518 −0.677590 0.735439i \(-0.736976\pi\)
−0.677590 + 0.735439i \(0.736976\pi\)
\(38\) −20.0000 −0.0853797
\(39\) −520.000 −2.13504
\(40\) 0 0
\(41\) −438.000 −1.66839 −0.834196 0.551467i \(-0.814068\pi\)
−0.834196 + 0.551467i \(0.814068\pi\)
\(42\) 140.000 0.514344
\(43\) −353.000 −1.25191 −0.625953 0.779860i \(-0.715290\pi\)
−0.625953 + 0.779860i \(0.715290\pi\)
\(44\) 36.0000 0.123346
\(45\) 0 0
\(46\) −150.000 −0.480789
\(47\) 486.000 1.50831 0.754153 0.656699i \(-0.228048\pi\)
0.754153 + 0.656699i \(0.228048\pi\)
\(48\) −160.000 −0.481125
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 960.000 2.63582
\(52\) 208.000 0.554700
\(53\) 354.000 0.917465 0.458732 0.888574i \(-0.348304\pi\)
0.458732 + 0.888574i \(0.348304\pi\)
\(54\) −920.000 −2.31845
\(55\) 0 0
\(56\) −56.0000 −0.133631
\(57\) 100.000 0.232374
\(58\) 378.000 0.855756
\(59\) −672.000 −1.48283 −0.741415 0.671047i \(-0.765845\pi\)
−0.741415 + 0.671047i \(0.765845\pi\)
\(60\) 0 0
\(61\) 206.000 0.432387 0.216193 0.976351i \(-0.430636\pi\)
0.216193 + 0.976351i \(0.430636\pi\)
\(62\) −464.000 −0.950453
\(63\) −511.000 −1.02190
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) −180.000 −0.335704
\(67\) −599.000 −1.09223 −0.546116 0.837710i \(-0.683894\pi\)
−0.546116 + 0.837710i \(0.683894\pi\)
\(68\) −384.000 −0.684806
\(69\) 750.000 1.30854
\(70\) 0 0
\(71\) −471.000 −0.787288 −0.393644 0.919263i \(-0.628786\pi\)
−0.393644 + 0.919263i \(0.628786\pi\)
\(72\) 584.000 0.955904
\(73\) −614.000 −0.984428 −0.492214 0.870474i \(-0.663812\pi\)
−0.492214 + 0.870474i \(0.663812\pi\)
\(74\) −610.000 −0.958258
\(75\) 0 0
\(76\) −40.0000 −0.0603726
\(77\) −63.0000 −0.0932405
\(78\) −1040.00 −1.50970
\(79\) 743.000 1.05815 0.529076 0.848574i \(-0.322539\pi\)
0.529076 + 0.848574i \(0.322539\pi\)
\(80\) 0 0
\(81\) 2629.00 3.60631
\(82\) −876.000 −1.17973
\(83\) −996.000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 280.000 0.363696
\(85\) 0 0
\(86\) −706.000 −0.885232
\(87\) −1890.00 −2.32907
\(88\) 72.0000 0.0872185
\(89\) 180.000 0.214382 0.107191 0.994238i \(-0.465814\pi\)
0.107191 + 0.994238i \(0.465814\pi\)
\(90\) 0 0
\(91\) −364.000 −0.419314
\(92\) −300.000 −0.339969
\(93\) 2320.00 2.58680
\(94\) 972.000 1.06653
\(95\) 0 0
\(96\) −320.000 −0.340207
\(97\) 184.000 0.192602 0.0963009 0.995352i \(-0.469299\pi\)
0.0963009 + 0.995352i \(0.469299\pi\)
\(98\) 98.0000 0.101015
\(99\) 657.000 0.666980
\(100\) 0 0
\(101\) −726.000 −0.715245 −0.357622 0.933866i \(-0.616412\pi\)
−0.357622 + 0.933866i \(0.616412\pi\)
\(102\) 1920.00 1.86381
\(103\) 1798.00 1.72002 0.860011 0.510276i \(-0.170457\pi\)
0.860011 + 0.510276i \(0.170457\pi\)
\(104\) 416.000 0.392232
\(105\) 0 0
\(106\) 708.000 0.648746
\(107\) −876.000 −0.791459 −0.395730 0.918367i \(-0.629508\pi\)
−0.395730 + 0.918367i \(0.629508\pi\)
\(108\) −1840.00 −1.63939
\(109\) −691.000 −0.607209 −0.303605 0.952798i \(-0.598190\pi\)
−0.303605 + 0.952798i \(0.598190\pi\)
\(110\) 0 0
\(111\) 3050.00 2.60805
\(112\) −112.000 −0.0944911
\(113\) 1521.00 1.26623 0.633113 0.774059i \(-0.281777\pi\)
0.633113 + 0.774059i \(0.281777\pi\)
\(114\) 200.000 0.164313
\(115\) 0 0
\(116\) 756.000 0.605111
\(117\) 3796.00 2.99949
\(118\) −1344.00 −1.04852
\(119\) 672.000 0.517665
\(120\) 0 0
\(121\) −1250.00 −0.939144
\(122\) 412.000 0.305744
\(123\) 4380.00 3.21082
\(124\) −928.000 −0.672071
\(125\) 0 0
\(126\) −1022.00 −0.722595
\(127\) −1031.00 −0.720366 −0.360183 0.932882i \(-0.617286\pi\)
−0.360183 + 0.932882i \(0.617286\pi\)
\(128\) 128.000 0.0883883
\(129\) 3530.00 2.40930
\(130\) 0 0
\(131\) −1116.00 −0.744316 −0.372158 0.928169i \(-0.621382\pi\)
−0.372158 + 0.928169i \(0.621382\pi\)
\(132\) −360.000 −0.237379
\(133\) 70.0000 0.0456374
\(134\) −1198.00 −0.772324
\(135\) 0 0
\(136\) −768.000 −0.484231
\(137\) 1398.00 0.871819 0.435909 0.899991i \(-0.356427\pi\)
0.435909 + 0.899991i \(0.356427\pi\)
\(138\) 1500.00 0.925279
\(139\) 674.000 0.411280 0.205640 0.978628i \(-0.434072\pi\)
0.205640 + 0.978628i \(0.434072\pi\)
\(140\) 0 0
\(141\) −4860.00 −2.90274
\(142\) −942.000 −0.556696
\(143\) 468.000 0.273679
\(144\) 1168.00 0.675926
\(145\) 0 0
\(146\) −1228.00 −0.696096
\(147\) −490.000 −0.274929
\(148\) −1220.00 −0.677590
\(149\) −1281.00 −0.704320 −0.352160 0.935940i \(-0.614553\pi\)
−0.352160 + 0.935940i \(0.614553\pi\)
\(150\) 0 0
\(151\) 953.000 0.513603 0.256801 0.966464i \(-0.417331\pi\)
0.256801 + 0.966464i \(0.417331\pi\)
\(152\) −80.0000 −0.0426898
\(153\) −7008.00 −3.70303
\(154\) −126.000 −0.0659310
\(155\) 0 0
\(156\) −2080.00 −1.06752
\(157\) −650.000 −0.330418 −0.165209 0.986259i \(-0.552830\pi\)
−0.165209 + 0.986259i \(0.552830\pi\)
\(158\) 1486.00 0.748227
\(159\) −3540.00 −1.76566
\(160\) 0 0
\(161\) 525.000 0.256993
\(162\) 5258.00 2.55005
\(163\) −932.000 −0.447852 −0.223926 0.974606i \(-0.571887\pi\)
−0.223926 + 0.974606i \(0.571887\pi\)
\(164\) −1752.00 −0.834196
\(165\) 0 0
\(166\) −1992.00 −0.931381
\(167\) 180.000 0.0834061 0.0417030 0.999130i \(-0.486722\pi\)
0.0417030 + 0.999130i \(0.486722\pi\)
\(168\) 560.000 0.257172
\(169\) 507.000 0.230769
\(170\) 0 0
\(171\) −730.000 −0.326459
\(172\) −1412.00 −0.625953
\(173\) 834.000 0.366519 0.183260 0.983065i \(-0.441335\pi\)
0.183260 + 0.983065i \(0.441335\pi\)
\(174\) −3780.00 −1.64690
\(175\) 0 0
\(176\) 144.000 0.0616728
\(177\) 6720.00 2.85371
\(178\) 360.000 0.151591
\(179\) −648.000 −0.270580 −0.135290 0.990806i \(-0.543197\pi\)
−0.135290 + 0.990806i \(0.543197\pi\)
\(180\) 0 0
\(181\) −2914.00 −1.19666 −0.598331 0.801249i \(-0.704169\pi\)
−0.598331 + 0.801249i \(0.704169\pi\)
\(182\) −728.000 −0.296500
\(183\) −2060.00 −0.832129
\(184\) −600.000 −0.240394
\(185\) 0 0
\(186\) 4640.00 1.82915
\(187\) −864.000 −0.337871
\(188\) 1944.00 0.754153
\(189\) 3220.00 1.23926
\(190\) 0 0
\(191\) −876.000 −0.331859 −0.165930 0.986138i \(-0.553062\pi\)
−0.165930 + 0.986138i \(0.553062\pi\)
\(192\) −640.000 −0.240563
\(193\) 601.000 0.224150 0.112075 0.993700i \(-0.464250\pi\)
0.112075 + 0.993700i \(0.464250\pi\)
\(194\) 368.000 0.136190
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) 2013.00 0.728022 0.364011 0.931395i \(-0.381407\pi\)
0.364011 + 0.931395i \(0.381407\pi\)
\(198\) 1314.00 0.471626
\(199\) 326.000 0.116128 0.0580641 0.998313i \(-0.481507\pi\)
0.0580641 + 0.998313i \(0.481507\pi\)
\(200\) 0 0
\(201\) 5990.00 2.10200
\(202\) −1452.00 −0.505754
\(203\) −1323.00 −0.457421
\(204\) 3840.00 1.31791
\(205\) 0 0
\(206\) 3596.00 1.21624
\(207\) −5475.00 −1.83835
\(208\) 832.000 0.277350
\(209\) −90.0000 −0.0297867
\(210\) 0 0
\(211\) −5956.00 −1.94326 −0.971630 0.236505i \(-0.923998\pi\)
−0.971630 + 0.236505i \(0.923998\pi\)
\(212\) 1416.00 0.458732
\(213\) 4710.00 1.51514
\(214\) −1752.00 −0.559646
\(215\) 0 0
\(216\) −3680.00 −1.15922
\(217\) 1624.00 0.508038
\(218\) −1382.00 −0.429362
\(219\) 6140.00 1.89453
\(220\) 0 0
\(221\) −4992.00 −1.51945
\(222\) 6100.00 1.84417
\(223\) 3118.00 0.936308 0.468154 0.883647i \(-0.344919\pi\)
0.468154 + 0.883647i \(0.344919\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) 3042.00 0.895358
\(227\) 6.00000 0.00175433 0.000877167 1.00000i \(-0.499721\pi\)
0.000877167 1.00000i \(0.499721\pi\)
\(228\) 400.000 0.116187
\(229\) −586.000 −0.169100 −0.0845502 0.996419i \(-0.526945\pi\)
−0.0845502 + 0.996419i \(0.526945\pi\)
\(230\) 0 0
\(231\) 630.000 0.179441
\(232\) 1512.00 0.427878
\(233\) −1293.00 −0.363550 −0.181775 0.983340i \(-0.558184\pi\)
−0.181775 + 0.983340i \(0.558184\pi\)
\(234\) 7592.00 2.12096
\(235\) 0 0
\(236\) −2688.00 −0.741415
\(237\) −7430.00 −2.03642
\(238\) 1344.00 0.366044
\(239\) −5376.00 −1.45500 −0.727499 0.686109i \(-0.759317\pi\)
−0.727499 + 0.686109i \(0.759317\pi\)
\(240\) 0 0
\(241\) −670.000 −0.179081 −0.0895404 0.995983i \(-0.528540\pi\)
−0.0895404 + 0.995983i \(0.528540\pi\)
\(242\) −2500.00 −0.664075
\(243\) −13870.0 −3.66157
\(244\) 824.000 0.216193
\(245\) 0 0
\(246\) 8760.00 2.27040
\(247\) −520.000 −0.133955
\(248\) −1856.00 −0.475226
\(249\) 9960.00 2.53490
\(250\) 0 0
\(251\) 1380.00 0.347031 0.173516 0.984831i \(-0.444487\pi\)
0.173516 + 0.984831i \(0.444487\pi\)
\(252\) −2044.00 −0.510952
\(253\) −675.000 −0.167735
\(254\) −2062.00 −0.509376
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 3576.00 0.867956 0.433978 0.900923i \(-0.357110\pi\)
0.433978 + 0.900923i \(0.357110\pi\)
\(258\) 7060.00 1.70363
\(259\) 2135.00 0.512210
\(260\) 0 0
\(261\) 13797.0 3.27208
\(262\) −2232.00 −0.526311
\(263\) 5919.00 1.38776 0.693881 0.720090i \(-0.255900\pi\)
0.693881 + 0.720090i \(0.255900\pi\)
\(264\) −720.000 −0.167852
\(265\) 0 0
\(266\) 140.000 0.0322705
\(267\) −1800.00 −0.412578
\(268\) −2396.00 −0.546116
\(269\) −1764.00 −0.399825 −0.199913 0.979814i \(-0.564066\pi\)
−0.199913 + 0.979814i \(0.564066\pi\)
\(270\) 0 0
\(271\) −340.000 −0.0762123 −0.0381061 0.999274i \(-0.512132\pi\)
−0.0381061 + 0.999274i \(0.512132\pi\)
\(272\) −1536.00 −0.342403
\(273\) 3640.00 0.806970
\(274\) 2796.00 0.616469
\(275\) 0 0
\(276\) 3000.00 0.654271
\(277\) −4706.00 −1.02078 −0.510390 0.859943i \(-0.670499\pi\)
−0.510390 + 0.859943i \(0.670499\pi\)
\(278\) 1348.00 0.290819
\(279\) −16936.0 −3.63416
\(280\) 0 0
\(281\) 6681.00 1.41835 0.709173 0.705035i \(-0.249069\pi\)
0.709173 + 0.705035i \(0.249069\pi\)
\(282\) −9720.00 −2.05254
\(283\) 226.000 0.0474710 0.0237355 0.999718i \(-0.492444\pi\)
0.0237355 + 0.999718i \(0.492444\pi\)
\(284\) −1884.00 −0.393644
\(285\) 0 0
\(286\) 936.000 0.193520
\(287\) 3066.00 0.630593
\(288\) 2336.00 0.477952
\(289\) 4303.00 0.875840
\(290\) 0 0
\(291\) −1840.00 −0.370662
\(292\) −2456.00 −0.492214
\(293\) −4320.00 −0.861355 −0.430678 0.902506i \(-0.641725\pi\)
−0.430678 + 0.902506i \(0.641725\pi\)
\(294\) −980.000 −0.194404
\(295\) 0 0
\(296\) −2440.00 −0.479129
\(297\) −4140.00 −0.808846
\(298\) −2562.00 −0.498029
\(299\) −3900.00 −0.754324
\(300\) 0 0
\(301\) 2471.00 0.473176
\(302\) 1906.00 0.363172
\(303\) 7260.00 1.37649
\(304\) −160.000 −0.0301863
\(305\) 0 0
\(306\) −14016.0 −2.61844
\(307\) 6604.00 1.22772 0.613860 0.789415i \(-0.289616\pi\)
0.613860 + 0.789415i \(0.289616\pi\)
\(308\) −252.000 −0.0466202
\(309\) −17980.0 −3.31018
\(310\) 0 0
\(311\) 6036.00 1.10055 0.550274 0.834984i \(-0.314523\pi\)
0.550274 + 0.834984i \(0.314523\pi\)
\(312\) −4160.00 −0.754851
\(313\) −9146.00 −1.65164 −0.825819 0.563936i \(-0.809287\pi\)
−0.825819 + 0.563936i \(0.809287\pi\)
\(314\) −1300.00 −0.233641
\(315\) 0 0
\(316\) 2972.00 0.529076
\(317\) 4449.00 0.788267 0.394134 0.919053i \(-0.371045\pi\)
0.394134 + 0.919053i \(0.371045\pi\)
\(318\) −7080.00 −1.24851
\(319\) 1701.00 0.298551
\(320\) 0 0
\(321\) 8760.00 1.52316
\(322\) 1050.00 0.181721
\(323\) 960.000 0.165374
\(324\) 10516.0 1.80316
\(325\) 0 0
\(326\) −1864.00 −0.316679
\(327\) 6910.00 1.16857
\(328\) −3504.00 −0.589866
\(329\) −3402.00 −0.570086
\(330\) 0 0
\(331\) −10081.0 −1.67402 −0.837012 0.547185i \(-0.815700\pi\)
−0.837012 + 0.547185i \(0.815700\pi\)
\(332\) −3984.00 −0.658586
\(333\) −22265.0 −3.66401
\(334\) 360.000 0.0589770
\(335\) 0 0
\(336\) 1120.00 0.181848
\(337\) −7778.00 −1.25725 −0.628627 0.777707i \(-0.716383\pi\)
−0.628627 + 0.777707i \(0.716383\pi\)
\(338\) 1014.00 0.163178
\(339\) −15210.0 −2.43685
\(340\) 0 0
\(341\) −2088.00 −0.331588
\(342\) −1460.00 −0.230841
\(343\) −343.000 −0.0539949
\(344\) −2824.00 −0.442616
\(345\) 0 0
\(346\) 1668.00 0.259168
\(347\) −1017.00 −0.157336 −0.0786678 0.996901i \(-0.525067\pi\)
−0.0786678 + 0.996901i \(0.525067\pi\)
\(348\) −7560.00 −1.16454
\(349\) 10370.0 1.59053 0.795263 0.606265i \(-0.207333\pi\)
0.795263 + 0.606265i \(0.207333\pi\)
\(350\) 0 0
\(351\) −23920.0 −3.63748
\(352\) 288.000 0.0436092
\(353\) 9432.00 1.42214 0.711069 0.703122i \(-0.248211\pi\)
0.711069 + 0.703122i \(0.248211\pi\)
\(354\) 13440.0 2.01788
\(355\) 0 0
\(356\) 720.000 0.107191
\(357\) −6720.00 −0.996247
\(358\) −1296.00 −0.191329
\(359\) 7557.00 1.11098 0.555492 0.831522i \(-0.312530\pi\)
0.555492 + 0.831522i \(0.312530\pi\)
\(360\) 0 0
\(361\) −6759.00 −0.985421
\(362\) −5828.00 −0.846168
\(363\) 12500.0 1.80738
\(364\) −1456.00 −0.209657
\(365\) 0 0
\(366\) −4120.00 −0.588404
\(367\) 11662.0 1.65872 0.829362 0.558712i \(-0.188704\pi\)
0.829362 + 0.558712i \(0.188704\pi\)
\(368\) −1200.00 −0.169985
\(369\) −31974.0 −4.51084
\(370\) 0 0
\(371\) −2478.00 −0.346769
\(372\) 9280.00 1.29340
\(373\) 2377.00 0.329964 0.164982 0.986297i \(-0.447243\pi\)
0.164982 + 0.986297i \(0.447243\pi\)
\(374\) −1728.00 −0.238911
\(375\) 0 0
\(376\) 3888.00 0.533267
\(377\) 9828.00 1.34262
\(378\) 6440.00 0.876291
\(379\) 4427.00 0.599999 0.300000 0.953939i \(-0.403013\pi\)
0.300000 + 0.953939i \(0.403013\pi\)
\(380\) 0 0
\(381\) 10310.0 1.38634
\(382\) −1752.00 −0.234660
\(383\) −4608.00 −0.614772 −0.307386 0.951585i \(-0.599454\pi\)
−0.307386 + 0.951585i \(0.599454\pi\)
\(384\) −1280.00 −0.170103
\(385\) 0 0
\(386\) 1202.00 0.158498
\(387\) −25769.0 −3.38479
\(388\) 736.000 0.0963009
\(389\) −699.000 −0.0911072 −0.0455536 0.998962i \(-0.514505\pi\)
−0.0455536 + 0.998962i \(0.514505\pi\)
\(390\) 0 0
\(391\) 7200.00 0.931252
\(392\) 392.000 0.0505076
\(393\) 11160.0 1.43244
\(394\) 4026.00 0.514789
\(395\) 0 0
\(396\) 2628.00 0.333490
\(397\) 7630.00 0.964581 0.482291 0.876011i \(-0.339805\pi\)
0.482291 + 0.876011i \(0.339805\pi\)
\(398\) 652.000 0.0821151
\(399\) −700.000 −0.0878292
\(400\) 0 0
\(401\) 5601.00 0.697508 0.348754 0.937214i \(-0.386605\pi\)
0.348754 + 0.937214i \(0.386605\pi\)
\(402\) 11980.0 1.48634
\(403\) −12064.0 −1.49119
\(404\) −2904.00 −0.357622
\(405\) 0 0
\(406\) −2646.00 −0.323445
\(407\) −2745.00 −0.334311
\(408\) 7680.00 0.931904
\(409\) 4670.00 0.564588 0.282294 0.959328i \(-0.408905\pi\)
0.282294 + 0.959328i \(0.408905\pi\)
\(410\) 0 0
\(411\) −13980.0 −1.67782
\(412\) 7192.00 0.860011
\(413\) 4704.00 0.560457
\(414\) −10950.0 −1.29991
\(415\) 0 0
\(416\) 1664.00 0.196116
\(417\) −6740.00 −0.791509
\(418\) −180.000 −0.0210624
\(419\) 36.0000 0.00419741 0.00209871 0.999998i \(-0.499332\pi\)
0.00209871 + 0.999998i \(0.499332\pi\)
\(420\) 0 0
\(421\) 5495.00 0.636128 0.318064 0.948069i \(-0.396967\pi\)
0.318064 + 0.948069i \(0.396967\pi\)
\(422\) −11912.0 −1.37409
\(423\) 35478.0 4.07801
\(424\) 2832.00 0.324373
\(425\) 0 0
\(426\) 9420.00 1.07136
\(427\) −1442.00 −0.163427
\(428\) −3504.00 −0.395730
\(429\) −4680.00 −0.526696
\(430\) 0 0
\(431\) 2700.00 0.301750 0.150875 0.988553i \(-0.451791\pi\)
0.150875 + 0.988553i \(0.451791\pi\)
\(432\) −7360.00 −0.819695
\(433\) −15104.0 −1.67633 −0.838166 0.545415i \(-0.816372\pi\)
−0.838166 + 0.545415i \(0.816372\pi\)
\(434\) 3248.00 0.359237
\(435\) 0 0
\(436\) −2764.00 −0.303605
\(437\) 750.000 0.0820992
\(438\) 12280.0 1.33964
\(439\) 14948.0 1.62512 0.812562 0.582875i \(-0.198072\pi\)
0.812562 + 0.582875i \(0.198072\pi\)
\(440\) 0 0
\(441\) 3577.00 0.386243
\(442\) −9984.00 −1.07441
\(443\) −4980.00 −0.534101 −0.267051 0.963682i \(-0.586049\pi\)
−0.267051 + 0.963682i \(0.586049\pi\)
\(444\) 12200.0 1.30402
\(445\) 0 0
\(446\) 6236.00 0.662070
\(447\) 12810.0 1.35546
\(448\) −448.000 −0.0472456
\(449\) 12375.0 1.30070 0.650348 0.759637i \(-0.274623\pi\)
0.650348 + 0.759637i \(0.274623\pi\)
\(450\) 0 0
\(451\) −3942.00 −0.411578
\(452\) 6084.00 0.633113
\(453\) −9530.00 −0.988429
\(454\) 12.0000 0.00124050
\(455\) 0 0
\(456\) 800.000 0.0821567
\(457\) −10835.0 −1.10906 −0.554529 0.832164i \(-0.687102\pi\)
−0.554529 + 0.832164i \(0.687102\pi\)
\(458\) −1172.00 −0.119572
\(459\) 44160.0 4.49066
\(460\) 0 0
\(461\) 5700.00 0.575869 0.287934 0.957650i \(-0.407032\pi\)
0.287934 + 0.957650i \(0.407032\pi\)
\(462\) 1260.00 0.126884
\(463\) −6128.00 −0.615102 −0.307551 0.951532i \(-0.599509\pi\)
−0.307551 + 0.951532i \(0.599509\pi\)
\(464\) 3024.00 0.302555
\(465\) 0 0
\(466\) −2586.00 −0.257069
\(467\) 9810.00 0.972061 0.486031 0.873942i \(-0.338444\pi\)
0.486031 + 0.873942i \(0.338444\pi\)
\(468\) 15184.0 1.49974
\(469\) 4193.00 0.412825
\(470\) 0 0
\(471\) 6500.00 0.635890
\(472\) −5376.00 −0.524259
\(473\) −3177.00 −0.308834
\(474\) −14860.0 −1.43996
\(475\) 0 0
\(476\) 2688.00 0.258833
\(477\) 25842.0 2.48055
\(478\) −10752.0 −1.02884
\(479\) −204.000 −0.0194593 −0.00972964 0.999953i \(-0.503097\pi\)
−0.00972964 + 0.999953i \(0.503097\pi\)
\(480\) 0 0
\(481\) −15860.0 −1.50344
\(482\) −1340.00 −0.126629
\(483\) −5250.00 −0.494582
\(484\) −5000.00 −0.469572
\(485\) 0 0
\(486\) −27740.0 −2.58912
\(487\) −15401.0 −1.43303 −0.716515 0.697571i \(-0.754264\pi\)
−0.716515 + 0.697571i \(0.754264\pi\)
\(488\) 1648.00 0.152872
\(489\) 9320.00 0.861892
\(490\) 0 0
\(491\) 3897.00 0.358186 0.179093 0.983832i \(-0.442684\pi\)
0.179093 + 0.983832i \(0.442684\pi\)
\(492\) 17520.0 1.60541
\(493\) −18144.0 −1.65753
\(494\) −1040.00 −0.0947203
\(495\) 0 0
\(496\) −3712.00 −0.336036
\(497\) 3297.00 0.297567
\(498\) 19920.0 1.79244
\(499\) 8132.00 0.729536 0.364768 0.931098i \(-0.381148\pi\)
0.364768 + 0.931098i \(0.381148\pi\)
\(500\) 0 0
\(501\) −1800.00 −0.160515
\(502\) 2760.00 0.245388
\(503\) 10998.0 0.974904 0.487452 0.873150i \(-0.337926\pi\)
0.487452 + 0.873150i \(0.337926\pi\)
\(504\) −4088.00 −0.361298
\(505\) 0 0
\(506\) −1350.00 −0.118606
\(507\) −5070.00 −0.444116
\(508\) −4124.00 −0.360183
\(509\) 5940.00 0.517261 0.258631 0.965976i \(-0.416729\pi\)
0.258631 + 0.965976i \(0.416729\pi\)
\(510\) 0 0
\(511\) 4298.00 0.372079
\(512\) 512.000 0.0441942
\(513\) 4600.00 0.395897
\(514\) 7152.00 0.613738
\(515\) 0 0
\(516\) 14120.0 1.20465
\(517\) 4374.00 0.372086
\(518\) 4270.00 0.362187
\(519\) −8340.00 −0.705367
\(520\) 0 0
\(521\) 17022.0 1.43138 0.715688 0.698420i \(-0.246113\pi\)
0.715688 + 0.698420i \(0.246113\pi\)
\(522\) 27594.0 2.31371
\(523\) 15748.0 1.31666 0.658329 0.752730i \(-0.271264\pi\)
0.658329 + 0.752730i \(0.271264\pi\)
\(524\) −4464.00 −0.372158
\(525\) 0 0
\(526\) 11838.0 0.981295
\(527\) 22272.0 1.84096
\(528\) −1440.00 −0.118689
\(529\) −6542.00 −0.537684
\(530\) 0 0
\(531\) −49056.0 −4.00913
\(532\) 280.000 0.0228187
\(533\) −22776.0 −1.85092
\(534\) −3600.00 −0.291736
\(535\) 0 0
\(536\) −4792.00 −0.386162
\(537\) 6480.00 0.520731
\(538\) −3528.00 −0.282719
\(539\) 441.000 0.0352416
\(540\) 0 0
\(541\) −3373.00 −0.268053 −0.134026 0.990978i \(-0.542791\pi\)
−0.134026 + 0.990978i \(0.542791\pi\)
\(542\) −680.000 −0.0538902
\(543\) 29140.0 2.30298
\(544\) −3072.00 −0.242116
\(545\) 0 0
\(546\) 7280.00 0.570614
\(547\) 14389.0 1.12473 0.562367 0.826888i \(-0.309891\pi\)
0.562367 + 0.826888i \(0.309891\pi\)
\(548\) 5592.00 0.435909
\(549\) 15038.0 1.16905
\(550\) 0 0
\(551\) −1890.00 −0.146128
\(552\) 6000.00 0.462639
\(553\) −5201.00 −0.399944
\(554\) −9412.00 −0.721801
\(555\) 0 0
\(556\) 2696.00 0.205640
\(557\) 4929.00 0.374952 0.187476 0.982269i \(-0.439969\pi\)
0.187476 + 0.982269i \(0.439969\pi\)
\(558\) −33872.0 −2.56974
\(559\) −18356.0 −1.38887
\(560\) 0 0
\(561\) 8640.00 0.650234
\(562\) 13362.0 1.00292
\(563\) −15678.0 −1.17362 −0.586811 0.809724i \(-0.699617\pi\)
−0.586811 + 0.809724i \(0.699617\pi\)
\(564\) −19440.0 −1.45137
\(565\) 0 0
\(566\) 452.000 0.0335671
\(567\) −18403.0 −1.36306
\(568\) −3768.00 −0.278348
\(569\) −14499.0 −1.06824 −0.534121 0.845408i \(-0.679357\pi\)
−0.534121 + 0.845408i \(0.679357\pi\)
\(570\) 0 0
\(571\) −9457.00 −0.693105 −0.346553 0.938031i \(-0.612648\pi\)
−0.346553 + 0.938031i \(0.612648\pi\)
\(572\) 1872.00 0.136840
\(573\) 8760.00 0.638664
\(574\) 6132.00 0.445897
\(575\) 0 0
\(576\) 4672.00 0.337963
\(577\) −10370.0 −0.748195 −0.374098 0.927389i \(-0.622048\pi\)
−0.374098 + 0.927389i \(0.622048\pi\)
\(578\) 8606.00 0.619312
\(579\) −6010.00 −0.431377
\(580\) 0 0
\(581\) 6972.00 0.497844
\(582\) −3680.00 −0.262098
\(583\) 3186.00 0.226330
\(584\) −4912.00 −0.348048
\(585\) 0 0
\(586\) −8640.00 −0.609070
\(587\) 12126.0 0.852630 0.426315 0.904575i \(-0.359812\pi\)
0.426315 + 0.904575i \(0.359812\pi\)
\(588\) −1960.00 −0.137464
\(589\) 2320.00 0.162299
\(590\) 0 0
\(591\) −20130.0 −1.40108
\(592\) −4880.00 −0.338795
\(593\) −1068.00 −0.0739587 −0.0369793 0.999316i \(-0.511774\pi\)
−0.0369793 + 0.999316i \(0.511774\pi\)
\(594\) −8280.00 −0.571940
\(595\) 0 0
\(596\) −5124.00 −0.352160
\(597\) −3260.00 −0.223489
\(598\) −7800.00 −0.533387
\(599\) 3375.00 0.230215 0.115107 0.993353i \(-0.463279\pi\)
0.115107 + 0.993353i \(0.463279\pi\)
\(600\) 0 0
\(601\) −27448.0 −1.86294 −0.931470 0.363817i \(-0.881473\pi\)
−0.931470 + 0.363817i \(0.881473\pi\)
\(602\) 4942.00 0.334586
\(603\) −43727.0 −2.95307
\(604\) 3812.00 0.256801
\(605\) 0 0
\(606\) 14520.0 0.973325
\(607\) −3884.00 −0.259714 −0.129857 0.991533i \(-0.541452\pi\)
−0.129857 + 0.991533i \(0.541452\pi\)
\(608\) −320.000 −0.0213449
\(609\) 13230.0 0.880306
\(610\) 0 0
\(611\) 25272.0 1.67332
\(612\) −28032.0 −1.85151
\(613\) 3643.00 0.240032 0.120016 0.992772i \(-0.461705\pi\)
0.120016 + 0.992772i \(0.461705\pi\)
\(614\) 13208.0 0.868129
\(615\) 0 0
\(616\) −504.000 −0.0329655
\(617\) −30369.0 −1.98154 −0.990770 0.135555i \(-0.956718\pi\)
−0.990770 + 0.135555i \(0.956718\pi\)
\(618\) −35960.0 −2.34065
\(619\) −10888.0 −0.706988 −0.353494 0.935437i \(-0.615007\pi\)
−0.353494 + 0.935437i \(0.615007\pi\)
\(620\) 0 0
\(621\) 34500.0 2.22937
\(622\) 12072.0 0.778204
\(623\) −1260.00 −0.0810286
\(624\) −8320.00 −0.533761
\(625\) 0 0
\(626\) −18292.0 −1.16788
\(627\) 900.000 0.0573246
\(628\) −2600.00 −0.165209
\(629\) 29280.0 1.85607
\(630\) 0 0
\(631\) 28499.0 1.79798 0.898992 0.437966i \(-0.144301\pi\)
0.898992 + 0.437966i \(0.144301\pi\)
\(632\) 5944.00 0.374113
\(633\) 59560.0 3.73981
\(634\) 8898.00 0.557389
\(635\) 0 0
\(636\) −14160.0 −0.882831
\(637\) 2548.00 0.158486
\(638\) 3402.00 0.211107
\(639\) −34383.0 −2.12859
\(640\) 0 0
\(641\) 5817.00 0.358436 0.179218 0.983809i \(-0.442643\pi\)
0.179218 + 0.983809i \(0.442643\pi\)
\(642\) 17520.0 1.07704
\(643\) −22376.0 −1.37235 −0.686177 0.727435i \(-0.740712\pi\)
−0.686177 + 0.727435i \(0.740712\pi\)
\(644\) 2100.00 0.128496
\(645\) 0 0
\(646\) 1920.00 0.116937
\(647\) −3018.00 −0.183385 −0.0916923 0.995787i \(-0.529228\pi\)
−0.0916923 + 0.995787i \(0.529228\pi\)
\(648\) 21032.0 1.27502
\(649\) −6048.00 −0.365801
\(650\) 0 0
\(651\) −16240.0 −0.977720
\(652\) −3728.00 −0.223926
\(653\) 29682.0 1.77878 0.889392 0.457145i \(-0.151128\pi\)
0.889392 + 0.457145i \(0.151128\pi\)
\(654\) 13820.0 0.826307
\(655\) 0 0
\(656\) −7008.00 −0.417098
\(657\) −44822.0 −2.66160
\(658\) −6804.00 −0.403112
\(659\) 2052.00 0.121297 0.0606484 0.998159i \(-0.480683\pi\)
0.0606484 + 0.998159i \(0.480683\pi\)
\(660\) 0 0
\(661\) 14222.0 0.836871 0.418435 0.908247i \(-0.362579\pi\)
0.418435 + 0.908247i \(0.362579\pi\)
\(662\) −20162.0 −1.18371
\(663\) 49920.0 2.92418
\(664\) −7968.00 −0.465690
\(665\) 0 0
\(666\) −44530.0 −2.59084
\(667\) −14175.0 −0.822876
\(668\) 720.000 0.0417030
\(669\) −31180.0 −1.80193
\(670\) 0 0
\(671\) 1854.00 0.106666
\(672\) 2240.00 0.128586
\(673\) −20942.0 −1.19949 −0.599744 0.800192i \(-0.704731\pi\)
−0.599744 + 0.800192i \(0.704731\pi\)
\(674\) −15556.0 −0.889013
\(675\) 0 0
\(676\) 2028.00 0.115385
\(677\) −13074.0 −0.742208 −0.371104 0.928591i \(-0.621021\pi\)
−0.371104 + 0.928591i \(0.621021\pi\)
\(678\) −30420.0 −1.72312
\(679\) −1288.00 −0.0727966
\(680\) 0 0
\(681\) −60.0000 −0.00337622
\(682\) −4176.00 −0.234468
\(683\) 31383.0 1.75818 0.879090 0.476656i \(-0.158151\pi\)
0.879090 + 0.476656i \(0.158151\pi\)
\(684\) −2920.00 −0.163230
\(685\) 0 0
\(686\) −686.000 −0.0381802
\(687\) 5860.00 0.325434
\(688\) −5648.00 −0.312977
\(689\) 18408.0 1.01784
\(690\) 0 0
\(691\) −622.000 −0.0342431 −0.0171216 0.999853i \(-0.505450\pi\)
−0.0171216 + 0.999853i \(0.505450\pi\)
\(692\) 3336.00 0.183260
\(693\) −4599.00 −0.252095
\(694\) −2034.00 −0.111253
\(695\) 0 0
\(696\) −15120.0 −0.823451
\(697\) 42048.0 2.28505
\(698\) 20740.0 1.12467
\(699\) 12930.0 0.699653
\(700\) 0 0
\(701\) 7782.00 0.419290 0.209645 0.977778i \(-0.432769\pi\)
0.209645 + 0.977778i \(0.432769\pi\)
\(702\) −47840.0 −2.57209
\(703\) 3050.00 0.163631
\(704\) 576.000 0.0308364
\(705\) 0 0
\(706\) 18864.0 1.00560
\(707\) 5082.00 0.270337
\(708\) 26880.0 1.42685
\(709\) 7502.00 0.397382 0.198691 0.980062i \(-0.436331\pi\)
0.198691 + 0.980062i \(0.436331\pi\)
\(710\) 0 0
\(711\) 54239.0 2.86093
\(712\) 1440.00 0.0757953
\(713\) 17400.0 0.913934
\(714\) −13440.0 −0.704453
\(715\) 0 0
\(716\) −2592.00 −0.135290
\(717\) 53760.0 2.80015
\(718\) 15114.0 0.785584
\(719\) −20814.0 −1.07960 −0.539799 0.841794i \(-0.681500\pi\)
−0.539799 + 0.841794i \(0.681500\pi\)
\(720\) 0 0
\(721\) −12586.0 −0.650107
\(722\) −13518.0 −0.696798
\(723\) 6700.00 0.344641
\(724\) −11656.0 −0.598331
\(725\) 0 0
\(726\) 25000.0 1.27801
\(727\) −14360.0 −0.732576 −0.366288 0.930501i \(-0.619372\pi\)
−0.366288 + 0.930501i \(0.619372\pi\)
\(728\) −2912.00 −0.148250
\(729\) 67717.0 3.44038
\(730\) 0 0
\(731\) 33888.0 1.71463
\(732\) −8240.00 −0.416064
\(733\) 1588.00 0.0800193 0.0400096 0.999199i \(-0.487261\pi\)
0.0400096 + 0.999199i \(0.487261\pi\)
\(734\) 23324.0 1.17289
\(735\) 0 0
\(736\) −2400.00 −0.120197
\(737\) −5391.00 −0.269444
\(738\) −63948.0 −3.18965
\(739\) 2957.00 0.147192 0.0735961 0.997288i \(-0.476552\pi\)
0.0735961 + 0.997288i \(0.476552\pi\)
\(740\) 0 0
\(741\) 5200.00 0.257796
\(742\) −4956.00 −0.245203
\(743\) 12384.0 0.611474 0.305737 0.952116i \(-0.401097\pi\)
0.305737 + 0.952116i \(0.401097\pi\)
\(744\) 18560.0 0.914573
\(745\) 0 0
\(746\) 4754.00 0.233319
\(747\) −72708.0 −3.56124
\(748\) −3456.00 −0.168936
\(749\) 6132.00 0.299143
\(750\) 0 0
\(751\) −20236.0 −0.983252 −0.491626 0.870806i \(-0.663597\pi\)
−0.491626 + 0.870806i \(0.663597\pi\)
\(752\) 7776.00 0.377077
\(753\) −13800.0 −0.667862
\(754\) 19656.0 0.949376
\(755\) 0 0
\(756\) 12880.0 0.619631
\(757\) −37601.0 −1.80533 −0.902663 0.430348i \(-0.858391\pi\)
−0.902663 + 0.430348i \(0.858391\pi\)
\(758\) 8854.00 0.424264
\(759\) 6750.00 0.322806
\(760\) 0 0
\(761\) −13392.0 −0.637923 −0.318962 0.947768i \(-0.603334\pi\)
−0.318962 + 0.947768i \(0.603334\pi\)
\(762\) 20620.0 0.980294
\(763\) 4837.00 0.229503
\(764\) −3504.00 −0.165930
\(765\) 0 0
\(766\) −9216.00 −0.434710
\(767\) −34944.0 −1.64505
\(768\) −2560.00 −0.120281
\(769\) 22430.0 1.05182 0.525908 0.850541i \(-0.323726\pi\)
0.525908 + 0.850541i \(0.323726\pi\)
\(770\) 0 0
\(771\) −35760.0 −1.67038
\(772\) 2404.00 0.112075
\(773\) −34704.0 −1.61477 −0.807384 0.590026i \(-0.799118\pi\)
−0.807384 + 0.590026i \(0.799118\pi\)
\(774\) −51538.0 −2.39340
\(775\) 0 0
\(776\) 1472.00 0.0680950
\(777\) −21350.0 −0.985749
\(778\) −1398.00 −0.0644225
\(779\) 4380.00 0.201450
\(780\) 0 0
\(781\) −4239.00 −0.194217
\(782\) 14400.0 0.658495
\(783\) −86940.0 −3.96805
\(784\) 784.000 0.0357143
\(785\) 0 0
\(786\) 22320.0 1.01289
\(787\) −37646.0 −1.70513 −0.852564 0.522624i \(-0.824953\pi\)
−0.852564 + 0.522624i \(0.824953\pi\)
\(788\) 8052.00 0.364011
\(789\) −59190.0 −2.67075
\(790\) 0 0
\(791\) −10647.0 −0.478589
\(792\) 5256.00 0.235813
\(793\) 10712.0 0.479690
\(794\) 15260.0 0.682062
\(795\) 0 0
\(796\) 1304.00 0.0580641
\(797\) 8988.00 0.399462 0.199731 0.979851i \(-0.435993\pi\)
0.199731 + 0.979851i \(0.435993\pi\)
\(798\) −1400.00 −0.0621046
\(799\) −46656.0 −2.06580
\(800\) 0 0
\(801\) 13140.0 0.579624
\(802\) 11202.0 0.493212
\(803\) −5526.00 −0.242850
\(804\) 23960.0 1.05100
\(805\) 0 0
\(806\) −24128.0 −1.05443
\(807\) 17640.0 0.769464
\(808\) −5808.00 −0.252877
\(809\) −28029.0 −1.21811 −0.609053 0.793130i \(-0.708450\pi\)
−0.609053 + 0.793130i \(0.708450\pi\)
\(810\) 0 0
\(811\) 8078.00 0.349762 0.174881 0.984590i \(-0.444046\pi\)
0.174881 + 0.984590i \(0.444046\pi\)
\(812\) −5292.00 −0.228710
\(813\) 3400.00 0.146671
\(814\) −5490.00 −0.236394
\(815\) 0 0
\(816\) 15360.0 0.658955
\(817\) 3530.00 0.151162
\(818\) 9340.00 0.399224
\(819\) −26572.0 −1.13370
\(820\) 0 0
\(821\) −35574.0 −1.51223 −0.756115 0.654439i \(-0.772905\pi\)
−0.756115 + 0.654439i \(0.772905\pi\)
\(822\) −27960.0 −1.18640
\(823\) −6599.00 −0.279498 −0.139749 0.990187i \(-0.544630\pi\)
−0.139749 + 0.990187i \(0.544630\pi\)
\(824\) 14384.0 0.608119
\(825\) 0 0
\(826\) 9408.00 0.396303
\(827\) 663.000 0.0278776 0.0139388 0.999903i \(-0.495563\pi\)
0.0139388 + 0.999903i \(0.495563\pi\)
\(828\) −21900.0 −0.919176
\(829\) −22564.0 −0.945332 −0.472666 0.881242i \(-0.656708\pi\)
−0.472666 + 0.881242i \(0.656708\pi\)
\(830\) 0 0
\(831\) 47060.0 1.96449
\(832\) 3328.00 0.138675
\(833\) −4704.00 −0.195659
\(834\) −13480.0 −0.559681
\(835\) 0 0
\(836\) −360.000 −0.0148934
\(837\) 106720. 4.40715
\(838\) 72.0000 0.00296802
\(839\) −294.000 −0.0120977 −0.00604887 0.999982i \(-0.501925\pi\)
−0.00604887 + 0.999982i \(0.501925\pi\)
\(840\) 0 0
\(841\) 11332.0 0.464636
\(842\) 10990.0 0.449810
\(843\) −66810.0 −2.72961
\(844\) −23824.0 −0.971630
\(845\) 0 0
\(846\) 70956.0 2.88359
\(847\) 8750.00 0.354963
\(848\) 5664.00 0.229366
\(849\) −2260.00 −0.0913581
\(850\) 0 0
\(851\) 22875.0 0.921439
\(852\) 18840.0 0.757568
\(853\) 28852.0 1.15812 0.579058 0.815286i \(-0.303420\pi\)
0.579058 + 0.815286i \(0.303420\pi\)
\(854\) −2884.00 −0.115560
\(855\) 0 0
\(856\) −7008.00 −0.279823
\(857\) 7422.00 0.295835 0.147918 0.989000i \(-0.452743\pi\)
0.147918 + 0.989000i \(0.452743\pi\)
\(858\) −9360.00 −0.372430
\(859\) 8138.00 0.323242 0.161621 0.986853i \(-0.448328\pi\)
0.161621 + 0.986853i \(0.448328\pi\)
\(860\) 0 0
\(861\) −30660.0 −1.21358
\(862\) 5400.00 0.213370
\(863\) 32199.0 1.27007 0.635033 0.772485i \(-0.280987\pi\)
0.635033 + 0.772485i \(0.280987\pi\)
\(864\) −14720.0 −0.579612
\(865\) 0 0
\(866\) −30208.0 −1.18535
\(867\) −43030.0 −1.68555
\(868\) 6496.00 0.254019
\(869\) 6687.00 0.261037
\(870\) 0 0
\(871\) −31148.0 −1.21172
\(872\) −5528.00 −0.214681
\(873\) 13432.0 0.520738
\(874\) 1500.00 0.0580529
\(875\) 0 0
\(876\) 24560.0 0.947267
\(877\) 11158.0 0.429622 0.214811 0.976656i \(-0.431086\pi\)
0.214811 + 0.976656i \(0.431086\pi\)
\(878\) 29896.0 1.14914
\(879\) 43200.0 1.65768
\(880\) 0 0
\(881\) 16272.0 0.622267 0.311134 0.950366i \(-0.399291\pi\)
0.311134 + 0.950366i \(0.399291\pi\)
\(882\) 7154.00 0.273115
\(883\) −9071.00 −0.345712 −0.172856 0.984947i \(-0.555299\pi\)
−0.172856 + 0.984947i \(0.555299\pi\)
\(884\) −19968.0 −0.759725
\(885\) 0 0
\(886\) −9960.00 −0.377667
\(887\) 30138.0 1.14085 0.570426 0.821349i \(-0.306778\pi\)
0.570426 + 0.821349i \(0.306778\pi\)
\(888\) 24400.0 0.922084
\(889\) 7217.00 0.272273
\(890\) 0 0
\(891\) 23661.0 0.889645
\(892\) 12472.0 0.468154
\(893\) −4860.00 −0.182121
\(894\) 25620.0 0.958457
\(895\) 0 0
\(896\) −896.000 −0.0334077
\(897\) 39000.0 1.45170
\(898\) 24750.0 0.919731
\(899\) −43848.0 −1.62671
\(900\) 0 0
\(901\) −33984.0 −1.25657
\(902\) −7884.00 −0.291029
\(903\) −24710.0 −0.910628
\(904\) 12168.0 0.447679
\(905\) 0 0
\(906\) −19060.0 −0.698925
\(907\) −25844.0 −0.946126 −0.473063 0.881029i \(-0.656852\pi\)
−0.473063 + 0.881029i \(0.656852\pi\)
\(908\) 24.0000 0.000877167 0
\(909\) −52998.0 −1.93381
\(910\) 0 0
\(911\) 40815.0 1.48437 0.742185 0.670195i \(-0.233790\pi\)
0.742185 + 0.670195i \(0.233790\pi\)
\(912\) 1600.00 0.0580935
\(913\) −8964.00 −0.324934
\(914\) −21670.0 −0.784223
\(915\) 0 0
\(916\) −2344.00 −0.0845502
\(917\) 7812.00 0.281325
\(918\) 88320.0 3.17538
\(919\) −5389.00 −0.193435 −0.0967175 0.995312i \(-0.530834\pi\)
−0.0967175 + 0.995312i \(0.530834\pi\)
\(920\) 0 0
\(921\) −66040.0 −2.36275
\(922\) 11400.0 0.407201
\(923\) −24492.0 −0.873417
\(924\) 2520.00 0.0897207
\(925\) 0 0
\(926\) −12256.0 −0.434943
\(927\) 131254. 4.65043
\(928\) 6048.00 0.213939
\(929\) 43662.0 1.54198 0.770992 0.636844i \(-0.219761\pi\)
0.770992 + 0.636844i \(0.219761\pi\)
\(930\) 0 0
\(931\) −490.000 −0.0172493
\(932\) −5172.00 −0.181775
\(933\) −60360.0 −2.11800
\(934\) 19620.0 0.687351
\(935\) 0 0
\(936\) 30368.0 1.06048
\(937\) 11950.0 0.416638 0.208319 0.978061i \(-0.433201\pi\)
0.208319 + 0.978061i \(0.433201\pi\)
\(938\) 8386.00 0.291911
\(939\) 91460.0 3.17858
\(940\) 0 0
\(941\) −8448.00 −0.292664 −0.146332 0.989236i \(-0.546747\pi\)
−0.146332 + 0.989236i \(0.546747\pi\)
\(942\) 13000.0 0.449642
\(943\) 32850.0 1.13440
\(944\) −10752.0 −0.370707
\(945\) 0 0
\(946\) −6354.00 −0.218379
\(947\) −25692.0 −0.881603 −0.440801 0.897605i \(-0.645306\pi\)
−0.440801 + 0.897605i \(0.645306\pi\)
\(948\) −29720.0 −1.01821
\(949\) −31928.0 −1.09213
\(950\) 0 0
\(951\) −44490.0 −1.51702
\(952\) 5376.00 0.183022
\(953\) −47547.0 −1.61616 −0.808079 0.589074i \(-0.799493\pi\)
−0.808079 + 0.589074i \(0.799493\pi\)
\(954\) 51684.0 1.75402
\(955\) 0 0
\(956\) −21504.0 −0.727499
\(957\) −17010.0 −0.574561
\(958\) −408.000 −0.0137598
\(959\) −9786.00 −0.329517
\(960\) 0 0
\(961\) 24033.0 0.806720
\(962\) −31720.0 −1.06309
\(963\) −63948.0 −2.13987
\(964\) −2680.00 −0.0895404
\(965\) 0 0
\(966\) −10500.0 −0.349723
\(967\) −51608.0 −1.71624 −0.858119 0.513452i \(-0.828367\pi\)
−0.858119 + 0.513452i \(0.828367\pi\)
\(968\) −10000.0 −0.332037
\(969\) −9600.00 −0.318263
\(970\) 0 0
\(971\) −11754.0 −0.388469 −0.194235 0.980955i \(-0.562222\pi\)
−0.194235 + 0.980955i \(0.562222\pi\)
\(972\) −55480.0 −1.83078
\(973\) −4718.00 −0.155449
\(974\) −30802.0 −1.01331
\(975\) 0 0
\(976\) 3296.00 0.108097
\(977\) −12765.0 −0.418003 −0.209001 0.977915i \(-0.567021\pi\)
−0.209001 + 0.977915i \(0.567021\pi\)
\(978\) 18640.0 0.609449
\(979\) 1620.00 0.0528860
\(980\) 0 0
\(981\) −50443.0 −1.64171
\(982\) 7794.00 0.253275
\(983\) 32112.0 1.04193 0.520963 0.853579i \(-0.325573\pi\)
0.520963 + 0.853579i \(0.325573\pi\)
\(984\) 35040.0 1.13520
\(985\) 0 0
\(986\) −36288.0 −1.17205
\(987\) 34020.0 1.09713
\(988\) −2080.00 −0.0669773
\(989\) 26475.0 0.851219
\(990\) 0 0
\(991\) −42505.0 −1.36248 −0.681239 0.732061i \(-0.738559\pi\)
−0.681239 + 0.732061i \(0.738559\pi\)
\(992\) −7424.00 −0.237613
\(993\) 100810. 3.22166
\(994\) 6594.00 0.210411
\(995\) 0 0
\(996\) 39840.0 1.26745
\(997\) −59654.0 −1.89495 −0.947473 0.319836i \(-0.896372\pi\)
−0.947473 + 0.319836i \(0.896372\pi\)
\(998\) 16264.0 0.515860
\(999\) 140300. 4.44334
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 350.4.a.k.1.1 yes 1
5.2 odd 4 350.4.c.a.99.2 2
5.3 odd 4 350.4.c.a.99.1 2
5.4 even 2 350.4.a.j.1.1 1
7.6 odd 2 2450.4.a.bp.1.1 1
35.34 odd 2 2450.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.4.a.j.1.1 1 5.4 even 2
350.4.a.k.1.1 yes 1 1.1 even 1 trivial
350.4.c.a.99.1 2 5.3 odd 4
350.4.c.a.99.2 2 5.2 odd 4
2450.4.a.a.1.1 1 35.34 odd 2
2450.4.a.bp.1.1 1 7.6 odd 2