Properties

Label 2450.4.a.bf.1.1
Level $2450$
Weight $4$
Character 2450.1
Self dual yes
Analytic conductor $144.555$
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] = [2450,4,Mod(1,2450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2450, 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("2450.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2450.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: \(144.554679514\)
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 \(\chi\) \(=\) 2450.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -1.00000 q^{3} +4.00000 q^{4} -2.00000 q^{6} +8.00000 q^{8} -26.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -1.00000 q^{3} +4.00000 q^{4} -2.00000 q^{6} +8.00000 q^{8} -26.0000 q^{9} +35.0000 q^{11} -4.00000 q^{12} +66.0000 q^{13} +16.0000 q^{16} +59.0000 q^{17} -52.0000 q^{18} -137.000 q^{19} +70.0000 q^{22} +7.00000 q^{23} -8.00000 q^{24} +132.000 q^{26} +53.0000 q^{27} +106.000 q^{29} -75.0000 q^{31} +32.0000 q^{32} -35.0000 q^{33} +118.000 q^{34} -104.000 q^{36} -11.0000 q^{37} -274.000 q^{38} -66.0000 q^{39} +498.000 q^{41} -260.000 q^{43} +140.000 q^{44} +14.0000 q^{46} -171.000 q^{47} -16.0000 q^{48} -59.0000 q^{51} +264.000 q^{52} +417.000 q^{53} +106.000 q^{54} +137.000 q^{57} +212.000 q^{58} +17.0000 q^{59} -51.0000 q^{61} -150.000 q^{62} +64.0000 q^{64} -70.0000 q^{66} -439.000 q^{67} +236.000 q^{68} -7.00000 q^{69} -784.000 q^{71} -208.000 q^{72} +295.000 q^{73} -22.0000 q^{74} -548.000 q^{76} -132.000 q^{78} -495.000 q^{79} +649.000 q^{81} +996.000 q^{82} +932.000 q^{83} -520.000 q^{86} -106.000 q^{87} +280.000 q^{88} +873.000 q^{89} +28.0000 q^{92} +75.0000 q^{93} -342.000 q^{94} -32.0000 q^{96} -290.000 q^{97} -910.000 q^{99} +O(q^{100})\)

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
\(3\) −1.00000 −0.192450 −0.0962250 0.995360i \(-0.530677\pi\)
−0.0962250 + 0.995360i \(0.530677\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −2.00000 −0.136083
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) 35.0000 0.959354 0.479677 0.877445i \(-0.340754\pi\)
0.479677 + 0.877445i \(0.340754\pi\)
\(12\) −4.00000 −0.0962250
\(13\) 66.0000 1.40809 0.704043 0.710158i \(-0.251376\pi\)
0.704043 + 0.710158i \(0.251376\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 59.0000 0.841741 0.420871 0.907121i \(-0.361725\pi\)
0.420871 + 0.907121i \(0.361725\pi\)
\(18\) −52.0000 −0.680918
\(19\) −137.000 −1.65421 −0.827104 0.562049i \(-0.810013\pi\)
−0.827104 + 0.562049i \(0.810013\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 70.0000 0.678366
\(23\) 7.00000 0.0634609 0.0317305 0.999496i \(-0.489898\pi\)
0.0317305 + 0.999496i \(0.489898\pi\)
\(24\) −8.00000 −0.0680414
\(25\) 0 0
\(26\) 132.000 0.995667
\(27\) 53.0000 0.377772
\(28\) 0 0
\(29\) 106.000 0.678748 0.339374 0.940651i \(-0.389785\pi\)
0.339374 + 0.940651i \(0.389785\pi\)
\(30\) 0 0
\(31\) −75.0000 −0.434529 −0.217264 0.976113i \(-0.569713\pi\)
−0.217264 + 0.976113i \(0.569713\pi\)
\(32\) 32.0000 0.176777
\(33\) −35.0000 −0.184628
\(34\) 118.000 0.595201
\(35\) 0 0
\(36\) −104.000 −0.481481
\(37\) −11.0000 −0.0488754 −0.0244377 0.999701i \(-0.507780\pi\)
−0.0244377 + 0.999701i \(0.507780\pi\)
\(38\) −274.000 −1.16970
\(39\) −66.0000 −0.270986
\(40\) 0 0
\(41\) 498.000 1.89694 0.948470 0.316867i \(-0.102631\pi\)
0.948470 + 0.316867i \(0.102631\pi\)
\(42\) 0 0
\(43\) −260.000 −0.922084 −0.461042 0.887378i \(-0.652524\pi\)
−0.461042 + 0.887378i \(0.652524\pi\)
\(44\) 140.000 0.479677
\(45\) 0 0
\(46\) 14.0000 0.0448736
\(47\) −171.000 −0.530700 −0.265350 0.964152i \(-0.585488\pi\)
−0.265350 + 0.964152i \(0.585488\pi\)
\(48\) −16.0000 −0.0481125
\(49\) 0 0
\(50\) 0 0
\(51\) −59.0000 −0.161993
\(52\) 264.000 0.704043
\(53\) 417.000 1.08074 0.540371 0.841427i \(-0.318284\pi\)
0.540371 + 0.841427i \(0.318284\pi\)
\(54\) 106.000 0.267125
\(55\) 0 0
\(56\) 0 0
\(57\) 137.000 0.318353
\(58\) 212.000 0.479948
\(59\) 17.0000 0.0375121 0.0187560 0.999824i \(-0.494029\pi\)
0.0187560 + 0.999824i \(0.494029\pi\)
\(60\) 0 0
\(61\) −51.0000 −0.107047 −0.0535236 0.998567i \(-0.517045\pi\)
−0.0535236 + 0.998567i \(0.517045\pi\)
\(62\) −150.000 −0.307258
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) −70.0000 −0.130552
\(67\) −439.000 −0.800483 −0.400242 0.916410i \(-0.631074\pi\)
−0.400242 + 0.916410i \(0.631074\pi\)
\(68\) 236.000 0.420871
\(69\) −7.00000 −0.0122131
\(70\) 0 0
\(71\) −784.000 −1.31047 −0.655237 0.755423i \(-0.727431\pi\)
−0.655237 + 0.755423i \(0.727431\pi\)
\(72\) −208.000 −0.340459
\(73\) 295.000 0.472974 0.236487 0.971635i \(-0.424004\pi\)
0.236487 + 0.971635i \(0.424004\pi\)
\(74\) −22.0000 −0.0345601
\(75\) 0 0
\(76\) −548.000 −0.827104
\(77\) 0 0
\(78\) −132.000 −0.191616
\(79\) −495.000 −0.704960 −0.352480 0.935819i \(-0.614662\pi\)
−0.352480 + 0.935819i \(0.614662\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 996.000 1.34134
\(83\) 932.000 1.23253 0.616267 0.787537i \(-0.288644\pi\)
0.616267 + 0.787537i \(0.288644\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −520.000 −0.652012
\(87\) −106.000 −0.130625
\(88\) 280.000 0.339183
\(89\) 873.000 1.03975 0.519875 0.854242i \(-0.325978\pi\)
0.519875 + 0.854242i \(0.325978\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 28.0000 0.0317305
\(93\) 75.0000 0.0836251
\(94\) −342.000 −0.375262
\(95\) 0 0
\(96\) −32.0000 −0.0340207
\(97\) −290.000 −0.303557 −0.151779 0.988415i \(-0.548500\pi\)
−0.151779 + 0.988415i \(0.548500\pi\)
\(98\) 0 0
\(99\) −910.000 −0.923823
\(100\) 0 0
\(101\) 1085.00 1.06893 0.534463 0.845192i \(-0.320514\pi\)
0.534463 + 0.845192i \(0.320514\pi\)
\(102\) −118.000 −0.114546
\(103\) 1553.00 1.48565 0.742823 0.669487i \(-0.233486\pi\)
0.742823 + 0.669487i \(0.233486\pi\)
\(104\) 528.000 0.497833
\(105\) 0 0
\(106\) 834.000 0.764200
\(107\) −129.000 −0.116550 −0.0582752 0.998301i \(-0.518560\pi\)
−0.0582752 + 0.998301i \(0.518560\pi\)
\(108\) 212.000 0.188886
\(109\) −965.000 −0.847984 −0.423992 0.905666i \(-0.639372\pi\)
−0.423992 + 0.905666i \(0.639372\pi\)
\(110\) 0 0
\(111\) 11.0000 0.00940607
\(112\) 0 0
\(113\) 50.0000 0.0416248 0.0208124 0.999783i \(-0.493375\pi\)
0.0208124 + 0.999783i \(0.493375\pi\)
\(114\) 274.000 0.225109
\(115\) 0 0
\(116\) 424.000 0.339374
\(117\) −1716.00 −1.35593
\(118\) 34.0000 0.0265250
\(119\) 0 0
\(120\) 0 0
\(121\) −106.000 −0.0796394
\(122\) −102.000 −0.0756938
\(123\) −498.000 −0.365066
\(124\) −300.000 −0.217264
\(125\) 0 0
\(126\) 0 0
\(127\) −936.000 −0.653989 −0.326994 0.945026i \(-0.606036\pi\)
−0.326994 + 0.945026i \(0.606036\pi\)
\(128\) 128.000 0.0883883
\(129\) 260.000 0.177455
\(130\) 0 0
\(131\) 755.000 0.503547 0.251773 0.967786i \(-0.418986\pi\)
0.251773 + 0.967786i \(0.418986\pi\)
\(132\) −140.000 −0.0923139
\(133\) 0 0
\(134\) −878.000 −0.566027
\(135\) 0 0
\(136\) 472.000 0.297600
\(137\) 2357.00 1.46987 0.734935 0.678138i \(-0.237213\pi\)
0.734935 + 0.678138i \(0.237213\pi\)
\(138\) −14.0000 −0.00863594
\(139\) −28.0000 −0.0170858 −0.00854291 0.999964i \(-0.502719\pi\)
−0.00854291 + 0.999964i \(0.502719\pi\)
\(140\) 0 0
\(141\) 171.000 0.102133
\(142\) −1568.00 −0.926645
\(143\) 2310.00 1.35085
\(144\) −416.000 −0.240741
\(145\) 0 0
\(146\) 590.000 0.334443
\(147\) 0 0
\(148\) −44.0000 −0.0244377
\(149\) 2295.00 1.26184 0.630919 0.775849i \(-0.282678\pi\)
0.630919 + 0.775849i \(0.282678\pi\)
\(150\) 0 0
\(151\) −1109.00 −0.597676 −0.298838 0.954304i \(-0.596599\pi\)
−0.298838 + 0.954304i \(0.596599\pi\)
\(152\) −1096.00 −0.584851
\(153\) −1534.00 −0.810566
\(154\) 0 0
\(155\) 0 0
\(156\) −264.000 −0.135493
\(157\) 1559.00 0.792495 0.396248 0.918144i \(-0.370312\pi\)
0.396248 + 0.918144i \(0.370312\pi\)
\(158\) −990.000 −0.498482
\(159\) −417.000 −0.207989
\(160\) 0 0
\(161\) 0 0
\(162\) 1298.00 0.629509
\(163\) 2251.00 1.08167 0.540834 0.841129i \(-0.318109\pi\)
0.540834 + 0.841129i \(0.318109\pi\)
\(164\) 1992.00 0.948470
\(165\) 0 0
\(166\) 1864.00 0.871533
\(167\) 2788.00 1.29187 0.645934 0.763393i \(-0.276468\pi\)
0.645934 + 0.763393i \(0.276468\pi\)
\(168\) 0 0
\(169\) 2159.00 0.982704
\(170\) 0 0
\(171\) 3562.00 1.59294
\(172\) −1040.00 −0.461042
\(173\) 1579.00 0.693926 0.346963 0.937879i \(-0.387213\pi\)
0.346963 + 0.937879i \(0.387213\pi\)
\(174\) −212.000 −0.0923660
\(175\) 0 0
\(176\) 560.000 0.239839
\(177\) −17.0000 −0.00721920
\(178\) 1746.00 0.735215
\(179\) 2451.00 1.02344 0.511722 0.859151i \(-0.329008\pi\)
0.511722 + 0.859151i \(0.329008\pi\)
\(180\) 0 0
\(181\) 1170.00 0.480472 0.240236 0.970715i \(-0.422775\pi\)
0.240236 + 0.970715i \(0.422775\pi\)
\(182\) 0 0
\(183\) 51.0000 0.0206012
\(184\) 56.0000 0.0224368
\(185\) 0 0
\(186\) 150.000 0.0591319
\(187\) 2065.00 0.807528
\(188\) −684.000 −0.265350
\(189\) 0 0
\(190\) 0 0
\(191\) −1275.00 −0.483014 −0.241507 0.970399i \(-0.577642\pi\)
−0.241507 + 0.970399i \(0.577642\pi\)
\(192\) −64.0000 −0.0240563
\(193\) −35.0000 −0.0130537 −0.00652683 0.999979i \(-0.502078\pi\)
−0.00652683 + 0.999979i \(0.502078\pi\)
\(194\) −580.000 −0.214647
\(195\) 0 0
\(196\) 0 0
\(197\) 2734.00 0.988779 0.494389 0.869241i \(-0.335392\pi\)
0.494389 + 0.869241i \(0.335392\pi\)
\(198\) −1820.00 −0.653241
\(199\) −2243.00 −0.799005 −0.399503 0.916732i \(-0.630817\pi\)
−0.399503 + 0.916732i \(0.630817\pi\)
\(200\) 0 0
\(201\) 439.000 0.154053
\(202\) 2170.00 0.755845
\(203\) 0 0
\(204\) −236.000 −0.0809966
\(205\) 0 0
\(206\) 3106.00 1.05051
\(207\) −182.000 −0.0611105
\(208\) 1056.00 0.352021
\(209\) −4795.00 −1.58697
\(210\) 0 0
\(211\) 1172.00 0.382388 0.191194 0.981552i \(-0.438764\pi\)
0.191194 + 0.981552i \(0.438764\pi\)
\(212\) 1668.00 0.540371
\(213\) 784.000 0.252201
\(214\) −258.000 −0.0824136
\(215\) 0 0
\(216\) 424.000 0.133563
\(217\) 0 0
\(218\) −1930.00 −0.599615
\(219\) −295.000 −0.0910240
\(220\) 0 0
\(221\) 3894.00 1.18524
\(222\) 22.0000 0.00665110
\(223\) 2024.00 0.607790 0.303895 0.952706i \(-0.401713\pi\)
0.303895 + 0.952706i \(0.401713\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 100.000 0.0294332
\(227\) 2571.00 0.751732 0.375866 0.926674i \(-0.377345\pi\)
0.375866 + 0.926674i \(0.377345\pi\)
\(228\) 548.000 0.159176
\(229\) −895.000 −0.258268 −0.129134 0.991627i \(-0.541220\pi\)
−0.129134 + 0.991627i \(0.541220\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 848.000 0.239974
\(233\) −1787.00 −0.502447 −0.251224 0.967929i \(-0.580833\pi\)
−0.251224 + 0.967929i \(0.580833\pi\)
\(234\) −3432.00 −0.958790
\(235\) 0 0
\(236\) 68.0000 0.0187560
\(237\) 495.000 0.135670
\(238\) 0 0
\(239\) −5100.00 −1.38030 −0.690150 0.723667i \(-0.742455\pi\)
−0.690150 + 0.723667i \(0.742455\pi\)
\(240\) 0 0
\(241\) 4177.00 1.11645 0.558225 0.829690i \(-0.311483\pi\)
0.558225 + 0.829690i \(0.311483\pi\)
\(242\) −212.000 −0.0563135
\(243\) −2080.00 −0.549103
\(244\) −204.000 −0.0535236
\(245\) 0 0
\(246\) −996.000 −0.258141
\(247\) −9042.00 −2.32927
\(248\) −600.000 −0.153629
\(249\) −932.000 −0.237201
\(250\) 0 0
\(251\) 4680.00 1.17689 0.588444 0.808538i \(-0.299741\pi\)
0.588444 + 0.808538i \(0.299741\pi\)
\(252\) 0 0
\(253\) 245.000 0.0608815
\(254\) −1872.00 −0.462440
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −1749.00 −0.424512 −0.212256 0.977214i \(-0.568081\pi\)
−0.212256 + 0.977214i \(0.568081\pi\)
\(258\) 520.000 0.125480
\(259\) 0 0
\(260\) 0 0
\(261\) −2756.00 −0.653610
\(262\) 1510.00 0.356061
\(263\) 4473.00 1.04873 0.524367 0.851492i \(-0.324302\pi\)
0.524367 + 0.851492i \(0.324302\pi\)
\(264\) −280.000 −0.0652758
\(265\) 0 0
\(266\) 0 0
\(267\) −873.000 −0.200100
\(268\) −1756.00 −0.400242
\(269\) −1975.00 −0.447650 −0.223825 0.974629i \(-0.571854\pi\)
−0.223825 + 0.974629i \(0.571854\pi\)
\(270\) 0 0
\(271\) 8439.00 1.89163 0.945817 0.324701i \(-0.105264\pi\)
0.945817 + 0.324701i \(0.105264\pi\)
\(272\) 944.000 0.210435
\(273\) 0 0
\(274\) 4714.00 1.03935
\(275\) 0 0
\(276\) −28.0000 −0.00610653
\(277\) −527.000 −0.114312 −0.0571559 0.998365i \(-0.518203\pi\)
−0.0571559 + 0.998365i \(0.518203\pi\)
\(278\) −56.0000 −0.0120815
\(279\) 1950.00 0.418435
\(280\) 0 0
\(281\) −202.000 −0.0428837 −0.0214418 0.999770i \(-0.506826\pi\)
−0.0214418 + 0.999770i \(0.506826\pi\)
\(282\) 342.000 0.0722192
\(283\) −7949.00 −1.66968 −0.834839 0.550494i \(-0.814439\pi\)
−0.834839 + 0.550494i \(0.814439\pi\)
\(284\) −3136.00 −0.655237
\(285\) 0 0
\(286\) 4620.00 0.955197
\(287\) 0 0
\(288\) −832.000 −0.170229
\(289\) −1432.00 −0.291472
\(290\) 0 0
\(291\) 290.000 0.0584196
\(292\) 1180.00 0.236487
\(293\) 318.000 0.0634053 0.0317027 0.999497i \(-0.489907\pi\)
0.0317027 + 0.999497i \(0.489907\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −88.0000 −0.0172801
\(297\) 1855.00 0.362418
\(298\) 4590.00 0.892254
\(299\) 462.000 0.0893584
\(300\) 0 0
\(301\) 0 0
\(302\) −2218.00 −0.422621
\(303\) −1085.00 −0.205715
\(304\) −2192.00 −0.413552
\(305\) 0 0
\(306\) −3068.00 −0.573156
\(307\) −8132.00 −1.51178 −0.755892 0.654696i \(-0.772797\pi\)
−0.755892 + 0.654696i \(0.772797\pi\)
\(308\) 0 0
\(309\) −1553.00 −0.285913
\(310\) 0 0
\(311\) 929.000 0.169385 0.0846925 0.996407i \(-0.473009\pi\)
0.0846925 + 0.996407i \(0.473009\pi\)
\(312\) −528.000 −0.0958081
\(313\) −209.000 −0.0377424 −0.0188712 0.999822i \(-0.506007\pi\)
−0.0188712 + 0.999822i \(0.506007\pi\)
\(314\) 3118.00 0.560379
\(315\) 0 0
\(316\) −1980.00 −0.352480
\(317\) −7131.00 −1.26346 −0.631730 0.775188i \(-0.717655\pi\)
−0.631730 + 0.775188i \(0.717655\pi\)
\(318\) −834.000 −0.147070
\(319\) 3710.00 0.651160
\(320\) 0 0
\(321\) 129.000 0.0224301
\(322\) 0 0
\(323\) −8083.00 −1.39242
\(324\) 2596.00 0.445130
\(325\) 0 0
\(326\) 4502.00 0.764855
\(327\) 965.000 0.163195
\(328\) 3984.00 0.670670
\(329\) 0 0
\(330\) 0 0
\(331\) −6571.00 −1.09116 −0.545581 0.838058i \(-0.683691\pi\)
−0.545581 + 0.838058i \(0.683691\pi\)
\(332\) 3728.00 0.616267
\(333\) 286.000 0.0470652
\(334\) 5576.00 0.913488
\(335\) 0 0
\(336\) 0 0
\(337\) 11466.0 1.85339 0.926696 0.375813i \(-0.122636\pi\)
0.926696 + 0.375813i \(0.122636\pi\)
\(338\) 4318.00 0.694876
\(339\) −50.0000 −0.00801070
\(340\) 0 0
\(341\) −2625.00 −0.416867
\(342\) 7124.00 1.12638
\(343\) 0 0
\(344\) −2080.00 −0.326006
\(345\) 0 0
\(346\) 3158.00 0.490680
\(347\) 9777.00 1.51256 0.756278 0.654251i \(-0.227016\pi\)
0.756278 + 0.654251i \(0.227016\pi\)
\(348\) −424.000 −0.0653126
\(349\) −11914.0 −1.82734 −0.913670 0.406456i \(-0.866764\pi\)
−0.913670 + 0.406456i \(0.866764\pi\)
\(350\) 0 0
\(351\) 3498.00 0.531936
\(352\) 1120.00 0.169591
\(353\) 9123.00 1.37555 0.687774 0.725925i \(-0.258588\pi\)
0.687774 + 0.725925i \(0.258588\pi\)
\(354\) −34.0000 −0.00510474
\(355\) 0 0
\(356\) 3492.00 0.519875
\(357\) 0 0
\(358\) 4902.00 0.723684
\(359\) 8149.00 1.19802 0.599008 0.800743i \(-0.295562\pi\)
0.599008 + 0.800743i \(0.295562\pi\)
\(360\) 0 0
\(361\) 11910.0 1.73640
\(362\) 2340.00 0.339745
\(363\) 106.000 0.0153266
\(364\) 0 0
\(365\) 0 0
\(366\) 102.000 0.0145673
\(367\) 9671.00 1.37554 0.687769 0.725930i \(-0.258590\pi\)
0.687769 + 0.725930i \(0.258590\pi\)
\(368\) 112.000 0.0158652
\(369\) −12948.0 −1.82668
\(370\) 0 0
\(371\) 0 0
\(372\) 300.000 0.0418126
\(373\) 4109.00 0.570391 0.285196 0.958469i \(-0.407941\pi\)
0.285196 + 0.958469i \(0.407941\pi\)
\(374\) 4130.00 0.571009
\(375\) 0 0
\(376\) −1368.00 −0.187631
\(377\) 6996.00 0.955736
\(378\) 0 0
\(379\) −3488.00 −0.472735 −0.236367 0.971664i \(-0.575957\pi\)
−0.236367 + 0.971664i \(0.575957\pi\)
\(380\) 0 0
\(381\) 936.000 0.125860
\(382\) −2550.00 −0.341543
\(383\) 8717.00 1.16297 0.581485 0.813557i \(-0.302472\pi\)
0.581485 + 0.813557i \(0.302472\pi\)
\(384\) −128.000 −0.0170103
\(385\) 0 0
\(386\) −70.0000 −0.00923033
\(387\) 6760.00 0.887933
\(388\) −1160.00 −0.151779
\(389\) 163.000 0.0212453 0.0106227 0.999944i \(-0.496619\pi\)
0.0106227 + 0.999944i \(0.496619\pi\)
\(390\) 0 0
\(391\) 413.000 0.0534177
\(392\) 0 0
\(393\) −755.000 −0.0969077
\(394\) 5468.00 0.699172
\(395\) 0 0
\(396\) −3640.00 −0.461911
\(397\) 999.000 0.126293 0.0631466 0.998004i \(-0.479886\pi\)
0.0631466 + 0.998004i \(0.479886\pi\)
\(398\) −4486.00 −0.564982
\(399\) 0 0
\(400\) 0 0
\(401\) −14757.0 −1.83773 −0.918865 0.394573i \(-0.870893\pi\)
−0.918865 + 0.394573i \(0.870893\pi\)
\(402\) 878.000 0.108932
\(403\) −4950.00 −0.611854
\(404\) 4340.00 0.534463
\(405\) 0 0
\(406\) 0 0
\(407\) −385.000 −0.0468888
\(408\) −472.000 −0.0572732
\(409\) 133.000 0.0160793 0.00803964 0.999968i \(-0.497441\pi\)
0.00803964 + 0.999968i \(0.497441\pi\)
\(410\) 0 0
\(411\) −2357.00 −0.282876
\(412\) 6212.00 0.742823
\(413\) 0 0
\(414\) −364.000 −0.0432117
\(415\) 0 0
\(416\) 2112.00 0.248917
\(417\) 28.0000 0.00328817
\(418\) −9590.00 −1.12216
\(419\) 6420.00 0.748538 0.374269 0.927320i \(-0.377894\pi\)
0.374269 + 0.927320i \(0.377894\pi\)
\(420\) 0 0
\(421\) 10266.0 1.18844 0.594221 0.804302i \(-0.297460\pi\)
0.594221 + 0.804302i \(0.297460\pi\)
\(422\) 2344.00 0.270389
\(423\) 4446.00 0.511045
\(424\) 3336.00 0.382100
\(425\) 0 0
\(426\) 1568.00 0.178333
\(427\) 0 0
\(428\) −516.000 −0.0582752
\(429\) −2310.00 −0.259972
\(430\) 0 0
\(431\) −15213.0 −1.70020 −0.850098 0.526625i \(-0.823457\pi\)
−0.850098 + 0.526625i \(0.823457\pi\)
\(432\) 848.000 0.0944431
\(433\) −1378.00 −0.152939 −0.0764693 0.997072i \(-0.524365\pi\)
−0.0764693 + 0.997072i \(0.524365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3860.00 −0.423992
\(437\) −959.000 −0.104978
\(438\) −590.000 −0.0643637
\(439\) 2763.00 0.300389 0.150195 0.988656i \(-0.452010\pi\)
0.150195 + 0.988656i \(0.452010\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 7788.00 0.838094
\(443\) −5849.00 −0.627301 −0.313651 0.949538i \(-0.601552\pi\)
−0.313651 + 0.949538i \(0.601552\pi\)
\(444\) 44.0000 0.00470304
\(445\) 0 0
\(446\) 4048.00 0.429772
\(447\) −2295.00 −0.242841
\(448\) 0 0
\(449\) 4582.00 0.481599 0.240799 0.970575i \(-0.422590\pi\)
0.240799 + 0.970575i \(0.422590\pi\)
\(450\) 0 0
\(451\) 17430.0 1.81984
\(452\) 200.000 0.0208124
\(453\) 1109.00 0.115023
\(454\) 5142.00 0.531555
\(455\) 0 0
\(456\) 1096.00 0.112555
\(457\) −11551.0 −1.18235 −0.591174 0.806544i \(-0.701335\pi\)
−0.591174 + 0.806544i \(0.701335\pi\)
\(458\) −1790.00 −0.182623
\(459\) 3127.00 0.317987
\(460\) 0 0
\(461\) 9494.00 0.959175 0.479587 0.877494i \(-0.340786\pi\)
0.479587 + 0.877494i \(0.340786\pi\)
\(462\) 0 0
\(463\) 10160.0 1.01982 0.509908 0.860229i \(-0.329679\pi\)
0.509908 + 0.860229i \(0.329679\pi\)
\(464\) 1696.00 0.169687
\(465\) 0 0
\(466\) −3574.00 −0.355284
\(467\) −1307.00 −0.129509 −0.0647545 0.997901i \(-0.520626\pi\)
−0.0647545 + 0.997901i \(0.520626\pi\)
\(468\) −6864.00 −0.677967
\(469\) 0 0
\(470\) 0 0
\(471\) −1559.00 −0.152516
\(472\) 136.000 0.0132625
\(473\) −9100.00 −0.884606
\(474\) 990.000 0.0959329
\(475\) 0 0
\(476\) 0 0
\(477\) −10842.0 −1.04072
\(478\) −10200.0 −0.976019
\(479\) −18287.0 −1.74437 −0.872186 0.489174i \(-0.837298\pi\)
−0.872186 + 0.489174i \(0.837298\pi\)
\(480\) 0 0
\(481\) −726.000 −0.0688207
\(482\) 8354.00 0.789449
\(483\) 0 0
\(484\) −424.000 −0.0398197
\(485\) 0 0
\(486\) −4160.00 −0.388275
\(487\) 14953.0 1.39135 0.695673 0.718359i \(-0.255106\pi\)
0.695673 + 0.718359i \(0.255106\pi\)
\(488\) −408.000 −0.0378469
\(489\) −2251.00 −0.208167
\(490\) 0 0
\(491\) 14352.0 1.31914 0.659569 0.751644i \(-0.270739\pi\)
0.659569 + 0.751644i \(0.270739\pi\)
\(492\) −1992.00 −0.182533
\(493\) 6254.00 0.571331
\(494\) −18084.0 −1.64704
\(495\) 0 0
\(496\) −1200.00 −0.108632
\(497\) 0 0
\(498\) −1864.00 −0.167727
\(499\) −5531.00 −0.496196 −0.248098 0.968735i \(-0.579805\pi\)
−0.248098 + 0.968735i \(0.579805\pi\)
\(500\) 0 0
\(501\) −2788.00 −0.248620
\(502\) 9360.00 0.832186
\(503\) 8400.00 0.744607 0.372304 0.928111i \(-0.378568\pi\)
0.372304 + 0.928111i \(0.378568\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 490.000 0.0430497
\(507\) −2159.00 −0.189121
\(508\) −3744.00 −0.326994
\(509\) 2385.00 0.207688 0.103844 0.994594i \(-0.466886\pi\)
0.103844 + 0.994594i \(0.466886\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −7261.00 −0.624914
\(514\) −3498.00 −0.300175
\(515\) 0 0
\(516\) 1040.00 0.0887276
\(517\) −5985.00 −0.509130
\(518\) 0 0
\(519\) −1579.00 −0.133546
\(520\) 0 0
\(521\) 9153.00 0.769674 0.384837 0.922985i \(-0.374258\pi\)
0.384837 + 0.922985i \(0.374258\pi\)
\(522\) −5512.00 −0.462172
\(523\) −13807.0 −1.15437 −0.577187 0.816612i \(-0.695850\pi\)
−0.577187 + 0.816612i \(0.695850\pi\)
\(524\) 3020.00 0.251773
\(525\) 0 0
\(526\) 8946.00 0.741567
\(527\) −4425.00 −0.365761
\(528\) −560.000 −0.0461570
\(529\) −12118.0 −0.995973
\(530\) 0 0
\(531\) −442.000 −0.0361227
\(532\) 0 0
\(533\) 32868.0 2.67105
\(534\) −1746.00 −0.141492
\(535\) 0 0
\(536\) −3512.00 −0.283014
\(537\) −2451.00 −0.196962
\(538\) −3950.00 −0.316536
\(539\) 0 0
\(540\) 0 0
\(541\) 8175.00 0.649669 0.324834 0.945771i \(-0.394691\pi\)
0.324834 + 0.945771i \(0.394691\pi\)
\(542\) 16878.0 1.33759
\(543\) −1170.00 −0.0924669
\(544\) 1888.00 0.148800
\(545\) 0 0
\(546\) 0 0
\(547\) −4656.00 −0.363942 −0.181971 0.983304i \(-0.558248\pi\)
−0.181971 + 0.983304i \(0.558248\pi\)
\(548\) 9428.00 0.734935
\(549\) 1326.00 0.103083
\(550\) 0 0
\(551\) −14522.0 −1.12279
\(552\) −56.0000 −0.00431797
\(553\) 0 0
\(554\) −1054.00 −0.0808306
\(555\) 0 0
\(556\) −112.000 −0.00854291
\(557\) −7003.00 −0.532723 −0.266361 0.963873i \(-0.585821\pi\)
−0.266361 + 0.963873i \(0.585821\pi\)
\(558\) 3900.00 0.295878
\(559\) −17160.0 −1.29837
\(560\) 0 0
\(561\) −2065.00 −0.155409
\(562\) −404.000 −0.0303233
\(563\) −19753.0 −1.47867 −0.739334 0.673339i \(-0.764859\pi\)
−0.739334 + 0.673339i \(0.764859\pi\)
\(564\) 684.000 0.0510667
\(565\) 0 0
\(566\) −15898.0 −1.18064
\(567\) 0 0
\(568\) −6272.00 −0.463323
\(569\) −6897.00 −0.508150 −0.254075 0.967185i \(-0.581771\pi\)
−0.254075 + 0.967185i \(0.581771\pi\)
\(570\) 0 0
\(571\) 24915.0 1.82603 0.913013 0.407932i \(-0.133750\pi\)
0.913013 + 0.407932i \(0.133750\pi\)
\(572\) 9240.00 0.675426
\(573\) 1275.00 0.0929562
\(574\) 0 0
\(575\) 0 0
\(576\) −1664.00 −0.120370
\(577\) 127.000 0.00916305 0.00458152 0.999990i \(-0.498542\pi\)
0.00458152 + 0.999990i \(0.498542\pi\)
\(578\) −2864.00 −0.206102
\(579\) 35.0000 0.00251218
\(580\) 0 0
\(581\) 0 0
\(582\) 580.000 0.0413089
\(583\) 14595.0 1.03681
\(584\) 2360.00 0.167222
\(585\) 0 0
\(586\) 636.000 0.0448343
\(587\) 9044.00 0.635921 0.317961 0.948104i \(-0.397002\pi\)
0.317961 + 0.948104i \(0.397002\pi\)
\(588\) 0 0
\(589\) 10275.0 0.718801
\(590\) 0 0
\(591\) −2734.00 −0.190291
\(592\) −176.000 −0.0122188
\(593\) −10701.0 −0.741041 −0.370521 0.928824i \(-0.620821\pi\)
−0.370521 + 0.928824i \(0.620821\pi\)
\(594\) 3710.00 0.256268
\(595\) 0 0
\(596\) 9180.00 0.630919
\(597\) 2243.00 0.153769
\(598\) 924.000 0.0631859
\(599\) 20799.0 1.41874 0.709369 0.704837i \(-0.248980\pi\)
0.709369 + 0.704837i \(0.248980\pi\)
\(600\) 0 0
\(601\) 1402.00 0.0951560 0.0475780 0.998868i \(-0.484850\pi\)
0.0475780 + 0.998868i \(0.484850\pi\)
\(602\) 0 0
\(603\) 11414.0 0.770836
\(604\) −4436.00 −0.298838
\(605\) 0 0
\(606\) −2170.00 −0.145462
\(607\) 6525.00 0.436312 0.218156 0.975914i \(-0.429996\pi\)
0.218156 + 0.975914i \(0.429996\pi\)
\(608\) −4384.00 −0.292425
\(609\) 0 0
\(610\) 0 0
\(611\) −11286.0 −0.747271
\(612\) −6136.00 −0.405283
\(613\) −15051.0 −0.991687 −0.495844 0.868412i \(-0.665141\pi\)
−0.495844 + 0.868412i \(0.665141\pi\)
\(614\) −16264.0 −1.06899
\(615\) 0 0
\(616\) 0 0
\(617\) −11150.0 −0.727524 −0.363762 0.931492i \(-0.618508\pi\)
−0.363762 + 0.931492i \(0.618508\pi\)
\(618\) −3106.00 −0.202171
\(619\) −3415.00 −0.221745 −0.110873 0.993835i \(-0.535365\pi\)
−0.110873 + 0.993835i \(0.535365\pi\)
\(620\) 0 0
\(621\) 371.000 0.0239738
\(622\) 1858.00 0.119773
\(623\) 0 0
\(624\) −1056.00 −0.0677465
\(625\) 0 0
\(626\) −418.000 −0.0266879
\(627\) 4795.00 0.305413
\(628\) 6236.00 0.396248
\(629\) −649.000 −0.0411404
\(630\) 0 0
\(631\) −21184.0 −1.33648 −0.668242 0.743944i \(-0.732953\pi\)
−0.668242 + 0.743944i \(0.732953\pi\)
\(632\) −3960.00 −0.249241
\(633\) −1172.00 −0.0735905
\(634\) −14262.0 −0.893401
\(635\) 0 0
\(636\) −1668.00 −0.103995
\(637\) 0 0
\(638\) 7420.00 0.460440
\(639\) 20384.0 1.26194
\(640\) 0 0
\(641\) −10705.0 −0.659629 −0.329814 0.944046i \(-0.606986\pi\)
−0.329814 + 0.944046i \(0.606986\pi\)
\(642\) 258.000 0.0158605
\(643\) 6860.00 0.420734 0.210367 0.977622i \(-0.432534\pi\)
0.210367 + 0.977622i \(0.432534\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −16166.0 −0.984586
\(647\) 14463.0 0.878824 0.439412 0.898286i \(-0.355187\pi\)
0.439412 + 0.898286i \(0.355187\pi\)
\(648\) 5192.00 0.314755
\(649\) 595.000 0.0359874
\(650\) 0 0
\(651\) 0 0
\(652\) 9004.00 0.540834
\(653\) −5979.00 −0.358310 −0.179155 0.983821i \(-0.557336\pi\)
−0.179155 + 0.983821i \(0.557336\pi\)
\(654\) 1930.00 0.115396
\(655\) 0 0
\(656\) 7968.00 0.474235
\(657\) −7670.00 −0.455457
\(658\) 0 0
\(659\) −6940.00 −0.410234 −0.205117 0.978737i \(-0.565757\pi\)
−0.205117 + 0.978737i \(0.565757\pi\)
\(660\) 0 0
\(661\) −13399.0 −0.788443 −0.394221 0.919015i \(-0.628986\pi\)
−0.394221 + 0.919015i \(0.628986\pi\)
\(662\) −13142.0 −0.771568
\(663\) −3894.00 −0.228100
\(664\) 7456.00 0.435766
\(665\) 0 0
\(666\) 572.000 0.0332801
\(667\) 742.000 0.0430740
\(668\) 11152.0 0.645934
\(669\) −2024.00 −0.116969
\(670\) 0 0
\(671\) −1785.00 −0.102696
\(672\) 0 0
\(673\) −29510.0 −1.69023 −0.845117 0.534582i \(-0.820469\pi\)
−0.845117 + 0.534582i \(0.820469\pi\)
\(674\) 22932.0 1.31055
\(675\) 0 0
\(676\) 8636.00 0.491352
\(677\) −26001.0 −1.47607 −0.738035 0.674762i \(-0.764246\pi\)
−0.738035 + 0.674762i \(0.764246\pi\)
\(678\) −100.000 −0.00566442
\(679\) 0 0
\(680\) 0 0
\(681\) −2571.00 −0.144671
\(682\) −5250.00 −0.294770
\(683\) 8805.00 0.493285 0.246643 0.969106i \(-0.420673\pi\)
0.246643 + 0.969106i \(0.420673\pi\)
\(684\) 14248.0 0.796471
\(685\) 0 0
\(686\) 0 0
\(687\) 895.000 0.0497036
\(688\) −4160.00 −0.230521
\(689\) 27522.0 1.52178
\(690\) 0 0
\(691\) −28685.0 −1.57920 −0.789601 0.613620i \(-0.789713\pi\)
−0.789601 + 0.613620i \(0.789713\pi\)
\(692\) 6316.00 0.346963
\(693\) 0 0
\(694\) 19554.0 1.06954
\(695\) 0 0
\(696\) −848.000 −0.0461830
\(697\) 29382.0 1.59673
\(698\) −23828.0 −1.29212
\(699\) 1787.00 0.0966961
\(700\) 0 0
\(701\) −3146.00 −0.169505 −0.0847523 0.996402i \(-0.527010\pi\)
−0.0847523 + 0.996402i \(0.527010\pi\)
\(702\) 6996.00 0.376135
\(703\) 1507.00 0.0808500
\(704\) 2240.00 0.119919
\(705\) 0 0
\(706\) 18246.0 0.972659
\(707\) 0 0
\(708\) −68.0000 −0.00360960
\(709\) 1259.00 0.0666893 0.0333447 0.999444i \(-0.489384\pi\)
0.0333447 + 0.999444i \(0.489384\pi\)
\(710\) 0 0
\(711\) 12870.0 0.678851
\(712\) 6984.00 0.367607
\(713\) −525.000 −0.0275756
\(714\) 0 0
\(715\) 0 0
\(716\) 9804.00 0.511722
\(717\) 5100.00 0.265639
\(718\) 16298.0 0.847125
\(719\) −16425.0 −0.851946 −0.425973 0.904736i \(-0.640068\pi\)
−0.425973 + 0.904736i \(0.640068\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 23820.0 1.22782
\(723\) −4177.00 −0.214861
\(724\) 4680.00 0.240236
\(725\) 0 0
\(726\) 212.000 0.0108375
\(727\) −6032.00 −0.307723 −0.153861 0.988092i \(-0.549171\pi\)
−0.153861 + 0.988092i \(0.549171\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) −15340.0 −0.776156
\(732\) 204.000 0.0103006
\(733\) 15243.0 0.768094 0.384047 0.923314i \(-0.374530\pi\)
0.384047 + 0.923314i \(0.374530\pi\)
\(734\) 19342.0 0.972652
\(735\) 0 0
\(736\) 224.000 0.0112184
\(737\) −15365.0 −0.767947
\(738\) −25896.0 −1.29166
\(739\) −10053.0 −0.500414 −0.250207 0.968192i \(-0.580499\pi\)
−0.250207 + 0.968192i \(0.580499\pi\)
\(740\) 0 0
\(741\) 9042.00 0.448267
\(742\) 0 0
\(743\) −24384.0 −1.20399 −0.601993 0.798501i \(-0.705627\pi\)
−0.601993 + 0.798501i \(0.705627\pi\)
\(744\) 600.000 0.0295660
\(745\) 0 0
\(746\) 8218.00 0.403328
\(747\) −24232.0 −1.18688
\(748\) 8260.00 0.403764
\(749\) 0 0
\(750\) 0 0
\(751\) 11589.0 0.563101 0.281550 0.959546i \(-0.409151\pi\)
0.281550 + 0.959546i \(0.409151\pi\)
\(752\) −2736.00 −0.132675
\(753\) −4680.00 −0.226492
\(754\) 13992.0 0.675807
\(755\) 0 0
\(756\) 0 0
\(757\) −14562.0 −0.699161 −0.349581 0.936906i \(-0.613676\pi\)
−0.349581 + 0.936906i \(0.613676\pi\)
\(758\) −6976.00 −0.334274
\(759\) −245.000 −0.0117166
\(760\) 0 0
\(761\) 22765.0 1.08440 0.542201 0.840249i \(-0.317591\pi\)
0.542201 + 0.840249i \(0.317591\pi\)
\(762\) 1872.00 0.0889966
\(763\) 0 0
\(764\) −5100.00 −0.241507
\(765\) 0 0
\(766\) 17434.0 0.822345
\(767\) 1122.00 0.0528202
\(768\) −256.000 −0.0120281
\(769\) −3766.00 −0.176600 −0.0883000 0.996094i \(-0.528143\pi\)
−0.0883000 + 0.996094i \(0.528143\pi\)
\(770\) 0 0
\(771\) 1749.00 0.0816974
\(772\) −140.000 −0.00652683
\(773\) −26861.0 −1.24984 −0.624918 0.780691i \(-0.714868\pi\)
−0.624918 + 0.780691i \(0.714868\pi\)
\(774\) 13520.0 0.627864
\(775\) 0 0
\(776\) −2320.00 −0.107324
\(777\) 0 0
\(778\) 326.000 0.0150227
\(779\) −68226.0 −3.13793
\(780\) 0 0
\(781\) −27440.0 −1.25721
\(782\) 826.000 0.0377720
\(783\) 5618.00 0.256412
\(784\) 0 0
\(785\) 0 0
\(786\) −1510.00 −0.0685241
\(787\) −2097.00 −0.0949809 −0.0474905 0.998872i \(-0.515122\pi\)
−0.0474905 + 0.998872i \(0.515122\pi\)
\(788\) 10936.0 0.494389
\(789\) −4473.00 −0.201829
\(790\) 0 0
\(791\) 0 0
\(792\) −7280.00 −0.326621
\(793\) −3366.00 −0.150732
\(794\) 1998.00 0.0893027
\(795\) 0 0
\(796\) −8972.00 −0.399503
\(797\) −35334.0 −1.57038 −0.785191 0.619254i \(-0.787435\pi\)
−0.785191 + 0.619254i \(0.787435\pi\)
\(798\) 0 0
\(799\) −10089.0 −0.446712
\(800\) 0 0
\(801\) −22698.0 −1.00124
\(802\) −29514.0 −1.29947
\(803\) 10325.0 0.453750
\(804\) 1756.00 0.0770265
\(805\) 0 0
\(806\) −9900.00 −0.432646
\(807\) 1975.00 0.0861503
\(808\) 8680.00 0.377922
\(809\) 42535.0 1.84852 0.924259 0.381766i \(-0.124684\pi\)
0.924259 + 0.381766i \(0.124684\pi\)
\(810\) 0 0
\(811\) −30676.0 −1.32821 −0.664106 0.747638i \(-0.731188\pi\)
−0.664106 + 0.747638i \(0.731188\pi\)
\(812\) 0 0
\(813\) −8439.00 −0.364045
\(814\) −770.000 −0.0331554
\(815\) 0 0
\(816\) −944.000 −0.0404983
\(817\) 35620.0 1.52532
\(818\) 266.000 0.0113698
\(819\) 0 0
\(820\) 0 0
\(821\) 37343.0 1.58743 0.793715 0.608290i \(-0.208144\pi\)
0.793715 + 0.608290i \(0.208144\pi\)
\(822\) −4714.00 −0.200024
\(823\) −2815.00 −0.119228 −0.0596141 0.998222i \(-0.518987\pi\)
−0.0596141 + 0.998222i \(0.518987\pi\)
\(824\) 12424.0 0.525256
\(825\) 0 0
\(826\) 0 0
\(827\) 9276.00 0.390034 0.195017 0.980800i \(-0.437524\pi\)
0.195017 + 0.980800i \(0.437524\pi\)
\(828\) −728.000 −0.0305553
\(829\) −18571.0 −0.778043 −0.389021 0.921229i \(-0.627187\pi\)
−0.389021 + 0.921229i \(0.627187\pi\)
\(830\) 0 0
\(831\) 527.000 0.0219993
\(832\) 4224.00 0.176011
\(833\) 0 0
\(834\) 56.0000 0.00232509
\(835\) 0 0
\(836\) −19180.0 −0.793486
\(837\) −3975.00 −0.164153
\(838\) 12840.0 0.529296
\(839\) −29048.0 −1.19529 −0.597645 0.801761i \(-0.703897\pi\)
−0.597645 + 0.801761i \(0.703897\pi\)
\(840\) 0 0
\(841\) −13153.0 −0.539301
\(842\) 20532.0 0.840356
\(843\) 202.000 0.00825297
\(844\) 4688.00 0.191194
\(845\) 0 0
\(846\) 8892.00 0.361363
\(847\) 0 0
\(848\) 6672.00 0.270186
\(849\) 7949.00 0.321330
\(850\) 0 0
\(851\) −77.0000 −0.00310168
\(852\) 3136.00 0.126100
\(853\) 32090.0 1.28809 0.644045 0.764988i \(-0.277255\pi\)
0.644045 + 0.764988i \(0.277255\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1032.00 −0.0412068
\(857\) −24537.0 −0.978026 −0.489013 0.872277i \(-0.662643\pi\)
−0.489013 + 0.872277i \(0.662643\pi\)
\(858\) −4620.00 −0.183828
\(859\) −20825.0 −0.827171 −0.413585 0.910465i \(-0.635724\pi\)
−0.413585 + 0.910465i \(0.635724\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −30426.0 −1.20222
\(863\) 22847.0 0.901183 0.450591 0.892730i \(-0.351213\pi\)
0.450591 + 0.892730i \(0.351213\pi\)
\(864\) 1696.00 0.0667814
\(865\) 0 0
\(866\) −2756.00 −0.108144
\(867\) 1432.00 0.0560937
\(868\) 0 0
\(869\) −17325.0 −0.676307
\(870\) 0 0
\(871\) −28974.0 −1.12715
\(872\) −7720.00 −0.299808
\(873\) 7540.00 0.292314
\(874\) −1918.00 −0.0742303
\(875\) 0 0
\(876\) −1180.00 −0.0455120
\(877\) 42737.0 1.64553 0.822763 0.568385i \(-0.192432\pi\)
0.822763 + 0.568385i \(0.192432\pi\)
\(878\) 5526.00 0.212407
\(879\) −318.000 −0.0122024
\(880\) 0 0
\(881\) −6162.00 −0.235645 −0.117822 0.993035i \(-0.537591\pi\)
−0.117822 + 0.993035i \(0.537591\pi\)
\(882\) 0 0
\(883\) −7748.00 −0.295290 −0.147645 0.989040i \(-0.547169\pi\)
−0.147645 + 0.989040i \(0.547169\pi\)
\(884\) 15576.0 0.592622
\(885\) 0 0
\(886\) −11698.0 −0.443569
\(887\) −25923.0 −0.981296 −0.490648 0.871358i \(-0.663240\pi\)
−0.490648 + 0.871358i \(0.663240\pi\)
\(888\) 88.0000 0.00332555
\(889\) 0 0
\(890\) 0 0
\(891\) 22715.0 0.854075
\(892\) 8096.00 0.303895
\(893\) 23427.0 0.877889
\(894\) −4590.00 −0.171714
\(895\) 0 0
\(896\) 0 0
\(897\) −462.000 −0.0171970
\(898\) 9164.00 0.340542
\(899\) −7950.00 −0.294936
\(900\) 0 0
\(901\) 24603.0 0.909706
\(902\) 34860.0 1.28682
\(903\) 0 0
\(904\) 400.000 0.0147166
\(905\) 0 0
\(906\) 2218.00 0.0813335
\(907\) −31935.0 −1.16911 −0.584556 0.811353i \(-0.698731\pi\)
−0.584556 + 0.811353i \(0.698731\pi\)
\(908\) 10284.0 0.375866
\(909\) −28210.0 −1.02934
\(910\) 0 0
\(911\) 3408.00 0.123943 0.0619715 0.998078i \(-0.480261\pi\)
0.0619715 + 0.998078i \(0.480261\pi\)
\(912\) 2192.00 0.0795881
\(913\) 32620.0 1.18244
\(914\) −23102.0 −0.836046
\(915\) 0 0
\(916\) −3580.00 −0.129134
\(917\) 0 0
\(918\) 6254.00 0.224850
\(919\) 13909.0 0.499255 0.249628 0.968342i \(-0.419692\pi\)
0.249628 + 0.968342i \(0.419692\pi\)
\(920\) 0 0
\(921\) 8132.00 0.290943
\(922\) 18988.0 0.678239
\(923\) −51744.0 −1.84526
\(924\) 0 0
\(925\) 0 0
\(926\) 20320.0 0.721119
\(927\) −40378.0 −1.43062
\(928\) 3392.00 0.119987
\(929\) 24537.0 0.866559 0.433279 0.901260i \(-0.357356\pi\)
0.433279 + 0.901260i \(0.357356\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −7148.00 −0.251224
\(933\) −929.000 −0.0325982
\(934\) −2614.00 −0.0915768
\(935\) 0 0
\(936\) −13728.0 −0.479395
\(937\) −32758.0 −1.14211 −0.571055 0.820912i \(-0.693466\pi\)
−0.571055 + 0.820912i \(0.693466\pi\)
\(938\) 0 0
\(939\) 209.000 0.00726353
\(940\) 0 0
\(941\) 38561.0 1.33587 0.667934 0.744220i \(-0.267179\pi\)
0.667934 + 0.744220i \(0.267179\pi\)
\(942\) −3118.00 −0.107845
\(943\) 3486.00 0.120382
\(944\) 272.000 0.00937801
\(945\) 0 0
\(946\) −18200.0 −0.625511
\(947\) −39661.0 −1.36094 −0.680470 0.732776i \(-0.738224\pi\)
−0.680470 + 0.732776i \(0.738224\pi\)
\(948\) 1980.00 0.0678348
\(949\) 19470.0 0.665988
\(950\) 0 0
\(951\) 7131.00 0.243153
\(952\) 0 0
\(953\) 46618.0 1.58458 0.792290 0.610144i \(-0.208889\pi\)
0.792290 + 0.610144i \(0.208889\pi\)
\(954\) −21684.0 −0.735897
\(955\) 0 0
\(956\) −20400.0 −0.690150
\(957\) −3710.00 −0.125316
\(958\) −36574.0 −1.23346
\(959\) 0 0
\(960\) 0 0
\(961\) −24166.0 −0.811185
\(962\) −1452.00 −0.0486636
\(963\) 3354.00 0.112234
\(964\) 16708.0 0.558225
\(965\) 0 0
\(966\) 0 0
\(967\) −14816.0 −0.492710 −0.246355 0.969180i \(-0.579233\pi\)
−0.246355 + 0.969180i \(0.579233\pi\)
\(968\) −848.000 −0.0281568
\(969\) 8083.00 0.267970
\(970\) 0 0
\(971\) 16875.0 0.557718 0.278859 0.960332i \(-0.410044\pi\)
0.278859 + 0.960332i \(0.410044\pi\)
\(972\) −8320.00 −0.274552
\(973\) 0 0
\(974\) 29906.0 0.983830
\(975\) 0 0
\(976\) −816.000 −0.0267618
\(977\) 15837.0 0.518598 0.259299 0.965797i \(-0.416508\pi\)
0.259299 + 0.965797i \(0.416508\pi\)
\(978\) −4502.00 −0.147196
\(979\) 30555.0 0.997489
\(980\) 0 0
\(981\) 25090.0 0.816577
\(982\) 28704.0 0.932771
\(983\) 9915.00 0.321708 0.160854 0.986978i \(-0.448575\pi\)
0.160854 + 0.986978i \(0.448575\pi\)
\(984\) −3984.00 −0.129070
\(985\) 0 0
\(986\) 12508.0 0.403992
\(987\) 0 0
\(988\) −36168.0 −1.16463
\(989\) −1820.00 −0.0585163
\(990\) 0 0
\(991\) −43681.0 −1.40017 −0.700087 0.714057i \(-0.746856\pi\)
−0.700087 + 0.714057i \(0.746856\pi\)
\(992\) −2400.00 −0.0768146
\(993\) 6571.00 0.209994
\(994\) 0 0
\(995\) 0 0
\(996\) −3728.00 −0.118601
\(997\) −47113.0 −1.49657 −0.748287 0.663375i \(-0.769123\pi\)
−0.748287 + 0.663375i \(0.769123\pi\)
\(998\) −11062.0 −0.350863
\(999\) −583.000 −0.0184638
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 2450.4.a.bf.1.1 1
5.4 even 2 98.4.a.c.1.1 1
7.3 odd 6 350.4.e.b.51.1 2
7.5 odd 6 350.4.e.b.151.1 2
7.6 odd 2 2450.4.a.bh.1.1 1
15.14 odd 2 882.4.a.p.1.1 1
20.19 odd 2 784.4.a.j.1.1 1
35.3 even 12 350.4.j.d.149.2 4
35.4 even 6 98.4.c.e.79.1 2
35.9 even 6 98.4.c.e.67.1 2
35.12 even 12 350.4.j.d.249.2 4
35.17 even 12 350.4.j.d.149.1 4
35.19 odd 6 14.4.c.b.11.1 yes 2
35.24 odd 6 14.4.c.b.9.1 2
35.33 even 12 350.4.j.d.249.1 4
35.34 odd 2 98.4.a.b.1.1 1
105.44 odd 6 882.4.g.d.361.1 2
105.59 even 6 126.4.g.c.37.1 2
105.74 odd 6 882.4.g.d.667.1 2
105.89 even 6 126.4.g.c.109.1 2
105.104 even 2 882.4.a.k.1.1 1
140.19 even 6 112.4.i.b.81.1 2
140.59 even 6 112.4.i.b.65.1 2
140.139 even 2 784.4.a.l.1.1 1
280.19 even 6 448.4.i.d.193.1 2
280.59 even 6 448.4.i.d.65.1 2
280.229 odd 6 448.4.i.c.193.1 2
280.269 odd 6 448.4.i.c.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.b.9.1 2 35.24 odd 6
14.4.c.b.11.1 yes 2 35.19 odd 6
98.4.a.b.1.1 1 35.34 odd 2
98.4.a.c.1.1 1 5.4 even 2
98.4.c.e.67.1 2 35.9 even 6
98.4.c.e.79.1 2 35.4 even 6
112.4.i.b.65.1 2 140.59 even 6
112.4.i.b.81.1 2 140.19 even 6
126.4.g.c.37.1 2 105.59 even 6
126.4.g.c.109.1 2 105.89 even 6
350.4.e.b.51.1 2 7.3 odd 6
350.4.e.b.151.1 2 7.5 odd 6
350.4.j.d.149.1 4 35.17 even 12
350.4.j.d.149.2 4 35.3 even 12
350.4.j.d.249.1 4 35.33 even 12
350.4.j.d.249.2 4 35.12 even 12
448.4.i.c.65.1 2 280.269 odd 6
448.4.i.c.193.1 2 280.229 odd 6
448.4.i.d.65.1 2 280.59 even 6
448.4.i.d.193.1 2 280.19 even 6
784.4.a.j.1.1 1 20.19 odd 2
784.4.a.l.1.1 1 140.139 even 2
882.4.a.k.1.1 1 105.104 even 2
882.4.a.p.1.1 1 15.14 odd 2
882.4.g.d.361.1 2 105.44 odd 6
882.4.g.d.667.1 2 105.74 odd 6
2450.4.a.bf.1.1 1 1.1 even 1 trivial
2450.4.a.bh.1.1 1 7.6 odd 2