Properties

Label 529.4.a.g.1.3
Level $529$
Weight $4$
Character 529.1
Self dual yes
Analytic conductor $31.212$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [529,4,Mod(1,529)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(529, 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("529.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 529 = 23^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 529.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: \(31.2120103930\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.334189.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 16x^{2} - 5x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 23)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.83969\) of defining polynomial
Character \(\chi\) \(=\) 529.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.86845 q^{2} +3.43737 q^{3} +0.228032 q^{4} +17.9704 q^{5} +9.85995 q^{6} -32.7301 q^{7} -22.2935 q^{8} -15.1845 q^{9} +51.5473 q^{10} -26.7049 q^{11} +0.783832 q^{12} -14.4956 q^{13} -93.8848 q^{14} +61.7710 q^{15} -65.7723 q^{16} -24.7016 q^{17} -43.5560 q^{18} -94.6224 q^{19} +4.09784 q^{20} -112.505 q^{21} -76.6018 q^{22} -76.6312 q^{24} +197.935 q^{25} -41.5801 q^{26} -145.004 q^{27} -7.46352 q^{28} -57.5965 q^{29} +177.187 q^{30} +88.8691 q^{31} -10.3165 q^{32} -91.7948 q^{33} -70.8553 q^{34} -588.173 q^{35} -3.46255 q^{36} +305.467 q^{37} -271.420 q^{38} -49.8269 q^{39} -400.624 q^{40} -179.205 q^{41} -322.717 q^{42} +96.5826 q^{43} -6.08959 q^{44} -272.871 q^{45} +218.484 q^{47} -226.084 q^{48} +728.258 q^{49} +567.769 q^{50} -84.9085 q^{51} -3.30548 q^{52} +519.174 q^{53} -415.937 q^{54} -479.898 q^{55} +729.669 q^{56} -325.252 q^{57} -165.213 q^{58} -37.2884 q^{59} +14.0858 q^{60} -96.3052 q^{61} +254.917 q^{62} +496.989 q^{63} +496.586 q^{64} -260.493 q^{65} -263.309 q^{66} -497.552 q^{67} -5.63276 q^{68} -1687.15 q^{70} -19.6235 q^{71} +338.515 q^{72} -208.235 q^{73} +876.219 q^{74} +680.378 q^{75} -21.5770 q^{76} +874.054 q^{77} -142.926 q^{78} +446.200 q^{79} -1181.95 q^{80} -88.4513 q^{81} -514.042 q^{82} -501.151 q^{83} -25.6549 q^{84} -443.897 q^{85} +277.043 q^{86} -197.981 q^{87} +595.347 q^{88} -1102.82 q^{89} -782.718 q^{90} +474.444 q^{91} +305.476 q^{93} +626.711 q^{94} -1700.40 q^{95} -35.4615 q^{96} -1814.37 q^{97} +2088.98 q^{98} +405.500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 7 q^{3} + 20 q^{4} - 14 q^{5} - 17 q^{6} - 16 q^{7} - 63 q^{8} - 33 q^{9} + 70 q^{10} - 8 q^{11} - 67 q^{12} + 111 q^{13} + 144 q^{14} - 10 q^{15} + 64 q^{16} - 98 q^{17} + 49 q^{18} - 96 q^{19}+ \cdots + 1498 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.86845 1.01415 0.507076 0.861901i \(-0.330726\pi\)
0.507076 + 0.861901i \(0.330726\pi\)
\(3\) 3.43737 0.661523 0.330761 0.943714i \(-0.392694\pi\)
0.330761 + 0.943714i \(0.392694\pi\)
\(4\) 0.228032 0.0285041
\(5\) 17.9704 1.60732 0.803661 0.595087i \(-0.202883\pi\)
0.803661 + 0.595087i \(0.202883\pi\)
\(6\) 9.85995 0.670885
\(7\) −32.7301 −1.76726 −0.883629 0.468187i \(-0.844907\pi\)
−0.883629 + 0.468187i \(0.844907\pi\)
\(8\) −22.2935 −0.985244
\(9\) −15.1845 −0.562388
\(10\) 51.5473 1.63007
\(11\) −26.7049 −0.731985 −0.365993 0.930618i \(-0.619270\pi\)
−0.365993 + 0.930618i \(0.619270\pi\)
\(12\) 0.783832 0.0188561
\(13\) −14.4956 −0.309259 −0.154630 0.987973i \(-0.549418\pi\)
−0.154630 + 0.987973i \(0.549418\pi\)
\(14\) −93.8848 −1.79227
\(15\) 61.7710 1.06328
\(16\) −65.7723 −1.02769
\(17\) −24.7016 −0.352412 −0.176206 0.984353i \(-0.556383\pi\)
−0.176206 + 0.984353i \(0.556383\pi\)
\(18\) −43.5560 −0.570347
\(19\) −94.6224 −1.14252 −0.571259 0.820770i \(-0.693545\pi\)
−0.571259 + 0.820770i \(0.693545\pi\)
\(20\) 4.09784 0.0458152
\(21\) −112.505 −1.16908
\(22\) −76.6018 −0.742344
\(23\) 0 0
\(24\) −76.6312 −0.651762
\(25\) 197.935 1.58348
\(26\) −41.5801 −0.313636
\(27\) −145.004 −1.03355
\(28\) −7.46352 −0.0503740
\(29\) −57.5965 −0.368807 −0.184403 0.982851i \(-0.559035\pi\)
−0.184403 + 0.982851i \(0.559035\pi\)
\(30\) 177.187 1.07833
\(31\) 88.8691 0.514882 0.257441 0.966294i \(-0.417121\pi\)
0.257441 + 0.966294i \(0.417121\pi\)
\(32\) −10.3165 −0.0569909
\(33\) −91.7948 −0.484225
\(34\) −70.8553 −0.357400
\(35\) −588.173 −2.84055
\(36\) −3.46255 −0.0160303
\(37\) 305.467 1.35726 0.678629 0.734482i \(-0.262575\pi\)
0.678629 + 0.734482i \(0.262575\pi\)
\(38\) −271.420 −1.15869
\(39\) −49.8269 −0.204582
\(40\) −400.624 −1.58360
\(41\) −179.205 −0.682613 −0.341306 0.939952i \(-0.610869\pi\)
−0.341306 + 0.939952i \(0.610869\pi\)
\(42\) −322.717 −1.18563
\(43\) 96.5826 0.342528 0.171264 0.985225i \(-0.445215\pi\)
0.171264 + 0.985225i \(0.445215\pi\)
\(44\) −6.08959 −0.0208645
\(45\) −272.871 −0.903938
\(46\) 0 0
\(47\) 218.484 0.678067 0.339034 0.940774i \(-0.389900\pi\)
0.339034 + 0.940774i \(0.389900\pi\)
\(48\) −226.084 −0.679841
\(49\) 728.258 2.12320
\(50\) 567.769 1.60589
\(51\) −84.9085 −0.233129
\(52\) −3.30548 −0.00881514
\(53\) 519.174 1.34555 0.672774 0.739848i \(-0.265103\pi\)
0.672774 + 0.739848i \(0.265103\pi\)
\(54\) −415.937 −1.04818
\(55\) −479.898 −1.17654
\(56\) 729.669 1.74118
\(57\) −325.252 −0.755802
\(58\) −165.213 −0.374026
\(59\) −37.2884 −0.0822803 −0.0411401 0.999153i \(-0.513099\pi\)
−0.0411401 + 0.999153i \(0.513099\pi\)
\(60\) 14.0858 0.0303078
\(61\) −96.3052 −0.202141 −0.101071 0.994879i \(-0.532227\pi\)
−0.101071 + 0.994879i \(0.532227\pi\)
\(62\) 254.917 0.522169
\(63\) 496.989 0.993884
\(64\) 496.586 0.969894
\(65\) −260.493 −0.497079
\(66\) −263.309 −0.491077
\(67\) −497.552 −0.907248 −0.453624 0.891193i \(-0.649869\pi\)
−0.453624 + 0.891193i \(0.649869\pi\)
\(68\) −5.63276 −0.0100452
\(69\) 0 0
\(70\) −1687.15 −2.88075
\(71\) −19.6235 −0.0328011 −0.0164005 0.999866i \(-0.505221\pi\)
−0.0164005 + 0.999866i \(0.505221\pi\)
\(72\) 338.515 0.554089
\(73\) −208.235 −0.333865 −0.166932 0.985968i \(-0.553386\pi\)
−0.166932 + 0.985968i \(0.553386\pi\)
\(74\) 876.219 1.37647
\(75\) 680.378 1.04751
\(76\) −21.5770 −0.0325664
\(77\) 874.054 1.29361
\(78\) −142.926 −0.207477
\(79\) 446.200 0.635461 0.317730 0.948181i \(-0.397079\pi\)
0.317730 + 0.948181i \(0.397079\pi\)
\(80\) −1181.95 −1.65183
\(81\) −88.4513 −0.121332
\(82\) −514.042 −0.692273
\(83\) −501.151 −0.662752 −0.331376 0.943499i \(-0.607513\pi\)
−0.331376 + 0.943499i \(0.607513\pi\)
\(84\) −25.6549 −0.0333236
\(85\) −443.897 −0.566440
\(86\) 277.043 0.347375
\(87\) −197.981 −0.243974
\(88\) 595.347 0.721184
\(89\) −1102.82 −1.31347 −0.656733 0.754124i \(-0.728062\pi\)
−0.656733 + 0.754124i \(0.728062\pi\)
\(90\) −782.718 −0.916731
\(91\) 474.444 0.546541
\(92\) 0 0
\(93\) 305.476 0.340606
\(94\) 626.711 0.687663
\(95\) −1700.40 −1.83640
\(96\) −35.4615 −0.0377008
\(97\) −1814.37 −1.89919 −0.949595 0.313478i \(-0.898506\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(98\) 2088.98 2.15325
\(99\) 405.500 0.411659
\(100\) 45.1357 0.0451357
\(101\) −1386.24 −1.36570 −0.682852 0.730557i \(-0.739261\pi\)
−0.682852 + 0.730557i \(0.739261\pi\)
\(102\) −243.556 −0.236428
\(103\) −1372.33 −1.31281 −0.656407 0.754407i \(-0.727925\pi\)
−0.656407 + 0.754407i \(0.727925\pi\)
\(104\) 323.159 0.304696
\(105\) −2021.77 −1.87909
\(106\) 1489.23 1.36459
\(107\) −1657.83 −1.49784 −0.748919 0.662662i \(-0.769427\pi\)
−0.748919 + 0.662662i \(0.769427\pi\)
\(108\) −33.0656 −0.0294605
\(109\) 821.369 0.721770 0.360885 0.932610i \(-0.382475\pi\)
0.360885 + 0.932610i \(0.382475\pi\)
\(110\) −1376.57 −1.19319
\(111\) 1050.01 0.897857
\(112\) 2152.73 1.81620
\(113\) 267.142 0.222395 0.111197 0.993798i \(-0.464531\pi\)
0.111197 + 0.993798i \(0.464531\pi\)
\(114\) −932.972 −0.766498
\(115\) 0 0
\(116\) −13.1339 −0.0105125
\(117\) 220.109 0.173924
\(118\) −106.960 −0.0834447
\(119\) 808.484 0.622803
\(120\) −1377.09 −1.04759
\(121\) −617.847 −0.464198
\(122\) −276.247 −0.205002
\(123\) −615.995 −0.451564
\(124\) 20.2650 0.0146762
\(125\) 1310.68 0.937846
\(126\) 1425.59 1.00795
\(127\) −1446.21 −1.01048 −0.505239 0.862979i \(-0.668596\pi\)
−0.505239 + 0.862979i \(0.668596\pi\)
\(128\) 1506.97 1.04061
\(129\) 331.990 0.226590
\(130\) −747.211 −0.504114
\(131\) 1459.33 0.973297 0.486649 0.873598i \(-0.338219\pi\)
0.486649 + 0.873598i \(0.338219\pi\)
\(132\) −20.9322 −0.0138024
\(133\) 3097.00 2.01913
\(134\) −1427.20 −0.920088
\(135\) −2605.78 −1.66126
\(136\) 550.685 0.347212
\(137\) 1889.31 1.17821 0.589105 0.808056i \(-0.299480\pi\)
0.589105 + 0.808056i \(0.299480\pi\)
\(138\) 0 0
\(139\) −1506.31 −0.919159 −0.459580 0.888137i \(-0.652000\pi\)
−0.459580 + 0.888137i \(0.652000\pi\)
\(140\) −134.122 −0.0809673
\(141\) 751.011 0.448557
\(142\) −56.2890 −0.0332653
\(143\) 387.105 0.226373
\(144\) 998.717 0.577961
\(145\) −1035.03 −0.592791
\(146\) −597.314 −0.338589
\(147\) 2503.30 1.40455
\(148\) 69.6565 0.0386873
\(149\) 2946.38 1.61998 0.809989 0.586444i \(-0.199473\pi\)
0.809989 + 0.586444i \(0.199473\pi\)
\(150\) 1951.63 1.06233
\(151\) 1979.37 1.06675 0.533374 0.845880i \(-0.320924\pi\)
0.533374 + 0.845880i \(0.320924\pi\)
\(152\) 2109.47 1.12566
\(153\) 375.080 0.198192
\(154\) 2507.18 1.31191
\(155\) 1597.01 0.827582
\(156\) −11.3622 −0.00583142
\(157\) −505.403 −0.256915 −0.128457 0.991715i \(-0.541003\pi\)
−0.128457 + 0.991715i \(0.541003\pi\)
\(158\) 1279.90 0.644454
\(159\) 1784.59 0.890110
\(160\) −185.391 −0.0916027
\(161\) 0 0
\(162\) −253.719 −0.123049
\(163\) −2604.26 −1.25142 −0.625711 0.780055i \(-0.715191\pi\)
−0.625711 + 0.780055i \(0.715191\pi\)
\(164\) −40.8646 −0.0194572
\(165\) −1649.59 −0.778305
\(166\) −1437.53 −0.672131
\(167\) −845.304 −0.391686 −0.195843 0.980635i \(-0.562744\pi\)
−0.195843 + 0.980635i \(0.562744\pi\)
\(168\) 2508.15 1.15183
\(169\) −1986.88 −0.904359
\(170\) −1273.30 −0.574456
\(171\) 1436.79 0.642539
\(172\) 22.0240 0.00976343
\(173\) 886.843 0.389742 0.194871 0.980829i \(-0.437571\pi\)
0.194871 + 0.980829i \(0.437571\pi\)
\(174\) −567.898 −0.247427
\(175\) −6478.44 −2.79842
\(176\) 1756.44 0.752255
\(177\) −128.174 −0.0544303
\(178\) −3163.38 −1.33205
\(179\) 1103.01 0.460575 0.230288 0.973123i \(-0.426033\pi\)
0.230288 + 0.973123i \(0.426033\pi\)
\(180\) −62.2234 −0.0257659
\(181\) 1200.43 0.492967 0.246483 0.969147i \(-0.420725\pi\)
0.246483 + 0.969147i \(0.420725\pi\)
\(182\) 1360.92 0.554275
\(183\) −331.037 −0.133721
\(184\) 0 0
\(185\) 5489.37 2.18155
\(186\) 876.244 0.345427
\(187\) 659.653 0.257961
\(188\) 49.8214 0.0193277
\(189\) 4745.98 1.82656
\(190\) −4877.53 −1.86238
\(191\) −2415.93 −0.915237 −0.457618 0.889149i \(-0.651297\pi\)
−0.457618 + 0.889149i \(0.651297\pi\)
\(192\) 1706.95 0.641607
\(193\) 232.884 0.0868568 0.0434284 0.999057i \(-0.486172\pi\)
0.0434284 + 0.999057i \(0.486172\pi\)
\(194\) −5204.44 −1.92607
\(195\) −895.410 −0.328829
\(196\) 166.067 0.0605199
\(197\) −1418.48 −0.513008 −0.256504 0.966543i \(-0.582571\pi\)
−0.256504 + 0.966543i \(0.582571\pi\)
\(198\) 1163.16 0.417485
\(199\) −1068.21 −0.380520 −0.190260 0.981734i \(-0.560933\pi\)
−0.190260 + 0.981734i \(0.560933\pi\)
\(200\) −4412.68 −1.56012
\(201\) −1710.27 −0.600165
\(202\) −3976.37 −1.38503
\(203\) 1885.14 0.651777
\(204\) −19.3619 −0.00664511
\(205\) −3220.39 −1.09718
\(206\) −3936.47 −1.33139
\(207\) 0 0
\(208\) 953.412 0.317823
\(209\) 2526.88 0.836307
\(210\) −5799.35 −1.90568
\(211\) −1537.74 −0.501717 −0.250859 0.968024i \(-0.580713\pi\)
−0.250859 + 0.968024i \(0.580713\pi\)
\(212\) 118.388 0.0383535
\(213\) −67.4532 −0.0216987
\(214\) −4755.41 −1.51903
\(215\) 1735.63 0.550553
\(216\) 3232.65 1.01830
\(217\) −2908.69 −0.909930
\(218\) 2356.06 0.731984
\(219\) −715.783 −0.220859
\(220\) −109.432 −0.0335360
\(221\) 358.065 0.108987
\(222\) 3011.89 0.910563
\(223\) −5359.68 −1.60946 −0.804732 0.593638i \(-0.797691\pi\)
−0.804732 + 0.593638i \(0.797691\pi\)
\(224\) 337.658 0.100718
\(225\) −3005.54 −0.890532
\(226\) 766.285 0.225542
\(227\) −1108.36 −0.324072 −0.162036 0.986785i \(-0.551806\pi\)
−0.162036 + 0.986785i \(0.551806\pi\)
\(228\) −74.1681 −0.0215434
\(229\) 5046.34 1.45621 0.728104 0.685467i \(-0.240402\pi\)
0.728104 + 0.685467i \(0.240402\pi\)
\(230\) 0 0
\(231\) 3004.45 0.855750
\(232\) 1284.03 0.363365
\(233\) 7102.11 1.99689 0.998444 0.0557635i \(-0.0177593\pi\)
0.998444 + 0.0557635i \(0.0177593\pi\)
\(234\) 631.372 0.176385
\(235\) 3926.25 1.08987
\(236\) −8.50296 −0.00234532
\(237\) 1533.75 0.420372
\(238\) 2319.10 0.631617
\(239\) 1556.22 0.421187 0.210594 0.977574i \(-0.432460\pi\)
0.210594 + 0.977574i \(0.432460\pi\)
\(240\) −4062.82 −1.09272
\(241\) −3028.88 −0.809573 −0.404787 0.914411i \(-0.632654\pi\)
−0.404787 + 0.914411i \(0.632654\pi\)
\(242\) −1772.27 −0.470767
\(243\) 3611.06 0.953291
\(244\) −21.9607 −0.00576184
\(245\) 13087.1 3.41267
\(246\) −1766.95 −0.457954
\(247\) 1371.61 0.353334
\(248\) −1981.21 −0.507285
\(249\) −1722.64 −0.438426
\(250\) 3759.63 0.951118
\(251\) −1449.39 −0.364480 −0.182240 0.983254i \(-0.558335\pi\)
−0.182240 + 0.983254i \(0.558335\pi\)
\(252\) 113.330 0.0283297
\(253\) 0 0
\(254\) −4148.40 −1.02478
\(255\) −1525.84 −0.374713
\(256\) 349.976 0.0854433
\(257\) −3099.62 −0.752332 −0.376166 0.926552i \(-0.622758\pi\)
−0.376166 + 0.926552i \(0.622758\pi\)
\(258\) 952.299 0.229797
\(259\) −9997.97 −2.39862
\(260\) −59.4008 −0.0141688
\(261\) 874.572 0.207412
\(262\) 4186.01 0.987071
\(263\) 1087.92 0.255073 0.127537 0.991834i \(-0.459293\pi\)
0.127537 + 0.991834i \(0.459293\pi\)
\(264\) 2046.43 0.477080
\(265\) 9329.76 2.16273
\(266\) 8883.60 2.04770
\(267\) −3790.79 −0.868887
\(268\) −113.458 −0.0258603
\(269\) 4721.01 1.07006 0.535028 0.844834i \(-0.320301\pi\)
0.535028 + 0.844834i \(0.320301\pi\)
\(270\) −7474.55 −1.68477
\(271\) 1401.15 0.314074 0.157037 0.987593i \(-0.449806\pi\)
0.157037 + 0.987593i \(0.449806\pi\)
\(272\) 1624.68 0.362171
\(273\) 1630.84 0.361549
\(274\) 5419.41 1.19488
\(275\) −5285.85 −1.15909
\(276\) 0 0
\(277\) 4122.82 0.894283 0.447142 0.894463i \(-0.352442\pi\)
0.447142 + 0.894463i \(0.352442\pi\)
\(278\) −4320.77 −0.932167
\(279\) −1349.43 −0.289564
\(280\) 13112.5 2.79864
\(281\) −803.897 −0.170664 −0.0853318 0.996353i \(-0.527195\pi\)
−0.0853318 + 0.996353i \(0.527195\pi\)
\(282\) 2154.24 0.454905
\(283\) 3147.53 0.661134 0.330567 0.943782i \(-0.392760\pi\)
0.330567 + 0.943782i \(0.392760\pi\)
\(284\) −4.47479 −0.000934964 0
\(285\) −5844.92 −1.21482
\(286\) 1110.39 0.229577
\(287\) 5865.40 1.20635
\(288\) 156.650 0.0320510
\(289\) −4302.83 −0.875806
\(290\) −2968.94 −0.601181
\(291\) −6236.67 −1.25636
\(292\) −47.4844 −0.00951649
\(293\) 2812.88 0.560854 0.280427 0.959875i \(-0.409524\pi\)
0.280427 + 0.959875i \(0.409524\pi\)
\(294\) 7180.59 1.42442
\(295\) −670.088 −0.132251
\(296\) −6809.95 −1.33723
\(297\) 3872.31 0.756547
\(298\) 8451.56 1.64290
\(299\) 0 0
\(300\) 155.148 0.0298583
\(301\) −3161.15 −0.605335
\(302\) 5677.73 1.08184
\(303\) −4765.02 −0.903444
\(304\) 6223.53 1.17416
\(305\) −1730.64 −0.324906
\(306\) 1075.90 0.200997
\(307\) −7885.52 −1.46596 −0.732981 0.680249i \(-0.761872\pi\)
−0.732981 + 0.680249i \(0.761872\pi\)
\(308\) 199.313 0.0368730
\(309\) −4717.22 −0.868457
\(310\) 4580.96 0.839294
\(311\) −1904.46 −0.347240 −0.173620 0.984813i \(-0.555547\pi\)
−0.173620 + 0.984813i \(0.555547\pi\)
\(312\) 1110.82 0.201563
\(313\) 3854.89 0.696137 0.348069 0.937469i \(-0.386838\pi\)
0.348069 + 0.937469i \(0.386838\pi\)
\(314\) −1449.73 −0.260550
\(315\) 8931.09 1.59749
\(316\) 101.748 0.0181132
\(317\) 1878.70 0.332865 0.166432 0.986053i \(-0.446775\pi\)
0.166432 + 0.986053i \(0.446775\pi\)
\(318\) 5119.03 0.902707
\(319\) 1538.11 0.269961
\(320\) 8923.85 1.55893
\(321\) −5698.58 −0.990853
\(322\) 0 0
\(323\) 2337.32 0.402638
\(324\) −20.1698 −0.00345846
\(325\) −2869.20 −0.489707
\(326\) −7470.21 −1.26913
\(327\) 2823.35 0.477467
\(328\) 3995.11 0.672541
\(329\) −7151.00 −1.19832
\(330\) −4731.77 −0.789320
\(331\) 6829.96 1.13417 0.567083 0.823661i \(-0.308072\pi\)
0.567083 + 0.823661i \(0.308072\pi\)
\(332\) −114.279 −0.0188911
\(333\) −4638.36 −0.763305
\(334\) −2424.72 −0.397229
\(335\) −8941.21 −1.45824
\(336\) 7399.74 1.20146
\(337\) −11048.9 −1.78597 −0.892985 0.450087i \(-0.851393\pi\)
−0.892985 + 0.450087i \(0.851393\pi\)
\(338\) −5699.26 −0.917157
\(339\) 918.267 0.147119
\(340\) −101.223 −0.0161458
\(341\) −2373.24 −0.376886
\(342\) 4121.37 0.651632
\(343\) −12609.5 −1.98499
\(344\) −2153.17 −0.337474
\(345\) 0 0
\(346\) 2543.87 0.395258
\(347\) −7093.14 −1.09735 −0.548674 0.836037i \(-0.684867\pi\)
−0.548674 + 0.836037i \(0.684867\pi\)
\(348\) −45.1460 −0.00695425
\(349\) −5363.16 −0.822588 −0.411294 0.911503i \(-0.634923\pi\)
−0.411294 + 0.911503i \(0.634923\pi\)
\(350\) −18583.1 −2.83803
\(351\) 2101.92 0.319636
\(352\) 275.500 0.0417165
\(353\) 11789.3 1.77757 0.888787 0.458320i \(-0.151549\pi\)
0.888787 + 0.458320i \(0.151549\pi\)
\(354\) −367.662 −0.0552006
\(355\) −352.642 −0.0527219
\(356\) −251.478 −0.0374391
\(357\) 2779.06 0.411999
\(358\) 3163.94 0.467093
\(359\) 2645.66 0.388949 0.194474 0.980908i \(-0.437700\pi\)
0.194474 + 0.980908i \(0.437700\pi\)
\(360\) 6083.26 0.890600
\(361\) 2094.39 0.305349
\(362\) 3443.37 0.499943
\(363\) −2123.77 −0.307077
\(364\) 108.189 0.0155786
\(365\) −3742.07 −0.536628
\(366\) −949.564 −0.135613
\(367\) 9775.68 1.39043 0.695213 0.718804i \(-0.255310\pi\)
0.695213 + 0.718804i \(0.255310\pi\)
\(368\) 0 0
\(369\) 2721.13 0.383893
\(370\) 15746.0 2.21242
\(371\) −16992.6 −2.37793
\(372\) 69.6585 0.00970866
\(373\) −10981.1 −1.52435 −0.762174 0.647373i \(-0.775868\pi\)
−0.762174 + 0.647373i \(0.775868\pi\)
\(374\) 1892.19 0.261611
\(375\) 4505.30 0.620407
\(376\) −4870.78 −0.668062
\(377\) 834.899 0.114057
\(378\) 13613.6 1.85241
\(379\) 2313.77 0.313589 0.156795 0.987631i \(-0.449884\pi\)
0.156795 + 0.987631i \(0.449884\pi\)
\(380\) −387.747 −0.0523447
\(381\) −4971.18 −0.668455
\(382\) −6929.97 −0.928189
\(383\) −9219.25 −1.22998 −0.614989 0.788535i \(-0.710840\pi\)
−0.614989 + 0.788535i \(0.710840\pi\)
\(384\) 5180.00 0.688388
\(385\) 15707.1 2.07924
\(386\) 668.017 0.0880860
\(387\) −1466.55 −0.192633
\(388\) −413.736 −0.0541346
\(389\) −5876.90 −0.765991 −0.382996 0.923750i \(-0.625108\pi\)
−0.382996 + 0.923750i \(0.625108\pi\)
\(390\) −2568.44 −0.333483
\(391\) 0 0
\(392\) −16235.5 −2.09187
\(393\) 5016.25 0.643858
\(394\) −4068.85 −0.520268
\(395\) 8018.39 1.02139
\(396\) 92.4671 0.0117340
\(397\) 14268.6 1.80383 0.901916 0.431911i \(-0.142160\pi\)
0.901916 + 0.431911i \(0.142160\pi\)
\(398\) −3064.12 −0.385905
\(399\) 10645.5 1.33570
\(400\) −13018.7 −1.62733
\(401\) 11556.1 1.43911 0.719557 0.694434i \(-0.244345\pi\)
0.719557 + 0.694434i \(0.244345\pi\)
\(402\) −4905.84 −0.608659
\(403\) −1288.21 −0.159232
\(404\) −316.108 −0.0389281
\(405\) −1589.51 −0.195020
\(406\) 5407.43 0.661001
\(407\) −8157.48 −0.993492
\(408\) 1892.91 0.229689
\(409\) −14148.3 −1.71049 −0.855245 0.518223i \(-0.826594\pi\)
−0.855245 + 0.518223i \(0.826594\pi\)
\(410\) −9237.54 −1.11271
\(411\) 6494.27 0.779413
\(412\) −312.936 −0.0374205
\(413\) 1220.45 0.145410
\(414\) 0 0
\(415\) −9005.88 −1.06526
\(416\) 149.544 0.0176250
\(417\) −5177.73 −0.608045
\(418\) 7248.25 0.848142
\(419\) 2222.16 0.259092 0.129546 0.991573i \(-0.458648\pi\)
0.129546 + 0.991573i \(0.458648\pi\)
\(420\) −461.029 −0.0535617
\(421\) −2518.51 −0.291555 −0.145777 0.989317i \(-0.546568\pi\)
−0.145777 + 0.989317i \(0.546568\pi\)
\(422\) −4410.94 −0.508818
\(423\) −3317.56 −0.381337
\(424\) −11574.2 −1.32569
\(425\) −4889.31 −0.558039
\(426\) −193.486 −0.0220057
\(427\) 3152.08 0.357236
\(428\) −378.039 −0.0426944
\(429\) 1330.62 0.149751
\(430\) 4978.57 0.558344
\(431\) −9935.17 −1.11035 −0.555174 0.831734i \(-0.687348\pi\)
−0.555174 + 0.831734i \(0.687348\pi\)
\(432\) 9537.22 1.06218
\(433\) 8427.47 0.935331 0.467665 0.883906i \(-0.345095\pi\)
0.467665 + 0.883906i \(0.345095\pi\)
\(434\) −8343.45 −0.922807
\(435\) −3557.79 −0.392145
\(436\) 187.299 0.0205734
\(437\) 0 0
\(438\) −2053.19 −0.223985
\(439\) 4886.04 0.531203 0.265601 0.964083i \(-0.414430\pi\)
0.265601 + 0.964083i \(0.414430\pi\)
\(440\) 10698.6 1.15918
\(441\) −11058.2 −1.19406
\(442\) 1027.09 0.110529
\(443\) 9724.04 1.04290 0.521448 0.853283i \(-0.325392\pi\)
0.521448 + 0.853283i \(0.325392\pi\)
\(444\) 239.435 0.0255926
\(445\) −19818.1 −2.11116
\(446\) −15374.0 −1.63224
\(447\) 10127.8 1.07165
\(448\) −16253.3 −1.71405
\(449\) −10093.7 −1.06091 −0.530457 0.847712i \(-0.677980\pi\)
−0.530457 + 0.847712i \(0.677980\pi\)
\(450\) −8621.27 −0.903134
\(451\) 4785.66 0.499662
\(452\) 60.9171 0.00633915
\(453\) 6803.83 0.705678
\(454\) −3179.28 −0.328658
\(455\) 8525.95 0.878467
\(456\) 7251.02 0.744650
\(457\) −3561.77 −0.364578 −0.182289 0.983245i \(-0.558351\pi\)
−0.182289 + 0.983245i \(0.558351\pi\)
\(458\) 14475.2 1.47682
\(459\) 3581.82 0.364237
\(460\) 0 0
\(461\) −7492.00 −0.756914 −0.378457 0.925619i \(-0.623545\pi\)
−0.378457 + 0.925619i \(0.623545\pi\)
\(462\) 8618.13 0.867861
\(463\) 15427.0 1.54849 0.774247 0.632884i \(-0.218129\pi\)
0.774247 + 0.632884i \(0.218129\pi\)
\(464\) 3788.25 0.379020
\(465\) 5489.53 0.547464
\(466\) 20372.1 2.02515
\(467\) −11868.7 −1.17606 −0.588028 0.808841i \(-0.700096\pi\)
−0.588028 + 0.808841i \(0.700096\pi\)
\(468\) 50.1919 0.00495753
\(469\) 16284.9 1.60334
\(470\) 11262.3 1.10530
\(471\) −1737.26 −0.169955
\(472\) 831.290 0.0810662
\(473\) −2579.23 −0.250725
\(474\) 4399.51 0.426321
\(475\) −18729.1 −1.80916
\(476\) 184.361 0.0177524
\(477\) −7883.38 −0.756719
\(478\) 4463.96 0.427148
\(479\) −697.153 −0.0665005 −0.0332503 0.999447i \(-0.510586\pi\)
−0.0332503 + 0.999447i \(0.510586\pi\)
\(480\) −637.258 −0.0605973
\(481\) −4427.95 −0.419744
\(482\) −8688.20 −0.821030
\(483\) 0 0
\(484\) −140.889 −0.0132315
\(485\) −32605.0 −3.05261
\(486\) 10358.2 0.966782
\(487\) 14414.0 1.34119 0.670597 0.741822i \(-0.266038\pi\)
0.670597 + 0.741822i \(0.266038\pi\)
\(488\) 2146.98 0.199159
\(489\) −8951.83 −0.827844
\(490\) 37539.7 3.46096
\(491\) 17538.9 1.61206 0.806029 0.591876i \(-0.201612\pi\)
0.806029 + 0.591876i \(0.201612\pi\)
\(492\) −140.467 −0.0128714
\(493\) 1422.72 0.129972
\(494\) 3934.41 0.358335
\(495\) 7287.00 0.661669
\(496\) −5845.12 −0.529140
\(497\) 642.278 0.0579680
\(498\) −4941.32 −0.444630
\(499\) −18798.6 −1.68645 −0.843226 0.537559i \(-0.819347\pi\)
−0.843226 + 0.537559i \(0.819347\pi\)
\(500\) 298.878 0.0267324
\(501\) −2905.62 −0.259109
\(502\) −4157.50 −0.369638
\(503\) −4634.11 −0.410785 −0.205392 0.978680i \(-0.565847\pi\)
−0.205392 + 0.978680i \(0.565847\pi\)
\(504\) −11079.6 −0.979219
\(505\) −24911.3 −2.19513
\(506\) 0 0
\(507\) −6829.63 −0.598254
\(508\) −329.784 −0.0288027
\(509\) −2193.57 −0.191018 −0.0955092 0.995429i \(-0.530448\pi\)
−0.0955092 + 0.995429i \(0.530448\pi\)
\(510\) −4376.80 −0.380016
\(511\) 6815.56 0.590025
\(512\) −11051.8 −0.953958
\(513\) 13720.6 1.18086
\(514\) −8891.13 −0.762979
\(515\) −24661.4 −2.11012
\(516\) 75.7045 0.00645873
\(517\) −5834.60 −0.496335
\(518\) −28678.7 −2.43257
\(519\) 3048.41 0.257823
\(520\) 5807.30 0.489744
\(521\) 4401.81 0.370147 0.185074 0.982725i \(-0.440748\pi\)
0.185074 + 0.982725i \(0.440748\pi\)
\(522\) 2508.67 0.210348
\(523\) 9974.09 0.833913 0.416957 0.908926i \(-0.363097\pi\)
0.416957 + 0.908926i \(0.363097\pi\)
\(524\) 332.774 0.0277429
\(525\) −22268.8 −1.85122
\(526\) 3120.66 0.258683
\(527\) −2195.20 −0.181451
\(528\) 6037.55 0.497634
\(529\) 0 0
\(530\) 26762.0 2.19333
\(531\) 566.204 0.0462734
\(532\) 706.216 0.0575533
\(533\) 2597.69 0.211104
\(534\) −10873.7 −0.881183
\(535\) −29791.9 −2.40751
\(536\) 11092.2 0.893861
\(537\) 3791.46 0.304681
\(538\) 13542.0 1.08520
\(539\) −19448.1 −1.55415
\(540\) −594.201 −0.0473525
\(541\) −9161.72 −0.728083 −0.364042 0.931383i \(-0.618603\pi\)
−0.364042 + 0.931383i \(0.618603\pi\)
\(542\) 4019.15 0.318519
\(543\) 4126.31 0.326109
\(544\) 254.833 0.0200843
\(545\) 14760.3 1.16012
\(546\) 4677.99 0.366666
\(547\) 1113.51 0.0870390 0.0435195 0.999053i \(-0.486143\pi\)
0.0435195 + 0.999053i \(0.486143\pi\)
\(548\) 430.825 0.0335838
\(549\) 1462.34 0.113682
\(550\) −15162.2 −1.17549
\(551\) 5449.92 0.421369
\(552\) 0 0
\(553\) −14604.2 −1.12302
\(554\) 11826.1 0.906939
\(555\) 18869.0 1.44314
\(556\) −343.486 −0.0261998
\(557\) 7660.96 0.582775 0.291387 0.956605i \(-0.405883\pi\)
0.291387 + 0.956605i \(0.405883\pi\)
\(558\) −3870.78 −0.293661
\(559\) −1400.03 −0.105930
\(560\) 38685.5 2.91921
\(561\) 2267.47 0.170647
\(562\) −2305.94 −0.173079
\(563\) −17217.7 −1.28888 −0.644441 0.764654i \(-0.722910\pi\)
−0.644441 + 0.764654i \(0.722910\pi\)
\(564\) 171.255 0.0127857
\(565\) 4800.65 0.357460
\(566\) 9028.54 0.670491
\(567\) 2895.02 0.214426
\(568\) 437.476 0.0323171
\(569\) 2385.63 0.175766 0.0878830 0.996131i \(-0.471990\pi\)
0.0878830 + 0.996131i \(0.471990\pi\)
\(570\) −16765.9 −1.23201
\(571\) −16927.9 −1.24065 −0.620323 0.784347i \(-0.712998\pi\)
−0.620323 + 0.784347i \(0.712998\pi\)
\(572\) 88.2725 0.00645255
\(573\) −8304.44 −0.605450
\(574\) 16824.6 1.22343
\(575\) 0 0
\(576\) −7540.39 −0.545457
\(577\) 2886.69 0.208275 0.104137 0.994563i \(-0.466792\pi\)
0.104137 + 0.994563i \(0.466792\pi\)
\(578\) −12342.5 −0.888200
\(579\) 800.509 0.0574578
\(580\) −236.021 −0.0168970
\(581\) 16402.7 1.17125
\(582\) −17889.6 −1.27414
\(583\) −13864.5 −0.984920
\(584\) 4642.30 0.328938
\(585\) 3955.44 0.279551
\(586\) 8068.62 0.568791
\(587\) 503.810 0.0354250 0.0177125 0.999843i \(-0.494362\pi\)
0.0177125 + 0.999843i \(0.494362\pi\)
\(588\) 570.832 0.0400353
\(589\) −8409.00 −0.588263
\(590\) −1922.12 −0.134122
\(591\) −4875.85 −0.339366
\(592\) −20091.3 −1.39484
\(593\) −7654.92 −0.530101 −0.265050 0.964235i \(-0.585389\pi\)
−0.265050 + 0.964235i \(0.585389\pi\)
\(594\) 11107.6 0.767253
\(595\) 14528.8 1.00105
\(596\) 671.870 0.0461760
\(597\) −3671.84 −0.251723
\(598\) 0 0
\(599\) 17366.5 1.18460 0.592301 0.805717i \(-0.298220\pi\)
0.592301 + 0.805717i \(0.298220\pi\)
\(600\) −15168.0 −1.03205
\(601\) 3872.81 0.262854 0.131427 0.991326i \(-0.458044\pi\)
0.131427 + 0.991326i \(0.458044\pi\)
\(602\) −9067.63 −0.613902
\(603\) 7555.06 0.510225
\(604\) 451.361 0.0304066
\(605\) −11103.0 −0.746115
\(606\) −13668.3 −0.916229
\(607\) −12823.3 −0.857464 −0.428732 0.903432i \(-0.641039\pi\)
−0.428732 + 0.903432i \(0.641039\pi\)
\(608\) 976.167 0.0651132
\(609\) 6479.92 0.431165
\(610\) −4964.27 −0.329504
\(611\) −3167.07 −0.209699
\(612\) 85.5304 0.00564928
\(613\) 17226.4 1.13502 0.567509 0.823367i \(-0.307907\pi\)
0.567509 + 0.823367i \(0.307907\pi\)
\(614\) −22619.3 −1.48671
\(615\) −11069.7 −0.725809
\(616\) −19485.8 −1.27452
\(617\) 5892.12 0.384454 0.192227 0.981351i \(-0.438429\pi\)
0.192227 + 0.981351i \(0.438429\pi\)
\(618\) −13531.1 −0.880747
\(619\) 13036.6 0.846503 0.423251 0.906012i \(-0.360889\pi\)
0.423251 + 0.906012i \(0.360889\pi\)
\(620\) 364.171 0.0235894
\(621\) 0 0
\(622\) −5462.84 −0.352154
\(623\) 36095.3 2.32123
\(624\) 3277.23 0.210247
\(625\) −1188.48 −0.0760630
\(626\) 11057.6 0.705989
\(627\) 8685.84 0.553236
\(628\) −115.248 −0.00732310
\(629\) −7545.52 −0.478314
\(630\) 25618.4 1.62010
\(631\) 10044.6 0.633707 0.316853 0.948475i \(-0.397374\pi\)
0.316853 + 0.948475i \(0.397374\pi\)
\(632\) −9947.37 −0.626084
\(633\) −5285.79 −0.331898
\(634\) 5388.95 0.337575
\(635\) −25989.1 −1.62416
\(636\) 406.945 0.0253717
\(637\) −10556.6 −0.656620
\(638\) 4412.00 0.273782
\(639\) 297.972 0.0184469
\(640\) 27080.8 1.67260
\(641\) −4583.33 −0.282419 −0.141209 0.989980i \(-0.545099\pi\)
−0.141209 + 0.989980i \(0.545099\pi\)
\(642\) −16346.1 −1.00488
\(643\) −19260.0 −1.18125 −0.590623 0.806948i \(-0.701118\pi\)
−0.590623 + 0.806948i \(0.701118\pi\)
\(644\) 0 0
\(645\) 5966.00 0.364203
\(646\) 6704.50 0.408336
\(647\) −1771.91 −0.107667 −0.0538337 0.998550i \(-0.517144\pi\)
−0.0538337 + 0.998550i \(0.517144\pi\)
\(648\) 1971.89 0.119542
\(649\) 995.784 0.0602279
\(650\) −8230.18 −0.496637
\(651\) −9998.26 −0.601940
\(652\) −593.857 −0.0356706
\(653\) −28000.8 −1.67803 −0.839017 0.544106i \(-0.816869\pi\)
−0.839017 + 0.544106i \(0.816869\pi\)
\(654\) 8098.66 0.484224
\(655\) 26224.7 1.56440
\(656\) 11786.7 0.701515
\(657\) 3161.94 0.187761
\(658\) −20512.3 −1.21528
\(659\) 27664.0 1.63526 0.817629 0.575745i \(-0.195288\pi\)
0.817629 + 0.575745i \(0.195288\pi\)
\(660\) −376.160 −0.0221848
\(661\) −23392.1 −1.37647 −0.688234 0.725489i \(-0.741614\pi\)
−0.688234 + 0.725489i \(0.741614\pi\)
\(662\) 19591.4 1.15022
\(663\) 1230.80 0.0720972
\(664\) 11172.4 0.652973
\(665\) 55654.3 3.24539
\(666\) −13304.9 −0.774107
\(667\) 0 0
\(668\) −192.757 −0.0111646
\(669\) −18423.2 −1.06470
\(670\) −25647.5 −1.47888
\(671\) 2571.82 0.147964
\(672\) 1160.66 0.0666270
\(673\) 4318.41 0.247344 0.123672 0.992323i \(-0.460533\pi\)
0.123672 + 0.992323i \(0.460533\pi\)
\(674\) −31693.3 −1.81124
\(675\) −28701.4 −1.63662
\(676\) −453.072 −0.0257779
\(677\) −18272.8 −1.03734 −0.518671 0.854974i \(-0.673573\pi\)
−0.518671 + 0.854974i \(0.673573\pi\)
\(678\) 2634.01 0.149201
\(679\) 59384.5 3.35636
\(680\) 9896.04 0.558082
\(681\) −3809.84 −0.214381
\(682\) −6807.53 −0.382220
\(683\) −7245.38 −0.405910 −0.202955 0.979188i \(-0.565055\pi\)
−0.202955 + 0.979188i \(0.565055\pi\)
\(684\) 327.635 0.0183150
\(685\) 33951.7 1.89376
\(686\) −36169.9 −2.01308
\(687\) 17346.2 0.963314
\(688\) −6352.45 −0.352013
\(689\) −7525.76 −0.416123
\(690\) 0 0
\(691\) −12055.2 −0.663679 −0.331839 0.943336i \(-0.607669\pi\)
−0.331839 + 0.943336i \(0.607669\pi\)
\(692\) 202.229 0.0111092
\(693\) −13272.0 −0.727509
\(694\) −20346.3 −1.11288
\(695\) −27068.9 −1.47738
\(696\) 4413.69 0.240374
\(697\) 4426.64 0.240561
\(698\) −15384.0 −0.834229
\(699\) 24412.6 1.32099
\(700\) −1477.30 −0.0797664
\(701\) 15301.9 0.824455 0.412228 0.911081i \(-0.364751\pi\)
0.412228 + 0.911081i \(0.364751\pi\)
\(702\) 6029.27 0.324160
\(703\) −28904.0 −1.55069
\(704\) −13261.3 −0.709948
\(705\) 13496.0 0.720975
\(706\) 33817.2 1.80273
\(707\) 45371.8 2.41355
\(708\) −29.2279 −0.00155148
\(709\) 12173.6 0.644835 0.322418 0.946597i \(-0.395504\pi\)
0.322418 + 0.946597i \(0.395504\pi\)
\(710\) −1011.54 −0.0534680
\(711\) −6775.30 −0.357375
\(712\) 24585.7 1.29408
\(713\) 0 0
\(714\) 7971.61 0.417829
\(715\) 6956.44 0.363854
\(716\) 251.522 0.0131283
\(717\) 5349.32 0.278625
\(718\) 7588.95 0.394453
\(719\) 2639.63 0.136914 0.0684572 0.997654i \(-0.478192\pi\)
0.0684572 + 0.997654i \(0.478192\pi\)
\(720\) 17947.3 0.928970
\(721\) 44916.5 2.32008
\(722\) 6007.67 0.309671
\(723\) −10411.4 −0.535551
\(724\) 273.736 0.0140515
\(725\) −11400.4 −0.584000
\(726\) −6091.94 −0.311423
\(727\) 32759.5 1.67123 0.835613 0.549319i \(-0.185113\pi\)
0.835613 + 0.549319i \(0.185113\pi\)
\(728\) −10577.0 −0.538476
\(729\) 14800.7 0.751956
\(730\) −10734.0 −0.544222
\(731\) −2385.74 −0.120711
\(732\) −75.4871 −0.00381159
\(733\) −29178.0 −1.47028 −0.735139 0.677917i \(-0.762883\pi\)
−0.735139 + 0.677917i \(0.762883\pi\)
\(734\) 28041.1 1.41010
\(735\) 44985.2 2.25756
\(736\) 0 0
\(737\) 13287.1 0.664092
\(738\) 7805.45 0.389326
\(739\) −13704.9 −0.682194 −0.341097 0.940028i \(-0.610798\pi\)
−0.341097 + 0.940028i \(0.610798\pi\)
\(740\) 1251.75 0.0621830
\(741\) 4714.74 0.233739
\(742\) −48742.5 −2.41158
\(743\) 991.593 0.0489610 0.0244805 0.999700i \(-0.492207\pi\)
0.0244805 + 0.999700i \(0.492207\pi\)
\(744\) −6810.14 −0.335581
\(745\) 52947.6 2.60383
\(746\) −31498.9 −1.54592
\(747\) 7609.71 0.372724
\(748\) 150.422 0.00735292
\(749\) 54260.9 2.64706
\(750\) 12923.2 0.629186
\(751\) −9440.73 −0.458718 −0.229359 0.973342i \(-0.573663\pi\)
−0.229359 + 0.973342i \(0.573663\pi\)
\(752\) −14370.2 −0.696844
\(753\) −4982.09 −0.241112
\(754\) 2394.87 0.115671
\(755\) 35570.1 1.71461
\(756\) 1082.24 0.0520643
\(757\) −10480.1 −0.503177 −0.251589 0.967834i \(-0.580953\pi\)
−0.251589 + 0.967834i \(0.580953\pi\)
\(758\) 6636.94 0.318027
\(759\) 0 0
\(760\) 37908.0 1.80930
\(761\) −31314.9 −1.49168 −0.745838 0.666128i \(-0.767951\pi\)
−0.745838 + 0.666128i \(0.767951\pi\)
\(762\) −14259.6 −0.677915
\(763\) −26883.5 −1.27555
\(764\) −550.909 −0.0260880
\(765\) 6740.34 0.318559
\(766\) −26445.0 −1.24739
\(767\) 540.519 0.0254459
\(768\) 1203.00 0.0565227
\(769\) 20862.1 0.978292 0.489146 0.872202i \(-0.337309\pi\)
0.489146 + 0.872202i \(0.337309\pi\)
\(770\) 45055.1 2.10867
\(771\) −10654.6 −0.497684
\(772\) 53.1051 0.00247577
\(773\) 20340.2 0.946426 0.473213 0.880948i \(-0.343094\pi\)
0.473213 + 0.880948i \(0.343094\pi\)
\(774\) −4206.75 −0.195360
\(775\) 17590.3 0.815308
\(776\) 40448.8 1.87117
\(777\) −34366.8 −1.58674
\(778\) −16857.6 −0.776832
\(779\) 16956.8 0.779898
\(780\) −204.183 −0.00937296
\(781\) 524.043 0.0240099
\(782\) 0 0
\(783\) 8351.71 0.381182
\(784\) −47899.2 −2.18200
\(785\) −9082.30 −0.412944
\(786\) 14388.9 0.652970
\(787\) −31293.8 −1.41741 −0.708707 0.705503i \(-0.750721\pi\)
−0.708707 + 0.705503i \(0.750721\pi\)
\(788\) −323.460 −0.0146228
\(789\) 3739.60 0.168737
\(790\) 23000.4 1.03584
\(791\) −8743.58 −0.393029
\(792\) −9040.03 −0.405585
\(793\) 1396.01 0.0625140
\(794\) 40928.9 1.82936
\(795\) 32069.9 1.43069
\(796\) −243.587 −0.0108464
\(797\) −32015.4 −1.42289 −0.711446 0.702741i \(-0.751959\pi\)
−0.711446 + 0.702741i \(0.751959\pi\)
\(798\) 30536.2 1.35460
\(799\) −5396.89 −0.238959
\(800\) −2041.99 −0.0902442
\(801\) 16745.7 0.738677
\(802\) 33148.2 1.45948
\(803\) 5560.91 0.244384
\(804\) −389.997 −0.0171071
\(805\) 0 0
\(806\) −3695.19 −0.161486
\(807\) 16227.9 0.707867
\(808\) 30904.2 1.34555
\(809\) 5234.16 0.227470 0.113735 0.993511i \(-0.463719\pi\)
0.113735 + 0.993511i \(0.463719\pi\)
\(810\) −4559.43 −0.197780
\(811\) −2377.40 −0.102937 −0.0514685 0.998675i \(-0.516390\pi\)
−0.0514685 + 0.998675i \(0.516390\pi\)
\(812\) 429.873 0.0185783
\(813\) 4816.29 0.207767
\(814\) −23399.4 −1.00755
\(815\) −46799.7 −2.01144
\(816\) 5584.62 0.239584
\(817\) −9138.87 −0.391345
\(818\) −40583.9 −1.73470
\(819\) −7204.18 −0.307368
\(820\) −734.353 −0.0312740
\(821\) 5174.70 0.219974 0.109987 0.993933i \(-0.464919\pi\)
0.109987 + 0.993933i \(0.464919\pi\)
\(822\) 18628.5 0.790443
\(823\) 44178.3 1.87115 0.935576 0.353126i \(-0.114881\pi\)
0.935576 + 0.353126i \(0.114881\pi\)
\(824\) 30594.1 1.29344
\(825\) −18169.4 −0.766762
\(826\) 3500.81 0.147468
\(827\) −5766.56 −0.242470 −0.121235 0.992624i \(-0.538686\pi\)
−0.121235 + 0.992624i \(0.538686\pi\)
\(828\) 0 0
\(829\) 38465.6 1.61154 0.805770 0.592229i \(-0.201752\pi\)
0.805770 + 0.592229i \(0.201752\pi\)
\(830\) −25833.0 −1.08033
\(831\) 14171.7 0.591589
\(832\) −7198.33 −0.299949
\(833\) −17989.1 −0.748242
\(834\) −14852.1 −0.616650
\(835\) −15190.5 −0.629566
\(836\) 576.211 0.0238381
\(837\) −12886.3 −0.532159
\(838\) 6374.17 0.262759
\(839\) 17261.8 0.710301 0.355151 0.934809i \(-0.384430\pi\)
0.355151 + 0.934809i \(0.384430\pi\)
\(840\) 45072.4 1.85136
\(841\) −21071.6 −0.863981
\(842\) −7224.22 −0.295681
\(843\) −2763.29 −0.112898
\(844\) −350.655 −0.0143010
\(845\) −35705.0 −1.45360
\(846\) −9516.28 −0.386733
\(847\) 20222.2 0.820358
\(848\) −34147.2 −1.38281
\(849\) 10819.2 0.437355
\(850\) −14024.8 −0.565936
\(851\) 0 0
\(852\) −15.3815 −0.000618500 0
\(853\) 29038.7 1.16561 0.582805 0.812612i \(-0.301955\pi\)
0.582805 + 0.812612i \(0.301955\pi\)
\(854\) 9041.59 0.362291
\(855\) 25819.7 1.03277
\(856\) 36958.9 1.47574
\(857\) −9865.16 −0.393217 −0.196609 0.980482i \(-0.562993\pi\)
−0.196609 + 0.980482i \(0.562993\pi\)
\(858\) 3816.84 0.151870
\(859\) −24476.6 −0.972214 −0.486107 0.873899i \(-0.661584\pi\)
−0.486107 + 0.873899i \(0.661584\pi\)
\(860\) 395.779 0.0156930
\(861\) 20161.6 0.798030
\(862\) −28498.6 −1.12606
\(863\) −37353.6 −1.47339 −0.736693 0.676227i \(-0.763614\pi\)
−0.736693 + 0.676227i \(0.763614\pi\)
\(864\) 1495.92 0.0589032
\(865\) 15936.9 0.626442
\(866\) 24173.8 0.948567
\(867\) −14790.4 −0.579365
\(868\) −663.276 −0.0259367
\(869\) −11915.7 −0.465148
\(870\) −10205.4 −0.397695
\(871\) 7212.34 0.280575
\(872\) −18311.2 −0.711120
\(873\) 27550.3 1.06808
\(874\) 0 0
\(875\) −42898.7 −1.65742
\(876\) −163.222 −0.00629538
\(877\) −25920.7 −0.998040 −0.499020 0.866590i \(-0.666307\pi\)
−0.499020 + 0.866590i \(0.666307\pi\)
\(878\) 14015.4 0.538720
\(879\) 9668.92 0.371018
\(880\) 31564.0 1.20912
\(881\) 9337.06 0.357064 0.178532 0.983934i \(-0.442865\pi\)
0.178532 + 0.983934i \(0.442865\pi\)
\(882\) −31720.0 −1.21096
\(883\) −70.8656 −0.00270081 −0.00135041 0.999999i \(-0.500430\pi\)
−0.00135041 + 0.999999i \(0.500430\pi\)
\(884\) 81.6505 0.00310656
\(885\) −2303.34 −0.0874870
\(886\) 27893.0 1.05765
\(887\) −1058.85 −0.0400819 −0.0200409 0.999799i \(-0.506380\pi\)
−0.0200409 + 0.999799i \(0.506380\pi\)
\(888\) −23408.3 −0.884608
\(889\) 47334.7 1.78578
\(890\) −56847.2 −2.14104
\(891\) 2362.08 0.0888135
\(892\) −1222.18 −0.0458762
\(893\) −20673.5 −0.774705
\(894\) 29051.2 1.08682
\(895\) 19821.6 0.740293
\(896\) −49323.1 −1.83903
\(897\) 0 0
\(898\) −28953.3 −1.07593
\(899\) −5118.55 −0.189892
\(900\) −685.362 −0.0253838
\(901\) −12824.4 −0.474187
\(902\) 13727.4 0.506734
\(903\) −10866.1 −0.400443
\(904\) −5955.54 −0.219113
\(905\) 21572.1 0.792356
\(906\) 19516.5 0.715664
\(907\) −29050.2 −1.06350 −0.531751 0.846900i \(-0.678466\pi\)
−0.531751 + 0.846900i \(0.678466\pi\)
\(908\) −252.742 −0.00923736
\(909\) 21049.3 0.768055
\(910\) 24456.3 0.890899
\(911\) −16041.6 −0.583404 −0.291702 0.956509i \(-0.594222\pi\)
−0.291702 + 0.956509i \(0.594222\pi\)
\(912\) 21392.6 0.776732
\(913\) 13383.2 0.485125
\(914\) −10216.8 −0.369738
\(915\) −5948.87 −0.214933
\(916\) 1150.73 0.0415078
\(917\) −47763.9 −1.72007
\(918\) 10274.3 0.369392
\(919\) 30151.2 1.08226 0.541130 0.840939i \(-0.317997\pi\)
0.541130 + 0.840939i \(0.317997\pi\)
\(920\) 0 0
\(921\) −27105.5 −0.969767
\(922\) −21490.5 −0.767626
\(923\) 284.455 0.0101440
\(924\) 685.112 0.0243923
\(925\) 60462.8 2.14919
\(926\) 44251.6 1.57041
\(927\) 20838.1 0.738311
\(928\) 594.192 0.0210186
\(929\) 43339.8 1.53061 0.765303 0.643670i \(-0.222589\pi\)
0.765303 + 0.643670i \(0.222589\pi\)
\(930\) 15746.5 0.555212
\(931\) −68909.5 −2.42580
\(932\) 1619.51 0.0569194
\(933\) −6546.32 −0.229707
\(934\) −34044.8 −1.19270
\(935\) 11854.2 0.414626
\(936\) −4907.00 −0.171357
\(937\) −27291.9 −0.951533 −0.475766 0.879572i \(-0.657829\pi\)
−0.475766 + 0.879572i \(0.657829\pi\)
\(938\) 46712.5 1.62603
\(939\) 13250.7 0.460511
\(940\) 895.311 0.0310658
\(941\) 4358.15 0.150980 0.0754898 0.997147i \(-0.475948\pi\)
0.0754898 + 0.997147i \(0.475948\pi\)
\(942\) −4983.25 −0.172360
\(943\) 0 0
\(944\) 2452.54 0.0845587
\(945\) 85287.3 2.93587
\(946\) −7398.40 −0.254274
\(947\) 39067.8 1.34059 0.670293 0.742097i \(-0.266169\pi\)
0.670293 + 0.742097i \(0.266169\pi\)
\(948\) 349.746 0.0119823
\(949\) 3018.51 0.103251
\(950\) −53723.6 −1.83476
\(951\) 6457.78 0.220197
\(952\) −18024.0 −0.613614
\(953\) 52563.8 1.78668 0.893341 0.449379i \(-0.148355\pi\)
0.893341 + 0.449379i \(0.148355\pi\)
\(954\) −22613.1 −0.767428
\(955\) −43415.2 −1.47108
\(956\) 354.869 0.0120055
\(957\) 5287.06 0.178585
\(958\) −1999.75 −0.0674416
\(959\) −61837.4 −2.08220
\(960\) 30674.6 1.03127
\(961\) −21893.3 −0.734896
\(962\) −12701.4 −0.425684
\(963\) 25173.3 0.842365
\(964\) −690.682 −0.0230761
\(965\) 4185.02 0.139607
\(966\) 0 0
\(967\) −2440.46 −0.0811580 −0.0405790 0.999176i \(-0.512920\pi\)
−0.0405790 + 0.999176i \(0.512920\pi\)
\(968\) 13774.0 0.457348
\(969\) 8034.24 0.266354
\(970\) −93525.9 −3.09581
\(971\) −45490.7 −1.50347 −0.751733 0.659468i \(-0.770782\pi\)
−0.751733 + 0.659468i \(0.770782\pi\)
\(972\) 823.439 0.0271727
\(973\) 49301.5 1.62439
\(974\) 41345.9 1.36017
\(975\) −9862.52 −0.323952
\(976\) 6334.21 0.207739
\(977\) 33244.4 1.08862 0.544311 0.838884i \(-0.316791\pi\)
0.544311 + 0.838884i \(0.316791\pi\)
\(978\) −25677.9 −0.839559
\(979\) 29450.6 0.961437
\(980\) 2984.28 0.0972749
\(981\) −12472.1 −0.405914
\(982\) 50309.6 1.63487
\(983\) −1171.32 −0.0380053 −0.0190027 0.999819i \(-0.506049\pi\)
−0.0190027 + 0.999819i \(0.506049\pi\)
\(984\) 13732.7 0.444901
\(985\) −25490.7 −0.824569
\(986\) 4081.02 0.131811
\(987\) −24580.6 −0.792716
\(988\) 312.772 0.0100715
\(989\) 0 0
\(990\) 20902.4 0.671033
\(991\) −3714.32 −0.119061 −0.0595304 0.998226i \(-0.518960\pi\)
−0.0595304 + 0.998226i \(0.518960\pi\)
\(992\) −916.814 −0.0293436
\(993\) 23477.1 0.750276
\(994\) 1842.34 0.0587883
\(995\) −19196.2 −0.611618
\(996\) −392.818 −0.0124969
\(997\) 19521.0 0.620098 0.310049 0.950721i \(-0.399655\pi\)
0.310049 + 0.950721i \(0.399655\pi\)
\(998\) −53922.9 −1.71032
\(999\) −44293.9 −1.40280
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 529.4.a.g.1.3 4
23.22 odd 2 23.4.a.b.1.3 4
69.68 even 2 207.4.a.e.1.2 4
92.91 even 2 368.4.a.l.1.2 4
115.22 even 4 575.4.b.g.24.6 8
115.68 even 4 575.4.b.g.24.3 8
115.114 odd 2 575.4.a.i.1.2 4
161.160 even 2 1127.4.a.c.1.3 4
184.45 odd 2 1472.4.a.y.1.2 4
184.91 even 2 1472.4.a.bf.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.4.a.b.1.3 4 23.22 odd 2
207.4.a.e.1.2 4 69.68 even 2
368.4.a.l.1.2 4 92.91 even 2
529.4.a.g.1.3 4 1.1 even 1 trivial
575.4.a.i.1.2 4 115.114 odd 2
575.4.b.g.24.3 8 115.68 even 4
575.4.b.g.24.6 8 115.22 even 4
1127.4.a.c.1.3 4 161.160 even 2
1472.4.a.y.1.2 4 184.45 odd 2
1472.4.a.bf.1.3 4 184.91 even 2