Properties

Label 2151.4.a.d.1.9
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
Dimension $32$
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] = [2151,4,Mod(1,2151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2151, 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("2151.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.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: \(126.913108422\)
Analytic rank: \(1\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 717)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 2151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.63855 q^{2} +5.23901 q^{4} -13.7159 q^{5} +7.38539 q^{7} +10.0460 q^{8} +O(q^{10})\) \(q-3.63855 q^{2} +5.23901 q^{4} -13.7159 q^{5} +7.38539 q^{7} +10.0460 q^{8} +49.9058 q^{10} -66.1642 q^{11} +26.6111 q^{13} -26.8721 q^{14} -78.4648 q^{16} +49.9563 q^{17} -9.84240 q^{19} -71.8575 q^{20} +240.742 q^{22} -14.3919 q^{23} +63.1246 q^{25} -96.8256 q^{26} +38.6922 q^{28} -39.4988 q^{29} -203.855 q^{31} +205.130 q^{32} -181.768 q^{34} -101.297 q^{35} +386.423 q^{37} +35.8120 q^{38} -137.789 q^{40} +380.605 q^{41} +84.5120 q^{43} -346.635 q^{44} +52.3657 q^{46} -79.4396 q^{47} -288.456 q^{49} -229.682 q^{50} +139.416 q^{52} -549.481 q^{53} +907.499 q^{55} +74.1934 q^{56} +143.718 q^{58} -375.200 q^{59} +461.499 q^{61} +741.737 q^{62} -118.657 q^{64} -364.993 q^{65} -141.327 q^{67} +261.722 q^{68} +368.573 q^{70} +164.404 q^{71} -830.189 q^{73} -1406.02 q^{74} -51.5645 q^{76} -488.649 q^{77} +979.054 q^{79} +1076.21 q^{80} -1384.85 q^{82} +933.690 q^{83} -685.193 q^{85} -307.501 q^{86} -664.684 q^{88} +647.053 q^{89} +196.533 q^{91} -75.3995 q^{92} +289.044 q^{94} +134.997 q^{95} +559.455 q^{97} +1049.56 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 11 q^{2} + 147 q^{4} - 66 q^{5} + 58 q^{7} - 153 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 11 q^{2} + 147 q^{4} - 66 q^{5} + 58 q^{7} - 153 q^{8} + 52 q^{10} - 270 q^{11} + 48 q^{13} - 184 q^{14} + 775 q^{16} - 384 q^{17} + 216 q^{19} - 534 q^{20} + 437 q^{22} - 712 q^{23} + 1190 q^{25} - 436 q^{26} + 598 q^{28} - 562 q^{29} + 384 q^{31} - 1770 q^{32} + 452 q^{34} - 1026 q^{35} + 770 q^{37} - 733 q^{38} + 877 q^{40} - 1648 q^{41} + 1592 q^{43} - 1595 q^{44} + 532 q^{46} - 1540 q^{47} + 2134 q^{49} - 1646 q^{50} - 144 q^{52} - 1708 q^{53} + 1282 q^{55} - 2155 q^{56} + 1086 q^{58} - 2396 q^{59} + 364 q^{61} - 2180 q^{62} + 1663 q^{64} - 1520 q^{65} + 2728 q^{67} - 1545 q^{68} - 4609 q^{70} - 3322 q^{71} - 188 q^{73} - 1111 q^{74} - 3134 q^{76} - 556 q^{77} - 462 q^{79} - 6076 q^{80} - 7965 q^{82} - 4604 q^{83} - 852 q^{85} - 549 q^{86} - 1127 q^{88} - 6742 q^{89} + 1390 q^{91} - 1802 q^{92} - 2796 q^{94} - 448 q^{95} - 1322 q^{97} - 1000 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.63855 −1.28642 −0.643210 0.765690i \(-0.722398\pi\)
−0.643210 + 0.765690i \(0.722398\pi\)
\(3\) 0 0
\(4\) 5.23901 0.654877
\(5\) −13.7159 −1.22678 −0.613392 0.789779i \(-0.710195\pi\)
−0.613392 + 0.789779i \(0.710195\pi\)
\(6\) 0 0
\(7\) 7.38539 0.398774 0.199387 0.979921i \(-0.436105\pi\)
0.199387 + 0.979921i \(0.436105\pi\)
\(8\) 10.0460 0.443973
\(9\) 0 0
\(10\) 49.9058 1.57816
\(11\) −66.1642 −1.81357 −0.906785 0.421594i \(-0.861471\pi\)
−0.906785 + 0.421594i \(0.861471\pi\)
\(12\) 0 0
\(13\) 26.6111 0.567737 0.283869 0.958863i \(-0.408382\pi\)
0.283869 + 0.958863i \(0.408382\pi\)
\(14\) −26.8721 −0.512990
\(15\) 0 0
\(16\) −78.4648 −1.22601
\(17\) 49.9563 0.712716 0.356358 0.934349i \(-0.384018\pi\)
0.356358 + 0.934349i \(0.384018\pi\)
\(18\) 0 0
\(19\) −9.84240 −0.118842 −0.0594211 0.998233i \(-0.518925\pi\)
−0.0594211 + 0.998233i \(0.518925\pi\)
\(20\) −71.8575 −0.803392
\(21\) 0 0
\(22\) 240.742 2.33301
\(23\) −14.3919 −0.130475 −0.0652375 0.997870i \(-0.520780\pi\)
−0.0652375 + 0.997870i \(0.520780\pi\)
\(24\) 0 0
\(25\) 63.1246 0.504997
\(26\) −96.8256 −0.730348
\(27\) 0 0
\(28\) 38.6922 0.261148
\(29\) −39.4988 −0.252922 −0.126461 0.991972i \(-0.540362\pi\)
−0.126461 + 0.991972i \(0.540362\pi\)
\(30\) 0 0
\(31\) −203.855 −1.18108 −0.590541 0.807008i \(-0.701085\pi\)
−0.590541 + 0.807008i \(0.701085\pi\)
\(32\) 205.130 1.13319
\(33\) 0 0
\(34\) −181.768 −0.916852
\(35\) −101.297 −0.489209
\(36\) 0 0
\(37\) 386.423 1.71696 0.858481 0.512845i \(-0.171408\pi\)
0.858481 + 0.512845i \(0.171408\pi\)
\(38\) 35.8120 0.152881
\(39\) 0 0
\(40\) −137.789 −0.544659
\(41\) 380.605 1.44977 0.724883 0.688871i \(-0.241894\pi\)
0.724883 + 0.688871i \(0.241894\pi\)
\(42\) 0 0
\(43\) 84.5120 0.299720 0.149860 0.988707i \(-0.452118\pi\)
0.149860 + 0.988707i \(0.452118\pi\)
\(44\) −346.635 −1.18766
\(45\) 0 0
\(46\) 52.3657 0.167846
\(47\) −79.4396 −0.246542 −0.123271 0.992373i \(-0.539338\pi\)
−0.123271 + 0.992373i \(0.539338\pi\)
\(48\) 0 0
\(49\) −288.456 −0.840980
\(50\) −229.682 −0.649638
\(51\) 0 0
\(52\) 139.416 0.371798
\(53\) −549.481 −1.42409 −0.712047 0.702132i \(-0.752232\pi\)
−0.712047 + 0.702132i \(0.752232\pi\)
\(54\) 0 0
\(55\) 907.499 2.22486
\(56\) 74.1934 0.177045
\(57\) 0 0
\(58\) 143.718 0.325364
\(59\) −375.200 −0.827914 −0.413957 0.910296i \(-0.635854\pi\)
−0.413957 + 0.910296i \(0.635854\pi\)
\(60\) 0 0
\(61\) 461.499 0.968670 0.484335 0.874883i \(-0.339062\pi\)
0.484335 + 0.874883i \(0.339062\pi\)
\(62\) 741.737 1.51937
\(63\) 0 0
\(64\) −118.657 −0.231751
\(65\) −364.993 −0.696490
\(66\) 0 0
\(67\) −141.327 −0.257699 −0.128849 0.991664i \(-0.541128\pi\)
−0.128849 + 0.991664i \(0.541128\pi\)
\(68\) 261.722 0.466741
\(69\) 0 0
\(70\) 368.573 0.629328
\(71\) 164.404 0.274805 0.137402 0.990515i \(-0.456125\pi\)
0.137402 + 0.990515i \(0.456125\pi\)
\(72\) 0 0
\(73\) −830.189 −1.33105 −0.665523 0.746378i \(-0.731791\pi\)
−0.665523 + 0.746378i \(0.731791\pi\)
\(74\) −1406.02 −2.20874
\(75\) 0 0
\(76\) −51.5645 −0.0778270
\(77\) −488.649 −0.723204
\(78\) 0 0
\(79\) 979.054 1.39433 0.697166 0.716910i \(-0.254444\pi\)
0.697166 + 0.716910i \(0.254444\pi\)
\(80\) 1076.21 1.50405
\(81\) 0 0
\(82\) −1384.85 −1.86501
\(83\) 933.690 1.23477 0.617384 0.786662i \(-0.288192\pi\)
0.617384 + 0.786662i \(0.288192\pi\)
\(84\) 0 0
\(85\) −685.193 −0.874348
\(86\) −307.501 −0.385566
\(87\) 0 0
\(88\) −664.684 −0.805177
\(89\) 647.053 0.770646 0.385323 0.922782i \(-0.374090\pi\)
0.385323 + 0.922782i \(0.374090\pi\)
\(90\) 0 0
\(91\) 196.533 0.226399
\(92\) −75.3995 −0.0854450
\(93\) 0 0
\(94\) 289.044 0.317156
\(95\) 134.997 0.145794
\(96\) 0 0
\(97\) 559.455 0.585608 0.292804 0.956172i \(-0.405412\pi\)
0.292804 + 0.956172i \(0.405412\pi\)
\(98\) 1049.56 1.08185
\(99\) 0 0
\(100\) 330.711 0.330711
\(101\) 1070.07 1.05422 0.527110 0.849797i \(-0.323276\pi\)
0.527110 + 0.849797i \(0.323276\pi\)
\(102\) 0 0
\(103\) −1260.22 −1.20557 −0.602784 0.797904i \(-0.705942\pi\)
−0.602784 + 0.797904i \(0.705942\pi\)
\(104\) 267.334 0.252060
\(105\) 0 0
\(106\) 1999.31 1.83198
\(107\) 1776.77 1.60530 0.802648 0.596453i \(-0.203424\pi\)
0.802648 + 0.596453i \(0.203424\pi\)
\(108\) 0 0
\(109\) 1002.40 0.880853 0.440426 0.897789i \(-0.354827\pi\)
0.440426 + 0.897789i \(0.354827\pi\)
\(110\) −3301.98 −2.86210
\(111\) 0 0
\(112\) −579.493 −0.488902
\(113\) −936.016 −0.779230 −0.389615 0.920978i \(-0.627392\pi\)
−0.389615 + 0.920978i \(0.627392\pi\)
\(114\) 0 0
\(115\) 197.397 0.160064
\(116\) −206.935 −0.165633
\(117\) 0 0
\(118\) 1365.18 1.06505
\(119\) 368.946 0.284212
\(120\) 0 0
\(121\) 3046.71 2.28903
\(122\) −1679.18 −1.24612
\(123\) 0 0
\(124\) −1068.00 −0.773463
\(125\) 848.674 0.607262
\(126\) 0 0
\(127\) −66.9696 −0.0467921 −0.0233960 0.999726i \(-0.507448\pi\)
−0.0233960 + 0.999726i \(0.507448\pi\)
\(128\) −1209.30 −0.835065
\(129\) 0 0
\(130\) 1328.05 0.895979
\(131\) −438.635 −0.292548 −0.146274 0.989244i \(-0.546728\pi\)
−0.146274 + 0.989244i \(0.546728\pi\)
\(132\) 0 0
\(133\) −72.6899 −0.0473911
\(134\) 514.224 0.331509
\(135\) 0 0
\(136\) 501.859 0.316427
\(137\) 694.908 0.433358 0.216679 0.976243i \(-0.430478\pi\)
0.216679 + 0.976243i \(0.430478\pi\)
\(138\) 0 0
\(139\) −2166.57 −1.32206 −0.661030 0.750359i \(-0.729881\pi\)
−0.661030 + 0.750359i \(0.729881\pi\)
\(140\) −530.696 −0.320371
\(141\) 0 0
\(142\) −598.190 −0.353514
\(143\) −1760.70 −1.02963
\(144\) 0 0
\(145\) 541.760 0.310281
\(146\) 3020.68 1.71228
\(147\) 0 0
\(148\) 2024.48 1.12440
\(149\) −129.578 −0.0712448 −0.0356224 0.999365i \(-0.511341\pi\)
−0.0356224 + 0.999365i \(0.511341\pi\)
\(150\) 0 0
\(151\) 1086.93 0.585784 0.292892 0.956145i \(-0.405382\pi\)
0.292892 + 0.956145i \(0.405382\pi\)
\(152\) −98.8764 −0.0527627
\(153\) 0 0
\(154\) 1777.97 0.930344
\(155\) 2796.05 1.44893
\(156\) 0 0
\(157\) −840.599 −0.427306 −0.213653 0.976910i \(-0.568536\pi\)
−0.213653 + 0.976910i \(0.568536\pi\)
\(158\) −3562.33 −1.79370
\(159\) 0 0
\(160\) −2813.53 −1.39018
\(161\) −106.290 −0.0520300
\(162\) 0 0
\(163\) 1448.81 0.696191 0.348096 0.937459i \(-0.386828\pi\)
0.348096 + 0.937459i \(0.386828\pi\)
\(164\) 1993.99 0.949419
\(165\) 0 0
\(166\) −3397.27 −1.58843
\(167\) 2941.59 1.36304 0.681519 0.731801i \(-0.261320\pi\)
0.681519 + 0.731801i \(0.261320\pi\)
\(168\) 0 0
\(169\) −1488.85 −0.677675
\(170\) 2493.10 1.12478
\(171\) 0 0
\(172\) 442.759 0.196280
\(173\) 929.288 0.408396 0.204198 0.978930i \(-0.434541\pi\)
0.204198 + 0.978930i \(0.434541\pi\)
\(174\) 0 0
\(175\) 466.200 0.201379
\(176\) 5191.57 2.22346
\(177\) 0 0
\(178\) −2354.33 −0.991374
\(179\) 3981.41 1.66248 0.831242 0.555910i \(-0.187630\pi\)
0.831242 + 0.555910i \(0.187630\pi\)
\(180\) 0 0
\(181\) 467.477 0.191974 0.0959870 0.995383i \(-0.469399\pi\)
0.0959870 + 0.995383i \(0.469399\pi\)
\(182\) −715.095 −0.291244
\(183\) 0 0
\(184\) −144.581 −0.0579274
\(185\) −5300.13 −2.10634
\(186\) 0 0
\(187\) −3305.32 −1.29256
\(188\) −416.185 −0.161454
\(189\) 0 0
\(190\) −491.192 −0.187552
\(191\) 252.008 0.0954695 0.0477347 0.998860i \(-0.484800\pi\)
0.0477347 + 0.998860i \(0.484800\pi\)
\(192\) 0 0
\(193\) −3575.36 −1.33347 −0.666735 0.745295i \(-0.732309\pi\)
−0.666735 + 0.745295i \(0.732309\pi\)
\(194\) −2035.60 −0.753338
\(195\) 0 0
\(196\) −1511.23 −0.550738
\(197\) −5474.34 −1.97985 −0.989924 0.141596i \(-0.954776\pi\)
−0.989924 + 0.141596i \(0.954776\pi\)
\(198\) 0 0
\(199\) 4376.75 1.55909 0.779547 0.626343i \(-0.215449\pi\)
0.779547 + 0.626343i \(0.215449\pi\)
\(200\) 634.148 0.224205
\(201\) 0 0
\(202\) −3893.51 −1.35617
\(203\) −291.714 −0.100859
\(204\) 0 0
\(205\) −5220.32 −1.77855
\(206\) 4585.38 1.55087
\(207\) 0 0
\(208\) −2088.03 −0.696053
\(209\) 651.215 0.215528
\(210\) 0 0
\(211\) 1372.80 0.447902 0.223951 0.974600i \(-0.428105\pi\)
0.223951 + 0.974600i \(0.428105\pi\)
\(212\) −2878.74 −0.932607
\(213\) 0 0
\(214\) −6464.85 −2.06509
\(215\) −1159.15 −0.367691
\(216\) 0 0
\(217\) −1505.55 −0.470984
\(218\) −3647.30 −1.13315
\(219\) 0 0
\(220\) 4754.40 1.45701
\(221\) 1329.39 0.404635
\(222\) 0 0
\(223\) −810.858 −0.243494 −0.121747 0.992561i \(-0.538850\pi\)
−0.121747 + 0.992561i \(0.538850\pi\)
\(224\) 1514.97 0.451888
\(225\) 0 0
\(226\) 3405.74 1.00242
\(227\) 3355.29 0.981049 0.490525 0.871427i \(-0.336805\pi\)
0.490525 + 0.871427i \(0.336805\pi\)
\(228\) 0 0
\(229\) −3126.00 −0.902061 −0.451031 0.892508i \(-0.648944\pi\)
−0.451031 + 0.892508i \(0.648944\pi\)
\(230\) −718.240 −0.205910
\(231\) 0 0
\(232\) −396.804 −0.112291
\(233\) −2978.06 −0.837335 −0.418667 0.908140i \(-0.637503\pi\)
−0.418667 + 0.908140i \(0.637503\pi\)
\(234\) 0 0
\(235\) 1089.58 0.302453
\(236\) −1965.68 −0.542182
\(237\) 0 0
\(238\) −1342.43 −0.365616
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −3128.78 −0.836276 −0.418138 0.908383i \(-0.637317\pi\)
−0.418138 + 0.908383i \(0.637317\pi\)
\(242\) −11085.6 −2.94466
\(243\) 0 0
\(244\) 2417.80 0.634360
\(245\) 3956.42 1.03170
\(246\) 0 0
\(247\) −261.917 −0.0674711
\(248\) −2047.93 −0.524369
\(249\) 0 0
\(250\) −3087.94 −0.781194
\(251\) 4509.62 1.13404 0.567021 0.823703i \(-0.308096\pi\)
0.567021 + 0.823703i \(0.308096\pi\)
\(252\) 0 0
\(253\) 952.231 0.236625
\(254\) 243.672 0.0601943
\(255\) 0 0
\(256\) 5349.36 1.30600
\(257\) 5048.58 1.22538 0.612688 0.790324i \(-0.290088\pi\)
0.612688 + 0.790324i \(0.290088\pi\)
\(258\) 0 0
\(259\) 2853.89 0.684679
\(260\) −1912.21 −0.456115
\(261\) 0 0
\(262\) 1595.99 0.376339
\(263\) 4417.95 1.03583 0.517913 0.855433i \(-0.326709\pi\)
0.517913 + 0.855433i \(0.326709\pi\)
\(264\) 0 0
\(265\) 7536.60 1.74706
\(266\) 264.486 0.0609649
\(267\) 0 0
\(268\) −740.413 −0.168761
\(269\) −2139.43 −0.484919 −0.242460 0.970161i \(-0.577954\pi\)
−0.242460 + 0.970161i \(0.577954\pi\)
\(270\) 0 0
\(271\) 3607.43 0.808619 0.404310 0.914622i \(-0.367512\pi\)
0.404310 + 0.914622i \(0.367512\pi\)
\(272\) −3919.81 −0.873799
\(273\) 0 0
\(274\) −2528.46 −0.557480
\(275\) −4176.59 −0.915847
\(276\) 0 0
\(277\) −8502.58 −1.84430 −0.922149 0.386835i \(-0.873568\pi\)
−0.922149 + 0.386835i \(0.873568\pi\)
\(278\) 7883.18 1.70073
\(279\) 0 0
\(280\) −1017.63 −0.217196
\(281\) −1837.65 −0.390124 −0.195062 0.980791i \(-0.562491\pi\)
−0.195062 + 0.980791i \(0.562491\pi\)
\(282\) 0 0
\(283\) 7370.66 1.54820 0.774099 0.633064i \(-0.218203\pi\)
0.774099 + 0.633064i \(0.218203\pi\)
\(284\) 861.313 0.179963
\(285\) 0 0
\(286\) 6406.39 1.32454
\(287\) 2810.91 0.578129
\(288\) 0 0
\(289\) −2417.37 −0.492036
\(290\) −1971.22 −0.399152
\(291\) 0 0
\(292\) −4349.37 −0.871671
\(293\) −952.999 −0.190016 −0.0950081 0.995476i \(-0.530288\pi\)
−0.0950081 + 0.995476i \(0.530288\pi\)
\(294\) 0 0
\(295\) 5146.19 1.01567
\(296\) 3882.00 0.762286
\(297\) 0 0
\(298\) 471.477 0.0916508
\(299\) −382.984 −0.0740755
\(300\) 0 0
\(301\) 624.154 0.119520
\(302\) −3954.86 −0.753565
\(303\) 0 0
\(304\) 772.282 0.145702
\(305\) −6329.85 −1.18835
\(306\) 0 0
\(307\) −949.397 −0.176498 −0.0882491 0.996098i \(-0.528127\pi\)
−0.0882491 + 0.996098i \(0.528127\pi\)
\(308\) −2560.04 −0.473609
\(309\) 0 0
\(310\) −10173.6 −1.86393
\(311\) −5917.05 −1.07886 −0.539429 0.842031i \(-0.681360\pi\)
−0.539429 + 0.842031i \(0.681360\pi\)
\(312\) 0 0
\(313\) 1078.16 0.194701 0.0973506 0.995250i \(-0.468963\pi\)
0.0973506 + 0.995250i \(0.468963\pi\)
\(314\) 3058.56 0.549695
\(315\) 0 0
\(316\) 5129.28 0.913115
\(317\) −6420.27 −1.13753 −0.568767 0.822499i \(-0.692579\pi\)
−0.568767 + 0.822499i \(0.692579\pi\)
\(318\) 0 0
\(319\) 2613.41 0.458692
\(320\) 1627.48 0.284308
\(321\) 0 0
\(322\) 386.741 0.0669324
\(323\) −491.689 −0.0847007
\(324\) 0 0
\(325\) 1679.81 0.286705
\(326\) −5271.54 −0.895595
\(327\) 0 0
\(328\) 3823.54 0.643658
\(329\) −586.692 −0.0983142
\(330\) 0 0
\(331\) −2171.66 −0.360620 −0.180310 0.983610i \(-0.557710\pi\)
−0.180310 + 0.983610i \(0.557710\pi\)
\(332\) 4891.61 0.808621
\(333\) 0 0
\(334\) −10703.1 −1.75344
\(335\) 1938.42 0.316140
\(336\) 0 0
\(337\) −4470.30 −0.722591 −0.361295 0.932451i \(-0.617665\pi\)
−0.361295 + 0.932451i \(0.617665\pi\)
\(338\) 5417.25 0.871774
\(339\) 0 0
\(340\) −3589.73 −0.572590
\(341\) 13487.9 2.14197
\(342\) 0 0
\(343\) −4663.55 −0.734134
\(344\) 849.005 0.133068
\(345\) 0 0
\(346\) −3381.26 −0.525369
\(347\) −275.767 −0.0426626 −0.0213313 0.999772i \(-0.506790\pi\)
−0.0213313 + 0.999772i \(0.506790\pi\)
\(348\) 0 0
\(349\) −6311.44 −0.968033 −0.484017 0.875059i \(-0.660823\pi\)
−0.484017 + 0.875059i \(0.660823\pi\)
\(350\) −1696.29 −0.259058
\(351\) 0 0
\(352\) −13572.3 −2.05513
\(353\) −452.697 −0.0682568 −0.0341284 0.999417i \(-0.510866\pi\)
−0.0341284 + 0.999417i \(0.510866\pi\)
\(354\) 0 0
\(355\) −2254.94 −0.337126
\(356\) 3389.92 0.504678
\(357\) 0 0
\(358\) −14486.6 −2.13865
\(359\) −4.87452 −0.000716622 0 −0.000358311 1.00000i \(-0.500114\pi\)
−0.000358311 1.00000i \(0.500114\pi\)
\(360\) 0 0
\(361\) −6762.13 −0.985877
\(362\) −1700.94 −0.246959
\(363\) 0 0
\(364\) 1029.64 0.148263
\(365\) 11386.8 1.63290
\(366\) 0 0
\(367\) −13316.3 −1.89402 −0.947012 0.321198i \(-0.895914\pi\)
−0.947012 + 0.321198i \(0.895914\pi\)
\(368\) 1129.26 0.159964
\(369\) 0 0
\(370\) 19284.7 2.70964
\(371\) −4058.13 −0.567891
\(372\) 0 0
\(373\) −7061.40 −0.980229 −0.490115 0.871658i \(-0.663045\pi\)
−0.490115 + 0.871658i \(0.663045\pi\)
\(374\) 12026.5 1.66278
\(375\) 0 0
\(376\) −798.048 −0.109458
\(377\) −1051.11 −0.143593
\(378\) 0 0
\(379\) 13537.7 1.83479 0.917393 0.397982i \(-0.130289\pi\)
0.917393 + 0.397982i \(0.130289\pi\)
\(380\) 707.250 0.0954768
\(381\) 0 0
\(382\) −916.943 −0.122814
\(383\) −6264.10 −0.835720 −0.417860 0.908511i \(-0.637220\pi\)
−0.417860 + 0.908511i \(0.637220\pi\)
\(384\) 0 0
\(385\) 6702.23 0.887214
\(386\) 13009.1 1.71540
\(387\) 0 0
\(388\) 2930.99 0.383501
\(389\) 6724.40 0.876455 0.438227 0.898864i \(-0.355607\pi\)
0.438227 + 0.898864i \(0.355607\pi\)
\(390\) 0 0
\(391\) −718.967 −0.0929916
\(392\) −2897.82 −0.373373
\(393\) 0 0
\(394\) 19918.6 2.54692
\(395\) −13428.6 −1.71054
\(396\) 0 0
\(397\) 4578.31 0.578788 0.289394 0.957210i \(-0.406546\pi\)
0.289394 + 0.957210i \(0.406546\pi\)
\(398\) −15925.0 −2.00565
\(399\) 0 0
\(400\) −4953.06 −0.619133
\(401\) −299.242 −0.0372654 −0.0186327 0.999826i \(-0.505931\pi\)
−0.0186327 + 0.999826i \(0.505931\pi\)
\(402\) 0 0
\(403\) −5424.81 −0.670544
\(404\) 5606.13 0.690384
\(405\) 0 0
\(406\) 1061.42 0.129747
\(407\) −25567.4 −3.11383
\(408\) 0 0
\(409\) 2314.81 0.279854 0.139927 0.990162i \(-0.455313\pi\)
0.139927 + 0.990162i \(0.455313\pi\)
\(410\) 18994.4 2.28796
\(411\) 0 0
\(412\) −6602.33 −0.789499
\(413\) −2771.00 −0.330150
\(414\) 0 0
\(415\) −12806.4 −1.51479
\(416\) 5458.73 0.643357
\(417\) 0 0
\(418\) −2369.47 −0.277260
\(419\) −13789.0 −1.60773 −0.803864 0.594813i \(-0.797226\pi\)
−0.803864 + 0.594813i \(0.797226\pi\)
\(420\) 0 0
\(421\) −6168.28 −0.714071 −0.357035 0.934091i \(-0.616212\pi\)
−0.357035 + 0.934091i \(0.616212\pi\)
\(422\) −4994.98 −0.576190
\(423\) 0 0
\(424\) −5520.07 −0.632260
\(425\) 3153.47 0.359919
\(426\) 0 0
\(427\) 3408.35 0.386280
\(428\) 9308.52 1.05127
\(429\) 0 0
\(430\) 4217.63 0.473005
\(431\) −4839.40 −0.540849 −0.270424 0.962741i \(-0.587164\pi\)
−0.270424 + 0.962741i \(0.587164\pi\)
\(432\) 0 0
\(433\) 5275.54 0.585512 0.292756 0.956187i \(-0.405428\pi\)
0.292756 + 0.956187i \(0.405428\pi\)
\(434\) 5478.02 0.605883
\(435\) 0 0
\(436\) 5251.61 0.576850
\(437\) 141.651 0.0155059
\(438\) 0 0
\(439\) −8024.63 −0.872425 −0.436212 0.899844i \(-0.643680\pi\)
−0.436212 + 0.899844i \(0.643680\pi\)
\(440\) 9116.71 0.987777
\(441\) 0 0
\(442\) −4837.04 −0.520531
\(443\) −10024.2 −1.07509 −0.537544 0.843236i \(-0.680648\pi\)
−0.537544 + 0.843236i \(0.680648\pi\)
\(444\) 0 0
\(445\) −8874.88 −0.945415
\(446\) 2950.35 0.313235
\(447\) 0 0
\(448\) −876.325 −0.0924163
\(449\) −11626.0 −1.22197 −0.610984 0.791643i \(-0.709226\pi\)
−0.610984 + 0.791643i \(0.709226\pi\)
\(450\) 0 0
\(451\) −25182.4 −2.62925
\(452\) −4903.80 −0.510300
\(453\) 0 0
\(454\) −12208.4 −1.26204
\(455\) −2695.62 −0.277742
\(456\) 0 0
\(457\) 8569.20 0.877134 0.438567 0.898698i \(-0.355486\pi\)
0.438567 + 0.898698i \(0.355486\pi\)
\(458\) 11374.1 1.16043
\(459\) 0 0
\(460\) 1034.17 0.104822
\(461\) −15878.4 −1.60419 −0.802095 0.597197i \(-0.796281\pi\)
−0.802095 + 0.597197i \(0.796281\pi\)
\(462\) 0 0
\(463\) 11333.4 1.13759 0.568796 0.822478i \(-0.307409\pi\)
0.568796 + 0.822478i \(0.307409\pi\)
\(464\) 3099.27 0.310086
\(465\) 0 0
\(466\) 10835.8 1.07716
\(467\) 6065.43 0.601016 0.300508 0.953779i \(-0.402844\pi\)
0.300508 + 0.953779i \(0.402844\pi\)
\(468\) 0 0
\(469\) −1043.75 −0.102763
\(470\) −3964.49 −0.389082
\(471\) 0 0
\(472\) −3769.25 −0.367572
\(473\) −5591.67 −0.543563
\(474\) 0 0
\(475\) −621.297 −0.0600149
\(476\) 1932.92 0.186124
\(477\) 0 0
\(478\) 869.612 0.0832116
\(479\) 5215.54 0.497504 0.248752 0.968567i \(-0.419980\pi\)
0.248752 + 0.968567i \(0.419980\pi\)
\(480\) 0 0
\(481\) 10283.1 0.974783
\(482\) 11384.2 1.07580
\(483\) 0 0
\(484\) 15961.7 1.49904
\(485\) −7673.40 −0.718414
\(486\) 0 0
\(487\) −15569.3 −1.44869 −0.724347 0.689435i \(-0.757859\pi\)
−0.724347 + 0.689435i \(0.757859\pi\)
\(488\) 4636.20 0.430064
\(489\) 0 0
\(490\) −14395.6 −1.32720
\(491\) −1285.69 −0.118172 −0.0590859 0.998253i \(-0.518819\pi\)
−0.0590859 + 0.998253i \(0.518819\pi\)
\(492\) 0 0
\(493\) −1973.21 −0.180262
\(494\) 952.996 0.0867962
\(495\) 0 0
\(496\) 15995.5 1.44802
\(497\) 1214.18 0.109585
\(498\) 0 0
\(499\) 2343.62 0.210250 0.105125 0.994459i \(-0.466476\pi\)
0.105125 + 0.994459i \(0.466476\pi\)
\(500\) 4446.22 0.397682
\(501\) 0 0
\(502\) −16408.4 −1.45885
\(503\) −8604.12 −0.762701 −0.381351 0.924430i \(-0.624541\pi\)
−0.381351 + 0.924430i \(0.624541\pi\)
\(504\) 0 0
\(505\) −14677.0 −1.29330
\(506\) −3464.73 −0.304400
\(507\) 0 0
\(508\) −350.855 −0.0306430
\(509\) −12151.5 −1.05817 −0.529083 0.848570i \(-0.677464\pi\)
−0.529083 + 0.848570i \(0.677464\pi\)
\(510\) 0 0
\(511\) −6131.27 −0.530786
\(512\) −9789.46 −0.844994
\(513\) 0 0
\(514\) −18369.5 −1.57635
\(515\) 17285.0 1.47897
\(516\) 0 0
\(517\) 5256.06 0.447120
\(518\) −10384.0 −0.880785
\(519\) 0 0
\(520\) −3666.71 −0.309223
\(521\) −20447.1 −1.71939 −0.859695 0.510808i \(-0.829346\pi\)
−0.859695 + 0.510808i \(0.829346\pi\)
\(522\) 0 0
\(523\) 20329.0 1.69967 0.849833 0.527052i \(-0.176703\pi\)
0.849833 + 0.527052i \(0.176703\pi\)
\(524\) −2298.02 −0.191583
\(525\) 0 0
\(526\) −16074.9 −1.33251
\(527\) −10183.9 −0.841776
\(528\) 0 0
\(529\) −11959.9 −0.982976
\(530\) −27422.3 −2.24745
\(531\) 0 0
\(532\) −380.824 −0.0310353
\(533\) 10128.3 0.823087
\(534\) 0 0
\(535\) −24369.9 −1.96935
\(536\) −1419.76 −0.114411
\(537\) 0 0
\(538\) 7784.41 0.623810
\(539\) 19085.5 1.52518
\(540\) 0 0
\(541\) −14893.6 −1.18360 −0.591799 0.806085i \(-0.701582\pi\)
−0.591799 + 0.806085i \(0.701582\pi\)
\(542\) −13125.8 −1.04022
\(543\) 0 0
\(544\) 10247.5 0.807646
\(545\) −13748.8 −1.08062
\(546\) 0 0
\(547\) −12312.0 −0.962383 −0.481192 0.876615i \(-0.659796\pi\)
−0.481192 + 0.876615i \(0.659796\pi\)
\(548\) 3640.64 0.283796
\(549\) 0 0
\(550\) 15196.7 1.17816
\(551\) 388.763 0.0300578
\(552\) 0 0
\(553\) 7230.70 0.556022
\(554\) 30937.0 2.37254
\(555\) 0 0
\(556\) −11350.7 −0.865787
\(557\) 8573.98 0.652229 0.326114 0.945330i \(-0.394261\pi\)
0.326114 + 0.945330i \(0.394261\pi\)
\(558\) 0 0
\(559\) 2248.95 0.170162
\(560\) 7948.25 0.599776
\(561\) 0 0
\(562\) 6686.36 0.501863
\(563\) −6372.85 −0.477058 −0.238529 0.971135i \(-0.576665\pi\)
−0.238529 + 0.971135i \(0.576665\pi\)
\(564\) 0 0
\(565\) 12838.3 0.955947
\(566\) −26818.5 −1.99163
\(567\) 0 0
\(568\) 1651.59 0.122006
\(569\) 6730.36 0.495873 0.247936 0.968776i \(-0.420248\pi\)
0.247936 + 0.968776i \(0.420248\pi\)
\(570\) 0 0
\(571\) 8502.34 0.623138 0.311569 0.950224i \(-0.399145\pi\)
0.311569 + 0.950224i \(0.399145\pi\)
\(572\) −9224.34 −0.674281
\(573\) 0 0
\(574\) −10227.6 −0.743716
\(575\) −908.484 −0.0658894
\(576\) 0 0
\(577\) 2908.85 0.209874 0.104937 0.994479i \(-0.466536\pi\)
0.104937 + 0.994479i \(0.466536\pi\)
\(578\) 8795.72 0.632965
\(579\) 0 0
\(580\) 2838.29 0.203196
\(581\) 6895.66 0.492393
\(582\) 0 0
\(583\) 36356.0 2.58269
\(584\) −8340.06 −0.590949
\(585\) 0 0
\(586\) 3467.53 0.244441
\(587\) −17116.3 −1.20352 −0.601760 0.798677i \(-0.705534\pi\)
−0.601760 + 0.798677i \(0.705534\pi\)
\(588\) 0 0
\(589\) 2006.43 0.140362
\(590\) −18724.7 −1.30658
\(591\) 0 0
\(592\) −30320.6 −2.10502
\(593\) −17817.9 −1.23389 −0.616943 0.787008i \(-0.711629\pi\)
−0.616943 + 0.787008i \(0.711629\pi\)
\(594\) 0 0
\(595\) −5060.41 −0.348667
\(596\) −678.863 −0.0466566
\(597\) 0 0
\(598\) 1393.51 0.0952922
\(599\) −21014.6 −1.43344 −0.716722 0.697359i \(-0.754358\pi\)
−0.716722 + 0.697359i \(0.754358\pi\)
\(600\) 0 0
\(601\) −24286.8 −1.64839 −0.824194 0.566308i \(-0.808371\pi\)
−0.824194 + 0.566308i \(0.808371\pi\)
\(602\) −2271.01 −0.153753
\(603\) 0 0
\(604\) 5694.46 0.383617
\(605\) −41788.2 −2.80815
\(606\) 0 0
\(607\) 3487.33 0.233190 0.116595 0.993180i \(-0.462802\pi\)
0.116595 + 0.993180i \(0.462802\pi\)
\(608\) −2018.97 −0.134671
\(609\) 0 0
\(610\) 23031.4 1.52871
\(611\) −2113.97 −0.139971
\(612\) 0 0
\(613\) −3348.02 −0.220596 −0.110298 0.993899i \(-0.535180\pi\)
−0.110298 + 0.993899i \(0.535180\pi\)
\(614\) 3454.42 0.227051
\(615\) 0 0
\(616\) −4908.95 −0.321083
\(617\) −415.752 −0.0271273 −0.0135636 0.999908i \(-0.504318\pi\)
−0.0135636 + 0.999908i \(0.504318\pi\)
\(618\) 0 0
\(619\) −20765.7 −1.34837 −0.674187 0.738561i \(-0.735506\pi\)
−0.674187 + 0.738561i \(0.735506\pi\)
\(620\) 14648.6 0.948871
\(621\) 0 0
\(622\) 21529.4 1.38787
\(623\) 4778.74 0.307313
\(624\) 0 0
\(625\) −19530.9 −1.24998
\(626\) −3922.95 −0.250467
\(627\) 0 0
\(628\) −4403.91 −0.279833
\(629\) 19304.3 1.22371
\(630\) 0 0
\(631\) 18583.1 1.17239 0.586197 0.810168i \(-0.300624\pi\)
0.586197 + 0.810168i \(0.300624\pi\)
\(632\) 9835.55 0.619046
\(633\) 0 0
\(634\) 23360.4 1.46335
\(635\) 918.545 0.0574037
\(636\) 0 0
\(637\) −7676.12 −0.477455
\(638\) −9509.01 −0.590071
\(639\) 0 0
\(640\) 16586.6 1.02444
\(641\) 10050.2 0.619279 0.309639 0.950854i \(-0.399792\pi\)
0.309639 + 0.950854i \(0.399792\pi\)
\(642\) 0 0
\(643\) −27887.6 −1.71039 −0.855193 0.518310i \(-0.826561\pi\)
−0.855193 + 0.518310i \(0.826561\pi\)
\(644\) −556.855 −0.0340732
\(645\) 0 0
\(646\) 1789.03 0.108961
\(647\) −17596.4 −1.06922 −0.534610 0.845099i \(-0.679542\pi\)
−0.534610 + 0.845099i \(0.679542\pi\)
\(648\) 0 0
\(649\) 24824.8 1.50148
\(650\) −6112.07 −0.368823
\(651\) 0 0
\(652\) 7590.31 0.455920
\(653\) −7842.61 −0.469993 −0.234996 0.971996i \(-0.575508\pi\)
−0.234996 + 0.971996i \(0.575508\pi\)
\(654\) 0 0
\(655\) 6016.26 0.358893
\(656\) −29864.1 −1.77743
\(657\) 0 0
\(658\) 2134.71 0.126473
\(659\) −3967.06 −0.234499 −0.117249 0.993102i \(-0.537408\pi\)
−0.117249 + 0.993102i \(0.537408\pi\)
\(660\) 0 0
\(661\) 13012.7 0.765710 0.382855 0.923808i \(-0.374941\pi\)
0.382855 + 0.923808i \(0.374941\pi\)
\(662\) 7901.68 0.463908
\(663\) 0 0
\(664\) 9379.82 0.548204
\(665\) 997.004 0.0581386
\(666\) 0 0
\(667\) 568.464 0.0330000
\(668\) 15411.0 0.892622
\(669\) 0 0
\(670\) −7053.02 −0.406689
\(671\) −30534.7 −1.75675
\(672\) 0 0
\(673\) 22159.3 1.26921 0.634605 0.772837i \(-0.281163\pi\)
0.634605 + 0.772837i \(0.281163\pi\)
\(674\) 16265.4 0.929555
\(675\) 0 0
\(676\) −7800.11 −0.443793
\(677\) −16452.8 −0.934019 −0.467010 0.884252i \(-0.654669\pi\)
−0.467010 + 0.884252i \(0.654669\pi\)
\(678\) 0 0
\(679\) 4131.79 0.233525
\(680\) −6883.43 −0.388187
\(681\) 0 0
\(682\) −49076.5 −2.75548
\(683\) −6703.67 −0.375562 −0.187781 0.982211i \(-0.560130\pi\)
−0.187781 + 0.982211i \(0.560130\pi\)
\(684\) 0 0
\(685\) −9531.26 −0.531636
\(686\) 16968.5 0.944405
\(687\) 0 0
\(688\) −6631.22 −0.367460
\(689\) −14622.3 −0.808511
\(690\) 0 0
\(691\) 23807.8 1.31069 0.655347 0.755328i \(-0.272522\pi\)
0.655347 + 0.755328i \(0.272522\pi\)
\(692\) 4868.55 0.267449
\(693\) 0 0
\(694\) 1003.39 0.0548821
\(695\) 29716.4 1.62188
\(696\) 0 0
\(697\) 19013.6 1.03327
\(698\) 22964.5 1.24530
\(699\) 0 0
\(700\) 2442.43 0.131879
\(701\) 15905.9 0.856999 0.428499 0.903542i \(-0.359042\pi\)
0.428499 + 0.903542i \(0.359042\pi\)
\(702\) 0 0
\(703\) −3803.33 −0.204047
\(704\) 7850.82 0.420297
\(705\) 0 0
\(706\) 1647.16 0.0878069
\(707\) 7902.90 0.420395
\(708\) 0 0
\(709\) 19476.5 1.03167 0.515836 0.856687i \(-0.327481\pi\)
0.515836 + 0.856687i \(0.327481\pi\)
\(710\) 8204.69 0.433685
\(711\) 0 0
\(712\) 6500.27 0.342146
\(713\) 2933.87 0.154102
\(714\) 0 0
\(715\) 24149.5 1.26313
\(716\) 20858.7 1.08872
\(717\) 0 0
\(718\) 17.7362 0.000921877 0
\(719\) −19269.8 −0.999504 −0.499752 0.866168i \(-0.666576\pi\)
−0.499752 + 0.866168i \(0.666576\pi\)
\(720\) 0 0
\(721\) −9307.24 −0.480749
\(722\) 24604.3 1.26825
\(723\) 0 0
\(724\) 2449.12 0.125719
\(725\) −2493.35 −0.127725
\(726\) 0 0
\(727\) 18301.4 0.933645 0.466823 0.884351i \(-0.345399\pi\)
0.466823 + 0.884351i \(0.345399\pi\)
\(728\) 1974.37 0.100515
\(729\) 0 0
\(730\) −41431.2 −2.10060
\(731\) 4221.90 0.213615
\(732\) 0 0
\(733\) 16411.7 0.826986 0.413493 0.910507i \(-0.364309\pi\)
0.413493 + 0.910507i \(0.364309\pi\)
\(734\) 48452.1 2.43651
\(735\) 0 0
\(736\) −2952.22 −0.147853
\(737\) 9350.77 0.467354
\(738\) 0 0
\(739\) 27984.1 1.39298 0.696489 0.717568i \(-0.254745\pi\)
0.696489 + 0.717568i \(0.254745\pi\)
\(740\) −27767.4 −1.37939
\(741\) 0 0
\(742\) 14765.7 0.730547
\(743\) 8620.47 0.425645 0.212823 0.977091i \(-0.431734\pi\)
0.212823 + 0.977091i \(0.431734\pi\)
\(744\) 0 0
\(745\) 1777.28 0.0874019
\(746\) 25693.2 1.26099
\(747\) 0 0
\(748\) −17316.6 −0.846468
\(749\) 13122.1 0.640150
\(750\) 0 0
\(751\) 26617.5 1.29333 0.646663 0.762776i \(-0.276164\pi\)
0.646663 + 0.762776i \(0.276164\pi\)
\(752\) 6233.21 0.302263
\(753\) 0 0
\(754\) 3824.50 0.184721
\(755\) −14908.2 −0.718630
\(756\) 0 0
\(757\) 18198.8 0.873775 0.436888 0.899516i \(-0.356081\pi\)
0.436888 + 0.899516i \(0.356081\pi\)
\(758\) −49257.5 −2.36031
\(759\) 0 0
\(760\) 1356.17 0.0647284
\(761\) −7352.93 −0.350254 −0.175127 0.984546i \(-0.556034\pi\)
−0.175127 + 0.984546i \(0.556034\pi\)
\(762\) 0 0
\(763\) 7403.15 0.351261
\(764\) 1320.27 0.0625207
\(765\) 0 0
\(766\) 22792.2 1.07509
\(767\) −9984.48 −0.470038
\(768\) 0 0
\(769\) 24387.8 1.14362 0.571811 0.820385i \(-0.306241\pi\)
0.571811 + 0.820385i \(0.306241\pi\)
\(770\) −24386.4 −1.14133
\(771\) 0 0
\(772\) −18731.3 −0.873259
\(773\) 6489.66 0.301962 0.150981 0.988537i \(-0.451757\pi\)
0.150981 + 0.988537i \(0.451757\pi\)
\(774\) 0 0
\(775\) −12868.3 −0.596442
\(776\) 5620.27 0.259995
\(777\) 0 0
\(778\) −24467.1 −1.12749
\(779\) −3746.06 −0.172293
\(780\) 0 0
\(781\) −10877.6 −0.498377
\(782\) 2615.99 0.119626
\(783\) 0 0
\(784\) 22633.7 1.03105
\(785\) 11529.5 0.524212
\(786\) 0 0
\(787\) −11896.6 −0.538840 −0.269420 0.963023i \(-0.586832\pi\)
−0.269420 + 0.963023i \(0.586832\pi\)
\(788\) −28680.1 −1.29656
\(789\) 0 0
\(790\) 48860.4 2.20048
\(791\) −6912.85 −0.310736
\(792\) 0 0
\(793\) 12281.0 0.549950
\(794\) −16658.4 −0.744565
\(795\) 0 0
\(796\) 22929.9 1.02102
\(797\) 13147.1 0.584310 0.292155 0.956371i \(-0.405628\pi\)
0.292155 + 0.956371i \(0.405628\pi\)
\(798\) 0 0
\(799\) −3968.50 −0.175714
\(800\) 12948.8 0.572259
\(801\) 0 0
\(802\) 1088.80 0.0479389
\(803\) 54928.8 2.41394
\(804\) 0 0
\(805\) 1457.86 0.0638295
\(806\) 19738.4 0.862601
\(807\) 0 0
\(808\) 10749.9 0.468046
\(809\) −27417.7 −1.19154 −0.595770 0.803155i \(-0.703153\pi\)
−0.595770 + 0.803155i \(0.703153\pi\)
\(810\) 0 0
\(811\) −26093.5 −1.12980 −0.564899 0.825160i \(-0.691085\pi\)
−0.564899 + 0.825160i \(0.691085\pi\)
\(812\) −1528.30 −0.0660501
\(813\) 0 0
\(814\) 93028.2 4.00569
\(815\) −19871.6 −0.854076
\(816\) 0 0
\(817\) −831.800 −0.0356193
\(818\) −8422.55 −0.360009
\(819\) 0 0
\(820\) −27349.3 −1.16473
\(821\) −7728.72 −0.328544 −0.164272 0.986415i \(-0.552527\pi\)
−0.164272 + 0.986415i \(0.552527\pi\)
\(822\) 0 0
\(823\) 1290.35 0.0546521 0.0273260 0.999627i \(-0.491301\pi\)
0.0273260 + 0.999627i \(0.491301\pi\)
\(824\) −12660.2 −0.535240
\(825\) 0 0
\(826\) 10082.4 0.424712
\(827\) −6519.87 −0.274145 −0.137073 0.990561i \(-0.543769\pi\)
−0.137073 + 0.990561i \(0.543769\pi\)
\(828\) 0 0
\(829\) −45033.9 −1.88672 −0.943361 0.331768i \(-0.892355\pi\)
−0.943361 + 0.331768i \(0.892355\pi\)
\(830\) 46596.5 1.94866
\(831\) 0 0
\(832\) −3157.58 −0.131574
\(833\) −14410.2 −0.599380
\(834\) 0 0
\(835\) −40346.4 −1.67215
\(836\) 3411.72 0.141145
\(837\) 0 0
\(838\) 50172.0 2.06821
\(839\) −6258.20 −0.257517 −0.128759 0.991676i \(-0.541099\pi\)
−0.128759 + 0.991676i \(0.541099\pi\)
\(840\) 0 0
\(841\) −22828.8 −0.936030
\(842\) 22443.6 0.918595
\(843\) 0 0
\(844\) 7192.10 0.293320
\(845\) 20420.9 0.831360
\(846\) 0 0
\(847\) 22501.1 0.912807
\(848\) 43114.9 1.74596
\(849\) 0 0
\(850\) −11474.0 −0.463007
\(851\) −5561.38 −0.224021
\(852\) 0 0
\(853\) 44415.9 1.78285 0.891424 0.453169i \(-0.149707\pi\)
0.891424 + 0.453169i \(0.149707\pi\)
\(854\) −12401.4 −0.496918
\(855\) 0 0
\(856\) 17849.4 0.712709
\(857\) 36097.5 1.43882 0.719409 0.694587i \(-0.244413\pi\)
0.719409 + 0.694587i \(0.244413\pi\)
\(858\) 0 0
\(859\) 44430.9 1.76480 0.882399 0.470501i \(-0.155927\pi\)
0.882399 + 0.470501i \(0.155927\pi\)
\(860\) −6072.82 −0.240792
\(861\) 0 0
\(862\) 17608.4 0.695759
\(863\) 6970.04 0.274928 0.137464 0.990507i \(-0.456105\pi\)
0.137464 + 0.990507i \(0.456105\pi\)
\(864\) 0 0
\(865\) −12746.0 −0.501013
\(866\) −19195.3 −0.753214
\(867\) 0 0
\(868\) −7887.61 −0.308437
\(869\) −64778.4 −2.52872
\(870\) 0 0
\(871\) −3760.86 −0.146305
\(872\) 10070.1 0.391075
\(873\) 0 0
\(874\) −515.404 −0.0199471
\(875\) 6267.79 0.242160
\(876\) 0 0
\(877\) 20920.2 0.805500 0.402750 0.915310i \(-0.368054\pi\)
0.402750 + 0.915310i \(0.368054\pi\)
\(878\) 29198.0 1.12231
\(879\) 0 0
\(880\) −71206.7 −2.72770
\(881\) 44357.8 1.69631 0.848157 0.529746i \(-0.177713\pi\)
0.848157 + 0.529746i \(0.177713\pi\)
\(882\) 0 0
\(883\) −25872.0 −0.986028 −0.493014 0.870021i \(-0.664105\pi\)
−0.493014 + 0.870021i \(0.664105\pi\)
\(884\) 6964.69 0.264986
\(885\) 0 0
\(886\) 36473.5 1.38301
\(887\) −1291.93 −0.0489052 −0.0244526 0.999701i \(-0.507784\pi\)
−0.0244526 + 0.999701i \(0.507784\pi\)
\(888\) 0 0
\(889\) −494.597 −0.0186594
\(890\) 32291.7 1.21620
\(891\) 0 0
\(892\) −4248.10 −0.159458
\(893\) 781.876 0.0292995
\(894\) 0 0
\(895\) −54608.5 −2.03951
\(896\) −8931.18 −0.333002
\(897\) 0 0
\(898\) 42301.6 1.57196
\(899\) 8052.05 0.298722
\(900\) 0 0
\(901\) −27450.0 −1.01497
\(902\) 91627.3 3.38232
\(903\) 0 0
\(904\) −9403.20 −0.345958
\(905\) −6411.85 −0.235511
\(906\) 0 0
\(907\) 2998.23 0.109762 0.0548812 0.998493i \(-0.482522\pi\)
0.0548812 + 0.998493i \(0.482522\pi\)
\(908\) 17578.4 0.642466
\(909\) 0 0
\(910\) 9808.13 0.357293
\(911\) −10463.1 −0.380524 −0.190262 0.981733i \(-0.560934\pi\)
−0.190262 + 0.981733i \(0.560934\pi\)
\(912\) 0 0
\(913\) −61776.9 −2.23934
\(914\) −31179.4 −1.12836
\(915\) 0 0
\(916\) −16377.2 −0.590739
\(917\) −3239.49 −0.116660
\(918\) 0 0
\(919\) 50998.5 1.83056 0.915280 0.402818i \(-0.131969\pi\)
0.915280 + 0.402818i \(0.131969\pi\)
\(920\) 1983.05 0.0710644
\(921\) 0 0
\(922\) 57774.3 2.06366
\(923\) 4374.96 0.156017
\(924\) 0 0
\(925\) 24392.8 0.867060
\(926\) −41236.9 −1.46342
\(927\) 0 0
\(928\) −8102.40 −0.286610
\(929\) 9821.02 0.346843 0.173421 0.984848i \(-0.444518\pi\)
0.173421 + 0.984848i \(0.444518\pi\)
\(930\) 0 0
\(931\) 2839.10 0.0999438
\(932\) −15602.1 −0.548351
\(933\) 0 0
\(934\) −22069.3 −0.773159
\(935\) 45335.2 1.58569
\(936\) 0 0
\(937\) 25597.2 0.892449 0.446225 0.894921i \(-0.352768\pi\)
0.446225 + 0.894921i \(0.352768\pi\)
\(938\) 3797.74 0.132197
\(939\) 0 0
\(940\) 5708.33 0.198069
\(941\) 51229.7 1.77475 0.887375 0.461049i \(-0.152527\pi\)
0.887375 + 0.461049i \(0.152527\pi\)
\(942\) 0 0
\(943\) −5477.63 −0.189158
\(944\) 29440.0 1.01503
\(945\) 0 0
\(946\) 20345.5 0.699250
\(947\) 8813.28 0.302422 0.151211 0.988502i \(-0.451683\pi\)
0.151211 + 0.988502i \(0.451683\pi\)
\(948\) 0 0
\(949\) −22092.2 −0.755684
\(950\) 2260.62 0.0772043
\(951\) 0 0
\(952\) 3706.43 0.126183
\(953\) −41702.5 −1.41750 −0.708749 0.705460i \(-0.750740\pi\)
−0.708749 + 0.705460i \(0.750740\pi\)
\(954\) 0 0
\(955\) −3456.51 −0.117120
\(956\) −1252.12 −0.0423605
\(957\) 0 0
\(958\) −18977.0 −0.639999
\(959\) 5132.17 0.172812
\(960\) 0 0
\(961\) 11766.1 0.394953
\(962\) −37415.7 −1.25398
\(963\) 0 0
\(964\) −16391.7 −0.547658
\(965\) 49039.1 1.63588
\(966\) 0 0
\(967\) −49400.1 −1.64281 −0.821407 0.570342i \(-0.806811\pi\)
−0.821407 + 0.570342i \(0.806811\pi\)
\(968\) 30607.1 1.01627
\(969\) 0 0
\(970\) 27920.0 0.924183
\(971\) 51272.8 1.69456 0.847282 0.531143i \(-0.178237\pi\)
0.847282 + 0.531143i \(0.178237\pi\)
\(972\) 0 0
\(973\) −16001.0 −0.527203
\(974\) 56649.8 1.86363
\(975\) 0 0
\(976\) −36211.4 −1.18760
\(977\) −4073.15 −0.133379 −0.0666896 0.997774i \(-0.521244\pi\)
−0.0666896 + 0.997774i \(0.521244\pi\)
\(978\) 0 0
\(979\) −42811.8 −1.39762
\(980\) 20727.7 0.675636
\(981\) 0 0
\(982\) 4678.04 0.152019
\(983\) −27220.7 −0.883219 −0.441609 0.897207i \(-0.645592\pi\)
−0.441609 + 0.897207i \(0.645592\pi\)
\(984\) 0 0
\(985\) 75085.2 2.42885
\(986\) 7179.63 0.231892
\(987\) 0 0
\(988\) −1372.19 −0.0441852
\(989\) −1216.29 −0.0391059
\(990\) 0 0
\(991\) 57200.3 1.83353 0.916765 0.399428i \(-0.130791\pi\)
0.916765 + 0.399428i \(0.130791\pi\)
\(992\) −41816.9 −1.33840
\(993\) 0 0
\(994\) −4417.87 −0.140972
\(995\) −60030.9 −1.91267
\(996\) 0 0
\(997\) −14610.2 −0.464103 −0.232051 0.972704i \(-0.574544\pi\)
−0.232051 + 0.972704i \(0.574544\pi\)
\(998\) −8527.36 −0.270470
\(999\) 0 0
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 2151.4.a.d.1.9 32
3.2 odd 2 717.4.a.d.1.24 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
717.4.a.d.1.24 32 3.2 odd 2
2151.4.a.d.1.9 32 1.1 even 1 trivial