Properties

Label 2151.4.a.b.1.14
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
Dimension $28$
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: \(28\)
Twist minimal: no (minimal twist has level 717)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
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)
 
\(f(q)\) \(=\) \(q+0.410040 q^{2} -7.83187 q^{4} +19.1512 q^{5} -11.0347 q^{7} -6.49170 q^{8} +O(q^{10})\) \(q+0.410040 q^{2} -7.83187 q^{4} +19.1512 q^{5} -11.0347 q^{7} -6.49170 q^{8} +7.85278 q^{10} -19.6472 q^{11} -19.5272 q^{13} -4.52467 q^{14} +59.9931 q^{16} -102.431 q^{17} +15.5918 q^{19} -149.990 q^{20} -8.05612 q^{22} +153.505 q^{23} +241.770 q^{25} -8.00694 q^{26} +86.4224 q^{28} -5.88022 q^{29} +209.861 q^{31} +76.5332 q^{32} -42.0008 q^{34} -211.328 q^{35} +289.738 q^{37} +6.39328 q^{38} -124.324 q^{40} +189.759 q^{41} -380.254 q^{43} +153.874 q^{44} +62.9430 q^{46} +61.6120 q^{47} -221.235 q^{49} +99.1354 q^{50} +152.934 q^{52} -499.156 q^{53} -376.267 q^{55} +71.6341 q^{56} -2.41113 q^{58} -806.008 q^{59} +231.215 q^{61} +86.0514 q^{62} -448.563 q^{64} -373.970 q^{65} -1037.28 q^{67} +802.225 q^{68} -86.6531 q^{70} -253.204 q^{71} -597.809 q^{73} +118.804 q^{74} -122.113 q^{76} +216.801 q^{77} +590.837 q^{79} +1148.94 q^{80} +77.8089 q^{82} +856.619 q^{83} -1961.68 q^{85} -155.919 q^{86} +127.543 q^{88} +425.114 q^{89} +215.477 q^{91} -1202.23 q^{92} +25.2634 q^{94} +298.603 q^{95} +1191.43 q^{97} -90.7153 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 5 q^{2} + 103 q^{4} - 6 q^{5} - 68 q^{7} + 39 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 5 q^{2} + 103 q^{4} - 6 q^{5} - 68 q^{7} + 39 q^{8} - 88 q^{10} + 110 q^{11} - 82 q^{13} - 126 q^{14} + 271 q^{16} - 100 q^{17} - 292 q^{19} + 52 q^{20} - 351 q^{22} + 276 q^{23} + 386 q^{25} - 84 q^{26} - 1010 q^{28} + 38 q^{29} - 432 q^{31} + 452 q^{32} - 524 q^{34} + 166 q^{35} - 936 q^{37} + 41 q^{38} - 1183 q^{40} - 1054 q^{41} - 1804 q^{43} + 341 q^{44} - 888 q^{46} + 560 q^{47} + 1074 q^{49} + 1054 q^{50} - 632 q^{52} + 160 q^{53} - 842 q^{55} - 509 q^{56} - 1266 q^{58} - 846 q^{59} - 2220 q^{61} - 82 q^{62} - 1565 q^{64} - 296 q^{65} - 4752 q^{67} + 1719 q^{68} - 5601 q^{70} + 802 q^{71} - 2732 q^{73} + 4581 q^{74} - 5614 q^{76} + 1008 q^{77} - 3172 q^{79} + 732 q^{80} - 9709 q^{82} + 4780 q^{83} - 4624 q^{85} + 2009 q^{86} - 9331 q^{88} - 4372 q^{89} - 7398 q^{91} + 6138 q^{92} - 7068 q^{94} + 3160 q^{95} - 4846 q^{97} + 3772 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.410040 0.144971 0.0724855 0.997369i \(-0.476907\pi\)
0.0724855 + 0.997369i \(0.476907\pi\)
\(3\) 0 0
\(4\) −7.83187 −0.978983
\(5\) 19.1512 1.71294 0.856469 0.516198i \(-0.172653\pi\)
0.856469 + 0.516198i \(0.172653\pi\)
\(6\) 0 0
\(7\) −11.0347 −0.595818 −0.297909 0.954594i \(-0.596289\pi\)
−0.297909 + 0.954594i \(0.596289\pi\)
\(8\) −6.49170 −0.286895
\(9\) 0 0
\(10\) 7.85278 0.248327
\(11\) −19.6472 −0.538531 −0.269266 0.963066i \(-0.586781\pi\)
−0.269266 + 0.963066i \(0.586781\pi\)
\(12\) 0 0
\(13\) −19.5272 −0.416606 −0.208303 0.978064i \(-0.566794\pi\)
−0.208303 + 0.978064i \(0.566794\pi\)
\(14\) −4.52467 −0.0863764
\(15\) 0 0
\(16\) 59.9931 0.937392
\(17\) −102.431 −1.46136 −0.730680 0.682720i \(-0.760797\pi\)
−0.730680 + 0.682720i \(0.760797\pi\)
\(18\) 0 0
\(19\) 15.5918 0.188264 0.0941319 0.995560i \(-0.469992\pi\)
0.0941319 + 0.995560i \(0.469992\pi\)
\(20\) −149.990 −1.67694
\(21\) 0 0
\(22\) −8.05612 −0.0780714
\(23\) 153.505 1.39165 0.695824 0.718212i \(-0.255039\pi\)
0.695824 + 0.718212i \(0.255039\pi\)
\(24\) 0 0
\(25\) 241.770 1.93416
\(26\) −8.00694 −0.0603958
\(27\) 0 0
\(28\) 86.4224 0.583296
\(29\) −5.88022 −0.0376528 −0.0188264 0.999823i \(-0.505993\pi\)
−0.0188264 + 0.999823i \(0.505993\pi\)
\(30\) 0 0
\(31\) 209.861 1.21588 0.607938 0.793985i \(-0.291997\pi\)
0.607938 + 0.793985i \(0.291997\pi\)
\(32\) 76.5332 0.422790
\(33\) 0 0
\(34\) −42.0008 −0.211855
\(35\) −211.328 −1.02060
\(36\) 0 0
\(37\) 289.738 1.28737 0.643684 0.765291i \(-0.277405\pi\)
0.643684 + 0.765291i \(0.277405\pi\)
\(38\) 6.39328 0.0272928
\(39\) 0 0
\(40\) −124.324 −0.491434
\(41\) 189.759 0.722815 0.361407 0.932408i \(-0.382296\pi\)
0.361407 + 0.932408i \(0.382296\pi\)
\(42\) 0 0
\(43\) −380.254 −1.34856 −0.674281 0.738475i \(-0.735546\pi\)
−0.674281 + 0.738475i \(0.735546\pi\)
\(44\) 153.874 0.527213
\(45\) 0 0
\(46\) 62.9430 0.201749
\(47\) 61.6120 0.191213 0.0956067 0.995419i \(-0.469521\pi\)
0.0956067 + 0.995419i \(0.469521\pi\)
\(48\) 0 0
\(49\) −221.235 −0.645000
\(50\) 99.1354 0.280397
\(51\) 0 0
\(52\) 152.934 0.407850
\(53\) −499.156 −1.29367 −0.646834 0.762631i \(-0.723907\pi\)
−0.646834 + 0.762631i \(0.723907\pi\)
\(54\) 0 0
\(55\) −376.267 −0.922471
\(56\) 71.6341 0.170938
\(57\) 0 0
\(58\) −2.41113 −0.00545856
\(59\) −806.008 −1.77853 −0.889265 0.457392i \(-0.848784\pi\)
−0.889265 + 0.457392i \(0.848784\pi\)
\(60\) 0 0
\(61\) 231.215 0.485313 0.242657 0.970112i \(-0.421981\pi\)
0.242657 + 0.970112i \(0.421981\pi\)
\(62\) 86.0514 0.176267
\(63\) 0 0
\(64\) −448.563 −0.876099
\(65\) −373.970 −0.713620
\(66\) 0 0
\(67\) −1037.28 −1.89139 −0.945697 0.325050i \(-0.894619\pi\)
−0.945697 + 0.325050i \(0.894619\pi\)
\(68\) 802.225 1.43065
\(69\) 0 0
\(70\) −86.6531 −0.147958
\(71\) −253.204 −0.423236 −0.211618 0.977352i \(-0.567873\pi\)
−0.211618 + 0.977352i \(0.567873\pi\)
\(72\) 0 0
\(73\) −597.809 −0.958469 −0.479234 0.877687i \(-0.659086\pi\)
−0.479234 + 0.877687i \(0.659086\pi\)
\(74\) 118.804 0.186631
\(75\) 0 0
\(76\) −122.113 −0.184307
\(77\) 216.801 0.320867
\(78\) 0 0
\(79\) 590.837 0.841447 0.420724 0.907189i \(-0.361776\pi\)
0.420724 + 0.907189i \(0.361776\pi\)
\(80\) 1148.94 1.60569
\(81\) 0 0
\(82\) 77.8089 0.104787
\(83\) 856.619 1.13284 0.566422 0.824115i \(-0.308327\pi\)
0.566422 + 0.824115i \(0.308327\pi\)
\(84\) 0 0
\(85\) −1961.68 −2.50322
\(86\) −155.919 −0.195502
\(87\) 0 0
\(88\) 127.543 0.154502
\(89\) 425.114 0.506314 0.253157 0.967425i \(-0.418531\pi\)
0.253157 + 0.967425i \(0.418531\pi\)
\(90\) 0 0
\(91\) 215.477 0.248221
\(92\) −1202.23 −1.36240
\(93\) 0 0
\(94\) 25.2634 0.0277204
\(95\) 298.603 0.322484
\(96\) 0 0
\(97\) 1191.43 1.24713 0.623566 0.781771i \(-0.285683\pi\)
0.623566 + 0.781771i \(0.285683\pi\)
\(98\) −90.7153 −0.0935064
\(99\) 0 0
\(100\) −1893.51 −1.89351
\(101\) −278.923 −0.274791 −0.137395 0.990516i \(-0.543873\pi\)
−0.137395 + 0.990516i \(0.543873\pi\)
\(102\) 0 0
\(103\) 30.6207 0.0292927 0.0146463 0.999893i \(-0.495338\pi\)
0.0146463 + 0.999893i \(0.495338\pi\)
\(104\) 126.765 0.119522
\(105\) 0 0
\(106\) −204.674 −0.187544
\(107\) 13.2134 0.0119382 0.00596910 0.999982i \(-0.498100\pi\)
0.00596910 + 0.999982i \(0.498100\pi\)
\(108\) 0 0
\(109\) 300.208 0.263804 0.131902 0.991263i \(-0.457892\pi\)
0.131902 + 0.991263i \(0.457892\pi\)
\(110\) −154.285 −0.133732
\(111\) 0 0
\(112\) −662.006 −0.558515
\(113\) −1058.39 −0.881108 −0.440554 0.897726i \(-0.645218\pi\)
−0.440554 + 0.897726i \(0.645218\pi\)
\(114\) 0 0
\(115\) 2939.80 2.38381
\(116\) 46.0531 0.0368614
\(117\) 0 0
\(118\) −330.496 −0.257835
\(119\) 1130.30 0.870706
\(120\) 0 0
\(121\) −944.989 −0.709984
\(122\) 94.8076 0.0703564
\(123\) 0 0
\(124\) −1643.60 −1.19032
\(125\) 2236.29 1.60016
\(126\) 0 0
\(127\) 2694.61 1.88274 0.941369 0.337378i \(-0.109540\pi\)
0.941369 + 0.337378i \(0.109540\pi\)
\(128\) −796.194 −0.549799
\(129\) 0 0
\(130\) −153.343 −0.103454
\(131\) 502.907 0.335414 0.167707 0.985837i \(-0.446364\pi\)
0.167707 + 0.985837i \(0.446364\pi\)
\(132\) 0 0
\(133\) −172.051 −0.112171
\(134\) −425.325 −0.274197
\(135\) 0 0
\(136\) 664.951 0.419258
\(137\) −1986.88 −1.23905 −0.619527 0.784976i \(-0.712675\pi\)
−0.619527 + 0.784976i \(0.712675\pi\)
\(138\) 0 0
\(139\) 554.567 0.338401 0.169201 0.985582i \(-0.445881\pi\)
0.169201 + 0.985582i \(0.445881\pi\)
\(140\) 1655.10 0.999151
\(141\) 0 0
\(142\) −103.824 −0.0613570
\(143\) 383.654 0.224355
\(144\) 0 0
\(145\) −112.614 −0.0644969
\(146\) −245.126 −0.138950
\(147\) 0 0
\(148\) −2269.19 −1.26031
\(149\) −1389.90 −0.764196 −0.382098 0.924122i \(-0.624798\pi\)
−0.382098 + 0.924122i \(0.624798\pi\)
\(150\) 0 0
\(151\) −3690.17 −1.98876 −0.994378 0.105892i \(-0.966230\pi\)
−0.994378 + 0.105892i \(0.966230\pi\)
\(152\) −101.218 −0.0540120
\(153\) 0 0
\(154\) 88.8970 0.0465164
\(155\) 4019.10 2.08272
\(156\) 0 0
\(157\) −1878.88 −0.955101 −0.477550 0.878604i \(-0.658475\pi\)
−0.477550 + 0.878604i \(0.658475\pi\)
\(158\) 242.267 0.121985
\(159\) 0 0
\(160\) 1465.71 0.724214
\(161\) −1693.88 −0.829170
\(162\) 0 0
\(163\) −2899.69 −1.39338 −0.696691 0.717372i \(-0.745345\pi\)
−0.696691 + 0.717372i \(0.745345\pi\)
\(164\) −1486.17 −0.707624
\(165\) 0 0
\(166\) 351.248 0.164230
\(167\) 687.351 0.318496 0.159248 0.987239i \(-0.449093\pi\)
0.159248 + 0.987239i \(0.449093\pi\)
\(168\) 0 0
\(169\) −1815.69 −0.826440
\(170\) −804.367 −0.362895
\(171\) 0 0
\(172\) 2978.10 1.32022
\(173\) 255.193 0.112150 0.0560751 0.998427i \(-0.482141\pi\)
0.0560751 + 0.998427i \(0.482141\pi\)
\(174\) 0 0
\(175\) −2667.86 −1.15241
\(176\) −1178.69 −0.504815
\(177\) 0 0
\(178\) 174.314 0.0734009
\(179\) −4686.20 −1.95678 −0.978388 0.206777i \(-0.933703\pi\)
−0.978388 + 0.206777i \(0.933703\pi\)
\(180\) 0 0
\(181\) −1470.17 −0.603741 −0.301870 0.953349i \(-0.597611\pi\)
−0.301870 + 0.953349i \(0.597611\pi\)
\(182\) 88.3542 0.0359849
\(183\) 0 0
\(184\) −996.506 −0.399257
\(185\) 5548.84 2.20518
\(186\) 0 0
\(187\) 2012.48 0.786988
\(188\) −482.537 −0.187195
\(189\) 0 0
\(190\) 122.439 0.0467509
\(191\) −1676.69 −0.635187 −0.317594 0.948227i \(-0.602875\pi\)
−0.317594 + 0.948227i \(0.602875\pi\)
\(192\) 0 0
\(193\) −3509.26 −1.30882 −0.654410 0.756140i \(-0.727083\pi\)
−0.654410 + 0.756140i \(0.727083\pi\)
\(194\) 488.536 0.180798
\(195\) 0 0
\(196\) 1732.68 0.631445
\(197\) 899.057 0.325153 0.162577 0.986696i \(-0.448020\pi\)
0.162577 + 0.986696i \(0.448020\pi\)
\(198\) 0 0
\(199\) 2940.66 1.04753 0.523763 0.851864i \(-0.324528\pi\)
0.523763 + 0.851864i \(0.324528\pi\)
\(200\) −1569.50 −0.554901
\(201\) 0 0
\(202\) −114.370 −0.0398367
\(203\) 64.8866 0.0224342
\(204\) 0 0
\(205\) 3634.12 1.23814
\(206\) 12.5557 0.00424659
\(207\) 0 0
\(208\) −1171.50 −0.390523
\(209\) −306.335 −0.101386
\(210\) 0 0
\(211\) 399.675 0.130402 0.0652008 0.997872i \(-0.479231\pi\)
0.0652008 + 0.997872i \(0.479231\pi\)
\(212\) 3909.32 1.26648
\(213\) 0 0
\(214\) 5.41802 0.00173069
\(215\) −7282.33 −2.31000
\(216\) 0 0
\(217\) −2315.75 −0.724441
\(218\) 123.097 0.0382440
\(219\) 0 0
\(220\) 2946.88 0.903083
\(221\) 2000.19 0.608811
\(222\) 0 0
\(223\) −4539.97 −1.36331 −0.681657 0.731672i \(-0.738740\pi\)
−0.681657 + 0.731672i \(0.738740\pi\)
\(224\) −844.522 −0.251906
\(225\) 0 0
\(226\) −433.983 −0.127735
\(227\) 3502.99 1.02424 0.512118 0.858915i \(-0.328861\pi\)
0.512118 + 0.858915i \(0.328861\pi\)
\(228\) 0 0
\(229\) −5815.73 −1.67823 −0.839114 0.543956i \(-0.816926\pi\)
−0.839114 + 0.543956i \(0.816926\pi\)
\(230\) 1205.44 0.345583
\(231\) 0 0
\(232\) 38.1727 0.0108024
\(233\) 4023.74 1.13135 0.565673 0.824630i \(-0.308616\pi\)
0.565673 + 0.824630i \(0.308616\pi\)
\(234\) 0 0
\(235\) 1179.95 0.327537
\(236\) 6312.55 1.74115
\(237\) 0 0
\(238\) 463.466 0.126227
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 2859.61 0.764330 0.382165 0.924094i \(-0.375179\pi\)
0.382165 + 0.924094i \(0.375179\pi\)
\(242\) −387.484 −0.102927
\(243\) 0 0
\(244\) −1810.85 −0.475113
\(245\) −4236.93 −1.10485
\(246\) 0 0
\(247\) −304.465 −0.0784318
\(248\) −1362.35 −0.348829
\(249\) 0 0
\(250\) 916.968 0.231977
\(251\) 454.207 0.114220 0.0571101 0.998368i \(-0.481811\pi\)
0.0571101 + 0.998368i \(0.481811\pi\)
\(252\) 0 0
\(253\) −3015.93 −0.749446
\(254\) 1104.90 0.272943
\(255\) 0 0
\(256\) 3262.03 0.796395
\(257\) 1391.28 0.337687 0.168843 0.985643i \(-0.445997\pi\)
0.168843 + 0.985643i \(0.445997\pi\)
\(258\) 0 0
\(259\) −3197.18 −0.767038
\(260\) 2928.88 0.698622
\(261\) 0 0
\(262\) 206.212 0.0486253
\(263\) −5779.48 −1.35505 −0.677525 0.735500i \(-0.736947\pi\)
−0.677525 + 0.735500i \(0.736947\pi\)
\(264\) 0 0
\(265\) −9559.46 −2.21597
\(266\) −70.5480 −0.0162616
\(267\) 0 0
\(268\) 8123.80 1.85164
\(269\) 1726.44 0.391311 0.195656 0.980673i \(-0.437317\pi\)
0.195656 + 0.980673i \(0.437317\pi\)
\(270\) 0 0
\(271\) 1584.05 0.355072 0.177536 0.984114i \(-0.443187\pi\)
0.177536 + 0.984114i \(0.443187\pi\)
\(272\) −6145.14 −1.36987
\(273\) 0 0
\(274\) −814.699 −0.179627
\(275\) −4750.09 −1.04160
\(276\) 0 0
\(277\) −1591.17 −0.345140 −0.172570 0.984997i \(-0.555207\pi\)
−0.172570 + 0.984997i \(0.555207\pi\)
\(278\) 227.395 0.0490584
\(279\) 0 0
\(280\) 1371.88 0.292806
\(281\) 113.733 0.0241451 0.0120725 0.999927i \(-0.496157\pi\)
0.0120725 + 0.999927i \(0.496157\pi\)
\(282\) 0 0
\(283\) 1352.24 0.284036 0.142018 0.989864i \(-0.454641\pi\)
0.142018 + 0.989864i \(0.454641\pi\)
\(284\) 1983.06 0.414341
\(285\) 0 0
\(286\) 157.314 0.0325250
\(287\) −2093.94 −0.430666
\(288\) 0 0
\(289\) 5579.08 1.13558
\(290\) −46.1761 −0.00935018
\(291\) 0 0
\(292\) 4681.96 0.938325
\(293\) −6661.54 −1.32823 −0.664115 0.747630i \(-0.731192\pi\)
−0.664115 + 0.747630i \(0.731192\pi\)
\(294\) 0 0
\(295\) −15436.0 −3.04651
\(296\) −1880.89 −0.369340
\(297\) 0 0
\(298\) −569.916 −0.110786
\(299\) −2997.51 −0.579768
\(300\) 0 0
\(301\) 4195.99 0.803498
\(302\) −1513.12 −0.288312
\(303\) 0 0
\(304\) 935.403 0.176477
\(305\) 4428.06 0.831312
\(306\) 0 0
\(307\) −6091.74 −1.13249 −0.566245 0.824237i \(-0.691604\pi\)
−0.566245 + 0.824237i \(0.691604\pi\)
\(308\) −1697.95 −0.314123
\(309\) 0 0
\(310\) 1647.99 0.301934
\(311\) −964.699 −0.175894 −0.0879471 0.996125i \(-0.528031\pi\)
−0.0879471 + 0.996125i \(0.528031\pi\)
\(312\) 0 0
\(313\) 1734.62 0.313247 0.156623 0.987658i \(-0.449939\pi\)
0.156623 + 0.987658i \(0.449939\pi\)
\(314\) −770.416 −0.138462
\(315\) 0 0
\(316\) −4627.35 −0.823763
\(317\) −1182.23 −0.209466 −0.104733 0.994500i \(-0.533399\pi\)
−0.104733 + 0.994500i \(0.533399\pi\)
\(318\) 0 0
\(319\) 115.530 0.0202772
\(320\) −8590.54 −1.50070
\(321\) 0 0
\(322\) −694.558 −0.120206
\(323\) −1597.09 −0.275121
\(324\) 0 0
\(325\) −4721.09 −0.805781
\(326\) −1188.99 −0.202000
\(327\) 0 0
\(328\) −1231.86 −0.207372
\(329\) −679.871 −0.113928
\(330\) 0 0
\(331\) −5918.46 −0.982804 −0.491402 0.870933i \(-0.663515\pi\)
−0.491402 + 0.870933i \(0.663515\pi\)
\(332\) −6708.92 −1.10904
\(333\) 0 0
\(334\) 281.841 0.0461727
\(335\) −19865.1 −3.23984
\(336\) 0 0
\(337\) −4897.54 −0.791650 −0.395825 0.918326i \(-0.629541\pi\)
−0.395825 + 0.918326i \(0.629541\pi\)
\(338\) −744.505 −0.119810
\(339\) 0 0
\(340\) 15363.6 2.45061
\(341\) −4123.17 −0.654786
\(342\) 0 0
\(343\) 6226.17 0.980122
\(344\) 2468.49 0.386896
\(345\) 0 0
\(346\) 104.640 0.0162585
\(347\) 9378.30 1.45087 0.725437 0.688288i \(-0.241637\pi\)
0.725437 + 0.688288i \(0.241637\pi\)
\(348\) 0 0
\(349\) 671.157 0.102941 0.0514703 0.998675i \(-0.483609\pi\)
0.0514703 + 0.998675i \(0.483609\pi\)
\(350\) −1093.93 −0.167066
\(351\) 0 0
\(352\) −1503.66 −0.227686
\(353\) −173.097 −0.0260992 −0.0130496 0.999915i \(-0.504154\pi\)
−0.0130496 + 0.999915i \(0.504154\pi\)
\(354\) 0 0
\(355\) −4849.17 −0.724978
\(356\) −3329.43 −0.495673
\(357\) 0 0
\(358\) −1921.53 −0.283676
\(359\) −7107.06 −1.04484 −0.522418 0.852689i \(-0.674970\pi\)
−0.522418 + 0.852689i \(0.674970\pi\)
\(360\) 0 0
\(361\) −6615.89 −0.964557
\(362\) −602.830 −0.0875250
\(363\) 0 0
\(364\) −1687.59 −0.243004
\(365\) −11448.8 −1.64180
\(366\) 0 0
\(367\) 9164.35 1.30347 0.651737 0.758445i \(-0.274041\pi\)
0.651737 + 0.758445i \(0.274041\pi\)
\(368\) 9209.21 1.30452
\(369\) 0 0
\(370\) 2275.25 0.319688
\(371\) 5508.04 0.770791
\(372\) 0 0
\(373\) 4223.88 0.586338 0.293169 0.956061i \(-0.405290\pi\)
0.293169 + 0.956061i \(0.405290\pi\)
\(374\) 825.196 0.114091
\(375\) 0 0
\(376\) −399.967 −0.0548583
\(377\) 114.824 0.0156863
\(378\) 0 0
\(379\) −1150.78 −0.155967 −0.0779834 0.996955i \(-0.524848\pi\)
−0.0779834 + 0.996955i \(0.524848\pi\)
\(380\) −2338.62 −0.315707
\(381\) 0 0
\(382\) −687.509 −0.0920838
\(383\) −9157.79 −1.22178 −0.610889 0.791716i \(-0.709188\pi\)
−0.610889 + 0.791716i \(0.709188\pi\)
\(384\) 0 0
\(385\) 4152.00 0.549625
\(386\) −1438.94 −0.189741
\(387\) 0 0
\(388\) −9331.15 −1.22092
\(389\) 2370.80 0.309008 0.154504 0.987992i \(-0.450622\pi\)
0.154504 + 0.987992i \(0.450622\pi\)
\(390\) 0 0
\(391\) −15723.6 −2.03370
\(392\) 1436.19 0.185048
\(393\) 0 0
\(394\) 368.649 0.0471378
\(395\) 11315.3 1.44135
\(396\) 0 0
\(397\) 4487.57 0.567316 0.283658 0.958926i \(-0.408452\pi\)
0.283658 + 0.958926i \(0.408452\pi\)
\(398\) 1205.79 0.151861
\(399\) 0 0
\(400\) 14504.5 1.81306
\(401\) −13496.7 −1.68079 −0.840393 0.541977i \(-0.817676\pi\)
−0.840393 + 0.541977i \(0.817676\pi\)
\(402\) 0 0
\(403\) −4098.00 −0.506540
\(404\) 2184.49 0.269016
\(405\) 0 0
\(406\) 26.6061 0.00325231
\(407\) −5692.53 −0.693288
\(408\) 0 0
\(409\) −5635.52 −0.681317 −0.340658 0.940187i \(-0.610650\pi\)
−0.340658 + 0.940187i \(0.610650\pi\)
\(410\) 1490.14 0.179494
\(411\) 0 0
\(412\) −239.817 −0.0286770
\(413\) 8894.06 1.05968
\(414\) 0 0
\(415\) 16405.3 1.94049
\(416\) −1494.48 −0.176137
\(417\) 0 0
\(418\) −125.610 −0.0146980
\(419\) 15387.8 1.79414 0.897068 0.441892i \(-0.145693\pi\)
0.897068 + 0.441892i \(0.145693\pi\)
\(420\) 0 0
\(421\) −7068.70 −0.818308 −0.409154 0.912465i \(-0.634176\pi\)
−0.409154 + 0.912465i \(0.634176\pi\)
\(422\) 163.883 0.0189045
\(423\) 0 0
\(424\) 3240.37 0.371147
\(425\) −24764.7 −2.82650
\(426\) 0 0
\(427\) −2551.40 −0.289158
\(428\) −103.486 −0.0116873
\(429\) 0 0
\(430\) −2986.05 −0.334884
\(431\) 12414.8 1.38747 0.693736 0.720230i \(-0.255964\pi\)
0.693736 + 0.720230i \(0.255964\pi\)
\(432\) 0 0
\(433\) −9540.57 −1.05887 −0.529435 0.848351i \(-0.677596\pi\)
−0.529435 + 0.848351i \(0.677596\pi\)
\(434\) −949.552 −0.105023
\(435\) 0 0
\(436\) −2351.19 −0.258260
\(437\) 2393.42 0.261997
\(438\) 0 0
\(439\) −12109.2 −1.31650 −0.658248 0.752801i \(-0.728702\pi\)
−0.658248 + 0.752801i \(0.728702\pi\)
\(440\) 2442.62 0.264653
\(441\) 0 0
\(442\) 820.158 0.0882600
\(443\) 10745.2 1.15241 0.576205 0.817305i \(-0.304533\pi\)
0.576205 + 0.817305i \(0.304533\pi\)
\(444\) 0 0
\(445\) 8141.45 0.867285
\(446\) −1861.57 −0.197641
\(447\) 0 0
\(448\) 4949.76 0.521996
\(449\) −12251.4 −1.28771 −0.643854 0.765149i \(-0.722665\pi\)
−0.643854 + 0.765149i \(0.722665\pi\)
\(450\) 0 0
\(451\) −3728.23 −0.389258
\(452\) 8289.19 0.862590
\(453\) 0 0
\(454\) 1436.37 0.148485
\(455\) 4126.65 0.425188
\(456\) 0 0
\(457\) 9561.13 0.978667 0.489334 0.872097i \(-0.337240\pi\)
0.489334 + 0.872097i \(0.337240\pi\)
\(458\) −2384.68 −0.243294
\(459\) 0 0
\(460\) −23024.1 −2.33371
\(461\) −9185.83 −0.928041 −0.464021 0.885824i \(-0.653594\pi\)
−0.464021 + 0.885824i \(0.653594\pi\)
\(462\) 0 0
\(463\) −3944.19 −0.395900 −0.197950 0.980212i \(-0.563428\pi\)
−0.197950 + 0.980212i \(0.563428\pi\)
\(464\) −352.773 −0.0352954
\(465\) 0 0
\(466\) 1649.89 0.164013
\(467\) 12677.7 1.25622 0.628111 0.778124i \(-0.283828\pi\)
0.628111 + 0.778124i \(0.283828\pi\)
\(468\) 0 0
\(469\) 11446.0 1.12693
\(470\) 483.825 0.0474834
\(471\) 0 0
\(472\) 5232.36 0.510252
\(473\) 7470.91 0.726242
\(474\) 0 0
\(475\) 3769.64 0.364132
\(476\) −8852.32 −0.852406
\(477\) 0 0
\(478\) −97.9996 −0.00937740
\(479\) −5220.89 −0.498013 −0.249007 0.968502i \(-0.580104\pi\)
−0.249007 + 0.968502i \(0.580104\pi\)
\(480\) 0 0
\(481\) −5657.77 −0.536325
\(482\) 1172.55 0.110806
\(483\) 0 0
\(484\) 7401.03 0.695063
\(485\) 22817.4 2.13626
\(486\) 0 0
\(487\) −12640.9 −1.17621 −0.588106 0.808784i \(-0.700126\pi\)
−0.588106 + 0.808784i \(0.700126\pi\)
\(488\) −1500.98 −0.139234
\(489\) 0 0
\(490\) −1737.31 −0.160171
\(491\) 1322.37 0.121543 0.0607715 0.998152i \(-0.480644\pi\)
0.0607715 + 0.998152i \(0.480644\pi\)
\(492\) 0 0
\(493\) 602.316 0.0550243
\(494\) −124.843 −0.0113703
\(495\) 0 0
\(496\) 12590.2 1.13975
\(497\) 2794.03 0.252172
\(498\) 0 0
\(499\) 1861.29 0.166980 0.0834900 0.996509i \(-0.473393\pi\)
0.0834900 + 0.996509i \(0.473393\pi\)
\(500\) −17514.3 −1.56653
\(501\) 0 0
\(502\) 186.243 0.0165586
\(503\) −10146.4 −0.899412 −0.449706 0.893177i \(-0.648471\pi\)
−0.449706 + 0.893177i \(0.648471\pi\)
\(504\) 0 0
\(505\) −5341.72 −0.470700
\(506\) −1236.65 −0.108648
\(507\) 0 0
\(508\) −21103.8 −1.84317
\(509\) 10573.5 0.920750 0.460375 0.887724i \(-0.347715\pi\)
0.460375 + 0.887724i \(0.347715\pi\)
\(510\) 0 0
\(511\) 6596.65 0.571073
\(512\) 7707.12 0.665253
\(513\) 0 0
\(514\) 570.480 0.0489548
\(515\) 586.424 0.0501766
\(516\) 0 0
\(517\) −1210.50 −0.102974
\(518\) −1310.97 −0.111198
\(519\) 0 0
\(520\) 2427.70 0.204734
\(521\) 569.399 0.0478806 0.0239403 0.999713i \(-0.492379\pi\)
0.0239403 + 0.999713i \(0.492379\pi\)
\(522\) 0 0
\(523\) 15735.2 1.31559 0.657793 0.753199i \(-0.271490\pi\)
0.657793 + 0.753199i \(0.271490\pi\)
\(524\) −3938.70 −0.328365
\(525\) 0 0
\(526\) −2369.82 −0.196443
\(527\) −21496.2 −1.77683
\(528\) 0 0
\(529\) 11396.6 0.936685
\(530\) −3919.76 −0.321252
\(531\) 0 0
\(532\) 1347.48 0.109814
\(533\) −3705.47 −0.301129
\(534\) 0 0
\(535\) 253.053 0.0204494
\(536\) 6733.68 0.542632
\(537\) 0 0
\(538\) 707.908 0.0567288
\(539\) 4346.64 0.347353
\(540\) 0 0
\(541\) −17202.3 −1.36707 −0.683533 0.729919i \(-0.739558\pi\)
−0.683533 + 0.729919i \(0.739558\pi\)
\(542\) 649.526 0.0514751
\(543\) 0 0
\(544\) −7839.36 −0.617849
\(545\) 5749.35 0.451881
\(546\) 0 0
\(547\) −24396.8 −1.90700 −0.953501 0.301390i \(-0.902549\pi\)
−0.953501 + 0.301390i \(0.902549\pi\)
\(548\) 15561.0 1.21301
\(549\) 0 0
\(550\) −1947.73 −0.151003
\(551\) −91.6835 −0.00708865
\(552\) 0 0
\(553\) −6519.71 −0.501350
\(554\) −652.442 −0.0500354
\(555\) 0 0
\(556\) −4343.30 −0.331289
\(557\) 17490.8 1.33054 0.665268 0.746604i \(-0.268317\pi\)
0.665268 + 0.746604i \(0.268317\pi\)
\(558\) 0 0
\(559\) 7425.29 0.561818
\(560\) −12678.2 −0.956702
\(561\) 0 0
\(562\) 46.6352 0.00350034
\(563\) 5212.73 0.390213 0.195107 0.980782i \(-0.437495\pi\)
0.195107 + 0.980782i \(0.437495\pi\)
\(564\) 0 0
\(565\) −20269.5 −1.50928
\(566\) 554.472 0.0411770
\(567\) 0 0
\(568\) 1643.72 0.121425
\(569\) 7606.26 0.560406 0.280203 0.959941i \(-0.409598\pi\)
0.280203 + 0.959941i \(0.409598\pi\)
\(570\) 0 0
\(571\) −16718.9 −1.22533 −0.612665 0.790343i \(-0.709902\pi\)
−0.612665 + 0.790343i \(0.709902\pi\)
\(572\) −3004.73 −0.219640
\(573\) 0 0
\(574\) −858.599 −0.0624342
\(575\) 37112.8 2.69167
\(576\) 0 0
\(577\) −12336.2 −0.890059 −0.445029 0.895516i \(-0.646807\pi\)
−0.445029 + 0.895516i \(0.646807\pi\)
\(578\) 2287.65 0.164626
\(579\) 0 0
\(580\) 881.974 0.0631414
\(581\) −9452.54 −0.674970
\(582\) 0 0
\(583\) 9807.00 0.696680
\(584\) 3880.80 0.274980
\(585\) 0 0
\(586\) −2731.50 −0.192555
\(587\) 7213.07 0.507181 0.253590 0.967312i \(-0.418388\pi\)
0.253590 + 0.967312i \(0.418388\pi\)
\(588\) 0 0
\(589\) 3272.12 0.228905
\(590\) −6329.40 −0.441656
\(591\) 0 0
\(592\) 17382.3 1.20677
\(593\) −16759.1 −1.16057 −0.580283 0.814415i \(-0.697058\pi\)
−0.580283 + 0.814415i \(0.697058\pi\)
\(594\) 0 0
\(595\) 21646.6 1.49147
\(596\) 10885.5 0.748136
\(597\) 0 0
\(598\) −1229.10 −0.0840497
\(599\) 18652.0 1.27229 0.636143 0.771571i \(-0.280529\pi\)
0.636143 + 0.771571i \(0.280529\pi\)
\(600\) 0 0
\(601\) 11696.1 0.793833 0.396916 0.917855i \(-0.370080\pi\)
0.396916 + 0.917855i \(0.370080\pi\)
\(602\) 1720.52 0.116484
\(603\) 0 0
\(604\) 28900.9 1.94696
\(605\) −18097.7 −1.21616
\(606\) 0 0
\(607\) 7834.42 0.523871 0.261935 0.965085i \(-0.415639\pi\)
0.261935 + 0.965085i \(0.415639\pi\)
\(608\) 1193.29 0.0795961
\(609\) 0 0
\(610\) 1815.68 0.120516
\(611\) −1203.11 −0.0796606
\(612\) 0 0
\(613\) 21976.9 1.44802 0.724012 0.689787i \(-0.242296\pi\)
0.724012 + 0.689787i \(0.242296\pi\)
\(614\) −2497.86 −0.164178
\(615\) 0 0
\(616\) −1407.41 −0.0920552
\(617\) 24333.9 1.58776 0.793879 0.608076i \(-0.208058\pi\)
0.793879 + 0.608076i \(0.208058\pi\)
\(618\) 0 0
\(619\) 21713.5 1.40992 0.704960 0.709247i \(-0.250965\pi\)
0.704960 + 0.709247i \(0.250965\pi\)
\(620\) −31477.0 −2.03895
\(621\) 0 0
\(622\) −395.565 −0.0254996
\(623\) −4691.01 −0.301671
\(624\) 0 0
\(625\) 12606.4 0.806812
\(626\) 711.262 0.0454117
\(627\) 0 0
\(628\) 14715.1 0.935028
\(629\) −29678.1 −1.88131
\(630\) 0 0
\(631\) −17221.7 −1.08651 −0.543253 0.839569i \(-0.682808\pi\)
−0.543253 + 0.839569i \(0.682808\pi\)
\(632\) −3835.54 −0.241407
\(633\) 0 0
\(634\) −484.762 −0.0303665
\(635\) 51605.1 3.22502
\(636\) 0 0
\(637\) 4320.10 0.268711
\(638\) 47.3718 0.00293960
\(639\) 0 0
\(640\) −15248.1 −0.941772
\(641\) 10816.8 0.666516 0.333258 0.942836i \(-0.391852\pi\)
0.333258 + 0.942836i \(0.391852\pi\)
\(642\) 0 0
\(643\) 205.221 0.0125865 0.00629326 0.999980i \(-0.497997\pi\)
0.00629326 + 0.999980i \(0.497997\pi\)
\(644\) 13266.2 0.811743
\(645\) 0 0
\(646\) −654.869 −0.0398847
\(647\) −12818.8 −0.778916 −0.389458 0.921044i \(-0.627338\pi\)
−0.389458 + 0.921044i \(0.627338\pi\)
\(648\) 0 0
\(649\) 15835.8 0.957794
\(650\) −1935.84 −0.116815
\(651\) 0 0
\(652\) 22710.0 1.36410
\(653\) −18071.7 −1.08300 −0.541501 0.840700i \(-0.682144\pi\)
−0.541501 + 0.840700i \(0.682144\pi\)
\(654\) 0 0
\(655\) 9631.30 0.574543
\(656\) 11384.2 0.677561
\(657\) 0 0
\(658\) −278.774 −0.0165163
\(659\) 25375.3 1.49997 0.749985 0.661455i \(-0.230061\pi\)
0.749985 + 0.661455i \(0.230061\pi\)
\(660\) 0 0
\(661\) −24947.5 −1.46800 −0.733998 0.679152i \(-0.762348\pi\)
−0.733998 + 0.679152i \(0.762348\pi\)
\(662\) −2426.81 −0.142478
\(663\) 0 0
\(664\) −5560.91 −0.325008
\(665\) −3295.00 −0.192142
\(666\) 0 0
\(667\) −902.641 −0.0523994
\(668\) −5383.24 −0.311802
\(669\) 0 0
\(670\) −8145.49 −0.469683
\(671\) −4542.73 −0.261356
\(672\) 0 0
\(673\) −10576.2 −0.605768 −0.302884 0.953027i \(-0.597950\pi\)
−0.302884 + 0.953027i \(0.597950\pi\)
\(674\) −2008.19 −0.114766
\(675\) 0 0
\(676\) 14220.2 0.809071
\(677\) 27468.3 1.55937 0.779684 0.626174i \(-0.215380\pi\)
0.779684 + 0.626174i \(0.215380\pi\)
\(678\) 0 0
\(679\) −13147.1 −0.743064
\(680\) 12734.6 0.718163
\(681\) 0 0
\(682\) −1690.67 −0.0949251
\(683\) 28341.1 1.58776 0.793881 0.608074i \(-0.208057\pi\)
0.793881 + 0.608074i \(0.208057\pi\)
\(684\) 0 0
\(685\) −38051.1 −2.12242
\(686\) 2552.98 0.142089
\(687\) 0 0
\(688\) −22812.6 −1.26413
\(689\) 9747.12 0.538949
\(690\) 0 0
\(691\) −7519.91 −0.413995 −0.206998 0.978341i \(-0.566369\pi\)
−0.206998 + 0.978341i \(0.566369\pi\)
\(692\) −1998.64 −0.109793
\(693\) 0 0
\(694\) 3845.48 0.210335
\(695\) 10620.6 0.579660
\(696\) 0 0
\(697\) −19437.2 −1.05629
\(698\) 275.202 0.0149234
\(699\) 0 0
\(700\) 20894.3 1.12819
\(701\) −11013.6 −0.593406 −0.296703 0.954970i \(-0.595887\pi\)
−0.296703 + 0.954970i \(0.595887\pi\)
\(702\) 0 0
\(703\) 4517.55 0.242365
\(704\) 8812.99 0.471807
\(705\) 0 0
\(706\) −70.9766 −0.00378363
\(707\) 3077.84 0.163726
\(708\) 0 0
\(709\) −15265.0 −0.808587 −0.404293 0.914629i \(-0.632482\pi\)
−0.404293 + 0.914629i \(0.632482\pi\)
\(710\) −1988.35 −0.105101
\(711\) 0 0
\(712\) −2759.71 −0.145259
\(713\) 32214.6 1.69207
\(714\) 0 0
\(715\) 7347.45 0.384306
\(716\) 36701.7 1.91565
\(717\) 0 0
\(718\) −2914.18 −0.151471
\(719\) 10445.5 0.541797 0.270898 0.962608i \(-0.412679\pi\)
0.270898 + 0.962608i \(0.412679\pi\)
\(720\) 0 0
\(721\) −337.890 −0.0174531
\(722\) −2712.78 −0.139833
\(723\) 0 0
\(724\) 11514.2 0.591052
\(725\) −1421.66 −0.0728264
\(726\) 0 0
\(727\) 11779.3 0.600923 0.300462 0.953794i \(-0.402859\pi\)
0.300462 + 0.953794i \(0.402859\pi\)
\(728\) −1398.81 −0.0712135
\(729\) 0 0
\(730\) −4694.46 −0.238013
\(731\) 38949.7 1.97074
\(732\) 0 0
\(733\) −4037.13 −0.203431 −0.101715 0.994814i \(-0.532433\pi\)
−0.101715 + 0.994814i \(0.532433\pi\)
\(734\) 3757.75 0.188966
\(735\) 0 0
\(736\) 11748.2 0.588375
\(737\) 20379.5 1.01857
\(738\) 0 0
\(739\) −32609.4 −1.62322 −0.811609 0.584201i \(-0.801408\pi\)
−0.811609 + 0.584201i \(0.801408\pi\)
\(740\) −43457.8 −2.15884
\(741\) 0 0
\(742\) 2258.52 0.111742
\(743\) 10619.4 0.524343 0.262171 0.965021i \(-0.415561\pi\)
0.262171 + 0.965021i \(0.415561\pi\)
\(744\) 0 0
\(745\) −26618.4 −1.30902
\(746\) 1731.96 0.0850021
\(747\) 0 0
\(748\) −15761.4 −0.770448
\(749\) −145.806 −0.00711300
\(750\) 0 0
\(751\) −8276.31 −0.402139 −0.201070 0.979577i \(-0.564442\pi\)
−0.201070 + 0.979577i \(0.564442\pi\)
\(752\) 3696.29 0.179242
\(753\) 0 0
\(754\) 47.0826 0.00227407
\(755\) −70671.4 −3.40662
\(756\) 0 0
\(757\) 237.768 0.0114159 0.00570794 0.999984i \(-0.498183\pi\)
0.00570794 + 0.999984i \(0.498183\pi\)
\(758\) −471.864 −0.0226107
\(759\) 0 0
\(760\) −1938.44 −0.0925193
\(761\) −41263.6 −1.96558 −0.982789 0.184730i \(-0.940859\pi\)
−0.982789 + 0.184730i \(0.940859\pi\)
\(762\) 0 0
\(763\) −3312.71 −0.157180
\(764\) 13131.6 0.621838
\(765\) 0 0
\(766\) −3755.06 −0.177123
\(767\) 15739.1 0.740945
\(768\) 0 0
\(769\) 14056.7 0.659165 0.329582 0.944127i \(-0.393092\pi\)
0.329582 + 0.944127i \(0.393092\pi\)
\(770\) 1702.49 0.0796797
\(771\) 0 0
\(772\) 27484.1 1.28131
\(773\) 12138.6 0.564806 0.282403 0.959296i \(-0.408868\pi\)
0.282403 + 0.959296i \(0.408868\pi\)
\(774\) 0 0
\(775\) 50738.0 2.35170
\(776\) −7734.43 −0.357796
\(777\) 0 0
\(778\) 972.122 0.0447972
\(779\) 2958.70 0.136080
\(780\) 0 0
\(781\) 4974.74 0.227926
\(782\) −6447.31 −0.294828
\(783\) 0 0
\(784\) −13272.6 −0.604618
\(785\) −35982.9 −1.63603
\(786\) 0 0
\(787\) 34214.6 1.54971 0.774854 0.632140i \(-0.217823\pi\)
0.774854 + 0.632140i \(0.217823\pi\)
\(788\) −7041.29 −0.318319
\(789\) 0 0
\(790\) 4639.71 0.208954
\(791\) 11679.1 0.524980
\(792\) 0 0
\(793\) −4514.99 −0.202184
\(794\) 1840.08 0.0822444
\(795\) 0 0
\(796\) −23030.8 −1.02551
\(797\) −20283.0 −0.901458 −0.450729 0.892661i \(-0.648836\pi\)
−0.450729 + 0.892661i \(0.648836\pi\)
\(798\) 0 0
\(799\) −6310.97 −0.279432
\(800\) 18503.4 0.817743
\(801\) 0 0
\(802\) −5534.21 −0.243665
\(803\) 11745.2 0.516165
\(804\) 0 0
\(805\) −32439.9 −1.42032
\(806\) −1680.34 −0.0734337
\(807\) 0 0
\(808\) 1810.69 0.0788363
\(809\) −22553.6 −0.980153 −0.490076 0.871680i \(-0.663031\pi\)
−0.490076 + 0.871680i \(0.663031\pi\)
\(810\) 0 0
\(811\) 13204.3 0.571722 0.285861 0.958271i \(-0.407720\pi\)
0.285861 + 0.958271i \(0.407720\pi\)
\(812\) −508.183 −0.0219627
\(813\) 0 0
\(814\) −2334.17 −0.100507
\(815\) −55532.6 −2.38678
\(816\) 0 0
\(817\) −5928.86 −0.253885
\(818\) −2310.79 −0.0987713
\(819\) 0 0
\(820\) −28462.0 −1.21212
\(821\) −27494.5 −1.16877 −0.584387 0.811475i \(-0.698665\pi\)
−0.584387 + 0.811475i \(0.698665\pi\)
\(822\) 0 0
\(823\) −33702.9 −1.42747 −0.713737 0.700414i \(-0.752999\pi\)
−0.713737 + 0.700414i \(0.752999\pi\)
\(824\) −198.780 −0.00840393
\(825\) 0 0
\(826\) 3646.92 0.153623
\(827\) −42658.3 −1.79368 −0.896842 0.442352i \(-0.854144\pi\)
−0.896842 + 0.442352i \(0.854144\pi\)
\(828\) 0 0
\(829\) 17343.7 0.726625 0.363312 0.931667i \(-0.381646\pi\)
0.363312 + 0.931667i \(0.381646\pi\)
\(830\) 6726.84 0.281316
\(831\) 0 0
\(832\) 8759.18 0.364988
\(833\) 22661.3 0.942578
\(834\) 0 0
\(835\) 13163.6 0.545564
\(836\) 2399.18 0.0992552
\(837\) 0 0
\(838\) 6309.61 0.260098
\(839\) −26880.4 −1.10610 −0.553048 0.833149i \(-0.686535\pi\)
−0.553048 + 0.833149i \(0.686535\pi\)
\(840\) 0 0
\(841\) −24354.4 −0.998582
\(842\) −2898.45 −0.118631
\(843\) 0 0
\(844\) −3130.20 −0.127661
\(845\) −34772.7 −1.41564
\(846\) 0 0
\(847\) 10427.7 0.423022
\(848\) −29945.9 −1.21267
\(849\) 0 0
\(850\) −10154.5 −0.409761
\(851\) 44476.1 1.79156
\(852\) 0 0
\(853\) −20392.0 −0.818535 −0.409267 0.912415i \(-0.634216\pi\)
−0.409267 + 0.912415i \(0.634216\pi\)
\(854\) −1046.17 −0.0419196
\(855\) 0 0
\(856\) −85.7774 −0.00342501
\(857\) −32975.6 −1.31438 −0.657190 0.753725i \(-0.728255\pi\)
−0.657190 + 0.753725i \(0.728255\pi\)
\(858\) 0 0
\(859\) 3473.29 0.137960 0.0689798 0.997618i \(-0.478026\pi\)
0.0689798 + 0.997618i \(0.478026\pi\)
\(860\) 57034.2 2.26146
\(861\) 0 0
\(862\) 5090.57 0.201143
\(863\) 21960.8 0.866226 0.433113 0.901340i \(-0.357415\pi\)
0.433113 + 0.901340i \(0.357415\pi\)
\(864\) 0 0
\(865\) 4887.27 0.192106
\(866\) −3912.02 −0.153505
\(867\) 0 0
\(868\) 18136.7 0.709215
\(869\) −11608.3 −0.453145
\(870\) 0 0
\(871\) 20255.1 0.787965
\(872\) −1948.86 −0.0756843
\(873\) 0 0
\(874\) 981.398 0.0379820
\(875\) −24676.8 −0.953403
\(876\) 0 0
\(877\) 45991.0 1.77082 0.885408 0.464815i \(-0.153879\pi\)
0.885408 + 0.464815i \(0.153879\pi\)
\(878\) −4965.27 −0.190854
\(879\) 0 0
\(880\) −22573.4 −0.864716
\(881\) 21002.8 0.803181 0.401591 0.915819i \(-0.368458\pi\)
0.401591 + 0.915819i \(0.368458\pi\)
\(882\) 0 0
\(883\) −6205.12 −0.236488 −0.118244 0.992985i \(-0.537727\pi\)
−0.118244 + 0.992985i \(0.537727\pi\)
\(884\) −15665.2 −0.596016
\(885\) 0 0
\(886\) 4405.95 0.167066
\(887\) 21820.0 0.825980 0.412990 0.910735i \(-0.364484\pi\)
0.412990 + 0.910735i \(0.364484\pi\)
\(888\) 0 0
\(889\) −29734.2 −1.12177
\(890\) 3338.32 0.125731
\(891\) 0 0
\(892\) 35556.5 1.33466
\(893\) 960.644 0.0359986
\(894\) 0 0
\(895\) −89746.5 −3.35184
\(896\) 8785.77 0.327580
\(897\) 0 0
\(898\) −5023.58 −0.186680
\(899\) −1234.03 −0.0457811
\(900\) 0 0
\(901\) 51129.0 1.89051
\(902\) −1528.72 −0.0564312
\(903\) 0 0
\(904\) 6870.77 0.252786
\(905\) −28155.6 −1.03417
\(906\) 0 0
\(907\) 6136.19 0.224640 0.112320 0.993672i \(-0.464172\pi\)
0.112320 + 0.993672i \(0.464172\pi\)
\(908\) −27435.0 −1.00271
\(909\) 0 0
\(910\) 1692.09 0.0616399
\(911\) −33424.3 −1.21558 −0.607791 0.794097i \(-0.707944\pi\)
−0.607791 + 0.794097i \(0.707944\pi\)
\(912\) 0 0
\(913\) −16830.1 −0.610072
\(914\) 3920.45 0.141878
\(915\) 0 0
\(916\) 45548.0 1.64296
\(917\) −5549.44 −0.199846
\(918\) 0 0
\(919\) 31125.9 1.11724 0.558622 0.829422i \(-0.311330\pi\)
0.558622 + 0.829422i \(0.311330\pi\)
\(920\) −19084.3 −0.683904
\(921\) 0 0
\(922\) −3766.56 −0.134539
\(923\) 4944.37 0.176323
\(924\) 0 0
\(925\) 70049.9 2.48998
\(926\) −1617.27 −0.0573941
\(927\) 0 0
\(928\) −450.032 −0.0159192
\(929\) −49957.1 −1.76431 −0.882153 0.470963i \(-0.843906\pi\)
−0.882153 + 0.470963i \(0.843906\pi\)
\(930\) 0 0
\(931\) −3449.46 −0.121430
\(932\) −31513.4 −1.10757
\(933\) 0 0
\(934\) 5198.38 0.182116
\(935\) 38541.4 1.34806
\(936\) 0 0
\(937\) 46502.5 1.62131 0.810656 0.585522i \(-0.199110\pi\)
0.810656 + 0.585522i \(0.199110\pi\)
\(938\) 4693.33 0.163372
\(939\) 0 0
\(940\) −9241.18 −0.320653
\(941\) −6850.70 −0.237329 −0.118664 0.992934i \(-0.537861\pi\)
−0.118664 + 0.992934i \(0.537861\pi\)
\(942\) 0 0
\(943\) 29128.9 1.00590
\(944\) −48354.9 −1.66718
\(945\) 0 0
\(946\) 3063.37 0.105284
\(947\) 17782.3 0.610187 0.305093 0.952322i \(-0.401312\pi\)
0.305093 + 0.952322i \(0.401312\pi\)
\(948\) 0 0
\(949\) 11673.5 0.399303
\(950\) 1545.70 0.0527887
\(951\) 0 0
\(952\) −7337.54 −0.249801
\(953\) 43227.9 1.46935 0.734675 0.678420i \(-0.237335\pi\)
0.734675 + 0.678420i \(0.237335\pi\)
\(954\) 0 0
\(955\) −32110.6 −1.08804
\(956\) 1871.82 0.0633252
\(957\) 0 0
\(958\) −2140.77 −0.0721976
\(959\) 21924.6 0.738251
\(960\) 0 0
\(961\) 14250.6 0.478352
\(962\) −2319.91 −0.0777516
\(963\) 0 0
\(964\) −22396.1 −0.748267
\(965\) −67206.7 −2.24193
\(966\) 0 0
\(967\) 15458.1 0.514062 0.257031 0.966403i \(-0.417256\pi\)
0.257031 + 0.966403i \(0.417256\pi\)
\(968\) 6134.59 0.203691
\(969\) 0 0
\(970\) 9356.06 0.309696
\(971\) 37978.0 1.25517 0.627586 0.778548i \(-0.284043\pi\)
0.627586 + 0.778548i \(0.284043\pi\)
\(972\) 0 0
\(973\) −6119.49 −0.201626
\(974\) −5183.29 −0.170517
\(975\) 0 0
\(976\) 13871.3 0.454929
\(977\) 8636.65 0.282816 0.141408 0.989951i \(-0.454837\pi\)
0.141408 + 0.989951i \(0.454837\pi\)
\(978\) 0 0
\(979\) −8352.28 −0.272666
\(980\) 33183.0 1.08163
\(981\) 0 0
\(982\) 542.223 0.0176202
\(983\) 25884.9 0.839877 0.419939 0.907552i \(-0.362052\pi\)
0.419939 + 0.907552i \(0.362052\pi\)
\(984\) 0 0
\(985\) 17218.0 0.556967
\(986\) 246.974 0.00797693
\(987\) 0 0
\(988\) 2384.53 0.0767834
\(989\) −58370.7 −1.87672
\(990\) 0 0
\(991\) −18732.3 −0.600457 −0.300228 0.953867i \(-0.597063\pi\)
−0.300228 + 0.953867i \(0.597063\pi\)
\(992\) 16061.3 0.514060
\(993\) 0 0
\(994\) 1145.67 0.0365577
\(995\) 56317.3 1.79435
\(996\) 0 0
\(997\) −47122.4 −1.49687 −0.748436 0.663207i \(-0.769195\pi\)
−0.748436 + 0.663207i \(0.769195\pi\)
\(998\) 763.206 0.0242073
\(999\) 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.b.1.14 28
3.2 odd 2 717.4.a.b.1.15 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
717.4.a.b.1.15 28 3.2 odd 2
2151.4.a.b.1.14 28 1.1 even 1 trivial