Properties

Label 2254.4.a.u.1.9
Level $2254$
Weight $4$
Character 2254.1
Self dual yes
Analytic conductor $132.990$
Analytic rank $0$
Dimension $11$
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] = [2254,4,Mod(1,2254)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2254, 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("2254.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2254.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: \(132.990305153\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 234 x^{9} - 105 x^{8} + 18997 x^{7} + 16513 x^{6} - 621598 x^{5} - 743169 x^{4} + \cdots - 12103441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 7 \)
Twist minimal: no (minimal twist has level 322)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(7.30492\) of defining polynomial
Character \(\chi\) \(=\) 2254.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +7.30492 q^{3} +4.00000 q^{4} +7.55338 q^{5} -14.6098 q^{6} -8.00000 q^{8} +26.3619 q^{9} -15.1068 q^{10} +56.3122 q^{11} +29.2197 q^{12} +65.8379 q^{13} +55.1768 q^{15} +16.0000 q^{16} -108.835 q^{17} -52.7238 q^{18} +92.3659 q^{19} +30.2135 q^{20} -112.624 q^{22} +23.0000 q^{23} -58.4394 q^{24} -67.9465 q^{25} -131.676 q^{26} -4.66115 q^{27} +58.1564 q^{29} -110.354 q^{30} +234.881 q^{31} -32.0000 q^{32} +411.356 q^{33} +217.669 q^{34} +105.448 q^{36} -122.911 q^{37} -184.732 q^{38} +480.941 q^{39} -60.4270 q^{40} +359.331 q^{41} -33.0320 q^{43} +225.249 q^{44} +199.121 q^{45} -46.0000 q^{46} -147.849 q^{47} +116.879 q^{48} +135.893 q^{50} -795.028 q^{51} +263.352 q^{52} +640.721 q^{53} +9.32230 q^{54} +425.347 q^{55} +674.726 q^{57} -116.313 q^{58} -402.029 q^{59} +220.707 q^{60} -240.394 q^{61} -469.762 q^{62} +64.0000 q^{64} +497.298 q^{65} -822.713 q^{66} +112.885 q^{67} -435.338 q^{68} +168.013 q^{69} +171.363 q^{71} -210.895 q^{72} +361.719 q^{73} +245.823 q^{74} -496.344 q^{75} +369.464 q^{76} -961.881 q^{78} -842.316 q^{79} +120.854 q^{80} -745.821 q^{81} -718.661 q^{82} +1374.29 q^{83} -822.069 q^{85} +66.0640 q^{86} +424.828 q^{87} -450.498 q^{88} -1241.11 q^{89} -398.243 q^{90} +92.0000 q^{92} +1715.79 q^{93} +295.699 q^{94} +697.674 q^{95} -233.758 q^{96} -997.907 q^{97} +1484.50 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 22 q^{2} + 44 q^{4} + 23 q^{5} - 88 q^{8} + 171 q^{9} - 46 q^{10} - 48 q^{11} + 77 q^{13} + 104 q^{15} + 176 q^{16} + 97 q^{17} - 342 q^{18} + 138 q^{19} + 92 q^{20} + 96 q^{22} + 253 q^{23} + 30 q^{25}+ \cdots - 2545 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 7.30492 1.40583 0.702917 0.711272i \(-0.251881\pi\)
0.702917 + 0.711272i \(0.251881\pi\)
\(4\) 4.00000 0.500000
\(5\) 7.55338 0.675595 0.337797 0.941219i \(-0.390318\pi\)
0.337797 + 0.941219i \(0.390318\pi\)
\(6\) −14.6098 −0.994074
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 26.3619 0.976367
\(10\) −15.1068 −0.477717
\(11\) 56.3122 1.54352 0.771762 0.635911i \(-0.219376\pi\)
0.771762 + 0.635911i \(0.219376\pi\)
\(12\) 29.2197 0.702917
\(13\) 65.8379 1.40463 0.702313 0.711868i \(-0.252151\pi\)
0.702313 + 0.711868i \(0.252151\pi\)
\(14\) 0 0
\(15\) 55.1768 0.949773
\(16\) 16.0000 0.250000
\(17\) −108.835 −1.55272 −0.776361 0.630289i \(-0.782936\pi\)
−0.776361 + 0.630289i \(0.782936\pi\)
\(18\) −52.7238 −0.690396
\(19\) 92.3659 1.11527 0.557637 0.830085i \(-0.311708\pi\)
0.557637 + 0.830085i \(0.311708\pi\)
\(20\) 30.2135 0.337797
\(21\) 0 0
\(22\) −112.624 −1.09144
\(23\) 23.0000 0.208514
\(24\) −58.4394 −0.497037
\(25\) −67.9465 −0.543572
\(26\) −131.676 −0.993221
\(27\) −4.66115 −0.0332236
\(28\) 0 0
\(29\) 58.1564 0.372392 0.186196 0.982513i \(-0.440384\pi\)
0.186196 + 0.982513i \(0.440384\pi\)
\(30\) −110.354 −0.671591
\(31\) 234.881 1.36083 0.680417 0.732825i \(-0.261799\pi\)
0.680417 + 0.732825i \(0.261799\pi\)
\(32\) −32.0000 −0.176777
\(33\) 411.356 2.16994
\(34\) 217.669 1.09794
\(35\) 0 0
\(36\) 105.448 0.488184
\(37\) −122.911 −0.546122 −0.273061 0.961997i \(-0.588036\pi\)
−0.273061 + 0.961997i \(0.588036\pi\)
\(38\) −184.732 −0.788617
\(39\) 480.941 1.97467
\(40\) −60.4270 −0.238859
\(41\) 359.331 1.36873 0.684366 0.729139i \(-0.260079\pi\)
0.684366 + 0.729139i \(0.260079\pi\)
\(42\) 0 0
\(43\) −33.0320 −0.117147 −0.0585736 0.998283i \(-0.518655\pi\)
−0.0585736 + 0.998283i \(0.518655\pi\)
\(44\) 225.249 0.771762
\(45\) 199.121 0.659628
\(46\) −46.0000 −0.147442
\(47\) −147.849 −0.458852 −0.229426 0.973326i \(-0.573685\pi\)
−0.229426 + 0.973326i \(0.573685\pi\)
\(48\) 116.879 0.351458
\(49\) 0 0
\(50\) 135.893 0.384363
\(51\) −795.028 −2.18287
\(52\) 263.352 0.702313
\(53\) 640.721 1.66056 0.830281 0.557345i \(-0.188180\pi\)
0.830281 + 0.557345i \(0.188180\pi\)
\(54\) 9.32230 0.0234927
\(55\) 425.347 1.04280
\(56\) 0 0
\(57\) 674.726 1.56789
\(58\) −116.313 −0.263321
\(59\) −402.029 −0.887115 −0.443557 0.896246i \(-0.646284\pi\)
−0.443557 + 0.896246i \(0.646284\pi\)
\(60\) 220.707 0.474887
\(61\) −240.394 −0.504580 −0.252290 0.967652i \(-0.581184\pi\)
−0.252290 + 0.967652i \(0.581184\pi\)
\(62\) −469.762 −0.962255
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 497.298 0.948958
\(66\) −822.713 −1.53438
\(67\) 112.885 0.205838 0.102919 0.994690i \(-0.467182\pi\)
0.102919 + 0.994690i \(0.467182\pi\)
\(68\) −435.338 −0.776361
\(69\) 168.013 0.293137
\(70\) 0 0
\(71\) 171.363 0.286437 0.143219 0.989691i \(-0.454255\pi\)
0.143219 + 0.989691i \(0.454255\pi\)
\(72\) −210.895 −0.345198
\(73\) 361.719 0.579946 0.289973 0.957035i \(-0.406354\pi\)
0.289973 + 0.957035i \(0.406354\pi\)
\(74\) 245.823 0.386166
\(75\) −496.344 −0.764172
\(76\) 369.464 0.557637
\(77\) 0 0
\(78\) −961.881 −1.39630
\(79\) −842.316 −1.19959 −0.599797 0.800152i \(-0.704752\pi\)
−0.599797 + 0.800152i \(0.704752\pi\)
\(80\) 120.854 0.168899
\(81\) −745.821 −1.02307
\(82\) −718.661 −0.967840
\(83\) 1374.29 1.81744 0.908721 0.417404i \(-0.137060\pi\)
0.908721 + 0.417404i \(0.137060\pi\)
\(84\) 0 0
\(85\) −822.069 −1.04901
\(86\) 66.0640 0.0828356
\(87\) 424.828 0.523521
\(88\) −450.498 −0.545718
\(89\) −1241.11 −1.47818 −0.739088 0.673608i \(-0.764743\pi\)
−0.739088 + 0.673608i \(0.764743\pi\)
\(90\) −398.243 −0.466428
\(91\) 0 0
\(92\) 92.0000 0.104257
\(93\) 1715.79 1.91311
\(94\) 295.699 0.324457
\(95\) 697.674 0.753472
\(96\) −233.758 −0.248519
\(97\) −997.907 −1.04456 −0.522279 0.852775i \(-0.674918\pi\)
−0.522279 + 0.852775i \(0.674918\pi\)
\(98\) 0 0
\(99\) 1484.50 1.50705
\(100\) −271.786 −0.271786
\(101\) −946.648 −0.932624 −0.466312 0.884620i \(-0.654418\pi\)
−0.466312 + 0.884620i \(0.654418\pi\)
\(102\) 1590.06 1.54352
\(103\) −422.213 −0.403902 −0.201951 0.979396i \(-0.564728\pi\)
−0.201951 + 0.979396i \(0.564728\pi\)
\(104\) −526.703 −0.496610
\(105\) 0 0
\(106\) −1281.44 −1.17419
\(107\) 588.846 0.532018 0.266009 0.963971i \(-0.414295\pi\)
0.266009 + 0.963971i \(0.414295\pi\)
\(108\) −18.6446 −0.0166118
\(109\) 106.854 0.0938969 0.0469484 0.998897i \(-0.485050\pi\)
0.0469484 + 0.998897i \(0.485050\pi\)
\(110\) −850.694 −0.737368
\(111\) −897.858 −0.767756
\(112\) 0 0
\(113\) 21.1869 0.0176380 0.00881901 0.999961i \(-0.497193\pi\)
0.00881901 + 0.999961i \(0.497193\pi\)
\(114\) −1349.45 −1.10866
\(115\) 173.728 0.140871
\(116\) 232.625 0.186196
\(117\) 1735.61 1.37143
\(118\) 804.059 0.627285
\(119\) 0 0
\(120\) −441.415 −0.335796
\(121\) 1840.06 1.38247
\(122\) 480.789 0.356792
\(123\) 2624.88 1.92421
\(124\) 939.524 0.680417
\(125\) −1457.40 −1.04283
\(126\) 0 0
\(127\) 2173.95 1.51895 0.759475 0.650536i \(-0.225456\pi\)
0.759475 + 0.650536i \(0.225456\pi\)
\(128\) −128.000 −0.0883883
\(129\) −241.296 −0.164689
\(130\) −994.597 −0.671015
\(131\) 2455.77 1.63788 0.818939 0.573881i \(-0.194563\pi\)
0.818939 + 0.573881i \(0.194563\pi\)
\(132\) 1645.43 1.08497
\(133\) 0 0
\(134\) −225.770 −0.145549
\(135\) −35.2074 −0.0224457
\(136\) 870.677 0.548970
\(137\) 1021.29 0.636896 0.318448 0.947940i \(-0.396838\pi\)
0.318448 + 0.947940i \(0.396838\pi\)
\(138\) −336.027 −0.207279
\(139\) −418.904 −0.255619 −0.127809 0.991799i \(-0.540795\pi\)
−0.127809 + 0.991799i \(0.540795\pi\)
\(140\) 0 0
\(141\) −1080.03 −0.645069
\(142\) −342.726 −0.202542
\(143\) 3707.48 2.16807
\(144\) 421.791 0.244092
\(145\) 439.277 0.251586
\(146\) −723.438 −0.410083
\(147\) 0 0
\(148\) −491.645 −0.273061
\(149\) 984.319 0.541199 0.270599 0.962692i \(-0.412778\pi\)
0.270599 + 0.962692i \(0.412778\pi\)
\(150\) 992.688 0.540351
\(151\) 2004.99 1.08056 0.540278 0.841486i \(-0.318319\pi\)
0.540278 + 0.841486i \(0.318319\pi\)
\(152\) −738.927 −0.394309
\(153\) −2869.09 −1.51603
\(154\) 0 0
\(155\) 1774.14 0.919372
\(156\) 1923.76 0.987335
\(157\) 385.868 0.196150 0.0980752 0.995179i \(-0.468731\pi\)
0.0980752 + 0.995179i \(0.468731\pi\)
\(158\) 1684.63 0.848242
\(159\) 4680.42 2.33447
\(160\) −241.708 −0.119429
\(161\) 0 0
\(162\) 1491.64 0.723423
\(163\) −2397.38 −1.15201 −0.576003 0.817448i \(-0.695388\pi\)
−0.576003 + 0.817448i \(0.695388\pi\)
\(164\) 1437.32 0.684366
\(165\) 3107.13 1.46600
\(166\) −2748.58 −1.28513
\(167\) −3438.93 −1.59349 −0.796743 0.604318i \(-0.793446\pi\)
−0.796743 + 0.604318i \(0.793446\pi\)
\(168\) 0 0
\(169\) 2137.63 0.972975
\(170\) 1644.14 0.741762
\(171\) 2434.94 1.08892
\(172\) −132.128 −0.0585736
\(173\) −2008.99 −0.882894 −0.441447 0.897287i \(-0.645535\pi\)
−0.441447 + 0.897287i \(0.645535\pi\)
\(174\) −849.656 −0.370185
\(175\) 0 0
\(176\) 900.995 0.385881
\(177\) −2936.79 −1.24714
\(178\) 2482.23 1.04523
\(179\) 4012.23 1.67535 0.837677 0.546166i \(-0.183913\pi\)
0.837677 + 0.546166i \(0.183913\pi\)
\(180\) 796.486 0.329814
\(181\) −2231.44 −0.916361 −0.458181 0.888859i \(-0.651499\pi\)
−0.458181 + 0.888859i \(0.651499\pi\)
\(182\) 0 0
\(183\) −1756.06 −0.709355
\(184\) −184.000 −0.0737210
\(185\) −928.395 −0.368957
\(186\) −3431.57 −1.35277
\(187\) −6128.71 −2.39666
\(188\) −591.397 −0.229426
\(189\) 0 0
\(190\) −1395.35 −0.532785
\(191\) 130.667 0.0495011 0.0247505 0.999694i \(-0.492121\pi\)
0.0247505 + 0.999694i \(0.492121\pi\)
\(192\) 467.515 0.175729
\(193\) −3443.32 −1.28423 −0.642113 0.766610i \(-0.721942\pi\)
−0.642113 + 0.766610i \(0.721942\pi\)
\(194\) 1995.81 0.738614
\(195\) 3632.73 1.33408
\(196\) 0 0
\(197\) −2976.33 −1.07642 −0.538211 0.842810i \(-0.680900\pi\)
−0.538211 + 0.842810i \(0.680900\pi\)
\(198\) −2968.99 −1.06564
\(199\) 902.959 0.321653 0.160827 0.986983i \(-0.448584\pi\)
0.160827 + 0.986983i \(0.448584\pi\)
\(200\) 543.572 0.192182
\(201\) 824.618 0.289374
\(202\) 1893.30 0.659465
\(203\) 0 0
\(204\) −3180.11 −1.09143
\(205\) 2714.16 0.924708
\(206\) 844.426 0.285602
\(207\) 606.324 0.203587
\(208\) 1053.41 0.351157
\(209\) 5201.33 1.72145
\(210\) 0 0
\(211\) −2439.95 −0.796081 −0.398041 0.917368i \(-0.630310\pi\)
−0.398041 + 0.917368i \(0.630310\pi\)
\(212\) 2562.88 0.830281
\(213\) 1251.79 0.402683
\(214\) −1177.69 −0.376194
\(215\) −249.503 −0.0791440
\(216\) 37.2892 0.0117463
\(217\) 0 0
\(218\) −213.708 −0.0663951
\(219\) 2642.33 0.815307
\(220\) 1701.39 0.521398
\(221\) −7165.44 −2.18099
\(222\) 1795.72 0.542885
\(223\) 5414.35 1.62588 0.812941 0.582346i \(-0.197865\pi\)
0.812941 + 0.582346i \(0.197865\pi\)
\(224\) 0 0
\(225\) −1791.20 −0.530726
\(226\) −42.3738 −0.0124720
\(227\) −4479.54 −1.30977 −0.654884 0.755729i \(-0.727283\pi\)
−0.654884 + 0.755729i \(0.727283\pi\)
\(228\) 2698.90 0.783944
\(229\) 3627.89 1.04689 0.523445 0.852059i \(-0.324646\pi\)
0.523445 + 0.852059i \(0.324646\pi\)
\(230\) −347.455 −0.0996110
\(231\) 0 0
\(232\) −465.251 −0.131660
\(233\) −3682.73 −1.03547 −0.517734 0.855542i \(-0.673224\pi\)
−0.517734 + 0.855542i \(0.673224\pi\)
\(234\) −3471.23 −0.969748
\(235\) −1116.76 −0.309998
\(236\) −1608.12 −0.443557
\(237\) −6153.06 −1.68643
\(238\) 0 0
\(239\) 1289.59 0.349025 0.174512 0.984655i \(-0.444165\pi\)
0.174512 + 0.984655i \(0.444165\pi\)
\(240\) 882.829 0.237443
\(241\) 664.153 0.177518 0.0887590 0.996053i \(-0.471710\pi\)
0.0887590 + 0.996053i \(0.471710\pi\)
\(242\) −3680.13 −0.977552
\(243\) −5322.32 −1.40505
\(244\) −961.578 −0.252290
\(245\) 0 0
\(246\) −5249.77 −1.36062
\(247\) 6081.17 1.56654
\(248\) −1879.05 −0.481128
\(249\) 10039.1 2.55502
\(250\) 2914.80 0.737391
\(251\) −4771.08 −1.19979 −0.599896 0.800078i \(-0.704791\pi\)
−0.599896 + 0.800078i \(0.704791\pi\)
\(252\) 0 0
\(253\) 1295.18 0.321847
\(254\) −4347.90 −1.07406
\(255\) −6005.15 −1.47473
\(256\) 256.000 0.0625000
\(257\) 2134.29 0.518028 0.259014 0.965874i \(-0.416602\pi\)
0.259014 + 0.965874i \(0.416602\pi\)
\(258\) 482.592 0.116453
\(259\) 0 0
\(260\) 1989.19 0.474479
\(261\) 1533.11 0.363591
\(262\) −4911.55 −1.15815
\(263\) 6810.24 1.59672 0.798360 0.602180i \(-0.205701\pi\)
0.798360 + 0.602180i \(0.205701\pi\)
\(264\) −3290.85 −0.767189
\(265\) 4839.61 1.12187
\(266\) 0 0
\(267\) −9066.24 −2.07807
\(268\) 451.541 0.102919
\(269\) 6693.13 1.51705 0.758526 0.651643i \(-0.225920\pi\)
0.758526 + 0.651643i \(0.225920\pi\)
\(270\) 70.4148 0.0158715
\(271\) 8641.37 1.93699 0.968497 0.249024i \(-0.0801097\pi\)
0.968497 + 0.249024i \(0.0801097\pi\)
\(272\) −1741.35 −0.388180
\(273\) 0 0
\(274\) −2042.58 −0.450353
\(275\) −3826.22 −0.839017
\(276\) 672.053 0.146568
\(277\) −7493.58 −1.62544 −0.812718 0.582658i \(-0.802013\pi\)
−0.812718 + 0.582658i \(0.802013\pi\)
\(278\) 837.808 0.180750
\(279\) 6191.91 1.32867
\(280\) 0 0
\(281\) 1976.73 0.419651 0.209825 0.977739i \(-0.432710\pi\)
0.209825 + 0.977739i \(0.432710\pi\)
\(282\) 2160.06 0.456133
\(283\) −6154.61 −1.29277 −0.646384 0.763012i \(-0.723720\pi\)
−0.646384 + 0.763012i \(0.723720\pi\)
\(284\) 685.452 0.143219
\(285\) 5096.46 1.05926
\(286\) −7414.95 −1.53306
\(287\) 0 0
\(288\) −843.581 −0.172599
\(289\) 6931.97 1.41094
\(290\) −878.554 −0.177898
\(291\) −7289.63 −1.46847
\(292\) 1446.88 0.289973
\(293\) 1905.58 0.379950 0.189975 0.981789i \(-0.439159\pi\)
0.189975 + 0.981789i \(0.439159\pi\)
\(294\) 0 0
\(295\) −3036.68 −0.599330
\(296\) 983.291 0.193083
\(297\) −262.479 −0.0512815
\(298\) −1968.64 −0.382685
\(299\) 1514.27 0.292885
\(300\) −1985.38 −0.382086
\(301\) 0 0
\(302\) −4009.99 −0.764069
\(303\) −6915.20 −1.31111
\(304\) 1477.85 0.278818
\(305\) −1815.79 −0.340891
\(306\) 5738.18 1.07199
\(307\) −643.667 −0.119661 −0.0598307 0.998209i \(-0.519056\pi\)
−0.0598307 + 0.998209i \(0.519056\pi\)
\(308\) 0 0
\(309\) −3084.23 −0.567818
\(310\) −3548.29 −0.650094
\(311\) 5131.05 0.935547 0.467773 0.883848i \(-0.345056\pi\)
0.467773 + 0.883848i \(0.345056\pi\)
\(312\) −3847.53 −0.698151
\(313\) −4845.93 −0.875106 −0.437553 0.899193i \(-0.644155\pi\)
−0.437553 + 0.899193i \(0.644155\pi\)
\(314\) −771.736 −0.138699
\(315\) 0 0
\(316\) −3369.27 −0.599797
\(317\) 2149.07 0.380769 0.190384 0.981710i \(-0.439027\pi\)
0.190384 + 0.981710i \(0.439027\pi\)
\(318\) −9360.84 −1.65072
\(319\) 3274.91 0.574796
\(320\) 483.416 0.0844493
\(321\) 4301.48 0.747929
\(322\) 0 0
\(323\) −10052.6 −1.73171
\(324\) −2983.28 −0.511537
\(325\) −4473.45 −0.763516
\(326\) 4794.75 0.814591
\(327\) 780.561 0.132003
\(328\) −2874.64 −0.483920
\(329\) 0 0
\(330\) −6214.26 −1.03662
\(331\) 733.344 0.121777 0.0608886 0.998145i \(-0.480607\pi\)
0.0608886 + 0.998145i \(0.480607\pi\)
\(332\) 5497.15 0.908721
\(333\) −3240.18 −0.533215
\(334\) 6877.86 1.12677
\(335\) 852.665 0.139063
\(336\) 0 0
\(337\) −1922.41 −0.310743 −0.155372 0.987856i \(-0.549657\pi\)
−0.155372 + 0.987856i \(0.549657\pi\)
\(338\) −4275.25 −0.687997
\(339\) 154.769 0.0247961
\(340\) −3288.27 −0.524505
\(341\) 13226.7 2.10048
\(342\) −4869.88 −0.769980
\(343\) 0 0
\(344\) 264.256 0.0414178
\(345\) 1269.07 0.198041
\(346\) 4017.98 0.624300
\(347\) 11309.5 1.74964 0.874821 0.484446i \(-0.160979\pi\)
0.874821 + 0.484446i \(0.160979\pi\)
\(348\) 1699.31 0.261760
\(349\) −5202.37 −0.797927 −0.398963 0.916967i \(-0.630630\pi\)
−0.398963 + 0.916967i \(0.630630\pi\)
\(350\) 0 0
\(351\) −306.880 −0.0466668
\(352\) −1801.99 −0.272859
\(353\) −6302.68 −0.950306 −0.475153 0.879903i \(-0.657607\pi\)
−0.475153 + 0.879903i \(0.657607\pi\)
\(354\) 5873.59 0.881858
\(355\) 1294.37 0.193515
\(356\) −4964.45 −0.739088
\(357\) 0 0
\(358\) −8024.47 −1.18465
\(359\) −12797.9 −1.88147 −0.940733 0.339148i \(-0.889861\pi\)
−0.940733 + 0.339148i \(0.889861\pi\)
\(360\) −1592.97 −0.233214
\(361\) 1672.46 0.243834
\(362\) 4462.87 0.647965
\(363\) 13441.5 1.94352
\(364\) 0 0
\(365\) 2732.20 0.391808
\(366\) 3512.13 0.501590
\(367\) 7794.73 1.10867 0.554335 0.832294i \(-0.312973\pi\)
0.554335 + 0.832294i \(0.312973\pi\)
\(368\) 368.000 0.0521286
\(369\) 9472.64 1.33639
\(370\) 1856.79 0.260892
\(371\) 0 0
\(372\) 6863.15 0.956553
\(373\) 9352.02 1.29820 0.649101 0.760703i \(-0.275145\pi\)
0.649101 + 0.760703i \(0.275145\pi\)
\(374\) 12257.4 1.69470
\(375\) −10646.2 −1.46604
\(376\) 1182.79 0.162229
\(377\) 3828.89 0.523072
\(378\) 0 0
\(379\) −671.508 −0.0910107 −0.0455054 0.998964i \(-0.514490\pi\)
−0.0455054 + 0.998964i \(0.514490\pi\)
\(380\) 2790.70 0.376736
\(381\) 15880.5 2.13539
\(382\) −261.333 −0.0350026
\(383\) −5923.13 −0.790230 −0.395115 0.918632i \(-0.629295\pi\)
−0.395115 + 0.918632i \(0.629295\pi\)
\(384\) −935.030 −0.124259
\(385\) 0 0
\(386\) 6886.64 0.908085
\(387\) −870.787 −0.114379
\(388\) −3991.63 −0.522279
\(389\) −3452.45 −0.449991 −0.224995 0.974360i \(-0.572237\pi\)
−0.224995 + 0.974360i \(0.572237\pi\)
\(390\) −7265.45 −0.943335
\(391\) −2503.20 −0.323765
\(392\) 0 0
\(393\) 17939.2 2.30258
\(394\) 5952.67 0.761145
\(395\) −6362.33 −0.810440
\(396\) 5937.99 0.753523
\(397\) 2462.71 0.311334 0.155667 0.987810i \(-0.450247\pi\)
0.155667 + 0.987810i \(0.450247\pi\)
\(398\) −1805.92 −0.227443
\(399\) 0 0
\(400\) −1087.14 −0.135893
\(401\) −12628.0 −1.57260 −0.786301 0.617843i \(-0.788007\pi\)
−0.786301 + 0.617843i \(0.788007\pi\)
\(402\) −1649.24 −0.204618
\(403\) 15464.1 1.91146
\(404\) −3786.59 −0.466312
\(405\) −5633.47 −0.691183
\(406\) 0 0
\(407\) −6921.41 −0.842952
\(408\) 6360.23 0.771760
\(409\) −9857.74 −1.19177 −0.595885 0.803070i \(-0.703199\pi\)
−0.595885 + 0.803070i \(0.703199\pi\)
\(410\) −5428.32 −0.653867
\(411\) 7460.45 0.895370
\(412\) −1688.85 −0.201951
\(413\) 0 0
\(414\) −1212.65 −0.143958
\(415\) 10380.5 1.22785
\(416\) −2106.81 −0.248305
\(417\) −3060.06 −0.359357
\(418\) −10402.7 −1.21725
\(419\) 15594.0 1.81818 0.909090 0.416599i \(-0.136778\pi\)
0.909090 + 0.416599i \(0.136778\pi\)
\(420\) 0 0
\(421\) −2429.98 −0.281306 −0.140653 0.990059i \(-0.544920\pi\)
−0.140653 + 0.990059i \(0.544920\pi\)
\(422\) 4879.90 0.562914
\(423\) −3897.59 −0.448008
\(424\) −5125.77 −0.587097
\(425\) 7394.93 0.844016
\(426\) −2503.59 −0.284740
\(427\) 0 0
\(428\) 2355.39 0.266009
\(429\) 27082.8 3.04795
\(430\) 499.006 0.0559633
\(431\) −4540.29 −0.507420 −0.253710 0.967280i \(-0.581651\pi\)
−0.253710 + 0.967280i \(0.581651\pi\)
\(432\) −74.5784 −0.00830591
\(433\) 15322.6 1.70060 0.850299 0.526300i \(-0.176421\pi\)
0.850299 + 0.526300i \(0.176421\pi\)
\(434\) 0 0
\(435\) 3208.88 0.353688
\(436\) 427.416 0.0469484
\(437\) 2124.42 0.232551
\(438\) −5284.66 −0.576509
\(439\) 5141.79 0.559008 0.279504 0.960145i \(-0.409830\pi\)
0.279504 + 0.960145i \(0.409830\pi\)
\(440\) −3402.78 −0.368684
\(441\) 0 0
\(442\) 14330.9 1.54220
\(443\) −7538.33 −0.808480 −0.404240 0.914653i \(-0.632464\pi\)
−0.404240 + 0.914653i \(0.632464\pi\)
\(444\) −3591.43 −0.383878
\(445\) −9374.60 −0.998648
\(446\) −10828.7 −1.14967
\(447\) 7190.38 0.760835
\(448\) 0 0
\(449\) −7253.14 −0.762354 −0.381177 0.924502i \(-0.624481\pi\)
−0.381177 + 0.924502i \(0.624481\pi\)
\(450\) 3582.40 0.375280
\(451\) 20234.7 2.11267
\(452\) 84.7476 0.00881901
\(453\) 14646.3 1.51908
\(454\) 8959.08 0.926146
\(455\) 0 0
\(456\) −5397.81 −0.554332
\(457\) −14113.4 −1.44464 −0.722319 0.691561i \(-0.756924\pi\)
−0.722319 + 0.691561i \(0.756924\pi\)
\(458\) −7255.79 −0.740264
\(459\) 507.294 0.0515871
\(460\) 694.911 0.0704356
\(461\) −1996.06 −0.201662 −0.100831 0.994904i \(-0.532150\pi\)
−0.100831 + 0.994904i \(0.532150\pi\)
\(462\) 0 0
\(463\) 8301.53 0.833271 0.416636 0.909074i \(-0.363209\pi\)
0.416636 + 0.909074i \(0.363209\pi\)
\(464\) 930.502 0.0930980
\(465\) 12960.0 1.29248
\(466\) 7365.47 0.732186
\(467\) 4517.84 0.447668 0.223834 0.974627i \(-0.428143\pi\)
0.223834 + 0.974627i \(0.428143\pi\)
\(468\) 6942.45 0.685716
\(469\) 0 0
\(470\) 2233.52 0.219202
\(471\) 2818.74 0.275755
\(472\) 3216.24 0.313642
\(473\) −1860.10 −0.180820
\(474\) 12306.1 1.19249
\(475\) −6275.94 −0.606231
\(476\) 0 0
\(477\) 16890.6 1.62132
\(478\) −2579.19 −0.246798
\(479\) 16515.6 1.57540 0.787702 0.616056i \(-0.211271\pi\)
0.787702 + 0.616056i \(0.211271\pi\)
\(480\) −1765.66 −0.167898
\(481\) −8092.22 −0.767097
\(482\) −1328.31 −0.125524
\(483\) 0 0
\(484\) 7360.25 0.691233
\(485\) −7537.57 −0.705697
\(486\) 10644.6 0.993519
\(487\) 9053.08 0.842370 0.421185 0.906975i \(-0.361614\pi\)
0.421185 + 0.906975i \(0.361614\pi\)
\(488\) 1923.16 0.178396
\(489\) −17512.6 −1.61953
\(490\) 0 0
\(491\) −7398.88 −0.680055 −0.340027 0.940416i \(-0.610436\pi\)
−0.340027 + 0.940416i \(0.610436\pi\)
\(492\) 10499.5 0.962105
\(493\) −6329.42 −0.578221
\(494\) −12162.3 −1.10771
\(495\) 11213.0 1.01815
\(496\) 3758.09 0.340209
\(497\) 0 0
\(498\) −20078.1 −1.80667
\(499\) −717.821 −0.0643970 −0.0321985 0.999481i \(-0.510251\pi\)
−0.0321985 + 0.999481i \(0.510251\pi\)
\(500\) −5829.59 −0.521414
\(501\) −25121.1 −2.24018
\(502\) 9542.15 0.848381
\(503\) 1927.68 0.170877 0.0854385 0.996343i \(-0.472771\pi\)
0.0854385 + 0.996343i \(0.472771\pi\)
\(504\) 0 0
\(505\) −7150.39 −0.630076
\(506\) −2590.36 −0.227580
\(507\) 15615.2 1.36784
\(508\) 8695.79 0.759475
\(509\) 7804.87 0.679656 0.339828 0.940488i \(-0.389631\pi\)
0.339828 + 0.940488i \(0.389631\pi\)
\(510\) 12010.3 1.04279
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −430.531 −0.0370534
\(514\) −4268.58 −0.366301
\(515\) −3189.13 −0.272874
\(516\) −965.185 −0.0823447
\(517\) −8325.72 −0.708249
\(518\) 0 0
\(519\) −14675.5 −1.24120
\(520\) −3978.39 −0.335507
\(521\) 21406.8 1.80010 0.900049 0.435789i \(-0.143531\pi\)
0.900049 + 0.435789i \(0.143531\pi\)
\(522\) −3066.23 −0.257098
\(523\) −11327.8 −0.947098 −0.473549 0.880768i \(-0.657027\pi\)
−0.473549 + 0.880768i \(0.657027\pi\)
\(524\) 9823.10 0.818939
\(525\) 0 0
\(526\) −13620.5 −1.12905
\(527\) −25563.2 −2.11300
\(528\) 6581.70 0.542484
\(529\) 529.000 0.0434783
\(530\) −9679.21 −0.793279
\(531\) −10598.3 −0.866150
\(532\) 0 0
\(533\) 23657.6 1.92256
\(534\) 18132.5 1.46942
\(535\) 4447.78 0.359428
\(536\) −903.082 −0.0727746
\(537\) 29309.1 2.35527
\(538\) −13386.3 −1.07272
\(539\) 0 0
\(540\) −140.830 −0.0112229
\(541\) −8508.86 −0.676201 −0.338100 0.941110i \(-0.609784\pi\)
−0.338100 + 0.941110i \(0.609784\pi\)
\(542\) −17282.7 −1.36966
\(543\) −16300.5 −1.28825
\(544\) 3482.71 0.274485
\(545\) 807.109 0.0634362
\(546\) 0 0
\(547\) 7097.86 0.554813 0.277406 0.960753i \(-0.410525\pi\)
0.277406 + 0.960753i \(0.410525\pi\)
\(548\) 4085.16 0.318448
\(549\) −6337.26 −0.492655
\(550\) 7652.43 0.593274
\(551\) 5371.66 0.415319
\(552\) −1344.11 −0.103639
\(553\) 0 0
\(554\) 14987.2 1.14936
\(555\) −6781.86 −0.518692
\(556\) −1675.62 −0.127809
\(557\) 269.957 0.0205358 0.0102679 0.999947i \(-0.496732\pi\)
0.0102679 + 0.999947i \(0.496732\pi\)
\(558\) −12383.8 −0.939514
\(559\) −2174.76 −0.164548
\(560\) 0 0
\(561\) −44769.8 −3.36931
\(562\) −3953.46 −0.296738
\(563\) 22749.5 1.70298 0.851491 0.524370i \(-0.175699\pi\)
0.851491 + 0.524370i \(0.175699\pi\)
\(564\) −4320.11 −0.322535
\(565\) 160.033 0.0119161
\(566\) 12309.2 0.914126
\(567\) 0 0
\(568\) −1370.90 −0.101271
\(569\) −93.7196 −0.00690498 −0.00345249 0.999994i \(-0.501099\pi\)
−0.00345249 + 0.999994i \(0.501099\pi\)
\(570\) −10192.9 −0.749007
\(571\) 3511.92 0.257389 0.128695 0.991684i \(-0.458921\pi\)
0.128695 + 0.991684i \(0.458921\pi\)
\(572\) 14829.9 1.08404
\(573\) 954.510 0.0695903
\(574\) 0 0
\(575\) −1562.77 −0.113343
\(576\) 1687.16 0.122046
\(577\) 3643.87 0.262905 0.131453 0.991322i \(-0.458036\pi\)
0.131453 + 0.991322i \(0.458036\pi\)
\(578\) −13863.9 −0.997688
\(579\) −25153.2 −1.80541
\(580\) 1757.11 0.125793
\(581\) 0 0
\(582\) 14579.3 1.03837
\(583\) 36080.4 2.56312
\(584\) −2893.75 −0.205042
\(585\) 13109.7 0.926531
\(586\) −3811.16 −0.268665
\(587\) −12611.0 −0.886730 −0.443365 0.896341i \(-0.646216\pi\)
−0.443365 + 0.896341i \(0.646216\pi\)
\(588\) 0 0
\(589\) 21695.0 1.51770
\(590\) 6073.36 0.423790
\(591\) −21741.9 −1.51327
\(592\) −1966.58 −0.136530
\(593\) 516.853 0.0357919 0.0178959 0.999840i \(-0.494303\pi\)
0.0178959 + 0.999840i \(0.494303\pi\)
\(594\) 524.959 0.0362615
\(595\) 0 0
\(596\) 3937.28 0.270599
\(597\) 6596.04 0.452191
\(598\) −3028.54 −0.207101
\(599\) −6239.98 −0.425640 −0.212820 0.977091i \(-0.568265\pi\)
−0.212820 + 0.977091i \(0.568265\pi\)
\(600\) 3970.75 0.270176
\(601\) 22085.1 1.49895 0.749477 0.662031i \(-0.230305\pi\)
0.749477 + 0.662031i \(0.230305\pi\)
\(602\) 0 0
\(603\) 2975.87 0.200973
\(604\) 8019.97 0.540278
\(605\) 13898.7 0.933987
\(606\) 13830.4 0.927098
\(607\) −23388.3 −1.56393 −0.781963 0.623325i \(-0.785782\pi\)
−0.781963 + 0.623325i \(0.785782\pi\)
\(608\) −2955.71 −0.197154
\(609\) 0 0
\(610\) 3631.58 0.241046
\(611\) −9734.09 −0.644516
\(612\) −11476.4 −0.758013
\(613\) 23195.2 1.52830 0.764149 0.645039i \(-0.223159\pi\)
0.764149 + 0.645039i \(0.223159\pi\)
\(614\) 1287.33 0.0846134
\(615\) 19826.7 1.29999
\(616\) 0 0
\(617\) −4370.58 −0.285175 −0.142588 0.989782i \(-0.545542\pi\)
−0.142588 + 0.989782i \(0.545542\pi\)
\(618\) 6168.47 0.401508
\(619\) −5754.61 −0.373663 −0.186831 0.982392i \(-0.559822\pi\)
−0.186831 + 0.982392i \(0.559822\pi\)
\(620\) 7096.58 0.459686
\(621\) −107.206 −0.00692761
\(622\) −10262.1 −0.661531
\(623\) 0 0
\(624\) 7695.05 0.493668
\(625\) −2514.96 −0.160957
\(626\) 9691.86 0.618793
\(627\) 37995.3 2.42007
\(628\) 1543.47 0.0980752
\(629\) 13377.0 0.847975
\(630\) 0 0
\(631\) −10487.6 −0.661658 −0.330829 0.943691i \(-0.607328\pi\)
−0.330829 + 0.943691i \(0.607328\pi\)
\(632\) 6738.53 0.424121
\(633\) −17823.7 −1.11916
\(634\) −4298.14 −0.269244
\(635\) 16420.7 1.02619
\(636\) 18721.7 1.16724
\(637\) 0 0
\(638\) −6549.82 −0.406442
\(639\) 4517.46 0.279668
\(640\) −966.832 −0.0597147
\(641\) 22643.5 1.39526 0.697631 0.716457i \(-0.254237\pi\)
0.697631 + 0.716457i \(0.254237\pi\)
\(642\) −8602.96 −0.528865
\(643\) 8247.48 0.505830 0.252915 0.967488i \(-0.418611\pi\)
0.252915 + 0.967488i \(0.418611\pi\)
\(644\) 0 0
\(645\) −1822.60 −0.111263
\(646\) 20105.2 1.22450
\(647\) −3358.18 −0.204055 −0.102027 0.994782i \(-0.532533\pi\)
−0.102027 + 0.994782i \(0.532533\pi\)
\(648\) 5966.57 0.361711
\(649\) −22639.2 −1.36928
\(650\) 8946.91 0.539887
\(651\) 0 0
\(652\) −9589.50 −0.576003
\(653\) −11243.5 −0.673802 −0.336901 0.941540i \(-0.609379\pi\)
−0.336901 + 0.941540i \(0.609379\pi\)
\(654\) −1561.12 −0.0933405
\(655\) 18549.4 1.10654
\(656\) 5749.29 0.342183
\(657\) 9535.61 0.566240
\(658\) 0 0
\(659\) 28375.7 1.67733 0.838664 0.544650i \(-0.183337\pi\)
0.838664 + 0.544650i \(0.183337\pi\)
\(660\) 12428.5 0.732999
\(661\) 26521.0 1.56058 0.780292 0.625415i \(-0.215070\pi\)
0.780292 + 0.625415i \(0.215070\pi\)
\(662\) −1466.69 −0.0861094
\(663\) −52343.0 −3.06611
\(664\) −10994.3 −0.642563
\(665\) 0 0
\(666\) 6480.36 0.377040
\(667\) 1337.60 0.0776491
\(668\) −13755.7 −0.796743
\(669\) 39551.4 2.28572
\(670\) −1705.33 −0.0983323
\(671\) −13537.1 −0.778831
\(672\) 0 0
\(673\) −11574.0 −0.662921 −0.331460 0.943469i \(-0.607541\pi\)
−0.331460 + 0.943469i \(0.607541\pi\)
\(674\) 3844.82 0.219729
\(675\) 316.709 0.0180594
\(676\) 8550.51 0.486488
\(677\) −19964.6 −1.13338 −0.566692 0.823930i \(-0.691777\pi\)
−0.566692 + 0.823930i \(0.691777\pi\)
\(678\) −309.537 −0.0175335
\(679\) 0 0
\(680\) 6576.55 0.370881
\(681\) −32722.7 −1.84132
\(682\) −26453.3 −1.48526
\(683\) 30955.7 1.73424 0.867120 0.498099i \(-0.165968\pi\)
0.867120 + 0.498099i \(0.165968\pi\)
\(684\) 9739.77 0.544458
\(685\) 7714.19 0.430283
\(686\) 0 0
\(687\) 26501.5 1.47175
\(688\) −528.512 −0.0292868
\(689\) 42183.7 2.33247
\(690\) −2538.13 −0.140036
\(691\) 10356.0 0.570133 0.285066 0.958508i \(-0.407984\pi\)
0.285066 + 0.958508i \(0.407984\pi\)
\(692\) −8035.96 −0.441447
\(693\) 0 0
\(694\) −22619.0 −1.23718
\(695\) −3164.14 −0.172694
\(696\) −3398.62 −0.185093
\(697\) −39107.6 −2.12526
\(698\) 10404.7 0.564220
\(699\) −26902.1 −1.45569
\(700\) 0 0
\(701\) −736.621 −0.0396887 −0.0198444 0.999803i \(-0.506317\pi\)
−0.0198444 + 0.999803i \(0.506317\pi\)
\(702\) 613.760 0.0329984
\(703\) −11352.8 −0.609075
\(704\) 3603.98 0.192941
\(705\) −8157.86 −0.435805
\(706\) 12605.4 0.671968
\(707\) 0 0
\(708\) −11747.2 −0.623568
\(709\) −32277.6 −1.70975 −0.854873 0.518838i \(-0.826365\pi\)
−0.854873 + 0.518838i \(0.826365\pi\)
\(710\) −2588.74 −0.136836
\(711\) −22205.1 −1.17125
\(712\) 9928.91 0.522614
\(713\) 5402.26 0.283754
\(714\) 0 0
\(715\) 28004.0 1.46474
\(716\) 16048.9 0.837677
\(717\) 9420.39 0.490671
\(718\) 25595.8 1.33040
\(719\) −34790.7 −1.80455 −0.902277 0.431156i \(-0.858106\pi\)
−0.902277 + 0.431156i \(0.858106\pi\)
\(720\) 3185.94 0.164907
\(721\) 0 0
\(722\) −3344.92 −0.172417
\(723\) 4851.59 0.249561
\(724\) −8925.75 −0.458181
\(725\) −3951.52 −0.202422
\(726\) −26883.0 −1.37427
\(727\) −21693.3 −1.10668 −0.553341 0.832955i \(-0.686647\pi\)
−0.553341 + 0.832955i \(0.686647\pi\)
\(728\) 0 0
\(729\) −18741.9 −0.952189
\(730\) −5464.40 −0.277050
\(731\) 3595.02 0.181897
\(732\) −7024.25 −0.354677
\(733\) −18264.6 −0.920352 −0.460176 0.887828i \(-0.652214\pi\)
−0.460176 + 0.887828i \(0.652214\pi\)
\(734\) −15589.5 −0.783948
\(735\) 0 0
\(736\) −736.000 −0.0368605
\(737\) 6356.82 0.317715
\(738\) −18945.3 −0.944967
\(739\) 10487.5 0.522040 0.261020 0.965333i \(-0.415941\pi\)
0.261020 + 0.965333i \(0.415941\pi\)
\(740\) −3713.58 −0.184478
\(741\) 44422.5 2.20230
\(742\) 0 0
\(743\) 6519.14 0.321889 0.160945 0.986963i \(-0.448546\pi\)
0.160945 + 0.986963i \(0.448546\pi\)
\(744\) −13726.3 −0.676385
\(745\) 7434.93 0.365631
\(746\) −18704.0 −0.917967
\(747\) 36228.9 1.77449
\(748\) −24514.9 −1.19833
\(749\) 0 0
\(750\) 21292.4 1.03665
\(751\) −24410.9 −1.18611 −0.593053 0.805164i \(-0.702077\pi\)
−0.593053 + 0.805164i \(0.702077\pi\)
\(752\) −2365.59 −0.114713
\(753\) −34852.4 −1.68671
\(754\) −7657.78 −0.369867
\(755\) 15144.5 0.730018
\(756\) 0 0
\(757\) −36222.9 −1.73916 −0.869580 0.493793i \(-0.835610\pi\)
−0.869580 + 0.493793i \(0.835610\pi\)
\(758\) 1343.02 0.0643543
\(759\) 9461.19 0.452463
\(760\) −5581.39 −0.266393
\(761\) −10363.5 −0.493660 −0.246830 0.969059i \(-0.579389\pi\)
−0.246830 + 0.969059i \(0.579389\pi\)
\(762\) −31761.1 −1.50995
\(763\) 0 0
\(764\) 522.667 0.0247505
\(765\) −21671.3 −1.02422
\(766\) 11846.3 0.558777
\(767\) −26468.8 −1.24607
\(768\) 1870.06 0.0878646
\(769\) 3915.55 0.183613 0.0918065 0.995777i \(-0.470736\pi\)
0.0918065 + 0.995777i \(0.470736\pi\)
\(770\) 0 0
\(771\) 15590.8 0.728262
\(772\) −13773.3 −0.642113
\(773\) −28820.3 −1.34100 −0.670500 0.741910i \(-0.733920\pi\)
−0.670500 + 0.741910i \(0.733920\pi\)
\(774\) 1741.57 0.0808780
\(775\) −15959.3 −0.739711
\(776\) 7983.25 0.369307
\(777\) 0 0
\(778\) 6904.91 0.318191
\(779\) 33189.9 1.52651
\(780\) 14530.9 0.667038
\(781\) 9649.82 0.442123
\(782\) 5006.39 0.228936
\(783\) −271.075 −0.0123722
\(784\) 0 0
\(785\) 2914.61 0.132518
\(786\) −35878.5 −1.62817
\(787\) −23146.5 −1.04839 −0.524196 0.851598i \(-0.675634\pi\)
−0.524196 + 0.851598i \(0.675634\pi\)
\(788\) −11905.3 −0.538211
\(789\) 49748.3 2.24472
\(790\) 12724.7 0.573067
\(791\) 0 0
\(792\) −11876.0 −0.532821
\(793\) −15827.1 −0.708746
\(794\) −4925.42 −0.220147
\(795\) 35353.0 1.57716
\(796\) 3611.83 0.160827
\(797\) −8804.30 −0.391298 −0.195649 0.980674i \(-0.562681\pi\)
−0.195649 + 0.980674i \(0.562681\pi\)
\(798\) 0 0
\(799\) 16091.1 0.712469
\(800\) 2174.29 0.0960909
\(801\) −32718.1 −1.44324
\(802\) 25256.1 1.11200
\(803\) 20369.2 0.895160
\(804\) 3298.47 0.144687
\(805\) 0 0
\(806\) −30928.1 −1.35161
\(807\) 48892.8 2.13272
\(808\) 7573.19 0.329732
\(809\) −16308.6 −0.708752 −0.354376 0.935103i \(-0.615307\pi\)
−0.354376 + 0.935103i \(0.615307\pi\)
\(810\) 11266.9 0.488740
\(811\) −8308.25 −0.359731 −0.179866 0.983691i \(-0.557566\pi\)
−0.179866 + 0.983691i \(0.557566\pi\)
\(812\) 0 0
\(813\) 63124.5 2.72309
\(814\) 13842.8 0.596057
\(815\) −18108.3 −0.778289
\(816\) −12720.5 −0.545717
\(817\) −3051.03 −0.130651
\(818\) 19715.5 0.842709
\(819\) 0 0
\(820\) 10856.6 0.462354
\(821\) 28618.8 1.21657 0.608284 0.793720i \(-0.291858\pi\)
0.608284 + 0.793720i \(0.291858\pi\)
\(822\) −14920.9 −0.633122
\(823\) 1464.41 0.0620244 0.0310122 0.999519i \(-0.490127\pi\)
0.0310122 + 0.999519i \(0.490127\pi\)
\(824\) 3377.70 0.142801
\(825\) −27950.2 −1.17952
\(826\) 0 0
\(827\) −38045.8 −1.59974 −0.799869 0.600175i \(-0.795098\pi\)
−0.799869 + 0.600175i \(0.795098\pi\)
\(828\) 2425.30 0.101793
\(829\) −23247.3 −0.973961 −0.486980 0.873413i \(-0.661902\pi\)
−0.486980 + 0.873413i \(0.661902\pi\)
\(830\) −20761.0 −0.868224
\(831\) −54740.0 −2.28509
\(832\) 4213.62 0.175578
\(833\) 0 0
\(834\) 6120.12 0.254104
\(835\) −25975.5 −1.07655
\(836\) 20805.3 0.860725
\(837\) −1094.81 −0.0452119
\(838\) −31188.0 −1.28565
\(839\) −10511.6 −0.432539 −0.216270 0.976334i \(-0.569389\pi\)
−0.216270 + 0.976334i \(0.569389\pi\)
\(840\) 0 0
\(841\) −21006.8 −0.861324
\(842\) 4859.96 0.198914
\(843\) 14439.9 0.589959
\(844\) −9759.80 −0.398041
\(845\) 16146.3 0.657337
\(846\) 7795.18 0.316790
\(847\) 0 0
\(848\) 10251.5 0.415141
\(849\) −44959.0 −1.81742
\(850\) −14789.9 −0.596809
\(851\) −2826.96 −0.113874
\(852\) 5007.17 0.201341
\(853\) −10457.1 −0.419748 −0.209874 0.977728i \(-0.567305\pi\)
−0.209874 + 0.977728i \(0.567305\pi\)
\(854\) 0 0
\(855\) 18392.0 0.735666
\(856\) −4710.77 −0.188097
\(857\) 17615.4 0.702135 0.351067 0.936350i \(-0.385819\pi\)
0.351067 + 0.936350i \(0.385819\pi\)
\(858\) −54165.7 −2.15523
\(859\) 16600.7 0.659381 0.329691 0.944089i \(-0.393056\pi\)
0.329691 + 0.944089i \(0.393056\pi\)
\(860\) −998.012 −0.0395720
\(861\) 0 0
\(862\) 9080.57 0.358800
\(863\) −11013.9 −0.434436 −0.217218 0.976123i \(-0.569698\pi\)
−0.217218 + 0.976123i \(0.569698\pi\)
\(864\) 149.157 0.00587317
\(865\) −15174.7 −0.596478
\(866\) −30645.3 −1.20250
\(867\) 50637.5 1.98355
\(868\) 0 0
\(869\) −47432.7 −1.85160
\(870\) −6417.77 −0.250095
\(871\) 7432.13 0.289125
\(872\) −854.832 −0.0331976
\(873\) −26306.7 −1.01987
\(874\) −4248.83 −0.164438
\(875\) 0 0
\(876\) 10569.3 0.407653
\(877\) 22076.0 0.850003 0.425002 0.905193i \(-0.360274\pi\)
0.425002 + 0.905193i \(0.360274\pi\)
\(878\) −10283.6 −0.395278
\(879\) 13920.1 0.534146
\(880\) 6805.55 0.260699
\(881\) −9443.65 −0.361140 −0.180570 0.983562i \(-0.557794\pi\)
−0.180570 + 0.983562i \(0.557794\pi\)
\(882\) 0 0
\(883\) 31677.0 1.20727 0.603633 0.797262i \(-0.293719\pi\)
0.603633 + 0.797262i \(0.293719\pi\)
\(884\) −28661.8 −1.09050
\(885\) −22182.7 −0.842558
\(886\) 15076.7 0.571682
\(887\) 96.4492 0.00365101 0.00182551 0.999998i \(-0.499419\pi\)
0.00182551 + 0.999998i \(0.499419\pi\)
\(888\) 7182.86 0.271443
\(889\) 0 0
\(890\) 18749.2 0.706151
\(891\) −41998.8 −1.57914
\(892\) 21657.4 0.812941
\(893\) −13656.2 −0.511745
\(894\) −14380.8 −0.537992
\(895\) 30305.9 1.13186
\(896\) 0 0
\(897\) 11061.6 0.411747
\(898\) 14506.3 0.539065
\(899\) 13659.8 0.506764
\(900\) −7164.80 −0.265363
\(901\) −69732.6 −2.57839
\(902\) −40469.4 −1.49388
\(903\) 0 0
\(904\) −169.495 −0.00623598
\(905\) −16854.9 −0.619088
\(906\) −29292.6 −1.07415
\(907\) −34721.3 −1.27112 −0.635559 0.772053i \(-0.719230\pi\)
−0.635559 + 0.772053i \(0.719230\pi\)
\(908\) −17918.2 −0.654884
\(909\) −24955.5 −0.910584
\(910\) 0 0
\(911\) 23562.8 0.856938 0.428469 0.903557i \(-0.359053\pi\)
0.428469 + 0.903557i \(0.359053\pi\)
\(912\) 10795.6 0.391972
\(913\) 77389.2 2.80527
\(914\) 28226.9 1.02151
\(915\) −13264.2 −0.479236
\(916\) 14511.6 0.523445
\(917\) 0 0
\(918\) −1014.59 −0.0364776
\(919\) −26368.7 −0.946487 −0.473244 0.880932i \(-0.656917\pi\)
−0.473244 + 0.880932i \(0.656917\pi\)
\(920\) −1389.82 −0.0498055
\(921\) −4701.94 −0.168224
\(922\) 3992.13 0.142596
\(923\) 11282.2 0.402337
\(924\) 0 0
\(925\) 8351.39 0.296856
\(926\) −16603.1 −0.589212
\(927\) −11130.3 −0.394356
\(928\) −1861.00 −0.0658302
\(929\) 36036.3 1.27267 0.636336 0.771412i \(-0.280449\pi\)
0.636336 + 0.771412i \(0.280449\pi\)
\(930\) −25920.0 −0.913924
\(931\) 0 0
\(932\) −14730.9 −0.517734
\(933\) 37481.9 1.31522
\(934\) −9035.68 −0.316549
\(935\) −46292.5 −1.61917
\(936\) −13884.9 −0.484874
\(937\) −13236.3 −0.461483 −0.230742 0.973015i \(-0.574115\pi\)
−0.230742 + 0.973015i \(0.574115\pi\)
\(938\) 0 0
\(939\) −35399.2 −1.23025
\(940\) −4467.05 −0.154999
\(941\) 14141.9 0.489918 0.244959 0.969533i \(-0.421225\pi\)
0.244959 + 0.969533i \(0.421225\pi\)
\(942\) −5637.47 −0.194988
\(943\) 8264.60 0.285400
\(944\) −6432.47 −0.221779
\(945\) 0 0
\(946\) 3720.21 0.127859
\(947\) 48138.7 1.65185 0.825923 0.563782i \(-0.190654\pi\)
0.825923 + 0.563782i \(0.190654\pi\)
\(948\) −24612.2 −0.843215
\(949\) 23814.8 0.814607
\(950\) 12551.9 0.428670
\(951\) 15698.8 0.535298
\(952\) 0 0
\(953\) −35613.3 −1.21052 −0.605262 0.796027i \(-0.706932\pi\)
−0.605262 + 0.796027i \(0.706932\pi\)
\(954\) −33781.3 −1.14645
\(955\) 986.974 0.0334427
\(956\) 5158.38 0.174512
\(957\) 23923.0 0.808067
\(958\) −33031.3 −1.11398
\(959\) 0 0
\(960\) 3531.32 0.118722
\(961\) 25378.0 0.851869
\(962\) 16184.4 0.542419
\(963\) 15523.1 0.519445
\(964\) 2656.61 0.0887590
\(965\) −26008.7 −0.867616
\(966\) 0 0
\(967\) −19501.2 −0.648518 −0.324259 0.945968i \(-0.605115\pi\)
−0.324259 + 0.945968i \(0.605115\pi\)
\(968\) −14720.5 −0.488776
\(969\) −73433.5 −2.43449
\(970\) 15075.1 0.499003
\(971\) 8769.76 0.289840 0.144920 0.989443i \(-0.453707\pi\)
0.144920 + 0.989443i \(0.453707\pi\)
\(972\) −21289.3 −0.702524
\(973\) 0 0
\(974\) −18106.2 −0.595646
\(975\) −32678.2 −1.07338
\(976\) −3846.31 −0.126145
\(977\) −4744.61 −0.155367 −0.0776835 0.996978i \(-0.524752\pi\)
−0.0776835 + 0.996978i \(0.524752\pi\)
\(978\) 35025.3 1.14518
\(979\) −69889.8 −2.28160
\(980\) 0 0
\(981\) 2816.88 0.0916779
\(982\) 14797.8 0.480871
\(983\) 55524.2 1.80157 0.900787 0.434262i \(-0.142991\pi\)
0.900787 + 0.434262i \(0.142991\pi\)
\(984\) −20999.1 −0.680311
\(985\) −22481.4 −0.727225
\(986\) 12658.8 0.408864
\(987\) 0 0
\(988\) 24324.7 0.783271
\(989\) −759.736 −0.0244269
\(990\) −22425.9 −0.719942
\(991\) −16769.6 −0.537543 −0.268771 0.963204i \(-0.586618\pi\)
−0.268771 + 0.963204i \(0.586618\pi\)
\(992\) −7516.19 −0.240564
\(993\) 5357.02 0.171198
\(994\) 0 0
\(995\) 6820.39 0.217307
\(996\) 40156.3 1.27751
\(997\) −14619.4 −0.464394 −0.232197 0.972669i \(-0.574591\pi\)
−0.232197 + 0.972669i \(0.574591\pi\)
\(998\) 1435.64 0.0455356
\(999\) 572.908 0.0181441
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 2254.4.a.u.1.9 11
7.3 odd 6 322.4.e.d.93.9 22
7.5 odd 6 322.4.e.d.277.9 yes 22
7.6 odd 2 2254.4.a.r.1.3 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.e.d.93.9 22 7.3 odd 6
322.4.e.d.277.9 yes 22 7.5 odd 6
2254.4.a.r.1.3 11 7.6 odd 2
2254.4.a.u.1.9 11 1.1 even 1 trivial