Properties

Label 289.4.a.h.1.8
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $1$
Dimension $12$
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] = [289,4,Mod(1,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.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: \(17.0515519917\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3}\cdot 17^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-1.26162\) of defining polynomial
Character \(\chi\) \(=\) 289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.26162 q^{2} +6.09538 q^{3} -6.40830 q^{4} -13.2627 q^{5} +7.69007 q^{6} +27.2593 q^{7} -18.1779 q^{8} +10.1536 q^{9} +O(q^{10})\) \(q+1.26162 q^{2} +6.09538 q^{3} -6.40830 q^{4} -13.2627 q^{5} +7.69007 q^{6} +27.2593 q^{7} -18.1779 q^{8} +10.1536 q^{9} -16.7325 q^{10} -45.5149 q^{11} -39.0610 q^{12} -52.5379 q^{13} +34.3910 q^{14} -80.8409 q^{15} +28.3328 q^{16} +12.8100 q^{18} +3.08418 q^{19} +84.9911 q^{20} +166.156 q^{21} -57.4227 q^{22} -112.369 q^{23} -110.801 q^{24} +50.8981 q^{25} -66.2831 q^{26} -102.685 q^{27} -174.686 q^{28} +18.6294 q^{29} -101.991 q^{30} -238.763 q^{31} +181.168 q^{32} -277.430 q^{33} -361.531 q^{35} -65.0674 q^{36} +162.717 q^{37} +3.89108 q^{38} -320.238 q^{39} +241.087 q^{40} -383.816 q^{41} +209.626 q^{42} +468.761 q^{43} +291.673 q^{44} -134.664 q^{45} -141.767 q^{46} -199.727 q^{47} +172.699 q^{48} +400.071 q^{49} +64.2142 q^{50} +336.679 q^{52} -105.679 q^{53} -129.550 q^{54} +603.649 q^{55} -495.516 q^{56} +18.7993 q^{57} +23.5033 q^{58} +207.142 q^{59} +518.053 q^{60} -586.101 q^{61} -301.230 q^{62} +276.780 q^{63} +1.90375 q^{64} +696.792 q^{65} -350.013 q^{66} +401.953 q^{67} -684.930 q^{69} -456.116 q^{70} +481.559 q^{71} -184.571 q^{72} +725.281 q^{73} +205.287 q^{74} +310.243 q^{75} -19.7644 q^{76} -1240.71 q^{77} -404.020 q^{78} +382.621 q^{79} -375.768 q^{80} -900.052 q^{81} -484.231 q^{82} -182.391 q^{83} -1064.78 q^{84} +591.401 q^{86} +113.553 q^{87} +827.364 q^{88} -623.009 q^{89} -169.895 q^{90} -1432.15 q^{91} +720.094 q^{92} -1455.35 q^{93} -251.981 q^{94} -40.9045 q^{95} +1104.29 q^{96} +369.544 q^{97} +504.739 q^{98} -462.140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26162 0.446051 0.223026 0.974813i \(-0.428407\pi\)
0.223026 + 0.974813i \(0.428407\pi\)
\(3\) 6.09538 1.17306 0.586528 0.809929i \(-0.300494\pi\)
0.586528 + 0.809929i \(0.300494\pi\)
\(4\) −6.40830 −0.801038
\(5\) −13.2627 −1.18625 −0.593124 0.805111i \(-0.702106\pi\)
−0.593124 + 0.805111i \(0.702106\pi\)
\(6\) 7.69007 0.523243
\(7\) 27.2593 1.47186 0.735932 0.677055i \(-0.236744\pi\)
0.735932 + 0.677055i \(0.236744\pi\)
\(8\) −18.1779 −0.803356
\(9\) 10.1536 0.376059
\(10\) −16.7325 −0.529128
\(11\) −45.5149 −1.24757 −0.623785 0.781596i \(-0.714406\pi\)
−0.623785 + 0.781596i \(0.714406\pi\)
\(12\) −39.0610 −0.939662
\(13\) −52.5379 −1.12088 −0.560438 0.828196i \(-0.689367\pi\)
−0.560438 + 0.828196i \(0.689367\pi\)
\(14\) 34.3910 0.656527
\(15\) −80.8409 −1.39153
\(16\) 28.3328 0.442700
\(17\) 0 0
\(18\) 12.8100 0.167742
\(19\) 3.08418 0.0372400 0.0186200 0.999827i \(-0.494073\pi\)
0.0186200 + 0.999827i \(0.494073\pi\)
\(20\) 84.9911 0.950230
\(21\) 166.156 1.72658
\(22\) −57.4227 −0.556480
\(23\) −112.369 −1.01872 −0.509359 0.860554i \(-0.670118\pi\)
−0.509359 + 0.860554i \(0.670118\pi\)
\(24\) −110.801 −0.942381
\(25\) 50.8981 0.407185
\(26\) −66.2831 −0.499968
\(27\) −102.685 −0.731917
\(28\) −174.686 −1.17902
\(29\) 18.6294 0.119290 0.0596448 0.998220i \(-0.481003\pi\)
0.0596448 + 0.998220i \(0.481003\pi\)
\(30\) −101.991 −0.620696
\(31\) −238.763 −1.38333 −0.691664 0.722219i \(-0.743122\pi\)
−0.691664 + 0.722219i \(0.743122\pi\)
\(32\) 181.168 1.00082
\(33\) −277.430 −1.46347
\(34\) 0 0
\(35\) −361.531 −1.74600
\(36\) −65.0674 −0.301238
\(37\) 162.717 0.722986 0.361493 0.932375i \(-0.382267\pi\)
0.361493 + 0.932375i \(0.382267\pi\)
\(38\) 3.89108 0.0166110
\(39\) −320.238 −1.31485
\(40\) 241.087 0.952979
\(41\) −383.816 −1.46200 −0.730999 0.682378i \(-0.760946\pi\)
−0.730999 + 0.682378i \(0.760946\pi\)
\(42\) 209.626 0.770143
\(43\) 468.761 1.66245 0.831226 0.555935i \(-0.187640\pi\)
0.831226 + 0.555935i \(0.187640\pi\)
\(44\) 291.673 0.999350
\(45\) −134.664 −0.446100
\(46\) −141.767 −0.454401
\(47\) −199.727 −0.619856 −0.309928 0.950760i \(-0.600305\pi\)
−0.309928 + 0.950760i \(0.600305\pi\)
\(48\) 172.699 0.519312
\(49\) 400.071 1.16639
\(50\) 64.2142 0.181625
\(51\) 0 0
\(52\) 336.679 0.897864
\(53\) −105.679 −0.273889 −0.136944 0.990579i \(-0.543728\pi\)
−0.136944 + 0.990579i \(0.543728\pi\)
\(54\) −129.550 −0.326473
\(55\) 603.649 1.47993
\(56\) −495.516 −1.18243
\(57\) 18.7993 0.0436846
\(58\) 23.5033 0.0532093
\(59\) 207.142 0.457078 0.228539 0.973535i \(-0.426605\pi\)
0.228539 + 0.973535i \(0.426605\pi\)
\(60\) 518.053 1.11467
\(61\) −586.101 −1.23021 −0.615103 0.788447i \(-0.710886\pi\)
−0.615103 + 0.788447i \(0.710886\pi\)
\(62\) −301.230 −0.617036
\(63\) 276.780 0.553508
\(64\) 1.90375 0.00371826
\(65\) 696.792 1.32964
\(66\) −350.013 −0.652782
\(67\) 401.953 0.732931 0.366466 0.930432i \(-0.380568\pi\)
0.366466 + 0.930432i \(0.380568\pi\)
\(68\) 0 0
\(69\) −684.930 −1.19501
\(70\) −456.116 −0.778805
\(71\) 481.559 0.804937 0.402468 0.915434i \(-0.368152\pi\)
0.402468 + 0.915434i \(0.368152\pi\)
\(72\) −184.571 −0.302109
\(73\) 725.281 1.16285 0.581423 0.813602i \(-0.302496\pi\)
0.581423 + 0.813602i \(0.302496\pi\)
\(74\) 205.287 0.322489
\(75\) 310.243 0.477650
\(76\) −19.7644 −0.0298307
\(77\) −1240.71 −1.83625
\(78\) −404.020 −0.586491
\(79\) 382.621 0.544914 0.272457 0.962168i \(-0.412164\pi\)
0.272457 + 0.962168i \(0.412164\pi\)
\(80\) −375.768 −0.525152
\(81\) −900.052 −1.23464
\(82\) −484.231 −0.652127
\(83\) −182.391 −0.241204 −0.120602 0.992701i \(-0.538483\pi\)
−0.120602 + 0.992701i \(0.538483\pi\)
\(84\) −1064.78 −1.38306
\(85\) 0 0
\(86\) 591.401 0.741539
\(87\) 113.553 0.139933
\(88\) 827.364 1.00224
\(89\) −623.009 −0.742010 −0.371005 0.928631i \(-0.620987\pi\)
−0.371005 + 0.928631i \(0.620987\pi\)
\(90\) −169.895 −0.198983
\(91\) −1432.15 −1.64978
\(92\) 720.094 0.816032
\(93\) −1455.35 −1.62272
\(94\) −251.981 −0.276488
\(95\) −40.9045 −0.0441759
\(96\) 1104.29 1.17402
\(97\) 369.544 0.386820 0.193410 0.981118i \(-0.438045\pi\)
0.193410 + 0.981118i \(0.438045\pi\)
\(98\) 504.739 0.520268
\(99\) −462.140 −0.469160
\(100\) −326.170 −0.326170
\(101\) 810.381 0.798375 0.399188 0.916869i \(-0.369292\pi\)
0.399188 + 0.916869i \(0.369292\pi\)
\(102\) 0 0
\(103\) 772.683 0.739172 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(104\) 955.026 0.900462
\(105\) −2203.67 −2.04815
\(106\) −133.327 −0.122169
\(107\) 996.966 0.900751 0.450375 0.892839i \(-0.351290\pi\)
0.450375 + 0.892839i \(0.351290\pi\)
\(108\) 658.038 0.586293
\(109\) −700.996 −0.615993 −0.307996 0.951388i \(-0.599658\pi\)
−0.307996 + 0.951388i \(0.599658\pi\)
\(110\) 761.578 0.660123
\(111\) 991.820 0.848102
\(112\) 772.333 0.651595
\(113\) −1459.26 −1.21483 −0.607415 0.794384i \(-0.707794\pi\)
−0.607415 + 0.794384i \(0.707794\pi\)
\(114\) 23.7176 0.0194856
\(115\) 1490.31 1.20845
\(116\) −119.383 −0.0955554
\(117\) −533.449 −0.421516
\(118\) 261.335 0.203880
\(119\) 0 0
\(120\) 1469.51 1.11790
\(121\) 740.607 0.556429
\(122\) −739.439 −0.548735
\(123\) −2339.50 −1.71501
\(124\) 1530.07 1.10810
\(125\) 982.788 0.703226
\(126\) 349.193 0.246893
\(127\) 426.418 0.297941 0.148970 0.988842i \(-0.452404\pi\)
0.148970 + 0.988842i \(0.452404\pi\)
\(128\) −1446.94 −0.999164
\(129\) 2857.28 1.95015
\(130\) 879.089 0.593086
\(131\) 19.9037 0.0132747 0.00663737 0.999978i \(-0.497887\pi\)
0.00663737 + 0.999978i \(0.497887\pi\)
\(132\) 1777.86 1.17229
\(133\) 84.0728 0.0548123
\(134\) 507.114 0.326925
\(135\) 1361.88 0.868235
\(136\) 0 0
\(137\) −1824.89 −1.13804 −0.569019 0.822324i \(-0.692677\pi\)
−0.569019 + 0.822324i \(0.692677\pi\)
\(138\) −864.125 −0.533037
\(139\) −1803.87 −1.10074 −0.550368 0.834922i \(-0.685512\pi\)
−0.550368 + 0.834922i \(0.685512\pi\)
\(140\) 2316.80 1.39861
\(141\) −1217.41 −0.727126
\(142\) 607.546 0.359043
\(143\) 2391.26 1.39837
\(144\) 287.680 0.166482
\(145\) −247.076 −0.141507
\(146\) 915.032 0.518689
\(147\) 2438.58 1.36824
\(148\) −1042.74 −0.579139
\(149\) 2742.46 1.50786 0.753929 0.656955i \(-0.228156\pi\)
0.753929 + 0.656955i \(0.228156\pi\)
\(150\) 391.410 0.213057
\(151\) 2085.22 1.12379 0.561896 0.827208i \(-0.310072\pi\)
0.561896 + 0.827208i \(0.310072\pi\)
\(152\) −56.0639 −0.0299170
\(153\) 0 0
\(154\) −1565.30 −0.819063
\(155\) 3166.64 1.64097
\(156\) 2052.18 1.05324
\(157\) −2703.53 −1.37430 −0.687149 0.726516i \(-0.741138\pi\)
−0.687149 + 0.726516i \(0.741138\pi\)
\(158\) 482.724 0.243060
\(159\) −644.152 −0.321287
\(160\) −2402.77 −1.18722
\(161\) −3063.10 −1.49942
\(162\) −1135.53 −0.550712
\(163\) −2923.57 −1.40486 −0.702428 0.711755i \(-0.747901\pi\)
−0.702428 + 0.711755i \(0.747901\pi\)
\(164\) 2459.61 1.17112
\(165\) 3679.46 1.73604
\(166\) −230.108 −0.107590
\(167\) −2419.31 −1.12103 −0.560514 0.828145i \(-0.689397\pi\)
−0.560514 + 0.828145i \(0.689397\pi\)
\(168\) −3020.36 −1.38706
\(169\) 563.229 0.256363
\(170\) 0 0
\(171\) 31.3156 0.0140045
\(172\) −3003.97 −1.33169
\(173\) −393.655 −0.173000 −0.0865000 0.996252i \(-0.527568\pi\)
−0.0865000 + 0.996252i \(0.527568\pi\)
\(174\) 143.262 0.0624174
\(175\) 1387.45 0.599321
\(176\) −1289.57 −0.552299
\(177\) 1262.61 0.536178
\(178\) −786.004 −0.330975
\(179\) 1918.60 0.801133 0.400567 0.916268i \(-0.368813\pi\)
0.400567 + 0.916268i \(0.368813\pi\)
\(180\) 862.966 0.357343
\(181\) −1677.03 −0.688688 −0.344344 0.938844i \(-0.611899\pi\)
−0.344344 + 0.938844i \(0.611899\pi\)
\(182\) −1806.83 −0.735886
\(183\) −3572.51 −1.44310
\(184\) 2042.63 0.818393
\(185\) −2158.06 −0.857640
\(186\) −1836.11 −0.723817
\(187\) 0 0
\(188\) 1279.91 0.496529
\(189\) −2799.13 −1.07728
\(190\) −51.6061 −0.0197047
\(191\) 2347.19 0.889196 0.444598 0.895730i \(-0.353347\pi\)
0.444598 + 0.895730i \(0.353347\pi\)
\(192\) 11.6041 0.00436173
\(193\) 650.982 0.242791 0.121396 0.992604i \(-0.461263\pi\)
0.121396 + 0.992604i \(0.461263\pi\)
\(194\) 466.226 0.172542
\(195\) 4247.21 1.55974
\(196\) −2563.77 −0.934320
\(197\) −2681.01 −0.969614 −0.484807 0.874621i \(-0.661110\pi\)
−0.484807 + 0.874621i \(0.661110\pi\)
\(198\) −583.047 −0.209269
\(199\) −1784.74 −0.635762 −0.317881 0.948131i \(-0.602971\pi\)
−0.317881 + 0.948131i \(0.602971\pi\)
\(200\) −925.218 −0.327114
\(201\) 2450.06 0.859769
\(202\) 1022.40 0.356116
\(203\) 507.825 0.175578
\(204\) 0 0
\(205\) 5090.42 1.73429
\(206\) 974.835 0.329709
\(207\) −1140.95 −0.383099
\(208\) −1488.55 −0.496212
\(209\) −140.376 −0.0464595
\(210\) −2780.20 −0.913581
\(211\) 68.5651 0.0223707 0.0111853 0.999937i \(-0.496440\pi\)
0.0111853 + 0.999937i \(0.496440\pi\)
\(212\) 677.222 0.219395
\(213\) 2935.28 0.944235
\(214\) 1257.80 0.401781
\(215\) −6217.02 −1.97208
\(216\) 1866.60 0.587990
\(217\) −6508.53 −2.03607
\(218\) −884.393 −0.274765
\(219\) 4420.86 1.36408
\(220\) −3868.36 −1.18548
\(221\) 0 0
\(222\) 1251.30 0.378297
\(223\) 4734.22 1.42164 0.710822 0.703372i \(-0.248323\pi\)
0.710822 + 0.703372i \(0.248323\pi\)
\(224\) 4938.52 1.47308
\(225\) 516.799 0.153126
\(226\) −1841.04 −0.541877
\(227\) 1722.86 0.503745 0.251873 0.967760i \(-0.418954\pi\)
0.251873 + 0.967760i \(0.418954\pi\)
\(228\) −120.471 −0.0349930
\(229\) −313.375 −0.0904297 −0.0452149 0.998977i \(-0.514397\pi\)
−0.0452149 + 0.998977i \(0.514397\pi\)
\(230\) 1880.21 0.539032
\(231\) −7562.57 −2.15403
\(232\) −338.643 −0.0958319
\(233\) −2101.61 −0.590905 −0.295453 0.955357i \(-0.595470\pi\)
−0.295453 + 0.955357i \(0.595470\pi\)
\(234\) −673.012 −0.188018
\(235\) 2648.92 0.735303
\(236\) −1327.43 −0.366137
\(237\) 2332.22 0.639215
\(238\) 0 0
\(239\) −5525.44 −1.49544 −0.747721 0.664013i \(-0.768852\pi\)
−0.747721 + 0.664013i \(0.768852\pi\)
\(240\) −2290.45 −0.616033
\(241\) 2005.92 0.536153 0.268076 0.963398i \(-0.413612\pi\)
0.268076 + 0.963398i \(0.413612\pi\)
\(242\) 934.367 0.248196
\(243\) −2713.65 −0.716383
\(244\) 3755.91 0.985442
\(245\) −5306.00 −1.38362
\(246\) −2951.57 −0.764981
\(247\) −162.037 −0.0417414
\(248\) 4340.21 1.11130
\(249\) −1111.74 −0.282946
\(250\) 1239.91 0.313675
\(251\) 4427.81 1.11347 0.556735 0.830690i \(-0.312054\pi\)
0.556735 + 0.830690i \(0.312054\pi\)
\(252\) −1773.69 −0.443381
\(253\) 5114.46 1.27092
\(254\) 537.979 0.132897
\(255\) 0 0
\(256\) −1840.73 −0.449397
\(257\) −6198.01 −1.50436 −0.752182 0.658956i \(-0.770998\pi\)
−0.752182 + 0.658956i \(0.770998\pi\)
\(258\) 3604.81 0.869867
\(259\) 4435.55 1.06414
\(260\) −4465.26 −1.06509
\(261\) 189.156 0.0448599
\(262\) 25.1109 0.00592122
\(263\) 477.072 0.111854 0.0559269 0.998435i \(-0.482189\pi\)
0.0559269 + 0.998435i \(0.482189\pi\)
\(264\) 5043.09 1.17569
\(265\) 1401.58 0.324900
\(266\) 106.068 0.0244491
\(267\) −3797.48 −0.870419
\(268\) −2575.84 −0.587106
\(269\) −7583.93 −1.71896 −0.859481 0.511168i \(-0.829213\pi\)
−0.859481 + 0.511168i \(0.829213\pi\)
\(270\) 1718.18 0.387278
\(271\) −5431.92 −1.21759 −0.608793 0.793329i \(-0.708346\pi\)
−0.608793 + 0.793329i \(0.708346\pi\)
\(272\) 0 0
\(273\) −8729.47 −1.93528
\(274\) −2302.33 −0.507624
\(275\) −2316.62 −0.507991
\(276\) 4389.24 0.957251
\(277\) −4091.98 −0.887594 −0.443797 0.896127i \(-0.646369\pi\)
−0.443797 + 0.896127i \(0.646369\pi\)
\(278\) −2275.81 −0.490985
\(279\) −2424.31 −0.520213
\(280\) 6571.86 1.40266
\(281\) −3410.26 −0.723983 −0.361991 0.932181i \(-0.617903\pi\)
−0.361991 + 0.932181i \(0.617903\pi\)
\(282\) −1535.92 −0.324336
\(283\) 4322.86 0.908011 0.454006 0.890999i \(-0.349995\pi\)
0.454006 + 0.890999i \(0.349995\pi\)
\(284\) −3085.97 −0.644785
\(285\) −249.328 −0.0518208
\(286\) 3016.87 0.623745
\(287\) −10462.6 −2.15186
\(288\) 1839.51 0.376369
\(289\) 0 0
\(290\) −311.716 −0.0631194
\(291\) 2252.51 0.453761
\(292\) −4647.82 −0.931484
\(293\) 3073.56 0.612831 0.306416 0.951898i \(-0.400870\pi\)
0.306416 + 0.951898i \(0.400870\pi\)
\(294\) 3076.57 0.610304
\(295\) −2747.26 −0.542208
\(296\) −2957.84 −0.580815
\(297\) 4673.70 0.913117
\(298\) 3459.95 0.672583
\(299\) 5903.62 1.14186
\(300\) −1988.13 −0.382616
\(301\) 12778.1 2.44690
\(302\) 2630.76 0.501269
\(303\) 4939.57 0.936538
\(304\) 87.3836 0.0164862
\(305\) 7773.26 1.45933
\(306\) 0 0
\(307\) −3954.45 −0.735154 −0.367577 0.929993i \(-0.619813\pi\)
−0.367577 + 0.929993i \(0.619813\pi\)
\(308\) 7950.82 1.47091
\(309\) 4709.79 0.867089
\(310\) 3995.11 0.731957
\(311\) −8984.40 −1.63813 −0.819065 0.573701i \(-0.805507\pi\)
−0.819065 + 0.573701i \(0.805507\pi\)
\(312\) 5821.24 1.05629
\(313\) −1737.01 −0.313680 −0.156840 0.987624i \(-0.550131\pi\)
−0.156840 + 0.987624i \(0.550131\pi\)
\(314\) −3410.83 −0.613008
\(315\) −3670.84 −0.656598
\(316\) −2451.95 −0.436497
\(317\) −8232.55 −1.45863 −0.729316 0.684177i \(-0.760162\pi\)
−0.729316 + 0.684177i \(0.760162\pi\)
\(318\) −812.678 −0.143310
\(319\) −847.916 −0.148822
\(320\) −25.2488 −0.00441078
\(321\) 6076.88 1.05663
\(322\) −3864.48 −0.668817
\(323\) 0 0
\(324\) 5767.81 0.988993
\(325\) −2674.08 −0.456403
\(326\) −3688.44 −0.626638
\(327\) −4272.83 −0.722594
\(328\) 6976.95 1.17451
\(329\) −5444.44 −0.912345
\(330\) 4642.10 0.774361
\(331\) −4153.12 −0.689655 −0.344828 0.938666i \(-0.612063\pi\)
−0.344828 + 0.938666i \(0.612063\pi\)
\(332\) 1168.81 0.193214
\(333\) 1652.16 0.271885
\(334\) −3052.26 −0.500037
\(335\) −5330.97 −0.869439
\(336\) 4707.66 0.764357
\(337\) −6569.49 −1.06191 −0.530954 0.847401i \(-0.678166\pi\)
−0.530954 + 0.847401i \(0.678166\pi\)
\(338\) 710.584 0.114351
\(339\) −8894.75 −1.42506
\(340\) 0 0
\(341\) 10867.3 1.72580
\(342\) 39.5085 0.00624671
\(343\) 1555.70 0.244898
\(344\) −8521.08 −1.33554
\(345\) 9084.00 1.41758
\(346\) −496.644 −0.0771669
\(347\) 2038.58 0.315380 0.157690 0.987489i \(-0.449595\pi\)
0.157690 + 0.987489i \(0.449595\pi\)
\(348\) −727.684 −0.112092
\(349\) −1791.21 −0.274731 −0.137365 0.990520i \(-0.543863\pi\)
−0.137365 + 0.990520i \(0.543863\pi\)
\(350\) 1750.44 0.267328
\(351\) 5394.86 0.820388
\(352\) −8245.86 −1.24860
\(353\) −5928.71 −0.893919 −0.446959 0.894554i \(-0.647493\pi\)
−0.446959 + 0.894554i \(0.647493\pi\)
\(354\) 1592.94 0.239163
\(355\) −6386.75 −0.954854
\(356\) 3992.43 0.594378
\(357\) 0 0
\(358\) 2420.55 0.357347
\(359\) 413.998 0.0608634 0.0304317 0.999537i \(-0.490312\pi\)
0.0304317 + 0.999537i \(0.490312\pi\)
\(360\) 2447.90 0.358377
\(361\) −6849.49 −0.998613
\(362\) −2115.78 −0.307190
\(363\) 4514.28 0.652722
\(364\) 9177.63 1.32154
\(365\) −9619.15 −1.37942
\(366\) −4507.16 −0.643697
\(367\) −6979.15 −0.992667 −0.496334 0.868132i \(-0.665321\pi\)
−0.496334 + 0.868132i \(0.665321\pi\)
\(368\) −3183.73 −0.450987
\(369\) −3897.11 −0.549798
\(370\) −2722.66 −0.382552
\(371\) −2880.73 −0.403127
\(372\) 9326.34 1.29986
\(373\) 6855.64 0.951667 0.475833 0.879535i \(-0.342147\pi\)
0.475833 + 0.879535i \(0.342147\pi\)
\(374\) 0 0
\(375\) 5990.46 0.824923
\(376\) 3630.62 0.497965
\(377\) −978.750 −0.133709
\(378\) −3531.45 −0.480524
\(379\) 8206.78 1.11228 0.556140 0.831089i \(-0.312282\pi\)
0.556140 + 0.831089i \(0.312282\pi\)
\(380\) 262.128 0.0353866
\(381\) 2599.18 0.349501
\(382\) 2961.27 0.396627
\(383\) −889.401 −0.118659 −0.0593293 0.998238i \(-0.518896\pi\)
−0.0593293 + 0.998238i \(0.518896\pi\)
\(384\) −8819.67 −1.17208
\(385\) 16455.1 2.17825
\(386\) 821.294 0.108297
\(387\) 4759.62 0.625180
\(388\) −2368.15 −0.309857
\(389\) −12992.8 −1.69347 −0.846736 0.532013i \(-0.821436\pi\)
−0.846736 + 0.532013i \(0.821436\pi\)
\(390\) 5358.38 0.695723
\(391\) 0 0
\(392\) −7272.43 −0.937023
\(393\) 121.320 0.0155720
\(394\) −3382.42 −0.432498
\(395\) −5074.57 −0.646403
\(396\) 2961.54 0.375815
\(397\) −4325.29 −0.546801 −0.273400 0.961900i \(-0.588148\pi\)
−0.273400 + 0.961900i \(0.588148\pi\)
\(398\) −2251.67 −0.283583
\(399\) 512.455 0.0642979
\(400\) 1442.09 0.180261
\(401\) 11849.1 1.47560 0.737798 0.675022i \(-0.235866\pi\)
0.737798 + 0.675022i \(0.235866\pi\)
\(402\) 3091.05 0.383501
\(403\) 12544.1 1.55054
\(404\) −5193.17 −0.639529
\(405\) 11937.1 1.46459
\(406\) 640.685 0.0783168
\(407\) −7406.04 −0.901975
\(408\) 0 0
\(409\) 7677.24 0.928154 0.464077 0.885795i \(-0.346386\pi\)
0.464077 + 0.885795i \(0.346386\pi\)
\(410\) 6422.19 0.773584
\(411\) −11123.4 −1.33498
\(412\) −4951.59 −0.592105
\(413\) 5646.55 0.672757
\(414\) −1439.45 −0.170882
\(415\) 2418.98 0.286128
\(416\) −9518.20 −1.12180
\(417\) −10995.3 −1.29122
\(418\) −177.102 −0.0207233
\(419\) 3235.83 0.377280 0.188640 0.982046i \(-0.439592\pi\)
0.188640 + 0.982046i \(0.439592\pi\)
\(420\) 14121.8 1.64065
\(421\) 14496.6 1.67820 0.839100 0.543977i \(-0.183082\pi\)
0.839100 + 0.543977i \(0.183082\pi\)
\(422\) 86.5033 0.00997848
\(423\) −2027.95 −0.233103
\(424\) 1921.02 0.220030
\(425\) 0 0
\(426\) 3703.22 0.421178
\(427\) −15976.7 −1.81070
\(428\) −6388.86 −0.721536
\(429\) 14575.6 1.64037
\(430\) −7843.54 −0.879649
\(431\) −7136.25 −0.797543 −0.398771 0.917050i \(-0.630563\pi\)
−0.398771 + 0.917050i \(0.630563\pi\)
\(432\) −2909.36 −0.324020
\(433\) 11434.3 1.26904 0.634521 0.772905i \(-0.281197\pi\)
0.634521 + 0.772905i \(0.281197\pi\)
\(434\) −8211.32 −0.908193
\(435\) −1506.02 −0.165996
\(436\) 4492.20 0.493434
\(437\) −346.566 −0.0379371
\(438\) 5577.46 0.608451
\(439\) 13308.0 1.44682 0.723412 0.690417i \(-0.242573\pi\)
0.723412 + 0.690417i \(0.242573\pi\)
\(440\) −10973.0 −1.18891
\(441\) 4062.16 0.438630
\(442\) 0 0
\(443\) −10897.9 −1.16880 −0.584398 0.811467i \(-0.698669\pi\)
−0.584398 + 0.811467i \(0.698669\pi\)
\(444\) −6355.88 −0.679362
\(445\) 8262.76 0.880208
\(446\) 5972.80 0.634126
\(447\) 16716.3 1.76880
\(448\) 51.8949 0.00547278
\(449\) 16756.4 1.76121 0.880603 0.473855i \(-0.157138\pi\)
0.880603 + 0.473855i \(0.157138\pi\)
\(450\) 652.006 0.0683019
\(451\) 17469.3 1.82394
\(452\) 9351.40 0.973126
\(453\) 12710.2 1.31827
\(454\) 2173.60 0.224696
\(455\) 18994.1 1.95705
\(456\) −341.730 −0.0350943
\(457\) 13561.8 1.38817 0.694087 0.719891i \(-0.255808\pi\)
0.694087 + 0.719891i \(0.255808\pi\)
\(458\) −395.361 −0.0403363
\(459\) 0 0
\(460\) −9550.36 −0.968017
\(461\) 15516.4 1.56762 0.783810 0.621000i \(-0.213273\pi\)
0.783810 + 0.621000i \(0.213273\pi\)
\(462\) −9541.11 −0.960807
\(463\) −15186.4 −1.52435 −0.762174 0.647372i \(-0.775868\pi\)
−0.762174 + 0.647372i \(0.775868\pi\)
\(464\) 527.824 0.0528095
\(465\) 19301.8 1.92495
\(466\) −2651.44 −0.263574
\(467\) 10544.3 1.04482 0.522412 0.852693i \(-0.325032\pi\)
0.522412 + 0.852693i \(0.325032\pi\)
\(468\) 3418.50 0.337650
\(469\) 10957.0 1.07878
\(470\) 3341.94 0.327983
\(471\) −16479.0 −1.61213
\(472\) −3765.40 −0.367196
\(473\) −21335.6 −2.07402
\(474\) 2942.38 0.285123
\(475\) 156.979 0.0151636
\(476\) 0 0
\(477\) −1073.02 −0.102998
\(478\) −6971.02 −0.667044
\(479\) 5762.22 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(480\) −14645.8 −1.39268
\(481\) −8548.79 −0.810377
\(482\) 2530.72 0.239152
\(483\) −18670.7 −1.75890
\(484\) −4746.03 −0.445721
\(485\) −4901.14 −0.458864
\(486\) −3423.61 −0.319544
\(487\) −5369.36 −0.499608 −0.249804 0.968296i \(-0.580366\pi\)
−0.249804 + 0.968296i \(0.580366\pi\)
\(488\) 10654.1 0.988293
\(489\) −17820.2 −1.64797
\(490\) −6694.18 −0.617167
\(491\) 17878.0 1.64322 0.821611 0.570049i \(-0.193076\pi\)
0.821611 + 0.570049i \(0.193076\pi\)
\(492\) 14992.2 1.37378
\(493\) 0 0
\(494\) −204.429 −0.0186188
\(495\) 6129.21 0.556540
\(496\) −6764.84 −0.612400
\(497\) 13127.0 1.18476
\(498\) −1402.60 −0.126209
\(499\) 3507.03 0.314622 0.157311 0.987549i \(-0.449718\pi\)
0.157311 + 0.987549i \(0.449718\pi\)
\(500\) −6298.01 −0.563311
\(501\) −14746.6 −1.31503
\(502\) 5586.23 0.496665
\(503\) −1207.56 −0.107043 −0.0535214 0.998567i \(-0.517045\pi\)
−0.0535214 + 0.998567i \(0.517045\pi\)
\(504\) −5031.27 −0.444664
\(505\) −10747.8 −0.947071
\(506\) 6452.52 0.566897
\(507\) 3433.09 0.300728
\(508\) −2732.62 −0.238662
\(509\) −14092.1 −1.22716 −0.613578 0.789634i \(-0.710270\pi\)
−0.613578 + 0.789634i \(0.710270\pi\)
\(510\) 0 0
\(511\) 19770.7 1.71155
\(512\) 9253.25 0.798710
\(513\) −316.700 −0.0272566
\(514\) −7819.56 −0.671023
\(515\) −10247.8 −0.876841
\(516\) −18310.3 −1.56214
\(517\) 9090.58 0.773314
\(518\) 5595.99 0.474660
\(519\) −2399.47 −0.202939
\(520\) −12666.2 −1.06817
\(521\) −10080.1 −0.847635 −0.423818 0.905748i \(-0.639310\pi\)
−0.423818 + 0.905748i \(0.639310\pi\)
\(522\) 238.643 0.0200098
\(523\) 12330.2 1.03090 0.515452 0.856919i \(-0.327624\pi\)
0.515452 + 0.856919i \(0.327624\pi\)
\(524\) −127.549 −0.0106336
\(525\) 8457.01 0.703036
\(526\) 601.886 0.0498925
\(527\) 0 0
\(528\) −7860.38 −0.647877
\(529\) 459.760 0.0377875
\(530\) 1768.27 0.144922
\(531\) 2103.24 0.171888
\(532\) −538.764 −0.0439067
\(533\) 20164.9 1.63872
\(534\) −4790.99 −0.388252
\(535\) −13222.4 −1.06851
\(536\) −7306.65 −0.588805
\(537\) 11694.6 0.939774
\(538\) −9568.07 −0.766745
\(539\) −18209.2 −1.45515
\(540\) −8727.33 −0.695490
\(541\) 7122.72 0.566044 0.283022 0.959113i \(-0.408663\pi\)
0.283022 + 0.959113i \(0.408663\pi\)
\(542\) −6853.04 −0.543106
\(543\) −10222.1 −0.807869
\(544\) 0 0
\(545\) 9297.07 0.730720
\(546\) −11013.3 −0.863235
\(547\) 14919.7 1.16622 0.583109 0.812394i \(-0.301836\pi\)
0.583109 + 0.812394i \(0.301836\pi\)
\(548\) 11694.5 0.911612
\(549\) −5951.04 −0.462630
\(550\) −2922.70 −0.226590
\(551\) 57.4566 0.00444234
\(552\) 12450.6 0.960021
\(553\) 10430.0 0.802040
\(554\) −5162.55 −0.395913
\(555\) −13154.2 −1.00606
\(556\) 11559.7 0.881731
\(557\) −18935.0 −1.44039 −0.720197 0.693769i \(-0.755949\pi\)
−0.720197 + 0.693769i \(0.755949\pi\)
\(558\) −3058.57 −0.232042
\(559\) −24627.7 −1.86340
\(560\) −10243.2 −0.772953
\(561\) 0 0
\(562\) −4302.47 −0.322934
\(563\) 8150.42 0.610123 0.305062 0.952333i \(-0.401323\pi\)
0.305062 + 0.952333i \(0.401323\pi\)
\(564\) 7801.56 0.582456
\(565\) 19353.7 1.44109
\(566\) 5453.82 0.405020
\(567\) −24534.8 −1.81722
\(568\) −8753.71 −0.646650
\(569\) 18218.2 1.34226 0.671131 0.741338i \(-0.265809\pi\)
0.671131 + 0.741338i \(0.265809\pi\)
\(570\) −314.558 −0.0231147
\(571\) 2443.35 0.179073 0.0895367 0.995984i \(-0.471461\pi\)
0.0895367 + 0.995984i \(0.471461\pi\)
\(572\) −15323.9 −1.12015
\(573\) 14307.0 1.04308
\(574\) −13199.8 −0.959842
\(575\) −5719.36 −0.414806
\(576\) 19.3299 0.00139829
\(577\) −852.752 −0.0615261 −0.0307630 0.999527i \(-0.509794\pi\)
−0.0307630 + 0.999527i \(0.509794\pi\)
\(578\) 0 0
\(579\) 3967.98 0.284807
\(580\) 1583.34 0.113352
\(581\) −4971.84 −0.355020
\(582\) 2841.82 0.202401
\(583\) 4809.96 0.341695
\(584\) −13184.1 −0.934179
\(585\) 7074.95 0.500022
\(586\) 3877.68 0.273354
\(587\) 900.272 0.0633019 0.0316509 0.999499i \(-0.489924\pi\)
0.0316509 + 0.999499i \(0.489924\pi\)
\(588\) −15627.2 −1.09601
\(589\) −736.390 −0.0515152
\(590\) −3466.00 −0.241853
\(591\) −16341.7 −1.13741
\(592\) 4610.22 0.320066
\(593\) −25007.2 −1.73174 −0.865870 0.500268i \(-0.833235\pi\)
−0.865870 + 0.500268i \(0.833235\pi\)
\(594\) 5896.46 0.407297
\(595\) 0 0
\(596\) −17574.5 −1.20785
\(597\) −10878.6 −0.745784
\(598\) 7448.15 0.509327
\(599\) −3448.82 −0.235251 −0.117625 0.993058i \(-0.537528\pi\)
−0.117625 + 0.993058i \(0.537528\pi\)
\(600\) −5639.55 −0.383723
\(601\) 942.873 0.0639943 0.0319972 0.999488i \(-0.489813\pi\)
0.0319972 + 0.999488i \(0.489813\pi\)
\(602\) 16121.2 1.09145
\(603\) 4081.27 0.275626
\(604\) −13362.7 −0.900201
\(605\) −9822.41 −0.660063
\(606\) 6231.89 0.417744
\(607\) −10173.9 −0.680306 −0.340153 0.940370i \(-0.610479\pi\)
−0.340153 + 0.940370i \(0.610479\pi\)
\(608\) 558.756 0.0372707
\(609\) 3095.39 0.205963
\(610\) 9806.93 0.650936
\(611\) 10493.3 0.694782
\(612\) 0 0
\(613\) −17327.0 −1.14165 −0.570824 0.821073i \(-0.693376\pi\)
−0.570824 + 0.821073i \(0.693376\pi\)
\(614\) −4989.03 −0.327916
\(615\) 31028.0 2.03442
\(616\) 22553.4 1.47516
\(617\) −19782.8 −1.29080 −0.645401 0.763844i \(-0.723310\pi\)
−0.645401 + 0.763844i \(0.723310\pi\)
\(618\) 5941.98 0.386766
\(619\) −15033.2 −0.976147 −0.488074 0.872802i \(-0.662300\pi\)
−0.488074 + 0.872802i \(0.662300\pi\)
\(620\) −20292.8 −1.31448
\(621\) 11538.6 0.745618
\(622\) −11334.9 −0.730690
\(623\) −16982.8 −1.09214
\(624\) −9073.25 −0.582084
\(625\) −19396.6 −1.24139
\(626\) −2191.46 −0.139917
\(627\) −855.647 −0.0544996
\(628\) 17325.0 1.10087
\(629\) 0 0
\(630\) −4631.22 −0.292877
\(631\) −24060.5 −1.51796 −0.758979 0.651115i \(-0.774302\pi\)
−0.758979 + 0.651115i \(0.774302\pi\)
\(632\) −6955.23 −0.437760
\(633\) 417.930 0.0262421
\(634\) −10386.4 −0.650625
\(635\) −5655.44 −0.353432
\(636\) 4127.92 0.257363
\(637\) −21018.9 −1.30737
\(638\) −1069.75 −0.0663822
\(639\) 4889.55 0.302704
\(640\) 19190.3 1.18526
\(641\) 4886.07 0.301074 0.150537 0.988604i \(-0.451900\pi\)
0.150537 + 0.988604i \(0.451900\pi\)
\(642\) 7666.74 0.471312
\(643\) 24508.4 1.50314 0.751568 0.659655i \(-0.229298\pi\)
0.751568 + 0.659655i \(0.229298\pi\)
\(644\) 19629.3 1.20109
\(645\) −37895.1 −2.31336
\(646\) 0 0
\(647\) 2932.50 0.178189 0.0890947 0.996023i \(-0.471603\pi\)
0.0890947 + 0.996023i \(0.471603\pi\)
\(648\) 16361.0 0.991854
\(649\) −9428.06 −0.570237
\(650\) −3373.68 −0.203579
\(651\) −39671.9 −2.38843
\(652\) 18735.1 1.12534
\(653\) −19977.8 −1.19723 −0.598617 0.801035i \(-0.704283\pi\)
−0.598617 + 0.801035i \(0.704283\pi\)
\(654\) −5390.71 −0.322314
\(655\) −263.975 −0.0157471
\(656\) −10874.6 −0.647227
\(657\) 7364.21 0.437299
\(658\) −6868.83 −0.406953
\(659\) 28222.7 1.66829 0.834143 0.551548i \(-0.185963\pi\)
0.834143 + 0.551548i \(0.185963\pi\)
\(660\) −23579.1 −1.39063
\(661\) 20712.8 1.21881 0.609405 0.792859i \(-0.291408\pi\)
0.609405 + 0.792859i \(0.291408\pi\)
\(662\) −5239.67 −0.307622
\(663\) 0 0
\(664\) 3315.47 0.193773
\(665\) −1115.03 −0.0650210
\(666\) 2084.41 0.121275
\(667\) −2093.37 −0.121522
\(668\) 15503.7 0.897987
\(669\) 28856.8 1.66767
\(670\) −6725.68 −0.387814
\(671\) 26676.3 1.53477
\(672\) 30102.2 1.72800
\(673\) −395.468 −0.0226511 −0.0113255 0.999936i \(-0.503605\pi\)
−0.0113255 + 0.999936i \(0.503605\pi\)
\(674\) −8288.23 −0.473666
\(675\) −5226.48 −0.298025
\(676\) −3609.34 −0.205356
\(677\) 2297.47 0.130427 0.0652135 0.997871i \(-0.479227\pi\)
0.0652135 + 0.997871i \(0.479227\pi\)
\(678\) −11221.8 −0.635652
\(679\) 10073.5 0.569347
\(680\) 0 0
\(681\) 10501.5 0.590921
\(682\) 13710.4 0.769794
\(683\) 28611.7 1.60292 0.801461 0.598048i \(-0.204057\pi\)
0.801461 + 0.598048i \(0.204057\pi\)
\(684\) −200.680 −0.0112181
\(685\) 24202.9 1.35000
\(686\) 1962.71 0.109237
\(687\) −1910.14 −0.106079
\(688\) 13281.3 0.735968
\(689\) 5552.14 0.306995
\(690\) 11460.6 0.632315
\(691\) −4902.87 −0.269919 −0.134959 0.990851i \(-0.543090\pi\)
−0.134959 + 0.990851i \(0.543090\pi\)
\(692\) 2522.66 0.138580
\(693\) −12597.6 −0.690540
\(694\) 2571.93 0.140676
\(695\) 23924.1 1.30575
\(696\) −2064.16 −0.112416
\(697\) 0 0
\(698\) −2259.83 −0.122544
\(699\) −12810.1 −0.693165
\(700\) −8891.18 −0.480079
\(701\) 1714.99 0.0924027 0.0462014 0.998932i \(-0.485288\pi\)
0.0462014 + 0.998932i \(0.485288\pi\)
\(702\) 6806.28 0.365935
\(703\) 501.849 0.0269240
\(704\) −86.6490 −0.00463879
\(705\) 16146.1 0.862552
\(706\) −7479.80 −0.398734
\(707\) 22090.4 1.17510
\(708\) −8091.18 −0.429499
\(709\) 13939.8 0.738393 0.369196 0.929351i \(-0.379633\pi\)
0.369196 + 0.929351i \(0.379633\pi\)
\(710\) −8057.67 −0.425914
\(711\) 3884.98 0.204920
\(712\) 11325.0 0.596098
\(713\) 26829.6 1.40922
\(714\) 0 0
\(715\) −31714.4 −1.65881
\(716\) −12295.0 −0.641738
\(717\) −33679.6 −1.75424
\(718\) 522.310 0.0271482
\(719\) 1779.18 0.0922839 0.0461419 0.998935i \(-0.485307\pi\)
0.0461419 + 0.998935i \(0.485307\pi\)
\(720\) −3815.40 −0.197488
\(721\) 21062.8 1.08796
\(722\) −8641.48 −0.445433
\(723\) 12226.9 0.628937
\(724\) 10746.9 0.551665
\(725\) 948.201 0.0485729
\(726\) 5695.32 0.291148
\(727\) 9141.02 0.466330 0.233165 0.972437i \(-0.425092\pi\)
0.233165 + 0.972437i \(0.425092\pi\)
\(728\) 26033.4 1.32536
\(729\) 7760.65 0.394282
\(730\) −12135.8 −0.615294
\(731\) 0 0
\(732\) 22893.7 1.15598
\(733\) 12176.0 0.613547 0.306773 0.951783i \(-0.400751\pi\)
0.306773 + 0.951783i \(0.400751\pi\)
\(734\) −8805.07 −0.442781
\(735\) −32342.1 −1.62307
\(736\) −20357.7 −1.01956
\(737\) −18294.9 −0.914383
\(738\) −4916.69 −0.245238
\(739\) 25025.4 1.24570 0.622852 0.782339i \(-0.285974\pi\)
0.622852 + 0.782339i \(0.285974\pi\)
\(740\) 13829.5 0.687003
\(741\) −987.673 −0.0489650
\(742\) −3634.40 −0.179816
\(743\) 10781.3 0.532339 0.266170 0.963926i \(-0.414242\pi\)
0.266170 + 0.963926i \(0.414242\pi\)
\(744\) 26455.2 1.30362
\(745\) −36372.3 −1.78869
\(746\) 8649.24 0.424492
\(747\) −1851.92 −0.0907072
\(748\) 0 0
\(749\) 27176.6 1.32578
\(750\) 7557.71 0.367958
\(751\) −33910.7 −1.64769 −0.823847 0.566812i \(-0.808177\pi\)
−0.823847 + 0.566812i \(0.808177\pi\)
\(752\) −5658.84 −0.274410
\(753\) 26989.2 1.30616
\(754\) −1234.81 −0.0596410
\(755\) −27655.5 −1.33310
\(756\) 17937.7 0.862945
\(757\) −31545.0 −1.51456 −0.757281 0.653090i \(-0.773472\pi\)
−0.757281 + 0.653090i \(0.773472\pi\)
\(758\) 10353.9 0.496134
\(759\) 31174.5 1.49086
\(760\) 743.556 0.0354890
\(761\) 9150.51 0.435881 0.217941 0.975962i \(-0.430066\pi\)
0.217941 + 0.975962i \(0.430066\pi\)
\(762\) 3279.19 0.155895
\(763\) −19108.7 −0.906658
\(764\) −15041.5 −0.712280
\(765\) 0 0
\(766\) −1122.09 −0.0529279
\(767\) −10882.8 −0.512328
\(768\) −11219.9 −0.527168
\(769\) 33797.5 1.58488 0.792438 0.609952i \(-0.208811\pi\)
0.792438 + 0.609952i \(0.208811\pi\)
\(770\) 20760.1 0.971612
\(771\) −37779.2 −1.76470
\(772\) −4171.69 −0.194485
\(773\) −33969.4 −1.58059 −0.790295 0.612727i \(-0.790073\pi\)
−0.790295 + 0.612727i \(0.790073\pi\)
\(774\) 6004.85 0.278863
\(775\) −12152.6 −0.563270
\(776\) −6717.52 −0.310754
\(777\) 27036.3 1.24829
\(778\) −16392.0 −0.755376
\(779\) −1183.76 −0.0544449
\(780\) −27217.4 −1.24941
\(781\) −21918.1 −1.00421
\(782\) 0 0
\(783\) −1912.96 −0.0873100
\(784\) 11335.1 0.516359
\(785\) 35856.0 1.63026
\(786\) 153.061 0.00694592
\(787\) 10962.7 0.496543 0.248271 0.968691i \(-0.420138\pi\)
0.248271 + 0.968691i \(0.420138\pi\)
\(788\) 17180.7 0.776698
\(789\) 2907.93 0.131211
\(790\) −6402.20 −0.288329
\(791\) −39778.5 −1.78807
\(792\) 8400.72 0.376902
\(793\) 30792.5 1.37891
\(794\) −5456.89 −0.243901
\(795\) 8543.17 0.381126
\(796\) 11437.1 0.509270
\(797\) −8041.29 −0.357386 −0.178693 0.983905i \(-0.557187\pi\)
−0.178693 + 0.983905i \(0.557187\pi\)
\(798\) 646.526 0.0286802
\(799\) 0 0
\(800\) 9221.12 0.407520
\(801\) −6325.79 −0.279040
\(802\) 14949.1 0.658192
\(803\) −33011.1 −1.45073
\(804\) −15700.7 −0.688708
\(805\) 40624.8 1.77868
\(806\) 15826.0 0.691620
\(807\) −46226.9 −2.01644
\(808\) −14731.0 −0.641379
\(809\) −36568.0 −1.58920 −0.794599 0.607134i \(-0.792319\pi\)
−0.794599 + 0.607134i \(0.792319\pi\)
\(810\) 15060.1 0.653282
\(811\) −37315.7 −1.61570 −0.807849 0.589390i \(-0.799368\pi\)
−0.807849 + 0.589390i \(0.799368\pi\)
\(812\) −3254.30 −0.140645
\(813\) −33109.6 −1.42830
\(814\) −9343.64 −0.402327
\(815\) 38774.3 1.66651
\(816\) 0 0
\(817\) 1445.75 0.0619097
\(818\) 9685.79 0.414005
\(819\) −14541.4 −0.620414
\(820\) −32620.9 −1.38924
\(821\) 27365.1 1.16328 0.581638 0.813448i \(-0.302412\pi\)
0.581638 + 0.813448i \(0.302412\pi\)
\(822\) −14033.6 −0.595471
\(823\) 21138.4 0.895308 0.447654 0.894207i \(-0.352260\pi\)
0.447654 + 0.894207i \(0.352260\pi\)
\(824\) −14045.7 −0.593818
\(825\) −14120.7 −0.595902
\(826\) 7123.83 0.300084
\(827\) 43453.3 1.82711 0.913554 0.406717i \(-0.133327\pi\)
0.913554 + 0.406717i \(0.133327\pi\)
\(828\) 7311.55 0.306877
\(829\) 36460.2 1.52752 0.763760 0.645501i \(-0.223351\pi\)
0.763760 + 0.645501i \(0.223351\pi\)
\(830\) 3051.85 0.127628
\(831\) −24942.2 −1.04120
\(832\) −100.019 −0.00416771
\(833\) 0 0
\(834\) −13871.9 −0.575952
\(835\) 32086.5 1.32982
\(836\) 899.575 0.0372158
\(837\) 24517.4 1.01248
\(838\) 4082.39 0.168286
\(839\) −20236.0 −0.832687 −0.416344 0.909207i \(-0.636689\pi\)
−0.416344 + 0.909207i \(0.636689\pi\)
\(840\) 40058.0 1.64539
\(841\) −24041.9 −0.985770
\(842\) 18289.3 0.748564
\(843\) −20786.8 −0.849272
\(844\) −439.386 −0.0179198
\(845\) −7469.92 −0.304110
\(846\) −2558.51 −0.103976
\(847\) 20188.4 0.818988
\(848\) −2994.18 −0.121251
\(849\) 26349.4 1.06515
\(850\) 0 0
\(851\) −18284.3 −0.736519
\(852\) −18810.2 −0.756368
\(853\) 6934.19 0.278338 0.139169 0.990269i \(-0.455557\pi\)
0.139169 + 0.990269i \(0.455557\pi\)
\(854\) −20156.6 −0.807664
\(855\) −415.328 −0.0166128
\(856\) −18122.7 −0.723623
\(857\) 19207.8 0.765607 0.382803 0.923830i \(-0.374959\pi\)
0.382803 + 0.923830i \(0.374959\pi\)
\(858\) 18388.9 0.731688
\(859\) −9954.55 −0.395395 −0.197698 0.980263i \(-0.563346\pi\)
−0.197698 + 0.980263i \(0.563346\pi\)
\(860\) 39840.6 1.57971
\(861\) −63773.2 −2.52426
\(862\) −9003.26 −0.355745
\(863\) −33698.0 −1.32919 −0.664596 0.747203i \(-0.731396\pi\)
−0.664596 + 0.747203i \(0.731396\pi\)
\(864\) −18603.3 −0.732519
\(865\) 5220.91 0.205221
\(866\) 14425.7 0.566058
\(867\) 0 0
\(868\) 41708.6 1.63097
\(869\) −17415.0 −0.679818
\(870\) −1900.03 −0.0740425
\(871\) −21117.8 −0.821525
\(872\) 12742.6 0.494861
\(873\) 3752.20 0.145467
\(874\) −437.236 −0.0169219
\(875\) 26790.1 1.03505
\(876\) −28330.2 −1.09268
\(877\) 4469.65 0.172097 0.0860487 0.996291i \(-0.472576\pi\)
0.0860487 + 0.996291i \(0.472576\pi\)
\(878\) 16789.7 0.645358
\(879\) 18734.5 0.718885
\(880\) 17103.1 0.655164
\(881\) 2081.32 0.0795930 0.0397965 0.999208i \(-0.487329\pi\)
0.0397965 + 0.999208i \(0.487329\pi\)
\(882\) 5124.91 0.195652
\(883\) 10124.4 0.385857 0.192929 0.981213i \(-0.438201\pi\)
0.192929 + 0.981213i \(0.438201\pi\)
\(884\) 0 0
\(885\) −16745.6 −0.636040
\(886\) −13749.1 −0.521343
\(887\) −42725.3 −1.61733 −0.808666 0.588268i \(-0.799810\pi\)
−0.808666 + 0.588268i \(0.799810\pi\)
\(888\) −18029.2 −0.681328
\(889\) 11623.9 0.438529
\(890\) 10424.5 0.392618
\(891\) 40965.8 1.54030
\(892\) −30338.3 −1.13879
\(893\) −615.996 −0.0230835
\(894\) 21089.7 0.788977
\(895\) −25445.7 −0.950343
\(896\) −39442.7 −1.47063
\(897\) 35984.8 1.33946
\(898\) 21140.2 0.785588
\(899\) −4448.02 −0.165017
\(900\) −3311.80 −0.122659
\(901\) 0 0
\(902\) 22039.7 0.813573
\(903\) 77887.4 2.87036
\(904\) 26526.3 0.975941
\(905\) 22241.8 0.816954
\(906\) 16035.5 0.588017
\(907\) −21767.6 −0.796893 −0.398446 0.917192i \(-0.630450\pi\)
−0.398446 + 0.917192i \(0.630450\pi\)
\(908\) −11040.6 −0.403519
\(909\) 8228.28 0.300236
\(910\) 23963.4 0.872943
\(911\) −21654.2 −0.787524 −0.393762 0.919212i \(-0.628827\pi\)
−0.393762 + 0.919212i \(0.628827\pi\)
\(912\) 532.636 0.0193392
\(913\) 8301.49 0.300919
\(914\) 17109.9 0.619197
\(915\) 47380.9 1.71187
\(916\) 2008.20 0.0724376
\(917\) 542.560 0.0195386
\(918\) 0 0
\(919\) 21445.1 0.769760 0.384880 0.922967i \(-0.374243\pi\)
0.384880 + 0.922967i \(0.374243\pi\)
\(920\) −27090.6 −0.970818
\(921\) −24103.8 −0.862376
\(922\) 19575.9 0.699239
\(923\) −25300.1 −0.902234
\(924\) 48463.2 1.72546
\(925\) 8281.97 0.294389
\(926\) −19159.6 −0.679938
\(927\) 7845.51 0.277972
\(928\) 3375.06 0.119388
\(929\) 24271.4 0.857177 0.428589 0.903500i \(-0.359011\pi\)
0.428589 + 0.903500i \(0.359011\pi\)
\(930\) 24351.7 0.858626
\(931\) 1233.89 0.0434363
\(932\) 13467.7 0.473338
\(933\) −54763.3 −1.92162
\(934\) 13303.0 0.466046
\(935\) 0 0
\(936\) 9696.96 0.338627
\(937\) 38491.5 1.34201 0.671005 0.741453i \(-0.265863\pi\)
0.671005 + 0.741453i \(0.265863\pi\)
\(938\) 13823.6 0.481190
\(939\) −10587.7 −0.367964
\(940\) −16975.1 −0.589006
\(941\) 31323.4 1.08514 0.542568 0.840012i \(-0.317452\pi\)
0.542568 + 0.840012i \(0.317452\pi\)
\(942\) −20790.3 −0.719092
\(943\) 43128.9 1.48937
\(944\) 5868.92 0.202349
\(945\) 37123.9 1.27793
\(946\) −26917.5 −0.925121
\(947\) 32096.4 1.10136 0.550682 0.834715i \(-0.314368\pi\)
0.550682 + 0.834715i \(0.314368\pi\)
\(948\) −14945.6 −0.512035
\(949\) −38104.7 −1.30341
\(950\) 198.049 0.00676373
\(951\) −50180.5 −1.71106
\(952\) 0 0
\(953\) 10493.3 0.356675 0.178338 0.983969i \(-0.442928\pi\)
0.178338 + 0.983969i \(0.442928\pi\)
\(954\) −1353.75 −0.0459426
\(955\) −31129.9 −1.05481
\(956\) 35408.7 1.19791
\(957\) −5168.37 −0.174576
\(958\) 7269.75 0.245172
\(959\) −49745.4 −1.67504
\(960\) −153.901 −0.00517409
\(961\) 27217.0 0.913597
\(962\) −10785.4 −0.361470
\(963\) 10122.8 0.338736
\(964\) −12854.6 −0.429479
\(965\) −8633.74 −0.288010
\(966\) −23555.4 −0.784559
\(967\) 31468.2 1.04648 0.523242 0.852184i \(-0.324722\pi\)
0.523242 + 0.852184i \(0.324722\pi\)
\(968\) −13462.6 −0.447010
\(969\) 0 0
\(970\) −6183.39 −0.204677
\(971\) −46923.8 −1.55083 −0.775415 0.631452i \(-0.782459\pi\)
−0.775415 + 0.631452i \(0.782459\pi\)
\(972\) 17389.9 0.573850
\(973\) −49172.3 −1.62013
\(974\) −6774.11 −0.222851
\(975\) −16299.5 −0.535387
\(976\) −16605.9 −0.544612
\(977\) 8666.25 0.283785 0.141893 0.989882i \(-0.454681\pi\)
0.141893 + 0.989882i \(0.454681\pi\)
\(978\) −22482.4 −0.735081
\(979\) 28356.2 0.925709
\(980\) 34002.5 1.10834
\(981\) −7117.63 −0.231650
\(982\) 22555.3 0.732961
\(983\) −35155.3 −1.14067 −0.570336 0.821412i \(-0.693187\pi\)
−0.570336 + 0.821412i \(0.693187\pi\)
\(984\) 42527.1 1.37776
\(985\) 35557.3 1.15020
\(986\) 0 0
\(987\) −33185.9 −1.07023
\(988\) 1038.38 0.0334365
\(989\) −52674.2 −1.69357
\(990\) 7732.75 0.248246
\(991\) 11236.2 0.360170 0.180085 0.983651i \(-0.442363\pi\)
0.180085 + 0.983651i \(0.442363\pi\)
\(992\) −43256.3 −1.38447
\(993\) −25314.8 −0.809004
\(994\) 16561.3 0.528463
\(995\) 23670.4 0.754172
\(996\) 7124.36 0.226651
\(997\) −18825.0 −0.597987 −0.298994 0.954255i \(-0.596651\pi\)
−0.298994 + 0.954255i \(0.596651\pi\)
\(998\) 4424.56 0.140338
\(999\) −16708.6 −0.529166
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 289.4.a.h.1.8 12
17.4 even 4 289.4.b.f.288.10 24
17.13 even 4 289.4.b.f.288.9 24
17.16 even 2 289.4.a.i.1.8 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.8 12 1.1 even 1 trivial
289.4.a.i.1.8 yes 12 17.16 even 2
289.4.b.f.288.9 24 17.13 even 4
289.4.b.f.288.10 24 17.4 even 4