Properties

Label 289.4.a.h.1.5
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 1.5
Root \(1.07125\) 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)
 
\(f(q)\) \(=\) \(q-1.07125 q^{2} +5.02012 q^{3} -6.85243 q^{4} -4.32398 q^{5} -5.37778 q^{6} -4.44673 q^{7} +15.9106 q^{8} -1.79838 q^{9} +O(q^{10})\) \(q-1.07125 q^{2} +5.02012 q^{3} -6.85243 q^{4} -4.32398 q^{5} -5.37778 q^{6} -4.44673 q^{7} +15.9106 q^{8} -1.79838 q^{9} +4.63204 q^{10} +68.9570 q^{11} -34.4000 q^{12} -27.1960 q^{13} +4.76354 q^{14} -21.7069 q^{15} +37.7753 q^{16} +1.92651 q^{18} -123.839 q^{19} +29.6298 q^{20} -22.3231 q^{21} -73.8698 q^{22} -98.6310 q^{23} +79.8731 q^{24} -106.303 q^{25} +29.1336 q^{26} -144.571 q^{27} +30.4709 q^{28} -21.9952 q^{29} +23.2534 q^{30} -241.893 q^{31} -167.751 q^{32} +346.172 q^{33} +19.2276 q^{35} +12.3233 q^{36} -324.851 q^{37} +132.662 q^{38} -136.527 q^{39} -68.7971 q^{40} +164.148 q^{41} +23.9135 q^{42} +383.332 q^{43} -472.523 q^{44} +7.77618 q^{45} +105.658 q^{46} +411.060 q^{47} +189.637 q^{48} -323.227 q^{49} +113.877 q^{50} +186.359 q^{52} -380.053 q^{53} +154.871 q^{54} -298.169 q^{55} -70.7501 q^{56} -621.685 q^{57} +23.5623 q^{58} +63.3150 q^{59} +148.745 q^{60} +37.1265 q^{61} +259.127 q^{62} +7.99693 q^{63} -122.499 q^{64} +117.595 q^{65} -370.836 q^{66} -48.2971 q^{67} -495.139 q^{69} -20.5974 q^{70} -672.362 q^{71} -28.6134 q^{72} -562.892 q^{73} +347.996 q^{74} -533.655 q^{75} +848.596 q^{76} -306.633 q^{77} +146.254 q^{78} +461.229 q^{79} -163.340 q^{80} -677.209 q^{81} -175.843 q^{82} +972.576 q^{83} +152.968 q^{84} -410.643 q^{86} -110.419 q^{87} +1097.15 q^{88} +16.0131 q^{89} -8.33020 q^{90} +120.933 q^{91} +675.862 q^{92} -1214.33 q^{93} -440.346 q^{94} +535.476 q^{95} -842.133 q^{96} -598.704 q^{97} +346.255 q^{98} -124.011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07125 −0.378742 −0.189371 0.981906i \(-0.560645\pi\)
−0.189371 + 0.981906i \(0.560645\pi\)
\(3\) 5.02012 0.966123 0.483061 0.875586i \(-0.339525\pi\)
0.483061 + 0.875586i \(0.339525\pi\)
\(4\) −6.85243 −0.856554
\(5\) −4.32398 −0.386749 −0.193374 0.981125i \(-0.561943\pi\)
−0.193374 + 0.981125i \(0.561943\pi\)
\(6\) −5.37778 −0.365912
\(7\) −4.44673 −0.240101 −0.120050 0.992768i \(-0.538306\pi\)
−0.120050 + 0.992768i \(0.538306\pi\)
\(8\) 15.9106 0.703156
\(9\) −1.79838 −0.0666068
\(10\) 4.63204 0.146478
\(11\) 68.9570 1.89012 0.945059 0.326899i \(-0.106004\pi\)
0.945059 + 0.326899i \(0.106004\pi\)
\(12\) −34.4000 −0.827536
\(13\) −27.1960 −0.580217 −0.290108 0.956994i \(-0.593691\pi\)
−0.290108 + 0.956994i \(0.593691\pi\)
\(14\) 4.76354 0.0909363
\(15\) −21.7069 −0.373647
\(16\) 37.7753 0.590239
\(17\) 0 0
\(18\) 1.92651 0.0252268
\(19\) −123.839 −1.49529 −0.747646 0.664098i \(-0.768816\pi\)
−0.747646 + 0.664098i \(0.768816\pi\)
\(20\) 29.6298 0.331271
\(21\) −22.3231 −0.231967
\(22\) −73.8698 −0.715868
\(23\) −98.6310 −0.894173 −0.447086 0.894491i \(-0.647538\pi\)
−0.447086 + 0.894491i \(0.647538\pi\)
\(24\) 79.8731 0.679335
\(25\) −106.303 −0.850426
\(26\) 29.1336 0.219753
\(27\) −144.571 −1.03047
\(28\) 30.4709 0.205659
\(29\) −21.9952 −0.140842 −0.0704209 0.997517i \(-0.522434\pi\)
−0.0704209 + 0.997517i \(0.522434\pi\)
\(30\) 23.2534 0.141516
\(31\) −241.893 −1.40146 −0.700730 0.713426i \(-0.747142\pi\)
−0.700730 + 0.713426i \(0.747142\pi\)
\(32\) −167.751 −0.926705
\(33\) 346.172 1.82609
\(34\) 0 0
\(35\) 19.2276 0.0928586
\(36\) 12.3233 0.0570524
\(37\) −324.851 −1.44338 −0.721692 0.692214i \(-0.756636\pi\)
−0.721692 + 0.692214i \(0.756636\pi\)
\(38\) 132.662 0.566330
\(39\) −136.527 −0.560561
\(40\) −68.7971 −0.271945
\(41\) 164.148 0.625260 0.312630 0.949875i \(-0.398790\pi\)
0.312630 + 0.949875i \(0.398790\pi\)
\(42\) 23.9135 0.0878557
\(43\) 383.332 1.35948 0.679739 0.733454i \(-0.262093\pi\)
0.679739 + 0.733454i \(0.262093\pi\)
\(44\) −472.523 −1.61899
\(45\) 7.77618 0.0257601
\(46\) 105.658 0.338661
\(47\) 411.060 1.27573 0.637865 0.770148i \(-0.279818\pi\)
0.637865 + 0.770148i \(0.279818\pi\)
\(48\) 189.637 0.570243
\(49\) −323.227 −0.942352
\(50\) 113.877 0.322092
\(51\) 0 0
\(52\) 186.359 0.496987
\(53\) −380.053 −0.984987 −0.492493 0.870316i \(-0.663914\pi\)
−0.492493 + 0.870316i \(0.663914\pi\)
\(54\) 154.871 0.390284
\(55\) −298.169 −0.731001
\(56\) −70.7501 −0.168828
\(57\) −621.685 −1.44464
\(58\) 23.5623 0.0533428
\(59\) 63.3150 0.139710 0.0698552 0.997557i \(-0.477746\pi\)
0.0698552 + 0.997557i \(0.477746\pi\)
\(60\) 148.745 0.320049
\(61\) 37.1265 0.0779272 0.0389636 0.999241i \(-0.487594\pi\)
0.0389636 + 0.999241i \(0.487594\pi\)
\(62\) 259.127 0.530793
\(63\) 7.99693 0.0159924
\(64\) −122.499 −0.239257
\(65\) 117.595 0.224398
\(66\) −370.836 −0.691617
\(67\) −48.2971 −0.0880660 −0.0440330 0.999030i \(-0.514021\pi\)
−0.0440330 + 0.999030i \(0.514021\pi\)
\(68\) 0 0
\(69\) −495.139 −0.863881
\(70\) −20.5974 −0.0351695
\(71\) −672.362 −1.12387 −0.561934 0.827182i \(-0.689943\pi\)
−0.561934 + 0.827182i \(0.689943\pi\)
\(72\) −28.6134 −0.0468350
\(73\) −562.892 −0.902486 −0.451243 0.892401i \(-0.649019\pi\)
−0.451243 + 0.892401i \(0.649019\pi\)
\(74\) 347.996 0.546671
\(75\) −533.655 −0.821615
\(76\) 848.596 1.28080
\(77\) −306.633 −0.453819
\(78\) 146.254 0.212308
\(79\) 461.229 0.656864 0.328432 0.944528i \(-0.393480\pi\)
0.328432 + 0.944528i \(0.393480\pi\)
\(80\) −163.340 −0.228274
\(81\) −677.209 −0.928957
\(82\) −175.843 −0.236812
\(83\) 972.576 1.28619 0.643097 0.765785i \(-0.277649\pi\)
0.643097 + 0.765785i \(0.277649\pi\)
\(84\) 152.968 0.198692
\(85\) 0 0
\(86\) −410.643 −0.514892
\(87\) −110.419 −0.136071
\(88\) 1097.15 1.32905
\(89\) 16.0131 0.0190717 0.00953587 0.999955i \(-0.496965\pi\)
0.00953587 + 0.999955i \(0.496965\pi\)
\(90\) −8.33020 −0.00975645
\(91\) 120.933 0.139311
\(92\) 675.862 0.765907
\(93\) −1214.33 −1.35398
\(94\) −440.346 −0.483173
\(95\) 535.476 0.578302
\(96\) −842.133 −0.895310
\(97\) −598.704 −0.626693 −0.313346 0.949639i \(-0.601450\pi\)
−0.313346 + 0.949639i \(0.601450\pi\)
\(98\) 346.255 0.356909
\(99\) −124.011 −0.125895
\(100\) 728.436 0.728436
\(101\) −1545.14 −1.52225 −0.761124 0.648607i \(-0.775352\pi\)
−0.761124 + 0.648607i \(0.775352\pi\)
\(102\) 0 0
\(103\) 1045.57 1.00022 0.500111 0.865961i \(-0.333292\pi\)
0.500111 + 0.865961i \(0.333292\pi\)
\(104\) −432.705 −0.407983
\(105\) 96.5247 0.0897128
\(106\) 407.130 0.373056
\(107\) 815.729 0.737005 0.368502 0.929627i \(-0.379871\pi\)
0.368502 + 0.929627i \(0.379871\pi\)
\(108\) 990.666 0.882656
\(109\) −438.510 −0.385336 −0.192668 0.981264i \(-0.561714\pi\)
−0.192668 + 0.981264i \(0.561714\pi\)
\(110\) 319.412 0.276861
\(111\) −1630.79 −1.39449
\(112\) −167.977 −0.141717
\(113\) −665.416 −0.553956 −0.276978 0.960876i \(-0.589333\pi\)
−0.276978 + 0.960876i \(0.589333\pi\)
\(114\) 665.977 0.547145
\(115\) 426.478 0.345820
\(116\) 150.721 0.120639
\(117\) 48.9089 0.0386464
\(118\) −67.8259 −0.0529143
\(119\) 0 0
\(120\) −345.370 −0.262732
\(121\) 3424.06 2.57255
\(122\) −39.7716 −0.0295143
\(123\) 824.044 0.604077
\(124\) 1657.56 1.20043
\(125\) 1000.15 0.715649
\(126\) −8.56667 −0.00605698
\(127\) −524.835 −0.366706 −0.183353 0.983047i \(-0.558695\pi\)
−0.183353 + 0.983047i \(0.558695\pi\)
\(128\) 1473.24 1.01732
\(129\) 1924.37 1.31342
\(130\) −125.973 −0.0849891
\(131\) 129.359 0.0862760 0.0431380 0.999069i \(-0.486264\pi\)
0.0431380 + 0.999069i \(0.486264\pi\)
\(132\) −2372.12 −1.56414
\(133\) 550.677 0.359021
\(134\) 51.7380 0.0333543
\(135\) 625.124 0.398534
\(136\) 0 0
\(137\) 760.804 0.474452 0.237226 0.971455i \(-0.423762\pi\)
0.237226 + 0.971455i \(0.423762\pi\)
\(138\) 530.416 0.327188
\(139\) 859.570 0.524516 0.262258 0.964998i \(-0.415533\pi\)
0.262258 + 0.964998i \(0.415533\pi\)
\(140\) −131.756 −0.0795384
\(141\) 2063.57 1.23251
\(142\) 720.265 0.425657
\(143\) −1875.36 −1.09668
\(144\) −67.9345 −0.0393140
\(145\) 95.1070 0.0544704
\(146\) 602.995 0.341810
\(147\) −1622.64 −0.910427
\(148\) 2226.02 1.23634
\(149\) 2709.00 1.48946 0.744730 0.667366i \(-0.232578\pi\)
0.744730 + 0.667366i \(0.232578\pi\)
\(150\) 571.675 0.311181
\(151\) 406.811 0.219244 0.109622 0.993973i \(-0.465036\pi\)
0.109622 + 0.993973i \(0.465036\pi\)
\(152\) −1970.35 −1.05142
\(153\) 0 0
\(154\) 328.479 0.171881
\(155\) 1045.94 0.542013
\(156\) 935.544 0.480151
\(157\) −2314.18 −1.17638 −0.588191 0.808722i \(-0.700160\pi\)
−0.588191 + 0.808722i \(0.700160\pi\)
\(158\) −494.089 −0.248782
\(159\) −1907.91 −0.951618
\(160\) 725.354 0.358402
\(161\) 438.585 0.214692
\(162\) 725.457 0.351835
\(163\) 2046.67 0.983481 0.491741 0.870742i \(-0.336361\pi\)
0.491741 + 0.870742i \(0.336361\pi\)
\(164\) −1124.81 −0.535569
\(165\) −1496.84 −0.706237
\(166\) −1041.87 −0.487136
\(167\) 821.932 0.380856 0.190428 0.981701i \(-0.439012\pi\)
0.190428 + 0.981701i \(0.439012\pi\)
\(168\) −355.174 −0.163109
\(169\) −1457.38 −0.663348
\(170\) 0 0
\(171\) 222.710 0.0995967
\(172\) −2626.76 −1.16447
\(173\) −1450.84 −0.637603 −0.318802 0.947821i \(-0.603280\pi\)
−0.318802 + 0.947821i \(0.603280\pi\)
\(174\) 118.286 0.0515357
\(175\) 472.701 0.204188
\(176\) 2604.87 1.11562
\(177\) 317.849 0.134977
\(178\) −17.1539 −0.00722327
\(179\) −2841.91 −1.18667 −0.593337 0.804954i \(-0.702190\pi\)
−0.593337 + 0.804954i \(0.702190\pi\)
\(180\) −53.2858 −0.0220649
\(181\) 4019.94 1.65083 0.825414 0.564528i \(-0.190942\pi\)
0.825414 + 0.564528i \(0.190942\pi\)
\(182\) −129.549 −0.0527628
\(183\) 186.379 0.0752872
\(184\) −1569.28 −0.628743
\(185\) 1404.65 0.558227
\(186\) 1300.85 0.512811
\(187\) 0 0
\(188\) −2816.76 −1.09273
\(189\) 642.870 0.247417
\(190\) −573.626 −0.219027
\(191\) 3374.10 1.27823 0.639113 0.769113i \(-0.279301\pi\)
0.639113 + 0.769113i \(0.279301\pi\)
\(192\) −614.962 −0.231151
\(193\) −343.680 −0.128179 −0.0640897 0.997944i \(-0.520414\pi\)
−0.0640897 + 0.997944i \(0.520414\pi\)
\(194\) 641.359 0.237355
\(195\) 590.342 0.216796
\(196\) 2214.89 0.807175
\(197\) −4600.65 −1.66387 −0.831935 0.554873i \(-0.812767\pi\)
−0.831935 + 0.554873i \(0.812767\pi\)
\(198\) 132.846 0.0476817
\(199\) −1018.79 −0.362914 −0.181457 0.983399i \(-0.558081\pi\)
−0.181457 + 0.983399i \(0.558081\pi\)
\(200\) −1691.35 −0.597982
\(201\) −242.457 −0.0850826
\(202\) 1655.22 0.576540
\(203\) 97.8069 0.0338162
\(204\) 0 0
\(205\) −709.774 −0.241818
\(206\) −1120.06 −0.378827
\(207\) 177.376 0.0595580
\(208\) −1027.34 −0.342467
\(209\) −8539.54 −2.82628
\(210\) −103.402 −0.0339781
\(211\) −2498.29 −0.815115 −0.407557 0.913180i \(-0.633619\pi\)
−0.407557 + 0.913180i \(0.633619\pi\)
\(212\) 2604.29 0.843694
\(213\) −3375.34 −1.08580
\(214\) −873.846 −0.279135
\(215\) −1657.52 −0.525776
\(216\) −2300.22 −0.724583
\(217\) 1075.63 0.336492
\(218\) 469.752 0.145943
\(219\) −2825.78 −0.871912
\(220\) 2043.18 0.626142
\(221\) 0 0
\(222\) 1746.98 0.528151
\(223\) −4252.54 −1.27700 −0.638500 0.769622i \(-0.720445\pi\)
−0.638500 + 0.769622i \(0.720445\pi\)
\(224\) 745.945 0.222502
\(225\) 191.174 0.0566442
\(226\) 712.823 0.209807
\(227\) −6652.94 −1.94525 −0.972623 0.232387i \(-0.925347\pi\)
−0.972623 + 0.232387i \(0.925347\pi\)
\(228\) 4260.06 1.23741
\(229\) −3364.85 −0.970984 −0.485492 0.874241i \(-0.661359\pi\)
−0.485492 + 0.874241i \(0.661359\pi\)
\(230\) −456.863 −0.130977
\(231\) −1539.33 −0.438445
\(232\) −349.958 −0.0990338
\(233\) 1944.15 0.546634 0.273317 0.961924i \(-0.411879\pi\)
0.273317 + 0.961924i \(0.411879\pi\)
\(234\) −52.3935 −0.0146370
\(235\) −1777.42 −0.493387
\(236\) −433.862 −0.119670
\(237\) 2315.42 0.634612
\(238\) 0 0
\(239\) −392.233 −0.106157 −0.0530783 0.998590i \(-0.516903\pi\)
−0.0530783 + 0.998590i \(0.516903\pi\)
\(240\) −819.985 −0.220541
\(241\) −1163.20 −0.310905 −0.155453 0.987843i \(-0.549684\pi\)
−0.155453 + 0.987843i \(0.549684\pi\)
\(242\) −3668.01 −0.974334
\(243\) 503.754 0.132987
\(244\) −254.407 −0.0667488
\(245\) 1397.63 0.364453
\(246\) −882.753 −0.228790
\(247\) 3367.92 0.867594
\(248\) −3848.66 −0.985445
\(249\) 4882.45 1.24262
\(250\) −1071.41 −0.271047
\(251\) 2743.17 0.689831 0.344915 0.938634i \(-0.387908\pi\)
0.344915 + 0.938634i \(0.387908\pi\)
\(252\) −54.7984 −0.0136983
\(253\) −6801.29 −1.69009
\(254\) 562.227 0.138887
\(255\) 0 0
\(256\) −598.204 −0.146046
\(257\) 689.924 0.167456 0.0837282 0.996489i \(-0.473317\pi\)
0.0837282 + 0.996489i \(0.473317\pi\)
\(258\) −2061.48 −0.497449
\(259\) 1444.53 0.346558
\(260\) −805.813 −0.192209
\(261\) 39.5559 0.00938103
\(262\) −138.575 −0.0326764
\(263\) 4670.18 1.09497 0.547483 0.836817i \(-0.315586\pi\)
0.547483 + 0.836817i \(0.315586\pi\)
\(264\) 5507.81 1.28402
\(265\) 1643.34 0.380942
\(266\) −589.910 −0.135976
\(267\) 80.3876 0.0184256
\(268\) 330.952 0.0754333
\(269\) 868.931 0.196951 0.0984753 0.995140i \(-0.468603\pi\)
0.0984753 + 0.995140i \(0.468603\pi\)
\(270\) −669.661 −0.150942
\(271\) 6730.27 1.50862 0.754308 0.656521i \(-0.227973\pi\)
0.754308 + 0.656521i \(0.227973\pi\)
\(272\) 0 0
\(273\) 607.100 0.134591
\(274\) −815.008 −0.179695
\(275\) −7330.35 −1.60741
\(276\) 3392.91 0.739961
\(277\) 3264.04 0.708005 0.354003 0.935244i \(-0.384820\pi\)
0.354003 + 0.935244i \(0.384820\pi\)
\(278\) −920.810 −0.198657
\(279\) 435.017 0.0933469
\(280\) 305.922 0.0652941
\(281\) 8205.96 1.74209 0.871044 0.491205i \(-0.163443\pi\)
0.871044 + 0.491205i \(0.163443\pi\)
\(282\) −2210.59 −0.466805
\(283\) 2958.69 0.621469 0.310734 0.950497i \(-0.399425\pi\)
0.310734 + 0.950497i \(0.399425\pi\)
\(284\) 4607.32 0.962654
\(285\) 2688.15 0.558711
\(286\) 2008.97 0.415359
\(287\) −729.922 −0.150125
\(288\) 301.682 0.0617249
\(289\) 0 0
\(290\) −101.883 −0.0206303
\(291\) −3005.57 −0.605462
\(292\) 3857.18 0.773028
\(293\) −5413.44 −1.07937 −0.539687 0.841866i \(-0.681457\pi\)
−0.539687 + 0.841866i \(0.681457\pi\)
\(294\) 1738.24 0.344817
\(295\) −273.773 −0.0540328
\(296\) −5168.58 −1.01492
\(297\) −9969.20 −1.94772
\(298\) −2902.00 −0.564122
\(299\) 2682.37 0.518814
\(300\) 3656.83 0.703758
\(301\) −1704.57 −0.326412
\(302\) −435.795 −0.0830370
\(303\) −7756.78 −1.47068
\(304\) −4678.04 −0.882580
\(305\) −160.534 −0.0301382
\(306\) 0 0
\(307\) 7347.01 1.36585 0.682925 0.730488i \(-0.260707\pi\)
0.682925 + 0.730488i \(0.260707\pi\)
\(308\) 2101.18 0.388721
\(309\) 5248.88 0.966338
\(310\) −1120.46 −0.205283
\(311\) −4971.09 −0.906381 −0.453190 0.891414i \(-0.649714\pi\)
−0.453190 + 0.891414i \(0.649714\pi\)
\(312\) −2172.23 −0.394162
\(313\) 6935.73 1.25249 0.626247 0.779625i \(-0.284590\pi\)
0.626247 + 0.779625i \(0.284590\pi\)
\(314\) 2479.06 0.445546
\(315\) −34.5786 −0.00618502
\(316\) −3160.54 −0.562640
\(317\) −7667.25 −1.35847 −0.679236 0.733920i \(-0.737689\pi\)
−0.679236 + 0.733920i \(0.737689\pi\)
\(318\) 2043.84 0.360418
\(319\) −1516.73 −0.266208
\(320\) 529.685 0.0925322
\(321\) 4095.06 0.712037
\(322\) −469.832 −0.0813128
\(323\) 0 0
\(324\) 4640.53 0.795702
\(325\) 2891.02 0.493431
\(326\) −2192.48 −0.372486
\(327\) −2201.37 −0.372282
\(328\) 2611.70 0.439655
\(329\) −1827.87 −0.306304
\(330\) 1603.49 0.267482
\(331\) 1425.58 0.236728 0.118364 0.992970i \(-0.462235\pi\)
0.118364 + 0.992970i \(0.462235\pi\)
\(332\) −6664.51 −1.10169
\(333\) 584.208 0.0961393
\(334\) −880.491 −0.144246
\(335\) 208.836 0.0340594
\(336\) −843.262 −0.136916
\(337\) 2472.94 0.399732 0.199866 0.979823i \(-0.435949\pi\)
0.199866 + 0.979823i \(0.435949\pi\)
\(338\) 1561.21 0.251238
\(339\) −3340.47 −0.535190
\(340\) 0 0
\(341\) −16680.2 −2.64893
\(342\) −238.577 −0.0377215
\(343\) 2962.53 0.466360
\(344\) 6099.04 0.955925
\(345\) 2140.97 0.334105
\(346\) 1554.21 0.241487
\(347\) −3930.28 −0.608036 −0.304018 0.952666i \(-0.598328\pi\)
−0.304018 + 0.952666i \(0.598328\pi\)
\(348\) 756.637 0.116552
\(349\) −6606.93 −1.01336 −0.506678 0.862136i \(-0.669127\pi\)
−0.506678 + 0.862136i \(0.669127\pi\)
\(350\) −506.379 −0.0773346
\(351\) 3931.77 0.597898
\(352\) −11567.6 −1.75158
\(353\) −6336.87 −0.955461 −0.477731 0.878506i \(-0.658541\pi\)
−0.477731 + 0.878506i \(0.658541\pi\)
\(354\) −340.494 −0.0511217
\(355\) 2907.28 0.434655
\(356\) −109.729 −0.0163360
\(357\) 0 0
\(358\) 3044.39 0.449444
\(359\) −3060.68 −0.449963 −0.224982 0.974363i \(-0.572232\pi\)
−0.224982 + 0.974363i \(0.572232\pi\)
\(360\) 123.724 0.0181134
\(361\) 8477.02 1.23590
\(362\) −4306.34 −0.625238
\(363\) 17189.2 2.48540
\(364\) −828.688 −0.119327
\(365\) 2433.93 0.349035
\(366\) −199.658 −0.0285145
\(367\) 5391.79 0.766892 0.383446 0.923563i \(-0.374737\pi\)
0.383446 + 0.923563i \(0.374737\pi\)
\(368\) −3725.81 −0.527776
\(369\) −295.202 −0.0416466
\(370\) −1504.73 −0.211424
\(371\) 1689.99 0.236496
\(372\) 8321.13 1.15976
\(373\) −1509.56 −0.209550 −0.104775 0.994496i \(-0.533412\pi\)
−0.104775 + 0.994496i \(0.533412\pi\)
\(374\) 0 0
\(375\) 5020.88 0.691405
\(376\) 6540.22 0.897037
\(377\) 598.183 0.0817189
\(378\) −688.671 −0.0937075
\(379\) 4111.54 0.557244 0.278622 0.960401i \(-0.410122\pi\)
0.278622 + 0.960401i \(0.410122\pi\)
\(380\) −3669.31 −0.495347
\(381\) −2634.74 −0.354283
\(382\) −3614.49 −0.484119
\(383\) −6538.64 −0.872347 −0.436173 0.899863i \(-0.643667\pi\)
−0.436173 + 0.899863i \(0.643667\pi\)
\(384\) 7395.84 0.982857
\(385\) 1325.87 0.175514
\(386\) 368.166 0.0485470
\(387\) −689.378 −0.0905506
\(388\) 4102.58 0.536796
\(389\) 7955.67 1.03694 0.518468 0.855097i \(-0.326502\pi\)
0.518468 + 0.855097i \(0.326502\pi\)
\(390\) −632.401 −0.0821099
\(391\) 0 0
\(392\) −5142.73 −0.662620
\(393\) 649.398 0.0833532
\(394\) 4928.42 0.630178
\(395\) −1994.34 −0.254041
\(396\) 849.778 0.107836
\(397\) −2375.20 −0.300271 −0.150136 0.988665i \(-0.547971\pi\)
−0.150136 + 0.988665i \(0.547971\pi\)
\(398\) 1091.37 0.137451
\(399\) 2764.46 0.346858
\(400\) −4015.64 −0.501954
\(401\) −434.525 −0.0541125 −0.0270563 0.999634i \(-0.508613\pi\)
−0.0270563 + 0.999634i \(0.508613\pi\)
\(402\) 259.731 0.0322244
\(403\) 6578.53 0.813151
\(404\) 10588.0 1.30389
\(405\) 2928.24 0.359273
\(406\) −104.775 −0.0128076
\(407\) −22400.8 −2.72817
\(408\) 0 0
\(409\) −3564.54 −0.430942 −0.215471 0.976510i \(-0.569129\pi\)
−0.215471 + 0.976510i \(0.569129\pi\)
\(410\) 760.342 0.0915868
\(411\) 3819.33 0.458378
\(412\) −7164.69 −0.856745
\(413\) −281.545 −0.0335446
\(414\) −190.014 −0.0225572
\(415\) −4205.40 −0.497434
\(416\) 4562.17 0.537690
\(417\) 4315.14 0.506747
\(418\) 9147.94 1.07043
\(419\) −16502.8 −1.92414 −0.962072 0.272797i \(-0.912051\pi\)
−0.962072 + 0.272797i \(0.912051\pi\)
\(420\) −661.429 −0.0768439
\(421\) −11424.1 −1.32251 −0.661255 0.750161i \(-0.729976\pi\)
−0.661255 + 0.750161i \(0.729976\pi\)
\(422\) 2676.28 0.308718
\(423\) −739.245 −0.0849724
\(424\) −6046.87 −0.692599
\(425\) 0 0
\(426\) 3615.82 0.411237
\(427\) −165.091 −0.0187104
\(428\) −5589.73 −0.631284
\(429\) −9414.51 −1.05953
\(430\) 1775.61 0.199134
\(431\) 7929.24 0.886167 0.443083 0.896480i \(-0.353885\pi\)
0.443083 + 0.896480i \(0.353885\pi\)
\(432\) −5461.23 −0.608226
\(433\) −377.380 −0.0418839 −0.0209419 0.999781i \(-0.506667\pi\)
−0.0209419 + 0.999781i \(0.506667\pi\)
\(434\) −1152.27 −0.127444
\(435\) 477.449 0.0526251
\(436\) 3004.86 0.330061
\(437\) 12214.3 1.33705
\(438\) 3027.11 0.330230
\(439\) −4049.99 −0.440308 −0.220154 0.975465i \(-0.570656\pi\)
−0.220154 + 0.975465i \(0.570656\pi\)
\(440\) −4744.04 −0.514008
\(441\) 581.286 0.0627671
\(442\) 0 0
\(443\) 3944.38 0.423032 0.211516 0.977374i \(-0.432160\pi\)
0.211516 + 0.977374i \(0.432160\pi\)
\(444\) 11174.9 1.19445
\(445\) −69.2403 −0.00737596
\(446\) 4555.51 0.483654
\(447\) 13599.5 1.43900
\(448\) 544.722 0.0574457
\(449\) −2830.17 −0.297470 −0.148735 0.988877i \(-0.547520\pi\)
−0.148735 + 0.988877i \(0.547520\pi\)
\(450\) −204.794 −0.0214535
\(451\) 11319.2 1.18181
\(452\) 4559.72 0.474493
\(453\) 2042.24 0.211817
\(454\) 7126.93 0.736748
\(455\) −522.913 −0.0538781
\(456\) −9891.38 −1.01580
\(457\) 8796.64 0.900414 0.450207 0.892924i \(-0.351350\pi\)
0.450207 + 0.892924i \(0.351350\pi\)
\(458\) 3604.58 0.367753
\(459\) 0 0
\(460\) −2922.41 −0.296214
\(461\) 10424.8 1.05321 0.526606 0.850110i \(-0.323464\pi\)
0.526606 + 0.850110i \(0.323464\pi\)
\(462\) 1649.00 0.166058
\(463\) 6847.90 0.687362 0.343681 0.939086i \(-0.388326\pi\)
0.343681 + 0.939086i \(0.388326\pi\)
\(464\) −830.877 −0.0831304
\(465\) 5250.75 0.523651
\(466\) −2082.67 −0.207033
\(467\) 14390.7 1.42596 0.712979 0.701186i \(-0.247346\pi\)
0.712979 + 0.701186i \(0.247346\pi\)
\(468\) −335.145 −0.0331028
\(469\) 214.764 0.0211447
\(470\) 1904.05 0.186867
\(471\) −11617.5 −1.13653
\(472\) 1007.38 0.0982382
\(473\) 26433.4 2.56958
\(474\) −2480.39 −0.240354
\(475\) 13164.4 1.27163
\(476\) 0 0
\(477\) 683.482 0.0656069
\(478\) 420.178 0.0402060
\(479\) −7163.29 −0.683296 −0.341648 0.939828i \(-0.610985\pi\)
−0.341648 + 0.939828i \(0.610985\pi\)
\(480\) 3641.36 0.346260
\(481\) 8834.67 0.837476
\(482\) 1246.07 0.117753
\(483\) 2201.75 0.207418
\(484\) −23463.2 −2.20353
\(485\) 2588.79 0.242373
\(486\) −539.644 −0.0503678
\(487\) −14830.1 −1.37991 −0.689957 0.723850i \(-0.742371\pi\)
−0.689957 + 0.723850i \(0.742371\pi\)
\(488\) 590.704 0.0547949
\(489\) 10274.5 0.950164
\(490\) −1497.20 −0.138034
\(491\) −9634.41 −0.885529 −0.442765 0.896638i \(-0.646002\pi\)
−0.442765 + 0.896638i \(0.646002\pi\)
\(492\) −5646.71 −0.517425
\(493\) 0 0
\(494\) −3607.87 −0.328595
\(495\) 536.222 0.0486897
\(496\) −9137.59 −0.827197
\(497\) 2989.81 0.269842
\(498\) −5230.30 −0.470633
\(499\) −2033.72 −0.182449 −0.0912244 0.995830i \(-0.529078\pi\)
−0.0912244 + 0.995830i \(0.529078\pi\)
\(500\) −6853.46 −0.612993
\(501\) 4126.20 0.367954
\(502\) −2938.61 −0.261268
\(503\) −6715.07 −0.595249 −0.297625 0.954683i \(-0.596194\pi\)
−0.297625 + 0.954683i \(0.596194\pi\)
\(504\) 127.236 0.0112451
\(505\) 6681.15 0.588727
\(506\) 7285.85 0.640110
\(507\) −7316.20 −0.640876
\(508\) 3596.40 0.314103
\(509\) −1060.04 −0.0923096 −0.0461548 0.998934i \(-0.514697\pi\)
−0.0461548 + 0.998934i \(0.514697\pi\)
\(510\) 0 0
\(511\) 2503.03 0.216688
\(512\) −11145.1 −0.962007
\(513\) 17903.5 1.54086
\(514\) −739.078 −0.0634228
\(515\) −4521.02 −0.386835
\(516\) −13186.6 −1.12502
\(517\) 28345.5 2.41128
\(518\) −1547.44 −0.131256
\(519\) −7283.39 −0.616003
\(520\) 1871.01 0.157787
\(521\) 3742.36 0.314694 0.157347 0.987543i \(-0.449706\pi\)
0.157347 + 0.987543i \(0.449706\pi\)
\(522\) −42.3741 −0.00355300
\(523\) −11603.1 −0.970113 −0.485057 0.874483i \(-0.661201\pi\)
−0.485057 + 0.874483i \(0.661201\pi\)
\(524\) −886.425 −0.0739001
\(525\) 2373.02 0.197270
\(526\) −5002.91 −0.414710
\(527\) 0 0
\(528\) 13076.8 1.07783
\(529\) −2438.93 −0.200455
\(530\) −1760.42 −0.144279
\(531\) −113.865 −0.00930567
\(532\) −3773.48 −0.307521
\(533\) −4464.18 −0.362786
\(534\) −86.1149 −0.00697857
\(535\) −3527.20 −0.285035
\(536\) −768.435 −0.0619242
\(537\) −14266.8 −1.14647
\(538\) −930.839 −0.0745935
\(539\) −22288.7 −1.78116
\(540\) −4283.62 −0.341366
\(541\) −24094.9 −1.91483 −0.957415 0.288717i \(-0.906771\pi\)
−0.957415 + 0.288717i \(0.906771\pi\)
\(542\) −7209.77 −0.571377
\(543\) 20180.6 1.59490
\(544\) 0 0
\(545\) 1896.11 0.149028
\(546\) −650.353 −0.0509754
\(547\) 11145.9 0.871234 0.435617 0.900132i \(-0.356530\pi\)
0.435617 + 0.900132i \(0.356530\pi\)
\(548\) −5213.36 −0.406393
\(549\) −66.7677 −0.00519048
\(550\) 7852.60 0.608793
\(551\) 2723.86 0.210600
\(552\) −7877.96 −0.607443
\(553\) −2050.96 −0.157714
\(554\) −3496.59 −0.268152
\(555\) 7051.52 0.539316
\(556\) −5890.14 −0.449276
\(557\) −1634.29 −0.124322 −0.0621609 0.998066i \(-0.519799\pi\)
−0.0621609 + 0.998066i \(0.519799\pi\)
\(558\) −466.010 −0.0353544
\(559\) −10425.1 −0.788793
\(560\) 726.327 0.0548088
\(561\) 0 0
\(562\) −8790.60 −0.659803
\(563\) −17760.1 −1.32948 −0.664741 0.747074i \(-0.731458\pi\)
−0.664741 + 0.747074i \(0.731458\pi\)
\(564\) −14140.5 −1.05571
\(565\) 2877.24 0.214242
\(566\) −3169.48 −0.235377
\(567\) 3011.37 0.223043
\(568\) −10697.7 −0.790255
\(569\) 7497.30 0.552378 0.276189 0.961103i \(-0.410928\pi\)
0.276189 + 0.961103i \(0.410928\pi\)
\(570\) −2879.67 −0.211607
\(571\) −11381.8 −0.834172 −0.417086 0.908867i \(-0.636949\pi\)
−0.417086 + 0.908867i \(0.636949\pi\)
\(572\) 12850.7 0.939365
\(573\) 16938.4 1.23492
\(574\) 781.926 0.0568588
\(575\) 10484.8 0.760427
\(576\) 220.301 0.0159361
\(577\) 14264.6 1.02919 0.514596 0.857433i \(-0.327942\pi\)
0.514596 + 0.857433i \(0.327942\pi\)
\(578\) 0 0
\(579\) −1725.32 −0.123837
\(580\) −651.715 −0.0466569
\(581\) −4324.78 −0.308816
\(582\) 3219.70 0.229314
\(583\) −26207.3 −1.86174
\(584\) −8955.94 −0.634588
\(585\) −211.481 −0.0149464
\(586\) 5799.12 0.408805
\(587\) 15284.6 1.07472 0.537361 0.843353i \(-0.319421\pi\)
0.537361 + 0.843353i \(0.319421\pi\)
\(588\) 11119.0 0.779830
\(589\) 29955.7 2.09559
\(590\) 293.278 0.0204645
\(591\) −23095.8 −1.60750
\(592\) −12271.4 −0.851942
\(593\) 22175.8 1.53566 0.767832 0.640651i \(-0.221335\pi\)
0.767832 + 0.640651i \(0.221335\pi\)
\(594\) 10679.5 0.737683
\(595\) 0 0
\(596\) −18563.2 −1.27580
\(597\) −5114.43 −0.350619
\(598\) −2873.48 −0.196497
\(599\) −5573.44 −0.380175 −0.190087 0.981767i \(-0.560877\pi\)
−0.190087 + 0.981767i \(0.560877\pi\)
\(600\) −8490.77 −0.577724
\(601\) −11936.4 −0.810144 −0.405072 0.914285i \(-0.632754\pi\)
−0.405072 + 0.914285i \(0.632754\pi\)
\(602\) 1826.02 0.123626
\(603\) 86.8567 0.00586580
\(604\) −2787.65 −0.187794
\(605\) −14805.6 −0.994930
\(606\) 8309.41 0.557008
\(607\) −18129.9 −1.21230 −0.606152 0.795349i \(-0.707288\pi\)
−0.606152 + 0.795349i \(0.707288\pi\)
\(608\) 20774.1 1.38569
\(609\) 491.002 0.0326706
\(610\) 171.971 0.0114146
\(611\) −11179.2 −0.740200
\(612\) 0 0
\(613\) 14680.7 0.967289 0.483644 0.875265i \(-0.339313\pi\)
0.483644 + 0.875265i \(0.339313\pi\)
\(614\) −7870.45 −0.517306
\(615\) −3563.15 −0.233626
\(616\) −4878.71 −0.319105
\(617\) 1056.15 0.0689123 0.0344561 0.999406i \(-0.489030\pi\)
0.0344561 + 0.999406i \(0.489030\pi\)
\(618\) −5622.84 −0.365993
\(619\) −11068.5 −0.718707 −0.359353 0.933202i \(-0.617003\pi\)
−0.359353 + 0.933202i \(0.617003\pi\)
\(620\) −7167.24 −0.464263
\(621\) 14259.2 0.921421
\(622\) 5325.25 0.343285
\(623\) −71.2059 −0.00457914
\(624\) −5157.36 −0.330865
\(625\) 8963.27 0.573649
\(626\) −7429.86 −0.474372
\(627\) −42869.5 −2.73053
\(628\) 15857.8 1.00763
\(629\) 0 0
\(630\) 37.0421 0.00234253
\(631\) −15903.0 −1.00331 −0.501655 0.865068i \(-0.667275\pi\)
−0.501655 + 0.865068i \(0.667275\pi\)
\(632\) 7338.43 0.461878
\(633\) −12541.7 −0.787501
\(634\) 8213.50 0.514511
\(635\) 2269.38 0.141823
\(636\) 13073.8 0.815112
\(637\) 8790.48 0.546768
\(638\) 1624.79 0.100824
\(639\) 1209.17 0.0748574
\(640\) −6370.25 −0.393448
\(641\) 3380.02 0.208272 0.104136 0.994563i \(-0.466792\pi\)
0.104136 + 0.994563i \(0.466792\pi\)
\(642\) −4386.81 −0.269679
\(643\) 19441.2 1.19236 0.596178 0.802852i \(-0.296685\pi\)
0.596178 + 0.802852i \(0.296685\pi\)
\(644\) −3005.37 −0.183895
\(645\) −8320.95 −0.507965
\(646\) 0 0
\(647\) 4778.18 0.290339 0.145170 0.989407i \(-0.453627\pi\)
0.145170 + 0.989407i \(0.453627\pi\)
\(648\) −10774.8 −0.653201
\(649\) 4366.01 0.264069
\(650\) −3097.00 −0.186883
\(651\) 5399.81 0.325092
\(652\) −14024.7 −0.842405
\(653\) 24415.5 1.46317 0.731587 0.681749i \(-0.238780\pi\)
0.731587 + 0.681749i \(0.238780\pi\)
\(654\) 2358.21 0.140999
\(655\) −559.346 −0.0333671
\(656\) 6200.75 0.369053
\(657\) 1012.30 0.0601118
\(658\) 1958.10 0.116010
\(659\) 3212.43 0.189891 0.0949457 0.995482i \(-0.469732\pi\)
0.0949457 + 0.995482i \(0.469732\pi\)
\(660\) 10257.0 0.604930
\(661\) −6486.27 −0.381674 −0.190837 0.981622i \(-0.561120\pi\)
−0.190837 + 0.981622i \(0.561120\pi\)
\(662\) −1527.15 −0.0896591
\(663\) 0 0
\(664\) 15474.3 0.904395
\(665\) −2381.12 −0.138851
\(666\) −625.830 −0.0364120
\(667\) 2169.41 0.125937
\(668\) −5632.23 −0.326224
\(669\) −21348.2 −1.23374
\(670\) −223.714 −0.0128997
\(671\) 2560.13 0.147292
\(672\) 3744.73 0.214965
\(673\) −25244.2 −1.44590 −0.722952 0.690898i \(-0.757215\pi\)
−0.722952 + 0.690898i \(0.757215\pi\)
\(674\) −2649.13 −0.151396
\(675\) 15368.4 0.876341
\(676\) 9986.57 0.568194
\(677\) −9817.09 −0.557314 −0.278657 0.960391i \(-0.589889\pi\)
−0.278657 + 0.960391i \(0.589889\pi\)
\(678\) 3578.46 0.202699
\(679\) 2662.28 0.150469
\(680\) 0 0
\(681\) −33398.6 −1.87935
\(682\) 17868.6 1.00326
\(683\) −26082.8 −1.46125 −0.730624 0.682780i \(-0.760771\pi\)
−0.730624 + 0.682780i \(0.760771\pi\)
\(684\) −1526.10 −0.0853099
\(685\) −3289.70 −0.183493
\(686\) −3173.60 −0.176630
\(687\) −16891.9 −0.938090
\(688\) 14480.5 0.802417
\(689\) 10335.9 0.571506
\(690\) −2293.51 −0.126540
\(691\) −23259.6 −1.28052 −0.640258 0.768160i \(-0.721173\pi\)
−0.640258 + 0.768160i \(0.721173\pi\)
\(692\) 9941.79 0.546142
\(693\) 551.444 0.0302275
\(694\) 4210.29 0.230289
\(695\) −3716.76 −0.202856
\(696\) −1756.83 −0.0956788
\(697\) 0 0
\(698\) 7077.64 0.383801
\(699\) 9759.88 0.528115
\(700\) −3239.15 −0.174898
\(701\) 17022.9 0.917183 0.458592 0.888647i \(-0.348354\pi\)
0.458592 + 0.888647i \(0.348354\pi\)
\(702\) −4211.89 −0.226449
\(703\) 40229.2 2.15828
\(704\) −8447.19 −0.452224
\(705\) −8922.85 −0.476672
\(706\) 6788.35 0.361874
\(707\) 6870.81 0.365493
\(708\) −2178.04 −0.115615
\(709\) 4322.81 0.228980 0.114490 0.993424i \(-0.463477\pi\)
0.114490 + 0.993424i \(0.463477\pi\)
\(710\) −3114.41 −0.164622
\(711\) −829.467 −0.0437517
\(712\) 254.778 0.0134104
\(713\) 23858.1 1.25315
\(714\) 0 0
\(715\) 8109.00 0.424139
\(716\) 19474.0 1.01645
\(717\) −1969.06 −0.102560
\(718\) 3278.74 0.170420
\(719\) −6228.36 −0.323058 −0.161529 0.986868i \(-0.551642\pi\)
−0.161529 + 0.986868i \(0.551642\pi\)
\(720\) 293.748 0.0152046
\(721\) −4649.36 −0.240154
\(722\) −9080.97 −0.468087
\(723\) −5839.39 −0.300373
\(724\) −27546.4 −1.41402
\(725\) 2338.16 0.119776
\(726\) −18413.9 −0.941326
\(727\) 24426.4 1.24611 0.623057 0.782176i \(-0.285890\pi\)
0.623057 + 0.782176i \(0.285890\pi\)
\(728\) 1924.12 0.0979570
\(729\) 20813.6 1.05744
\(730\) −2607.34 −0.132194
\(731\) 0 0
\(732\) −1277.15 −0.0644876
\(733\) 16963.6 0.854793 0.427396 0.904064i \(-0.359431\pi\)
0.427396 + 0.904064i \(0.359431\pi\)
\(734\) −5775.93 −0.290455
\(735\) 7016.25 0.352106
\(736\) 16545.5 0.828634
\(737\) −3330.42 −0.166455
\(738\) 316.233 0.0157733
\(739\) −8021.02 −0.399266 −0.199633 0.979871i \(-0.563975\pi\)
−0.199633 + 0.979871i \(0.563975\pi\)
\(740\) −9625.28 −0.478152
\(741\) 16907.4 0.838202
\(742\) −1810.40 −0.0895711
\(743\) 9925.69 0.490092 0.245046 0.969511i \(-0.421197\pi\)
0.245046 + 0.969511i \(0.421197\pi\)
\(744\) −19320.8 −0.952061
\(745\) −11713.6 −0.576047
\(746\) 1617.11 0.0793655
\(747\) −1749.07 −0.0856693
\(748\) 0 0
\(749\) −3627.32 −0.176955
\(750\) −5378.59 −0.261865
\(751\) 16444.3 0.799018 0.399509 0.916729i \(-0.369181\pi\)
0.399509 + 0.916729i \(0.369181\pi\)
\(752\) 15527.9 0.752986
\(753\) 13771.1 0.666461
\(754\) −640.801 −0.0309504
\(755\) −1759.04 −0.0847923
\(756\) −4405.22 −0.211926
\(757\) −10727.3 −0.515047 −0.257523 0.966272i \(-0.582906\pi\)
−0.257523 + 0.966272i \(0.582906\pi\)
\(758\) −4404.47 −0.211052
\(759\) −34143.3 −1.63284
\(760\) 8519.75 0.406636
\(761\) 2379.78 0.113360 0.0566801 0.998392i \(-0.481948\pi\)
0.0566801 + 0.998392i \(0.481948\pi\)
\(762\) 2822.45 0.134182
\(763\) 1949.93 0.0925194
\(764\) −23120.8 −1.09487
\(765\) 0 0
\(766\) 7004.49 0.330395
\(767\) −1721.92 −0.0810623
\(768\) −3003.06 −0.141098
\(769\) −7698.01 −0.360985 −0.180492 0.983576i \(-0.557769\pi\)
−0.180492 + 0.983576i \(0.557769\pi\)
\(770\) −1420.34 −0.0664745
\(771\) 3463.50 0.161783
\(772\) 2355.05 0.109793
\(773\) 217.026 0.0100981 0.00504907 0.999987i \(-0.498393\pi\)
0.00504907 + 0.999987i \(0.498393\pi\)
\(774\) 738.493 0.0342953
\(775\) 25714.0 1.19184
\(776\) −9525.75 −0.440663
\(777\) 7251.69 0.334817
\(778\) −8522.47 −0.392732
\(779\) −20327.9 −0.934945
\(780\) −4045.28 −0.185698
\(781\) −46364.0 −2.12425
\(782\) 0 0
\(783\) 3179.88 0.145134
\(784\) −12210.0 −0.556213
\(785\) 10006.5 0.454964
\(786\) −695.665 −0.0315694
\(787\) −14718.5 −0.666657 −0.333329 0.942811i \(-0.608172\pi\)
−0.333329 + 0.942811i \(0.608172\pi\)
\(788\) 31525.6 1.42520
\(789\) 23444.9 1.05787
\(790\) 2136.43 0.0962162
\(791\) 2958.92 0.133005
\(792\) −1973.09 −0.0885237
\(793\) −1009.69 −0.0452147
\(794\) 2544.42 0.113725
\(795\) 8249.78 0.368037
\(796\) 6981.17 0.310855
\(797\) 24288.0 1.07945 0.539727 0.841840i \(-0.318527\pi\)
0.539727 + 0.841840i \(0.318527\pi\)
\(798\) −2961.42 −0.131370
\(799\) 0 0
\(800\) 17832.5 0.788093
\(801\) −28.7977 −0.00127031
\(802\) 465.483 0.0204947
\(803\) −38815.3 −1.70581
\(804\) 1661.42 0.0728779
\(805\) −1896.43 −0.0830317
\(806\) −7047.22 −0.307975
\(807\) 4362.14 0.190278
\(808\) −24584.1 −1.07038
\(809\) 29816.7 1.29580 0.647898 0.761727i \(-0.275648\pi\)
0.647898 + 0.761727i \(0.275648\pi\)
\(810\) −3136.86 −0.136072
\(811\) −27414.4 −1.18699 −0.593495 0.804838i \(-0.702252\pi\)
−0.593495 + 0.804838i \(0.702252\pi\)
\(812\) −670.215 −0.0289654
\(813\) 33786.8 1.45751
\(814\) 23996.7 1.03327
\(815\) −8849.76 −0.380360
\(816\) 0 0
\(817\) −47471.3 −2.03282
\(818\) 3818.50 0.163216
\(819\) −217.485 −0.00927904
\(820\) 4863.68 0.207130
\(821\) 36258.7 1.54134 0.770668 0.637236i \(-0.219922\pi\)
0.770668 + 0.637236i \(0.219922\pi\)
\(822\) −4091.44 −0.173607
\(823\) −4167.25 −0.176502 −0.0882511 0.996098i \(-0.528128\pi\)
−0.0882511 + 0.996098i \(0.528128\pi\)
\(824\) 16635.6 0.703312
\(825\) −36799.2 −1.55295
\(826\) 301.603 0.0127048
\(827\) 32608.4 1.37111 0.685553 0.728023i \(-0.259561\pi\)
0.685553 + 0.728023i \(0.259561\pi\)
\(828\) −1215.46 −0.0510147
\(829\) −23614.7 −0.989351 −0.494676 0.869078i \(-0.664713\pi\)
−0.494676 + 0.869078i \(0.664713\pi\)
\(830\) 4505.01 0.188399
\(831\) 16385.9 0.684020
\(832\) 3331.50 0.138821
\(833\) 0 0
\(834\) −4622.58 −0.191927
\(835\) −3554.02 −0.147296
\(836\) 58516.6 2.42086
\(837\) 34970.8 1.44417
\(838\) 17678.6 0.728755
\(839\) 13162.0 0.541600 0.270800 0.962636i \(-0.412712\pi\)
0.270800 + 0.962636i \(0.412712\pi\)
\(840\) 1535.77 0.0630821
\(841\) −23905.2 −0.980164
\(842\) 12238.0 0.500891
\(843\) 41194.9 1.68307
\(844\) 17119.3 0.698190
\(845\) 6301.67 0.256549
\(846\) 791.912 0.0321826
\(847\) −15225.9 −0.617671
\(848\) −14356.6 −0.581378
\(849\) 14853.0 0.600415
\(850\) 0 0
\(851\) 32040.4 1.29064
\(852\) 23129.3 0.930042
\(853\) −27360.7 −1.09826 −0.549129 0.835738i \(-0.685040\pi\)
−0.549129 + 0.835738i \(0.685040\pi\)
\(854\) 176.853 0.00708641
\(855\) −962.992 −0.0385189
\(856\) 12978.7 0.518229
\(857\) −46845.7 −1.86723 −0.933617 0.358272i \(-0.883366\pi\)
−0.933617 + 0.358272i \(0.883366\pi\)
\(858\) 10085.3 0.401288
\(859\) 15314.6 0.608299 0.304149 0.952624i \(-0.401628\pi\)
0.304149 + 0.952624i \(0.401628\pi\)
\(860\) 11358.0 0.450356
\(861\) −3664.30 −0.145039
\(862\) −8494.16 −0.335629
\(863\) −39481.1 −1.55730 −0.778651 0.627458i \(-0.784096\pi\)
−0.778651 + 0.627458i \(0.784096\pi\)
\(864\) 24252.1 0.954944
\(865\) 6273.41 0.246592
\(866\) 404.266 0.0158632
\(867\) 0 0
\(868\) −7370.70 −0.288223
\(869\) 31804.9 1.24155
\(870\) −511.465 −0.0199314
\(871\) 1313.49 0.0510974
\(872\) −6976.95 −0.270951
\(873\) 1076.70 0.0417420
\(874\) −13084.5 −0.506397
\(875\) −4447.40 −0.171828
\(876\) 19363.5 0.746840
\(877\) 30914.9 1.19033 0.595166 0.803603i \(-0.297086\pi\)
0.595166 + 0.803603i \(0.297086\pi\)
\(878\) 4338.53 0.166763
\(879\) −27176.1 −1.04281
\(880\) −11263.4 −0.431465
\(881\) −5477.01 −0.209450 −0.104725 0.994501i \(-0.533396\pi\)
−0.104725 + 0.994501i \(0.533396\pi\)
\(882\) −622.700 −0.0237726
\(883\) −24324.0 −0.927029 −0.463515 0.886089i \(-0.653412\pi\)
−0.463515 + 0.886089i \(0.653412\pi\)
\(884\) 0 0
\(885\) −1374.37 −0.0522023
\(886\) −4225.40 −0.160220
\(887\) 22552.0 0.853688 0.426844 0.904325i \(-0.359625\pi\)
0.426844 + 0.904325i \(0.359625\pi\)
\(888\) −25946.9 −0.980542
\(889\) 2333.80 0.0880463
\(890\) 74.1733 0.00279359
\(891\) −46698.3 −1.75584
\(892\) 29140.2 1.09382
\(893\) −50905.2 −1.90759
\(894\) −14568.4 −0.545011
\(895\) 12288.4 0.458944
\(896\) −6551.09 −0.244260
\(897\) 13465.8 0.501238
\(898\) 3031.80 0.112664
\(899\) 5320.50 0.197384
\(900\) −1310.01 −0.0485188
\(901\) 0 0
\(902\) −12125.6 −0.447603
\(903\) −8557.16 −0.315354
\(904\) −10587.2 −0.389517
\(905\) −17382.1 −0.638455
\(906\) −2187.74 −0.0802239
\(907\) 8057.54 0.294979 0.147490 0.989064i \(-0.452881\pi\)
0.147490 + 0.989064i \(0.452881\pi\)
\(908\) 45588.8 1.66621
\(909\) 2778.75 0.101392
\(910\) 560.169 0.0204059
\(911\) −22191.3 −0.807058 −0.403529 0.914967i \(-0.632217\pi\)
−0.403529 + 0.914967i \(0.632217\pi\)
\(912\) −23484.3 −0.852680
\(913\) 67065.9 2.43106
\(914\) −9423.36 −0.341025
\(915\) −805.901 −0.0291172
\(916\) 23057.4 0.831700
\(917\) −575.225 −0.0207149
\(918\) 0 0
\(919\) 18688.4 0.670810 0.335405 0.942074i \(-0.391127\pi\)
0.335405 + 0.942074i \(0.391127\pi\)
\(920\) 6785.53 0.243165
\(921\) 36882.9 1.31958
\(922\) −11167.5 −0.398896
\(923\) 18285.6 0.652088
\(924\) 10548.2 0.375552
\(925\) 34532.7 1.22749
\(926\) −7335.78 −0.260333
\(927\) −1880.33 −0.0666217
\(928\) 3689.73 0.130519
\(929\) 46.6711 0.00164826 0.000824128 1.00000i \(-0.499738\pi\)
0.000824128 1.00000i \(0.499738\pi\)
\(930\) −5624.84 −0.198329
\(931\) 40028.0 1.40909
\(932\) −13322.2 −0.468222
\(933\) −24955.5 −0.875675
\(934\) −15416.0 −0.540071
\(935\) 0 0
\(936\) 778.170 0.0271745
\(937\) −1778.92 −0.0620222 −0.0310111 0.999519i \(-0.509873\pi\)
−0.0310111 + 0.999519i \(0.509873\pi\)
\(938\) −230.065 −0.00800840
\(939\) 34818.2 1.21006
\(940\) 12179.6 0.422612
\(941\) −47634.0 −1.65018 −0.825092 0.564998i \(-0.808877\pi\)
−0.825092 + 0.564998i \(0.808877\pi\)
\(942\) 12445.2 0.430452
\(943\) −16190.1 −0.559090
\(944\) 2391.74 0.0824625
\(945\) −2779.76 −0.0956883
\(946\) −28316.7 −0.973208
\(947\) −21092.5 −0.723776 −0.361888 0.932222i \(-0.617868\pi\)
−0.361888 + 0.932222i \(0.617868\pi\)
\(948\) −15866.3 −0.543579
\(949\) 15308.4 0.523638
\(950\) −14102.4 −0.481622
\(951\) −38490.5 −1.31245
\(952\) 0 0
\(953\) 45019.9 1.53026 0.765130 0.643876i \(-0.222675\pi\)
0.765130 + 0.643876i \(0.222675\pi\)
\(954\) −732.177 −0.0248481
\(955\) −14589.5 −0.494352
\(956\) 2687.75 0.0909289
\(957\) −7614.15 −0.257190
\(958\) 7673.64 0.258793
\(959\) −3383.09 −0.113916
\(960\) 2659.09 0.0893975
\(961\) 28721.3 0.964092
\(962\) −9464.10 −0.317188
\(963\) −1466.99 −0.0490896
\(964\) 7970.74 0.266307
\(965\) 1486.07 0.0495732
\(966\) −2358.61 −0.0785582
\(967\) −16583.3 −0.551482 −0.275741 0.961232i \(-0.588923\pi\)
−0.275741 + 0.961232i \(0.588923\pi\)
\(968\) 54478.9 1.80890
\(969\) 0 0
\(970\) −2773.23 −0.0917968
\(971\) 19060.7 0.629957 0.314978 0.949099i \(-0.398003\pi\)
0.314978 + 0.949099i \(0.398003\pi\)
\(972\) −3451.94 −0.113911
\(973\) −3822.27 −0.125937
\(974\) 15886.7 0.522632
\(975\) 14513.3 0.476715
\(976\) 1402.46 0.0459957
\(977\) −44082.8 −1.44353 −0.721767 0.692136i \(-0.756670\pi\)
−0.721767 + 0.692136i \(0.756670\pi\)
\(978\) −11006.5 −0.359867
\(979\) 1104.21 0.0360478
\(980\) −9577.14 −0.312174
\(981\) 788.609 0.0256660
\(982\) 10320.8 0.335388
\(983\) −39309.6 −1.27546 −0.637732 0.770258i \(-0.720127\pi\)
−0.637732 + 0.770258i \(0.720127\pi\)
\(984\) 13111.0 0.424761
\(985\) 19893.1 0.643500
\(986\) 0 0
\(987\) −9176.15 −0.295927
\(988\) −23078.4 −0.743141
\(989\) −37808.4 −1.21561
\(990\) −574.425 −0.0184408
\(991\) −24889.9 −0.797834 −0.398917 0.916987i \(-0.630614\pi\)
−0.398917 + 0.916987i \(0.630614\pi\)
\(992\) 40577.9 1.29874
\(993\) 7156.59 0.228709
\(994\) −3202.82 −0.102201
\(995\) 4405.21 0.140356
\(996\) −33456.7 −1.06437
\(997\) 10612.3 0.337105 0.168552 0.985693i \(-0.446091\pi\)
0.168552 + 0.985693i \(0.446091\pi\)
\(998\) 2178.62 0.0691011
\(999\) 46964.2 1.48737
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.1.5 12
17.4 even 4 289.4.b.f.288.16 24
17.13 even 4 289.4.b.f.288.15 24
17.16 even 2 289.4.a.i.1.5 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.5 12 1.1 even 1 trivial
289.4.a.i.1.5 yes 12 17.16 even 2
289.4.b.f.288.15 24 17.13 even 4
289.4.b.f.288.16 24 17.4 even 4