Properties

Label 289.4.a.h.1.4
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 1.4
Root \(2.16473\) 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)
 
\(f(q)\) \(=\) \(q-2.16473 q^{2} -9.14133 q^{3} -3.31395 q^{4} -16.2298 q^{5} +19.7885 q^{6} -12.2246 q^{7} +24.4916 q^{8} +56.5639 q^{9} +O(q^{10})\) \(q-2.16473 q^{2} -9.14133 q^{3} -3.31395 q^{4} -16.2298 q^{5} +19.7885 q^{6} -12.2246 q^{7} +24.4916 q^{8} +56.5639 q^{9} +35.1331 q^{10} +11.1761 q^{11} +30.2939 q^{12} +28.9000 q^{13} +26.4629 q^{14} +148.362 q^{15} -26.5061 q^{16} -122.445 q^{18} -79.5850 q^{19} +53.7848 q^{20} +111.749 q^{21} -24.1932 q^{22} +45.0447 q^{23} -223.886 q^{24} +138.406 q^{25} -62.5606 q^{26} -270.253 q^{27} +40.5117 q^{28} -20.3774 q^{29} -321.163 q^{30} -1.03839 q^{31} -138.555 q^{32} -102.164 q^{33} +198.402 q^{35} -187.450 q^{36} +219.921 q^{37} +172.280 q^{38} -264.184 q^{39} -397.494 q^{40} +310.992 q^{41} -241.906 q^{42} +483.760 q^{43} -37.0371 q^{44} -918.020 q^{45} -97.5095 q^{46} -632.422 q^{47} +242.301 q^{48} -193.560 q^{49} -299.612 q^{50} -95.7732 q^{52} +490.172 q^{53} +585.024 q^{54} -181.386 q^{55} -299.400 q^{56} +727.512 q^{57} +44.1115 q^{58} +147.956 q^{59} -491.665 q^{60} -176.395 q^{61} +2.24783 q^{62} -691.469 q^{63} +511.982 q^{64} -469.041 q^{65} +221.158 q^{66} +809.312 q^{67} -411.768 q^{69} -429.487 q^{70} -714.189 q^{71} +1385.34 q^{72} -780.184 q^{73} -476.070 q^{74} -1265.22 q^{75} +263.741 q^{76} -136.623 q^{77} +571.887 q^{78} +230.265 q^{79} +430.188 q^{80} +943.248 q^{81} -673.213 q^{82} +236.046 q^{83} -370.330 q^{84} -1047.21 q^{86} +186.276 q^{87} +273.721 q^{88} -688.557 q^{89} +1987.26 q^{90} -353.290 q^{91} -149.276 q^{92} +9.49224 q^{93} +1369.02 q^{94} +1291.65 q^{95} +1266.57 q^{96} +1846.11 q^{97} +419.004 q^{98} +632.164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.16473 −0.765347 −0.382673 0.923884i \(-0.624997\pi\)
−0.382673 + 0.923884i \(0.624997\pi\)
\(3\) −9.14133 −1.75925 −0.879625 0.475668i \(-0.842206\pi\)
−0.879625 + 0.475668i \(0.842206\pi\)
\(4\) −3.31395 −0.414244
\(5\) −16.2298 −1.45164 −0.725819 0.687886i \(-0.758539\pi\)
−0.725819 + 0.687886i \(0.758539\pi\)
\(6\) 19.7885 1.34644
\(7\) −12.2246 −0.660065 −0.330032 0.943970i \(-0.607060\pi\)
−0.330032 + 0.943970i \(0.607060\pi\)
\(8\) 24.4916 1.08239
\(9\) 56.5639 2.09496
\(10\) 35.1331 1.11101
\(11\) 11.1761 0.306338 0.153169 0.988200i \(-0.451052\pi\)
0.153169 + 0.988200i \(0.451052\pi\)
\(12\) 30.2939 0.728759
\(13\) 28.9000 0.616570 0.308285 0.951294i \(-0.400245\pi\)
0.308285 + 0.951294i \(0.400245\pi\)
\(14\) 26.4629 0.505178
\(15\) 148.362 2.55379
\(16\) −26.5061 −0.414158
\(17\) 0 0
\(18\) −122.445 −1.60337
\(19\) −79.5850 −0.960950 −0.480475 0.877009i \(-0.659536\pi\)
−0.480475 + 0.877009i \(0.659536\pi\)
\(20\) 53.7848 0.601332
\(21\) 111.749 1.16122
\(22\) −24.1932 −0.234455
\(23\) 45.0447 0.408368 0.204184 0.978933i \(-0.434546\pi\)
0.204184 + 0.978933i \(0.434546\pi\)
\(24\) −223.886 −1.90419
\(25\) 138.406 1.10725
\(26\) −62.5606 −0.471890
\(27\) −270.253 −1.92631
\(28\) 40.5117 0.273428
\(29\) −20.3774 −0.130482 −0.0652411 0.997870i \(-0.520782\pi\)
−0.0652411 + 0.997870i \(0.520782\pi\)
\(30\) −321.163 −1.95454
\(31\) −1.03839 −0.00601613 −0.00300806 0.999995i \(-0.500957\pi\)
−0.00300806 + 0.999995i \(0.500957\pi\)
\(32\) −138.555 −0.765413
\(33\) −102.164 −0.538926
\(34\) 0 0
\(35\) 198.402 0.958175
\(36\) −187.450 −0.867824
\(37\) 219.921 0.977159 0.488579 0.872520i \(-0.337515\pi\)
0.488579 + 0.872520i \(0.337515\pi\)
\(38\) 172.280 0.735460
\(39\) −264.184 −1.08470
\(40\) −397.494 −1.57123
\(41\) 310.992 1.18460 0.592302 0.805716i \(-0.298219\pi\)
0.592302 + 0.805716i \(0.298219\pi\)
\(42\) −241.906 −0.888735
\(43\) 483.760 1.71564 0.857822 0.513947i \(-0.171817\pi\)
0.857822 + 0.513947i \(0.171817\pi\)
\(44\) −37.0371 −0.126899
\(45\) −918.020 −3.04112
\(46\) −97.5095 −0.312543
\(47\) −632.422 −1.96273 −0.981364 0.192156i \(-0.938452\pi\)
−0.981364 + 0.192156i \(0.938452\pi\)
\(48\) 242.301 0.728606
\(49\) −193.560 −0.564315
\(50\) −299.612 −0.847431
\(51\) 0 0
\(52\) −95.7732 −0.255411
\(53\) 490.172 1.27038 0.635192 0.772354i \(-0.280921\pi\)
0.635192 + 0.772354i \(0.280921\pi\)
\(54\) 585.024 1.47429
\(55\) −181.386 −0.444692
\(56\) −299.400 −0.714446
\(57\) 727.512 1.69055
\(58\) 44.1115 0.0998642
\(59\) 147.956 0.326478 0.163239 0.986587i \(-0.447806\pi\)
0.163239 + 0.986587i \(0.447806\pi\)
\(60\) −491.665 −1.05789
\(61\) −176.395 −0.370246 −0.185123 0.982715i \(-0.559268\pi\)
−0.185123 + 0.982715i \(0.559268\pi\)
\(62\) 2.24783 0.00460442
\(63\) −691.469 −1.38281
\(64\) 511.982 0.999964
\(65\) −469.041 −0.895037
\(66\) 221.158 0.412465
\(67\) 809.312 1.47572 0.737860 0.674954i \(-0.235836\pi\)
0.737860 + 0.674954i \(0.235836\pi\)
\(68\) 0 0
\(69\) −411.768 −0.718421
\(70\) −429.487 −0.733336
\(71\) −714.189 −1.19378 −0.596892 0.802322i \(-0.703598\pi\)
−0.596892 + 0.802322i \(0.703598\pi\)
\(72\) 1385.34 2.26756
\(73\) −780.184 −1.25087 −0.625436 0.780276i \(-0.715079\pi\)
−0.625436 + 0.780276i \(0.715079\pi\)
\(74\) −476.070 −0.747865
\(75\) −1265.22 −1.94793
\(76\) 263.741 0.398068
\(77\) −136.623 −0.202203
\(78\) 571.887 0.830172
\(79\) 230.265 0.327935 0.163968 0.986466i \(-0.447571\pi\)
0.163968 + 0.986466i \(0.447571\pi\)
\(80\) 430.188 0.601207
\(81\) 943.248 1.29389
\(82\) −673.213 −0.906633
\(83\) 236.046 0.312161 0.156080 0.987744i \(-0.450114\pi\)
0.156080 + 0.987744i \(0.450114\pi\)
\(84\) −370.330 −0.481028
\(85\) 0 0
\(86\) −1047.21 −1.31306
\(87\) 186.276 0.229551
\(88\) 273.721 0.331577
\(89\) −688.557 −0.820078 −0.410039 0.912068i \(-0.634485\pi\)
−0.410039 + 0.912068i \(0.634485\pi\)
\(90\) 1987.26 2.32751
\(91\) −353.290 −0.406976
\(92\) −149.276 −0.169164
\(93\) 9.49224 0.0105839
\(94\) 1369.02 1.50217
\(95\) 1291.65 1.39495
\(96\) 1266.57 1.34655
\(97\) 1846.11 1.93241 0.966205 0.257775i \(-0.0829893\pi\)
0.966205 + 0.257775i \(0.0829893\pi\)
\(98\) 419.004 0.431896
\(99\) 632.164 0.641766
\(100\) −458.672 −0.458672
\(101\) −735.748 −0.724848 −0.362424 0.932013i \(-0.618051\pi\)
−0.362424 + 0.932013i \(0.618051\pi\)
\(102\) 0 0
\(103\) 387.334 0.370535 0.185268 0.982688i \(-0.440685\pi\)
0.185268 + 0.982688i \(0.440685\pi\)
\(104\) 707.808 0.667368
\(105\) −1813.66 −1.68567
\(106\) −1061.09 −0.972284
\(107\) −793.424 −0.716852 −0.358426 0.933558i \(-0.616686\pi\)
−0.358426 + 0.933558i \(0.616686\pi\)
\(108\) 895.606 0.797961
\(109\) 1709.67 1.50236 0.751178 0.660100i \(-0.229486\pi\)
0.751178 + 0.660100i \(0.229486\pi\)
\(110\) 392.651 0.340344
\(111\) −2010.37 −1.71907
\(112\) 324.025 0.273371
\(113\) −42.1279 −0.0350713 −0.0175357 0.999846i \(-0.505582\pi\)
−0.0175357 + 0.999846i \(0.505582\pi\)
\(114\) −1574.87 −1.29386
\(115\) −731.066 −0.592802
\(116\) 67.5297 0.0540515
\(117\) 1634.70 1.29169
\(118\) −320.284 −0.249869
\(119\) 0 0
\(120\) 3633.63 2.76419
\(121\) −1206.09 −0.906157
\(122\) 381.846 0.283367
\(123\) −2842.88 −2.08401
\(124\) 3.44117 0.00249215
\(125\) −217.583 −0.155690
\(126\) 1496.84 1.05833
\(127\) −1536.78 −1.07376 −0.536878 0.843660i \(-0.680397\pi\)
−0.536878 + 0.843660i \(0.680397\pi\)
\(128\) 0.135867 9.38207e−5 0
\(129\) −4422.21 −3.01825
\(130\) 1015.35 0.685013
\(131\) 264.718 0.176554 0.0882768 0.996096i \(-0.471864\pi\)
0.0882768 + 0.996096i \(0.471864\pi\)
\(132\) 338.568 0.223247
\(133\) 972.892 0.634289
\(134\) −1751.94 −1.12944
\(135\) 4386.15 2.79630
\(136\) 0 0
\(137\) 686.450 0.428083 0.214042 0.976825i \(-0.431337\pi\)
0.214042 + 0.976825i \(0.431337\pi\)
\(138\) 891.366 0.549841
\(139\) 43.2364 0.0263832 0.0131916 0.999913i \(-0.495801\pi\)
0.0131916 + 0.999913i \(0.495801\pi\)
\(140\) −657.496 −0.396918
\(141\) 5781.18 3.45293
\(142\) 1546.02 0.913659
\(143\) 322.989 0.188879
\(144\) −1499.29 −0.867643
\(145\) 330.721 0.189413
\(146\) 1688.89 0.957350
\(147\) 1769.39 0.992770
\(148\) −728.810 −0.404782
\(149\) 335.407 0.184413 0.0922067 0.995740i \(-0.470608\pi\)
0.0922067 + 0.995740i \(0.470608\pi\)
\(150\) 2738.85 1.49084
\(151\) −2432.29 −1.31084 −0.655421 0.755264i \(-0.727509\pi\)
−0.655421 + 0.755264i \(0.727509\pi\)
\(152\) −1949.17 −1.04012
\(153\) 0 0
\(154\) 295.752 0.154756
\(155\) 16.8528 0.00873324
\(156\) 875.494 0.449331
\(157\) 2706.98 1.37605 0.688026 0.725686i \(-0.258477\pi\)
0.688026 + 0.725686i \(0.258477\pi\)
\(158\) −498.462 −0.250984
\(159\) −4480.83 −2.23492
\(160\) 2248.71 1.11110
\(161\) −550.652 −0.269549
\(162\) −2041.87 −0.990277
\(163\) 190.765 0.0916678 0.0458339 0.998949i \(-0.485405\pi\)
0.0458339 + 0.998949i \(0.485405\pi\)
\(164\) −1030.61 −0.490715
\(165\) 1658.11 0.782325
\(166\) −510.974 −0.238911
\(167\) −2757.18 −1.27759 −0.638793 0.769379i \(-0.720566\pi\)
−0.638793 + 0.769379i \(0.720566\pi\)
\(168\) 2736.91 1.25689
\(169\) −1361.79 −0.619841
\(170\) 0 0
\(171\) −4501.63 −2.01315
\(172\) −1603.16 −0.710696
\(173\) −1453.00 −0.638554 −0.319277 0.947661i \(-0.603440\pi\)
−0.319277 + 0.947661i \(0.603440\pi\)
\(174\) −403.238 −0.175686
\(175\) −1691.96 −0.730858
\(176\) −296.235 −0.126872
\(177\) −1352.51 −0.574356
\(178\) 1490.54 0.627644
\(179\) −1171.47 −0.489160 −0.244580 0.969629i \(-0.578650\pi\)
−0.244580 + 0.969629i \(0.578650\pi\)
\(180\) 3042.28 1.25977
\(181\) 2737.41 1.12414 0.562072 0.827089i \(-0.310005\pi\)
0.562072 + 0.827089i \(0.310005\pi\)
\(182\) 764.776 0.311478
\(183\) 1612.48 0.651355
\(184\) 1103.22 0.442012
\(185\) −3569.28 −1.41848
\(186\) −20.5481 −0.00810033
\(187\) 0 0
\(188\) 2095.82 0.813049
\(189\) 3303.73 1.27149
\(190\) −2796.07 −1.06762
\(191\) −1345.56 −0.509744 −0.254872 0.966975i \(-0.582033\pi\)
−0.254872 + 0.966975i \(0.582033\pi\)
\(192\) −4680.19 −1.75919
\(193\) 3787.61 1.41263 0.706317 0.707896i \(-0.250355\pi\)
0.706317 + 0.707896i \(0.250355\pi\)
\(194\) −3996.32 −1.47896
\(195\) 4287.66 1.57459
\(196\) 641.448 0.233764
\(197\) 72.4095 0.0261876 0.0130938 0.999914i \(-0.495832\pi\)
0.0130938 + 0.999914i \(0.495832\pi\)
\(198\) −1368.46 −0.491174
\(199\) 2703.59 0.963077 0.481539 0.876425i \(-0.340078\pi\)
0.481539 + 0.876425i \(0.340078\pi\)
\(200\) 3389.80 1.19847
\(201\) −7398.19 −2.59616
\(202\) 1592.69 0.554760
\(203\) 249.105 0.0861267
\(204\) 0 0
\(205\) −5047.33 −1.71962
\(206\) −838.472 −0.283588
\(207\) 2547.90 0.855514
\(208\) −766.025 −0.255357
\(209\) −889.450 −0.294376
\(210\) 3926.08 1.29012
\(211\) −2338.29 −0.762911 −0.381456 0.924387i \(-0.624577\pi\)
−0.381456 + 0.924387i \(0.624577\pi\)
\(212\) −1624.41 −0.526249
\(213\) 6528.64 2.10016
\(214\) 1717.55 0.548640
\(215\) −7851.33 −2.49049
\(216\) −6618.94 −2.08501
\(217\) 12.6938 0.00397103
\(218\) −3700.97 −1.14982
\(219\) 7131.91 2.20059
\(220\) 601.105 0.184211
\(221\) 0 0
\(222\) 4351.91 1.31568
\(223\) 1737.70 0.521815 0.260908 0.965364i \(-0.415978\pi\)
0.260908 + 0.965364i \(0.415978\pi\)
\(224\) 1693.77 0.505222
\(225\) 7828.80 2.31965
\(226\) 91.1954 0.0268417
\(227\) −4480.83 −1.31015 −0.655073 0.755565i \(-0.727362\pi\)
−0.655073 + 0.755565i \(0.727362\pi\)
\(228\) −2410.94 −0.700301
\(229\) −3917.73 −1.13053 −0.565264 0.824910i \(-0.691226\pi\)
−0.565264 + 0.824910i \(0.691226\pi\)
\(230\) 1582.56 0.453699
\(231\) 1248.92 0.355726
\(232\) −499.075 −0.141232
\(233\) −4166.02 −1.17135 −0.585675 0.810546i \(-0.699171\pi\)
−0.585675 + 0.810546i \(0.699171\pi\)
\(234\) −3538.67 −0.988590
\(235\) 10264.1 2.84917
\(236\) −490.318 −0.135242
\(237\) −2104.93 −0.576920
\(238\) 0 0
\(239\) −1780.06 −0.481768 −0.240884 0.970554i \(-0.577437\pi\)
−0.240884 + 0.970554i \(0.577437\pi\)
\(240\) −3932.49 −1.05767
\(241\) −2469.12 −0.659958 −0.329979 0.943988i \(-0.607042\pi\)
−0.329979 + 0.943988i \(0.607042\pi\)
\(242\) 2610.87 0.693524
\(243\) −1325.70 −0.349975
\(244\) 584.563 0.153372
\(245\) 3141.44 0.819180
\(246\) 6154.06 1.59499
\(247\) −2300.00 −0.592493
\(248\) −25.4318 −0.00651178
\(249\) −2157.77 −0.549169
\(250\) 471.009 0.119157
\(251\) −4824.05 −1.21311 −0.606557 0.795040i \(-0.707450\pi\)
−0.606557 + 0.795040i \(0.707450\pi\)
\(252\) 2291.50 0.572820
\(253\) 503.424 0.125099
\(254\) 3326.71 0.821796
\(255\) 0 0
\(256\) −4096.15 −1.00004
\(257\) 5558.77 1.34921 0.674604 0.738180i \(-0.264314\pi\)
0.674604 + 0.738180i \(0.264314\pi\)
\(258\) 9572.88 2.31000
\(259\) −2688.45 −0.644988
\(260\) 1554.38 0.370764
\(261\) −1152.62 −0.273355
\(262\) −573.043 −0.135125
\(263\) −3172.23 −0.743757 −0.371878 0.928281i \(-0.621286\pi\)
−0.371878 + 0.928281i \(0.621286\pi\)
\(264\) −2502.17 −0.583326
\(265\) −7955.40 −1.84414
\(266\) −2106.05 −0.485451
\(267\) 6294.33 1.44272
\(268\) −2682.02 −0.611309
\(269\) −2849.92 −0.645959 −0.322979 0.946406i \(-0.604684\pi\)
−0.322979 + 0.946406i \(0.604684\pi\)
\(270\) −9494.83 −2.14014
\(271\) −2565.11 −0.574980 −0.287490 0.957784i \(-0.592821\pi\)
−0.287490 + 0.957784i \(0.592821\pi\)
\(272\) 0 0
\(273\) 3229.54 0.715973
\(274\) −1485.98 −0.327632
\(275\) 1546.84 0.339194
\(276\) 1364.58 0.297602
\(277\) −6260.95 −1.35806 −0.679032 0.734108i \(-0.737600\pi\)
−0.679032 + 0.734108i \(0.737600\pi\)
\(278\) −93.5951 −0.0201923
\(279\) −58.7352 −0.0126035
\(280\) 4859.20 1.03712
\(281\) −1807.59 −0.383744 −0.191872 0.981420i \(-0.561456\pi\)
−0.191872 + 0.981420i \(0.561456\pi\)
\(282\) −12514.7 −2.64269
\(283\) 1264.09 0.265521 0.132761 0.991148i \(-0.457616\pi\)
0.132761 + 0.991148i \(0.457616\pi\)
\(284\) 2366.79 0.494518
\(285\) −11807.4 −2.45407
\(286\) −699.184 −0.144558
\(287\) −3801.74 −0.781915
\(288\) −7837.18 −1.60351
\(289\) 0 0
\(290\) −715.921 −0.144967
\(291\) −16875.9 −3.39959
\(292\) 2585.49 0.518166
\(293\) 3708.40 0.739410 0.369705 0.929149i \(-0.379459\pi\)
0.369705 + 0.929149i \(0.379459\pi\)
\(294\) −3830.26 −0.759813
\(295\) −2401.29 −0.473927
\(296\) 5386.24 1.05766
\(297\) −3020.38 −0.590101
\(298\) −726.065 −0.141140
\(299\) 1301.79 0.251788
\(300\) 4192.88 0.806919
\(301\) −5913.76 −1.13244
\(302\) 5265.25 1.00325
\(303\) 6725.71 1.27519
\(304\) 2109.49 0.397985
\(305\) 2862.85 0.537463
\(306\) 0 0
\(307\) 4689.47 0.871799 0.435899 0.899995i \(-0.356430\pi\)
0.435899 + 0.899995i \(0.356430\pi\)
\(308\) 452.763 0.0837615
\(309\) −3540.75 −0.651864
\(310\) −36.4818 −0.00668396
\(311\) 2725.79 0.496995 0.248497 0.968633i \(-0.420063\pi\)
0.248497 + 0.968633i \(0.420063\pi\)
\(312\) −6470.30 −1.17407
\(313\) 1406.42 0.253980 0.126990 0.991904i \(-0.459468\pi\)
0.126990 + 0.991904i \(0.459468\pi\)
\(314\) −5859.87 −1.05316
\(315\) 11222.4 2.00734
\(316\) −763.089 −0.135845
\(317\) 836.717 0.148248 0.0741241 0.997249i \(-0.476384\pi\)
0.0741241 + 0.997249i \(0.476384\pi\)
\(318\) 9699.77 1.71049
\(319\) −227.740 −0.0399717
\(320\) −8309.36 −1.45159
\(321\) 7252.95 1.26112
\(322\) 1192.01 0.206299
\(323\) 0 0
\(324\) −3125.88 −0.535987
\(325\) 3999.94 0.682698
\(326\) −412.954 −0.0701577
\(327\) −15628.7 −2.64302
\(328\) 7616.70 1.28220
\(329\) 7731.09 1.29553
\(330\) −3589.35 −0.598750
\(331\) 2544.99 0.422614 0.211307 0.977420i \(-0.432228\pi\)
0.211307 + 0.977420i \(0.432228\pi\)
\(332\) −782.244 −0.129311
\(333\) 12439.6 2.04711
\(334\) 5968.54 0.977796
\(335\) −13135.0 −2.14221
\(336\) −2962.02 −0.480927
\(337\) 9258.04 1.49649 0.748246 0.663422i \(-0.230896\pi\)
0.748246 + 0.663422i \(0.230896\pi\)
\(338\) 2947.91 0.474393
\(339\) 385.105 0.0616992
\(340\) 0 0
\(341\) −11.6051 −0.00184297
\(342\) 9744.81 1.54076
\(343\) 6559.21 1.03255
\(344\) 11848.1 1.85699
\(345\) 6682.92 1.04289
\(346\) 3145.36 0.488716
\(347\) −11972.3 −1.85217 −0.926087 0.377310i \(-0.876849\pi\)
−0.926087 + 0.377310i \(0.876849\pi\)
\(348\) −617.311 −0.0950901
\(349\) 1887.57 0.289511 0.144755 0.989467i \(-0.453760\pi\)
0.144755 + 0.989467i \(0.453760\pi\)
\(350\) 3662.63 0.559360
\(351\) −7810.31 −1.18770
\(352\) −1548.50 −0.234475
\(353\) 7441.02 1.12194 0.560971 0.827836i \(-0.310428\pi\)
0.560971 + 0.827836i \(0.310428\pi\)
\(354\) 2927.82 0.439581
\(355\) 11591.1 1.73294
\(356\) 2281.85 0.339712
\(357\) 0 0
\(358\) 2535.91 0.374377
\(359\) 11518.8 1.69342 0.846711 0.532052i \(-0.178579\pi\)
0.846711 + 0.532052i \(0.178579\pi\)
\(360\) −22483.8 −3.29167
\(361\) −525.233 −0.0765757
\(362\) −5925.74 −0.860359
\(363\) 11025.3 1.59416
\(364\) 1170.79 0.168588
\(365\) 12662.2 1.81581
\(366\) −3490.58 −0.498513
\(367\) 702.580 0.0999302 0.0499651 0.998751i \(-0.484089\pi\)
0.0499651 + 0.998751i \(0.484089\pi\)
\(368\) −1193.96 −0.169129
\(369\) 17590.9 2.48170
\(370\) 7726.52 1.08563
\(371\) −5992.15 −0.838536
\(372\) −31.4569 −0.00438431
\(373\) 8797.32 1.22120 0.610600 0.791939i \(-0.290928\pi\)
0.610600 + 0.791939i \(0.290928\pi\)
\(374\) 0 0
\(375\) 1989.00 0.273897
\(376\) −15489.0 −2.12443
\(377\) −588.906 −0.0804515
\(378\) −7151.67 −0.973128
\(379\) 3113.75 0.422012 0.211006 0.977485i \(-0.432326\pi\)
0.211006 + 0.977485i \(0.432326\pi\)
\(380\) −4280.46 −0.577850
\(381\) 14048.2 1.88901
\(382\) 2912.77 0.390131
\(383\) −9735.60 −1.29887 −0.649434 0.760418i \(-0.724994\pi\)
−0.649434 + 0.760418i \(0.724994\pi\)
\(384\) −1.24200 −0.000165054 0
\(385\) 2217.37 0.293526
\(386\) −8199.15 −1.08115
\(387\) 27363.3 3.59420
\(388\) −6117.91 −0.800490
\(389\) −1772.22 −0.230990 −0.115495 0.993308i \(-0.536845\pi\)
−0.115495 + 0.993308i \(0.536845\pi\)
\(390\) −9281.61 −1.20511
\(391\) 0 0
\(392\) −4740.60 −0.610807
\(393\) −2419.88 −0.310602
\(394\) −156.747 −0.0200426
\(395\) −3737.16 −0.476043
\(396\) −2094.96 −0.265848
\(397\) −1201.80 −0.151931 −0.0759653 0.997110i \(-0.524204\pi\)
−0.0759653 + 0.997110i \(0.524204\pi\)
\(398\) −5852.54 −0.737088
\(399\) −8893.53 −1.11587
\(400\) −3668.61 −0.458576
\(401\) 13633.2 1.69778 0.848892 0.528566i \(-0.177270\pi\)
0.848892 + 0.528566i \(0.177270\pi\)
\(402\) 16015.1 1.98696
\(403\) −30.0094 −0.00370937
\(404\) 2438.23 0.300264
\(405\) −15308.7 −1.87826
\(406\) −539.244 −0.0659168
\(407\) 2457.87 0.299341
\(408\) 0 0
\(409\) 7345.95 0.888103 0.444051 0.896001i \(-0.353541\pi\)
0.444051 + 0.896001i \(0.353541\pi\)
\(410\) 10926.1 1.31610
\(411\) −6275.07 −0.753105
\(412\) −1283.61 −0.153492
\(413\) −1808.69 −0.215496
\(414\) −5515.51 −0.654765
\(415\) −3830.97 −0.453145
\(416\) −4004.23 −0.471931
\(417\) −395.238 −0.0464146
\(418\) 1925.42 0.225300
\(419\) 3293.55 0.384011 0.192005 0.981394i \(-0.438501\pi\)
0.192005 + 0.981394i \(0.438501\pi\)
\(420\) 6010.39 0.698278
\(421\) −9775.57 −1.13167 −0.565834 0.824519i \(-0.691446\pi\)
−0.565834 + 0.824519i \(0.691446\pi\)
\(422\) 5061.75 0.583892
\(423\) −35772.2 −4.11184
\(424\) 12005.1 1.37505
\(425\) 0 0
\(426\) −14132.7 −1.60735
\(427\) 2156.35 0.244386
\(428\) 2629.37 0.296952
\(429\) −2952.55 −0.332286
\(430\) 16996.0 1.90609
\(431\) −7842.98 −0.876527 −0.438263 0.898847i \(-0.644406\pi\)
−0.438263 + 0.898847i \(0.644406\pi\)
\(432\) 7163.35 0.797794
\(433\) −5178.49 −0.574740 −0.287370 0.957820i \(-0.592781\pi\)
−0.287370 + 0.957820i \(0.592781\pi\)
\(434\) −27.4787 −0.00303922
\(435\) −3023.23 −0.333225
\(436\) −5665.77 −0.622342
\(437\) −3584.88 −0.392421
\(438\) −15438.7 −1.68422
\(439\) −5661.88 −0.615550 −0.307775 0.951459i \(-0.599584\pi\)
−0.307775 + 0.951459i \(0.599584\pi\)
\(440\) −4442.44 −0.481329
\(441\) −10948.5 −1.18222
\(442\) 0 0
\(443\) −3020.29 −0.323924 −0.161962 0.986797i \(-0.551782\pi\)
−0.161962 + 0.986797i \(0.551782\pi\)
\(444\) 6662.29 0.712113
\(445\) 11175.1 1.19046
\(446\) −3761.64 −0.399370
\(447\) −3066.06 −0.324429
\(448\) −6258.76 −0.660041
\(449\) 13308.6 1.39883 0.699413 0.714718i \(-0.253445\pi\)
0.699413 + 0.714718i \(0.253445\pi\)
\(450\) −16947.2 −1.77533
\(451\) 3475.68 0.362890
\(452\) 139.610 0.0145281
\(453\) 22234.4 2.30610
\(454\) 9699.78 1.00272
\(455\) 5733.82 0.590782
\(456\) 17818.0 1.82983
\(457\) 7260.23 0.743150 0.371575 0.928403i \(-0.378818\pi\)
0.371575 + 0.928403i \(0.378818\pi\)
\(458\) 8480.83 0.865247
\(459\) 0 0
\(460\) 2422.72 0.245565
\(461\) −2580.20 −0.260677 −0.130338 0.991470i \(-0.541606\pi\)
−0.130338 + 0.991470i \(0.541606\pi\)
\(462\) −2703.56 −0.272254
\(463\) 14392.8 1.44469 0.722345 0.691533i \(-0.243064\pi\)
0.722345 + 0.691533i \(0.243064\pi\)
\(464\) 540.125 0.0540402
\(465\) −154.057 −0.0153639
\(466\) 9018.29 0.896490
\(467\) −11696.0 −1.15894 −0.579471 0.814993i \(-0.696741\pi\)
−0.579471 + 0.814993i \(0.696741\pi\)
\(468\) −5417.30 −0.535075
\(469\) −9893.50 −0.974071
\(470\) −22218.9 −2.18060
\(471\) −24745.4 −2.42082
\(472\) 3623.68 0.353375
\(473\) 5406.55 0.525568
\(474\) 4556.61 0.441544
\(475\) −11015.1 −1.06401
\(476\) 0 0
\(477\) 27726.0 2.66140
\(478\) 3853.35 0.368720
\(479\) −13997.5 −1.33520 −0.667599 0.744521i \(-0.732678\pi\)
−0.667599 + 0.744521i \(0.732678\pi\)
\(480\) −20556.2 −1.95471
\(481\) 6355.73 0.602487
\(482\) 5344.97 0.505097
\(483\) 5033.69 0.474205
\(484\) 3996.94 0.375370
\(485\) −29961.9 −2.80516
\(486\) 2869.78 0.267852
\(487\) −2888.42 −0.268761 −0.134381 0.990930i \(-0.542905\pi\)
−0.134381 + 0.990930i \(0.542905\pi\)
\(488\) −4320.19 −0.400750
\(489\) −1743.84 −0.161267
\(490\) −6800.36 −0.626957
\(491\) −9420.11 −0.865832 −0.432916 0.901434i \(-0.642515\pi\)
−0.432916 + 0.901434i \(0.642515\pi\)
\(492\) 9421.17 0.863291
\(493\) 0 0
\(494\) 4978.88 0.453463
\(495\) −10259.9 −0.931612
\(496\) 27.5236 0.00249162
\(497\) 8730.65 0.787975
\(498\) 4670.98 0.420305
\(499\) −713.936 −0.0640484 −0.0320242 0.999487i \(-0.510195\pi\)
−0.0320242 + 0.999487i \(0.510195\pi\)
\(500\) 721.061 0.0644937
\(501\) 25204.3 2.24759
\(502\) 10442.8 0.928453
\(503\) −17604.4 −1.56052 −0.780260 0.625456i \(-0.784913\pi\)
−0.780260 + 0.625456i \(0.784913\pi\)
\(504\) −16935.2 −1.49673
\(505\) 11941.0 1.05222
\(506\) −1089.78 −0.0957440
\(507\) 12448.6 1.09046
\(508\) 5092.81 0.444797
\(509\) 12291.2 1.07033 0.535165 0.844748i \(-0.320249\pi\)
0.535165 + 0.844748i \(0.320249\pi\)
\(510\) 0 0
\(511\) 9537.41 0.825656
\(512\) 8865.96 0.765280
\(513\) 21508.1 1.85108
\(514\) −12033.2 −1.03261
\(515\) −6286.35 −0.537883
\(516\) 14655.0 1.25029
\(517\) −7068.02 −0.601259
\(518\) 5819.75 0.493639
\(519\) 13282.4 1.12338
\(520\) −11487.6 −0.968776
\(521\) −8736.73 −0.734670 −0.367335 0.930089i \(-0.619730\pi\)
−0.367335 + 0.930089i \(0.619730\pi\)
\(522\) 2495.12 0.209211
\(523\) −2513.00 −0.210107 −0.105053 0.994467i \(-0.533501\pi\)
−0.105053 + 0.994467i \(0.533501\pi\)
\(524\) −877.264 −0.0731363
\(525\) 15466.8 1.28576
\(526\) 6867.01 0.569232
\(527\) 0 0
\(528\) 2707.98 0.223200
\(529\) −10138.0 −0.833236
\(530\) 17221.3 1.41140
\(531\) 8368.95 0.683957
\(532\) −3224.12 −0.262751
\(533\) 8987.66 0.730392
\(534\) −13625.5 −1.10418
\(535\) 12877.1 1.04061
\(536\) 19821.4 1.59730
\(537\) 10708.8 0.860554
\(538\) 6169.31 0.494383
\(539\) −2163.25 −0.172871
\(540\) −14535.5 −1.15835
\(541\) −9702.15 −0.771031 −0.385516 0.922701i \(-0.625976\pi\)
−0.385516 + 0.922701i \(0.625976\pi\)
\(542\) 5552.77 0.440059
\(543\) −25023.5 −1.97765
\(544\) 0 0
\(545\) −27747.6 −2.18088
\(546\) −6991.07 −0.547968
\(547\) −16198.6 −1.26618 −0.633092 0.774077i \(-0.718215\pi\)
−0.633092 + 0.774077i \(0.718215\pi\)
\(548\) −2274.86 −0.177331
\(549\) −9977.56 −0.775650
\(550\) −3348.50 −0.259601
\(551\) 1621.73 0.125387
\(552\) −10084.9 −0.777610
\(553\) −2814.90 −0.216459
\(554\) 13553.2 1.03939
\(555\) 32628.0 2.49546
\(556\) −143.283 −0.0109291
\(557\) −9873.27 −0.751066 −0.375533 0.926809i \(-0.622540\pi\)
−0.375533 + 0.926809i \(0.622540\pi\)
\(558\) 127.146 0.00964608
\(559\) 13980.7 1.05782
\(560\) −5258.87 −0.396835
\(561\) 0 0
\(562\) 3912.95 0.293697
\(563\) 3283.56 0.245801 0.122900 0.992419i \(-0.460780\pi\)
0.122900 + 0.992419i \(0.460780\pi\)
\(564\) −19158.6 −1.43036
\(565\) 683.727 0.0509108
\(566\) −2736.42 −0.203216
\(567\) −11530.8 −0.854053
\(568\) −17491.7 −1.29214
\(569\) −15065.3 −1.10996 −0.554982 0.831862i \(-0.687275\pi\)
−0.554982 + 0.831862i \(0.687275\pi\)
\(570\) 25559.8 1.87821
\(571\) 2567.87 0.188200 0.0941000 0.995563i \(-0.470003\pi\)
0.0941000 + 0.995563i \(0.470003\pi\)
\(572\) −1070.37 −0.0782421
\(573\) 12300.2 0.896767
\(574\) 8229.73 0.598436
\(575\) 6234.47 0.452166
\(576\) 28959.7 2.09488
\(577\) −23042.3 −1.66250 −0.831249 0.555900i \(-0.812374\pi\)
−0.831249 + 0.555900i \(0.812374\pi\)
\(578\) 0 0
\(579\) −34623.8 −2.48517
\(580\) −1095.99 −0.0784632
\(581\) −2885.56 −0.206046
\(582\) 36531.7 2.60187
\(583\) 5478.22 0.389167
\(584\) −19108.0 −1.35393
\(585\) −26530.8 −1.87506
\(586\) −8027.68 −0.565905
\(587\) −4094.68 −0.287914 −0.143957 0.989584i \(-0.545983\pi\)
−0.143957 + 0.989584i \(0.545983\pi\)
\(588\) −5863.69 −0.411249
\(589\) 82.6401 0.00578120
\(590\) 5198.14 0.362719
\(591\) −661.919 −0.0460706
\(592\) −5829.26 −0.404698
\(593\) −25698.4 −1.77961 −0.889803 0.456344i \(-0.849159\pi\)
−0.889803 + 0.456344i \(0.849159\pi\)
\(594\) 6538.30 0.451632
\(595\) 0 0
\(596\) −1111.52 −0.0763922
\(597\) −24714.4 −1.69429
\(598\) −2818.02 −0.192705
\(599\) 1085.55 0.0740472 0.0370236 0.999314i \(-0.488212\pi\)
0.0370236 + 0.999314i \(0.488212\pi\)
\(600\) −30987.3 −2.10842
\(601\) 11163.9 0.757713 0.378857 0.925455i \(-0.376317\pi\)
0.378857 + 0.925455i \(0.376317\pi\)
\(602\) 12801.7 0.866706
\(603\) 45777.8 3.09157
\(604\) 8060.50 0.543008
\(605\) 19574.7 1.31541
\(606\) −14559.3 −0.975961
\(607\) 167.486 0.0111994 0.00559971 0.999984i \(-0.498218\pi\)
0.00559971 + 0.999984i \(0.498218\pi\)
\(608\) 11026.9 0.735524
\(609\) −2277.15 −0.151518
\(610\) −6197.29 −0.411346
\(611\) −18277.0 −1.21016
\(612\) 0 0
\(613\) −6533.58 −0.430487 −0.215244 0.976560i \(-0.569055\pi\)
−0.215244 + 0.976560i \(0.569055\pi\)
\(614\) −10151.4 −0.667228
\(615\) 46139.3 3.02523
\(616\) −3346.12 −0.218862
\(617\) −9073.82 −0.592056 −0.296028 0.955179i \(-0.595662\pi\)
−0.296028 + 0.955179i \(0.595662\pi\)
\(618\) 7664.75 0.498902
\(619\) −26617.2 −1.72833 −0.864163 0.503212i \(-0.832151\pi\)
−0.864163 + 0.503212i \(0.832151\pi\)
\(620\) −55.8495 −0.00361769
\(621\) −12173.5 −0.786641
\(622\) −5900.60 −0.380374
\(623\) 8417.32 0.541304
\(624\) 7002.49 0.449237
\(625\) −13769.5 −0.881246
\(626\) −3044.52 −0.194383
\(627\) 8130.76 0.517881
\(628\) −8970.79 −0.570022
\(629\) 0 0
\(630\) −24293.5 −1.53631
\(631\) 5977.98 0.377147 0.188573 0.982059i \(-0.439614\pi\)
0.188573 + 0.982059i \(0.439614\pi\)
\(632\) 5639.58 0.354953
\(633\) 21375.0 1.34215
\(634\) −1811.26 −0.113461
\(635\) 24941.6 1.55870
\(636\) 14849.2 0.925803
\(637\) −5593.88 −0.347940
\(638\) 492.995 0.0305922
\(639\) −40397.3 −2.50093
\(640\) −2.20509 −0.000136194 0
\(641\) 7927.25 0.488467 0.244234 0.969716i \(-0.421464\pi\)
0.244234 + 0.969716i \(0.421464\pi\)
\(642\) −15700.7 −0.965195
\(643\) 9197.33 0.564086 0.282043 0.959402i \(-0.408988\pi\)
0.282043 + 0.959402i \(0.408988\pi\)
\(644\) 1824.83 0.111659
\(645\) 71771.5 4.38140
\(646\) 0 0
\(647\) 19035.8 1.15669 0.578343 0.815794i \(-0.303700\pi\)
0.578343 + 0.815794i \(0.303700\pi\)
\(648\) 23101.7 1.40049
\(649\) 1653.57 0.100013
\(650\) −8658.79 −0.522501
\(651\) −116.039 −0.00698604
\(652\) −632.186 −0.0379729
\(653\) −19349.6 −1.15958 −0.579792 0.814764i \(-0.696866\pi\)
−0.579792 + 0.814764i \(0.696866\pi\)
\(654\) 33831.8 2.02283
\(655\) −4296.32 −0.256292
\(656\) −8243.17 −0.490613
\(657\) −44130.2 −2.62052
\(658\) −16735.7 −0.991528
\(659\) 16666.8 0.985201 0.492600 0.870256i \(-0.336046\pi\)
0.492600 + 0.870256i \(0.336046\pi\)
\(660\) −5494.90 −0.324074
\(661\) −6024.30 −0.354490 −0.177245 0.984167i \(-0.556719\pi\)
−0.177245 + 0.984167i \(0.556719\pi\)
\(662\) −5509.21 −0.323446
\(663\) 0 0
\(664\) 5781.14 0.337879
\(665\) −15789.8 −0.920758
\(666\) −26928.4 −1.56675
\(667\) −917.893 −0.0532848
\(668\) 9137.16 0.529232
\(669\) −15884.9 −0.918003
\(670\) 28433.7 1.63953
\(671\) −1971.40 −0.113421
\(672\) −15483.3 −0.888812
\(673\) 27296.1 1.56343 0.781714 0.623637i \(-0.214346\pi\)
0.781714 + 0.623637i \(0.214346\pi\)
\(674\) −20041.1 −1.14534
\(675\) −37404.8 −2.13290
\(676\) 4512.91 0.256766
\(677\) −13081.5 −0.742632 −0.371316 0.928507i \(-0.621093\pi\)
−0.371316 + 0.928507i \(0.621093\pi\)
\(678\) −833.647 −0.0472213
\(679\) −22567.9 −1.27552
\(680\) 0 0
\(681\) 40960.8 2.30487
\(682\) 25.1220 0.00141051
\(683\) 15698.0 0.879452 0.439726 0.898132i \(-0.355075\pi\)
0.439726 + 0.898132i \(0.355075\pi\)
\(684\) 14918.2 0.833936
\(685\) −11140.9 −0.621422
\(686\) −14198.9 −0.790258
\(687\) 35813.3 1.98888
\(688\) −12822.6 −0.710547
\(689\) 14166.0 0.783281
\(690\) −14466.7 −0.798170
\(691\) −13621.7 −0.749919 −0.374959 0.927041i \(-0.622343\pi\)
−0.374959 + 0.927041i \(0.622343\pi\)
\(692\) 4815.19 0.264517
\(693\) −7727.93 −0.423607
\(694\) 25916.7 1.41756
\(695\) −701.718 −0.0382988
\(696\) 4562.21 0.248463
\(697\) 0 0
\(698\) −4086.08 −0.221576
\(699\) 38082.9 2.06070
\(700\) 5607.07 0.302753
\(701\) 5733.01 0.308892 0.154446 0.988001i \(-0.450641\pi\)
0.154446 + 0.988001i \(0.450641\pi\)
\(702\) 16907.2 0.909004
\(703\) −17502.4 −0.939000
\(704\) 5721.96 0.306327
\(705\) −93827.4 −5.01240
\(706\) −16107.8 −0.858674
\(707\) 8994.20 0.478447
\(708\) 4482.16 0.237924
\(709\) −25474.5 −1.34939 −0.674694 0.738097i \(-0.735725\pi\)
−0.674694 + 0.738097i \(0.735725\pi\)
\(710\) −25091.7 −1.32630
\(711\) 13024.7 0.687011
\(712\) −16863.9 −0.887642
\(713\) −46.7739 −0.00245679
\(714\) 0 0
\(715\) −5242.05 −0.274184
\(716\) 3882.19 0.202632
\(717\) 16272.1 0.847551
\(718\) −24935.1 −1.29606
\(719\) −15508.0 −0.804380 −0.402190 0.915556i \(-0.631751\pi\)
−0.402190 + 0.915556i \(0.631751\pi\)
\(720\) 24333.1 1.25950
\(721\) −4734.99 −0.244577
\(722\) 1136.99 0.0586070
\(723\) 22571.0 1.16103
\(724\) −9071.64 −0.465670
\(725\) −2820.36 −0.144477
\(726\) −23866.8 −1.22008
\(727\) −32127.0 −1.63896 −0.819481 0.573106i \(-0.805738\pi\)
−0.819481 + 0.573106i \(0.805738\pi\)
\(728\) −8652.65 −0.440506
\(729\) −13349.0 −0.678200
\(730\) −27410.3 −1.38973
\(731\) 0 0
\(732\) −5343.68 −0.269820
\(733\) 1723.27 0.0868353 0.0434177 0.999057i \(-0.486175\pi\)
0.0434177 + 0.999057i \(0.486175\pi\)
\(734\) −1520.89 −0.0764812
\(735\) −28716.9 −1.44114
\(736\) −6241.15 −0.312570
\(737\) 9044.96 0.452070
\(738\) −38079.5 −1.89936
\(739\) 22411.5 1.11559 0.557796 0.829978i \(-0.311647\pi\)
0.557796 + 0.829978i \(0.311647\pi\)
\(740\) 11828.4 0.587597
\(741\) 21025.1 1.04234
\(742\) 12971.4 0.641771
\(743\) 23971.3 1.18361 0.591804 0.806082i \(-0.298416\pi\)
0.591804 + 0.806082i \(0.298416\pi\)
\(744\) 232.481 0.0114558
\(745\) −5443.59 −0.267701
\(746\) −19043.8 −0.934642
\(747\) 13351.7 0.653964
\(748\) 0 0
\(749\) 9699.26 0.473169
\(750\) −4305.64 −0.209627
\(751\) −26268.1 −1.27635 −0.638175 0.769892i \(-0.720310\pi\)
−0.638175 + 0.769892i \(0.720310\pi\)
\(752\) 16763.0 0.812879
\(753\) 44098.3 2.13417
\(754\) 1274.82 0.0615733
\(755\) 39475.6 1.90287
\(756\) −10948.4 −0.526706
\(757\) −345.842 −0.0166048 −0.00830239 0.999966i \(-0.502643\pi\)
−0.00830239 + 0.999966i \(0.502643\pi\)
\(758\) −6740.42 −0.322986
\(759\) −4601.97 −0.220080
\(760\) 31634.6 1.50988
\(761\) 28929.2 1.37803 0.689015 0.724747i \(-0.258043\pi\)
0.689015 + 0.724747i \(0.258043\pi\)
\(762\) −30410.5 −1.44574
\(763\) −20900.0 −0.991652
\(764\) 4459.11 0.211159
\(765\) 0 0
\(766\) 21074.9 0.994084
\(767\) 4275.92 0.201297
\(768\) 37444.2 1.75931
\(769\) −29320.3 −1.37492 −0.687462 0.726221i \(-0.741275\pi\)
−0.687462 + 0.726221i \(0.741275\pi\)
\(770\) −4799.99 −0.224649
\(771\) −50814.6 −2.37359
\(772\) −12552.0 −0.585175
\(773\) 25830.3 1.20188 0.600938 0.799296i \(-0.294794\pi\)
0.600938 + 0.799296i \(0.294794\pi\)
\(774\) −59234.2 −2.75081
\(775\) −143.720 −0.00666137
\(776\) 45214.2 2.09162
\(777\) 24576.0 1.13469
\(778\) 3836.37 0.176787
\(779\) −24750.3 −1.13834
\(780\) −14209.1 −0.652266
\(781\) −7981.85 −0.365702
\(782\) 0 0
\(783\) 5507.05 0.251349
\(784\) 5130.51 0.233715
\(785\) −43933.7 −1.99753
\(786\) 5238.37 0.237718
\(787\) −13639.9 −0.617801 −0.308900 0.951094i \(-0.599961\pi\)
−0.308900 + 0.951094i \(0.599961\pi\)
\(788\) −239.962 −0.0108481
\(789\) 28998.4 1.30845
\(790\) 8089.94 0.364338
\(791\) 514.995 0.0231493
\(792\) 15482.7 0.694640
\(793\) −5097.80 −0.228283
\(794\) 2601.56 0.116280
\(795\) 72722.9 3.24430
\(796\) −8959.57 −0.398949
\(797\) 35932.1 1.59697 0.798483 0.602017i \(-0.205636\pi\)
0.798483 + 0.602017i \(0.205636\pi\)
\(798\) 19252.1 0.854030
\(799\) 0 0
\(800\) −19176.8 −0.847505
\(801\) −38947.5 −1.71803
\(802\) −29512.3 −1.29939
\(803\) −8719.42 −0.383190
\(804\) 24517.3 1.07544
\(805\) 8936.97 0.391288
\(806\) 64.9622 0.00283895
\(807\) 26052.1 1.13640
\(808\) −18019.7 −0.784566
\(809\) −19296.4 −0.838598 −0.419299 0.907848i \(-0.637724\pi\)
−0.419299 + 0.907848i \(0.637724\pi\)
\(810\) 33139.2 1.43752
\(811\) 5464.45 0.236600 0.118300 0.992978i \(-0.462256\pi\)
0.118300 + 0.992978i \(0.462256\pi\)
\(812\) −825.522 −0.0356775
\(813\) 23448.6 1.01153
\(814\) −5320.61 −0.229100
\(815\) −3096.08 −0.133068
\(816\) 0 0
\(817\) −38500.0 −1.64865
\(818\) −15902.0 −0.679707
\(819\) −19983.4 −0.852598
\(820\) 16726.6 0.712341
\(821\) −16693.5 −0.709631 −0.354816 0.934936i \(-0.615456\pi\)
−0.354816 + 0.934936i \(0.615456\pi\)
\(822\) 13583.8 0.576387
\(823\) 5833.41 0.247072 0.123536 0.992340i \(-0.460577\pi\)
0.123536 + 0.992340i \(0.460577\pi\)
\(824\) 9486.44 0.401063
\(825\) −14140.2 −0.596726
\(826\) 3915.33 0.164930
\(827\) 11048.3 0.464556 0.232278 0.972649i \(-0.425382\pi\)
0.232278 + 0.972649i \(0.425382\pi\)
\(828\) −8443.63 −0.354392
\(829\) −26287.1 −1.10131 −0.550657 0.834732i \(-0.685623\pi\)
−0.550657 + 0.834732i \(0.685623\pi\)
\(830\) 8293.01 0.346813
\(831\) 57233.4 2.38917
\(832\) 14796.3 0.616548
\(833\) 0 0
\(834\) 855.583 0.0355233
\(835\) 44748.4 1.85459
\(836\) 2947.60 0.121943
\(837\) 280.628 0.0115889
\(838\) −7129.64 −0.293901
\(839\) 8311.95 0.342027 0.171013 0.985269i \(-0.445296\pi\)
0.171013 + 0.985269i \(0.445296\pi\)
\(840\) −44419.5 −1.82455
\(841\) −23973.8 −0.982974
\(842\) 21161.5 0.866119
\(843\) 16523.8 0.675101
\(844\) 7748.97 0.316032
\(845\) 22101.6 0.899785
\(846\) 77437.2 3.14698
\(847\) 14744.0 0.598122
\(848\) −12992.5 −0.526139
\(849\) −11555.5 −0.467118
\(850\) 0 0
\(851\) 9906.29 0.399040
\(852\) −21635.6 −0.869981
\(853\) 3875.16 0.155549 0.0777743 0.996971i \(-0.475219\pi\)
0.0777743 + 0.996971i \(0.475219\pi\)
\(854\) −4667.91 −0.187040
\(855\) 73060.6 2.92236
\(856\) −19432.2 −0.775912
\(857\) −31317.9 −1.24831 −0.624154 0.781301i \(-0.714556\pi\)
−0.624154 + 0.781301i \(0.714556\pi\)
\(858\) 6391.47 0.254314
\(859\) 35801.6 1.42204 0.711021 0.703171i \(-0.248233\pi\)
0.711021 + 0.703171i \(0.248233\pi\)
\(860\) 26018.9 1.03167
\(861\) 34753.0 1.37558
\(862\) 16977.9 0.670847
\(863\) −5935.67 −0.234128 −0.117064 0.993124i \(-0.537348\pi\)
−0.117064 + 0.993124i \(0.537348\pi\)
\(864\) 37444.8 1.47442
\(865\) 23582.0 0.926950
\(866\) 11210.0 0.439875
\(867\) 0 0
\(868\) −42.0668 −0.00164498
\(869\) 2573.47 0.100459
\(870\) 6544.46 0.255032
\(871\) 23389.1 0.909885
\(872\) 41872.6 1.62613
\(873\) 104423. 4.04832
\(874\) 7760.29 0.300338
\(875\) 2659.86 0.102765
\(876\) −23634.8 −0.911583
\(877\) 43699.3 1.68258 0.841290 0.540585i \(-0.181797\pi\)
0.841290 + 0.540585i \(0.181797\pi\)
\(878\) 12256.4 0.471110
\(879\) −33899.7 −1.30081
\(880\) 4807.83 0.184173
\(881\) 30329.5 1.15985 0.579924 0.814671i \(-0.303082\pi\)
0.579924 + 0.814671i \(0.303082\pi\)
\(882\) 23700.5 0.904805
\(883\) 35558.7 1.35521 0.677603 0.735428i \(-0.263019\pi\)
0.677603 + 0.735428i \(0.263019\pi\)
\(884\) 0 0
\(885\) 21951.0 0.833757
\(886\) 6538.11 0.247914
\(887\) −23689.6 −0.896752 −0.448376 0.893845i \(-0.647997\pi\)
−0.448376 + 0.893845i \(0.647997\pi\)
\(888\) −49237.3 −1.86069
\(889\) 18786.5 0.708749
\(890\) −24191.1 −0.911111
\(891\) 10541.8 0.396369
\(892\) −5758.65 −0.216159
\(893\) 50331.3 1.88608
\(894\) 6637.19 0.248301
\(895\) 19012.7 0.710083
\(896\) −1.66091 −6.19277e−5 0
\(897\) −11900.1 −0.442957
\(898\) −28809.6 −1.07059
\(899\) 21.1596 0.000784998 0
\(900\) −25944.3 −0.960900
\(901\) 0 0
\(902\) −7523.90 −0.277737
\(903\) 54059.6 1.99224
\(904\) −1031.78 −0.0379608
\(905\) −44427.6 −1.63185
\(906\) −48131.4 −1.76496
\(907\) −12176.0 −0.445752 −0.222876 0.974847i \(-0.571544\pi\)
−0.222876 + 0.974847i \(0.571544\pi\)
\(908\) 14849.3 0.542721
\(909\) −41616.8 −1.51853
\(910\) −12412.2 −0.452153
\(911\) −34830.5 −1.26673 −0.633363 0.773855i \(-0.718326\pi\)
−0.633363 + 0.773855i \(0.718326\pi\)
\(912\) −19283.5 −0.700154
\(913\) 2638.07 0.0956269
\(914\) −15716.4 −0.568767
\(915\) −26170.2 −0.945531
\(916\) 12983.2 0.468315
\(917\) −3236.07 −0.116537
\(918\) 0 0
\(919\) −15886.7 −0.570244 −0.285122 0.958491i \(-0.592034\pi\)
−0.285122 + 0.958491i \(0.592034\pi\)
\(920\) −17905.0 −0.641642
\(921\) −42868.0 −1.53371
\(922\) 5585.44 0.199508
\(923\) −20640.1 −0.736052
\(924\) −4138.85 −0.147357
\(925\) 30438.5 1.08196
\(926\) −31156.6 −1.10569
\(927\) 21909.1 0.776256
\(928\) 2823.38 0.0998728
\(929\) 14115.7 0.498514 0.249257 0.968437i \(-0.419814\pi\)
0.249257 + 0.968437i \(0.419814\pi\)
\(930\) 333.492 0.0117587
\(931\) 15404.5 0.542278
\(932\) 13806.0 0.485225
\(933\) −24917.4 −0.874338
\(934\) 25318.6 0.886993
\(935\) 0 0
\(936\) 40036.4 1.39811
\(937\) −39312.3 −1.37063 −0.685314 0.728248i \(-0.740335\pi\)
−0.685314 + 0.728248i \(0.740335\pi\)
\(938\) 21416.7 0.745502
\(939\) −12856.6 −0.446814
\(940\) −34014.7 −1.18025
\(941\) −30478.0 −1.05585 −0.527924 0.849291i \(-0.677030\pi\)
−0.527924 + 0.849291i \(0.677030\pi\)
\(942\) 53567.0 1.85277
\(943\) 14008.5 0.483754
\(944\) −3921.73 −0.135213
\(945\) −53618.8 −1.84574
\(946\) −11703.7 −0.402242
\(947\) −45331.1 −1.55551 −0.777753 0.628570i \(-0.783640\pi\)
−0.777753 + 0.628570i \(0.783640\pi\)
\(948\) 6975.65 0.238986
\(949\) −22547.3 −0.771250
\(950\) 23844.6 0.814339
\(951\) −7648.70 −0.260806
\(952\) 0 0
\(953\) 33782.9 1.14830 0.574152 0.818748i \(-0.305332\pi\)
0.574152 + 0.818748i \(0.305332\pi\)
\(954\) −60019.3 −2.03690
\(955\) 21838.1 0.739964
\(956\) 5899.04 0.199570
\(957\) 2081.84 0.0703202
\(958\) 30300.7 1.02189
\(959\) −8391.56 −0.282563
\(960\) 75958.6 2.55370
\(961\) −29789.9 −0.999964
\(962\) −13758.4 −0.461111
\(963\) −44879.1 −1.50178
\(964\) 8182.55 0.273384
\(965\) −61472.2 −2.05063
\(966\) −10896.6 −0.362931
\(967\) −45742.7 −1.52119 −0.760593 0.649229i \(-0.775092\pi\)
−0.760593 + 0.649229i \(0.775092\pi\)
\(968\) −29539.2 −0.980813
\(969\) 0 0
\(970\) 64859.5 2.14692
\(971\) 7001.98 0.231415 0.115708 0.993283i \(-0.463086\pi\)
0.115708 + 0.993283i \(0.463086\pi\)
\(972\) 4393.31 0.144975
\(973\) −528.547 −0.0174146
\(974\) 6252.64 0.205696
\(975\) −36564.8 −1.20104
\(976\) 4675.53 0.153340
\(977\) 36142.8 1.18353 0.591767 0.806109i \(-0.298431\pi\)
0.591767 + 0.806109i \(0.298431\pi\)
\(978\) 3774.95 0.123425
\(979\) −7695.39 −0.251221
\(980\) −10410.6 −0.339341
\(981\) 96705.6 3.14737
\(982\) 20392.0 0.662662
\(983\) 21919.3 0.711207 0.355603 0.934637i \(-0.384275\pi\)
0.355603 + 0.934637i \(0.384275\pi\)
\(984\) −69626.7 −2.25571
\(985\) −1175.19 −0.0380150
\(986\) 0 0
\(987\) −70672.4 −2.27916
\(988\) 7622.11 0.245437
\(989\) 21790.8 0.700614
\(990\) 22209.9 0.713006
\(991\) −19931.0 −0.638880 −0.319440 0.947607i \(-0.603495\pi\)
−0.319440 + 0.947607i \(0.603495\pi\)
\(992\) 143.873 0.00460482
\(993\) −23264.6 −0.743483
\(994\) −18899.5 −0.603074
\(995\) −43878.7 −1.39804
\(996\) 7150.75 0.227490
\(997\) −18298.2 −0.581253 −0.290626 0.956837i \(-0.593864\pi\)
−0.290626 + 0.956837i \(0.593864\pi\)
\(998\) 1545.48 0.0490193
\(999\) −59434.5 −1.88231
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.1.4 12
17.4 even 4 289.4.b.f.288.18 24
17.13 even 4 289.4.b.f.288.17 24
17.16 even 2 289.4.a.i.1.4 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.4 12 1.1 even 1 trivial
289.4.a.i.1.4 yes 12 17.16 even 2
289.4.b.f.288.17 24 17.13 even 4
289.4.b.f.288.18 24 17.4 even 4