Properties

Label 2254.4.a.u.1.6
Level $2254$
Weight $4$
Character 2254.1
Self dual yes
Analytic conductor $132.990$
Analytic rank $0$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2254,4,Mod(1,2254)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2254.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2254.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(132.990305153\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 234 x^{9} - 105 x^{8} + 18997 x^{7} + 16513 x^{6} - 621598 x^{5} - 743169 x^{4} + \cdots - 12103441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 7 \)
Twist minimal: no (minimal twist has level 322)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.423740\) of defining polynomial
Character \(\chi\) \(=\) 2254.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -0.423740 q^{3} +4.00000 q^{4} +18.0271 q^{5} +0.847481 q^{6} -8.00000 q^{8} -26.8204 q^{9} -36.0542 q^{10} +10.8276 q^{11} -1.69496 q^{12} +20.0082 q^{13} -7.63881 q^{15} +16.0000 q^{16} +109.597 q^{17} +53.6409 q^{18} -16.0076 q^{19} +72.1084 q^{20} -21.6553 q^{22} +23.0000 q^{23} +3.38992 q^{24} +199.976 q^{25} -40.0163 q^{26} +22.8059 q^{27} +174.550 q^{29} +15.2776 q^{30} -285.169 q^{31} -32.0000 q^{32} -4.58811 q^{33} -219.195 q^{34} -107.282 q^{36} +201.953 q^{37} +32.0152 q^{38} -8.47827 q^{39} -144.217 q^{40} +72.7492 q^{41} -22.4963 q^{43} +43.3106 q^{44} -483.495 q^{45} -46.0000 q^{46} +26.1314 q^{47} -6.77984 q^{48} -399.953 q^{50} -46.4408 q^{51} +80.0327 q^{52} -299.634 q^{53} -45.6118 q^{54} +195.191 q^{55} +6.78307 q^{57} -349.100 q^{58} -571.609 q^{59} -30.5552 q^{60} +493.219 q^{61} +570.337 q^{62} +64.0000 q^{64} +360.689 q^{65} +9.17622 q^{66} +853.087 q^{67} +438.390 q^{68} -9.74603 q^{69} -275.485 q^{71} +214.564 q^{72} +405.694 q^{73} -403.905 q^{74} -84.7381 q^{75} -64.0305 q^{76} +16.9565 q^{78} -49.0626 q^{79} +288.434 q^{80} +714.488 q^{81} -145.498 q^{82} -537.134 q^{83} +1975.72 q^{85} +44.9927 q^{86} -73.9639 q^{87} -86.6212 q^{88} -408.857 q^{89} +966.990 q^{90} +92.0000 q^{92} +120.837 q^{93} -52.2629 q^{94} -288.571 q^{95} +13.5597 q^{96} -1164.89 q^{97} -290.402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 22 q^{2} + 44 q^{4} + 23 q^{5} - 88 q^{8} + 171 q^{9} - 46 q^{10} - 48 q^{11} + 77 q^{13} + 104 q^{15} + 176 q^{16} + 97 q^{17} - 342 q^{18} + 138 q^{19} + 92 q^{20} + 96 q^{22} + 253 q^{23} + 30 q^{25}+ \cdots - 2545 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −0.423740 −0.0815489 −0.0407744 0.999168i \(-0.512983\pi\)
−0.0407744 + 0.999168i \(0.512983\pi\)
\(4\) 4.00000 0.500000
\(5\) 18.0271 1.61239 0.806197 0.591648i \(-0.201522\pi\)
0.806197 + 0.591648i \(0.201522\pi\)
\(6\) 0.847481 0.0576637
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −26.8204 −0.993350
\(10\) −36.0542 −1.14013
\(11\) 10.8276 0.296787 0.148394 0.988928i \(-0.452590\pi\)
0.148394 + 0.988928i \(0.452590\pi\)
\(12\) −1.69496 −0.0407744
\(13\) 20.0082 0.426867 0.213433 0.976958i \(-0.431535\pi\)
0.213433 + 0.976958i \(0.431535\pi\)
\(14\) 0 0
\(15\) −7.63881 −0.131489
\(16\) 16.0000 0.250000
\(17\) 109.597 1.56360 0.781802 0.623527i \(-0.214301\pi\)
0.781802 + 0.623527i \(0.214301\pi\)
\(18\) 53.6409 0.702404
\(19\) −16.0076 −0.193284 −0.0966421 0.995319i \(-0.530810\pi\)
−0.0966421 + 0.995319i \(0.530810\pi\)
\(20\) 72.1084 0.806197
\(21\) 0 0
\(22\) −21.6553 −0.209860
\(23\) 23.0000 0.208514
\(24\) 3.38992 0.0288319
\(25\) 199.976 1.59981
\(26\) −40.0163 −0.301840
\(27\) 22.8059 0.162555
\(28\) 0 0
\(29\) 174.550 1.11769 0.558847 0.829271i \(-0.311244\pi\)
0.558847 + 0.829271i \(0.311244\pi\)
\(30\) 15.2776 0.0929766
\(31\) −285.169 −1.65219 −0.826093 0.563533i \(-0.809442\pi\)
−0.826093 + 0.563533i \(0.809442\pi\)
\(32\) −32.0000 −0.176777
\(33\) −4.58811 −0.0242026
\(34\) −219.195 −1.10564
\(35\) 0 0
\(36\) −107.282 −0.496675
\(37\) 201.953 0.897319 0.448659 0.893703i \(-0.351902\pi\)
0.448659 + 0.893703i \(0.351902\pi\)
\(38\) 32.0152 0.136673
\(39\) −8.47827 −0.0348105
\(40\) −144.217 −0.570067
\(41\) 72.7492 0.277110 0.138555 0.990355i \(-0.455754\pi\)
0.138555 + 0.990355i \(0.455754\pi\)
\(42\) 0 0
\(43\) −22.4963 −0.0797827 −0.0398914 0.999204i \(-0.512701\pi\)
−0.0398914 + 0.999204i \(0.512701\pi\)
\(44\) 43.3106 0.148394
\(45\) −483.495 −1.60167
\(46\) −46.0000 −0.147442
\(47\) 26.1314 0.0810992 0.0405496 0.999178i \(-0.487089\pi\)
0.0405496 + 0.999178i \(0.487089\pi\)
\(48\) −6.77984 −0.0203872
\(49\) 0 0
\(50\) −399.953 −1.13124
\(51\) −46.4408 −0.127510
\(52\) 80.0327 0.213433
\(53\) −299.634 −0.776565 −0.388282 0.921540i \(-0.626931\pi\)
−0.388282 + 0.921540i \(0.626931\pi\)
\(54\) −45.6118 −0.114944
\(55\) 195.191 0.478537
\(56\) 0 0
\(57\) 6.78307 0.0157621
\(58\) −349.100 −0.790330
\(59\) −571.609 −1.26131 −0.630654 0.776064i \(-0.717213\pi\)
−0.630654 + 0.776064i \(0.717213\pi\)
\(60\) −30.5552 −0.0657444
\(61\) 493.219 1.03525 0.517625 0.855608i \(-0.326816\pi\)
0.517625 + 0.855608i \(0.326816\pi\)
\(62\) 570.337 1.16827
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 360.689 0.688277
\(66\) 9.17622 0.0171139
\(67\) 853.087 1.55554 0.777770 0.628550i \(-0.216351\pi\)
0.777770 + 0.628550i \(0.216351\pi\)
\(68\) 438.390 0.781802
\(69\) −9.74603 −0.0170041
\(70\) 0 0
\(71\) −275.485 −0.460480 −0.230240 0.973134i \(-0.573951\pi\)
−0.230240 + 0.973134i \(0.573951\pi\)
\(72\) 214.564 0.351202
\(73\) 405.694 0.650451 0.325225 0.945637i \(-0.394560\pi\)
0.325225 + 0.945637i \(0.394560\pi\)
\(74\) −403.905 −0.634500
\(75\) −84.7381 −0.130463
\(76\) −64.0305 −0.0966421
\(77\) 0 0
\(78\) 16.9565 0.0246147
\(79\) −49.0626 −0.0698731 −0.0349365 0.999390i \(-0.511123\pi\)
−0.0349365 + 0.999390i \(0.511123\pi\)
\(80\) 288.434 0.403098
\(81\) 714.488 0.980094
\(82\) −145.498 −0.195946
\(83\) −537.134 −0.710339 −0.355170 0.934802i \(-0.615577\pi\)
−0.355170 + 0.934802i \(0.615577\pi\)
\(84\) 0 0
\(85\) 1975.72 2.52114
\(86\) 44.9927 0.0564149
\(87\) −73.9639 −0.0911467
\(88\) −86.6212 −0.104930
\(89\) −408.857 −0.486952 −0.243476 0.969907i \(-0.578288\pi\)
−0.243476 + 0.969907i \(0.578288\pi\)
\(90\) 966.990 1.13255
\(91\) 0 0
\(92\) 92.0000 0.104257
\(93\) 120.837 0.134734
\(94\) −52.2629 −0.0573458
\(95\) −288.571 −0.311650
\(96\) 13.5597 0.0144159
\(97\) −1164.89 −1.21935 −0.609675 0.792651i \(-0.708700\pi\)
−0.609675 + 0.792651i \(0.708700\pi\)
\(98\) 0 0
\(99\) −290.402 −0.294813
\(100\) 799.906 0.799906
\(101\) 1888.04 1.86006 0.930032 0.367478i \(-0.119779\pi\)
0.930032 + 0.367478i \(0.119779\pi\)
\(102\) 92.8817 0.0901633
\(103\) 732.800 0.701019 0.350510 0.936559i \(-0.386008\pi\)
0.350510 + 0.936559i \(0.386008\pi\)
\(104\) −160.065 −0.150920
\(105\) 0 0
\(106\) 599.269 0.549114
\(107\) 29.3551 0.0265221 0.0132610 0.999912i \(-0.495779\pi\)
0.0132610 + 0.999912i \(0.495779\pi\)
\(108\) 91.2236 0.0812777
\(109\) 1504.64 1.32219 0.661094 0.750303i \(-0.270092\pi\)
0.661094 + 0.750303i \(0.270092\pi\)
\(110\) −390.382 −0.338377
\(111\) −85.5754 −0.0731753
\(112\) 0 0
\(113\) −215.494 −0.179398 −0.0896990 0.995969i \(-0.528591\pi\)
−0.0896990 + 0.995969i \(0.528591\pi\)
\(114\) −13.5661 −0.0111455
\(115\) 414.623 0.336207
\(116\) 698.201 0.558847
\(117\) −536.628 −0.424028
\(118\) 1143.22 0.891880
\(119\) 0 0
\(120\) 61.1105 0.0464883
\(121\) −1213.76 −0.911917
\(122\) −986.439 −0.732032
\(123\) −30.8268 −0.0225980
\(124\) −1140.67 −0.826093
\(125\) 1351.61 0.967132
\(126\) 0 0
\(127\) 1680.34 1.17406 0.587032 0.809564i \(-0.300296\pi\)
0.587032 + 0.809564i \(0.300296\pi\)
\(128\) −128.000 −0.0883883
\(129\) 9.53260 0.00650619
\(130\) −721.378 −0.486685
\(131\) 1838.25 1.22602 0.613009 0.790076i \(-0.289959\pi\)
0.613009 + 0.790076i \(0.289959\pi\)
\(132\) −18.3524 −0.0121013
\(133\) 0 0
\(134\) −1706.17 −1.09993
\(135\) 411.124 0.262103
\(136\) −876.779 −0.552818
\(137\) 2530.78 1.57824 0.789120 0.614239i \(-0.210537\pi\)
0.789120 + 0.614239i \(0.210537\pi\)
\(138\) 19.4921 0.0120237
\(139\) 235.342 0.143607 0.0718037 0.997419i \(-0.477124\pi\)
0.0718037 + 0.997419i \(0.477124\pi\)
\(140\) 0 0
\(141\) −11.0729 −0.00661354
\(142\) 550.970 0.325608
\(143\) 216.641 0.126688
\(144\) −429.127 −0.248337
\(145\) 3146.63 1.80216
\(146\) −811.388 −0.459938
\(147\) 0 0
\(148\) 807.810 0.448659
\(149\) −1681.29 −0.924406 −0.462203 0.886774i \(-0.652941\pi\)
−0.462203 + 0.886774i \(0.652941\pi\)
\(150\) 169.476 0.0922511
\(151\) −539.920 −0.290980 −0.145490 0.989360i \(-0.546476\pi\)
−0.145490 + 0.989360i \(0.546476\pi\)
\(152\) 128.061 0.0683363
\(153\) −2939.45 −1.55321
\(154\) 0 0
\(155\) −5140.76 −2.66397
\(156\) −33.9131 −0.0174052
\(157\) 1042.01 0.529692 0.264846 0.964291i \(-0.414679\pi\)
0.264846 + 0.964291i \(0.414679\pi\)
\(158\) 98.1252 0.0494077
\(159\) 126.967 0.0633280
\(160\) −576.867 −0.285034
\(161\) 0 0
\(162\) −1428.98 −0.693031
\(163\) 851.681 0.409257 0.204628 0.978840i \(-0.434401\pi\)
0.204628 + 0.978840i \(0.434401\pi\)
\(164\) 290.997 0.138555
\(165\) −82.7103 −0.0390242
\(166\) 1074.27 0.502286
\(167\) −3658.62 −1.69528 −0.847642 0.530568i \(-0.821979\pi\)
−0.847642 + 0.530568i \(0.821979\pi\)
\(168\) 0 0
\(169\) −1796.67 −0.817785
\(170\) −3951.45 −1.78272
\(171\) 429.331 0.191999
\(172\) −89.9853 −0.0398914
\(173\) 46.2925 0.0203442 0.0101721 0.999948i \(-0.496762\pi\)
0.0101721 + 0.999948i \(0.496762\pi\)
\(174\) 147.928 0.0644505
\(175\) 0 0
\(176\) 173.242 0.0741968
\(177\) 242.214 0.102858
\(178\) 817.714 0.344327
\(179\) −2996.72 −1.25131 −0.625657 0.780098i \(-0.715169\pi\)
−0.625657 + 0.780098i \(0.715169\pi\)
\(180\) −1933.98 −0.800835
\(181\) −1333.04 −0.547426 −0.273713 0.961811i \(-0.588252\pi\)
−0.273713 + 0.961811i \(0.588252\pi\)
\(182\) 0 0
\(183\) −208.997 −0.0844235
\(184\) −184.000 −0.0737210
\(185\) 3640.62 1.44683
\(186\) −241.675 −0.0952713
\(187\) 1186.68 0.464058
\(188\) 104.526 0.0405496
\(189\) 0 0
\(190\) 577.142 0.220370
\(191\) −3098.01 −1.17363 −0.586816 0.809720i \(-0.699619\pi\)
−0.586816 + 0.809720i \(0.699619\pi\)
\(192\) −27.1194 −0.0101936
\(193\) 3065.90 1.14346 0.571732 0.820440i \(-0.306272\pi\)
0.571732 + 0.820440i \(0.306272\pi\)
\(194\) 2329.79 0.862211
\(195\) −152.839 −0.0561282
\(196\) 0 0
\(197\) 503.114 0.181956 0.0909781 0.995853i \(-0.471001\pi\)
0.0909781 + 0.995853i \(0.471001\pi\)
\(198\) 580.804 0.208465
\(199\) 1269.09 0.452078 0.226039 0.974118i \(-0.427422\pi\)
0.226039 + 0.974118i \(0.427422\pi\)
\(200\) −1599.81 −0.565619
\(201\) −361.487 −0.126852
\(202\) −3776.07 −1.31526
\(203\) 0 0
\(204\) −185.763 −0.0637551
\(205\) 1311.46 0.446810
\(206\) −1465.60 −0.495695
\(207\) −616.870 −0.207128
\(208\) 320.131 0.106717
\(209\) −173.325 −0.0573642
\(210\) 0 0
\(211\) −3149.06 −1.02744 −0.513722 0.857957i \(-0.671734\pi\)
−0.513722 + 0.857957i \(0.671734\pi\)
\(212\) −1198.54 −0.388282
\(213\) 116.734 0.0375516
\(214\) −58.7102 −0.0187539
\(215\) −405.544 −0.128641
\(216\) −182.447 −0.0574720
\(217\) 0 0
\(218\) −3009.28 −0.934928
\(219\) −171.909 −0.0530435
\(220\) 780.764 0.239269
\(221\) 2192.84 0.667451
\(222\) 171.151 0.0517428
\(223\) −475.283 −0.142723 −0.0713617 0.997451i \(-0.522734\pi\)
−0.0713617 + 0.997451i \(0.522734\pi\)
\(224\) 0 0
\(225\) −5363.46 −1.58917
\(226\) 430.988 0.126854
\(227\) 4923.88 1.43969 0.719845 0.694135i \(-0.244213\pi\)
0.719845 + 0.694135i \(0.244213\pi\)
\(228\) 27.1323 0.00788105
\(229\) −3098.75 −0.894198 −0.447099 0.894484i \(-0.647543\pi\)
−0.447099 + 0.894484i \(0.647543\pi\)
\(230\) −829.247 −0.237734
\(231\) 0 0
\(232\) −1396.40 −0.395165
\(233\) 6838.24 1.92270 0.961348 0.275335i \(-0.0887889\pi\)
0.961348 + 0.275335i \(0.0887889\pi\)
\(234\) 1073.26 0.299833
\(235\) 471.074 0.130764
\(236\) −2286.44 −0.630654
\(237\) 20.7898 0.00569807
\(238\) 0 0
\(239\) −4248.98 −1.14997 −0.574987 0.818163i \(-0.694993\pi\)
−0.574987 + 0.818163i \(0.694993\pi\)
\(240\) −122.221 −0.0328722
\(241\) −4234.73 −1.13188 −0.565939 0.824447i \(-0.691486\pi\)
−0.565939 + 0.824447i \(0.691486\pi\)
\(242\) 2427.52 0.644823
\(243\) −918.516 −0.242481
\(244\) 1972.88 0.517625
\(245\) 0 0
\(246\) 61.6535 0.0159792
\(247\) −320.283 −0.0825066
\(248\) 2281.35 0.584136
\(249\) 227.605 0.0579273
\(250\) −2703.22 −0.683866
\(251\) 2246.31 0.564885 0.282442 0.959284i \(-0.408855\pi\)
0.282442 + 0.959284i \(0.408855\pi\)
\(252\) 0 0
\(253\) 249.036 0.0618844
\(254\) −3360.68 −0.830188
\(255\) −837.194 −0.205596
\(256\) 256.000 0.0625000
\(257\) 3129.11 0.759489 0.379744 0.925091i \(-0.376012\pi\)
0.379744 + 0.925091i \(0.376012\pi\)
\(258\) −19.0652 −0.00460057
\(259\) 0 0
\(260\) 1442.76 0.344138
\(261\) −4681.51 −1.11026
\(262\) −3676.49 −0.866925
\(263\) 5978.66 1.40175 0.700875 0.713284i \(-0.252793\pi\)
0.700875 + 0.713284i \(0.252793\pi\)
\(264\) 36.7049 0.00855693
\(265\) −5401.54 −1.25213
\(266\) 0 0
\(267\) 173.249 0.0397104
\(268\) 3412.35 0.777770
\(269\) −6190.03 −1.40302 −0.701511 0.712659i \(-0.747491\pi\)
−0.701511 + 0.712659i \(0.747491\pi\)
\(270\) −822.248 −0.185335
\(271\) −2570.30 −0.576142 −0.288071 0.957609i \(-0.593014\pi\)
−0.288071 + 0.957609i \(0.593014\pi\)
\(272\) 1753.56 0.390901
\(273\) 0 0
\(274\) −5061.55 −1.11598
\(275\) 2165.27 0.474803
\(276\) −38.9841 −0.00850206
\(277\) −3305.91 −0.717086 −0.358543 0.933513i \(-0.616726\pi\)
−0.358543 + 0.933513i \(0.616726\pi\)
\(278\) −470.684 −0.101546
\(279\) 7648.35 1.64120
\(280\) 0 0
\(281\) 4740.20 1.00632 0.503162 0.864192i \(-0.332170\pi\)
0.503162 + 0.864192i \(0.332170\pi\)
\(282\) 22.1459 0.00467648
\(283\) 8775.14 1.84321 0.921605 0.388130i \(-0.126879\pi\)
0.921605 + 0.388130i \(0.126879\pi\)
\(284\) −1101.94 −0.230240
\(285\) 122.279 0.0254147
\(286\) −433.283 −0.0895823
\(287\) 0 0
\(288\) 858.254 0.175601
\(289\) 7098.59 1.44486
\(290\) −6293.27 −1.27432
\(291\) 493.612 0.0994366
\(292\) 1622.78 0.325225
\(293\) −2717.70 −0.541875 −0.270938 0.962597i \(-0.587334\pi\)
−0.270938 + 0.962597i \(0.587334\pi\)
\(294\) 0 0
\(295\) −10304.5 −2.03372
\(296\) −1615.62 −0.317250
\(297\) 246.934 0.0482443
\(298\) 3362.57 0.653653
\(299\) 460.188 0.0890078
\(300\) −338.952 −0.0652314
\(301\) 0 0
\(302\) 1079.84 0.205754
\(303\) −800.037 −0.151686
\(304\) −256.122 −0.0483210
\(305\) 8891.32 1.66923
\(306\) 5878.90 1.09828
\(307\) 7532.14 1.40027 0.700133 0.714012i \(-0.253124\pi\)
0.700133 + 0.714012i \(0.253124\pi\)
\(308\) 0 0
\(309\) −310.517 −0.0571673
\(310\) 10281.5 1.88371
\(311\) 10918.9 1.99085 0.995425 0.0955425i \(-0.0304586\pi\)
0.995425 + 0.0955425i \(0.0304586\pi\)
\(312\) 67.8261 0.0123074
\(313\) 7687.50 1.38825 0.694126 0.719853i \(-0.255791\pi\)
0.694126 + 0.719853i \(0.255791\pi\)
\(314\) −2084.03 −0.374549
\(315\) 0 0
\(316\) −196.250 −0.0349365
\(317\) −9269.22 −1.64231 −0.821153 0.570708i \(-0.806669\pi\)
−0.821153 + 0.570708i \(0.806669\pi\)
\(318\) −253.934 −0.0447796
\(319\) 1889.97 0.331717
\(320\) 1153.73 0.201549
\(321\) −12.4389 −0.00216285
\(322\) 0 0
\(323\) −1754.39 −0.302220
\(324\) 2857.95 0.490047
\(325\) 4001.16 0.682906
\(326\) −1703.36 −0.289388
\(327\) −637.577 −0.107823
\(328\) −581.993 −0.0979732
\(329\) 0 0
\(330\) 165.421 0.0275943
\(331\) 9939.55 1.65054 0.825268 0.564742i \(-0.191024\pi\)
0.825268 + 0.564742i \(0.191024\pi\)
\(332\) −2148.54 −0.355170
\(333\) −5416.46 −0.891351
\(334\) 7317.24 1.19875
\(335\) 15378.7 2.50814
\(336\) 0 0
\(337\) −921.909 −0.149020 −0.0745098 0.997220i \(-0.523739\pi\)
−0.0745098 + 0.997220i \(0.523739\pi\)
\(338\) 3593.35 0.578261
\(339\) 91.3135 0.0146297
\(340\) 7902.89 1.26057
\(341\) −3087.70 −0.490348
\(342\) −858.663 −0.135764
\(343\) 0 0
\(344\) 179.971 0.0282075
\(345\) −175.693 −0.0274173
\(346\) −92.5850 −0.0143855
\(347\) 7343.80 1.13613 0.568063 0.822985i \(-0.307693\pi\)
0.568063 + 0.822985i \(0.307693\pi\)
\(348\) −295.856 −0.0455734
\(349\) 7623.29 1.16924 0.584621 0.811306i \(-0.301243\pi\)
0.584621 + 0.811306i \(0.301243\pi\)
\(350\) 0 0
\(351\) 456.304 0.0693895
\(352\) −346.485 −0.0524650
\(353\) −1935.30 −0.291801 −0.145900 0.989299i \(-0.546608\pi\)
−0.145900 + 0.989299i \(0.546608\pi\)
\(354\) −484.428 −0.0727318
\(355\) −4966.20 −0.742475
\(356\) −1635.43 −0.243476
\(357\) 0 0
\(358\) 5993.44 0.884813
\(359\) −1420.86 −0.208887 −0.104443 0.994531i \(-0.533306\pi\)
−0.104443 + 0.994531i \(0.533306\pi\)
\(360\) 3867.96 0.566276
\(361\) −6602.76 −0.962641
\(362\) 2666.08 0.387089
\(363\) 514.320 0.0743658
\(364\) 0 0
\(365\) 7313.49 1.04878
\(366\) 417.994 0.0596964
\(367\) −6740.90 −0.958779 −0.479390 0.877602i \(-0.659142\pi\)
−0.479390 + 0.877602i \(0.659142\pi\)
\(368\) 368.000 0.0521286
\(369\) −1951.17 −0.275267
\(370\) −7281.24 −1.02306
\(371\) 0 0
\(372\) 483.350 0.0673670
\(373\) 5369.88 0.745420 0.372710 0.927948i \(-0.378429\pi\)
0.372710 + 0.927948i \(0.378429\pi\)
\(374\) −2373.36 −0.328138
\(375\) −572.731 −0.0788685
\(376\) −209.051 −0.0286729
\(377\) 3492.43 0.477107
\(378\) 0 0
\(379\) 2510.75 0.340286 0.170143 0.985419i \(-0.445577\pi\)
0.170143 + 0.985419i \(0.445577\pi\)
\(380\) −1154.28 −0.155825
\(381\) −712.028 −0.0957435
\(382\) 6196.01 0.829884
\(383\) 9436.92 1.25902 0.629509 0.776993i \(-0.283256\pi\)
0.629509 + 0.776993i \(0.283256\pi\)
\(384\) 54.2388 0.00720797
\(385\) 0 0
\(386\) −6131.81 −0.808551
\(387\) 603.361 0.0792522
\(388\) −4659.57 −0.609675
\(389\) −3025.19 −0.394301 −0.197151 0.980373i \(-0.563169\pi\)
−0.197151 + 0.980373i \(0.563169\pi\)
\(390\) 305.677 0.0396886
\(391\) 2520.74 0.326034
\(392\) 0 0
\(393\) −778.939 −0.0999803
\(394\) −1006.23 −0.128662
\(395\) −884.456 −0.112663
\(396\) −1161.61 −0.147407
\(397\) 13999.3 1.76979 0.884895 0.465791i \(-0.154230\pi\)
0.884895 + 0.465791i \(0.154230\pi\)
\(398\) −2538.18 −0.319668
\(399\) 0 0
\(400\) 3199.62 0.399953
\(401\) 3017.67 0.375799 0.187900 0.982188i \(-0.439832\pi\)
0.187900 + 0.982188i \(0.439832\pi\)
\(402\) 722.974 0.0896982
\(403\) −5705.70 −0.705263
\(404\) 7552.14 0.930032
\(405\) 12880.2 1.58030
\(406\) 0 0
\(407\) 2186.67 0.266313
\(408\) 371.527 0.0450816
\(409\) 6741.78 0.815060 0.407530 0.913192i \(-0.366390\pi\)
0.407530 + 0.913192i \(0.366390\pi\)
\(410\) −2622.91 −0.315943
\(411\) −1072.39 −0.128704
\(412\) 2931.20 0.350510
\(413\) 0 0
\(414\) 1233.74 0.146461
\(415\) −9682.98 −1.14535
\(416\) −640.261 −0.0754601
\(417\) −99.7238 −0.0117110
\(418\) 346.650 0.0405626
\(419\) 2505.65 0.292146 0.146073 0.989274i \(-0.453337\pi\)
0.146073 + 0.989274i \(0.453337\pi\)
\(420\) 0 0
\(421\) 7665.96 0.887449 0.443724 0.896163i \(-0.353657\pi\)
0.443724 + 0.896163i \(0.353657\pi\)
\(422\) 6298.13 0.726512
\(423\) −700.856 −0.0805598
\(424\) 2397.07 0.274557
\(425\) 21916.9 2.50147
\(426\) −233.468 −0.0265530
\(427\) 0 0
\(428\) 117.420 0.0132610
\(429\) −91.7996 −0.0103313
\(430\) 811.087 0.0909630
\(431\) −3735.71 −0.417501 −0.208751 0.977969i \(-0.566940\pi\)
−0.208751 + 0.977969i \(0.566940\pi\)
\(432\) 364.894 0.0406388
\(433\) −13124.0 −1.45658 −0.728289 0.685270i \(-0.759684\pi\)
−0.728289 + 0.685270i \(0.759684\pi\)
\(434\) 0 0
\(435\) −1333.36 −0.146964
\(436\) 6018.57 0.661094
\(437\) −368.175 −0.0403025
\(438\) 343.818 0.0375074
\(439\) 10836.5 1.17813 0.589066 0.808085i \(-0.299496\pi\)
0.589066 + 0.808085i \(0.299496\pi\)
\(440\) −1561.53 −0.169189
\(441\) 0 0
\(442\) −4385.69 −0.471959
\(443\) −8521.87 −0.913964 −0.456982 0.889476i \(-0.651070\pi\)
−0.456982 + 0.889476i \(0.651070\pi\)
\(444\) −342.302 −0.0365877
\(445\) −7370.51 −0.785159
\(446\) 950.567 0.100921
\(447\) 712.429 0.0753842
\(448\) 0 0
\(449\) −12286.0 −1.29134 −0.645671 0.763616i \(-0.723422\pi\)
−0.645671 + 0.763616i \(0.723422\pi\)
\(450\) 10726.9 1.12371
\(451\) 787.702 0.0822427
\(452\) −861.977 −0.0896990
\(453\) 228.786 0.0237291
\(454\) −9847.77 −1.01801
\(455\) 0 0
\(456\) −54.2646 −0.00557275
\(457\) 6936.85 0.710049 0.355024 0.934857i \(-0.384473\pi\)
0.355024 + 0.934857i \(0.384473\pi\)
\(458\) 6197.51 0.632293
\(459\) 2499.47 0.254172
\(460\) 1658.49 0.168104
\(461\) −6741.05 −0.681045 −0.340523 0.940236i \(-0.610604\pi\)
−0.340523 + 0.940236i \(0.610604\pi\)
\(462\) 0 0
\(463\) 5242.34 0.526203 0.263102 0.964768i \(-0.415255\pi\)
0.263102 + 0.964768i \(0.415255\pi\)
\(464\) 2792.80 0.279424
\(465\) 2178.35 0.217244
\(466\) −13676.5 −1.35955
\(467\) 825.259 0.0817740 0.0408870 0.999164i \(-0.486982\pi\)
0.0408870 + 0.999164i \(0.486982\pi\)
\(468\) −2146.51 −0.212014
\(469\) 0 0
\(470\) −942.148 −0.0924639
\(471\) −441.543 −0.0431958
\(472\) 4572.87 0.445940
\(473\) −243.582 −0.0236785
\(474\) −41.5796 −0.00402914
\(475\) −3201.15 −0.309218
\(476\) 0 0
\(477\) 8036.32 0.771400
\(478\) 8497.96 0.813154
\(479\) 10998.2 1.04911 0.524553 0.851378i \(-0.324233\pi\)
0.524553 + 0.851378i \(0.324233\pi\)
\(480\) 244.442 0.0232442
\(481\) 4040.70 0.383035
\(482\) 8469.46 0.800359
\(483\) 0 0
\(484\) −4855.05 −0.455959
\(485\) −20999.7 −1.96607
\(486\) 1837.03 0.171460
\(487\) −5976.46 −0.556097 −0.278048 0.960567i \(-0.589688\pi\)
−0.278048 + 0.960567i \(0.589688\pi\)
\(488\) −3945.75 −0.366016
\(489\) −360.892 −0.0333744
\(490\) 0 0
\(491\) −1119.29 −0.102878 −0.0514389 0.998676i \(-0.516381\pi\)
−0.0514389 + 0.998676i \(0.516381\pi\)
\(492\) −123.307 −0.0112990
\(493\) 19130.2 1.74763
\(494\) 640.566 0.0583410
\(495\) −5235.11 −0.475355
\(496\) −4562.70 −0.413047
\(497\) 0 0
\(498\) −455.211 −0.0409608
\(499\) 7057.72 0.633160 0.316580 0.948566i \(-0.397465\pi\)
0.316580 + 0.948566i \(0.397465\pi\)
\(500\) 5406.43 0.483566
\(501\) 1550.31 0.138249
\(502\) −4492.63 −0.399434
\(503\) −9822.07 −0.870665 −0.435332 0.900270i \(-0.643369\pi\)
−0.435332 + 0.900270i \(0.643369\pi\)
\(504\) 0 0
\(505\) 34035.8 2.99916
\(506\) −498.072 −0.0437589
\(507\) 761.323 0.0666894
\(508\) 6721.36 0.587032
\(509\) 10971.9 0.955445 0.477722 0.878511i \(-0.341462\pi\)
0.477722 + 0.878511i \(0.341462\pi\)
\(510\) 1674.39 0.145379
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −365.068 −0.0314194
\(514\) −6258.22 −0.537040
\(515\) 13210.3 1.13032
\(516\) 38.1304 0.00325310
\(517\) 282.942 0.0240692
\(518\) 0 0
\(519\) −19.6160 −0.00165905
\(520\) −2885.51 −0.243343
\(521\) 11404.8 0.959027 0.479514 0.877534i \(-0.340813\pi\)
0.479514 + 0.877534i \(0.340813\pi\)
\(522\) 9363.03 0.785074
\(523\) −8931.53 −0.746747 −0.373373 0.927681i \(-0.621799\pi\)
−0.373373 + 0.927681i \(0.621799\pi\)
\(524\) 7352.99 0.613009
\(525\) 0 0
\(526\) −11957.3 −0.991186
\(527\) −31253.7 −2.58337
\(528\) −73.4097 −0.00605066
\(529\) 529.000 0.0434783
\(530\) 10803.1 0.885388
\(531\) 15330.8 1.25292
\(532\) 0 0
\(533\) 1455.58 0.118289
\(534\) −346.498 −0.0280795
\(535\) 529.187 0.0427640
\(536\) −6824.69 −0.549966
\(537\) 1269.83 0.102043
\(538\) 12380.1 0.992086
\(539\) 0 0
\(540\) 1644.50 0.131052
\(541\) 6503.89 0.516865 0.258433 0.966029i \(-0.416794\pi\)
0.258433 + 0.966029i \(0.416794\pi\)
\(542\) 5140.59 0.407394
\(543\) 564.863 0.0446420
\(544\) −3507.12 −0.276409
\(545\) 27124.3 2.13189
\(546\) 0 0
\(547\) −14483.9 −1.13215 −0.566077 0.824352i \(-0.691540\pi\)
−0.566077 + 0.824352i \(0.691540\pi\)
\(548\) 10123.1 0.789120
\(549\) −13228.4 −1.02837
\(550\) −4330.55 −0.335737
\(551\) −2794.13 −0.216033
\(552\) 77.9682 0.00601186
\(553\) 0 0
\(554\) 6611.82 0.507056
\(555\) −1542.68 −0.117987
\(556\) 941.367 0.0718037
\(557\) 19776.6 1.50442 0.752210 0.658924i \(-0.228988\pi\)
0.752210 + 0.658924i \(0.228988\pi\)
\(558\) −15296.7 −1.16050
\(559\) −450.110 −0.0340566
\(560\) 0 0
\(561\) −502.845 −0.0378434
\(562\) −9480.41 −0.711578
\(563\) −11618.4 −0.869727 −0.434863 0.900496i \(-0.643203\pi\)
−0.434863 + 0.900496i \(0.643203\pi\)
\(564\) −44.2918 −0.00330677
\(565\) −3884.74 −0.289260
\(566\) −17550.3 −1.30335
\(567\) 0 0
\(568\) 2203.88 0.162804
\(569\) −21913.2 −1.61449 −0.807247 0.590213i \(-0.799044\pi\)
−0.807247 + 0.590213i \(0.799044\pi\)
\(570\) −244.558 −0.0179709
\(571\) 7580.99 0.555612 0.277806 0.960637i \(-0.410393\pi\)
0.277806 + 0.960637i \(0.410393\pi\)
\(572\) 866.565 0.0633442
\(573\) 1312.75 0.0957084
\(574\) 0 0
\(575\) 4599.46 0.333584
\(576\) −1716.51 −0.124169
\(577\) 5057.21 0.364877 0.182439 0.983217i \(-0.441601\pi\)
0.182439 + 0.983217i \(0.441601\pi\)
\(578\) −14197.2 −1.02167
\(579\) −1299.15 −0.0932482
\(580\) 12586.5 0.901082
\(581\) 0 0
\(582\) −987.225 −0.0703123
\(583\) −3244.33 −0.230474
\(584\) −3245.55 −0.229969
\(585\) −9673.85 −0.683700
\(586\) 5435.39 0.383164
\(587\) 9108.51 0.640457 0.320229 0.947340i \(-0.396240\pi\)
0.320229 + 0.947340i \(0.396240\pi\)
\(588\) 0 0
\(589\) 4564.87 0.319342
\(590\) 20608.9 1.43806
\(591\) −213.190 −0.0148383
\(592\) 3231.24 0.224330
\(593\) −11793.9 −0.816721 −0.408361 0.912821i \(-0.633899\pi\)
−0.408361 + 0.912821i \(0.633899\pi\)
\(594\) −493.868 −0.0341139
\(595\) 0 0
\(596\) −6725.15 −0.462203
\(597\) −537.766 −0.0368665
\(598\) −920.376 −0.0629381
\(599\) −27046.3 −1.84488 −0.922440 0.386140i \(-0.873808\pi\)
−0.922440 + 0.386140i \(0.873808\pi\)
\(600\) 677.905 0.0461256
\(601\) −19013.2 −1.29046 −0.645230 0.763989i \(-0.723238\pi\)
−0.645230 + 0.763989i \(0.723238\pi\)
\(602\) 0 0
\(603\) −22880.2 −1.54519
\(604\) −2159.68 −0.145490
\(605\) −21880.6 −1.47037
\(606\) 1600.07 0.107258
\(607\) 1868.60 0.124949 0.0624745 0.998047i \(-0.480101\pi\)
0.0624745 + 0.998047i \(0.480101\pi\)
\(608\) 512.244 0.0341681
\(609\) 0 0
\(610\) −17782.6 −1.18032
\(611\) 522.842 0.0346185
\(612\) −11757.8 −0.776603
\(613\) −735.324 −0.0484493 −0.0242247 0.999707i \(-0.507712\pi\)
−0.0242247 + 0.999707i \(0.507712\pi\)
\(614\) −15064.3 −0.990138
\(615\) −555.717 −0.0364369
\(616\) 0 0
\(617\) −10128.6 −0.660876 −0.330438 0.943828i \(-0.607196\pi\)
−0.330438 + 0.943828i \(0.607196\pi\)
\(618\) 621.034 0.0404234
\(619\) 6555.19 0.425647 0.212823 0.977091i \(-0.431734\pi\)
0.212823 + 0.977091i \(0.431734\pi\)
\(620\) −20563.1 −1.33199
\(621\) 524.535 0.0338951
\(622\) −21837.8 −1.40774
\(623\) 0 0
\(624\) −135.652 −0.00870262
\(625\) −631.476 −0.0404144
\(626\) −15375.0 −0.981643
\(627\) 73.4447 0.00467799
\(628\) 4168.05 0.264846
\(629\) 22133.5 1.40305
\(630\) 0 0
\(631\) −26053.0 −1.64367 −0.821833 0.569728i \(-0.807049\pi\)
−0.821833 + 0.569728i \(0.807049\pi\)
\(632\) 392.501 0.0247039
\(633\) 1334.39 0.0837868
\(634\) 18538.4 1.16129
\(635\) 30291.7 1.89305
\(636\) 507.868 0.0316640
\(637\) 0 0
\(638\) −3779.93 −0.234560
\(639\) 7388.63 0.457418
\(640\) −2307.47 −0.142517
\(641\) 7834.67 0.482763 0.241381 0.970430i \(-0.422400\pi\)
0.241381 + 0.970430i \(0.422400\pi\)
\(642\) 24.8779 0.00152936
\(643\) −22205.5 −1.36190 −0.680949 0.732331i \(-0.738433\pi\)
−0.680949 + 0.732331i \(0.738433\pi\)
\(644\) 0 0
\(645\) 171.845 0.0104905
\(646\) 3508.79 0.213702
\(647\) 28757.5 1.74741 0.873704 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(648\) −5715.91 −0.346515
\(649\) −6189.18 −0.374340
\(650\) −8002.32 −0.482888
\(651\) 0 0
\(652\) 3406.73 0.204628
\(653\) 23477.2 1.40694 0.703471 0.710724i \(-0.251633\pi\)
0.703471 + 0.710724i \(0.251633\pi\)
\(654\) 1275.15 0.0762423
\(655\) 33138.3 1.97682
\(656\) 1163.99 0.0692775
\(657\) −10880.9 −0.646125
\(658\) 0 0
\(659\) −82.2052 −0.00485927 −0.00242964 0.999997i \(-0.500773\pi\)
−0.00242964 + 0.999997i \(0.500773\pi\)
\(660\) −330.841 −0.0195121
\(661\) 32371.0 1.90482 0.952411 0.304818i \(-0.0985957\pi\)
0.952411 + 0.304818i \(0.0985957\pi\)
\(662\) −19879.1 −1.16710
\(663\) −929.196 −0.0544298
\(664\) 4297.07 0.251143
\(665\) 0 0
\(666\) 10832.9 0.630280
\(667\) 4014.65 0.233055
\(668\) −14634.5 −0.847642
\(669\) 201.397 0.0116389
\(670\) −30757.4 −1.77352
\(671\) 5340.40 0.307249
\(672\) 0 0
\(673\) −10946.9 −0.627001 −0.313501 0.949588i \(-0.601502\pi\)
−0.313501 + 0.949588i \(0.601502\pi\)
\(674\) 1843.82 0.105373
\(675\) 4560.64 0.260058
\(676\) −7186.69 −0.408892
\(677\) 17975.5 1.02046 0.510232 0.860037i \(-0.329559\pi\)
0.510232 + 0.860037i \(0.329559\pi\)
\(678\) −182.627 −0.0103448
\(679\) 0 0
\(680\) −15805.8 −0.891359
\(681\) −2086.45 −0.117405
\(682\) 6175.41 0.346728
\(683\) −24747.0 −1.38641 −0.693204 0.720741i \(-0.743801\pi\)
−0.693204 + 0.720741i \(0.743801\pi\)
\(684\) 1717.33 0.0959994
\(685\) 45622.6 2.54474
\(686\) 0 0
\(687\) 1313.07 0.0729208
\(688\) −359.941 −0.0199457
\(689\) −5995.13 −0.331490
\(690\) 351.385 0.0193870
\(691\) −22534.5 −1.24060 −0.620299 0.784365i \(-0.712989\pi\)
−0.620299 + 0.784365i \(0.712989\pi\)
\(692\) 185.170 0.0101721
\(693\) 0 0
\(694\) −14687.6 −0.803362
\(695\) 4242.53 0.231552
\(696\) 591.711 0.0322252
\(697\) 7973.12 0.433290
\(698\) −15246.6 −0.826779
\(699\) −2897.64 −0.156794
\(700\) 0 0
\(701\) 33521.9 1.80614 0.903069 0.429495i \(-0.141308\pi\)
0.903069 + 0.429495i \(0.141308\pi\)
\(702\) −912.608 −0.0490658
\(703\) −3232.78 −0.173437
\(704\) 692.969 0.0370984
\(705\) −199.613 −0.0106636
\(706\) 3870.60 0.206334
\(707\) 0 0
\(708\) 968.856 0.0514291
\(709\) 6358.64 0.336818 0.168409 0.985717i \(-0.446137\pi\)
0.168409 + 0.985717i \(0.446137\pi\)
\(710\) 9932.40 0.525009
\(711\) 1315.88 0.0694084
\(712\) 3270.86 0.172164
\(713\) −6558.88 −0.344505
\(714\) 0 0
\(715\) 3905.41 0.204272
\(716\) −11986.9 −0.625657
\(717\) 1800.46 0.0937790
\(718\) 2841.73 0.147705
\(719\) −23439.4 −1.21577 −0.607887 0.794024i \(-0.707983\pi\)
−0.607887 + 0.794024i \(0.707983\pi\)
\(720\) −7735.92 −0.400418
\(721\) 0 0
\(722\) 13205.5 0.680690
\(723\) 1794.42 0.0923034
\(724\) −5332.16 −0.273713
\(725\) 34905.9 1.78810
\(726\) −1028.64 −0.0525846
\(727\) −19080.9 −0.973415 −0.486708 0.873565i \(-0.661802\pi\)
−0.486708 + 0.873565i \(0.661802\pi\)
\(728\) 0 0
\(729\) −18902.0 −0.960320
\(730\) −14627.0 −0.741601
\(731\) −2465.54 −0.124749
\(732\) −835.988 −0.0422117
\(733\) 7975.41 0.401881 0.200940 0.979603i \(-0.435600\pi\)
0.200940 + 0.979603i \(0.435600\pi\)
\(734\) 13481.8 0.677959
\(735\) 0 0
\(736\) −736.000 −0.0368605
\(737\) 9236.92 0.461664
\(738\) 3902.33 0.194643
\(739\) 12646.3 0.629502 0.314751 0.949174i \(-0.398079\pi\)
0.314751 + 0.949174i \(0.398079\pi\)
\(740\) 14562.5 0.723415
\(741\) 135.717 0.00672832
\(742\) 0 0
\(743\) 21893.7 1.08103 0.540514 0.841335i \(-0.318230\pi\)
0.540514 + 0.841335i \(0.318230\pi\)
\(744\) −966.699 −0.0476356
\(745\) −30308.7 −1.49051
\(746\) −10739.8 −0.527092
\(747\) 14406.2 0.705615
\(748\) 4746.73 0.232029
\(749\) 0 0
\(750\) 1145.46 0.0557685
\(751\) 29541.1 1.43538 0.717689 0.696363i \(-0.245200\pi\)
0.717689 + 0.696363i \(0.245200\pi\)
\(752\) 418.103 0.0202748
\(753\) −951.853 −0.0460657
\(754\) −6984.86 −0.337365
\(755\) −9733.19 −0.469175
\(756\) 0 0
\(757\) −18772.7 −0.901326 −0.450663 0.892694i \(-0.648812\pi\)
−0.450663 + 0.892694i \(0.648812\pi\)
\(758\) −5021.49 −0.240618
\(759\) −105.527 −0.00504660
\(760\) 2308.57 0.110185
\(761\) 27796.9 1.32410 0.662049 0.749461i \(-0.269687\pi\)
0.662049 + 0.749461i \(0.269687\pi\)
\(762\) 1424.06 0.0677009
\(763\) 0 0
\(764\) −12392.0 −0.586816
\(765\) −52989.8 −2.50438
\(766\) −18873.8 −0.890260
\(767\) −11436.9 −0.538410
\(768\) −108.478 −0.00509680
\(769\) 3876.68 0.181790 0.0908950 0.995860i \(-0.471027\pi\)
0.0908950 + 0.995860i \(0.471027\pi\)
\(770\) 0 0
\(771\) −1325.93 −0.0619354
\(772\) 12263.6 0.571732
\(773\) 25970.4 1.20840 0.604198 0.796834i \(-0.293493\pi\)
0.604198 + 0.796834i \(0.293493\pi\)
\(774\) −1206.72 −0.0560397
\(775\) −57027.0 −2.64319
\(776\) 9319.15 0.431106
\(777\) 0 0
\(778\) 6050.38 0.278813
\(779\) −1164.54 −0.0535610
\(780\) −611.354 −0.0280641
\(781\) −2982.85 −0.136664
\(782\) −5041.48 −0.230541
\(783\) 3980.77 0.181687
\(784\) 0 0
\(785\) 18784.5 0.854072
\(786\) 1557.88 0.0706968
\(787\) 38804.8 1.75761 0.878806 0.477180i \(-0.158341\pi\)
0.878806 + 0.477180i \(0.158341\pi\)
\(788\) 2012.46 0.0909781
\(789\) −2533.40 −0.114311
\(790\) 1768.91 0.0796647
\(791\) 0 0
\(792\) 2323.22 0.104232
\(793\) 9868.41 0.441914
\(794\) −27998.7 −1.25143
\(795\) 2288.85 0.102110
\(796\) 5076.37 0.226039
\(797\) 28345.3 1.25978 0.629888 0.776686i \(-0.283101\pi\)
0.629888 + 0.776686i \(0.283101\pi\)
\(798\) 0 0
\(799\) 2863.94 0.126807
\(800\) −6399.25 −0.282809
\(801\) 10965.7 0.483714
\(802\) −6035.35 −0.265730
\(803\) 4392.71 0.193045
\(804\) −1445.95 −0.0634262
\(805\) 0 0
\(806\) 11411.4 0.498696
\(807\) 2622.97 0.114415
\(808\) −15104.3 −0.657632
\(809\) −20784.8 −0.903282 −0.451641 0.892200i \(-0.649161\pi\)
−0.451641 + 0.892200i \(0.649161\pi\)
\(810\) −25760.3 −1.11744
\(811\) 10577.0 0.457963 0.228981 0.973431i \(-0.426461\pi\)
0.228981 + 0.973431i \(0.426461\pi\)
\(812\) 0 0
\(813\) 1089.14 0.0469837
\(814\) −4373.34 −0.188311
\(815\) 15353.3 0.659883
\(816\) −743.053 −0.0318775
\(817\) 360.113 0.0154207
\(818\) −13483.6 −0.576335
\(819\) 0 0
\(820\) 5245.83 0.223405
\(821\) 1446.68 0.0614975 0.0307488 0.999527i \(-0.490211\pi\)
0.0307488 + 0.999527i \(0.490211\pi\)
\(822\) 2144.78 0.0910072
\(823\) −37849.9 −1.60311 −0.801557 0.597918i \(-0.795995\pi\)
−0.801557 + 0.597918i \(0.795995\pi\)
\(824\) −5862.40 −0.247848
\(825\) −917.514 −0.0387197
\(826\) 0 0
\(827\) 24988.6 1.05071 0.525355 0.850883i \(-0.323932\pi\)
0.525355 + 0.850883i \(0.323932\pi\)
\(828\) −2467.48 −0.103564
\(829\) −25002.4 −1.04749 −0.523744 0.851876i \(-0.675465\pi\)
−0.523744 + 0.851876i \(0.675465\pi\)
\(830\) 19366.0 0.809882
\(831\) 1400.85 0.0584776
\(832\) 1280.52 0.0533583
\(833\) 0 0
\(834\) 199.448 0.00828094
\(835\) −65954.3 −2.73347
\(836\) −693.299 −0.0286821
\(837\) −6503.52 −0.268572
\(838\) −5011.30 −0.206578
\(839\) −12191.6 −0.501671 −0.250836 0.968030i \(-0.580705\pi\)
−0.250836 + 0.968030i \(0.580705\pi\)
\(840\) 0 0
\(841\) 6078.75 0.249242
\(842\) −15331.9 −0.627521
\(843\) −2008.61 −0.0820645
\(844\) −12596.3 −0.513722
\(845\) −32388.8 −1.31859
\(846\) 1401.71 0.0569644
\(847\) 0 0
\(848\) −4794.15 −0.194141
\(849\) −3718.38 −0.150312
\(850\) −43833.8 −1.76881
\(851\) 4644.91 0.187104
\(852\) 466.937 0.0187758
\(853\) −27618.4 −1.10860 −0.554300 0.832317i \(-0.687014\pi\)
−0.554300 + 0.832317i \(0.687014\pi\)
\(854\) 0 0
\(855\) 7739.60 0.309578
\(856\) −234.841 −0.00937697
\(857\) 12648.6 0.504164 0.252082 0.967706i \(-0.418885\pi\)
0.252082 + 0.967706i \(0.418885\pi\)
\(858\) 183.599 0.00730533
\(859\) 5293.51 0.210259 0.105129 0.994459i \(-0.466474\pi\)
0.105129 + 0.994459i \(0.466474\pi\)
\(860\) −1622.17 −0.0643206
\(861\) 0 0
\(862\) 7471.43 0.295218
\(863\) 40972.6 1.61614 0.808068 0.589089i \(-0.200513\pi\)
0.808068 + 0.589089i \(0.200513\pi\)
\(864\) −729.789 −0.0287360
\(865\) 834.520 0.0328029
\(866\) 26248.0 1.02996
\(867\) −3007.96 −0.117827
\(868\) 0 0
\(869\) −531.232 −0.0207374
\(870\) 2666.71 0.103919
\(871\) 17068.7 0.664008
\(872\) −12037.1 −0.467464
\(873\) 31243.0 1.21124
\(874\) 736.350 0.0284982
\(875\) 0 0
\(876\) −687.636 −0.0265217
\(877\) 50035.4 1.92654 0.963269 0.268537i \(-0.0865403\pi\)
0.963269 + 0.268537i \(0.0865403\pi\)
\(878\) −21673.1 −0.833066
\(879\) 1151.60 0.0441893
\(880\) 3123.06 0.119634
\(881\) −11129.7 −0.425618 −0.212809 0.977094i \(-0.568261\pi\)
−0.212809 + 0.977094i \(0.568261\pi\)
\(882\) 0 0
\(883\) 10184.5 0.388149 0.194074 0.980987i \(-0.437830\pi\)
0.194074 + 0.980987i \(0.437830\pi\)
\(884\) 8771.37 0.333725
\(885\) 4366.41 0.165848
\(886\) 17043.7 0.646270
\(887\) −36749.2 −1.39111 −0.695556 0.718472i \(-0.744842\pi\)
−0.695556 + 0.718472i \(0.744842\pi\)
\(888\) 684.603 0.0258714
\(889\) 0 0
\(890\) 14741.0 0.555191
\(891\) 7736.22 0.290879
\(892\) −1901.13 −0.0713617
\(893\) −418.302 −0.0156752
\(894\) −1424.86 −0.0533047
\(895\) −54022.2 −2.01761
\(896\) 0 0
\(897\) −195.000 −0.00725849
\(898\) 24572.0 0.913117
\(899\) −49776.2 −1.84664
\(900\) −21453.8 −0.794586
\(901\) −32839.1 −1.21424
\(902\) −1575.40 −0.0581544
\(903\) 0 0
\(904\) 1723.95 0.0634268
\(905\) −24030.9 −0.882666
\(906\) −457.571 −0.0167790
\(907\) −3161.83 −0.115752 −0.0578759 0.998324i \(-0.518433\pi\)
−0.0578759 + 0.998324i \(0.518433\pi\)
\(908\) 19695.5 0.719845
\(909\) −50637.9 −1.84769
\(910\) 0 0
\(911\) −7515.86 −0.273339 −0.136669 0.990617i \(-0.543640\pi\)
−0.136669 + 0.990617i \(0.543640\pi\)
\(912\) 108.529 0.00394053
\(913\) −5815.90 −0.210819
\(914\) −13873.7 −0.502080
\(915\) −3767.61 −0.136124
\(916\) −12395.0 −0.447099
\(917\) 0 0
\(918\) −4998.93 −0.179727
\(919\) −3072.55 −0.110287 −0.0551437 0.998478i \(-0.517562\pi\)
−0.0551437 + 0.998478i \(0.517562\pi\)
\(920\) −3316.99 −0.118867
\(921\) −3191.67 −0.114190
\(922\) 13482.1 0.481572
\(923\) −5511.95 −0.196563
\(924\) 0 0
\(925\) 40385.7 1.43554
\(926\) −10484.7 −0.372082
\(927\) −19654.0 −0.696357
\(928\) −5585.60 −0.197582
\(929\) 12994.6 0.458924 0.229462 0.973318i \(-0.426303\pi\)
0.229462 + 0.973318i \(0.426303\pi\)
\(930\) −4356.70 −0.153615
\(931\) 0 0
\(932\) 27353.0 0.961348
\(933\) −4626.78 −0.162352
\(934\) −1650.52 −0.0578229
\(935\) 21392.4 0.748243
\(936\) 4293.02 0.149916
\(937\) −28457.1 −0.992161 −0.496080 0.868277i \(-0.665228\pi\)
−0.496080 + 0.868277i \(0.665228\pi\)
\(938\) 0 0
\(939\) −3257.50 −0.113210
\(940\) 1884.30 0.0653819
\(941\) −38435.1 −1.33151 −0.665754 0.746172i \(-0.731890\pi\)
−0.665754 + 0.746172i \(0.731890\pi\)
\(942\) 883.086 0.0305440
\(943\) 1673.23 0.0577814
\(944\) −9145.75 −0.315327
\(945\) 0 0
\(946\) 487.164 0.0167432
\(947\) −50283.5 −1.72544 −0.862722 0.505679i \(-0.831242\pi\)
−0.862722 + 0.505679i \(0.831242\pi\)
\(948\) 83.1592 0.00284903
\(949\) 8117.19 0.277656
\(950\) 6402.29 0.218650
\(951\) 3927.74 0.133928
\(952\) 0 0
\(953\) −3339.05 −0.113497 −0.0567483 0.998389i \(-0.518073\pi\)
−0.0567483 + 0.998389i \(0.518073\pi\)
\(954\) −16072.6 −0.545462
\(955\) −55848.1 −1.89236
\(956\) −16995.9 −0.574987
\(957\) −800.855 −0.0270512
\(958\) −21996.4 −0.741830
\(959\) 0 0
\(960\) −488.884 −0.0164361
\(961\) 51530.1 1.72972
\(962\) −8081.40 −0.270847
\(963\) −787.316 −0.0263457
\(964\) −16938.9 −0.565939
\(965\) 55269.4 1.84371
\(966\) 0 0
\(967\) 44743.8 1.48797 0.743983 0.668198i \(-0.232934\pi\)
0.743983 + 0.668198i \(0.232934\pi\)
\(968\) 9710.10 0.322412
\(969\) 743.407 0.0246457
\(970\) 41999.3 1.39022
\(971\) 592.085 0.0195684 0.00978420 0.999952i \(-0.496886\pi\)
0.00978420 + 0.999952i \(0.496886\pi\)
\(972\) −3674.07 −0.121240
\(973\) 0 0
\(974\) 11952.9 0.393220
\(975\) −1695.45 −0.0556902
\(976\) 7891.51 0.258813
\(977\) 7513.33 0.246031 0.123016 0.992405i \(-0.460743\pi\)
0.123016 + 0.992405i \(0.460743\pi\)
\(978\) 721.783 0.0235993
\(979\) −4426.96 −0.144521
\(980\) 0 0
\(981\) −40355.1 −1.31340
\(982\) 2238.59 0.0727456
\(983\) 12122.1 0.393321 0.196660 0.980472i \(-0.436990\pi\)
0.196660 + 0.980472i \(0.436990\pi\)
\(984\) 246.614 0.00798960
\(985\) 9069.69 0.293385
\(986\) −38260.5 −1.23576
\(987\) 0 0
\(988\) −1281.13 −0.0412533
\(989\) −517.415 −0.0166358
\(990\) 10470.2 0.336127
\(991\) −1562.94 −0.0500995 −0.0250497 0.999686i \(-0.507974\pi\)
−0.0250497 + 0.999686i \(0.507974\pi\)
\(992\) 9125.39 0.292068
\(993\) −4211.79 −0.134599
\(994\) 0 0
\(995\) 22878.1 0.728928
\(996\) 910.422 0.0289637
\(997\) −58687.6 −1.86425 −0.932124 0.362138i \(-0.882047\pi\)
−0.932124 + 0.362138i \(0.882047\pi\)
\(998\) −14115.4 −0.447712
\(999\) 4605.71 0.145864
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2254.4.a.u.1.6 11
7.3 odd 6 322.4.e.d.93.6 22
7.5 odd 6 322.4.e.d.277.6 yes 22
7.6 odd 2 2254.4.a.r.1.6 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.e.d.93.6 22 7.3 odd 6
322.4.e.d.277.6 yes 22 7.5 odd 6
2254.4.a.r.1.6 11 7.6 odd 2
2254.4.a.u.1.6 11 1.1 even 1 trivial