Properties

Label 1452.4.a.t.1.5
Level $1452$
Weight $4$
Character 1452.1
Self dual yes
Analytic conductor $85.671$
Analytic rank $1$
Dimension $6$
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] = [1452,4,Mod(1,1452)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1452, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1452.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1452.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: \(85.6707733283\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 174x^{4} + 63x^{3} + 7614x^{2} + 1579x - 12611 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 11 \)
Twist minimal: no (minimal twist has level 132)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.20018\) of defining polynomial
Character \(\chi\) \(=\) 1452.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} +10.3377 q^{5} +5.80080 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +10.3377 q^{5} +5.80080 q^{7} +9.00000 q^{9} -47.3044 q^{13} +31.0132 q^{15} -109.726 q^{17} -11.8417 q^{19} +17.4024 q^{21} -7.30324 q^{23} -18.1315 q^{25} +27.0000 q^{27} -36.1125 q^{29} +117.587 q^{31} +59.9671 q^{35} -396.848 q^{37} -141.913 q^{39} -256.630 q^{41} -351.237 q^{43} +93.0395 q^{45} -354.461 q^{47} -309.351 q^{49} -329.178 q^{51} -162.775 q^{53} -35.5251 q^{57} +285.636 q^{59} +36.8307 q^{61} +52.2072 q^{63} -489.020 q^{65} +856.929 q^{67} -21.9097 q^{69} +516.892 q^{71} +639.252 q^{73} -54.3946 q^{75} -613.584 q^{79} +81.0000 q^{81} -478.395 q^{83} -1134.32 q^{85} -108.338 q^{87} -46.9014 q^{89} -274.404 q^{91} +352.761 q^{93} -122.416 q^{95} +163.330 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 18 q^{3} + 13 q^{5} - 23 q^{7} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 18 q^{3} + 13 q^{5} - 23 q^{7} + 54 q^{9} - 66 q^{13} + 39 q^{15} - 44 q^{17} - 270 q^{19} - 69 q^{21} - 124 q^{23} + 131 q^{25} + 162 q^{27} - 141 q^{29} - 253 q^{31} - 884 q^{35} + 288 q^{37} - 198 q^{39} - 428 q^{41} - 1006 q^{43} + 117 q^{45} - 674 q^{47} + 181 q^{49} - 132 q^{51} - 773 q^{53} - 810 q^{57} - 17 q^{59} - 1016 q^{61} - 207 q^{63} - 1220 q^{65} + 1836 q^{67} - 372 q^{69} - 208 q^{71} - 1521 q^{73} + 393 q^{75} - 1425 q^{79} + 486 q^{81} - 3065 q^{83} - 1304 q^{85} - 423 q^{87} + 1444 q^{89} + 1328 q^{91} - 759 q^{93} - 1760 q^{95} - 3887 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 10.3377 0.924634 0.462317 0.886715i \(-0.347018\pi\)
0.462317 + 0.886715i \(0.347018\pi\)
\(6\) 0 0
\(7\) 5.80080 0.313214 0.156607 0.987661i \(-0.449944\pi\)
0.156607 + 0.987661i \(0.449944\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −47.3044 −1.00922 −0.504611 0.863347i \(-0.668364\pi\)
−0.504611 + 0.863347i \(0.668364\pi\)
\(14\) 0 0
\(15\) 31.0132 0.533838
\(16\) 0 0
\(17\) −109.726 −1.56544 −0.782719 0.622376i \(-0.786168\pi\)
−0.782719 + 0.622376i \(0.786168\pi\)
\(18\) 0 0
\(19\) −11.8417 −0.142983 −0.0714914 0.997441i \(-0.522776\pi\)
−0.0714914 + 0.997441i \(0.522776\pi\)
\(20\) 0 0
\(21\) 17.4024 0.180834
\(22\) 0 0
\(23\) −7.30324 −0.0662101 −0.0331050 0.999452i \(-0.510540\pi\)
−0.0331050 + 0.999452i \(0.510540\pi\)
\(24\) 0 0
\(25\) −18.1315 −0.145052
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −36.1125 −0.231239 −0.115619 0.993294i \(-0.536885\pi\)
−0.115619 + 0.993294i \(0.536885\pi\)
\(30\) 0 0
\(31\) 117.587 0.681265 0.340633 0.940196i \(-0.389359\pi\)
0.340633 + 0.940196i \(0.389359\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 59.9671 0.289608
\(36\) 0 0
\(37\) −396.848 −1.76328 −0.881641 0.471921i \(-0.843561\pi\)
−0.881641 + 0.471921i \(0.843561\pi\)
\(38\) 0 0
\(39\) −141.913 −0.582675
\(40\) 0 0
\(41\) −256.630 −0.977535 −0.488767 0.872414i \(-0.662553\pi\)
−0.488767 + 0.872414i \(0.662553\pi\)
\(42\) 0 0
\(43\) −351.237 −1.24565 −0.622827 0.782359i \(-0.714016\pi\)
−0.622827 + 0.782359i \(0.714016\pi\)
\(44\) 0 0
\(45\) 93.0395 0.308211
\(46\) 0 0
\(47\) −354.461 −1.10007 −0.550037 0.835140i \(-0.685387\pi\)
−0.550037 + 0.835140i \(0.685387\pi\)
\(48\) 0 0
\(49\) −309.351 −0.901897
\(50\) 0 0
\(51\) −329.178 −0.903805
\(52\) 0 0
\(53\) −162.775 −0.421865 −0.210932 0.977501i \(-0.567650\pi\)
−0.210932 + 0.977501i \(0.567650\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −35.5251 −0.0825512
\(58\) 0 0
\(59\) 285.636 0.630282 0.315141 0.949045i \(-0.397948\pi\)
0.315141 + 0.949045i \(0.397948\pi\)
\(60\) 0 0
\(61\) 36.8307 0.0773063 0.0386532 0.999253i \(-0.487693\pi\)
0.0386532 + 0.999253i \(0.487693\pi\)
\(62\) 0 0
\(63\) 52.2072 0.104405
\(64\) 0 0
\(65\) −489.020 −0.933161
\(66\) 0 0
\(67\) 856.929 1.56255 0.781273 0.624190i \(-0.214571\pi\)
0.781273 + 0.624190i \(0.214571\pi\)
\(68\) 0 0
\(69\) −21.9097 −0.0382264
\(70\) 0 0
\(71\) 516.892 0.863998 0.431999 0.901874i \(-0.357808\pi\)
0.431999 + 0.901874i \(0.357808\pi\)
\(72\) 0 0
\(73\) 639.252 1.02492 0.512458 0.858713i \(-0.328735\pi\)
0.512458 + 0.858713i \(0.328735\pi\)
\(74\) 0 0
\(75\) −54.3946 −0.0837459
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −613.584 −0.873842 −0.436921 0.899500i \(-0.643931\pi\)
−0.436921 + 0.899500i \(0.643931\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −478.395 −0.632658 −0.316329 0.948649i \(-0.602450\pi\)
−0.316329 + 0.948649i \(0.602450\pi\)
\(84\) 0 0
\(85\) −1134.32 −1.44746
\(86\) 0 0
\(87\) −108.338 −0.133506
\(88\) 0 0
\(89\) −46.9014 −0.0558599 −0.0279300 0.999610i \(-0.508892\pi\)
−0.0279300 + 0.999610i \(0.508892\pi\)
\(90\) 0 0
\(91\) −274.404 −0.316103
\(92\) 0 0
\(93\) 352.761 0.393329
\(94\) 0 0
\(95\) −122.416 −0.132207
\(96\) 0 0
\(97\) 163.330 0.170966 0.0854828 0.996340i \(-0.472757\pi\)
0.0854828 + 0.996340i \(0.472757\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −804.911 −0.792986 −0.396493 0.918038i \(-0.629773\pi\)
−0.396493 + 0.918038i \(0.629773\pi\)
\(102\) 0 0
\(103\) 1007.34 0.963652 0.481826 0.876267i \(-0.339974\pi\)
0.481826 + 0.876267i \(0.339974\pi\)
\(104\) 0 0
\(105\) 179.901 0.167205
\(106\) 0 0
\(107\) −1019.41 −0.921032 −0.460516 0.887651i \(-0.652336\pi\)
−0.460516 + 0.887651i \(0.652336\pi\)
\(108\) 0 0
\(109\) 2252.23 1.97913 0.989564 0.144097i \(-0.0460279\pi\)
0.989564 + 0.144097i \(0.0460279\pi\)
\(110\) 0 0
\(111\) −1190.54 −1.01803
\(112\) 0 0
\(113\) 250.192 0.208284 0.104142 0.994562i \(-0.466790\pi\)
0.104142 + 0.994562i \(0.466790\pi\)
\(114\) 0 0
\(115\) −75.4989 −0.0612201
\(116\) 0 0
\(117\) −425.740 −0.336407
\(118\) 0 0
\(119\) −636.498 −0.490317
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −769.891 −0.564380
\(124\) 0 0
\(125\) −1479.65 −1.05875
\(126\) 0 0
\(127\) −1650.86 −1.15347 −0.576734 0.816932i \(-0.695673\pi\)
−0.576734 + 0.816932i \(0.695673\pi\)
\(128\) 0 0
\(129\) −1053.71 −0.719179
\(130\) 0 0
\(131\) 730.497 0.487204 0.243602 0.969875i \(-0.421671\pi\)
0.243602 + 0.969875i \(0.421671\pi\)
\(132\) 0 0
\(133\) −68.6915 −0.0447842
\(134\) 0 0
\(135\) 279.118 0.177946
\(136\) 0 0
\(137\) 2859.50 1.78324 0.891619 0.452787i \(-0.149570\pi\)
0.891619 + 0.452787i \(0.149570\pi\)
\(138\) 0 0
\(139\) 1000.88 0.610744 0.305372 0.952233i \(-0.401219\pi\)
0.305372 + 0.952233i \(0.401219\pi\)
\(140\) 0 0
\(141\) −1063.38 −0.635129
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −373.321 −0.213811
\(146\) 0 0
\(147\) −928.052 −0.520710
\(148\) 0 0
\(149\) 2557.52 1.40617 0.703087 0.711104i \(-0.251804\pi\)
0.703087 + 0.711104i \(0.251804\pi\)
\(150\) 0 0
\(151\) −84.9460 −0.0457802 −0.0228901 0.999738i \(-0.507287\pi\)
−0.0228901 + 0.999738i \(0.507287\pi\)
\(152\) 0 0
\(153\) −987.533 −0.521812
\(154\) 0 0
\(155\) 1215.58 0.629921
\(156\) 0 0
\(157\) −1480.21 −0.752444 −0.376222 0.926530i \(-0.622777\pi\)
−0.376222 + 0.926530i \(0.622777\pi\)
\(158\) 0 0
\(159\) −488.324 −0.243564
\(160\) 0 0
\(161\) −42.3647 −0.0207379
\(162\) 0 0
\(163\) −3378.78 −1.62360 −0.811799 0.583937i \(-0.801512\pi\)
−0.811799 + 0.583937i \(0.801512\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1950.75 −0.903915 −0.451957 0.892039i \(-0.649274\pi\)
−0.451957 + 0.892039i \(0.649274\pi\)
\(168\) 0 0
\(169\) 40.7099 0.0185298
\(170\) 0 0
\(171\) −106.575 −0.0476610
\(172\) 0 0
\(173\) −2230.90 −0.980417 −0.490209 0.871605i \(-0.663079\pi\)
−0.490209 + 0.871605i \(0.663079\pi\)
\(174\) 0 0
\(175\) −105.177 −0.0454324
\(176\) 0 0
\(177\) 856.908 0.363893
\(178\) 0 0
\(179\) 2305.48 0.962680 0.481340 0.876534i \(-0.340150\pi\)
0.481340 + 0.876534i \(0.340150\pi\)
\(180\) 0 0
\(181\) 3311.70 1.35998 0.679992 0.733220i \(-0.261983\pi\)
0.679992 + 0.733220i \(0.261983\pi\)
\(182\) 0 0
\(183\) 110.492 0.0446328
\(184\) 0 0
\(185\) −4102.50 −1.63039
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 156.622 0.0602781
\(190\) 0 0
\(191\) −1474.55 −0.558609 −0.279305 0.960203i \(-0.590104\pi\)
−0.279305 + 0.960203i \(0.590104\pi\)
\(192\) 0 0
\(193\) −2989.62 −1.11501 −0.557506 0.830173i \(-0.688242\pi\)
−0.557506 + 0.830173i \(0.688242\pi\)
\(194\) 0 0
\(195\) −1467.06 −0.538761
\(196\) 0 0
\(197\) −259.625 −0.0938962 −0.0469481 0.998897i \(-0.514950\pi\)
−0.0469481 + 0.998897i \(0.514950\pi\)
\(198\) 0 0
\(199\) 2831.47 1.00863 0.504316 0.863519i \(-0.331745\pi\)
0.504316 + 0.863519i \(0.331745\pi\)
\(200\) 0 0
\(201\) 2570.79 0.902136
\(202\) 0 0
\(203\) −209.482 −0.0724273
\(204\) 0 0
\(205\) −2652.97 −0.903862
\(206\) 0 0
\(207\) −65.7292 −0.0220700
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −2382.75 −0.777418 −0.388709 0.921361i \(-0.627079\pi\)
−0.388709 + 0.921361i \(0.627079\pi\)
\(212\) 0 0
\(213\) 1550.68 0.498829
\(214\) 0 0
\(215\) −3630.99 −1.15177
\(216\) 0 0
\(217\) 682.098 0.213382
\(218\) 0 0
\(219\) 1917.76 0.591735
\(220\) 0 0
\(221\) 5190.52 1.57987
\(222\) 0 0
\(223\) −2035.27 −0.611173 −0.305587 0.952164i \(-0.598853\pi\)
−0.305587 + 0.952164i \(0.598853\pi\)
\(224\) 0 0
\(225\) −163.184 −0.0483507
\(226\) 0 0
\(227\) 499.392 0.146017 0.0730083 0.997331i \(-0.476740\pi\)
0.0730083 + 0.997331i \(0.476740\pi\)
\(228\) 0 0
\(229\) −2858.85 −0.824970 −0.412485 0.910964i \(-0.635339\pi\)
−0.412485 + 0.910964i \(0.635339\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5477.76 1.54017 0.770086 0.637940i \(-0.220213\pi\)
0.770086 + 0.637940i \(0.220213\pi\)
\(234\) 0 0
\(235\) −3664.32 −1.01717
\(236\) 0 0
\(237\) −1840.75 −0.504513
\(238\) 0 0
\(239\) −7023.21 −1.90081 −0.950406 0.311013i \(-0.899332\pi\)
−0.950406 + 0.311013i \(0.899332\pi\)
\(240\) 0 0
\(241\) 3611.41 0.965276 0.482638 0.875820i \(-0.339679\pi\)
0.482638 + 0.875820i \(0.339679\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) −3197.98 −0.833925
\(246\) 0 0
\(247\) 560.166 0.144302
\(248\) 0 0
\(249\) −1435.18 −0.365265
\(250\) 0 0
\(251\) 2039.84 0.512961 0.256481 0.966549i \(-0.417437\pi\)
0.256481 + 0.966549i \(0.417437\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −3402.95 −0.835689
\(256\) 0 0
\(257\) −7104.54 −1.72439 −0.862197 0.506573i \(-0.830912\pi\)
−0.862197 + 0.506573i \(0.830912\pi\)
\(258\) 0 0
\(259\) −2302.04 −0.552284
\(260\) 0 0
\(261\) −325.013 −0.0770797
\(262\) 0 0
\(263\) 6912.17 1.62062 0.810309 0.586002i \(-0.199299\pi\)
0.810309 + 0.586002i \(0.199299\pi\)
\(264\) 0 0
\(265\) −1682.72 −0.390071
\(266\) 0 0
\(267\) −140.704 −0.0322507
\(268\) 0 0
\(269\) 6260.31 1.41895 0.709476 0.704730i \(-0.248932\pi\)
0.709476 + 0.704730i \(0.248932\pi\)
\(270\) 0 0
\(271\) −1718.19 −0.385140 −0.192570 0.981283i \(-0.561682\pi\)
−0.192570 + 0.981283i \(0.561682\pi\)
\(272\) 0 0
\(273\) −823.211 −0.182502
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −5471.15 −1.18675 −0.593374 0.804927i \(-0.702205\pi\)
−0.593374 + 0.804927i \(0.702205\pi\)
\(278\) 0 0
\(279\) 1058.28 0.227088
\(280\) 0 0
\(281\) −4059.40 −0.861792 −0.430896 0.902402i \(-0.641802\pi\)
−0.430896 + 0.902402i \(0.641802\pi\)
\(282\) 0 0
\(283\) −4290.06 −0.901122 −0.450561 0.892746i \(-0.648776\pi\)
−0.450561 + 0.892746i \(0.648776\pi\)
\(284\) 0 0
\(285\) −367.249 −0.0763296
\(286\) 0 0
\(287\) −1488.66 −0.306178
\(288\) 0 0
\(289\) 7126.76 1.45059
\(290\) 0 0
\(291\) 489.991 0.0987071
\(292\) 0 0
\(293\) −944.438 −0.188309 −0.0941547 0.995558i \(-0.530015\pi\)
−0.0941547 + 0.995558i \(0.530015\pi\)
\(294\) 0 0
\(295\) 2952.82 0.582780
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 345.476 0.0668207
\(300\) 0 0
\(301\) −2037.46 −0.390157
\(302\) 0 0
\(303\) −2414.73 −0.457831
\(304\) 0 0
\(305\) 380.745 0.0714800
\(306\) 0 0
\(307\) −7598.46 −1.41260 −0.706298 0.707915i \(-0.749636\pi\)
−0.706298 + 0.707915i \(0.749636\pi\)
\(308\) 0 0
\(309\) 3022.02 0.556365
\(310\) 0 0
\(311\) −8962.47 −1.63413 −0.817066 0.576544i \(-0.804401\pi\)
−0.817066 + 0.576544i \(0.804401\pi\)
\(312\) 0 0
\(313\) 4071.50 0.735255 0.367628 0.929973i \(-0.380170\pi\)
0.367628 + 0.929973i \(0.380170\pi\)
\(314\) 0 0
\(315\) 539.704 0.0965361
\(316\) 0 0
\(317\) −4668.14 −0.827095 −0.413548 0.910483i \(-0.635710\pi\)
−0.413548 + 0.910483i \(0.635710\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −3058.24 −0.531758
\(322\) 0 0
\(323\) 1299.34 0.223831
\(324\) 0 0
\(325\) 857.701 0.146390
\(326\) 0 0
\(327\) 6756.70 1.14265
\(328\) 0 0
\(329\) −2056.16 −0.344559
\(330\) 0 0
\(331\) 5769.39 0.958049 0.479025 0.877801i \(-0.340990\pi\)
0.479025 + 0.877801i \(0.340990\pi\)
\(332\) 0 0
\(333\) −3571.63 −0.587760
\(334\) 0 0
\(335\) 8858.69 1.44478
\(336\) 0 0
\(337\) −1623.09 −0.262360 −0.131180 0.991359i \(-0.541877\pi\)
−0.131180 + 0.991359i \(0.541877\pi\)
\(338\) 0 0
\(339\) 750.576 0.120253
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −3784.16 −0.595701
\(344\) 0 0
\(345\) −226.497 −0.0353454
\(346\) 0 0
\(347\) 10953.5 1.69457 0.847286 0.531137i \(-0.178235\pi\)
0.847286 + 0.531137i \(0.178235\pi\)
\(348\) 0 0
\(349\) −10715.5 −1.64351 −0.821756 0.569840i \(-0.807005\pi\)
−0.821756 + 0.569840i \(0.807005\pi\)
\(350\) 0 0
\(351\) −1277.22 −0.194225
\(352\) 0 0
\(353\) −2850.20 −0.429748 −0.214874 0.976642i \(-0.568934\pi\)
−0.214874 + 0.976642i \(0.568934\pi\)
\(354\) 0 0
\(355\) 5343.49 0.798881
\(356\) 0 0
\(357\) −1909.49 −0.283085
\(358\) 0 0
\(359\) 10213.7 1.50156 0.750780 0.660552i \(-0.229678\pi\)
0.750780 + 0.660552i \(0.229678\pi\)
\(360\) 0 0
\(361\) −6718.77 −0.979556
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6608.41 0.947671
\(366\) 0 0
\(367\) 7540.97 1.07258 0.536288 0.844035i \(-0.319826\pi\)
0.536288 + 0.844035i \(0.319826\pi\)
\(368\) 0 0
\(369\) −2309.67 −0.325845
\(370\) 0 0
\(371\) −944.225 −0.132134
\(372\) 0 0
\(373\) 1860.38 0.258249 0.129125 0.991628i \(-0.458783\pi\)
0.129125 + 0.991628i \(0.458783\pi\)
\(374\) 0 0
\(375\) −4438.96 −0.611272
\(376\) 0 0
\(377\) 1708.28 0.233372
\(378\) 0 0
\(379\) −13838.8 −1.87560 −0.937798 0.347181i \(-0.887139\pi\)
−0.937798 + 0.347181i \(0.887139\pi\)
\(380\) 0 0
\(381\) −4952.59 −0.665955
\(382\) 0 0
\(383\) −1588.30 −0.211901 −0.105951 0.994371i \(-0.533789\pi\)
−0.105951 + 0.994371i \(0.533789\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3161.13 −0.415218
\(388\) 0 0
\(389\) −3988.03 −0.519797 −0.259899 0.965636i \(-0.583689\pi\)
−0.259899 + 0.965636i \(0.583689\pi\)
\(390\) 0 0
\(391\) 801.355 0.103648
\(392\) 0 0
\(393\) 2191.49 0.281288
\(394\) 0 0
\(395\) −6343.06 −0.807984
\(396\) 0 0
\(397\) −7791.14 −0.984952 −0.492476 0.870326i \(-0.663908\pi\)
−0.492476 + 0.870326i \(0.663908\pi\)
\(398\) 0 0
\(399\) −206.074 −0.0258562
\(400\) 0 0
\(401\) −8427.18 −1.04946 −0.524730 0.851269i \(-0.675834\pi\)
−0.524730 + 0.851269i \(0.675834\pi\)
\(402\) 0 0
\(403\) −5562.38 −0.687548
\(404\) 0 0
\(405\) 837.355 0.102737
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −3638.77 −0.439916 −0.219958 0.975509i \(-0.570592\pi\)
−0.219958 + 0.975509i \(0.570592\pi\)
\(410\) 0 0
\(411\) 8578.50 1.02955
\(412\) 0 0
\(413\) 1656.92 0.197413
\(414\) 0 0
\(415\) −4945.51 −0.584977
\(416\) 0 0
\(417\) 3002.64 0.352613
\(418\) 0 0
\(419\) 13673.5 1.59426 0.797131 0.603806i \(-0.206350\pi\)
0.797131 + 0.603806i \(0.206350\pi\)
\(420\) 0 0
\(421\) 11459.3 1.32658 0.663290 0.748363i \(-0.269160\pi\)
0.663290 + 0.748363i \(0.269160\pi\)
\(422\) 0 0
\(423\) −3190.15 −0.366692
\(424\) 0 0
\(425\) 1989.50 0.227070
\(426\) 0 0
\(427\) 213.648 0.0242134
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8091.69 0.904322 0.452161 0.891936i \(-0.350653\pi\)
0.452161 + 0.891936i \(0.350653\pi\)
\(432\) 0 0
\(433\) 11446.8 1.27044 0.635219 0.772332i \(-0.280910\pi\)
0.635219 + 0.772332i \(0.280910\pi\)
\(434\) 0 0
\(435\) −1119.96 −0.123444
\(436\) 0 0
\(437\) 86.4829 0.00946691
\(438\) 0 0
\(439\) −3451.69 −0.375262 −0.187631 0.982240i \(-0.560081\pi\)
−0.187631 + 0.982240i \(0.560081\pi\)
\(440\) 0 0
\(441\) −2784.16 −0.300632
\(442\) 0 0
\(443\) −16907.5 −1.81332 −0.906660 0.421862i \(-0.861377\pi\)
−0.906660 + 0.421862i \(0.861377\pi\)
\(444\) 0 0
\(445\) −484.853 −0.0516500
\(446\) 0 0
\(447\) 7672.55 0.811855
\(448\) 0 0
\(449\) 13840.8 1.45476 0.727379 0.686236i \(-0.240738\pi\)
0.727379 + 0.686236i \(0.240738\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −254.838 −0.0264312
\(454\) 0 0
\(455\) −2836.71 −0.292279
\(456\) 0 0
\(457\) 9205.28 0.942242 0.471121 0.882068i \(-0.343849\pi\)
0.471121 + 0.882068i \(0.343849\pi\)
\(458\) 0 0
\(459\) −2962.60 −0.301268
\(460\) 0 0
\(461\) 13321.0 1.34581 0.672906 0.739728i \(-0.265046\pi\)
0.672906 + 0.739728i \(0.265046\pi\)
\(462\) 0 0
\(463\) −13999.1 −1.40517 −0.702587 0.711598i \(-0.747972\pi\)
−0.702587 + 0.711598i \(0.747972\pi\)
\(464\) 0 0
\(465\) 3646.74 0.363685
\(466\) 0 0
\(467\) 10414.4 1.03195 0.515974 0.856604i \(-0.327430\pi\)
0.515974 + 0.856604i \(0.327430\pi\)
\(468\) 0 0
\(469\) 4970.88 0.489411
\(470\) 0 0
\(471\) −4440.63 −0.434424
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 214.708 0.0207400
\(476\) 0 0
\(477\) −1464.97 −0.140622
\(478\) 0 0
\(479\) 5668.18 0.540680 0.270340 0.962765i \(-0.412864\pi\)
0.270340 + 0.962765i \(0.412864\pi\)
\(480\) 0 0
\(481\) 18772.7 1.77954
\(482\) 0 0
\(483\) −127.094 −0.0119730
\(484\) 0 0
\(485\) 1688.46 0.158081
\(486\) 0 0
\(487\) −13476.1 −1.25392 −0.626962 0.779050i \(-0.715702\pi\)
−0.626962 + 0.779050i \(0.715702\pi\)
\(488\) 0 0
\(489\) −10136.3 −0.937385
\(490\) 0 0
\(491\) 14327.0 1.31684 0.658422 0.752649i \(-0.271224\pi\)
0.658422 + 0.752649i \(0.271224\pi\)
\(492\) 0 0
\(493\) 3962.48 0.361990
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2998.39 0.270616
\(498\) 0 0
\(499\) −3777.61 −0.338896 −0.169448 0.985539i \(-0.554198\pi\)
−0.169448 + 0.985539i \(0.554198\pi\)
\(500\) 0 0
\(501\) −5852.26 −0.521876
\(502\) 0 0
\(503\) 8501.39 0.753595 0.376797 0.926296i \(-0.377025\pi\)
0.376797 + 0.926296i \(0.377025\pi\)
\(504\) 0 0
\(505\) −8320.95 −0.733222
\(506\) 0 0
\(507\) 122.130 0.0106982
\(508\) 0 0
\(509\) 10108.6 0.880264 0.440132 0.897933i \(-0.354932\pi\)
0.440132 + 0.897933i \(0.354932\pi\)
\(510\) 0 0
\(511\) 3708.18 0.321018
\(512\) 0 0
\(513\) −319.726 −0.0275171
\(514\) 0 0
\(515\) 10413.6 0.891026
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −6692.70 −0.566044
\(520\) 0 0
\(521\) −4239.14 −0.356468 −0.178234 0.983988i \(-0.557038\pi\)
−0.178234 + 0.983988i \(0.557038\pi\)
\(522\) 0 0
\(523\) −21202.0 −1.77266 −0.886328 0.463058i \(-0.846752\pi\)
−0.886328 + 0.463058i \(0.846752\pi\)
\(524\) 0 0
\(525\) −315.532 −0.0262304
\(526\) 0 0
\(527\) −12902.3 −1.06648
\(528\) 0 0
\(529\) −12113.7 −0.995616
\(530\) 0 0
\(531\) 2570.72 0.210094
\(532\) 0 0
\(533\) 12139.8 0.986550
\(534\) 0 0
\(535\) −10538.4 −0.851618
\(536\) 0 0
\(537\) 6916.44 0.555804
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9056.61 −0.719730 −0.359865 0.933004i \(-0.617177\pi\)
−0.359865 + 0.933004i \(0.617177\pi\)
\(542\) 0 0
\(543\) 9935.11 0.785187
\(544\) 0 0
\(545\) 23283.0 1.82997
\(546\) 0 0
\(547\) 14424.4 1.12750 0.563750 0.825945i \(-0.309358\pi\)
0.563750 + 0.825945i \(0.309358\pi\)
\(548\) 0 0
\(549\) 331.476 0.0257688
\(550\) 0 0
\(551\) 427.634 0.0330632
\(552\) 0 0
\(553\) −3559.28 −0.273700
\(554\) 0 0
\(555\) −12307.5 −0.941306
\(556\) 0 0
\(557\) 4890.52 0.372025 0.186013 0.982547i \(-0.440443\pi\)
0.186013 + 0.982547i \(0.440443\pi\)
\(558\) 0 0
\(559\) 16615.1 1.25714
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18383.9 1.37618 0.688089 0.725626i \(-0.258450\pi\)
0.688089 + 0.725626i \(0.258450\pi\)
\(564\) 0 0
\(565\) 2586.41 0.192586
\(566\) 0 0
\(567\) 469.865 0.0348016
\(568\) 0 0
\(569\) 6468.56 0.476584 0.238292 0.971194i \(-0.423413\pi\)
0.238292 + 0.971194i \(0.423413\pi\)
\(570\) 0 0
\(571\) −7277.86 −0.533395 −0.266698 0.963780i \(-0.585933\pi\)
−0.266698 + 0.963780i \(0.585933\pi\)
\(572\) 0 0
\(573\) −4423.64 −0.322513
\(574\) 0 0
\(575\) 132.419 0.00960391
\(576\) 0 0
\(577\) −8614.28 −0.621521 −0.310760 0.950488i \(-0.600584\pi\)
−0.310760 + 0.950488i \(0.600584\pi\)
\(578\) 0 0
\(579\) −8968.85 −0.643752
\(580\) 0 0
\(581\) −2775.07 −0.198157
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −4401.18 −0.311054
\(586\) 0 0
\(587\) −10053.9 −0.706931 −0.353466 0.935447i \(-0.614997\pi\)
−0.353466 + 0.935447i \(0.614997\pi\)
\(588\) 0 0
\(589\) −1392.43 −0.0974093
\(590\) 0 0
\(591\) −778.876 −0.0542110
\(592\) 0 0
\(593\) 4391.04 0.304078 0.152039 0.988374i \(-0.451416\pi\)
0.152039 + 0.988374i \(0.451416\pi\)
\(594\) 0 0
\(595\) −6579.94 −0.453364
\(596\) 0 0
\(597\) 8494.41 0.582333
\(598\) 0 0
\(599\) −14435.7 −0.984683 −0.492341 0.870402i \(-0.663859\pi\)
−0.492341 + 0.870402i \(0.663859\pi\)
\(600\) 0 0
\(601\) −23485.3 −1.59398 −0.796992 0.603989i \(-0.793577\pi\)
−0.796992 + 0.603989i \(0.793577\pi\)
\(602\) 0 0
\(603\) 7712.36 0.520848
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 12645.1 0.845551 0.422776 0.906234i \(-0.361056\pi\)
0.422776 + 0.906234i \(0.361056\pi\)
\(608\) 0 0
\(609\) −628.445 −0.0418159
\(610\) 0 0
\(611\) 16767.6 1.11022
\(612\) 0 0
\(613\) 26361.9 1.73695 0.868473 0.495737i \(-0.165102\pi\)
0.868473 + 0.495737i \(0.165102\pi\)
\(614\) 0 0
\(615\) −7958.92 −0.521845
\(616\) 0 0
\(617\) 8960.83 0.584683 0.292342 0.956314i \(-0.405566\pi\)
0.292342 + 0.956314i \(0.405566\pi\)
\(618\) 0 0
\(619\) −10404.1 −0.675569 −0.337784 0.941223i \(-0.609677\pi\)
−0.337784 + 0.941223i \(0.609677\pi\)
\(620\) 0 0
\(621\) −197.188 −0.0127421
\(622\) 0 0
\(623\) −272.066 −0.0174961
\(624\) 0 0
\(625\) −13029.8 −0.833908
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 43544.5 2.76031
\(630\) 0 0
\(631\) 5110.14 0.322395 0.161198 0.986922i \(-0.448464\pi\)
0.161198 + 0.986922i \(0.448464\pi\)
\(632\) 0 0
\(633\) −7148.24 −0.448842
\(634\) 0 0
\(635\) −17066.2 −1.06654
\(636\) 0 0
\(637\) 14633.7 0.910215
\(638\) 0 0
\(639\) 4652.03 0.287999
\(640\) 0 0
\(641\) −6648.67 −0.409683 −0.204841 0.978795i \(-0.565668\pi\)
−0.204841 + 0.978795i \(0.565668\pi\)
\(642\) 0 0
\(643\) −24388.2 −1.49576 −0.747881 0.663832i \(-0.768929\pi\)
−0.747881 + 0.663832i \(0.768929\pi\)
\(644\) 0 0
\(645\) −10893.0 −0.664977
\(646\) 0 0
\(647\) 11901.3 0.723165 0.361582 0.932340i \(-0.382237\pi\)
0.361582 + 0.932340i \(0.382237\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 2046.30 0.123196
\(652\) 0 0
\(653\) −8684.07 −0.520419 −0.260210 0.965552i \(-0.583792\pi\)
−0.260210 + 0.965552i \(0.583792\pi\)
\(654\) 0 0
\(655\) 7551.67 0.450486
\(656\) 0 0
\(657\) 5753.27 0.341638
\(658\) 0 0
\(659\) −14795.9 −0.874608 −0.437304 0.899314i \(-0.644067\pi\)
−0.437304 + 0.899314i \(0.644067\pi\)
\(660\) 0 0
\(661\) 17801.5 1.04750 0.523751 0.851872i \(-0.324532\pi\)
0.523751 + 0.851872i \(0.324532\pi\)
\(662\) 0 0
\(663\) 15571.6 0.912141
\(664\) 0 0
\(665\) −710.113 −0.0414090
\(666\) 0 0
\(667\) 263.739 0.0153103
\(668\) 0 0
\(669\) −6105.81 −0.352861
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 16885.1 0.967120 0.483560 0.875311i \(-0.339343\pi\)
0.483560 + 0.875311i \(0.339343\pi\)
\(674\) 0 0
\(675\) −489.551 −0.0279153
\(676\) 0 0
\(677\) −17446.3 −0.990423 −0.495211 0.868772i \(-0.664909\pi\)
−0.495211 + 0.868772i \(0.664909\pi\)
\(678\) 0 0
\(679\) 947.447 0.0535488
\(680\) 0 0
\(681\) 1498.18 0.0843028
\(682\) 0 0
\(683\) −12819.4 −0.718187 −0.359093 0.933302i \(-0.616914\pi\)
−0.359093 + 0.933302i \(0.616914\pi\)
\(684\) 0 0
\(685\) 29560.7 1.64884
\(686\) 0 0
\(687\) −8576.55 −0.476297
\(688\) 0 0
\(689\) 7699.97 0.425755
\(690\) 0 0
\(691\) 34174.6 1.88142 0.940712 0.339207i \(-0.110159\pi\)
0.940712 + 0.339207i \(0.110159\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10346.8 0.564715
\(696\) 0 0
\(697\) 28159.0 1.53027
\(698\) 0 0
\(699\) 16433.3 0.889219
\(700\) 0 0
\(701\) 28160.4 1.51727 0.758633 0.651519i \(-0.225868\pi\)
0.758633 + 0.651519i \(0.225868\pi\)
\(702\) 0 0
\(703\) 4699.36 0.252119
\(704\) 0 0
\(705\) −10993.0 −0.587261
\(706\) 0 0
\(707\) −4669.13 −0.248374
\(708\) 0 0
\(709\) −21986.4 −1.16462 −0.582310 0.812967i \(-0.697851\pi\)
−0.582310 + 0.812967i \(0.697851\pi\)
\(710\) 0 0
\(711\) −5522.25 −0.291281
\(712\) 0 0
\(713\) −858.765 −0.0451066
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −21069.6 −1.09743
\(718\) 0 0
\(719\) −7096.66 −0.368095 −0.184048 0.982917i \(-0.558920\pi\)
−0.184048 + 0.982917i \(0.558920\pi\)
\(720\) 0 0
\(721\) 5843.38 0.301829
\(722\) 0 0
\(723\) 10834.2 0.557303
\(724\) 0 0
\(725\) 654.775 0.0335417
\(726\) 0 0
\(727\) 9445.16 0.481845 0.240923 0.970544i \(-0.422550\pi\)
0.240923 + 0.970544i \(0.422550\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 38539.8 1.94999
\(732\) 0 0
\(733\) 31148.3 1.56956 0.784782 0.619772i \(-0.212775\pi\)
0.784782 + 0.619772i \(0.212775\pi\)
\(734\) 0 0
\(735\) −9593.94 −0.481467
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −20736.7 −1.03222 −0.516112 0.856521i \(-0.672621\pi\)
−0.516112 + 0.856521i \(0.672621\pi\)
\(740\) 0 0
\(741\) 1680.50 0.0833125
\(742\) 0 0
\(743\) 29538.6 1.45850 0.729252 0.684246i \(-0.239868\pi\)
0.729252 + 0.684246i \(0.239868\pi\)
\(744\) 0 0
\(745\) 26438.9 1.30020
\(746\) 0 0
\(747\) −4305.55 −0.210886
\(748\) 0 0
\(749\) −5913.42 −0.288480
\(750\) 0 0
\(751\) 10499.3 0.510153 0.255076 0.966921i \(-0.417899\pi\)
0.255076 + 0.966921i \(0.417899\pi\)
\(752\) 0 0
\(753\) 6119.51 0.296158
\(754\) 0 0
\(755\) −878.148 −0.0423299
\(756\) 0 0
\(757\) −17677.9 −0.848762 −0.424381 0.905484i \(-0.639508\pi\)
−0.424381 + 0.905484i \(0.639508\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 35393.9 1.68598 0.842988 0.537933i \(-0.180795\pi\)
0.842988 + 0.537933i \(0.180795\pi\)
\(762\) 0 0
\(763\) 13064.8 0.619890
\(764\) 0 0
\(765\) −10208.8 −0.482485
\(766\) 0 0
\(767\) −13511.8 −0.636094
\(768\) 0 0
\(769\) 23789.1 1.11555 0.557774 0.829993i \(-0.311656\pi\)
0.557774 + 0.829993i \(0.311656\pi\)
\(770\) 0 0
\(771\) −21313.6 −0.995579
\(772\) 0 0
\(773\) −24763.8 −1.15225 −0.576127 0.817360i \(-0.695437\pi\)
−0.576127 + 0.817360i \(0.695437\pi\)
\(774\) 0 0
\(775\) −2132.03 −0.0988190
\(776\) 0 0
\(777\) −6906.11 −0.318862
\(778\) 0 0
\(779\) 3038.94 0.139771
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −975.039 −0.0445020
\(784\) 0 0
\(785\) −15302.0 −0.695735
\(786\) 0 0
\(787\) −21994.6 −0.996218 −0.498109 0.867114i \(-0.665972\pi\)
−0.498109 + 0.867114i \(0.665972\pi\)
\(788\) 0 0
\(789\) 20736.5 0.935665
\(790\) 0 0
\(791\) 1451.31 0.0652374
\(792\) 0 0
\(793\) −1742.25 −0.0780193
\(794\) 0 0
\(795\) −5048.16 −0.225207
\(796\) 0 0
\(797\) 13140.9 0.584031 0.292016 0.956414i \(-0.405674\pi\)
0.292016 + 0.956414i \(0.405674\pi\)
\(798\) 0 0
\(799\) 38893.6 1.72210
\(800\) 0 0
\(801\) −422.112 −0.0186200
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −437.954 −0.0191750
\(806\) 0 0
\(807\) 18780.9 0.819232
\(808\) 0 0
\(809\) 37687.4 1.63785 0.818923 0.573904i \(-0.194572\pi\)
0.818923 + 0.573904i \(0.194572\pi\)
\(810\) 0 0
\(811\) 4997.61 0.216387 0.108193 0.994130i \(-0.465493\pi\)
0.108193 + 0.994130i \(0.465493\pi\)
\(812\) 0 0
\(813\) −5154.58 −0.222361
\(814\) 0 0
\(815\) −34928.9 −1.50123
\(816\) 0 0
\(817\) 4159.25 0.178107
\(818\) 0 0
\(819\) −2469.63 −0.105368
\(820\) 0 0
\(821\) 10964.7 0.466103 0.233052 0.972464i \(-0.425129\pi\)
0.233052 + 0.972464i \(0.425129\pi\)
\(822\) 0 0
\(823\) 30075.8 1.27385 0.636923 0.770927i \(-0.280207\pi\)
0.636923 + 0.770927i \(0.280207\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5494.60 −0.231035 −0.115518 0.993305i \(-0.536853\pi\)
−0.115518 + 0.993305i \(0.536853\pi\)
\(828\) 0 0
\(829\) −27154.2 −1.13764 −0.568820 0.822462i \(-0.692600\pi\)
−0.568820 + 0.822462i \(0.692600\pi\)
\(830\) 0 0
\(831\) −16413.4 −0.685170
\(832\) 0 0
\(833\) 33943.8 1.41186
\(834\) 0 0
\(835\) −20166.3 −0.835790
\(836\) 0 0
\(837\) 3174.85 0.131110
\(838\) 0 0
\(839\) −1708.86 −0.0703176 −0.0351588 0.999382i \(-0.511194\pi\)
−0.0351588 + 0.999382i \(0.511194\pi\)
\(840\) 0 0
\(841\) −23084.9 −0.946529
\(842\) 0 0
\(843\) −12178.2 −0.497556
\(844\) 0 0
\(845\) 420.847 0.0171332
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −12870.2 −0.520263
\(850\) 0 0
\(851\) 2898.28 0.116747
\(852\) 0 0
\(853\) 13274.7 0.532844 0.266422 0.963857i \(-0.414159\pi\)
0.266422 + 0.963857i \(0.414159\pi\)
\(854\) 0 0
\(855\) −1101.75 −0.0440689
\(856\) 0 0
\(857\) 37451.0 1.49277 0.746384 0.665516i \(-0.231788\pi\)
0.746384 + 0.665516i \(0.231788\pi\)
\(858\) 0 0
\(859\) −23124.2 −0.918497 −0.459249 0.888308i \(-0.651881\pi\)
−0.459249 + 0.888308i \(0.651881\pi\)
\(860\) 0 0
\(861\) −4465.99 −0.176772
\(862\) 0 0
\(863\) −38457.7 −1.51694 −0.758468 0.651710i \(-0.774052\pi\)
−0.758468 + 0.651710i \(0.774052\pi\)
\(864\) 0 0
\(865\) −23062.4 −0.906527
\(866\) 0 0
\(867\) 21380.3 0.837500
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −40536.5 −1.57696
\(872\) 0 0
\(873\) 1469.97 0.0569886
\(874\) 0 0
\(875\) −8583.18 −0.331617
\(876\) 0 0
\(877\) −26863.9 −1.03435 −0.517177 0.855879i \(-0.673017\pi\)
−0.517177 + 0.855879i \(0.673017\pi\)
\(878\) 0 0
\(879\) −2833.32 −0.108721
\(880\) 0 0
\(881\) −7486.46 −0.286294 −0.143147 0.989701i \(-0.545722\pi\)
−0.143147 + 0.989701i \(0.545722\pi\)
\(882\) 0 0
\(883\) 7391.59 0.281707 0.140853 0.990030i \(-0.455015\pi\)
0.140853 + 0.990030i \(0.455015\pi\)
\(884\) 0 0
\(885\) 8858.47 0.336468
\(886\) 0 0
\(887\) 6738.05 0.255064 0.127532 0.991834i \(-0.459294\pi\)
0.127532 + 0.991834i \(0.459294\pi\)
\(888\) 0 0
\(889\) −9576.34 −0.361283
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4197.43 0.157292
\(894\) 0 0
\(895\) 23833.4 0.890127
\(896\) 0 0
\(897\) 1036.43 0.0385789
\(898\) 0 0
\(899\) −4246.36 −0.157535
\(900\) 0 0
\(901\) 17860.6 0.660403
\(902\) 0 0
\(903\) −6112.37 −0.225257
\(904\) 0 0
\(905\) 34235.5 1.25749
\(906\) 0 0
\(907\) −22365.9 −0.818794 −0.409397 0.912356i \(-0.634261\pi\)
−0.409397 + 0.912356i \(0.634261\pi\)
\(908\) 0 0
\(909\) −7244.20 −0.264329
\(910\) 0 0
\(911\) −27646.2 −1.00544 −0.502722 0.864448i \(-0.667668\pi\)
−0.502722 + 0.864448i \(0.667668\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 1142.24 0.0412690
\(916\) 0 0
\(917\) 4237.47 0.152599
\(918\) 0 0
\(919\) 36196.0 1.29923 0.649617 0.760262i \(-0.274929\pi\)
0.649617 + 0.760262i \(0.274929\pi\)
\(920\) 0 0
\(921\) −22795.4 −0.815563
\(922\) 0 0
\(923\) −24451.3 −0.871966
\(924\) 0 0
\(925\) 7195.46 0.255768
\(926\) 0 0
\(927\) 9066.06 0.321217
\(928\) 0 0
\(929\) 33046.5 1.16708 0.583542 0.812083i \(-0.301666\pi\)
0.583542 + 0.812083i \(0.301666\pi\)
\(930\) 0 0
\(931\) 3663.24 0.128956
\(932\) 0 0
\(933\) −26887.4 −0.943466
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 44197.4 1.54095 0.770473 0.637473i \(-0.220020\pi\)
0.770473 + 0.637473i \(0.220020\pi\)
\(938\) 0 0
\(939\) 12214.5 0.424500
\(940\) 0 0
\(941\) −47.7548 −0.00165437 −0.000827186 1.00000i \(-0.500263\pi\)
−0.000827186 1.00000i \(0.500263\pi\)
\(942\) 0 0
\(943\) 1874.23 0.0647226
\(944\) 0 0
\(945\) 1619.11 0.0557351
\(946\) 0 0
\(947\) 56761.5 1.94773 0.973865 0.227129i \(-0.0729339\pi\)
0.973865 + 0.227129i \(0.0729339\pi\)
\(948\) 0 0
\(949\) −30239.5 −1.03437
\(950\) 0 0
\(951\) −14004.4 −0.477524
\(952\) 0 0
\(953\) −11388.8 −0.387115 −0.193558 0.981089i \(-0.562003\pi\)
−0.193558 + 0.981089i \(0.562003\pi\)
\(954\) 0 0
\(955\) −15243.4 −0.516509
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 16587.4 0.558535
\(960\) 0 0
\(961\) −15964.3 −0.535878
\(962\) 0 0
\(963\) −9174.72 −0.307011
\(964\) 0 0
\(965\) −30905.8 −1.03098
\(966\) 0 0
\(967\) −56463.5 −1.87771 −0.938853 0.344317i \(-0.888110\pi\)
−0.938853 + 0.344317i \(0.888110\pi\)
\(968\) 0 0
\(969\) 3898.03 0.129229
\(970\) 0 0
\(971\) −35149.3 −1.16169 −0.580843 0.814016i \(-0.697277\pi\)
−0.580843 + 0.814016i \(0.697277\pi\)
\(972\) 0 0
\(973\) 5805.90 0.191294
\(974\) 0 0
\(975\) 2573.10 0.0845182
\(976\) 0 0
\(977\) 42770.8 1.40057 0.700287 0.713862i \(-0.253056\pi\)
0.700287 + 0.713862i \(0.253056\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 20270.1 0.659709
\(982\) 0 0
\(983\) 10045.0 0.325927 0.162964 0.986632i \(-0.447895\pi\)
0.162964 + 0.986632i \(0.447895\pi\)
\(984\) 0 0
\(985\) −2683.93 −0.0868196
\(986\) 0 0
\(987\) −6168.49 −0.198931
\(988\) 0 0
\(989\) 2565.17 0.0824749
\(990\) 0 0
\(991\) −3259.52 −0.104482 −0.0522412 0.998634i \(-0.516636\pi\)
−0.0522412 + 0.998634i \(0.516636\pi\)
\(992\) 0 0
\(993\) 17308.2 0.553130
\(994\) 0 0
\(995\) 29270.9 0.932614
\(996\) 0 0
\(997\) 5967.81 0.189571 0.0947856 0.995498i \(-0.469783\pi\)
0.0947856 + 0.995498i \(0.469783\pi\)
\(998\) 0 0
\(999\) −10714.9 −0.339344
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 1452.4.a.t.1.5 6
11.2 odd 10 132.4.i.c.37.1 yes 12
11.6 odd 10 132.4.i.c.25.1 12
11.10 odd 2 1452.4.a.u.1.5 6
33.2 even 10 396.4.j.c.37.3 12
33.17 even 10 396.4.j.c.289.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
132.4.i.c.25.1 12 11.6 odd 10
132.4.i.c.37.1 yes 12 11.2 odd 10
396.4.j.c.37.3 12 33.2 even 10
396.4.j.c.289.3 12 33.17 even 10
1452.4.a.t.1.5 6 1.1 even 1 trivial
1452.4.a.u.1.5 6 11.10 odd 2