Properties

Label 1160.4.a.c.1.1
Level $1160$
Weight $4$
Character 1160.1
Self dual yes
Analytic conductor $68.442$
Analytic rank $1$
Dimension $7$
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] = [1160,4,Mod(1,1160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1160.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1160.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: \(68.4422156067\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 121x^{5} + 38x^{4} + 4100x^{3} + 836x^{2} - 34400x - 6912 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-7.91868\) of defining polynomial
Character \(\chi\) \(=\) 1160.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-7.91868 q^{3} -5.00000 q^{5} +30.1700 q^{7} +35.7055 q^{9} -41.5009 q^{11} +20.4606 q^{13} +39.5934 q^{15} -44.4259 q^{17} -139.197 q^{19} -238.907 q^{21} +164.416 q^{23} +25.0000 q^{25} -68.9361 q^{27} -29.0000 q^{29} +143.019 q^{31} +328.632 q^{33} -150.850 q^{35} -178.297 q^{37} -162.021 q^{39} +283.451 q^{41} -400.334 q^{43} -178.527 q^{45} +66.1270 q^{47} +567.231 q^{49} +351.794 q^{51} +707.089 q^{53} +207.504 q^{55} +1102.26 q^{57} -385.448 q^{59} +207.613 q^{61} +1077.24 q^{63} -102.303 q^{65} +1007.51 q^{67} -1301.96 q^{69} -4.72980 q^{71} +259.868 q^{73} -197.967 q^{75} -1252.08 q^{77} -954.754 q^{79} -418.166 q^{81} -883.835 q^{83} +222.129 q^{85} +229.642 q^{87} +1256.60 q^{89} +617.297 q^{91} -1132.53 q^{93} +695.984 q^{95} -396.847 q^{97} -1481.81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{3} - 35 q^{5} + 65 q^{7} + 54 q^{9} - 14 q^{11} - 137 q^{13} - 5 q^{15} - 181 q^{17} + 14 q^{19} - 84 q^{21} + 279 q^{23} + 175 q^{25} + 196 q^{27} - 203 q^{29} - 55 q^{31} - 656 q^{33} - 325 q^{35}+ \cdots - 5216 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −7.91868 −1.52395 −0.761975 0.647606i \(-0.775770\pi\)
−0.761975 + 0.647606i \(0.775770\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) 30.1700 1.62903 0.814514 0.580144i \(-0.197004\pi\)
0.814514 + 0.580144i \(0.197004\pi\)
\(8\) 0 0
\(9\) 35.7055 1.32243
\(10\) 0 0
\(11\) −41.5009 −1.13754 −0.568772 0.822495i \(-0.692581\pi\)
−0.568772 + 0.822495i \(0.692581\pi\)
\(12\) 0 0
\(13\) 20.4606 0.436519 0.218260 0.975891i \(-0.429962\pi\)
0.218260 + 0.975891i \(0.429962\pi\)
\(14\) 0 0
\(15\) 39.5934 0.681531
\(16\) 0 0
\(17\) −44.4259 −0.633815 −0.316907 0.948456i \(-0.602644\pi\)
−0.316907 + 0.948456i \(0.602644\pi\)
\(18\) 0 0
\(19\) −139.197 −1.68073 −0.840367 0.542018i \(-0.817660\pi\)
−0.840367 + 0.542018i \(0.817660\pi\)
\(20\) 0 0
\(21\) −238.907 −2.48256
\(22\) 0 0
\(23\) 164.416 1.49057 0.745286 0.666745i \(-0.232313\pi\)
0.745286 + 0.666745i \(0.232313\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) −68.9361 −0.491361
\(28\) 0 0
\(29\) −29.0000 −0.185695
\(30\) 0 0
\(31\) 143.019 0.828614 0.414307 0.910137i \(-0.364024\pi\)
0.414307 + 0.910137i \(0.364024\pi\)
\(32\) 0 0
\(33\) 328.632 1.73356
\(34\) 0 0
\(35\) −150.850 −0.728524
\(36\) 0 0
\(37\) −178.297 −0.792212 −0.396106 0.918205i \(-0.629639\pi\)
−0.396106 + 0.918205i \(0.629639\pi\)
\(38\) 0 0
\(39\) −162.021 −0.665234
\(40\) 0 0
\(41\) 283.451 1.07970 0.539850 0.841761i \(-0.318481\pi\)
0.539850 + 0.841761i \(0.318481\pi\)
\(42\) 0 0
\(43\) −400.334 −1.41978 −0.709888 0.704314i \(-0.751255\pi\)
−0.709888 + 0.704314i \(0.751255\pi\)
\(44\) 0 0
\(45\) −178.527 −0.591407
\(46\) 0 0
\(47\) 66.1270 0.205226 0.102613 0.994721i \(-0.467280\pi\)
0.102613 + 0.994721i \(0.467280\pi\)
\(48\) 0 0
\(49\) 567.231 1.65373
\(50\) 0 0
\(51\) 351.794 0.965903
\(52\) 0 0
\(53\) 707.089 1.83257 0.916285 0.400527i \(-0.131173\pi\)
0.916285 + 0.400527i \(0.131173\pi\)
\(54\) 0 0
\(55\) 207.504 0.508725
\(56\) 0 0
\(57\) 1102.26 2.56136
\(58\) 0 0
\(59\) −385.448 −0.850526 −0.425263 0.905070i \(-0.639818\pi\)
−0.425263 + 0.905070i \(0.639818\pi\)
\(60\) 0 0
\(61\) 207.613 0.435772 0.217886 0.975974i \(-0.430084\pi\)
0.217886 + 0.975974i \(0.430084\pi\)
\(62\) 0 0
\(63\) 1077.24 2.15427
\(64\) 0 0
\(65\) −102.303 −0.195217
\(66\) 0 0
\(67\) 1007.51 1.83712 0.918560 0.395282i \(-0.129353\pi\)
0.918560 + 0.395282i \(0.129353\pi\)
\(68\) 0 0
\(69\) −1301.96 −2.27156
\(70\) 0 0
\(71\) −4.72980 −0.00790597 −0.00395299 0.999992i \(-0.501258\pi\)
−0.00395299 + 0.999992i \(0.501258\pi\)
\(72\) 0 0
\(73\) 259.868 0.416647 0.208324 0.978060i \(-0.433199\pi\)
0.208324 + 0.978060i \(0.433199\pi\)
\(74\) 0 0
\(75\) −197.967 −0.304790
\(76\) 0 0
\(77\) −1252.08 −1.85309
\(78\) 0 0
\(79\) −954.754 −1.35972 −0.679862 0.733340i \(-0.737960\pi\)
−0.679862 + 0.733340i \(0.737960\pi\)
\(80\) 0 0
\(81\) −418.166 −0.573616
\(82\) 0 0
\(83\) −883.835 −1.16884 −0.584419 0.811452i \(-0.698678\pi\)
−0.584419 + 0.811452i \(0.698678\pi\)
\(84\) 0 0
\(85\) 222.129 0.283451
\(86\) 0 0
\(87\) 229.642 0.282991
\(88\) 0 0
\(89\) 1256.60 1.49663 0.748313 0.663346i \(-0.230864\pi\)
0.748313 + 0.663346i \(0.230864\pi\)
\(90\) 0 0
\(91\) 617.297 0.711103
\(92\) 0 0
\(93\) −1132.53 −1.26277
\(94\) 0 0
\(95\) 695.984 0.751647
\(96\) 0 0
\(97\) −396.847 −0.415399 −0.207699 0.978193i \(-0.566598\pi\)
−0.207699 + 0.978193i \(0.566598\pi\)
\(98\) 0 0
\(99\) −1481.81 −1.50432
\(100\) 0 0
\(101\) 1362.77 1.34258 0.671289 0.741195i \(-0.265741\pi\)
0.671289 + 0.741195i \(0.265741\pi\)
\(102\) 0 0
\(103\) −1953.67 −1.86894 −0.934470 0.356042i \(-0.884126\pi\)
−0.934470 + 0.356042i \(0.884126\pi\)
\(104\) 0 0
\(105\) 1194.53 1.11023
\(106\) 0 0
\(107\) 1773.39 1.60225 0.801123 0.598499i \(-0.204236\pi\)
0.801123 + 0.598499i \(0.204236\pi\)
\(108\) 0 0
\(109\) −1705.45 −1.49865 −0.749323 0.662205i \(-0.769621\pi\)
−0.749323 + 0.662205i \(0.769621\pi\)
\(110\) 0 0
\(111\) 1411.88 1.20729
\(112\) 0 0
\(113\) −1540.09 −1.28212 −0.641060 0.767490i \(-0.721505\pi\)
−0.641060 + 0.767490i \(0.721505\pi\)
\(114\) 0 0
\(115\) −822.081 −0.666604
\(116\) 0 0
\(117\) 730.556 0.577265
\(118\) 0 0
\(119\) −1340.33 −1.03250
\(120\) 0 0
\(121\) 391.325 0.294008
\(122\) 0 0
\(123\) −2244.56 −1.64541
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1521.76 −1.06326 −0.531630 0.846977i \(-0.678420\pi\)
−0.531630 + 0.846977i \(0.678420\pi\)
\(128\) 0 0
\(129\) 3170.12 2.16367
\(130\) 0 0
\(131\) −319.260 −0.212931 −0.106465 0.994316i \(-0.533953\pi\)
−0.106465 + 0.994316i \(0.533953\pi\)
\(132\) 0 0
\(133\) −4199.57 −2.73796
\(134\) 0 0
\(135\) 344.680 0.219743
\(136\) 0 0
\(137\) −1680.02 −1.04769 −0.523847 0.851812i \(-0.675504\pi\)
−0.523847 + 0.851812i \(0.675504\pi\)
\(138\) 0 0
\(139\) −567.983 −0.346587 −0.173294 0.984870i \(-0.555441\pi\)
−0.173294 + 0.984870i \(0.555441\pi\)
\(140\) 0 0
\(141\) −523.639 −0.312754
\(142\) 0 0
\(143\) −849.134 −0.496560
\(144\) 0 0
\(145\) 145.000 0.0830455
\(146\) 0 0
\(147\) −4491.72 −2.52021
\(148\) 0 0
\(149\) 2330.64 1.28143 0.640716 0.767778i \(-0.278638\pi\)
0.640716 + 0.767778i \(0.278638\pi\)
\(150\) 0 0
\(151\) −2335.72 −1.25880 −0.629398 0.777083i \(-0.716698\pi\)
−0.629398 + 0.777083i \(0.716698\pi\)
\(152\) 0 0
\(153\) −1586.25 −0.838173
\(154\) 0 0
\(155\) −715.097 −0.370568
\(156\) 0 0
\(157\) −598.686 −0.304333 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(158\) 0 0
\(159\) −5599.22 −2.79275
\(160\) 0 0
\(161\) 4960.44 2.42818
\(162\) 0 0
\(163\) −2355.82 −1.13204 −0.566018 0.824393i \(-0.691517\pi\)
−0.566018 + 0.824393i \(0.691517\pi\)
\(164\) 0 0
\(165\) −1643.16 −0.775273
\(166\) 0 0
\(167\) −975.190 −0.451871 −0.225936 0.974142i \(-0.572544\pi\)
−0.225936 + 0.974142i \(0.572544\pi\)
\(168\) 0 0
\(169\) −1778.36 −0.809451
\(170\) 0 0
\(171\) −4970.09 −2.22265
\(172\) 0 0
\(173\) 1750.07 0.769106 0.384553 0.923103i \(-0.374356\pi\)
0.384553 + 0.923103i \(0.374356\pi\)
\(174\) 0 0
\(175\) 754.251 0.325806
\(176\) 0 0
\(177\) 3052.24 1.29616
\(178\) 0 0
\(179\) 215.951 0.0901728 0.0450864 0.998983i \(-0.485644\pi\)
0.0450864 + 0.998983i \(0.485644\pi\)
\(180\) 0 0
\(181\) 369.011 0.151538 0.0757690 0.997125i \(-0.475859\pi\)
0.0757690 + 0.997125i \(0.475859\pi\)
\(182\) 0 0
\(183\) −1644.02 −0.664096
\(184\) 0 0
\(185\) 891.485 0.354288
\(186\) 0 0
\(187\) 1843.71 0.720993
\(188\) 0 0
\(189\) −2079.80 −0.800441
\(190\) 0 0
\(191\) −2981.01 −1.12931 −0.564655 0.825327i \(-0.690991\pi\)
−0.564655 + 0.825327i \(0.690991\pi\)
\(192\) 0 0
\(193\) −1421.80 −0.530277 −0.265138 0.964210i \(-0.585418\pi\)
−0.265138 + 0.964210i \(0.585418\pi\)
\(194\) 0 0
\(195\) 810.105 0.297502
\(196\) 0 0
\(197\) 866.654 0.313434 0.156717 0.987644i \(-0.449909\pi\)
0.156717 + 0.987644i \(0.449909\pi\)
\(198\) 0 0
\(199\) −2936.39 −1.04601 −0.523003 0.852331i \(-0.675188\pi\)
−0.523003 + 0.852331i \(0.675188\pi\)
\(200\) 0 0
\(201\) −7978.16 −2.79968
\(202\) 0 0
\(203\) −874.931 −0.302503
\(204\) 0 0
\(205\) −1417.26 −0.482856
\(206\) 0 0
\(207\) 5870.56 1.97117
\(208\) 0 0
\(209\) 5776.79 1.91191
\(210\) 0 0
\(211\) −242.085 −0.0789851 −0.0394925 0.999220i \(-0.512574\pi\)
−0.0394925 + 0.999220i \(0.512574\pi\)
\(212\) 0 0
\(213\) 37.4538 0.0120483
\(214\) 0 0
\(215\) 2001.67 0.634943
\(216\) 0 0
\(217\) 4314.90 1.34984
\(218\) 0 0
\(219\) −2057.81 −0.634950
\(220\) 0 0
\(221\) −908.980 −0.276673
\(222\) 0 0
\(223\) −725.560 −0.217879 −0.108940 0.994048i \(-0.534746\pi\)
−0.108940 + 0.994048i \(0.534746\pi\)
\(224\) 0 0
\(225\) 892.637 0.264485
\(226\) 0 0
\(227\) −6224.96 −1.82011 −0.910055 0.414487i \(-0.863961\pi\)
−0.910055 + 0.414487i \(0.863961\pi\)
\(228\) 0 0
\(229\) 4182.45 1.20692 0.603459 0.797394i \(-0.293789\pi\)
0.603459 + 0.797394i \(0.293789\pi\)
\(230\) 0 0
\(231\) 9914.85 2.82402
\(232\) 0 0
\(233\) −3487.32 −0.980524 −0.490262 0.871575i \(-0.663099\pi\)
−0.490262 + 0.871575i \(0.663099\pi\)
\(234\) 0 0
\(235\) −330.635 −0.0917798
\(236\) 0 0
\(237\) 7560.39 2.07215
\(238\) 0 0
\(239\) −1596.56 −0.432104 −0.216052 0.976382i \(-0.569318\pi\)
−0.216052 + 0.976382i \(0.569318\pi\)
\(240\) 0 0
\(241\) 6924.23 1.85074 0.925371 0.379062i \(-0.123753\pi\)
0.925371 + 0.379062i \(0.123753\pi\)
\(242\) 0 0
\(243\) 5172.60 1.36552
\(244\) 0 0
\(245\) −2836.15 −0.739572
\(246\) 0 0
\(247\) −2848.05 −0.733673
\(248\) 0 0
\(249\) 6998.81 1.78125
\(250\) 0 0
\(251\) 5781.91 1.45399 0.726994 0.686644i \(-0.240917\pi\)
0.726994 + 0.686644i \(0.240917\pi\)
\(252\) 0 0
\(253\) −6823.42 −1.69559
\(254\) 0 0
\(255\) −1758.97 −0.431965
\(256\) 0 0
\(257\) −145.551 −0.0353277 −0.0176639 0.999844i \(-0.505623\pi\)
−0.0176639 + 0.999844i \(0.505623\pi\)
\(258\) 0 0
\(259\) −5379.22 −1.29054
\(260\) 0 0
\(261\) −1035.46 −0.245568
\(262\) 0 0
\(263\) 3122.63 0.732128 0.366064 0.930590i \(-0.380705\pi\)
0.366064 + 0.930590i \(0.380705\pi\)
\(264\) 0 0
\(265\) −3535.45 −0.819550
\(266\) 0 0
\(267\) −9950.64 −2.28078
\(268\) 0 0
\(269\) 750.382 0.170080 0.0850402 0.996378i \(-0.472898\pi\)
0.0850402 + 0.996378i \(0.472898\pi\)
\(270\) 0 0
\(271\) −4817.42 −1.07984 −0.539921 0.841715i \(-0.681546\pi\)
−0.539921 + 0.841715i \(0.681546\pi\)
\(272\) 0 0
\(273\) −4888.18 −1.08369
\(274\) 0 0
\(275\) −1037.52 −0.227509
\(276\) 0 0
\(277\) −2441.36 −0.529556 −0.264778 0.964309i \(-0.585299\pi\)
−0.264778 + 0.964309i \(0.585299\pi\)
\(278\) 0 0
\(279\) 5106.58 1.09578
\(280\) 0 0
\(281\) 5596.93 1.18820 0.594101 0.804391i \(-0.297508\pi\)
0.594101 + 0.804391i \(0.297508\pi\)
\(282\) 0 0
\(283\) −2573.05 −0.540467 −0.270234 0.962795i \(-0.587101\pi\)
−0.270234 + 0.962795i \(0.587101\pi\)
\(284\) 0 0
\(285\) −5511.28 −1.14547
\(286\) 0 0
\(287\) 8551.74 1.75886
\(288\) 0 0
\(289\) −2939.34 −0.598279
\(290\) 0 0
\(291\) 3142.50 0.633047
\(292\) 0 0
\(293\) −4699.84 −0.937090 −0.468545 0.883440i \(-0.655222\pi\)
−0.468545 + 0.883440i \(0.655222\pi\)
\(294\) 0 0
\(295\) 1927.24 0.380367
\(296\) 0 0
\(297\) 2860.91 0.558945
\(298\) 0 0
\(299\) 3364.06 0.650664
\(300\) 0 0
\(301\) −12078.1 −2.31286
\(302\) 0 0
\(303\) −10791.3 −2.04602
\(304\) 0 0
\(305\) −1038.06 −0.194883
\(306\) 0 0
\(307\) −2818.58 −0.523989 −0.261995 0.965069i \(-0.584380\pi\)
−0.261995 + 0.965069i \(0.584380\pi\)
\(308\) 0 0
\(309\) 15470.5 2.84817
\(310\) 0 0
\(311\) 340.672 0.0621148 0.0310574 0.999518i \(-0.490113\pi\)
0.0310574 + 0.999518i \(0.490113\pi\)
\(312\) 0 0
\(313\) −6854.04 −1.23774 −0.618871 0.785492i \(-0.712410\pi\)
−0.618871 + 0.785492i \(0.712410\pi\)
\(314\) 0 0
\(315\) −5386.18 −0.963419
\(316\) 0 0
\(317\) −6510.76 −1.15357 −0.576783 0.816897i \(-0.695692\pi\)
−0.576783 + 0.816897i \(0.695692\pi\)
\(318\) 0 0
\(319\) 1203.53 0.211237
\(320\) 0 0
\(321\) −14042.9 −2.44174
\(322\) 0 0
\(323\) 6183.94 1.06527
\(324\) 0 0
\(325\) 511.515 0.0873039
\(326\) 0 0
\(327\) 13504.9 2.28386
\(328\) 0 0
\(329\) 1995.05 0.334319
\(330\) 0 0
\(331\) −3135.36 −0.520649 −0.260324 0.965521i \(-0.583829\pi\)
−0.260324 + 0.965521i \(0.583829\pi\)
\(332\) 0 0
\(333\) −6366.18 −1.04764
\(334\) 0 0
\(335\) −5037.55 −0.821585
\(336\) 0 0
\(337\) 5459.28 0.882451 0.441225 0.897396i \(-0.354544\pi\)
0.441225 + 0.897396i \(0.354544\pi\)
\(338\) 0 0
\(339\) 12195.5 1.95389
\(340\) 0 0
\(341\) −5935.43 −0.942586
\(342\) 0 0
\(343\) 6765.04 1.06495
\(344\) 0 0
\(345\) 6509.80 1.01587
\(346\) 0 0
\(347\) −4476.98 −0.692613 −0.346306 0.938121i \(-0.612564\pi\)
−0.346306 + 0.938121i \(0.612564\pi\)
\(348\) 0 0
\(349\) −3769.50 −0.578157 −0.289078 0.957305i \(-0.593349\pi\)
−0.289078 + 0.957305i \(0.593349\pi\)
\(350\) 0 0
\(351\) −1410.47 −0.214489
\(352\) 0 0
\(353\) 10801.6 1.62865 0.814323 0.580412i \(-0.197109\pi\)
0.814323 + 0.580412i \(0.197109\pi\)
\(354\) 0 0
\(355\) 23.6490 0.00353566
\(356\) 0 0
\(357\) 10613.6 1.57348
\(358\) 0 0
\(359\) −83.1926 −0.0122305 −0.00611523 0.999981i \(-0.501947\pi\)
−0.00611523 + 0.999981i \(0.501947\pi\)
\(360\) 0 0
\(361\) 12516.8 1.82487
\(362\) 0 0
\(363\) −3098.77 −0.448054
\(364\) 0 0
\(365\) −1299.34 −0.186330
\(366\) 0 0
\(367\) −5161.95 −0.734201 −0.367101 0.930181i \(-0.619649\pi\)
−0.367101 + 0.930181i \(0.619649\pi\)
\(368\) 0 0
\(369\) 10120.8 1.42782
\(370\) 0 0
\(371\) 21332.9 2.98531
\(372\) 0 0
\(373\) −3535.69 −0.490807 −0.245403 0.969421i \(-0.578920\pi\)
−0.245403 + 0.969421i \(0.578920\pi\)
\(374\) 0 0
\(375\) 989.835 0.136306
\(376\) 0 0
\(377\) −593.358 −0.0810596
\(378\) 0 0
\(379\) 10014.9 1.35734 0.678668 0.734445i \(-0.262558\pi\)
0.678668 + 0.734445i \(0.262558\pi\)
\(380\) 0 0
\(381\) 12050.3 1.62035
\(382\) 0 0
\(383\) −2999.55 −0.400183 −0.200091 0.979777i \(-0.564124\pi\)
−0.200091 + 0.979777i \(0.564124\pi\)
\(384\) 0 0
\(385\) 6260.42 0.828728
\(386\) 0 0
\(387\) −14294.1 −1.87755
\(388\) 0 0
\(389\) −3981.88 −0.518996 −0.259498 0.965744i \(-0.583557\pi\)
−0.259498 + 0.965744i \(0.583557\pi\)
\(390\) 0 0
\(391\) −7304.33 −0.944747
\(392\) 0 0
\(393\) 2528.12 0.324496
\(394\) 0 0
\(395\) 4773.77 0.608087
\(396\) 0 0
\(397\) −4023.09 −0.508597 −0.254298 0.967126i \(-0.581845\pi\)
−0.254298 + 0.967126i \(0.581845\pi\)
\(398\) 0 0
\(399\) 33255.1 4.17252
\(400\) 0 0
\(401\) −15809.5 −1.96881 −0.984403 0.175930i \(-0.943707\pi\)
−0.984403 + 0.175930i \(0.943707\pi\)
\(402\) 0 0
\(403\) 2926.27 0.361706
\(404\) 0 0
\(405\) 2090.83 0.256529
\(406\) 0 0
\(407\) 7399.49 0.901177
\(408\) 0 0
\(409\) −8040.42 −0.972061 −0.486031 0.873942i \(-0.661556\pi\)
−0.486031 + 0.873942i \(0.661556\pi\)
\(410\) 0 0
\(411\) 13303.6 1.59663
\(412\) 0 0
\(413\) −11629.0 −1.38553
\(414\) 0 0
\(415\) 4419.18 0.522720
\(416\) 0 0
\(417\) 4497.67 0.528182
\(418\) 0 0
\(419\) −16378.7 −1.90967 −0.954833 0.297142i \(-0.903967\pi\)
−0.954833 + 0.297142i \(0.903967\pi\)
\(420\) 0 0
\(421\) 11576.6 1.34016 0.670082 0.742287i \(-0.266259\pi\)
0.670082 + 0.742287i \(0.266259\pi\)
\(422\) 0 0
\(423\) 2361.10 0.271396
\(424\) 0 0
\(425\) −1110.65 −0.126763
\(426\) 0 0
\(427\) 6263.69 0.709886
\(428\) 0 0
\(429\) 6724.02 0.756734
\(430\) 0 0
\(431\) 747.175 0.0835039 0.0417519 0.999128i \(-0.486706\pi\)
0.0417519 + 0.999128i \(0.486706\pi\)
\(432\) 0 0
\(433\) 8711.47 0.966851 0.483425 0.875386i \(-0.339392\pi\)
0.483425 + 0.875386i \(0.339392\pi\)
\(434\) 0 0
\(435\) −1148.21 −0.126557
\(436\) 0 0
\(437\) −22886.2 −2.50525
\(438\) 0 0
\(439\) −2056.40 −0.223568 −0.111784 0.993733i \(-0.535657\pi\)
−0.111784 + 0.993733i \(0.535657\pi\)
\(440\) 0 0
\(441\) 20253.2 2.18694
\(442\) 0 0
\(443\) −16175.5 −1.73481 −0.867404 0.497605i \(-0.834213\pi\)
−0.867404 + 0.497605i \(0.834213\pi\)
\(444\) 0 0
\(445\) −6283.02 −0.669312
\(446\) 0 0
\(447\) −18455.6 −1.95284
\(448\) 0 0
\(449\) −11865.6 −1.24715 −0.623575 0.781764i \(-0.714320\pi\)
−0.623575 + 0.781764i \(0.714320\pi\)
\(450\) 0 0
\(451\) −11763.5 −1.22821
\(452\) 0 0
\(453\) 18495.8 1.91834
\(454\) 0 0
\(455\) −3086.49 −0.318015
\(456\) 0 0
\(457\) −7236.71 −0.740742 −0.370371 0.928884i \(-0.620769\pi\)
−0.370371 + 0.928884i \(0.620769\pi\)
\(458\) 0 0
\(459\) 3062.54 0.311432
\(460\) 0 0
\(461\) −8760.00 −0.885019 −0.442509 0.896764i \(-0.645912\pi\)
−0.442509 + 0.896764i \(0.645912\pi\)
\(462\) 0 0
\(463\) −14811.5 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(464\) 0 0
\(465\) 5662.63 0.564727
\(466\) 0 0
\(467\) 568.520 0.0563340 0.0281670 0.999603i \(-0.491033\pi\)
0.0281670 + 0.999603i \(0.491033\pi\)
\(468\) 0 0
\(469\) 30396.6 2.99272
\(470\) 0 0
\(471\) 4740.80 0.463789
\(472\) 0 0
\(473\) 16614.2 1.61506
\(474\) 0 0
\(475\) −3479.92 −0.336147
\(476\) 0 0
\(477\) 25247.0 2.42344
\(478\) 0 0
\(479\) −14218.8 −1.35631 −0.678157 0.734917i \(-0.737221\pi\)
−0.678157 + 0.734917i \(0.737221\pi\)
\(480\) 0 0
\(481\) −3648.07 −0.345816
\(482\) 0 0
\(483\) −39280.2 −3.70043
\(484\) 0 0
\(485\) 1984.23 0.185772
\(486\) 0 0
\(487\) −2724.74 −0.253532 −0.126766 0.991933i \(-0.540460\pi\)
−0.126766 + 0.991933i \(0.540460\pi\)
\(488\) 0 0
\(489\) 18655.0 1.72517
\(490\) 0 0
\(491\) 21133.2 1.94242 0.971209 0.238231i \(-0.0765674\pi\)
0.971209 + 0.238231i \(0.0765674\pi\)
\(492\) 0 0
\(493\) 1288.35 0.117696
\(494\) 0 0
\(495\) 7409.05 0.672752
\(496\) 0 0
\(497\) −142.698 −0.0128791
\(498\) 0 0
\(499\) 11748.1 1.05394 0.526970 0.849884i \(-0.323328\pi\)
0.526970 + 0.849884i \(0.323328\pi\)
\(500\) 0 0
\(501\) 7722.22 0.688629
\(502\) 0 0
\(503\) 20052.9 1.77757 0.888783 0.458328i \(-0.151552\pi\)
0.888783 + 0.458328i \(0.151552\pi\)
\(504\) 0 0
\(505\) −6813.84 −0.600419
\(506\) 0 0
\(507\) 14082.3 1.23356
\(508\) 0 0
\(509\) −17437.0 −1.51843 −0.759214 0.650841i \(-0.774417\pi\)
−0.759214 + 0.650841i \(0.774417\pi\)
\(510\) 0 0
\(511\) 7840.23 0.678731
\(512\) 0 0
\(513\) 9595.68 0.825847
\(514\) 0 0
\(515\) 9768.35 0.835815
\(516\) 0 0
\(517\) −2744.33 −0.233454
\(518\) 0 0
\(519\) −13858.2 −1.17208
\(520\) 0 0
\(521\) 13465.5 1.13231 0.566154 0.824299i \(-0.308431\pi\)
0.566154 + 0.824299i \(0.308431\pi\)
\(522\) 0 0
\(523\) −226.324 −0.0189224 −0.00946122 0.999955i \(-0.503012\pi\)
−0.00946122 + 0.999955i \(0.503012\pi\)
\(524\) 0 0
\(525\) −5972.67 −0.496512
\(526\) 0 0
\(527\) −6353.76 −0.525188
\(528\) 0 0
\(529\) 14865.7 1.22180
\(530\) 0 0
\(531\) −13762.6 −1.12476
\(532\) 0 0
\(533\) 5799.59 0.471310
\(534\) 0 0
\(535\) −8866.96 −0.716546
\(536\) 0 0
\(537\) −1710.05 −0.137419
\(538\) 0 0
\(539\) −23540.6 −1.88120
\(540\) 0 0
\(541\) 1099.62 0.0873866 0.0436933 0.999045i \(-0.486088\pi\)
0.0436933 + 0.999045i \(0.486088\pi\)
\(542\) 0 0
\(543\) −2922.08 −0.230936
\(544\) 0 0
\(545\) 8527.24 0.670215
\(546\) 0 0
\(547\) −325.266 −0.0254248 −0.0127124 0.999919i \(-0.504047\pi\)
−0.0127124 + 0.999919i \(0.504047\pi\)
\(548\) 0 0
\(549\) 7412.92 0.576277
\(550\) 0 0
\(551\) 4036.71 0.312104
\(552\) 0 0
\(553\) −28805.0 −2.21503
\(554\) 0 0
\(555\) −7059.38 −0.539917
\(556\) 0 0
\(557\) −11078.0 −0.842715 −0.421357 0.906895i \(-0.638446\pi\)
−0.421357 + 0.906895i \(0.638446\pi\)
\(558\) 0 0
\(559\) −8191.08 −0.619760
\(560\) 0 0
\(561\) −14599.8 −1.09876
\(562\) 0 0
\(563\) −4301.09 −0.321971 −0.160985 0.986957i \(-0.551467\pi\)
−0.160985 + 0.986957i \(0.551467\pi\)
\(564\) 0 0
\(565\) 7700.46 0.573382
\(566\) 0 0
\(567\) −12616.1 −0.934436
\(568\) 0 0
\(569\) −13912.2 −1.02501 −0.512503 0.858686i \(-0.671282\pi\)
−0.512503 + 0.858686i \(0.671282\pi\)
\(570\) 0 0
\(571\) 5249.89 0.384765 0.192383 0.981320i \(-0.438379\pi\)
0.192383 + 0.981320i \(0.438379\pi\)
\(572\) 0 0
\(573\) 23605.7 1.72101
\(574\) 0 0
\(575\) 4110.41 0.298114
\(576\) 0 0
\(577\) 23793.2 1.71668 0.858338 0.513085i \(-0.171497\pi\)
0.858338 + 0.513085i \(0.171497\pi\)
\(578\) 0 0
\(579\) 11258.8 0.808116
\(580\) 0 0
\(581\) −26665.3 −1.90407
\(582\) 0 0
\(583\) −29344.8 −2.08463
\(584\) 0 0
\(585\) −3652.78 −0.258161
\(586\) 0 0
\(587\) 1345.64 0.0946174 0.0473087 0.998880i \(-0.484936\pi\)
0.0473087 + 0.998880i \(0.484936\pi\)
\(588\) 0 0
\(589\) −19907.9 −1.39268
\(590\) 0 0
\(591\) −6862.76 −0.477659
\(592\) 0 0
\(593\) −12716.6 −0.880618 −0.440309 0.897846i \(-0.645131\pi\)
−0.440309 + 0.897846i \(0.645131\pi\)
\(594\) 0 0
\(595\) 6701.65 0.461749
\(596\) 0 0
\(597\) 23252.3 1.59406
\(598\) 0 0
\(599\) −20205.6 −1.37826 −0.689131 0.724637i \(-0.742008\pi\)
−0.689131 + 0.724637i \(0.742008\pi\)
\(600\) 0 0
\(601\) −5770.48 −0.391652 −0.195826 0.980639i \(-0.562739\pi\)
−0.195826 + 0.980639i \(0.562739\pi\)
\(602\) 0 0
\(603\) 35973.7 2.42945
\(604\) 0 0
\(605\) −1956.62 −0.131484
\(606\) 0 0
\(607\) 3069.56 0.205255 0.102627 0.994720i \(-0.467275\pi\)
0.102627 + 0.994720i \(0.467275\pi\)
\(608\) 0 0
\(609\) 6928.30 0.461000
\(610\) 0 0
\(611\) 1353.00 0.0895851
\(612\) 0 0
\(613\) −15942.9 −1.05045 −0.525227 0.850962i \(-0.676020\pi\)
−0.525227 + 0.850962i \(0.676020\pi\)
\(614\) 0 0
\(615\) 11222.8 0.735849
\(616\) 0 0
\(617\) 7071.49 0.461406 0.230703 0.973024i \(-0.425897\pi\)
0.230703 + 0.973024i \(0.425897\pi\)
\(618\) 0 0
\(619\) 14764.2 0.958679 0.479339 0.877630i \(-0.340876\pi\)
0.479339 + 0.877630i \(0.340876\pi\)
\(620\) 0 0
\(621\) −11334.2 −0.732409
\(622\) 0 0
\(623\) 37911.8 2.43805
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −45744.6 −2.91366
\(628\) 0 0
\(629\) 7921.00 0.502116
\(630\) 0 0
\(631\) 28574.8 1.80277 0.901383 0.433023i \(-0.142553\pi\)
0.901383 + 0.433023i \(0.142553\pi\)
\(632\) 0 0
\(633\) 1917.00 0.120369
\(634\) 0 0
\(635\) 7608.78 0.475504
\(636\) 0 0
\(637\) 11605.9 0.721887
\(638\) 0 0
\(639\) −168.880 −0.0104551
\(640\) 0 0
\(641\) −24087.2 −1.48422 −0.742112 0.670276i \(-0.766176\pi\)
−0.742112 + 0.670276i \(0.766176\pi\)
\(642\) 0 0
\(643\) 1460.69 0.0895865 0.0447932 0.998996i \(-0.485737\pi\)
0.0447932 + 0.998996i \(0.485737\pi\)
\(644\) 0 0
\(645\) −15850.6 −0.967623
\(646\) 0 0
\(647\) 6718.59 0.408246 0.204123 0.978945i \(-0.434566\pi\)
0.204123 + 0.978945i \(0.434566\pi\)
\(648\) 0 0
\(649\) 15996.4 0.967512
\(650\) 0 0
\(651\) −34168.3 −2.05708
\(652\) 0 0
\(653\) −98.3814 −0.00589580 −0.00294790 0.999996i \(-0.500938\pi\)
−0.00294790 + 0.999996i \(0.500938\pi\)
\(654\) 0 0
\(655\) 1596.30 0.0952254
\(656\) 0 0
\(657\) 9278.72 0.550985
\(658\) 0 0
\(659\) 14606.4 0.863408 0.431704 0.902015i \(-0.357913\pi\)
0.431704 + 0.902015i \(0.357913\pi\)
\(660\) 0 0
\(661\) 89.9790 0.00529467 0.00264734 0.999996i \(-0.499157\pi\)
0.00264734 + 0.999996i \(0.499157\pi\)
\(662\) 0 0
\(663\) 7197.92 0.421635
\(664\) 0 0
\(665\) 20997.9 1.22445
\(666\) 0 0
\(667\) −4768.07 −0.276792
\(668\) 0 0
\(669\) 5745.48 0.332038
\(670\) 0 0
\(671\) −8616.12 −0.495711
\(672\) 0 0
\(673\) −13820.9 −0.791613 −0.395806 0.918334i \(-0.629535\pi\)
−0.395806 + 0.918334i \(0.629535\pi\)
\(674\) 0 0
\(675\) −1723.40 −0.0982722
\(676\) 0 0
\(677\) 32389.0 1.83871 0.919357 0.393423i \(-0.128709\pi\)
0.919357 + 0.393423i \(0.128709\pi\)
\(678\) 0 0
\(679\) −11972.9 −0.676697
\(680\) 0 0
\(681\) 49293.5 2.77376
\(682\) 0 0
\(683\) 12912.1 0.723379 0.361689 0.932299i \(-0.382200\pi\)
0.361689 + 0.932299i \(0.382200\pi\)
\(684\) 0 0
\(685\) 8400.12 0.468543
\(686\) 0 0
\(687\) −33119.5 −1.83928
\(688\) 0 0
\(689\) 14467.5 0.799952
\(690\) 0 0
\(691\) 2598.12 0.143035 0.0715176 0.997439i \(-0.477216\pi\)
0.0715176 + 0.997439i \(0.477216\pi\)
\(692\) 0 0
\(693\) −44706.3 −2.45058
\(694\) 0 0
\(695\) 2839.91 0.154999
\(696\) 0 0
\(697\) −12592.6 −0.684329
\(698\) 0 0
\(699\) 27615.0 1.49427
\(700\) 0 0
\(701\) −14722.0 −0.793212 −0.396606 0.917989i \(-0.629812\pi\)
−0.396606 + 0.917989i \(0.629812\pi\)
\(702\) 0 0
\(703\) 24818.4 1.33150
\(704\) 0 0
\(705\) 2618.19 0.139868
\(706\) 0 0
\(707\) 41114.7 2.18710
\(708\) 0 0
\(709\) −20819.7 −1.10282 −0.551410 0.834234i \(-0.685910\pi\)
−0.551410 + 0.834234i \(0.685910\pi\)
\(710\) 0 0
\(711\) −34090.0 −1.79813
\(712\) 0 0
\(713\) 23514.7 1.23511
\(714\) 0 0
\(715\) 4245.67 0.222069
\(716\) 0 0
\(717\) 12642.7 0.658506
\(718\) 0 0
\(719\) 9197.06 0.477041 0.238520 0.971137i \(-0.423338\pi\)
0.238520 + 0.971137i \(0.423338\pi\)
\(720\) 0 0
\(721\) −58942.3 −3.04456
\(722\) 0 0
\(723\) −54830.8 −2.82044
\(724\) 0 0
\(725\) −725.000 −0.0371391
\(726\) 0 0
\(727\) −7105.85 −0.362505 −0.181253 0.983437i \(-0.558015\pi\)
−0.181253 + 0.983437i \(0.558015\pi\)
\(728\) 0 0
\(729\) −29669.7 −1.50737
\(730\) 0 0
\(731\) 17785.2 0.899876
\(732\) 0 0
\(733\) −999.375 −0.0503585 −0.0251792 0.999683i \(-0.508016\pi\)
−0.0251792 + 0.999683i \(0.508016\pi\)
\(734\) 0 0
\(735\) 22458.6 1.12707
\(736\) 0 0
\(737\) −41812.6 −2.08981
\(738\) 0 0
\(739\) 31121.4 1.54914 0.774572 0.632486i \(-0.217965\pi\)
0.774572 + 0.632486i \(0.217965\pi\)
\(740\) 0 0
\(741\) 22552.8 1.11808
\(742\) 0 0
\(743\) −3438.14 −0.169762 −0.0848811 0.996391i \(-0.527051\pi\)
−0.0848811 + 0.996391i \(0.527051\pi\)
\(744\) 0 0
\(745\) −11653.2 −0.573073
\(746\) 0 0
\(747\) −31557.8 −1.54570
\(748\) 0 0
\(749\) 53503.3 2.61010
\(750\) 0 0
\(751\) −12142.4 −0.589992 −0.294996 0.955499i \(-0.595318\pi\)
−0.294996 + 0.955499i \(0.595318\pi\)
\(752\) 0 0
\(753\) −45785.1 −2.21581
\(754\) 0 0
\(755\) 11678.6 0.562951
\(756\) 0 0
\(757\) 18697.6 0.897722 0.448861 0.893602i \(-0.351830\pi\)
0.448861 + 0.893602i \(0.351830\pi\)
\(758\) 0 0
\(759\) 54032.5 2.58400
\(760\) 0 0
\(761\) −1401.86 −0.0667772 −0.0333886 0.999442i \(-0.510630\pi\)
−0.0333886 + 0.999442i \(0.510630\pi\)
\(762\) 0 0
\(763\) −51453.4 −2.44134
\(764\) 0 0
\(765\) 7931.24 0.374842
\(766\) 0 0
\(767\) −7886.50 −0.371271
\(768\) 0 0
\(769\) 12563.3 0.589134 0.294567 0.955631i \(-0.404825\pi\)
0.294567 + 0.955631i \(0.404825\pi\)
\(770\) 0 0
\(771\) 1152.57 0.0538377
\(772\) 0 0
\(773\) 22987.3 1.06960 0.534798 0.844980i \(-0.320388\pi\)
0.534798 + 0.844980i \(0.320388\pi\)
\(774\) 0 0
\(775\) 3575.49 0.165723
\(776\) 0 0
\(777\) 42596.4 1.96671
\(778\) 0 0
\(779\) −39455.5 −1.81469
\(780\) 0 0
\(781\) 196.291 0.00899340
\(782\) 0 0
\(783\) 1999.15 0.0912435
\(784\) 0 0
\(785\) 2993.43 0.136102
\(786\) 0 0
\(787\) −13115.7 −0.594058 −0.297029 0.954868i \(-0.595996\pi\)
−0.297029 + 0.954868i \(0.595996\pi\)
\(788\) 0 0
\(789\) −24727.1 −1.11573
\(790\) 0 0
\(791\) −46464.6 −2.08861
\(792\) 0 0
\(793\) 4247.89 0.190223
\(794\) 0 0
\(795\) 27996.1 1.24895
\(796\) 0 0
\(797\) 6717.43 0.298549 0.149274 0.988796i \(-0.452306\pi\)
0.149274 + 0.988796i \(0.452306\pi\)
\(798\) 0 0
\(799\) −2937.75 −0.130075
\(800\) 0 0
\(801\) 44867.7 1.97918
\(802\) 0 0
\(803\) −10784.8 −0.473955
\(804\) 0 0
\(805\) −24802.2 −1.08592
\(806\) 0 0
\(807\) −5942.04 −0.259194
\(808\) 0 0
\(809\) 19473.0 0.846270 0.423135 0.906067i \(-0.360930\pi\)
0.423135 + 0.906067i \(0.360930\pi\)
\(810\) 0 0
\(811\) 217.936 0.00943623 0.00471811 0.999989i \(-0.498498\pi\)
0.00471811 + 0.999989i \(0.498498\pi\)
\(812\) 0 0
\(813\) 38147.6 1.64563
\(814\) 0 0
\(815\) 11779.1 0.506262
\(816\) 0 0
\(817\) 55725.3 2.38627
\(818\) 0 0
\(819\) 22040.9 0.940380
\(820\) 0 0
\(821\) −6337.86 −0.269419 −0.134709 0.990885i \(-0.543010\pi\)
−0.134709 + 0.990885i \(0.543010\pi\)
\(822\) 0 0
\(823\) 33154.8 1.40426 0.702128 0.712051i \(-0.252233\pi\)
0.702128 + 0.712051i \(0.252233\pi\)
\(824\) 0 0
\(825\) 8215.81 0.346712
\(826\) 0 0
\(827\) −20191.4 −0.849003 −0.424501 0.905427i \(-0.639551\pi\)
−0.424501 + 0.905427i \(0.639551\pi\)
\(828\) 0 0
\(829\) −28296.8 −1.18551 −0.592756 0.805382i \(-0.701960\pi\)
−0.592756 + 0.805382i \(0.701960\pi\)
\(830\) 0 0
\(831\) 19332.3 0.807017
\(832\) 0 0
\(833\) −25199.7 −1.04816
\(834\) 0 0
\(835\) 4875.95 0.202083
\(836\) 0 0
\(837\) −9859.20 −0.407149
\(838\) 0 0
\(839\) 38620.6 1.58919 0.794596 0.607138i \(-0.207683\pi\)
0.794596 + 0.607138i \(0.207683\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) 0 0
\(843\) −44320.3 −1.81076
\(844\) 0 0
\(845\) 8891.82 0.361997
\(846\) 0 0
\(847\) 11806.3 0.478947
\(848\) 0 0
\(849\) 20375.2 0.823645
\(850\) 0 0
\(851\) −29314.9 −1.18085
\(852\) 0 0
\(853\) −25417.1 −1.02024 −0.510119 0.860104i \(-0.670399\pi\)
−0.510119 + 0.860104i \(0.670399\pi\)
\(854\) 0 0
\(855\) 24850.5 0.993997
\(856\) 0 0
\(857\) 25926.0 1.03339 0.516695 0.856170i \(-0.327162\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(858\) 0 0
\(859\) −7972.29 −0.316660 −0.158330 0.987386i \(-0.550611\pi\)
−0.158330 + 0.987386i \(0.550611\pi\)
\(860\) 0 0
\(861\) −67718.5 −2.68042
\(862\) 0 0
\(863\) −10304.2 −0.406440 −0.203220 0.979133i \(-0.565141\pi\)
−0.203220 + 0.979133i \(0.565141\pi\)
\(864\) 0 0
\(865\) −8750.34 −0.343954
\(866\) 0 0
\(867\) 23275.7 0.911747
\(868\) 0 0
\(869\) 39623.2 1.54675
\(870\) 0 0
\(871\) 20614.3 0.801939
\(872\) 0 0
\(873\) −14169.6 −0.549334
\(874\) 0 0
\(875\) −3771.25 −0.145705
\(876\) 0 0
\(877\) −6900.23 −0.265683 −0.132842 0.991137i \(-0.542410\pi\)
−0.132842 + 0.991137i \(0.542410\pi\)
\(878\) 0 0
\(879\) 37216.5 1.42808
\(880\) 0 0
\(881\) −28477.9 −1.08904 −0.544521 0.838747i \(-0.683288\pi\)
−0.544521 + 0.838747i \(0.683288\pi\)
\(882\) 0 0
\(883\) −16775.0 −0.639326 −0.319663 0.947531i \(-0.603570\pi\)
−0.319663 + 0.947531i \(0.603570\pi\)
\(884\) 0 0
\(885\) −15261.2 −0.579661
\(886\) 0 0
\(887\) 20332.1 0.769657 0.384829 0.922988i \(-0.374261\pi\)
0.384829 + 0.922988i \(0.374261\pi\)
\(888\) 0 0
\(889\) −45911.4 −1.73208
\(890\) 0 0
\(891\) 17354.3 0.652513
\(892\) 0 0
\(893\) −9204.67 −0.344930
\(894\) 0 0
\(895\) −1079.75 −0.0403265
\(896\) 0 0
\(897\) −26638.9 −0.991579
\(898\) 0 0
\(899\) −4147.56 −0.153870
\(900\) 0 0
\(901\) −31413.1 −1.16151
\(902\) 0 0
\(903\) 95642.6 3.52468
\(904\) 0 0
\(905\) −1845.05 −0.0677698
\(906\) 0 0
\(907\) 33419.1 1.22344 0.611722 0.791073i \(-0.290477\pi\)
0.611722 + 0.791073i \(0.290477\pi\)
\(908\) 0 0
\(909\) 48658.3 1.77546
\(910\) 0 0
\(911\) 9108.80 0.331271 0.165636 0.986187i \(-0.447032\pi\)
0.165636 + 0.986187i \(0.447032\pi\)
\(912\) 0 0
\(913\) 36680.0 1.32961
\(914\) 0 0
\(915\) 8220.10 0.296993
\(916\) 0 0
\(917\) −9632.09 −0.346870
\(918\) 0 0
\(919\) 26246.3 0.942095 0.471047 0.882108i \(-0.343876\pi\)
0.471047 + 0.882108i \(0.343876\pi\)
\(920\) 0 0
\(921\) 22319.4 0.798534
\(922\) 0 0
\(923\) −96.7746 −0.00345111
\(924\) 0 0
\(925\) −4457.42 −0.158442
\(926\) 0 0
\(927\) −69756.8 −2.47153
\(928\) 0 0
\(929\) 20844.2 0.736143 0.368072 0.929797i \(-0.380018\pi\)
0.368072 + 0.929797i \(0.380018\pi\)
\(930\) 0 0
\(931\) −78956.7 −2.77949
\(932\) 0 0
\(933\) −2697.67 −0.0946600
\(934\) 0 0
\(935\) −9218.57 −0.322438
\(936\) 0 0
\(937\) −19289.8 −0.672540 −0.336270 0.941766i \(-0.609166\pi\)
−0.336270 + 0.941766i \(0.609166\pi\)
\(938\) 0 0
\(939\) 54275.0 1.88626
\(940\) 0 0
\(941\) 10216.4 0.353926 0.176963 0.984217i \(-0.443373\pi\)
0.176963 + 0.984217i \(0.443373\pi\)
\(942\) 0 0
\(943\) 46604.0 1.60937
\(944\) 0 0
\(945\) 10399.0 0.357968
\(946\) 0 0
\(947\) −28349.2 −0.972783 −0.486391 0.873741i \(-0.661687\pi\)
−0.486391 + 0.873741i \(0.661687\pi\)
\(948\) 0 0
\(949\) 5317.06 0.181875
\(950\) 0 0
\(951\) 51556.6 1.75798
\(952\) 0 0
\(953\) −7660.89 −0.260399 −0.130200 0.991488i \(-0.541562\pi\)
−0.130200 + 0.991488i \(0.541562\pi\)
\(954\) 0 0
\(955\) 14905.0 0.505043
\(956\) 0 0
\(957\) −9530.34 −0.321914
\(958\) 0 0
\(959\) −50686.4 −1.70672
\(960\) 0 0
\(961\) −9336.44 −0.313398
\(962\) 0 0
\(963\) 63319.9 2.11885
\(964\) 0 0
\(965\) 7109.00 0.237147
\(966\) 0 0
\(967\) 46016.5 1.53029 0.765145 0.643858i \(-0.222667\pi\)
0.765145 + 0.643858i \(0.222667\pi\)
\(968\) 0 0
\(969\) −48968.6 −1.62343
\(970\) 0 0
\(971\) −41993.2 −1.38787 −0.693937 0.720036i \(-0.744125\pi\)
−0.693937 + 0.720036i \(0.744125\pi\)
\(972\) 0 0
\(973\) −17136.1 −0.564601
\(974\) 0 0
\(975\) −4050.53 −0.133047
\(976\) 0 0
\(977\) 8008.89 0.262259 0.131130 0.991365i \(-0.458140\pi\)
0.131130 + 0.991365i \(0.458140\pi\)
\(978\) 0 0
\(979\) −52150.2 −1.70248
\(980\) 0 0
\(981\) −60893.9 −1.98185
\(982\) 0 0
\(983\) −36234.8 −1.17570 −0.587849 0.808971i \(-0.700025\pi\)
−0.587849 + 0.808971i \(0.700025\pi\)
\(984\) 0 0
\(985\) −4333.27 −0.140172
\(986\) 0 0
\(987\) −15798.2 −0.509485
\(988\) 0 0
\(989\) −65821.4 −2.11628
\(990\) 0 0
\(991\) −28132.9 −0.901786 −0.450893 0.892578i \(-0.648894\pi\)
−0.450893 + 0.892578i \(0.648894\pi\)
\(992\) 0 0
\(993\) 24827.9 0.793443
\(994\) 0 0
\(995\) 14682.0 0.467788
\(996\) 0 0
\(997\) −33.2275 −0.00105549 −0.000527746 1.00000i \(-0.500168\pi\)
−0.000527746 1.00000i \(0.500168\pi\)
\(998\) 0 0
\(999\) 12291.1 0.389262
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 1160.4.a.c.1.1 7
4.3 odd 2 2320.4.a.r.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1160.4.a.c.1.1 7 1.1 even 1 trivial
2320.4.a.r.1.7 7 4.3 odd 2