Properties

Label 1859.4.a.e.1.7
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $0$
Dimension $11$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, 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("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
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: \( x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + 68209 x^{3} - 90926 x^{2} - 1672 x + 16256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.778412\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.221588 q^{2} -7.13795 q^{3} -7.95090 q^{4} -6.37060 q^{5} +1.58168 q^{6} +23.0480 q^{7} +3.53453 q^{8} +23.9503 q^{9} +O(q^{10})\) \(q-0.221588 q^{2} -7.13795 q^{3} -7.95090 q^{4} -6.37060 q^{5} +1.58168 q^{6} +23.0480 q^{7} +3.53453 q^{8} +23.9503 q^{9} +1.41165 q^{10} -11.0000 q^{11} +56.7531 q^{12} -5.10717 q^{14} +45.4730 q^{15} +62.8240 q^{16} +73.4783 q^{17} -5.30710 q^{18} +12.9866 q^{19} +50.6520 q^{20} -164.516 q^{21} +2.43747 q^{22} +132.964 q^{23} -25.2293 q^{24} -84.4155 q^{25} +21.7686 q^{27} -183.253 q^{28} +283.903 q^{29} -10.0763 q^{30} +225.356 q^{31} -42.1973 q^{32} +78.5174 q^{33} -16.2819 q^{34} -146.830 q^{35} -190.426 q^{36} +89.8050 q^{37} -2.87768 q^{38} -22.5170 q^{40} +127.456 q^{41} +36.4547 q^{42} -477.108 q^{43} +87.4599 q^{44} -152.578 q^{45} -29.4632 q^{46} -402.605 q^{47} -448.434 q^{48} +188.212 q^{49} +18.7055 q^{50} -524.484 q^{51} +533.370 q^{53} -4.82366 q^{54} +70.0766 q^{55} +81.4639 q^{56} -92.6980 q^{57} -62.9095 q^{58} -1.69034 q^{59} -361.551 q^{60} +522.467 q^{61} -49.9362 q^{62} +552.007 q^{63} -493.241 q^{64} -17.3985 q^{66} -873.364 q^{67} -584.218 q^{68} -949.089 q^{69} +32.5357 q^{70} +253.773 q^{71} +84.6530 q^{72} -542.512 q^{73} -19.8997 q^{74} +602.553 q^{75} -103.255 q^{76} -253.528 q^{77} -139.158 q^{79} -400.226 q^{80} -802.041 q^{81} -28.2427 q^{82} +454.213 q^{83} +1308.05 q^{84} -468.100 q^{85} +105.721 q^{86} -2026.49 q^{87} -38.8798 q^{88} -430.013 q^{89} +33.8094 q^{90} -1057.18 q^{92} -1608.58 q^{93} +89.2125 q^{94} -82.7326 q^{95} +301.202 q^{96} -1490.83 q^{97} -41.7055 q^{98} -263.453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.221588 −0.0783432 −0.0391716 0.999232i \(-0.512472\pi\)
−0.0391716 + 0.999232i \(0.512472\pi\)
\(3\) −7.13795 −1.37370 −0.686849 0.726800i \(-0.741007\pi\)
−0.686849 + 0.726800i \(0.741007\pi\)
\(4\) −7.95090 −0.993862
\(5\) −6.37060 −0.569803 −0.284902 0.958557i \(-0.591961\pi\)
−0.284902 + 0.958557i \(0.591961\pi\)
\(6\) 1.58168 0.107620
\(7\) 23.0480 1.24448 0.622239 0.782828i \(-0.286223\pi\)
0.622239 + 0.782828i \(0.286223\pi\)
\(8\) 3.53453 0.156206
\(9\) 23.9503 0.887048
\(10\) 1.41165 0.0446402
\(11\) −11.0000 −0.301511
\(12\) 56.7531 1.36527
\(13\) 0 0
\(14\) −5.10717 −0.0974963
\(15\) 45.4730 0.782738
\(16\) 62.8240 0.981625
\(17\) 73.4783 1.04830 0.524150 0.851626i \(-0.324383\pi\)
0.524150 + 0.851626i \(0.324383\pi\)
\(18\) −5.30710 −0.0694942
\(19\) 12.9866 0.156807 0.0784037 0.996922i \(-0.475018\pi\)
0.0784037 + 0.996922i \(0.475018\pi\)
\(20\) 50.6520 0.566306
\(21\) −164.516 −1.70954
\(22\) 2.43747 0.0236214
\(23\) 132.964 1.20543 0.602715 0.797957i \(-0.294086\pi\)
0.602715 + 0.797957i \(0.294086\pi\)
\(24\) −25.2293 −0.214579
\(25\) −84.4155 −0.675324
\(26\) 0 0
\(27\) 21.7686 0.155162
\(28\) −183.253 −1.23684
\(29\) 283.903 1.81791 0.908957 0.416890i \(-0.136880\pi\)
0.908957 + 0.416890i \(0.136880\pi\)
\(30\) −10.0763 −0.0613222
\(31\) 225.356 1.30565 0.652825 0.757509i \(-0.273584\pi\)
0.652825 + 0.757509i \(0.273584\pi\)
\(32\) −42.1973 −0.233109
\(33\) 78.5174 0.414186
\(34\) −16.2819 −0.0821271
\(35\) −146.830 −0.709107
\(36\) −190.426 −0.881604
\(37\) 89.8050 0.399023 0.199511 0.979895i \(-0.436064\pi\)
0.199511 + 0.979895i \(0.436064\pi\)
\(38\) −2.87768 −0.0122848
\(39\) 0 0
\(40\) −22.5170 −0.0890065
\(41\) 127.456 0.485495 0.242747 0.970090i \(-0.421951\pi\)
0.242747 + 0.970090i \(0.421951\pi\)
\(42\) 36.4547 0.133931
\(43\) −477.108 −1.69205 −0.846027 0.533140i \(-0.821012\pi\)
−0.846027 + 0.533140i \(0.821012\pi\)
\(44\) 87.4599 0.299661
\(45\) −152.578 −0.505443
\(46\) −29.4632 −0.0944372
\(47\) −402.605 −1.24949 −0.624745 0.780829i \(-0.714797\pi\)
−0.624745 + 0.780829i \(0.714797\pi\)
\(48\) −448.434 −1.34846
\(49\) 188.212 0.548723
\(50\) 18.7055 0.0529070
\(51\) −524.484 −1.44005
\(52\) 0 0
\(53\) 533.370 1.38234 0.691169 0.722693i \(-0.257096\pi\)
0.691169 + 0.722693i \(0.257096\pi\)
\(54\) −4.82366 −0.0121559
\(55\) 70.0766 0.171802
\(56\) 81.4639 0.194394
\(57\) −92.6980 −0.215406
\(58\) −62.9095 −0.142421
\(59\) −1.69034 −0.00372988 −0.00186494 0.999998i \(-0.500594\pi\)
−0.00186494 + 0.999998i \(0.500594\pi\)
\(60\) −361.551 −0.777934
\(61\) 522.467 1.09664 0.548320 0.836269i \(-0.315268\pi\)
0.548320 + 0.836269i \(0.315268\pi\)
\(62\) −49.9362 −0.102289
\(63\) 552.007 1.10391
\(64\) −493.241 −0.963362
\(65\) 0 0
\(66\) −17.3985 −0.0324486
\(67\) −873.364 −1.59251 −0.796257 0.604959i \(-0.793190\pi\)
−0.796257 + 0.604959i \(0.793190\pi\)
\(68\) −584.218 −1.04187
\(69\) −949.089 −1.65590
\(70\) 32.5357 0.0555537
\(71\) 253.773 0.424188 0.212094 0.977249i \(-0.431972\pi\)
0.212094 + 0.977249i \(0.431972\pi\)
\(72\) 84.6530 0.138562
\(73\) −542.512 −0.869811 −0.434905 0.900476i \(-0.643218\pi\)
−0.434905 + 0.900476i \(0.643218\pi\)
\(74\) −19.8997 −0.0312607
\(75\) 602.553 0.927692
\(76\) −103.255 −0.155845
\(77\) −253.528 −0.375224
\(78\) 0 0
\(79\) −139.158 −0.198183 −0.0990914 0.995078i \(-0.531594\pi\)
−0.0990914 + 0.995078i \(0.531594\pi\)
\(80\) −400.226 −0.559333
\(81\) −802.041 −1.10019
\(82\) −28.2427 −0.0380352
\(83\) 454.213 0.600678 0.300339 0.953832i \(-0.402900\pi\)
0.300339 + 0.953832i \(0.402900\pi\)
\(84\) 1308.05 1.69904
\(85\) −468.100 −0.597325
\(86\) 105.721 0.132561
\(87\) −2026.49 −2.49727
\(88\) −38.8798 −0.0470977
\(89\) −430.013 −0.512149 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(90\) 33.8094 0.0395980
\(91\) 0 0
\(92\) −1057.18 −1.19803
\(93\) −1608.58 −1.79357
\(94\) 89.2125 0.0978890
\(95\) −82.7326 −0.0893494
\(96\) 301.202 0.320222
\(97\) −1490.83 −1.56053 −0.780263 0.625452i \(-0.784915\pi\)
−0.780263 + 0.625452i \(0.784915\pi\)
\(98\) −41.7055 −0.0429887
\(99\) −263.453 −0.267455
\(100\) 671.179 0.671179
\(101\) 1293.51 1.27435 0.637173 0.770720i \(-0.280104\pi\)
0.637173 + 0.770720i \(0.280104\pi\)
\(102\) 116.219 0.112818
\(103\) 584.488 0.559139 0.279569 0.960125i \(-0.409808\pi\)
0.279569 + 0.960125i \(0.409808\pi\)
\(104\) 0 0
\(105\) 1048.06 0.974100
\(106\) −118.188 −0.108297
\(107\) 1700.46 1.53635 0.768174 0.640241i \(-0.221165\pi\)
0.768174 + 0.640241i \(0.221165\pi\)
\(108\) −173.080 −0.154209
\(109\) 714.703 0.628038 0.314019 0.949417i \(-0.398324\pi\)
0.314019 + 0.949417i \(0.398324\pi\)
\(110\) −15.5281 −0.0134595
\(111\) −641.023 −0.548137
\(112\) 1447.97 1.22161
\(113\) −1022.39 −0.851132 −0.425566 0.904927i \(-0.639925\pi\)
−0.425566 + 0.904927i \(0.639925\pi\)
\(114\) 20.5408 0.0168756
\(115\) −847.059 −0.686858
\(116\) −2257.29 −1.80676
\(117\) 0 0
\(118\) 0.374558 0.000292211 0
\(119\) 1693.53 1.30458
\(120\) 160.726 0.122268
\(121\) 121.000 0.0909091
\(122\) −115.772 −0.0859142
\(123\) −909.775 −0.666924
\(124\) −1791.78 −1.29764
\(125\) 1334.10 0.954605
\(126\) −122.318 −0.0864839
\(127\) 1021.58 0.713784 0.356892 0.934146i \(-0.383836\pi\)
0.356892 + 0.934146i \(0.383836\pi\)
\(128\) 446.874 0.308582
\(129\) 3405.57 2.32437
\(130\) 0 0
\(131\) −225.024 −0.150080 −0.0750398 0.997181i \(-0.523908\pi\)
−0.0750398 + 0.997181i \(0.523908\pi\)
\(132\) −624.284 −0.411644
\(133\) 299.317 0.195143
\(134\) 193.527 0.124763
\(135\) −138.679 −0.0884117
\(136\) 259.711 0.163750
\(137\) −1654.80 −1.03197 −0.515983 0.856599i \(-0.672573\pi\)
−0.515983 + 0.856599i \(0.672573\pi\)
\(138\) 210.307 0.129728
\(139\) −699.725 −0.426978 −0.213489 0.976945i \(-0.568483\pi\)
−0.213489 + 0.976945i \(0.568483\pi\)
\(140\) 1167.43 0.704755
\(141\) 2873.78 1.71642
\(142\) −56.2331 −0.0332323
\(143\) 0 0
\(144\) 1504.65 0.870748
\(145\) −1808.63 −1.03585
\(146\) 120.214 0.0681438
\(147\) −1343.45 −0.753781
\(148\) −714.030 −0.396574
\(149\) −1244.63 −0.684325 −0.342162 0.939641i \(-0.611159\pi\)
−0.342162 + 0.939641i \(0.611159\pi\)
\(150\) −133.519 −0.0726783
\(151\) −1148.93 −0.619197 −0.309598 0.950867i \(-0.600195\pi\)
−0.309598 + 0.950867i \(0.600195\pi\)
\(152\) 45.9016 0.0244942
\(153\) 1759.83 0.929892
\(154\) 56.1789 0.0293962
\(155\) −1435.65 −0.743964
\(156\) 0 0
\(157\) 2141.94 1.08883 0.544413 0.838817i \(-0.316752\pi\)
0.544413 + 0.838817i \(0.316752\pi\)
\(158\) 30.8356 0.0155263
\(159\) −3807.17 −1.89892
\(160\) 268.822 0.132826
\(161\) 3064.56 1.50013
\(162\) 177.723 0.0861927
\(163\) 2952.91 1.41895 0.709477 0.704728i \(-0.248931\pi\)
0.709477 + 0.704728i \(0.248931\pi\)
\(164\) −1013.39 −0.482515
\(165\) −500.203 −0.236004
\(166\) −100.648 −0.0470591
\(167\) −898.670 −0.416414 −0.208207 0.978085i \(-0.566763\pi\)
−0.208207 + 0.978085i \(0.566763\pi\)
\(168\) −581.485 −0.267039
\(169\) 0 0
\(170\) 103.725 0.0467963
\(171\) 311.034 0.139096
\(172\) 3793.44 1.68167
\(173\) −2344.10 −1.03017 −0.515083 0.857140i \(-0.672239\pi\)
−0.515083 + 0.857140i \(0.672239\pi\)
\(174\) 449.045 0.195644
\(175\) −1945.61 −0.840425
\(176\) −691.064 −0.295971
\(177\) 12.0655 0.00512373
\(178\) 95.2857 0.0401234
\(179\) 1418.35 0.592247 0.296123 0.955150i \(-0.404306\pi\)
0.296123 + 0.955150i \(0.404306\pi\)
\(180\) 1213.13 0.502341
\(181\) −3048.87 −1.25205 −0.626025 0.779803i \(-0.715319\pi\)
−0.626025 + 0.779803i \(0.715319\pi\)
\(182\) 0 0
\(183\) −3729.34 −1.50645
\(184\) 469.965 0.188295
\(185\) −572.111 −0.227365
\(186\) 356.442 0.140514
\(187\) −808.261 −0.316074
\(188\) 3201.07 1.24182
\(189\) 501.723 0.193095
\(190\) 18.3326 0.00699991
\(191\) 1481.95 0.561412 0.280706 0.959794i \(-0.409431\pi\)
0.280706 + 0.959794i \(0.409431\pi\)
\(192\) 3520.73 1.32337
\(193\) 4950.57 1.84637 0.923187 0.384352i \(-0.125575\pi\)
0.923187 + 0.384352i \(0.125575\pi\)
\(194\) 330.350 0.122257
\(195\) 0 0
\(196\) −1496.46 −0.545356
\(197\) −787.234 −0.284711 −0.142356 0.989816i \(-0.545468\pi\)
−0.142356 + 0.989816i \(0.545468\pi\)
\(198\) 58.3781 0.0209533
\(199\) −37.2673 −0.0132754 −0.00663770 0.999978i \(-0.502113\pi\)
−0.00663770 + 0.999978i \(0.502113\pi\)
\(200\) −298.369 −0.105489
\(201\) 6234.03 2.18763
\(202\) −286.626 −0.0998364
\(203\) 6543.41 2.26235
\(204\) 4170.12 1.43121
\(205\) −811.971 −0.276637
\(206\) −129.516 −0.0438047
\(207\) 3184.53 1.06927
\(208\) 0 0
\(209\) −142.853 −0.0472792
\(210\) −232.238 −0.0763141
\(211\) 3594.70 1.17284 0.586420 0.810007i \(-0.300537\pi\)
0.586420 + 0.810007i \(0.300537\pi\)
\(212\) −4240.77 −1.37385
\(213\) −1811.42 −0.582707
\(214\) −376.801 −0.120362
\(215\) 3039.46 0.964138
\(216\) 76.9417 0.0242371
\(217\) 5194.02 1.62485
\(218\) −158.370 −0.0492025
\(219\) 3872.42 1.19486
\(220\) −557.172 −0.170748
\(221\) 0 0
\(222\) 142.043 0.0429428
\(223\) 5262.76 1.58036 0.790180 0.612874i \(-0.209987\pi\)
0.790180 + 0.612874i \(0.209987\pi\)
\(224\) −972.564 −0.290099
\(225\) −2021.78 −0.599045
\(226\) 226.548 0.0666804
\(227\) 645.666 0.188786 0.0943928 0.995535i \(-0.469909\pi\)
0.0943928 + 0.995535i \(0.469909\pi\)
\(228\) 737.032 0.214084
\(229\) 2614.26 0.754391 0.377195 0.926134i \(-0.376889\pi\)
0.377195 + 0.926134i \(0.376889\pi\)
\(230\) 187.698 0.0538107
\(231\) 1809.67 0.515445
\(232\) 1003.46 0.283968
\(233\) 5317.46 1.49510 0.747551 0.664205i \(-0.231230\pi\)
0.747551 + 0.664205i \(0.231230\pi\)
\(234\) 0 0
\(235\) 2564.84 0.711964
\(236\) 13.4397 0.00370699
\(237\) 993.299 0.272244
\(238\) −375.266 −0.102205
\(239\) −3337.77 −0.903357 −0.451678 0.892181i \(-0.649175\pi\)
−0.451678 + 0.892181i \(0.649175\pi\)
\(240\) 2856.79 0.768355
\(241\) −3795.52 −1.01449 −0.507243 0.861803i \(-0.669335\pi\)
−0.507243 + 0.861803i \(0.669335\pi\)
\(242\) −26.8121 −0.00712211
\(243\) 5137.18 1.35617
\(244\) −4154.08 −1.08991
\(245\) −1199.02 −0.312664
\(246\) 201.595 0.0522489
\(247\) 0 0
\(248\) 796.527 0.203950
\(249\) −3242.15 −0.825151
\(250\) −295.621 −0.0747868
\(251\) −2238.10 −0.562820 −0.281410 0.959588i \(-0.590802\pi\)
−0.281410 + 0.959588i \(0.590802\pi\)
\(252\) −4388.96 −1.09714
\(253\) −1462.60 −0.363451
\(254\) −226.370 −0.0559201
\(255\) 3341.28 0.820544
\(256\) 3846.91 0.939187
\(257\) −5554.35 −1.34814 −0.674068 0.738670i \(-0.735454\pi\)
−0.674068 + 0.738670i \(0.735454\pi\)
\(258\) −754.634 −0.182099
\(259\) 2069.83 0.496575
\(260\) 0 0
\(261\) 6799.57 1.61258
\(262\) 49.8626 0.0117577
\(263\) 2945.49 0.690595 0.345297 0.938493i \(-0.387778\pi\)
0.345297 + 0.938493i \(0.387778\pi\)
\(264\) 277.522 0.0646981
\(265\) −3397.88 −0.787661
\(266\) −66.3250 −0.0152881
\(267\) 3069.41 0.703538
\(268\) 6944.03 1.58274
\(269\) −4153.67 −0.941463 −0.470731 0.882277i \(-0.656010\pi\)
−0.470731 + 0.882277i \(0.656010\pi\)
\(270\) 30.7296 0.00692645
\(271\) 6141.93 1.37674 0.688369 0.725361i \(-0.258327\pi\)
0.688369 + 0.725361i \(0.258327\pi\)
\(272\) 4616.20 1.02904
\(273\) 0 0
\(274\) 366.685 0.0808475
\(275\) 928.571 0.203618
\(276\) 7546.11 1.64573
\(277\) 3715.68 0.805969 0.402984 0.915207i \(-0.367973\pi\)
0.402984 + 0.915207i \(0.367973\pi\)
\(278\) 155.051 0.0334508
\(279\) 5397.35 1.15817
\(280\) −518.974 −0.110766
\(281\) 635.949 0.135009 0.0675045 0.997719i \(-0.478496\pi\)
0.0675045 + 0.997719i \(0.478496\pi\)
\(282\) −636.794 −0.134470
\(283\) 4253.77 0.893500 0.446750 0.894659i \(-0.352581\pi\)
0.446750 + 0.894659i \(0.352581\pi\)
\(284\) −2017.73 −0.421585
\(285\) 590.541 0.122739
\(286\) 0 0
\(287\) 2937.61 0.604187
\(288\) −1010.64 −0.206779
\(289\) 486.053 0.0989321
\(290\) 400.771 0.0811521
\(291\) 10641.5 2.14369
\(292\) 4313.46 0.864472
\(293\) 3946.01 0.786787 0.393394 0.919370i \(-0.371301\pi\)
0.393394 + 0.919370i \(0.371301\pi\)
\(294\) 297.692 0.0590536
\(295\) 10.7684 0.00212530
\(296\) 317.418 0.0623296
\(297\) −239.454 −0.0467830
\(298\) 275.796 0.0536122
\(299\) 0 0
\(300\) −4790.84 −0.921998
\(301\) −10996.4 −2.10572
\(302\) 254.589 0.0485099
\(303\) −9233.00 −1.75057
\(304\) 815.873 0.153926
\(305\) −3328.42 −0.624869
\(306\) −389.956 −0.0728507
\(307\) −5882.41 −1.09357 −0.546786 0.837272i \(-0.684149\pi\)
−0.546786 + 0.837272i \(0.684149\pi\)
\(308\) 2015.78 0.372921
\(309\) −4172.04 −0.768088
\(310\) 318.123 0.0582845
\(311\) −2040.41 −0.372029 −0.186015 0.982547i \(-0.559557\pi\)
−0.186015 + 0.982547i \(0.559557\pi\)
\(312\) 0 0
\(313\) 4695.38 0.847918 0.423959 0.905681i \(-0.360640\pi\)
0.423959 + 0.905681i \(0.360640\pi\)
\(314\) −474.629 −0.0853021
\(315\) −3516.62 −0.629012
\(316\) 1106.43 0.196966
\(317\) −10244.2 −1.81504 −0.907522 0.420004i \(-0.862029\pi\)
−0.907522 + 0.420004i \(0.862029\pi\)
\(318\) 843.622 0.148767
\(319\) −3122.94 −0.548122
\(320\) 3142.24 0.548927
\(321\) −12137.8 −2.11048
\(322\) −679.069 −0.117525
\(323\) 954.236 0.164381
\(324\) 6376.95 1.09344
\(325\) 0 0
\(326\) −654.329 −0.111165
\(327\) −5101.51 −0.862735
\(328\) 450.497 0.0758370
\(329\) −9279.26 −1.55496
\(330\) 110.839 0.0184893
\(331\) 6762.25 1.12292 0.561460 0.827504i \(-0.310240\pi\)
0.561460 + 0.827504i \(0.310240\pi\)
\(332\) −3611.40 −0.596992
\(333\) 2150.86 0.353953
\(334\) 199.135 0.0326232
\(335\) 5563.85 0.907420
\(336\) −10335.5 −1.67812
\(337\) 3074.22 0.496923 0.248462 0.968642i \(-0.420075\pi\)
0.248462 + 0.968642i \(0.420075\pi\)
\(338\) 0 0
\(339\) 7297.73 1.16920
\(340\) 3721.82 0.593659
\(341\) −2478.92 −0.393668
\(342\) −68.9214 −0.0108972
\(343\) −3567.56 −0.561603
\(344\) −1686.35 −0.264308
\(345\) 6046.27 0.943536
\(346\) 519.424 0.0807064
\(347\) −6003.78 −0.928819 −0.464409 0.885621i \(-0.653733\pi\)
−0.464409 + 0.885621i \(0.653733\pi\)
\(348\) 16112.4 2.48194
\(349\) 3081.09 0.472570 0.236285 0.971684i \(-0.424070\pi\)
0.236285 + 0.971684i \(0.424070\pi\)
\(350\) 431.124 0.0658416
\(351\) 0 0
\(352\) 464.170 0.0702851
\(353\) −5235.28 −0.789365 −0.394683 0.918817i \(-0.629145\pi\)
−0.394683 + 0.918817i \(0.629145\pi\)
\(354\) −2.67358 −0.000401410 0
\(355\) −1616.69 −0.241704
\(356\) 3418.99 0.509006
\(357\) −12088.3 −1.79211
\(358\) −314.289 −0.0463985
\(359\) −6812.64 −1.00155 −0.500776 0.865577i \(-0.666952\pi\)
−0.500776 + 0.865577i \(0.666952\pi\)
\(360\) −539.290 −0.0789530
\(361\) −6690.35 −0.975411
\(362\) 675.593 0.0980895
\(363\) −863.692 −0.124882
\(364\) 0 0
\(365\) 3456.12 0.495621
\(366\) 826.377 0.118020
\(367\) 3729.39 0.530443 0.265222 0.964187i \(-0.414555\pi\)
0.265222 + 0.964187i \(0.414555\pi\)
\(368\) 8353.32 1.18328
\(369\) 3052.61 0.430657
\(370\) 126.773 0.0178125
\(371\) 12293.1 1.72029
\(372\) 12789.7 1.78256
\(373\) 4450.76 0.617833 0.308916 0.951089i \(-0.400034\pi\)
0.308916 + 0.951089i \(0.400034\pi\)
\(374\) 179.101 0.0247623
\(375\) −9522.75 −1.31134
\(376\) −1423.02 −0.195177
\(377\) 0 0
\(378\) −111.176 −0.0151277
\(379\) −3667.51 −0.497065 −0.248532 0.968624i \(-0.579948\pi\)
−0.248532 + 0.968624i \(0.579948\pi\)
\(380\) 657.799 0.0888010
\(381\) −7291.98 −0.980524
\(382\) −328.381 −0.0439828
\(383\) −10896.7 −1.45378 −0.726889 0.686755i \(-0.759035\pi\)
−0.726889 + 0.686755i \(0.759035\pi\)
\(384\) −3189.77 −0.423899
\(385\) 1615.13 0.213804
\(386\) −1096.99 −0.144651
\(387\) −11426.9 −1.50093
\(388\) 11853.4 1.55095
\(389\) −6688.53 −0.871778 −0.435889 0.900000i \(-0.643566\pi\)
−0.435889 + 0.900000i \(0.643566\pi\)
\(390\) 0 0
\(391\) 9769.95 1.26365
\(392\) 665.241 0.0857136
\(393\) 1606.21 0.206164
\(394\) 174.442 0.0223052
\(395\) 886.516 0.112925
\(396\) 2094.69 0.265814
\(397\) 2533.80 0.320322 0.160161 0.987091i \(-0.448799\pi\)
0.160161 + 0.987091i \(0.448799\pi\)
\(398\) 8.25798 0.00104004
\(399\) −2136.51 −0.268068
\(400\) −5303.32 −0.662915
\(401\) 14014.4 1.74525 0.872625 0.488391i \(-0.162416\pi\)
0.872625 + 0.488391i \(0.162416\pi\)
\(402\) −1381.39 −0.171386
\(403\) 0 0
\(404\) −10284.6 −1.26653
\(405\) 5109.48 0.626894
\(406\) −1449.94 −0.177240
\(407\) −987.855 −0.120310
\(408\) −1853.80 −0.224943
\(409\) 6090.96 0.736378 0.368189 0.929751i \(-0.379978\pi\)
0.368189 + 0.929751i \(0.379978\pi\)
\(410\) 179.923 0.0216726
\(411\) 11811.9 1.41761
\(412\) −4647.20 −0.555707
\(413\) −38.9589 −0.00464175
\(414\) −705.653 −0.0837704
\(415\) −2893.60 −0.342269
\(416\) 0 0
\(417\) 4994.60 0.586539
\(418\) 31.6545 0.00370400
\(419\) −454.104 −0.0529462 −0.0264731 0.999650i \(-0.508428\pi\)
−0.0264731 + 0.999650i \(0.508428\pi\)
\(420\) −8333.04 −0.968121
\(421\) −3809.92 −0.441055 −0.220528 0.975381i \(-0.570778\pi\)
−0.220528 + 0.975381i \(0.570778\pi\)
\(422\) −796.542 −0.0918840
\(423\) −9642.52 −1.10836
\(424\) 1885.21 0.215929
\(425\) −6202.70 −0.707942
\(426\) 401.389 0.0456511
\(427\) 12041.8 1.36474
\(428\) −13520.2 −1.52692
\(429\) 0 0
\(430\) −673.508 −0.0755336
\(431\) −12074.5 −1.34944 −0.674721 0.738073i \(-0.735736\pi\)
−0.674721 + 0.738073i \(0.735736\pi\)
\(432\) 1367.59 0.152311
\(433\) 7121.85 0.790426 0.395213 0.918590i \(-0.370671\pi\)
0.395213 + 0.918590i \(0.370671\pi\)
\(434\) −1150.93 −0.127296
\(435\) 12909.9 1.42295
\(436\) −5682.53 −0.624183
\(437\) 1726.75 0.189020
\(438\) −858.082 −0.0936090
\(439\) −9344.80 −1.01595 −0.507976 0.861371i \(-0.669606\pi\)
−0.507976 + 0.861371i \(0.669606\pi\)
\(440\) 247.688 0.0268365
\(441\) 4507.74 0.486744
\(442\) 0 0
\(443\) 9584.79 1.02796 0.513981 0.857802i \(-0.328170\pi\)
0.513981 + 0.857802i \(0.328170\pi\)
\(444\) 5096.71 0.544773
\(445\) 2739.44 0.291824
\(446\) −1166.16 −0.123810
\(447\) 8884.14 0.940056
\(448\) −11368.2 −1.19888
\(449\) −4321.80 −0.454251 −0.227125 0.973866i \(-0.572933\pi\)
−0.227125 + 0.973866i \(0.572933\pi\)
\(450\) 448.001 0.0469311
\(451\) −1402.02 −0.146382
\(452\) 8128.88 0.845908
\(453\) 8201.01 0.850590
\(454\) −143.072 −0.0147901
\(455\) 0 0
\(456\) −327.644 −0.0336476
\(457\) −16281.7 −1.66658 −0.833291 0.552834i \(-0.813546\pi\)
−0.833291 + 0.552834i \(0.813546\pi\)
\(458\) −579.290 −0.0591014
\(459\) 1599.52 0.162656
\(460\) 6734.88 0.682642
\(461\) 6835.80 0.690618 0.345309 0.938489i \(-0.387774\pi\)
0.345309 + 0.938489i \(0.387774\pi\)
\(462\) −401.002 −0.0403816
\(463\) 614.185 0.0616492 0.0308246 0.999525i \(-0.490187\pi\)
0.0308246 + 0.999525i \(0.490187\pi\)
\(464\) 17835.9 1.78451
\(465\) 10247.6 1.02198
\(466\) −1178.29 −0.117131
\(467\) −17077.5 −1.69218 −0.846092 0.533037i \(-0.821051\pi\)
−0.846092 + 0.533037i \(0.821051\pi\)
\(468\) 0 0
\(469\) −20129.3 −1.98185
\(470\) −568.337 −0.0557775
\(471\) −15289.1 −1.49572
\(472\) −5.97454 −0.000582628 0
\(473\) 5248.19 0.510173
\(474\) −220.103 −0.0213284
\(475\) −1096.27 −0.105896
\(476\) −13465.1 −1.29658
\(477\) 12774.4 1.22620
\(478\) 739.609 0.0707719
\(479\) −15654.5 −1.49326 −0.746632 0.665237i \(-0.768331\pi\)
−0.746632 + 0.665237i \(0.768331\pi\)
\(480\) −1918.84 −0.182463
\(481\) 0 0
\(482\) 841.042 0.0794780
\(483\) −21874.6 −2.06073
\(484\) −962.059 −0.0903511
\(485\) 9497.48 0.889193
\(486\) −1138.34 −0.106247
\(487\) −14358.5 −1.33603 −0.668014 0.744149i \(-0.732855\pi\)
−0.668014 + 0.744149i \(0.732855\pi\)
\(488\) 1846.67 0.171301
\(489\) −21077.7 −1.94922
\(490\) 265.689 0.0244951
\(491\) 9150.12 0.841017 0.420508 0.907289i \(-0.361852\pi\)
0.420508 + 0.907289i \(0.361852\pi\)
\(492\) 7233.53 0.662830
\(493\) 20860.7 1.90572
\(494\) 0 0
\(495\) 1678.35 0.152397
\(496\) 14157.8 1.28166
\(497\) 5848.98 0.527892
\(498\) 718.421 0.0646450
\(499\) 11822.2 1.06059 0.530296 0.847813i \(-0.322081\pi\)
0.530296 + 0.847813i \(0.322081\pi\)
\(500\) −10607.3 −0.948746
\(501\) 6414.66 0.572028
\(502\) 495.936 0.0440931
\(503\) −4441.37 −0.393700 −0.196850 0.980434i \(-0.563071\pi\)
−0.196850 + 0.980434i \(0.563071\pi\)
\(504\) 1951.09 0.172437
\(505\) −8240.43 −0.726127
\(506\) 324.095 0.0284739
\(507\) 0 0
\(508\) −8122.48 −0.709403
\(509\) 9760.01 0.849912 0.424956 0.905214i \(-0.360290\pi\)
0.424956 + 0.905214i \(0.360290\pi\)
\(510\) −740.387 −0.0642841
\(511\) −12503.8 −1.08246
\(512\) −4427.42 −0.382161
\(513\) 282.701 0.0243305
\(514\) 1230.78 0.105617
\(515\) −3723.54 −0.318599
\(516\) −27077.4 −2.31011
\(517\) 4428.66 0.376735
\(518\) −458.649 −0.0389033
\(519\) 16732.1 1.41514
\(520\) 0 0
\(521\) 15982.5 1.34397 0.671984 0.740566i \(-0.265442\pi\)
0.671984 + 0.740566i \(0.265442\pi\)
\(522\) −1506.70 −0.126334
\(523\) 502.803 0.0420383 0.0210191 0.999779i \(-0.493309\pi\)
0.0210191 + 0.999779i \(0.493309\pi\)
\(524\) 1789.14 0.149158
\(525\) 13887.7 1.15449
\(526\) −652.684 −0.0541034
\(527\) 16558.8 1.36871
\(528\) 4932.78 0.406575
\(529\) 5512.40 0.453061
\(530\) 752.930 0.0617079
\(531\) −40.4840 −0.00330858
\(532\) −2379.84 −0.193945
\(533\) 0 0
\(534\) −680.144 −0.0551174
\(535\) −10832.9 −0.875417
\(536\) −3086.93 −0.248759
\(537\) −10124.1 −0.813569
\(538\) 920.403 0.0737572
\(539\) −2070.33 −0.165446
\(540\) 1102.62 0.0878691
\(541\) −16867.2 −1.34044 −0.670220 0.742163i \(-0.733800\pi\)
−0.670220 + 0.742163i \(0.733800\pi\)
\(542\) −1360.98 −0.107858
\(543\) 21762.7 1.71994
\(544\) −3100.58 −0.244368
\(545\) −4553.08 −0.357858
\(546\) 0 0
\(547\) 9104.87 0.711693 0.355846 0.934544i \(-0.384193\pi\)
0.355846 + 0.934544i \(0.384193\pi\)
\(548\) 13157.2 1.02563
\(549\) 12513.2 0.972772
\(550\) −205.760 −0.0159521
\(551\) 3686.95 0.285062
\(552\) −3354.58 −0.258660
\(553\) −3207.31 −0.246634
\(554\) −823.349 −0.0631422
\(555\) 4083.70 0.312330
\(556\) 5563.44 0.424357
\(557\) 5185.09 0.394433 0.197217 0.980360i \(-0.436810\pi\)
0.197217 + 0.980360i \(0.436810\pi\)
\(558\) −1195.99 −0.0907351
\(559\) 0 0
\(560\) −9224.43 −0.696077
\(561\) 5769.32 0.434191
\(562\) −140.919 −0.0105770
\(563\) 3523.48 0.263760 0.131880 0.991266i \(-0.457899\pi\)
0.131880 + 0.991266i \(0.457899\pi\)
\(564\) −22849.1 −1.70589
\(565\) 6513.20 0.484978
\(566\) −942.585 −0.0699996
\(567\) −18485.5 −1.36917
\(568\) 896.969 0.0662605
\(569\) 14692.9 1.08253 0.541265 0.840852i \(-0.317945\pi\)
0.541265 + 0.840852i \(0.317945\pi\)
\(570\) −130.857 −0.00961577
\(571\) −20772.1 −1.52239 −0.761196 0.648522i \(-0.775387\pi\)
−0.761196 + 0.648522i \(0.775387\pi\)
\(572\) 0 0
\(573\) −10578.0 −0.771212
\(574\) −650.940 −0.0473340
\(575\) −11224.2 −0.814056
\(576\) −11813.3 −0.854549
\(577\) 19163.9 1.38267 0.691336 0.722533i \(-0.257022\pi\)
0.691336 + 0.722533i \(0.257022\pi\)
\(578\) −107.704 −0.00775066
\(579\) −35336.9 −2.53636
\(580\) 14380.3 1.02950
\(581\) 10468.7 0.747531
\(582\) −2358.02 −0.167944
\(583\) −5867.07 −0.416791
\(584\) −1917.52 −0.135869
\(585\) 0 0
\(586\) −874.390 −0.0616394
\(587\) 25419.4 1.78734 0.893672 0.448722i \(-0.148121\pi\)
0.893672 + 0.448722i \(0.148121\pi\)
\(588\) 10681.6 0.749154
\(589\) 2926.62 0.204736
\(590\) −2.38616 −0.000166503 0
\(591\) 5619.24 0.391107
\(592\) 5641.91 0.391691
\(593\) −22771.2 −1.57690 −0.788451 0.615098i \(-0.789116\pi\)
−0.788451 + 0.615098i \(0.789116\pi\)
\(594\) 53.0602 0.00366513
\(595\) −10788.8 −0.743357
\(596\) 9895.96 0.680125
\(597\) 266.012 0.0182364
\(598\) 0 0
\(599\) −14844.0 −1.01253 −0.506267 0.862377i \(-0.668975\pi\)
−0.506267 + 0.862377i \(0.668975\pi\)
\(600\) 2129.74 0.144911
\(601\) 1152.87 0.0782475 0.0391237 0.999234i \(-0.487543\pi\)
0.0391237 + 0.999234i \(0.487543\pi\)
\(602\) 2436.67 0.164969
\(603\) −20917.3 −1.41264
\(604\) 9135.04 0.615396
\(605\) −770.842 −0.0518003
\(606\) 2045.92 0.137145
\(607\) −10559.8 −0.706112 −0.353056 0.935602i \(-0.614858\pi\)
−0.353056 + 0.935602i \(0.614858\pi\)
\(608\) −548.001 −0.0365532
\(609\) −46706.5 −3.10779
\(610\) 737.539 0.0489542
\(611\) 0 0
\(612\) −13992.2 −0.924185
\(613\) 26620.7 1.75400 0.876998 0.480495i \(-0.159543\pi\)
0.876998 + 0.480495i \(0.159543\pi\)
\(614\) 1303.47 0.0856739
\(615\) 5795.81 0.380015
\(616\) −896.103 −0.0586121
\(617\) 12506.8 0.816053 0.408026 0.912970i \(-0.366217\pi\)
0.408026 + 0.912970i \(0.366217\pi\)
\(618\) 924.475 0.0601745
\(619\) 11013.3 0.715121 0.357561 0.933890i \(-0.383609\pi\)
0.357561 + 0.933890i \(0.383609\pi\)
\(620\) 11414.7 0.739398
\(621\) 2894.44 0.187037
\(622\) 452.130 0.0291459
\(623\) −9910.95 −0.637358
\(624\) 0 0
\(625\) 2052.92 0.131387
\(626\) −1040.44 −0.0664286
\(627\) 1019.68 0.0649474
\(628\) −17030.4 −1.08214
\(629\) 6598.71 0.418296
\(630\) 779.240 0.0492788
\(631\) −3315.53 −0.209174 −0.104587 0.994516i \(-0.533352\pi\)
−0.104587 + 0.994516i \(0.533352\pi\)
\(632\) −491.856 −0.0309573
\(633\) −25658.8 −1.61113
\(634\) 2269.98 0.142196
\(635\) −6508.07 −0.406716
\(636\) 30270.4 1.88726
\(637\) 0 0
\(638\) 692.005 0.0429416
\(639\) 6077.95 0.376275
\(640\) −2846.86 −0.175831
\(641\) 18082.3 1.11421 0.557103 0.830443i \(-0.311913\pi\)
0.557103 + 0.830443i \(0.311913\pi\)
\(642\) 2689.58 0.165342
\(643\) 16694.9 1.02392 0.511961 0.859009i \(-0.328919\pi\)
0.511961 + 0.859009i \(0.328919\pi\)
\(644\) −24366.0 −1.49092
\(645\) −21695.5 −1.32443
\(646\) −211.447 −0.0128781
\(647\) 17734.1 1.07759 0.538795 0.842437i \(-0.318880\pi\)
0.538795 + 0.842437i \(0.318880\pi\)
\(648\) −2834.84 −0.171856
\(649\) 18.5937 0.00112460
\(650\) 0 0
\(651\) −37074.6 −2.23206
\(652\) −23478.3 −1.41025
\(653\) 19094.7 1.14431 0.572153 0.820147i \(-0.306108\pi\)
0.572153 + 0.820147i \(0.306108\pi\)
\(654\) 1130.43 0.0675894
\(655\) 1433.54 0.0855159
\(656\) 8007.30 0.476574
\(657\) −12993.3 −0.771564
\(658\) 2056.17 0.121821
\(659\) −5756.24 −0.340260 −0.170130 0.985422i \(-0.554419\pi\)
−0.170130 + 0.985422i \(0.554419\pi\)
\(660\) 3977.06 0.234556
\(661\) 30596.6 1.80041 0.900205 0.435466i \(-0.143417\pi\)
0.900205 + 0.435466i \(0.143417\pi\)
\(662\) −1498.43 −0.0879732
\(663\) 0 0
\(664\) 1605.43 0.0938293
\(665\) −1906.83 −0.111193
\(666\) −476.604 −0.0277298
\(667\) 37748.9 2.19137
\(668\) 7145.24 0.413859
\(669\) −37565.3 −2.17094
\(670\) −1232.88 −0.0710902
\(671\) −5747.13 −0.330649
\(672\) 6942.11 0.398509
\(673\) −19024.1 −1.08963 −0.544817 0.838555i \(-0.683401\pi\)
−0.544817 + 0.838555i \(0.683401\pi\)
\(674\) −681.209 −0.0389306
\(675\) −1837.61 −0.104784
\(676\) 0 0
\(677\) 14655.3 0.831976 0.415988 0.909370i \(-0.363436\pi\)
0.415988 + 0.909370i \(0.363436\pi\)
\(678\) −1617.09 −0.0915988
\(679\) −34360.7 −1.94204
\(680\) −1654.51 −0.0933054
\(681\) −4608.73 −0.259335
\(682\) 549.298 0.0308412
\(683\) −5137.72 −0.287832 −0.143916 0.989590i \(-0.545970\pi\)
−0.143916 + 0.989590i \(0.545970\pi\)
\(684\) −2473.00 −0.138242
\(685\) 10542.1 0.588018
\(686\) 790.528 0.0439978
\(687\) −18660.5 −1.03631
\(688\) −29973.8 −1.66096
\(689\) 0 0
\(690\) −1339.78 −0.0739196
\(691\) 18074.2 0.995046 0.497523 0.867451i \(-0.334243\pi\)
0.497523 + 0.867451i \(0.334243\pi\)
\(692\) 18637.7 1.02384
\(693\) −6072.08 −0.332842
\(694\) 1330.37 0.0727666
\(695\) 4457.67 0.243293
\(696\) −7162.67 −0.390087
\(697\) 9365.25 0.508944
\(698\) −682.732 −0.0370226
\(699\) −37955.8 −2.05382
\(700\) 15469.4 0.835267
\(701\) 17200.1 0.926733 0.463366 0.886167i \(-0.346641\pi\)
0.463366 + 0.886167i \(0.346641\pi\)
\(702\) 0 0
\(703\) 1166.26 0.0625697
\(704\) 5425.66 0.290465
\(705\) −18307.7 −0.978023
\(706\) 1160.08 0.0618414
\(707\) 29812.9 1.58590
\(708\) −95.9318 −0.00509228
\(709\) 22222.6 1.17713 0.588565 0.808450i \(-0.299693\pi\)
0.588565 + 0.808450i \(0.299693\pi\)
\(710\) 358.239 0.0189359
\(711\) −3332.86 −0.175798
\(712\) −1519.89 −0.0800005
\(713\) 29964.2 1.57387
\(714\) 2678.63 0.140399
\(715\) 0 0
\(716\) −11277.1 −0.588612
\(717\) 23824.8 1.24094
\(718\) 1509.60 0.0784648
\(719\) 23179.8 1.20231 0.601154 0.799133i \(-0.294708\pi\)
0.601154 + 0.799133i \(0.294708\pi\)
\(720\) −9585.54 −0.496155
\(721\) 13471.3 0.695836
\(722\) 1482.50 0.0764168
\(723\) 27092.2 1.39360
\(724\) 24241.3 1.24436
\(725\) −23965.8 −1.22768
\(726\) 191.384 0.00978363
\(727\) −27170.8 −1.38612 −0.693059 0.720880i \(-0.743738\pi\)
−0.693059 + 0.720880i \(0.743738\pi\)
\(728\) 0 0
\(729\) −15013.8 −0.762779
\(730\) −765.835 −0.0388285
\(731\) −35057.1 −1.77378
\(732\) 29651.6 1.49721
\(733\) −17639.9 −0.888872 −0.444436 0.895811i \(-0.646596\pi\)
−0.444436 + 0.895811i \(0.646596\pi\)
\(734\) −826.389 −0.0415566
\(735\) 8558.57 0.429507
\(736\) −5610.71 −0.280997
\(737\) 9607.01 0.480161
\(738\) −676.422 −0.0337391
\(739\) −7869.41 −0.391720 −0.195860 0.980632i \(-0.562750\pi\)
−0.195860 + 0.980632i \(0.562750\pi\)
\(740\) 4548.80 0.225969
\(741\) 0 0
\(742\) −2724.01 −0.134773
\(743\) −16096.4 −0.794779 −0.397389 0.917650i \(-0.630084\pi\)
−0.397389 + 0.917650i \(0.630084\pi\)
\(744\) −5685.57 −0.280166
\(745\) 7929.06 0.389931
\(746\) −986.235 −0.0484030
\(747\) 10878.5 0.532831
\(748\) 6426.40 0.314134
\(749\) 39192.2 1.91195
\(750\) 2110.13 0.102735
\(751\) −10069.4 −0.489263 −0.244632 0.969616i \(-0.578667\pi\)
−0.244632 + 0.969616i \(0.578667\pi\)
\(752\) −25293.3 −1.22653
\(753\) 15975.4 0.773144
\(754\) 0 0
\(755\) 7319.38 0.352820
\(756\) −3989.15 −0.191910
\(757\) −35438.8 −1.70151 −0.850757 0.525559i \(-0.823856\pi\)
−0.850757 + 0.525559i \(0.823856\pi\)
\(758\) 812.677 0.0389416
\(759\) 10440.0 0.499272
\(760\) −292.421 −0.0139569
\(761\) 21534.0 1.02577 0.512883 0.858458i \(-0.328577\pi\)
0.512883 + 0.858458i \(0.328577\pi\)
\(762\) 1615.82 0.0768174
\(763\) 16472.5 0.781578
\(764\) −11782.8 −0.557967
\(765\) −11211.1 −0.529856
\(766\) 2414.59 0.113894
\(767\) 0 0
\(768\) −27459.0 −1.29016
\(769\) −24991.8 −1.17195 −0.585974 0.810330i \(-0.699288\pi\)
−0.585974 + 0.810330i \(0.699288\pi\)
\(770\) −357.893 −0.0167501
\(771\) 39646.7 1.85193
\(772\) −39361.5 −1.83504
\(773\) 16709.6 0.777493 0.388746 0.921345i \(-0.372908\pi\)
0.388746 + 0.921345i \(0.372908\pi\)
\(774\) 2532.06 0.117588
\(775\) −19023.5 −0.881737
\(776\) −5269.38 −0.243763
\(777\) −14774.3 −0.682144
\(778\) 1482.10 0.0682979
\(779\) 1655.23 0.0761292
\(780\) 0 0
\(781\) −2791.51 −0.127898
\(782\) −2164.90 −0.0989985
\(783\) 6180.17 0.282071
\(784\) 11824.2 0.538640
\(785\) −13645.5 −0.620417
\(786\) −355.917 −0.0161516
\(787\) 39178.5 1.77454 0.887270 0.461251i \(-0.152599\pi\)
0.887270 + 0.461251i \(0.152599\pi\)
\(788\) 6259.22 0.282964
\(789\) −21024.7 −0.948669
\(790\) −196.441 −0.00884693
\(791\) −23564.0 −1.05921
\(792\) −931.183 −0.0417780
\(793\) 0 0
\(794\) −561.459 −0.0250950
\(795\) 24253.9 1.08201
\(796\) 296.308 0.0131939
\(797\) −43194.1 −1.91972 −0.959858 0.280487i \(-0.909504\pi\)
−0.959858 + 0.280487i \(0.909504\pi\)
\(798\) 473.424 0.0210013
\(799\) −29582.7 −1.30984
\(800\) 3562.10 0.157424
\(801\) −10298.9 −0.454301
\(802\) −3105.42 −0.136728
\(803\) 5967.63 0.262258
\(804\) −49566.1 −2.17421
\(805\) −19523.1 −0.854779
\(806\) 0 0
\(807\) 29648.7 1.29329
\(808\) 4571.95 0.199060
\(809\) 30480.9 1.32466 0.662330 0.749212i \(-0.269568\pi\)
0.662330 + 0.749212i \(0.269568\pi\)
\(810\) −1132.20 −0.0491129
\(811\) −38120.8 −1.65056 −0.825279 0.564725i \(-0.808982\pi\)
−0.825279 + 0.564725i \(0.808982\pi\)
\(812\) −52026.0 −2.24847
\(813\) −43840.8 −1.89122
\(814\) 218.897 0.00942546
\(815\) −18811.8 −0.808525
\(816\) −32950.2 −1.41359
\(817\) −6196.03 −0.265326
\(818\) −1349.68 −0.0576902
\(819\) 0 0
\(820\) 6455.90 0.274939
\(821\) 27818.9 1.18257 0.591284 0.806464i \(-0.298621\pi\)
0.591284 + 0.806464i \(0.298621\pi\)
\(822\) −2617.38 −0.111060
\(823\) 37786.8 1.60044 0.800222 0.599704i \(-0.204715\pi\)
0.800222 + 0.599704i \(0.204715\pi\)
\(824\) 2065.89 0.0873406
\(825\) −6628.09 −0.279710
\(826\) 8.63283 0.000363650 0
\(827\) −43364.7 −1.82338 −0.911692 0.410873i \(-0.865224\pi\)
−0.911692 + 0.410873i \(0.865224\pi\)
\(828\) −25319.8 −1.06271
\(829\) 1244.35 0.0521327 0.0260664 0.999660i \(-0.491702\pi\)
0.0260664 + 0.999660i \(0.491702\pi\)
\(830\) 641.188 0.0268144
\(831\) −26522.3 −1.10716
\(832\) 0 0
\(833\) 13829.5 0.575227
\(834\) −1106.74 −0.0459513
\(835\) 5725.07 0.237274
\(836\) 1135.81 0.0469890
\(837\) 4905.68 0.202587
\(838\) 100.624 0.00414797
\(839\) −23769.0 −0.978064 −0.489032 0.872266i \(-0.662650\pi\)
−0.489032 + 0.872266i \(0.662650\pi\)
\(840\) 3704.41 0.152160
\(841\) 56212.0 2.30481
\(842\) 844.233 0.0345537
\(843\) −4539.37 −0.185462
\(844\) −28581.1 −1.16564
\(845\) 0 0
\(846\) 2136.67 0.0868323
\(847\) 2788.81 0.113134
\(848\) 33508.4 1.35694
\(849\) −30363.2 −1.22740
\(850\) 1374.44 0.0554624
\(851\) 11940.8 0.480994
\(852\) 14402.4 0.579130
\(853\) 42511.5 1.70641 0.853204 0.521577i \(-0.174656\pi\)
0.853204 + 0.521577i \(0.174656\pi\)
\(854\) −2668.33 −0.106918
\(855\) −1981.47 −0.0792572
\(856\) 6010.31 0.239986
\(857\) 15326.8 0.610915 0.305457 0.952206i \(-0.401191\pi\)
0.305457 + 0.952206i \(0.401191\pi\)
\(858\) 0 0
\(859\) 18415.6 0.731471 0.365736 0.930719i \(-0.380817\pi\)
0.365736 + 0.930719i \(0.380817\pi\)
\(860\) −24166.5 −0.958220
\(861\) −20968.5 −0.829971
\(862\) 2675.57 0.105720
\(863\) 2893.68 0.114139 0.0570695 0.998370i \(-0.481824\pi\)
0.0570695 + 0.998370i \(0.481824\pi\)
\(864\) −918.575 −0.0361696
\(865\) 14933.3 0.586992
\(866\) −1578.12 −0.0619245
\(867\) −3469.42 −0.135903
\(868\) −41297.1 −1.61488
\(869\) 1530.73 0.0597544
\(870\) −2860.68 −0.111478
\(871\) 0 0
\(872\) 2526.14 0.0981030
\(873\) −35705.8 −1.38426
\(874\) −382.628 −0.0148085
\(875\) 30748.4 1.18798
\(876\) −30789.2 −1.18752
\(877\) −43023.3 −1.65655 −0.828275 0.560323i \(-0.810677\pi\)
−0.828275 + 0.560323i \(0.810677\pi\)
\(878\) 2070.70 0.0795929
\(879\) −28166.4 −1.08081
\(880\) 4402.49 0.168645
\(881\) −30466.0 −1.16507 −0.582534 0.812806i \(-0.697939\pi\)
−0.582534 + 0.812806i \(0.697939\pi\)
\(882\) −998.860 −0.0381331
\(883\) 39398.2 1.50153 0.750767 0.660567i \(-0.229684\pi\)
0.750767 + 0.660567i \(0.229684\pi\)
\(884\) 0 0
\(885\) −76.8646 −0.00291952
\(886\) −2123.87 −0.0805338
\(887\) 6077.46 0.230058 0.115029 0.993362i \(-0.463304\pi\)
0.115029 + 0.993362i \(0.463304\pi\)
\(888\) −2265.71 −0.0856221
\(889\) 23545.4 0.888288
\(890\) −607.026 −0.0228624
\(891\) 8822.45 0.331721
\(892\) −41843.7 −1.57066
\(893\) −5228.49 −0.195929
\(894\) −1968.62 −0.0736470
\(895\) −9035.71 −0.337464
\(896\) 10299.6 0.384023
\(897\) 0 0
\(898\) 957.660 0.0355874
\(899\) 63979.3 2.37356
\(900\) 16074.9 0.595368
\(901\) 39191.1 1.44911
\(902\) 310.670 0.0114681
\(903\) 78491.8 2.89263
\(904\) −3613.65 −0.132952
\(905\) 19423.1 0.713422
\(906\) −1817.25 −0.0666379
\(907\) 10979.6 0.401954 0.200977 0.979596i \(-0.435588\pi\)
0.200977 + 0.979596i \(0.435588\pi\)
\(908\) −5133.62 −0.187627
\(909\) 30979.9 1.13041
\(910\) 0 0
\(911\) −2625.11 −0.0954706 −0.0477353 0.998860i \(-0.515200\pi\)
−0.0477353 + 0.998860i \(0.515200\pi\)
\(912\) −5823.66 −0.211448
\(913\) −4996.34 −0.181111
\(914\) 3607.84 0.130565
\(915\) 23758.1 0.858382
\(916\) −20785.8 −0.749760
\(917\) −5186.36 −0.186771
\(918\) −354.434 −0.0127430
\(919\) 27772.9 0.996892 0.498446 0.866921i \(-0.333904\pi\)
0.498446 + 0.866921i \(0.333904\pi\)
\(920\) −2993.95 −0.107291
\(921\) 41988.3 1.50224
\(922\) −1514.73 −0.0541052
\(923\) 0 0
\(924\) −14388.5 −0.512281
\(925\) −7580.93 −0.269470
\(926\) −136.096 −0.00482980
\(927\) 13998.7 0.495983
\(928\) −11979.9 −0.423772
\(929\) −41116.0 −1.45207 −0.726034 0.687658i \(-0.758639\pi\)
−0.726034 + 0.687658i \(0.758639\pi\)
\(930\) −2270.75 −0.0800653
\(931\) 2444.24 0.0860439
\(932\) −42278.6 −1.48593
\(933\) 14564.3 0.511056
\(934\) 3784.16 0.132571
\(935\) 5149.10 0.180100
\(936\) 0 0
\(937\) 13015.6 0.453790 0.226895 0.973919i \(-0.427143\pi\)
0.226895 + 0.973919i \(0.427143\pi\)
\(938\) 4460.42 0.155264
\(939\) −33515.3 −1.16478
\(940\) −20392.7 −0.707594
\(941\) 40088.4 1.38878 0.694392 0.719597i \(-0.255673\pi\)
0.694392 + 0.719597i \(0.255673\pi\)
\(942\) 3387.88 0.117179
\(943\) 16947.1 0.585230
\(944\) −106.194 −0.00366134
\(945\) −3196.28 −0.110026
\(946\) −1162.94 −0.0399686
\(947\) −44753.7 −1.53569 −0.767846 0.640634i \(-0.778671\pi\)
−0.767846 + 0.640634i \(0.778671\pi\)
\(948\) −7897.62 −0.270573
\(949\) 0 0
\(950\) 242.921 0.00829621
\(951\) 73122.2 2.49332
\(952\) 5985.83 0.203783
\(953\) 2835.36 0.0963762 0.0481881 0.998838i \(-0.484655\pi\)
0.0481881 + 0.998838i \(0.484655\pi\)
\(954\) −2830.65 −0.0960645
\(955\) −9440.87 −0.319895
\(956\) 26538.3 0.897812
\(957\) 22291.3 0.752954
\(958\) 3468.86 0.116987
\(959\) −38140.0 −1.28426
\(960\) −22429.2 −0.754060
\(961\) 20994.4 0.704722
\(962\) 0 0
\(963\) 40726.4 1.36282
\(964\) 30177.8 1.00826
\(965\) −31538.1 −1.05207
\(966\) 4847.16 0.161444
\(967\) −24439.5 −0.812741 −0.406371 0.913708i \(-0.633206\pi\)
−0.406371 + 0.913708i \(0.633206\pi\)
\(968\) 427.678 0.0142005
\(969\) −6811.28 −0.225810
\(970\) −2104.53 −0.0696622
\(971\) −1845.66 −0.0609989 −0.0304994 0.999535i \(-0.509710\pi\)
−0.0304994 + 0.999535i \(0.509710\pi\)
\(972\) −40845.2 −1.34785
\(973\) −16127.3 −0.531364
\(974\) 3181.67 0.104669
\(975\) 0 0
\(976\) 32823.4 1.07649
\(977\) 25442.8 0.833151 0.416575 0.909101i \(-0.363230\pi\)
0.416575 + 0.909101i \(0.363230\pi\)
\(978\) 4670.57 0.152708
\(979\) 4730.14 0.154419
\(980\) 9533.31 0.310745
\(981\) 17117.3 0.557100
\(982\) −2027.56 −0.0658879
\(983\) −44900.2 −1.45686 −0.728430 0.685121i \(-0.759749\pi\)
−0.728430 + 0.685121i \(0.759749\pi\)
\(984\) −3215.62 −0.104177
\(985\) 5015.15 0.162229
\(986\) −4622.48 −0.149300
\(987\) 66234.9 2.13605
\(988\) 0 0
\(989\) −63438.1 −2.03965
\(990\) −371.903 −0.0119393
\(991\) 8954.53 0.287033 0.143517 0.989648i \(-0.454159\pi\)
0.143517 + 0.989648i \(0.454159\pi\)
\(992\) −9509.41 −0.304359
\(993\) −48268.6 −1.54255
\(994\) −1296.06 −0.0413568
\(995\) 237.415 0.00756437
\(996\) 25778.0 0.820087
\(997\) 270.402 0.00858950 0.00429475 0.999991i \(-0.498633\pi\)
0.00429475 + 0.999991i \(0.498633\pi\)
\(998\) −2619.66 −0.0830901
\(999\) 1954.93 0.0619131
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 1859.4.a.e.1.7 11
13.12 even 2 143.4.a.d.1.5 11
39.38 odd 2 1287.4.a.m.1.7 11
52.51 odd 2 2288.4.a.u.1.10 11
143.142 odd 2 1573.4.a.f.1.7 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.a.d.1.5 11 13.12 even 2
1287.4.a.m.1.7 11 39.38 odd 2
1573.4.a.f.1.7 11 143.142 odd 2
1859.4.a.e.1.7 11 1.1 even 1 trivial
2288.4.a.u.1.10 11 52.51 odd 2