Properties

Label 1859.4.a.n.1.13
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $1$
Dimension $39$
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: \(1\)
Dimension: \(39\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
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)
 
\(f(q)\) \(=\) \(q-2.30249 q^{2} +4.54839 q^{3} -2.69855 q^{4} -4.16672 q^{5} -10.4726 q^{6} -17.3608 q^{7} +24.6333 q^{8} -6.31212 q^{9} +O(q^{10})\) \(q-2.30249 q^{2} +4.54839 q^{3} -2.69855 q^{4} -4.16672 q^{5} -10.4726 q^{6} -17.3608 q^{7} +24.6333 q^{8} -6.31212 q^{9} +9.59382 q^{10} +11.0000 q^{11} -12.2741 q^{12} +39.9730 q^{14} -18.9519 q^{15} -35.1294 q^{16} +1.39107 q^{17} +14.5336 q^{18} +58.9335 q^{19} +11.2441 q^{20} -78.9636 q^{21} -25.3274 q^{22} +46.6310 q^{23} +112.042 q^{24} -107.638 q^{25} -151.517 q^{27} +46.8489 q^{28} +175.166 q^{29} +43.6364 q^{30} -33.3275 q^{31} -116.181 q^{32} +50.0323 q^{33} -3.20293 q^{34} +72.3375 q^{35} +17.0336 q^{36} +376.578 q^{37} -135.694 q^{38} -102.640 q^{40} -270.238 q^{41} +181.813 q^{42} -125.758 q^{43} -29.6840 q^{44} +26.3008 q^{45} -107.367 q^{46} +562.550 q^{47} -159.782 q^{48} -41.6034 q^{49} +247.836 q^{50} +6.32715 q^{51} -356.005 q^{53} +348.865 q^{54} -45.8339 q^{55} -427.653 q^{56} +268.053 q^{57} -403.317 q^{58} +138.690 q^{59} +51.1426 q^{60} +358.274 q^{61} +76.7362 q^{62} +109.583 q^{63} +548.541 q^{64} -115.199 q^{66} +291.047 q^{67} -3.75388 q^{68} +212.096 q^{69} -166.556 q^{70} +90.2883 q^{71} -155.488 q^{72} +366.526 q^{73} -867.067 q^{74} -489.582 q^{75} -159.035 q^{76} -190.969 q^{77} +270.365 q^{79} +146.374 q^{80} -518.730 q^{81} +622.219 q^{82} -746.776 q^{83} +213.087 q^{84} -5.79621 q^{85} +289.556 q^{86} +796.722 q^{87} +270.966 q^{88} +1485.51 q^{89} -60.5574 q^{90} -125.836 q^{92} -151.587 q^{93} -1295.26 q^{94} -245.559 q^{95} -528.438 q^{96} +869.043 q^{97} +95.7913 q^{98} -69.4334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30249 −0.814052 −0.407026 0.913416i \(-0.633434\pi\)
−0.407026 + 0.913416i \(0.633434\pi\)
\(3\) 4.54839 0.875339 0.437669 0.899136i \(-0.355804\pi\)
0.437669 + 0.899136i \(0.355804\pi\)
\(4\) −2.69855 −0.337319
\(5\) −4.16672 −0.372683 −0.186341 0.982485i \(-0.559663\pi\)
−0.186341 + 0.982485i \(0.559663\pi\)
\(6\) −10.4726 −0.712571
\(7\) −17.3608 −0.937394 −0.468697 0.883359i \(-0.655276\pi\)
−0.468697 + 0.883359i \(0.655276\pi\)
\(8\) 24.6333 1.08865
\(9\) −6.31212 −0.233782
\(10\) 9.59382 0.303383
\(11\) 11.0000 0.301511
\(12\) −12.2741 −0.295268
\(13\) 0 0
\(14\) 39.9730 0.763088
\(15\) −18.9519 −0.326223
\(16\) −35.1294 −0.548897
\(17\) 1.39107 0.0198462 0.00992308 0.999951i \(-0.496841\pi\)
0.00992308 + 0.999951i \(0.496841\pi\)
\(18\) 14.5336 0.190311
\(19\) 58.9335 0.711593 0.355797 0.934563i \(-0.384210\pi\)
0.355797 + 0.934563i \(0.384210\pi\)
\(20\) 11.2441 0.125713
\(21\) −78.9636 −0.820537
\(22\) −25.3274 −0.245446
\(23\) 46.6310 0.422749 0.211375 0.977405i \(-0.432206\pi\)
0.211375 + 0.977405i \(0.432206\pi\)
\(24\) 112.042 0.952935
\(25\) −107.638 −0.861108
\(26\) 0 0
\(27\) −151.517 −1.07998
\(28\) 46.8489 0.316200
\(29\) 175.166 1.12164 0.560818 0.827939i \(-0.310487\pi\)
0.560818 + 0.827939i \(0.310487\pi\)
\(30\) 43.6364 0.265563
\(31\) −33.3275 −0.193090 −0.0965452 0.995329i \(-0.530779\pi\)
−0.0965452 + 0.995329i \(0.530779\pi\)
\(32\) −116.181 −0.641816
\(33\) 50.0323 0.263925
\(34\) −3.20293 −0.0161558
\(35\) 72.3375 0.349350
\(36\) 17.0336 0.0788592
\(37\) 376.578 1.67322 0.836610 0.547799i \(-0.184534\pi\)
0.836610 + 0.547799i \(0.184534\pi\)
\(38\) −135.694 −0.579274
\(39\) 0 0
\(40\) −102.640 −0.405720
\(41\) −270.238 −1.02937 −0.514683 0.857380i \(-0.672090\pi\)
−0.514683 + 0.857380i \(0.672090\pi\)
\(42\) 181.813 0.667960
\(43\) −125.758 −0.445997 −0.222998 0.974819i \(-0.571584\pi\)
−0.222998 + 0.974819i \(0.571584\pi\)
\(44\) −29.6840 −0.101705
\(45\) 26.3008 0.0871266
\(46\) −107.367 −0.344140
\(47\) 562.550 1.74588 0.872940 0.487828i \(-0.162211\pi\)
0.872940 + 0.487828i \(0.162211\pi\)
\(48\) −159.782 −0.480471
\(49\) −41.6034 −0.121293
\(50\) 247.836 0.700987
\(51\) 6.32715 0.0173721
\(52\) 0 0
\(53\) −356.005 −0.922662 −0.461331 0.887228i \(-0.652628\pi\)
−0.461331 + 0.887228i \(0.652628\pi\)
\(54\) 348.865 0.879158
\(55\) −45.8339 −0.112368
\(56\) −427.653 −1.02049
\(57\) 268.053 0.622885
\(58\) −403.317 −0.913070
\(59\) 138.690 0.306032 0.153016 0.988224i \(-0.451101\pi\)
0.153016 + 0.988224i \(0.451101\pi\)
\(60\) 51.1426 0.110041
\(61\) 358.274 0.752006 0.376003 0.926619i \(-0.377298\pi\)
0.376003 + 0.926619i \(0.377298\pi\)
\(62\) 76.7362 0.157186
\(63\) 109.583 0.219146
\(64\) 548.541 1.07137
\(65\) 0 0
\(66\) −115.199 −0.214848
\(67\) 291.047 0.530703 0.265351 0.964152i \(-0.414512\pi\)
0.265351 + 0.964152i \(0.414512\pi\)
\(68\) −3.75388 −0.00669448
\(69\) 212.096 0.370049
\(70\) −166.556 −0.284389
\(71\) 90.2883 0.150919 0.0754595 0.997149i \(-0.475958\pi\)
0.0754595 + 0.997149i \(0.475958\pi\)
\(72\) −155.488 −0.254507
\(73\) 366.526 0.587652 0.293826 0.955859i \(-0.405071\pi\)
0.293826 + 0.955859i \(0.405071\pi\)
\(74\) −867.067 −1.36209
\(75\) −489.582 −0.753761
\(76\) −159.035 −0.240034
\(77\) −190.969 −0.282635
\(78\) 0 0
\(79\) 270.365 0.385044 0.192522 0.981293i \(-0.438333\pi\)
0.192522 + 0.981293i \(0.438333\pi\)
\(80\) 146.374 0.204564
\(81\) −518.730 −0.711563
\(82\) 622.219 0.837958
\(83\) −746.776 −0.987583 −0.493791 0.869580i \(-0.664389\pi\)
−0.493791 + 0.869580i \(0.664389\pi\)
\(84\) 213.087 0.276782
\(85\) −5.79621 −0.00739632
\(86\) 289.556 0.363065
\(87\) 796.722 0.981811
\(88\) 270.966 0.328240
\(89\) 1485.51 1.76926 0.884628 0.466297i \(-0.154412\pi\)
0.884628 + 0.466297i \(0.154412\pi\)
\(90\) −60.5574 −0.0709256
\(91\) 0 0
\(92\) −125.836 −0.142601
\(93\) −151.587 −0.169019
\(94\) −1295.26 −1.42124
\(95\) −245.559 −0.265198
\(96\) −528.438 −0.561807
\(97\) 869.043 0.909670 0.454835 0.890576i \(-0.349698\pi\)
0.454835 + 0.890576i \(0.349698\pi\)
\(98\) 95.7913 0.0987386
\(99\) −69.4334 −0.0704880
\(100\) 290.468 0.290468
\(101\) −676.974 −0.666945 −0.333472 0.942760i \(-0.608220\pi\)
−0.333472 + 0.942760i \(0.608220\pi\)
\(102\) −14.5682 −0.0141418
\(103\) −145.684 −0.139365 −0.0696827 0.997569i \(-0.522199\pi\)
−0.0696827 + 0.997569i \(0.522199\pi\)
\(104\) 0 0
\(105\) 329.019 0.305800
\(106\) 819.698 0.751095
\(107\) −1759.90 −1.59005 −0.795027 0.606574i \(-0.792543\pi\)
−0.795027 + 0.606574i \(0.792543\pi\)
\(108\) 408.875 0.364297
\(109\) −1586.57 −1.39418 −0.697090 0.716984i \(-0.745522\pi\)
−0.697090 + 0.716984i \(0.745522\pi\)
\(110\) 105.532 0.0914735
\(111\) 1712.83 1.46463
\(112\) 609.874 0.514533
\(113\) −1328.52 −1.10599 −0.552995 0.833185i \(-0.686515\pi\)
−0.552995 + 0.833185i \(0.686515\pi\)
\(114\) −617.188 −0.507061
\(115\) −194.298 −0.157551
\(116\) −472.693 −0.378349
\(117\) 0 0
\(118\) −319.332 −0.249126
\(119\) −24.1501 −0.0186037
\(120\) −466.847 −0.355142
\(121\) 121.000 0.0909091
\(122\) −824.923 −0.612172
\(123\) −1229.15 −0.901044
\(124\) 89.9360 0.0651330
\(125\) 969.339 0.693602
\(126\) −252.314 −0.178396
\(127\) 587.994 0.410835 0.205417 0.978674i \(-0.434145\pi\)
0.205417 + 0.978674i \(0.434145\pi\)
\(128\) −333.560 −0.230335
\(129\) −571.995 −0.390398
\(130\) 0 0
\(131\) −579.068 −0.386209 −0.193104 0.981178i \(-0.561856\pi\)
−0.193104 + 0.981178i \(0.561856\pi\)
\(132\) −135.015 −0.0890267
\(133\) −1023.13 −0.667043
\(134\) −670.133 −0.432020
\(135\) 631.327 0.402489
\(136\) 34.2667 0.0216055
\(137\) −1413.01 −0.881178 −0.440589 0.897709i \(-0.645230\pi\)
−0.440589 + 0.897709i \(0.645230\pi\)
\(138\) −488.348 −0.301239
\(139\) 1506.31 0.919162 0.459581 0.888136i \(-0.348000\pi\)
0.459581 + 0.888136i \(0.348000\pi\)
\(140\) −195.206 −0.117842
\(141\) 2558.70 1.52824
\(142\) −207.888 −0.122856
\(143\) 0 0
\(144\) 221.741 0.128323
\(145\) −729.866 −0.418014
\(146\) −843.921 −0.478379
\(147\) −189.229 −0.106172
\(148\) −1016.22 −0.564408
\(149\) −592.565 −0.325804 −0.162902 0.986642i \(-0.552085\pi\)
−0.162902 + 0.986642i \(0.552085\pi\)
\(150\) 1127.26 0.613601
\(151\) −687.583 −0.370561 −0.185281 0.982686i \(-0.559319\pi\)
−0.185281 + 0.982686i \(0.559319\pi\)
\(152\) 1451.73 0.774674
\(153\) −8.78063 −0.00463968
\(154\) 439.703 0.230080
\(155\) 138.866 0.0719614
\(156\) 0 0
\(157\) −304.141 −0.154606 −0.0773029 0.997008i \(-0.524631\pi\)
−0.0773029 + 0.997008i \(0.524631\pi\)
\(158\) −622.513 −0.313446
\(159\) −1619.25 −0.807642
\(160\) 484.094 0.239194
\(161\) −809.550 −0.396282
\(162\) 1194.37 0.579250
\(163\) −3724.50 −1.78972 −0.894862 0.446343i \(-0.852726\pi\)
−0.894862 + 0.446343i \(0.852726\pi\)
\(164\) 729.250 0.347225
\(165\) −208.471 −0.0983601
\(166\) 1719.44 0.803944
\(167\) 1404.56 0.650826 0.325413 0.945572i \(-0.394497\pi\)
0.325413 + 0.945572i \(0.394497\pi\)
\(168\) −1945.13 −0.893276
\(169\) 0 0
\(170\) 13.3457 0.00602099
\(171\) −371.996 −0.166358
\(172\) 339.363 0.150443
\(173\) 1353.10 0.594650 0.297325 0.954776i \(-0.403906\pi\)
0.297325 + 0.954776i \(0.403906\pi\)
\(174\) −1834.44 −0.799246
\(175\) 1868.69 0.807197
\(176\) −386.424 −0.165499
\(177\) 630.816 0.267882
\(178\) −3420.37 −1.44027
\(179\) −3628.19 −1.51499 −0.757496 0.652840i \(-0.773577\pi\)
−0.757496 + 0.652840i \(0.773577\pi\)
\(180\) −70.9741 −0.0293894
\(181\) −2868.20 −1.17785 −0.588927 0.808186i \(-0.700450\pi\)
−0.588927 + 0.808186i \(0.700450\pi\)
\(182\) 0 0
\(183\) 1629.57 0.658260
\(184\) 1148.67 0.460225
\(185\) −1569.10 −0.623580
\(186\) 349.027 0.137591
\(187\) 15.3018 0.00598384
\(188\) −1518.07 −0.588918
\(189\) 2630.45 1.01236
\(190\) 565.397 0.215885
\(191\) 563.116 0.213328 0.106664 0.994295i \(-0.465983\pi\)
0.106664 + 0.994295i \(0.465983\pi\)
\(192\) 2494.98 0.937811
\(193\) −713.977 −0.266286 −0.133143 0.991097i \(-0.542507\pi\)
−0.133143 + 0.991097i \(0.542507\pi\)
\(194\) −2000.96 −0.740519
\(195\) 0 0
\(196\) 112.269 0.0409143
\(197\) −1436.96 −0.519692 −0.259846 0.965650i \(-0.583672\pi\)
−0.259846 + 0.965650i \(0.583672\pi\)
\(198\) 159.869 0.0573810
\(199\) −1614.93 −0.575273 −0.287637 0.957740i \(-0.592870\pi\)
−0.287637 + 0.957740i \(0.592870\pi\)
\(200\) −2651.49 −0.937443
\(201\) 1323.80 0.464545
\(202\) 1558.72 0.542928
\(203\) −3041.01 −1.05141
\(204\) −17.0741 −0.00585994
\(205\) 1126.00 0.383627
\(206\) 335.435 0.113451
\(207\) −294.340 −0.0988313
\(208\) 0 0
\(209\) 648.268 0.214553
\(210\) −757.563 −0.248937
\(211\) −1856.32 −0.605660 −0.302830 0.953045i \(-0.597931\pi\)
−0.302830 + 0.953045i \(0.597931\pi\)
\(212\) 960.698 0.311231
\(213\) 410.666 0.132105
\(214\) 4052.14 1.29439
\(215\) 523.997 0.166215
\(216\) −3732.35 −1.17571
\(217\) 578.592 0.181002
\(218\) 3653.05 1.13494
\(219\) 1667.10 0.514394
\(220\) 123.685 0.0379038
\(221\) 0 0
\(222\) −3943.76 −1.19229
\(223\) 323.796 0.0972332 0.0486166 0.998818i \(-0.484519\pi\)
0.0486166 + 0.998818i \(0.484519\pi\)
\(224\) 2017.00 0.601635
\(225\) 679.427 0.201312
\(226\) 3058.90 0.900333
\(227\) 1514.68 0.442875 0.221438 0.975175i \(-0.428925\pi\)
0.221438 + 0.975175i \(0.428925\pi\)
\(228\) −723.353 −0.210111
\(229\) −3454.15 −0.996755 −0.498378 0.866960i \(-0.666071\pi\)
−0.498378 + 0.866960i \(0.666071\pi\)
\(230\) 447.369 0.128255
\(231\) −868.600 −0.247401
\(232\) 4314.90 1.22107
\(233\) −6965.84 −1.95857 −0.979287 0.202479i \(-0.935100\pi\)
−0.979287 + 0.202479i \(0.935100\pi\)
\(234\) 0 0
\(235\) −2343.99 −0.650659
\(236\) −374.262 −0.103230
\(237\) 1229.73 0.337044
\(238\) 55.6053 0.0151444
\(239\) −2194.92 −0.594048 −0.297024 0.954870i \(-0.595994\pi\)
−0.297024 + 0.954870i \(0.595994\pi\)
\(240\) 665.768 0.179063
\(241\) 6112.18 1.63369 0.816847 0.576855i \(-0.195720\pi\)
0.816847 + 0.576855i \(0.195720\pi\)
\(242\) −278.601 −0.0740048
\(243\) 1731.56 0.457118
\(244\) −966.821 −0.253666
\(245\) 173.350 0.0452037
\(246\) 2830.10 0.733497
\(247\) 0 0
\(248\) −820.967 −0.210207
\(249\) −3396.63 −0.864469
\(250\) −2231.89 −0.564629
\(251\) −3005.30 −0.755749 −0.377874 0.925857i \(-0.623345\pi\)
−0.377874 + 0.925857i \(0.623345\pi\)
\(252\) −295.716 −0.0739221
\(253\) 512.941 0.127464
\(254\) −1353.85 −0.334441
\(255\) −26.3634 −0.00647428
\(256\) −3620.31 −0.883865
\(257\) 3397.11 0.824537 0.412269 0.911062i \(-0.364737\pi\)
0.412269 + 0.911062i \(0.364737\pi\)
\(258\) 1317.01 0.317805
\(259\) −6537.69 −1.56847
\(260\) 0 0
\(261\) −1105.67 −0.262219
\(262\) 1333.30 0.314394
\(263\) 103.229 0.0242028 0.0121014 0.999927i \(-0.496148\pi\)
0.0121014 + 0.999927i \(0.496148\pi\)
\(264\) 1232.46 0.287321
\(265\) 1483.37 0.343860
\(266\) 2355.75 0.543008
\(267\) 6756.69 1.54870
\(268\) −785.406 −0.179016
\(269\) −64.7352 −0.0146728 −0.00733638 0.999973i \(-0.502335\pi\)
−0.00733638 + 0.999973i \(0.502335\pi\)
\(270\) −1453.62 −0.327647
\(271\) 2540.69 0.569506 0.284753 0.958601i \(-0.408088\pi\)
0.284753 + 0.958601i \(0.408088\pi\)
\(272\) −48.8676 −0.0108935
\(273\) 0 0
\(274\) 3253.43 0.717325
\(275\) −1184.02 −0.259634
\(276\) −572.351 −0.124824
\(277\) 563.954 0.122327 0.0611637 0.998128i \(-0.480519\pi\)
0.0611637 + 0.998128i \(0.480519\pi\)
\(278\) −3468.26 −0.748246
\(279\) 210.368 0.0451411
\(280\) 1781.91 0.380319
\(281\) 1398.31 0.296855 0.148427 0.988923i \(-0.452579\pi\)
0.148427 + 0.988923i \(0.452579\pi\)
\(282\) −5891.37 −1.24406
\(283\) 6039.06 1.26850 0.634249 0.773129i \(-0.281310\pi\)
0.634249 + 0.773129i \(0.281310\pi\)
\(284\) −243.647 −0.0509078
\(285\) −1116.90 −0.232138
\(286\) 0 0
\(287\) 4691.53 0.964922
\(288\) 733.350 0.150045
\(289\) −4911.06 −0.999606
\(290\) 1680.51 0.340285
\(291\) 3952.75 0.796269
\(292\) −989.088 −0.198226
\(293\) 4006.30 0.798807 0.399404 0.916775i \(-0.369217\pi\)
0.399404 + 0.916775i \(0.369217\pi\)
\(294\) 435.697 0.0864297
\(295\) −577.882 −0.114053
\(296\) 9276.36 1.82155
\(297\) −1666.68 −0.325625
\(298\) 1364.37 0.265222
\(299\) 0 0
\(300\) 1321.16 0.254258
\(301\) 2183.25 0.418075
\(302\) 1583.15 0.301656
\(303\) −3079.14 −0.583803
\(304\) −2070.30 −0.390592
\(305\) −1492.83 −0.280259
\(306\) 20.2173 0.00377695
\(307\) −3450.64 −0.641492 −0.320746 0.947165i \(-0.603934\pi\)
−0.320746 + 0.947165i \(0.603934\pi\)
\(308\) 515.338 0.0953380
\(309\) −662.626 −0.121992
\(310\) −319.738 −0.0585804
\(311\) −928.020 −0.169206 −0.0846032 0.996415i \(-0.526962\pi\)
−0.0846032 + 0.996415i \(0.526962\pi\)
\(312\) 0 0
\(313\) 8253.90 1.49054 0.745268 0.666765i \(-0.232321\pi\)
0.745268 + 0.666765i \(0.232321\pi\)
\(314\) 700.281 0.125857
\(315\) −456.603 −0.0816720
\(316\) −729.594 −0.129883
\(317\) −8757.50 −1.55164 −0.775820 0.630954i \(-0.782664\pi\)
−0.775820 + 0.630954i \(0.782664\pi\)
\(318\) 3728.31 0.657463
\(319\) 1926.82 0.338186
\(320\) −2285.62 −0.399281
\(321\) −8004.71 −1.39184
\(322\) 1863.98 0.322595
\(323\) 81.9808 0.0141224
\(324\) 1399.82 0.240024
\(325\) 0 0
\(326\) 8575.60 1.45693
\(327\) −7216.33 −1.22038
\(328\) −6656.84 −1.12062
\(329\) −9766.30 −1.63658
\(330\) 480.001 0.0800702
\(331\) −884.985 −0.146958 −0.0734791 0.997297i \(-0.523410\pi\)
−0.0734791 + 0.997297i \(0.523410\pi\)
\(332\) 2015.21 0.333130
\(333\) −2377.01 −0.391169
\(334\) −3233.98 −0.529807
\(335\) −1212.71 −0.197784
\(336\) 2773.95 0.450391
\(337\) 1403.28 0.226829 0.113414 0.993548i \(-0.463821\pi\)
0.113414 + 0.993548i \(0.463821\pi\)
\(338\) 0 0
\(339\) −6042.64 −0.968115
\(340\) 15.6414 0.00249492
\(341\) −366.603 −0.0582189
\(342\) 856.515 0.135424
\(343\) 6677.01 1.05109
\(344\) −3097.82 −0.485533
\(345\) −883.744 −0.137911
\(346\) −3115.50 −0.484076
\(347\) −5649.13 −0.873952 −0.436976 0.899473i \(-0.643951\pi\)
−0.436976 + 0.899473i \(0.643951\pi\)
\(348\) −2149.99 −0.331183
\(349\) −9445.14 −1.44867 −0.724336 0.689447i \(-0.757854\pi\)
−0.724336 + 0.689447i \(0.757854\pi\)
\(350\) −4302.63 −0.657101
\(351\) 0 0
\(352\) −1277.99 −0.193515
\(353\) 8070.52 1.21686 0.608429 0.793609i \(-0.291800\pi\)
0.608429 + 0.793609i \(0.291800\pi\)
\(354\) −1452.45 −0.218070
\(355\) −376.206 −0.0562449
\(356\) −4008.72 −0.596803
\(357\) −109.844 −0.0162845
\(358\) 8353.86 1.23328
\(359\) −13277.5 −1.95198 −0.975989 0.217820i \(-0.930106\pi\)
−0.975989 + 0.217820i \(0.930106\pi\)
\(360\) 647.876 0.0948502
\(361\) −3385.84 −0.493635
\(362\) 6604.00 0.958835
\(363\) 550.356 0.0795762
\(364\) 0 0
\(365\) −1527.21 −0.219008
\(366\) −3752.07 −0.535858
\(367\) −13420.1 −1.90878 −0.954390 0.298562i \(-0.903493\pi\)
−0.954390 + 0.298562i \(0.903493\pi\)
\(368\) −1638.12 −0.232046
\(369\) 1705.77 0.240648
\(370\) 3612.82 0.507627
\(371\) 6180.53 0.864898
\(372\) 409.064 0.0570134
\(373\) 5921.20 0.821951 0.410976 0.911646i \(-0.365188\pi\)
0.410976 + 0.911646i \(0.365188\pi\)
\(374\) −35.2322 −0.00487116
\(375\) 4408.93 0.607137
\(376\) 13857.5 1.90065
\(377\) 0 0
\(378\) −6056.57 −0.824117
\(379\) 7455.99 1.01052 0.505262 0.862966i \(-0.331396\pi\)
0.505262 + 0.862966i \(0.331396\pi\)
\(380\) 662.654 0.0894564
\(381\) 2674.43 0.359620
\(382\) −1296.57 −0.173660
\(383\) −9968.01 −1.32987 −0.664937 0.746900i \(-0.731542\pi\)
−0.664937 + 0.746900i \(0.731542\pi\)
\(384\) −1517.16 −0.201621
\(385\) 795.712 0.105333
\(386\) 1643.92 0.216771
\(387\) 793.798 0.104266
\(388\) −2345.16 −0.306849
\(389\) 5260.84 0.685694 0.342847 0.939391i \(-0.388609\pi\)
0.342847 + 0.939391i \(0.388609\pi\)
\(390\) 0 0
\(391\) 64.8671 0.00838995
\(392\) −1024.83 −0.132045
\(393\) −2633.83 −0.338064
\(394\) 3308.59 0.423057
\(395\) −1126.54 −0.143499
\(396\) 187.369 0.0237769
\(397\) −14345.3 −1.81352 −0.906761 0.421644i \(-0.861453\pi\)
−0.906761 + 0.421644i \(0.861453\pi\)
\(398\) 3718.36 0.468302
\(399\) −4653.60 −0.583889
\(400\) 3781.28 0.472660
\(401\) −3703.40 −0.461195 −0.230597 0.973049i \(-0.574068\pi\)
−0.230597 + 0.973049i \(0.574068\pi\)
\(402\) −3048.03 −0.378164
\(403\) 0 0
\(404\) 1826.85 0.224973
\(405\) 2161.40 0.265187
\(406\) 7001.89 0.855907
\(407\) 4142.36 0.504495
\(408\) 155.858 0.0189121
\(409\) −8793.65 −1.06312 −0.531562 0.847019i \(-0.678395\pi\)
−0.531562 + 0.847019i \(0.678395\pi\)
\(410\) −2592.61 −0.312292
\(411\) −6426.91 −0.771329
\(412\) 393.134 0.0470105
\(413\) −2407.77 −0.286873
\(414\) 677.715 0.0804538
\(415\) 3111.61 0.368055
\(416\) 0 0
\(417\) 6851.29 0.804578
\(418\) −1492.63 −0.174658
\(419\) −1247.40 −0.145440 −0.0727201 0.997352i \(-0.523168\pi\)
−0.0727201 + 0.997352i \(0.523168\pi\)
\(420\) −887.875 −0.103152
\(421\) 1060.57 0.122776 0.0613881 0.998114i \(-0.480447\pi\)
0.0613881 + 0.998114i \(0.480447\pi\)
\(422\) 4274.15 0.493039
\(423\) −3550.89 −0.408156
\(424\) −8769.58 −1.00445
\(425\) −149.733 −0.0170897
\(426\) −945.555 −0.107541
\(427\) −6219.92 −0.704925
\(428\) 4749.17 0.536355
\(429\) 0 0
\(430\) −1206.50 −0.135308
\(431\) −15286.8 −1.70844 −0.854222 0.519909i \(-0.825966\pi\)
−0.854222 + 0.519909i \(0.825966\pi\)
\(432\) 5322.69 0.592797
\(433\) −8781.08 −0.974577 −0.487288 0.873241i \(-0.662014\pi\)
−0.487288 + 0.873241i \(0.662014\pi\)
\(434\) −1332.20 −0.147345
\(435\) −3319.72 −0.365904
\(436\) 4281.43 0.470283
\(437\) 2748.13 0.300825
\(438\) −3838.48 −0.418744
\(439\) −1906.09 −0.207227 −0.103614 0.994618i \(-0.533041\pi\)
−0.103614 + 0.994618i \(0.533041\pi\)
\(440\) −1129.04 −0.122329
\(441\) 262.606 0.0283561
\(442\) 0 0
\(443\) −4620.37 −0.495532 −0.247766 0.968820i \(-0.579696\pi\)
−0.247766 + 0.968820i \(0.579696\pi\)
\(444\) −4622.15 −0.494048
\(445\) −6189.70 −0.659371
\(446\) −745.537 −0.0791529
\(447\) −2695.22 −0.285189
\(448\) −9523.10 −1.00430
\(449\) −8833.44 −0.928454 −0.464227 0.885716i \(-0.653668\pi\)
−0.464227 + 0.885716i \(0.653668\pi\)
\(450\) −1564.37 −0.163878
\(451\) −2972.61 −0.310366
\(452\) 3585.08 0.373071
\(453\) −3127.40 −0.324366
\(454\) −3487.53 −0.360524
\(455\) 0 0
\(456\) 6603.02 0.678102
\(457\) −9240.25 −0.945822 −0.472911 0.881110i \(-0.656797\pi\)
−0.472911 + 0.881110i \(0.656797\pi\)
\(458\) 7953.15 0.811411
\(459\) −210.771 −0.0214334
\(460\) 524.323 0.0531450
\(461\) 9390.04 0.948672 0.474336 0.880344i \(-0.342688\pi\)
0.474336 + 0.880344i \(0.342688\pi\)
\(462\) 1999.94 0.201398
\(463\) −7817.84 −0.784721 −0.392360 0.919812i \(-0.628341\pi\)
−0.392360 + 0.919812i \(0.628341\pi\)
\(464\) −6153.47 −0.615663
\(465\) 631.619 0.0629906
\(466\) 16038.8 1.59438
\(467\) −16645.0 −1.64933 −0.824666 0.565620i \(-0.808637\pi\)
−0.824666 + 0.565620i \(0.808637\pi\)
\(468\) 0 0
\(469\) −5052.81 −0.497478
\(470\) 5397.00 0.529670
\(471\) −1383.35 −0.135332
\(472\) 3416.39 0.333161
\(473\) −1383.33 −0.134473
\(474\) −2831.43 −0.274371
\(475\) −6343.51 −0.612758
\(476\) 65.1703 0.00627537
\(477\) 2247.15 0.215702
\(478\) 5053.77 0.483586
\(479\) 245.962 0.0234620 0.0117310 0.999931i \(-0.496266\pi\)
0.0117310 + 0.999931i \(0.496266\pi\)
\(480\) 2201.85 0.209375
\(481\) 0 0
\(482\) −14073.2 −1.32991
\(483\) −3682.15 −0.346881
\(484\) −326.525 −0.0306653
\(485\) −3621.06 −0.339018
\(486\) −3986.90 −0.372118
\(487\) −240.346 −0.0223637 −0.0111818 0.999937i \(-0.503559\pi\)
−0.0111818 + 0.999937i \(0.503559\pi\)
\(488\) 8825.48 0.818669
\(489\) −16940.5 −1.56661
\(490\) −399.135 −0.0367982
\(491\) 5208.20 0.478702 0.239351 0.970933i \(-0.423065\pi\)
0.239351 + 0.970933i \(0.423065\pi\)
\(492\) 3316.91 0.303939
\(493\) 243.668 0.0222602
\(494\) 0 0
\(495\) 289.309 0.0262697
\(496\) 1170.78 0.105987
\(497\) −1567.47 −0.141471
\(498\) 7820.70 0.703723
\(499\) −13603.3 −1.22037 −0.610186 0.792258i \(-0.708905\pi\)
−0.610186 + 0.792258i \(0.708905\pi\)
\(500\) −2615.81 −0.233965
\(501\) 6388.48 0.569693
\(502\) 6919.67 0.615219
\(503\) 9041.72 0.801491 0.400746 0.916189i \(-0.368751\pi\)
0.400746 + 0.916189i \(0.368751\pi\)
\(504\) 2699.40 0.238573
\(505\) 2820.76 0.248559
\(506\) −1181.04 −0.103762
\(507\) 0 0
\(508\) −1586.73 −0.138582
\(509\) 8952.50 0.779593 0.389796 0.920901i \(-0.372545\pi\)
0.389796 + 0.920901i \(0.372545\pi\)
\(510\) 60.7015 0.00527041
\(511\) −6363.17 −0.550861
\(512\) 11004.2 0.949847
\(513\) −8929.40 −0.768505
\(514\) −7821.81 −0.671216
\(515\) 607.022 0.0519390
\(516\) 1543.56 0.131689
\(517\) 6188.05 0.526402
\(518\) 15053.0 1.27681
\(519\) 6154.44 0.520520
\(520\) 0 0
\(521\) −8131.19 −0.683751 −0.341875 0.939745i \(-0.611062\pi\)
−0.341875 + 0.939745i \(0.611062\pi\)
\(522\) 2545.79 0.213460
\(523\) −13541.4 −1.13217 −0.566084 0.824347i \(-0.691542\pi\)
−0.566084 + 0.824347i \(0.691542\pi\)
\(524\) 1562.64 0.130276
\(525\) 8499.52 0.706571
\(526\) −237.683 −0.0197024
\(527\) −46.3610 −0.00383210
\(528\) −1757.61 −0.144867
\(529\) −9992.55 −0.821283
\(530\) −3415.45 −0.279920
\(531\) −875.428 −0.0715449
\(532\) 2760.97 0.225006
\(533\) 0 0
\(534\) −15557.2 −1.26072
\(535\) 7333.00 0.592585
\(536\) 7169.45 0.577748
\(537\) −16502.4 −1.32613
\(538\) 149.052 0.0119444
\(539\) −457.637 −0.0365711
\(540\) −1703.67 −0.135767
\(541\) 20393.5 1.62068 0.810338 0.585963i \(-0.199283\pi\)
0.810338 + 0.585963i \(0.199283\pi\)
\(542\) −5849.91 −0.463607
\(543\) −13045.7 −1.03102
\(544\) −161.616 −0.0127376
\(545\) 6610.78 0.519586
\(546\) 0 0
\(547\) −14378.3 −1.12390 −0.561949 0.827172i \(-0.689948\pi\)
−0.561949 + 0.827172i \(0.689948\pi\)
\(548\) 3813.07 0.297238
\(549\) −2261.47 −0.175806
\(550\) 2726.20 0.211355
\(551\) 10323.1 0.798148
\(552\) 5224.62 0.402852
\(553\) −4693.75 −0.360938
\(554\) −1298.50 −0.0995809
\(555\) −7136.86 −0.545843
\(556\) −4064.85 −0.310050
\(557\) −17107.4 −1.30137 −0.650686 0.759347i \(-0.725519\pi\)
−0.650686 + 0.759347i \(0.725519\pi\)
\(558\) −484.369 −0.0367472
\(559\) 0 0
\(560\) −2541.17 −0.191757
\(561\) 69.5986 0.00523789
\(562\) −3219.59 −0.241655
\(563\) 5524.08 0.413521 0.206760 0.978392i \(-0.433708\pi\)
0.206760 + 0.978392i \(0.433708\pi\)
\(564\) −6904.77 −0.515503
\(565\) 5535.57 0.412183
\(566\) −13904.9 −1.03262
\(567\) 9005.55 0.667015
\(568\) 2224.10 0.164298
\(569\) 18693.4 1.37727 0.688635 0.725108i \(-0.258210\pi\)
0.688635 + 0.725108i \(0.258210\pi\)
\(570\) 2571.65 0.188973
\(571\) 23031.5 1.68798 0.843992 0.536355i \(-0.180199\pi\)
0.843992 + 0.536355i \(0.180199\pi\)
\(572\) 0 0
\(573\) 2561.27 0.186734
\(574\) −10802.2 −0.785497
\(575\) −5019.29 −0.364033
\(576\) −3462.46 −0.250467
\(577\) 8356.41 0.602915 0.301458 0.953480i \(-0.402527\pi\)
0.301458 + 0.953480i \(0.402527\pi\)
\(578\) 11307.7 0.813732
\(579\) −3247.45 −0.233090
\(580\) 1969.58 0.141004
\(581\) 12964.6 0.925754
\(582\) −9101.16 −0.648205
\(583\) −3916.06 −0.278193
\(584\) 9028.73 0.639746
\(585\) 0 0
\(586\) −9224.46 −0.650271
\(587\) 14373.2 1.01064 0.505321 0.862932i \(-0.331374\pi\)
0.505321 + 0.862932i \(0.331374\pi\)
\(588\) 510.643 0.0358139
\(589\) −1964.11 −0.137402
\(590\) 1330.57 0.0928450
\(591\) −6535.87 −0.454907
\(592\) −13229.0 −0.918426
\(593\) 5370.38 0.371898 0.185949 0.982559i \(-0.440464\pi\)
0.185949 + 0.982559i \(0.440464\pi\)
\(594\) 3837.52 0.265076
\(595\) 100.627 0.00693326
\(596\) 1599.07 0.109900
\(597\) −7345.34 −0.503559
\(598\) 0 0
\(599\) 6427.64 0.438441 0.219220 0.975675i \(-0.429649\pi\)
0.219220 + 0.975675i \(0.429649\pi\)
\(600\) −12060.0 −0.820580
\(601\) 20326.7 1.37961 0.689804 0.723996i \(-0.257696\pi\)
0.689804 + 0.723996i \(0.257696\pi\)
\(602\) −5026.91 −0.340335
\(603\) −1837.13 −0.124069
\(604\) 1855.48 0.124997
\(605\) −504.173 −0.0338802
\(606\) 7089.69 0.475246
\(607\) 2402.92 0.160678 0.0803390 0.996768i \(-0.474400\pi\)
0.0803390 + 0.996768i \(0.474400\pi\)
\(608\) −6846.96 −0.456712
\(609\) −13831.7 −0.920344
\(610\) 3437.22 0.228146
\(611\) 0 0
\(612\) 23.6950 0.00156505
\(613\) 3076.49 0.202705 0.101352 0.994851i \(-0.467683\pi\)
0.101352 + 0.994851i \(0.467683\pi\)
\(614\) 7945.05 0.522208
\(615\) 5121.51 0.335803
\(616\) −4704.18 −0.307690
\(617\) −23027.3 −1.50250 −0.751251 0.660017i \(-0.770549\pi\)
−0.751251 + 0.660017i \(0.770549\pi\)
\(618\) 1525.69 0.0993078
\(619\) 10155.0 0.659391 0.329695 0.944087i \(-0.393054\pi\)
0.329695 + 0.944087i \(0.393054\pi\)
\(620\) −374.738 −0.0242739
\(621\) −7065.37 −0.456559
\(622\) 2136.76 0.137743
\(623\) −25789.6 −1.65849
\(624\) 0 0
\(625\) 9415.85 0.602614
\(626\) −19004.5 −1.21338
\(627\) 2948.58 0.187807
\(628\) 820.740 0.0521514
\(629\) 523.848 0.0332070
\(630\) 1051.32 0.0664853
\(631\) −5762.78 −0.363570 −0.181785 0.983338i \(-0.558188\pi\)
−0.181785 + 0.983338i \(0.558188\pi\)
\(632\) 6659.99 0.419177
\(633\) −8443.26 −0.530157
\(634\) 20164.0 1.26312
\(635\) −2450.00 −0.153111
\(636\) 4369.63 0.272433
\(637\) 0 0
\(638\) −4436.48 −0.275301
\(639\) −569.911 −0.0352822
\(640\) 1389.85 0.0858417
\(641\) −13564.2 −0.835811 −0.417906 0.908490i \(-0.637236\pi\)
−0.417906 + 0.908490i \(0.637236\pi\)
\(642\) 18430.7 1.13303
\(643\) 390.407 0.0239442 0.0119721 0.999928i \(-0.496189\pi\)
0.0119721 + 0.999928i \(0.496189\pi\)
\(644\) 2184.61 0.133673
\(645\) 2383.34 0.145495
\(646\) −188.760 −0.0114964
\(647\) 14443.1 0.877612 0.438806 0.898582i \(-0.355402\pi\)
0.438806 + 0.898582i \(0.355402\pi\)
\(648\) −12778.0 −0.774642
\(649\) 1525.59 0.0922721
\(650\) 0 0
\(651\) 2631.66 0.158438
\(652\) 10050.7 0.603707
\(653\) 21664.2 1.29829 0.649147 0.760663i \(-0.275126\pi\)
0.649147 + 0.760663i \(0.275126\pi\)
\(654\) 16615.5 0.993453
\(655\) 2412.81 0.143933
\(656\) 9493.29 0.565017
\(657\) −2313.56 −0.137383
\(658\) 22486.8 1.33226
\(659\) 2002.80 0.118389 0.0591943 0.998246i \(-0.481147\pi\)
0.0591943 + 0.998246i \(0.481147\pi\)
\(660\) 562.568 0.0331787
\(661\) 5664.78 0.333335 0.166668 0.986013i \(-0.446699\pi\)
0.166668 + 0.986013i \(0.446699\pi\)
\(662\) 2037.67 0.119632
\(663\) 0 0
\(664\) −18395.6 −1.07513
\(665\) 4263.10 0.248595
\(666\) 5473.04 0.318432
\(667\) 8168.14 0.474171
\(668\) −3790.27 −0.219536
\(669\) 1472.75 0.0851120
\(670\) 2792.26 0.161006
\(671\) 3941.02 0.226738
\(672\) 9174.09 0.526634
\(673\) −25837.7 −1.47989 −0.739947 0.672665i \(-0.765150\pi\)
−0.739947 + 0.672665i \(0.765150\pi\)
\(674\) −3231.02 −0.184650
\(675\) 16309.0 0.929977
\(676\) 0 0
\(677\) 30528.7 1.73311 0.866553 0.499085i \(-0.166330\pi\)
0.866553 + 0.499085i \(0.166330\pi\)
\(678\) 13913.1 0.788096
\(679\) −15087.3 −0.852719
\(680\) −142.780 −0.00805198
\(681\) 6889.35 0.387666
\(682\) 844.099 0.0473933
\(683\) 15284.7 0.856298 0.428149 0.903708i \(-0.359166\pi\)
0.428149 + 0.903708i \(0.359166\pi\)
\(684\) 1003.85 0.0561157
\(685\) 5887.60 0.328399
\(686\) −15373.7 −0.855645
\(687\) −15710.8 −0.872498
\(688\) 4417.80 0.244807
\(689\) 0 0
\(690\) 2034.81 0.112266
\(691\) 26541.3 1.46119 0.730593 0.682813i \(-0.239244\pi\)
0.730593 + 0.682813i \(0.239244\pi\)
\(692\) −3651.41 −0.200587
\(693\) 1205.42 0.0660751
\(694\) 13007.1 0.711443
\(695\) −6276.36 −0.342556
\(696\) 19625.9 1.06885
\(697\) −375.920 −0.0204290
\(698\) 21747.3 1.17930
\(699\) −31683.4 −1.71441
\(700\) −5042.75 −0.272283
\(701\) −23167.2 −1.24823 −0.624117 0.781331i \(-0.714541\pi\)
−0.624117 + 0.781331i \(0.714541\pi\)
\(702\) 0 0
\(703\) 22193.1 1.19065
\(704\) 6033.95 0.323030
\(705\) −10661.4 −0.569547
\(706\) −18582.3 −0.990586
\(707\) 11752.8 0.625190
\(708\) −1702.29 −0.0903615
\(709\) −15225.3 −0.806484 −0.403242 0.915093i \(-0.632117\pi\)
−0.403242 + 0.915093i \(0.632117\pi\)
\(710\) 866.209 0.0457863
\(711\) −1706.58 −0.0900165
\(712\) 36593.0 1.92610
\(713\) −1554.10 −0.0816288
\(714\) 252.915 0.0132564
\(715\) 0 0
\(716\) 9790.85 0.511035
\(717\) −9983.34 −0.519993
\(718\) 30571.3 1.58901
\(719\) 711.358 0.0368973 0.0184487 0.999830i \(-0.494127\pi\)
0.0184487 + 0.999830i \(0.494127\pi\)
\(720\) −923.934 −0.0478236
\(721\) 2529.18 0.130640
\(722\) 7795.86 0.401845
\(723\) 27800.6 1.43003
\(724\) 7739.98 0.397312
\(725\) −18854.6 −0.965849
\(726\) −1267.19 −0.0647792
\(727\) −7249.37 −0.369827 −0.184914 0.982755i \(-0.559201\pi\)
−0.184914 + 0.982755i \(0.559201\pi\)
\(728\) 0 0
\(729\) 21881.5 1.11170
\(730\) 3516.38 0.178284
\(731\) −174.938 −0.00885133
\(732\) −4397.48 −0.222043
\(733\) −20158.7 −1.01579 −0.507897 0.861418i \(-0.669577\pi\)
−0.507897 + 0.861418i \(0.669577\pi\)
\(734\) 30899.6 1.55385
\(735\) 788.462 0.0395685
\(736\) −5417.64 −0.271327
\(737\) 3201.52 0.160013
\(738\) −3927.52 −0.195900
\(739\) 20211.8 1.00610 0.503048 0.864259i \(-0.332212\pi\)
0.503048 + 0.864259i \(0.332212\pi\)
\(740\) 4234.28 0.210345
\(741\) 0 0
\(742\) −14230.6 −0.704072
\(743\) 30489.9 1.50547 0.752736 0.658322i \(-0.228734\pi\)
0.752736 + 0.658322i \(0.228734\pi\)
\(744\) −3734.08 −0.184003
\(745\) 2469.05 0.121422
\(746\) −13633.5 −0.669111
\(747\) 4713.75 0.230879
\(748\) −41.2927 −0.00201846
\(749\) 30553.2 1.49051
\(750\) −10151.5 −0.494241
\(751\) −13731.3 −0.667193 −0.333596 0.942716i \(-0.608262\pi\)
−0.333596 + 0.942716i \(0.608262\pi\)
\(752\) −19762.1 −0.958309
\(753\) −13669.3 −0.661536
\(754\) 0 0
\(755\) 2864.96 0.138102
\(756\) −7098.39 −0.341489
\(757\) 17226.4 0.827085 0.413543 0.910485i \(-0.364291\pi\)
0.413543 + 0.910485i \(0.364291\pi\)
\(758\) −17167.3 −0.822619
\(759\) 2333.06 0.111574
\(760\) −6048.93 −0.288708
\(761\) −524.915 −0.0250041 −0.0125021 0.999922i \(-0.503980\pi\)
−0.0125021 + 0.999922i \(0.503980\pi\)
\(762\) −6157.84 −0.292749
\(763\) 27544.0 1.30690
\(764\) −1519.60 −0.0719596
\(765\) 36.5864 0.00172913
\(766\) 22951.2 1.08259
\(767\) 0 0
\(768\) −16466.6 −0.773681
\(769\) −23219.0 −1.08882 −0.544408 0.838821i \(-0.683246\pi\)
−0.544408 + 0.838821i \(0.683246\pi\)
\(770\) −1832.12 −0.0857467
\(771\) 15451.4 0.721749
\(772\) 1926.70 0.0898232
\(773\) −20012.5 −0.931175 −0.465588 0.885002i \(-0.654157\pi\)
−0.465588 + 0.885002i \(0.654157\pi\)
\(774\) −1827.71 −0.0848782
\(775\) 3587.32 0.166272
\(776\) 21407.4 0.990310
\(777\) −29736.0 −1.37294
\(778\) −12113.0 −0.558191
\(779\) −15926.0 −0.732490
\(780\) 0 0
\(781\) 993.171 0.0455038
\(782\) −149.356 −0.00682986
\(783\) −26540.5 −1.21134
\(784\) 1461.50 0.0665773
\(785\) 1267.27 0.0576189
\(786\) 6064.36 0.275202
\(787\) −27618.3 −1.25093 −0.625467 0.780250i \(-0.715092\pi\)
−0.625467 + 0.780250i \(0.715092\pi\)
\(788\) 3877.72 0.175302
\(789\) 469.524 0.0211857
\(790\) 2593.84 0.116816
\(791\) 23064.2 1.03675
\(792\) −1710.37 −0.0767366
\(793\) 0 0
\(794\) 33029.8 1.47630
\(795\) 6746.97 0.300994
\(796\) 4357.97 0.194050
\(797\) 29515.2 1.31177 0.655885 0.754861i \(-0.272296\pi\)
0.655885 + 0.754861i \(0.272296\pi\)
\(798\) 10714.9 0.475316
\(799\) 782.548 0.0346490
\(800\) 12505.6 0.552673
\(801\) −9376.73 −0.413621
\(802\) 8527.03 0.375436
\(803\) 4031.78 0.177184
\(804\) −3572.33 −0.156700
\(805\) 3373.17 0.147688
\(806\) 0 0
\(807\) −294.441 −0.0128436
\(808\) −16676.1 −0.726068
\(809\) 27669.7 1.20249 0.601246 0.799064i \(-0.294671\pi\)
0.601246 + 0.799064i \(0.294671\pi\)
\(810\) −4976.60 −0.215876
\(811\) 11063.8 0.479040 0.239520 0.970891i \(-0.423010\pi\)
0.239520 + 0.970891i \(0.423010\pi\)
\(812\) 8206.32 0.354662
\(813\) 11556.1 0.498510
\(814\) −9537.74 −0.410685
\(815\) 15518.9 0.666999
\(816\) −222.269 −0.00953551
\(817\) −7411.34 −0.317368
\(818\) 20247.3 0.865439
\(819\) 0 0
\(820\) −3038.58 −0.129405
\(821\) 15354.0 0.652691 0.326346 0.945251i \(-0.394183\pi\)
0.326346 + 0.945251i \(0.394183\pi\)
\(822\) 14797.9 0.627902
\(823\) 16823.2 0.712539 0.356269 0.934383i \(-0.384049\pi\)
0.356269 + 0.934383i \(0.384049\pi\)
\(824\) −3588.66 −0.151720
\(825\) −5385.40 −0.227267
\(826\) 5543.85 0.233529
\(827\) −35426.2 −1.48959 −0.744795 0.667294i \(-0.767453\pi\)
−0.744795 + 0.667294i \(0.767453\pi\)
\(828\) 794.292 0.0333376
\(829\) −42315.2 −1.77282 −0.886410 0.462901i \(-0.846809\pi\)
−0.886410 + 0.462901i \(0.846809\pi\)
\(830\) −7164.44 −0.299616
\(831\) 2565.08 0.107078
\(832\) 0 0
\(833\) −57.8734 −0.00240719
\(834\) −15775.0 −0.654968
\(835\) −5852.40 −0.242552
\(836\) −1749.38 −0.0723729
\(837\) 5049.68 0.208533
\(838\) 2872.12 0.118396
\(839\) −15519.4 −0.638606 −0.319303 0.947653i \(-0.603449\pi\)
−0.319303 + 0.947653i \(0.603449\pi\)
\(840\) 8104.82 0.332908
\(841\) 6294.00 0.258067
\(842\) −2441.94 −0.0999463
\(843\) 6360.07 0.259848
\(844\) 5009.36 0.204300
\(845\) 0 0
\(846\) 8175.87 0.332260
\(847\) −2100.65 −0.0852176
\(848\) 12506.3 0.506447
\(849\) 27468.0 1.11036
\(850\) 344.758 0.0139119
\(851\) 17560.2 0.707352
\(852\) −1108.20 −0.0445615
\(853\) −1499.09 −0.0601732 −0.0300866 0.999547i \(-0.509578\pi\)
−0.0300866 + 0.999547i \(0.509578\pi\)
\(854\) 14321.3 0.573846
\(855\) 1550.00 0.0619987
\(856\) −43352.1 −1.73101
\(857\) 7709.00 0.307275 0.153637 0.988127i \(-0.450901\pi\)
0.153637 + 0.988127i \(0.450901\pi\)
\(858\) 0 0
\(859\) 32493.2 1.29063 0.645316 0.763916i \(-0.276726\pi\)
0.645316 + 0.763916i \(0.276726\pi\)
\(860\) −1414.03 −0.0560675
\(861\) 21338.9 0.844633
\(862\) 35197.7 1.39076
\(863\) 10257.0 0.404582 0.202291 0.979325i \(-0.435161\pi\)
0.202291 + 0.979325i \(0.435161\pi\)
\(864\) 17603.4 0.693147
\(865\) −5637.99 −0.221616
\(866\) 20218.3 0.793356
\(867\) −22337.5 −0.874994
\(868\) −1561.36 −0.0610553
\(869\) 2974.02 0.116095
\(870\) 7643.61 0.297865
\(871\) 0 0
\(872\) −39082.4 −1.51777
\(873\) −5485.51 −0.212665
\(874\) −6327.53 −0.244888
\(875\) −16828.5 −0.650179
\(876\) −4498.76 −0.173515
\(877\) −45870.2 −1.76616 −0.883082 0.469219i \(-0.844536\pi\)
−0.883082 + 0.469219i \(0.844536\pi\)
\(878\) 4388.75 0.168694
\(879\) 18222.2 0.699227
\(880\) 1610.12 0.0616785
\(881\) −6836.28 −0.261430 −0.130715 0.991420i \(-0.541727\pi\)
−0.130715 + 0.991420i \(0.541727\pi\)
\(882\) −604.647 −0.0230834
\(883\) −17094.1 −0.651487 −0.325744 0.945458i \(-0.605615\pi\)
−0.325744 + 0.945458i \(0.605615\pi\)
\(884\) 0 0
\(885\) −2628.43 −0.0998348
\(886\) 10638.4 0.403389
\(887\) 28116.2 1.06432 0.532159 0.846644i \(-0.321381\pi\)
0.532159 + 0.846644i \(0.321381\pi\)
\(888\) 42192.5 1.59447
\(889\) −10208.0 −0.385114
\(890\) 14251.7 0.536763
\(891\) −5706.03 −0.214544
\(892\) −873.781 −0.0327986
\(893\) 33153.0 1.24236
\(894\) 6205.71 0.232159
\(895\) 15117.6 0.564611
\(896\) 5790.86 0.215914
\(897\) 0 0
\(898\) 20338.9 0.755810
\(899\) −5837.84 −0.216577
\(900\) −1833.47 −0.0679062
\(901\) −495.230 −0.0183113
\(902\) 6844.41 0.252654
\(903\) 9930.29 0.365957
\(904\) −32725.8 −1.20403
\(905\) 11951.0 0.438966
\(906\) 7200.80 0.264051
\(907\) −23330.1 −0.854095 −0.427047 0.904229i \(-0.640446\pi\)
−0.427047 + 0.904229i \(0.640446\pi\)
\(908\) −4087.43 −0.149390
\(909\) 4273.14 0.155920
\(910\) 0 0
\(911\) −25834.6 −0.939560 −0.469780 0.882784i \(-0.655667\pi\)
−0.469780 + 0.882784i \(0.655667\pi\)
\(912\) −9416.54 −0.341900
\(913\) −8214.54 −0.297767
\(914\) 21275.6 0.769949
\(915\) −6789.97 −0.245322
\(916\) 9321.21 0.336224
\(917\) 10053.1 0.362030
\(918\) 485.297 0.0174479
\(919\) 31228.6 1.12093 0.560466 0.828177i \(-0.310622\pi\)
0.560466 + 0.828177i \(0.310622\pi\)
\(920\) −4786.20 −0.171518
\(921\) −15694.8 −0.561523
\(922\) −21620.4 −0.772268
\(923\) 0 0
\(924\) 2343.96 0.0834531
\(925\) −40534.3 −1.44082
\(926\) 18000.5 0.638804
\(927\) 919.573 0.0325812
\(928\) −20350.9 −0.719884
\(929\) 4317.75 0.152487 0.0762437 0.997089i \(-0.475707\pi\)
0.0762437 + 0.997089i \(0.475707\pi\)
\(930\) −1454.30 −0.0512777
\(931\) −2451.83 −0.0863111
\(932\) 18797.7 0.660663
\(933\) −4221.00 −0.148113
\(934\) 38324.9 1.34264
\(935\) −63.7583 −0.00223007
\(936\) 0 0
\(937\) 40522.5 1.41282 0.706409 0.707804i \(-0.250314\pi\)
0.706409 + 0.707804i \(0.250314\pi\)
\(938\) 11634.0 0.404973
\(939\) 37542.0 1.30472
\(940\) 6325.36 0.219479
\(941\) 50791.1 1.75956 0.879778 0.475384i \(-0.157691\pi\)
0.879778 + 0.475384i \(0.157691\pi\)
\(942\) 3185.15 0.110168
\(943\) −12601.4 −0.435164
\(944\) −4872.10 −0.167980
\(945\) −10960.3 −0.377290
\(946\) 3185.11 0.109468
\(947\) 16851.5 0.578248 0.289124 0.957292i \(-0.406636\pi\)
0.289124 + 0.957292i \(0.406636\pi\)
\(948\) −3318.48 −0.113691
\(949\) 0 0
\(950\) 14605.9 0.498817
\(951\) −39832.5 −1.35821
\(952\) −594.896 −0.0202528
\(953\) −19119.0 −0.649868 −0.324934 0.945737i \(-0.605342\pi\)
−0.324934 + 0.945737i \(0.605342\pi\)
\(954\) −5174.04 −0.175593
\(955\) −2346.35 −0.0795037
\(956\) 5923.09 0.200383
\(957\) 8763.94 0.296027
\(958\) −566.324 −0.0190993
\(959\) 24530.9 0.826010
\(960\) −10395.9 −0.349506
\(961\) −28680.3 −0.962716
\(962\) 0 0
\(963\) 11108.7 0.371727
\(964\) −16494.0 −0.551075
\(965\) 2974.94 0.0992401
\(966\) 8478.11 0.282380
\(967\) 12584.8 0.418511 0.209256 0.977861i \(-0.432896\pi\)
0.209256 + 0.977861i \(0.432896\pi\)
\(968\) 2980.63 0.0989680
\(969\) 372.881 0.0123619
\(970\) 8337.44 0.275979
\(971\) −4243.01 −0.140231 −0.0701156 0.997539i \(-0.522337\pi\)
−0.0701156 + 0.997539i \(0.522337\pi\)
\(972\) −4672.71 −0.154195
\(973\) −26150.7 −0.861617
\(974\) 553.394 0.0182052
\(975\) 0 0
\(976\) −12586.0 −0.412774
\(977\) 50395.4 1.65025 0.825123 0.564953i \(-0.191106\pi\)
0.825123 + 0.564953i \(0.191106\pi\)
\(978\) 39005.2 1.27531
\(979\) 16340.6 0.533451
\(980\) −467.793 −0.0152480
\(981\) 10014.6 0.325935
\(982\) −11991.8 −0.389689
\(983\) −31148.7 −1.01067 −0.505335 0.862923i \(-0.668631\pi\)
−0.505335 + 0.862923i \(0.668631\pi\)
\(984\) −30277.9 −0.980919
\(985\) 5987.42 0.193680
\(986\) −561.043 −0.0181209
\(987\) −44421.0 −1.43256
\(988\) 0 0
\(989\) −5864.20 −0.188545
\(990\) −666.131 −0.0213849
\(991\) 25818.0 0.827584 0.413792 0.910371i \(-0.364204\pi\)
0.413792 + 0.910371i \(0.364204\pi\)
\(992\) 3872.03 0.123929
\(993\) −4025.26 −0.128638
\(994\) 3609.09 0.115164
\(995\) 6728.96 0.214394
\(996\) 9165.98 0.291602
\(997\) −25082.9 −0.796773 −0.398386 0.917218i \(-0.630430\pi\)
−0.398386 + 0.917218i \(0.630430\pi\)
\(998\) 31321.4 0.993448
\(999\) −57057.9 −1.80704
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.n.1.13 39
13.12 even 2 1859.4.a.o.1.27 yes 39
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.4.a.n.1.13 39 1.1 even 1 trivial
1859.4.a.o.1.27 yes 39 13.12 even 2