Properties

Label 1859.4.a.o.1.4
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 1.4
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)
 
\(f(q)\) \(=\) \(q-4.86773 q^{2} -7.77085 q^{3} +15.6948 q^{4} -6.79003 q^{5} +37.8264 q^{6} +12.1965 q^{7} -37.4563 q^{8} +33.3861 q^{9} +O(q^{10})\) \(q-4.86773 q^{2} -7.77085 q^{3} +15.6948 q^{4} -6.79003 q^{5} +37.8264 q^{6} +12.1965 q^{7} -37.4563 q^{8} +33.3861 q^{9} +33.0520 q^{10} -11.0000 q^{11} -121.962 q^{12} -59.3695 q^{14} +52.7643 q^{15} +56.7686 q^{16} +31.0773 q^{17} -162.514 q^{18} +110.731 q^{19} -106.568 q^{20} -94.7775 q^{21} +53.5450 q^{22} +84.4283 q^{23} +291.067 q^{24} -78.8955 q^{25} -49.6251 q^{27} +191.422 q^{28} +21.9448 q^{29} -256.842 q^{30} -83.3657 q^{31} +23.3160 q^{32} +85.4793 q^{33} -151.276 q^{34} -82.8149 q^{35} +523.988 q^{36} -303.283 q^{37} -539.010 q^{38} +254.329 q^{40} +242.328 q^{41} +461.351 q^{42} -325.927 q^{43} -172.643 q^{44} -226.692 q^{45} -410.975 q^{46} +474.115 q^{47} -441.140 q^{48} -194.244 q^{49} +384.042 q^{50} -241.497 q^{51} -267.590 q^{53} +241.562 q^{54} +74.6903 q^{55} -456.837 q^{56} -860.475 q^{57} -106.821 q^{58} -564.798 q^{59} +828.125 q^{60} +60.8398 q^{61} +405.802 q^{62} +407.195 q^{63} -567.644 q^{64} -416.090 q^{66} -851.817 q^{67} +487.752 q^{68} -656.080 q^{69} +403.121 q^{70} -743.888 q^{71} -1250.52 q^{72} +1049.77 q^{73} +1476.30 q^{74} +613.085 q^{75} +1737.90 q^{76} -134.162 q^{77} -739.430 q^{79} -385.460 q^{80} -515.795 q^{81} -1179.59 q^{82} +161.060 q^{83} -1487.51 q^{84} -211.016 q^{85} +1586.53 q^{86} -170.529 q^{87} +412.019 q^{88} +922.681 q^{89} +1103.48 q^{90} +1325.09 q^{92} +647.822 q^{93} -2307.87 q^{94} -751.868 q^{95} -181.185 q^{96} +1639.37 q^{97} +945.529 q^{98} -367.247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.86773 −1.72100 −0.860501 0.509448i \(-0.829850\pi\)
−0.860501 + 0.509448i \(0.829850\pi\)
\(3\) −7.77085 −1.49550 −0.747750 0.663980i \(-0.768866\pi\)
−0.747750 + 0.663980i \(0.768866\pi\)
\(4\) 15.6948 1.96185
\(5\) −6.79003 −0.607319 −0.303659 0.952781i \(-0.598208\pi\)
−0.303659 + 0.952781i \(0.598208\pi\)
\(6\) 37.8264 2.57376
\(7\) 12.1965 0.658552 0.329276 0.944234i \(-0.393195\pi\)
0.329276 + 0.944234i \(0.393195\pi\)
\(8\) −37.4563 −1.65535
\(9\) 33.3861 1.23652
\(10\) 33.0520 1.04520
\(11\) −11.0000 −0.301511
\(12\) −121.962 −2.93395
\(13\) 0 0
\(14\) −59.3695 −1.13337
\(15\) 52.7643 0.908245
\(16\) 56.7686 0.887009
\(17\) 31.0773 0.443373 0.221687 0.975118i \(-0.428844\pi\)
0.221687 + 0.975118i \(0.428844\pi\)
\(18\) −162.514 −2.12806
\(19\) 110.731 1.33702 0.668512 0.743701i \(-0.266931\pi\)
0.668512 + 0.743701i \(0.266931\pi\)
\(20\) −106.568 −1.19147
\(21\) −94.7775 −0.984864
\(22\) 53.5450 0.518902
\(23\) 84.4283 0.765414 0.382707 0.923870i \(-0.374992\pi\)
0.382707 + 0.923870i \(0.374992\pi\)
\(24\) 291.067 2.47557
\(25\) −78.8955 −0.631164
\(26\) 0 0
\(27\) −49.6251 −0.353717
\(28\) 191.422 1.29198
\(29\) 21.9448 0.140519 0.0702593 0.997529i \(-0.477617\pi\)
0.0702593 + 0.997529i \(0.477617\pi\)
\(30\) −256.842 −1.56309
\(31\) −83.3657 −0.482997 −0.241499 0.970401i \(-0.577639\pi\)
−0.241499 + 0.970401i \(0.577639\pi\)
\(32\) 23.3160 0.128804
\(33\) 85.4793 0.450910
\(34\) −151.276 −0.763047
\(35\) −82.8149 −0.399951
\(36\) 523.988 2.42587
\(37\) −303.283 −1.34755 −0.673775 0.738937i \(-0.735328\pi\)
−0.673775 + 0.738937i \(0.735328\pi\)
\(38\) −539.010 −2.30102
\(39\) 0 0
\(40\) 254.329 1.00532
\(41\) 242.328 0.923056 0.461528 0.887126i \(-0.347301\pi\)
0.461528 + 0.887126i \(0.347301\pi\)
\(42\) 461.351 1.69495
\(43\) −325.927 −1.15589 −0.577947 0.816074i \(-0.696146\pi\)
−0.577947 + 0.816074i \(0.696146\pi\)
\(44\) −172.643 −0.591520
\(45\) −226.692 −0.750962
\(46\) −410.975 −1.31728
\(47\) 474.115 1.47142 0.735711 0.677296i \(-0.236848\pi\)
0.735711 + 0.677296i \(0.236848\pi\)
\(48\) −441.140 −1.32652
\(49\) −194.244 −0.566310
\(50\) 384.042 1.08623
\(51\) −241.497 −0.663065
\(52\) 0 0
\(53\) −267.590 −0.693515 −0.346757 0.937955i \(-0.612717\pi\)
−0.346757 + 0.937955i \(0.612717\pi\)
\(54\) 241.562 0.608748
\(55\) 74.6903 0.183114
\(56\) −456.837 −1.09013
\(57\) −860.475 −1.99952
\(58\) −106.821 −0.241833
\(59\) −564.798 −1.24628 −0.623139 0.782111i \(-0.714143\pi\)
−0.623139 + 0.782111i \(0.714143\pi\)
\(60\) 828.125 1.78184
\(61\) 60.8398 0.127701 0.0638503 0.997959i \(-0.479662\pi\)
0.0638503 + 0.997959i \(0.479662\pi\)
\(62\) 405.802 0.831240
\(63\) 407.195 0.814313
\(64\) −567.644 −1.10868
\(65\) 0 0
\(66\) −416.090 −0.776018
\(67\) −851.817 −1.55322 −0.776612 0.629980i \(-0.783063\pi\)
−0.776612 + 0.629980i \(0.783063\pi\)
\(68\) 487.752 0.869832
\(69\) −656.080 −1.14468
\(70\) 403.121 0.688316
\(71\) −743.888 −1.24343 −0.621713 0.783245i \(-0.713563\pi\)
−0.621713 + 0.783245i \(0.713563\pi\)
\(72\) −1250.52 −2.04687
\(73\) 1049.77 1.68311 0.841553 0.540175i \(-0.181642\pi\)
0.841553 + 0.540175i \(0.181642\pi\)
\(74\) 1476.30 2.31914
\(75\) 613.085 0.943906
\(76\) 1737.90 2.62304
\(77\) −134.162 −0.198561
\(78\) 0 0
\(79\) −739.430 −1.05307 −0.526534 0.850154i \(-0.676509\pi\)
−0.526534 + 0.850154i \(0.676509\pi\)
\(80\) −385.460 −0.538697
\(81\) −515.795 −0.707537
\(82\) −1179.59 −1.58858
\(83\) 161.060 0.212996 0.106498 0.994313i \(-0.466036\pi\)
0.106498 + 0.994313i \(0.466036\pi\)
\(84\) −1487.51 −1.93216
\(85\) −211.016 −0.269269
\(86\) 1586.53 1.98930
\(87\) −170.529 −0.210146
\(88\) 412.019 0.499106
\(89\) 922.681 1.09892 0.549460 0.835520i \(-0.314833\pi\)
0.549460 + 0.835520i \(0.314833\pi\)
\(90\) 1103.48 1.29241
\(91\) 0 0
\(92\) 1325.09 1.50163
\(93\) 647.822 0.722323
\(94\) −2307.87 −2.53232
\(95\) −751.868 −0.812000
\(96\) −181.185 −0.192626
\(97\) 1639.37 1.71601 0.858005 0.513642i \(-0.171704\pi\)
0.858005 + 0.513642i \(0.171704\pi\)
\(98\) 945.529 0.974621
\(99\) −367.247 −0.372825
\(100\) −1238.25 −1.23825
\(101\) −285.763 −0.281529 −0.140765 0.990043i \(-0.544956\pi\)
−0.140765 + 0.990043i \(0.544956\pi\)
\(102\) 1175.54 1.14114
\(103\) −533.704 −0.510558 −0.255279 0.966867i \(-0.582167\pi\)
−0.255279 + 0.966867i \(0.582167\pi\)
\(104\) 0 0
\(105\) 643.542 0.598126
\(106\) 1302.56 1.19354
\(107\) 1512.59 1.36661 0.683306 0.730132i \(-0.260541\pi\)
0.683306 + 0.730132i \(0.260541\pi\)
\(108\) −778.856 −0.693940
\(109\) −150.230 −0.132013 −0.0660064 0.997819i \(-0.521026\pi\)
−0.0660064 + 0.997819i \(0.521026\pi\)
\(110\) −363.573 −0.315139
\(111\) 2356.76 2.01526
\(112\) 692.381 0.584141
\(113\) −273.090 −0.227347 −0.113673 0.993518i \(-0.536262\pi\)
−0.113673 + 0.993518i \(0.536262\pi\)
\(114\) 4188.56 3.44118
\(115\) −573.271 −0.464850
\(116\) 344.419 0.275677
\(117\) 0 0
\(118\) 2749.28 2.14485
\(119\) 379.035 0.291984
\(120\) −1976.35 −1.50346
\(121\) 121.000 0.0909091
\(122\) −296.152 −0.219773
\(123\) −1883.09 −1.38043
\(124\) −1308.41 −0.947569
\(125\) 1384.46 0.990636
\(126\) −1982.11 −1.40143
\(127\) −1639.81 −1.14574 −0.572872 0.819645i \(-0.694171\pi\)
−0.572872 + 0.819645i \(0.694171\pi\)
\(128\) 2576.61 1.77924
\(129\) 2532.73 1.72864
\(130\) 0 0
\(131\) 1478.05 0.985783 0.492891 0.870091i \(-0.335940\pi\)
0.492891 + 0.870091i \(0.335940\pi\)
\(132\) 1341.58 0.884619
\(133\) 1350.54 0.880500
\(134\) 4146.41 2.67310
\(135\) 336.956 0.214819
\(136\) −1164.04 −0.733937
\(137\) 2959.08 1.84534 0.922670 0.385591i \(-0.126002\pi\)
0.922670 + 0.385591i \(0.126002\pi\)
\(138\) 3193.62 1.96999
\(139\) 665.710 0.406222 0.203111 0.979156i \(-0.434895\pi\)
0.203111 + 0.979156i \(0.434895\pi\)
\(140\) −1299.76 −0.784644
\(141\) −3684.28 −2.20051
\(142\) 3621.05 2.13994
\(143\) 0 0
\(144\) 1895.28 1.09680
\(145\) −149.006 −0.0853396
\(146\) −5110.02 −2.89663
\(147\) 1509.44 0.846916
\(148\) −4759.96 −2.64369
\(149\) 2466.98 1.35639 0.678197 0.734880i \(-0.262762\pi\)
0.678197 + 0.734880i \(0.262762\pi\)
\(150\) −2984.33 −1.62446
\(151\) 455.869 0.245683 0.122841 0.992426i \(-0.460799\pi\)
0.122841 + 0.992426i \(0.460799\pi\)
\(152\) −4147.58 −2.21324
\(153\) 1037.55 0.548240
\(154\) 653.065 0.341724
\(155\) 566.056 0.293333
\(156\) 0 0
\(157\) −2164.39 −1.10024 −0.550119 0.835086i \(-0.685418\pi\)
−0.550119 + 0.835086i \(0.685418\pi\)
\(158\) 3599.35 1.81233
\(159\) 2079.40 1.03715
\(160\) −158.316 −0.0782250
\(161\) 1029.73 0.504065
\(162\) 2510.75 1.21767
\(163\) −883.355 −0.424477 −0.212238 0.977218i \(-0.568075\pi\)
−0.212238 + 0.977218i \(0.568075\pi\)
\(164\) 3803.29 1.81090
\(165\) −580.407 −0.273846
\(166\) −783.999 −0.366567
\(167\) −2156.89 −0.999430 −0.499715 0.866190i \(-0.666562\pi\)
−0.499715 + 0.866190i \(0.666562\pi\)
\(168\) 3550.01 1.63029
\(169\) 0 0
\(170\) 1027.17 0.463413
\(171\) 3696.88 1.65326
\(172\) −5115.37 −2.26769
\(173\) 634.892 0.279017 0.139508 0.990221i \(-0.455448\pi\)
0.139508 + 0.990221i \(0.455448\pi\)
\(174\) 830.091 0.361661
\(175\) −962.252 −0.415654
\(176\) −624.454 −0.267443
\(177\) 4388.96 1.86381
\(178\) −4491.36 −1.89125
\(179\) −917.912 −0.383285 −0.191642 0.981465i \(-0.561381\pi\)
−0.191642 + 0.981465i \(0.561381\pi\)
\(180\) −3557.89 −1.47328
\(181\) −3805.60 −1.56281 −0.781404 0.624026i \(-0.785496\pi\)
−0.781404 + 0.624026i \(0.785496\pi\)
\(182\) 0 0
\(183\) −472.776 −0.190976
\(184\) −3162.37 −1.26703
\(185\) 2059.30 0.818392
\(186\) −3153.42 −1.24312
\(187\) −341.850 −0.133682
\(188\) 7441.15 2.88671
\(189\) −605.255 −0.232941
\(190\) 3659.89 1.39745
\(191\) −4327.49 −1.63940 −0.819702 0.572790i \(-0.805861\pi\)
−0.819702 + 0.572790i \(0.805861\pi\)
\(192\) 4411.08 1.65803
\(193\) 826.347 0.308196 0.154098 0.988056i \(-0.450753\pi\)
0.154098 + 0.988056i \(0.450753\pi\)
\(194\) −7980.02 −2.95326
\(195\) 0 0
\(196\) −3048.63 −1.11102
\(197\) 2643.51 0.956052 0.478026 0.878346i \(-0.341352\pi\)
0.478026 + 0.878346i \(0.341352\pi\)
\(198\) 1787.66 0.641633
\(199\) 2737.38 0.975116 0.487558 0.873091i \(-0.337888\pi\)
0.487558 + 0.873091i \(0.337888\pi\)
\(200\) 2955.13 1.04480
\(201\) 6619.34 2.32285
\(202\) 1391.02 0.484513
\(203\) 267.650 0.0925388
\(204\) −3790.24 −1.30083
\(205\) −1645.41 −0.560589
\(206\) 2597.93 0.878671
\(207\) 2818.73 0.946451
\(208\) 0 0
\(209\) −1218.04 −0.403128
\(210\) −3132.59 −1.02938
\(211\) 5313.85 1.73375 0.866874 0.498528i \(-0.166126\pi\)
0.866874 + 0.498528i \(0.166126\pi\)
\(212\) −4199.77 −1.36057
\(213\) 5780.64 1.85954
\(214\) −7362.88 −2.35194
\(215\) 2213.06 0.701996
\(216\) 1858.77 0.585525
\(217\) −1016.77 −0.318079
\(218\) 731.278 0.227194
\(219\) −8157.63 −2.51708
\(220\) 1172.25 0.359241
\(221\) 0 0
\(222\) −11472.1 −3.46827
\(223\) −479.582 −0.144014 −0.0720071 0.997404i \(-0.522940\pi\)
−0.0720071 + 0.997404i \(0.522940\pi\)
\(224\) 284.375 0.0848240
\(225\) −2634.01 −0.780447
\(226\) 1329.33 0.391264
\(227\) 3870.68 1.13175 0.565873 0.824493i \(-0.308539\pi\)
0.565873 + 0.824493i \(0.308539\pi\)
\(228\) −13505.0 −3.92276
\(229\) −943.994 −0.272406 −0.136203 0.990681i \(-0.543490\pi\)
−0.136203 + 0.990681i \(0.543490\pi\)
\(230\) 2790.53 0.800009
\(231\) 1042.55 0.296948
\(232\) −821.969 −0.232607
\(233\) −2082.41 −0.585506 −0.292753 0.956188i \(-0.594571\pi\)
−0.292753 + 0.956188i \(0.594571\pi\)
\(234\) 0 0
\(235\) −3219.26 −0.893622
\(236\) −8864.40 −2.44501
\(237\) 5746.00 1.57486
\(238\) −1845.04 −0.502506
\(239\) 6593.08 1.78440 0.892199 0.451643i \(-0.149162\pi\)
0.892199 + 0.451643i \(0.149162\pi\)
\(240\) 2995.35 0.805622
\(241\) 788.446 0.210740 0.105370 0.994433i \(-0.466397\pi\)
0.105370 + 0.994433i \(0.466397\pi\)
\(242\) −588.996 −0.156455
\(243\) 5348.04 1.41184
\(244\) 954.868 0.250529
\(245\) 1318.92 0.343931
\(246\) 9166.40 2.37572
\(247\) 0 0
\(248\) 3122.57 0.799529
\(249\) −1251.58 −0.318536
\(250\) −6739.16 −1.70489
\(251\) −84.4314 −0.0212321 −0.0106161 0.999944i \(-0.503379\pi\)
−0.0106161 + 0.999944i \(0.503379\pi\)
\(252\) 6390.84 1.59756
\(253\) −928.712 −0.230781
\(254\) 7982.14 1.97183
\(255\) 1639.77 0.402692
\(256\) −8001.10 −1.95339
\(257\) 6409.97 1.55581 0.777904 0.628383i \(-0.216283\pi\)
0.777904 + 0.628383i \(0.216283\pi\)
\(258\) −12328.7 −2.97499
\(259\) −3699.00 −0.887431
\(260\) 0 0
\(261\) 732.649 0.173754
\(262\) −7194.73 −1.69653
\(263\) 3669.52 0.860351 0.430176 0.902745i \(-0.358452\pi\)
0.430176 + 0.902745i \(0.358452\pi\)
\(264\) −3201.74 −0.746414
\(265\) 1816.94 0.421185
\(266\) −6574.05 −1.51534
\(267\) −7170.01 −1.64344
\(268\) −13369.1 −3.04719
\(269\) −8172.06 −1.85226 −0.926132 0.377199i \(-0.876887\pi\)
−0.926132 + 0.377199i \(0.876887\pi\)
\(270\) −1640.21 −0.369704
\(271\) 1854.49 0.415692 0.207846 0.978162i \(-0.433355\pi\)
0.207846 + 0.978162i \(0.433355\pi\)
\(272\) 1764.21 0.393276
\(273\) 0 0
\(274\) −14404.0 −3.17584
\(275\) 867.850 0.190303
\(276\) −10297.0 −2.24569
\(277\) 3214.95 0.697355 0.348678 0.937243i \(-0.386631\pi\)
0.348678 + 0.937243i \(0.386631\pi\)
\(278\) −3240.50 −0.699109
\(279\) −2783.25 −0.597236
\(280\) 3101.94 0.662058
\(281\) −8553.21 −1.81581 −0.907904 0.419178i \(-0.862318\pi\)
−0.907904 + 0.419178i \(0.862318\pi\)
\(282\) 17934.1 3.78709
\(283\) −813.492 −0.170873 −0.0854366 0.996344i \(-0.527229\pi\)
−0.0854366 + 0.996344i \(0.527229\pi\)
\(284\) −11675.2 −2.43942
\(285\) 5842.65 1.21435
\(286\) 0 0
\(287\) 2955.57 0.607880
\(288\) 778.429 0.159269
\(289\) −3947.20 −0.803420
\(290\) 725.319 0.146870
\(291\) −12739.3 −2.56629
\(292\) 16476.0 3.30200
\(293\) −3994.34 −0.796422 −0.398211 0.917294i \(-0.630369\pi\)
−0.398211 + 0.917294i \(0.630369\pi\)
\(294\) −7347.56 −1.45755
\(295\) 3835.00 0.756888
\(296\) 11359.8 2.23066
\(297\) 545.876 0.106650
\(298\) −12008.6 −2.33436
\(299\) 0 0
\(300\) 9622.25 1.85180
\(301\) −3975.19 −0.761216
\(302\) −2219.05 −0.422821
\(303\) 2220.62 0.421027
\(304\) 6286.05 1.18595
\(305\) −413.104 −0.0775549
\(306\) −5050.50 −0.943523
\(307\) 8207.46 1.52581 0.762906 0.646510i \(-0.223772\pi\)
0.762906 + 0.646510i \(0.223772\pi\)
\(308\) −2105.65 −0.389547
\(309\) 4147.33 0.763539
\(310\) −2755.41 −0.504828
\(311\) −3572.46 −0.651369 −0.325684 0.945479i \(-0.605595\pi\)
−0.325684 + 0.945479i \(0.605595\pi\)
\(312\) 0 0
\(313\) 3214.48 0.580490 0.290245 0.956952i \(-0.406263\pi\)
0.290245 + 0.956952i \(0.406263\pi\)
\(314\) 10535.7 1.89351
\(315\) −2764.86 −0.494547
\(316\) −11605.2 −2.06596
\(317\) −9457.67 −1.67570 −0.837848 0.545903i \(-0.816187\pi\)
−0.837848 + 0.545903i \(0.816187\pi\)
\(318\) −10122.0 −1.78494
\(319\) −241.392 −0.0423680
\(320\) 3854.32 0.673323
\(321\) −11754.1 −2.04377
\(322\) −5012.47 −0.867497
\(323\) 3441.22 0.592801
\(324\) −8095.30 −1.38808
\(325\) 0 0
\(326\) 4299.93 0.730526
\(327\) 1167.41 0.197425
\(328\) −9076.70 −1.52798
\(329\) 5782.57 0.969007
\(330\) 2825.27 0.471290
\(331\) −1982.64 −0.329231 −0.164616 0.986358i \(-0.552638\pi\)
−0.164616 + 0.986358i \(0.552638\pi\)
\(332\) 2527.81 0.417867
\(333\) −10125.4 −1.66627
\(334\) 10499.1 1.72002
\(335\) 5783.86 0.943302
\(336\) −5380.38 −0.873583
\(337\) 4257.10 0.688128 0.344064 0.938946i \(-0.388196\pi\)
0.344064 + 0.938946i \(0.388196\pi\)
\(338\) 0 0
\(339\) 2122.14 0.339997
\(340\) −3311.85 −0.528266
\(341\) 917.023 0.145629
\(342\) −17995.4 −2.84526
\(343\) −6552.52 −1.03150
\(344\) 12208.0 1.91341
\(345\) 4454.80 0.695184
\(346\) −3090.48 −0.480189
\(347\) −2527.84 −0.391070 −0.195535 0.980697i \(-0.562644\pi\)
−0.195535 + 0.980697i \(0.562644\pi\)
\(348\) −2676.43 −0.412274
\(349\) −4817.10 −0.738835 −0.369418 0.929264i \(-0.620443\pi\)
−0.369418 + 0.929264i \(0.620443\pi\)
\(350\) 4683.99 0.715342
\(351\) 0 0
\(352\) −256.476 −0.0388358
\(353\) −3702.54 −0.558262 −0.279131 0.960253i \(-0.590046\pi\)
−0.279131 + 0.960253i \(0.590046\pi\)
\(354\) −21364.3 −3.20762
\(355\) 5051.02 0.755156
\(356\) 14481.3 2.15592
\(357\) −2945.43 −0.436662
\(358\) 4468.15 0.659634
\(359\) −4293.48 −0.631201 −0.315600 0.948892i \(-0.602206\pi\)
−0.315600 + 0.948892i \(0.602206\pi\)
\(360\) 8491.05 1.24310
\(361\) 5402.39 0.787635
\(362\) 18524.6 2.68960
\(363\) −940.272 −0.135955
\(364\) 0 0
\(365\) −7127.99 −1.02218
\(366\) 2301.35 0.328671
\(367\) 9320.93 1.32575 0.662873 0.748732i \(-0.269337\pi\)
0.662873 + 0.748732i \(0.269337\pi\)
\(368\) 4792.88 0.678929
\(369\) 8090.38 1.14138
\(370\) −10024.1 −1.40846
\(371\) −3263.67 −0.456715
\(372\) 10167.4 1.41709
\(373\) 6547.67 0.908915 0.454458 0.890768i \(-0.349833\pi\)
0.454458 + 0.890768i \(0.349833\pi\)
\(374\) 1664.03 0.230067
\(375\) −10758.4 −1.48150
\(376\) −17758.6 −2.43572
\(377\) 0 0
\(378\) 2946.22 0.400892
\(379\) −7238.33 −0.981024 −0.490512 0.871434i \(-0.663190\pi\)
−0.490512 + 0.871434i \(0.663190\pi\)
\(380\) −11800.4 −1.59302
\(381\) 12742.7 1.71346
\(382\) 21065.1 2.82142
\(383\) 755.065 0.100736 0.0503682 0.998731i \(-0.483961\pi\)
0.0503682 + 0.998731i \(0.483961\pi\)
\(384\) −20022.5 −2.66085
\(385\) 910.964 0.120590
\(386\) −4022.43 −0.530405
\(387\) −10881.4 −1.42929
\(388\) 25729.6 3.36655
\(389\) −4097.38 −0.534050 −0.267025 0.963690i \(-0.586041\pi\)
−0.267025 + 0.963690i \(0.586041\pi\)
\(390\) 0 0
\(391\) 2623.80 0.339364
\(392\) 7275.66 0.937440
\(393\) −11485.7 −1.47424
\(394\) −12867.9 −1.64537
\(395\) 5020.75 0.639548
\(396\) −5763.87 −0.731427
\(397\) 10460.5 1.32241 0.661203 0.750207i \(-0.270046\pi\)
0.661203 + 0.750207i \(0.270046\pi\)
\(398\) −13324.9 −1.67818
\(399\) −10494.8 −1.31679
\(400\) −4478.78 −0.559848
\(401\) −6046.58 −0.752997 −0.376499 0.926417i \(-0.622872\pi\)
−0.376499 + 0.926417i \(0.622872\pi\)
\(402\) −32221.2 −3.99762
\(403\) 0 0
\(404\) −4485.00 −0.552319
\(405\) 3502.26 0.429701
\(406\) −1302.85 −0.159259
\(407\) 3336.11 0.406302
\(408\) 9045.56 1.09760
\(409\) −6524.91 −0.788841 −0.394421 0.918930i \(-0.629055\pi\)
−0.394421 + 0.918930i \(0.629055\pi\)
\(410\) 8009.44 0.964775
\(411\) −22994.6 −2.75971
\(412\) −8376.39 −1.00164
\(413\) −6888.59 −0.820739
\(414\) −13720.8 −1.62884
\(415\) −1093.61 −0.129357
\(416\) 0 0
\(417\) −5173.13 −0.607505
\(418\) 5929.10 0.693785
\(419\) −13509.6 −1.57514 −0.787572 0.616223i \(-0.788662\pi\)
−0.787572 + 0.616223i \(0.788662\pi\)
\(420\) 10100.3 1.17344
\(421\) −8784.45 −1.01693 −0.508465 0.861082i \(-0.669787\pi\)
−0.508465 + 0.861082i \(0.669787\pi\)
\(422\) −25866.4 −2.98378
\(423\) 15828.8 1.81944
\(424\) 10022.9 1.14801
\(425\) −2451.86 −0.279841
\(426\) −28138.6 −3.20028
\(427\) 742.035 0.0840974
\(428\) 23739.8 2.68109
\(429\) 0 0
\(430\) −10772.6 −1.20814
\(431\) −7124.99 −0.796285 −0.398142 0.917324i \(-0.630345\pi\)
−0.398142 + 0.917324i \(0.630345\pi\)
\(432\) −2817.15 −0.313750
\(433\) −6400.92 −0.710412 −0.355206 0.934788i \(-0.615589\pi\)
−0.355206 + 0.934788i \(0.615589\pi\)
\(434\) 4949.38 0.547415
\(435\) 1157.90 0.127625
\(436\) −2357.83 −0.258990
\(437\) 9348.85 1.02338
\(438\) 39709.1 4.33191
\(439\) 7615.19 0.827912 0.413956 0.910297i \(-0.364147\pi\)
0.413956 + 0.910297i \(0.364147\pi\)
\(440\) −2797.62 −0.303117
\(441\) −6485.05 −0.700254
\(442\) 0 0
\(443\) −403.957 −0.0433241 −0.0216620 0.999765i \(-0.506896\pi\)
−0.0216620 + 0.999765i \(0.506896\pi\)
\(444\) 36988.9 3.95364
\(445\) −6265.03 −0.667395
\(446\) 2334.47 0.247849
\(447\) −19170.5 −2.02849
\(448\) −6923.30 −0.730123
\(449\) 12544.9 1.31855 0.659275 0.751902i \(-0.270863\pi\)
0.659275 + 0.751902i \(0.270863\pi\)
\(450\) 12821.6 1.34315
\(451\) −2665.61 −0.278312
\(452\) −4286.10 −0.446020
\(453\) −3542.49 −0.367419
\(454\) −18841.4 −1.94774
\(455\) 0 0
\(456\) 32230.2 3.30990
\(457\) −15475.2 −1.58403 −0.792013 0.610504i \(-0.790967\pi\)
−0.792013 + 0.610504i \(0.790967\pi\)
\(458\) 4595.11 0.468811
\(459\) −1542.21 −0.156829
\(460\) −8997.38 −0.911967
\(461\) −15071.8 −1.52269 −0.761347 0.648344i \(-0.775462\pi\)
−0.761347 + 0.648344i \(0.775462\pi\)
\(462\) −5074.87 −0.511048
\(463\) 2467.06 0.247633 0.123817 0.992305i \(-0.460487\pi\)
0.123817 + 0.992305i \(0.460487\pi\)
\(464\) 1245.77 0.124641
\(465\) −4398.73 −0.438680
\(466\) 10136.6 1.00766
\(467\) −10906.3 −1.08070 −0.540348 0.841442i \(-0.681707\pi\)
−0.540348 + 0.841442i \(0.681707\pi\)
\(468\) 0 0
\(469\) −10389.2 −1.02288
\(470\) 15670.5 1.53793
\(471\) 16819.2 1.64541
\(472\) 21155.2 2.06303
\(473\) 3585.20 0.348515
\(474\) −27970.0 −2.71035
\(475\) −8736.19 −0.843882
\(476\) 5948.89 0.572829
\(477\) −8933.77 −0.857545
\(478\) −32093.3 −3.07095
\(479\) 9696.41 0.924927 0.462464 0.886638i \(-0.346966\pi\)
0.462464 + 0.886638i \(0.346966\pi\)
\(480\) 1230.25 0.116985
\(481\) 0 0
\(482\) −3837.94 −0.362684
\(483\) −8001.91 −0.753829
\(484\) 1899.07 0.178350
\(485\) −11131.4 −1.04216
\(486\) −26032.8 −2.42978
\(487\) −8851.15 −0.823581 −0.411790 0.911279i \(-0.635096\pi\)
−0.411790 + 0.911279i \(0.635096\pi\)
\(488\) −2278.83 −0.211389
\(489\) 6864.42 0.634805
\(490\) −6420.17 −0.591905
\(491\) −6581.76 −0.604950 −0.302475 0.953157i \(-0.597813\pi\)
−0.302475 + 0.953157i \(0.597813\pi\)
\(492\) −29554.8 −2.70820
\(493\) 681.983 0.0623022
\(494\) 0 0
\(495\) 2493.62 0.226424
\(496\) −4732.55 −0.428423
\(497\) −9072.87 −0.818861
\(498\) 6092.33 0.548201
\(499\) 9264.63 0.831146 0.415573 0.909560i \(-0.363581\pi\)
0.415573 + 0.909560i \(0.363581\pi\)
\(500\) 21728.8 1.94348
\(501\) 16760.8 1.49465
\(502\) 410.990 0.0365406
\(503\) −1265.32 −0.112163 −0.0560814 0.998426i \(-0.517861\pi\)
−0.0560814 + 0.998426i \(0.517861\pi\)
\(504\) −15252.0 −1.34797
\(505\) 1940.34 0.170978
\(506\) 4520.72 0.397175
\(507\) 0 0
\(508\) −25736.5 −2.24778
\(509\) 12585.4 1.09595 0.547976 0.836494i \(-0.315399\pi\)
0.547976 + 0.836494i \(0.315399\pi\)
\(510\) −7981.96 −0.693034
\(511\) 12803.6 1.10841
\(512\) 18334.3 1.58256
\(513\) −5495.04 −0.472928
\(514\) −31202.0 −2.67755
\(515\) 3623.87 0.310071
\(516\) 39750.7 3.39133
\(517\) −5215.27 −0.443650
\(518\) 18005.7 1.52727
\(519\) −4933.65 −0.417270
\(520\) 0 0
\(521\) 6595.77 0.554637 0.277318 0.960778i \(-0.410554\pi\)
0.277318 + 0.960778i \(0.410554\pi\)
\(522\) −3566.34 −0.299031
\(523\) 18286.4 1.52889 0.764445 0.644688i \(-0.223013\pi\)
0.764445 + 0.644688i \(0.223013\pi\)
\(524\) 23197.7 1.93396
\(525\) 7477.52 0.621611
\(526\) −17862.2 −1.48067
\(527\) −2590.78 −0.214148
\(528\) 4852.54 0.399961
\(529\) −5038.85 −0.414141
\(530\) −8844.39 −0.724860
\(531\) −18856.4 −1.54105
\(532\) 21196.4 1.72741
\(533\) 0 0
\(534\) 34901.7 2.82836
\(535\) −10270.5 −0.829970
\(536\) 31905.9 2.57113
\(537\) 7132.95 0.573202
\(538\) 39779.4 3.18775
\(539\) 2136.69 0.170749
\(540\) 5288.46 0.421443
\(541\) −6494.33 −0.516106 −0.258053 0.966131i \(-0.583081\pi\)
−0.258053 + 0.966131i \(0.583081\pi\)
\(542\) −9027.18 −0.715407
\(543\) 29572.8 2.33718
\(544\) 724.597 0.0571082
\(545\) 1020.06 0.0801739
\(546\) 0 0
\(547\) −7095.02 −0.554591 −0.277295 0.960785i \(-0.589438\pi\)
−0.277295 + 0.960785i \(0.589438\pi\)
\(548\) 46442.3 3.62028
\(549\) 2031.20 0.157904
\(550\) −4224.46 −0.327512
\(551\) 2429.97 0.187877
\(552\) 24574.3 1.89484
\(553\) −9018.49 −0.693500
\(554\) −15649.5 −1.20015
\(555\) −16002.5 −1.22391
\(556\) 10448.2 0.796947
\(557\) −13753.5 −1.04624 −0.523120 0.852259i \(-0.675232\pi\)
−0.523120 + 0.852259i \(0.675232\pi\)
\(558\) 13548.1 1.02785
\(559\) 0 0
\(560\) −4701.28 −0.354760
\(561\) 2656.46 0.199922
\(562\) 41634.7 3.12501
\(563\) 13735.7 1.02822 0.514112 0.857723i \(-0.328122\pi\)
0.514112 + 0.857723i \(0.328122\pi\)
\(564\) −57824.0 −4.31708
\(565\) 1854.29 0.138072
\(566\) 3959.86 0.294073
\(567\) −6290.91 −0.465950
\(568\) 27863.3 2.05830
\(569\) 21279.1 1.56778 0.783890 0.620899i \(-0.213232\pi\)
0.783890 + 0.620899i \(0.213232\pi\)
\(570\) −28440.5 −2.08989
\(571\) 9365.84 0.686424 0.343212 0.939258i \(-0.388485\pi\)
0.343212 + 0.939258i \(0.388485\pi\)
\(572\) 0 0
\(573\) 33628.3 2.45173
\(574\) −14386.9 −1.04616
\(575\) −6661.02 −0.483102
\(576\) −18951.4 −1.37091
\(577\) 22068.2 1.59222 0.796110 0.605153i \(-0.206888\pi\)
0.796110 + 0.605153i \(0.206888\pi\)
\(578\) 19213.9 1.38269
\(579\) −6421.41 −0.460907
\(580\) −2338.61 −0.167424
\(581\) 1964.38 0.140269
\(582\) 62011.5 4.41660
\(583\) 2943.49 0.209103
\(584\) −39320.6 −2.78613
\(585\) 0 0
\(586\) 19443.4 1.37064
\(587\) 11150.9 0.784065 0.392033 0.919951i \(-0.371772\pi\)
0.392033 + 0.919951i \(0.371772\pi\)
\(588\) 23690.4 1.66152
\(589\) −9231.18 −0.645780
\(590\) −18667.7 −1.30261
\(591\) −20542.3 −1.42978
\(592\) −17216.9 −1.19529
\(593\) −16730.2 −1.15856 −0.579280 0.815129i \(-0.696666\pi\)
−0.579280 + 0.815129i \(0.696666\pi\)
\(594\) −2657.18 −0.183544
\(595\) −2573.66 −0.177327
\(596\) 38718.7 2.66104
\(597\) −21271.8 −1.45829
\(598\) 0 0
\(599\) 21934.5 1.49619 0.748097 0.663590i \(-0.230968\pi\)
0.748097 + 0.663590i \(0.230968\pi\)
\(600\) −22963.9 −1.56249
\(601\) 4434.24 0.300959 0.150479 0.988613i \(-0.451918\pi\)
0.150479 + 0.988613i \(0.451918\pi\)
\(602\) 19350.1 1.31005
\(603\) −28438.8 −1.92059
\(604\) 7154.78 0.481993
\(605\) −821.594 −0.0552108
\(606\) −10809.4 −0.724589
\(607\) 22581.3 1.50996 0.754982 0.655745i \(-0.227646\pi\)
0.754982 + 0.655745i \(0.227646\pi\)
\(608\) 2581.81 0.172214
\(609\) −2079.87 −0.138392
\(610\) 2010.88 0.133472
\(611\) 0 0
\(612\) 16284.1 1.07557
\(613\) −24639.4 −1.62345 −0.811727 0.584037i \(-0.801472\pi\)
−0.811727 + 0.584037i \(0.801472\pi\)
\(614\) −39951.7 −2.62593
\(615\) 12786.3 0.838361
\(616\) 5025.21 0.328687
\(617\) 9756.74 0.636615 0.318308 0.947988i \(-0.396886\pi\)
0.318308 + 0.947988i \(0.396886\pi\)
\(618\) −20188.1 −1.31405
\(619\) 18965.9 1.23151 0.615755 0.787937i \(-0.288851\pi\)
0.615755 + 0.787937i \(0.288851\pi\)
\(620\) 8884.14 0.575477
\(621\) −4189.76 −0.270740
\(622\) 17389.8 1.12101
\(623\) 11253.5 0.723696
\(624\) 0 0
\(625\) 461.433 0.0295317
\(626\) −15647.2 −0.999025
\(627\) 9465.22 0.602878
\(628\) −33969.8 −2.15850
\(629\) −9425.19 −0.597468
\(630\) 13458.6 0.851118
\(631\) −15836.3 −0.999102 −0.499551 0.866285i \(-0.666502\pi\)
−0.499551 + 0.866285i \(0.666502\pi\)
\(632\) 27696.3 1.74320
\(633\) −41293.1 −2.59282
\(634\) 46037.4 2.88388
\(635\) 11134.3 0.695832
\(636\) 32635.8 2.03474
\(637\) 0 0
\(638\) 1175.03 0.0729154
\(639\) −24835.5 −1.53752
\(640\) −17495.3 −1.08057
\(641\) 3727.95 0.229711 0.114856 0.993382i \(-0.463359\pi\)
0.114856 + 0.993382i \(0.463359\pi\)
\(642\) 57215.8 3.51733
\(643\) 16971.4 1.04088 0.520440 0.853898i \(-0.325768\pi\)
0.520440 + 0.853898i \(0.325768\pi\)
\(644\) 16161.5 0.988900
\(645\) −17197.3 −1.04984
\(646\) −16750.9 −1.02021
\(647\) 2460.07 0.149483 0.0747414 0.997203i \(-0.476187\pi\)
0.0747414 + 0.997203i \(0.476187\pi\)
\(648\) 19319.7 1.17122
\(649\) 6212.78 0.375767
\(650\) 0 0
\(651\) 7901.19 0.475687
\(652\) −13864.1 −0.832760
\(653\) −7568.89 −0.453589 −0.226794 0.973943i \(-0.572825\pi\)
−0.226794 + 0.973943i \(0.572825\pi\)
\(654\) −5682.65 −0.339769
\(655\) −10036.0 −0.598684
\(656\) 13756.6 0.818758
\(657\) 35047.8 2.08119
\(658\) −28148.0 −1.66766
\(659\) 1352.39 0.0799415 0.0399708 0.999201i \(-0.487274\pi\)
0.0399708 + 0.999201i \(0.487274\pi\)
\(660\) −9109.38 −0.537246
\(661\) −3444.05 −0.202660 −0.101330 0.994853i \(-0.532310\pi\)
−0.101330 + 0.994853i \(0.532310\pi\)
\(662\) 9650.93 0.566608
\(663\) 0 0
\(664\) −6032.72 −0.352583
\(665\) −9170.19 −0.534744
\(666\) 49287.8 2.86766
\(667\) 1852.76 0.107555
\(668\) −33851.9 −1.96073
\(669\) 3726.76 0.215373
\(670\) −28154.3 −1.62343
\(671\) −669.237 −0.0385032
\(672\) −2209.83 −0.126854
\(673\) −21330.5 −1.22174 −0.610869 0.791732i \(-0.709180\pi\)
−0.610869 + 0.791732i \(0.709180\pi\)
\(674\) −20722.4 −1.18427
\(675\) 3915.20 0.223253
\(676\) 0 0
\(677\) −17214.8 −0.977278 −0.488639 0.872486i \(-0.662506\pi\)
−0.488639 + 0.872486i \(0.662506\pi\)
\(678\) −10330.0 −0.585136
\(679\) 19994.7 1.13008
\(680\) 7903.86 0.445734
\(681\) −30078.5 −1.69253
\(682\) −4463.82 −0.250628
\(683\) 26914.9 1.50786 0.753930 0.656955i \(-0.228156\pi\)
0.753930 + 0.656955i \(0.228156\pi\)
\(684\) 58021.8 3.24345
\(685\) −20092.3 −1.12071
\(686\) 31895.9 1.77521
\(687\) 7335.64 0.407383
\(688\) −18502.4 −1.02529
\(689\) 0 0
\(690\) −21684.8 −1.19641
\(691\) −29556.4 −1.62717 −0.813587 0.581443i \(-0.802488\pi\)
−0.813587 + 0.581443i \(0.802488\pi\)
\(692\) 9964.51 0.547390
\(693\) −4479.14 −0.245525
\(694\) 12304.8 0.673033
\(695\) −4520.19 −0.246706
\(696\) 6387.39 0.347864
\(697\) 7530.89 0.409258
\(698\) 23448.4 1.27154
\(699\) 16182.1 0.875625
\(700\) −15102.4 −0.815451
\(701\) 17864.1 0.962507 0.481253 0.876582i \(-0.340182\pi\)
0.481253 + 0.876582i \(0.340182\pi\)
\(702\) 0 0
\(703\) −33582.8 −1.80171
\(704\) 6244.09 0.334280
\(705\) 25016.4 1.33641
\(706\) 18023.0 0.960770
\(707\) −3485.32 −0.185402
\(708\) 68883.9 3.65652
\(709\) −30283.0 −1.60409 −0.802046 0.597263i \(-0.796255\pi\)
−0.802046 + 0.597263i \(0.796255\pi\)
\(710\) −24587.0 −1.29963
\(711\) −24686.7 −1.30214
\(712\) −34560.2 −1.81910
\(713\) −7038.43 −0.369693
\(714\) 14337.5 0.751497
\(715\) 0 0
\(716\) −14406.5 −0.751948
\(717\) −51233.8 −2.66857
\(718\) 20899.5 1.08630
\(719\) −6678.03 −0.346382 −0.173191 0.984888i \(-0.555408\pi\)
−0.173191 + 0.984888i \(0.555408\pi\)
\(720\) −12869.0 −0.666110
\(721\) −6509.35 −0.336229
\(722\) −26297.4 −1.35552
\(723\) −6126.89 −0.315161
\(724\) −59728.2 −3.06600
\(725\) −1731.34 −0.0886903
\(726\) 4576.99 0.233978
\(727\) 15670.1 0.799409 0.399705 0.916644i \(-0.369113\pi\)
0.399705 + 0.916644i \(0.369113\pi\)
\(728\) 0 0
\(729\) −27632.3 −1.40387
\(730\) 34697.2 1.75918
\(731\) −10128.9 −0.512492
\(732\) −7420.14 −0.374667
\(733\) 9590.61 0.483270 0.241635 0.970367i \(-0.422316\pi\)
0.241635 + 0.970367i \(0.422316\pi\)
\(734\) −45371.8 −2.28161
\(735\) −10249.2 −0.514348
\(736\) 1968.53 0.0985883
\(737\) 9369.98 0.468314
\(738\) −39381.8 −1.96431
\(739\) 12190.9 0.606834 0.303417 0.952858i \(-0.401872\pi\)
0.303417 + 0.952858i \(0.401872\pi\)
\(740\) 32320.3 1.60556
\(741\) 0 0
\(742\) 15886.7 0.786008
\(743\) −5903.11 −0.291473 −0.145736 0.989323i \(-0.546555\pi\)
−0.145736 + 0.989323i \(0.546555\pi\)
\(744\) −24265.0 −1.19570
\(745\) −16750.9 −0.823764
\(746\) −31872.3 −1.56425
\(747\) 5377.17 0.263374
\(748\) −5365.27 −0.262264
\(749\) 18448.4 0.899985
\(750\) 52369.0 2.54966
\(751\) −11178.9 −0.543173 −0.271587 0.962414i \(-0.587548\pi\)
−0.271587 + 0.962414i \(0.587548\pi\)
\(752\) 26914.8 1.30516
\(753\) 656.104 0.0317527
\(754\) 0 0
\(755\) −3095.37 −0.149208
\(756\) −9499.36 −0.456995
\(757\) −21033.9 −1.00990 −0.504948 0.863150i \(-0.668488\pi\)
−0.504948 + 0.863150i \(0.668488\pi\)
\(758\) 35234.3 1.68835
\(759\) 7216.88 0.345133
\(760\) 28162.2 1.34414
\(761\) 882.086 0.0420179 0.0210089 0.999779i \(-0.493312\pi\)
0.0210089 + 0.999779i \(0.493312\pi\)
\(762\) −62028.0 −2.94887
\(763\) −1832.28 −0.0869373
\(764\) −67919.1 −3.21627
\(765\) −7044.98 −0.332957
\(766\) −3675.45 −0.173367
\(767\) 0 0
\(768\) 62175.4 2.92130
\(769\) 26048.5 1.22150 0.610751 0.791823i \(-0.290868\pi\)
0.610751 + 0.791823i \(0.290868\pi\)
\(770\) −4434.33 −0.207535
\(771\) −49810.9 −2.32671
\(772\) 12969.4 0.604634
\(773\) −4753.72 −0.221189 −0.110595 0.993866i \(-0.535276\pi\)
−0.110595 + 0.993866i \(0.535276\pi\)
\(774\) 52967.9 2.45981
\(775\) 6577.18 0.304851
\(776\) −61404.7 −2.84059
\(777\) 28744.4 1.32715
\(778\) 19944.9 0.919101
\(779\) 26833.3 1.23415
\(780\) 0 0
\(781\) 8182.77 0.374907
\(782\) −12772.0 −0.584047
\(783\) −1089.01 −0.0497038
\(784\) −11027.0 −0.502322
\(785\) 14696.3 0.668196
\(786\) 55909.2 2.53717
\(787\) 34950.3 1.58303 0.791514 0.611151i \(-0.209293\pi\)
0.791514 + 0.611151i \(0.209293\pi\)
\(788\) 41489.4 1.87563
\(789\) −28515.3 −1.28666
\(790\) −24439.7 −1.10066
\(791\) −3330.76 −0.149720
\(792\) 13755.7 0.617155
\(793\) 0 0
\(794\) −50918.7 −2.27586
\(795\) −14119.2 −0.629882
\(796\) 42962.7 1.91303
\(797\) 2517.67 0.111895 0.0559476 0.998434i \(-0.482182\pi\)
0.0559476 + 0.998434i \(0.482182\pi\)
\(798\) 51086.0 2.26620
\(799\) 14734.2 0.652389
\(800\) −1839.53 −0.0812963
\(801\) 30804.7 1.35884
\(802\) 29433.1 1.29591
\(803\) −11547.5 −0.507475
\(804\) 103889. 4.55708
\(805\) −6991.93 −0.306128
\(806\) 0 0
\(807\) 63503.8 2.77006
\(808\) 10703.6 0.466029
\(809\) −1840.70 −0.0799946 −0.0399973 0.999200i \(-0.512735\pi\)
−0.0399973 + 0.999200i \(0.512735\pi\)
\(810\) −17048.1 −0.739516
\(811\) −36003.3 −1.55888 −0.779438 0.626480i \(-0.784495\pi\)
−0.779438 + 0.626480i \(0.784495\pi\)
\(812\) 4200.72 0.181547
\(813\) −14411.0 −0.621667
\(814\) −16239.3 −0.699246
\(815\) 5998.01 0.257793
\(816\) −13709.4 −0.588144
\(817\) −36090.3 −1.54546
\(818\) 31761.5 1.35760
\(819\) 0 0
\(820\) −25824.5 −1.09979
\(821\) 39115.2 1.66276 0.831382 0.555701i \(-0.187550\pi\)
0.831382 + 0.555701i \(0.187550\pi\)
\(822\) 111931. 4.74946
\(823\) 13571.6 0.574820 0.287410 0.957808i \(-0.407206\pi\)
0.287410 + 0.957808i \(0.407206\pi\)
\(824\) 19990.6 0.845151
\(825\) −6743.93 −0.284598
\(826\) 33531.8 1.41249
\(827\) 32945.2 1.38527 0.692634 0.721289i \(-0.256450\pi\)
0.692634 + 0.721289i \(0.256450\pi\)
\(828\) 44239.4 1.85680
\(829\) −11996.8 −0.502613 −0.251306 0.967908i \(-0.580860\pi\)
−0.251306 + 0.967908i \(0.580860\pi\)
\(830\) 5323.38 0.222623
\(831\) −24982.9 −1.04290
\(832\) 0 0
\(833\) −6036.58 −0.251087
\(834\) 25181.4 1.04552
\(835\) 14645.3 0.606973
\(836\) −19116.9 −0.790877
\(837\) 4137.03 0.170844
\(838\) 65760.9 2.71083
\(839\) 21000.6 0.864148 0.432074 0.901838i \(-0.357782\pi\)
0.432074 + 0.901838i \(0.357782\pi\)
\(840\) −24104.7 −0.990108
\(841\) −23907.4 −0.980255
\(842\) 42760.3 1.75014
\(843\) 66465.7 2.71554
\(844\) 83399.9 3.40135
\(845\) 0 0
\(846\) −77050.5 −3.13127
\(847\) 1475.78 0.0598683
\(848\) −15190.7 −0.615154
\(849\) 6321.52 0.255541
\(850\) 11935.0 0.481607
\(851\) −25605.6 −1.03143
\(852\) 90726.1 3.64815
\(853\) −40511.4 −1.62612 −0.813061 0.582178i \(-0.802201\pi\)
−0.813061 + 0.582178i \(0.802201\pi\)
\(854\) −3612.03 −0.144732
\(855\) −25101.9 −1.00406
\(856\) −56656.0 −2.26222
\(857\) −19156.1 −0.763546 −0.381773 0.924256i \(-0.624686\pi\)
−0.381773 + 0.924256i \(0.624686\pi\)
\(858\) 0 0
\(859\) −38727.4 −1.53825 −0.769127 0.639096i \(-0.779309\pi\)
−0.769127 + 0.639096i \(0.779309\pi\)
\(860\) 34733.5 1.37721
\(861\) −22967.2 −0.909084
\(862\) 34682.5 1.37041
\(863\) −36280.3 −1.43105 −0.715524 0.698588i \(-0.753812\pi\)
−0.715524 + 0.698588i \(0.753812\pi\)
\(864\) −1157.06 −0.0455601
\(865\) −4310.94 −0.169452
\(866\) 31158.0 1.22262
\(867\) 30673.1 1.20152
\(868\) −15958.1 −0.624023
\(869\) 8133.73 0.317512
\(870\) −5636.34 −0.219644
\(871\) 0 0
\(872\) 5627.04 0.218527
\(873\) 54732.1 2.12188
\(874\) −45507.7 −1.76124
\(875\) 16885.6 0.652385
\(876\) −128032. −4.93814
\(877\) −51747.7 −1.99247 −0.996234 0.0867073i \(-0.972365\pi\)
−0.996234 + 0.0867073i \(0.972365\pi\)
\(878\) −37068.7 −1.42484
\(879\) 31039.4 1.19105
\(880\) 4240.06 0.162423
\(881\) −24397.8 −0.933009 −0.466505 0.884519i \(-0.654487\pi\)
−0.466505 + 0.884519i \(0.654487\pi\)
\(882\) 31567.5 1.20514
\(883\) −28537.3 −1.08761 −0.543804 0.839212i \(-0.683016\pi\)
−0.543804 + 0.839212i \(0.683016\pi\)
\(884\) 0 0
\(885\) −29801.2 −1.13193
\(886\) 1966.35 0.0745609
\(887\) −29577.4 −1.11963 −0.559814 0.828618i \(-0.689128\pi\)
−0.559814 + 0.828618i \(0.689128\pi\)
\(888\) −88275.5 −3.33596
\(889\) −20000.0 −0.754531
\(890\) 30496.5 1.14859
\(891\) 5673.74 0.213331
\(892\) −7526.94 −0.282534
\(893\) 52499.3 1.96733
\(894\) 93316.9 3.49103
\(895\) 6232.65 0.232776
\(896\) 31425.8 1.17172
\(897\) 0 0
\(898\) −61065.0 −2.26923
\(899\) −1829.44 −0.0678701
\(900\) −41340.3 −1.53112
\(901\) −8315.96 −0.307486
\(902\) 12975.5 0.478975
\(903\) 30890.6 1.13840
\(904\) 10228.9 0.376338
\(905\) 25840.2 0.949122
\(906\) 17243.9 0.632329
\(907\) 3029.84 0.110920 0.0554599 0.998461i \(-0.482338\pi\)
0.0554599 + 0.998461i \(0.482338\pi\)
\(908\) 60749.6 2.22032
\(909\) −9540.50 −0.348117
\(910\) 0 0
\(911\) −27762.9 −1.00969 −0.504844 0.863211i \(-0.668450\pi\)
−0.504844 + 0.863211i \(0.668450\pi\)
\(912\) −48847.9 −1.77359
\(913\) −1771.66 −0.0642207
\(914\) 75329.2 2.72611
\(915\) 3210.17 0.115983
\(916\) −14815.8 −0.534419
\(917\) 18027.1 0.649189
\(918\) 7507.07 0.269902
\(919\) −4346.97 −0.156032 −0.0780159 0.996952i \(-0.524858\pi\)
−0.0780159 + 0.996952i \(0.524858\pi\)
\(920\) 21472.6 0.769490
\(921\) −63778.9 −2.28185
\(922\) 73365.3 2.62056
\(923\) 0 0
\(924\) 16362.7 0.582567
\(925\) 23927.6 0.850525
\(926\) −12009.0 −0.426178
\(927\) −17818.3 −0.631315
\(928\) 511.664 0.0180993
\(929\) −2228.75 −0.0787115 −0.0393558 0.999225i \(-0.512531\pi\)
−0.0393558 + 0.999225i \(0.512531\pi\)
\(930\) 21411.8 0.754970
\(931\) −21508.9 −0.757170
\(932\) −32683.0 −1.14868
\(933\) 27761.1 0.974122
\(934\) 53089.1 1.85988
\(935\) 2321.17 0.0811876
\(936\) 0 0
\(937\) −3718.86 −0.129658 −0.0648291 0.997896i \(-0.520650\pi\)
−0.0648291 + 0.997896i \(0.520650\pi\)
\(938\) 50571.9 1.76038
\(939\) −24979.3 −0.868123
\(940\) −50525.6 −1.75315
\(941\) −38302.8 −1.32693 −0.663463 0.748209i \(-0.730914\pi\)
−0.663463 + 0.748209i \(0.730914\pi\)
\(942\) −81871.3 −2.83175
\(943\) 20459.4 0.706520
\(944\) −32062.8 −1.10546
\(945\) 4109.70 0.141469
\(946\) −17451.8 −0.599796
\(947\) −12761.7 −0.437907 −0.218954 0.975735i \(-0.570264\pi\)
−0.218954 + 0.975735i \(0.570264\pi\)
\(948\) 90182.3 3.08965
\(949\) 0 0
\(950\) 42525.4 1.45232
\(951\) 73494.1 2.50600
\(952\) −14197.2 −0.483336
\(953\) 28280.0 0.961258 0.480629 0.876924i \(-0.340408\pi\)
0.480629 + 0.876924i \(0.340408\pi\)
\(954\) 43487.2 1.47584
\(955\) 29383.8 0.995641
\(956\) 103477. 3.50072
\(957\) 1875.82 0.0633613
\(958\) −47199.5 −1.59180
\(959\) 36090.6 1.21525
\(960\) −29951.4 −1.00695
\(961\) −22841.2 −0.766713
\(962\) 0 0
\(963\) 50499.4 1.68985
\(964\) 12374.5 0.413440
\(965\) −5610.92 −0.187173
\(966\) 38951.1 1.29734
\(967\) −43554.8 −1.44842 −0.724212 0.689577i \(-0.757796\pi\)
−0.724212 + 0.689577i \(0.757796\pi\)
\(968\) −4532.21 −0.150486
\(969\) −26741.2 −0.886534
\(970\) 54184.6 1.79357
\(971\) 38867.6 1.28457 0.642286 0.766465i \(-0.277986\pi\)
0.642286 + 0.766465i \(0.277986\pi\)
\(972\) 83936.4 2.76982
\(973\) 8119.37 0.267518
\(974\) 43085.0 1.41739
\(975\) 0 0
\(976\) 3453.79 0.113272
\(977\) −25776.3 −0.844071 −0.422036 0.906579i \(-0.638684\pi\)
−0.422036 + 0.906579i \(0.638684\pi\)
\(978\) −33414.1 −1.09250
\(979\) −10149.5 −0.331337
\(980\) 20700.3 0.674741
\(981\) −5015.58 −0.163237
\(982\) 32038.2 1.04112
\(983\) 10135.6 0.328867 0.164433 0.986388i \(-0.447420\pi\)
0.164433 + 0.986388i \(0.447420\pi\)
\(984\) 70533.7 2.28509
\(985\) −17949.5 −0.580629
\(986\) −3319.71 −0.107222
\(987\) −44935.5 −1.44915
\(988\) 0 0
\(989\) −27517.5 −0.884738
\(990\) −12138.3 −0.389676
\(991\) 34291.6 1.09920 0.549601 0.835427i \(-0.314780\pi\)
0.549601 + 0.835427i \(0.314780\pi\)
\(992\) −1943.75 −0.0622119
\(993\) 15406.8 0.492365
\(994\) 44164.3 1.40926
\(995\) −18586.9 −0.592206
\(996\) −19643.2 −0.624920
\(997\) −11783.3 −0.374305 −0.187153 0.982331i \(-0.559926\pi\)
−0.187153 + 0.982331i \(0.559926\pi\)
\(998\) −45097.7 −1.43040
\(999\) 15050.4 0.476651
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.o.1.4 yes 39
13.12 even 2 1859.4.a.n.1.36 39
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.4.a.n.1.36 39 13.12 even 2
1859.4.a.o.1.4 yes 39 1.1 even 1 trivial