Properties

Label 1441.4.a.a.1.10
Level $1441$
Weight $4$
Character 1441.1
Self dual yes
Analytic conductor $85.022$
Analytic rank $1$
Dimension $77$
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] = [1441,4,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, 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("1441.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(85.0217523183\)
Analytic rank: \(1\)
Dimension: \(77\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 1441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.59373 q^{2} +3.62650 q^{3} +13.1024 q^{4} -18.1051 q^{5} -16.6592 q^{6} +32.3039 q^{7} -23.4390 q^{8} -13.8485 q^{9} +O(q^{10})\) \(q-4.59373 q^{2} +3.62650 q^{3} +13.1024 q^{4} -18.1051 q^{5} -16.6592 q^{6} +32.3039 q^{7} -23.4390 q^{8} -13.8485 q^{9} +83.1700 q^{10} -11.0000 q^{11} +47.5158 q^{12} -58.9805 q^{13} -148.396 q^{14} -65.6582 q^{15} +2.85335 q^{16} +39.7546 q^{17} +63.6162 q^{18} +69.6703 q^{19} -237.220 q^{20} +117.150 q^{21} +50.5311 q^{22} +96.1871 q^{23} -85.0015 q^{24} +202.795 q^{25} +270.941 q^{26} -148.137 q^{27} +423.259 q^{28} -195.274 q^{29} +301.616 q^{30} +138.590 q^{31} +174.404 q^{32} -39.8915 q^{33} -182.622 q^{34} -584.866 q^{35} -181.448 q^{36} +274.090 q^{37} -320.047 q^{38} -213.893 q^{39} +424.365 q^{40} -188.058 q^{41} -538.157 q^{42} -102.168 q^{43} -144.126 q^{44} +250.728 q^{45} -441.858 q^{46} -483.643 q^{47} +10.3477 q^{48} +700.545 q^{49} -931.584 q^{50} +144.170 q^{51} -772.785 q^{52} +97.5033 q^{53} +680.502 q^{54} +199.156 q^{55} -757.171 q^{56} +252.660 q^{57} +897.038 q^{58} +224.646 q^{59} -860.279 q^{60} +365.823 q^{61} -636.647 q^{62} -447.360 q^{63} -823.994 q^{64} +1067.85 q^{65} +183.251 q^{66} +984.876 q^{67} +520.880 q^{68} +348.823 q^{69} +2686.72 q^{70} -679.941 q^{71} +324.594 q^{72} -1090.10 q^{73} -1259.10 q^{74} +735.435 q^{75} +912.847 q^{76} -355.343 q^{77} +982.567 q^{78} -581.652 q^{79} -51.6601 q^{80} -163.311 q^{81} +863.890 q^{82} +671.747 q^{83} +1534.95 q^{84} -719.760 q^{85} +469.330 q^{86} -708.163 q^{87} +257.829 q^{88} +554.120 q^{89} -1151.78 q^{90} -1905.30 q^{91} +1260.28 q^{92} +502.598 q^{93} +2221.72 q^{94} -1261.39 q^{95} +632.478 q^{96} -374.347 q^{97} -3218.11 q^{98} +152.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.59373 −1.62413 −0.812065 0.583567i \(-0.801657\pi\)
−0.812065 + 0.583567i \(0.801657\pi\)
\(3\) 3.62650 0.697921 0.348960 0.937137i \(-0.386535\pi\)
0.348960 + 0.937137i \(0.386535\pi\)
\(4\) 13.1024 1.63780
\(5\) −18.1051 −1.61937 −0.809685 0.586865i \(-0.800362\pi\)
−0.809685 + 0.586865i \(0.800362\pi\)
\(6\) −16.6592 −1.13351
\(7\) 32.3039 1.74425 0.872124 0.489284i \(-0.162742\pi\)
0.872124 + 0.489284i \(0.162742\pi\)
\(8\) −23.4390 −1.03587
\(9\) −13.8485 −0.512906
\(10\) 83.1700 2.63007
\(11\) −11.0000 −0.301511
\(12\) 47.5158 1.14305
\(13\) −58.9805 −1.25833 −0.629163 0.777273i \(-0.716602\pi\)
−0.629163 + 0.777273i \(0.716602\pi\)
\(14\) −148.396 −2.83289
\(15\) −65.6582 −1.13019
\(16\) 2.85335 0.0445836
\(17\) 39.7546 0.567171 0.283585 0.958947i \(-0.408476\pi\)
0.283585 + 0.958947i \(0.408476\pi\)
\(18\) 63.6162 0.833027
\(19\) 69.6703 0.841235 0.420617 0.907238i \(-0.361813\pi\)
0.420617 + 0.907238i \(0.361813\pi\)
\(20\) −237.220 −2.65220
\(21\) 117.150 1.21735
\(22\) 50.5311 0.489694
\(23\) 96.1871 0.872017 0.436009 0.899943i \(-0.356392\pi\)
0.436009 + 0.899943i \(0.356392\pi\)
\(24\) −85.0015 −0.722953
\(25\) 202.795 1.62236
\(26\) 270.941 2.04369
\(27\) −148.137 −1.05589
\(28\) 423.259 2.85673
\(29\) −195.274 −1.25040 −0.625199 0.780466i \(-0.714982\pi\)
−0.625199 + 0.780466i \(0.714982\pi\)
\(30\) 301.616 1.83558
\(31\) 138.590 0.802954 0.401477 0.915869i \(-0.368497\pi\)
0.401477 + 0.915869i \(0.368497\pi\)
\(32\) 174.404 0.963457
\(33\) −39.8915 −0.210431
\(34\) −182.622 −0.921159
\(35\) −584.866 −2.82458
\(36\) −181.448 −0.840037
\(37\) 274.090 1.21784 0.608921 0.793231i \(-0.291603\pi\)
0.608921 + 0.793231i \(0.291603\pi\)
\(38\) −320.047 −1.36627
\(39\) −213.893 −0.878212
\(40\) 424.365 1.67745
\(41\) −188.058 −0.716337 −0.358168 0.933657i \(-0.616599\pi\)
−0.358168 + 0.933657i \(0.616599\pi\)
\(42\) −538.157 −1.97713
\(43\) −102.168 −0.362335 −0.181167 0.983452i \(-0.557988\pi\)
−0.181167 + 0.983452i \(0.557988\pi\)
\(44\) −144.126 −0.493815
\(45\) 250.728 0.830585
\(46\) −441.858 −1.41627
\(47\) −483.643 −1.50099 −0.750495 0.660876i \(-0.770185\pi\)
−0.750495 + 0.660876i \(0.770185\pi\)
\(48\) 10.3477 0.0311158
\(49\) 700.545 2.04240
\(50\) −931.584 −2.63492
\(51\) 144.170 0.395840
\(52\) −772.785 −2.06088
\(53\) 97.5033 0.252700 0.126350 0.991986i \(-0.459674\pi\)
0.126350 + 0.991986i \(0.459674\pi\)
\(54\) 680.502 1.71490
\(55\) 199.156 0.488258
\(56\) −757.171 −1.80681
\(57\) 252.660 0.587115
\(58\) 897.038 2.03081
\(59\) 224.646 0.495702 0.247851 0.968798i \(-0.420276\pi\)
0.247851 + 0.968798i \(0.420276\pi\)
\(60\) −860.279 −1.85102
\(61\) 365.823 0.767850 0.383925 0.923364i \(-0.374572\pi\)
0.383925 + 0.923364i \(0.374572\pi\)
\(62\) −636.647 −1.30410
\(63\) −447.360 −0.894637
\(64\) −823.994 −1.60936
\(65\) 1067.85 2.03770
\(66\) 183.251 0.341767
\(67\) 984.876 1.79585 0.897923 0.440152i \(-0.145075\pi\)
0.897923 + 0.440152i \(0.145075\pi\)
\(68\) 520.880 0.928911
\(69\) 348.823 0.608599
\(70\) 2686.72 4.58749
\(71\) −679.941 −1.13654 −0.568269 0.822843i \(-0.692387\pi\)
−0.568269 + 0.822843i \(0.692387\pi\)
\(72\) 324.594 0.531303
\(73\) −1090.10 −1.74775 −0.873877 0.486147i \(-0.838402\pi\)
−0.873877 + 0.486147i \(0.838402\pi\)
\(74\) −1259.10 −1.97793
\(75\) 735.435 1.13228
\(76\) 912.847 1.37777
\(77\) −355.343 −0.525911
\(78\) 982.567 1.42633
\(79\) −581.652 −0.828366 −0.414183 0.910194i \(-0.635933\pi\)
−0.414183 + 0.910194i \(0.635933\pi\)
\(80\) −51.6601 −0.0721972
\(81\) −163.311 −0.224020
\(82\) 863.890 1.16342
\(83\) 671.747 0.888359 0.444180 0.895938i \(-0.353495\pi\)
0.444180 + 0.895938i \(0.353495\pi\)
\(84\) 1534.95 1.99377
\(85\) −719.760 −0.918458
\(86\) 469.330 0.588479
\(87\) −708.163 −0.872679
\(88\) 257.829 0.312325
\(89\) 554.120 0.659962 0.329981 0.943988i \(-0.392958\pi\)
0.329981 + 0.943988i \(0.392958\pi\)
\(90\) −1151.78 −1.34898
\(91\) −1905.30 −2.19483
\(92\) 1260.28 1.42819
\(93\) 502.598 0.560398
\(94\) 2221.72 2.43780
\(95\) −1261.39 −1.36227
\(96\) 632.478 0.672417
\(97\) −374.347 −0.391847 −0.195924 0.980619i \(-0.562771\pi\)
−0.195924 + 0.980619i \(0.562771\pi\)
\(98\) −3218.11 −3.31713
\(99\) 152.333 0.154647
\(100\) 2657.09 2.65709
\(101\) 434.204 0.427771 0.213886 0.976859i \(-0.431388\pi\)
0.213886 + 0.976859i \(0.431388\pi\)
\(102\) −662.279 −0.642896
\(103\) −964.644 −0.922808 −0.461404 0.887190i \(-0.652654\pi\)
−0.461404 + 0.887190i \(0.652654\pi\)
\(104\) 1382.44 1.30346
\(105\) −2121.02 −1.97134
\(106\) −447.904 −0.410418
\(107\) 498.850 0.450707 0.225354 0.974277i \(-0.427646\pi\)
0.225354 + 0.974277i \(0.427646\pi\)
\(108\) −1940.95 −1.72933
\(109\) 1748.15 1.53617 0.768086 0.640347i \(-0.221209\pi\)
0.768086 + 0.640347i \(0.221209\pi\)
\(110\) −914.870 −0.792995
\(111\) 993.988 0.849957
\(112\) 92.1744 0.0777648
\(113\) −1952.14 −1.62515 −0.812573 0.582859i \(-0.801934\pi\)
−0.812573 + 0.582859i \(0.801934\pi\)
\(114\) −1160.65 −0.953552
\(115\) −1741.48 −1.41212
\(116\) −2558.56 −2.04790
\(117\) 816.790 0.645404
\(118\) −1031.96 −0.805084
\(119\) 1284.23 0.989287
\(120\) 1538.96 1.17073
\(121\) 121.000 0.0909091
\(122\) −1680.49 −1.24709
\(123\) −681.995 −0.499946
\(124\) 1815.86 1.31508
\(125\) −1408.48 −1.00782
\(126\) 2055.05 1.45301
\(127\) −395.076 −0.276042 −0.138021 0.990429i \(-0.544074\pi\)
−0.138021 + 0.990429i \(0.544074\pi\)
\(128\) 2389.97 1.65036
\(129\) −370.511 −0.252881
\(130\) −4905.41 −3.30948
\(131\) 131.000 0.0873704
\(132\) −522.674 −0.344643
\(133\) 2250.63 1.46732
\(134\) −4524.26 −2.91669
\(135\) 2682.04 1.70987
\(136\) −931.806 −0.587513
\(137\) 2423.84 1.51155 0.755775 0.654832i \(-0.227260\pi\)
0.755775 + 0.654832i \(0.227260\pi\)
\(138\) −1602.40 −0.988444
\(139\) −1904.44 −1.16211 −0.581053 0.813866i \(-0.697359\pi\)
−0.581053 + 0.813866i \(0.697359\pi\)
\(140\) −7663.14 −4.62610
\(141\) −1753.93 −1.04757
\(142\) 3123.47 1.84588
\(143\) 648.785 0.379400
\(144\) −39.5145 −0.0228672
\(145\) 3535.46 2.02486
\(146\) 5007.61 2.83858
\(147\) 2540.53 1.42544
\(148\) 3591.23 1.99458
\(149\) −1.40500 −0.000772496 0 −0.000386248 1.00000i \(-0.500123\pi\)
−0.000386248 1.00000i \(0.500123\pi\)
\(150\) −3378.39 −1.83896
\(151\) 1440.02 0.776075 0.388038 0.921644i \(-0.373153\pi\)
0.388038 + 0.921644i \(0.373153\pi\)
\(152\) −1633.00 −0.871407
\(153\) −550.540 −0.290905
\(154\) 1632.35 0.854147
\(155\) −2509.19 −1.30028
\(156\) −2802.51 −1.43833
\(157\) 1358.03 0.690334 0.345167 0.938541i \(-0.387822\pi\)
0.345167 + 0.938541i \(0.387822\pi\)
\(158\) 2671.95 1.34537
\(159\) 353.596 0.176365
\(160\) −3157.61 −1.56019
\(161\) 3107.22 1.52101
\(162\) 750.207 0.363838
\(163\) −386.881 −0.185907 −0.0929536 0.995670i \(-0.529631\pi\)
−0.0929536 + 0.995670i \(0.529631\pi\)
\(164\) −2464.01 −1.17321
\(165\) 722.240 0.340766
\(166\) −3085.83 −1.44281
\(167\) 416.683 0.193077 0.0965385 0.995329i \(-0.469223\pi\)
0.0965385 + 0.995329i \(0.469223\pi\)
\(168\) −2745.88 −1.26101
\(169\) 1281.70 0.583386
\(170\) 3306.39 1.49170
\(171\) −964.828 −0.431475
\(172\) −1338.64 −0.593431
\(173\) 217.165 0.0954376 0.0477188 0.998861i \(-0.484805\pi\)
0.0477188 + 0.998861i \(0.484805\pi\)
\(174\) 3253.11 1.41734
\(175\) 6551.06 2.82979
\(176\) −31.3868 −0.0134424
\(177\) 814.679 0.345961
\(178\) −2545.48 −1.07186
\(179\) −1678.93 −0.701058 −0.350529 0.936552i \(-0.613998\pi\)
−0.350529 + 0.936552i \(0.613998\pi\)
\(180\) 3285.13 1.36033
\(181\) −2528.26 −1.03825 −0.519127 0.854697i \(-0.673743\pi\)
−0.519127 + 0.854697i \(0.673743\pi\)
\(182\) 8752.45 3.56470
\(183\) 1326.66 0.535898
\(184\) −2254.53 −0.903293
\(185\) −4962.43 −1.97213
\(186\) −2308.80 −0.910159
\(187\) −437.300 −0.171008
\(188\) −6336.87 −2.45832
\(189\) −4785.41 −1.84173
\(190\) 5794.48 2.21250
\(191\) −810.342 −0.306986 −0.153493 0.988150i \(-0.549052\pi\)
−0.153493 + 0.988150i \(0.549052\pi\)
\(192\) −2988.22 −1.12321
\(193\) −2801.65 −1.04491 −0.522454 0.852667i \(-0.674984\pi\)
−0.522454 + 0.852667i \(0.674984\pi\)
\(194\) 1719.65 0.636411
\(195\) 3872.55 1.42215
\(196\) 9178.80 3.34504
\(197\) −4516.03 −1.63327 −0.816634 0.577156i \(-0.804163\pi\)
−0.816634 + 0.577156i \(0.804163\pi\)
\(198\) −699.778 −0.251167
\(199\) 5388.06 1.91934 0.959672 0.281120i \(-0.0907060\pi\)
0.959672 + 0.281120i \(0.0907060\pi\)
\(200\) −4753.30 −1.68054
\(201\) 3571.66 1.25336
\(202\) −1994.62 −0.694756
\(203\) −6308.13 −2.18100
\(204\) 1888.97 0.648306
\(205\) 3404.82 1.16001
\(206\) 4431.32 1.49876
\(207\) −1332.04 −0.447263
\(208\) −168.292 −0.0561007
\(209\) −766.373 −0.253642
\(210\) 9743.39 3.20170
\(211\) 3916.21 1.27774 0.638870 0.769314i \(-0.279402\pi\)
0.638870 + 0.769314i \(0.279402\pi\)
\(212\) 1277.53 0.413872
\(213\) −2465.81 −0.793213
\(214\) −2291.58 −0.732007
\(215\) 1849.75 0.586754
\(216\) 3472.18 1.09376
\(217\) 4477.01 1.40055
\(218\) −8030.55 −2.49494
\(219\) −3953.24 −1.21979
\(220\) 2609.42 0.799668
\(221\) −2344.74 −0.713686
\(222\) −4566.12 −1.38044
\(223\) −5735.99 −1.72247 −0.861233 0.508210i \(-0.830307\pi\)
−0.861233 + 0.508210i \(0.830307\pi\)
\(224\) 5633.95 1.68051
\(225\) −2808.40 −0.832117
\(226\) 8967.60 2.63945
\(227\) 368.988 0.107888 0.0539441 0.998544i \(-0.482821\pi\)
0.0539441 + 0.998544i \(0.482821\pi\)
\(228\) 3310.44 0.961576
\(229\) 529.455 0.152783 0.0763916 0.997078i \(-0.475660\pi\)
0.0763916 + 0.997078i \(0.475660\pi\)
\(230\) 7999.88 2.29346
\(231\) −1288.65 −0.367044
\(232\) 4577.03 1.29524
\(233\) −4632.58 −1.30254 −0.651268 0.758848i \(-0.725762\pi\)
−0.651268 + 0.758848i \(0.725762\pi\)
\(234\) −3752.11 −1.04822
\(235\) 8756.40 2.43066
\(236\) 2943.40 0.811859
\(237\) −2109.36 −0.578134
\(238\) −5899.41 −1.60673
\(239\) −536.451 −0.145189 −0.0725944 0.997362i \(-0.523128\pi\)
−0.0725944 + 0.997362i \(0.523128\pi\)
\(240\) −187.346 −0.0503880
\(241\) −5934.44 −1.58619 −0.793093 0.609100i \(-0.791531\pi\)
−0.793093 + 0.609100i \(0.791531\pi\)
\(242\) −555.842 −0.147648
\(243\) 3407.45 0.899540
\(244\) 4793.15 1.25758
\(245\) −12683.4 −3.30741
\(246\) 3132.90 0.811978
\(247\) −4109.19 −1.05855
\(248\) −3248.42 −0.831753
\(249\) 2436.09 0.620005
\(250\) 6470.17 1.63684
\(251\) −1674.40 −0.421064 −0.210532 0.977587i \(-0.567520\pi\)
−0.210532 + 0.977587i \(0.567520\pi\)
\(252\) −5861.49 −1.46523
\(253\) −1058.06 −0.262923
\(254\) 1814.87 0.448328
\(255\) −2610.21 −0.641011
\(256\) −4386.94 −1.07103
\(257\) 674.774 0.163779 0.0818896 0.996641i \(-0.473905\pi\)
0.0818896 + 0.996641i \(0.473905\pi\)
\(258\) 1702.03 0.410712
\(259\) 8854.19 2.12422
\(260\) 13991.3 3.33733
\(261\) 2704.25 0.641337
\(262\) −601.779 −0.141901
\(263\) −6969.05 −1.63395 −0.816977 0.576670i \(-0.804352\pi\)
−0.816977 + 0.576670i \(0.804352\pi\)
\(264\) 935.017 0.217978
\(265\) −1765.31 −0.409215
\(266\) −10338.8 −2.38312
\(267\) 2009.52 0.460601
\(268\) 12904.2 2.94123
\(269\) −4193.78 −0.950554 −0.475277 0.879836i \(-0.657652\pi\)
−0.475277 + 0.879836i \(0.657652\pi\)
\(270\) −12320.6 −2.77706
\(271\) 1107.09 0.248158 0.124079 0.992272i \(-0.460402\pi\)
0.124079 + 0.992272i \(0.460402\pi\)
\(272\) 113.434 0.0252865
\(273\) −6909.58 −1.53182
\(274\) −11134.5 −2.45495
\(275\) −2230.74 −0.489159
\(276\) 4570.41 0.996762
\(277\) −5691.73 −1.23460 −0.617298 0.786729i \(-0.711773\pi\)
−0.617298 + 0.786729i \(0.711773\pi\)
\(278\) 8748.50 1.88741
\(279\) −1919.27 −0.411840
\(280\) 13708.7 2.92589
\(281\) 8965.19 1.90327 0.951634 0.307234i \(-0.0994034\pi\)
0.951634 + 0.307234i \(0.0994034\pi\)
\(282\) 8057.09 1.70139
\(283\) −2207.05 −0.463588 −0.231794 0.972765i \(-0.574460\pi\)
−0.231794 + 0.972765i \(0.574460\pi\)
\(284\) −8908.84 −1.86142
\(285\) −4574.43 −0.950757
\(286\) −2980.35 −0.616194
\(287\) −6075.03 −1.24947
\(288\) −2415.23 −0.494163
\(289\) −3332.57 −0.678318
\(290\) −16241.0 −3.28863
\(291\) −1357.57 −0.273479
\(292\) −14282.9 −2.86247
\(293\) −4345.90 −0.866519 −0.433260 0.901269i \(-0.642637\pi\)
−0.433260 + 0.901269i \(0.642637\pi\)
\(294\) −11670.5 −2.31509
\(295\) −4067.24 −0.802724
\(296\) −6424.39 −1.26152
\(297\) 1629.51 0.318363
\(298\) 6.45418 0.00125463
\(299\) −5673.16 −1.09728
\(300\) 9635.95 1.85444
\(301\) −3300.41 −0.632002
\(302\) −6615.08 −1.26045
\(303\) 1574.64 0.298550
\(304\) 198.794 0.0375052
\(305\) −6623.26 −1.24343
\(306\) 2529.03 0.472468
\(307\) 2845.14 0.528927 0.264464 0.964396i \(-0.414805\pi\)
0.264464 + 0.964396i \(0.414805\pi\)
\(308\) −4655.84 −0.861336
\(309\) −3498.29 −0.644047
\(310\) 11526.6 2.11182
\(311\) 902.017 0.164465 0.0822327 0.996613i \(-0.473795\pi\)
0.0822327 + 0.996613i \(0.473795\pi\)
\(312\) 5013.43 0.909710
\(313\) −7517.88 −1.35762 −0.678811 0.734313i \(-0.737505\pi\)
−0.678811 + 0.734313i \(0.737505\pi\)
\(314\) −6238.42 −1.12119
\(315\) 8099.50 1.44875
\(316\) −7621.02 −1.35670
\(317\) −9025.87 −1.59919 −0.799595 0.600540i \(-0.794952\pi\)
−0.799595 + 0.600540i \(0.794952\pi\)
\(318\) −1624.33 −0.286439
\(319\) 2148.02 0.377009
\(320\) 14918.5 2.60615
\(321\) 1809.08 0.314558
\(322\) −14273.7 −2.47033
\(323\) 2769.71 0.477124
\(324\) −2139.76 −0.366900
\(325\) −11960.9 −2.04145
\(326\) 1777.23 0.301937
\(327\) 6339.68 1.07213
\(328\) 4407.90 0.742029
\(329\) −15623.6 −2.61810
\(330\) −3317.78 −0.553447
\(331\) −9045.70 −1.50210 −0.751052 0.660243i \(-0.770453\pi\)
−0.751052 + 0.660243i \(0.770453\pi\)
\(332\) 8801.49 1.45495
\(333\) −3795.73 −0.624639
\(334\) −1914.13 −0.313582
\(335\) −17831.3 −2.90814
\(336\) 334.271 0.0542737
\(337\) 6694.79 1.08216 0.541081 0.840971i \(-0.318015\pi\)
0.541081 + 0.840971i \(0.318015\pi\)
\(338\) −5887.78 −0.947494
\(339\) −7079.43 −1.13422
\(340\) −9430.57 −1.50425
\(341\) −1524.49 −0.242100
\(342\) 4432.16 0.700771
\(343\) 11550.1 1.81821
\(344\) 2394.70 0.375331
\(345\) −6315.47 −0.985546
\(346\) −997.596 −0.155003
\(347\) −9541.54 −1.47613 −0.738065 0.674730i \(-0.764260\pi\)
−0.738065 + 0.674730i \(0.764260\pi\)
\(348\) −9278.62 −1.42927
\(349\) 1839.41 0.282125 0.141062 0.990001i \(-0.454948\pi\)
0.141062 + 0.990001i \(0.454948\pi\)
\(350\) −30093.8 −4.59595
\(351\) 8737.20 1.32865
\(352\) −1918.45 −0.290493
\(353\) 7673.58 1.15701 0.578503 0.815680i \(-0.303637\pi\)
0.578503 + 0.815680i \(0.303637\pi\)
\(354\) −3742.42 −0.561885
\(355\) 12310.4 1.84047
\(356\) 7260.30 1.08088
\(357\) 4657.26 0.690444
\(358\) 7712.58 1.13861
\(359\) −7420.53 −1.09092 −0.545461 0.838136i \(-0.683645\pi\)
−0.545461 + 0.838136i \(0.683645\pi\)
\(360\) −5876.81 −0.860375
\(361\) −2005.05 −0.292324
\(362\) 11614.2 1.68626
\(363\) 438.807 0.0634473
\(364\) −24964.0 −3.59470
\(365\) 19736.3 2.83026
\(366\) −6094.31 −0.870368
\(367\) 7846.49 1.11603 0.558016 0.829830i \(-0.311563\pi\)
0.558016 + 0.829830i \(0.311563\pi\)
\(368\) 274.455 0.0388776
\(369\) 2604.32 0.367414
\(370\) 22796.1 3.20300
\(371\) 3149.74 0.440772
\(372\) 6585.24 0.917819
\(373\) 10319.3 1.43248 0.716238 0.697856i \(-0.245863\pi\)
0.716238 + 0.697856i \(0.245863\pi\)
\(374\) 2008.84 0.277740
\(375\) −5107.85 −0.703382
\(376\) 11336.1 1.55482
\(377\) 11517.4 1.57341
\(378\) 21982.9 2.99121
\(379\) −811.104 −0.109930 −0.0549652 0.998488i \(-0.517505\pi\)
−0.0549652 + 0.998488i \(0.517505\pi\)
\(380\) −16527.2 −2.23112
\(381\) −1432.74 −0.192655
\(382\) 3722.49 0.498585
\(383\) −6367.04 −0.849453 −0.424726 0.905322i \(-0.639630\pi\)
−0.424726 + 0.905322i \(0.639630\pi\)
\(384\) 8667.24 1.15182
\(385\) 6433.53 0.851644
\(386\) 12870.0 1.69707
\(387\) 1414.86 0.185844
\(388\) −4904.84 −0.641767
\(389\) −9823.30 −1.28036 −0.640182 0.768224i \(-0.721141\pi\)
−0.640182 + 0.768224i \(0.721141\pi\)
\(390\) −17789.5 −2.30976
\(391\) 3823.88 0.494582
\(392\) −16420.0 −2.11566
\(393\) 475.072 0.0609776
\(394\) 20745.4 2.65264
\(395\) 10530.9 1.34143
\(396\) 1995.93 0.253281
\(397\) −11297.4 −1.42821 −0.714105 0.700039i \(-0.753166\pi\)
−0.714105 + 0.700039i \(0.753166\pi\)
\(398\) −24751.3 −3.11727
\(399\) 8161.90 1.02408
\(400\) 578.643 0.0723304
\(401\) −11002.2 −1.37013 −0.685065 0.728482i \(-0.740226\pi\)
−0.685065 + 0.728482i \(0.740226\pi\)
\(402\) −16407.2 −2.03562
\(403\) −8174.13 −1.01038
\(404\) 5689.10 0.700603
\(405\) 2956.76 0.362772
\(406\) 28977.9 3.54223
\(407\) −3014.99 −0.367193
\(408\) −3379.20 −0.410037
\(409\) −3883.19 −0.469466 −0.234733 0.972060i \(-0.575422\pi\)
−0.234733 + 0.972060i \(0.575422\pi\)
\(410\) −15640.8 −1.88401
\(411\) 8790.05 1.05494
\(412\) −12639.1 −1.51137
\(413\) 7256.95 0.864627
\(414\) 6119.06 0.726413
\(415\) −12162.0 −1.43858
\(416\) −10286.5 −1.21234
\(417\) −6906.47 −0.811058
\(418\) 3520.51 0.411947
\(419\) 4884.16 0.569467 0.284734 0.958607i \(-0.408095\pi\)
0.284734 + 0.958607i \(0.408095\pi\)
\(420\) −27790.4 −3.22865
\(421\) −3879.96 −0.449163 −0.224581 0.974455i \(-0.572101\pi\)
−0.224581 + 0.974455i \(0.572101\pi\)
\(422\) −17990.0 −2.07522
\(423\) 6697.71 0.769867
\(424\) −2285.38 −0.261764
\(425\) 8062.01 0.920153
\(426\) 11327.3 1.28828
\(427\) 11817.5 1.33932
\(428\) 6536.12 0.738167
\(429\) 2352.82 0.264791
\(430\) −8497.27 −0.952965
\(431\) 8673.91 0.969391 0.484695 0.874683i \(-0.338930\pi\)
0.484695 + 0.874683i \(0.338930\pi\)
\(432\) −422.687 −0.0470753
\(433\) −12252.4 −1.35985 −0.679924 0.733283i \(-0.737987\pi\)
−0.679924 + 0.733283i \(0.737987\pi\)
\(434\) −20566.2 −2.27468
\(435\) 12821.4 1.41319
\(436\) 22905.0 2.51594
\(437\) 6701.38 0.733571
\(438\) 18160.1 1.98110
\(439\) −14320.4 −1.55690 −0.778448 0.627709i \(-0.783993\pi\)
−0.778448 + 0.627709i \(0.783993\pi\)
\(440\) −4668.01 −0.505770
\(441\) −9701.47 −1.04756
\(442\) 10771.1 1.15912
\(443\) −2874.85 −0.308325 −0.154163 0.988045i \(-0.549268\pi\)
−0.154163 + 0.988045i \(0.549268\pi\)
\(444\) 13023.6 1.39206
\(445\) −10032.4 −1.06872
\(446\) 26349.6 2.79751
\(447\) −5.09523 −0.000539141 0
\(448\) −26618.2 −2.80713
\(449\) −726.986 −0.0764112 −0.0382056 0.999270i \(-0.512164\pi\)
−0.0382056 + 0.999270i \(0.512164\pi\)
\(450\) 12901.0 1.35147
\(451\) 2068.64 0.215984
\(452\) −25577.6 −2.66166
\(453\) 5222.25 0.541639
\(454\) −1695.03 −0.175224
\(455\) 34495.7 3.55425
\(456\) −5922.08 −0.608173
\(457\) −473.509 −0.0484678 −0.0242339 0.999706i \(-0.507715\pi\)
−0.0242339 + 0.999706i \(0.507715\pi\)
\(458\) −2432.17 −0.248140
\(459\) −5889.13 −0.598869
\(460\) −22817.5 −2.31276
\(461\) −11551.7 −1.16706 −0.583531 0.812091i \(-0.698329\pi\)
−0.583531 + 0.812091i \(0.698329\pi\)
\(462\) 5919.73 0.596127
\(463\) −15168.1 −1.52251 −0.761255 0.648453i \(-0.775416\pi\)
−0.761255 + 0.648453i \(0.775416\pi\)
\(464\) −557.186 −0.0557472
\(465\) −9099.59 −0.907491
\(466\) 21280.9 2.11549
\(467\) 144.213 0.0142899 0.00714493 0.999974i \(-0.497726\pi\)
0.00714493 + 0.999974i \(0.497726\pi\)
\(468\) 10701.9 1.05704
\(469\) 31815.4 3.13240
\(470\) −40224.5 −3.94770
\(471\) 4924.90 0.481799
\(472\) −5265.47 −0.513481
\(473\) 1123.84 0.109248
\(474\) 9689.84 0.938965
\(475\) 14128.8 1.36478
\(476\) 16826.5 1.62025
\(477\) −1350.27 −0.129612
\(478\) 2464.31 0.235806
\(479\) 10302.9 0.982778 0.491389 0.870940i \(-0.336489\pi\)
0.491389 + 0.870940i \(0.336489\pi\)
\(480\) −11451.1 −1.08889
\(481\) −16166.0 −1.53244
\(482\) 27261.2 2.57617
\(483\) 11268.3 1.06155
\(484\) 1585.39 0.148891
\(485\) 6777.59 0.634546
\(486\) −15652.9 −1.46097
\(487\) −20568.3 −1.91383 −0.956917 0.290361i \(-0.906225\pi\)
−0.956917 + 0.290361i \(0.906225\pi\)
\(488\) −8574.51 −0.795389
\(489\) −1403.03 −0.129748
\(490\) 58264.3 5.37166
\(491\) −9273.92 −0.852395 −0.426198 0.904630i \(-0.640147\pi\)
−0.426198 + 0.904630i \(0.640147\pi\)
\(492\) −8935.75 −0.818811
\(493\) −7763.05 −0.709189
\(494\) 18876.5 1.71922
\(495\) −2758.01 −0.250431
\(496\) 395.446 0.0357985
\(497\) −21964.8 −1.98240
\(498\) −11190.8 −1.00697
\(499\) −12293.6 −1.10288 −0.551438 0.834216i \(-0.685921\pi\)
−0.551438 + 0.834216i \(0.685921\pi\)
\(500\) −18454.4 −1.65061
\(501\) 1511.10 0.134752
\(502\) 7691.73 0.683862
\(503\) −7386.50 −0.654767 −0.327383 0.944892i \(-0.606167\pi\)
−0.327383 + 0.944892i \(0.606167\pi\)
\(504\) 10485.7 0.926724
\(505\) −7861.30 −0.692719
\(506\) 4860.43 0.427021
\(507\) 4648.08 0.407157
\(508\) −5176.44 −0.452101
\(509\) 16470.8 1.43430 0.717148 0.696920i \(-0.245447\pi\)
0.717148 + 0.696920i \(0.245447\pi\)
\(510\) 11990.6 1.04109
\(511\) −35214.4 −3.04852
\(512\) 1032.67 0.0891369
\(513\) −10320.8 −0.888251
\(514\) −3099.73 −0.265999
\(515\) 17465.0 1.49437
\(516\) −4854.57 −0.414168
\(517\) 5320.07 0.452565
\(518\) −40673.8 −3.45001
\(519\) 787.548 0.0666079
\(520\) −25029.3 −2.11078
\(521\) −11500.3 −0.967057 −0.483529 0.875329i \(-0.660645\pi\)
−0.483529 + 0.875329i \(0.660645\pi\)
\(522\) −12422.6 −1.04161
\(523\) 13606.4 1.13761 0.568803 0.822474i \(-0.307407\pi\)
0.568803 + 0.822474i \(0.307407\pi\)
\(524\) 1716.41 0.143095
\(525\) 23757.5 1.97497
\(526\) 32014.0 2.65376
\(527\) 5509.60 0.455412
\(528\) −113.824 −0.00938177
\(529\) −2915.05 −0.239586
\(530\) 8109.35 0.664618
\(531\) −3111.00 −0.254249
\(532\) 29488.6 2.40318
\(533\) 11091.8 0.901385
\(534\) −9231.19 −0.748076
\(535\) −9031.73 −0.729861
\(536\) −23084.5 −1.86026
\(537\) −6088.66 −0.489283
\(538\) 19265.1 1.54382
\(539\) −7705.99 −0.615808
\(540\) 35141.1 2.80043
\(541\) 5423.43 0.431001 0.215501 0.976504i \(-0.430862\pi\)
0.215501 + 0.976504i \(0.430862\pi\)
\(542\) −5085.68 −0.403042
\(543\) −9168.74 −0.724620
\(544\) 6933.37 0.546444
\(545\) −31650.5 −2.48763
\(546\) 31740.8 2.48788
\(547\) 9026.78 0.705589 0.352795 0.935701i \(-0.385231\pi\)
0.352795 + 0.935701i \(0.385231\pi\)
\(548\) 31758.0 2.47561
\(549\) −5066.09 −0.393835
\(550\) 10247.4 0.794457
\(551\) −13604.8 −1.05188
\(552\) −8176.05 −0.630427
\(553\) −18789.6 −1.44488
\(554\) 26146.3 2.00514
\(555\) −17996.3 −1.37639
\(556\) −24952.7 −1.90329
\(557\) −15918.6 −1.21094 −0.605468 0.795869i \(-0.707014\pi\)
−0.605468 + 0.795869i \(0.707014\pi\)
\(558\) 8816.59 0.668882
\(559\) 6025.89 0.455936
\(560\) −1668.83 −0.125930
\(561\) −1585.87 −0.119350
\(562\) −41183.7 −3.09115
\(563\) 19016.9 1.42356 0.711782 0.702401i \(-0.247889\pi\)
0.711782 + 0.702401i \(0.247889\pi\)
\(564\) −22980.7 −1.71571
\(565\) 35343.6 2.63171
\(566\) 10138.6 0.752928
\(567\) −5275.59 −0.390747
\(568\) 15937.1 1.17730
\(569\) −10773.7 −0.793776 −0.396888 0.917867i \(-0.629910\pi\)
−0.396888 + 0.917867i \(0.629910\pi\)
\(570\) 21013.7 1.54415
\(571\) 19005.4 1.39291 0.696453 0.717602i \(-0.254761\pi\)
0.696453 + 0.717602i \(0.254761\pi\)
\(572\) 8500.63 0.621380
\(573\) −2938.71 −0.214252
\(574\) 27907.1 2.02930
\(575\) 19506.2 1.41472
\(576\) 11411.1 0.825452
\(577\) 12089.2 0.872235 0.436117 0.899890i \(-0.356353\pi\)
0.436117 + 0.899890i \(0.356353\pi\)
\(578\) 15309.0 1.10168
\(579\) −10160.2 −0.729264
\(580\) 46323.0 3.31630
\(581\) 21700.1 1.54952
\(582\) 6236.32 0.444165
\(583\) −1072.54 −0.0761920
\(584\) 25550.7 1.81044
\(585\) −14788.1 −1.04515
\(586\) 19963.9 1.40734
\(587\) 5657.90 0.397830 0.198915 0.980017i \(-0.436258\pi\)
0.198915 + 0.980017i \(0.436258\pi\)
\(588\) 33287.0 2.33458
\(589\) 9655.63 0.675473
\(590\) 18683.8 1.30373
\(591\) −16377.4 −1.13989
\(592\) 782.074 0.0542957
\(593\) 1814.29 0.125639 0.0628195 0.998025i \(-0.479991\pi\)
0.0628195 + 0.998025i \(0.479991\pi\)
\(594\) −7485.53 −0.517062
\(595\) −23251.1 −1.60202
\(596\) −18.4088 −0.00126519
\(597\) 19539.8 1.33955
\(598\) 26061.0 1.78213
\(599\) 10468.4 0.714070 0.357035 0.934091i \(-0.383788\pi\)
0.357035 + 0.934091i \(0.383788\pi\)
\(600\) −17237.8 −1.17289
\(601\) −3466.70 −0.235291 −0.117645 0.993056i \(-0.537535\pi\)
−0.117645 + 0.993056i \(0.537535\pi\)
\(602\) 15161.2 1.02645
\(603\) −13639.0 −0.921102
\(604\) 18867.7 1.27105
\(605\) −2190.72 −0.147215
\(606\) −7233.48 −0.484885
\(607\) 24467.1 1.63606 0.818032 0.575173i \(-0.195065\pi\)
0.818032 + 0.575173i \(0.195065\pi\)
\(608\) 12150.8 0.810494
\(609\) −22876.5 −1.52217
\(610\) 30425.5 2.01949
\(611\) 28525.5 1.88874
\(612\) −7213.39 −0.476444
\(613\) 4635.69 0.305439 0.152719 0.988270i \(-0.451197\pi\)
0.152719 + 0.988270i \(0.451197\pi\)
\(614\) −13069.8 −0.859047
\(615\) 12347.6 0.809597
\(616\) 8328.88 0.544773
\(617\) −21768.8 −1.42039 −0.710194 0.704006i \(-0.751393\pi\)
−0.710194 + 0.704006i \(0.751393\pi\)
\(618\) 16070.2 1.04602
\(619\) −10131.7 −0.657882 −0.328941 0.944350i \(-0.606692\pi\)
−0.328941 + 0.944350i \(0.606692\pi\)
\(620\) −32876.4 −2.12959
\(621\) −14248.9 −0.920753
\(622\) −4143.63 −0.267113
\(623\) 17900.3 1.15114
\(624\) −610.311 −0.0391538
\(625\) 151.310 0.00968386
\(626\) 34535.2 2.20496
\(627\) −2779.26 −0.177022
\(628\) 17793.4 1.13063
\(629\) 10896.3 0.690724
\(630\) −37206.9 −2.35295
\(631\) 588.064 0.0371006 0.0185503 0.999828i \(-0.494095\pi\)
0.0185503 + 0.999828i \(0.494095\pi\)
\(632\) 13633.3 0.858076
\(633\) 14202.2 0.891762
\(634\) 41462.4 2.59729
\(635\) 7152.89 0.447014
\(636\) 4632.95 0.288850
\(637\) −41318.5 −2.57001
\(638\) −9867.42 −0.612312
\(639\) 9416.14 0.582937
\(640\) −43270.7 −2.67254
\(641\) 5438.26 0.335099 0.167549 0.985864i \(-0.446415\pi\)
0.167549 + 0.985864i \(0.446415\pi\)
\(642\) −8310.44 −0.510883
\(643\) 24143.0 1.48073 0.740364 0.672207i \(-0.234653\pi\)
0.740364 + 0.672207i \(0.234653\pi\)
\(644\) 40712.0 2.49111
\(645\) 6708.13 0.409508
\(646\) −12723.3 −0.774911
\(647\) 22789.0 1.38474 0.692370 0.721543i \(-0.256567\pi\)
0.692370 + 0.721543i \(0.256567\pi\)
\(648\) 3827.84 0.232055
\(649\) −2471.10 −0.149460
\(650\) 54945.3 3.31559
\(651\) 16235.9 0.977474
\(652\) −5069.06 −0.304478
\(653\) 7687.12 0.460674 0.230337 0.973111i \(-0.426017\pi\)
0.230337 + 0.973111i \(0.426017\pi\)
\(654\) −29122.8 −1.74127
\(655\) −2371.77 −0.141485
\(656\) −536.596 −0.0319368
\(657\) 15096.2 0.896435
\(658\) 71770.5 4.25213
\(659\) 1478.67 0.0874062 0.0437031 0.999045i \(-0.486084\pi\)
0.0437031 + 0.999045i \(0.486084\pi\)
\(660\) 9463.07 0.558105
\(661\) 253.566 0.0149207 0.00746035 0.999972i \(-0.497625\pi\)
0.00746035 + 0.999972i \(0.497625\pi\)
\(662\) 41553.5 2.43961
\(663\) −8503.22 −0.498096
\(664\) −15745.1 −0.920221
\(665\) −40747.8 −2.37614
\(666\) 17436.6 1.01449
\(667\) −18782.9 −1.09037
\(668\) 5459.53 0.316221
\(669\) −20801.6 −1.20215
\(670\) 81912.1 4.72320
\(671\) −4024.05 −0.231515
\(672\) 20431.5 1.17286
\(673\) 11530.3 0.660417 0.330209 0.943908i \(-0.392881\pi\)
0.330209 + 0.943908i \(0.392881\pi\)
\(674\) −30754.1 −1.75757
\(675\) −30041.4 −1.71303
\(676\) 16793.3 0.955468
\(677\) −1862.76 −0.105748 −0.0528741 0.998601i \(-0.516838\pi\)
−0.0528741 + 0.998601i \(0.516838\pi\)
\(678\) 32521.0 1.84213
\(679\) −12092.9 −0.683480
\(680\) 16870.4 0.951400
\(681\) 1338.14 0.0752974
\(682\) 7003.12 0.393201
\(683\) 18395.7 1.03059 0.515294 0.857013i \(-0.327683\pi\)
0.515294 + 0.857013i \(0.327683\pi\)
\(684\) −12641.5 −0.706669
\(685\) −43883.8 −2.44776
\(686\) −53058.1 −2.95301
\(687\) 1920.07 0.106631
\(688\) −291.519 −0.0161542
\(689\) −5750.79 −0.317979
\(690\) 29011.6 1.60065
\(691\) 21621.6 1.19034 0.595170 0.803600i \(-0.297085\pi\)
0.595170 + 0.803600i \(0.297085\pi\)
\(692\) 2845.37 0.156308
\(693\) 4920.96 0.269743
\(694\) 43831.3 2.39743
\(695\) 34480.1 1.88188
\(696\) 16598.6 0.903978
\(697\) −7476.18 −0.406285
\(698\) −8449.77 −0.458207
\(699\) −16800.1 −0.909067
\(700\) 85834.5 4.63463
\(701\) 1405.85 0.0757464 0.0378732 0.999283i \(-0.487942\pi\)
0.0378732 + 0.999283i \(0.487942\pi\)
\(702\) −40136.4 −2.15791
\(703\) 19095.9 1.02449
\(704\) 9063.93 0.485241
\(705\) 31755.1 1.69641
\(706\) −35250.4 −1.87913
\(707\) 14026.5 0.746139
\(708\) 10674.2 0.566613
\(709\) −28703.0 −1.52040 −0.760201 0.649688i \(-0.774900\pi\)
−0.760201 + 0.649688i \(0.774900\pi\)
\(710\) −56550.7 −2.98917
\(711\) 8054.99 0.424874
\(712\) −12988.0 −0.683633
\(713\) 13330.6 0.700189
\(714\) −21394.2 −1.12137
\(715\) −11746.3 −0.614388
\(716\) −21998.0 −1.14819
\(717\) −1945.44 −0.101330
\(718\) 34087.9 1.77180
\(719\) 35372.0 1.83471 0.917353 0.398075i \(-0.130322\pi\)
0.917353 + 0.398075i \(0.130322\pi\)
\(720\) 715.414 0.0370304
\(721\) −31161.8 −1.60961
\(722\) 9210.66 0.474772
\(723\) −21521.3 −1.10703
\(724\) −33126.2 −1.70045
\(725\) −39600.6 −2.02859
\(726\) −2015.76 −0.103047
\(727\) −38127.7 −1.94509 −0.972543 0.232724i \(-0.925236\pi\)
−0.972543 + 0.232724i \(0.925236\pi\)
\(728\) 44658.3 2.27356
\(729\) 16766.5 0.851828
\(730\) −90663.3 −4.59671
\(731\) −4061.63 −0.205506
\(732\) 17382.4 0.877693
\(733\) −9573.10 −0.482388 −0.241194 0.970477i \(-0.577539\pi\)
−0.241194 + 0.970477i \(0.577539\pi\)
\(734\) −36044.7 −1.81258
\(735\) −45996.5 −2.30831
\(736\) 16775.4 0.840151
\(737\) −10833.6 −0.541468
\(738\) −11963.6 −0.596727
\(739\) −8470.31 −0.421631 −0.210816 0.977526i \(-0.567612\pi\)
−0.210816 + 0.977526i \(0.567612\pi\)
\(740\) −65019.6 −3.22996
\(741\) −14902.0 −0.738783
\(742\) −14469.1 −0.715871
\(743\) 2325.07 0.114803 0.0574013 0.998351i \(-0.481719\pi\)
0.0574013 + 0.998351i \(0.481719\pi\)
\(744\) −11780.4 −0.580497
\(745\) 25.4376 0.00125096
\(746\) −47404.1 −2.32653
\(747\) −9302.67 −0.455645
\(748\) −5729.67 −0.280077
\(749\) 16114.8 0.786145
\(750\) 23464.1 1.14238
\(751\) 24549.9 1.19286 0.596431 0.802664i \(-0.296585\pi\)
0.596431 + 0.802664i \(0.296585\pi\)
\(752\) −1380.00 −0.0669195
\(753\) −6072.20 −0.293869
\(754\) −52907.7 −2.55542
\(755\) −26071.7 −1.25675
\(756\) −62700.3 −3.01639
\(757\) 9628.86 0.462308 0.231154 0.972917i \(-0.425750\pi\)
0.231154 + 0.972917i \(0.425750\pi\)
\(758\) 3725.99 0.178541
\(759\) −3837.05 −0.183499
\(760\) 29565.6 1.41113
\(761\) −34572.3 −1.64684 −0.823420 0.567433i \(-0.807937\pi\)
−0.823420 + 0.567433i \(0.807937\pi\)
\(762\) 6581.64 0.312897
\(763\) 56472.2 2.67947
\(764\) −10617.4 −0.502780
\(765\) 9967.58 0.471083
\(766\) 29248.5 1.37962
\(767\) −13249.7 −0.623755
\(768\) −15909.3 −0.747495
\(769\) −7895.86 −0.370263 −0.185131 0.982714i \(-0.559271\pi\)
−0.185131 + 0.982714i \(0.559271\pi\)
\(770\) −29553.9 −1.38318
\(771\) 2447.07 0.114305
\(772\) −36708.3 −1.71135
\(773\) 2264.52 0.105368 0.0526838 0.998611i \(-0.483222\pi\)
0.0526838 + 0.998611i \(0.483222\pi\)
\(774\) −6499.51 −0.301835
\(775\) 28105.4 1.30268
\(776\) 8774.32 0.405902
\(777\) 32109.7 1.48254
\(778\) 45125.6 2.07948
\(779\) −13102.1 −0.602607
\(780\) 50739.7 2.32919
\(781\) 7479.35 0.342679
\(782\) −17565.9 −0.803266
\(783\) 28927.4 1.32028
\(784\) 1998.90 0.0910576
\(785\) −24587.2 −1.11791
\(786\) −2182.35 −0.0990356
\(787\) −12234.3 −0.554135 −0.277068 0.960850i \(-0.589363\pi\)
−0.277068 + 0.960850i \(0.589363\pi\)
\(788\) −59170.8 −2.67496
\(789\) −25273.3 −1.14037
\(790\) −48376.0 −2.17866
\(791\) −63061.7 −2.83466
\(792\) −3570.54 −0.160194
\(793\) −21576.4 −0.966205
\(794\) 51897.1 2.31960
\(795\) −6401.89 −0.285600
\(796\) 70596.5 3.14350
\(797\) −34297.0 −1.52429 −0.762147 0.647404i \(-0.775855\pi\)
−0.762147 + 0.647404i \(0.775855\pi\)
\(798\) −37493.6 −1.66323
\(799\) −19227.0 −0.851317
\(800\) 35368.2 1.56307
\(801\) −7673.72 −0.338499
\(802\) 50541.1 2.22527
\(803\) 11991.1 0.526968
\(804\) 46797.2 2.05275
\(805\) −56256.5 −2.46308
\(806\) 37549.8 1.64098
\(807\) −15208.7 −0.663412
\(808\) −10177.3 −0.443114
\(809\) −13392.4 −0.582016 −0.291008 0.956721i \(-0.593991\pi\)
−0.291008 + 0.956721i \(0.593991\pi\)
\(810\) −13582.6 −0.589188
\(811\) −17875.0 −0.773953 −0.386976 0.922090i \(-0.626481\pi\)
−0.386976 + 0.922090i \(0.626481\pi\)
\(812\) −82651.5 −3.57204
\(813\) 4014.87 0.173195
\(814\) 13850.1 0.596369
\(815\) 7004.52 0.301052
\(816\) 411.367 0.0176480
\(817\) −7118.04 −0.304809
\(818\) 17838.4 0.762474
\(819\) 26385.5 1.12574
\(820\) 44611.2 1.89987
\(821\) 27091.3 1.15163 0.575817 0.817579i \(-0.304684\pi\)
0.575817 + 0.817579i \(0.304684\pi\)
\(822\) −40379.1 −1.71336
\(823\) 9454.93 0.400459 0.200230 0.979749i \(-0.435831\pi\)
0.200230 + 0.979749i \(0.435831\pi\)
\(824\) 22610.3 0.955906
\(825\) −8089.79 −0.341394
\(826\) −33336.5 −1.40427
\(827\) 5966.77 0.250888 0.125444 0.992101i \(-0.459964\pi\)
0.125444 + 0.992101i \(0.459964\pi\)
\(828\) −17453.0 −0.732527
\(829\) 30513.2 1.27837 0.639183 0.769054i \(-0.279272\pi\)
0.639183 + 0.769054i \(0.279272\pi\)
\(830\) 55869.2 2.33644
\(831\) −20641.1 −0.861650
\(832\) 48599.5 2.02510
\(833\) 27849.8 1.15839
\(834\) 31726.5 1.31726
\(835\) −7544.08 −0.312663
\(836\) −10041.3 −0.415414
\(837\) −20530.4 −0.847830
\(838\) −22436.5 −0.924889
\(839\) 36892.3 1.51807 0.759037 0.651048i \(-0.225670\pi\)
0.759037 + 0.651048i \(0.225670\pi\)
\(840\) 49714.5 2.04204
\(841\) 13743.1 0.563494
\(842\) 17823.5 0.729498
\(843\) 32512.3 1.32833
\(844\) 51311.7 2.09268
\(845\) −23205.3 −0.944717
\(846\) −30767.5 −1.25036
\(847\) 3908.78 0.158568
\(848\) 278.211 0.0112663
\(849\) −8003.88 −0.323548
\(850\) −37034.7 −1.49445
\(851\) 26363.9 1.06198
\(852\) −32308.0 −1.29912
\(853\) −1880.79 −0.0754948 −0.0377474 0.999287i \(-0.512018\pi\)
−0.0377474 + 0.999287i \(0.512018\pi\)
\(854\) −54286.5 −2.17523
\(855\) 17468.3 0.698717
\(856\) −11692.5 −0.466872
\(857\) −29396.5 −1.17172 −0.585861 0.810412i \(-0.699243\pi\)
−0.585861 + 0.810412i \(0.699243\pi\)
\(858\) −10808.2 −0.430055
\(859\) 25201.3 1.00100 0.500499 0.865737i \(-0.333150\pi\)
0.500499 + 0.865737i \(0.333150\pi\)
\(860\) 24236.2 0.960984
\(861\) −22031.1 −0.872031
\(862\) −39845.6 −1.57442
\(863\) 4903.67 0.193422 0.0967108 0.995313i \(-0.469168\pi\)
0.0967108 + 0.995313i \(0.469168\pi\)
\(864\) −25835.8 −1.01730
\(865\) −3931.78 −0.154549
\(866\) 56284.4 2.20857
\(867\) −12085.6 −0.473412
\(868\) 58659.6 2.29382
\(869\) 6398.17 0.249762
\(870\) −58897.9 −2.29520
\(871\) −58088.5 −2.25976
\(872\) −40974.9 −1.59127
\(873\) 5184.14 0.200981
\(874\) −30784.4 −1.19141
\(875\) −45499.4 −1.75790
\(876\) −51796.8 −1.99778
\(877\) −18951.8 −0.729710 −0.364855 0.931064i \(-0.618881\pi\)
−0.364855 + 0.931064i \(0.618881\pi\)
\(878\) 65784.3 2.52860
\(879\) −15760.4 −0.604762
\(880\) 568.262 0.0217683
\(881\) 41138.9 1.57322 0.786609 0.617452i \(-0.211835\pi\)
0.786609 + 0.617452i \(0.211835\pi\)
\(882\) 44566.0 1.70138
\(883\) −21304.9 −0.811967 −0.405984 0.913880i \(-0.633071\pi\)
−0.405984 + 0.913880i \(0.633071\pi\)
\(884\) −30721.7 −1.16887
\(885\) −14749.8 −0.560238
\(886\) 13206.3 0.500760
\(887\) −8578.08 −0.324717 −0.162358 0.986732i \(-0.551910\pi\)
−0.162358 + 0.986732i \(0.551910\pi\)
\(888\) −23298.1 −0.880442
\(889\) −12762.5 −0.481486
\(890\) 46086.2 1.73574
\(891\) 1796.42 0.0675447
\(892\) −75155.1 −2.82105
\(893\) −33695.5 −1.26268
\(894\) 23.4061 0.000875635 0
\(895\) 30397.3 1.13527
\(896\) 77205.5 2.87863
\(897\) −20573.7 −0.765816
\(898\) 3339.58 0.124102
\(899\) −27063.1 −1.00401
\(900\) −36796.7 −1.36284
\(901\) 3876.20 0.143324
\(902\) −9502.79 −0.350785
\(903\) −11969.0 −0.441088
\(904\) 45756.1 1.68343
\(905\) 45774.4 1.68132
\(906\) −23989.6 −0.879692
\(907\) −4897.99 −0.179311 −0.0896556 0.995973i \(-0.528577\pi\)
−0.0896556 + 0.995973i \(0.528577\pi\)
\(908\) 4834.62 0.176699
\(909\) −6013.06 −0.219407
\(910\) −158464. −5.77256
\(911\) −5563.86 −0.202348 −0.101174 0.994869i \(-0.532260\pi\)
−0.101174 + 0.994869i \(0.532260\pi\)
\(912\) 720.926 0.0261757
\(913\) −7389.22 −0.267850
\(914\) 2175.17 0.0787181
\(915\) −24019.3 −0.867817
\(916\) 6937.12 0.250228
\(917\) 4231.82 0.152396
\(918\) 27053.1 0.972641
\(919\) −49598.3 −1.78030 −0.890150 0.455667i \(-0.849401\pi\)
−0.890150 + 0.455667i \(0.849401\pi\)
\(920\) 40818.4 1.46276
\(921\) 10317.9 0.369149
\(922\) 53065.4 1.89546
\(923\) 40103.2 1.43013
\(924\) −16884.4 −0.601144
\(925\) 55584.0 1.97577
\(926\) 69678.3 2.47275
\(927\) 13358.9 0.473314
\(928\) −34056.7 −1.20470
\(929\) −905.345 −0.0319735 −0.0159868 0.999872i \(-0.505089\pi\)
−0.0159868 + 0.999872i \(0.505089\pi\)
\(930\) 41801.1 1.47388
\(931\) 48807.2 1.71814
\(932\) −60697.9 −2.13329
\(933\) 3271.17 0.114784
\(934\) −662.475 −0.0232086
\(935\) 7917.36 0.276926
\(936\) −19144.7 −0.668552
\(937\) 22056.5 0.769002 0.384501 0.923125i \(-0.374374\pi\)
0.384501 + 0.923125i \(0.374374\pi\)
\(938\) −146151. −5.08743
\(939\) −27263.6 −0.947513
\(940\) 114730. 3.98092
\(941\) 18429.7 0.638460 0.319230 0.947677i \(-0.396576\pi\)
0.319230 + 0.947677i \(0.396576\pi\)
\(942\) −22623.7 −0.782504
\(943\) −18088.8 −0.624658
\(944\) 640.993 0.0221001
\(945\) 86640.4 2.98245
\(946\) −5162.63 −0.177433
\(947\) 23340.5 0.800912 0.400456 0.916316i \(-0.368852\pi\)
0.400456 + 0.916316i \(0.368852\pi\)
\(948\) −27637.7 −0.946866
\(949\) 64294.4 2.19925
\(950\) −64903.7 −2.21658
\(951\) −32732.3 −1.11611
\(952\) −30101.0 −1.02477
\(953\) 34053.3 1.15750 0.578748 0.815506i \(-0.303541\pi\)
0.578748 + 0.815506i \(0.303541\pi\)
\(954\) 6202.79 0.210506
\(955\) 14671.3 0.497123
\(956\) −7028.79 −0.237790
\(957\) 7789.79 0.263122
\(958\) −47328.7 −1.59616
\(959\) 78299.5 2.63652
\(960\) 54101.9 1.81889
\(961\) −10583.7 −0.355265
\(962\) 74262.1 2.48888
\(963\) −6908.31 −0.231171
\(964\) −77755.3 −2.59785
\(965\) 50724.2 1.69209
\(966\) −51763.8 −1.72409
\(967\) −3932.44 −0.130774 −0.0653871 0.997860i \(-0.520828\pi\)
−0.0653871 + 0.997860i \(0.520828\pi\)
\(968\) −2836.12 −0.0941697
\(969\) 10044.4 0.332995
\(970\) −31134.5 −1.03058
\(971\) −7261.24 −0.239984 −0.119992 0.992775i \(-0.538287\pi\)
−0.119992 + 0.992775i \(0.538287\pi\)
\(972\) 44645.8 1.47327
\(973\) −61521.0 −2.02700
\(974\) 94485.1 3.10832
\(975\) −43376.3 −1.42477
\(976\) 1043.82 0.0342335
\(977\) −32946.0 −1.07885 −0.539424 0.842034i \(-0.681358\pi\)
−0.539424 + 0.842034i \(0.681358\pi\)
\(978\) 6445.12 0.210728
\(979\) −6095.32 −0.198986
\(980\) −166183. −5.41686
\(981\) −24209.3 −0.787912
\(982\) 42601.9 1.38440
\(983\) −14071.9 −0.456585 −0.228293 0.973593i \(-0.573314\pi\)
−0.228293 + 0.973593i \(0.573314\pi\)
\(984\) 15985.3 0.517877
\(985\) 81763.2 2.64486
\(986\) 35661.4 1.15181
\(987\) −56658.9 −1.82723
\(988\) −53840.2 −1.73369
\(989\) −9827.20 −0.315962
\(990\) 12669.6 0.406732
\(991\) −22138.1 −0.709625 −0.354813 0.934937i \(-0.615455\pi\)
−0.354813 + 0.934937i \(0.615455\pi\)
\(992\) 24170.8 0.773611
\(993\) −32804.3 −1.04835
\(994\) 100900. 3.21968
\(995\) −97551.4 −3.10813
\(996\) 31918.6 1.01544
\(997\) 27681.9 0.879333 0.439667 0.898161i \(-0.355097\pi\)
0.439667 + 0.898161i \(0.355097\pi\)
\(998\) 56473.3 1.79121
\(999\) −40602.9 −1.28591
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 1441.4.a.a.1.10 77
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.4.a.a.1.10 77 1.1 even 1 trivial