Properties

Label 547.4.a.b.1.11
Level $547$
Weight $4$
Character 547.1
Self dual yes
Analytic conductor $32.274$
Analytic rank $0$
Dimension $71$
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] = [547,4,Mod(1,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("547.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 547.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: \(32.2740447731\)
Analytic rank: \(0\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 547.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.13291 q^{2} +8.01594 q^{3} +9.08096 q^{4} -4.43214 q^{5} -33.1292 q^{6} +17.8969 q^{7} -4.46750 q^{8} +37.2553 q^{9} +O(q^{10})\) \(q-4.13291 q^{2} +8.01594 q^{3} +9.08096 q^{4} -4.43214 q^{5} -33.1292 q^{6} +17.8969 q^{7} -4.46750 q^{8} +37.2553 q^{9} +18.3177 q^{10} +54.6583 q^{11} +72.7924 q^{12} +85.9516 q^{13} -73.9664 q^{14} -35.5278 q^{15} -54.1839 q^{16} +34.7132 q^{17} -153.973 q^{18} +7.75375 q^{19} -40.2481 q^{20} +143.461 q^{21} -225.898 q^{22} -13.5082 q^{23} -35.8112 q^{24} -105.356 q^{25} -355.230 q^{26} +82.2062 q^{27} +162.521 q^{28} +22.5537 q^{29} +146.833 q^{30} -192.016 q^{31} +259.677 q^{32} +438.137 q^{33} -143.467 q^{34} -79.3217 q^{35} +338.314 q^{36} +145.256 q^{37} -32.0455 q^{38} +688.983 q^{39} +19.8006 q^{40} +455.088 q^{41} -592.910 q^{42} -287.889 q^{43} +496.349 q^{44} -165.121 q^{45} +55.8281 q^{46} -339.202 q^{47} -434.335 q^{48} -22.7004 q^{49} +435.427 q^{50} +278.259 q^{51} +780.522 q^{52} +163.091 q^{53} -339.751 q^{54} -242.253 q^{55} -79.9545 q^{56} +62.1536 q^{57} -93.2122 q^{58} +63.0464 q^{59} -322.626 q^{60} -257.410 q^{61} +793.584 q^{62} +666.756 q^{63} -639.752 q^{64} -380.950 q^{65} -1810.78 q^{66} -488.364 q^{67} +315.229 q^{68} -108.281 q^{69} +327.830 q^{70} -298.165 q^{71} -166.438 q^{72} +512.834 q^{73} -600.330 q^{74} -844.528 q^{75} +70.4114 q^{76} +978.214 q^{77} -2847.50 q^{78} -371.381 q^{79} +240.151 q^{80} -346.934 q^{81} -1880.84 q^{82} -444.044 q^{83} +1302.76 q^{84} -153.854 q^{85} +1189.82 q^{86} +180.789 q^{87} -244.186 q^{88} +261.381 q^{89} +682.430 q^{90} +1538.27 q^{91} -122.667 q^{92} -1539.19 q^{93} +1401.89 q^{94} -34.3657 q^{95} +2081.56 q^{96} +267.187 q^{97} +93.8188 q^{98} +2036.31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.13291 −1.46120 −0.730602 0.682803i \(-0.760761\pi\)
−0.730602 + 0.682803i \(0.760761\pi\)
\(3\) 8.01594 1.54267 0.771334 0.636430i \(-0.219590\pi\)
0.771334 + 0.636430i \(0.219590\pi\)
\(4\) 9.08096 1.13512
\(5\) −4.43214 −0.396423 −0.198211 0.980159i \(-0.563513\pi\)
−0.198211 + 0.980159i \(0.563513\pi\)
\(6\) −33.1292 −2.25416
\(7\) 17.8969 0.966343 0.483171 0.875526i \(-0.339485\pi\)
0.483171 + 0.875526i \(0.339485\pi\)
\(8\) −4.46750 −0.197437
\(9\) 37.2553 1.37983
\(10\) 18.3177 0.579255
\(11\) 54.6583 1.49819 0.749095 0.662463i \(-0.230489\pi\)
0.749095 + 0.662463i \(0.230489\pi\)
\(12\) 72.7924 1.75111
\(13\) 85.9516 1.83374 0.916872 0.399181i \(-0.130706\pi\)
0.916872 + 0.399181i \(0.130706\pi\)
\(14\) −73.9664 −1.41202
\(15\) −35.5278 −0.611549
\(16\) −54.1839 −0.846623
\(17\) 34.7132 0.495247 0.247623 0.968856i \(-0.420350\pi\)
0.247623 + 0.968856i \(0.420350\pi\)
\(18\) −153.973 −2.01621
\(19\) 7.75375 0.0936227 0.0468114 0.998904i \(-0.485094\pi\)
0.0468114 + 0.998904i \(0.485094\pi\)
\(20\) −40.2481 −0.449987
\(21\) 143.461 1.49075
\(22\) −225.898 −2.18916
\(23\) −13.5082 −0.122463 −0.0612315 0.998124i \(-0.519503\pi\)
−0.0612315 + 0.998124i \(0.519503\pi\)
\(24\) −35.8112 −0.304581
\(25\) −105.356 −0.842849
\(26\) −355.230 −2.67948
\(27\) 82.2062 0.585948
\(28\) 162.521 1.09691
\(29\) 22.5537 0.144418 0.0722088 0.997390i \(-0.476995\pi\)
0.0722088 + 0.997390i \(0.476995\pi\)
\(30\) 146.833 0.893599
\(31\) −192.016 −1.11248 −0.556242 0.831020i \(-0.687757\pi\)
−0.556242 + 0.831020i \(0.687757\pi\)
\(32\) 259.677 1.43453
\(33\) 438.137 2.31121
\(34\) −143.467 −0.723657
\(35\) −79.3217 −0.383080
\(36\) 338.314 1.56627
\(37\) 145.256 0.645404 0.322702 0.946501i \(-0.395409\pi\)
0.322702 + 0.946501i \(0.395409\pi\)
\(38\) −32.0455 −0.136802
\(39\) 688.983 2.82886
\(40\) 19.8006 0.0782687
\(41\) 455.088 1.73348 0.866742 0.498756i \(-0.166210\pi\)
0.866742 + 0.498756i \(0.166210\pi\)
\(42\) −592.910 −2.17829
\(43\) −287.889 −1.02099 −0.510497 0.859880i \(-0.670539\pi\)
−0.510497 + 0.859880i \(0.670539\pi\)
\(44\) 496.349 1.70062
\(45\) −165.121 −0.546995
\(46\) 55.8281 0.178943
\(47\) −339.202 −1.05272 −0.526359 0.850263i \(-0.676443\pi\)
−0.526359 + 0.850263i \(0.676443\pi\)
\(48\) −434.335 −1.30606
\(49\) −22.7004 −0.0661820
\(50\) 435.427 1.23157
\(51\) 278.259 0.764002
\(52\) 780.522 2.08152
\(53\) 163.091 0.422686 0.211343 0.977412i \(-0.432216\pi\)
0.211343 + 0.977412i \(0.432216\pi\)
\(54\) −339.751 −0.856189
\(55\) −242.253 −0.593917
\(56\) −79.9545 −0.190792
\(57\) 62.1536 0.144429
\(58\) −93.2122 −0.211024
\(59\) 63.0464 0.139118 0.0695588 0.997578i \(-0.477841\pi\)
0.0695588 + 0.997578i \(0.477841\pi\)
\(60\) −322.626 −0.694182
\(61\) −257.410 −0.540295 −0.270147 0.962819i \(-0.587072\pi\)
−0.270147 + 0.962819i \(0.587072\pi\)
\(62\) 793.584 1.62557
\(63\) 666.756 1.33339
\(64\) −639.752 −1.24952
\(65\) −380.950 −0.726938
\(66\) −1810.78 −3.37715
\(67\) −488.364 −0.890495 −0.445247 0.895408i \(-0.646884\pi\)
−0.445247 + 0.895408i \(0.646884\pi\)
\(68\) 315.229 0.562164
\(69\) −108.281 −0.188920
\(70\) 327.830 0.559759
\(71\) −298.165 −0.498389 −0.249195 0.968453i \(-0.580166\pi\)
−0.249195 + 0.968453i \(0.580166\pi\)
\(72\) −166.438 −0.272430
\(73\) 512.834 0.822229 0.411114 0.911584i \(-0.365140\pi\)
0.411114 + 0.911584i \(0.365140\pi\)
\(74\) −600.330 −0.943067
\(75\) −844.528 −1.30024
\(76\) 70.4114 0.106273
\(77\) 978.214 1.44776
\(78\) −2847.50 −4.13354
\(79\) −371.381 −0.528907 −0.264454 0.964398i \(-0.585192\pi\)
−0.264454 + 0.964398i \(0.585192\pi\)
\(80\) 240.151 0.335621
\(81\) −346.934 −0.475904
\(82\) −1880.84 −2.53298
\(83\) −444.044 −0.587231 −0.293615 0.955924i \(-0.594858\pi\)
−0.293615 + 0.955924i \(0.594858\pi\)
\(84\) 1302.76 1.69218
\(85\) −153.854 −0.196327
\(86\) 1189.82 1.49188
\(87\) 180.789 0.222788
\(88\) −244.186 −0.295799
\(89\) 261.381 0.311307 0.155653 0.987812i \(-0.450252\pi\)
0.155653 + 0.987812i \(0.450252\pi\)
\(90\) 682.430 0.799272
\(91\) 1538.27 1.77203
\(92\) −122.667 −0.139010
\(93\) −1539.19 −1.71620
\(94\) 1401.89 1.53824
\(95\) −34.3657 −0.0371142
\(96\) 2081.56 2.21300
\(97\) 267.187 0.279678 0.139839 0.990174i \(-0.455341\pi\)
0.139839 + 0.990174i \(0.455341\pi\)
\(98\) 93.8188 0.0967054
\(99\) 2036.31 2.06724
\(100\) −956.734 −0.956734
\(101\) 1716.53 1.69110 0.845552 0.533893i \(-0.179271\pi\)
0.845552 + 0.533893i \(0.179271\pi\)
\(102\) −1150.02 −1.11636
\(103\) −156.424 −0.149640 −0.0748200 0.997197i \(-0.523838\pi\)
−0.0748200 + 0.997197i \(0.523838\pi\)
\(104\) −383.989 −0.362050
\(105\) −635.838 −0.590966
\(106\) −674.043 −0.617630
\(107\) 540.532 0.488366 0.244183 0.969729i \(-0.421480\pi\)
0.244183 + 0.969729i \(0.421480\pi\)
\(108\) 746.511 0.665121
\(109\) 1635.85 1.43749 0.718745 0.695274i \(-0.244717\pi\)
0.718745 + 0.695274i \(0.244717\pi\)
\(110\) 1001.21 0.867834
\(111\) 1164.36 0.995645
\(112\) −969.724 −0.818128
\(113\) 1058.53 0.881222 0.440611 0.897698i \(-0.354762\pi\)
0.440611 + 0.897698i \(0.354762\pi\)
\(114\) −256.875 −0.211040
\(115\) 59.8701 0.0485471
\(116\) 204.809 0.163931
\(117\) 3202.15 2.53025
\(118\) −260.565 −0.203279
\(119\) 621.260 0.478578
\(120\) 158.720 0.120743
\(121\) 1656.52 1.24457
\(122\) 1063.85 0.789481
\(123\) 3647.96 2.67419
\(124\) −1743.69 −1.26280
\(125\) 1020.97 0.730548
\(126\) −2755.64 −1.94835
\(127\) −1020.54 −0.713059 −0.356530 0.934284i \(-0.616040\pi\)
−0.356530 + 0.934284i \(0.616040\pi\)
\(128\) 566.620 0.391270
\(129\) −2307.71 −1.57506
\(130\) 1574.43 1.06221
\(131\) −2641.60 −1.76181 −0.880907 0.473289i \(-0.843067\pi\)
−0.880907 + 0.473289i \(0.843067\pi\)
\(132\) 3978.71 2.62350
\(133\) 138.768 0.0904716
\(134\) 2018.36 1.30120
\(135\) −364.349 −0.232283
\(136\) −155.081 −0.0977803
\(137\) −2542.74 −1.58570 −0.792849 0.609418i \(-0.791403\pi\)
−0.792849 + 0.609418i \(0.791403\pi\)
\(138\) 447.515 0.276050
\(139\) 968.563 0.591025 0.295512 0.955339i \(-0.404510\pi\)
0.295512 + 0.955339i \(0.404510\pi\)
\(140\) −720.317 −0.434842
\(141\) −2719.02 −1.62399
\(142\) 1232.29 0.728249
\(143\) 4697.96 2.74730
\(144\) −2018.64 −1.16819
\(145\) −99.9610 −0.0572504
\(146\) −2119.50 −1.20144
\(147\) −181.965 −0.102097
\(148\) 1319.06 0.732611
\(149\) 1314.64 0.722818 0.361409 0.932407i \(-0.382296\pi\)
0.361409 + 0.932407i \(0.382296\pi\)
\(150\) 3490.36 1.89991
\(151\) 302.259 0.162897 0.0814486 0.996678i \(-0.474045\pi\)
0.0814486 + 0.996678i \(0.474045\pi\)
\(152\) −34.6399 −0.0184846
\(153\) 1293.25 0.683355
\(154\) −4042.87 −2.11548
\(155\) 851.041 0.441015
\(156\) 6256.62 3.21109
\(157\) −3444.31 −1.75087 −0.875434 0.483338i \(-0.839424\pi\)
−0.875434 + 0.483338i \(0.839424\pi\)
\(158\) 1534.89 0.772842
\(159\) 1307.33 0.652064
\(160\) −1150.93 −0.568679
\(161\) −241.755 −0.118341
\(162\) 1433.85 0.695393
\(163\) −3457.41 −1.66138 −0.830691 0.556733i \(-0.812055\pi\)
−0.830691 + 0.556733i \(0.812055\pi\)
\(164\) 4132.64 1.96771
\(165\) −1941.89 −0.916217
\(166\) 1835.19 0.858064
\(167\) 3672.32 1.70163 0.850817 0.525462i \(-0.176107\pi\)
0.850817 + 0.525462i \(0.176107\pi\)
\(168\) −640.910 −0.294329
\(169\) 5190.67 2.36262
\(170\) 635.865 0.286874
\(171\) 288.868 0.129183
\(172\) −2614.31 −1.15895
\(173\) 1001.42 0.440094 0.220047 0.975489i \(-0.429379\pi\)
0.220047 + 0.975489i \(0.429379\pi\)
\(174\) −747.184 −0.325539
\(175\) −1885.55 −0.814481
\(176\) −2961.60 −1.26840
\(177\) 505.376 0.214612
\(178\) −1080.26 −0.454883
\(179\) 2549.94 1.06476 0.532378 0.846507i \(-0.321298\pi\)
0.532378 + 0.846507i \(0.321298\pi\)
\(180\) −1499.46 −0.620905
\(181\) 820.681 0.337020 0.168510 0.985700i \(-0.446104\pi\)
0.168510 + 0.985700i \(0.446104\pi\)
\(182\) −6357.52 −2.58929
\(183\) −2063.38 −0.833496
\(184\) 60.3477 0.0241788
\(185\) −643.796 −0.255853
\(186\) 6361.32 2.50771
\(187\) 1897.36 0.741973
\(188\) −3080.28 −1.19496
\(189\) 1471.24 0.566226
\(190\) 142.030 0.0542314
\(191\) −4354.94 −1.64980 −0.824902 0.565276i \(-0.808770\pi\)
−0.824902 + 0.565276i \(0.808770\pi\)
\(192\) −5128.21 −1.92759
\(193\) −1466.15 −0.546816 −0.273408 0.961898i \(-0.588151\pi\)
−0.273408 + 0.961898i \(0.588151\pi\)
\(194\) −1104.26 −0.408667
\(195\) −3053.67 −1.12142
\(196\) −206.142 −0.0751245
\(197\) 712.470 0.257672 0.128836 0.991666i \(-0.458876\pi\)
0.128836 + 0.991666i \(0.458876\pi\)
\(198\) −8415.90 −3.02066
\(199\) 860.619 0.306571 0.153286 0.988182i \(-0.451015\pi\)
0.153286 + 0.988182i \(0.451015\pi\)
\(200\) 470.678 0.166410
\(201\) −3914.70 −1.37374
\(202\) −7094.28 −2.47105
\(203\) 403.641 0.139557
\(204\) 2526.86 0.867233
\(205\) −2017.02 −0.687193
\(206\) 646.487 0.218655
\(207\) −503.251 −0.168978
\(208\) −4657.19 −1.55249
\(209\) 423.806 0.140265
\(210\) 2627.86 0.863523
\(211\) 2090.15 0.681952 0.340976 0.940072i \(-0.389242\pi\)
0.340976 + 0.940072i \(0.389242\pi\)
\(212\) 1481.03 0.479799
\(213\) −2390.07 −0.768849
\(214\) −2233.97 −0.713603
\(215\) 1275.97 0.404745
\(216\) −367.256 −0.115688
\(217\) −3436.49 −1.07504
\(218\) −6760.84 −2.10047
\(219\) 4110.85 1.26843
\(220\) −2199.89 −0.674166
\(221\) 2983.66 0.908156
\(222\) −4812.21 −1.45484
\(223\) −63.0624 −0.0189371 −0.00946854 0.999955i \(-0.503014\pi\)
−0.00946854 + 0.999955i \(0.503014\pi\)
\(224\) 4647.42 1.38624
\(225\) −3925.08 −1.16299
\(226\) −4374.81 −1.28765
\(227\) 2042.66 0.597252 0.298626 0.954370i \(-0.403472\pi\)
0.298626 + 0.954370i \(0.403472\pi\)
\(228\) 564.414 0.163944
\(229\) 1044.91 0.301526 0.150763 0.988570i \(-0.451827\pi\)
0.150763 + 0.988570i \(0.451827\pi\)
\(230\) −247.438 −0.0709373
\(231\) 7841.31 2.23342
\(232\) −100.758 −0.0285134
\(233\) 3215.45 0.904083 0.452041 0.891997i \(-0.350696\pi\)
0.452041 + 0.891997i \(0.350696\pi\)
\(234\) −13234.2 −3.69721
\(235\) 1503.39 0.417321
\(236\) 572.522 0.157915
\(237\) −2976.97 −0.815928
\(238\) −2567.61 −0.699301
\(239\) 1090.37 0.295105 0.147553 0.989054i \(-0.452860\pi\)
0.147553 + 0.989054i \(0.452860\pi\)
\(240\) 1925.03 0.517752
\(241\) 575.585 0.153845 0.0769225 0.997037i \(-0.475491\pi\)
0.0769225 + 0.997037i \(0.475491\pi\)
\(242\) −6846.27 −1.81857
\(243\) −5000.57 −1.32011
\(244\) −2337.53 −0.613299
\(245\) 100.612 0.0262361
\(246\) −15076.7 −3.90754
\(247\) 666.447 0.171680
\(248\) 857.830 0.219646
\(249\) −3559.43 −0.905903
\(250\) −4219.58 −1.06748
\(251\) −6966.67 −1.75192 −0.875960 0.482383i \(-0.839771\pi\)
−0.875960 + 0.482383i \(0.839771\pi\)
\(252\) 6054.78 1.51355
\(253\) −738.333 −0.183473
\(254\) 4217.81 1.04193
\(255\) −1233.28 −0.302868
\(256\) 2776.22 0.677789
\(257\) −3245.89 −0.787834 −0.393917 0.919146i \(-0.628880\pi\)
−0.393917 + 0.919146i \(0.628880\pi\)
\(258\) 9537.54 2.30148
\(259\) 2599.64 0.623681
\(260\) −3459.39 −0.825162
\(261\) 840.244 0.199271
\(262\) 10917.5 2.57437
\(263\) 7790.93 1.82665 0.913326 0.407229i \(-0.133505\pi\)
0.913326 + 0.407229i \(0.133505\pi\)
\(264\) −1957.38 −0.456319
\(265\) −722.845 −0.167562
\(266\) −573.516 −0.132198
\(267\) 2095.21 0.480243
\(268\) −4434.81 −1.01082
\(269\) −6258.67 −1.41858 −0.709289 0.704918i \(-0.750984\pi\)
−0.709289 + 0.704918i \(0.750984\pi\)
\(270\) 1505.82 0.339413
\(271\) −4577.50 −1.02606 −0.513032 0.858369i \(-0.671478\pi\)
−0.513032 + 0.858369i \(0.671478\pi\)
\(272\) −1880.90 −0.419287
\(273\) 12330.7 2.73365
\(274\) 10508.9 2.31703
\(275\) −5758.58 −1.26275
\(276\) −983.292 −0.214447
\(277\) 1188.20 0.257733 0.128866 0.991662i \(-0.458866\pi\)
0.128866 + 0.991662i \(0.458866\pi\)
\(278\) −4002.99 −0.863608
\(279\) −7153.61 −1.53504
\(280\) 354.370 0.0756344
\(281\) 5759.46 1.22271 0.611354 0.791358i \(-0.290625\pi\)
0.611354 + 0.791358i \(0.290625\pi\)
\(282\) 11237.5 2.37299
\(283\) −3166.41 −0.665102 −0.332551 0.943085i \(-0.607909\pi\)
−0.332551 + 0.943085i \(0.607909\pi\)
\(284\) −2707.62 −0.565731
\(285\) −275.474 −0.0572549
\(286\) −19416.3 −4.01436
\(287\) 8144.68 1.67514
\(288\) 9674.36 1.97940
\(289\) −3707.99 −0.754731
\(290\) 413.130 0.0836546
\(291\) 2141.76 0.431451
\(292\) 4657.03 0.933328
\(293\) −8113.37 −1.61771 −0.808853 0.588011i \(-0.799911\pi\)
−0.808853 + 0.588011i \(0.799911\pi\)
\(294\) 752.046 0.149184
\(295\) −279.431 −0.0551494
\(296\) −648.931 −0.127427
\(297\) 4493.25 0.877860
\(298\) −5433.31 −1.05619
\(299\) −1161.05 −0.224566
\(300\) −7669.13 −1.47592
\(301\) −5152.33 −0.986630
\(302\) −1249.21 −0.238026
\(303\) 13759.6 2.60881
\(304\) −420.128 −0.0792631
\(305\) 1140.88 0.214185
\(306\) −5344.90 −0.998522
\(307\) 257.041 0.0477853 0.0238926 0.999715i \(-0.492394\pi\)
0.0238926 + 0.999715i \(0.492394\pi\)
\(308\) 8883.12 1.64339
\(309\) −1253.89 −0.230845
\(310\) −3517.28 −0.644413
\(311\) 1137.07 0.207322 0.103661 0.994613i \(-0.466944\pi\)
0.103661 + 0.994613i \(0.466944\pi\)
\(312\) −3078.03 −0.558523
\(313\) 6607.47 1.19321 0.596607 0.802533i \(-0.296515\pi\)
0.596607 + 0.802533i \(0.296515\pi\)
\(314\) 14235.0 2.55838
\(315\) −2955.16 −0.528585
\(316\) −3372.50 −0.600373
\(317\) 2277.77 0.403571 0.201786 0.979430i \(-0.435326\pi\)
0.201786 + 0.979430i \(0.435326\pi\)
\(318\) −5403.09 −0.952799
\(319\) 1232.74 0.216365
\(320\) 2835.47 0.495336
\(321\) 4332.87 0.753387
\(322\) 999.150 0.172921
\(323\) 269.158 0.0463663
\(324\) −3150.49 −0.540208
\(325\) −9055.52 −1.54557
\(326\) 14289.2 2.42762
\(327\) 13112.9 2.21757
\(328\) −2033.11 −0.342255
\(329\) −6070.67 −1.01729
\(330\) 8025.65 1.33878
\(331\) −5412.68 −0.898814 −0.449407 0.893327i \(-0.648365\pi\)
−0.449407 + 0.893327i \(0.648365\pi\)
\(332\) −4032.34 −0.666577
\(333\) 5411.56 0.890546
\(334\) −15177.4 −2.48644
\(335\) 2164.50 0.353013
\(336\) −7773.25 −1.26210
\(337\) −4295.39 −0.694316 −0.347158 0.937807i \(-0.612853\pi\)
−0.347158 + 0.937807i \(0.612853\pi\)
\(338\) −21452.6 −3.45227
\(339\) 8485.11 1.35943
\(340\) −1397.14 −0.222855
\(341\) −10495.2 −1.66671
\(342\) −1193.87 −0.188763
\(343\) −6544.91 −1.03030
\(344\) 1286.15 0.201582
\(345\) 479.916 0.0748921
\(346\) −4138.76 −0.643067
\(347\) 2284.59 0.353439 0.176719 0.984261i \(-0.443452\pi\)
0.176719 + 0.984261i \(0.443452\pi\)
\(348\) 1641.74 0.252891
\(349\) −6204.33 −0.951605 −0.475802 0.879552i \(-0.657842\pi\)
−0.475802 + 0.879552i \(0.657842\pi\)
\(350\) 7792.81 1.19012
\(351\) 7065.75 1.07448
\(352\) 14193.5 2.14919
\(353\) −6615.29 −0.997440 −0.498720 0.866763i \(-0.666196\pi\)
−0.498720 + 0.866763i \(0.666196\pi\)
\(354\) −2088.68 −0.313593
\(355\) 1321.51 0.197573
\(356\) 2373.59 0.353370
\(357\) 4979.98 0.738287
\(358\) −10538.7 −1.55583
\(359\) 3926.62 0.577267 0.288634 0.957440i \(-0.406799\pi\)
0.288634 + 0.957440i \(0.406799\pi\)
\(360\) 737.678 0.107997
\(361\) −6798.88 −0.991235
\(362\) −3391.80 −0.492456
\(363\) 13278.6 1.91996
\(364\) 13968.9 2.01146
\(365\) −2272.95 −0.325950
\(366\) 8527.78 1.21791
\(367\) 3312.85 0.471197 0.235598 0.971851i \(-0.424295\pi\)
0.235598 + 0.971851i \(0.424295\pi\)
\(368\) 731.925 0.103680
\(369\) 16954.5 2.39191
\(370\) 2660.75 0.373854
\(371\) 2918.83 0.408459
\(372\) −13977.3 −1.94809
\(373\) −8350.37 −1.15916 −0.579579 0.814916i \(-0.696783\pi\)
−0.579579 + 0.814916i \(0.696783\pi\)
\(374\) −7841.64 −1.08418
\(375\) 8184.05 1.12699
\(376\) 1515.39 0.207846
\(377\) 1938.52 0.264825
\(378\) −6080.49 −0.827372
\(379\) 3866.52 0.524036 0.262018 0.965063i \(-0.415612\pi\)
0.262018 + 0.965063i \(0.415612\pi\)
\(380\) −312.074 −0.0421290
\(381\) −8180.61 −1.10001
\(382\) 17998.6 2.41070
\(383\) 460.086 0.0613820 0.0306910 0.999529i \(-0.490229\pi\)
0.0306910 + 0.999529i \(0.490229\pi\)
\(384\) 4541.99 0.603600
\(385\) −4335.59 −0.573927
\(386\) 6059.46 0.799011
\(387\) −10725.4 −1.40879
\(388\) 2426.32 0.317468
\(389\) 13981.6 1.82235 0.911175 0.412019i \(-0.135176\pi\)
0.911175 + 0.412019i \(0.135176\pi\)
\(390\) 12620.5 1.63863
\(391\) −468.912 −0.0606494
\(392\) 101.414 0.0130668
\(393\) −21174.9 −2.71790
\(394\) −2944.58 −0.376512
\(395\) 1646.01 0.209671
\(396\) 18491.7 2.34657
\(397\) −7238.31 −0.915064 −0.457532 0.889193i \(-0.651266\pi\)
−0.457532 + 0.889193i \(0.651266\pi\)
\(398\) −3556.86 −0.447963
\(399\) 1112.36 0.139568
\(400\) 5708.60 0.713575
\(401\) 4187.60 0.521493 0.260747 0.965407i \(-0.416031\pi\)
0.260747 + 0.965407i \(0.416031\pi\)
\(402\) 16179.1 2.00731
\(403\) −16504.0 −2.04001
\(404\) 15587.8 1.91961
\(405\) 1537.66 0.188659
\(406\) −1668.21 −0.203921
\(407\) 7939.44 0.966937
\(408\) −1243.12 −0.150843
\(409\) 9828.49 1.18823 0.594117 0.804379i \(-0.297502\pi\)
0.594117 + 0.804379i \(0.297502\pi\)
\(410\) 8336.15 1.00413
\(411\) −20382.4 −2.44621
\(412\) −1420.48 −0.169859
\(413\) 1128.34 0.134435
\(414\) 2079.89 0.246911
\(415\) 1968.07 0.232792
\(416\) 22319.7 2.63056
\(417\) 7763.95 0.911755
\(418\) −1751.55 −0.204955
\(419\) −1703.49 −0.198618 −0.0993092 0.995057i \(-0.531663\pi\)
−0.0993092 + 0.995057i \(0.531663\pi\)
\(420\) −5774.02 −0.670817
\(421\) −1139.44 −0.131907 −0.0659536 0.997823i \(-0.521009\pi\)
−0.0659536 + 0.997823i \(0.521009\pi\)
\(422\) −8638.41 −0.996472
\(423\) −12637.1 −1.45257
\(424\) −728.611 −0.0834540
\(425\) −3657.25 −0.417418
\(426\) 9877.95 1.12345
\(427\) −4606.84 −0.522110
\(428\) 4908.54 0.554354
\(429\) 37658.6 4.23817
\(430\) −5273.46 −0.591416
\(431\) −8359.34 −0.934235 −0.467118 0.884195i \(-0.654708\pi\)
−0.467118 + 0.884195i \(0.654708\pi\)
\(432\) −4454.25 −0.496077
\(433\) −4342.97 −0.482009 −0.241004 0.970524i \(-0.577477\pi\)
−0.241004 + 0.970524i \(0.577477\pi\)
\(434\) 14202.7 1.57086
\(435\) −801.282 −0.0883184
\(436\) 14855.1 1.63172
\(437\) −104.739 −0.0114653
\(438\) −16989.8 −1.85343
\(439\) 14668.0 1.59469 0.797343 0.603527i \(-0.206238\pi\)
0.797343 + 0.603527i \(0.206238\pi\)
\(440\) 1082.27 0.117261
\(441\) −845.712 −0.0913197
\(442\) −12331.2 −1.32700
\(443\) −15972.8 −1.71308 −0.856538 0.516084i \(-0.827389\pi\)
−0.856538 + 0.516084i \(0.827389\pi\)
\(444\) 10573.5 1.13018
\(445\) −1158.48 −0.123409
\(446\) 260.631 0.0276710
\(447\) 10538.1 1.11507
\(448\) −11449.6 −1.20746
\(449\) 10764.5 1.13142 0.565711 0.824604i \(-0.308602\pi\)
0.565711 + 0.824604i \(0.308602\pi\)
\(450\) 16222.0 1.69936
\(451\) 24874.3 2.59709
\(452\) 9612.46 1.00029
\(453\) 2422.89 0.251296
\(454\) −8442.14 −0.872707
\(455\) −6817.82 −0.702471
\(456\) −277.671 −0.0285157
\(457\) 3048.91 0.312083 0.156042 0.987750i \(-0.450127\pi\)
0.156042 + 0.987750i \(0.450127\pi\)
\(458\) −4318.52 −0.440592
\(459\) 2853.64 0.290189
\(460\) 543.678 0.0551068
\(461\) −10219.5 −1.03247 −0.516237 0.856446i \(-0.672667\pi\)
−0.516237 + 0.856446i \(0.672667\pi\)
\(462\) −32407.4 −3.26349
\(463\) −10323.3 −1.03621 −0.518103 0.855318i \(-0.673362\pi\)
−0.518103 + 0.855318i \(0.673362\pi\)
\(464\) −1222.04 −0.122267
\(465\) 6821.90 0.680339
\(466\) −13289.2 −1.32105
\(467\) 3566.38 0.353388 0.176694 0.984266i \(-0.443460\pi\)
0.176694 + 0.984266i \(0.443460\pi\)
\(468\) 29078.6 2.87214
\(469\) −8740.21 −0.860523
\(470\) −6213.39 −0.609792
\(471\) −27609.4 −2.70101
\(472\) −281.660 −0.0274670
\(473\) −15735.5 −1.52964
\(474\) 12303.6 1.19224
\(475\) −816.905 −0.0789098
\(476\) 5641.63 0.543243
\(477\) 6076.03 0.583233
\(478\) −4506.40 −0.431209
\(479\) −15365.2 −1.46567 −0.732834 0.680407i \(-0.761803\pi\)
−0.732834 + 0.680407i \(0.761803\pi\)
\(480\) −9225.76 −0.877284
\(481\) 12485.0 1.18351
\(482\) −2378.84 −0.224799
\(483\) −1937.89 −0.182561
\(484\) 15042.8 1.41274
\(485\) −1184.21 −0.110871
\(486\) 20666.9 1.92895
\(487\) 12202.4 1.13540 0.567702 0.823234i \(-0.307833\pi\)
0.567702 + 0.823234i \(0.307833\pi\)
\(488\) 1149.98 0.106674
\(489\) −27714.4 −2.56296
\(490\) −415.818 −0.0383363
\(491\) −7775.84 −0.714702 −0.357351 0.933970i \(-0.616320\pi\)
−0.357351 + 0.933970i \(0.616320\pi\)
\(492\) 33127.0 3.03553
\(493\) 782.910 0.0715223
\(494\) −2754.36 −0.250860
\(495\) −9025.22 −0.819502
\(496\) 10404.2 0.941855
\(497\) −5336.23 −0.481615
\(498\) 14710.8 1.32371
\(499\) −10285.6 −0.922738 −0.461369 0.887208i \(-0.652642\pi\)
−0.461369 + 0.887208i \(0.652642\pi\)
\(500\) 9271.40 0.829259
\(501\) 29437.1 2.62506
\(502\) 28792.6 2.55992
\(503\) −16257.7 −1.44114 −0.720572 0.693380i \(-0.756121\pi\)
−0.720572 + 0.693380i \(0.756121\pi\)
\(504\) −2978.73 −0.263260
\(505\) −7607.93 −0.670393
\(506\) 3051.46 0.268091
\(507\) 41608.1 3.64474
\(508\) −9267.51 −0.809408
\(509\) 17537.6 1.52720 0.763598 0.645692i \(-0.223431\pi\)
0.763598 + 0.645692i \(0.223431\pi\)
\(510\) 5097.06 0.442552
\(511\) 9178.15 0.794555
\(512\) −16006.8 −1.38166
\(513\) 637.406 0.0548580
\(514\) 13415.0 1.15119
\(515\) 693.294 0.0593207
\(516\) −20956.2 −1.78788
\(517\) −18540.2 −1.57717
\(518\) −10744.1 −0.911326
\(519\) 8027.29 0.678919
\(520\) 1701.89 0.143525
\(521\) 982.730 0.0826376 0.0413188 0.999146i \(-0.486844\pi\)
0.0413188 + 0.999146i \(0.486844\pi\)
\(522\) −3472.65 −0.291176
\(523\) 6047.59 0.505626 0.252813 0.967515i \(-0.418644\pi\)
0.252813 + 0.967515i \(0.418644\pi\)
\(524\) −23988.3 −1.99987
\(525\) −15114.5 −1.25647
\(526\) −32199.2 −2.66911
\(527\) −6665.48 −0.550955
\(528\) −23740.0 −1.95672
\(529\) −11984.5 −0.985003
\(530\) 2987.45 0.244843
\(531\) 2348.81 0.191958
\(532\) 1260.15 0.102696
\(533\) 39115.6 3.17877
\(534\) −8659.33 −0.701734
\(535\) −2395.71 −0.193599
\(536\) 2181.77 0.175817
\(537\) 20440.2 1.64257
\(538\) 25866.5 2.07283
\(539\) −1240.77 −0.0991531
\(540\) −3308.64 −0.263669
\(541\) −21044.1 −1.67238 −0.836191 0.548439i \(-0.815222\pi\)
−0.836191 + 0.548439i \(0.815222\pi\)
\(542\) 18918.4 1.49929
\(543\) 6578.53 0.519911
\(544\) 9014.23 0.710445
\(545\) −7250.34 −0.569854
\(546\) −50961.6 −3.99442
\(547\) −547.000 −0.0427569
\(548\) −23090.5 −1.79996
\(549\) −9589.89 −0.745513
\(550\) 23799.7 1.84513
\(551\) 174.875 0.0135208
\(552\) 483.744 0.0372998
\(553\) −6646.58 −0.511105
\(554\) −4910.73 −0.376601
\(555\) −5160.63 −0.394696
\(556\) 8795.48 0.670884
\(557\) −21175.6 −1.61084 −0.805420 0.592704i \(-0.798060\pi\)
−0.805420 + 0.592704i \(0.798060\pi\)
\(558\) 29565.2 2.24300
\(559\) −24744.5 −1.87224
\(560\) 4297.96 0.324325
\(561\) 15209.2 1.14462
\(562\) −23803.3 −1.78663
\(563\) 13176.6 0.986371 0.493186 0.869924i \(-0.335832\pi\)
0.493186 + 0.869924i \(0.335832\pi\)
\(564\) −24691.3 −1.84343
\(565\) −4691.55 −0.349337
\(566\) 13086.5 0.971850
\(567\) −6209.05 −0.459886
\(568\) 1332.05 0.0984007
\(569\) −2414.54 −0.177896 −0.0889478 0.996036i \(-0.528350\pi\)
−0.0889478 + 0.996036i \(0.528350\pi\)
\(570\) 1138.51 0.0836611
\(571\) 585.979 0.0429465 0.0214733 0.999769i \(-0.493164\pi\)
0.0214733 + 0.999769i \(0.493164\pi\)
\(572\) 42662.0 3.11851
\(573\) −34909.0 −2.54510
\(574\) −33661.2 −2.44772
\(575\) 1423.17 0.103218
\(576\) −23834.2 −1.72411
\(577\) 27231.6 1.96476 0.982381 0.186891i \(-0.0598412\pi\)
0.982381 + 0.186891i \(0.0598412\pi\)
\(578\) 15324.8 1.10282
\(579\) −11752.5 −0.843557
\(580\) −907.742 −0.0649861
\(581\) −7947.02 −0.567466
\(582\) −8851.70 −0.630438
\(583\) 8914.30 0.633263
\(584\) −2291.09 −0.162339
\(585\) −14192.4 −1.00305
\(586\) 33531.8 2.36380
\(587\) −13881.2 −0.976042 −0.488021 0.872832i \(-0.662281\pi\)
−0.488021 + 0.872832i \(0.662281\pi\)
\(588\) −1652.42 −0.115892
\(589\) −1488.84 −0.104154
\(590\) 1154.86 0.0805846
\(591\) 5711.12 0.397503
\(592\) −7870.54 −0.546414
\(593\) −13743.6 −0.951740 −0.475870 0.879516i \(-0.657867\pi\)
−0.475870 + 0.879516i \(0.657867\pi\)
\(594\) −18570.2 −1.28273
\(595\) −2753.51 −0.189719
\(596\) 11938.2 0.820485
\(597\) 6898.67 0.472938
\(598\) 4798.51 0.328136
\(599\) 23063.7 1.57322 0.786610 0.617450i \(-0.211834\pi\)
0.786610 + 0.617450i \(0.211834\pi\)
\(600\) 3772.93 0.256715
\(601\) −21928.1 −1.48830 −0.744148 0.668015i \(-0.767144\pi\)
−0.744148 + 0.668015i \(0.767144\pi\)
\(602\) 21294.1 1.44167
\(603\) −18194.2 −1.22873
\(604\) 2744.80 0.184908
\(605\) −7341.96 −0.493377
\(606\) −56867.4 −3.81201
\(607\) 18710.7 1.25114 0.625571 0.780167i \(-0.284866\pi\)
0.625571 + 0.780167i \(0.284866\pi\)
\(608\) 2013.47 0.134304
\(609\) 3235.56 0.215290
\(610\) −4715.15 −0.312968
\(611\) −29155.0 −1.93041
\(612\) 11744.0 0.775690
\(613\) 19774.9 1.30294 0.651468 0.758676i \(-0.274153\pi\)
0.651468 + 0.758676i \(0.274153\pi\)
\(614\) −1062.33 −0.0698241
\(615\) −16168.3 −1.06011
\(616\) −4370.17 −0.285843
\(617\) −9684.87 −0.631926 −0.315963 0.948772i \(-0.602328\pi\)
−0.315963 + 0.948772i \(0.602328\pi\)
\(618\) 5182.20 0.337312
\(619\) −16148.3 −1.04855 −0.524277 0.851548i \(-0.675664\pi\)
−0.524277 + 0.851548i \(0.675664\pi\)
\(620\) 7728.27 0.500604
\(621\) −1110.45 −0.0717569
\(622\) −4699.39 −0.302939
\(623\) 4677.91 0.300829
\(624\) −37331.8 −2.39498
\(625\) 8644.42 0.553243
\(626\) −27308.1 −1.74353
\(627\) 3397.21 0.216382
\(628\) −31277.7 −1.98744
\(629\) 5042.31 0.319634
\(630\) 12213.4 0.772371
\(631\) −13912.3 −0.877720 −0.438860 0.898556i \(-0.644618\pi\)
−0.438860 + 0.898556i \(0.644618\pi\)
\(632\) 1659.15 0.104426
\(633\) 16754.5 1.05203
\(634\) −9413.81 −0.589701
\(635\) 4523.19 0.282673
\(636\) 11871.8 0.740171
\(637\) −1951.14 −0.121361
\(638\) −5094.82 −0.316153
\(639\) −11108.2 −0.687691
\(640\) −2511.34 −0.155108
\(641\) 21571.1 1.32918 0.664591 0.747207i \(-0.268606\pi\)
0.664591 + 0.747207i \(0.268606\pi\)
\(642\) −17907.4 −1.10085
\(643\) −14895.6 −0.913567 −0.456783 0.889578i \(-0.650999\pi\)
−0.456783 + 0.889578i \(0.650999\pi\)
\(644\) −2195.36 −0.134331
\(645\) 10228.1 0.624388
\(646\) −1112.40 −0.0677507
\(647\) 31426.1 1.90956 0.954782 0.297307i \(-0.0960884\pi\)
0.954782 + 0.297307i \(0.0960884\pi\)
\(648\) 1549.93 0.0939613
\(649\) 3446.01 0.208425
\(650\) 37425.7 2.25839
\(651\) −27546.7 −1.65843
\(652\) −31396.6 −1.88587
\(653\) 16387.0 0.982041 0.491020 0.871148i \(-0.336624\pi\)
0.491020 + 0.871148i \(0.336624\pi\)
\(654\) −54194.5 −3.24032
\(655\) 11708.0 0.698424
\(656\) −24658.5 −1.46761
\(657\) 19105.8 1.13453
\(658\) 25089.5 1.48646
\(659\) 23831.3 1.40870 0.704350 0.709852i \(-0.251238\pi\)
0.704350 + 0.709852i \(0.251238\pi\)
\(660\) −17634.2 −1.04002
\(661\) 31788.5 1.87054 0.935271 0.353932i \(-0.115156\pi\)
0.935271 + 0.353932i \(0.115156\pi\)
\(662\) 22370.1 1.31335
\(663\) 23916.8 1.40098
\(664\) 1983.77 0.115941
\(665\) −615.040 −0.0358650
\(666\) −22365.5 −1.30127
\(667\) −304.659 −0.0176858
\(668\) 33348.2 1.93156
\(669\) −505.504 −0.0292136
\(670\) −8945.68 −0.515824
\(671\) −14069.6 −0.809464
\(672\) 37253.5 2.13852
\(673\) −19746.6 −1.13102 −0.565510 0.824742i \(-0.691321\pi\)
−0.565510 + 0.824742i \(0.691321\pi\)
\(674\) 17752.4 1.01454
\(675\) −8660.92 −0.493865
\(676\) 47136.3 2.68185
\(677\) −21362.6 −1.21275 −0.606376 0.795178i \(-0.707377\pi\)
−0.606376 + 0.795178i \(0.707377\pi\)
\(678\) −35068.2 −1.98641
\(679\) 4781.83 0.270265
\(680\) 687.343 0.0387623
\(681\) 16373.9 0.921362
\(682\) 43375.9 2.43541
\(683\) 814.972 0.0456575 0.0228287 0.999739i \(-0.492733\pi\)
0.0228287 + 0.999739i \(0.492733\pi\)
\(684\) 2623.20 0.146638
\(685\) 11269.8 0.628607
\(686\) 27049.5 1.50548
\(687\) 8375.93 0.465155
\(688\) 15599.0 0.864397
\(689\) 14018.0 0.775097
\(690\) −1983.45 −0.109433
\(691\) 25662.9 1.41282 0.706412 0.707801i \(-0.250313\pi\)
0.706412 + 0.707801i \(0.250313\pi\)
\(692\) 9093.81 0.499559
\(693\) 36443.7 1.99766
\(694\) −9442.01 −0.516446
\(695\) −4292.81 −0.234296
\(696\) −807.674 −0.0439868
\(697\) 15797.6 0.858503
\(698\) 25641.9 1.39049
\(699\) 25774.9 1.39470
\(700\) −17122.6 −0.924533
\(701\) 25978.0 1.39968 0.699840 0.714300i \(-0.253255\pi\)
0.699840 + 0.714300i \(0.253255\pi\)
\(702\) −29202.1 −1.57003
\(703\) 1126.28 0.0604245
\(704\) −34967.7 −1.87201
\(705\) 12051.1 0.643789
\(706\) 27340.4 1.45746
\(707\) 30720.7 1.63419
\(708\) 4589.30 0.243611
\(709\) −15753.7 −0.834474 −0.417237 0.908798i \(-0.637002\pi\)
−0.417237 + 0.908798i \(0.637002\pi\)
\(710\) −5461.68 −0.288694
\(711\) −13835.9 −0.729800
\(712\) −1167.72 −0.0614636
\(713\) 2593.78 0.136238
\(714\) −20581.8 −1.07879
\(715\) −20822.0 −1.08909
\(716\) 23155.9 1.20863
\(717\) 8740.34 0.455250
\(718\) −16228.4 −0.843506
\(719\) −17232.3 −0.893820 −0.446910 0.894579i \(-0.647476\pi\)
−0.446910 + 0.894579i \(0.647476\pi\)
\(720\) 8946.89 0.463099
\(721\) −2799.51 −0.144603
\(722\) 28099.2 1.44840
\(723\) 4613.85 0.237332
\(724\) 7452.56 0.382559
\(725\) −2376.16 −0.121722
\(726\) −54879.3 −2.80546
\(727\) 4356.85 0.222265 0.111132 0.993806i \(-0.464552\pi\)
0.111132 + 0.993806i \(0.464552\pi\)
\(728\) −6872.21 −0.349864
\(729\) −30717.1 −1.56059
\(730\) 9393.92 0.476280
\(731\) −9993.57 −0.505644
\(732\) −18737.5 −0.946117
\(733\) 21830.1 1.10002 0.550008 0.835159i \(-0.314625\pi\)
0.550008 + 0.835159i \(0.314625\pi\)
\(734\) −13691.7 −0.688515
\(735\) 806.496 0.0404735
\(736\) −3507.76 −0.175676
\(737\) −26693.1 −1.33413
\(738\) −70071.3 −3.49507
\(739\) −18445.7 −0.918184 −0.459092 0.888389i \(-0.651825\pi\)
−0.459092 + 0.888389i \(0.651825\pi\)
\(740\) −5846.28 −0.290424
\(741\) 5342.20 0.264846
\(742\) −12063.3 −0.596842
\(743\) 10726.7 0.529641 0.264821 0.964298i \(-0.414687\pi\)
0.264821 + 0.964298i \(0.414687\pi\)
\(744\) 6876.31 0.338841
\(745\) −5826.69 −0.286542
\(746\) 34511.4 1.69377
\(747\) −16543.0 −0.810277
\(748\) 17229.9 0.842229
\(749\) 9673.85 0.471929
\(750\) −33823.9 −1.64677
\(751\) −2105.22 −0.102291 −0.0511455 0.998691i \(-0.516287\pi\)
−0.0511455 + 0.998691i \(0.516287\pi\)
\(752\) 18379.3 0.891255
\(753\) −55844.4 −2.70263
\(754\) −8011.74 −0.386963
\(755\) −1339.65 −0.0645762
\(756\) 13360.2 0.642734
\(757\) 35718.3 1.71493 0.857467 0.514539i \(-0.172037\pi\)
0.857467 + 0.514539i \(0.172037\pi\)
\(758\) −15980.0 −0.765725
\(759\) −5918.43 −0.283038
\(760\) 153.529 0.00732773
\(761\) −21571.1 −1.02753 −0.513766 0.857930i \(-0.671750\pi\)
−0.513766 + 0.857930i \(0.671750\pi\)
\(762\) 33809.7 1.60735
\(763\) 29276.7 1.38911
\(764\) −39547.0 −1.87273
\(765\) −5731.88 −0.270898
\(766\) −1901.49 −0.0896916
\(767\) 5418.94 0.255106
\(768\) 22254.1 1.04560
\(769\) −32715.7 −1.53415 −0.767074 0.641558i \(-0.778288\pi\)
−0.767074 + 0.641558i \(0.778288\pi\)
\(770\) 17918.6 0.838625
\(771\) −26018.9 −1.21537
\(772\) −13314.0 −0.620702
\(773\) 14274.8 0.664201 0.332100 0.943244i \(-0.392243\pi\)
0.332100 + 0.943244i \(0.392243\pi\)
\(774\) 44327.2 2.05854
\(775\) 20230.0 0.937657
\(776\) −1193.66 −0.0552189
\(777\) 20838.5 0.962134
\(778\) −57784.6 −2.66283
\(779\) 3528.64 0.162294
\(780\) −27730.2 −1.27295
\(781\) −16297.2 −0.746681
\(782\) 1937.97 0.0886212
\(783\) 1854.05 0.0846211
\(784\) 1230.00 0.0560312
\(785\) 15265.7 0.694084
\(786\) 87514.1 3.97140
\(787\) −154.800 −0.00701147 −0.00350574 0.999994i \(-0.501116\pi\)
−0.00350574 + 0.999994i \(0.501116\pi\)
\(788\) 6469.91 0.292489
\(789\) 62451.7 2.81792
\(790\) −6802.83 −0.306372
\(791\) 18944.4 0.851562
\(792\) −9097.22 −0.408151
\(793\) −22124.8 −0.990762
\(794\) 29915.3 1.33710
\(795\) −5794.28 −0.258493
\(796\) 7815.25 0.347995
\(797\) 1210.82 0.0538136 0.0269068 0.999638i \(-0.491434\pi\)
0.0269068 + 0.999638i \(0.491434\pi\)
\(798\) −4597.27 −0.203937
\(799\) −11774.8 −0.521355
\(800\) −27358.6 −1.20909
\(801\) 9737.83 0.429550
\(802\) −17307.0 −0.762008
\(803\) 28030.6 1.23185
\(804\) −35549.2 −1.55936
\(805\) 1071.49 0.0469131
\(806\) 68209.8 2.98088
\(807\) −50169.1 −2.18840
\(808\) −7668.62 −0.333887
\(809\) −24108.3 −1.04772 −0.523859 0.851805i \(-0.675508\pi\)
−0.523859 + 0.851805i \(0.675508\pi\)
\(810\) −6355.02 −0.275670
\(811\) −28376.6 −1.22865 −0.614326 0.789052i \(-0.710572\pi\)
−0.614326 + 0.789052i \(0.710572\pi\)
\(812\) 3665.44 0.158414
\(813\) −36693.0 −1.58288
\(814\) −32813.0 −1.41289
\(815\) 15323.7 0.658610
\(816\) −15077.2 −0.646822
\(817\) −2232.22 −0.0955882
\(818\) −40620.3 −1.73625
\(819\) 57308.7 2.44509
\(820\) −18316.4 −0.780046
\(821\) 32553.3 1.38382 0.691911 0.721983i \(-0.256769\pi\)
0.691911 + 0.721983i \(0.256769\pi\)
\(822\) 84238.8 3.57441
\(823\) 42105.4 1.78335 0.891677 0.452672i \(-0.149529\pi\)
0.891677 + 0.452672i \(0.149529\pi\)
\(824\) 698.824 0.0295445
\(825\) −46160.5 −1.94800
\(826\) −4663.31 −0.196438
\(827\) −16938.3 −0.712215 −0.356107 0.934445i \(-0.615896\pi\)
−0.356107 + 0.934445i \(0.615896\pi\)
\(828\) −4570.00 −0.191810
\(829\) −27507.1 −1.15243 −0.576214 0.817299i \(-0.695470\pi\)
−0.576214 + 0.817299i \(0.695470\pi\)
\(830\) −8133.84 −0.340156
\(831\) 9524.54 0.397597
\(832\) −54987.7 −2.29129
\(833\) −788.005 −0.0327764
\(834\) −32087.7 −1.33226
\(835\) −16276.3 −0.674567
\(836\) 3848.57 0.159217
\(837\) −15784.9 −0.651858
\(838\) 7040.39 0.290222
\(839\) −15189.7 −0.625036 −0.312518 0.949912i \(-0.601173\pi\)
−0.312518 + 0.949912i \(0.601173\pi\)
\(840\) 2840.61 0.116679
\(841\) −23880.3 −0.979144
\(842\) 4709.20 0.192743
\(843\) 46167.5 1.88623
\(844\) 18980.6 0.774097
\(845\) −23005.8 −0.936596
\(846\) 52228.0 2.12250
\(847\) 29646.7 1.20268
\(848\) −8836.93 −0.357855
\(849\) −25381.8 −1.02603
\(850\) 15115.1 0.609933
\(851\) −1962.14 −0.0790381
\(852\) −21704.1 −0.872736
\(853\) 40128.8 1.61077 0.805384 0.592753i \(-0.201959\pi\)
0.805384 + 0.592753i \(0.201959\pi\)
\(854\) 19039.7 0.762909
\(855\) −1280.31 −0.0512112
\(856\) −2414.82 −0.0964217
\(857\) 22634.7 0.902201 0.451101 0.892473i \(-0.351032\pi\)
0.451101 + 0.892473i \(0.351032\pi\)
\(858\) −155640. −6.19283
\(859\) 31716.0 1.25976 0.629880 0.776692i \(-0.283104\pi\)
0.629880 + 0.776692i \(0.283104\pi\)
\(860\) 11587.0 0.459434
\(861\) 65287.3 2.58419
\(862\) 34548.4 1.36511
\(863\) 23915.4 0.943324 0.471662 0.881780i \(-0.343654\pi\)
0.471662 + 0.881780i \(0.343654\pi\)
\(864\) 21347.1 0.840558
\(865\) −4438.42 −0.174463
\(866\) 17949.1 0.704314
\(867\) −29723.0 −1.16430
\(868\) −31206.6 −1.22030
\(869\) −20299.1 −0.792403
\(870\) 3311.63 0.129051
\(871\) −41975.6 −1.63294
\(872\) −7308.18 −0.283814
\(873\) 9954.16 0.385907
\(874\) 432.877 0.0167532
\(875\) 18272.2 0.705959
\(876\) 37330.4 1.43982
\(877\) 26014.0 1.00163 0.500816 0.865554i \(-0.333033\pi\)
0.500816 + 0.865554i \(0.333033\pi\)
\(878\) −60621.7 −2.33016
\(879\) −65036.3 −2.49558
\(880\) 13126.2 0.502824
\(881\) 25233.4 0.964965 0.482483 0.875905i \(-0.339735\pi\)
0.482483 + 0.875905i \(0.339735\pi\)
\(882\) 3495.25 0.133437
\(883\) −18268.5 −0.696244 −0.348122 0.937449i \(-0.613180\pi\)
−0.348122 + 0.937449i \(0.613180\pi\)
\(884\) 27094.5 1.03087
\(885\) −2239.90 −0.0850773
\(886\) 66014.3 2.50315
\(887\) −5992.15 −0.226828 −0.113414 0.993548i \(-0.536179\pi\)
−0.113414 + 0.993548i \(0.536179\pi\)
\(888\) −5201.80 −0.196578
\(889\) −18264.6 −0.689060
\(890\) 4787.88 0.180326
\(891\) −18962.8 −0.712995
\(892\) −572.667 −0.0214959
\(893\) −2630.09 −0.0985582
\(894\) −43553.1 −1.62934
\(895\) −11301.7 −0.422094
\(896\) 10140.7 0.378101
\(897\) −9306.89 −0.346431
\(898\) −44488.7 −1.65324
\(899\) −4330.65 −0.160662
\(900\) −35643.5 −1.32013
\(901\) 5661.43 0.209334
\(902\) −102803. −3.79488
\(903\) −41300.8 −1.52204
\(904\) −4728.98 −0.173986
\(905\) −3637.37 −0.133603
\(906\) −10013.6 −0.367196
\(907\) 10017.5 0.366730 0.183365 0.983045i \(-0.441301\pi\)
0.183365 + 0.983045i \(0.441301\pi\)
\(908\) 18549.3 0.677952
\(909\) 63950.1 2.33343
\(910\) 28177.5 1.02645
\(911\) −28206.8 −1.02583 −0.512915 0.858439i \(-0.671434\pi\)
−0.512915 + 0.858439i \(0.671434\pi\)
\(912\) −3367.72 −0.122277
\(913\) −24270.7 −0.879783
\(914\) −12600.9 −0.456018
\(915\) 9145.21 0.330417
\(916\) 9488.78 0.342269
\(917\) −47276.5 −1.70252
\(918\) −11793.8 −0.424025
\(919\) 15141.5 0.543496 0.271748 0.962368i \(-0.412398\pi\)
0.271748 + 0.962368i \(0.412398\pi\)
\(920\) −267.470 −0.00958502
\(921\) 2060.42 0.0737169
\(922\) 42236.3 1.50865
\(923\) −25627.7 −0.913918
\(924\) 71206.6 2.53520
\(925\) −15303.6 −0.543978
\(926\) 42665.2 1.51411
\(927\) −5827.63 −0.206477
\(928\) 5856.67 0.207171
\(929\) −28368.3 −1.00187 −0.500933 0.865486i \(-0.667010\pi\)
−0.500933 + 0.865486i \(0.667010\pi\)
\(930\) −28194.3 −0.994115
\(931\) −176.013 −0.00619614
\(932\) 29199.4 1.02624
\(933\) 9114.65 0.319829
\(934\) −14739.5 −0.516372
\(935\) −8409.39 −0.294135
\(936\) −14305.6 −0.499566
\(937\) 11298.3 0.393917 0.196958 0.980412i \(-0.436894\pi\)
0.196958 + 0.980412i \(0.436894\pi\)
\(938\) 36122.5 1.25740
\(939\) 52965.1 1.84074
\(940\) 13652.2 0.473710
\(941\) −49135.8 −1.70221 −0.851106 0.524993i \(-0.824068\pi\)
−0.851106 + 0.524993i \(0.824068\pi\)
\(942\) 114107. 3.94673
\(943\) −6147.41 −0.212288
\(944\) −3416.10 −0.117780
\(945\) −6520.73 −0.224465
\(946\) 65033.6 2.23512
\(947\) −40776.4 −1.39921 −0.699607 0.714528i \(-0.746642\pi\)
−0.699607 + 0.714528i \(0.746642\pi\)
\(948\) −27033.7 −0.926176
\(949\) 44078.9 1.50776
\(950\) 3376.19 0.115303
\(951\) 18258.4 0.622577
\(952\) −2775.48 −0.0944892
\(953\) 57911.4 1.96845 0.984225 0.176922i \(-0.0566140\pi\)
0.984225 + 0.176922i \(0.0566140\pi\)
\(954\) −25111.7 −0.852223
\(955\) 19301.7 0.654020
\(956\) 9901.60 0.334980
\(957\) 9881.60 0.333779
\(958\) 63503.1 2.14164
\(959\) −45507.1 −1.53233
\(960\) 22729.0 0.764140
\(961\) 7079.02 0.237623
\(962\) −51599.3 −1.72934
\(963\) 20137.7 0.673861
\(964\) 5226.86 0.174633
\(965\) 6498.17 0.216771
\(966\) 8009.13 0.266759
\(967\) −10786.0 −0.358691 −0.179346 0.983786i \(-0.557398\pi\)
−0.179346 + 0.983786i \(0.557398\pi\)
\(968\) −7400.52 −0.245725
\(969\) 2157.55 0.0715279
\(970\) 4894.25 0.162005
\(971\) −31577.6 −1.04364 −0.521820 0.853056i \(-0.674747\pi\)
−0.521820 + 0.853056i \(0.674747\pi\)
\(972\) −45410.0 −1.49848
\(973\) 17334.3 0.571132
\(974\) −50431.3 −1.65906
\(975\) −72588.5 −2.38430
\(976\) 13947.5 0.457426
\(977\) 10340.3 0.338603 0.169301 0.985564i \(-0.445849\pi\)
0.169301 + 0.985564i \(0.445849\pi\)
\(978\) 114541. 3.74501
\(979\) 14286.6 0.466397
\(980\) 913.649 0.0297811
\(981\) 60944.3 1.98349
\(982\) 32136.9 1.04433
\(983\) 22041.8 0.715184 0.357592 0.933878i \(-0.383598\pi\)
0.357592 + 0.933878i \(0.383598\pi\)
\(984\) −16297.3 −0.527986
\(985\) −3157.77 −0.102147
\(986\) −3235.70 −0.104509
\(987\) −48662.2 −1.56933
\(988\) 6051.97 0.194877
\(989\) 3888.86 0.125034
\(990\) 37300.5 1.19746
\(991\) −24259.6 −0.777632 −0.388816 0.921315i \(-0.627116\pi\)
−0.388816 + 0.921315i \(0.627116\pi\)
\(992\) −49862.1 −1.59589
\(993\) −43387.7 −1.38657
\(994\) 22054.2 0.703738
\(995\) −3814.39 −0.121532
\(996\) −32323.0 −1.02831
\(997\) 17540.2 0.557175 0.278587 0.960411i \(-0.410134\pi\)
0.278587 + 0.960411i \(0.410134\pi\)
\(998\) 42509.4 1.34831
\(999\) 11940.9 0.378173
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 547.4.a.b.1.11 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.4.a.b.1.11 71 1.1 even 1 trivial