Properties

Label 8021.2.a.c.1.5
Level $8021$
Weight $2$
Character 8021.1
Self dual yes
Analytic conductor $64.048$
Analytic rank $0$
Dimension $169$
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] = [8021,2,Mod(1,8021)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8021, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8021.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8021 = 13 \cdot 617 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8021.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: \(64.0480074613\)
Analytic rank: \(0\)
Dimension: \(169\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 8021.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.75686 q^{2} -1.90538 q^{3} +5.60028 q^{4} -0.896577 q^{5} +5.25287 q^{6} +2.47327 q^{7} -9.92547 q^{8} +0.630474 q^{9} +O(q^{10})\) \(q-2.75686 q^{2} -1.90538 q^{3} +5.60028 q^{4} -0.896577 q^{5} +5.25287 q^{6} +2.47327 q^{7} -9.92547 q^{8} +0.630474 q^{9} +2.47174 q^{10} -0.829573 q^{11} -10.6707 q^{12} -1.00000 q^{13} -6.81845 q^{14} +1.70832 q^{15} +16.1626 q^{16} -2.26874 q^{17} -1.73813 q^{18} -3.69629 q^{19} -5.02108 q^{20} -4.71251 q^{21} +2.28702 q^{22} -5.25182 q^{23} +18.9118 q^{24} -4.19615 q^{25} +2.75686 q^{26} +4.51485 q^{27} +13.8510 q^{28} -6.49921 q^{29} -4.70960 q^{30} -2.31862 q^{31} -24.7070 q^{32} +1.58065 q^{33} +6.25461 q^{34} -2.21747 q^{35} +3.53083 q^{36} -7.02474 q^{37} +10.1902 q^{38} +1.90538 q^{39} +8.89895 q^{40} -5.48491 q^{41} +12.9917 q^{42} -9.24004 q^{43} -4.64584 q^{44} -0.565269 q^{45} +14.4785 q^{46} +4.56715 q^{47} -30.7958 q^{48} -0.882952 q^{49} +11.5682 q^{50} +4.32282 q^{51} -5.60028 q^{52} -10.1469 q^{53} -12.4468 q^{54} +0.743777 q^{55} -24.5483 q^{56} +7.04284 q^{57} +17.9174 q^{58} -2.24047 q^{59} +9.56707 q^{60} +8.47940 q^{61} +6.39211 q^{62} +1.55933 q^{63} +35.7886 q^{64} +0.896577 q^{65} -4.35764 q^{66} -14.5732 q^{67} -12.7056 q^{68} +10.0067 q^{69} +6.11327 q^{70} -13.9707 q^{71} -6.25775 q^{72} -4.21314 q^{73} +19.3662 q^{74} +7.99526 q^{75} -20.7003 q^{76} -2.05176 q^{77} -5.25287 q^{78} -3.34200 q^{79} -14.4910 q^{80} -10.4939 q^{81} +15.1211 q^{82} +0.491916 q^{83} -26.3914 q^{84} +2.03410 q^{85} +25.4735 q^{86} +12.3835 q^{87} +8.23390 q^{88} -15.4847 q^{89} +1.55837 q^{90} -2.47327 q^{91} -29.4117 q^{92} +4.41785 q^{93} -12.5910 q^{94} +3.31401 q^{95} +47.0762 q^{96} +16.3692 q^{97} +2.43418 q^{98} -0.523024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75686 −1.94939 −0.974697 0.223529i \(-0.928242\pi\)
−0.974697 + 0.223529i \(0.928242\pi\)
\(3\) −1.90538 −1.10007 −0.550036 0.835141i \(-0.685386\pi\)
−0.550036 + 0.835141i \(0.685386\pi\)
\(4\) 5.60028 2.80014
\(5\) −0.896577 −0.400962 −0.200481 0.979698i \(-0.564250\pi\)
−0.200481 + 0.979698i \(0.564250\pi\)
\(6\) 5.25287 2.14447
\(7\) 2.47327 0.934807 0.467403 0.884044i \(-0.345190\pi\)
0.467403 + 0.884044i \(0.345190\pi\)
\(8\) −9.92547 −3.50918
\(9\) 0.630474 0.210158
\(10\) 2.47174 0.781632
\(11\) −0.829573 −0.250126 −0.125063 0.992149i \(-0.539913\pi\)
−0.125063 + 0.992149i \(0.539913\pi\)
\(12\) −10.6707 −3.08035
\(13\) −1.00000 −0.277350
\(14\) −6.81845 −1.82231
\(15\) 1.70832 0.441087
\(16\) 16.1626 4.04064
\(17\) −2.26874 −0.550251 −0.275126 0.961408i \(-0.588719\pi\)
−0.275126 + 0.961408i \(0.588719\pi\)
\(18\) −1.73813 −0.409681
\(19\) −3.69629 −0.847987 −0.423994 0.905665i \(-0.639372\pi\)
−0.423994 + 0.905665i \(0.639372\pi\)
\(20\) −5.02108 −1.12275
\(21\) −4.71251 −1.02835
\(22\) 2.28702 0.487594
\(23\) −5.25182 −1.09508 −0.547541 0.836779i \(-0.684436\pi\)
−0.547541 + 0.836779i \(0.684436\pi\)
\(24\) 18.9118 3.86035
\(25\) −4.19615 −0.839230
\(26\) 2.75686 0.540665
\(27\) 4.51485 0.868883
\(28\) 13.8510 2.61759
\(29\) −6.49921 −1.20687 −0.603437 0.797411i \(-0.706202\pi\)
−0.603437 + 0.797411i \(0.706202\pi\)
\(30\) −4.70960 −0.859852
\(31\) −2.31862 −0.416436 −0.208218 0.978082i \(-0.566766\pi\)
−0.208218 + 0.978082i \(0.566766\pi\)
\(32\) −24.7070 −4.36762
\(33\) 1.58065 0.275156
\(34\) 6.25461 1.07266
\(35\) −2.21747 −0.374822
\(36\) 3.53083 0.588472
\(37\) −7.02474 −1.15486 −0.577430 0.816440i \(-0.695944\pi\)
−0.577430 + 0.816440i \(0.695944\pi\)
\(38\) 10.1902 1.65306
\(39\) 1.90538 0.305105
\(40\) 8.89895 1.40705
\(41\) −5.48491 −0.856599 −0.428299 0.903637i \(-0.640887\pi\)
−0.428299 + 0.903637i \(0.640887\pi\)
\(42\) 12.9917 2.00467
\(43\) −9.24004 −1.40909 −0.704546 0.709658i \(-0.748849\pi\)
−0.704546 + 0.709658i \(0.748849\pi\)
\(44\) −4.64584 −0.700387
\(45\) −0.565269 −0.0842653
\(46\) 14.4785 2.13475
\(47\) 4.56715 0.666187 0.333093 0.942894i \(-0.391908\pi\)
0.333093 + 0.942894i \(0.391908\pi\)
\(48\) −30.7958 −4.44500
\(49\) −0.882952 −0.126136
\(50\) 11.5682 1.63599
\(51\) 4.32282 0.605316
\(52\) −5.60028 −0.776619
\(53\) −10.1469 −1.39378 −0.696889 0.717179i \(-0.745433\pi\)
−0.696889 + 0.717179i \(0.745433\pi\)
\(54\) −12.4468 −1.69380
\(55\) 0.743777 0.100291
\(56\) −24.5483 −3.28041
\(57\) 7.04284 0.932847
\(58\) 17.9174 2.35267
\(59\) −2.24047 −0.291685 −0.145842 0.989308i \(-0.546589\pi\)
−0.145842 + 0.989308i \(0.546589\pi\)
\(60\) 9.56707 1.23510
\(61\) 8.47940 1.08568 0.542838 0.839837i \(-0.317350\pi\)
0.542838 + 0.839837i \(0.317350\pi\)
\(62\) 6.39211 0.811798
\(63\) 1.55933 0.196457
\(64\) 35.7886 4.47358
\(65\) 0.896577 0.111207
\(66\) −4.35764 −0.536388
\(67\) −14.5732 −1.78039 −0.890197 0.455576i \(-0.849433\pi\)
−0.890197 + 0.455576i \(0.849433\pi\)
\(68\) −12.7056 −1.54078
\(69\) 10.0067 1.20467
\(70\) 6.11327 0.730675
\(71\) −13.9707 −1.65802 −0.829008 0.559237i \(-0.811094\pi\)
−0.829008 + 0.559237i \(0.811094\pi\)
\(72\) −6.25775 −0.737483
\(73\) −4.21314 −0.493111 −0.246556 0.969129i \(-0.579299\pi\)
−0.246556 + 0.969129i \(0.579299\pi\)
\(74\) 19.3662 2.25128
\(75\) 7.99526 0.923213
\(76\) −20.7003 −2.37448
\(77\) −2.05176 −0.233819
\(78\) −5.25287 −0.594770
\(79\) −3.34200 −0.376005 −0.188002 0.982169i \(-0.560201\pi\)
−0.188002 + 0.982169i \(0.560201\pi\)
\(80\) −14.4910 −1.62014
\(81\) −10.4939 −1.16599
\(82\) 15.1211 1.66985
\(83\) 0.491916 0.0539948 0.0269974 0.999636i \(-0.491405\pi\)
0.0269974 + 0.999636i \(0.491405\pi\)
\(84\) −26.3914 −2.87954
\(85\) 2.03410 0.220630
\(86\) 25.4735 2.74688
\(87\) 12.3835 1.32765
\(88\) 8.23390 0.877737
\(89\) −15.4847 −1.64137 −0.820687 0.571378i \(-0.806409\pi\)
−0.820687 + 0.571378i \(0.806409\pi\)
\(90\) 1.55837 0.164266
\(91\) −2.47327 −0.259269
\(92\) −29.4117 −3.06638
\(93\) 4.41785 0.458110
\(94\) −12.5910 −1.29866
\(95\) 3.31401 0.340010
\(96\) 47.0762 4.80470
\(97\) 16.3692 1.66204 0.831019 0.556243i \(-0.187758\pi\)
0.831019 + 0.556243i \(0.187758\pi\)
\(98\) 2.43418 0.245889
\(99\) −0.523024 −0.0525659
\(100\) −23.4996 −2.34996
\(101\) 9.30569 0.925951 0.462976 0.886371i \(-0.346782\pi\)
0.462976 + 0.886371i \(0.346782\pi\)
\(102\) −11.9174 −1.18000
\(103\) −1.23021 −0.121216 −0.0606081 0.998162i \(-0.519304\pi\)
−0.0606081 + 0.998162i \(0.519304\pi\)
\(104\) 9.92547 0.973272
\(105\) 4.22513 0.412331
\(106\) 27.9735 2.71702
\(107\) −17.2946 −1.67193 −0.835966 0.548782i \(-0.815092\pi\)
−0.835966 + 0.548782i \(0.815092\pi\)
\(108\) 25.2844 2.43299
\(109\) 17.4148 1.66804 0.834020 0.551735i \(-0.186034\pi\)
0.834020 + 0.551735i \(0.186034\pi\)
\(110\) −2.05049 −0.195506
\(111\) 13.3848 1.27043
\(112\) 39.9743 3.77722
\(113\) 1.71682 0.161505 0.0807526 0.996734i \(-0.474268\pi\)
0.0807526 + 0.996734i \(0.474268\pi\)
\(114\) −19.4161 −1.81849
\(115\) 4.70867 0.439085
\(116\) −36.3974 −3.37941
\(117\) −0.630474 −0.0582873
\(118\) 6.17667 0.568609
\(119\) −5.61121 −0.514379
\(120\) −16.9559 −1.54785
\(121\) −10.3118 −0.937437
\(122\) −23.3765 −2.11641
\(123\) 10.4508 0.942320
\(124\) −12.9849 −1.16608
\(125\) 8.24506 0.737461
\(126\) −4.29885 −0.382972
\(127\) −8.86184 −0.786362 −0.393181 0.919461i \(-0.628625\pi\)
−0.393181 + 0.919461i \(0.628625\pi\)
\(128\) −49.2503 −4.35315
\(129\) 17.6058 1.55010
\(130\) −2.47174 −0.216786
\(131\) 5.06912 0.442891 0.221445 0.975173i \(-0.428923\pi\)
0.221445 + 0.975173i \(0.428923\pi\)
\(132\) 8.85209 0.770476
\(133\) −9.14191 −0.792705
\(134\) 40.1761 3.47069
\(135\) −4.04791 −0.348389
\(136\) 22.5183 1.93093
\(137\) −9.67626 −0.826699 −0.413349 0.910572i \(-0.635641\pi\)
−0.413349 + 0.910572i \(0.635641\pi\)
\(138\) −27.5871 −2.34837
\(139\) 18.4780 1.56728 0.783641 0.621214i \(-0.213360\pi\)
0.783641 + 0.621214i \(0.213360\pi\)
\(140\) −12.4185 −1.04955
\(141\) −8.70215 −0.732853
\(142\) 38.5152 3.23213
\(143\) 0.829573 0.0693724
\(144\) 10.1901 0.849173
\(145\) 5.82704 0.483910
\(146\) 11.6151 0.961268
\(147\) 1.68236 0.138759
\(148\) −39.3405 −3.23377
\(149\) 23.0464 1.88804 0.944019 0.329891i \(-0.107012\pi\)
0.944019 + 0.329891i \(0.107012\pi\)
\(150\) −22.0418 −1.79971
\(151\) 5.42506 0.441485 0.220743 0.975332i \(-0.429152\pi\)
0.220743 + 0.975332i \(0.429152\pi\)
\(152\) 36.6874 2.97574
\(153\) −1.43038 −0.115640
\(154\) 5.65640 0.455806
\(155\) 2.07882 0.166975
\(156\) 10.6707 0.854337
\(157\) −4.01511 −0.320441 −0.160220 0.987081i \(-0.551220\pi\)
−0.160220 + 0.987081i \(0.551220\pi\)
\(158\) 9.21344 0.732982
\(159\) 19.3336 1.53326
\(160\) 22.1517 1.75125
\(161\) −12.9892 −1.02369
\(162\) 28.9303 2.27298
\(163\) −7.57930 −0.593657 −0.296828 0.954931i \(-0.595929\pi\)
−0.296828 + 0.954931i \(0.595929\pi\)
\(164\) −30.7170 −2.39860
\(165\) −1.41718 −0.110327
\(166\) −1.35614 −0.105257
\(167\) −15.9189 −1.23184 −0.615921 0.787808i \(-0.711216\pi\)
−0.615921 + 0.787808i \(0.711216\pi\)
\(168\) 46.7739 3.60868
\(169\) 1.00000 0.0769231
\(170\) −5.60774 −0.430094
\(171\) −2.33042 −0.178211
\(172\) −51.7468 −3.94566
\(173\) 7.54878 0.573923 0.286962 0.957942i \(-0.407355\pi\)
0.286962 + 0.957942i \(0.407355\pi\)
\(174\) −34.1395 −2.58811
\(175\) −10.3782 −0.784518
\(176\) −13.4080 −1.01067
\(177\) 4.26895 0.320874
\(178\) 42.6891 3.19968
\(179\) −11.8518 −0.885844 −0.442922 0.896560i \(-0.646058\pi\)
−0.442922 + 0.896560i \(0.646058\pi\)
\(180\) −3.16566 −0.235954
\(181\) 8.31162 0.617798 0.308899 0.951095i \(-0.400040\pi\)
0.308899 + 0.951095i \(0.400040\pi\)
\(182\) 6.81845 0.505417
\(183\) −16.1565 −1.19432
\(184\) 52.1268 3.84284
\(185\) 6.29822 0.463054
\(186\) −12.1794 −0.893036
\(187\) 1.88209 0.137632
\(188\) 25.5773 1.86542
\(189\) 11.1664 0.812238
\(190\) −9.13627 −0.662814
\(191\) 6.50624 0.470775 0.235388 0.971902i \(-0.424364\pi\)
0.235388 + 0.971902i \(0.424364\pi\)
\(192\) −68.1910 −4.92126
\(193\) 21.8143 1.57023 0.785114 0.619351i \(-0.212604\pi\)
0.785114 + 0.619351i \(0.212604\pi\)
\(194\) −45.1276 −3.23997
\(195\) −1.70832 −0.122335
\(196\) −4.94478 −0.353198
\(197\) −19.7563 −1.40758 −0.703788 0.710410i \(-0.748510\pi\)
−0.703788 + 0.710410i \(0.748510\pi\)
\(198\) 1.44190 0.102472
\(199\) 14.2734 1.01182 0.505908 0.862588i \(-0.331158\pi\)
0.505908 + 0.862588i \(0.331158\pi\)
\(200\) 41.6487 2.94501
\(201\) 27.7674 1.95856
\(202\) −25.6545 −1.80504
\(203\) −16.0743 −1.12819
\(204\) 24.2090 1.69497
\(205\) 4.91764 0.343463
\(206\) 3.39152 0.236298
\(207\) −3.31114 −0.230140
\(208\) −16.1626 −1.12067
\(209\) 3.06634 0.212103
\(210\) −11.6481 −0.803795
\(211\) 14.7070 1.01247 0.506235 0.862396i \(-0.331037\pi\)
0.506235 + 0.862396i \(0.331037\pi\)
\(212\) −56.8252 −3.90277
\(213\) 26.6195 1.82394
\(214\) 47.6788 3.25925
\(215\) 8.28441 0.564992
\(216\) −44.8120 −3.04907
\(217\) −5.73456 −0.389287
\(218\) −48.0103 −3.25167
\(219\) 8.02764 0.542458
\(220\) 4.16536 0.280828
\(221\) 2.26874 0.152612
\(222\) −36.9000 −2.47657
\(223\) 11.3078 0.757227 0.378613 0.925555i \(-0.376401\pi\)
0.378613 + 0.925555i \(0.376401\pi\)
\(224\) −61.1070 −4.08288
\(225\) −2.64556 −0.176371
\(226\) −4.73304 −0.314837
\(227\) 24.8073 1.64652 0.823260 0.567664i \(-0.192153\pi\)
0.823260 + 0.567664i \(0.192153\pi\)
\(228\) 39.4419 2.61210
\(229\) 19.4057 1.28237 0.641183 0.767388i \(-0.278444\pi\)
0.641183 + 0.767388i \(0.278444\pi\)
\(230\) −12.9811 −0.855951
\(231\) 3.90937 0.257218
\(232\) 64.5077 4.23514
\(233\) 4.98730 0.326729 0.163365 0.986566i \(-0.447765\pi\)
0.163365 + 0.986566i \(0.447765\pi\)
\(234\) 1.73813 0.113625
\(235\) −4.09480 −0.267115
\(236\) −12.5473 −0.816758
\(237\) 6.36779 0.413632
\(238\) 15.4693 1.00273
\(239\) −22.3202 −1.44378 −0.721888 0.692010i \(-0.756725\pi\)
−0.721888 + 0.692010i \(0.756725\pi\)
\(240\) 27.6109 1.78227
\(241\) −14.2876 −0.920342 −0.460171 0.887830i \(-0.652212\pi\)
−0.460171 + 0.887830i \(0.652212\pi\)
\(242\) 28.4282 1.82743
\(243\) 6.45037 0.413791
\(244\) 47.4870 3.04005
\(245\) 0.791635 0.0505757
\(246\) −28.8115 −1.83695
\(247\) 3.69629 0.235189
\(248\) 23.0134 1.46135
\(249\) −0.937288 −0.0593982
\(250\) −22.7305 −1.43760
\(251\) −14.6923 −0.927369 −0.463685 0.886000i \(-0.653473\pi\)
−0.463685 + 0.886000i \(0.653473\pi\)
\(252\) 8.73268 0.550107
\(253\) 4.35677 0.273908
\(254\) 24.4309 1.53293
\(255\) −3.87574 −0.242708
\(256\) 64.1988 4.01243
\(257\) −7.53700 −0.470145 −0.235073 0.971978i \(-0.575533\pi\)
−0.235073 + 0.971978i \(0.575533\pi\)
\(258\) −48.5367 −3.02176
\(259\) −17.3740 −1.07957
\(260\) 5.02108 0.311394
\(261\) −4.09758 −0.253634
\(262\) −13.9749 −0.863369
\(263\) −23.9422 −1.47634 −0.738170 0.674614i \(-0.764310\pi\)
−0.738170 + 0.674614i \(0.764310\pi\)
\(264\) −15.6887 −0.965573
\(265\) 9.09744 0.558851
\(266\) 25.2030 1.54529
\(267\) 29.5042 1.80563
\(268\) −81.6137 −4.98535
\(269\) −25.6418 −1.56341 −0.781704 0.623649i \(-0.785649\pi\)
−0.781704 + 0.623649i \(0.785649\pi\)
\(270\) 11.1595 0.679147
\(271\) 26.7658 1.62591 0.812954 0.582327i \(-0.197858\pi\)
0.812954 + 0.582327i \(0.197858\pi\)
\(272\) −36.6687 −2.22337
\(273\) 4.71251 0.285214
\(274\) 26.6761 1.61156
\(275\) 3.48101 0.209913
\(276\) 56.0404 3.37324
\(277\) −28.5995 −1.71838 −0.859189 0.511658i \(-0.829032\pi\)
−0.859189 + 0.511658i \(0.829032\pi\)
\(278\) −50.9412 −3.05525
\(279\) −1.46183 −0.0875173
\(280\) 22.0095 1.31532
\(281\) −7.13971 −0.425919 −0.212960 0.977061i \(-0.568310\pi\)
−0.212960 + 0.977061i \(0.568310\pi\)
\(282\) 23.9906 1.42862
\(283\) −9.76934 −0.580727 −0.290363 0.956916i \(-0.593776\pi\)
−0.290363 + 0.956916i \(0.593776\pi\)
\(284\) −78.2397 −4.64267
\(285\) −6.31445 −0.374036
\(286\) −2.28702 −0.135234
\(287\) −13.5656 −0.800754
\(288\) −15.5771 −0.917891
\(289\) −11.8528 −0.697224
\(290\) −16.0643 −0.943331
\(291\) −31.1895 −1.82836
\(292\) −23.5948 −1.38078
\(293\) −5.95696 −0.348009 −0.174005 0.984745i \(-0.555671\pi\)
−0.174005 + 0.984745i \(0.555671\pi\)
\(294\) −4.63803 −0.270495
\(295\) 2.00876 0.116954
\(296\) 69.7238 4.05261
\(297\) −3.74540 −0.217330
\(298\) −63.5358 −3.68053
\(299\) 5.25182 0.303721
\(300\) 44.7757 2.58513
\(301\) −22.8531 −1.31723
\(302\) −14.9561 −0.860629
\(303\) −17.7309 −1.01861
\(304\) −59.7416 −3.42641
\(305\) −7.60244 −0.435314
\(306\) 3.94337 0.225427
\(307\) −6.31397 −0.360357 −0.180179 0.983634i \(-0.557668\pi\)
−0.180179 + 0.983634i \(0.557668\pi\)
\(308\) −11.4904 −0.654727
\(309\) 2.34402 0.133347
\(310\) −5.73102 −0.325500
\(311\) 32.7829 1.85895 0.929474 0.368888i \(-0.120261\pi\)
0.929474 + 0.368888i \(0.120261\pi\)
\(312\) −18.9118 −1.07067
\(313\) −17.2502 −0.975037 −0.487518 0.873113i \(-0.662098\pi\)
−0.487518 + 0.873113i \(0.662098\pi\)
\(314\) 11.0691 0.624665
\(315\) −1.39806 −0.0787718
\(316\) −18.7162 −1.05287
\(317\) 8.77899 0.493077 0.246539 0.969133i \(-0.420707\pi\)
0.246539 + 0.969133i \(0.420707\pi\)
\(318\) −53.3001 −2.98892
\(319\) 5.39157 0.301870
\(320\) −32.0873 −1.79373
\(321\) 32.9528 1.83924
\(322\) 35.8093 1.99557
\(323\) 8.38594 0.466606
\(324\) −58.7689 −3.26494
\(325\) 4.19615 0.232760
\(326\) 20.8951 1.15727
\(327\) −33.1819 −1.83496
\(328\) 54.4403 3.00596
\(329\) 11.2958 0.622756
\(330\) 3.90696 0.215071
\(331\) −25.3258 −1.39203 −0.696015 0.718027i \(-0.745045\pi\)
−0.696015 + 0.718027i \(0.745045\pi\)
\(332\) 2.75487 0.151193
\(333\) −4.42891 −0.242703
\(334\) 43.8862 2.40135
\(335\) 13.0660 0.713869
\(336\) −76.1663 −4.15521
\(337\) −15.4794 −0.843218 −0.421609 0.906778i \(-0.638534\pi\)
−0.421609 + 0.906778i \(0.638534\pi\)
\(338\) −2.75686 −0.149953
\(339\) −3.27120 −0.177667
\(340\) 11.3916 0.617794
\(341\) 1.92346 0.104161
\(342\) 6.42463 0.347404
\(343\) −19.4966 −1.05272
\(344\) 91.7117 4.94476
\(345\) −8.97180 −0.483026
\(346\) −20.8109 −1.11880
\(347\) −18.0490 −0.968920 −0.484460 0.874813i \(-0.660984\pi\)
−0.484460 + 0.874813i \(0.660984\pi\)
\(348\) 69.3509 3.71760
\(349\) −13.7918 −0.738257 −0.369128 0.929378i \(-0.620344\pi\)
−0.369128 + 0.929378i \(0.620344\pi\)
\(350\) 28.6112 1.52933
\(351\) −4.51485 −0.240985
\(352\) 20.4963 1.09245
\(353\) 35.4270 1.88559 0.942794 0.333376i \(-0.108188\pi\)
0.942794 + 0.333376i \(0.108188\pi\)
\(354\) −11.7689 −0.625510
\(355\) 12.5258 0.664801
\(356\) −86.7186 −4.59607
\(357\) 10.6915 0.565853
\(358\) 32.6737 1.72686
\(359\) −16.5285 −0.872342 −0.436171 0.899864i \(-0.643666\pi\)
−0.436171 + 0.899864i \(0.643666\pi\)
\(360\) 5.61055 0.295702
\(361\) −5.33743 −0.280917
\(362\) −22.9140 −1.20433
\(363\) 19.6479 1.03125
\(364\) −13.8510 −0.725989
\(365\) 3.77741 0.197719
\(366\) 44.5412 2.32820
\(367\) −11.7670 −0.614232 −0.307116 0.951672i \(-0.599364\pi\)
−0.307116 + 0.951672i \(0.599364\pi\)
\(368\) −84.8830 −4.42483
\(369\) −3.45809 −0.180021
\(370\) −17.3633 −0.902676
\(371\) −25.0959 −1.30291
\(372\) 24.7412 1.28277
\(373\) 8.31865 0.430723 0.215362 0.976534i \(-0.430907\pi\)
0.215362 + 0.976534i \(0.430907\pi\)
\(374\) −5.18866 −0.268299
\(375\) −15.7100 −0.811259
\(376\) −45.3311 −2.33777
\(377\) 6.49921 0.334726
\(378\) −30.7843 −1.58337
\(379\) −20.1478 −1.03492 −0.517462 0.855706i \(-0.673123\pi\)
−0.517462 + 0.855706i \(0.673123\pi\)
\(380\) 18.5594 0.952077
\(381\) 16.8852 0.865054
\(382\) −17.9368 −0.917727
\(383\) 33.0288 1.68769 0.843846 0.536585i \(-0.180286\pi\)
0.843846 + 0.536585i \(0.180286\pi\)
\(384\) 93.8405 4.78878
\(385\) 1.83956 0.0937525
\(386\) −60.1390 −3.06100
\(387\) −5.82560 −0.296132
\(388\) 91.6720 4.65394
\(389\) 12.0130 0.609083 0.304541 0.952499i \(-0.401497\pi\)
0.304541 + 0.952499i \(0.401497\pi\)
\(390\) 4.70960 0.238480
\(391\) 11.9150 0.602570
\(392\) 8.76371 0.442634
\(393\) −9.65860 −0.487212
\(394\) 54.4653 2.74392
\(395\) 2.99637 0.150764
\(396\) −2.92908 −0.147192
\(397\) −19.5818 −0.982780 −0.491390 0.870940i \(-0.663511\pi\)
−0.491390 + 0.870940i \(0.663511\pi\)
\(398\) −39.3498 −1.97243
\(399\) 17.4188 0.872032
\(400\) −67.8205 −3.39103
\(401\) −5.12431 −0.255896 −0.127948 0.991781i \(-0.540839\pi\)
−0.127948 + 0.991781i \(0.540839\pi\)
\(402\) −76.5508 −3.81801
\(403\) 2.31862 0.115499
\(404\) 52.1145 2.59279
\(405\) 9.40861 0.467518
\(406\) 44.3145 2.19929
\(407\) 5.82753 0.288860
\(408\) −42.9060 −2.12416
\(409\) 3.81835 0.188805 0.0944026 0.995534i \(-0.469906\pi\)
0.0944026 + 0.995534i \(0.469906\pi\)
\(410\) −13.5573 −0.669545
\(411\) 18.4370 0.909428
\(412\) −6.88952 −0.339422
\(413\) −5.54129 −0.272669
\(414\) 9.12835 0.448634
\(415\) −0.441041 −0.0216499
\(416\) 24.7070 1.21136
\(417\) −35.2076 −1.72412
\(418\) −8.45348 −0.413473
\(419\) −3.62208 −0.176950 −0.0884750 0.996078i \(-0.528199\pi\)
−0.0884750 + 0.996078i \(0.528199\pi\)
\(420\) 23.6619 1.15458
\(421\) 12.9561 0.631444 0.315722 0.948852i \(-0.397753\pi\)
0.315722 + 0.948852i \(0.397753\pi\)
\(422\) −40.5450 −1.97370
\(423\) 2.87947 0.140004
\(424\) 100.712 4.89102
\(425\) 9.51999 0.461787
\(426\) −73.3862 −3.55557
\(427\) 20.9718 1.01490
\(428\) −96.8545 −4.68164
\(429\) −1.58065 −0.0763146
\(430\) −22.8390 −1.10139
\(431\) 31.7530 1.52949 0.764745 0.644334i \(-0.222865\pi\)
0.764745 + 0.644334i \(0.222865\pi\)
\(432\) 72.9715 3.51084
\(433\) −5.35980 −0.257576 −0.128788 0.991672i \(-0.541109\pi\)
−0.128788 + 0.991672i \(0.541109\pi\)
\(434\) 15.8094 0.758875
\(435\) −11.1027 −0.532335
\(436\) 97.5280 4.67074
\(437\) 19.4123 0.928615
\(438\) −22.1311 −1.05746
\(439\) −30.2345 −1.44302 −0.721508 0.692406i \(-0.756551\pi\)
−0.721508 + 0.692406i \(0.756551\pi\)
\(440\) −7.38233 −0.351939
\(441\) −0.556678 −0.0265085
\(442\) −6.25461 −0.297501
\(443\) 21.0515 1.00019 0.500093 0.865971i \(-0.333299\pi\)
0.500093 + 0.865971i \(0.333299\pi\)
\(444\) 74.9586 3.55738
\(445\) 13.8832 0.658128
\(446\) −31.1740 −1.47613
\(447\) −43.9122 −2.07698
\(448\) 88.5148 4.18193
\(449\) −26.9075 −1.26984 −0.634921 0.772577i \(-0.718967\pi\)
−0.634921 + 0.772577i \(0.718967\pi\)
\(450\) 7.29345 0.343816
\(451\) 4.55013 0.214257
\(452\) 9.61469 0.452237
\(453\) −10.3368 −0.485666
\(454\) −68.3904 −3.20972
\(455\) 2.21747 0.103957
\(456\) −69.9035 −3.27353
\(457\) −28.6732 −1.34128 −0.670638 0.741784i \(-0.733980\pi\)
−0.670638 + 0.741784i \(0.733980\pi\)
\(458\) −53.4989 −2.49984
\(459\) −10.2430 −0.478104
\(460\) 26.3699 1.22950
\(461\) 2.13682 0.0995219 0.0497609 0.998761i \(-0.484154\pi\)
0.0497609 + 0.998761i \(0.484154\pi\)
\(462\) −10.7776 −0.501419
\(463\) 5.53612 0.257285 0.128643 0.991691i \(-0.458938\pi\)
0.128643 + 0.991691i \(0.458938\pi\)
\(464\) −105.044 −4.87654
\(465\) −3.96094 −0.183684
\(466\) −13.7493 −0.636924
\(467\) −40.5622 −1.87699 −0.938496 0.345289i \(-0.887781\pi\)
−0.938496 + 0.345289i \(0.887781\pi\)
\(468\) −3.53083 −0.163213
\(469\) −36.0433 −1.66432
\(470\) 11.2888 0.520713
\(471\) 7.65031 0.352508
\(472\) 22.2377 1.02357
\(473\) 7.66529 0.352450
\(474\) −17.5551 −0.806333
\(475\) 15.5102 0.711656
\(476\) −31.4243 −1.44033
\(477\) −6.39733 −0.292913
\(478\) 61.5338 2.81449
\(479\) 37.2373 1.70142 0.850708 0.525638i \(-0.176174\pi\)
0.850708 + 0.525638i \(0.176174\pi\)
\(480\) −42.2075 −1.92650
\(481\) 7.02474 0.320300
\(482\) 39.3888 1.79411
\(483\) 24.7493 1.12613
\(484\) −57.7490 −2.62495
\(485\) −14.6762 −0.666414
\(486\) −17.7828 −0.806643
\(487\) −24.2374 −1.09830 −0.549151 0.835723i \(-0.685049\pi\)
−0.549151 + 0.835723i \(0.685049\pi\)
\(488\) −84.1620 −3.80984
\(489\) 14.4414 0.653065
\(490\) −2.18243 −0.0985920
\(491\) −33.4164 −1.50806 −0.754030 0.656839i \(-0.771893\pi\)
−0.754030 + 0.656839i \(0.771893\pi\)
\(492\) 58.5276 2.63863
\(493\) 14.7450 0.664083
\(494\) −10.1902 −0.458477
\(495\) 0.468932 0.0210769
\(496\) −37.4748 −1.68267
\(497\) −34.5532 −1.54992
\(498\) 2.58397 0.115791
\(499\) 17.3723 0.777689 0.388845 0.921303i \(-0.372874\pi\)
0.388845 + 0.921303i \(0.372874\pi\)
\(500\) 46.1746 2.06499
\(501\) 30.3316 1.35511
\(502\) 40.5046 1.80781
\(503\) −23.6472 −1.05438 −0.527189 0.849748i \(-0.676754\pi\)
−0.527189 + 0.849748i \(0.676754\pi\)
\(504\) −15.4771 −0.689404
\(505\) −8.34327 −0.371271
\(506\) −12.0110 −0.533955
\(507\) −1.90538 −0.0846209
\(508\) −49.6288 −2.20192
\(509\) −9.68169 −0.429133 −0.214567 0.976709i \(-0.568834\pi\)
−0.214567 + 0.976709i \(0.568834\pi\)
\(510\) 10.6849 0.473134
\(511\) −10.4202 −0.460964
\(512\) −78.4867 −3.46865
\(513\) −16.6882 −0.736802
\(514\) 20.7785 0.916499
\(515\) 1.10298 0.0486030
\(516\) 98.5973 4.34051
\(517\) −3.78878 −0.166630
\(518\) 47.8978 2.10451
\(519\) −14.3833 −0.631357
\(520\) −8.89895 −0.390245
\(521\) 6.18500 0.270970 0.135485 0.990779i \(-0.456741\pi\)
0.135485 + 0.990779i \(0.456741\pi\)
\(522\) 11.2965 0.494433
\(523\) −9.44238 −0.412887 −0.206443 0.978459i \(-0.566189\pi\)
−0.206443 + 0.978459i \(0.566189\pi\)
\(524\) 28.3885 1.24016
\(525\) 19.7744 0.863026
\(526\) 66.0054 2.87797
\(527\) 5.26035 0.229144
\(528\) 25.5474 1.11181
\(529\) 4.58166 0.199203
\(530\) −25.0804 −1.08942
\(531\) −1.41256 −0.0612999
\(532\) −51.1973 −2.21968
\(533\) 5.48491 0.237578
\(534\) −81.3390 −3.51988
\(535\) 15.5059 0.670380
\(536\) 144.645 6.24773
\(537\) 22.5822 0.974492
\(538\) 70.6909 3.04770
\(539\) 0.732473 0.0315499
\(540\) −22.6694 −0.975537
\(541\) 26.2027 1.12654 0.563271 0.826272i \(-0.309543\pi\)
0.563271 + 0.826272i \(0.309543\pi\)
\(542\) −73.7897 −3.16954
\(543\) −15.8368 −0.679622
\(544\) 56.0539 2.40329
\(545\) −15.6138 −0.668820
\(546\) −12.9917 −0.555995
\(547\) −12.0358 −0.514612 −0.257306 0.966330i \(-0.582835\pi\)
−0.257306 + 0.966330i \(0.582835\pi\)
\(548\) −54.1898 −2.31487
\(549\) 5.34604 0.228163
\(550\) −9.59667 −0.409203
\(551\) 24.0230 1.02341
\(552\) −99.3214 −4.22740
\(553\) −8.26567 −0.351492
\(554\) 78.8449 3.34980
\(555\) −12.0005 −0.509393
\(556\) 103.482 4.38861
\(557\) −21.6892 −0.918999 −0.459500 0.888178i \(-0.651971\pi\)
−0.459500 + 0.888178i \(0.651971\pi\)
\(558\) 4.03006 0.170606
\(559\) 9.24004 0.390812
\(560\) −35.8401 −1.51452
\(561\) −3.58609 −0.151405
\(562\) 19.6832 0.830285
\(563\) 43.0617 1.81483 0.907416 0.420233i \(-0.138052\pi\)
0.907416 + 0.420233i \(0.138052\pi\)
\(564\) −48.7345 −2.05209
\(565\) −1.53926 −0.0647574
\(566\) 26.9327 1.13207
\(567\) −25.9543 −1.08998
\(568\) 138.666 5.81828
\(569\) 31.2329 1.30935 0.654675 0.755910i \(-0.272805\pi\)
0.654675 + 0.755910i \(0.272805\pi\)
\(570\) 17.4081 0.729143
\(571\) 22.9090 0.958712 0.479356 0.877620i \(-0.340870\pi\)
0.479356 + 0.877620i \(0.340870\pi\)
\(572\) 4.64584 0.194252
\(573\) −12.3969 −0.517887
\(574\) 37.3986 1.56099
\(575\) 22.0374 0.919025
\(576\) 22.5638 0.940158
\(577\) −37.8639 −1.57630 −0.788148 0.615485i \(-0.788960\pi\)
−0.788148 + 0.615485i \(0.788960\pi\)
\(578\) 32.6765 1.35916
\(579\) −41.5646 −1.72736
\(580\) 32.6331 1.35501
\(581\) 1.21664 0.0504747
\(582\) 85.9851 3.56420
\(583\) 8.41756 0.348620
\(584\) 41.8174 1.73042
\(585\) 0.565269 0.0233710
\(586\) 16.4225 0.678407
\(587\) 8.26364 0.341077 0.170539 0.985351i \(-0.445449\pi\)
0.170539 + 0.985351i \(0.445449\pi\)
\(588\) 9.42168 0.388544
\(589\) 8.57029 0.353133
\(590\) −5.53786 −0.227990
\(591\) 37.6432 1.54843
\(592\) −113.538 −4.66637
\(593\) 15.2281 0.625345 0.312673 0.949861i \(-0.398776\pi\)
0.312673 + 0.949861i \(0.398776\pi\)
\(594\) 10.3255 0.423662
\(595\) 5.03088 0.206246
\(596\) 129.067 5.28677
\(597\) −27.1963 −1.11307
\(598\) −14.4785 −0.592072
\(599\) −21.1014 −0.862179 −0.431089 0.902309i \(-0.641871\pi\)
−0.431089 + 0.902309i \(0.641871\pi\)
\(600\) −79.3567 −3.23972
\(601\) −46.0284 −1.87754 −0.938770 0.344546i \(-0.888033\pi\)
−0.938770 + 0.344546i \(0.888033\pi\)
\(602\) 63.0027 2.56780
\(603\) −9.18799 −0.374164
\(604\) 30.3819 1.23622
\(605\) 9.24533 0.375876
\(606\) 48.8816 1.98568
\(607\) 28.4268 1.15381 0.576904 0.816812i \(-0.304261\pi\)
0.576904 + 0.816812i \(0.304261\pi\)
\(608\) 91.3243 3.70369
\(609\) 30.6276 1.24109
\(610\) 20.9589 0.848600
\(611\) −4.56715 −0.184767
\(612\) −8.01055 −0.323807
\(613\) 31.3037 1.26435 0.632173 0.774827i \(-0.282163\pi\)
0.632173 + 0.774827i \(0.282163\pi\)
\(614\) 17.4067 0.702478
\(615\) −9.36998 −0.377834
\(616\) 20.3646 0.820514
\(617\) 1.00000 0.0402585
\(618\) −6.46213 −0.259945
\(619\) −6.63834 −0.266818 −0.133409 0.991061i \(-0.542592\pi\)
−0.133409 + 0.991061i \(0.542592\pi\)
\(620\) 11.6420 0.467553
\(621\) −23.7112 −0.951497
\(622\) −90.3779 −3.62382
\(623\) −38.2978 −1.53437
\(624\) 30.7958 1.23282
\(625\) 13.5884 0.543536
\(626\) 47.5563 1.90073
\(627\) −5.84255 −0.233329
\(628\) −22.4857 −0.897278
\(629\) 15.9373 0.635463
\(630\) 3.85426 0.153557
\(631\) 23.7435 0.945212 0.472606 0.881274i \(-0.343313\pi\)
0.472606 + 0.881274i \(0.343313\pi\)
\(632\) 33.1710 1.31947
\(633\) −28.0224 −1.11379
\(634\) −24.2024 −0.961202
\(635\) 7.94533 0.315301
\(636\) 108.274 4.29333
\(637\) 0.882952 0.0349838
\(638\) −14.8638 −0.588464
\(639\) −8.80815 −0.348445
\(640\) 44.1567 1.74545
\(641\) −26.0610 −1.02935 −0.514674 0.857386i \(-0.672087\pi\)
−0.514674 + 0.857386i \(0.672087\pi\)
\(642\) −90.8462 −3.58541
\(643\) −11.2452 −0.443466 −0.221733 0.975107i \(-0.571171\pi\)
−0.221733 + 0.975107i \(0.571171\pi\)
\(644\) −72.7429 −2.86647
\(645\) −15.7850 −0.621532
\(646\) −23.1189 −0.909599
\(647\) −16.4529 −0.646831 −0.323416 0.946257i \(-0.604831\pi\)
−0.323416 + 0.946257i \(0.604831\pi\)
\(648\) 104.157 4.09168
\(649\) 1.85864 0.0729579
\(650\) −11.5682 −0.453742
\(651\) 10.9265 0.428244
\(652\) −42.4462 −1.66232
\(653\) −18.6852 −0.731209 −0.365604 0.930770i \(-0.619138\pi\)
−0.365604 + 0.930770i \(0.619138\pi\)
\(654\) 91.4778 3.57707
\(655\) −4.54486 −0.177582
\(656\) −88.6502 −3.46121
\(657\) −2.65628 −0.103631
\(658\) −31.1409 −1.21400
\(659\) 19.7470 0.769234 0.384617 0.923076i \(-0.374333\pi\)
0.384617 + 0.923076i \(0.374333\pi\)
\(660\) −7.93659 −0.308931
\(661\) 40.6988 1.58300 0.791500 0.611169i \(-0.209300\pi\)
0.791500 + 0.611169i \(0.209300\pi\)
\(662\) 69.8196 2.71362
\(663\) −4.32282 −0.167884
\(664\) −4.88250 −0.189478
\(665\) 8.19643 0.317844
\(666\) 12.2099 0.473124
\(667\) 34.1327 1.32162
\(668\) −89.1503 −3.44933
\(669\) −21.5457 −0.833004
\(670\) −36.0210 −1.39161
\(671\) −7.03429 −0.271556
\(672\) 116.432 4.49147
\(673\) −3.18889 −0.122923 −0.0614613 0.998109i \(-0.519576\pi\)
−0.0614613 + 0.998109i \(0.519576\pi\)
\(674\) 42.6746 1.64376
\(675\) −18.9450 −0.729192
\(676\) 5.60028 0.215395
\(677\) −22.9844 −0.883362 −0.441681 0.897172i \(-0.645618\pi\)
−0.441681 + 0.897172i \(0.645618\pi\)
\(678\) 9.01824 0.346344
\(679\) 40.4854 1.55369
\(680\) −20.1894 −0.774229
\(681\) −47.2674 −1.81129
\(682\) −5.30272 −0.203052
\(683\) 25.7789 0.986404 0.493202 0.869915i \(-0.335826\pi\)
0.493202 + 0.869915i \(0.335826\pi\)
\(684\) −13.0510 −0.499017
\(685\) 8.67552 0.331474
\(686\) 53.7495 2.05217
\(687\) −36.9753 −1.41070
\(688\) −149.343 −5.69364
\(689\) 10.1469 0.386564
\(690\) 24.7340 0.941607
\(691\) −30.1322 −1.14628 −0.573141 0.819457i \(-0.694275\pi\)
−0.573141 + 0.819457i \(0.694275\pi\)
\(692\) 42.2753 1.60707
\(693\) −1.29358 −0.0491390
\(694\) 49.7585 1.88881
\(695\) −16.5669 −0.628420
\(696\) −122.912 −4.65896
\(697\) 12.4438 0.471344
\(698\) 38.0220 1.43915
\(699\) −9.50271 −0.359425
\(700\) −58.1208 −2.19676
\(701\) 32.5446 1.22919 0.614597 0.788841i \(-0.289319\pi\)
0.614597 + 0.788841i \(0.289319\pi\)
\(702\) 12.4468 0.469774
\(703\) 25.9655 0.979307
\(704\) −29.6893 −1.11896
\(705\) 7.80215 0.293846
\(706\) −97.6672 −3.67575
\(707\) 23.0155 0.865586
\(708\) 23.9073 0.898492
\(709\) 5.36266 0.201399 0.100699 0.994917i \(-0.467892\pi\)
0.100699 + 0.994917i \(0.467892\pi\)
\(710\) −34.5319 −1.29596
\(711\) −2.10705 −0.0790204
\(712\) 153.693 5.75988
\(713\) 12.1770 0.456031
\(714\) −29.4749 −1.10307
\(715\) −0.743777 −0.0278157
\(716\) −66.3733 −2.48049
\(717\) 42.5285 1.58826
\(718\) 45.5668 1.70054
\(719\) −49.1337 −1.83238 −0.916188 0.400748i \(-0.868750\pi\)
−0.916188 + 0.400748i \(0.868750\pi\)
\(720\) −9.13619 −0.340486
\(721\) −3.04264 −0.113314
\(722\) 14.7145 0.547619
\(723\) 27.2232 1.01244
\(724\) 46.5474 1.72992
\(725\) 27.2717 1.01284
\(726\) −54.1666 −2.01031
\(727\) −9.75190 −0.361678 −0.180839 0.983513i \(-0.557881\pi\)
−0.180839 + 0.983513i \(0.557881\pi\)
\(728\) 24.5483 0.909821
\(729\) 19.1914 0.710791
\(730\) −10.4138 −0.385432
\(731\) 20.9633 0.775355
\(732\) −90.4808 −3.34427
\(733\) −11.5395 −0.426222 −0.213111 0.977028i \(-0.568360\pi\)
−0.213111 + 0.977028i \(0.568360\pi\)
\(734\) 32.4400 1.19738
\(735\) −1.50837 −0.0556369
\(736\) 129.757 4.78290
\(737\) 12.0895 0.445322
\(738\) 9.53347 0.350932
\(739\) 23.7484 0.873600 0.436800 0.899559i \(-0.356112\pi\)
0.436800 + 0.899559i \(0.356112\pi\)
\(740\) 35.2718 1.29662
\(741\) −7.04284 −0.258725
\(742\) 69.1858 2.53989
\(743\) 19.7555 0.724758 0.362379 0.932031i \(-0.381965\pi\)
0.362379 + 0.932031i \(0.381965\pi\)
\(744\) −43.8492 −1.60759
\(745\) −20.6629 −0.757031
\(746\) −22.9333 −0.839649
\(747\) 0.310140 0.0113474
\(748\) 10.5402 0.385389
\(749\) −42.7741 −1.56293
\(750\) 43.3102 1.58146
\(751\) 11.2707 0.411275 0.205638 0.978628i \(-0.434073\pi\)
0.205638 + 0.978628i \(0.434073\pi\)
\(752\) 73.8168 2.69182
\(753\) 27.9944 1.02017
\(754\) −17.9174 −0.652514
\(755\) −4.86399 −0.177019
\(756\) 62.5351 2.27438
\(757\) −21.6872 −0.788234 −0.394117 0.919060i \(-0.628950\pi\)
−0.394117 + 0.919060i \(0.628950\pi\)
\(758\) 55.5447 2.01747
\(759\) −8.30131 −0.301318
\(760\) −32.8931 −1.19316
\(761\) −28.3931 −1.02925 −0.514624 0.857416i \(-0.672068\pi\)
−0.514624 + 0.857416i \(0.672068\pi\)
\(762\) −46.5501 −1.68633
\(763\) 43.0715 1.55929
\(764\) 36.4368 1.31824
\(765\) 1.28245 0.0463671
\(766\) −91.0558 −3.28998
\(767\) 2.24047 0.0808988
\(768\) −122.323 −4.41396
\(769\) 11.4571 0.413155 0.206578 0.978430i \(-0.433767\pi\)
0.206578 + 0.978430i \(0.433767\pi\)
\(770\) −5.07140 −0.182761
\(771\) 14.3609 0.517194
\(772\) 122.166 4.39686
\(773\) 39.3912 1.41680 0.708402 0.705809i \(-0.249416\pi\)
0.708402 + 0.705809i \(0.249416\pi\)
\(774\) 16.0604 0.577278
\(775\) 9.72927 0.349486
\(776\) −162.472 −5.83240
\(777\) 33.1042 1.18761
\(778\) −33.1181 −1.18734
\(779\) 20.2738 0.726385
\(780\) −9.56707 −0.342556
\(781\) 11.5897 0.414712
\(782\) −32.8481 −1.17465
\(783\) −29.3429 −1.04863
\(784\) −14.2708 −0.509670
\(785\) 3.59986 0.128484
\(786\) 26.6274 0.949768
\(787\) −15.5583 −0.554594 −0.277297 0.960784i \(-0.589439\pi\)
−0.277297 + 0.960784i \(0.589439\pi\)
\(788\) −110.641 −3.94141
\(789\) 45.6190 1.62408
\(790\) −8.26056 −0.293898
\(791\) 4.24616 0.150976
\(792\) 5.19126 0.184463
\(793\) −8.47940 −0.301112
\(794\) 53.9842 1.91583
\(795\) −17.3341 −0.614777
\(796\) 79.9351 2.83323
\(797\) 39.1590 1.38708 0.693542 0.720416i \(-0.256049\pi\)
0.693542 + 0.720416i \(0.256049\pi\)
\(798\) −48.0213 −1.69993
\(799\) −10.3617 −0.366570
\(800\) 103.674 3.66544
\(801\) −9.76269 −0.344948
\(802\) 14.1270 0.498842
\(803\) 3.49511 0.123340
\(804\) 155.505 5.48424
\(805\) 11.6458 0.410460
\(806\) −6.39211 −0.225152
\(807\) 48.8574 1.71986
\(808\) −92.3634 −3.24933
\(809\) −3.98605 −0.140142 −0.0700711 0.997542i \(-0.522323\pi\)
−0.0700711 + 0.997542i \(0.522323\pi\)
\(810\) −25.9382 −0.911377
\(811\) −27.1271 −0.952562 −0.476281 0.879293i \(-0.658016\pi\)
−0.476281 + 0.879293i \(0.658016\pi\)
\(812\) −90.0205 −3.15910
\(813\) −50.9991 −1.78862
\(814\) −16.0657 −0.563102
\(815\) 6.79543 0.238033
\(816\) 69.8679 2.44586
\(817\) 34.1539 1.19489
\(818\) −10.5267 −0.368056
\(819\) −1.55933 −0.0544874
\(820\) 27.5402 0.961745
\(821\) 51.9286 1.81232 0.906161 0.422934i \(-0.139000\pi\)
0.906161 + 0.422934i \(0.139000\pi\)
\(822\) −50.8281 −1.77283
\(823\) −29.8238 −1.03959 −0.519796 0.854290i \(-0.673992\pi\)
−0.519796 + 0.854290i \(0.673992\pi\)
\(824\) 12.2104 0.425370
\(825\) −6.63265 −0.230919
\(826\) 15.2766 0.531539
\(827\) 25.2158 0.876839 0.438419 0.898770i \(-0.355538\pi\)
0.438419 + 0.898770i \(0.355538\pi\)
\(828\) −18.5433 −0.644424
\(829\) 5.19751 0.180517 0.0902586 0.995918i \(-0.471231\pi\)
0.0902586 + 0.995918i \(0.471231\pi\)
\(830\) 1.21589 0.0422041
\(831\) 54.4930 1.89034
\(832\) −35.7886 −1.24075
\(833\) 2.00319 0.0694065
\(834\) 97.0623 3.36099
\(835\) 14.2725 0.493921
\(836\) 17.1724 0.593919
\(837\) −10.4682 −0.361834
\(838\) 9.98556 0.344946
\(839\) 17.9428 0.619453 0.309727 0.950826i \(-0.399762\pi\)
0.309727 + 0.950826i \(0.399762\pi\)
\(840\) −41.9364 −1.44694
\(841\) 13.2397 0.456543
\(842\) −35.7183 −1.23093
\(843\) 13.6039 0.468542
\(844\) 82.3631 2.83505
\(845\) −0.896577 −0.0308432
\(846\) −7.93829 −0.272924
\(847\) −25.5039 −0.876323
\(848\) −163.999 −5.63176
\(849\) 18.6143 0.638841
\(850\) −26.2453 −0.900205
\(851\) 36.8927 1.26467
\(852\) 149.076 5.10728
\(853\) −15.3351 −0.525064 −0.262532 0.964923i \(-0.584558\pi\)
−0.262532 + 0.964923i \(0.584558\pi\)
\(854\) −57.8164 −1.97844
\(855\) 2.08940 0.0714559
\(856\) 171.657 5.86711
\(857\) −21.4849 −0.733909 −0.366955 0.930239i \(-0.619600\pi\)
−0.366955 + 0.930239i \(0.619600\pi\)
\(858\) 4.35764 0.148767
\(859\) 19.0104 0.648627 0.324314 0.945950i \(-0.394867\pi\)
0.324314 + 0.945950i \(0.394867\pi\)
\(860\) 46.3950 1.58206
\(861\) 25.8477 0.880887
\(862\) −87.5386 −2.98158
\(863\) −24.3660 −0.829429 −0.414714 0.909952i \(-0.636119\pi\)
−0.414714 + 0.909952i \(0.636119\pi\)
\(864\) −111.548 −3.79495
\(865\) −6.76807 −0.230121
\(866\) 14.7762 0.502116
\(867\) 22.5841 0.766996
\(868\) −32.1151 −1.09006
\(869\) 2.77244 0.0940485
\(870\) 30.6087 1.03773
\(871\) 14.5732 0.493792
\(872\) −172.850 −5.85345
\(873\) 10.3203 0.349291
\(874\) −53.5169 −1.81024
\(875\) 20.3922 0.689383
\(876\) 44.9570 1.51896
\(877\) −52.0935 −1.75907 −0.879537 0.475831i \(-0.842147\pi\)
−0.879537 + 0.475831i \(0.842147\pi\)
\(878\) 83.3524 2.81301
\(879\) 11.3503 0.382835
\(880\) 12.0213 0.405239
\(881\) −18.6743 −0.629153 −0.314576 0.949232i \(-0.601862\pi\)
−0.314576 + 0.949232i \(0.601862\pi\)
\(882\) 1.53468 0.0516755
\(883\) 38.9810 1.31181 0.655907 0.754841i \(-0.272286\pi\)
0.655907 + 0.754841i \(0.272286\pi\)
\(884\) 12.7056 0.427335
\(885\) −3.82745 −0.128658
\(886\) −58.0360 −1.94976
\(887\) −21.2810 −0.714547 −0.357273 0.934000i \(-0.616294\pi\)
−0.357273 + 0.934000i \(0.616294\pi\)
\(888\) −132.850 −4.45817
\(889\) −21.9177 −0.735096
\(890\) −38.2741 −1.28295
\(891\) 8.70548 0.291644
\(892\) 63.3269 2.12034
\(893\) −16.8815 −0.564918
\(894\) 121.060 4.04885
\(895\) 10.6260 0.355189
\(896\) −121.809 −4.06935
\(897\) −10.0067 −0.334115
\(898\) 74.1802 2.47542
\(899\) 15.0692 0.502585
\(900\) −14.8159 −0.493863
\(901\) 23.0206 0.766928
\(902\) −12.5441 −0.417672
\(903\) 43.5438 1.44905
\(904\) −17.0403 −0.566751
\(905\) −7.45201 −0.247713
\(906\) 28.4971 0.946754
\(907\) 36.2069 1.20223 0.601116 0.799162i \(-0.294723\pi\)
0.601116 + 0.799162i \(0.294723\pi\)
\(908\) 138.928 4.61049
\(909\) 5.86700 0.194596
\(910\) −6.11327 −0.202653
\(911\) −23.8016 −0.788582 −0.394291 0.918986i \(-0.629010\pi\)
−0.394291 + 0.918986i \(0.629010\pi\)
\(912\) 113.830 3.76930
\(913\) −0.408081 −0.0135055
\(914\) 79.0481 2.61468
\(915\) 14.4855 0.478877
\(916\) 108.677 3.59080
\(917\) 12.5373 0.414018
\(918\) 28.2386 0.932013
\(919\) 56.0665 1.84946 0.924732 0.380619i \(-0.124289\pi\)
0.924732 + 0.380619i \(0.124289\pi\)
\(920\) −46.7357 −1.54083
\(921\) 12.0305 0.396419
\(922\) −5.89093 −0.194007
\(923\) 13.9707 0.459851
\(924\) 21.8936 0.720246
\(925\) 29.4768 0.969193
\(926\) −15.2623 −0.501551
\(927\) −0.775615 −0.0254745
\(928\) 160.576 5.27117
\(929\) 44.0479 1.44517 0.722583 0.691284i \(-0.242955\pi\)
0.722583 + 0.691284i \(0.242955\pi\)
\(930\) 10.9198 0.358073
\(931\) 3.26365 0.106962
\(932\) 27.9303 0.914887
\(933\) −62.4639 −2.04498
\(934\) 111.824 3.65900
\(935\) −1.68744 −0.0551851
\(936\) 6.25775 0.204541
\(937\) −59.5467 −1.94531 −0.972653 0.232262i \(-0.925387\pi\)
−0.972653 + 0.232262i \(0.925387\pi\)
\(938\) 99.3663 3.24443
\(939\) 32.8681 1.07261
\(940\) −22.9320 −0.747960
\(941\) −47.9447 −1.56295 −0.781477 0.623934i \(-0.785533\pi\)
−0.781477 + 0.623934i \(0.785533\pi\)
\(942\) −21.0908 −0.687177
\(943\) 28.8058 0.938045
\(944\) −36.2118 −1.17859
\(945\) −10.0116 −0.325676
\(946\) −21.1321 −0.687065
\(947\) 35.8937 1.16639 0.583194 0.812333i \(-0.301803\pi\)
0.583194 + 0.812333i \(0.301803\pi\)
\(948\) 35.6614 1.15823
\(949\) 4.21314 0.136764
\(950\) −42.7594 −1.38730
\(951\) −16.7273 −0.542420
\(952\) 55.6939 1.80505
\(953\) 9.76399 0.316287 0.158143 0.987416i \(-0.449449\pi\)
0.158143 + 0.987416i \(0.449449\pi\)
\(954\) 17.6365 0.571004
\(955\) −5.83335 −0.188763
\(956\) −125.000 −4.04277
\(957\) −10.2730 −0.332079
\(958\) −102.658 −3.31673
\(959\) −23.9320 −0.772804
\(960\) 61.1385 1.97324
\(961\) −25.6240 −0.826581
\(962\) −19.3662 −0.624392
\(963\) −10.9038 −0.351370
\(964\) −80.0143 −2.57709
\(965\) −19.5582 −0.629601
\(966\) −68.2304 −2.19528
\(967\) −45.6133 −1.46682 −0.733412 0.679785i \(-0.762073\pi\)
−0.733412 + 0.679785i \(0.762073\pi\)
\(968\) 102.350 3.28964
\(969\) −15.9784 −0.513300
\(970\) 40.4603 1.29910
\(971\) 10.1981 0.327273 0.163637 0.986521i \(-0.447678\pi\)
0.163637 + 0.986521i \(0.447678\pi\)
\(972\) 36.1239 1.15867
\(973\) 45.7010 1.46511
\(974\) 66.8191 2.14102
\(975\) −7.99526 −0.256053
\(976\) 137.049 4.38683
\(977\) 7.28968 0.233218 0.116609 0.993178i \(-0.462798\pi\)
0.116609 + 0.993178i \(0.462798\pi\)
\(978\) −39.8131 −1.27308
\(979\) 12.8457 0.410550
\(980\) 4.43338 0.141619
\(981\) 10.9796 0.350552
\(982\) 92.1243 2.93981
\(983\) 57.3648 1.82965 0.914826 0.403849i \(-0.132328\pi\)
0.914826 + 0.403849i \(0.132328\pi\)
\(984\) −103.729 −3.30677
\(985\) 17.7130 0.564384
\(986\) −40.6500 −1.29456
\(987\) −21.5227 −0.685076
\(988\) 20.7003 0.658563
\(989\) 48.5271 1.54307
\(990\) −1.29278 −0.0410872
\(991\) −30.2611 −0.961276 −0.480638 0.876919i \(-0.659595\pi\)
−0.480638 + 0.876919i \(0.659595\pi\)
\(992\) 57.2861 1.81884
\(993\) 48.2552 1.53133
\(994\) 95.2584 3.02141
\(995\) −12.7972 −0.405699
\(996\) −5.24907 −0.166323
\(997\) −54.9786 −1.74119 −0.870595 0.492001i \(-0.836266\pi\)
−0.870595 + 0.492001i \(0.836266\pi\)
\(998\) −47.8929 −1.51602
\(999\) −31.7156 −1.00344
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 8021.2.a.c.1.5 169
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8021.2.a.c.1.5 169 1.1 even 1 trivial