Properties

Label 8014.2.a.d.1.11
Level $8014$
Weight $2$
Character 8014.1
Self dual yes
Analytic conductor $63.992$
Analytic rank $0$
Dimension $88$
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] = [8014,2,Mod(1,8014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8014 = 2 \cdot 4007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8014.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: \(63.9921121799\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 8014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.45668 q^{3} +1.00000 q^{4} -0.657543 q^{5} -2.45668 q^{6} +4.85111 q^{7} +1.00000 q^{8} +3.03526 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.45668 q^{3} +1.00000 q^{4} -0.657543 q^{5} -2.45668 q^{6} +4.85111 q^{7} +1.00000 q^{8} +3.03526 q^{9} -0.657543 q^{10} +4.65548 q^{11} -2.45668 q^{12} -5.27842 q^{13} +4.85111 q^{14} +1.61537 q^{15} +1.00000 q^{16} +3.71623 q^{17} +3.03526 q^{18} +7.87815 q^{19} -0.657543 q^{20} -11.9176 q^{21} +4.65548 q^{22} -3.85376 q^{23} -2.45668 q^{24} -4.56764 q^{25} -5.27842 q^{26} -0.0866199 q^{27} +4.85111 q^{28} +7.72413 q^{29} +1.61537 q^{30} -1.67549 q^{31} +1.00000 q^{32} -11.4370 q^{33} +3.71623 q^{34} -3.18982 q^{35} +3.03526 q^{36} +9.74450 q^{37} +7.87815 q^{38} +12.9674 q^{39} -0.657543 q^{40} +8.25622 q^{41} -11.9176 q^{42} +0.474388 q^{43} +4.65548 q^{44} -1.99581 q^{45} -3.85376 q^{46} -3.65590 q^{47} -2.45668 q^{48} +16.5333 q^{49} -4.56764 q^{50} -9.12958 q^{51} -5.27842 q^{52} +1.25043 q^{53} -0.0866199 q^{54} -3.06118 q^{55} +4.85111 q^{56} -19.3541 q^{57} +7.72413 q^{58} -8.73589 q^{59} +1.61537 q^{60} -11.7977 q^{61} -1.67549 q^{62} +14.7244 q^{63} +1.00000 q^{64} +3.47079 q^{65} -11.4370 q^{66} -3.40005 q^{67} +3.71623 q^{68} +9.46744 q^{69} -3.18982 q^{70} +4.45021 q^{71} +3.03526 q^{72} +5.84736 q^{73} +9.74450 q^{74} +11.2212 q^{75} +7.87815 q^{76} +22.5843 q^{77} +12.9674 q^{78} +13.7681 q^{79} -0.657543 q^{80} -8.89298 q^{81} +8.25622 q^{82} -0.0309457 q^{83} -11.9176 q^{84} -2.44358 q^{85} +0.474388 q^{86} -18.9757 q^{87} +4.65548 q^{88} -11.2309 q^{89} -1.99581 q^{90} -25.6062 q^{91} -3.85376 q^{92} +4.11615 q^{93} -3.65590 q^{94} -5.18022 q^{95} -2.45668 q^{96} +4.35610 q^{97} +16.5333 q^{98} +14.1306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.45668 −1.41836 −0.709181 0.705026i \(-0.750935\pi\)
−0.709181 + 0.705026i \(0.750935\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.657543 −0.294062 −0.147031 0.989132i \(-0.546972\pi\)
−0.147031 + 0.989132i \(0.546972\pi\)
\(6\) −2.45668 −1.00293
\(7\) 4.85111 1.83355 0.916774 0.399405i \(-0.130783\pi\)
0.916774 + 0.399405i \(0.130783\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.03526 1.01175
\(10\) −0.657543 −0.207933
\(11\) 4.65548 1.40368 0.701840 0.712334i \(-0.252362\pi\)
0.701840 + 0.712334i \(0.252362\pi\)
\(12\) −2.45668 −0.709181
\(13\) −5.27842 −1.46397 −0.731985 0.681321i \(-0.761406\pi\)
−0.731985 + 0.681321i \(0.761406\pi\)
\(14\) 4.85111 1.29651
\(15\) 1.61537 0.417087
\(16\) 1.00000 0.250000
\(17\) 3.71623 0.901319 0.450660 0.892696i \(-0.351189\pi\)
0.450660 + 0.892696i \(0.351189\pi\)
\(18\) 3.03526 0.715417
\(19\) 7.87815 1.80737 0.903686 0.428197i \(-0.140851\pi\)
0.903686 + 0.428197i \(0.140851\pi\)
\(20\) −0.657543 −0.147031
\(21\) −11.9176 −2.60064
\(22\) 4.65548 0.992552
\(23\) −3.85376 −0.803565 −0.401782 0.915735i \(-0.631609\pi\)
−0.401782 + 0.915735i \(0.631609\pi\)
\(24\) −2.45668 −0.501467
\(25\) −4.56764 −0.913527
\(26\) −5.27842 −1.03518
\(27\) −0.0866199 −0.0166700
\(28\) 4.85111 0.916774
\(29\) 7.72413 1.43434 0.717168 0.696901i \(-0.245438\pi\)
0.717168 + 0.696901i \(0.245438\pi\)
\(30\) 1.61537 0.294925
\(31\) −1.67549 −0.300928 −0.150464 0.988616i \(-0.548077\pi\)
−0.150464 + 0.988616i \(0.548077\pi\)
\(32\) 1.00000 0.176777
\(33\) −11.4370 −1.99093
\(34\) 3.71623 0.637329
\(35\) −3.18982 −0.539177
\(36\) 3.03526 0.505876
\(37\) 9.74450 1.60199 0.800993 0.598674i \(-0.204305\pi\)
0.800993 + 0.598674i \(0.204305\pi\)
\(38\) 7.87815 1.27800
\(39\) 12.9674 2.07644
\(40\) −0.657543 −0.103967
\(41\) 8.25622 1.28941 0.644703 0.764433i \(-0.276981\pi\)
0.644703 + 0.764433i \(0.276981\pi\)
\(42\) −11.9176 −1.83893
\(43\) 0.474388 0.0723435 0.0361718 0.999346i \(-0.488484\pi\)
0.0361718 + 0.999346i \(0.488484\pi\)
\(44\) 4.65548 0.701840
\(45\) −1.99581 −0.297518
\(46\) −3.85376 −0.568206
\(47\) −3.65590 −0.533268 −0.266634 0.963798i \(-0.585911\pi\)
−0.266634 + 0.963798i \(0.585911\pi\)
\(48\) −2.45668 −0.354591
\(49\) 16.5333 2.36190
\(50\) −4.56764 −0.645961
\(51\) −9.12958 −1.27840
\(52\) −5.27842 −0.731985
\(53\) 1.25043 0.171760 0.0858802 0.996305i \(-0.472630\pi\)
0.0858802 + 0.996305i \(0.472630\pi\)
\(54\) −0.0866199 −0.0117875
\(55\) −3.06118 −0.412769
\(56\) 4.85111 0.648257
\(57\) −19.3541 −2.56351
\(58\) 7.72413 1.01423
\(59\) −8.73589 −1.13732 −0.568658 0.822574i \(-0.692537\pi\)
−0.568658 + 0.822574i \(0.692537\pi\)
\(60\) 1.61537 0.208543
\(61\) −11.7977 −1.51054 −0.755272 0.655412i \(-0.772495\pi\)
−0.755272 + 0.655412i \(0.772495\pi\)
\(62\) −1.67549 −0.212788
\(63\) 14.7244 1.85510
\(64\) 1.00000 0.125000
\(65\) 3.47079 0.430498
\(66\) −11.4370 −1.40780
\(67\) −3.40005 −0.415382 −0.207691 0.978194i \(-0.566595\pi\)
−0.207691 + 0.978194i \(0.566595\pi\)
\(68\) 3.71623 0.450660
\(69\) 9.46744 1.13975
\(70\) −3.18982 −0.381256
\(71\) 4.45021 0.528142 0.264071 0.964503i \(-0.414935\pi\)
0.264071 + 0.964503i \(0.414935\pi\)
\(72\) 3.03526 0.357709
\(73\) 5.84736 0.684382 0.342191 0.939630i \(-0.388831\pi\)
0.342191 + 0.939630i \(0.388831\pi\)
\(74\) 9.74450 1.13277
\(75\) 11.2212 1.29571
\(76\) 7.87815 0.903686
\(77\) 22.5843 2.57372
\(78\) 12.9674 1.46826
\(79\) 13.7681 1.54904 0.774518 0.632552i \(-0.217992\pi\)
0.774518 + 0.632552i \(0.217992\pi\)
\(80\) −0.657543 −0.0735155
\(81\) −8.89298 −0.988109
\(82\) 8.25622 0.911747
\(83\) −0.0309457 −0.00339673 −0.00169836 0.999999i \(-0.500541\pi\)
−0.00169836 + 0.999999i \(0.500541\pi\)
\(84\) −11.9176 −1.30032
\(85\) −2.44358 −0.265044
\(86\) 0.474388 0.0511546
\(87\) −18.9757 −2.03441
\(88\) 4.65548 0.496276
\(89\) −11.2309 −1.19047 −0.595237 0.803550i \(-0.702942\pi\)
−0.595237 + 0.803550i \(0.702942\pi\)
\(90\) −1.99581 −0.210377
\(91\) −25.6062 −2.68426
\(92\) −3.85376 −0.401782
\(93\) 4.11615 0.426824
\(94\) −3.65590 −0.377077
\(95\) −5.18022 −0.531479
\(96\) −2.45668 −0.250733
\(97\) 4.35610 0.442295 0.221148 0.975240i \(-0.429020\pi\)
0.221148 + 0.975240i \(0.429020\pi\)
\(98\) 16.5333 1.67012
\(99\) 14.1306 1.42018
\(100\) −4.56764 −0.456764
\(101\) −1.82482 −0.181576 −0.0907881 0.995870i \(-0.528939\pi\)
−0.0907881 + 0.995870i \(0.528939\pi\)
\(102\) −9.12958 −0.903964
\(103\) −10.8846 −1.07249 −0.536245 0.844063i \(-0.680158\pi\)
−0.536245 + 0.844063i \(0.680158\pi\)
\(104\) −5.27842 −0.517591
\(105\) 7.83635 0.764749
\(106\) 1.25043 0.121453
\(107\) −16.0350 −1.55016 −0.775081 0.631862i \(-0.782291\pi\)
−0.775081 + 0.631862i \(0.782291\pi\)
\(108\) −0.0866199 −0.00833500
\(109\) 5.14174 0.492489 0.246244 0.969208i \(-0.420803\pi\)
0.246244 + 0.969208i \(0.420803\pi\)
\(110\) −3.06118 −0.291872
\(111\) −23.9391 −2.27220
\(112\) 4.85111 0.458387
\(113\) 8.10135 0.762111 0.381055 0.924552i \(-0.375561\pi\)
0.381055 + 0.924552i \(0.375561\pi\)
\(114\) −19.3541 −1.81267
\(115\) 2.53401 0.236298
\(116\) 7.72413 0.717168
\(117\) −16.0214 −1.48118
\(118\) −8.73589 −0.804203
\(119\) 18.0279 1.65261
\(120\) 1.61537 0.147462
\(121\) 10.6735 0.970319
\(122\) −11.7977 −1.06812
\(123\) −20.2829 −1.82884
\(124\) −1.67549 −0.150464
\(125\) 6.29113 0.562696
\(126\) 14.7244 1.31175
\(127\) −8.49939 −0.754199 −0.377099 0.926173i \(-0.623078\pi\)
−0.377099 + 0.926173i \(0.623078\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.16542 −0.102609
\(130\) 3.47079 0.304408
\(131\) −5.87777 −0.513543 −0.256772 0.966472i \(-0.582659\pi\)
−0.256772 + 0.966472i \(0.582659\pi\)
\(132\) −11.4370 −0.995464
\(133\) 38.2178 3.31390
\(134\) −3.40005 −0.293720
\(135\) 0.0569563 0.00490202
\(136\) 3.71623 0.318664
\(137\) 12.7165 1.08645 0.543223 0.839589i \(-0.317204\pi\)
0.543223 + 0.839589i \(0.317204\pi\)
\(138\) 9.46744 0.805922
\(139\) 8.41180 0.713480 0.356740 0.934204i \(-0.383888\pi\)
0.356740 + 0.934204i \(0.383888\pi\)
\(140\) −3.18982 −0.269589
\(141\) 8.98136 0.756367
\(142\) 4.45021 0.373453
\(143\) −24.5736 −2.05495
\(144\) 3.03526 0.252938
\(145\) −5.07895 −0.421784
\(146\) 5.84736 0.483931
\(147\) −40.6170 −3.35003
\(148\) 9.74450 0.800993
\(149\) 12.3235 1.00958 0.504790 0.863242i \(-0.331570\pi\)
0.504790 + 0.863242i \(0.331570\pi\)
\(150\) 11.2212 0.916208
\(151\) −11.7387 −0.955285 −0.477643 0.878554i \(-0.658509\pi\)
−0.477643 + 0.878554i \(0.658509\pi\)
\(152\) 7.87815 0.639002
\(153\) 11.2797 0.911912
\(154\) 22.5843 1.81989
\(155\) 1.10171 0.0884914
\(156\) 12.9674 1.03822
\(157\) 13.4078 1.07006 0.535028 0.844834i \(-0.320301\pi\)
0.535028 + 0.844834i \(0.320301\pi\)
\(158\) 13.7681 1.09533
\(159\) −3.07191 −0.243618
\(160\) −0.657543 −0.0519833
\(161\) −18.6950 −1.47338
\(162\) −8.89298 −0.698698
\(163\) −8.49718 −0.665551 −0.332775 0.943006i \(-0.607985\pi\)
−0.332775 + 0.943006i \(0.607985\pi\)
\(164\) 8.25622 0.644703
\(165\) 7.52033 0.585457
\(166\) −0.0309457 −0.00240185
\(167\) −18.4665 −1.42898 −0.714490 0.699646i \(-0.753341\pi\)
−0.714490 + 0.699646i \(0.753341\pi\)
\(168\) −11.9176 −0.919464
\(169\) 14.8617 1.14321
\(170\) −2.44358 −0.187414
\(171\) 23.9122 1.82861
\(172\) 0.474388 0.0361718
\(173\) −7.14070 −0.542897 −0.271449 0.962453i \(-0.587503\pi\)
−0.271449 + 0.962453i \(0.587503\pi\)
\(174\) −18.9757 −1.43854
\(175\) −22.1581 −1.67500
\(176\) 4.65548 0.350920
\(177\) 21.4612 1.61313
\(178\) −11.2309 −0.841793
\(179\) 0.549358 0.0410610 0.0205305 0.999789i \(-0.493464\pi\)
0.0205305 + 0.999789i \(0.493464\pi\)
\(180\) −1.99581 −0.148759
\(181\) −23.6930 −1.76108 −0.880542 0.473967i \(-0.842821\pi\)
−0.880542 + 0.473967i \(0.842821\pi\)
\(182\) −25.6062 −1.89806
\(183\) 28.9832 2.14250
\(184\) −3.85376 −0.284103
\(185\) −6.40743 −0.471083
\(186\) 4.11615 0.301810
\(187\) 17.3009 1.26516
\(188\) −3.65590 −0.266634
\(189\) −0.420203 −0.0305653
\(190\) −5.18022 −0.375813
\(191\) −0.682066 −0.0493525 −0.0246763 0.999695i \(-0.507855\pi\)
−0.0246763 + 0.999695i \(0.507855\pi\)
\(192\) −2.45668 −0.177295
\(193\) −25.0276 −1.80153 −0.900763 0.434312i \(-0.856992\pi\)
−0.900763 + 0.434312i \(0.856992\pi\)
\(194\) 4.35610 0.312750
\(195\) −8.52660 −0.610602
\(196\) 16.5333 1.18095
\(197\) −19.0279 −1.35568 −0.677841 0.735209i \(-0.737084\pi\)
−0.677841 + 0.735209i \(0.737084\pi\)
\(198\) 14.1306 1.00422
\(199\) −5.36205 −0.380106 −0.190053 0.981774i \(-0.560866\pi\)
−0.190053 + 0.981774i \(0.560866\pi\)
\(200\) −4.56764 −0.322981
\(201\) 8.35283 0.589163
\(202\) −1.82482 −0.128394
\(203\) 37.4706 2.62992
\(204\) −9.12958 −0.639199
\(205\) −5.42882 −0.379165
\(206\) −10.8846 −0.758365
\(207\) −11.6972 −0.813009
\(208\) −5.27842 −0.365992
\(209\) 36.6766 2.53697
\(210\) 7.83635 0.540759
\(211\) 27.9985 1.92750 0.963748 0.266815i \(-0.0859714\pi\)
0.963748 + 0.266815i \(0.0859714\pi\)
\(212\) 1.25043 0.0858802
\(213\) −10.9327 −0.749098
\(214\) −16.0350 −1.09613
\(215\) −0.311931 −0.0212735
\(216\) −0.0866199 −0.00589373
\(217\) −8.12801 −0.551765
\(218\) 5.14174 0.348242
\(219\) −14.3651 −0.970701
\(220\) −3.06118 −0.206385
\(221\) −19.6158 −1.31950
\(222\) −23.9391 −1.60669
\(223\) −1.62148 −0.108582 −0.0542912 0.998525i \(-0.517290\pi\)
−0.0542912 + 0.998525i \(0.517290\pi\)
\(224\) 4.85111 0.324129
\(225\) −13.8640 −0.924264
\(226\) 8.10135 0.538894
\(227\) 9.46216 0.628026 0.314013 0.949419i \(-0.398327\pi\)
0.314013 + 0.949419i \(0.398327\pi\)
\(228\) −19.3541 −1.28175
\(229\) −1.53149 −0.101204 −0.0506019 0.998719i \(-0.516114\pi\)
−0.0506019 + 0.998719i \(0.516114\pi\)
\(230\) 2.53401 0.167088
\(231\) −55.4823 −3.65046
\(232\) 7.72413 0.507114
\(233\) −13.1802 −0.863461 −0.431731 0.902003i \(-0.642097\pi\)
−0.431731 + 0.902003i \(0.642097\pi\)
\(234\) −16.0214 −1.04735
\(235\) 2.40391 0.156814
\(236\) −8.73589 −0.568658
\(237\) −33.8239 −2.19710
\(238\) 18.0279 1.16857
\(239\) 19.4289 1.25675 0.628374 0.777911i \(-0.283721\pi\)
0.628374 + 0.777911i \(0.283721\pi\)
\(240\) 1.61537 0.104272
\(241\) −9.95609 −0.641328 −0.320664 0.947193i \(-0.603906\pi\)
−0.320664 + 0.947193i \(0.603906\pi\)
\(242\) 10.6735 0.686119
\(243\) 22.1070 1.41817
\(244\) −11.7977 −0.755272
\(245\) −10.8714 −0.694546
\(246\) −20.2829 −1.29319
\(247\) −41.5841 −2.64594
\(248\) −1.67549 −0.106394
\(249\) 0.0760234 0.00481779
\(250\) 6.29113 0.397886
\(251\) 29.0730 1.83507 0.917535 0.397656i \(-0.130176\pi\)
0.917535 + 0.397656i \(0.130176\pi\)
\(252\) 14.7244 0.927549
\(253\) −17.9411 −1.12795
\(254\) −8.49939 −0.533299
\(255\) 6.00309 0.375928
\(256\) 1.00000 0.0625000
\(257\) −3.63027 −0.226450 −0.113225 0.993569i \(-0.536118\pi\)
−0.113225 + 0.993569i \(0.536118\pi\)
\(258\) −1.16542 −0.0725558
\(259\) 47.2717 2.93732
\(260\) 3.47079 0.215249
\(261\) 23.4447 1.45119
\(262\) −5.87777 −0.363130
\(263\) 14.2500 0.878695 0.439347 0.898317i \(-0.355210\pi\)
0.439347 + 0.898317i \(0.355210\pi\)
\(264\) −11.4370 −0.703899
\(265\) −0.822214 −0.0505082
\(266\) 38.2178 2.34328
\(267\) 27.5907 1.68853
\(268\) −3.40005 −0.207691
\(269\) −15.8136 −0.964171 −0.482085 0.876124i \(-0.660121\pi\)
−0.482085 + 0.876124i \(0.660121\pi\)
\(270\) 0.0569563 0.00346625
\(271\) −2.72575 −0.165577 −0.0827887 0.996567i \(-0.526383\pi\)
−0.0827887 + 0.996567i \(0.526383\pi\)
\(272\) 3.71623 0.225330
\(273\) 62.9062 3.80725
\(274\) 12.7165 0.768233
\(275\) −21.2646 −1.28230
\(276\) 9.46744 0.569873
\(277\) −3.79366 −0.227939 −0.113970 0.993484i \(-0.536357\pi\)
−0.113970 + 0.993484i \(0.536357\pi\)
\(278\) 8.41180 0.504506
\(279\) −5.08556 −0.304464
\(280\) −3.18982 −0.190628
\(281\) 6.39000 0.381195 0.190598 0.981668i \(-0.438957\pi\)
0.190598 + 0.981668i \(0.438957\pi\)
\(282\) 8.98136 0.534832
\(283\) 7.11658 0.423037 0.211518 0.977374i \(-0.432159\pi\)
0.211518 + 0.977374i \(0.432159\pi\)
\(284\) 4.45021 0.264071
\(285\) 12.7261 0.753831
\(286\) −24.5736 −1.45307
\(287\) 40.0519 2.36419
\(288\) 3.03526 0.178854
\(289\) −3.18960 −0.187624
\(290\) −5.07895 −0.298246
\(291\) −10.7015 −0.627335
\(292\) 5.84736 0.342191
\(293\) 23.5193 1.37401 0.687007 0.726651i \(-0.258924\pi\)
0.687007 + 0.726651i \(0.258924\pi\)
\(294\) −40.6170 −2.36883
\(295\) 5.74422 0.334441
\(296\) 9.74450 0.566387
\(297\) −0.403257 −0.0233994
\(298\) 12.3235 0.713881
\(299\) 20.3418 1.17639
\(300\) 11.2212 0.647857
\(301\) 2.30131 0.132645
\(302\) −11.7387 −0.675489
\(303\) 4.48299 0.257541
\(304\) 7.87815 0.451843
\(305\) 7.75751 0.444194
\(306\) 11.2797 0.644819
\(307\) −4.26127 −0.243203 −0.121602 0.992579i \(-0.538803\pi\)
−0.121602 + 0.992579i \(0.538803\pi\)
\(308\) 22.5843 1.28686
\(309\) 26.7399 1.52118
\(310\) 1.10171 0.0625729
\(311\) −2.05998 −0.116811 −0.0584054 0.998293i \(-0.518602\pi\)
−0.0584054 + 0.998293i \(0.518602\pi\)
\(312\) 12.9674 0.734132
\(313\) −4.77654 −0.269986 −0.134993 0.990847i \(-0.543101\pi\)
−0.134993 + 0.990847i \(0.543101\pi\)
\(314\) 13.4078 0.756644
\(315\) −9.68192 −0.545514
\(316\) 13.7681 0.774518
\(317\) 24.9167 1.39946 0.699731 0.714406i \(-0.253303\pi\)
0.699731 + 0.714406i \(0.253303\pi\)
\(318\) −3.07191 −0.172264
\(319\) 35.9596 2.01335
\(320\) −0.657543 −0.0367578
\(321\) 39.3928 2.19869
\(322\) −18.6950 −1.04183
\(323\) 29.2770 1.62902
\(324\) −8.89298 −0.494054
\(325\) 24.1099 1.33738
\(326\) −8.49718 −0.470615
\(327\) −12.6316 −0.698528
\(328\) 8.25622 0.455874
\(329\) −17.7352 −0.977772
\(330\) 7.52033 0.413980
\(331\) 29.1738 1.60353 0.801767 0.597636i \(-0.203893\pi\)
0.801767 + 0.597636i \(0.203893\pi\)
\(332\) −0.0309457 −0.00169836
\(333\) 29.5771 1.62081
\(334\) −18.4665 −1.01044
\(335\) 2.23568 0.122148
\(336\) −11.9176 −0.650159
\(337\) −5.77401 −0.314530 −0.157265 0.987556i \(-0.550268\pi\)
−0.157265 + 0.987556i \(0.550268\pi\)
\(338\) 14.8617 0.808369
\(339\) −19.9024 −1.08095
\(340\) −2.44358 −0.132522
\(341\) −7.80023 −0.422406
\(342\) 23.9122 1.29302
\(343\) 46.2472 2.49711
\(344\) 0.474388 0.0255773
\(345\) −6.22525 −0.335156
\(346\) −7.14070 −0.383886
\(347\) 16.8513 0.904623 0.452311 0.891860i \(-0.350600\pi\)
0.452311 + 0.891860i \(0.350600\pi\)
\(348\) −18.9757 −1.01720
\(349\) 18.2569 0.977272 0.488636 0.872488i \(-0.337495\pi\)
0.488636 + 0.872488i \(0.337495\pi\)
\(350\) −22.1581 −1.18440
\(351\) 0.457216 0.0244044
\(352\) 4.65548 0.248138
\(353\) −19.7042 −1.04875 −0.524374 0.851488i \(-0.675701\pi\)
−0.524374 + 0.851488i \(0.675701\pi\)
\(354\) 21.4612 1.14065
\(355\) −2.92620 −0.155307
\(356\) −11.2309 −0.595237
\(357\) −44.2887 −2.34400
\(358\) 0.549358 0.0290345
\(359\) −22.2212 −1.17279 −0.586396 0.810024i \(-0.699454\pi\)
−0.586396 + 0.810024i \(0.699454\pi\)
\(360\) −1.99581 −0.105189
\(361\) 43.0652 2.26659
\(362\) −23.6930 −1.24527
\(363\) −26.2214 −1.37626
\(364\) −25.6062 −1.34213
\(365\) −3.84489 −0.201251
\(366\) 28.9832 1.51498
\(367\) 31.0026 1.61832 0.809160 0.587588i \(-0.199922\pi\)
0.809160 + 0.587588i \(0.199922\pi\)
\(368\) −3.85376 −0.200891
\(369\) 25.0598 1.30456
\(370\) −6.40743 −0.333106
\(371\) 6.06600 0.314931
\(372\) 4.11615 0.213412
\(373\) 0.0557758 0.00288796 0.00144398 0.999999i \(-0.499540\pi\)
0.00144398 + 0.999999i \(0.499540\pi\)
\(374\) 17.3009 0.894606
\(375\) −15.4553 −0.798107
\(376\) −3.65590 −0.188539
\(377\) −40.7712 −2.09982
\(378\) −0.420203 −0.0216129
\(379\) −23.4822 −1.20620 −0.603099 0.797666i \(-0.706068\pi\)
−0.603099 + 0.797666i \(0.706068\pi\)
\(380\) −5.18022 −0.265740
\(381\) 20.8802 1.06973
\(382\) −0.682066 −0.0348975
\(383\) 28.1050 1.43610 0.718049 0.695992i \(-0.245035\pi\)
0.718049 + 0.695992i \(0.245035\pi\)
\(384\) −2.45668 −0.125367
\(385\) −14.8501 −0.756833
\(386\) −25.0276 −1.27387
\(387\) 1.43989 0.0731938
\(388\) 4.35610 0.221148
\(389\) 27.4912 1.39386 0.696929 0.717140i \(-0.254549\pi\)
0.696929 + 0.717140i \(0.254549\pi\)
\(390\) −8.52660 −0.431761
\(391\) −14.3215 −0.724268
\(392\) 16.5333 0.835058
\(393\) 14.4398 0.728391
\(394\) −19.0279 −0.958612
\(395\) −9.05314 −0.455513
\(396\) 14.1306 0.710089
\(397\) 37.7034 1.89228 0.946141 0.323755i \(-0.104946\pi\)
0.946141 + 0.323755i \(0.104946\pi\)
\(398\) −5.36205 −0.268775
\(399\) −93.8888 −4.70032
\(400\) −4.56764 −0.228382
\(401\) 0.289242 0.0144441 0.00722203 0.999974i \(-0.497701\pi\)
0.00722203 + 0.999974i \(0.497701\pi\)
\(402\) 8.35283 0.416601
\(403\) 8.84395 0.440549
\(404\) −1.82482 −0.0907881
\(405\) 5.84752 0.290565
\(406\) 37.4706 1.85964
\(407\) 45.3653 2.24868
\(408\) −9.12958 −0.451982
\(409\) 17.2439 0.852658 0.426329 0.904568i \(-0.359807\pi\)
0.426329 + 0.904568i \(0.359807\pi\)
\(410\) −5.42882 −0.268110
\(411\) −31.2404 −1.54097
\(412\) −10.8846 −0.536245
\(413\) −42.3788 −2.08532
\(414\) −11.6972 −0.574884
\(415\) 0.0203481 0.000998849 0
\(416\) −5.27842 −0.258796
\(417\) −20.6651 −1.01197
\(418\) 36.6766 1.79391
\(419\) 11.8682 0.579798 0.289899 0.957057i \(-0.406378\pi\)
0.289899 + 0.957057i \(0.406378\pi\)
\(420\) 7.83635 0.382375
\(421\) 17.9260 0.873662 0.436831 0.899544i \(-0.356101\pi\)
0.436831 + 0.899544i \(0.356101\pi\)
\(422\) 27.9985 1.36294
\(423\) −11.0966 −0.539535
\(424\) 1.25043 0.0607264
\(425\) −16.9744 −0.823380
\(426\) −10.9327 −0.529692
\(427\) −57.2321 −2.76966
\(428\) −16.0350 −0.775081
\(429\) 60.3693 2.91466
\(430\) −0.311931 −0.0150426
\(431\) 23.7562 1.14430 0.572148 0.820150i \(-0.306110\pi\)
0.572148 + 0.820150i \(0.306110\pi\)
\(432\) −0.0866199 −0.00416750
\(433\) −10.5516 −0.507075 −0.253538 0.967326i \(-0.581594\pi\)
−0.253538 + 0.967326i \(0.581594\pi\)
\(434\) −8.12801 −0.390157
\(435\) 12.4773 0.598242
\(436\) 5.14174 0.246244
\(437\) −30.3605 −1.45234
\(438\) −14.3651 −0.686390
\(439\) 13.2659 0.633148 0.316574 0.948568i \(-0.397467\pi\)
0.316574 + 0.948568i \(0.397467\pi\)
\(440\) −3.06118 −0.145936
\(441\) 50.1829 2.38966
\(442\) −19.6158 −0.933030
\(443\) −10.4100 −0.494595 −0.247298 0.968940i \(-0.579543\pi\)
−0.247298 + 0.968940i \(0.579543\pi\)
\(444\) −23.9391 −1.13610
\(445\) 7.38481 0.350074
\(446\) −1.62148 −0.0767793
\(447\) −30.2748 −1.43195
\(448\) 4.85111 0.229194
\(449\) −17.3246 −0.817597 −0.408799 0.912625i \(-0.634052\pi\)
−0.408799 + 0.912625i \(0.634052\pi\)
\(450\) −13.8640 −0.653553
\(451\) 38.4367 1.80991
\(452\) 8.10135 0.381055
\(453\) 28.8383 1.35494
\(454\) 9.46216 0.444081
\(455\) 16.8372 0.789339
\(456\) −19.3541 −0.906337
\(457\) −20.1850 −0.944215 −0.472108 0.881541i \(-0.656507\pi\)
−0.472108 + 0.881541i \(0.656507\pi\)
\(458\) −1.53149 −0.0715619
\(459\) −0.321900 −0.0150250
\(460\) 2.53401 0.118149
\(461\) 1.41661 0.0659779 0.0329889 0.999456i \(-0.489497\pi\)
0.0329889 + 0.999456i \(0.489497\pi\)
\(462\) −55.4823 −2.58127
\(463\) 19.8843 0.924101 0.462051 0.886854i \(-0.347114\pi\)
0.462051 + 0.886854i \(0.347114\pi\)
\(464\) 7.72413 0.358584
\(465\) −2.70654 −0.125513
\(466\) −13.1802 −0.610559
\(467\) −33.2983 −1.54086 −0.770431 0.637524i \(-0.779959\pi\)
−0.770431 + 0.637524i \(0.779959\pi\)
\(468\) −16.0214 −0.740588
\(469\) −16.4940 −0.761624
\(470\) 2.40391 0.110884
\(471\) −32.9385 −1.51773
\(472\) −8.73589 −0.402102
\(473\) 2.20851 0.101547
\(474\) −33.8239 −1.55358
\(475\) −35.9845 −1.65108
\(476\) 18.0279 0.826306
\(477\) 3.79539 0.173779
\(478\) 19.4289 0.888655
\(479\) −19.5149 −0.891660 −0.445830 0.895118i \(-0.647091\pi\)
−0.445830 + 0.895118i \(0.647091\pi\)
\(480\) 1.61537 0.0737312
\(481\) −51.4355 −2.34526
\(482\) −9.95609 −0.453487
\(483\) 45.9277 2.08978
\(484\) 10.6735 0.485159
\(485\) −2.86432 −0.130062
\(486\) 22.1070 1.00280
\(487\) 2.43265 0.110234 0.0551169 0.998480i \(-0.482447\pi\)
0.0551169 + 0.998480i \(0.482447\pi\)
\(488\) −11.7977 −0.534058
\(489\) 20.8748 0.943992
\(490\) −10.8714 −0.491118
\(491\) 26.1573 1.18046 0.590231 0.807234i \(-0.299036\pi\)
0.590231 + 0.807234i \(0.299036\pi\)
\(492\) −20.2829 −0.914422
\(493\) 28.7047 1.29279
\(494\) −41.5841 −1.87096
\(495\) −9.29147 −0.417621
\(496\) −1.67549 −0.0752319
\(497\) 21.5885 0.968375
\(498\) 0.0760234 0.00340669
\(499\) 13.2342 0.592444 0.296222 0.955119i \(-0.404273\pi\)
0.296222 + 0.955119i \(0.404273\pi\)
\(500\) 6.29113 0.281348
\(501\) 45.3662 2.02681
\(502\) 29.0730 1.29759
\(503\) −29.2876 −1.30587 −0.652934 0.757415i \(-0.726462\pi\)
−0.652934 + 0.757415i \(0.726462\pi\)
\(504\) 14.7244 0.655876
\(505\) 1.19990 0.0533947
\(506\) −17.9411 −0.797580
\(507\) −36.5103 −1.62148
\(508\) −8.49939 −0.377099
\(509\) 27.6933 1.22748 0.613742 0.789507i \(-0.289664\pi\)
0.613742 + 0.789507i \(0.289664\pi\)
\(510\) 6.00309 0.265821
\(511\) 28.3662 1.25485
\(512\) 1.00000 0.0441942
\(513\) −0.682404 −0.0301289
\(514\) −3.63027 −0.160124
\(515\) 7.15708 0.315379
\(516\) −1.16542 −0.0513047
\(517\) −17.0200 −0.748537
\(518\) 47.2717 2.07700
\(519\) 17.5424 0.770025
\(520\) 3.47079 0.152204
\(521\) −30.6888 −1.34450 −0.672250 0.740324i \(-0.734672\pi\)
−0.672250 + 0.740324i \(0.734672\pi\)
\(522\) 23.4447 1.02615
\(523\) −0.0449696 −0.00196638 −0.000983191 1.00000i \(-0.500313\pi\)
−0.000983191 1.00000i \(0.500313\pi\)
\(524\) −5.87777 −0.256772
\(525\) 54.4354 2.37575
\(526\) 14.2500 0.621331
\(527\) −6.22653 −0.271232
\(528\) −11.4370 −0.497732
\(529\) −8.14852 −0.354284
\(530\) −0.822214 −0.0357147
\(531\) −26.5157 −1.15068
\(532\) 38.2178 1.65695
\(533\) −43.5798 −1.88765
\(534\) 27.5907 1.19397
\(535\) 10.5437 0.455844
\(536\) −3.40005 −0.146860
\(537\) −1.34960 −0.0582393
\(538\) −15.8136 −0.681772
\(539\) 76.9705 3.31536
\(540\) 0.0569563 0.00245101
\(541\) 30.4047 1.30720 0.653599 0.756841i \(-0.273258\pi\)
0.653599 + 0.756841i \(0.273258\pi\)
\(542\) −2.72575 −0.117081
\(543\) 58.2060 2.49786
\(544\) 3.71623 0.159332
\(545\) −3.38091 −0.144822
\(546\) 62.9062 2.69213
\(547\) −3.01713 −0.129003 −0.0645015 0.997918i \(-0.520546\pi\)
−0.0645015 + 0.997918i \(0.520546\pi\)
\(548\) 12.7165 0.543223
\(549\) −35.8091 −1.52830
\(550\) −21.2646 −0.906723
\(551\) 60.8519 2.59238
\(552\) 9.46744 0.402961
\(553\) 66.7908 2.84023
\(554\) −3.79366 −0.161177
\(555\) 15.7410 0.668167
\(556\) 8.41180 0.356740
\(557\) 28.2522 1.19708 0.598541 0.801092i \(-0.295747\pi\)
0.598541 + 0.801092i \(0.295747\pi\)
\(558\) −5.08556 −0.215289
\(559\) −2.50402 −0.105909
\(560\) −3.18982 −0.134794
\(561\) −42.5026 −1.79446
\(562\) 6.39000 0.269546
\(563\) −0.798961 −0.0336722 −0.0168361 0.999858i \(-0.505359\pi\)
−0.0168361 + 0.999858i \(0.505359\pi\)
\(564\) 8.98136 0.378184
\(565\) −5.32698 −0.224108
\(566\) 7.11658 0.299132
\(567\) −43.1409 −1.81175
\(568\) 4.45021 0.186727
\(569\) −26.0163 −1.09066 −0.545331 0.838221i \(-0.683596\pi\)
−0.545331 + 0.838221i \(0.683596\pi\)
\(570\) 12.7261 0.533039
\(571\) −33.2937 −1.39330 −0.696650 0.717411i \(-0.745327\pi\)
−0.696650 + 0.717411i \(0.745327\pi\)
\(572\) −24.5736 −1.02747
\(573\) 1.67561 0.0699998
\(574\) 40.0519 1.67173
\(575\) 17.6026 0.734078
\(576\) 3.03526 0.126469
\(577\) −5.13287 −0.213684 −0.106842 0.994276i \(-0.534074\pi\)
−0.106842 + 0.994276i \(0.534074\pi\)
\(578\) −3.18960 −0.132670
\(579\) 61.4847 2.55522
\(580\) −5.07895 −0.210892
\(581\) −0.150121 −0.00622806
\(582\) −10.7015 −0.443593
\(583\) 5.82137 0.241097
\(584\) 5.84736 0.241965
\(585\) 10.5347 0.435558
\(586\) 23.5193 0.971574
\(587\) 3.97512 0.164071 0.0820354 0.996629i \(-0.473858\pi\)
0.0820354 + 0.996629i \(0.473858\pi\)
\(588\) −40.6170 −1.67502
\(589\) −13.1998 −0.543888
\(590\) 5.74422 0.236486
\(591\) 46.7454 1.92285
\(592\) 9.74450 0.400496
\(593\) −12.3895 −0.508776 −0.254388 0.967102i \(-0.581874\pi\)
−0.254388 + 0.967102i \(0.581874\pi\)
\(594\) −0.403257 −0.0165458
\(595\) −11.8541 −0.485971
\(596\) 12.3235 0.504790
\(597\) 13.1728 0.539128
\(598\) 20.3418 0.831836
\(599\) 28.5977 1.16847 0.584236 0.811584i \(-0.301394\pi\)
0.584236 + 0.811584i \(0.301394\pi\)
\(600\) 11.2212 0.458104
\(601\) −24.5799 −1.00264 −0.501318 0.865263i \(-0.667151\pi\)
−0.501318 + 0.865263i \(0.667151\pi\)
\(602\) 2.30131 0.0937945
\(603\) −10.3200 −0.420264
\(604\) −11.7387 −0.477643
\(605\) −7.01829 −0.285334
\(606\) 4.48299 0.182109
\(607\) −43.2003 −1.75345 −0.876723 0.480995i \(-0.840275\pi\)
−0.876723 + 0.480995i \(0.840275\pi\)
\(608\) 7.87815 0.319501
\(609\) −92.0533 −3.73019
\(610\) 7.75751 0.314092
\(611\) 19.2974 0.780688
\(612\) 11.2797 0.455956
\(613\) −20.8148 −0.840703 −0.420351 0.907361i \(-0.638093\pi\)
−0.420351 + 0.907361i \(0.638093\pi\)
\(614\) −4.26127 −0.171971
\(615\) 13.3369 0.537794
\(616\) 22.5843 0.909946
\(617\) 14.5617 0.586233 0.293117 0.956077i \(-0.405308\pi\)
0.293117 + 0.956077i \(0.405308\pi\)
\(618\) 26.7399 1.07564
\(619\) −33.2360 −1.33587 −0.667934 0.744221i \(-0.732821\pi\)
−0.667934 + 0.744221i \(0.732821\pi\)
\(620\) 1.10171 0.0442457
\(621\) 0.333812 0.0133954
\(622\) −2.05998 −0.0825977
\(623\) −54.4825 −2.18279
\(624\) 12.9674 0.519110
\(625\) 18.7015 0.748060
\(626\) −4.77654 −0.190909
\(627\) −90.1025 −3.59835
\(628\) 13.4078 0.535028
\(629\) 36.2128 1.44390
\(630\) −9.68192 −0.385737
\(631\) 21.7958 0.867679 0.433839 0.900990i \(-0.357158\pi\)
0.433839 + 0.900990i \(0.357158\pi\)
\(632\) 13.7681 0.547667
\(633\) −68.7832 −2.73389
\(634\) 24.9167 0.989569
\(635\) 5.58871 0.221781
\(636\) −3.07191 −0.121809
\(637\) −87.2697 −3.45775
\(638\) 35.9596 1.42365
\(639\) 13.5075 0.534350
\(640\) −0.657543 −0.0259917
\(641\) 13.0221 0.514344 0.257172 0.966366i \(-0.417209\pi\)
0.257172 + 0.966366i \(0.417209\pi\)
\(642\) 39.3928 1.55471
\(643\) −24.7405 −0.975670 −0.487835 0.872936i \(-0.662213\pi\)
−0.487835 + 0.872936i \(0.662213\pi\)
\(644\) −18.6950 −0.736688
\(645\) 0.766313 0.0301735
\(646\) 29.2770 1.15189
\(647\) 48.5747 1.90967 0.954835 0.297137i \(-0.0960318\pi\)
0.954835 + 0.297137i \(0.0960318\pi\)
\(648\) −8.89298 −0.349349
\(649\) −40.6698 −1.59643
\(650\) 24.1099 0.945668
\(651\) 19.9679 0.782604
\(652\) −8.49718 −0.332775
\(653\) −28.2937 −1.10722 −0.553609 0.832777i \(-0.686750\pi\)
−0.553609 + 0.832777i \(0.686750\pi\)
\(654\) −12.6316 −0.493934
\(655\) 3.86489 0.151014
\(656\) 8.25622 0.322351
\(657\) 17.7482 0.692425
\(658\) −17.7352 −0.691390
\(659\) −20.0225 −0.779966 −0.389983 0.920822i \(-0.627519\pi\)
−0.389983 + 0.920822i \(0.627519\pi\)
\(660\) 7.52033 0.292728
\(661\) 8.46135 0.329108 0.164554 0.986368i \(-0.447381\pi\)
0.164554 + 0.986368i \(0.447381\pi\)
\(662\) 29.1738 1.13387
\(663\) 48.1897 1.87153
\(664\) −0.0309457 −0.00120092
\(665\) −25.1298 −0.974494
\(666\) 29.5771 1.14609
\(667\) −29.7670 −1.15258
\(668\) −18.4665 −0.714490
\(669\) 3.98345 0.154009
\(670\) 2.23568 0.0863718
\(671\) −54.9241 −2.12032
\(672\) −11.9176 −0.459732
\(673\) −13.2386 −0.510311 −0.255155 0.966900i \(-0.582127\pi\)
−0.255155 + 0.966900i \(0.582127\pi\)
\(674\) −5.77401 −0.222407
\(675\) 0.395648 0.0152285
\(676\) 14.8617 0.571603
\(677\) 28.0768 1.07908 0.539540 0.841960i \(-0.318598\pi\)
0.539540 + 0.841960i \(0.318598\pi\)
\(678\) −19.9024 −0.764347
\(679\) 21.1319 0.810970
\(680\) −2.44358 −0.0937072
\(681\) −23.2455 −0.890768
\(682\) −7.80023 −0.298686
\(683\) −16.6571 −0.637366 −0.318683 0.947861i \(-0.603241\pi\)
−0.318683 + 0.947861i \(0.603241\pi\)
\(684\) 23.9122 0.914307
\(685\) −8.36166 −0.319482
\(686\) 46.2472 1.76573
\(687\) 3.76238 0.143544
\(688\) 0.474388 0.0180859
\(689\) −6.60031 −0.251452
\(690\) −6.22525 −0.236991
\(691\) 45.7787 1.74150 0.870752 0.491722i \(-0.163632\pi\)
0.870752 + 0.491722i \(0.163632\pi\)
\(692\) −7.14070 −0.271449
\(693\) 68.5491 2.60397
\(694\) 16.8513 0.639665
\(695\) −5.53112 −0.209807
\(696\) −18.9757 −0.719272
\(697\) 30.6821 1.16217
\(698\) 18.2569 0.691035
\(699\) 32.3794 1.22470
\(700\) −22.1581 −0.837499
\(701\) 5.42076 0.204739 0.102370 0.994746i \(-0.467358\pi\)
0.102370 + 0.994746i \(0.467358\pi\)
\(702\) 0.457216 0.0172565
\(703\) 76.7686 2.89538
\(704\) 4.65548 0.175460
\(705\) −5.90563 −0.222419
\(706\) −19.7042 −0.741577
\(707\) −8.85240 −0.332929
\(708\) 21.4612 0.806563
\(709\) −19.8950 −0.747173 −0.373587 0.927595i \(-0.621872\pi\)
−0.373587 + 0.927595i \(0.621872\pi\)
\(710\) −2.92620 −0.109818
\(711\) 41.7899 1.56724
\(712\) −11.2309 −0.420896
\(713\) 6.45695 0.241815
\(714\) −44.2887 −1.65746
\(715\) 16.1582 0.604282
\(716\) 0.549358 0.0205305
\(717\) −47.7304 −1.78252
\(718\) −22.2212 −0.829289
\(719\) 16.2096 0.604517 0.302259 0.953226i \(-0.402259\pi\)
0.302259 + 0.953226i \(0.402259\pi\)
\(720\) −1.99581 −0.0743796
\(721\) −52.8023 −1.96646
\(722\) 43.0652 1.60272
\(723\) 24.4589 0.909636
\(724\) −23.6930 −0.880542
\(725\) −35.2810 −1.31030
\(726\) −26.2214 −0.973166
\(727\) −25.5839 −0.948854 −0.474427 0.880295i \(-0.657345\pi\)
−0.474427 + 0.880295i \(0.657345\pi\)
\(728\) −25.6062 −0.949029
\(729\) −27.6309 −1.02337
\(730\) −3.84489 −0.142306
\(731\) 1.76294 0.0652046
\(732\) 28.9832 1.07125
\(733\) −26.4630 −0.977432 −0.488716 0.872443i \(-0.662535\pi\)
−0.488716 + 0.872443i \(0.662535\pi\)
\(734\) 31.0026 1.14433
\(735\) 26.7074 0.985118
\(736\) −3.85376 −0.142052
\(737\) −15.8289 −0.583064
\(738\) 25.0598 0.922463
\(739\) 4.76143 0.175152 0.0875760 0.996158i \(-0.472088\pi\)
0.0875760 + 0.996158i \(0.472088\pi\)
\(740\) −6.40743 −0.235542
\(741\) 102.159 3.75290
\(742\) 6.06600 0.222690
\(743\) −42.7383 −1.56791 −0.783957 0.620815i \(-0.786802\pi\)
−0.783957 + 0.620815i \(0.786802\pi\)
\(744\) 4.11615 0.150905
\(745\) −8.10323 −0.296879
\(746\) 0.0557758 0.00204210
\(747\) −0.0939281 −0.00343665
\(748\) 17.3009 0.632582
\(749\) −77.7876 −2.84230
\(750\) −15.4553 −0.564347
\(751\) 0.0611600 0.00223176 0.00111588 0.999999i \(-0.499645\pi\)
0.00111588 + 0.999999i \(0.499645\pi\)
\(752\) −3.65590 −0.133317
\(753\) −71.4229 −2.60279
\(754\) −40.7712 −1.48480
\(755\) 7.71873 0.280913
\(756\) −0.420203 −0.0152826
\(757\) 28.9890 1.05362 0.526811 0.849982i \(-0.323388\pi\)
0.526811 + 0.849982i \(0.323388\pi\)
\(758\) −23.4822 −0.852911
\(759\) 44.0755 1.59984
\(760\) −5.18022 −0.187906
\(761\) 6.54394 0.237218 0.118609 0.992941i \(-0.462157\pi\)
0.118609 + 0.992941i \(0.462157\pi\)
\(762\) 20.8802 0.756411
\(763\) 24.9432 0.903003
\(764\) −0.682066 −0.0246763
\(765\) −7.41691 −0.268159
\(766\) 28.1050 1.01548
\(767\) 46.1116 1.66499
\(768\) −2.45668 −0.0886477
\(769\) −48.0782 −1.73374 −0.866872 0.498530i \(-0.833873\pi\)
−0.866872 + 0.498530i \(0.833873\pi\)
\(770\) −14.8501 −0.535162
\(771\) 8.91840 0.321188
\(772\) −25.0276 −0.900763
\(773\) 13.0824 0.470541 0.235271 0.971930i \(-0.424402\pi\)
0.235271 + 0.971930i \(0.424402\pi\)
\(774\) 1.43989 0.0517558
\(775\) 7.65305 0.274906
\(776\) 4.35610 0.156375
\(777\) −116.131 −4.16618
\(778\) 27.4912 0.985606
\(779\) 65.0437 2.33043
\(780\) −8.52660 −0.305301
\(781\) 20.7179 0.741343
\(782\) −14.3215 −0.512135
\(783\) −0.669063 −0.0239104
\(784\) 16.5333 0.590475
\(785\) −8.81618 −0.314663
\(786\) 14.4398 0.515050
\(787\) −49.4331 −1.76210 −0.881050 0.473022i \(-0.843163\pi\)
−0.881050 + 0.473022i \(0.843163\pi\)
\(788\) −19.0279 −0.677841
\(789\) −35.0077 −1.24631
\(790\) −9.05314 −0.322096
\(791\) 39.3006 1.39737
\(792\) 14.1306 0.502109
\(793\) 62.2733 2.21139
\(794\) 37.7034 1.33805
\(795\) 2.01991 0.0716390
\(796\) −5.36205 −0.190053
\(797\) 37.6259 1.33278 0.666389 0.745605i \(-0.267839\pi\)
0.666389 + 0.745605i \(0.267839\pi\)
\(798\) −93.8888 −3.32363
\(799\) −13.5862 −0.480644
\(800\) −4.56764 −0.161490
\(801\) −34.0887 −1.20447
\(802\) 0.289242 0.0102135
\(803\) 27.2223 0.960653
\(804\) 8.35283 0.294581
\(805\) 12.2928 0.433264
\(806\) 8.84395 0.311515
\(807\) 38.8488 1.36754
\(808\) −1.82482 −0.0641969
\(809\) −12.0141 −0.422395 −0.211197 0.977443i \(-0.567736\pi\)
−0.211197 + 0.977443i \(0.567736\pi\)
\(810\) 5.84752 0.205461
\(811\) 6.50765 0.228515 0.114257 0.993451i \(-0.463551\pi\)
0.114257 + 0.993451i \(0.463551\pi\)
\(812\) 37.4706 1.31496
\(813\) 6.69628 0.234849
\(814\) 45.3653 1.59005
\(815\) 5.58726 0.195713
\(816\) −9.12958 −0.319599
\(817\) 3.73730 0.130752
\(818\) 17.2439 0.602921
\(819\) −77.7215 −2.71581
\(820\) −5.42882 −0.189583
\(821\) −13.4854 −0.470644 −0.235322 0.971917i \(-0.575614\pi\)
−0.235322 + 0.971917i \(0.575614\pi\)
\(822\) −31.2404 −1.08963
\(823\) 17.5977 0.613417 0.306708 0.951804i \(-0.400772\pi\)
0.306708 + 0.951804i \(0.400772\pi\)
\(824\) −10.8846 −0.379182
\(825\) 52.2401 1.81877
\(826\) −42.3788 −1.47455
\(827\) −7.38576 −0.256828 −0.128414 0.991721i \(-0.540989\pi\)
−0.128414 + 0.991721i \(0.540989\pi\)
\(828\) −11.6972 −0.406505
\(829\) 23.0075 0.799083 0.399541 0.916715i \(-0.369169\pi\)
0.399541 + 0.916715i \(0.369169\pi\)
\(830\) 0.0203481 0.000706293 0
\(831\) 9.31981 0.323300
\(832\) −5.27842 −0.182996
\(833\) 61.4417 2.12883
\(834\) −20.6651 −0.715573
\(835\) 12.1425 0.420209
\(836\) 36.6766 1.26849
\(837\) 0.145131 0.00501646
\(838\) 11.8682 0.409979
\(839\) 37.2965 1.28762 0.643810 0.765186i \(-0.277353\pi\)
0.643810 + 0.765186i \(0.277353\pi\)
\(840\) 7.83635 0.270380
\(841\) 30.6622 1.05732
\(842\) 17.9260 0.617772
\(843\) −15.6982 −0.540673
\(844\) 27.9985 0.963748
\(845\) −9.77219 −0.336174
\(846\) −11.0966 −0.381509
\(847\) 51.7784 1.77913
\(848\) 1.25043 0.0429401
\(849\) −17.4831 −0.600020
\(850\) −16.9744 −0.582217
\(851\) −37.5530 −1.28730
\(852\) −10.9327 −0.374549
\(853\) 14.7541 0.505170 0.252585 0.967575i \(-0.418719\pi\)
0.252585 + 0.967575i \(0.418719\pi\)
\(854\) −57.2321 −1.95844
\(855\) −15.7233 −0.537726
\(856\) −16.0350 −0.548065
\(857\) 2.80112 0.0956844 0.0478422 0.998855i \(-0.484766\pi\)
0.0478422 + 0.998855i \(0.484766\pi\)
\(858\) 60.3693 2.06097
\(859\) −20.7412 −0.707679 −0.353840 0.935306i \(-0.615124\pi\)
−0.353840 + 0.935306i \(0.615124\pi\)
\(860\) −0.311931 −0.0106367
\(861\) −98.3945 −3.35328
\(862\) 23.7562 0.809140
\(863\) −28.2525 −0.961726 −0.480863 0.876796i \(-0.659676\pi\)
−0.480863 + 0.876796i \(0.659676\pi\)
\(864\) −0.0866199 −0.00294687
\(865\) 4.69532 0.159646
\(866\) −10.5516 −0.358556
\(867\) 7.83583 0.266119
\(868\) −8.12801 −0.275883
\(869\) 64.0973 2.17435
\(870\) 12.4773 0.423021
\(871\) 17.9469 0.608107
\(872\) 5.14174 0.174121
\(873\) 13.2219 0.447493
\(874\) −30.3605 −1.02696
\(875\) 30.5190 1.03173
\(876\) −14.3651 −0.485351
\(877\) 13.8321 0.467078 0.233539 0.972347i \(-0.424969\pi\)
0.233539 + 0.972347i \(0.424969\pi\)
\(878\) 13.2659 0.447703
\(879\) −57.7794 −1.94885
\(880\) −3.06118 −0.103192
\(881\) 15.1747 0.511248 0.255624 0.966776i \(-0.417719\pi\)
0.255624 + 0.966776i \(0.417719\pi\)
\(882\) 50.1829 1.68975
\(883\) −43.4233 −1.46131 −0.730656 0.682746i \(-0.760786\pi\)
−0.730656 + 0.682746i \(0.760786\pi\)
\(884\) −19.6158 −0.659752
\(885\) −14.1117 −0.474359
\(886\) −10.4100 −0.349732
\(887\) −31.6996 −1.06437 −0.532184 0.846629i \(-0.678628\pi\)
−0.532184 + 0.846629i \(0.678628\pi\)
\(888\) −23.9391 −0.803343
\(889\) −41.2315 −1.38286
\(890\) 7.38481 0.247539
\(891\) −41.4011 −1.38699
\(892\) −1.62148 −0.0542912
\(893\) −28.8017 −0.963813
\(894\) −30.2748 −1.01254
\(895\) −0.361227 −0.0120745
\(896\) 4.85111 0.162064
\(897\) −49.9731 −1.66855
\(898\) −17.3246 −0.578129
\(899\) −12.9417 −0.431631
\(900\) −13.8640 −0.462132
\(901\) 4.64691 0.154811
\(902\) 38.4367 1.27980
\(903\) −5.65358 −0.188139
\(904\) 8.10135 0.269447
\(905\) 15.5791 0.517868
\(906\) 28.8383 0.958088
\(907\) −20.0221 −0.664822 −0.332411 0.943135i \(-0.607862\pi\)
−0.332411 + 0.943135i \(0.607862\pi\)
\(908\) 9.46216 0.314013
\(909\) −5.53879 −0.183710
\(910\) 16.8372 0.558147
\(911\) −57.5661 −1.90725 −0.953625 0.300996i \(-0.902681\pi\)
−0.953625 + 0.300996i \(0.902681\pi\)
\(912\) −19.3541 −0.640877
\(913\) −0.144067 −0.00476792
\(914\) −20.1850 −0.667661
\(915\) −19.0577 −0.630028
\(916\) −1.53149 −0.0506019
\(917\) −28.5137 −0.941607
\(918\) −0.321900 −0.0106243
\(919\) −35.7330 −1.17872 −0.589362 0.807869i \(-0.700621\pi\)
−0.589362 + 0.807869i \(0.700621\pi\)
\(920\) 2.53401 0.0835440
\(921\) 10.4686 0.344951
\(922\) 1.41661 0.0466534
\(923\) −23.4900 −0.773184
\(924\) −55.4823 −1.82523
\(925\) −44.5093 −1.46346
\(926\) 19.8843 0.653438
\(927\) −33.0375 −1.08509
\(928\) 7.72413 0.253557
\(929\) 43.7375 1.43498 0.717490 0.696568i \(-0.245291\pi\)
0.717490 + 0.696568i \(0.245291\pi\)
\(930\) −2.70654 −0.0887510
\(931\) 130.252 4.26883
\(932\) −13.1802 −0.431731
\(933\) 5.06071 0.165680
\(934\) −33.2983 −1.08955
\(935\) −11.3761 −0.372037
\(936\) −16.0214 −0.523675
\(937\) −9.17833 −0.299843 −0.149922 0.988698i \(-0.547902\pi\)
−0.149922 + 0.988698i \(0.547902\pi\)
\(938\) −16.4940 −0.538549
\(939\) 11.7344 0.382938
\(940\) 2.40391 0.0784069
\(941\) −10.8151 −0.352561 −0.176280 0.984340i \(-0.556407\pi\)
−0.176280 + 0.984340i \(0.556407\pi\)
\(942\) −32.9385 −1.07320
\(943\) −31.8175 −1.03612
\(944\) −8.73589 −0.284329
\(945\) 0.276301 0.00898809
\(946\) 2.20851 0.0718047
\(947\) 39.6293 1.28778 0.643889 0.765119i \(-0.277320\pi\)
0.643889 + 0.765119i \(0.277320\pi\)
\(948\) −33.8239 −1.09855
\(949\) −30.8648 −1.00191
\(950\) −35.9845 −1.16749
\(951\) −61.2123 −1.98495
\(952\) 18.0279 0.584287
\(953\) −51.2464 −1.66004 −0.830018 0.557737i \(-0.811670\pi\)
−0.830018 + 0.557737i \(0.811670\pi\)
\(954\) 3.79539 0.122880
\(955\) 0.448487 0.0145127
\(956\) 19.4289 0.628374
\(957\) −88.3410 −2.85566
\(958\) −19.5149 −0.630499
\(959\) 61.6893 1.99205
\(960\) 1.61537 0.0521359
\(961\) −28.1927 −0.909443
\(962\) −51.4355 −1.65835
\(963\) −48.6704 −1.56838
\(964\) −9.95609 −0.320664
\(965\) 16.4567 0.529760
\(966\) 45.9277 1.47770
\(967\) −45.8410 −1.47415 −0.737074 0.675812i \(-0.763793\pi\)
−0.737074 + 0.675812i \(0.763793\pi\)
\(968\) 10.6735 0.343060
\(969\) −71.9242 −2.31054
\(970\) −2.86432 −0.0919679
\(971\) 37.6783 1.20916 0.604578 0.796546i \(-0.293342\pi\)
0.604578 + 0.796546i \(0.293342\pi\)
\(972\) 22.1070 0.709083
\(973\) 40.8066 1.30820
\(974\) 2.43265 0.0779470
\(975\) −59.2302 −1.89688
\(976\) −11.7977 −0.377636
\(977\) 2.94293 0.0941527 0.0470764 0.998891i \(-0.485010\pi\)
0.0470764 + 0.998891i \(0.485010\pi\)
\(978\) 20.8748 0.667503
\(979\) −52.2853 −1.67105
\(980\) −10.8714 −0.347273
\(981\) 15.6065 0.498277
\(982\) 26.1573 0.834713
\(983\) 21.5954 0.688787 0.344393 0.938825i \(-0.388085\pi\)
0.344393 + 0.938825i \(0.388085\pi\)
\(984\) −20.2829 −0.646594
\(985\) 12.5117 0.398655
\(986\) 28.7047 0.914143
\(987\) 43.5696 1.38684
\(988\) −41.5841 −1.32297
\(989\) −1.82818 −0.0581327
\(990\) −9.29147 −0.295302
\(991\) 21.1106 0.670599 0.335299 0.942112i \(-0.391163\pi\)
0.335299 + 0.942112i \(0.391163\pi\)
\(992\) −1.67549 −0.0531970
\(993\) −71.6705 −2.27439
\(994\) 21.5885 0.684744
\(995\) 3.52578 0.111775
\(996\) 0.0760234 0.00240890
\(997\) −8.65940 −0.274246 −0.137123 0.990554i \(-0.543786\pi\)
−0.137123 + 0.990554i \(0.543786\pi\)
\(998\) 13.2342 0.418921
\(999\) −0.844067 −0.0267051
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 8014.2.a.d.1.11 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8014.2.a.d.1.11 88 1.1 even 1 trivial