Properties

Label 8007.2.a.j.1.48
Level $8007$
Weight $2$
Character 8007.1
Self dual yes
Analytic conductor $63.936$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8007,2,Mod(1,8007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8007.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: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.48
Character \(\chi\) \(=\) 8007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.79853 q^{2} -1.00000 q^{3} +1.23470 q^{4} +4.43407 q^{5} -1.79853 q^{6} -4.49904 q^{7} -1.37641 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.79853 q^{2} -1.00000 q^{3} +1.23470 q^{4} +4.43407 q^{5} -1.79853 q^{6} -4.49904 q^{7} -1.37641 q^{8} +1.00000 q^{9} +7.97480 q^{10} -4.62856 q^{11} -1.23470 q^{12} -2.91661 q^{13} -8.09166 q^{14} -4.43407 q^{15} -4.94491 q^{16} +1.00000 q^{17} +1.79853 q^{18} -0.480190 q^{19} +5.47476 q^{20} +4.49904 q^{21} -8.32460 q^{22} +3.05235 q^{23} +1.37641 q^{24} +14.6610 q^{25} -5.24561 q^{26} -1.00000 q^{27} -5.55499 q^{28} +9.94458 q^{29} -7.97480 q^{30} +3.58031 q^{31} -6.14076 q^{32} +4.62856 q^{33} +1.79853 q^{34} -19.9491 q^{35} +1.23470 q^{36} -4.58724 q^{37} -0.863636 q^{38} +2.91661 q^{39} -6.10308 q^{40} +5.50600 q^{41} +8.09166 q^{42} +6.63207 q^{43} -5.71491 q^{44} +4.43407 q^{45} +5.48974 q^{46} -5.29067 q^{47} +4.94491 q^{48} +13.2414 q^{49} +26.3681 q^{50} -1.00000 q^{51} -3.60116 q^{52} +7.85674 q^{53} -1.79853 q^{54} -20.5234 q^{55} +6.19251 q^{56} +0.480190 q^{57} +17.8856 q^{58} -11.4881 q^{59} -5.47476 q^{60} -15.0640 q^{61} +6.43929 q^{62} -4.49904 q^{63} -1.15450 q^{64} -12.9325 q^{65} +8.32460 q^{66} +5.55181 q^{67} +1.23470 q^{68} -3.05235 q^{69} -35.8789 q^{70} +7.98950 q^{71} -1.37641 q^{72} +2.71710 q^{73} -8.25028 q^{74} -14.6610 q^{75} -0.592893 q^{76} +20.8241 q^{77} +5.24561 q^{78} +13.5994 q^{79} -21.9261 q^{80} +1.00000 q^{81} +9.90269 q^{82} +4.67665 q^{83} +5.55499 q^{84} +4.43407 q^{85} +11.9280 q^{86} -9.94458 q^{87} +6.37078 q^{88} -9.95473 q^{89} +7.97480 q^{90} +13.1220 q^{91} +3.76875 q^{92} -3.58031 q^{93} -9.51543 q^{94} -2.12920 q^{95} +6.14076 q^{96} +14.9666 q^{97} +23.8150 q^{98} -4.62856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79853 1.27175 0.635876 0.771791i \(-0.280639\pi\)
0.635876 + 0.771791i \(0.280639\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.23470 0.617352
\(5\) 4.43407 1.98298 0.991488 0.130202i \(-0.0415625\pi\)
0.991488 + 0.130202i \(0.0415625\pi\)
\(6\) −1.79853 −0.734246
\(7\) −4.49904 −1.70048 −0.850239 0.526397i \(-0.823543\pi\)
−0.850239 + 0.526397i \(0.823543\pi\)
\(8\) −1.37641 −0.486633
\(9\) 1.00000 0.333333
\(10\) 7.97480 2.52185
\(11\) −4.62856 −1.39556 −0.697782 0.716310i \(-0.745830\pi\)
−0.697782 + 0.716310i \(0.745830\pi\)
\(12\) −1.23470 −0.356428
\(13\) −2.91661 −0.808923 −0.404462 0.914555i \(-0.632541\pi\)
−0.404462 + 0.914555i \(0.632541\pi\)
\(14\) −8.09166 −2.16259
\(15\) −4.43407 −1.14487
\(16\) −4.94491 −1.23623
\(17\) 1.00000 0.242536
\(18\) 1.79853 0.423917
\(19\) −0.480190 −0.110163 −0.0550816 0.998482i \(-0.517542\pi\)
−0.0550816 + 0.998482i \(0.517542\pi\)
\(20\) 5.47476 1.22419
\(21\) 4.49904 0.981772
\(22\) −8.32460 −1.77481
\(23\) 3.05235 0.636460 0.318230 0.948014i \(-0.396912\pi\)
0.318230 + 0.948014i \(0.396912\pi\)
\(24\) 1.37641 0.280958
\(25\) 14.6610 2.93219
\(26\) −5.24561 −1.02875
\(27\) −1.00000 −0.192450
\(28\) −5.55499 −1.04979
\(29\) 9.94458 1.84666 0.923332 0.384004i \(-0.125455\pi\)
0.923332 + 0.384004i \(0.125455\pi\)
\(30\) −7.97480 −1.45599
\(31\) 3.58031 0.643043 0.321521 0.946902i \(-0.395806\pi\)
0.321521 + 0.946902i \(0.395806\pi\)
\(32\) −6.14076 −1.08554
\(33\) 4.62856 0.805729
\(34\) 1.79853 0.308445
\(35\) −19.9491 −3.37201
\(36\) 1.23470 0.205784
\(37\) −4.58724 −0.754137 −0.377069 0.926185i \(-0.623068\pi\)
−0.377069 + 0.926185i \(0.623068\pi\)
\(38\) −0.863636 −0.140100
\(39\) 2.91661 0.467032
\(40\) −6.10308 −0.964981
\(41\) 5.50600 0.859892 0.429946 0.902855i \(-0.358533\pi\)
0.429946 + 0.902855i \(0.358533\pi\)
\(42\) 8.09166 1.24857
\(43\) 6.63207 1.01138 0.505691 0.862715i \(-0.331238\pi\)
0.505691 + 0.862715i \(0.331238\pi\)
\(44\) −5.71491 −0.861555
\(45\) 4.43407 0.660992
\(46\) 5.48974 0.809419
\(47\) −5.29067 −0.771724 −0.385862 0.922556i \(-0.626096\pi\)
−0.385862 + 0.922556i \(0.626096\pi\)
\(48\) 4.94491 0.713737
\(49\) 13.2414 1.89163
\(50\) 26.3681 3.72902
\(51\) −1.00000 −0.140028
\(52\) −3.60116 −0.499391
\(53\) 7.85674 1.07921 0.539603 0.841920i \(-0.318574\pi\)
0.539603 + 0.841920i \(0.318574\pi\)
\(54\) −1.79853 −0.244749
\(55\) −20.5234 −2.76737
\(56\) 6.19251 0.827509
\(57\) 0.480190 0.0636028
\(58\) 17.8856 2.34850
\(59\) −11.4881 −1.49563 −0.747814 0.663908i \(-0.768897\pi\)
−0.747814 + 0.663908i \(0.768897\pi\)
\(60\) −5.47476 −0.706789
\(61\) −15.0640 −1.92875 −0.964376 0.264536i \(-0.914781\pi\)
−0.964376 + 0.264536i \(0.914781\pi\)
\(62\) 6.43929 0.817791
\(63\) −4.49904 −0.566826
\(64\) −1.15450 −0.144312
\(65\) −12.9325 −1.60407
\(66\) 8.32460 1.02469
\(67\) 5.55181 0.678262 0.339131 0.940739i \(-0.389867\pi\)
0.339131 + 0.940739i \(0.389867\pi\)
\(68\) 1.23470 0.149730
\(69\) −3.05235 −0.367460
\(70\) −35.8789 −4.28835
\(71\) 7.98950 0.948179 0.474089 0.880477i \(-0.342777\pi\)
0.474089 + 0.880477i \(0.342777\pi\)
\(72\) −1.37641 −0.162211
\(73\) 2.71710 0.318012 0.159006 0.987278i \(-0.449171\pi\)
0.159006 + 0.987278i \(0.449171\pi\)
\(74\) −8.25028 −0.959075
\(75\) −14.6610 −1.69290
\(76\) −0.592893 −0.0680095
\(77\) 20.8241 2.37313
\(78\) 5.24561 0.593949
\(79\) 13.5994 1.53005 0.765023 0.644002i \(-0.222727\pi\)
0.765023 + 0.644002i \(0.222727\pi\)
\(80\) −21.9261 −2.45141
\(81\) 1.00000 0.111111
\(82\) 9.90269 1.09357
\(83\) 4.67665 0.513329 0.256665 0.966501i \(-0.417376\pi\)
0.256665 + 0.966501i \(0.417376\pi\)
\(84\) 5.55499 0.606099
\(85\) 4.43407 0.480942
\(86\) 11.9280 1.28623
\(87\) −9.94458 −1.06617
\(88\) 6.37078 0.679128
\(89\) −9.95473 −1.05520 −0.527600 0.849493i \(-0.676908\pi\)
−0.527600 + 0.849493i \(0.676908\pi\)
\(90\) 7.97480 0.840617
\(91\) 13.1220 1.37556
\(92\) 3.76875 0.392920
\(93\) −3.58031 −0.371261
\(94\) −9.51543 −0.981441
\(95\) −2.12920 −0.218451
\(96\) 6.14076 0.626738
\(97\) 14.9666 1.51963 0.759816 0.650138i \(-0.225289\pi\)
0.759816 + 0.650138i \(0.225289\pi\)
\(98\) 23.8150 2.40568
\(99\) −4.62856 −0.465188
\(100\) 18.1019 1.81019
\(101\) 9.97039 0.992090 0.496045 0.868297i \(-0.334785\pi\)
0.496045 + 0.868297i \(0.334785\pi\)
\(102\) −1.79853 −0.178081
\(103\) 4.71678 0.464758 0.232379 0.972625i \(-0.425349\pi\)
0.232379 + 0.972625i \(0.425349\pi\)
\(104\) 4.01445 0.393649
\(105\) 19.9491 1.94683
\(106\) 14.1306 1.37248
\(107\) 17.4959 1.69140 0.845698 0.533661i \(-0.179184\pi\)
0.845698 + 0.533661i \(0.179184\pi\)
\(108\) −1.23470 −0.118809
\(109\) 9.60614 0.920102 0.460051 0.887893i \(-0.347831\pi\)
0.460051 + 0.887893i \(0.347831\pi\)
\(110\) −36.9118 −3.51941
\(111\) 4.58724 0.435401
\(112\) 22.2474 2.10218
\(113\) 7.49558 0.705125 0.352562 0.935788i \(-0.385310\pi\)
0.352562 + 0.935788i \(0.385310\pi\)
\(114\) 0.863636 0.0808869
\(115\) 13.5343 1.26208
\(116\) 12.2786 1.14004
\(117\) −2.91661 −0.269641
\(118\) −20.6617 −1.90207
\(119\) −4.49904 −0.412427
\(120\) 6.10308 0.557132
\(121\) 10.4236 0.947599
\(122\) −27.0931 −2.45289
\(123\) −5.50600 −0.496459
\(124\) 4.42063 0.396984
\(125\) 42.8373 3.83148
\(126\) −8.09166 −0.720862
\(127\) 0.893378 0.0792745 0.0396372 0.999214i \(-0.487380\pi\)
0.0396372 + 0.999214i \(0.487380\pi\)
\(128\) 10.2051 0.902013
\(129\) −6.63207 −0.583921
\(130\) −23.2594 −2.03998
\(131\) −7.91024 −0.691121 −0.345560 0.938397i \(-0.612311\pi\)
−0.345560 + 0.938397i \(0.612311\pi\)
\(132\) 5.71491 0.497419
\(133\) 2.16040 0.187330
\(134\) 9.98509 0.862581
\(135\) −4.43407 −0.381624
\(136\) −1.37641 −0.118026
\(137\) 7.49347 0.640210 0.320105 0.947382i \(-0.396282\pi\)
0.320105 + 0.947382i \(0.396282\pi\)
\(138\) −5.48974 −0.467318
\(139\) −14.4874 −1.22881 −0.614404 0.788991i \(-0.710604\pi\)
−0.614404 + 0.788991i \(0.710604\pi\)
\(140\) −24.6312 −2.08172
\(141\) 5.29067 0.445555
\(142\) 14.3693 1.20585
\(143\) 13.4997 1.12890
\(144\) −4.94491 −0.412076
\(145\) 44.0950 3.66189
\(146\) 4.88677 0.404432
\(147\) −13.2414 −1.09213
\(148\) −5.66388 −0.465568
\(149\) −14.9281 −1.22295 −0.611477 0.791262i \(-0.709424\pi\)
−0.611477 + 0.791262i \(0.709424\pi\)
\(150\) −26.3681 −2.15295
\(151\) 21.4229 1.74337 0.871687 0.490064i \(-0.163027\pi\)
0.871687 + 0.490064i \(0.163027\pi\)
\(152\) 0.660937 0.0536091
\(153\) 1.00000 0.0808452
\(154\) 37.4527 3.01803
\(155\) 15.8753 1.27514
\(156\) 3.60116 0.288323
\(157\) −1.00000 −0.0798087
\(158\) 24.4588 1.94584
\(159\) −7.85674 −0.623080
\(160\) −27.2285 −2.15260
\(161\) −13.7327 −1.08229
\(162\) 1.79853 0.141306
\(163\) −19.7354 −1.54579 −0.772897 0.634531i \(-0.781193\pi\)
−0.772897 + 0.634531i \(0.781193\pi\)
\(164\) 6.79828 0.530856
\(165\) 20.5234 1.59774
\(166\) 8.41109 0.652827
\(167\) 5.51825 0.427015 0.213508 0.976941i \(-0.431511\pi\)
0.213508 + 0.976941i \(0.431511\pi\)
\(168\) −6.19251 −0.477762
\(169\) −4.49336 −0.345643
\(170\) 7.97480 0.611639
\(171\) −0.480190 −0.0367211
\(172\) 8.18864 0.624378
\(173\) −19.2886 −1.46648 −0.733241 0.679969i \(-0.761993\pi\)
−0.733241 + 0.679969i \(0.761993\pi\)
\(174\) −17.8856 −1.35591
\(175\) −65.9602 −4.98613
\(176\) 22.8878 1.72524
\(177\) 11.4881 0.863501
\(178\) −17.9039 −1.34195
\(179\) 11.0243 0.823993 0.411997 0.911185i \(-0.364832\pi\)
0.411997 + 0.911185i \(0.364832\pi\)
\(180\) 5.47476 0.408065
\(181\) −12.2257 −0.908727 −0.454363 0.890816i \(-0.650133\pi\)
−0.454363 + 0.890816i \(0.650133\pi\)
\(182\) 23.6002 1.74937
\(183\) 15.0640 1.11357
\(184\) −4.20128 −0.309722
\(185\) −20.3401 −1.49543
\(186\) −6.43929 −0.472152
\(187\) −4.62856 −0.338474
\(188\) −6.53242 −0.476426
\(189\) 4.49904 0.327257
\(190\) −3.82942 −0.277815
\(191\) 18.8444 1.36353 0.681765 0.731571i \(-0.261213\pi\)
0.681765 + 0.731571i \(0.261213\pi\)
\(192\) 1.15450 0.0833186
\(193\) −25.5147 −1.83659 −0.918295 0.395897i \(-0.870434\pi\)
−0.918295 + 0.395897i \(0.870434\pi\)
\(194\) 26.9179 1.93260
\(195\) 12.9325 0.926113
\(196\) 16.3492 1.16780
\(197\) 5.86540 0.417892 0.208946 0.977927i \(-0.432997\pi\)
0.208946 + 0.977927i \(0.432997\pi\)
\(198\) −8.32460 −0.591604
\(199\) −19.4004 −1.37526 −0.687629 0.726063i \(-0.741348\pi\)
−0.687629 + 0.726063i \(0.741348\pi\)
\(200\) −20.1794 −1.42690
\(201\) −5.55181 −0.391595
\(202\) 17.9320 1.26169
\(203\) −44.7411 −3.14021
\(204\) −1.23470 −0.0864466
\(205\) 24.4140 1.70514
\(206\) 8.48327 0.591057
\(207\) 3.05235 0.212153
\(208\) 14.4224 1.00001
\(209\) 2.22259 0.153740
\(210\) 35.8789 2.47588
\(211\) 12.5811 0.866121 0.433061 0.901365i \(-0.357434\pi\)
0.433061 + 0.901365i \(0.357434\pi\)
\(212\) 9.70075 0.666250
\(213\) −7.98950 −0.547431
\(214\) 31.4670 2.15104
\(215\) 29.4070 2.00554
\(216\) 1.37641 0.0936526
\(217\) −16.1080 −1.09348
\(218\) 17.2769 1.17014
\(219\) −2.71710 −0.183604
\(220\) −25.3403 −1.70844
\(221\) −2.91661 −0.196193
\(222\) 8.25028 0.553722
\(223\) −21.5299 −1.44175 −0.720875 0.693065i \(-0.756260\pi\)
−0.720875 + 0.693065i \(0.756260\pi\)
\(224\) 27.6275 1.84594
\(225\) 14.6610 0.977397
\(226\) 13.4810 0.896743
\(227\) −12.9210 −0.857596 −0.428798 0.903401i \(-0.641063\pi\)
−0.428798 + 0.903401i \(0.641063\pi\)
\(228\) 0.592893 0.0392653
\(229\) 19.0280 1.25741 0.628703 0.777645i \(-0.283586\pi\)
0.628703 + 0.777645i \(0.283586\pi\)
\(230\) 24.3419 1.60506
\(231\) −20.8241 −1.37013
\(232\) −13.6878 −0.898647
\(233\) 18.8820 1.23700 0.618501 0.785784i \(-0.287740\pi\)
0.618501 + 0.785784i \(0.287740\pi\)
\(234\) −5.24561 −0.342917
\(235\) −23.4592 −1.53031
\(236\) −14.1845 −0.923329
\(237\) −13.5994 −0.883373
\(238\) −8.09166 −0.524504
\(239\) −16.2674 −1.05225 −0.526126 0.850407i \(-0.676356\pi\)
−0.526126 + 0.850407i \(0.676356\pi\)
\(240\) 21.9261 1.41532
\(241\) 4.33551 0.279274 0.139637 0.990203i \(-0.455406\pi\)
0.139637 + 0.990203i \(0.455406\pi\)
\(242\) 18.7471 1.20511
\(243\) −1.00000 −0.0641500
\(244\) −18.5996 −1.19072
\(245\) 58.7132 3.75105
\(246\) −9.90269 −0.631373
\(247\) 1.40053 0.0891136
\(248\) −4.92796 −0.312926
\(249\) −4.67665 −0.296371
\(250\) 77.0441 4.87270
\(251\) 6.99084 0.441258 0.220629 0.975358i \(-0.429189\pi\)
0.220629 + 0.975358i \(0.429189\pi\)
\(252\) −5.55499 −0.349931
\(253\) −14.1280 −0.888220
\(254\) 1.60677 0.100817
\(255\) −4.43407 −0.277672
\(256\) 20.6632 1.29145
\(257\) 18.7213 1.16780 0.583901 0.811825i \(-0.301526\pi\)
0.583901 + 0.811825i \(0.301526\pi\)
\(258\) −11.9280 −0.742603
\(259\) 20.6382 1.28239
\(260\) −15.9678 −0.990279
\(261\) 9.94458 0.615554
\(262\) −14.2268 −0.878934
\(263\) 12.9078 0.795928 0.397964 0.917401i \(-0.369717\pi\)
0.397964 + 0.917401i \(0.369717\pi\)
\(264\) −6.37078 −0.392094
\(265\) 34.8373 2.14004
\(266\) 3.88554 0.238238
\(267\) 9.95473 0.609219
\(268\) 6.85485 0.418726
\(269\) 4.68577 0.285697 0.142848 0.989745i \(-0.454374\pi\)
0.142848 + 0.989745i \(0.454374\pi\)
\(270\) −7.97480 −0.485331
\(271\) −3.35006 −0.203502 −0.101751 0.994810i \(-0.532444\pi\)
−0.101751 + 0.994810i \(0.532444\pi\)
\(272\) −4.94491 −0.299829
\(273\) −13.1220 −0.794178
\(274\) 13.4772 0.814189
\(275\) −67.8591 −4.09206
\(276\) −3.76875 −0.226852
\(277\) 28.3758 1.70494 0.852469 0.522778i \(-0.175104\pi\)
0.852469 + 0.522778i \(0.175104\pi\)
\(278\) −26.0561 −1.56274
\(279\) 3.58031 0.214348
\(280\) 27.4580 1.64093
\(281\) −16.2369 −0.968613 −0.484307 0.874898i \(-0.660928\pi\)
−0.484307 + 0.874898i \(0.660928\pi\)
\(282\) 9.51543 0.566636
\(283\) −10.7145 −0.636909 −0.318455 0.947938i \(-0.603164\pi\)
−0.318455 + 0.947938i \(0.603164\pi\)
\(284\) 9.86467 0.585360
\(285\) 2.12920 0.126123
\(286\) 24.2797 1.43569
\(287\) −24.7717 −1.46223
\(288\) −6.14076 −0.361848
\(289\) 1.00000 0.0588235
\(290\) 79.3060 4.65701
\(291\) −14.9666 −0.877360
\(292\) 3.35481 0.196325
\(293\) −26.3958 −1.54206 −0.771028 0.636801i \(-0.780257\pi\)
−0.771028 + 0.636801i \(0.780257\pi\)
\(294\) −23.8150 −1.38892
\(295\) −50.9392 −2.96579
\(296\) 6.31390 0.366988
\(297\) 4.62856 0.268576
\(298\) −26.8485 −1.55529
\(299\) −8.90254 −0.514847
\(300\) −18.1019 −1.04512
\(301\) −29.8380 −1.71983
\(302\) 38.5297 2.21714
\(303\) −9.97039 −0.572784
\(304\) 2.37450 0.136187
\(305\) −66.7949 −3.82467
\(306\) 1.79853 0.102815
\(307\) −19.1507 −1.09299 −0.546493 0.837464i \(-0.684037\pi\)
−0.546493 + 0.837464i \(0.684037\pi\)
\(308\) 25.7116 1.46505
\(309\) −4.71678 −0.268328
\(310\) 28.5522 1.62166
\(311\) 1.52003 0.0861929 0.0430965 0.999071i \(-0.486278\pi\)
0.0430965 + 0.999071i \(0.486278\pi\)
\(312\) −4.01445 −0.227273
\(313\) 8.83884 0.499601 0.249800 0.968297i \(-0.419635\pi\)
0.249800 + 0.968297i \(0.419635\pi\)
\(314\) −1.79853 −0.101497
\(315\) −19.9491 −1.12400
\(316\) 16.7912 0.944578
\(317\) −0.200835 −0.0112800 −0.00564000 0.999984i \(-0.501795\pi\)
−0.00564000 + 0.999984i \(0.501795\pi\)
\(318\) −14.1306 −0.792403
\(319\) −46.0291 −2.57714
\(320\) −5.11912 −0.286167
\(321\) −17.4959 −0.976528
\(322\) −24.6986 −1.37640
\(323\) −0.480190 −0.0267185
\(324\) 1.23470 0.0685947
\(325\) −42.7603 −2.37192
\(326\) −35.4947 −1.96587
\(327\) −9.60614 −0.531221
\(328\) −7.57849 −0.418452
\(329\) 23.8030 1.31230
\(330\) 36.9118 2.03193
\(331\) 17.9318 0.985620 0.492810 0.870137i \(-0.335970\pi\)
0.492810 + 0.870137i \(0.335970\pi\)
\(332\) 5.77428 0.316905
\(333\) −4.58724 −0.251379
\(334\) 9.92473 0.543057
\(335\) 24.6171 1.34498
\(336\) −22.2474 −1.21369
\(337\) 3.11678 0.169782 0.0848910 0.996390i \(-0.472946\pi\)
0.0848910 + 0.996390i \(0.472946\pi\)
\(338\) −8.08144 −0.439572
\(339\) −7.49558 −0.407104
\(340\) 5.47476 0.296911
\(341\) −16.5717 −0.897408
\(342\) −0.863636 −0.0467001
\(343\) −28.0803 −1.51619
\(344\) −9.12842 −0.492171
\(345\) −13.5343 −0.728664
\(346\) −34.6910 −1.86500
\(347\) 17.4388 0.936162 0.468081 0.883686i \(-0.344946\pi\)
0.468081 + 0.883686i \(0.344946\pi\)
\(348\) −12.2786 −0.658203
\(349\) 1.72202 0.0921775 0.0460888 0.998937i \(-0.485324\pi\)
0.0460888 + 0.998937i \(0.485324\pi\)
\(350\) −118.631 −6.34111
\(351\) 2.91661 0.155677
\(352\) 28.4229 1.51494
\(353\) 34.7628 1.85024 0.925119 0.379678i \(-0.123965\pi\)
0.925119 + 0.379678i \(0.123965\pi\)
\(354\) 20.6617 1.09816
\(355\) 35.4260 1.88021
\(356\) −12.2911 −0.651429
\(357\) 4.49904 0.238115
\(358\) 19.8275 1.04791
\(359\) 21.8667 1.15408 0.577041 0.816715i \(-0.304207\pi\)
0.577041 + 0.816715i \(0.304207\pi\)
\(360\) −6.10308 −0.321660
\(361\) −18.7694 −0.987864
\(362\) −21.9882 −1.15567
\(363\) −10.4236 −0.547097
\(364\) 16.2018 0.849203
\(365\) 12.0478 0.630610
\(366\) 27.0931 1.41618
\(367\) −22.8011 −1.19021 −0.595104 0.803648i \(-0.702889\pi\)
−0.595104 + 0.803648i \(0.702889\pi\)
\(368\) −15.0936 −0.786810
\(369\) 5.50600 0.286631
\(370\) −36.5823 −1.90182
\(371\) −35.3478 −1.83517
\(372\) −4.42063 −0.229199
\(373\) 2.51016 0.129971 0.0649855 0.997886i \(-0.479300\pi\)
0.0649855 + 0.997886i \(0.479300\pi\)
\(374\) −8.32460 −0.430455
\(375\) −42.8373 −2.21211
\(376\) 7.28212 0.375546
\(377\) −29.0045 −1.49381
\(378\) 8.09166 0.416190
\(379\) −27.5901 −1.41721 −0.708605 0.705606i \(-0.750675\pi\)
−0.708605 + 0.705606i \(0.750675\pi\)
\(380\) −2.62893 −0.134861
\(381\) −0.893378 −0.0457691
\(382\) 33.8921 1.73407
\(383\) 26.7908 1.36894 0.684472 0.729039i \(-0.260033\pi\)
0.684472 + 0.729039i \(0.260033\pi\)
\(384\) −10.2051 −0.520778
\(385\) 92.3355 4.70585
\(386\) −45.8890 −2.33569
\(387\) 6.63207 0.337127
\(388\) 18.4794 0.938149
\(389\) 15.6700 0.794501 0.397251 0.917710i \(-0.369964\pi\)
0.397251 + 0.917710i \(0.369964\pi\)
\(390\) 23.2594 1.17779
\(391\) 3.05235 0.154364
\(392\) −18.2255 −0.920528
\(393\) 7.91024 0.399019
\(394\) 10.5491 0.531455
\(395\) 60.3005 3.03404
\(396\) −5.71491 −0.287185
\(397\) −1.79232 −0.0899539 −0.0449769 0.998988i \(-0.514321\pi\)
−0.0449769 + 0.998988i \(0.514321\pi\)
\(398\) −34.8921 −1.74899
\(399\) −2.16040 −0.108155
\(400\) −72.4971 −3.62486
\(401\) 22.9717 1.14715 0.573577 0.819152i \(-0.305555\pi\)
0.573577 + 0.819152i \(0.305555\pi\)
\(402\) −9.98509 −0.498011
\(403\) −10.4424 −0.520172
\(404\) 12.3105 0.612469
\(405\) 4.43407 0.220331
\(406\) −80.4682 −3.99357
\(407\) 21.2323 1.05245
\(408\) 1.37641 0.0681422
\(409\) −21.0186 −1.03930 −0.519650 0.854379i \(-0.673938\pi\)
−0.519650 + 0.854379i \(0.673938\pi\)
\(410\) 43.9092 2.16852
\(411\) −7.49347 −0.369626
\(412\) 5.82383 0.286920
\(413\) 51.6856 2.54328
\(414\) 5.48974 0.269806
\(415\) 20.7366 1.01792
\(416\) 17.9102 0.878121
\(417\) 14.4874 0.709453
\(418\) 3.99739 0.195519
\(419\) −11.4970 −0.561667 −0.280833 0.959757i \(-0.590611\pi\)
−0.280833 + 0.959757i \(0.590611\pi\)
\(420\) 24.6312 1.20188
\(421\) −7.29663 −0.355616 −0.177808 0.984065i \(-0.556901\pi\)
−0.177808 + 0.984065i \(0.556901\pi\)
\(422\) 22.6275 1.10149
\(423\) −5.29067 −0.257241
\(424\) −10.8141 −0.525177
\(425\) 14.6610 0.711161
\(426\) −14.3693 −0.696197
\(427\) 67.7737 3.27980
\(428\) 21.6023 1.04419
\(429\) −13.4997 −0.651773
\(430\) 52.8894 2.55055
\(431\) 18.1705 0.875244 0.437622 0.899159i \(-0.355821\pi\)
0.437622 + 0.899159i \(0.355821\pi\)
\(432\) 4.94491 0.237912
\(433\) 40.7831 1.95991 0.979956 0.199215i \(-0.0638393\pi\)
0.979956 + 0.199215i \(0.0638393\pi\)
\(434\) −28.9706 −1.39064
\(435\) −44.0950 −2.11419
\(436\) 11.8607 0.568027
\(437\) −1.46571 −0.0701145
\(438\) −4.88677 −0.233499
\(439\) 5.50731 0.262850 0.131425 0.991326i \(-0.458045\pi\)
0.131425 + 0.991326i \(0.458045\pi\)
\(440\) 28.2485 1.34669
\(441\) 13.2414 0.630542
\(442\) −5.24561 −0.249508
\(443\) 5.92484 0.281498 0.140749 0.990045i \(-0.455049\pi\)
0.140749 + 0.990045i \(0.455049\pi\)
\(444\) 5.66388 0.268796
\(445\) −44.1399 −2.09243
\(446\) −38.7222 −1.83355
\(447\) 14.9281 0.706073
\(448\) 5.19413 0.245400
\(449\) 28.6750 1.35326 0.676629 0.736324i \(-0.263440\pi\)
0.676629 + 0.736324i \(0.263440\pi\)
\(450\) 26.3681 1.24301
\(451\) −25.4849 −1.20003
\(452\) 9.25482 0.435310
\(453\) −21.4229 −1.00654
\(454\) −23.2387 −1.09065
\(455\) 58.1837 2.72769
\(456\) −0.660937 −0.0309512
\(457\) −8.43914 −0.394766 −0.197383 0.980326i \(-0.563244\pi\)
−0.197383 + 0.980326i \(0.563244\pi\)
\(458\) 34.2224 1.59911
\(459\) −1.00000 −0.0466760
\(460\) 16.7109 0.779150
\(461\) −22.5120 −1.04849 −0.524244 0.851568i \(-0.675652\pi\)
−0.524244 + 0.851568i \(0.675652\pi\)
\(462\) −37.4527 −1.74246
\(463\) 2.83629 0.131814 0.0659068 0.997826i \(-0.479006\pi\)
0.0659068 + 0.997826i \(0.479006\pi\)
\(464\) −49.1751 −2.28290
\(465\) −15.8753 −0.736201
\(466\) 33.9599 1.57316
\(467\) −8.53724 −0.395056 −0.197528 0.980297i \(-0.563291\pi\)
−0.197528 + 0.980297i \(0.563291\pi\)
\(468\) −3.60116 −0.166464
\(469\) −24.9778 −1.15337
\(470\) −42.1920 −1.94617
\(471\) 1.00000 0.0460776
\(472\) 15.8123 0.727822
\(473\) −30.6969 −1.41145
\(474\) −24.4588 −1.12343
\(475\) −7.04005 −0.323020
\(476\) −5.55499 −0.254612
\(477\) 7.85674 0.359735
\(478\) −29.2574 −1.33820
\(479\) 10.4534 0.477630 0.238815 0.971065i \(-0.423241\pi\)
0.238815 + 0.971065i \(0.423241\pi\)
\(480\) 27.2285 1.24281
\(481\) 13.3792 0.610039
\(482\) 7.79753 0.355168
\(483\) 13.7327 0.624858
\(484\) 12.8701 0.585002
\(485\) 66.3631 3.01339
\(486\) −1.79853 −0.0815829
\(487\) −18.6985 −0.847311 −0.423656 0.905823i \(-0.639253\pi\)
−0.423656 + 0.905823i \(0.639253\pi\)
\(488\) 20.7342 0.938594
\(489\) 19.7354 0.892465
\(490\) 105.597 4.77040
\(491\) −17.6434 −0.796234 −0.398117 0.917335i \(-0.630336\pi\)
−0.398117 + 0.917335i \(0.630336\pi\)
\(492\) −6.79828 −0.306490
\(493\) 9.94458 0.447882
\(494\) 2.51889 0.113330
\(495\) −20.5234 −0.922456
\(496\) −17.7043 −0.794948
\(497\) −35.9451 −1.61236
\(498\) −8.41109 −0.376910
\(499\) −21.8744 −0.979232 −0.489616 0.871938i \(-0.662863\pi\)
−0.489616 + 0.871938i \(0.662863\pi\)
\(500\) 52.8914 2.36538
\(501\) −5.51825 −0.246537
\(502\) 12.5732 0.561171
\(503\) 3.90620 0.174169 0.0870844 0.996201i \(-0.472245\pi\)
0.0870844 + 0.996201i \(0.472245\pi\)
\(504\) 6.19251 0.275836
\(505\) 44.2094 1.96729
\(506\) −25.4096 −1.12960
\(507\) 4.49336 0.199557
\(508\) 1.10306 0.0489403
\(509\) −10.7392 −0.476006 −0.238003 0.971264i \(-0.576493\pi\)
−0.238003 + 0.971264i \(0.576493\pi\)
\(510\) −7.97480 −0.353130
\(511\) −12.2243 −0.540772
\(512\) 16.7531 0.740389
\(513\) 0.480190 0.0212009
\(514\) 33.6708 1.48515
\(515\) 20.9145 0.921604
\(516\) −8.18864 −0.360485
\(517\) 24.4882 1.07699
\(518\) 37.1183 1.63089
\(519\) 19.2886 0.846673
\(520\) 17.8003 0.780596
\(521\) 30.2274 1.32428 0.662142 0.749378i \(-0.269647\pi\)
0.662142 + 0.749378i \(0.269647\pi\)
\(522\) 17.8856 0.782832
\(523\) −4.06532 −0.177764 −0.0888819 0.996042i \(-0.528329\pi\)
−0.0888819 + 0.996042i \(0.528329\pi\)
\(524\) −9.76680 −0.426665
\(525\) 65.9602 2.87874
\(526\) 23.2150 1.01222
\(527\) 3.58031 0.155961
\(528\) −22.8878 −0.996066
\(529\) −13.6831 −0.594919
\(530\) 62.6559 2.72160
\(531\) −11.4881 −0.498543
\(532\) 2.66745 0.115649
\(533\) −16.0589 −0.695587
\(534\) 17.9039 0.774776
\(535\) 77.5782 3.35400
\(536\) −7.64155 −0.330065
\(537\) −11.0243 −0.475733
\(538\) 8.42749 0.363335
\(539\) −61.2886 −2.63989
\(540\) −5.47476 −0.235596
\(541\) 28.1350 1.20962 0.604809 0.796371i \(-0.293249\pi\)
0.604809 + 0.796371i \(0.293249\pi\)
\(542\) −6.02518 −0.258803
\(543\) 12.2257 0.524654
\(544\) −6.14076 −0.263283
\(545\) 42.5943 1.82454
\(546\) −23.6002 −1.01000
\(547\) −8.99143 −0.384446 −0.192223 0.981351i \(-0.561570\pi\)
−0.192223 + 0.981351i \(0.561570\pi\)
\(548\) 9.25222 0.395235
\(549\) −15.0640 −0.642917
\(550\) −122.047 −5.20408
\(551\) −4.77529 −0.203434
\(552\) 4.20128 0.178818
\(553\) −61.1841 −2.60181
\(554\) 51.0347 2.16826
\(555\) 20.3401 0.863390
\(556\) −17.8877 −0.758608
\(557\) 3.12893 0.132577 0.0662886 0.997800i \(-0.478884\pi\)
0.0662886 + 0.997800i \(0.478884\pi\)
\(558\) 6.43929 0.272597
\(559\) −19.3432 −0.818130
\(560\) 98.6464 4.16857
\(561\) 4.62856 0.195418
\(562\) −29.2025 −1.23184
\(563\) 44.6983 1.88381 0.941905 0.335881i \(-0.109034\pi\)
0.941905 + 0.335881i \(0.109034\pi\)
\(564\) 6.53242 0.275064
\(565\) 33.2359 1.39824
\(566\) −19.2703 −0.809990
\(567\) −4.49904 −0.188942
\(568\) −10.9968 −0.461415
\(569\) 8.69913 0.364686 0.182343 0.983235i \(-0.441632\pi\)
0.182343 + 0.983235i \(0.441632\pi\)
\(570\) 3.82942 0.160397
\(571\) −7.25869 −0.303767 −0.151883 0.988398i \(-0.548534\pi\)
−0.151883 + 0.988398i \(0.548534\pi\)
\(572\) 16.6682 0.696932
\(573\) −18.8444 −0.787234
\(574\) −44.5526 −1.85959
\(575\) 44.7504 1.86622
\(576\) −1.15450 −0.0481040
\(577\) 17.7464 0.738790 0.369395 0.929272i \(-0.379565\pi\)
0.369395 + 0.929272i \(0.379565\pi\)
\(578\) 1.79853 0.0748089
\(579\) 25.5147 1.06036
\(580\) 54.4442 2.26067
\(581\) −21.0405 −0.872905
\(582\) −26.9179 −1.11578
\(583\) −36.3654 −1.50610
\(584\) −3.73983 −0.154755
\(585\) −12.9325 −0.534692
\(586\) −47.4735 −1.96111
\(587\) 21.6272 0.892652 0.446326 0.894871i \(-0.352732\pi\)
0.446326 + 0.894871i \(0.352732\pi\)
\(588\) −16.3492 −0.674230
\(589\) −1.71923 −0.0708397
\(590\) −91.6155 −3.77175
\(591\) −5.86540 −0.241270
\(592\) 22.6835 0.932286
\(593\) 32.8863 1.35048 0.675239 0.737599i \(-0.264041\pi\)
0.675239 + 0.737599i \(0.264041\pi\)
\(594\) 8.32460 0.341563
\(595\) −19.9491 −0.817832
\(596\) −18.4317 −0.754993
\(597\) 19.4004 0.794005
\(598\) −16.0115 −0.654758
\(599\) 42.8417 1.75046 0.875232 0.483703i \(-0.160708\pi\)
0.875232 + 0.483703i \(0.160708\pi\)
\(600\) 20.1794 0.823821
\(601\) −16.5388 −0.674630 −0.337315 0.941392i \(-0.609519\pi\)
−0.337315 + 0.941392i \(0.609519\pi\)
\(602\) −53.6644 −2.18720
\(603\) 5.55181 0.226087
\(604\) 26.4510 1.07628
\(605\) 46.2189 1.87907
\(606\) −17.9320 −0.728439
\(607\) −8.56208 −0.347524 −0.173762 0.984788i \(-0.555592\pi\)
−0.173762 + 0.984788i \(0.555592\pi\)
\(608\) 2.94873 0.119587
\(609\) 44.7411 1.81300
\(610\) −120.133 −4.86403
\(611\) 15.4309 0.624266
\(612\) 1.23470 0.0499100
\(613\) −3.50829 −0.141698 −0.0708492 0.997487i \(-0.522571\pi\)
−0.0708492 + 0.997487i \(0.522571\pi\)
\(614\) −34.4430 −1.39001
\(615\) −24.4140 −0.984466
\(616\) −28.6624 −1.15484
\(617\) −0.200006 −0.00805192 −0.00402596 0.999992i \(-0.501282\pi\)
−0.00402596 + 0.999992i \(0.501282\pi\)
\(618\) −8.48327 −0.341247
\(619\) −42.9788 −1.72746 −0.863731 0.503953i \(-0.831879\pi\)
−0.863731 + 0.503953i \(0.831879\pi\)
\(620\) 19.6014 0.787209
\(621\) −3.05235 −0.122487
\(622\) 2.73382 0.109616
\(623\) 44.7868 1.79434
\(624\) −14.4224 −0.577358
\(625\) 116.639 4.66555
\(626\) 15.8969 0.635368
\(627\) −2.22259 −0.0887618
\(628\) −1.23470 −0.0492701
\(629\) −4.58724 −0.182905
\(630\) −35.8789 −1.42945
\(631\) −37.2254 −1.48192 −0.740959 0.671550i \(-0.765629\pi\)
−0.740959 + 0.671550i \(0.765629\pi\)
\(632\) −18.7182 −0.744571
\(633\) −12.5811 −0.500055
\(634\) −0.361207 −0.0143454
\(635\) 3.96130 0.157199
\(636\) −9.70075 −0.384660
\(637\) −38.6200 −1.53018
\(638\) −82.7847 −3.27748
\(639\) 7.98950 0.316060
\(640\) 45.2502 1.78867
\(641\) −28.6641 −1.13216 −0.566082 0.824349i \(-0.691542\pi\)
−0.566082 + 0.824349i \(0.691542\pi\)
\(642\) −31.4670 −1.24190
\(643\) −5.73294 −0.226085 −0.113042 0.993590i \(-0.536060\pi\)
−0.113042 + 0.993590i \(0.536060\pi\)
\(644\) −16.9558 −0.668152
\(645\) −29.4070 −1.15790
\(646\) −0.863636 −0.0339793
\(647\) −1.19976 −0.0471674 −0.0235837 0.999722i \(-0.507508\pi\)
−0.0235837 + 0.999722i \(0.507508\pi\)
\(648\) −1.37641 −0.0540703
\(649\) 53.1736 2.08724
\(650\) −76.9057 −3.01649
\(651\) 16.1080 0.631321
\(652\) −24.3674 −0.954300
\(653\) −36.5691 −1.43106 −0.715529 0.698583i \(-0.753814\pi\)
−0.715529 + 0.698583i \(0.753814\pi\)
\(654\) −17.2769 −0.675581
\(655\) −35.0745 −1.37047
\(656\) −27.2267 −1.06302
\(657\) 2.71710 0.106004
\(658\) 42.8103 1.66892
\(659\) 18.2835 0.712224 0.356112 0.934443i \(-0.384102\pi\)
0.356112 + 0.934443i \(0.384102\pi\)
\(660\) 25.3403 0.986369
\(661\) −17.6781 −0.687600 −0.343800 0.939043i \(-0.611714\pi\)
−0.343800 + 0.939043i \(0.611714\pi\)
\(662\) 32.2508 1.25346
\(663\) 2.91661 0.113272
\(664\) −6.43697 −0.249803
\(665\) 9.57935 0.371471
\(666\) −8.25028 −0.319692
\(667\) 30.3544 1.17533
\(668\) 6.81341 0.263619
\(669\) 21.5299 0.832395
\(670\) 44.2746 1.71048
\(671\) 69.7248 2.69170
\(672\) −27.6275 −1.06575
\(673\) −18.0466 −0.695646 −0.347823 0.937560i \(-0.613079\pi\)
−0.347823 + 0.937560i \(0.613079\pi\)
\(674\) 5.60562 0.215921
\(675\) −14.6610 −0.564300
\(676\) −5.54797 −0.213384
\(677\) −39.0457 −1.50065 −0.750324 0.661071i \(-0.770102\pi\)
−0.750324 + 0.661071i \(0.770102\pi\)
\(678\) −13.4810 −0.517735
\(679\) −67.3356 −2.58410
\(680\) −6.10308 −0.234042
\(681\) 12.9210 0.495133
\(682\) −29.8047 −1.14128
\(683\) −18.5600 −0.710180 −0.355090 0.934832i \(-0.615550\pi\)
−0.355090 + 0.934832i \(0.615550\pi\)
\(684\) −0.592893 −0.0226698
\(685\) 33.2266 1.26952
\(686\) −50.5032 −1.92822
\(687\) −19.0280 −0.725964
\(688\) −32.7950 −1.25030
\(689\) −22.9151 −0.872995
\(690\) −24.3419 −0.926680
\(691\) 10.7549 0.409137 0.204569 0.978852i \(-0.434421\pi\)
0.204569 + 0.978852i \(0.434421\pi\)
\(692\) −23.8157 −0.905335
\(693\) 20.8241 0.791042
\(694\) 31.3641 1.19057
\(695\) −64.2383 −2.43670
\(696\) 13.6878 0.518834
\(697\) 5.50600 0.208555
\(698\) 3.09710 0.117227
\(699\) −18.8820 −0.714184
\(700\) −81.4414 −3.07820
\(701\) 0.220501 0.00832820 0.00416410 0.999991i \(-0.498675\pi\)
0.00416410 + 0.999991i \(0.498675\pi\)
\(702\) 5.24561 0.197983
\(703\) 2.20275 0.0830782
\(704\) 5.34366 0.201397
\(705\) 23.4592 0.883525
\(706\) 62.5219 2.35304
\(707\) −44.8572 −1.68703
\(708\) 14.1845 0.533084
\(709\) 14.1040 0.529685 0.264843 0.964292i \(-0.414680\pi\)
0.264843 + 0.964292i \(0.414680\pi\)
\(710\) 63.7146 2.39117
\(711\) 13.5994 0.510016
\(712\) 13.7017 0.513495
\(713\) 10.9284 0.409271
\(714\) 8.09166 0.302823
\(715\) 59.8587 2.23859
\(716\) 13.6117 0.508694
\(717\) 16.2674 0.607518
\(718\) 39.3279 1.46771
\(719\) 11.3720 0.424105 0.212053 0.977258i \(-0.431985\pi\)
0.212053 + 0.977258i \(0.431985\pi\)
\(720\) −21.9261 −0.817137
\(721\) −21.2210 −0.790312
\(722\) −33.7573 −1.25632
\(723\) −4.33551 −0.161239
\(724\) −15.0951 −0.561004
\(725\) 145.797 5.41477
\(726\) −18.7471 −0.695771
\(727\) 39.8861 1.47929 0.739647 0.672995i \(-0.234993\pi\)
0.739647 + 0.672995i \(0.234993\pi\)
\(728\) −18.0612 −0.669391
\(729\) 1.00000 0.0370370
\(730\) 21.6683 0.801979
\(731\) 6.63207 0.245296
\(732\) 18.5996 0.687462
\(733\) −0.00413344 −0.000152672 0 −7.63360e−5 1.00000i \(-0.500024\pi\)
−7.63360e−5 1.00000i \(0.500024\pi\)
\(734\) −41.0085 −1.51365
\(735\) −58.7132 −2.16567
\(736\) −18.7438 −0.690904
\(737\) −25.6969 −0.946558
\(738\) 9.90269 0.364523
\(739\) −38.5093 −1.41659 −0.708294 0.705917i \(-0.750535\pi\)
−0.708294 + 0.705917i \(0.750535\pi\)
\(740\) −25.1140 −0.923210
\(741\) −1.40053 −0.0514498
\(742\) −63.5740 −2.33388
\(743\) 36.2308 1.32918 0.664590 0.747209i \(-0.268606\pi\)
0.664590 + 0.747209i \(0.268606\pi\)
\(744\) 4.92796 0.180668
\(745\) −66.1920 −2.42509
\(746\) 4.51459 0.165291
\(747\) 4.67665 0.171110
\(748\) −5.71491 −0.208958
\(749\) −78.7150 −2.87618
\(750\) −77.0441 −2.81325
\(751\) 6.15872 0.224735 0.112367 0.993667i \(-0.464157\pi\)
0.112367 + 0.993667i \(0.464157\pi\)
\(752\) 26.1619 0.954027
\(753\) −6.99084 −0.254761
\(754\) −52.1655 −1.89975
\(755\) 94.9907 3.45707
\(756\) 5.55499 0.202033
\(757\) −25.7039 −0.934224 −0.467112 0.884198i \(-0.654706\pi\)
−0.467112 + 0.884198i \(0.654706\pi\)
\(758\) −49.6216 −1.80234
\(759\) 14.1280 0.512814
\(760\) 2.93064 0.106305
\(761\) −17.1978 −0.623420 −0.311710 0.950177i \(-0.600902\pi\)
−0.311710 + 0.950177i \(0.600902\pi\)
\(762\) −1.60677 −0.0582070
\(763\) −43.2185 −1.56461
\(764\) 23.2672 0.841778
\(765\) 4.43407 0.160314
\(766\) 48.1840 1.74096
\(767\) 33.5065 1.20985
\(768\) −20.6632 −0.745619
\(769\) 11.3752 0.410199 0.205099 0.978741i \(-0.434248\pi\)
0.205099 + 0.978741i \(0.434248\pi\)
\(770\) 166.068 5.98467
\(771\) −18.7213 −0.674231
\(772\) −31.5031 −1.13382
\(773\) −22.3853 −0.805144 −0.402572 0.915388i \(-0.631884\pi\)
−0.402572 + 0.915388i \(0.631884\pi\)
\(774\) 11.9280 0.428742
\(775\) 52.4908 1.88552
\(776\) −20.6002 −0.739503
\(777\) −20.6382 −0.740390
\(778\) 28.1830 1.01041
\(779\) −2.64393 −0.0947285
\(780\) 15.9678 0.571738
\(781\) −36.9799 −1.32324
\(782\) 5.48974 0.196313
\(783\) −9.94458 −0.355390
\(784\) −65.4775 −2.33848
\(785\) −4.43407 −0.158259
\(786\) 14.2268 0.507453
\(787\) −18.0978 −0.645118 −0.322559 0.946549i \(-0.604543\pi\)
−0.322559 + 0.946549i \(0.604543\pi\)
\(788\) 7.24203 0.257987
\(789\) −12.9078 −0.459529
\(790\) 108.452 3.85855
\(791\) −33.7229 −1.19905
\(792\) 6.37078 0.226376
\(793\) 43.9360 1.56021
\(794\) −3.22354 −0.114399
\(795\) −34.8373 −1.23555
\(796\) −23.9537 −0.849018
\(797\) 33.1451 1.17406 0.587030 0.809565i \(-0.300297\pi\)
0.587030 + 0.809565i \(0.300297\pi\)
\(798\) −3.88554 −0.137546
\(799\) −5.29067 −0.187171
\(800\) −90.0293 −3.18302
\(801\) −9.95473 −0.351733
\(802\) 41.3153 1.45889
\(803\) −12.5762 −0.443806
\(804\) −6.85485 −0.241752
\(805\) −60.8916 −2.14615
\(806\) −18.7809 −0.661530
\(807\) −4.68577 −0.164947
\(808\) −13.7233 −0.482784
\(809\) −15.2505 −0.536180 −0.268090 0.963394i \(-0.586393\pi\)
−0.268090 + 0.963394i \(0.586393\pi\)
\(810\) 7.97480 0.280206
\(811\) 10.8230 0.380046 0.190023 0.981780i \(-0.439144\pi\)
0.190023 + 0.981780i \(0.439144\pi\)
\(812\) −55.2421 −1.93862
\(813\) 3.35006 0.117492
\(814\) 38.1869 1.33845
\(815\) −87.5080 −3.06527
\(816\) 4.94491 0.173107
\(817\) −3.18466 −0.111417
\(818\) −37.8025 −1.32173
\(819\) 13.1220 0.458519
\(820\) 30.1440 1.05267
\(821\) −3.73030 −0.130188 −0.0650942 0.997879i \(-0.520735\pi\)
−0.0650942 + 0.997879i \(0.520735\pi\)
\(822\) −13.4772 −0.470072
\(823\) 34.3619 1.19778 0.598890 0.800832i \(-0.295609\pi\)
0.598890 + 0.800832i \(0.295609\pi\)
\(824\) −6.49221 −0.226167
\(825\) 67.8591 2.36255
\(826\) 92.9581 3.23442
\(827\) 9.47172 0.329364 0.164682 0.986347i \(-0.447340\pi\)
0.164682 + 0.986347i \(0.447340\pi\)
\(828\) 3.76875 0.130973
\(829\) 46.5525 1.61684 0.808418 0.588609i \(-0.200324\pi\)
0.808418 + 0.588609i \(0.200324\pi\)
\(830\) 37.2953 1.29454
\(831\) −28.3758 −0.984346
\(832\) 3.36722 0.116737
\(833\) 13.2414 0.458787
\(834\) 26.0561 0.902248
\(835\) 24.4683 0.846760
\(836\) 2.74424 0.0949116
\(837\) −3.58031 −0.123754
\(838\) −20.6777 −0.714301
\(839\) −24.3179 −0.839546 −0.419773 0.907629i \(-0.637890\pi\)
−0.419773 + 0.907629i \(0.637890\pi\)
\(840\) −27.4580 −0.947391
\(841\) 69.8948 2.41016
\(842\) −13.1232 −0.452255
\(843\) 16.2369 0.559229
\(844\) 15.5340 0.534702
\(845\) −19.9239 −0.685402
\(846\) −9.51543 −0.327147
\(847\) −46.8962 −1.61137
\(848\) −38.8509 −1.33415
\(849\) 10.7145 0.367720
\(850\) 26.3681 0.904420
\(851\) −14.0019 −0.479978
\(852\) −9.86467 −0.337958
\(853\) −48.6664 −1.66631 −0.833153 0.553043i \(-0.813467\pi\)
−0.833153 + 0.553043i \(0.813467\pi\)
\(854\) 121.893 4.17109
\(855\) −2.12920 −0.0728170
\(856\) −24.0815 −0.823090
\(857\) 44.9890 1.53679 0.768397 0.639973i \(-0.221055\pi\)
0.768397 + 0.639973i \(0.221055\pi\)
\(858\) −24.2797 −0.828894
\(859\) −9.22248 −0.314667 −0.157333 0.987546i \(-0.550290\pi\)
−0.157333 + 0.987546i \(0.550290\pi\)
\(860\) 36.3090 1.23813
\(861\) 24.7717 0.844218
\(862\) 32.6802 1.11309
\(863\) −4.34652 −0.147957 −0.0739786 0.997260i \(-0.523570\pi\)
−0.0739786 + 0.997260i \(0.523570\pi\)
\(864\) 6.14076 0.208913
\(865\) −85.5267 −2.90800
\(866\) 73.3496 2.49252
\(867\) −1.00000 −0.0339618
\(868\) −19.8886 −0.675063
\(869\) −62.9455 −2.13528
\(870\) −79.3060 −2.68873
\(871\) −16.1925 −0.548662
\(872\) −13.2220 −0.447752
\(873\) 14.9666 0.506544
\(874\) −2.63612 −0.0891682
\(875\) −192.727 −6.51536
\(876\) −3.35481 −0.113348
\(877\) −13.2669 −0.447991 −0.223995 0.974590i \(-0.571910\pi\)
−0.223995 + 0.974590i \(0.571910\pi\)
\(878\) 9.90505 0.334279
\(879\) 26.3958 0.890307
\(880\) 101.486 3.42110
\(881\) −24.6111 −0.829168 −0.414584 0.910011i \(-0.636073\pi\)
−0.414584 + 0.910011i \(0.636073\pi\)
\(882\) 23.8150 0.801893
\(883\) 32.7570 1.10236 0.551180 0.834386i \(-0.314178\pi\)
0.551180 + 0.834386i \(0.314178\pi\)
\(884\) −3.60116 −0.121120
\(885\) 50.9392 1.71230
\(886\) 10.6560 0.357995
\(887\) 26.9699 0.905560 0.452780 0.891622i \(-0.350432\pi\)
0.452780 + 0.891622i \(0.350432\pi\)
\(888\) −6.31390 −0.211881
\(889\) −4.01935 −0.134805
\(890\) −79.3869 −2.66106
\(891\) −4.62856 −0.155063
\(892\) −26.5831 −0.890068
\(893\) 2.54053 0.0850156
\(894\) 26.8485 0.897949
\(895\) 48.8824 1.63396
\(896\) −45.9133 −1.53385
\(897\) 8.90254 0.297247
\(898\) 51.5728 1.72101
\(899\) 35.6047 1.18748
\(900\) 18.1019 0.603398
\(901\) 7.85674 0.261746
\(902\) −45.8352 −1.52615
\(903\) 29.8380 0.992945
\(904\) −10.3170 −0.343137
\(905\) −54.2094 −1.80198
\(906\) −38.5297 −1.28007
\(907\) 30.1573 1.00136 0.500678 0.865634i \(-0.333084\pi\)
0.500678 + 0.865634i \(0.333084\pi\)
\(908\) −15.9536 −0.529438
\(909\) 9.97039 0.330697
\(910\) 104.645 3.46895
\(911\) −34.8651 −1.15513 −0.577566 0.816344i \(-0.695998\pi\)
−0.577566 + 0.816344i \(0.695998\pi\)
\(912\) −2.37450 −0.0786276
\(913\) −21.6462 −0.716384
\(914\) −15.1780 −0.502045
\(915\) 66.7949 2.20817
\(916\) 23.4940 0.776263
\(917\) 35.5885 1.17524
\(918\) −1.79853 −0.0593603
\(919\) −30.9380 −1.02055 −0.510274 0.860012i \(-0.670456\pi\)
−0.510274 + 0.860012i \(0.670456\pi\)
\(920\) −18.6287 −0.614172
\(921\) 19.1507 0.631036
\(922\) −40.4885 −1.33342
\(923\) −23.3023 −0.767004
\(924\) −25.7116 −0.845850
\(925\) −67.2532 −2.21127
\(926\) 5.10115 0.167634
\(927\) 4.71678 0.154919
\(928\) −61.0673 −2.00463
\(929\) −41.1794 −1.35105 −0.675526 0.737336i \(-0.736083\pi\)
−0.675526 + 0.737336i \(0.736083\pi\)
\(930\) −28.5522 −0.936265
\(931\) −6.35839 −0.208388
\(932\) 23.3137 0.763666
\(933\) −1.52003 −0.0497635
\(934\) −15.3545 −0.502414
\(935\) −20.5234 −0.671186
\(936\) 4.01445 0.131216
\(937\) −5.48833 −0.179296 −0.0896480 0.995974i \(-0.528574\pi\)
−0.0896480 + 0.995974i \(0.528574\pi\)
\(938\) −44.9234 −1.46680
\(939\) −8.83884 −0.288445
\(940\) −28.9652 −0.944740
\(941\) −28.5263 −0.929930 −0.464965 0.885329i \(-0.653933\pi\)
−0.464965 + 0.885329i \(0.653933\pi\)
\(942\) 1.79853 0.0585992
\(943\) 16.8063 0.547287
\(944\) 56.8078 1.84894
\(945\) 19.9491 0.648943
\(946\) −55.2093 −1.79501
\(947\) 50.0379 1.62601 0.813007 0.582254i \(-0.197829\pi\)
0.813007 + 0.582254i \(0.197829\pi\)
\(948\) −16.7912 −0.545352
\(949\) −7.92472 −0.257247
\(950\) −12.6617 −0.410801
\(951\) 0.200835 0.00651251
\(952\) 6.19251 0.200700
\(953\) 49.6915 1.60966 0.804832 0.593503i \(-0.202255\pi\)
0.804832 + 0.593503i \(0.202255\pi\)
\(954\) 14.1306 0.457494
\(955\) 83.5572 2.70385
\(956\) −20.0854 −0.649610
\(957\) 46.0291 1.48791
\(958\) 18.8008 0.607427
\(959\) −33.7134 −1.08866
\(960\) 5.11912 0.165219
\(961\) −18.1814 −0.586496
\(962\) 24.0629 0.775818
\(963\) 17.4959 0.563799
\(964\) 5.35307 0.172411
\(965\) −113.134 −3.64191
\(966\) 24.6986 0.794664
\(967\) 11.9168 0.383218 0.191609 0.981471i \(-0.438629\pi\)
0.191609 + 0.981471i \(0.438629\pi\)
\(968\) −14.3471 −0.461133
\(969\) 0.480190 0.0154259
\(970\) 119.356 3.83229
\(971\) −41.4905 −1.33149 −0.665747 0.746178i \(-0.731887\pi\)
−0.665747 + 0.746178i \(0.731887\pi\)
\(972\) −1.23470 −0.0396032
\(973\) 65.1796 2.08956
\(974\) −33.6298 −1.07757
\(975\) 42.7603 1.36943
\(976\) 74.4903 2.38438
\(977\) −20.5042 −0.655987 −0.327993 0.944680i \(-0.606372\pi\)
−0.327993 + 0.944680i \(0.606372\pi\)
\(978\) 35.4947 1.13499
\(979\) 46.0761 1.47260
\(980\) 72.4934 2.31572
\(981\) 9.60614 0.306701
\(982\) −31.7321 −1.01261
\(983\) 20.1667 0.643219 0.321610 0.946872i \(-0.395776\pi\)
0.321610 + 0.946872i \(0.395776\pi\)
\(984\) 7.57849 0.241593
\(985\) 26.0076 0.828670
\(986\) 17.8856 0.569594
\(987\) −23.8030 −0.757657
\(988\) 1.72924 0.0550145
\(989\) 20.2434 0.643703
\(990\) −36.9118 −1.17314
\(991\) 49.8803 1.58450 0.792250 0.610197i \(-0.208910\pi\)
0.792250 + 0.610197i \(0.208910\pi\)
\(992\) −21.9858 −0.698050
\(993\) −17.9318 −0.569048
\(994\) −64.6483 −2.05052
\(995\) −86.0226 −2.72710
\(996\) −5.77428 −0.182965
\(997\) −12.2513 −0.388001 −0.194001 0.981001i \(-0.562146\pi\)
−0.194001 + 0.981001i \(0.562146\pi\)
\(998\) −39.3417 −1.24534
\(999\) 4.58724 0.145134
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 8007.2.a.j.1.48 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.j.1.48 64 1.1 even 1 trivial