Properties

Label 81.2.e.a.37.2
Level $81$
Weight $2$
Character 81.37
Analytic conductor $0.647$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,2,Mod(10,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.e (of order \(9\), degree \(6\), not minimal)

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: no
Analytic conductor: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.2
Root \(0.500000 - 0.258654i\) of defining polynomial
Character \(\chi\) \(=\) 81.37
Dual form 81.2.e.a.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.62143 - 1.36054i) q^{2} +(0.430663 - 2.44241i) q^{4} +(-2.52129 + 0.917674i) q^{5} +(0.168844 + 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +O(q^{10})\) \(q+(1.62143 - 1.36054i) q^{2} +(0.430663 - 2.44241i) q^{4} +(-2.52129 + 0.917674i) q^{5} +(0.168844 + 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-2.83955 + 4.91825i) q^{10} +(-0.297791 - 0.108387i) q^{11} +(-1.15981 - 0.973200i) q^{13} +(1.57657 + 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(0.587342 - 1.01731i) q^{17} +(-3.11040 - 5.38737i) q^{19} +(1.15551 + 6.55323i) q^{20} +(-0.630310 + 0.229414i) q^{22} +(-0.375556 + 2.12988i) q^{23} +(1.68454 - 1.41350i) q^{25} -3.20463 q^{26} +2.41147 q^{28} +(3.37436 - 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(7.49746 - 2.72885i) q^{32} +(-0.431752 - 2.44859i) q^{34} +(-1.30443 - 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(-12.3730 - 4.50341i) q^{38} +(2.08861 + 1.75255i) q^{40} +(-4.47767 - 3.75721i) q^{41} +(-5.25381 - 1.91223i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(0.429965 + 2.43845i) q^{47} +(5.68943 - 2.07078i) q^{49} +(0.808243 - 4.58377i) q^{50} +(-2.87645 + 2.41362i) q^{52} +10.8920 q^{53} +0.850279 q^{55} +(0.756896 - 0.635111i) q^{56} +(1.61901 - 9.18189i) q^{58} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(9.17898 + 15.8985i) q^{62} +(5.63455 - 9.75933i) q^{64} +(3.81731 + 1.38939i) q^{65} +(0.656156 + 0.550580i) q^{67} +(-2.23174 - 1.87265i) q^{68} +(-5.18896 - 1.88863i) q^{70} +(-4.79788 + 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(-1.64171 - 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.0535070 - 0.303453i) q^{77} +(-8.59024 + 7.20807i) q^{79} -7.53771 q^{80} -12.3721 q^{82} +(-3.58886 + 3.01141i) q^{83} +(-0.547303 + 3.10391i) q^{85} +(-11.1203 + 4.04747i) q^{86} +(0.0559194 + 0.317135i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(5.04032 + 1.83453i) q^{92} +(4.01476 + 3.36879i) q^{94} +(12.7861 + 10.7288i) q^{95} +(5.21481 + 1.89804i) q^{97} +(6.40762 - 11.0983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62143 1.36054i 1.14652 0.962046i 0.146889 0.989153i \(-0.453074\pi\)
0.999633 + 0.0271067i \(0.00862938\pi\)
\(3\) 0 0
\(4\) 0.430663 2.44241i 0.215332 1.22121i
\(5\) −2.52129 + 0.917674i −1.12755 + 0.410396i −0.837404 0.546585i \(-0.815928\pi\)
−0.290150 + 0.956981i \(0.593705\pi\)
\(6\) 0 0
\(7\) 0.168844 + 0.957561i 0.0638170 + 0.361924i 0.999947 + 0.0102706i \(0.00326930\pi\)
−0.936130 + 0.351653i \(0.885620\pi\)
\(8\) −0.508086 0.880031i −0.179636 0.311138i
\(9\) 0 0
\(10\) −2.83955 + 4.91825i −0.897945 + 1.55529i
\(11\) −0.297791 0.108387i −0.0897872 0.0326799i 0.296736 0.954960i \(-0.404102\pi\)
−0.386523 + 0.922280i \(0.626324\pi\)
\(12\) 0 0
\(13\) −1.15981 0.973200i −0.321675 0.269917i 0.467623 0.883928i \(-0.345111\pi\)
−0.789297 + 0.614011i \(0.789555\pi\)
\(14\) 1.57657 + 1.32290i 0.421355 + 0.353559i
\(15\) 0 0
\(16\) 2.63991 + 0.960847i 0.659977 + 0.240212i
\(17\) 0.587342 1.01731i 0.142451 0.246733i −0.785968 0.618267i \(-0.787835\pi\)
0.928419 + 0.371534i \(0.121168\pi\)
\(18\) 0 0
\(19\) −3.11040 5.38737i −0.713575 1.23595i −0.963507 0.267685i \(-0.913741\pi\)
0.249931 0.968264i \(-0.419592\pi\)
\(20\) 1.15551 + 6.55323i 0.258380 + 1.46535i
\(21\) 0 0
\(22\) −0.630310 + 0.229414i −0.134383 + 0.0489113i
\(23\) −0.375556 + 2.12988i −0.0783089 + 0.444112i 0.920292 + 0.391232i \(0.127951\pi\)
−0.998601 + 0.0528796i \(0.983160\pi\)
\(24\) 0 0
\(25\) 1.68454 1.41350i 0.336909 0.282700i
\(26\) −3.20463 −0.628480
\(27\) 0 0
\(28\) 2.41147 0.455726
\(29\) 3.37436 2.83142i 0.626602 0.525782i −0.273269 0.961938i \(-0.588105\pi\)
0.899871 + 0.436156i \(0.143660\pi\)
\(30\) 0 0
\(31\) −1.50609 + 8.54146i −0.270502 + 1.53409i 0.482395 + 0.875954i \(0.339767\pi\)
−0.752897 + 0.658138i \(0.771344\pi\)
\(32\) 7.49746 2.72885i 1.32538 0.482398i
\(33\) 0 0
\(34\) −0.431752 2.44859i −0.0740449 0.419930i
\(35\) −1.30443 2.25934i −0.220489 0.381899i
\(36\) 0 0
\(37\) 2.23332 3.86823i 0.367156 0.635933i −0.621964 0.783046i \(-0.713665\pi\)
0.989120 + 0.147113i \(0.0469982\pi\)
\(38\) −12.3730 4.50341i −2.00717 0.730550i
\(39\) 0 0
\(40\) 2.08861 + 1.75255i 0.330239 + 0.277103i
\(41\) −4.47767 3.75721i −0.699295 0.586778i 0.222278 0.974983i \(-0.428651\pi\)
−0.921573 + 0.388205i \(0.873095\pi\)
\(42\) 0 0
\(43\) −5.25381 1.91223i −0.801199 0.291613i −0.0912158 0.995831i \(-0.529075\pi\)
−0.709983 + 0.704219i \(0.751298\pi\)
\(44\) −0.392973 + 0.680649i −0.0592429 + 0.102612i
\(45\) 0 0
\(46\) 2.28885 + 3.96441i 0.337473 + 0.584521i
\(47\) 0.429965 + 2.43845i 0.0627168 + 0.355685i 0.999975 + 0.00704911i \(0.00224382\pi\)
−0.937258 + 0.348636i \(0.886645\pi\)
\(48\) 0 0
\(49\) 5.68943 2.07078i 0.812776 0.295826i
\(50\) 0.808243 4.58377i 0.114303 0.648243i
\(51\) 0 0
\(52\) −2.87645 + 2.41362i −0.398891 + 0.334710i
\(53\) 10.8920 1.49613 0.748063 0.663628i \(-0.230984\pi\)
0.748063 + 0.663628i \(0.230984\pi\)
\(54\) 0 0
\(55\) 0.850279 0.114652
\(56\) 0.756896 0.635111i 0.101145 0.0848703i
\(57\) 0 0
\(58\) 1.61901 9.18189i 0.212587 1.20564i
\(59\) −1.62023 + 0.589715i −0.210936 + 0.0767743i −0.445327 0.895368i \(-0.646913\pi\)
0.234391 + 0.972142i \(0.424690\pi\)
\(60\) 0 0
\(61\) 0.176214 + 0.999361i 0.0225619 + 0.127955i 0.994008 0.109304i \(-0.0348621\pi\)
−0.971446 + 0.237259i \(0.923751\pi\)
\(62\) 9.17898 + 15.8985i 1.16573 + 2.01911i
\(63\) 0 0
\(64\) 5.63455 9.75933i 0.704319 1.21992i
\(65\) 3.81731 + 1.38939i 0.473478 + 0.172332i
\(66\) 0 0
\(67\) 0.656156 + 0.550580i 0.0801622 + 0.0672641i 0.681988 0.731363i \(-0.261116\pi\)
−0.601826 + 0.798627i \(0.705560\pi\)
\(68\) −2.23174 1.87265i −0.270638 0.227092i
\(69\) 0 0
\(70\) −5.18896 1.88863i −0.620200 0.225734i
\(71\) −4.79788 + 8.31018i −0.569404 + 0.986237i 0.427221 + 0.904147i \(0.359493\pi\)
−0.996625 + 0.0820894i \(0.973841\pi\)
\(72\) 0 0
\(73\) 7.62091 + 13.1998i 0.891960 + 1.54492i 0.837522 + 0.546404i \(0.184004\pi\)
0.0544385 + 0.998517i \(0.482663\pi\)
\(74\) −1.64171 9.31057i −0.190844 1.08233i
\(75\) 0 0
\(76\) −14.4977 + 5.27674i −1.66300 + 0.605284i
\(77\) 0.0535070 0.303453i 0.00609768 0.0345817i
\(78\) 0 0
\(79\) −8.59024 + 7.20807i −0.966478 + 0.810971i −0.981995 0.188908i \(-0.939505\pi\)
0.0155168 + 0.999880i \(0.495061\pi\)
\(80\) −7.53771 −0.842741
\(81\) 0 0
\(82\) −12.3721 −1.36626
\(83\) −3.58886 + 3.01141i −0.393929 + 0.330546i −0.818141 0.575017i \(-0.804995\pi\)
0.424212 + 0.905563i \(0.360551\pi\)
\(84\) 0 0
\(85\) −0.547303 + 3.10391i −0.0593633 + 0.336666i
\(86\) −11.1203 + 4.04747i −1.19914 + 0.436450i
\(87\) 0 0
\(88\) 0.0559194 + 0.317135i 0.00596103 + 0.0338067i
\(89\) −7.74976 13.4230i −0.821473 1.42283i −0.904586 0.426292i \(-0.859820\pi\)
0.0831130 0.996540i \(-0.473514\pi\)
\(90\) 0 0
\(91\) 0.736071 1.27491i 0.0771612 0.133647i
\(92\) 5.04032 + 1.83453i 0.525490 + 0.191263i
\(93\) 0 0
\(94\) 4.01476 + 3.36879i 0.414091 + 0.347464i
\(95\) 12.7861 + 10.7288i 1.31182 + 1.10075i
\(96\) 0 0
\(97\) 5.21481 + 1.89804i 0.529484 + 0.192716i 0.592908 0.805270i \(-0.297980\pi\)
−0.0634241 + 0.997987i \(0.520202\pi\)
\(98\) 6.40762 11.0983i 0.647267 1.12110i
\(99\) 0 0
\(100\) −2.72688 4.72309i −0.272688 0.472309i
\(101\) 1.76063 + 9.98501i 0.175189 + 0.993546i 0.937926 + 0.346836i \(0.112744\pi\)
−0.762737 + 0.646709i \(0.776145\pi\)
\(102\) 0 0
\(103\) 9.25906 3.37002i 0.912323 0.332058i 0.157143 0.987576i \(-0.449772\pi\)
0.755180 + 0.655518i \(0.227549\pi\)
\(104\) −0.267160 + 1.51514i −0.0261972 + 0.148572i
\(105\) 0 0
\(106\) 17.6605 14.8189i 1.71534 1.43934i
\(107\) −5.17080 −0.499880 −0.249940 0.968261i \(-0.580411\pi\)
−0.249940 + 0.968261i \(0.580411\pi\)
\(108\) 0 0
\(109\) −7.31065 −0.700234 −0.350117 0.936706i \(-0.613858\pi\)
−0.350117 + 0.936706i \(0.613858\pi\)
\(110\) 1.37867 1.15684i 0.131451 0.110300i
\(111\) 0 0
\(112\) −0.474338 + 2.69010i −0.0448207 + 0.254191i
\(113\) 9.74991 3.54868i 0.917195 0.333832i 0.160073 0.987105i \(-0.448827\pi\)
0.757122 + 0.653274i \(0.226605\pi\)
\(114\) 0 0
\(115\) −1.00765 5.71469i −0.0939642 0.532898i
\(116\) −5.46229 9.46096i −0.507161 0.878428i
\(117\) 0 0
\(118\) −1.82475 + 3.16056i −0.167982 + 0.290953i
\(119\) 1.07330 + 0.390650i 0.0983894 + 0.0358108i
\(120\) 0 0
\(121\) −8.34956 7.00611i −0.759051 0.636919i
\(122\) 1.64539 + 1.38064i 0.148966 + 0.124998i
\(123\) 0 0
\(124\) 20.2132 + 7.35699i 1.81520 + 0.660677i
\(125\) 3.75766 6.50846i 0.336095 0.582134i
\(126\) 0 0
\(127\) −2.61372 4.52709i −0.231930 0.401714i 0.726446 0.687223i \(-0.241171\pi\)
−0.958376 + 0.285509i \(0.907837\pi\)
\(128\) −1.37098 7.77522i −0.121179 0.687239i
\(129\) 0 0
\(130\) 8.07980 2.94081i 0.708645 0.257926i
\(131\) 1.25622 7.12440i 0.109757 0.622461i −0.879457 0.475979i \(-0.842094\pi\)
0.989213 0.146482i \(-0.0467951\pi\)
\(132\) 0 0
\(133\) 4.63357 3.88802i 0.401781 0.337134i
\(134\) 1.81300 0.156619
\(135\) 0 0
\(136\) −1.19368 −0.102357
\(137\) −8.61748 + 7.23092i −0.736241 + 0.617779i −0.931825 0.362907i \(-0.881784\pi\)
0.195584 + 0.980687i \(0.437340\pi\)
\(138\) 0 0
\(139\) 1.62885 9.23766i 0.138157 0.783528i −0.834452 0.551081i \(-0.814216\pi\)
0.972609 0.232447i \(-0.0746733\pi\)
\(140\) −6.08002 + 2.21295i −0.513855 + 0.187028i
\(141\) 0 0
\(142\) 3.52690 + 20.0021i 0.295971 + 1.67854i
\(143\) 0.239900 + 0.415518i 0.0200614 + 0.0347474i
\(144\) 0 0
\(145\) −5.90940 + 10.2354i −0.490749 + 0.850003i
\(146\) 30.3156 + 11.0340i 2.50894 + 0.913179i
\(147\) 0 0
\(148\) −8.48600 7.12060i −0.697545 0.585310i
\(149\) −14.5941 12.2459i −1.19560 1.00322i −0.999745 0.0225899i \(-0.992809\pi\)
−0.195851 0.980634i \(-0.562747\pi\)
\(150\) 0 0
\(151\) −3.77193 1.37287i −0.306955 0.111723i 0.183950 0.982936i \(-0.441112\pi\)
−0.490905 + 0.871213i \(0.663334\pi\)
\(152\) −3.16070 + 5.47450i −0.256367 + 0.444041i
\(153\) 0 0
\(154\) −0.326102 0.564825i −0.0262780 0.0455149i
\(155\) −4.04099 22.9176i −0.324580 1.84078i
\(156\) 0 0
\(157\) −6.83713 + 2.48851i −0.545662 + 0.198605i −0.600118 0.799911i \(-0.704880\pi\)
0.0544560 + 0.998516i \(0.482658\pi\)
\(158\) −4.12159 + 23.3747i −0.327896 + 1.85959i
\(159\) 0 0
\(160\) −16.3991 + 13.7604i −1.29646 + 1.08786i
\(161\) −2.10290 −0.165732
\(162\) 0 0
\(163\) 12.4492 0.975094 0.487547 0.873097i \(-0.337892\pi\)
0.487547 + 0.873097i \(0.337892\pi\)
\(164\) −11.1050 + 9.31823i −0.867157 + 0.727632i
\(165\) 0 0
\(166\) −1.72194 + 9.76558i −0.133648 + 0.757956i
\(167\) −2.19126 + 0.797553i −0.169565 + 0.0617165i −0.425408 0.905002i \(-0.639869\pi\)
0.255843 + 0.966718i \(0.417647\pi\)
\(168\) 0 0
\(169\) −1.85937 10.5450i −0.143029 0.811157i
\(170\) 3.33558 + 5.77739i 0.255827 + 0.443106i
\(171\) 0 0
\(172\) −6.93308 + 12.0085i −0.528643 + 0.915636i
\(173\) −3.36623 1.22521i −0.255930 0.0931509i 0.210869 0.977514i \(-0.432371\pi\)
−0.466799 + 0.884363i \(0.654593\pi\)
\(174\) 0 0
\(175\) 1.63794 + 1.37439i 0.123816 + 0.103894i
\(176\) −0.681996 0.572262i −0.0514074 0.0431359i
\(177\) 0 0
\(178\) −30.8281 11.2205i −2.31067 0.841014i
\(179\) −9.99785 + 17.3168i −0.747275 + 1.29432i 0.201850 + 0.979416i \(0.435305\pi\)
−0.949124 + 0.314901i \(0.898029\pi\)
\(180\) 0 0
\(181\) −4.86616 8.42844i −0.361699 0.626481i 0.626542 0.779388i \(-0.284470\pi\)
−0.988241 + 0.152907i \(0.951136\pi\)
\(182\) −0.541082 3.06863i −0.0401077 0.227462i
\(183\) 0 0
\(184\) 2.06518 0.751664i 0.152247 0.0554134i
\(185\) −2.08108 + 11.8024i −0.153004 + 0.867728i
\(186\) 0 0
\(187\) −0.285168 + 0.239284i −0.0208535 + 0.0174982i
\(188\) 6.14088 0.447869
\(189\) 0 0
\(190\) 35.3286 2.56301
\(191\) 13.6023 11.4137i 0.984227 0.825864i −0.000494763 1.00000i \(-0.500157\pi\)
0.984722 + 0.174135i \(0.0557130\pi\)
\(192\) 0 0
\(193\) 1.83795 10.4235i 0.132299 0.750303i −0.844404 0.535706i \(-0.820045\pi\)
0.976703 0.214596i \(-0.0688435\pi\)
\(194\) 11.0378 4.01743i 0.792467 0.288434i
\(195\) 0 0
\(196\) −2.60748 14.7878i −0.186249 1.05627i
\(197\) 7.07945 + 12.2620i 0.504390 + 0.873628i 0.999987 + 0.00507615i \(0.00161579\pi\)
−0.495597 + 0.868552i \(0.665051\pi\)
\(198\) 0 0
\(199\) −3.77010 + 6.53000i −0.267255 + 0.462899i −0.968152 0.250363i \(-0.919450\pi\)
0.700897 + 0.713263i \(0.252783\pi\)
\(200\) −2.09982 0.764271i −0.148479 0.0540421i
\(201\) 0 0
\(202\) 16.4397 + 13.7946i 1.15669 + 0.970582i
\(203\) 3.28100 + 2.75308i 0.230281 + 0.193229i
\(204\) 0 0
\(205\) 14.7374 + 5.36397i 1.02930 + 0.374636i
\(206\) 10.4278 18.0616i 0.726543 1.25841i
\(207\) 0 0
\(208\) −2.12670 3.68356i −0.147460 0.255409i
\(209\) 0.342328 + 1.94144i 0.0236793 + 0.134292i
\(210\) 0 0
\(211\) −4.89922 + 1.78317i −0.337276 + 0.122758i −0.505106 0.863058i \(-0.668546\pi\)
0.167829 + 0.985816i \(0.446324\pi\)
\(212\) 4.69077 26.6027i 0.322163 1.82708i
\(213\) 0 0
\(214\) −8.38408 + 7.03508i −0.573124 + 0.480908i
\(215\) 15.0012 1.02307
\(216\) 0 0
\(217\) −8.43326 −0.572487
\(218\) −11.8537 + 9.94643i −0.802833 + 0.673657i
\(219\) 0 0
\(220\) 0.366184 2.07673i 0.0246881 0.140013i
\(221\) −1.67125 + 0.608285i −0.112420 + 0.0409177i
\(222\) 0 0
\(223\) 3.07250 + 17.4250i 0.205750 + 1.16686i 0.896256 + 0.443537i \(0.146277\pi\)
−0.690506 + 0.723326i \(0.742612\pi\)
\(224\) 3.87894 + 6.71853i 0.259173 + 0.448901i
\(225\) 0 0
\(226\) 10.9807 19.0191i 0.730423 1.26513i
\(227\) −14.8208 5.39434i −0.983692 0.358035i −0.200418 0.979711i \(-0.564230\pi\)
−0.783275 + 0.621676i \(0.786452\pi\)
\(228\) 0 0
\(229\) −1.35350 1.13572i −0.0894415 0.0750504i 0.596971 0.802263i \(-0.296371\pi\)
−0.686412 + 0.727213i \(0.740815\pi\)
\(230\) −9.40889 7.89500i −0.620404 0.520581i
\(231\) 0 0
\(232\) −4.20620 1.53093i −0.276151 0.100511i
\(233\) −6.94920 + 12.0364i −0.455257 + 0.788529i −0.998703 0.0509157i \(-0.983786\pi\)
0.543446 + 0.839444i \(0.317119\pi\)
\(234\) 0 0
\(235\) −3.32177 5.75347i −0.216688 0.375315i
\(236\) 0.742554 + 4.21123i 0.0483362 + 0.274128i
\(237\) 0 0
\(238\) 2.27177 0.826858i 0.147257 0.0535973i
\(239\) 3.44391 19.5314i 0.222768 1.26338i −0.644138 0.764909i \(-0.722784\pi\)
0.866906 0.498471i \(-0.166105\pi\)
\(240\) 0 0
\(241\) 14.8419 12.4538i 0.956050 0.802221i −0.0242563 0.999706i \(-0.507722\pi\)
0.980306 + 0.197485i \(0.0632773\pi\)
\(242\) −23.0703 −1.48301
\(243\) 0 0
\(244\) 2.51674 0.161118
\(245\) −12.4444 + 10.4421i −0.795043 + 0.667120i
\(246\) 0 0
\(247\) −1.63550 + 9.27540i −0.104065 + 0.590179i
\(248\) 8.28198 3.01439i 0.525906 0.191414i
\(249\) 0 0
\(250\) −2.76224 15.6654i −0.174699 0.990769i
\(251\) −2.73786 4.74212i −0.172812 0.299320i 0.766590 0.642137i \(-0.221952\pi\)
−0.939402 + 0.342818i \(0.888619\pi\)
\(252\) 0 0
\(253\) 0.342689 0.593554i 0.0215447 0.0373164i
\(254\) −10.3972 3.78428i −0.652380 0.237447i
\(255\) 0 0
\(256\) 4.46383 + 3.74560i 0.278989 + 0.234100i
\(257\) 8.85943 + 7.43395i 0.552636 + 0.463717i 0.875833 0.482615i \(-0.160313\pi\)
−0.323196 + 0.946332i \(0.604757\pi\)
\(258\) 0 0
\(259\) 4.08115 + 1.48542i 0.253590 + 0.0922993i
\(260\) 5.03743 8.72508i 0.312408 0.541107i
\(261\) 0 0
\(262\) −7.65614 13.2608i −0.472998 0.819257i
\(263\) −1.12488 6.37952i −0.0693632 0.393378i −0.999648 0.0265395i \(-0.991551\pi\)
0.930285 0.366839i \(-0.119560\pi\)
\(264\) 0 0
\(265\) −27.4618 + 9.99526i −1.68696 + 0.614004i
\(266\) 2.22318 12.6083i 0.136312 0.773064i
\(267\) 0 0
\(268\) 1.62733 1.36549i 0.0994048 0.0834106i
\(269\) 13.8387 0.843758 0.421879 0.906652i \(-0.361371\pi\)
0.421879 + 0.906652i \(0.361371\pi\)
\(270\) 0 0
\(271\) 1.94536 0.118172 0.0590860 0.998253i \(-0.481181\pi\)
0.0590860 + 0.998253i \(0.481181\pi\)
\(272\) 2.52800 2.12125i 0.153283 0.128619i
\(273\) 0 0
\(274\) −4.13466 + 23.4488i −0.249784 + 1.41660i
\(275\) −0.654846 + 0.238344i −0.0394887 + 0.0143727i
\(276\) 0 0
\(277\) 2.16586 + 12.2832i 0.130134 + 0.738026i 0.978125 + 0.208016i \(0.0667007\pi\)
−0.847991 + 0.530010i \(0.822188\pi\)
\(278\) −9.92713 17.1943i −0.595390 1.03125i
\(279\) 0 0
\(280\) −1.32553 + 2.29588i −0.0792154 + 0.137205i
\(281\) 9.16752 + 3.33670i 0.546888 + 0.199051i 0.600663 0.799502i \(-0.294903\pi\)
−0.0537751 + 0.998553i \(0.517125\pi\)
\(282\) 0 0
\(283\) 20.3547 + 17.0797i 1.20996 + 1.01528i 0.999288 + 0.0377246i \(0.0120110\pi\)
0.210676 + 0.977556i \(0.432433\pi\)
\(284\) 18.2306 + 15.2973i 1.08179 + 0.907728i
\(285\) 0 0
\(286\) 0.954309 + 0.347340i 0.0564295 + 0.0205386i
\(287\) 2.84173 4.92202i 0.167742 0.290538i
\(288\) 0 0
\(289\) 7.81006 + 13.5274i 0.459415 + 0.795730i
\(290\) 4.34397 + 24.6359i 0.255087 + 1.44667i
\(291\) 0 0
\(292\) 35.5214 12.9287i 2.07873 0.756598i
\(293\) −2.12849 + 12.0712i −0.124347 + 0.705210i 0.857346 + 0.514741i \(0.172112\pi\)
−0.981693 + 0.190469i \(0.938999\pi\)
\(294\) 0 0
\(295\) 3.54389 2.97368i 0.206334 0.173134i
\(296\) −4.53888 −0.263817
\(297\) 0 0
\(298\) −40.3243 −2.33592
\(299\) 2.50838 2.10478i 0.145063 0.121723i
\(300\) 0 0
\(301\) 0.944004 5.35371i 0.0544115 0.308583i
\(302\) −7.98375 + 2.90585i −0.459413 + 0.167213i
\(303\) 0 0
\(304\) −3.03473 17.2108i −0.174053 0.987106i
\(305\) −1.36137 2.35797i −0.0779521 0.135017i
\(306\) 0 0
\(307\) 13.2370 22.9271i 0.755475 1.30852i −0.189663 0.981849i \(-0.560740\pi\)
0.945138 0.326671i \(-0.105927\pi\)
\(308\) −0.718114 0.261372i −0.0409184 0.0148931i
\(309\) 0 0
\(310\) −37.7324 31.6613i −2.14306 1.79824i
\(311\) 13.5280 + 11.3513i 0.767100 + 0.643673i 0.939964 0.341272i \(-0.110858\pi\)
−0.172865 + 0.984946i \(0.555302\pi\)
\(312\) 0 0
\(313\) −9.06541 3.29954i −0.512407 0.186501i 0.0728589 0.997342i \(-0.476788\pi\)
−0.585266 + 0.810841i \(0.699010\pi\)
\(314\) −7.70019 + 13.3371i −0.434547 + 0.752657i
\(315\) 0 0
\(316\) 13.9056 + 24.0852i 0.782250 + 1.35490i
\(317\) 0.644320 + 3.65412i 0.0361886 + 0.205236i 0.997541 0.0700850i \(-0.0223270\pi\)
−0.961352 + 0.275321i \(0.911216\pi\)
\(318\) 0 0
\(319\) −1.31174 + 0.477435i −0.0734434 + 0.0267312i
\(320\) −5.25044 + 29.7767i −0.293509 + 1.66457i
\(321\) 0 0
\(322\) −3.40971 + 2.86108i −0.190016 + 0.159442i
\(323\) −7.30748 −0.406599
\(324\) 0 0
\(325\) −3.32937 −0.184680
\(326\) 20.1854 16.9376i 1.11797 0.938085i
\(327\) 0 0
\(328\) −1.03142 + 5.84948i −0.0569507 + 0.322983i
\(329\) −2.26237 + 0.823435i −0.124728 + 0.0453974i
\(330\) 0 0
\(331\) −0.245329 1.39133i −0.0134845 0.0764745i 0.977323 0.211755i \(-0.0679177\pi\)
−0.990807 + 0.135280i \(0.956807\pi\)
\(332\) 5.80953 + 10.0624i 0.318839 + 0.552246i
\(333\) 0 0
\(334\) −2.46786 + 4.27446i −0.135035 + 0.233888i
\(335\) −2.15961 0.786034i −0.117992 0.0429456i
\(336\) 0 0
\(337\) −9.95097 8.34986i −0.542064 0.454846i 0.330179 0.943918i \(-0.392891\pi\)
−0.872243 + 0.489073i \(0.837335\pi\)
\(338\) −17.3618 14.5683i −0.944356 0.792409i
\(339\) 0 0
\(340\) 7.34533 + 2.67348i 0.398356 + 0.144990i
\(341\) 1.37428 2.38033i 0.0744215 0.128902i
\(342\) 0 0
\(343\) 6.34669 + 10.9928i 0.342689 + 0.593555i
\(344\) 0.986567 + 5.59510i 0.0531921 + 0.301667i
\(345\) 0 0
\(346\) −7.12504 + 2.59330i −0.383045 + 0.139417i
\(347\) 0.833591 4.72753i 0.0447495 0.253787i −0.954224 0.299094i \(-0.903316\pi\)
0.998973 + 0.0453070i \(0.0144266\pi\)
\(348\) 0 0
\(349\) −17.2954 + 14.5126i −0.925803 + 0.776841i −0.975059 0.221946i \(-0.928759\pi\)
0.0492565 + 0.998786i \(0.484315\pi\)
\(350\) 4.52571 0.241909
\(351\) 0 0
\(352\) −2.52845 −0.134767
\(353\) 22.7565 19.0950i 1.21121 1.01632i 0.211972 0.977276i \(-0.432012\pi\)
0.999237 0.0390490i \(-0.0124328\pi\)
\(354\) 0 0
\(355\) 4.47081 25.3552i 0.237286 1.34572i
\(356\) −36.1220 + 13.1473i −1.91446 + 0.696807i
\(357\) 0 0
\(358\) 7.34937 + 41.6804i 0.388427 + 2.20288i
\(359\) 6.70991 + 11.6219i 0.354136 + 0.613381i 0.986970 0.160906i \(-0.0514418\pi\)
−0.632834 + 0.774288i \(0.718108\pi\)
\(360\) 0 0
\(361\) −9.84920 + 17.0593i −0.518379 + 0.897858i
\(362\) −19.3573 7.04550i −1.01740 0.370303i
\(363\) 0 0
\(364\) −2.79686 2.34685i −0.146595 0.123008i
\(365\) −31.3276 26.2870i −1.63976 1.37592i
\(366\) 0 0
\(367\) 7.47054 + 2.71905i 0.389959 + 0.141933i 0.529556 0.848275i \(-0.322359\pi\)
−0.139597 + 0.990208i \(0.544581\pi\)
\(368\) −3.03793 + 5.26184i −0.158363 + 0.274293i
\(369\) 0 0
\(370\) 12.6833 + 21.9681i 0.659372 + 1.14207i
\(371\) 1.83904 + 10.4297i 0.0954782 + 0.541484i
\(372\) 0 0
\(373\) 10.7318 3.90604i 0.555670 0.202247i −0.0488939 0.998804i \(-0.515570\pi\)
0.604564 + 0.796557i \(0.293347\pi\)
\(374\) −0.136823 + 0.775963i −0.00707496 + 0.0401241i
\(375\) 0 0
\(376\) 1.92745 1.61733i 0.0994009 0.0834072i
\(377\) −6.66917 −0.343480
\(378\) 0 0
\(379\) −24.1705 −1.24155 −0.620777 0.783987i \(-0.713183\pi\)
−0.620777 + 0.783987i \(0.713183\pi\)
\(380\) 31.7106 26.6084i 1.62672 1.36498i
\(381\) 0 0
\(382\) 6.52637 37.0129i 0.333918 1.89374i
\(383\) 8.87378 3.22979i 0.453429 0.165035i −0.105202 0.994451i \(-0.533549\pi\)
0.558631 + 0.829416i \(0.311327\pi\)
\(384\) 0 0
\(385\) 0.143564 + 0.814194i 0.00731672 + 0.0414952i
\(386\) −11.2015 19.4016i −0.570143 0.987516i
\(387\) 0 0
\(388\) 6.88162 11.9193i 0.349361 0.605111i
\(389\) −2.39406 0.871367i −0.121384 0.0441801i 0.280614 0.959821i \(-0.409462\pi\)
−0.401998 + 0.915641i \(0.631684\pi\)
\(390\) 0 0
\(391\) 1.94617 + 1.63303i 0.0984218 + 0.0825857i
\(392\) −4.71308 3.95474i −0.238046 0.199745i
\(393\) 0 0
\(394\) 28.1617 + 10.2500i 1.41876 + 0.516388i
\(395\) 15.0438 26.0567i 0.756937 1.31105i
\(396\) 0 0
\(397\) −1.83759 3.18279i −0.0922258 0.159740i 0.816222 0.577739i \(-0.196065\pi\)
−0.908447 + 0.417999i \(0.862731\pi\)
\(398\) 2.77138 + 15.7173i 0.138917 + 0.787836i
\(399\) 0 0
\(400\) 5.80519 2.11292i 0.290260 0.105646i
\(401\) −2.80420 + 15.9034i −0.140035 + 0.794177i 0.831186 + 0.555995i \(0.187663\pi\)
−0.971220 + 0.238182i \(0.923448\pi\)
\(402\) 0 0
\(403\) 10.0593 8.44078i 0.501091 0.420465i
\(404\) 25.1458 1.25105
\(405\) 0 0
\(406\) 9.06558 0.449917
\(407\) −1.08433 + 0.909859i −0.0537481 + 0.0451000i
\(408\) 0 0
\(409\) 1.59443 9.04248i 0.0788396 0.447122i −0.919677 0.392676i \(-0.871550\pi\)
0.998517 0.0544462i \(-0.0173393\pi\)
\(410\) 31.1935 11.3535i 1.54054 0.560710i
\(411\) 0 0
\(412\) −4.24345 24.0658i −0.209060 1.18564i
\(413\) −0.838253 1.45190i −0.0412477 0.0714432i
\(414\) 0 0
\(415\) 6.28506 10.8860i 0.308522 0.534375i
\(416\) −11.3514 4.13157i −0.556548 0.202567i
\(417\) 0 0
\(418\) 3.19646 + 2.68215i 0.156344 + 0.131188i
\(419\) 5.34613 + 4.48594i 0.261176 + 0.219152i 0.763967 0.645256i \(-0.223249\pi\)
−0.502791 + 0.864408i \(0.667694\pi\)
\(420\) 0 0
\(421\) −28.9525 10.5379i −1.41106 0.513584i −0.479619 0.877477i \(-0.659225\pi\)
−0.931441 + 0.363894i \(0.881447\pi\)
\(422\) −5.51765 + 9.55686i −0.268595 + 0.465221i
\(423\) 0 0
\(424\) −5.53405 9.58526i −0.268757 0.465502i
\(425\) −0.448559 2.54390i −0.0217583 0.123397i
\(426\) 0 0
\(427\) −0.927196 + 0.337472i −0.0448702 + 0.0163314i
\(428\) −2.22687 + 12.6292i −0.107640 + 0.610457i
\(429\) 0 0
\(430\) 24.3233 20.4097i 1.17297 0.984242i
\(431\) −27.8971 −1.34376 −0.671879 0.740661i \(-0.734513\pi\)
−0.671879 + 0.740661i \(0.734513\pi\)
\(432\) 0 0
\(433\) 19.1706 0.921278 0.460639 0.887588i \(-0.347620\pi\)
0.460639 + 0.887588i \(0.347620\pi\)
\(434\) −13.6739 + 11.4738i −0.656369 + 0.550759i
\(435\) 0 0
\(436\) −3.14843 + 17.8556i −0.150782 + 0.855130i
\(437\) 12.6426 4.60154i 0.604778 0.220121i
\(438\) 0 0
\(439\) −4.12397 23.3882i −0.196826 1.11626i −0.909794 0.415060i \(-0.863761\pi\)
0.712968 0.701197i \(-0.247351\pi\)
\(440\) −0.432015 0.748272i −0.0205955 0.0356725i
\(441\) 0 0
\(442\) −1.88221 + 3.26009i −0.0895278 + 0.155067i
\(443\) 21.9496 + 7.98900i 1.04286 + 0.379569i 0.805962 0.591967i \(-0.201648\pi\)
0.236894 + 0.971536i \(0.423871\pi\)
\(444\) 0 0
\(445\) 31.8573 + 26.7314i 1.51018 + 1.26719i
\(446\) 28.6892 + 24.0731i 1.35847 + 1.13989i
\(447\) 0 0
\(448\) 10.2965 + 3.74762i 0.486464 + 0.177059i
\(449\) 2.40953 4.17343i 0.113713 0.196956i −0.803552 0.595235i \(-0.797059\pi\)
0.917264 + 0.398279i \(0.130392\pi\)
\(450\) 0 0
\(451\) 0.926176 + 1.60418i 0.0436119 + 0.0755380i
\(452\) −4.46841 25.3416i −0.210176 1.19197i
\(453\) 0 0
\(454\) −31.3701 + 11.4178i −1.47227 + 0.535863i
\(455\) −0.685893 + 3.88989i −0.0321552 + 0.182361i
\(456\) 0 0
\(457\) −3.74872 + 3.14555i −0.175358 + 0.147142i −0.726242 0.687439i \(-0.758735\pi\)
0.550885 + 0.834581i \(0.314290\pi\)
\(458\) −3.73978 −0.174749
\(459\) 0 0
\(460\) −14.3916 −0.671012
\(461\) −21.4419 + 17.9919i −0.998650 + 0.837967i −0.986797 0.161963i \(-0.948218\pi\)
−0.0118535 + 0.999930i \(0.503773\pi\)
\(462\) 0 0
\(463\) −4.77104 + 27.0579i −0.221729 + 1.25749i 0.647111 + 0.762396i \(0.275977\pi\)
−0.868840 + 0.495093i \(0.835134\pi\)
\(464\) 11.6285 4.23245i 0.539842 0.196486i
\(465\) 0 0
\(466\) 5.10832 + 28.9707i 0.236639 + 1.34204i
\(467\) −10.6232 18.4000i −0.491585 0.851450i 0.508368 0.861140i \(-0.330249\pi\)
−0.999953 + 0.00968963i \(0.996916\pi\)
\(468\) 0 0
\(469\) −0.416426 + 0.721272i −0.0192288 + 0.0333052i
\(470\) −13.2138 4.80944i −0.609508 0.221843i
\(471\) 0 0
\(472\) 1.34218 + 1.12623i 0.0617790 + 0.0518387i
\(473\) 1.35728 + 1.13889i 0.0624076 + 0.0523662i
\(474\) 0 0
\(475\) −12.8547 4.67871i −0.589812 0.214674i
\(476\) 1.41636 2.45321i 0.0649188 0.112443i
\(477\) 0 0
\(478\) −20.9892 36.3543i −0.960022 1.66281i
\(479\) 7.23745 + 41.0456i 0.330688 + 1.87542i 0.466248 + 0.884654i \(0.345606\pi\)
−0.135560 + 0.990769i \(0.543283\pi\)
\(480\) 0 0
\(481\) −6.35480 + 2.31296i −0.289754 + 0.105462i
\(482\) 7.12113 40.3859i 0.324358 1.83953i
\(483\) 0 0
\(484\) −20.7077 + 17.3758i −0.941258 + 0.789809i
\(485\) −14.8898 −0.676112
\(486\) 0 0
\(487\) 4.02801 0.182527 0.0912634 0.995827i \(-0.470909\pi\)
0.0912634 + 0.995827i \(0.470909\pi\)
\(488\) 0.789937 0.662836i 0.0357588 0.0300052i
\(489\) 0 0
\(490\) −5.97081 + 33.8622i −0.269734 + 1.52974i
\(491\) −36.2922 + 13.2093i −1.63784 + 0.596126i −0.986660 0.162793i \(-0.947950\pi\)
−0.651184 + 0.758920i \(0.725727\pi\)
\(492\) 0 0
\(493\) −0.898521 5.09577i −0.0404674 0.229502i
\(494\) 9.96769 + 17.2645i 0.448468 + 0.776769i
\(495\) 0 0
\(496\) −12.1830 + 21.1015i −0.547032 + 0.947487i
\(497\) −8.76759 3.19114i −0.393280 0.143142i
\(498\) 0 0
\(499\) −3.11922 2.61734i −0.139636 0.117168i 0.570295 0.821440i \(-0.306829\pi\)
−0.709930 + 0.704272i \(0.751274\pi\)
\(500\) −14.2781 11.9807i −0.638534 0.535794i
\(501\) 0 0
\(502\) −10.8911 3.96403i −0.486093 0.176923i
\(503\) −1.71297 + 2.96695i −0.0763775 + 0.132290i −0.901684 0.432395i \(-0.857669\pi\)
0.825307 + 0.564684i \(0.191002\pi\)
\(504\) 0 0
\(505\) −13.6020 23.5594i −0.605282 1.04838i
\(506\) −0.251909 1.42865i −0.0111987 0.0635111i
\(507\) 0 0
\(508\) −12.1827 + 4.43412i −0.540518 + 0.196732i
\(509\) 2.12952 12.0771i 0.0943893 0.535308i −0.900543 0.434766i \(-0.856831\pi\)
0.994933 0.100542i \(-0.0320578\pi\)
\(510\) 0 0
\(511\) −11.3529 + 9.52619i −0.502222 + 0.421414i
\(512\) 28.1241 1.24292
\(513\) 0 0
\(514\) 24.4791 1.07973
\(515\) −20.2522 + 16.9936i −0.892418 + 0.748827i
\(516\) 0 0
\(517\) 0.136257 0.772750i 0.00599257 0.0339855i
\(518\) 8.63825 3.14407i 0.379543 0.138142i
\(519\) 0 0
\(520\) −0.716818 4.06528i −0.0314345 0.178274i
\(521\) 7.04117 + 12.1957i 0.308479 + 0.534302i 0.978030 0.208465i \(-0.0668466\pi\)
−0.669551 + 0.742766i \(0.733513\pi\)
\(522\) 0 0
\(523\) −4.88956 + 8.46897i −0.213806 + 0.370322i −0.952902 0.303277i \(-0.901919\pi\)
0.739097 + 0.673599i \(0.235253\pi\)
\(524\) −16.8597 6.13643i −0.736520 0.268071i
\(525\) 0 0
\(526\) −10.5035 8.81348i −0.457974 0.384286i
\(527\) 7.80469 + 6.54892i 0.339978 + 0.285275i
\(528\) 0 0
\(529\) 17.2176 + 6.26668i 0.748590 + 0.272464i
\(530\) −30.9283 + 53.5694i −1.34344 + 2.32691i
\(531\) 0 0
\(532\) −7.50065 12.9915i −0.325195 0.563254i
\(533\) 1.53675 + 8.71534i 0.0665640 + 0.377503i
\(534\) 0 0
\(535\) 13.0371 4.74511i 0.563642 0.205149i
\(536\) 0.151144 0.857180i 0.00652843 0.0370245i
\(537\) 0 0
\(538\) 22.4384 18.8280i 0.967387 0.811734i
\(539\) −1.91871 −0.0826445
\(540\) 0 0
\(541\) 40.9454 1.76038 0.880189 0.474623i \(-0.157416\pi\)
0.880189 + 0.474623i \(0.157416\pi\)
\(542\) 3.15426 2.64674i 0.135487 0.113687i
\(543\) 0 0
\(544\) 1.62750 9.22999i 0.0697783 0.395732i
\(545\) 18.4323 6.70879i 0.789551 0.287373i
\(546\) 0 0
\(547\) 0.192798 + 1.09341i 0.00824343 + 0.0467508i 0.988652 0.150224i \(-0.0479994\pi\)
−0.980409 + 0.196975i \(0.936888\pi\)
\(548\) 13.9497 + 24.1615i 0.595900 + 1.03213i
\(549\) 0 0
\(550\) −0.737508 + 1.27740i −0.0314474 + 0.0544686i
\(551\) −25.7495 9.37206i −1.09697 0.399263i
\(552\) 0 0
\(553\) −8.35257 7.00864i −0.355188 0.298038i
\(554\) 20.2236 + 16.9696i 0.859216 + 0.720968i
\(555\) 0 0
\(556\) −21.8607 7.95664i −0.927100 0.337437i
\(557\) 17.5201 30.3458i 0.742352 1.28579i −0.209070 0.977901i \(-0.567044\pi\)
0.951422 0.307890i \(-0.0996230\pi\)
\(558\) 0 0
\(559\) 4.23247 + 7.33084i 0.179014 + 0.310062i
\(560\) −1.27269 7.21781i −0.0537812 0.305008i
\(561\) 0 0
\(562\) 19.4042 7.06254i 0.818516 0.297915i
\(563\) 6.73255 38.1822i 0.283743 1.60919i −0.425998 0.904724i \(-0.640077\pi\)
0.709741 0.704463i \(-0.248812\pi\)
\(564\) 0 0
\(565\) −21.3258 + 17.8945i −0.897183 + 0.752826i
\(566\) 56.2413 2.36400
\(567\) 0 0
\(568\) 9.75095 0.409141
\(569\) 26.0213 21.8344i 1.09087 0.915347i 0.0940904 0.995564i \(-0.470006\pi\)
0.996777 + 0.0802169i \(0.0255613\pi\)
\(570\) 0 0
\(571\) 1.75191 9.93559i 0.0733153 0.415792i −0.925956 0.377631i \(-0.876739\pi\)
0.999272 0.0381610i \(-0.0121500\pi\)
\(572\) 1.11818 0.406986i 0.0467536 0.0170169i
\(573\) 0 0
\(574\) −2.08894 11.8470i −0.0871908 0.494484i
\(575\) 2.37795 + 4.11873i 0.0991674 + 0.171763i
\(576\) 0 0
\(577\) 6.06615 10.5069i 0.252537 0.437407i −0.711687 0.702497i \(-0.752068\pi\)
0.964224 + 0.265090i \(0.0854017\pi\)
\(578\) 31.0680 + 11.3078i 1.29226 + 0.470344i
\(579\) 0 0
\(580\) 22.4541 + 18.8412i 0.932355 + 0.782339i
\(581\) −3.48957 2.92810i −0.144772 0.121478i
\(582\) 0 0
\(583\) −3.24352 1.18055i −0.134333 0.0488932i
\(584\) 7.74416 13.4133i 0.320456 0.555046i
\(585\) 0 0
\(586\) 12.9722 + 22.4685i 0.535877 + 0.928167i
\(587\) −5.51319 31.2669i −0.227554 1.29052i −0.857743 0.514079i \(-0.828134\pi\)
0.630189 0.776442i \(-0.282977\pi\)
\(588\) 0 0
\(589\) 50.7006 18.4535i 2.08908 0.760363i
\(590\) 1.70036 9.64321i 0.0700027 0.397005i
\(591\) 0 0
\(592\) 9.61254 8.06588i 0.395073 0.331506i
\(593\) −13.4906 −0.553993 −0.276996 0.960871i \(-0.589339\pi\)
−0.276996 + 0.960871i \(0.589339\pi\)
\(594\) 0 0
\(595\) −3.06459 −0.125636
\(596\) −36.1947 + 30.3710i −1.48259 + 1.24404i
\(597\) 0 0
\(598\) 1.20352 6.82550i 0.0492156 0.279115i
\(599\) −39.8715 + 14.5120i −1.62911 + 0.592946i −0.985086 0.172063i \(-0.944957\pi\)
−0.644020 + 0.765009i \(0.722735\pi\)
\(600\) 0 0
\(601\) −3.43906 19.5039i −0.140282 0.795579i −0.971035 0.238938i \(-0.923201\pi\)
0.830753 0.556641i \(-0.187910\pi\)
\(602\) −5.75330 9.96501i −0.234487 0.406144i
\(603\) 0 0
\(604\) −4.97755 + 8.62136i −0.202533 + 0.350798i
\(605\) 27.4810 + 10.0022i 1.11726 + 0.406649i
\(606\) 0 0
\(607\) −27.5769 23.1397i −1.11931 0.939213i −0.120741 0.992684i \(-0.538527\pi\)
−0.998569 + 0.0534715i \(0.982971\pi\)
\(608\) −38.0215 31.9038i −1.54197 1.29387i
\(609\) 0 0
\(610\) −5.41548 1.97107i −0.219266 0.0798064i
\(611\) 1.87442 3.24659i 0.0758310 0.131343i
\(612\) 0 0
\(613\) −13.2314 22.9175i −0.534411 0.925627i −0.999192 0.0402013i \(-0.987200\pi\)
0.464780 0.885426i \(-0.346133\pi\)
\(614\) −9.73045 55.1841i −0.392689 2.22705i
\(615\) 0 0
\(616\) −0.294234 + 0.107093i −0.0118550 + 0.00431488i
\(617\) −8.52903 + 48.3705i −0.343366 + 1.94732i −0.0239406 + 0.999713i \(0.507621\pi\)
−0.319425 + 0.947611i \(0.603490\pi\)
\(618\) 0 0
\(619\) −18.5430 + 15.5595i −0.745307 + 0.625387i −0.934257 0.356600i \(-0.883936\pi\)
0.188950 + 0.981987i \(0.439492\pi\)
\(620\) −57.7145 −2.31787
\(621\) 0 0
\(622\) 37.3785 1.49874
\(623\) 11.5448 9.68725i 0.462533 0.388111i
\(624\) 0 0
\(625\) −5.41077 + 30.6860i −0.216431 + 1.22744i
\(626\) −19.1881 + 6.98388i −0.766909 + 0.279132i
\(627\) 0 0
\(628\) 3.13347 + 17.7708i 0.125039 + 0.709132i
\(629\) −2.62345 4.54395i −0.104604 0.181179i
\(630\) 0 0
\(631\) −8.84842 + 15.3259i −0.352250 + 0.610115i −0.986643 0.162895i \(-0.947917\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(632\) 10.7079 + 3.89736i 0.425938 + 0.155029i
\(633\) 0 0
\(634\) 6.01629 + 5.04827i 0.238937 + 0.200492i
\(635\) 10.7443 + 9.01555i 0.426375 + 0.357771i
\(636\) 0 0
\(637\) −8.61398 3.13523i −0.341298 0.124222i
\(638\) −1.47732 + 2.55880i −0.0584878 + 0.101304i
\(639\) 0 0
\(640\) 10.5917 + 18.3454i 0.418676 + 0.725167i
\(641\) −6.60738 37.4723i −0.260976 1.48007i −0.780254 0.625463i \(-0.784910\pi\)
0.519278 0.854605i \(-0.326201\pi\)
\(642\) 0 0
\(643\) −44.1115 + 16.0553i −1.73959 + 0.633158i −0.999237 0.0390615i \(-0.987563\pi\)
−0.740352 + 0.672220i \(0.765341\pi\)
\(644\) −0.905644 + 5.13616i −0.0356874 + 0.202393i
\(645\) 0 0
\(646\) −11.8485 + 9.94211i −0.466175 + 0.391167i
\(647\) 28.2333 1.10997 0.554983 0.831862i \(-0.312725\pi\)
0.554983 + 0.831862i \(0.312725\pi\)
\(648\) 0 0
\(649\) 0.546406 0.0214483
\(650\) −5.39834 + 4.52974i −0.211740 + 0.177671i
\(651\) 0 0
\(652\) 5.36140 30.4060i 0.209969 1.19079i
\(653\) 33.1779 12.0758i 1.29835 0.472562i 0.401893 0.915687i \(-0.368353\pi\)
0.896460 + 0.443125i \(0.146130\pi\)
\(654\) 0 0
\(655\) 3.37057 + 19.1155i 0.131699 + 0.746902i
\(656\) −8.21052 14.2210i −0.320567 0.555239i
\(657\) 0 0
\(658\) −2.54795 + 4.41318i −0.0993295 + 0.172044i
\(659\) 39.1793 + 14.2601i 1.52621 + 0.555494i 0.962689 0.270609i \(-0.0872250\pi\)
0.563519 + 0.826103i \(0.309447\pi\)
\(660\) 0 0
\(661\) 0.975874 + 0.818856i 0.0379571 + 0.0318498i 0.661569 0.749884i \(-0.269891\pi\)
−0.623612 + 0.781734i \(0.714335\pi\)
\(662\) −2.29075 1.92216i −0.0890324 0.0747070i
\(663\) 0 0
\(664\) 4.47359 + 1.62825i 0.173609 + 0.0631885i
\(665\) −8.11461 + 14.0549i −0.314671 + 0.545027i
\(666\) 0 0
\(667\) 4.76334 + 8.25035i 0.184437 + 0.319455i
\(668\) 1.00426 + 5.69543i 0.0388559 + 0.220363i
\(669\) 0 0
\(670\) −4.57108 + 1.66374i −0.176596 + 0.0642758i
\(671\) 0.0558427 0.316700i 0.00215578 0.0122261i
\(672\) 0 0
\(673\) 27.2963 22.9043i 1.05219 0.882896i 0.0588715 0.998266i \(-0.481250\pi\)
0.993323 + 0.115370i \(0.0368053\pi\)
\(674\) −27.4951 −1.05907
\(675\) 0 0
\(676\) −26.5561 −1.02139
\(677\) −13.7902 + 11.5714i −0.530002 + 0.444725i −0.868102 0.496386i \(-0.834660\pi\)
0.338100 + 0.941110i \(0.390216\pi\)
\(678\) 0 0
\(679\) −0.936996 + 5.31397i −0.0359586 + 0.203931i
\(680\) 3.00961 1.09541i 0.115413 0.0420071i
\(681\) 0 0
\(682\) −1.01023 5.72929i −0.0386836 0.219386i
\(683\) 19.8807 + 34.4344i 0.760715 + 1.31760i 0.942483 + 0.334255i \(0.108485\pi\)
−0.181768 + 0.983341i \(0.558182\pi\)
\(684\) 0 0
\(685\) 15.0915 26.1393i 0.576617 0.998730i
\(686\) 25.2468 + 9.18909i 0.963928 + 0.350841i
\(687\) 0 0
\(688\) −12.0322 10.0962i −0.458724 0.384915i
\(689\) −12.6327 10.6001i −0.481266 0.403830i
\(690\) 0 0
\(691\) 15.8251 + 5.75986i 0.602015 + 0.219115i 0.625006 0.780620i \(-0.285097\pi\)
−0.0229909 + 0.999736i \(0.507319\pi\)
\(692\) −4.44218 + 7.69408i −0.168866 + 0.292485i
\(693\) 0 0
\(694\) −5.08038 8.79948i −0.192849 0.334024i
\(695\) 4.37036 + 24.7855i 0.165777 + 0.940169i
\(696\) 0 0
\(697\) −6.45216 + 2.34839i −0.244393 + 0.0889518i
\(698\) −8.29833 + 47.0622i −0.314097 + 1.78133i
\(699\) 0 0
\(700\) 4.06223 3.40862i 0.153538 0.128834i
\(701\) 8.96921 0.338762 0.169381 0.985551i \(-0.445823\pi\)
0.169381 + 0.985551i \(0.445823\pi\)
\(702\) 0 0
\(703\) −27.7861 −1.04797
\(704\) −2.73570 + 2.29552i −0.103106 + 0.0865158i
\(705\) 0 0
\(706\) 10.9186 61.9223i 0.410926 2.33048i
\(707\) −9.26398 + 3.37181i −0.348408 + 0.126810i
\(708\) 0 0
\(709\) 3.15026 + 17.8660i 0.118311 + 0.670973i 0.985058 + 0.172225i \(0.0550955\pi\)
−0.866747 + 0.498748i \(0.833793\pi\)
\(710\) −27.2477 47.1944i −1.02259 1.77117i
\(711\) 0 0
\(712\) −7.87509 + 13.6401i −0.295131 + 0.511183i
\(713\) −17.6267 6.41560i −0.660125 0.240266i
\(714\) 0 0
\(715\) −0.986166 0.827492i −0.0368805 0.0309464i
\(716\) 37.9890 + 31.8766i 1.41972 + 1.19128i
\(717\) 0 0
\(718\) 26.6917 + 9.71498i 0.996125 + 0.362560i
\(719\) 15.7860 27.3421i 0.588718 1.01969i −0.405683 0.914014i \(-0.632966\pi\)
0.994401 0.105675i \(-0.0337004\pi\)
\(720\) 0 0
\(721\) 4.79034 + 8.29711i 0.178402 + 0.309001i
\(722\) 7.24010 + 41.0606i 0.269449 + 1.52812i
\(723\) 0 0
\(724\) −22.6814 + 8.25536i −0.842948 + 0.306808i
\(725\) 1.68204 9.53930i 0.0624693 0.354281i
\(726\) 0 0
\(727\) 29.4232 24.6890i 1.09125 0.915664i 0.0944407 0.995530i \(-0.469894\pi\)
0.996806 + 0.0798662i \(0.0254493\pi\)
\(728\) −1.49595 −0.0554436
\(729\) 0 0
\(730\) −86.5599 −3.20373
\(731\) −5.03111 + 4.22160i −0.186082 + 0.156142i
\(732\) 0 0
\(733\) −5.26680 + 29.8695i −0.194534 + 1.10326i 0.718547 + 0.695478i \(0.244807\pi\)
−0.913081 + 0.407778i \(0.866304\pi\)
\(734\) 15.8123 5.75521i 0.583643 0.212429i
\(735\) 0 0
\(736\) 2.99643 + 16.9936i 0.110450 + 0.626391i
\(737\) −0.135721 0.235076i −0.00499936 0.00865915i
\(738\) 0 0
\(739\) −5.00127 + 8.66245i −0.183975 + 0.318653i −0.943230 0.332139i \(-0.892230\pi\)
0.759256 + 0.650792i \(0.225563\pi\)
\(740\) 27.9300 + 10.1657i 1.02673 + 0.373699i
\(741\) 0 0
\(742\) 17.1719 + 14.4089i 0.630400 + 0.528969i
\(743\) −27.7873 23.3163i −1.01942 0.855394i −0.0298642 0.999554i \(-0.509507\pi\)
−0.989554 + 0.144160i \(0.953952\pi\)
\(744\) 0 0
\(745\) 48.0337 + 17.4828i 1.75982 + 0.640521i
\(746\) 12.0865 20.9344i 0.442517 0.766461i
\(747\) 0 0
\(748\) 0.461619 + 0.799548i 0.0168785 + 0.0292344i
\(749\) −0.873058 4.95136i −0.0319008 0.180919i
\(750\) 0 0
\(751\) 13.6766 4.97788i 0.499067 0.181646i −0.0802073 0.996778i \(-0.525558\pi\)
0.579274 + 0.815133i \(0.303336\pi\)
\(752\) −1.20791 + 6.85041i −0.0440480 + 0.249809i
\(753\) 0 0
\(754\) −10.8136 + 9.07366i −0.393807 + 0.330443i
\(755\) 10.7700 0.391959
\(756\) 0 0
\(757\) −45.5754 −1.65646 −0.828232 0.560385i \(-0.810653\pi\)
−0.828232 + 0.560385i \(0.810653\pi\)
\(758\) −39.1907 + 32.8849i −1.42347 + 1.19443i
\(759\) 0 0
\(760\) 2.94524 16.7033i 0.106835 0.605892i
\(761\) 20.9040 7.60843i 0.757769 0.275805i 0.0658978 0.997826i \(-0.479009\pi\)
0.691871 + 0.722021i \(0.256787\pi\)
\(762\) 0 0
\(763\) −1.23436 7.00040i −0.0446868 0.253431i
\(764\) −22.0189 38.1379i −0.796616 1.37978i
\(765\) 0 0
\(766\) 9.99393 17.3100i 0.361096 0.625436i
\(767\) 2.45307 + 0.892846i 0.0885754 + 0.0322388i
\(768\) 0 0
\(769\) 10.4679 + 8.78365i 0.377484 + 0.316747i 0.811714 0.584056i \(-0.198535\pi\)
−0.434230 + 0.900802i \(0.642979\pi\)
\(770\) 1.34052 + 1.12483i 0.0483091 + 0.0405361i
\(771\) 0 0
\(772\) −24.6670 8.97807i −0.887786 0.323128i
\(773\) −10.3270 + 17.8869i −0.371436 + 0.643345i −0.989787 0.142557i \(-0.954468\pi\)
0.618351 + 0.785902i \(0.287801\pi\)
\(774\) 0 0
\(775\) 9.53628 + 16.5173i 0.342553 + 0.593319i
\(776\) −0.979243 5.55356i −0.0351528 0.199361i
\(777\) 0 0
\(778\) −5.06732 + 1.84436i −0.181672 + 0.0661233i
\(779\) −6.31415 + 35.8093i −0.226228 + 1.28300i
\(780\) 0 0
\(781\) 2.32948 1.95466i 0.0833553 0.0699434i
\(782\) 5.37736 0.192294
\(783\) 0 0
\(784\) 17.0093 0.607474
\(785\) 14.9547 12.5485i 0.533757 0.447875i
\(786\) 0 0
\(787\) −4.28970 + 24.3281i −0.152911 + 0.867202i 0.807759 + 0.589512i \(0.200680\pi\)
−0.960671 + 0.277690i \(0.910431\pi\)
\(788\) 32.9976 12.0102i 1.17549 0.427844i
\(789\) 0 0
\(790\) −11.0586 62.7167i −0.393449 2.23136i
\(791\) 5.04429 + 8.73696i 0.179354 + 0.310651i
\(792\) 0 0
\(793\) 0.768202 1.33057i 0.0272797 0.0472498i
\(794\) −7.30983 2.66056i −0.259416 0.0944197i
\(795\) 0 0
\(796\) 14.3253 + 12.0204i 0.507747 + 0.426051i
\(797\) 23.4148 + 19.6473i 0.829393 + 0.695943i 0.955152 0.296117i \(-0.0956920\pi\)
−0.125758 + 0.992061i \(0.540136\pi\)
\(798\) 0 0
\(799\) 2.73319 + 0.994799i 0.0966933 + 0.0351935i
\(800\) 8.77257 15.1945i 0.310157 0.537208i
\(801\) 0 0
\(802\) 17.0904 + 29.6014i 0.603482 + 1.04526i
\(803\) −0.838750 4.75679i −0.0295988 0.167863i
\(804\) 0 0
\(805\) 5.30203 1.92978i 0.186872 0.0680158i
\(806\) 4.82646 27.3722i 0.170005 0.964146i
\(807\) 0 0
\(808\) 7.89257 6.62265i 0.277660 0.232984i
\(809\) −46.8599 −1.64751 −0.823753 0.566949i \(-0.808124\pi\)
−0.823753 + 0.566949i \(0.808124\pi\)
\(810\) 0 0
\(811\) 10.9984 0.386206 0.193103 0.981178i \(-0.438145\pi\)
0.193103 + 0.981178i \(0.438145\pi\)
\(812\) 8.13717 6.82790i 0.285559 0.239612i
\(813\) 0 0
\(814\) −0.520260 + 2.95054i −0.0182351 + 0.103416i
\(815\) −31.3879 + 11.4243i −1.09947 + 0.400175i
\(816\) 0 0
\(817\) 6.03956 + 34.2521i 0.211298 + 1.19833i
\(818\) −9.71738 16.8310i −0.339760 0.588482i
\(819\) 0 0
\(820\) 19.4479 33.6847i 0.679150 1.17632i
\(821\) −33.8133 12.3070i −1.18009 0.429518i −0.323857 0.946106i \(-0.604980\pi\)
−0.856234 + 0.516588i \(0.827202\pi\)
\(822\) 0 0
\(823\) −37.5259 31.4880i −1.30807 1.09760i −0.988689 0.149977i \(-0.952080\pi\)
−0.319383 0.947626i \(-0.603476\pi\)
\(824\) −7.67013 6.43600i −0.267202 0.224209i
\(825\) 0 0
\(826\) −3.33453 1.21367i −0.116023 0.0422290i
\(827\) −7.80533 + 13.5192i −0.271418 + 0.470109i −0.969225 0.246176i \(-0.920826\pi\)
0.697807 + 0.716286i \(0.254159\pi\)
\(828\) 0 0
\(829\) −5.73541 9.93401i −0.199199 0.345023i 0.749070 0.662491i \(-0.230501\pi\)
−0.948269 + 0.317468i \(0.897167\pi\)
\(830\) −4.62012 26.2020i −0.160367 0.909485i
\(831\) 0 0
\(832\) −16.0328 + 5.83547i −0.555838 + 0.202308i
\(833\) 1.23502 7.00416i 0.0427910 0.242680i
\(834\) 0 0
\(835\) 4.79290 4.02172i 0.165865 0.139177i
\(836\) 4.88922 0.169097
\(837\) 0 0
\(838\) 14.7716 0.510278
\(839\) 0.517329 0.434090i 0.0178602 0.0149865i −0.633814 0.773486i \(-0.718511\pi\)
0.651674 + 0.758499i \(0.274067\pi\)
\(840\) 0 0
\(841\) −1.66646 + 9.45097i −0.0574642 + 0.325895i
\(842\) −61.2815 + 22.3047i −2.11190 + 0.768669i
\(843\) 0 0
\(844\) 2.24532 + 12.7339i 0.0772872 + 0.438318i
\(845\) 14.3649 + 24.8808i 0.494168 + 0.855925i
\(846\) 0 0
\(847\) 5.29901 9.17815i 0.182076 0.315365i
\(848\) 28.7537 + 10.4655i 0.987408 + 0.359387i
\(849\) 0 0
\(850\) −4.18838 3.51447i −0.143660 0.120545i
\(851\) 7.40014 + 6.20946i 0.253674 + 0.212857i
\(852\) 0 0
\(853\) −36.9823 13.4605i −1.26625 0.460877i −0.380388 0.924827i \(-0.624210\pi\)
−0.885862 + 0.463949i \(0.846432\pi\)
\(854\) −1.04424 + 1.80867i −0.0357331 + 0.0618915i
\(855\) 0 0
\(856\) 2.62721 + 4.55047i 0.0897963 + 0.155532i
\(857\) −5.67172 32.1659i −0.193742 1.09877i −0.914199 0.405266i \(-0.867179\pi\)
0.720457 0.693500i \(-0.243932\pi\)
\(858\) 0 0
\(859\) 31.1946 11.3539i 1.06435 0.387391i 0.250287 0.968172i \(-0.419475\pi\)
0.814060 + 0.580781i \(0.197253\pi\)
\(860\) 6.46046 36.6391i 0.220300 1.24938i
\(861\) 0 0
\(862\) −45.2332 + 37.9551i −1.54065 + 1.29276i
\(863\) −22.6796 −0.772024 −0.386012 0.922494i \(-0.626148\pi\)
−0.386012 + 0.922494i \(0.626148\pi\)
\(864\) 0 0
\(865\) 9.61158 0.326804
\(866\) 31.0837 26.0823i 1.05627 0.886312i
\(867\) 0 0
\(868\) −3.63190 + 20.5975i −0.123275 + 0.699125i
\(869\) 3.33935 1.21543i 0.113280 0.0412305i
\(870\) 0 0
\(871\) −0.225195 1.27714i −0.00763043 0.0432743i
\(872\) 3.71444 + 6.43360i 0.125787 + 0.217869i
\(873\) 0 0
\(874\) 14.2385 24.6618i 0.481625 0.834199i
\(875\) 6.86670 + 2.49927i 0.232137 + 0.0844909i
\(876\) 0 0
\(877\) 7.08113 + 5.94178i 0.239113 + 0.200640i 0.754467 0.656338i \(-0.227895\pi\)
−0.515354 + 0.856977i \(0.672340\pi\)
\(878\) −38.5072 32.3114i −1.29956 1.09046i
\(879\) 0 0
\(880\) 2.24466 + 0.816989i 0.0756674 + 0.0275407i
\(881\) 3.89378 6.74422i 0.131185 0.227219i −0.792949 0.609288i \(-0.791455\pi\)
0.924134 + 0.382070i \(0.124789\pi\)
\(882\) 0 0
\(883\) 16.2309 + 28.1127i 0.546213 + 0.946068i 0.998530 + 0.0542106i \(0.0172642\pi\)
−0.452317 + 0.891857i \(0.649402\pi\)
\(884\) 0.765938 + 4.34385i 0.0257613 + 0.146099i
\(885\) 0 0
\(886\) 46.4590 16.9097i 1.56082 0.568092i
\(887\) 5.87759 33.3334i 0.197350 1.11923i −0.711682 0.702502i \(-0.752066\pi\)
0.909032 0.416726i \(-0.136823\pi\)
\(888\) 0 0
\(889\) 3.89365 3.26716i 0.130589 0.109577i
\(890\) 88.0234 2.95055
\(891\) 0 0
\(892\) 43.8822 1.46929
\(893\) 11.7995 9.90095i 0.394855 0.331323i
\(894\) 0 0
\(895\) 9.31630 52.8354i 0.311410 1.76609i
\(896\) 7.21376 2.62560i 0.240995 0.0877150i
\(897\) 0 0
\(898\) −1.77124 10.0452i −0.0591069 0.335212i
\(899\) 19.1024 + 33.0863i 0.637101 + 1.10349i
\(900\) 0 0
\(901\) 6.39731 11.0805i 0.213125 0.369144i
\(902\) 3.68428 + 1.34097i 0.122673 + 0.0446494i
\(903\) 0 0
\(904\) −8.07674 6.77719i −0.268629 0.225406i
\(905\) 20.0035 + 16.7850i 0.664940 + 0.557951i
\(906\) 0 0
\(907\) 10.3929 + 3.78269i 0.345089 + 0.125602i 0.508750 0.860915i \(-0.330108\pi\)
−0.163660 + 0.986517i \(0.552330\pi\)
\(908\) −19.5580 + 33.8754i −0.649054 + 1.12420i
\(909\) 0 0
\(910\) 4.18022 + 7.24036i 0.138573 + 0.240016i
\(911\) −2.17845 12.3546i −0.0721751 0.409325i −0.999394 0.0348058i \(-0.988919\pi\)
0.927219 0.374520i \(-0.122192\pi\)
\(912\) 0 0
\(913\) 1.39513 0.507785i 0.0461720 0.0168052i
\(914\) −1.79863 + 10.2005i −0.0594934 + 0.337404i
\(915\) 0 0
\(916\) −3.35679 + 2.81668i −0.110912 + 0.0930659i
\(917\) 7.03415 0.232288
\(918\) 0 0
\(919\) −5.92909 −0.195583 −0.0977913 0.995207i \(-0.531178\pi\)
−0.0977913 + 0.995207i \(0.531178\pi\)
\(920\) −4.51713 + 3.79032i −0.148925 + 0.124963i
\(921\) 0 0
\(922\) −10.2878 + 58.3452i −0.338812 + 1.92150i
\(923\) 13.6521 4.96897i 0.449365 0.163555i
\(924\) 0 0
\(925\) −1.70561 9.67300i −0.0560801 0.318046i
\(926\) 29.0775 + 50.3636i 0.955545 + 1.65505i
\(927\) 0 0
\(928\) 17.5726 30.4366i 0.576848 0.999131i
\(929\) −9.42772 3.43141i −0.309314 0.112581i 0.182699 0.983169i \(-0.441517\pi\)
−0.492013 + 0.870588i \(0.663739\pi\)
\(930\) 0 0
\(931\) −28.8525 24.2101i −0.945603 0.793455i
\(932\) 26.4050 + 22.1564i 0.864925 + 0.725758i
\(933\) 0 0
\(934\) −42.2587 15.3809i −1.38275 0.503279i
\(935\) 0.499405 0.864995i 0.0163323 0.0282883i
\(936\) 0 0
\(937\) 11.7671 + 20.3811i 0.384413 + 0.665823i 0.991688 0.128669i \(-0.0410705\pi\)
−0.607274 + 0.794492i \(0.707737\pi\)
\(938\) 0.306113 + 1.73605i 0.00999494 + 0.0566841i
\(939\) 0 0
\(940\) −15.4829 + 5.63532i −0.504997 + 0.183804i
\(941\) 5.08781 28.8544i 0.165858 0.940627i −0.782317 0.622880i \(-0.785962\pi\)
0.948175 0.317747i \(-0.102926\pi\)
\(942\) 0 0
\(943\) 9.68405 8.12588i 0.315356 0.264615i
\(944\) −4.84388 −0.157655
\(945\) 0 0
\(946\) 3.75023 0.121930
\(947\) −41.1074 + 34.4932i −1.33581 + 1.12088i −0.353130 + 0.935574i \(0.614883\pi\)
−0.982681 + 0.185304i \(0.940673\pi\)
\(948\) 0 0
\(949\) 4.00721 22.7260i 0.130079 0.737717i
\(950\) −27.2084 + 9.90307i −0.882759 + 0.321298i
\(951\) 0 0
\(952\) −0.201546 1.14302i −0.00653214 0.0370456i
\(953\) −2.44828 4.24055i −0.0793076 0.137365i 0.823644 0.567108i \(-0.191938\pi\)
−0.902951 + 0.429743i \(0.858604\pi\)
\(954\) 0 0
\(955\) −23.8212 + 41.2596i −0.770837 + 1.33513i
\(956\) −46.2205 16.8229i −1.49488 0.544092i
\(957\) 0 0
\(958\) 67.5792 + 56.7057i 2.18338 + 1.83208i
\(959\) −8.37906 7.03086i −0.270574 0.227038i
\(960\) 0 0
\(961\) −41.5578 15.1258i −1.34057 0.487929i
\(962\) −7.15698 + 12.3962i −0.230750 + 0.399671i
\(963\) 0 0
\(964\) −24.0255 41.6134i −0.773810 1.34028i
\(965\) 4.93140 + 27.9674i 0.158747 + 0.900302i
\(966\) 0 0
\(967\) −15.9683 + 5.81200i −0.513507 + 0.186901i −0.585759 0.810485i \(-0.699204\pi\)
0.0722523 + 0.997386i \(0.476981\pi\)
\(968\) −1.92330 + 10.9076i −0.0618172 + 0.350583i
\(969\) 0 0
\(970\) −24.1427 + 20.2582i −0.775177 + 0.650451i
\(971\) 2.68374 0.0861253 0.0430627 0.999072i \(-0.486288\pi\)
0.0430627 + 0.999072i \(0.486288\pi\)
\(972\) 0 0
\(973\) 9.12064 0.292394
\(974\) 6.53113 5.48027i 0.209271 0.175599i
\(975\) 0 0
\(976\) −0.495044 + 2.80753i −0.0158460 + 0.0898670i
\(977\) 10.3301 3.75984i 0.330488 0.120288i −0.171446 0.985193i \(-0.554844\pi\)
0.501935 + 0.864906i \(0.332622\pi\)
\(978\) 0 0
\(979\) 0.852930 + 4.83721i 0.0272598 + 0.154598i
\(980\) 20.1445 + 34.8914i 0.643494 + 1.11456i
\(981\) 0 0
\(982\) −40.8734 + 70.7948i −1.30432 + 2.25915i
\(983\) −44.8944 16.3402i −1.43191 0.521172i −0.494431 0.869217i \(-0.664624\pi\)
−0.937478 + 0.348044i \(0.886846\pi\)
\(984\) 0 0
\(985\) −29.1018 24.4193i −0.927260 0.778064i
\(986\) −8.38988 7.03994i −0.267188 0.224197i
\(987\) 0 0
\(988\) 21.9500 + 7.98915i 0.698323 + 0.254169i
\(989\) 6.04594 10.4719i 0.192250 0.332986i
\(990\) 0 0
\(991\) −27.7503 48.0649i −0.881517 1.52683i −0.849654 0.527340i \(-0.823189\pi\)
−0.0318627 0.999492i \(-0.510144\pi\)
\(992\) 12.0165 + 68.1492i 0.381526 + 2.16374i
\(993\) 0 0
\(994\) −18.5577 + 6.75445i −0.588614 + 0.214238i
\(995\) 3.51309 19.9237i 0.111372 0.631624i
\(996\) 0 0
\(997\) −34.5078 + 28.9555i −1.09287 + 0.917029i −0.996925 0.0783575i \(-0.975032\pi\)
−0.0959472 + 0.995386i \(0.530588\pi\)
\(998\) −8.61859 −0.272817
\(999\) 0 0
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 81.2.e.a.37.2 12
3.2 odd 2 27.2.e.a.22.1 yes 12
9.2 odd 6 243.2.e.c.190.2 12
9.4 even 3 243.2.e.a.28.2 12
9.5 odd 6 243.2.e.d.28.1 12
9.7 even 3 243.2.e.b.190.1 12
12.11 even 2 432.2.u.c.49.2 12
15.2 even 4 675.2.u.b.49.1 24
15.8 even 4 675.2.u.b.49.4 24
15.14 odd 2 675.2.l.c.76.2 12
27.2 odd 18 243.2.e.c.55.2 12
27.4 even 9 729.2.a.d.1.5 6
27.5 odd 18 729.2.c.e.244.5 12
27.7 even 9 243.2.e.a.217.2 12
27.11 odd 18 27.2.e.a.16.1 12
27.13 even 9 729.2.c.b.487.2 12
27.14 odd 18 729.2.c.e.487.5 12
27.16 even 9 inner 81.2.e.a.46.2 12
27.20 odd 18 243.2.e.d.217.1 12
27.22 even 9 729.2.c.b.244.2 12
27.23 odd 18 729.2.a.a.1.2 6
27.25 even 9 243.2.e.b.55.1 12
108.11 even 18 432.2.u.c.97.2 12
135.38 even 36 675.2.u.b.124.1 24
135.92 even 36 675.2.u.b.124.4 24
135.119 odd 18 675.2.l.c.151.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.1 12 27.11 odd 18
27.2.e.a.22.1 yes 12 3.2 odd 2
81.2.e.a.37.2 12 1.1 even 1 trivial
81.2.e.a.46.2 12 27.16 even 9 inner
243.2.e.a.28.2 12 9.4 even 3
243.2.e.a.217.2 12 27.7 even 9
243.2.e.b.55.1 12 27.25 even 9
243.2.e.b.190.1 12 9.7 even 3
243.2.e.c.55.2 12 27.2 odd 18
243.2.e.c.190.2 12 9.2 odd 6
243.2.e.d.28.1 12 9.5 odd 6
243.2.e.d.217.1 12 27.20 odd 18
432.2.u.c.49.2 12 12.11 even 2
432.2.u.c.97.2 12 108.11 even 18
675.2.l.c.76.2 12 15.14 odd 2
675.2.l.c.151.2 12 135.119 odd 18
675.2.u.b.49.1 24 15.2 even 4
675.2.u.b.49.4 24 15.8 even 4
675.2.u.b.124.1 24 135.38 even 36
675.2.u.b.124.4 24 135.92 even 36
729.2.a.a.1.2 6 27.23 odd 18
729.2.a.d.1.5 6 27.4 even 9
729.2.c.b.244.2 12 27.22 even 9
729.2.c.b.487.2 12 27.13 even 9
729.2.c.e.244.5 12 27.5 odd 18
729.2.c.e.487.5 12 27.14 odd 18