Properties

Label 567.2.bd.a.17.19
Level $567$
Weight $2$
Character 567.17
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
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] = [567,2,Mod(17,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.bd (of order \(18\), 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 17.19
Character \(\chi\) \(=\) 567.17
Dual form 567.2.bd.a.467.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.06025 - 0.363278i) q^{2} +(2.23328 - 0.812849i) q^{4} +(-0.338534 + 0.123216i) q^{5} +(1.84499 - 1.89632i) q^{7} +(0.682329 - 0.393943i) q^{8} +O(q^{10})\) \(q+(2.06025 - 0.363278i) q^{2} +(2.23328 - 0.812849i) q^{4} +(-0.338534 + 0.123216i) q^{5} +(1.84499 - 1.89632i) q^{7} +(0.682329 - 0.393943i) q^{8} +(-0.652704 + 0.376839i) q^{10} +(2.14028 - 5.88038i) q^{11} +(0.429890 + 1.18111i) q^{13} +(3.11225 - 4.57714i) q^{14} +(-2.37852 + 1.99582i) q^{16} +(0.468609 + 0.811655i) q^{17} +(6.61941 + 3.82172i) q^{19} +(-0.655887 + 0.550354i) q^{20} +(2.27331 - 12.8926i) q^{22} +(-1.68421 - 0.296971i) q^{23} +(-3.73080 + 3.13051i) q^{25} +(1.31476 + 2.27722i) q^{26} +(2.57896 - 5.73471i) q^{28} +(0.731568 - 2.00997i) q^{29} +(1.98478 + 5.45314i) q^{31} +(-5.18821 + 6.18306i) q^{32} +(1.26031 + 1.50198i) q^{34} +(-0.390934 + 0.869301i) q^{35} -3.33513 q^{37} +(15.0260 + 5.46902i) q^{38} +(-0.182451 + 0.217437i) q^{40} +(-8.66669 + 3.15442i) q^{41} +(-0.688669 - 3.90564i) q^{43} -14.8723i q^{44} -3.57777 q^{46} +(-4.74048 - 1.72539i) q^{47} +(-0.192044 - 6.99737i) q^{49} +(-6.54914 + 7.80496i) q^{50} +(1.92013 + 2.28833i) q^{52} +(-3.01037 - 1.73804i) q^{53} +2.25443i q^{55} +(0.511847 - 2.02073i) q^{56} +(0.777037 - 4.40680i) q^{58} +(-4.89583 - 4.10809i) q^{59} +(-3.57768 + 9.82960i) q^{61} +(6.07015 + 10.5138i) q^{62} +(-5.33790 + 9.24552i) q^{64} +(-0.291065 - 0.346878i) q^{65} +(-0.0504771 + 0.286270i) q^{67} +(1.70629 + 1.43175i) q^{68} +(-0.489624 + 1.93300i) q^{70} +(4.18316 + 2.41515i) q^{71} -3.69086i q^{73} +(-6.87121 + 1.21158i) q^{74} +(17.8895 + 3.15440i) q^{76} +(-7.20228 - 14.9079i) q^{77} +(1.79265 + 10.1666i) q^{79} +(0.559294 - 0.968725i) q^{80} +(-16.7096 + 9.64732i) q^{82} +(6.06917 + 2.20900i) q^{83} +(-0.258650 - 0.217033i) q^{85} +(-2.83766 - 7.79642i) q^{86} +(-0.856156 - 4.85550i) q^{88} +(-2.56195 + 4.43743i) q^{89} +(3.03291 + 1.36393i) q^{91} +(-4.00271 + 0.705785i) q^{92} +(-10.3934 - 1.83263i) q^{94} +(-2.71179 - 0.478163i) q^{95} +(7.91567 - 1.39575i) q^{97} +(-2.93765 - 14.3466i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.06025 0.363278i 1.45682 0.256876i 0.611545 0.791210i \(-0.290548\pi\)
0.845274 + 0.534333i \(0.179437\pi\)
\(3\) 0 0
\(4\) 2.23328 0.812849i 1.11664 0.406425i
\(5\) −0.338534 + 0.123216i −0.151397 + 0.0551040i −0.416607 0.909087i \(-0.636781\pi\)
0.265210 + 0.964191i \(0.414559\pi\)
\(6\) 0 0
\(7\) 1.84499 1.89632i 0.697340 0.716741i
\(8\) 0.682329 0.393943i 0.241240 0.139280i
\(9\) 0 0
\(10\) −0.652704 + 0.376839i −0.206403 + 0.119167i
\(11\) 2.14028 5.88038i 0.645320 1.77300i 0.0109905 0.999940i \(-0.496502\pi\)
0.634330 0.773063i \(-0.281276\pi\)
\(12\) 0 0
\(13\) 0.429890 + 1.18111i 0.119230 + 0.327582i 0.984923 0.172994i \(-0.0553440\pi\)
−0.865693 + 0.500576i \(0.833122\pi\)
\(14\) 3.11225 4.57714i 0.831784 1.22329i
\(15\) 0 0
\(16\) −2.37852 + 1.99582i −0.594631 + 0.498954i
\(17\) 0.468609 + 0.811655i 0.113654 + 0.196855i 0.917241 0.398332i \(-0.130411\pi\)
−0.803587 + 0.595188i \(0.797078\pi\)
\(18\) 0 0
\(19\) 6.61941 + 3.82172i 1.51860 + 0.876762i 0.999760 + 0.0218885i \(0.00696789\pi\)
0.518836 + 0.854874i \(0.326365\pi\)
\(20\) −0.655887 + 0.550354i −0.146661 + 0.123063i
\(21\) 0 0
\(22\) 2.27331 12.8926i 0.484672 2.74871i
\(23\) −1.68421 0.296971i −0.351181 0.0619228i −0.00472501 0.999989i \(-0.501504\pi\)
−0.346456 + 0.938066i \(0.612615\pi\)
\(24\) 0 0
\(25\) −3.73080 + 3.13051i −0.746160 + 0.626102i
\(26\) 1.31476 + 2.27722i 0.257845 + 0.446600i
\(27\) 0 0
\(28\) 2.57896 5.73471i 0.487378 1.08376i
\(29\) 0.731568 2.00997i 0.135849 0.373241i −0.853051 0.521828i \(-0.825250\pi\)
0.988899 + 0.148587i \(0.0474725\pi\)
\(30\) 0 0
\(31\) 1.98478 + 5.45314i 0.356477 + 0.979412i 0.980242 + 0.197801i \(0.0633799\pi\)
−0.623765 + 0.781612i \(0.714398\pi\)
\(32\) −5.18821 + 6.18306i −0.917154 + 1.09302i
\(33\) 0 0
\(34\) 1.26031 + 1.50198i 0.216141 + 0.257587i
\(35\) −0.390934 + 0.869301i −0.0660799 + 0.146939i
\(36\) 0 0
\(37\) −3.33513 −0.548292 −0.274146 0.961688i \(-0.588395\pi\)
−0.274146 + 0.961688i \(0.588395\pi\)
\(38\) 15.0260 + 5.46902i 2.43754 + 0.887192i
\(39\) 0 0
\(40\) −0.182451 + 0.217437i −0.0288481 + 0.0343798i
\(41\) −8.66669 + 3.15442i −1.35351 + 0.492637i −0.914041 0.405621i \(-0.867055\pi\)
−0.439468 + 0.898258i \(0.644833\pi\)
\(42\) 0 0
\(43\) −0.688669 3.90564i −0.105021 0.595604i −0.991212 0.132284i \(-0.957769\pi\)
0.886191 0.463320i \(-0.153342\pi\)
\(44\) 14.8723i 2.24208i
\(45\) 0 0
\(46\) −3.57777 −0.527514
\(47\) −4.74048 1.72539i −0.691470 0.251674i −0.0277052 0.999616i \(-0.508820\pi\)
−0.663764 + 0.747942i \(0.731042\pi\)
\(48\) 0 0
\(49\) −0.192044 6.99737i −0.0274348 0.999624i
\(50\) −6.54914 + 7.80496i −0.926189 + 1.10379i
\(51\) 0 0
\(52\) 1.92013 + 2.28833i 0.266275 + 0.317334i
\(53\) −3.01037 1.73804i −0.413506 0.238738i 0.278789 0.960352i \(-0.410067\pi\)
−0.692295 + 0.721614i \(0.743400\pi\)
\(54\) 0 0
\(55\) 2.25443i 0.303987i
\(56\) 0.511847 2.02073i 0.0683984 0.270032i
\(57\) 0 0
\(58\) 0.777037 4.40680i 0.102030 0.578641i
\(59\) −4.89583 4.10809i −0.637383 0.534828i 0.265830 0.964020i \(-0.414354\pi\)
−0.903213 + 0.429192i \(0.858798\pi\)
\(60\) 0 0
\(61\) −3.57768 + 9.82960i −0.458075 + 1.25855i 0.468840 + 0.883283i \(0.344672\pi\)
−0.926916 + 0.375269i \(0.877550\pi\)
\(62\) 6.07015 + 10.5138i 0.770910 + 1.33526i
\(63\) 0 0
\(64\) −5.33790 + 9.24552i −0.667238 + 1.15569i
\(65\) −0.291065 0.346878i −0.0361022 0.0430249i
\(66\) 0 0
\(67\) −0.0504771 + 0.286270i −0.00616676 + 0.0349734i −0.987736 0.156134i \(-0.950097\pi\)
0.981569 + 0.191108i \(0.0612079\pi\)
\(68\) 1.70629 + 1.43175i 0.206918 + 0.173625i
\(69\) 0 0
\(70\) −0.489624 + 1.93300i −0.0585213 + 0.231037i
\(71\) 4.18316 + 2.41515i 0.496450 + 0.286625i 0.727246 0.686377i \(-0.240800\pi\)
−0.230797 + 0.973002i \(0.574133\pi\)
\(72\) 0 0
\(73\) 3.69086i 0.431983i −0.976395 0.215992i \(-0.930702\pi\)
0.976395 0.215992i \(-0.0692984\pi\)
\(74\) −6.87121 + 1.21158i −0.798762 + 0.140843i
\(75\) 0 0
\(76\) 17.8895 + 3.15440i 2.05207 + 0.361835i
\(77\) −7.20228 14.9079i −0.820776 1.69891i
\(78\) 0 0
\(79\) 1.79265 + 10.1666i 0.201689 + 1.14384i 0.902565 + 0.430553i \(0.141682\pi\)
−0.700876 + 0.713283i \(0.747207\pi\)
\(80\) 0.559294 0.968725i 0.0625309 0.108307i
\(81\) 0 0
\(82\) −16.7096 + 9.64732i −1.84527 + 1.06537i
\(83\) 6.06917 + 2.20900i 0.666178 + 0.242469i 0.652901 0.757443i \(-0.273552\pi\)
0.0132766 + 0.999912i \(0.495774\pi\)
\(84\) 0 0
\(85\) −0.258650 0.217033i −0.0280545 0.0235405i
\(86\) −2.83766 7.79642i −0.305993 0.840709i
\(87\) 0 0
\(88\) −0.856156 4.85550i −0.0912665 0.517598i
\(89\) −2.56195 + 4.43743i −0.271566 + 0.470367i −0.969263 0.246026i \(-0.920875\pi\)
0.697697 + 0.716393i \(0.254208\pi\)
\(90\) 0 0
\(91\) 3.03291 + 1.36393i 0.317935 + 0.142979i
\(92\) −4.00271 + 0.705785i −0.417311 + 0.0735832i
\(93\) 0 0
\(94\) −10.3934 1.83263i −1.07199 0.189022i
\(95\) −2.71179 0.478163i −0.278224 0.0490584i
\(96\) 0 0
\(97\) 7.91567 1.39575i 0.803714 0.141717i 0.243324 0.969945i \(-0.421762\pi\)
0.560390 + 0.828229i \(0.310651\pi\)
\(98\) −2.93765 14.3466i −0.296747 1.44922i
\(99\) 0 0
\(100\) −5.78730 + 10.0239i −0.578730 + 1.00239i
\(101\) 2.47268 + 14.0233i 0.246041 + 1.39537i 0.818062 + 0.575130i \(0.195048\pi\)
−0.572021 + 0.820239i \(0.693840\pi\)
\(102\) 0 0
\(103\) −2.18829 6.01227i −0.215618 0.592406i 0.783979 0.620787i \(-0.213187\pi\)
−0.999597 + 0.0283812i \(0.990965\pi\)
\(104\) 0.758617 + 0.636556i 0.0743886 + 0.0624194i
\(105\) 0 0
\(106\) −6.83352 2.48720i −0.663730 0.241578i
\(107\) −2.81413 + 1.62474i −0.272053 + 0.157070i −0.629820 0.776741i \(-0.716871\pi\)
0.357767 + 0.933811i \(0.383538\pi\)
\(108\) 0 0
\(109\) 6.30335 10.9177i 0.603751 1.04573i −0.388496 0.921450i \(-0.627005\pi\)
0.992247 0.124278i \(-0.0396613\pi\)
\(110\) 0.818985 + 4.64469i 0.0780871 + 0.442854i
\(111\) 0 0
\(112\) −0.603640 + 8.19269i −0.0570386 + 0.774137i
\(113\) 14.5530 + 2.56609i 1.36903 + 0.241397i 0.809358 0.587315i \(-0.199815\pi\)
0.559674 + 0.828713i \(0.310926\pi\)
\(114\) 0 0
\(115\) 0.606753 0.106987i 0.0565800 0.00997659i
\(116\) 5.08348i 0.471989i
\(117\) 0 0
\(118\) −11.5790 6.68515i −1.06594 0.615418i
\(119\) 2.40374 + 0.608861i 0.220350 + 0.0558142i
\(120\) 0 0
\(121\) −21.5716 18.1007i −1.96105 1.64552i
\(122\) −3.80005 + 21.5512i −0.344041 + 1.95115i
\(123\) 0 0
\(124\) 8.86515 + 10.5651i 0.796114 + 0.948772i
\(125\) 1.77792 3.07945i 0.159022 0.275435i
\(126\) 0 0
\(127\) 7.01123 + 12.1438i 0.622146 + 1.07759i 0.989085 + 0.147344i \(0.0470724\pi\)
−0.366939 + 0.930245i \(0.619594\pi\)
\(128\) −2.11756 + 5.81795i −0.187168 + 0.514239i
\(129\) 0 0
\(130\) −0.725681 0.608918i −0.0636464 0.0534057i
\(131\) −0.455349 + 2.58241i −0.0397841 + 0.225627i −0.998217 0.0596917i \(-0.980988\pi\)
0.958433 + 0.285318i \(0.0920993\pi\)
\(132\) 0 0
\(133\) 19.4599 5.50148i 1.68739 0.477039i
\(134\) 0.608125i 0.0525340i
\(135\) 0 0
\(136\) 0.639491 + 0.369210i 0.0548359 + 0.0316595i
\(137\) 6.26152 + 7.46219i 0.534958 + 0.637538i 0.964049 0.265723i \(-0.0856107\pi\)
−0.429092 + 0.903261i \(0.641166\pi\)
\(138\) 0 0
\(139\) −0.0836111 + 0.0996438i −0.00709180 + 0.00845168i −0.769579 0.638552i \(-0.779534\pi\)
0.762487 + 0.647004i \(0.223978\pi\)
\(140\) −0.166456 + 2.25917i −0.0140681 + 0.190934i
\(141\) 0 0
\(142\) 9.49573 + 3.45616i 0.796864 + 0.290035i
\(143\) 7.86549 0.657745
\(144\) 0 0
\(145\) 0.770583i 0.0639934i
\(146\) −1.34081 7.60411i −0.110966 0.629321i
\(147\) 0 0
\(148\) −7.44829 + 2.71096i −0.612246 + 0.222839i
\(149\) 9.24727 11.0205i 0.757566 0.902832i −0.240125 0.970742i \(-0.577189\pi\)
0.997691 + 0.0679097i \(0.0216330\pi\)
\(150\) 0 0
\(151\) −19.0335 6.92763i −1.54892 0.563762i −0.580759 0.814075i \(-0.697244\pi\)
−0.968165 + 0.250313i \(0.919466\pi\)
\(152\) 6.02215 0.488461
\(153\) 0 0
\(154\) −20.2542 28.0976i −1.63213 2.26417i
\(155\) −1.34383 1.60152i −0.107939 0.128637i
\(156\) 0 0
\(157\) 2.54977 3.03870i 0.203494 0.242515i −0.654640 0.755941i \(-0.727180\pi\)
0.858134 + 0.513426i \(0.171624\pi\)
\(158\) 7.38664 + 20.2946i 0.587649 + 1.61455i
\(159\) 0 0
\(160\) 0.994530 2.73245i 0.0786245 0.216019i
\(161\) −3.67049 + 2.64588i −0.289275 + 0.208525i
\(162\) 0 0
\(163\) −8.65872 14.9973i −0.678203 1.17468i −0.975522 0.219904i \(-0.929426\pi\)
0.297318 0.954778i \(-0.403908\pi\)
\(164\) −16.7911 + 14.0894i −1.31117 + 1.10020i
\(165\) 0 0
\(166\) 13.3065 + 2.34630i 1.03279 + 0.182108i
\(167\) 2.13178 12.0899i 0.164962 0.935548i −0.784141 0.620583i \(-0.786896\pi\)
0.949103 0.314965i \(-0.101993\pi\)
\(168\) 0 0
\(169\) 8.74835 7.34074i 0.672950 0.564672i
\(170\) −0.611727 0.353181i −0.0469173 0.0270877i
\(171\) 0 0
\(172\) −4.71269 8.16261i −0.359339 0.622393i
\(173\) −16.1769 + 13.5741i −1.22991 + 1.03202i −0.231664 + 0.972796i \(0.574417\pi\)
−0.998245 + 0.0592207i \(0.981138\pi\)
\(174\) 0 0
\(175\) −0.946831 + 12.8505i −0.0715737 + 0.971409i
\(176\) 6.64546 + 18.2582i 0.500920 + 1.37627i
\(177\) 0 0
\(178\) −3.66625 + 10.0729i −0.274797 + 0.754998i
\(179\) −8.13538 + 4.69697i −0.608067 + 0.351068i −0.772209 0.635369i \(-0.780848\pi\)
0.164141 + 0.986437i \(0.447515\pi\)
\(180\) 0 0
\(181\) 8.05463 4.65035i 0.598696 0.345657i −0.169832 0.985473i \(-0.554323\pi\)
0.768529 + 0.639816i \(0.220989\pi\)
\(182\) 6.74405 + 1.70825i 0.499902 + 0.126624i
\(183\) 0 0
\(184\) −1.26617 + 0.460849i −0.0933434 + 0.0339742i
\(185\) 1.12906 0.410943i 0.0830098 0.0302131i
\(186\) 0 0
\(187\) 5.77580 1.01843i 0.422369 0.0744750i
\(188\) −11.9893 −0.874411
\(189\) 0 0
\(190\) −5.76069 −0.417924
\(191\) −8.98811 + 1.58485i −0.650357 + 0.114675i −0.489087 0.872235i \(-0.662670\pi\)
−0.161270 + 0.986910i \(0.551559\pi\)
\(192\) 0 0
\(193\) 3.29363 1.19878i 0.237081 0.0862902i −0.220748 0.975331i \(-0.570850\pi\)
0.457828 + 0.889041i \(0.348627\pi\)
\(194\) 15.8012 5.75118i 1.13446 0.412911i
\(195\) 0 0
\(196\) −6.11669 15.4710i −0.436906 1.10507i
\(197\) 17.0883 9.86593i 1.21749 0.702918i 0.253110 0.967438i \(-0.418547\pi\)
0.964380 + 0.264519i \(0.0852132\pi\)
\(198\) 0 0
\(199\) 9.64829 5.57044i 0.683949 0.394878i −0.117392 0.993086i \(-0.537453\pi\)
0.801341 + 0.598207i \(0.204120\pi\)
\(200\) −1.31239 + 3.60576i −0.0927999 + 0.254966i
\(201\) 0 0
\(202\) 10.1887 + 27.9932i 0.716875 + 1.96960i
\(203\) −2.46180 5.09564i −0.172785 0.357644i
\(204\) 0 0
\(205\) 2.54530 2.13576i 0.177771 0.149168i
\(206\) −6.69255 11.5918i −0.466292 0.807641i
\(207\) 0 0
\(208\) −3.37979 1.95132i −0.234346 0.135300i
\(209\) 36.6406 30.7451i 2.53448 2.12668i
\(210\) 0 0
\(211\) −1.40219 + 7.95221i −0.0965307 + 0.547453i 0.897737 + 0.440532i \(0.145210\pi\)
−0.994268 + 0.106921i \(0.965901\pi\)
\(212\) −8.13578 1.43456i −0.558767 0.0985258i
\(213\) 0 0
\(214\) −5.20759 + 4.36969i −0.355984 + 0.298706i
\(215\) 0.714376 + 1.23734i 0.0487201 + 0.0843856i
\(216\) 0 0
\(217\) 14.0028 + 6.29720i 0.950570 + 0.427481i
\(218\) 9.02032 24.7831i 0.610933 1.67853i
\(219\) 0 0
\(220\) 1.83251 + 5.03478i 0.123548 + 0.339445i
\(221\) −0.757207 + 0.902404i −0.0509352 + 0.0607023i
\(222\) 0 0
\(223\) −4.16647 4.96540i −0.279007 0.332508i 0.608282 0.793721i \(-0.291859\pi\)
−0.887290 + 0.461213i \(0.847414\pi\)
\(224\) 2.15288 + 21.2462i 0.143845 + 1.41957i
\(225\) 0 0
\(226\) 30.9151 2.05644
\(227\) −6.51828 2.37246i −0.432634 0.157466i 0.116518 0.993189i \(-0.462827\pi\)
−0.549152 + 0.835723i \(0.685049\pi\)
\(228\) 0 0
\(229\) −11.8635 + 14.1384i −0.783964 + 0.934292i −0.999105 0.0422913i \(-0.986534\pi\)
0.215142 + 0.976583i \(0.430979\pi\)
\(230\) 1.21120 0.440840i 0.0798641 0.0290682i
\(231\) 0 0
\(232\) −0.292641 1.65965i −0.0192129 0.108962i
\(233\) 24.0601i 1.57623i −0.615529 0.788115i \(-0.711057\pi\)
0.615529 0.788115i \(-0.288943\pi\)
\(234\) 0 0
\(235\) 1.81741 0.118555
\(236\) −14.2730 5.19496i −0.929096 0.338163i
\(237\) 0 0
\(238\) 5.17349 + 0.381184i 0.335347 + 0.0247085i
\(239\) 3.56306 4.24628i 0.230475 0.274669i −0.638396 0.769708i \(-0.720402\pi\)
0.868871 + 0.495039i \(0.164846\pi\)
\(240\) 0 0
\(241\) −6.55253 7.80900i −0.422086 0.503022i 0.512536 0.858666i \(-0.328706\pi\)
−0.934622 + 0.355644i \(0.884262\pi\)
\(242\) −51.0185 29.4556i −3.27960 1.89348i
\(243\) 0 0
\(244\) 24.8604i 1.59153i
\(245\) 0.927203 + 2.34518i 0.0592368 + 0.149828i
\(246\) 0 0
\(247\) −1.66826 + 9.46120i −0.106149 + 0.602001i
\(248\) 3.50249 + 2.93894i 0.222409 + 0.186623i
\(249\) 0 0
\(250\) 2.54427 6.99034i 0.160914 0.442108i
\(251\) 10.3890 + 17.9942i 0.655746 + 1.13579i 0.981706 + 0.190402i \(0.0609792\pi\)
−0.325960 + 0.945384i \(0.605688\pi\)
\(252\) 0 0
\(253\) −5.35099 + 9.26818i −0.336414 + 0.582685i
\(254\) 18.8565 + 22.4723i 1.18316 + 1.41004i
\(255\) 0 0
\(256\) 1.45849 8.27153i 0.0911558 0.516970i
\(257\) −19.4196 16.2950i −1.21136 1.01645i −0.999231 0.0392104i \(-0.987516\pi\)
−0.212129 0.977242i \(-0.568040\pi\)
\(258\) 0 0
\(259\) −6.15327 + 6.32447i −0.382346 + 0.392983i
\(260\) −0.931991 0.538085i −0.0577996 0.0333706i
\(261\) 0 0
\(262\) 5.48585i 0.338917i
\(263\) −3.91251 + 0.689881i −0.241256 + 0.0425399i −0.292968 0.956122i \(-0.594643\pi\)
0.0517128 + 0.998662i \(0.483532\pi\)
\(264\) 0 0
\(265\) 1.23327 + 0.217458i 0.0757591 + 0.0133584i
\(266\) 38.0938 18.4038i 2.33568 1.12841i
\(267\) 0 0
\(268\) 0.119964 + 0.680352i 0.00732799 + 0.0415591i
\(269\) −2.35052 + 4.07121i −0.143313 + 0.248226i −0.928742 0.370726i \(-0.879109\pi\)
0.785429 + 0.618952i \(0.212442\pi\)
\(270\) 0 0
\(271\) −7.44995 + 4.30123i −0.452552 + 0.261281i −0.708907 0.705302i \(-0.750812\pi\)
0.256355 + 0.966583i \(0.417478\pi\)
\(272\) −2.73451 0.995282i −0.165804 0.0603478i
\(273\) 0 0
\(274\) 15.6112 + 13.0993i 0.943105 + 0.791359i
\(275\) 10.4236 + 28.6387i 0.628569 + 1.72698i
\(276\) 0 0
\(277\) 2.75863 + 15.6450i 0.165750 + 0.940015i 0.948288 + 0.317412i \(0.102814\pi\)
−0.782538 + 0.622603i \(0.786075\pi\)
\(278\) −0.136062 + 0.235665i −0.00816043 + 0.0141343i
\(279\) 0 0
\(280\) 0.0757094 + 0.747154i 0.00452450 + 0.0446510i
\(281\) −21.2686 + 3.75023i −1.26878 + 0.223720i −0.767208 0.641398i \(-0.778355\pi\)
−0.501569 + 0.865118i \(0.667244\pi\)
\(282\) 0 0
\(283\) −4.47736 0.789480i −0.266152 0.0469297i 0.0389797 0.999240i \(-0.487589\pi\)
−0.305131 + 0.952310i \(0.598700\pi\)
\(284\) 11.3053 + 1.99344i 0.670848 + 0.118289i
\(285\) 0 0
\(286\) 16.2049 2.85736i 0.958216 0.168959i
\(287\) −10.0082 + 22.2547i −0.590763 + 1.31365i
\(288\) 0 0
\(289\) 8.06081 13.9617i 0.474165 0.821278i
\(290\) 0.279936 + 1.58760i 0.0164384 + 0.0932268i
\(291\) 0 0
\(292\) −3.00012 8.24275i −0.175568 0.482370i
\(293\) −6.06074 5.08556i −0.354072 0.297102i 0.448351 0.893858i \(-0.352012\pi\)
−0.802423 + 0.596756i \(0.796456\pi\)
\(294\) 0 0
\(295\) 2.16359 + 0.787482i 0.125969 + 0.0458490i
\(296\) −2.27565 + 1.31385i −0.132270 + 0.0763660i
\(297\) 0 0
\(298\) 15.0482 26.0643i 0.871720 1.50986i
\(299\) −0.373267 2.11690i −0.0215866 0.122424i
\(300\) 0 0
\(301\) −8.67691 5.89991i −0.500129 0.340065i
\(302\) −41.7305 7.35821i −2.40132 0.423417i
\(303\) 0 0
\(304\) −23.3719 + 4.12109i −1.34047 + 0.236361i
\(305\) 3.76849i 0.215783i
\(306\) 0 0
\(307\) −16.6860 9.63367i −0.952321 0.549823i −0.0585197 0.998286i \(-0.518638\pi\)
−0.893801 + 0.448464i \(0.851971\pi\)
\(308\) −28.2026 27.4392i −1.60699 1.56349i
\(309\) 0 0
\(310\) −3.35043 2.81134i −0.190292 0.159674i
\(311\) 2.30794 13.0890i 0.130871 0.742208i −0.846775 0.531951i \(-0.821459\pi\)
0.977646 0.210257i \(-0.0674300\pi\)
\(312\) 0 0
\(313\) −9.61460 11.4582i −0.543449 0.647658i 0.422508 0.906359i \(-0.361150\pi\)
−0.965957 + 0.258701i \(0.916705\pi\)
\(314\) 4.14928 7.18676i 0.234157 0.405573i
\(315\) 0 0
\(316\) 12.2675 + 21.2479i 0.690098 + 1.19528i
\(317\) −5.67633 + 15.5956i −0.318815 + 0.875936i 0.671981 + 0.740569i \(0.265444\pi\)
−0.990795 + 0.135367i \(0.956779\pi\)
\(318\) 0 0
\(319\) −10.2536 8.60379i −0.574092 0.481720i
\(320\) 0.667863 3.78764i 0.0373347 0.211736i
\(321\) 0 0
\(322\) −6.60095 + 6.78460i −0.367856 + 0.378091i
\(323\) 7.16357i 0.398592i
\(324\) 0 0
\(325\) −5.30133 3.06072i −0.294065 0.169778i
\(326\) −23.2874 27.7528i −1.28977 1.53708i
\(327\) 0 0
\(328\) −4.67087 + 5.56653i −0.257906 + 0.307360i
\(329\) −12.0180 + 5.80612i −0.662574 + 0.320102i
\(330\) 0 0
\(331\) 21.5799 + 7.85444i 1.18614 + 0.431719i 0.858366 0.513037i \(-0.171480\pi\)
0.327773 + 0.944757i \(0.393702\pi\)
\(332\) 15.3498 0.842428
\(333\) 0 0
\(334\) 25.6828i 1.40530i
\(335\) −0.0181849 0.103132i −0.000993547 0.00563469i
\(336\) 0 0
\(337\) 25.8190 9.39733i 1.40645 0.511905i 0.476363 0.879249i \(-0.341955\pi\)
0.930085 + 0.367344i \(0.119733\pi\)
\(338\) 15.3571 18.3019i 0.835315 0.995490i
\(339\) 0 0
\(340\) −0.754053 0.274453i −0.0408943 0.0148843i
\(341\) 36.3145 1.96654
\(342\) 0 0
\(343\) −13.6235 12.5459i −0.735602 0.677414i
\(344\) −2.00849 2.39363i −0.108291 0.129056i
\(345\) 0 0
\(346\) −28.3974 + 33.8427i −1.52665 + 1.81940i
\(347\) 3.41079 + 9.37108i 0.183101 + 0.503066i 0.996953 0.0780065i \(-0.0248555\pi\)
−0.813852 + 0.581072i \(0.802633\pi\)
\(348\) 0 0
\(349\) 9.55483 26.2517i 0.511458 1.40522i −0.368259 0.929723i \(-0.620046\pi\)
0.879717 0.475497i \(-0.157732\pi\)
\(350\) 2.71761 + 26.8193i 0.145262 + 1.43355i
\(351\) 0 0
\(352\) 25.2545 + 43.7421i 1.34607 + 2.33146i
\(353\) 18.1012 15.1887i 0.963429 0.808413i −0.0180788 0.999837i \(-0.505755\pi\)
0.981507 + 0.191424i \(0.0613105\pi\)
\(354\) 0 0
\(355\) −1.71373 0.302177i −0.0909552 0.0160379i
\(356\) −2.11461 + 11.9925i −0.112074 + 0.635603i
\(357\) 0 0
\(358\) −15.0546 + 12.6323i −0.795662 + 0.667640i
\(359\) −0.0258053 0.0148987i −0.00136195 0.000786324i 0.499319 0.866418i \(-0.333584\pi\)
−0.500681 + 0.865632i \(0.666917\pi\)
\(360\) 0 0
\(361\) 19.7111 + 34.1405i 1.03742 + 1.79687i
\(362\) 14.9052 12.5070i 0.783401 0.657351i
\(363\) 0 0
\(364\) 7.88202 + 0.580749i 0.413130 + 0.0304395i
\(365\) 0.454775 + 1.24948i 0.0238040 + 0.0654010i
\(366\) 0 0
\(367\) 5.36231 14.7328i 0.279910 0.769047i −0.717462 0.696598i \(-0.754696\pi\)
0.997372 0.0724491i \(-0.0230815\pi\)
\(368\) 4.59862 2.65502i 0.239720 0.138402i
\(369\) 0 0
\(370\) 2.17685 1.25681i 0.113169 0.0653383i
\(371\) −8.84997 + 2.50196i −0.459467 + 0.129895i
\(372\) 0 0
\(373\) −14.4007 + 5.24143i −0.745640 + 0.271391i −0.686770 0.726875i \(-0.740972\pi\)
−0.0588703 + 0.998266i \(0.518750\pi\)
\(374\) 11.5296 4.19645i 0.596183 0.216993i
\(375\) 0 0
\(376\) −3.91427 + 0.690191i −0.201863 + 0.0355939i
\(377\) 2.68849 0.138464
\(378\) 0 0
\(379\) 17.9559 0.922330 0.461165 0.887314i \(-0.347432\pi\)
0.461165 + 0.887314i \(0.347432\pi\)
\(380\) −6.44488 + 1.13641i −0.330616 + 0.0582964i
\(381\) 0 0
\(382\) −17.9420 + 6.53037i −0.917995 + 0.334123i
\(383\) 32.4762 11.8204i 1.65945 0.603992i 0.669177 0.743103i \(-0.266647\pi\)
0.990277 + 0.139111i \(0.0444245\pi\)
\(384\) 0 0
\(385\) 4.27511 + 4.15939i 0.217880 + 0.211982i
\(386\) 6.35021 3.66630i 0.323217 0.186610i
\(387\) 0 0
\(388\) 16.5434 9.55134i 0.839864 0.484896i
\(389\) −0.118139 + 0.324583i −0.00598986 + 0.0164570i −0.942652 0.333779i \(-0.891676\pi\)
0.936662 + 0.350236i \(0.113898\pi\)
\(390\) 0 0
\(391\) −0.548197 1.50616i −0.0277235 0.0761697i
\(392\) −2.88760 4.69885i −0.145846 0.237328i
\(393\) 0 0
\(394\) 31.6221 26.5341i 1.59310 1.33677i
\(395\) −1.85957 3.22087i −0.0935652 0.162060i
\(396\) 0 0
\(397\) 2.27062 + 1.31094i 0.113959 + 0.0657943i 0.555896 0.831252i \(-0.312375\pi\)
−0.441937 + 0.897046i \(0.645709\pi\)
\(398\) 17.8543 14.9815i 0.894955 0.750956i
\(399\) 0 0
\(400\) 2.62586 14.8920i 0.131293 0.744599i
\(401\) −17.0025 2.99801i −0.849066 0.149713i −0.267848 0.963461i \(-0.586313\pi\)
−0.581218 + 0.813748i \(0.697424\pi\)
\(402\) 0 0
\(403\) −5.58754 + 4.68850i −0.278335 + 0.233551i
\(404\) 16.9210 + 29.3081i 0.841852 + 1.45813i
\(405\) 0 0
\(406\) −6.92307 9.60400i −0.343586 0.476638i
\(407\) −7.13813 + 19.6118i −0.353824 + 0.972123i
\(408\) 0 0
\(409\) −7.89678 21.6962i −0.390471 1.07281i −0.966787 0.255583i \(-0.917733\pi\)
0.576317 0.817227i \(-0.304490\pi\)
\(410\) 4.46808 5.32485i 0.220663 0.262975i
\(411\) 0 0
\(412\) −9.77413 11.6484i −0.481537 0.573873i
\(413\) −16.8230 + 1.70468i −0.827805 + 0.0838817i
\(414\) 0 0
\(415\) −2.32681 −0.114218
\(416\) −9.53326 3.46982i −0.467406 0.170122i
\(417\) 0 0
\(418\) 64.3198 76.6534i 3.14599 3.74924i
\(419\) 21.7961 7.93314i 1.06481 0.387559i 0.250577 0.968097i \(-0.419380\pi\)
0.814234 + 0.580537i \(0.197157\pi\)
\(420\) 0 0
\(421\) −3.28202 18.6133i −0.159956 0.907156i −0.954114 0.299444i \(-0.903199\pi\)
0.794158 0.607712i \(-0.207912\pi\)
\(422\) 16.8929i 0.822336i
\(423\) 0 0
\(424\) −2.73875 −0.133005
\(425\) −4.28918 1.56114i −0.208056 0.0757262i
\(426\) 0 0
\(427\) 12.0393 + 24.9199i 0.582621 + 1.20596i
\(428\) −4.96409 + 5.91598i −0.239949 + 0.285959i
\(429\) 0 0
\(430\) 1.92129 + 2.28971i 0.0926530 + 0.110420i
\(431\) 35.0297 + 20.2244i 1.68732 + 0.974175i 0.956557 + 0.291545i \(0.0941692\pi\)
0.730764 + 0.682630i \(0.239164\pi\)
\(432\) 0 0
\(433\) 5.57490i 0.267912i 0.990987 + 0.133956i \(0.0427681\pi\)
−0.990987 + 0.133956i \(0.957232\pi\)
\(434\) 31.1369 + 7.88691i 1.49462 + 0.378584i
\(435\) 0 0
\(436\) 5.20271 29.5060i 0.249165 1.41308i
\(437\) −10.0135 8.40234i −0.479011 0.401938i
\(438\) 0 0
\(439\) −11.6900 + 32.1181i −0.557934 + 1.53291i 0.264694 + 0.964332i \(0.414729\pi\)
−0.822628 + 0.568580i \(0.807493\pi\)
\(440\) 0.888115 + 1.53826i 0.0423392 + 0.0733337i
\(441\) 0 0
\(442\) −1.23221 + 2.13426i −0.0586104 + 0.101516i
\(443\) 8.54217 + 10.1802i 0.405851 + 0.483674i 0.929795 0.368079i \(-0.119984\pi\)
−0.523944 + 0.851753i \(0.675540\pi\)
\(444\) 0 0
\(445\) 0.320544 1.81790i 0.0151953 0.0861766i
\(446\) −10.3878 8.71640i −0.491876 0.412733i
\(447\) 0 0
\(448\) 7.68408 + 27.1802i 0.363039 + 1.28414i
\(449\) 10.5259 + 6.07712i 0.496747 + 0.286797i 0.727369 0.686247i \(-0.240743\pi\)
−0.230622 + 0.973043i \(0.574076\pi\)
\(450\) 0 0
\(451\) 57.7148i 2.71768i
\(452\) 34.5869 6.09860i 1.62683 0.286854i
\(453\) 0 0
\(454\) −14.2912 2.51992i −0.670718 0.118266i
\(455\) −1.19480 0.0880333i −0.0560132 0.00412707i
\(456\) 0 0
\(457\) −2.48520 14.0943i −0.116253 0.659303i −0.986122 0.166021i \(-0.946908\pi\)
0.869869 0.493282i \(-0.164203\pi\)
\(458\) −19.3057 + 33.4384i −0.902095 + 1.56248i
\(459\) 0 0
\(460\) 1.26809 0.732131i 0.0591249 0.0341358i
\(461\) −23.2811 8.47362i −1.08431 0.394656i −0.262798 0.964851i \(-0.584645\pi\)
−0.821509 + 0.570195i \(0.806868\pi\)
\(462\) 0 0
\(463\) −13.5051 11.3321i −0.627634 0.526647i 0.272559 0.962139i \(-0.412130\pi\)
−0.900193 + 0.435492i \(0.856574\pi\)
\(464\) 2.27147 + 6.24082i 0.105450 + 0.289723i
\(465\) 0 0
\(466\) −8.74050 49.5699i −0.404896 2.29628i
\(467\) −1.78544 + 3.09247i −0.0826202 + 0.143102i −0.904375 0.426739i \(-0.859662\pi\)
0.821754 + 0.569842i \(0.192996\pi\)
\(468\) 0 0
\(469\) 0.449729 + 0.623884i 0.0207665 + 0.0288083i
\(470\) 3.74432 0.660225i 0.172713 0.0304539i
\(471\) 0 0
\(472\) −4.95892 0.874391i −0.228253 0.0402471i
\(473\) −24.4406 4.30953i −1.12378 0.198153i
\(474\) 0 0
\(475\) −36.6596 + 6.46408i −1.68206 + 0.296592i
\(476\) 5.86314 0.594113i 0.268736 0.0272311i
\(477\) 0 0
\(478\) 5.79821 10.0428i 0.265204 0.459347i
\(479\) −1.11594 6.32882i −0.0509887 0.289171i 0.948642 0.316352i \(-0.102458\pi\)
−0.999631 + 0.0271809i \(0.991347\pi\)
\(480\) 0 0
\(481\) −1.43374 3.93917i −0.0653729 0.179611i
\(482\) −16.3367 13.7081i −0.744117 0.624388i
\(483\) 0 0
\(484\) −62.8887 22.8896i −2.85858 1.04044i
\(485\) −2.50775 + 1.44785i −0.113871 + 0.0657434i
\(486\) 0 0
\(487\) 8.85684 15.3405i 0.401342 0.695144i −0.592546 0.805536i \(-0.701877\pi\)
0.993888 + 0.110392i \(0.0352107\pi\)
\(488\) 1.43114 + 8.11642i 0.0647848 + 0.367413i
\(489\) 0 0
\(490\) 2.76223 + 4.49484i 0.124785 + 0.203056i
\(491\) −12.0720 2.12862i −0.544803 0.0960634i −0.105528 0.994416i \(-0.533653\pi\)
−0.439274 + 0.898353i \(0.644764\pi\)
\(492\) 0 0
\(493\) 1.97422 0.348108i 0.0889143 0.0156780i
\(494\) 20.0985i 0.904274i
\(495\) 0 0
\(496\) −15.6043 9.00915i −0.700654 0.404523i
\(497\) 12.2978 3.47668i 0.551630 0.155951i
\(498\) 0 0
\(499\) 3.82390 + 3.20863i 0.171181 + 0.143638i 0.724353 0.689429i \(-0.242138\pi\)
−0.553172 + 0.833067i \(0.686583\pi\)
\(500\) 1.46748 8.32248i 0.0656276 0.372193i
\(501\) 0 0
\(502\) 27.9408 + 33.2986i 1.24706 + 1.48619i
\(503\) −10.5236 + 18.2273i −0.469222 + 0.812717i −0.999381 0.0351814i \(-0.988799\pi\)
0.530158 + 0.847899i \(0.322132\pi\)
\(504\) 0 0
\(505\) −2.56499 4.44269i −0.114140 0.197697i
\(506\) −7.65746 + 21.0387i −0.340415 + 0.935284i
\(507\) 0 0
\(508\) 25.5292 + 21.4215i 1.13267 + 0.950426i
\(509\) −4.75075 + 26.9428i −0.210573 + 1.19422i 0.677852 + 0.735198i \(0.262911\pi\)
−0.888425 + 0.459021i \(0.848200\pi\)
\(510\) 0 0
\(511\) −6.99905 6.80960i −0.309620 0.301239i
\(512\) 29.9539i 1.32379i
\(513\) 0 0
\(514\) −45.9289 26.5170i −2.02583 1.16962i
\(515\) 1.48162 + 1.76573i 0.0652879 + 0.0778071i
\(516\) 0 0
\(517\) −20.2919 + 24.1830i −0.892438 + 1.06357i
\(518\) −10.3798 + 15.2653i −0.456060 + 0.670721i
\(519\) 0 0
\(520\) −0.335252 0.122022i −0.0147018 0.00535101i
\(521\) −37.9904 −1.66439 −0.832194 0.554485i \(-0.812915\pi\)
−0.832194 + 0.554485i \(0.812915\pi\)
\(522\) 0 0
\(523\) 0.849579i 0.0371495i 0.999827 + 0.0185747i \(0.00591287\pi\)
−0.999827 + 0.0185747i \(0.994087\pi\)
\(524\) 1.08219 + 6.13740i 0.0472756 + 0.268113i
\(525\) 0 0
\(526\) −7.81014 + 2.84266i −0.340538 + 0.123946i
\(527\) −3.49598 + 4.16635i −0.152287 + 0.181489i
\(528\) 0 0
\(529\) −18.8646 6.86614i −0.820199 0.298528i
\(530\) 2.61984 0.113799
\(531\) 0 0
\(532\) 38.9877 28.1044i 1.69033 1.21848i
\(533\) −7.45145 8.88030i −0.322758 0.384648i
\(534\) 0 0
\(535\) 0.752486 0.896778i 0.0325328 0.0387711i
\(536\) 0.0783319 + 0.215215i 0.00338342 + 0.00929587i
\(537\) 0 0
\(538\) −3.36367 + 9.24162i −0.145018 + 0.398434i
\(539\) −41.5582 13.8471i −1.79004 0.596435i
\(540\) 0 0
\(541\) 20.4690 + 35.4533i 0.880031 + 1.52426i 0.851305 + 0.524671i \(0.175812\pi\)
0.0287257 + 0.999587i \(0.490855\pi\)
\(542\) −13.7862 + 11.5680i −0.592169 + 0.496889i
\(543\) 0 0
\(544\) −7.44976 1.31359i −0.319406 0.0563198i
\(545\) −0.788657 + 4.47270i −0.0337824 + 0.191589i
\(546\) 0 0
\(547\) −9.03807 + 7.58384i −0.386440 + 0.324262i −0.815224 0.579145i \(-0.803386\pi\)
0.428784 + 0.903407i \(0.358942\pi\)
\(548\) 20.0494 + 11.5755i 0.856468 + 0.494482i
\(549\) 0 0
\(550\) 31.8792 + 55.2163i 1.35933 + 2.35443i
\(551\) 12.5241 10.5089i 0.533543 0.447696i
\(552\) 0 0
\(553\) 22.5866 + 15.3579i 0.960480 + 0.653084i
\(554\) 11.3670 + 31.2304i 0.482935 + 1.32685i
\(555\) 0 0
\(556\) −0.105732 + 0.290496i −0.00448403 + 0.0123198i
\(557\) 27.0274 15.6043i 1.14519 0.661175i 0.197478 0.980307i \(-0.436725\pi\)
0.947710 + 0.319132i \(0.103391\pi\)
\(558\) 0 0
\(559\) 4.31695 2.49239i 0.182587 0.105417i
\(560\) −0.805121 2.84788i −0.0340226 0.120345i
\(561\) 0 0
\(562\) −42.4563 + 15.4528i −1.79091 + 0.651838i
\(563\) 15.5954 5.67626i 0.657268 0.239226i 0.00821159 0.999966i \(-0.497386\pi\)
0.649056 + 0.760740i \(0.275164\pi\)
\(564\) 0 0
\(565\) −5.24288 + 0.924461i −0.220570 + 0.0388924i
\(566\) −9.51130 −0.399790
\(567\) 0 0
\(568\) 3.80572 0.159684
\(569\) −12.9515 + 2.28370i −0.542956 + 0.0957378i −0.438398 0.898781i \(-0.644454\pi\)
−0.104558 + 0.994519i \(0.533343\pi\)
\(570\) 0 0
\(571\) −13.3923 + 4.87441i −0.560452 + 0.203988i −0.606684 0.794943i \(-0.707501\pi\)
0.0462326 + 0.998931i \(0.485278\pi\)
\(572\) 17.5659 6.39346i 0.734466 0.267324i
\(573\) 0 0
\(574\) −12.5347 + 49.4860i −0.523188 + 2.06550i
\(575\) 7.21311 4.16449i 0.300807 0.173671i
\(576\) 0 0
\(577\) −0.474700 + 0.274068i −0.0197620 + 0.0114096i −0.509848 0.860264i \(-0.670299\pi\)
0.490086 + 0.871674i \(0.336965\pi\)
\(578\) 11.5353 31.6930i 0.479806 1.31826i
\(579\) 0 0
\(580\) 0.626368 + 1.72093i 0.0260085 + 0.0714578i
\(581\) 15.3865 7.43350i 0.638340 0.308394i
\(582\) 0 0
\(583\) −16.6634 + 13.9822i −0.690127 + 0.579085i
\(584\) −1.45399 2.51838i −0.0601665 0.104211i
\(585\) 0 0
\(586\) −14.3341 8.27581i −0.592137 0.341871i
\(587\) −19.8533 + 16.6589i −0.819432 + 0.687585i −0.952839 0.303476i \(-0.901853\pi\)
0.133407 + 0.991061i \(0.457408\pi\)
\(588\) 0 0
\(589\) −7.70228 + 43.6818i −0.317367 + 1.79988i
\(590\) 4.74362 + 0.836428i 0.195292 + 0.0344352i
\(591\) 0 0
\(592\) 7.93268 6.65631i 0.326031 0.273573i
\(593\) −1.71212 2.96547i −0.0703082 0.121777i 0.828728 0.559651i \(-0.189065\pi\)
−0.899036 + 0.437874i \(0.855732\pi\)
\(594\) 0 0
\(595\) −0.888768 + 0.0900591i −0.0364359 + 0.00369206i
\(596\) 11.6938 32.1285i 0.478997 1.31603i
\(597\) 0 0
\(598\) −1.53805 4.22576i −0.0628956 0.172804i
\(599\) −17.8781 + 21.3063i −0.730479 + 0.870550i −0.995604 0.0936635i \(-0.970142\pi\)
0.265125 + 0.964214i \(0.414587\pi\)
\(600\) 0 0
\(601\) −4.26455 5.08229i −0.173955 0.207311i 0.672022 0.740531i \(-0.265426\pi\)
−0.845976 + 0.533220i \(0.820982\pi\)
\(602\) −20.0199 9.00318i −0.815952 0.366942i
\(603\) 0 0
\(604\) −48.1383 −1.95872
\(605\) 9.53303 + 3.46974i 0.387573 + 0.141065i
\(606\) 0 0
\(607\) −23.5073 + 28.0149i −0.954133 + 1.13709i 0.0363338 + 0.999340i \(0.488432\pi\)
−0.990467 + 0.137752i \(0.956012\pi\)
\(608\) −57.9728 + 21.1004i −2.35111 + 0.855733i
\(609\) 0 0
\(610\) −1.36901 7.76403i −0.0554295 0.314357i
\(611\) 6.34077i 0.256520i
\(612\) 0 0
\(613\) −15.8053 −0.638369 −0.319185 0.947693i \(-0.603409\pi\)
−0.319185 + 0.947693i \(0.603409\pi\)
\(614\) −37.8771 13.7861i −1.52860 0.556363i
\(615\) 0 0
\(616\) −10.7872 7.33480i −0.434628 0.295527i
\(617\) −10.9448 + 13.0434i −0.440619 + 0.525109i −0.939955 0.341299i \(-0.889133\pi\)
0.499336 + 0.866409i \(0.333577\pi\)
\(618\) 0 0
\(619\) 15.2802 + 18.2102i 0.614163 + 0.731931i 0.980055 0.198726i \(-0.0636805\pi\)
−0.365892 + 0.930657i \(0.619236\pi\)
\(620\) −4.30295 2.48431i −0.172811 0.0997722i
\(621\) 0 0
\(622\) 27.8050i 1.11488i
\(623\) 3.68801 + 13.0453i 0.147757 + 0.522648i
\(624\) 0 0
\(625\) 4.00607 22.7195i 0.160243 0.908782i
\(626\) −23.9710 20.1141i −0.958075 0.803920i
\(627\) 0 0
\(628\) 3.22436 8.85886i 0.128666 0.353507i
\(629\) −1.56287 2.70698i −0.0623158 0.107934i
\(630\) 0 0
\(631\) 21.9990 38.1033i 0.875765 1.51687i 0.0198191 0.999804i \(-0.493691\pi\)
0.855946 0.517066i \(-0.172976\pi\)
\(632\) 5.22825 + 6.23079i 0.207969 + 0.247847i
\(633\) 0 0
\(634\) −6.02914 + 34.1930i −0.239448 + 1.35798i
\(635\) −3.86986 3.24720i −0.153571 0.128861i
\(636\) 0 0
\(637\) 8.18213 3.23492i 0.324188 0.128172i
\(638\) −24.2506 14.0011i −0.960090 0.554308i
\(639\) 0 0
\(640\) 2.23049i 0.0881679i
\(641\) −26.1576 + 4.61228i −1.03316 + 0.182174i −0.664421 0.747358i \(-0.731322\pi\)
−0.368740 + 0.929532i \(0.620211\pi\)
\(642\) 0 0
\(643\) 21.8428 + 3.85147i 0.861394 + 0.151887i 0.586858 0.809690i \(-0.300365\pi\)
0.274536 + 0.961577i \(0.411476\pi\)
\(644\) −6.04655 + 8.89257i −0.238267 + 0.350416i
\(645\) 0 0
\(646\) 2.60237 + 14.7588i 0.102389 + 0.580676i
\(647\) −6.41692 + 11.1144i −0.252275 + 0.436954i −0.964152 0.265351i \(-0.914512\pi\)
0.711877 + 0.702305i \(0.247846\pi\)
\(648\) 0 0
\(649\) −34.6356 + 19.9969i −1.35957 + 0.784946i
\(650\) −12.0340 4.38000i −0.472011 0.171798i
\(651\) 0 0
\(652\) −31.5280 26.4551i −1.23473 1.03606i
\(653\) −3.64829 10.0236i −0.142769 0.392254i 0.847613 0.530615i \(-0.178039\pi\)
−0.990382 + 0.138361i \(0.955817\pi\)
\(654\) 0 0
\(655\) −0.164044 0.930342i −0.00640975 0.0363515i
\(656\) 14.3183 24.8000i 0.559035 0.968277i
\(657\) 0 0
\(658\) −22.6509 + 16.3280i −0.883024 + 0.636530i
\(659\) −12.4568 + 2.19647i −0.485248 + 0.0855623i −0.410920 0.911672i \(-0.634792\pi\)
−0.0743281 + 0.997234i \(0.523681\pi\)
\(660\) 0 0
\(661\) 32.7769 + 5.77946i 1.27487 + 0.224795i 0.769802 0.638282i \(-0.220355\pi\)
0.505072 + 0.863077i \(0.331466\pi\)
\(662\) 47.3134 + 8.34263i 1.83889 + 0.324246i
\(663\) 0 0
\(664\) 5.01139 0.883643i 0.194479 0.0342920i
\(665\) −5.90997 + 4.26022i −0.229179 + 0.165204i
\(666\) 0 0
\(667\) −1.82901 + 3.16794i −0.0708196 + 0.122663i
\(668\) −5.06642 28.7331i −0.196026 1.11172i
\(669\) 0 0
\(670\) −0.0749310 0.205871i −0.00289484 0.00795350i
\(671\) 50.1446 + 42.0763i 1.93581 + 1.62434i
\(672\) 0 0
\(673\) 21.0468 + 7.66040i 0.811294 + 0.295287i 0.714158 0.699984i \(-0.246810\pi\)
0.0971357 + 0.995271i \(0.469032\pi\)
\(674\) 49.7797 28.7403i 1.91744 1.10704i
\(675\) 0 0
\(676\) 13.5706 23.5051i 0.521948 0.904040i
\(677\) 8.03399 + 45.5630i 0.308771 + 1.75113i 0.605199 + 0.796074i \(0.293094\pi\)
−0.296427 + 0.955055i \(0.595795\pi\)
\(678\) 0 0
\(679\) 11.9575 17.5858i 0.458888 0.674879i
\(680\) −0.261982 0.0461946i −0.0100466 0.00177148i
\(681\) 0 0
\(682\) 74.8171 13.1923i 2.86489 0.505158i
\(683\) 8.70104i 0.332936i −0.986047 0.166468i \(-0.946764\pi\)
0.986047 0.166468i \(-0.0532362\pi\)
\(684\) 0 0
\(685\) −3.03920 1.75468i −0.116122 0.0670431i
\(686\) −32.6256 20.8985i −1.24565 0.797910i
\(687\) 0 0
\(688\) 9.43295 + 7.91518i 0.359628 + 0.301764i
\(689\) 0.758692 4.30276i 0.0289039 0.163922i
\(690\) 0 0
\(691\) −7.31456 8.71715i −0.278259 0.331616i 0.608755 0.793358i \(-0.291669\pi\)
−0.887014 + 0.461742i \(0.847225\pi\)
\(692\) −25.0940 + 43.4641i −0.953932 + 1.65226i
\(693\) 0 0
\(694\) 10.4314 + 18.0677i 0.395971 + 0.685841i
\(695\) 0.0160275 0.0440351i 0.000607956 0.00167035i
\(696\) 0 0
\(697\) −6.62159 5.55618i −0.250811 0.210455i
\(698\) 10.1487 57.5561i 0.384134 2.17853i
\(699\) 0 0
\(700\) 8.33100 + 29.4685i 0.314882 + 1.11381i
\(701\) 19.8586i 0.750050i −0.927015 0.375025i \(-0.877634\pi\)
0.927015 0.375025i \(-0.122366\pi\)
\(702\) 0 0
\(703\) −22.0766 12.7459i −0.832634 0.480722i
\(704\) 42.9426 + 51.1769i 1.61846 + 1.92880i
\(705\) 0 0
\(706\) 31.7753 37.8683i 1.19588 1.42519i
\(707\) 31.1547 + 21.1838i 1.17169 + 0.796698i
\(708\) 0 0
\(709\) −19.2290 6.99878i −0.722160 0.262845i −0.0453176 0.998973i \(-0.514430\pi\)
−0.676843 + 0.736128i \(0.736652\pi\)
\(710\) −3.64049 −0.136625
\(711\) 0 0
\(712\) 4.03705i 0.151295i
\(713\) −1.72335 9.77363i −0.0645402 0.366025i
\(714\) 0 0
\(715\) −2.66274 + 0.969157i −0.0995807 + 0.0362444i
\(716\) −14.3507 + 17.1025i −0.536311 + 0.639150i
\(717\) 0 0
\(718\) −0.0585778 0.0213206i −0.00218611 0.000795677i
\(719\) −22.3708 −0.834292 −0.417146 0.908840i \(-0.636970\pi\)
−0.417146 + 0.908840i \(0.636970\pi\)
\(720\) 0 0
\(721\) −15.4385 6.94287i −0.574961 0.258566i
\(722\) 53.0123 + 63.1776i 1.97291 + 2.35123i
\(723\) 0 0
\(724\) 14.2083 16.9327i 0.528046 0.629301i
\(725\) 3.56289 + 9.78896i 0.132322 + 0.363553i
\(726\) 0 0
\(727\) 2.58356 7.09828i 0.0958190 0.263261i −0.882518 0.470278i \(-0.844154\pi\)
0.978337 + 0.207018i \(0.0663758\pi\)
\(728\) 2.60675 0.264143i 0.0966126 0.00978978i
\(729\) 0 0
\(730\) 1.39086 + 2.40904i 0.0514781 + 0.0891627i
\(731\) 2.84731 2.38918i 0.105312 0.0883670i
\(732\) 0 0
\(733\) 16.7724 + 2.95743i 0.619503 + 0.109235i 0.474586 0.880209i \(-0.342598\pi\)
0.144916 + 0.989444i \(0.453709\pi\)
\(734\) 5.69560 32.3013i 0.210228 1.19226i
\(735\) 0 0
\(736\) 10.5742 8.87281i 0.389770 0.327056i
\(737\) 1.57534 + 0.909523i 0.0580284 + 0.0335027i
\(738\) 0 0
\(739\) −3.49112 6.04680i −0.128423 0.222435i 0.794643 0.607077i \(-0.207658\pi\)
−0.923066 + 0.384642i \(0.874325\pi\)
\(740\) 2.18747 1.83550i 0.0804129 0.0674745i
\(741\) 0 0
\(742\) −17.3243 + 8.36967i −0.635994 + 0.307260i
\(743\) 0.493042 + 1.35462i 0.0180880 + 0.0496962i 0.948408 0.317052i \(-0.102693\pi\)
−0.930320 + 0.366749i \(0.880471\pi\)
\(744\) 0 0
\(745\) −1.77262 + 4.87022i −0.0649436 + 0.178431i
\(746\) −27.7650 + 16.0301i −1.01655 + 0.586905i
\(747\) 0 0
\(748\) 12.0712 6.96930i 0.441366 0.254823i
\(749\) −2.11102 + 8.33412i −0.0771349 + 0.304522i
\(750\) 0 0
\(751\) 17.6380 6.41970i 0.643619 0.234258i 0.000470879 1.00000i \(-0.499850\pi\)
0.643148 + 0.765742i \(0.277628\pi\)
\(752\) 14.7189 5.35724i 0.536743 0.195358i
\(753\) 0 0
\(754\) 5.53897 0.976670i 0.201717 0.0355682i
\(755\) 7.29709 0.265568
\(756\) 0 0
\(757\) −6.53601 −0.237555 −0.118778 0.992921i \(-0.537898\pi\)
−0.118778 + 0.992921i \(0.537898\pi\)
\(758\) 36.9936 6.52297i 1.34367 0.236925i
\(759\) 0 0
\(760\) −2.03870 + 0.742027i −0.0739515 + 0.0269162i
\(761\) 3.33224 1.21283i 0.120793 0.0439652i −0.280916 0.959732i \(-0.590638\pi\)
0.401710 + 0.915767i \(0.368416\pi\)
\(762\) 0 0
\(763\) −9.07387 32.0962i −0.328496 1.16196i
\(764\) −18.7848 + 10.8454i −0.679609 + 0.392373i
\(765\) 0 0
\(766\) 62.6150 36.1508i 2.26237 1.30618i
\(767\) 2.74745 7.54856i 0.0992047 0.272563i
\(768\) 0 0
\(769\) −3.05429 8.39159i −0.110141 0.302609i 0.872361 0.488862i \(-0.162588\pi\)
−0.982502 + 0.186253i \(0.940366\pi\)
\(770\) 10.3188 + 7.01634i 0.371865 + 0.252852i
\(771\) 0 0
\(772\) 6.38118 5.35444i 0.229664 0.192711i
\(773\) −0.840279 1.45541i −0.0302227 0.0523473i 0.850518 0.525945i \(-0.176288\pi\)
−0.880741 + 0.473598i \(0.842955\pi\)
\(774\) 0 0
\(775\) −24.4759 14.1312i −0.879201 0.507607i
\(776\) 4.85124 4.07068i 0.174149 0.146129i
\(777\) 0 0
\(778\) −0.125481 + 0.711640i −0.00449872 + 0.0255135i
\(779\) −69.4237 12.2413i −2.48736 0.438589i
\(780\) 0 0
\(781\) 23.1551 19.4295i 0.828556 0.695241i
\(782\) −1.67658 2.90392i −0.0599543 0.103844i
\(783\) 0 0
\(784\) 14.4222 + 16.2601i 0.515080 + 0.580718i
\(785\) −0.488767 + 1.34288i −0.0174449 + 0.0479293i
\(786\) 0 0
\(787\) −6.73495 18.5041i −0.240075 0.659600i −0.999955 0.00953653i \(-0.996964\pi\)
0.759880 0.650064i \(-0.225258\pi\)
\(788\) 30.1435 35.9236i 1.07382 1.27973i
\(789\) 0 0
\(790\) −5.00126 5.96027i −0.177937 0.212057i
\(791\) 31.7163 22.8627i 1.12770 0.812906i
\(792\) 0 0
\(793\) −13.1479 −0.466895
\(794\) 5.15428 + 1.87601i 0.182919 + 0.0665769i
\(795\) 0 0
\(796\) 17.0194 20.2830i 0.603238 0.718912i
\(797\) −6.04013 + 2.19843i −0.213952 + 0.0778723i −0.446773 0.894647i \(-0.647427\pi\)
0.232820 + 0.972520i \(0.425205\pi\)
\(798\) 0 0
\(799\) −0.821008 4.65617i −0.0290452 0.164723i
\(800\) 39.3095i 1.38980i
\(801\) 0 0
\(802\) −36.1186 −1.27539
\(803\) −21.7037 7.89950i −0.765907 0.278767i
\(804\) 0 0
\(805\) 0.916571 1.34799i 0.0323049 0.0475103i
\(806\) −9.80851 + 11.6893i −0.345490 + 0.411739i
\(807\) 0 0
\(808\) 7.21155 + 8.59439i 0.253701 + 0.302350i
\(809\) 18.3341 + 10.5852i 0.644592 + 0.372155i 0.786381 0.617741i \(-0.211952\pi\)
−0.141789 + 0.989897i \(0.545285\pi\)
\(810\) 0 0
\(811\) 36.0138i 1.26461i 0.774718 + 0.632307i \(0.217892\pi\)
−0.774718 + 0.632307i \(0.782108\pi\)
\(812\) −9.63989 9.37895i −0.338294 0.329137i
\(813\) 0 0
\(814\) −7.58179 + 42.9985i −0.265742 + 1.50710i
\(815\) 4.77919 + 4.01022i 0.167408 + 0.140472i
\(816\) 0 0
\(817\) 10.3677 28.4849i 0.362718 0.996561i
\(818\) −24.1511 41.8310i −0.844424 1.46259i
\(819\) 0 0
\(820\) 3.94832 6.83869i 0.137881 0.238818i
\(821\) 18.5058 + 22.0543i 0.645855 + 0.769700i 0.985283 0.170932i \(-0.0546778\pi\)
−0.339428 + 0.940632i \(0.610233\pi\)
\(822\) 0 0
\(823\) −3.40065 + 19.2861i −0.118539 + 0.672270i 0.866397 + 0.499355i \(0.166430\pi\)
−0.984937 + 0.172915i \(0.944681\pi\)
\(824\) −3.86162 3.24028i −0.134526 0.112881i
\(825\) 0 0
\(826\) −34.0403 + 9.62349i −1.18441 + 0.334844i
\(827\) −13.9928 8.07875i −0.486577 0.280925i 0.236576 0.971613i \(-0.423975\pi\)
−0.723153 + 0.690687i \(0.757308\pi\)
\(828\) 0 0
\(829\) 32.1140i 1.11537i 0.830054 + 0.557683i \(0.188310\pi\)
−0.830054 + 0.557683i \(0.811690\pi\)
\(830\) −4.79381 + 0.845278i −0.166396 + 0.0293400i
\(831\) 0 0
\(832\) −13.2147 2.33011i −0.458138 0.0807821i
\(833\) 5.58946 3.43490i 0.193663 0.119012i
\(834\) 0 0
\(835\) 0.767997 + 4.35553i 0.0265776 + 0.150729i
\(836\) 56.8377 98.4458i 1.96577 3.40482i
\(837\) 0 0
\(838\) 42.0236 24.2623i 1.45168 0.838128i
\(839\) −4.91418 1.78862i −0.169656 0.0617499i 0.255795 0.966731i \(-0.417663\pi\)
−0.425452 + 0.904981i \(0.639885\pi\)
\(840\) 0 0
\(841\) 18.7105 + 15.7000i 0.645190 + 0.541379i
\(842\) −13.5236 37.1558i −0.466054 1.28047i
\(843\) 0 0
\(844\) 3.33246 + 18.8993i 0.114708 + 0.650541i
\(845\) −2.05712 + 3.56303i −0.0707670 + 0.122572i
\(846\) 0 0
\(847\) −74.1241 + 7.51101i −2.54693 + 0.258081i
\(848\) 10.6290 1.87419i 0.365003 0.0643598i
\(849\) 0 0
\(850\) −9.40393 1.65817i −0.322552 0.0568746i
\(851\) 5.61705 + 0.990437i 0.192550 + 0.0339518i
\(852\) 0 0
\(853\) 39.1762 6.90782i 1.34137 0.236519i 0.543529 0.839391i \(-0.317088\pi\)
0.797838 + 0.602871i \(0.205977\pi\)
\(854\) 33.8568 + 46.9677i 1.15856 + 1.60720i
\(855\) 0 0
\(856\) −1.28011 + 2.21721i −0.0437532 + 0.0757828i
\(857\) −7.52170 42.6577i −0.256936 1.45716i −0.791053 0.611747i \(-0.790467\pi\)
0.534117 0.845410i \(-0.320644\pi\)
\(858\) 0 0
\(859\) 4.68725 + 12.8781i 0.159927 + 0.439395i 0.993613 0.112844i \(-0.0359959\pi\)
−0.833686 + 0.552239i \(0.813774\pi\)
\(860\) 2.60117 + 2.18264i 0.0886993 + 0.0744275i
\(861\) 0 0
\(862\) 79.5171 + 28.9419i 2.70836 + 0.985764i
\(863\) 24.1671 13.9529i 0.822659 0.474962i −0.0286735 0.999589i \(-0.509128\pi\)
0.851333 + 0.524626i \(0.175795\pi\)
\(864\) 0 0
\(865\) 3.80390 6.58855i 0.129336 0.224017i
\(866\) 2.02524 + 11.4857i 0.0688204 + 0.390300i
\(867\) 0 0
\(868\) 36.3908 + 2.68129i 1.23519 + 0.0910088i
\(869\) 63.6205 + 11.2180i 2.15818 + 0.380545i
\(870\) 0 0
\(871\) −0.359817 + 0.0634454i −0.0121919 + 0.00214976i
\(872\) 9.93263i 0.336361i
\(873\) 0 0
\(874\) −23.6828 13.6732i −0.801081 0.462504i
\(875\) −2.55938 9.05306i −0.0865228 0.306049i
\(876\) 0 0
\(877\) −28.2148 23.6751i −0.952748 0.799450i 0.0270106 0.999635i \(-0.491401\pi\)
−0.979758 + 0.200185i \(0.935846\pi\)
\(878\) −12.4166 + 70.4181i −0.419040 + 2.37649i
\(879\) 0 0
\(880\) −4.49943 5.36221i −0.151676 0.180760i
\(881\) 23.0421 39.9101i 0.776309 1.34461i −0.157747 0.987480i \(-0.550423\pi\)
0.934056 0.357127i \(-0.116244\pi\)
\(882\) 0 0
\(883\) −18.9002 32.7361i −0.636043 1.10166i −0.986293 0.165002i \(-0.947237\pi\)
0.350251 0.936656i \(-0.386096\pi\)
\(884\) −0.957540 + 2.63082i −0.0322056 + 0.0884840i
\(885\) 0 0
\(886\) 21.2973 + 17.8705i 0.715495 + 0.600372i
\(887\) 0.236461 1.34104i 0.00793958 0.0450276i −0.980581 0.196117i \(-0.937167\pi\)
0.988520 + 0.151089i \(0.0482780\pi\)
\(888\) 0 0
\(889\) 35.9642 + 9.10965i 1.20620 + 0.305528i
\(890\) 3.86177i 0.129447i
\(891\) 0 0
\(892\) −13.3410 7.70245i −0.446691 0.257897i
\(893\) −24.7852 29.5378i −0.829405 0.988446i
\(894\) 0 0
\(895\) 2.17536 2.59250i 0.0727143 0.0866576i
\(896\) 7.12581 + 14.7496i 0.238057 + 0.492750i
\(897\) 0 0
\(898\) 23.8936 + 8.69657i 0.797341 + 0.290208i
\(899\) 12.4126 0.413984
\(900\) 0 0
\(901\) 3.25784i 0.108535i
\(902\) 20.9665 + 118.907i 0.698109 + 3.95917i
\(903\) 0 0
\(904\) 10.9408 3.98214i 0.363887 0.132444i
\(905\) −2.15377 + 2.56676i −0.0715938 + 0.0853221i
\(906\) 0 0
\(907\) 29.4991 + 10.7368i 0.979502 + 0.356510i 0.781647 0.623722i \(-0.214380\pi\)
0.197855 + 0.980231i \(0.436602\pi\)
\(908\) −16.4856 −0.547095
\(909\) 0 0
\(910\) −2.49357 + 0.252675i −0.0826612 + 0.00837608i
\(911\) 23.0479 + 27.4674i 0.763610 + 0.910034i 0.998070 0.0620911i \(-0.0197769\pi\)
−0.234461 + 0.972126i \(0.575332\pi\)
\(912\) 0 0
\(913\) 25.9795 30.9612i 0.859796 1.02467i
\(914\) −10.2403 28.1350i −0.338719 0.930622i
\(915\) 0 0
\(916\) −15.0022 + 41.2183i −0.495688 + 1.36189i
\(917\) 4.05697 + 5.62801i 0.133973 + 0.185853i
\(918\) 0 0
\(919\) −10.7450 18.6110i −0.354446 0.613919i 0.632577 0.774498i \(-0.281997\pi\)
−0.987023 + 0.160579i \(0.948664\pi\)
\(920\) 0.371858 0.312026i 0.0122598 0.0102872i
\(921\) 0 0
\(922\) −51.0432 9.00029i −1.68102 0.296409i
\(923\) −1.05427 + 5.97904i −0.0347016 + 0.196802i
\(924\) 0 0
\(925\) 12.4427 10.4407i 0.409113 0.343287i
\(926\) −31.9406 18.4409i −1.04963 0.606005i
\(927\) 0 0
\(928\) 8.63222 + 14.9514i 0.283366 + 0.490805i
\(929\) −30.1571 + 25.3048i −0.989422 + 0.830224i −0.985484 0.169769i \(-0.945698\pi\)
−0.00393798 + 0.999992i \(0.501253\pi\)
\(930\) 0 0
\(931\) 25.4707 47.0524i 0.834770 1.54208i
\(932\) −19.5572 53.7330i −0.640618 1.76008i
\(933\) 0 0
\(934\) −2.55503 + 7.01988i −0.0836031 + 0.229697i
\(935\) −1.82982 + 1.05645i −0.0598415 + 0.0345495i
\(936\) 0 0
\(937\) 42.7796 24.6988i 1.39755 0.806875i 0.403413 0.915018i \(-0.367824\pi\)
0.994135 + 0.108143i \(0.0344905\pi\)
\(938\) 1.15320 + 1.12198i 0.0376533 + 0.0366340i
\(939\) 0 0
\(940\) 4.05879 1.47728i 0.132383 0.0481836i
\(941\) −14.3771 + 5.23283i −0.468679 + 0.170585i −0.565554 0.824711i \(-0.691338\pi\)
0.0968746 + 0.995297i \(0.469115\pi\)
\(942\) 0 0
\(943\) 15.5333 2.73893i 0.505833 0.0891920i
\(944\) 19.8438 0.645862
\(945\) 0 0
\(946\) −51.9193 −1.68804
\(947\) −8.19844 + 1.44561i −0.266413 + 0.0469759i −0.305259 0.952269i \(-0.598743\pi\)
0.0388456 + 0.999245i \(0.487632\pi\)
\(948\) 0 0
\(949\) 4.35933 1.58667i 0.141510 0.0515054i
\(950\) −73.1798 + 26.6353i −2.37427 + 0.864162i
\(951\) 0 0
\(952\) 1.87999 0.531490i 0.0609309 0.0172257i
\(953\) 11.5050 6.64241i 0.372683 0.215169i −0.301947 0.953325i \(-0.597637\pi\)
0.674630 + 0.738156i \(0.264303\pi\)
\(954\) 0 0
\(955\) 2.84750 1.64401i 0.0921431 0.0531988i
\(956\) 4.50573 12.3794i 0.145726 0.400378i
\(957\) 0 0
\(958\) −4.59825 12.6336i −0.148563 0.408172i
\(959\) 25.7031 + 1.89381i 0.829997 + 0.0611544i
\(960\) 0 0
\(961\) −2.04997 + 1.72013i −0.0661281 + 0.0554881i
\(962\) −4.38488 7.59484i −0.141374 0.244867i
\(963\) 0 0
\(964\) −20.9812 12.1135i −0.675759 0.390150i
\(965\) −0.967296 + 0.811658i −0.0311384 + 0.0261282i
\(966\) 0 0
\(967\) −2.63510 + 14.9444i −0.0847390 + 0.480579i 0.912674 + 0.408689i \(0.134014\pi\)
−0.997413 + 0.0718894i \(0.977097\pi\)
\(968\) −21.8496 3.85267i −0.702272 0.123829i
\(969\) 0 0
\(970\) −4.64062 + 3.89394i −0.149001 + 0.125027i
\(971\) −1.28302 2.22225i −0.0411740 0.0713155i 0.844704 0.535234i \(-0.179776\pi\)
−0.885878 + 0.463918i \(0.846443\pi\)
\(972\) 0 0
\(973\) 0.0346950 + 0.342395i 0.00111227 + 0.0109767i
\(974\) 12.6745 34.8228i 0.406116 1.11579i
\(975\) 0 0
\(976\) −11.1085 30.5203i −0.355574 0.976932i
\(977\) 7.16223 8.53562i 0.229140 0.273079i −0.639208 0.769034i \(-0.720738\pi\)
0.868348 + 0.495955i \(0.165182\pi\)
\(978\) 0 0
\(979\) 20.6105 + 24.5626i 0.658714 + 0.785025i
\(980\) 3.97699 + 4.48379i 0.127040 + 0.143229i
\(981\) 0 0
\(982\) −25.6447 −0.818355
\(983\) 45.0396 + 16.3931i 1.43654 + 0.522858i 0.938798 0.344468i \(-0.111941\pi\)
0.497742 + 0.867325i \(0.334163\pi\)
\(984\) 0 0
\(985\) −4.56933 + 5.44551i −0.145591 + 0.173508i
\(986\) 3.94093 1.43438i 0.125505 0.0456800i
\(987\) 0 0
\(988\) 3.96482 + 22.4856i 0.126138 + 0.715362i
\(989\) 6.78241i 0.215668i
\(990\) 0 0
\(991\) 22.6953 0.720940 0.360470 0.932771i \(-0.382616\pi\)
0.360470 + 0.932771i \(0.382616\pi\)
\(992\) −44.0145 16.0200i −1.39746 0.508635i
\(993\) 0 0
\(994\) 24.0735 11.6304i 0.763565 0.368892i
\(995\) −2.57991 + 3.07461i −0.0817885 + 0.0974718i
\(996\) 0 0
\(997\) −12.8968 15.3698i −0.408446 0.486767i 0.522130 0.852866i \(-0.325138\pi\)
−0.930576 + 0.366099i \(0.880693\pi\)
\(998\) 9.04381 + 5.22145i 0.286277 + 0.165282i
\(999\) 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 567.2.bd.a.17.19 132
3.2 odd 2 189.2.bd.a.185.4 yes 132
7.5 odd 6 567.2.ba.a.341.4 132
21.5 even 6 189.2.ba.a.131.19 yes 132
27.7 even 9 189.2.ba.a.101.19 132
27.20 odd 18 567.2.ba.a.143.4 132
189.47 even 18 inner 567.2.bd.a.467.19 132
189.61 odd 18 189.2.bd.a.47.4 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.ba.a.101.19 132 27.7 even 9
189.2.ba.a.131.19 yes 132 21.5 even 6
189.2.bd.a.47.4 yes 132 189.61 odd 18
189.2.bd.a.185.4 yes 132 3.2 odd 2
567.2.ba.a.143.4 132 27.20 odd 18
567.2.ba.a.341.4 132 7.5 odd 6
567.2.bd.a.17.19 132 1.1 even 1 trivial
567.2.bd.a.467.19 132 189.47 even 18 inner