Properties

Label 729.2.e.t.406.2
Level $729$
Weight $2$
Character 729.406
Analytic conductor $5.821$
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] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, 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("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 406.2
Root \(-1.13697i\) of defining polynomial
Character \(\chi\) \(=\) 729.406
Dual form 729.2.e.t.325.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.595778 + 0.499917i) q^{2} +(-0.242262 - 1.37394i) q^{4} +(-2.23304 - 0.812759i) q^{5} +(-0.434359 + 2.46337i) q^{7} +(1.32025 - 2.28674i) q^{8} +O(q^{10})\) \(q+(0.595778 + 0.499917i) q^{2} +(-0.242262 - 1.37394i) q^{4} +(-2.23304 - 0.812759i) q^{5} +(-0.434359 + 2.46337i) q^{7} +(1.32025 - 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(-2.95192 + 1.07441i) q^{11} +(1.02392 - 0.859169i) q^{13} +(-1.49026 + 1.25048i) q^{14} +(-0.692233 + 0.251952i) q^{16} +(-3.13726 - 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(-0.575699 + 3.26495i) q^{20} +(-2.29581 - 0.835605i) q^{22} +(0.704074 + 3.99300i) q^{23} +(0.495652 + 0.415902i) q^{25} +1.03954 q^{26} +3.48975 q^{28} +(-7.11443 - 5.96971i) q^{29} +(0.491741 + 2.78880i) q^{31} +(-5.50090 - 2.00216i) q^{32} +(0.847385 - 4.80576i) q^{34} +(2.97207 - 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(-5.89391 + 2.14521i) q^{38} +(-4.80674 + 4.03334i) q^{40} +(-5.44333 + 4.56750i) q^{41} +(-2.19597 + 0.799267i) q^{43} +(2.19131 + 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(-0.801248 + 4.54411i) q^{47} +(0.698301 + 0.254161i) q^{49} +(0.0873823 + 0.495570i) q^{50} +(-1.42850 - 1.19865i) q^{52} +0.135496 q^{53} +7.46499 q^{55} +(5.05964 + 4.24554i) q^{56} +(-1.25426 - 7.11324i) q^{58} +(3.75759 + 1.36765i) q^{59} +(0.0593526 - 0.336605i) q^{61} +(-1.10120 + 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(-2.98474 + 1.08636i) q^{65} +(7.75461 - 6.50689i) q^{67} +(-6.70579 + 5.62682i) q^{68} +(4.34415 - 1.58114i) q^{70} +(-4.09540 - 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(0.747095 - 4.23698i) q^{74} +(10.5728 + 3.84817i) q^{76} +(-1.36448 - 7.73837i) q^{77} +(3.12600 + 2.62302i) q^{79} +1.75056 q^{80} -5.52638 q^{82} +(0.699573 + 0.587012i) q^{83} +(2.58917 + 14.6839i) q^{85} +(-1.70788 - 0.621616i) q^{86} +(-1.44038 + 8.16879i) q^{88} +(1.86437 - 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(5.31556 - 1.93471i) q^{92} +(-2.74904 + 2.30672i) q^{94} +(14.6809 - 12.3187i) q^{95} +(5.63467 - 2.05085i) q^{97} +(0.288973 + 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.595778 + 0.499917i 0.421278 + 0.353495i 0.828649 0.559768i \(-0.189110\pi\)
−0.407371 + 0.913263i \(0.633554\pi\)
\(3\) 0 0
\(4\) −0.242262 1.37394i −0.121131 0.686969i
\(5\) −2.23304 0.812759i −0.998644 0.363477i −0.209583 0.977791i \(-0.567211\pi\)
−0.789062 + 0.614314i \(0.789433\pi\)
\(6\) 0 0
\(7\) −0.434359 + 2.46337i −0.164172 + 0.931068i 0.785741 + 0.618555i \(0.212282\pi\)
−0.949914 + 0.312513i \(0.898829\pi\)
\(8\) 1.32025 2.28674i 0.466780 0.808486i
\(9\) 0 0
\(10\) −0.924081 1.60056i −0.292220 0.506140i
\(11\) −2.95192 + 1.07441i −0.890038 + 0.323947i −0.746254 0.665662i \(-0.768149\pi\)
−0.143784 + 0.989609i \(0.545927\pi\)
\(12\) 0 0
\(13\) 1.02392 0.859169i 0.283984 0.238291i −0.489657 0.871915i \(-0.662878\pi\)
0.773641 + 0.633624i \(0.218434\pi\)
\(14\) −1.49026 + 1.25048i −0.398290 + 0.334205i
\(15\) 0 0
\(16\) −0.692233 + 0.251952i −0.173058 + 0.0629881i
\(17\) −3.13726 5.43389i −0.760897 1.31791i −0.942389 0.334520i \(-0.891426\pi\)
0.181492 0.983392i \(-0.441907\pi\)
\(18\) 0 0
\(19\) −4.03234 + 6.98422i −0.925083 + 1.60229i −0.133656 + 0.991028i \(0.542672\pi\)
−0.791427 + 0.611263i \(0.790662\pi\)
\(20\) −0.575699 + 3.26495i −0.128730 + 0.730066i
\(21\) 0 0
\(22\) −2.29581 0.835605i −0.489467 0.178152i
\(23\) 0.704074 + 3.99300i 0.146810 + 0.832598i 0.965896 + 0.258929i \(0.0833695\pi\)
−0.819087 + 0.573669i \(0.805519\pi\)
\(24\) 0 0
\(25\) 0.495652 + 0.415902i 0.0991305 + 0.0831803i
\(26\) 1.03954 0.203871
\(27\) 0 0
\(28\) 3.48975 0.659501
\(29\) −7.11443 5.96971i −1.32112 1.10855i −0.986067 0.166347i \(-0.946803\pi\)
−0.335049 0.942201i \(-0.608753\pi\)
\(30\) 0 0
\(31\) 0.491741 + 2.78880i 0.0883192 + 0.500883i 0.996591 + 0.0825022i \(0.0262912\pi\)
−0.908272 + 0.418381i \(0.862598\pi\)
\(32\) −5.50090 2.00216i −0.972430 0.353936i
\(33\) 0 0
\(34\) 0.847385 4.80576i 0.145325 0.824181i
\(35\) 2.97207 5.14778i 0.502372 0.870133i
\(36\) 0 0
\(37\) −2.76596 4.79078i −0.454720 0.787599i 0.543952 0.839117i \(-0.316927\pi\)
−0.998672 + 0.0515178i \(0.983594\pi\)
\(38\) −5.89391 + 2.14521i −0.956119 + 0.347999i
\(39\) 0 0
\(40\) −4.80674 + 4.03334i −0.760013 + 0.637726i
\(41\) −5.44333 + 4.56750i −0.850105 + 0.713323i −0.959813 0.280641i \(-0.909453\pi\)
0.109708 + 0.993964i \(0.465009\pi\)
\(42\) 0 0
\(43\) −2.19597 + 0.799267i −0.334882 + 0.121887i −0.503988 0.863711i \(-0.668134\pi\)
0.169106 + 0.985598i \(0.445912\pi\)
\(44\) 2.19131 + 3.79547i 0.330353 + 0.572188i
\(45\) 0 0
\(46\) −1.57670 + 2.73092i −0.232471 + 0.402652i
\(47\) −0.801248 + 4.54411i −0.116874 + 0.662826i 0.868931 + 0.494933i \(0.164807\pi\)
−0.985805 + 0.167893i \(0.946304\pi\)
\(48\) 0 0
\(49\) 0.698301 + 0.254161i 0.0997573 + 0.0363087i
\(50\) 0.0873823 + 0.495570i 0.0123577 + 0.0700842i
\(51\) 0 0
\(52\) −1.42850 1.19865i −0.198097 0.166224i
\(53\) 0.135496 0.0186118 0.00930588 0.999957i \(-0.497038\pi\)
0.00930588 + 0.999957i \(0.497038\pi\)
\(54\) 0 0
\(55\) 7.46499 1.00658
\(56\) 5.05964 + 4.24554i 0.676123 + 0.567335i
\(57\) 0 0
\(58\) −1.25426 7.11324i −0.164692 0.934015i
\(59\) 3.75759 + 1.36765i 0.489196 + 0.178053i 0.574828 0.818274i \(-0.305069\pi\)
−0.0856324 + 0.996327i \(0.527291\pi\)
\(60\) 0 0
\(61\) 0.0593526 0.336605i 0.00759932 0.0430979i −0.980772 0.195156i \(-0.937479\pi\)
0.988372 + 0.152058i \(0.0485899\pi\)
\(62\) −1.10120 + 1.90733i −0.139852 + 0.242232i
\(63\) 0 0
\(64\) −1.53974 2.66690i −0.192467 0.333363i
\(65\) −2.98474 + 1.08636i −0.370212 + 0.134746i
\(66\) 0 0
\(67\) 7.75461 6.50689i 0.947376 0.794943i −0.0314778 0.999504i \(-0.510021\pi\)
0.978854 + 0.204562i \(0.0655769\pi\)
\(68\) −6.70579 + 5.62682i −0.813196 + 0.682353i
\(69\) 0 0
\(70\) 4.34415 1.58114i 0.519225 0.188983i
\(71\) −4.09540 7.09344i −0.486035 0.841837i 0.513837 0.857888i \(-0.328224\pi\)
−0.999871 + 0.0160515i \(0.994890\pi\)
\(72\) 0 0
\(73\) 6.15722 10.6646i 0.720648 1.24820i −0.240092 0.970750i \(-0.577178\pi\)
0.960740 0.277449i \(-0.0894890\pi\)
\(74\) 0.747095 4.23698i 0.0868480 0.492539i
\(75\) 0 0
\(76\) 10.5728 + 3.84817i 1.21278 + 0.441416i
\(77\) −1.36448 7.73837i −0.155497 0.881869i
\(78\) 0 0
\(79\) 3.12600 + 2.62302i 0.351702 + 0.295113i 0.801473 0.598031i \(-0.204050\pi\)
−0.449771 + 0.893144i \(0.648494\pi\)
\(80\) 1.75056 0.195718
\(81\) 0 0
\(82\) −5.52638 −0.610287
\(83\) 0.699573 + 0.587012i 0.0767881 + 0.0644329i 0.680374 0.732865i \(-0.261817\pi\)
−0.603586 + 0.797298i \(0.706262\pi\)
\(84\) 0 0
\(85\) 2.58917 + 14.6839i 0.280835 + 1.59269i
\(86\) −1.70788 0.621616i −0.184165 0.0670306i
\(87\) 0 0
\(88\) −1.44038 + 8.16879i −0.153545 + 0.870795i
\(89\) 1.86437 3.22919i 0.197623 0.342293i −0.750134 0.661286i \(-0.770011\pi\)
0.947757 + 0.318992i \(0.103344\pi\)
\(90\) 0 0
\(91\) 1.67171 + 2.89548i 0.175243 + 0.303529i
\(92\) 5.31556 1.93471i 0.554186 0.201707i
\(93\) 0 0
\(94\) −2.74904 + 2.30672i −0.283542 + 0.237920i
\(95\) 14.6809 12.3187i 1.50622 1.26387i
\(96\) 0 0
\(97\) 5.63467 2.05085i 0.572115 0.208233i −0.0397303 0.999210i \(-0.512650\pi\)
0.611845 + 0.790978i \(0.290428\pi\)
\(98\) 0.288973 + 0.500515i 0.0291907 + 0.0505597i
\(99\) 0 0
\(100\) 0.451345 0.781752i 0.0451345 0.0781752i
\(101\) 1.77498 10.0664i 0.176617 1.00165i −0.759643 0.650340i \(-0.774626\pi\)
0.936261 0.351306i \(-0.114262\pi\)
\(102\) 0 0
\(103\) −8.01939 2.91882i −0.790174 0.287600i −0.0847658 0.996401i \(-0.527014\pi\)
−0.705409 + 0.708801i \(0.749236\pi\)
\(104\) −0.612870 3.47576i −0.0600968 0.340826i
\(105\) 0 0
\(106\) 0.0807253 + 0.0677366i 0.00784073 + 0.00657916i
\(107\) −7.74500 −0.748738 −0.374369 0.927280i \(-0.622141\pi\)
−0.374369 + 0.927280i \(0.622141\pi\)
\(108\) 0 0
\(109\) 1.25438 0.120148 0.0600738 0.998194i \(-0.480866\pi\)
0.0600738 + 0.998194i \(0.480866\pi\)
\(110\) 4.44747 + 3.73187i 0.424050 + 0.355820i
\(111\) 0 0
\(112\) −0.319975 1.81467i −0.0302348 0.171470i
\(113\) 16.6897 + 6.07454i 1.57003 + 0.571445i 0.973006 0.230778i \(-0.0741271\pi\)
0.597025 + 0.802223i \(0.296349\pi\)
\(114\) 0 0
\(115\) 1.67312 9.48876i 0.156020 0.884831i
\(116\) −6.47846 + 11.2210i −0.601509 + 1.04185i
\(117\) 0 0
\(118\) 1.55497 + 2.69329i 0.143147 + 0.247938i
\(119\) 14.7484 5.36798i 1.35198 0.492082i
\(120\) 0 0
\(121\) −0.867002 + 0.727501i −0.0788184 + 0.0661365i
\(122\) 0.203636 0.170871i 0.0184363 0.0154699i
\(123\) 0 0
\(124\) 3.71250 1.35124i 0.333393 0.121345i
\(125\) 5.17209 + 8.95832i 0.462606 + 0.801256i
\(126\) 0 0
\(127\) 1.98279 3.43429i 0.175944 0.304744i −0.764543 0.644572i \(-0.777036\pi\)
0.940488 + 0.339828i \(0.110369\pi\)
\(128\) −1.61716 + 9.17137i −0.142938 + 0.810643i
\(129\) 0 0
\(130\) −2.32133 0.844896i −0.203594 0.0741022i
\(131\) −0.0177987 0.100941i −0.00155508 0.00881927i 0.984020 0.178056i \(-0.0569808\pi\)
−0.985575 + 0.169237i \(0.945870\pi\)
\(132\) 0 0
\(133\) −15.4533 12.9668i −1.33997 1.12437i
\(134\) 7.87292 0.680117
\(135\) 0 0
\(136\) −16.5679 −1.42068
\(137\) −5.83691 4.89775i −0.498681 0.418443i 0.358444 0.933551i \(-0.383307\pi\)
−0.857125 + 0.515108i \(0.827752\pi\)
\(138\) 0 0
\(139\) −1.81301 10.2821i −0.153778 0.872117i −0.959895 0.280361i \(-0.909546\pi\)
0.806117 0.591756i \(-0.201565\pi\)
\(140\) −7.79274 2.83633i −0.658607 0.239713i
\(141\) 0 0
\(142\) 1.10618 6.27347i 0.0928288 0.526458i
\(143\) −2.09943 + 3.63631i −0.175563 + 0.304084i
\(144\) 0 0
\(145\) 11.0348 + 19.1129i 0.916394 + 1.58724i
\(146\) 8.99975 3.27564i 0.744825 0.271094i
\(147\) 0 0
\(148\) −5.91214 + 4.96087i −0.485975 + 0.407781i
\(149\) 6.91936 5.80603i 0.566856 0.475648i −0.313745 0.949507i \(-0.601584\pi\)
0.880601 + 0.473859i \(0.157139\pi\)
\(150\) 0 0
\(151\) −22.4496 + 8.17099i −1.82692 + 0.664946i −0.833216 + 0.552948i \(0.813503\pi\)
−0.993708 + 0.111998i \(0.964275\pi\)
\(152\) 10.6474 + 18.4419i 0.863620 + 1.49583i
\(153\) 0 0
\(154\) 3.05561 5.29248i 0.246228 0.426480i
\(155\) 1.16855 6.62716i 0.0938599 0.532306i
\(156\) 0 0
\(157\) −2.54843 0.927554i −0.203387 0.0740269i 0.238318 0.971187i \(-0.423404\pi\)
−0.441705 + 0.897160i \(0.645626\pi\)
\(158\) 0.551105 + 3.12547i 0.0438436 + 0.248649i
\(159\) 0 0
\(160\) 10.6564 + 8.94180i 0.842465 + 0.706912i
\(161\) −10.1421 −0.799308
\(162\) 0 0
\(163\) −22.0489 −1.72701 −0.863504 0.504343i \(-0.831735\pi\)
−0.863504 + 0.504343i \(0.831735\pi\)
\(164\) 7.59416 + 6.37226i 0.593005 + 0.497590i
\(165\) 0 0
\(166\) 0.123333 + 0.699457i 0.00957251 + 0.0542884i
\(167\) 8.41101 + 3.06136i 0.650863 + 0.236895i 0.646287 0.763095i \(-0.276321\pi\)
0.00457649 + 0.999990i \(0.498543\pi\)
\(168\) 0 0
\(169\) −1.94719 + 11.0431i −0.149784 + 0.849466i
\(170\) −5.79816 + 10.0427i −0.444699 + 0.770241i
\(171\) 0 0
\(172\) 1.63014 + 2.82349i 0.124297 + 0.215289i
\(173\) 2.47538 0.900966i 0.188200 0.0684992i −0.246201 0.969219i \(-0.579182\pi\)
0.434401 + 0.900720i \(0.356960\pi\)
\(174\) 0 0
\(175\) −1.23981 + 1.04033i −0.0937211 + 0.0786413i
\(176\) 1.77272 1.48749i 0.133624 0.112124i
\(177\) 0 0
\(178\) 2.72508 0.991847i 0.204253 0.0743421i
\(179\) 1.84227 + 3.19090i 0.137697 + 0.238499i 0.926625 0.375988i \(-0.122697\pi\)
−0.788927 + 0.614487i \(0.789363\pi\)
\(180\) 0 0
\(181\) 0.134255 0.232536i 0.00997906 0.0172842i −0.860993 0.508617i \(-0.830157\pi\)
0.870972 + 0.491333i \(0.163490\pi\)
\(182\) −0.451534 + 2.56078i −0.0334699 + 0.189817i
\(183\) 0 0
\(184\) 10.0605 + 3.66173i 0.741672 + 0.269946i
\(185\) 2.28273 + 12.9460i 0.167830 + 0.951811i
\(186\) 0 0
\(187\) 15.0992 + 12.6697i 1.10416 + 0.926502i
\(188\) 6.43743 0.469498
\(189\) 0 0
\(190\) 14.9049 1.08131
\(191\) 1.83696 + 1.54140i 0.132918 + 0.111531i 0.706823 0.707390i \(-0.250128\pi\)
−0.573905 + 0.818922i \(0.694572\pi\)
\(192\) 0 0
\(193\) 0.0861647 + 0.488664i 0.00620227 + 0.0351748i 0.987752 0.156033i \(-0.0498706\pi\)
−0.981550 + 0.191208i \(0.938760\pi\)
\(194\) 4.38227 + 1.59502i 0.314629 + 0.114515i
\(195\) 0 0
\(196\) 0.180029 1.02099i 0.0128592 0.0729282i
\(197\) −11.0734 + 19.1797i −0.788946 + 1.36649i 0.137667 + 0.990479i \(0.456040\pi\)
−0.926613 + 0.376016i \(0.877294\pi\)
\(198\) 0 0
\(199\) −1.06624 1.84677i −0.0755834 0.130914i 0.825756 0.564027i \(-0.190749\pi\)
−0.901340 + 0.433113i \(0.857415\pi\)
\(200\) 1.60545 0.584335i 0.113522 0.0413187i
\(201\) 0 0
\(202\) 6.08987 5.11001i 0.428482 0.359539i
\(203\) 17.7959 14.9325i 1.24902 1.04806i
\(204\) 0 0
\(205\) 15.8674 5.77527i 1.10823 0.403362i
\(206\) −3.31861 5.74800i −0.231218 0.400482i
\(207\) 0 0
\(208\) −0.492320 + 0.852724i −0.0341363 + 0.0591257i
\(209\) 4.39923 24.9493i 0.304301 1.72578i
\(210\) 0 0
\(211\) −18.8019 6.84334i −1.29438 0.471115i −0.399216 0.916857i \(-0.630718\pi\)
−0.895162 + 0.445742i \(0.852940\pi\)
\(212\) −0.0328255 0.186163i −0.00225446 0.0127857i
\(213\) 0 0
\(214\) −4.61430 3.87186i −0.315427 0.264675i
\(215\) 5.55329 0.378731
\(216\) 0 0
\(217\) −7.08345 −0.480856
\(218\) 0.747330 + 0.627084i 0.0506156 + 0.0424715i
\(219\) 0 0
\(220\) −1.80848 10.2564i −0.121928 0.691488i
\(221\) −7.88093 2.86842i −0.530129 0.192951i
\(222\) 0 0
\(223\) −2.30578 + 13.0767i −0.154407 + 0.875683i 0.804920 + 0.593384i \(0.202208\pi\)
−0.959326 + 0.282299i \(0.908903\pi\)
\(224\) 7.32144 12.6811i 0.489185 0.847292i
\(225\) 0 0
\(226\) 6.90656 + 11.9625i 0.459418 + 0.795735i
\(227\) −11.7188 + 4.26531i −0.777807 + 0.283099i −0.700258 0.713890i \(-0.746932\pi\)
−0.0775490 + 0.996989i \(0.524709\pi\)
\(228\) 0 0
\(229\) 19.6579 16.4949i 1.29903 1.09002i 0.308719 0.951153i \(-0.400100\pi\)
0.990312 0.138862i \(-0.0443445\pi\)
\(230\) 5.74040 4.81677i 0.378511 0.317608i
\(231\) 0 0
\(232\) −23.0440 + 8.38735i −1.51292 + 0.550656i
\(233\) −2.69821 4.67344i −0.176766 0.306167i 0.764005 0.645210i \(-0.223230\pi\)
−0.940771 + 0.339043i \(0.889897\pi\)
\(234\) 0 0
\(235\) 5.48248 9.49593i 0.357637 0.619446i
\(236\) 0.968743 5.49402i 0.0630598 0.357630i
\(237\) 0 0
\(238\) 11.4703 + 4.17485i 0.743510 + 0.270616i
\(239\) −1.45362 8.24387i −0.0940266 0.533252i −0.995041 0.0994629i \(-0.968288\pi\)
0.901015 0.433789i \(-0.142824\pi\)
\(240\) 0 0
\(241\) −0.338737 0.284234i −0.0218200 0.0183091i 0.631812 0.775121i \(-0.282311\pi\)
−0.653632 + 0.756812i \(0.726756\pi\)
\(242\) −0.880231 −0.0565834
\(243\) 0 0
\(244\) −0.476854 −0.0305274
\(245\) −1.35276 1.13510i −0.0864246 0.0725189i
\(246\) 0 0
\(247\) 1.87184 + 10.6157i 0.119102 + 0.675463i
\(248\) 7.02649 + 2.55743i 0.446183 + 0.162397i
\(249\) 0 0
\(250\) −1.39700 + 7.92278i −0.0883540 + 0.501080i
\(251\) 8.51427 14.7471i 0.537416 0.930832i −0.461626 0.887074i \(-0.652734\pi\)
0.999042 0.0437571i \(-0.0139328\pi\)
\(252\) 0 0
\(253\) −6.36850 11.0306i −0.400384 0.693486i
\(254\) 2.89816 1.05484i 0.181847 0.0661869i
\(255\) 0 0
\(256\) −10.2664 + 8.61455i −0.641651 + 0.538409i
\(257\) −15.9925 + 13.4193i −0.997584 + 0.837073i −0.986648 0.162867i \(-0.947926\pi\)
−0.0109365 + 0.999940i \(0.503481\pi\)
\(258\) 0 0
\(259\) 13.0029 4.73267i 0.807961 0.294074i
\(260\) 2.21568 + 3.83767i 0.137411 + 0.238002i
\(261\) 0 0
\(262\) 0.0398582 0.0690364i 0.00246245 0.00426508i
\(263\) −3.36731 + 19.0970i −0.207637 + 1.17757i 0.685599 + 0.727980i \(0.259541\pi\)
−0.893236 + 0.449589i \(0.851571\pi\)
\(264\) 0 0
\(265\) −0.302567 0.110125i −0.0185865 0.00676495i
\(266\) −2.72438 15.4507i −0.167042 0.947343i
\(267\) 0 0
\(268\) −10.8187 9.07797i −0.660857 0.554525i
\(269\) −18.6791 −1.13889 −0.569443 0.822031i \(-0.692841\pi\)
−0.569443 + 0.822031i \(0.692841\pi\)
\(270\) 0 0
\(271\) 12.9378 0.785917 0.392958 0.919556i \(-0.371452\pi\)
0.392958 + 0.919556i \(0.371452\pi\)
\(272\) 3.54080 + 2.97108i 0.214692 + 0.180148i
\(273\) 0 0
\(274\) −1.02903 5.83594i −0.0621662 0.352562i
\(275\) −1.90998 0.695175i −0.115176 0.0419206i
\(276\) 0 0
\(277\) 1.81312 10.2827i 0.108940 0.617828i −0.880634 0.473798i \(-0.842883\pi\)
0.989573 0.144030i \(-0.0460061\pi\)
\(278\) 4.06005 7.03221i 0.243505 0.421764i
\(279\) 0 0
\(280\) −7.84776 13.5927i −0.468994 0.812321i
\(281\) 13.4806 4.90655i 0.804187 0.292700i 0.0929668 0.995669i \(-0.470365\pi\)
0.711221 + 0.702969i \(0.248143\pi\)
\(282\) 0 0
\(283\) −14.3194 + 12.0154i −0.851198 + 0.714240i −0.960053 0.279818i \(-0.909726\pi\)
0.108855 + 0.994058i \(0.465282\pi\)
\(284\) −8.75378 + 7.34530i −0.519441 + 0.435863i
\(285\) 0 0
\(286\) −3.06864 + 1.11689i −0.181453 + 0.0660434i
\(287\) −8.88709 15.3929i −0.524588 0.908614i
\(288\) 0 0
\(289\) −11.1848 + 19.3726i −0.657929 + 1.13957i
\(290\) −2.98055 + 16.9035i −0.175024 + 0.992610i
\(291\) 0 0
\(292\) −16.1442 5.87600i −0.944766 0.343867i
\(293\) 1.87335 + 10.6243i 0.109442 + 0.620677i 0.989353 + 0.145538i \(0.0464913\pi\)
−0.879911 + 0.475139i \(0.842398\pi\)
\(294\) 0 0
\(295\) −7.27926 6.10802i −0.423815 0.355623i
\(296\) −14.6070 −0.849017
\(297\) 0 0
\(298\) 7.02493 0.406943
\(299\) 4.15158 + 3.48359i 0.240092 + 0.201461i
\(300\) 0 0
\(301\) −1.01506 5.75666i −0.0585068 0.331809i
\(302\) −17.4598 6.35485i −1.00470 0.365680i
\(303\) 0 0
\(304\) 1.03163 5.85067i 0.0591681 0.335559i
\(305\) −0.406116 + 0.703413i −0.0232541 + 0.0402773i
\(306\) 0 0
\(307\) −0.0248747 0.0430843i −0.00141967 0.00245895i 0.865315 0.501229i \(-0.167119\pi\)
−0.866734 + 0.498770i \(0.833785\pi\)
\(308\) −10.3015 + 3.74943i −0.586981 + 0.213644i
\(309\) 0 0
\(310\) 4.00922 3.36413i 0.227708 0.191070i
\(311\) −10.1389 + 8.50759i −0.574927 + 0.482421i −0.883277 0.468852i \(-0.844668\pi\)
0.308350 + 0.951273i \(0.400223\pi\)
\(312\) 0 0
\(313\) 14.1733 5.15866i 0.801123 0.291585i 0.0911710 0.995835i \(-0.470939\pi\)
0.709952 + 0.704250i \(0.248717\pi\)
\(314\) −1.05460 1.82662i −0.0595145 0.103082i
\(315\) 0 0
\(316\) 2.84656 4.93038i 0.160131 0.277356i
\(317\) −1.49873 + 8.49970i −0.0841769 + 0.477391i 0.913354 + 0.407166i \(0.133483\pi\)
−0.997531 + 0.0702251i \(0.977628\pi\)
\(318\) 0 0
\(319\) 27.4152 + 9.97831i 1.53496 + 0.558678i
\(320\) 1.27074 + 7.20673i 0.0710365 + 0.402868i
\(321\) 0 0
\(322\) −6.04242 5.07019i −0.336731 0.282551i
\(323\) 50.6020 2.81557
\(324\) 0 0
\(325\) 0.864837 0.0479725
\(326\) −13.1363 11.0226i −0.727551 0.610488i
\(327\) 0 0
\(328\) 3.25812 + 18.4777i 0.179900 + 1.02026i
\(329\) −10.8458 3.94755i −0.597949 0.217636i
\(330\) 0 0
\(331\) 5.38752 30.5541i 0.296125 1.67941i −0.366471 0.930430i \(-0.619434\pi\)
0.662596 0.748977i \(-0.269455\pi\)
\(332\) 0.637037 1.10338i 0.0349619 0.0605559i
\(333\) 0 0
\(334\) 3.48067 + 6.02869i 0.190454 + 0.329875i
\(335\) −22.6048 + 8.22749i −1.23503 + 0.449516i
\(336\) 0 0
\(337\) −18.2834 + 15.3416i −0.995962 + 0.835711i −0.986420 0.164243i \(-0.947482\pi\)
−0.00954207 + 0.999954i \(0.503037\pi\)
\(338\) −6.68070 + 5.60578i −0.363382 + 0.304914i
\(339\) 0 0
\(340\) 19.5475 7.11471i 1.06011 0.385850i
\(341\) −4.44790 7.70399i −0.240867 0.417194i
\(342\) 0 0
\(343\) −9.68422 + 16.7736i −0.522899 + 0.905688i
\(344\) −1.07151 + 6.07685i −0.0577721 + 0.327642i
\(345\) 0 0
\(346\) 1.92519 + 0.700711i 0.103499 + 0.0376704i
\(347\) −3.80485 21.5784i −0.204255 1.15839i −0.898608 0.438752i \(-0.855420\pi\)
0.694353 0.719634i \(-0.255691\pi\)
\(348\) 0 0
\(349\) 12.1394 + 10.1862i 0.649807 + 0.545253i 0.907012 0.421104i \(-0.138357\pi\)
−0.257205 + 0.966357i \(0.582802\pi\)
\(350\) −1.25873 −0.0672819
\(351\) 0 0
\(352\) 18.3894 0.980157
\(353\) −9.88725 8.29639i −0.526245 0.441572i 0.340557 0.940224i \(-0.389384\pi\)
−0.866802 + 0.498652i \(0.833829\pi\)
\(354\) 0 0
\(355\) 3.37992 + 19.1685i 0.179388 + 1.01736i
\(356\) −4.88837 1.77922i −0.259083 0.0942985i
\(357\) 0 0
\(358\) −0.497603 + 2.82204i −0.0262991 + 0.149150i
\(359\) 12.9142 22.3681i 0.681588 1.18054i −0.292909 0.956140i \(-0.594623\pi\)
0.974496 0.224404i \(-0.0720435\pi\)
\(360\) 0 0
\(361\) −23.0196 39.8711i −1.21156 2.09848i
\(362\) 0.196234 0.0714235i 0.0103138 0.00375393i
\(363\) 0 0
\(364\) 3.57322 2.99829i 0.187288 0.157153i
\(365\) −22.4171 + 18.8101i −1.17336 + 0.984568i
\(366\) 0 0
\(367\) −15.0112 + 5.46363i −0.783578 + 0.285199i −0.702664 0.711522i \(-0.748006\pi\)
−0.0809141 + 0.996721i \(0.525784\pi\)
\(368\) −1.49343 2.58669i −0.0778503 0.134841i
\(369\) 0 0
\(370\) −5.11194 + 8.85413i −0.265757 + 0.460304i
\(371\) −0.0588538 + 0.333777i −0.00305554 + 0.0173288i
\(372\) 0 0
\(373\) −1.71641 0.624722i −0.0888724 0.0323469i 0.297201 0.954815i \(-0.403947\pi\)
−0.386074 + 0.922468i \(0.626169\pi\)
\(374\) 2.66195 + 15.0967i 0.137646 + 0.780630i
\(375\) 0 0
\(376\) 9.33336 + 7.83162i 0.481331 + 0.403885i
\(377\) −12.4136 −0.639332
\(378\) 0 0
\(379\) 1.14694 0.0589141 0.0294571 0.999566i \(-0.490622\pi\)
0.0294571 + 0.999566i \(0.490622\pi\)
\(380\) −20.4817 17.1862i −1.05069 0.881635i
\(381\) 0 0
\(382\) 0.323852 + 1.83666i 0.0165697 + 0.0939716i
\(383\) 20.5112 + 7.46546i 1.04807 + 0.381467i 0.807935 0.589272i \(-0.200585\pi\)
0.240138 + 0.970739i \(0.422807\pi\)
\(384\) 0 0
\(385\) −3.24249 + 18.3891i −0.165253 + 0.937194i
\(386\) −0.192957 + 0.334210i −0.00982123 + 0.0170109i
\(387\) 0 0
\(388\) −4.18281 7.24484i −0.212350 0.367801i
\(389\) −24.6164 + 8.95962i −1.24810 + 0.454271i −0.879759 0.475420i \(-0.842296\pi\)
−0.368340 + 0.929691i \(0.620074\pi\)
\(390\) 0 0
\(391\) 19.4887 16.3529i 0.985584 0.827003i
\(392\) 1.50313 1.26128i 0.0759197 0.0637042i
\(393\) 0 0
\(394\) −16.1855 + 5.89104i −0.815414 + 0.296787i
\(395\) −4.84858 8.39798i −0.243958 0.422548i
\(396\) 0 0
\(397\) −2.09915 + 3.63584i −0.105353 + 0.182478i −0.913883 0.405979i \(-0.866931\pi\)
0.808529 + 0.588456i \(0.200264\pi\)
\(398\) 0.287994 1.63330i 0.0144358 0.0818697i
\(399\) 0 0
\(400\) −0.447894 0.163020i −0.0223947 0.00815101i
\(401\) 1.35963 + 7.71086i 0.0678968 + 0.385062i 0.999753 + 0.0222335i \(0.00707774\pi\)
−0.931856 + 0.362828i \(0.881811\pi\)
\(402\) 0 0
\(403\) 2.89955 + 2.43301i 0.144437 + 0.121197i
\(404\) −14.2606 −0.709493
\(405\) 0 0
\(406\) 18.0674 0.896669
\(407\) 13.3122 + 11.1702i 0.659859 + 0.553687i
\(408\) 0 0
\(409\) −3.02651 17.1642i −0.149651 0.848716i −0.963514 0.267658i \(-0.913750\pi\)
0.813863 0.581057i \(-0.197361\pi\)
\(410\) 12.3406 + 4.49161i 0.609459 + 0.221825i
\(411\) 0 0
\(412\) −2.06748 + 11.7253i −0.101857 + 0.577662i
\(413\) −5.00118 + 8.66229i −0.246092 + 0.426243i
\(414\) 0 0
\(415\) −1.08507 1.87940i −0.0532642 0.0922563i
\(416\) −7.35266 + 2.67615i −0.360494 + 0.131209i
\(417\) 0 0
\(418\) 15.0935 12.6650i 0.738249 0.619464i
\(419\) −8.79662 + 7.38124i −0.429743 + 0.360597i −0.831855 0.554993i \(-0.812721\pi\)
0.402112 + 0.915591i \(0.368276\pi\)
\(420\) 0 0
\(421\) −6.85151 + 2.49375i −0.333922 + 0.121538i −0.503539 0.863972i \(-0.667969\pi\)
0.169617 + 0.985510i \(0.445747\pi\)
\(422\) −7.78066 13.4765i −0.378757 0.656026i
\(423\) 0 0
\(424\) 0.178889 0.309844i 0.00868759 0.0150474i
\(425\) 0.704975 3.99811i 0.0341963 0.193937i
\(426\) 0 0
\(427\) 0.803405 + 0.292416i 0.0388795 + 0.0141510i
\(428\) 1.87632 + 10.6411i 0.0906954 + 0.514359i
\(429\) 0 0
\(430\) 3.30853 + 2.77618i 0.159551 + 0.133879i
\(431\) −0.389084 −0.0187415 −0.00937075 0.999956i \(-0.502983\pi\)
−0.00937075 + 0.999956i \(0.502983\pi\)
\(432\) 0 0
\(433\) 24.1011 1.15822 0.579112 0.815248i \(-0.303400\pi\)
0.579112 + 0.815248i \(0.303400\pi\)
\(434\) −4.22016 3.54113i −0.202574 0.169980i
\(435\) 0 0
\(436\) −0.303888 1.72344i −0.0145536 0.0825376i
\(437\) −30.7271 11.1837i −1.46988 0.534991i
\(438\) 0 0
\(439\) 6.36691 36.1086i 0.303876 1.72337i −0.324871 0.945758i \(-0.605321\pi\)
0.628748 0.777609i \(-0.283568\pi\)
\(440\) 9.85567 17.0705i 0.469851 0.813805i
\(441\) 0 0
\(442\) −3.26131 5.64875i −0.155125 0.268684i
\(443\) −35.5078 + 12.9238i −1.68703 + 0.614028i −0.994246 0.107118i \(-0.965838\pi\)
−0.692782 + 0.721147i \(0.743615\pi\)
\(444\) 0 0
\(445\) −6.78776 + 5.69561i −0.321771 + 0.269998i
\(446\) −7.91101 + 6.63813i −0.374597 + 0.314324i
\(447\) 0 0
\(448\) 7.23838 2.63456i 0.341981 0.124471i
\(449\) 5.89289 + 10.2068i 0.278103 + 0.481688i 0.970913 0.239432i \(-0.0769611\pi\)
−0.692811 + 0.721120i \(0.743628\pi\)
\(450\) 0 0
\(451\) 11.1609 19.3313i 0.525547 0.910274i
\(452\) 4.30276 24.4022i 0.202385 1.14778i
\(453\) 0 0
\(454\) −9.11412 3.31727i −0.427747 0.155687i
\(455\) −1.37965 7.82441i −0.0646792 0.366814i
\(456\) 0 0
\(457\) −15.2105 12.7631i −0.711517 0.597034i 0.213507 0.976942i \(-0.431511\pi\)
−0.925024 + 0.379908i \(0.875956\pi\)
\(458\) 19.9578 0.932568
\(459\) 0 0
\(460\) −13.4423 −0.626750
\(461\) 5.85398 + 4.91207i 0.272647 + 0.228778i 0.768851 0.639428i \(-0.220829\pi\)
−0.496204 + 0.868206i \(0.665273\pi\)
\(462\) 0 0
\(463\) −2.77046 15.7120i −0.128754 0.730200i −0.979007 0.203826i \(-0.934662\pi\)
0.850253 0.526374i \(-0.176449\pi\)
\(464\) 6.42893 + 2.33994i 0.298455 + 0.108629i
\(465\) 0 0
\(466\) 0.728797 4.13321i 0.0337609 0.191467i
\(467\) 13.0703 22.6385i 0.604822 1.04758i −0.387257 0.921972i \(-0.626577\pi\)
0.992080 0.125611i \(-0.0400892\pi\)
\(468\) 0 0
\(469\) 12.6606 + 21.9288i 0.584613 + 1.01258i
\(470\) 8.01351 2.91668i 0.369636 0.134536i
\(471\) 0 0
\(472\) 8.08842 6.78699i 0.372300 0.312397i
\(473\) 5.62359 4.71875i 0.258573 0.216968i
\(474\) 0 0
\(475\) −4.90339 + 1.78469i −0.224983 + 0.0818871i
\(476\) −10.9483 18.9629i −0.501812 0.869164i
\(477\) 0 0
\(478\) 3.25522 5.63820i 0.148890 0.257885i
\(479\) −6.83310 + 38.7525i −0.312213 + 1.77065i 0.275229 + 0.961379i \(0.411246\pi\)
−0.587442 + 0.809267i \(0.699865\pi\)
\(480\) 0 0
\(481\) −6.94820 2.52894i −0.316811 0.115310i
\(482\) −0.0597185 0.338680i −0.00272010 0.0154265i
\(483\) 0 0
\(484\) 1.20958 + 1.01496i 0.0549811 + 0.0461346i
\(485\) −14.2493 −0.647027
\(486\) 0 0
\(487\) 11.7133 0.530779 0.265389 0.964141i \(-0.414500\pi\)
0.265389 + 0.964141i \(0.414500\pi\)
\(488\) −0.691370 0.580128i −0.0312968 0.0262612i
\(489\) 0 0
\(490\) −0.238488 1.35253i −0.0107738 0.0611013i
\(491\) −36.2250 13.1848i −1.63481 0.595023i −0.648691 0.761052i \(-0.724683\pi\)
−0.986121 + 0.166030i \(0.946905\pi\)
\(492\) 0 0
\(493\) −10.1190 + 57.3876i −0.455736 + 2.58461i
\(494\) −4.19178 + 7.26038i −0.188597 + 0.326660i
\(495\) 0 0
\(496\) −1.04304 1.80660i −0.0468340 0.0811189i
\(497\) 19.2527 7.00740i 0.863601 0.314325i
\(498\) 0 0
\(499\) −22.6455 + 19.0018i −1.01375 + 0.850638i −0.988830 0.149051i \(-0.952378\pi\)
−0.0249220 + 0.999689i \(0.507934\pi\)
\(500\) 11.0552 9.27638i 0.494402 0.414853i
\(501\) 0 0
\(502\) 12.4450 4.52959i 0.555445 0.202166i
\(503\) 17.7888 + 30.8110i 0.793161 + 1.37380i 0.924000 + 0.382392i \(0.124900\pi\)
−0.130839 + 0.991404i \(0.541767\pi\)
\(504\) 0 0
\(505\) −12.1452 + 21.0361i −0.540453 + 0.936092i
\(506\) 1.72015 9.75548i 0.0764702 0.433684i
\(507\) 0 0
\(508\) −5.19886 1.89223i −0.230662 0.0839541i
\(509\) 4.92854 + 27.9512i 0.218454 + 1.23891i 0.874812 + 0.484463i \(0.160985\pi\)
−0.656358 + 0.754450i \(0.727904\pi\)
\(510\) 0 0
\(511\) 23.5965 + 19.7998i 1.04385 + 0.875892i
\(512\) 8.20265 0.362510
\(513\) 0 0
\(514\) −16.2365 −0.716161
\(515\) 15.5353 + 13.0357i 0.684567 + 0.574420i
\(516\) 0 0
\(517\) −2.51702 14.2747i −0.110698 0.627801i
\(518\) 10.1128 + 3.68075i 0.444330 + 0.161723i
\(519\) 0 0
\(520\) −1.45639 + 8.25961i −0.0638670 + 0.362208i
\(521\) −12.7176 + 22.0275i −0.557167 + 0.965041i 0.440565 + 0.897721i \(0.354778\pi\)
−0.997731 + 0.0673204i \(0.978555\pi\)
\(522\) 0 0
\(523\) −4.20395 7.28145i −0.183826 0.318396i 0.759354 0.650677i \(-0.225515\pi\)
−0.943180 + 0.332282i \(0.892182\pi\)
\(524\) −0.134375 + 0.0489085i −0.00587020 + 0.00213658i
\(525\) 0 0
\(526\) −11.5531 + 9.69416i −0.503737 + 0.422686i
\(527\) 13.6113 11.4212i 0.592918 0.497517i
\(528\) 0 0
\(529\) 6.16460 2.24373i 0.268026 0.0975535i
\(530\) −0.125209 0.216868i −0.00543873 0.00942016i
\(531\) 0 0
\(532\) −14.0719 + 24.3732i −0.610093 + 1.05671i
\(533\) −1.64927 + 9.35348i −0.0714379 + 0.405144i
\(534\) 0 0
\(535\) 17.2949 + 6.29482i 0.747723 + 0.272149i
\(536\) −4.64155 26.3235i −0.200484 1.13700i
\(537\) 0 0
\(538\) −11.1286 9.33801i −0.479788 0.402590i
\(539\) −2.33440 −0.100550
\(540\) 0 0
\(541\) −12.8635 −0.553043 −0.276522 0.961008i \(-0.589182\pi\)
−0.276522 + 0.961008i \(0.589182\pi\)
\(542\) 7.70806 + 6.46783i 0.331090 + 0.277817i
\(543\) 0 0
\(544\) 6.37820 + 36.1726i 0.273463 + 1.55089i
\(545\) −2.80107 1.01951i −0.119985 0.0436708i
\(546\) 0 0
\(547\) 2.27340 12.8931i 0.0972034 0.551268i −0.896847 0.442342i \(-0.854148\pi\)
0.994050 0.108926i \(-0.0347411\pi\)
\(548\) −5.31514 + 9.20609i −0.227051 + 0.393265i
\(549\) 0 0
\(550\) −0.790392 1.36900i −0.0337024 0.0583743i
\(551\) 70.3817 25.6168i 2.99836 1.09131i
\(552\) 0 0
\(553\) −7.81929 + 6.56116i −0.332510 + 0.279009i
\(554\) 6.22071 5.21980i 0.264293 0.221768i
\(555\) 0 0
\(556\) −13.6878 + 4.98193i −0.580490 + 0.211281i
\(557\) 2.29110 + 3.96830i 0.0970769 + 0.168142i 0.910474 0.413567i \(-0.135717\pi\)
−0.813397 + 0.581710i \(0.802384\pi\)
\(558\) 0 0
\(559\) −1.56179 + 2.70509i −0.0660565 + 0.114413i
\(560\) −0.760371 + 4.31228i −0.0321316 + 0.182227i
\(561\) 0 0
\(562\) 10.4843 + 3.81598i 0.442255 + 0.160968i
\(563\) −2.13308 12.0973i −0.0898986 0.509840i −0.996192 0.0871905i \(-0.972211\pi\)
0.906293 0.422650i \(-0.138900\pi\)
\(564\) 0 0
\(565\) −32.3315 27.1293i −1.36020 1.14134i
\(566\) −14.5378 −0.611071
\(567\) 0 0
\(568\) −21.6278 −0.907484
\(569\) −11.1028 9.31634i −0.465453 0.390561i 0.379680 0.925118i \(-0.376034\pi\)
−0.845133 + 0.534557i \(0.820479\pi\)
\(570\) 0 0
\(571\) −3.82814 21.7104i −0.160203 0.908554i −0.953874 0.300207i \(-0.902944\pi\)
0.793672 0.608346i \(-0.208167\pi\)
\(572\) 5.50467 + 2.00354i 0.230162 + 0.0837721i
\(573\) 0 0
\(574\) 2.40044 13.6135i 0.100192 0.568218i
\(575\) −1.31172 + 2.27197i −0.0547025 + 0.0947475i
\(576\) 0 0
\(577\) 15.7418 + 27.2655i 0.655338 + 1.13508i 0.981809 + 0.189872i \(0.0608072\pi\)
−0.326471 + 0.945207i \(0.605859\pi\)
\(578\) −16.3483 + 5.95031i −0.680001 + 0.247500i
\(579\) 0 0
\(580\) 23.5866 19.7915i 0.979380 0.821798i
\(581\) −1.74990 + 1.46834i −0.0725979 + 0.0609169i
\(582\) 0 0
\(583\) −0.399973 + 0.145578i −0.0165652 + 0.00602923i
\(584\) −16.2582 28.1600i −0.672768 1.16527i
\(585\) 0 0
\(586\) −4.19516 + 7.26623i −0.173300 + 0.300165i
\(587\) 2.49523 14.1511i 0.102989 0.584080i −0.889015 0.457877i \(-0.848610\pi\)
0.992004 0.126203i \(-0.0402790\pi\)
\(588\) 0 0
\(589\) −21.4605 7.81097i −0.884263 0.321845i
\(590\) −1.28332 7.27804i −0.0528333 0.299632i
\(591\) 0 0
\(592\) 3.12173 + 2.61944i 0.128302 + 0.107659i
\(593\) 41.0988 1.68772 0.843862 0.536560i \(-0.180276\pi\)
0.843862 + 0.536560i \(0.180276\pi\)
\(594\) 0 0
\(595\) −37.2966 −1.52901
\(596\) −9.65342 8.10018i −0.395419 0.331796i
\(597\) 0 0
\(598\) 0.731913 + 4.15089i 0.0299301 + 0.169742i
\(599\) 8.04580 + 2.92843i 0.328742 + 0.119652i 0.501118 0.865379i \(-0.332922\pi\)
−0.172376 + 0.985031i \(0.555144\pi\)
\(600\) 0 0
\(601\) −0.283951 + 1.61037i −0.0115826 + 0.0656883i −0.990051 0.140707i \(-0.955062\pi\)
0.978469 + 0.206396i \(0.0661734\pi\)
\(602\) 2.27311 3.93713i 0.0926449 0.160466i
\(603\) 0 0
\(604\) 16.6651 + 28.8648i 0.678094 + 1.17449i
\(605\) 2.52733 0.919873i 0.102751 0.0373982i
\(606\) 0 0
\(607\) 5.03248 4.22275i 0.204262 0.171396i −0.534918 0.844904i \(-0.679658\pi\)
0.739180 + 0.673508i \(0.235213\pi\)
\(608\) 36.1651 30.3461i 1.46669 1.23070i
\(609\) 0 0
\(610\) −0.593602 + 0.216054i −0.0240343 + 0.00874775i
\(611\) 3.08374 + 5.34120i 0.124755 + 0.216082i
\(612\) 0 0
\(613\) 13.1363 22.7527i 0.530569 0.918973i −0.468795 0.883307i \(-0.655312\pi\)
0.999364 0.0356656i \(-0.0113551\pi\)
\(614\) 0.00671875 0.0381039i 0.000271147 0.00153775i
\(615\) 0 0
\(616\) −19.4971 7.09638i −0.785562 0.285921i
\(617\) 1.08930 + 6.17772i 0.0438535 + 0.248706i 0.998852 0.0479054i \(-0.0152546\pi\)
−0.954998 + 0.296611i \(0.904143\pi\)
\(618\) 0 0
\(619\) 3.78493 + 3.17593i 0.152129 + 0.127651i 0.715676 0.698433i \(-0.246119\pi\)
−0.563546 + 0.826084i \(0.690563\pi\)
\(620\) −9.38839 −0.377047
\(621\) 0 0
\(622\) −10.2936 −0.412738
\(623\) 7.14489 + 5.99528i 0.286254 + 0.240196i
\(624\) 0 0
\(625\) −4.83028 27.3939i −0.193211 1.09576i
\(626\) 11.0230 + 4.01206i 0.440569 + 0.160354i
\(627\) 0 0
\(628\) −0.657012 + 3.72610i −0.0262176 + 0.148688i
\(629\) −17.3550 + 30.0598i −0.691991 + 1.19856i
\(630\) 0 0
\(631\) 3.46210 + 5.99653i 0.137824 + 0.238718i 0.926673 0.375869i \(-0.122656\pi\)
−0.788849 + 0.614587i \(0.789322\pi\)
\(632\) 10.1253 3.68530i 0.402762 0.146593i
\(633\) 0 0
\(634\) −5.14205 + 4.31469i −0.204217 + 0.171358i
\(635\) −7.21889 + 6.05737i −0.286473 + 0.240379i
\(636\) 0 0
\(637\) 0.933370 0.339719i 0.0369815 0.0134601i
\(638\) 11.3450 + 19.6502i 0.449154 + 0.777957i
\(639\) 0 0
\(640\) 11.0653 19.1657i 0.437394 0.757589i
\(641\) 5.88995 33.4036i 0.232639 1.31936i −0.614890 0.788613i \(-0.710800\pi\)
0.847529 0.530749i \(-0.178089\pi\)
\(642\) 0 0
\(643\) −7.25745 2.64150i −0.286206 0.104170i 0.194928 0.980818i \(-0.437553\pi\)
−0.481134 + 0.876647i \(0.659775\pi\)
\(644\) 2.45704 + 13.9346i 0.0968210 + 0.549099i
\(645\) 0 0
\(646\) 30.1476 + 25.2968i 1.18614 + 0.995289i
\(647\) −35.1862 −1.38331 −0.691655 0.722228i \(-0.743118\pi\)
−0.691655 + 0.722228i \(0.743118\pi\)
\(648\) 0 0
\(649\) −12.5615 −0.493083
\(650\) 0.515251 + 0.432347i 0.0202098 + 0.0169580i
\(651\) 0 0
\(652\) 5.34163 + 30.2939i 0.209194 + 1.18640i
\(653\) 18.3353 + 6.67349i 0.717514 + 0.261154i 0.674870 0.737937i \(-0.264200\pi\)
0.0426440 + 0.999090i \(0.486422\pi\)
\(654\) 0 0
\(655\) −0.0422958 + 0.239871i −0.00165263 + 0.00937255i
\(656\) 2.61726 4.53323i 0.102187 0.176993i
\(657\) 0 0
\(658\) −4.48824 7.77386i −0.174970 0.303057i
\(659\) 21.6942 7.89603i 0.845085 0.307586i 0.117050 0.993126i \(-0.462656\pi\)
0.728035 + 0.685540i \(0.240434\pi\)
\(660\) 0 0
\(661\) −5.26760 + 4.42004i −0.204886 + 0.171920i −0.739457 0.673204i \(-0.764918\pi\)
0.534571 + 0.845123i \(0.320473\pi\)
\(662\) 18.4843 15.5102i 0.718412 0.602819i
\(663\) 0 0
\(664\) 2.26596 0.824741i 0.0879362 0.0320062i
\(665\) 23.9688 + 41.5152i 0.929471 + 1.60989i
\(666\) 0 0
\(667\) 18.8280 32.6110i 0.729023 1.26270i
\(668\) 2.16844 12.2978i 0.0838995 0.475818i
\(669\) 0 0
\(670\) −17.5805 6.39879i −0.679195 0.247207i
\(671\) 0.186449 + 1.05740i 0.00719777 + 0.0408206i
\(672\) 0 0
\(673\) −23.4964 19.7158i −0.905718 0.759988i 0.0655815 0.997847i \(-0.479110\pi\)
−0.971300 + 0.237859i \(0.923554\pi\)
\(674\) −18.5624 −0.714997
\(675\) 0 0
\(676\) 15.6442 0.601700
\(677\) 10.4059 + 8.73161i 0.399932 + 0.335583i 0.820467 0.571693i \(-0.193713\pi\)
−0.420535 + 0.907276i \(0.638158\pi\)
\(678\) 0 0
\(679\) 2.60455 + 14.7711i 0.0999534 + 0.566864i
\(680\) 36.9967 + 13.4657i 1.41876 + 0.516386i
\(681\) 0 0
\(682\) 1.20139 6.81344i 0.0460037 0.260900i
\(683\) −3.03350 + 5.25418i −0.116074 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203698\pi\)
\(684\) 0 0
\(685\) 9.05335 + 15.6809i 0.345911 + 0.599135i
\(686\) −14.1550 + 5.15201i −0.540442 + 0.196705i
\(687\) 0 0
\(688\) 1.31875 1.10656i 0.0502767 0.0421871i
\(689\) 0.138736 0.116414i 0.00528544 0.00443501i
\(690\) 0 0
\(691\) −19.4188 + 7.06787i −0.738727 + 0.268875i −0.683854 0.729619i \(-0.739698\pi\)
−0.0548728 + 0.998493i \(0.517475\pi\)
\(692\) −1.83756 3.18275i −0.0698537 0.120990i
\(693\) 0 0
\(694\) 8.52054 14.7580i 0.323435 0.560206i
\(695\) −4.30835 + 24.4339i −0.163425 + 0.926830i
\(696\) 0 0
\(697\) 41.8964 + 15.2490i 1.58694 + 0.577599i
\(698\) 2.14015 + 12.1374i 0.0810058 + 0.459407i
\(699\) 0 0
\(700\) 1.72970 + 1.45139i 0.0653766 + 0.0548575i
\(701\) −11.0222 −0.416303 −0.208151 0.978097i \(-0.566745\pi\)
−0.208151 + 0.978097i \(0.566745\pi\)
\(702\) 0 0
\(703\) 44.6131 1.68262
\(704\) 7.41054 + 6.21818i 0.279295 + 0.234356i
\(705\) 0 0
\(706\) −1.74310 9.88560i −0.0656024 0.372050i
\(707\) 24.0264 + 8.74489i 0.903605 + 0.328885i
\(708\) 0 0
\(709\) −1.90795 + 10.8205i −0.0716546 + 0.406373i 0.927792 + 0.373099i \(0.121705\pi\)
−0.999446 + 0.0332746i \(0.989406\pi\)
\(710\) −7.56897 + 13.1098i −0.284058 + 0.492003i
\(711\) 0 0
\(712\) −4.92288 8.52669i −0.184493 0.319551i
\(713\) −10.7895 + 3.92704i −0.404068 + 0.147069i
\(714\) 0 0
\(715\) 7.64354 6.41369i 0.285852 0.239858i
\(716\) 3.93778 3.30419i 0.147162 0.123483i
\(717\) 0 0
\(718\) 18.8762 6.87038i 0.704454 0.256400i
\(719\) 16.3529 + 28.3240i 0.609859 + 1.05631i 0.991263 + 0.131898i \(0.0421072\pi\)
−0.381404 + 0.924408i \(0.624559\pi\)
\(720\) 0 0
\(721\) 10.6734 18.4870i 0.397500 0.688490i
\(722\) 6.21768 35.2622i 0.231398 1.31232i
\(723\) 0 0
\(724\) −0.352014 0.128123i −0.0130825 0.00476164i
\(725\) −1.04347 5.91781i −0.0387535 0.219782i
\(726\) 0 0
\(727\) 29.4625 + 24.7220i 1.09271 + 0.916888i 0.996913 0.0785129i \(-0.0250172\pi\)
0.0957920 + 0.995401i \(0.469462\pi\)
\(728\) 8.82830 0.327199
\(729\) 0 0
\(730\) −22.7591 −0.842352
\(731\) 11.2325 + 9.42515i 0.415447 + 0.348602i
\(732\) 0 0
\(733\) 2.44978 + 13.8934i 0.0904849 + 0.513165i 0.996038 + 0.0889317i \(0.0283453\pi\)
−0.905553 + 0.424233i \(0.860544\pi\)
\(734\) −11.6747 4.24924i −0.430921 0.156842i
\(735\) 0 0
\(736\) 4.12160 23.3748i 0.151924 0.861605i
\(737\) −15.8999 + 27.5395i −0.585681 + 1.01443i
\(738\) 0 0
\(739\) 5.92286 + 10.2587i 0.217876 + 0.377372i 0.954158 0.299302i \(-0.0967539\pi\)
−0.736283 + 0.676674i \(0.763421\pi\)
\(740\) 17.2340 6.27267i 0.633535 0.230588i
\(741\) 0 0
\(742\) −0.201924 + 0.169435i −0.00741288 + 0.00622014i
\(743\) 16.6749 13.9919i 0.611743 0.513314i −0.283453 0.958986i \(-0.591480\pi\)
0.895196 + 0.445673i \(0.147035\pi\)
\(744\) 0 0
\(745\) −20.1701 + 7.34131i −0.738974 + 0.268965i
\(746\) −0.710290 1.23026i −0.0260056 0.0450429i
\(747\) 0 0
\(748\) 13.7494 23.8147i 0.502729 0.870753i
\(749\) 3.36412 19.0788i 0.122922 0.697126i
\(750\) 0 0
\(751\) 39.9830 + 14.5526i 1.45900 + 0.531033i 0.945090 0.326811i \(-0.105974\pi\)
0.513911 + 0.857844i \(0.328196\pi\)
\(752\) −0.590247 3.34746i −0.0215241 0.122069i
\(753\) 0 0
\(754\) −7.39574 6.20576i −0.269337 0.226000i
\(755\) 56.7719 2.06614
\(756\) 0 0
\(757\) −20.6382 −0.750110 −0.375055 0.927003i \(-0.622376\pi\)
−0.375055 + 0.927003i \(0.622376\pi\)
\(758\) 0.683318 + 0.573372i 0.0248192 + 0.0208258i
\(759\) 0 0
\(760\) −8.78728 49.8352i −0.318748 1.80771i
\(761\) −46.4631 16.9112i −1.68429 0.613030i −0.690400 0.723428i \(-0.742565\pi\)
−0.993887 + 0.110398i \(0.964787\pi\)
\(762\) 0 0
\(763\) −0.544851 + 3.09000i −0.0197249 + 0.111866i
\(764\) 1.67275 2.89729i 0.0605181 0.104820i
\(765\) 0 0
\(766\) 8.48799 + 14.7016i 0.306684 + 0.531192i
\(767\) 5.02250 1.82804i 0.181352 0.0660067i
\(768\) 0 0
\(769\) 16.9553 14.2272i 0.611424 0.513046i −0.283670 0.958922i \(-0.591552\pi\)
0.895095 + 0.445876i \(0.147108\pi\)
\(770\) −11.1248 + 9.33482i −0.400910 + 0.336403i
\(771\) 0 0
\(772\) 0.650520 0.236770i 0.0234127 0.00852153i
\(773\) 10.9836 + 19.0241i 0.395051 + 0.684248i 0.993108 0.117206i \(-0.0373936\pi\)
−0.598057 + 0.801454i \(0.704060\pi\)
\(774\) 0 0
\(775\) −0.916134 + 1.58679i −0.0329085 + 0.0569992i
\(776\) 2.74941 15.5927i 0.0986982 0.559745i
\(777\) 0 0
\(778\) −19.1449 6.96819i −0.686379 0.249822i
\(779\) −9.95104 56.4351i −0.356533 2.02200i
\(780\) 0 0
\(781\) 19.7106 + 16.5391i 0.705300 + 0.591817i
\(782\) 19.7860 0.707547
\(783\) 0 0
\(784\) −0.547423 −0.0195508
\(785\) 4.93687 + 4.14253i 0.176204 + 0.147853i
\(786\) 0 0
\(787\) 0.0929939 + 0.527395i 0.00331488 + 0.0187996i 0.986420 0.164240i \(-0.0525173\pi\)
−0.983105 + 0.183040i \(0.941406\pi\)
\(788\) 29.0343 + 10.5676i 1.03430 + 0.376456i
\(789\) 0 0
\(790\) 1.30962 7.42721i 0.0465941 0.264248i
\(791\) −22.2132 + 38.4744i −0.789810 + 1.36799i
\(792\) 0 0
\(793\) −0.228429 0.395650i −0.00811174 0.0140500i
\(794\) −3.06825 + 1.11675i −0.108888 + 0.0396320i
\(795\) 0 0
\(796\) −2.27904 + 1.91234i −0.0807785 + 0.0677812i
\(797\) −30.7176 + 25.7751i −1.08807 + 0.913001i −0.996566 0.0828030i \(-0.973613\pi\)
−0.0915068 + 0.995804i \(0.529168\pi\)
\(798\) 0 0
\(799\) 27.2059 9.90214i 0.962476 0.350312i
\(800\) −1.89383 3.28021i −0.0669570 0.115973i
\(801\) 0 0
\(802\) −3.04475 + 5.27366i −0.107514 + 0.186219i
\(803\) −6.71744 + 38.0965i −0.237053 + 1.34440i
\(804\) 0 0
\(805\) 22.6476 + 8.24306i 0.798224 + 0.290530i
\(806\) 0.511184 + 2.89907i 0.0180057 + 0.102115i
\(807\) 0 0
\(808\) −20.6759 17.3491i −0.727376 0.610341i
\(809\) −17.1826 −0.604110 −0.302055 0.953291i \(-0.597673\pi\)
−0.302055 + 0.953291i \(0.597673\pi\)
\(810\) 0 0
\(811\) −19.6169 −0.688842 −0.344421 0.938815i \(-0.611925\pi\)
−0.344421 + 0.938815i \(0.611925\pi\)
\(812\) −24.8276 20.8328i −0.871277 0.731089i
\(813\) 0 0
\(814\) 2.34690 + 13.3099i 0.0822588 + 0.466513i
\(815\) 49.2361 + 17.9205i 1.72467 + 0.627727i
\(816\) 0 0
\(817\) 3.27264 18.5601i 0.114495 0.649334i
\(818\) 6.77755 11.7391i 0.236971 0.410446i
\(819\) 0 0
\(820\) −11.7789 20.4017i −0.411338 0.712459i
\(821\) 33.7405 12.2806i 1.17755 0.428594i 0.322216 0.946666i \(-0.395572\pi\)
0.855337 + 0.518072i \(0.173350\pi\)
\(822\) 0 0
\(823\) −19.7778 + 16.5955i −0.689410 + 0.578484i −0.918739 0.394865i \(-0.870791\pi\)
0.229329 + 0.973349i \(0.426347\pi\)
\(824\) −17.2622 + 14.4847i −0.601358 + 0.504599i
\(825\) 0 0
\(826\) −7.31001 + 2.66063i −0.254348 + 0.0925750i
\(827\) −12.4793 21.6148i −0.433948 0.751619i 0.563261 0.826279i \(-0.309546\pi\)
−0.997209 + 0.0746593i \(0.976213\pi\)
\(828\) 0 0
\(829\) −1.39964 + 2.42424i −0.0486114 + 0.0841974i −0.889307 0.457310i \(-0.848813\pi\)
0.840696 + 0.541508i \(0.182146\pi\)
\(830\) 0.293082 1.66215i 0.0101730 0.0576942i
\(831\) 0 0
\(832\) −3.86789 1.40780i −0.134095 0.0488065i
\(833\) −0.809669 4.59186i −0.0280534 0.159098i
\(834\) 0 0
\(835\) −16.2939 13.6722i −0.563875 0.473147i
\(836\) −35.3445 −1.22242
\(837\) 0 0
\(838\) −8.93083 −0.308511
\(839\) 34.2482 + 28.7377i 1.18238 + 0.992134i 0.999960 + 0.00891362i \(0.00283733\pi\)
0.182419 + 0.983221i \(0.441607\pi\)
\(840\) 0 0
\(841\) 9.94181 + 56.3828i 0.342821 + 1.94423i
\(842\) −5.32864 1.93947i −0.183637 0.0668385i
\(843\) 0 0
\(844\) −4.84732 + 27.4905i −0.166852 + 0.946263i
\(845\) 13.3235 23.0770i 0.458342 0.793872i
\(846\) 0 0
\(847\) −1.41552 2.45175i −0.0486378 0.0842431i
\(848\) −0.0937946 + 0.0341384i −0.00322092 + 0.00117232i
\(849\) 0 0
\(850\) 2.41873 2.02956i 0.0829618 0.0696132i
\(851\) 17.1821 14.4175i 0.588996 0.494226i
\(852\) 0 0
\(853\) 40.8907 14.8830i 1.40007 0.509584i 0.471871 0.881668i \(-0.343579\pi\)
0.928199 + 0.372084i \(0.121357\pi\)
\(854\) 0.332467 + 0.575850i 0.0113768 + 0.0197052i
\(855\) 0 0
\(856\) −10.2254 + 17.7108i −0.349496 + 0.605344i
\(857\) −1.26945 + 7.19944i −0.0433638 + 0.245928i −0.998783 0.0493252i \(-0.984293\pi\)
0.955419 + 0.295253i \(0.0954040\pi\)
\(858\) 0 0
\(859\) 9.08034 + 3.30497i 0.309817 + 0.112764i 0.492249 0.870454i \(-0.336175\pi\)
−0.182432 + 0.983218i \(0.558397\pi\)
\(860\) −1.34535 7.62987i −0.0458761 0.260176i
\(861\) 0 0
\(862\) −0.231807 0.194510i −0.00789539 0.00662502i
\(863\) −3.15525 −0.107406 −0.0537030 0.998557i \(-0.517102\pi\)
−0.0537030 + 0.998557i \(0.517102\pi\)
\(864\) 0 0
\(865\) −6.25989 −0.212843
\(866\) 14.3589 + 12.0485i 0.487934 + 0.409426i
\(867\) 0 0
\(868\) 1.71605 + 9.73221i 0.0582466 + 0.330333i
\(869\) −12.0459 4.38435i −0.408629 0.148729i
\(870\) 0 0
\(871\) 2.34956 13.3250i 0.0796119 0.451502i
\(872\) 1.65609 2.86844i 0.0560824 0.0971376i
\(873\) 0 0
\(874\) −12.7156 22.0240i −0.430110 0.744973i
\(875\) −24.3142 + 8.84966i −0.821971 + 0.299173i
\(876\) 0 0
\(877\) −40.5413 + 34.0182i −1.36898 + 1.14871i −0.395888 + 0.918299i \(0.629563\pi\)
−0.973093 + 0.230413i \(0.925992\pi\)
\(878\) 21.8445 18.3297i 0.737218 0.618599i
\(879\) 0 0
\(880\) −5.16751 + 1.88082i −0.174197 + 0.0634024i
\(881\) −18.3507 31.7843i −0.618250 1.07084i −0.989805 0.142430i \(-0.954508\pi\)
0.371555 0.928411i \(-0.378825\pi\)
\(882\) 0 0
\(883\) −14.9551 + 25.9031i −0.503280 + 0.871707i 0.496712 + 0.867915i \(0.334540\pi\)
−0.999993 + 0.00379204i \(0.998793\pi\)
\(884\) −2.03178 + 11.5228i −0.0683362 + 0.387554i
\(885\) 0 0
\(886\) −27.6156 10.0513i −0.927764 0.337679i
\(887\) 9.68114 + 54.9045i 0.325061 + 1.84351i 0.509246 + 0.860621i \(0.329924\pi\)
−0.184185 + 0.982892i \(0.558965\pi\)
\(888\) 0 0
\(889\) 7.59871 + 6.37607i 0.254852 + 0.213847i
\(890\) −6.89133 −0.230998
\(891\) 0 0
\(892\) 18.5252 0.620270
\(893\) −28.5061 23.9195i −0.953922 0.800435i
\(894\) 0 0
\(895\) −1.52042 8.62271i −0.0508219 0.288225i
\(896\) −21.8901 7.96735i −0.731297 0.266170i
\(897\) 0 0
\(898\) −1.59169 + 9.02693i −0.0531154 + 0.301233i
\(899\) 13.1499 22.7763i 0.438573 0.759631i
\(900\) 0 0
\(901\) −0.425085 0.736269i −0.0141616 0.0245287i
\(902\) 16.3134 5.93761i 0.543178 0.197701i
\(903\) 0 0
\(904\) 35.9255 30.1451i 1.19486 1.00261i
\(905\) −0.488791 + 0.410144i −0.0162480 + 0.0136337i
\(906\) 0 0
\(907\) −33.8305 + 12.3133i −1.12332 + 0.408856i −0.835864 0.548937i \(-0.815033\pi\)
−0.287459 + 0.957793i \(0.592811\pi\)
\(908\) 8.69930 + 15.0676i 0.288696 + 0.500037i
\(909\) 0 0
\(910\) 3.08959 5.35132i 0.102419 0.177395i
\(911\) −2.84381 + 16.1280i −0.0942195 + 0.534345i 0.900764 + 0.434308i \(0.143007\pi\)
−0.994984 + 0.100037i \(0.968104\pi\)
\(912\) 0 0
\(913\) −2.69578 0.981183i −0.0892173 0.0324724i
\(914\) −2.68158 15.2080i −0.0886986 0.503035i
\(915\) 0 0
\(916\) −27.4254 23.0126i −0.906160 0.760358i
\(917\) 0.256387 0.00846665
\(918\) 0 0
\(919\) 19.5368 0.644461 0.322231 0.946661i \(-0.395567\pi\)
0.322231 + 0.946661i \(0.395567\pi\)
\(920\) −19.4894 16.3536i −0.642547 0.539161i
\(921\) 0 0
\(922\) 1.03204 + 5.85301i 0.0339885 + 0.192758i
\(923\) −10.2878 3.74446i −0.338628 0.123250i
\(924\) 0 0
\(925\) 0.621539 3.52493i 0.0204361 0.115899i
\(926\) 6.20413 10.7459i 0.203880 0.353131i
\(927\) 0 0
\(928\) 27.1834 + 47.0830i 0.892339 + 1.54558i
\(929\) 10.1028 3.67710i 0.331461 0.120642i −0.170929 0.985283i \(-0.554677\pi\)
0.502389 + 0.864642i \(0.332454\pi\)
\(930\) 0 0
\(931\) −4.59090 + 3.85223i −0.150461 + 0.126252i
\(932\) −5.76734 + 4.83937i −0.188915 + 0.158519i
\(933\) 0 0
\(934\) 19.1043 6.95341i 0.625113 0.227523i
\(935\) −23.4196 40.5639i −0.765903 1.32658i
\(936\) 0 0
\(937\) 14.2219 24.6330i 0.464609 0.804727i −0.534575 0.845121i \(-0.679528\pi\)
0.999184 + 0.0403947i \(0.0128615\pi\)
\(938\) −3.41968 + 19.3940i −0.111656 + 0.633235i
\(939\) 0 0
\(940\) −14.3750 5.23208i −0.468861 0.170651i
\(941\) −4.82057 27.3388i −0.157146 0.891219i −0.956798 0.290755i \(-0.906094\pi\)
0.799652 0.600464i \(-0.205018\pi\)
\(942\) 0 0
\(943\) −22.0705 18.5194i −0.718715 0.603073i
\(944\) −2.94571 −0.0958746
\(945\) 0 0
\(946\) 5.70939 0.185628
\(947\) −32.5381 27.3027i −1.05735 0.887220i −0.0635006 0.997982i \(-0.520226\pi\)
−0.993847 + 0.110762i \(0.964671\pi\)
\(948\) 0 0
\(949\) −2.85822 16.2098i −0.0927818 0.526192i
\(950\) −3.81353 1.38801i −0.123727 0.0450330i
\(951\) 0 0
\(952\) 7.19642 40.8129i 0.233237 1.32275i
\(953\) 24.5758 42.5665i 0.796088 1.37886i −0.126058 0.992023i \(-0.540233\pi\)
0.922146 0.386842i \(-0.126434\pi\)
\(954\) 0 0
\(955\) −2.84922 4.93500i −0.0921987 0.159693i
\(956\) −10.9744 + 3.99436i −0.354937 + 0.129187i
\(957\) 0 0
\(958\) −23.4440 + 19.6719i −0.757442 + 0.635569i
\(959\) 14.6003 12.2511i 0.471469 0.395609i
\(960\) 0 0
\(961\) 21.5949 7.85989i 0.696609 0.253545i
\(962\) −2.87532 4.98021i −0.0927041 0.160568i
\(963\) 0 0
\(964\) −0.308456 + 0.534262i −0.00993471 + 0.0172074i
\(965\) 0.204757 1.16124i 0.00659137 0.0373815i
\(966\) 0 0
\(967\) −45.0930 16.4125i −1.45009 0.527791i −0.507476 0.861666i \(-0.669422\pi\)
−0.942617 + 0.333875i \(0.891644\pi\)
\(968\) 0.518948 + 2.94310i 0.0166796 + 0.0945947i
\(969\) 0 0
\(970\) −8.48940 7.12346i −0.272578 0.228720i
\(971\) 28.9682 0.929633 0.464817 0.885407i \(-0.346120\pi\)
0.464817 + 0.885407i \(0.346120\pi\)
\(972\) 0 0
\(973\) 26.1162 0.837247
\(974\) 6.97850 + 5.85566i 0.223606 + 0.187627i
\(975\) 0 0
\(976\) 0.0437226 + 0.247963i 0.00139953 + 0.00793712i
\(977\) −14.2807 5.19774i −0.456879 0.166290i 0.103320 0.994648i \(-0.467053\pi\)
−0.560199 + 0.828358i \(0.689276\pi\)
\(978\) 0 0
\(979\) −2.03401 + 11.5354i −0.0650071 + 0.368674i
\(980\) −1.23183 + 2.13360i −0.0393495 + 0.0681553i
\(981\) 0 0
\(982\) −14.9907 25.9647i −0.478373 0.828567i
\(983\) −36.2460 + 13.1925i −1.15607 + 0.420774i −0.847691 0.530490i \(-0.822008\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(984\) 0 0
\(985\) 40.3157 33.8289i 1.28457 1.07788i
\(986\) −34.7177 + 29.1316i −1.10564 + 0.927739i
\(987\) 0 0
\(988\) 14.1319 5.14358i 0.449595 0.163639i
\(989\) −4.73760 8.20576i −0.150647 0.260928i
\(990\) 0 0
\(991\) −25.5171 + 44.1968i −0.810576 + 1.40396i 0.101885 + 0.994796i \(0.467512\pi\)
−0.912461 + 0.409163i \(0.865821\pi\)
\(992\) 2.87862 16.3254i 0.0913961 0.518333i
\(993\) 0 0
\(994\) 14.9734 + 5.44988i 0.474928 + 0.172860i
\(995\) 0.879961 + 4.99050i 0.0278966 + 0.158210i
\(996\) 0 0
\(997\) 24.3581 + 20.4389i 0.771429 + 0.647306i 0.941075 0.338199i \(-0.109818\pi\)
−0.169645 + 0.985505i \(0.554262\pi\)
\(998\) −22.9910 −0.727768
\(999\) 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 729.2.e.t.406.2 12
3.2 odd 2 729.2.e.k.406.1 12
9.2 odd 6 729.2.e.u.649.1 12
9.4 even 3 729.2.e.s.163.1 12
9.5 odd 6 729.2.e.l.163.2 12
9.7 even 3 729.2.e.j.649.2 12
27.2 odd 18 729.2.c.a.244.5 12
27.4 even 9 729.2.e.j.82.2 12
27.5 odd 18 729.2.e.k.325.1 12
27.7 even 9 729.2.a.b.1.5 6
27.11 odd 18 729.2.c.a.487.5 12
27.13 even 9 729.2.e.s.568.1 12
27.14 odd 18 729.2.e.l.568.2 12
27.16 even 9 729.2.c.d.487.2 12
27.20 odd 18 729.2.a.e.1.2 yes 6
27.22 even 9 inner 729.2.e.t.325.2 12
27.23 odd 18 729.2.e.u.82.1 12
27.25 even 9 729.2.c.d.244.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.5 6 27.7 even 9
729.2.a.e.1.2 yes 6 27.20 odd 18
729.2.c.a.244.5 12 27.2 odd 18
729.2.c.a.487.5 12 27.11 odd 18
729.2.c.d.244.2 12 27.25 even 9
729.2.c.d.487.2 12 27.16 even 9
729.2.e.j.82.2 12 27.4 even 9
729.2.e.j.649.2 12 9.7 even 3
729.2.e.k.325.1 12 27.5 odd 18
729.2.e.k.406.1 12 3.2 odd 2
729.2.e.l.163.2 12 9.5 odd 6
729.2.e.l.568.2 12 27.14 odd 18
729.2.e.s.163.1 12 9.4 even 3
729.2.e.s.568.1 12 27.13 even 9
729.2.e.t.325.2 12 27.22 even 9 inner
729.2.e.t.406.2 12 1.1 even 1 trivial
729.2.e.u.82.1 12 27.23 odd 18
729.2.e.u.649.1 12 9.2 odd 6