Properties

Label 729.2.e.u.82.1
Level $729$
Weight $2$
Character 729.82
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 82.1
Root \(1.13697i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.u.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.135052 - 0.765917i) q^{2} +(1.31100 - 0.477163i) q^{4} +(-1.82039 - 1.52749i) q^{5} +(2.35052 + 0.855521i) q^{7} +(-1.32025 - 2.28674i) q^{8} +O(q^{10})\) \(q+(-0.135052 - 0.765917i) q^{2} +(1.31100 - 0.477163i) q^{4} +(-1.82039 - 1.52749i) q^{5} +(2.35052 + 0.855521i) q^{7} +(-1.32025 - 2.28674i) q^{8} +(-0.924081 + 1.60056i) q^{10} +(-2.40643 + 2.01923i) q^{11} +(0.232103 - 1.31632i) q^{13} +(0.337815 - 1.91585i) q^{14} +(0.564314 - 0.473515i) q^{16} +(3.13726 - 5.43389i) q^{17} +(-4.03234 - 6.98422i) q^{19} +(-3.11538 - 1.13391i) q^{20} +(1.87156 + 1.57042i) q^{22} +(3.81008 - 1.38675i) q^{23} +(0.112355 + 0.637198i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(1.61271 + 9.14613i) q^{29} +(-2.66104 + 0.968540i) q^{31} +(-4.48437 - 3.76284i) q^{32} +(-4.58560 - 1.66902i) q^{34} +(-2.97207 - 5.14778i) q^{35} +(-2.76596 + 4.79078i) q^{37} +(-4.80476 + 4.03167i) q^{38} +(-1.08960 + 6.17943i) q^{40} +(1.23390 - 6.99781i) q^{41} +(1.79017 - 1.50213i) q^{43} +(-2.19131 + 3.79547i) q^{44} +(-1.57670 - 2.73092i) q^{46} +(-4.33594 - 1.57815i) q^{47} +(-0.569260 - 0.477666i) q^{49} +(0.472867 - 0.172110i) q^{50} +(-0.323815 - 1.83645i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-1.14693 - 6.50455i) q^{56} +(6.78738 - 2.47040i) q^{58} +(3.06321 + 2.57034i) q^{59} +(-0.321185 - 0.116902i) q^{61} +(1.10120 + 1.90733i) q^{62} +(-1.53974 + 2.66690i) q^{64} +(-2.43319 + 2.04168i) q^{65} +(1.75783 - 9.96913i) q^{67} +(1.52008 - 8.62079i) q^{68} +(-3.54139 + 2.97158i) q^{70} +(4.09540 - 7.09344i) q^{71} +(6.15722 + 10.6646i) q^{73} +(4.04288 + 1.47149i) q^{74} +(-8.61900 - 7.23220i) q^{76} +(-7.38387 + 2.68751i) q^{77} +(0.708606 + 4.01870i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.158580 - 0.899354i) q^{83} +(-14.0112 + 5.09967i) q^{85} +(-1.39227 - 1.16826i) q^{86} +(7.79456 + 2.83699i) q^{88} +(-1.86437 - 3.22919i) q^{89} +(1.67171 - 2.89548i) q^{91} +(4.33328 - 3.63606i) q^{92} +(-0.623157 + 3.53410i) q^{94} +(-3.32788 + 18.8734i) q^{95} +(-4.59343 + 3.85434i) q^{97} +(-0.288973 + 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 3 q^{13} - 15 q^{14} - 36 q^{16} + 9 q^{17} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 6 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 54 q^{32} - 9 q^{34} - 30 q^{35} - 3 q^{37} - 42 q^{38} - 57 q^{40} - 24 q^{41} + 6 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} + 33 q^{49} - 21 q^{50} + 45 q^{52} - 18 q^{53} + 30 q^{55} - 3 q^{56} + 33 q^{58} - 15 q^{59} + 33 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} + 42 q^{67} + 18 q^{68} + 24 q^{70} - 12 q^{73} + 3 q^{74} - 87 q^{76} + 57 q^{77} - 48 q^{79} - 42 q^{80} - 42 q^{82} - 12 q^{83} - 36 q^{85} + 30 q^{86} + 30 q^{88} + 9 q^{89} - 18 q^{91} + 48 q^{92} + 33 q^{94} - 30 q^{95} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.135052 0.765917i −0.0954961 0.541585i −0.994594 0.103838i \(-0.966888\pi\)
0.899098 0.437747i \(-0.144223\pi\)
\(3\) 0 0
\(4\) 1.31100 0.477163i 0.655498 0.238582i
\(5\) −1.82039 1.52749i −0.814102 0.683113i 0.137481 0.990504i \(-0.456099\pi\)
−0.951583 + 0.307392i \(0.900544\pi\)
\(6\) 0 0
\(7\) 2.35052 + 0.855521i 0.888415 + 0.323357i 0.745601 0.666393i \(-0.232163\pi\)
0.142814 + 0.989750i \(0.454385\pi\)
\(8\) −1.32025 2.28674i −0.466780 0.808486i
\(9\) 0 0
\(10\) −0.924081 + 1.60056i −0.292220 + 0.506140i
\(11\) −2.40643 + 2.01923i −0.725566 + 0.608822i −0.928919 0.370284i \(-0.879261\pi\)
0.203353 + 0.979105i \(0.434816\pi\)
\(12\) 0 0
\(13\) 0.232103 1.31632i 0.0643739 0.365082i −0.935555 0.353180i \(-0.885100\pi\)
0.999929 0.0119022i \(-0.00378867\pi\)
\(14\) 0.337815 1.91585i 0.0902850 0.512031i
\(15\) 0 0
\(16\) 0.564314 0.473515i 0.141078 0.118379i
\(17\) 3.13726 5.43389i 0.760897 1.31791i −0.181492 0.983392i \(-0.558093\pi\)
0.942389 0.334520i \(-0.108574\pi\)
\(18\) 0 0
\(19\) −4.03234 6.98422i −0.925083 1.60229i −0.791427 0.611263i \(-0.790662\pi\)
−0.133656 0.991028i \(-0.542672\pi\)
\(20\) −3.11538 1.13391i −0.696620 0.253549i
\(21\) 0 0
\(22\) 1.87156 + 1.57042i 0.399018 + 0.334815i
\(23\) 3.81008 1.38675i 0.794456 0.289158i 0.0872688 0.996185i \(-0.472186\pi\)
0.707187 + 0.707027i \(0.249964\pi\)
\(24\) 0 0
\(25\) 0.112355 + 0.637198i 0.0224711 + 0.127440i
\(26\) −1.03954 −0.203871
\(27\) 0 0
\(28\) 3.48975 0.659501
\(29\) 1.61271 + 9.14613i 0.299473 + 1.69839i 0.648445 + 0.761261i \(0.275420\pi\)
−0.348972 + 0.937133i \(0.613469\pi\)
\(30\) 0 0
\(31\) −2.66104 + 0.968540i −0.477937 + 0.173955i −0.569744 0.821822i \(-0.692958\pi\)
0.0918074 + 0.995777i \(0.470736\pi\)
\(32\) −4.48437 3.76284i −0.792733 0.665182i
\(33\) 0 0
\(34\) −4.58560 1.66902i −0.786424 0.286235i
\(35\) −2.97207 5.14778i −0.502372 0.870133i
\(36\) 0 0
\(37\) −2.76596 + 4.79078i −0.454720 + 0.787599i −0.998672 0.0515178i \(-0.983594\pi\)
0.543952 + 0.839117i \(0.316927\pi\)
\(38\) −4.80476 + 4.03167i −0.779435 + 0.654024i
\(39\) 0 0
\(40\) −1.08960 + 6.17943i −0.172281 + 0.977053i
\(41\) 1.23390 6.99781i 0.192703 1.09287i −0.722949 0.690902i \(-0.757214\pi\)
0.915652 0.401972i \(-0.131675\pi\)
\(42\) 0 0
\(43\) 1.79017 1.50213i 0.272998 0.229073i −0.496002 0.868322i \(-0.665199\pi\)
0.769000 + 0.639249i \(0.220755\pi\)
\(44\) −2.19131 + 3.79547i −0.330353 + 0.572188i
\(45\) 0 0
\(46\) −1.57670 2.73092i −0.232471 0.402652i
\(47\) −4.33594 1.57815i −0.632461 0.230197i 0.00584102 0.999983i \(-0.498141\pi\)
−0.638302 + 0.769786i \(0.720363\pi\)
\(48\) 0 0
\(49\) −0.569260 0.477666i −0.0813229 0.0682380i
\(50\) 0.472867 0.172110i 0.0668735 0.0243400i
\(51\) 0 0
\(52\) −0.323815 1.83645i −0.0449050 0.254669i
\(53\) −0.135496 −0.0186118 −0.00930588 0.999957i \(-0.502962\pi\)
−0.00930588 + 0.999957i \(0.502962\pi\)
\(54\) 0 0
\(55\) 7.46499 1.00658
\(56\) −1.14693 6.50455i −0.153265 0.869207i
\(57\) 0 0
\(58\) 6.78738 2.47040i 0.891226 0.324380i
\(59\) 3.06321 + 2.57034i 0.398796 + 0.334630i 0.820028 0.572323i \(-0.193958\pi\)
−0.421232 + 0.906953i \(0.638402\pi\)
\(60\) 0 0
\(61\) −0.321185 0.116902i −0.0411235 0.0149677i 0.321376 0.946952i \(-0.395855\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(62\) 1.10120 + 1.90733i 0.139852 + 0.242232i
\(63\) 0 0
\(64\) −1.53974 + 2.66690i −0.192467 + 0.333363i
\(65\) −2.43319 + 2.04168i −0.301799 + 0.253240i
\(66\) 0 0
\(67\) 1.75783 9.96913i 0.214753 1.21792i −0.666582 0.745431i \(-0.732244\pi\)
0.881335 0.472492i \(-0.156645\pi\)
\(68\) 1.52008 8.62079i 0.184337 1.04542i
\(69\) 0 0
\(70\) −3.54139 + 2.97158i −0.423276 + 0.355171i
\(71\) 4.09540 7.09344i 0.486035 0.841837i −0.513837 0.857888i \(-0.671776\pi\)
0.999871 + 0.0160515i \(0.00510955\pi\)
\(72\) 0 0
\(73\) 6.15722 + 10.6646i 0.720648 + 1.24820i 0.960740 + 0.277449i \(0.0894890\pi\)
−0.240092 + 0.970750i \(0.577178\pi\)
\(74\) 4.04288 + 1.47149i 0.469976 + 0.171057i
\(75\) 0 0
\(76\) −8.61900 7.23220i −0.988667 0.829590i
\(77\) −7.38387 + 2.68751i −0.841470 + 0.306270i
\(78\) 0 0
\(79\) 0.708606 + 4.01870i 0.0797244 + 0.452139i 0.998371 + 0.0570587i \(0.0181722\pi\)
−0.918646 + 0.395081i \(0.870717\pi\)
\(80\) −1.75056 −0.195718
\(81\) 0 0
\(82\) −5.52638 −0.610287
\(83\) −0.158580 0.899354i −0.0174065 0.0987169i 0.974867 0.222788i \(-0.0715159\pi\)
−0.992273 + 0.124071i \(0.960405\pi\)
\(84\) 0 0
\(85\) −14.0112 + 5.09967i −1.51973 + 0.553137i
\(86\) −1.39227 1.16826i −0.150133 0.125976i
\(87\) 0 0
\(88\) 7.79456 + 2.83699i 0.830903 + 0.302424i
\(89\) −1.86437 3.22919i −0.197623 0.342293i 0.750134 0.661286i \(-0.229989\pi\)
−0.947757 + 0.318992i \(0.896656\pi\)
\(90\) 0 0
\(91\) 1.67171 2.89548i 0.175243 0.303529i
\(92\) 4.33328 3.63606i 0.451776 0.379085i
\(93\) 0 0
\(94\) −0.623157 + 3.53410i −0.0642737 + 0.364514i
\(95\) −3.32788 + 18.8734i −0.341433 + 1.93636i
\(96\) 0 0
\(97\) −4.59343 + 3.85434i −0.466392 + 0.391349i −0.845476 0.534013i \(-0.820683\pi\)
0.379084 + 0.925362i \(0.376239\pi\)
\(98\) −0.288973 + 0.500515i −0.0291907 + 0.0505597i
\(99\) 0 0
\(100\) 0.451345 + 0.781752i 0.0451345 + 0.0781752i
\(101\) 9.60527 + 3.49603i 0.955760 + 0.347868i 0.772371 0.635172i \(-0.219071\pi\)
0.183389 + 0.983040i \(0.441293\pi\)
\(102\) 0 0
\(103\) 6.53747 + 5.48559i 0.644156 + 0.540511i 0.905291 0.424791i \(-0.139652\pi\)
−0.261135 + 0.965302i \(0.584097\pi\)
\(104\) −3.31653 + 1.20712i −0.325213 + 0.118368i
\(105\) 0 0
\(106\) 0.0182989 + 0.103778i 0.00177735 + 0.0100799i
\(107\) 7.74500 0.748738 0.374369 0.927280i \(-0.377859\pi\)
0.374369 + 0.927280i \(0.377859\pi\)
\(108\) 0 0
\(109\) 1.25438 0.120148 0.0600738 0.998194i \(-0.480866\pi\)
0.0600738 + 0.998194i \(0.480866\pi\)
\(110\) −1.00816 5.71756i −0.0961243 0.545148i
\(111\) 0 0
\(112\) 1.73154 0.630227i 0.163615 0.0595509i
\(113\) 13.6055 + 11.4164i 1.27990 + 1.07396i 0.993258 + 0.115928i \(0.0369840\pi\)
0.286644 + 0.958037i \(0.407460\pi\)
\(114\) 0 0
\(115\) −9.05407 3.29541i −0.844296 0.307299i
\(116\) 6.47846 + 11.2210i 0.601509 + 1.04185i
\(117\) 0 0
\(118\) 1.55497 2.69329i 0.143147 0.247938i
\(119\) 12.0230 10.0885i 1.10215 0.924812i
\(120\) 0 0
\(121\) −0.196534 + 1.11460i −0.0178667 + 0.101327i
\(122\) −0.0461605 + 0.261789i −0.00417917 + 0.0237013i
\(123\) 0 0
\(124\) −3.02646 + 2.53950i −0.271784 + 0.228054i
\(125\) −5.17209 + 8.95832i −0.462606 + 0.801256i
\(126\) 0 0
\(127\) 1.98279 + 3.43429i 0.175944 + 0.304744i 0.940488 0.339828i \(-0.110369\pi\)
−0.764543 + 0.644572i \(0.777036\pi\)
\(128\) −8.75122 3.18518i −0.773506 0.281533i
\(129\) 0 0
\(130\) 1.89237 + 1.58788i 0.165972 + 0.139267i
\(131\) −0.0963170 + 0.0350565i −0.00841525 + 0.00306290i −0.346224 0.938152i \(-0.612536\pi\)
0.337809 + 0.941215i \(0.390314\pi\)
\(132\) 0 0
\(133\) −3.50297 19.8663i −0.303746 1.72263i
\(134\) −7.87292 −0.680117
\(135\) 0 0
\(136\) −16.5679 −1.42068
\(137\) 1.32312 + 7.50379i 0.113042 + 0.641092i 0.987701 + 0.156354i \(0.0499740\pi\)
−0.874659 + 0.484738i \(0.838915\pi\)
\(138\) 0 0
\(139\) 9.81108 3.57094i 0.832165 0.302883i 0.109418 0.993996i \(-0.465101\pi\)
0.722747 + 0.691113i \(0.242879\pi\)
\(140\) −6.35270 5.33055i −0.536901 0.450514i
\(141\) 0 0
\(142\) −5.98608 2.17875i −0.502341 0.182837i
\(143\) 2.09943 + 3.63631i 0.175563 + 0.304084i
\(144\) 0 0
\(145\) 11.0348 19.1129i 0.916394 1.58724i
\(146\) 7.33667 6.15619i 0.607187 0.509490i
\(147\) 0 0
\(148\) −1.34017 + 7.60050i −0.110162 + 0.624757i
\(149\) −1.56849 + 8.89535i −0.128496 + 0.728736i 0.850674 + 0.525693i \(0.176194\pi\)
−0.979170 + 0.203042i \(0.934917\pi\)
\(150\) 0 0
\(151\) 18.3011 15.3564i 1.48932 1.24969i 0.593848 0.804578i \(-0.297608\pi\)
0.895475 0.445112i \(-0.146836\pi\)
\(152\) −10.6474 + 18.4419i −0.863620 + 1.49583i
\(153\) 0 0
\(154\) 3.05561 + 5.29248i 0.246228 + 0.426480i
\(155\) 6.32356 + 2.30159i 0.507920 + 0.184868i
\(156\) 0 0
\(157\) 2.07750 + 1.74323i 0.165803 + 0.139125i 0.721914 0.691983i \(-0.243263\pi\)
−0.556111 + 0.831108i \(0.687707\pi\)
\(158\) 2.98229 1.08547i 0.237258 0.0863550i
\(159\) 0 0
\(160\) 2.41562 + 13.6996i 0.190971 + 1.08305i
\(161\) 10.1421 0.799308
\(162\) 0 0
\(163\) −22.0489 −1.72701 −0.863504 0.504343i \(-0.831735\pi\)
−0.863504 + 0.504343i \(0.831735\pi\)
\(164\) −1.72146 9.76287i −0.134423 0.762352i
\(165\) 0 0
\(166\) −0.667414 + 0.242919i −0.0518014 + 0.0188542i
\(167\) 6.85671 + 5.75347i 0.530589 + 0.445217i 0.868305 0.496031i \(-0.165210\pi\)
−0.337716 + 0.941248i \(0.609654\pi\)
\(168\) 0 0
\(169\) 10.5372 + 3.83522i 0.810551 + 0.295017i
\(170\) 5.79816 + 10.0427i 0.444699 + 0.770241i
\(171\) 0 0
\(172\) 1.63014 2.82349i 0.124297 0.215289i
\(173\) 2.01795 1.69326i 0.153422 0.128736i −0.562846 0.826562i \(-0.690293\pi\)
0.716268 + 0.697826i \(0.245849\pi\)
\(174\) 0 0
\(175\) −0.281043 + 1.59387i −0.0212448 + 0.120485i
\(176\) −0.401843 + 2.27896i −0.0302900 + 0.171783i
\(177\) 0 0
\(178\) −2.22150 + 1.86406i −0.166509 + 0.139717i
\(179\) −1.84227 + 3.19090i −0.137697 + 0.238499i −0.926625 0.375988i \(-0.877303\pi\)
0.788927 + 0.614487i \(0.210637\pi\)
\(180\) 0 0
\(181\) 0.134255 + 0.232536i 0.00997906 + 0.0172842i 0.870972 0.491333i \(-0.163490\pi\)
−0.860993 + 0.508617i \(0.830157\pi\)
\(182\) −2.44347 0.889349i −0.181122 0.0659229i
\(183\) 0 0
\(184\) −8.20141 6.88180i −0.604616 0.507333i
\(185\) 12.3530 4.49611i 0.908208 0.330561i
\(186\) 0 0
\(187\) 3.42271 + 19.4111i 0.250293 + 1.41948i
\(188\) −6.43743 −0.469498
\(189\) 0 0
\(190\) 14.9049 1.08131
\(191\) −0.416406 2.36155i −0.0301301 0.170876i 0.966030 0.258432i \(-0.0832056\pi\)
−0.996160 + 0.0875554i \(0.972095\pi\)
\(192\) 0 0
\(193\) −0.466278 + 0.169711i −0.0335634 + 0.0122161i −0.358747 0.933435i \(-0.616796\pi\)
0.325184 + 0.945651i \(0.394574\pi\)
\(194\) 3.57246 + 2.99765i 0.256488 + 0.215219i
\(195\) 0 0
\(196\) −0.974222 0.354588i −0.0695873 0.0253277i
\(197\) 11.0734 + 19.1797i 0.788946 + 1.36649i 0.926613 + 0.376016i \(0.122706\pi\)
−0.137667 + 0.990479i \(0.543960\pi\)
\(198\) 0 0
\(199\) −1.06624 + 1.84677i −0.0755834 + 0.130914i −0.901340 0.433113i \(-0.857415\pi\)
0.825756 + 0.564027i \(0.190749\pi\)
\(200\) 1.30877 1.09819i 0.0925442 0.0776538i
\(201\) 0 0
\(202\) 1.38046 7.82898i 0.0971289 0.550845i
\(203\) −4.03399 + 22.8779i −0.283131 + 1.60572i
\(204\) 0 0
\(205\) −12.9352 + 10.8540i −0.903437 + 0.758073i
\(206\) 3.31861 5.74800i 0.231218 0.400482i
\(207\) 0 0
\(208\) −0.492320 0.852724i −0.0341363 0.0591257i
\(209\) 23.8063 + 8.66480i 1.64672 + 0.599357i
\(210\) 0 0
\(211\) 15.3275 + 12.8613i 1.05519 + 0.885406i 0.993629 0.112697i \(-0.0359490\pi\)
0.0615569 + 0.998104i \(0.480393\pi\)
\(212\) −0.177634 + 0.0646536i −0.0122000 + 0.00444043i
\(213\) 0 0
\(214\) −1.04598 5.93203i −0.0715015 0.405505i
\(215\) −5.55329 −0.378731
\(216\) 0 0
\(217\) −7.08345 −0.480856
\(218\) −0.169406 0.960749i −0.0114736 0.0650701i
\(219\) 0 0
\(220\) 9.78657 3.56202i 0.659810 0.240151i
\(221\) −6.42459 5.39087i −0.432165 0.362629i
\(222\) 0 0
\(223\) 12.4777 + 4.54150i 0.835567 + 0.304122i 0.724142 0.689651i \(-0.242236\pi\)
0.111425 + 0.993773i \(0.464458\pi\)
\(224\) −7.32144 12.6811i −0.489185 0.847292i
\(225\) 0 0
\(226\) 6.90656 11.9625i 0.459418 0.795735i
\(227\) −9.55329 + 8.01616i −0.634074 + 0.532051i −0.902192 0.431335i \(-0.858043\pi\)
0.268118 + 0.963386i \(0.413598\pi\)
\(228\) 0 0
\(229\) 4.45608 25.2717i 0.294466 1.67000i −0.374898 0.927066i \(-0.622322\pi\)
0.669364 0.742935i \(-0.266567\pi\)
\(230\) −1.30124 + 7.37971i −0.0858014 + 0.486604i
\(231\) 0 0
\(232\) 18.7857 15.7631i 1.23334 1.03490i
\(233\) 2.69821 4.67344i 0.176766 0.306167i −0.764005 0.645210i \(-0.776770\pi\)
0.940771 + 0.339043i \(0.110103\pi\)
\(234\) 0 0
\(235\) 5.48248 + 9.49593i 0.357637 + 0.619446i
\(236\) 5.24233 + 1.90805i 0.341247 + 0.124204i
\(237\) 0 0
\(238\) −9.35069 7.84616i −0.606115 0.508591i
\(239\) −7.86621 + 2.86307i −0.508823 + 0.185196i −0.583658 0.812000i \(-0.698379\pi\)
0.0748353 + 0.997196i \(0.476157\pi\)
\(240\) 0 0
\(241\) −0.0767854 0.435472i −0.00494618 0.0280512i 0.982235 0.187656i \(-0.0600891\pi\)
−0.987181 + 0.159605i \(0.948978\pi\)
\(242\) 0.880231 0.0565834
\(243\) 0 0
\(244\) −0.476854 −0.0305274
\(245\) 0.306646 + 1.73907i 0.0195909 + 0.111105i
\(246\) 0 0
\(247\) −10.1294 + 3.68681i −0.644520 + 0.234586i
\(248\) 5.72805 + 4.80640i 0.363731 + 0.305207i
\(249\) 0 0
\(250\) 7.55983 + 2.75155i 0.478125 + 0.174023i
\(251\) −8.51427 14.7471i −0.537416 0.930832i −0.999042 0.0437571i \(-0.986067\pi\)
0.461626 0.887074i \(-0.347266\pi\)
\(252\) 0 0
\(253\) −6.36850 + 11.0306i −0.400384 + 0.693486i
\(254\) 2.36260 1.98246i 0.148243 0.124391i
\(255\) 0 0
\(256\) −2.32721 + 13.1983i −0.145451 + 0.824891i
\(257\) 3.62520 20.5596i 0.226134 1.28247i −0.634371 0.773028i \(-0.718741\pi\)
0.860505 0.509441i \(-0.170148\pi\)
\(258\) 0 0
\(259\) −10.6001 + 8.89450i −0.658656 + 0.552678i
\(260\) −2.21568 + 3.83767i −0.137411 + 0.238002i
\(261\) 0 0
\(262\) 0.0398582 + 0.0690364i 0.00246245 + 0.00426508i
\(263\) −18.2221 6.63230i −1.12362 0.408965i −0.287650 0.957736i \(-0.592874\pi\)
−0.835973 + 0.548770i \(0.815096\pi\)
\(264\) 0 0
\(265\) 0.246655 + 0.206968i 0.0151519 + 0.0127139i
\(266\) −14.7429 + 5.36597i −0.903945 + 0.329009i
\(267\) 0 0
\(268\) −2.45240 13.9083i −0.149804 0.849582i
\(269\) 18.6791 1.13889 0.569443 0.822031i \(-0.307159\pi\)
0.569443 + 0.822031i \(0.307159\pi\)
\(270\) 0 0
\(271\) 12.9378 0.785917 0.392958 0.919556i \(-0.371452\pi\)
0.392958 + 0.919556i \(0.371452\pi\)
\(272\) −0.802633 4.55196i −0.0486668 0.276003i
\(273\) 0 0
\(274\) 5.56859 2.02680i 0.336411 0.122444i
\(275\) −1.55703 1.30650i −0.0938923 0.0787850i
\(276\) 0 0
\(277\) −9.81164 3.57114i −0.589524 0.214569i 0.0299959 0.999550i \(-0.490451\pi\)
−0.619520 + 0.784981i \(0.712673\pi\)
\(278\) −4.06005 7.03221i −0.243505 0.421764i
\(279\) 0 0
\(280\) −7.84776 + 13.5927i −0.468994 + 0.812321i
\(281\) 10.9895 9.22130i 0.655580 0.550097i −0.253179 0.967420i \(-0.581476\pi\)
0.908758 + 0.417323i \(0.137032\pi\)
\(282\) 0 0
\(283\) −3.24594 + 18.4086i −0.192951 + 1.09428i 0.722356 + 0.691522i \(0.243059\pi\)
−0.915307 + 0.402758i \(0.868052\pi\)
\(284\) 1.98432 11.2536i 0.117748 0.667781i
\(285\) 0 0
\(286\) 2.50158 2.09908i 0.147922 0.124121i
\(287\) 8.88709 15.3929i 0.524588 0.908614i
\(288\) 0 0
\(289\) −11.1848 19.3726i −0.657929 1.13957i
\(290\) −16.1292 5.87054i −0.947138 0.344730i
\(291\) 0 0
\(292\) 13.1609 + 11.0433i 0.770181 + 0.646258i
\(293\) 10.1376 3.68978i 0.592243 0.215559i −0.0284724 0.999595i \(-0.509064\pi\)
0.620716 + 0.784036i \(0.286842\pi\)
\(294\) 0 0
\(295\) −1.65007 9.35803i −0.0960710 0.544846i
\(296\) 14.6070 0.849017
\(297\) 0 0
\(298\) 7.02493 0.406943
\(299\) −0.941086 5.33716i −0.0544244 0.308656i
\(300\) 0 0
\(301\) 5.49295 1.99927i 0.316608 0.115236i
\(302\) −14.2334 11.9432i −0.819038 0.687254i
\(303\) 0 0
\(304\) −5.58264 2.03192i −0.320187 0.116538i
\(305\) 0.406116 + 0.703413i 0.0232541 + 0.0402773i
\(306\) 0 0
\(307\) −0.0248747 + 0.0430843i −0.00141967 + 0.00245895i −0.866734 0.498770i \(-0.833785\pi\)
0.865315 + 0.501229i \(0.167119\pi\)
\(308\) −8.39784 + 7.04662i −0.478511 + 0.401519i
\(309\) 0 0
\(310\) 0.908816 5.15415i 0.0516173 0.292736i
\(311\) 2.29831 13.0344i 0.130325 0.739112i −0.847676 0.530514i \(-0.821999\pi\)
0.978001 0.208598i \(-0.0668900\pi\)
\(312\) 0 0
\(313\) −11.5542 + 9.69511i −0.653081 + 0.548000i −0.908004 0.418961i \(-0.862394\pi\)
0.254923 + 0.966961i \(0.417950\pi\)
\(314\) 1.05460 1.82662i 0.0595145 0.103082i
\(315\) 0 0
\(316\) 2.84656 + 4.93038i 0.160131 + 0.277356i
\(317\) −8.11032 2.95192i −0.455521 0.165796i 0.104061 0.994571i \(-0.466816\pi\)
−0.559582 + 0.828775i \(0.689038\pi\)
\(318\) 0 0
\(319\) −22.3491 18.7531i −1.25131 1.04997i
\(320\) 6.87658 2.50287i 0.384412 0.139915i
\(321\) 0 0
\(322\) −1.36971 7.76799i −0.0763307 0.432893i
\(323\) −50.6020 −2.81557
\(324\) 0 0
\(325\) 0.864837 0.0479725
\(326\) 2.97775 + 16.8877i 0.164922 + 0.935321i
\(327\) 0 0
\(328\) −17.6313 + 6.41725i −0.973523 + 0.354334i
\(329\) −8.84158 7.41897i −0.487452 0.409021i
\(330\) 0 0
\(331\) −29.1544 10.6113i −1.60247 0.583252i −0.622540 0.782588i \(-0.713899\pi\)
−0.979931 + 0.199336i \(0.936121\pi\)
\(332\) −0.637037 1.10338i −0.0349619 0.0605559i
\(333\) 0 0
\(334\) 3.48067 6.02869i 0.190454 0.329875i
\(335\) −18.4276 + 15.4626i −1.00681 + 0.844813i
\(336\) 0 0
\(337\) −4.14452 + 23.5047i −0.225766 + 1.28038i 0.635449 + 0.772143i \(0.280815\pi\)
−0.861215 + 0.508241i \(0.830296\pi\)
\(338\) 1.51439 8.58855i 0.0823721 0.467155i
\(339\) 0 0
\(340\) −15.9353 + 13.3713i −0.864212 + 0.725160i
\(341\) 4.44790 7.70399i 0.240867 0.417194i
\(342\) 0 0
\(343\) −9.68422 16.7736i −0.522899 0.905688i
\(344\) −5.79847 2.11047i −0.312632 0.113789i
\(345\) 0 0
\(346\) −1.56943 1.31691i −0.0843729 0.0707973i
\(347\) −20.5898 + 7.49409i −1.10532 + 0.402304i −0.829275 0.558841i \(-0.811246\pi\)
−0.276045 + 0.961145i \(0.589024\pi\)
\(348\) 0 0
\(349\) 2.75178 + 15.6061i 0.147299 + 0.835376i 0.965492 + 0.260432i \(0.0838651\pi\)
−0.818193 + 0.574944i \(0.805024\pi\)
\(350\) 1.25873 0.0672819
\(351\) 0 0
\(352\) 18.3894 0.980157
\(353\) 2.24126 + 12.7108i 0.119290 + 0.676528i 0.984536 + 0.175181i \(0.0560509\pi\)
−0.865246 + 0.501347i \(0.832838\pi\)
\(354\) 0 0
\(355\) −18.2904 + 6.65715i −0.970751 + 0.353325i
\(356\) −3.98503 3.34384i −0.211206 0.177223i
\(357\) 0 0
\(358\) 2.69276 + 0.980086i 0.142317 + 0.0517991i
\(359\) −12.9142 22.3681i −0.681588 1.18054i −0.974496 0.224404i \(-0.927956\pi\)
0.292909 0.956140i \(-0.405377\pi\)
\(360\) 0 0
\(361\) −23.0196 + 39.8711i −1.21156 + 2.09848i
\(362\) 0.159972 0.134232i 0.00840793 0.00705509i
\(363\) 0 0
\(364\) 0.809983 4.59364i 0.0424546 0.240772i
\(365\) 5.08153 28.8188i 0.265980 1.50845i
\(366\) 0 0
\(367\) 12.2372 10.2683i 0.638778 0.535999i −0.264864 0.964286i \(-0.585327\pi\)
0.903643 + 0.428287i \(0.140883\pi\)
\(368\) 1.49343 2.58669i 0.0778503 0.134841i
\(369\) 0 0
\(370\) −5.11194 8.85413i −0.265757 0.460304i
\(371\) −0.318486 0.115919i −0.0165350 0.00601824i
\(372\) 0 0
\(373\) 1.39923 + 1.17409i 0.0724494 + 0.0607923i 0.678293 0.734791i \(-0.262720\pi\)
−0.605844 + 0.795584i \(0.707164\pi\)
\(374\) 14.4051 5.24302i 0.744869 0.271110i
\(375\) 0 0
\(376\) 2.11570 + 11.9987i 0.109109 + 0.618787i
\(377\) 12.4136 0.639332
\(378\) 0 0
\(379\) 1.14694 0.0589141 0.0294571 0.999566i \(-0.490622\pi\)
0.0294571 + 0.999566i \(0.490622\pi\)
\(380\) 4.64283 + 26.3308i 0.238172 + 1.35074i
\(381\) 0 0
\(382\) −1.75252 + 0.637865i −0.0896666 + 0.0326360i
\(383\) 16.7209 + 14.0305i 0.854397 + 0.716924i 0.960753 0.277404i \(-0.0894741\pi\)
−0.106357 + 0.994328i \(0.533919\pi\)
\(384\) 0 0
\(385\) 17.5466 + 6.38646i 0.894260 + 0.325484i
\(386\) 0.192957 + 0.334210i 0.00982123 + 0.0170109i
\(387\) 0 0
\(388\) −4.18281 + 7.24484i −0.212350 + 0.367801i
\(389\) −20.0674 + 16.8386i −1.01746 + 0.853750i −0.989306 0.145854i \(-0.953407\pi\)
−0.0281533 + 0.999604i \(0.508963\pi\)
\(390\) 0 0
\(391\) 4.41772 25.0541i 0.223414 1.26704i
\(392\) −0.340733 + 1.93239i −0.0172096 + 0.0976005i
\(393\) 0 0
\(394\) 13.1945 11.0715i 0.664732 0.557776i
\(395\) 4.84858 8.39798i 0.243958 0.422548i
\(396\) 0 0
\(397\) −2.09915 3.63584i −0.105353 0.182478i 0.808529 0.588456i \(-0.200264\pi\)
−0.913883 + 0.405979i \(0.866931\pi\)
\(398\) 1.55847 + 0.567237i 0.0781191 + 0.0284330i
\(399\) 0 0
\(400\) 0.365127 + 0.306378i 0.0182563 + 0.0153189i
\(401\) 7.35761 2.67795i 0.367422 0.133731i −0.151709 0.988425i \(-0.548478\pi\)
0.519131 + 0.854695i \(0.326256\pi\)
\(402\) 0 0
\(403\) 0.657275 + 3.72759i 0.0327412 + 0.185685i
\(404\) 14.2606 0.709493
\(405\) 0 0
\(406\) 18.0674 0.896669
\(407\) −3.01762 17.1138i −0.149578 0.848298i
\(408\) 0 0
\(409\) 16.3779 5.96107i 0.809835 0.294756i 0.0962793 0.995354i \(-0.469306\pi\)
0.713556 + 0.700599i \(0.247084\pi\)
\(410\) 10.0602 + 8.44147i 0.496836 + 0.416895i
\(411\) 0 0
\(412\) 11.1881 + 4.07214i 0.551199 + 0.200620i
\(413\) 5.00118 + 8.66229i 0.246092 + 0.426243i
\(414\) 0 0
\(415\) −1.08507 + 1.87940i −0.0532642 + 0.0922563i
\(416\) −5.99395 + 5.02952i −0.293877 + 0.246592i
\(417\) 0 0
\(418\) 3.42143 19.4039i 0.167347 0.949074i
\(419\) 1.99403 11.3087i 0.0974148 0.552467i −0.896566 0.442911i \(-0.853946\pi\)
0.993981 0.109556i \(-0.0349430\pi\)
\(420\) 0 0
\(421\) 5.58540 4.68671i 0.272216 0.228416i −0.496452 0.868064i \(-0.665364\pi\)
0.768668 + 0.639648i \(0.220920\pi\)
\(422\) 7.78066 13.4765i 0.378757 0.656026i
\(423\) 0 0
\(424\) 0.178889 + 0.309844i 0.00868759 + 0.0150474i
\(425\) 3.81495 + 1.38853i 0.185052 + 0.0673536i
\(426\) 0 0
\(427\) −0.654942 0.549561i −0.0316949 0.0265951i
\(428\) 10.1537 3.69563i 0.490796 0.178635i
\(429\) 0 0
\(430\) 0.749982 + 4.25336i 0.0361673 + 0.205115i
\(431\) 0.389084 0.0187415 0.00937075 0.999956i \(-0.497017\pi\)
0.00937075 + 0.999956i \(0.497017\pi\)
\(432\) 0 0
\(433\) 24.1011 1.15822 0.579112 0.815248i \(-0.303400\pi\)
0.579112 + 0.815248i \(0.303400\pi\)
\(434\) 0.956633 + 5.42533i 0.0459198 + 0.260424i
\(435\) 0 0
\(436\) 1.64448 0.598543i 0.0787564 0.0286650i
\(437\) −25.0489 21.0186i −1.19825 1.00545i
\(438\) 0 0
\(439\) −34.4544 12.5404i −1.64442 0.598519i −0.656615 0.754226i \(-0.728012\pi\)
−0.987803 + 0.155707i \(0.950235\pi\)
\(440\) −9.85567 17.0705i −0.469851 0.813805i
\(441\) 0 0
\(442\) −3.26131 + 5.64875i −0.155125 + 0.268684i
\(443\) −28.9463 + 24.2888i −1.37528 + 1.15400i −0.404356 + 0.914602i \(0.632504\pi\)
−0.970923 + 0.239394i \(0.923051\pi\)
\(444\) 0 0
\(445\) −1.53866 + 8.72618i −0.0729395 + 0.413661i
\(446\) 1.79328 10.1702i 0.0849143 0.481573i
\(447\) 0 0
\(448\) −5.90078 + 4.95134i −0.278786 + 0.233929i
\(449\) −5.89289 + 10.2068i −0.278103 + 0.481688i −0.970913 0.239432i \(-0.923039\pi\)
0.692811 + 0.721120i \(0.256372\pi\)
\(450\) 0 0
\(451\) 11.1609 + 19.3313i 0.525547 + 0.910274i
\(452\) 23.2843 + 8.47479i 1.09520 + 0.398621i
\(453\) 0 0
\(454\) 7.42990 + 6.23443i 0.348703 + 0.292596i
\(455\) −7.46597 + 2.71739i −0.350010 + 0.127393i
\(456\) 0 0
\(457\) −3.44794 19.5542i −0.161288 0.914709i −0.952810 0.303568i \(-0.901822\pi\)
0.791522 0.611141i \(-0.209289\pi\)
\(458\) −19.9578 −0.932568
\(459\) 0 0
\(460\) −13.4423 −0.626750
\(461\) −1.32699 7.52573i −0.0618041 0.350508i −0.999990 0.00437770i \(-0.998607\pi\)
0.938186 0.346131i \(-0.112505\pi\)
\(462\) 0 0
\(463\) 14.9922 5.45673i 0.696749 0.253596i 0.0307267 0.999528i \(-0.490218\pi\)
0.666022 + 0.745932i \(0.267996\pi\)
\(464\) 5.24091 + 4.39764i 0.243303 + 0.204155i
\(465\) 0 0
\(466\) −3.94387 1.43545i −0.182696 0.0664959i
\(467\) −13.0703 22.6385i −0.604822 1.04758i −0.992080 0.125611i \(-0.959911\pi\)
0.387257 0.921972i \(-0.373423\pi\)
\(468\) 0 0
\(469\) 12.6606 21.9288i 0.584613 1.01258i
\(470\) 6.53268 5.48157i 0.301330 0.252846i
\(471\) 0 0
\(472\) 1.83350 10.3983i 0.0843935 0.478619i
\(473\) −1.27476 + 7.22955i −0.0586137 + 0.332415i
\(474\) 0 0
\(475\) 3.99728 3.35412i 0.183408 0.153897i
\(476\) 10.9483 18.9629i 0.501812 0.869164i
\(477\) 0 0
\(478\) 3.25522 + 5.63820i 0.148890 + 0.257885i
\(479\) −36.9772 13.4586i −1.68953 0.614939i −0.694964 0.719045i \(-0.744580\pi\)
−0.994566 + 0.104106i \(0.966802\pi\)
\(480\) 0 0
\(481\) 5.66422 + 4.75285i 0.258266 + 0.216711i
\(482\) −0.323165 + 0.117622i −0.0147198 + 0.00535756i
\(483\) 0 0
\(484\) 0.274190 + 1.55501i 0.0124632 + 0.0706823i
\(485\) 14.2493 0.647027
\(486\) 0 0
\(487\) 11.7133 0.530779 0.265389 0.964141i \(-0.414500\pi\)
0.265389 + 0.964141i \(0.414500\pi\)
\(488\) 0.156721 + 0.888808i 0.00709442 + 0.0402345i
\(489\) 0 0
\(490\) 1.29057 0.469730i 0.0583022 0.0212203i
\(491\) −29.5309 24.7794i −1.33271 1.11828i −0.983436 0.181256i \(-0.941984\pi\)
−0.349275 0.937020i \(-0.613572\pi\)
\(492\) 0 0
\(493\) 54.7586 + 19.9305i 2.46620 + 0.897624i
\(494\) 4.19178 + 7.26038i 0.188597 + 0.326660i
\(495\) 0 0
\(496\) −1.04304 + 1.80660i −0.0468340 + 0.0811189i
\(497\) 15.6949 13.1696i 0.704014 0.590738i
\(498\) 0 0
\(499\) −5.13332 + 29.1125i −0.229799 + 1.30325i 0.623497 + 0.781826i \(0.285712\pi\)
−0.853295 + 0.521428i \(0.825400\pi\)
\(500\) −2.50600 + 14.2122i −0.112072 + 0.635591i
\(501\) 0 0
\(502\) −10.1452 + 8.51285i −0.452803 + 0.379947i
\(503\) −17.7888 + 30.8110i −0.793161 + 1.37380i 0.130839 + 0.991404i \(0.458233\pi\)
−0.924000 + 0.382392i \(0.875100\pi\)
\(504\) 0 0
\(505\) −12.1452 21.0361i −0.540453 0.936092i
\(506\) 9.30857 + 3.38804i 0.413816 + 0.150617i
\(507\) 0 0
\(508\) 4.23815 + 3.55623i 0.188037 + 0.157782i
\(509\) 26.6707 9.70733i 1.18216 0.430270i 0.325194 0.945647i \(-0.394570\pi\)
0.856963 + 0.515377i \(0.172348\pi\)
\(510\) 0 0
\(511\) 5.34889 + 30.3351i 0.236621 + 1.34195i
\(512\) −8.20265 −0.362510
\(513\) 0 0
\(514\) −16.2365 −0.716161
\(515\) −3.52157 19.9718i −0.155179 0.880062i
\(516\) 0 0
\(517\) 13.6208 4.95756i 0.599041 0.218033i
\(518\) 8.24401 + 6.91754i 0.362221 + 0.303939i
\(519\) 0 0
\(520\) 7.88123 + 2.86853i 0.345615 + 0.125793i
\(521\) 12.7176 + 22.0275i 0.557167 + 0.965041i 0.997731 + 0.0673204i \(0.0214450\pi\)
−0.440565 + 0.897721i \(0.645222\pi\)
\(522\) 0 0
\(523\) −4.20395 + 7.28145i −0.183826 + 0.318396i −0.943180 0.332282i \(-0.892182\pi\)
0.759354 + 0.650677i \(0.225515\pi\)
\(524\) −0.109543 + 0.0919179i −0.00478543 + 0.00401545i
\(525\) 0 0
\(526\) −2.61886 + 14.8523i −0.114188 + 0.647592i
\(527\) −3.08543 + 17.4984i −0.134404 + 0.762241i
\(528\) 0 0
\(529\) −5.02543 + 4.21683i −0.218497 + 0.183341i
\(530\) 0.125209 0.216868i 0.00543873 0.00942016i
\(531\) 0 0
\(532\) −14.0719 24.3732i −0.610093 1.05671i
\(533\) −8.92499 3.24843i −0.386584 0.140705i
\(534\) 0 0
\(535\) −14.0989 11.8304i −0.609549 0.511472i
\(536\) −25.1176 + 9.14207i −1.08492 + 0.394877i
\(537\) 0 0
\(538\) −2.52265 14.3067i −0.108759 0.616804i
\(539\) 2.33440 0.100550
\(540\) 0 0
\(541\) −12.8635 −0.553043 −0.276522 0.961008i \(-0.589182\pi\)
−0.276522 + 0.961008i \(0.589182\pi\)
\(542\) −1.74728 9.90930i −0.0750519 0.425641i
\(543\) 0 0
\(544\) −34.5155 + 12.5626i −1.47984 + 0.538617i
\(545\) −2.28345 1.91604i −0.0978124 0.0820743i
\(546\) 0 0
\(547\) −12.3024 4.47771i −0.526013 0.191453i 0.0653440 0.997863i \(-0.479186\pi\)
−0.591357 + 0.806410i \(0.701408\pi\)
\(548\) 5.31514 + 9.20609i 0.227051 + 0.393265i
\(549\) 0 0
\(550\) −0.790392 + 1.36900i −0.0337024 + 0.0583743i
\(551\) 57.3756 48.1439i 2.44428 2.05100i
\(552\) 0 0
\(553\) −1.77249 + 10.0523i −0.0753739 + 0.427467i
\(554\) −1.41012 + 7.99719i −0.0599103 + 0.339768i
\(555\) 0 0
\(556\) 11.1584 9.36297i 0.473220 0.397079i
\(557\) −2.29110 + 3.96830i −0.0970769 + 0.168142i −0.910474 0.413567i \(-0.864283\pi\)
0.813397 + 0.581710i \(0.197616\pi\)
\(558\) 0 0
\(559\) −1.56179 2.70509i −0.0660565 0.114413i
\(560\) −4.11473 1.49764i −0.173879 0.0632868i
\(561\) 0 0
\(562\) −8.54690 7.17170i −0.360529 0.302520i
\(563\) −11.5431 + 4.20135i −0.486484 + 0.177066i −0.573605 0.819132i \(-0.694456\pi\)
0.0871210 + 0.996198i \(0.472233\pi\)
\(564\) 0 0
\(565\) −7.32895 41.5646i −0.308331 1.74863i
\(566\) 14.5378 0.611071
\(567\) 0 0
\(568\) −21.6278 −0.907484
\(569\) 2.51680 + 14.2735i 0.105510 + 0.598375i 0.991016 + 0.133747i \(0.0427009\pi\)
−0.885506 + 0.464628i \(0.846188\pi\)
\(570\) 0 0
\(571\) 20.7159 7.53996i 0.866932 0.315537i 0.130008 0.991513i \(-0.458500\pi\)
0.736924 + 0.675976i \(0.236278\pi\)
\(572\) 4.48745 + 3.76542i 0.187630 + 0.157440i
\(573\) 0 0
\(574\) −12.9899 4.72794i −0.542188 0.197340i
\(575\) 1.31172 + 2.27197i 0.0547025 + 0.0947475i
\(576\) 0 0
\(577\) 15.7418 27.2655i 0.655338 1.13508i −0.326471 0.945207i \(-0.605859\pi\)
0.981809 0.189872i \(-0.0608072\pi\)
\(578\) −13.3273 + 11.1829i −0.554342 + 0.465148i
\(579\) 0 0
\(580\) 5.34665 30.3224i 0.222008 1.25907i
\(581\) 0.396669 2.24962i 0.0164566 0.0933301i
\(582\) 0 0
\(583\) 0.326061 0.273598i 0.0135041 0.0113313i
\(584\) 16.2582 28.1600i 0.672768 1.16527i
\(585\) 0 0
\(586\) −4.19516 7.26623i −0.173300 0.300165i
\(587\) 13.5029 + 4.91464i 0.557323 + 0.202849i 0.605297 0.796000i \(-0.293054\pi\)
−0.0479743 + 0.998849i \(0.515277\pi\)
\(588\) 0 0
\(589\) 17.4947 + 14.6798i 0.720858 + 0.604872i
\(590\) −6.94463 + 2.52764i −0.285906 + 0.104061i
\(591\) 0 0
\(592\) 0.707639 + 4.01322i 0.0290838 + 0.164942i
\(593\) −41.0988 −1.68772 −0.843862 0.536560i \(-0.819724\pi\)
−0.843862 + 0.536560i \(0.819724\pi\)
\(594\) 0 0
\(595\) −37.2966 −1.52901
\(596\) 2.18825 + 12.4102i 0.0896343 + 0.508341i
\(597\) 0 0
\(598\) −3.96073 + 1.44159i −0.161966 + 0.0589509i
\(599\) 6.55899 + 5.50365i 0.267993 + 0.224873i 0.766874 0.641798i \(-0.221811\pi\)
−0.498881 + 0.866671i \(0.666255\pi\)
\(600\) 0 0
\(601\) 1.53660 + 0.559275i 0.0626790 + 0.0228133i 0.373169 0.927763i \(-0.378271\pi\)
−0.310490 + 0.950577i \(0.600493\pi\)
\(602\) −2.27311 3.93713i −0.0926449 0.160466i
\(603\) 0 0
\(604\) 16.6651 28.8648i 0.678094 1.17449i
\(605\) 2.06030 1.72880i 0.0837631 0.0702856i
\(606\) 0 0
\(607\) 1.14077 6.46963i 0.0463024 0.262594i −0.952865 0.303395i \(-0.901880\pi\)
0.999167 + 0.0408009i \(0.0129909\pi\)
\(608\) −8.19795 + 46.4929i −0.332471 + 1.88554i
\(609\) 0 0
\(610\) 0.483909 0.406048i 0.0195929 0.0164404i
\(611\) −3.08374 + 5.34120i −0.124755 + 0.216082i
\(612\) 0 0
\(613\) 13.1363 + 22.7527i 0.530569 + 0.918973i 0.999364 + 0.0356656i \(0.0113551\pi\)
−0.468795 + 0.883307i \(0.655312\pi\)
\(614\) 0.0363583 + 0.0132334i 0.00146730 + 0.000534055i
\(615\) 0 0
\(616\) 15.8942 + 13.3368i 0.640396 + 0.537356i
\(617\) 5.89472 2.14550i 0.237312 0.0863746i −0.220626 0.975358i \(-0.570810\pi\)
0.457939 + 0.888984i \(0.348588\pi\)
\(618\) 0 0
\(619\) 0.857974 + 4.86581i 0.0344849 + 0.195573i 0.997183 0.0750033i \(-0.0238967\pi\)
−0.962698 + 0.270577i \(0.912786\pi\)
\(620\) 9.38839 0.377047
\(621\) 0 0
\(622\) −10.2936 −0.412738
\(623\) −1.61962 9.18530i −0.0648885 0.368001i
\(624\) 0 0
\(625\) 26.1390 9.51380i 1.04556 0.380552i
\(626\) 8.98606 + 7.54020i 0.359155 + 0.301367i
\(627\) 0 0
\(628\) 3.55540 + 1.29406i 0.141876 + 0.0516387i
\(629\) 17.3550 + 30.0598i 0.691991 + 1.19856i
\(630\) 0 0
\(631\) 3.46210 5.99653i 0.137824 0.238718i −0.788849 0.614587i \(-0.789322\pi\)
0.926673 + 0.375869i \(0.122656\pi\)
\(632\) 8.25420 6.92610i 0.328335 0.275505i
\(633\) 0 0
\(634\) −1.16561 + 6.61049i −0.0462922 + 0.262536i
\(635\) 1.63639 9.28043i 0.0649382 0.368283i
\(636\) 0 0
\(637\) −0.760890 + 0.638463i −0.0301476 + 0.0252968i
\(638\) −11.3450 + 19.6502i −0.449154 + 0.777957i
\(639\) 0 0
\(640\) 11.0653 + 19.1657i 0.437394 + 0.757589i
\(641\) 31.8733 + 11.6009i 1.25892 + 0.458210i 0.883407 0.468607i \(-0.155244\pi\)
0.375514 + 0.926817i \(0.377466\pi\)
\(642\) 0 0
\(643\) 5.91633 + 4.96439i 0.233317 + 0.195776i 0.751949 0.659221i \(-0.229114\pi\)
−0.518632 + 0.854998i \(0.673558\pi\)
\(644\) 13.2962 4.83943i 0.523944 0.190700i
\(645\) 0 0
\(646\) 6.83390 + 38.7569i 0.268876 + 1.52487i
\(647\) 35.1862 1.38331 0.691655 0.722228i \(-0.256882\pi\)
0.691655 + 0.722228i \(0.256882\pi\)
\(648\) 0 0
\(649\) −12.5615 −0.493083
\(650\) −0.116798 0.662393i −0.00458119 0.0259812i
\(651\) 0 0
\(652\) −28.9061 + 10.5210i −1.13205 + 0.412032i
\(653\) 14.9470 + 12.5421i 0.584923 + 0.490808i 0.886560 0.462614i \(-0.153089\pi\)
−0.301637 + 0.953423i \(0.597533\pi\)
\(654\) 0 0
\(655\) 0.228883 + 0.0833065i 0.00894318 + 0.00325505i
\(656\) −2.61726 4.53323i −0.102187 0.176993i
\(657\) 0 0
\(658\) −4.48824 + 7.77386i −0.174970 + 0.303057i
\(659\) 17.6852 14.8397i 0.688919 0.578072i −0.229678 0.973267i \(-0.573767\pi\)
0.918597 + 0.395195i \(0.129323\pi\)
\(660\) 0 0
\(661\) −1.19407 + 6.77189i −0.0464438 + 0.263396i −0.999184 0.0403905i \(-0.987140\pi\)
0.952740 + 0.303786i \(0.0982509\pi\)
\(662\) −4.19005 + 23.7629i −0.162851 + 0.923573i
\(663\) 0 0
\(664\) −1.84723 + 1.55001i −0.0716863 + 0.0601519i
\(665\) −23.9688 + 41.5152i −0.929471 + 1.60989i
\(666\) 0 0
\(667\) 18.8280 + 32.6110i 0.729023 + 1.26270i
\(668\) 11.7345 + 4.27100i 0.454020 + 0.165250i
\(669\) 0 0
\(670\) 14.3318 + 12.0258i 0.553685 + 0.464597i
\(671\) 1.00896 0.367232i 0.0389505 0.0141768i
\(672\) 0 0
\(673\) −5.32619 30.2063i −0.205310 1.16437i −0.896952 0.442128i \(-0.854224\pi\)
0.691642 0.722240i \(-0.256888\pi\)
\(674\) 18.5624 0.714997
\(675\) 0 0
\(676\) 15.6442 0.601700
\(677\) −2.35883 13.3776i −0.0906572 0.514143i −0.995992 0.0894438i \(-0.971491\pi\)
0.905335 0.424699i \(-0.139620\pi\)
\(678\) 0 0
\(679\) −14.0944 + 5.12996i −0.540895 + 0.196870i
\(680\) 30.1600 + 25.3072i 1.15658 + 0.970488i
\(681\) 0 0
\(682\) −6.50131 2.36628i −0.248948 0.0906097i
\(683\) 3.03350 + 5.25418i 0.116074 + 0.201045i 0.918208 0.396098i \(-0.129636\pi\)
−0.802135 + 0.597143i \(0.796302\pi\)
\(684\) 0 0
\(685\) 9.05335 15.6809i 0.345911 0.599135i
\(686\) −11.5393 + 9.68261i −0.440572 + 0.369684i
\(687\) 0 0
\(688\) 0.298935 1.69535i 0.0113968 0.0646345i
\(689\) −0.0314490 + 0.178356i −0.00119811 + 0.00679483i
\(690\) 0 0
\(691\) 15.8304 13.2833i 0.602216 0.505319i −0.289941 0.957044i \(-0.593636\pi\)
0.892157 + 0.451725i \(0.149191\pi\)
\(692\) 1.83756 3.18275i 0.0698537 0.120990i
\(693\) 0 0
\(694\) 8.52054 + 14.7580i 0.323435 + 0.560206i
\(695\) −23.3145 8.48580i −0.884371 0.321885i
\(696\) 0 0
\(697\) −34.1543 28.6588i −1.29368 1.08553i
\(698\) 11.5814 4.21527i 0.438361 0.159550i
\(699\) 0 0
\(700\) 0.392092 + 2.22366i 0.0148197 + 0.0840466i
\(701\) 11.0222 0.416303 0.208151 0.978097i \(-0.433255\pi\)
0.208151 + 0.978097i \(0.433255\pi\)
\(702\) 0 0
\(703\) 44.6131 1.68262
\(704\) −1.67983 9.52680i −0.0633111 0.359055i
\(705\) 0 0
\(706\) 9.43273 3.43323i 0.355006 0.129211i
\(707\) 19.5865 + 16.4350i 0.736626 + 0.618103i
\(708\) 0 0
\(709\) 10.3248 + 3.75793i 0.387757 + 0.141132i 0.528540 0.848909i \(-0.322740\pi\)
−0.140783 + 0.990040i \(0.544962\pi\)
\(710\) 7.56897 + 13.1098i 0.284058 + 0.492003i
\(711\) 0 0
\(712\) −4.92288 + 8.52669i −0.184493 + 0.319551i
\(713\) −8.79564 + 7.38042i −0.329399 + 0.276399i
\(714\) 0 0
\(715\) 1.73265 9.82634i 0.0647974 0.367484i
\(716\) −0.892623 + 5.06231i −0.0333589 + 0.189188i
\(717\) 0 0
\(718\) −15.3880 + 12.9121i −0.574276 + 0.481875i
\(719\) −16.3529 + 28.3240i −0.609859 + 1.05631i 0.381404 + 0.924408i \(0.375441\pi\)
−0.991263 + 0.131898i \(0.957893\pi\)
\(720\) 0 0
\(721\) 10.6734 + 18.4870i 0.397500 + 0.688490i
\(722\) 33.6468 + 12.2464i 1.25220 + 0.455765i
\(723\) 0 0
\(724\) 0.286965 + 0.240792i 0.0106650 + 0.00894896i
\(725\) −5.64670 + 2.05523i −0.209713 + 0.0763294i
\(726\) 0 0
\(727\) 6.67862 + 37.8763i 0.247696 + 1.40475i 0.814147 + 0.580659i \(0.197205\pi\)
−0.566451 + 0.824096i \(0.691684\pi\)
\(728\) −8.82830 −0.327199
\(729\) 0 0
\(730\) −22.7591 −0.842352
\(731\) −2.54619 14.4402i −0.0941743 0.534089i
\(732\) 0 0
\(733\) −13.2569 + 4.82513i −0.489656 + 0.178220i −0.575036 0.818128i \(-0.695012\pi\)
0.0853795 + 0.996349i \(0.472790\pi\)
\(734\) −9.51729 7.98596i −0.351290 0.294767i
\(735\) 0 0
\(736\) −22.3039 8.11797i −0.822134 0.299232i
\(737\) 15.8999 + 27.5395i 0.585681 + 1.01443i
\(738\) 0 0
\(739\) 5.92286 10.2587i 0.217876 0.377372i −0.736283 0.676674i \(-0.763421\pi\)
0.954158 + 0.299302i \(0.0967539\pi\)
\(740\) 14.0493 11.7888i 0.516462 0.433363i
\(741\) 0 0
\(742\) −0.0457725 + 0.259589i −0.00168036 + 0.00952981i
\(743\) −3.77990 + 21.4369i −0.138671 + 0.786442i 0.833562 + 0.552426i \(0.186298\pi\)
−0.972233 + 0.234016i \(0.924813\pi\)
\(744\) 0 0
\(745\) 16.4428 13.7971i 0.602417 0.505488i
\(746\) 0.710290 1.23026i 0.0260056 0.0450429i
\(747\) 0 0
\(748\) 13.7494 + 23.8147i 0.502729 + 0.870753i
\(749\) 18.2048 + 6.62601i 0.665190 + 0.242109i
\(750\) 0 0
\(751\) −32.5944 27.3500i −1.18939 0.998015i −0.999870 0.0161380i \(-0.994863\pi\)
−0.189518 0.981877i \(-0.560693\pi\)
\(752\) −3.19411 + 1.16256i −0.116477 + 0.0423942i
\(753\) 0 0
\(754\) −1.67648 9.50778i −0.0610537 0.346253i
\(755\) −56.7719 −2.06614
\(756\) 0 0
\(757\) −20.6382 −0.750110 −0.375055 0.927003i \(-0.622376\pi\)
−0.375055 + 0.927003i \(0.622376\pi\)
\(758\) −0.154896 0.878457i −0.00562607 0.0319070i
\(759\) 0 0
\(760\) 47.5522 17.3076i 1.72490 0.627812i
\(761\) −37.8771 31.7827i −1.37304 1.15212i −0.971707 0.236189i \(-0.924101\pi\)
−0.401336 0.915931i \(-0.631454\pi\)
\(762\) 0 0
\(763\) 2.94844 + 1.07315i 0.106741 + 0.0388505i
\(764\) −1.67275 2.89729i −0.0605181 0.104820i
\(765\) 0 0
\(766\) 8.48799 14.7016i 0.306684 0.531192i
\(767\) 4.09438 3.43559i 0.147840 0.124052i
\(768\) 0 0
\(769\) 3.84346 21.7973i 0.138599 0.786032i −0.833687 0.552237i \(-0.813774\pi\)
0.972286 0.233795i \(-0.0751145\pi\)
\(770\) 2.52179 14.3018i 0.0908789 0.515400i
\(771\) 0 0
\(772\) −0.530309 + 0.444982i −0.0190862 + 0.0160152i
\(773\) −10.9836 + 19.0241i −0.395051 + 0.684248i −0.993108 0.117206i \(-0.962606\pi\)
0.598057 + 0.801454i \(0.295940\pi\)
\(774\) 0 0
\(775\) −0.916134 1.58679i −0.0329085 0.0569992i
\(776\) 14.8784 + 5.41529i 0.534103 + 0.194398i
\(777\) 0 0
\(778\) 15.6071 + 13.0959i 0.559541 + 0.469511i
\(779\) −53.8498 + 19.5997i −1.92937 + 0.702233i
\(780\) 0 0
\(781\) 4.46803 + 25.3394i 0.159879 + 0.906716i
\(782\) −19.7860 −0.707547
\(783\) 0 0
\(784\) −0.547423 −0.0195508
\(785\) −1.11910 6.34672i −0.0399423 0.226524i
\(786\) 0 0
\(787\) −0.503234 + 0.183162i −0.0179384 + 0.00652903i −0.350974 0.936385i \(-0.614149\pi\)
0.333035 + 0.942914i \(0.391927\pi\)
\(788\) 23.6690 + 19.8606i 0.843173 + 0.707506i
\(789\) 0 0
\(790\) −7.08697 2.57944i −0.252143 0.0917725i
\(791\) 22.2132 + 38.4744i 0.789810 + 1.36799i
\(792\) 0 0
\(793\) −0.228429 + 0.395650i −0.00811174 + 0.0140500i
\(794\) −2.50126 + 2.09880i −0.0887663 + 0.0744837i
\(795\) 0 0
\(796\) −0.516617 + 2.92988i −0.0183110 + 0.103847i
\(797\) 6.96311 39.4898i 0.246646 1.39880i −0.569992 0.821650i \(-0.693054\pi\)
0.816639 0.577149i \(-0.195835\pi\)
\(798\) 0 0
\(799\) −22.1785 + 18.6099i −0.784617 + 0.658372i
\(800\) 1.89383 3.28021i 0.0669570 0.115973i
\(801\) 0 0
\(802\) −3.04475 5.27366i −0.107514 0.186219i
\(803\) −36.3513 13.2308i −1.28281 0.466904i
\(804\) 0 0
\(805\) −18.4625 15.4919i −0.650718 0.546017i
\(806\) 2.76626 1.00684i 0.0974373 0.0354643i
\(807\) 0 0
\(808\) −4.68685 26.5804i −0.164883 0.935096i
\(809\) 17.1826 0.604110 0.302055 0.953291i \(-0.402327\pi\)
0.302055 + 0.953291i \(0.402327\pi\)
\(810\) 0 0
\(811\) −19.6169 −0.688842 −0.344421 0.938815i \(-0.611925\pi\)
−0.344421 + 0.938815i \(0.611925\pi\)
\(812\) 5.62796 + 31.9177i 0.197503 + 1.12009i
\(813\) 0 0
\(814\) −12.7002 + 4.62249i −0.445142 + 0.162018i
\(815\) 40.1376 + 33.6795i 1.40596 + 1.17974i
\(816\) 0 0
\(817\) −17.7098 6.44584i −0.619588 0.225511i
\(818\) −6.77755 11.7391i −0.236971 0.410446i
\(819\) 0 0
\(820\) −11.7789 + 20.4017i −0.411338 + 0.712459i
\(821\) 27.5055 23.0799i 0.959950 0.805494i −0.0209950 0.999780i \(-0.506683\pi\)
0.980945 + 0.194286i \(0.0622390\pi\)
\(822\) 0 0
\(823\) −4.48326 + 25.4258i −0.156277 + 0.886288i 0.801333 + 0.598219i \(0.204125\pi\)
−0.957609 + 0.288070i \(0.906986\pi\)
\(824\) 3.91303 22.1919i 0.136317 0.773091i
\(825\) 0 0
\(826\) 5.95918 5.00034i 0.207346 0.173984i
\(827\) 12.4793 21.6148i 0.433948 0.751619i −0.563261 0.826279i \(-0.690454\pi\)
0.997209 + 0.0746593i \(0.0237869\pi\)
\(828\) 0 0
\(829\) −1.39964 2.42424i −0.0486114 0.0841974i 0.840696 0.541508i \(-0.182146\pi\)
−0.889307 + 0.457310i \(0.848813\pi\)
\(830\) 1.58601 + 0.577260i 0.0550511 + 0.0200370i
\(831\) 0 0
\(832\) 3.15313 + 2.64579i 0.109315 + 0.0917263i
\(833\) −4.38150 + 1.59474i −0.151810 + 0.0552543i
\(834\) 0 0
\(835\) −3.69354 20.9471i −0.127820 0.724904i
\(836\) 35.3445 1.22242
\(837\) 0 0
\(838\) −8.93083 −0.308511
\(839\) −7.76344 44.0287i −0.268024 1.52004i −0.760284 0.649590i \(-0.774940\pi\)
0.492261 0.870448i \(-0.336171\pi\)
\(840\) 0 0
\(841\) −53.7998 + 19.5815i −1.85517 + 0.675225i
\(842\) −4.34395 3.64501i −0.149702 0.125615i
\(843\) 0 0
\(844\) 26.2312 + 9.54736i 0.902914 + 0.328634i
\(845\) −13.3235 23.0770i −0.458342 0.793872i
\(846\) 0 0
\(847\) −1.41552 + 2.45175i −0.0486378 + 0.0842431i
\(848\) −0.0764621 + 0.0641593i −0.00262572 + 0.00220324i
\(849\) 0 0
\(850\) 0.548282 3.10946i 0.0188059 0.106654i
\(851\) −3.89487 + 22.0889i −0.133515 + 0.757199i
\(852\) 0 0
\(853\) −33.3344 + 27.9709i −1.14135 + 0.957704i −0.999482 0.0321814i \(-0.989755\pi\)
−0.141866 + 0.989886i \(0.545310\pi\)
\(854\) −0.332467 + 0.575850i −0.0113768 + 0.0197052i
\(855\) 0 0
\(856\) −10.2254 17.7108i −0.349496 0.605344i
\(857\) −6.86962 2.50034i −0.234662 0.0854099i 0.222013 0.975044i \(-0.428737\pi\)
−0.456674 + 0.889634i \(0.650960\pi\)
\(858\) 0 0
\(859\) −7.40236 6.21132i −0.252565 0.211928i 0.507711 0.861528i \(-0.330492\pi\)
−0.760276 + 0.649600i \(0.774936\pi\)
\(860\) −7.28034 + 2.64983i −0.248258 + 0.0903583i
\(861\) 0 0
\(862\) −0.0525465 0.298006i −0.00178974 0.0101501i
\(863\) 3.15525 0.107406 0.0537030 0.998557i \(-0.482898\pi\)
0.0537030 + 0.998557i \(0.482898\pi\)
\(864\) 0 0
\(865\) −6.25989 −0.212843
\(866\) −3.25489 18.4594i −0.110606 0.627276i
\(867\) 0 0
\(868\) −9.28637 + 3.37996i −0.315200 + 0.114723i
\(869\) −9.81991 8.23988i −0.333118 0.279519i
\(870\) 0 0
\(871\) −12.7146 4.62774i −0.430818 0.156805i
\(872\) −1.65609 2.86844i −0.0560824 0.0971376i
\(873\) 0 0
\(874\) −12.7156 + 22.0240i −0.430110 + 0.744973i
\(875\) −19.8211 + 16.6319i −0.670077 + 0.562262i
\(876\) 0 0
\(877\) −9.18996 + 52.1188i −0.310323 + 1.75993i 0.287003 + 0.957930i \(0.407341\pi\)
−0.597326 + 0.801999i \(0.703770\pi\)
\(878\) −4.95176 + 28.0828i −0.167114 + 0.947749i
\(879\) 0 0
\(880\) 4.21259 3.53479i 0.142007 0.119158i
\(881\) 18.3507 31.7843i 0.618250 1.07084i −0.371555 0.928411i \(-0.621175\pi\)
0.989805 0.142430i \(-0.0454915\pi\)
\(882\) 0 0
\(883\) −14.9551 25.9031i −0.503280 0.871707i −0.999993 0.00379204i \(-0.998793\pi\)
0.496712 0.867915i \(-0.334540\pi\)
\(884\) −10.9949 4.00183i −0.369800 0.134596i
\(885\) 0 0
\(886\) 22.5124 + 18.8902i 0.756320 + 0.634628i
\(887\) 52.3893 19.0681i 1.75906 0.640245i 0.759116 0.650955i \(-0.225631\pi\)
0.999943 + 0.0107097i \(0.00340908\pi\)
\(888\) 0 0
\(889\) 1.72249 + 9.76871i 0.0577704 + 0.327632i
\(890\) 6.89133 0.230998
\(891\) 0 0
\(892\) 18.5252 0.620270
\(893\) 6.46182 + 36.6468i 0.216237 + 1.22634i
\(894\) 0 0
\(895\) 8.22769 2.99463i 0.275021 0.100100i
\(896\) −17.8450 14.9737i −0.596159 0.500237i
\(897\) 0 0
\(898\) 8.61340 + 3.13502i 0.287433 + 0.104617i
\(899\) −13.1499 22.7763i −0.438573 0.759631i
\(900\) 0 0
\(901\) −0.425085 + 0.736269i −0.0141616 + 0.0245287i
\(902\) 13.2988 11.1591i 0.442803 0.371556i
\(903\) 0 0
\(904\) 8.14365 46.1849i 0.270854 1.53609i
\(905\) 0.110800 0.628377i 0.00368311 0.0208880i
\(906\) 0 0
\(907\) 27.5789 23.1414i 0.915741 0.768398i −0.0574613 0.998348i \(-0.518301\pi\)
0.973203 + 0.229950i \(0.0738561\pi\)
\(908\) −8.69930 + 15.0676i −0.288696 + 0.500037i
\(909\) 0 0
\(910\) 3.08959 + 5.35132i 0.102419 + 0.177395i
\(911\) −15.3892 5.60121i −0.509866 0.185576i 0.0742599 0.997239i \(-0.476341\pi\)
−0.584126 + 0.811663i \(0.698563\pi\)
\(912\) 0 0
\(913\) 2.19762 + 1.84402i 0.0727306 + 0.0610282i
\(914\) −14.5113 + 5.28167i −0.479990 + 0.174702i
\(915\) 0 0
\(916\) −6.21683 35.2574i −0.205410 1.16494i
\(917\) −0.256387 −0.00846665
\(918\) 0 0
\(919\) 19.5368 0.644461 0.322231 0.946661i \(-0.395567\pi\)
0.322231 + 0.946661i \(0.395567\pi\)
\(920\) 4.41789 + 25.0551i 0.145654 + 0.826042i
\(921\) 0 0
\(922\) −5.58487 + 2.03273i −0.183928 + 0.0669443i
\(923\) −8.38671 7.03728i −0.276052 0.231635i
\(924\) 0 0
\(925\) −3.36344 1.22419i −0.110589 0.0402512i
\(926\) −6.20413 10.7459i −0.203880 0.353131i
\(927\) 0 0
\(928\) 27.1834 47.0830i 0.892339 1.54558i
\(929\) 8.23584 6.91069i 0.270209 0.226732i −0.497607 0.867403i \(-0.665788\pi\)
0.767816 + 0.640670i \(0.221343\pi\)
\(930\) 0 0
\(931\) −1.04067 + 5.90195i −0.0341067 + 0.193429i
\(932\) 1.30735 7.41435i 0.0428237 0.242865i
\(933\) 0 0
\(934\) −15.5740 + 13.0681i −0.509597 + 0.427603i
\(935\) 23.4196 40.5639i 0.765903 1.32658i
\(936\) 0 0
\(937\) 14.2219 + 24.6330i 0.464609 + 0.804727i 0.999184 0.0403947i \(-0.0128615\pi\)
−0.534575 + 0.845121i \(0.679528\pi\)
\(938\) −18.5055 6.73545i −0.604226 0.219920i
\(939\) 0 0
\(940\) 11.7186 + 9.83309i 0.382219 + 0.320720i
\(941\) −26.0864 + 9.49466i −0.850391 + 0.309517i −0.730200 0.683234i \(-0.760573\pi\)
−0.120191 + 0.992751i \(0.538351\pi\)
\(942\) 0 0
\(943\) −5.00298 28.3733i −0.162919 0.923962i
\(944\) 2.94571 0.0958746
\(945\) 0 0
\(946\) 5.70939 0.185628
\(947\) 7.37580 + 41.8302i 0.239681 + 1.35930i 0.832527 + 0.553984i \(0.186893\pi\)
−0.592846 + 0.805316i \(0.701996\pi\)
\(948\) 0 0
\(949\) 15.4672 5.62960i 0.502087 0.182745i
\(950\) −3.10882 2.60861i −0.100863 0.0846343i
\(951\) 0 0
\(952\) −38.9432 14.1742i −1.26216 0.459388i
\(953\) −24.5758 42.5665i −0.796088 1.37886i −0.922146 0.386842i \(-0.873566\pi\)
0.126058 0.992023i \(-0.459767\pi\)
\(954\) 0 0
\(955\) −2.84922 + 4.93500i −0.0921987 + 0.159693i
\(956\) −8.94641 + 7.50693i −0.289348 + 0.242792i
\(957\) 0 0
\(958\) −5.31433 + 30.1390i −0.171698 + 0.973748i
\(959\) −3.30962 + 18.7698i −0.106873 + 0.606109i
\(960\) 0 0
\(961\) −17.6043 + 14.7718i −0.567881 + 0.476509i
\(962\) 2.87532 4.98021i 0.0927041 0.160568i
\(963\) 0 0
\(964\) −0.308456 0.534262i −0.00993471 0.0172074i
\(965\) 1.10804 + 0.403293i 0.0356690 + 0.0129825i
\(966\) 0 0
\(967\) 36.7602 + 30.8454i 1.18213 + 0.991923i 0.999963 + 0.00865458i \(0.00275487\pi\)
0.182165 + 0.983268i \(0.441690\pi\)
\(968\) 2.80827 1.02213i 0.0902613 0.0328524i
\(969\) 0 0
\(970\) −1.92439 10.9138i −0.0617885 0.350420i
\(971\) −28.9682 −0.929633 −0.464817 0.885407i \(-0.653880\pi\)
−0.464817 + 0.885407i \(0.653880\pi\)
\(972\) 0 0
\(973\) 26.1162 0.837247
\(974\) −1.58190 8.97139i −0.0506873 0.287462i
\(975\) 0 0
\(976\) −0.236604 + 0.0861168i −0.00757351 + 0.00275653i
\(977\) −11.6417 9.76855i −0.372451 0.312524i 0.437279 0.899326i \(-0.355942\pi\)
−0.809730 + 0.586802i \(0.800387\pi\)
\(978\) 0 0
\(979\) 11.0070 + 4.00621i 0.351784 + 0.128039i
\(980\) 1.23183 + 2.13360i 0.0393495 + 0.0681553i
\(981\) 0 0
\(982\) −14.9907 + 25.9647i −0.478373 + 0.828567i
\(983\) −29.5480 + 24.7937i −0.942435 + 0.790797i −0.978007 0.208570i \(-0.933119\pi\)
0.0355724 + 0.999367i \(0.488675\pi\)
\(984\) 0 0
\(985\) 9.13883 51.8289i 0.291187 1.65141i
\(986\) 7.86986 44.6322i 0.250627 1.42138i
\(987\) 0 0
\(988\) −11.5204 + 9.66678i −0.366513 + 0.307541i
\(989\) 4.73760 8.20576i 0.150647 0.260928i
\(990\) 0 0
\(991\) −25.5171 44.1968i −0.810576 1.40396i −0.912461 0.409163i \(-0.865821\pi\)
0.101885 0.994796i \(-0.467512\pi\)
\(992\) 15.5776 + 5.66977i 0.494588 + 0.180015i
\(993\) 0 0
\(994\) −12.2065 10.2424i −0.387165 0.324870i
\(995\) 4.76188 1.73318i 0.150962 0.0549456i
\(996\) 0 0
\(997\) 5.52154 + 31.3142i 0.174869 + 0.991730i 0.938295 + 0.345835i \(0.112404\pi\)
−0.763426 + 0.645895i \(0.776484\pi\)
\(998\) 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.u.82.1 12
3.2 odd 2 729.2.e.j.82.2 12
9.2 odd 6 729.2.e.t.325.2 12
9.4 even 3 729.2.e.l.568.2 12
9.5 odd 6 729.2.e.s.568.1 12
9.7 even 3 729.2.e.k.325.1 12
27.2 odd 18 729.2.e.j.649.2 12
27.4 even 9 729.2.c.a.487.5 12
27.5 odd 18 729.2.a.b.1.5 6
27.7 even 9 729.2.e.k.406.1 12
27.11 odd 18 729.2.e.s.163.1 12
27.13 even 9 729.2.c.a.244.5 12
27.14 odd 18 729.2.c.d.244.2 12
27.16 even 9 729.2.e.l.163.2 12
27.20 odd 18 729.2.e.t.406.2 12
27.22 even 9 729.2.a.e.1.2 yes 6
27.23 odd 18 729.2.c.d.487.2 12
27.25 even 9 inner 729.2.e.u.649.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.5 6 27.5 odd 18
729.2.a.e.1.2 yes 6 27.22 even 9
729.2.c.a.244.5 12 27.13 even 9
729.2.c.a.487.5 12 27.4 even 9
729.2.c.d.244.2 12 27.14 odd 18
729.2.c.d.487.2 12 27.23 odd 18
729.2.e.j.82.2 12 3.2 odd 2
729.2.e.j.649.2 12 27.2 odd 18
729.2.e.k.325.1 12 9.7 even 3
729.2.e.k.406.1 12 27.7 even 9
729.2.e.l.163.2 12 27.16 even 9
729.2.e.l.568.2 12 9.4 even 3
729.2.e.s.163.1 12 27.11 odd 18
729.2.e.s.568.1 12 9.5 odd 6
729.2.e.t.325.2 12 9.2 odd 6
729.2.e.t.406.2 12 27.20 odd 18
729.2.e.u.82.1 12 1.1 even 1 trivial
729.2.e.u.649.1 12 27.25 even 9 inner