Properties

Label 729.2.e.s.82.1
Level $729$
Weight $2$
Character 729.82
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 \(-1.37340i\) of defining polynomial
Character \(\chi\) \(=\) 729.82
Dual form 729.2.e.s.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.469730 - 2.66397i) q^{2} +(-4.99670 + 1.81865i) q^{4} +(1.28112 + 1.07499i) q^{5} +(-0.470402 - 0.171212i) q^{7} +(4.48686 + 7.77147i) q^{8} +O(q^{10})\) \(q+(-0.469730 - 2.66397i) q^{2} +(-4.99670 + 1.81865i) q^{4} +(1.28112 + 1.07499i) q^{5} +(-0.470402 - 0.171212i) q^{7} +(4.48686 + 7.77147i) q^{8} +(2.26195 - 3.91782i) q^{10} +(1.46906 - 1.23269i) q^{11} +(0.540469 - 3.06515i) q^{13} +(-0.235142 + 1.33356i) q^{14} +(10.4486 - 8.76745i) q^{16} +(1.33234 - 2.30767i) q^{17} +(-2.89832 - 5.02003i) q^{19} +(-8.35640 - 3.04148i) q^{20} +(-3.97390 - 3.33449i) q^{22} +(-4.36569 + 1.58898i) q^{23} +(-0.382569 - 2.16966i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(0.454102 + 2.57534i) q^{29} +(4.33631 - 1.57829i) q^{31} +(-14.5157 - 12.1801i) q^{32} +(-6.77341 - 2.46532i) q^{34} +(-0.418591 - 0.725020i) q^{35} +(2.42934 - 4.20773i) q^{37} +(-12.0118 + 10.0791i) q^{38} +(-2.60603 + 14.7795i) q^{40} +(2.00532 - 11.3727i) q^{41} +(-6.89772 + 5.78788i) q^{43} +(-5.09861 + 8.83106i) q^{44} +(6.28369 + 10.8837i) q^{46} +(6.42020 + 2.33676i) q^{47} +(-5.17035 - 4.33844i) q^{49} +(-5.60020 + 2.03831i) q^{50} +(2.87388 + 16.2986i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(-0.780056 - 4.42392i) q^{56} +(6.64732 - 2.41943i) q^{58} +(1.67864 + 1.40855i) q^{59} +(-6.42781 - 2.33953i) q^{61} +(-6.24140 - 10.8104i) q^{62} +(-11.9893 + 20.7661i) q^{64} +(3.98741 - 3.34583i) q^{65} +(2.16775 - 12.2939i) q^{67} +(-2.46043 + 13.9538i) q^{68} +(-1.73481 + 1.45568i) q^{70} +(-1.41784 + 2.45578i) q^{71} +(-4.96749 - 8.60394i) q^{73} +(-12.3504 - 4.49518i) q^{74} +(23.6117 + 19.8126i) q^{76} +(-0.902098 + 0.328337i) q^{77} +(0.922282 + 5.23052i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(0.473738 + 2.68670i) q^{83} +(4.18761 - 1.52416i) q^{85} +(18.6588 + 15.6566i) q^{86} +(16.1712 + 5.88584i) q^{88} +(5.60945 + 9.71585i) q^{89} +(-0.779029 + 1.34932i) q^{91} +(18.9242 - 15.8793i) q^{92} +(3.20930 - 18.2009i) q^{94} +(1.68338 - 9.54693i) q^{95} +(-5.27739 + 4.42826i) q^{97} +(-9.12879 + 15.8115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.469730 2.66397i −0.332149 1.88371i −0.453746 0.891131i \(-0.649913\pi\)
0.121597 0.992580i \(-0.461198\pi\)
\(3\) 0 0
\(4\) −4.99670 + 1.81865i −2.49835 + 0.909325i
\(5\) 1.28112 + 1.07499i 0.572935 + 0.480749i 0.882618 0.470090i \(-0.155779\pi\)
−0.309684 + 0.950840i \(0.600223\pi\)
\(6\) 0 0
\(7\) −0.470402 0.171212i −0.177795 0.0647122i 0.251589 0.967834i \(-0.419047\pi\)
−0.429384 + 0.903122i \(0.641269\pi\)
\(8\) 4.48686 + 7.77147i 1.58634 + 2.74763i
\(9\) 0 0
\(10\) 2.26195 3.91782i 0.715293 1.23892i
\(11\) 1.46906 1.23269i 0.442937 0.371669i −0.393870 0.919166i \(-0.628864\pi\)
0.836807 + 0.547498i \(0.184419\pi\)
\(12\) 0 0
\(13\) 0.540469 3.06515i 0.149899 0.850120i −0.813403 0.581700i \(-0.802388\pi\)
0.963302 0.268419i \(-0.0865013\pi\)
\(14\) −0.235142 + 1.33356i −0.0628445 + 0.356409i
\(15\) 0 0
\(16\) 10.4486 8.76745i 2.61216 2.19186i
\(17\) 1.33234 2.30767i 0.323139 0.559693i −0.657995 0.753022i \(-0.728595\pi\)
0.981134 + 0.193329i \(0.0619285\pi\)
\(18\) 0 0
\(19\) −2.89832 5.02003i −0.664920 1.15167i −0.979307 0.202380i \(-0.935132\pi\)
0.314387 0.949295i \(-0.398201\pi\)
\(20\) −8.35640 3.04148i −1.86855 0.680096i
\(21\) 0 0
\(22\) −3.97390 3.33449i −0.847237 0.710917i
\(23\) −4.36569 + 1.58898i −0.910309 + 0.331325i −0.754376 0.656442i \(-0.772061\pi\)
−0.155933 + 0.987768i \(0.549838\pi\)
\(24\) 0 0
\(25\) −0.382569 2.16966i −0.0765139 0.433932i
\(26\) −8.41934 −1.65117
\(27\) 0 0
\(28\) 2.66183 0.503039
\(29\) 0.454102 + 2.57534i 0.0843247 + 0.478229i 0.997500 + 0.0706626i \(0.0225114\pi\)
−0.913176 + 0.407566i \(0.866378\pi\)
\(30\) 0 0
\(31\) 4.33631 1.57829i 0.778824 0.283469i 0.0781418 0.996942i \(-0.475101\pi\)
0.700682 + 0.713473i \(0.252879\pi\)
\(32\) −14.5157 12.1801i −2.56604 2.15316i
\(33\) 0 0
\(34\) −6.77341 2.46532i −1.16163 0.422799i
\(35\) −0.418591 0.725020i −0.0707547 0.122551i
\(36\) 0 0
\(37\) 2.42934 4.20773i 0.399381 0.691747i −0.594269 0.804266i \(-0.702559\pi\)
0.993650 + 0.112519i \(0.0358919\pi\)
\(38\) −12.0118 + 10.0791i −1.94857 + 1.63504i
\(39\) 0 0
\(40\) −2.60603 + 14.7795i −0.412049 + 2.33685i
\(41\) 2.00532 11.3727i 0.313178 1.77612i −0.269082 0.963117i \(-0.586720\pi\)
0.582260 0.813003i \(-0.302169\pi\)
\(42\) 0 0
\(43\) −6.89772 + 5.78788i −1.05189 + 0.882643i −0.993291 0.115639i \(-0.963109\pi\)
−0.0586014 + 0.998281i \(0.518664\pi\)
\(44\) −5.09861 + 8.83106i −0.768645 + 1.33133i
\(45\) 0 0
\(46\) 6.28369 + 10.8837i 0.926479 + 1.60471i
\(47\) 6.42020 + 2.33676i 0.936483 + 0.340852i 0.764776 0.644296i \(-0.222850\pi\)
0.171707 + 0.985148i \(0.445072\pi\)
\(48\) 0 0
\(49\) −5.17035 4.33844i −0.738621 0.619777i
\(50\) −5.60020 + 2.03831i −0.791988 + 0.288260i
\(51\) 0 0
\(52\) 2.87388 + 16.2986i 0.398535 + 2.26020i
\(53\) 5.43322 0.746309 0.373155 0.927769i \(-0.378276\pi\)
0.373155 + 0.927769i \(0.378276\pi\)
\(54\) 0 0
\(55\) 3.20716 0.432454
\(56\) −0.780056 4.42392i −0.104239 0.591171i
\(57\) 0 0
\(58\) 6.64732 2.41943i 0.872836 0.317686i
\(59\) 1.67864 + 1.40855i 0.218541 + 0.183377i 0.745485 0.666522i \(-0.232218\pi\)
−0.526944 + 0.849900i \(0.676662\pi\)
\(60\) 0 0
\(61\) −6.42781 2.33953i −0.822997 0.299547i −0.104016 0.994576i \(-0.533169\pi\)
−0.718982 + 0.695029i \(0.755391\pi\)
\(62\) −6.24140 10.8104i −0.792659 1.37293i
\(63\) 0 0
\(64\) −11.9893 + 20.7661i −1.49866 + 2.59576i
\(65\) 3.98741 3.34583i 0.494577 0.414999i
\(66\) 0 0
\(67\) 2.16775 12.2939i 0.264833 1.50194i −0.504676 0.863309i \(-0.668388\pi\)
0.769509 0.638635i \(-0.220501\pi\)
\(68\) −2.46043 + 13.9538i −0.298371 + 1.69215i
\(69\) 0 0
\(70\) −1.73481 + 1.45568i −0.207349 + 0.173986i
\(71\) −1.41784 + 2.45578i −0.168267 + 0.291447i −0.937811 0.347147i \(-0.887150\pi\)
0.769544 + 0.638594i \(0.220484\pi\)
\(72\) 0 0
\(73\) −4.96749 8.60394i −0.581400 1.00701i −0.995314 0.0966986i \(-0.969172\pi\)
0.413913 0.910316i \(-0.364162\pi\)
\(74\) −12.3504 4.49518i −1.43571 0.522554i
\(75\) 0 0
\(76\) 23.6117 + 19.8126i 2.70845 + 2.27266i
\(77\) −0.902098 + 0.328337i −0.102804 + 0.0374175i
\(78\) 0 0
\(79\) 0.922282 + 5.23052i 0.103765 + 0.588480i 0.991706 + 0.128524i \(0.0410238\pi\)
−0.887942 + 0.459956i \(0.847865\pi\)
\(80\) 22.8109 2.55033
\(81\) 0 0
\(82\) −31.2385 −3.44972
\(83\) 0.473738 + 2.68670i 0.0519995 + 0.294904i 0.999706 0.0242387i \(-0.00771617\pi\)
−0.947707 + 0.319143i \(0.896605\pi\)
\(84\) 0 0
\(85\) 4.18761 1.52416i 0.454210 0.165319i
\(86\) 18.6588 + 15.6566i 2.01203 + 1.68829i
\(87\) 0 0
\(88\) 16.1712 + 5.88584i 1.72386 + 0.627433i
\(89\) 5.60945 + 9.71585i 0.594600 + 1.02988i 0.993603 + 0.112928i \(0.0360230\pi\)
−0.399003 + 0.916950i \(0.630644\pi\)
\(90\) 0 0
\(91\) −0.779029 + 1.34932i −0.0816644 + 0.141447i
\(92\) 18.9242 15.8793i 1.97299 1.65553i
\(93\) 0 0
\(94\) 3.20930 18.2009i 0.331014 1.87728i
\(95\) 1.68338 9.54693i 0.172711 0.979494i
\(96\) 0 0
\(97\) −5.27739 + 4.42826i −0.535838 + 0.449621i −0.870112 0.492855i \(-0.835953\pi\)
0.334274 + 0.942476i \(0.391509\pi\)
\(98\) −9.12879 + 15.8115i −0.922147 + 1.59721i
\(99\) 0 0
\(100\) 5.85743 + 10.1454i 0.585743 + 1.01454i
\(101\) 3.50472 + 1.27561i 0.348733 + 0.126928i 0.510447 0.859909i \(-0.329480\pi\)
−0.161714 + 0.986838i \(0.551702\pi\)
\(102\) 0 0
\(103\) 5.88383 + 4.93712i 0.579751 + 0.486469i 0.884865 0.465847i \(-0.154250\pi\)
−0.305114 + 0.952316i \(0.598695\pi\)
\(104\) 26.2457 9.55266i 2.57360 0.936715i
\(105\) 0 0
\(106\) −2.55214 14.4739i −0.247886 1.40583i
\(107\) 10.7658 1.04077 0.520383 0.853933i \(-0.325789\pi\)
0.520383 + 0.853933i \(0.325789\pi\)
\(108\) 0 0
\(109\) 12.2298 1.17141 0.585703 0.810526i \(-0.300819\pi\)
0.585703 + 0.810526i \(0.300819\pi\)
\(110\) −1.50650 8.54378i −0.143639 0.814618i
\(111\) 0 0
\(112\) −6.41616 + 2.33529i −0.606270 + 0.220664i
\(113\) 1.48915 + 1.24955i 0.140088 + 0.117547i 0.710139 0.704062i \(-0.248632\pi\)
−0.570051 + 0.821609i \(0.693077\pi\)
\(114\) 0 0
\(115\) −7.30111 2.65739i −0.680832 0.247803i
\(116\) −6.95266 12.0424i −0.645538 1.11810i
\(117\) 0 0
\(118\) 2.96382 5.13349i 0.272842 0.472576i
\(119\) −1.02184 + 0.857422i −0.0936715 + 0.0785997i
\(120\) 0 0
\(121\) −1.27151 + 7.21111i −0.115592 + 0.655556i
\(122\) −3.21311 + 18.2224i −0.290901 + 1.64978i
\(123\) 0 0
\(124\) −18.7969 + 15.7725i −1.68801 + 1.41641i
\(125\) 6.02320 10.4325i 0.538732 0.933110i
\(126\) 0 0
\(127\) −1.17217 2.03025i −0.104013 0.180156i 0.809322 0.587366i \(-0.199835\pi\)
−0.913335 + 0.407210i \(0.866502\pi\)
\(128\) 25.3396 + 9.22286i 2.23973 + 0.815194i
\(129\) 0 0
\(130\) −10.7862 9.05069i −0.946012 0.793798i
\(131\) −16.0710 + 5.84936i −1.40413 + 0.511061i −0.929401 0.369072i \(-0.879676\pi\)
−0.474728 + 0.880133i \(0.657453\pi\)
\(132\) 0 0
\(133\) 0.503883 + 2.85766i 0.0436922 + 0.247791i
\(134\) −33.7689 −2.91719
\(135\) 0 0
\(136\) 23.9120 2.05044
\(137\) −2.41843 13.7156i −0.206620 1.17180i −0.894870 0.446327i \(-0.852732\pi\)
0.688250 0.725474i \(-0.258379\pi\)
\(138\) 0 0
\(139\) −7.43920 + 2.70765i −0.630985 + 0.229660i −0.637660 0.770318i \(-0.720098\pi\)
0.00667492 + 0.999978i \(0.497875\pi\)
\(140\) 3.41013 + 2.86144i 0.288208 + 0.241836i
\(141\) 0 0
\(142\) 7.20811 + 2.62354i 0.604891 + 0.220162i
\(143\) −2.98439 5.16911i −0.249567 0.432263i
\(144\) 0 0
\(145\) −2.18670 + 3.78748i −0.181596 + 0.314533i
\(146\) −20.5872 + 17.2748i −1.70381 + 1.42967i
\(147\) 0 0
\(148\) −4.48627 + 25.4429i −0.368769 + 2.09139i
\(149\) −0.126439 + 0.717072i −0.0103583 + 0.0587449i −0.989549 0.144198i \(-0.953940\pi\)
0.979190 + 0.202943i \(0.0650507\pi\)
\(150\) 0 0
\(151\) 3.32623 2.79104i 0.270685 0.227132i −0.497333 0.867560i \(-0.665687\pi\)
0.768018 + 0.640428i \(0.221243\pi\)
\(152\) 26.0087 45.0484i 2.10958 3.65390i
\(153\) 0 0
\(154\) 1.29842 + 2.24893i 0.104630 + 0.181224i
\(155\) 7.25198 + 2.63950i 0.582493 + 0.212010i
\(156\) 0 0
\(157\) −11.8915 9.97816i −0.949046 0.796344i 0.0300908 0.999547i \(-0.490420\pi\)
−0.979137 + 0.203203i \(0.934865\pi\)
\(158\) 13.5007 4.91386i 1.07406 0.390926i
\(159\) 0 0
\(160\) −5.50289 31.2085i −0.435042 2.46725i
\(161\) 2.32568 0.183289
\(162\) 0 0
\(163\) 8.49738 0.665566 0.332783 0.943003i \(-0.392012\pi\)
0.332783 + 0.943003i \(0.392012\pi\)
\(164\) 10.6630 + 60.4730i 0.832642 + 4.72215i
\(165\) 0 0
\(166\) 6.93477 2.52405i 0.538242 0.195904i
\(167\) −17.7278 14.8754i −1.37182 1.15109i −0.972131 0.234436i \(-0.924676\pi\)
−0.399684 0.916653i \(-0.630880\pi\)
\(168\) 0 0
\(169\) 3.11296 + 1.13303i 0.239459 + 0.0871559i
\(170\) −6.02737 10.4397i −0.462278 0.800689i
\(171\) 0 0
\(172\) 23.9397 41.4648i 1.82539 3.16166i
\(173\) 1.97523 1.65741i 0.150174 0.126011i −0.564605 0.825361i \(-0.690972\pi\)
0.714779 + 0.699350i \(0.246527\pi\)
\(174\) 0 0
\(175\) −0.191511 + 1.08611i −0.0144769 + 0.0821023i
\(176\) 4.54214 25.7598i 0.342377 1.94172i
\(177\) 0 0
\(178\) 23.2478 19.5072i 1.74250 1.46213i
\(179\) −4.44806 + 7.70427i −0.332464 + 0.575844i −0.982994 0.183636i \(-0.941213\pi\)
0.650530 + 0.759480i \(0.274547\pi\)
\(180\) 0 0
\(181\) −3.95592 6.85185i −0.294041 0.509294i 0.680720 0.732543i \(-0.261667\pi\)
−0.974761 + 0.223250i \(0.928334\pi\)
\(182\) 3.96047 + 1.44149i 0.293570 + 0.106851i
\(183\) 0 0
\(184\) −31.9369 26.7983i −2.35442 1.97559i
\(185\) 7.63554 2.77911i 0.561376 0.204324i
\(186\) 0 0
\(187\) −0.887358 5.03246i −0.0648900 0.368010i
\(188\) −36.3296 −2.64961
\(189\) 0 0
\(190\) −26.2235 −1.90245
\(191\) 2.76055 + 15.6558i 0.199746 + 1.13282i 0.905496 + 0.424355i \(0.139499\pi\)
−0.705750 + 0.708461i \(0.749390\pi\)
\(192\) 0 0
\(193\) 4.30828 1.56809i 0.310117 0.112873i −0.182273 0.983248i \(-0.558346\pi\)
0.492390 + 0.870375i \(0.336123\pi\)
\(194\) 14.2757 + 11.9787i 1.02493 + 0.860022i
\(195\) 0 0
\(196\) 33.7248 + 12.2748i 2.40891 + 0.876772i
\(197\) 1.49708 + 2.59303i 0.106663 + 0.184745i 0.914416 0.404775i \(-0.132650\pi\)
−0.807754 + 0.589520i \(0.799317\pi\)
\(198\) 0 0
\(199\) −7.44425 + 12.8938i −0.527709 + 0.914018i 0.471770 + 0.881722i \(0.343615\pi\)
−0.999478 + 0.0322965i \(0.989718\pi\)
\(200\) 15.1449 12.7081i 1.07091 0.898597i
\(201\) 0 0
\(202\) 1.75193 9.93566i 0.123265 0.699071i
\(203\) 0.227320 1.28919i 0.0159547 0.0904836i
\(204\) 0 0
\(205\) 14.7946 12.4141i 1.03330 0.867041i
\(206\) 10.3885 17.9935i 0.723803 1.25366i
\(207\) 0 0
\(208\) −21.2264 36.7652i −1.47179 2.54921i
\(209\) −10.4459 3.80200i −0.722559 0.262990i
\(210\) 0 0
\(211\) 10.6319 + 8.92122i 0.731930 + 0.614162i 0.930657 0.365893i \(-0.119236\pi\)
−0.198727 + 0.980055i \(0.563681\pi\)
\(212\) −27.1481 + 9.88111i −1.86454 + 0.678638i
\(213\) 0 0
\(214\) −5.05699 28.6796i −0.345689 1.96050i
\(215\) −15.0587 −1.02700
\(216\) 0 0
\(217\) −2.31003 −0.156815
\(218\) −5.74472 32.5799i −0.389081 2.20659i
\(219\) 0 0
\(220\) −16.0252 + 5.83271i −1.08042 + 0.393241i
\(221\) −6.35328 5.33104i −0.427368 0.358604i
\(222\) 0 0
\(223\) 6.40117 + 2.32983i 0.428654 + 0.156017i 0.547332 0.836916i \(-0.315643\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(224\) 4.74283 + 8.21483i 0.316894 + 0.548876i
\(225\) 0 0
\(226\) 2.62925 4.55400i 0.174895 0.302928i
\(227\) 7.46192 6.26129i 0.495265 0.415577i −0.360644 0.932704i \(-0.617443\pi\)
0.855909 + 0.517127i \(0.172999\pi\)
\(228\) 0 0
\(229\) −2.43886 + 13.8315i −0.161165 + 0.914009i 0.791767 + 0.610823i \(0.209161\pi\)
−0.952931 + 0.303186i \(0.901950\pi\)
\(230\) −3.64965 + 20.6982i −0.240651 + 1.36480i
\(231\) 0 0
\(232\) −17.9767 + 15.0842i −1.18023 + 0.990328i
\(233\) 2.66167 4.61014i 0.174372 0.302020i −0.765572 0.643350i \(-0.777544\pi\)
0.939944 + 0.341330i \(0.110877\pi\)
\(234\) 0 0
\(235\) 5.71307 + 9.89532i 0.372679 + 0.645499i
\(236\) −10.9493 3.98523i −0.712741 0.259416i
\(237\) 0 0
\(238\) 2.76413 + 2.31938i 0.179172 + 0.150343i
\(239\) 16.7016 6.07890i 1.08034 0.393211i 0.260305 0.965526i \(-0.416177\pi\)
0.820034 + 0.572315i \(0.193955\pi\)
\(240\) 0 0
\(241\) −0.348476 1.97631i −0.0224473 0.127305i 0.971525 0.236938i \(-0.0761437\pi\)
−0.993972 + 0.109633i \(0.965033\pi\)
\(242\) 19.8075 1.27327
\(243\) 0 0
\(244\) 36.3726 2.32852
\(245\) −1.96007 11.1161i −0.125224 0.710183i
\(246\) 0 0
\(247\) −16.9536 + 6.17061i −1.07873 + 0.392626i
\(248\) 31.7220 + 26.6179i 2.01435 + 1.69024i
\(249\) 0 0
\(250\) −30.6211 11.1452i −1.93665 0.704883i
\(251\) 11.7822 + 20.4073i 0.743683 + 1.28810i 0.950808 + 0.309782i \(0.100256\pi\)
−0.207125 + 0.978314i \(0.566411\pi\)
\(252\) 0 0
\(253\) −4.45473 + 7.71582i −0.280067 + 0.485090i
\(254\) −4.85793 + 4.07628i −0.304813 + 0.255769i
\(255\) 0 0
\(256\) 4.33897 24.6075i 0.271186 1.53797i
\(257\) −1.02011 + 5.78532i −0.0636326 + 0.360878i 0.936320 + 0.351148i \(0.114208\pi\)
−0.999953 + 0.00973053i \(0.996903\pi\)
\(258\) 0 0
\(259\) −1.86318 + 1.56339i −0.115772 + 0.0971446i
\(260\) −13.8390 + 23.9698i −0.858257 + 1.48654i
\(261\) 0 0
\(262\) 23.1315 + 40.0650i 1.42907 + 2.47522i
\(263\) 20.6527 + 7.51696i 1.27350 + 0.463516i 0.888277 0.459308i \(-0.151903\pi\)
0.385222 + 0.922824i \(0.374125\pi\)
\(264\) 0 0
\(265\) 6.96061 + 5.84064i 0.427587 + 0.358788i
\(266\) 7.37603 2.68466i 0.452253 0.164607i
\(267\) 0 0
\(268\) 11.5268 + 65.3715i 0.704109 + 3.99320i
\(269\) 30.6026 1.86587 0.932937 0.360041i \(-0.117237\pi\)
0.932937 + 0.360041i \(0.117237\pi\)
\(270\) 0 0
\(271\) −16.0823 −0.976928 −0.488464 0.872584i \(-0.662443\pi\)
−0.488464 + 0.872584i \(0.662443\pi\)
\(272\) −6.31131 35.7932i −0.382680 2.17028i
\(273\) 0 0
\(274\) −35.4019 + 12.8852i −2.13870 + 0.778425i
\(275\) −3.23652 2.71577i −0.195170 0.163767i
\(276\) 0 0
\(277\) 19.5584 + 7.11866i 1.17515 + 0.427719i 0.854486 0.519475i \(-0.173872\pi\)
0.320662 + 0.947194i \(0.396095\pi\)
\(278\) 10.7075 + 18.5459i 0.642194 + 1.11231i
\(279\) 0 0
\(280\) 3.75631 6.50612i 0.224483 0.388815i
\(281\) −9.39192 + 7.88075i −0.560275 + 0.470126i −0.878403 0.477921i \(-0.841390\pi\)
0.318128 + 0.948048i \(0.396946\pi\)
\(282\) 0 0
\(283\) 0.794020 4.50311i 0.0471996 0.267682i −0.952071 0.305878i \(-0.901050\pi\)
0.999270 + 0.0381959i \(0.0121611\pi\)
\(284\) 2.61834 14.8493i 0.155370 0.881145i
\(285\) 0 0
\(286\) −12.3685 + 10.3784i −0.731364 + 0.613687i
\(287\) −2.89045 + 5.00641i −0.170618 + 0.295519i
\(288\) 0 0
\(289\) 4.94976 + 8.57324i 0.291162 + 0.504308i
\(290\) 11.1169 + 4.04621i 0.652806 + 0.237602i
\(291\) 0 0
\(292\) 40.4686 + 33.9572i 2.36824 + 1.98719i
\(293\) 24.5480 8.93473i 1.43411 0.521973i 0.496002 0.868321i \(-0.334801\pi\)
0.938106 + 0.346348i \(0.112579\pi\)
\(294\) 0 0
\(295\) 0.636372 + 3.60904i 0.0370510 + 0.210127i
\(296\) 43.6004 2.53422
\(297\) 0 0
\(298\) 1.96965 0.114099
\(299\) 2.51095 + 14.2403i 0.145212 + 0.823537i
\(300\) 0 0
\(301\) 4.23566 1.54165i 0.244139 0.0888594i
\(302\) −8.99768 7.54995i −0.517758 0.434451i
\(303\) 0 0
\(304\) −74.2964 27.0417i −4.26119 1.55095i
\(305\) −5.71984 9.90705i −0.327517 0.567276i
\(306\) 0 0
\(307\) −1.64638 + 2.85162i −0.0939641 + 0.162751i −0.909176 0.416412i \(-0.863287\pi\)
0.815212 + 0.579163i \(0.196621\pi\)
\(308\) 3.91038 3.28120i 0.222815 0.186964i
\(309\) 0 0
\(310\) 3.62509 20.5589i 0.205891 1.16767i
\(311\) −6.04168 + 34.2641i −0.342592 + 1.94294i −0.00975457 + 0.999952i \(0.503105\pi\)
−0.332838 + 0.942984i \(0.608006\pi\)
\(312\) 0 0
\(313\) 8.14139 6.83144i 0.460179 0.386136i −0.383018 0.923741i \(-0.625115\pi\)
0.843197 + 0.537605i \(0.180671\pi\)
\(314\) −20.9957 + 36.3657i −1.18486 + 2.05223i
\(315\) 0 0
\(316\) −14.1209 24.4580i −0.794360 1.37587i
\(317\) −14.5654 5.30139i −0.818077 0.297756i −0.101121 0.994874i \(-0.532243\pi\)
−0.716956 + 0.697118i \(0.754465\pi\)
\(318\) 0 0
\(319\) 3.84169 + 3.22356i 0.215093 + 0.180485i
\(320\) −37.6831 + 13.7155i −2.10655 + 0.766720i
\(321\) 0 0
\(322\) −1.09244 6.19554i −0.0608794 0.345264i
\(323\) −15.4461 −0.859446
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) −3.99147 22.6368i −0.221067 1.25373i
\(327\) 0 0
\(328\) 97.3803 35.4435i 5.37693 1.95704i
\(329\) −2.61999 2.19844i −0.144445 0.121204i
\(330\) 0 0
\(331\) 13.6916 + 4.98333i 0.752557 + 0.273908i 0.689682 0.724113i \(-0.257751\pi\)
0.0628759 + 0.998021i \(0.479973\pi\)
\(332\) −7.25330 12.5631i −0.398077 0.689489i
\(333\) 0 0
\(334\) −31.3002 + 54.2136i −1.71267 + 2.96644i
\(335\) 15.9930 13.4197i 0.873791 0.733198i
\(336\) 0 0
\(337\) −3.57972 + 20.3016i −0.195000 + 1.10590i 0.717419 + 0.696641i \(0.245323\pi\)
−0.912419 + 0.409257i \(0.865788\pi\)
\(338\) 1.55610 8.82506i 0.0846404 0.480020i
\(339\) 0 0
\(340\) −18.1523 + 15.2316i −0.984446 + 0.826048i
\(341\) 4.42475 7.66390i 0.239614 0.415023i
\(342\) 0 0
\(343\) 3.44142 + 5.96071i 0.185819 + 0.321848i
\(344\) −75.9294 27.6360i −4.09384 1.49004i
\(345\) 0 0
\(346\) −5.34312 4.48341i −0.287248 0.241030i
\(347\) −19.9060 + 7.24520i −1.06861 + 0.388943i −0.815657 0.578536i \(-0.803624\pi\)
−0.252954 + 0.967478i \(0.581402\pi\)
\(348\) 0 0
\(349\) −0.803291 4.55569i −0.0429992 0.243861i 0.955731 0.294242i \(-0.0950673\pi\)
−0.998730 + 0.0503818i \(0.983956\pi\)
\(350\) 2.98333 0.159466
\(351\) 0 0
\(352\) −36.3387 −1.93686
\(353\) 2.36915 + 13.4361i 0.126097 + 0.715133i 0.980650 + 0.195769i \(0.0627202\pi\)
−0.854553 + 0.519365i \(0.826169\pi\)
\(354\) 0 0
\(355\) −4.45636 + 1.62198i −0.236519 + 0.0860858i
\(356\) −45.6984 38.3456i −2.42201 2.03231i
\(357\) 0 0
\(358\) 22.6133 + 8.23058i 1.19515 + 0.435000i
\(359\) −14.1223 24.4606i −0.745349 1.29098i −0.950032 0.312153i \(-0.898950\pi\)
0.204683 0.978828i \(-0.434384\pi\)
\(360\) 0 0
\(361\) −7.30050 + 12.6448i −0.384237 + 0.665517i
\(362\) −16.3949 + 13.7570i −0.861697 + 0.723049i
\(363\) 0 0
\(364\) 1.43864 8.15891i 0.0754050 0.427643i
\(365\) 2.88518 16.3627i 0.151017 0.856462i
\(366\) 0 0
\(367\) 26.7198 22.4206i 1.39476 1.17034i 0.431393 0.902164i \(-0.358022\pi\)
0.963369 0.268180i \(-0.0864221\pi\)
\(368\) −31.6842 + 54.8786i −1.65165 + 2.86075i
\(369\) 0 0
\(370\) −10.9901 19.0354i −0.571348 0.989604i
\(371\) −2.55579 0.930233i −0.132690 0.0482953i
\(372\) 0 0
\(373\) 2.34367 + 1.96657i 0.121350 + 0.101825i 0.701443 0.712725i \(-0.252539\pi\)
−0.580093 + 0.814550i \(0.696984\pi\)
\(374\) −12.9895 + 4.72779i −0.671670 + 0.244468i
\(375\) 0 0
\(376\) 10.6465 + 60.3791i 0.549050 + 3.11382i
\(377\) 8.13924 0.419192
\(378\) 0 0
\(379\) −7.67705 −0.394344 −0.197172 0.980369i \(-0.563176\pi\)
−0.197172 + 0.980369i \(0.563176\pi\)
\(380\) 8.95117 + 50.7646i 0.459185 + 2.60417i
\(381\) 0 0
\(382\) 40.4099 14.7080i 2.06755 0.752528i
\(383\) −7.93771 6.66053i −0.405598 0.340337i 0.417055 0.908881i \(-0.363062\pi\)
−0.822653 + 0.568544i \(0.807507\pi\)
\(384\) 0 0
\(385\) −1.50866 0.549106i −0.0768882 0.0279850i
\(386\) −6.20106 10.7406i −0.315626 0.546680i
\(387\) 0 0
\(388\) 18.3161 31.7244i 0.929858 1.61056i
\(389\) 0.327064 0.274439i 0.0165828 0.0139146i −0.634459 0.772957i \(-0.718777\pi\)
0.651041 + 0.759042i \(0.274332\pi\)
\(390\) 0 0
\(391\) −2.14972 + 12.1916i −0.108716 + 0.616558i
\(392\) 10.5174 59.6471i 0.531209 3.01263i
\(393\) 0 0
\(394\) 6.20452 5.20621i 0.312579 0.262285i
\(395\) −4.44119 + 7.69238i −0.223461 + 0.387045i
\(396\) 0 0
\(397\) 13.5445 + 23.4598i 0.679781 + 1.17741i 0.975047 + 0.221999i \(0.0712583\pi\)
−0.295266 + 0.955415i \(0.595408\pi\)
\(398\) 37.8455 + 13.7746i 1.89702 + 0.690460i
\(399\) 0 0
\(400\) −23.0197 19.3158i −1.15099 0.965791i
\(401\) 27.5898 10.0419i 1.37777 0.501467i 0.456268 0.889842i \(-0.349186\pi\)
0.921501 + 0.388375i \(0.126963\pi\)
\(402\) 0 0
\(403\) −2.49405 14.1445i −0.124237 0.704585i
\(404\) −19.8319 −0.986675
\(405\) 0 0
\(406\) −3.54115 −0.175744
\(407\) −1.61798 9.17601i −0.0802002 0.454838i
\(408\) 0 0
\(409\) 18.9667 6.90331i 0.937842 0.341347i 0.172529 0.985004i \(-0.444806\pi\)
0.765313 + 0.643658i \(0.222584\pi\)
\(410\) −40.0203 33.5810i −1.97646 1.65845i
\(411\) 0 0
\(412\) −38.3786 13.9687i −1.89078 0.688187i
\(413\) −0.548476 0.949988i −0.0269887 0.0467459i
\(414\) 0 0
\(415\) −2.28126 + 3.95126i −0.111983 + 0.193960i
\(416\) −45.1792 + 37.9099i −2.21509 + 1.85869i
\(417\) 0 0
\(418\) −5.22166 + 29.6135i −0.255400 + 1.44844i
\(419\) −4.23186 + 24.0001i −0.206740 + 1.17248i 0.687938 + 0.725769i \(0.258516\pi\)
−0.894678 + 0.446711i \(0.852595\pi\)
\(420\) 0 0
\(421\) −20.0509 + 16.8247i −0.977219 + 0.819984i −0.983668 0.179995i \(-0.942392\pi\)
0.00644834 + 0.999979i \(0.497947\pi\)
\(422\) 18.7717 32.5136i 0.913794 1.58274i
\(423\) 0 0
\(424\) 24.3781 + 42.2240i 1.18390 + 2.05058i
\(425\) −5.51658 2.00787i −0.267593 0.0973960i
\(426\) 0 0
\(427\) 2.62310 + 2.20104i 0.126941 + 0.106516i
\(428\) −53.7932 + 19.5791i −2.60019 + 0.946393i
\(429\) 0 0
\(430\) 7.07352 + 40.1159i 0.341116 + 1.93456i
\(431\) −31.9185 −1.53746 −0.768731 0.639572i \(-0.779111\pi\)
−0.768731 + 0.639572i \(0.779111\pi\)
\(432\) 0 0
\(433\) 0.0123080 0.000591484 0.000295742 1.00000i \(-0.499906\pi\)
0.000295742 1.00000i \(0.499906\pi\)
\(434\) 1.08509 + 6.15385i 0.0520860 + 0.295394i
\(435\) 0 0
\(436\) −61.1088 + 22.2418i −2.92658 + 1.06519i
\(437\) 20.6299 + 17.3105i 0.986862 + 0.828075i
\(438\) 0 0
\(439\) −4.98489 1.81435i −0.237916 0.0865942i 0.220311 0.975430i \(-0.429293\pi\)
−0.458226 + 0.888836i \(0.651515\pi\)
\(440\) 14.3901 + 24.9244i 0.686020 + 1.18822i
\(441\) 0 0
\(442\) −11.2174 + 19.4291i −0.533557 + 0.924147i
\(443\) −31.1752 + 26.1591i −1.48118 + 1.24286i −0.576264 + 0.817264i \(0.695490\pi\)
−0.904915 + 0.425593i \(0.860066\pi\)
\(444\) 0 0
\(445\) −3.25804 + 18.4773i −0.154446 + 0.875907i
\(446\) 3.19979 18.1469i 0.151514 0.859281i
\(447\) 0 0
\(448\) 9.19520 7.71569i 0.434432 0.364532i
\(449\) 7.71401 13.3611i 0.364047 0.630547i −0.624576 0.780964i \(-0.714728\pi\)
0.988623 + 0.150417i \(0.0480615\pi\)
\(450\) 0 0
\(451\) −11.0731 19.1791i −0.521410 0.903109i
\(452\) −9.71333 3.53536i −0.456877 0.166289i
\(453\) 0 0
\(454\) −20.1850 16.9372i −0.947328 0.794902i
\(455\) −2.44853 + 0.891192i −0.114789 + 0.0417797i
\(456\) 0 0
\(457\) 0.414801 + 2.35246i 0.0194036 + 0.110043i 0.992971 0.118355i \(-0.0377622\pi\)
−0.973568 + 0.228399i \(0.926651\pi\)
\(458\) 37.9922 1.77526
\(459\) 0 0
\(460\) 41.3143 1.92629
\(461\) −5.64076 31.9904i −0.262717 1.48994i −0.775459 0.631397i \(-0.782482\pi\)
0.512743 0.858542i \(-0.328629\pi\)
\(462\) 0 0
\(463\) −31.8354 + 11.5871i −1.47952 + 0.538500i −0.950666 0.310215i \(-0.899599\pi\)
−0.528850 + 0.848715i \(0.677377\pi\)
\(464\) 27.3239 + 22.9275i 1.26848 + 1.06438i
\(465\) 0 0
\(466\) −13.5315 4.92508i −0.626836 0.228150i
\(467\) −6.90133 11.9535i −0.319356 0.553140i 0.660998 0.750388i \(-0.270133\pi\)
−0.980354 + 0.197247i \(0.936800\pi\)
\(468\) 0 0
\(469\) −3.12459 + 5.41195i −0.144280 + 0.249901i
\(470\) 23.6772 19.8676i 1.09215 0.916422i
\(471\) 0 0
\(472\) −3.41466 + 19.3655i −0.157172 + 0.891368i
\(473\) −2.99852 + 17.0054i −0.137872 + 0.781911i
\(474\) 0 0
\(475\) −9.78295 + 8.20887i −0.448873 + 0.376649i
\(476\) 3.54645 6.14264i 0.162551 0.281547i
\(477\) 0 0
\(478\) −24.0392 41.6372i −1.09953 1.90444i
\(479\) 5.53584 + 2.01488i 0.252939 + 0.0920623i 0.465378 0.885112i \(-0.345918\pi\)
−0.212439 + 0.977174i \(0.568141\pi\)
\(480\) 0 0
\(481\) −11.5844 9.72043i −0.528201 0.443214i
\(482\) −5.10113 + 1.85666i −0.232350 + 0.0845685i
\(483\) 0 0
\(484\) −6.76112 38.3442i −0.307324 1.74292i
\(485\) −11.5213 −0.523155
\(486\) 0 0
\(487\) 29.0299 1.31547 0.657736 0.753249i \(-0.271514\pi\)
0.657736 + 0.753249i \(0.271514\pi\)
\(488\) −10.6591 60.4507i −0.482514 2.73647i
\(489\) 0 0
\(490\) −28.6923 + 10.4431i −1.29619 + 0.471773i
\(491\) −3.35796 2.81766i −0.151543 0.127159i 0.563864 0.825868i \(-0.309314\pi\)
−0.715407 + 0.698708i \(0.753759\pi\)
\(492\) 0 0
\(493\) 6.54806 + 2.38330i 0.294910 + 0.107338i
\(494\) 24.4019 + 42.2654i 1.09789 + 1.90161i
\(495\) 0 0
\(496\) 31.4710 54.5093i 1.41309 2.44754i
\(497\) 1.08741 0.912449i 0.0487772 0.0409289i
\(498\) 0 0
\(499\) 6.13734 34.8066i 0.274745 1.55816i −0.465026 0.885297i \(-0.653955\pi\)
0.739771 0.672859i \(-0.234934\pi\)
\(500\) −11.1231 + 63.0821i −0.497439 + 2.82112i
\(501\) 0 0
\(502\) 48.8299 40.9732i 2.17939 1.82872i
\(503\) −4.18829 + 7.25434i −0.186747 + 0.323455i −0.944164 0.329477i \(-0.893128\pi\)
0.757417 + 0.652932i \(0.226461\pi\)
\(504\) 0 0
\(505\) 3.11870 + 5.40175i 0.138780 + 0.240375i
\(506\) 22.6472 + 8.24292i 1.00679 + 0.366442i
\(507\) 0 0
\(508\) 9.54928 + 8.01280i 0.423681 + 0.355510i
\(509\) −3.61121 + 1.31437i −0.160064 + 0.0582586i −0.420809 0.907149i \(-0.638254\pi\)
0.260745 + 0.965408i \(0.416032\pi\)
\(510\) 0 0
\(511\) 0.863615 + 4.89780i 0.0382041 + 0.216666i
\(512\) −13.6601 −0.603699
\(513\) 0 0
\(514\) 15.8911 0.700925
\(515\) 2.23055 + 12.6501i 0.0982899 + 0.557430i
\(516\) 0 0
\(517\) 12.3121 4.48125i 0.541487 0.197085i
\(518\) 5.04002 + 4.22908i 0.221446 + 0.185815i
\(519\) 0 0
\(520\) 43.8929 + 15.9757i 1.92483 + 0.700582i
\(521\) 9.82615 + 17.0194i 0.430491 + 0.745633i 0.996916 0.0784810i \(-0.0250070\pi\)
−0.566424 + 0.824114i \(0.691674\pi\)
\(522\) 0 0
\(523\) 19.8051 34.3035i 0.866018 1.49999i −1.41543e−5 1.00000i \(-0.500005\pi\)
0.866032 0.499988i \(-0.166662\pi\)
\(524\) 69.6639 58.4550i 3.04328 2.55362i
\(525\) 0 0
\(526\) 10.3238 58.5491i 0.450138 2.55286i
\(527\) 2.13525 12.1096i 0.0930129 0.527502i
\(528\) 0 0
\(529\) −1.08465 + 0.910127i −0.0471586 + 0.0395707i
\(530\) 12.2897 21.2864i 0.533830 0.924620i
\(531\) 0 0
\(532\) −7.71483 13.3625i −0.334480 0.579337i
\(533\) −33.7753 12.2932i −1.46297 0.532477i
\(534\) 0 0
\(535\) 13.7922 + 11.5731i 0.596290 + 0.500347i
\(536\) 105.268 38.3146i 4.54690 1.65494i
\(537\) 0 0
\(538\) −14.3749 81.5244i −0.619748 3.51476i
\(539\) −12.9435 −0.557514
\(540\) 0 0
\(541\) −41.8257 −1.79823 −0.899115 0.437713i \(-0.855788\pi\)
−0.899115 + 0.437713i \(0.855788\pi\)
\(542\) 7.55432 + 42.8427i 0.324486 + 1.84025i
\(543\) 0 0
\(544\) −47.4476 + 17.2695i −2.03430 + 0.740424i
\(545\) 15.6679 + 13.1469i 0.671139 + 0.563153i
\(546\) 0 0
\(547\) 16.0070 + 5.82608i 0.684411 + 0.249105i 0.660740 0.750615i \(-0.270242\pi\)
0.0236708 + 0.999720i \(0.492465\pi\)
\(548\) 37.0280 + 64.1343i 1.58176 + 2.73968i
\(549\) 0 0
\(550\) −5.71442 + 9.89767i −0.243664 + 0.422038i
\(551\) 11.6122 9.74377i 0.494695 0.415098i
\(552\) 0 0
\(553\) 0.461686 2.61835i 0.0196329 0.111344i
\(554\) 9.77675 55.4467i 0.415374 2.35571i
\(555\) 0 0
\(556\) 32.2472 27.0586i 1.36759 1.14754i
\(557\) −16.8840 + 29.2439i −0.715398 + 1.23911i 0.247408 + 0.968911i \(0.420421\pi\)
−0.962806 + 0.270194i \(0.912912\pi\)
\(558\) 0 0
\(559\) 14.0127 + 24.2707i 0.592674 + 1.02654i
\(560\) −10.7303 3.90550i −0.453437 0.165038i
\(561\) 0 0
\(562\) 25.4057 + 21.3180i 1.07168 + 0.899244i
\(563\) −21.3416 + 7.76771i −0.899442 + 0.327370i −0.750029 0.661405i \(-0.769961\pi\)
−0.149413 + 0.988775i \(0.547738\pi\)
\(564\) 0 0
\(565\) 0.564536 + 3.20164i 0.0237502 + 0.134694i
\(566\) −12.3691 −0.519913
\(567\) 0 0
\(568\) −25.4466 −1.06772
\(569\) −1.88781 10.7063i −0.0791410 0.448831i −0.998468 0.0553359i \(-0.982377\pi\)
0.919327 0.393495i \(-0.128734\pi\)
\(570\) 0 0
\(571\) −13.9861 + 5.09053i −0.585300 + 0.213032i −0.617661 0.786444i \(-0.711920\pi\)
0.0323607 + 0.999476i \(0.489697\pi\)
\(572\) 24.3129 + 20.4009i 1.01657 + 0.853006i
\(573\) 0 0
\(574\) 14.6947 + 5.34842i 0.613343 + 0.223239i
\(575\) 5.11772 + 8.86416i 0.213424 + 0.369661i
\(576\) 0 0
\(577\) 18.5582 32.1437i 0.772586 1.33816i −0.163555 0.986534i \(-0.552296\pi\)
0.936141 0.351624i \(-0.114371\pi\)
\(578\) 20.5138 17.2131i 0.853261 0.715971i
\(579\) 0 0
\(580\) 4.03819 22.9017i 0.167677 0.950943i
\(581\) 0.237149 1.34494i 0.00983861 0.0557975i
\(582\) 0 0
\(583\) 7.98170 6.69745i 0.330568 0.277380i
\(584\) 44.5768 77.2093i 1.84460 3.19494i
\(585\) 0 0
\(586\) −35.3328 61.1981i −1.45958 2.52807i
\(587\) 13.7601 + 5.00828i 0.567941 + 0.206714i 0.610000 0.792401i \(-0.291169\pi\)
−0.0420588 + 0.999115i \(0.513392\pi\)
\(588\) 0 0
\(589\) −20.4911 17.1940i −0.844319 0.708468i
\(590\) 9.31545 3.39055i 0.383511 0.139587i
\(591\) 0 0
\(592\) −11.5078 65.2642i −0.472969 2.68234i
\(593\) 36.4392 1.49638 0.748189 0.663485i \(-0.230924\pi\)
0.748189 + 0.663485i \(0.230924\pi\)
\(594\) 0 0
\(595\) −2.23081 −0.0914544
\(596\) −0.672325 3.81294i −0.0275395 0.156184i
\(597\) 0 0
\(598\) 36.7562 13.3782i 1.50307 0.547074i
\(599\) 21.0623 + 17.6734i 0.860583 + 0.722115i 0.962094 0.272720i \(-0.0879232\pi\)
−0.101511 + 0.994834i \(0.532368\pi\)
\(600\) 0 0
\(601\) −42.4525 15.4514i −1.73167 0.630277i −0.732925 0.680309i \(-0.761846\pi\)
−0.998748 + 0.0500315i \(0.984068\pi\)
\(602\) −6.09653 10.5595i −0.248476 0.430373i
\(603\) 0 0
\(604\) −11.5443 + 19.9953i −0.469729 + 0.813595i
\(605\) −9.38083 + 7.87145i −0.381385 + 0.320020i
\(606\) 0 0
\(607\) 2.97584 16.8768i 0.120786 0.685009i −0.862937 0.505312i \(-0.831377\pi\)
0.983722 0.179697i \(-0.0575116\pi\)
\(608\) −19.0735 + 108.171i −0.773534 + 4.38693i
\(609\) 0 0
\(610\) −23.7053 + 19.8911i −0.959799 + 0.805367i
\(611\) 10.6324 18.4159i 0.430143 0.745029i
\(612\) 0 0
\(613\) 0.234380 + 0.405959i 0.00946653 + 0.0163965i 0.870720 0.491779i \(-0.163653\pi\)
−0.861253 + 0.508176i \(0.830320\pi\)
\(614\) 8.36998 + 3.04643i 0.337785 + 0.122944i
\(615\) 0 0
\(616\) −6.59925 5.53742i −0.265891 0.223109i
\(617\) 2.00610 0.730161i 0.0807626 0.0293952i −0.301323 0.953522i \(-0.597428\pi\)
0.382086 + 0.924127i \(0.375206\pi\)
\(618\) 0 0
\(619\) 1.48254 + 8.40790i 0.0595883 + 0.337942i 0.999998 0.00210213i \(-0.000669129\pi\)
−0.940410 + 0.340044i \(0.889558\pi\)
\(620\) −41.0363 −1.64806
\(621\) 0 0
\(622\) 94.1163 3.77372
\(623\) −0.975222 5.53076i −0.0390715 0.221585i
\(624\) 0 0
\(625\) 8.57993 3.12284i 0.343197 0.124914i
\(626\) −22.0230 18.4795i −0.880216 0.738589i
\(627\) 0 0
\(628\) 77.5651 + 28.2314i 3.09518 + 1.12655i
\(629\) −6.47339 11.2122i −0.258111 0.447061i
\(630\) 0 0
\(631\) 5.93539 10.2804i 0.236284 0.409256i −0.723361 0.690470i \(-0.757404\pi\)
0.959645 + 0.281214i \(0.0907370\pi\)
\(632\) −36.5107 + 30.6361i −1.45232 + 1.21864i
\(633\) 0 0
\(634\) −7.28091 + 41.2921i −0.289162 + 1.63992i
\(635\) 0.680810 3.86106i 0.0270171 0.153222i
\(636\) 0 0
\(637\) −16.0924 + 13.5031i −0.637603 + 0.535012i
\(638\) 6.78291 11.7483i 0.268538 0.465121i
\(639\) 0 0
\(640\) 22.5486 + 39.0554i 0.891313 + 1.54380i
\(641\) −4.98381 1.81396i −0.196849 0.0716470i 0.241715 0.970347i \(-0.422290\pi\)
−0.438563 + 0.898700i \(0.644512\pi\)
\(642\) 0 0
\(643\) −0.631120 0.529573i −0.0248889 0.0208843i 0.630258 0.776386i \(-0.282949\pi\)
−0.655147 + 0.755501i \(0.727393\pi\)
\(644\) −11.6207 + 4.22960i −0.457921 + 0.166670i
\(645\) 0 0
\(646\) 7.25551 + 41.1480i 0.285464 + 1.61895i
\(647\) −40.8373 −1.60548 −0.802740 0.596329i \(-0.796626\pi\)
−0.802740 + 0.596329i \(0.796626\pi\)
\(648\) 0 0
\(649\) 4.20232 0.164955
\(650\) 3.22098 + 18.2671i 0.126337 + 0.716494i
\(651\) 0 0
\(652\) −42.4589 + 15.4538i −1.66282 + 0.605216i
\(653\) 0.819175 + 0.687369i 0.0320568 + 0.0268988i 0.658675 0.752427i \(-0.271117\pi\)
−0.626618 + 0.779326i \(0.715562\pi\)
\(654\) 0 0
\(655\) −26.8769 9.78238i −1.05017 0.382229i
\(656\) −78.7569 136.411i −3.07494 5.32595i
\(657\) 0 0
\(658\) −4.62587 + 8.01225i −0.180335 + 0.312350i
\(659\) −21.9581 + 18.4250i −0.855367 + 0.717738i −0.960965 0.276671i \(-0.910769\pi\)
0.105598 + 0.994409i \(0.466324\pi\)
\(660\) 0 0
\(661\) −0.780673 + 4.42742i −0.0303647 + 0.172207i −0.996219 0.0868799i \(-0.972310\pi\)
0.965854 + 0.259086i \(0.0834215\pi\)
\(662\) 6.84409 38.8148i 0.266003 1.50858i
\(663\) 0 0
\(664\) −18.7540 + 15.7365i −0.727797 + 0.610695i
\(665\) −2.42642 + 4.20268i −0.0940924 + 0.162973i
\(666\) 0 0
\(667\) −6.07464 10.5216i −0.235211 0.407397i
\(668\) 115.633 + 42.0871i 4.47399 + 1.62840i
\(669\) 0 0
\(670\) −43.2621 36.3012i −1.67136 1.40244i
\(671\) −12.3267 + 4.48656i −0.475868 + 0.173202i
\(672\) 0 0
\(673\) 3.13584 + 17.7842i 0.120878 + 0.685532i 0.983671 + 0.179975i \(0.0576017\pi\)
−0.862793 + 0.505557i \(0.831287\pi\)
\(674\) 55.7643 2.14796
\(675\) 0 0
\(676\) −17.6151 −0.677505
\(677\) 2.73308 + 15.5001i 0.105041 + 0.595716i 0.991204 + 0.132343i \(0.0422499\pi\)
−0.886163 + 0.463373i \(0.846639\pi\)
\(678\) 0 0
\(679\) 3.24066 1.17951i 0.124365 0.0452653i
\(680\) 30.6342 + 25.7051i 1.17477 + 0.985747i
\(681\) 0 0
\(682\) −22.4948 8.18745i −0.861371 0.313514i
\(683\) 1.38059 + 2.39125i 0.0528268 + 0.0914987i 0.891230 0.453552i \(-0.149844\pi\)
−0.838403 + 0.545051i \(0.816510\pi\)
\(684\) 0 0
\(685\) 11.6458 20.1711i 0.444963 0.770698i
\(686\) 14.2626 11.9677i 0.544549 0.456931i
\(687\) 0 0
\(688\) −21.3269 + 120.951i −0.813081 + 4.61121i
\(689\) 2.93648 16.6536i 0.111871 0.634452i
\(690\) 0 0
\(691\) −26.4481 + 22.1926i −1.00613 + 0.844246i −0.987822 0.155586i \(-0.950273\pi\)
−0.0183109 + 0.999832i \(0.505829\pi\)
\(692\) −6.85537 + 11.8738i −0.260602 + 0.451376i
\(693\) 0 0
\(694\) 28.6514 + 49.6257i 1.08759 + 1.88377i
\(695\) −12.4412 4.52823i −0.471922 0.171766i
\(696\) 0 0
\(697\) −23.5728 19.7799i −0.892882 0.749217i
\(698\) −11.7589 + 4.27989i −0.445081 + 0.161996i
\(699\) 0 0
\(700\) −1.01834 5.77527i −0.0384894 0.218285i
\(701\) −20.7410 −0.783378 −0.391689 0.920098i \(-0.628109\pi\)
−0.391689 + 0.920098i \(0.628109\pi\)
\(702\) 0 0
\(703\) −28.1640 −1.06222
\(704\) 7.98508 + 45.2856i 0.300949 + 1.70677i
\(705\) 0 0
\(706\) 34.6806 12.6227i 1.30522 0.475062i
\(707\) −1.43023 1.20010i −0.0537892 0.0451345i
\(708\) 0 0
\(709\) −26.0362 9.47639i −0.977809 0.355893i −0.196821 0.980439i \(-0.563062\pi\)
−0.780988 + 0.624546i \(0.785284\pi\)
\(710\) 6.41419 + 11.1097i 0.240720 + 0.416940i
\(711\) 0 0
\(712\) −50.3376 + 87.1873i −1.88648 + 3.26748i
\(713\) −16.4231 + 13.7806i −0.615050 + 0.516088i
\(714\) 0 0
\(715\) 1.73337 9.83044i 0.0648244 0.367637i
\(716\) 8.21426 46.5854i 0.306981 1.74098i
\(717\) 0 0
\(718\) −58.5286 + 49.1113i −2.18427 + 1.83282i
\(719\) −16.5657 + 28.6927i −0.617797 + 1.07006i 0.372090 + 0.928197i \(0.378641\pi\)
−0.989887 + 0.141859i \(0.954692\pi\)
\(720\) 0 0
\(721\) −1.92247 3.32981i −0.0715965 0.124009i
\(722\) 37.1147 + 13.5086i 1.38127 + 0.502740i
\(723\) 0 0
\(724\) 32.2276 + 27.0422i 1.19773 + 1.00502i
\(725\) 5.41389 1.97049i 0.201067 0.0731823i
\(726\) 0 0
\(727\) −0.0143443 0.0813505i −0.000532000 0.00301712i 0.984541 0.175157i \(-0.0560432\pi\)
−0.985073 + 0.172139i \(0.944932\pi\)
\(728\) −13.9816 −0.518191
\(729\) 0 0
\(730\) −44.9449 −1.66349
\(731\) 4.16645 + 23.6291i 0.154102 + 0.873953i
\(732\) 0 0
\(733\) 29.9926 10.9164i 1.10780 0.403207i 0.277616 0.960692i \(-0.410456\pi\)
0.830187 + 0.557485i \(0.188234\pi\)
\(734\) −72.2788 60.6491i −2.66786 2.23860i
\(735\) 0 0
\(736\) 82.7251 + 30.1095i 3.04929 + 1.10985i
\(737\) −11.9700 20.7327i −0.440921 0.763698i
\(738\) 0 0
\(739\) 17.8960 30.9967i 0.658314 1.14023i −0.322738 0.946488i \(-0.604603\pi\)
0.981052 0.193745i \(-0.0620634\pi\)
\(740\) −33.0983 + 27.7727i −1.21672 + 1.02095i
\(741\) 0 0
\(742\) −1.27758 + 7.24551i −0.0469014 + 0.265991i
\(743\) 3.43457 19.4784i 0.126002 0.714593i −0.854706 0.519113i \(-0.826262\pi\)
0.980708 0.195480i \(-0.0626264\pi\)
\(744\) 0 0
\(745\) −0.932828 + 0.782736i −0.0341762 + 0.0286772i
\(746\) 4.13799 7.16721i 0.151503 0.262410i
\(747\) 0 0
\(748\) 13.5861 + 23.5319i 0.496758 + 0.860411i
\(749\) −5.06423 1.84323i −0.185043 0.0673501i
\(750\) 0 0
\(751\) 23.4261 + 19.6568i 0.854829 + 0.717287i 0.960848 0.277077i \(-0.0893658\pi\)
−0.106018 + 0.994364i \(0.533810\pi\)
\(752\) 87.5699 31.8728i 3.19334 1.16228i
\(753\) 0 0
\(754\) −3.82324 21.6827i −0.139234 0.789636i
\(755\) 7.26165 0.264278
\(756\) 0 0
\(757\) 25.4129 0.923647 0.461824 0.886972i \(-0.347195\pi\)
0.461824 + 0.886972i \(0.347195\pi\)
\(758\) 3.60614 + 20.4514i 0.130981 + 0.742829i
\(759\) 0 0
\(760\) 81.7467 29.7534i 2.96527 1.07927i
\(761\) 35.8646 + 30.0940i 1.30009 + 1.09091i 0.990129 + 0.140159i \(0.0447612\pi\)
0.309963 + 0.950749i \(0.399683\pi\)
\(762\) 0 0
\(763\) −5.75294 2.09390i −0.208270 0.0758042i
\(764\) −42.2661 73.2070i −1.52913 2.64854i
\(765\) 0 0
\(766\) −14.0149 + 24.2744i −0.506377 + 0.877071i
\(767\) 5.22467 4.38402i 0.188652 0.158298i
\(768\) 0 0
\(769\) 2.52926 14.3441i 0.0912074 0.517263i −0.904636 0.426184i \(-0.859857\pi\)
0.995844 0.0910785i \(-0.0290314\pi\)
\(770\) −0.754140 + 4.27694i −0.0271773 + 0.154130i
\(771\) 0 0
\(772\) −18.6754 + 15.6705i −0.672142 + 0.563994i
\(773\) 12.1767 21.0906i 0.437964 0.758576i −0.559568 0.828784i \(-0.689033\pi\)
0.997532 + 0.0702080i \(0.0223663\pi\)
\(774\) 0 0
\(775\) −5.08328 8.80451i −0.182597 0.316267i
\(776\) −58.0929 21.1441i −2.08541 0.759029i
\(777\) 0 0
\(778\) −0.884728 0.742375i −0.0317190 0.0266154i
\(779\) −62.9035 + 22.8950i −2.25375 + 0.820298i
\(780\) 0 0
\(781\) 0.944306 + 5.35543i 0.0337899 + 0.191632i
\(782\) 33.4879 1.19753
\(783\) 0 0
\(784\) −92.0601 −3.28786
\(785\) −4.50806 25.5665i −0.160899 0.912506i
\(786\) 0 0
\(787\) 25.9047 9.42853i 0.923402 0.336091i 0.163811 0.986492i \(-0.447621\pi\)
0.759591 + 0.650401i \(0.225399\pi\)
\(788\) −12.1963 10.2339i −0.434475 0.364568i
\(789\) 0 0
\(790\) 22.5784 + 8.21787i 0.803304 + 0.292379i
\(791\) −0.486562 0.842750i −0.0173001 0.0299647i
\(792\) 0 0
\(793\) −10.6451 + 18.4378i −0.378017 + 0.654744i
\(794\) 56.1340 47.1020i 1.99212 1.67159i
\(795\) 0 0
\(796\) 13.7473 77.9650i 0.487261 2.76340i
\(797\) 1.14902 6.51639i 0.0407002 0.230822i −0.957672 0.287863i \(-0.907055\pi\)
0.998372 + 0.0570404i \(0.0181664\pi\)
\(798\) 0 0
\(799\) 13.9464 11.7024i 0.493387 0.414000i
\(800\) −20.8735 + 36.1539i −0.737989 + 1.27823i
\(801\) 0 0
\(802\) −39.7110 68.7815i −1.40224 2.42876i
\(803\) −17.9035 6.51633i −0.631800 0.229956i
\(804\) 0 0
\(805\) 2.97948 + 2.50008i 0.105013 + 0.0881162i
\(806\) −36.5089 + 13.2881i −1.28597 + 0.468055i
\(807\) 0 0
\(808\) 5.81179 + 32.9603i 0.204458 + 1.15954i
\(809\) 8.61362 0.302839 0.151419 0.988470i \(-0.451616\pi\)
0.151419 + 0.988470i \(0.451616\pi\)
\(810\) 0 0
\(811\) −9.58716 −0.336651 −0.168325 0.985732i \(-0.553836\pi\)
−0.168325 + 0.985732i \(0.553836\pi\)
\(812\) 1.20874 + 6.85512i 0.0424186 + 0.240568i
\(813\) 0 0
\(814\) −23.6846 + 8.62049i −0.830145 + 0.302148i
\(815\) 10.8862 + 9.13459i 0.381326 + 0.319971i
\(816\) 0 0
\(817\) 49.0471 + 17.8517i 1.71594 + 0.624552i
\(818\) −27.2994 47.2840i −0.954502 1.65325i
\(819\) 0 0
\(820\) −51.3472 + 88.9359i −1.79312 + 3.10578i
\(821\) 10.6200 8.91127i 0.370642 0.311005i −0.438374 0.898793i \(-0.644445\pi\)
0.809015 + 0.587787i \(0.200001\pi\)
\(822\) 0 0
\(823\) 8.30485 47.0992i 0.289489 1.64177i −0.399307 0.916817i \(-0.630749\pi\)
0.688795 0.724956i \(-0.258140\pi\)
\(824\) −11.9688 + 67.8782i −0.416951 + 2.36465i
\(825\) 0 0
\(826\) −2.27310 + 1.90736i −0.0790914 + 0.0663655i
\(827\) −21.2209 + 36.7556i −0.737921 + 1.27812i 0.215508 + 0.976502i \(0.430859\pi\)
−0.953430 + 0.301615i \(0.902474\pi\)
\(828\) 0 0
\(829\) −13.0018 22.5199i −0.451573 0.782147i 0.546911 0.837191i \(-0.315804\pi\)
−0.998484 + 0.0550437i \(0.982470\pi\)
\(830\) 11.5976 + 4.22118i 0.402558 + 0.146519i
\(831\) 0 0
\(832\) 57.1713 + 47.9724i 1.98206 + 1.66315i
\(833\) −16.9003 + 6.15122i −0.585562 + 0.213127i
\(834\) 0 0
\(835\) −6.72057 38.1143i −0.232575 1.31900i
\(836\) 59.1096 2.04435
\(837\) 0 0
\(838\) 65.9233 2.27728
\(839\) −0.218150 1.23719i −0.00753138 0.0427126i 0.980810 0.194964i \(-0.0624589\pi\)
−0.988342 + 0.152251i \(0.951348\pi\)
\(840\) 0 0
\(841\) 20.8249 7.57965i 0.718100 0.261367i
\(842\) 54.2389 + 45.5118i 1.86920 + 1.56844i
\(843\) 0 0
\(844\) −69.3490 25.2410i −2.38709 0.868830i
\(845\) 2.77009 + 4.79794i 0.0952941 + 0.165054i
\(846\) 0 0
\(847\) 1.83275 3.17442i 0.0629742 0.109074i
\(848\) 56.7697 47.6354i 1.94948 1.63581i
\(849\) 0 0
\(850\) −2.75760 + 15.6391i −0.0945850 + 0.536418i
\(851\) −3.91972 + 22.2298i −0.134366 + 0.762029i
\(852\) 0 0
\(853\) 1.11409 0.934836i 0.0381459 0.0320082i −0.623515 0.781811i \(-0.714296\pi\)
0.661661 + 0.749803i \(0.269852\pi\)
\(854\) 4.63136 8.02175i 0.158482 0.274499i
\(855\) 0 0
\(856\) 48.3044 + 83.6657i 1.65101 + 2.85964i
\(857\) −49.1550 17.8910i −1.67910 0.611144i −0.685917 0.727680i \(-0.740599\pi\)
−0.993187 + 0.116536i \(0.962821\pi\)
\(858\) 0 0
\(859\) −16.0903 13.5013i −0.548992 0.460659i 0.325607 0.945505i \(-0.394431\pi\)
−0.874600 + 0.484846i \(0.838876\pi\)
\(860\) 75.2439 27.3865i 2.56579 0.933873i
\(861\) 0 0
\(862\) 14.9931 + 85.0300i 0.510666 + 2.89613i
\(863\) −12.9813 −0.441890 −0.220945 0.975286i \(-0.570914\pi\)
−0.220945 + 0.975286i \(0.570914\pi\)
\(864\) 0 0
\(865\) 4.31221 0.146619
\(866\) −0.00578142 0.0327881i −0.000196461 0.00111418i
\(867\) 0 0
\(868\) 11.5425 4.20113i 0.391779 0.142596i
\(869\) 7.80247 + 6.54705i 0.264681 + 0.222094i
\(870\) 0 0
\(871\) −36.5112 13.2890i −1.23713 0.450280i
\(872\) 54.8735 + 95.0438i 1.85825 + 3.21859i
\(873\) 0 0
\(874\) 36.4243 63.0887i 1.23207 2.13401i
\(875\) −4.61950 + 3.87622i −0.156167 + 0.131040i
\(876\) 0 0
\(877\) 5.39102 30.5740i 0.182042 1.03241i −0.747655 0.664087i \(-0.768821\pi\)
0.929697 0.368324i \(-0.120068\pi\)
\(878\) −2.49182 + 14.1318i −0.0840950 + 0.476926i
\(879\) 0 0
\(880\) 33.5105 28.1186i 1.12964 0.947879i
\(881\) 9.64783 16.7105i 0.325044 0.562992i −0.656478 0.754346i \(-0.727954\pi\)
0.981521 + 0.191353i \(0.0612877\pi\)
\(882\) 0 0
\(883\) 4.91194 + 8.50773i 0.165300 + 0.286308i 0.936762 0.349968i \(-0.113807\pi\)
−0.771462 + 0.636276i \(0.780474\pi\)
\(884\) 41.4407 + 15.0832i 1.39380 + 0.507302i
\(885\) 0 0
\(886\) 84.3309 + 70.7621i 2.83315 + 2.37730i
\(887\) 41.4529 15.0876i 1.39185 0.506593i 0.466104 0.884730i \(-0.345657\pi\)
0.925750 + 0.378137i \(0.123435\pi\)
\(888\) 0 0
\(889\) 0.203785 + 1.15572i 0.00683474 + 0.0387617i
\(890\) 50.7533 1.70125
\(891\) 0 0
\(892\) −36.2219 −1.21280
\(893\) −6.87716 39.0023i −0.230135 1.30516i
\(894\) 0 0
\(895\) −13.9805 + 5.08849i −0.467317 + 0.170089i
\(896\) −10.3407 8.67690i −0.345460 0.289875i
\(897\) 0 0
\(898\) −39.2169 14.2738i −1.30869 0.476323i
\(899\) 6.03376 + 10.4508i 0.201237 + 0.348553i
\(900\) 0 0
\(901\) 7.23887 12.5381i 0.241162 0.417704i
\(902\) −45.8912 + 38.5073i −1.52801 + 1.28215i
\(903\) 0 0
\(904\) −3.02920 + 17.1794i −0.100750 + 0.571379i
\(905\) 2.29765 13.0306i 0.0763764 0.433152i
\(906\) 0 0
\(907\) −32.4898 + 27.2622i −1.07881 + 0.905225i −0.995821 0.0913259i \(-0.970890\pi\)
−0.0829841 + 0.996551i \(0.526445\pi\)
\(908\) −25.8979 + 44.8564i −0.859451 + 1.48861i
\(909\) 0 0
\(910\) 3.52426 + 6.10419i 0.116828 + 0.202352i
\(911\) 34.4965 + 12.5557i 1.14292 + 0.415988i 0.842967 0.537966i \(-0.180807\pi\)
0.299952 + 0.953954i \(0.403029\pi\)
\(912\) 0 0
\(913\) 4.00781 + 3.36295i 0.132639 + 0.111297i
\(914\) 6.07203 2.21004i 0.200845 0.0731015i
\(915\) 0 0
\(916\) −12.9683 73.5471i −0.428486 2.43007i
\(917\) 8.56130 0.282719
\(918\) 0 0
\(919\) −14.0589 −0.463761 −0.231881 0.972744i \(-0.574488\pi\)
−0.231881 + 0.972744i \(0.574488\pi\)
\(920\) −12.1073 68.6637i −0.399164 2.26377i
\(921\) 0 0
\(922\) −82.5717 + 30.0536i −2.71935 + 0.989764i
\(923\) 6.76102 + 5.67317i 0.222542 + 0.186735i
\(924\) 0 0
\(925\) −10.0587 3.66108i −0.330729 0.120376i
\(926\) 45.8218 + 79.3657i 1.50580 + 2.60812i
\(927\) 0 0
\(928\) 24.7764 42.9140i 0.813325 1.40872i
\(929\) 14.1852 11.9028i 0.465402 0.390519i −0.379712 0.925105i \(-0.623977\pi\)
0.845114 + 0.534586i \(0.179532\pi\)
\(930\) 0 0
\(931\) −6.79379 + 38.5295i −0.222657 + 1.26275i
\(932\) −4.91531 + 27.8761i −0.161006 + 0.913113i
\(933\) 0 0
\(934\) −28.6019 + 23.9998i −0.935882 + 0.785298i
\(935\) 4.27302 7.40108i 0.139743 0.242041i
\(936\) 0 0
\(937\) −2.23409 3.86955i −0.0729845 0.126413i 0.827224 0.561873i \(-0.189919\pi\)
−0.900208 + 0.435460i \(0.856586\pi\)
\(938\) 15.8850 + 5.78166i 0.518663 + 0.188778i
\(939\) 0 0
\(940\) −46.5426 39.0539i −1.51805 1.27380i
\(941\) −1.88301 + 0.685360i −0.0613844 + 0.0223421i −0.372530 0.928020i \(-0.621510\pi\)
0.311145 + 0.950362i \(0.399287\pi\)
\(942\) 0 0
\(943\) 9.31644 + 52.8362i 0.303385 + 1.72058i
\(944\) 29.8889 0.972801
\(945\) 0 0
\(946\) 46.7105 1.51869
\(947\) 2.18516 + 12.3926i 0.0710081 + 0.402707i 0.999508 + 0.0313735i \(0.00998814\pi\)
−0.928500 + 0.371333i \(0.878901\pi\)
\(948\) 0 0
\(949\) −29.0571 + 10.5759i −0.943235 + 0.343309i
\(950\) 26.4635 + 22.2055i 0.858590 + 0.720443i
\(951\) 0 0
\(952\) −11.2483 4.09403i −0.364558 0.132688i
\(953\) −9.98205 17.2894i −0.323350 0.560059i 0.657827 0.753169i \(-0.271476\pi\)
−0.981177 + 0.193110i \(0.938143\pi\)
\(954\) 0 0
\(955\) −13.2932 + 23.0246i −0.430159 + 0.745058i
\(956\) −72.3976 + 60.7488i −2.34151 + 1.96476i
\(957\) 0 0
\(958\) 2.76723 15.6938i 0.0894052 0.507042i
\(959\) −1.21064 + 6.86590i −0.0390937 + 0.221711i
\(960\) 0 0
\(961\) −7.43480 + 6.23853i −0.239832 + 0.201243i
\(962\) −20.4534 + 35.4263i −0.659444 + 1.14219i
\(963\) 0 0
\(964\) 5.33544 + 9.24125i 0.171843 + 0.297640i
\(965\) 7.20511 + 2.62244i 0.231941 + 0.0844195i
\(966\) 0 0
\(967\) −24.6732 20.7033i −0.793437 0.665773i 0.153157 0.988202i \(-0.451056\pi\)
−0.946594 + 0.322429i \(0.895501\pi\)
\(968\) −61.7460 + 22.4737i −1.98459 + 0.722333i
\(969\) 0 0
\(970\) 5.41189 + 30.6924i 0.173765 + 0.985473i
\(971\) 6.62934 0.212746 0.106373 0.994326i \(-0.466076\pi\)
0.106373 + 0.994326i \(0.466076\pi\)
\(972\) 0 0
\(973\) 3.96300 0.127048
\(974\) −13.6362 77.3348i −0.436932 2.47797i
\(975\) 0 0
\(976\) −87.6737 + 31.9106i −2.80637 + 1.02143i
\(977\) −9.08272 7.62130i −0.290582 0.243827i 0.485830 0.874054i \(-0.338518\pi\)
−0.776411 + 0.630226i \(0.782962\pi\)
\(978\) 0 0
\(979\) 20.2172 + 7.35845i 0.646144 + 0.235177i
\(980\) 30.0102 + 51.9792i 0.958642 + 1.66042i
\(981\) 0 0
\(982\) −5.92884 + 10.2690i −0.189197 + 0.327698i
\(983\) 39.8841 33.4667i 1.27211 1.06742i 0.277824 0.960632i \(-0.410387\pi\)
0.994281 0.106791i \(-0.0340576\pi\)
\(984\) 0 0
\(985\) −0.869526 + 4.93133i −0.0277054 + 0.157125i
\(986\) 3.27322 18.5633i 0.104241 0.591177i
\(987\) 0 0
\(988\) 73.4899 61.6654i 2.33803 1.96184i
\(989\) 20.9165 36.2284i 0.665105 1.15200i
\(990\) 0 0
\(991\) −0.735575 1.27405i −0.0233663 0.0404716i 0.854106 0.520099i \(-0.174105\pi\)
−0.877472 + 0.479628i \(0.840772\pi\)
\(992\) −82.1684 29.9069i −2.60885 0.949544i
\(993\) 0 0
\(994\) −2.94153 2.46823i −0.0932996 0.0782876i
\(995\) −23.3977 + 8.51606i −0.741756 + 0.269977i
\(996\) 0 0
\(997\) −4.58801 26.0199i −0.145304 0.824058i −0.967123 0.254310i \(-0.918152\pi\)
0.821819 0.569748i \(-0.192959\pi\)
\(998\) −95.6065 −3.02637
\(999\) 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.s.82.1 12
3.2 odd 2 729.2.e.l.82.2 12
9.2 odd 6 729.2.e.u.325.2 12
9.4 even 3 729.2.e.t.568.2 12
9.5 odd 6 729.2.e.k.568.1 12
9.7 even 3 729.2.e.j.325.1 12
27.2 odd 18 729.2.e.l.649.2 12
27.4 even 9 729.2.c.d.487.6 12
27.5 odd 18 729.2.a.e.1.6 yes 6
27.7 even 9 729.2.e.j.406.1 12
27.11 odd 18 729.2.e.k.163.1 12
27.13 even 9 729.2.c.d.244.6 12
27.14 odd 18 729.2.c.a.244.1 12
27.16 even 9 729.2.e.t.163.2 12
27.20 odd 18 729.2.e.u.406.2 12
27.22 even 9 729.2.a.b.1.1 6
27.23 odd 18 729.2.c.a.487.1 12
27.25 even 9 inner 729.2.e.s.649.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.1 6 27.22 even 9
729.2.a.e.1.6 yes 6 27.5 odd 18
729.2.c.a.244.1 12 27.14 odd 18
729.2.c.a.487.1 12 27.23 odd 18
729.2.c.d.244.6 12 27.13 even 9
729.2.c.d.487.6 12 27.4 even 9
729.2.e.j.325.1 12 9.7 even 3
729.2.e.j.406.1 12 27.7 even 9
729.2.e.k.163.1 12 27.11 odd 18
729.2.e.k.568.1 12 9.5 odd 6
729.2.e.l.82.2 12 3.2 odd 2
729.2.e.l.649.2 12 27.2 odd 18
729.2.e.s.82.1 12 1.1 even 1 trivial
729.2.e.s.649.1 12 27.25 even 9 inner
729.2.e.t.163.2 12 27.16 even 9
729.2.e.t.568.2 12 9.4 even 3
729.2.e.u.325.2 12 9.2 odd 6
729.2.e.u.406.2 12 27.20 odd 18