Properties

Label 539.2.q.f.214.1
Level $539$
Weight $2$
Character 539.214
Analytic conductor $4.304$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(214,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.q (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 214.1
Character \(\chi\) \(=\) 539.214
Dual form 539.2.q.f.471.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.62629 + 1.80618i) q^{2} +(-1.31021 + 0.583344i) q^{3} +(-0.408403 - 3.88570i) q^{4} +(1.23113 - 0.261684i) q^{5} +(1.07716 - 3.31516i) q^{6} +(3.74989 + 2.72445i) q^{8} +(-0.631025 + 0.700825i) q^{9} +O(q^{10})\) \(q+(-1.62629 + 1.80618i) q^{2} +(-1.31021 + 0.583344i) q^{3} +(-0.408403 - 3.88570i) q^{4} +(1.23113 - 0.261684i) q^{5} +(1.07716 - 3.31516i) q^{6} +(3.74989 + 2.72445i) q^{8} +(-0.631025 + 0.700825i) q^{9} +(-1.52952 + 2.64921i) q^{10} +(-2.39780 + 2.29141i) q^{11} +(2.80179 + 4.85285i) q^{12} +(0.982152 + 3.02275i) q^{13} +(-1.46039 + 1.06103i) q^{15} +(-3.37581 + 0.717551i) q^{16} +(-3.96405 - 4.40252i) q^{17} +(-0.239584 - 2.27949i) q^{18} +(0.299183 - 2.84654i) q^{19} +(-1.51962 - 4.67691i) q^{20} +(-0.239188 - 8.05735i) q^{22} +(-3.38171 - 5.85730i) q^{23} +(-6.50244 - 1.38214i) q^{24} +(-3.12053 + 1.38935i) q^{25} +(-7.05689 - 3.14193i) q^{26} +(1.74754 - 5.37837i) q^{27} +(-3.63693 + 2.64238i) q^{29} +(0.458598 - 4.36326i) q^{30} +(9.51494 + 2.02246i) q^{31} +(-0.441092 + 0.763993i) q^{32} +(1.80494 - 4.40098i) q^{33} +14.3984 q^{34} +(2.98090 + 2.16575i) q^{36} +(-4.98335 - 2.21873i) q^{37} +(4.65480 + 5.16968i) q^{38} +(-3.05013 - 3.38751i) q^{39} +(5.32953 + 2.37286i) q^{40} +(-0.254423 - 0.184849i) q^{41} -0.132562 q^{43} +(9.88300 + 8.38129i) q^{44} +(-0.593478 + 1.02793i) q^{45} +(16.0790 + 3.41769i) q^{46} +(0.979960 - 9.32369i) q^{47} +(4.00445 - 2.90940i) q^{48} +(2.56548 - 7.89572i) q^{50} +(7.76194 + 3.45584i) q^{51} +(11.3444 - 5.05084i) q^{52} +(-4.25682 - 0.904816i) q^{53} +(6.87229 + 11.9032i) q^{54} +(-2.35237 + 3.44849i) q^{55} +(1.26852 + 3.90410i) q^{57} +(1.14209 - 10.8662i) q^{58} +(-0.726144 - 6.90880i) q^{59} +(4.71928 + 5.24129i) q^{60} +(-2.39857 + 0.509832i) q^{61} +(-19.1270 + 13.8966i) q^{62} +(-2.79554 - 8.60379i) q^{64} +(2.00016 + 3.46438i) q^{65} +(5.01360 + 10.4173i) q^{66} +(4.70993 - 8.15784i) q^{67} +(-15.4879 + 17.2011i) q^{68} +(7.84759 + 5.70161i) q^{69} +(-0.0360345 + 0.110903i) q^{71} +(-4.27564 + 0.908815i) q^{72} +(0.0642883 + 0.611662i) q^{73} +(12.1118 - 5.39252i) q^{74} +(3.27809 - 3.64069i) q^{75} -11.1830 q^{76} +11.0789 q^{78} +(5.70720 - 6.33849i) q^{79} +(-3.96828 + 1.76679i) q^{80} +(0.552066 + 5.25256i) q^{81} +(0.747637 - 0.158915i) q^{82} +(-0.293731 + 0.904010i) q^{83} +(-6.03232 - 4.38274i) q^{85} +(0.215584 - 0.239431i) q^{86} +(3.22373 - 5.58367i) q^{87} +(-15.2343 + 2.05986i) q^{88} +(5.02758 + 8.70803i) q^{89} +(-0.891464 - 2.74364i) q^{90} +(-21.3786 + 15.5325i) q^{92} +(-13.6464 + 2.90063i) q^{93} +(15.2466 + 16.9330i) q^{94} +(-0.376561 - 3.58274i) q^{95} +(0.132253 - 1.25830i) q^{96} +(-5.43159 - 16.7167i) q^{97} +(-0.0928085 - 3.12637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 3 q^{2} - 2 q^{3} + 11 q^{4} - 5 q^{5} - 6 q^{6} - 10 q^{8} + 12 q^{9} + 12 q^{10} + 3 q^{11} + 18 q^{12} + 14 q^{13} - 36 q^{15} - 17 q^{16} - 5 q^{17} - 11 q^{18} + 19 q^{19} - 2 q^{20} - 66 q^{22} - 32 q^{23} - 35 q^{24} - 7 q^{25} - 27 q^{26} - 20 q^{27} + 6 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 26 q^{33} + 48 q^{34} + 104 q^{36} - 4 q^{37} - 5 q^{38} - 11 q^{39} - 10 q^{40} + 20 q^{41} - 16 q^{43} + 38 q^{44} + 70 q^{45} + 42 q^{46} - 23 q^{47} + 72 q^{48} + 104 q^{50} + 29 q^{51} + 33 q^{52} - 4 q^{53} + 60 q^{54} + 24 q^{55} - 22 q^{57} - 20 q^{58} + 17 q^{59} + 30 q^{60} - 7 q^{61} - 158 q^{62} + 14 q^{64} + 8 q^{65} + 8 q^{66} + 38 q^{67} - 2 q^{68} - 20 q^{69} - 28 q^{71} - 35 q^{73} + 29 q^{74} + 9 q^{75} - 104 q^{76} - 116 q^{78} - 15 q^{79} - 87 q^{80} + 14 q^{81} + 19 q^{82} - 10 q^{83} + 12 q^{85} + 52 q^{86} - 72 q^{87} - 55 q^{88} + 74 q^{89} + 28 q^{90} - 110 q^{92} - 32 q^{93} - 24 q^{94} - 32 q^{95} - 42 q^{96} - 40 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.62629 + 1.80618i −1.14996 + 1.27716i −0.194876 + 0.980828i \(0.562430\pi\)
−0.955085 + 0.296333i \(0.904236\pi\)
\(3\) −1.31021 + 0.583344i −0.756452 + 0.336794i −0.748465 0.663174i \(-0.769209\pi\)
−0.00798646 + 0.999968i \(0.502542\pi\)
\(4\) −0.408403 3.88570i −0.204202 1.94285i
\(5\) 1.23113 0.261684i 0.550577 0.117029i 0.0757806 0.997125i \(-0.475855\pi\)
0.474796 + 0.880096i \(0.342522\pi\)
\(6\) 1.07716 3.31516i 0.439750 1.35341i
\(7\) 0 0
\(8\) 3.74989 + 2.72445i 1.32579 + 0.963239i
\(9\) −0.631025 + 0.700825i −0.210342 + 0.233608i
\(10\) −1.52952 + 2.64921i −0.483677 + 0.837754i
\(11\) −2.39780 + 2.29141i −0.722963 + 0.690887i
\(12\) 2.80179 + 4.85285i 0.808808 + 1.40090i
\(13\) 0.982152 + 3.02275i 0.272400 + 0.838361i 0.989896 + 0.141798i \(0.0452882\pi\)
−0.717496 + 0.696563i \(0.754712\pi\)
\(14\) 0 0
\(15\) −1.46039 + 1.06103i −0.377070 + 0.273957i
\(16\) −3.37581 + 0.717551i −0.843953 + 0.179388i
\(17\) −3.96405 4.40252i −0.961424 1.06777i −0.997656 0.0684256i \(-0.978202\pi\)
0.0362327 0.999343i \(-0.488464\pi\)
\(18\) −0.239584 2.27949i −0.0564705 0.537281i
\(19\) 0.299183 2.84654i 0.0686373 0.653041i −0.905074 0.425254i \(-0.860185\pi\)
0.973711 0.227786i \(-0.0731487\pi\)
\(20\) −1.51962 4.67691i −0.339798 1.04579i
\(21\) 0 0
\(22\) −0.239188 8.05735i −0.0509950 1.71783i
\(23\) −3.38171 5.85730i −0.705136 1.22133i −0.966642 0.256130i \(-0.917552\pi\)
0.261506 0.965202i \(-0.415781\pi\)
\(24\) −6.50244 1.38214i −1.32731 0.282127i
\(25\) −3.12053 + 1.38935i −0.624106 + 0.277870i
\(26\) −7.05689 3.14193i −1.38397 0.616183i
\(27\) 1.74754 5.37837i 0.336314 1.03507i
\(28\) 0 0
\(29\) −3.63693 + 2.64238i −0.675361 + 0.490678i −0.871815 0.489834i \(-0.837057\pi\)
0.196454 + 0.980513i \(0.437057\pi\)
\(30\) 0.458598 4.36326i 0.0837281 0.796620i
\(31\) 9.51494 + 2.02246i 1.70893 + 0.363245i 0.955663 0.294464i \(-0.0951412\pi\)
0.753272 + 0.657709i \(0.228475\pi\)
\(32\) −0.441092 + 0.763993i −0.0779748 + 0.135056i
\(33\) 1.80494 4.40098i 0.314200 0.766112i
\(34\) 14.3984 2.46931
\(35\) 0 0
\(36\) 2.98090 + 2.16575i 0.496817 + 0.360959i
\(37\) −4.98335 2.21873i −0.819257 0.364757i −0.0460730 0.998938i \(-0.514671\pi\)
−0.773184 + 0.634181i \(0.781337\pi\)
\(38\) 4.65480 + 5.16968i 0.755108 + 0.838632i
\(39\) −3.05013 3.38751i −0.488412 0.542437i
\(40\) 5.32953 + 2.37286i 0.842673 + 0.375182i
\(41\) −0.254423 0.184849i −0.0397342 0.0288686i 0.567741 0.823207i \(-0.307818\pi\)
−0.607475 + 0.794339i \(0.707818\pi\)
\(42\) 0 0
\(43\) −0.132562 −0.0202155 −0.0101078 0.999949i \(-0.503217\pi\)
−0.0101078 + 0.999949i \(0.503217\pi\)
\(44\) 9.88300 + 8.38129i 1.48992 + 1.26353i
\(45\) −0.593478 + 1.02793i −0.0884704 + 0.153235i
\(46\) 16.0790 + 3.41769i 2.37072 + 0.503911i
\(47\) 0.979960 9.32369i 0.142942 1.36000i −0.654252 0.756277i \(-0.727016\pi\)
0.797194 0.603724i \(-0.206317\pi\)
\(48\) 4.00445 2.90940i 0.577993 0.419936i
\(49\) 0 0
\(50\) 2.56548 7.89572i 0.362813 1.11662i
\(51\) 7.76194 + 3.45584i 1.08689 + 0.483914i
\(52\) 11.3444 5.05084i 1.57318 0.700426i
\(53\) −4.25682 0.904816i −0.584720 0.124286i −0.0939524 0.995577i \(-0.529950\pi\)
−0.490767 + 0.871291i \(0.663283\pi\)
\(54\) 6.87229 + 11.9032i 0.935200 + 1.61981i
\(55\) −2.35237 + 3.44849i −0.317193 + 0.464994i
\(56\) 0 0
\(57\) 1.26852 + 3.90410i 0.168019 + 0.517110i
\(58\) 1.14209 10.8662i 0.149963 1.42681i
\(59\) −0.726144 6.90880i −0.0945359 0.899449i −0.934298 0.356494i \(-0.883972\pi\)
0.839762 0.542955i \(-0.182695\pi\)
\(60\) 4.71928 + 5.24129i 0.609256 + 0.676647i
\(61\) −2.39857 + 0.509832i −0.307105 + 0.0652772i −0.358886 0.933381i \(-0.616843\pi\)
0.0517812 + 0.998658i \(0.483510\pi\)
\(62\) −19.1270 + 13.8966i −2.42913 + 1.76487i
\(63\) 0 0
\(64\) −2.79554 8.60379i −0.349443 1.07547i
\(65\) 2.00016 + 3.46438i 0.248089 + 0.429703i
\(66\) 5.01360 + 10.4173i 0.617131 + 1.28228i
\(67\) 4.70993 8.15784i 0.575410 0.996639i −0.420587 0.907252i \(-0.638176\pi\)
0.995997 0.0893871i \(-0.0284908\pi\)
\(68\) −15.4879 + 17.2011i −1.87819 + 2.08594i
\(69\) 7.84759 + 5.70161i 0.944739 + 0.686393i
\(70\) 0 0
\(71\) −0.0360345 + 0.110903i −0.00427651 + 0.0131617i −0.953172 0.302429i \(-0.902203\pi\)
0.948895 + 0.315590i \(0.102203\pi\)
\(72\) −4.27564 + 0.908815i −0.503889 + 0.107105i
\(73\) 0.0642883 + 0.611662i 0.00752438 + 0.0715897i 0.997640 0.0686659i \(-0.0218742\pi\)
−0.990115 + 0.140256i \(0.955208\pi\)
\(74\) 12.1118 5.39252i 1.40797 0.626867i
\(75\) 3.27809 3.64069i 0.378521 0.420391i
\(76\) −11.1830 −1.28277
\(77\) 0 0
\(78\) 11.0789 1.25443
\(79\) 5.70720 6.33849i 0.642111 0.713136i −0.330960 0.943645i \(-0.607372\pi\)
0.973070 + 0.230509i \(0.0740391\pi\)
\(80\) −3.96828 + 1.76679i −0.443667 + 0.197533i
\(81\) 0.552066 + 5.25256i 0.0613407 + 0.583618i
\(82\) 0.747637 0.158915i 0.0825627 0.0175492i
\(83\) −0.293731 + 0.904010i −0.0322411 + 0.0992280i −0.965882 0.258982i \(-0.916613\pi\)
0.933641 + 0.358210i \(0.116613\pi\)
\(84\) 0 0
\(85\) −6.03232 4.38274i −0.654297 0.475375i
\(86\) 0.215584 0.239431i 0.0232471 0.0258185i
\(87\) 3.22373 5.58367i 0.345620 0.598632i
\(88\) −15.2343 + 2.05986i −1.62398 + 0.219582i
\(89\) 5.02758 + 8.70803i 0.532923 + 0.923049i 0.999261 + 0.0384427i \(0.0122397\pi\)
−0.466338 + 0.884607i \(0.654427\pi\)
\(90\) −0.891464 2.74364i −0.0939686 0.289206i
\(91\) 0 0
\(92\) −21.3786 + 15.5325i −2.22887 + 1.61937i
\(93\) −13.6464 + 2.90063i −1.41506 + 0.300781i
\(94\) 15.2466 + 16.9330i 1.57256 + 1.74651i
\(95\) −0.376561 3.58274i −0.0386344 0.367582i
\(96\) 0.132253 1.25830i 0.0134980 0.128425i
\(97\) −5.43159 16.7167i −0.551495 1.69733i −0.705025 0.709182i \(-0.749064\pi\)
0.153530 0.988144i \(-0.450936\pi\)
\(98\) 0 0
\(99\) −0.0928085 3.12637i −0.00932760 0.314212i
\(100\) 6.67303 + 11.5580i 0.667303 + 1.15580i
\(101\) −12.2035 2.59394i −1.21429 0.258106i −0.444137 0.895959i \(-0.646490\pi\)
−0.770158 + 0.637853i \(0.779823\pi\)
\(102\) −18.8650 + 8.39925i −1.86792 + 0.831649i
\(103\) −7.50754 3.34257i −0.739740 0.329353i 0.00203908 0.999998i \(-0.499351\pi\)
−0.741779 + 0.670645i \(0.766018\pi\)
\(104\) −4.55239 + 14.0108i −0.446398 + 1.37387i
\(105\) 0 0
\(106\) 8.55709 6.21709i 0.831138 0.603857i
\(107\) −1.27405 + 12.1218i −0.123167 + 1.17185i 0.742011 + 0.670388i \(0.233872\pi\)
−0.865177 + 0.501466i \(0.832794\pi\)
\(108\) −21.6124 4.59386i −2.07965 0.442044i
\(109\) −0.443044 + 0.767375i −0.0424359 + 0.0735012i −0.886463 0.462799i \(-0.846845\pi\)
0.844027 + 0.536300i \(0.180178\pi\)
\(110\) −2.40295 9.85703i −0.229112 0.939831i
\(111\) 7.82353 0.742577
\(112\) 0 0
\(113\) −3.67700 2.67149i −0.345903 0.251313i 0.401245 0.915971i \(-0.368577\pi\)
−0.747148 + 0.664658i \(0.768577\pi\)
\(114\) −9.11447 4.05802i −0.853649 0.380069i
\(115\) −5.69608 6.32614i −0.531163 0.589916i
\(116\) 11.7528 + 13.0528i 1.09122 + 1.21193i
\(117\) −2.73818 1.21912i −0.253145 0.112707i
\(118\) 13.6594 + 9.92416i 1.25745 + 0.913593i
\(119\) 0 0
\(120\) −8.36702 −0.763801
\(121\) 0.498853 10.9887i 0.0453503 0.998971i
\(122\) 2.97992 5.16138i 0.269789 0.467289i
\(123\) 0.441179 + 0.0937755i 0.0397798 + 0.00845546i
\(124\) 3.97275 37.7982i 0.356763 3.39437i
\(125\) −8.56947 + 6.22608i −0.766477 + 0.556878i
\(126\) 0 0
\(127\) −2.48072 + 7.63488i −0.220129 + 0.677486i 0.778621 + 0.627494i \(0.215919\pi\)
−0.998750 + 0.0499916i \(0.984081\pi\)
\(128\) 18.4745 + 8.22538i 1.63293 + 0.727028i
\(129\) 0.173684 0.0773293i 0.0152921 0.00680846i
\(130\) −9.51012 2.02144i −0.834093 0.177292i
\(131\) 0.0507303 + 0.0878675i 0.00443233 + 0.00767702i 0.868233 0.496157i \(-0.165256\pi\)
−0.863801 + 0.503834i \(0.831922\pi\)
\(132\) −17.8380 5.21608i −1.55260 0.454001i
\(133\) 0 0
\(134\) 7.07480 + 21.7740i 0.611170 + 1.88099i
\(135\) 0.744007 7.07876i 0.0640340 0.609242i
\(136\) −2.87027 27.3088i −0.246124 2.34171i
\(137\) −3.05397 3.39178i −0.260919 0.289779i 0.598424 0.801179i \(-0.295794\pi\)
−0.859343 + 0.511400i \(0.829127\pi\)
\(138\) −23.0606 + 4.90168i −1.96305 + 0.417258i
\(139\) −3.09475 + 2.24847i −0.262494 + 0.190713i −0.711246 0.702944i \(-0.751869\pi\)
0.448752 + 0.893656i \(0.351869\pi\)
\(140\) 0 0
\(141\) 4.15497 + 12.7877i 0.349911 + 1.07692i
\(142\) −0.141708 0.245445i −0.0118918 0.0205973i
\(143\) −9.28137 4.99743i −0.776147 0.417906i
\(144\) 1.62734 2.81864i 0.135612 0.234887i
\(145\) −3.78605 + 4.20484i −0.314415 + 0.349193i
\(146\) −1.20932 0.878624i −0.100084 0.0727155i
\(147\) 0 0
\(148\) −6.58609 + 20.2699i −0.541374 + 1.66618i
\(149\) 4.76576 1.01299i 0.390427 0.0829877i −0.00851575 0.999964i \(-0.502711\pi\)
0.398942 + 0.916976i \(0.369377\pi\)
\(150\) 1.24461 + 11.8416i 0.101622 + 0.966865i
\(151\) −15.5064 + 6.90389i −1.26189 + 0.561831i −0.925091 0.379745i \(-0.876012\pi\)
−0.336802 + 0.941576i \(0.609345\pi\)
\(152\) 8.87716 9.85909i 0.720033 0.799677i
\(153\) 5.58681 0.451667
\(154\) 0 0
\(155\) 12.2434 0.983410
\(156\) −11.9172 + 13.2354i −0.954137 + 1.05968i
\(157\) −2.05075 + 0.913055i −0.163668 + 0.0728697i −0.486935 0.873438i \(-0.661885\pi\)
0.323267 + 0.946308i \(0.395219\pi\)
\(158\) 2.16688 + 20.6165i 0.172387 + 1.64016i
\(159\) 6.10516 1.29769i 0.484171 0.102914i
\(160\) −0.343115 + 1.05600i −0.0271256 + 0.0834841i
\(161\) 0 0
\(162\) −10.3849 7.54506i −0.815913 0.592796i
\(163\) −10.5972 + 11.7694i −0.830036 + 0.921848i −0.997953 0.0639530i \(-0.979629\pi\)
0.167917 + 0.985801i \(0.446296\pi\)
\(164\) −0.614361 + 1.06410i −0.0479735 + 0.0830926i
\(165\) 1.07044 5.89049i 0.0833340 0.458574i
\(166\) −1.15511 2.00071i −0.0896540 0.155285i
\(167\) −6.40950 19.7264i −0.495982 1.52647i −0.815421 0.578868i \(-0.803495\pi\)
0.319440 0.947607i \(-0.396505\pi\)
\(168\) 0 0
\(169\) 2.34481 1.70361i 0.180370 0.131047i
\(170\) 17.7263 3.76784i 1.35955 0.288980i
\(171\) 1.80613 + 2.00591i 0.138118 + 0.153396i
\(172\) 0.0541387 + 0.515096i 0.00412804 + 0.0392757i
\(173\) −2.25315 + 21.4373i −0.171304 + 1.62985i 0.484410 + 0.874841i \(0.339034\pi\)
−0.655714 + 0.755009i \(0.727632\pi\)
\(174\) 4.84238 + 14.9033i 0.367100 + 1.12982i
\(175\) 0 0
\(176\) 6.45030 9.45592i 0.486210 0.712767i
\(177\) 4.98161 + 8.62840i 0.374441 + 0.648550i
\(178\) −23.9046 5.08107i −1.79172 0.380842i
\(179\) 4.36822 1.94485i 0.326496 0.145365i −0.236942 0.971524i \(-0.576145\pi\)
0.563438 + 0.826159i \(0.309478\pi\)
\(180\) 4.23662 + 1.88626i 0.315779 + 0.140594i
\(181\) 2.42666 7.46850i 0.180372 0.555129i −0.819466 0.573128i \(-0.805730\pi\)
0.999838 + 0.0179992i \(0.00572963\pi\)
\(182\) 0 0
\(183\) 2.84523 2.06718i 0.210325 0.152810i
\(184\) 3.27689 31.1775i 0.241576 2.29844i
\(185\) −6.71574 1.42747i −0.493751 0.104950i
\(186\) 16.9539 29.3651i 1.24312 2.15315i
\(187\) 19.5930 + 1.47308i 1.43278 + 0.107722i
\(188\) −36.6293 −2.67146
\(189\) 0 0
\(190\) 7.08347 + 5.14644i 0.513889 + 0.373362i
\(191\) −8.06687 3.59160i −0.583698 0.259879i 0.0935733 0.995612i \(-0.470171\pi\)
−0.677271 + 0.735733i \(0.736838\pi\)
\(192\) 8.68173 + 9.64203i 0.626550 + 0.695854i
\(193\) 17.1313 + 19.0262i 1.23313 + 1.36954i 0.905285 + 0.424805i \(0.139657\pi\)
0.327850 + 0.944730i \(0.393676\pi\)
\(194\) 39.0267 + 17.3758i 2.80196 + 1.24751i
\(195\) −4.64156 3.37229i −0.332389 0.241495i
\(196\) 0 0
\(197\) −11.1977 −0.797802 −0.398901 0.916994i \(-0.630608\pi\)
−0.398901 + 0.916994i \(0.630608\pi\)
\(198\) 5.79772 + 4.91676i 0.412026 + 0.349419i
\(199\) −6.12514 + 10.6091i −0.434200 + 0.752056i −0.997230 0.0743802i \(-0.976302\pi\)
0.563030 + 0.826436i \(0.309635\pi\)
\(200\) −15.4869 3.29183i −1.09509 0.232768i
\(201\) −1.41218 + 13.4360i −0.0996077 + 0.947704i
\(202\) 24.5316 17.8232i 1.72603 1.25404i
\(203\) 0 0
\(204\) 10.2583 31.5719i 0.718227 2.21048i
\(205\) −0.361599 0.160994i −0.0252552 0.0112443i
\(206\) 18.2467 8.12396i 1.27131 0.566023i
\(207\) 6.23889 + 1.32612i 0.433633 + 0.0921715i
\(208\) −5.48454 9.49949i −0.380284 0.658671i
\(209\) 5.80521 + 7.51097i 0.401555 + 0.519545i
\(210\) 0 0
\(211\) −4.40769 13.5655i −0.303438 0.933887i −0.980255 0.197736i \(-0.936641\pi\)
0.676817 0.736151i \(-0.263359\pi\)
\(212\) −1.77734 + 16.9103i −0.122068 + 1.16140i
\(213\) −0.0174817 0.166327i −0.00119782 0.0113965i
\(214\) −19.8221 22.0146i −1.35501 1.50489i
\(215\) −0.163201 + 0.0346894i −0.0111302 + 0.00236580i
\(216\) 21.2062 15.4072i 1.44290 1.04833i
\(217\) 0 0
\(218\) −0.665497 2.04819i −0.0450732 0.138721i
\(219\) −0.441041 0.763905i −0.0298028 0.0516199i
\(220\) 14.3605 + 7.73220i 0.968183 + 0.521305i
\(221\) 9.41444 16.3063i 0.633284 1.09688i
\(222\) −12.7233 + 14.1307i −0.853934 + 0.948390i
\(223\) −2.39793 1.74220i −0.160577 0.116666i 0.504595 0.863356i \(-0.331642\pi\)
−0.665172 + 0.746690i \(0.731642\pi\)
\(224\) 0 0
\(225\) 0.995444 3.06366i 0.0663629 0.204244i
\(226\) 10.8051 2.29669i 0.718742 0.152773i
\(227\) 0.862993 + 8.21083i 0.0572788 + 0.544972i 0.985104 + 0.171957i \(0.0550091\pi\)
−0.927826 + 0.373014i \(0.878324\pi\)
\(228\) 14.6521 6.52352i 0.970357 0.432031i
\(229\) −8.77104 + 9.74122i −0.579607 + 0.643718i −0.959632 0.281258i \(-0.909248\pi\)
0.380026 + 0.924976i \(0.375915\pi\)
\(230\) 20.6896 1.36423
\(231\) 0 0
\(232\) −20.8371 −1.36802
\(233\) −8.58339 + 9.53282i −0.562317 + 0.624516i −0.955517 0.294937i \(-0.904701\pi\)
0.393200 + 0.919453i \(0.371368\pi\)
\(234\) 6.65502 2.96301i 0.435052 0.193698i
\(235\) −1.23341 11.7351i −0.0804586 0.765513i
\(236\) −26.5489 + 5.64315i −1.72819 + 0.367338i
\(237\) −3.78013 + 11.6340i −0.245546 + 0.755712i
\(238\) 0 0
\(239\) 4.02979 + 2.92781i 0.260665 + 0.189384i 0.710440 0.703758i \(-0.248496\pi\)
−0.449775 + 0.893142i \(0.648496\pi\)
\(240\) 4.16864 4.62975i 0.269085 0.298849i
\(241\) −1.31343 + 2.27492i −0.0846053 + 0.146541i −0.905223 0.424937i \(-0.860296\pi\)
0.820618 + 0.571478i \(0.193630\pi\)
\(242\) 19.0362 + 18.7718i 1.22370 + 1.20670i
\(243\) 4.69535 + 8.13258i 0.301207 + 0.521706i
\(244\) 2.96063 + 9.11189i 0.189535 + 0.583329i
\(245\) 0 0
\(246\) −0.886861 + 0.644342i −0.0565442 + 0.0410818i
\(247\) 8.89822 1.89138i 0.566180 0.120345i
\(248\) 30.1699 + 33.5070i 1.91579 + 2.12770i
\(249\) −0.142499 1.35579i −0.00903053 0.0859198i
\(250\) 2.69103 25.6034i 0.170195 1.61930i
\(251\) 8.10332 + 24.9395i 0.511477 + 1.57417i 0.789601 + 0.613620i \(0.210287\pi\)
−0.278124 + 0.960545i \(0.589713\pi\)
\(252\) 0 0
\(253\) 21.5302 + 6.29571i 1.35359 + 0.395808i
\(254\) −9.75558 16.8972i −0.612119 1.06022i
\(255\) 10.4603 + 2.22340i 0.655047 + 0.139235i
\(256\) −28.3725 + 12.6323i −1.77328 + 0.789517i
\(257\) −27.3623 12.1825i −1.70681 0.759923i −0.998542 0.0539837i \(-0.982808\pi\)
−0.708273 0.705939i \(-0.750525\pi\)
\(258\) −0.142791 + 0.439465i −0.00888977 + 0.0273599i
\(259\) 0 0
\(260\) 12.6446 9.18688i 0.784188 0.569746i
\(261\) 0.443147 4.21626i 0.0274301 0.260980i
\(262\) −0.241207 0.0512701i −0.0149018 0.00316747i
\(263\) −1.66854 + 2.89000i −0.102887 + 0.178205i −0.912873 0.408244i \(-0.866141\pi\)
0.809986 + 0.586449i \(0.199475\pi\)
\(264\) 18.7586 11.5857i 1.15451 0.713050i
\(265\) −5.47747 −0.336478
\(266\) 0 0
\(267\) −11.6670 8.47656i −0.714008 0.518757i
\(268\) −33.6225 14.9697i −2.05382 0.914419i
\(269\) 1.16149 + 1.28996i 0.0708170 + 0.0786502i 0.777512 0.628868i \(-0.216481\pi\)
−0.706695 + 0.707518i \(0.749815\pi\)
\(270\) 11.5755 + 12.8559i 0.704464 + 0.782387i
\(271\) 2.26190 + 1.00706i 0.137401 + 0.0611747i 0.474285 0.880371i \(-0.342707\pi\)
−0.336885 + 0.941546i \(0.609373\pi\)
\(272\) 16.5409 + 12.0177i 1.00294 + 0.728679i
\(273\) 0 0
\(274\) 11.0928 0.670141
\(275\) 4.29882 10.4818i 0.259229 0.632077i
\(276\) 18.9497 32.8219i 1.14064 1.97565i
\(277\) −5.04304 1.07193i −0.303007 0.0644061i 0.0538991 0.998546i \(-0.482835\pi\)
−0.356906 + 0.934140i \(0.616168\pi\)
\(278\) 0.971830 9.24634i 0.0582865 0.554559i
\(279\) −7.42156 + 5.39208i −0.444317 + 0.322815i
\(280\) 0 0
\(281\) −6.97467 + 21.4658i −0.416074 + 1.28054i 0.495213 + 0.868772i \(0.335090\pi\)
−0.911287 + 0.411772i \(0.864910\pi\)
\(282\) −29.8540 13.2919i −1.77778 0.791519i
\(283\) 7.75378 3.45221i 0.460914 0.205212i −0.163125 0.986605i \(-0.552157\pi\)
0.624039 + 0.781393i \(0.285491\pi\)
\(284\) 0.445651 + 0.0947261i 0.0264445 + 0.00562096i
\(285\) 2.58335 + 4.47449i 0.153024 + 0.265046i
\(286\) 24.1205 8.63654i 1.42627 0.510690i
\(287\) 0 0
\(288\) −0.257085 0.791227i −0.0151489 0.0466235i
\(289\) −1.89154 + 17.9968i −0.111267 + 1.05863i
\(290\) −1.43747 13.6766i −0.0844109 0.803116i
\(291\) 16.8681 + 18.7340i 0.988828 + 1.09821i
\(292\) 2.35048 0.499610i 0.137551 0.0292374i
\(293\) 19.9229 14.4749i 1.16391 0.845630i 0.173643 0.984809i \(-0.444446\pi\)
0.990267 + 0.139178i \(0.0444462\pi\)
\(294\) 0 0
\(295\) −2.70190 8.31559i −0.157311 0.484152i
\(296\) −12.6422 21.8969i −0.734811 1.27273i
\(297\) 8.13382 + 16.9006i 0.471972 + 0.980670i
\(298\) −5.92087 + 10.2552i −0.342987 + 0.594070i
\(299\) 14.3838 15.9748i 0.831837 0.923849i
\(300\) −15.4854 11.2508i −0.894050 0.649565i
\(301\) 0 0
\(302\) 12.7482 39.2351i 0.733579 2.25772i
\(303\) 17.5024 3.72024i 1.00548 0.213722i
\(304\) 1.03255 + 9.82405i 0.0592208 + 0.563448i
\(305\) −2.81953 + 1.25533i −0.161446 + 0.0718803i
\(306\) −9.08578 + 10.0908i −0.519400 + 0.576852i
\(307\) −4.59391 −0.262188 −0.131094 0.991370i \(-0.541849\pi\)
−0.131094 + 0.991370i \(0.541849\pi\)
\(308\) 0 0
\(309\) 11.7863 0.670502
\(310\) −19.9112 + 22.1137i −1.13088 + 1.25597i
\(311\) 2.01960 0.899186i 0.114521 0.0509882i −0.348676 0.937243i \(-0.613369\pi\)
0.463198 + 0.886255i \(0.346702\pi\)
\(312\) −2.20853 21.0127i −0.125033 1.18961i
\(313\) −9.48733 + 2.01659i −0.536256 + 0.113985i −0.468076 0.883688i \(-0.655053\pi\)
−0.0681799 + 0.997673i \(0.521719\pi\)
\(314\) 1.68598 5.18892i 0.0951455 0.292828i
\(315\) 0 0
\(316\) −26.9603 19.5878i −1.51664 1.10190i
\(317\) 4.31950 4.79729i 0.242607 0.269443i −0.609528 0.792765i \(-0.708641\pi\)
0.852135 + 0.523322i \(0.175308\pi\)
\(318\) −7.58490 + 13.1374i −0.425340 + 0.736711i
\(319\) 2.66582 14.6696i 0.149257 0.821340i
\(320\) −5.69314 9.86081i −0.318256 0.551236i
\(321\) −5.40188 16.6253i −0.301504 0.927933i
\(322\) 0 0
\(323\) −13.7179 + 9.96666i −0.763286 + 0.554560i
\(324\) 20.1844 4.29033i 1.12136 0.238351i
\(325\) −7.26450 8.06804i −0.402962 0.447534i
\(326\) −4.02348 38.2808i −0.222840 2.12018i
\(327\) 0.132838 1.26387i 0.00734597 0.0698922i
\(328\) −0.450445 1.38633i −0.0248717 0.0765471i
\(329\) 0 0
\(330\) 8.89842 + 11.5131i 0.489842 + 0.633773i
\(331\) −1.81038 3.13567i −0.0995075 0.172352i 0.811973 0.583694i \(-0.198393\pi\)
−0.911481 + 0.411342i \(0.865060\pi\)
\(332\) 3.63267 + 0.772147i 0.199369 + 0.0423771i
\(333\) 4.69956 2.09238i 0.257534 0.114662i
\(334\) 46.0531 + 20.5042i 2.51991 + 1.12194i
\(335\) 3.66375 11.2759i 0.200172 0.616066i
\(336\) 0 0
\(337\) 5.18183 3.76482i 0.282272 0.205083i −0.437636 0.899152i \(-0.644184\pi\)
0.719908 + 0.694070i \(0.244184\pi\)
\(338\) −0.736330 + 7.00571i −0.0400511 + 0.381060i
\(339\) 6.37605 + 1.35527i 0.346299 + 0.0736082i
\(340\) −14.5664 + 25.2297i −0.789972 + 1.36827i
\(341\) −27.4492 + 16.9532i −1.48646 + 0.918068i
\(342\) −6.56033 −0.354742
\(343\) 0 0
\(344\) −0.497093 0.361159i −0.0268014 0.0194724i
\(345\) 11.1534 + 4.96581i 0.600479 + 0.267350i
\(346\) −35.0554 38.9329i −1.88459 2.09305i
\(347\) −11.6830 12.9753i −0.627177 0.696551i 0.342893 0.939374i \(-0.388593\pi\)
−0.970070 + 0.242823i \(0.921926\pi\)
\(348\) −23.0130 10.2461i −1.23363 0.549246i
\(349\) −17.4949 12.7108i −0.936481 0.680393i 0.0110900 0.999939i \(-0.496470\pi\)
−0.947571 + 0.319545i \(0.896470\pi\)
\(350\) 0 0
\(351\) 17.9738 0.959371
\(352\) −0.692976 2.84262i −0.0369358 0.151512i
\(353\) 2.20075 3.81181i 0.117134 0.202882i −0.801497 0.597999i \(-0.795963\pi\)
0.918631 + 0.395117i \(0.129296\pi\)
\(354\) −23.6860 5.03461i −1.25890 0.267586i
\(355\) −0.0153416 + 0.145965i −0.000814245 + 0.00774703i
\(356\) 31.7835 23.0920i 1.68452 1.22388i
\(357\) 0 0
\(358\) −3.59123 + 11.0527i −0.189802 + 0.584152i
\(359\) −9.75825 4.34465i −0.515021 0.229302i 0.132733 0.991152i \(-0.457625\pi\)
−0.647754 + 0.761850i \(0.724291\pi\)
\(360\) −5.02603 + 2.23773i −0.264895 + 0.117939i
\(361\) 10.5715 + 2.24705i 0.556397 + 0.118266i
\(362\) 9.54298 + 16.5289i 0.501568 + 0.868741i
\(363\) 5.75658 + 14.6885i 0.302142 + 0.770947i
\(364\) 0 0
\(365\) 0.239209 + 0.736211i 0.0125208 + 0.0385350i
\(366\) −0.893472 + 8.50082i −0.0467025 + 0.444345i
\(367\) 1.06794 + 10.1608i 0.0557460 + 0.530388i 0.986385 + 0.164450i \(0.0525850\pi\)
−0.930639 + 0.365938i \(0.880748\pi\)
\(368\) 15.6189 + 17.3466i 0.814194 + 0.904254i
\(369\) 0.290094 0.0616615i 0.0151017 0.00320997i
\(370\) 13.5000 9.80834i 0.701833 0.509911i
\(371\) 0 0
\(372\) 16.8442 + 51.8411i 0.873331 + 2.68784i
\(373\) 13.9425 + 24.1492i 0.721917 + 1.25040i 0.960231 + 0.279208i \(0.0900720\pi\)
−0.238314 + 0.971188i \(0.576595\pi\)
\(374\) −34.5245 + 32.9928i −1.78522 + 1.70602i
\(375\) 7.59588 13.1564i 0.392249 0.679396i
\(376\) 29.0767 32.2929i 1.49952 1.66538i
\(377\) −11.5593 8.39832i −0.595334 0.432535i
\(378\) 0 0
\(379\) 0.354761 1.09184i 0.0182228 0.0560841i −0.941532 0.336925i \(-0.890613\pi\)
0.959754 + 0.280841i \(0.0906132\pi\)
\(380\) −13.7677 + 2.92641i −0.706266 + 0.150121i
\(381\) −1.20349 11.4504i −0.0616566 0.586623i
\(382\) 19.6061 8.72922i 1.00314 0.446626i
\(383\) 13.3502 14.8269i 0.682165 0.757621i −0.298266 0.954483i \(-0.596408\pi\)
0.980431 + 0.196861i \(0.0630749\pi\)
\(384\) −29.0038 −1.48009
\(385\) 0 0
\(386\) −62.2251 −3.16717
\(387\) 0.0836500 0.0929027i 0.00425217 0.00472251i
\(388\) −62.7378 + 27.9327i −3.18503 + 1.41807i
\(389\) −0.271774 2.58576i −0.0137795 0.131103i 0.985469 0.169853i \(-0.0543292\pi\)
−0.999249 + 0.0387496i \(0.987663\pi\)
\(390\) 13.6395 2.89916i 0.690662 0.146805i
\(391\) −12.3816 + 38.1067i −0.626166 + 1.92714i
\(392\) 0 0
\(393\) −0.117725 0.0855319i −0.00593842 0.00431451i
\(394\) 18.2107 20.2250i 0.917441 1.01892i
\(395\) 5.36761 9.29697i 0.270074 0.467782i
\(396\) −12.1102 + 1.63745i −0.608562 + 0.0822848i
\(397\) 4.38618 + 7.59709i 0.220136 + 0.381287i 0.954849 0.297091i \(-0.0960165\pi\)
−0.734713 + 0.678378i \(0.762683\pi\)
\(398\) −9.20059 28.3165i −0.461184 1.41938i
\(399\) 0 0
\(400\) 9.53740 6.92932i 0.476870 0.346466i
\(401\) −27.7339 + 5.89502i −1.38496 + 0.294383i −0.839322 0.543634i \(-0.817048\pi\)
−0.545643 + 0.838018i \(0.683714\pi\)
\(402\) −21.9712 24.4015i −1.09583 1.21704i
\(403\) 3.23171 + 30.7477i 0.160983 + 1.53165i
\(404\) −5.09530 + 48.4785i −0.253501 + 2.41190i
\(405\) 2.05418 + 6.32210i 0.102073 + 0.314148i
\(406\) 0 0
\(407\) 17.0331 6.09885i 0.844298 0.302309i
\(408\) 19.6911 + 34.1060i 0.974856 + 1.68850i
\(409\) 19.4705 + 4.13859i 0.962756 + 0.204640i 0.662369 0.749178i \(-0.269551\pi\)
0.300386 + 0.953818i \(0.402884\pi\)
\(410\) 0.878850 0.391289i 0.0434033 0.0193244i
\(411\) 5.97993 + 2.66244i 0.294968 + 0.131328i
\(412\) −9.92212 + 30.5371i −0.488828 + 1.50446i
\(413\) 0 0
\(414\) −12.5414 + 9.11189i −0.616379 + 0.447825i
\(415\) −0.125055 + 1.18982i −0.00613869 + 0.0584057i
\(416\) −2.74258 0.582954i −0.134466 0.0285817i
\(417\) 2.74315 4.75128i 0.134333 0.232671i
\(418\) −23.0071 1.72977i −1.12531 0.0846057i
\(419\) 30.8957 1.50935 0.754676 0.656097i \(-0.227794\pi\)
0.754676 + 0.656097i \(0.227794\pi\)
\(420\) 0 0
\(421\) 19.5727 + 14.2204i 0.953913 + 0.693058i 0.951729 0.306939i \(-0.0993049\pi\)
0.00218371 + 0.999998i \(0.499305\pi\)
\(422\) 31.6699 + 14.1003i 1.54167 + 0.686394i
\(423\) 5.91589 + 6.57027i 0.287641 + 0.319457i
\(424\) −13.4975 14.9905i −0.655496 0.728002i
\(425\) 18.4866 + 8.23076i 0.896732 + 0.399251i
\(426\) 0.328846 + 0.238921i 0.0159326 + 0.0115757i
\(427\) 0 0
\(428\) 47.6218 2.30188
\(429\) 15.0758 + 1.13346i 0.727866 + 0.0547239i
\(430\) 0.202756 0.351184i 0.00977778 0.0169356i
\(431\) −18.9761 4.03350i −0.914047 0.194287i −0.273202 0.961957i \(-0.588083\pi\)
−0.640845 + 0.767670i \(0.721416\pi\)
\(432\) −2.04010 + 19.4103i −0.0981546 + 0.933878i
\(433\) −17.3030 + 12.5714i −0.831530 + 0.604142i −0.919992 0.391937i \(-0.871805\pi\)
0.0884616 + 0.996080i \(0.471805\pi\)
\(434\) 0 0
\(435\) 2.50767 7.71780i 0.120233 0.370040i
\(436\) 3.16273 + 1.40814i 0.151467 + 0.0674375i
\(437\) −17.6848 + 7.87377i −0.845978 + 0.376654i
\(438\) 2.09701 + 0.445733i 0.100199 + 0.0212980i
\(439\) −15.8658 27.4803i −0.757232 1.31156i −0.944257 0.329209i \(-0.893218\pi\)
0.187025 0.982355i \(-0.440115\pi\)
\(440\) −18.2163 + 6.52252i −0.868430 + 0.310949i
\(441\) 0 0
\(442\) 14.1415 + 43.5229i 0.672640 + 2.07017i
\(443\) 0.174155 1.65698i 0.00827437 0.0787254i −0.989605 0.143809i \(-0.954065\pi\)
0.997880 + 0.0650839i \(0.0207315\pi\)
\(444\) −3.19515 30.3999i −0.151635 1.44271i
\(445\) 8.46835 + 9.40505i 0.401438 + 0.445842i
\(446\) 7.04644 1.49777i 0.333659 0.0709213i
\(447\) −5.65324 + 4.10732i −0.267389 + 0.194270i
\(448\) 0 0
\(449\) −5.31070 16.3447i −0.250627 0.771352i −0.994660 0.103208i \(-0.967089\pi\)
0.744032 0.668144i \(-0.232911\pi\)
\(450\) 3.91464 + 6.78035i 0.184538 + 0.319629i
\(451\) 1.03362 0.139758i 0.0486713 0.00658093i
\(452\) −8.87892 + 15.3787i −0.417629 + 0.723355i
\(453\) 16.2893 18.0911i 0.765340 0.849996i
\(454\) −16.2337 11.7945i −0.761885 0.553542i
\(455\) 0 0
\(456\) −5.87973 + 18.0959i −0.275343 + 0.847420i
\(457\) −9.99729 + 2.12499i −0.467654 + 0.0994029i −0.435711 0.900087i \(-0.643503\pi\)
−0.0319431 + 0.999490i \(0.510170\pi\)
\(458\) −3.33013 31.6841i −0.155607 1.48050i
\(459\) −30.6057 + 13.6265i −1.42855 + 0.636033i
\(460\) −22.2552 + 24.7169i −1.03765 + 1.15243i
\(461\) 22.1160 1.03004 0.515022 0.857177i \(-0.327784\pi\)
0.515022 + 0.857177i \(0.327784\pi\)
\(462\) 0 0
\(463\) −30.3717 −1.41149 −0.705747 0.708464i \(-0.749389\pi\)
−0.705747 + 0.708464i \(0.749389\pi\)
\(464\) 10.3815 11.5299i 0.481951 0.535261i
\(465\) −16.0414 + 7.14209i −0.743902 + 0.331206i
\(466\) −3.25889 31.0063i −0.150965 1.43634i
\(467\) 24.6404 5.23748i 1.14022 0.242362i 0.401166 0.916005i \(-0.368605\pi\)
0.739056 + 0.673644i \(0.235272\pi\)
\(468\) −3.61884 + 11.1376i −0.167281 + 0.514837i
\(469\) 0 0
\(470\) 23.2015 + 16.8569i 1.07021 + 0.777551i
\(471\) 2.15430 2.39259i 0.0992648 0.110245i
\(472\) 16.0997 27.8856i 0.741050 1.28354i
\(473\) 0.317857 0.303754i 0.0146151 0.0139666i
\(474\) −14.8656 25.7479i −0.682798 1.18264i
\(475\) 3.02123 + 9.29838i 0.138623 + 0.426639i
\(476\) 0 0
\(477\) 3.32028 2.41233i 0.152025 0.110453i
\(478\) −11.8418 + 2.51704i −0.541629 + 0.115127i
\(479\) 14.1882 + 15.7576i 0.648277 + 0.719985i 0.974269 0.225388i \(-0.0723649\pi\)
−0.325992 + 0.945373i \(0.605698\pi\)
\(480\) −0.166458 1.58374i −0.00759772 0.0722874i
\(481\) 1.81227 17.2426i 0.0826322 0.786193i
\(482\) −1.97290 6.07197i −0.0898633 0.276571i
\(483\) 0 0
\(484\) −42.9024 + 2.54942i −1.95011 + 0.115883i
\(485\) −11.0615 19.1591i −0.502276 0.869968i
\(486\) −22.3249 4.74530i −1.01268 0.215251i
\(487\) −15.3656 + 6.84121i −0.696283 + 0.310005i −0.724185 0.689606i \(-0.757784\pi\)
0.0279025 + 0.999611i \(0.491117\pi\)
\(488\) −10.3834 4.62298i −0.470033 0.209272i
\(489\) 7.01897 21.6022i 0.317409 0.976884i
\(490\) 0 0
\(491\) −3.91406 + 2.84373i −0.176639 + 0.128336i −0.672592 0.740014i \(-0.734819\pi\)
0.495953 + 0.868350i \(0.334819\pi\)
\(492\) 0.184204 1.75259i 0.00830457 0.0790127i
\(493\) 26.0501 + 5.53713i 1.17324 + 0.249380i
\(494\) −11.0549 + 19.1477i −0.497385 + 0.861496i
\(495\) −0.932382 3.82468i −0.0419074 0.171906i
\(496\) −33.5719 −1.50742
\(497\) 0 0
\(498\) 2.68055 + 1.94753i 0.120118 + 0.0872709i
\(499\) 27.9395 + 12.4395i 1.25074 + 0.556866i 0.921867 0.387507i \(-0.126664\pi\)
0.328876 + 0.944373i \(0.393330\pi\)
\(500\) 27.6925 + 30.7556i 1.23845 + 1.37543i
\(501\) 19.9051 + 22.1068i 0.889293 + 0.987660i
\(502\) −58.2235 25.9228i −2.59864 1.15699i
\(503\) −22.8472 16.5994i −1.01871 0.740133i −0.0526880 0.998611i \(-0.516779\pi\)
−0.966017 + 0.258478i \(0.916779\pi\)
\(504\) 0 0
\(505\) −15.7029 −0.698768
\(506\) −46.3855 + 28.6487i −2.06209 + 1.27359i
\(507\) −2.07842 + 3.59992i −0.0923057 + 0.159878i
\(508\) 30.6800 + 6.52123i 1.36120 + 0.289333i
\(509\) −0.439087 + 4.17764i −0.0194622 + 0.185170i −0.999934 0.0114893i \(-0.996343\pi\)
0.980472 + 0.196660i \(0.0630094\pi\)
\(510\) −21.0273 + 15.2772i −0.931104 + 0.676486i
\(511\) 0 0
\(512\) 10.8274 33.3234i 0.478509 1.47270i
\(513\) −14.7869 6.58355i −0.652857 0.290671i
\(514\) 66.5028 29.6090i 2.93331 1.30600i
\(515\) −10.1174 2.15053i −0.445827 0.0947635i
\(516\) −0.371411 0.643303i −0.0163505 0.0283198i
\(517\) 19.0147 + 24.6018i 0.836265 + 1.08199i
\(518\) 0 0
\(519\) −9.55323 29.4018i −0.419340 1.29060i
\(520\) −1.93816 + 18.4404i −0.0849940 + 0.808664i
\(521\) −2.15819 20.5339i −0.0945522 0.899604i −0.934266 0.356576i \(-0.883944\pi\)
0.839714 0.543029i \(-0.182722\pi\)
\(522\) 6.89464 + 7.65727i 0.301770 + 0.335150i
\(523\) −22.1395 + 4.70589i −0.968091 + 0.205774i −0.664715 0.747097i \(-0.731447\pi\)
−0.303376 + 0.952871i \(0.598114\pi\)
\(524\) 0.320708 0.233008i 0.0140102 0.0101790i
\(525\) 0 0
\(526\) −2.50632 7.71367i −0.109281 0.336332i
\(527\) −28.8138 49.9069i −1.25515 2.17398i
\(528\) −2.93521 + 16.1520i −0.127739 + 0.702926i
\(529\) −11.3720 + 19.6969i −0.494434 + 0.856385i
\(530\) 8.90795 9.89328i 0.386937 0.429737i
\(531\) 5.30007 + 3.85073i 0.230003 + 0.167107i
\(532\) 0 0
\(533\) 0.308871 0.950608i 0.0133787 0.0411754i
\(534\) 34.2841 7.28730i 1.48362 0.315353i
\(535\) 1.60356 + 15.2568i 0.0693278 + 0.659610i
\(536\) 39.8874 17.7590i 1.72287 0.767072i
\(537\) −4.58877 + 5.09635i −0.198020 + 0.219924i
\(538\) −4.21881 −0.181886
\(539\) 0 0
\(540\) −27.8098 −1.19674
\(541\) 28.5828 31.7444i 1.22887 1.36480i 0.320163 0.947363i \(-0.396262\pi\)
0.908707 0.417435i \(-0.137071\pi\)
\(542\) −5.49744 + 2.44762i −0.236135 + 0.105134i
\(543\) 1.17726 + 11.2009i 0.0505212 + 0.480677i
\(544\) 5.11201 1.08659i 0.219176 0.0465872i
\(545\) −0.344634 + 1.06067i −0.0147625 + 0.0454343i
\(546\) 0 0
\(547\) −35.9873 26.1463i −1.53870 1.11793i −0.951141 0.308756i \(-0.900087\pi\)
−0.587563 0.809178i \(-0.699913\pi\)
\(548\) −11.9322 + 13.2520i −0.509717 + 0.566098i
\(549\) 1.15626 2.00269i 0.0493478 0.0854728i
\(550\) 11.9409 + 24.8109i 0.509161 + 1.05794i
\(551\) 6.43354 + 11.1432i 0.274078 + 0.474717i
\(552\) 13.8938 + 42.7608i 0.591360 + 1.82002i
\(553\) 0 0
\(554\) 10.1376 7.36536i 0.430703 0.312924i
\(555\) 9.63176 2.04729i 0.408845 0.0869028i
\(556\) 10.0008 + 11.1070i 0.424128 + 0.471041i
\(557\) 2.61228 + 24.8542i 0.110686 + 1.05311i 0.899035 + 0.437878i \(0.144270\pi\)
−0.788349 + 0.615229i \(0.789064\pi\)
\(558\) 2.33056 22.1738i 0.0986603 0.938690i
\(559\) −0.130196 0.400702i −0.00550670 0.0169479i
\(560\) 0 0
\(561\) −26.5303 + 9.49941i −1.12011 + 0.401065i
\(562\) −27.4283 47.5072i −1.15699 2.00397i
\(563\) 8.81316 + 1.87330i 0.371431 + 0.0789500i 0.389845 0.920880i \(-0.372529\pi\)
−0.0184146 + 0.999830i \(0.505862\pi\)
\(564\) 47.9921 21.3675i 2.02083 0.899733i
\(565\) −5.22594 2.32674i −0.219857 0.0978866i
\(566\) −6.37460 + 19.6190i −0.267944 + 0.824648i
\(567\) 0 0
\(568\) −0.437275 + 0.317699i −0.0183476 + 0.0133303i
\(569\) −3.04950 + 29.0140i −0.127842 + 1.21633i 0.722977 + 0.690872i \(0.242773\pi\)
−0.850819 + 0.525459i \(0.823893\pi\)
\(570\) −12.2830 2.61083i −0.514478 0.109356i
\(571\) −0.894970 + 1.55013i −0.0374533 + 0.0648711i −0.884144 0.467214i \(-0.845258\pi\)
0.846691 + 0.532085i \(0.178591\pi\)
\(572\) −15.6279 + 38.1056i −0.653437 + 1.59327i
\(573\) 12.6645 0.529065
\(574\) 0 0
\(575\) 18.6906 + 13.5795i 0.779452 + 0.566305i
\(576\) 7.79381 + 3.47003i 0.324742 + 0.144584i
\(577\) 14.4432 + 16.0408i 0.601277 + 0.667785i 0.964551 0.263897i \(-0.0850078\pi\)
−0.363274 + 0.931682i \(0.618341\pi\)
\(578\) −29.4292 32.6845i −1.22409 1.35949i
\(579\) −33.5444 14.9349i −1.39406 0.620675i
\(580\) 17.8850 + 12.9942i 0.742633 + 0.539554i
\(581\) 0 0
\(582\) −61.2694 −2.53970
\(583\) 12.2803 7.58458i 0.508598 0.314121i
\(584\) −1.42537 + 2.46881i −0.0589823 + 0.102160i
\(585\) −3.69007 0.784349i −0.152566 0.0324288i
\(586\) −6.25630 + 59.5247i −0.258445 + 2.45894i
\(587\) 4.46865 3.24666i 0.184441 0.134004i −0.491734 0.870746i \(-0.663637\pi\)
0.676174 + 0.736742i \(0.263637\pi\)
\(588\) 0 0
\(589\) 8.60373 26.4796i 0.354511 1.09107i
\(590\) 19.4135 + 8.64345i 0.799241 + 0.355845i
\(591\) 14.6713 6.53210i 0.603499 0.268695i
\(592\) 18.4149 + 3.91421i 0.756847 + 0.160873i
\(593\) −20.3933 35.3223i −0.837454 1.45051i −0.892017 0.452002i \(-0.850710\pi\)
0.0545633 0.998510i \(-0.482623\pi\)
\(594\) −43.7534 12.7941i −1.79522 0.524948i
\(595\) 0 0
\(596\) −5.88254 18.1046i −0.240958 0.741593i
\(597\) 1.83651 17.4732i 0.0751632 0.715130i
\(598\) 5.46116 + 51.9595i 0.223323 + 2.12478i
\(599\) −17.7419 19.7044i −0.724916 0.805101i 0.262216 0.965009i \(-0.415547\pi\)
−0.987132 + 0.159908i \(0.948880\pi\)
\(600\) 22.2114 4.72117i 0.906775 0.192741i
\(601\) −30.5565 + 22.2006i −1.24643 + 0.905581i −0.998009 0.0630720i \(-0.979910\pi\)
−0.248417 + 0.968653i \(0.579910\pi\)
\(602\) 0 0
\(603\) 2.74513 + 8.44864i 0.111790 + 0.344055i
\(604\) 33.1593 + 57.4336i 1.34923 + 2.33694i
\(605\) −2.26141 13.6590i −0.0919395 0.555318i
\(606\) −21.7445 + 37.6626i −0.883310 + 1.52994i
\(607\) 18.5512 20.6032i 0.752971 0.836259i −0.237870 0.971297i \(-0.576449\pi\)
0.990840 + 0.135038i \(0.0431157\pi\)
\(608\) 2.04277 + 1.48416i 0.0828452 + 0.0601906i
\(609\) 0 0
\(610\) 2.31801 7.13411i 0.0938536 0.288852i
\(611\) 29.1457 6.19511i 1.17911 0.250627i
\(612\) −2.28167 21.7087i −0.0922311 0.877521i
\(613\) 33.0945 14.7346i 1.33667 0.595126i 0.391045 0.920372i \(-0.372114\pi\)
0.945630 + 0.325246i \(0.105447\pi\)
\(614\) 7.47102 8.29741i 0.301506 0.334856i
\(615\) 0.567687 0.0228914
\(616\) 0 0
\(617\) 41.1920 1.65833 0.829163 0.559007i \(-0.188817\pi\)
0.829163 + 0.559007i \(0.188817\pi\)
\(618\) −19.1680 + 21.2882i −0.771051 + 0.856338i
\(619\) 32.6497 14.5366i 1.31230 0.584274i 0.373148 0.927772i \(-0.378278\pi\)
0.939154 + 0.343497i \(0.111612\pi\)
\(620\) −5.00022 47.5739i −0.200814 1.91062i
\(621\) −37.4124 + 7.95225i −1.50131 + 0.319113i
\(622\) −1.66037 + 5.11010i −0.0665749 + 0.204897i
\(623\) 0 0
\(624\) 12.7274 + 9.24698i 0.509503 + 0.370176i
\(625\) 2.50740 2.78475i 0.100296 0.111390i
\(626\) 11.7868 20.4154i 0.471096 0.815963i
\(627\) −11.9875 6.45453i −0.478736 0.257769i
\(628\) 4.38539 + 7.59571i 0.174996 + 0.303102i
\(629\) 9.98623 + 30.7345i 0.398177 + 1.22546i
\(630\) 0 0
\(631\) −2.23700 + 1.62527i −0.0890534 + 0.0647011i −0.631421 0.775440i \(-0.717528\pi\)
0.542368 + 0.840141i \(0.317528\pi\)
\(632\) 38.6703 8.21962i 1.53822 0.326959i
\(633\) 13.6884 + 15.2025i 0.544064 + 0.604244i
\(634\) 1.64000 + 15.6036i 0.0651328 + 0.619697i
\(635\) −1.05616 + 10.0487i −0.0419123 + 0.398769i
\(636\) −7.53581 23.1928i −0.298814 0.919655i
\(637\) 0 0
\(638\) 22.1605 + 28.6720i 0.877344 + 1.13514i
\(639\) −0.0549848 0.0952364i −0.00217516 0.00376749i
\(640\) 24.8969 + 5.29200i 0.984137 + 0.209185i
\(641\) 35.1591 15.6538i 1.38870 0.618290i 0.430032 0.902813i \(-0.358502\pi\)
0.958669 + 0.284524i \(0.0918355\pi\)
\(642\) 38.8132 + 17.2808i 1.53184 + 0.682018i
\(643\) 8.15130 25.0871i 0.321456 0.989339i −0.651559 0.758598i \(-0.725885\pi\)
0.973015 0.230741i \(-0.0741151\pi\)
\(644\) 0 0
\(645\) 0.193592 0.140653i 0.00762267 0.00553819i
\(646\) 4.30777 40.9857i 0.169487 1.61256i
\(647\) −26.7241 5.68037i −1.05063 0.223319i −0.349932 0.936775i \(-0.613795\pi\)
−0.700699 + 0.713457i \(0.747129\pi\)
\(648\) −12.2402 + 21.2006i −0.480839 + 0.832838i
\(649\) 17.5721 + 14.9020i 0.689763 + 0.584954i
\(650\) 26.3865 1.03496
\(651\) 0 0
\(652\) 50.0601 + 36.3708i 1.96051 + 1.42439i
\(653\) −7.73011 3.44166i −0.302502 0.134683i 0.249872 0.968279i \(-0.419611\pi\)
−0.552374 + 0.833596i \(0.686278\pi\)
\(654\) 2.06674 + 2.29535i 0.0808160 + 0.0897553i
\(655\) 0.0854490 + 0.0949008i 0.00333877 + 0.00370808i
\(656\) 0.991523 + 0.441455i 0.0387125 + 0.0172359i
\(657\) −0.469236 0.340920i −0.0183066 0.0133005i
\(658\) 0 0
\(659\) −5.29247 −0.206165 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(660\) −23.3258 1.75373i −0.907956 0.0682638i
\(661\) −9.63501 + 16.6883i −0.374759 + 0.649101i −0.990291 0.139011i \(-0.955608\pi\)
0.615532 + 0.788112i \(0.288941\pi\)
\(662\) 8.60778 + 1.82964i 0.334551 + 0.0711110i
\(663\) −2.82274 + 26.8566i −0.109626 + 1.04302i
\(664\) −3.56439 + 2.58968i −0.138325 + 0.100499i
\(665\) 0 0
\(666\) −3.86364 + 11.8911i −0.149713 + 0.460769i
\(667\) 27.7763 + 12.3668i 1.07550 + 0.478845i
\(668\) −74.0331 + 32.9617i −2.86443 + 1.27533i
\(669\) 4.15809 + 0.883830i 0.160761 + 0.0341708i
\(670\) 14.4079 + 24.9552i 0.556625 + 0.964104i
\(671\) 4.58304 6.71858i 0.176926 0.259368i
\(672\) 0 0
\(673\) −5.86892 18.0627i −0.226230 0.696265i −0.998164 0.0605625i \(-0.980711\pi\)
0.771934 0.635702i \(-0.219289\pi\)
\(674\) −1.62722 + 15.4820i −0.0626783 + 0.596344i
\(675\) 2.01919 + 19.2113i 0.0777187 + 0.739444i
\(676\) −7.57733 8.41548i −0.291436 0.323672i
\(677\) 31.7134 6.74089i 1.21884 0.259073i 0.446795 0.894636i \(-0.352565\pi\)
0.772049 + 0.635563i \(0.219232\pi\)
\(678\) −12.8172 + 9.31222i −0.492240 + 0.357633i
\(679\) 0 0
\(680\) −10.6800 32.8695i −0.409558 1.26049i
\(681\) −5.92044 10.2545i −0.226872 0.392954i
\(682\) 14.0198 77.1490i 0.536847 2.95419i
\(683\) −7.56298 + 13.0995i −0.289389 + 0.501237i −0.973664 0.227987i \(-0.926786\pi\)
0.684275 + 0.729224i \(0.260119\pi\)
\(684\) 7.05674 7.83730i 0.269821 0.299667i
\(685\) −4.64740 3.37654i −0.177568 0.129011i
\(686\) 0 0
\(687\) 5.80944 17.8796i 0.221644 0.682150i
\(688\) 0.447504 0.0951200i 0.0170609 0.00362641i
\(689\) −1.44581 13.7560i −0.0550811 0.524061i
\(690\) −27.1078 + 12.0692i −1.03198 + 0.459466i
\(691\) 21.0179 23.3428i 0.799559 0.888000i −0.196147 0.980575i \(-0.562843\pi\)
0.995706 + 0.0925742i \(0.0295095\pi\)
\(692\) 84.2192 3.20153
\(693\) 0 0
\(694\) 42.4357 1.61084
\(695\) −3.22165 + 3.57800i −0.122204 + 0.135721i
\(696\) 27.3011 12.1552i 1.03484 0.460742i
\(697\) 0.194743 + 1.85286i 0.00737642 + 0.0701819i
\(698\) 51.4098 10.9275i 1.94589 0.413611i
\(699\) 5.68515 17.4971i 0.215032 0.661801i
\(700\) 0 0
\(701\) 12.9966 + 9.44259i 0.490875 + 0.356642i 0.805521 0.592568i \(-0.201886\pi\)
−0.314646 + 0.949209i \(0.601886\pi\)
\(702\) −29.2306 + 32.4639i −1.10324 + 1.22527i
\(703\) −7.80663 + 13.5215i −0.294433 + 0.509972i
\(704\) 26.4180 + 14.2244i 0.995665 + 0.536102i
\(705\) 8.46162 + 14.6560i 0.318683 + 0.551975i
\(706\) 3.30575 + 10.1741i 0.124414 + 0.382906i
\(707\) 0 0
\(708\) 31.4928 22.8809i 1.18357 0.859916i
\(709\) −38.8303 + 8.25363i −1.45830 + 0.309972i −0.867739 0.497020i \(-0.834428\pi\)
−0.590563 + 0.806992i \(0.701094\pi\)
\(710\) −0.238689 0.265091i −0.00895785 0.00994870i
\(711\) 0.840781 + 7.99950i 0.0315318 + 0.300005i
\(712\) −4.87174 + 46.3515i −0.182576 + 1.73710i
\(713\) −20.3306 62.5713i −0.761389 2.34331i
\(714\) 0 0
\(715\) −12.7343 3.72368i −0.476236 0.139258i
\(716\) −9.34111 16.1793i −0.349094 0.604648i
\(717\) −6.98780 1.48530i −0.260964 0.0554696i
\(718\) 23.7170 10.5595i 0.885109 0.394076i
\(719\) 9.00976 + 4.01140i 0.336007 + 0.149600i 0.567803 0.823164i \(-0.307793\pi\)
−0.231796 + 0.972764i \(0.574460\pi\)
\(720\) 1.26587 3.89596i 0.0471763 0.145194i
\(721\) 0 0
\(722\) −21.2510 + 15.4397i −0.790879 + 0.574607i
\(723\) 0.393806 3.74681i 0.0146458 0.139346i
\(724\) −30.0114 6.37911i −1.11536 0.237078i
\(725\) 7.67796 13.2986i 0.285152 0.493898i
\(726\) −35.8919 13.4904i −1.33207 0.500675i
\(727\) 31.5764 1.17111 0.585553 0.810634i \(-0.300878\pi\)
0.585553 + 0.810634i \(0.300878\pi\)
\(728\) 0 0
\(729\) −23.7145 17.2296i −0.878313 0.638132i
\(730\) −1.71875 0.765238i −0.0636139 0.0283227i
\(731\) 0.525482 + 0.583607i 0.0194357 + 0.0215855i
\(732\) −9.19443 10.2114i −0.339836 0.377426i
\(733\) −37.7226 16.7952i −1.39332 0.620345i −0.433547 0.901131i \(-0.642738\pi\)
−0.959770 + 0.280786i \(0.909405\pi\)
\(734\) −20.0889 14.5955i −0.741496 0.538729i
\(735\) 0 0
\(736\) 5.96659 0.219931
\(737\) 7.39953 + 30.3533i 0.272565 + 1.11808i
\(738\) −0.360406 + 0.624242i −0.0132667 + 0.0229787i
\(739\) −34.6358 7.36206i −1.27410 0.270818i −0.479278 0.877663i \(-0.659101\pi\)
−0.794820 + 0.606846i \(0.792435\pi\)
\(740\) −2.80400 + 26.6783i −0.103077 + 0.980714i
\(741\) −10.5552 + 7.66883i −0.387756 + 0.281722i
\(742\) 0 0
\(743\) −1.24351 + 3.82713i −0.0456200 + 0.140404i −0.971272 0.237972i \(-0.923517\pi\)
0.925652 + 0.378376i \(0.123517\pi\)
\(744\) −59.0751 26.3019i −2.16580 0.964275i
\(745\) 5.60218 2.49425i 0.205248 0.0913822i
\(746\) −66.2923 14.0909i −2.42713 0.515903i
\(747\) −0.448201 0.776307i −0.0163988 0.0284036i
\(748\) −2.27790 76.7340i −0.0832882 2.80567i
\(749\) 0 0
\(750\) 11.4098 + 35.1157i 0.416626 + 1.28224i
\(751\) −2.55248 + 24.2852i −0.0931413 + 0.886180i 0.843792 + 0.536671i \(0.180318\pi\)
−0.936933 + 0.349509i \(0.886348\pi\)
\(752\) 3.38206 + 32.1782i 0.123331 + 1.17342i
\(753\) −25.1654 27.9490i −0.917077 1.01852i
\(754\) 33.9676 7.22004i 1.23703 0.262938i
\(755\) −17.2837 + 12.5573i −0.629019 + 0.457009i
\(756\) 0 0
\(757\) −0.407046 1.25276i −0.0147943 0.0455323i 0.943387 0.331695i \(-0.107620\pi\)
−0.958181 + 0.286162i \(0.907620\pi\)
\(758\) 1.39512 + 2.41641i 0.0506729 + 0.0877680i
\(759\) −31.8817 + 4.31077i −1.15723 + 0.156471i
\(760\) 8.34895 14.4608i 0.302848 0.524548i
\(761\) 4.84721 5.38337i 0.175711 0.195147i −0.648856 0.760911i \(-0.724752\pi\)
0.824567 + 0.565764i \(0.191419\pi\)
\(762\) 22.6387 + 16.4480i 0.820115 + 0.595848i
\(763\) 0 0
\(764\) −10.6613 + 32.8122i −0.385714 + 1.18710i
\(765\) 6.87808 1.46198i 0.248677 0.0528580i
\(766\) 5.06874 + 48.2258i 0.183141 + 1.74247i
\(767\) 20.1704 8.98044i 0.728311 0.324265i
\(768\) 29.8051 33.1019i 1.07550 1.19446i
\(769\) −44.3139 −1.59800 −0.798999 0.601332i \(-0.794637\pi\)
−0.798999 + 0.601332i \(0.794637\pi\)
\(770\) 0 0
\(771\) 42.9570 1.54706
\(772\) 66.9335 74.3372i 2.40899 2.67546i
\(773\) −17.4085 + 7.75075i −0.626139 + 0.278775i −0.695177 0.718839i \(-0.744674\pi\)
0.0690374 + 0.997614i \(0.478007\pi\)
\(774\) 0.0317597 + 0.302174i 0.00114158 + 0.0108614i
\(775\) −32.5016 + 6.90843i −1.16749 + 0.248158i
\(776\) 25.1761 77.4839i 0.903768 2.78151i
\(777\) 0 0
\(778\) 5.11232 + 3.71432i 0.183286 + 0.133165i
\(779\) −0.602300 + 0.668922i −0.0215796 + 0.0239666i
\(780\) −11.2081 + 19.4129i −0.401313 + 0.695095i
\(781\) −0.167721 0.348492i −0.00600152 0.0124700i
\(782\) −48.6914 84.3360i −1.74120 3.01585i
\(783\) 7.85604 + 24.1784i 0.280752 + 0.864066i
\(784\) 0 0
\(785\) −2.28581 + 1.66074i −0.0815840 + 0.0592742i
\(786\) 0.345940 0.0735318i 0.0123393 0.00262279i
\(787\) −21.0509 23.3793i −0.750382 0.833384i 0.240140 0.970738i \(-0.422807\pi\)
−0.990522 + 0.137355i \(0.956140\pi\)
\(788\) 4.57317 + 43.5108i 0.162912 + 1.55001i
\(789\) 0.500280 4.75985i 0.0178105 0.169455i
\(790\) 8.06270 + 24.8144i 0.286858 + 0.882858i
\(791\) 0 0
\(792\) 8.16964 11.9764i 0.290295 0.425563i
\(793\) −3.89685 6.74955i −0.138381 0.239683i
\(794\) −20.8549 4.43285i −0.740113 0.157316i
\(795\) 7.17665 3.19525i 0.254529 0.113324i
\(796\) 43.7251 + 19.4677i 1.54980 + 0.690013i
\(797\) 3.87670 11.9313i 0.137320 0.422627i −0.858624 0.512606i \(-0.828680\pi\)
0.995944 + 0.0899793i \(0.0286801\pi\)
\(798\) 0 0
\(799\) −44.9324 + 32.6453i −1.58959 + 1.15491i
\(800\) 0.314987 2.99690i 0.0111365 0.105956i
\(801\) −9.27533 1.97153i −0.327728 0.0696607i
\(802\) 34.4559 59.6794i 1.21668 2.10735i
\(803\) −1.55572 1.31933i −0.0549002 0.0465582i
\(804\) 52.7850 1.86159
\(805\) 0 0
\(806\) −60.7915 44.1676i −2.14129 1.55574i
\(807\) −2.27428 1.01258i −0.0800585 0.0356444i
\(808\) −38.6947 42.9749i −1.36128 1.51185i
\(809\) −3.60008 3.99830i −0.126572 0.140573i 0.676527 0.736417i \(-0.263484\pi\)
−0.803100 + 0.595845i \(0.796817\pi\)
\(810\) −14.7595 6.57137i −0.518597 0.230894i
\(811\) 11.0835 + 8.05262i 0.389194 + 0.282766i 0.765125 0.643882i \(-0.222677\pi\)
−0.375931 + 0.926647i \(0.622677\pi\)
\(812\) 0 0
\(813\) −3.55103 −0.124540
\(814\) −16.6851 + 40.6833i −0.584813 + 1.42595i
\(815\) −9.96663 + 17.2627i −0.349116 + 0.604686i
\(816\) −28.6826 6.09667i −1.00409 0.213426i
\(817\) −0.0396603 + 0.377343i −0.00138754 + 0.0132016i
\(818\) −39.1398 + 28.4367i −1.36849 + 0.994266i
\(819\) 0 0
\(820\) −0.477897 + 1.47082i −0.0166889 + 0.0513631i
\(821\) −8.43308 3.75465i −0.294317 0.131038i 0.254267 0.967134i \(-0.418166\pi\)
−0.548583 + 0.836096i \(0.684833\pi\)
\(822\) −14.5339 + 6.47092i −0.506929 + 0.225699i
\(823\) 12.1708 + 2.58698i 0.424246 + 0.0901763i 0.415087 0.909782i \(-0.363751\pi\)
0.00915927 + 0.999958i \(0.497084\pi\)
\(824\) −19.0457 32.9882i −0.663490 1.14920i
\(825\) 0.482127 + 16.2411i 0.0167855 + 0.565442i
\(826\) 0 0
\(827\) −1.38559 4.26441i −0.0481817 0.148288i 0.924071 0.382221i \(-0.124841\pi\)
−0.972253 + 0.233932i \(0.924841\pi\)
\(828\) 2.60491 24.7840i 0.0905267 0.861304i
\(829\) −3.85475 36.6755i −0.133881 1.27379i −0.830770 0.556615i \(-0.812100\pi\)
0.696889 0.717179i \(-0.254567\pi\)
\(830\) −1.94564 2.16086i −0.0675343 0.0750044i
\(831\) 7.23276 1.53737i 0.250902 0.0533308i
\(832\) 23.2615 16.9005i 0.806447 0.585918i
\(833\) 0 0
\(834\) 4.12050 + 12.6816i 0.142681 + 0.439127i
\(835\) −13.0530 22.6084i −0.451717 0.782397i
\(836\) 26.8145 25.6248i 0.927398 0.886252i
\(837\) 27.5053 47.6405i 0.950721 1.64670i
\(838\) −50.2453 + 55.8031i −1.73570 + 1.92769i
\(839\) 7.41389 + 5.38651i 0.255956 + 0.185963i 0.708362 0.705849i \(-0.249434\pi\)
−0.452406 + 0.891812i \(0.649434\pi\)
\(840\) 0 0
\(841\) −2.71643 + 8.36030i −0.0936699 + 0.288286i
\(842\) −57.5153 + 12.2253i −1.98211 + 0.421310i
\(843\) −3.38367 32.1934i −0.116540 1.10880i
\(844\) −50.9112 + 22.6671i −1.75244 + 0.780235i
\(845\) 2.44096 2.71096i 0.0839715 0.0932598i
\(846\) −21.4880 −0.738774
\(847\) 0 0
\(848\) 15.0195 0.515771
\(849\) −8.14528 + 9.04625i −0.279545 + 0.310466i
\(850\) −44.9308 + 20.0045i −1.54111 + 0.686148i
\(851\) 3.85649 + 36.6921i 0.132199 + 1.25779i
\(852\) −0.639156 + 0.135857i −0.0218971 + 0.00465438i
\(853\) −2.01494 + 6.20135i −0.0689903 + 0.212330i −0.979608 0.200921i \(-0.935607\pi\)
0.910617 + 0.413251i \(0.135607\pi\)
\(854\) 0 0
\(855\) 2.74849 + 1.99690i 0.0939965 + 0.0682924i
\(856\) −37.8027 + 41.9841i −1.29207 + 1.43499i
\(857\) 24.0368 41.6330i 0.821082 1.42216i −0.0837952 0.996483i \(-0.526704\pi\)
0.904877 0.425673i \(-0.139962\pi\)
\(858\) −26.5648 + 25.3862i −0.906909 + 0.866672i
\(859\) −0.158149 0.273922i −0.00539598 0.00934610i 0.863315 0.504666i \(-0.168384\pi\)
−0.868711 + 0.495320i \(0.835051\pi\)
\(860\) 0.201444 + 0.619981i 0.00686918 + 0.0211412i
\(861\) 0 0
\(862\) 38.1459 27.7146i 1.29925 0.943963i
\(863\) −3.54767 + 0.754081i −0.120764 + 0.0256692i −0.267897 0.963447i \(-0.586329\pi\)
0.147133 + 0.989117i \(0.452995\pi\)
\(864\) 3.33821 + 3.70746i 0.113568 + 0.126130i
\(865\) 2.83589 + 26.9817i 0.0964232 + 0.917405i
\(866\) 5.43358 51.6971i 0.184641 1.75674i
\(867\) −8.02000 24.6830i −0.272374 0.838280i
\(868\) 0 0
\(869\) 0.839391 + 28.2760i 0.0284744 + 0.959197i
\(870\) 9.86154 + 17.0807i 0.334337 + 0.579089i
\(871\) 29.2850 + 6.22472i 0.992285 + 0.210917i
\(872\) −3.75204 + 1.67052i −0.127060 + 0.0565708i
\(873\) 15.1430 + 6.74208i 0.512512 + 0.228185i
\(874\) 14.5392 44.7469i 0.491794 1.51359i
\(875\) 0 0
\(876\) −2.78818 + 2.02573i −0.0942039 + 0.0684432i
\(877\) −2.79171 + 26.5613i −0.0942692 + 0.896911i 0.840537 + 0.541754i \(0.182239\pi\)
−0.934806 + 0.355158i \(0.884427\pi\)
\(878\) 75.4367 + 16.0346i 2.54587 + 0.541140i
\(879\) −17.6595 + 30.5871i −0.595639 + 1.03168i
\(880\) 5.46668 13.3294i 0.184282 0.449333i
\(881\) −2.91937 −0.0983560 −0.0491780 0.998790i \(-0.515660\pi\)
−0.0491780 + 0.998790i \(0.515660\pi\)
\(882\) 0 0
\(883\) 36.5331 + 26.5429i 1.22944 + 0.893238i 0.996848 0.0793369i \(-0.0252803\pi\)
0.232589 + 0.972575i \(0.425280\pi\)
\(884\) −67.2062 29.9221i −2.26039 1.00639i
\(885\) 8.39091 + 9.31905i 0.282057 + 0.313256i
\(886\) 2.70957 + 3.00928i 0.0910298 + 0.101099i
\(887\) 21.9478 + 9.77179i 0.736935 + 0.328105i 0.740652 0.671889i \(-0.234517\pi\)
−0.00371735 + 0.999993i \(0.501183\pi\)
\(888\) 29.3373 + 21.3148i 0.984497 + 0.715279i
\(889\) 0 0
\(890\) −30.7592 −1.03105
\(891\) −13.3595 11.3296i −0.447561 0.379555i
\(892\) −5.79032 + 10.0291i −0.193874 + 0.335800i
\(893\) −26.2471 5.57898i −0.878324 0.186694i
\(894\) 1.77526 16.8905i 0.0593735 0.564901i
\(895\) 4.86889 3.53746i 0.162749 0.118244i
\(896\) 0 0
\(897\) −9.52702 + 29.3212i −0.318098 + 0.979005i
\(898\) 38.1581 + 16.9891i 1.27335 + 0.566933i
\(899\) −39.9493 + 17.7866i −1.33238 + 0.593216i
\(900\) −12.3110 2.61678i −0.410367 0.0872261i
\(901\) 12.8908 + 22.3275i 0.429455 + 0.743837i
\(902\) −1.42854 + 2.09419i −0.0475652 + 0.0697289i
\(903\) 0 0
\(904\) −6.50996 20.0356i −0.216518 0.666374i
\(905\) 1.03314 9.82969i 0.0343428 0.326750i
\(906\) 6.18464 + 58.8429i 0.205471 + 1.95492i
\(907\) −10.7241 11.9104i −0.356089 0.395477i 0.538310 0.842747i \(-0.319063\pi\)
−0.894399 + 0.447270i \(0.852396\pi\)
\(908\) 31.5523 6.70665i 1.04710 0.222568i
\(909\) 9.51862 6.91568i 0.315713 0.229379i
\(910\) 0 0
\(911\) −5.06922 15.6014i −0.167951 0.516899i 0.831291 0.555838i \(-0.187602\pi\)
−0.999242 + 0.0389385i \(0.987602\pi\)
\(912\) −7.08366 12.2693i −0.234564 0.406276i
\(913\) −1.36715 2.84069i −0.0452462 0.0940131i
\(914\) 12.4204 21.5127i 0.410830 0.711578i
\(915\) 2.96189 3.28951i 0.0979170 0.108748i
\(916\) 41.4336 + 30.1032i 1.36900 + 0.994639i
\(917\) 0 0
\(918\) 25.1618 77.4401i 0.830464 2.55590i
\(919\) −31.6139 + 6.71973i −1.04284 + 0.221664i −0.697330 0.716750i \(-0.745629\pi\)
−0.345515 + 0.938413i \(0.612296\pi\)
\(920\) −4.12440 39.2410i −0.135977 1.29374i
\(921\) 6.01899 2.67983i 0.198333 0.0883033i
\(922\) −35.9670 + 39.9454i −1.18451 + 1.31553i
\(923\) −0.370623 −0.0121992
\(924\) 0 0
\(925\) 18.6333 0.612659
\(926\) 49.3933 54.8568i 1.62316 1.80271i
\(927\) 7.08000 3.15222i 0.232538 0.103533i
\(928\) −0.414544 3.94412i −0.0136081 0.129472i
\(929\) −8.01622 + 1.70390i −0.263004 + 0.0559032i −0.337526 0.941316i \(-0.609590\pi\)
0.0745223 + 0.997219i \(0.476257\pi\)
\(930\) 13.1881 40.5887i 0.432454 1.33096i
\(931\) 0 0
\(932\) 40.5471 + 29.4592i 1.32817 + 0.964969i
\(933\) −2.12158 + 2.35625i −0.0694573 + 0.0771402i
\(934\) −30.6126 + 53.0226i −1.00168 + 1.73495i
\(935\) 24.5069 3.31363i 0.801463 0.108367i
\(936\) −6.94645 12.0316i −0.227052 0.393265i
\(937\) −10.5490 32.4666i −0.344622 1.06064i −0.961786 0.273803i \(-0.911718\pi\)
0.617164 0.786835i \(-0.288282\pi\)
\(938\) 0 0
\(939\) 11.2541 8.17655i 0.367262 0.266831i
\(940\) −45.0953 + 9.58530i −1.47085 + 0.312638i
\(941\) −0.655327 0.727814i −0.0213630 0.0237261i 0.732369 0.680908i \(-0.238415\pi\)
−0.753732 + 0.657182i \(0.771748\pi\)
\(942\) 0.817931 + 7.78210i 0.0266496 + 0.253554i
\(943\) −0.222331 + 2.11534i −0.00724010 + 0.0688850i
\(944\) 7.40874 + 22.8017i 0.241134 + 0.742134i
\(945\) 0 0
\(946\) 0.0317072 + 1.06810i 0.00103089 + 0.0347269i
\(947\) −0.467800 0.810253i −0.0152014 0.0263297i 0.858325 0.513107i \(-0.171506\pi\)
−0.873526 + 0.486777i \(0.838172\pi\)
\(948\) 46.7501 + 9.93705i 1.51837 + 0.322740i
\(949\) −1.78576 + 0.795073i −0.0579683 + 0.0258092i
\(950\) −21.7079 9.66499i −0.704298 0.313574i
\(951\) −2.86099 + 8.80523i −0.0927740 + 0.285529i
\(952\) 0 0
\(953\) −13.5365 + 9.83486i −0.438491 + 0.318582i −0.785035 0.619451i \(-0.787355\pi\)
0.346544 + 0.938034i \(0.387355\pi\)
\(954\) −1.04265 + 9.92016i −0.0337571 + 0.321177i
\(955\) −10.8712 2.31075i −0.351784 0.0747740i
\(956\) 9.73081 16.8543i 0.314717 0.545106i
\(957\) 5.06464 + 20.7754i 0.163716 + 0.671573i
\(958\) −51.5353 −1.66503
\(959\) 0 0
\(960\) 13.2115 + 9.59870i 0.426399 + 0.309797i
\(961\) 58.1239 + 25.8784i 1.87496 + 0.834788i
\(962\) 28.1959 + 31.3147i 0.909071 + 1.00963i
\(963\) −7.69127 8.54202i −0.247848 0.275263i
\(964\) 9.37607 + 4.17450i 0.301983 + 0.134451i
\(965\) 26.0696 + 18.9407i 0.839210 + 0.609722i
\(966\) 0 0
\(967\) 36.4439 1.17196 0.585978 0.810327i \(-0.300710\pi\)
0.585978 + 0.810327i \(0.300710\pi\)
\(968\) 31.8088 39.8472i 1.02237 1.28074i
\(969\) 12.1594 21.0607i 0.390617 0.676568i
\(970\) 52.5938 + 11.1792i 1.68869 + 0.358941i
\(971\) −3.47471 + 33.0596i −0.111509 + 1.06093i 0.785482 + 0.618885i \(0.212415\pi\)
−0.896991 + 0.442050i \(0.854252\pi\)
\(972\) 29.6832 21.5661i 0.952088 0.691732i
\(973\) 0 0
\(974\) 12.6325 38.8788i 0.404771 1.24576i
\(975\) 14.2245 + 6.33315i 0.455548 + 0.202823i
\(976\) 7.73128 3.44219i 0.247472 0.110182i
\(977\) −22.0735 4.69186i −0.706193 0.150106i −0.159204 0.987246i \(-0.550893\pi\)
−0.546989 + 0.837140i \(0.684226\pi\)
\(978\) 27.6025 + 47.8089i 0.882631 + 1.52876i
\(979\) −32.0088 9.35981i −1.02301 0.299141i
\(980\) 0 0
\(981\) −0.258223 0.794729i −0.00824443 0.0253737i
\(982\) 1.22911 11.6942i 0.0392225 0.373178i
\(983\) −1.57888 15.0220i −0.0503584 0.479128i −0.990416 0.138114i \(-0.955896\pi\)
0.940058 0.341015i \(-0.110771\pi\)
\(984\) 1.39889 + 1.55362i 0.0445948 + 0.0495276i
\(985\) −13.7858 + 2.93026i −0.439251 + 0.0933657i
\(986\) −52.3661 + 38.0462i −1.66768 + 1.21164i
\(987\) 0 0
\(988\) −10.9834 33.8033i −0.349428 1.07543i
\(989\) 0.448287 + 0.776456i 0.0142547 + 0.0246899i
\(990\) 8.42437 + 4.53599i 0.267744 + 0.144163i
\(991\) 27.5767 47.7643i 0.876003 1.51728i 0.0203128 0.999794i \(-0.493534\pi\)
0.855690 0.517488i \(-0.173133\pi\)
\(992\) −5.74211 + 6.37726i −0.182312 + 0.202478i
\(993\) 4.20116 + 3.05232i 0.133320 + 0.0968624i
\(994\) 0 0
\(995\) −4.76461 + 14.6639i −0.151048 + 0.464878i
\(996\) −5.20999 + 1.10742i −0.165085 + 0.0350899i
\(997\) 5.19556 + 49.4325i 0.164545 + 1.56554i 0.695740 + 0.718293i \(0.255076\pi\)
−0.531195 + 0.847249i \(0.678257\pi\)
\(998\) −67.9056 + 30.2335i −2.14951 + 0.957025i
\(999\) −20.6417 + 22.9250i −0.653076 + 0.725314i
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 539.2.q.f.214.1 32
7.2 even 3 inner 539.2.q.f.324.4 32
7.3 odd 6 77.2.f.b.71.1 yes 16
7.4 even 3 539.2.f.e.148.1 16
7.5 odd 6 539.2.q.g.324.4 32
7.6 odd 2 539.2.q.g.214.1 32
11.9 even 5 inner 539.2.q.f.361.4 32
21.17 even 6 693.2.m.i.379.4 16
77.3 odd 30 847.2.a.p.1.1 8
77.9 even 15 inner 539.2.q.f.471.1 32
77.10 even 6 847.2.f.x.148.4 16
77.17 even 30 847.2.f.v.323.1 16
77.20 odd 10 539.2.q.g.361.4 32
77.24 even 30 847.2.f.x.372.4 16
77.25 even 15 5929.2.a.bt.1.1 8
77.31 odd 30 77.2.f.b.64.1 16
77.38 odd 30 847.2.f.w.323.4 16
77.52 even 30 847.2.a.o.1.8 8
77.53 even 15 539.2.f.e.295.1 16
77.59 odd 30 847.2.f.w.729.4 16
77.73 even 30 847.2.f.v.729.1 16
77.74 odd 30 5929.2.a.bs.1.8 8
77.75 odd 30 539.2.q.g.471.1 32
231.80 even 30 7623.2.a.ct.1.8 8
231.185 even 30 693.2.m.i.64.4 16
231.206 odd 30 7623.2.a.cw.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.1 16 77.31 odd 30
77.2.f.b.71.1 yes 16 7.3 odd 6
539.2.f.e.148.1 16 7.4 even 3
539.2.f.e.295.1 16 77.53 even 15
539.2.q.f.214.1 32 1.1 even 1 trivial
539.2.q.f.324.4 32 7.2 even 3 inner
539.2.q.f.361.4 32 11.9 even 5 inner
539.2.q.f.471.1 32 77.9 even 15 inner
539.2.q.g.214.1 32 7.6 odd 2
539.2.q.g.324.4 32 7.5 odd 6
539.2.q.g.361.4 32 77.20 odd 10
539.2.q.g.471.1 32 77.75 odd 30
693.2.m.i.64.4 16 231.185 even 30
693.2.m.i.379.4 16 21.17 even 6
847.2.a.o.1.8 8 77.52 even 30
847.2.a.p.1.1 8 77.3 odd 30
847.2.f.v.323.1 16 77.17 even 30
847.2.f.v.729.1 16 77.73 even 30
847.2.f.w.323.4 16 77.38 odd 30
847.2.f.w.729.4 16 77.59 odd 30
847.2.f.x.148.4 16 77.10 even 6
847.2.f.x.372.4 16 77.24 even 30
5929.2.a.bs.1.8 8 77.74 odd 30
5929.2.a.bt.1.1 8 77.25 even 15
7623.2.a.ct.1.8 8 231.80 even 30
7623.2.a.cw.1.1 8 231.206 odd 30