Properties

Label 672.2.bo.a.125.6
Level $672$
Weight $2$
Character 672.125
Analytic conductor $5.366$
Analytic rank $0$
Dimension $496$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [672,2,Mod(125,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.bo (of order \(8\), degree \(4\), 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: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(496\)
Relative dimension: \(124\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 125.6
Character \(\chi\) \(=\) 672.125
Dual form 672.2.bo.a.629.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39741 + 0.217363i) q^{2} +(0.679260 + 1.59330i) q^{3} +(1.90551 - 0.607491i) q^{4} +(-0.491250 - 1.18598i) q^{5} +(-1.29553 - 2.07885i) q^{6} +(-2.64335 - 0.112587i) q^{7} +(-2.53073 + 1.26310i) q^{8} +(-2.07721 + 2.16453i) q^{9} +O(q^{10})\) \(q+(-1.39741 + 0.217363i) q^{2} +(0.679260 + 1.59330i) q^{3} +(1.90551 - 0.607491i) q^{4} +(-0.491250 - 1.18598i) q^{5} +(-1.29553 - 2.07885i) q^{6} +(-2.64335 - 0.112587i) q^{7} +(-2.53073 + 1.26310i) q^{8} +(-2.07721 + 2.16453i) q^{9} +(0.944266 + 1.55052i) q^{10} +(-1.77535 - 4.28607i) q^{11} +(2.26225 + 2.62340i) q^{12} +(0.783054 + 0.324352i) q^{13} +(3.71832 - 0.417238i) q^{14} +(1.55594 - 1.58830i) q^{15} +(3.26191 - 2.31516i) q^{16} -1.90168i q^{17} +(2.43223 - 3.47624i) q^{18} +(7.09674 + 2.93957i) q^{19} +(-1.65655 - 1.96147i) q^{20} +(-1.61614 - 4.28813i) q^{21} +(3.41252 + 5.60350i) q^{22} +(5.55180 - 5.55180i) q^{23} +(-3.73152 - 3.17423i) q^{24} +(2.37031 - 2.37031i) q^{25} +(-1.16475 - 0.283045i) q^{26} +(-4.85971 - 1.83935i) q^{27} +(-5.10532 + 1.39128i) q^{28} +(1.32060 - 3.18821i) q^{29} +(-1.82905 + 2.55771i) q^{30} +3.29238i q^{31} +(-4.05499 + 3.94424i) q^{32} +(5.62307 - 5.74002i) q^{33} +(0.413355 + 2.65742i) q^{34} +(1.16502 + 3.19028i) q^{35} +(-2.64321 + 5.38641i) q^{36} +(-3.68551 - 8.89762i) q^{37} +(-10.5560 - 2.56521i) q^{38} +(0.0151074 + 1.46796i) q^{39} +(2.74123 + 2.38090i) q^{40} +(-2.07087 - 2.07087i) q^{41} +(3.19049 + 5.64099i) q^{42} +(-1.34745 + 0.558131i) q^{43} +(-5.98669 - 7.08863i) q^{44} +(3.58752 + 1.40021i) q^{45} +(-6.55137 + 8.96489i) q^{46} +3.10014i q^{47} +(5.90442 + 3.62461i) q^{48} +(6.97465 + 0.595214i) q^{49} +(-2.79707 + 3.82751i) q^{50} +(3.02994 - 1.29173i) q^{51} +(1.68916 + 0.142356i) q^{52} +(-2.74572 - 6.62876i) q^{53} +(7.19081 + 1.51400i) q^{54} +(-4.21106 + 4.21106i) q^{55} +(6.83182 - 3.05390i) q^{56} +(0.136917 + 13.3040i) q^{57} +(-1.15242 + 4.74228i) q^{58} +(3.16388 + 7.63828i) q^{59} +(1.99998 - 3.97173i) q^{60} +(5.90476 - 14.2553i) q^{61} +(-0.715642 - 4.60080i) q^{62} +(5.73451 - 5.48775i) q^{63} +(4.80915 - 6.39312i) q^{64} -1.08803i q^{65} +(-6.61007 + 9.24340i) q^{66} +(-0.559933 - 0.231932i) q^{67} +(-1.15525 - 3.62366i) q^{68} +(12.6168 + 5.07457i) q^{69} +(-2.32146 - 4.20489i) q^{70} +(-2.74586 - 2.74586i) q^{71} +(2.52284 - 8.10156i) q^{72} +(-6.19930 + 6.19930i) q^{73} +(7.08419 + 11.6325i) q^{74} +(5.38667 + 2.16656i) q^{75} +(15.3086 + 1.29016i) q^{76} +(4.21032 + 11.5295i) q^{77} +(-0.340192 - 2.04806i) q^{78} -7.15778i q^{79} +(-4.34814 - 2.73125i) q^{80} +(-0.370373 - 8.99238i) q^{81} +(3.34398 + 2.44372i) q^{82} +(-4.51977 + 10.9117i) q^{83} +(-5.68457 - 7.18928i) q^{84} +(-2.25535 + 0.934198i) q^{85} +(1.76162 - 1.07282i) q^{86} +(5.97680 - 0.0615097i) q^{87} +(9.90666 + 8.60443i) q^{88} +(8.06313 - 8.06313i) q^{89} +(-5.31759 - 1.17687i) q^{90} +(-2.03337 - 0.945538i) q^{91} +(7.20632 - 13.9516i) q^{92} +(-5.24575 + 2.23638i) q^{93} +(-0.673856 - 4.33216i) q^{94} -9.86067i q^{95} +(-9.03875 - 3.78166i) q^{96} -7.95920i q^{97} +(-9.87582 + 0.684275i) q^{98} +(12.9651 + 5.06029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39741 + 0.217363i −0.988118 + 0.153699i
\(3\) 0.679260 + 1.59330i 0.392171 + 0.919892i
\(4\) 1.90551 0.607491i 0.952753 0.303745i
\(5\) −0.491250 1.18598i −0.219694 0.530387i 0.775154 0.631773i \(-0.217672\pi\)
−0.994847 + 0.101386i \(0.967672\pi\)
\(6\) −1.29553 2.07885i −0.528897 0.848686i
\(7\) −2.64335 0.112587i −0.999094 0.0425538i
\(8\) −2.53073 + 1.26310i −0.894747 + 0.446573i
\(9\) −2.07721 + 2.16453i −0.692404 + 0.721510i
\(10\) 0.944266 + 1.55052i 0.298603 + 0.490318i
\(11\) −1.77535 4.28607i −0.535288 1.29230i −0.927980 0.372629i \(-0.878456\pi\)
0.392693 0.919670i \(-0.371544\pi\)
\(12\) 2.26225 + 2.62340i 0.653055 + 0.757310i
\(13\) 0.783054 + 0.324352i 0.217180 + 0.0899590i 0.488621 0.872496i \(-0.337500\pi\)
−0.271441 + 0.962455i \(0.587500\pi\)
\(14\) 3.71832 0.417238i 0.993763 0.111512i
\(15\) 1.55594 1.58830i 0.401742 0.410097i
\(16\) 3.26191 2.31516i 0.815477 0.578789i
\(17\) 1.90168i 0.461224i −0.973046 0.230612i \(-0.925927\pi\)
0.973046 0.230612i \(-0.0740729\pi\)
\(18\) 2.43223 3.47624i 0.573282 0.819358i
\(19\) 7.09674 + 2.93957i 1.62810 + 0.674383i 0.995018 0.0996979i \(-0.0317876\pi\)
0.633087 + 0.774081i \(0.281788\pi\)
\(20\) −1.65655 1.96147i −0.370416 0.438597i
\(21\) −1.61614 4.28813i −0.352671 0.935748i
\(22\) 3.41252 + 5.60350i 0.727552 + 1.19467i
\(23\) 5.55180 5.55180i 1.15763 1.15763i 0.172645 0.984984i \(-0.444769\pi\)
0.984984 0.172645i \(-0.0552314\pi\)
\(24\) −3.73152 3.17423i −0.761693 0.647938i
\(25\) 2.37031 2.37031i 0.474062 0.474062i
\(26\) −1.16475 0.283045i −0.228426 0.0555097i
\(27\) −4.85971 1.83935i −0.935252 0.353983i
\(28\) −5.10532 + 1.39128i −0.964816 + 0.262927i
\(29\) 1.32060 3.18821i 0.245229 0.592035i −0.752558 0.658526i \(-0.771180\pi\)
0.997787 + 0.0664910i \(0.0211804\pi\)
\(30\) −1.82905 + 2.55771i −0.333937 + 0.466971i
\(31\) 3.29238i 0.591329i 0.955292 + 0.295664i \(0.0955410\pi\)
−0.955292 + 0.295664i \(0.904459\pi\)
\(32\) −4.05499 + 3.94424i −0.716828 + 0.697250i
\(33\) 5.62307 5.74002i 0.978852 0.999209i
\(34\) 0.413355 + 2.65742i 0.0708897 + 0.455744i
\(35\) 1.16502 + 3.19028i 0.196925 + 0.539255i
\(36\) −2.64321 + 5.38641i −0.440535 + 0.897735i
\(37\) −3.68551 8.89762i −0.605895 1.46276i −0.867427 0.497565i \(-0.834228\pi\)
0.261532 0.965195i \(-0.415772\pi\)
\(38\) −10.5560 2.56521i −1.71241 0.416132i
\(39\) 0.0151074 + 1.46796i 0.00241912 + 0.235062i
\(40\) 2.74123 + 2.38090i 0.433427 + 0.376453i
\(41\) −2.07087 2.07087i −0.323415 0.323415i 0.526661 0.850076i \(-0.323444\pi\)
−0.850076 + 0.526661i \(0.823444\pi\)
\(42\) 3.19049 + 5.64099i 0.492303 + 0.870424i
\(43\) −1.34745 + 0.558131i −0.205484 + 0.0851142i −0.483052 0.875592i \(-0.660472\pi\)
0.277568 + 0.960706i \(0.410472\pi\)
\(44\) −5.98669 7.08863i −0.902527 1.06865i
\(45\) 3.58752 + 1.40021i 0.534796 + 0.208731i
\(46\) −6.55137 + 8.96489i −0.965948 + 1.32180i
\(47\) 3.10014i 0.452202i 0.974104 + 0.226101i \(0.0725979\pi\)
−0.974104 + 0.226101i \(0.927402\pi\)
\(48\) 5.90442 + 3.62461i 0.852230 + 0.523167i
\(49\) 6.97465 + 0.595214i 0.996378 + 0.0850305i
\(50\) −2.79707 + 3.82751i −0.395566 + 0.541291i
\(51\) 3.02994 1.29173i 0.424277 0.180879i
\(52\) 1.68916 + 0.142356i 0.234244 + 0.0197412i
\(53\) −2.74572 6.62876i −0.377154 0.910530i −0.992497 0.122270i \(-0.960983\pi\)
0.615343 0.788259i \(-0.289017\pi\)
\(54\) 7.19081 + 1.51400i 0.978546 + 0.206029i
\(55\) −4.21106 + 4.21106i −0.567819 + 0.567819i
\(56\) 6.83182 3.05390i 0.912940 0.408094i
\(57\) 0.136917 + 13.3040i 0.0181351 + 1.76215i
\(58\) −1.15242 + 4.74228i −0.151320 + 0.622692i
\(59\) 3.16388 + 7.63828i 0.411902 + 0.994420i 0.984627 + 0.174672i \(0.0558865\pi\)
−0.572724 + 0.819748i \(0.694114\pi\)
\(60\) 1.99998 3.97173i 0.258196 0.512748i
\(61\) 5.90476 14.2553i 0.756027 1.82521i 0.234119 0.972208i \(-0.424779\pi\)
0.521907 0.853002i \(-0.325221\pi\)
\(62\) −0.715642 4.60080i −0.0908866 0.584302i
\(63\) 5.73451 5.48775i 0.722480 0.691392i
\(64\) 4.80915 6.39312i 0.601144 0.799141i
\(65\) 1.08803i 0.134953i
\(66\) −6.61007 + 9.24340i −0.813643 + 1.13778i
\(67\) −0.559933 0.231932i −0.0684068 0.0283350i 0.348218 0.937414i \(-0.386787\pi\)
−0.416624 + 0.909079i \(0.636787\pi\)
\(68\) −1.15525 3.62366i −0.140095 0.439433i
\(69\) 12.6168 + 5.07457i 1.51888 + 0.610906i
\(70\) −2.32146 4.20489i −0.277468 0.502581i
\(71\) −2.74586 2.74586i −0.325874 0.325874i 0.525141 0.851015i \(-0.324012\pi\)
−0.851015 + 0.525141i \(0.824012\pi\)
\(72\) 2.52284 8.10156i 0.297320 0.954778i
\(73\) −6.19930 + 6.19930i −0.725573 + 0.725573i −0.969735 0.244161i \(-0.921487\pi\)
0.244161 + 0.969735i \(0.421487\pi\)
\(74\) 7.08419 + 11.6325i 0.823520 + 1.35225i
\(75\) 5.38667 + 2.16656i 0.621999 + 0.250173i
\(76\) 15.3086 + 1.29016i 1.75602 + 0.147991i
\(77\) 4.21032 + 11.5295i 0.479811 + 1.31391i
\(78\) −0.340192 2.04806i −0.0385191 0.231897i
\(79\) 7.15778i 0.805313i −0.915351 0.402657i \(-0.868087\pi\)
0.915351 0.402657i \(-0.131913\pi\)
\(80\) −4.34814 2.73125i −0.486137 0.305363i
\(81\) −0.370373 8.99238i −0.0411526 0.999153i
\(82\) 3.34398 + 2.44372i 0.369280 + 0.269863i
\(83\) −4.51977 + 10.9117i −0.496110 + 1.19771i 0.455453 + 0.890260i \(0.349477\pi\)
−0.951563 + 0.307455i \(0.900523\pi\)
\(84\) −5.68457 7.18928i −0.620237 0.784414i
\(85\) −2.25535 + 0.934198i −0.244627 + 0.101328i
\(86\) 1.76162 1.07282i 0.189960 0.115686i
\(87\) 5.97680 0.0615097i 0.640780 0.00659453i
\(88\) 9.90666 + 8.60443i 1.05605 + 0.917235i
\(89\) 8.06313 8.06313i 0.854690 0.854690i −0.136016 0.990707i \(-0.543430\pi\)
0.990707 + 0.136016i \(0.0434300\pi\)
\(90\) −5.31759 1.17687i −0.560523 0.124053i
\(91\) −2.03337 0.945538i −0.213155 0.0991193i
\(92\) 7.20632 13.9516i 0.751310 1.45456i
\(93\) −5.24575 + 2.23638i −0.543959 + 0.231902i
\(94\) −0.673856 4.33216i −0.0695030 0.446829i
\(95\) 9.86067i 1.01168i
\(96\) −9.03875 3.78166i −0.922514 0.385964i
\(97\) 7.95920i 0.808134i −0.914729 0.404067i \(-0.867596\pi\)
0.914729 0.404067i \(-0.132404\pi\)
\(98\) −9.87582 + 0.684275i −0.997608 + 0.0691222i
\(99\) 12.9651 + 5.06029i 1.30304 + 0.508578i
\(100\) 3.07670 5.95658i 0.307670 0.595658i
\(101\) −1.75253 4.23099i −0.174383 0.420999i 0.812388 0.583117i \(-0.198167\pi\)
−0.986771 + 0.162119i \(0.948167\pi\)
\(102\) −3.95330 + 2.46368i −0.391435 + 0.243940i
\(103\) −7.27569 7.27569i −0.716895 0.716895i 0.251073 0.967968i \(-0.419217\pi\)
−0.967968 + 0.251073i \(0.919217\pi\)
\(104\) −2.39138 + 0.168231i −0.234495 + 0.0164964i
\(105\) −4.29172 + 4.02326i −0.418829 + 0.392630i
\(106\) 5.27774 + 8.66627i 0.512620 + 0.841742i
\(107\) 5.28270 + 12.7536i 0.510697 + 1.23293i 0.943479 + 0.331434i \(0.107532\pi\)
−0.432781 + 0.901499i \(0.642468\pi\)
\(108\) −10.3776 0.552657i −0.998585 0.0531795i
\(109\) −1.81003 + 4.36979i −0.173369 + 0.418550i −0.986550 0.163461i \(-0.947734\pi\)
0.813181 + 0.582012i \(0.197734\pi\)
\(110\) 4.96925 6.79991i 0.473799 0.648346i
\(111\) 11.6732 11.9159i 1.10797 1.13101i
\(112\) −8.88304 + 5.75253i −0.839368 + 0.543563i
\(113\) −12.5662 −1.18213 −0.591063 0.806625i \(-0.701292\pi\)
−0.591063 + 0.806625i \(0.701292\pi\)
\(114\) −3.08312 18.5613i −0.288761 1.73843i
\(115\) −9.31164 3.85701i −0.868315 0.359668i
\(116\) 0.579602 6.87740i 0.0538147 0.638550i
\(117\) −2.32864 + 1.02120i −0.215283 + 0.0944096i
\(118\) −6.08152 9.98610i −0.559849 0.919295i
\(119\) −0.214104 + 5.02681i −0.0196268 + 0.460807i
\(120\) −1.93148 + 5.98485i −0.176319 + 0.546340i
\(121\) −7.44036 + 7.44036i −0.676396 + 0.676396i
\(122\) −5.15278 + 21.2040i −0.466510 + 1.91972i
\(123\) 1.89286 4.70617i 0.170673 0.424341i
\(124\) 2.00009 + 6.27365i 0.179613 + 0.563390i
\(125\) −9.90546 4.10298i −0.885972 0.366981i
\(126\) −6.82062 + 8.91511i −0.607629 + 0.794221i
\(127\) −5.03806 −0.447056 −0.223528 0.974698i \(-0.571757\pi\)
−0.223528 + 0.974698i \(0.571757\pi\)
\(128\) −5.33073 + 9.97915i −0.471174 + 0.882040i
\(129\) −1.80454 1.76777i −0.158881 0.155644i
\(130\) 0.236497 + 1.52042i 0.0207421 + 0.133349i
\(131\) 17.1820 + 7.11704i 1.50120 + 0.621818i 0.973720 0.227748i \(-0.0731361\pi\)
0.527482 + 0.849566i \(0.323136\pi\)
\(132\) 7.22780 14.3536i 0.629099 1.24932i
\(133\) −18.4283 8.56932i −1.59793 0.743054i
\(134\) 0.832870 + 0.202395i 0.0719490 + 0.0174843i
\(135\) 0.205900 + 6.66711i 0.0177211 + 0.573813i
\(136\) 2.40201 + 4.81262i 0.205971 + 0.412679i
\(137\) −0.943247 + 0.943247i −0.0805870 + 0.0805870i −0.746251 0.665664i \(-0.768148\pi\)
0.665664 + 0.746251i \(0.268148\pi\)
\(138\) −18.7338 4.34882i −1.59473 0.370196i
\(139\) 2.05898 + 4.97081i 0.174640 + 0.421619i 0.986827 0.161779i \(-0.0517231\pi\)
−0.812187 + 0.583397i \(0.801723\pi\)
\(140\) 4.15802 + 5.37136i 0.351417 + 0.453962i
\(141\) −4.93945 + 2.10580i −0.415977 + 0.177340i
\(142\) 4.43394 + 3.24024i 0.372088 + 0.271915i
\(143\) 3.93206i 0.328816i
\(144\) −1.76446 + 11.8696i −0.147038 + 0.989131i
\(145\) −4.42990 −0.367883
\(146\) 7.31546 10.0105i 0.605432 0.828472i
\(147\) 3.78924 + 11.5170i 0.312531 + 0.949907i
\(148\) −12.4280 14.7156i −1.02157 1.20961i
\(149\) 4.62948 + 11.1765i 0.379262 + 0.915618i 0.992105 + 0.125414i \(0.0400258\pi\)
−0.612843 + 0.790205i \(0.709974\pi\)
\(150\) −7.99831 1.85671i −0.653059 0.151599i
\(151\) −3.50043 3.50043i −0.284861 0.284861i 0.550183 0.835044i \(-0.314558\pi\)
−0.835044 + 0.550183i \(0.814558\pi\)
\(152\) −21.6729 + 1.52466i −1.75790 + 0.123666i
\(153\) 4.11623 + 3.95019i 0.332778 + 0.319354i
\(154\) −8.38963 15.1962i −0.676055 1.22455i
\(155\) 3.90470 1.61738i 0.313633 0.129911i
\(156\) 0.920559 + 2.78803i 0.0737037 + 0.223221i
\(157\) −0.602088 + 1.45357i −0.0480519 + 0.116008i −0.946083 0.323925i \(-0.894998\pi\)
0.898031 + 0.439932i \(0.144998\pi\)
\(158\) 1.55584 + 10.0024i 0.123776 + 0.795744i
\(159\) 8.69654 8.87740i 0.689681 0.704024i
\(160\) 6.66981 + 2.87154i 0.527295 + 0.227015i
\(161\) −15.3004 + 14.0503i −1.20584 + 1.10732i
\(162\) 2.47217 + 12.4855i 0.194232 + 0.980956i
\(163\) 17.1307 + 7.09575i 1.34178 + 0.555782i 0.933991 0.357295i \(-0.116301\pi\)
0.407786 + 0.913078i \(0.366301\pi\)
\(164\) −5.20408 2.68802i −0.406370 0.209899i
\(165\) −9.56989 3.84908i −0.745015 0.299651i
\(166\) 3.94417 16.2305i 0.306127 1.25973i
\(167\) 3.54510 3.54510i 0.274328 0.274328i −0.556512 0.830840i \(-0.687861\pi\)
0.830840 + 0.556512i \(0.187861\pi\)
\(168\) 9.50635 + 8.81075i 0.733431 + 0.679764i
\(169\) −8.68442 8.68442i −0.668032 0.668032i
\(170\) 2.94859 1.79569i 0.226147 0.137723i
\(171\) −21.1042 + 9.25500i −1.61388 + 0.707748i
\(172\) −2.22851 + 1.88208i −0.169922 + 0.143508i
\(173\) −2.94986 + 7.12159i −0.224273 + 0.541444i −0.995462 0.0951631i \(-0.969663\pi\)
0.771188 + 0.636607i \(0.219663\pi\)
\(174\) −8.33866 + 1.38509i −0.632152 + 0.105003i
\(175\) −6.53243 + 5.99870i −0.493805 + 0.453459i
\(176\) −15.7139 9.87056i −1.18448 0.744022i
\(177\) −10.0210 + 10.2294i −0.753223 + 0.768888i
\(178\) −9.51487 + 13.0201i −0.713169 + 0.975900i
\(179\) −1.69333 0.701401i −0.126566 0.0524252i 0.318502 0.947922i \(-0.396820\pi\)
−0.445067 + 0.895497i \(0.646820\pi\)
\(180\) 7.68666 + 0.488726i 0.572930 + 0.0364275i
\(181\) 8.08486 + 19.5186i 0.600943 + 1.45080i 0.872612 + 0.488414i \(0.162424\pi\)
−0.271669 + 0.962391i \(0.587576\pi\)
\(182\) 3.04698 + 0.879323i 0.225857 + 0.0651798i
\(183\) 26.7239 0.275027i 1.97549 0.0203306i
\(184\) −7.03760 + 21.0626i −0.518819 + 1.55275i
\(185\) −8.74191 + 8.74191i −0.642718 + 0.642718i
\(186\) 6.84435 4.26537i 0.501852 0.312752i
\(187\) −8.15072 + 3.37614i −0.596040 + 0.246888i
\(188\) 1.88331 + 5.90733i 0.137354 + 0.430837i
\(189\) 12.6389 + 5.40919i 0.919342 + 0.393460i
\(190\) 2.14335 + 13.7794i 0.155495 + 0.999662i
\(191\) 5.77863i 0.418127i −0.977902 0.209063i \(-0.932958\pi\)
0.977902 0.209063i \(-0.0670415\pi\)
\(192\) 13.4528 + 3.31984i 0.970875 + 0.239589i
\(193\) −1.27730 −0.0919422 −0.0459711 0.998943i \(-0.514638\pi\)
−0.0459711 + 0.998943i \(0.514638\pi\)
\(194\) 1.73004 + 11.1223i 0.124209 + 0.798532i
\(195\) 1.73355 0.739052i 0.124142 0.0529246i
\(196\) 13.6518 3.10285i 0.975130 0.221632i
\(197\) 13.0945 5.42391i 0.932942 0.386437i 0.136148 0.990688i \(-0.456528\pi\)
0.796794 + 0.604251i \(0.206528\pi\)
\(198\) −19.2175 4.25316i −1.36573 0.302259i
\(199\) −16.8514 16.8514i −1.19456 1.19456i −0.975772 0.218792i \(-0.929788\pi\)
−0.218792 0.975772i \(-0.570212\pi\)
\(200\) −3.00466 + 8.99254i −0.212462 + 0.635868i
\(201\) −0.0108027 1.04968i −0.000761966 0.0740390i
\(202\) 3.36866 + 5.53148i 0.237018 + 0.389194i
\(203\) −3.84976 + 8.27888i −0.270200 + 0.581063i
\(204\) 4.98886 4.30207i 0.349290 0.301205i
\(205\) −1.43870 + 3.47332i −0.100483 + 0.242587i
\(206\) 11.7486 + 8.58565i 0.818563 + 0.598191i
\(207\) 0.484762 + 23.5493i 0.0336933 + 1.63679i
\(208\) 3.30518 0.754886i 0.229173 0.0523420i
\(209\) 35.6359i 2.46499i
\(210\) 5.12278 6.55500i 0.353506 0.452338i
\(211\) 3.67199 8.86497i 0.252790 0.610290i −0.745637 0.666352i \(-0.767855\pi\)
0.998427 + 0.0560627i \(0.0178547\pi\)
\(212\) −9.25890 10.9631i −0.635904 0.752951i
\(213\) 2.50983 6.24013i 0.171971 0.427567i
\(214\) −10.1542 16.6737i −0.694130 1.13979i
\(215\) 1.32387 + 1.32387i 0.0902870 + 0.0902870i
\(216\) 14.6219 1.48342i 0.994893 0.100934i
\(217\) 0.370678 8.70292i 0.0251633 0.590793i
\(218\) 1.57952 6.49982i 0.106978 0.440224i
\(219\) −14.0883 5.66641i −0.951998 0.382901i
\(220\) −5.46602 + 10.5824i −0.368519 + 0.713464i
\(221\) 0.616812 1.48912i 0.0414913 0.100169i
\(222\) −13.7221 + 19.1887i −0.920967 + 1.28786i
\(223\) 12.6315i 0.845868i 0.906160 + 0.422934i \(0.139000\pi\)
−0.906160 + 0.422934i \(0.861000\pi\)
\(224\) 11.1629 9.96949i 0.745850 0.666114i
\(225\) 0.206967 + 10.0542i 0.0137978 + 0.670282i
\(226\) 17.5601 2.73142i 1.16808 0.181692i
\(227\) −22.2132 9.20100i −1.47434 0.610692i −0.506496 0.862242i \(-0.669060\pi\)
−0.967844 + 0.251550i \(0.919060\pi\)
\(228\) 8.34294 + 25.2676i 0.552525 + 1.67339i
\(229\) 4.16120 1.72363i 0.274980 0.113900i −0.240932 0.970542i \(-0.577453\pi\)
0.515912 + 0.856642i \(0.327453\pi\)
\(230\) 13.8506 + 3.36581i 0.913278 + 0.221935i
\(231\) −15.5100 + 14.5398i −1.02049 + 0.956650i
\(232\) 0.684952 + 9.73652i 0.0449693 + 0.639234i
\(233\) 13.3240 13.3240i 0.872885 0.872885i −0.119901 0.992786i \(-0.538258\pi\)
0.992786 + 0.119901i \(0.0382576\pi\)
\(234\) 3.03209 1.93319i 0.198214 0.126377i
\(235\) 3.67671 1.52294i 0.239842 0.0993458i
\(236\) 10.6690 + 12.6328i 0.694492 + 0.822323i
\(237\) 11.4045 4.86199i 0.740802 0.315820i
\(238\) −0.793452 7.07104i −0.0514319 0.458348i
\(239\) −23.8830 −1.54486 −0.772430 0.635099i \(-0.780959\pi\)
−0.772430 + 0.635099i \(0.780959\pi\)
\(240\) 1.39818 8.78312i 0.0902519 0.566948i
\(241\) −7.77549 −0.500863 −0.250432 0.968134i \(-0.580573\pi\)
−0.250432 + 0.968134i \(0.580573\pi\)
\(242\) 8.77996 12.0145i 0.564397 0.772320i
\(243\) 14.0760 6.69827i 0.902974 0.429694i
\(244\) 2.59156 30.7507i 0.165908 1.96861i
\(245\) −2.72038 8.56420i −0.173799 0.547147i
\(246\) −1.62215 + 6.98788i −0.103424 + 0.445531i
\(247\) 4.60368 + 4.60368i 0.292925 + 0.292925i
\(248\) −4.15860 8.33211i −0.264072 0.529089i
\(249\) −20.4557 + 0.210518i −1.29633 + 0.0133411i
\(250\) 14.7338 + 3.58046i 0.931849 + 0.226448i
\(251\) −6.98708 16.8683i −0.441020 1.06472i −0.975591 0.219594i \(-0.929527\pi\)
0.534571 0.845124i \(-0.320473\pi\)
\(252\) 7.59338 13.9406i 0.478338 0.878176i
\(253\) −33.6517 13.9390i −2.11567 0.876338i
\(254\) 7.04023 1.09509i 0.441743 0.0687120i
\(255\) −3.02043 2.95889i −0.189147 0.185293i
\(256\) 5.28011 15.1037i 0.330007 0.943979i
\(257\) −19.2639 −1.20165 −0.600824 0.799381i \(-0.705161\pi\)
−0.600824 + 0.799381i \(0.705161\pi\)
\(258\) 2.90593 + 2.07806i 0.180915 + 0.129375i
\(259\) 8.74037 + 23.9345i 0.543100 + 1.48722i
\(260\) −0.660966 2.07324i −0.0409913 0.128577i
\(261\) 4.15780 + 9.48105i 0.257361 + 0.586862i
\(262\) −25.5573 6.21067i −1.57894 0.383696i
\(263\) 4.93554 + 4.93554i 0.304339 + 0.304339i 0.842709 0.538370i \(-0.180960\pi\)
−0.538370 + 0.842709i \(0.680960\pi\)
\(264\) −6.98025 + 21.6289i −0.429604 + 1.33117i
\(265\) −6.51275 + 6.51275i −0.400075 + 0.400075i
\(266\) 27.6145 + 7.96922i 1.69315 + 0.488624i
\(267\) 18.3239 + 7.37003i 1.12141 + 0.451039i
\(268\) −1.20785 0.101794i −0.0737814 0.00621803i
\(269\) −2.33774 + 5.64380i −0.142534 + 0.344108i −0.978985 0.203935i \(-0.934627\pi\)
0.836450 + 0.548043i \(0.184627\pi\)
\(270\) −1.73691 9.27192i −0.105705 0.564271i
\(271\) 6.46559 0.392757 0.196378 0.980528i \(-0.437082\pi\)
0.196378 + 0.980528i \(0.437082\pi\)
\(272\) −4.40268 6.20310i −0.266952 0.376118i
\(273\) 0.125339 3.88204i 0.00758584 0.234952i
\(274\) 1.11307 1.52313i 0.0672433 0.0920156i
\(275\) −14.3674 5.95118i −0.866388 0.358870i
\(276\) 27.1241 + 2.00504i 1.63268 + 0.120689i
\(277\) 30.1826 12.5021i 1.81350 0.751176i 0.833399 0.552672i \(-0.186392\pi\)
0.980100 0.198504i \(-0.0636083\pi\)
\(278\) −3.95770 6.49871i −0.237367 0.389767i
\(279\) −7.12645 6.83897i −0.426649 0.409438i
\(280\) −6.97799 6.60218i −0.417015 0.394556i
\(281\) −2.86206 2.86206i −0.170736 0.170736i 0.616567 0.787303i \(-0.288523\pi\)
−0.787303 + 0.616567i \(0.788523\pi\)
\(282\) 6.44471 4.01632i 0.383777 0.239168i
\(283\) 11.3994 4.72179i 0.677625 0.280681i −0.0172088 0.999852i \(-0.505478\pi\)
0.694834 + 0.719171i \(0.255478\pi\)
\(284\) −6.90034 3.56417i −0.409460 0.211495i
\(285\) 15.7110 6.69795i 0.930640 0.396753i
\(286\) 0.854686 + 5.49470i 0.0505386 + 0.324908i
\(287\) 5.24088 + 5.70718i 0.309359 + 0.336884i
\(288\) −0.114336 16.9702i −0.00673732 0.999977i
\(289\) 13.3836 0.787272
\(290\) 6.19038 0.962896i 0.363512 0.0565432i
\(291\) 12.6814 5.40636i 0.743397 0.316927i
\(292\) −8.04679 + 15.5788i −0.470903 + 0.911682i
\(293\) 1.18499 + 2.86082i 0.0692279 + 0.167131i 0.954706 0.297549i \(-0.0961693\pi\)
−0.885479 + 0.464680i \(0.846169\pi\)
\(294\) −7.79850 15.2703i −0.454818 0.890585i
\(295\) 7.50461 7.50461i 0.436935 0.436935i
\(296\) 20.5656 + 17.8623i 1.19535 + 1.03822i
\(297\) 0.744111 + 24.0945i 0.0431777 + 1.39811i
\(298\) −8.89865 14.6119i −0.515485 0.846447i
\(299\) 6.14809 2.54662i 0.355553 0.147275i
\(300\) 11.5805 + 0.856040i 0.668600 + 0.0494235i
\(301\) 3.62462 1.32363i 0.208920 0.0762930i
\(302\) 5.65240 + 4.13067i 0.325259 + 0.237693i
\(303\) 5.55081 5.66625i 0.318886 0.325517i
\(304\) 29.9545 6.84146i 1.71801 0.392385i
\(305\) −19.8073 −1.13416
\(306\) −6.61069 4.62531i −0.377908 0.264411i
\(307\) 22.8449 + 9.46268i 1.30383 + 0.540064i 0.923078 0.384614i \(-0.125665\pi\)
0.380752 + 0.924677i \(0.375665\pi\)
\(308\) 15.0268 + 19.4118i 0.856234 + 1.10609i
\(309\) 6.65028 16.5344i 0.378321 0.940612i
\(310\) −5.10491 + 3.10888i −0.289939 + 0.176572i
\(311\) 15.4859 + 15.4859i 0.878123 + 0.878123i 0.993340 0.115218i \(-0.0367566\pi\)
−0.115218 + 0.993340i \(0.536757\pi\)
\(312\) −1.89241 3.69592i −0.107137 0.209240i
\(313\) −18.3792 18.3792i −1.03885 1.03885i −0.999214 0.0396384i \(-0.987379\pi\)
−0.0396384 0.999214i \(-0.512621\pi\)
\(314\) 0.525411 2.16210i 0.0296507 0.122015i
\(315\) −9.32545 4.10516i −0.525429 0.231300i
\(316\) −4.34829 13.6392i −0.244610 0.767265i
\(317\) −8.39124 + 20.2582i −0.471299 + 1.13782i 0.492291 + 0.870431i \(0.336160\pi\)
−0.963590 + 0.267385i \(0.913840\pi\)
\(318\) −10.2230 + 14.2957i −0.573278 + 0.801662i
\(319\) −16.0094 −0.896354
\(320\) −9.94462 2.56295i −0.555921 0.143273i
\(321\) −16.7319 + 17.0799i −0.933885 + 0.953307i
\(322\) 18.3269 22.9598i 1.02132 1.27950i
\(323\) 5.59011 13.4957i 0.311042 0.750921i
\(324\) −6.16853 16.9100i −0.342696 0.939446i
\(325\) 2.62489 1.08727i 0.145603 0.0603107i
\(326\) −25.4809 6.19210i −1.41126 0.342948i
\(327\) −8.19187 + 0.0843060i −0.453012 + 0.00466213i
\(328\) 7.85651 + 2.62508i 0.433803 + 0.144946i
\(329\) 0.349035 8.19477i 0.0192429 0.451792i
\(330\) 14.2097 + 3.29860i 0.782218 + 0.181582i
\(331\) −3.26758 + 1.35348i −0.179603 + 0.0743938i −0.470673 0.882308i \(-0.655989\pi\)
0.291070 + 0.956702i \(0.405989\pi\)
\(332\) −1.98370 + 23.5380i −0.108870 + 1.29182i
\(333\) 26.9148 + 10.5048i 1.47492 + 0.575662i
\(334\) −4.18338 + 5.72453i −0.228905 + 0.313232i
\(335\) 0.778007i 0.0425071i
\(336\) −15.1994 10.2459i −0.829195 0.558959i
\(337\) 8.46912i 0.461342i 0.973032 + 0.230671i \(0.0740921\pi\)
−0.973032 + 0.230671i \(0.925908\pi\)
\(338\) 14.0234 + 10.2480i 0.762770 + 0.557419i
\(339\) −8.53569 20.0217i −0.463595 1.08743i
\(340\) −3.73007 + 3.15023i −0.202292 + 0.170845i
\(341\) 14.1114 5.84512i 0.764173 0.316531i
\(342\) 27.4795 17.5203i 1.48592 0.947390i
\(343\) −18.3695 2.35861i −0.991857 0.127353i
\(344\) 2.70505 3.11444i 0.145846 0.167919i
\(345\) −0.179649 17.4562i −0.00967195 0.939808i
\(346\) 2.57419 10.5930i 0.138389 0.569481i
\(347\) −23.7703 + 9.84599i −1.27606 + 0.528561i −0.914801 0.403906i \(-0.867652\pi\)
−0.361257 + 0.932466i \(0.617652\pi\)
\(348\) 11.3515 3.74806i 0.608502 0.200917i
\(349\) −6.85875 + 16.5585i −0.367141 + 0.886356i 0.627076 + 0.778958i \(0.284252\pi\)
−0.994216 + 0.107397i \(0.965748\pi\)
\(350\) 7.82458 9.80255i 0.418242 0.523968i
\(351\) −3.20882 3.01656i −0.171274 0.161012i
\(352\) 24.1043 + 10.3776i 1.28476 + 0.553127i
\(353\) 33.6488 1.79095 0.895474 0.445114i \(-0.146837\pi\)
0.895474 + 0.445114i \(0.146837\pi\)
\(354\) 11.7799 16.4728i 0.626096 0.875522i
\(355\) −1.90764 + 4.60544i −0.101247 + 0.244432i
\(356\) 10.4661 20.2626i 0.554701 1.07392i
\(357\) −8.15464 + 3.07337i −0.431590 + 0.162660i
\(358\) 2.51874 + 0.612076i 0.133119 + 0.0323492i
\(359\) 10.1805 + 10.1805i 0.537304 + 0.537304i 0.922736 0.385432i \(-0.125948\pi\)
−0.385432 + 0.922736i \(0.625948\pi\)
\(360\) −10.8476 + 0.987847i −0.571721 + 0.0520641i
\(361\) 28.2877 + 28.2877i 1.48883 + 1.48883i
\(362\) −15.5405 25.5181i −0.816789 1.34120i
\(363\) −16.9087 6.80079i −0.887474 0.356949i
\(364\) −4.44901 0.566474i −0.233191 0.0296913i
\(365\) 10.3977 + 4.30685i 0.544238 + 0.225431i
\(366\) −37.2845 + 6.19312i −1.94889 + 0.323720i
\(367\) 0.466030 0.0243266 0.0121633 0.999926i \(-0.496128\pi\)
0.0121633 + 0.999926i \(0.496128\pi\)
\(368\) 5.25618 30.9627i 0.273998 1.61404i
\(369\) 8.78408 0.180820i 0.457281 0.00941313i
\(370\) 10.3159 14.1162i 0.536296 0.733866i
\(371\) 6.51160 + 17.8313i 0.338066 + 0.925754i
\(372\) −8.63723 + 7.44818i −0.447819 + 0.386170i
\(373\) −18.3001 + 7.58017i −0.947545 + 0.392486i −0.802308 0.596911i \(-0.796395\pi\)
−0.145238 + 0.989397i \(0.546395\pi\)
\(374\) 10.6560 6.48951i 0.551011 0.335565i
\(375\) −0.191105 18.5694i −0.00986862 0.958918i
\(376\) −3.91579 7.84560i −0.201941 0.404606i
\(377\) 2.06820 2.06820i 0.106518 0.106518i
\(378\) −18.8374 4.81163i −0.968892 0.247483i
\(379\) −3.99179 9.63704i −0.205045 0.495022i 0.787585 0.616206i \(-0.211331\pi\)
−0.992630 + 0.121184i \(0.961331\pi\)
\(380\) −5.99027 18.7896i −0.307294 0.963884i
\(381\) −3.42215 8.02714i −0.175322 0.411243i
\(382\) 1.25606 + 8.07511i 0.0642657 + 0.413159i
\(383\) 26.2038 1.33895 0.669475 0.742835i \(-0.266519\pi\)
0.669475 + 0.742835i \(0.266519\pi\)
\(384\) −19.5207 1.71502i −0.996163 0.0875193i
\(385\) 11.6054 10.6572i 0.591468 0.543142i
\(386\) 1.78491 0.277639i 0.0908497 0.0141314i
\(387\) 1.59084 4.07595i 0.0808672 0.207192i
\(388\) −4.83514 15.1663i −0.245467 0.769953i
\(389\) 19.7437 8.17811i 1.00105 0.414647i 0.178865 0.983874i \(-0.442757\pi\)
0.822180 + 0.569227i \(0.192757\pi\)
\(390\) −2.26184 + 1.40957i −0.114533 + 0.0713763i
\(391\) −10.5577 10.5577i −0.533927 0.533927i
\(392\) −18.4027 + 7.30336i −0.929479 + 0.368875i
\(393\) 0.331491 + 32.2105i 0.0167215 + 1.62480i
\(394\) −17.1194 + 10.4257i −0.862462 + 0.525238i
\(395\) −8.48900 + 3.51626i −0.427128 + 0.176922i
\(396\) 27.7792 + 1.76623i 1.39596 + 0.0887563i
\(397\) −5.98962 2.48098i −0.300610 0.124517i 0.227280 0.973829i \(-0.427017\pi\)
−0.527890 + 0.849313i \(0.677017\pi\)
\(398\) 27.2112 + 19.8854i 1.36397 + 0.996766i
\(399\) 1.13593 35.1825i 0.0568677 1.76133i
\(400\) 2.24410 13.2194i 0.112205 0.660968i
\(401\) 0.816177 0.0407579 0.0203790 0.999792i \(-0.493513\pi\)
0.0203790 + 0.999792i \(0.493513\pi\)
\(402\) 0.243259 + 1.46449i 0.0121326 + 0.0730422i
\(403\) −1.06789 + 2.57811i −0.0531953 + 0.128425i
\(404\) −5.90975 6.99752i −0.294021 0.348140i
\(405\) −10.4828 + 4.85676i −0.520897 + 0.241334i
\(406\) 3.58017 12.4058i 0.177681 0.615688i
\(407\) −31.5927 + 31.5927i −1.56599 + 1.56599i
\(408\) −6.03637 + 7.09614i −0.298845 + 0.351311i
\(409\) 21.8709 + 21.8709i 1.08145 + 1.08145i 0.996375 + 0.0850724i \(0.0271122\pi\)
0.0850724 + 0.996375i \(0.472888\pi\)
\(410\) 1.25548 5.16637i 0.0620035 0.255149i
\(411\) −2.14358 0.862166i −0.105735 0.0425275i
\(412\) −18.2838 9.44396i −0.900778 0.465270i
\(413\) −7.50329 20.5469i −0.369213 1.01105i
\(414\) −5.79616 32.8026i −0.284866 1.61216i
\(415\) 15.1614 0.744244
\(416\) −4.45460 + 1.77331i −0.218405 + 0.0869436i
\(417\) −6.52141 + 6.65704i −0.319355 + 0.325997i
\(418\) 7.74593 + 49.7979i 0.378866 + 2.43570i
\(419\) 15.9496 + 6.60654i 0.779189 + 0.322751i 0.736588 0.676342i \(-0.236436\pi\)
0.0426007 + 0.999092i \(0.486436\pi\)
\(420\) −5.73381 + 10.2735i −0.279781 + 0.501297i
\(421\) 1.41426 + 3.41432i 0.0689267 + 0.166404i 0.954589 0.297927i \(-0.0962950\pi\)
−0.885662 + 0.464330i \(0.846295\pi\)
\(422\) −3.20436 + 13.1861i −0.155986 + 0.641892i
\(423\) −6.71034 6.43965i −0.326268 0.313106i
\(424\) 15.3215 + 13.3074i 0.744076 + 0.646267i
\(425\) −4.50756 4.50756i −0.218649 0.218649i
\(426\) −2.15088 + 9.26557i −0.104211 + 0.448918i
\(427\) −17.2133 + 37.0171i −0.833012 + 1.79138i
\(428\) 17.8139 + 21.0928i 0.861066 + 1.01956i
\(429\) 6.26496 2.67089i 0.302475 0.128952i
\(430\) −2.13774 1.56222i −0.103091 0.0753371i
\(431\) −11.9755 −0.576841 −0.288421 0.957504i \(-0.593130\pi\)
−0.288421 + 0.957504i \(0.593130\pi\)
\(432\) −20.1103 + 5.25121i −0.967558 + 0.252649i
\(433\) −2.07294 −0.0996192 −0.0498096 0.998759i \(-0.515861\pi\)
−0.0498096 + 0.998759i \(0.515861\pi\)
\(434\) 1.37371 + 12.2421i 0.0659400 + 0.587640i
\(435\) −3.00905 7.05816i −0.144273 0.338413i
\(436\) −0.794410 + 9.42625i −0.0380453 + 0.451435i
\(437\) 55.7195 23.0798i 2.66543 1.10406i
\(438\) 20.9188 + 4.85603i 0.999537 + 0.232030i
\(439\) 4.89937 4.89937i 0.233834 0.233834i −0.580457 0.814291i \(-0.697126\pi\)
0.814291 + 0.580457i \(0.197126\pi\)
\(440\) 5.33805 15.9760i 0.254482 0.761628i
\(441\) −15.7762 + 13.8604i −0.751247 + 0.660021i
\(442\) −0.538260 + 2.21498i −0.0256024 + 0.105356i
\(443\) −4.47527 + 1.85372i −0.212626 + 0.0880728i −0.486455 0.873706i \(-0.661710\pi\)
0.273828 + 0.961779i \(0.411710\pi\)
\(444\) 15.0045 29.7972i 0.712081 1.41411i
\(445\) −13.5237 5.60171i −0.641087 0.265547i
\(446\) −2.74562 17.6514i −0.130009 0.835817i
\(447\) −14.6630 + 14.9679i −0.693535 + 0.707959i
\(448\) −13.4321 + 16.3578i −0.634606 + 0.772836i
\(449\) 1.12904i 0.0532829i −0.999645 0.0266415i \(-0.991519\pi\)
0.999645 0.0266415i \(-0.00848124\pi\)
\(450\) −2.47464 14.0049i −0.116656 0.660197i
\(451\) −5.19937 + 12.5524i −0.244829 + 0.591068i
\(452\) −23.9449 + 7.63384i −1.12627 + 0.359065i
\(453\) 3.19954 7.95494i 0.150327 0.373756i
\(454\) 33.0409 + 8.02924i 1.55068 + 0.376831i
\(455\) −0.122497 + 2.87604i −0.00574276 + 0.134831i
\(456\) −17.1508 33.4958i −0.803158 1.56858i
\(457\) 16.3309 + 16.3309i 0.763926 + 0.763926i 0.977030 0.213104i \(-0.0683572\pi\)
−0.213104 + 0.977030i \(0.568357\pi\)
\(458\) −5.44025 + 3.31310i −0.254206 + 0.154811i
\(459\) −3.49784 + 9.24160i −0.163265 + 0.431361i
\(460\) −20.0865 1.69282i −0.936538 0.0789280i
\(461\) −7.06664 + 17.0604i −0.329126 + 0.794581i 0.669532 + 0.742784i \(0.266495\pi\)
−0.998658 + 0.0517970i \(0.983505\pi\)
\(462\) 18.5134 23.6894i 0.861323 1.10213i
\(463\) 26.4029i 1.22705i −0.789676 0.613524i \(-0.789752\pi\)
0.789676 0.613524i \(-0.210248\pi\)
\(464\) −3.07352 13.4570i −0.142685 0.624727i
\(465\) 5.22928 + 5.12274i 0.242502 + 0.237561i
\(466\) −15.7230 + 21.5153i −0.728352 + 0.996675i
\(467\) −0.141822 + 0.342388i −0.00656273 + 0.0158438i −0.927127 0.374747i \(-0.877729\pi\)
0.920564 + 0.390591i \(0.127729\pi\)
\(468\) −3.81687 + 3.36052i −0.176435 + 0.155340i
\(469\) 1.45399 + 0.676120i 0.0671390 + 0.0312203i
\(470\) −4.80683 + 2.92736i −0.221723 + 0.135029i
\(471\) −2.72495 + 0.0280436i −0.125559 + 0.00129218i
\(472\) −17.6548 15.3341i −0.812630 0.705810i
\(473\) 4.78438 + 4.78438i 0.219986 + 0.219986i
\(474\) −14.8799 + 9.27311i −0.683458 + 0.425928i
\(475\) 23.7891 9.85379i 1.09152 0.452123i
\(476\) 2.64576 + 9.70868i 0.121268 + 0.444997i
\(477\) 20.0516 + 7.82615i 0.918099 + 0.358335i
\(478\) 33.3743 5.19128i 1.52650 0.237444i
\(479\) 5.11883 0.233885 0.116943 0.993139i \(-0.462691\pi\)
0.116943 + 0.993139i \(0.462691\pi\)
\(480\) −0.0446967 + 12.5775i −0.00204011 + 0.574083i
\(481\) 8.16272i 0.372188i
\(482\) 10.8655 1.69011i 0.494912 0.0769822i
\(483\) −32.7793 14.8344i −1.49151 0.674987i
\(484\) −9.65770 + 18.6976i −0.438986 + 0.849891i
\(485\) −9.43946 + 3.90995i −0.428624 + 0.177542i
\(486\) −18.2139 + 12.4198i −0.826201 + 0.563375i
\(487\) −5.87578 + 5.87578i −0.266257 + 0.266257i −0.827590 0.561333i \(-0.810289\pi\)
0.561333 + 0.827590i \(0.310289\pi\)
\(488\) 3.06261 + 43.5347i 0.138638 + 1.97072i
\(489\) 0.330500 + 32.1142i 0.0149457 + 1.45225i
\(490\) 5.66303 + 11.3764i 0.255830 + 0.513933i
\(491\) 12.6872 + 30.6295i 0.572564 + 1.38229i 0.899365 + 0.437198i \(0.144029\pi\)
−0.326801 + 0.945093i \(0.605971\pi\)
\(492\) 0.747896 10.1175i 0.0337178 0.456133i
\(493\) −6.06294 2.51135i −0.273061 0.113106i
\(494\) −7.43390 5.43256i −0.334467 0.244422i
\(495\) −0.367694 17.8622i −0.0165266 0.802848i
\(496\) 7.62237 + 10.7394i 0.342254 + 0.482215i
\(497\) 6.94914 + 7.56743i 0.311711 + 0.339446i
\(498\) 28.5392 4.74050i 1.27887 0.212427i
\(499\) −4.88317 + 11.7890i −0.218601 + 0.527749i −0.994695 0.102868i \(-0.967198\pi\)
0.776094 + 0.630617i \(0.217198\pi\)
\(500\) −21.3674 1.80077i −0.955581 0.0805329i
\(501\) 8.05646 + 3.24037i 0.359936 + 0.144769i
\(502\) 13.4304 + 22.0532i 0.599426 + 0.984282i
\(503\) 6.94461 + 6.94461i 0.309645 + 0.309645i 0.844772 0.535127i \(-0.179736\pi\)
−0.535127 + 0.844772i \(0.679736\pi\)
\(504\) −7.58089 + 21.1313i −0.337680 + 0.941261i
\(505\) −4.15694 + 4.15694i −0.184981 + 0.184981i
\(506\) 50.0551 + 12.1639i 2.22522 + 0.540749i
\(507\) 7.93791 19.7359i 0.352535 0.876500i
\(508\) −9.60006 + 3.06058i −0.425934 + 0.135791i
\(509\) −13.6808 5.66678i −0.606391 0.251176i 0.0582934 0.998299i \(-0.481434\pi\)
−0.664685 + 0.747124i \(0.731434\pi\)
\(510\) 4.86393 + 3.47826i 0.215378 + 0.154020i
\(511\) 17.0849 15.6890i 0.755792 0.694040i
\(512\) −4.09550 + 22.2537i −0.180997 + 0.983484i
\(513\) −29.0812 27.3388i −1.28397 1.20704i
\(514\) 26.9195 4.18726i 1.18737 0.184692i
\(515\) −5.05465 + 12.2030i −0.222735 + 0.537729i
\(516\) −4.51246 2.27226i −0.198650 0.100031i
\(517\) 13.2874 5.50383i 0.584380 0.242058i
\(518\) −17.4164 31.5465i −0.765231 1.38607i
\(519\) −13.3505 + 0.137396i −0.586024 + 0.00603101i
\(520\) 1.37429 + 2.75350i 0.0602664 + 0.120749i
\(521\) −4.41255 4.41255i −0.193317 0.193317i 0.603811 0.797128i \(-0.293648\pi\)
−0.797128 + 0.603811i \(0.793648\pi\)
\(522\) −7.87098 12.3452i −0.344504 0.540333i
\(523\) −9.66135 23.3246i −0.422461 1.01991i −0.981619 0.190851i \(-0.938875\pi\)
0.559158 0.829061i \(-0.311125\pi\)
\(524\) 37.0640 + 3.12362i 1.61915 + 0.136456i
\(525\) −13.9949 6.33345i −0.610789 0.276414i
\(526\) −7.96978 5.82417i −0.347499 0.253946i
\(527\) 6.26104 0.272735
\(528\) 5.05293 31.7417i 0.219901 1.38138i
\(529\) 38.6449i 1.68021i
\(530\) 7.68535 10.5166i 0.333830 0.456812i
\(531\) −23.1053 9.01803i −1.00269 0.391349i
\(532\) −40.3209 5.13390i −1.74813 0.222583i
\(533\) −0.949911 2.29329i −0.0411452 0.0993333i
\(534\) −27.2080 6.31600i −1.17741 0.273320i
\(535\) 12.5304 12.5304i 0.541735 0.541735i
\(536\) 1.70999 0.120296i 0.0738604 0.00519598i
\(537\) −0.0326693 3.17442i −0.00140978 0.136986i
\(538\) 2.04002 8.39484i 0.0879516 0.361927i
\(539\) −9.83130 30.9505i −0.423464 1.33313i
\(540\) 4.44255 + 12.5791i 0.191177 + 0.541320i
\(541\) 7.42860 + 3.07703i 0.319381 + 0.132292i 0.536614 0.843828i \(-0.319703\pi\)
−0.217233 + 0.976120i \(0.569703\pi\)
\(542\) −9.03508 + 1.40538i −0.388090 + 0.0603663i
\(543\) −25.6072 + 26.1398i −1.09891 + 1.12177i
\(544\) 7.50067 + 7.71129i 0.321589 + 0.330619i
\(545\) 6.07167 0.260082
\(546\) 0.668663 + 5.45204i 0.0286161 + 0.233326i
\(547\) 2.47351 + 1.02456i 0.105760 + 0.0438071i 0.434936 0.900461i \(-0.356771\pi\)
−0.329176 + 0.944268i \(0.606771\pi\)
\(548\) −1.22435 + 2.37038i −0.0523016 + 0.101257i
\(549\) 18.5907 + 42.3924i 0.793431 + 1.80926i
\(550\) 21.3707 + 5.19329i 0.911252 + 0.221443i
\(551\) 18.7439 18.7439i 0.798516 0.798516i
\(552\) −38.3393 + 3.09393i −1.63183 + 0.131686i
\(553\) −0.805871 + 18.9206i −0.0342691 + 0.804584i
\(554\) −39.4600 + 24.0311i −1.67650 + 1.02098i
\(555\) −19.8665 7.99046i −0.843286 0.339176i
\(556\) 6.94311 + 8.22110i 0.294454 + 0.348652i
\(557\) −6.26019 2.59306i −0.265253 0.109871i 0.246093 0.969246i \(-0.420853\pi\)
−0.511346 + 0.859375i \(0.670853\pi\)
\(558\) 11.4451 + 8.00781i 0.484510 + 0.338998i
\(559\) −1.23616 −0.0522838
\(560\) 11.1862 + 7.70919i 0.472703 + 0.325773i
\(561\) −10.9157 10.6933i −0.460859 0.451470i
\(562\) 4.62157 + 3.37736i 0.194949 + 0.142465i
\(563\) −3.37074 + 8.13769i −0.142060 + 0.342963i −0.978856 0.204552i \(-0.934426\pi\)
0.836796 + 0.547515i \(0.184426\pi\)
\(564\) −8.13291 + 7.01329i −0.342457 + 0.295313i
\(565\) 6.17313 + 14.9033i 0.259706 + 0.626985i
\(566\) −14.9033 + 9.07609i −0.626433 + 0.381496i
\(567\) −0.0333947 + 23.8117i −0.00140244 + 0.999999i
\(568\) 10.4173 + 3.48072i 0.437101 + 0.146048i
\(569\) 0.670180 + 0.670180i 0.0280954 + 0.0280954i 0.721015 0.692920i \(-0.243676\pi\)
−0.692920 + 0.721015i \(0.743676\pi\)
\(570\) −20.4988 + 12.7748i −0.858601 + 0.535077i
\(571\) 16.2279 + 39.1777i 0.679118 + 1.63953i 0.765628 + 0.643284i \(0.222429\pi\)
−0.0865100 + 0.996251i \(0.527571\pi\)
\(572\) −2.38869 7.49257i −0.0998762 0.313280i
\(573\) 9.20709 3.92519i 0.384632 0.163977i
\(574\) −8.56419 6.83610i −0.357462 0.285333i
\(575\) 26.3189i 1.09758i
\(576\) 3.84847 + 23.6894i 0.160353 + 0.987060i
\(577\) 10.2989i 0.428750i −0.976751 0.214375i \(-0.931229\pi\)
0.976751 0.214375i \(-0.0687715\pi\)
\(578\) −18.7024 + 2.90911i −0.777917 + 0.121003i
\(579\) −0.867620 2.03513i −0.0360570 0.0845770i
\(580\) −8.44120 + 2.69112i −0.350502 + 0.111743i
\(581\) 13.1759 28.3346i 0.546628 1.17552i
\(582\) −16.5460 + 10.3114i −0.685852 + 0.427420i
\(583\) −23.5367 + 23.5367i −0.974791 + 0.974791i
\(584\) 7.85839 23.5191i 0.325183 0.973226i
\(585\) 2.35506 + 2.26006i 0.0973699 + 0.0934420i
\(586\) −2.27775 3.74016i −0.0940932 0.154505i
\(587\) −3.22485 + 1.33578i −0.133104 + 0.0551333i −0.448241 0.893913i \(-0.647949\pi\)
0.315137 + 0.949046i \(0.397949\pi\)
\(588\) 14.2169 + 19.6438i 0.586295 + 0.810097i
\(589\) −9.67817 + 23.3652i −0.398782 + 0.962745i
\(590\) −8.85579 + 12.1182i −0.364587 + 0.498900i
\(591\) 17.5365 + 17.1792i 0.721353 + 0.706657i
\(592\) −32.6212 20.4907i −1.34072 0.842162i
\(593\) 12.7937i 0.525373i 0.964881 + 0.262686i \(0.0846085\pi\)
−0.964881 + 0.262686i \(0.915392\pi\)
\(594\) −6.27710 33.5082i −0.257552 1.37486i
\(595\) 6.06688 2.21549i 0.248718 0.0908264i
\(596\) 15.6112 + 18.4846i 0.639458 + 0.757159i
\(597\) 15.4029 38.2958i 0.630397 1.56734i
\(598\) −8.03786 + 4.89504i −0.328692 + 0.200173i
\(599\) 9.46156 9.46156i 0.386589 0.386589i −0.486880 0.873469i \(-0.661865\pi\)
0.873469 + 0.486880i \(0.161865\pi\)
\(600\) −16.3688 + 1.32093i −0.668252 + 0.0539269i
\(601\) −26.5750 26.5750i −1.08402 1.08402i −0.996130 0.0878866i \(-0.971989\pi\)
−0.0878866 0.996130i \(-0.528011\pi\)
\(602\) −4.77737 + 2.63752i −0.194711 + 0.107497i
\(603\) 1.66512 0.730220i 0.0678091 0.0297369i
\(604\) −8.79658 4.54362i −0.357928 0.184877i
\(605\) 12.4792 + 5.16905i 0.507352 + 0.210152i
\(606\) −6.52512 + 9.12461i −0.265065 + 0.370662i
\(607\) 25.9850i 1.05470i 0.849649 + 0.527348i \(0.176814\pi\)
−0.849649 + 0.527348i \(0.823186\pi\)
\(608\) −40.3716 + 16.0713i −1.63728 + 0.651778i
\(609\) −15.8057 0.510316i −0.640480 0.0206791i
\(610\) 27.6789 4.30538i 1.12069 0.174320i
\(611\) −1.00554 + 2.42758i −0.0406796 + 0.0982092i
\(612\) 10.2432 + 5.02653i 0.414057 + 0.203186i
\(613\) 14.5692 + 35.1731i 0.588443 + 1.42063i 0.884991 + 0.465609i \(0.154165\pi\)
−0.296548 + 0.955018i \(0.595835\pi\)
\(614\) −33.9806 8.25759i −1.37134 0.333249i
\(615\) −6.51129 + 0.0670104i −0.262561 + 0.00270212i
\(616\) −25.2181 23.8599i −1.01606 0.961343i
\(617\) 24.4432 24.4432i 0.984048 0.984048i −0.0158270 0.999875i \(-0.505038\pi\)
0.999875 + 0.0158270i \(0.00503809\pi\)
\(618\) −5.69918 + 24.5509i −0.229255 + 0.987582i
\(619\) −16.9475 40.9150i −0.681179 1.64451i −0.761836 0.647770i \(-0.775702\pi\)
0.0806567 0.996742i \(-0.474298\pi\)
\(620\) 6.45789 5.45400i 0.259355 0.219038i
\(621\) −37.1918 + 16.7684i −1.49246 + 0.672895i
\(622\) −25.0061 18.2740i −1.00265 0.732722i
\(623\) −22.2215 + 20.4059i −0.890286 + 0.817546i
\(624\) 3.44783 + 4.75338i 0.138024 + 0.190287i
\(625\) 2.99732i 0.119893i
\(626\) 29.6782 + 21.6883i 1.18618 + 0.866838i
\(627\) 56.7787 24.2060i 2.26752 0.966695i
\(628\) −0.264253 + 3.13555i −0.0105448 + 0.125122i
\(629\) −16.9204 + 7.00866i −0.674660 + 0.279454i
\(630\) 13.9238 + 3.70959i 0.554737 + 0.147793i
\(631\) −23.5625 23.5625i −0.938008 0.938008i 0.0601800 0.998188i \(-0.480833\pi\)
−0.998188 + 0.0601800i \(0.980833\pi\)
\(632\) 9.04100 + 18.1144i 0.359632 + 0.720552i
\(633\) 16.6188 0.171031i 0.660538 0.00679787i
\(634\) 7.32260 30.1330i 0.290817 1.19673i
\(635\) 2.47495 + 5.97505i 0.0982152 + 0.237112i
\(636\) 11.1784 22.1990i 0.443252 0.880249i
\(637\) 5.26847 + 2.72832i 0.208744 + 0.108100i
\(638\) 22.3717 3.47985i 0.885703 0.137769i
\(639\) 11.6472 0.239758i 0.460757 0.00948470i
\(640\) 14.4538 + 1.41989i 0.571337 + 0.0561262i
\(641\) 6.47610i 0.255790i 0.991788 + 0.127895i \(0.0408221\pi\)
−0.991788 + 0.127895i \(0.959178\pi\)
\(642\) 19.6688 27.5045i 0.776266 1.08552i
\(643\) 8.28119 19.9926i 0.326578 0.788430i −0.672263 0.740312i \(-0.734678\pi\)
0.998842 0.0481179i \(-0.0153223\pi\)
\(644\) −20.6196 + 36.0678i −0.812527 + 1.42127i
\(645\) −1.21007 + 3.00857i −0.0476464 + 0.118462i
\(646\) −4.87820 + 20.0741i −0.191930 + 0.789806i
\(647\) −21.0983 + 21.0983i −0.829458 + 0.829458i −0.987442 0.157984i \(-0.949501\pi\)
0.157984 + 0.987442i \(0.449501\pi\)
\(648\) 12.2956 + 22.2894i 0.483016 + 0.875611i
\(649\) 27.1212 27.1212i 1.06460 1.06460i
\(650\) −3.43172 + 2.08991i −0.134603 + 0.0819731i
\(651\) 14.1182 5.32094i 0.553334 0.208544i
\(652\) 36.9532 + 3.11428i 1.44720 + 0.121965i
\(653\) 21.3062 + 8.82533i 0.833778 + 0.345362i 0.758397 0.651793i \(-0.225983\pi\)
0.0753805 + 0.997155i \(0.475983\pi\)
\(654\) 11.4291 1.89842i 0.446912 0.0742342i
\(655\) 23.8738i 0.932828i
\(656\) −11.5494 1.96060i −0.450926 0.0765486i
\(657\) −0.541300 26.2958i −0.0211181 1.02590i
\(658\) 1.29350 + 11.5273i 0.0504258 + 0.449381i
\(659\) 16.3666 + 6.77928i 0.637553 + 0.264083i 0.677959 0.735100i \(-0.262865\pi\)
−0.0404052 + 0.999183i \(0.512865\pi\)
\(660\) −20.5738 1.52083i −0.800833 0.0591982i
\(661\) 12.5870 + 30.3878i 0.489579 + 1.18195i 0.954933 + 0.296823i \(0.0959270\pi\)
−0.465354 + 0.885125i \(0.654073\pi\)
\(662\) 4.27196 2.60161i 0.166034 0.101115i
\(663\) 2.79158 0.0287294i 0.108416 0.00111576i
\(664\) −2.34426 33.3235i −0.0909750 1.29320i
\(665\) −1.11018 + 26.0652i −0.0430510 + 1.01077i
\(666\) −39.8943 8.82929i −1.54587 0.342128i
\(667\) −10.3686 25.0319i −0.401473 0.969241i
\(668\) 4.60160 8.90883i 0.178041 0.344693i
\(669\) −20.1258 + 8.58007i −0.778108 + 0.331725i
\(670\) −0.169110 1.08719i −0.00653330 0.0420020i
\(671\) −71.5824 −2.76341
\(672\) 23.4669 + 11.0139i 0.905254 + 0.424871i
\(673\) −35.4030 −1.36469 −0.682343 0.731032i \(-0.739039\pi\)
−0.682343 + 0.731032i \(0.739039\pi\)
\(674\) −1.84087 11.8348i −0.0709078 0.455860i
\(675\) −15.8788 + 7.15919i −0.611177 + 0.275558i
\(676\) −21.8239 11.2725i −0.839382 0.433558i
\(677\) 8.22253 + 19.8509i 0.316017 + 0.762933i 0.999458 + 0.0329271i \(0.0104829\pi\)
−0.683440 + 0.730006i \(0.739517\pi\)
\(678\) 16.2798 + 26.1232i 0.625223 + 1.00325i
\(679\) −0.896101 + 21.0390i −0.0343892 + 0.807402i
\(680\) 4.52770 5.21294i 0.173629 0.199907i
\(681\) −0.428557 41.6421i −0.0164223 1.59573i
\(682\) −18.4488 + 11.2353i −0.706442 + 0.430222i
\(683\) 0.314108 + 0.758323i 0.0120190 + 0.0290164i 0.929775 0.368128i \(-0.120001\pi\)
−0.917756 + 0.397144i \(0.870001\pi\)
\(684\) −34.5919 + 30.4561i −1.32265 + 1.16452i
\(685\) 1.58204 + 0.655304i 0.0604468 + 0.0250379i
\(686\) 26.1823 0.696895i 0.999646 0.0266076i
\(687\) 5.57279 + 5.45925i 0.212615 + 0.208284i
\(688\) −3.10309 + 4.94012i −0.118304 + 0.188340i
\(689\) 6.08125i 0.231677i
\(690\) 4.04537 + 24.3544i 0.154005 + 0.927154i
\(691\) 20.4739 + 8.48058i 0.778865 + 0.322616i 0.736457 0.676484i \(-0.236497\pi\)
0.0424075 + 0.999100i \(0.486497\pi\)
\(692\) −1.29467 + 15.3622i −0.0492161 + 0.583985i
\(693\) −33.7016 14.8358i −1.28022 0.563567i
\(694\) 31.0767 18.9257i 1.17966 0.718409i
\(695\) 4.88382 4.88382i 0.185254 0.185254i
\(696\) −15.0479 + 7.70496i −0.570391 + 0.292056i
\(697\) −3.93812 + 3.93812i −0.149167 + 0.149167i
\(698\) 5.98528 24.6298i 0.226546 0.932253i
\(699\) 30.2796 + 12.1787i 1.14528 + 0.460641i
\(700\) −8.80343 + 15.3990i −0.332738 + 0.582026i
\(701\) 15.2144 36.7308i 0.574640 1.38730i −0.322927 0.946424i \(-0.604667\pi\)
0.897567 0.440879i \(-0.145333\pi\)
\(702\) 5.13973 + 3.51790i 0.193987 + 0.132774i
\(703\) 73.9779i 2.79013i
\(704\) −35.9393 9.26235i −1.35451 0.349088i
\(705\) 4.92394 + 4.82363i 0.185446 + 0.181668i
\(706\) −47.0212 + 7.31402i −1.76967 + 0.275267i
\(707\) 4.15621 + 11.3813i 0.156310 + 0.428038i
\(708\) −12.8808 + 25.5798i −0.484090 + 0.961349i
\(709\) −12.2861 29.6612i −0.461414 1.11395i −0.967817 0.251654i \(-0.919025\pi\)
0.506404 0.862297i \(-0.330975\pi\)
\(710\) 1.66470 6.85034i 0.0624749 0.257089i
\(711\) 15.4932 + 14.8682i 0.581041 + 0.557602i
\(712\) −10.2210 + 30.5901i −0.383049 + 1.14641i
\(713\) 18.2786 + 18.2786i 0.684539 + 0.684539i
\(714\) 10.7273 6.06728i 0.401461 0.227062i
\(715\) −4.66335 + 1.93162i −0.174400 + 0.0722386i
\(716\) −3.65275 0.307841i −0.136510 0.0115045i
\(717\) −16.2227 38.0527i −0.605849 1.42111i
\(718\) −16.4391 12.0134i −0.613503 0.448337i
\(719\) 11.5801i 0.431864i −0.976408 0.215932i \(-0.930721\pi\)
0.976408 0.215932i \(-0.0692789\pi\)
\(720\) 14.9439 3.73831i 0.556926 0.139318i
\(721\) 18.4131 + 20.0514i 0.685739 + 0.746752i
\(722\) −45.6782 33.3808i −1.69997 1.24230i
\(723\) −5.28158 12.3887i −0.196424 0.460740i
\(724\) 27.2631 + 32.2813i 1.01323 + 1.19972i
\(725\) −4.42680 10.6872i −0.164407 0.396914i
\(726\) 25.1066 + 5.82817i 0.931792 + 0.216304i
\(727\) −18.8079 + 18.8079i −0.697547 + 0.697547i −0.963881 0.266334i \(-0.914188\pi\)
0.266334 + 0.963881i \(0.414188\pi\)
\(728\) 6.34022 0.175455i 0.234984 0.00650281i
\(729\) 20.2336 + 17.8774i 0.749393 + 0.662126i
\(730\) −15.4659 3.75837i −0.572420 0.139103i
\(731\) 1.06139 + 2.56241i 0.0392567 + 0.0947742i
\(732\) 50.7555 16.7586i 1.87598 0.619416i
\(733\) 6.12274 14.7816i 0.226148 0.545971i −0.769554 0.638582i \(-0.779521\pi\)
0.995702 + 0.0926112i \(0.0295214\pi\)
\(734\) −0.651235 + 0.101298i −0.0240375 + 0.00373897i
\(735\) 11.7975 10.1517i 0.435158 0.374451i
\(736\) −0.614885 + 44.4101i −0.0226650 + 1.63698i
\(737\) 2.81167i 0.103569i
\(738\) −12.2356 + 2.16202i −0.450400 + 0.0795849i
\(739\) −33.2434 13.7699i −1.22288 0.506533i −0.324555 0.945867i \(-0.605214\pi\)
−0.898324 + 0.439334i \(0.855214\pi\)
\(740\) −11.3471 + 21.9684i −0.417129 + 0.807574i
\(741\) −4.20795 + 10.4621i −0.154583 + 0.384336i
\(742\) −12.9752 23.5022i −0.476336 0.862794i
\(743\) 21.7102 + 21.7102i 0.796472 + 0.796472i 0.982537 0.186066i \(-0.0595737\pi\)
−0.186066 + 0.982537i \(0.559574\pi\)
\(744\) 10.4508 12.2856i 0.383144 0.450411i
\(745\) 10.9810 10.9810i 0.402311 0.402311i
\(746\) 23.9251 14.5704i 0.875962 0.533459i
\(747\) −14.2302 32.4491i −0.520654 1.18725i
\(748\) −13.4803 + 11.3847i −0.492888 + 0.416267i
\(749\) −12.5282 34.3069i −0.457769 1.25355i
\(750\) 4.30335 + 25.9075i 0.157136 + 0.946007i
\(751\) 38.7252i 1.41310i −0.707662 0.706551i \(-0.750250\pi\)
0.707662 0.706551i \(-0.249750\pi\)
\(752\) 7.17730 + 10.1124i 0.261729 + 0.368760i
\(753\) 22.1302 22.5905i 0.806470 0.823242i
\(754\) −2.44057 + 3.33967i −0.0888803 + 0.121624i
\(755\) −2.43186 + 5.87103i −0.0885045 + 0.213669i
\(756\) 27.3695 + 2.62925i 0.995417 + 0.0956249i
\(757\) 32.8313 13.5992i 1.19327 0.494271i 0.304455 0.952527i \(-0.401526\pi\)
0.888820 + 0.458256i \(0.151526\pi\)
\(758\) 7.67291 + 12.5992i 0.278693 + 0.457624i
\(759\) −0.649240 63.0856i −0.0235659 2.28986i
\(760\) 12.4550 + 24.9547i 0.451791 + 0.905201i
\(761\) 0.854654 0.854654i 0.0309812 0.0309812i −0.691446 0.722428i \(-0.743026\pi\)
0.722428 + 0.691446i \(0.243026\pi\)
\(762\) 6.52695 + 10.4734i 0.236446 + 0.379410i
\(763\) 5.27653 11.3471i 0.191023 0.410794i
\(764\) −3.51046 11.0112i −0.127004 0.398372i
\(765\) 2.66275 6.82231i 0.0962720 0.246661i
\(766\) −36.6174 + 5.69574i −1.32304 + 0.205795i
\(767\) 7.00740i 0.253023i
\(768\) 27.6512 1.84650i 0.997778 0.0666299i
\(769\) 10.2705i 0.370364i 0.982704 + 0.185182i \(0.0592874\pi\)
−0.982704 + 0.185182i \(0.940713\pi\)
\(770\) −13.9011 + 17.4151i −0.500959 + 0.627596i
\(771\) −13.0852 30.6932i −0.471251 1.10539i
\(772\) −2.43391 + 0.775949i −0.0875982 + 0.0279270i
\(773\) −11.8746 28.6679i −0.427101 1.03111i −0.980202 0.197999i \(-0.936556\pi\)
0.553102 0.833114i \(-0.313444\pi\)
\(774\) −1.33710 + 6.04156i −0.0480611 + 0.217159i
\(775\) 7.80395 + 7.80395i 0.280326 + 0.280326i
\(776\) 10.0533 + 20.1426i 0.360891 + 0.723076i
\(777\) −32.1979 + 30.1838i −1.15509 + 1.08284i
\(778\) −25.8124 + 15.7197i −0.925420 + 0.563579i
\(779\) −8.60895 20.7838i −0.308448 0.744659i
\(780\) 2.85433 2.46138i 0.102201 0.0881317i
\(781\) −6.89409 + 16.6438i −0.246690 + 0.595562i
\(782\) 17.0483 + 12.4586i 0.609647 + 0.445519i
\(783\) −12.2819 + 13.0647i −0.438921 + 0.466895i
\(784\) 24.1287 14.2059i 0.861739 0.507352i
\(785\) 2.01968 0.0720856
\(786\) −7.46460 44.9392i −0.266254 1.60293i
\(787\) 24.2088 + 10.0276i 0.862951 + 0.357446i 0.769861 0.638212i \(-0.220326\pi\)
0.0930901 + 0.995658i \(0.470326\pi\)
\(788\) 21.6566 18.2901i 0.771485 0.651556i
\(789\) −4.51129 + 11.2163i −0.160606 + 0.399312i
\(790\) 11.0983 6.75885i 0.394860 0.240469i
\(791\) 33.2169 + 1.41479i 1.18106 + 0.0503040i
\(792\) −39.2028 + 3.57002i −1.39301 + 0.126855i
\(793\) 9.24749 9.24749i 0.328388 0.328388i
\(794\) 8.90922 + 2.16502i 0.316176 + 0.0768338i
\(795\) −14.8006 5.95292i −0.524924 0.211128i
\(796\) −42.3475 21.8734i −1.50097 0.775281i
\(797\) 7.49626 + 3.10505i 0.265531 + 0.109987i 0.511477 0.859297i \(-0.329099\pi\)
−0.245946 + 0.969284i \(0.579099\pi\)
\(798\) 6.06003 + 49.4113i 0.214523 + 1.74914i
\(799\) 5.89546 0.208566
\(800\) −0.262522 + 18.9606i −0.00928154 + 0.670360i
\(801\) 0.704043 + 34.2017i 0.0248761 + 1.20846i
\(802\) −1.14053 + 0.177407i −0.0402736 + 0.00626445i
\(803\) 37.5765 + 15.5647i 1.32605 + 0.549267i
\(804\) −0.658258 1.99362i −0.0232150 0.0703095i
\(805\) 24.1797 + 11.2438i 0.852224 + 0.396292i
\(806\) 0.931891 3.83480i 0.0328245 0.135075i
\(807\) −10.5802 + 0.108885i −0.372441 + 0.00383294i
\(808\) 9.77934 + 8.49384i 0.344036 + 0.298812i
\(809\) 15.6991 15.6991i 0.551951 0.551951i −0.375053 0.927003i \(-0.622375\pi\)
0.927003 + 0.375053i \(0.122375\pi\)
\(810\) 13.5931 9.06546i 0.477615 0.318528i
\(811\) 2.36034 + 5.69837i 0.0828829 + 0.200097i 0.959888 0.280384i \(-0.0904620\pi\)
−0.877005 + 0.480481i \(0.840462\pi\)
\(812\) −2.30640 + 18.1141i −0.0809387 + 0.635682i
\(813\) 4.39182 + 10.3016i 0.154028 + 0.361294i
\(814\) 37.2809 51.0151i 1.30669 1.78808i
\(815\) 23.8024i 0.833763i
\(816\) 6.89284 11.2283i 0.241298 0.393069i
\(817\) −11.2032 −0.391949
\(818\) −35.3166 25.8087i −1.23481 0.902380i
\(819\) 6.27039 2.43721i 0.219105 0.0851630i
\(820\) −0.631435 + 7.49243i −0.0220507 + 0.261647i
\(821\) 13.1530 + 31.7541i 0.459041 + 1.10822i 0.968786 + 0.247898i \(0.0797399\pi\)
−0.509745 + 0.860326i \(0.670260\pi\)
\(822\) 3.18287 + 0.738863i 0.111015 + 0.0257708i
\(823\) 32.5081 + 32.5081i 1.13316 + 1.13316i 0.989649 + 0.143511i \(0.0458392\pi\)
0.143511 + 0.989649i \(0.454161\pi\)
\(824\) 27.6027 + 9.22285i 0.961586 + 0.321293i
\(825\) −0.277189 26.9340i −0.00965049 0.937722i
\(826\) 14.9513 + 27.0815i 0.520223 + 0.942286i
\(827\) 8.61595 3.56884i 0.299606 0.124101i −0.227816 0.973704i \(-0.573159\pi\)
0.527422 + 0.849603i \(0.323159\pi\)
\(828\) 15.2297 + 44.5788i 0.529268 + 1.54922i
\(829\) −20.9131 + 50.4888i −0.726344 + 1.75355i −0.0719329 + 0.997409i \(0.522917\pi\)
−0.654411 + 0.756139i \(0.727083\pi\)
\(830\) −21.1867 + 3.29553i −0.735401 + 0.114390i
\(831\) 40.4214 + 39.5979i 1.40220 + 1.37363i
\(832\) 5.83945 3.44631i 0.202446 0.119479i
\(833\) 1.13190 13.2635i 0.0392181 0.459554i
\(834\) 7.66609 10.7201i 0.265455 0.371208i
\(835\) −5.94595 2.46290i −0.205768 0.0852320i
\(836\) −21.6485 67.9044i −0.748728 2.34852i
\(837\) 6.05583 16.0000i 0.209320 0.553041i
\(838\) −23.7241 5.76519i −0.819537 0.199155i
\(839\) −22.7361 + 22.7361i −0.784937 + 0.784937i −0.980659 0.195723i \(-0.937295\pi\)
0.195723 + 0.980659i \(0.437295\pi\)
\(840\) 5.77939 15.6026i 0.199408 0.538342i
\(841\) 12.0854 + 12.0854i 0.416739 + 0.416739i
\(842\) −2.71845 4.46380i −0.0936838 0.153833i
\(843\) 2.61604 6.50420i 0.0901011 0.224016i
\(844\) 1.61161 19.1230i 0.0554740 0.658239i
\(845\) −6.03334 + 14.5658i −0.207553 + 0.501078i
\(846\) 10.7768 + 7.54024i 0.370515 + 0.259239i
\(847\) 20.5052 18.8298i 0.704567 0.647000i
\(848\) −24.3029 15.2656i −0.834565 0.524224i
\(849\) 15.2664 + 14.9554i 0.523941 + 0.513267i
\(850\) 7.27868 + 5.31913i 0.249657 + 0.182445i
\(851\) −69.8590 28.9365i −2.39474 0.991932i
\(852\) 0.991671 13.4153i 0.0339741 0.459601i
\(853\) 6.58810 + 15.9051i 0.225572 + 0.544580i 0.995629 0.0933956i \(-0.0297721\pi\)
−0.770057 + 0.637975i \(0.779772\pi\)
\(854\) 16.0079 55.4696i 0.547779 1.89813i
\(855\) 21.3437 + 20.4827i 0.729939 + 0.700494i
\(856\) −29.4781 25.6032i −1.00754 0.875099i
\(857\) −6.47594 + 6.47594i −0.221214 + 0.221214i −0.809010 0.587796i \(-0.799996\pi\)
0.587796 + 0.809010i \(0.299996\pi\)
\(858\) −8.17416 + 5.09410i −0.279061 + 0.173910i
\(859\) 39.4456 16.3389i 1.34587 0.557476i 0.410728 0.911758i \(-0.365275\pi\)
0.935139 + 0.354281i \(0.115275\pi\)
\(860\) 3.32687 + 1.71840i 0.113445 + 0.0585969i
\(861\) −5.53334 + 12.2270i −0.188576 + 0.416694i
\(862\) 16.7347 2.60304i 0.569987 0.0886600i
\(863\) 21.6558i 0.737172i −0.929594 0.368586i \(-0.879842\pi\)
0.929594 0.368586i \(-0.120158\pi\)
\(864\) 26.9609 11.7093i 0.917229 0.398359i
\(865\) 9.89519 0.336446
\(866\) 2.89675 0.450581i 0.0984355 0.0153114i
\(867\) 9.09096 + 21.3241i 0.308745 + 0.724206i
\(868\) −4.58062 16.8087i −0.155476 0.570523i
\(869\) −30.6787 + 12.7076i −1.04071 + 0.431074i
\(870\) 5.73906 + 9.20908i 0.194572 + 0.312217i
\(871\) −0.363231 0.363231i −0.0123076 0.0123076i
\(872\) −0.938803 13.3450i −0.0317919 0.451919i
\(873\) 17.2279 + 16.5330i 0.583077 + 0.559556i
\(874\) −72.8463 + 44.3633i −2.46406 + 1.50061i
\(875\) 25.7217 + 11.9608i 0.869553 + 0.404350i
\(876\) −30.2876 2.23889i −1.02332 0.0756449i
\(877\) 3.55455 8.58145i 0.120029 0.289775i −0.852433 0.522836i \(-0.824874\pi\)
0.972462 + 0.233061i \(0.0748741\pi\)
\(878\) −5.78148 + 7.91137i −0.195116 + 0.266996i
\(879\) −3.75323 + 3.83129i −0.126593 + 0.129226i
\(880\) −3.98684 + 23.4854i −0.134396 + 0.791691i
\(881\) 32.6691i 1.10065i 0.834951 + 0.550325i \(0.185496\pi\)
−0.834951 + 0.550325i \(0.814504\pi\)
\(882\) 19.0330 22.7979i 0.640876 0.767645i
\(883\) −18.5221 + 44.7163i −0.623318 + 1.50482i 0.224467 + 0.974482i \(0.427936\pi\)
−0.847785 + 0.530340i \(0.822064\pi\)
\(884\) 0.270715 3.21223i 0.00910513 0.108039i
\(885\) 17.0547 + 6.85952i 0.573287 + 0.230580i
\(886\) 5.85085 3.56316i 0.196563 0.119707i
\(887\) −5.07169 5.07169i −0.170291 0.170291i 0.616816 0.787107i \(-0.288422\pi\)
−0.787107 + 0.616816i \(0.788422\pi\)
\(888\) −14.4906 + 44.9003i −0.486272 + 1.50676i
\(889\) 13.3174 + 0.567219i 0.446651 + 0.0190239i
\(890\) 20.1158 + 4.88833i 0.674283 + 0.163857i
\(891\) −37.8844 + 17.5520i −1.26918 + 0.588016i
\(892\) 7.67352 + 24.0694i 0.256929 + 0.805904i
\(893\) −9.11307 + 22.0009i −0.304957 + 0.736232i
\(894\) 17.2367 24.1035i 0.576482 0.806142i
\(895\) 2.35282i 0.0786462i
\(896\) 15.2145 25.7783i 0.508282 0.861191i
\(897\) 8.23368 + 8.06594i 0.274915 + 0.269314i
\(898\) 0.245413 + 1.57774i 0.00818953 + 0.0526498i
\(899\) 10.4968 + 4.34791i 0.350087 + 0.145011i
\(900\) 6.50223 + 19.0327i 0.216741 + 0.634423i
\(901\) −12.6058 + 5.22147i −0.419959 + 0.173953i
\(902\) 4.53722 18.6710i 0.151073 0.621675i
\(903\) 4.57100 + 4.87602i 0.152114 + 0.162264i
\(904\) 31.8016 15.8723i 1.05770 0.527906i
\(905\) 19.1770 19.1770i 0.637465 0.637465i
\(906\) −2.74195 + 11.8118i −0.0910953 + 0.392420i
\(907\) −7.19146 + 2.97880i −0.238789 + 0.0989095i −0.498869 0.866678i \(-0.666251\pi\)
0.260080 + 0.965587i \(0.416251\pi\)
\(908\) −47.9169 4.03826i −1.59018 0.134014i
\(909\) 12.7985 + 4.99525i 0.424499 + 0.165682i
\(910\) −0.453966 4.04563i −0.0150488 0.134111i
\(911\) 2.06944 0.0685637 0.0342819 0.999412i \(-0.489086\pi\)
0.0342819 + 0.999412i \(0.489086\pi\)
\(912\) 31.2474 + 43.0794i 1.03470 + 1.42650i
\(913\) 54.7925 1.81337
\(914\) −26.3706 19.2712i −0.872263 0.637434i
\(915\) −13.4543 31.5590i −0.444785 1.04331i
\(916\) 6.88211 5.81227i 0.227391 0.192043i
\(917\) −44.6170 20.7473i −1.47338 0.685137i
\(918\) 2.87914 13.6746i 0.0950256 0.451329i
\(919\) 2.31318 + 2.31318i 0.0763047 + 0.0763047i 0.744229 0.667924i \(-0.232817\pi\)
−0.667924 + 0.744229i \(0.732817\pi\)
\(920\) 28.4370 2.00051i 0.937541 0.0659548i
\(921\) 0.440745 + 42.8265i 0.0145230 + 1.41118i
\(922\) 6.16669 25.3764i 0.203089 0.835726i
\(923\) −1.25953 3.04078i −0.0414580 0.100089i
\(924\) −20.7217 + 37.1279i −0.681692 + 1.22142i
\(925\) −29.8259 12.3543i −0.980670 0.406207i
\(926\) 5.73902 + 36.8957i 0.188596 + 1.21247i
\(927\) 30.8616 0.635286i 1.01363 0.0208655i
\(928\) 7.22003 + 18.1369i 0.237009 + 0.595373i
\(929\) 23.9455 0.785627 0.392813 0.919618i \(-0.371502\pi\)
0.392813 + 0.919618i \(0.371502\pi\)
\(930\) −8.42094 6.02191i −0.276133 0.197466i
\(931\) 47.7476 + 24.7265i 1.56486 + 0.810379i
\(932\) 17.2948 33.4832i 0.566509 1.09678i
\(933\) −14.1547 + 35.1925i −0.463404 + 1.15215i
\(934\) 0.123761 0.509283i 0.00404957 0.0166643i
\(935\) 8.00808 + 8.00808i 0.261892 + 0.261892i
\(936\) 4.60327 5.52567i 0.150463 0.180612i
\(937\) −5.00364 + 5.00364i −0.163462 + 0.163462i −0.784098 0.620637i \(-0.786874\pi\)
0.620637 + 0.784098i \(0.286874\pi\)
\(938\) −2.17878 0.628772i −0.0711398 0.0205301i
\(939\) 16.7993 41.7678i 0.548225 1.36304i
\(940\) 6.08082 5.13554i 0.198334 0.167503i
\(941\) 0.454949 1.09834i 0.0148309 0.0358050i −0.916291 0.400514i \(-0.868832\pi\)
0.931122 + 0.364709i \(0.118832\pi\)
\(942\) 3.80177 0.631492i 0.123868 0.0205751i
\(943\) −22.9940 −0.748789
\(944\) 28.0041 + 17.5905i 0.911456 + 0.572523i
\(945\) 0.206361 17.6467i 0.00671293 0.574048i
\(946\) −7.72568 5.64579i −0.251184 0.183560i
\(947\) −22.5818 9.35369i −0.733810 0.303954i −0.0156932 0.999877i \(-0.504996\pi\)
−0.718116 + 0.695923i \(0.754996\pi\)
\(948\) 18.7777 16.1927i 0.609872 0.525914i
\(949\) −6.86514 + 2.84363i −0.222852 + 0.0923083i
\(950\) −31.1013 + 18.9407i −1.00906 + 0.614516i
\(951\) −37.9773 + 0.390840i −1.23150 + 0.0126739i
\(952\) −5.80752 12.9919i −0.188223 0.421070i
\(953\) −6.17054 6.17054i −0.199883 0.199883i 0.600067 0.799950i \(-0.295141\pi\)
−0.799950 + 0.600067i \(0.795141\pi\)
\(954\) −29.7214 6.57785i −0.962266 0.212966i
\(955\) −6.85335 + 2.83875i −0.221769 + 0.0918598i
\(956\) −45.5092 + 14.5087i −1.47187 + 0.469244i
\(957\) −10.8745 25.5078i −0.351524 0.824549i
\(958\) −7.15310 + 1.11265i −0.231106 + 0.0359479i
\(959\) 2.59953 2.38714i 0.0839433 0.0770847i
\(960\) −2.67143 17.5857i −0.0862202 0.567575i
\(961\) 20.1602 0.650331
\(962\) 1.77428 + 11.4067i 0.0572049 + 0.367766i
\(963\) −38.5787 15.0573i −1.24318 0.485215i
\(964\) −14.8162 + 4.72354i −0.477199 + 0.152135i
\(965\) 0.627474 + 1.51486i 0.0201991 + 0.0487650i
\(966\) 49.0306 + 13.6047i 1.57753 + 0.437723i
\(967\) −16.5213 + 16.5213i −0.531290 + 0.531290i −0.920956 0.389666i \(-0.872590\pi\)
0.389666 + 0.920956i \(0.372590\pi\)
\(968\) 9.43159 28.2274i 0.303143 0.907264i
\(969\) 25.2999 0.260371i 0.812748 0.00836433i
\(970\) 12.3409 7.51560i 0.396243 0.241311i
\(971\) −21.4043 + 8.86594i −0.686896 + 0.284522i −0.698706 0.715409i \(-0.746241\pi\)
0.0118104 + 0.999930i \(0.496241\pi\)
\(972\) 22.7527 21.3146i 0.729794 0.683667i
\(973\) −4.88296 13.3714i −0.156540 0.428668i
\(974\) 6.93369 9.48805i 0.222170 0.304017i
\(975\) 3.51532 + 3.44371i 0.112580 + 0.110287i
\(976\) −13.7426 60.1701i −0.439889 1.92600i
\(977\) 12.2739 0.392678 0.196339 0.980536i \(-0.437095\pi\)
0.196339 + 0.980536i \(0.437095\pi\)
\(978\) −7.44228 44.8048i −0.237978 1.43270i
\(979\) −48.8740 20.2443i −1.56202 0.647010i
\(980\) −10.3864 14.6665i −0.331781 0.468505i
\(981\) −5.69873 12.9948i −0.181947 0.414894i
\(982\) −24.3869 40.0443i −0.778217 1.27786i
\(983\) −9.50897 9.50897i −0.303289 0.303289i 0.539010 0.842299i \(-0.318798\pi\)
−0.842299 + 0.539010i \(0.818798\pi\)
\(984\) 1.15406 + 14.3009i 0.0367901 + 0.455896i
\(985\) −12.8653 12.8653i −0.409923 0.409923i
\(986\) 9.01828 + 2.19153i 0.287201 + 0.0697924i
\(987\) 13.2938 5.01026i 0.423147 0.159478i
\(988\) 11.5690 + 5.97565i 0.368060 + 0.190111i
\(989\) −4.38212 + 10.5794i −0.139343 + 0.336405i
\(990\) 4.39641 + 24.8809i 0.139727 + 0.790768i
\(991\) 61.1699 1.94313 0.971563 0.236782i \(-0.0760928\pi\)
0.971563 + 0.236782i \(0.0760928\pi\)
\(992\) −12.9859 13.3506i −0.412304 0.423881i
\(993\) −4.37603 4.28688i −0.138869 0.136040i
\(994\) −11.3557 9.06431i −0.360180 0.287503i
\(995\) −11.7072 + 28.2637i −0.371143 + 0.896019i
\(996\) −38.8506 + 12.8278i −1.23103 + 0.406465i
\(997\) −19.2385 + 7.96884i −0.609289 + 0.252376i −0.665924 0.746019i \(-0.731963\pi\)
0.0566357 + 0.998395i \(0.481963\pi\)
\(998\) 4.26129 17.5355i 0.134889 0.555077i
\(999\) 1.54473 + 50.0188i 0.0488731 + 1.58253i
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 672.2.bo.a.125.6 yes 496
3.2 odd 2 inner 672.2.bo.a.125.119 yes 496
7.6 odd 2 inner 672.2.bo.a.125.5 496
21.20 even 2 inner 672.2.bo.a.125.120 yes 496
32.21 even 8 inner 672.2.bo.a.629.120 yes 496
96.53 odd 8 inner 672.2.bo.a.629.5 yes 496
224.181 odd 8 inner 672.2.bo.a.629.119 yes 496
672.629 even 8 inner 672.2.bo.a.629.6 yes 496
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.bo.a.125.5 496 7.6 odd 2 inner
672.2.bo.a.125.6 yes 496 1.1 even 1 trivial
672.2.bo.a.125.119 yes 496 3.2 odd 2 inner
672.2.bo.a.125.120 yes 496 21.20 even 2 inner
672.2.bo.a.629.5 yes 496 96.53 odd 8 inner
672.2.bo.a.629.6 yes 496 672.629 even 8 inner
672.2.bo.a.629.119 yes 496 224.181 odd 8 inner
672.2.bo.a.629.120 yes 496 32.21 even 8 inner