Properties

Label 539.2.f.d.295.1
Level $539$
Weight $2$
Character 539.295
Analytic conductor $4.304$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(148,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.f (of order \(5\), 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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 295.1
Root \(-0.628998 - 0.456994i\) of defining polynomial
Character \(\chi\) \(=\) 539.295
Dual form 539.2.f.d.148.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.240256 + 0.739431i) q^{2} +(0.500000 - 0.363271i) q^{3} +(1.12900 + 0.820265i) q^{4} +(0.0687611 + 0.211625i) q^{5} +(0.148486 + 0.456994i) q^{6} +(-2.13577 + 1.55173i) q^{8} +(-0.809017 + 2.48990i) q^{9} +O(q^{10})\) \(q+(-0.240256 + 0.739431i) q^{2} +(0.500000 - 0.363271i) q^{3} +(1.12900 + 0.820265i) q^{4} +(0.0687611 + 0.211625i) q^{5} +(0.148486 + 0.456994i) q^{6} +(-2.13577 + 1.55173i) q^{8} +(-0.809017 + 2.48990i) q^{9} -0.173002 q^{10} +(0.660531 - 3.25018i) q^{11} +0.862478 q^{12} +(-2.01774 + 6.20997i) q^{13} +(0.111258 + 0.0808336i) q^{15} +(0.228211 + 0.702362i) q^{16} +(1.33947 + 4.12246i) q^{17} +(-1.64674 - 1.19643i) q^{18} +(2.35829 - 1.71340i) q^{19} +(-0.0959574 + 0.295327i) q^{20} +(2.24459 + 1.26929i) q^{22} -3.89796 q^{23} +(-0.504188 + 1.55173i) q^{24} +(4.00503 - 2.90982i) q^{25} +(-4.10707 - 2.98396i) q^{26} +(1.07295 + 3.30220i) q^{27} +(3.05322 + 2.21829i) q^{29} +(-0.0865012 + 0.0628468i) q^{30} +(2.12900 - 6.55238i) q^{31} -5.85410 q^{32} +(-0.850433 - 1.86504i) q^{33} -3.37009 q^{34} +(-2.95576 + 2.14748i) q^{36} +(4.57379 + 3.32305i) q^{37} +(0.700347 + 2.15545i) q^{38} +(1.24703 + 3.83797i) q^{39} +(-0.475243 - 0.345285i) q^{40} +(1.08255 - 0.786521i) q^{41} -4.70820 q^{43} +(3.41175 - 3.12764i) q^{44} -0.582554 q^{45} +(0.936507 - 2.88227i) q^{46} +(4.89094 - 3.55348i) q^{47} +(0.369254 + 0.268279i) q^{48} +(1.18938 + 3.66055i) q^{50} +(2.16731 + 1.57464i) q^{51} +(-7.37184 + 5.35596i) q^{52} +(-0.530865 + 1.63383i) q^{53} -2.69953 q^{54} +(0.733239 - 0.0837016i) q^{55} +(0.556717 - 1.71340i) q^{57} +(-2.37383 + 1.72469i) q^{58} +(-7.71239 - 5.60338i) q^{59} +(0.0593050 + 0.182522i) q^{60} +(2.97566 + 9.15813i) q^{61} +(4.33353 + 3.14850i) q^{62} +(0.950059 - 2.92398i) q^{64} -1.45293 q^{65} +(1.58339 - 0.180749i) q^{66} +1.27155 q^{67} +(-1.86925 + 5.75297i) q^{68} +(-1.94898 + 1.41602i) q^{69} +(-2.87670 - 8.85357i) q^{71} +(-2.13577 - 6.57324i) q^{72} +(4.52169 + 3.28520i) q^{73} +(-3.55605 + 2.58362i) q^{74} +(0.945459 - 2.90982i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-1.39971 + 4.30785i) q^{79} +(-0.132945 + 0.0965905i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(0.321489 + 0.989441i) q^{82} +(-3.48688 - 10.7315i) q^{83} +(-0.780313 + 0.566931i) q^{85} +(1.13117 - 3.48139i) q^{86} +2.33245 q^{87} +(3.63267 + 7.96663i) q^{88} -7.92157 q^{89} +(0.139962 - 0.430759i) q^{90} +(-4.40079 - 3.19736i) q^{92} +(-1.31579 - 4.04959i) q^{93} +(1.45248 + 4.47026i) q^{94} +(0.524757 + 0.381258i) q^{95} +(-2.92705 + 2.12663i) q^{96} +(2.79781 - 8.61078i) q^{97} +(7.55825 + 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.240256 + 0.739431i −0.169887 + 0.522857i −0.999363 0.0356845i \(-0.988639\pi\)
0.829477 + 0.558542i \(0.188639\pi\)
\(3\) 0.500000 0.363271i 0.288675 0.209735i −0.434017 0.900905i \(-0.642904\pi\)
0.722692 + 0.691170i \(0.242904\pi\)
\(4\) 1.12900 + 0.820265i 0.564499 + 0.410133i
\(5\) 0.0687611 + 0.211625i 0.0307509 + 0.0946416i 0.965254 0.261313i \(-0.0841556\pi\)
−0.934503 + 0.355955i \(0.884156\pi\)
\(6\) 0.148486 + 0.456994i 0.0606193 + 0.186567i
\(7\) 0 0
\(8\) −2.13577 + 1.55173i −0.755110 + 0.548620i
\(9\) −0.809017 + 2.48990i −0.269672 + 0.829966i
\(10\) −0.173002 −0.0547082
\(11\) 0.660531 3.25018i 0.199158 0.979967i
\(12\) 0.862478 0.248976
\(13\) −2.01774 + 6.20997i −0.559620 + 1.72233i 0.123798 + 0.992307i \(0.460493\pi\)
−0.683418 + 0.730027i \(0.739507\pi\)
\(14\) 0 0
\(15\) 0.111258 + 0.0808336i 0.0287267 + 0.0208711i
\(16\) 0.228211 + 0.702362i 0.0570529 + 0.175591i
\(17\) 1.33947 + 4.12246i 0.324869 + 0.999844i 0.971500 + 0.237041i \(0.0761775\pi\)
−0.646631 + 0.762803i \(0.723822\pi\)
\(18\) −1.64674 1.19643i −0.388140 0.282000i
\(19\) 2.35829 1.71340i 0.541029 0.393080i −0.283438 0.958991i \(-0.591475\pi\)
0.824467 + 0.565910i \(0.191475\pi\)
\(20\) −0.0959574 + 0.295327i −0.0214567 + 0.0660370i
\(21\) 0 0
\(22\) 2.24459 + 1.26929i 0.478549 + 0.270614i
\(23\) −3.89796 −0.812780 −0.406390 0.913700i \(-0.633213\pi\)
−0.406390 + 0.913700i \(0.633213\pi\)
\(24\) −0.504188 + 1.55173i −0.102917 + 0.316746i
\(25\) 4.00503 2.90982i 0.801006 0.581965i
\(26\) −4.10707 2.98396i −0.805463 0.585203i
\(27\) 1.07295 + 3.30220i 0.206489 + 0.635508i
\(28\) 0 0
\(29\) 3.05322 + 2.21829i 0.566969 + 0.411927i 0.834003 0.551760i \(-0.186044\pi\)
−0.267034 + 0.963687i \(0.586044\pi\)
\(30\) −0.0865012 + 0.0628468i −0.0157929 + 0.0114742i
\(31\) 2.12900 6.55238i 0.382379 1.17684i −0.555984 0.831193i \(-0.687659\pi\)
0.938364 0.345650i \(-0.112341\pi\)
\(32\) −5.85410 −1.03487
\(33\) −0.850433 1.86504i −0.148041 0.324662i
\(34\) −3.37009 −0.577966
\(35\) 0 0
\(36\) −2.95576 + 2.14748i −0.492626 + 0.357914i
\(37\) 4.57379 + 3.32305i 0.751926 + 0.546306i 0.896423 0.443199i \(-0.146156\pi\)
−0.144497 + 0.989505i \(0.546156\pi\)
\(38\) 0.700347 + 2.15545i 0.113611 + 0.349660i
\(39\) 1.24703 + 3.83797i 0.199685 + 0.614567i
\(40\) −0.475243 0.345285i −0.0751426 0.0545943i
\(41\) 1.08255 0.786521i 0.169066 0.122834i −0.500035 0.866005i \(-0.666679\pi\)
0.669101 + 0.743171i \(0.266679\pi\)
\(42\) 0 0
\(43\) −4.70820 −0.717994 −0.358997 0.933339i \(-0.616881\pi\)
−0.358997 + 0.933339i \(0.616881\pi\)
\(44\) 3.41175 3.12764i 0.514341 0.471510i
\(45\) −0.582554 −0.0868420
\(46\) 0.936507 2.88227i 0.138080 0.424968i
\(47\) 4.89094 3.55348i 0.713417 0.518328i −0.170857 0.985296i \(-0.554654\pi\)
0.884274 + 0.466968i \(0.154654\pi\)
\(48\) 0.369254 + 0.268279i 0.0532972 + 0.0387227i
\(49\) 0 0
\(50\) 1.18938 + 3.66055i 0.168204 + 0.517679i
\(51\) 2.16731 + 1.57464i 0.303484 + 0.220494i
\(52\) −7.37184 + 5.35596i −1.02229 + 0.742738i
\(53\) −0.530865 + 1.63383i −0.0729199 + 0.224424i −0.980873 0.194646i \(-0.937644\pi\)
0.907954 + 0.419071i \(0.137644\pi\)
\(54\) −2.69953 −0.367360
\(55\) 0.733239 0.0837016i 0.0988700 0.0112863i
\(56\) 0 0
\(57\) 0.556717 1.71340i 0.0737389 0.226945i
\(58\) −2.37383 + 1.72469i −0.311699 + 0.226463i
\(59\) −7.71239 5.60338i −1.00407 0.729498i −0.0411113 0.999155i \(-0.513090\pi\)
−0.962957 + 0.269657i \(0.913090\pi\)
\(60\) 0.0593050 + 0.182522i 0.00765624 + 0.0235635i
\(61\) 2.97566 + 9.15813i 0.380994 + 1.17258i 0.939345 + 0.342974i \(0.111434\pi\)
−0.558351 + 0.829605i \(0.688566\pi\)
\(62\) 4.33353 + 3.14850i 0.550359 + 0.399859i
\(63\) 0 0
\(64\) 0.950059 2.92398i 0.118757 0.365498i
\(65\) −1.45293 −0.180213
\(66\) 1.58339 0.180749i 0.194902 0.0222487i
\(67\) 1.27155 0.155344 0.0776722 0.996979i \(-0.475251\pi\)
0.0776722 + 0.996979i \(0.475251\pi\)
\(68\) −1.86925 + 5.75297i −0.226680 + 0.697650i
\(69\) −1.94898 + 1.41602i −0.234629 + 0.170468i
\(70\) 0 0
\(71\) −2.87670 8.85357i −0.341401 1.05072i −0.963482 0.267772i \(-0.913713\pi\)
0.622081 0.782953i \(-0.286287\pi\)
\(72\) −2.13577 6.57324i −0.251703 0.774663i
\(73\) 4.52169 + 3.28520i 0.529223 + 0.384503i 0.820067 0.572267i \(-0.193936\pi\)
−0.290844 + 0.956771i \(0.593936\pi\)
\(74\) −3.55605 + 2.58362i −0.413382 + 0.300340i
\(75\) 0.945459 2.90982i 0.109172 0.335997i
\(76\) 4.06794 0.466625
\(77\) 0 0
\(78\) −3.13752 −0.355254
\(79\) −1.39971 + 4.30785i −0.157479 + 0.484671i −0.998404 0.0564813i \(-0.982012\pi\)
0.840924 + 0.541153i \(0.182012\pi\)
\(80\) −0.132945 + 0.0965905i −0.0148638 + 0.0107991i
\(81\) −4.61803 3.35520i −0.513115 0.372800i
\(82\) 0.321489 + 0.989441i 0.0355025 + 0.109265i
\(83\) −3.48688 10.7315i −0.382734 1.17793i −0.938111 0.346336i \(-0.887426\pi\)
0.555376 0.831599i \(-0.312574\pi\)
\(84\) 0 0
\(85\) −0.780313 + 0.566931i −0.0846368 + 0.0614922i
\(86\) 1.13117 3.48139i 0.121978 0.375408i
\(87\) 2.33245 0.250065
\(88\) 3.63267 + 7.96663i 0.387244 + 0.849245i
\(89\) −7.92157 −0.839684 −0.419842 0.907597i \(-0.637915\pi\)
−0.419842 + 0.907597i \(0.637915\pi\)
\(90\) 0.139962 0.430759i 0.0147533 0.0454059i
\(91\) 0 0
\(92\) −4.40079 3.19736i −0.458814 0.333348i
\(93\) −1.31579 4.04959i −0.136441 0.419923i
\(94\) 1.45248 + 4.47026i 0.149811 + 0.461072i
\(95\) 0.524757 + 0.381258i 0.0538389 + 0.0391162i
\(96\) −2.92705 + 2.12663i −0.298741 + 0.217048i
\(97\) 2.79781 8.61078i 0.284075 0.874292i −0.702600 0.711585i \(-0.747977\pi\)
0.986674 0.162707i \(-0.0520225\pi\)
\(98\) 0 0
\(99\) 7.55825 + 4.27411i 0.759633 + 0.429564i
\(100\) 6.90849 0.690849
\(101\) 5.93627 18.2700i 0.590681 1.81793i 0.0155316 0.999879i \(-0.495056\pi\)
0.575149 0.818049i \(-0.304944\pi\)
\(102\) −1.68505 + 1.22426i −0.166845 + 0.121220i
\(103\) 13.1371 + 9.54464i 1.29443 + 0.940461i 0.999885 0.0151755i \(-0.00483070\pi\)
0.294549 + 0.955636i \(0.404831\pi\)
\(104\) −5.32676 16.3941i −0.522332 1.60757i
\(105\) 0 0
\(106\) −1.08057 0.785077i −0.104954 0.0762534i
\(107\) 4.36332 3.17014i 0.421818 0.306469i −0.356551 0.934276i \(-0.616047\pi\)
0.778369 + 0.627807i \(0.216047\pi\)
\(108\) −1.49732 + 4.60828i −0.144080 + 0.443432i
\(109\) 5.39901 0.517132 0.258566 0.965994i \(-0.416750\pi\)
0.258566 + 0.965994i \(0.416750\pi\)
\(110\) −0.114273 + 0.562290i −0.0108955 + 0.0536122i
\(111\) 3.49406 0.331642
\(112\) 0 0
\(113\) 13.3457 9.69624i 1.25546 0.912145i 0.256935 0.966429i \(-0.417287\pi\)
0.998526 + 0.0542834i \(0.0172875\pi\)
\(114\) 1.13319 + 0.823308i 0.106133 + 0.0771098i
\(115\) −0.268028 0.824906i −0.0249937 0.0769228i
\(116\) 1.62749 + 5.00890i 0.151109 + 0.465065i
\(117\) −13.8298 10.0479i −1.27857 0.928932i
\(118\) 5.99626 4.35654i 0.552001 0.401052i
\(119\) 0 0
\(120\) −0.363054 −0.0331421
\(121\) −10.1274 4.29369i −0.920673 0.390336i
\(122\) −7.48673 −0.677816
\(123\) 0.255556 0.786521i 0.0230427 0.0709182i
\(124\) 7.77832 5.65128i 0.698514 0.507500i
\(125\) 1.79128 + 1.30144i 0.160217 + 0.116404i
\(126\) 0 0
\(127\) 0.617194 + 1.89953i 0.0547671 + 0.168556i 0.974699 0.223523i \(-0.0717559\pi\)
−0.919931 + 0.392079i \(0.871756\pi\)
\(128\) −7.53831 5.47690i −0.666299 0.484094i
\(129\) −2.35410 + 1.71036i −0.207267 + 0.150588i
\(130\) 0.349074 1.07434i 0.0306158 0.0942258i
\(131\) −1.37009 −0.119706 −0.0598528 0.998207i \(-0.519063\pi\)
−0.0598528 + 0.998207i \(0.519063\pi\)
\(132\) 0.569693 2.80321i 0.0495854 0.243988i
\(133\) 0 0
\(134\) −0.305497 + 0.940223i −0.0263909 + 0.0812229i
\(135\) −0.625051 + 0.454126i −0.0537958 + 0.0390849i
\(136\) −9.25776 6.72615i −0.793846 0.576763i
\(137\) 0.772308 + 2.37692i 0.0659827 + 0.203074i 0.978612 0.205714i \(-0.0659516\pi\)
−0.912629 + 0.408788i \(0.865952\pi\)
\(138\) −0.578793 1.78134i −0.0492702 0.151638i
\(139\) −3.85302 2.79938i −0.326809 0.237441i 0.412266 0.911063i \(-0.364737\pi\)
−0.739075 + 0.673623i \(0.764737\pi\)
\(140\) 0 0
\(141\) 1.15459 3.55348i 0.0972344 0.299257i
\(142\) 7.23775 0.607378
\(143\) 18.8508 + 10.6599i 1.57638 + 0.891426i
\(144\) −1.93344 −0.161120
\(145\) −0.259504 + 0.798670i −0.0215506 + 0.0663260i
\(146\) −3.51554 + 2.55419i −0.290948 + 0.211386i
\(147\) 0 0
\(148\) 2.43801 + 7.50344i 0.200404 + 0.616779i
\(149\) −2.23415 6.87600i −0.183028 0.563304i 0.816880 0.576807i \(-0.195702\pi\)
−0.999909 + 0.0135034i \(0.995702\pi\)
\(150\) 1.92446 + 1.39820i 0.157132 + 0.114163i
\(151\) −6.58514 + 4.78439i −0.535891 + 0.389348i −0.822557 0.568683i \(-0.807453\pi\)
0.286666 + 0.958031i \(0.407453\pi\)
\(152\) −2.37804 + 7.31886i −0.192885 + 0.593638i
\(153\) −11.3482 −0.917445
\(154\) 0 0
\(155\) 1.53304 0.123137
\(156\) −1.74026 + 5.35596i −0.139332 + 0.428820i
\(157\) 16.3028 11.8447i 1.30111 0.945311i 0.301143 0.953579i \(-0.402632\pi\)
0.999966 + 0.00826862i \(0.00263201\pi\)
\(158\) −2.84907 2.06997i −0.226660 0.164678i
\(159\) 0.328093 + 1.00977i 0.0260194 + 0.0800796i
\(160\) −0.402535 1.23887i −0.0318232 0.0979416i
\(161\) 0 0
\(162\) 3.59045 2.60861i 0.282092 0.204952i
\(163\) 2.29739 7.07062i 0.179945 0.553814i −0.819880 0.572536i \(-0.805960\pi\)
0.999825 + 0.0187219i \(0.00595970\pi\)
\(164\) 1.86736 0.145816
\(165\) 0.336213 0.308216i 0.0261742 0.0239945i
\(166\) 8.77295 0.680913
\(167\) 0.683275 2.10290i 0.0528734 0.162728i −0.921133 0.389248i \(-0.872735\pi\)
0.974006 + 0.226520i \(0.0727350\pi\)
\(168\) 0 0
\(169\) −23.9752 17.4190i −1.84424 1.33992i
\(170\) −0.231732 0.713196i −0.0177730 0.0546997i
\(171\) 2.35829 + 7.25807i 0.180343 + 0.555038i
\(172\) −5.31555 3.86198i −0.405307 0.294473i
\(173\) −8.38320 + 6.09075i −0.637363 + 0.463071i −0.858943 0.512071i \(-0.828878\pi\)
0.221581 + 0.975142i \(0.428878\pi\)
\(174\) −0.560385 + 1.72469i −0.0424827 + 0.130748i
\(175\) 0 0
\(176\) 2.43355 0.277797i 0.183436 0.0209398i
\(177\) −5.89174 −0.442851
\(178\) 1.90320 5.85746i 0.142651 0.439035i
\(179\) 18.9386 13.7597i 1.41554 1.02845i 0.423051 0.906106i \(-0.360959\pi\)
0.992488 0.122343i \(-0.0390408\pi\)
\(180\) −0.657702 0.477849i −0.0490222 0.0356167i
\(181\) 4.23851 + 13.0448i 0.315046 + 0.969611i 0.975736 + 0.218952i \(0.0702639\pi\)
−0.660690 + 0.750659i \(0.729736\pi\)
\(182\) 0 0
\(183\) 4.81471 + 3.49809i 0.355914 + 0.258587i
\(184\) 8.32516 6.04858i 0.613739 0.445907i
\(185\) −0.388742 + 1.19643i −0.0285809 + 0.0879629i
\(186\) 3.31052 0.242739
\(187\) 14.2835 1.63051i 1.04451 0.119235i
\(188\) 8.43666 0.615306
\(189\) 0 0
\(190\) −0.407990 + 0.296422i −0.0295987 + 0.0215047i
\(191\) 9.72838 + 7.06808i 0.703921 + 0.511429i 0.881207 0.472731i \(-0.156732\pi\)
−0.177286 + 0.984159i \(0.556732\pi\)
\(192\) −0.587169 1.80712i −0.0423753 0.130418i
\(193\) 4.90840 + 15.1065i 0.353315 + 1.08739i 0.956980 + 0.290153i \(0.0937062\pi\)
−0.603666 + 0.797238i \(0.706294\pi\)
\(194\) 5.69489 + 4.13758i 0.408869 + 0.297061i
\(195\) −0.726463 + 0.527806i −0.0520231 + 0.0377970i
\(196\) 0 0
\(197\) 12.3035 0.876590 0.438295 0.898831i \(-0.355582\pi\)
0.438295 + 0.898831i \(0.355582\pi\)
\(198\) −4.97632 + 4.56193i −0.353652 + 0.324202i
\(199\) −15.2615 −1.08186 −0.540929 0.841068i \(-0.681927\pi\)
−0.540929 + 0.841068i \(0.681927\pi\)
\(200\) −4.03857 + 12.4294i −0.285570 + 0.878895i
\(201\) 0.635774 0.461917i 0.0448440 0.0325811i
\(202\) 12.0832 + 8.77892i 0.850168 + 0.617683i
\(203\) 0 0
\(204\) 1.15526 + 3.55553i 0.0808845 + 0.248937i
\(205\) 0.240885 + 0.175013i 0.0168242 + 0.0122235i
\(206\) −10.2139 + 7.42080i −0.711633 + 0.517032i
\(207\) 3.15351 9.70552i 0.219184 0.674580i
\(208\) −4.82212 −0.334354
\(209\) −4.01114 8.79663i −0.277456 0.608476i
\(210\) 0 0
\(211\) 2.76058 8.49620i 0.190046 0.584903i −0.809952 0.586496i \(-0.800507\pi\)
0.999999 + 0.00159295i \(0.000507051\pi\)
\(212\) −1.93952 + 1.40915i −0.133207 + 0.0967805i
\(213\) −4.65459 3.38176i −0.318928 0.231714i
\(214\) 1.29579 + 3.98802i 0.0885781 + 0.272615i
\(215\) −0.323742 0.996374i −0.0220790 0.0679521i
\(216\) −7.41570 5.38782i −0.504574 0.366595i
\(217\) 0 0
\(218\) −1.29714 + 3.99220i −0.0878537 + 0.270386i
\(219\) 3.45426 0.233417
\(220\) 0.896483 + 0.506952i 0.0604409 + 0.0341787i
\(221\) −28.3031 −1.90387
\(222\) −0.839469 + 2.58362i −0.0563415 + 0.173401i
\(223\) 0.578645 0.420410i 0.0387489 0.0281527i −0.568242 0.822861i \(-0.692376\pi\)
0.606991 + 0.794709i \(0.292376\pi\)
\(224\) 0 0
\(225\) 4.00503 + 12.3262i 0.267002 + 0.821747i
\(226\) 3.96331 + 12.1978i 0.263636 + 0.811387i
\(227\) −4.30528 3.12797i −0.285751 0.207611i 0.435671 0.900106i \(-0.356511\pi\)
−0.721422 + 0.692496i \(0.756511\pi\)
\(228\) 2.03397 1.47777i 0.134703 0.0978675i
\(229\) 2.04208 6.28489i 0.134945 0.415317i −0.860637 0.509219i \(-0.829934\pi\)
0.995581 + 0.0939024i \(0.0299341\pi\)
\(230\) 0.674356 0.0444657
\(231\) 0 0
\(232\) −9.96318 −0.654115
\(233\) −2.95332 + 9.08937i −0.193478 + 0.595464i 0.806513 + 0.591217i \(0.201352\pi\)
−0.999991 + 0.00424788i \(0.998648\pi\)
\(234\) 10.7524 7.81211i 0.702910 0.510694i
\(235\) 1.08831 + 0.790705i 0.0709936 + 0.0515799i
\(236\) −4.11102 12.6524i −0.267604 0.823602i
\(237\) 0.865066 + 2.66240i 0.0561921 + 0.172941i
\(238\) 0 0
\(239\) −21.7194 + 15.7801i −1.40491 + 1.02073i −0.410872 + 0.911693i \(0.634776\pi\)
−0.994038 + 0.109034i \(0.965224\pi\)
\(240\) −0.0313842 + 0.0965905i −0.00202584 + 0.00623489i
\(241\) −18.8663 −1.21529 −0.607643 0.794210i \(-0.707885\pi\)
−0.607643 + 0.794210i \(0.707885\pi\)
\(242\) 5.60806 6.45693i 0.360500 0.415067i
\(243\) −13.9443 −0.894525
\(244\) −4.15258 + 12.7803i −0.265842 + 0.818177i
\(245\) 0 0
\(246\) 0.520180 + 0.377933i 0.0331654 + 0.0240961i
\(247\) 5.88173 + 18.1021i 0.374245 + 1.15181i
\(248\) 5.62047 + 17.2980i 0.356900 + 1.09843i
\(249\) −5.64188 4.09907i −0.357540 0.259768i
\(250\) −1.39269 + 1.01185i −0.0880814 + 0.0639949i
\(251\) −9.07680 + 27.9355i −0.572923 + 1.76328i 0.0702229 + 0.997531i \(0.477629\pi\)
−0.643146 + 0.765744i \(0.722371\pi\)
\(252\) 0 0
\(253\) −2.57472 + 12.6691i −0.161871 + 0.796498i
\(254\) −1.55285 −0.0974348
\(255\) −0.184207 + 0.566931i −0.0115355 + 0.0355026i
\(256\) 10.8355 7.87245i 0.677218 0.492028i
\(257\) −13.6856 9.94320i −0.853687 0.620240i 0.0724730 0.997370i \(-0.476911\pi\)
−0.926160 + 0.377130i \(0.876911\pi\)
\(258\) −0.699104 2.15162i −0.0435243 0.133954i
\(259\) 0 0
\(260\) −1.64035 1.19178i −0.101730 0.0739114i
\(261\) −7.99343 + 5.80757i −0.494781 + 0.359480i
\(262\) 0.329173 1.01309i 0.0203364 0.0625889i
\(263\) −8.18034 −0.504421 −0.252211 0.967672i \(-0.581158\pi\)
−0.252211 + 0.967672i \(0.581158\pi\)
\(264\) 4.71038 + 2.66367i 0.289904 + 0.163938i
\(265\) −0.382263 −0.0234822
\(266\) 0 0
\(267\) −3.96078 + 2.87768i −0.242396 + 0.176111i
\(268\) 1.43558 + 1.04301i 0.0876917 + 0.0637118i
\(269\) 1.93048 + 5.94140i 0.117703 + 0.362254i 0.992501 0.122234i \(-0.0390059\pi\)
−0.874798 + 0.484488i \(0.839006\pi\)
\(270\) −0.185623 0.571288i −0.0112966 0.0347675i
\(271\) 6.36444 + 4.62403i 0.386612 + 0.280890i 0.764066 0.645138i \(-0.223200\pi\)
−0.377454 + 0.926028i \(0.623200\pi\)
\(272\) −2.58978 + 1.88159i −0.157029 + 0.114088i
\(273\) 0 0
\(274\) −1.94312 −0.117388
\(275\) −6.81202 14.9391i −0.410780 0.900862i
\(276\) −3.36190 −0.202363
\(277\) 3.72293 11.4580i 0.223689 0.688444i −0.774733 0.632289i \(-0.782116\pi\)
0.998422 0.0561556i \(-0.0178843\pi\)
\(278\) 2.99566 2.17648i 0.179668 0.130536i
\(279\) 14.5924 + 10.6020i 0.873622 + 0.634724i
\(280\) 0 0
\(281\) 6.53723 + 20.1195i 0.389978 + 1.20023i 0.932804 + 0.360384i \(0.117354\pi\)
−0.542826 + 0.839846i \(0.682646\pi\)
\(282\) 2.35015 + 1.70749i 0.139950 + 0.101679i
\(283\) −20.2281 + 14.6966i −1.20244 + 0.873623i −0.994522 0.104524i \(-0.966668\pi\)
−0.207916 + 0.978147i \(0.566668\pi\)
\(284\) 4.01448 12.3553i 0.238216 0.733153i
\(285\) 0.400878 0.0237460
\(286\) −12.4113 + 11.3777i −0.733894 + 0.672780i
\(287\) 0 0
\(288\) 4.73607 14.5761i 0.279075 0.858906i
\(289\) −1.44723 + 1.05147i −0.0851312 + 0.0618515i
\(290\) −0.528215 0.383770i −0.0310178 0.0225358i
\(291\) −1.72914 5.32176i −0.101364 0.311967i
\(292\) 2.41024 + 7.41796i 0.141049 + 0.434104i
\(293\) −0.368173 0.267494i −0.0215089 0.0156271i 0.576979 0.816759i \(-0.304231\pi\)
−0.598488 + 0.801132i \(0.704231\pi\)
\(294\) 0 0
\(295\) 0.655503 2.01743i 0.0381648 0.117459i
\(296\) −14.9251 −0.867502
\(297\) 11.4415 1.30608i 0.663901 0.0757864i
\(298\) 5.62110 0.325621
\(299\) 7.86507 24.2062i 0.454849 1.39988i
\(300\) 3.45425 2.50966i 0.199431 0.144895i
\(301\) 0 0
\(302\) −1.95561 6.01874i −0.112533 0.346339i
\(303\) −3.66881 11.2915i −0.210768 0.648677i
\(304\) 1.74162 + 1.26536i 0.0998885 + 0.0725732i
\(305\) −1.73348 + 1.25945i −0.0992588 + 0.0721157i
\(306\) 2.72646 8.39119i 0.155862 0.479692i
\(307\) 8.03578 0.458626 0.229313 0.973353i \(-0.426352\pi\)
0.229313 + 0.973353i \(0.426352\pi\)
\(308\) 0 0
\(309\) 10.0358 0.570918
\(310\) −0.368322 + 1.13358i −0.0209193 + 0.0643829i
\(311\) 0.110807 0.0805059i 0.00628328 0.00456507i −0.584639 0.811293i \(-0.698764\pi\)
0.590922 + 0.806728i \(0.298764\pi\)
\(312\) −8.61887 6.26198i −0.487948 0.354515i
\(313\) 4.72485 + 14.5416i 0.267064 + 0.821939i 0.991211 + 0.132293i \(0.0422340\pi\)
−0.724146 + 0.689646i \(0.757766\pi\)
\(314\) 4.84150 + 14.9006i 0.273221 + 0.840889i
\(315\) 0 0
\(316\) −5.11385 + 3.71543i −0.287676 + 0.209009i
\(317\) −10.1953 + 31.3778i −0.572622 + 1.76235i 0.0715138 + 0.997440i \(0.477217\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(318\) −0.825478 −0.0462905
\(319\) 9.22661 8.45828i 0.516591 0.473573i
\(320\) 0.684115 0.0382432
\(321\) 1.03004 3.17014i 0.0574912 0.176940i
\(322\) 0 0
\(323\) 10.2223 + 7.42692i 0.568783 + 0.413245i
\(324\) −2.46160 7.57602i −0.136756 0.420890i
\(325\) 9.98880 + 30.7424i 0.554079 + 1.70528i
\(326\) 4.67628 + 3.39752i 0.258995 + 0.188171i
\(327\) 2.69951 1.96131i 0.149283 0.108461i
\(328\) −1.09162 + 3.35966i −0.0602747 + 0.185506i
\(329\) 0 0
\(330\) 0.147127 + 0.322657i 0.00809908 + 0.0177617i
\(331\) 29.5335 1.62331 0.811653 0.584140i \(-0.198568\pi\)
0.811653 + 0.584140i \(0.198568\pi\)
\(332\) 4.86600 14.9760i 0.267056 0.821915i
\(333\) −11.9743 + 8.69986i −0.656190 + 0.476750i
\(334\) 1.39079 + 1.01047i 0.0761008 + 0.0552905i
\(335\) 0.0874331 + 0.269091i 0.00477698 + 0.0147020i
\(336\) 0 0
\(337\) −4.55497 3.30938i −0.248125 0.180273i 0.456770 0.889585i \(-0.349006\pi\)
−0.704895 + 0.709311i \(0.749006\pi\)
\(338\) 18.6403 13.5430i 1.01390 0.736641i
\(339\) 3.15050 9.69624i 0.171112 0.526627i
\(340\) −1.34600 −0.0729974
\(341\) −19.8902 11.2477i −1.07711 0.609096i
\(342\) −5.93344 −0.320844
\(343\) 0 0
\(344\) 10.0557 7.30586i 0.542165 0.393906i
\(345\) −0.433679 0.315086i −0.0233485 0.0169637i
\(346\) −2.48958 7.66214i −0.133841 0.411919i
\(347\) 2.69791 + 8.30331i 0.144831 + 0.445745i 0.996989 0.0775398i \(-0.0247065\pi\)
−0.852158 + 0.523285i \(0.824706\pi\)
\(348\) 2.63333 + 1.91323i 0.141162 + 0.102560i
\(349\) 14.9401 10.8546i 0.799724 0.581034i −0.111109 0.993808i \(-0.535440\pi\)
0.910833 + 0.412774i \(0.135440\pi\)
\(350\) 0 0
\(351\) −22.6715 −1.21011
\(352\) −3.86681 + 19.0269i −0.206102 + 1.01414i
\(353\) 23.4857 1.25002 0.625009 0.780618i \(-0.285095\pi\)
0.625009 + 0.780618i \(0.285095\pi\)
\(354\) 1.41553 4.35654i 0.0752343 0.231547i
\(355\) 1.67583 1.21756i 0.0889439 0.0646215i
\(356\) −8.94343 6.49778i −0.474001 0.344382i
\(357\) 0 0
\(358\) 5.62425 + 17.3097i 0.297251 + 0.914844i
\(359\) −12.0391 8.74695i −0.635402 0.461647i 0.222865 0.974849i \(-0.428459\pi\)
−0.858267 + 0.513203i \(0.828459\pi\)
\(360\) 1.24420 0.903967i 0.0655753 0.0476432i
\(361\) −3.24552 + 9.98870i −0.170817 + 0.525721i
\(362\) −10.6641 −0.560490
\(363\) −6.62347 + 1.53215i −0.347642 + 0.0804168i
\(364\) 0 0
\(365\) −0.384314 + 1.18280i −0.0201159 + 0.0619104i
\(366\) −3.74336 + 2.71971i −0.195669 + 0.142162i
\(367\) −27.6894 20.1175i −1.44537 1.05012i −0.986885 0.161424i \(-0.948391\pi\)
−0.458487 0.888701i \(-0.651609\pi\)
\(368\) −0.889558 2.73778i −0.0463714 0.142717i
\(369\) 1.08255 + 3.33176i 0.0563555 + 0.173444i
\(370\) −0.791277 0.574896i −0.0411365 0.0298874i
\(371\) 0 0
\(372\) 1.83621 5.65128i 0.0952032 0.293005i
\(373\) 3.01739 0.156235 0.0781173 0.996944i \(-0.475109\pi\)
0.0781173 + 0.996944i \(0.475109\pi\)
\(374\) −2.22605 + 10.9534i −0.115106 + 0.566388i
\(375\) 1.36841 0.0706646
\(376\) −4.93191 + 15.1788i −0.254344 + 0.782789i
\(377\) −19.9361 + 14.4845i −1.02676 + 0.745987i
\(378\) 0 0
\(379\) −1.89252 5.82457i −0.0972121 0.299188i 0.890612 0.454764i \(-0.150277\pi\)
−0.987824 + 0.155576i \(0.950277\pi\)
\(380\) 0.279717 + 0.860879i 0.0143492 + 0.0441622i
\(381\) 0.998641 + 0.725555i 0.0511619 + 0.0371713i
\(382\) −7.56367 + 5.49532i −0.386991 + 0.281165i
\(383\) −1.35689 + 4.17607i −0.0693338 + 0.213387i −0.979720 0.200373i \(-0.935785\pi\)
0.910386 + 0.413760i \(0.135785\pi\)
\(384\) −5.75876 −0.293875
\(385\) 0 0
\(386\) −12.3495 −0.628573
\(387\) 3.80902 11.7229i 0.193623 0.595911i
\(388\) 10.2218 7.42661i 0.518936 0.377029i
\(389\) −8.49145 6.16940i −0.430533 0.312801i 0.351329 0.936252i \(-0.385730\pi\)
−0.781862 + 0.623451i \(0.785730\pi\)
\(390\) −0.215740 0.663978i −0.0109244 0.0336218i
\(391\) −5.22119 16.0692i −0.264047 0.812654i
\(392\) 0 0
\(393\) −0.685047 + 0.497716i −0.0345560 + 0.0251064i
\(394\) −2.95600 + 9.09762i −0.148921 + 0.458331i
\(395\) −1.00789 −0.0507127
\(396\) 5.02734 + 11.0252i 0.252634 + 0.554038i
\(397\) −11.3888 −0.571589 −0.285794 0.958291i \(-0.592257\pi\)
−0.285794 + 0.958291i \(0.592257\pi\)
\(398\) 3.66666 11.2848i 0.183793 0.565657i
\(399\) 0 0
\(400\) 2.95774 + 2.14893i 0.147887 + 0.107446i
\(401\) −1.46009 4.49370i −0.0729135 0.224405i 0.907958 0.419061i \(-0.137641\pi\)
−0.980871 + 0.194657i \(0.937641\pi\)
\(402\) 0.188807 + 0.581090i 0.00941686 + 0.0289821i
\(403\) 36.3943 + 26.4420i 1.81293 + 1.31717i
\(404\) 21.6882 15.7574i 1.07903 0.783961i
\(405\) 0.392503 1.20800i 0.0195036 0.0600260i
\(406\) 0 0
\(407\) 13.8217 12.6707i 0.685114 0.628062i
\(408\) −7.07230 −0.350131
\(409\) −0.761863 + 2.34477i −0.0376717 + 0.115942i −0.968124 0.250472i \(-0.919414\pi\)
0.930452 + 0.366413i \(0.119414\pi\)
\(410\) −0.187285 + 0.136070i −0.00924932 + 0.00672003i
\(411\) 1.24962 + 0.907902i 0.0616392 + 0.0447835i
\(412\) 7.00259 + 21.5518i 0.344993 + 1.06178i
\(413\) 0 0
\(414\) 6.41892 + 4.66362i 0.315472 + 0.229204i
\(415\) 2.03129 1.47582i 0.0997122 0.0724452i
\(416\) 11.8121 36.3538i 0.579134 1.78239i
\(417\) −2.94345 −0.144141
\(418\) 7.46820 0.852519i 0.365282 0.0416981i
\(419\) 14.3399 0.700548 0.350274 0.936647i \(-0.386088\pi\)
0.350274 + 0.936647i \(0.386088\pi\)
\(420\) 0 0
\(421\) 14.0087 10.1779i 0.682744 0.496043i −0.191523 0.981488i \(-0.561343\pi\)
0.874267 + 0.485446i \(0.161343\pi\)
\(422\) 5.61911 + 4.08253i 0.273534 + 0.198734i
\(423\) 4.89094 + 15.0528i 0.237806 + 0.731891i
\(424\) −1.40146 4.31326i −0.0680611 0.209470i
\(425\) 17.3602 + 12.6130i 0.842096 + 0.611818i
\(426\) 3.61887 2.62927i 0.175335 0.127388i
\(427\) 0 0
\(428\) 7.52653 0.363808
\(429\) 13.2978 1.51799i 0.642024 0.0732891i
\(430\) 0.814531 0.0392802
\(431\) 8.61919 26.5272i 0.415172 1.27777i −0.496925 0.867794i \(-0.665538\pi\)
0.912097 0.409975i \(-0.134462\pi\)
\(432\) −2.07448 + 1.50720i −0.0998085 + 0.0725151i
\(433\) −23.9040 17.3673i −1.14875 0.834619i −0.160440 0.987046i \(-0.551291\pi\)
−0.988315 + 0.152426i \(0.951291\pi\)
\(434\) 0 0
\(435\) 0.160382 + 0.493605i 0.00768973 + 0.0236666i
\(436\) 6.09548 + 4.42862i 0.291920 + 0.212093i
\(437\) −9.19251 + 6.67875i −0.439738 + 0.319488i
\(438\) −0.829907 + 2.55419i −0.0396545 + 0.122044i
\(439\) 33.6655 1.60677 0.803384 0.595461i \(-0.203030\pi\)
0.803384 + 0.595461i \(0.203030\pi\)
\(440\) −1.43615 + 1.31656i −0.0684658 + 0.0627644i
\(441\) 0 0
\(442\) 6.79997 20.9282i 0.323442 0.995451i
\(443\) −8.35449 + 6.06989i −0.396934 + 0.288389i −0.768291 0.640101i \(-0.778893\pi\)
0.371357 + 0.928490i \(0.378893\pi\)
\(444\) 3.94479 + 2.86606i 0.187211 + 0.136017i
\(445\) −0.544696 1.67640i −0.0258211 0.0794691i
\(446\) 0.171842 + 0.528874i 0.00813694 + 0.0250429i
\(447\) −3.61493 2.62640i −0.170980 0.124224i
\(448\) 0 0
\(449\) −0.852224 + 2.62287i −0.0402189 + 0.123781i −0.969150 0.246471i \(-0.920729\pi\)
0.928931 + 0.370253i \(0.120729\pi\)
\(450\) −10.0766 −0.475016
\(451\) −1.84128 4.03802i −0.0867025 0.190143i
\(452\) 23.0208 1.08281
\(453\) −1.55454 + 4.78439i −0.0730387 + 0.224790i
\(454\) 3.34729 2.43195i 0.157096 0.114137i
\(455\) 0 0
\(456\) 1.46971 + 4.52331i 0.0688255 + 0.211823i
\(457\) −12.4628 38.3566i −0.582986 1.79425i −0.607213 0.794539i \(-0.707713\pi\)
0.0242276 0.999706i \(-0.492287\pi\)
\(458\) 4.15662 + 3.01996i 0.194226 + 0.141114i
\(459\) −12.1760 + 8.84638i −0.568327 + 0.412914i
\(460\) 0.374038 1.15117i 0.0174396 0.0536736i
\(461\) 34.2251 1.59402 0.797011 0.603965i \(-0.206413\pi\)
0.797011 + 0.603965i \(0.206413\pi\)
\(462\) 0 0
\(463\) 0.707349 0.0328733 0.0164367 0.999865i \(-0.494768\pi\)
0.0164367 + 0.999865i \(0.494768\pi\)
\(464\) −0.861267 + 2.65071i −0.0399833 + 0.123056i
\(465\) 0.766520 0.556910i 0.0355465 0.0258261i
\(466\) −6.01142 4.36755i −0.278473 0.202323i
\(467\) 8.83555 + 27.1930i 0.408860 + 1.25834i 0.917629 + 0.397439i \(0.130101\pi\)
−0.508768 + 0.860904i \(0.669899\pi\)
\(468\) −7.37184 22.6882i −0.340764 1.04876i
\(469\) 0 0
\(470\) −0.846145 + 0.614760i −0.0390298 + 0.0283568i
\(471\) 3.84858 11.8447i 0.177333 0.545775i
\(472\) 25.1669 1.15840
\(473\) −3.10991 + 15.3025i −0.142994 + 0.703611i
\(474\) −2.17650 −0.0999699
\(475\) 4.45933 13.7244i 0.204608 0.629719i
\(476\) 0 0
\(477\) −3.63860 2.64360i −0.166600 0.121042i
\(478\) −6.45006 19.8512i −0.295019 0.907975i
\(479\) 1.57511 + 4.84769i 0.0719686 + 0.221497i 0.980571 0.196166i \(-0.0628493\pi\)
−0.908602 + 0.417663i \(0.862849\pi\)
\(480\) −0.651315 0.473208i −0.0297283 0.0215989i
\(481\) −29.8648 + 21.6980i −1.36172 + 0.989344i
\(482\) 4.53274 13.9503i 0.206461 0.635421i
\(483\) 0 0
\(484\) −7.91185 13.1547i −0.359629 0.597942i
\(485\) 2.01464 0.0914800
\(486\) 3.35019 10.3108i 0.151968 0.467709i
\(487\) −23.6138 + 17.1564i −1.07004 + 0.777433i −0.975920 0.218128i \(-0.930005\pi\)
−0.0941240 + 0.995560i \(0.530005\pi\)
\(488\) −20.5663 14.9423i −0.930992 0.676405i
\(489\) −1.41986 4.36989i −0.0642084 0.197613i
\(490\) 0 0
\(491\) −24.3870 17.7182i −1.10057 0.799610i −0.119416 0.992844i \(-0.538102\pi\)
−0.981153 + 0.193235i \(0.938102\pi\)
\(492\) 0.933679 0.678357i 0.0420935 0.0305827i
\(493\) −5.05514 + 15.5581i −0.227672 + 0.700703i
\(494\) −14.7984 −0.665810
\(495\) −0.384795 + 1.89341i −0.0172952 + 0.0851023i
\(496\) 5.08801 0.228458
\(497\) 0 0
\(498\) 4.38647 3.18696i 0.196563 0.142811i
\(499\) −4.81450 3.49794i −0.215526 0.156589i 0.474784 0.880102i \(-0.342526\pi\)
−0.690311 + 0.723513i \(0.742526\pi\)
\(500\) 0.954823 + 2.93864i 0.0427010 + 0.131420i
\(501\) −0.422287 1.29967i −0.0188664 0.0580648i
\(502\) −18.4757 13.4233i −0.824609 0.599113i
\(503\) −4.02773 + 2.92632i −0.179588 + 0.130478i −0.673947 0.738779i \(-0.735403\pi\)
0.494360 + 0.869257i \(0.335403\pi\)
\(504\) 0 0
\(505\) 4.27456 0.190216
\(506\) −8.74933 4.94765i −0.388955 0.219950i
\(507\) −18.3154 −0.813416
\(508\) −0.861305 + 2.65083i −0.0382142 + 0.117611i
\(509\) −17.2551 + 12.5366i −0.764821 + 0.555675i −0.900385 0.435094i \(-0.856715\pi\)
0.135565 + 0.990769i \(0.456715\pi\)
\(510\) −0.374949 0.272417i −0.0166030 0.0120628i
\(511\) 0 0
\(512\) −2.54091 7.82012i −0.112293 0.345604i
\(513\) 8.18830 + 5.94915i 0.361522 + 0.262661i
\(514\) 10.6404 7.73068i 0.469327 0.340986i
\(515\) −1.11656 + 3.43643i −0.0492017 + 0.151427i
\(516\) −4.06072 −0.178763
\(517\) −8.31884 18.2436i −0.365862 0.802354i
\(518\) 0 0
\(519\) −1.97900 + 6.09075i −0.0868686 + 0.267354i
\(520\) 3.10312 2.25455i 0.136081 0.0988686i
\(521\) −17.9103 13.0126i −0.784664 0.570092i 0.121711 0.992566i \(-0.461162\pi\)
−0.906375 + 0.422473i \(0.861162\pi\)
\(522\) −2.37383 7.30590i −0.103900 0.319771i
\(523\) −1.51773 4.67108i −0.0663655 0.204252i 0.912375 0.409356i \(-0.134247\pi\)
−0.978740 + 0.205104i \(0.934247\pi\)
\(524\) −1.54683 1.12384i −0.0675737 0.0490952i
\(525\) 0 0
\(526\) 1.96537 6.04880i 0.0856944 0.263740i
\(527\) 29.8637 1.30088
\(528\) 1.11586 1.02294i 0.0485615 0.0445176i
\(529\) −7.80592 −0.339388
\(530\) 0.0918410 0.282657i 0.00398932 0.0122779i
\(531\) 20.1913 14.6698i 0.876228 0.636617i
\(532\) 0 0
\(533\) 2.69996 + 8.30962i 0.116948 + 0.359929i
\(534\) −1.17624 3.62011i −0.0509010 0.156657i
\(535\) 0.970907 + 0.705405i 0.0419760 + 0.0304973i
\(536\) −2.71574 + 1.97310i −0.117302 + 0.0852250i
\(537\) 4.47080 13.7597i 0.192929 0.593775i
\(538\) −4.85707 −0.209403
\(539\) 0 0
\(540\) −1.07818 −0.0463977
\(541\) 5.99013 18.4357i 0.257536 0.792614i −0.735784 0.677217i \(-0.763186\pi\)
0.993319 0.115397i \(-0.0368141\pi\)
\(542\) −4.94825 + 3.59511i −0.212546 + 0.154423i
\(543\) 6.85805 + 4.98266i 0.294307 + 0.213827i
\(544\) −7.84139 24.1333i −0.336197 1.03471i
\(545\) 0.371242 + 1.14257i 0.0159023 + 0.0489422i
\(546\) 0 0
\(547\) −11.6904 + 8.49354i −0.499843 + 0.363158i −0.808957 0.587868i \(-0.799968\pi\)
0.309114 + 0.951025i \(0.399968\pi\)
\(548\) −1.07777 + 3.31703i −0.0460400 + 0.141697i
\(549\) −25.2102 −1.07594
\(550\) 12.6831 1.44781i 0.540808 0.0617349i
\(551\) 11.0012 0.468667
\(552\) 1.96530 6.04858i 0.0836489 0.257445i
\(553\) 0 0
\(554\) 7.57795 + 5.50570i 0.321956 + 0.233915i
\(555\) 0.240256 + 0.739431i 0.0101983 + 0.0313871i
\(556\) −2.05382 6.32100i −0.0871012 0.268070i
\(557\) −14.9432 10.8569i −0.633164 0.460021i 0.224331 0.974513i \(-0.427980\pi\)
−0.857495 + 0.514492i \(0.827980\pi\)
\(558\) −11.3453 + 8.24287i −0.480286 + 0.348949i
\(559\) 9.49993 29.2378i 0.401804 1.23663i
\(560\) 0 0
\(561\) 6.54945 6.00405i 0.276518 0.253491i
\(562\) −16.4476 −0.693801
\(563\) −9.66724 + 29.7527i −0.407426 + 1.25393i 0.511427 + 0.859327i \(0.329117\pi\)
−0.918853 + 0.394600i \(0.870883\pi\)
\(564\) 4.21833 3.06479i 0.177624 0.129051i
\(565\) 2.96963 + 2.15757i 0.124933 + 0.0907695i
\(566\) −6.00720 18.4883i −0.252502 0.777120i
\(567\) 0 0
\(568\) 19.8823 + 14.4454i 0.834244 + 0.606114i
\(569\) −1.40449 + 1.02042i −0.0588794 + 0.0427784i −0.616836 0.787092i \(-0.711586\pi\)
0.557956 + 0.829870i \(0.311586\pi\)
\(570\) −0.0963134 + 0.296422i −0.00403412 + 0.0124158i
\(571\) 12.5309 0.524403 0.262201 0.965013i \(-0.415551\pi\)
0.262201 + 0.965013i \(0.415551\pi\)
\(572\) 12.5385 + 27.4976i 0.524262 + 1.14973i
\(573\) 7.43182 0.310469
\(574\) 0 0
\(575\) −15.6114 + 11.3424i −0.651042 + 0.473009i
\(576\) 6.51180 + 4.73110i 0.271325 + 0.197129i
\(577\) −6.23893 19.2015i −0.259730 0.799368i −0.992861 0.119280i \(-0.961942\pi\)
0.733130 0.680088i \(-0.238058\pi\)
\(578\) −0.429788 1.32275i −0.0178768 0.0550192i
\(579\) 7.94196 + 5.77017i 0.330057 + 0.239800i
\(580\) −0.948101 + 0.688835i −0.0393677 + 0.0286023i
\(581\) 0 0
\(582\) 4.35051 0.180334
\(583\) 4.95961 + 2.80461i 0.205406 + 0.116155i
\(584\) −14.7550 −0.610568
\(585\) 1.17544 3.61764i 0.0485986 0.149571i
\(586\) 0.286249 0.207972i 0.0118248 0.00859125i
\(587\) −0.00677611 0.00492314i −0.000279680 0.000203200i 0.587645 0.809119i \(-0.300055\pi\)
−0.587925 + 0.808915i \(0.700055\pi\)
\(588\) 0 0
\(589\) −6.20604 19.1002i −0.255716 0.787012i
\(590\) 1.33426 + 0.969399i 0.0549307 + 0.0399095i
\(591\) 6.15177 4.46952i 0.253050 0.183851i
\(592\) −1.29020 + 3.97082i −0.0530267 + 0.163200i
\(593\) 0.439298 0.0180398 0.00901989 0.999959i \(-0.497129\pi\)
0.00901989 + 0.999959i \(0.497129\pi\)
\(594\) −1.78312 + 8.77397i −0.0731624 + 0.360001i
\(595\) 0 0
\(596\) 3.11779 9.59558i 0.127710 0.393050i
\(597\) −7.63075 + 5.54406i −0.312306 + 0.226903i
\(598\) 16.0092 + 11.6314i 0.654664 + 0.475641i
\(599\) 13.9572 + 42.9558i 0.570275 + 1.75512i 0.651734 + 0.758448i \(0.274042\pi\)
−0.0814591 + 0.996677i \(0.525958\pi\)
\(600\) 2.49598 + 7.68182i 0.101898 + 0.313609i
\(601\) 9.01541 + 6.55008i 0.367746 + 0.267183i 0.756276 0.654253i \(-0.227017\pi\)
−0.388529 + 0.921436i \(0.627017\pi\)
\(602\) 0 0
\(603\) −1.02870 + 3.16603i −0.0418921 + 0.128931i
\(604\) −11.3591 −0.462194
\(605\) 0.212282 2.43845i 0.00863047 0.0991371i
\(606\) 9.23071 0.374972
\(607\) 11.0318 33.9525i 0.447768 1.37809i −0.431651 0.902041i \(-0.642069\pi\)
0.879419 0.476049i \(-0.157931\pi\)
\(608\) −13.8057 + 10.0304i −0.559894 + 0.406787i
\(609\) 0 0
\(610\) −0.514796 1.58438i −0.0208435 0.0641496i
\(611\) 12.1983 + 37.5426i 0.493491 + 1.51881i
\(612\) −12.8121 9.30850i −0.517897 0.376274i
\(613\) −13.9135 + 10.1087i −0.561960 + 0.408288i −0.832176 0.554512i \(-0.812905\pi\)
0.270216 + 0.962800i \(0.412905\pi\)
\(614\) −1.93064 + 5.94191i −0.0779144 + 0.239796i
\(615\) 0.184020 0.00742040
\(616\) 0 0
\(617\) −16.8852 −0.679774 −0.339887 0.940466i \(-0.610389\pi\)
−0.339887 + 0.940466i \(0.610389\pi\)
\(618\) −2.41117 + 7.42080i −0.0969913 + 0.298509i
\(619\) 25.1355 18.2620i 1.01028 0.734013i 0.0460139 0.998941i \(-0.485348\pi\)
0.964268 + 0.264928i \(0.0853481\pi\)
\(620\) 1.73080 + 1.25750i 0.0695106 + 0.0505024i
\(621\) −4.18231 12.8718i −0.167830 0.516529i
\(622\) 0.0329066 + 0.101276i 0.00131943 + 0.00406080i
\(623\) 0 0
\(624\) −2.41106 + 1.75174i −0.0965196 + 0.0701256i
\(625\) 7.49668 23.0724i 0.299867 0.922896i
\(626\) −11.8877 −0.475127
\(627\) −5.20113 2.94118i −0.207713 0.117460i
\(628\) 28.1217 1.12218
\(629\) −7.57271 + 23.3064i −0.301944 + 0.929287i
\(630\) 0 0
\(631\) −5.86832 4.26359i −0.233614 0.169731i 0.464819 0.885406i \(-0.346119\pi\)
−0.698434 + 0.715675i \(0.746119\pi\)
\(632\) −3.69517 11.3726i −0.146986 0.452376i
\(633\) −1.70613 5.25094i −0.0678128 0.208706i
\(634\) −20.7522 15.0774i −0.824176 0.598799i
\(635\) −0.359549 + 0.261227i −0.0142683 + 0.0103665i
\(636\) −0.457859 + 1.40915i −0.0181553 + 0.0558763i
\(637\) 0 0
\(638\) 4.03757 + 8.85460i 0.159849 + 0.350557i
\(639\) 24.3718 0.964132
\(640\) 0.640707 1.97189i 0.0253262 0.0779459i
\(641\) 16.7870 12.1965i 0.663047 0.481732i −0.204643 0.978837i \(-0.565603\pi\)
0.867691 + 0.497104i \(0.165603\pi\)
\(642\) 2.09663 + 1.52329i 0.0827472 + 0.0601194i
\(643\) −2.19750 6.76322i −0.0866611 0.266715i 0.898330 0.439322i \(-0.144781\pi\)
−0.984991 + 0.172606i \(0.944781\pi\)
\(644\) 0 0
\(645\) −0.523825 0.380581i −0.0206256 0.0149854i
\(646\) −7.94766 + 5.77431i −0.312696 + 0.227187i
\(647\) −8.52234 + 26.2291i −0.335048 + 1.03117i 0.631651 + 0.775253i \(0.282378\pi\)
−0.966699 + 0.255918i \(0.917622\pi\)
\(648\) 15.0694 0.591984
\(649\) −23.3063 + 21.3655i −0.914852 + 0.838669i
\(650\) −25.1317 −0.985748
\(651\) 0 0
\(652\) 8.39353 6.09826i 0.328716 0.238826i
\(653\) −13.0690 9.49516i −0.511428 0.371574i 0.301937 0.953328i \(-0.402367\pi\)
−0.813365 + 0.581753i \(0.802367\pi\)
\(654\) 0.801680 + 2.46732i 0.0313482 + 0.0964797i
\(655\) −0.0942092 0.289946i −0.00368106 0.0113291i
\(656\) 0.799474 + 0.580852i 0.0312142 + 0.0226785i
\(657\) −11.8379 + 8.60076i −0.461842 + 0.335548i
\(658\) 0 0
\(659\) −13.2085 −0.514531 −0.257266 0.966341i \(-0.582822\pi\)
−0.257266 + 0.966341i \(0.582822\pi\)
\(660\) 0.632403 0.0721907i 0.0246162 0.00281002i
\(661\) 4.90660 0.190845 0.0954223 0.995437i \(-0.469580\pi\)
0.0954223 + 0.995437i \(0.469580\pi\)
\(662\) −7.09559 + 21.8380i −0.275778 + 0.848757i
\(663\) −14.1515 + 10.2817i −0.549600 + 0.399308i
\(664\) 24.0996 + 17.5094i 0.935245 + 0.679495i
\(665\) 0 0
\(666\) −3.55605 10.9444i −0.137794 0.424087i
\(667\) −11.9013 8.64682i −0.460821 0.334806i
\(668\) 2.49635 1.81371i 0.0965869 0.0701745i
\(669\) 0.136599 0.420410i 0.00528124 0.0162540i
\(670\) −0.219981 −0.00849861
\(671\) 31.7311 3.62221i 1.22497 0.139834i
\(672\) 0 0
\(673\) −9.26654 + 28.5195i −0.357199 + 1.09935i 0.597524 + 0.801851i \(0.296151\pi\)
−0.954723 + 0.297495i \(0.903849\pi\)
\(674\) 3.54142 2.57299i 0.136410 0.0991079i
\(675\) 13.9060 + 10.1033i 0.535242 + 0.388876i
\(676\) −12.7797 39.3320i −0.491528 1.51277i
\(677\) −3.89019 11.9728i −0.149512 0.460151i 0.848051 0.529914i \(-0.177776\pi\)
−0.997564 + 0.0697626i \(0.977776\pi\)
\(678\) 6.41278 + 4.65916i 0.246281 + 0.178934i
\(679\) 0 0
\(680\) 0.786849 2.42167i 0.0301743 0.0928668i
\(681\) −3.28894 −0.126033
\(682\) 13.0956 12.0051i 0.501457 0.459699i
\(683\) −28.5342 −1.09183 −0.545916 0.837840i \(-0.683818\pi\)
−0.545916 + 0.837840i \(0.683818\pi\)
\(684\) −3.29104 + 10.1288i −0.125836 + 0.387283i
\(685\) −0.449911 + 0.326879i −0.0171902 + 0.0124894i
\(686\) 0 0
\(687\) −1.26208 3.88427i −0.0481513 0.148194i
\(688\) −1.07447 3.30687i −0.0409636 0.126073i
\(689\) −9.07491 6.59331i −0.345726 0.251185i
\(690\) 0.337178 0.244974i 0.0128362 0.00932601i
\(691\) −7.84107 + 24.1323i −0.298288 + 0.918037i 0.683809 + 0.729661i \(0.260322\pi\)
−0.982097 + 0.188376i \(0.939678\pi\)
\(692\) −14.4606 −0.549711
\(693\) 0 0
\(694\) −6.78791 −0.257666
\(695\) 0.327482 1.00788i 0.0124221 0.0382312i
\(696\) −4.98159 + 3.61934i −0.188827 + 0.137191i
\(697\) 4.69245 + 3.40927i 0.177739 + 0.129135i
\(698\) 4.43679 + 13.6551i 0.167935 + 0.516851i
\(699\) 1.82525 + 5.61754i 0.0690373 + 0.212475i
\(700\) 0 0
\(701\) 36.9738 26.8630i 1.39648 1.01460i 0.401363 0.915919i \(-0.368537\pi\)
0.995119 0.0986843i \(-0.0314634\pi\)
\(702\) 5.44695 16.7640i 0.205582 0.632716i
\(703\) 16.4800 0.621556
\(704\) −8.87594 5.01925i −0.334525 0.189170i
\(705\) 0.831396 0.0313122
\(706\) −5.64257 + 17.3661i −0.212361 + 0.653580i
\(707\) 0 0
\(708\) −6.65177 4.83279i −0.249989 0.181627i
\(709\) 11.9065 + 36.6446i 0.447160 + 1.37622i 0.880098 + 0.474793i \(0.157477\pi\)
−0.432938 + 0.901424i \(0.642523\pi\)
\(710\) 0.497676 + 1.53169i 0.0186774 + 0.0574833i
\(711\) −9.59373 6.97025i −0.359793 0.261405i
\(712\) 16.9187 12.2921i 0.634054 0.460667i
\(713\) −8.29874 + 25.5409i −0.310790 + 0.956515i
\(714\) 0 0
\(715\) −0.959703 + 4.72228i −0.0358908 + 0.176603i
\(716\) 32.6683 1.22087
\(717\) −5.12725 + 15.7801i −0.191481 + 0.589317i
\(718\) 9.36025 6.80062i 0.349321 0.253797i
\(719\) 4.61312 + 3.35163i 0.172040 + 0.124995i 0.670473 0.741934i \(-0.266091\pi\)
−0.498433 + 0.866928i \(0.666091\pi\)
\(720\) −0.132945 0.409164i −0.00495458 0.0152486i
\(721\) 0 0
\(722\) −6.60620 4.79969i −0.245857 0.178626i
\(723\) −9.43316 + 6.85359i −0.350823 + 0.254888i
\(724\) −5.91491 + 18.2042i −0.219826 + 0.676555i
\(725\) 18.6831 0.693872
\(726\) 0.458411 5.26571i 0.0170132 0.195429i
\(727\) −11.8221 −0.438458 −0.219229 0.975673i \(-0.570354\pi\)
−0.219229 + 0.975673i \(0.570354\pi\)
\(728\) 0 0
\(729\) 6.88197 5.00004i 0.254888 0.185187i
\(730\) −0.782263 0.568347i −0.0289529 0.0210355i
\(731\) −6.30649 19.4094i −0.233254 0.717882i
\(732\) 2.56644 + 7.89868i 0.0948582 + 0.291944i
\(733\) 7.12900 + 5.17952i 0.263316 + 0.191310i 0.711607 0.702577i \(-0.247967\pi\)
−0.448292 + 0.893887i \(0.647967\pi\)
\(734\) 21.5280 15.6410i 0.794614 0.577321i
\(735\) 0 0
\(736\) 22.8190 0.841121
\(737\) 0.839897 4.13277i 0.0309380 0.152232i
\(738\) −2.72370 −0.100261
\(739\) 0.148578 0.457276i 0.00546553 0.0168212i −0.948287 0.317416i \(-0.897185\pi\)
0.953752 + 0.300594i \(0.0971850\pi\)
\(740\) −1.42027 + 1.03189i −0.0522103 + 0.0379330i
\(741\) 9.51683 + 6.91438i 0.349610 + 0.254006i
\(742\) 0 0
\(743\) 10.2730 + 31.6172i 0.376881 + 1.15992i 0.942201 + 0.335049i \(0.108753\pi\)
−0.565319 + 0.824872i \(0.691247\pi\)
\(744\) 9.09412 + 6.60726i 0.333407 + 0.242234i
\(745\) 1.30151 0.945603i 0.0476837 0.0346442i
\(746\) −0.724946 + 2.23116i −0.0265422 + 0.0816884i
\(747\) 29.5413 1.08086
\(748\) 17.4635 + 9.87543i 0.638530 + 0.361082i
\(749\) 0 0
\(750\) −0.328769 + 1.01185i −0.0120050 + 0.0369475i
\(751\) −22.6578 + 16.4619i −0.826796 + 0.600703i −0.918651 0.395070i \(-0.870720\pi\)
0.0918547 + 0.995772i \(0.470720\pi\)
\(752\) 3.61200 + 2.62427i 0.131716 + 0.0956973i
\(753\) 5.60977 + 17.2651i 0.204432 + 0.629176i
\(754\) −5.92049 18.2214i −0.215611 0.663584i
\(755\) −1.46530 1.06460i −0.0533276 0.0387448i
\(756\) 0 0
\(757\) −6.87465 + 21.1580i −0.249863 + 0.769001i 0.744935 + 0.667137i \(0.232481\pi\)
−0.994798 + 0.101864i \(0.967519\pi\)
\(758\) 4.76156 0.172948
\(759\) 3.31495 + 7.26986i 0.120325 + 0.263879i
\(760\) −1.71237 −0.0621142
\(761\) 14.9025 45.8651i 0.540214 1.66261i −0.191891 0.981416i \(-0.561462\pi\)
0.732105 0.681192i \(-0.238538\pi\)
\(762\) −0.776427 + 0.564108i −0.0281270 + 0.0204355i
\(763\) 0 0
\(764\) 5.18562 + 15.9597i 0.187609 + 0.577402i
\(765\) −0.780313 2.40156i −0.0282123 0.0868284i
\(766\) −2.76192 2.00665i −0.0997922 0.0725033i
\(767\) 50.3584 36.5875i 1.81834 1.32110i
\(768\) 2.55791 7.87245i 0.0923007 0.284072i
\(769\) −43.6883 −1.57544 −0.787721 0.616032i \(-0.788739\pi\)
−0.787721 + 0.616032i \(0.788739\pi\)
\(770\) 0 0
\(771\) −10.4549 −0.376524
\(772\) −6.84977 + 21.0814i −0.246528 + 0.758737i
\(773\) −0.473736 + 0.344189i −0.0170391 + 0.0123796i −0.596272 0.802782i \(-0.703352\pi\)
0.579233 + 0.815162i \(0.303352\pi\)
\(774\) 7.75318 + 5.63301i 0.278682 + 0.202475i
\(775\) −10.5396 32.4375i −0.378593 1.16519i
\(776\) 7.38612 + 22.7321i 0.265146 + 0.816036i
\(777\) 0 0
\(778\) 6.60197 4.79661i 0.236692 0.171967i
\(779\) 1.20535 3.70969i 0.0431862 0.132913i
\(780\) −1.25312 −0.0448688
\(781\) −30.6759 + 3.50175i −1.09767 + 0.125302i
\(782\) 13.1365 0.469760
\(783\) −4.04930 + 12.4625i −0.144710 + 0.445372i
\(784\) 0 0
\(785\) 3.62764 + 2.63563i 0.129476 + 0.0940698i
\(786\) −0.203440 0.626124i −0.00725647 0.0223331i
\(787\) −9.49195 29.2132i −0.338351 1.04134i −0.965048 0.262075i \(-0.915593\pi\)
0.626696 0.779264i \(-0.284407\pi\)
\(788\) 13.8907 + 10.0922i 0.494834 + 0.359518i
\(789\) −4.09017 + 2.97168i −0.145614 + 0.105795i
\(790\) 0.242153 0.745269i 0.00861540 0.0265155i
\(791\) 0 0
\(792\) −22.7750 + 2.59984i −0.809274 + 0.0923811i
\(793\) −62.8758 −2.23278
\(794\) 2.73623 8.42125i 0.0971052 0.298859i
\(795\) −0.191132 + 0.138865i −0.00677874 + 0.00492504i
\(796\) −17.2302 12.5185i −0.610708 0.443705i
\(797\) 3.34767 + 10.3031i 0.118581 + 0.364953i 0.992677 0.120799i \(-0.0385456\pi\)
−0.874096 + 0.485752i \(0.838546\pi\)
\(798\) 0 0
\(799\) 21.2003 + 15.4029i 0.750014 + 0.544917i
\(800\) −23.4458 + 17.0344i −0.828936 + 0.602257i
\(801\) 6.40868 19.7239i 0.226440 0.696910i
\(802\) 3.67358 0.129719
\(803\) 13.6642 12.5263i 0.482200 0.442045i
\(804\) 1.09668 0.0386770
\(805\) 0 0
\(806\) −28.2960 + 20.5582i −0.996684 + 0.724133i
\(807\) 3.12358 + 2.26941i 0.109955 + 0.0798872i
\(808\) 15.6715 + 48.2320i 0.551322 + 1.69679i
\(809\) −11.9250 36.7013i −0.419260 1.29035i −0.908385 0.418136i \(-0.862684\pi\)
0.489125 0.872214i \(-0.337316\pi\)
\(810\) 0.798931 + 0.580458i 0.0280716 + 0.0203952i
\(811\) −41.1737 + 29.9144i −1.44580 + 1.05044i −0.459015 + 0.888428i \(0.651798\pi\)
−0.986789 + 0.162010i \(0.948202\pi\)
\(812\) 0 0
\(813\) 4.86200 0.170518
\(814\) 6.04836 + 13.2644i 0.211995 + 0.464916i
\(815\) 1.65429 0.0579473
\(816\) −0.611364 + 1.88159i −0.0214020 + 0.0658687i
\(817\) −11.1033 + 8.06703i −0.388456 + 0.282230i
\(818\) −1.55076 1.12669i −0.0542209 0.0393938i
\(819\) 0 0
\(820\) 0.128402 + 0.395180i 0.00448398 + 0.0138003i
\(821\) 32.6110 + 23.6933i 1.13813 + 0.826901i 0.986858 0.161590i \(-0.0516623\pi\)
0.151274 + 0.988492i \(0.451662\pi\)
\(822\) −0.971560 + 0.705880i −0.0338870 + 0.0246204i
\(823\) 7.93609 24.4248i 0.276635 0.851395i −0.712147 0.702030i \(-0.752277\pi\)
0.988782 0.149365i \(-0.0477228\pi\)
\(824\) −42.8685 −1.49340
\(825\) −8.83296 4.99494i −0.307524 0.173902i
\(826\) 0 0
\(827\) −9.87486 + 30.3917i −0.343382 + 1.05682i 0.619062 + 0.785342i \(0.287513\pi\)
−0.962444 + 0.271480i \(0.912487\pi\)
\(828\) 11.5214 8.37079i 0.400397 0.290905i
\(829\) 39.1566 + 28.4489i 1.35996 + 0.988072i 0.998447 + 0.0557070i \(0.0177413\pi\)
0.361518 + 0.932365i \(0.382259\pi\)
\(830\) 0.603238 + 1.85658i 0.0209387 + 0.0644427i
\(831\) −2.30090 7.08143i −0.0798172 0.245652i
\(832\) 16.2409 + 11.7997i 0.563050 + 0.409080i
\(833\) 0 0
\(834\) 0.707180 2.17648i 0.0244876 0.0753652i
\(835\) 0.492010 0.0170267
\(836\) 2.68700 13.2216i 0.0929319 0.457278i
\(837\) 23.9216 0.826850
\(838\) −3.44524 + 10.6033i −0.119014 + 0.366287i
\(839\) −30.5133 + 22.1692i −1.05344 + 0.765366i −0.972863 0.231382i \(-0.925675\pi\)
−0.0805734 + 0.996749i \(0.525675\pi\)
\(840\) 0 0
\(841\) −4.56017 14.0348i −0.157247 0.483957i
\(842\) 4.16021 + 12.8038i 0.143370 + 0.441248i
\(843\) 10.5775 + 7.68497i 0.364307 + 0.264685i
\(844\) 10.0858 7.32779i 0.347169 0.252233i
\(845\) 2.03773 6.27150i 0.0701001 0.215746i
\(846\) −12.3056 −0.423074
\(847\) 0 0
\(848\) −1.26869 −0.0435671
\(849\) −4.77522 + 14.6966i −0.163885 + 0.504386i
\(850\) −13.4973 + 9.80638i −0.462954 + 0.336356i
\(851\) −17.8284 12.9531i −0.611151 0.444027i
\(852\) −2.48109 7.63600i −0.0850007 0.261605i
\(853\) −2.87035 8.83403i −0.0982789 0.302471i 0.889815 0.456321i \(-0.150833\pi\)
−0.988094 + 0.153849i \(0.950833\pi\)
\(854\) 0 0
\(855\) −1.37383 + 0.998146i −0.0469840 + 0.0341359i
\(856\) −4.39986 + 13.5414i −0.150384 + 0.462835i
\(857\) 29.7644 1.01673 0.508365 0.861141i \(-0.330250\pi\)
0.508365 + 0.861141i \(0.330250\pi\)
\(858\) −2.07243 + 10.1975i −0.0707516 + 0.348138i
\(859\) −33.2611 −1.13485 −0.567427 0.823424i \(-0.692061\pi\)
−0.567427 + 0.823424i \(0.692061\pi\)
\(860\) 0.451787 1.39046i 0.0154058 0.0474142i
\(861\) 0 0
\(862\) 17.5442 + 12.7466i 0.597558 + 0.434151i
\(863\) −5.73772 17.6589i −0.195314 0.601116i −0.999973 0.00737787i \(-0.997652\pi\)
0.804658 0.593738i \(-0.202348\pi\)
\(864\) −6.28115 19.3314i −0.213689 0.657668i
\(865\) −1.86539 1.35529i −0.0634253 0.0460812i
\(866\) 18.5850 13.5028i 0.631544 0.458844i
\(867\) −0.341645 + 1.05147i −0.0116029 + 0.0357100i
\(868\) 0 0
\(869\) 13.0768 + 7.39477i 0.443599 + 0.250850i
\(870\) −0.403520 −0.0136806
\(871\) −2.56565 + 7.89627i −0.0869339 + 0.267555i
\(872\) −11.5311 + 8.37782i −0.390491 + 0.283709i
\(873\) 19.1765 + 13.9325i 0.649026 + 0.471545i
\(874\) −2.72992 8.40184i −0.0923411 0.284197i
\(875\) 0 0
\(876\) 3.89985 + 2.83341i 0.131764 + 0.0957321i
\(877\) 18.1965 13.2205i 0.614452 0.446426i −0.236527 0.971625i \(-0.576009\pi\)
0.850979 + 0.525199i \(0.176009\pi\)
\(878\) −8.08834 + 24.8934i −0.272968 + 0.840110i
\(879\) −0.281259 −0.00948664
\(880\) 0.226122 + 0.495898i 0.00762259 + 0.0167167i
\(881\) −7.06565 −0.238048 −0.119024 0.992891i \(-0.537977\pi\)
−0.119024 + 0.992891i \(0.537977\pi\)
\(882\) 0 0
\(883\) 16.1304 11.7194i 0.542830 0.394389i −0.282305 0.959325i \(-0.591099\pi\)
0.825135 + 0.564936i \(0.191099\pi\)
\(884\) −31.9541 23.2160i −1.07473 0.780839i
\(885\) −0.405123 1.24684i −0.0136181 0.0419121i
\(886\) −2.48105 7.63590i −0.0833527 0.256533i
\(887\) 5.62656 + 4.08793i 0.188921 + 0.137259i 0.678226 0.734854i \(-0.262749\pi\)
−0.489304 + 0.872113i \(0.662749\pi\)
\(888\) −7.46253 + 5.42185i −0.250426 + 0.181945i
\(889\) 0 0
\(890\) 1.37045 0.0459376
\(891\) −13.9554 + 12.7933i −0.467522 + 0.428590i
\(892\) 0.998136 0.0334201
\(893\) 5.44574 16.7603i 0.182235 0.560861i
\(894\) 2.81055 2.04198i 0.0939988 0.0682941i
\(895\) 4.21414 + 3.06175i 0.140863 + 0.102343i
\(896\) 0 0
\(897\) −4.86088 14.9602i −0.162300 0.499508i
\(898\) −1.73468 1.26032i −0.0578872 0.0420575i
\(899\) 21.0354 15.2831i 0.701570 0.509721i
\(900\) −5.58909 + 17.2014i −0.186303 + 0.573382i
\(901\) −7.44650 −0.248079
\(902\) 3.42822 0.391342i 0.114147 0.0130303i
\(903\) 0 0
\(904\) −13.4575 + 41.4179i −0.447590 + 1.37754i
\(905\) −2.46916 + 1.79395i −0.0820776 + 0.0596329i
\(906\) −3.16424 2.29895i −0.105125 0.0763776i
\(907\) −7.24340 22.2929i −0.240513 0.740224i −0.996342 0.0854543i \(-0.972766\pi\)
0.755829 0.654769i \(-0.227234\pi\)
\(908\) −2.29489 7.06294i −0.0761586 0.234392i
\(909\) 40.6878 + 29.5614i 1.34953 + 0.980490i
\(910\) 0 0
\(911\) 14.4650 44.5186i 0.479246 1.47497i −0.360899 0.932605i \(-0.617530\pi\)
0.840145 0.542362i \(-0.182470\pi\)
\(912\) 1.33048 0.0440564
\(913\) −37.1825 + 4.24450i −1.23056 + 0.140473i
\(914\) 31.3563 1.03718
\(915\) −0.409219 + 1.25945i −0.0135284 + 0.0416360i
\(916\) 7.46078 5.42058i 0.246511 0.179101i
\(917\) 0 0
\(918\) −3.61594 11.1287i −0.119344 0.367302i
\(919\) 3.28402 + 10.1072i 0.108330 + 0.333405i 0.990498 0.137530i \(-0.0439165\pi\)
−0.882168 + 0.470935i \(0.843916\pi\)
\(920\) 1.85248 + 1.34590i 0.0610744 + 0.0443732i
\(921\) 4.01789 2.91917i 0.132394 0.0961898i
\(922\) −8.22278 + 25.3071i −0.270803 + 0.833445i
\(923\) 60.7848 2.00075
\(924\) 0 0
\(925\) 27.9876 0.920228
\(926\) −0.169945 + 0.523036i −0.00558473 + 0.0171880i
\(927\) −34.3933 + 24.9882i −1.12962 + 0.820720i
\(928\) −17.8739 12.9861i −0.586738 0.426290i
\(929\) 11.3319 + 34.8762i 0.371789 + 1.14425i 0.945619 + 0.325275i \(0.105457\pi\)
−0.573830 + 0.818974i \(0.694543\pi\)
\(930\) 0.227635 + 0.700590i 0.00746446 + 0.0229733i
\(931\) 0 0
\(932\) −10.7900 + 7.83938i −0.353438 + 0.256787i
\(933\) 0.0261579 0.0805059i 0.000856373 0.00263564i
\(934\) −22.2302 −0.727393
\(935\) 1.32721 + 2.91064i 0.0434043 + 0.0951880i
\(936\) 45.1290 1.47509
\(937\) 12.4278 38.2490i 0.406000 1.24954i −0.514057 0.857756i \(-0.671858\pi\)
0.920057 0.391784i \(-0.128142\pi\)
\(938\) 0 0
\(939\) 7.64497 + 5.55439i 0.249484 + 0.181261i
\(940\) 0.580114 + 1.78541i 0.0189212 + 0.0582336i
\(941\) −7.69751 23.6905i −0.250932 0.772288i −0.994604 0.103744i \(-0.966918\pi\)
0.743672 0.668544i \(-0.233082\pi\)
\(942\) 7.83371 + 5.69152i 0.255236 + 0.185440i
\(943\) −4.21975 + 3.06583i −0.137414 + 0.0998371i
\(944\) 2.17555 6.69565i 0.0708081 0.217925i
\(945\) 0 0
\(946\) −10.5680 5.97609i −0.343595 0.194299i
\(947\) −32.2061 −1.04656 −0.523279 0.852161i \(-0.675292\pi\)
−0.523279 + 0.852161i \(0.675292\pi\)
\(948\) −1.20722 + 3.71543i −0.0392085 + 0.120671i
\(949\) −29.5246 + 21.4508i −0.958408 + 0.696324i
\(950\) 9.07688 + 6.59474i 0.294493 + 0.213962i
\(951\) 6.30101 + 19.3925i 0.204324 + 0.628846i
\(952\) 0 0
\(953\) −36.4552 26.4863i −1.18090 0.857975i −0.188628 0.982049i \(-0.560404\pi\)
−0.992273 + 0.124074i \(0.960404\pi\)
\(954\) 2.82896 2.05536i 0.0915908 0.0665446i
\(955\) −0.826849 + 2.54478i −0.0267562 + 0.0823471i
\(956\) −37.4650 −1.21170
\(957\) 1.54066 7.58090i 0.0498024 0.245056i
\(958\) −3.96296 −0.128038
\(959\) 0 0
\(960\) 0.342058 0.248519i 0.0110399 0.00802093i
\(961\) −13.3216 9.67867i −0.429727 0.312215i
\(962\) −8.86901 27.2960i −0.285948 0.880059i
\(963\) 4.36332 + 13.4289i 0.140606 + 0.432741i
\(964\) −21.3000 15.4754i −0.686028 0.498428i
\(965\) −2.85941 + 2.07748i −0.0920476 + 0.0668765i
\(966\) 0 0
\(967\) 1.81387 0.0583300 0.0291650 0.999575i \(-0.490715\pi\)
0.0291650 + 0.999575i \(0.490715\pi\)
\(968\) 28.2925 6.54464i 0.909355 0.210353i
\(969\) 7.80912 0.250865
\(970\) −0.484029 + 1.48969i −0.0155412 + 0.0478310i
\(971\) 18.6510 13.5507i 0.598539 0.434864i −0.246821 0.969061i \(-0.579386\pi\)
0.845360 + 0.534197i \(0.179386\pi\)
\(972\) −15.7431 11.4380i −0.504959 0.366874i
\(973\) 0 0
\(974\) −7.01266 21.5827i −0.224700 0.691555i
\(975\) 16.1622 + 11.7425i 0.517605 + 0.376062i
\(976\) −5.75325 + 4.17998i −0.184157 + 0.133798i
\(977\) −2.19232 + 6.74726i −0.0701385 + 0.215864i −0.979981 0.199089i \(-0.936202\pi\)
0.909843 + 0.414953i \(0.136202\pi\)
\(978\) 3.57236 0.114232
\(979\) −5.23244 + 25.7466i −0.167229 + 0.822863i
\(980\) 0 0
\(981\) −4.36789 + 13.4430i −0.139456 + 0.429202i
\(982\) 18.9605 13.7756i 0.605053 0.439597i
\(983\) 31.0260 + 22.5417i 0.989576 + 0.718969i 0.959828 0.280589i \(-0.0905297\pi\)
0.0297474 + 0.999557i \(0.490530\pi\)
\(984\) 0.674659 + 2.07639i 0.0215073 + 0.0661928i
\(985\) 0.846005 + 2.60374i 0.0269560 + 0.0829619i
\(986\) −10.2896 7.47586i −0.327689 0.238080i
\(987\) 0 0
\(988\) −8.20806 + 25.2618i −0.261133 + 0.803685i
\(989\) 18.3524 0.583572
\(990\) −1.30760 0.739431i −0.0415581 0.0235007i
\(991\) 20.2722 0.643967 0.321984 0.946745i \(-0.395650\pi\)
0.321984 + 0.946745i \(0.395650\pi\)
\(992\) −12.4634 + 38.3583i −0.395712 + 1.21788i
\(993\) 14.7667 10.7287i 0.468608 0.340464i
\(994\) 0 0
\(995\) −1.04940 3.22971i −0.0332681 0.102389i
\(996\) −3.00735 9.25568i −0.0952916 0.293277i
\(997\) 12.4675 + 9.05819i 0.394851 + 0.286876i 0.767440 0.641120i \(-0.221530\pi\)
−0.372590 + 0.927996i \(0.621530\pi\)
\(998\) 3.74319 2.71959i 0.118489 0.0860871i
\(999\) −6.06593 + 18.6690i −0.191918 + 0.590662i
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.f.d.295.1 8
7.2 even 3 539.2.q.b.361.2 16
7.3 odd 6 539.2.q.c.471.1 16
7.4 even 3 539.2.q.b.471.1 16
7.5 odd 6 539.2.q.c.361.2 16
7.6 odd 2 77.2.f.a.64.1 8
11.4 even 5 5929.2.a.bi.1.2 4
11.5 even 5 inner 539.2.f.d.148.1 8
11.7 odd 10 5929.2.a.bb.1.3 4
21.20 even 2 693.2.m.g.64.2 8
77.5 odd 30 539.2.q.c.214.1 16
77.6 even 10 847.2.f.q.148.2 8
77.13 even 10 847.2.f.s.729.1 8
77.16 even 15 539.2.q.b.214.1 16
77.20 odd 10 847.2.f.p.729.2 8
77.27 odd 10 77.2.f.a.71.1 yes 8
77.38 odd 30 539.2.q.c.324.2 16
77.41 even 10 847.2.f.s.323.1 8
77.48 odd 10 847.2.a.l.1.2 4
77.60 even 15 539.2.q.b.324.2 16
77.62 even 10 847.2.a.k.1.3 4
77.69 odd 10 847.2.f.p.323.2 8
77.76 even 2 847.2.f.q.372.2 8
231.62 odd 10 7623.2.a.co.1.2 4
231.104 even 10 693.2.m.g.379.2 8
231.125 even 10 7623.2.a.ch.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.64.1 8 7.6 odd 2
77.2.f.a.71.1 yes 8 77.27 odd 10
539.2.f.d.148.1 8 11.5 even 5 inner
539.2.f.d.295.1 8 1.1 even 1 trivial
539.2.q.b.214.1 16 77.16 even 15
539.2.q.b.324.2 16 77.60 even 15
539.2.q.b.361.2 16 7.2 even 3
539.2.q.b.471.1 16 7.4 even 3
539.2.q.c.214.1 16 77.5 odd 30
539.2.q.c.324.2 16 77.38 odd 30
539.2.q.c.361.2 16 7.5 odd 6
539.2.q.c.471.1 16 7.3 odd 6
693.2.m.g.64.2 8 21.20 even 2
693.2.m.g.379.2 8 231.104 even 10
847.2.a.k.1.3 4 77.62 even 10
847.2.a.l.1.2 4 77.48 odd 10
847.2.f.p.323.2 8 77.69 odd 10
847.2.f.p.729.2 8 77.20 odd 10
847.2.f.q.148.2 8 77.6 even 10
847.2.f.q.372.2 8 77.76 even 2
847.2.f.s.323.1 8 77.41 even 10
847.2.f.s.729.1 8 77.13 even 10
5929.2.a.bb.1.3 4 11.7 odd 10
5929.2.a.bi.1.2 4 11.4 even 5
7623.2.a.ch.1.3 4 231.125 even 10
7623.2.a.co.1.2 4 231.62 odd 10