Properties

Label 539.2.q.g.361.2
Level $539$
Weight $2$
Character 539.361
Analytic conductor $4.304$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 361.2
Character \(\chi\) \(=\) 539.361
Dual form 539.2.q.g.324.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.655108 + 0.139248i) q^{2} +(-0.328196 - 3.12257i) q^{3} +(-1.41731 + 0.631029i) q^{4} +(1.43447 - 1.59314i) q^{5} +(0.649815 + 1.99992i) q^{6} +(1.92429 - 1.39808i) q^{8} +(-6.70831 + 1.42589i) q^{9} +O(q^{10})\) \(q+(-0.655108 + 0.139248i) q^{2} +(-0.328196 - 3.12257i) q^{3} +(-1.41731 + 0.631029i) q^{4} +(1.43447 - 1.59314i) q^{5} +(0.649815 + 1.99992i) q^{6} +(1.92429 - 1.39808i) q^{8} +(-6.70831 + 1.42589i) q^{9} +(-0.717891 + 1.24342i) q^{10} +(-2.17218 - 2.50631i) q^{11} +(2.43559 + 4.21857i) q^{12} +(0.781276 - 2.40452i) q^{13} +(-5.44548 - 3.95637i) q^{15} +(1.01029 - 1.12205i) q^{16} +(1.75178 + 0.372353i) q^{17} +(4.19612 - 1.86823i) q^{18} +(-6.14579 - 2.73628i) q^{19} +(-1.02778 + 3.16317i) q^{20} +(1.77201 + 1.33944i) q^{22} +(1.58214 + 2.74035i) q^{23} +(-4.99715 - 5.54990i) q^{24} +(0.0422518 + 0.401999i) q^{25} +(-0.176997 + 1.68401i) q^{26} +(3.74337 + 11.5209i) q^{27} +(0.747669 + 0.543213i) q^{29} +(4.11829 + 1.83358i) q^{30} +(2.00858 + 2.23076i) q^{31} +(-2.88417 + 4.99553i) q^{32} +(-7.11325 + 7.60537i) q^{33} -1.19946 q^{34} +(8.60800 - 6.25408i) q^{36} +(0.157543 - 1.49892i) q^{37} +(4.40718 + 0.936774i) q^{38} +(-7.76470 - 1.65044i) q^{39} +(0.533001 - 5.07117i) q^{40} +(-4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(4.66022 + 2.18152i) q^{44} +(-7.35120 + 12.7327i) q^{45} +(-1.41806 - 1.57492i) q^{46} +(4.01751 + 1.78871i) q^{47} +(-3.83525 - 2.78647i) q^{48} +(-0.0836570 - 0.257470i) q^{50} +(0.587772 - 5.59228i) q^{51} +(0.410008 + 3.90097i) q^{52} +(0.446592 + 0.495990i) q^{53} +(-4.05657 - 7.02619i) q^{54} +(-7.10883 - 0.134639i) q^{55} +(-6.52722 + 20.0887i) q^{57} +(-0.565445 - 0.251753i) q^{58} +(-0.336514 + 0.149826i) q^{59} +(10.2145 + 2.17117i) q^{60} +(3.35334 - 3.72426i) q^{61} +(-1.62647 - 1.18170i) q^{62} +(0.260682 - 0.802296i) q^{64} +(-2.71002 - 4.69389i) q^{65} +(3.60092 - 5.97284i) q^{66} +(0.451065 - 0.781267i) q^{67} +(-2.71779 + 0.577685i) q^{68} +(8.03770 - 5.83973i) q^{69} +(-4.59489 - 14.1416i) q^{71} +(-10.9152 + 12.1226i) q^{72} +(7.34322 - 3.26941i) q^{73} +(0.105514 + 1.00389i) q^{74} +(1.24141 - 0.263869i) q^{75} +10.4372 q^{76} +5.31654 q^{78} +(-3.96803 + 0.843431i) q^{79} +(-0.338339 - 3.21908i) q^{80} +(15.9505 - 7.10164i) q^{81} +(2.49216 - 2.76782i) q^{82} +(-1.25193 - 3.85305i) q^{83} +(3.10609 - 2.25670i) q^{85} +(5.52246 - 1.17384i) q^{86} +(1.45084 - 2.51293i) q^{87} +(-7.68395 - 1.78600i) q^{88} +(4.15363 + 7.19431i) q^{89} +(3.04284 - 9.36491i) q^{90} +(-3.97163 - 2.88556i) q^{92} +(6.30650 - 7.00408i) q^{93} +(-2.88097 - 0.612370i) q^{94} +(-13.1752 + 5.86598i) q^{95} +(16.5455 + 7.36652i) q^{96} +(2.63154 - 8.09904i) q^{97} +(18.1454 + 13.7158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 3 q^{2} + 2 q^{3} + 11 q^{4} + 5 q^{5} + 6 q^{6} - 10 q^{8} + 12 q^{9} - 12 q^{10} + 3 q^{11} - 18 q^{12} - 14 q^{13} - 36 q^{15} - 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + 2 q^{20} - 66 q^{22} - 32 q^{23} + 35 q^{24} - 7 q^{25} + 27 q^{26} + 20 q^{27} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 32 q^{32} + 26 q^{33} - 48 q^{34} + 104 q^{36} - 4 q^{37} + 5 q^{38} - 11 q^{39} + 10 q^{40} - 20 q^{41} - 16 q^{43} + 38 q^{44} - 70 q^{45} + 42 q^{46} + 23 q^{47} - 72 q^{48} + 104 q^{50} + 29 q^{51} - 33 q^{52} - 4 q^{53} - 60 q^{54} - 24 q^{55} - 22 q^{57} - 20 q^{58} - 17 q^{59} + 30 q^{60} + 7 q^{61} + 158 q^{62} + 14 q^{64} + 8 q^{65} - 8 q^{66} + 38 q^{67} + 2 q^{68} + 20 q^{69} - 28 q^{71} + 35 q^{73} + 29 q^{74} - 9 q^{75} + 104 q^{76} - 116 q^{78} - 15 q^{79} + 87 q^{80} + 14 q^{81} - 19 q^{82} + 10 q^{83} + 12 q^{85} + 52 q^{86} + 72 q^{87} - 55 q^{88} - 74 q^{89} - 28 q^{90} - 110 q^{92} - 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 40 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.655108 + 0.139248i −0.463232 + 0.0984629i −0.433615 0.901098i \(-0.642762\pi\)
−0.0296169 + 0.999561i \(0.509429\pi\)
\(3\) −0.328196 3.12257i −0.189484 1.80282i −0.514903 0.857249i \(-0.672172\pi\)
0.325419 0.945570i \(-0.394495\pi\)
\(4\) −1.41731 + 0.631029i −0.708657 + 0.315514i
\(5\) 1.43447 1.59314i 0.641514 0.712473i −0.331439 0.943477i \(-0.607534\pi\)
0.972953 + 0.231004i \(0.0742009\pi\)
\(6\) 0.649815 + 1.99992i 0.265286 + 0.816465i
\(7\) 0 0
\(8\) 1.92429 1.39808i 0.680340 0.494296i
\(9\) −6.70831 + 1.42589i −2.23610 + 0.475298i
\(10\) −0.717891 + 1.24342i −0.227017 + 0.393205i
\(11\) −2.17218 2.50631i −0.654938 0.755682i
\(12\) 2.43559 + 4.21857i 0.703094 + 1.21779i
\(13\) 0.781276 2.40452i 0.216687 0.666894i −0.782343 0.622848i \(-0.785975\pi\)
0.999030 0.0440455i \(-0.0140247\pi\)
\(14\) 0 0
\(15\) −5.44548 3.95637i −1.40602 1.02153i
\(16\) 1.01029 1.12205i 0.252574 0.280512i
\(17\) 1.75178 + 0.372353i 0.424870 + 0.0903089i 0.415384 0.909646i \(-0.363647\pi\)
0.00948587 + 0.999955i \(0.496981\pi\)
\(18\) 4.19612 1.86823i 0.989034 0.440346i
\(19\) −6.14579 2.73628i −1.40994 0.627746i −0.446284 0.894891i \(-0.647253\pi\)
−0.963656 + 0.267146i \(0.913920\pi\)
\(20\) −1.02778 + 3.16317i −0.229818 + 0.707306i
\(21\) 0 0
\(22\) 1.77201 + 1.33944i 0.377795 + 0.285569i
\(23\) 1.58214 + 2.74035i 0.329900 + 0.571403i 0.982492 0.186307i \(-0.0596518\pi\)
−0.652592 + 0.757709i \(0.726318\pi\)
\(24\) −4.99715 5.54990i −1.02004 1.13287i
\(25\) 0.0422518 + 0.401999i 0.00845037 + 0.0803999i
\(26\) −0.176997 + 1.68401i −0.0347119 + 0.330262i
\(27\) 3.74337 + 11.5209i 0.720412 + 2.21720i
\(28\) 0 0
\(29\) 0.747669 + 0.543213i 0.138839 + 0.100872i 0.655037 0.755597i \(-0.272653\pi\)
−0.516198 + 0.856469i \(0.672653\pi\)
\(30\) 4.11829 + 1.83358i 0.751894 + 0.334765i
\(31\) 2.00858 + 2.23076i 0.360752 + 0.400656i 0.896011 0.444032i \(-0.146452\pi\)
−0.535258 + 0.844688i \(0.679786\pi\)
\(32\) −2.88417 + 4.99553i −0.509854 + 0.883092i
\(33\) −7.11325 + 7.60537i −1.23826 + 1.32392i
\(34\) −1.19946 −0.205705
\(35\) 0 0
\(36\) 8.60800 6.25408i 1.43467 1.04235i
\(37\) 0.157543 1.49892i 0.0258999 0.246421i −0.973910 0.226934i \(-0.927130\pi\)
0.999810 0.0194875i \(-0.00620346\pi\)
\(38\) 4.40718 + 0.936774i 0.714938 + 0.151965i
\(39\) −7.76470 1.65044i −1.24335 0.264282i
\(40\) 0.533001 5.07117i 0.0842749 0.801822i
\(41\) −4.49897 + 3.26870i −0.702622 + 0.510485i −0.880785 0.473516i \(-0.842984\pi\)
0.178163 + 0.984001i \(0.442984\pi\)
\(42\) 0 0
\(43\) −8.42985 −1.28554 −0.642770 0.766059i \(-0.722215\pi\)
−0.642770 + 0.766059i \(0.722215\pi\)
\(44\) 4.66022 + 2.18152i 0.702555 + 0.328877i
\(45\) −7.35120 + 12.7327i −1.09585 + 1.89807i
\(46\) −1.41806 1.57492i −0.209082 0.232209i
\(47\) 4.01751 + 1.78871i 0.586013 + 0.260910i 0.678255 0.734827i \(-0.262737\pi\)
−0.0922416 + 0.995737i \(0.529403\pi\)
\(48\) −3.83525 2.78647i −0.553570 0.402192i
\(49\) 0 0
\(50\) −0.0836570 0.257470i −0.0118309 0.0364117i
\(51\) 0.587772 5.59228i 0.0823046 0.783076i
\(52\) 0.410008 + 3.90097i 0.0568579 + 0.540967i
\(53\) 0.446592 + 0.495990i 0.0613441 + 0.0681295i 0.773036 0.634362i \(-0.218737\pi\)
−0.711692 + 0.702492i \(0.752071\pi\)
\(54\) −4.05657 7.02619i −0.552029 0.956143i
\(55\) −7.10883 0.134639i −0.958555 0.0181547i
\(56\) 0 0
\(57\) −6.52722 + 20.0887i −0.864551 + 2.66081i
\(58\) −0.565445 0.251753i −0.0742466 0.0330567i
\(59\) −0.336514 + 0.149826i −0.0438104 + 0.0195056i −0.428525 0.903530i \(-0.640967\pi\)
0.384715 + 0.923036i \(0.374300\pi\)
\(60\) 10.2145 + 2.17117i 1.31869 + 0.280296i
\(61\) 3.35334 3.72426i 0.429351 0.476843i −0.489185 0.872180i \(-0.662706\pi\)
0.918536 + 0.395337i \(0.129372\pi\)
\(62\) −1.62647 1.18170i −0.206562 0.150076i
\(63\) 0 0
\(64\) 0.260682 0.802296i 0.0325852 0.100287i
\(65\) −2.71002 4.69389i −0.336136 0.582205i
\(66\) 3.60092 5.97284i 0.443243 0.735206i
\(67\) 0.451065 0.781267i 0.0551063 0.0954469i −0.837156 0.546964i \(-0.815784\pi\)
0.892263 + 0.451517i \(0.149117\pi\)
\(68\) −2.71779 + 0.577685i −0.329581 + 0.0700546i
\(69\) 8.03770 5.83973i 0.967625 0.703021i
\(70\) 0 0
\(71\) −4.59489 14.1416i −0.545313 1.67830i −0.720245 0.693720i \(-0.755971\pi\)
0.174932 0.984580i \(-0.444029\pi\)
\(72\) −10.9152 + 12.1226i −1.28637 + 1.42866i
\(73\) 7.34322 3.26941i 0.859459 0.382656i 0.0708031 0.997490i \(-0.477444\pi\)
0.788656 + 0.614834i \(0.210777\pi\)
\(74\) 0.105514 + 1.00389i 0.0122657 + 0.116700i
\(75\) 1.24141 0.263869i 0.143345 0.0304690i
\(76\) 10.4372 1.19723
\(77\) 0 0
\(78\) 5.31654 0.601980
\(79\) −3.96803 + 0.843431i −0.446438 + 0.0948934i −0.425645 0.904890i \(-0.639953\pi\)
−0.0207937 + 0.999784i \(0.506619\pi\)
\(80\) −0.338339 3.21908i −0.0378274 0.359904i
\(81\) 15.9505 7.10164i 1.77228 0.789071i
\(82\) 2.49216 2.76782i 0.275213 0.305655i
\(83\) −1.25193 3.85305i −0.137418 0.422928i 0.858541 0.512745i \(-0.171372\pi\)
−0.995958 + 0.0898178i \(0.971372\pi\)
\(84\) 0 0
\(85\) 3.10609 2.25670i 0.336902 0.244774i
\(86\) 5.52246 1.17384i 0.595503 0.126578i
\(87\) 1.45084 2.51293i 0.155547 0.269415i
\(88\) −7.68395 1.78600i −0.819112 0.190388i
\(89\) 4.15363 + 7.19431i 0.440284 + 0.762595i 0.997710 0.0676317i \(-0.0215443\pi\)
−0.557426 + 0.830227i \(0.688211\pi\)
\(90\) 3.04284 9.36491i 0.320744 0.987148i
\(91\) 0 0
\(92\) −3.97163 2.88556i −0.414071 0.300840i
\(93\) 6.30650 7.00408i 0.653954 0.726289i
\(94\) −2.88097 0.612370i −0.297150 0.0631611i
\(95\) −13.1752 + 5.86598i −1.35175 + 0.601837i
\(96\) 16.5455 + 7.36652i 1.68866 + 0.751842i
\(97\) 2.63154 8.09904i 0.267192 0.822333i −0.723988 0.689812i \(-0.757693\pi\)
0.991180 0.132520i \(-0.0423070\pi\)
\(98\) 0 0
\(99\) 18.1454 + 13.7158i 1.82368 + 1.37849i
\(100\) −0.313557 0.543097i −0.0313557 0.0543097i
\(101\) −2.69463 2.99269i −0.268126 0.297784i 0.594013 0.804455i \(-0.297543\pi\)
−0.862140 + 0.506671i \(0.830876\pi\)
\(102\) 0.393657 + 3.74539i 0.0389778 + 0.370849i
\(103\) 1.84240 17.5293i 0.181537 1.72721i −0.402445 0.915444i \(-0.631839\pi\)
0.583982 0.811767i \(-0.301494\pi\)
\(104\) −1.85831 5.71929i −0.182222 0.560822i
\(105\) 0 0
\(106\) −0.361631 0.262741i −0.0351248 0.0255196i
\(107\) −14.0720 6.26526i −1.36039 0.605685i −0.408680 0.912678i \(-0.634011\pi\)
−0.951712 + 0.306992i \(0.900677\pi\)
\(108\) −12.5756 13.9666i −1.21008 1.34393i
\(109\) 9.46326 16.3908i 0.906416 1.56996i 0.0874110 0.996172i \(-0.472141\pi\)
0.819005 0.573786i \(-0.194526\pi\)
\(110\) 4.67580 0.901685i 0.445821 0.0859723i
\(111\) −4.73220 −0.449161
\(112\) 0 0
\(113\) −1.35965 + 0.987844i −0.127905 + 0.0929286i −0.649898 0.760021i \(-0.725189\pi\)
0.521993 + 0.852950i \(0.325189\pi\)
\(114\) 1.47873 14.0692i 0.138496 1.31770i
\(115\) 6.63529 + 1.41037i 0.618744 + 0.131518i
\(116\) −1.40247 0.298103i −0.130216 0.0276782i
\(117\) −1.81245 + 17.2443i −0.167561 + 1.59423i
\(118\) 0.199590 0.145011i 0.0183738 0.0133493i
\(119\) 0 0
\(120\) −16.0100 −1.46151
\(121\) −1.56323 + 10.8884i −0.142112 + 0.989851i
\(122\) −1.67821 + 2.90674i −0.151938 + 0.263164i
\(123\) 11.6833 + 12.9756i 1.05345 + 1.16997i
\(124\) −4.25447 1.89421i −0.382063 0.170105i
\(125\) 9.37282 + 6.80975i 0.838330 + 0.609082i
\(126\) 0 0
\(127\) 5.42848 + 16.7071i 0.481699 + 1.48252i 0.836705 + 0.547654i \(0.184479\pi\)
−0.355006 + 0.934864i \(0.615521\pi\)
\(128\) 1.14685 10.9116i 0.101368 0.964457i
\(129\) 2.76664 + 26.3228i 0.243589 + 2.31759i
\(130\) 2.42897 + 2.69764i 0.213035 + 0.236599i
\(131\) −3.36278 5.82451i −0.293808 0.508890i 0.680899 0.732377i \(-0.261589\pi\)
−0.974707 + 0.223487i \(0.928256\pi\)
\(132\) 5.28250 15.2679i 0.459783 1.32890i
\(133\) 0 0
\(134\) −0.186707 + 0.574624i −0.0161290 + 0.0496400i
\(135\) 23.7241 + 10.5627i 2.04185 + 0.909089i
\(136\) 3.89153 1.73262i 0.333696 0.148571i
\(137\) −13.5646 2.88324i −1.15890 0.246332i −0.411947 0.911208i \(-0.635151\pi\)
−0.746954 + 0.664876i \(0.768484\pi\)
\(138\) −4.45239 + 4.94488i −0.379013 + 0.420937i
\(139\) −11.5453 8.38812i −0.979256 0.711471i −0.0217140 0.999764i \(-0.506912\pi\)
−0.957542 + 0.288293i \(0.906912\pi\)
\(140\) 0 0
\(141\) 4.26685 13.1320i 0.359333 1.10591i
\(142\) 4.97933 + 8.62446i 0.417856 + 0.723749i
\(143\) −7.72356 + 3.26494i −0.645877 + 0.273028i
\(144\) −5.17745 + 8.96761i −0.431454 + 0.747300i
\(145\) 1.93792 0.411918i 0.160936 0.0342079i
\(146\) −4.35535 + 3.16435i −0.360451 + 0.261883i
\(147\) 0 0
\(148\) 0.722575 + 2.22386i 0.0593953 + 0.182800i
\(149\) 1.75508 1.94921i 0.143782 0.159686i −0.666952 0.745100i \(-0.732402\pi\)
0.810734 + 0.585415i \(0.199068\pi\)
\(150\) −0.776512 + 0.345725i −0.0634019 + 0.0282284i
\(151\) 0.312498 + 2.97322i 0.0254307 + 0.241957i 0.999852 + 0.0172265i \(0.00548363\pi\)
−0.974421 + 0.224731i \(0.927850\pi\)
\(152\) −15.6518 + 3.32690i −1.26953 + 0.269847i
\(153\) −12.2824 −0.992977
\(154\) 0 0
\(155\) 6.43516 0.516884
\(156\) 12.0465 2.56056i 0.964491 0.205009i
\(157\) −1.17644 11.1930i −0.0938898 0.893302i −0.935526 0.353257i \(-0.885074\pi\)
0.841636 0.540045i \(-0.181593\pi\)
\(158\) 2.48204 1.10508i 0.197461 0.0879152i
\(159\) 1.40220 1.55730i 0.111201 0.123502i
\(160\) 3.82131 + 11.7608i 0.302101 + 0.929773i
\(161\) 0 0
\(162\) −9.46045 + 6.87342i −0.743283 + 0.540027i
\(163\) 17.8052 3.78461i 1.39461 0.296433i 0.551500 0.834175i \(-0.314056\pi\)
0.843110 + 0.537742i \(0.180723\pi\)
\(164\) 4.31382 7.47175i 0.336853 0.583446i
\(165\) 1.91267 + 22.2420i 0.148901 + 1.73154i
\(166\) 1.35668 + 2.34984i 0.105299 + 0.182383i
\(167\) 6.15909 18.9557i 0.476605 1.46684i −0.367176 0.930151i \(-0.619675\pi\)
0.843781 0.536687i \(-0.180325\pi\)
\(168\) 0 0
\(169\) 5.34590 + 3.88402i 0.411223 + 0.298771i
\(170\) −1.72058 + 1.91090i −0.131963 + 0.146559i
\(171\) 45.1295 + 9.59257i 3.45114 + 0.733562i
\(172\) 11.9477 5.31948i 0.911007 0.405606i
\(173\) 5.47221 + 2.43638i 0.416044 + 0.185235i 0.604074 0.796929i \(-0.293543\pi\)
−0.188029 + 0.982163i \(0.560210\pi\)
\(174\) −0.600539 + 1.84827i −0.0455267 + 0.140117i
\(175\) 0 0
\(176\) −5.00675 0.0948260i −0.377398 0.00714778i
\(177\) 0.578284 + 1.00162i 0.0434665 + 0.0752861i
\(178\) −3.72287 4.13467i −0.279041 0.309906i
\(179\) 0.169225 + 1.61007i 0.0126485 + 0.120342i 0.999024 0.0441658i \(-0.0140630\pi\)
−0.986376 + 0.164508i \(0.947396\pi\)
\(180\) 2.38429 22.6850i 0.177714 1.69084i
\(181\) 0.749929 + 2.30804i 0.0557418 + 0.171556i 0.975051 0.221980i \(-0.0712519\pi\)
−0.919309 + 0.393535i \(0.871252\pi\)
\(182\) 0 0
\(183\) −12.7298 9.24876i −0.941016 0.683688i
\(184\) 6.87574 + 3.06128i 0.506886 + 0.225680i
\(185\) −2.16200 2.40114i −0.158953 0.176536i
\(186\) −3.15614 + 5.46660i −0.231419 + 0.400830i
\(187\) −2.87196 5.19934i −0.210019 0.380214i
\(188\) −6.82279 −0.497603
\(189\) 0 0
\(190\) 7.81436 5.67747i 0.566914 0.411887i
\(191\) −1.32761 + 12.6313i −0.0960623 + 0.913972i 0.835279 + 0.549826i \(0.185306\pi\)
−0.931342 + 0.364146i \(0.881361\pi\)
\(192\) −2.59078 0.550688i −0.186974 0.0397425i
\(193\) 1.72087 + 0.365781i 0.123871 + 0.0263295i 0.269430 0.963020i \(-0.413165\pi\)
−0.145559 + 0.989350i \(0.546498\pi\)
\(194\) −0.596171 + 5.67218i −0.0428025 + 0.407239i
\(195\) −13.7676 + 10.0027i −0.985918 + 0.716311i
\(196\) 0 0
\(197\) −0.903053 −0.0643399 −0.0321699 0.999482i \(-0.510242\pi\)
−0.0321699 + 0.999482i \(0.510242\pi\)
\(198\) −13.7971 6.45865i −0.980518 0.458996i
\(199\) 7.81479 13.5356i 0.553976 0.959515i −0.444006 0.896024i \(-0.646443\pi\)
0.997982 0.0634910i \(-0.0202234\pi\)
\(200\) 0.643333 + 0.714493i 0.0454905 + 0.0505223i
\(201\) −2.58760 1.15207i −0.182515 0.0812610i
\(202\) 2.18200 + 1.58532i 0.153525 + 0.111543i
\(203\) 0 0
\(204\) 2.69583 + 8.29691i 0.188746 + 0.580900i
\(205\) −1.24615 + 11.8563i −0.0870349 + 0.828082i
\(206\) 1.23394 + 11.7401i 0.0859725 + 0.817973i
\(207\) −14.5210 16.1272i −1.00928 1.12091i
\(208\) −1.90866 3.30590i −0.132342 0.229223i
\(209\) 6.49180 + 21.3470i 0.449047 + 1.47660i
\(210\) 0 0
\(211\) 4.56378 14.0459i 0.314184 0.966958i −0.661905 0.749587i \(-0.730252\pi\)
0.976089 0.217371i \(-0.0697480\pi\)
\(212\) −0.945945 0.421162i −0.0649678 0.0289255i
\(213\) −42.6502 + 18.9891i −2.92234 + 1.30111i
\(214\) 10.0911 + 2.14493i 0.689814 + 0.146624i
\(215\) −12.0923 + 13.4299i −0.824691 + 0.915912i
\(216\) 23.3105 + 16.9361i 1.58608 + 1.15235i
\(217\) 0 0
\(218\) −3.91708 + 12.0555i −0.265298 + 0.816503i
\(219\) −12.6190 21.8567i −0.852713 1.47694i
\(220\) 10.1604 4.29505i 0.685015 0.289572i
\(221\) 2.26396 3.92129i 0.152290 0.263774i
\(222\) 3.10010 0.658948i 0.208065 0.0442257i
\(223\) 1.49293 1.08468i 0.0999743 0.0726356i −0.536675 0.843789i \(-0.680320\pi\)
0.636649 + 0.771153i \(0.280320\pi\)
\(224\) 0 0
\(225\) −0.856647 2.63649i −0.0571098 0.175766i
\(226\) 0.753164 0.836473i 0.0500997 0.0556414i
\(227\) −20.0431 + 8.92378i −1.33031 + 0.592292i −0.943960 0.330061i \(-0.892931\pi\)
−0.386349 + 0.922352i \(0.626264\pi\)
\(228\) −3.42544 32.5909i −0.226855 2.15838i
\(229\) 19.8092 4.21058i 1.30903 0.278243i 0.500009 0.866020i \(-0.333330\pi\)
0.809023 + 0.587777i \(0.199997\pi\)
\(230\) −4.54323 −0.299571
\(231\) 0 0
\(232\) 2.19819 0.144318
\(233\) −20.6023 + 4.37916i −1.34970 + 0.286888i −0.825354 0.564616i \(-0.809024\pi\)
−0.524349 + 0.851504i \(0.675691\pi\)
\(234\) −1.21388 11.5493i −0.0793535 0.754998i
\(235\) 8.61264 3.83459i 0.561827 0.250141i
\(236\) 0.382401 0.424700i 0.0248922 0.0276456i
\(237\) 3.93597 + 12.1137i 0.255668 + 0.786867i
\(238\) 0 0
\(239\) −12.5370 + 9.10863i −0.810948 + 0.589188i −0.914105 0.405477i \(-0.867106\pi\)
0.103157 + 0.994665i \(0.467106\pi\)
\(240\) −9.94077 + 2.11297i −0.641674 + 0.136392i
\(241\) −7.04241 + 12.1978i −0.453641 + 0.785730i −0.998609 0.0527271i \(-0.983209\pi\)
0.544967 + 0.838457i \(0.316542\pi\)
\(242\) −0.492093 7.35073i −0.0316329 0.472523i
\(243\) −9.23960 16.0035i −0.592721 1.02662i
\(244\) −2.40262 + 7.39450i −0.153812 + 0.473384i
\(245\) 0 0
\(246\) −9.46064 6.87356i −0.603188 0.438242i
\(247\) −11.3810 + 12.6399i −0.724156 + 0.804256i
\(248\) 6.98389 + 1.48447i 0.443477 + 0.0942640i
\(249\) −11.6206 + 5.17381i −0.736423 + 0.327877i
\(250\) −7.08845 3.15598i −0.448313 0.199602i
\(251\) −0.332894 + 1.02454i −0.0210121 + 0.0646686i −0.961013 0.276504i \(-0.910824\pi\)
0.940001 + 0.341173i \(0.110824\pi\)
\(252\) 0 0
\(253\) 3.43148 9.91790i 0.215735 0.623533i
\(254\) −5.88267 10.1891i −0.369111 0.639320i
\(255\) −8.06613 8.95834i −0.505121 0.560993i
\(256\) 0.944455 + 8.98589i 0.0590284 + 0.561618i
\(257\) −1.36734 + 13.0094i −0.0852922 + 0.811501i 0.865341 + 0.501184i \(0.167102\pi\)
−0.950633 + 0.310317i \(0.899565\pi\)
\(258\) −5.47784 16.8591i −0.341035 1.04960i
\(259\) 0 0
\(260\) 6.80292 + 4.94261i 0.421899 + 0.306528i
\(261\) −5.79016 2.57795i −0.358402 0.159571i
\(262\) 3.01404 + 3.34743i 0.186208 + 0.206805i
\(263\) 4.78608 8.28973i 0.295122 0.511167i −0.679891 0.733313i \(-0.737973\pi\)
0.975013 + 0.222146i \(0.0713062\pi\)
\(264\) −3.05506 + 24.5799i −0.188026 + 1.51279i
\(265\) 1.43080 0.0878935
\(266\) 0 0
\(267\) 21.1015 15.3312i 1.29139 0.938252i
\(268\) −0.146298 + 1.39193i −0.00893659 + 0.0850260i
\(269\) 4.66433 + 0.991434i 0.284389 + 0.0604488i 0.347898 0.937533i \(-0.386896\pi\)
−0.0635085 + 0.997981i \(0.520229\pi\)
\(270\) −17.0127 3.61616i −1.03536 0.220073i
\(271\) 2.09603 19.9424i 0.127325 1.21142i −0.725128 0.688614i \(-0.758220\pi\)
0.852453 0.522803i \(-0.175114\pi\)
\(272\) 2.18762 1.58940i 0.132644 0.0963713i
\(273\) 0 0
\(274\) 9.28776 0.561094
\(275\) 0.915758 0.979113i 0.0552223 0.0590427i
\(276\) −7.70690 + 13.3487i −0.463901 + 0.803500i
\(277\) −7.76355 8.62230i −0.466467 0.518064i 0.463306 0.886199i \(-0.346663\pi\)
−0.929772 + 0.368135i \(0.879997\pi\)
\(278\) 8.73142 + 3.88748i 0.523676 + 0.233156i
\(279\) −16.6550 12.1006i −0.997111 0.724443i
\(280\) 0 0
\(281\) 3.73256 + 11.4876i 0.222666 + 0.685295i 0.998520 + 0.0543830i \(0.0173192\pi\)
−0.775854 + 0.630912i \(0.782681\pi\)
\(282\) −0.966647 + 9.19703i −0.0575630 + 0.547675i
\(283\) −2.29892 21.8727i −0.136656 1.30020i −0.820953 0.570996i \(-0.806557\pi\)
0.684297 0.729204i \(-0.260109\pi\)
\(284\) 15.4362 + 17.1436i 0.915968 + 1.01729i
\(285\) 22.6410 + 39.2154i 1.34114 + 2.32292i
\(286\) 4.60513 3.21438i 0.272307 0.190070i
\(287\) 0 0
\(288\) 12.2248 37.6240i 0.720353 2.21702i
\(289\) −12.6002 5.60996i −0.741187 0.329998i
\(290\) −1.21219 + 0.539702i −0.0711822 + 0.0316924i
\(291\) −26.1535 5.55910i −1.53315 0.325880i
\(292\) −8.34456 + 9.26757i −0.488328 + 0.542344i
\(293\) −1.14654 0.833014i −0.0669819 0.0486652i 0.553790 0.832656i \(-0.313181\pi\)
−0.620772 + 0.783991i \(0.713181\pi\)
\(294\) 0 0
\(295\) −0.244025 + 0.751033i −0.0142077 + 0.0437268i
\(296\) −1.79246 3.10463i −0.104184 0.180453i
\(297\) 20.7437 34.4076i 1.20367 1.99653i
\(298\) −0.878343 + 1.52133i −0.0508810 + 0.0881286i
\(299\) 7.82532 1.66332i 0.452550 0.0961925i
\(300\) −1.59295 + 1.15735i −0.0919691 + 0.0668195i
\(301\) 0 0
\(302\) −0.618734 1.90427i −0.0356041 0.109578i
\(303\) −8.46054 + 9.39638i −0.486045 + 0.539808i
\(304\) −9.27929 + 4.13141i −0.532204 + 0.236952i
\(305\) −1.12300 10.6847i −0.0643030 0.611802i
\(306\) 8.04633 1.71030i 0.459978 0.0977714i
\(307\) 29.4646 1.68163 0.840817 0.541319i \(-0.182075\pi\)
0.840817 + 0.541319i \(0.182075\pi\)
\(308\) 0 0
\(309\) −55.3411 −3.14825
\(310\) −4.21573 + 0.896080i −0.239437 + 0.0508939i
\(311\) −2.80959 26.7314i −0.159317 1.51580i −0.723600 0.690219i \(-0.757514\pi\)
0.564283 0.825581i \(-0.309153\pi\)
\(312\) −17.2490 + 7.67975i −0.976533 + 0.434780i
\(313\) −3.00620 + 3.33873i −0.169921 + 0.188716i −0.822090 0.569357i \(-0.807192\pi\)
0.652170 + 0.758073i \(0.273859\pi\)
\(314\) 2.32930 + 7.16884i 0.131450 + 0.404561i
\(315\) 0 0
\(316\) 5.09172 3.69935i 0.286431 0.208105i
\(317\) 10.7108 2.27665i 0.601577 0.127869i 0.102951 0.994686i \(-0.467171\pi\)
0.498626 + 0.866817i \(0.333838\pi\)
\(318\) −0.701741 + 1.21545i −0.0393517 + 0.0681591i
\(319\) −0.262611 3.05385i −0.0147034 0.170983i
\(320\) −0.904228 1.56617i −0.0505479 0.0875515i
\(321\) −14.9454 + 45.9971i −0.834169 + 2.56731i
\(322\) 0 0
\(323\) −9.74723 7.08177i −0.542350 0.394040i
\(324\) −18.1256 + 20.1305i −1.00698 + 1.11836i
\(325\) 0.999626 + 0.212477i 0.0554493 + 0.0117861i
\(326\) −11.1373 + 4.95866i −0.616839 + 0.274635i
\(327\) −54.2874 24.1703i −3.00210 1.33662i
\(328\) −4.08744 + 12.5799i −0.225691 + 0.694607i
\(329\) 0 0
\(330\) −4.35016 14.3046i −0.239468 0.787443i
\(331\) −8.26132 14.3090i −0.454083 0.786495i 0.544552 0.838727i \(-0.316700\pi\)
−0.998635 + 0.0522322i \(0.983366\pi\)
\(332\) 4.20577 + 4.67098i 0.230822 + 0.256353i
\(333\) 1.08046 + 10.2799i 0.0592088 + 0.563334i
\(334\) −1.39533 + 13.2757i −0.0763492 + 0.726414i
\(335\) −0.597628 1.83931i −0.0326519 0.100492i
\(336\) 0 0
\(337\) 9.80588 + 7.12439i 0.534160 + 0.388090i 0.821912 0.569615i \(-0.192908\pi\)
−0.287751 + 0.957705i \(0.592908\pi\)
\(338\) −4.04298 1.80005i −0.219909 0.0979099i
\(339\) 3.53085 + 3.92140i 0.191769 + 0.212981i
\(340\) −2.97826 + 5.15849i −0.161519 + 0.279758i
\(341\) 1.22797 9.87977i 0.0664983 0.535019i
\(342\) −30.9004 −1.67090
\(343\) 0 0
\(344\) −16.2215 + 11.7856i −0.874605 + 0.635437i
\(345\) 2.22632 21.1821i 0.119861 1.14040i
\(346\) −3.92415 0.834104i −0.210964 0.0448417i
\(347\) 23.7544 + 5.04916i 1.27521 + 0.271053i 0.795273 0.606252i \(-0.207328\pi\)
0.479933 + 0.877305i \(0.340661\pi\)
\(348\) −0.470566 + 4.47714i −0.0252250 + 0.240000i
\(349\) 2.68497 1.95074i 0.143723 0.104421i −0.513600 0.858030i \(-0.671689\pi\)
0.657323 + 0.753609i \(0.271689\pi\)
\(350\) 0 0
\(351\) 30.6269 1.63474
\(352\) 18.7853 3.62257i 1.00126 0.193084i
\(353\) −10.1636 + 17.6039i −0.540955 + 0.936962i 0.457894 + 0.889007i \(0.348604\pi\)
−0.998849 + 0.0479552i \(0.984730\pi\)
\(354\) −0.518311 0.575643i −0.0275479 0.0305951i
\(355\) −29.1208 12.9654i −1.54557 0.688132i
\(356\) −10.4268 7.57553i −0.552620 0.401502i
\(357\) 0 0
\(358\) −0.335059 1.03121i −0.0177084 0.0545009i
\(359\) −3.03564 + 28.8821i −0.160215 + 1.52434i 0.558774 + 0.829320i \(0.311272\pi\)
−0.718989 + 0.695021i \(0.755395\pi\)
\(360\) 3.65542 + 34.7790i 0.192657 + 1.83301i
\(361\) 17.5700 + 19.5134i 0.924736 + 1.02702i
\(362\) −0.812674 1.40759i −0.0427132 0.0739814i
\(363\) 34.5127 + 1.30779i 1.81145 + 0.0686410i
\(364\) 0 0
\(365\) 5.32499 16.3886i 0.278723 0.857821i
\(366\) 9.62728 + 4.28634i 0.503226 + 0.224051i
\(367\) −20.7912 + 9.25683i −1.08529 + 0.483203i −0.869851 0.493314i \(-0.835785\pi\)
−0.215440 + 0.976517i \(0.569119\pi\)
\(368\) 4.67323 + 0.993326i 0.243609 + 0.0517807i
\(369\) 25.5197 28.3425i 1.32850 1.47545i
\(370\) 1.75070 + 1.27196i 0.0910145 + 0.0661259i
\(371\) 0 0
\(372\) −4.51852 + 13.9066i −0.234274 + 0.721022i
\(373\) 11.1206 + 19.2614i 0.575802 + 0.997319i 0.995954 + 0.0898652i \(0.0286436\pi\)
−0.420151 + 0.907454i \(0.638023\pi\)
\(374\) 2.60544 + 3.00622i 0.134724 + 0.155448i
\(375\) 18.1878 31.5022i 0.939215 1.62677i
\(376\) 10.2316 2.17480i 0.527655 0.112157i
\(377\) 1.89030 1.37339i 0.0973556 0.0707330i
\(378\) 0 0
\(379\) 10.3430 + 31.8325i 0.531285 + 1.63513i 0.751543 + 0.659685i \(0.229310\pi\)
−0.220258 + 0.975442i \(0.570690\pi\)
\(380\) 14.9718 16.6279i 0.768037 0.852992i
\(381\) 50.3876 22.4340i 2.58144 1.14933i
\(382\) −0.889157 8.45977i −0.0454932 0.432839i
\(383\) 6.01162 1.27781i 0.307179 0.0652930i −0.0517429 0.998660i \(-0.516478\pi\)
0.358922 + 0.933367i \(0.383144\pi\)
\(384\) −34.4486 −1.75795
\(385\) 0 0
\(386\) −1.17829 −0.0599733
\(387\) 56.5500 12.0201i 2.87460 0.611015i
\(388\) 1.38101 + 13.1395i 0.0701103 + 0.667055i
\(389\) 6.76357 3.01133i 0.342926 0.152681i −0.228045 0.973651i \(-0.573233\pi\)
0.570971 + 0.820970i \(0.306567\pi\)
\(390\) 7.62641 8.46998i 0.386178 0.428894i
\(391\) 1.75119 + 5.38962i 0.0885617 + 0.272565i
\(392\) 0 0
\(393\) −17.0838 + 12.4121i −0.861765 + 0.626109i
\(394\) 0.591598 0.125748i 0.0298043 0.00633509i
\(395\) −4.34831 + 7.53150i −0.218787 + 0.378951i
\(396\) −34.3728 7.98935i −1.72730 0.401480i
\(397\) −8.90394 15.4221i −0.446876 0.774012i 0.551305 0.834304i \(-0.314130\pi\)
−0.998181 + 0.0602921i \(0.980797\pi\)
\(398\) −3.23473 + 9.95549i −0.162143 + 0.499024i
\(399\) 0 0
\(400\) 0.493749 + 0.358729i 0.0246874 + 0.0179365i
\(401\) 17.1825 19.0831i 0.858054 0.952965i −0.141261 0.989972i \(-0.545116\pi\)
0.999315 + 0.0370073i \(0.0117825\pi\)
\(402\) 1.85558 + 0.394416i 0.0925480 + 0.0196717i
\(403\) 6.93317 3.08684i 0.345366 0.153767i
\(404\) 5.70762 + 2.54120i 0.283965 + 0.126429i
\(405\) 11.5667 35.5985i 0.574752 1.76890i
\(406\) 0 0
\(407\) −4.09899 + 2.86108i −0.203179 + 0.141819i
\(408\) −6.68741 11.5829i −0.331076 0.573441i
\(409\) 0.894992 + 0.993990i 0.0442545 + 0.0491496i 0.764866 0.644190i \(-0.222805\pi\)
−0.720611 + 0.693339i \(0.756139\pi\)
\(410\) −0.834601 7.94070i −0.0412180 0.392163i
\(411\) −4.55130 + 43.3027i −0.224499 + 2.13596i
\(412\) 8.45022 + 26.0071i 0.416312 + 1.28128i
\(413\) 0 0
\(414\) 11.7585 + 8.54303i 0.577897 + 0.419867i
\(415\) −7.93431 3.53258i −0.389480 0.173408i
\(416\) 9.75851 + 10.8379i 0.478450 + 0.531373i
\(417\) −22.4034 + 38.8039i −1.09710 + 1.90023i
\(418\) −7.22535 13.0806i −0.353403 0.639794i
\(419\) 37.4618 1.83013 0.915064 0.403310i \(-0.132140\pi\)
0.915064 + 0.403310i \(0.132140\pi\)
\(420\) 0 0
\(421\) −6.68374 + 4.85602i −0.325746 + 0.236668i −0.738623 0.674118i \(-0.764524\pi\)
0.412878 + 0.910787i \(0.364524\pi\)
\(422\) −1.03392 + 9.83707i −0.0503303 + 0.478861i
\(423\) −29.5012 6.27067i −1.43440 0.304890i
\(424\) 1.55281 + 0.330060i 0.0754110 + 0.0160291i
\(425\) −0.0756696 + 0.719949i −0.00367052 + 0.0349226i
\(426\) 25.2963 18.3788i 1.22561 0.890458i
\(427\) 0 0
\(428\) 23.8980 1.15515
\(429\) 12.7298 + 23.0458i 0.614603 + 1.11266i
\(430\) 6.05171 10.4819i 0.291840 0.505481i
\(431\) 21.8514 + 24.2685i 1.05255 + 1.16897i 0.985229 + 0.171239i \(0.0547772\pi\)
0.0673168 + 0.997732i \(0.478556\pi\)
\(432\) 16.7089 + 7.43928i 0.803907 + 0.357922i
\(433\) −12.7786 9.28422i −0.614102 0.446171i 0.236754 0.971570i \(-0.423916\pi\)
−0.850856 + 0.525398i \(0.823916\pi\)
\(434\) 0 0
\(435\) −1.92226 5.91611i −0.0921654 0.283656i
\(436\) −3.06931 + 29.2026i −0.146993 + 1.39855i
\(437\) −2.22514 21.1708i −0.106443 1.01274i
\(438\) 11.3103 + 12.5614i 0.540428 + 0.600206i
\(439\) 10.3471 + 17.9217i 0.493839 + 0.855354i 0.999975 0.00709942i \(-0.00225984\pi\)
−0.506136 + 0.862454i \(0.668927\pi\)
\(440\) −13.8677 + 9.67964i −0.661118 + 0.461459i
\(441\) 0 0
\(442\) −0.937107 + 2.88412i −0.0445737 + 0.137184i
\(443\) 27.4936 + 12.2409i 1.30626 + 0.581584i 0.937514 0.347947i \(-0.113121\pi\)
0.368745 + 0.929531i \(0.379788\pi\)
\(444\) 6.70701 2.98616i 0.318301 0.141717i
\(445\) 17.4198 + 3.70269i 0.825777 + 0.175524i
\(446\) −0.826995 + 0.918470i −0.0391593 + 0.0434908i
\(447\) −6.66256 4.84063i −0.315128 0.228954i
\(448\) 0 0
\(449\) 11.2465 34.6132i 0.530755 1.63350i −0.221892 0.975071i \(-0.571223\pi\)
0.752647 0.658424i \(-0.228777\pi\)
\(450\) 0.928321 + 1.60790i 0.0437615 + 0.0757971i
\(451\) 17.9650 + 4.17564i 0.845938 + 0.196623i
\(452\) 1.30369 2.25806i 0.0613206 0.106210i
\(453\) 9.18154 1.95160i 0.431386 0.0916940i
\(454\) 11.8878 8.63700i 0.557922 0.405354i
\(455\) 0 0
\(456\) 15.5254 + 47.7821i 0.727041 + 2.23760i
\(457\) −6.55347 + 7.27837i −0.306559 + 0.340468i −0.876663 0.481104i \(-0.840236\pi\)
0.570105 + 0.821572i \(0.306903\pi\)
\(458\) −12.3909 + 5.51678i −0.578988 + 0.257782i
\(459\) 2.26773 + 21.5760i 0.105848 + 1.00708i
\(460\) −10.2943 + 2.18812i −0.479973 + 0.102021i
\(461\) −21.8596 −1.01810 −0.509052 0.860736i \(-0.670004\pi\)
−0.509052 + 0.860736i \(0.670004\pi\)
\(462\) 0 0
\(463\) 6.75889 0.314112 0.157056 0.987590i \(-0.449800\pi\)
0.157056 + 0.987590i \(0.449800\pi\)
\(464\) 1.36488 0.290114i 0.0633628 0.0134682i
\(465\) −2.11199 20.0943i −0.0979412 0.931849i
\(466\) 12.8870 5.73765i 0.596977 0.265791i
\(467\) −20.0894 + 22.3116i −0.929628 + 1.03246i 0.0697626 + 0.997564i \(0.477776\pi\)
−0.999391 + 0.0348933i \(0.988891\pi\)
\(468\) −8.31283 25.5843i −0.384261 1.18263i
\(469\) 0 0
\(470\) −5.10826 + 3.71136i −0.235626 + 0.171192i
\(471\) −34.5650 + 7.34701i −1.59267 + 0.338533i
\(472\) −0.438083 + 0.758782i −0.0201644 + 0.0349258i
\(473\) 18.3112 + 21.1279i 0.841949 + 0.971460i
\(474\) −4.26528 7.38768i −0.195911 0.339328i
\(475\) 0.840312 2.58622i 0.0385562 0.118664i
\(476\) 0 0
\(477\) −3.70311 2.69046i −0.169554 0.123188i
\(478\) 6.94471 7.71288i 0.317644 0.352779i
\(479\) 5.87234 + 1.24820i 0.268314 + 0.0570319i 0.340104 0.940388i \(-0.389538\pi\)
−0.0717898 + 0.997420i \(0.522871\pi\)
\(480\) 35.4698 15.7922i 1.61897 0.720811i
\(481\) −3.48111 1.54989i −0.158725 0.0706688i
\(482\) 2.91503 8.97153i 0.132776 0.408642i
\(483\) 0 0
\(484\) −4.65528 16.4187i −0.211604 0.746303i
\(485\) −9.12803 15.8102i −0.414483 0.717905i
\(486\) 8.28138 + 9.19741i 0.375651 + 0.417203i
\(487\) −0.665556 6.33235i −0.0301592 0.286946i −0.999198 0.0400380i \(-0.987252\pi\)
0.969039 0.246908i \(-0.0794146\pi\)
\(488\) 1.24599 11.8548i 0.0564033 0.536642i
\(489\) −17.6613 54.3559i −0.798671 2.45806i
\(490\) 0 0
\(491\) −10.0131 7.27496i −0.451886 0.328314i 0.338454 0.940983i \(-0.390096\pi\)
−0.790340 + 0.612669i \(0.790096\pi\)
\(492\) −24.7469 11.0180i −1.11567 0.496730i
\(493\) 1.10749 + 1.22999i 0.0498787 + 0.0553959i
\(494\) 5.69571 9.86527i 0.256262 0.443859i
\(495\) 47.8802 9.23325i 2.15206 0.415004i
\(496\) 4.53228 0.203505
\(497\) 0 0
\(498\) 6.89229 5.00754i 0.308851 0.224393i
\(499\) 1.49263 14.2014i 0.0668193 0.635743i −0.908945 0.416917i \(-0.863111\pi\)
0.975764 0.218826i \(-0.0702228\pi\)
\(500\) −17.5814 3.73704i −0.786263 0.167125i
\(501\) −61.2121 13.0110i −2.73475 0.581290i
\(502\) 0.0754167 0.717542i 0.00336601 0.0320255i
\(503\) −4.79402 + 3.48306i −0.213755 + 0.155302i −0.689511 0.724275i \(-0.742174\pi\)
0.475756 + 0.879577i \(0.342174\pi\)
\(504\) 0 0
\(505\) −8.63314 −0.384170
\(506\) −0.866947 + 6.97512i −0.0385405 + 0.310082i
\(507\) 10.3736 17.9677i 0.460709 0.797972i
\(508\) −18.2365 20.2537i −0.809115 0.898614i
\(509\) 28.2043 + 12.5574i 1.25014 + 0.556596i 0.921690 0.387927i \(-0.126809\pi\)
0.328445 + 0.944523i \(0.393475\pi\)
\(510\) 6.53162 + 4.74550i 0.289225 + 0.210134i
\(511\) 0 0
\(512\) 4.91089 + 15.1142i 0.217033 + 0.667958i
\(513\) 8.51848 81.0479i 0.376100 3.57835i
\(514\) −0.915767 8.71294i −0.0403927 0.384311i
\(515\) −25.2837 28.0804i −1.11413 1.23737i
\(516\) −20.5317 35.5619i −0.903856 1.56552i
\(517\) −4.24370 13.9545i −0.186637 0.613720i
\(518\) 0 0
\(519\) 5.81183 17.8870i 0.255111 0.785151i
\(520\) −11.7773 5.24359i −0.516469 0.229947i
\(521\) 17.2541 7.68202i 0.755916 0.336555i 0.00766428 0.999971i \(-0.497560\pi\)
0.748251 + 0.663415i \(0.230894\pi\)
\(522\) 4.15216 + 0.882568i 0.181735 + 0.0386289i
\(523\) −5.31429 + 5.90212i −0.232378 + 0.258082i −0.848045 0.529925i \(-0.822220\pi\)
0.615667 + 0.788007i \(0.288887\pi\)
\(524\) 8.44156 + 6.13315i 0.368771 + 0.267928i
\(525\) 0 0
\(526\) −1.98108 + 6.09712i −0.0863790 + 0.265847i
\(527\) 2.68798 + 4.65571i 0.117090 + 0.202806i
\(528\) 1.34709 + 15.6651i 0.0586246 + 0.681734i
\(529\) 6.49365 11.2473i 0.282333 0.489014i
\(530\) −0.937331 + 0.199236i −0.0407150 + 0.00865425i
\(531\) 2.04380 1.48491i 0.0886935 0.0644396i
\(532\) 0 0
\(533\) 4.34471 + 13.3716i 0.188190 + 0.579190i
\(534\) −11.6890 + 12.9819i −0.505831 + 0.561782i
\(535\) −30.1673 + 13.4313i −1.30424 + 0.580687i
\(536\) −0.224294 2.13401i −0.00968801 0.0921752i
\(537\) 4.97202 1.05684i 0.214559 0.0456058i
\(538\) −3.19370 −0.137690
\(539\) 0 0
\(540\) −40.2899 −1.73380
\(541\) −7.43554 + 1.58047i −0.319679 + 0.0679498i −0.364956 0.931025i \(-0.618916\pi\)
0.0452777 + 0.998974i \(0.485583\pi\)
\(542\) 1.40381 + 13.3563i 0.0602986 + 0.573703i
\(543\) 6.96091 3.09920i 0.298721 0.132999i
\(544\) −6.91254 + 7.67715i −0.296373 + 0.329155i
\(545\) −12.5381 38.5884i −0.537075 1.65295i
\(546\) 0 0
\(547\) −17.5548 + 12.7543i −0.750590 + 0.545335i −0.896010 0.444035i \(-0.853547\pi\)
0.145420 + 0.989370i \(0.453547\pi\)
\(548\) 21.0447 4.47319i 0.898984 0.191085i
\(549\) −17.1848 + 29.7650i −0.733431 + 1.27034i
\(550\) −0.463582 + 0.768942i −0.0197672 + 0.0327878i
\(551\) −3.10863 5.38431i −0.132432 0.229379i
\(552\) 7.30247 22.4747i 0.310814 0.956587i
\(553\) 0 0
\(554\) 6.28660 + 4.56749i 0.267092 + 0.194054i
\(555\) −6.78819 + 7.53905i −0.288143 + 0.320015i
\(556\) 21.6564 + 4.60321i 0.918436 + 0.195220i
\(557\) −37.1022 + 16.5189i −1.57207 + 0.699930i −0.993300 0.115562i \(-0.963133\pi\)
−0.578769 + 0.815492i \(0.696467\pi\)
\(558\) 12.5958 + 5.60803i 0.533224 + 0.237407i
\(559\) −6.58604 + 20.2697i −0.278560 + 0.857319i
\(560\) 0 0
\(561\) −15.2928 + 10.6743i −0.645661 + 0.450670i
\(562\) −4.04486 7.00590i −0.170622 0.295526i
\(563\) −15.6772 17.4113i −0.660717 0.733800i 0.315899 0.948793i \(-0.397694\pi\)
−0.976616 + 0.214993i \(0.931027\pi\)
\(564\) 2.23921 + 21.3047i 0.0942878 + 0.897088i
\(565\) −0.376603 + 3.58314i −0.0158438 + 0.150744i
\(566\) 4.55177 + 14.0089i 0.191325 + 0.588838i
\(567\) 0 0
\(568\) −28.6130 20.7886i −1.20058 0.872269i
\(569\) −10.1818 4.53322i −0.426842 0.190043i 0.182060 0.983287i \(-0.441723\pi\)
−0.608903 + 0.793245i \(0.708390\pi\)
\(570\) −20.2929 22.5376i −0.849978 0.943996i
\(571\) 3.07923 5.33338i 0.128862 0.223195i −0.794374 0.607429i \(-0.792201\pi\)
0.923236 + 0.384234i \(0.125534\pi\)
\(572\) 8.88644 9.50123i 0.371561 0.397266i
\(573\) 39.8780 1.66593
\(574\) 0 0
\(575\) −1.03477 + 0.751805i −0.0431529 + 0.0313524i
\(576\) −0.604744 + 5.75375i −0.0251977 + 0.239740i
\(577\) 14.1676 + 3.01142i 0.589807 + 0.125367i 0.493141 0.869950i \(-0.335849\pi\)
0.0966659 + 0.995317i \(0.469182\pi\)
\(578\) 9.03565 + 1.92059i 0.375834 + 0.0798859i
\(579\) 0.577398 5.49358i 0.0239959 0.228305i
\(580\) −2.48671 + 1.80670i −0.103255 + 0.0750192i
\(581\) 0 0
\(582\) 17.9075 0.742288
\(583\) 0.273028 2.19668i 0.0113077 0.0909773i
\(584\) 9.55961 16.5577i 0.395580 0.685164i
\(585\) 24.8726 + 27.6238i 1.02836 + 1.14211i
\(586\) 0.867106 + 0.386061i 0.0358198 + 0.0159480i
\(587\) −12.8285 9.32048i −0.529491 0.384698i 0.290676 0.956821i \(-0.406120\pi\)
−0.820167 + 0.572124i \(0.806120\pi\)
\(588\) 0 0
\(589\) −6.24035 19.2058i −0.257129 0.791362i
\(590\) 0.0552836 0.525988i 0.00227599 0.0216546i
\(591\) 0.296378 + 2.81985i 0.0121914 + 0.115993i
\(592\) −1.52270 1.69112i −0.0625824 0.0695048i
\(593\) −11.4642 19.8566i −0.470780 0.815415i 0.528662 0.848833i \(-0.322694\pi\)
−0.999441 + 0.0334179i \(0.989361\pi\)
\(594\) −8.79822 + 25.4292i −0.360995 + 1.04337i
\(595\) 0 0
\(596\) −1.25749 + 3.87015i −0.0515087 + 0.158527i
\(597\) −44.8307 19.9599i −1.83480 0.816906i
\(598\) −4.89482 + 2.17931i −0.200164 + 0.0891188i
\(599\) −12.8638 2.73429i −0.525601 0.111720i −0.0625335 0.998043i \(-0.519918\pi\)
−0.463068 + 0.886323i \(0.653251\pi\)
\(600\) 2.01992 2.24335i 0.0824628 0.0915842i
\(601\) −22.1286 16.0774i −0.902645 0.655810i 0.0364993 0.999334i \(-0.488379\pi\)
−0.939144 + 0.343524i \(0.888379\pi\)
\(602\) 0 0
\(603\) −1.91188 + 5.88415i −0.0778576 + 0.239621i
\(604\) −2.31910 4.01679i −0.0943627 0.163441i
\(605\) 15.1043 + 18.1094i 0.614075 + 0.736253i
\(606\) 4.23415 7.33376i 0.172001 0.297914i
\(607\) 45.8500 9.74572i 1.86099 0.395567i 0.866395 0.499359i \(-0.166431\pi\)
0.994599 + 0.103792i \(0.0330977\pi\)
\(608\) 31.3946 22.8095i 1.27322 0.925049i
\(609\) 0 0
\(610\) 2.22350 + 6.84324i 0.0900270 + 0.277075i
\(611\) 7.43977 8.26270i 0.300981 0.334273i
\(612\) 17.4081 7.75057i 0.703680 0.313298i
\(613\) 2.13964 + 20.3573i 0.0864192 + 0.822223i 0.948782 + 0.315932i \(0.102317\pi\)
−0.862363 + 0.506291i \(0.831016\pi\)
\(614\) −19.3025 + 4.10288i −0.778986 + 0.165579i
\(615\) 37.4312 1.50937
\(616\) 0 0
\(617\) 44.1691 1.77818 0.889090 0.457733i \(-0.151338\pi\)
0.889090 + 0.457733i \(0.151338\pi\)
\(618\) 36.2544 7.70612i 1.45837 0.309986i
\(619\) −0.0712449 0.677850i −0.00286357 0.0272451i 0.992997 0.118141i \(-0.0376935\pi\)
−0.995860 + 0.0908961i \(0.971027\pi\)
\(620\) −9.12064 + 4.06077i −0.366294 + 0.163084i
\(621\) −25.6488 + 28.4859i −1.02925 + 1.14310i
\(622\) 5.56287 + 17.1208i 0.223051 + 0.686480i
\(623\) 0 0
\(624\) −9.69651 + 7.04492i −0.388171 + 0.282023i
\(625\) 22.3170 4.74362i 0.892679 0.189745i
\(626\) 1.50448 2.60584i 0.0601311 0.104150i
\(627\) 64.5269 27.2771i 2.57696 1.08934i
\(628\) 8.73051 + 15.1217i 0.348385 + 0.603421i
\(629\) 0.834110 2.56713i 0.0332582 0.102358i
\(630\) 0 0
\(631\) 29.8299 + 21.6727i 1.18751 + 0.862776i 0.992999 0.118124i \(-0.0376880\pi\)
0.194511 + 0.980900i \(0.437688\pi\)
\(632\) −6.45647 + 7.17064i −0.256825 + 0.285233i
\(633\) −45.3571 9.64095i −1.80278 0.383193i
\(634\) −6.69970 + 2.98290i −0.266079 + 0.118466i
\(635\) 34.4037 + 15.3175i 1.36527 + 0.607858i
\(636\) −1.00465 + 3.09201i −0.0398371 + 0.122606i
\(637\) 0 0
\(638\) 0.597281 + 1.96404i 0.0236466 + 0.0777570i
\(639\) 50.9884 + 88.3144i 2.01707 + 3.49367i
\(640\) −15.7385 17.4794i −0.622120 0.690934i
\(641\) 2.14415 + 20.4003i 0.0846890 + 0.805762i 0.951608 + 0.307314i \(0.0994301\pi\)
−0.866919 + 0.498449i \(0.833903\pi\)
\(642\) 3.38585 32.2142i 0.133629 1.27139i
\(643\) −2.35984 7.26283i −0.0930629 0.286418i 0.893681 0.448703i \(-0.148114\pi\)
−0.986744 + 0.162284i \(0.948114\pi\)
\(644\) 0 0
\(645\) 45.9045 + 33.3516i 1.80749 + 1.31322i
\(646\) 7.37161 + 3.28205i 0.290032 + 0.129131i
\(647\) 9.82473 + 10.9115i 0.386250 + 0.428974i 0.904644 0.426168i \(-0.140137\pi\)
−0.518394 + 0.855142i \(0.673470\pi\)
\(648\) 20.7649 35.9658i 0.815721 1.41287i
\(649\) 1.10648 + 0.517961i 0.0434331 + 0.0203317i
\(650\) −0.684450 −0.0268463
\(651\) 0 0
\(652\) −22.8473 + 16.5996i −0.894770 + 0.650089i
\(653\) −0.117807 + 1.12086i −0.00461015 + 0.0438627i −0.996585 0.0825717i \(-0.973687\pi\)
0.991975 + 0.126434i \(0.0403533\pi\)
\(654\) 38.9298 + 8.27479i 1.52228 + 0.323570i
\(655\) −14.1031 2.99770i −0.551052 0.117130i
\(656\) −0.877663 + 8.35040i −0.0342670 + 0.326028i
\(657\) −44.5988 + 32.4029i −1.73996 + 1.26416i
\(658\) 0 0
\(659\) 10.0215 0.390384 0.195192 0.980765i \(-0.437467\pi\)
0.195192 + 0.980765i \(0.437467\pi\)
\(660\) −16.7462 30.3170i −0.651846 1.18009i
\(661\) −7.86853 + 13.6287i −0.306050 + 0.530095i −0.977495 0.210960i \(-0.932341\pi\)
0.671444 + 0.741055i \(0.265674\pi\)
\(662\) 7.40456 + 8.22359i 0.287786 + 0.319619i
\(663\) −12.9875 5.78242i −0.504394 0.224571i
\(664\) −7.79597 5.66410i −0.302542 0.219810i
\(665\) 0 0
\(666\) −2.13927 6.58398i −0.0828949 0.255124i
\(667\) −0.305676 + 2.90832i −0.0118358 + 0.112611i
\(668\) 3.23225 + 30.7528i 0.125059 + 1.18986i
\(669\) −3.87697 4.30581i −0.149892 0.166472i
\(670\) 0.647631 + 1.12173i 0.0250202 + 0.0433362i
\(671\) −16.6182 0.314744i −0.641540 0.0121505i
\(672\) 0 0
\(673\) 9.89226 30.4452i 0.381319 1.17358i −0.557797 0.829977i \(-0.688353\pi\)
0.939116 0.343601i \(-0.111647\pi\)
\(674\) −7.41597 3.30180i −0.285652 0.127181i
\(675\) −4.47323 + 1.99161i −0.172175 + 0.0766572i
\(676\) −10.0277 2.13146i −0.385682 0.0819793i
\(677\) −10.2645 + 11.3999i −0.394496 + 0.438133i −0.907371 0.420331i \(-0.861914\pi\)
0.512874 + 0.858464i \(0.328581\pi\)
\(678\) −2.85913 2.07728i −0.109804 0.0797775i
\(679\) 0 0
\(680\) 2.82197 8.68512i 0.108218 0.333059i
\(681\) 34.4432 + 59.6574i 1.31987 + 2.28608i
\(682\) 0.571281 + 6.64331i 0.0218755 + 0.254385i
\(683\) −0.523820 + 0.907282i −0.0200434 + 0.0347162i −0.875873 0.482541i \(-0.839714\pi\)
0.855830 + 0.517258i \(0.173047\pi\)
\(684\) −70.0158 + 14.8823i −2.67712 + 0.569040i
\(685\) −24.0514 + 17.4743i −0.918955 + 0.667660i
\(686\) 0 0
\(687\) −19.6492 60.4739i −0.749663 2.30722i
\(688\) −8.51663 + 9.45868i −0.324694 + 0.360609i
\(689\) 1.54153 0.686334i 0.0587276 0.0261472i
\(690\) 1.49107 + 14.1866i 0.0567640 + 0.540073i
\(691\) −28.5505 + 6.06859i −1.08611 + 0.230860i −0.715981 0.698120i \(-0.754020\pi\)
−0.370131 + 0.928980i \(0.620687\pi\)
\(692\) −9.29326 −0.353277
\(693\) 0 0
\(694\) −16.2648 −0.617404
\(695\) −29.9247 + 6.36070i −1.13511 + 0.241275i
\(696\) −0.721437 6.86401i −0.0273460 0.260180i
\(697\) −9.09834 + 4.05084i −0.344624 + 0.153437i
\(698\) −1.48731 + 1.65182i −0.0562955 + 0.0625224i
\(699\) 20.4358 + 62.8950i 0.772954 + 2.37891i
\(700\) 0 0
\(701\) −10.3380 + 7.51100i −0.390461 + 0.283687i −0.765644 0.643264i \(-0.777580\pi\)
0.375183 + 0.926951i \(0.377580\pi\)
\(702\) −20.0639 + 4.26472i −0.757263 + 0.160961i
\(703\) −5.06970 + 8.78098i −0.191207 + 0.331181i
\(704\) −2.57705 + 1.08938i −0.0971264 + 0.0410577i
\(705\) −14.8004 25.6351i −0.557417 0.965474i
\(706\) 4.20697 12.9477i 0.158332 0.487294i
\(707\) 0 0
\(708\) −1.45166 1.05469i −0.0545567 0.0396377i
\(709\) 25.4744 28.2922i 0.956713 1.06254i −0.0412760 0.999148i \(-0.513142\pi\)
0.997989 0.0633895i \(-0.0201910\pi\)
\(710\) 20.8826 + 4.43874i 0.783712 + 0.166583i
\(711\) 25.4161 11.3160i 0.953179 0.424383i
\(712\) 18.0510 + 8.03684i 0.676491 + 0.301193i
\(713\) −2.93520 + 9.03361i −0.109924 + 0.338311i
\(714\) 0 0
\(715\) −5.87770 + 16.9881i −0.219814 + 0.635321i
\(716\) −1.25585 2.17519i −0.0469332 0.0812906i
\(717\) 32.5569 + 36.1581i 1.21586 + 1.35035i
\(718\) −2.03310 19.3436i −0.0758746 0.721898i
\(719\) 4.10477 39.0542i 0.153082 1.45648i −0.600764 0.799426i \(-0.705137\pi\)
0.753846 0.657051i \(-0.228196\pi\)
\(720\) 6.85975 + 21.1121i 0.255648 + 0.786803i
\(721\) 0 0
\(722\) −14.2274 10.3368i −0.529491 0.384697i
\(723\) 40.3998 + 17.9872i 1.50249 + 0.668950i
\(724\) −2.51933 2.79800i −0.0936300 0.103987i
\(725\) −0.186781 + 0.323514i −0.00693687 + 0.0120150i
\(726\) −22.7917 + 3.94907i −0.845879 + 0.146564i
\(727\) −28.4699 −1.05589 −0.527946 0.849278i \(-0.677037\pi\)
−0.527946 + 0.849278i \(0.677037\pi\)
\(728\) 0 0
\(729\) −4.56314 + 3.31531i −0.169005 + 0.122789i
\(730\) −1.20637 + 11.4778i −0.0446497 + 0.424813i
\(731\) −14.7673 3.13888i −0.546187 0.116096i
\(732\) 23.8784 + 5.07551i 0.882571 + 0.187596i
\(733\) 0.312892 2.97697i 0.0115569 0.109957i −0.987223 0.159347i \(-0.949061\pi\)
0.998780 + 0.0493902i \(0.0157278\pi\)
\(734\) 12.3315 8.95935i 0.455163 0.330696i
\(735\) 0 0
\(736\) −18.2527 −0.672802
\(737\) −2.93790 + 0.566546i −0.108219 + 0.0208690i
\(738\) −12.7715 + 22.1210i −0.470127 + 0.814284i
\(739\) −33.9469 37.7019i −1.24876 1.38689i −0.891589 0.452846i \(-0.850409\pi\)
−0.357169 0.934040i \(-0.616258\pi\)
\(740\) 4.57942 + 2.03889i 0.168343 + 0.0749511i
\(741\) 43.2041 + 31.3896i 1.58714 + 1.15313i
\(742\) 0 0
\(743\) −0.118625 0.365089i −0.00435191 0.0133938i 0.948857 0.315706i \(-0.102241\pi\)
−0.953209 + 0.302312i \(0.902241\pi\)
\(744\) 2.34329 22.2949i 0.0859091 0.817371i
\(745\) −0.587760 5.59216i −0.0215339 0.204881i
\(746\) −9.96730 11.0698i −0.364929 0.405295i
\(747\) 13.8924 + 24.0624i 0.508297 + 0.880395i
\(748\) 7.35141 + 5.55681i 0.268794 + 0.203177i
\(749\) 0 0
\(750\) −7.52839 + 23.1700i −0.274898 + 0.846048i
\(751\) −35.9544 16.0079i −1.31199 0.584137i −0.372923 0.927862i \(-0.621645\pi\)
−0.939070 + 0.343725i \(0.888311\pi\)
\(752\) 6.06588 2.70070i 0.221200 0.0984845i
\(753\) 3.30847 + 0.703236i 0.120567 + 0.0256274i
\(754\) −1.04711 + 1.16294i −0.0381336 + 0.0423517i
\(755\) 5.18502 + 3.76714i 0.188702 + 0.137100i
\(756\) 0 0
\(757\) 3.51868 10.8294i 0.127889 0.393600i −0.866528 0.499129i \(-0.833653\pi\)
0.994416 + 0.105528i \(0.0336534\pi\)
\(758\) −11.2084 19.4135i −0.407107 0.705130i
\(759\) −32.0956 7.46003i −1.16499 0.270782i
\(760\) −17.1518 + 29.7079i −0.622163 + 1.07762i
\(761\) 7.31816 1.55552i 0.265283 0.0563876i −0.0733498 0.997306i \(-0.523369\pi\)
0.338633 + 0.940919i \(0.390036\pi\)
\(762\) −29.8855 + 21.7131i −1.08264 + 0.786582i
\(763\) 0 0
\(764\) −6.08911 18.7403i −0.220296 0.678002i
\(765\) −17.6188 + 19.5676i −0.637008 + 0.707469i
\(766\) −3.76033 + 1.67421i −0.135866 + 0.0604916i
\(767\) 0.0973485 + 0.926209i 0.00351505 + 0.0334435i
\(768\) 27.7491 5.89826i 1.00131 0.212835i
\(769\) −26.8378 −0.967798 −0.483899 0.875124i \(-0.660780\pi\)
−0.483899 + 0.875124i \(0.660780\pi\)
\(770\) 0 0
\(771\) 41.0714 1.47915
\(772\) −2.66983 + 0.567489i −0.0960891 + 0.0204244i
\(773\) −0.467013 4.44333i −0.0167973 0.159816i 0.982908 0.184098i \(-0.0589365\pi\)
−0.999705 + 0.0242827i \(0.992270\pi\)
\(774\) −35.3726 + 15.7489i −1.27144 + 0.566083i
\(775\) −0.811897 + 0.901703i −0.0291642 + 0.0323901i
\(776\) −6.25926 19.2640i −0.224694 0.691538i
\(777\) 0 0
\(778\) −4.01155 + 2.91456i −0.143821 + 0.104492i
\(779\) 36.5938 7.77825i 1.31111 0.278685i
\(780\) 13.2010 22.8648i 0.472671 0.818690i
\(781\) −25.4624 + 42.2344i −0.911116 + 1.51127i
\(782\) −1.89771 3.28694i −0.0678621 0.117541i
\(783\) −3.45951 + 10.6473i −0.123633 + 0.380503i
\(784\) 0 0
\(785\) −19.5196 14.1818i −0.696685 0.506171i
\(786\) 9.46340 10.5102i 0.337548 0.374885i
\(787\) 13.1912 + 2.80388i 0.470217 + 0.0999476i 0.436925 0.899498i \(-0.356068\pi\)
0.0332918 + 0.999446i \(0.489401\pi\)
\(788\) 1.27991 0.569853i 0.0455949 0.0203002i
\(789\) −27.4561 12.2242i −0.977462 0.435194i
\(790\) 1.79987 5.53944i 0.0640366 0.197084i
\(791\) 0 0
\(792\) 54.0930 + 1.02450i 1.92211 + 0.0364041i
\(793\) −6.33518 10.9728i −0.224969 0.389657i
\(794\) 7.98053 + 8.86328i 0.283218 + 0.314546i
\(795\) −0.469583 4.46779i −0.0166544 0.158456i
\(796\) −2.53465 + 24.1156i −0.0898383 + 0.854754i
\(797\) 16.2250 + 49.9354i 0.574719 + 1.76880i 0.637134 + 0.770753i \(0.280120\pi\)
−0.0624156 + 0.998050i \(0.519880\pi\)
\(798\) 0 0
\(799\) 6.37177 + 4.62936i 0.225417 + 0.163775i
\(800\) −2.13006 0.948363i −0.0753090 0.0335297i
\(801\) −38.1222 42.3390i −1.34698 1.49597i
\(802\) −8.59913 + 14.8941i −0.303646 + 0.525930i
\(803\) −24.1450 11.3027i −0.852059 0.398862i
\(804\) 4.39443 0.154980
\(805\) 0 0
\(806\) −4.11214 + 2.98764i −0.144844 + 0.105235i
\(807\) 1.56501 14.8901i 0.0550910 0.524156i
\(808\) −9.36930 1.99151i −0.329611 0.0700609i
\(809\) 1.26166 + 0.268173i 0.0443575 + 0.00942847i 0.230037 0.973182i \(-0.426115\pi\)
−0.185680 + 0.982610i \(0.559449\pi\)
\(810\) −2.62041 + 24.9315i −0.0920717 + 0.876004i
\(811\) 27.6585 20.0951i 0.971220 0.705633i 0.0154910 0.999880i \(-0.495069\pi\)
0.955729 + 0.294247i \(0.0950689\pi\)
\(812\) 0 0
\(813\) −62.9596 −2.20809
\(814\) 2.28688 2.44509i 0.0801551 0.0857005i
\(815\) 19.5116 33.7950i 0.683460 1.18379i
\(816\) −5.68097 6.30936i −0.198874 0.220872i
\(817\) 51.8080 + 23.0664i 1.81253 + 0.806992i
\(818\) −0.724728 0.526545i −0.0253395 0.0184102i
\(819\) 0 0
\(820\) −5.71550 17.5905i −0.199594 0.614287i
\(821\) −4.14559 + 39.4427i −0.144682 + 1.37656i 0.645534 + 0.763731i \(0.276635\pi\)
−0.790217 + 0.612828i \(0.790032\pi\)
\(822\) −3.04820 29.0017i −0.106318 1.01155i
\(823\) −6.17416 6.85710i −0.215218 0.239024i 0.625863 0.779933i \(-0.284747\pi\)
−0.841081 + 0.540909i \(0.818080\pi\)
\(824\) −20.9620 36.3073i −0.730247 1.26482i
\(825\) −3.35790 2.53818i −0.116907 0.0883681i
\(826\) 0 0
\(827\) −7.94043 + 24.4381i −0.276116 + 0.849797i 0.712806 + 0.701361i \(0.247424\pi\)
−0.988922 + 0.148436i \(0.952576\pi\)
\(828\) 30.7574 + 13.6941i 1.06890 + 0.475903i
\(829\) 9.99284 4.44910i 0.347066 0.154524i −0.225798 0.974174i \(-0.572499\pi\)
0.572864 + 0.819651i \(0.305832\pi\)
\(830\) 5.68973 + 1.20939i 0.197494 + 0.0419785i
\(831\) −24.3758 + 27.0721i −0.845587 + 0.939120i
\(832\) −1.72547 1.25363i −0.0598200 0.0434618i
\(833\) 0 0
\(834\) 9.27333 28.5404i 0.321109 0.988272i
\(835\) −21.3641 37.0037i −0.739334 1.28056i
\(836\) −22.6715 26.1589i −0.784110 0.904723i
\(837\) −18.1815 + 31.4913i −0.628444 + 1.08850i
\(838\) −24.5415 + 5.21646i −0.847773 + 0.180200i
\(839\) 28.1031 20.4181i 0.970228 0.704912i 0.0147243 0.999892i \(-0.495313\pi\)
0.955503 + 0.294980i \(0.0953129\pi\)
\(840\) 0 0
\(841\) −8.69756 26.7684i −0.299916 0.923047i
\(842\) 3.70239 4.11192i 0.127593 0.141706i
\(843\) 34.6460 15.4254i 1.19327 0.531279i
\(844\) 2.39504 + 22.7873i 0.0824407 + 0.784371i
\(845\) 13.8563 2.94525i 0.476671 0.101320i
\(846\) 20.1996 0.694478
\(847\) 0 0
\(848\) 1.00771 0.0346050
\(849\) −67.5447 + 14.3571i −2.31813 + 0.492733i
\(850\) −0.0506793 0.482181i −0.00173828 0.0165387i
\(851\) 4.35683 1.93979i 0.149350 0.0664950i
\(852\) 48.4660 53.8270i 1.66042 1.84408i
\(853\) −6.37880 19.6319i −0.218406 0.672185i −0.998894 0.0470143i \(-0.985029\pi\)
0.780488 0.625171i \(-0.214971\pi\)
\(854\) 0 0
\(855\) 80.0191 58.1373i 2.73659 1.98825i
\(856\) −35.8380 + 7.61760i −1.22492 + 0.260364i
\(857\) 17.0756 29.5758i 0.583291 1.01029i −0.411795 0.911276i \(-0.635098\pi\)
0.995086 0.0990131i \(-0.0315686\pi\)
\(858\) −11.5485 13.3249i −0.394260 0.454905i
\(859\) 16.7246 + 28.9679i 0.570637 + 0.988373i 0.996501 + 0.0835852i \(0.0266371\pi\)
−0.425863 + 0.904787i \(0.640030\pi\)
\(860\) 8.66399 26.6650i 0.295440 0.909269i
\(861\) 0 0
\(862\) −17.6944 12.8557i −0.602673 0.437868i
\(863\) −22.7732 + 25.2922i −0.775208 + 0.860956i −0.993371 0.114956i \(-0.963327\pi\)
0.218162 + 0.975913i \(0.429994\pi\)
\(864\) −68.3495 14.5281i −2.32530 0.494257i
\(865\) 11.7312 5.22307i 0.398873 0.177590i
\(866\) 9.66420 + 4.30278i 0.328403 + 0.146214i
\(867\) −13.3822 + 41.1861i −0.454483 + 1.39875i
\(868\) 0 0
\(869\) 10.7332 + 8.11305i 0.364099 + 0.275216i
\(870\) 2.08309 + 3.60802i 0.0706235 + 0.122323i
\(871\) −1.52617 1.69498i −0.0517122 0.0574322i
\(872\) −4.70564 44.7712i −0.159353 1.51614i
\(873\) −6.10478 + 58.0831i −0.206616 + 1.96582i
\(874\) 4.40569 + 13.5593i 0.149025 + 0.458651i
\(875\) 0 0
\(876\) 31.6773 + 23.0149i 1.07028 + 0.777602i
\(877\) 7.18692 + 3.19982i 0.242685 + 0.108050i 0.524475 0.851426i \(-0.324262\pi\)
−0.281790 + 0.959476i \(0.590928\pi\)
\(878\) −9.27401 10.2998i −0.312983 0.347602i
\(879\) −2.22485 + 3.85356i −0.0750425 + 0.129977i
\(880\) −7.33309 + 7.84041i −0.247198 + 0.264300i
\(881\) 13.3289 0.449063 0.224531 0.974467i \(-0.427915\pi\)
0.224531 + 0.974467i \(0.427915\pi\)
\(882\) 0 0
\(883\) 13.8340 10.0510i 0.465552 0.338243i −0.330153 0.943927i \(-0.607100\pi\)
0.795705 + 0.605684i \(0.207100\pi\)
\(884\) −0.734292 + 6.98632i −0.0246969 + 0.234975i
\(885\) 2.42524 + 0.515501i 0.0815237 + 0.0173284i
\(886\) −19.7158 4.19072i −0.662365 0.140790i
\(887\) 2.77193 26.3732i 0.0930724 0.885525i −0.843989 0.536361i \(-0.819799\pi\)
0.937061 0.349165i \(-0.113535\pi\)
\(888\) −9.10614 + 6.61600i −0.305582 + 0.222018i
\(889\) 0 0
\(890\) −11.9274 −0.399808
\(891\) −52.4465 24.5510i −1.75702 0.822490i
\(892\) −1.43149 + 2.47942i −0.0479299 + 0.0830170i
\(893\) −19.7963 21.9860i −0.662459 0.735735i
\(894\) 5.03875 + 2.24339i 0.168521 + 0.0750303i
\(895\) 2.80781 + 2.03999i 0.0938548 + 0.0681895i
\(896\) 0 0
\(897\) −7.76209 23.8892i −0.259168 0.797639i
\(898\) −2.54788 + 24.2414i −0.0850237 + 0.808946i
\(899\) 0.289978 + 2.75896i 0.00967132 + 0.0920165i
\(900\) 2.87784 + 3.19616i 0.0959279 + 0.106539i
\(901\) 0.597649 + 1.03516i 0.0199106 + 0.0344861i
\(902\) −12.3505 0.233913i −0.411225 0.00778846i
\(903\) 0 0
\(904\) −1.23528 + 3.80180i −0.0410848 + 0.126446i
\(905\) 4.75278 + 2.11607i 0.157988 + 0.0703407i
\(906\) −5.74315 + 2.55702i −0.190803 + 0.0849511i
\(907\) −8.65911 1.84055i −0.287521 0.0611145i 0.0618934 0.998083i \(-0.480286\pi\)
−0.349414 + 0.936968i \(0.613619\pi\)
\(908\) 22.7762 25.2956i 0.755856 0.839463i
\(909\) 22.3437 + 16.2337i 0.741094 + 0.538436i
\(910\) 0 0
\(911\) −17.2740 + 53.1639i −0.572313 + 1.76140i 0.0728381 + 0.997344i \(0.476794\pi\)
−0.645151 + 0.764055i \(0.723206\pi\)
\(912\) 15.9460 + 27.6194i 0.528026 + 0.914568i
\(913\) −6.93754 + 11.5073i −0.229599 + 0.380836i
\(914\) 3.27974 5.68068i 0.108484 0.187900i
\(915\) −32.9951 + 7.01332i −1.09078 + 0.231853i
\(916\) −25.4189 + 18.4679i −0.839865 + 0.610197i
\(917\) 0 0
\(918\) −4.49001 13.8188i −0.148192 0.456090i
\(919\) 32.3709 35.9516i 1.06782 1.18593i 0.0859639 0.996298i \(-0.472603\pi\)
0.981855 0.189634i \(-0.0607303\pi\)
\(920\) 14.7401 6.56270i 0.485966 0.216366i
\(921\) −9.67016 92.0054i −0.318643 3.03168i
\(922\) 14.3204 3.04390i 0.471618 0.100246i
\(923\) −37.5937 −1.23741
\(924\) 0 0
\(925\) 0.609223 0.0200311
\(926\) −4.42781 + 0.941159i −0.145507 + 0.0309284i
\(927\) 12.6355 + 120.219i 0.415005 + 3.94851i
\(928\) −4.87004 + 2.16828i −0.159867 + 0.0711773i
\(929\) 0.578326 0.642296i 0.0189743 0.0210731i −0.733583 0.679600i \(-0.762153\pi\)
0.752557 + 0.658527i \(0.228820\pi\)
\(930\) 4.18166 + 12.8698i 0.137122 + 0.422018i
\(931\) 0 0
\(932\) 26.4366 19.2073i 0.865959 0.629156i
\(933\) −82.5488 + 17.5463i −2.70253 + 0.574440i
\(934\) 10.0539 17.4139i 0.328975 0.569801i
\(935\) −12.4030 2.88285i −0.405622 0.0942794i
\(936\) 20.6212 + 35.7170i 0.674026 + 1.16745i
\(937\) 16.5194 50.8416i 0.539667 1.66092i −0.193678 0.981065i \(-0.562042\pi\)
0.733344 0.679858i \(-0.237958\pi\)
\(938\) 0 0
\(939\) 11.4120 + 8.29134i 0.372418 + 0.270578i
\(940\) −9.78708 + 10.8696i −0.319219 + 0.354529i
\(941\) −13.4006 2.84839i −0.436848 0.0928548i −0.0157621 0.999876i \(-0.505017\pi\)
−0.421086 + 0.907021i \(0.638351\pi\)
\(942\) 21.6208 9.62618i 0.704442 0.313638i
\(943\) −16.0754 7.15723i −0.523487 0.233071i
\(944\) −0.171867 + 0.528952i −0.00559379 + 0.0172159i
\(945\) 0 0
\(946\) −14.9378 11.2912i −0.485670 0.367110i
\(947\) −15.8222 27.4049i −0.514152 0.890538i −0.999865 0.0164197i \(-0.994773\pi\)
0.485713 0.874119i \(-0.338560\pi\)
\(948\) −13.2226 14.6851i −0.429449 0.476951i
\(949\) −2.12429 20.2112i −0.0689573 0.656085i
\(950\) −0.190371 + 1.81126i −0.00617646 + 0.0587651i
\(951\) −10.6242 32.6980i −0.344514 1.06031i
\(952\) 0 0
\(953\) −26.4856 19.2429i −0.857951 0.623338i 0.0693755 0.997591i \(-0.477899\pi\)
−0.927327 + 0.374253i \(0.877899\pi\)
\(954\) 2.80058 + 1.24690i 0.0906720 + 0.0403698i
\(955\) 18.2191 + 20.2343i 0.589555 + 0.654767i
\(956\) 12.0210 20.8210i 0.388787 0.673398i
\(957\) −9.44970 + 1.82228i −0.305465 + 0.0589061i
\(958\) −4.02083 −0.129907
\(959\) 0 0
\(960\) −4.59371 + 3.33753i −0.148261 + 0.107718i
\(961\) 2.29851 21.8688i 0.0741454 0.705446i
\(962\) 2.49632 + 0.530609i 0.0804846 + 0.0171075i
\(963\) 103.333 + 21.9641i 3.32986 + 0.707783i
\(964\) 2.28413 21.7321i 0.0735670 0.699943i
\(965\) 3.05127 2.21688i 0.0982238 0.0713637i
\(966\) 0 0
\(967\) −32.3487 −1.04026 −0.520132 0.854086i \(-0.674117\pi\)
−0.520132 + 0.854086i \(0.674117\pi\)
\(968\) 12.2147 + 23.1379i 0.392595 + 0.743681i
\(969\) −18.9144 + 32.7606i −0.607617 + 1.05242i
\(970\) 8.18138 + 9.08635i 0.262688 + 0.291745i
\(971\) −26.8829 11.9690i −0.862714 0.384105i −0.0728173 0.997345i \(-0.523199\pi\)
−0.789896 + 0.613240i \(0.789866\pi\)
\(972\) 23.1941 + 16.8515i 0.743950 + 0.540511i
\(973\) 0 0
\(974\) 1.31778 + 4.05570i 0.0422243 + 0.129953i
\(975\) 0.335402 3.19114i 0.0107415 0.102198i
\(976\) −0.790931 7.52520i −0.0253171 0.240876i
\(977\) 9.16337 + 10.1770i 0.293162 + 0.325590i 0.871676 0.490083i \(-0.163034\pi\)
−0.578513 + 0.815673i \(0.696367\pi\)
\(978\) 19.1390 + 33.1497i 0.611997 + 1.06001i
\(979\) 9.00874 26.0377i 0.287920 0.832168i
\(980\) 0 0
\(981\) −40.1108 + 123.448i −1.28064 + 3.94141i
\(982\) 7.57270 + 3.37158i 0.241654 + 0.107592i
\(983\) 15.5595 6.92751i 0.496269 0.220953i −0.143311 0.989678i \(-0.545775\pi\)
0.639580 + 0.768724i \(0.279108\pi\)
\(984\) 40.6230 + 8.63469i 1.29501 + 0.275264i
\(985\) −1.29540 + 1.43869i −0.0412749 + 0.0458404i
\(986\) −0.896797 0.651561i −0.0285598 0.0207499i
\(987\) 0 0
\(988\) 8.15432 25.0964i 0.259423 0.798423i
\(989\) −13.3372 23.1007i −0.424099 0.734561i
\(990\) −30.0810 + 12.7160i −0.956038 + 0.404141i
\(991\) −11.6101 + 20.1093i −0.368807 + 0.638792i −0.989379 0.145357i \(-0.953567\pi\)
0.620572 + 0.784149i \(0.286900\pi\)
\(992\) −16.9369 + 3.60005i −0.537747 + 0.114302i
\(993\) −41.9696 + 30.4927i −1.33187 + 0.967657i
\(994\) 0 0
\(995\) −10.3540 31.8665i −0.328245 1.01023i
\(996\) 13.2052 14.6658i 0.418422 0.464704i
\(997\) −16.7888 + 7.47485i −0.531706 + 0.236731i −0.654986 0.755641i \(-0.727325\pi\)
0.123280 + 0.992372i \(0.460659\pi\)
\(998\) 0.999680 + 9.51132i 0.0316443 + 0.301076i
\(999\) 17.8587 3.79598i 0.565024 0.120100i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 539.2.q.g.361.2 32
7.2 even 3 inner 539.2.q.g.471.3 32
7.3 odd 6 539.2.f.e.295.3 16
7.4 even 3 77.2.f.b.64.3 16
7.5 odd 6 539.2.q.f.471.3 32
7.6 odd 2 539.2.q.f.361.2 32
11.5 even 5 inner 539.2.q.g.214.3 32
21.11 odd 6 693.2.m.i.64.2 16
77.4 even 15 847.2.a.p.1.5 8
77.5 odd 30 539.2.q.f.324.2 32
77.16 even 15 inner 539.2.q.g.324.2 32
77.18 odd 30 847.2.a.o.1.4 8
77.25 even 15 847.2.f.w.323.2 16
77.27 odd 10 539.2.q.f.214.3 32
77.32 odd 6 847.2.f.x.372.2 16
77.38 odd 30 539.2.f.e.148.3 16
77.39 odd 30 847.2.f.x.148.2 16
77.46 odd 30 847.2.f.v.729.3 16
77.53 even 15 847.2.f.w.729.2 16
77.59 odd 30 5929.2.a.bt.1.5 8
77.60 even 15 77.2.f.b.71.3 yes 16
77.73 even 30 5929.2.a.bs.1.4 8
77.74 odd 30 847.2.f.v.323.3 16
231.95 even 30 7623.2.a.cw.1.5 8
231.137 odd 30 693.2.m.i.379.2 16
231.158 odd 30 7623.2.a.ct.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.b.64.3 16 7.4 even 3
77.2.f.b.71.3 yes 16 77.60 even 15
539.2.f.e.148.3 16 77.38 odd 30
539.2.f.e.295.3 16 7.3 odd 6
539.2.q.f.214.3 32 77.27 odd 10
539.2.q.f.324.2 32 77.5 odd 30
539.2.q.f.361.2 32 7.6 odd 2
539.2.q.f.471.3 32 7.5 odd 6
539.2.q.g.214.3 32 11.5 even 5 inner
539.2.q.g.324.2 32 77.16 even 15 inner
539.2.q.g.361.2 32 1.1 even 1 trivial
539.2.q.g.471.3 32 7.2 even 3 inner
693.2.m.i.64.2 16 21.11 odd 6
693.2.m.i.379.2 16 231.137 odd 30
847.2.a.o.1.4 8 77.18 odd 30
847.2.a.p.1.5 8 77.4 even 15
847.2.f.v.323.3 16 77.74 odd 30
847.2.f.v.729.3 16 77.46 odd 30
847.2.f.w.323.2 16 77.25 even 15
847.2.f.w.729.2 16 77.53 even 15
847.2.f.x.148.2 16 77.39 odd 30
847.2.f.x.372.2 16 77.32 odd 6
5929.2.a.bs.1.4 8 77.73 even 30
5929.2.a.bt.1.5 8 77.59 odd 30
7623.2.a.ct.1.4 8 231.158 odd 30
7623.2.a.cw.1.5 8 231.95 even 30