Properties

Label 462.2.w.a.239.7
Level $462$
Weight $2$
Character 462.239
Analytic conductor $3.689$
Analytic rank $0$
Dimension $48$
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] = [462,2,Mod(29,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.w (of order \(10\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 239.7
Character \(\chi\) \(=\) 462.239
Dual form 462.2.w.a.29.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.261877 + 1.71214i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.43689 - 1.97771i) q^{5} +(-1.21823 - 1.23122i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-2.86284 + 0.896741i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.261877 + 1.71214i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.43689 - 1.97771i) q^{5} +(-1.21823 - 1.23122i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-2.86284 + 0.896741i) q^{9} +2.44458i q^{10} +(1.53536 - 2.93984i) q^{11} +(1.70927 + 0.280020i) q^{12} +(4.02784 + 5.54385i) q^{13} +(0.951057 - 0.309017i) q^{14} +(3.76240 + 1.94224i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.36689 + 0.993107i) q^{17} +(1.78900 - 2.40821i) q^{18} +(6.15014 - 1.99830i) q^{19} +(-1.43689 - 1.97771i) q^{20} +(0.280020 - 1.70927i) q^{21} +(0.485860 + 3.28084i) q^{22} +5.69092i q^{23} +(-1.54742 + 0.778140i) q^{24} +(-0.301591 - 0.928202i) q^{25} +(-6.51718 - 2.11756i) q^{26} +(-2.28506 - 4.66675i) q^{27} +(-0.587785 + 0.809017i) q^{28} +(1.73027 - 5.32522i) q^{29} +(-4.18546 + 0.640180i) q^{30} +(-0.638022 + 0.463550i) q^{31} +1.00000 q^{32} +(5.43549 + 1.85888i) q^{33} -1.68957 q^{34} +(-1.97771 + 1.43689i) q^{35} +(-0.0318154 + 2.99983i) q^{36} +(2.12167 - 6.52982i) q^{37} +(-3.80100 + 5.23162i) q^{38} +(-8.43704 + 8.34803i) q^{39} +(2.32493 + 0.755417i) q^{40} +(2.79393 + 8.59884i) q^{41} +(0.778140 + 1.54742i) q^{42} +6.16717i q^{43} +(-2.32150 - 2.36868i) q^{44} +(-2.34009 + 6.95037i) q^{45} +(-3.34504 - 4.60405i) q^{46} +(-4.81667 + 1.56503i) q^{47} +(0.794507 - 1.53908i) q^{48} +(0.809017 + 0.587785i) q^{49} +(0.789576 + 0.573660i) q^{50} +(-1.34238 + 2.60039i) q^{51} +(6.51718 - 2.11756i) q^{52} +(0.765951 + 1.05424i) q^{53} +(4.59169 + 2.43235i) q^{54} +(-3.60800 - 7.26072i) q^{55} -1.00000i q^{56} +(5.03195 + 10.0066i) q^{57} +(1.73027 + 5.32522i) q^{58} +(-13.0119 - 4.22781i) q^{59} +(3.00982 - 2.97807i) q^{60} +(5.87948 - 8.09241i) q^{61} +(0.243703 - 0.750040i) q^{62} +(2.99983 + 0.0318154i) q^{63} +(-0.809017 + 0.587785i) q^{64} +16.7517 q^{65} +(-5.49003 + 1.69104i) q^{66} -1.03374 q^{67} +(1.36689 - 0.993107i) q^{68} +(-9.74364 + 1.49032i) q^{69} +(0.755417 - 2.32493i) q^{70} +(-4.46190 + 6.14128i) q^{71} +(-1.73752 - 2.44562i) q^{72} +(0.108422 + 0.0352283i) q^{73} +(2.12167 + 6.52982i) q^{74} +(1.51023 - 0.759441i) q^{75} -6.46664i q^{76} +(-2.36868 + 2.32150i) q^{77} +(1.91886 - 11.7129i) q^{78} +(-6.14287 - 8.45493i) q^{79} +(-2.32493 + 0.755417i) q^{80} +(7.39171 - 5.13445i) q^{81} +(-7.31461 - 5.31438i) q^{82} +(-2.09224 - 1.52010i) q^{83} +(-1.53908 - 0.794507i) q^{84} +(3.92815 - 1.27633i) q^{85} +(-3.62497 - 4.98935i) q^{86} +(9.57063 + 1.56791i) q^{87} +(3.27041 + 0.551756i) q^{88} -11.7971i q^{89} +(-2.19215 - 6.99844i) q^{90} +(-2.11756 - 6.51718i) q^{91} +(5.41238 + 1.75859i) q^{92} +(-0.960746 - 0.970989i) q^{93} +(2.97687 - 4.09731i) q^{94} +(4.88501 - 15.0345i) q^{95} +(0.261877 + 1.71214i) q^{96} +(0.828161 - 0.601694i) q^{97} -1.00000 q^{98} +(-1.75923 + 9.79312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 12 q^{2} - 4 q^{3} - 12 q^{4} + 6 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{11} + 6 q^{12} + 36 q^{15} - 12 q^{16} - 24 q^{17} + 30 q^{19} - 8 q^{22} - 4 q^{24} + 18 q^{25} - 20 q^{26} - 22 q^{27} + 8 q^{29} - 24 q^{30} - 32 q^{31} + 48 q^{32} - 14 q^{33} - 4 q^{34} + 6 q^{35} - 10 q^{36} - 20 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{44} + 12 q^{45} + 20 q^{46} + 20 q^{47} - 4 q^{48} + 12 q^{49} + 28 q^{50} + 8 q^{51} + 20 q^{52} + 20 q^{53} + 18 q^{54} + 16 q^{55} - 2 q^{57} + 8 q^{58} + 30 q^{59} - 4 q^{60} - 20 q^{61} + 8 q^{62} + 4 q^{63} - 12 q^{64} - 14 q^{66} + 36 q^{67} - 24 q^{68} - 70 q^{69} - 4 q^{70} + 10 q^{72} - 20 q^{73} - 20 q^{74} - 30 q^{75} - 16 q^{77} - 16 q^{78} - 20 q^{79} + 26 q^{81} - 10 q^{82} - 46 q^{83} - 10 q^{84} + 10 q^{85} - 30 q^{86} + 8 q^{87} - 8 q^{88} - 38 q^{90} - 36 q^{91} + 10 q^{92} - 36 q^{93} + 50 q^{95} - 4 q^{96} - 2 q^{97} - 48 q^{98} + 70 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0.261877 + 1.71214i 0.151195 + 0.988504i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 1.43689 1.97771i 0.642596 0.884457i −0.356155 0.934427i \(-0.615912\pi\)
0.998751 + 0.0499697i \(0.0159125\pi\)
\(6\) −1.21823 1.23122i −0.497342 0.502644i
\(7\) −0.951057 0.309017i −0.359466 0.116797i
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) −2.86284 + 0.896741i −0.954280 + 0.298914i
\(10\) 2.44458i 0.773044i
\(11\) 1.53536 2.93984i 0.462929 0.886395i
\(12\) 1.70927 + 0.280020i 0.493422 + 0.0808348i
\(13\) 4.02784 + 5.54385i 1.11712 + 1.53759i 0.810484 + 0.585761i \(0.199204\pi\)
0.306638 + 0.951826i \(0.400796\pi\)
\(14\) 0.951057 0.309017i 0.254181 0.0825883i
\(15\) 3.76240 + 1.94224i 0.971447 + 0.501483i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 1.36689 + 0.993107i 0.331521 + 0.240864i 0.741076 0.671422i \(-0.234316\pi\)
−0.409555 + 0.912285i \(0.634316\pi\)
\(18\) 1.78900 2.40821i 0.421670 0.567621i
\(19\) 6.15014 1.99830i 1.41094 0.458442i 0.498227 0.867046i \(-0.333984\pi\)
0.912712 + 0.408605i \(0.133984\pi\)
\(20\) −1.43689 1.97771i −0.321298 0.442229i
\(21\) 0.280020 1.70927i 0.0611054 0.372992i
\(22\) 0.485860 + 3.28084i 0.103586 + 0.699478i
\(23\) 5.69092i 1.18664i 0.804967 + 0.593319i \(0.202183\pi\)
−0.804967 + 0.593319i \(0.797817\pi\)
\(24\) −1.54742 + 0.778140i −0.315865 + 0.158837i
\(25\) −0.301591 0.928202i −0.0603182 0.185640i
\(26\) −6.51718 2.11756i −1.27812 0.415288i
\(27\) −2.28506 4.66675i −0.439760 0.898116i
\(28\) −0.587785 + 0.809017i −0.111081 + 0.152890i
\(29\) 1.73027 5.32522i 0.321303 0.988868i −0.651779 0.758409i \(-0.725977\pi\)
0.973082 0.230459i \(-0.0740229\pi\)
\(30\) −4.18546 + 0.640180i −0.764157 + 0.116880i
\(31\) −0.638022 + 0.463550i −0.114592 + 0.0832561i −0.643605 0.765358i \(-0.722562\pi\)
0.529013 + 0.848614i \(0.322562\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.43549 + 1.85888i 0.946198 + 0.323589i
\(34\) −1.68957 −0.289760
\(35\) −1.97771 + 1.43689i −0.334293 + 0.242878i
\(36\) −0.0318154 + 2.99983i −0.00530257 + 0.499972i
\(37\) 2.12167 6.52982i 0.348800 1.07350i −0.610718 0.791848i \(-0.709119\pi\)
0.959518 0.281648i \(-0.0908809\pi\)
\(38\) −3.80100 + 5.23162i −0.616603 + 0.848681i
\(39\) −8.43704 + 8.34803i −1.35101 + 1.33675i
\(40\) 2.32493 + 0.755417i 0.367604 + 0.119442i
\(41\) 2.79393 + 8.59884i 0.436339 + 1.34291i 0.891708 + 0.452611i \(0.149507\pi\)
−0.455369 + 0.890303i \(0.650493\pi\)
\(42\) 0.778140 + 1.54742i 0.120070 + 0.238772i
\(43\) 6.16717i 0.940485i 0.882537 + 0.470242i \(0.155833\pi\)
−0.882537 + 0.470242i \(0.844167\pi\)
\(44\) −2.32150 2.36868i −0.349979 0.357092i
\(45\) −2.34009 + 6.95037i −0.348840 + 1.03610i
\(46\) −3.34504 4.60405i −0.493199 0.678830i
\(47\) −4.81667 + 1.56503i −0.702584 + 0.228283i −0.638456 0.769658i \(-0.720427\pi\)
−0.0641278 + 0.997942i \(0.520427\pi\)
\(48\) 0.794507 1.53908i 0.114677 0.222147i
\(49\) 0.809017 + 0.587785i 0.115574 + 0.0839693i
\(50\) 0.789576 + 0.573660i 0.111663 + 0.0811278i
\(51\) −1.34238 + 2.60039i −0.187971 + 0.364127i
\(52\) 6.51718 2.11756i 0.903771 0.293653i
\(53\) 0.765951 + 1.05424i 0.105212 + 0.144811i 0.858376 0.513021i \(-0.171474\pi\)
−0.753165 + 0.657832i \(0.771474\pi\)
\(54\) 4.59169 + 2.43235i 0.624850 + 0.331001i
\(55\) −3.60800 7.26072i −0.486502 0.979035i
\(56\) 1.00000i 0.133631i
\(57\) 5.03195 + 10.0066i 0.666498 + 1.32540i
\(58\) 1.73027 + 5.32522i 0.227195 + 0.699235i
\(59\) −13.0119 4.22781i −1.69400 0.550414i −0.706456 0.707757i \(-0.749707\pi\)
−0.987544 + 0.157343i \(0.949707\pi\)
\(60\) 3.00982 2.97807i 0.388566 0.384467i
\(61\) 5.87948 8.09241i 0.752790 1.03613i −0.244990 0.969526i \(-0.578785\pi\)
0.997780 0.0666007i \(-0.0212154\pi\)
\(62\) 0.243703 0.750040i 0.0309503 0.0952552i
\(63\) 2.99983 + 0.0318154i 0.377943 + 0.00400837i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 16.7517 2.07779
\(66\) −5.49003 + 1.69104i −0.675776 + 0.208152i
\(67\) −1.03374 −0.126292 −0.0631459 0.998004i \(-0.520113\pi\)
−0.0631459 + 0.998004i \(0.520113\pi\)
\(68\) 1.36689 0.993107i 0.165760 0.120432i
\(69\) −9.74364 + 1.49032i −1.17300 + 0.179414i
\(70\) 0.755417 2.32493i 0.0902896 0.277883i
\(71\) −4.46190 + 6.14128i −0.529531 + 0.728836i −0.987059 0.160359i \(-0.948735\pi\)
0.457528 + 0.889195i \(0.348735\pi\)
\(72\) −1.73752 2.44562i −0.204768 0.288219i
\(73\) 0.108422 + 0.0352283i 0.0126898 + 0.00412316i 0.315355 0.948974i \(-0.397876\pi\)
−0.302665 + 0.953097i \(0.597876\pi\)
\(74\) 2.12167 + 6.52982i 0.246639 + 0.759076i
\(75\) 1.51023 0.759441i 0.174386 0.0876927i
\(76\) 6.46664i 0.741774i
\(77\) −2.36868 + 2.32150i −0.269936 + 0.264560i
\(78\) 1.91886 11.7129i 0.217268 1.32622i
\(79\) −6.14287 8.45493i −0.691127 0.951254i −1.00000 0.000151201i \(-0.999952\pi\)
0.308873 0.951103i \(-0.400048\pi\)
\(80\) −2.32493 + 0.755417i −0.259935 + 0.0844581i
\(81\) 7.39171 5.13445i 0.821301 0.570495i
\(82\) −7.31461 5.31438i −0.807764 0.586875i
\(83\) −2.09224 1.52010i −0.229653 0.166852i 0.467008 0.884253i \(-0.345332\pi\)
−0.696661 + 0.717401i \(0.745332\pi\)
\(84\) −1.53908 0.794507i −0.167927 0.0866878i
\(85\) 3.92815 1.27633i 0.426067 0.138438i
\(86\) −3.62497 4.98935i −0.390891 0.538015i
\(87\) 9.57063 + 1.56791i 1.02608 + 0.168097i
\(88\) 3.27041 + 0.551756i 0.348627 + 0.0588174i
\(89\) 11.7971i 1.25049i −0.780428 0.625245i \(-0.784999\pi\)
0.780428 0.625245i \(-0.215001\pi\)
\(90\) −2.19215 6.99844i −0.231073 0.737701i
\(91\) −2.11756 6.51718i −0.221981 0.683187i
\(92\) 5.41238 + 1.75859i 0.564280 + 0.183346i
\(93\) −0.960746 0.970989i −0.0996247 0.100687i
\(94\) 2.97687 4.09731i 0.307040 0.422605i
\(95\) 4.88501 15.0345i 0.501191 1.54251i
\(96\) 0.261877 + 1.71214i 0.0267277 + 0.174744i
\(97\) 0.828161 0.601694i 0.0840870 0.0610928i −0.544947 0.838470i \(-0.683450\pi\)
0.629034 + 0.777377i \(0.283450\pi\)
\(98\) −1.00000 −0.101015
\(99\) −1.75923 + 9.79312i −0.176809 + 0.984245i
\(100\) −0.975969 −0.0975969
\(101\) 10.4795 7.61383i 1.04275 0.757605i 0.0719321 0.997410i \(-0.477084\pi\)
0.970821 + 0.239805i \(0.0770835\pi\)
\(102\) −0.442461 2.89279i −0.0438102 0.286429i
\(103\) 0.879825 2.70782i 0.0866917 0.266810i −0.898308 0.439367i \(-0.855203\pi\)
0.985000 + 0.172557i \(0.0552029\pi\)
\(104\) −4.02784 + 5.54385i −0.394962 + 0.543619i
\(105\) −2.97807 3.00982i −0.290630 0.293728i
\(106\) −1.23934 0.402684i −0.120375 0.0391122i
\(107\) −2.43057 7.48053i −0.234972 0.723170i −0.997125 0.0757729i \(-0.975858\pi\)
0.762153 0.647397i \(-0.224142\pi\)
\(108\) −5.14446 + 0.731115i −0.495026 + 0.0703516i
\(109\) 9.74860i 0.933747i 0.884324 + 0.466873i \(0.154620\pi\)
−0.884324 + 0.466873i \(0.845380\pi\)
\(110\) 7.18667 + 3.75332i 0.685222 + 0.357865i
\(111\) 11.7356 + 1.92258i 1.11389 + 0.182483i
\(112\) 0.587785 + 0.809017i 0.0555405 + 0.0764449i
\(113\) −11.5838 + 3.76380i −1.08971 + 0.354068i −0.798135 0.602479i \(-0.794180\pi\)
−0.291576 + 0.956548i \(0.594180\pi\)
\(114\) −9.95266 5.13779i −0.932152 0.481198i
\(115\) 11.2550 + 8.17721i 1.04953 + 0.762529i
\(116\) −4.52990 3.29117i −0.420591 0.305577i
\(117\) −16.5025 12.2592i −1.52565 1.13337i
\(118\) 13.0119 4.22781i 1.19784 0.389201i
\(119\) −0.993107 1.36689i −0.0910380 0.125303i
\(120\) −0.684531 + 4.17844i −0.0624889 + 0.381437i
\(121\) −6.28532 9.02744i −0.571393 0.820677i
\(122\) 10.0028i 0.905608i
\(123\) −13.9908 + 7.03545i −1.26150 + 0.634365i
\(124\) 0.243703 + 0.750040i 0.0218852 + 0.0673556i
\(125\) 9.35560 + 3.03982i 0.836791 + 0.271890i
\(126\) −2.44562 + 1.73752i −0.217873 + 0.154790i
\(127\) −4.60952 + 6.34446i −0.409029 + 0.562980i −0.962981 0.269569i \(-0.913119\pi\)
0.553953 + 0.832548i \(0.313119\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) −10.5591 + 1.61504i −0.929673 + 0.142196i
\(130\) −13.5524 + 9.84638i −1.18862 + 0.863585i
\(131\) −17.0271 −1.48766 −0.743830 0.668369i \(-0.766993\pi\)
−0.743830 + 0.668369i \(0.766993\pi\)
\(132\) 3.44756 4.59504i 0.300071 0.399946i
\(133\) −6.46664 −0.560729
\(134\) 0.836316 0.607619i 0.0722467 0.0524903i
\(135\) −12.5128 2.18642i −1.07693 0.188177i
\(136\) −0.522107 + 1.60688i −0.0447703 + 0.137789i
\(137\) 0.370586 0.510068i 0.0316613 0.0435781i −0.792893 0.609361i \(-0.791426\pi\)
0.824554 + 0.565783i \(0.191426\pi\)
\(138\) 7.00678 6.93286i 0.596457 0.590165i
\(139\) −1.18245 0.384201i −0.100294 0.0325875i 0.258440 0.966027i \(-0.416792\pi\)
−0.358734 + 0.933440i \(0.616792\pi\)
\(140\) 0.755417 + 2.32493i 0.0638444 + 0.196493i
\(141\) −3.94093 7.83697i −0.331886 0.659992i
\(142\) 7.59104i 0.637026i
\(143\) 22.4822 3.32939i 1.88006 0.278418i
\(144\) 2.84318 + 0.957257i 0.236931 + 0.0797714i
\(145\) −8.04552 11.0737i −0.668144 0.919621i
\(146\) −0.108422 + 0.0352283i −0.00897303 + 0.00291552i
\(147\) −0.794507 + 1.53908i −0.0655298 + 0.126941i
\(148\) −5.55460 4.03565i −0.456585 0.331728i
\(149\) 16.0997 + 11.6971i 1.31894 + 0.958268i 0.999945 + 0.0105120i \(0.00334614\pi\)
0.318997 + 0.947756i \(0.396654\pi\)
\(150\) −0.775414 + 1.50209i −0.0633123 + 0.122645i
\(151\) 5.95714 1.93559i 0.484785 0.157516i −0.0564196 0.998407i \(-0.517968\pi\)
0.541205 + 0.840891i \(0.317968\pi\)
\(152\) 3.80100 + 5.23162i 0.308301 + 0.424341i
\(153\) −4.80376 1.61736i −0.388361 0.130756i
\(154\) 0.551756 3.27041i 0.0444618 0.263537i
\(155\) 1.92789i 0.154852i
\(156\) 5.33226 + 10.6038i 0.426923 + 0.848982i
\(157\) −4.09345 12.5983i −0.326693 1.00546i −0.970671 0.240413i \(-0.922717\pi\)
0.643978 0.765044i \(-0.277283\pi\)
\(158\) 9.93937 + 3.22950i 0.790734 + 0.256925i
\(159\) −1.60442 + 1.58750i −0.127239 + 0.125897i
\(160\) 1.43689 1.97771i 0.113596 0.156351i
\(161\) 1.75859 5.41238i 0.138596 0.426556i
\(162\) −2.96207 + 8.49860i −0.232722 + 0.667713i
\(163\) 5.90734 4.29194i 0.462699 0.336170i −0.331890 0.943318i \(-0.607686\pi\)
0.794589 + 0.607148i \(0.207686\pi\)
\(164\) 9.04136 0.706012
\(165\) 11.4865 8.07881i 0.894223 0.628934i
\(166\) 2.58614 0.200724
\(167\) −10.4925 + 7.62322i −0.811931 + 0.589903i −0.914390 0.404835i \(-0.867329\pi\)
0.102459 + 0.994737i \(0.467329\pi\)
\(168\) 1.71214 0.261877i 0.132094 0.0202043i
\(169\) −10.4935 + 32.2957i −0.807194 + 2.48429i
\(170\) −2.42773 + 3.34148i −0.186198 + 0.256280i
\(171\) −15.8149 + 11.2359i −1.20940 + 0.859231i
\(172\) 5.86533 + 1.90576i 0.447227 + 0.145313i
\(173\) −5.26759 16.2120i −0.400488 1.23257i −0.924605 0.380928i \(-0.875605\pi\)
0.524117 0.851646i \(-0.324395\pi\)
\(174\) −8.66440 + 4.35701i −0.656846 + 0.330304i
\(175\) 0.975969i 0.0737763i
\(176\) −2.97013 + 1.47592i −0.223882 + 0.111251i
\(177\) 3.83109 23.3853i 0.287962 1.75775i
\(178\) 6.93417 + 9.54406i 0.519738 + 0.715358i
\(179\) −5.27534 + 1.71406i −0.394297 + 0.128115i −0.499453 0.866341i \(-0.666466\pi\)
0.105156 + 0.994456i \(0.466466\pi\)
\(180\) 5.88707 + 4.37334i 0.438796 + 0.325970i
\(181\) −12.4538 9.04821i −0.925684 0.672548i 0.0192486 0.999815i \(-0.493873\pi\)
−0.944932 + 0.327266i \(0.893873\pi\)
\(182\) 5.54385 + 4.02784i 0.410937 + 0.298563i
\(183\) 15.3950 + 7.94726i 1.13803 + 0.587479i
\(184\) −5.41238 + 1.75859i −0.399006 + 0.129645i
\(185\) −9.86547 13.5787i −0.725324 0.998323i
\(186\) 1.34799 + 0.220835i 0.0988396 + 0.0161924i
\(187\) 5.01825 2.49367i 0.366971 0.182355i
\(188\) 5.06455i 0.369370i
\(189\) 0.731115 + 5.14446i 0.0531808 + 0.374204i
\(190\) 4.88501 + 15.0345i 0.354396 + 1.09072i
\(191\) 10.5754 + 3.43614i 0.765206 + 0.248630i 0.665511 0.746388i \(-0.268213\pi\)
0.0996944 + 0.995018i \(0.468213\pi\)
\(192\) −1.21823 1.23122i −0.0879184 0.0888558i
\(193\) −7.60485 + 10.4672i −0.547409 + 0.753444i −0.989658 0.143448i \(-0.954181\pi\)
0.442249 + 0.896892i \(0.354181\pi\)
\(194\) −0.316329 + 0.973561i −0.0227111 + 0.0698976i
\(195\) 4.38688 + 28.6812i 0.314151 + 2.05390i
\(196\) 0.809017 0.587785i 0.0577869 0.0419847i
\(197\) 15.6454 1.11469 0.557344 0.830282i \(-0.311820\pi\)
0.557344 + 0.830282i \(0.311820\pi\)
\(198\) −4.33301 8.95684i −0.307933 0.636535i
\(199\) 11.9147 0.844610 0.422305 0.906454i \(-0.361221\pi\)
0.422305 + 0.906454i \(0.361221\pi\)
\(200\) 0.789576 0.573660i 0.0558314 0.0405639i
\(201\) −0.270714 1.76991i −0.0190947 0.124840i
\(202\) −4.00283 + 12.3194i −0.281638 + 0.866793i
\(203\) −3.29117 + 4.52990i −0.230995 + 0.317937i
\(204\) 2.05830 + 2.08024i 0.144110 + 0.145646i
\(205\) 21.0206 + 6.82999i 1.46814 + 0.477027i
\(206\) 0.879825 + 2.70782i 0.0613003 + 0.188663i
\(207\) −5.10328 16.2922i −0.354702 1.13239i
\(208\) 6.85257i 0.475140i
\(209\) 3.56801 21.1485i 0.246804 1.46288i
\(210\) 4.17844 + 0.684531i 0.288339 + 0.0472371i
\(211\) −4.81494 6.62720i −0.331474 0.456235i 0.610453 0.792053i \(-0.290987\pi\)
−0.941927 + 0.335817i \(0.890987\pi\)
\(212\) 1.23934 0.402684i 0.0851179 0.0276565i
\(213\) −11.6832 6.03114i −0.800520 0.413247i
\(214\) 6.36332 + 4.62322i 0.434987 + 0.316037i
\(215\) 12.1969 + 8.86153i 0.831818 + 0.604351i
\(216\) 3.73222 3.61532i 0.253945 0.245992i
\(217\) 0.750040 0.243703i 0.0509160 0.0165436i
\(218\) −5.73009 7.88679i −0.388090 0.534161i
\(219\) −0.0319226 + 0.194858i −0.00215713 + 0.0131673i
\(220\) −8.02029 + 1.18772i −0.540728 + 0.0800763i
\(221\) 11.5779i 0.778816i
\(222\) −10.6243 + 5.34260i −0.713059 + 0.358572i
\(223\) −3.07683 9.46952i −0.206040 0.634126i −0.999669 0.0257240i \(-0.991811\pi\)
0.793629 0.608402i \(-0.208189\pi\)
\(224\) −0.951057 0.309017i −0.0635451 0.0206471i
\(225\) 1.69576 + 2.38685i 0.113051 + 0.159123i
\(226\) 7.15917 9.85375i 0.476221 0.655462i
\(227\) 0.944859 2.90798i 0.0627125 0.193009i −0.914791 0.403927i \(-0.867645\pi\)
0.977504 + 0.210917i \(0.0676451\pi\)
\(228\) 11.0718 1.69347i 0.733247 0.112153i
\(229\) −12.4393 + 9.03770i −0.822013 + 0.597228i −0.917289 0.398223i \(-0.869627\pi\)
0.0952751 + 0.995451i \(0.469627\pi\)
\(230\) −13.9119 −0.917323
\(231\) −4.59504 3.44756i −0.302331 0.226833i
\(232\) 5.59927 0.367610
\(233\) −17.7401 + 12.8889i −1.16219 + 0.844381i −0.990053 0.140692i \(-0.955067\pi\)
−0.172137 + 0.985073i \(0.555067\pi\)
\(234\) 20.5566 + 0.218018i 1.34382 + 0.0142523i
\(235\) −3.82584 + 11.7747i −0.249571 + 0.768099i
\(236\) −8.04177 + 11.0685i −0.523475 + 0.720501i
\(237\) 12.8673 12.7316i 0.835824 0.827006i
\(238\) 1.60688 + 0.522107i 0.104159 + 0.0338432i
\(239\) 0.523908 + 1.61242i 0.0338888 + 0.104299i 0.966570 0.256403i \(-0.0825373\pi\)
−0.932681 + 0.360702i \(0.882537\pi\)
\(240\) −1.90223 3.78278i −0.122788 0.244178i
\(241\) 27.1182i 1.74684i 0.486968 + 0.873420i \(0.338103\pi\)
−0.486968 + 0.873420i \(0.661897\pi\)
\(242\) 10.3911 + 3.60894i 0.667967 + 0.231991i
\(243\) 10.7266 + 11.3110i 0.688113 + 0.725604i
\(244\) −5.87948 8.09241i −0.376395 0.518063i
\(245\) 2.32493 0.755417i 0.148535 0.0482618i
\(246\) 7.18342 13.9154i 0.457998 0.887210i
\(247\) 35.8501 + 26.0466i 2.28109 + 1.65731i
\(248\) −0.638022 0.463550i −0.0405144 0.0294355i
\(249\) 2.05471 3.98028i 0.130212 0.252240i
\(250\) −9.35560 + 3.03982i −0.591700 + 0.192255i
\(251\) −13.7703 18.9533i −0.869176 1.19632i −0.979303 0.202401i \(-0.935126\pi\)
0.110126 0.993918i \(-0.464874\pi\)
\(252\) 0.957257 2.84318i 0.0603015 0.179103i
\(253\) 16.7304 + 8.73762i 1.05183 + 0.549330i
\(254\) 7.84218i 0.492062i
\(255\) 3.21395 + 6.39129i 0.201265 + 0.400238i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −11.2161 3.64432i −0.699640 0.227327i −0.0624661 0.998047i \(-0.519897\pi\)
−0.637173 + 0.770720i \(0.719897\pi\)
\(258\) 7.59316 7.51305i 0.472729 0.467742i
\(259\) −4.03565 + 5.55460i −0.250763 + 0.345146i
\(260\) 5.17655 15.9318i 0.321036 0.988047i
\(261\) −0.178143 + 16.7969i −0.0110268 + 1.03970i
\(262\) 13.7752 10.0083i 0.851033 0.618312i
\(263\) −19.8086 −1.22145 −0.610726 0.791842i \(-0.709122\pi\)
−0.610726 + 0.791842i \(0.709122\pi\)
\(264\) −0.0882381 + 5.74388i −0.00543068 + 0.353512i
\(265\) 3.18557 0.195688
\(266\) 5.23162 3.80100i 0.320771 0.233054i
\(267\) 20.1983 3.08939i 1.23612 0.189068i
\(268\) −0.319444 + 0.983149i −0.0195132 + 0.0600554i
\(269\) −14.0766 + 19.3748i −0.858268 + 1.18130i 0.123712 + 0.992318i \(0.460520\pi\)
−0.981980 + 0.188986i \(0.939480\pi\)
\(270\) 11.4082 5.58600i 0.694283 0.339953i
\(271\) −21.0861 6.85128i −1.28089 0.416186i −0.411995 0.911186i \(-0.635168\pi\)
−0.868893 + 0.495001i \(0.835168\pi\)
\(272\) −0.522107 1.60688i −0.0316574 0.0974315i
\(273\) 10.6038 5.33226i 0.641770 0.322723i
\(274\) 0.630479i 0.0380886i
\(275\) −3.19182 0.538497i −0.192474 0.0324726i
\(276\) −1.59357 + 9.72729i −0.0959217 + 0.585514i
\(277\) 12.8606 + 17.7012i 0.772721 + 1.06356i 0.996048 + 0.0888160i \(0.0283083\pi\)
−0.223327 + 0.974744i \(0.571692\pi\)
\(278\) 1.18245 0.384201i 0.0709186 0.0230428i
\(279\) 1.41087 1.89921i 0.0844667 0.113703i
\(280\) −1.97771 1.43689i −0.118191 0.0858705i
\(281\) 2.91966 + 2.12126i 0.174172 + 0.126544i 0.671456 0.741044i \(-0.265669\pi\)
−0.497284 + 0.867588i \(0.665669\pi\)
\(282\) 7.79473 + 4.02382i 0.464169 + 0.239615i
\(283\) 6.66653 2.16609i 0.396284 0.128761i −0.104094 0.994567i \(-0.533194\pi\)
0.500378 + 0.865807i \(0.333194\pi\)
\(284\) 4.46190 + 6.14128i 0.264765 + 0.364418i
\(285\) 27.0204 + 4.42662i 1.60055 + 0.262210i
\(286\) −16.2315 + 15.9083i −0.959791 + 0.940675i
\(287\) 9.04136i 0.533695i
\(288\) −2.86284 + 0.896741i −0.168695 + 0.0528409i
\(289\) −4.37115 13.4530i −0.257126 0.791354i
\(290\) 13.0179 + 4.22978i 0.764438 + 0.248381i
\(291\) 1.24706 + 1.26036i 0.0731040 + 0.0738834i
\(292\) 0.0670082 0.0922289i 0.00392136 0.00539729i
\(293\) 4.67047 14.3742i 0.272852 0.839751i −0.716928 0.697147i \(-0.754452\pi\)
0.989780 0.142604i \(-0.0455475\pi\)
\(294\) −0.261877 1.71214i −0.0152730 0.0998540i
\(295\) −27.0579 + 19.6587i −1.57537 + 1.14458i
\(296\) 6.86586 0.399070
\(297\) −17.2279 0.447444i −0.999663 0.0259633i
\(298\) −19.9004 −1.15280
\(299\) −31.5496 + 22.9221i −1.82456 + 1.32562i
\(300\) −0.255584 1.67100i −0.0147562 0.0964750i
\(301\) 1.90576 5.86533i 0.109846 0.338072i
\(302\) −3.68171 + 5.06744i −0.211859 + 0.291599i
\(303\) 15.7803 + 15.9485i 0.906554 + 0.916220i
\(304\) −6.15014 1.99830i −0.352735 0.114610i
\(305\) −7.55625 23.2558i −0.432670 1.33162i
\(306\) 4.83698 1.51511i 0.276512 0.0866131i
\(307\) 2.78519i 0.158959i 0.996836 + 0.0794796i \(0.0253258\pi\)
−0.996836 + 0.0794796i \(0.974674\pi\)
\(308\) 1.47592 + 2.97013i 0.0840982 + 0.169239i
\(309\) 4.86658 + 0.797266i 0.276850 + 0.0453549i
\(310\) −1.13319 1.55970i −0.0643606 0.0885848i
\(311\) −1.60899 + 0.522792i −0.0912374 + 0.0296448i −0.354280 0.935139i \(-0.615274\pi\)
0.263043 + 0.964784i \(0.415274\pi\)
\(312\) −10.5466 5.44442i −0.597086 0.308229i
\(313\) −2.84236 2.06509i −0.160660 0.116726i 0.504551 0.863382i \(-0.331658\pi\)
−0.665210 + 0.746656i \(0.731658\pi\)
\(314\) 10.7168 + 7.78620i 0.604783 + 0.439401i
\(315\) 4.37334 5.88707i 0.246410 0.331699i
\(316\) −9.93937 + 3.22950i −0.559133 + 0.181673i
\(317\) 6.23541 + 8.58231i 0.350216 + 0.482031i 0.947390 0.320081i \(-0.103710\pi\)
−0.597175 + 0.802111i \(0.703710\pi\)
\(318\) 0.364898 2.22737i 0.0204625 0.124905i
\(319\) −12.9987 13.2629i −0.727787 0.742577i
\(320\) 2.44458i 0.136656i
\(321\) 12.1712 6.12046i 0.679330 0.341611i
\(322\) 1.75859 + 5.41238i 0.0980024 + 0.301620i
\(323\) 10.3911 + 3.37628i 0.578177 + 0.187861i
\(324\) −2.59899 8.61657i −0.144388 0.478698i
\(325\) 3.93105 5.41063i 0.218055 0.300127i
\(326\) −2.25640 + 6.94450i −0.124971 + 0.384620i
\(327\) −16.6910 + 2.55294i −0.923013 + 0.141178i
\(328\) −7.31461 + 5.31438i −0.403882 + 0.293437i
\(329\) 5.06455 0.279218
\(330\) −4.54417 + 13.2875i −0.250149 + 0.731452i
\(331\) −23.1537 −1.27264 −0.636320 0.771425i \(-0.719544\pi\)
−0.636320 + 0.771425i \(0.719544\pi\)
\(332\) −2.09224 + 1.52010i −0.114826 + 0.0834262i
\(333\) −0.218440 + 20.5964i −0.0119705 + 1.12868i
\(334\) 4.00776 12.3346i 0.219295 0.674921i
\(335\) −1.48537 + 2.04444i −0.0811546 + 0.111700i
\(336\) −1.23122 + 1.21823i −0.0671687 + 0.0664601i
\(337\) −28.9289 9.39956i −1.57586 0.512027i −0.614871 0.788628i \(-0.710792\pi\)
−0.960985 + 0.276601i \(0.910792\pi\)
\(338\) −10.4935 32.2957i −0.570772 1.75666i
\(339\) −9.47768 18.8474i −0.514757 1.02365i
\(340\) 4.13030i 0.223997i
\(341\) 0.383168 + 2.58740i 0.0207497 + 0.140116i
\(342\) 6.19024 18.3858i 0.334730 0.994191i
\(343\) −0.587785 0.809017i −0.0317374 0.0436828i
\(344\) −5.86533 + 1.90576i −0.316237 + 0.102752i
\(345\) −11.0531 + 21.4115i −0.595079 + 1.15276i
\(346\) 13.7907 + 10.0196i 0.741395 + 0.538655i
\(347\) 22.6140 + 16.4300i 1.21398 + 0.882009i 0.995586 0.0938516i \(-0.0299179\pi\)
0.218395 + 0.975860i \(0.429918\pi\)
\(348\) 4.44866 8.61770i 0.238473 0.461957i
\(349\) −15.8310 + 5.14379i −0.847412 + 0.275341i −0.700362 0.713788i \(-0.746978\pi\)
−0.147050 + 0.989129i \(0.546978\pi\)
\(350\) −0.573660 0.789576i −0.0306634 0.0422046i
\(351\) 16.6679 31.4649i 0.889665 1.67947i
\(352\) 1.53536 2.93984i 0.0818351 0.156694i
\(353\) 29.5840i 1.57460i −0.616571 0.787299i \(-0.711479\pi\)
0.616571 0.787299i \(-0.288521\pi\)
\(354\) 10.6461 + 21.1709i 0.565834 + 1.12522i
\(355\) 5.73440 + 17.6487i 0.304350 + 0.936694i
\(356\) −11.2197 3.64551i −0.594644 0.193211i
\(357\) 2.08024 2.05830i 0.110098 0.108937i
\(358\) 3.26034 4.48747i 0.172314 0.237170i
\(359\) −1.43780 + 4.42509i −0.0758842 + 0.233547i −0.981802 0.189905i \(-0.939182\pi\)
0.905918 + 0.423453i \(0.139182\pi\)
\(360\) −7.33333 0.0777754i −0.386500 0.00409912i
\(361\) 18.4597 13.4117i 0.971563 0.705882i
\(362\) 15.3937 0.809077
\(363\) 13.8103 13.1254i 0.724850 0.688906i
\(364\) −6.85257 −0.359172
\(365\) 0.225461 0.163807i 0.0118012 0.00857405i
\(366\) −17.1261 + 2.61950i −0.895197 + 0.136923i
\(367\) 8.06717 24.8282i 0.421103 1.29602i −0.485574 0.874195i \(-0.661389\pi\)
0.906677 0.421826i \(-0.138611\pi\)
\(368\) 3.34504 4.60405i 0.174372 0.240003i
\(369\) −15.7095 22.1117i −0.817805 1.15109i
\(370\) 15.9627 + 5.18658i 0.829859 + 0.269638i
\(371\) −0.402684 1.23934i −0.0209063 0.0643431i
\(372\) −1.22035 + 0.613671i −0.0632723 + 0.0318174i
\(373\) 19.1643i 0.992288i −0.868240 0.496144i \(-0.834749\pi\)
0.868240 0.496144i \(-0.165251\pi\)
\(374\) −2.59411 + 4.96708i −0.134138 + 0.256842i
\(375\) −2.75457 + 16.8142i −0.142246 + 0.868279i
\(376\) −2.97687 4.09731i −0.153520 0.211302i
\(377\) 36.4914 11.8568i 1.87940 0.610656i
\(378\) −3.61532 3.73222i −0.185952 0.191965i
\(379\) −2.13006 1.54758i −0.109414 0.0794936i 0.531733 0.846912i \(-0.321541\pi\)
−0.641147 + 0.767418i \(0.721541\pi\)
\(380\) −12.7891 9.29184i −0.656068 0.476661i
\(381\) −12.0697 6.23067i −0.618351 0.319207i
\(382\) −10.5754 + 3.43614i −0.541082 + 0.175808i
\(383\) 6.08296 + 8.37247i 0.310825 + 0.427813i 0.935638 0.352961i \(-0.114825\pi\)
−0.624814 + 0.780774i \(0.714825\pi\)
\(384\) 1.70927 + 0.280020i 0.0872256 + 0.0142897i
\(385\) 1.18772 + 8.02029i 0.0605320 + 0.408752i
\(386\) 12.9381i 0.658534i
\(387\) −5.53035 17.6556i −0.281124 0.897486i
\(388\) −0.316329 0.973561i −0.0160592 0.0494251i
\(389\) 12.7308 + 4.13649i 0.645478 + 0.209729i 0.613419 0.789757i \(-0.289794\pi\)
0.0320590 + 0.999486i \(0.489794\pi\)
\(390\) −20.4074 20.6250i −1.03337 1.04439i
\(391\) −5.65169 + 7.77888i −0.285818 + 0.393395i
\(392\) −0.309017 + 0.951057i −0.0156077 + 0.0480356i
\(393\) −4.45900 29.1527i −0.224927 1.47056i
\(394\) −12.6574 + 9.19613i −0.637670 + 0.463295i
\(395\) −25.5480 −1.28546
\(396\) 8.77018 + 4.69936i 0.440718 + 0.236152i
\(397\) 9.55818 0.479711 0.239856 0.970809i \(-0.422900\pi\)
0.239856 + 0.970809i \(0.422900\pi\)
\(398\) −9.63919 + 7.00328i −0.483169 + 0.351043i
\(399\) −1.69347 11.0718i −0.0847793 0.554283i
\(400\) −0.301591 + 0.928202i −0.0150796 + 0.0464101i
\(401\) −11.4308 + 15.7331i −0.570825 + 0.785674i −0.992652 0.121003i \(-0.961389\pi\)
0.421827 + 0.906676i \(0.361389\pi\)
\(402\) 1.25934 + 1.27277i 0.0628102 + 0.0634799i
\(403\) −5.13970 1.66999i −0.256027 0.0831882i
\(404\) −4.00283 12.3194i −0.199148 0.612915i
\(405\) 0.466626 21.9963i 0.0231868 1.09300i
\(406\) 5.59927i 0.277887i
\(407\) −15.9391 16.2630i −0.790072 0.806127i
\(408\) −2.88793 0.473115i −0.142974 0.0234227i
\(409\) −2.14037 2.94597i −0.105835 0.145669i 0.752814 0.658233i \(-0.228696\pi\)
−0.858649 + 0.512564i \(0.828696\pi\)
\(410\) −21.0206 + 6.82999i −1.03813 + 0.337309i
\(411\) 0.970356 + 0.500920i 0.0478641 + 0.0247086i
\(412\) −2.30341 1.67353i −0.113481 0.0824487i
\(413\) 11.0685 + 8.04177i 0.544648 + 0.395710i
\(414\) 13.7049 + 10.1810i 0.673561 + 0.500370i
\(415\) −6.01261 + 1.95362i −0.295148 + 0.0958993i
\(416\) 4.02784 + 5.54385i 0.197481 + 0.271810i
\(417\) 0.348149 2.12513i 0.0170489 0.104068i
\(418\) 9.54422 + 19.2068i 0.466823 + 0.939433i
\(419\) 21.8005i 1.06503i 0.846422 + 0.532513i \(0.178752\pi\)
−0.846422 + 0.532513i \(0.821248\pi\)
\(420\) −3.78278 + 1.90223i −0.184581 + 0.0928191i
\(421\) −4.81466 14.8180i −0.234652 0.722184i −0.997167 0.0752144i \(-0.976036\pi\)
0.762515 0.646970i \(-0.223964\pi\)
\(422\) 7.79074 + 2.53136i 0.379247 + 0.123225i
\(423\) 12.3859 8.79974i 0.602225 0.427858i
\(424\) −0.765951 + 1.05424i −0.0371979 + 0.0511985i
\(425\) 0.509561 1.56827i 0.0247173 0.0760721i
\(426\) 12.9969 1.98792i 0.629703 0.0963151i
\(427\) −8.09241 + 5.87948i −0.391619 + 0.284528i
\(428\) −7.86549 −0.380193
\(429\) 11.5880 + 37.6208i 0.559472 + 1.81635i
\(430\) −15.0761 −0.727036
\(431\) 13.4407 9.76525i 0.647416 0.470375i −0.214974 0.976620i \(-0.568967\pi\)
0.862390 + 0.506244i \(0.168967\pi\)
\(432\) −0.894394 + 5.11860i −0.0430315 + 0.246269i
\(433\) 2.90462 8.93950i 0.139587 0.429605i −0.856688 0.515835i \(-0.827482\pi\)
0.996275 + 0.0862296i \(0.0274819\pi\)
\(434\) −0.463550 + 0.638022i −0.0222511 + 0.0306260i
\(435\) 16.8528 16.6750i 0.808029 0.799505i
\(436\) 9.27147 + 3.01248i 0.444023 + 0.144272i
\(437\) 11.3722 + 34.9999i 0.544005 + 1.67427i
\(438\) −0.0887089 0.176407i −0.00423868 0.00842907i
\(439\) 7.73871i 0.369349i 0.982800 + 0.184674i \(0.0591230\pi\)
−0.982800 + 0.184674i \(0.940877\pi\)
\(440\) 5.79042 5.67509i 0.276047 0.270549i
\(441\) −2.84318 0.957257i −0.135389 0.0455837i
\(442\) −6.80534 9.36674i −0.323697 0.445531i
\(443\) −12.3655 + 4.01780i −0.587503 + 0.190891i −0.587659 0.809109i \(-0.699950\pi\)
0.000156063 1.00000i \(0.499950\pi\)
\(444\) 5.45497 10.5671i 0.258882 0.501492i
\(445\) −23.3312 16.9511i −1.10601 0.803560i
\(446\) 8.05525 + 5.85248i 0.381427 + 0.277123i
\(447\) −15.8110 + 30.6282i −0.747834 + 1.44866i
\(448\) 0.951057 0.309017i 0.0449332 0.0145997i
\(449\) 1.34634 + 1.85308i 0.0635378 + 0.0874523i 0.839603 0.543200i \(-0.182787\pi\)
−0.776066 + 0.630652i \(0.782787\pi\)
\(450\) −2.77485 0.934254i −0.130808 0.0440411i
\(451\) 29.5689 + 4.98863i 1.39235 + 0.234905i
\(452\) 12.1799i 0.572895i
\(453\) 4.87404 + 9.69256i 0.229002 + 0.455396i
\(454\) 0.944859 + 2.90798i 0.0443444 + 0.136478i
\(455\) −15.9318 5.17655i −0.746893 0.242680i
\(456\) −7.96187 + 7.87788i −0.372849 + 0.368915i
\(457\) −0.00249035 + 0.00342767i −0.000116494 + 0.000160340i −0.809075 0.587705i \(-0.800032\pi\)
0.808959 + 0.587865i \(0.200032\pi\)
\(458\) 4.75140 14.6233i 0.222018 0.683302i
\(459\) 1.51114 8.64825i 0.0705342 0.403666i
\(460\) 11.2550 8.17721i 0.524765 0.381264i
\(461\) 3.55278 0.165469 0.0827346 0.996572i \(-0.473635\pi\)
0.0827346 + 0.996572i \(0.473635\pi\)
\(462\) 5.74388 + 0.0882381i 0.267230 + 0.00410521i
\(463\) 12.9691 0.602725 0.301362 0.953510i \(-0.402559\pi\)
0.301362 + 0.953510i \(0.402559\pi\)
\(464\) −4.52990 + 3.29117i −0.210295 + 0.152789i
\(465\) −3.30082 + 0.504871i −0.153072 + 0.0234128i
\(466\) 6.77610 20.8547i 0.313897 0.966075i
\(467\) −0.0877085 + 0.120720i −0.00405866 + 0.00558627i −0.811042 0.584989i \(-0.801099\pi\)
0.806983 + 0.590575i \(0.201099\pi\)
\(468\) −16.7588 + 11.9065i −0.774674 + 0.550376i
\(469\) 0.983149 + 0.319444i 0.0453976 + 0.0147506i
\(470\) −3.82584 11.7747i −0.176473 0.543128i
\(471\) 20.4981 10.3078i 0.944504 0.474957i
\(472\) 13.6815i 0.629741i
\(473\) 18.1305 + 9.46884i 0.833641 + 0.435378i
\(474\) −2.92645 + 17.8633i −0.134416 + 0.820489i
\(475\) −3.70965 5.10590i −0.170211 0.234275i
\(476\) −1.60688 + 0.522107i −0.0736513 + 0.0239307i
\(477\) −3.13818 2.33127i −0.143687 0.106741i
\(478\) −1.37161 0.996532i −0.0627359 0.0455803i
\(479\) 12.0900 + 8.78393i 0.552408 + 0.401348i 0.828672 0.559734i \(-0.189097\pi\)
−0.276265 + 0.961082i \(0.589097\pi\)
\(480\) 3.76240 + 1.94224i 0.171729 + 0.0886505i
\(481\) 44.7461 14.5389i 2.04025 0.662916i
\(482\) −15.9397 21.9391i −0.726033 0.999299i
\(483\) 9.72729 + 1.59357i 0.442607 + 0.0725100i
\(484\) −10.5279 + 3.18806i −0.478540 + 0.144912i
\(485\) 2.50243i 0.113629i
\(486\) −15.3265 2.84588i −0.695223 0.129092i
\(487\) −10.3721 31.9219i −0.470003 1.44652i −0.852580 0.522597i \(-0.824963\pi\)
0.382577 0.923924i \(-0.375037\pi\)
\(488\) 9.51319 + 3.09102i 0.430642 + 0.139924i
\(489\) 8.89539 + 8.99024i 0.402264 + 0.406553i
\(490\) −1.43689 + 1.97771i −0.0649120 + 0.0893437i
\(491\) 4.19669 12.9161i 0.189394 0.582895i −0.810602 0.585597i \(-0.800860\pi\)
0.999996 + 0.00270204i \(0.000860088\pi\)
\(492\) 2.36773 + 15.4801i 0.106745 + 0.697895i
\(493\) 7.65360 5.56067i 0.344701 0.250440i
\(494\) −44.3131 −1.99374
\(495\) 16.8401 + 17.5508i 0.756906 + 0.788852i
\(496\) 0.788639 0.0354109
\(497\) 6.14128 4.46190i 0.275474 0.200144i
\(498\) 0.677252 + 4.42784i 0.0303484 + 0.198416i
\(499\) −10.2184 + 31.4489i −0.457437 + 1.40785i 0.410813 + 0.911720i \(0.365245\pi\)
−0.868250 + 0.496127i \(0.834755\pi\)
\(500\) 5.78208 7.95835i 0.258583 0.355908i
\(501\) −15.7998 15.9682i −0.705881 0.713407i
\(502\) 22.2809 + 7.23950i 0.994444 + 0.323115i
\(503\) 5.58010 + 17.1738i 0.248805 + 0.765742i 0.994987 + 0.100001i \(0.0318845\pi\)
−0.746183 + 0.665741i \(0.768116\pi\)
\(504\) 0.896741 + 2.86284i 0.0399440 + 0.127521i
\(505\) 31.6657i 1.40910i
\(506\) −18.6710 + 2.76499i −0.830028 + 0.122919i
\(507\) −58.0428 9.50885i −2.57777 0.422303i
\(508\) 4.60952 + 6.34446i 0.204514 + 0.281490i
\(509\) 6.11971 1.98841i 0.271251 0.0881349i −0.170233 0.985404i \(-0.554452\pi\)
0.441484 + 0.897269i \(0.354452\pi\)
\(510\) −6.35685 3.28155i −0.281486 0.145310i
\(511\) −0.0922289 0.0670082i −0.00407997 0.00296427i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) −23.3790 24.1349i −1.03221 1.06558i
\(514\) 11.2161 3.64432i 0.494720 0.160744i
\(515\) −4.09107 5.63087i −0.180274 0.248126i
\(516\) −1.72693 + 10.5413i −0.0760239 + 0.464056i
\(517\) −2.79440 + 16.5631i −0.122897 + 0.728446i
\(518\) 6.86586i 0.301669i
\(519\) 26.3777 13.2644i 1.15785 0.582243i
\(520\) 5.17655 + 15.9318i 0.227007 + 0.698655i
\(521\) 18.2045 + 5.91501i 0.797555 + 0.259141i 0.679318 0.733844i \(-0.262276\pi\)
0.118237 + 0.992985i \(0.462276\pi\)
\(522\) −9.72882 13.6936i −0.425819 0.599355i
\(523\) 17.4102 23.9631i 0.761294 1.04783i −0.235811 0.971799i \(-0.575775\pi\)
0.997105 0.0760326i \(-0.0242253\pi\)
\(524\) −5.26165 + 16.1937i −0.229856 + 0.707425i
\(525\) −1.67100 + 0.255584i −0.0729282 + 0.0111546i
\(526\) 16.0255 11.6432i 0.698746 0.507669i
\(527\) −1.33246 −0.0580430
\(528\) −3.30478 4.69877i −0.143822 0.204488i
\(529\) −9.38653 −0.408110
\(530\) −2.57718 + 1.87243i −0.111945 + 0.0813331i
\(531\) 41.0421 + 0.435282i 1.78108 + 0.0188896i
\(532\) −1.99830 + 6.15014i −0.0866374 + 0.266642i
\(533\) −36.4172 + 50.1239i −1.57740 + 2.17111i
\(534\) −14.5249 + 14.3716i −0.628552 + 0.621921i
\(535\) −18.2867 5.94172i −0.790605 0.256883i
\(536\) −0.319444 0.983149i −0.0137979 0.0424655i
\(537\) −4.31620 8.58324i −0.186258 0.370394i
\(538\) 23.9486i 1.03250i
\(539\) 2.97013 1.47592i 0.127933 0.0635722i
\(540\) −5.94608 + 11.2248i −0.255879 + 0.483037i
\(541\) 1.41587 + 1.94878i 0.0608731 + 0.0837847i 0.838368 0.545104i \(-0.183510\pi\)
−0.777495 + 0.628889i \(0.783510\pi\)
\(542\) 21.0861 6.85128i 0.905724 0.294288i
\(543\) 12.2304 23.6922i 0.524858 1.01673i
\(544\) 1.36689 + 0.993107i 0.0586051 + 0.0425791i
\(545\) 19.2799 + 14.0077i 0.825859 + 0.600022i
\(546\) −5.44442 + 10.5466i −0.233000 + 0.451354i
\(547\) 2.93829 0.954710i 0.125632 0.0408204i −0.245526 0.969390i \(-0.578961\pi\)
0.371158 + 0.928570i \(0.378961\pi\)
\(548\) −0.370586 0.510068i −0.0158307 0.0217890i
\(549\) −9.57522 + 28.4396i −0.408660 + 1.21377i
\(550\) 2.89876 1.44045i 0.123603 0.0614210i
\(551\) 36.2084i 1.54253i
\(552\) −4.42833 8.80622i −0.188482 0.374818i
\(553\) 3.22950 + 9.93937i 0.137332 + 0.422665i
\(554\) −20.8090 6.76124i −0.884088 0.287258i
\(555\) 20.6650 20.4470i 0.877181 0.867927i
\(556\) −0.730794 + 1.00585i −0.0309926 + 0.0426576i
\(557\) −13.0949 + 40.3020i −0.554849 + 1.70765i 0.141492 + 0.989939i \(0.454810\pi\)
−0.696341 + 0.717711i \(0.745190\pi\)
\(558\) −0.0250909 + 2.36578i −0.00106218 + 0.100152i
\(559\) −34.1899 + 24.8404i −1.44608 + 1.05064i
\(560\) 2.44458 0.103302
\(561\) 5.58368 + 7.93891i 0.235743 + 0.335181i
\(562\) −3.60890 −0.152232
\(563\) 21.5555 15.6610i 0.908456 0.660032i −0.0321679 0.999482i \(-0.510241\pi\)
0.940624 + 0.339451i \(0.110241\pi\)
\(564\) −8.67121 + 1.32629i −0.365124 + 0.0558469i
\(565\) −9.20091 + 28.3175i −0.387085 + 1.19133i
\(566\) −4.12014 + 5.67089i −0.173182 + 0.238365i
\(567\) −8.61657 + 2.59899i −0.361862 + 0.109147i
\(568\) −7.21951 2.34576i −0.302924 0.0984260i
\(569\) 2.88942 + 8.89271i 0.121131 + 0.372802i 0.993176 0.116623i \(-0.0372069\pi\)
−0.872046 + 0.489425i \(0.837207\pi\)
\(570\) −24.4619 + 12.3010i −1.02460 + 0.515232i
\(571\) 11.7998i 0.493804i 0.969040 + 0.246902i \(0.0794126\pi\)
−0.969040 + 0.246902i \(0.920587\pi\)
\(572\) 3.78095 22.4107i 0.158089 0.937039i
\(573\) −3.11371 + 19.0063i −0.130077 + 0.794001i
\(574\) 5.31438 + 7.31461i 0.221818 + 0.305306i
\(575\) 5.28232 1.71633i 0.220288 0.0715759i
\(576\) 1.78900 2.40821i 0.0745415 0.100342i
\(577\) −12.2283 8.88435i −0.509069 0.369860i 0.303401 0.952863i \(-0.401878\pi\)
−0.812470 + 0.583002i \(0.801878\pi\)
\(578\) 11.4438 + 8.31442i 0.476000 + 0.345834i
\(579\) −19.9128 10.2794i −0.827548 0.427199i
\(580\) −13.0179 + 4.22978i −0.540540 + 0.175632i
\(581\) 1.52010 + 2.09224i 0.0630643 + 0.0868005i
\(582\) −1.74971 0.286646i −0.0725279 0.0118819i
\(583\) 4.27531 0.633131i 0.177065 0.0262216i
\(584\) 0.114001i 0.00471740i
\(585\) −47.9573 + 15.0219i −1.98279 + 0.621079i
\(586\) 4.67047 + 14.3742i 0.192935 + 0.593794i
\(587\) −10.6792 3.46988i −0.440778 0.143217i 0.0802165 0.996777i \(-0.474439\pi\)
−0.520995 + 0.853560i \(0.674439\pi\)
\(588\) 1.21823 + 1.23122i 0.0502391 + 0.0507747i
\(589\) −2.99761 + 4.12586i −0.123514 + 0.170003i
\(590\) 10.3352 31.8085i 0.425494 1.30954i
\(591\) 4.09717 + 26.7871i 0.168535 + 1.10187i
\(592\) −5.55460 + 4.03565i −0.228293 + 0.165864i
\(593\) −14.3949 −0.591129 −0.295565 0.955323i \(-0.595508\pi\)
−0.295565 + 0.955323i \(0.595508\pi\)
\(594\) 14.2006 9.76430i 0.582660 0.400634i
\(595\) −4.13030 −0.169326
\(596\) 16.0997 11.6971i 0.659471 0.479134i
\(597\) 3.12019 + 20.3996i 0.127701 + 0.834900i
\(598\) 12.0509 37.0887i 0.492796 1.51667i
\(599\) 21.9616 30.2276i 0.897327 1.23506i −0.0739859 0.997259i \(-0.523572\pi\)
0.971313 0.237805i \(-0.0764280\pi\)
\(600\) 1.18896 + 1.20163i 0.0485390 + 0.0490565i
\(601\) 2.99070 + 0.971739i 0.121993 + 0.0396381i 0.369377 0.929279i \(-0.379571\pi\)
−0.247384 + 0.968917i \(0.579571\pi\)
\(602\) 1.90576 + 5.86533i 0.0776730 + 0.239053i
\(603\) 2.95944 0.927000i 0.120518 0.0377503i
\(604\) 6.26370i 0.254867i
\(605\) −26.8849 0.540902i −1.09303 0.0219908i
\(606\) −22.1408 3.62722i −0.899410 0.147346i
\(607\) 26.6210 + 36.6406i 1.08051 + 1.48720i 0.858955 + 0.512050i \(0.171114\pi\)
0.221557 + 0.975147i \(0.428886\pi\)
\(608\) 6.15014 1.99830i 0.249421 0.0810418i
\(609\) −8.61770 4.44866i −0.349207 0.180269i
\(610\) 19.7825 + 14.3728i 0.800971 + 0.581940i
\(611\) −28.0771 20.3992i −1.13588 0.825263i
\(612\) −3.02264 + 4.06886i −0.122183 + 0.164474i
\(613\) −5.29933 + 1.72186i −0.214038 + 0.0695451i −0.414073 0.910244i \(-0.635894\pi\)
0.200035 + 0.979789i \(0.435894\pi\)
\(614\) −1.63709 2.25327i −0.0660677 0.0909344i
\(615\) −6.18909 + 37.7787i −0.249568 + 1.52339i
\(616\) −2.93984 1.53536i −0.118450 0.0618615i
\(617\) 16.5004i 0.664279i 0.943230 + 0.332140i \(0.107771\pi\)
−0.943230 + 0.332140i \(0.892229\pi\)
\(618\) −4.40576 + 2.21550i −0.177226 + 0.0891205i
\(619\) −4.67155 14.3776i −0.187766 0.577883i 0.812219 0.583352i \(-0.198259\pi\)
−0.999985 + 0.00546885i \(0.998259\pi\)
\(620\) 1.83353 + 0.595751i 0.0736364 + 0.0239259i
\(621\) 26.5581 13.0041i 1.06574 0.521835i
\(622\) 0.994410 1.36869i 0.0398722 0.0548794i
\(623\) −3.64551 + 11.2197i −0.146054 + 0.449508i
\(624\) 11.7326 1.79453i 0.469678 0.0718388i
\(625\) 23.4027 17.0031i 0.936108 0.680122i
\(626\) 3.51335 0.140422
\(627\) 37.1436 + 0.570604i 1.48337 + 0.0227877i
\(628\) −13.2467 −0.528600
\(629\) 9.38491 6.81853i 0.374201 0.271873i
\(630\) −0.0777754 + 7.33333i −0.00309864 + 0.292167i
\(631\) 2.90419 8.93819i 0.115614 0.355824i −0.876460 0.481474i \(-0.840102\pi\)
0.992075 + 0.125650i \(0.0401016\pi\)
\(632\) 6.14287 8.45493i 0.244350 0.336319i
\(633\) 10.0858 9.97936i 0.400873 0.396644i
\(634\) −10.0891 3.27815i −0.400690 0.130192i
\(635\) 5.92411 + 18.2325i 0.235091 + 0.723537i
\(636\) 1.01401 + 2.01646i 0.0402079 + 0.0799579i
\(637\) 6.85257i 0.271509i
\(638\) 18.3119 + 3.08943i 0.724974 + 0.122312i
\(639\) 7.26658 21.5827i 0.287462 0.853798i
\(640\) −1.43689 1.97771i −0.0567980 0.0781757i
\(641\) −12.7697 + 4.14913i −0.504373 + 0.163881i −0.550142 0.835071i \(-0.685426\pi\)
0.0457687 + 0.998952i \(0.485426\pi\)
\(642\) −6.24919 + 12.1056i −0.246636 + 0.477770i
\(643\) 37.4732 + 27.2259i 1.47780 + 1.07368i 0.978257 + 0.207394i \(0.0664983\pi\)
0.499542 + 0.866290i \(0.333502\pi\)
\(644\) −4.60405 3.34504i −0.181425 0.131813i
\(645\) −11.9781 + 23.2033i −0.471637 + 0.913631i
\(646\) −10.3911 + 3.37628i −0.408833 + 0.132838i
\(647\) −15.7613 21.6936i −0.619640 0.852862i 0.377686 0.925934i \(-0.376720\pi\)
−0.997327 + 0.0730717i \(0.976720\pi\)
\(648\) 7.16732 + 5.44330i 0.281559 + 0.213833i
\(649\) −32.4070 + 31.7616i −1.27209 + 1.24675i
\(650\) 6.68790i 0.262321i
\(651\) 0.613671 + 1.22035i 0.0240517 + 0.0478294i
\(652\) −2.25640 6.94450i −0.0883676 0.271968i
\(653\) 25.7723 + 8.37394i 1.00855 + 0.327698i 0.766277 0.642511i \(-0.222107\pi\)
0.242273 + 0.970208i \(0.422107\pi\)
\(654\) 12.0027 11.8761i 0.469343 0.464391i
\(655\) −24.4660 + 33.6745i −0.955964 + 1.31577i
\(656\) 2.79393 8.59884i 0.109085 0.335728i
\(657\) −0.341984 0.00362700i −0.0133421 0.000141503i
\(658\) −4.09731 + 2.97687i −0.159730 + 0.116050i
\(659\) 35.2260 1.37221 0.686104 0.727503i \(-0.259319\pi\)
0.686104 + 0.727503i \(0.259319\pi\)
\(660\) −4.13388 13.4208i −0.160911 0.522404i
\(661\) 30.9201 1.20265 0.601327 0.799003i \(-0.294639\pi\)
0.601327 + 0.799003i \(0.294639\pi\)
\(662\) 18.7317 13.6094i 0.728029 0.528944i
\(663\) −19.8230 + 3.03200i −0.769863 + 0.117753i
\(664\) 0.799163 2.45957i 0.0310135 0.0954498i
\(665\) −9.29184 + 12.7891i −0.360322 + 0.495941i
\(666\) −11.9296 16.7912i −0.462261 0.650648i
\(667\) 30.3054 + 9.84681i 1.17343 + 0.381270i
\(668\) 4.00776 + 12.3346i 0.155065 + 0.477241i
\(669\) 15.4074 7.74782i 0.595684 0.299548i
\(670\) 2.52707i 0.0976292i
\(671\) −14.7632 29.7095i −0.569929 1.14692i
\(672\) 0.280020 1.70927i 0.0108020 0.0659364i
\(673\) −7.02197 9.66491i −0.270677 0.372555i 0.651941 0.758270i \(-0.273955\pi\)
−0.922618 + 0.385715i \(0.873955\pi\)
\(674\) 28.9289 9.39956i 1.11430 0.362057i
\(675\) −3.64253 + 3.52844i −0.140201 + 0.135810i
\(676\) 27.4724 + 19.9599i 1.05663 + 0.767687i
\(677\) 7.82771 + 5.68716i 0.300843 + 0.218575i 0.727958 0.685622i \(-0.240470\pi\)
−0.427114 + 0.904198i \(0.640470\pi\)
\(678\) 18.7458 + 9.67702i 0.719929 + 0.371644i
\(679\) −0.973561 + 0.316329i −0.0373619 + 0.0121396i
\(680\) 2.42773 + 3.34148i 0.0930992 + 0.128140i
\(681\) 5.22630 + 0.856197i 0.200272 + 0.0328095i
\(682\) −1.83083 1.86803i −0.0701059 0.0715306i
\(683\) 26.4240i 1.01109i 0.862801 + 0.505544i \(0.168708\pi\)
−0.862801 + 0.505544i \(0.831292\pi\)
\(684\) 5.79890 + 18.5130i 0.221726 + 0.707861i
\(685\) −0.476274 1.46582i −0.0181975 0.0560062i
\(686\) 0.951057 + 0.309017i 0.0363115 + 0.0117983i
\(687\) −18.7314 18.9311i −0.714646 0.722266i
\(688\) 3.62497 4.98935i 0.138201 0.190217i
\(689\) −2.75942 + 8.49263i −0.105126 + 0.323544i
\(690\) −3.64321 23.8191i −0.138695 0.906778i
\(691\) 24.4068 17.7326i 0.928479 0.674579i −0.0171410 0.999853i \(-0.505456\pi\)
0.945620 + 0.325274i \(0.105456\pi\)
\(692\) −17.0463 −0.648003
\(693\) 4.69936 8.77018i 0.178514 0.333151i
\(694\) −27.9524 −1.06106
\(695\) −2.45888 + 1.78648i −0.0932708 + 0.0677652i
\(696\) 1.46632 + 9.58672i 0.0555807 + 0.363384i
\(697\) −4.72056 + 14.5284i −0.178804 + 0.550302i
\(698\) 9.78407 13.4666i 0.370332 0.509719i
\(699\) −26.7133 26.9981i −1.01039 1.02116i
\(700\) 0.928202 + 0.301591i 0.0350827 + 0.0113991i
\(701\) 2.36639 + 7.28299i 0.0893772 + 0.275075i 0.985748 0.168231i \(-0.0538055\pi\)
−0.896370 + 0.443306i \(0.853806\pi\)
\(702\) 5.01002 + 35.2528i 0.189091 + 1.33053i
\(703\) 44.3990i 1.67454i
\(704\) 0.485860 + 3.28084i 0.0183115 + 0.123651i
\(705\) −21.1619 3.46684i −0.797003 0.130569i
\(706\) 17.3890 + 23.9340i 0.654445 + 0.900767i
\(707\) −12.3194 + 4.00283i −0.463320 + 0.150542i
\(708\) −21.0569 10.8700i −0.791365 0.408521i
\(709\) −18.1988 13.2222i −0.683469 0.496569i 0.191038 0.981583i \(-0.438815\pi\)
−0.874507 + 0.485014i \(0.838815\pi\)
\(710\) −15.0129 10.9075i −0.563422 0.409350i
\(711\) 25.1679 + 18.6966i 0.943871 + 0.701176i
\(712\) 11.2197 3.64551i 0.420477 0.136621i
\(713\) −2.63803 3.63093i −0.0987948 0.135979i
\(714\) −0.473115 + 2.88793i −0.0177059 + 0.108078i
\(715\) 25.7199 49.2472i 0.961869 1.84174i
\(716\) 5.54682i 0.207294i
\(717\) −2.62349 + 1.31926i −0.0979761 + 0.0492687i
\(718\) −1.43780 4.42509i −0.0536582 0.165143i
\(719\) 17.4737 + 5.67754i 0.651658 + 0.211737i 0.616145 0.787633i \(-0.288693\pi\)
0.0355131 + 0.999369i \(0.488693\pi\)
\(720\) 5.97850 4.24750i 0.222806 0.158295i
\(721\) −1.67353 + 2.30341i −0.0623254 + 0.0857835i
\(722\) −7.05097 + 21.7007i −0.262410 + 0.807615i
\(723\) −46.4302 + 7.10165i −1.72676 + 0.264113i
\(724\) −12.4538 + 9.04821i −0.462842 + 0.336274i
\(725\) −5.46471 −0.202954
\(726\) −3.45780 + 18.7362i −0.128331 + 0.695364i
\(727\) 41.2564 1.53011 0.765057 0.643963i \(-0.222711\pi\)
0.765057 + 0.643963i \(0.222711\pi\)
\(728\) 5.54385 4.02784i 0.205469 0.149282i
\(729\) −16.5570 + 21.3276i −0.613223 + 0.789910i
\(730\) −0.0861184 + 0.265045i −0.00318738 + 0.00980976i
\(731\) −6.12466 + 8.42987i −0.226529 + 0.311790i
\(732\) 12.3156 12.1857i 0.455199 0.450396i
\(733\) −29.2033 9.48872i −1.07865 0.350474i −0.284797 0.958588i \(-0.591926\pi\)
−0.793850 + 0.608114i \(0.791926\pi\)
\(734\) 8.06717 + 24.8282i 0.297765 + 0.916425i
\(735\) 1.90223 + 3.78278i 0.0701646 + 0.139530i
\(736\) 5.69092i 0.209770i
\(737\) −1.58717 + 3.03904i −0.0584642 + 0.111945i
\(738\) 25.7062 + 8.65491i 0.946258 + 0.318592i
\(739\) −6.91915 9.52339i −0.254525 0.350324i 0.662565 0.749005i \(-0.269468\pi\)
−0.917090 + 0.398681i \(0.869468\pi\)
\(740\) −15.9627 + 5.18658i −0.586799 + 0.190663i
\(741\) −35.2071 + 68.2013i −1.29336 + 2.50544i
\(742\) 1.05424 + 0.765951i 0.0387024 + 0.0281190i
\(743\) −12.7090 9.23363i −0.466248 0.338749i 0.329729 0.944076i \(-0.393043\pi\)
−0.795977 + 0.605327i \(0.793043\pi\)
\(744\) 0.626579 1.21378i 0.0229715 0.0444992i
\(745\) 46.2670 15.0331i 1.69509 0.550769i
\(746\) 11.2645 + 15.5042i 0.412422 + 0.567650i
\(747\) 7.35287 + 2.47561i 0.269027 + 0.0905777i
\(748\) −0.820897 5.54323i −0.0300150 0.202681i
\(749\) 7.86549i 0.287399i
\(750\) −7.65461 15.2220i −0.279507 0.555830i
\(751\) −4.88687 15.0402i −0.178325 0.548826i 0.821445 0.570288i \(-0.193168\pi\)
−0.999770 + 0.0214610i \(0.993168\pi\)
\(752\) 4.81667 + 1.56503i 0.175646 + 0.0570708i
\(753\) 28.8445 28.5402i 1.05115 1.04006i
\(754\) −22.5530 + 31.0415i −0.821330 + 1.13046i
\(755\) 4.73171 14.5627i 0.172204 0.529991i
\(756\) 5.11860 + 0.894394i 0.186162 + 0.0325288i
\(757\) 31.5210 22.9013i 1.14565 0.832363i 0.157753 0.987479i \(-0.449575\pi\)
0.987896 + 0.155115i \(0.0495749\pi\)
\(758\) 2.63289 0.0956310
\(759\) −10.5787 + 30.9329i −0.383983 + 1.12279i
\(760\) 15.8082 0.573424
\(761\) 30.5972 22.2302i 1.10915 0.805843i 0.126618 0.991952i \(-0.459588\pi\)
0.982529 + 0.186109i \(0.0595878\pi\)
\(762\) 13.4269 2.05369i 0.486405 0.0743973i
\(763\) 3.01248 9.27147i 0.109059 0.335650i
\(764\) 6.53593 8.99593i 0.236462 0.325462i
\(765\) −10.1011 + 7.17647i −0.365207 + 0.259466i
\(766\) −9.84243 3.19800i −0.355621 0.115548i
\(767\) −28.9714 89.1647i −1.04610 3.21955i
\(768\) −1.54742 + 0.778140i −0.0558376 + 0.0280787i
\(769\) 3.68574i 0.132911i −0.997789 0.0664557i \(-0.978831\pi\)
0.997789 0.0664557i \(-0.0211691\pi\)
\(770\) −5.67509 5.79042i −0.204516 0.208672i
\(771\) 3.30235 20.1578i 0.118931 0.725967i
\(772\) 7.60485 + 10.4672i 0.273705 + 0.376722i
\(773\) −9.39362 + 3.05217i −0.337865 + 0.109779i −0.473036 0.881043i \(-0.656842\pi\)
0.135170 + 0.990822i \(0.456842\pi\)
\(774\) 14.8519 + 11.0330i 0.533839 + 0.396574i
\(775\) 0.622690 + 0.452411i 0.0223677 + 0.0162511i
\(776\) 0.828161 + 0.601694i 0.0297292 + 0.0215996i
\(777\) −10.5671 5.45497i −0.379092 0.195696i
\(778\) −12.7308 + 4.13649i −0.456422 + 0.148301i
\(779\) 34.3662 + 47.3010i 1.23130 + 1.69473i
\(780\) 28.6330 + 4.69080i 1.02523 + 0.167958i
\(781\) 11.2038 + 22.5464i 0.400902 + 0.806773i
\(782\) 9.61523i 0.343840i
\(783\) −28.8052 + 4.09371i −1.02941 + 0.146297i
\(784\) −0.309017 0.951057i −0.0110363 0.0339663i
\(785\) −30.7976 10.0068i −1.09921 0.357157i
\(786\) 20.7429 + 20.9641i 0.739876 + 0.747764i
\(787\) −14.0841 + 19.3852i −0.502046 + 0.691007i −0.982553 0.185984i \(-0.940453\pi\)
0.480507 + 0.876991i \(0.340453\pi\)
\(788\) 4.83469 14.8797i 0.172229 0.530066i
\(789\) −5.18743 33.9151i −0.184677 1.20741i
\(790\) 20.6688 15.0167i 0.735361 0.534271i
\(791\) 12.1799 0.433068
\(792\) −9.85744 + 1.35312i −0.350269 + 0.0480809i
\(793\) 68.5447 2.43409
\(794\) −7.73273 + 5.61816i −0.274424 + 0.199381i
\(795\) 0.834227 + 5.45413i 0.0295870 + 0.193438i
\(796\) 3.68184 11.3315i 0.130499 0.401636i
\(797\) −3.78402 + 5.20826i −0.134037 + 0.184486i −0.870760 0.491709i \(-0.836372\pi\)
0.736723 + 0.676195i \(0.236372\pi\)
\(798\) 7.87788 + 7.96187i 0.278874 + 0.281847i
\(799\) −8.13813 2.64424i −0.287906 0.0935464i
\(800\) −0.301591 0.928202i −0.0106629 0.0328169i
\(801\) 10.5789 + 33.7732i 0.373789 + 1.19332i
\(802\) 19.4472i 0.686704i
\(803\) 0.270032 0.264654i 0.00952922 0.00933943i
\(804\) −1.76694 0.289469i −0.0623152 0.0102088i
\(805\) −8.17721 11.2550i −0.288209 0.396685i
\(806\) 5.13970 1.66999i 0.181038 0.0588229i
\(807\) −36.8587 19.0273i −1.29749 0.669794i
\(808\) 10.4795 + 7.61383i 0.368669 + 0.267854i
\(809\) −25.9234 18.8345i −0.911419 0.662184i 0.0299547 0.999551i \(-0.490464\pi\)
−0.941373 + 0.337367i \(0.890464\pi\)
\(810\) 12.5516 + 18.0696i 0.441017 + 0.634902i
\(811\) −0.324068 + 0.105296i −0.0113796 + 0.00369744i −0.314701 0.949191i \(-0.601904\pi\)
0.303322 + 0.952888i \(0.401904\pi\)
\(812\) 3.29117 + 4.52990i 0.115497 + 0.158968i
\(813\) 6.20838 37.8965i 0.217737 1.32909i
\(814\) 22.4542 + 3.78828i 0.787018 + 0.132779i
\(815\) 17.8500i 0.625259i
\(816\) 2.61448 1.31473i 0.0915249 0.0460246i
\(817\) 12.3239 + 37.9290i 0.431157 + 1.32697i
\(818\) 3.46320 + 1.12526i 0.121088 + 0.0393438i
\(819\) 11.9065 + 16.7588i 0.416046 + 0.585598i
\(820\) 12.9914 17.8812i 0.453680 0.624437i
\(821\) 14.3461 44.1526i 0.500681 1.54094i −0.307231 0.951635i \(-0.599403\pi\)
0.807912 0.589303i \(-0.200597\pi\)
\(822\) −1.07947 + 0.165108i −0.0376508 + 0.00575881i
\(823\) −1.73949 + 1.26382i −0.0606350 + 0.0440539i −0.617690 0.786422i \(-0.711931\pi\)
0.557055 + 0.830476i \(0.311931\pi\)
\(824\) 2.84717 0.0991860
\(825\) 0.0861177 5.60586i 0.00299823 0.195171i
\(826\) −13.6815 −0.476039
\(827\) 4.99138 3.62645i 0.173567 0.126104i −0.497610 0.867401i \(-0.665789\pi\)
0.671177 + 0.741297i \(0.265789\pi\)
\(828\) −17.0718 0.181059i −0.593286 0.00629223i
\(829\) −4.42631 + 13.6228i −0.153732 + 0.473139i −0.998030 0.0627351i \(-0.980018\pi\)
0.844298 + 0.535874i \(0.180018\pi\)
\(830\) 3.71600 5.11464i 0.128984 0.177532i
\(831\) −26.9389 + 26.6547i −0.934501 + 0.924643i
\(832\) −6.51718 2.11756i −0.225943 0.0734132i
\(833\) 0.522107 + 1.60688i 0.0180899 + 0.0556751i
\(834\) 0.967462 + 1.92390i 0.0335005 + 0.0666193i
\(835\) 31.7047i 1.09719i
\(836\) −19.0109 9.92864i −0.657505 0.343389i
\(837\) 3.62119 + 1.91825i 0.125167 + 0.0663043i
\(838\) −12.8140 17.6370i −0.442653 0.609260i
\(839\) 29.8415 9.69608i 1.03024 0.334746i 0.255356 0.966847i \(-0.417807\pi\)
0.774886 + 0.632101i \(0.217807\pi\)
\(840\) 1.94224 3.76240i 0.0670135 0.129815i
\(841\) −1.90262 1.38234i −0.0656076 0.0476667i
\(842\) 12.6049 + 9.15802i 0.434395 + 0.315606i
\(843\) −2.86730 + 5.55438i −0.0987550 + 0.191303i
\(844\) −7.79074 + 2.53136i −0.268168 + 0.0871332i
\(845\) 48.7935 + 67.1585i 1.67855 + 2.31032i
\(846\) −4.84807 + 14.3994i −0.166680 + 0.495062i
\(847\) 3.18806 + 10.5279i 0.109543 + 0.361742i
\(848\) 1.30311i 0.0447491i
\(849\) 5.45445 + 10.8468i 0.187196 + 0.372260i
\(850\) 0.509561 + 1.56827i 0.0174778 + 0.0537911i
\(851\) 37.1607 + 12.0742i 1.27385 + 0.413899i
\(852\) −9.34626 + 9.24766i −0.320198 + 0.316820i
\(853\) 13.5038 18.5863i 0.462360 0.636384i −0.512636 0.858606i \(-0.671331\pi\)
0.974996 + 0.222222i \(0.0713311\pi\)
\(854\) 3.09102 9.51319i 0.105773 0.325535i
\(855\) −0.502945 + 47.4220i −0.0172004 + 1.62180i
\(856\) 6.36332 4.62322i 0.217494 0.158018i
\(857\) −26.1192 −0.892216 −0.446108 0.894979i \(-0.647190\pi\)
−0.446108 + 0.894979i \(0.647190\pi\)
\(858\) −31.4878 23.6246i −1.07498 0.806532i
\(859\) −11.6855 −0.398704 −0.199352 0.979928i \(-0.563884\pi\)
−0.199352 + 0.979928i \(0.563884\pi\)
\(860\) 12.1969 8.86153i 0.415909 0.302176i
\(861\) 15.4801 2.36773i 0.527559 0.0806919i
\(862\) −5.13390 + 15.8005i −0.174861 + 0.538167i
\(863\) −7.14496 + 9.83420i −0.243217 + 0.334760i −0.913121 0.407688i \(-0.866335\pi\)
0.669904 + 0.742448i \(0.266335\pi\)
\(864\) −2.28506 4.66675i −0.0777392 0.158766i
\(865\) −39.6315 12.8770i −1.34751 0.437833i
\(866\) 2.90462 + 8.93950i 0.0987030 + 0.303777i
\(867\) 21.8887 11.0071i 0.743380 0.373819i
\(868\) 0.788639i 0.0267681i
\(869\) −34.2877 + 5.07766i −1.16313 + 0.172248i
\(870\) −3.83287 + 23.3962i −0.129947 + 0.793204i
\(871\) −4.16375 5.73092i −0.141083 0.194185i
\(872\) −9.27147 + 3.01248i −0.313972 + 0.102016i
\(873\) −1.83133 + 2.46520i −0.0619811 + 0.0834344i
\(874\) −29.7727 21.6311i −1.00708 0.731684i
\(875\) −7.95835 5.78208i −0.269041 0.195470i
\(876\) 0.175457 + 0.0905747i 0.00592813 + 0.00306024i
\(877\) −35.9116 + 11.6684i −1.21265 + 0.394013i −0.844399 0.535715i \(-0.820042\pi\)
−0.368248 + 0.929728i \(0.620042\pi\)
\(878\) −4.54870 6.26075i −0.153511 0.211290i
\(879\) 25.8338 + 4.23221i 0.871351 + 0.142749i
\(880\) −1.34881 + 7.99477i −0.0454684 + 0.269504i
\(881\) 3.27777i 0.110431i −0.998474 0.0552154i \(-0.982415\pi\)
0.998474 0.0552154i \(-0.0175846\pi\)
\(882\) 2.86284 0.896741i 0.0963969 0.0301948i
\(883\) −14.5064 44.6461i −0.488180 1.50246i −0.827322 0.561727i \(-0.810137\pi\)
0.339143 0.940735i \(-0.389863\pi\)
\(884\) 11.0113 + 3.57778i 0.370349 + 0.120334i
\(885\) −40.7444 41.1788i −1.36961 1.38421i
\(886\) 7.64230 10.5187i 0.256748 0.353384i
\(887\) −6.27720 + 19.3192i −0.210768 + 0.648676i 0.788659 + 0.614830i \(0.210776\pi\)
−0.999427 + 0.0338460i \(0.989224\pi\)
\(888\) 1.79801 + 11.7553i 0.0603373 + 0.394482i
\(889\) 6.34446 4.60952i 0.212786 0.154598i
\(890\) 28.8390 0.966684
\(891\) −3.74550 29.6137i −0.125479 0.992096i
\(892\) −9.95684 −0.333380
\(893\) −26.4958 + 19.2503i −0.886648 + 0.644188i
\(894\) −5.21146 34.0722i −0.174297 1.13955i
\(895\) −4.19016 + 12.8960i −0.140062 + 0.431065i
\(896\) −0.587785 + 0.809017i −0.0196365 + 0.0270274i
\(897\) −47.5079 48.0145i −1.58624 1.60316i
\(898\) −2.17843 0.707814i −0.0726951 0.0236201i
\(899\) 1.36456 + 4.19967i 0.0455105 + 0.140067i
\(900\) 2.79404 0.875191i 0.0931348 0.0291730i
\(901\) 2.20171i 0.0733495i
\(902\) −26.8540 + 13.3443i −0.894141 + 0.444317i
\(903\) 10.5413 + 1.72693i 0.350794 + 0.0574687i
\(904\) −7.15917 9.85375i −0.238111 0.327731i
\(905\) −35.7894 + 11.6287i −1.18968 + 0.386551i
\(906\) −9.64032 4.97656i −0.320278 0.165335i
\(907\) −26.2280 19.0557i −0.870885 0.632735i 0.0599389 0.998202i \(-0.480909\pi\)
−0.930824 + 0.365467i \(0.880909\pi\)
\(908\) −2.47367 1.79723i −0.0820917 0.0596431i
\(909\) −23.1736 + 31.1946i −0.768620 + 1.03466i
\(910\) 15.9318 5.17655i 0.528133 0.171601i
\(911\) 21.0081 + 28.9151i 0.696028 + 0.958001i 0.999986 + 0.00531529i \(0.00169192\pi\)
−0.303957 + 0.952686i \(0.598308\pi\)
\(912\) 1.81079 11.0532i 0.0599612 0.366008i
\(913\) −7.68118 + 3.81694i −0.254210 + 0.126322i
\(914\) 0.00423683i 0.000140142i
\(915\) 37.8383 19.0275i 1.25089 0.629030i
\(916\) 4.75140 + 14.6233i 0.156991 + 0.483167i
\(917\) 16.1937 + 5.26165i 0.534763 + 0.173755i
\(918\) 3.86077 + 7.88481i 0.127425 + 0.260238i
\(919\) 9.13863 12.5782i 0.301455 0.414918i −0.631237 0.775590i \(-0.717453\pi\)
0.932693 + 0.360672i \(0.117453\pi\)
\(920\) −4.29901 + 13.2310i −0.141734 + 0.436213i
\(921\) −4.76863 + 0.729378i −0.157132 + 0.0240338i
\(922\) −2.87426 + 2.08827i −0.0946586 + 0.0687735i
\(923\) −52.0182 −1.71220
\(924\) −4.69877 + 3.30478i −0.154578 + 0.108719i
\(925\) −6.70087 −0.220323
\(926\) −10.4922 + 7.62304i −0.344795 + 0.250509i
\(927\) −0.0905841 + 8.54104i −0.00297517 + 0.280525i
\(928\) 1.73027 5.32522i 0.0567988 0.174809i
\(929\) 14.7725 20.3326i 0.484671 0.667092i −0.494723 0.869051i \(-0.664731\pi\)
0.979394 + 0.201958i \(0.0647305\pi\)
\(930\) 2.37366 2.34862i 0.0778354 0.0770143i
\(931\) 6.15014 + 1.99830i 0.201563 + 0.0654917i
\(932\) 6.77610 + 20.8547i 0.221959 + 0.683118i
\(933\) −1.31645 2.61791i −0.0430987 0.0857064i
\(934\) 0.149219i 0.00488258i
\(935\) 2.27892 13.5078i 0.0745286 0.441751i
\(936\) 6.55967 19.4831i 0.214410 0.636824i
\(937\) −11.0094 15.1532i −0.359662 0.495033i 0.590392 0.807116i \(-0.298973\pi\)
−0.950055 + 0.312084i \(0.898973\pi\)
\(938\) −0.983149 + 0.319444i −0.0321009 + 0.0104302i
\(939\) 2.79138 5.40731i 0.0910932 0.176461i
\(940\) 10.0162 + 7.27719i 0.326692 + 0.237356i
\(941\) −15.7918 11.4734i −0.514798 0.374022i 0.299843 0.953989i \(-0.403066\pi\)
−0.814641 + 0.579966i \(0.803066\pi\)
\(942\) −10.5246 + 20.3877i −0.342909 + 0.664266i
\(943\) −48.9353 + 15.9000i −1.59355 + 0.517777i
\(944\) 8.04177 + 11.0685i 0.261737 + 0.360251i
\(945\) 11.2248 + 5.94608i 0.365142 + 0.193426i
\(946\) −20.2335 + 2.99638i −0.657849 + 0.0974208i
\(947\) 26.6868i 0.867205i 0.901104 + 0.433602i \(0.142758\pi\)
−0.901104 + 0.433602i \(0.857242\pi\)
\(948\) −8.13224 16.1719i −0.264123 0.525237i
\(949\) 0.241405 + 0.742967i 0.00783632 + 0.0241177i
\(950\) 6.00235 + 1.95028i 0.194742 + 0.0632755i
\(951\) −13.0612 + 12.9234i −0.423538 + 0.419070i
\(952\) 0.993107 1.36689i 0.0321868 0.0443013i
\(953\) 0.522708 1.60873i 0.0169322 0.0521119i −0.942233 0.334957i \(-0.891278\pi\)
0.959166 + 0.282845i \(0.0912782\pi\)
\(954\) 3.90912 + 0.0414591i 0.126563 + 0.00134229i
\(955\) 21.9913 15.9776i 0.711621 0.517023i
\(956\) 1.69540 0.0548332
\(957\) 19.3038 25.7288i 0.624003 0.831695i
\(958\) −14.9441 −0.482822
\(959\) −0.510068 + 0.370586i −0.0164710 + 0.0119669i
\(960\) −4.18546 + 0.640180i −0.135085 + 0.0206617i
\(961\) −9.38733 + 28.8912i −0.302817 + 0.931976i
\(962\) −27.6546 + 38.0633i −0.891620 + 1.22721i
\(963\) 13.6664 + 19.2360i 0.440395 + 0.619870i
\(964\) 25.7910 + 8.38000i 0.830671 + 0.269901i
\(965\) 9.77369 + 30.0803i 0.314626 + 0.968320i
\(966\) −8.80622 + 4.42833i −0.283335 + 0.142479i
\(967\) 40.5364i 1.30356i 0.758406 + 0.651782i \(0.225978\pi\)
−0.758406 + 0.651782i \(0.774022\pi\)
\(968\) 6.64334 8.76733i 0.213525 0.281793i
\(969\) −3.05946 + 18.6752i −0.0982841 + 0.599934i
\(970\) 1.47089 + 2.02450i 0.0472274 + 0.0650029i
\(971\) −51.2857 + 16.6637i −1.64584 + 0.534764i −0.977832 0.209393i \(-0.932851\pi\)
−0.668004 + 0.744158i \(0.732851\pi\)
\(972\) 14.0721 6.70631i 0.451364 0.215105i
\(973\) 1.00585 + 0.730794i 0.0322461 + 0.0234282i
\(974\) 27.1544 + 19.7288i 0.870084 + 0.632153i
\(975\) 10.2932 + 5.31358i 0.329646 + 0.170171i
\(976\) −9.51319 + 3.09102i −0.304510 + 0.0989413i
\(977\) 3.31542 + 4.56329i 0.106070 + 0.145992i 0.858752 0.512391i \(-0.171240\pi\)
−0.752682 + 0.658384i \(0.771240\pi\)
\(978\) −12.4809 2.04467i −0.399094 0.0653814i
\(979\) −34.6816 18.1128i −1.10843 0.578889i
\(980\) 2.44458i 0.0780892i
\(981\) −8.74197 27.9087i −0.279110 0.891056i
\(982\) 4.19669 + 12.9161i 0.133922 + 0.412169i
\(983\) 23.8404 + 7.74622i 0.760391 + 0.247066i 0.663447 0.748224i \(-0.269093\pi\)
0.0969448 + 0.995290i \(0.469093\pi\)
\(984\) −11.0145 11.1319i −0.351129 0.354873i
\(985\) 22.4807 30.9420i 0.716294 0.985894i
\(986\) −2.92342 + 8.99735i −0.0931006 + 0.286534i
\(987\) 1.32629 + 8.67121i 0.0422163 + 0.276008i
\(988\) 35.8501 26.0466i 1.14054 0.828653i
\(989\) −35.0968 −1.11601
\(990\) −23.9401 4.30057i −0.760865 0.136681i
\(991\) 57.1725 1.81615 0.908073 0.418812i \(-0.137553\pi\)
0.908073 + 0.418812i \(0.137553\pi\)
\(992\) −0.638022 + 0.463550i −0.0202572 + 0.0147177i
\(993\) −6.06342 39.6423i −0.192417 1.25801i
\(994\) −2.34576 + 7.21951i −0.0744030 + 0.228989i
\(995\) 17.1201 23.5638i 0.542743 0.747021i
\(996\) −3.15053 3.18412i −0.0998283 0.100893i
\(997\) 48.2832 + 15.6882i 1.52914 + 0.496849i 0.948357 0.317206i \(-0.102745\pi\)
0.580788 + 0.814055i \(0.302745\pi\)
\(998\) −10.2184 31.4489i −0.323457 0.995498i
\(999\) −35.3211 + 5.01973i −1.11751 + 0.158817i
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 462.2.w.a.239.7 yes 48
3.2 odd 2 462.2.w.b.239.8 yes 48
11.7 odd 10 462.2.w.b.29.8 yes 48
33.29 even 10 inner 462.2.w.a.29.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.w.a.29.7 48 33.29 even 10 inner
462.2.w.a.239.7 yes 48 1.1 even 1 trivial
462.2.w.b.29.8 yes 48 11.7 odd 10
462.2.w.b.239.8 yes 48 3.2 odd 2