Properties

Label 420.2.l.h.239.13
Level $420$
Weight $2$
Character 420.239
Analytic conductor $3.354$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [420,2,Mod(239,420)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(420, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("420.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.l (of order \(2\), degree \(1\), 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: \(3.35371688489\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 9 x^{14} - 16 x^{13} + 18 x^{12} - 4 x^{11} - 36 x^{10} + 102 x^{9} - 170 x^{8} + 204 x^{7} - 144 x^{6} - 32 x^{5} + 288 x^{4} - 512 x^{3} + 576 x^{2} - 512 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.13
Root \(-0.167106 + 1.40431i\) of defining polynomial
Character \(\chi\) \(=\) 420.239
Dual form 420.2.l.h.239.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.25945 - 0.643263i) q^{2} +(1.48716 - 0.887900i) q^{3} +(1.17242 - 1.62032i) q^{4} +(-2.05223 + 0.887900i) q^{5} +(1.30184 - 2.07490i) q^{6} +1.00000 q^{7} +(0.434319 - 2.79488i) q^{8} +(1.42327 - 2.64089i) q^{9} +O(q^{10})\) \(q+(1.25945 - 0.643263i) q^{2} +(1.48716 - 0.887900i) q^{3} +(1.17242 - 1.62032i) q^{4} +(-2.05223 + 0.887900i) q^{5} +(1.30184 - 2.07490i) q^{6} +1.00000 q^{7} +(0.434319 - 2.79488i) q^{8} +(1.42327 - 2.64089i) q^{9} +(-2.01352 + 2.43839i) q^{10} +2.75993 q^{11} +(0.304900 - 3.45066i) q^{12} +1.90761i q^{13} +(1.25945 - 0.643263i) q^{14} +(-2.26361 + 3.14262i) q^{15} +(-1.25084 - 3.79939i) q^{16} -5.03780 q^{17} +(0.0937425 - 4.24160i) q^{18} -1.90761i q^{19} +(-0.967402 + 4.36625i) q^{20} +(1.48716 - 0.887900i) q^{21} +(3.47600 - 1.77536i) q^{22} +2.05073i q^{23} +(-1.83568 - 4.54206i) q^{24} +(3.42327 - 3.64434i) q^{25} +(1.22710 + 2.40254i) q^{26} +(-0.228229 - 5.19114i) q^{27} +(1.17242 - 1.62032i) q^{28} +4.94433i q^{29} +(-0.829376 + 5.41407i) q^{30} +6.92361i q^{31} +(-4.01938 - 3.98052i) q^{32} +(4.10445 - 2.45055i) q^{33} +(-6.34485 + 3.24063i) q^{34} +(-2.05223 + 0.887900i) q^{35} +(-2.61041 - 5.40239i) q^{36} +6.48126i q^{37} +(-1.22710 - 2.40254i) q^{38} +(1.69377 + 2.83692i) q^{39} +(1.59025 + 6.12136i) q^{40} +11.1795i q^{41} +(1.30184 - 2.07490i) q^{42} -9.36439 q^{43} +(3.23581 - 4.47196i) q^{44} +(-0.576017 + 6.68343i) q^{45} +(1.31916 + 2.58279i) q^{46} -7.51739i q^{47} +(-5.23368 - 4.53967i) q^{48} +1.00000 q^{49} +(1.96716 - 6.79193i) q^{50} +(-7.49199 + 4.47306i) q^{51} +(3.09093 + 2.23653i) q^{52} +6.14747 q^{53} +(-3.62671 - 6.39116i) q^{54} +(-5.66401 + 2.45055i) q^{55} +(0.434319 - 2.79488i) q^{56} +(-1.69377 - 2.83692i) q^{57} +(3.18051 + 6.22714i) q^{58} +0.716916 q^{59} +(2.43812 + 7.35225i) q^{60} +5.13115 q^{61} +(4.45370 + 8.71993i) q^{62} +(1.42327 - 2.64089i) q^{63} +(-7.62273 - 2.42774i) q^{64} +(-1.69377 - 3.91485i) q^{65} +(3.59300 - 5.72658i) q^{66} +3.58761 q^{67} +(-5.90644 + 8.16282i) q^{68} +(1.82085 + 3.04976i) q^{69} +(-2.01352 + 2.43839i) q^{70} +4.49721 q^{71} +(-6.76283 - 5.12485i) q^{72} +6.11618i q^{73} +(4.16916 + 8.16282i) q^{74} +(1.85512 - 8.45923i) q^{75} +(-3.09093 - 2.23653i) q^{76} +2.75993 q^{77} +(3.95810 + 2.48341i) q^{78} -14.6546i q^{79} +(5.94049 + 6.68659i) q^{80} +(-4.94862 - 7.51739i) q^{81} +(7.19138 + 14.0800i) q^{82} +7.71558i q^{83} +(0.304900 - 3.45066i) q^{84} +(10.3387 - 4.47306i) q^{85} +(-11.7940 + 6.02377i) q^{86} +(4.39007 + 7.35300i) q^{87} +(1.19869 - 7.71369i) q^{88} -13.5677i q^{89} +(3.57374 + 8.78797i) q^{90} +1.90761i q^{91} +(3.32283 + 2.40433i) q^{92} +(6.14747 + 10.2965i) q^{93} +(-4.83566 - 9.46777i) q^{94} +(1.69377 + 3.91485i) q^{95} +(-9.51176 - 2.35085i) q^{96} -16.6772i q^{97} +(1.25945 - 0.643263i) q^{98} +(3.92812 - 7.28869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(241\) \(281\) \(337\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.25945 0.643263i 0.890565 0.454856i
\(3\) 1.48716 0.887900i 0.858610 0.512629i
\(4\) 1.17242 1.62032i 0.586212 0.810158i
\(5\) −2.05223 + 0.887900i −0.917784 + 0.397081i
\(6\) 1.30184 2.07490i 0.531476 0.847074i
\(7\) 1.00000 0.377964
\(8\) 0.434319 2.79488i 0.153555 0.988140i
\(9\) 1.42327 2.64089i 0.474422 0.880297i
\(10\) −2.01352 + 2.43839i −0.636731 + 0.771086i
\(11\) 2.75993 0.832151 0.416076 0.909330i \(-0.363405\pi\)
0.416076 + 0.909330i \(0.363405\pi\)
\(12\) 0.304900 3.45066i 0.0880170 0.996119i
\(13\) 1.90761i 0.529076i 0.964375 + 0.264538i \(0.0852195\pi\)
−0.964375 + 0.264538i \(0.914781\pi\)
\(14\) 1.25945 0.643263i 0.336602 0.171919i
\(15\) −2.26361 + 3.14262i −0.584463 + 0.811421i
\(16\) −1.25084 3.79939i −0.312711 0.949848i
\(17\) −5.03780 −1.22185 −0.610923 0.791690i \(-0.709201\pi\)
−0.610923 + 0.791690i \(0.709201\pi\)
\(18\) 0.0937425 4.24160i 0.0220953 0.999756i
\(19\) 1.90761i 0.437636i −0.975766 0.218818i \(-0.929780\pi\)
0.975766 0.218818i \(-0.0702201\pi\)
\(20\) −0.967402 + 4.36625i −0.216318 + 0.976323i
\(21\) 1.48716 0.887900i 0.324524 0.193756i
\(22\) 3.47600 1.77536i 0.741085 0.378509i
\(23\) 2.05073i 0.427607i 0.976877 + 0.213804i \(0.0685853\pi\)
−0.976877 + 0.213804i \(0.931415\pi\)
\(24\) −1.83568 4.54206i −0.374706 0.927144i
\(25\) 3.42327 3.64434i 0.684653 0.728869i
\(26\) 1.22710 + 2.40254i 0.240653 + 0.471177i
\(27\) −0.228229 5.19114i −0.0439227 0.999035i
\(28\) 1.17242 1.62032i 0.221567 0.306211i
\(29\) 4.94433i 0.918140i 0.888400 + 0.459070i \(0.151817\pi\)
−0.888400 + 0.459070i \(0.848183\pi\)
\(30\) −0.829376 + 5.41407i −0.151423 + 0.988469i
\(31\) 6.92361i 1.24352i 0.783209 + 0.621758i \(0.213581\pi\)
−0.783209 + 0.621758i \(0.786419\pi\)
\(32\) −4.01938 3.98052i −0.710533 0.703664i
\(33\) 4.10445 2.45055i 0.714494 0.426585i
\(34\) −6.34485 + 3.24063i −1.08813 + 0.555764i
\(35\) −2.05223 + 0.887900i −0.346890 + 0.150083i
\(36\) −2.61041 5.40239i −0.435068 0.900398i
\(37\) 6.48126i 1.06551i 0.846269 + 0.532756i \(0.178844\pi\)
−0.846269 + 0.532756i \(0.821156\pi\)
\(38\) −1.22710 2.40254i −0.199061 0.389743i
\(39\) 1.69377 + 2.83692i 0.271220 + 0.454270i
\(40\) 1.59025 + 6.12136i 0.251441 + 0.967873i
\(41\) 11.1795i 1.74595i 0.487766 + 0.872975i \(0.337812\pi\)
−0.487766 + 0.872975i \(0.662188\pi\)
\(42\) 1.30184 2.07490i 0.200879 0.320164i
\(43\) −9.36439 −1.42806 −0.714028 0.700117i \(-0.753131\pi\)
−0.714028 + 0.700117i \(0.753131\pi\)
\(44\) 3.23581 4.47196i 0.487817 0.674174i
\(45\) −0.576017 + 6.68343i −0.0858675 + 0.996307i
\(46\) 1.31916 + 2.58279i 0.194500 + 0.380812i
\(47\) 7.51739i 1.09652i −0.836307 0.548262i \(-0.815290\pi\)
0.836307 0.548262i \(-0.184710\pi\)
\(48\) −5.23368 4.53967i −0.755417 0.655245i
\(49\) 1.00000 0.142857
\(50\) 1.96716 6.79193i 0.278198 0.960524i
\(51\) −7.49199 + 4.47306i −1.04909 + 0.626354i
\(52\) 3.09093 + 2.23653i 0.428635 + 0.310151i
\(53\) 6.14747 0.844420 0.422210 0.906498i \(-0.361254\pi\)
0.422210 + 0.906498i \(0.361254\pi\)
\(54\) −3.62671 6.39116i −0.493533 0.869727i
\(55\) −5.66401 + 2.45055i −0.763735 + 0.330432i
\(56\) 0.434319 2.79488i 0.0580384 0.373482i
\(57\) −1.69377 2.83692i −0.224345 0.375759i
\(58\) 3.18051 + 6.22714i 0.417621 + 0.817663i
\(59\) 0.716916 0.0933345 0.0466672 0.998910i \(-0.485140\pi\)
0.0466672 + 0.998910i \(0.485140\pi\)
\(60\) 2.43812 + 7.35225i 0.314759 + 0.949172i
\(61\) 5.13115 0.656976 0.328488 0.944508i \(-0.393461\pi\)
0.328488 + 0.944508i \(0.393461\pi\)
\(62\) 4.45370 + 8.71993i 0.565621 + 1.10743i
\(63\) 1.42327 2.64089i 0.179315 0.332721i
\(64\) −7.62273 2.42774i −0.952842 0.303468i
\(65\) −1.69377 3.91485i −0.210086 0.485577i
\(66\) 3.59300 5.72658i 0.442268 0.704894i
\(67\) 3.58761 0.438296 0.219148 0.975692i \(-0.429672\pi\)
0.219148 + 0.975692i \(0.429672\pi\)
\(68\) −5.90644 + 8.16282i −0.716261 + 0.989887i
\(69\) 1.82085 + 3.04976i 0.219204 + 0.367148i
\(70\) −2.01352 + 2.43839i −0.240662 + 0.291443i
\(71\) 4.49721 0.533721 0.266860 0.963735i \(-0.414014\pi\)
0.266860 + 0.963735i \(0.414014\pi\)
\(72\) −6.76283 5.12485i −0.797007 0.603970i
\(73\) 6.11618i 0.715845i 0.933751 + 0.357922i \(0.116515\pi\)
−0.933751 + 0.357922i \(0.883485\pi\)
\(74\) 4.16916 + 8.16282i 0.484655 + 0.948908i
\(75\) 1.85512 8.45923i 0.214211 0.976788i
\(76\) −3.09093 2.23653i −0.354554 0.256548i
\(77\) 2.75993 0.314524
\(78\) 3.95810 + 2.48341i 0.448167 + 0.281191i
\(79\) 14.6546i 1.64878i −0.566025 0.824388i \(-0.691520\pi\)
0.566025 0.824388i \(-0.308480\pi\)
\(80\) 5.94049 + 6.68659i 0.664167 + 0.747584i
\(81\) −4.94862 7.51739i −0.549847 0.835265i
\(82\) 7.19138 + 14.0800i 0.794155 + 1.55488i
\(83\) 7.71558i 0.846895i 0.905921 + 0.423448i \(0.139180\pi\)
−0.905921 + 0.423448i \(0.860820\pi\)
\(84\) 0.304900 3.45066i 0.0332673 0.376498i
\(85\) 10.3387 4.47306i 1.12139 0.485172i
\(86\) −11.7940 + 6.02377i −1.27178 + 0.649560i
\(87\) 4.39007 + 7.35300i 0.470665 + 0.788324i
\(88\) 1.19869 7.71369i 0.127781 0.822282i
\(89\) 13.5677i 1.43817i −0.694920 0.719087i \(-0.744560\pi\)
0.694920 0.719087i \(-0.255440\pi\)
\(90\) 3.57374 + 8.78797i 0.376705 + 0.926333i
\(91\) 1.90761i 0.199972i
\(92\) 3.32283 + 2.40433i 0.346429 + 0.250669i
\(93\) 6.14747 + 10.2965i 0.637463 + 1.06770i
\(94\) −4.83566 9.46777i −0.498760 0.976526i
\(95\) 1.69377 + 3.91485i 0.173777 + 0.401655i
\(96\) −9.51176 2.35085i −0.970790 0.239932i
\(97\) 16.6772i 1.69331i −0.532143 0.846654i \(-0.678613\pi\)
0.532143 0.846654i \(-0.321387\pi\)
\(98\) 1.25945 0.643263i 0.127224 0.0649794i
\(99\) 3.92812 7.28869i 0.394791 0.732541i
\(100\) −1.89147 9.81949i −0.189147 0.981949i
\(101\) 7.71558i 0.767729i 0.923389 + 0.383865i \(0.125407\pi\)
−0.923389 + 0.383865i \(0.874593\pi\)
\(102\) −6.55842 + 10.4529i −0.649381 + 1.03499i
\(103\) −20.2109 −1.99144 −0.995721 0.0924150i \(-0.970541\pi\)
−0.995721 + 0.0924150i \(0.970541\pi\)
\(104\) 5.33155 + 0.828513i 0.522801 + 0.0812424i
\(105\) −2.26361 + 3.14262i −0.220906 + 0.306688i
\(106\) 7.74243 3.95444i 0.752011 0.384089i
\(107\) 1.27396i 0.123158i 0.998102 + 0.0615791i \(0.0196136\pi\)
−0.998102 + 0.0615791i \(0.980386\pi\)
\(108\) −8.67886 5.71641i −0.835124 0.550062i
\(109\) −14.6383 −1.40210 −0.701048 0.713114i \(-0.747284\pi\)
−0.701048 + 0.713114i \(0.747284\pi\)
\(110\) −5.55719 + 6.72979i −0.529857 + 0.641660i
\(111\) 5.75471 + 9.63865i 0.546213 + 0.914860i
\(112\) −1.25084 3.79939i −0.118193 0.359009i
\(113\) 8.83651 0.831269 0.415634 0.909532i \(-0.363560\pi\)
0.415634 + 0.909532i \(0.363560\pi\)
\(114\) −3.95810 2.48341i −0.370710 0.232593i
\(115\) −1.82085 4.20857i −0.169795 0.392451i
\(116\) 8.01138 + 5.79686i 0.743838 + 0.538225i
\(117\) 5.03780 + 2.71504i 0.465744 + 0.251006i
\(118\) 0.902919 0.461166i 0.0831204 0.0424537i
\(119\) −5.03780 −0.461814
\(120\) 7.80012 + 7.69144i 0.712050 + 0.702129i
\(121\) −3.38276 −0.307524
\(122\) 6.46242 3.30068i 0.585080 0.298830i
\(123\) 9.92631 + 16.6257i 0.895025 + 1.49909i
\(124\) 11.2184 + 8.11740i 1.00744 + 0.728964i
\(125\) −3.78950 + 10.5185i −0.338944 + 0.940807i
\(126\) 0.0937425 4.24160i 0.00835125 0.377872i
\(127\) −2.15684 −0.191388 −0.0956941 0.995411i \(-0.530507\pi\)
−0.0956941 + 0.995411i \(0.530507\pi\)
\(128\) −11.1621 + 1.84581i −0.986602 + 0.163148i
\(129\) −13.9263 + 8.31464i −1.22614 + 0.732063i
\(130\) −4.65150 3.84102i −0.407963 0.336879i
\(131\) −2.93626 −0.256543 −0.128271 0.991739i \(-0.540943\pi\)
−0.128271 + 0.991739i \(0.540943\pi\)
\(132\) 0.841504 9.52359i 0.0732435 0.828922i
\(133\) 1.90761i 0.165411i
\(134\) 4.51841 2.30778i 0.390331 0.199361i
\(135\) 5.07759 + 10.4507i 0.437009 + 0.899457i
\(136\) −2.18801 + 14.0800i −0.187621 + 1.20735i
\(137\) −16.4887 −1.40873 −0.704363 0.709840i \(-0.748767\pi\)
−0.704363 + 0.709840i \(0.748767\pi\)
\(138\) 4.25506 + 2.66973i 0.362215 + 0.227263i
\(139\) 10.8537i 0.920602i −0.887763 0.460301i \(-0.847742\pi\)
0.887763 0.460301i \(-0.152258\pi\)
\(140\) −0.967402 + 4.36625i −0.0817604 + 0.369015i
\(141\) −6.67469 11.1795i −0.562110 0.941486i
\(142\) 5.66401 2.89289i 0.475313 0.242766i
\(143\) 5.26488i 0.440272i
\(144\) −11.8141 2.10421i −0.984506 0.175351i
\(145\) −4.39007 10.1469i −0.364576 0.842654i
\(146\) 3.93431 + 7.70302i 0.325606 + 0.637506i
\(147\) 1.48716 0.887900i 0.122659 0.0732328i
\(148\) 10.5017 + 7.59879i 0.863233 + 0.624617i
\(149\) 13.6420i 1.11760i −0.829303 0.558800i \(-0.811262\pi\)
0.829303 0.558800i \(-0.188738\pi\)
\(150\) −3.10509 11.8473i −0.253529 0.967328i
\(151\) 1.35036i 0.109891i 0.998489 + 0.0549455i \(0.0174985\pi\)
−0.998489 + 0.0549455i \(0.982501\pi\)
\(152\) −5.33155 0.828513i −0.432446 0.0672013i
\(153\) −7.17013 + 13.3043i −0.579670 + 1.07559i
\(154\) 3.47600 1.77536i 0.280104 0.143063i
\(155\) −6.14747 14.2088i −0.493777 1.14128i
\(156\) 6.58251 + 0.581631i 0.527023 + 0.0465677i
\(157\) 1.90761i 0.152244i −0.997099 0.0761220i \(-0.975746\pi\)
0.997099 0.0761220i \(-0.0242538\pi\)
\(158\) −9.42679 18.4568i −0.749955 1.46834i
\(159\) 9.14225 5.45834i 0.725028 0.432875i
\(160\) 11.7830 + 4.60012i 0.931527 + 0.363672i
\(161\) 2.05073i 0.161620i
\(162\) −11.0682 6.28450i −0.869600 0.493757i
\(163\) 24.4368 1.91404 0.957021 0.290019i \(-0.0936617\pi\)
0.957021 + 0.290019i \(0.0936617\pi\)
\(164\) 18.1144 + 13.1072i 1.41449 + 1.02350i
\(165\) −6.24743 + 8.67342i −0.486361 + 0.675225i
\(166\) 4.96315 + 9.71739i 0.385215 + 0.754215i
\(167\) 3.53470i 0.273523i 0.990604 + 0.136762i \(0.0436694\pi\)
−0.990604 + 0.136762i \(0.956331\pi\)
\(168\) −1.83568 4.54206i −0.141625 0.350427i
\(169\) 9.36102 0.720078
\(170\) 10.1437 12.2841i 0.777987 0.942147i
\(171\) −5.03780 2.71504i −0.385250 0.207624i
\(172\) −10.9790 + 15.1733i −0.837144 + 1.15695i
\(173\) 16.8691 1.28253 0.641266 0.767318i \(-0.278409\pi\)
0.641266 + 0.767318i \(0.278409\pi\)
\(174\) 10.2590 + 6.43675i 0.777732 + 0.487969i
\(175\) 3.42327 3.64434i 0.258775 0.275487i
\(176\) −3.45224 10.4861i −0.260223 0.790418i
\(177\) 1.06617 0.636550i 0.0801379 0.0478460i
\(178\) −8.72761 17.0878i −0.654162 1.28079i
\(179\) 4.19377 0.313457 0.156728 0.987642i \(-0.449905\pi\)
0.156728 + 0.987642i \(0.449905\pi\)
\(180\) 10.1539 + 8.76914i 0.756829 + 0.653613i
\(181\) −9.70038 −0.721023 −0.360512 0.932755i \(-0.617398\pi\)
−0.360512 + 0.932755i \(0.617398\pi\)
\(182\) 1.22710 + 2.40254i 0.0909585 + 0.178088i
\(183\) 7.63082 4.55595i 0.564086 0.336785i
\(184\) 5.73155 + 0.890673i 0.422536 + 0.0656613i
\(185\) −5.75471 13.3010i −0.423095 0.977910i
\(186\) 14.3658 + 9.01345i 1.05335 + 0.660899i
\(187\) −13.9040 −1.01676
\(188\) −12.1805 8.81357i −0.888357 0.642796i
\(189\) −0.228229 5.19114i −0.0166012 0.377600i
\(190\) 4.65150 + 3.84102i 0.337455 + 0.278657i
\(191\) −7.79773 −0.564224 −0.282112 0.959381i \(-0.591035\pi\)
−0.282112 + 0.959381i \(0.591035\pi\)
\(192\) −13.4918 + 3.15779i −0.973686 + 0.227894i
\(193\) 2.15779i 0.155321i −0.996980 0.0776606i \(-0.975255\pi\)
0.996980 0.0776606i \(-0.0247451\pi\)
\(194\) −10.7278 21.0040i −0.770211 1.50800i
\(195\) −5.99489 4.31810i −0.429303 0.309225i
\(196\) 1.17242 1.62032i 0.0837446 0.115737i
\(197\) 14.9679 1.06642 0.533208 0.845984i \(-0.320986\pi\)
0.533208 + 0.845984i \(0.320986\pi\)
\(198\) 0.258723 11.7066i 0.0183867 0.831948i
\(199\) 10.7388i 0.761255i 0.924728 + 0.380628i \(0.124292\pi\)
−0.924728 + 0.380628i \(0.875708\pi\)
\(200\) −8.69872 11.1504i −0.615093 0.788455i
\(201\) 5.33533 3.18544i 0.376325 0.224683i
\(202\) 4.96315 + 9.71739i 0.349206 + 0.683713i
\(203\) 4.94433i 0.347024i
\(204\) −1.53602 + 17.3837i −0.107543 + 1.21710i
\(205\) −9.92631 22.9429i −0.693283 1.60240i
\(206\) −25.4546 + 13.0009i −1.77351 + 0.905819i
\(207\) 5.41576 + 2.91874i 0.376422 + 0.202866i
\(208\) 7.24777 2.38612i 0.502542 0.165448i
\(209\) 5.26488i 0.364180i
\(210\) −0.829376 + 5.41407i −0.0572324 + 0.373606i
\(211\) 13.5827i 0.935073i −0.883974 0.467536i \(-0.845142\pi\)
0.883974 0.467536i \(-0.154858\pi\)
\(212\) 7.20745 9.96084i 0.495009 0.684113i
\(213\) 6.68806 3.99308i 0.458258 0.273601i
\(214\) 0.819491 + 1.60449i 0.0560192 + 0.109680i
\(215\) 19.2178 8.31464i 1.31065 0.567054i
\(216\) −14.6077 1.61674i −0.993931 0.110005i
\(217\) 6.92361i 0.470005i
\(218\) −18.4362 + 9.41630i −1.24866 + 0.637752i
\(219\) 5.43056 + 9.09571i 0.366963 + 0.614631i
\(220\) −2.66997 + 12.0506i −0.180009 + 0.812449i
\(221\) 9.61016i 0.646449i
\(222\) 13.4480 + 8.43759i 0.902568 + 0.566294i
\(223\) −11.6417 −0.779585 −0.389793 0.920903i \(-0.627453\pi\)
−0.389793 + 0.920903i \(0.627453\pi\)
\(224\) −4.01938 3.98052i −0.268556 0.265960i
\(225\) −4.75210 14.2274i −0.316807 0.948490i
\(226\) 11.1291 5.68420i 0.740299 0.378108i
\(227\) 3.16030i 0.209756i −0.994485 0.104878i \(-0.966555\pi\)
0.994485 0.104878i \(-0.0334453\pi\)
\(228\) −6.58251 0.581631i −0.435938 0.0385194i
\(229\) −3.43808 −0.227195 −0.113597 0.993527i \(-0.536237\pi\)
−0.113597 + 0.993527i \(0.536237\pi\)
\(230\) −5.00048 4.12919i −0.329722 0.272271i
\(231\) 4.10445 2.45055i 0.270053 0.161234i
\(232\) 13.8188 + 2.14742i 0.907251 + 0.140985i
\(233\) −17.5699 −1.15104 −0.575520 0.817787i \(-0.695200\pi\)
−0.575520 + 0.817787i \(0.695200\pi\)
\(234\) 8.09133 + 0.178824i 0.528947 + 0.0116901i
\(235\) 6.67469 + 15.4274i 0.435409 + 1.00637i
\(236\) 0.840529 1.16163i 0.0547138 0.0756156i
\(237\) −13.0119 21.7937i −0.845211 1.41566i
\(238\) −6.34485 + 3.24063i −0.411275 + 0.210059i
\(239\) −17.5275 −1.13376 −0.566879 0.823801i \(-0.691849\pi\)
−0.566879 + 0.823801i \(0.691849\pi\)
\(240\) 14.7715 + 4.66944i 0.953494 + 0.301411i
\(241\) 6.21092 0.400081 0.200040 0.979788i \(-0.435893\pi\)
0.200040 + 0.979788i \(0.435893\pi\)
\(242\) −4.26042 + 2.17601i −0.273870 + 0.139879i
\(243\) −14.0341 6.78564i −0.900286 0.435299i
\(244\) 6.01588 8.31408i 0.385127 0.532254i
\(245\) −2.05223 + 0.887900i −0.131112 + 0.0567259i
\(246\) 23.1964 + 14.5540i 1.47895 + 0.927929i
\(247\) 3.63898 0.231543
\(248\) 19.3507 + 3.00706i 1.22877 + 0.190948i
\(249\) 6.85067 + 11.4743i 0.434143 + 0.727153i
\(250\) 1.99350 + 15.6852i 0.126080 + 0.992020i
\(251\) 22.4760 1.41867 0.709335 0.704871i \(-0.248995\pi\)
0.709335 + 0.704871i \(0.248995\pi\)
\(252\) −2.61041 5.40239i −0.164440 0.340318i
\(253\) 5.65989i 0.355834i
\(254\) −2.71642 + 1.38741i −0.170444 + 0.0870541i
\(255\) 11.4036 15.8319i 0.714123 0.991430i
\(256\) −12.8708 + 9.50488i −0.804424 + 0.594055i
\(257\) −7.25715 −0.452688 −0.226344 0.974047i \(-0.572677\pi\)
−0.226344 + 0.974047i \(0.572677\pi\)
\(258\) −12.1910 + 19.4302i −0.758977 + 1.20967i
\(259\) 6.48126i 0.402726i
\(260\) −8.32911 1.84543i −0.516549 0.114449i
\(261\) 13.0575 + 7.03711i 0.808236 + 0.435586i
\(262\) −3.69808 + 1.88879i −0.228468 + 0.116690i
\(263\) 16.3928i 1.01082i −0.862878 0.505412i \(-0.831341\pi\)
0.862878 0.505412i \(-0.168659\pi\)
\(264\) −5.06634 12.5358i −0.311812 0.771524i
\(265\) −12.6160 + 5.45834i −0.774995 + 0.335303i
\(266\) −1.22710 2.40254i −0.0752381 0.147309i
\(267\) −12.0468 20.1773i −0.737251 1.23483i
\(268\) 4.20620 5.81305i 0.256934 0.355089i
\(269\) 4.53372i 0.276426i −0.990403 0.138213i \(-0.955864\pi\)
0.990403 0.138213i \(-0.0441359\pi\)
\(270\) 13.1175 + 9.89595i 0.798309 + 0.602249i
\(271\) 27.5166i 1.67151i −0.549100 0.835756i \(-0.685030\pi\)
0.549100 0.835756i \(-0.314970\pi\)
\(272\) 6.30149 + 19.1406i 0.382084 + 1.16057i
\(273\) 1.69377 + 2.83692i 0.102512 + 0.171698i
\(274\) −20.7667 + 10.6066i −1.25456 + 0.640767i
\(275\) 9.44799 10.0582i 0.569735 0.606529i
\(276\) 7.07637 + 0.625268i 0.425948 + 0.0376367i
\(277\) 24.3449i 1.46274i 0.681980 + 0.731371i \(0.261119\pi\)
−0.681980 + 0.731371i \(0.738881\pi\)
\(278\) −6.98181 13.6697i −0.418741 0.819856i
\(279\) 18.2845 + 9.85414i 1.09466 + 0.589952i
\(280\) 1.59025 + 6.12136i 0.0950359 + 0.365821i
\(281\) 10.5636i 0.630170i −0.949064 0.315085i \(-0.897967\pi\)
0.949064 0.315085i \(-0.102033\pi\)
\(282\) −15.5978 9.78646i −0.928836 0.582775i
\(283\) −5.53680 −0.329129 −0.164564 0.986366i \(-0.552622\pi\)
−0.164564 + 0.986366i \(0.552622\pi\)
\(284\) 5.27264 7.28690i 0.312874 0.432398i
\(285\) 5.99489 + 4.31810i 0.355107 + 0.255782i
\(286\) 3.38671 + 6.63085i 0.200260 + 0.392090i
\(287\) 11.1795i 0.659907i
\(288\) −16.2328 + 4.94941i −0.956526 + 0.291647i
\(289\) 8.37939 0.492906
\(290\) −12.0562 9.95552i −0.707965 0.584608i
\(291\) −14.8076 24.8015i −0.868040 1.45389i
\(292\) 9.91014 + 7.17076i 0.579947 + 0.419637i
\(293\) 25.2198 1.47336 0.736678 0.676244i \(-0.236393\pi\)
0.736678 + 0.676244i \(0.236393\pi\)
\(294\) 1.30184 2.07490i 0.0759251 0.121011i
\(295\) −1.47127 + 0.636550i −0.0856608 + 0.0370613i
\(296\) 18.1144 + 2.81494i 1.05288 + 0.163615i
\(297\) −0.629897 14.3272i −0.0365504 0.831348i
\(298\) −8.77543 17.1815i −0.508347 0.995295i
\(299\) −3.91200 −0.226237
\(300\) −11.5316 12.9237i −0.665779 0.746149i
\(301\) −9.36439 −0.539754
\(302\) 0.868639 + 1.70071i 0.0499846 + 0.0978650i
\(303\) 6.85067 + 11.4743i 0.393561 + 0.659180i
\(304\) −7.24777 + 2.38612i −0.415688 + 0.136853i
\(305\) −10.5303 + 4.55595i −0.602962 + 0.260873i
\(306\) −0.472256 + 21.3683i −0.0269971 + 1.22155i
\(307\) 19.0825 1.08909 0.544547 0.838730i \(-0.316701\pi\)
0.544547 + 0.838730i \(0.316701\pi\)
\(308\) 3.23581 4.47196i 0.184378 0.254814i
\(309\) −30.0568 + 17.9453i −1.70987 + 1.02087i
\(310\) −16.8824 13.9408i −0.958858 0.791786i
\(311\) −6.95370 −0.394308 −0.197154 0.980373i \(-0.563170\pi\)
−0.197154 + 0.980373i \(0.563170\pi\)
\(312\) 8.66448 3.50176i 0.490530 0.198248i
\(313\) 34.5408i 1.95236i −0.216963 0.976180i \(-0.569615\pi\)
0.216963 0.976180i \(-0.430385\pi\)
\(314\) −1.22710 2.40254i −0.0692491 0.135583i
\(315\) −0.576017 + 6.68343i −0.0324549 + 0.376568i
\(316\) −23.7451 17.1815i −1.33577 0.966533i
\(317\) 8.19278 0.460153 0.230076 0.973173i \(-0.426102\pi\)
0.230076 + 0.973173i \(0.426102\pi\)
\(318\) 8.00305 12.7554i 0.448789 0.715286i
\(319\) 13.6460i 0.764031i
\(320\) 17.7992 1.78595i 0.995004 0.0998375i
\(321\) 1.13115 + 1.89458i 0.0631345 + 0.105745i
\(322\) 1.31916 + 2.58279i 0.0735140 + 0.143933i
\(323\) 9.61016i 0.534724i
\(324\) −17.9824 0.795237i −0.999024 0.0441799i
\(325\) 6.95199 + 6.53026i 0.385627 + 0.362234i
\(326\) 30.7770 15.7193i 1.70458 0.870613i
\(327\) −21.7695 + 12.9974i −1.20385 + 0.718756i
\(328\) 31.2455 + 4.85549i 1.72524 + 0.268099i
\(329\) 7.51739i 0.414447i
\(330\) −2.28902 + 14.9425i −0.126007 + 0.822556i
\(331\) 4.63660i 0.254850i 0.991848 + 0.127425i \(0.0406713\pi\)
−0.991848 + 0.127425i \(0.959329\pi\)
\(332\) 12.5017 + 9.04594i 0.686119 + 0.496460i
\(333\) 17.1163 + 9.22456i 0.937968 + 0.505503i
\(334\) 2.27374 + 4.45177i 0.124414 + 0.243590i
\(335\) −7.36258 + 3.18544i −0.402261 + 0.174039i
\(336\) −5.23368 4.53967i −0.285521 0.247659i
\(337\) 18.4352i 1.00423i 0.864801 + 0.502114i \(0.167444\pi\)
−0.864801 + 0.502114i \(0.832556\pi\)
\(338\) 11.7897 6.02160i 0.641277 0.327532i
\(339\) 13.1413 7.84594i 0.713736 0.426133i
\(340\) 4.87358 21.9963i 0.264307 1.19292i
\(341\) 19.1087i 1.03479i
\(342\) −8.09133 0.178824i −0.437529 0.00966971i
\(343\) 1.00000 0.0539949
\(344\) −4.06714 + 26.1724i −0.219285 + 1.41112i
\(345\) −6.44467 4.64207i −0.346969 0.249920i
\(346\) 21.2458 10.8513i 1.14218 0.583368i
\(347\) 2.86847i 0.153987i 0.997032 + 0.0769936i \(0.0245321\pi\)
−0.997032 + 0.0769936i \(0.975468\pi\)
\(348\) 17.0612 + 1.50753i 0.914576 + 0.0808119i
\(349\) −2.76610 −0.148066 −0.0740330 0.997256i \(-0.523587\pi\)
−0.0740330 + 0.997256i \(0.523587\pi\)
\(350\) 1.96716 6.79193i 0.105149 0.363044i
\(351\) 9.90267 0.435373i 0.528566 0.0232385i
\(352\) −11.0932 10.9860i −0.591271 0.585555i
\(353\) 23.6750 1.26009 0.630045 0.776558i \(-0.283036\pi\)
0.630045 + 0.776558i \(0.283036\pi\)
\(354\) 0.933312 1.48753i 0.0496050 0.0790612i
\(355\) −9.22930 + 3.99308i −0.489840 + 0.211930i
\(356\) −21.9840 15.9071i −1.16515 0.843075i
\(357\) −7.49199 + 4.47306i −0.396518 + 0.236739i
\(358\) 5.28183 2.69770i 0.279154 0.142578i
\(359\) −15.7410 −0.830778 −0.415389 0.909644i \(-0.636355\pi\)
−0.415389 + 0.909644i \(0.636355\pi\)
\(360\) 18.4292 + 4.51264i 0.971305 + 0.237837i
\(361\) 15.3610 0.808475
\(362\) −12.2171 + 6.23990i −0.642118 + 0.327962i
\(363\) −5.03070 + 3.00356i −0.264043 + 0.157646i
\(364\) 3.09093 + 2.23653i 0.162009 + 0.117226i
\(365\) −5.43056 12.5518i −0.284248 0.656990i
\(366\) 6.67995 10.6466i 0.349167 0.556507i
\(367\) 19.3280 1.00891 0.504457 0.863437i \(-0.331693\pi\)
0.504457 + 0.863437i \(0.331693\pi\)
\(368\) 7.79154 2.56514i 0.406162 0.133717i
\(369\) 29.5239 + 15.9114i 1.53695 + 0.828317i
\(370\) −15.8038 13.0502i −0.821602 0.678445i
\(371\) 6.14747 0.319161
\(372\) 23.8910 + 2.11101i 1.23869 + 0.109451i
\(373\) 34.4749i 1.78504i 0.451007 + 0.892520i \(0.351065\pi\)
−0.451007 + 0.892520i \(0.648935\pi\)
\(374\) −17.5114 + 8.94393i −0.905491 + 0.462479i
\(375\) 3.70383 + 19.0074i 0.191265 + 0.981538i
\(376\) −21.0102 3.26495i −1.08352 0.168377i
\(377\) −9.43187 −0.485766
\(378\) −3.62671 6.39116i −0.186538 0.328726i
\(379\) 16.3121i 0.837895i 0.908010 + 0.418947i \(0.137601\pi\)
−0.908010 + 0.418947i \(0.862399\pi\)
\(380\) 8.32911 + 1.84543i 0.427274 + 0.0946684i
\(381\) −3.20755 + 1.91505i −0.164328 + 0.0981112i
\(382\) −9.82085 + 5.01599i −0.502478 + 0.256641i
\(383\) 20.4691i 1.04592i −0.852356 0.522962i \(-0.824827\pi\)
0.852356 0.522962i \(-0.175173\pi\)
\(384\) −14.9609 + 12.6559i −0.763472 + 0.645841i
\(385\) −5.66401 + 2.45055i −0.288665 + 0.124891i
\(386\) −1.38803 2.71763i −0.0706488 0.138324i
\(387\) −13.3280 + 24.7303i −0.677501 + 1.25711i
\(388\) −27.0222 19.5527i −1.37185 0.992638i
\(389\) 12.5062i 0.634088i 0.948411 + 0.317044i \(0.102690\pi\)
−0.948411 + 0.317044i \(0.897310\pi\)
\(390\) −10.3279 1.58213i −0.522976 0.0801141i
\(391\) 10.3312i 0.522470i
\(392\) 0.434319 2.79488i 0.0219364 0.141163i
\(393\) −4.36668 + 2.60711i −0.220270 + 0.131511i
\(394\) 18.8513 9.62828i 0.949713 0.485066i
\(395\) 13.0119 + 30.0746i 0.654698 + 1.51322i
\(396\) −7.20455 14.9102i −0.362042 0.749267i
\(397\) 7.33769i 0.368268i 0.982901 + 0.184134i \(0.0589481\pi\)
−0.982901 + 0.184134i \(0.941052\pi\)
\(398\) 6.90790 + 13.5250i 0.346262 + 0.677947i
\(399\) −1.69377 2.83692i −0.0847945 0.142023i
\(400\) −18.1283 8.44784i −0.906413 0.422392i
\(401\) 11.3403i 0.566310i −0.959074 0.283155i \(-0.908619\pi\)
0.959074 0.283155i \(-0.0913810\pi\)
\(402\) 4.67050 7.44392i 0.232944 0.371269i
\(403\) −13.2076 −0.657915
\(404\) 12.5017 + 9.04594i 0.621982 + 0.450052i
\(405\) 16.8304 + 11.0335i 0.836309 + 0.548259i
\(406\) 3.18051 + 6.22714i 0.157846 + 0.309048i
\(407\) 17.8879i 0.886668i
\(408\) 9.24776 + 22.8820i 0.457832 + 1.13283i
\(409\) 10.5692 0.522615 0.261307 0.965256i \(-0.415846\pi\)
0.261307 + 0.965256i \(0.415846\pi\)
\(410\) −27.2600 22.5102i −1.34628 1.11170i
\(411\) −24.5213 + 14.6403i −1.20955 + 0.722154i
\(412\) −23.6958 + 32.7481i −1.16741 + 1.61338i
\(413\) 0.716916 0.0352771
\(414\) 8.69840 + 0.192241i 0.427503 + 0.00944812i
\(415\) −6.85067 15.8341i −0.336286 0.777267i
\(416\) 7.59329 7.66742i 0.372292 0.375926i
\(417\) −9.63703 16.1412i −0.471927 0.790438i
\(418\) −3.38671 6.63085i −0.165649 0.324326i
\(419\) −39.1526 −1.91273 −0.956365 0.292175i \(-0.905621\pi\)
−0.956365 + 0.292175i \(0.905621\pi\)
\(420\) 2.43812 + 7.35225i 0.118968 + 0.358753i
\(421\) 28.0122 1.36523 0.682614 0.730779i \(-0.260843\pi\)
0.682614 + 0.730779i \(0.260843\pi\)
\(422\) −8.73727 17.1067i −0.425323 0.832743i
\(423\) −19.8526 10.6992i −0.965267 0.520215i
\(424\) 2.66997 17.1815i 0.129665 0.834405i
\(425\) −17.2457 + 18.3595i −0.836540 + 0.890565i
\(426\) 5.85467 9.33126i 0.283660 0.452101i
\(427\) 5.13115 0.248314
\(428\) 2.06421 + 1.49362i 0.0997776 + 0.0721968i
\(429\) 4.67469 + 7.82970i 0.225696 + 0.378022i
\(430\) 18.8554 22.8340i 0.909288 1.10115i
\(431\) −37.8527 −1.82330 −0.911650 0.410967i \(-0.865191\pi\)
−0.911650 + 0.410967i \(0.865191\pi\)
\(432\) −19.4377 + 7.36043i −0.935197 + 0.354129i
\(433\) 18.2920i 0.879058i 0.898228 + 0.439529i \(0.144855\pi\)
−0.898228 + 0.439529i \(0.855145\pi\)
\(434\) 4.45370 + 8.71993i 0.213785 + 0.418570i
\(435\) −15.5382 11.1921i −0.744997 0.536618i
\(436\) −17.1623 + 23.7187i −0.821926 + 1.13592i
\(437\) 3.91200 0.187136
\(438\) 12.6904 + 7.96231i 0.606373 + 0.380454i
\(439\) 12.5549i 0.599211i 0.954063 + 0.299605i \(0.0968550\pi\)
−0.954063 + 0.299605i \(0.903145\pi\)
\(440\) 4.38900 + 16.8946i 0.209237 + 0.805417i
\(441\) 1.42327 2.64089i 0.0677746 0.125757i
\(442\) −6.18186 12.1035i −0.294041 0.575705i
\(443\) 29.7757i 1.41468i 0.706872 + 0.707342i \(0.250106\pi\)
−0.706872 + 0.707342i \(0.749894\pi\)
\(444\) 22.3646 + 1.97614i 1.06138 + 0.0937833i
\(445\) 12.0468 + 27.8440i 0.571072 + 1.31993i
\(446\) −14.6621 + 7.48867i −0.694271 + 0.354599i
\(447\) −12.1128 20.2878i −0.572914 0.959582i
\(448\) −7.62273 2.42774i −0.360140 0.114700i
\(449\) 23.7253i 1.11967i 0.828605 + 0.559834i \(0.189135\pi\)
−0.828605 + 0.559834i \(0.810865\pi\)
\(450\) −15.1370 14.8618i −0.713563 0.700591i
\(451\) 30.8548i 1.45289i
\(452\) 10.3601 14.3179i 0.487300 0.673459i
\(453\) 1.19899 + 2.00820i 0.0563333 + 0.0943535i
\(454\) −2.03290 3.98024i −0.0954090 0.186802i
\(455\) −1.69377 3.91485i −0.0794051 0.183531i
\(456\) −8.66448 + 3.50176i −0.405752 + 0.163985i
\(457\) 5.67383i 0.265411i 0.991156 + 0.132705i \(0.0423664\pi\)
−0.991156 + 0.132705i \(0.957634\pi\)
\(458\) −4.33009 + 2.21159i −0.202332 + 0.103341i
\(459\) 1.14977 + 26.1519i 0.0536668 + 1.22067i
\(460\) −8.95401 1.98388i −0.417483 0.0924990i
\(461\) 12.2891i 0.572360i −0.958176 0.286180i \(-0.907614\pi\)
0.958176 0.286180i \(-0.0923856\pi\)
\(462\) 3.59300 5.72658i 0.167162 0.266425i
\(463\) 0.893880 0.0415421 0.0207711 0.999784i \(-0.493388\pi\)
0.0207711 + 0.999784i \(0.493388\pi\)
\(464\) 18.7855 6.18458i 0.872094 0.287112i
\(465\) −21.7583 15.6724i −1.00901 0.726789i
\(466\) −22.1284 + 11.3021i −1.02508 + 0.523558i
\(467\) 29.0874i 1.34601i −0.739640 0.673003i \(-0.765004\pi\)
0.739640 0.673003i \(-0.234996\pi\)
\(468\) 10.3057 4.97964i 0.476379 0.230184i
\(469\) 3.58761 0.165660
\(470\) 18.3303 + 15.1364i 0.845514 + 0.698191i
\(471\) −1.69377 2.83692i −0.0780447 0.130718i
\(472\) 0.311370 2.00369i 0.0143320 0.0922275i
\(473\) −25.8451 −1.18836
\(474\) −30.4069 19.0781i −1.39663 0.876284i
\(475\) −6.95199 6.53026i −0.318979 0.299629i
\(476\) −5.90644 + 8.16282i −0.270721 + 0.374142i
\(477\) 8.74949 16.2348i 0.400612 0.743341i
\(478\) −22.0750 + 11.2748i −1.00969 + 0.515697i
\(479\) −24.2741 −1.10911 −0.554555 0.832147i \(-0.687111\pi\)
−0.554555 + 0.832147i \(0.687111\pi\)
\(480\) 21.6076 3.62102i 0.986247 0.165276i
\(481\) −12.3637 −0.563737
\(482\) 7.82234 3.99526i 0.356298 0.181979i
\(483\) 1.82085 + 3.04976i 0.0828513 + 0.138769i
\(484\) −3.96603 + 5.48114i −0.180274 + 0.249143i
\(485\) 14.8076 + 34.2253i 0.672381 + 1.55409i
\(486\) −22.0402 + 0.481428i −0.999762 + 0.0218380i
\(487\) 38.1623 1.72930 0.864648 0.502378i \(-0.167541\pi\)
0.864648 + 0.502378i \(0.167541\pi\)
\(488\) 2.22856 14.3410i 0.100882 0.649184i
\(489\) 36.3414 21.6975i 1.64342 0.981194i
\(490\) −2.01352 + 2.43839i −0.0909616 + 0.110155i
\(491\) 26.4225 1.19243 0.596216 0.802824i \(-0.296670\pi\)
0.596216 + 0.802824i \(0.296670\pi\)
\(492\) 38.5767 + 3.40864i 1.73917 + 0.153673i
\(493\) 24.9085i 1.12182i
\(494\) 4.58311 2.34082i 0.206204 0.105319i
\(495\) −1.58977 + 18.4458i −0.0714547 + 0.829078i
\(496\) 26.3055 8.66034i 1.18115 0.388861i
\(497\) 4.49721 0.201728
\(498\) 16.0091 + 10.0445i 0.717383 + 0.450104i
\(499\) 34.9059i 1.56260i 0.624155 + 0.781300i \(0.285443\pi\)
−0.624155 + 0.781300i \(0.714557\pi\)
\(500\) 12.6004 + 18.4724i 0.563509 + 0.826110i
\(501\) 3.13846 + 5.25665i 0.140216 + 0.234850i
\(502\) 28.3073 14.4580i 1.26342 0.645291i
\(503\) 8.03971i 0.358473i −0.983806 0.179236i \(-0.942637\pi\)
0.983806 0.179236i \(-0.0573627\pi\)
\(504\) −6.76283 5.12485i −0.301240 0.228279i
\(505\) −6.85067 15.8341i −0.304851 0.704609i
\(506\) 3.64080 + 7.12834i 0.161853 + 0.316893i
\(507\) 13.9213 8.31165i 0.618266 0.369133i
\(508\) −2.52873 + 3.49475i −0.112194 + 0.155055i
\(509\) 5.53741i 0.245441i −0.992441 0.122721i \(-0.960838\pi\)
0.992441 0.122721i \(-0.0391619\pi\)
\(510\) 4.17823 27.2750i 0.185015 1.20776i
\(511\) 6.11618i 0.270564i
\(512\) −10.0960 + 20.2502i −0.446183 + 0.894942i
\(513\) −9.90267 + 0.435373i −0.437214 + 0.0192222i
\(514\) −9.14001 + 4.66826i −0.403148 + 0.205908i
\(515\) 41.4774 17.9453i 1.82771 0.790763i
\(516\) −2.85520 + 32.3133i −0.125693 + 1.42251i
\(517\) 20.7475i 0.912474i
\(518\) 4.16916 + 8.16282i 0.183182 + 0.358654i
\(519\) 25.0870 14.9781i 1.10120 0.657464i
\(520\) −11.6772 + 3.03359i −0.512078 + 0.133032i
\(521\) 12.7331i 0.557846i 0.960313 + 0.278923i \(0.0899775\pi\)
−0.960313 + 0.278923i \(0.910023\pi\)
\(522\) 20.9719 + 0.463494i 0.917916 + 0.0202866i
\(523\) 22.8415 0.998791 0.499396 0.866374i \(-0.333555\pi\)
0.499396 + 0.866374i \(0.333555\pi\)
\(524\) −3.44255 + 4.75767i −0.150388 + 0.207840i
\(525\) 1.85512 8.45923i 0.0809640 0.369191i
\(526\) −10.5449 20.6459i −0.459779 0.900205i
\(527\) 34.8797i 1.51938i
\(528\) −14.4446 12.5292i −0.628621 0.545263i
\(529\) 18.7945 0.817152
\(530\) −12.3781 + 14.9899i −0.537669 + 0.651120i
\(531\) 1.02036 1.89330i 0.0442799 0.0821621i
\(532\) −3.09093 2.23653i −0.134009 0.0969659i
\(533\) −21.3262 −0.923740
\(534\) −28.1516 17.6630i −1.21824 0.764355i
\(535\) −1.13115 2.61445i −0.0489038 0.113033i
\(536\) 1.55817 10.0269i 0.0673026 0.433098i
\(537\) 6.23678 3.72364i 0.269137 0.160687i
\(538\) −2.91638 5.71000i −0.125734 0.246175i
\(539\) 2.75993 0.118879
\(540\) 22.8866 + 4.02541i 0.984882 + 0.173226i
\(541\) −16.5179 −0.710158 −0.355079 0.934836i \(-0.615546\pi\)
−0.355079 + 0.934836i \(0.615546\pi\)
\(542\) −17.7004 34.6557i −0.760297 1.48859i
\(543\) −14.4260 + 8.61297i −0.619078 + 0.369618i
\(544\) 20.2488 + 20.0531i 0.868162 + 0.859768i
\(545\) 30.0412 12.9974i 1.28682 0.556746i
\(546\) 3.95810 + 2.48341i 0.169391 + 0.106280i
\(547\) −22.5719 −0.965106 −0.482553 0.875867i \(-0.660290\pi\)
−0.482553 + 0.875867i \(0.660290\pi\)
\(548\) −19.3318 + 26.7169i −0.825812 + 1.14129i
\(549\) 7.30299 13.5508i 0.311684 0.578334i
\(550\) 5.42922 18.7453i 0.231503 0.799301i
\(551\) 9.43187 0.401811
\(552\) 9.31455 3.76448i 0.396453 0.160227i
\(553\) 14.6546i 0.623179i
\(554\) 15.6602 + 30.6611i 0.665337 + 1.30267i
\(555\) −20.3681 14.6711i −0.864579 0.622752i
\(556\) −17.5865 12.7252i −0.745832 0.539668i
\(557\) −9.27395 −0.392950 −0.196475 0.980509i \(-0.562949\pi\)
−0.196475 + 0.980509i \(0.562949\pi\)
\(558\) 29.3672 + 0.649036i 1.24321 + 0.0274759i
\(559\) 17.8636i 0.755550i
\(560\) 5.94049 + 6.68659i 0.251032 + 0.282560i
\(561\) −20.6774 + 12.3454i −0.873000 + 0.521221i
\(562\) −6.79516 13.3043i −0.286636 0.561207i
\(563\) 13.5713i 0.571962i 0.958235 + 0.285981i \(0.0923194\pi\)
−0.958235 + 0.285981i \(0.907681\pi\)
\(564\) −25.9399 2.29205i −1.09227 0.0965128i
\(565\) −18.1345 + 7.84594i −0.762925 + 0.330081i
\(566\) −6.97332 + 3.56162i −0.293111 + 0.149706i
\(567\) −4.94862 7.51739i −0.207823 0.315701i
\(568\) 1.95323 12.5692i 0.0819556 0.527391i
\(569\) 16.4865i 0.691148i 0.938392 + 0.345574i \(0.112316\pi\)
−0.938392 + 0.345574i \(0.887684\pi\)
\(570\) 10.3279 + 1.58213i 0.432590 + 0.0662680i
\(571\) 7.86631i 0.329195i 0.986361 + 0.164597i \(0.0526325\pi\)
−0.986361 + 0.164597i \(0.947368\pi\)
\(572\) 8.53077 + 6.17268i 0.356689 + 0.258093i
\(573\) −11.5964 + 6.92361i −0.484448 + 0.289238i
\(574\) 7.19138 + 14.0800i 0.300162 + 0.587690i
\(575\) 7.47357 + 7.02020i 0.311670 + 0.292763i
\(576\) −17.2606 + 16.6755i −0.719191 + 0.694812i
\(577\) 31.2545i 1.30114i 0.759445 + 0.650572i \(0.225471\pi\)
−0.759445 + 0.650572i \(0.774529\pi\)
\(578\) 10.5534 5.39016i 0.438964 0.224201i
\(579\) −1.91590 3.20897i −0.0796222 0.133360i
\(580\) −21.5882 4.78316i −0.896401 0.198610i
\(581\) 7.71558i 0.320096i
\(582\) −34.6034 21.7111i −1.43436 0.899952i
\(583\) 16.9666 0.702685
\(584\) 17.0940 + 2.65638i 0.707355 + 0.109922i
\(585\) −12.7494 1.09882i −0.527122 0.0454304i
\(586\) 31.7630 16.2230i 1.31212 0.670164i
\(587\) 2.10458i 0.0868654i 0.999056 + 0.0434327i \(0.0138294\pi\)
−0.999056 + 0.0434327i \(0.986171\pi\)
\(588\) 0.304900 3.45066i 0.0125739 0.142303i
\(589\) 13.2076 0.544208
\(590\) −1.44352 + 1.74812i −0.0594290 + 0.0719689i
\(591\) 22.2595 13.2900i 0.915635 0.546676i
\(592\) 24.6249 8.10703i 1.01208 0.333197i
\(593\) −3.52377 −0.144704 −0.0723520 0.997379i \(-0.523050\pi\)
−0.0723520 + 0.997379i \(0.523050\pi\)
\(594\) −10.0095 17.6392i −0.410694 0.723745i
\(595\) 10.3387 4.47306i 0.423845 0.183378i
\(596\) −22.1044 15.9943i −0.905432 0.655151i
\(597\) 9.53501 + 15.9703i 0.390242 + 0.653622i
\(598\) −4.92697 + 2.51645i −0.201479 + 0.102905i
\(599\) −13.1436 −0.537031 −0.268516 0.963275i \(-0.586533\pi\)
−0.268516 + 0.963275i \(0.586533\pi\)
\(600\) −22.8368 8.85884i −0.932310 0.361661i
\(601\) −15.5022 −0.632347 −0.316174 0.948701i \(-0.602398\pi\)
−0.316174 + 0.948701i \(0.602398\pi\)
\(602\) −11.7940 + 6.02377i −0.480686 + 0.245510i
\(603\) 5.10612 9.47448i 0.207937 0.385831i
\(604\) 2.18801 + 1.58320i 0.0890290 + 0.0644194i
\(605\) 6.94220 3.00356i 0.282240 0.122112i
\(606\) 16.0091 + 10.0445i 0.650323 + 0.408029i
\(607\) 8.78015 0.356375 0.178188 0.983997i \(-0.442977\pi\)
0.178188 + 0.983997i \(0.442977\pi\)
\(608\) −7.59329 + 7.66742i −0.307949 + 0.310955i
\(609\) 4.39007 + 7.35300i 0.177895 + 0.297958i
\(610\) −10.3317 + 12.5117i −0.418317 + 0.506585i
\(611\) 14.3403 0.580145
\(612\) 13.1507 + 27.2161i 0.531585 + 1.10015i
\(613\) 7.21143i 0.291267i 0.989339 + 0.145633i \(0.0465220\pi\)
−0.989339 + 0.145633i \(0.953478\pi\)
\(614\) 24.0334 12.2751i 0.969910 0.495381i
\(615\) −35.1330 25.3061i −1.41670 1.02044i
\(616\) 1.19869 7.71369i 0.0482967 0.310793i
\(617\) −4.53960 −0.182758 −0.0913788 0.995816i \(-0.529127\pi\)
−0.0913788 + 0.995816i \(0.529127\pi\)
\(618\) −26.3115 + 41.9356i −1.05840 + 1.68690i
\(619\) 18.1564i 0.729766i −0.931053 0.364883i \(-0.881109\pi\)
0.931053 0.364883i \(-0.118891\pi\)
\(620\) −30.2302 6.69791i −1.21407 0.268995i
\(621\) 10.6456 0.468037i 0.427195 0.0187817i
\(622\) −8.75783 + 4.47306i −0.351157 + 0.179353i
\(623\) 13.5677i 0.543579i
\(624\) 8.65992 9.98383i 0.346674 0.399673i
\(625\) −1.56249 24.9511i −0.0624997 0.998045i
\(626\) −22.2188 43.5023i −0.888042 1.73870i
\(627\) −4.67469 7.82970i −0.186689 0.312688i
\(628\) −3.09093 2.23653i −0.123342 0.0892473i
\(629\) 32.6513i 1.30189i
\(630\) 3.57374 + 8.78797i 0.142381 + 0.350121i
\(631\) 46.0384i 1.83276i 0.400310 + 0.916380i \(0.368902\pi\)
−0.400310 + 0.916380i \(0.631098\pi\)
\(632\) −40.9580 6.36480i −1.62922 0.253178i
\(633\) −12.0601 20.1996i −0.479346 0.802863i
\(634\) 10.3184 5.27012i 0.409796 0.209303i
\(635\) 4.42632 1.91505i 0.175653 0.0759966i
\(636\) 1.87436 21.2128i 0.0743234 0.841143i
\(637\) 1.90761i 0.0755823i
\(638\) 8.77800 + 17.1865i 0.347524 + 0.680420i
\(639\) 6.40073 11.8767i 0.253209 0.469833i
\(640\) 21.2683 13.6989i 0.840704 0.541495i
\(641\) 28.5533i 1.12779i −0.825847 0.563894i \(-0.809303\pi\)
0.825847 0.563894i \(-0.190697\pi\)
\(642\) 2.64333 + 1.65849i 0.104324 + 0.0654556i
\(643\) 28.9229 1.14061 0.570305 0.821433i \(-0.306825\pi\)
0.570305 + 0.821433i \(0.306825\pi\)
\(644\) 3.32283 + 2.40433i 0.130938 + 0.0947438i
\(645\) 21.1974 29.4287i 0.834645 1.15875i
\(646\) 6.18186 + 12.1035i 0.243222 + 0.476206i
\(647\) 5.44152i 0.213928i −0.994263 0.106964i \(-0.965887\pi\)
0.994263 0.106964i \(-0.0341130\pi\)
\(648\) −23.1595 + 10.5659i −0.909791 + 0.415067i
\(649\) 1.97864 0.0776684
\(650\) 12.9564 + 3.75257i 0.508190 + 0.147188i
\(651\) 6.14747 + 10.2965i 0.240938 + 0.403551i
\(652\) 28.6504 39.5954i 1.12203 1.55068i
\(653\) −36.5529 −1.43042 −0.715212 0.698907i \(-0.753670\pi\)
−0.715212 + 0.698907i \(0.753670\pi\)
\(654\) −19.0568 + 30.3730i −0.745180 + 1.18768i
\(655\) 6.02588 2.60711i 0.235451 0.101868i
\(656\) 42.4754 13.9838i 1.65839 0.545977i
\(657\) 16.1522 + 8.70495i 0.630156 + 0.339613i
\(658\) −4.83566 9.46777i −0.188514 0.369092i
\(659\) 9.10215 0.354570 0.177285 0.984160i \(-0.443269\pi\)
0.177285 + 0.984160i \(0.443269\pi\)
\(660\) 6.72904 + 20.2917i 0.261927 + 0.789854i
\(661\) −1.54757 −0.0601935 −0.0300968 0.999547i \(-0.509582\pi\)
−0.0300968 + 0.999547i \(0.509582\pi\)
\(662\) 2.98255 + 5.83956i 0.115920 + 0.226961i
\(663\) −8.53286 14.2918i −0.331389 0.555048i
\(664\) 21.5641 + 3.35103i 0.836851 + 0.130045i
\(665\) 1.69377 + 3.91485i 0.0656815 + 0.151811i
\(666\) 27.4909 + 0.607570i 1.06525 + 0.0235428i
\(667\) −10.1395 −0.392603
\(668\) 5.72732 + 4.14417i 0.221597 + 0.160343i
\(669\) −17.3130 + 10.3367i −0.669360 + 0.399638i
\(670\) −7.22372 + 8.74797i −0.279077 + 0.337964i
\(671\) 14.1616 0.546704
\(672\) −9.51176 2.35085i −0.366924 0.0906859i
\(673\) 3.16034i 0.121822i −0.998143 0.0609110i \(-0.980599\pi\)
0.998143 0.0609110i \(-0.0194006\pi\)
\(674\) 11.8587 + 23.2182i 0.456779 + 0.894330i
\(675\) −19.6996 16.9389i −0.758237 0.651979i
\(676\) 10.9751 15.1678i 0.422119 0.583377i
\(677\) 11.8437 0.455189 0.227595 0.973756i \(-0.426914\pi\)
0.227595 + 0.973756i \(0.426914\pi\)
\(678\) 11.5038 18.3349i 0.441799 0.704146i
\(679\) 16.6772i 0.640010i
\(680\) −8.01138 30.8382i −0.307222 1.18259i
\(681\) −2.80603 4.69986i −0.107527 0.180099i
\(682\) 12.2919 + 24.0664i 0.470682 + 0.921551i
\(683\) 4.05943i 0.155330i −0.996980 0.0776648i \(-0.975254\pi\)
0.996980 0.0776648i \(-0.0247464\pi\)
\(684\) −10.3057 + 4.97964i −0.394047 + 0.190401i
\(685\) 33.8386 14.6403i 1.29291 0.559378i
\(686\) 1.25945 0.643263i 0.0480860 0.0245599i
\(687\) −5.11296 + 3.05267i −0.195072 + 0.116467i
\(688\) 11.7134 + 35.5790i 0.446568 + 1.35644i
\(689\) 11.7270i 0.446763i
\(690\) −11.1028 1.70083i −0.422677 0.0647494i
\(691\) 40.8932i 1.55565i −0.628481 0.777825i \(-0.716323\pi\)
0.628481 0.777825i \(-0.283677\pi\)
\(692\) 19.7777 27.3332i 0.751836 1.03905i
\(693\) 3.92812 7.28869i 0.149217 0.276874i
\(694\) 1.84518 + 3.61269i 0.0700420 + 0.137136i
\(695\) 9.63703 + 22.2743i 0.365553 + 0.844913i
\(696\) 22.4575 9.07619i 0.851248 0.344032i
\(697\) 56.3202i 2.13328i
\(698\) −3.48376 + 1.77933i −0.131862 + 0.0673487i
\(699\) −26.1292 + 15.6003i −0.988295 + 0.590057i
\(700\) −1.89147 9.81949i −0.0714907 0.371142i
\(701\) 34.0369i 1.28555i 0.766053 + 0.642777i \(0.222218\pi\)
−0.766053 + 0.642777i \(0.777782\pi\)
\(702\) 12.1919 6.91836i 0.460152 0.261117i
\(703\) 12.3637 0.466307
\(704\) −21.0382 6.70041i −0.792909 0.252531i
\(705\) 23.6243 + 17.0165i 0.889742 + 0.640877i
\(706\) 29.8174 15.2292i 1.12219 0.573160i
\(707\) 7.71558i 0.290174i
\(708\) 0.218588 2.47383i 0.00821502 0.0929722i
\(709\) −38.5746 −1.44870 −0.724351 0.689432i \(-0.757860\pi\)
−0.724351 + 0.689432i \(0.757860\pi\)
\(710\) −9.05523 + 10.9659i −0.339837 + 0.411545i
\(711\) −38.7013 20.8575i −1.45141 0.782216i
\(712\) −37.9202 5.89272i −1.42112 0.220839i
\(713\) −14.1985 −0.531737
\(714\) −6.55842 + 10.4529i −0.245443 + 0.391191i
\(715\) −4.67469 10.8047i −0.174823 0.404074i
\(716\) 4.91687 6.79522i 0.183752 0.253949i
\(717\) −26.0661 + 15.5627i −0.973457 + 0.581198i
\(718\) −19.8250 + 10.1256i −0.739862 + 0.377884i
\(719\) 10.8657 0.405222 0.202611 0.979259i \(-0.435057\pi\)
0.202611 + 0.979259i \(0.435057\pi\)
\(720\) 26.1135 6.17140i 0.973192 0.229994i
\(721\) −20.2109 −0.752694
\(722\) 19.3464 9.88118i 0.719999 0.367739i
\(723\) 9.23661 5.51468i 0.343513 0.205093i
\(724\) −11.3730 + 15.7177i −0.422673 + 0.584143i
\(725\) 18.0189 + 16.9258i 0.669203 + 0.628607i
\(726\) −4.40383 + 7.01889i −0.163441 + 0.260495i
\(727\) 4.65736 0.172732 0.0863659 0.996263i \(-0.472475\pi\)
0.0863659 + 0.996263i \(0.472475\pi\)
\(728\) 5.33155 + 0.828513i 0.197600 + 0.0307067i
\(729\) −26.8958 + 2.36954i −0.996142 + 0.0877607i
\(730\) −14.9136 12.3151i −0.551978 0.455801i
\(731\) 47.1759 1.74486
\(732\) 1.56449 17.7058i 0.0578251 0.654426i
\(733\) 7.36632i 0.272081i −0.990703 0.136041i \(-0.956562\pi\)
0.990703 0.136041i \(-0.0434378\pi\)
\(734\) 24.3427 12.4330i 0.898504 0.458911i
\(735\) −2.26361 + 3.14262i −0.0834947 + 0.115917i
\(736\) 8.16299 8.24268i 0.300892 0.303829i
\(737\) 9.90156 0.364729
\(738\) 47.4191 + 1.04800i 1.74552 + 0.0385773i
\(739\) 33.9459i 1.24872i −0.781137 0.624360i \(-0.785360\pi\)
0.781137 0.624360i \(-0.214640\pi\)
\(740\) −28.2988 6.26999i −1.04028 0.230489i
\(741\) 5.41173 3.23105i 0.198805 0.118696i
\(742\) 7.74243 3.95444i 0.284233 0.145172i
\(743\) 5.51110i 0.202183i −0.994877 0.101091i \(-0.967767\pi\)
0.994877 0.101091i \(-0.0322334\pi\)
\(744\) 31.4474 12.7095i 1.15292 0.465953i
\(745\) 12.1128 + 27.9966i 0.443778 + 1.02571i
\(746\) 22.1764 + 43.4193i 0.811936 + 1.58970i
\(747\) 20.3760 + 10.9813i 0.745520 + 0.401786i
\(748\) −16.3014 + 22.5288i −0.596037 + 0.823736i
\(749\) 1.27396i 0.0465494i
\(750\) 16.8916 + 21.5563i 0.616792 + 0.787126i
\(751\) 19.4438i 0.709514i −0.934959 0.354757i \(-0.884564\pi\)
0.934959 0.354757i \(-0.115436\pi\)
\(752\) −28.5615 + 9.40307i −1.04153 + 0.342895i
\(753\) 33.4253 19.9564i 1.21808 0.727252i
\(754\) −11.8790 + 6.06718i −0.432606 + 0.220954i
\(755\) −1.19899 2.77125i −0.0436356 0.100856i
\(756\) −8.67886 5.71641i −0.315647 0.207904i
\(757\) 26.8731i 0.976718i 0.872643 + 0.488359i \(0.162404\pi\)
−0.872643 + 0.488359i \(0.837596\pi\)
\(758\) 10.4930 + 20.5442i 0.381121 + 0.746200i
\(759\) 5.02541 + 8.41713i 0.182411 + 0.305523i
\(760\) 11.6772 3.03359i 0.423576 0.110040i
\(761\) 43.9086i 1.59169i −0.605503 0.795843i \(-0.707028\pi\)
0.605503 0.795843i \(-0.292972\pi\)
\(762\) −2.80786 + 4.47521i −0.101718 + 0.162120i
\(763\) −14.6383 −0.529943
\(764\) −9.14225 + 12.6348i −0.330755 + 0.457110i
\(765\) 2.90185 33.6697i 0.104917 1.21733i
\(766\) −13.1670 25.7798i −0.475745 0.931464i
\(767\) 1.36760i 0.0493811i
\(768\) −10.7015 + 25.5632i −0.386156 + 0.922433i
\(769\) −24.2477 −0.874393 −0.437197 0.899366i \(-0.644029\pi\)
−0.437197 + 0.899366i \(0.644029\pi\)
\(770\) −5.55719 + 6.72979i −0.200267 + 0.242525i
\(771\) −10.7925 + 6.44362i −0.388683 + 0.232061i
\(772\) −3.49630 2.52985i −0.125835 0.0910512i
\(773\) −17.0431 −0.612998 −0.306499 0.951871i \(-0.599158\pi\)
−0.306499 + 0.951871i \(0.599158\pi\)
\(774\) −0.877841 + 39.7200i −0.0315533 + 1.42771i
\(775\) 25.2320 + 23.7014i 0.906360 + 0.851378i
\(776\) −46.6107 7.24321i −1.67323 0.260016i
\(777\) 5.75471 + 9.63865i 0.206449 + 0.345785i
\(778\) 8.04476 + 15.7509i 0.288419 + 0.564696i
\(779\) 21.3262 0.764090
\(780\) −14.0252 + 4.65098i −0.502184 + 0.166532i
\(781\) 12.4120 0.444137
\(782\) −6.64566 13.0116i −0.237648 0.465293i
\(783\) 25.6667 1.12844i 0.917254 0.0403272i
\(784\) −1.25084 3.79939i −0.0446729 0.135693i
\(785\) 1.69377 + 3.91485i 0.0604532 + 0.139727i
\(786\) −3.82256 + 6.09245i −0.136346 + 0.217311i
\(787\) −11.5435 −0.411483 −0.205741 0.978606i \(-0.565961\pi\)
−0.205741 + 0.978606i \(0.565961\pi\)
\(788\) 17.5487 24.2526i 0.625146 0.863965i
\(789\) −14.5552 24.3787i −0.518178 0.867904i
\(790\) 35.7337 + 29.5074i 1.27135 + 1.04983i
\(791\) 8.83651 0.314190
\(792\) −18.6650 14.1443i −0.663231 0.502594i
\(793\) 9.78824i 0.347590i
\(794\) 4.72007 + 9.24145i 0.167509 + 0.327967i
\(795\) −13.9155 + 19.3192i −0.493532 + 0.685180i
\(796\) 17.4003 + 12.5905i 0.616737 + 0.446257i
\(797\) 8.66018 0.306759 0.153380 0.988167i \(-0.450984\pi\)
0.153380 + 0.988167i \(0.450984\pi\)
\(798\) −3.95810 2.48341i −0.140115 0.0879118i
\(799\) 37.8711i 1.33978i
\(800\) −28.2658 + 1.02163i −0.999347 + 0.0361200i
\(801\) −35.8309 19.3105i −1.26602 0.682302i
\(802\) −7.29483 14.2826i −0.257589 0.504336i
\(803\) 16.8802i 0.595691i
\(804\) 1.09386 12.3796i 0.0385775 0.436595i
\(805\) −1.82085 4.20857i −0.0641764 0.148332i
\(806\) −16.6342 + 8.49593i −0.585916 + 0.299257i
\(807\) −4.02550 6.74236i −0.141704 0.237342i
\(808\) 21.5641 + 3.35103i 0.758624 + 0.117889i
\(809\) 29.1441i 1.02465i −0.858791 0.512326i \(-0.828784\pi\)
0.858791 0.512326i \(-0.171216\pi\)
\(810\) 28.2945 + 3.06976i 0.994166 + 0.107860i
\(811\) 37.4623i 1.31548i 0.753246 + 0.657739i \(0.228487\pi\)
−0.753246 + 0.657739i \(0.771513\pi\)
\(812\) 8.01138 + 5.79686i 0.281144 + 0.203430i
\(813\) −24.4320 40.9214i −0.856867 1.43518i
\(814\) 11.5066 + 22.5288i 0.403306 + 0.789635i
\(815\) −50.1499 + 21.6975i −1.75668 + 0.760030i
\(816\) 26.3662 + 22.8699i 0.923002 + 0.800608i
\(817\) 17.8636i 0.624969i
\(818\) 13.3114 6.79880i 0.465422 0.237714i
\(819\) 5.03780 + 2.71504i 0.176035 + 0.0948712i
\(820\) −48.8126 10.8151i −1.70461 0.377680i
\(821\) 22.2823i 0.777658i 0.921310 + 0.388829i \(0.127120\pi\)
−0.921310 + 0.388829i \(0.872880\pi\)
\(822\) −21.4657 + 34.2124i −0.748703 + 1.19329i
\(823\) −12.5937 −0.438988 −0.219494 0.975614i \(-0.570441\pi\)
−0.219494 + 0.975614i \(0.570441\pi\)
\(824\) −8.77800 + 56.4871i −0.305796 + 1.96782i
\(825\) 5.12000 23.3469i 0.178256 0.812835i
\(826\) 0.902919 0.461166i 0.0314166 0.0160460i
\(827\) 32.6595i 1.13568i 0.823138 + 0.567841i \(0.192221\pi\)
−0.823138 + 0.567841i \(0.807779\pi\)
\(828\) 11.0788 5.35324i 0.385017 0.186038i
\(829\) −19.9927 −0.694375 −0.347187 0.937796i \(-0.612863\pi\)
−0.347187 + 0.937796i \(0.612863\pi\)
\(830\) −18.8136 15.5355i −0.653029 0.539245i
\(831\) 21.6158 + 36.2046i 0.749844 + 1.25592i
\(832\) 4.63119 14.5412i 0.160558 0.504126i
\(833\) −5.03780 −0.174549
\(834\) −22.5204 14.1299i −0.779817 0.489277i
\(835\) −3.13846 7.25400i −0.108611 0.251035i
\(836\) −8.53077 6.17268i −0.295043 0.213486i
\(837\) 35.9414 1.58017i 1.24232 0.0546186i
\(838\) −49.3107 + 25.1854i −1.70341 + 0.870016i
\(839\) −7.38656 −0.255012 −0.127506 0.991838i \(-0.540697\pi\)
−0.127506 + 0.991838i \(0.540697\pi\)
\(840\) 7.80012 + 7.69144i 0.269130 + 0.265380i
\(841\) 4.55356 0.157019
\(842\) 35.2799 18.0192i 1.21583 0.620982i
\(843\) −9.37939 15.7097i −0.323044 0.541070i
\(844\) −22.0083 15.9247i −0.757556 0.548151i
\(845\) −19.2109 + 8.31165i −0.660876 + 0.285929i
\(846\) −31.8858 0.704699i −1.09626 0.0242280i
\(847\) −3.38276 −0.116233
\(848\) −7.68952 23.3567i −0.264059 0.802071i
\(849\) −8.23409 + 4.91613i −0.282593 + 0.168721i
\(850\) −9.91014 + 34.2164i −0.339915 + 1.17361i
\(851\) −13.2913 −0.455621
\(852\) 1.37120 15.5183i 0.0469765 0.531649i
\(853\) 0.362131i 0.0123991i 0.999981 + 0.00619956i \(0.00197339\pi\)
−0.999981 + 0.00619956i \(0.998027\pi\)
\(854\) 6.46242 3.30068i 0.221139 0.112947i
\(855\) 12.7494 + 1.09882i 0.436020 + 0.0375787i
\(856\) 3.56056 + 0.553305i 0.121698 + 0.0189116i
\(857\) −4.56811 −0.156044 −0.0780218 0.996952i \(-0.524860\pi\)
−0.0780218 + 0.996952i \(0.524860\pi\)
\(858\) 10.9241 + 6.85405i 0.372942 + 0.233994i
\(859\) 16.7842i 0.572669i −0.958130 0.286334i \(-0.907563\pi\)
0.958130 0.286334i \(-0.0924368\pi\)
\(860\) 9.05913 40.8872i 0.308914 1.39424i
\(861\) 9.92631 + 16.6257i 0.338288 + 0.566602i
\(862\) −47.6736 + 24.3493i −1.62377 + 0.829339i
\(863\) 26.2477i 0.893481i −0.894664 0.446741i \(-0.852585\pi\)
0.894664 0.446741i \(-0.147415\pi\)
\(864\) −19.7461 + 21.7736i −0.671776 + 0.740754i
\(865\) −34.6192 + 14.9781i −1.17709 + 0.509269i
\(866\) 11.7666 + 23.0379i 0.399845 + 0.782858i
\(867\) 12.4615 7.44007i 0.423214 0.252678i
\(868\) 11.2184 + 8.11740i 0.380778 + 0.275523i
\(869\) 40.4458i 1.37203i
\(870\) −26.7690 4.10071i −0.907553 0.139027i
\(871\) 6.84376i 0.231892i
\(872\) −6.35771 + 40.9124i −0.215299 + 1.38547i
\(873\) −44.0426 23.7360i −1.49062 0.803343i
\(874\) 4.92697 2.51645i 0.166657 0.0851201i
\(875\) −3.78950 + 10.5185i −0.128109 + 0.355592i
\(876\) 21.1048 + 1.86482i 0.713066 + 0.0630065i
\(877\) 30.5051i 1.03008i −0.857165 0.515042i \(-0.827776\pi\)
0.857165 0.515042i \(-0.172224\pi\)
\(878\) 8.07608 + 15.8122i 0.272555 + 0.533636i
\(879\) 37.5058 22.3926i 1.26504 0.755285i
\(880\) 16.3954 + 18.4546i 0.552688 + 0.622103i
\(881\) 21.4921i 0.724088i 0.932161 + 0.362044i \(0.117921\pi\)
−0.932161 + 0.362044i \(0.882079\pi\)
\(882\) 0.0937425 4.24160i 0.00315647 0.142822i
\(883\) 26.3164 0.885617 0.442808 0.896616i \(-0.353982\pi\)
0.442808 + 0.896616i \(0.353982\pi\)
\(884\) −15.5715 11.2672i −0.523726 0.378956i
\(885\) −1.62282 + 2.25299i −0.0545505 + 0.0757335i
\(886\) 19.1536 + 37.5009i 0.643477 + 1.25987i
\(887\) 58.2531i 1.95595i 0.208727 + 0.977974i \(0.433068\pi\)
−0.208727 + 0.977974i \(0.566932\pi\)
\(888\) 29.4383 11.8975i 0.987883 0.399254i
\(889\) −2.15684 −0.0723379
\(890\) 33.0833 + 27.3189i 1.10896 + 0.915731i
\(891\) −13.6579 20.7475i −0.457556 0.695067i
\(892\) −13.6490 + 18.8632i −0.457002 + 0.631587i
\(893\) −14.3403 −0.479878
\(894\) −28.3058 17.7598i −0.946689 0.593977i
\(895\) −8.60656 + 3.72364i −0.287685 + 0.124468i
\(896\) −11.1621 + 1.84581i −0.372900 + 0.0616641i
\(897\) −5.81776 + 3.47347i −0.194249 + 0.115976i
\(898\) 15.2616 + 29.8808i 0.509287 + 0.997137i
\(899\) −34.2326 −1.14172
\(900\) −28.6243 8.98059i −0.954142 0.299353i
\(901\) −30.9697 −1.03175
\(902\) 19.8477 + 38.8600i 0.660857 + 1.29390i
\(903\) −13.9263 + 8.31464i −0.463438 + 0.276694i
\(904\) 3.83787 24.6970i 0.127646 0.821410i
\(905\) 19.9074 8.61297i 0.661743 0.286305i
\(906\) 2.80187 + 1.75796i 0.0930857 + 0.0584044i
\(907\) −28.7261 −0.953833 −0.476917 0.878949i \(-0.658246\pi\)
−0.476917 + 0.878949i \(0.658246\pi\)
\(908\) −5.12068 3.70521i −0.169936 0.122962i
\(909\) 20.3760 + 10.9813i 0.675830 + 0.364228i
\(910\) −4.65150 3.84102i −0.154196 0.127328i
\(911\) −1.93202 −0.0640108 −0.0320054 0.999488i \(-0.510189\pi\)
−0.0320054 + 0.999488i \(0.510189\pi\)
\(912\) −8.65992 + 9.98383i −0.286759 + 0.330598i
\(913\) 21.2945i 0.704745i
\(914\) 3.64977 + 7.14590i 0.120724 + 0.236365i
\(915\) −11.6149 + 16.1252i −0.383978 + 0.533084i
\(916\) −4.03089 + 5.57078i −0.133184 + 0.184064i
\(917\) −2.93626 −0.0969640
\(918\) 18.2706 + 32.1974i 0.603021 + 1.06267i
\(919\) 39.8495i 1.31451i 0.753666 + 0.657257i \(0.228283\pi\)
−0.753666 + 0.657257i \(0.771717\pi\)
\(920\) −12.5533 + 3.26119i −0.413869 + 0.107518i
\(921\) 28.3786 16.9433i 0.935108 0.558302i
\(922\) −7.90513 15.4775i −0.260341 0.509724i
\(923\) 8.57893i 0.282379i
\(924\) 0.841504 9.52359i 0.0276834 0.313303i
\(925\) 23.6199 + 22.1871i 0.776619 + 0.729507i
\(926\) 1.12580 0.575000i 0.0369960 0.0188957i
\(927\) −28.7655 + 53.3749i −0.944784 + 1.75306i
\(928\) 19.6810 19.8732i 0.646062 0.652369i
\(929\) 33.7414i 1.10702i 0.832842 + 0.553510i \(0.186712\pi\)
−0.832842 + 0.553510i \(0.813288\pi\)
\(930\) −37.4849 5.74227i −1.22918 0.188297i
\(931\) 1.90761i 0.0625194i
\(932\) −20.5994 + 28.4687i −0.674754 + 0.932525i
\(933\) −10.3412 + 6.17419i −0.338557 + 0.202134i
\(934\) −18.7109 36.6341i −0.612239 1.19871i
\(935\) 28.5341 12.3454i 0.933166 0.403736i
\(936\) 9.77623 12.9009i 0.319546 0.421678i
\(937\) 2.95584i 0.0965631i 0.998834 + 0.0482816i \(0.0153745\pi\)
−0.998834 + 0.0482816i \(0.984626\pi\)
\(938\) 4.51841 2.30778i 0.147531 0.0753516i
\(939\) −30.6688 51.3675i −1.00084 1.67632i
\(940\) 32.8228 + 7.27234i 1.07056 + 0.237197i
\(941\) 10.7787i 0.351375i −0.984446 0.175687i \(-0.943785\pi\)
0.984446 0.175687i \(-0.0562148\pi\)
\(942\) −3.95810 2.48341i −0.128962 0.0809139i
\(943\) −22.9262 −0.746580
\(944\) −0.896748 2.72384i −0.0291867 0.0886536i
\(945\) 5.07759 + 10.4507i 0.165174 + 0.339963i
\(946\) −32.5506 + 16.6252i −1.05831 + 0.540532i
\(947\) 34.5592i 1.12302i 0.827469 + 0.561511i \(0.189780\pi\)
−0.827469 + 0.561511i \(0.810220\pi\)
\(948\) −50.5681 4.46820i −1.64238 0.145120i
\(949\) −11.6673 −0.378736
\(950\) −12.9564 3.75257i −0.420360 0.121749i
\(951\) 12.1839 7.27437i 0.395092 0.235888i
\(952\) −2.18801 + 14.0800i −0.0709139 + 0.456337i
\(953\) 32.9065 1.06595 0.532973 0.846132i \(-0.321075\pi\)
0.532973 + 0.846132i \(0.321075\pi\)
\(954\) 0.576279 26.0751i 0.0186577 0.844214i
\(955\) 16.0027 6.92361i 0.517836 0.224043i
\(956\) −20.5497 + 28.4001i −0.664623 + 0.918523i
\(957\) 12.1163 + 20.2938i 0.391665 + 0.656005i
\(958\) −30.5719 + 15.6146i −0.987735 + 0.504485i
\(959\) −16.4887 −0.532448
\(960\) 24.8844 18.4599i 0.803141 0.595790i
\(961\) −16.9363 −0.546333
\(962\) −15.5715 + 7.95313i −0.502045 + 0.256419i
\(963\) 3.36439 + 1.81318i 0.108416 + 0.0584290i
\(964\) 7.28183 10.0636i 0.234532 0.324128i
\(965\) 1.91590 + 4.42828i 0.0616751 + 0.142551i
\(966\) 4.25506 + 2.66973i 0.136904 + 0.0858972i
\(967\) 0.335417 0.0107863 0.00539314 0.999985i \(-0.498283\pi\)
0.00539314 + 0.999985i \(0.498283\pi\)
\(968\) −1.46920 + 9.45443i −0.0472219 + 0.303877i
\(969\) 8.53286 + 14.2918i 0.274115 + 0.459119i
\(970\) 40.6654 + 33.5798i 1.30569 + 1.07818i
\(971\) −56.6148 −1.81685 −0.908427 0.418044i \(-0.862716\pi\)
−0.908427 + 0.418044i \(0.862716\pi\)
\(972\) −27.4488 + 14.7840i −0.880420 + 0.474196i
\(973\) 10.8537i 0.347955i
\(974\) 48.0634 24.5484i 1.54005 0.786581i
\(975\) 16.1369 + 3.53884i 0.516795 + 0.113334i
\(976\) −6.41826 19.4953i −0.205443 0.624028i
\(977\) 59.0104 1.88791 0.943955 0.330073i \(-0.107073\pi\)
0.943955 + 0.330073i \(0.107073\pi\)
\(978\) 31.8130 50.7040i 1.01727 1.62133i
\(979\) 37.4460i 1.19678i
\(980\) −0.967402 + 4.36625i −0.0309025 + 0.139475i
\(981\) −20.8342 + 38.6582i −0.665186 + 1.23426i
\(982\) 33.2778 16.9966i 1.06194 0.542384i
\(983\) 37.6136i 1.19969i −0.800117 0.599844i \(-0.795229\pi\)
0.800117 0.599844i \(-0.204771\pi\)
\(984\) 50.7781 20.5220i 1.61875 0.654217i
\(985\) −30.7174 + 13.2900i −0.978739 + 0.423453i
\(986\) −16.0228 31.3711i −0.510269 0.999058i
\(987\) −6.67469 11.1795i −0.212458 0.355848i
\(988\) 4.26643 5.89630i 0.135733 0.187586i
\(989\) 19.2038i 0.610647i
\(990\) 9.86329 + 24.2542i 0.313476 + 0.770849i
\(991\) 45.8372i 1.45607i −0.685541 0.728034i \(-0.740434\pi\)
0.685541 0.728034i \(-0.259566\pi\)
\(992\) 27.5596 27.8286i 0.875017 0.883560i
\(993\) 4.11684 + 6.89535i 0.130644 + 0.218817i
\(994\) 5.66401 2.89289i 0.179651 0.0917570i
\(995\) −9.53501 22.0385i −0.302280 0.698668i
\(996\) 26.6238 + 2.35248i 0.843609 + 0.0745412i
\(997\) 13.7556i 0.435645i −0.975988 0.217823i \(-0.930105\pi\)
0.975988 0.217823i \(-0.0698954\pi\)
\(998\) 22.4537 + 43.9621i 0.710758 + 1.39160i
\(999\) 33.6451 1.47921i 1.06448 0.0468002i
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 420.2.l.h.239.13 yes 16
3.2 odd 2 inner 420.2.l.h.239.4 yes 16
4.3 odd 2 420.2.l.g.239.14 yes 16
5.4 even 2 420.2.l.g.239.4 yes 16
12.11 even 2 420.2.l.g.239.3 16
15.14 odd 2 420.2.l.g.239.13 yes 16
20.19 odd 2 inner 420.2.l.h.239.3 yes 16
60.59 even 2 inner 420.2.l.h.239.14 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
420.2.l.g.239.3 16 12.11 even 2
420.2.l.g.239.4 yes 16 5.4 even 2
420.2.l.g.239.13 yes 16 15.14 odd 2
420.2.l.g.239.14 yes 16 4.3 odd 2
420.2.l.h.239.3 yes 16 20.19 odd 2 inner
420.2.l.h.239.4 yes 16 3.2 odd 2 inner
420.2.l.h.239.13 yes 16 1.1 even 1 trivial
420.2.l.h.239.14 yes 16 60.59 even 2 inner