Properties

Label 280.2.w.a.267.6
Level $280$
Weight $2$
Character 280.267
Analytic conductor $2.236$
Analytic rank $0$
Dimension $72$
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] = [280,2,Mod(43,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.w (of order \(4\), degree \(2\), 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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 267.6
Character \(\chi\) \(=\) 280.267
Dual form 280.2.w.a.43.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25279 - 0.656136i) q^{2} +(0.683238 - 0.683238i) q^{3} +(1.13897 + 1.64400i) q^{4} +(-2.03938 + 0.917023i) q^{5} +(-1.30425 + 0.407657i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.348203 - 2.80691i) q^{8} +2.06637i q^{9} +O(q^{10})\) \(q+(-1.25279 - 0.656136i) q^{2} +(0.683238 - 0.683238i) q^{3} +(1.13897 + 1.64400i) q^{4} +(-2.03938 + 0.917023i) q^{5} +(-1.30425 + 0.407657i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.348203 - 2.80691i) q^{8} +2.06637i q^{9} +(3.15661 + 0.189272i) q^{10} +5.41441 q^{11} +(1.90143 + 0.345057i) q^{12} +(3.15744 + 3.15744i) q^{13} +(1.34982 - 0.421899i) q^{14} +(-0.766836 + 2.01993i) q^{15} +(-1.40549 + 3.74494i) q^{16} +(-2.46948 - 2.46948i) q^{17} +(1.35582 - 2.58873i) q^{18} +3.87964i q^{19} +(-3.83038 - 2.30828i) q^{20} +0.966244i q^{21} +(-6.78313 - 3.55259i) q^{22} +(0.659207 + 0.659207i) q^{23} +(-2.15569 - 1.67988i) q^{24} +(3.31814 - 3.74032i) q^{25} +(-1.88390 - 6.02733i) q^{26} +(3.46154 + 3.46154i) q^{27} +(-1.96786 - 0.357112i) q^{28} +5.76955 q^{29} +(2.28603 - 2.02740i) q^{30} +3.09841i q^{31} +(4.21798 - 3.76944i) q^{32} +(3.69933 - 3.69933i) q^{33} +(1.47343 + 4.71405i) q^{34} +(0.793626 - 2.09049i) q^{35} +(-3.39712 + 2.35354i) q^{36} +(-0.680801 + 0.680801i) q^{37} +(2.54557 - 4.86038i) q^{38} +4.31457 q^{39} +(3.28412 + 5.40505i) q^{40} -7.39465 q^{41} +(0.633988 - 1.21050i) q^{42} +(-0.0846505 + 0.0846505i) q^{43} +(6.16686 + 8.90131i) q^{44} +(-1.89491 - 4.21412i) q^{45} +(-0.393319 - 1.25838i) q^{46} +(2.32683 - 2.32683i) q^{47} +(1.59840 + 3.51897i) q^{48} -1.00000i q^{49} +(-6.61109 + 2.50869i) q^{50} -3.37448 q^{51} +(-1.59461 + 8.78708i) q^{52} +(-8.08545 - 8.08545i) q^{53} +(-2.06534 - 6.60782i) q^{54} +(-11.0420 + 4.96514i) q^{55} +(2.23100 + 1.73857i) q^{56} +(2.65072 + 2.65072i) q^{57} +(-7.22804 - 3.78561i) q^{58} +7.94305i q^{59} +(-4.19417 + 1.03996i) q^{60} -4.20293i q^{61} +(2.03298 - 3.88167i) q^{62} +(-1.46115 - 1.46115i) q^{63} +(-7.75751 + 1.95475i) q^{64} +(-9.33468 - 3.54378i) q^{65} +(-7.06175 + 2.20722i) q^{66} +(7.82159 + 7.82159i) q^{67} +(1.24716 - 6.87249i) q^{68} +0.900790 q^{69} +(-2.36589 + 2.09822i) q^{70} -2.85514i q^{71} +(5.80013 - 0.719517i) q^{72} +(1.45516 - 1.45516i) q^{73} +(1.29960 - 0.406203i) q^{74} +(-0.288449 - 4.82260i) q^{75} +(-6.37814 + 4.41880i) q^{76} +(-3.82857 + 3.82857i) q^{77} +(-5.40525 - 2.83095i) q^{78} -12.8568 q^{79} +(-0.567870 - 8.92623i) q^{80} -1.46901 q^{81} +(9.26395 + 4.85190i) q^{82} +(-3.88328 + 3.88328i) q^{83} +(-1.58851 + 1.10052i) q^{84} +(7.30077 + 2.77163i) q^{85} +(0.161592 - 0.0505071i) q^{86} +(3.94197 - 3.94197i) q^{87} +(-1.88531 - 15.1978i) q^{88} -1.96589i q^{89} +(-0.391106 + 6.52273i) q^{90} -4.46530 q^{91} +(-0.332921 + 1.83455i) q^{92} +(2.11695 + 2.11695i) q^{93} +(-4.44175 + 1.38832i) q^{94} +(-3.55772 - 7.91206i) q^{95} +(0.306460 - 5.45730i) q^{96} +(-13.2788 - 13.2788i) q^{97} +(-0.656136 + 1.25279i) q^{98} +11.1882i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25279 0.656136i −0.885857 0.463958i
\(3\) 0.683238 0.683238i 0.394468 0.394468i −0.481809 0.876276i \(-0.660020\pi\)
0.876276 + 0.481809i \(0.160020\pi\)
\(4\) 1.13897 + 1.64400i 0.569485 + 0.822001i
\(5\) −2.03938 + 0.917023i −0.912038 + 0.410105i
\(6\) −1.30425 + 0.407657i −0.532458 + 0.166425i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.348203 2.80691i −0.123108 0.992393i
\(9\) 2.06637i 0.688791i
\(10\) 3.15661 + 0.189272i 0.998207 + 0.0598530i
\(11\) 5.41441 1.63251 0.816253 0.577694i \(-0.196047\pi\)
0.816253 + 0.577694i \(0.196047\pi\)
\(12\) 1.90143 + 0.345057i 0.548896 + 0.0996094i
\(13\) 3.15744 + 3.15744i 0.875717 + 0.875717i 0.993088 0.117371i \(-0.0374466\pi\)
−0.117371 + 0.993088i \(0.537447\pi\)
\(14\) 1.34982 0.421899i 0.360753 0.112757i
\(15\) −0.766836 + 2.01993i −0.197996 + 0.521543i
\(16\) −1.40549 + 3.74494i −0.351373 + 0.936236i
\(17\) −2.46948 2.46948i −0.598936 0.598936i 0.341093 0.940029i \(-0.389203\pi\)
−0.940029 + 0.341093i \(0.889203\pi\)
\(18\) 1.35582 2.58873i 0.319570 0.610170i
\(19\) 3.87964i 0.890051i 0.895518 + 0.445025i \(0.146805\pi\)
−0.895518 + 0.445025i \(0.853195\pi\)
\(20\) −3.83038 2.30828i −0.856500 0.516148i
\(21\) 0.966244i 0.210852i
\(22\) −6.78313 3.55259i −1.44617 0.757415i
\(23\) 0.659207 + 0.659207i 0.137454 + 0.137454i 0.772486 0.635032i \(-0.219013\pi\)
−0.635032 + 0.772486i \(0.719013\pi\)
\(24\) −2.15569 1.67988i −0.440029 0.342905i
\(25\) 3.31814 3.74032i 0.663627 0.748063i
\(26\) −1.88390 6.02733i −0.369464 1.18206i
\(27\) 3.46154 + 3.46154i 0.666173 + 0.666173i
\(28\) −1.96786 0.357112i −0.371891 0.0674877i
\(29\) 5.76955 1.07138 0.535689 0.844415i \(-0.320052\pi\)
0.535689 + 0.844415i \(0.320052\pi\)
\(30\) 2.28603 2.02740i 0.417370 0.370150i
\(31\) 3.09841i 0.556492i 0.960510 + 0.278246i \(0.0897530\pi\)
−0.960510 + 0.278246i \(0.910247\pi\)
\(32\) 4.21798 3.76944i 0.745640 0.666349i
\(33\) 3.69933 3.69933i 0.643971 0.643971i
\(34\) 1.47343 + 4.71405i 0.252690 + 0.808453i
\(35\) 0.793626 2.09049i 0.134147 0.353358i
\(36\) −3.39712 + 2.35354i −0.566187 + 0.392256i
\(37\) −0.680801 + 0.680801i −0.111923 + 0.111923i −0.760850 0.648927i \(-0.775218\pi\)
0.648927 + 0.760850i \(0.275218\pi\)
\(38\) 2.54557 4.86038i 0.412946 0.788458i
\(39\) 4.31457 0.690884
\(40\) 3.28412 + 5.40505i 0.519265 + 0.854613i
\(41\) −7.39465 −1.15485 −0.577425 0.816444i \(-0.695942\pi\)
−0.577425 + 0.816444i \(0.695942\pi\)
\(42\) 0.633988 1.21050i 0.0978264 0.186785i
\(43\) −0.0846505 + 0.0846505i −0.0129091 + 0.0129091i −0.713532 0.700623i \(-0.752906\pi\)
0.700623 + 0.713532i \(0.252906\pi\)
\(44\) 6.16686 + 8.90131i 0.929689 + 1.34192i
\(45\) −1.89491 4.21412i −0.282477 0.628203i
\(46\) −0.393319 1.25838i −0.0579917 0.185538i
\(47\) 2.32683 2.32683i 0.339403 0.339403i −0.516740 0.856143i \(-0.672854\pi\)
0.856143 + 0.516740i \(0.172854\pi\)
\(48\) 1.59840 + 3.51897i 0.230709 + 0.507920i
\(49\) 1.00000i 0.142857i
\(50\) −6.61109 + 2.50869i −0.934949 + 0.354782i
\(51\) −3.37448 −0.472522
\(52\) −1.59461 + 8.78708i −0.221133 + 1.21855i
\(53\) −8.08545 8.08545i −1.11062 1.11062i −0.993066 0.117556i \(-0.962494\pi\)
−0.117556 0.993066i \(-0.537506\pi\)
\(54\) −2.06534 6.60782i −0.281058 0.899211i
\(55\) −11.0420 + 4.96514i −1.48891 + 0.669500i
\(56\) 2.23100 + 1.73857i 0.298130 + 0.232326i
\(57\) 2.65072 + 2.65072i 0.351096 + 0.351096i
\(58\) −7.22804 3.78561i −0.949088 0.497075i
\(59\) 7.94305i 1.03410i 0.855956 + 0.517049i \(0.172969\pi\)
−0.855956 + 0.517049i \(0.827031\pi\)
\(60\) −4.19417 + 1.03996i −0.541465 + 0.134258i
\(61\) 4.20293i 0.538130i −0.963122 0.269065i \(-0.913285\pi\)
0.963122 0.269065i \(-0.0867147\pi\)
\(62\) 2.03298 3.88167i 0.258189 0.492972i
\(63\) −1.46115 1.46115i −0.184087 0.184087i
\(64\) −7.75751 + 1.95475i −0.969689 + 0.244344i
\(65\) −9.33468 3.54378i −1.15782 0.439551i
\(66\) −7.06175 + 2.20722i −0.869242 + 0.271690i
\(67\) 7.82159 + 7.82159i 0.955559 + 0.955559i 0.999054 0.0434947i \(-0.0138491\pi\)
−0.0434947 + 0.999054i \(0.513849\pi\)
\(68\) 1.24716 6.87249i 0.151241 0.833412i
\(69\) 0.900790 0.108442
\(70\) −2.36589 + 2.09822i −0.282778 + 0.250786i
\(71\) 2.85514i 0.338842i −0.985544 0.169421i \(-0.945810\pi\)
0.985544 0.169421i \(-0.0541898\pi\)
\(72\) 5.80013 0.719517i 0.683551 0.0847958i
\(73\) 1.45516 1.45516i 0.170314 0.170314i −0.616803 0.787117i \(-0.711573\pi\)
0.787117 + 0.616803i \(0.211573\pi\)
\(74\) 1.29960 0.406203i 0.151075 0.0472202i
\(75\) −0.288449 4.82260i −0.0333073 0.556866i
\(76\) −6.37814 + 4.41880i −0.731623 + 0.506871i
\(77\) −3.82857 + 3.82857i −0.436306 + 0.436306i
\(78\) −5.40525 2.83095i −0.612025 0.320541i
\(79\) −12.8568 −1.44650 −0.723249 0.690587i \(-0.757352\pi\)
−0.723249 + 0.690587i \(0.757352\pi\)
\(80\) −0.567870 8.92623i −0.0634898 0.997982i
\(81\) −1.46901 −0.163223
\(82\) 9.26395 + 4.85190i 1.02303 + 0.535802i
\(83\) −3.88328 + 3.88328i −0.426245 + 0.426245i −0.887347 0.461102i \(-0.847454\pi\)
0.461102 + 0.887347i \(0.347454\pi\)
\(84\) −1.58851 + 1.10052i −0.173320 + 0.120077i
\(85\) 7.30077 + 2.77163i 0.791879 + 0.300626i
\(86\) 0.161592 0.0505071i 0.0174249 0.00544632i
\(87\) 3.94197 3.94197i 0.422624 0.422624i
\(88\) −1.88531 15.1978i −0.200975 1.62009i
\(89\) 1.96589i 0.208384i −0.994557 0.104192i \(-0.966774\pi\)
0.994557 0.104192i \(-0.0332256\pi\)
\(90\) −0.391106 + 6.52273i −0.0412262 + 0.687556i
\(91\) −4.46530 −0.468091
\(92\) −0.332921 + 1.83455i −0.0347094 + 0.191266i
\(93\) 2.11695 + 2.11695i 0.219518 + 0.219518i
\(94\) −4.44175 + 1.38832i −0.458132 + 0.143194i
\(95\) −3.55772 7.91206i −0.365015 0.811760i
\(96\) 0.306460 5.45730i 0.0312780 0.556984i
\(97\) −13.2788 13.2788i −1.34826 1.34826i −0.887552 0.460707i \(-0.847596\pi\)
−0.460707 0.887552i \(-0.652404\pi\)
\(98\) −0.656136 + 1.25279i −0.0662798 + 0.126551i
\(99\) 11.1882i 1.12446i
\(100\) 9.92835 + 1.19491i 0.992835 + 0.119491i
\(101\) 12.7251i 1.26619i −0.774073 0.633097i \(-0.781784\pi\)
0.774073 0.633097i \(-0.218216\pi\)
\(102\) 4.22752 + 2.21412i 0.418587 + 0.219230i
\(103\) 8.27848 + 8.27848i 0.815703 + 0.815703i 0.985482 0.169779i \(-0.0543054\pi\)
−0.169779 + 0.985482i \(0.554305\pi\)
\(104\) 7.76324 9.96210i 0.761248 0.976864i
\(105\) −0.886068 1.97054i −0.0864714 0.192305i
\(106\) 4.82422 + 15.4345i 0.468570 + 1.49913i
\(107\) −4.27215 4.27215i −0.413004 0.413004i 0.469780 0.882784i \(-0.344333\pi\)
−0.882784 + 0.469780i \(0.844333\pi\)
\(108\) −1.74819 + 9.63337i −0.168219 + 0.926971i
\(109\) 18.5611 1.77783 0.888915 0.458073i \(-0.151460\pi\)
0.888915 + 0.458073i \(0.151460\pi\)
\(110\) 17.0912 + 1.02480i 1.62958 + 0.0977105i
\(111\) 0.930298i 0.0883000i
\(112\) −1.65424 3.64191i −0.156311 0.344128i
\(113\) −7.33321 + 7.33321i −0.689851 + 0.689851i −0.962199 0.272348i \(-0.912200\pi\)
0.272348 + 0.962199i \(0.412200\pi\)
\(114\) −1.58156 5.06003i −0.148127 0.473915i
\(115\) −1.94888 0.739865i −0.181734 0.0689927i
\(116\) 6.57135 + 9.48516i 0.610134 + 0.880675i
\(117\) −6.52445 + 6.52445i −0.603186 + 0.603186i
\(118\) 5.21172 9.95099i 0.479778 0.916063i
\(119\) 3.49237 0.320145
\(120\) 5.93677 + 1.44910i 0.541950 + 0.132284i
\(121\) 18.3159 1.66508
\(122\) −2.75770 + 5.26540i −0.249670 + 0.476707i
\(123\) −5.05230 + 5.05230i −0.455551 + 0.455551i
\(124\) −5.09380 + 3.52900i −0.457437 + 0.316914i
\(125\) −3.33698 + 10.6707i −0.298469 + 0.954419i
\(126\) 0.871800 + 2.78922i 0.0776661 + 0.248484i
\(127\) 15.8188 15.8188i 1.40369 1.40369i 0.615754 0.787938i \(-0.288851\pi\)
0.787938 0.615754i \(-0.211149\pi\)
\(128\) 11.0011 + 2.64109i 0.972371 + 0.233442i
\(129\) 0.115673i 0.0101844i
\(130\) 9.36920 + 10.5644i 0.821733 + 0.926562i
\(131\) 8.12773 0.710123 0.355062 0.934843i \(-0.384460\pi\)
0.355062 + 0.934843i \(0.384460\pi\)
\(132\) 10.2951 + 1.86828i 0.896077 + 0.162613i
\(133\) −2.74332 2.74332i −0.237876 0.237876i
\(134\) −4.66679 14.9308i −0.403149 1.28983i
\(135\) −10.2337 3.88508i −0.880776 0.334374i
\(136\) −6.07172 + 7.79148i −0.520646 + 0.668114i
\(137\) 4.20821 + 4.20821i 0.359531 + 0.359531i 0.863640 0.504109i \(-0.168179\pi\)
−0.504109 + 0.863640i \(0.668179\pi\)
\(138\) −1.12850 0.591041i −0.0960644 0.0503127i
\(139\) 21.7350i 1.84354i −0.387741 0.921769i \(-0.626744\pi\)
0.387741 0.921769i \(-0.373256\pi\)
\(140\) 4.34069 1.07629i 0.366855 0.0909628i
\(141\) 3.17956i 0.267767i
\(142\) −1.87336 + 3.57689i −0.157209 + 0.300166i
\(143\) 17.0957 + 17.0957i 1.42961 + 1.42961i
\(144\) −7.73845 2.90427i −0.644870 0.242022i
\(145\) −11.7663 + 5.29081i −0.977138 + 0.439378i
\(146\) −2.77780 + 0.868230i −0.229892 + 0.0718552i
\(147\) −0.683238 0.683238i −0.0563525 0.0563525i
\(148\) −1.89465 0.343826i −0.155739 0.0282623i
\(149\) 13.2830 1.08818 0.544092 0.839025i \(-0.316874\pi\)
0.544092 + 0.839025i \(0.316874\pi\)
\(150\) −2.80292 + 6.23097i −0.228857 + 0.508757i
\(151\) 10.5109i 0.855365i −0.903929 0.427682i \(-0.859330\pi\)
0.903929 0.427682i \(-0.140670\pi\)
\(152\) 10.8898 1.35090i 0.883280 0.109573i
\(153\) 5.10286 5.10286i 0.412542 0.412542i
\(154\) 7.30846 2.28433i 0.588932 0.184077i
\(155\) −2.84132 6.31884i −0.228220 0.507542i
\(156\) 4.91417 + 7.09317i 0.393448 + 0.567908i
\(157\) −14.7455 + 14.7455i −1.17682 + 1.17682i −0.196273 + 0.980549i \(0.562884\pi\)
−0.980549 + 0.196273i \(0.937116\pi\)
\(158\) 16.1068 + 8.43578i 1.28139 + 0.671115i
\(159\) −11.0486 −0.876209
\(160\) −5.14540 + 11.5553i −0.406779 + 0.913526i
\(161\) −0.932259 −0.0734723
\(162\) 1.84036 + 0.963871i 0.144593 + 0.0757289i
\(163\) 6.86932 6.86932i 0.538047 0.538047i −0.384908 0.922955i \(-0.625767\pi\)
0.922955 + 0.384908i \(0.125767\pi\)
\(164\) −8.42229 12.1568i −0.657670 0.949289i
\(165\) −4.15197 + 10.9367i −0.323230 + 0.851422i
\(166\) 7.41290 2.31698i 0.575352 0.179832i
\(167\) −3.08533 + 3.08533i −0.238750 + 0.238750i −0.816332 0.577583i \(-0.803996\pi\)
0.577583 + 0.816332i \(0.303996\pi\)
\(168\) 2.71216 0.336449i 0.209248 0.0259576i
\(169\) 6.93890i 0.533762i
\(170\) −7.32777 8.26257i −0.562014 0.633710i
\(171\) −8.01678 −0.613059
\(172\) −0.235580 0.0427512i −0.0179628 0.00325975i
\(173\) −6.45046 6.45046i −0.490419 0.490419i 0.418019 0.908438i \(-0.362725\pi\)
−0.908438 + 0.418019i \(0.862725\pi\)
\(174\) −7.52494 + 2.35200i −0.570464 + 0.178305i
\(175\) 0.298526 + 4.99108i 0.0225665 + 0.377290i
\(176\) −7.60991 + 20.2767i −0.573618 + 1.52841i
\(177\) 5.42700 + 5.42700i 0.407918 + 0.407918i
\(178\) −1.28989 + 2.46285i −0.0966814 + 0.184598i
\(179\) 19.1642i 1.43240i −0.697895 0.716201i \(-0.745880\pi\)
0.697895 0.716201i \(-0.254120\pi\)
\(180\) 4.76977 7.91500i 0.355518 0.589949i
\(181\) 13.4361i 0.998700i −0.866400 0.499350i \(-0.833572\pi\)
0.866400 0.499350i \(-0.166428\pi\)
\(182\) 5.59409 + 2.92984i 0.414661 + 0.217175i
\(183\) −2.87160 2.87160i −0.212275 0.212275i
\(184\) 1.62080 2.07987i 0.119487 0.153330i
\(185\) 0.764101 2.01272i 0.0561778 0.147978i
\(186\) −1.26309 4.04111i −0.0926143 0.296309i
\(187\) −13.3708 13.3708i −0.977767 0.977767i
\(188\) 6.47551 + 1.17512i 0.472275 + 0.0857047i
\(189\) −4.89535 −0.356084
\(190\) −0.734307 + 12.2465i −0.0532723 + 0.888455i
\(191\) 0.448780i 0.0324726i −0.999868 0.0162363i \(-0.994832\pi\)
0.999868 0.0162363i \(-0.00516839\pi\)
\(192\) −3.96467 + 6.63578i −0.286125 + 0.478896i
\(193\) −2.00162 + 2.00162i −0.144080 + 0.144080i −0.775467 0.631388i \(-0.782486\pi\)
0.631388 + 0.775467i \(0.282486\pi\)
\(194\) 7.92287 + 25.3483i 0.568829 + 1.81990i
\(195\) −8.79904 + 3.95656i −0.630113 + 0.283335i
\(196\) 1.64400 1.13897i 0.117429 0.0813551i
\(197\) 9.07212 9.07212i 0.646362 0.646362i −0.305750 0.952112i \(-0.598907\pi\)
0.952112 + 0.305750i \(0.0989072\pi\)
\(198\) 7.34098 14.0165i 0.521700 0.996107i
\(199\) 18.1441 1.28620 0.643101 0.765781i \(-0.277647\pi\)
0.643101 + 0.765781i \(0.277647\pi\)
\(200\) −11.6541 8.01133i −0.824071 0.566487i
\(201\) 10.6880 0.753874
\(202\) −8.34939 + 15.9419i −0.587461 + 1.12167i
\(203\) −4.07969 + 4.07969i −0.286338 + 0.286338i
\(204\) −3.84343 5.54765i −0.269094 0.388413i
\(205\) 15.0805 6.78107i 1.05327 0.473610i
\(206\) −4.93940 15.8030i −0.344144 1.10105i
\(207\) −1.36217 + 1.36217i −0.0946771 + 0.0946771i
\(208\) −16.2622 + 7.38669i −1.12758 + 0.512175i
\(209\) 21.0060i 1.45301i
\(210\) −0.182883 + 3.05005i −0.0126201 + 0.210474i
\(211\) 13.0722 0.899929 0.449964 0.893046i \(-0.351437\pi\)
0.449964 + 0.893046i \(0.351437\pi\)
\(212\) 4.08341 22.5016i 0.280450 1.54542i
\(213\) −1.95074 1.95074i −0.133662 0.133662i
\(214\) 2.54900 + 8.15522i 0.174246 + 0.557479i
\(215\) 0.0950080 0.250261i 0.00647949 0.0170677i
\(216\) 8.51091 10.9215i 0.579094 0.743117i
\(217\) −2.19091 2.19091i −0.148729 0.148729i
\(218\) −23.2532 12.1786i −1.57490 0.824839i
\(219\) 1.98844i 0.134367i
\(220\) −20.7393 12.4980i −1.39824 0.842615i
\(221\) 15.5945i 1.04900i
\(222\) 0.610402 1.16547i 0.0409675 0.0782211i
\(223\) −6.46091 6.46091i −0.432655 0.432655i 0.456876 0.889531i \(-0.348968\pi\)
−0.889531 + 0.456876i \(0.848968\pi\)
\(224\) −0.317167 + 5.64796i −0.0211916 + 0.377370i
\(225\) 7.72889 + 6.85651i 0.515259 + 0.457100i
\(226\) 13.9986 4.37540i 0.931171 0.291047i
\(227\) 6.74613 + 6.74613i 0.447756 + 0.447756i 0.894608 0.446852i \(-0.147455\pi\)
−0.446852 + 0.894608i \(0.647455\pi\)
\(228\) −1.33870 + 7.37688i −0.0886574 + 0.488546i
\(229\) −20.4172 −1.34921 −0.674603 0.738181i \(-0.735685\pi\)
−0.674603 + 0.738181i \(0.735685\pi\)
\(230\) 1.95609 + 2.20563i 0.128981 + 0.145435i
\(231\) 5.23164i 0.344217i
\(232\) −2.00897 16.1946i −0.131896 1.06323i
\(233\) −9.85773 + 9.85773i −0.645802 + 0.645802i −0.951976 0.306174i \(-0.900951\pi\)
0.306174 + 0.951976i \(0.400951\pi\)
\(234\) 12.4547 3.89285i 0.814190 0.254483i
\(235\) −2.61153 + 6.87905i −0.170358 + 0.448740i
\(236\) −13.0584 + 9.04691i −0.850030 + 0.588904i
\(237\) −8.78422 + 8.78422i −0.570597 + 0.570597i
\(238\) −4.37521 2.29147i −0.283603 0.148534i
\(239\) −4.45737 −0.288324 −0.144162 0.989554i \(-0.546049\pi\)
−0.144162 + 0.989554i \(0.546049\pi\)
\(240\) −6.48673 5.71075i −0.418716 0.368627i
\(241\) 5.85350 0.377057 0.188529 0.982068i \(-0.439628\pi\)
0.188529 + 0.982068i \(0.439628\pi\)
\(242\) −22.9459 12.0177i −1.47502 0.772527i
\(243\) −11.3883 + 11.3883i −0.730559 + 0.730559i
\(244\) 6.90963 4.78702i 0.442344 0.306457i
\(245\) 0.917023 + 2.03938i 0.0585865 + 0.130291i
\(246\) 9.64448 3.01448i 0.614910 0.192196i
\(247\) −12.2498 + 12.2498i −0.779433 + 0.779433i
\(248\) 8.69698 1.07888i 0.552259 0.0685087i
\(249\) 5.30641i 0.336280i
\(250\) 11.1820 11.1787i 0.707211 0.707002i
\(251\) 4.36889 0.275762 0.137881 0.990449i \(-0.455971\pi\)
0.137881 + 0.990449i \(0.455971\pi\)
\(252\) 0.737926 4.06633i 0.0464849 0.256155i
\(253\) 3.56922 + 3.56922i 0.224395 + 0.224395i
\(254\) −30.1970 + 9.43837i −1.89473 + 0.592216i
\(255\) 6.88184 3.09448i 0.430958 0.193784i
\(256\) −12.0492 10.5270i −0.753074 0.657935i
\(257\) −6.53348 6.53348i −0.407547 0.407547i 0.473335 0.880882i \(-0.343050\pi\)
−0.880882 + 0.473335i \(0.843050\pi\)
\(258\) 0.0758971 0.144914i 0.00472515 0.00902194i
\(259\) 0.962798i 0.0598254i
\(260\) −4.80594 19.3825i −0.298052 1.20205i
\(261\) 11.9220i 0.737956i
\(262\) −10.1824 5.33290i −0.629068 0.329468i
\(263\) 11.5702 + 11.5702i 0.713446 + 0.713446i 0.967254 0.253808i \(-0.0816833\pi\)
−0.253808 + 0.967254i \(0.581683\pi\)
\(264\) −11.6718 9.09558i −0.718350 0.559794i
\(265\) 23.9038 + 9.07476i 1.46840 + 0.557458i
\(266\) 1.63682 + 5.23680i 0.100360 + 0.321089i
\(267\) −1.34317 1.34317i −0.0822006 0.0822006i
\(268\) −3.95015 + 21.7673i −0.241294 + 1.32965i
\(269\) −15.9197 −0.970644 −0.485322 0.874336i \(-0.661298\pi\)
−0.485322 + 0.874336i \(0.661298\pi\)
\(270\) 10.2715 + 11.5819i 0.625106 + 0.704851i
\(271\) 20.8120i 1.26424i 0.774872 + 0.632119i \(0.217814\pi\)
−0.774872 + 0.632119i \(0.782186\pi\)
\(272\) 12.7189 5.77722i 0.771195 0.350295i
\(273\) −3.05086 + 3.05086i −0.184647 + 0.184647i
\(274\) −2.51085 8.03316i −0.151686 0.485301i
\(275\) 17.9658 20.2516i 1.08338 1.22122i
\(276\) 1.02597 + 1.48090i 0.0617563 + 0.0891398i
\(277\) −14.4770 + 14.4770i −0.869840 + 0.869840i −0.992454 0.122615i \(-0.960872\pi\)
0.122615 + 0.992454i \(0.460872\pi\)
\(278\) −14.2611 + 27.2294i −0.855324 + 1.63311i
\(279\) −6.40248 −0.383306
\(280\) −6.14417 1.49972i −0.367184 0.0896255i
\(281\) 22.0154 1.31333 0.656664 0.754184i \(-0.271967\pi\)
0.656664 + 0.754184i \(0.271967\pi\)
\(282\) −2.08622 + 3.98332i −0.124233 + 0.237203i
\(283\) 0.00141407 0.00141407i 8.40579e−5 8.40579e-5i −0.707065 0.707149i \(-0.749981\pi\)
0.707149 + 0.707065i \(0.249981\pi\)
\(284\) 4.69385 3.25192i 0.278529 0.192966i
\(285\) −7.83659 2.97505i −0.464199 0.176227i
\(286\) −10.2002 32.6344i −0.603152 1.92972i
\(287\) 5.22881 5.22881i 0.308647 0.308647i
\(288\) 7.78906 + 8.71591i 0.458975 + 0.513590i
\(289\) 4.80337i 0.282551i
\(290\) 18.2122 + 1.09201i 1.06946 + 0.0641253i
\(291\) −18.1452 −1.06369
\(292\) 4.04968 + 0.734904i 0.236990 + 0.0430070i
\(293\) 13.2135 + 13.2135i 0.771940 + 0.771940i 0.978445 0.206505i \(-0.0662091\pi\)
−0.206505 + 0.978445i \(0.566209\pi\)
\(294\) 0.407657 + 1.30425i 0.0237751 + 0.0760655i
\(295\) −7.28397 16.1989i −0.424089 0.943137i
\(296\) 2.14801 + 1.67389i 0.124850 + 0.0972930i
\(297\) 18.7422 + 18.7422i 1.08753 + 1.08753i
\(298\) −16.6408 8.71545i −0.963976 0.504872i
\(299\) 4.16282i 0.240742i
\(300\) 7.59984 5.96701i 0.438777 0.344506i
\(301\) 0.119714i 0.00690019i
\(302\) −6.89658 + 13.1680i −0.396854 + 0.757731i
\(303\) −8.69426 8.69426i −0.499472 0.499472i
\(304\) −14.5290 5.45280i −0.833297 0.312740i
\(305\) 3.85419 + 8.57137i 0.220690 + 0.490795i
\(306\) −9.74098 + 3.04465i −0.556855 + 0.174051i
\(307\) −15.4316 15.4316i −0.880731 0.880731i 0.112878 0.993609i \(-0.463993\pi\)
−0.993609 + 0.112878i \(0.963993\pi\)
\(308\) −10.6548 1.93355i −0.607114 0.110174i
\(309\) 11.3123 0.643537
\(310\) −0.586443 + 9.78048i −0.0333077 + 0.555494i
\(311\) 22.4892i 1.27524i −0.770349 0.637622i \(-0.779918\pi\)
0.770349 0.637622i \(-0.220082\pi\)
\(312\) −1.50235 12.1106i −0.0850536 0.685629i
\(313\) 10.8617 10.8617i 0.613942 0.613942i −0.330029 0.943971i \(-0.607058\pi\)
0.943971 + 0.330029i \(0.107058\pi\)
\(314\) 28.1482 8.79800i 1.58849 0.496500i
\(315\) 4.31974 + 1.63993i 0.243390 + 0.0923994i
\(316\) −14.6435 21.1365i −0.823760 1.18902i
\(317\) −5.29117 + 5.29117i −0.297182 + 0.297182i −0.839909 0.542727i \(-0.817392\pi\)
0.542727 + 0.839909i \(0.317392\pi\)
\(318\) 13.8416 + 7.24937i 0.776196 + 0.406524i
\(319\) 31.2387 1.74903
\(320\) 14.0280 11.1003i 0.784187 0.620525i
\(321\) −5.83778 −0.325833
\(322\) 1.16793 + 0.611689i 0.0650860 + 0.0340881i
\(323\) 9.58068 9.58068i 0.533083 0.533083i
\(324\) −1.67316 2.41506i −0.0929534 0.134170i
\(325\) 22.2867 1.33301i 1.23624 0.0739421i
\(326\) −13.1130 + 4.09861i −0.726264 + 0.227001i
\(327\) 12.6816 12.6816i 0.701296 0.701296i
\(328\) 2.57484 + 20.7561i 0.142172 + 1.14607i
\(329\) 3.29064i 0.181419i
\(330\) 12.3775 10.9772i 0.681360 0.604273i
\(331\) −6.80525 −0.374050 −0.187025 0.982355i \(-0.559885\pi\)
−0.187025 + 0.982355i \(0.559885\pi\)
\(332\) −10.8071 1.96118i −0.593115 0.107634i
\(333\) −1.40679 1.40679i −0.0770915 0.0770915i
\(334\) 5.88966 1.84088i 0.322268 0.100728i
\(335\) −23.1238 8.77861i −1.26339 0.479627i
\(336\) −3.61853 1.35805i −0.197407 0.0740876i
\(337\) −18.9299 18.9299i −1.03118 1.03118i −0.999498 0.0316788i \(-0.989915\pi\)
−0.0316788 0.999498i \(-0.510085\pi\)
\(338\) 4.55286 8.69300i 0.247643 0.472837i
\(339\) 10.0207i 0.544247i
\(340\) 3.75879 + 15.1593i 0.203849 + 0.822128i
\(341\) 16.7761i 0.908476i
\(342\) 10.0434 + 5.26010i 0.543082 + 0.284434i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 0.267082 + 0.208131i 0.0144001 + 0.0112217i
\(345\) −1.83705 + 0.826045i −0.0989036 + 0.0444728i
\(346\) 3.84870 + 12.3135i 0.206907 + 0.661975i
\(347\) 12.1708 + 12.1708i 0.653362 + 0.653362i 0.953801 0.300439i \(-0.0971333\pi\)
−0.300439 + 0.953801i \(0.597133\pi\)
\(348\) 10.9704 + 1.99082i 0.588076 + 0.106719i
\(349\) 15.7645 0.843856 0.421928 0.906629i \(-0.361353\pi\)
0.421928 + 0.906629i \(0.361353\pi\)
\(350\) 2.90084 6.44865i 0.155056 0.344695i
\(351\) 21.8592i 1.16676i
\(352\) 22.8379 20.4093i 1.21726 1.08782i
\(353\) −12.5792 + 12.5792i −0.669525 + 0.669525i −0.957606 0.288081i \(-0.906983\pi\)
0.288081 + 0.957606i \(0.406983\pi\)
\(354\) −3.23804 10.3597i −0.172100 0.550614i
\(355\) 2.61823 + 5.82271i 0.138961 + 0.309037i
\(356\) 3.23193 2.23909i 0.171292 0.118672i
\(357\) 2.38612 2.38612i 0.126287 0.126287i
\(358\) −12.5743 + 24.0088i −0.664574 + 1.26890i
\(359\) −33.7490 −1.78120 −0.890602 0.454784i \(-0.849716\pi\)
−0.890602 + 0.454784i \(0.849716\pi\)
\(360\) −11.1688 + 6.78622i −0.588650 + 0.357665i
\(361\) 3.94838 0.207810
\(362\) −8.81594 + 16.8327i −0.463355 + 0.884706i
\(363\) 12.5141 12.5141i 0.656819 0.656819i
\(364\) −5.08585 7.34097i −0.266571 0.384771i
\(365\) −1.63321 + 4.30205i −0.0854861 + 0.225179i
\(366\) 1.71336 + 5.48168i 0.0895585 + 0.286532i
\(367\) 2.19334 2.19334i 0.114491 0.114491i −0.647540 0.762031i \(-0.724202\pi\)
0.762031 + 0.647540i \(0.224202\pi\)
\(368\) −3.39520 + 1.54218i −0.176987 + 0.0803918i
\(369\) 15.2801i 0.795450i
\(370\) −2.27788 + 2.02017i −0.118421 + 0.105023i
\(371\) 11.4346 0.593652
\(372\) −1.06913 + 5.89143i −0.0554318 + 0.305456i
\(373\) 5.66659 + 5.66659i 0.293405 + 0.293405i 0.838424 0.545019i \(-0.183478\pi\)
−0.545019 + 0.838424i \(0.683478\pi\)
\(374\) 7.97773 + 25.5238i 0.412519 + 1.31980i
\(375\) 5.01070 + 9.57060i 0.258751 + 0.494224i
\(376\) −7.34142 5.72100i −0.378605 0.295038i
\(377\) 18.2170 + 18.2170i 0.938225 + 0.938225i
\(378\) 6.13285 + 3.21202i 0.315440 + 0.165208i
\(379\) 9.13563i 0.469266i 0.972084 + 0.234633i \(0.0753888\pi\)
−0.972084 + 0.234633i \(0.924611\pi\)
\(380\) 8.95531 14.8605i 0.459398 0.762328i
\(381\) 21.6160i 1.10742i
\(382\) −0.294461 + 0.562227i −0.0150659 + 0.0287660i
\(383\) 7.64787 + 7.64787i 0.390788 + 0.390788i 0.874968 0.484180i \(-0.160882\pi\)
−0.484180 + 0.874968i \(0.660882\pi\)
\(384\) 9.32087 5.71189i 0.475654 0.291484i
\(385\) 4.29702 11.3188i 0.218996 0.576859i
\(386\) 3.82095 1.19428i 0.194481 0.0607871i
\(387\) −0.174919 0.174919i −0.00889165 0.00889165i
\(388\) 6.70623 36.9546i 0.340457 1.87609i
\(389\) −27.8987 −1.41452 −0.707261 0.706952i \(-0.750070\pi\)
−0.707261 + 0.706952i \(0.750070\pi\)
\(390\) 13.6194 + 0.816627i 0.689645 + 0.0413515i
\(391\) 3.25579i 0.164652i
\(392\) −2.80691 + 0.348203i −0.141770 + 0.0175869i
\(393\) 5.55317 5.55317i 0.280121 0.280121i
\(394\) −17.3180 + 5.41292i −0.872469 + 0.272699i
\(395\) 26.2198 11.7899i 1.31926 0.593216i
\(396\) −18.3934 + 12.7430i −0.924304 + 0.640361i
\(397\) −8.36699 + 8.36699i −0.419927 + 0.419927i −0.885179 0.465251i \(-0.845964\pi\)
0.465251 + 0.885179i \(0.345964\pi\)
\(398\) −22.7308 11.9050i −1.13939 0.596744i
\(399\) −3.74868 −0.187669
\(400\) 9.34366 + 17.6832i 0.467183 + 0.884161i
\(401\) −34.4862 −1.72216 −0.861080 0.508470i \(-0.830211\pi\)
−0.861080 + 0.508470i \(0.830211\pi\)
\(402\) −13.3898 7.01279i −0.667825 0.349766i
\(403\) −9.78307 + 9.78307i −0.487329 + 0.487329i
\(404\) 20.9201 14.4935i 1.04081 0.721079i
\(405\) 2.99587 1.34712i 0.148866 0.0669388i
\(406\) 7.78783 2.43417i 0.386503 0.120806i
\(407\) −3.68614 + 3.68614i −0.182715 + 0.182715i
\(408\) 1.17500 + 9.47187i 0.0581713 + 0.468927i
\(409\) 24.8534i 1.22892i −0.788947 0.614461i \(-0.789374\pi\)
0.788947 0.614461i \(-0.210626\pi\)
\(410\) −23.3420 1.39960i −1.15278 0.0691213i
\(411\) 5.75041 0.283647
\(412\) −4.18090 + 23.0388i −0.205978 + 1.13504i
\(413\) −5.61659 5.61659i −0.276374 0.276374i
\(414\) 2.60028 0.812743i 0.127797 0.0399442i
\(415\) 4.35842 11.4805i 0.213947 0.563557i
\(416\) 25.2198 + 1.41624i 1.23650 + 0.0694371i
\(417\) −14.8502 14.8502i −0.727216 0.727216i
\(418\) 13.7828 26.3161i 0.674138 1.28716i
\(419\) 1.88796i 0.0922330i 0.998936 + 0.0461165i \(0.0146845\pi\)
−0.998936 + 0.0461165i \(0.985315\pi\)
\(420\) 2.23036 3.70108i 0.108831 0.180594i
\(421\) 1.78407i 0.0869500i 0.999055 + 0.0434750i \(0.0138429\pi\)
−0.999055 + 0.0434750i \(0.986157\pi\)
\(422\) −16.3768 8.57716i −0.797208 0.417529i
\(423\) 4.80810 + 4.80810i 0.233778 + 0.233778i
\(424\) −19.8798 + 25.5105i −0.965447 + 1.23890i
\(425\) −17.4307 + 1.04256i −0.845512 + 0.0505718i
\(426\) 1.16392 + 3.72382i 0.0563920 + 0.180419i
\(427\) 2.97192 + 2.97192i 0.143821 + 0.143821i
\(428\) 2.15757 11.8893i 0.104290 0.574690i
\(429\) 23.3609 1.12787
\(430\) −0.283230 + 0.251186i −0.0136586 + 0.0121133i
\(431\) 32.0625i 1.54439i 0.635383 + 0.772197i \(0.280842\pi\)
−0.635383 + 0.772197i \(0.719158\pi\)
\(432\) −17.8284 + 8.09810i −0.857770 + 0.389620i
\(433\) 22.4346 22.4346i 1.07814 1.07814i 0.0814590 0.996677i \(-0.474042\pi\)
0.996677 0.0814590i \(-0.0259580\pi\)
\(434\) 1.30722 + 4.18229i 0.0627484 + 0.200756i
\(435\) −4.42430 + 11.6541i −0.212129 + 0.558770i
\(436\) 21.1405 + 30.5145i 1.01245 + 1.46138i
\(437\) −2.55749 + 2.55749i −0.122341 + 0.122341i
\(438\) −1.30469 + 2.49110i −0.0623405 + 0.119030i
\(439\) 15.5671 0.742977 0.371489 0.928438i \(-0.378847\pi\)
0.371489 + 0.928438i \(0.378847\pi\)
\(440\) 17.7816 + 29.2652i 0.847704 + 1.39516i
\(441\) 2.06637 0.0983987
\(442\) −10.2321 + 19.5366i −0.486691 + 0.929262i
\(443\) −22.7365 + 22.7365i −1.08025 + 1.08025i −0.0837592 + 0.996486i \(0.526693\pi\)
−0.996486 + 0.0837592i \(0.973307\pi\)
\(444\) −1.52941 + 1.05958i −0.0725827 + 0.0502855i
\(445\) 1.80277 + 4.00919i 0.0854593 + 0.190054i
\(446\) 3.85494 + 12.3334i 0.182537 + 0.584004i
\(447\) 9.07544 9.07544i 0.429254 0.429254i
\(448\) 4.10317 6.86760i 0.193857 0.324464i
\(449\) 7.97082i 0.376166i 0.982153 + 0.188083i \(0.0602274\pi\)
−0.982153 + 0.188083i \(0.939773\pi\)
\(450\) −5.18388 13.6610i −0.244370 0.643984i
\(451\) −40.0377 −1.88530
\(452\) −20.4081 3.70351i −0.959918 0.174198i
\(453\) −7.18144 7.18144i −0.337414 0.337414i
\(454\) −4.02511 12.8779i −0.188908 0.604388i
\(455\) 9.10644 4.09478i 0.426917 0.191966i
\(456\) 6.51734 8.36332i 0.305203 0.391648i
\(457\) 3.30838 + 3.30838i 0.154759 + 0.154759i 0.780240 0.625480i \(-0.215097\pi\)
−0.625480 + 0.780240i \(0.715097\pi\)
\(458\) 25.5785 + 13.3965i 1.19520 + 0.625975i
\(459\) 17.0964i 0.797990i
\(460\) −1.00338 4.04665i −0.0467827 0.188676i
\(461\) 12.0107i 0.559393i −0.960088 0.279697i \(-0.909766\pi\)
0.960088 0.279697i \(-0.0902339\pi\)
\(462\) 3.43267 6.55416i 0.159702 0.304927i
\(463\) 2.07725 + 2.07725i 0.0965380 + 0.0965380i 0.753726 0.657188i \(-0.228254\pi\)
−0.657188 + 0.753726i \(0.728254\pi\)
\(464\) −8.10905 + 21.6066i −0.376453 + 1.00306i
\(465\) −6.25857 2.37598i −0.290234 0.110183i
\(466\) 18.8177 5.88167i 0.871713 0.272463i
\(467\) −5.60472 5.60472i −0.259356 0.259356i 0.565436 0.824792i \(-0.308708\pi\)
−0.824792 + 0.565436i \(0.808708\pi\)
\(468\) −18.1574 3.29506i −0.839325 0.152314i
\(469\) −11.0614 −0.510768
\(470\) 7.78530 6.90449i 0.359109 0.318480i
\(471\) 20.1494i 0.928437i
\(472\) 22.2955 2.76579i 1.02623 0.127306i
\(473\) −0.458333 + 0.458333i −0.0210742 + 0.0210742i
\(474\) 16.7684 5.24115i 0.770200 0.240734i
\(475\) 14.5111 + 12.8732i 0.665814 + 0.590662i
\(476\) 3.97770 + 5.74146i 0.182318 + 0.263159i
\(477\) 16.7076 16.7076i 0.764986 0.764986i
\(478\) 5.58416 + 2.92464i 0.255413 + 0.133770i
\(479\) −30.2393 −1.38167 −0.690835 0.723013i \(-0.742757\pi\)
−0.690835 + 0.723013i \(0.742757\pi\)
\(480\) 4.37949 + 11.4105i 0.199895 + 0.520818i
\(481\) −4.29918 −0.196026
\(482\) −7.33321 3.84069i −0.334019 0.174939i
\(483\) −0.636955 + 0.636955i −0.0289824 + 0.0289824i
\(484\) 20.8612 + 30.1113i 0.948237 + 1.36870i
\(485\) 39.2575 + 14.9036i 1.78259 + 0.676736i
\(486\) 21.7394 6.79488i 0.986120 0.308222i
\(487\) 5.59965 5.59965i 0.253745 0.253745i −0.568759 0.822504i \(-0.692576\pi\)
0.822504 + 0.568759i \(0.192576\pi\)
\(488\) −11.7973 + 1.46347i −0.534037 + 0.0662483i
\(489\) 9.38676i 0.424484i
\(490\) 0.189272 3.15661i 0.00855044 0.142601i
\(491\) 11.2713 0.508667 0.254333 0.967117i \(-0.418144\pi\)
0.254333 + 0.967117i \(0.418144\pi\)
\(492\) −14.0604 2.55158i −0.633893 0.115034i
\(493\) −14.2478 14.2478i −0.641687 0.641687i
\(494\) 23.3839 7.30887i 1.05209 0.328842i
\(495\) −10.2598 22.8170i −0.461145 1.02555i
\(496\) −11.6034 4.35479i −0.521007 0.195536i
\(497\) 2.01889 + 2.01889i 0.0905594 + 0.0905594i
\(498\) 3.48172 6.64782i 0.156020 0.297896i
\(499\) 7.04115i 0.315205i 0.987503 + 0.157603i \(0.0503765\pi\)
−0.987503 + 0.157603i \(0.949623\pi\)
\(500\) −21.3434 + 6.66765i −0.954508 + 0.298186i
\(501\) 4.21602i 0.188358i
\(502\) −5.47331 2.86659i −0.244286 0.127942i
\(503\) 13.7302 + 13.7302i 0.612199 + 0.612199i 0.943518 0.331320i \(-0.107494\pi\)
−0.331320 + 0.943518i \(0.607494\pi\)
\(504\) −3.59253 + 4.61008i −0.160024 + 0.205349i
\(505\) 11.6692 + 25.9513i 0.519273 + 1.15482i
\(506\) −2.12959 6.81337i −0.0946718 0.302891i
\(507\) 4.74092 + 4.74092i 0.210552 + 0.210552i
\(508\) 44.0233 + 7.98901i 1.95322 + 0.354455i
\(509\) −4.91505 −0.217856 −0.108928 0.994050i \(-0.534742\pi\)
−0.108928 + 0.994050i \(0.534742\pi\)
\(510\) −10.6519 0.638694i −0.471674 0.0282819i
\(511\) 2.05791i 0.0910366i
\(512\) 8.18800 + 21.0940i 0.361862 + 0.932232i
\(513\) −13.4295 + 13.4295i −0.592928 + 0.592928i
\(514\) 3.89823 + 12.4719i 0.171944 + 0.550114i
\(515\) −24.4745 9.29140i −1.07848 0.409428i
\(516\) −0.190166 + 0.131748i −0.00837161 + 0.00579988i
\(517\) 12.5984 12.5984i 0.554078 0.554078i
\(518\) −0.631726 + 1.20618i −0.0277565 + 0.0529967i
\(519\) −8.81439 −0.386909
\(520\) −6.69671 + 27.4356i −0.293670 + 1.20313i
\(521\) 6.55084 0.286998 0.143499 0.989650i \(-0.454165\pi\)
0.143499 + 0.989650i \(0.454165\pi\)
\(522\) 7.82248 14.9358i 0.342381 0.653723i
\(523\) 18.1480 18.1480i 0.793556 0.793556i −0.188514 0.982070i \(-0.560367\pi\)
0.982070 + 0.188514i \(0.0603671\pi\)
\(524\) 9.25725 + 13.3620i 0.404405 + 0.583722i
\(525\) 3.61406 + 3.20613i 0.157730 + 0.139927i
\(526\) −6.90339 22.0866i −0.301002 0.963020i
\(527\) 7.65146 7.65146i 0.333303 0.333303i
\(528\) 8.65441 + 19.0532i 0.376635 + 0.829182i
\(529\) 22.1309i 0.962213i
\(530\) −23.9923 27.0530i −1.04216 1.17511i
\(531\) −16.4133 −0.712277
\(532\) 1.38546 7.63459i 0.0600675 0.331001i
\(533\) −23.3482 23.3482i −1.01132 1.01132i
\(534\) 0.801409 + 2.56401i 0.0346803 + 0.110956i
\(535\) 12.6302 + 4.79487i 0.546051 + 0.207300i
\(536\) 19.2310 24.6780i 0.830653 1.06593i
\(537\) −13.0937 13.0937i −0.565036 0.565036i
\(538\) 19.9441 + 10.4455i 0.859851 + 0.450338i
\(539\) 5.41441i 0.233215i
\(540\) −5.26880 21.2492i −0.226733 0.914421i
\(541\) 7.99669i 0.343805i −0.985114 0.171902i \(-0.945009\pi\)
0.985114 0.171902i \(-0.0549913\pi\)
\(542\) 13.6555 26.0730i 0.586553 1.11993i
\(543\) −9.18008 9.18008i −0.393955 0.393955i
\(544\) −19.7247 1.10766i −0.845691 0.0474906i
\(545\) −37.8531 + 17.0209i −1.62145 + 0.729097i
\(546\) 5.82387 1.82031i 0.249239 0.0779021i
\(547\) 11.2540 + 11.2540i 0.481186 + 0.481186i 0.905510 0.424324i \(-0.139488\pi\)
−0.424324 + 0.905510i \(0.639488\pi\)
\(548\) −2.12528 + 11.7113i −0.0907875 + 0.500283i
\(549\) 8.68482 0.370659
\(550\) −35.7952 + 13.5831i −1.52631 + 0.579184i
\(551\) 22.3838i 0.953581i
\(552\) −0.313658 2.52844i −0.0133502 0.107617i
\(553\) 9.09110 9.09110i 0.386593 0.386593i
\(554\) 27.6356 8.63778i 1.17412 0.366984i
\(555\) −0.853105 1.89723i −0.0362123 0.0805329i
\(556\) 35.7324 24.7555i 1.51539 1.04987i
\(557\) 1.87320 1.87320i 0.0793700 0.0793700i −0.666307 0.745677i \(-0.732126\pi\)
0.745677 + 0.666307i \(0.232126\pi\)
\(558\) 8.02097 + 4.20090i 0.339555 + 0.177838i
\(559\) −0.534558 −0.0226094
\(560\) 6.71334 + 5.91025i 0.283690 + 0.249754i
\(561\) −18.2708 −0.771395
\(562\) −27.5807 14.4451i −1.16342 0.609329i
\(563\) 18.2779 18.2779i 0.770322 0.770322i −0.207840 0.978163i \(-0.566643\pi\)
0.978163 + 0.207840i \(0.0666434\pi\)
\(564\) 5.22720 3.62142i 0.220105 0.152489i
\(565\) 8.23048 21.6799i 0.346259 0.912082i
\(566\) −0.00269936 0.000843713i −0.000113463 3.54639e-5i
\(567\) 1.03875 1.03875i 0.0436233 0.0436233i
\(568\) −8.01412 + 0.994167i −0.336265 + 0.0417143i
\(569\) 0.0832566i 0.00349030i −0.999998 0.00174515i \(-0.999445\pi\)
0.999998 0.00174515i \(-0.000555499\pi\)
\(570\) 7.86557 + 8.86898i 0.329453 + 0.371481i
\(571\) −7.17301 −0.300181 −0.150091 0.988672i \(-0.547957\pi\)
−0.150091 + 0.988672i \(0.547957\pi\)
\(572\) −8.63388 + 47.5769i −0.361001 + 1.98929i
\(573\) −0.306623 0.306623i −0.0128094 0.0128094i
\(574\) −9.98141 + 3.11979i −0.416616 + 0.130218i
\(575\) 4.65298 0.278304i 0.194043 0.0116061i
\(576\) −4.03924 16.0299i −0.168302 0.667913i
\(577\) −3.54999 3.54999i −0.147788 0.147788i 0.629341 0.777129i \(-0.283325\pi\)
−0.777129 + 0.629341i \(0.783325\pi\)
\(578\) −3.15167 + 6.01762i −0.131092 + 0.250300i
\(579\) 2.73517i 0.113670i
\(580\) −22.0996 13.3178i −0.917635 0.552990i
\(581\) 5.49179i 0.227838i
\(582\) 22.7321 + 11.9057i 0.942276 + 0.493507i
\(583\) −43.7780 43.7780i −1.81310 1.81310i
\(584\) −4.59120 3.57782i −0.189985 0.148051i
\(585\) 7.32276 19.2889i 0.302759 0.797498i
\(586\) −7.88389 25.2236i −0.325681 1.04198i
\(587\) 18.7905 + 18.7905i 0.775568 + 0.775568i 0.979074 0.203505i \(-0.0652334\pi\)
−0.203505 + 0.979074i \(0.565233\pi\)
\(588\) 0.345057 1.90143i 0.0142299 0.0784138i
\(589\) −12.0207 −0.495306
\(590\) −1.50340 + 25.0731i −0.0618939 + 1.03224i
\(591\) 12.3968i 0.509937i
\(592\) −1.59270 3.50642i −0.0654596 0.144113i
\(593\) −7.24799 + 7.24799i −0.297639 + 0.297639i −0.840088 0.542449i \(-0.817497\pi\)
0.542449 + 0.840088i \(0.317497\pi\)
\(594\) −11.1826 35.7775i −0.458828 1.46797i
\(595\) −7.12226 + 3.20258i −0.291984 + 0.131293i
\(596\) 15.1289 + 21.8373i 0.619705 + 0.894490i
\(597\) 12.3967 12.3967i 0.507365 0.507365i
\(598\) 2.73137 5.21514i 0.111694 0.213263i
\(599\) −20.5332 −0.838963 −0.419482 0.907764i \(-0.637788\pi\)
−0.419482 + 0.907764i \(0.637788\pi\)
\(600\) −13.4362 + 2.48890i −0.548530 + 0.101609i
\(601\) −27.1276 −1.10656 −0.553280 0.832995i \(-0.686624\pi\)
−0.553280 + 0.832995i \(0.686624\pi\)
\(602\) −0.0785486 + 0.149976i −0.00320140 + 0.00611258i
\(603\) −16.1623 + 16.1623i −0.658180 + 0.658180i
\(604\) 17.2800 11.9716i 0.703111 0.487118i
\(605\) −37.3530 + 16.7961i −1.51861 + 0.682857i
\(606\) 5.18747 + 16.5967i 0.210727 + 0.674195i
\(607\) 12.6435 12.6435i 0.513185 0.513185i −0.402316 0.915501i \(-0.631795\pi\)
0.915501 + 0.402316i \(0.131795\pi\)
\(608\) 14.6241 + 16.3642i 0.593084 + 0.663658i
\(609\) 5.57479i 0.225902i
\(610\) 0.795497 13.2670i 0.0322087 0.537166i
\(611\) 14.6937 0.594442
\(612\) 14.2011 + 2.57711i 0.574046 + 0.104173i
\(613\) −0.474128 0.474128i −0.0191498 0.0191498i 0.697467 0.716617i \(-0.254310\pi\)
−0.716617 + 0.697467i \(0.754310\pi\)
\(614\) 9.20737 + 29.4579i 0.371579 + 1.18882i
\(615\) 5.67048 14.9366i 0.228656 0.602304i
\(616\) 12.0796 + 9.41333i 0.486700 + 0.379274i
\(617\) −34.0848 34.0848i −1.37220 1.37220i −0.857171 0.515032i \(-0.827780\pi\)
−0.515032 0.857171i \(-0.672220\pi\)
\(618\) −14.1720 7.42244i −0.570081 0.298574i
\(619\) 29.0177i 1.16632i 0.812357 + 0.583161i \(0.198184\pi\)
−0.812357 + 0.583161i \(0.801816\pi\)
\(620\) 7.15202 11.8681i 0.287232 0.476635i
\(621\) 4.56374i 0.183136i
\(622\) −14.7560 + 28.1742i −0.591660 + 1.12968i
\(623\) 1.39009 + 1.39009i 0.0556929 + 0.0556929i
\(624\) −6.06409 + 16.1578i −0.242758 + 0.646830i
\(625\) −2.97994 24.8218i −0.119197 0.992871i
\(626\) −20.7343 + 6.48071i −0.828708 + 0.259021i
\(627\) 14.3521 + 14.3521i 0.573167 + 0.573167i
\(628\) −41.0365 7.44697i −1.63753 0.297167i
\(629\) 3.36244 0.134069
\(630\) −4.33571 4.88882i −0.172739 0.194775i
\(631\) 24.5158i 0.975960i 0.872855 + 0.487980i \(0.162266\pi\)
−0.872855 + 0.487980i \(0.837734\pi\)
\(632\) 4.47676 + 36.0878i 0.178076 + 1.43549i
\(633\) 8.93144 8.93144i 0.354993 0.354993i
\(634\) 10.1005 3.15700i 0.401141 0.125381i
\(635\) −17.7543 + 46.7668i −0.704559 + 1.85588i
\(636\) −12.5840 18.1639i −0.498988 0.720245i
\(637\) 3.15744 3.15744i 0.125102 0.125102i
\(638\) −39.1356 20.4969i −1.54939 0.811478i
\(639\) 5.89978 0.233392
\(640\) −24.8574 + 4.70210i −0.982575 + 0.185867i
\(641\) −42.5065 −1.67891 −0.839453 0.543432i \(-0.817125\pi\)
−0.839453 + 0.543432i \(0.817125\pi\)
\(642\) 7.31352 + 3.83038i 0.288642 + 0.151173i
\(643\) −3.14215 + 3.14215i −0.123914 + 0.123914i −0.766344 0.642430i \(-0.777926\pi\)
0.642430 + 0.766344i \(0.277926\pi\)
\(644\) −1.06182 1.53264i −0.0418414 0.0603943i
\(645\) −0.106075 0.235901i −0.00417669 0.00928858i
\(646\) −18.2888 + 5.71636i −0.719564 + 0.224907i
\(647\) 10.1457 10.1457i 0.398867 0.398867i −0.478966 0.877833i \(-0.658988\pi\)
0.877833 + 0.478966i \(0.158988\pi\)
\(648\) 0.511514 + 4.12338i 0.0200942 + 0.161982i
\(649\) 43.0070i 1.68817i
\(650\) −28.7952 12.9531i −1.12944 0.508063i
\(651\) −2.99382 −0.117337
\(652\) 19.1171 + 3.46923i 0.748685 + 0.135865i
\(653\) 5.20264 + 5.20264i 0.203595 + 0.203595i 0.801538 0.597943i \(-0.204015\pi\)
−0.597943 + 0.801538i \(0.704015\pi\)
\(654\) −24.2083 + 7.56656i −0.946620 + 0.295876i
\(655\) −16.5755 + 7.45332i −0.647660 + 0.291225i
\(656\) 10.3931 27.6925i 0.405783 1.08121i
\(657\) 3.00691 + 3.00691i 0.117311 + 0.117311i
\(658\) 2.15910 4.12248i 0.0841707 0.160711i
\(659\) 45.6133i 1.77684i −0.459032 0.888420i \(-0.651804\pi\)
0.459032 0.888420i \(-0.348196\pi\)
\(660\) −22.7090 + 5.63075i −0.883945 + 0.219177i
\(661\) 45.1240i 1.75512i 0.479465 + 0.877561i \(0.340831\pi\)
−0.479465 + 0.877561i \(0.659169\pi\)
\(662\) 8.52556 + 4.46517i 0.331355 + 0.173544i
\(663\) −10.6547 10.6547i −0.413795 0.413795i
\(664\) 12.2522 + 9.54785i 0.475477 + 0.370529i
\(665\) 8.11036 + 3.07898i 0.314506 + 0.119398i
\(666\) 0.839367 + 2.68546i 0.0325248 + 0.104059i
\(667\) 3.80333 + 3.80333i 0.147265 + 0.147265i
\(668\) −8.58638 1.55819i −0.332217 0.0602881i
\(669\) −8.82868 −0.341337
\(670\) 23.2093 + 26.1701i 0.896653 + 1.01104i
\(671\) 22.7564i 0.878501i
\(672\) 3.64220 + 4.07560i 0.140501 + 0.157220i
\(673\) 5.25412 5.25412i 0.202532 0.202532i −0.598552 0.801084i \(-0.704257\pi\)
0.801084 + 0.598552i \(0.204257\pi\)
\(674\) 11.2946 + 36.1358i 0.435052 + 1.39190i
\(675\) 24.4331 1.46139i 0.940430 0.0562490i
\(676\) −11.4076 + 7.90321i −0.438753 + 0.303970i
\(677\) 26.8547 26.8547i 1.03211 1.03211i 0.0326441 0.999467i \(-0.489607\pi\)
0.999467 0.0326441i \(-0.0103928\pi\)
\(678\) 6.57492 12.5538i 0.252508 0.482125i
\(679\) 18.7791 0.720675
\(680\) 5.23758 21.4577i 0.200852 0.822865i
\(681\) 9.21842 0.353251
\(682\) 11.0074 21.0169i 0.421495 0.804780i
\(683\) 11.7713 11.7713i 0.450416 0.450416i −0.445077 0.895492i \(-0.646824\pi\)
0.895492 + 0.445077i \(0.146824\pi\)
\(684\) −9.13088 13.1796i −0.349128 0.503935i
\(685\) −12.4412 4.72311i −0.475352 0.180461i
\(686\) −0.421899 1.34982i −0.0161082 0.0515362i
\(687\) −13.9498 + 13.9498i −0.532218 + 0.532218i
\(688\) −0.198036 0.435987i −0.00755004 0.0166218i
\(689\) 51.0587i 1.94518i
\(690\) 2.84344 + 0.170494i 0.108248 + 0.00649061i
\(691\) 32.1658 1.22364 0.611822 0.790995i \(-0.290437\pi\)
0.611822 + 0.790995i \(0.290437\pi\)
\(692\) 3.25769 17.9515i 0.123839 0.682412i
\(693\) −7.91125 7.91125i −0.300523 0.300523i
\(694\) −7.26175 23.2331i −0.275652 0.881917i
\(695\) 19.9315 + 44.3259i 0.756044 + 1.68138i
\(696\) −12.4374 9.69217i −0.471438 0.367381i
\(697\) 18.2609 + 18.2609i 0.691681 + 0.691681i
\(698\) −19.7497 10.3437i −0.747536 0.391514i
\(699\) 13.4704i 0.509496i
\(700\) −7.86534 + 6.17547i −0.297282 + 0.233411i
\(701\) 36.5604i 1.38087i 0.723396 + 0.690433i \(0.242580\pi\)
−0.723396 + 0.690433i \(0.757420\pi\)
\(702\) 14.3426 27.3850i 0.541327 1.03358i
\(703\) −2.64126 2.64126i −0.0996171 0.0996171i
\(704\) −42.0024 + 10.5838i −1.58302 + 0.398893i
\(705\) 2.91573 + 6.48432i 0.109813 + 0.244214i
\(706\) 24.0128 7.50546i 0.903734 0.282472i
\(707\) 8.99799 + 8.99799i 0.338404 + 0.338404i
\(708\) −2.74081 + 15.1032i −0.103006 + 0.567612i
\(709\) −13.0843 −0.491390 −0.245695 0.969347i \(-0.579016\pi\)
−0.245695 + 0.969347i \(0.579016\pi\)
\(710\) 0.540397 9.01255i 0.0202808 0.338235i
\(711\) 26.5668i 0.996335i
\(712\) −5.51808 + 0.684528i −0.206799 + 0.0256538i
\(713\) −2.04250 + 2.04250i −0.0764921 + 0.0764921i
\(714\) −4.55492 + 1.42369i −0.170464 + 0.0532802i
\(715\) −50.5418 19.1875i −1.89016 0.717571i
\(716\) 31.5060 21.8275i 1.17744 0.815732i
\(717\) −3.04545 + 3.04545i −0.113734 + 0.113734i
\(718\) 42.2804 + 22.1439i 1.57789 + 0.826404i
\(719\) 18.4708 0.688843 0.344422 0.938815i \(-0.388075\pi\)
0.344422 + 0.938815i \(0.388075\pi\)
\(720\) 18.4449 1.17343i 0.687401 0.0437312i
\(721\) −11.7075 −0.436012
\(722\) −4.94650 2.59068i −0.184090 0.0964150i
\(723\) 3.99933 3.99933i 0.148737 0.148737i
\(724\) 22.0890 15.3034i 0.820933 0.568745i
\(725\) 19.1442 21.5799i 0.710996 0.801459i
\(726\) −23.8885 + 7.46659i −0.886584 + 0.277111i
\(727\) −25.3587 + 25.3587i −0.940503 + 0.940503i −0.998327 0.0578241i \(-0.981584\pi\)
0.0578241 + 0.998327i \(0.481584\pi\)
\(728\) 1.55483 + 12.5337i 0.0576258 + 0.464530i
\(729\) 11.1548i 0.413140i
\(730\) 4.86880 4.31796i 0.180202 0.159815i
\(731\) 0.418085 0.0154634
\(732\) 1.45025 7.99159i 0.0536028 0.295378i
\(733\) 24.6327 + 24.6327i 0.909830 + 0.909830i 0.996258 0.0864280i \(-0.0275453\pi\)
−0.0864280 + 0.996258i \(0.527545\pi\)
\(734\) −4.18693 + 1.30867i −0.154542 + 0.0483038i
\(735\) 2.01993 + 0.766836i 0.0745061 + 0.0282852i
\(736\) 5.26536 + 0.295681i 0.194084 + 0.0108990i
\(737\) 42.3493 + 42.3493i 1.55996 + 1.55996i
\(738\) −10.0258 + 19.1428i −0.369056 + 0.704655i
\(739\) 23.4559i 0.862838i 0.902152 + 0.431419i \(0.141987\pi\)
−0.902152 + 0.431419i \(0.858013\pi\)
\(740\) 4.17921 1.03625i 0.153631 0.0380932i
\(741\) 16.7390i 0.614922i
\(742\) −14.3251 7.50262i −0.525891 0.275430i
\(743\) −9.17537 9.17537i −0.336612 0.336612i 0.518479 0.855090i \(-0.326498\pi\)
−0.855090 + 0.518479i \(0.826498\pi\)
\(744\) 5.20497 6.67923i 0.190824 0.244873i
\(745\) −27.0891 + 12.1808i −0.992466 + 0.446270i
\(746\) −3.38100 10.8171i −0.123787 0.396042i
\(747\) −8.02430 8.02430i −0.293594 0.293594i
\(748\) 6.75266 37.2105i 0.246902 1.36055i
\(749\) 6.04173 0.220760
\(750\) 0.00226196 15.2777i 8.25952e−5 0.557861i
\(751\) 34.6985i 1.26617i −0.774084 0.633083i \(-0.781789\pi\)
0.774084 0.633083i \(-0.218211\pi\)
\(752\) 5.44351 + 11.9842i 0.198504 + 0.437018i
\(753\) 2.98499 2.98499i 0.108779 0.108779i
\(754\) −10.8693 34.7750i −0.395836 1.26643i
\(755\) 9.63874 + 21.4357i 0.350790 + 0.780126i
\(756\) −5.57566 8.04797i −0.202785 0.292702i
\(757\) −11.2942 + 11.2942i −0.410495 + 0.410495i −0.881911 0.471416i \(-0.843743\pi\)
0.471416 + 0.881911i \(0.343743\pi\)
\(758\) 5.99421 11.4450i 0.217720 0.415702i
\(759\) 4.87725 0.177033
\(760\) −20.9697 + 12.7412i −0.760649 + 0.462172i
\(761\) 51.7952 1.87757 0.938787 0.344499i \(-0.111951\pi\)
0.938787 + 0.344499i \(0.111951\pi\)
\(762\) −14.1831 + 27.0804i −0.513798 + 0.981018i
\(763\) −13.1247 + 13.1247i −0.475145 + 0.475145i
\(764\) 0.737795 0.511147i 0.0266925 0.0184926i
\(765\) −5.72722 + 15.0861i −0.207068 + 0.545439i
\(766\) −4.56314 14.5992i −0.164873 0.527492i
\(767\) −25.0797 + 25.0797i −0.905577 + 0.905577i
\(768\) −15.4249 + 1.04004i −0.556598 + 0.0375293i
\(769\) 7.52971i 0.271528i −0.990741 0.135764i \(-0.956651\pi\)
0.990741 0.135764i \(-0.0433490\pi\)
\(770\) −12.8099 + 11.3606i −0.461638 + 0.409409i
\(771\) −8.92784 −0.321528
\(772\) −5.57046 1.01088i −0.200485 0.0363825i
\(773\) −6.95427 6.95427i −0.250128 0.250128i 0.570895 0.821023i \(-0.306596\pi\)
−0.821023 + 0.570895i \(0.806596\pi\)
\(774\) 0.104367 + 0.333908i 0.00375138 + 0.0120021i
\(775\) 11.5891 + 10.2810i 0.416291 + 0.369303i
\(776\) −32.6487 + 41.8962i −1.17202 + 1.50399i
\(777\) −0.657820 0.657820i −0.0235992 0.0235992i
\(778\) 34.9513 + 18.3054i 1.25306 + 0.656279i
\(779\) 28.6886i 1.02788i
\(780\) −16.5265 9.95925i −0.591742 0.356598i
\(781\) 15.4589i 0.553162i
\(782\) −2.13624 + 4.07883i −0.0763919 + 0.145858i
\(783\) 19.9715 + 19.9715i 0.713724 + 0.713724i
\(784\) 3.74494 + 1.40549i 0.133748 + 0.0501961i
\(785\) 16.5498 43.5938i 0.590686 1.55593i
\(786\) −10.6006 + 3.31333i −0.378111 + 0.118183i
\(787\) −12.5412 12.5412i −0.447047 0.447047i 0.447325 0.894372i \(-0.352377\pi\)
−0.894372 + 0.447325i \(0.852377\pi\)
\(788\) 25.2475 + 4.58171i 0.899404 + 0.163217i
\(789\) 15.8103 0.562863
\(790\) −40.5837 2.43342i −1.44390 0.0865773i
\(791\) 10.3707i 0.368741i
\(792\) 31.4043 3.89576i 1.11590 0.138430i
\(793\) 13.2705 13.2705i 0.471250 0.471250i
\(794\) 15.9720 4.99220i 0.566824 0.177167i
\(795\) 22.5322 10.1318i 0.799136 0.359338i
\(796\) 20.6656 + 29.8290i 0.732474 + 1.05726i
\(797\) 21.9527 21.9527i 0.777606 0.777606i −0.201817 0.979423i \(-0.564685\pi\)
0.979423 + 0.201817i \(0.0646846\pi\)
\(798\) 4.69631 + 2.45964i 0.166248 + 0.0870705i
\(799\) −11.4921 −0.406562
\(800\) −0.103059 28.2841i −0.00364369 0.999993i
\(801\) 4.06226 0.143533
\(802\) 43.2040 + 22.6277i 1.52559 + 0.799010i
\(803\) 7.87885 7.87885i 0.278039 0.278039i
\(804\) 12.1733 + 17.5711i 0.429320 + 0.619686i
\(805\) 1.90123 0.854903i 0.0670095 0.0301314i
\(806\) 18.6752 5.83712i 0.657805 0.205604i
\(807\) −10.8770 + 10.8770i −0.382887 + 0.382887i
\(808\) −35.7182 + 4.43091i −1.25656 + 0.155879i
\(809\) 15.6233i 0.549285i −0.961546 0.274642i \(-0.911441\pi\)
0.961546 0.274642i \(-0.0885595\pi\)
\(810\) −4.63709 0.278043i −0.162931 0.00976942i
\(811\) 12.8151 0.450000 0.225000 0.974359i \(-0.427762\pi\)
0.225000 + 0.974359i \(0.427762\pi\)
\(812\) −11.3537 2.06037i −0.398435 0.0723049i
\(813\) 14.2195 + 14.2195i 0.498700 + 0.498700i
\(814\) 7.03657 2.19935i 0.246632 0.0770872i
\(815\) −7.70982 + 20.3085i −0.270063 + 0.711375i
\(816\) 4.74280 12.6372i 0.166031 0.442392i
\(817\) −0.328414 0.328414i −0.0114897 0.0114897i
\(818\) −16.3072 + 31.1361i −0.570168 + 1.08865i
\(819\) 9.22697i 0.322416i
\(820\) 28.3243 + 17.0689i 0.989129 + 0.596073i
\(821\) 1.83369i 0.0639962i −0.999488 0.0319981i \(-0.989813\pi\)
0.999488 0.0319981i \(-0.0101871\pi\)
\(822\) −7.20407 3.77305i −0.251271 0.131600i
\(823\) −9.77602 9.77602i −0.340770 0.340770i 0.515886 0.856657i \(-0.327463\pi\)
−0.856657 + 0.515886i \(0.827463\pi\)
\(824\) 20.3544 26.1196i 0.709078 0.909918i
\(825\) −1.56178 26.1116i −0.0543743 0.909088i
\(826\) 3.35116 + 10.7217i 0.116602 + 0.373054i
\(827\) 9.46776 + 9.46776i 0.329226 + 0.329226i 0.852292 0.523066i \(-0.175212\pi\)
−0.523066 + 0.852292i \(0.675212\pi\)
\(828\) −3.79087 0.687938i −0.131742 0.0239075i
\(829\) 29.4393 1.02247 0.511234 0.859442i \(-0.329189\pi\)
0.511234 + 0.859442i \(0.329189\pi\)
\(830\) −12.9930 + 11.5230i −0.450993 + 0.399969i
\(831\) 19.7825i 0.686247i
\(832\) −30.6659 18.3219i −1.06315 0.635197i
\(833\) −2.46948 + 2.46948i −0.0855623 + 0.0855623i
\(834\) 8.86042 + 28.3479i 0.306811 + 0.981607i
\(835\) 3.46284 9.12147i 0.119836 0.315661i
\(836\) −34.5339 + 23.9252i −1.19438 + 0.827470i
\(837\) −10.7253 + 10.7253i −0.370720 + 0.370720i
\(838\) 1.23876 2.36522i 0.0427923 0.0817052i
\(839\) 8.19787 0.283022 0.141511 0.989937i \(-0.454804\pi\)
0.141511 + 0.989937i \(0.454804\pi\)
\(840\) −5.22260 + 3.17326i −0.180197 + 0.109488i
\(841\) 4.28771 0.147852
\(842\) 1.17059 2.23506i 0.0403412 0.0770253i
\(843\) 15.0417 15.0417i 0.518065 0.518065i
\(844\) 14.8889 + 21.4908i 0.512496 + 0.739743i
\(845\) −6.36314 14.1511i −0.218899 0.486811i
\(846\) −2.86878 9.17831i −0.0986305 0.315557i
\(847\) −12.9513 + 12.9513i −0.445011 + 0.445011i
\(848\) 41.6436 18.9155i 1.43005 0.649562i
\(849\) 0.00193230i 6.63162e-5i
\(850\) 22.5211 + 10.1308i 0.772466 + 0.347483i
\(851\) −0.897577 −0.0307685
\(852\) 0.985185 5.42885i 0.0337519 0.185989i
\(853\) −12.0948 12.0948i −0.414118 0.414118i 0.469053 0.883170i \(-0.344595\pi\)
−0.883170 + 0.469053i \(0.844595\pi\)
\(854\) −1.77321 5.67318i −0.0606781 0.194132i
\(855\) 16.3493 7.35158i 0.559133 0.251419i
\(856\) −10.5040 + 13.4791i −0.359018 + 0.460707i
\(857\) 13.0039 + 13.0039i 0.444205 + 0.444205i 0.893422 0.449218i \(-0.148297\pi\)
−0.449218 + 0.893422i \(0.648297\pi\)
\(858\) −29.2663 15.3279i −0.999134 0.523286i
\(859\) 46.0549i 1.57137i 0.618624 + 0.785687i \(0.287690\pi\)
−0.618624 + 0.785687i \(0.712310\pi\)
\(860\) 0.519641 0.128846i 0.0177196 0.00439363i
\(861\) 7.14504i 0.243502i
\(862\) 21.0373 40.1676i 0.716535 1.36811i
\(863\) 8.93749 + 8.93749i 0.304236 + 0.304236i 0.842669 0.538433i \(-0.180983\pi\)
−0.538433 + 0.842669i \(0.680983\pi\)
\(864\) 27.6487 + 1.55264i 0.940629 + 0.0528220i
\(865\) 19.0701 + 7.23971i 0.648405 + 0.246158i
\(866\) −42.8259 + 13.3857i −1.45528 + 0.454864i
\(867\) −3.28185 3.28185i −0.111457 0.111457i
\(868\) 1.10648 6.09724i 0.0375564 0.206954i
\(869\) −69.6118 −2.36142
\(870\) 13.1894 11.6972i 0.447162 0.396571i
\(871\) 49.3924i 1.67360i
\(872\) −6.46302 52.0993i −0.218866 1.76431i
\(873\) 27.4390 27.4390i 0.928669 0.928669i
\(874\) 4.88205 1.52594i 0.165138 0.0516156i
\(875\) −5.18574 9.90495i −0.175310 0.334848i
\(876\) 3.26901 2.26478i 0.110450 0.0765198i
\(877\) −5.94628 + 5.94628i −0.200792 + 0.200792i −0.800339 0.599547i \(-0.795347\pi\)
0.599547 + 0.800339i \(0.295347\pi\)
\(878\) −19.5023 10.2141i −0.658172 0.344710i
\(879\) 18.0559 0.609011
\(880\) −3.07468 48.3303i −0.103648 1.62921i
\(881\) 23.6599 0.797122 0.398561 0.917142i \(-0.369510\pi\)
0.398561 + 0.917142i \(0.369510\pi\)
\(882\) −2.58873 1.35582i −0.0871672 0.0456529i
\(883\) 21.7857 21.7857i 0.733148 0.733148i −0.238094 0.971242i \(-0.576523\pi\)
0.971242 + 0.238094i \(0.0765227\pi\)
\(884\) 25.6373 17.7616i 0.862277 0.597389i
\(885\) −16.0444 6.09102i −0.539326 0.204747i
\(886\) 43.4024 13.5659i 1.45813 0.455754i
\(887\) 34.7838 34.7838i 1.16793 1.16793i 0.185230 0.982695i \(-0.440697\pi\)
0.982695 0.185230i \(-0.0593030\pi\)
\(888\) 2.61126 0.323932i 0.0876283 0.0108705i
\(889\) 22.3712i 0.750305i
\(890\) 0.372088 6.20554i 0.0124724 0.208010i
\(891\) −7.95383 −0.266463
\(892\) 3.26297 17.9806i 0.109252 0.602033i
\(893\) 9.02727 + 9.02727i 0.302086 + 0.302086i
\(894\) −17.3244 + 5.41491i −0.579413 + 0.181102i
\(895\) 17.5740 + 39.0831i 0.587435 + 1.30640i
\(896\) −9.64650 + 5.91143i −0.322267 + 0.197487i
\(897\) 2.84419 + 2.84419i 0.0949648 + 0.0949648i
\(898\) 5.22994 9.98577i 0.174525 0.333229i
\(899\) 17.8765i 0.596213i
\(900\) −2.46914 + 20.5157i −0.0823046 + 0.683856i
\(901\) 39.9337i 1.33038i
\(902\) 50.1588 + 26.2702i 1.67011 + 0.874701i
\(903\) −0.0817930 0.0817930i −0.00272190 0.00272190i
\(904\) 23.1371 + 18.0302i 0.769530 + 0.599677i
\(905\) 12.3213 + 27.4014i 0.409572 + 0.910853i
\(906\) 4.28484 + 13.7089i 0.142354 + 0.455446i
\(907\) 6.75591 + 6.75591i 0.224326 + 0.224326i 0.810317 0.585991i \(-0.199295\pi\)
−0.585991 + 0.810317i \(0.699295\pi\)
\(908\) −3.40701 + 18.7743i −0.113066 + 0.623047i
\(909\) 26.2948 0.872142
\(910\) −14.0952 0.845156i −0.467251 0.0280167i
\(911\) 24.7078i 0.818605i −0.912399 0.409302i \(-0.865772\pi\)
0.912399 0.409302i \(-0.134228\pi\)
\(912\) −13.6523 + 6.20123i −0.452074 + 0.205343i
\(913\) −21.0257 + 21.0257i −0.695848 + 0.695848i
\(914\) −1.97396 6.31545i −0.0652928 0.208897i
\(915\) 8.48961 + 3.22296i 0.280658 + 0.106548i
\(916\) −23.2546 33.5659i −0.768353 1.10905i
\(917\) −5.74717 + 5.74717i −0.189788 + 0.189788i
\(918\) −11.2175 + 21.4182i −0.370234 + 0.706905i
\(919\) −1.05781 −0.0348938 −0.0174469 0.999848i \(-0.505554\pi\)
−0.0174469 + 0.999848i \(0.505554\pi\)
\(920\) −1.39813 + 5.72796i −0.0460950 + 0.188845i
\(921\) −21.0870 −0.694839
\(922\) −7.88064 + 15.0469i −0.259535 + 0.495543i
\(923\) 9.01493 9.01493i 0.296730 0.296730i
\(924\) −8.60084 + 5.95869i −0.282947 + 0.196026i
\(925\) 0.287420 + 4.80540i 0.00945033 + 0.158001i
\(926\) −1.23940 3.96532i −0.0407292 0.130308i
\(927\) −17.1064 + 17.1064i −0.561849 + 0.561849i
\(928\) 24.3358 21.7480i 0.798863 0.713912i
\(929\) 17.9400i 0.588591i 0.955714 + 0.294296i \(0.0950850\pi\)
−0.955714 + 0.294296i \(0.904915\pi\)
\(930\) 6.28171 + 7.08307i 0.205986 + 0.232263i
\(931\) 3.87964 0.127150
\(932\) −27.4338 4.97847i −0.898624 0.163075i
\(933\) −15.3655 15.3655i −0.503043 0.503043i
\(934\) 3.34409 + 10.6990i 0.109422 + 0.350082i
\(935\) 39.5294 + 15.0068i 1.29275 + 0.490773i
\(936\) 20.5854 + 16.0417i 0.672855 + 0.524341i
\(937\) 7.24822 + 7.24822i 0.236789 + 0.236789i 0.815519 0.578730i \(-0.196452\pi\)
−0.578730 + 0.815519i \(0.696452\pi\)
\(938\) 13.8576 + 7.25778i 0.452467 + 0.236975i
\(939\) 14.8423i 0.484360i
\(940\) −14.2836 + 3.54167i −0.465881 + 0.115516i
\(941\) 31.3685i 1.02259i 0.859407 + 0.511293i \(0.170833\pi\)
−0.859407 + 0.511293i \(0.829167\pi\)
\(942\) 13.2208 25.2430i 0.430756 0.822462i
\(943\) −4.87460 4.87460i −0.158739 0.158739i
\(944\) −29.7463 11.1639i −0.968159 0.363354i
\(945\) 9.98348 4.48915i 0.324763 0.146032i
\(946\) 0.874923 0.273466i 0.0284462 0.00889116i
\(947\) 10.5999 + 10.5999i 0.344450 + 0.344450i 0.858037 0.513587i \(-0.171684\pi\)
−0.513587 + 0.858037i \(0.671684\pi\)
\(948\) −24.4463 4.43631i −0.793978 0.144085i
\(949\) 9.18919 0.298294
\(950\) −9.73280 25.6487i −0.315774 0.832152i
\(951\) 7.23026i 0.234457i
\(952\) −1.21605 9.80277i −0.0394125 0.317710i
\(953\) 6.64018 6.64018i 0.215097 0.215097i −0.591332 0.806428i \(-0.701398\pi\)
0.806428 + 0.591332i \(0.201398\pi\)
\(954\) −31.8935 + 9.96864i −1.03259 + 0.322747i
\(955\) 0.411541 + 0.915232i 0.0133172 + 0.0296162i
\(956\) −5.07682 7.32794i −0.164196 0.237002i
\(957\) 21.3435 21.3435i 0.689936 0.689936i
\(958\) 37.8835 + 19.8411i 1.22396 + 0.641037i
\(959\) −5.95131 −0.192178
\(960\) 2.00029 17.1686i 0.0645591 0.554113i
\(961\) 21.3998 0.690317
\(962\) 5.38598 + 2.82085i 0.173651 + 0.0909478i
\(963\) 8.82784 8.82784i 0.284473 0.284473i
\(964\) 6.66697 + 9.62317i 0.214729 + 0.309941i
\(965\) 2.24653 5.91760i 0.0723184 0.190494i
\(966\) 1.21590 0.380042i 0.0391209 0.0122277i
\(967\) −29.9303 + 29.9303i −0.962495 + 0.962495i −0.999322 0.0368270i \(-0.988275\pi\)
0.0368270 + 0.999322i \(0.488275\pi\)
\(968\) −6.37763 51.4110i −0.204985 1.65241i
\(969\) 13.0918i 0.420568i
\(970\) −39.4027 44.4293i −1.26514 1.42654i
\(971\) −27.5224 −0.883237 −0.441618 0.897203i \(-0.645595\pi\)
−0.441618 + 0.897203i \(0.645595\pi\)
\(972\) −31.6933 5.75145i −1.01656 0.184478i
\(973\) 15.3690 + 15.3690i 0.492706 + 0.492706i
\(974\) −10.6893 + 3.34106i −0.342508 + 0.107055i
\(975\) 14.3163 16.1379i 0.458490 0.516825i
\(976\) 15.7397 + 5.90718i 0.503817 + 0.189084i
\(977\) 16.9569 + 16.9569i 0.542499 + 0.542499i 0.924261 0.381762i \(-0.124682\pi\)
−0.381762 + 0.924261i \(0.624682\pi\)
\(978\) −6.15899 + 11.7596i −0.196943 + 0.376032i
\(979\) 10.6441i 0.340188i
\(980\) −2.30828 + 3.83038i −0.0737354 + 0.122357i
\(981\) 38.3541i 1.22455i
\(982\) −14.1206 7.39551i −0.450606 0.236000i
\(983\) −29.2243 29.2243i −0.932109 0.932109i 0.0657283 0.997838i \(-0.479063\pi\)
−0.997838 + 0.0657283i \(0.979063\pi\)
\(984\) 15.9406 + 12.4221i 0.508168 + 0.396004i
\(985\) −10.1821 + 26.8208i −0.324430 + 0.854583i
\(986\) 8.50100 + 27.1980i 0.270727 + 0.866159i
\(987\) 2.24829 + 2.24829i 0.0715638 + 0.0715638i
\(988\) −34.0907 6.18652i −1.08457 0.196819i
\(989\) −0.111604 −0.00354881
\(990\) −2.11761 + 35.3167i −0.0673021 + 1.12244i
\(991\) 17.2817i 0.548972i −0.961591 0.274486i \(-0.911492\pi\)
0.961591 0.274486i \(-0.0885077\pi\)
\(992\) 11.6793 + 13.0690i 0.370817 + 0.414943i
\(993\) −4.64961 + 4.64961i −0.147551 + 0.147551i
\(994\) −1.20458 3.85391i −0.0382069 0.122239i
\(995\) −37.0027 + 16.6386i −1.17307 + 0.527478i
\(996\) −8.72375 + 6.04384i −0.276422 + 0.191506i
\(997\) 1.00560 1.00560i 0.0318476 0.0318476i −0.691004 0.722851i \(-0.742831\pi\)
0.722851 + 0.691004i \(0.242831\pi\)
\(998\) 4.61995 8.82109i 0.146242 0.279227i
\(999\) −4.71324 −0.149120
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 280.2.w.a.267.6 yes 72
4.3 odd 2 1120.2.bi.a.687.11 72
5.3 odd 4 inner 280.2.w.a.43.14 yes 72
8.3 odd 2 inner 280.2.w.a.267.14 yes 72
8.5 even 2 1120.2.bi.a.687.12 72
20.3 even 4 1120.2.bi.a.463.12 72
40.3 even 4 inner 280.2.w.a.43.6 72
40.13 odd 4 1120.2.bi.a.463.11 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.w.a.43.6 72 40.3 even 4 inner
280.2.w.a.43.14 yes 72 5.3 odd 4 inner
280.2.w.a.267.6 yes 72 1.1 even 1 trivial
280.2.w.a.267.14 yes 72 8.3 odd 2 inner
1120.2.bi.a.463.11 72 40.13 odd 4
1120.2.bi.a.463.12 72 20.3 even 4
1120.2.bi.a.687.11 72 4.3 odd 2
1120.2.bi.a.687.12 72 8.5 even 2