Properties

Label 756.2.cf.a.659.18
Level $756$
Weight $2$
Character 756.659
Analytic conductor $6.037$
Analytic rank $0$
Dimension $648$
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] = [756,2,Mod(155,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.cf (of order \(18\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(108\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 659.18
Character \(\chi\) \(=\) 756.659
Dual form 756.2.cf.a.491.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20815 + 0.735107i) q^{2} +(-0.0154386 - 1.73198i) q^{3} +(0.919237 - 1.77623i) q^{4} +(0.565100 - 1.55260i) q^{5} +(1.29184 + 2.08114i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(0.195148 + 2.82169i) q^{8} +(-2.99952 + 0.0534788i) q^{9} +O(q^{10})\) \(q+(-1.20815 + 0.735107i) q^{2} +(-0.0154386 - 1.73198i) q^{3} +(0.919237 - 1.77623i) q^{4} +(0.565100 - 1.55260i) q^{5} +(1.29184 + 2.08114i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(0.195148 + 2.82169i) q^{8} +(-2.99952 + 0.0534788i) q^{9} +(0.458603 + 2.29118i) q^{10} +(-1.46920 + 0.534745i) q^{11} +(-3.09060 - 1.56468i) q^{12} +(-3.24265 + 2.72090i) q^{13} +(1.31744 - 0.514146i) q^{14} +(-2.69780 - 0.954773i) q^{15} +(-2.31001 - 3.26556i) q^{16} +(-7.00335 + 4.04339i) q^{17} +(3.58455 - 2.26958i) q^{18} +(3.42098 + 1.97510i) q^{19} +(-2.23832 - 2.43096i) q^{20} +(-0.285551 + 1.70835i) q^{21} +(1.38191 - 1.72607i) q^{22} +(-1.09268 - 6.19691i) q^{23} +(4.88410 - 0.381556i) q^{24} +(1.73899 + 1.45919i) q^{25} +(1.91744 - 5.67094i) q^{26} +(0.138933 + 5.19429i) q^{27} +(-1.21371 + 1.58962i) q^{28} +(-4.72272 + 5.62832i) q^{29} +(3.96120 - 0.829664i) q^{30} +(5.25140 - 0.925964i) q^{31} +(5.19136 + 2.24717i) q^{32} +(0.948851 + 2.53637i) q^{33} +(5.48876 - 10.0332i) q^{34} +(-0.826121 + 1.43088i) q^{35} +(-2.66228 + 5.37701i) q^{36} +(-2.34082 - 4.05441i) q^{37} +(-5.58495 + 0.128570i) q^{38} +(4.76262 + 5.57420i) q^{39} +(4.49123 + 1.29155i) q^{40} +(3.60168 + 4.29231i) q^{41} +(-0.910831 - 2.27385i) q^{42} +(-0.952210 - 2.61617i) q^{43} +(-0.400710 + 3.10120i) q^{44} +(-1.61200 + 4.68728i) q^{45} +(5.87551 + 6.68354i) q^{46} +(0.239097 - 1.35599i) q^{47} +(-5.62022 + 4.05131i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-3.17362 - 0.484568i) q^{50} +(7.11120 + 12.0673i) q^{51} +(1.85220 + 8.26085i) q^{52} +8.39705i q^{53} +(-3.98621 - 6.17334i) q^{54} +2.58326i q^{55} +(0.297797 - 2.81271i) q^{56} +(3.36803 - 5.95556i) q^{57} +(1.56832 - 10.2715i) q^{58} +(-11.2209 - 4.08408i) q^{59} +(-4.17582 + 3.91426i) q^{60} +(1.87298 - 10.6222i) q^{61} +(-5.66378 + 4.97904i) q^{62} +(2.96324 + 0.468195i) q^{63} +(-7.92383 + 1.10129i) q^{64} +(2.39205 + 6.57211i) q^{65} +(-3.01085 - 2.36680i) q^{66} +(0.894801 + 1.06638i) q^{67} +(0.744261 + 16.1564i) q^{68} +(-10.7161 + 1.98818i) q^{69} +(-0.0537767 - 2.33601i) q^{70} +(4.18994 + 7.25719i) q^{71} +(-0.736252 - 8.45328i) q^{72} +(1.37971 - 2.38973i) q^{73} +(5.80847 + 3.17757i) q^{74} +(2.50044 - 3.03443i) q^{75} +(6.65293 - 4.26087i) q^{76} +(1.53974 - 0.271497i) q^{77} +(-9.85157 - 3.23342i) q^{78} +(-6.76929 + 8.06733i) q^{79} +(-6.37549 + 1.74115i) q^{80} +(8.99428 - 0.320822i) q^{81} +(-7.50666 - 2.53813i) q^{82} +(-13.3029 - 11.1624i) q^{83} +(2.77194 + 2.07758i) q^{84} +(2.32017 + 13.1583i) q^{85} +(3.07358 + 2.46075i) q^{86} +(9.82106 + 8.09278i) q^{87} +(-1.79559 - 4.04127i) q^{88} +(-14.3593 - 8.29033i) q^{89} +(-1.49812 - 6.84792i) q^{90} +(3.66586 - 2.11649i) q^{91} +(-12.0116 - 3.75557i) q^{92} +(-1.68483 - 9.08104i) q^{93} +(0.707931 + 1.81399i) q^{94} +(4.99974 - 4.19528i) q^{95} +(3.81191 - 9.02604i) q^{96} +(-11.0251 + 4.01281i) q^{97} +(-1.38671 + 0.277564i) q^{98} +(4.37830 - 1.68255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q+O(q^{10}) \) Copy content Toggle raw display \( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20815 + 0.735107i −0.854289 + 0.519799i
\(3\) −0.0154386 1.73198i −0.00891349 0.999960i
\(4\) 0.919237 1.77623i 0.459618 0.888117i
\(5\) 0.565100 1.55260i 0.252721 0.694344i −0.746849 0.664994i \(-0.768434\pi\)
0.999569 0.0293499i \(-0.00934370\pi\)
\(6\) 1.29184 + 2.08114i 0.527393 + 0.849622i
\(7\) −0.984808 0.173648i −0.372222 0.0656328i
\(8\) 0.195148 + 2.82169i 0.0689953 + 0.997617i
\(9\) −2.99952 + 0.0534788i −0.999841 + 0.0178263i
\(10\) 0.458603 + 2.29118i 0.145023 + 0.724534i
\(11\) −1.46920 + 0.534745i −0.442980 + 0.161232i −0.553874 0.832601i \(-0.686851\pi\)
0.110894 + 0.993832i \(0.464629\pi\)
\(12\) −3.09060 1.56468i −0.892178 0.451684i
\(13\) −3.24265 + 2.72090i −0.899348 + 0.754643i −0.970063 0.242854i \(-0.921916\pi\)
0.0707148 + 0.997497i \(0.477472\pi\)
\(14\) 1.31744 0.514146i 0.352101 0.137411i
\(15\) −2.69780 0.954773i −0.696569 0.246521i
\(16\) −2.31001 3.26556i −0.577502 0.816389i
\(17\) −7.00335 + 4.04339i −1.69856 + 0.980666i −0.751436 + 0.659806i \(0.770638\pi\)
−0.947127 + 0.320859i \(0.896028\pi\)
\(18\) 3.58455 2.26958i 0.844887 0.534945i
\(19\) 3.42098 + 1.97510i 0.784826 + 0.453119i 0.838138 0.545459i \(-0.183644\pi\)
−0.0533120 + 0.998578i \(0.516978\pi\)
\(20\) −2.23832 2.43096i −0.500503 0.543578i
\(21\) −0.285551 + 1.70835i −0.0623124 + 0.372793i
\(22\) 1.38191 1.72607i 0.294625 0.367999i
\(23\) −1.09268 6.19691i −0.227840 1.29214i −0.857181 0.515016i \(-0.827786\pi\)
0.629341 0.777129i \(-0.283325\pi\)
\(24\) 4.88410 0.381556i 0.996962 0.0778848i
\(25\) 1.73899 + 1.45919i 0.347799 + 0.291838i
\(26\) 1.91744 5.67094i 0.376040 1.11216i
\(27\) 0.138933 + 5.19429i 0.0267376 + 0.999642i
\(28\) −1.21371 + 1.58962i −0.229370 + 0.300411i
\(29\) −4.72272 + 5.62832i −0.876988 + 1.04515i 0.121629 + 0.992576i \(0.461188\pi\)
−0.998617 + 0.0525775i \(0.983256\pi\)
\(30\) 3.96120 0.829664i 0.723213 0.151475i
\(31\) 5.25140 0.925964i 0.943179 0.166308i 0.319146 0.947706i \(-0.396604\pi\)
0.624033 + 0.781398i \(0.285493\pi\)
\(32\) 5.19136 + 2.24717i 0.917712 + 0.397247i
\(33\) 0.948851 + 2.53637i 0.165174 + 0.441525i
\(34\) 5.48876 10.0332i 0.941314 1.72068i
\(35\) −0.826121 + 1.43088i −0.139640 + 0.241864i
\(36\) −2.66228 + 5.37701i −0.443713 + 0.896169i
\(37\) −2.34082 4.05441i −0.384828 0.666541i 0.606918 0.794765i \(-0.292406\pi\)
−0.991745 + 0.128224i \(0.959072\pi\)
\(38\) −5.58495 + 0.128570i −0.905999 + 0.0208568i
\(39\) 4.76262 + 5.57420i 0.762629 + 0.892586i
\(40\) 4.49123 + 1.29155i 0.710126 + 0.204212i
\(41\) 3.60168 + 4.29231i 0.562488 + 0.670347i 0.970071 0.242821i \(-0.0780729\pi\)
−0.407583 + 0.913168i \(0.633628\pi\)
\(42\) −0.910831 2.27385i −0.140544 0.350862i
\(43\) −0.952210 2.61617i −0.145211 0.398963i 0.845670 0.533706i \(-0.179201\pi\)
−0.990881 + 0.134743i \(0.956979\pi\)
\(44\) −0.400710 + 3.10120i −0.0604093 + 0.467523i
\(45\) −1.61200 + 4.68728i −0.240303 + 0.698739i
\(46\) 5.87551 + 6.68354i 0.866297 + 0.985434i
\(47\) 0.239097 1.35599i 0.0348759 0.197791i −0.962392 0.271666i \(-0.912425\pi\)
0.997268 + 0.0738749i \(0.0235365\pi\)
\(48\) −5.62022 + 4.05131i −0.811209 + 0.584756i
\(49\) 0.939693 + 0.342020i 0.134242 + 0.0488600i
\(50\) −3.17362 0.484568i −0.448817 0.0685283i
\(51\) 7.11120 + 12.0673i 0.995767 + 1.68975i
\(52\) 1.85220 + 8.26085i 0.256854 + 1.14557i
\(53\) 8.39705i 1.15342i 0.816948 + 0.576711i \(0.195664\pi\)
−0.816948 + 0.576711i \(0.804336\pi\)
\(54\) −3.98621 6.17334i −0.542455 0.840085i
\(55\) 2.58326i 0.348327i
\(56\) 0.297797 2.81271i 0.0397948 0.375864i
\(57\) 3.36803 5.95556i 0.446106 0.788834i
\(58\) 1.56832 10.2715i 0.205931 1.34872i
\(59\) −11.2209 4.08408i −1.46084 0.531701i −0.515241 0.857045i \(-0.672298\pi\)
−0.945596 + 0.325344i \(0.894520\pi\)
\(60\) −4.17582 + 3.91426i −0.539096 + 0.505329i
\(61\) 1.87298 10.6222i 0.239811 1.36003i −0.592431 0.805621i \(-0.701832\pi\)
0.832242 0.554412i \(-0.187057\pi\)
\(62\) −5.66378 + 4.97904i −0.719301 + 0.632339i
\(63\) 2.96324 + 0.468195i 0.373333 + 0.0589871i
\(64\) −7.92383 + 1.10129i −0.990479 + 0.137662i
\(65\) 2.39205 + 6.57211i 0.296698 + 0.815171i
\(66\) −3.01085 2.36680i −0.370610 0.291333i
\(67\) 0.894801 + 1.06638i 0.109317 + 0.130279i 0.817929 0.575320i \(-0.195122\pi\)
−0.708611 + 0.705599i \(0.750678\pi\)
\(68\) 0.744261 + 16.1564i 0.0902549 + 1.95925i
\(69\) −10.7161 + 1.98818i −1.29006 + 0.239348i
\(70\) −0.0537767 2.33601i −0.00642754 0.279206i
\(71\) 4.18994 + 7.25719i 0.497255 + 0.861270i 0.999995 0.00316730i \(-0.00100818\pi\)
−0.502740 + 0.864437i \(0.667675\pi\)
\(72\) −0.736252 8.45328i −0.0867681 0.996229i
\(73\) 1.37971 2.38973i 0.161483 0.279697i −0.773918 0.633286i \(-0.781706\pi\)
0.935401 + 0.353589i \(0.115039\pi\)
\(74\) 5.80847 + 3.17757i 0.675221 + 0.369386i
\(75\) 2.50044 3.03443i 0.288726 0.350386i
\(76\) 6.65293 4.26087i 0.763143 0.488755i
\(77\) 1.53974 0.271497i 0.175469 0.0309400i
\(78\) −9.85157 3.23342i −1.11547 0.366112i
\(79\) −6.76929 + 8.06733i −0.761605 + 0.907645i −0.997948 0.0640242i \(-0.979607\pi\)
0.236343 + 0.971670i \(0.424051\pi\)
\(80\) −6.37549 + 1.74115i −0.712802 + 0.194667i
\(81\) 8.99428 0.320822i 0.999364 0.0356469i
\(82\) −7.50666 2.53813i −0.828972 0.280289i
\(83\) −13.3029 11.1624i −1.46018 1.22524i −0.924705 0.380683i \(-0.875689\pi\)
−0.535473 0.844552i \(-0.679867\pi\)
\(84\) 2.77194 + 2.07758i 0.302443 + 0.226683i
\(85\) 2.32017 + 13.1583i 0.251658 + 1.42722i
\(86\) 3.07358 + 2.46075i 0.331432 + 0.265349i
\(87\) 9.82106 + 8.09278i 1.05293 + 0.867637i
\(88\) −1.79559 4.04127i −0.191411 0.430800i
\(89\) −14.3593 8.29033i −1.52208 0.878773i −0.999660 0.0260850i \(-0.991696\pi\)
−0.522420 0.852688i \(-0.674971\pi\)
\(90\) −1.49812 6.84792i −0.157916 0.721834i
\(91\) 3.66586 2.11649i 0.384287 0.221868i
\(92\) −12.0116 3.75557i −1.25229 0.391545i
\(93\) −1.68483 9.08104i −0.174708 0.941660i
\(94\) 0.707931 + 1.81399i 0.0730175 + 0.187099i
\(95\) 4.99974 4.19528i 0.512962 0.430426i
\(96\) 3.81191 9.02604i 0.389051 0.921216i
\(97\) −11.0251 + 4.01281i −1.11943 + 0.407439i −0.834444 0.551092i \(-0.814211\pi\)
−0.284986 + 0.958532i \(0.591989\pi\)
\(98\) −1.38671 + 0.277564i −0.140079 + 0.0280382i
\(99\) 4.37830 1.68255i 0.440036 0.169103i
\(100\) 4.19041 1.74752i 0.419041 0.174752i
\(101\) −7.01688 1.23727i −0.698206 0.123113i −0.186732 0.982411i \(-0.559789\pi\)
−0.511475 + 0.859298i \(0.670901\pi\)
\(102\) −17.4621 9.35153i −1.72900 0.925939i
\(103\) −3.01638 + 8.28744i −0.297213 + 0.816585i 0.697750 + 0.716341i \(0.254185\pi\)
−0.994963 + 0.100244i \(0.968038\pi\)
\(104\) −8.31033 8.61875i −0.814895 0.845138i
\(105\) 2.49102 + 1.40874i 0.243099 + 0.137479i
\(106\) −6.17272 10.1449i −0.599548 0.985356i
\(107\) −3.65217 −0.353069 −0.176534 0.984294i \(-0.556489\pi\)
−0.176534 + 0.984294i \(0.556489\pi\)
\(108\) 9.35399 + 4.52801i 0.900088 + 0.435708i
\(109\) 6.69227 0.641003 0.320502 0.947248i \(-0.396149\pi\)
0.320502 + 0.947248i \(0.396149\pi\)
\(110\) −1.89897 3.12096i −0.181060 0.297572i
\(111\) −6.98603 + 4.11684i −0.663084 + 0.390754i
\(112\) 1.70786 + 3.61707i 0.161377 + 0.341781i
\(113\) −2.96759 + 8.15338i −0.279167 + 0.767005i 0.718291 + 0.695743i \(0.244925\pi\)
−0.997458 + 0.0712619i \(0.977297\pi\)
\(114\) 0.308905 + 9.67105i 0.0289316 + 0.905777i
\(115\) −10.2388 1.80538i −0.954773 0.168352i
\(116\) 5.65591 + 13.5624i 0.525138 + 1.25924i
\(117\) 9.58088 8.33482i 0.885753 0.770555i
\(118\) 16.5587 3.31440i 1.52435 0.305115i
\(119\) 7.59908 2.76584i 0.696607 0.253544i
\(120\) 2.16760 7.79867i 0.197874 0.711918i
\(121\) −6.55390 + 5.49937i −0.595809 + 0.499943i
\(122\) 5.54561 + 14.2100i 0.502076 + 1.28651i
\(123\) 7.37860 6.30431i 0.665306 0.568440i
\(124\) 3.18255 10.1789i 0.285802 0.914091i
\(125\) 10.4027 6.00598i 0.930442 0.537191i
\(126\) −3.92420 + 1.61265i −0.349596 + 0.143666i
\(127\) −9.14140 5.27779i −0.811168 0.468328i 0.0361930 0.999345i \(-0.488477\pi\)
−0.847361 + 0.531016i \(0.821810\pi\)
\(128\) 8.76359 7.15539i 0.774599 0.632453i
\(129\) −4.51647 + 1.68960i −0.397653 + 0.148761i
\(130\) −7.72116 6.18166i −0.677190 0.542168i
\(131\) 0.497411 + 2.82096i 0.0434590 + 0.246468i 0.998796 0.0490492i \(-0.0156191\pi\)
−0.955337 + 0.295517i \(0.904508\pi\)
\(132\) 5.37740 + 0.646145i 0.468043 + 0.0562397i
\(133\) −3.02603 2.53914i −0.262390 0.220172i
\(134\) −1.86496 0.630572i −0.161108 0.0544732i
\(135\) 8.14317 + 2.71959i 0.700853 + 0.234065i
\(136\) −12.7759 18.9722i −1.09552 1.62685i
\(137\) −0.381352 + 0.454478i −0.0325811 + 0.0388287i −0.782089 0.623167i \(-0.785846\pi\)
0.749508 + 0.661995i \(0.230290\pi\)
\(138\) 11.4851 10.2795i 0.977673 0.875046i
\(139\) 18.1038 3.19219i 1.53555 0.270758i 0.659025 0.752121i \(-0.270969\pi\)
0.876522 + 0.481362i \(0.159858\pi\)
\(140\) 1.78218 + 2.78271i 0.150622 + 0.235181i
\(141\) −2.35224 0.393177i −0.198094 0.0331115i
\(142\) −10.3969 5.68770i −0.872486 0.477301i
\(143\) 3.30910 5.73154i 0.276721 0.479295i
\(144\) 7.10356 + 9.67158i 0.591963 + 0.805965i
\(145\) 6.06972 + 10.5131i 0.504063 + 0.873063i
\(146\) 0.0898129 + 3.90138i 0.00743297 + 0.322881i
\(147\) 0.577865 1.63281i 0.0476615 0.134672i
\(148\) −9.35334 + 0.430871i −0.768840 + 0.0354174i
\(149\) 2.55929 + 3.05005i 0.209665 + 0.249870i 0.860621 0.509247i \(-0.170076\pi\)
−0.650955 + 0.759116i \(0.725631\pi\)
\(150\) −0.790267 + 5.50413i −0.0645251 + 0.449410i
\(151\) −1.11752 3.07037i −0.0909427 0.249863i 0.885879 0.463915i \(-0.153556\pi\)
−0.976822 + 0.214052i \(0.931334\pi\)
\(152\) −4.90552 + 10.0384i −0.397890 + 0.814219i
\(153\) 20.7905 12.5028i 1.68081 1.01079i
\(154\) −1.66065 + 1.45988i −0.133819 + 0.117640i
\(155\) 1.52992 8.67659i 0.122886 0.696920i
\(156\) 14.2790 3.33551i 1.14324 0.267055i
\(157\) −7.16688 2.60853i −0.571980 0.208184i 0.0398057 0.999207i \(-0.487326\pi\)
−0.611785 + 0.791024i \(0.709548\pi\)
\(158\) 2.24795 14.7227i 0.178837 1.17127i
\(159\) 14.5435 0.129639i 1.15338 0.0102810i
\(160\) 6.42259 6.79023i 0.507751 0.536815i
\(161\) 6.29251i 0.495919i
\(162\) −10.6306 + 6.99935i −0.835217 + 0.549921i
\(163\) 5.05964i 0.396302i 0.980172 + 0.198151i \(0.0634936\pi\)
−0.980172 + 0.198151i \(0.936506\pi\)
\(164\) 10.9349 2.45177i 0.853876 0.191451i
\(165\) 4.47417 0.0398820i 0.348313 0.00310481i
\(166\) 24.2774 + 3.70683i 1.88429 + 0.287706i
\(167\) 2.17925 + 0.793181i 0.168635 + 0.0613782i 0.424958 0.905213i \(-0.360289\pi\)
−0.256323 + 0.966591i \(0.582511\pi\)
\(168\) −4.87615 0.472355i −0.376203 0.0364430i
\(169\) 0.854012 4.84334i 0.0656933 0.372565i
\(170\) −12.4759 14.1916i −0.956856 1.08845i
\(171\) −10.3669 5.74141i −0.792779 0.439057i
\(172\) −5.52224 0.713537i −0.421067 0.0544067i
\(173\) −1.01181 2.77993i −0.0769267 0.211354i 0.895268 0.445528i \(-0.146984\pi\)
−0.972195 + 0.234173i \(0.924762\pi\)
\(174\) −17.8143 2.55773i −1.35050 0.193901i
\(175\) −1.45919 1.73899i −0.110304 0.131456i
\(176\) 5.14010 + 3.56249i 0.387450 + 0.268533i
\(177\) −6.90031 + 19.4975i −0.518659 + 1.46552i
\(178\) 23.4424 0.539662i 1.75708 0.0404494i
\(179\) −11.1364 19.2889i −0.832377 1.44172i −0.896149 0.443754i \(-0.853646\pi\)
0.0637721 0.997964i \(-0.479687\pi\)
\(180\) 6.84389 + 7.17201i 0.510114 + 0.534570i
\(181\) −3.29282 + 5.70333i −0.244753 + 0.423925i −0.962062 0.272830i \(-0.912040\pi\)
0.717309 + 0.696755i \(0.245374\pi\)
\(182\) −2.87306 + 5.25183i −0.212965 + 0.389291i
\(183\) −18.4264 3.07998i −1.36212 0.227678i
\(184\) 17.2725 4.29252i 1.27335 0.316449i
\(185\) −7.61768 + 1.34320i −0.560063 + 0.0987542i
\(186\) 8.71105 + 9.73270i 0.638725 + 0.713636i
\(187\) 8.12714 9.68555i 0.594315 0.708277i
\(188\) −2.18876 1.67116i −0.159632 0.121882i
\(189\) 0.765158 5.13951i 0.0556570 0.373844i
\(190\) −2.95644 + 8.74385i −0.214483 + 0.634346i
\(191\) 16.0210 + 13.4433i 1.15924 + 0.972720i 0.999895 0.0145029i \(-0.00461659\pi\)
0.159347 + 0.987223i \(0.449061\pi\)
\(192\) 2.02975 + 13.7069i 0.146485 + 0.989213i
\(193\) −0.0180859 0.102570i −0.00130185 0.00738317i 0.984150 0.177339i \(-0.0567488\pi\)
−0.985452 + 0.169955i \(0.945638\pi\)
\(194\) 10.3701 12.9527i 0.744530 0.929949i
\(195\) 11.3459 4.24446i 0.812494 0.303952i
\(196\) 1.47131 1.35472i 0.105093 0.0967654i
\(197\) 17.7001 + 10.2191i 1.26108 + 0.728084i 0.973283 0.229608i \(-0.0737444\pi\)
0.287795 + 0.957692i \(0.407078\pi\)
\(198\) −4.05277 + 5.25128i −0.288018 + 0.373193i
\(199\) −5.08140 + 2.93375i −0.360211 + 0.207968i −0.669173 0.743106i \(-0.733352\pi\)
0.308962 + 0.951074i \(0.400018\pi\)
\(200\) −3.77801 + 5.19165i −0.267146 + 0.367105i
\(201\) 1.83314 1.56624i 0.129300 0.110474i
\(202\) 9.38695 3.66336i 0.660463 0.257753i
\(203\) 5.62832 4.72272i 0.395031 0.331470i
\(204\) 27.9711 1.53848i 1.95837 0.107715i
\(205\) 8.69956 3.16638i 0.607603 0.221150i
\(206\) −2.44792 12.2298i −0.170555 0.852091i
\(207\) 3.60893 + 18.5293i 0.250838 + 1.28788i
\(208\) 16.3758 + 4.30374i 1.13546 + 0.298410i
\(209\) −6.08227 1.07247i −0.420719 0.0741842i
\(210\) −4.04509 + 0.129205i −0.279138 + 0.00891598i
\(211\) −5.89874 + 16.2067i −0.406086 + 1.11571i 0.553144 + 0.833086i \(0.313428\pi\)
−0.959230 + 0.282627i \(0.908794\pi\)
\(212\) 14.9151 + 7.71887i 1.02437 + 0.530134i
\(213\) 12.5046 7.36894i 0.856804 0.504912i
\(214\) 4.41236 2.68474i 0.301623 0.183525i
\(215\) −4.59997 −0.313715
\(216\) −14.6296 + 1.40568i −0.995416 + 0.0956445i
\(217\) −5.33241 −0.361988
\(218\) −8.08524 + 4.91953i −0.547602 + 0.333193i
\(219\) −4.16028 2.35274i −0.281125 0.158984i
\(220\) 4.58848 + 2.37463i 0.309355 + 0.160098i
\(221\) 11.7077 32.1667i 0.787547 2.16377i
\(222\) 5.41383 10.1092i 0.363352 0.678487i
\(223\) −17.5128 3.08797i −1.17274 0.206786i −0.446859 0.894604i \(-0.647457\pi\)
−0.725883 + 0.687818i \(0.758569\pi\)
\(224\) −4.72228 3.11450i −0.315520 0.208096i
\(225\) −5.29419 4.28387i −0.352946 0.285591i
\(226\) −2.40832 12.0320i −0.160199 0.800354i
\(227\) −15.9139 + 5.79220i −1.05624 + 0.384442i −0.811016 0.585024i \(-0.801085\pi\)
−0.245228 + 0.969465i \(0.578863\pi\)
\(228\) −7.48246 11.4570i −0.495538 0.758756i
\(229\) −0.338886 + 0.284359i −0.0223942 + 0.0187910i −0.653916 0.756567i \(-0.726875\pi\)
0.631522 + 0.775358i \(0.282431\pi\)
\(230\) 13.6971 5.34545i 0.903161 0.352468i
\(231\) −0.493999 2.66260i −0.0325028 0.175186i
\(232\) −16.8030 12.2277i −1.10317 0.802787i
\(233\) 16.3996 9.46829i 1.07437 0.620288i 0.144998 0.989432i \(-0.453682\pi\)
0.929372 + 0.369144i \(0.120349\pi\)
\(234\) −5.44812 + 17.1127i −0.356155 + 1.11869i
\(235\) −1.97019 1.13749i −0.128521 0.0742017i
\(236\) −17.5689 + 16.1767i −1.14364 + 1.05301i
\(237\) 14.0770 + 11.5997i 0.914398 + 0.753484i
\(238\) −7.14762 + 8.92768i −0.463311 + 0.578695i
\(239\) −1.70811 9.68719i −0.110489 0.626612i −0.988885 0.148680i \(-0.952498\pi\)
0.878397 0.477932i \(-0.158614\pi\)
\(240\) 3.11407 + 11.0154i 0.201013 + 0.711038i
\(241\) −2.50601 2.10279i −0.161427 0.135453i 0.558496 0.829507i \(-0.311378\pi\)
−0.719923 + 0.694054i \(0.755823\pi\)
\(242\) 3.87544 11.4619i 0.249123 0.736796i
\(243\) −0.694517 15.5730i −0.0445533 0.999007i
\(244\) −17.1458 13.0912i −1.09765 0.838076i
\(245\) 1.06204 1.26569i 0.0678513 0.0808620i
\(246\) −4.28010 + 13.0406i −0.272889 + 0.831438i
\(247\) −16.4671 + 2.90359i −1.04777 + 0.184751i
\(248\) 3.63758 + 14.6371i 0.230987 + 0.929457i
\(249\) −19.1277 + 23.2126i −1.21217 + 1.47104i
\(250\) −8.15291 + 14.9032i −0.515635 + 0.942559i
\(251\) 6.00657 10.4037i 0.379131 0.656675i −0.611805 0.791009i \(-0.709556\pi\)
0.990936 + 0.134334i \(0.0428895\pi\)
\(252\) 3.55554 4.83302i 0.223978 0.304452i
\(253\) 4.91913 + 8.52019i 0.309263 + 0.535660i
\(254\) 14.9239 0.343560i 0.936409 0.0215569i
\(255\) 22.7542 4.22164i 1.42492 0.264369i
\(256\) −5.32772 + 15.0869i −0.332983 + 0.942933i
\(257\) −6.06624 7.22946i −0.378402 0.450962i 0.542907 0.839793i \(-0.317323\pi\)
−0.921309 + 0.388831i \(0.872879\pi\)
\(258\) 4.21452 5.36137i 0.262384 0.333784i
\(259\) 1.60121 + 4.39929i 0.0994945 + 0.273359i
\(260\) 13.8725 + 1.79248i 0.860334 + 0.111165i
\(261\) 13.8649 17.1348i 0.858217 1.06062i
\(262\) −2.67465 3.04248i −0.165240 0.187965i
\(263\) 0.624826 3.54357i 0.0385285 0.218506i −0.959465 0.281829i \(-0.909059\pi\)
0.997993 + 0.0633234i \(0.0201700\pi\)
\(264\) −6.97168 + 3.17233i −0.429077 + 0.195243i
\(265\) 13.0373 + 4.74517i 0.800872 + 0.291494i
\(266\) 5.52243 + 0.843200i 0.338602 + 0.0516999i
\(267\) −14.1370 + 24.9980i −0.865171 + 1.52985i
\(268\) 2.71668 0.609118i 0.165948 0.0372078i
\(269\) 25.8695i 1.57729i −0.614849 0.788645i \(-0.710783\pi\)
0.614849 0.788645i \(-0.289217\pi\)
\(270\) −11.8373 + 2.70044i −0.720397 + 0.164343i
\(271\) 22.2867i 1.35382i −0.736065 0.676911i \(-0.763318\pi\)
0.736065 0.676911i \(-0.236682\pi\)
\(272\) 29.3817 + 13.5296i 1.78153 + 0.820352i
\(273\) −3.72231 6.31653i −0.225285 0.382294i
\(274\) 0.126640 0.829411i 0.00765059 0.0501065i
\(275\) −3.33522 1.21392i −0.201121 0.0732022i
\(276\) −6.31913 + 20.8618i −0.380367 + 1.25574i
\(277\) 0.277840 1.57571i 0.0166938 0.0946751i −0.975323 0.220785i \(-0.929138\pi\)
0.992016 + 0.126110i \(0.0402492\pi\)
\(278\) −19.5255 + 17.1649i −1.17106 + 1.02948i
\(279\) −15.7022 + 3.05829i −0.940065 + 0.183095i
\(280\) −4.19872 2.05182i −0.250922 0.122620i
\(281\) 8.17438 + 22.4589i 0.487642 + 1.33979i 0.902809 + 0.430041i \(0.141501\pi\)
−0.415167 + 0.909745i \(0.636277\pi\)
\(282\) 3.13087 1.25413i 0.186441 0.0746823i
\(283\) −16.1599 19.2586i −0.960604 1.14480i −0.989400 0.145218i \(-0.953612\pi\)
0.0287959 0.999585i \(-0.490833\pi\)
\(284\) 16.7420 0.771237i 0.993456 0.0457645i
\(285\) −7.34334 8.59469i −0.434982 0.509105i
\(286\) 0.215407 + 9.35708i 0.0127373 + 0.553296i
\(287\) −2.80161 4.85253i −0.165374 0.286436i
\(288\) −15.6918 6.46281i −0.924647 0.380825i
\(289\) 24.1980 41.9121i 1.42341 2.46542i
\(290\) −15.0613 8.23943i −0.884432 0.483836i
\(291\) 7.12033 + 19.0333i 0.417401 + 1.11575i
\(292\) −2.97644 4.64742i −0.174183 0.271970i
\(293\) 3.69781 0.652024i 0.216028 0.0380916i −0.0645864 0.997912i \(-0.520573\pi\)
0.280615 + 0.959820i \(0.409462\pi\)
\(294\) 0.502144 + 2.39747i 0.0292856 + 0.139823i
\(295\) −12.6819 + 15.1137i −0.738367 + 0.879952i
\(296\) 10.9835 7.39626i 0.638401 0.429899i
\(297\) −2.98174 7.55716i −0.173018 0.438511i
\(298\) −5.33411 1.80355i −0.308997 0.104477i
\(299\) 20.4044 + 17.1213i 1.18002 + 0.990150i
\(300\) −3.09136 7.23073i −0.178480 0.417466i
\(301\) 0.483449 + 2.74178i 0.0278656 + 0.158033i
\(302\) 3.60718 + 2.88796i 0.207570 + 0.166183i
\(303\) −2.03459 + 12.1722i −0.116884 + 0.699276i
\(304\) −1.45268 15.7339i −0.0833167 0.902401i
\(305\) −15.4336 8.91060i −0.883726 0.510219i
\(306\) −15.9271 + 30.3884i −0.910491 + 1.73719i
\(307\) −13.1506 + 7.59249i −0.750543 + 0.433326i −0.825890 0.563831i \(-0.809327\pi\)
0.0753472 + 0.997157i \(0.475993\pi\)
\(308\) 0.933140 2.98450i 0.0531706 0.170058i
\(309\) 14.4003 + 5.09637i 0.819202 + 0.289922i
\(310\) 4.52985 + 11.6072i 0.257278 + 0.659247i
\(311\) 21.4201 17.9736i 1.21462 1.01919i 0.215537 0.976496i \(-0.430850\pi\)
0.999088 0.0426955i \(-0.0135945\pi\)
\(312\) −14.7992 + 14.5264i −0.837841 + 0.822396i
\(313\) −5.11983 + 1.86347i −0.289390 + 0.105329i −0.482636 0.875821i \(-0.660321\pi\)
0.193246 + 0.981150i \(0.438098\pi\)
\(314\) 10.5762 2.11693i 0.596849 0.119466i
\(315\) 2.40145 4.33615i 0.135306 0.244314i
\(316\) 8.10688 + 19.4396i 0.456047 + 1.09356i
\(317\) −31.9544 5.63442i −1.79474 0.316461i −0.825837 0.563909i \(-0.809297\pi\)
−0.968901 + 0.247448i \(0.920408\pi\)
\(318\) −17.4754 + 10.8477i −0.979973 + 0.608307i
\(319\) 3.92890 10.7946i 0.219976 0.604380i
\(320\) −2.76789 + 12.9249i −0.154730 + 0.722523i
\(321\) 0.0563844 + 6.32549i 0.00314707 + 0.353055i
\(322\) −4.62566 7.60227i −0.257778 0.423658i
\(323\) −31.9444 −1.77743
\(324\) 7.69802 16.2708i 0.427668 0.903936i
\(325\) −9.60925 −0.533025
\(326\) −3.71938 6.11279i −0.205997 0.338556i
\(327\) −0.103319 11.5909i −0.00571357 0.640978i
\(328\) −11.4087 + 11.0004i −0.629940 + 0.607398i
\(329\) −0.470929 + 1.29387i −0.0259632 + 0.0713332i
\(330\) −5.37613 + 3.33717i −0.295946 + 0.183705i
\(331\) −21.4238 3.77760i −1.17756 0.207636i −0.449584 0.893238i \(-0.648428\pi\)
−0.727976 + 0.685603i \(0.759539\pi\)
\(332\) −32.0555 + 13.3681i −1.75928 + 0.733668i
\(333\) 7.23816 + 12.0361i 0.396648 + 0.659575i
\(334\) −3.21592 + 0.643700i −0.175968 + 0.0352217i
\(335\) 2.16132 0.786656i 0.118085 0.0429796i
\(336\) 6.23834 3.01382i 0.340329 0.164417i
\(337\) −18.7214 + 15.7091i −1.01982 + 0.855730i −0.989605 0.143813i \(-0.954064\pi\)
−0.0302148 + 0.999543i \(0.509619\pi\)
\(338\) 2.52860 + 6.47926i 0.137538 + 0.352425i
\(339\) 14.1673 + 5.01393i 0.769463 + 0.272319i
\(340\) 25.5050 + 7.97446i 1.38320 + 0.432476i
\(341\) −7.22020 + 4.16858i −0.390996 + 0.225741i
\(342\) 16.7453 0.684325i 0.905483 0.0370041i
\(343\) −0.866025 0.500000i −0.0467610 0.0269975i
\(344\) 7.19620 3.19738i 0.387993 0.172391i
\(345\) −2.96881 + 17.7613i −0.159835 + 0.956235i
\(346\) 3.26596 + 2.61477i 0.175579 + 0.140571i
\(347\) −2.84102 16.1122i −0.152514 0.864949i −0.961024 0.276466i \(-0.910837\pi\)
0.808510 0.588483i \(-0.200275\pi\)
\(348\) 23.4025 10.0053i 1.25451 0.536342i
\(349\) −10.0326 8.41832i −0.537031 0.450622i 0.333490 0.942754i \(-0.391774\pi\)
−0.870521 + 0.492131i \(0.836218\pi\)
\(350\) 3.04126 + 1.02830i 0.162562 + 0.0549649i
\(351\) −14.5837 16.4652i −0.778419 0.878849i
\(352\) −8.82880 0.525486i −0.470577 0.0280085i
\(353\) −7.25486 + 8.64600i −0.386137 + 0.460180i −0.923741 0.383017i \(-0.874885\pi\)
0.537604 + 0.843197i \(0.319329\pi\)
\(354\) −5.99612 28.6282i −0.318690 1.52157i
\(355\) 13.6353 2.40426i 0.723684 0.127605i
\(356\) −27.9251 + 17.8846i −1.48003 + 0.947884i
\(357\) −4.90770 13.1188i −0.259743 0.694319i
\(358\) 27.6338 + 15.1173i 1.46049 + 0.798975i
\(359\) −6.94936 + 12.0366i −0.366773 + 0.635270i −0.989059 0.147520i \(-0.952871\pi\)
0.622286 + 0.782790i \(0.286204\pi\)
\(360\) −13.5406 3.63385i −0.713653 0.191520i
\(361\) −1.69795 2.94093i −0.0893656 0.154786i
\(362\) −0.214347 9.31104i −0.0112658 0.489377i
\(363\) 9.62599 + 11.2663i 0.505234 + 0.591329i
\(364\) −0.389579 8.45698i −0.0204195 0.443266i
\(365\) −2.93062 3.49258i −0.153396 0.182810i
\(366\) 24.5259 9.82429i 1.28199 0.513524i
\(367\) 2.53393 + 6.96191i 0.132270 + 0.363409i 0.988093 0.153861i \(-0.0491707\pi\)
−0.855823 + 0.517270i \(0.826948\pi\)
\(368\) −17.7123 + 17.8831i −0.923315 + 0.932222i
\(369\) −11.0329 12.6823i −0.574348 0.660213i
\(370\) 8.21587 7.22259i 0.427123 0.375484i
\(371\) 1.45813 8.26948i 0.0757024 0.429330i
\(372\) −17.6788 5.35498i −0.916603 0.277643i
\(373\) 34.0155 + 12.3806i 1.76125 + 0.641044i 0.999973 0.00737632i \(-0.00234798\pi\)
0.761282 + 0.648421i \(0.224570\pi\)
\(374\) −2.69887 + 17.6759i −0.139555 + 0.913998i
\(375\) −10.5629 17.9245i −0.545463 0.925617i
\(376\) 3.87283 + 0.410039i 0.199726 + 0.0211461i
\(377\) 31.1007i 1.60177i
\(378\) 2.85366 + 6.77175i 0.146777 + 0.348301i
\(379\) 7.32802i 0.376415i 0.982129 + 0.188208i \(0.0602678\pi\)
−0.982129 + 0.188208i \(0.939732\pi\)
\(380\) −2.85585 12.7372i −0.146502 0.653402i
\(381\) −8.99991 + 15.9142i −0.461079 + 0.815311i
\(382\) −29.2380 4.46424i −1.49595 0.228411i
\(383\) 16.6788 + 6.07059i 0.852248 + 0.310193i 0.730957 0.682424i \(-0.239074\pi\)
0.121291 + 0.992617i \(0.461296\pi\)
\(384\) −12.5283 15.0679i −0.639332 0.768931i
\(385\) 0.448579 2.54402i 0.0228617 0.129655i
\(386\) 0.0972505 + 0.110625i 0.00494992 + 0.00563066i
\(387\) 2.99608 + 7.79635i 0.152300 + 0.396311i
\(388\) −3.00699 + 23.2719i −0.152657 + 1.18145i
\(389\) 5.76201 + 15.8310i 0.292145 + 0.802663i 0.995752 + 0.0920735i \(0.0293495\pi\)
−0.703607 + 0.710590i \(0.748428\pi\)
\(390\) −10.5873 + 13.4683i −0.536110 + 0.681996i
\(391\) 32.7089 + 38.9810i 1.65416 + 1.97135i
\(392\) −0.781694 + 2.71826i −0.0394815 + 0.137293i
\(393\) 4.87817 0.905058i 0.246071 0.0456542i
\(394\) −28.8965 + 0.665219i −1.45578 + 0.0335132i
\(395\) 8.70001 + 15.0689i 0.437745 + 0.758196i
\(396\) 1.03609 9.32354i 0.0520655 0.468526i
\(397\) 5.66940 9.81968i 0.284539 0.492836i −0.687958 0.725750i \(-0.741493\pi\)
0.972497 + 0.232914i \(0.0748262\pi\)
\(398\) 3.98246 7.27977i 0.199623 0.364902i
\(399\) −4.35103 + 5.28023i −0.217824 + 0.264342i
\(400\) 0.747974 9.04952i 0.0373987 0.452476i
\(401\) −6.36241 + 1.12186i −0.317723 + 0.0560232i −0.330236 0.943899i \(-0.607128\pi\)
0.0125123 + 0.999922i \(0.496017\pi\)
\(402\) −1.06335 + 3.23981i −0.0530350 + 0.161587i
\(403\) −14.5090 + 17.2911i −0.722743 + 0.861332i
\(404\) −8.64785 + 11.3263i −0.430247 + 0.563504i
\(405\) 4.58456 14.1458i 0.227809 0.702911i
\(406\) −3.32813 + 9.84316i −0.165172 + 0.488508i
\(407\) 5.60720 + 4.70500i 0.277939 + 0.233218i
\(408\) −32.6623 + 22.4205i −1.61702 + 1.10998i
\(409\) 5.30308 + 30.0753i 0.262220 + 1.48713i 0.776835 + 0.629704i \(0.216824\pi\)
−0.514614 + 0.857422i \(0.672065\pi\)
\(410\) −8.18271 + 10.2206i −0.404115 + 0.504757i
\(411\) 0.793035 + 0.653479i 0.0391175 + 0.0322337i
\(412\) 11.9477 + 12.9759i 0.588619 + 0.639277i
\(413\) 10.3412 + 5.97052i 0.508859 + 0.293790i
\(414\) −17.9812 19.7332i −0.883726 0.969834i
\(415\) −24.8482 + 14.3461i −1.21975 + 0.704224i
\(416\) −22.9481 + 6.83842i −1.12512 + 0.335281i
\(417\) −5.80832 31.3062i −0.284435 1.53307i
\(418\) 8.13665 3.17542i 0.397977 0.155315i
\(419\) −7.40736 + 6.21551i −0.361873 + 0.303648i −0.805537 0.592546i \(-0.798123\pi\)
0.443664 + 0.896193i \(0.353678\pi\)
\(420\) 4.79208 3.12967i 0.233830 0.152712i
\(421\) 19.9523 7.26203i 0.972414 0.353930i 0.193528 0.981095i \(-0.438007\pi\)
0.778887 + 0.627165i \(0.215785\pi\)
\(422\) −4.78708 23.9162i −0.233031 1.16422i
\(423\) −0.644661 + 4.08010i −0.0313445 + 0.198381i
\(424\) −23.6938 + 1.63867i −1.15067 + 0.0795807i
\(425\) −18.0788 3.18779i −0.876953 0.154630i
\(426\) −9.69048 + 18.0950i −0.469505 + 0.876706i
\(427\) −3.68905 + 10.1356i −0.178526 + 0.490495i
\(428\) −3.35721 + 6.48711i −0.162277 + 0.313566i
\(429\) −9.97800 5.64282i −0.481743 0.272438i
\(430\) 5.55743 3.38147i 0.268003 0.163069i
\(431\) 6.38558 0.307583 0.153791 0.988103i \(-0.450852\pi\)
0.153791 + 0.988103i \(0.450852\pi\)
\(432\) 16.6413 12.4526i 0.800656 0.599124i
\(433\) −27.4746 −1.32035 −0.660173 0.751113i \(-0.729517\pi\)
−0.660173 + 0.751113i \(0.729517\pi\)
\(434\) 6.44234 3.91989i 0.309242 0.188161i
\(435\) 18.1147 10.6750i 0.868535 0.511825i
\(436\) 6.15178 11.8870i 0.294617 0.569286i
\(437\) 8.50149 23.3576i 0.406681 1.11735i
\(438\) 6.75574 0.215786i 0.322802 0.0103107i
\(439\) 25.9615 + 4.57771i 1.23907 + 0.218482i 0.754518 0.656279i \(-0.227871\pi\)
0.484555 + 0.874761i \(0.338982\pi\)
\(440\) −7.28916 + 0.504119i −0.347497 + 0.0240329i
\(441\) −2.83692 0.975644i −0.135091 0.0464592i
\(442\) 9.50131 + 47.4685i 0.451931 + 2.25785i
\(443\) −4.22710 + 1.53854i −0.200835 + 0.0730981i −0.440479 0.897763i \(-0.645192\pi\)
0.239644 + 0.970861i \(0.422969\pi\)
\(444\) 0.890663 + 16.1932i 0.0422690 + 0.768494i
\(445\) −20.9860 + 17.6093i −0.994832 + 0.834763i
\(446\) 23.4280 9.14303i 1.10935 0.432935i
\(447\) 5.24311 4.47974i 0.247991 0.211884i
\(448\) 7.99469 + 0.291397i 0.377714 + 0.0137672i
\(449\) 4.84883 2.79947i 0.228830 0.132115i −0.381202 0.924492i \(-0.624490\pi\)
0.610032 + 0.792377i \(0.291156\pi\)
\(450\) 9.54525 + 1.28375i 0.449968 + 0.0605167i
\(451\) −7.58687 4.38028i −0.357252 0.206260i
\(452\) 11.7544 + 12.7660i 0.552880 + 0.600462i
\(453\) −5.30057 + 1.98293i −0.249042 + 0.0931662i
\(454\) 14.9685 18.6963i 0.702506 0.877459i
\(455\) −1.21448 6.88765i −0.0569356 0.322898i
\(456\) 17.4620 + 8.34130i 0.817733 + 0.390617i
\(457\) −12.3883 10.3951i −0.579502 0.486260i 0.305281 0.952262i \(-0.401250\pi\)
−0.884784 + 0.466002i \(0.845694\pi\)
\(458\) 0.200389 0.592664i 0.00936358 0.0276934i
\(459\) −21.9755 35.8157i −1.02573 1.67173i
\(460\) −12.6186 + 16.5269i −0.588347 + 0.770572i
\(461\) −3.89085 + 4.63693i −0.181215 + 0.215963i −0.849003 0.528388i \(-0.822797\pi\)
0.667788 + 0.744351i \(0.267241\pi\)
\(462\) 2.55412 + 2.85367i 0.118828 + 0.132765i
\(463\) 21.0289 3.70796i 0.977296 0.172324i 0.337884 0.941188i \(-0.390289\pi\)
0.639412 + 0.768864i \(0.279178\pi\)
\(464\) 29.2891 + 2.42085i 1.35971 + 0.112385i
\(465\) −15.0513 2.51583i −0.697988 0.116669i
\(466\) −12.8529 + 23.4945i −0.595398 + 1.08836i
\(467\) 14.8018 25.6374i 0.684944 1.18636i −0.288510 0.957477i \(-0.593160\pi\)
0.973454 0.228881i \(-0.0735067\pi\)
\(468\) −5.99749 24.6796i −0.277234 1.14081i
\(469\) −0.696032 1.20556i −0.0321398 0.0556677i
\(470\) 3.21646 0.0740454i 0.148364 0.00341546i
\(471\) −4.40728 + 12.4532i −0.203077 + 0.573813i
\(472\) 9.33424 32.4589i 0.429643 1.49404i
\(473\) 2.79797 + 3.33449i 0.128651 + 0.153320i
\(474\) −25.5341 3.66611i −1.17282 0.168390i
\(475\) 3.06701 + 8.42654i 0.140724 + 0.386636i
\(476\) 2.07258 16.0402i 0.0949965 0.735202i
\(477\) −0.449064 25.1871i −0.0205612 1.15324i
\(478\) 9.18477 + 10.4479i 0.420102 + 0.477876i
\(479\) −0.153089 + 0.868210i −0.00699480 + 0.0396695i −0.988105 0.153778i \(-0.950856\pi\)
0.981111 + 0.193448i \(0.0619670\pi\)
\(480\) −11.8597 11.0190i −0.541320 0.502946i
\(481\) 18.6221 + 6.77789i 0.849094 + 0.309045i
\(482\) 4.57341 + 0.698298i 0.208313 + 0.0318066i
\(483\) 10.8985 0.0971476i 0.495899 0.00442037i
\(484\) 3.74358 + 16.6965i 0.170163 + 0.758930i
\(485\) 19.3852i 0.880238i
\(486\) 12.2869 + 18.3039i 0.557344 + 0.830282i
\(487\) 16.9787i 0.769376i 0.923047 + 0.384688i \(0.125691\pi\)
−0.923047 + 0.384688i \(0.874309\pi\)
\(488\) 30.3380 + 3.21206i 1.37334 + 0.145403i
\(489\) 8.76321 0.0781138i 0.396286 0.00353243i
\(490\) −0.352683 + 2.30985i −0.0159326 + 0.104349i
\(491\) 16.2139 + 5.90137i 0.731723 + 0.266325i 0.680894 0.732382i \(-0.261592\pi\)
0.0508288 + 0.998707i \(0.483814\pi\)
\(492\) −4.41524 18.9013i −0.199054 0.852135i
\(493\) 10.3174 58.5129i 0.464673 2.63529i
\(494\) 17.7602 15.6130i 0.799069 0.702463i
\(495\) −0.138150 7.74856i −0.00620937 0.348272i
\(496\) −15.1546 15.0098i −0.680460 0.673958i
\(497\) −2.86609 7.87451i −0.128562 0.353220i
\(498\) 6.04535 42.1052i 0.270898 1.88678i
\(499\) −19.6998 23.4773i −0.881882 1.05099i −0.998329 0.0577894i \(-0.981595\pi\)
0.116447 0.993197i \(-0.462850\pi\)
\(500\) −1.10551 23.9985i −0.0494400 1.07324i
\(501\) 1.34013 3.78666i 0.0598727 0.169176i
\(502\) 0.391000 + 16.9847i 0.0174512 + 0.758062i
\(503\) 4.58157 + 7.93551i 0.204282 + 0.353827i 0.949904 0.312543i \(-0.101181\pi\)
−0.745622 + 0.666370i \(0.767847\pi\)
\(504\) −0.742830 + 8.45270i −0.0330883 + 0.376513i
\(505\) −5.88622 + 10.1952i −0.261933 + 0.453682i
\(506\) −12.2063 6.67755i −0.542635 0.296853i
\(507\) −8.40177 1.40436i −0.373136 0.0623698i
\(508\) −17.7777 + 11.3857i −0.788758 + 0.505160i
\(509\) 14.9011 2.62746i 0.660479 0.116460i 0.166646 0.986017i \(-0.446706\pi\)
0.493833 + 0.869557i \(0.335595\pi\)
\(510\) −24.3870 + 21.8271i −1.07988 + 0.966520i
\(511\) −1.77373 + 2.11384i −0.0784650 + 0.0935109i
\(512\) −4.65383 22.1437i −0.205672 0.978621i
\(513\) −9.78397 + 18.0440i −0.431973 + 0.796661i
\(514\) 12.6433 + 4.27492i 0.557674 + 0.188559i
\(515\) 11.1625 + 9.36647i 0.491879 + 0.412736i
\(516\) −1.15058 + 9.57544i −0.0506513 + 0.421535i
\(517\) 0.373826 + 2.12007i 0.0164408 + 0.0932406i
\(518\) −5.16845 4.13793i −0.227089 0.181810i
\(519\) −4.79917 + 1.79536i −0.210660 + 0.0788075i
\(520\) −18.0776 + 8.03216i −0.792757 + 0.352234i
\(521\) 26.1153 + 15.0777i 1.14413 + 0.660566i 0.947451 0.319902i \(-0.103650\pi\)
0.196682 + 0.980467i \(0.436983\pi\)
\(522\) −4.15492 + 30.8936i −0.181856 + 1.35218i
\(523\) 1.54254 0.890588i 0.0674508 0.0389427i −0.465895 0.884840i \(-0.654268\pi\)
0.533346 + 0.845897i \(0.320934\pi\)
\(524\) 5.46792 + 1.70961i 0.238867 + 0.0746846i
\(525\) −2.98938 + 2.55414i −0.130467 + 0.111472i
\(526\) 1.85002 + 4.74046i 0.0806646 + 0.206694i
\(527\) −33.0334 + 27.7183i −1.43896 + 1.20743i
\(528\) 6.09081 8.95756i 0.265068 0.389828i
\(529\) −15.5948 + 5.67604i −0.678035 + 0.246784i
\(530\) −19.2391 + 3.85091i −0.835694 + 0.167273i
\(531\) 33.8758 + 11.6502i 1.47008 + 0.505576i
\(532\) −7.29175 + 3.04087i −0.316137 + 0.131838i
\(533\) −23.3579 4.11863i −1.01174 0.178398i
\(534\) −1.29660 40.5935i −0.0561095 1.75665i
\(535\) −2.06384 + 5.67036i −0.0892277 + 0.245151i
\(536\) −2.83438 + 2.73295i −0.122427 + 0.118046i
\(537\) −33.2361 + 19.5859i −1.43424 + 0.845194i
\(538\) 19.0168 + 31.2541i 0.819873 + 1.34746i
\(539\) −1.56349 −0.0673442
\(540\) 12.3161 11.9642i 0.530002 0.514858i
\(541\) 28.7555 1.23630 0.618148 0.786061i \(-0.287883\pi\)
0.618148 + 0.786061i \(0.287883\pi\)
\(542\) 16.3831 + 26.9256i 0.703715 + 1.15655i
\(543\) 9.92891 + 5.61506i 0.426090 + 0.240965i
\(544\) −45.4431 + 5.25297i −1.94836 + 0.225219i
\(545\) 3.78180 10.3904i 0.161995 0.445077i
\(546\) 9.14042 + 4.89500i 0.391174 + 0.209487i
\(547\) 17.0077 + 2.99891i 0.727195 + 0.128224i 0.524977 0.851116i \(-0.324074\pi\)
0.202218 + 0.979340i \(0.435185\pi\)
\(548\) 0.456706 + 1.09514i 0.0195095 + 0.0467822i
\(549\) −5.04999 + 31.9617i −0.215528 + 1.36409i
\(550\) 4.92180 0.985148i 0.209866 0.0420069i
\(551\) −27.2728 + 9.92650i −1.16186 + 0.422883i
\(552\) −7.70124 29.8494i −0.327786 1.27047i
\(553\) 8.06733 6.76929i 0.343058 0.287860i
\(554\) 0.822642 + 2.10793i 0.0349507 + 0.0895573i
\(555\) 2.44401 + 13.1729i 0.103742 + 0.559160i
\(556\) 10.9716 35.0910i 0.465301 1.48819i
\(557\) 31.7693 18.3420i 1.34611 0.777175i 0.358411 0.933564i \(-0.383319\pi\)
0.987696 + 0.156389i \(0.0499853\pi\)
\(558\) 16.7224 15.2376i 0.707914 0.645061i
\(559\) 10.2060 + 5.89246i 0.431669 + 0.249224i
\(560\) 6.58098 0.607608i 0.278097 0.0256761i
\(561\) −16.9007 13.9265i −0.713547 0.587978i
\(562\) −26.3855 21.1246i −1.11301 0.891088i
\(563\) −2.64668 15.0101i −0.111544 0.632599i −0.988403 0.151852i \(-0.951476\pi\)
0.876859 0.480748i \(-0.159635\pi\)
\(564\) −2.86064 + 3.81670i −0.120455 + 0.160712i
\(565\) 10.9819 + 9.21495i 0.462014 + 0.387676i
\(566\) 33.6806 + 11.3880i 1.41570 + 0.478672i
\(567\) −8.91335 1.24589i −0.374325 0.0523226i
\(568\) −19.6599 + 13.2389i −0.824909 + 0.555493i
\(569\) −6.41106 + 7.64040i −0.268766 + 0.320302i −0.883499 0.468432i \(-0.844819\pi\)
0.614734 + 0.788735i \(0.289263\pi\)
\(570\) 15.1898 + 4.98551i 0.636232 + 0.208820i
\(571\) 22.3551 3.94181i 0.935533 0.164960i 0.314957 0.949106i \(-0.398010\pi\)
0.620576 + 0.784146i \(0.286899\pi\)
\(572\) −7.13869 11.1464i −0.298484 0.466053i
\(573\) 23.0361 27.9557i 0.962348 1.16787i
\(574\) 6.95188 + 3.80308i 0.290166 + 0.158738i
\(575\) 7.14229 12.3708i 0.297854 0.515899i
\(576\) 23.7088 3.72711i 0.987868 0.155296i
\(577\) 9.91684 + 17.1765i 0.412843 + 0.715066i 0.995199 0.0978681i \(-0.0312023\pi\)
−0.582356 + 0.812934i \(0.697869\pi\)
\(578\) 1.57518 + 68.4241i 0.0655187 + 2.84607i
\(579\) −0.177371 + 0.0329080i −0.00737127 + 0.00136761i
\(580\) 24.2532 1.11725i 1.00706 0.0463911i
\(581\) 11.1624 + 13.3029i 0.463095 + 0.551896i
\(582\) −22.5939 17.7609i −0.936549 0.736211i
\(583\) −4.49028 12.3369i −0.185968 0.510943i
\(584\) 7.01233 + 3.42677i 0.290172 + 0.141801i
\(585\) −7.52649 19.5853i −0.311182 0.809752i
\(586\) −3.98819 + 3.50602i −0.164751 + 0.144833i
\(587\) −3.69588 + 20.9604i −0.152545 + 0.865128i 0.808450 + 0.588565i \(0.200307\pi\)
−0.960996 + 0.276563i \(0.910804\pi\)
\(588\) −2.36906 2.52736i −0.0976983 0.104227i
\(589\) 19.7938 + 7.20435i 0.815589 + 0.296850i
\(590\) 4.21140 27.5821i 0.173381 1.13554i
\(591\) 17.4261 30.8140i 0.716814 1.26752i
\(592\) −7.83261 + 17.0098i −0.321918 + 0.699098i
\(593\) 32.8945i 1.35082i 0.737444 + 0.675409i \(0.236033\pi\)
−0.737444 + 0.675409i \(0.763967\pi\)
\(594\) 9.15770 + 6.93826i 0.375745 + 0.284680i
\(595\) 13.3613i 0.547761i
\(596\) 7.77019 1.74219i 0.318279 0.0713627i
\(597\) 5.15965 + 8.75560i 0.211170 + 0.358343i
\(598\) −37.2374 5.68565i −1.52275 0.232504i
\(599\) −8.71921 3.17353i −0.356257 0.129667i 0.157690 0.987489i \(-0.449595\pi\)
−0.513948 + 0.857822i \(0.671817\pi\)
\(600\) 9.05018 + 6.46330i 0.369472 + 0.263863i
\(601\) −5.40918 + 30.6770i −0.220645 + 1.25134i 0.650193 + 0.759769i \(0.274688\pi\)
−0.870838 + 0.491570i \(0.836423\pi\)
\(602\) −2.59958 2.95708i −0.105951 0.120522i
\(603\) −2.74101 3.15079i −0.111622 0.128310i
\(604\) −6.48096 0.837414i −0.263706 0.0340739i
\(605\) 4.83472 + 13.2833i 0.196559 + 0.540042i
\(606\) −6.48979 16.2015i −0.263630 0.658140i
\(607\) −19.8203 23.6209i −0.804481 0.958743i 0.195277 0.980748i \(-0.437439\pi\)
−0.999758 + 0.0220053i \(0.992995\pi\)
\(608\) 13.3211 + 17.9410i 0.540243 + 0.727603i
\(609\) −8.26656 9.67524i −0.334978 0.392060i
\(610\) 25.1963 0.580039i 1.02017 0.0234851i
\(611\) 2.91420 + 5.04754i 0.117896 + 0.204202i
\(612\) −3.09645 48.4217i −0.125167 1.95733i
\(613\) −0.962163 + 1.66651i −0.0388614 + 0.0673099i −0.884802 0.465967i \(-0.845706\pi\)
0.845941 + 0.533277i \(0.179040\pi\)
\(614\) 10.3065 18.8399i 0.415938 0.760317i
\(615\) −5.61842 15.0186i −0.226557 0.605608i
\(616\) 1.06656 + 4.29167i 0.0429728 + 0.172916i
\(617\) 16.7852 2.95969i 0.675748 0.119153i 0.174766 0.984610i \(-0.444083\pi\)
0.500982 + 0.865458i \(0.332972\pi\)
\(618\) −21.1440 + 4.42856i −0.850536 + 0.178143i
\(619\) 26.8887 32.0447i 1.08075 1.28798i 0.125527 0.992090i \(-0.459938\pi\)
0.955221 0.295895i \(-0.0956177\pi\)
\(620\) −14.0053 10.6933i −0.562466 0.429454i
\(621\) 32.0368 6.53667i 1.28559 0.262307i
\(622\) −12.6661 + 37.4609i −0.507866 + 1.50204i
\(623\) 12.7015 + 10.6578i 0.508876 + 0.426997i
\(624\) 7.20117 28.4290i 0.288278 1.13807i
\(625\) −1.47535 8.36712i −0.0590140 0.334685i
\(626\) 4.81566 6.01497i 0.192473 0.240406i
\(627\) −1.76359 + 10.5509i −0.0704312 + 0.421364i
\(628\) −11.2214 + 10.3322i −0.447784 + 0.412300i
\(629\) 32.7871 + 18.9296i 1.30731 + 0.754775i
\(630\) 0.286231 + 7.00403i 0.0114037 + 0.279047i
\(631\) 3.48832 2.01398i 0.138868 0.0801754i −0.428956 0.903325i \(-0.641119\pi\)
0.567824 + 0.823150i \(0.307785\pi\)
\(632\) −24.0845 17.5265i −0.958030 0.697167i
\(633\) 28.1607 + 9.96631i 1.11929 + 0.396125i
\(634\) 42.7475 16.6827i 1.69772 0.662554i
\(635\) −13.3601 + 11.2105i −0.530180 + 0.444874i
\(636\) 13.1387 25.9519i 0.520982 1.02906i
\(637\) −3.97769 + 1.44776i −0.157602 + 0.0573624i
\(638\) 3.18847 + 15.9296i 0.126233 + 0.630659i
\(639\) −12.9559 21.5440i −0.512529 0.852269i
\(640\) −6.15715 17.6499i −0.243383 0.697672i
\(641\) 9.14268 + 1.61210i 0.361114 + 0.0636741i 0.351262 0.936277i \(-0.385753\pi\)
0.00985232 + 0.999951i \(0.496864\pi\)
\(642\) −4.71803 7.60068i −0.186206 0.299975i
\(643\) 0.144574 0.397215i 0.00570145 0.0156646i −0.936809 0.349841i \(-0.886236\pi\)
0.942511 + 0.334176i \(0.108458\pi\)
\(644\) 11.1770 + 5.78430i 0.440434 + 0.227933i
\(645\) 0.0710171 + 7.96706i 0.00279630 + 0.313703i
\(646\) 38.5935 23.4825i 1.51844 0.923908i
\(647\) 0.676200 0.0265842 0.0132921 0.999912i \(-0.495769\pi\)
0.0132921 + 0.999912i \(0.495769\pi\)
\(648\) 2.66048 + 25.3164i 0.104513 + 0.994523i
\(649\) 18.6697 0.732849
\(650\) 11.6094 7.06382i 0.455357 0.277066i
\(651\) 0.0823250 + 9.23564i 0.00322657 + 0.361973i
\(652\) 8.98710 + 4.65101i 0.351962 + 0.182148i
\(653\) −6.66796 + 18.3201i −0.260938 + 0.716920i 0.738167 + 0.674618i \(0.235692\pi\)
−0.999105 + 0.0423024i \(0.986531\pi\)
\(654\) 8.64537 + 13.9275i 0.338061 + 0.544610i
\(655\) 4.66091 + 0.821843i 0.182117 + 0.0321121i
\(656\) 5.69689 21.6768i 0.222426 0.846336i
\(657\) −4.01068 + 7.24185i −0.156472 + 0.282531i
\(658\) −0.382179 1.90937i −0.0148989 0.0744348i
\(659\) −9.79320 + 3.56443i −0.381489 + 0.138851i −0.525644 0.850704i \(-0.676176\pi\)
0.144155 + 0.989555i \(0.453954\pi\)
\(660\) 4.04198 7.98382i 0.157334 0.310770i
\(661\) 9.40273 7.88983i 0.365724 0.306879i −0.441343 0.897338i \(-0.645498\pi\)
0.807067 + 0.590459i \(0.201053\pi\)
\(662\) 28.6600 11.1849i 1.11390 0.434713i
\(663\) −55.8929 19.7810i −2.17070 0.768229i
\(664\) 28.9008 39.7148i 1.12157 1.54123i
\(665\) −5.65228 + 3.26335i −0.219186 + 0.126547i
\(666\) −17.5926 9.22058i −0.681699 0.357290i
\(667\) 40.0386 + 23.1163i 1.55030 + 0.895067i
\(668\) 3.41212 3.14173i 0.132019 0.121557i
\(669\) −5.07794 + 30.3795i −0.196325 + 1.17454i
\(670\) −2.03291 + 2.53920i −0.0785383 + 0.0980977i
\(671\) 2.92838 + 16.6077i 0.113049 + 0.641133i
\(672\) −5.32135 + 8.22698i −0.205276 + 0.317363i
\(673\) −31.4391 26.3805i −1.21189 1.01689i −0.999209 0.0397720i \(-0.987337\pi\)
−0.212679 0.977122i \(-0.568219\pi\)
\(674\) 11.0703 32.7411i 0.426413 1.26114i
\(675\) −7.33785 + 9.23557i −0.282434 + 0.355477i
\(676\) −7.81787 5.96910i −0.300687 0.229581i
\(677\) −8.08906 + 9.64016i −0.310888 + 0.370502i −0.898751 0.438458i \(-0.855525\pi\)
0.587864 + 0.808960i \(0.299969\pi\)
\(678\) −20.8020 + 4.35693i −0.798895 + 0.167327i
\(679\) 11.5544 2.03736i 0.443418 0.0781866i
\(680\) −36.6759 + 9.11461i −1.40646 + 0.349529i
\(681\) 10.2777 + 27.4732i 0.393841 + 1.05278i
\(682\) 5.65871 10.3439i 0.216683 0.396087i
\(683\) 9.44667 16.3621i 0.361467 0.626079i −0.626736 0.779232i \(-0.715609\pi\)
0.988202 + 0.153153i \(0.0489428\pi\)
\(684\) −19.7277 + 13.1364i −0.754309 + 0.502281i
\(685\) 0.490120 + 0.848913i 0.0187265 + 0.0324353i
\(686\) 1.41384 0.0325477i 0.0539806 0.00124268i
\(687\) 0.497736 + 0.582554i 0.0189898 + 0.0222258i
\(688\) −6.34365 + 9.15288i −0.241850 + 0.348950i
\(689\) −22.8475 27.2286i −0.870422 1.03733i
\(690\) −9.46968 23.6406i −0.360505 0.899983i
\(691\) −6.86255 18.8547i −0.261064 0.717267i −0.999096 0.0425019i \(-0.986467\pi\)
0.738033 0.674765i \(-0.235755\pi\)
\(692\) −5.86790 0.758200i −0.223064 0.0288224i
\(693\) −4.60395 + 0.896705i −0.174890 + 0.0340630i
\(694\) 15.2766 + 17.3775i 0.579891 + 0.659640i
\(695\) 5.27428 29.9119i 0.200065 1.13462i
\(696\) −20.9187 + 29.2913i −0.792922 + 1.11028i
\(697\) −42.5793 15.4976i −1.61281 0.587014i
\(698\) 18.3092 + 2.79556i 0.693012 + 0.105814i
\(699\) −16.6521 28.2576i −0.629840 1.06880i
\(700\) −4.43020 + 0.993313i −0.167446 + 0.0375437i
\(701\) 18.4249i 0.695898i −0.937513 0.347949i \(-0.886878\pi\)
0.937513 0.347949i \(-0.113122\pi\)
\(702\) 29.7229 + 9.17186i 1.12182 + 0.346169i
\(703\) 18.4934i 0.697492i
\(704\) 11.0528 5.85525i 0.416567 0.220678i
\(705\) −1.93970 + 3.42990i −0.0730532 + 0.129177i
\(706\) 2.40920 15.7787i 0.0906713 0.593840i
\(707\) 6.69543 + 2.43694i 0.251808 + 0.0916505i
\(708\) 28.2890 + 30.1793i 1.06317 + 1.13421i
\(709\) −6.73450 + 38.1932i −0.252919 + 1.43438i 0.548438 + 0.836191i \(0.315223\pi\)
−0.801357 + 0.598186i \(0.795888\pi\)
\(710\) −14.7060 + 12.9281i −0.551906 + 0.485182i
\(711\) 19.8732 24.5602i 0.745304 0.921078i
\(712\) 20.5905 42.1352i 0.771663 1.57908i
\(713\) −11.4762 31.5307i −0.429788 1.18083i
\(714\) 15.5729 + 12.2417i 0.582802 + 0.458135i
\(715\) −7.02881 8.37661i −0.262862 0.313267i
\(716\) −44.4986 + 2.04987i −1.66299 + 0.0766072i
\(717\) −16.7517 + 3.10798i −0.625602 + 0.116070i
\(718\) −0.452371 19.6506i −0.0168823 0.733352i
\(719\) −13.7740 23.8573i −0.513684 0.889726i −0.999874 0.0158734i \(-0.994947\pi\)
0.486190 0.873853i \(-0.338386\pi\)
\(720\) 19.0303 5.56358i 0.709218 0.207342i
\(721\) 4.40965 7.63774i 0.164224 0.284444i
\(722\) 4.21327 + 2.30490i 0.156802 + 0.0857796i
\(723\) −3.60331 + 4.37283i −0.134009 + 0.162627i
\(724\) 7.10357 + 11.0915i 0.264002 + 0.412214i
\(725\) −16.4256 + 2.89627i −0.610030 + 0.107565i
\(726\) −19.9116 6.53524i −0.738987 0.242546i
\(727\) −29.1372 + 34.7244i −1.08064 + 1.28786i −0.125373 + 0.992110i \(0.540013\pi\)
−0.955266 + 0.295747i \(0.904432\pi\)
\(728\) 6.68745 + 9.93089i 0.247853 + 0.368063i
\(729\) −26.9614 + 1.44332i −0.998570 + 0.0534561i
\(730\) 6.10804 + 2.06523i 0.226069 + 0.0764376i
\(731\) 17.2469 + 14.4718i 0.637898 + 0.535260i
\(732\) −22.4090 + 29.8983i −0.828259 + 1.10507i
\(733\) 6.41359 + 36.3733i 0.236891 + 1.34348i 0.838594 + 0.544758i \(0.183378\pi\)
−0.601702 + 0.798721i \(0.705511\pi\)
\(734\) −8.17911 6.54831i −0.301896 0.241702i
\(735\) −2.20855 1.81990i −0.0814636 0.0671279i
\(736\) 8.25300 34.6258i 0.304209 1.27633i
\(737\) −1.88488 1.08824i −0.0694306 0.0400858i
\(738\) 22.6521 + 7.21172i 0.833837 + 0.265467i
\(739\) −35.0394 + 20.2300i −1.28895 + 0.744173i −0.978466 0.206406i \(-0.933823\pi\)
−0.310480 + 0.950580i \(0.600490\pi\)
\(740\) −4.61661 + 14.7655i −0.169710 + 0.542790i
\(741\) 5.28319 + 28.4758i 0.194083 + 1.04609i
\(742\) 4.31731 + 11.0626i 0.158493 + 0.406122i
\(743\) −4.01296 + 3.36727i −0.147221 + 0.123533i −0.713424 0.700733i \(-0.752856\pi\)
0.566202 + 0.824266i \(0.308412\pi\)
\(744\) 25.2951 6.52620i 0.927362 0.239262i
\(745\) 6.18176 2.24998i 0.226482 0.0824328i
\(746\) −50.1968 + 10.0474i −1.83783 + 0.367861i
\(747\) 40.4992 + 32.7705i 1.48179 + 1.19901i
\(748\) −9.73303 23.3390i −0.355875 0.853358i
\(749\) 3.59669 + 0.634193i 0.131420 + 0.0231729i
\(750\) 25.9379 + 13.8906i 0.947118 + 0.507213i
\(751\) 1.03619 2.84692i 0.0378112 0.103886i −0.919350 0.393440i \(-0.871285\pi\)
0.957162 + 0.289554i \(0.0935071\pi\)
\(752\) −4.98037 + 2.35156i −0.181615 + 0.0857524i
\(753\) −18.1117 10.2427i −0.660028 0.373263i
\(754\) 22.8623 + 37.5742i 0.832597 + 1.36837i
\(755\) −5.39857 −0.196474
\(756\) −8.42560 6.08352i −0.306436 0.221256i
\(757\) −6.60355 −0.240010 −0.120005 0.992773i \(-0.538291\pi\)
−0.120005 + 0.992773i \(0.538291\pi\)
\(758\) −5.38687 8.85332i −0.195660 0.321567i
\(759\) 14.6809 8.65139i 0.532882 0.314026i
\(760\) 12.8135 + 13.2890i 0.464793 + 0.482042i
\(761\) −4.72889 + 12.9925i −0.171422 + 0.470978i −0.995418 0.0956172i \(-0.969518\pi\)
0.823996 + 0.566595i \(0.191740\pi\)
\(762\) −0.825444 25.8426i −0.0299027 0.936179i
\(763\) −6.59060 1.16210i −0.238596 0.0420709i
\(764\) 38.6055 16.0996i 1.39670 0.582462i
\(765\) −7.66309 39.3446i −0.277060 1.42251i
\(766\) −24.6130 + 4.92654i −0.889304 + 0.178003i
\(767\) 47.4978 17.2878i 1.71505 0.624226i
\(768\) 26.2125 + 8.99460i 0.945864 + 0.324565i
\(769\) −25.5920 + 21.4742i −0.922869 + 0.774379i −0.974523 0.224286i \(-0.927995\pi\)
0.0516541 + 0.998665i \(0.483551\pi\)
\(770\) 1.32817 + 3.40330i 0.0478641 + 0.122646i
\(771\) −12.4276 + 10.6182i −0.447571 + 0.382406i
\(772\) −0.198814 0.0621615i −0.00715547 0.00223724i
\(773\) 22.8426 13.1882i 0.821592 0.474346i −0.0293733 0.999569i \(-0.509351\pi\)
0.850965 + 0.525222i \(0.176018\pi\)
\(774\) −9.35086 7.21670i −0.336110 0.259399i
\(775\) 10.4833 + 6.05254i 0.376571 + 0.217414i
\(776\) −13.4744 30.3263i −0.483704 1.08865i
\(777\) 7.59478 2.84119i 0.272461 0.101927i
\(778\) −18.5988 14.8905i −0.666800 0.533849i
\(779\) 3.84350 + 21.7976i 0.137708 + 0.780980i
\(780\) 2.89038 24.0545i 0.103492 0.861291i
\(781\) −10.0366 8.42171i −0.359138 0.301352i
\(782\) −68.1724 23.0502i −2.43784 0.824274i
\(783\) −29.8913 23.7493i −1.06823 0.848729i
\(784\) −1.05381 3.85869i −0.0376361 0.137810i
\(785\) −8.10002 + 9.65322i −0.289102 + 0.344538i
\(786\) −5.22823 + 4.67942i −0.186485 + 0.166909i
\(787\) −0.0485998 + 0.00856946i −0.00173240 + 0.000305468i −0.174514 0.984655i \(-0.555836\pi\)
0.172782 + 0.984960i \(0.444724\pi\)
\(788\) 34.4221 22.0457i 1.22624 0.785344i
\(789\) −6.14704 1.02748i −0.218840 0.0365793i
\(790\) −21.5881 11.8100i −0.768070 0.420179i
\(791\) 4.33832 7.51419i 0.154253 0.267174i
\(792\) 5.60205 + 12.0258i 0.199060 + 0.427320i
\(793\) 22.8286 + 39.5402i 0.810666 + 1.40411i
\(794\) 0.369051 + 16.0312i 0.0130971 + 0.568927i
\(795\) 8.01728 22.6535i 0.284343 0.803439i
\(796\) 0.540011 + 11.7226i 0.0191402 + 0.415495i
\(797\) −14.4014 17.1629i −0.510122 0.607940i 0.448093 0.893987i \(-0.352103\pi\)
−0.958216 + 0.286047i \(0.907659\pi\)
\(798\) 1.37515 9.57777i 0.0486797 0.339049i
\(799\) 3.80830 + 10.4632i 0.134728 + 0.370162i
\(800\) 5.74870 + 11.4830i 0.203247 + 0.405985i
\(801\) 43.5143 + 24.0991i 1.53750 + 0.851501i
\(802\) 6.86203 6.03242i 0.242307 0.213012i
\(803\) −0.749176 + 4.24879i −0.0264378 + 0.149936i
\(804\) −1.09692 4.69583i −0.0386855 0.165609i
\(805\) 9.76975 + 3.55590i 0.344338 + 0.125329i
\(806\) 4.81815 31.5559i 0.169712 1.11151i
\(807\) −44.8055 + 0.399389i −1.57723 + 0.0140592i
\(808\) 2.12185 20.0409i 0.0746463 0.705036i
\(809\) 29.4891i 1.03678i 0.855144 + 0.518391i \(0.173469\pi\)
−0.855144 + 0.518391i \(0.826531\pi\)
\(810\) 4.85986 + 20.4604i 0.170758 + 0.718904i
\(811\) 27.6023i 0.969247i −0.874723 0.484623i \(-0.838957\pi\)
0.874723 0.484623i \(-0.161043\pi\)
\(812\) −3.21490 14.3385i −0.112821 0.503183i
\(813\) −38.6002 + 0.344076i −1.35377 + 0.0120673i
\(814\) −10.2330 1.56244i −0.358666 0.0547635i
\(815\) 7.85560 + 2.85920i 0.275170 + 0.100154i
\(816\) 22.9794 51.0975i 0.804440 1.78877i
\(817\) 1.90972 10.8306i 0.0668128 0.378914i
\(818\) −28.5154 32.4370i −0.997018 1.13413i
\(819\) −10.8827 + 6.54450i −0.380271 + 0.228683i
\(820\) 2.37272 18.3631i 0.0828590 0.641267i
\(821\) 3.40471 + 9.35436i 0.118825 + 0.326470i 0.984819 0.173586i \(-0.0555353\pi\)
−0.865994 + 0.500055i \(0.833313\pi\)
\(822\) −1.43848 0.206533i −0.0501727 0.00720366i
\(823\) −18.3335 21.8490i −0.639066 0.761609i 0.345156 0.938545i \(-0.387826\pi\)
−0.984222 + 0.176936i \(0.943381\pi\)
\(824\) −23.9732 6.89400i −0.835146 0.240164i
\(825\) −2.05100 + 5.79528i −0.0714066 + 0.201766i
\(826\) −16.8827 + 0.388653i −0.587424 + 0.0135230i
\(827\) 18.7079 + 32.4030i 0.650536 + 1.12676i 0.982993 + 0.183643i \(0.0587890\pi\)
−0.332457 + 0.943118i \(0.607878\pi\)
\(828\) 36.2299 + 10.6225i 1.25908 + 0.369159i
\(829\) 15.2067 26.3388i 0.528151 0.914785i −0.471310 0.881968i \(-0.656219\pi\)
0.999461 0.0328173i \(-0.0104479\pi\)
\(830\) 19.4744 35.5983i 0.675965 1.23564i
\(831\) −2.73339 0.456887i −0.0948201 0.0158492i
\(832\) 22.6977 25.1311i 0.786900 0.871264i
\(833\) −7.96392 + 1.40425i −0.275933 + 0.0486545i
\(834\) 30.0307 + 33.5528i 1.03988 + 1.16184i
\(835\) 2.46299 2.93527i 0.0852352 0.101579i
\(836\) −7.49600 + 9.81768i −0.259255 + 0.339552i
\(837\) 5.53932 + 27.1487i 0.191467 + 0.938396i
\(838\) 4.38011 12.9544i 0.151308 0.447504i
\(839\) 13.5528 + 11.3722i 0.467895 + 0.392611i 0.846026 0.533141i \(-0.178989\pi\)
−0.378131 + 0.925752i \(0.623433\pi\)
\(840\) −3.48890 + 7.30379i −0.120378 + 0.252005i
\(841\) −4.33810 24.6026i −0.149590 0.848365i
\(842\) −18.7669 + 23.4407i −0.646750 + 0.807818i
\(843\) 38.7722 14.5046i 1.33539 0.499565i
\(844\) 23.3645 + 25.3753i 0.804238 + 0.873454i
\(845\) −7.03718 4.06291i −0.242086 0.139769i
\(846\) −2.22046 5.40325i −0.0763411 0.185768i
\(847\) 7.40928 4.27775i 0.254586 0.146985i
\(848\) 27.4210 19.3972i 0.941642 0.666104i
\(849\) −33.1060 + 28.2859i −1.13620 + 0.970770i
\(850\) 24.1853 9.43856i 0.829548 0.323740i
\(851\) −22.5671 + 18.9360i −0.773589 + 0.649118i
\(852\) −1.59424 28.9850i −0.0546178 0.993008i
\(853\) −7.95668 + 2.89599i −0.272431 + 0.0991570i −0.474623 0.880189i \(-0.657416\pi\)
0.202192 + 0.979346i \(0.435194\pi\)
\(854\) −2.99382 14.9571i −0.102446 0.511822i
\(855\) −14.7725 + 12.8512i −0.505208 + 0.439502i
\(856\) −0.712714 10.3053i −0.0243601 0.352227i
\(857\) −40.5506 7.15016i −1.38518 0.244245i −0.569141 0.822240i \(-0.692724\pi\)
−0.816040 + 0.577995i \(0.803835\pi\)
\(858\) 16.2030 0.517542i 0.553160 0.0176686i
\(859\) −10.8385 + 29.7785i −0.369805 + 1.01603i 0.605631 + 0.795746i \(0.292921\pi\)
−0.975436 + 0.220285i \(0.929301\pi\)
\(860\) −4.22846 + 8.17061i −0.144189 + 0.278616i
\(861\) −8.36124 + 4.92725i −0.284950 + 0.167920i
\(862\) −7.71472 + 4.69408i −0.262764 + 0.159881i
\(863\) 33.2248 1.13099 0.565493 0.824753i \(-0.308686\pi\)
0.565493 + 0.824753i \(0.308686\pi\)
\(864\) −10.9512 + 27.2777i −0.372568 + 0.928005i
\(865\) −4.88790 −0.166193
\(866\) 33.1934 20.1968i 1.12796 0.686315i
\(867\) −72.9646 41.2634i −2.47801 1.40138i
\(868\) −4.90175 + 9.47161i −0.166376 + 0.321487i
\(869\) 5.63148 15.4724i 0.191035 0.524864i
\(870\) −14.0380 + 26.2132i −0.475934 + 0.888710i
\(871\) −5.80305 1.02323i −0.196629 0.0346710i
\(872\) 1.30598 + 18.8835i 0.0442262 + 0.639476i
\(873\) 32.8555 12.6261i 1.11199 0.427330i
\(874\) 6.89931 + 34.4690i 0.233373 + 1.16593i
\(875\) −11.2875 + 4.10833i −0.381589 + 0.138887i
\(876\) −8.00330 + 5.22689i −0.270406 + 0.176600i
\(877\) 17.4746 14.6629i 0.590076 0.495132i −0.298163 0.954515i \(-0.596374\pi\)
0.888238 + 0.459383i \(0.151929\pi\)
\(878\) −34.7303 + 13.5539i −1.17209 + 0.457422i
\(879\) −1.18638 6.39447i −0.0400157 0.215680i
\(880\) 8.43579 5.96736i 0.284371 0.201160i
\(881\) 11.5132 6.64717i 0.387891 0.223949i −0.293355 0.956004i \(-0.594772\pi\)
0.681246 + 0.732055i \(0.261438\pi\)
\(882\) 4.14462 0.906718i 0.139557 0.0305308i
\(883\) −9.32172 5.38190i −0.313701 0.181115i 0.334880 0.942261i \(-0.391304\pi\)
−0.648581 + 0.761145i \(0.724637\pi\)
\(884\) −46.3734 50.3645i −1.55971 1.69394i
\(885\) 26.3724 + 21.7314i 0.886498 + 0.730494i
\(886\) 3.97596 4.96615i 0.133575 0.166841i
\(887\) 4.99668 + 28.3376i 0.167772 + 0.951482i 0.946160 + 0.323699i \(0.104927\pi\)
−0.778388 + 0.627783i \(0.783962\pi\)
\(888\) −12.9798 18.9090i −0.435572 0.634544i
\(889\) 8.08605 + 6.78500i 0.271197 + 0.227562i
\(890\) 12.4094 36.7016i 0.415965 1.23024i
\(891\) −13.0428 + 5.28099i −0.436951 + 0.176920i
\(892\) −21.5833 + 28.2682i −0.722664 + 0.946489i
\(893\) 3.49616 4.16656i 0.116994 0.139429i
\(894\) −3.04136 + 9.26643i −0.101718 + 0.309916i
\(895\) −36.2411 + 6.39029i −1.21141 + 0.213604i
\(896\) −9.87297 + 5.52490i −0.329833 + 0.184574i
\(897\) 29.3388 35.6043i 0.979593 1.18879i
\(898\) −3.80018 + 6.94658i −0.126814 + 0.231810i
\(899\) −19.5893 + 33.9296i −0.653339 + 1.13162i
\(900\) −12.4758 + 5.46582i −0.415859 + 0.182194i
\(901\) −33.9525 58.8075i −1.13112 1.95916i
\(902\) 12.3860 0.285136i 0.412410 0.00949400i
\(903\) 4.74125 0.879655i 0.157779 0.0292731i
\(904\) −23.5854 6.78248i −0.784438 0.225582i
\(905\) 6.99422 + 8.33539i 0.232496 + 0.277078i
\(906\) 4.94620 6.29216i 0.164326 0.209043i
\(907\) 4.58983 + 12.6105i 0.152403 + 0.418724i 0.992275 0.124061i \(-0.0395920\pi\)
−0.839872 + 0.542785i \(0.817370\pi\)
\(908\) −4.34037 + 33.5912i −0.144040 + 1.11476i
\(909\) 21.1135 + 3.33595i 0.700290 + 0.110647i
\(910\) 6.53042 + 7.42852i 0.216481 + 0.246253i
\(911\) 0.484081 2.74536i 0.0160383 0.0909578i −0.975738 0.218942i \(-0.929740\pi\)
0.991776 + 0.127984i \(0.0408506\pi\)
\(912\) −27.2284 + 2.75892i −0.901622 + 0.0913570i
\(913\) 25.5136 + 9.28619i 0.844377 + 0.307328i
\(914\) 22.6084 + 3.45200i 0.747820 + 0.114182i
\(915\) −15.1947 + 26.8683i −0.502322 + 0.888239i
\(916\) 0.193571 + 0.863333i 0.00639578 + 0.0285253i
\(917\) 2.86448i 0.0945933i
\(918\) 52.8781 + 27.1163i 1.74524 + 0.894970i
\(919\) 23.8595i 0.787051i 0.919314 + 0.393526i \(0.128745\pi\)
−0.919314 + 0.393526i \(0.871255\pi\)
\(920\) 3.09612 29.2430i 0.102076 0.964113i
\(921\) 13.3531 + 22.6593i 0.439999 + 0.746651i
\(922\) 1.29208 8.46228i 0.0425522 0.278690i
\(923\) −33.3326 12.1321i −1.09716 0.399332i
\(924\) −5.18351 1.57010i −0.170525 0.0516526i
\(925\) 1.84549 10.4663i 0.0606793 0.344129i
\(926\) −22.6803 + 19.9382i −0.745319 + 0.655212i
\(927\) 8.60450 25.0197i 0.282609 0.821754i
\(928\) −37.1651 + 18.6059i −1.22001 + 0.610768i
\(929\) 1.78258 + 4.89760i 0.0584846 + 0.160685i 0.965494 0.260425i \(-0.0838627\pi\)
−0.907009 + 0.421110i \(0.861641\pi\)
\(930\) 20.0336 8.02482i 0.656928 0.263144i
\(931\) 2.53914 + 3.02603i 0.0832170 + 0.0991742i
\(932\) −1.74282 37.8330i −0.0570878 1.23926i
\(933\) −31.4607 36.8218i −1.02998 1.20549i
\(934\) 0.963526 + 41.8546i 0.0315275 + 1.36953i
\(935\) −10.4451 18.0915i −0.341592 0.591655i
\(936\) 25.3880 + 25.4077i 0.829831 + 0.830477i
\(937\) −8.41006 + 14.5666i −0.274745 + 0.475872i −0.970071 0.242823i \(-0.921927\pi\)
0.695326 + 0.718694i \(0.255260\pi\)
\(938\) 1.72713 + 0.944839i 0.0563927 + 0.0308501i
\(939\) 3.30653 + 8.83869i 0.107905 + 0.288440i
\(940\) −3.83152 + 2.45390i −0.124970 + 0.0800373i
\(941\) −41.9313 + 7.39363i −1.36692 + 0.241025i −0.808483 0.588520i \(-0.799711\pi\)
−0.558440 + 0.829545i \(0.688600\pi\)
\(942\) −3.82977 18.2851i −0.124781 0.595761i
\(943\) 22.6636 27.0094i 0.738028 0.879547i
\(944\) 12.5836 + 46.0767i 0.409561 + 1.49967i
\(945\) −7.54721 4.09232i −0.245511 0.133123i
\(946\) −5.83157 1.97175i −0.189601 0.0641071i
\(947\) 15.3512 + 12.8812i 0.498846 + 0.418582i 0.857184 0.515010i \(-0.172212\pi\)
−0.358338 + 0.933592i \(0.616656\pi\)
\(948\) 33.5439 14.3411i 1.08946 0.465777i
\(949\) 2.02831 + 11.5031i 0.0658418 + 0.373407i
\(950\) −9.89980 7.92591i −0.321192 0.257151i
\(951\) −9.26539 + 55.4314i −0.300451 + 1.79749i
\(952\) 9.28728 + 20.9025i 0.301003 + 0.677453i
\(953\) 52.7589 + 30.4604i 1.70903 + 0.986708i 0.935765 + 0.352624i \(0.114710\pi\)
0.773264 + 0.634085i \(0.218623\pi\)
\(954\) 19.0578 + 30.0996i 0.617018 + 0.974512i
\(955\) 29.9255 17.2775i 0.968366 0.559087i
\(956\) −18.7769 5.87081i −0.607287 0.189876i
\(957\) −18.7567 6.63814i −0.606317 0.214581i
\(958\) −0.453273 1.16146i −0.0146446 0.0375251i
\(959\) 0.454478 0.381352i 0.0146759 0.0123145i
\(960\) 22.4284 + 4.59440i 0.723874 + 0.148283i
\(961\) −2.41067 + 0.877412i −0.0777635 + 0.0283036i
\(962\) −27.4807 + 5.50054i −0.886013 + 0.177345i
\(963\) 10.9548 0.195314i 0.353013 0.00629390i
\(964\) −6.03867 + 2.51830i −0.194493 + 0.0811089i
\(965\) −0.169471 0.0298823i −0.00545546 0.000961945i
\(966\) −13.0956 + 8.12893i −0.421343 + 0.261544i
\(967\) 8.76806 24.0900i 0.281962 0.774684i −0.715167 0.698954i \(-0.753649\pi\)
0.997128 0.0757296i \(-0.0241286\pi\)
\(968\) −16.7965 17.4198i −0.539859 0.559895i
\(969\) 0.493177 + 55.3271i 0.0158431 + 1.77736i
\(970\) −14.2502 23.4202i −0.457547 0.751977i
\(971\) −28.1470 −0.903280 −0.451640 0.892200i \(-0.649161\pi\)
−0.451640 + 0.892200i \(0.649161\pi\)
\(972\) −28.2997 13.0816i −0.907712 0.419593i
\(973\) −18.3831 −0.589336
\(974\) −12.4811 20.5127i −0.399921 0.657270i
\(975\) 0.148353 + 16.6430i 0.00475111 + 0.533004i
\(976\) −39.0140 + 18.4210i −1.24881 + 0.589643i
\(977\) 4.05102 11.1301i 0.129604 0.356083i −0.857870 0.513867i \(-0.828213\pi\)
0.987474 + 0.157784i \(0.0504349\pi\)
\(978\) −10.5298 + 6.53627i −0.336706 + 0.209007i
\(979\) 25.5298 + 4.50160i 0.815937 + 0.143872i
\(980\) −1.27190 3.04990i −0.0406292 0.0974256i
\(981\) −20.0736 + 0.357895i −0.640901 + 0.0114267i
\(982\) −23.9269 + 4.78921i −0.763538 + 0.152830i
\(983\) −10.1156 + 3.68177i −0.322637 + 0.117430i −0.498261 0.867027i \(-0.666028\pi\)
0.175624 + 0.984457i \(0.443806\pi\)
\(984\) 19.2287 + 19.5898i 0.612989 + 0.624501i
\(985\) 25.8686 21.7063i 0.824241 0.691620i
\(986\) 30.5483 + 78.2766i 0.972856 + 2.49283i
\(987\) 2.24823 + 0.795666i 0.0715618 + 0.0253263i
\(988\) −9.97968 + 31.9184i −0.317496 + 1.01546i
\(989\) −15.1717 + 8.75940i −0.482433 + 0.278533i
\(990\) 5.86292 + 9.25984i 0.186336 + 0.294297i
\(991\) 45.5386 + 26.2917i 1.44658 + 0.835184i 0.998276 0.0586966i \(-0.0186945\pi\)
0.448305 + 0.893881i \(0.352028\pi\)
\(992\) 29.3427 + 6.99377i 0.931632 + 0.222053i
\(993\) −6.21198 + 37.1640i −0.197131 + 1.17936i
\(994\) 9.25126 + 7.40669i 0.293432 + 0.234926i
\(995\) 1.68344 + 9.54724i 0.0533685 + 0.302668i
\(996\) 23.6482 + 55.3132i 0.749321 + 1.75267i
\(997\) 9.88383 + 8.29352i 0.313024 + 0.262658i 0.785741 0.618556i \(-0.212282\pi\)
−0.472716 + 0.881215i \(0.656727\pi\)
\(998\) 41.0585 + 13.8825i 1.29968 + 0.439444i
\(999\) 20.7346 12.7222i 0.656013 0.402512i
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 756.2.cf.a.659.18 yes 648
4.3 odd 2 inner 756.2.cf.a.659.42 yes 648
27.5 odd 18 inner 756.2.cf.a.491.42 yes 648
108.59 even 18 inner 756.2.cf.a.491.18 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.cf.a.491.18 648 108.59 even 18 inner
756.2.cf.a.491.42 yes 648 27.5 odd 18 inner
756.2.cf.a.659.18 yes 648 1.1 even 1 trivial
756.2.cf.a.659.42 yes 648 4.3 odd 2 inner