Properties

Label 76.2.k.a.59.1
Level $76$
Weight $2$
Character 76.59
Analytic conductor $0.607$
Analytic rank $0$
Dimension $48$
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] = [76,2,Mod(3,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.k (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: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 59.1
Character \(\chi\) \(=\) 76.59
Dual form 76.2.k.a.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39408 + 0.237768i) q^{2} +(1.98545 + 1.66599i) q^{3} +(1.88693 - 0.662936i) q^{4} +(-2.53027 + 0.920944i) q^{5} +(-3.16400 - 1.85045i) q^{6} +(1.43753 - 0.829960i) q^{7} +(-2.47292 + 1.37284i) q^{8} +(0.645546 + 3.66107i) q^{9} +O(q^{10})\) \(q+(-1.39408 + 0.237768i) q^{2} +(1.98545 + 1.66599i) q^{3} +(1.88693 - 0.662936i) q^{4} +(-2.53027 + 0.920944i) q^{5} +(-3.16400 - 1.85045i) q^{6} +(1.43753 - 0.829960i) q^{7} +(-2.47292 + 1.37284i) q^{8} +(0.645546 + 3.66107i) q^{9} +(3.30844 - 1.88549i) q^{10} +(2.94034 + 1.69761i) q^{11} +(4.85086 + 1.82739i) q^{12} +(-2.17565 - 2.59283i) q^{13} +(-1.80670 + 1.49883i) q^{14} +(-6.55803 - 2.38693i) q^{15} +(3.12103 - 2.50183i) q^{16} +(1.03855 - 5.88992i) q^{17} +(-1.77043 - 4.95035i) q^{18} +(-4.28990 + 0.772510i) q^{19} +(-4.16393 + 3.41517i) q^{20} +(4.23686 + 0.747073i) q^{21} +(-4.50271 - 1.66749i) q^{22} +(2.01148 - 5.52649i) q^{23} +(-7.19700 - 1.39415i) q^{24} +(1.72393 - 1.44655i) q^{25} +(3.64952 + 3.09733i) q^{26} +(-0.929885 + 1.61061i) q^{27} +(2.16232 - 2.51907i) q^{28} +(-2.92975 + 0.516594i) q^{29} +(9.70996 + 1.76828i) q^{30} +(2.91510 + 5.04911i) q^{31} +(-3.75612 + 4.22984i) q^{32} +(3.00971 + 8.26910i) q^{33} +(-0.0473932 + 8.45798i) q^{34} +(-2.87301 + 3.42391i) q^{35} +(3.64516 + 6.48025i) q^{36} -0.798908i q^{37} +(5.79679 - 2.09694i) q^{38} -8.77256i q^{39} +(4.99284 - 5.75108i) q^{40} +(0.904276 - 1.07767i) q^{41} +(-6.08416 - 0.0340918i) q^{42} +(0.235045 + 0.645782i) q^{43} +(6.67363 + 1.25401i) q^{44} +(-5.00506 - 8.66901i) q^{45} +(-1.49014 + 8.18265i) q^{46} +(-6.47756 + 1.14217i) q^{47} +(10.3647 + 0.232345i) q^{48} +(-2.12233 + 3.67599i) q^{49} +(-2.05935 + 2.42650i) q^{50} +(11.8746 - 9.96394i) q^{51} +(-5.82418 - 3.45019i) q^{52} +(-2.91069 + 7.99704i) q^{53} +(0.913386 - 2.46642i) q^{54} +(-9.00327 - 1.58752i) q^{55} +(-2.41550 + 4.02592i) q^{56} +(-9.80439 - 5.61316i) q^{57} +(3.96148 - 1.41677i) q^{58} +(-0.838664 + 4.75630i) q^{59} +(-13.9569 - 0.156417i) q^{60} +(3.56100 + 1.29610i) q^{61} +(-5.26441 - 6.34575i) q^{62} +(3.96654 + 4.72714i) q^{63} +(4.23062 - 6.78983i) q^{64} +(7.89284 + 4.55693i) q^{65} +(-6.16191 - 10.8122i) q^{66} +(1.76401 + 10.0042i) q^{67} +(-1.94497 - 11.8024i) q^{68} +(13.2008 - 7.62148i) q^{69} +(3.19111 - 5.45633i) q^{70} +(-2.34943 + 0.855121i) q^{71} +(-6.62245 - 8.16730i) q^{72} +(-8.03196 - 6.73961i) q^{73} +(0.189955 + 1.11374i) q^{74} +5.83271 q^{75} +(-7.58263 + 4.30160i) q^{76} +5.63578 q^{77} +(2.08583 + 12.2297i) q^{78} +(6.98750 + 5.86321i) q^{79} +(-5.59302 + 9.20462i) q^{80} +(5.95057 - 2.16583i) q^{81} +(-1.00440 + 1.71737i) q^{82} +(6.78922 - 3.91976i) q^{83} +(8.48993 - 1.39909i) q^{84} +(2.79647 + 15.8596i) q^{85} +(-0.481219 - 0.844387i) q^{86} +(-6.67752 - 3.85527i) q^{87} +(-9.60176 - 0.161420i) q^{88} +(-7.99275 - 9.52539i) q^{89} +(9.03867 + 10.8953i) q^{90} +(-5.27951 - 1.92159i) q^{91} +(0.131813 - 11.7616i) q^{92} +(-2.62398 + 14.8813i) q^{93} +(8.75868 - 3.13243i) q^{94} +(10.1432 - 5.90542i) q^{95} +(-14.5045 + 2.14048i) q^{96} +(-8.40551 - 1.48212i) q^{97} +(2.08468 - 5.62925i) q^{98} +(-4.31694 + 11.8607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39408 + 0.237768i −0.985765 + 0.168127i
\(3\) 1.98545 + 1.66599i 1.14630 + 0.961861i 0.999627 0.0273235i \(-0.00869844\pi\)
0.146675 + 0.989185i \(0.453143\pi\)
\(4\) 1.88693 0.662936i 0.943466 0.331468i
\(5\) −2.53027 + 0.920944i −1.13157 + 0.411859i −0.838863 0.544342i \(-0.816779\pi\)
−0.292710 + 0.956201i \(0.594557\pi\)
\(6\) −3.16400 1.85045i −1.29170 0.755445i
\(7\) 1.43753 0.829960i 0.543336 0.313695i −0.203094 0.979159i \(-0.565100\pi\)
0.746430 + 0.665464i \(0.231766\pi\)
\(8\) −2.47292 + 1.37284i −0.874308 + 0.485372i
\(9\) 0.645546 + 3.66107i 0.215182 + 1.22036i
\(10\) 3.30844 1.88549i 1.04622 0.596245i
\(11\) 2.94034 + 1.69761i 0.886546 + 0.511848i 0.872811 0.488058i \(-0.162295\pi\)
0.0137349 + 0.999906i \(0.495628\pi\)
\(12\) 4.85086 + 1.82739i 1.40032 + 0.527521i
\(13\) −2.17565 2.59283i −0.603416 0.719123i 0.374709 0.927143i \(-0.377743\pi\)
−0.978125 + 0.208020i \(0.933298\pi\)
\(14\) −1.80670 + 1.49883i −0.482861 + 0.400580i
\(15\) −6.55803 2.38693i −1.69328 0.616302i
\(16\) 3.12103 2.50183i 0.780258 0.625458i
\(17\) 1.03855 5.88992i 0.251886 1.42852i −0.552055 0.833808i \(-0.686156\pi\)
0.803941 0.594709i \(-0.202733\pi\)
\(18\) −1.77043 4.95035i −0.417295 1.16681i
\(19\) −4.28990 + 0.772510i −0.984170 + 0.177226i
\(20\) −4.16393 + 3.41517i −0.931083 + 0.763655i
\(21\) 4.23686 + 0.747073i 0.924559 + 0.163025i
\(22\) −4.50271 1.66749i −0.959982 0.355509i
\(23\) 2.01148 5.52649i 0.419422 1.15235i −0.532611 0.846360i \(-0.678789\pi\)
0.952034 0.305993i \(-0.0989885\pi\)
\(24\) −7.19700 1.39415i −1.46908 0.284580i
\(25\) 1.72393 1.44655i 0.344785 0.289309i
\(26\) 3.64952 + 3.09733i 0.715731 + 0.607436i
\(27\) −0.929885 + 1.61061i −0.178957 + 0.309962i
\(28\) 2.16232 2.51907i 0.408640 0.476060i
\(29\) −2.92975 + 0.516594i −0.544040 + 0.0959290i −0.438913 0.898530i \(-0.644636\pi\)
−0.105128 + 0.994459i \(0.533525\pi\)
\(30\) 9.70996 + 1.76828i 1.77279 + 0.322843i
\(31\) 2.91510 + 5.04911i 0.523568 + 0.906846i 0.999624 + 0.0274312i \(0.00873273\pi\)
−0.476056 + 0.879415i \(0.657934\pi\)
\(32\) −3.75612 + 4.22984i −0.663994 + 0.747737i
\(33\) 3.00971 + 8.26910i 0.523923 + 1.43947i
\(34\) −0.0473932 + 8.45798i −0.00812787 + 1.45053i
\(35\) −2.87301 + 3.42391i −0.485627 + 0.578747i
\(36\) 3.64516 + 6.48025i 0.607527 + 1.08004i
\(37\) 0.798908i 0.131340i −0.997841 0.0656699i \(-0.979082\pi\)
0.997841 0.0656699i \(-0.0209184\pi\)
\(38\) 5.79679 2.09694i 0.940364 0.340169i
\(39\) 8.77256i 1.40473i
\(40\) 4.99284 5.75108i 0.789438 0.909325i
\(41\) 0.904276 1.07767i 0.141224 0.168304i −0.690796 0.723050i \(-0.742740\pi\)
0.832020 + 0.554745i \(0.187184\pi\)
\(42\) −6.08416 0.0340918i −0.938807 0.00526049i
\(43\) 0.235045 + 0.645782i 0.0358441 + 0.0984808i 0.956324 0.292310i \(-0.0944239\pi\)
−0.920480 + 0.390791i \(0.872202\pi\)
\(44\) 6.67363 + 1.25401i 1.00609 + 0.189049i
\(45\) −5.00506 8.66901i −0.746110 1.29230i
\(46\) −1.49014 + 8.18265i −0.219710 + 1.20647i
\(47\) −6.47756 + 1.14217i −0.944849 + 0.166602i −0.624788 0.780794i \(-0.714815\pi\)
−0.320061 + 0.947397i \(0.603704\pi\)
\(48\) 10.3647 + 0.232345i 1.49601 + 0.0335362i
\(49\) −2.12233 + 3.67599i −0.303190 + 0.525141i
\(50\) −2.05935 + 2.42650i −0.291237 + 0.343159i
\(51\) 11.8746 9.96394i 1.66277 1.39523i
\(52\) −5.82418 3.45019i −0.807669 0.478455i
\(53\) −2.91069 + 7.99704i −0.399813 + 1.09848i 0.562562 + 0.826755i \(0.309816\pi\)
−0.962375 + 0.271723i \(0.912406\pi\)
\(54\) 0.913386 2.46642i 0.124296 0.335637i
\(55\) −9.00327 1.58752i −1.21400 0.214061i
\(56\) −2.41550 + 4.02592i −0.322784 + 0.537987i
\(57\) −9.80439 5.61316i −1.29862 0.743481i
\(58\) 3.96148 1.41677i 0.520168 0.186032i
\(59\) −0.838664 + 4.75630i −0.109185 + 0.619218i 0.880281 + 0.474452i \(0.157354\pi\)
−0.989466 + 0.144765i \(0.953757\pi\)
\(60\) −13.9569 0.156417i −1.80183 0.0201933i
\(61\) 3.56100 + 1.29610i 0.455939 + 0.165948i 0.559772 0.828647i \(-0.310889\pi\)
−0.103833 + 0.994595i \(0.533111\pi\)
\(62\) −5.26441 6.34575i −0.668581 0.805912i
\(63\) 3.96654 + 4.72714i 0.499737 + 0.595563i
\(64\) 4.23062 6.78983i 0.528828 0.848729i
\(65\) 7.89284 + 4.55693i 0.978986 + 0.565218i
\(66\) −6.16191 10.8122i −0.758478 1.33089i
\(67\) 1.76401 + 10.0042i 0.215509 + 1.22221i 0.880022 + 0.474934i \(0.157528\pi\)
−0.664513 + 0.747277i \(0.731361\pi\)
\(68\) −1.94497 11.8024i −0.235862 1.43125i
\(69\) 13.2008 7.62148i 1.58919 0.917518i
\(70\) 3.19111 5.45633i 0.381411 0.652156i
\(71\) −2.34943 + 0.855121i −0.278825 + 0.101484i −0.477648 0.878551i \(-0.658511\pi\)
0.198822 + 0.980036i \(0.436288\pi\)
\(72\) −6.62245 8.16730i −0.780463 0.962525i
\(73\) −8.03196 6.73961i −0.940069 0.788812i 0.0375281 0.999296i \(-0.488052\pi\)
−0.977597 + 0.210484i \(0.932496\pi\)
\(74\) 0.189955 + 1.11374i 0.0220818 + 0.129470i
\(75\) 5.83271 0.673503
\(76\) −7.58263 + 4.30160i −0.869787 + 0.493428i
\(77\) 5.63578 0.642257
\(78\) 2.08583 + 12.2297i 0.236174 + 1.38474i
\(79\) 6.98750 + 5.86321i 0.786156 + 0.659663i 0.944791 0.327674i \(-0.106265\pi\)
−0.158635 + 0.987337i \(0.550709\pi\)
\(80\) −5.59302 + 9.20462i −0.625318 + 1.02911i
\(81\) 5.95057 2.16583i 0.661174 0.240648i
\(82\) −1.00440 + 1.71737i −0.110917 + 0.189652i
\(83\) 6.78922 3.91976i 0.745213 0.430249i −0.0787485 0.996895i \(-0.525092\pi\)
0.823962 + 0.566645i \(0.191759\pi\)
\(84\) 8.48993 1.39909i 0.926328 0.152653i
\(85\) 2.79647 + 15.8596i 0.303320 + 1.72021i
\(86\) −0.481219 0.844387i −0.0518911 0.0910526i
\(87\) −6.67752 3.85527i −0.715905 0.413328i
\(88\) −9.60176 0.161420i −1.02355 0.0172075i
\(89\) −7.99275 9.52539i −0.847230 1.00969i −0.999771 0.0213925i \(-0.993190\pi\)
0.152541 0.988297i \(-0.451254\pi\)
\(90\) 9.03867 + 10.8953i 0.952760 + 1.14846i
\(91\) −5.27951 1.92159i −0.553443 0.201437i
\(92\) 0.131813 11.7616i 0.0137425 1.22623i
\(93\) −2.62398 + 14.8813i −0.272094 + 1.54312i
\(94\) 8.75868 3.13243i 0.903389 0.323086i
\(95\) 10.1432 5.90542i 1.04067 0.605883i
\(96\) −14.5045 + 2.14048i −1.48036 + 0.218462i
\(97\) −8.40551 1.48212i −0.853451 0.150486i −0.270226 0.962797i \(-0.587098\pi\)
−0.583225 + 0.812311i \(0.698209\pi\)
\(98\) 2.08468 5.62925i 0.210584 0.568640i
\(99\) −4.31694 + 11.8607i −0.433869 + 1.19204i
\(100\) 2.29397 3.87239i 0.229397 0.387239i
\(101\) −0.0868957 + 0.0729142i −0.00864645 + 0.00725523i −0.647101 0.762405i \(-0.724019\pi\)
0.638454 + 0.769660i \(0.279574\pi\)
\(102\) −14.1850 + 16.7140i −1.40453 + 1.65493i
\(103\) 3.35278 5.80718i 0.330359 0.572199i −0.652223 0.758027i \(-0.726163\pi\)
0.982582 + 0.185828i \(0.0594968\pi\)
\(104\) 8.93974 + 3.42505i 0.876613 + 0.335853i
\(105\) −11.4084 + 2.01161i −1.11335 + 0.196313i
\(106\) 2.15630 11.8406i 0.209438 1.15006i
\(107\) −2.83864 4.91666i −0.274421 0.475312i 0.695568 0.718461i \(-0.255153\pi\)
−0.969989 + 0.243149i \(0.921820\pi\)
\(108\) −0.686900 + 3.65556i −0.0660970 + 0.351757i
\(109\) −2.68819 7.38575i −0.257482 0.707427i −0.999321 0.0368484i \(-0.988268\pi\)
0.741839 0.670579i \(-0.233954\pi\)
\(110\) 12.9288 + 0.0724447i 1.23271 + 0.00690733i
\(111\) 1.33098 1.58619i 0.126331 0.150555i
\(112\) 2.41016 6.18680i 0.227739 0.584597i
\(113\) 9.61911i 0.904890i 0.891792 + 0.452445i \(0.149448\pi\)
−0.891792 + 0.452445i \(0.850552\pi\)
\(114\) 15.0028 + 5.49404i 1.40514 + 0.514564i
\(115\) 15.8360i 1.47671i
\(116\) −5.18577 + 2.91701i −0.481487 + 0.270838i
\(117\) 8.08808 9.63900i 0.747743 0.891126i
\(118\) 0.0382715 6.83009i 0.00352318 0.628760i
\(119\) −3.39545 9.32892i −0.311260 0.855180i
\(120\) 19.4943 3.10045i 1.77958 0.283031i
\(121\) 0.263736 + 0.456803i 0.0239760 + 0.0415276i
\(122\) −5.27249 0.960175i −0.477349 0.0869302i
\(123\) 3.59079 0.633154i 0.323771 0.0570896i
\(124\) 8.84784 + 7.59480i 0.794559 + 0.682033i
\(125\) 3.70184 6.41177i 0.331102 0.573486i
\(126\) −6.65365 5.64691i −0.592754 0.503066i
\(127\) −6.20191 + 5.20402i −0.550331 + 0.461782i −0.875053 0.484027i \(-0.839174\pi\)
0.324722 + 0.945809i \(0.394729\pi\)
\(128\) −4.28343 + 10.4715i −0.378605 + 0.925558i
\(129\) −0.609196 + 1.67375i −0.0536367 + 0.147366i
\(130\) −12.0868 4.47608i −1.06008 0.392578i
\(131\) 5.31618 + 0.937385i 0.464476 + 0.0818997i 0.400989 0.916083i \(-0.368667\pi\)
0.0634875 + 0.997983i \(0.479778\pi\)
\(132\) 11.1610 + 13.6080i 0.971441 + 1.18442i
\(133\) −5.52572 + 4.67095i −0.479141 + 0.405023i
\(134\) −4.83787 13.5273i −0.417928 1.16858i
\(135\) 0.869584 4.93165i 0.0748418 0.424449i
\(136\) 5.51767 + 15.9911i 0.473136 + 1.37122i
\(137\) 10.8411 + 3.94583i 0.926216 + 0.337115i 0.760709 0.649093i \(-0.224852\pi\)
0.165507 + 0.986209i \(0.447074\pi\)
\(138\) −16.5908 + 13.7637i −1.41231 + 1.17164i
\(139\) −3.12723 3.72688i −0.265248 0.316110i 0.616938 0.787012i \(-0.288373\pi\)
−0.882186 + 0.470902i \(0.843929\pi\)
\(140\) −3.15133 + 8.36532i −0.266336 + 0.706998i
\(141\) −14.7637 8.52385i −1.24333 0.717837i
\(142\) 3.07197 1.75073i 0.257794 0.146918i
\(143\) −1.99553 11.3172i −0.166875 0.946393i
\(144\) 11.1742 + 9.81128i 0.931180 + 0.817607i
\(145\) 6.93731 4.00526i 0.576112 0.332619i
\(146\) 12.7997 + 7.48583i 1.05931 + 0.619532i
\(147\) −10.3380 + 3.76271i −0.852660 + 0.310343i
\(148\) −0.529625 1.50749i −0.0435349 0.123915i
\(149\) 14.3556 + 12.0458i 1.17606 + 0.986831i 0.999997 + 0.00245146i \(0.000780324\pi\)
0.176062 + 0.984379i \(0.443664\pi\)
\(150\) −8.13128 + 1.38683i −0.663916 + 0.113234i
\(151\) −6.11110 −0.497314 −0.248657 0.968592i \(-0.579989\pi\)
−0.248657 + 0.968592i \(0.579989\pi\)
\(152\) 9.54802 7.79970i 0.774447 0.632639i
\(153\) 22.2339 1.79750
\(154\) −7.85675 + 1.34001i −0.633115 + 0.107981i
\(155\) −12.0260 10.0910i −0.965948 0.810527i
\(156\) −5.81565 16.5532i −0.465624 1.32532i
\(157\) 3.67562 1.33782i 0.293347 0.106769i −0.191155 0.981560i \(-0.561223\pi\)
0.484501 + 0.874790i \(0.339001\pi\)
\(158\) −11.1352 6.51240i −0.885872 0.518099i
\(159\) −19.1020 + 11.0286i −1.51489 + 0.874622i
\(160\) 5.60856 14.1618i 0.443396 1.11959i
\(161\) −1.69520 9.61396i −0.133601 0.757686i
\(162\) −7.78062 + 4.43420i −0.611303 + 0.348383i
\(163\) −3.89527 2.24893i −0.305101 0.176150i 0.339631 0.940559i \(-0.389698\pi\)
−0.644732 + 0.764409i \(0.723031\pi\)
\(164\) 0.991879 2.63298i 0.0774527 0.205601i
\(165\) −15.2308 18.1513i −1.18571 1.41308i
\(166\) −8.53274 + 7.07872i −0.662269 + 0.549415i
\(167\) 14.9157 + 5.42887i 1.15421 + 0.420099i 0.847026 0.531551i \(-0.178391\pi\)
0.307185 + 0.951650i \(0.400613\pi\)
\(168\) −11.5030 + 3.96908i −0.887476 + 0.306221i
\(169\) 0.268073 1.52032i 0.0206210 0.116948i
\(170\) −7.66941 21.4446i −0.588217 1.64473i
\(171\) −5.59754 15.2069i −0.428055 1.16290i
\(172\) 0.871627 + 1.06273i 0.0664609 + 0.0810321i
\(173\) −4.51044 0.795312i −0.342922 0.0604664i −0.000465084 1.00000i \(-0.500148\pi\)
−0.342457 + 0.939533i \(0.611259\pi\)
\(174\) 10.2257 + 3.78686i 0.775206 + 0.287081i
\(175\) 1.27763 3.51025i 0.0965794 0.265350i
\(176\) 13.4240 2.05796i 1.01187 0.155124i
\(177\) −9.58909 + 8.04620i −0.720760 + 0.604790i
\(178\) 13.4074 + 11.3788i 1.00493 + 0.852875i
\(179\) 3.50718 6.07462i 0.262139 0.454039i −0.704671 0.709534i \(-0.748905\pi\)
0.966810 + 0.255496i \(0.0822387\pi\)
\(180\) −15.1912 13.0398i −1.13229 0.971930i
\(181\) 2.24482 0.395823i 0.166856 0.0294213i −0.0895957 0.995978i \(-0.528558\pi\)
0.256452 + 0.966557i \(0.417446\pi\)
\(182\) 7.81697 + 1.42355i 0.579432 + 0.105521i
\(183\) 4.91090 + 8.50593i 0.363024 + 0.628776i
\(184\) 2.61277 + 16.4280i 0.192616 + 1.21109i
\(185\) 0.735750 + 2.02146i 0.0540934 + 0.148620i
\(186\) 0.119742 21.3697i 0.00877992 1.56690i
\(187\) 13.0525 15.5553i 0.954491 1.13752i
\(188\) −11.4655 + 6.44941i −0.836210 + 0.470371i
\(189\) 3.08707i 0.224551i
\(190\) −12.7363 + 10.6444i −0.923989 + 0.772223i
\(191\) 23.8531i 1.72595i 0.505245 + 0.862976i \(0.331402\pi\)
−0.505245 + 0.862976i \(0.668598\pi\)
\(192\) 19.7115 6.43271i 1.42256 0.464241i
\(193\) 10.3925 12.3853i 0.748066 0.891511i −0.248965 0.968513i \(-0.580090\pi\)
0.997031 + 0.0770018i \(0.0245347\pi\)
\(194\) 12.0704 + 0.0676349i 0.866603 + 0.00485590i
\(195\) 8.07904 + 22.1970i 0.578552 + 1.58956i
\(196\) −1.56775 + 8.34331i −0.111982 + 0.595951i
\(197\) −1.59411 2.76108i −0.113576 0.196719i 0.803634 0.595124i \(-0.202897\pi\)
−0.917209 + 0.398405i \(0.869564\pi\)
\(198\) 3.19808 17.5612i 0.227277 1.24802i
\(199\) −11.2456 + 1.98291i −0.797183 + 0.140565i −0.557381 0.830257i \(-0.688194\pi\)
−0.239802 + 0.970822i \(0.577083\pi\)
\(200\) −2.27725 + 5.94386i −0.161026 + 0.420294i
\(201\) −13.1646 + 22.8018i −0.928559 + 1.60831i
\(202\) 0.103803 0.122309i 0.00730356 0.00860566i
\(203\) −3.78286 + 3.17419i −0.265505 + 0.222785i
\(204\) 15.8011 26.6734i 1.10629 1.86751i
\(205\) −1.29559 + 3.55960i −0.0904878 + 0.248613i
\(206\) −3.29329 + 8.89288i −0.229454 + 0.619596i
\(207\) 21.5314 + 3.79657i 1.49654 + 0.263880i
\(208\) −13.2771 2.64922i −0.920601 0.183690i
\(209\) −13.9252 5.01112i −0.963225 0.346626i
\(210\) 15.4260 5.51692i 1.06450 0.380703i
\(211\) 0.664785 3.77018i 0.0457657 0.259550i −0.953337 0.301909i \(-0.902376\pi\)
0.999102 + 0.0423589i \(0.0134873\pi\)
\(212\) −0.190739 + 17.0195i −0.0131000 + 1.16890i
\(213\) −6.08930 2.21632i −0.417232 0.151860i
\(214\) 5.12632 + 6.17930i 0.350428 + 0.422408i
\(215\) −1.18946 1.41754i −0.0811204 0.0966755i
\(216\) 0.0884199 5.25948i 0.00601621 0.357862i
\(217\) 8.38111 + 4.83884i 0.568947 + 0.328482i
\(218\) 5.50366 + 9.65719i 0.372755 + 0.654067i
\(219\) −4.71893 26.7624i −0.318875 1.80843i
\(220\) −18.0410 + 2.97305i −1.21632 + 0.200443i
\(221\) −17.5311 + 10.1216i −1.17927 + 0.680852i
\(222\) −1.47834 + 2.52775i −0.0992199 + 0.169651i
\(223\) 22.3608 8.13865i 1.49739 0.545004i 0.542004 0.840376i \(-0.317666\pi\)
0.955382 + 0.295372i \(0.0954435\pi\)
\(224\) −1.88895 + 9.19797i −0.126211 + 0.614565i
\(225\) 6.40879 + 5.37761i 0.427253 + 0.358507i
\(226\) −2.28712 13.4098i −0.152137 0.892009i
\(227\) −21.4255 −1.42206 −0.711031 0.703161i \(-0.751771\pi\)
−0.711031 + 0.703161i \(0.751771\pi\)
\(228\) −22.2214 4.09197i −1.47165 0.270997i
\(229\) −17.6065 −1.16347 −0.581735 0.813378i \(-0.697626\pi\)
−0.581735 + 0.813378i \(0.697626\pi\)
\(230\) −3.76529 22.0767i −0.248276 1.45569i
\(231\) 11.1896 + 9.38917i 0.736220 + 0.617762i
\(232\) 6.53582 5.29957i 0.429097 0.347934i
\(233\) 10.9408 3.98214i 0.716758 0.260879i 0.0422092 0.999109i \(-0.486560\pi\)
0.674549 + 0.738230i \(0.264338\pi\)
\(234\) −8.98361 + 15.3606i −0.587277 + 1.00416i
\(235\) 15.3381 8.85547i 1.00055 0.577667i
\(236\) 1.57062 + 9.53080i 0.102239 + 0.620402i
\(237\) 4.10529 + 23.2823i 0.266667 + 1.51235i
\(238\) 6.95165 + 12.1980i 0.450609 + 0.790676i
\(239\) 15.1464 + 8.74479i 0.979741 + 0.565654i 0.902192 0.431335i \(-0.141957\pi\)
0.0775489 + 0.996989i \(0.475291\pi\)
\(240\) −26.4395 + 8.95741i −1.70666 + 0.578198i
\(241\) 17.4817 + 20.8339i 1.12610 + 1.34203i 0.932593 + 0.360930i \(0.117541\pi\)
0.193504 + 0.981100i \(0.438015\pi\)
\(242\) −0.476282 0.574114i −0.0306166 0.0369054i
\(243\) 20.6657 + 7.52168i 1.32570 + 0.482516i
\(244\) 7.57859 + 0.0849340i 0.485169 + 0.00543734i
\(245\) 1.98470 11.2558i 0.126798 0.719107i
\(246\) −4.85532 + 1.73644i −0.309564 + 0.110712i
\(247\) 11.3363 + 9.44229i 0.721311 + 0.600798i
\(248\) −14.1404 8.48404i −0.897918 0.538737i
\(249\) 20.0099 + 3.52829i 1.26808 + 0.223597i
\(250\) −3.63615 + 9.81871i −0.229970 + 0.620990i
\(251\) −7.93890 + 21.8120i −0.501099 + 1.37676i 0.389103 + 0.921194i \(0.372785\pi\)
−0.890203 + 0.455565i \(0.849437\pi\)
\(252\) 10.6184 + 6.29023i 0.668895 + 0.396247i
\(253\) 15.2962 12.8351i 0.961666 0.806934i
\(254\) 7.40863 8.72945i 0.464859 0.547734i
\(255\) −20.8697 + 36.1473i −1.30691 + 2.26363i
\(256\) 3.48167 15.6166i 0.217604 0.976037i
\(257\) −8.80240 + 1.55210i −0.549079 + 0.0968174i −0.441303 0.897358i \(-0.645484\pi\)
−0.107775 + 0.994175i \(0.534373\pi\)
\(258\) 0.451305 2.47820i 0.0280970 0.154286i
\(259\) −0.663062 1.14846i −0.0412007 0.0713617i
\(260\) 17.9142 + 3.36618i 1.11099 + 0.208761i
\(261\) −3.78258 10.3925i −0.234136 0.643282i
\(262\) −7.63407 0.0427765i −0.471634 0.00264274i
\(263\) 0.382797 0.456200i 0.0236043 0.0281305i −0.754113 0.656744i \(-0.771933\pi\)
0.777717 + 0.628614i \(0.216377\pi\)
\(264\) −18.7949 16.3169i −1.15675 1.00424i
\(265\) 22.9153i 1.40768i
\(266\) 6.59271 7.82553i 0.404225 0.479814i
\(267\) 32.2281i 1.97233i
\(268\) 9.96074 + 17.7079i 0.608449 + 1.08168i
\(269\) 6.62803 7.89898i 0.404118 0.481609i −0.525153 0.851008i \(-0.675992\pi\)
0.929271 + 0.369399i \(0.120436\pi\)
\(270\) −0.0396825 + 7.08189i −0.00241500 + 0.430990i
\(271\) −4.03735 11.0925i −0.245252 0.673823i −0.999845 0.0176301i \(-0.994388\pi\)
0.754593 0.656193i \(-0.227834\pi\)
\(272\) −11.4942 20.9809i −0.696941 1.27216i
\(273\) −7.28088 12.6108i −0.440659 0.763243i
\(274\) −16.0516 2.92315i −0.969710 0.176594i
\(275\) 7.52460 1.32679i 0.453750 0.0800084i
\(276\) 19.8564 23.1325i 1.19522 1.39241i
\(277\) −14.1103 + 24.4398i −0.847807 + 1.46844i 0.0353540 + 0.999375i \(0.488744\pi\)
−0.883161 + 0.469070i \(0.844589\pi\)
\(278\) 5.24575 + 4.45203i 0.314619 + 0.267015i
\(279\) −16.6033 + 13.9318i −0.994015 + 0.834078i
\(280\) 2.40421 12.4112i 0.143679 0.741713i
\(281\) 1.73634 4.77054i 0.103581 0.284587i −0.877066 0.480370i \(-0.840503\pi\)
0.980647 + 0.195783i \(0.0627248\pi\)
\(282\) 22.6086 + 8.37260i 1.34632 + 0.498581i
\(283\) −4.41352 0.778223i −0.262357 0.0462605i 0.0409225 0.999162i \(-0.486970\pi\)
−0.303279 + 0.952902i \(0.598081\pi\)
\(284\) −3.86632 + 3.17107i −0.229424 + 0.188169i
\(285\) 29.9772 + 5.17353i 1.77570 + 0.306454i
\(286\) 5.47280 + 15.3027i 0.323614 + 0.904865i
\(287\) 0.405500 2.29971i 0.0239359 0.135747i
\(288\) −17.9105 11.0209i −1.05539 0.649411i
\(289\) −17.6378 6.41965i −1.03752 0.377626i
\(290\) −8.71886 + 7.23313i −0.511989 + 0.424744i
\(291\) −14.2195 16.9462i −0.833565 0.993404i
\(292\) −19.6237 7.39252i −1.14839 0.432614i
\(293\) −19.7434 11.3988i −1.15342 0.665928i −0.203702 0.979033i \(-0.565298\pi\)
−0.949719 + 0.313105i \(0.898631\pi\)
\(294\) 13.5173 7.70356i 0.788346 0.449281i
\(295\) −2.25824 12.8071i −0.131480 0.745659i
\(296\) 1.09677 + 1.97563i 0.0637487 + 0.114831i
\(297\) −5.46836 + 3.15716i −0.317306 + 0.183197i
\(298\) −22.8770 13.3795i −1.32523 0.775056i
\(299\) −18.7055 + 6.80826i −1.08177 + 0.393732i
\(300\) 11.0059 3.86671i 0.635428 0.223245i
\(301\) 0.873858 + 0.733254i 0.0503684 + 0.0422641i
\(302\) 8.51938 1.45302i 0.490235 0.0836121i
\(303\) −0.294002 −0.0168900
\(304\) −11.4562 + 13.1436i −0.657059 + 0.753839i
\(305\) −10.2039 −0.584275
\(306\) −30.9959 + 5.28650i −1.77192 + 0.302209i
\(307\) −25.9825 21.8019i −1.48290 1.24430i −0.903019 0.429602i \(-0.858654\pi\)
−0.579882 0.814700i \(-0.696902\pi\)
\(308\) 10.6343 3.73616i 0.605948 0.212888i
\(309\) 16.3315 5.94418i 0.929067 0.338153i
\(310\) 19.1645 + 11.2083i 1.08847 + 0.636587i
\(311\) 15.6547 9.03827i 0.887699 0.512513i 0.0145095 0.999895i \(-0.495381\pi\)
0.873189 + 0.487382i \(0.162048\pi\)
\(312\) 12.0433 + 21.6938i 0.681819 + 1.22817i
\(313\) 0.100851 + 0.571953i 0.00570042 + 0.0323287i 0.987525 0.157460i \(-0.0503307\pi\)
−0.981825 + 0.189789i \(0.939220\pi\)
\(314\) −4.80603 + 2.73897i −0.271220 + 0.154569i
\(315\) −14.3899 8.30799i −0.810777 0.468102i
\(316\) 17.0719 + 6.43122i 0.960369 + 0.361784i
\(317\) −0.495890 0.590979i −0.0278520 0.0331927i 0.751939 0.659233i \(-0.229119\pi\)
−0.779791 + 0.626040i \(0.784674\pi\)
\(318\) 24.0076 19.9166i 1.34628 1.11687i
\(319\) −9.49143 3.45460i −0.531418 0.193420i
\(320\) −4.45157 + 21.0763i −0.248850 + 1.17820i
\(321\) 2.55515 14.4909i 0.142614 0.808806i
\(322\) 4.64914 + 12.9996i 0.259087 + 0.724439i
\(323\) 0.0947395 + 26.0695i 0.00527145 + 1.45054i
\(324\) 9.79251 8.03162i 0.544028 0.446201i
\(325\) −7.50131 1.32268i −0.416098 0.0733693i
\(326\) 5.96505 + 2.20903i 0.330374 + 0.122347i
\(327\) 6.96733 19.1426i 0.385294 1.05859i
\(328\) −0.756724 + 3.90642i −0.0417831 + 0.215696i
\(329\) −8.36375 + 7.01802i −0.461109 + 0.386916i
\(330\) 25.5488 + 21.6831i 1.40641 + 1.19361i
\(331\) 11.5517 20.0081i 0.634937 1.09974i −0.351591 0.936154i \(-0.614359\pi\)
0.986528 0.163590i \(-0.0523073\pi\)
\(332\) 10.2122 11.8971i 0.560470 0.652940i
\(333\) 2.92486 0.515732i 0.160282 0.0282620i
\(334\) −22.0845 4.02182i −1.20841 0.220064i
\(335\) −13.6768 23.6889i −0.747242 1.29426i
\(336\) 15.0924 8.26828i 0.823359 0.451071i
\(337\) −1.58775 4.36231i −0.0864903 0.237630i 0.888906 0.458090i \(-0.151466\pi\)
−0.975396 + 0.220460i \(0.929244\pi\)
\(338\) −0.0122332 + 2.18319i −0.000665399 + 0.118750i
\(339\) −16.0254 + 19.0983i −0.870378 + 1.03728i
\(340\) 15.7906 + 28.0721i 0.856368 + 1.52242i
\(341\) 19.7948i 1.07195i
\(342\) 11.4192 + 19.8688i 0.617478 + 1.07438i
\(343\) 18.6652i 1.00783i
\(344\) −1.46780 1.27428i −0.0791386 0.0687048i
\(345\) −26.3827 + 31.4416i −1.42039 + 1.69276i
\(346\) 6.47702 + 0.0362932i 0.348207 + 0.00195113i
\(347\) 7.62858 + 20.9593i 0.409524 + 1.12516i 0.957442 + 0.288625i \(0.0931981\pi\)
−0.547919 + 0.836532i \(0.684580\pi\)
\(348\) −15.1558 2.84786i −0.812437 0.152661i
\(349\) 6.79776 + 11.7741i 0.363876 + 0.630251i 0.988595 0.150598i \(-0.0481200\pi\)
−0.624719 + 0.780849i \(0.714787\pi\)
\(350\) −0.946492 + 5.19735i −0.0505921 + 0.277810i
\(351\) 6.19914 1.09308i 0.330886 0.0583441i
\(352\) −18.2249 + 6.06076i −0.971389 + 0.323040i
\(353\) 12.5636 21.7608i 0.668692 1.15821i −0.309578 0.950874i \(-0.600188\pi\)
0.978270 0.207335i \(-0.0664789\pi\)
\(354\) 11.4549 13.4970i 0.608819 0.717360i
\(355\) 5.15717 4.32738i 0.273714 0.229674i
\(356\) −21.3965 12.6751i −1.13401 0.671779i
\(357\) 8.80041 24.1789i 0.465767 1.27968i
\(358\) −3.44496 + 9.30242i −0.182072 + 0.491648i
\(359\) −9.73513 1.71657i −0.513800 0.0905969i −0.0892644 0.996008i \(-0.528452\pi\)
−0.424536 + 0.905411i \(0.639563\pi\)
\(360\) 24.2782 + 14.5666i 1.27958 + 0.767727i
\(361\) 17.8065 6.62798i 0.937182 0.348841i
\(362\) −3.03536 + 1.08556i −0.159535 + 0.0570556i
\(363\) −0.237397 + 1.34634i −0.0124601 + 0.0706647i
\(364\) −11.2360 0.125923i −0.588925 0.00660014i
\(365\) 26.5299 + 9.65608i 1.38864 + 0.505422i
\(366\) −8.86864 10.6903i −0.463571 0.558792i
\(367\) 20.2739 + 24.1615i 1.05829 + 1.26122i 0.964064 + 0.265671i \(0.0855935\pi\)
0.0942270 + 0.995551i \(0.469962\pi\)
\(368\) −7.54847 22.2807i −0.393491 1.16146i
\(369\) 4.52920 + 2.61493i 0.235781 + 0.136128i
\(370\) −1.50633 2.64314i −0.0783106 0.137410i
\(371\) 2.45302 + 13.9118i 0.127354 + 0.722263i
\(372\) 4.91409 + 29.8195i 0.254784 + 1.54607i
\(373\) 17.2111 9.93681i 0.891155 0.514509i 0.0168350 0.999858i \(-0.494641\pi\)
0.874320 + 0.485350i \(0.161308\pi\)
\(374\) −14.4977 + 24.7889i −0.749656 + 1.28180i
\(375\) 18.0318 6.56303i 0.931157 0.338913i
\(376\) 14.4504 11.7171i 0.745225 0.604265i
\(377\) 7.71354 + 6.47243i 0.397267 + 0.333347i
\(378\) −0.734006 4.30363i −0.0377532 0.221355i
\(379\) 36.4793 1.87382 0.936909 0.349573i \(-0.113673\pi\)
0.936909 + 0.349573i \(0.113673\pi\)
\(380\) 15.2246 17.8674i 0.781005 0.916579i
\(381\) −20.9835 −1.07502
\(382\) −5.67151 33.2532i −0.290180 1.70138i
\(383\) 14.8965 + 12.4996i 0.761175 + 0.638702i 0.938432 0.345463i \(-0.112278\pi\)
−0.177258 + 0.984164i \(0.556723\pi\)
\(384\) −25.9500 + 13.6545i −1.32425 + 0.696803i
\(385\) −14.2601 + 5.19024i −0.726761 + 0.264519i
\(386\) −11.5431 + 19.7371i −0.587531 + 1.00459i
\(387\) −2.21252 + 1.27740i −0.112469 + 0.0649339i
\(388\) −16.8432 + 2.77566i −0.855083 + 0.140913i
\(389\) −1.67034 9.47298i −0.0846897 0.480299i −0.997423 0.0717435i \(-0.977144\pi\)
0.912733 0.408556i \(-0.133967\pi\)
\(390\) −16.5406 29.0235i −0.837565 1.46966i
\(391\) −30.4616 17.5870i −1.54051 0.889413i
\(392\) 0.201806 12.0040i 0.0101927 0.606295i
\(393\) 8.99334 + 10.7178i 0.453654 + 0.540644i
\(394\) 2.87881 + 3.47014i 0.145033 + 0.174823i
\(395\) −23.0800 8.40043i −1.16128 0.422671i
\(396\) −0.282892 + 25.2422i −0.0142158 + 1.26847i
\(397\) −0.0229782 + 0.130316i −0.00115324 + 0.00654036i −0.985379 0.170377i \(-0.945501\pi\)
0.984226 + 0.176917i \(0.0566125\pi\)
\(398\) 15.2059 5.43820i 0.762202 0.272592i
\(399\) −18.7528 + 0.0681499i −0.938815 + 0.00341176i
\(400\) 1.76141 8.82769i 0.0880706 0.441385i
\(401\) −1.91187 0.337113i −0.0954740 0.0168346i 0.125707 0.992067i \(-0.459880\pi\)
−0.221181 + 0.975233i \(0.570991\pi\)
\(402\) 12.9310 34.9176i 0.644940 1.74153i
\(403\) 6.74926 18.5435i 0.336205 0.923715i
\(404\) −0.115629 + 0.195190i −0.00575275 + 0.00971109i
\(405\) −13.0620 + 10.9603i −0.649054 + 0.544621i
\(406\) 4.51889 5.32453i 0.224269 0.264252i
\(407\) 1.35623 2.34906i 0.0672259 0.116439i
\(408\) −15.6859 + 40.9419i −0.776568 + 2.02692i
\(409\) −27.0452 + 4.76879i −1.33730 + 0.235802i −0.796136 0.605117i \(-0.793126\pi\)
−0.541161 + 0.840919i \(0.682015\pi\)
\(410\) 0.959799 5.27042i 0.0474011 0.260288i
\(411\) 14.9507 + 25.8954i 0.737465 + 1.27733i
\(412\) 2.47668 13.1804i 0.122017 0.649354i
\(413\) 2.74193 + 7.53340i 0.134922 + 0.370694i
\(414\) −30.9193 0.173252i −1.51960 0.00851488i
\(415\) −13.5687 + 16.1705i −0.666061 + 0.793781i
\(416\) 19.1393 + 0.536357i 0.938380 + 0.0262971i
\(417\) 12.6095i 0.617489i
\(418\) 20.6043 + 3.67495i 1.00779 + 0.179748i
\(419\) 6.34043i 0.309750i −0.987934 0.154875i \(-0.950503\pi\)
0.987934 0.154875i \(-0.0494975\pi\)
\(420\) −20.1934 + 11.3588i −0.985336 + 0.554255i
\(421\) 7.49154 8.92808i 0.365116 0.435128i −0.551942 0.833882i \(-0.686113\pi\)
0.917058 + 0.398755i \(0.130558\pi\)
\(422\) −0.0303367 + 5.41401i −0.00147677 + 0.263550i
\(423\) −8.36313 22.9775i −0.406629 1.11720i
\(424\) −3.78078 23.7719i −0.183611 1.15447i
\(425\) −6.72966 11.6561i −0.326436 0.565404i
\(426\) 9.01595 + 1.64190i 0.436824 + 0.0795502i
\(427\) 6.19476 1.09230i 0.299785 0.0528602i
\(428\) −8.61575 7.39558i −0.416458 0.357479i
\(429\) 14.8924 25.7943i 0.719010 1.24536i
\(430\) 1.99525 + 1.69335i 0.0962194 + 0.0816608i
\(431\) 17.1020 14.3503i 0.823775 0.691229i −0.130078 0.991504i \(-0.541523\pi\)
0.953853 + 0.300275i \(0.0970784\pi\)
\(432\) 1.12727 + 7.35318i 0.0542359 + 0.353780i
\(433\) −6.55454 + 18.0085i −0.314991 + 0.865431i 0.676638 + 0.736316i \(0.263436\pi\)
−0.991630 + 0.129116i \(0.958786\pi\)
\(434\) −12.8345 4.75298i −0.616075 0.228150i
\(435\) 20.4464 + 3.60526i 0.980331 + 0.172859i
\(436\) −9.96873 12.1543i −0.477415 0.582086i
\(437\) −4.35977 + 25.2620i −0.208556 + 1.20844i
\(438\) 12.9418 + 36.1869i 0.618383 + 1.72908i
\(439\) 0.638308 3.62002i 0.0304648 0.172774i −0.965779 0.259366i \(-0.916486\pi\)
0.996244 + 0.0865917i \(0.0275975\pi\)
\(440\) 24.4437 8.43425i 1.16531 0.402087i
\(441\) −14.8281 5.39700i −0.706101 0.257000i
\(442\) 22.0332 18.2787i 1.04801 0.869428i
\(443\) −14.4156 17.1798i −0.684905 0.816237i 0.305825 0.952088i \(-0.401068\pi\)
−0.990729 + 0.135850i \(0.956623\pi\)
\(444\) 1.45992 3.87539i 0.0692845 0.183918i
\(445\) 28.9962 + 16.7410i 1.37455 + 0.793598i
\(446\) −29.2376 + 16.6626i −1.38444 + 0.788998i
\(447\) 8.43420 + 47.8327i 0.398924 + 2.26241i
\(448\) 0.446367 13.2719i 0.0210888 0.627036i
\(449\) −32.5644 + 18.8011i −1.53681 + 0.887278i −0.537788 + 0.843080i \(0.680740\pi\)
−0.999023 + 0.0441984i \(0.985927\pi\)
\(450\) −10.2130 5.97303i −0.481446 0.281571i
\(451\) 4.48835 1.63362i 0.211348 0.0769244i
\(452\) 6.37686 + 18.1506i 0.299942 + 0.853733i
\(453\) −12.1333 10.1810i −0.570072 0.478347i
\(454\) 29.8689 5.09430i 1.40182 0.239087i
\(455\) 15.1283 0.709225
\(456\) 31.9514 + 0.421011i 1.49626 + 0.0197156i
\(457\) 40.6482 1.90144 0.950721 0.310047i \(-0.100345\pi\)
0.950721 + 0.310047i \(0.100345\pi\)
\(458\) 24.5449 4.18626i 1.14691 0.195611i
\(459\) 8.52063 + 7.14966i 0.397709 + 0.333717i
\(460\) 10.4983 + 29.8815i 0.489484 + 1.39323i
\(461\) −27.8951 + 10.1530i −1.29920 + 0.472871i −0.896737 0.442564i \(-0.854069\pi\)
−0.402466 + 0.915435i \(0.631847\pi\)
\(462\) −17.8316 10.4288i −0.829603 0.485190i
\(463\) −16.0546 + 9.26911i −0.746119 + 0.430772i −0.824290 0.566168i \(-0.808425\pi\)
0.0781706 + 0.996940i \(0.475092\pi\)
\(464\) −7.85140 + 8.94204i −0.364492 + 0.415124i
\(465\) −7.06548 40.0703i −0.327654 1.85822i
\(466\) −14.3056 + 8.15281i −0.662694 + 0.377672i
\(467\) 22.4178 + 12.9429i 1.03737 + 0.598926i 0.919087 0.394054i \(-0.128928\pi\)
0.118283 + 0.992980i \(0.462261\pi\)
\(468\) 8.87162 23.5500i 0.410091 1.08860i
\(469\) 10.8389 + 12.9173i 0.500496 + 0.596467i
\(470\) −19.2771 + 15.9922i −0.889185 + 0.737664i
\(471\) 9.52657 + 3.46739i 0.438961 + 0.159769i
\(472\) −4.45569 12.9133i −0.205090 0.594382i
\(473\) −0.405170 + 2.29783i −0.0186297 + 0.105654i
\(474\) −11.2589 31.4813i −0.517138 1.44598i
\(475\) −6.27800 + 7.53729i −0.288054 + 0.345834i
\(476\) −12.5915 15.3521i −0.577129 0.703661i
\(477\) −31.1568 5.49378i −1.42657 0.251543i
\(478\) −23.1946 8.58963i −1.06090 0.392881i
\(479\) 0.149158 0.409808i 0.00681519 0.0187246i −0.936238 0.351365i \(-0.885717\pi\)
0.943054 + 0.332641i \(0.107940\pi\)
\(480\) 34.7291 18.7738i 1.58516 0.856904i
\(481\) −2.07144 + 1.73814i −0.0944494 + 0.0792525i
\(482\) −29.3246 24.8876i −1.33570 1.13360i
\(483\) 12.6510 21.9123i 0.575643 0.997042i
\(484\) 0.800483 + 0.687118i 0.0363856 + 0.0312326i
\(485\) 22.6332 3.99084i 1.02772 0.181215i
\(486\) −30.5981 5.57222i −1.38796 0.252761i
\(487\) −2.67545 4.63401i −0.121236 0.209987i 0.799019 0.601305i \(-0.205352\pi\)
−0.920255 + 0.391318i \(0.872019\pi\)
\(488\) −10.5854 + 1.68354i −0.479177 + 0.0762103i
\(489\) −3.98716 10.9546i −0.180306 0.495386i
\(490\) −0.0905697 + 16.1634i −0.00409152 + 0.730189i
\(491\) −17.1929 + 20.4898i −0.775907 + 0.924690i −0.998741 0.0501666i \(-0.984025\pi\)
0.222834 + 0.974856i \(0.428469\pi\)
\(492\) 6.35585 3.57519i 0.286544 0.161182i
\(493\) 17.7925i 0.801334i
\(494\) −18.0488 10.4679i −0.812054 0.470974i
\(495\) 33.9865i 1.52758i
\(496\) 21.7301 + 8.46532i 0.975712 + 0.380104i
\(497\) −2.66766 + 3.17919i −0.119661 + 0.142606i
\(498\) −28.7344 0.161010i −1.28762 0.00721502i
\(499\) −1.54362 4.24107i −0.0691021 0.189856i 0.900334 0.435199i \(-0.143322\pi\)
−0.969437 + 0.245342i \(0.921100\pi\)
\(500\) 2.73452 14.5527i 0.122292 0.650815i
\(501\) 20.5700 + 35.6282i 0.918998 + 1.59175i
\(502\) 5.88131 32.2953i 0.262495 1.44141i
\(503\) −20.5559 + 3.62456i −0.916543 + 0.161611i −0.611973 0.790879i \(-0.709624\pi\)
−0.304570 + 0.952490i \(0.598513\pi\)
\(504\) −16.2985 6.24439i −0.725994 0.278147i
\(505\) 0.152720 0.264519i 0.00679595 0.0117709i
\(506\) −18.2725 + 21.5301i −0.812310 + 0.957130i
\(507\) 3.06508 2.57191i 0.136125 0.114223i
\(508\) −8.25265 + 13.9311i −0.366152 + 0.618093i
\(509\) 11.3786 31.2625i 0.504348 1.38569i −0.382642 0.923897i \(-0.624986\pi\)
0.886990 0.461789i \(-0.152792\pi\)
\(510\) 20.4994 55.3545i 0.907727 2.45114i
\(511\) −17.1398 3.02221i −0.758221 0.133695i
\(512\) −1.14061 + 22.5987i −0.0504085 + 0.998729i
\(513\) 2.74490 7.62769i 0.121190 0.336771i
\(514\) 11.9022 4.25668i 0.524985 0.187754i
\(515\) −3.13536 + 17.7815i −0.138160 + 0.783546i
\(516\) −0.0399210 + 3.56212i −0.00175742 + 0.156813i
\(517\) −20.9852 7.63798i −0.922928 0.335918i
\(518\) 1.19743 + 1.44339i 0.0526120 + 0.0634189i
\(519\) −7.63028 9.09341i −0.334932 0.399156i
\(520\) −25.7743 0.433305i −1.13028 0.0190017i
\(521\) 18.8289 + 10.8709i 0.824911 + 0.476262i 0.852107 0.523368i \(-0.175325\pi\)
−0.0271962 + 0.999630i \(0.508658\pi\)
\(522\) 7.74423 + 13.5887i 0.338956 + 0.594761i
\(523\) 3.60494 + 20.4446i 0.157633 + 0.893981i 0.956339 + 0.292260i \(0.0944072\pi\)
−0.798706 + 0.601722i \(0.794482\pi\)
\(524\) 10.6527 1.75550i 0.465365 0.0766895i
\(525\) 8.38471 4.84092i 0.365939 0.211275i
\(526\) −0.425181 + 0.726997i −0.0185388 + 0.0316986i
\(527\) 32.7663 11.9260i 1.42732 0.519504i
\(528\) 30.0813 + 18.2783i 1.30912 + 0.795463i
\(529\) −8.87704 7.44872i −0.385958 0.323858i
\(530\) 5.44852 + 31.9458i 0.236669 + 1.38764i
\(531\) −17.9546 −0.779162
\(532\) −7.33012 + 12.4770i −0.317801 + 0.540945i
\(533\) −4.76162 −0.206248
\(534\) 7.66280 + 44.9286i 0.331602 + 1.94425i
\(535\) 11.7105 + 9.82628i 0.506289 + 0.424827i
\(536\) −18.0965 22.3179i −0.781648 0.963986i
\(537\) 17.0836 6.21793i 0.737213 0.268324i
\(538\) −7.36190 + 12.5878i −0.317394 + 0.542697i
\(539\) −12.4808 + 7.20577i −0.537584 + 0.310375i
\(540\) −1.62853 9.88218i −0.0700806 0.425261i
\(541\) −6.88874 39.0680i −0.296170 1.67966i −0.662408 0.749143i \(-0.730465\pi\)
0.366238 0.930521i \(-0.380646\pi\)
\(542\) 8.26585 + 14.5040i 0.355049 + 0.622998i
\(543\) 5.11643 + 2.95397i 0.219567 + 0.126767i
\(544\) 21.0125 + 26.5162i 0.900904 + 1.13687i
\(545\) 13.6037 + 16.2123i 0.582720 + 0.694459i
\(546\) 13.1486 + 15.8494i 0.562708 + 0.678292i
\(547\) −14.4386 5.25520i −0.617348 0.224696i 0.0143672 0.999897i \(-0.495427\pi\)
−0.631715 + 0.775200i \(0.717649\pi\)
\(548\) 23.0722 + 0.258573i 0.985597 + 0.0110457i
\(549\) −2.44632 + 13.8738i −0.104406 + 0.592118i
\(550\) −10.1744 + 3.63876i −0.433840 + 0.155157i
\(551\) 12.1692 4.47939i 0.518427 0.190829i
\(552\) −22.1814 + 36.9698i −0.944102 + 1.57354i
\(553\) 14.9110 + 2.62921i 0.634080 + 0.111805i
\(554\) 13.8600 37.4261i 0.588853 1.59008i
\(555\) −1.90694 + 5.23926i −0.0809449 + 0.222394i
\(556\) −8.37155 4.95923i −0.355033 0.210318i
\(557\) 0.878070 0.736789i 0.0372050 0.0312187i −0.623996 0.781428i \(-0.714492\pi\)
0.661201 + 0.750209i \(0.270047\pi\)
\(558\) 19.8339 23.3699i 0.839634 0.989326i
\(559\) 1.16303 2.01443i 0.0491909 0.0852011i
\(560\) −0.400680 + 17.8739i −0.0169318 + 0.755311i
\(561\) 51.8301 9.13905i 2.18827 0.385851i
\(562\) −1.28631 + 7.06338i −0.0542599 + 0.297951i
\(563\) −13.2485 22.9471i −0.558358 0.967104i −0.997634 0.0687518i \(-0.978098\pi\)
0.439276 0.898352i \(-0.355235\pi\)
\(564\) −33.5089 6.29651i −1.41098 0.265131i
\(565\) −8.85867 24.3390i −0.372687 1.02395i
\(566\) 6.33785 + 0.0355133i 0.266400 + 0.00149274i
\(567\) 6.75658 8.05218i 0.283750 0.338160i
\(568\) 4.63599 5.34003i 0.194522 0.224063i
\(569\) 9.00969i 0.377706i −0.982005 0.188853i \(-0.939523\pi\)
0.982005 0.188853i \(-0.0604769\pi\)
\(570\) −43.0208 0.0847173i −1.80194 0.00354842i
\(571\) 12.9557i 0.542179i −0.962554 0.271089i \(-0.912616\pi\)
0.962554 0.271089i \(-0.0873839\pi\)
\(572\) −11.2680 20.0319i −0.471139 0.837576i
\(573\) −39.7391 + 47.3593i −1.66013 + 1.97846i
\(574\) −0.0185045 + 3.30239i −0.000772365 + 0.137839i
\(575\) −4.52668 12.4370i −0.188776 0.518657i
\(576\) 27.5892 + 11.1055i 1.14955 + 0.462728i
\(577\) 15.3414 + 26.5721i 0.638672 + 1.10621i 0.985725 + 0.168366i \(0.0538490\pi\)
−0.347053 + 0.937846i \(0.612818\pi\)
\(578\) 26.1150 + 4.75581i 1.08624 + 0.197816i
\(579\) 41.2675 7.27658i 1.71502 0.302404i
\(580\) 10.4350 12.1566i 0.433290 0.504777i
\(581\) 6.50648 11.2696i 0.269934 0.467540i
\(582\) 23.8525 + 20.2434i 0.988717 + 0.839118i
\(583\) −22.1342 + 18.5728i −0.916706 + 0.769208i
\(584\) 29.1148 + 5.63990i 1.20478 + 0.233381i
\(585\) −11.5881 + 31.8380i −0.479108 + 1.31634i
\(586\) 30.2342 + 11.1966i 1.24896 + 0.462527i
\(587\) −29.7939 5.25347i −1.22973 0.216834i −0.479218 0.877696i \(-0.659080\pi\)
−0.750508 + 0.660862i \(0.770191\pi\)
\(588\) −17.0126 + 13.9534i −0.701588 + 0.575428i
\(589\) −16.4060 19.4082i −0.675997 0.799701i
\(590\) 6.19329 + 17.3172i 0.254974 + 0.712939i
\(591\) 1.43491 8.13776i 0.0590242 0.334743i
\(592\) −1.99873 2.49342i −0.0821475 0.102479i
\(593\) −4.00540 1.45785i −0.164482 0.0598666i 0.258467 0.966020i \(-0.416783\pi\)
−0.422949 + 0.906154i \(0.639005\pi\)
\(594\) 6.87267 5.70154i 0.281989 0.233937i
\(595\) 17.1828 + 20.4777i 0.704427 + 0.839504i
\(596\) 35.0737 + 13.2128i 1.43667 + 0.541216i
\(597\) −25.6312 14.7982i −1.04902 0.605650i
\(598\) 24.4583 13.9389i 1.00017 0.570002i
\(599\) −0.748191 4.24320i −0.0305703 0.173373i 0.965700 0.259660i \(-0.0836106\pi\)
−0.996270 + 0.0862879i \(0.972500\pi\)
\(600\) −14.4238 + 8.00738i −0.588849 + 0.326900i
\(601\) 0.136310 0.0786987i 0.00556021 0.00321019i −0.497217 0.867626i \(-0.665645\pi\)
0.502778 + 0.864416i \(0.332311\pi\)
\(602\) −1.39257 0.814441i −0.0567571 0.0331942i
\(603\) −35.4875 + 12.9164i −1.44516 + 0.525996i
\(604\) −11.5312 + 4.05127i −0.469199 + 0.164844i
\(605\) −1.08801 0.912952i −0.0442341 0.0371168i
\(606\) 0.409863 0.0699042i 0.0166495 0.00283966i
\(607\) −23.1610 −0.940074 −0.470037 0.882647i \(-0.655760\pi\)
−0.470037 + 0.882647i \(0.655760\pi\)
\(608\) 12.8458 21.0472i 0.520965 0.853578i
\(609\) −12.7989 −0.518636
\(610\) 14.2251 2.42617i 0.575958 0.0982326i
\(611\) 17.0543 + 14.3103i 0.689945 + 0.578932i
\(612\) 41.9539 14.7396i 1.69588 0.595815i
\(613\) −45.1542 + 16.4348i −1.82376 + 0.663795i −0.829286 + 0.558825i \(0.811252\pi\)
−0.994475 + 0.104970i \(0.966525\pi\)
\(614\) 41.4056 + 24.2159i 1.67099 + 0.977273i
\(615\) −8.50259 + 4.90898i −0.342858 + 0.197949i
\(616\) −13.9368 + 7.73703i −0.561530 + 0.311734i
\(617\) −2.55508 14.4906i −0.102864 0.583369i −0.992052 0.125828i \(-0.959841\pi\)
0.889188 0.457541i \(-0.151270\pi\)
\(618\) −21.3541 + 12.1698i −0.858989 + 0.489541i
\(619\) 41.6191 + 24.0288i 1.67281 + 0.965800i 0.966052 + 0.258349i \(0.0831783\pi\)
0.706762 + 0.707451i \(0.250155\pi\)
\(620\) −29.3818 11.0686i −1.18000 0.444524i
\(621\) 7.03057 + 8.37871i 0.282127 + 0.336226i
\(622\) −19.6750 + 16.3223i −0.788895 + 0.654464i
\(623\) −19.3955 7.05940i −0.777066 0.282829i
\(624\) −21.9475 27.3794i −0.878602 1.09605i
\(625\) −5.41569 + 30.7139i −0.216628 + 1.22856i
\(626\) −0.276586 0.773371i −0.0110546 0.0309101i
\(627\) −19.2993 33.1486i −0.770740 1.32383i
\(628\) 6.04877 4.96107i 0.241372 0.197968i
\(629\) −4.70551 0.829708i −0.187621 0.0330826i
\(630\) 22.0360 + 8.16058i 0.877937 + 0.325125i
\(631\) 2.81681 7.73912i 0.112135 0.308090i −0.870913 0.491438i \(-0.836471\pi\)
0.983048 + 0.183348i \(0.0586937\pi\)
\(632\) −25.3288 4.90650i −1.00752 0.195170i
\(633\) 7.60099 6.37799i 0.302112 0.253502i
\(634\) 0.831828 + 0.705967i 0.0330361 + 0.0280375i
\(635\) 10.8999 18.8792i 0.432550 0.749199i
\(636\) −28.7330 + 33.4736i −1.13934 + 1.32731i
\(637\) 14.1487 2.49479i 0.560591 0.0988473i
\(638\) 14.0532 + 2.55924i 0.556373 + 0.101321i
\(639\) −4.64732 8.04940i −0.183845 0.318429i
\(640\) 1.19459 30.4406i 0.0472203 1.20327i
\(641\) 12.2993 + 33.7920i 0.485793 + 1.33471i 0.904457 + 0.426564i \(0.140276\pi\)
−0.418664 + 0.908141i \(0.637502\pi\)
\(642\) −0.116601 + 20.8091i −0.00460188 + 0.821270i
\(643\) 12.2592 14.6099i 0.483454 0.576158i −0.468086 0.883683i \(-0.655056\pi\)
0.951540 + 0.307525i \(0.0995008\pi\)
\(644\) −9.57217 17.0171i −0.377196 0.670567i
\(645\) 4.79609i 0.188846i
\(646\) −6.33056 36.3205i −0.249072 1.42901i
\(647\) 44.0542i 1.73195i −0.500089 0.865974i \(-0.666699\pi\)
0.500089 0.865974i \(-0.333301\pi\)
\(648\) −11.7419 + 13.5251i −0.461266 + 0.531316i
\(649\) −10.5403 + 12.5614i −0.413742 + 0.493079i
\(650\) 10.7719 + 0.0603592i 0.422510 + 0.00236748i
\(651\) 8.57884 + 23.5702i 0.336231 + 0.923787i
\(652\) −8.84101 1.66127i −0.346241 0.0650605i
\(653\) −14.7359 25.5233i −0.576660 0.998804i −0.995859 0.0909095i \(-0.971023\pi\)
0.419200 0.907894i \(-0.362311\pi\)
\(654\) −5.16154 + 28.3429i −0.201832 + 1.10830i
\(655\) −14.3147 + 2.52406i −0.559320 + 0.0986232i
\(656\) 0.126114 5.62580i 0.00492391 0.219651i
\(657\) 19.4892 33.7563i 0.760347 1.31696i
\(658\) 9.99110 11.7723i 0.389494 0.458933i
\(659\) 4.57370 3.83779i 0.178166 0.149499i −0.549344 0.835597i \(-0.685122\pi\)
0.727510 + 0.686098i \(0.240678\pi\)
\(660\) −40.7726 24.1533i −1.58707 0.940166i
\(661\) 14.8266 40.7359i 0.576690 1.58444i −0.217034 0.976164i \(-0.569638\pi\)
0.793724 0.608278i \(-0.208139\pi\)
\(662\) −11.3467 + 30.6395i −0.441002 + 1.19084i
\(663\) −51.6697 9.11077i −2.00669 0.353833i
\(664\) −11.4080 + 19.0137i −0.442715 + 0.737876i
\(665\) 9.67989 16.9077i 0.375370 0.655651i
\(666\) −3.95488 + 1.41441i −0.153248 + 0.0548074i
\(667\) −3.03817 + 17.2303i −0.117639 + 0.667162i
\(668\) 31.7439 + 0.355757i 1.22821 + 0.0137647i
\(669\) 57.9551 + 21.0939i 2.24067 + 0.815539i
\(670\) 24.6990 + 29.7723i 0.954206 + 1.15021i
\(671\) 8.27028 + 9.85613i 0.319271 + 0.380492i
\(672\) −19.0742 + 15.1152i −0.735802 + 0.583080i
\(673\) −29.6835 17.1378i −1.14421 0.660613i −0.196744 0.980455i \(-0.563037\pi\)
−0.947471 + 0.319842i \(0.896370\pi\)
\(674\) 3.25067 + 5.70390i 0.125211 + 0.219706i
\(675\) 0.726766 + 4.12169i 0.0279732 + 0.158644i
\(676\) −0.502038 3.04645i −0.0193091 0.117171i
\(677\) 22.0117 12.7085i 0.845978 0.488425i −0.0133139 0.999911i \(-0.504238\pi\)
0.859292 + 0.511486i \(0.170905\pi\)
\(678\) 17.7997 30.4349i 0.683594 1.16885i
\(679\) −13.3133 + 4.84565i −0.510918 + 0.185959i
\(680\) −28.6881 35.3803i −1.10014 1.35677i
\(681\) −42.5393 35.6947i −1.63011 1.36783i
\(682\) −4.70657 27.5956i −0.180224 1.05669i
\(683\) 1.72512 0.0660100 0.0330050 0.999455i \(-0.489492\pi\)
0.0330050 + 0.999455i \(0.489492\pi\)
\(684\) −20.6434 24.9837i −0.789321 0.955275i
\(685\) −31.0648 −1.18693
\(686\) −4.43800 26.0209i −0.169443 0.993482i
\(687\) −34.9569 29.3323i −1.33369 1.11910i
\(688\) 2.34922 + 1.42746i 0.0895632 + 0.0544214i
\(689\) 27.0676 9.85181i 1.03119 0.375324i
\(690\) 29.3038 50.1052i 1.11558 1.90747i
\(691\) −14.5248 + 8.38589i −0.552549 + 0.319014i −0.750149 0.661268i \(-0.770018\pi\)
0.197601 + 0.980283i \(0.436685\pi\)
\(692\) −9.03813 + 1.48943i −0.343578 + 0.0566197i
\(693\) 3.63816 + 20.6330i 0.138202 + 0.783784i
\(694\) −15.6183 27.4052i −0.592864 1.04029i
\(695\) 11.3450 + 6.55004i 0.430340 + 0.248457i
\(696\) 21.8056 + 0.366585i 0.826539 + 0.0138954i
\(697\) −5.40828 6.44534i −0.204853 0.244135i
\(698\) −12.2761 14.7977i −0.464658 0.560102i
\(699\) 28.3567 + 10.3210i 1.07255 + 0.390376i
\(700\) 0.0837236 7.47059i 0.00316445 0.282362i
\(701\) 1.08176 6.13496i 0.0408574 0.231714i −0.957540 0.288299i \(-0.906910\pi\)
0.998398 + 0.0565853i \(0.0180213\pi\)
\(702\) −8.38222 + 2.99780i −0.316366 + 0.113145i
\(703\) 0.617165 + 3.42724i 0.0232768 + 0.129261i
\(704\) 23.9659 12.7825i 0.903250 0.481758i
\(705\) 45.2063 + 7.97109i 1.70257 + 0.300209i
\(706\) −12.3407 + 33.3235i −0.464447 + 1.25415i
\(707\) −0.0643996 + 0.176936i −0.00242200 + 0.00665438i
\(708\) −12.7599 + 21.5396i −0.479545 + 0.809508i
\(709\) 34.9962 29.3653i 1.31431 1.10284i 0.326829 0.945083i \(-0.394020\pi\)
0.987479 0.157752i \(-0.0504247\pi\)
\(710\) −6.16061 + 7.25894i −0.231204 + 0.272423i
\(711\) −16.9549 + 29.3667i −0.635858 + 1.10134i
\(712\) 32.8422 + 12.5827i 1.23082 + 0.471557i
\(713\) 33.7675 5.95412i 1.26460 0.222984i
\(714\) −6.51952 + 35.7999i −0.243987 + 1.33978i
\(715\) 15.4718 + 26.7979i 0.578611 + 1.00218i
\(716\) 2.59074 13.7874i 0.0968203 0.515261i
\(717\) 15.5037 + 42.5962i 0.578998 + 1.59078i
\(718\) 13.9797 + 0.0783336i 0.521718 + 0.00292338i
\(719\) 30.0416 35.8022i 1.12036 1.33520i 0.184499 0.982833i \(-0.440934\pi\)
0.935863 0.352363i \(-0.114622\pi\)
\(720\) −37.3093 14.5344i −1.39044 0.541667i
\(721\) 11.1307i 0.414529i
\(722\) −23.2478 + 13.4738i −0.865192 + 0.501441i
\(723\) 70.4891i 2.62152i
\(724\) 3.97343 2.23507i 0.147671 0.0830656i
\(725\) −4.30339 + 5.12858i −0.159824 + 0.190471i
\(726\) 0.0108333 1.93336i 0.000402063 0.0717537i
\(727\) 12.7241 + 34.9591i 0.471910 + 1.29656i 0.916215 + 0.400687i \(0.131229\pi\)
−0.444305 + 0.895876i \(0.646549\pi\)
\(728\) 15.6938 2.49601i 0.581652 0.0925082i
\(729\) 19.0009 + 32.9106i 0.703738 + 1.21891i
\(730\) −39.2807 7.15342i −1.45384 0.264760i
\(731\) 4.04771 0.713721i 0.149710 0.0263979i
\(732\) 14.9054 + 12.7945i 0.550921 + 0.472899i
\(733\) −5.28816 + 9.15936i −0.195323 + 0.338309i −0.947006 0.321215i \(-0.895909\pi\)
0.751684 + 0.659524i \(0.229242\pi\)
\(734\) −34.0084 28.8627i −1.25527 1.06534i
\(735\) 22.6926 19.0414i 0.837030 0.702352i
\(736\) 15.8208 + 29.2664i 0.583164 + 1.07877i
\(737\) −11.7964 + 32.4104i −0.434527 + 1.19385i
\(738\) −6.93582 2.56854i −0.255311 0.0945491i
\(739\) 34.7564 + 6.12848i 1.27853 + 0.225440i 0.771357 0.636402i \(-0.219578\pi\)
0.507176 + 0.861842i \(0.330689\pi\)
\(740\) 2.72841 + 3.32660i 0.100298 + 0.122288i
\(741\) 6.77689 + 37.6334i 0.248955 + 1.38250i
\(742\) −6.72748 18.8109i −0.246974 0.690570i
\(743\) 3.19307 18.1088i 0.117142 0.664348i −0.868525 0.495646i \(-0.834931\pi\)
0.985667 0.168702i \(-0.0539575\pi\)
\(744\) −13.9408 40.4025i −0.511094 1.48123i
\(745\) −47.4172 17.2584i −1.73723 0.632301i
\(746\) −21.6310 + 17.9450i −0.791967 + 0.657012i
\(747\) 18.7333 + 22.3254i 0.685415 + 0.816845i
\(748\) 14.3169 38.0048i 0.523479 1.38959i
\(749\) −8.16127 4.71191i −0.298206 0.172169i
\(750\) −23.5773 + 13.4368i −0.860922 + 0.490642i
\(751\) −7.68759 43.5985i −0.280524 1.59093i −0.720848 0.693093i \(-0.756248\pi\)
0.440324 0.897839i \(-0.354863\pi\)
\(752\) −17.3592 + 19.7705i −0.633023 + 0.720957i
\(753\) −52.1009 + 30.0805i −1.89866 + 1.09619i
\(754\) −12.2922 7.18907i −0.447657 0.261810i
\(755\) 15.4628 5.62798i 0.562747 0.204823i
\(756\) 2.04653 + 5.82509i 0.0744316 + 0.211857i
\(757\) −4.01307 3.36736i −0.145857 0.122389i 0.566939 0.823760i \(-0.308127\pi\)
−0.712797 + 0.701371i \(0.752572\pi\)
\(758\) −50.8552 + 8.67362i −1.84714 + 0.315040i
\(759\) 51.7531 1.87852
\(760\) −16.9760 + 28.5286i −0.615785 + 1.03484i
\(761\) −35.8399 −1.29919 −0.649597 0.760279i \(-0.725062\pi\)
−0.649597 + 0.760279i \(0.725062\pi\)
\(762\) 29.2527 4.98919i 1.05971 0.180739i
\(763\) −9.99425 8.38617i −0.361816 0.303600i
\(764\) 15.8131 + 45.0093i 0.572098 + 1.62838i
\(765\) −56.2578 + 20.4762i −2.03401 + 0.740318i
\(766\) −23.7389 13.8836i −0.857723 0.501636i
\(767\) 14.1569 8.17351i 0.511178 0.295128i
\(768\) 32.9298 25.2056i 1.18825 0.909527i
\(769\) 5.00228 + 28.3693i 0.180387 + 1.02302i 0.931740 + 0.363125i \(0.118290\pi\)
−0.751354 + 0.659900i \(0.770599\pi\)
\(770\) 18.6456 10.6262i 0.671943 0.382942i
\(771\) −20.0625 11.5831i −0.722535 0.417156i
\(772\) 11.3993 30.2597i 0.410268 1.08907i
\(773\) 1.14807 + 1.36822i 0.0412933 + 0.0492114i 0.786296 0.617850i \(-0.211996\pi\)
−0.745003 + 0.667062i \(0.767552\pi\)
\(774\) 2.78071 2.30687i 0.0999507 0.0829187i
\(775\) 12.3292 + 4.48746i 0.442878 + 0.161194i
\(776\) 22.8208 7.87427i 0.819220 0.282670i
\(777\) 0.596843 3.38486i 0.0214116 0.121431i
\(778\) 4.58097 + 12.8090i 0.164236 + 0.459224i
\(779\) −3.04674 + 5.32168i −0.109161 + 0.190669i
\(780\) 29.9598 + 36.5283i 1.07273 + 1.30792i
\(781\) −8.35977 1.47405i −0.299136 0.0527458i
\(782\) 46.6476 + 17.2750i 1.66811 + 0.617751i
\(783\) 1.89230 5.19905i 0.0676253 0.185799i
\(784\) 2.57284 + 16.7826i 0.0918871 + 0.599378i
\(785\) −8.06828 + 6.77009i −0.287969 + 0.241635i
\(786\) −15.0858 12.8032i −0.538093 0.456676i
\(787\) −27.7835 + 48.1225i −0.990376 + 1.71538i −0.375327 + 0.926892i \(0.622470\pi\)
−0.615049 + 0.788489i \(0.710864\pi\)
\(788\) −4.83839 4.15317i −0.172361 0.147951i
\(789\) 1.52005 0.268026i 0.0541152 0.00954198i
\(790\) 34.1728 + 6.22321i 1.21581 + 0.221412i
\(791\) 7.98348 + 13.8278i 0.283860 + 0.491660i
\(792\) −5.60741 35.2569i −0.199250 1.25280i
\(793\) −4.38690 12.0529i −0.155784 0.428012i
\(794\) 0.00104858 0.187134i 3.72129e−5 0.00664115i
\(795\) 38.1767 45.4972i 1.35399 1.61362i
\(796\) −19.9052 + 11.1968i −0.705523 + 0.396859i
\(797\) 21.8514i 0.774016i −0.922076 0.387008i \(-0.873509\pi\)
0.922076 0.387008i \(-0.126491\pi\)
\(798\) 26.1268 4.55383i 0.924878 0.161204i
\(799\) 39.3385i 1.39170i
\(800\) −0.356614 + 12.7253i −0.0126082 + 0.449909i
\(801\) 29.7135 35.4112i 1.04987 1.25119i
\(802\) 2.74545 + 0.0153838i 0.0969453 + 0.000543221i
\(803\) −12.1755 33.4519i −0.429663 1.18049i
\(804\) −9.72460 + 51.7527i −0.342960 + 1.82518i
\(805\) 13.1432 + 22.7648i 0.463239 + 0.802353i
\(806\) −5.00000 + 27.4559i −0.176117 + 0.967092i
\(807\) 26.3193 4.64080i 0.926482 0.163364i
\(808\) 0.114786 0.299604i 0.00403817 0.0105400i
\(809\) −1.75120 + 3.03317i −0.0615690 + 0.106641i −0.895167 0.445731i \(-0.852944\pi\)
0.833598 + 0.552372i \(0.186277\pi\)
\(810\) 15.6034 18.3853i 0.548249 0.645992i
\(811\) −10.9054 + 9.15072i −0.382941 + 0.321325i −0.813856 0.581067i \(-0.802635\pi\)
0.430915 + 0.902393i \(0.358191\pi\)
\(812\) −5.03371 + 8.49728i −0.176649 + 0.298196i
\(813\) 10.4641 28.7499i 0.366992 1.00830i
\(814\) −1.33217 + 3.59726i −0.0466925 + 0.126084i
\(815\) 11.9272 + 2.10309i 0.417793 + 0.0736682i
\(816\) 12.1328 60.8060i 0.424732 2.12863i
\(817\) −1.50719 2.58876i −0.0527300 0.0905693i
\(818\) 36.5693 13.0786i 1.27862 0.457281i
\(819\) 3.62690 20.5692i 0.126734 0.718745i
\(820\) −0.0849007 + 7.57562i −0.00296486 + 0.264552i
\(821\) 7.20202 + 2.62132i 0.251352 + 0.0914847i 0.464624 0.885508i \(-0.346190\pi\)
−0.213271 + 0.976993i \(0.568412\pi\)
\(822\) −26.9997 32.5456i −0.941721 1.13516i
\(823\) 0.679981 + 0.810370i 0.0237027 + 0.0282477i 0.777766 0.628554i \(-0.216353\pi\)
−0.754063 + 0.656802i \(0.771909\pi\)
\(824\) −0.318806 + 18.9635i −0.0111061 + 0.660625i
\(825\) 17.1502 + 9.90164i 0.597092 + 0.344731i
\(826\) −5.61368 9.85024i −0.195325 0.342734i
\(827\) 4.31460 + 24.4693i 0.150033 + 0.850881i 0.963187 + 0.268832i \(0.0866377\pi\)
−0.813154 + 0.582049i \(0.802251\pi\)
\(828\) 43.1452 7.11008i 1.49940 0.247092i
\(829\) −7.34481 + 4.24053i −0.255096 + 0.147280i −0.622095 0.782941i \(-0.713718\pi\)
0.367000 + 0.930221i \(0.380385\pi\)
\(830\) 15.0711 25.7693i 0.523124 0.894465i
\(831\) −68.7319 + 25.0164i −2.38428 + 0.867808i
\(832\) −26.8093 + 3.80298i −0.929444 + 0.131845i
\(833\) 19.4471 + 16.3181i 0.673803 + 0.565388i
\(834\) 2.99813 + 17.5787i 0.103817 + 0.608699i
\(835\) −42.7405 −1.47910
\(836\) −29.5979 0.224136i −1.02367 0.00775189i
\(837\) −10.8428 −0.374784
\(838\) 1.50755 + 8.83908i 0.0520774 + 0.305341i
\(839\) −6.60696 5.54389i −0.228097 0.191396i 0.521575 0.853205i \(-0.325345\pi\)
−0.749673 + 0.661809i \(0.769789\pi\)
\(840\) 25.4505 20.6365i 0.878124 0.712027i
\(841\) −18.9345 + 6.89161i −0.652915 + 0.237642i
\(842\) −8.32102 + 14.2277i −0.286761 + 0.490320i
\(843\) 11.3951 6.57897i 0.392468 0.226592i
\(844\) −1.24499 7.55479i −0.0428542 0.260047i
\(845\) 0.721830 + 4.09370i 0.0248317 + 0.140828i
\(846\) 17.1222 + 30.0441i 0.588674 + 1.03294i
\(847\) 0.758257 + 0.437780i 0.0260540 + 0.0150423i
\(848\) 10.9229 + 32.2411i 0.375095 + 1.10716i
\(849\) −7.46632 8.89801i −0.256243 0.305379i
\(850\) 12.1531 + 14.6495i 0.416850 + 0.502473i
\(851\) −4.41516 1.60699i −0.151350 0.0550868i
\(852\) −12.9594 0.145237i −0.443981 0.00497574i
\(853\) 1.20460 6.83164i 0.0412448 0.233911i −0.957216 0.289375i \(-0.906553\pi\)
0.998461 + 0.0554639i \(0.0176638\pi\)
\(854\) −8.37629 + 2.99567i −0.286631 + 0.102510i
\(855\) 28.1681 + 33.3227i 0.963328 + 1.13961i
\(856\) 13.7695 + 8.26150i 0.470632 + 0.282372i
\(857\) −9.28874 1.63785i −0.317297 0.0559481i 0.0127315 0.999919i \(-0.495947\pi\)
−0.330029 + 0.943971i \(0.607058\pi\)
\(858\) −14.6281 + 39.5003i −0.499396 + 1.34852i
\(859\) −2.83749 + 7.79595i −0.0968140 + 0.265994i −0.978640 0.205580i \(-0.934092\pi\)
0.881826 + 0.471574i \(0.156314\pi\)
\(860\) −3.18417 1.88627i −0.108579 0.0643213i
\(861\) 4.63639 3.89040i 0.158008 0.132584i
\(862\) −20.4296 + 24.0718i −0.695834 + 0.819889i
\(863\) 11.3225 19.6112i 0.385423 0.667573i −0.606405 0.795156i \(-0.707389\pi\)
0.991828 + 0.127584i \(0.0407221\pi\)
\(864\) −3.31986 9.98291i −0.112944 0.339625i
\(865\) 12.1451 2.14151i 0.412945 0.0728134i
\(866\) 4.85574 26.6637i 0.165005 0.906071i
\(867\) −24.3240 42.1304i −0.826087 1.43082i
\(868\) 19.0224 + 3.57442i 0.645664 + 0.121324i
\(869\) 10.5922 + 29.1019i 0.359316 + 0.987213i
\(870\) −29.3612 0.164522i −0.995439 0.00557782i
\(871\) 22.1014 26.3395i 0.748878 0.892478i
\(872\) 16.7871 + 14.5739i 0.568484 + 0.493534i
\(873\) 31.7300i 1.07390i
\(874\) 0.0713918 36.2539i 0.00241486 1.22631i
\(875\) 12.2895i 0.415461i
\(876\) −26.6460 47.3704i −0.900286 1.60050i
\(877\) 12.8658 15.3329i 0.434448 0.517755i −0.503752 0.863848i \(-0.668048\pi\)
0.938200 + 0.346094i \(0.112492\pi\)
\(878\) −0.0291285 + 5.19838i −0.000983038 + 0.175437i
\(879\) −20.2092 55.5242i −0.681638 1.87279i
\(880\) −32.0712 + 17.5700i −1.08112 + 0.592284i
\(881\) −2.29906 3.98208i −0.0774572 0.134160i 0.824695 0.565578i \(-0.191347\pi\)
−0.902152 + 0.431418i \(0.858013\pi\)
\(882\) 21.9549 + 3.99821i 0.739259 + 0.134627i
\(883\) −24.2556 + 4.27692i −0.816266 + 0.143930i −0.566167 0.824291i \(-0.691574\pi\)
−0.250099 + 0.968220i \(0.580463\pi\)
\(884\) −26.3701 + 30.7208i −0.886922 + 1.03325i
\(885\) 16.8529 29.1901i 0.566505 0.981215i
\(886\) 24.1813 + 20.5225i 0.812387 + 0.689467i
\(887\) −34.9136 + 29.2960i −1.17229 + 0.983664i −0.999999 0.00138259i \(-0.999560\pi\)
−0.172286 + 0.985047i \(0.555115\pi\)
\(888\) −1.11380 + 5.74974i −0.0373766 + 0.192949i
\(889\) −4.59632 + 12.6283i −0.154156 + 0.423539i
\(890\) −44.4036 16.4439i −1.48841 0.551202i
\(891\) 21.1734 + 3.73344i 0.709336 + 0.125075i
\(892\) 36.7978 30.1808i 1.23208 1.01053i
\(893\) 26.9057 9.90377i 0.900366 0.331417i
\(894\) −23.1311 64.6774i −0.773619 2.16314i
\(895\) −3.27975 + 18.6004i −0.109630 + 0.621742i
\(896\) 2.53335 + 18.6082i 0.0846333 + 0.621656i
\(897\) −48.4815 17.6458i −1.61875 0.589177i
\(898\) 40.9272 33.9531i 1.36576 1.13303i
\(899\) −11.1489 13.2867i −0.371835 0.443136i
\(900\) 15.6580 + 5.89857i 0.521932 + 0.196619i
\(901\) 44.0791 + 25.4491i 1.46849 + 0.847831i
\(902\) −5.86870 + 3.34459i −0.195406 + 0.111363i
\(903\) 0.513408 + 2.91168i 0.0170852 + 0.0968947i
\(904\) −13.2055 23.7872i −0.439208 0.791152i
\(905\) −5.31549 + 3.06890i −0.176693 + 0.102014i
\(906\) 19.3355 + 11.3083i 0.642380 + 0.375693i
\(907\) 5.54925 2.01976i 0.184260 0.0670651i −0.248242 0.968698i \(-0.579853\pi\)
0.432502 + 0.901633i \(0.357631\pi\)
\(908\) −40.4285 + 14.2037i −1.34167 + 0.471368i
\(909\) −0.323039 0.271062i −0.0107145 0.00899057i
\(910\) −21.0901 + 3.59702i −0.699130 + 0.119240i
\(911\) −19.1178 −0.633401 −0.316700 0.948526i \(-0.602575\pi\)
−0.316700 + 0.948526i \(0.602575\pi\)
\(912\) −44.6430 + 7.01009i −1.47828 + 0.232127i
\(913\) 26.6168 0.880888
\(914\) −56.6670 + 9.66484i −1.87438 + 0.319684i
\(915\) −20.2594 16.9997i −0.669756 0.561992i
\(916\) −33.2223 + 11.6720i −1.09770 + 0.385653i
\(917\) 8.42017 3.06469i 0.278059 0.101205i
\(918\) −13.5784 7.94128i −0.448155 0.262101i
\(919\) −31.2360 + 18.0341i −1.03038 + 0.594890i −0.917093 0.398673i \(-0.869471\pi\)
−0.113286 + 0.993562i \(0.536138\pi\)
\(920\) −21.7403 39.1611i −0.716756 1.29110i
\(921\) −15.2652 86.5734i −0.503006 2.85269i
\(922\) 36.4740 20.7866i 1.20121 0.684571i
\(923\) 7.32871 + 4.23123i 0.241227 + 0.139273i
\(924\) 27.3384 + 10.2988i 0.899367 + 0.338804i
\(925\) −1.15566 1.37726i −0.0379978 0.0452840i
\(926\) 20.1775 16.7392i 0.663074 0.550083i
\(927\) 23.4249 + 8.52597i 0.769375 + 0.280030i
\(928\) 8.81937 14.3328i 0.289510 0.470496i
\(929\) −2.58424 + 14.6560i −0.0847862 + 0.480846i 0.912616 + 0.408817i \(0.134059\pi\)
−0.997403 + 0.0720292i \(0.977053\pi\)
\(930\) 19.3773 + 54.1814i 0.635406 + 1.77668i
\(931\) 6.26485 17.4091i 0.205322 0.570561i
\(932\) 18.0047 14.7671i 0.589764 0.483713i
\(933\) 46.1394 + 8.13562i 1.51054 + 0.266348i
\(934\) −34.3296 12.7133i −1.12330 0.415990i
\(935\) −18.7007 + 51.3799i −0.611580 + 1.68030i
\(936\) −6.76834 + 34.9401i −0.221230 + 1.14205i
\(937\) 24.7907 20.8019i 0.809877 0.679568i −0.140701 0.990052i \(-0.544936\pi\)
0.950579 + 0.310484i \(0.100491\pi\)
\(938\) −18.1817 15.4307i −0.593654 0.503830i
\(939\) −0.752635 + 1.30360i −0.0245613 + 0.0425414i
\(940\) 23.0714 26.8779i 0.752506 0.876660i
\(941\) −22.0071 + 3.88045i −0.717411 + 0.126499i −0.520425 0.853907i \(-0.674226\pi\)
−0.196986 + 0.980406i \(0.563115\pi\)
\(942\) −14.1053 2.56871i −0.459574 0.0836932i
\(943\) −4.13683 7.16519i −0.134714 0.233331i
\(944\) 9.28197 + 16.9428i 0.302102 + 0.551440i
\(945\) −2.84302 7.81114i −0.0924835 0.254096i
\(946\) 0.0184895 3.29970i 0.000601145 0.107283i
\(947\) −35.4036 + 42.1924i −1.15046 + 1.37107i −0.233374 + 0.972387i \(0.574977\pi\)
−0.917089 + 0.398682i \(0.869468\pi\)
\(948\) 23.1811 + 41.2105i 0.752886 + 1.33846i
\(949\) 35.4885i 1.15201i
\(950\) 6.95992 12.0003i 0.225810 0.389341i
\(951\) 1.99951i 0.0648386i
\(952\) 21.2038 + 18.4082i 0.687218 + 0.596614i
\(953\) −4.51618 + 5.38217i −0.146293 + 0.174346i −0.834215 0.551439i \(-0.814079\pi\)
0.687922 + 0.725785i \(0.258523\pi\)
\(954\) 44.7413 + 0.250702i 1.44855 + 0.00811679i
\(955\) −21.9674 60.3550i −0.710849 1.95304i
\(956\) 34.3775 + 6.45972i 1.11185 + 0.208922i
\(957\) −13.0894 22.6716i −0.423122 0.732868i
\(958\) −0.110499 + 0.606771i −0.00357007 + 0.0196039i
\(959\) 18.8593 3.32540i 0.608998 0.107383i
\(960\) −43.9514 + 34.4297i −1.41852 + 1.11121i
\(961\) −1.49565 + 2.59055i −0.0482469 + 0.0835661i
\(962\) 2.47448 2.91564i 0.0797804 0.0940039i
\(963\) 16.1678 13.5664i 0.521000 0.437171i
\(964\) 46.7984 + 27.7229i 1.50727 + 0.892895i
\(965\) −14.8897 + 40.9090i −0.479315 + 1.31691i
\(966\) −12.4266 + 33.5555i −0.399818 + 1.07963i
\(967\) 33.5782 + 5.92074i 1.07980 + 0.190398i 0.685127 0.728423i \(-0.259747\pi\)
0.394674 + 0.918821i \(0.370858\pi\)
\(968\) −1.27931 0.767570i −0.0411187 0.0246706i
\(969\) −43.2434 + 51.9175i −1.38918 + 1.66783i
\(970\) −30.6037 + 10.9450i −0.982624 + 0.351423i
\(971\) 0.272182 1.54362i 0.00873472 0.0495371i −0.980129 0.198362i \(-0.936438\pi\)
0.988864 + 0.148825i \(0.0475490\pi\)
\(972\) 43.9811 + 0.492901i 1.41069 + 0.0158098i
\(973\) −7.58866 2.76205i −0.243281 0.0885471i
\(974\) 4.83161 + 5.82405i 0.154815 + 0.186615i
\(975\) −12.6899 15.1232i −0.406402 0.484332i
\(976\) 14.3566 4.86386i 0.459543 0.155688i
\(977\) −15.5733 8.99124i −0.498233 0.287655i 0.229750 0.973250i \(-0.426209\pi\)
−0.727984 + 0.685594i \(0.759542\pi\)
\(978\) 8.16310 + 14.3237i 0.261027 + 0.458020i
\(979\) −7.33105 41.5765i −0.234301 1.32879i
\(980\) −3.71688 22.5547i −0.118731 0.720483i
\(981\) 25.3044 14.6095i 0.807909 0.466446i
\(982\) 19.0966 32.6523i 0.609396 1.04198i
\(983\) −47.5857 + 17.3198i −1.51775 + 0.552415i −0.960584 0.277988i \(-0.910332\pi\)
−0.557163 + 0.830403i \(0.688110\pi\)
\(984\) −8.01051 + 6.49532i −0.255366 + 0.207063i
\(985\) 6.57633 + 5.51820i 0.209539 + 0.175824i
\(986\) −4.23049 24.8042i −0.134726 0.789927i
\(987\) −28.2978 −0.900729
\(988\) 27.6505 + 10.3017i 0.879678 + 0.327742i
\(989\) 4.04170 0.128518
\(990\) 8.08089 + 47.3799i 0.256828 + 1.50583i
\(991\) 3.54873 + 2.97774i 0.112729 + 0.0945911i 0.697410 0.716672i \(-0.254336\pi\)
−0.584681 + 0.811264i \(0.698780\pi\)
\(992\) −32.3064 6.63463i −1.02573 0.210650i
\(993\) 56.2686 20.4801i 1.78563 0.649916i
\(994\) 2.96303 5.06634i 0.0939816 0.160695i
\(995\) 26.6284 15.3739i 0.844178 0.487386i
\(996\) 40.0965 6.60767i 1.27051 0.209372i
\(997\) 8.73220 + 49.5228i 0.276551 + 1.56840i 0.733990 + 0.679160i \(0.237656\pi\)
−0.457439 + 0.889241i \(0.651233\pi\)
\(998\) 3.16033 + 5.54538i 0.100039 + 0.175536i
\(999\) 1.28673 + 0.742893i 0.0407103 + 0.0235041i
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 76.2.k.a.59.1 48
3.2 odd 2 684.2.cf.a.667.8 48
4.3 odd 2 inner 76.2.k.a.59.2 yes 48
12.11 even 2 684.2.cf.a.667.7 48
19.10 odd 18 inner 76.2.k.a.67.2 yes 48
57.29 even 18 684.2.cf.a.523.7 48
76.67 even 18 inner 76.2.k.a.67.1 yes 48
228.143 odd 18 684.2.cf.a.523.8 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.2.k.a.59.1 48 1.1 even 1 trivial
76.2.k.a.59.2 yes 48 4.3 odd 2 inner
76.2.k.a.67.1 yes 48 76.67 even 18 inner
76.2.k.a.67.2 yes 48 19.10 odd 18 inner
684.2.cf.a.523.7 48 57.29 even 18
684.2.cf.a.523.8 48 228.143 odd 18
684.2.cf.a.667.7 48 12.11 even 2
684.2.cf.a.667.8 48 3.2 odd 2