Properties

Label 32.2.g.b.29.2
Level $32$
Weight $2$
Character 32.29
Analytic conductor $0.256$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [32,2,Mod(5,32)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(32, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("32.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.255521286468\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 29.2
Root \(0.500000 + 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 32.29
Dual form 32.2.g.b.21.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.11137 + 0.874559i) q^{2} +(-2.27882 - 0.943920i) q^{3} +(0.470294 + 1.94392i) q^{4} +(-0.707107 - 1.70711i) q^{5} +(-1.70711 - 3.04201i) q^{6} +(-0.665096 + 0.665096i) q^{7} +(-1.17740 + 2.57172i) q^{8} +(2.18073 + 2.18073i) q^{9} +O(q^{10})\) \(q+(1.11137 + 0.874559i) q^{2} +(-2.27882 - 0.943920i) q^{3} +(0.470294 + 1.94392i) q^{4} +(-0.707107 - 1.70711i) q^{5} +(-1.70711 - 3.04201i) q^{6} +(-0.665096 + 0.665096i) q^{7} +(-1.17740 + 2.57172i) q^{8} +(2.18073 + 2.18073i) q^{9} +(0.707107 - 2.51564i) q^{10} +(3.69304 - 1.52971i) q^{11} +(0.763187 - 4.87377i) q^{12} +(-1.76652 + 4.26475i) q^{13} +(-1.32083 + 0.157503i) q^{14} +4.55765i q^{15} +(-3.55765 + 1.82843i) q^{16} -3.61706i q^{17} +(0.516426 + 4.33078i) q^{18} +(0.194802 - 0.470294i) q^{19} +(2.98593 - 2.17740i) q^{20} +(2.14343 - 0.887839i) q^{21} +(5.44215 + 1.52971i) q^{22} +(-1.33490 - 1.33490i) q^{23} +(5.11058 - 4.74912i) q^{24} +(1.12132 - 1.12132i) q^{25} +(-5.69304 + 3.19480i) q^{26} +(-0.0793096 - 0.191470i) q^{27} +(-1.60568 - 0.980103i) q^{28} +(-5.73838 - 2.37691i) q^{29} +(-3.98593 + 5.06524i) q^{30} +1.17157 q^{31} +(-5.55294 - 1.07931i) q^{32} -9.85970 q^{33} +(3.16333 - 4.01990i) q^{34} +(1.60568 + 0.665096i) q^{35} +(-3.21358 + 5.26475i) q^{36} +(0.510925 + 1.23348i) q^{37} +(0.627797 - 0.352305i) q^{38} +(8.05117 - 8.05117i) q^{39} +(5.22274 + 0.191470i) q^{40} +(1.66981 + 1.66981i) q^{41} +(3.15862 + 0.887839i) q^{42} +(-2.54960 + 1.05608i) q^{43} +(4.71044 + 6.45956i) q^{44} +(2.18073 - 5.26475i) q^{45} +(-0.316122 - 2.65103i) q^{46} +1.49824i q^{47} +(9.83314 - 0.808530i) q^{48} +6.11529i q^{49} +(2.22686 - 0.265543i) q^{50} +(-3.41421 + 8.24264i) q^{51} +(-9.12112 - 1.42828i) q^{52} +(4.59495 - 1.90329i) q^{53} +(0.0793096 - 0.282156i) q^{54} +(-5.22274 - 5.22274i) q^{55} +(-0.927354 - 2.49352i) q^{56} +(-0.887839 + 0.887839i) q^{57} +(-4.29872 - 7.66019i) q^{58} +(2.04784 + 4.94392i) q^{59} +(-8.85970 + 2.14343i) q^{60} +(13.7102 + 5.67897i) q^{61} +(1.30205 + 1.02461i) q^{62} -2.90079 q^{63} +(-5.22746 - 6.05588i) q^{64} +8.52951 q^{65} +(-10.9578 - 8.62289i) q^{66} +(-3.40617 - 1.41088i) q^{67} +(7.03127 - 1.70108i) q^{68} +(1.78197 + 4.30205i) q^{69} +(1.20285 + 2.14343i) q^{70} +(-9.66157 + 9.66157i) q^{71} +(-8.17582 + 3.04063i) q^{72} +(-7.55765 - 7.55765i) q^{73} +(-0.510925 + 1.81769i) q^{74} +(-3.61373 + 1.49685i) q^{75} +(1.00583 + 0.157503i) q^{76} +(-1.43882 + 3.47363i) q^{77} +(15.9891 - 1.90662i) q^{78} -17.2176i q^{79} +(5.63696 + 4.78039i) q^{80} -8.74088i q^{81} +(0.395432 + 3.31612i) q^{82} +(4.82981 - 11.6602i) q^{83} +(2.73393 + 3.74912i) q^{84} +(-6.17471 + 2.55765i) q^{85} +(-3.75716 - 1.05608i) q^{86} +(10.8331 + 10.8331i) q^{87} +(-0.414214 + 11.2985i) q^{88} +(-5.43882 + 5.43882i) q^{89} +(7.02794 - 3.94392i) q^{90} +(-1.66157 - 4.01138i) q^{91} +(1.96715 - 3.22274i) q^{92} +(-2.66981 - 1.10587i) q^{93} +(-1.31029 + 1.66510i) q^{94} -0.940588 q^{95} +(11.6354 + 7.70108i) q^{96} +6.15862 q^{97} +(-5.34818 + 6.79637i) q^{98} +(11.3894 + 4.71765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{6} - 8 q^{7} - 4 q^{8} + 4 q^{11} + 12 q^{12} - 8 q^{13} + 12 q^{14} + 20 q^{18} + 4 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} - 8 q^{24} - 8 q^{25} - 20 q^{26} + 8 q^{27} - 16 q^{28} - 12 q^{30} + 32 q^{31} - 24 q^{32} - 16 q^{33} + 16 q^{35} - 40 q^{36} - 8 q^{37} + 8 q^{38} + 16 q^{39} + 16 q^{40} + 8 q^{41} + 8 q^{42} - 12 q^{43} + 20 q^{44} + 12 q^{46} + 48 q^{48} + 16 q^{50} - 16 q^{51} + 12 q^{52} + 8 q^{53} - 8 q^{54} - 16 q^{55} + 8 q^{56} + 16 q^{57} - 12 q^{58} - 20 q^{59} - 8 q^{60} + 24 q^{61} - 24 q^{62} - 40 q^{63} - 8 q^{64} - 28 q^{66} - 36 q^{67} + 16 q^{68} + 32 q^{69} - 8 q^{70} - 24 q^{71} + 12 q^{72} - 32 q^{73} + 8 q^{74} - 12 q^{75} - 20 q^{76} + 16 q^{77} + 28 q^{78} + 8 q^{80} - 20 q^{82} + 20 q^{83} + 8 q^{84} + 8 q^{85} + 4 q^{86} + 56 q^{87} + 8 q^{88} - 16 q^{89} + 28 q^{90} + 40 q^{91} - 16 q^{92} - 16 q^{93} - 24 q^{94} - 8 q^{95} - 16 q^{96} + 32 q^{97} - 24 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.11137 + 0.874559i 0.785858 + 0.618406i
\(3\) −2.27882 0.943920i −1.31568 0.544972i −0.389143 0.921177i \(-0.627229\pi\)
−0.926536 + 0.376205i \(0.877229\pi\)
\(4\) 0.470294 + 1.94392i 0.235147 + 0.971960i
\(5\) −0.707107 1.70711i −0.316228 0.763441i −0.999448 0.0332288i \(-0.989421\pi\)
0.683220 0.730213i \(-0.260579\pi\)
\(6\) −1.70711 3.04201i −0.696923 1.24190i
\(7\) −0.665096 + 0.665096i −0.251383 + 0.251383i −0.821537 0.570155i \(-0.806883\pi\)
0.570155 + 0.821537i \(0.306883\pi\)
\(8\) −1.17740 + 2.57172i −0.416274 + 0.909239i
\(9\) 2.18073 + 2.18073i 0.726911 + 0.726911i
\(10\) 0.707107 2.51564i 0.223607 0.795514i
\(11\) 3.69304 1.52971i 1.11349 0.461224i 0.251353 0.967895i \(-0.419124\pi\)
0.862139 + 0.506672i \(0.169124\pi\)
\(12\) 0.763187 4.87377i 0.220313 1.40694i
\(13\) −1.76652 + 4.26475i −0.489944 + 1.18283i 0.464804 + 0.885414i \(0.346125\pi\)
−0.954748 + 0.297416i \(0.903875\pi\)
\(14\) −1.32083 + 0.157503i −0.353008 + 0.0420945i
\(15\) 4.55765i 1.17678i
\(16\) −3.55765 + 1.82843i −0.889412 + 0.457107i
\(17\) 3.61706i 0.877266i −0.898666 0.438633i \(-0.855463\pi\)
0.898666 0.438633i \(-0.144537\pi\)
\(18\) 0.516426 + 4.33078i 0.121723 + 1.02078i
\(19\) 0.194802 0.470294i 0.0446907 0.107893i −0.899958 0.435977i \(-0.856403\pi\)
0.944649 + 0.328084i \(0.106403\pi\)
\(20\) 2.98593 2.17740i 0.667674 0.486882i
\(21\) 2.14343 0.887839i 0.467736 0.193742i
\(22\) 5.44215 + 1.52971i 1.16027 + 0.326134i
\(23\) −1.33490 1.33490i −0.278347 0.278347i 0.554102 0.832449i \(-0.313062\pi\)
−0.832449 + 0.554102i \(0.813062\pi\)
\(24\) 5.11058 4.74912i 1.04319 0.969410i
\(25\) 1.12132 1.12132i 0.224264 0.224264i
\(26\) −5.69304 + 3.19480i −1.11650 + 0.626552i
\(27\) −0.0793096 0.191470i −0.0152631 0.0368485i
\(28\) −1.60568 0.980103i −0.303446 0.185222i
\(29\) −5.73838 2.37691i −1.06559 0.441382i −0.220158 0.975464i \(-0.570657\pi\)
−0.845433 + 0.534082i \(0.820657\pi\)
\(30\) −3.98593 + 5.06524i −0.727728 + 0.924782i
\(31\) 1.17157 0.210421 0.105210 0.994450i \(-0.466448\pi\)
0.105210 + 0.994450i \(0.466448\pi\)
\(32\) −5.55294 1.07931i −0.981630 0.190797i
\(33\) −9.85970 −1.71635
\(34\) 3.16333 4.01990i 0.542507 0.689407i
\(35\) 1.60568 + 0.665096i 0.271410 + 0.112422i
\(36\) −3.21358 + 5.26475i −0.535597 + 0.877459i
\(37\) 0.510925 + 1.23348i 0.0839955 + 0.202783i 0.960297 0.278980i \(-0.0899965\pi\)
−0.876301 + 0.481763i \(0.839996\pi\)
\(38\) 0.627797 0.352305i 0.101842 0.0571515i
\(39\) 8.05117 8.05117i 1.28922 1.28922i
\(40\) 5.22274 + 0.191470i 0.825788 + 0.0302741i
\(41\) 1.66981 + 1.66981i 0.260780 + 0.260780i 0.825371 0.564591i \(-0.190966\pi\)
−0.564591 + 0.825371i \(0.690966\pi\)
\(42\) 3.15862 + 0.887839i 0.487386 + 0.136997i
\(43\) −2.54960 + 1.05608i −0.388811 + 0.161051i −0.568521 0.822669i \(-0.692484\pi\)
0.179710 + 0.983720i \(0.442484\pi\)
\(44\) 4.71044 + 6.45956i 0.710125 + 0.973815i
\(45\) 2.18073 5.26475i 0.325084 0.784823i
\(46\) −0.316122 2.65103i −0.0466097 0.390873i
\(47\) 1.49824i 0.218540i 0.994012 + 0.109270i \(0.0348513\pi\)
−0.994012 + 0.109270i \(0.965149\pi\)
\(48\) 9.83314 0.808530i 1.41929 0.116701i
\(49\) 6.11529i 0.873614i
\(50\) 2.22686 0.265543i 0.314926 0.0375535i
\(51\) −3.41421 + 8.24264i −0.478086 + 1.15420i
\(52\) −9.12112 1.42828i −1.26487 0.198067i
\(53\) 4.59495 1.90329i 0.631164 0.261437i −0.0440833 0.999028i \(-0.514037\pi\)
0.675248 + 0.737591i \(0.264037\pi\)
\(54\) 0.0793096 0.282156i 0.0107927 0.0383965i
\(55\) −5.22274 5.22274i −0.704235 0.704235i
\(56\) −0.927354 2.49352i −0.123923 0.333211i
\(57\) −0.887839 + 0.887839i −0.117597 + 0.117597i
\(58\) −4.29872 7.66019i −0.564450 1.00583i
\(59\) 2.04784 + 4.94392i 0.266606 + 0.643644i 0.999319 0.0368939i \(-0.0117464\pi\)
−0.732713 + 0.680537i \(0.761746\pi\)
\(60\) −8.85970 + 2.14343i −1.14378 + 0.276716i
\(61\) 13.7102 + 5.67897i 1.75542 + 0.727117i 0.997173 + 0.0751463i \(0.0239424\pi\)
0.758244 + 0.651971i \(0.226058\pi\)
\(62\) 1.30205 + 1.02461i 0.165361 + 0.130126i
\(63\) −2.90079 −0.365466
\(64\) −5.22746 6.05588i −0.653432 0.756985i
\(65\) 8.52951 1.05796
\(66\) −10.9578 8.62289i −1.34881 1.06140i
\(67\) −3.40617 1.41088i −0.416130 0.172367i 0.164788 0.986329i \(-0.447306\pi\)
−0.580918 + 0.813962i \(0.697306\pi\)
\(68\) 7.03127 1.70108i 0.852667 0.206286i
\(69\) 1.78197 + 4.30205i 0.214524 + 0.517906i
\(70\) 1.20285 + 2.14343i 0.143768 + 0.256189i
\(71\) −9.66157 + 9.66157i −1.14662 + 1.14662i −0.159403 + 0.987214i \(0.550957\pi\)
−0.987214 + 0.159403i \(0.949043\pi\)
\(72\) −8.17582 + 3.04063i −0.963530 + 0.358342i
\(73\) −7.55765 7.55765i −0.884556 0.884556i 0.109438 0.993994i \(-0.465095\pi\)
−0.993994 + 0.109438i \(0.965095\pi\)
\(74\) −0.510925 + 1.81769i −0.0593938 + 0.211302i
\(75\) −3.61373 + 1.49685i −0.417277 + 0.172842i
\(76\) 1.00583 + 0.157503i 0.115376 + 0.0180669i
\(77\) −1.43882 + 3.47363i −0.163969 + 0.395856i
\(78\) 15.9891 1.90662i 1.81041 0.215882i
\(79\) 17.2176i 1.93714i −0.248750 0.968568i \(-0.580020\pi\)
0.248750 0.968568i \(-0.419980\pi\)
\(80\) 5.63696 + 4.78039i 0.630231 + 0.534464i
\(81\) 8.74088i 0.971208i
\(82\) 0.395432 + 3.31612i 0.0436682 + 0.366204i
\(83\) 4.82981 11.6602i 0.530140 1.27987i −0.401290 0.915951i \(-0.631438\pi\)
0.931430 0.363921i \(-0.118562\pi\)
\(84\) 2.73393 + 3.74912i 0.298296 + 0.409062i
\(85\) −6.17471 + 2.55765i −0.669741 + 0.277416i
\(86\) −3.75716 1.05608i −0.405145 0.113880i
\(87\) 10.8331 + 10.8331i 1.16143 + 1.16143i
\(88\) −0.414214 + 11.2985i −0.0441553 + 1.20443i
\(89\) −5.43882 + 5.43882i −0.576514 + 0.576514i −0.933941 0.357427i \(-0.883654\pi\)
0.357427 + 0.933941i \(0.383654\pi\)
\(90\) 7.02794 3.94392i 0.740810 0.415726i
\(91\) −1.66157 4.01138i −0.174179 0.420506i
\(92\) 1.96715 3.22274i 0.205089 0.335994i
\(93\) −2.66981 1.10587i −0.276846 0.114673i
\(94\) −1.31029 + 1.66510i −0.135147 + 0.171742i
\(95\) −0.940588 −0.0965023
\(96\) 11.6354 + 7.70108i 1.18753 + 0.785988i
\(97\) 6.15862 0.625313 0.312657 0.949866i \(-0.398781\pi\)
0.312657 + 0.949866i \(0.398781\pi\)
\(98\) −5.34818 + 6.79637i −0.540248 + 0.686537i
\(99\) 11.3894 + 4.71765i 1.14468 + 0.474141i
\(100\) 2.70711 + 1.65241i 0.270711 + 0.165241i
\(101\) −3.09671 7.47612i −0.308134 0.743902i −0.999766 0.0216512i \(-0.993108\pi\)
0.691631 0.722251i \(-0.256892\pi\)
\(102\) −11.0031 + 6.17471i −1.08947 + 0.611387i
\(103\) −4.72764 + 4.72764i −0.465828 + 0.465828i −0.900560 0.434732i \(-0.856843\pi\)
0.434732 + 0.900560i \(0.356843\pi\)
\(104\) −8.88784 9.56431i −0.871524 0.937858i
\(105\) −3.03127 3.03127i −0.295822 0.295822i
\(106\) 6.77123 + 1.90329i 0.657680 + 0.184864i
\(107\) 2.57774 1.06774i 0.249200 0.103222i −0.254587 0.967050i \(-0.581940\pi\)
0.503787 + 0.863828i \(0.331940\pi\)
\(108\) 0.334904 0.244219i 0.0322262 0.0235000i
\(109\) 3.46094 8.35544i 0.331498 0.800306i −0.666976 0.745079i \(-0.732412\pi\)
0.998474 0.0552270i \(-0.0175882\pi\)
\(110\) −1.23681 10.3720i −0.117925 0.988932i
\(111\) 3.29316i 0.312573i
\(112\) 1.15010 3.58226i 0.108674 0.338491i
\(113\) 11.7757i 1.10776i 0.832596 + 0.553881i \(0.186854\pi\)
−0.832596 + 0.553881i \(0.813146\pi\)
\(114\) −1.76319 + 0.210252i −0.165138 + 0.0196919i
\(115\) −1.33490 + 3.22274i −0.124480 + 0.300522i
\(116\) 1.92181 12.2728i 0.178435 1.13950i
\(117\) −13.1526 + 5.44798i −1.21596 + 0.503666i
\(118\) −2.04784 + 7.28549i −0.188519 + 0.670683i
\(119\) 2.40569 + 2.40569i 0.220529 + 0.220529i
\(120\) −11.7210 5.36618i −1.06997 0.489863i
\(121\) 3.52035 3.52035i 0.320032 0.320032i
\(122\) 10.2706 + 18.3019i 0.929855 + 1.65697i
\(123\) −2.22903 5.38136i −0.200985 0.485221i
\(124\) 0.550984 + 2.27744i 0.0494798 + 0.204520i
\(125\) −11.2426 4.65685i −1.00557 0.416522i
\(126\) −3.22386 2.53691i −0.287204 0.226006i
\(127\) 13.0590 1.15880 0.579400 0.815043i \(-0.303287\pi\)
0.579400 + 0.815043i \(0.303287\pi\)
\(128\) −0.513421 11.3021i −0.0453804 0.998970i
\(129\) 6.80695 0.599319
\(130\) 9.47945 + 7.45956i 0.831403 + 0.654246i
\(131\) −6.52146 2.70128i −0.569783 0.236012i 0.0791431 0.996863i \(-0.474782\pi\)
−0.648926 + 0.760851i \(0.724782\pi\)
\(132\) −4.63696 19.1665i −0.403595 1.66823i
\(133\) 0.183228 + 0.442353i 0.0158879 + 0.0383568i
\(134\) −2.55162 4.54691i −0.220427 0.392793i
\(135\) −0.270780 + 0.270780i −0.0233050 + 0.0233050i
\(136\) 9.30205 + 4.25873i 0.797644 + 0.365183i
\(137\) 4.88118 + 4.88118i 0.417027 + 0.417027i 0.884178 0.467151i \(-0.154719\pi\)
−0.467151 + 0.884178i \(0.654719\pi\)
\(138\) −1.78197 + 6.33962i −0.151691 + 0.539664i
\(139\) −11.7837 + 4.88098i −0.999482 + 0.413999i −0.821607 0.570054i \(-0.806922\pi\)
−0.177875 + 0.984053i \(0.556922\pi\)
\(140\) −0.537750 + 3.43411i −0.0454482 + 0.290235i
\(141\) 1.41421 3.41421i 0.119098 0.287529i
\(142\) −19.1872 + 2.28798i −1.61015 + 0.192003i
\(143\) 18.4522i 1.54305i
\(144\) −11.7456 3.77097i −0.978799 0.314247i
\(145\) 11.4768i 0.953093i
\(146\) −1.78975 15.0090i −0.148121 1.24215i
\(147\) 5.77235 13.9357i 0.476095 1.14940i
\(148\) −2.15750 + 1.57329i −0.177346 + 0.129324i
\(149\) −5.73838 + 2.37691i −0.470106 + 0.194724i −0.605144 0.796116i \(-0.706884\pi\)
0.135038 + 0.990840i \(0.456884\pi\)
\(150\) −5.32528 1.49685i −0.434807 0.122218i
\(151\) 11.1504 + 11.1504i 0.907405 + 0.907405i 0.996062 0.0886573i \(-0.0282576\pi\)
−0.0886573 + 0.996062i \(0.528258\pi\)
\(152\) 0.980103 + 1.05470i 0.0794968 + 0.0855475i
\(153\) 7.88784 7.88784i 0.637694 0.637694i
\(154\) −4.63696 + 2.60215i −0.373657 + 0.209688i
\(155\) −0.828427 2.00000i −0.0665409 0.160644i
\(156\) 19.4372 + 11.8644i 1.55623 + 0.949913i
\(157\) 1.22496 + 0.507395i 0.0977624 + 0.0404945i 0.431029 0.902338i \(-0.358151\pi\)
−0.333266 + 0.942833i \(0.608151\pi\)
\(158\) 15.0578 19.1352i 1.19794 1.52231i
\(159\) −12.2676 −0.972886
\(160\) 2.08402 + 10.2426i 0.164756 + 0.809752i
\(161\) 1.77568 0.139943
\(162\) 7.64441 9.71436i 0.600602 0.763232i
\(163\) 21.3218 + 8.83176i 1.67005 + 0.691757i 0.998776 0.0494542i \(-0.0157482\pi\)
0.671272 + 0.741211i \(0.265748\pi\)
\(164\) −2.46067 + 4.03127i −0.192146 + 0.314790i
\(165\) 6.97186 + 16.8316i 0.542759 + 1.31034i
\(166\) 15.5652 8.73485i 1.20810 0.677956i
\(167\) 10.8863 10.8863i 0.842404 0.842404i −0.146767 0.989171i \(-0.546887\pi\)
0.989171 + 0.146767i \(0.0468867\pi\)
\(168\) −0.240409 + 6.55765i −0.0185480 + 0.505933i
\(169\) −5.87515 5.87515i −0.451935 0.451935i
\(170\) −9.09921 2.55765i −0.697877 0.196163i
\(171\) 1.45040 0.600774i 0.110915 0.0459423i
\(172\) −3.25200 4.45956i −0.247963 0.340038i
\(173\) 0.735246 1.77504i 0.0558997 0.134954i −0.893462 0.449138i \(-0.851731\pi\)
0.949362 + 0.314184i \(0.101731\pi\)
\(174\) 2.56543 + 21.5139i 0.194485 + 1.63096i
\(175\) 1.49157i 0.112752i
\(176\) −10.3416 + 12.1946i −0.779525 + 0.919203i
\(177\) 13.1993i 0.992121i
\(178\) −10.8011 + 1.28798i −0.809578 + 0.0965384i
\(179\) −1.87980 + 4.53823i −0.140503 + 0.339203i −0.978430 0.206578i \(-0.933767\pi\)
0.837928 + 0.545782i \(0.183767\pi\)
\(180\) 11.2598 + 1.76319i 0.839259 + 0.131420i
\(181\) 1.87868 0.778175i 0.139641 0.0578413i −0.311768 0.950158i \(-0.600921\pi\)
0.451410 + 0.892317i \(0.350921\pi\)
\(182\) 1.66157 5.91127i 0.123163 0.438172i
\(183\) −25.8827 25.8827i −1.91331 1.91331i
\(184\) 5.00471 1.86128i 0.368952 0.137215i
\(185\) 1.74441 1.74441i 0.128251 0.128251i
\(186\) −2.00000 3.56394i −0.146647 0.261321i
\(187\) −5.53304 13.3579i −0.404616 0.976829i
\(188\) −2.91245 + 0.704611i −0.212412 + 0.0513890i
\(189\) 0.180095 + 0.0745976i 0.0131000 + 0.00542618i
\(190\) −1.04534 0.822599i −0.0758371 0.0596776i
\(191\) −19.4022 −1.40389 −0.701946 0.712231i \(-0.747685\pi\)
−0.701946 + 0.712231i \(0.747685\pi\)
\(192\) 6.19618 + 18.7346i 0.447171 + 1.35205i
\(193\) −18.0461 −1.29898 −0.649492 0.760368i \(-0.725018\pi\)
−0.649492 + 0.760368i \(0.725018\pi\)
\(194\) 6.84451 + 5.38607i 0.491408 + 0.386698i
\(195\) −19.4372 8.05117i −1.39193 0.576556i
\(196\) −11.8876 + 2.87599i −0.849117 + 0.205428i
\(197\) −0.0865175 0.208872i −0.00616412 0.0148815i 0.920768 0.390112i \(-0.127564\pi\)
−0.926932 + 0.375230i \(0.877564\pi\)
\(198\) 8.53200 + 15.2038i 0.606343 + 1.08048i
\(199\) −11.8992 + 11.8992i −0.843513 + 0.843513i −0.989314 0.145801i \(-0.953424\pi\)
0.145801 + 0.989314i \(0.453424\pi\)
\(200\) 1.56348 + 4.20396i 0.110554 + 0.297265i
\(201\) 6.43030 + 6.43030i 0.453558 + 0.453558i
\(202\) 3.09671 11.0170i 0.217884 0.775154i
\(203\) 5.39745 2.23570i 0.378827 0.156915i
\(204\) −17.6287 2.76049i −1.23426 0.193273i
\(205\) 1.66981 4.03127i 0.116624 0.281556i
\(206\) −9.38877 + 1.11957i −0.654146 + 0.0780039i
\(207\) 5.82214i 0.404667i
\(208\) −1.51314 18.4024i −0.104917 1.27598i
\(209\) 2.03480i 0.140750i
\(210\) −0.717844 6.01990i −0.0495360 0.415412i
\(211\) −3.73060 + 9.00647i −0.256825 + 0.620031i −0.998725 0.0504799i \(-0.983925\pi\)
0.741900 + 0.670511i \(0.233925\pi\)
\(212\) 5.86082 + 8.03710i 0.402522 + 0.551990i
\(213\) 31.1367 12.8973i 2.13345 0.883706i
\(214\) 3.79863 + 1.06774i 0.259669 + 0.0729889i
\(215\) 3.60568 + 3.60568i 0.245906 + 0.245906i
\(216\) 0.585786 + 0.0214754i 0.0398577 + 0.00146122i
\(217\) −0.779208 + 0.779208i −0.0528961 + 0.0528961i
\(218\) 11.1537 6.25921i 0.755425 0.423927i
\(219\) 10.0887 + 24.3564i 0.681733 + 1.64585i
\(220\) 7.69637 12.6088i 0.518889 0.850086i
\(221\) 15.4259 + 6.38960i 1.03766 + 0.429811i
\(222\) 2.88006 3.65992i 0.193297 0.245638i
\(223\) 22.6174 1.51458 0.757288 0.653081i \(-0.226524\pi\)
0.757288 + 0.653081i \(0.226524\pi\)
\(224\) 4.41108 2.97539i 0.294728 0.198802i
\(225\) 4.89060 0.326040
\(226\) −10.2985 + 13.0872i −0.685048 + 0.870545i
\(227\) −9.51294 3.94039i −0.631396 0.261533i 0.0439500 0.999034i \(-0.486006\pi\)
−0.675346 + 0.737501i \(0.736006\pi\)
\(228\) −2.14343 1.30834i −0.141952 0.0866471i
\(229\) −6.53200 15.7697i −0.431647 1.04209i −0.978756 0.205027i \(-0.934272\pi\)
0.547109 0.837061i \(-0.315728\pi\)
\(230\) −4.30205 + 2.41421i −0.283669 + 0.159189i
\(231\) 6.55765 6.55765i 0.431462 0.431462i
\(232\) 12.8691 11.9589i 0.844899 0.785141i
\(233\) 10.4486 + 10.4486i 0.684512 + 0.684512i 0.961013 0.276502i \(-0.0891751\pi\)
−0.276502 + 0.961013i \(0.589175\pi\)
\(234\) −19.3820 5.44798i −1.26704 0.356146i
\(235\) 2.55765 1.05941i 0.166843 0.0691084i
\(236\) −8.64750 + 6.30593i −0.562904 + 0.410481i
\(237\) −16.2521 + 39.2360i −1.05569 + 2.54865i
\(238\) 0.569699 + 4.77754i 0.0369281 + 0.309682i
\(239\) 11.6733i 0.755085i −0.925992 0.377543i \(-0.876769\pi\)
0.925992 0.377543i \(-0.123231\pi\)
\(240\) −8.33333 16.2145i −0.537914 1.04664i
\(241\) 13.8288i 0.890791i −0.895334 0.445396i \(-0.853063\pi\)
0.895334 0.445396i \(-0.146937\pi\)
\(242\) 6.99117 0.833664i 0.449409 0.0535899i
\(243\) −8.48861 + 20.4933i −0.544545 + 1.31465i
\(244\) −4.59161 + 29.3224i −0.293948 + 1.87717i
\(245\) 10.4395 4.32417i 0.666953 0.276261i
\(246\) 2.22903 7.93011i 0.142118 0.505606i
\(247\) 1.66157 + 1.66157i 0.105723 + 0.105723i
\(248\) −1.37941 + 3.01295i −0.0875927 + 0.191323i
\(249\) −22.0126 + 22.0126i −1.39499 + 1.39499i
\(250\) −8.42206 15.0078i −0.532658 0.949180i
\(251\) 5.38745 + 13.0065i 0.340053 + 0.820961i 0.997710 + 0.0676429i \(0.0215479\pi\)
−0.657656 + 0.753318i \(0.728452\pi\)
\(252\) −1.36423 5.63891i −0.0859381 0.355218i
\(253\) −6.97186 2.88784i −0.438317 0.181557i
\(254\) 14.5134 + 11.4209i 0.910653 + 0.716610i
\(255\) 16.4853 1.03235
\(256\) 9.31371 13.0098i 0.582107 0.813112i
\(257\) −18.9043 −1.17922 −0.589609 0.807689i \(-0.700718\pi\)
−0.589609 + 0.807689i \(0.700718\pi\)
\(258\) 7.56505 + 5.95308i 0.470980 + 0.370623i
\(259\) −1.16020 0.480569i −0.0720911 0.0298611i
\(260\) 4.01138 + 16.5807i 0.248775 + 1.02829i
\(261\) −7.33046 17.6973i −0.453744 1.09543i
\(262\) −4.88534 8.70553i −0.301818 0.537829i
\(263\) 13.9086 13.9086i 0.857643 0.857643i −0.133417 0.991060i \(-0.542595\pi\)
0.991060 + 0.133417i \(0.0425948\pi\)
\(264\) 11.6088 25.3564i 0.714473 1.56058i
\(265\) −6.49824 6.49824i −0.399183 0.399183i
\(266\) −0.183228 + 0.651862i −0.0112345 + 0.0399682i
\(267\) 17.5279 7.26031i 1.07269 0.444324i
\(268\) 1.14074 7.28485i 0.0696818 0.444993i
\(269\) 5.05209 12.1968i 0.308031 0.743653i −0.691737 0.722149i \(-0.743154\pi\)
0.999769 0.0215042i \(-0.00684553\pi\)
\(270\) −0.537750 + 0.0641242i −0.0327264 + 0.00390247i
\(271\) 4.41512i 0.268199i 0.990968 + 0.134100i \(0.0428142\pi\)
−0.990968 + 0.134100i \(0.957186\pi\)
\(272\) 6.61353 + 12.8682i 0.401004 + 0.780251i
\(273\) 10.7096i 0.648175i
\(274\) 1.15593 + 9.69368i 0.0698320 + 0.585616i
\(275\) 2.42579 5.85637i 0.146280 0.353152i
\(276\) −7.52480 + 5.48723i −0.452940 + 0.330293i
\(277\) −23.0454 + 9.54573i −1.38467 + 0.573547i −0.945725 0.324969i \(-0.894646\pi\)
−0.438941 + 0.898516i \(0.644646\pi\)
\(278\) −17.3648 4.88098i −1.04147 0.292742i
\(279\) 2.55489 + 2.55489i 0.152957 + 0.152957i
\(280\) −3.60097 + 3.34628i −0.215199 + 0.199978i
\(281\) −5.83509 + 5.83509i −0.348092 + 0.348092i −0.859399 0.511306i \(-0.829162\pi\)
0.511306 + 0.859399i \(0.329162\pi\)
\(282\) 4.55765 2.55765i 0.271404 0.152306i
\(283\) 1.31992 + 3.18656i 0.0784609 + 0.189421i 0.958243 0.285957i \(-0.0923113\pi\)
−0.879782 + 0.475378i \(0.842311\pi\)
\(284\) −23.3251 14.2375i −1.38409 0.844842i
\(285\) 2.14343 + 0.887839i 0.126966 + 0.0525911i
\(286\) −16.1375 + 20.5072i −0.954230 + 1.21262i
\(287\) −2.22117 −0.131111
\(288\) −9.75578 14.4632i −0.574865 0.852249i
\(289\) 3.91688 0.230405
\(290\) −10.0371 + 12.7549i −0.589399 + 0.748996i
\(291\) −14.0344 5.81324i −0.822712 0.340778i
\(292\) 11.1371 18.2458i 0.651752 1.06775i
\(293\) 2.89663 + 6.99307i 0.169223 + 0.408540i 0.985626 0.168943i \(-0.0540353\pi\)
−0.816403 + 0.577482i \(0.804035\pi\)
\(294\) 18.6028 10.4395i 1.08494 0.608842i
\(295\) 6.99176 6.99176i 0.407076 0.407076i
\(296\) −3.77373 0.138348i −0.219343 0.00804132i
\(297\) −0.585786 0.585786i −0.0339908 0.0339908i
\(298\) −8.45622 2.37691i −0.489856 0.137691i
\(299\) 8.05117 3.33490i 0.465611 0.192862i
\(300\) −4.60928 6.32083i −0.266117 0.364934i
\(301\) 0.993336 2.39813i 0.0572550 0.138226i
\(302\) 2.64055 + 22.1439i 0.151947 + 1.27424i
\(303\) 19.9598i 1.14666i
\(304\) 0.166861 + 2.02932i 0.00957013 + 0.116390i
\(305\) 27.4205i 1.57009i
\(306\) 15.6647 1.86794i 0.895491 0.106783i
\(307\) −3.14481 + 7.59225i −0.179484 + 0.433313i −0.987859 0.155356i \(-0.950348\pi\)
0.808375 + 0.588668i \(0.200348\pi\)
\(308\) −7.42912 1.16333i −0.423313 0.0662869i
\(309\) 15.2360 6.31095i 0.866744 0.359017i
\(310\) 0.828427 2.94725i 0.0470515 0.167393i
\(311\) −15.0543 15.0543i −0.853651 0.853651i 0.136930 0.990581i \(-0.456277\pi\)
−0.990581 + 0.136930i \(0.956277\pi\)
\(312\) 11.2259 + 30.1848i 0.635540 + 1.70888i
\(313\) 18.3365 18.3365i 1.03644 1.03644i 0.0371274 0.999311i \(-0.488179\pi\)
0.999311 0.0371274i \(-0.0118208\pi\)
\(314\) 0.917639 + 1.63520i 0.0517853 + 0.0922798i
\(315\) 2.05117 + 4.95196i 0.115570 + 0.279012i
\(316\) 33.4697 8.09735i 1.88282 0.455511i
\(317\) −9.52348 3.94476i −0.534892 0.221560i 0.0988523 0.995102i \(-0.468483\pi\)
−0.633744 + 0.773543i \(0.718483\pi\)
\(318\) −13.6339 10.7288i −0.764551 0.601639i
\(319\) −24.8280 −1.39010
\(320\) −6.64167 + 13.2060i −0.371281 + 0.738237i
\(321\) −6.88208 −0.384120
\(322\) 1.97344 + 1.55294i 0.109975 + 0.0865417i
\(323\) −1.70108 0.704611i −0.0946507 0.0392056i
\(324\) 16.9916 4.11078i 0.943976 0.228377i
\(325\) 2.80132 + 6.76299i 0.155389 + 0.375143i
\(326\) 15.9725 + 28.4625i 0.884635 + 1.57639i
\(327\) −15.7737 + 15.7737i −0.872289 + 0.872289i
\(328\) −6.26031 + 2.32824i −0.345668 + 0.128556i
\(329\) −0.996470 0.996470i −0.0549372 0.0549372i
\(330\) −6.97186 + 24.8034i −0.383788 + 1.36538i
\(331\) 7.57421 3.13734i 0.416316 0.172444i −0.164685 0.986346i \(-0.552661\pi\)
0.581002 + 0.813902i \(0.302661\pi\)
\(332\) 24.9379 + 3.90504i 1.36864 + 0.214317i
\(333\) −1.57570 + 3.80408i −0.0863480 + 0.208462i
\(334\) 21.6194 2.57801i 1.18296 0.141062i
\(335\) 6.81234i 0.372198i
\(336\) −6.00223 + 7.07773i −0.327449 + 0.386122i
\(337\) 16.8910i 0.920110i 0.887890 + 0.460055i \(0.152170\pi\)
−0.887890 + 0.460055i \(0.847830\pi\)
\(338\) −1.39131 11.6676i −0.0756773 0.634636i
\(339\) 11.1153 26.8347i 0.603700 1.45746i
\(340\) −7.87579 10.8003i −0.427125 0.585728i
\(341\) 4.32666 1.79216i 0.234302 0.0970510i
\(342\) 2.13734 + 0.600774i 0.115574 + 0.0324861i
\(343\) −8.72293 8.72293i −0.470994 0.470994i
\(344\) 0.285965 7.80029i 0.0154182 0.420563i
\(345\) 6.08402 6.08402i 0.327553 0.327553i
\(346\) 2.36951 1.32971i 0.127386 0.0714859i
\(347\) −11.6582 28.1455i −0.625847 1.51093i −0.844739 0.535179i \(-0.820244\pi\)
0.218892 0.975749i \(-0.429756\pi\)
\(348\) −15.9640 + 26.1535i −0.855760 + 1.40198i
\(349\) 9.99044 + 4.13818i 0.534776 + 0.221512i 0.633694 0.773584i \(-0.281538\pi\)
−0.0989174 + 0.995096i \(0.531538\pi\)
\(350\) −1.30447 + 1.65769i −0.0697267 + 0.0886073i
\(351\) 0.956675 0.0510636
\(352\) −22.1582 + 4.50843i −1.18104 + 0.240300i
\(353\) 0.673711 0.0358580 0.0179290 0.999839i \(-0.494293\pi\)
0.0179290 + 0.999839i \(0.494293\pi\)
\(354\) 11.5436 14.6693i 0.613534 0.779667i
\(355\) 23.3251 + 9.66157i 1.23797 + 0.512783i
\(356\) −13.1305 8.01479i −0.695914 0.424783i
\(357\) −3.21137 7.75293i −0.169964 0.410328i
\(358\) −6.05810 + 3.39967i −0.320180 + 0.179678i
\(359\) 3.92568 3.92568i 0.207190 0.207190i −0.595882 0.803072i \(-0.703198\pi\)
0.803072 + 0.595882i \(0.203198\pi\)
\(360\) 10.9719 + 11.8070i 0.578268 + 0.622281i
\(361\) 13.2518 + 13.2518i 0.697463 + 0.697463i
\(362\) 2.76847 + 0.778175i 0.145508 + 0.0408999i
\(363\) −11.3452 + 4.69933i −0.595467 + 0.246651i
\(364\) 7.01637 5.11648i 0.367758 0.268176i
\(365\) −7.55765 + 18.2458i −0.395585 + 0.955027i
\(366\) −6.12936 51.4013i −0.320387 2.68679i
\(367\) 16.4759i 0.860033i 0.902821 + 0.430016i \(0.141492\pi\)
−0.902821 + 0.430016i \(0.858508\pi\)
\(368\) 7.18989 + 2.30834i 0.374799 + 0.120331i
\(369\) 7.28281i 0.379128i
\(370\) 3.46427 0.413098i 0.180099 0.0214759i
\(371\) −1.79021 + 4.32195i −0.0929431 + 0.224384i
\(372\) 0.894129 5.70998i 0.0463584 0.296048i
\(373\) −12.6790 + 5.25180i −0.656492 + 0.271928i −0.685962 0.727638i \(-0.740618\pi\)
0.0294695 + 0.999566i \(0.490618\pi\)
\(374\) 5.53304 19.6846i 0.286107 1.01787i
\(375\) 21.2243 + 21.2243i 1.09602 + 1.09602i
\(376\) −3.85304 1.76402i −0.198705 0.0909725i
\(377\) 20.2739 20.2739i 1.04416 1.04416i
\(378\) 0.134912 + 0.240409i 0.00693913 + 0.0123653i
\(379\) −5.06746 12.2339i −0.260298 0.628414i 0.738659 0.674079i \(-0.235459\pi\)
−0.998957 + 0.0456649i \(0.985459\pi\)
\(380\) −0.442353 1.82843i −0.0226922 0.0937963i
\(381\) −29.7592 12.3267i −1.52461 0.631514i
\(382\) −21.5630 16.9683i −1.10326 0.868175i
\(383\) 14.5667 0.744322 0.372161 0.928168i \(-0.378617\pi\)
0.372161 + 0.928168i \(0.378617\pi\)
\(384\) −9.49824 + 26.2400i −0.484705 + 1.33906i
\(385\) 6.94725 0.354065
\(386\) −20.0559 15.7823i −1.02082 0.803300i
\(387\) −7.86303 3.25697i −0.399700 0.165561i
\(388\) 2.89636 + 11.9719i 0.147040 + 0.607779i
\(389\) 14.2795 + 34.4739i 0.724002 + 1.74789i 0.661617 + 0.749842i \(0.269871\pi\)
0.0623850 + 0.998052i \(0.480129\pi\)
\(390\) −14.5608 25.9469i −0.737314 1.31387i
\(391\) −4.82843 + 4.82843i −0.244184 + 0.244184i
\(392\) −15.7268 7.20015i −0.794324 0.363663i
\(393\) 12.3115 + 12.3115i 0.621032 + 0.621032i
\(394\) 0.0865175 0.307799i 0.00435869 0.0155067i
\(395\) −29.3923 + 12.1747i −1.47889 + 0.612576i
\(396\) −3.81436 + 24.3588i −0.191679 + 1.22407i
\(397\) 8.88405 21.4480i 0.445877 1.07644i −0.527975 0.849260i \(-0.677048\pi\)
0.973852 0.227183i \(-0.0729516\pi\)
\(398\) −23.6310 + 2.81789i −1.18452 + 0.141248i
\(399\) 1.18100i 0.0591238i
\(400\) −1.93901 + 6.03951i −0.0969505 + 0.301976i
\(401\) 2.51509i 0.125598i 0.998026 + 0.0627989i \(0.0200027\pi\)
−0.998026 + 0.0627989i \(0.979997\pi\)
\(402\) 1.52278 + 12.7701i 0.0759493 + 0.636916i
\(403\) −2.06961 + 4.99647i −0.103094 + 0.248892i
\(404\) 13.0766 9.53573i 0.650586 0.474420i
\(405\) −14.9216 + 6.18073i −0.741461 + 0.307123i
\(406\) 7.95382 + 2.23570i 0.394742 + 0.110956i
\(407\) 3.77373 + 3.77373i 0.187057 + 0.187057i
\(408\) −17.1778 18.4853i −0.850430 0.915158i
\(409\) −5.32666 + 5.32666i −0.263386 + 0.263386i −0.826428 0.563042i \(-0.809631\pi\)
0.563042 + 0.826428i \(0.309631\pi\)
\(410\) 5.38136 3.01990i 0.265767 0.149142i
\(411\) −6.51590 15.7308i −0.321406 0.775942i
\(412\) −11.4135 6.96678i −0.562305 0.343228i
\(413\) −4.65019 1.92617i −0.228821 0.0947807i
\(414\) 5.09180 6.47056i 0.250248 0.318011i
\(415\) −23.3204 −1.14475
\(416\) 14.4124 21.7753i 0.706624 1.06762i
\(417\) 31.4603 1.54062
\(418\) 1.77955 2.26142i 0.0870409 0.110610i
\(419\) 10.5509 + 4.37032i 0.515444 + 0.213504i 0.625214 0.780453i \(-0.285012\pi\)
−0.109770 + 0.993957i \(0.535012\pi\)
\(420\) 4.46696 7.31814i 0.217965 0.357089i
\(421\) 1.72505 + 4.16464i 0.0840739 + 0.202972i 0.960326 0.278881i \(-0.0899636\pi\)
−0.876252 + 0.481854i \(0.839964\pi\)
\(422\) −12.0228 + 6.74690i −0.585259 + 0.328434i
\(423\) −3.26725 + 3.26725i −0.158859 + 0.158859i
\(424\) −0.515372 + 14.0578i −0.0250287 + 0.682709i
\(425\) −4.05588 4.05588i −0.196739 0.196739i
\(426\) 45.8839 + 12.8973i 2.22308 + 0.624874i
\(427\) −12.8957 + 5.34157i −0.624066 + 0.258497i
\(428\) 3.28789 + 4.50877i 0.158926 + 0.217940i
\(429\) 17.4173 42.0492i 0.840917 2.03015i
\(430\) 0.853872 + 7.16064i 0.0411774 + 0.345317i
\(431\) 16.9800i 0.817897i −0.912557 0.408949i \(-0.865896\pi\)
0.912557 0.408949i \(-0.134104\pi\)
\(432\) 0.632245 + 0.536172i 0.0304189 + 0.0257966i
\(433\) 16.9567i 0.814886i 0.913231 + 0.407443i \(0.133579\pi\)
−0.913231 + 0.407443i \(0.866421\pi\)
\(434\) −1.54745 + 0.184527i −0.0742802 + 0.00885756i
\(435\) 10.8331 26.1535i 0.519409 1.25396i
\(436\) 17.8700 + 2.79827i 0.855816 + 0.134013i
\(437\) −0.887839 + 0.367755i −0.0424711 + 0.0175921i
\(438\) −10.0887 + 35.8922i −0.482058 + 1.71499i
\(439\) 10.5596 + 10.5596i 0.503982 + 0.503982i 0.912673 0.408691i \(-0.134015\pi\)
−0.408691 + 0.912673i \(0.634015\pi\)
\(440\) 19.5807 7.28216i 0.933472 0.347163i
\(441\) −13.3358 + 13.3358i −0.635039 + 0.635039i
\(442\) 11.5558 + 20.5921i 0.549653 + 0.979464i
\(443\) 6.31087 + 15.2358i 0.299838 + 0.723874i 0.999952 + 0.00984190i \(0.00313282\pi\)
−0.700113 + 0.714032i \(0.746867\pi\)
\(444\) 6.40163 1.54875i 0.303808 0.0735005i
\(445\) 13.1305 + 5.43882i 0.622444 + 0.257825i
\(446\) 25.1364 + 19.7803i 1.19024 + 0.936623i
\(447\) 15.3204 0.724629
\(448\) 7.50450 + 0.550984i 0.354554 + 0.0260315i
\(449\) 8.07197 0.380940 0.190470 0.981693i \(-0.438999\pi\)
0.190470 + 0.981693i \(0.438999\pi\)
\(450\) 5.43527 + 4.27712i 0.256221 + 0.201625i
\(451\) 8.72098 + 3.61235i 0.410655 + 0.170099i
\(452\) −22.8910 + 5.53803i −1.07670 + 0.260487i
\(453\) −14.8847 35.9348i −0.699343 1.68836i
\(454\) −7.12631 12.6989i −0.334454 0.595987i
\(455\) −5.67294 + 5.67294i −0.265952 + 0.265952i
\(456\) −1.23793 3.32861i −0.0579713 0.155877i
\(457\) −7.68314 7.68314i −0.359402 0.359402i 0.504191 0.863592i \(-0.331791\pi\)
−0.863592 + 0.504191i \(0.831791\pi\)
\(458\) 6.53200 23.2386i 0.305221 1.08587i
\(459\) −0.692559 + 0.286867i −0.0323259 + 0.0133898i
\(460\) −6.89255 1.07931i −0.321367 0.0503231i
\(461\) −5.90199 + 14.2487i −0.274883 + 0.663627i −0.999679 0.0253371i \(-0.991934\pi\)
0.724796 + 0.688964i \(0.241934\pi\)
\(462\) 13.0230 1.55294i 0.605886 0.0722491i
\(463\) 27.3231i 1.26981i −0.772589 0.634907i \(-0.781038\pi\)
0.772589 0.634907i \(-0.218962\pi\)
\(464\) 24.7611 2.03599i 1.14951 0.0945182i
\(465\) 5.33962i 0.247619i
\(466\) 2.47437 + 20.7502i 0.114623 + 0.961236i
\(467\) −9.40577 + 22.7075i −0.435247 + 1.05078i 0.542323 + 0.840170i \(0.317545\pi\)
−0.977570 + 0.210610i \(0.932455\pi\)
\(468\) −16.7760 23.0054i −0.775472 1.06343i
\(469\) 3.20380 1.32706i 0.147938 0.0612779i
\(470\) 3.76901 + 1.05941i 0.173852 + 0.0488670i
\(471\) −2.31253 2.31253i −0.106556 0.106556i
\(472\) −15.1255 0.554513i −0.696207 0.0255235i
\(473\) −7.80029 + 7.80029i −0.358658 + 0.358658i
\(474\) −52.3762 + 29.3923i −2.40572 + 1.35003i
\(475\) −0.308915 0.745786i −0.0141740 0.0342190i
\(476\) −3.54509 + 5.80785i −0.162489 + 0.266203i
\(477\) 14.1709 + 5.86978i 0.648842 + 0.268759i
\(478\) 10.2090 12.9734i 0.466950 0.593390i
\(479\) 3.91155 0.178723 0.0893616 0.995999i \(-0.471517\pi\)
0.0893616 + 0.995999i \(0.471517\pi\)
\(480\) 4.91911 25.3083i 0.224526 1.15516i
\(481\) −6.16305 −0.281011
\(482\) 12.0941 15.3689i 0.550871 0.700036i
\(483\) −4.04646 1.67610i −0.184120 0.0762651i
\(484\) 8.49887 + 5.18768i 0.386312 + 0.235803i
\(485\) −4.35480 10.5134i −0.197741 0.477390i
\(486\) −27.3566 + 15.3519i −1.24092 + 0.696377i
\(487\) −8.14685 + 8.14685i −0.369169 + 0.369169i −0.867174 0.498005i \(-0.834066\pi\)
0.498005 + 0.867174i \(0.334066\pi\)
\(488\) −30.7471 + 28.5724i −1.39186 + 1.29341i
\(489\) −40.2520 40.2520i −1.82026 1.82026i
\(490\) 15.3839 + 4.32417i 0.694972 + 0.195346i
\(491\) 11.2886 4.67590i 0.509448 0.211020i −0.113127 0.993581i \(-0.536087\pi\)
0.622575 + 0.782560i \(0.286087\pi\)
\(492\) 9.41264 6.86388i 0.424354 0.309448i
\(493\) −8.59744 + 20.7561i −0.387209 + 0.934806i
\(494\) 0.393480 + 3.29975i 0.0177035 + 0.148463i
\(495\) 22.7788i 1.02383i
\(496\) −4.16804 + 2.14214i −0.187151 + 0.0961847i
\(497\) 12.8517i 0.576479i
\(498\) −43.7154 + 5.21286i −1.95893 + 0.233594i
\(499\) 12.4071 29.9533i 0.555417 1.34089i −0.357944 0.933743i \(-0.616522\pi\)
0.913361 0.407152i \(-0.133478\pi\)
\(500\) 3.76521 24.0449i 0.168385 1.07532i
\(501\) −35.0836 + 14.5321i −1.56742 + 0.649247i
\(502\) −5.38745 + 19.1667i −0.240454 + 0.855450i
\(503\) 8.77059 + 8.77059i 0.391061 + 0.391061i 0.875066 0.484004i \(-0.160818\pi\)
−0.484004 + 0.875066i \(0.660818\pi\)
\(504\) 3.41540 7.46002i 0.152134 0.332296i
\(505\) −10.5728 + 10.5728i −0.470485 + 0.470485i
\(506\) −5.22274 9.30676i −0.232179 0.413736i
\(507\) 7.84276 + 18.9341i 0.348309 + 0.840893i
\(508\) 6.14158 + 25.3857i 0.272488 + 1.12631i
\(509\) 20.0994 + 8.32546i 0.890892 + 0.369020i 0.780711 0.624892i \(-0.214857\pi\)
0.110181 + 0.993912i \(0.464857\pi\)
\(510\) 18.3213 + 14.4173i 0.811280 + 0.638411i
\(511\) 10.0531 0.444724
\(512\) 21.7288 6.31333i 0.960287 0.279013i
\(513\) −0.105497 −0.00465780
\(514\) −21.0097 16.5329i −0.926698 0.729236i
\(515\) 11.4135 + 4.72764i 0.502941 + 0.208325i
\(516\) 3.20127 + 13.2322i 0.140928 + 0.582514i
\(517\) 2.29186 + 5.53304i 0.100796 + 0.243343i
\(518\) −0.869124 1.54875i −0.0381871 0.0680483i
\(519\) −3.35099 + 3.35099i −0.147092 + 0.147092i
\(520\) −10.0426 + 21.9355i −0.440399 + 0.961934i
\(521\) −29.8910 29.8910i −1.30955 1.30955i −0.921741 0.387807i \(-0.873233\pi\)
−0.387807 0.921741i \(-0.626767\pi\)
\(522\) 7.33046 26.0792i 0.320845 1.14145i
\(523\) 32.7654 13.5719i 1.43273 0.593456i 0.474706 0.880144i \(-0.342554\pi\)
0.958024 + 0.286688i \(0.0925544\pi\)
\(524\) 2.18406 13.9476i 0.0954113 0.609304i
\(525\) 1.40792 3.39903i 0.0614468 0.148346i
\(526\) 27.6216 3.29374i 1.20436 0.143614i
\(527\) 4.23765i 0.184595i
\(528\) 35.0773 18.0277i 1.52655 0.784557i
\(529\) 19.4361i 0.845046i
\(530\) −1.53887 12.9050i −0.0668441 0.560559i
\(531\) −6.31558 + 15.2472i −0.274073 + 0.661670i
\(532\) −0.773727 + 0.564217i −0.0335453 + 0.0244619i
\(533\) −10.0711 + 4.17157i −0.436226 + 0.180691i
\(534\) 25.8296 + 7.26031i 1.11776 + 0.314184i
\(535\) −3.64548 3.64548i −0.157608 0.157608i
\(536\) 7.63881 7.09853i 0.329947 0.306610i
\(537\) 8.56744 8.56744i 0.369713 0.369713i
\(538\) 16.2816 9.13685i 0.701949 0.393918i
\(539\) 9.35460 + 22.5840i 0.402931 + 0.972762i
\(540\) −0.653720 0.399028i −0.0281316 0.0171714i
\(541\) −11.2925 4.67751i −0.485502 0.201102i 0.126486 0.991968i \(-0.459630\pi\)
−0.611988 + 0.790867i \(0.709630\pi\)
\(542\) −3.86128 + 4.90683i −0.165856 + 0.210767i
\(543\) −5.01571 −0.215245
\(544\) −3.90393 + 20.0853i −0.167379 + 0.861150i
\(545\) −16.7109 −0.715815
\(546\) −9.36618 + 11.9023i −0.400835 + 0.509374i
\(547\) −19.1256 7.92207i −0.817750 0.338723i −0.0657087 0.997839i \(-0.520931\pi\)
−0.752042 + 0.659116i \(0.770931\pi\)
\(548\) −7.19303 + 11.7842i −0.307271 + 0.503396i
\(549\) 17.5141 + 42.2827i 0.747482 + 1.80458i
\(550\) 7.81769 4.38711i 0.333347 0.187067i
\(551\) −2.23570 + 2.23570i −0.0952439 + 0.0952439i
\(552\) −13.1618 0.482521i −0.560201 0.0205375i
\(553\) 11.4514 + 11.4514i 0.486962 + 0.486962i
\(554\) −33.9603 9.54573i −1.44284 0.405559i
\(555\) −5.62177 + 2.32861i −0.238631 + 0.0988442i
\(556\) −15.0300 20.6111i −0.637416 0.874106i
\(557\) 12.3617 29.8439i 0.523783 1.26452i −0.411753 0.911295i \(-0.635084\pi\)
0.935537 0.353229i \(-0.114916\pi\)
\(558\) 0.605030 + 5.07383i 0.0256130 + 0.214792i
\(559\) 12.7390i 0.538803i
\(560\) −6.92854 + 0.569699i −0.292784 + 0.0240742i
\(561\) 35.6631i 1.50570i
\(562\) −11.5881 + 1.38182i −0.488814 + 0.0582888i
\(563\) −10.5540 + 25.4797i −0.444800 + 1.07384i 0.529444 + 0.848345i \(0.322400\pi\)
−0.974244 + 0.225497i \(0.927600\pi\)
\(564\) 7.30205 + 1.14343i 0.307472 + 0.0481472i
\(565\) 20.1023 8.32666i 0.845712 0.350305i
\(566\) −1.31992 + 4.69580i −0.0554802 + 0.197379i
\(567\) 5.81352 + 5.81352i 0.244145 + 0.244145i
\(568\) −13.4713 36.2223i −0.565242 1.51986i
\(569\) −23.7855 + 23.7855i −0.997139 + 0.997139i −0.999996 0.00285688i \(-0.999091\pi\)
0.00285688 + 0.999996i \(0.499091\pi\)
\(570\) 1.60568 + 2.86128i 0.0672547 + 0.119846i
\(571\) −0.904405 2.18343i −0.0378482 0.0913736i 0.903825 0.427902i \(-0.140747\pi\)
−0.941673 + 0.336528i \(0.890747\pi\)
\(572\) −35.8695 + 8.67793i −1.49978 + 0.362843i
\(573\) 44.2141 + 18.3141i 1.84707 + 0.765082i
\(574\) −2.46854 1.94254i −0.103035 0.0810800i
\(575\) −2.99371 −0.124846
\(576\) 1.80658 24.6059i 0.0752741 1.02525i
\(577\) 24.8839 1.03593 0.517965 0.855402i \(-0.326690\pi\)
0.517965 + 0.855402i \(0.326690\pi\)
\(578\) 4.35311 + 3.42554i 0.181066 + 0.142484i
\(579\) 41.1238 + 17.0340i 1.70905 + 0.707910i
\(580\) −22.3099 + 5.39745i −0.926368 + 0.224117i
\(581\) 4.54286 + 10.9674i 0.188469 + 0.455006i
\(582\) −10.5134 18.7346i −0.435795 0.776574i
\(583\) 14.0578 14.0578i 0.582216 0.582216i
\(584\) 28.3345 10.5377i 1.17249 0.436055i
\(585\) 18.6006 + 18.6006i 0.769039 + 0.769039i
\(586\) −2.89663 + 10.3052i −0.119658 + 0.425703i
\(587\) −40.1685 + 16.6383i −1.65793 + 0.686738i −0.997917 0.0645151i \(-0.979450\pi\)
−0.660015 + 0.751253i \(0.729450\pi\)
\(588\) 29.8045 + 4.66711i 1.22912 + 0.192469i
\(589\) 0.228225 0.550984i 0.00940384 0.0227029i
\(590\) 13.8851 1.65574i 0.571642 0.0681657i
\(591\) 0.557647i 0.0229385i
\(592\) −4.07302 3.45410i −0.167400 0.141963i
\(593\) 9.10197i 0.373773i −0.982382 0.186886i \(-0.940160\pi\)
0.982382 0.186886i \(-0.0598397\pi\)
\(594\) −0.138722 1.16333i −0.00569182 0.0477321i
\(595\) 2.40569 5.80785i 0.0986238 0.238099i
\(596\) −7.31926 10.0371i −0.299808 0.411136i
\(597\) 38.3481 15.8843i 1.56948 0.650102i
\(598\) 11.8644 + 3.33490i 0.485172 + 0.136374i
\(599\) 3.04488 + 3.04488i 0.124410 + 0.124410i 0.766571 0.642160i \(-0.221962\pi\)
−0.642160 + 0.766571i \(0.721962\pi\)
\(600\) 0.405318 11.0559i 0.0165470 0.451355i
\(601\) 9.53880 9.53880i 0.389096 0.389096i −0.485269 0.874365i \(-0.661278\pi\)
0.874365 + 0.485269i \(0.161278\pi\)
\(602\) 3.20127 1.79648i 0.130474 0.0732190i
\(603\) −4.35119 10.5047i −0.177194 0.427784i
\(604\) −16.4315 + 26.9194i −0.668588 + 1.09533i
\(605\) −8.49887 3.52035i −0.345528 0.143123i
\(606\) −17.4560 + 22.1828i −0.709103 + 0.901113i
\(607\) −3.66391 −0.148714 −0.0743568 0.997232i \(-0.523690\pi\)
−0.0743568 + 0.997232i \(0.523690\pi\)
\(608\) −1.58932 + 2.40126i −0.0644553 + 0.0973839i
\(609\) −14.4102 −0.583929
\(610\) 23.9808 30.4743i 0.970955 1.23387i
\(611\) −6.38960 2.64666i −0.258496 0.107072i
\(612\) 19.0429 + 11.6237i 0.769765 + 0.469861i
\(613\) −11.6012 28.0079i −0.468570 1.13123i −0.964788 0.263029i \(-0.915278\pi\)
0.496218 0.868198i \(-0.334722\pi\)
\(614\) −10.1349 + 5.68749i −0.409012 + 0.229528i
\(615\) −7.61040 + 7.61040i −0.306881 + 0.306881i
\(616\) −7.23911 7.79009i −0.291672 0.313872i
\(617\) 5.86100 + 5.86100i 0.235955 + 0.235955i 0.815173 0.579218i \(-0.196642\pi\)
−0.579218 + 0.815173i \(0.696642\pi\)
\(618\) 22.4521 + 6.31095i 0.903157 + 0.253864i
\(619\) −36.9173 + 15.2917i −1.48383 + 0.614624i −0.969965 0.243245i \(-0.921788\pi\)
−0.513868 + 0.857869i \(0.671788\pi\)
\(620\) 3.49824 2.55098i 0.140493 0.102450i
\(621\) −0.149724 + 0.361465i −0.00600821 + 0.0145051i
\(622\) −3.56505 29.8968i −0.142946 1.19875i
\(623\) 7.23468i 0.289851i
\(624\) −13.9222 + 43.3642i −0.557336 + 1.73596i
\(625\) 14.5563i 0.582254i
\(626\) 36.4149 4.34231i 1.45543 0.173554i
\(627\) −1.92069 + 4.63696i −0.0767050 + 0.185182i
\(628\) −0.410244 + 2.61985i −0.0163705 + 0.104543i
\(629\) 4.46157 1.84804i 0.177895 0.0736864i
\(630\) −2.05117 + 7.29734i −0.0817206 + 0.290733i
\(631\) −21.0543 21.0543i −0.838159 0.838159i 0.150458 0.988616i \(-0.451925\pi\)
−0.988616 + 0.150458i \(0.951925\pi\)
\(632\) 44.2789 + 20.2721i 1.76132 + 0.806379i
\(633\) 17.0028 17.0028i 0.675799 0.675799i
\(634\) −7.13421 12.7129i −0.283336 0.504895i
\(635\) −9.23412 22.2931i −0.366445 0.884676i
\(636\) −5.76939 23.8473i −0.228771 0.945606i
\(637\) −26.0802 10.8028i −1.03334 0.428022i
\(638\) −27.5932 21.7136i −1.09242 0.859649i
\(639\) −42.1386 −1.66698
\(640\) −18.9308 + 8.86822i −0.748304 + 0.350547i
\(641\) −6.57429 −0.259669 −0.129835 0.991536i \(-0.541445\pi\)
−0.129835 + 0.991536i \(0.541445\pi\)
\(642\) −7.64855 6.01878i −0.301864 0.237542i
\(643\) −24.1050 9.98462i −0.950608 0.393755i −0.147149 0.989114i \(-0.547010\pi\)
−0.803459 + 0.595360i \(0.797010\pi\)
\(644\) 0.835091 + 3.45178i 0.0329072 + 0.136019i
\(645\) −4.81324 11.6202i −0.189521 0.457545i
\(646\) −1.27431 2.27078i −0.0501370 0.0893426i
\(647\) 19.1598 19.1598i 0.753250 0.753250i −0.221835 0.975084i \(-0.571205\pi\)
0.975084 + 0.221835i \(0.0712046\pi\)
\(648\) 22.4791 + 10.2915i 0.883061 + 0.404289i
\(649\) 15.1255 + 15.1255i 0.593727 + 0.593727i
\(650\) −2.80132 + 9.96612i −0.109877 + 0.390903i
\(651\) 2.51119 1.04017i 0.0984212 0.0407674i
\(652\) −7.14074 + 45.6013i −0.279653 + 1.78588i
\(653\) −5.73339 + 13.8416i −0.224365 + 0.541665i −0.995474 0.0950389i \(-0.969702\pi\)
0.771109 + 0.636703i \(0.219702\pi\)
\(654\) −31.3255 + 3.73542i −1.22492 + 0.146067i
\(655\) 13.0429i 0.509629i
\(656\) −8.99371 2.88747i −0.351145 0.112737i
\(657\) 32.9624i 1.28599i
\(658\) −0.235977 1.97892i −0.00919934 0.0771464i
\(659\) −0.202554 + 0.489009i −0.00789039 + 0.0190491i −0.927776 0.373139i \(-0.878282\pi\)
0.919885 + 0.392188i \(0.128282\pi\)
\(660\) −29.4404 + 21.4685i −1.14597 + 0.835661i
\(661\) 6.45241 2.67268i 0.250970 0.103955i −0.253652 0.967295i \(-0.581632\pi\)
0.504622 + 0.863340i \(0.331632\pi\)
\(662\) 11.1616 + 3.13734i 0.433806 + 0.121936i
\(663\) −29.1216 29.1216i −1.13099 1.13099i
\(664\) 24.3001 + 26.1496i 0.943026 + 1.01480i
\(665\) 0.625581 0.625581i 0.0242590 0.0242590i
\(666\) −5.07808 + 2.84970i −0.196772 + 0.110424i
\(667\) 4.48723 + 10.8331i 0.173746 + 0.419461i
\(668\) 26.2818 + 16.0423i 1.01687 + 0.620694i
\(669\) −51.5411 21.3490i −1.99270 0.825402i
\(670\) −5.95779 + 7.57104i −0.230170 + 0.292495i
\(671\) 59.3196 2.29001
\(672\) −12.8606 + 2.61669i −0.496109 + 0.100941i
\(673\) −24.3285 −0.937793 −0.468897 0.883253i \(-0.655348\pi\)
−0.468897 + 0.883253i \(0.655348\pi\)
\(674\) −14.7721 + 18.7721i −0.569002 + 0.723076i
\(675\) −0.303631 0.125768i −0.0116868 0.00484081i
\(676\) 8.65777 14.1839i 0.332991 0.545533i
\(677\) 1.60737 + 3.88054i 0.0617763 + 0.149141i 0.951753 0.306864i \(-0.0992798\pi\)
−0.889977 + 0.456005i \(0.849280\pi\)
\(678\) 35.8217 20.1023i 1.37573 0.772026i
\(679\) −4.09607 + 4.09607i −0.157193 + 0.157193i
\(680\) 0.692559 18.8910i 0.0265584 0.724436i
\(681\) 17.9589 + 17.9589i 0.688187 + 0.688187i
\(682\) 6.37588 + 1.79216i 0.244145 + 0.0686254i
\(683\) 24.8133 10.2780i 0.949455 0.393277i 0.146429 0.989221i \(-0.453222\pi\)
0.803026 + 0.595944i \(0.203222\pi\)
\(684\) 1.84997 + 2.53691i 0.0707353 + 0.0970013i
\(685\) 4.88118 11.7842i 0.186500 0.450251i
\(686\) −2.06570 17.3231i −0.0788689 0.661400i
\(687\) 42.1019i 1.60629i
\(688\) 7.13962 8.41893i 0.272196 0.320969i
\(689\) 22.9585i 0.874650i
\(690\) 12.0824 1.44077i 0.459971 0.0548494i
\(691\) 8.56885 20.6870i 0.325974 0.786972i −0.672909 0.739725i \(-0.734955\pi\)
0.998883 0.0472463i \(-0.0150446\pi\)
\(692\) 3.79632 + 0.594468i 0.144314 + 0.0225983i
\(693\) −10.7127 + 4.43736i −0.406943 + 0.168561i
\(694\) 11.6582 41.4759i 0.442541 1.57440i
\(695\) 16.6647 + 16.6647i 0.632128 + 0.632128i
\(696\) −40.6147 + 15.1048i −1.53950 + 0.572547i
\(697\) 6.03979 6.03979i 0.228774 0.228774i
\(698\) 7.48402 + 13.3363i 0.283274 + 0.504786i
\(699\) −13.9479 33.6732i −0.527558 1.27364i
\(700\) −2.89949 + 0.701477i −0.109591 + 0.0265133i
\(701\) 28.1557 + 11.6625i 1.06343 + 0.440486i 0.844667 0.535293i \(-0.179799\pi\)
0.218760 + 0.975779i \(0.429799\pi\)
\(702\) 1.06322 + 0.836669i 0.0401287 + 0.0315780i
\(703\) 0.679628 0.0256326
\(704\) −28.5689 14.3681i −1.07673 0.541519i
\(705\) −6.82843 −0.257173
\(706\) 0.748744 + 0.589200i 0.0281793 + 0.0221748i
\(707\) 7.03195 + 2.91273i 0.264464 + 0.109544i
\(708\) 25.6584 6.20756i 0.964302 0.233294i
\(709\) 12.4408 + 30.0346i 0.467223 + 1.12797i 0.965370 + 0.260883i \(0.0840136\pi\)
−0.498148 + 0.867092i \(0.665986\pi\)
\(710\) 17.4732 + 31.1367i 0.655759 + 1.16854i
\(711\) 37.5471 37.5471i 1.40812 1.40812i
\(712\) −7.58344 20.3908i −0.284201 0.764177i
\(713\) −1.56394 1.56394i −0.0585699 0.0585699i
\(714\) 3.21137 11.4249i 0.120182 0.427567i
\(715\) 31.4998 13.0476i 1.17803 0.487954i
\(716\) −9.70601 1.51987i −0.362730 0.0568002i
\(717\) −11.0187 + 26.6015i −0.411501 + 0.993450i
\(718\) 7.79613 0.929652i 0.290949 0.0346943i
\(719\) 33.6333i 1.25431i 0.778894 + 0.627155i \(0.215781\pi\)
−0.778894 + 0.627155i \(0.784219\pi\)
\(720\) 1.86794 + 22.7174i 0.0696141 + 0.846629i
\(721\) 6.28867i 0.234202i
\(722\) 3.13820 + 26.3172i 0.116792 + 0.979423i
\(723\) −13.0533 + 31.5134i −0.485457 + 1.17200i
\(724\) 2.39624 + 3.28603i 0.0890556 + 0.122124i
\(725\) −9.09984 + 3.76928i −0.337960 + 0.139988i
\(726\) −16.7185 4.69933i −0.620484 0.174408i
\(727\) −7.43334 7.43334i −0.275687 0.275687i 0.555697 0.831385i \(-0.312451\pi\)
−0.831385 + 0.555697i \(0.812451\pi\)
\(728\) 12.2725 + 0.449919i 0.454847 + 0.0166751i
\(729\) 20.1459 20.1459i 0.746145 0.746145i
\(730\) −24.3564 + 13.6682i −0.901469 + 0.505884i
\(731\) 3.81991 + 9.22207i 0.141284 + 0.341090i
\(732\) 38.1415 62.4864i 1.40975 2.30957i
\(733\) −0.328598 0.136110i −0.0121371 0.00502733i 0.376607 0.926373i \(-0.377091\pi\)
−0.388744 + 0.921346i \(0.627091\pi\)
\(734\) −14.4091 + 18.3108i −0.531850 + 0.675864i
\(735\) −27.8714 −1.02805
\(736\) 5.97186 + 8.85341i 0.220126 + 0.326341i
\(737\) −14.7373 −0.542857
\(738\) −6.36924 + 8.09391i −0.234455 + 0.297941i
\(739\) −43.8857 18.1780i −1.61436 0.668690i −0.621008 0.783804i \(-0.713277\pi\)
−0.993352 + 0.115114i \(0.963277\pi\)
\(740\) 4.21137 + 2.57060i 0.154813 + 0.0944972i
\(741\) −2.21803 5.35480i −0.0814814 0.196714i
\(742\) −5.76939 + 3.23765i −0.211801 + 0.118858i
\(743\) −30.3220 + 30.3220i −1.11240 + 1.11240i −0.119580 + 0.992825i \(0.538155\pi\)
−0.992825 + 0.119580i \(0.961845\pi\)
\(744\) 5.98742 5.56394i 0.219509 0.203984i
\(745\) 8.11529 + 8.11529i 0.297321 + 0.297321i
\(746\) −18.6841 5.25180i −0.684072 0.192282i
\(747\) 35.9603 14.8952i 1.31572 0.544988i
\(748\) 23.3646 17.0379i 0.854294 0.622969i
\(749\) −1.00430 + 2.42459i −0.0366963 + 0.0885927i
\(750\) 5.02619 + 42.1500i 0.183530 + 1.53910i
\(751\) 51.3686i 1.87447i 0.348701 + 0.937234i \(0.386623\pi\)
−0.348701 + 0.937234i \(0.613377\pi\)
\(752\) −2.73941 5.33019i −0.0998961 0.194372i
\(753\) 34.7248i 1.26544i
\(754\) 40.2626 4.80112i 1.46628 0.174847i
\(755\) 11.1504 26.9194i 0.405804 0.979697i
\(756\) −0.0603144 + 0.385172i −0.00219361 + 0.0140086i
\(757\) 15.2644 6.32270i 0.554793 0.229803i −0.0876302 0.996153i \(-0.527929\pi\)
0.642423 + 0.766350i \(0.277929\pi\)
\(758\) 5.06746 18.0282i 0.184058 0.654814i
\(759\) 13.1618 + 13.1618i 0.477741 + 0.477741i
\(760\) 1.10745 2.41893i 0.0401714 0.0877437i
\(761\) 26.6859 26.6859i 0.967362 0.967362i −0.0321218 0.999484i \(-0.510226\pi\)
0.999484 + 0.0321218i \(0.0102264\pi\)
\(762\) −22.2931 39.7257i −0.807595 1.43911i
\(763\) 3.25531 + 7.85902i 0.117850 + 0.284516i
\(764\) −9.12472 37.7162i −0.330121 1.36453i
\(765\) −19.0429 7.88784i −0.688499 0.285185i
\(766\) 16.1890 + 12.7394i 0.584932 + 0.460294i
\(767\) −24.7021 −0.891943
\(768\) −33.5045 + 20.8556i −1.20899 + 0.752563i
\(769\) 44.0390 1.58809 0.794044 0.607861i \(-0.207972\pi\)
0.794044 + 0.607861i \(0.207972\pi\)
\(770\) 7.72098 + 6.07578i 0.278245 + 0.218956i
\(771\) 43.0796 + 17.8441i 1.55147 + 0.642641i
\(772\) −8.48695 35.0801i −0.305452 1.26256i
\(773\) −15.4001 37.1790i −0.553902 1.33724i −0.914526 0.404526i \(-0.867436\pi\)
0.360625 0.932711i \(-0.382564\pi\)
\(774\) −5.89034 10.4964i −0.211724 0.377285i
\(775\) 1.31371 1.31371i 0.0471898 0.0471898i
\(776\) −7.25116 + 15.8382i −0.260302 + 0.568559i
\(777\) 2.19027 + 2.19027i 0.0785754 + 0.0785754i
\(778\) −14.2795 + 50.8016i −0.511946 + 1.82132i
\(779\) 1.11058 0.460018i 0.0397908 0.0164819i
\(780\) 6.50961 41.5709i 0.233081 1.48848i
\(781\) −20.9012 + 50.4599i −0.747903 + 1.80560i
\(782\) −9.58892 + 1.14343i −0.342899 + 0.0408891i
\(783\) 1.28724i 0.0460022i
\(784\) −11.1814 21.7561i −0.399335 0.777002i
\(785\) 2.44992i 0.0874413i
\(786\) 2.91552 + 24.4497i 0.103993 + 0.872093i
\(787\) 0.948632 2.29020i 0.0338151 0.0816368i −0.906070 0.423128i \(-0.860932\pi\)
0.939885 + 0.341491i \(0.110932\pi\)
\(788\) 0.365341 0.266414i 0.0130147 0.00949061i
\(789\) −44.8240 + 18.5667i −1.59578 + 0.660992i
\(790\) −43.3133 12.1747i −1.54102 0.433157i
\(791\) −7.83196 7.83196i −0.278472 0.278472i
\(792\) −25.5423 + 23.7358i −0.907608 + 0.843414i
\(793\) −48.4388 + 48.4388i −1.72011 + 1.72011i
\(794\) 28.6310 16.0671i 1.01608 0.570199i
\(795\) 8.67452 + 20.9421i 0.307654 + 0.742741i
\(796\) −28.7272 17.5350i −1.01821 0.621511i
\(797\) −2.76562 1.14556i −0.0979632 0.0405777i 0.333164 0.942869i \(-0.391884\pi\)
−0.431127 + 0.902291i \(0.641884\pi\)
\(798\) 1.03285 1.31253i 0.0365625 0.0464629i
\(799\) 5.41921 0.191718
\(800\) −7.43687 + 5.01637i −0.262933 + 0.177355i
\(801\) −23.7212 −0.838149
\(802\) −2.19960 + 2.79520i −0.0776704 + 0.0987020i
\(803\) −39.4717 16.3497i −1.39292 0.576968i
\(804\) −9.47586 + 15.5241i −0.334188 + 0.547494i
\(805\) −1.25559 3.03127i −0.0442539 0.106838i
\(806\) −6.66981 + 3.74294i −0.234934 + 0.131840i
\(807\) −23.0256 + 23.0256i −0.810541 + 0.810541i
\(808\) 22.8725 + 0.838527i 0.804653 + 0.0294993i
\(809\) −7.12825 7.12825i −0.250616 0.250616i 0.570607 0.821223i \(-0.306708\pi\)
−0.821223 + 0.570607i \(0.806708\pi\)
\(810\) −21.9889 6.18073i −0.772610 0.217169i
\(811\) 27.4750 11.3805i 0.964777 0.399624i 0.156012 0.987755i \(-0.450136\pi\)
0.808765 + 0.588131i \(0.200136\pi\)
\(812\) 6.88440 + 9.44077i 0.241595 + 0.331306i
\(813\) 4.16751 10.0613i 0.146161 0.352864i
\(814\) 0.893667 + 7.49436i 0.0313230 + 0.262677i
\(815\) 42.6435i 1.49374i
\(816\) −2.92450 35.5670i −0.102378 1.24510i
\(817\) 1.40479i 0.0491474i
\(818\) −10.5784 + 1.26142i −0.369864 + 0.0441046i
\(819\) 5.12431 12.3712i 0.179058 0.432284i
\(820\) 8.62177 + 1.35009i 0.301085 + 0.0471472i
\(821\) 34.1861 14.1603i 1.19310 0.494199i 0.304339 0.952564i \(-0.401565\pi\)
0.888764 + 0.458364i \(0.151565\pi\)
\(822\) 6.51590 23.1813i 0.227268 0.808540i
\(823\) 27.3810 + 27.3810i 0.954440 + 0.954440i 0.999006 0.0445659i \(-0.0141905\pi\)
−0.0445659 + 0.999006i \(0.514190\pi\)
\(824\) −6.59183 17.7245i −0.229637 0.617462i
\(825\) −11.0559 + 11.0559i −0.384916 + 0.384916i
\(826\) −3.48354 6.20756i −0.121208 0.215989i
\(827\) 7.98030 + 19.2661i 0.277502 + 0.669950i 0.999765 0.0216689i \(-0.00689796\pi\)
−0.722263 + 0.691619i \(0.756898\pi\)
\(828\) 11.3178 2.73812i 0.393320 0.0951561i
\(829\) −3.59585 1.48945i −0.124889 0.0517307i 0.319364 0.947632i \(-0.396531\pi\)
−0.444253 + 0.895901i \(0.646531\pi\)
\(830\) −25.9176 20.3950i −0.899613 0.707922i
\(831\) 61.5269 2.13434
\(832\) 35.0612 11.5960i 1.21553 0.402018i
\(833\) 22.1194 0.766391
\(834\) 34.9641 + 27.5139i 1.21071 + 0.952727i
\(835\) −26.2818 10.8863i −0.909518 0.376735i
\(836\) 3.95549 0.956955i 0.136804 0.0330970i
\(837\) −0.0929169 0.224321i −0.00321168 0.00775368i
\(838\) 7.90385 + 14.0844i 0.273034 + 0.486538i
\(839\) 13.8461 13.8461i 0.478020 0.478020i −0.426478 0.904498i \(-0.640246\pi\)
0.904498 + 0.426478i \(0.140246\pi\)
\(840\) 11.3646 4.22655i 0.392116 0.145830i
\(841\) 6.77318 + 6.77318i 0.233558 + 0.233558i
\(842\) −1.72505 + 6.13713i −0.0594492 + 0.211499i
\(843\) 18.8050 7.78929i 0.647679 0.268277i
\(844\) −19.2623 3.01630i −0.663037 0.103825i
\(845\) −5.87515 + 14.1839i −0.202111 + 0.487940i
\(846\) −6.48853 + 0.773727i −0.223080 + 0.0266013i
\(847\) 4.68274i 0.160901i
\(848\) −12.8672 + 15.1728i −0.441861 + 0.521035i
\(849\) 8.50750i 0.291977i
\(850\) −0.960485 8.05470i −0.0329444 0.276274i
\(851\) 0.964543 2.32861i 0.0330641 0.0798239i
\(852\) 39.7147 + 54.4618i 1.36060 + 1.86583i
\(853\) 18.0597 7.48055i 0.618351 0.256129i −0.0514436 0.998676i \(-0.516382\pi\)
0.669794 + 0.742547i \(0.266382\pi\)
\(854\) −19.0034 5.34157i −0.650283 0.182785i
\(855\) −2.05117 2.05117i −0.0701485 0.0701485i
\(856\) −0.289121 + 7.88638i −0.00988196 + 0.269551i
\(857\) −6.35294 + 6.35294i −0.217012 + 0.217012i −0.807238 0.590226i \(-0.799039\pi\)
0.590226 + 0.807238i \(0.299039\pi\)
\(858\) 56.1316 31.4998i 1.91630 1.07539i
\(859\) 9.72800 + 23.4855i 0.331915 + 0.801314i 0.998440 + 0.0558315i \(0.0177810\pi\)
−0.666525 + 0.745483i \(0.732219\pi\)
\(860\) −5.31343 + 8.70489i −0.181186 + 0.296834i
\(861\) 5.06164 + 2.09660i 0.172500 + 0.0714520i
\(862\) 14.8500 18.8711i 0.505793 0.642751i
\(863\) −0.0884535 −0.00301099 −0.00150550 0.999999i \(-0.500479\pi\)
−0.00150550 + 0.999999i \(0.500479\pi\)
\(864\) 0.233745 + 1.14882i 0.00795218 + 0.0390837i
\(865\) −3.55008 −0.120706
\(866\) −14.8296 + 18.8452i −0.503931 + 0.640385i
\(867\) −8.92588 3.69722i −0.303139 0.125564i
\(868\) −1.88118 1.14826i −0.0638513 0.0389745i
\(869\) −26.3379 63.5854i −0.893453 2.15699i
\(870\) 34.9124 19.5921i 1.18364 0.664233i
\(871\) 12.0341 12.0341i 0.407761 0.407761i
\(872\) 17.4129 + 18.7382i 0.589676 + 0.634557i
\(873\) 13.4303 + 13.4303i 0.454547 + 0.454547i
\(874\) −1.30834 0.367755i −0.0442554 0.0124395i
\(875\) 10.5747 4.38018i 0.357490 0.148077i
\(876\) −42.6021 + 31.0663i −1.43939 + 1.04963i
\(877\) −4.24514 + 10.2487i −0.143348 + 0.346073i −0.979205 0.202875i \(-0.934971\pi\)
0.835857 + 0.548948i \(0.184971\pi\)
\(878\) 2.50065 + 20.9706i 0.0843928 + 0.707724i
\(879\) 18.6702i 0.629729i
\(880\) 28.1301 + 9.03127i 0.948265 + 0.304444i
\(881\) 23.9859i 0.808105i 0.914736 + 0.404052i \(0.132399\pi\)
−0.914736 + 0.404052i \(0.867601\pi\)
\(882\) −26.4840 + 3.15809i −0.891763 + 0.106339i
\(883\) −7.74892 + 18.7075i −0.260772 + 0.629559i −0.998987 0.0450067i \(-0.985669\pi\)
0.738215 + 0.674566i \(0.235669\pi\)
\(884\) −5.16619 + 32.9916i −0.173758 + 1.10963i
\(885\) −22.5326 + 9.33333i −0.757426 + 0.313736i
\(886\) −6.31087 + 22.4518i −0.212018 + 0.754284i
\(887\) −36.4494 36.4494i −1.22385 1.22385i −0.966252 0.257600i \(-0.917068\pi\)
−0.257600 0.966252i \(-0.582932\pi\)
\(888\) 8.46907 + 3.87737i 0.284203 + 0.130116i
\(889\) −8.68550 + 8.68550i −0.291302 + 0.291302i
\(890\) 9.83627 + 17.5279i 0.329713 + 0.587538i
\(891\) −13.3710 32.2804i −0.447944 1.08143i
\(892\) 10.6368 + 43.9665i 0.356148 + 1.47211i
\(893\) 0.704611 + 0.291859i 0.0235789 + 0.00976670i
\(894\) 17.0266 + 13.3986i 0.569456 + 0.448115i
\(895\) 9.07646 0.303392
\(896\) 7.85842 + 7.17548i 0.262532 + 0.239716i
\(897\) −21.4951 −0.717700
\(898\) 8.97096 + 7.05941i 0.299365 + 0.235576i
\(899\) −6.72293 2.78473i −0.224222 0.0928759i
\(900\) 2.30002 + 9.50693i 0.0766673 + 0.316898i
\(901\) −6.88431 16.6202i −0.229350 0.553699i
\(902\) 6.53304 + 11.6417i 0.217526 + 0.387625i
\(903\) −4.52728 + 4.52728i −0.150658 + 0.150658i
\(904\) −30.2837 13.8647i −1.00722 0.461133i
\(905\) −2.65685 2.65685i −0.0883168 0.0883168i
\(906\) 14.8847 52.9545i 0.494510 1.75929i
\(907\) −38.2753 + 15.8541i −1.27091 + 0.526428i −0.913241 0.407421i \(-0.866428\pi\)
−0.357669 + 0.933848i \(0.616428\pi\)
\(908\) 3.18592 20.3455i 0.105729 0.675190i
\(909\) 9.55032 23.0565i 0.316764 0.764737i
\(910\) −11.2661 + 1.34343i −0.373467 + 0.0445341i
\(911\) 12.5214i 0.414851i −0.978251 0.207426i \(-0.933492\pi\)
0.978251 0.207426i \(-0.0665085\pi\)
\(912\) 1.53527 4.78197i 0.0508379 0.158347i
\(913\) 50.4497i 1.66964i
\(914\) −1.81947 15.2582i −0.0601826 0.504695i
\(915\) −25.8827 + 62.4864i −0.855657 + 2.06574i
\(916\) 27.5830 20.1141i 0.911367 0.664587i
\(917\) 6.13401 2.54079i 0.202563 0.0839043i
\(918\) −1.02057 0.286867i −0.0336839 0.00946804i
\(919\) 1.19513 + 1.19513i 0.0394238 + 0.0394238i 0.726544 0.687120i \(-0.241125\pi\)
−0.687120 + 0.726544i \(0.741125\pi\)
\(920\) −6.71627 7.22746i −0.221429 0.238282i
\(921\) 14.3330 14.3330i 0.472287 0.472287i
\(922\) −19.0206 + 10.6739i −0.626410 + 0.351527i
\(923\) −24.1369 58.2715i −0.794475 1.91803i
\(924\) 15.8316 + 9.66352i 0.520820 + 0.317906i
\(925\) 1.95604 + 0.810217i 0.0643141 + 0.0266398i
\(926\) 23.8957 30.3662i 0.785261 0.997894i
\(927\) −20.6194 −0.677231
\(928\) 29.2994 + 19.3923i 0.961801 + 0.636585i
\(929\) 45.1410 1.48103 0.740514 0.672041i \(-0.234582\pi\)
0.740514 + 0.672041i \(0.234582\pi\)
\(930\) −4.66981 + 5.93430i −0.153129 + 0.194593i
\(931\) 2.87599 + 1.19127i 0.0942566 + 0.0390424i
\(932\) −15.3974 + 25.2252i −0.504357 + 0.826279i
\(933\) 20.0961 + 48.5162i 0.657915 + 1.58835i
\(934\) −30.3124 + 17.0106i −0.991852 + 0.556605i
\(935\) −18.8910 + 18.8910i −0.617801 + 0.617801i
\(936\) 1.47520 40.2392i 0.0482185 1.31526i
\(937\) 2.58002 + 2.58002i 0.0842857 + 0.0842857i 0.747993 0.663707i \(-0.231018\pi\)
−0.663707 + 0.747993i \(0.731018\pi\)
\(938\) 4.72120 + 1.32706i 0.154153 + 0.0433300i
\(939\) −59.0937 + 24.4774i −1.92845 + 0.798790i
\(940\) 3.26226 + 4.47363i 0.106403 + 0.145914i
\(941\) 2.24720 5.42523i 0.0732568 0.176857i −0.883009 0.469355i \(-0.844486\pi\)
0.956266 + 0.292498i \(0.0944864\pi\)
\(942\) −0.547636 4.59252i −0.0178429 0.149632i
\(943\) 4.45807i 0.145175i
\(944\) −16.3251 13.8444i −0.531336 0.450597i
\(945\) 0.360189i 0.0117170i
\(946\) −15.4908 + 1.84721i −0.503650 + 0.0600579i
\(947\) 17.5640 42.4032i 0.570753 1.37792i −0.330162 0.943924i \(-0.607103\pi\)
0.900915 0.433996i \(-0.142897\pi\)
\(948\) −83.9148 13.1403i −2.72543 0.426776i
\(949\) 45.5822 18.8808i 1.47966 0.612896i
\(950\) 0.308915 1.09901i 0.0100225 0.0356566i
\(951\) 17.9788 + 17.9788i 0.583003 + 0.583003i
\(952\) −9.01922 + 3.35430i −0.292315 + 0.108713i
\(953\) 14.8079 14.8079i 0.479673 0.479673i −0.425354 0.905027i \(-0.639850\pi\)
0.905027 + 0.425354i \(0.139850\pi\)
\(954\) 10.6157 + 18.9168i 0.343695 + 0.612454i
\(955\) 13.7194 + 33.1216i 0.443949 + 1.07179i
\(956\) 22.6920 5.48990i 0.733913 0.177556i
\(957\) 56.5787 + 23.4357i 1.82893 + 0.757568i
\(958\) 4.34718 + 3.42088i 0.140451 + 0.110524i
\(959\) −6.49290 −0.209667
\(960\) 27.6006 23.8249i 0.890805 0.768945i
\(961\) −29.6274 −0.955723
\(962\) −6.84944 5.38995i −0.220835 0.173779i
\(963\) 7.94981 + 3.29292i 0.256179 + 0.106113i
\(964\) 26.8821 6.50360i 0.865813 0.209467i
\(965\) 12.7605 + 30.8066i 0.410775 + 0.991698i
\(966\) −3.03127 5.40163i −0.0975296 0.173795i
\(967\) 24.8604 24.8604i 0.799455 0.799455i −0.183554 0.983010i \(-0.558760\pi\)
0.983010 + 0.183554i \(0.0587604\pi\)
\(968\) 4.90848 + 13.1982i 0.157764 + 0.424206i
\(969\) 3.21137 + 3.21137i 0.103164 + 0.103164i
\(970\) 4.35480 15.4928i 0.139824 0.497445i
\(971\) −23.3388 + 9.66725i −0.748978 + 0.310237i −0.724324 0.689459i \(-0.757848\pi\)
−0.0246533 + 0.999696i \(0.507848\pi\)
\(972\) −43.8295 6.86330i −1.40583 0.220140i
\(973\) 4.59099 11.0836i 0.147180 0.355325i
\(974\) −16.1791 + 1.92928i −0.518411 + 0.0618181i
\(975\) 18.0559i 0.578251i
\(976\) −59.1598 + 4.86441i −1.89366 + 0.155706i
\(977\) 54.7057i 1.75019i 0.483952 + 0.875094i \(0.339201\pi\)
−0.483952 + 0.875094i \(0.660799\pi\)
\(978\) −9.53220 79.9378i −0.304806 2.55613i
\(979\) −11.7660 + 28.4056i −0.376042 + 0.907846i
\(980\) 13.3154 + 18.2598i 0.425346 + 0.583289i
\(981\) 25.7684 10.6736i 0.822720 0.340782i
\(982\) 16.6352 + 4.67590i 0.530851 + 0.149214i
\(983\) −7.85315 7.85315i −0.250477 0.250477i 0.570689 0.821166i \(-0.306676\pi\)
−0.821166 + 0.570689i \(0.806676\pi\)
\(984\) 16.4638 + 0.603577i 0.524847 + 0.0192413i
\(985\) −0.295389 + 0.295389i −0.00941188 + 0.00941188i
\(986\) −27.7073 + 15.5487i −0.882382 + 0.495172i
\(987\) 1.33019 + 3.21137i 0.0423405 + 0.102219i
\(988\) −2.44853 + 4.01138i −0.0778980 + 0.127619i
\(989\) 4.81324 + 1.99371i 0.153052 + 0.0633963i
\(990\) 19.9214 25.3157i 0.633144 0.804587i
\(991\) −52.4878 −1.66733 −0.833665 0.552270i \(-0.813762\pi\)
−0.833665 + 0.552270i \(0.813762\pi\)
\(992\) −6.50567 1.26449i −0.206555 0.0401476i
\(993\) −20.2217 −0.641716
\(994\) 11.2396 14.2831i 0.356498 0.453031i
\(995\) 28.7272 + 11.8992i 0.910715 + 0.377230i
\(996\) −53.1430 32.4383i −1.68390 1.02785i
\(997\) 12.8431 + 31.0060i 0.406745 + 0.981970i 0.985988 + 0.166815i \(0.0533483\pi\)
−0.579243 + 0.815155i \(0.696652\pi\)
\(998\) 39.9848 22.4386i 1.26570 0.710280i
\(999\) 0.195654 0.195654i 0.00619021 0.00619021i
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 32.2.g.b.29.2 yes 8
3.2 odd 2 288.2.v.b.253.1 8
4.3 odd 2 128.2.g.b.81.2 8
5.2 odd 4 800.2.ba.d.349.1 8
5.3 odd 4 800.2.ba.c.349.2 8
5.4 even 2 800.2.y.b.701.1 8
8.3 odd 2 256.2.g.c.161.1 8
8.5 even 2 256.2.g.d.161.2 8
12.11 even 2 1152.2.v.b.721.1 8
16.3 odd 4 512.2.g.g.65.1 8
16.5 even 4 512.2.g.h.65.1 8
16.11 odd 4 512.2.g.f.65.2 8
16.13 even 4 512.2.g.e.65.2 8
32.3 odd 8 512.2.g.f.449.2 8
32.5 even 8 256.2.g.d.97.2 8
32.11 odd 8 128.2.g.b.49.2 8
32.13 even 8 512.2.g.e.449.2 8
32.19 odd 8 512.2.g.g.449.1 8
32.21 even 8 inner 32.2.g.b.21.2 8
32.27 odd 8 256.2.g.c.97.1 8
32.29 even 8 512.2.g.h.449.1 8
64.11 odd 16 4096.2.a.q.1.7 8
64.21 even 16 4096.2.a.k.1.7 8
64.43 odd 16 4096.2.a.q.1.2 8
64.53 even 16 4096.2.a.k.1.2 8
96.11 even 8 1152.2.v.b.433.1 8
96.53 odd 8 288.2.v.b.181.1 8
160.53 odd 8 800.2.ba.d.149.1 8
160.117 odd 8 800.2.ba.c.149.2 8
160.149 even 8 800.2.y.b.501.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.2.g.b.21.2 8 32.21 even 8 inner
32.2.g.b.29.2 yes 8 1.1 even 1 trivial
128.2.g.b.49.2 8 32.11 odd 8
128.2.g.b.81.2 8 4.3 odd 2
256.2.g.c.97.1 8 32.27 odd 8
256.2.g.c.161.1 8 8.3 odd 2
256.2.g.d.97.2 8 32.5 even 8
256.2.g.d.161.2 8 8.5 even 2
288.2.v.b.181.1 8 96.53 odd 8
288.2.v.b.253.1 8 3.2 odd 2
512.2.g.e.65.2 8 16.13 even 4
512.2.g.e.449.2 8 32.13 even 8
512.2.g.f.65.2 8 16.11 odd 4
512.2.g.f.449.2 8 32.3 odd 8
512.2.g.g.65.1 8 16.3 odd 4
512.2.g.g.449.1 8 32.19 odd 8
512.2.g.h.65.1 8 16.5 even 4
512.2.g.h.449.1 8 32.29 even 8
800.2.y.b.501.1 8 160.149 even 8
800.2.y.b.701.1 8 5.4 even 2
800.2.ba.c.149.2 8 160.117 odd 8
800.2.ba.c.349.2 8 5.3 odd 4
800.2.ba.d.149.1 8 160.53 odd 8
800.2.ba.d.349.1 8 5.2 odd 4
1152.2.v.b.433.1 8 96.11 even 8
1152.2.v.b.721.1 8 12.11 even 2
4096.2.a.k.1.2 8 64.53 even 16
4096.2.a.k.1.7 8 64.21 even 16
4096.2.a.q.1.2 8 64.43 odd 16
4096.2.a.q.1.7 8 64.11 odd 16