Properties

Label 175.2.s.a.13.4
Level $175$
Weight $2$
Character 175.13
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
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] = [175,2,Mod(13,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([19, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.s (of order \(20\), degree \(8\), 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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 13.4
Character \(\chi\) \(=\) 175.13
Dual form 175.2.s.a.27.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.26523 + 0.358778i) q^{2} +(2.54886 + 1.29871i) q^{3} +(3.10045 - 1.00740i) q^{4} +(0.855724 + 2.06585i) q^{5} +(-6.23972 - 2.02741i) q^{6} +(2.59686 - 0.506256i) q^{7} +(-2.57481 + 1.31193i) q^{8} +(3.04670 + 4.19343i) q^{9} +O(q^{10})\) \(q+(-2.26523 + 0.358778i) q^{2} +(2.54886 + 1.29871i) q^{3} +(3.10045 - 1.00740i) q^{4} +(0.855724 + 2.06585i) q^{5} +(-6.23972 - 2.02741i) q^{6} +(2.59686 - 0.506256i) q^{7} +(-2.57481 + 1.31193i) q^{8} +(3.04670 + 4.19343i) q^{9} +(-2.67959 - 4.37262i) q^{10} +(-4.34248 - 3.15500i) q^{11} +(9.21093 + 1.45887i) q^{12} +(0.642576 - 4.05707i) q^{13} +(-5.70087 + 2.07849i) q^{14} +(-0.501819 + 6.37691i) q^{15} +(0.0870603 - 0.0632530i) q^{16} +(0.0505344 - 0.0257486i) q^{17} +(-8.40600 - 8.40600i) q^{18} +(-0.554609 + 1.70691i) q^{19} +(4.73426 + 5.54301i) q^{20} +(7.27654 + 2.08220i) q^{21} +(10.9687 + 5.58882i) q^{22} +(0.609663 + 3.84926i) q^{23} -8.26666 q^{24} +(-3.53547 + 3.53559i) q^{25} +9.42074i q^{26} +(0.977065 + 6.16895i) q^{27} +(7.54144 - 4.18569i) q^{28} +(-2.79213 + 0.907218i) q^{29} +(-1.15116 - 14.6252i) q^{30} +(-4.44485 - 1.44422i) q^{31} +(3.91225 - 3.91225i) q^{32} +(-6.97097 - 13.6813i) q^{33} +(-0.105234 + 0.0764572i) q^{34} +(3.26805 + 4.93152i) q^{35} +(13.6706 + 9.93226i) q^{36} +(0.725477 - 4.58048i) q^{37} +(0.643917 - 4.06553i) q^{38} +(6.90680 - 9.50639i) q^{39} +(-4.91358 - 4.19652i) q^{40} +(-3.01811 - 4.15407i) q^{41} +(-17.2301 - 2.10601i) q^{42} +(-1.77629 - 1.77629i) q^{43} +(-16.6420 - 5.40730i) q^{44} +(-6.05585 + 9.88244i) q^{45} +(-2.76206 - 8.50074i) q^{46} +(-0.0826938 + 0.162296i) q^{47} +(0.304052 - 0.0481572i) q^{48} +(6.48741 - 2.62936i) q^{49} +(6.74018 - 9.27739i) q^{50} +0.162245 q^{51} +(-2.09480 - 13.2260i) q^{52} +(-3.33166 + 6.53875i) q^{53} +(-4.42656 - 13.6236i) q^{54} +(2.80179 - 11.6707i) q^{55} +(-6.02226 + 4.71042i) q^{56} +(-3.63041 + 3.63041i) q^{57} +(5.99934 - 3.05682i) q^{58} +(5.11223 - 3.71425i) q^{59} +(4.86821 + 20.2768i) q^{60} +(-2.77203 + 3.81537i) q^{61} +(10.5868 + 1.67678i) q^{62} +(10.0348 + 9.34735i) q^{63} +(-7.58503 + 10.4399i) q^{64} +(8.93116 - 2.14426i) q^{65} +(20.6994 + 28.4903i) q^{66} +(0.144637 + 0.283867i) q^{67} +(0.130740 - 0.130740i) q^{68} +(-3.44513 + 10.6030i) q^{69} +(-9.17221 - 9.99853i) q^{70} +(-3.23078 - 9.94332i) q^{71} +(-13.3462 - 6.80021i) q^{72} +(15.7935 - 2.50145i) q^{73} +10.6361i q^{74} +(-13.6032 + 4.42019i) q^{75} +5.85090i q^{76} +(-12.8741 - 5.99469i) q^{77} +(-12.2348 + 24.0122i) q^{78} +(-6.76190 + 2.19708i) q^{79} +(0.205171 + 0.125726i) q^{80} +(-0.716034 + 2.20373i) q^{81} +(8.32710 + 8.32710i) q^{82} +(2.84011 + 5.57403i) q^{83} +(24.6581 - 0.874609i) q^{84} +(0.0964362 + 0.0823629i) q^{85} +(4.66101 + 3.38642i) q^{86} +(-8.29498 - 1.31380i) q^{87} +(15.3202 + 2.42648i) q^{88} +(2.86263 + 2.07983i) q^{89} +(10.1723 - 24.5587i) q^{90} +(-0.385232 - 10.8610i) q^{91} +(5.76796 + 11.3203i) q^{92} +(-9.45369 - 9.45369i) q^{93} +(0.129093 - 0.397306i) q^{94} +(-4.00081 + 0.314905i) q^{95} +(15.0527 - 4.89090i) q^{96} +(-6.97738 + 13.6939i) q^{97} +(-13.7521 + 8.28365i) q^{98} -27.8222i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26523 + 0.358778i −1.60176 + 0.253694i −0.892432 0.451182i \(-0.851002\pi\)
−0.709330 + 0.704877i \(0.751002\pi\)
\(3\) 2.54886 + 1.29871i 1.47159 + 0.749811i 0.991827 0.127588i \(-0.0407237\pi\)
0.479760 + 0.877400i \(0.340724\pi\)
\(4\) 3.10045 1.00740i 1.55022 0.503698i
\(5\) 0.855724 + 2.06585i 0.382691 + 0.923876i
\(6\) −6.23972 2.02741i −2.54736 0.827686i
\(7\) 2.59686 0.506256i 0.981522 0.191347i
\(8\) −2.57481 + 1.31193i −0.910333 + 0.463838i
\(9\) 3.04670 + 4.19343i 1.01557 + 1.39781i
\(10\) −2.67959 4.37262i −0.847362 1.38274i
\(11\) −4.34248 3.15500i −1.30931 0.951268i −1.00000 0.000305816i \(-0.999903\pi\)
−0.309308 0.950962i \(-0.600097\pi\)
\(12\) 9.21093 + 1.45887i 2.65897 + 0.421139i
\(13\) 0.642576 4.05707i 0.178219 1.12523i −0.722675 0.691188i \(-0.757088\pi\)
0.900894 0.434040i \(-0.142912\pi\)
\(14\) −5.70087 + 2.07849i −1.52362 + 0.555499i
\(15\) −0.501819 + 6.37691i −0.129569 + 1.64651i
\(16\) 0.0870603 0.0632530i 0.0217651 0.0158133i
\(17\) 0.0505344 0.0257486i 0.0122564 0.00624495i −0.447852 0.894108i \(-0.647811\pi\)
0.460108 + 0.887863i \(0.347811\pi\)
\(18\) −8.40600 8.40600i −1.98131 1.98131i
\(19\) −0.554609 + 1.70691i −0.127236 + 0.391592i −0.994302 0.106601i \(-0.966003\pi\)
0.867066 + 0.498194i \(0.166003\pi\)
\(20\) 4.73426 + 5.54301i 1.05861 + 1.23945i
\(21\) 7.27654 + 2.08220i 1.58787 + 0.454373i
\(22\) 10.9687 + 5.58882i 2.33853 + 1.19154i
\(23\) 0.609663 + 3.84926i 0.127123 + 0.802626i 0.966045 + 0.258374i \(0.0831866\pi\)
−0.838922 + 0.544252i \(0.816813\pi\)
\(24\) −8.26666 −1.68743
\(25\) −3.53547 + 3.53559i −0.707095 + 0.707119i
\(26\) 9.42074i 1.84756i
\(27\) 0.977065 + 6.16895i 0.188036 + 1.18721i
\(28\) 7.54144 4.18569i 1.42520 0.791021i
\(29\) −2.79213 + 0.907218i −0.518486 + 0.168466i −0.556558 0.830809i \(-0.687878\pi\)
0.0380722 + 0.999275i \(0.487878\pi\)
\(30\) −1.15116 14.6252i −0.210171 2.67019i
\(31\) −4.44485 1.44422i −0.798318 0.259389i −0.118676 0.992933i \(-0.537865\pi\)
−0.679642 + 0.733544i \(0.737865\pi\)
\(32\) 3.91225 3.91225i 0.691594 0.691594i
\(33\) −6.97097 13.6813i −1.21349 2.38161i
\(34\) −0.105234 + 0.0764572i −0.0180475 + 0.0131123i
\(35\) 3.26805 + 4.93152i 0.552401 + 0.833579i
\(36\) 13.6706 + 9.93226i 2.27843 + 1.65538i
\(37\) 0.725477 4.58048i 0.119268 0.753026i −0.853474 0.521135i \(-0.825509\pi\)
0.972742 0.231891i \(-0.0744913\pi\)
\(38\) 0.643917 4.06553i 0.104457 0.659516i
\(39\) 6.90680 9.50639i 1.10597 1.52224i
\(40\) −4.91358 4.19652i −0.776905 0.663529i
\(41\) −3.01811 4.15407i −0.471349 0.648756i 0.505465 0.862847i \(-0.331321\pi\)
−0.976814 + 0.214091i \(0.931321\pi\)
\(42\) −17.2301 2.10601i −2.65866 0.324964i
\(43\) −1.77629 1.77629i −0.270882 0.270882i 0.558573 0.829455i \(-0.311349\pi\)
−0.829455 + 0.558573i \(0.811349\pi\)
\(44\) −16.6420 5.40730i −2.50887 0.815182i
\(45\) −6.05585 + 9.88244i −0.902753 + 1.47319i
\(46\) −2.76206 8.50074i −0.407243 1.25337i
\(47\) −0.0826938 + 0.162296i −0.0120621 + 0.0236733i −0.896959 0.442114i \(-0.854229\pi\)
0.884897 + 0.465787i \(0.154229\pi\)
\(48\) 0.304052 0.0481572i 0.0438862 0.00695089i
\(49\) 6.48741 2.62936i 0.926773 0.375623i
\(50\) 6.74018 9.27739i 0.953205 1.31202i
\(51\) 0.162245 0.0227189
\(52\) −2.09480 13.2260i −0.290497 1.83412i
\(53\) −3.33166 + 6.53875i −0.457639 + 0.898166i 0.540737 + 0.841192i \(0.318145\pi\)
−0.998376 + 0.0569747i \(0.981855\pi\)
\(54\) −4.42656 13.6236i −0.602378 1.85393i
\(55\) 2.80179 11.6707i 0.377793 1.57368i
\(56\) −6.02226 + 4.71042i −0.804759 + 0.629457i
\(57\) −3.63041 + 3.63041i −0.480859 + 0.480859i
\(58\) 5.99934 3.05682i 0.787752 0.401380i
\(59\) 5.11223 3.71425i 0.665555 0.483554i −0.202979 0.979183i \(-0.565062\pi\)
0.868534 + 0.495629i \(0.165062\pi\)
\(60\) 4.86821 + 20.2768i 0.628483 + 2.61772i
\(61\) −2.77203 + 3.81537i −0.354922 + 0.488509i −0.948725 0.316102i \(-0.897626\pi\)
0.593803 + 0.804610i \(0.297626\pi\)
\(62\) 10.5868 + 1.67678i 1.34452 + 0.212951i
\(63\) 10.0348 + 9.34735i 1.26427 + 1.17765i
\(64\) −7.58503 + 10.4399i −0.948128 + 1.30499i
\(65\) 8.93116 2.14426i 1.10777 0.265963i
\(66\) 20.6994 + 28.4903i 2.54792 + 3.50691i
\(67\) 0.144637 + 0.283867i 0.0176703 + 0.0346799i 0.899673 0.436565i \(-0.143805\pi\)
−0.882003 + 0.471244i \(0.843805\pi\)
\(68\) 0.130740 0.130740i 0.0158546 0.0158546i
\(69\) −3.44513 + 10.6030i −0.414745 + 1.27645i
\(70\) −9.17221 9.99853i −1.09629 1.19505i
\(71\) −3.23078 9.94332i −0.383423 1.18006i −0.937618 0.347668i \(-0.886974\pi\)
0.554194 0.832387i \(-0.313026\pi\)
\(72\) −13.3462 6.80021i −1.57286 0.801413i
\(73\) 15.7935 2.50145i 1.84849 0.292772i 0.869083 0.494665i \(-0.164709\pi\)
0.979408 + 0.201893i \(0.0647094\pi\)
\(74\) 10.6361i 1.23643i
\(75\) −13.6032 + 4.42019i −1.57076 + 0.510400i
\(76\) 5.85090i 0.671144i
\(77\) −12.8741 5.99469i −1.46714 0.683159i
\(78\) −12.2348 + 24.0122i −1.38532 + 2.71885i
\(79\) −6.76190 + 2.19708i −0.760774 + 0.247190i −0.663611 0.748078i \(-0.730977\pi\)
−0.0971630 + 0.995268i \(0.530977\pi\)
\(80\) 0.205171 + 0.125726i 0.0229388 + 0.0140566i
\(81\) −0.716034 + 2.20373i −0.0795593 + 0.244858i
\(82\) 8.32710 + 8.32710i 0.919574 + 0.919574i
\(83\) 2.84011 + 5.57403i 0.311742 + 0.611829i 0.992716 0.120479i \(-0.0384431\pi\)
−0.680974 + 0.732308i \(0.738443\pi\)
\(84\) 24.6581 0.874609i 2.69042 0.0954277i
\(85\) 0.0964362 + 0.0823629i 0.0104600 + 0.00893351i
\(86\) 4.66101 + 3.38642i 0.502609 + 0.365167i
\(87\) −8.29498 1.31380i −0.889315 0.140854i
\(88\) 15.3202 + 2.42648i 1.63314 + 0.258664i
\(89\) 2.86263 + 2.07983i 0.303439 + 0.220461i 0.729076 0.684433i \(-0.239950\pi\)
−0.425637 + 0.904894i \(0.639950\pi\)
\(90\) 10.1723 24.5587i 1.07226 2.58872i
\(91\) −0.385232 10.8610i −0.0403833 1.13854i
\(92\) 5.76796 + 11.3203i 0.601351 + 1.18022i
\(93\) −9.45369 9.45369i −0.980302 0.980302i
\(94\) 0.129093 0.397306i 0.0133149 0.0409790i
\(95\) −4.00081 + 0.314905i −0.410475 + 0.0323086i
\(96\) 15.0527 4.89090i 1.53631 0.499176i
\(97\) −6.97738 + 13.6939i −0.708446 + 1.39040i 0.203080 + 0.979162i \(0.434905\pi\)
−0.911526 + 0.411241i \(0.865095\pi\)
\(98\) −13.7521 + 8.28365i −1.38918 + 0.836775i
\(99\) 27.8222i 2.79624i
\(100\) −7.39980 + 14.5235i −0.739980 + 1.45235i
\(101\) 12.0690i 1.20091i −0.799657 0.600457i \(-0.794985\pi\)
0.799657 0.600457i \(-0.205015\pi\)
\(102\) −0.367524 + 0.0582100i −0.0363903 + 0.00576365i
\(103\) 1.29550 + 0.660088i 0.127649 + 0.0650404i 0.516649 0.856197i \(-0.327179\pi\)
−0.389000 + 0.921238i \(0.627179\pi\)
\(104\) 3.66808 + 11.2892i 0.359685 + 1.10700i
\(105\) 1.92519 + 16.8140i 0.187880 + 1.64088i
\(106\) 5.20103 16.0071i 0.505169 1.55475i
\(107\) 5.30900 5.30900i 0.513241 0.513241i −0.402277 0.915518i \(-0.631781\pi\)
0.915518 + 0.402277i \(0.131781\pi\)
\(108\) 9.24391 + 18.1422i 0.889496 + 1.74573i
\(109\) 3.28379 + 4.51975i 0.314530 + 0.432913i 0.936787 0.349899i \(-0.113784\pi\)
−0.622257 + 0.782813i \(0.713784\pi\)
\(110\) −2.15951 + 27.4421i −0.205901 + 2.61650i
\(111\) 7.79786 10.7328i 0.740140 1.01872i
\(112\) 0.194062 0.208334i 0.0183371 0.0196857i
\(113\) 13.7887 + 2.18391i 1.29713 + 0.205445i 0.766547 0.642189i \(-0.221973\pi\)
0.530582 + 0.847634i \(0.321973\pi\)
\(114\) 6.92121 9.52623i 0.648231 0.892213i
\(115\) −7.43029 + 4.55337i −0.692878 + 0.424604i
\(116\) −7.74293 + 5.62557i −0.718913 + 0.522321i
\(117\) 18.9707 9.66608i 1.75385 0.893629i
\(118\) −10.2478 + 10.2478i −0.943386 + 0.943386i
\(119\) 0.118196 0.0924490i 0.0108350 0.00847478i
\(120\) −7.07398 17.0777i −0.645763 1.55897i
\(121\) 5.50395 + 16.9394i 0.500359 + 1.53995i
\(122\) 4.91043 9.63725i 0.444569 0.872516i
\(123\) −2.29781 14.5078i −0.207186 1.30812i
\(124\) −15.2359 −1.36823
\(125\) −10.3294 4.27827i −0.923889 0.382660i
\(126\) −26.0848 17.5736i −2.32382 1.56558i
\(127\) −10.3518 + 1.63956i −0.918573 + 0.145488i −0.597778 0.801661i \(-0.703950\pi\)
−0.320794 + 0.947149i \(0.603950\pi\)
\(128\) 8.41262 16.5107i 0.743578 1.45935i
\(129\) −2.22064 6.83441i −0.195516 0.601737i
\(130\) −19.4618 + 8.06155i −1.70692 + 0.707045i
\(131\) 5.04701 + 1.63987i 0.440959 + 0.143276i 0.521078 0.853509i \(-0.325530\pi\)
−0.0801188 + 0.996785i \(0.525530\pi\)
\(132\) −35.3956 35.3956i −3.08079 3.08079i
\(133\) −0.576110 + 4.71339i −0.0499551 + 0.408703i
\(134\) −0.429483 0.591132i −0.0371017 0.0510660i
\(135\) −11.9080 + 7.29738i −1.02488 + 0.628059i
\(136\) −0.0963363 + 0.132595i −0.00826077 + 0.0113700i
\(137\) 0.772665 4.87841i 0.0660132 0.416791i −0.932446 0.361308i \(-0.882330\pi\)
0.998460 0.0554827i \(-0.0176698\pi\)
\(138\) 3.99989 25.2543i 0.340494 2.14979i
\(139\) 8.92635 + 6.48537i 0.757123 + 0.550082i 0.898027 0.439941i \(-0.145001\pi\)
−0.140903 + 0.990023i \(0.545001\pi\)
\(140\) 15.1004 + 11.9977i 1.27622 + 1.01399i
\(141\) −0.421550 + 0.306274i −0.0355010 + 0.0257930i
\(142\) 10.8859 + 21.3648i 0.913526 + 1.79290i
\(143\) −15.5904 + 15.5904i −1.30374 + 1.30374i
\(144\) 0.530494 + 0.172368i 0.0442078 + 0.0143640i
\(145\) −4.26347 4.99180i −0.354062 0.414546i
\(146\) −34.8785 + 11.3327i −2.88657 + 0.937903i
\(147\) 19.9503 + 1.72340i 1.64547 + 0.142143i
\(148\) −2.36506 14.9324i −0.194406 1.22743i
\(149\) 1.46183i 0.119758i 0.998206 + 0.0598791i \(0.0190715\pi\)
−0.998206 + 0.0598791i \(0.980928\pi\)
\(150\) 29.2285 14.8933i 2.38649 1.21603i
\(151\) −8.74281 −0.711480 −0.355740 0.934585i \(-0.615771\pi\)
−0.355740 + 0.934585i \(0.615771\pi\)
\(152\) −0.811337 5.12258i −0.0658081 0.415496i
\(153\) 0.261938 + 0.133464i 0.0211764 + 0.0107899i
\(154\) 31.3135 + 8.96045i 2.52332 + 0.722053i
\(155\) −0.820022 10.4182i −0.0658658 0.836813i
\(156\) 11.8375 36.4319i 0.947755 2.91689i
\(157\) 10.7327 + 10.7327i 0.856561 + 0.856561i 0.990931 0.134370i \(-0.0429012\pi\)
−0.134370 + 0.990931i \(0.542901\pi\)
\(158\) 14.5290 7.40291i 1.15587 0.588944i
\(159\) −16.9839 + 12.3395i −1.34691 + 0.978588i
\(160\) 11.4299 + 4.73431i 0.903614 + 0.374280i
\(161\) 3.53192 + 9.68736i 0.278355 + 0.763471i
\(162\) 0.831336 5.24885i 0.0653159 0.412389i
\(163\) −24.5231 3.88407i −1.92080 0.304224i −0.923879 0.382685i \(-0.875000\pi\)
−0.996917 + 0.0784605i \(0.975000\pi\)
\(164\) −13.5423 9.83903i −1.05747 0.768299i
\(165\) 22.2983 26.1084i 1.73592 2.03253i
\(166\) −8.43334 11.6075i −0.654554 0.900917i
\(167\) 8.47354 4.31748i 0.655702 0.334097i −0.0942888 0.995545i \(-0.530058\pi\)
0.749991 + 0.661448i \(0.230058\pi\)
\(168\) −21.4674 + 4.18505i −1.65625 + 0.322884i
\(169\) −3.68315 1.19673i −0.283319 0.0920560i
\(170\) −0.248001 0.151972i −0.0190208 0.0116557i
\(171\) −8.84753 + 2.87474i −0.676588 + 0.219837i
\(172\) −7.29672 3.71787i −0.556370 0.283485i
\(173\) −4.50515 + 0.713546i −0.342520 + 0.0542499i −0.325325 0.945602i \(-0.605474\pi\)
−0.0171954 + 0.999852i \(0.505474\pi\)
\(174\) 19.2614 1.46020
\(175\) −7.39123 + 10.9713i −0.558724 + 0.829353i
\(176\) −0.577621 −0.0435398
\(177\) 17.8541 2.82781i 1.34200 0.212551i
\(178\) −7.23073 3.68424i −0.541966 0.276146i
\(179\) 1.80988 0.588066i 0.135277 0.0439541i −0.240596 0.970625i \(-0.577343\pi\)
0.375873 + 0.926671i \(0.377343\pi\)
\(180\) −8.82032 + 36.7406i −0.657428 + 2.73849i
\(181\) 16.7826 + 5.45300i 1.24744 + 0.405318i 0.857003 0.515311i \(-0.172324\pi\)
0.390438 + 0.920629i \(0.372324\pi\)
\(182\) 4.76931 + 24.4644i 0.353525 + 1.81342i
\(183\) −12.0206 + 6.12480i −0.888588 + 0.452758i
\(184\) −6.61973 9.11128i −0.488013 0.671692i
\(185\) 10.0834 2.42090i 0.741346 0.177988i
\(186\) 24.8066 + 18.0230i 1.81891 + 1.32151i
\(187\) −0.300682 0.0476233i −0.0219880 0.00348256i
\(188\) −0.0928916 + 0.586495i −0.00677482 + 0.0427745i
\(189\) 5.66037 + 15.5253i 0.411731 + 1.12930i
\(190\) 8.94979 2.14874i 0.649286 0.155886i
\(191\) −8.89680 + 6.46390i −0.643750 + 0.467712i −0.861136 0.508374i \(-0.830247\pi\)
0.217387 + 0.976086i \(0.430247\pi\)
\(192\) −32.8916 + 16.7591i −2.37375 + 1.20948i
\(193\) 12.3378 + 12.3378i 0.888091 + 0.888091i 0.994340 0.106249i \(-0.0338840\pi\)
−0.106249 + 0.994340i \(0.533884\pi\)
\(194\) 10.8923 33.5232i 0.782024 2.40682i
\(195\) 25.5491 + 6.13356i 1.82961 + 0.439234i
\(196\) 17.4651 14.6876i 1.24750 1.04911i
\(197\) −11.1337 5.67291i −0.793245 0.404178i 0.00990859 0.999951i \(-0.496846\pi\)
−0.803153 + 0.595773i \(0.796846\pi\)
\(198\) 9.98199 + 63.0238i 0.709389 + 4.47891i
\(199\) −11.0246 −0.781513 −0.390756 0.920494i \(-0.627787\pi\)
−0.390756 + 0.920494i \(0.627787\pi\)
\(200\) 4.46472 13.7418i 0.315703 0.971691i
\(201\) 0.911381i 0.0642838i
\(202\) 4.33010 + 27.3392i 0.304665 + 1.92358i
\(203\) −6.79150 + 3.76946i −0.476670 + 0.264564i
\(204\) 0.503033 0.163445i 0.0352194 0.0114435i
\(205\) 5.99901 9.78969i 0.418989 0.683741i
\(206\) −3.17142 1.03046i −0.220964 0.0717954i
\(207\) −14.2841 + 14.2841i −0.992815 + 0.992815i
\(208\) −0.200679 0.393854i −0.0139146 0.0273089i
\(209\) 7.79368 5.66244i 0.539100 0.391679i
\(210\) −10.3935 37.3970i −0.717220 2.58064i
\(211\) −10.2803 7.46906i −0.707724 0.514191i 0.174715 0.984619i \(-0.444100\pi\)
−0.882439 + 0.470428i \(0.844100\pi\)
\(212\) −3.74252 + 23.6293i −0.257037 + 1.62287i
\(213\) 4.67868 29.5400i 0.320578 2.02405i
\(214\) −10.1214 + 13.9309i −0.691883 + 0.952295i
\(215\) 2.14954 5.18957i 0.146597 0.353925i
\(216\) −10.6090 14.6020i −0.721851 0.993542i
\(217\) −12.2738 1.50021i −0.833201 0.101841i
\(218\) −9.06013 9.06013i −0.613629 0.613629i
\(219\) 43.5042 + 14.1354i 2.93974 + 0.955179i
\(220\) −3.07025 39.0070i −0.206996 2.62985i
\(221\) −0.0719915 0.221567i −0.00484267 0.0149042i
\(222\) −13.8133 + 27.1101i −0.927086 + 1.81951i
\(223\) 4.62872 0.733118i 0.309962 0.0490932i 0.000484538 1.00000i \(-0.499846\pi\)
0.309478 + 0.950907i \(0.399846\pi\)
\(224\) 8.17897 12.1402i 0.546481 0.811149i
\(225\) −25.5978 4.05384i −1.70652 0.270256i
\(226\) −32.0181 −2.12981
\(227\) −4.23604 26.7453i −0.281156 1.77515i −0.573869 0.818947i \(-0.694558\pi\)
0.292713 0.956200i \(-0.405442\pi\)
\(228\) −7.59862 + 14.9131i −0.503231 + 0.987647i
\(229\) −0.678172 2.08720i −0.0448149 0.137926i 0.926145 0.377167i \(-0.123102\pi\)
−0.970960 + 0.239241i \(0.923102\pi\)
\(230\) 15.1977 12.9803i 1.00211 0.855894i
\(231\) −25.0289 31.9994i −1.64678 2.10540i
\(232\) 5.99900 5.99900i 0.393854 0.393854i
\(233\) −9.26793 + 4.72225i −0.607162 + 0.309365i −0.730408 0.683012i \(-0.760670\pi\)
0.123245 + 0.992376i \(0.460670\pi\)
\(234\) −39.5052 + 28.7022i −2.58254 + 1.87632i
\(235\) −0.406042 0.0319527i −0.0264872 0.00208436i
\(236\) 12.1085 16.6659i 0.788194 1.08486i
\(237\) −20.0885 3.18171i −1.30489 0.206674i
\(238\) −0.234572 + 0.251824i −0.0152051 + 0.0163234i
\(239\) −10.6903 + 14.7139i −0.691496 + 0.951763i 0.308503 + 0.951223i \(0.400172\pi\)
−1.00000 0.000539997i \(0.999828\pi\)
\(240\) 0.359670 + 0.586917i 0.0232166 + 0.0378854i
\(241\) 6.55615 + 9.02377i 0.422319 + 0.581272i 0.966169 0.257911i \(-0.0830340\pi\)
−0.543850 + 0.839182i \(0.683034\pi\)
\(242\) −18.5452 36.3971i −1.19213 2.33969i
\(243\) 8.56235 8.56235i 0.549275 0.549275i
\(244\) −4.75094 + 14.6219i −0.304148 + 0.936071i
\(245\) 10.9833 + 11.1520i 0.701697 + 0.712476i
\(246\) 10.4101 + 32.0391i 0.663727 + 2.04274i
\(247\) 6.56867 + 3.34691i 0.417955 + 0.212958i
\(248\) 13.3394 2.11275i 0.847050 0.134160i
\(249\) 17.8959i 1.13411i
\(250\) 24.9334 + 5.98532i 1.57693 + 0.378545i
\(251\) 4.27338i 0.269733i 0.990864 + 0.134867i \(0.0430606\pi\)
−0.990864 + 0.134867i \(0.956939\pi\)
\(252\) 40.5289 + 18.8719i 2.55308 + 1.18882i
\(253\) 9.49696 18.6388i 0.597069 1.17181i
\(254\) 22.8610 7.42798i 1.43442 0.466073i
\(255\) 0.138837 + 0.335175i 0.00869433 + 0.0209895i
\(256\) −5.15751 + 15.8732i −0.322344 + 0.992074i
\(257\) 12.9844 + 12.9844i 0.809943 + 0.809943i 0.984625 0.174682i \(-0.0558897\pi\)
−0.174682 + 0.984625i \(0.555890\pi\)
\(258\) 7.48229 + 14.6848i 0.465827 + 0.914237i
\(259\) −0.434932 12.2622i −0.0270254 0.761934i
\(260\) 25.5305 15.6454i 1.58333 0.970286i
\(261\) −12.3111 8.94457i −0.762041 0.553655i
\(262\) −12.0210 1.90394i −0.742660 0.117626i
\(263\) 7.31065 + 1.15789i 0.450794 + 0.0713988i 0.377704 0.925927i \(-0.376714\pi\)
0.0730905 + 0.997325i \(0.476714\pi\)
\(264\) 35.8978 + 26.0813i 2.20936 + 1.60519i
\(265\) −16.3591 1.28735i −1.00493 0.0790810i
\(266\) −0.386036 10.8836i −0.0236694 0.667318i
\(267\) 4.59537 + 9.01893i 0.281232 + 0.551949i
\(268\) 0.734407 + 0.734407i 0.0448611 + 0.0448611i
\(269\) −9.39419 + 28.9124i −0.572774 + 1.76282i 0.0708623 + 0.997486i \(0.477425\pi\)
−0.643636 + 0.765331i \(0.722575\pi\)
\(270\) 24.3563 20.8026i 1.48228 1.26601i
\(271\) −11.4914 + 3.73379i −0.698055 + 0.226812i −0.636483 0.771291i \(-0.719611\pi\)
−0.0615721 + 0.998103i \(0.519611\pi\)
\(272\) 0.00277087 0.00543814i 0.000168009 0.000329736i
\(273\) 13.1233 28.1834i 0.794261 1.70574i
\(274\) 11.3280i 0.684347i
\(275\) 26.5075 4.19884i 1.59846 0.253200i
\(276\) 36.3447i 2.18769i
\(277\) −2.58822 + 0.409934i −0.155511 + 0.0246306i −0.233705 0.972308i \(-0.575085\pi\)
0.0781933 + 0.996938i \(0.475085\pi\)
\(278\) −22.5471 11.4883i −1.35228 0.689023i
\(279\) −7.48590 23.0392i −0.448169 1.37932i
\(280\) −14.8844 8.41027i −0.889514 0.502610i
\(281\) −5.20949 + 16.0332i −0.310772 + 0.956458i 0.666688 + 0.745337i \(0.267711\pi\)
−0.977460 + 0.211121i \(0.932289\pi\)
\(282\) 0.845026 0.845026i 0.0503205 0.0503205i
\(283\) −3.88365 7.62209i −0.230859 0.453086i 0.746296 0.665614i \(-0.231830\pi\)
−0.977155 + 0.212528i \(0.931830\pi\)
\(284\) −20.0337 27.5741i −1.18878 1.63622i
\(285\) −10.6065 4.39325i −0.628275 0.260234i
\(286\) 29.7224 40.9094i 1.75752 2.41902i
\(287\) −9.94063 9.25961i −0.586777 0.546578i
\(288\) 28.3252 + 4.48626i 1.66908 + 0.264356i
\(289\) −9.99046 + 13.7507i −0.587674 + 0.808864i
\(290\) 11.4487 + 9.77795i 0.672291 + 0.574181i
\(291\) −35.5688 + 25.8423i −2.08508 + 1.51490i
\(292\) 46.4470 23.6659i 2.71811 1.38494i
\(293\) −11.3981 + 11.3981i −0.665885 + 0.665885i −0.956761 0.290876i \(-0.906053\pi\)
0.290876 + 0.956761i \(0.406053\pi\)
\(294\) −45.8104 + 3.25383i −2.67172 + 0.189767i
\(295\) 12.0477 + 7.38272i 0.701446 + 0.429839i
\(296\) 4.14131 + 12.7456i 0.240709 + 0.740826i
\(297\) 15.2201 29.8712i 0.883161 1.73330i
\(298\) −0.524474 3.31140i −0.0303819 0.191824i
\(299\) 16.0085 0.925793
\(300\) −37.7230 + 27.4083i −2.17794 + 1.58242i
\(301\) −5.51205 3.71353i −0.317709 0.214044i
\(302\) 19.8045 3.13673i 1.13962 0.180498i
\(303\) 15.6742 30.7624i 0.900459 1.76725i
\(304\) 0.0596828 + 0.183685i 0.00342305 + 0.0105351i
\(305\) −10.2541 2.46170i −0.587147 0.140956i
\(306\) −0.641235 0.208350i −0.0366570 0.0119106i
\(307\) −19.9969 19.9969i −1.14128 1.14128i −0.988216 0.153068i \(-0.951085\pi\)
−0.153068 0.988216i \(-0.548915\pi\)
\(308\) −45.9544 5.61693i −2.61850 0.320054i
\(309\) 2.44478 + 3.36495i 0.139079 + 0.191425i
\(310\) 5.59537 + 23.3055i 0.317796 + 1.32367i
\(311\) −11.4502 + 15.7599i −0.649282 + 0.893660i −0.999068 0.0431696i \(-0.986254\pi\)
0.349786 + 0.936830i \(0.386254\pi\)
\(312\) −5.31196 + 33.5384i −0.300731 + 1.89874i
\(313\) −4.52789 + 28.5880i −0.255931 + 1.61589i 0.440150 + 0.897924i \(0.354925\pi\)
−0.696081 + 0.717963i \(0.745075\pi\)
\(314\) −28.1627 20.4614i −1.58931 1.15470i
\(315\) −10.7232 + 28.7292i −0.604183 + 1.61871i
\(316\) −18.7516 + 13.6238i −1.05486 + 0.766401i
\(317\) −4.66373 9.15309i −0.261941 0.514089i 0.722153 0.691733i \(-0.243152\pi\)
−0.984095 + 0.177644i \(0.943152\pi\)
\(318\) 34.0453 34.0453i 1.90917 1.90917i
\(319\) 14.9871 + 4.86959i 0.839114 + 0.272645i
\(320\) −28.0579 6.73586i −1.56849 0.376546i
\(321\) 20.4268 6.63707i 1.14011 0.370445i
\(322\) −11.4762 20.6770i −0.639546 1.15228i
\(323\) 0.0159237 + 0.100538i 0.000886017 + 0.00559409i
\(324\) 7.55387i 0.419659i
\(325\) 12.0723 + 16.6155i 0.669652 + 0.921664i
\(326\) 56.9440 3.15384
\(327\) 2.50008 + 15.7849i 0.138255 + 0.872908i
\(328\) 13.2209 + 6.73639i 0.730002 + 0.371955i
\(329\) −0.132581 + 0.463324i −0.00730945 + 0.0255439i
\(330\) −41.1437 + 67.1417i −2.26489 + 3.69603i
\(331\) 0.0415942 0.128014i 0.00228622 0.00703627i −0.949907 0.312533i \(-0.898823\pi\)
0.952193 + 0.305497i \(0.0988225\pi\)
\(332\) 14.4209 + 14.4209i 0.791447 + 0.791447i
\(333\) 21.4182 10.9131i 1.17371 0.598036i
\(334\) −17.6455 + 12.8202i −0.965520 + 0.701492i
\(335\) −0.462657 + 0.541711i −0.0252776 + 0.0295968i
\(336\) 0.765203 0.278986i 0.0417452 0.0152199i
\(337\) 5.24151 33.0936i 0.285523 1.80272i −0.261063 0.965322i \(-0.584073\pi\)
0.546587 0.837402i \(-0.315927\pi\)
\(338\) 8.77256 + 1.38944i 0.477164 + 0.0755754i
\(339\) 32.3092 + 23.4740i 1.75479 + 1.27493i
\(340\) 0.381968 + 0.158212i 0.0207151 + 0.00858027i
\(341\) 14.7452 + 20.2950i 0.798495 + 1.09903i
\(342\) 19.0103 9.68625i 1.02796 0.523772i
\(343\) 15.5158 10.1124i 0.837774 0.546017i
\(344\) 6.90399 + 2.24324i 0.372238 + 0.120947i
\(345\) −24.8523 + 1.95613i −1.33800 + 0.105315i
\(346\) 9.94922 3.23270i 0.534873 0.173791i
\(347\) 9.23837 + 4.70718i 0.495942 + 0.252695i 0.684026 0.729458i \(-0.260228\pi\)
−0.188084 + 0.982153i \(0.560228\pi\)
\(348\) −27.0417 + 4.28298i −1.44958 + 0.229592i
\(349\) −33.1017 −1.77189 −0.885945 0.463790i \(-0.846489\pi\)
−0.885945 + 0.463790i \(0.846489\pi\)
\(350\) 12.8066 27.5044i 0.684541 1.47017i
\(351\) 25.6557 1.36940
\(352\) −29.3320 + 4.64573i −1.56340 + 0.247618i
\(353\) 27.0892 + 13.8026i 1.44181 + 0.734641i 0.987708 0.156307i \(-0.0499590\pi\)
0.454105 + 0.890948i \(0.349959\pi\)
\(354\) −39.4292 + 12.8113i −2.09564 + 0.680914i
\(355\) 17.7768 15.1831i 0.943493 0.805833i
\(356\) 10.9707 + 3.56458i 0.581444 + 0.188922i
\(357\) 0.421329 0.0821378i 0.0222991 0.00434719i
\(358\) −3.88882 + 1.98145i −0.205530 + 0.104723i
\(359\) −11.7260 16.1394i −0.618874 0.851807i 0.378396 0.925644i \(-0.376476\pi\)
−0.997270 + 0.0738368i \(0.976476\pi\)
\(360\) 2.62759 33.3903i 0.138486 1.75982i
\(361\) 12.7654 + 9.27458i 0.671862 + 0.488136i
\(362\) −39.9729 6.33109i −2.10093 0.332755i
\(363\) −7.97059 + 50.3244i −0.418348 + 2.64134i
\(364\) −12.1357 33.2857i −0.636083 1.74465i
\(365\) 18.6825 + 30.4865i 0.977887 + 1.59574i
\(366\) 25.0320 18.1868i 1.30844 0.950641i
\(367\) 15.1963 7.74290i 0.793241 0.404176i −0.00991110 0.999951i \(-0.503155\pi\)
0.803152 + 0.595775i \(0.203155\pi\)
\(368\) 0.296555 + 0.296555i 0.0154590 + 0.0154590i
\(369\) 8.22450 25.3124i 0.428150 1.31771i
\(370\) −21.9727 + 9.10160i −1.14230 + 0.473170i
\(371\) −5.34158 + 18.6669i −0.277321 + 0.969138i
\(372\) −38.8343 19.7870i −2.01346 1.02591i
\(373\) 2.14774 + 13.5603i 0.111206 + 0.702125i 0.978795 + 0.204843i \(0.0656685\pi\)
−0.867589 + 0.497282i \(0.834331\pi\)
\(374\) 0.698200 0.0361031
\(375\) −20.7720 24.3196i −1.07266 1.25586i
\(376\) 0.526369i 0.0271454i
\(377\) 1.88649 + 11.9108i 0.0971591 + 0.613438i
\(378\) −18.3922 33.1375i −0.945992 1.70441i
\(379\) 14.5474 4.72673i 0.747249 0.242796i 0.0894522 0.995991i \(-0.471488\pi\)
0.657797 + 0.753195i \(0.271488\pi\)
\(380\) −12.0871 + 5.00675i −0.620054 + 0.256841i
\(381\) −28.5146 9.26496i −1.46085 0.474658i
\(382\) 17.8342 17.8342i 0.912478 0.912478i
\(383\) 0.837922 + 1.64451i 0.0428158 + 0.0840307i 0.911423 0.411470i \(-0.134985\pi\)
−0.868607 + 0.495501i \(0.834985\pi\)
\(384\) 42.8853 31.1580i 2.18848 1.59002i
\(385\) 1.36749 31.7257i 0.0696936 1.61689i
\(386\) −32.3744 23.5214i −1.64781 1.19721i
\(387\) 2.03691 12.8606i 0.103542 0.653740i
\(388\) −7.83784 + 49.4862i −0.397906 + 2.51228i
\(389\) 18.1228 24.9439i 0.918862 1.26471i −0.0451865 0.998979i \(-0.514388\pi\)
0.964048 0.265726i \(-0.0856118\pi\)
\(390\) −60.0752 4.72751i −3.04203 0.239387i
\(391\) 0.129922 + 0.178822i 0.00657044 + 0.00904343i
\(392\) −13.2543 + 15.2811i −0.669444 + 0.771814i
\(393\) 10.7344 + 10.7344i 0.541480 + 0.541480i
\(394\) 27.2558 + 8.85594i 1.37313 + 0.446156i
\(395\) −10.3252 12.0890i −0.519515 0.608263i
\(396\) −28.0280 86.2613i −1.40846 4.33479i
\(397\) 9.21582 18.0871i 0.462529 0.907764i −0.535471 0.844553i \(-0.679866\pi\)
0.998000 0.0632105i \(-0.0201340\pi\)
\(398\) 24.9733 3.95538i 1.25180 0.198265i
\(399\) −7.58976 + 11.2656i −0.379963 + 0.563985i
\(400\) −0.0841625 + 0.531439i −0.00420812 + 0.0265720i
\(401\) 15.6422 0.781136 0.390568 0.920574i \(-0.372279\pi\)
0.390568 + 0.920574i \(0.372279\pi\)
\(402\) −0.326983 2.06449i −0.0163084 0.102967i
\(403\) −8.71544 + 17.1050i −0.434147 + 0.852062i
\(404\) −12.1583 37.4194i −0.604899 1.86169i
\(405\) −5.16529 + 0.406562i −0.256666 + 0.0202022i
\(406\) 14.0319 10.9753i 0.696393 0.544697i
\(407\) −17.6018 + 17.6018i −0.872488 + 0.872488i
\(408\) −0.417751 + 0.212855i −0.0206818 + 0.0105379i
\(409\) 3.25294 2.36340i 0.160848 0.116863i −0.504450 0.863441i \(-0.668305\pi\)
0.665298 + 0.746578i \(0.268305\pi\)
\(410\) −10.0768 + 24.3282i −0.497660 + 1.20149i
\(411\) 8.30507 11.4309i 0.409659 0.563847i
\(412\) 4.68159 + 0.741490i 0.230645 + 0.0365306i
\(413\) 11.3954 12.2335i 0.560731 0.601971i
\(414\) 27.2320 37.4817i 1.33838 1.84212i
\(415\) −9.08475 + 10.6371i −0.445953 + 0.522153i
\(416\) −13.3583 18.3862i −0.654946 0.901455i
\(417\) 14.3294 + 28.1231i 0.701715 + 1.37719i
\(418\) −15.6229 + 15.6229i −0.764143 + 0.764143i
\(419\) 11.7452 36.1479i 0.573788 1.76594i −0.0664797 0.997788i \(-0.521177\pi\)
0.640268 0.768151i \(-0.278823\pi\)
\(420\) 22.9073 + 50.1915i 1.11776 + 2.44910i
\(421\) −10.3327 31.8009i −0.503587 1.54988i −0.803133 0.595800i \(-0.796835\pi\)
0.299546 0.954082i \(-0.403165\pi\)
\(422\) 25.9670 + 13.2308i 1.26405 + 0.644067i
\(423\) −0.932518 + 0.147696i −0.0453406 + 0.00718124i
\(424\) 21.2070i 1.02990i
\(425\) −0.0876267 + 0.269703i −0.00425052 + 0.0130825i
\(426\) 68.5937i 3.32337i
\(427\) −5.26703 + 11.3114i −0.254890 + 0.547395i
\(428\) 11.1120 21.8086i 0.537119 1.05416i
\(429\) −59.9853 + 19.4904i −2.89612 + 0.941006i
\(430\) −3.00730 + 12.5268i −0.145025 + 0.604095i
\(431\) 8.50683 26.1813i 0.409760 1.26111i −0.507095 0.861890i \(-0.669281\pi\)
0.916855 0.399221i \(-0.130719\pi\)
\(432\) 0.475268 + 0.475268i 0.0228663 + 0.0228663i
\(433\) −8.35131 16.3904i −0.401338 0.787671i 0.598572 0.801069i \(-0.295735\pi\)
−0.999910 + 0.0133985i \(0.995735\pi\)
\(434\) 28.3413 1.00525i 1.36043 0.0482535i
\(435\) −4.38411 18.2604i −0.210202 0.875521i
\(436\) 14.7344 + 10.7052i 0.705649 + 0.512684i
\(437\) −6.90847 1.09419i −0.330477 0.0523424i
\(438\) −103.619 16.4116i −4.95109 0.784175i
\(439\) −3.15569 2.29274i −0.150613 0.109427i 0.509927 0.860218i \(-0.329672\pi\)
−0.660540 + 0.750791i \(0.729672\pi\)
\(440\) 8.09712 + 33.7257i 0.386015 + 1.60781i
\(441\) 30.7912 + 19.1936i 1.46625 + 0.913981i
\(442\) 0.242571 + 0.476072i 0.0115379 + 0.0226444i
\(443\) −11.0469 11.0469i −0.524854 0.524854i 0.394180 0.919033i \(-0.371029\pi\)
−0.919033 + 0.394180i \(0.871029\pi\)
\(444\) 13.3646 41.1321i 0.634258 1.95204i
\(445\) −1.84698 + 7.69353i −0.0875554 + 0.364708i
\(446\) −10.2221 + 3.32137i −0.484031 + 0.157271i
\(447\) −1.89850 + 3.72602i −0.0897960 + 0.176235i
\(448\) −14.4120 + 30.9510i −0.680904 + 1.46230i
\(449\) 18.5686i 0.876305i 0.898901 + 0.438153i \(0.144367\pi\)
−0.898901 + 0.438153i \(0.855633\pi\)
\(450\) 59.4394 0.00101082i 2.80200 4.76505e-5i
\(451\) 27.5611i 1.29780i
\(452\) 44.9511 7.11955i 2.11432 0.334876i
\(453\) −22.2842 11.3544i −1.04700 0.533476i
\(454\) 19.1912 + 59.0645i 0.900689 + 2.77204i
\(455\) 22.1075 10.0898i 1.03641 0.473018i
\(456\) 4.58477 14.1105i 0.214701 0.660783i
\(457\) −0.684871 + 0.684871i −0.0320369 + 0.0320369i −0.722944 0.690907i \(-0.757211\pi\)
0.690907 + 0.722944i \(0.257211\pi\)
\(458\) 2.28506 + 4.48468i 0.106774 + 0.209555i
\(459\) 0.208217 + 0.286586i 0.00971874 + 0.0133767i
\(460\) −18.4502 + 21.6027i −0.860243 + 1.00723i
\(461\) −17.3077 + 23.8220i −0.806098 + 1.10950i 0.185815 + 0.982585i \(0.440507\pi\)
−0.991914 + 0.126914i \(0.959493\pi\)
\(462\) 68.1769 + 63.5062i 3.17188 + 2.95458i
\(463\) −0.0892583 0.0141371i −0.00414818 0.000657008i 0.154360 0.988015i \(-0.450668\pi\)
−0.158508 + 0.987358i \(0.550668\pi\)
\(464\) −0.185700 + 0.255594i −0.00862089 + 0.0118656i
\(465\) 11.4402 27.6197i 0.530525 1.28083i
\(466\) 19.2998 14.0221i 0.894045 0.649562i
\(467\) −22.4185 + 11.4228i −1.03740 + 0.528584i −0.887833 0.460167i \(-0.847790\pi\)
−0.149572 + 0.988751i \(0.547790\pi\)
\(468\) 49.0802 49.0802i 2.26873 2.26873i
\(469\) 0.519313 + 0.663940i 0.0239797 + 0.0306579i
\(470\) 0.931243 0.0732984i 0.0429550 0.00338100i
\(471\) 13.4175 + 41.2948i 0.618245 + 1.90276i
\(472\) −8.29017 + 16.2704i −0.381586 + 0.748905i
\(473\) 2.10932 + 13.3177i 0.0969865 + 0.612349i
\(474\) 46.6468 2.14256
\(475\) −4.07414 7.99561i −0.186934 0.366864i
\(476\) 0.273327 0.405703i 0.0125279 0.0185954i
\(477\) −37.5703 + 5.95056i −1.72023 + 0.272457i
\(478\) 18.9369 37.1659i 0.866156 1.69993i
\(479\) 9.62665 + 29.6278i 0.439853 + 1.35373i 0.888031 + 0.459784i \(0.152073\pi\)
−0.448178 + 0.893944i \(0.647927\pi\)
\(480\) 22.9848 + 26.9113i 1.04911 + 1.22833i
\(481\) −18.1171 5.88662i −0.826071 0.268407i
\(482\) −18.0887 18.0887i −0.823919 0.823919i
\(483\) −3.57869 + 29.2787i −0.162836 + 1.33223i
\(484\) 34.1294 + 46.9751i 1.55134 + 2.13523i
\(485\) −34.2602 2.69605i −1.55568 0.122421i
\(486\) −16.3237 + 22.4677i −0.740460 + 1.01916i
\(487\) −1.44146 + 9.10101i −0.0653187 + 0.412406i 0.933264 + 0.359190i \(0.116947\pi\)
−0.998583 + 0.0532158i \(0.983053\pi\)
\(488\) 2.13195 13.4606i 0.0965087 0.609332i
\(489\) −57.4617 41.7484i −2.59851 1.88793i
\(490\) −28.8808 21.3213i −1.30470 0.963200i
\(491\) −15.1556 + 11.0112i −0.683962 + 0.496927i −0.874670 0.484719i \(-0.838922\pi\)
0.190708 + 0.981647i \(0.438922\pi\)
\(492\) −21.7393 42.6658i −0.980085 1.92353i
\(493\) −0.117739 + 0.117739i −0.00530271 + 0.00530271i
\(494\) −16.0804 5.22483i −0.723490 0.235076i
\(495\) 57.4765 23.8081i 2.58338 1.07010i
\(496\) −0.478321 + 0.155416i −0.0214773 + 0.00697838i
\(497\) −13.4238 24.1859i −0.602139 1.08488i
\(498\) −6.42065 40.5384i −0.287716 1.81657i
\(499\) 1.06987i 0.0478938i −0.999713 0.0239469i \(-0.992377\pi\)
0.999713 0.0239469i \(-0.00762326\pi\)
\(500\) −36.3357 2.85875i −1.62498 0.127847i
\(501\) 27.2051 1.21543
\(502\) −1.53319 9.68020i −0.0684298 0.432049i
\(503\) 9.71648 + 4.95080i 0.433237 + 0.220745i 0.656988 0.753901i \(-0.271830\pi\)
−0.223751 + 0.974646i \(0.571830\pi\)
\(504\) −38.1008 10.9026i −1.69715 0.485643i
\(505\) 24.9328 10.3278i 1.10950 0.459580i
\(506\) −14.8256 + 45.6286i −0.659079 + 2.02844i
\(507\) −7.83365 7.83365i −0.347905 0.347905i
\(508\) −30.4435 + 15.5117i −1.35071 + 0.688222i
\(509\) 9.57382 6.95579i 0.424352 0.308310i −0.355034 0.934853i \(-0.615531\pi\)
0.779387 + 0.626543i \(0.215531\pi\)
\(510\) −0.434752 0.709437i −0.0192511 0.0314144i
\(511\) 39.7472 14.4915i 1.75831 0.641065i
\(512\) 0.190435 1.20236i 0.00841611 0.0531372i
\(513\) −11.0717 1.75359i −0.488829 0.0774229i
\(514\) −34.0711 24.7541i −1.50281 1.09186i
\(515\) −0.255057 + 3.24115i −0.0112391 + 0.142822i
\(516\) −13.7699 18.9527i −0.606187 0.834345i
\(517\) 0.871139 0.443867i 0.0383127 0.0195213i
\(518\) 5.38461 + 27.6206i 0.236586 + 1.21358i
\(519\) −12.4097 4.03216i −0.544726 0.176992i
\(520\) −20.1829 + 17.2381i −0.885080 + 0.755943i
\(521\) 27.6845 8.99523i 1.21288 0.394088i 0.368395 0.929670i \(-0.379908\pi\)
0.844484 + 0.535582i \(0.179908\pi\)
\(522\) 31.0967 + 15.8446i 1.36107 + 0.693498i
\(523\) 19.9445 3.15890i 0.872111 0.138129i 0.295692 0.955283i \(-0.404450\pi\)
0.576419 + 0.817154i \(0.304450\pi\)
\(524\) 17.3000 0.755754
\(525\) −33.0878 + 18.3653i −1.44407 + 0.801528i
\(526\) −16.9758 −0.740178
\(527\) −0.261804 + 0.0414658i −0.0114044 + 0.00180628i
\(528\) −1.47228 0.750163i −0.0640727 0.0326467i
\(529\) 7.42919 2.41389i 0.323008 0.104952i
\(530\) 37.5190 2.95313i 1.62972 0.128276i
\(531\) 31.1509 + 10.1215i 1.35183 + 0.439237i
\(532\) 2.96205 + 15.1940i 0.128421 + 0.658743i
\(533\) −18.7927 + 9.57535i −0.814002 + 0.414755i
\(534\) −13.6454 18.7813i −0.590493 0.812745i
\(535\) 15.5106 + 6.42456i 0.670584 + 0.277758i
\(536\) −0.744828 0.541149i −0.0321717 0.0233741i
\(537\) 5.37687 + 0.851612i 0.232029 + 0.0367498i
\(538\) 10.9069 68.8637i 0.470231 2.96892i
\(539\) −36.4671 9.04982i −1.57075 0.389804i
\(540\) −29.5688 + 34.6212i −1.27244 + 1.48986i
\(541\) 18.0860 13.1402i 0.777577 0.564943i −0.126674 0.991944i \(-0.540430\pi\)
0.904251 + 0.427002i \(0.140430\pi\)
\(542\) 24.6912 12.5808i 1.06058 0.540391i
\(543\) 35.6947 + 35.6947i 1.53181 + 1.53181i
\(544\) 0.0969684 0.298438i 0.00415748 0.0127954i
\(545\) −6.52710 + 10.6515i −0.279590 + 0.456259i
\(546\) −19.6159 + 68.5504i −0.839481 + 2.93369i
\(547\) 36.0799 + 18.3836i 1.54267 + 0.786027i 0.998594 0.0530117i \(-0.0168821\pi\)
0.544071 + 0.839039i \(0.316882\pi\)
\(548\) −2.51889 15.9036i −0.107602 0.679370i
\(549\) −24.4450 −1.04329
\(550\) −58.5393 + 19.0217i −2.49612 + 0.811087i
\(551\) 5.26907i 0.224470i
\(552\) −5.03988 31.8205i −0.214511 1.35437i
\(553\) −16.4475 + 9.12876i −0.699417 + 0.388195i
\(554\) 5.71585 1.85719i 0.242843 0.0789046i
\(555\) 28.8453 + 6.92487i 1.22441 + 0.293944i
\(556\) 34.2090 + 11.1152i 1.45079 + 0.471389i
\(557\) −20.9995 + 20.9995i −0.889777 + 0.889777i −0.994501 0.104724i \(-0.966604\pi\)
0.104724 + 0.994501i \(0.466604\pi\)
\(558\) 25.2233 + 49.5035i 1.06779 + 2.09565i
\(559\) −8.34793 + 6.06513i −0.353080 + 0.256528i
\(560\) 0.596451 + 0.222626i 0.0252046 + 0.00940765i
\(561\) −0.704548 0.511884i −0.0297460 0.0216118i
\(562\) 6.04837 38.1879i 0.255135 1.61086i
\(563\) 0.662311 4.18167i 0.0279131 0.176236i −0.969793 0.243929i \(-0.921564\pi\)
0.997706 + 0.0676925i \(0.0215637\pi\)
\(564\) −0.998455 + 1.37426i −0.0420425 + 0.0578666i
\(565\) 7.28766 + 30.3541i 0.306594 + 1.27701i
\(566\) 11.5320 + 15.8724i 0.484726 + 0.667168i
\(567\) −0.743793 + 6.08527i −0.0312364 + 0.255557i
\(568\) 21.3636 + 21.3636i 0.896397 + 0.896397i
\(569\) −29.0875 9.45111i −1.21941 0.396211i −0.372544 0.928014i \(-0.621514\pi\)
−0.846868 + 0.531804i \(0.821514\pi\)
\(570\) 25.6024 + 6.14636i 1.07237 + 0.257443i
\(571\) −2.33913 7.19910i −0.0978895 0.301273i 0.890106 0.455753i \(-0.150630\pi\)
−0.987996 + 0.154480i \(0.950630\pi\)
\(572\) −32.6315 + 64.0430i −1.36439 + 2.67777i
\(573\) −31.0715 + 4.92124i −1.29803 + 0.205588i
\(574\) 25.8400 + 17.4087i 1.07854 + 0.726625i
\(575\) −15.7649 11.4534i −0.657440 0.477641i
\(576\) −66.8882 −2.78701
\(577\) 2.97088 + 18.7574i 0.123679 + 0.780881i 0.969080 + 0.246748i \(0.0793619\pi\)
−0.845400 + 0.534133i \(0.820638\pi\)
\(578\) 17.6973 34.7329i 0.736110 1.44470i
\(579\) 15.4241 + 47.4704i 0.641003 + 1.97280i
\(580\) −18.2474 11.1818i −0.757681 0.464299i
\(581\) 10.1973 + 13.0372i 0.423054 + 0.540873i
\(582\) 71.3000 71.3000i 2.95548 2.95548i
\(583\) 35.0974 17.8830i 1.45359 0.740639i
\(584\) −37.3836 + 27.1608i −1.54694 + 1.12392i
\(585\) 36.2024 + 30.9192i 1.49678 + 1.27835i
\(586\) 21.7300 29.9088i 0.897659 1.23552i
\(587\) 29.0722 + 4.60459i 1.19994 + 0.190052i 0.724235 0.689553i \(-0.242193\pi\)
0.475705 + 0.879605i \(0.342193\pi\)
\(588\) 63.5910 14.7546i 2.62245 0.608468i
\(589\) 4.93030 6.78598i 0.203150 0.279611i
\(590\) −29.9397 12.4011i −1.23260 0.510546i
\(591\) −21.0109 28.9190i −0.864271 1.18957i
\(592\) −0.226569 0.444667i −0.00931193 0.0182757i
\(593\) −6.33839 + 6.33839i −0.260287 + 0.260287i −0.825170 0.564884i \(-0.808921\pi\)
0.564884 + 0.825170i \(0.308921\pi\)
\(594\) −23.7600 + 73.1258i −0.974885 + 3.00039i
\(595\) 0.292129 + 0.165064i 0.0119761 + 0.00676696i
\(596\) 1.47265 + 4.53234i 0.0603220 + 0.185652i
\(597\) −28.1002 14.3178i −1.15006 0.585987i
\(598\) −36.2629 + 5.74348i −1.48290 + 0.234868i
\(599\) 24.9376i 1.01892i −0.860494 0.509461i \(-0.829845\pi\)
0.860494 0.509461i \(-0.170155\pi\)
\(600\) 29.2266 29.2276i 1.19317 1.19321i
\(601\) 36.8240i 1.50208i −0.660255 0.751041i \(-0.729552\pi\)
0.660255 0.751041i \(-0.270448\pi\)
\(602\) 13.8184 + 6.43441i 0.563196 + 0.262247i
\(603\) −0.749708 + 1.47138i −0.0305305 + 0.0599194i
\(604\) −27.1066 + 8.80747i −1.10295 + 0.358371i
\(605\) −30.2845 + 25.8658i −1.23124 + 1.05159i
\(606\) −24.4689 + 75.3075i −0.993980 + 3.05916i
\(607\) 4.23143 + 4.23143i 0.171749 + 0.171749i 0.787747 0.615999i \(-0.211247\pi\)
−0.615999 + 0.787747i \(0.711247\pi\)
\(608\) 4.50809 + 8.84762i 0.182827 + 0.358818i
\(609\) −22.2061 + 0.787636i −0.899835 + 0.0319166i
\(610\) 24.1111 + 1.89738i 0.976229 + 0.0768226i
\(611\) 0.605307 + 0.439782i 0.0244881 + 0.0177917i
\(612\) 0.946577 + 0.149923i 0.0382631 + 0.00606028i
\(613\) −26.5533 4.20564i −1.07248 0.169864i −0.404869 0.914375i \(-0.632683\pi\)
−0.667610 + 0.744511i \(0.732683\pi\)
\(614\) 52.4721 + 38.1232i 2.11760 + 1.53853i
\(615\) 28.0046 17.1616i 1.12926 0.692022i
\(616\) 41.0129 1.45471i 1.65246 0.0586118i
\(617\) 7.30125 + 14.3295i 0.293937 + 0.576885i 0.989995 0.141101i \(-0.0450643\pi\)
−0.696058 + 0.717986i \(0.745064\pi\)
\(618\) −6.74526 6.74526i −0.271334 0.271334i
\(619\) 5.89867 18.1542i 0.237087 0.729680i −0.759750 0.650215i \(-0.774679\pi\)
0.996838 0.0794650i \(-0.0253212\pi\)
\(620\) −13.0377 31.4751i −0.523608 1.26407i
\(621\) −23.1502 + 7.52195i −0.928985 + 0.301846i
\(622\) 20.2831 39.8079i 0.813279 1.59615i
\(623\) 8.48680 + 3.95180i 0.340016 + 0.158325i
\(624\) 1.26451i 0.0506207i
\(625\) −0.000850295 25.0000i −3.40118e−5 1.00000i
\(626\) 66.3829i 2.65319i
\(627\) 27.2189 4.31105i 1.08702 0.172167i
\(628\) 44.0882 + 22.4640i 1.75931 + 0.896413i
\(629\) −0.0812793 0.250152i −0.00324082 0.00997422i
\(630\) 13.9831 68.9255i 0.557101 2.74606i
\(631\) 2.62144 8.06796i 0.104358 0.321180i −0.885221 0.465170i \(-0.845993\pi\)
0.989579 + 0.143990i \(0.0459932\pi\)
\(632\) 14.5282 14.5282i 0.577901 0.577901i
\(633\) −16.5029 32.3887i −0.655931 1.28734i
\(634\) 13.8484 + 19.0606i 0.549989 + 0.756995i
\(635\) −12.2454 19.9822i −0.485942 0.792971i
\(636\) −40.2269 + 55.3675i −1.59510 + 2.19547i
\(637\) −6.49882 28.0094i −0.257493 1.10977i
\(638\) −35.6963 5.65373i −1.41323 0.223833i
\(639\) 31.8534 43.8424i 1.26010 1.73438i
\(640\) 41.3075 + 3.25062i 1.63282 + 0.128492i
\(641\) 10.6927 7.76870i 0.422336 0.306845i −0.356241 0.934394i \(-0.615942\pi\)
0.778577 + 0.627549i \(0.215942\pi\)
\(642\) −43.8902 + 22.3632i −1.73221 + 0.882604i
\(643\) −3.32589 + 3.32589i −0.131160 + 0.131160i −0.769639 0.638479i \(-0.779564\pi\)
0.638479 + 0.769639i \(0.279564\pi\)
\(644\) 20.7095 + 26.4771i 0.816071 + 1.04334i
\(645\) 12.2186 10.4359i 0.481108 0.410912i
\(646\) −0.0721417 0.222029i −0.00283838 0.00873563i
\(647\) −9.80554 + 19.2445i −0.385496 + 0.756578i −0.999463 0.0327531i \(-0.989572\pi\)
0.613968 + 0.789331i \(0.289572\pi\)
\(648\) −1.04749 6.61357i −0.0411491 0.259805i
\(649\) −33.9182 −1.33141
\(650\) −33.3079 33.3068i −1.30644 1.30640i
\(651\) −29.3359 19.7640i −1.14977 0.774611i
\(652\) −79.9453 + 12.6621i −3.13090 + 0.495886i
\(653\) −2.68139 + 5.26252i −0.104931 + 0.205938i −0.937502 0.347980i \(-0.886868\pi\)
0.832571 + 0.553918i \(0.186868\pi\)
\(654\) −11.3265 34.8595i −0.442903 1.36312i
\(655\) 0.931115 + 11.8296i 0.0363817 + 0.462223i
\(656\) −0.525515 0.170750i −0.0205179 0.00666667i
\(657\) 58.6078 + 58.6078i 2.28651 + 2.28651i
\(658\) 0.134097 1.09710i 0.00522766 0.0427696i
\(659\) −4.96825 6.83821i −0.193536 0.266379i 0.701210 0.712954i \(-0.252643\pi\)
−0.894746 + 0.446576i \(0.852643\pi\)
\(660\) 42.8331 103.411i 1.66728 4.02526i
\(661\) −20.7537 + 28.5651i −0.807227 + 1.11105i 0.184518 + 0.982829i \(0.440928\pi\)
−0.991745 + 0.128224i \(0.959072\pi\)
\(662\) −0.0482921 + 0.304904i −0.00187692 + 0.0118504i
\(663\) 0.104255 0.658240i 0.00404893 0.0255639i
\(664\) −14.6255 10.6260i −0.567579 0.412370i
\(665\) −10.2301 + 2.84320i −0.396708 + 0.110255i
\(666\) −44.6019 + 32.4052i −1.72829 + 1.25567i
\(667\) −5.19438 10.1945i −0.201127 0.394734i
\(668\) 21.9223 21.9223i 0.848201 0.848201i
\(669\) 12.7501 + 4.14276i 0.492947 + 0.160168i
\(670\) 0.853672 1.39309i 0.0329802 0.0538199i
\(671\) 24.0750 7.82244i 0.929405 0.301982i
\(672\) 36.6137 20.3215i 1.41240 0.783920i
\(673\) −4.34533 27.4353i −0.167500 1.05755i −0.917970 0.396650i \(-0.870173\pi\)
0.750470 0.660905i \(-0.229827\pi\)
\(674\) 76.8453i 2.95997i
\(675\) −25.2653 18.3556i −0.972461 0.706509i
\(676\) −12.6250 −0.485577
\(677\) −3.99765 25.2402i −0.153642 0.970059i −0.937213 0.348757i \(-0.886604\pi\)
0.783571 0.621302i \(-0.213396\pi\)
\(678\) −81.6097 41.5822i −3.13420 1.59696i
\(679\) −11.1867 + 39.0935i −0.429306 + 1.50027i
\(680\) −0.356360 0.0855512i −0.0136658 0.00328074i
\(681\) 23.9373 73.6715i 0.917280 2.82310i
\(682\) −40.6826 40.6826i −1.55782 1.55782i
\(683\) −14.7319 + 7.50627i −0.563700 + 0.287220i −0.712528 0.701644i \(-0.752450\pi\)
0.148828 + 0.988863i \(0.452450\pi\)
\(684\) −24.5353 + 17.8259i −0.938131 + 0.681592i
\(685\) 10.7393 2.57836i 0.410326 0.0985142i
\(686\) −31.5188 + 28.4736i −1.20339 + 1.08713i
\(687\) 0.982100 6.20074i 0.0374695 0.236573i
\(688\) −0.267000 0.0422887i −0.0101793 0.00161224i
\(689\) 24.3873 + 17.7184i 0.929082 + 0.675018i
\(690\) 55.5945 13.3476i 2.11645 0.508133i
\(691\) −22.2601 30.6384i −0.846815 1.16554i −0.984556 0.175072i \(-0.943984\pi\)
0.137741 0.990468i \(-0.456016\pi\)
\(692\) −13.2492 + 6.75079i −0.503658 + 0.256626i
\(693\) −14.0852 72.2505i −0.535051 2.74457i
\(694\) −22.6159 7.34835i −0.858488 0.278940i
\(695\) −5.75932 + 23.9902i −0.218463 + 0.910000i
\(696\) 23.0816 7.49967i 0.874906 0.284274i
\(697\) −0.259480 0.132211i −0.00982849 0.00500787i
\(698\) 74.9830 11.8761i 2.83815 0.449518i
\(699\) −29.7555 −1.12546
\(700\) −11.8637 + 41.4619i −0.448404 + 1.56711i
\(701\) 14.8175 0.559649 0.279824 0.960051i \(-0.409724\pi\)
0.279824 + 0.960051i \(0.409724\pi\)
\(702\) −58.1161 + 9.20468i −2.19345 + 0.347408i
\(703\) 7.41612 + 3.77870i 0.279704 + 0.142516i
\(704\) 65.8757 21.4043i 2.48278 0.806705i
\(705\) −0.993448 0.608774i −0.0374154 0.0229278i
\(706\) −66.3155 21.5472i −2.49582 0.810940i
\(707\) −6.11003 31.3417i −0.229791 1.17872i
\(708\) 52.5070 26.7536i 1.97333 1.00546i
\(709\) 0.625238 + 0.860567i 0.0234813 + 0.0323193i 0.820596 0.571508i \(-0.193642\pi\)
−0.797115 + 0.603828i \(0.793642\pi\)
\(710\) −34.8212 + 40.7711i −1.30682 + 1.53011i
\(711\) −29.8148 21.6617i −1.11814 0.812378i
\(712\) −10.0993 1.59958i −0.378488 0.0599467i
\(713\) 2.84931 17.9899i 0.106708 0.673725i
\(714\) −0.924940 + 0.337225i −0.0346150 + 0.0126203i
\(715\) −45.5485 18.8664i −1.70342 0.705562i
\(716\) 5.01902 3.64653i 0.187570 0.136277i
\(717\) −46.3572 + 23.6202i −1.73124 + 0.882111i
\(718\) 32.3526 + 32.3526i 1.20739 + 1.20739i
\(719\) −4.35217 + 13.3946i −0.162309 + 0.499535i −0.998828 0.0484027i \(-0.984587\pi\)
0.836519 + 0.547938i \(0.184587\pi\)
\(720\) 0.0978699 + 1.24342i 0.00364740 + 0.0463395i
\(721\) 3.69840 + 1.05831i 0.137736 + 0.0394134i
\(722\) −32.2441 16.4292i −1.20000 0.611430i
\(723\) 4.99147 + 31.5149i 0.185635 + 1.17205i
\(724\) 57.5269 2.13797
\(725\) 6.66395 13.0793i 0.247493 0.485753i
\(726\) 116.856i 4.33694i
\(727\) 7.48439 + 47.2546i 0.277581 + 1.75258i 0.594474 + 0.804115i \(0.297360\pi\)
−0.316893 + 0.948461i \(0.602640\pi\)
\(728\) 15.2407 + 27.4595i 0.564859 + 1.01772i
\(729\) 39.5555 12.8524i 1.46502 0.476013i
\(730\) −53.2581 62.3561i −1.97117 2.30790i
\(731\) −0.135501 0.0440269i −0.00501168 0.00162839i
\(732\) −31.0991 + 31.0991i −1.14946 + 1.14946i
\(733\) 4.62099 + 9.06920i 0.170680 + 0.334979i 0.960463 0.278408i \(-0.0898068\pi\)
−0.789783 + 0.613387i \(0.789807\pi\)
\(734\) −31.6452 + 22.9916i −1.16805 + 0.848635i
\(735\) 13.5117 + 42.6891i 0.498385 + 1.57461i
\(736\) 17.4444 + 12.6741i 0.643009 + 0.467173i
\(737\) 0.267514 1.68902i 0.00985401 0.0622158i
\(738\) −9.54888 + 60.2893i −0.351499 + 2.21928i
\(739\) −14.7151 + 20.2536i −0.541305 + 0.745042i −0.988800 0.149244i \(-0.952316\pi\)
0.447496 + 0.894286i \(0.352316\pi\)
\(740\) 28.8242 17.6638i 1.05960 0.649336i
\(741\) 12.3960 + 17.0616i 0.455378 + 0.626774i
\(742\) 5.40266 44.2014i 0.198338 1.62268i
\(743\) 26.4566 + 26.4566i 0.970599 + 0.970599i 0.999580 0.0289813i \(-0.00922634\pi\)
−0.0289813 + 0.999580i \(0.509226\pi\)
\(744\) 36.7441 + 11.9389i 1.34710 + 0.437700i
\(745\) −3.01993 + 1.25093i −0.110642 + 0.0458304i
\(746\) −9.73026 29.9467i −0.356250 1.09643i
\(747\) −14.7213 + 28.8922i −0.538624 + 1.05711i
\(748\) −0.980223 + 0.155252i −0.0358405 + 0.00567658i
\(749\) 11.0990 16.4745i 0.405550 0.601964i
\(750\) 55.7787 + 47.6371i 2.03675 + 1.73946i
\(751\) −21.6815 −0.791168 −0.395584 0.918430i \(-0.629458\pi\)
−0.395584 + 0.918430i \(0.629458\pi\)
\(752\) 0.00306635 + 0.0193602i 0.000111818 + 0.000705992i
\(753\) −5.54989 + 10.8923i −0.202249 + 0.396936i
\(754\) −8.54667 26.3040i −0.311251 0.957934i
\(755\) −7.48143 18.0613i −0.272277 0.657319i
\(756\) 33.1898 + 42.4330i 1.20710 + 1.54327i
\(757\) 33.5839 33.5839i 1.22063 1.22063i 0.253218 0.967409i \(-0.418511\pi\)
0.967409 0.253218i \(-0.0814890\pi\)
\(758\) −31.2574 + 15.9264i −1.13532 + 0.578474i
\(759\) 48.4129 35.1740i 1.75728 1.27674i
\(760\) 9.88821 6.05962i 0.358683 0.219805i
\(761\) −12.0369 + 16.5674i −0.436339 + 0.600569i −0.969394 0.245512i \(-0.921044\pi\)
0.533055 + 0.846081i \(0.321044\pi\)
\(762\) 67.9163 + 10.7569i 2.46035 + 0.389681i
\(763\) 10.8157 + 10.0747i 0.391555 + 0.364730i
\(764\) −21.0723 + 29.0036i −0.762371 + 1.04931i
\(765\) −0.0515703 + 0.655333i −0.00186453 + 0.0236936i
\(766\) −2.48810 3.42458i −0.0898988 0.123735i
\(767\) −11.7840 23.1273i −0.425494 0.835080i
\(768\) −33.7605 + 33.7605i −1.21823 + 1.21823i
\(769\) 5.82407 17.9246i 0.210021 0.646379i −0.789448 0.613817i \(-0.789633\pi\)
0.999470 0.0325622i \(-0.0103667\pi\)
\(770\) 8.28480 + 72.3568i 0.298564 + 2.60756i
\(771\) 16.2325 + 49.9584i 0.584598 + 1.79921i
\(772\) 50.6815 + 25.8235i 1.82407 + 0.929409i
\(773\) 20.1452 3.19069i 0.724574 0.114761i 0.216756 0.976226i \(-0.430452\pi\)
0.507818 + 0.861465i \(0.330452\pi\)
\(774\) 29.8630i 1.07340i
\(775\) 20.8208 10.6092i 0.747906 0.381093i
\(776\) 44.4130i 1.59433i
\(777\) 14.8164 31.8194i 0.531536 1.14152i
\(778\) −32.1030 + 63.0058i −1.15095 + 2.25887i
\(779\) 8.76449 2.84775i 0.314020 0.102031i
\(780\) 85.3925 6.72127i 3.05754 0.240660i
\(781\) −17.3416 + 53.3718i −0.620530 + 1.90979i
\(782\) −0.358461 0.358461i −0.0128185 0.0128185i
\(783\) −8.32467 16.3381i −0.297500 0.583876i
\(784\) 0.398481 0.639261i 0.0142315 0.0228308i
\(785\) −12.9879 + 31.3563i −0.463558 + 1.11915i
\(786\) −28.1672 20.4647i −1.00469 0.729952i
\(787\) −23.6819 3.75084i −0.844168 0.133703i −0.280653 0.959809i \(-0.590551\pi\)
−0.563514 + 0.826106i \(0.690551\pi\)
\(788\) −40.2344 6.37250i −1.43329 0.227011i
\(789\) 17.1301 + 12.4457i 0.609847 + 0.443080i
\(790\) 27.7261 + 23.6800i 0.986452 + 0.842495i
\(791\) 36.9129 1.30928i 1.31247 0.0465526i
\(792\) 36.5009 + 71.6370i 1.29700 + 2.54551i
\(793\) 13.6980 + 13.6980i 0.486430 + 0.486430i
\(794\) −14.3867 + 44.2779i −0.510567 + 1.57136i
\(795\) −40.0251 24.5270i −1.41954 0.869882i
\(796\) −34.1812 + 11.1061i −1.21152 + 0.393647i
\(797\) 7.21547 14.1612i 0.255585 0.501614i −0.727186 0.686440i \(-0.759172\pi\)
0.982771 + 0.184826i \(0.0591723\pi\)
\(798\) 13.1507 28.2422i 0.465531 0.999764i
\(799\) 0.0103308i 0.000365476i
\(800\) 0.000470447 27.6638i 1.66328e−5 0.978061i
\(801\) 18.3409i 0.648042i
\(802\) −35.4333 + 5.61208i −1.25119 + 0.198170i
\(803\) −76.4751 38.9660i −2.69875 1.37508i
\(804\) 0.918121 + 2.82569i 0.0323796 + 0.0996543i
\(805\) −16.9903 + 15.5861i −0.598829 + 0.549339i
\(806\) 13.6056 41.8738i 0.479237 1.47494i
\(807\) −61.4933 + 61.4933i −2.16467 + 2.16467i
\(808\) 15.8338 + 31.0755i 0.557030 + 1.09323i
\(809\) 2.34198 + 3.22346i 0.0823395 + 0.113331i 0.848200 0.529676i \(-0.177687\pi\)
−0.765860 + 0.643007i \(0.777687\pi\)
\(810\) 11.5547 2.77415i 0.405992 0.0974737i
\(811\) −15.2527 + 20.9936i −0.535596 + 0.737184i −0.987970 0.154644i \(-0.950577\pi\)
0.452375 + 0.891828i \(0.350577\pi\)
\(812\) −17.2594 + 18.5287i −0.605685 + 0.650231i
\(813\) −34.1392 5.40712i −1.19731 0.189636i
\(814\) 33.5570 46.1873i 1.17617 1.61886i
\(815\) −12.9611 53.9847i −0.454006 1.89100i
\(816\) 0.0141251 0.0102625i 0.000494479 0.000359260i
\(817\) 4.01712 2.04682i 0.140541 0.0716093i
\(818\) −6.52074 + 6.52074i −0.227992 + 0.227992i
\(819\) 44.3709 34.7056i 1.55045 1.21271i
\(820\) 8.73753 36.3958i 0.305128 1.27100i
\(821\) −11.1428 34.2941i −0.388887 1.19687i −0.933621 0.358262i \(-0.883369\pi\)
0.544734 0.838609i \(-0.316631\pi\)
\(822\) −14.7117 + 28.8734i −0.513131 + 1.00708i
\(823\) −5.88359 37.1475i −0.205089 1.29488i −0.848433 0.529303i \(-0.822453\pi\)
0.643344 0.765577i \(-0.277547\pi\)
\(824\) −4.20165 −0.146371
\(825\) 73.0172 + 23.7233i 2.54213 + 0.825941i
\(826\) −21.4241 + 31.8001i −0.745441 + 1.10647i
\(827\) 26.5100 4.19877i 0.921843 0.146006i 0.322566 0.946547i \(-0.395455\pi\)
0.599277 + 0.800542i \(0.295455\pi\)
\(828\) −29.8974 + 58.6769i −1.03901 + 2.03916i
\(829\) −11.9948 36.9162i −0.416596 1.28215i −0.910815 0.412814i \(-0.864546\pi\)
0.494219 0.869338i \(-0.335454\pi\)
\(830\) 16.7627 27.3548i 0.581843 0.949500i
\(831\) −7.12941 2.31649i −0.247317 0.0803580i
\(832\) 37.4814 + 37.4814i 1.29943 + 1.29943i
\(833\) 0.260135 0.299915i 0.00901316 0.0103914i
\(834\) −42.5494 58.5643i −1.47337 2.02792i
\(835\) 16.1703 + 13.8105i 0.559596 + 0.477932i
\(836\) 18.4596 25.4074i 0.638438 0.878734i
\(837\) 4.56640 28.8311i 0.157838 0.996549i
\(838\) −13.6365 + 86.0973i −0.471064 + 2.97418i
\(839\) 21.8117 + 15.8471i 0.753022 + 0.547102i 0.896762 0.442513i \(-0.145913\pi\)
−0.143740 + 0.989615i \(0.545913\pi\)
\(840\) −27.0159 40.7672i −0.932136 1.40660i
\(841\) −16.4885 + 11.9796i −0.568570 + 0.413091i
\(842\) 34.8155 + 68.3293i 1.19982 + 2.35478i
\(843\) −34.1007 + 34.1007i −1.17449 + 1.17449i
\(844\) −39.3978 12.8011i −1.35613 0.440632i
\(845\) −0.679498 8.63291i −0.0233755 0.296981i
\(846\) 2.05938 0.669134i 0.0708030 0.0230053i
\(847\) 22.8687 + 41.2030i 0.785778 + 1.41575i
\(848\) 0.123540 + 0.780003i 0.00424239 + 0.0267854i
\(849\) 24.4714i 0.839856i
\(850\) 0.101731 0.642378i 0.00348936 0.0220334i
\(851\) 18.0738 0.619560
\(852\) −15.2525 96.3006i −0.522543 3.29920i
\(853\) 29.9423 + 15.2564i 1.02521 + 0.522368i 0.883939 0.467603i \(-0.154882\pi\)
0.141267 + 0.989971i \(0.454882\pi\)
\(854\) 7.87279 27.5126i 0.269401 0.941461i
\(855\) −13.5098 15.8177i −0.462026 0.540954i
\(856\) −6.70463 + 20.6347i −0.229160 + 0.705281i
\(857\) −15.3250 15.3250i −0.523492 0.523492i 0.395132 0.918624i \(-0.370699\pi\)
−0.918624 + 0.395132i \(0.870699\pi\)
\(858\) 128.888 65.6717i 4.40016 2.24199i
\(859\) 1.28743 0.935370i 0.0439264 0.0319144i −0.565605 0.824676i \(-0.691357\pi\)
0.609532 + 0.792762i \(0.291357\pi\)
\(860\) 1.43658 18.2554i 0.0489868 0.622504i
\(861\) −13.3118 36.5115i −0.453664 1.24431i
\(862\) −9.87668 + 62.3589i −0.336401 + 2.12395i
\(863\) 48.5993 + 7.69737i 1.65434 + 0.262022i 0.912656 0.408729i \(-0.134028\pi\)
0.741683 + 0.670750i \(0.234028\pi\)
\(864\) 27.9569 + 20.3119i 0.951115 + 0.691025i
\(865\) −5.32925 8.69637i −0.181200 0.295686i
\(866\) 24.7982 + 34.1317i 0.842676 + 1.15984i
\(867\) −43.3225 + 22.0739i −1.47131 + 0.749669i
\(868\) −39.5656 + 7.71328i −1.34294 + 0.261806i
\(869\) 36.2952 + 11.7930i 1.23123 + 0.400051i
\(870\) 16.4825 + 39.7912i 0.558808 + 1.34905i
\(871\) 1.24461 0.404398i 0.0421719 0.0137025i
\(872\) −14.3847 7.32939i −0.487129 0.248204i
\(873\) −78.6823 + 12.4621i −2.66299 + 0.421777i
\(874\) 16.0419 0.542624
\(875\) −28.9899 5.88076i −0.980039 0.198806i
\(876\) 149.122 5.03838
\(877\) 54.0963 8.56801i 1.82670 0.289321i 0.853810 0.520585i \(-0.174286\pi\)
0.972891 + 0.231264i \(0.0742861\pi\)
\(878\) 7.97096 + 4.06141i 0.269007 + 0.137066i
\(879\) −43.8551 + 14.2494i −1.47920 + 0.480620i
\(880\) −0.494284 1.19328i −0.0166623 0.0402254i
\(881\) 35.4735 + 11.5260i 1.19513 + 0.388322i 0.837968 0.545719i \(-0.183743\pi\)
0.357165 + 0.934041i \(0.383743\pi\)
\(882\) −76.6355 32.4308i −2.58045 1.09200i
\(883\) 18.4308 9.39096i 0.620245 0.316031i −0.115481 0.993310i \(-0.536841\pi\)
0.735726 + 0.677279i \(0.236841\pi\)
\(884\) −0.446412 0.614433i −0.0150144 0.0206656i
\(885\) 21.1200 + 34.4641i 0.709942 + 1.15850i
\(886\) 28.9872 + 21.0604i 0.973843 + 0.707538i
\(887\) −27.3441 4.33089i −0.918126 0.145417i −0.320552 0.947231i \(-0.603869\pi\)
−0.597574 + 0.801814i \(0.703869\pi\)
\(888\) −5.99727 + 37.8653i −0.201255 + 1.27068i
\(889\) −26.0521 + 9.49838i −0.873761 + 0.318565i
\(890\) 1.42358 18.0903i 0.0477186 0.606388i
\(891\) 10.0621 7.31056i 0.337094 0.244913i
\(892\) 13.6126 6.93595i 0.455783 0.232233i
\(893\) −0.231162 0.231162i −0.00773553 0.00773553i
\(894\) 2.96374 9.12144i 0.0991221 0.305067i
\(895\) 2.76361 + 3.23572i 0.0923774 + 0.108158i
\(896\) 13.4878 47.1350i 0.450596 1.57467i
\(897\) 40.8034 + 20.7904i 1.36239 + 0.694170i
\(898\) −6.66199 42.0622i −0.222314 1.40363i
\(899\) 13.7208 0.457615
\(900\) −83.4484 + 13.2184i −2.78161 + 0.440613i
\(901\) 0.416218i 0.0138662i
\(902\) −9.88830 62.4323i −0.329244 2.07877i
\(903\) −9.22665 16.6238i −0.307044 0.553207i
\(904\) −38.3683 + 12.4666i −1.27611 + 0.414634i
\(905\) 3.09620 + 39.3366i 0.102921 + 1.30759i
\(906\) 54.5527 + 17.7252i 1.81239 + 0.588882i
\(907\) −16.0029 + 16.0029i −0.531366 + 0.531366i −0.920979 0.389613i \(-0.872609\pi\)
0.389613 + 0.920979i \(0.372609\pi\)
\(908\) −40.0767 78.6550i −1.32999 2.61026i
\(909\) 50.6106 36.7708i 1.67865 1.21961i
\(910\) −46.4586 + 30.7874i −1.54009 + 1.02059i
\(911\) −10.9211 7.93464i −0.361832 0.262886i 0.391984 0.919972i \(-0.371789\pi\)
−0.753816 + 0.657086i \(0.771789\pi\)
\(912\) −0.0864302 + 0.545699i −0.00286199 + 0.0180699i
\(913\) 5.25292 33.1656i 0.173846 1.09762i
\(914\) 1.30568 1.79711i 0.0431879 0.0594431i
\(915\) −22.9392 19.5916i −0.758348 0.647679i
\(916\) −4.20527 5.78806i −0.138946 0.191243i
\(917\) 13.9366 + 1.70345i 0.460227 + 0.0562528i
\(918\) −0.574481 0.574481i −0.0189607 0.0189607i
\(919\) −41.4501 13.4679i −1.36731 0.444266i −0.468834 0.883286i \(-0.655326\pi\)
−0.898477 + 0.439020i \(0.855326\pi\)
\(920\) 13.1579 21.4721i 0.433802 0.707915i
\(921\) −24.9992 76.9396i −0.823751 2.53525i
\(922\) 30.6591 60.1719i 1.00970 1.98166i
\(923\) −42.4168 + 6.71815i −1.39616 + 0.221131i
\(924\) −109.837 73.9983i −3.61337 2.43437i
\(925\) 13.6298 + 18.7592i 0.448146 + 0.616797i
\(926\) 0.207263 0.00681108
\(927\) 1.17896 + 7.44366i 0.0387221 + 0.244482i
\(928\) −7.37424 + 14.4728i −0.242071 + 0.475092i
\(929\) 10.5302 + 32.4087i 0.345486 + 1.06330i 0.961323 + 0.275423i \(0.0888178\pi\)
−0.615838 + 0.787873i \(0.711182\pi\)
\(930\) −16.0053 + 66.6694i −0.524835 + 2.18618i
\(931\) 0.890104 + 12.5317i 0.0291720 + 0.410710i
\(932\) −23.9776 + 23.9776i −0.785411 + 0.785411i
\(933\) −49.6526 + 25.2992i −1.62555 + 0.828260i
\(934\) 46.6849 33.9186i 1.52758 1.10985i
\(935\) −0.158918 0.661916i −0.00519717 0.0216470i
\(936\) −36.1649 + 49.7766i −1.18209 + 1.62700i
\(937\) 6.94271 + 1.09962i 0.226808 + 0.0359229i 0.268804 0.963195i \(-0.413372\pi\)
−0.0419957 + 0.999118i \(0.513372\pi\)
\(938\) −1.41457 1.31766i −0.0461874 0.0430232i
\(939\) −48.6685 + 66.9864i −1.58824 + 2.18602i
\(940\) −1.29110 + 0.309977i −0.0421110 + 0.0101103i
\(941\) 2.95089 + 4.06155i 0.0961962 + 0.132403i 0.854402 0.519613i \(-0.173924\pi\)
−0.758206 + 0.652015i \(0.773924\pi\)
\(942\) −45.2094 88.7284i −1.47300 2.89093i
\(943\) 14.1501 14.1501i 0.460789 0.460789i
\(944\) 0.210135 0.646728i 0.00683930 0.0210492i
\(945\) −27.2292 + 24.9788i −0.885765 + 0.812561i
\(946\) −9.55619 29.4109i −0.310699 0.956232i
\(947\) −30.3622 15.4703i −0.986638 0.502717i −0.115263 0.993335i \(-0.536771\pi\)
−0.871375 + 0.490618i \(0.836771\pi\)
\(948\) −65.4887 + 10.3724i −2.12697 + 0.336880i
\(949\) 65.6827i 2.13215i
\(950\) 12.0975 + 16.6502i 0.392495 + 0.540204i
\(951\) 29.3868i 0.952933i
\(952\) −0.183045 + 0.393103i −0.00593252 + 0.0127406i
\(953\) −12.6149 + 24.7581i −0.408636 + 0.801993i −0.999990 0.00441907i \(-0.998593\pi\)
0.591355 + 0.806412i \(0.298593\pi\)
\(954\) 82.9706 26.9588i 2.68627 0.872823i
\(955\) −20.9667 12.8481i −0.678465 0.415756i
\(956\) −18.3219 + 56.3890i −0.592573 + 1.82375i
\(957\) 31.8758 + 31.8758i 1.03040 + 1.03040i
\(958\) −32.4364 63.6600i −1.04797 2.05676i
\(959\) −0.463222 13.0597i −0.0149582 0.421721i
\(960\) −62.7679 53.6080i −2.02583 1.73019i
\(961\) −7.40863 5.38268i −0.238988 0.173635i
\(962\) 43.1515 + 6.83453i 1.39126 + 0.220354i
\(963\) 38.4379 + 6.08796i 1.23864 + 0.196182i
\(964\) 29.4175 + 21.3731i 0.947474 + 0.688380i
\(965\) −14.9302 + 36.0457i −0.480621 + 1.16035i
\(966\) −2.39798 67.6071i −0.0771539 2.17522i
\(967\) 5.66458 + 11.1174i 0.182161 + 0.357511i 0.963972 0.266005i \(-0.0857038\pi\)
−0.781811 + 0.623516i \(0.785704\pi\)
\(968\) −36.3950 36.3950i −1.16978 1.16978i
\(969\) −0.0899827 + 0.276938i −0.00289066 + 0.00889654i
\(970\) 78.5747 6.18463i 2.52288 0.198577i
\(971\) 56.5388 18.3706i 1.81442 0.589540i 0.814460 0.580220i \(-0.197033\pi\)
0.999957 0.00932016i \(-0.00296674\pi\)
\(972\) 17.9214 35.1728i 0.574831 1.12817i
\(973\) 26.4638 + 12.3226i 0.848390 + 0.395045i
\(974\) 21.1331i 0.677147i
\(975\) 9.19194 + 58.0292i 0.294378 + 1.85842i
\(976\) 0.507507i 0.0162449i
\(977\) 5.59602 0.886323i 0.179033 0.0283560i −0.0662744 0.997801i \(-0.521111\pi\)
0.245307 + 0.969445i \(0.421111\pi\)
\(978\) 145.143 + 73.9538i 4.64115 + 2.36478i
\(979\) −5.86909 18.0632i −0.187577 0.577303i
\(980\) 45.2876 + 23.5117i 1.44666 + 0.751054i
\(981\) −8.94850 + 27.5406i −0.285704 + 0.879305i
\(982\) 30.3804 30.3804i 0.969476 0.969476i
\(983\) 16.2624 + 31.9168i 0.518690 + 1.01799i 0.990658 + 0.136371i \(0.0435438\pi\)
−0.471968 + 0.881616i \(0.656456\pi\)
\(984\) 24.9497 + 34.3403i 0.795366 + 1.09473i
\(985\) 2.19200 27.8550i 0.0698430 0.887535i
\(986\) 0.224465 0.308949i 0.00714841 0.00983894i
\(987\) −0.939656 + 1.00877i −0.0299096 + 0.0321094i
\(988\) 23.7375 + 3.75965i 0.755190 + 0.119610i
\(989\) 5.75447 7.92034i 0.182981 0.251852i
\(990\) −121.656 + 74.5523i −3.86648 + 2.36943i
\(991\) −0.769865 + 0.559340i −0.0244556 + 0.0177680i −0.599946 0.800041i \(-0.704811\pi\)
0.575490 + 0.817809i \(0.304811\pi\)
\(992\) −23.0395 + 11.7392i −0.731504 + 0.372720i
\(993\) 0.272271 0.272271i 0.00864025 0.00864025i
\(994\) 39.0853 + 49.9705i 1.23971 + 1.58497i
\(995\) −9.43401 22.7752i −0.299078 0.722021i
\(996\) 18.0283 + 55.4853i 0.571248 + 1.75812i
\(997\) 1.85833 3.64717i 0.0588538 0.115507i −0.859706 0.510789i \(-0.829353\pi\)
0.918560 + 0.395282i \(0.129353\pi\)
\(998\) 0.383844 + 2.42350i 0.0121504 + 0.0767144i
\(999\) 28.9656 0.916430
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 175.2.s.a.13.4 yes 144
5.2 odd 4 875.2.s.b.832.4 144
5.3 odd 4 875.2.s.a.832.15 144
5.4 even 2 875.2.s.c.293.15 144
7.6 odd 2 inner 175.2.s.a.13.3 144
25.2 odd 20 inner 175.2.s.a.27.3 yes 144
25.11 even 5 875.2.s.b.468.3 144
25.14 even 10 875.2.s.a.468.16 144
25.23 odd 20 875.2.s.c.657.16 144
35.13 even 4 875.2.s.a.832.16 144
35.27 even 4 875.2.s.b.832.3 144
35.34 odd 2 875.2.s.c.293.16 144
175.27 even 20 inner 175.2.s.a.27.4 yes 144
175.48 even 20 875.2.s.c.657.15 144
175.111 odd 10 875.2.s.b.468.4 144
175.139 odd 10 875.2.s.a.468.15 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.s.a.13.3 144 7.6 odd 2 inner
175.2.s.a.13.4 yes 144 1.1 even 1 trivial
175.2.s.a.27.3 yes 144 25.2 odd 20 inner
175.2.s.a.27.4 yes 144 175.27 even 20 inner
875.2.s.a.468.15 144 175.139 odd 10
875.2.s.a.468.16 144 25.14 even 10
875.2.s.a.832.15 144 5.3 odd 4
875.2.s.a.832.16 144 35.13 even 4
875.2.s.b.468.3 144 25.11 even 5
875.2.s.b.468.4 144 175.111 odd 10
875.2.s.b.832.3 144 35.27 even 4
875.2.s.b.832.4 144 5.2 odd 4
875.2.s.c.293.15 144 5.4 even 2
875.2.s.c.293.16 144 35.34 odd 2
875.2.s.c.657.15 144 175.48 even 20
875.2.s.c.657.16 144 25.23 odd 20