Properties

Label 73.2.h.a.49.4
Level $73$
Weight $2$
Character 73.49
Analytic conductor $0.583$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [73,2,Mod(3,73)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(73, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("73.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 73.h (of order \(12\), 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: \(0.582907934755\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 28 x^{18} + 326 x^{16} + 2044 x^{14} + 7471 x^{12} + 16090 x^{10} + 19590 x^{8} + 12030 x^{6} + 2877 x^{4} + 230 x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.4
Root \(-0.0678852i\) of defining polynomial
Character \(\chi\) \(=\) 73.49
Dual form 73.2.h.a.3.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0339426 + 0.0587903i) q^{2} -1.73613i q^{3} +(0.997696 - 1.72806i) q^{4} +(-2.59207 + 0.694543i) q^{5} +(0.102067 - 0.0589286i) q^{6} +(0.823696 + 0.823696i) q^{7} +0.271228 q^{8} -0.0141334 q^{9} +O(q^{10})\) \(q+(0.0339426 + 0.0587903i) q^{2} -1.73613i q^{3} +(0.997696 - 1.72806i) q^{4} +(-2.59207 + 0.694543i) q^{5} +(0.102067 - 0.0589286i) q^{6} +(0.823696 + 0.823696i) q^{7} +0.271228 q^{8} -0.0141334 q^{9} +(-0.128814 - 0.128814i) q^{10} +(1.27209 + 4.74749i) q^{11} +(-3.00013 - 1.73213i) q^{12} +(4.09939 + 1.09843i) q^{13} +(-0.0204669 + 0.0763837i) q^{14} +(1.20581 + 4.50016i) q^{15} +(-1.98619 - 3.44017i) q^{16} +(-3.48348 - 3.48348i) q^{17} +(-0.000479724 - 0.000830906i) q^{18} +(-6.00388 + 3.46634i) q^{19} +(-1.38588 + 5.17219i) q^{20} +(1.43004 - 1.43004i) q^{21} +(-0.235928 + 0.235928i) q^{22} +(-0.846521 - 0.488739i) q^{23} -0.470886i q^{24} +(1.90630 - 1.10060i) q^{25} +(0.0745669 + 0.278287i) q^{26} -5.18384i q^{27} +(2.24519 - 0.601598i) q^{28} +(4.74401 + 1.27115i) q^{29} +(-0.223637 + 0.223637i) q^{30} +(-0.234430 - 0.0628153i) q^{31} +(0.406060 - 0.703317i) q^{32} +(8.24224 - 2.20850i) q^{33} +(0.0865564 - 0.323033i) q^{34} +(-2.70717 - 1.56298i) q^{35} +(-0.0141008 + 0.0244233i) q^{36} +(0.324066 - 0.561299i) q^{37} +(-0.407574 - 0.235313i) q^{38} +(1.90701 - 7.11705i) q^{39} +(-0.703041 + 0.188379i) q^{40} +(-3.76100 + 6.51424i) q^{41} +(0.132612 + 0.0355332i) q^{42} +(-3.45863 + 3.45863i) q^{43} +(9.47310 + 2.53831i) q^{44} +(0.0366347 - 0.00981624i) q^{45} -0.0663563i q^{46} +(-2.08759 - 7.79100i) q^{47} +(-5.97258 + 3.44827i) q^{48} -5.64305i q^{49} +(0.129410 + 0.0747146i) q^{50} +(-6.04775 + 6.04775i) q^{51} +(5.98809 - 5.98809i) q^{52} +(0.988907 - 3.69065i) q^{53} +(0.304759 - 0.175953i) q^{54} +(-6.59467 - 11.4223i) q^{55} +(0.223409 + 0.223409i) q^{56} +(6.01801 + 10.4235i) q^{57} +(0.0862925 + 0.322048i) q^{58} +(-1.75624 + 6.55437i) q^{59} +(8.97957 + 2.40607i) q^{60} +(9.03876 + 5.21853i) q^{61} +(-0.00426423 - 0.0159143i) q^{62} +(-0.0116416 - 0.0116416i) q^{63} -7.88961 q^{64} -11.3888 q^{65} +(0.409601 + 0.409601i) q^{66} +(-8.32687 + 4.80752i) q^{67} +(-9.49511 + 2.54421i) q^{68} +(-0.848513 + 1.46967i) q^{69} -0.212207i q^{70} +(2.40595 + 4.16722i) q^{71} -0.00383337 q^{72} +(5.64828 - 6.41069i) q^{73} +0.0439986 q^{74} +(-1.91079 - 3.30958i) q^{75} +13.8334i q^{76} +(-2.86267 + 4.95830i) q^{77} +(0.483142 - 0.129458i) q^{78} +(8.33547 - 4.81249i) q^{79} +(7.53767 + 7.53767i) q^{80} -9.04220 q^{81} -0.510632 q^{82} +(-5.35635 - 5.35635i) q^{83} +(-1.04445 - 3.89794i) q^{84} +(11.4488 + 6.60998i) q^{85} +(-0.320729 - 0.0859390i) q^{86} +(2.20688 - 8.23620i) q^{87} +(0.345025 + 1.28765i) q^{88} +(-6.08382 - 10.5375i) q^{89} +(0.00182058 + 0.00182058i) q^{90} +(2.47188 + 4.28142i) q^{91} +(-1.68914 + 0.975226i) q^{92} +(-0.109055 + 0.407000i) q^{93} +(0.387177 - 0.387177i) q^{94} +(13.1549 - 13.1549i) q^{95} +(-1.22105 - 0.704972i) q^{96} -7.81504i q^{97} +(0.331757 - 0.191540i) q^{98} +(-0.0179789 - 0.0670981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{2} - 8 q^{4} - 4 q^{5} + 6 q^{6} - 2 q^{7} + 12 q^{8} - 32 q^{9} - 12 q^{10} - 6 q^{11} + 30 q^{12} - 16 q^{13} - 8 q^{14} + 8 q^{15} - 4 q^{16} + 8 q^{17} + 4 q^{18} - 12 q^{19} + 8 q^{20} + 24 q^{21} + 8 q^{22} - 6 q^{23} - 36 q^{25} - 36 q^{26} - 12 q^{28} - 6 q^{29} + 34 q^{30} + 20 q^{31} - 6 q^{32} + 34 q^{33} + 36 q^{34} + 18 q^{35} + 18 q^{36} - 8 q^{37} - 66 q^{38} + 28 q^{39} - 2 q^{40} + 10 q^{41} - 56 q^{42} + 12 q^{43} + 34 q^{44} - 4 q^{45} - 20 q^{47} - 48 q^{48} + 30 q^{50} - 36 q^{51} + 80 q^{52} + 24 q^{53} + 24 q^{54} + 10 q^{55} + 10 q^{57} + 54 q^{58} - 18 q^{59} + 50 q^{60} + 42 q^{61} - 12 q^{62} - 48 q^{63} - 56 q^{64} - 44 q^{65} - 10 q^{66} - 42 q^{67} - 44 q^{68} + 24 q^{69} + 4 q^{71} - 112 q^{72} - 16 q^{73} - 96 q^{74} - 52 q^{75} + 52 q^{77} - 12 q^{78} + 54 q^{79} - 2 q^{80} + 60 q^{81} + 32 q^{82} - 30 q^{83} - 16 q^{84} + 6 q^{85} + 16 q^{86} + 32 q^{87} + 2 q^{88} - 22 q^{89} - 110 q^{90} - 8 q^{91} - 78 q^{92} + 78 q^{93} + 38 q^{94} + 38 q^{95} + 72 q^{96} + 138 q^{98} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/73\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0339426 + 0.0587903i 0.0240010 + 0.0415710i 0.877776 0.479070i \(-0.159026\pi\)
−0.853775 + 0.520641i \(0.825693\pi\)
\(3\) 1.73613i 1.00235i −0.865345 0.501176i \(-0.832901\pi\)
0.865345 0.501176i \(-0.167099\pi\)
\(4\) 0.997696 1.72806i 0.498848 0.864030i
\(5\) −2.59207 + 0.694543i −1.15921 + 0.310609i −0.786650 0.617400i \(-0.788186\pi\)
−0.372559 + 0.928009i \(0.621519\pi\)
\(6\) 0.102067 0.0589286i 0.0416688 0.0240575i
\(7\) 0.823696 + 0.823696i 0.311328 + 0.311328i 0.845424 0.534096i \(-0.179348\pi\)
−0.534096 + 0.845424i \(0.679348\pi\)
\(8\) 0.271228 0.0958935
\(9\) −0.0141334 −0.00471113
\(10\) −0.128814 0.128814i −0.0407345 0.0407345i
\(11\) 1.27209 + 4.74749i 0.383548 + 1.43142i 0.840443 + 0.541901i \(0.182295\pi\)
−0.456894 + 0.889521i \(0.651038\pi\)
\(12\) −3.00013 1.73213i −0.866063 0.500022i
\(13\) 4.09939 + 1.09843i 1.13696 + 0.304649i 0.777730 0.628598i \(-0.216371\pi\)
0.359235 + 0.933247i \(0.383038\pi\)
\(14\) −0.0204669 + 0.0763837i −0.00547002 + 0.0204144i
\(15\) 1.20581 + 4.50016i 0.311340 + 1.16194i
\(16\) −1.98619 3.44017i −0.496546 0.860044i
\(17\) −3.48348 3.48348i −0.844867 0.844867i 0.144620 0.989487i \(-0.453804\pi\)
−0.989487 + 0.144620i \(0.953804\pi\)
\(18\) −0.000479724 0 0.000830906i −0.000113072 0 0.000195846i
\(19\) −6.00388 + 3.46634i −1.37738 + 0.795233i −0.991844 0.127457i \(-0.959318\pi\)
−0.385541 + 0.922691i \(0.625985\pi\)
\(20\) −1.38588 + 5.17219i −0.309893 + 1.15654i
\(21\) 1.43004 1.43004i 0.312060 0.312060i
\(22\) −0.235928 + 0.235928i −0.0503001 + 0.0503001i
\(23\) −0.846521 0.488739i −0.176512 0.101909i 0.409141 0.912471i \(-0.365828\pi\)
−0.585653 + 0.810562i \(0.699162\pi\)
\(24\) 0.470886i 0.0961191i
\(25\) 1.90630 1.10060i 0.381260 0.220121i
\(26\) 0.0745669 + 0.278287i 0.0146238 + 0.0545767i
\(27\) 5.18384i 0.997631i
\(28\) 2.24519 0.601598i 0.424302 0.113691i
\(29\) 4.74401 + 1.27115i 0.880941 + 0.236047i 0.670813 0.741627i \(-0.265945\pi\)
0.210128 + 0.977674i \(0.432612\pi\)
\(30\) −0.223637 + 0.223637i −0.0408304 + 0.0408304i
\(31\) −0.234430 0.0628153i −0.0421048 0.0112820i 0.237705 0.971337i \(-0.423605\pi\)
−0.279810 + 0.960055i \(0.590271\pi\)
\(32\) 0.406060 0.703317i 0.0717820 0.124330i
\(33\) 8.24224 2.20850i 1.43479 0.384451i
\(34\) 0.0865564 0.323033i 0.0148443 0.0553997i
\(35\) −2.70717 1.56298i −0.457595 0.264192i
\(36\) −0.0141008 + 0.0244233i −0.00235014 + 0.00407056i
\(37\) 0.324066 0.561299i 0.0532762 0.0922771i −0.838157 0.545428i \(-0.816367\pi\)
0.891434 + 0.453151i \(0.149700\pi\)
\(38\) −0.407574 0.235313i −0.0661173 0.0381728i
\(39\) 1.90701 7.11705i 0.305366 1.13964i
\(40\) −0.703041 + 0.188379i −0.111161 + 0.0297854i
\(41\) −3.76100 + 6.51424i −0.587369 + 1.01735i 0.407207 + 0.913336i \(0.366503\pi\)
−0.994576 + 0.104017i \(0.966830\pi\)
\(42\) 0.132612 + 0.0355332i 0.0204624 + 0.00548289i
\(43\) −3.45863 + 3.45863i −0.527436 + 0.527436i −0.919807 0.392371i \(-0.871655\pi\)
0.392371 + 0.919807i \(0.371655\pi\)
\(44\) 9.47310 + 2.53831i 1.42812 + 0.382665i
\(45\) 0.0366347 0.00981624i 0.00546118 0.00146332i
\(46\) 0.0663563i 0.00978370i
\(47\) −2.08759 7.79100i −0.304507 1.13643i −0.933369 0.358917i \(-0.883146\pi\)
0.628863 0.777516i \(-0.283521\pi\)
\(48\) −5.97258 + 3.44827i −0.862067 + 0.497715i
\(49\) 5.64305i 0.806150i
\(50\) 0.129410 + 0.0747146i 0.0183013 + 0.0105662i
\(51\) −6.04775 + 6.04775i −0.846855 + 0.846855i
\(52\) 5.98809 5.98809i 0.830398 0.830398i
\(53\) 0.988907 3.69065i 0.135837 0.506950i −0.864156 0.503224i \(-0.832147\pi\)
0.999993 0.00372640i \(-0.00118615\pi\)
\(54\) 0.304759 0.175953i 0.0414725 0.0239442i
\(55\) −6.59467 11.4223i −0.889225 1.54018i
\(56\) 0.223409 + 0.223409i 0.0298543 + 0.0298543i
\(57\) 6.01801 + 10.4235i 0.797104 + 1.38063i
\(58\) 0.0862925 + 0.322048i 0.0113308 + 0.0422870i
\(59\) −1.75624 + 6.55437i −0.228643 + 0.853307i 0.752269 + 0.658856i \(0.228959\pi\)
−0.980912 + 0.194451i \(0.937707\pi\)
\(60\) 8.97957 + 2.40607i 1.15926 + 0.310622i
\(61\) 9.03876 + 5.21853i 1.15729 + 0.668164i 0.950654 0.310253i \(-0.100414\pi\)
0.206640 + 0.978417i \(0.433747\pi\)
\(62\) −0.00426423 0.0159143i −0.000541557 0.00202112i
\(63\) −0.0116416 0.0116416i −0.00146671 0.00146671i
\(64\) −7.88961 −0.986201
\(65\) −11.3888 −1.41261
\(66\) 0.409601 + 0.409601i 0.0504184 + 0.0504184i
\(67\) −8.32687 + 4.80752i −1.01729 + 0.587332i −0.913317 0.407248i \(-0.866488\pi\)
−0.103971 + 0.994580i \(0.533155\pi\)
\(68\) −9.49511 + 2.54421i −1.15145 + 0.308530i
\(69\) −0.848513 + 1.46967i −0.102149 + 0.176927i
\(70\) 0.212207i 0.0253636i
\(71\) 2.40595 + 4.16722i 0.285533 + 0.494558i 0.972738 0.231905i \(-0.0744960\pi\)
−0.687205 + 0.726463i \(0.741163\pi\)
\(72\) −0.00383337 −0.000451767
\(73\) 5.64828 6.41069i 0.661081 0.750315i
\(74\) 0.0439986 0.00511473
\(75\) −1.91079 3.30958i −0.220638 0.382157i
\(76\) 13.8334i 1.58680i
\(77\) −2.86267 + 4.95830i −0.326232 + 0.565050i
\(78\) 0.483142 0.129458i 0.0547051 0.0146582i
\(79\) 8.33547 4.81249i 0.937814 0.541447i 0.0485396 0.998821i \(-0.484543\pi\)
0.889274 + 0.457374i \(0.151210\pi\)
\(80\) 7.53767 + 7.53767i 0.842738 + 0.842738i
\(81\) −9.04220 −1.00469
\(82\) −0.510632 −0.0563898
\(83\) −5.35635 5.35635i −0.587935 0.587935i 0.349137 0.937072i \(-0.386475\pi\)
−0.937072 + 0.349137i \(0.886475\pi\)
\(84\) −1.04445 3.89794i −0.113959 0.425300i
\(85\) 11.4488 + 6.60998i 1.24180 + 0.716954i
\(86\) −0.320729 0.0859390i −0.0345850 0.00926704i
\(87\) 2.20688 8.23620i 0.236603 0.883014i
\(88\) 0.345025 + 1.28765i 0.0367798 + 0.137264i
\(89\) −6.08382 10.5375i −0.644884 1.11697i −0.984328 0.176345i \(-0.943573\pi\)
0.339445 0.940626i \(-0.389761\pi\)
\(90\) 0.00182058 + 0.00182058i 0.000191906 + 0.000191906i
\(91\) 2.47188 + 4.28142i 0.259123 + 0.448814i
\(92\) −1.68914 + 0.975226i −0.176105 + 0.101674i
\(93\) −0.109055 + 0.407000i −0.0113085 + 0.0422039i
\(94\) 0.387177 0.387177i 0.0399342 0.0399342i
\(95\) 13.1549 13.1549i 1.34967 1.34967i
\(96\) −1.22105 0.704972i −0.124623 0.0719509i
\(97\) 7.81504i 0.793497i −0.917927 0.396748i \(-0.870139\pi\)
0.917927 0.396748i \(-0.129861\pi\)
\(98\) 0.331757 0.191540i 0.0335125 0.0193484i
\(99\) −0.0179789 0.0670981i −0.00180695 0.00674361i
\(100\) 4.39227i 0.439227i
\(101\) 7.15774 1.91791i 0.712222 0.190839i 0.115523 0.993305i \(-0.463146\pi\)
0.596698 + 0.802466i \(0.296479\pi\)
\(102\) −0.560826 0.150273i −0.0555300 0.0148792i
\(103\) −11.3429 + 11.3429i −1.11765 + 1.11765i −0.125561 + 0.992086i \(0.540073\pi\)
−0.992086 + 0.125561i \(0.959927\pi\)
\(104\) 1.11187 + 0.297924i 0.109028 + 0.0292139i
\(105\) −2.71354 + 4.69998i −0.264814 + 0.458671i
\(106\) 0.250541 0.0671321i 0.0243347 0.00652045i
\(107\) 1.45576 5.43296i 0.140733 0.525224i −0.859175 0.511682i \(-0.829023\pi\)
0.999908 0.0135419i \(-0.00431066\pi\)
\(108\) −8.95799 5.17190i −0.861983 0.497666i
\(109\) −4.52854 + 7.84365i −0.433755 + 0.751286i −0.997193 0.0748725i \(-0.976145\pi\)
0.563438 + 0.826158i \(0.309478\pi\)
\(110\) 0.447680 0.775405i 0.0426846 0.0739319i
\(111\) −0.974487 0.562620i −0.0924942 0.0534015i
\(112\) 1.19764 4.46967i 0.113167 0.422344i
\(113\) 9.55680 2.56074i 0.899028 0.240894i 0.220429 0.975403i \(-0.429254\pi\)
0.678599 + 0.734509i \(0.262587\pi\)
\(114\) −0.408533 + 0.707601i −0.0382627 + 0.0662729i
\(115\) 2.53369 + 0.678900i 0.236268 + 0.0633078i
\(116\) 6.92971 6.92971i 0.643408 0.643408i
\(117\) −0.0579382 0.0155245i −0.00535639 0.00143524i
\(118\) −0.444945 + 0.119223i −0.0409605 + 0.0109753i
\(119\) 5.73865i 0.526061i
\(120\) 0.327050 + 1.22057i 0.0298555 + 0.111422i
\(121\) −11.3942 + 6.57843i −1.03583 + 0.598039i
\(122\) 0.708522i 0.0641465i
\(123\) 11.3095 + 6.52956i 1.01975 + 0.588751i
\(124\) −0.342438 + 0.342438i −0.0307519 + 0.0307519i
\(125\) 5.31078 5.31078i 0.475011 0.475011i
\(126\) 0.000289267 0.00107956i 2.57700e−5 9.61749e-5i
\(127\) 12.3743 7.14432i 1.09804 0.633956i 0.162338 0.986735i \(-0.448097\pi\)
0.935707 + 0.352779i \(0.114763\pi\)
\(128\) −1.07991 1.87047i −0.0954519 0.165327i
\(129\) 6.00461 + 6.00461i 0.528677 + 0.528677i
\(130\) −0.386565 0.669550i −0.0339040 0.0587234i
\(131\) 2.75065 + 10.2656i 0.240325 + 0.896906i 0.975676 + 0.219219i \(0.0703509\pi\)
−0.735351 + 0.677687i \(0.762982\pi\)
\(132\) 4.40682 16.4465i 0.383565 1.43148i
\(133\) −7.80058 2.09016i −0.676396 0.181240i
\(134\) −0.565271 0.326359i −0.0488320 0.0281931i
\(135\) 3.60040 + 13.4369i 0.309873 + 1.15646i
\(136\) −0.944816 0.944816i −0.0810173 0.0810173i
\(137\) 11.3379 0.968666 0.484333 0.874884i \(-0.339062\pi\)
0.484333 + 0.874884i \(0.339062\pi\)
\(138\) −0.115203 −0.00980672
\(139\) −2.05738 2.05738i −0.174505 0.174505i 0.614451 0.788955i \(-0.289378\pi\)
−0.788955 + 0.614451i \(0.789378\pi\)
\(140\) −5.40186 + 3.11876i −0.456540 + 0.263584i
\(141\) −13.5262 + 3.62432i −1.13911 + 0.305223i
\(142\) −0.163328 + 0.282892i −0.0137062 + 0.0237398i
\(143\) 20.8591i 1.74432i
\(144\) 0.0280715 + 0.0486213i 0.00233929 + 0.00405178i
\(145\) −13.1797 −1.09451
\(146\) 0.568604 + 0.114468i 0.0470580 + 0.00947346i
\(147\) −9.79705 −0.808047
\(148\) −0.646639 1.12001i −0.0531534 0.0920644i
\(149\) 24.2427i 1.98604i −0.117948 0.993020i \(-0.537632\pi\)
0.117948 0.993020i \(-0.462368\pi\)
\(150\) 0.129714 0.224671i 0.0105911 0.0183443i
\(151\) −15.4768 + 4.14699i −1.25948 + 0.337477i −0.825993 0.563681i \(-0.809385\pi\)
−0.433490 + 0.901158i \(0.642718\pi\)
\(152\) −1.62842 + 0.940169i −0.132082 + 0.0762577i
\(153\) 0.0492333 + 0.0492333i 0.00398028 + 0.00398028i
\(154\) −0.388666 −0.0313196
\(155\) 0.651286 0.0523125
\(156\) −10.3961 10.3961i −0.832352 0.832352i
\(157\) 5.81557 + 21.7040i 0.464133 + 1.73217i 0.659748 + 0.751487i \(0.270663\pi\)
−0.195614 + 0.980681i \(0.562670\pi\)
\(158\) 0.565855 + 0.326697i 0.0450170 + 0.0259906i
\(159\) −6.40744 1.71687i −0.508143 0.136156i
\(160\) −0.564052 + 2.10507i −0.0445923 + 0.166421i
\(161\) −0.294703 1.09985i −0.0232259 0.0866802i
\(162\) −0.306916 0.531594i −0.0241136 0.0417659i
\(163\) 3.31654 + 3.31654i 0.259771 + 0.259771i 0.824961 0.565190i \(-0.191197\pi\)
−0.565190 + 0.824961i \(0.691197\pi\)
\(164\) 7.50466 + 12.9985i 0.586015 + 1.01501i
\(165\) −19.8305 + 11.4492i −1.54381 + 0.891317i
\(166\) 0.133093 0.496709i 0.0103300 0.0385521i
\(167\) −0.992375 + 0.992375i −0.0767923 + 0.0767923i −0.744460 0.667667i \(-0.767293\pi\)
0.667667 + 0.744460i \(0.267293\pi\)
\(168\) 0.387866 0.387866i 0.0299245 0.0299245i
\(169\) 4.34009 + 2.50575i 0.333853 + 0.192750i
\(170\) 0.897440i 0.0688305i
\(171\) 0.0848552 0.0489912i 0.00648904 0.00374645i
\(172\) 2.52606 + 9.42738i 0.192610 + 0.718831i
\(173\) 3.22831i 0.245444i −0.992441 0.122722i \(-0.960838\pi\)
0.992441 0.122722i \(-0.0391624\pi\)
\(174\) 0.559116 0.149815i 0.0423865 0.0113574i
\(175\) 2.47677 + 0.663649i 0.187226 + 0.0501672i
\(176\) 13.8056 13.8056i 1.04064 1.04064i
\(177\) 11.3792 + 3.04905i 0.855314 + 0.229181i
\(178\) 0.413001 0.715339i 0.0309557 0.0536169i
\(179\) −6.59345 + 1.76671i −0.492817 + 0.132050i −0.496664 0.867943i \(-0.665442\pi\)
0.00384724 + 0.999993i \(0.498775\pi\)
\(180\) 0.0195872 0.0731006i 0.00145995 0.00544860i
\(181\) 4.70046 + 2.71381i 0.349382 + 0.201716i 0.664413 0.747365i \(-0.268682\pi\)
−0.315031 + 0.949081i \(0.602015\pi\)
\(182\) −0.167804 + 0.290645i −0.0124384 + 0.0215440i
\(183\) 9.06003 15.6924i 0.669736 1.16002i
\(184\) −0.229600 0.132560i −0.0169263 0.00977243i
\(185\) −0.450156 + 1.68000i −0.0330961 + 0.123516i
\(186\) −0.0276292 + 0.00740323i −0.00202587 + 0.000542831i
\(187\) 12.1065 20.9690i 0.885314 1.53341i
\(188\) −15.5461 4.16556i −1.13382 0.303805i
\(189\) 4.26991 4.26991i 0.310590 0.310590i
\(190\) 1.21990 + 0.326870i 0.0885005 + 0.0237136i
\(191\) 13.4214 3.59624i 0.971136 0.260215i 0.261829 0.965114i \(-0.415674\pi\)
0.709307 + 0.704899i \(0.249008\pi\)
\(192\) 13.6974i 0.988522i
\(193\) −2.76355 10.3137i −0.198924 0.742396i −0.991216 0.132253i \(-0.957779\pi\)
0.792292 0.610143i \(-0.208888\pi\)
\(194\) 0.459448 0.265263i 0.0329865 0.0190447i
\(195\) 19.7724i 1.41593i
\(196\) −9.75153 5.63005i −0.696538 0.402146i
\(197\) −0.587489 + 0.587489i −0.0418569 + 0.0418569i −0.727725 0.685869i \(-0.759422\pi\)
0.685869 + 0.727725i \(0.259422\pi\)
\(198\) 0.00333447 0.00333447i 0.000236970 0.000236970i
\(199\) −6.28620 + 23.4604i −0.445617 + 1.66306i 0.268687 + 0.963228i \(0.413410\pi\)
−0.714303 + 0.699836i \(0.753256\pi\)
\(200\) 0.517042 0.298514i 0.0365604 0.0211081i
\(201\) 8.34646 + 14.4565i 0.588714 + 1.01968i
\(202\) 0.355707 + 0.355707i 0.0250274 + 0.0250274i
\(203\) 2.86058 + 4.95467i 0.200773 + 0.347749i
\(204\) 4.41706 + 16.4847i 0.309256 + 1.15416i
\(205\) 5.22434 19.4975i 0.364884 1.36177i
\(206\) −1.05186 0.281844i −0.0732864 0.0196370i
\(207\) 0.0119642 + 0.00690754i 0.000831570 + 0.000480107i
\(208\) −4.36336 16.2843i −0.302545 1.12911i
\(209\) −24.0939 24.0939i −1.66661 1.66661i
\(210\) −0.368418 −0.0254232
\(211\) 14.6840 1.01089 0.505446 0.862858i \(-0.331328\pi\)
0.505446 + 0.862858i \(0.331328\pi\)
\(212\) −5.39104 5.39104i −0.370258 0.370258i
\(213\) 7.23482 4.17703i 0.495722 0.286205i
\(214\) 0.368817 0.0988243i 0.0252118 0.00675549i
\(215\) 6.56284 11.3672i 0.447582 0.775234i
\(216\) 1.40600i 0.0956663i
\(217\) −0.141358 0.244839i −0.00959601 0.0166208i
\(218\) −0.614841 −0.0416423
\(219\) −11.1298 9.80612i −0.752080 0.662636i
\(220\) −26.3179 −1.77435
\(221\) −10.4538 18.1065i −0.703196 1.21797i
\(222\) 0.0763871i 0.00512677i
\(223\) 10.6020 18.3632i 0.709963 1.22969i −0.254908 0.966965i \(-0.582045\pi\)
0.964870 0.262726i \(-0.0846216\pi\)
\(224\) 0.913789 0.244849i 0.0610551 0.0163597i
\(225\) −0.0269425 + 0.0155553i −0.00179617 + 0.00103702i
\(226\) 0.474929 + 0.474929i 0.0315918 + 0.0315918i
\(227\) −5.10954 −0.339132 −0.169566 0.985519i \(-0.554237\pi\)
−0.169566 + 0.985519i \(0.554237\pi\)
\(228\) 24.0166 1.59054
\(229\) 2.08710 + 2.08710i 0.137919 + 0.137919i 0.772696 0.634776i \(-0.218908\pi\)
−0.634776 + 0.772696i \(0.718908\pi\)
\(230\) 0.0460873 + 0.172000i 0.00303890 + 0.0113413i
\(231\) 8.60823 + 4.96996i 0.566380 + 0.327000i
\(232\) 1.28671 + 0.344772i 0.0844765 + 0.0226354i
\(233\) −6.30140 + 23.5172i −0.412819 + 1.54066i 0.376347 + 0.926479i \(0.377180\pi\)
−0.789165 + 0.614181i \(0.789486\pi\)
\(234\) −0.00105388 0.00393315i −6.88945e−5 0.000257118i
\(235\) 10.8224 + 18.7449i 0.705973 + 1.22278i
\(236\) 9.57416 + 9.57416i 0.623225 + 0.623225i
\(237\) −8.35508 14.4714i −0.542721 0.940020i
\(238\) 0.337377 0.194785i 0.0218689 0.0126260i
\(239\) −2.47547 + 9.23857i −0.160125 + 0.597594i 0.838487 + 0.544921i \(0.183441\pi\)
−0.998612 + 0.0526722i \(0.983226\pi\)
\(240\) 13.0864 13.0864i 0.844720 0.844720i
\(241\) 12.3733 12.3733i 0.797036 0.797036i −0.185591 0.982627i \(-0.559420\pi\)
0.982627 + 0.185591i \(0.0594200\pi\)
\(242\) −0.773495 0.446578i −0.0497221 0.0287071i
\(243\) 0.146877i 0.00942218i
\(244\) 18.0359 10.4130i 1.15463 0.666625i
\(245\) 3.91934 + 14.6272i 0.250397 + 0.934496i
\(246\) 0.886521i 0.0565225i
\(247\) −28.4197 + 7.61505i −1.80831 + 0.484534i
\(248\) −0.0635839 0.0170373i −0.00403758 0.00108187i
\(249\) −9.29929 + 9.29929i −0.589319 + 0.589319i
\(250\) 0.492484 + 0.131961i 0.0311474 + 0.00834593i
\(251\) 6.03319 10.4498i 0.380812 0.659585i −0.610367 0.792119i \(-0.708978\pi\)
0.991178 + 0.132534i \(0.0423113\pi\)
\(252\) −0.0317322 + 0.00850262i −0.00199894 + 0.000535614i
\(253\) 1.24344 4.64057i 0.0781742 0.291750i
\(254\) 0.840034 + 0.484994i 0.0527084 + 0.0304312i
\(255\) 11.4758 19.8766i 0.718640 1.24472i
\(256\) −7.81630 + 13.5382i −0.488519 + 0.846139i
\(257\) 6.79577 + 3.92354i 0.423908 + 0.244744i 0.696748 0.717316i \(-0.254630\pi\)
−0.272840 + 0.962060i \(0.587963\pi\)
\(258\) −0.149201 + 0.556825i −0.00928884 + 0.0346664i
\(259\) 0.729272 0.195408i 0.0453148 0.0121421i
\(260\) −11.3625 + 19.6805i −0.704675 + 1.22053i
\(261\) −0.0670490 0.0179657i −0.00415023 0.00111205i
\(262\) −0.510151 + 0.510151i −0.0315172 + 0.0315172i
\(263\) 2.11083 + 0.565594i 0.130159 + 0.0348760i 0.323310 0.946293i \(-0.395204\pi\)
−0.193151 + 0.981169i \(0.561871\pi\)
\(264\) 2.23552 0.599007i 0.137587 0.0368663i
\(265\) 10.2533i 0.629853i
\(266\) −0.141891 0.529544i −0.00869989 0.0324684i
\(267\) −18.2944 + 10.5623i −1.11960 + 0.646401i
\(268\) 19.1858i 1.17196i
\(269\) −16.8194 9.71070i −1.02550 0.592072i −0.109807 0.993953i \(-0.535023\pi\)
−0.915692 + 0.401881i \(0.868357\pi\)
\(270\) −0.667750 + 0.667750i −0.0406380 + 0.0406380i
\(271\) 4.72438 4.72438i 0.286986 0.286986i −0.548901 0.835887i \(-0.684954\pi\)
0.835887 + 0.548901i \(0.184954\pi\)
\(272\) −5.06493 + 18.9026i −0.307107 + 1.14614i
\(273\) 7.43308 4.29149i 0.449870 0.259733i
\(274\) 0.384839 + 0.666561i 0.0232490 + 0.0402684i
\(275\) 7.65008 + 7.65008i 0.461317 + 0.461317i
\(276\) 1.69312 + 2.93256i 0.101914 + 0.176519i
\(277\) 0.0121521 + 0.0453523i 0.000730149 + 0.00272495i 0.966290 0.257456i \(-0.0828843\pi\)
−0.965560 + 0.260181i \(0.916218\pi\)
\(278\) 0.0511211 0.190787i 0.00306604 0.0114426i
\(279\) 0.00331329 0.000887793i 0.000198361 5.31508e-5i
\(280\) −0.734259 0.423925i −0.0438804 0.0253343i
\(281\) 1.70030 + 6.34560i 0.101431 + 0.378547i 0.997916 0.0645281i \(-0.0205542\pi\)
−0.896485 + 0.443075i \(0.853888\pi\)
\(282\) −0.672188 0.672188i −0.0400282 0.0400282i
\(283\) −14.8899 −0.885111 −0.442556 0.896741i \(-0.645928\pi\)
−0.442556 + 0.896741i \(0.645928\pi\)
\(284\) 9.60161 0.569751
\(285\) −22.8386 22.8386i −1.35284 1.35284i
\(286\) −1.22631 + 0.708011i −0.0725133 + 0.0418656i
\(287\) −8.46366 + 2.26783i −0.499594 + 0.133866i
\(288\) −0.00573901 + 0.00994026i −0.000338174 + 0.000585735i
\(289\) 7.26921i 0.427601i
\(290\) −0.447352 0.774837i −0.0262694 0.0455000i
\(291\) −13.5679 −0.795364
\(292\) −5.44280 16.1565i −0.318516 0.945486i
\(293\) −18.3491 −1.07196 −0.535982 0.844229i \(-0.680059\pi\)
−0.535982 + 0.844229i \(0.680059\pi\)
\(294\) −0.332537 0.575971i −0.0193940 0.0335913i
\(295\) 18.2092i 1.06018i
\(296\) 0.0878958 0.152240i 0.00510884 0.00884877i
\(297\) 24.6102 6.59429i 1.42803 0.382640i
\(298\) 1.42524 0.822860i 0.0825617 0.0476670i
\(299\) −2.93337 2.93337i −0.169641 0.169641i
\(300\) −7.62553 −0.440260
\(301\) −5.69771 −0.328411
\(302\) −0.769125 0.769125i −0.0442582 0.0442582i
\(303\) −3.32973 12.4267i −0.191288 0.713897i
\(304\) 23.8496 + 13.7696i 1.36787 + 0.789741i
\(305\) −27.0536 7.24898i −1.54908 0.415076i
\(306\) −0.00122334 + 0.00456555i −6.99334e−5 + 0.000260995i
\(307\) 3.40947 + 12.7243i 0.194588 + 0.726214i 0.992373 + 0.123271i \(0.0393386\pi\)
−0.797785 + 0.602943i \(0.793995\pi\)
\(308\) 5.71216 + 9.89374i 0.325480 + 0.563748i
\(309\) 19.6927 + 19.6927i 1.12028 + 1.12028i
\(310\) 0.0221063 + 0.0382893i 0.00125555 + 0.00217468i
\(311\) 10.8432 6.26034i 0.614863 0.354991i −0.160004 0.987116i \(-0.551151\pi\)
0.774866 + 0.632125i \(0.217817\pi\)
\(312\) 0.517234 1.93034i 0.0292826 0.109284i
\(313\) −17.4969 + 17.4969i −0.988984 + 0.988984i −0.999940 0.0109555i \(-0.996513\pi\)
0.0109555 + 0.999940i \(0.496513\pi\)
\(314\) −1.07859 + 1.07859i −0.0608683 + 0.0608683i
\(315\) 0.0382614 + 0.0220903i 0.00215579 + 0.00124464i
\(316\) 19.2056i 1.08040i
\(317\) −23.5040 + 13.5701i −1.32012 + 0.762170i −0.983747 0.179560i \(-0.942533\pi\)
−0.336370 + 0.941730i \(0.609199\pi\)
\(318\) −0.116550 0.434970i −0.00653579 0.0243919i
\(319\) 24.1392i 1.35153i
\(320\) 20.4504 5.47967i 1.14321 0.306323i
\(321\) −9.43230 2.52738i −0.526459 0.141064i
\(322\) 0.0546574 0.0546574i 0.00304594 0.00304594i
\(323\) 32.9893 + 8.83946i 1.83557 + 0.491840i
\(324\) −9.02137 + 15.6255i −0.501187 + 0.868081i
\(325\) 9.02359 2.41786i 0.500539 0.134119i
\(326\) −0.0824083 + 0.307552i −0.00456418 + 0.0170337i
\(327\) 13.6176 + 7.86211i 0.753054 + 0.434776i
\(328\) −1.02009 + 1.76684i −0.0563249 + 0.0975575i
\(329\) 4.69787 8.13695i 0.259002 0.448605i
\(330\) −1.34620 0.777229i −0.0741059 0.0427850i
\(331\) 3.60692 13.4612i 0.198254 0.739895i −0.793146 0.609031i \(-0.791558\pi\)
0.991400 0.130864i \(-0.0417750\pi\)
\(332\) −14.6001 + 3.91208i −0.801284 + 0.214703i
\(333\) −0.00458016 + 0.00793307i −0.000250991 + 0.000434729i
\(334\) −0.0920258 0.0246582i −0.00503543 0.00134924i
\(335\) 18.2448 18.2448i 0.996819 0.996819i
\(336\) −7.75991 2.07926i −0.423338 0.113433i
\(337\) −3.19533 + 0.856187i −0.174061 + 0.0466395i −0.344797 0.938677i \(-0.612052\pi\)
0.170736 + 0.985317i \(0.445386\pi\)
\(338\) 0.340207i 0.0185048i
\(339\) −4.44576 16.5918i −0.241461 0.901144i
\(340\) 22.8449 13.1895i 1.23894 0.715302i
\(341\) 1.19286i 0.0645969i
\(342\) 0.00576041 + 0.00332577i 0.000311487 + 0.000179837i
\(343\) 10.4140 10.4140i 0.562305 0.562305i
\(344\) −0.938076 + 0.938076i −0.0505777 + 0.0505777i
\(345\) 1.17866 4.39881i 0.0634567 0.236824i
\(346\) 0.189793 0.109577i 0.0102034 0.00589091i
\(347\) 11.8006 + 20.4392i 0.633490 + 1.09724i 0.986833 + 0.161742i \(0.0517114\pi\)
−0.353343 + 0.935494i \(0.614955\pi\)
\(348\) −12.0309 12.0309i −0.644921 0.644921i
\(349\) 3.34960 + 5.80168i 0.179300 + 0.310557i 0.941641 0.336619i \(-0.109283\pi\)
−0.762341 + 0.647176i \(0.775950\pi\)
\(350\) 0.0450519 + 0.168136i 0.00240813 + 0.00898726i
\(351\) 5.69407 21.2506i 0.303927 1.13427i
\(352\) 3.85553 + 1.03309i 0.205501 + 0.0550637i
\(353\) 13.8082 + 7.97219i 0.734938 + 0.424317i 0.820226 0.572040i \(-0.193848\pi\)
−0.0852879 + 0.996356i \(0.527181\pi\)
\(354\) 0.206985 + 0.772480i 0.0110012 + 0.0410569i
\(355\) −9.13069 9.13069i −0.484607 0.484607i
\(356\) −24.2792 −1.28680
\(357\) −9.96302 −0.527299
\(358\) −0.327664 0.327664i −0.0173176 0.0173176i
\(359\) 8.24908 4.76261i 0.435370 0.251361i −0.266262 0.963901i \(-0.585789\pi\)
0.701632 + 0.712540i \(0.252455\pi\)
\(360\) 0.00993635 0.00266244i 0.000523692 0.000140323i
\(361\) 14.5311 25.1685i 0.764793 1.32466i
\(362\) 0.368455i 0.0193656i
\(363\) 11.4210 + 19.7817i 0.599446 + 1.03827i
\(364\) 9.86472 0.517052
\(365\) −10.1882 + 20.5399i −0.533276 + 1.07511i
\(366\) 1.23008 0.0642975
\(367\) −7.45781 12.9173i −0.389295 0.674278i 0.603060 0.797696i \(-0.293948\pi\)
−0.992355 + 0.123418i \(0.960615\pi\)
\(368\) 3.88291i 0.202411i
\(369\) 0.0531556 0.0920683i 0.00276717 0.00479288i
\(370\) −0.114047 + 0.0305589i −0.00592904 + 0.00158868i
\(371\) 3.85453 2.22542i 0.200117 0.115538i
\(372\) 0.594516 + 0.594516i 0.0308242 + 0.0308242i
\(373\) −17.9497 −0.929400 −0.464700 0.885468i \(-0.653838\pi\)
−0.464700 + 0.885468i \(0.653838\pi\)
\(374\) 1.64370 0.0849938
\(375\) −9.22019 9.22019i −0.476128 0.476128i
\(376\) −0.566213 2.11314i −0.0292002 0.108977i
\(377\) 18.0513 + 10.4219i 0.929687 + 0.536755i
\(378\) 0.395961 + 0.106097i 0.0203660 + 0.00545706i
\(379\) 4.38416 16.3619i 0.225199 0.840454i −0.757126 0.653269i \(-0.773397\pi\)
0.982325 0.187185i \(-0.0599364\pi\)
\(380\) −9.60790 35.8572i −0.492875 1.83943i
\(381\) −12.4034 21.4834i −0.635448 1.10063i
\(382\) 0.666980 + 0.666980i 0.0341257 + 0.0341257i
\(383\) 8.68209 + 15.0378i 0.443634 + 0.768396i 0.997956 0.0639059i \(-0.0203557\pi\)
−0.554322 + 0.832302i \(0.687022\pi\)
\(384\) −3.24737 + 1.87487i −0.165716 + 0.0956764i
\(385\) 3.97650 14.8405i 0.202661 0.756342i
\(386\) 0.512543 0.512543i 0.0260878 0.0260878i
\(387\) 0.0488822 0.0488822i 0.00248482 0.00248482i
\(388\) −13.5048 7.79703i −0.685605 0.395834i
\(389\) 9.07519i 0.460131i 0.973175 + 0.230065i \(0.0738940\pi\)
−0.973175 + 0.230065i \(0.926106\pi\)
\(390\) −1.16242 + 0.671125i −0.0588616 + 0.0339838i
\(391\) 1.24632 + 4.65135i 0.0630294 + 0.235229i
\(392\) 1.53055i 0.0773046i
\(393\) 17.8223 4.77547i 0.899016 0.240891i
\(394\) −0.0544796 0.0145978i −0.00274464 0.000735424i
\(395\) −18.2636 + 18.2636i −0.918943 + 0.918943i
\(396\) −0.133887 0.0358749i −0.00672808 0.00180278i
\(397\) −3.07886 + 5.33275i −0.154524 + 0.267643i −0.932886 0.360173i \(-0.882718\pi\)
0.778362 + 0.627816i \(0.216051\pi\)
\(398\) −1.59261 + 0.426740i −0.0798305 + 0.0213905i
\(399\) −3.62878 + 13.5428i −0.181666 + 0.677988i
\(400\) −7.57253 4.37200i −0.378627 0.218600i
\(401\) −19.3367 + 33.4921i −0.965629 + 1.67252i −0.257712 + 0.966222i \(0.582969\pi\)
−0.707917 + 0.706296i \(0.750365\pi\)
\(402\) −0.566601 + 0.981381i −0.0282595 + 0.0489469i
\(403\) −0.892020 0.515008i −0.0444347 0.0256544i
\(404\) 3.82698 14.2825i 0.190400 0.710581i
\(405\) 23.4380 6.28019i 1.16464 0.312065i
\(406\) −0.194191 + 0.336348i −0.00963753 + 0.0166927i
\(407\) 3.07700 + 0.824480i 0.152521 + 0.0408680i
\(408\) −1.64032 + 1.64032i −0.0812079 + 0.0812079i
\(409\) −7.75532 2.07803i −0.383476 0.102752i 0.0619307 0.998080i \(-0.480274\pi\)
−0.445407 + 0.895328i \(0.646941\pi\)
\(410\) 1.32359 0.354655i 0.0653676 0.0175152i
\(411\) 19.6841i 0.970945i
\(412\) 8.28443 + 30.9179i 0.408144 + 1.52322i
\(413\) −6.84542 + 3.95220i −0.336841 + 0.194475i
\(414\) 0 0.000937840i 0 4.60923e-5i
\(415\) 17.6042 + 10.1638i 0.864157 + 0.498921i
\(416\) 2.43714 2.43714i 0.119491 0.119491i
\(417\) −3.57187 + 3.57187i −0.174915 + 0.174915i
\(418\) 0.598677 2.23429i 0.0292823 0.109283i
\(419\) −2.94854 + 1.70234i −0.144045 + 0.0831647i −0.570291 0.821443i \(-0.693169\pi\)
0.426245 + 0.904608i \(0.359836\pi\)
\(420\) 5.41457 + 9.37831i 0.264204 + 0.457614i
\(421\) −9.14260 9.14260i −0.445583 0.445583i 0.448300 0.893883i \(-0.352030\pi\)
−0.893883 + 0.448300i \(0.852030\pi\)
\(422\) 0.498414 + 0.863279i 0.0242624 + 0.0420238i
\(423\) 0.0295047 + 0.110113i 0.00143457 + 0.00535389i
\(424\) 0.268219 1.00101i 0.0130259 0.0486132i
\(425\) −10.4745 2.80663i −0.508087 0.136141i
\(426\) 0.491137 + 0.283558i 0.0237957 + 0.0137384i
\(427\) 3.14671 + 11.7437i 0.152280 + 0.568316i
\(428\) −7.93607 7.93607i −0.383604 0.383604i
\(429\) 36.2140 1.74843
\(430\) 0.891038 0.0429697
\(431\) 1.42230 + 1.42230i 0.0685097 + 0.0685097i 0.740531 0.672022i \(-0.234574\pi\)
−0.672022 + 0.740531i \(0.734574\pi\)
\(432\) −17.8333 + 10.2961i −0.858006 + 0.495370i
\(433\) 30.4802 8.16715i 1.46479 0.392488i 0.563646 0.826016i \(-0.309398\pi\)
0.901140 + 0.433528i \(0.142731\pi\)
\(434\) 0.00959612 0.0166210i 0.000460629 0.000797832i
\(435\) 22.8816i 1.09709i
\(436\) 9.03620 + 15.6512i 0.432756 + 0.749555i
\(437\) 6.77655 0.324166
\(438\) 0.198731 0.987167i 0.00949575 0.0471687i
\(439\) 13.7315 0.655370 0.327685 0.944787i \(-0.393731\pi\)
0.327685 + 0.944787i \(0.393731\pi\)
\(440\) −1.78866 3.09804i −0.0852709 0.147693i
\(441\) 0.0797555i 0.00379788i
\(442\) 0.709656 1.22916i 0.0337549 0.0584652i
\(443\) −39.4586 + 10.5729i −1.87474 + 0.502334i −0.874898 + 0.484307i \(0.839072\pi\)
−0.999838 + 0.0180264i \(0.994262\pi\)
\(444\) −1.94448 + 1.12265i −0.0922810 + 0.0532785i
\(445\) 23.0884 + 23.0884i 1.09450 + 1.09450i
\(446\) 1.43944 0.0681594
\(447\) −42.0884 −1.99071
\(448\) −6.49864 6.49864i −0.307032 0.307032i
\(449\) −4.17761 15.5911i −0.197154 0.735787i −0.991699 0.128582i \(-0.958957\pi\)
0.794545 0.607205i \(-0.207709\pi\)
\(450\) −0.00182900 0.00105597i −8.62197e−5 4.97789e-5i
\(451\) −35.7106 9.56862i −1.68155 0.450569i
\(452\) 5.10967 19.0696i 0.240339 0.896957i
\(453\) 7.19970 + 26.8696i 0.338271 + 1.26245i
\(454\) −0.173431 0.300391i −0.00813951 0.0140981i
\(455\) −9.38090 9.38090i −0.439783 0.439783i
\(456\) 1.63225 + 2.82714i 0.0764372 + 0.132393i
\(457\) −12.1287 + 7.00252i −0.567358 + 0.327564i −0.756093 0.654464i \(-0.772894\pi\)
0.188736 + 0.982028i \(0.439561\pi\)
\(458\) −0.0518596 + 0.193543i −0.00242324 + 0.00904365i
\(459\) −18.0578 + 18.0578i −0.842865 + 0.842865i
\(460\) 3.70103 3.70103i 0.172562 0.172562i
\(461\) 21.7721 + 12.5701i 1.01403 + 0.585450i 0.912369 0.409369i \(-0.134251\pi\)
0.101660 + 0.994819i \(0.467585\pi\)
\(462\) 0.674774i 0.0313933i
\(463\) −17.8658 + 10.3148i −0.830293 + 0.479370i −0.853953 0.520350i \(-0.825801\pi\)
0.0236598 + 0.999720i \(0.492468\pi\)
\(464\) −5.04950 18.8450i −0.234417 0.874856i
\(465\) 1.13071i 0.0524356i
\(466\) −1.59647 + 0.427772i −0.0739549 + 0.0198161i
\(467\) 7.10274 + 1.90317i 0.328676 + 0.0880684i 0.419383 0.907809i \(-0.362246\pi\)
−0.0907079 + 0.995878i \(0.528913\pi\)
\(468\) −0.0846320 + 0.0846320i −0.00391211 + 0.00391211i
\(469\) −10.8187 2.89887i −0.499563 0.133857i
\(470\) −0.734678 + 1.27250i −0.0338882 + 0.0586960i
\(471\) 37.6809 10.0966i 1.73624 0.465225i
\(472\) −0.476341 + 1.77773i −0.0219254 + 0.0818266i
\(473\) −20.8195 12.0201i −0.957280 0.552686i
\(474\) 0.567186 0.982396i 0.0260517 0.0451229i
\(475\) −7.63013 + 13.2158i −0.350095 + 0.606381i
\(476\) −9.91673 5.72543i −0.454532 0.262424i
\(477\) −0.0139766 + 0.0521614i −0.000639945 + 0.00238831i
\(478\) −0.627162 + 0.168048i −0.0286857 + 0.00768632i
\(479\) −0.0885703 + 0.153408i −0.00404688 + 0.00700940i −0.868042 0.496491i \(-0.834621\pi\)
0.863995 + 0.503501i \(0.167955\pi\)
\(480\) 3.65467 + 0.979266i 0.166812 + 0.0446972i
\(481\) 1.94502 1.94502i 0.0886853 0.0886853i
\(482\) 1.14741 + 0.307449i 0.0522633 + 0.0140039i
\(483\) −1.90947 + 0.511642i −0.0868841 + 0.0232805i
\(484\) 26.2531i 1.19332i
\(485\) 5.42787 + 20.2571i 0.246467 + 0.919828i
\(486\) −0.00863496 + 0.00498540i −0.000391690 + 0.000226142i
\(487\) 8.57006i 0.388346i 0.980967 + 0.194173i \(0.0622024\pi\)
−0.980967 + 0.194173i \(0.937798\pi\)
\(488\) 2.45156 + 1.41541i 0.110977 + 0.0640726i
\(489\) 5.75793 5.75793i 0.260383 0.260383i
\(490\) −0.726903 + 0.726903i −0.0328381 + 0.0328381i
\(491\) 3.80705 14.2081i 0.171810 0.641203i −0.825263 0.564748i \(-0.808973\pi\)
0.997073 0.0764546i \(-0.0243600\pi\)
\(492\) 22.5670 13.0290i 1.01740 0.587394i
\(493\) −12.0976 20.9537i −0.544849 0.943707i
\(494\) −1.41233 1.41233i −0.0635438 0.0635438i
\(495\) 0.0932050 + 0.161436i 0.00418925 + 0.00725600i
\(496\) 0.249526 + 0.931242i 0.0112040 + 0.0418140i
\(497\) −1.45075 + 5.41429i −0.0650752 + 0.242864i
\(498\) −0.862350 0.231066i −0.0386428 0.0103543i
\(499\) −29.7346 17.1673i −1.33111 0.768514i −0.345636 0.938369i \(-0.612337\pi\)
−0.985469 + 0.169855i \(0.945670\pi\)
\(500\) −3.87880 14.4759i −0.173465 0.647382i
\(501\) 1.72289 + 1.72289i 0.0769730 + 0.0769730i
\(502\) 0.819128 0.0365595
\(503\) 0.390962 0.0174321 0.00871606 0.999962i \(-0.497226\pi\)
0.00871606 + 0.999962i \(0.497226\pi\)
\(504\) −0.00315753 0.00315753i −0.000140648 0.000140648i
\(505\) −17.2213 + 9.94271i −0.766337 + 0.442445i
\(506\) 0.315026 0.0844109i 0.0140046 0.00375252i
\(507\) 4.35030 7.53494i 0.193204 0.334638i
\(508\) 28.5114i 1.26499i
\(509\) 2.09332 + 3.62573i 0.0927846 + 0.160708i 0.908682 0.417489i \(-0.137090\pi\)
−0.815897 + 0.578197i \(0.803757\pi\)
\(510\) 1.55807 0.0689924
\(511\) 9.93292 0.627999i 0.439406 0.0277810i
\(512\) −5.38088 −0.237804
\(513\) 17.9690 + 31.1232i 0.793349 + 1.37412i
\(514\) 0.532700i 0.0234964i
\(515\) 21.5234 37.2796i 0.948434 1.64274i
\(516\) 16.3671 4.38555i 0.720522 0.193063i
\(517\) 34.3321 19.8216i 1.50992 0.871754i
\(518\) 0.0362415 + 0.0362415i 0.00159236 + 0.00159236i
\(519\) −5.60476 −0.246022
\(520\) −3.08896 −0.135460
\(521\) 25.2821 + 25.2821i 1.10763 + 1.10763i 0.993462 + 0.114167i \(0.0364199\pi\)
0.114167 + 0.993462i \(0.463580\pi\)
\(522\) −0.00121961 0.00455163i −5.33807e−5 0.000199219i
\(523\) 5.89561 + 3.40383i 0.257797 + 0.148839i 0.623329 0.781959i \(-0.285780\pi\)
−0.365532 + 0.930799i \(0.619113\pi\)
\(524\) 20.4838 + 5.48862i 0.894839 + 0.239771i
\(525\) 1.15218 4.29999i 0.0502852 0.187667i
\(526\) 0.0383954 + 0.143294i 0.00167412 + 0.00624791i
\(527\) 0.597815 + 1.03545i 0.0260412 + 0.0451047i
\(528\) −23.9682 23.9682i −1.04308 1.04308i
\(529\) −11.0223 19.0911i −0.479229 0.830049i
\(530\) −0.602792 + 0.348022i −0.0261836 + 0.0151171i
\(531\) 0.0248216 0.0926355i 0.00107717 0.00402004i
\(532\) −11.3945 + 11.3945i −0.494015 + 0.494015i
\(533\) −22.5732 + 22.5732i −0.977753 + 0.977753i
\(534\) −1.24192 0.717022i −0.0537431 0.0310286i
\(535\) 15.0937i 0.652557i
\(536\) −2.25848 + 1.30393i −0.0975514 + 0.0563213i
\(537\) 3.06723 + 11.4471i 0.132361 + 0.493977i
\(538\) 1.31843i 0.0568414i
\(539\) 26.7903 7.17845i 1.15394 0.309198i
\(540\) 26.8118 + 7.18420i 1.15380 + 0.309159i
\(541\) 22.0324 22.0324i 0.947247 0.947247i −0.0514300 0.998677i \(-0.516378\pi\)
0.998677 + 0.0514300i \(0.0163779\pi\)
\(542\) 0.438106 + 0.117390i 0.0188183 + 0.00504234i
\(543\) 4.71152 8.16059i 0.202191 0.350204i
\(544\) −3.86449 + 1.03549i −0.165689 + 0.0443961i
\(545\) 6.29052 23.4765i 0.269456 1.00562i
\(546\) 0.504596 + 0.291328i 0.0215947 + 0.0124677i
\(547\) 4.22370 7.31566i 0.180592 0.312795i −0.761490 0.648176i \(-0.775532\pi\)
0.942082 + 0.335382i \(0.108865\pi\)
\(548\) 11.3118 19.5927i 0.483217 0.836957i
\(549\) −0.127748 0.0737555i −0.00545217 0.00314781i
\(550\) −0.190087 + 0.709414i −0.00810533 + 0.0302495i
\(551\) −32.8887 + 8.81251i −1.40111 + 0.375426i
\(552\) −0.230140 + 0.398615i −0.00979542 + 0.0169662i
\(553\) 10.8299 + 2.90187i 0.460535 + 0.123400i
\(554\) −0.00225380 + 0.00225380i −9.57548e−5 + 9.57548e-5i
\(555\) 2.91670 + 0.781527i 0.123807 + 0.0331740i
\(556\) −5.60791 + 1.50264i −0.237829 + 0.0637260i
\(557\) 35.0915i 1.48687i −0.668806 0.743437i \(-0.733194\pi\)
0.668806 0.743437i \(-0.266806\pi\)
\(558\) 6.02680e−5 0 0.000224923i 2.55135e−6 0 9.52176e-6i
\(559\) −17.9773 + 10.3792i −0.760359 + 0.438993i
\(560\) 12.4175i 0.524735i
\(561\) −36.4049 21.0184i −1.53702 0.887397i
\(562\) −0.315347 + 0.315347i −0.0133021 + 0.0133021i
\(563\) −3.53281 + 3.53281i −0.148890 + 0.148890i −0.777622 0.628732i \(-0.783574\pi\)
0.628732 + 0.777622i \(0.283574\pi\)
\(564\) −7.23194 + 26.9900i −0.304520 + 1.13648i
\(565\) −22.9933 + 13.2752i −0.967337 + 0.558492i
\(566\) −0.505401 0.875380i −0.0212436 0.0367950i
\(567\) −7.44802 7.44802i −0.312787 0.312787i
\(568\) 0.652560 + 1.13027i 0.0273808 + 0.0474249i
\(569\) −0.994096 3.71002i −0.0416747 0.155532i 0.941953 0.335745i \(-0.108988\pi\)
−0.983628 + 0.180213i \(0.942321\pi\)
\(570\) 0.567488 2.11789i 0.0237694 0.0887088i
\(571\) 25.6435 + 6.87115i 1.07315 + 0.287549i 0.751785 0.659408i \(-0.229193\pi\)
0.321361 + 0.946957i \(0.395860\pi\)
\(572\) 36.0457 + 20.8110i 1.50715 + 0.870152i
\(573\) −6.24353 23.3012i −0.260827 0.973421i
\(574\) −0.420605 0.420605i −0.0175557 0.0175557i
\(575\) −2.15163 −0.0897292
\(576\) 0.111507 0.00464612
\(577\) 12.6989 + 12.6989i 0.528661 + 0.528661i 0.920173 0.391512i \(-0.128048\pi\)
−0.391512 + 0.920173i \(0.628048\pi\)
\(578\) −0.427359 + 0.246736i −0.0177758 + 0.0102629i
\(579\) −17.9059 + 4.79786i −0.744143 + 0.199392i
\(580\) −13.1493 + 22.7753i −0.545995 + 0.945691i
\(581\) 8.82400i 0.366081i
\(582\) −0.460529 0.797660i −0.0190895 0.0330641i
\(583\) 18.7793 0.777759
\(584\) 1.53197 1.73876i 0.0633934 0.0719503i
\(585\) 0.160962 0.00665497
\(586\) −0.622815 1.07875i −0.0257282 0.0445626i
\(587\) 16.5000i 0.681029i −0.940239 0.340514i \(-0.889399\pi\)
0.940239 0.340514i \(-0.110601\pi\)
\(588\) −9.77447 + 16.9299i −0.403092 + 0.698177i
\(589\) 1.62523 0.435478i 0.0669663 0.0179436i
\(590\) 1.07052 0.618066i 0.0440727 0.0254454i
\(591\) 1.01996 + 1.01996i 0.0419554 + 0.0419554i
\(592\) −2.57462 −0.105816
\(593\) 37.9912 1.56011 0.780055 0.625710i \(-0.215191\pi\)
0.780055 + 0.625710i \(0.215191\pi\)
\(594\) 1.22301 + 1.22301i 0.0501809 + 0.0501809i
\(595\) 3.98574 + 14.8750i 0.163399 + 0.609814i
\(596\) −41.8928 24.1868i −1.71600 0.990732i
\(597\) 40.7302 + 10.9136i 1.66698 + 0.446665i
\(598\) 0.0728875 0.272020i 0.00298059 0.0111237i
\(599\) −2.33275 8.70596i −0.0953137 0.355716i 0.901753 0.432252i \(-0.142281\pi\)
−0.997067 + 0.0765358i \(0.975614\pi\)
\(600\) −0.518258 0.897649i −0.0211578 0.0366464i
\(601\) −5.98344 5.98344i −0.244070 0.244070i 0.574462 0.818531i \(-0.305211\pi\)
−0.818531 + 0.574462i \(0.805211\pi\)
\(602\) −0.193395 0.334970i −0.00788220 0.0136524i
\(603\) 0.117687 0.0679466i 0.00479258 0.00276700i
\(604\) −8.27487 + 30.8822i −0.336700 + 1.25658i
\(605\) 24.9655 24.9655i 1.01499 1.01499i
\(606\) 0.617552 0.617552i 0.0250863 0.0250863i
\(607\) −22.9251 13.2358i −0.930501 0.537225i −0.0435311 0.999052i \(-0.513861\pi\)
−0.886970 + 0.461827i \(0.847194\pi\)
\(608\) 5.63018i 0.228334i
\(609\) 8.60192 4.96632i 0.348568 0.201246i
\(610\) −0.492098 1.83654i −0.0199245 0.0743592i
\(611\) 34.2314i 1.38485i
\(612\) 0.134198 0.0359583i 0.00542463 0.00145353i
\(613\) −3.51743 0.942493i −0.142068 0.0380669i 0.187084 0.982344i \(-0.440096\pi\)
−0.329152 + 0.944277i \(0.606763\pi\)
\(614\) −0.632339 + 0.632339i −0.0255191 + 0.0255191i
\(615\) −33.8501 9.07012i −1.36497 0.365742i
\(616\) −0.776437 + 1.34483i −0.0312835 + 0.0541847i
\(617\) 16.8950 4.52700i 0.680166 0.182250i 0.0978363 0.995203i \(-0.468808\pi\)
0.582330 + 0.812953i \(0.302141\pi\)
\(618\) −0.489317 + 1.82616i −0.0196832 + 0.0734588i
\(619\) 7.78318 + 4.49362i 0.312833 + 0.180614i 0.648193 0.761476i \(-0.275525\pi\)
−0.335361 + 0.942090i \(0.608858\pi\)
\(620\) 0.649785 1.12546i 0.0260960 0.0451996i
\(621\) −2.53355 + 4.38823i −0.101668 + 0.176094i
\(622\) 0.736094 + 0.424984i 0.0295147 + 0.0170403i
\(623\) 3.66846 13.6909i 0.146974 0.548514i
\(624\) −28.2716 + 7.57534i −1.13177 + 0.303256i
\(625\) −15.5804 + 26.9860i −0.623214 + 1.07944i
\(626\) −1.62254 0.434758i −0.0648497 0.0173764i
\(627\) −41.8300 + 41.8300i −1.67053 + 1.67053i
\(628\) 43.3080 + 11.6043i 1.72818 + 0.463064i
\(629\) −3.08415 + 0.826396i −0.122973 + 0.0329506i
\(630\) 0.00299920i 0.000119491i
\(631\) −2.86485 10.6918i −0.114048 0.425632i 0.885166 0.465275i \(-0.154045\pi\)
−0.999214 + 0.0396431i \(0.987378\pi\)
\(632\) 2.26081 1.30528i 0.0899303 0.0519213i
\(633\) 25.4934i 1.01327i
\(634\) −1.59557 0.921205i −0.0633684 0.0365857i
\(635\) −27.1131 + 27.1131i −1.07595 + 1.07595i
\(636\) −9.35952 + 9.35952i −0.371129 + 0.371129i
\(637\) 6.19848 23.1330i 0.245593 0.916564i
\(638\) −1.41915 + 0.819346i −0.0561846 + 0.0324382i
\(639\) −0.0340042 0.0588970i −0.00134518 0.00232993i
\(640\) 4.09833 + 4.09833i 0.162001 + 0.162001i
\(641\) 17.2076 + 29.8045i 0.679660 + 1.17721i 0.975083 + 0.221840i \(0.0712062\pi\)
−0.295423 + 0.955367i \(0.595460\pi\)
\(642\) −0.171571 0.640313i −0.00677138 0.0252711i
\(643\) −7.87286 + 29.3819i −0.310475 + 1.15871i 0.617653 + 0.786450i \(0.288083\pi\)
−0.928129 + 0.372259i \(0.878583\pi\)
\(644\) −2.19463 0.588049i −0.0864804 0.0231724i
\(645\) −19.7348 11.3939i −0.777058 0.448635i
\(646\) 0.600068 + 2.23948i 0.0236094 + 0.0881113i
\(647\) 24.0883 + 24.0883i 0.947007 + 0.947007i 0.998665 0.0516579i \(-0.0164505\pi\)
−0.0516579 + 0.998665i \(0.516451\pi\)
\(648\) −2.45250 −0.0963432
\(649\) −33.3509 −1.30914
\(650\) 0.448431 + 0.448431i 0.0175889 + 0.0175889i
\(651\) −0.425072 + 0.245416i −0.0166599 + 0.00961859i
\(652\) 9.04007 2.42228i 0.354037 0.0948638i
\(653\) −0.197265 + 0.341673i −0.00771957 + 0.0133707i −0.869859 0.493300i \(-0.835791\pi\)
0.862140 + 0.506670i \(0.169124\pi\)
\(654\) 1.06744i 0.0417403i
\(655\) −14.2597 24.6986i −0.557174 0.965053i
\(656\) 29.8801 1.16662
\(657\) −0.0798293 + 0.0906048i −0.00311444 + 0.00353483i
\(658\) 0.637832 0.0248653
\(659\) 3.49855 + 6.05967i 0.136284 + 0.236051i 0.926087 0.377309i \(-0.123151\pi\)
−0.789803 + 0.613361i \(0.789817\pi\)
\(660\) 45.6912i 1.77853i
\(661\) 3.53720 6.12661i 0.137581 0.238297i −0.788999 0.614394i \(-0.789401\pi\)
0.926580 + 0.376097i \(0.122734\pi\)
\(662\) 0.913817 0.244856i 0.0355165 0.00951661i
\(663\) −31.4351 + 18.1491i −1.22084 + 0.704851i
\(664\) −1.45279 1.45279i −0.0563792 0.0563792i
\(665\) 21.6713 0.840379
\(666\) −0.000621850 0 −2.40962e−5 0
\(667\) −3.39464 3.39464i −0.131441 0.131441i
\(668\) 0.724795 + 2.70497i 0.0280432 + 0.104659i
\(669\) −31.8809 18.4064i −1.23258 0.711633i
\(670\) 1.69189 + 0.453341i 0.0653634 + 0.0175141i
\(671\) −13.2768 + 49.5498i −0.512547 + 1.91285i
\(672\) −0.425089 1.58645i −0.0163982 0.0611988i
\(673\) 3.09080 + 5.35343i 0.119142 + 0.206359i 0.919428 0.393259i \(-0.128652\pi\)
−0.800286 + 0.599618i \(0.795319\pi\)
\(674\) −0.158793 0.158793i −0.00611649 0.00611649i
\(675\) −5.70535 9.88196i −0.219599 0.380357i
\(676\) 8.66018 4.99995i 0.333084 0.192306i
\(677\) −2.43095 + 9.07242i −0.0934289 + 0.348682i −0.996777 0.0802276i \(-0.974435\pi\)
0.903348 + 0.428909i \(0.141102\pi\)
\(678\) 0.824537 0.824537i 0.0316661 0.0316661i
\(679\) 6.43721 6.43721i 0.247037 0.247037i
\(680\) 3.10524 + 1.79281i 0.119081 + 0.0687512i
\(681\) 8.87080i 0.339930i
\(682\) 0.0701285 0.0404887i 0.00268536 0.00155039i
\(683\) −1.69603 6.32969i −0.0648969 0.242199i 0.925856 0.377876i \(-0.123346\pi\)
−0.990753 + 0.135678i \(0.956679\pi\)
\(684\) 0.195513i 0.00747563i
\(685\) −29.3887 + 7.87469i −1.12289 + 0.300876i
\(686\) 0.965722 + 0.258765i 0.0368715 + 0.00987968i
\(687\) 3.62347 3.62347i 0.138244 0.138244i
\(688\) 18.7678 + 5.02881i 0.715514 + 0.191721i
\(689\) 8.10782 14.0432i 0.308884 0.535002i
\(690\) 0.298614 0.0800133i 0.0113680 0.00304605i
\(691\) −2.21603 + 8.27032i −0.0843016 + 0.314618i −0.995181 0.0980547i \(-0.968738\pi\)
0.910879 + 0.412673i \(0.135405\pi\)
\(692\) −5.57872 3.22087i −0.212071 0.122439i
\(693\) 0.0404593 0.0700776i 0.00153692 0.00266203i
\(694\) −0.801086 + 1.38752i −0.0304088 + 0.0526696i
\(695\) 6.76181 + 3.90393i 0.256490 + 0.148085i
\(696\) 0.598568 2.23389i 0.0226887 0.0846753i
\(697\) 35.7935 9.59085i 1.35578 0.363279i
\(698\) −0.227388 + 0.393848i −0.00860678 + 0.0149074i
\(699\) 40.8287 + 10.9400i 1.54428 + 0.413790i
\(700\) 3.61789 3.61789i 0.136743 0.136743i
\(701\) −31.7054 8.49544i −1.19750 0.320868i −0.395652 0.918401i \(-0.629481\pi\)
−0.801845 + 0.597532i \(0.796148\pi\)
\(702\) 1.44260 0.386543i 0.0544473 0.0145891i
\(703\) 4.49330i 0.169468i
\(704\) −10.0363 37.4558i −0.378256 1.41167i
\(705\) 32.5435 18.7890i 1.22566 0.707634i
\(706\) 1.08239i 0.0407362i
\(707\) 7.47557 + 4.31602i 0.281148 + 0.162321i
\(708\) 16.6219 16.6219i 0.624691 0.624691i
\(709\) 13.5610 13.5610i 0.509294 0.509294i −0.405016 0.914310i \(-0.632734\pi\)
0.914310 + 0.405016i \(0.132734\pi\)
\(710\) 0.226877 0.846715i 0.00851453 0.0317766i
\(711\) −0.117808 + 0.0680168i −0.00441816 + 0.00255083i
\(712\) −1.65010 2.85806i −0.0618402 0.107110i
\(713\) 0.167749 + 0.167749i 0.00628227 + 0.00628227i
\(714\) −0.338171 0.585729i −0.0126557 0.0219203i
\(715\) −14.4875 54.0682i −0.541802 2.02203i
\(716\) −3.52528 + 13.1565i −0.131746 + 0.491682i
\(717\) 16.0393 + 4.29772i 0.599000 + 0.160501i
\(718\) 0.559990 + 0.323310i 0.0208986 + 0.0120658i
\(719\) 8.43708 + 31.4876i 0.314650 + 1.17429i 0.924315 + 0.381630i \(0.124637\pi\)
−0.609665 + 0.792659i \(0.708696\pi\)
\(720\) −0.106533 0.106533i −0.00397025 0.00397025i
\(721\) −18.6862 −0.695909
\(722\) 1.97289 0.0734232
\(723\) −21.4817 21.4817i −0.798911 0.798911i
\(724\) 9.37925 5.41511i 0.348577 0.201251i
\(725\) 10.4425 2.79807i 0.387826 0.103918i
\(726\) −0.775315 + 1.34288i −0.0287746 + 0.0498391i
\(727\) 0.0876925i 0.00325234i −0.999999 0.00162617i \(-0.999482\pi\)
0.999999 0.00162617i \(-0.000517625\pi\)
\(728\) 0.670442 + 1.16124i 0.0248482 + 0.0430384i
\(729\) −26.8716 −0.995245
\(730\) −1.55336 + 0.0982098i −0.0574925 + 0.00363491i
\(731\) 24.0961 0.891227
\(732\) −18.0783 31.3125i −0.668193 1.15734i
\(733\) 1.01752i 0.0375831i −0.999823 0.0187916i \(-0.994018\pi\)
0.999823 0.0187916i \(-0.00598189\pi\)
\(734\) 0.506275 0.876894i 0.0186869 0.0323667i
\(735\) 25.3946 6.80447i 0.936694 0.250987i
\(736\) −0.687477 + 0.396915i −0.0253408 + 0.0146305i
\(737\) −33.4161 33.4161i −1.23090 1.23090i
\(738\) 0.00721696 0.000265660
\(739\) −2.68830 −0.0988908 −0.0494454 0.998777i \(-0.515745\pi\)
−0.0494454 + 0.998777i \(0.515745\pi\)
\(740\) 2.45403 + 2.45403i 0.0902119 + 0.0902119i
\(741\) 13.2207 + 49.3403i 0.485674 + 1.81256i
\(742\) 0.261666 + 0.151073i 0.00960605 + 0.00554605i
\(743\) −8.56343 2.29456i −0.314162 0.0841794i 0.0982929 0.995158i \(-0.468662\pi\)
−0.412455 + 0.910978i \(0.635328\pi\)
\(744\) −0.0295788 + 0.110390i −0.00108441 + 0.00404708i
\(745\) 16.8376 + 62.8387i 0.616881 + 2.30223i
\(746\) −0.609259 1.05527i −0.0223066 0.0386361i
\(747\) 0.0757033 + 0.0757033i 0.00276984 + 0.00276984i
\(748\) −24.1572 41.8415i −0.883274 1.52988i
\(749\) 5.67420 3.27600i 0.207331 0.119703i
\(750\) 0.229100 0.855015i 0.00836557 0.0312207i
\(751\) 19.8398 19.8398i 0.723966 0.723966i −0.245445 0.969411i \(-0.578934\pi\)
0.969411 + 0.245445i \(0.0789341\pi\)
\(752\) −22.6560 + 22.6560i −0.826181 + 0.826181i
\(753\) −18.1422 10.4744i −0.661137 0.381708i
\(754\) 1.41499i 0.0515307i
\(755\) 37.2366 21.4986i 1.35518 0.782413i
\(756\) −3.11859 11.6387i −0.113422 0.423296i
\(757\) 29.6904i 1.07912i 0.841948 + 0.539558i \(0.181409\pi\)
−0.841948 + 0.539558i \(0.818591\pi\)
\(758\) 1.11073 0.297619i 0.0403435 0.0108100i
\(759\) −8.05661 2.15876i −0.292436 0.0783581i
\(760\) 3.56799 3.56799i 0.129425 0.129425i
\(761\) −16.7475 4.48748i −0.607097 0.162671i −0.0578417 0.998326i \(-0.518422\pi\)
−0.549255 + 0.835655i \(0.685089\pi\)
\(762\) 0.842010 1.45840i 0.0305028 0.0528324i
\(763\) −10.1909 + 2.73065i −0.368936 + 0.0988561i
\(764\) 7.17592 26.7809i 0.259616 0.968898i
\(765\) −0.161811 0.0934215i −0.00585028 0.00337766i
\(766\) −0.589385 + 1.02084i −0.0212953 + 0.0368846i
\(767\) −14.3990 + 24.9398i −0.519918 + 0.900524i
\(768\) 23.5041 + 13.5701i 0.848130 + 0.489668i
\(769\) −2.64260 + 9.86232i −0.0952946 + 0.355644i −0.997064 0.0765733i \(-0.975602\pi\)
0.901769 + 0.432218i \(0.142269\pi\)
\(770\) 1.00745 0.269945i 0.0363060 0.00972815i
\(771\) 6.81176 11.7983i 0.245319 0.424906i
\(772\) −20.5799 5.51436i −0.740685 0.198466i
\(773\) −2.90236 + 2.90236i −0.104391 + 0.104391i −0.757373 0.652982i \(-0.773518\pi\)
0.652982 + 0.757373i \(0.273518\pi\)
\(774\) 0.00453298 + 0.00121461i 0.000162935 + 4.36582e-5i
\(775\) −0.516028 + 0.138269i −0.0185363 + 0.00496678i
\(776\) 2.11966i 0.0760912i
\(777\) −0.339253 1.26611i −0.0121706 0.0454214i
\(778\) −0.533533 + 0.308036i −0.0191281 + 0.0110436i
\(779\) 52.1476i 1.86838i
\(780\) 34.1678 + 19.7268i 1.22341 + 0.706333i
\(781\) −16.7233 + 16.7233i −0.598405 + 0.598405i
\(782\) −0.231151 + 0.231151i −0.00826593 + 0.00826593i
\(783\) 6.58946 24.5922i 0.235488 0.878854i
\(784\) −19.4131 + 11.2081i −0.693324 + 0.400291i
\(785\) −30.1487 52.2191i −1.07605 1.86378i
\(786\) 0.885686 + 0.885686i 0.0315914 + 0.0315914i
\(787\) −23.3067 40.3685i −0.830796 1.43898i −0.897408 0.441201i \(-0.854552\pi\)
0.0666125 0.997779i \(-0.478781\pi\)
\(788\) 0.429081 + 1.60135i 0.0152854 + 0.0570458i
\(789\) 0.981943 3.66466i 0.0349581 0.130465i
\(790\) −1.69364 0.453809i −0.0602570 0.0161458i
\(791\) 9.98116 + 5.76263i 0.354889 + 0.204895i
\(792\) −0.00487637 0.0181989i −0.000173274 0.000646669i
\(793\) 31.3212 + 31.3212i 1.11225 + 1.11225i
\(794\) −0.418018 −0.0148349
\(795\) 17.8010 0.631335
\(796\) 34.2693 + 34.2693i 1.21464 + 1.21464i
\(797\) 25.7996 14.8954i 0.913869 0.527623i 0.0321951 0.999482i \(-0.489750\pi\)
0.881674 + 0.471859i \(0.156417\pi\)
\(798\) −0.919355 + 0.246340i −0.0325448 + 0.00872035i
\(799\) −19.8677 + 34.4118i −0.702868 + 1.21740i
\(800\) 1.78764i 0.0632028i
\(801\) 0.0859850 + 0.148930i 0.00303813 + 0.00526220i
\(802\) −2.62535 −0.0927043
\(803\) 37.6198 + 18.6602i 1.32757 + 0.658503i
\(804\) 33.3089 1.17471
\(805\) 1.52778 + 2.64620i 0.0538473 + 0.0932662i
\(806\) 0.0699228i 0.00246293i
\(807\) −16.8590 + 29.2007i −0.593465 + 1.02791i
\(808\) 1.94138 0.520191i 0.0682975 0.0183002i
\(809\) −9.73232 + 5.61896i −0.342170 + 0.197552i −0.661231 0.750182i \(-0.729966\pi\)
0.319061 + 0.947734i \(0.396632\pi\)
\(810\) 1.16476 + 1.16476i 0.0409255 + 0.0409255i
\(811\) 50.1731 1.76182 0.880909 0.473286i \(-0.156932\pi\)
0.880909 + 0.473286i \(0.156932\pi\)
\(812\) 11.4159 0.400621
\(813\) −8.20213 8.20213i −0.287661 0.287661i
\(814\) 0.0559700 + 0.208883i 0.00196175 + 0.00732134i
\(815\) −10.9002 6.29322i −0.381816 0.220442i
\(816\) 32.8173 + 8.79337i 1.14883 + 0.307829i
\(817\) 8.77640 32.7540i 0.307048 1.14592i
\(818\) −0.141068 0.526471i −0.00493231 0.0184076i
\(819\) −0.0349360 0.0605109i −0.00122076 0.00211442i
\(820\) −28.4806 28.4806i −0.994585 0.994585i
\(821\) 26.8381 + 46.4850i 0.936657 + 1.62234i 0.771651 + 0.636046i \(0.219431\pi\)
0.165006 + 0.986293i \(0.447236\pi\)
\(822\) 1.15723 0.668129i 0.0403632 0.0233037i
\(823\) 3.81120 14.2236i 0.132850 0.495804i −0.867147 0.498052i \(-0.834049\pi\)
0.999997 + 0.00224816i \(0.000715611\pi\)
\(824\) −3.07650 + 3.07650i −0.107175 + 0.107175i
\(825\) 13.2815 13.2815i 0.462402 0.462402i
\(826\) −0.464702 0.268296i −0.0161691 0.00933521i
\(827\) 32.4358i 1.12790i −0.825808 0.563952i \(-0.809280\pi\)
0.825808 0.563952i \(-0.190720\pi\)
\(828\) 0.0238733 0.0137833i 0.000829654 0.000479001i
\(829\) 4.52848 + 16.9005i 0.157281 + 0.586980i 0.998899 + 0.0469072i \(0.0149365\pi\)
−0.841619 + 0.540072i \(0.818397\pi\)
\(830\) 1.37994i 0.0478985i
\(831\) 0.0787373 0.0210976i 0.00273137 0.000731867i
\(832\) −32.3426 8.66616i −1.12128 0.300445i
\(833\) −19.6574 + 19.6574i −0.681090 + 0.681090i
\(834\) −0.331230 0.0887527i −0.0114695 0.00307326i
\(835\) 1.88306 3.26155i 0.0651659 0.112871i
\(836\) −65.6740 + 17.5973i −2.27138 + 0.608615i
\(837\) −0.325624 + 1.21525i −0.0112552 + 0.0420051i
\(838\) −0.200162 0.115564i −0.00691448 0.00399208i
\(839\) −7.89537 + 13.6752i −0.272578 + 0.472120i −0.969521 0.245007i \(-0.921210\pi\)
0.696943 + 0.717127i \(0.254543\pi\)
\(840\) −0.735987 + 1.27477i −0.0253939 + 0.0439836i
\(841\) −4.22492 2.43926i −0.145687 0.0841124i
\(842\) 0.227173 0.847820i 0.00782889 0.0292178i
\(843\) 11.0168 2.95193i 0.379437 0.101670i
\(844\) 14.6502 25.3749i 0.504281 0.873440i
\(845\) −12.9902 3.48070i −0.446875 0.119740i
\(846\) −0.00547212 + 0.00547212i −0.000188135 + 0.000188135i
\(847\) −14.8039 3.96671i −0.508670 0.136298i
\(848\) −14.6606 + 3.92831i −0.503448 + 0.134899i
\(849\) 25.8507i 0.887194i
\(850\) −0.190528 0.711062i −0.00653507 0.0243892i
\(851\) −0.548658 + 0.316768i −0.0188078 + 0.0108587i
\(852\) 16.6696i 0.571091i
\(853\) 18.4792 + 10.6690i 0.632716 + 0.365299i 0.781803 0.623525i \(-0.214300\pi\)
−0.149087 + 0.988824i \(0.547633\pi\)
\(854\) −0.583606 + 0.583606i −0.0199706 + 0.0199706i
\(855\) −0.185924 + 0.185924i −0.00635847 + 0.00635847i
\(856\) 0.394842 1.47357i 0.0134954 0.0503656i
\(857\) −28.3780 + 16.3841i −0.969375 + 0.559669i −0.899046 0.437855i \(-0.855738\pi\)
−0.0703294 + 0.997524i \(0.522405\pi\)
\(858\) 1.22920 + 2.12903i 0.0419641 + 0.0726839i
\(859\) 14.8137 + 14.8137i 0.505437 + 0.505437i 0.913123 0.407685i \(-0.133664\pi\)
−0.407685 + 0.913123i \(0.633664\pi\)
\(860\) −13.0954 22.6819i −0.446550 0.773448i
\(861\) 3.93724 + 14.6940i 0.134181 + 0.500770i
\(862\) −0.0353408 + 0.131894i −0.00120371 + 0.00449232i
\(863\) −40.8399 10.9430i −1.39020 0.372504i −0.515387 0.856957i \(-0.672352\pi\)
−0.874817 + 0.484453i \(0.839019\pi\)
\(864\) −3.64588 2.10495i −0.124036 0.0716119i
\(865\) 2.24220 + 8.36801i 0.0762371 + 0.284521i
\(866\) 1.51473 + 1.51473i 0.0514725 + 0.0514725i
\(867\) 12.6203 0.428607
\(868\) −0.564130 −0.0191478
\(869\) 33.4507 + 33.4507i 1.13474 + 1.13474i
\(870\) −1.34521 + 0.776660i −0.0456070 + 0.0263312i
\(871\) −39.4157 + 10.5614i −1.33555 + 0.357860i
\(872\) −1.22827 + 2.12742i −0.0415943 + 0.0720435i
\(873\) 0.110453i 0.00373827i
\(874\) 0.230014 + 0.398395i 0.00778033 + 0.0134759i
\(875\) 8.74894 0.295768
\(876\) −28.0497 + 9.44938i −0.947711 + 0.319265i
\(877\) 36.7816 1.24203 0.621014 0.783800i \(-0.286721\pi\)
0.621014 + 0.783800i \(0.286721\pi\)
\(878\) 0.466084 + 0.807281i 0.0157296 + 0.0272444i
\(879\) 31.8563i 1.07449i
\(880\) −26.1965 + 45.3736i −0.883082 + 1.52954i
\(881\) −51.6580 + 13.8417i −1.74040 + 0.466340i −0.982537 0.186069i \(-0.940425\pi\)
−0.757867 + 0.652409i \(0.773758\pi\)
\(882\) −0.00468885 + 0.00270711i −0.000157882 + 9.11530e-5i
\(883\) −6.23372 6.23372i −0.209781 0.209781i 0.594393 0.804175i \(-0.297392\pi\)
−0.804175 + 0.594393i \(0.797392\pi\)
\(884\) −41.7187 −1.40315
\(885\) −31.6134 −1.06267
\(886\) −1.96091 1.96091i −0.0658781 0.0658781i
\(887\) −7.38381 27.5567i −0.247924 0.925265i −0.971891 0.235430i \(-0.924350\pi\)
0.723967 0.689834i \(-0.242317\pi\)
\(888\) −0.264308 0.152598i −0.00886959 0.00512086i
\(889\) 16.0774 + 4.30793i 0.539220 + 0.144483i
\(890\) −0.573694 + 2.14105i −0.0192303 + 0.0717683i
\(891\) −11.5025 42.9277i −0.385347 1.43813i
\(892\) −21.1552 36.6418i −0.708327 1.22686i
\(893\) 39.5399 + 39.5399i 1.32315 + 1.32315i
\(894\) −1.42859 2.47439i −0.0477792 0.0827559i
\(895\) 15.8636 9.15886i 0.530262 0.306147i
\(896\) 0.651174 2.43022i 0.0217542 0.0811878i
\(897\) −5.09270 + 5.09270i −0.170040 + 0.170040i
\(898\) 0.774803 0.774803i 0.0258555 0.0258555i
\(899\) −1.03229 0.595993i −0.0344288 0.0198775i
\(900\) 0.0620776i 0.00206925i
\(901\) −16.3011 + 9.41146i −0.543070 + 0.313541i
\(902\) −0.649567 2.42422i −0.0216282 0.0807176i
\(903\) 9.89195i 0.329183i
\(904\) 2.59207 0.694543i 0.0862110 0.0231002i
\(905\) −14.0688 3.76971i −0.467661 0.125310i
\(906\) −1.33530 + 1.33530i −0.0443623 + 0.0443623i
\(907\) −35.9556 9.63428i −1.19389 0.319901i −0.393466 0.919339i \(-0.628724\pi\)
−0.800421 + 0.599438i \(0.795391\pi\)
\(908\) −5.09776 + 8.82958i −0.169175 + 0.293020i
\(909\) −0.101163 + 0.0271066i −0.00335537 + 0.000899069i
\(910\) 0.233094 0.869917i 0.00772698 0.0288375i
\(911\) 18.4573 + 10.6563i 0.611518 + 0.353060i 0.773559 0.633724i \(-0.218474\pi\)
−0.162041 + 0.986784i \(0.551808\pi\)
\(912\) 23.9058 41.4060i 0.791599 1.37109i
\(913\) 18.6155 32.2429i 0.616082 1.06708i
\(914\) −0.823360 0.475367i −0.0272343 0.0157238i
\(915\) −12.5851 + 46.9684i −0.416052 + 1.55273i
\(916\) 5.68892 1.52434i 0.187967 0.0503657i
\(917\) −6.19000 + 10.7214i −0.204412 + 0.354051i
\(918\) −1.67455 0.448694i −0.0552684 0.0148091i
\(919\) 18.8289 18.8289i 0.621109 0.621109i −0.324706 0.945815i \(-0.605265\pi\)
0.945815 + 0.324706i \(0.105265\pi\)
\(920\) 0.687207 + 0.184137i 0.0226566 + 0.00607081i
\(921\) 22.0910 5.91926i 0.727923 0.195046i
\(922\) 1.70665i 0.0562056i
\(923\) 5.28551 + 19.7258i 0.173975 + 0.649283i
\(924\) 17.1768 9.91702i 0.565075 0.326246i
\(925\) 1.42667i 0.0469087i
\(926\) −1.21282 0.700223i −0.0398558 0.0230108i
\(927\) 0.160313 0.160313i 0.00526538 0.00526538i
\(928\) 2.82038 2.82038i 0.0925835 0.0925835i
\(929\) 13.5796 50.6799i 0.445534 1.66275i −0.268989 0.963143i \(-0.586690\pi\)
0.714523 0.699612i \(-0.246644\pi\)
\(930\) 0.0664750 0.0383794i 0.00217980 0.00125851i
\(931\) 19.5607 + 33.8802i 0.641078 + 1.11038i
\(932\) 34.3522 + 34.3522i 1.12524 + 1.12524i
\(933\) −10.8687 18.8252i −0.355826 0.616309i
\(934\) 0.129197 + 0.482171i 0.00422746 + 0.0157771i
\(935\) −16.8169 + 62.7617i −0.549973 + 2.05253i
\(936\) −0.0157145 0.00421068i −0.000513643 0.000137630i
\(937\) −12.5538 7.24792i −0.410114 0.236779i 0.280725 0.959788i \(-0.409425\pi\)
−0.690839 + 0.723009i \(0.742758\pi\)
\(938\) −0.196790 0.734432i −0.00642543 0.0239800i
\(939\) 30.3769 + 30.3769i 0.991311 + 0.991311i
\(940\) 43.1897 1.40869
\(941\) 6.33171 0.206408 0.103204 0.994660i \(-0.467091\pi\)
0.103204 + 0.994660i \(0.467091\pi\)
\(942\) 1.87257 + 1.87257i 0.0610115 + 0.0610115i
\(943\) 6.36753 3.67629i 0.207355 0.119717i
\(944\) 26.0364 6.97643i 0.847413 0.227064i
\(945\) −8.10226 + 14.0335i −0.263566 + 0.456510i
\(946\) 1.63198i 0.0530601i
\(947\) −17.0649 29.5573i −0.554535 0.960483i −0.997940 0.0641614i \(-0.979563\pi\)
0.443404 0.896322i \(-0.353771\pi\)
\(948\) −33.3433 −1.08294
\(949\) 30.1961 20.0757i 0.980208 0.651684i
\(950\) −1.03595 −0.0336105
\(951\) 23.5593 + 40.8059i 0.763963 + 1.32322i
\(952\) 1.55648i 0.0504458i
\(953\) −7.28582 + 12.6194i −0.236011 + 0.408783i −0.959566 0.281484i \(-0.909173\pi\)
0.723555 + 0.690267i \(0.242507\pi\)
\(954\) −0.00354099 0.000948805i −0.000114644 3.07187e-5i
\(955\) −32.2914 + 18.6434i −1.04492 + 0.603287i
\(956\) 13.4950 + 13.4950i 0.436461 + 0.436461i
\(957\) 41.9086 1.35471
\(958\) −0.0120252 −0.000388517
\(959\) 9.33902 + 9.33902i 0.301573 + 0.301573i
\(960\) −9.51340 35.5045i −0.307044 1.14590i
\(961\) −26.7958 15.4705i −0.864380 0.499050i
\(962\) 0.180367 + 0.0483293i 0.00581527 + 0.00155820i
\(963\) −0.0205748 + 0.0767861i −0.000663013 + 0.00247440i
\(964\) −9.03703 33.7267i −0.291063 1.08626i
\(965\) 14.3266 + 24.8144i 0.461190 + 0.798804i
\(966\) −0.0948921 0.0948921i −0.00305310 0.00305310i
\(967\) 5.22036 + 9.04193i 0.167876 + 0.290769i 0.937673 0.347520i \(-0.112976\pi\)
−0.769797 + 0.638289i \(0.779643\pi\)
\(968\) −3.09042 + 1.78425i −0.0993297 + 0.0573480i
\(969\) 15.3464 57.2736i 0.492998 1.83989i
\(970\) −1.00668 + 1.00668i −0.0323227 + 0.0323227i
\(971\) 10.7584 10.7584i 0.345254 0.345254i −0.513084 0.858338i \(-0.671497\pi\)
0.858338 + 0.513084i \(0.171497\pi\)
\(972\) 0.253813 + 0.146539i 0.00814105 + 0.00470024i
\(973\) 3.38931i 0.108656i
\(974\) −0.503836 + 0.290890i −0.0161439 + 0.00932071i
\(975\) −4.19772 15.6661i −0.134435 0.501716i
\(976\) 41.4599i 1.32710i
\(977\) −43.7545 + 11.7240i −1.39983 + 0.375084i −0.878285 0.478138i \(-0.841312\pi\)
−0.521548 + 0.853222i \(0.674645\pi\)
\(978\) 0.533949 + 0.143071i 0.0170738 + 0.00457491i
\(979\) 42.2874 42.2874i 1.35151 1.35151i
\(980\) 29.1869 + 7.82062i 0.932342 + 0.249820i
\(981\) 0.0640036 0.110857i 0.00204348 0.00353941i
\(982\) 0.964520 0.258442i 0.0307791 0.00824722i
\(983\) −10.0281 + 37.4255i −0.319847 + 1.19369i 0.599543 + 0.800342i \(0.295349\pi\)
−0.919391 + 0.393345i \(0.871318\pi\)
\(984\) 3.06746 + 1.77100i 0.0977871 + 0.0564574i
\(985\) 1.11478 1.93085i 0.0355197 0.0615219i
\(986\) 0.821249 1.42244i 0.0261539 0.0452999i
\(987\) −14.1268 8.15610i −0.449660 0.259611i
\(988\) −15.1950 + 56.7085i −0.483417 + 1.80414i
\(989\) 4.61817 1.23743i 0.146849 0.0393481i
\(990\) −0.00632724 + 0.0109591i −0.000201093 + 0.000348303i
\(991\) −20.5181 5.49781i −0.651779 0.174644i −0.0822458 0.996612i \(-0.526209\pi\)
−0.569533 + 0.821968i \(0.692876\pi\)
\(992\) −0.139372 + 0.139372i −0.00442506 + 0.00442506i
\(993\) −23.3704 6.26207i −0.741636 0.198721i
\(994\) −0.367550 + 0.0984847i −0.0116580 + 0.00312374i
\(995\) 65.1770i 2.06625i
\(996\) 6.79187 + 25.3476i 0.215209 + 0.803169i
\(997\) −21.6549 + 12.5024i −0.685816 + 0.395956i −0.802043 0.597266i \(-0.796254\pi\)
0.116226 + 0.993223i \(0.462920\pi\)
\(998\) 2.33081i 0.0737805i
\(999\) −2.90969 1.67991i −0.0920584 0.0531500i
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 73.2.h.a.49.4 yes 20
3.2 odd 2 657.2.be.c.487.2 20
73.3 even 12 inner 73.2.h.a.3.4 20
73.21 odd 24 5329.2.a.m.1.8 20
73.52 odd 24 5329.2.a.m.1.7 20
219.149 odd 12 657.2.be.c.514.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
73.2.h.a.3.4 20 73.3 even 12 inner
73.2.h.a.49.4 yes 20 1.1 even 1 trivial
657.2.be.c.487.2 20 3.2 odd 2
657.2.be.c.514.2 20 219.149 odd 12
5329.2.a.m.1.7 20 73.52 odd 24
5329.2.a.m.1.8 20 73.21 odd 24