Properties

Label 525.2.bo.a.319.38
Level $525$
Weight $2$
Character 525.319
Analytic conductor $4.192$
Analytic rank $0$
Dimension $320$
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] = [525,2,Mod(4,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 3, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bo (of order \(30\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(320\)
Relative dimension: \(40\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 319.38
Character \(\chi\) \(=\) 525.319
Dual form 525.2.bo.a.79.38

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.92304 + 1.73151i) q^{2} +(0.994522 - 0.104528i) q^{3} +(0.490886 + 4.67047i) q^{4} +(0.450773 - 2.19016i) q^{5} +(2.09349 + 1.52101i) q^{6} +(-1.42574 + 2.22874i) q^{7} +(-4.10095 + 5.64447i) q^{8} +(0.978148 - 0.207912i) q^{9} +O(q^{10})\) \(q+(1.92304 + 1.73151i) q^{2} +(0.994522 - 0.104528i) q^{3} +(0.490886 + 4.67047i) q^{4} +(0.450773 - 2.19016i) q^{5} +(2.09349 + 1.52101i) q^{6} +(-1.42574 + 2.22874i) q^{7} +(-4.10095 + 5.64447i) q^{8} +(0.978148 - 0.207912i) q^{9} +(4.65914 - 3.43124i) q^{10} +(2.32661 + 0.494537i) q^{11} +(0.976394 + 4.59357i) q^{12} +(1.90422 + 0.618718i) q^{13} +(-6.60083 + 1.81726i) q^{14} +(0.219369 - 2.22528i) q^{15} +(-8.47259 + 1.80090i) q^{16} +(-1.91629 - 4.30407i) q^{17} +(2.24101 + 1.29385i) q^{18} +(-0.305504 + 2.90668i) q^{19} +(10.4504 + 1.03020i) q^{20} +(-1.18496 + 2.36556i) q^{21} +(3.61787 + 4.97957i) q^{22} +(-6.04068 - 5.43905i) q^{23} +(-3.48848 + 6.04222i) q^{24} +(-4.59361 - 1.97453i) q^{25} +(2.59057 + 4.48699i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-11.1091 - 5.56482i) q^{28} +(-5.97343 + 4.33995i) q^{29} +(4.27495 - 3.89946i) q^{30} +(8.80335 - 3.91950i) q^{31} +(-7.32694 - 4.23021i) q^{32} +(2.36556 + 0.248630i) q^{33} +(3.76743 - 11.5950i) q^{34} +(4.23861 + 4.12725i) q^{35} +(1.45120 + 4.46635i) q^{36} +(0.434165 + 2.04259i) q^{37} +(-5.62044 + 5.06067i) q^{38} +(1.95846 + 0.416284i) q^{39} +(10.5137 + 11.5261i) q^{40} +(0.548241 - 1.68731i) q^{41} +(-6.37471 + 2.49728i) q^{42} -5.86788i q^{43} +(-1.16762 + 11.1091i) q^{44} +(-0.0144379 - 2.23602i) q^{45} +(-2.19867 - 20.9190i) q^{46} +(4.58434 - 10.2966i) q^{47} +(-8.23793 + 2.67666i) q^{48} +(-2.93453 - 6.35520i) q^{49} +(-5.41476 - 11.7510i) q^{50} +(-2.35569 - 4.08018i) q^{51} +(-1.95495 + 9.19732i) q^{52} +(4.14423 - 0.435576i) q^{53} +(2.36398 + 1.05251i) q^{54} +(2.13189 - 4.87273i) q^{55} +(-6.73315 - 17.1875i) q^{56} +2.92269i q^{57} +(-19.0018 - 1.99717i) q^{58} +(-1.40731 - 1.56298i) q^{59} +(10.5008 - 0.0678032i) q^{60} +(-8.73722 + 9.70366i) q^{61} +(23.7158 + 7.70574i) q^{62} +(-0.931204 + 2.47646i) q^{63} +(-1.41200 - 4.34567i) q^{64} +(2.21346 - 3.89164i) q^{65} +(4.11855 + 4.57412i) q^{66} +(3.30558 + 7.42446i) q^{67} +(19.1613 - 11.0628i) q^{68} +(-6.57612 - 4.77783i) q^{69} +(1.00461 + 15.2760i) q^{70} +(0.106857 - 0.0776359i) q^{71} +(-2.83778 + 6.37376i) q^{72} +(-1.15893 + 5.45232i) q^{73} +(-2.70184 + 4.67973i) q^{74} +(-4.77484 - 1.48355i) q^{75} -13.7255 q^{76} +(-4.41934 + 4.48032i) q^{77} +(3.04539 + 4.19162i) q^{78} +(-9.72491 - 4.32981i) q^{79} +(0.125059 + 19.3681i) q^{80} +(0.913545 - 0.406737i) q^{81} +(3.97588 - 2.29548i) q^{82} +(6.24896 - 8.60095i) q^{83} +(-11.6299 - 4.37312i) q^{84} +(-10.2904 + 2.25684i) q^{85} +(10.1603 - 11.2842i) q^{86} +(-5.48706 + 4.94057i) q^{87} +(-12.3327 + 11.1044i) q^{88} +(-3.61063 + 4.01001i) q^{89} +(3.84393 - 4.32495i) q^{90} +(-4.09388 + 3.36187i) q^{91} +(22.4376 - 30.8828i) q^{92} +(8.34543 - 4.81823i) q^{93} +(26.6445 - 11.8629i) q^{94} +(6.22838 + 1.97935i) q^{95} +(-7.72898 - 3.44116i) q^{96} +(-4.22591 - 5.81646i) q^{97} +(5.36089 - 17.3024i) q^{98} +2.37859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92304 + 1.73151i 1.35979 + 1.22436i 0.950026 + 0.312172i \(0.101057\pi\)
0.409767 + 0.912190i \(0.365610\pi\)
\(3\) 0.994522 0.104528i 0.574187 0.0603495i
\(4\) 0.490886 + 4.67047i 0.245443 + 2.33524i
\(5\) 0.450773 2.19016i 0.201592 0.979470i
\(6\) 2.09349 + 1.52101i 0.854665 + 0.620951i
\(7\) −1.42574 + 2.22874i −0.538879 + 0.842383i
\(8\) −4.10095 + 5.64447i −1.44990 + 1.99562i
\(9\) 0.978148 0.207912i 0.326049 0.0693039i
\(10\) 4.65914 3.43124i 1.47335 1.08505i
\(11\) 2.32661 + 0.494537i 0.701500 + 0.149108i 0.544835 0.838543i \(-0.316592\pi\)
0.156665 + 0.987652i \(0.449926\pi\)
\(12\) 0.976394 + 4.59357i 0.281861 + 1.32605i
\(13\) 1.90422 + 0.618718i 0.528135 + 0.171602i 0.560934 0.827860i \(-0.310442\pi\)
−0.0327988 + 0.999462i \(0.510442\pi\)
\(14\) −6.60083 + 1.81726i −1.76415 + 0.485682i
\(15\) 0.219369 2.22528i 0.0566409 0.574565i
\(16\) −8.47259 + 1.80090i −2.11815 + 0.450226i
\(17\) −1.91629 4.30407i −0.464770 1.04389i −0.982144 0.188131i \(-0.939757\pi\)
0.517374 0.855759i \(-0.326910\pi\)
\(18\) 2.24101 + 1.29385i 0.528212 + 0.304963i
\(19\) −0.305504 + 2.90668i −0.0700875 + 0.666838i 0.901922 + 0.431898i \(0.142156\pi\)
−0.972010 + 0.234940i \(0.924511\pi\)
\(20\) 10.4504 + 1.03020i 2.33677 + 0.230360i
\(21\) −1.18496 + 2.36556i −0.258580 + 0.516207i
\(22\) 3.61787 + 4.97957i 0.771332 + 1.06165i
\(23\) −6.04068 5.43905i −1.25957 1.13412i −0.985000 0.172553i \(-0.944799\pi\)
−0.274568 0.961568i \(-0.588535\pi\)
\(24\) −3.48848 + 6.04222i −0.712082 + 1.23336i
\(25\) −4.59361 1.97453i −0.918722 0.394906i
\(26\) 2.59057 + 4.48699i 0.508052 + 0.879972i
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) −11.1091 5.56482i −2.09943 1.05165i
\(29\) −5.97343 + 4.33995i −1.10924 + 0.805908i −0.982543 0.186033i \(-0.940437\pi\)
−0.126694 + 0.991942i \(0.540437\pi\)
\(30\) 4.27495 3.89946i 0.780496 0.711940i
\(31\) 8.80335 3.91950i 1.58113 0.703964i 0.586742 0.809774i \(-0.300410\pi\)
0.994386 + 0.105810i \(0.0337435\pi\)
\(32\) −7.32694 4.23021i −1.29523 0.747803i
\(33\) 2.36556 + 0.248630i 0.411791 + 0.0432810i
\(34\) 3.76743 11.5950i 0.646109 1.98852i
\(35\) 4.23861 + 4.12725i 0.716455 + 0.697633i
\(36\) 1.45120 + 4.46635i 0.241867 + 0.744391i
\(37\) 0.434165 + 2.04259i 0.0713763 + 0.335799i 0.999318 0.0369263i \(-0.0117567\pi\)
−0.927942 + 0.372725i \(0.878423\pi\)
\(38\) −5.62044 + 5.06067i −0.911756 + 0.820948i
\(39\) 1.95846 + 0.416284i 0.313605 + 0.0666588i
\(40\) 10.5137 + 11.5261i 1.66236 + 1.82244i
\(41\) 0.548241 1.68731i 0.0856208 0.263514i −0.899075 0.437794i \(-0.855760\pi\)
0.984696 + 0.174280i \(0.0557599\pi\)
\(42\) −6.37471 + 2.49728i −0.983640 + 0.385338i
\(43\) 5.86788i 0.894844i −0.894323 0.447422i \(-0.852342\pi\)
0.894323 0.447422i \(-0.147658\pi\)
\(44\) −1.16762 + 11.1091i −0.176025 + 1.67477i
\(45\) −0.0144379 2.23602i −0.00215227 0.333326i
\(46\) −2.19867 20.9190i −0.324177 3.08434i
\(47\) 4.58434 10.2966i 0.668695 1.50191i −0.185874 0.982574i \(-0.559512\pi\)
0.854568 0.519339i \(-0.173822\pi\)
\(48\) −8.23793 + 2.67666i −1.18904 + 0.386343i
\(49\) −2.93453 6.35520i −0.419218 0.907886i
\(50\) −5.41476 11.7510i −0.765763 1.66184i
\(51\) −2.35569 4.08018i −0.329863 0.571340i
\(52\) −1.95495 + 9.19732i −0.271103 + 1.27544i
\(53\) 4.14423 0.435576i 0.569254 0.0598310i 0.184471 0.982838i \(-0.440943\pi\)
0.384783 + 0.923007i \(0.374276\pi\)
\(54\) 2.36398 + 1.05251i 0.321697 + 0.143229i
\(55\) 2.13189 4.87273i 0.287464 0.657039i
\(56\) −6.73315 17.1875i −0.899755 2.29677i
\(57\) 2.92269i 0.387120i
\(58\) −19.0018 1.99717i −2.49506 0.262241i
\(59\) −1.40731 1.56298i −0.183217 0.203483i 0.644539 0.764571i \(-0.277049\pi\)
−0.827756 + 0.561089i \(0.810383\pi\)
\(60\) 10.5008 0.0678032i 1.35565 0.00875335i
\(61\) −8.73722 + 9.70366i −1.11869 + 1.24243i −0.151473 + 0.988461i \(0.548402\pi\)
−0.967213 + 0.253966i \(0.918265\pi\)
\(62\) 23.7158 + 7.70574i 3.01191 + 0.978630i
\(63\) −0.931204 + 2.47646i −0.117321 + 0.312005i
\(64\) −1.41200 4.34567i −0.176499 0.543209i
\(65\) 2.21346 3.89164i 0.274546 0.482699i
\(66\) 4.11855 + 4.57412i 0.506959 + 0.563035i
\(67\) 3.30558 + 7.42446i 0.403841 + 0.907042i 0.994943 + 0.100445i \(0.0320266\pi\)
−0.591101 + 0.806597i \(0.701307\pi\)
\(68\) 19.1613 11.0628i 2.32365 1.34156i
\(69\) −6.57612 4.77783i −0.791672 0.575183i
\(70\) 1.00461 + 15.2760i 0.120074 + 1.82584i
\(71\) 0.106857 0.0776359i 0.0126816 0.00921369i −0.581426 0.813599i \(-0.697505\pi\)
0.594108 + 0.804385i \(0.297505\pi\)
\(72\) −2.83778 + 6.37376i −0.334436 + 0.751155i
\(73\) −1.15893 + 5.45232i −0.135642 + 0.638146i 0.856822 + 0.515612i \(0.172435\pi\)
−0.992464 + 0.122534i \(0.960898\pi\)
\(74\) −2.70184 + 4.67973i −0.314083 + 0.544007i
\(75\) −4.77484 1.48355i −0.551351 0.171306i
\(76\) −13.7255 −1.57443
\(77\) −4.41934 + 4.48032i −0.503630 + 0.510580i
\(78\) 3.04539 + 4.19162i 0.344823 + 0.474608i
\(79\) −9.72491 4.32981i −1.09414 0.487142i −0.221327 0.975200i \(-0.571039\pi\)
−0.872811 + 0.488058i \(0.837705\pi\)
\(80\) 0.125059 + 19.3681i 0.0139820 + 2.16542i
\(81\) 0.913545 0.406737i 0.101505 0.0451930i
\(82\) 3.97588 2.29548i 0.439063 0.253493i
\(83\) 6.24896 8.60095i 0.685912 0.944077i −0.314074 0.949399i \(-0.601694\pi\)
0.999986 + 0.00532133i \(0.00169384\pi\)
\(84\) −11.6299 4.37312i −1.26893 0.477146i
\(85\) −10.2904 + 2.25684i −1.11615 + 0.244788i
\(86\) 10.1603 11.2842i 1.09561 1.21680i
\(87\) −5.48706 + 4.94057i −0.588274 + 0.529684i
\(88\) −12.3327 + 11.1044i −1.31467 + 1.18374i
\(89\) −3.61063 + 4.01001i −0.382726 + 0.425060i −0.903469 0.428653i \(-0.858988\pi\)
0.520743 + 0.853713i \(0.325655\pi\)
\(90\) 3.84393 4.32495i 0.405186 0.455890i
\(91\) −4.09388 + 3.36187i −0.429155 + 0.352420i
\(92\) 22.4376 30.8828i 2.33929 3.21975i
\(93\) 8.34543 4.81823i 0.865380 0.499628i
\(94\) 26.6445 11.8629i 2.74817 1.22356i
\(95\) 6.22838 + 1.97935i 0.639018 + 0.203078i
\(96\) −7.72898 3.44116i −0.788836 0.351212i
\(97\) −4.22591 5.81646i −0.429076 0.590572i 0.538665 0.842520i \(-0.318929\pi\)
−0.967741 + 0.251948i \(0.918929\pi\)
\(98\) 5.36089 17.3024i 0.541531 1.74781i
\(99\) 2.37859 0.239057
\(100\) 6.96704 22.4236i 0.696704 2.24236i
\(101\) −3.66887 + 6.35467i −0.365066 + 0.632313i −0.988787 0.149334i \(-0.952287\pi\)
0.623721 + 0.781647i \(0.285620\pi\)
\(102\) 2.53479 11.9253i 0.250982 1.18078i
\(103\) −1.87567 + 4.21282i −0.184815 + 0.415102i −0.982064 0.188550i \(-0.939621\pi\)
0.797248 + 0.603651i \(0.206288\pi\)
\(104\) −11.3014 + 8.21098i −1.10820 + 0.805153i
\(105\) 4.64680 + 3.66159i 0.453481 + 0.357335i
\(106\) 8.72371 + 6.33815i 0.847321 + 0.615615i
\(107\) 4.16738 2.40604i 0.402876 0.232601i −0.284848 0.958573i \(-0.591943\pi\)
0.687724 + 0.725972i \(0.258610\pi\)
\(108\) 1.91012 + 4.29019i 0.183801 + 0.412824i
\(109\) 1.29182 + 1.43471i 0.123734 + 0.137420i 0.801828 0.597554i \(-0.203861\pi\)
−0.678095 + 0.734974i \(0.737194\pi\)
\(110\) 12.5369 5.67906i 1.19535 0.541477i
\(111\) 0.645295 + 1.98601i 0.0612487 + 0.188504i
\(112\) 8.06597 21.4508i 0.762163 2.02691i
\(113\) 15.0592 + 4.89302i 1.41665 + 0.460296i 0.914535 0.404506i \(-0.132557\pi\)
0.502112 + 0.864803i \(0.332557\pi\)
\(114\) −5.06067 + 5.62044i −0.473975 + 0.526402i
\(115\) −14.6354 + 10.7783i −1.36475 + 1.00508i
\(116\) −23.2019 25.7683i −2.15424 2.39253i
\(117\) 1.99125 + 0.209288i 0.184091 + 0.0193487i
\(118\) 5.44244i 0.501018i
\(119\) 12.3248 + 1.86557i 1.12981 + 0.171017i
\(120\) 11.6609 + 10.3640i 1.06449 + 0.946098i
\(121\) −4.88044 2.17291i −0.443676 0.197537i
\(122\) −33.6040 + 3.53192i −3.04236 + 0.319765i
\(123\) 0.368865 1.73538i 0.0332595 0.156474i
\(124\) 22.6274 + 39.1918i 2.03200 + 3.51952i
\(125\) −6.39521 + 9.17068i −0.572005 + 0.820250i
\(126\) −6.07876 + 3.14993i −0.541539 + 0.280619i
\(127\) −3.70660 + 1.20435i −0.328908 + 0.106869i −0.468816 0.883296i \(-0.655319\pi\)
0.139908 + 0.990164i \(0.455319\pi\)
\(128\) −2.07307 + 4.65619i −0.183235 + 0.411553i
\(129\) −0.613361 5.83574i −0.0540034 0.513808i
\(130\) 10.9950 3.65114i 0.964325 0.320226i
\(131\) 0.333613 3.17411i 0.0291479 0.277324i −0.970234 0.242169i \(-0.922141\pi\)
0.999382 0.0351543i \(-0.0111923\pi\)
\(132\) 11.1703i 0.972253i
\(133\) −6.04265 4.82506i −0.523964 0.418386i
\(134\) −6.49877 + 20.0012i −0.561408 + 1.72784i
\(135\) −0.248087 2.22226i −0.0213519 0.191262i
\(136\) 32.1528 + 6.83429i 2.75708 + 0.586036i
\(137\) −4.69837 + 4.23043i −0.401409 + 0.361430i −0.844970 0.534814i \(-0.820382\pi\)
0.443561 + 0.896244i \(0.353715\pi\)
\(138\) −4.37326 20.5746i −0.372277 1.75142i
\(139\) 4.87901 + 15.0161i 0.413832 + 1.27365i 0.913291 + 0.407307i \(0.133532\pi\)
−0.499459 + 0.866338i \(0.666468\pi\)
\(140\) −17.1955 + 21.8223i −1.45329 + 1.84432i
\(141\) 3.48294 10.7194i 0.293316 0.902735i
\(142\) 0.339917 + 0.0357267i 0.0285252 + 0.00299812i
\(143\) 4.12440 + 2.38122i 0.344900 + 0.199128i
\(144\) −7.91301 + 3.52310i −0.659418 + 0.293592i
\(145\) 6.81253 + 15.0391i 0.565750 + 1.24893i
\(146\) −11.6694 + 8.47832i −0.965767 + 0.701671i
\(147\) −3.58275 6.01364i −0.295500 0.495997i
\(148\) −9.32671 + 3.03043i −0.766651 + 0.249100i
\(149\) 10.6921 + 18.5192i 0.875929 + 1.51715i 0.855770 + 0.517356i \(0.173084\pi\)
0.0201586 + 0.999797i \(0.493583\pi\)
\(150\) −6.61341 11.1206i −0.539983 0.907993i
\(151\) −1.17736 + 2.03925i −0.0958122 + 0.165952i −0.909947 0.414724i \(-0.863878\pi\)
0.814135 + 0.580676i \(0.197211\pi\)
\(152\) −15.1538 13.6446i −1.22914 1.10672i
\(153\) −2.76929 3.81159i −0.223883 0.308149i
\(154\) −16.2563 + 0.963700i −1.30997 + 0.0776571i
\(155\) −4.61604 21.0476i −0.370769 1.69058i
\(156\) −0.982860 + 9.35128i −0.0786917 + 0.748702i
\(157\) −14.6820 8.47665i −1.17175 0.676510i −0.217658 0.976025i \(-0.569842\pi\)
−0.954092 + 0.299515i \(0.903175\pi\)
\(158\) −11.2043 25.1652i −0.891362 2.00203i
\(159\) 4.07600 0.866380i 0.323248 0.0687084i
\(160\) −12.5676 + 14.1403i −0.993558 + 1.11789i
\(161\) 20.7346 5.70840i 1.63412 0.449885i
\(162\) 2.46105 + 0.799644i 0.193358 + 0.0628259i
\(163\) 2.25397 + 10.6041i 0.176544 + 0.830575i 0.973884 + 0.227045i \(0.0729065\pi\)
−0.797340 + 0.603530i \(0.793760\pi\)
\(164\) 8.14966 + 1.73226i 0.636382 + 0.135267i
\(165\) 1.61087 5.06888i 0.125406 0.394612i
\(166\) 26.9096 5.71981i 2.08859 0.443944i
\(167\) −4.96719 + 6.83675i −0.384373 + 0.529043i −0.956736 0.290956i \(-0.906027\pi\)
0.572364 + 0.820000i \(0.306027\pi\)
\(168\) −8.49284 16.3895i −0.655237 1.26448i
\(169\) −7.27398 5.28486i −0.559537 0.406528i
\(170\) −23.6966 13.4780i −1.81744 1.03371i
\(171\) 0.305504 + 2.90668i 0.0233625 + 0.222279i
\(172\) 27.4058 2.88046i 2.08967 0.219633i
\(173\) 2.78886 + 2.51110i 0.212033 + 0.190916i 0.768303 0.640086i \(-0.221101\pi\)
−0.556270 + 0.831002i \(0.687768\pi\)
\(174\) −19.1065 −1.44846
\(175\) 10.9500 7.42277i 0.827742 0.561109i
\(176\) −20.6030 −1.55301
\(177\) −1.56298 1.40731i −0.117481 0.105780i
\(178\) −13.8867 + 1.45956i −1.04086 + 0.109398i
\(179\) 1.93875 + 18.4460i 0.144909 + 1.37872i 0.789294 + 0.614015i \(0.210447\pi\)
−0.644386 + 0.764701i \(0.722887\pi\)
\(180\) 10.4362 1.16506i 0.777867 0.0868387i
\(181\) −2.76025 2.00544i −0.205167 0.149063i 0.480457 0.877018i \(-0.340471\pi\)
−0.685625 + 0.727955i \(0.740471\pi\)
\(182\) −13.6938 0.623599i −1.01505 0.0462242i
\(183\) −7.67505 + 10.5638i −0.567356 + 0.780898i
\(184\) 55.4731 11.7912i 4.08953 0.869256i
\(185\) 4.66930 0.0301495i 0.343294 0.00221663i
\(186\) 24.3914 + 5.18455i 1.78846 + 0.380150i
\(187\) −2.32996 10.9616i −0.170383 0.801590i
\(188\) 50.3403 + 16.3566i 3.67145 + 1.19293i
\(189\) −0.667243 + 2.56023i −0.0485348 + 0.186229i
\(190\) 8.55013 + 14.5909i 0.620292 + 1.05853i
\(191\) −23.1330 + 4.91707i −1.67385 + 0.355787i −0.944539 0.328400i \(-0.893490\pi\)
−0.729307 + 0.684187i \(0.760157\pi\)
\(192\) −1.85851 4.17427i −0.134126 0.301252i
\(193\) 16.4640 + 9.50548i 1.18510 + 0.684219i 0.957189 0.289462i \(-0.0934765\pi\)
0.227913 + 0.973682i \(0.426810\pi\)
\(194\) 1.94469 18.5025i 0.139620 1.32840i
\(195\) 1.79455 4.10170i 0.128510 0.293729i
\(196\) 28.2412 16.8253i 2.01723 1.20181i
\(197\) −11.4071 15.7006i −0.812724 1.11862i −0.990897 0.134619i \(-0.957019\pi\)
0.178174 0.983999i \(-0.442981\pi\)
\(198\) 4.57412 + 4.11855i 0.325068 + 0.292693i
\(199\) −1.29272 + 2.23906i −0.0916388 + 0.158723i −0.908201 0.418535i \(-0.862544\pi\)
0.816562 + 0.577258i \(0.195877\pi\)
\(200\) 29.9833 17.8310i 2.12014 1.26085i
\(201\) 4.06354 + 7.03826i 0.286620 + 0.496441i
\(202\) −18.0585 + 5.86757i −1.27059 + 0.412841i
\(203\) −1.15604 19.5008i −0.0811383 1.36869i
\(204\) 17.9000 13.0051i 1.25325 0.910540i
\(205\) −3.44835 1.96133i −0.240843 0.136985i
\(206\) −10.9015 + 4.85367i −0.759545 + 0.338171i
\(207\) −7.03952 4.06427i −0.489280 0.282486i
\(208\) −17.2479 1.81283i −1.19593 0.125697i
\(209\) −2.14825 + 6.61163i −0.148598 + 0.457336i
\(210\) 2.59589 + 15.0874i 0.179133 + 1.04113i
\(211\) 0.172526 + 0.530980i 0.0118772 + 0.0365542i 0.956819 0.290683i \(-0.0938825\pi\)
−0.944942 + 0.327237i \(0.893882\pi\)
\(212\) 4.06869 + 19.1417i 0.279439 + 1.31466i
\(213\) 0.0981561 0.0883802i 0.00672555 0.00605571i
\(214\) 12.1801 + 2.58896i 0.832615 + 0.176978i
\(215\) −12.8516 2.64508i −0.876472 0.180393i
\(216\) −2.15600 + 6.63547i −0.146697 + 0.451487i
\(217\) −3.81576 + 25.2085i −0.259030 + 1.71127i
\(218\) 4.99579i 0.338357i
\(219\) −0.582655 + 5.54360i −0.0393722 + 0.374601i
\(220\) 23.8045 + 7.56497i 1.60490 + 0.510030i
\(221\) −0.986039 9.38154i −0.0663282 0.631070i
\(222\) −2.19788 + 4.93651i −0.147512 + 0.331317i
\(223\) 23.6766 7.69300i 1.58550 0.515161i 0.622036 0.782989i \(-0.286306\pi\)
0.963467 + 0.267827i \(0.0863057\pi\)
\(224\) 19.8743 10.2986i 1.32791 0.688106i
\(225\) −4.90375 0.976316i −0.326917 0.0650877i
\(226\) 20.4870 + 35.4845i 1.36278 + 2.36040i
\(227\) 5.91370 27.8218i 0.392506 1.84659i −0.126694 0.991942i \(-0.540437\pi\)
0.519200 0.854653i \(-0.326230\pi\)
\(228\) −13.6503 + 1.43471i −0.904016 + 0.0950159i
\(229\) 5.18249 + 2.30739i 0.342468 + 0.152477i 0.570762 0.821116i \(-0.306648\pi\)
−0.228294 + 0.973592i \(0.573315\pi\)
\(230\) −46.8070 4.61426i −3.08636 0.304255i
\(231\) −3.92681 + 4.91773i −0.258365 + 0.323563i
\(232\) 51.5147i 3.38211i
\(233\) 8.99850 + 0.945780i 0.589511 + 0.0619601i 0.394588 0.918858i \(-0.370887\pi\)
0.194924 + 0.980818i \(0.437554\pi\)
\(234\) 3.46685 + 3.85033i 0.226635 + 0.251704i
\(235\) −20.4847 14.6819i −1.33627 0.957739i
\(236\) 6.60902 7.34006i 0.430211 0.477797i
\(237\) −10.1242 3.28956i −0.657639 0.213680i
\(238\) 20.4707 + 24.9280i 1.32692 + 1.61584i
\(239\) −1.54596 4.75797i −0.0999997 0.307767i 0.888525 0.458829i \(-0.151731\pi\)
−0.988524 + 0.151061i \(0.951731\pi\)
\(240\) 2.14889 + 19.2489i 0.138711 + 1.24251i
\(241\) 1.25216 + 1.39066i 0.0806587 + 0.0895805i 0.782123 0.623124i \(-0.214137\pi\)
−0.701464 + 0.712704i \(0.747470\pi\)
\(242\) −5.62284 12.6291i −0.361450 0.811830i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −49.6097 36.0435i −3.17593 2.30745i
\(245\) −15.2417 + 3.56234i −0.973757 + 0.227589i
\(246\) 3.71416 2.69850i 0.236806 0.172050i
\(247\) −2.38016 + 5.34593i −0.151446 + 0.340154i
\(248\) −13.9786 + 65.7640i −0.887639 + 4.17602i
\(249\) 5.31568 9.20703i 0.336868 0.583472i
\(250\) −28.1773 + 6.56218i −1.78209 + 0.415029i
\(251\) 18.6506 1.17722 0.588608 0.808418i \(-0.299676\pi\)
0.588608 + 0.808418i \(0.299676\pi\)
\(252\) −12.0234 3.13350i −0.757400 0.197392i
\(253\) −11.3645 15.6419i −0.714480 0.983398i
\(254\) −9.21328 4.10201i −0.578092 0.257383i
\(255\) −9.99814 + 3.32012i −0.626108 + 0.207914i
\(256\) −20.3974 + 9.08150i −1.27484 + 0.567594i
\(257\) −5.58652 + 3.22538i −0.348478 + 0.201194i −0.664015 0.747720i \(-0.731149\pi\)
0.315537 + 0.948913i \(0.397815\pi\)
\(258\) 8.92512 12.2844i 0.555654 0.764792i
\(259\) −5.17139 1.94456i −0.321335 0.120829i
\(260\) 19.2624 + 8.42756i 1.19460 + 0.522655i
\(261\) −4.94057 + 5.48706i −0.305813 + 0.339640i
\(262\) 6.13756 5.52628i 0.379180 0.341415i
\(263\) −19.8872 + 17.9065i −1.22629 + 1.10416i −0.235069 + 0.971979i \(0.575532\pi\)
−0.991225 + 0.132182i \(0.957802\pi\)
\(264\) −11.1044 + 12.3327i −0.683430 + 0.759026i
\(265\) 0.914123 9.27287i 0.0561542 0.569628i
\(266\) −3.26560 19.7417i −0.200227 1.21044i
\(267\) −3.17169 + 4.36546i −0.194104 + 0.267162i
\(268\) −33.0531 + 19.0832i −2.01904 + 1.16569i
\(269\) 2.76121 1.22937i 0.168354 0.0749560i −0.320829 0.947137i \(-0.603962\pi\)
0.489183 + 0.872181i \(0.337295\pi\)
\(270\) 3.37079 4.70306i 0.205140 0.286219i
\(271\) −7.10871 3.16500i −0.431823 0.192260i 0.179302 0.983794i \(-0.442616\pi\)
−0.611125 + 0.791534i \(0.709283\pi\)
\(272\) 23.9872 + 33.0155i 1.45444 + 2.00186i
\(273\) −3.72004 + 3.77138i −0.225147 + 0.228254i
\(274\) −16.3602 −0.988354
\(275\) −9.71107 6.86567i −0.585600 0.414016i
\(276\) 19.0866 33.0589i 1.14888 1.98991i
\(277\) −5.11696 + 24.0734i −0.307448 + 1.44643i 0.504859 + 0.863202i \(0.331544\pi\)
−0.812308 + 0.583229i \(0.801789\pi\)
\(278\) −16.6179 + 37.3245i −0.996677 + 2.23857i
\(279\) 7.79607 5.66417i 0.466738 0.339105i
\(280\) −40.6785 + 6.99903i −2.43100 + 0.418272i
\(281\) 13.6801 + 9.93921i 0.816089 + 0.592923i 0.915590 0.402114i \(-0.131725\pi\)
−0.0995006 + 0.995038i \(0.531725\pi\)
\(282\) 25.2585 14.5830i 1.50412 0.868406i
\(283\) −9.44475 21.2133i −0.561432 1.26100i −0.941804 0.336164i \(-0.890870\pi\)
0.380371 0.924834i \(-0.375796\pi\)
\(284\) 0.415051 + 0.460960i 0.0246287 + 0.0273530i
\(285\) 6.40116 + 1.31747i 0.379172 + 0.0780401i
\(286\) 3.80826 + 11.7206i 0.225187 + 0.693055i
\(287\) 2.97892 + 3.62755i 0.175840 + 0.214128i
\(288\) −8.04634 2.61441i −0.474135 0.154056i
\(289\) −3.47760 + 3.86227i −0.204565 + 0.227192i
\(290\) −12.9396 + 40.7167i −0.759840 + 2.39097i
\(291\) −4.81074 5.34287i −0.282011 0.313205i
\(292\) −26.0338 2.73626i −1.52351 0.160128i
\(293\) 8.75186i 0.511289i −0.966771 0.255645i \(-0.917712\pi\)
0.966771 0.255645i \(-0.0822877\pi\)
\(294\) 3.52292 17.7680i 0.205461 1.03625i
\(295\) −4.05756 + 2.37769i −0.236240 + 0.138435i
\(296\) −13.3098 5.92591i −0.773617 0.344436i
\(297\) 2.36556 0.248630i 0.137264 0.0144270i
\(298\) −11.5050 + 54.1266i −0.666464 + 3.13547i
\(299\) −8.13753 14.0946i −0.470606 0.815113i
\(300\) 4.58497 23.0290i 0.264713 1.32958i
\(301\) 13.0780 + 8.36608i 0.753801 + 0.482213i
\(302\) −5.79508 + 1.88294i −0.333470 + 0.108351i
\(303\) −2.98453 + 6.70336i −0.171457 + 0.385098i
\(304\) −2.64624 25.1773i −0.151772 1.44402i
\(305\) 17.3141 + 23.5101i 0.991402 + 1.34618i
\(306\) 1.27438 12.1249i 0.0728512 0.693133i
\(307\) 20.4521i 1.16726i 0.812020 + 0.583630i \(0.198368\pi\)
−0.812020 + 0.583630i \(0.801632\pi\)
\(308\) −23.0946 18.4411i −1.31594 1.05078i
\(309\) −1.42503 + 4.38580i −0.0810674 + 0.249500i
\(310\) 27.5673 48.4679i 1.56571 2.75279i
\(311\) 3.87861 + 0.824424i 0.219936 + 0.0467488i 0.316561 0.948572i \(-0.397472\pi\)
−0.0966257 + 0.995321i \(0.530805\pi\)
\(312\) −10.3813 + 9.34732i −0.587723 + 0.529188i
\(313\) −4.20849 19.7994i −0.237878 1.11913i −0.921224 0.389033i \(-0.872809\pi\)
0.683346 0.730095i \(-0.260524\pi\)
\(314\) −13.5566 41.7229i −0.765043 2.35456i
\(315\) 5.00409 + 3.15581i 0.281948 + 0.177810i
\(316\) 15.4484 47.5453i 0.869041 2.67463i
\(317\) −4.38631 0.461020i −0.246360 0.0258935i −0.0194564 0.999811i \(-0.506194\pi\)
−0.226904 + 0.973917i \(0.572860\pi\)
\(318\) 9.33844 + 5.39155i 0.523673 + 0.302343i
\(319\) −16.0441 + 7.14330i −0.898298 + 0.399948i
\(320\) −10.1542 + 1.13359i −0.567638 + 0.0633694i
\(321\) 3.89305 2.82847i 0.217289 0.157870i
\(322\) 49.7576 + 24.9248i 2.77288 + 1.38900i
\(323\) 13.0960 4.25514i 0.728680 0.236762i
\(324\) 2.34810 + 4.06703i 0.130450 + 0.225946i
\(325\) −7.52556 6.60209i −0.417443 0.366218i
\(326\) −14.0266 + 24.2948i −0.776862 + 1.34556i
\(327\) 1.43471 + 1.29182i 0.0793395 + 0.0714376i
\(328\) 7.27568 + 10.0141i 0.401732 + 0.552937i
\(329\) 16.4123 + 24.8976i 0.904840 + 1.37265i
\(330\) 11.8746 6.95841i 0.653674 0.383048i
\(331\) −1.82229 + 17.3379i −0.100162 + 0.952978i 0.822864 + 0.568239i \(0.192375\pi\)
−0.923026 + 0.384739i \(0.874292\pi\)
\(332\) 43.2380 + 24.9635i 2.37299 + 1.37005i
\(333\) 0.849355 + 1.90768i 0.0465444 + 0.104540i
\(334\) −21.3900 + 4.54658i −1.17041 + 0.248778i
\(335\) 17.7508 3.89301i 0.969831 0.212698i
\(336\) 5.77957 22.1764i 0.315301 1.20982i
\(337\) −20.5012 6.66123i −1.11677 0.362861i −0.308236 0.951310i \(-0.599739\pi\)
−0.808534 + 0.588449i \(0.799739\pi\)
\(338\) −4.83735 22.7579i −0.263117 1.23787i
\(339\) 15.4881 + 3.29210i 0.841199 + 0.178802i
\(340\) −15.5919 46.9532i −0.845590 2.54640i
\(341\) 22.4203 4.76559i 1.21413 0.258071i
\(342\) −4.44545 + 6.11863i −0.240382 + 0.330858i
\(343\) 18.3479 + 2.52058i 0.990695 + 0.136098i
\(344\) 33.1211 + 24.0639i 1.78577 + 1.29744i
\(345\) −13.4286 + 12.2490i −0.722969 + 0.659467i
\(346\) 1.01508 + 9.65789i 0.0545713 + 0.519211i
\(347\) 17.5860 1.84837i 0.944068 0.0992255i 0.380030 0.924974i \(-0.375914\pi\)
0.564038 + 0.825749i \(0.309247\pi\)
\(348\) −25.7683 23.2019i −1.38133 1.24375i
\(349\) 11.3893 0.609655 0.304827 0.952408i \(-0.401401\pi\)
0.304827 + 0.952408i \(0.401401\pi\)
\(350\) 33.9099 + 4.68576i 1.81256 + 0.250465i
\(351\) 2.00221 0.106870
\(352\) −14.9550 13.4655i −0.797102 0.717714i
\(353\) −18.5823 + 1.95308i −0.989037 + 0.103952i −0.585208 0.810883i \(-0.698987\pi\)
−0.403828 + 0.914835i \(0.632321\pi\)
\(354\) −0.568890 5.41263i −0.0302362 0.287678i
\(355\) −0.121867 0.269029i −0.00646803 0.0142786i
\(356\) −20.5010 14.8949i −1.08655 0.789427i
\(357\) 12.4523 + 0.567061i 0.659044 + 0.0300121i
\(358\) −28.2111 + 38.8292i −1.49100 + 2.05219i
\(359\) −1.92151 + 0.408430i −0.101413 + 0.0215561i −0.258339 0.966054i \(-0.583175\pi\)
0.156925 + 0.987610i \(0.449842\pi\)
\(360\) 12.6804 + 9.08831i 0.668314 + 0.478996i
\(361\) 10.2294 + 2.17432i 0.538387 + 0.114438i
\(362\) −1.83562 8.63592i −0.0964781 0.453894i
\(363\) −5.08083 1.65086i −0.266675 0.0866478i
\(364\) −17.7111 17.4701i −0.928316 0.915680i
\(365\) 11.4191 + 4.99599i 0.597700 + 0.261502i
\(366\) −33.0507 + 7.02515i −1.72759 + 0.367210i
\(367\) −8.97349 20.1548i −0.468412 1.05207i −0.981101 0.193497i \(-0.938017\pi\)
0.512689 0.858575i \(-0.328649\pi\)
\(368\) 60.9754 + 35.2041i 3.17856 + 1.83514i
\(369\) 0.185449 1.76443i 0.00965407 0.0918523i
\(370\) 9.03144 + 8.02696i 0.469522 + 0.417302i
\(371\) −4.93781 + 9.85741i −0.256358 + 0.511771i
\(372\) 26.6001 + 36.6119i 1.37915 + 1.89824i
\(373\) −8.12249 7.31352i −0.420566 0.378680i 0.431500 0.902113i \(-0.357984\pi\)
−0.852067 + 0.523433i \(0.824651\pi\)
\(374\) 14.4995 25.1139i 0.749751 1.29861i
\(375\) −5.40158 + 9.78892i −0.278936 + 0.505498i
\(376\) 39.3187 + 68.1020i 2.02771 + 3.51209i
\(377\) −14.0599 + 4.56835i −0.724123 + 0.235282i
\(378\) −5.71620 + 3.76808i −0.294010 + 0.193809i
\(379\) 30.3119 22.0229i 1.55702 1.13124i 0.618614 0.785695i \(-0.287694\pi\)
0.938403 0.345544i \(-0.112306\pi\)
\(380\) −6.18709 + 30.0611i −0.317391 + 1.54210i
\(381\) −3.56041 + 1.58520i −0.182405 + 0.0812121i
\(382\) −52.9996 30.5993i −2.71169 1.56560i
\(383\) −9.31778 0.979338i −0.476116 0.0500418i −0.136569 0.990631i \(-0.543607\pi\)
−0.339548 + 0.940589i \(0.610274\pi\)
\(384\) −1.57501 + 4.84738i −0.0803743 + 0.247367i
\(385\) 7.82051 + 11.6987i 0.398570 + 0.596219i
\(386\) 15.2020 + 46.7869i 0.773761 + 2.38139i
\(387\) −1.22000 5.73966i −0.0620162 0.291763i
\(388\) 25.0912 22.5922i 1.27381 1.14694i
\(389\) 7.34897 + 1.56207i 0.372607 + 0.0792001i 0.390409 0.920641i \(-0.372333\pi\)
−0.0178019 + 0.999842i \(0.505667\pi\)
\(390\) 10.5531 4.78043i 0.534378 0.242067i
\(391\) −11.8343 + 36.4223i −0.598488 + 1.84196i
\(392\) 47.9061 + 9.49849i 2.41962 + 0.479746i
\(393\) 3.19160i 0.160995i
\(394\) 5.24936 49.9443i 0.264459 2.51616i
\(395\) −13.8667 + 19.3474i −0.697709 + 0.973471i
\(396\) 1.16762 + 11.1091i 0.0586750 + 0.558255i
\(397\) 6.87302 15.4371i 0.344947 0.774764i −0.654872 0.755740i \(-0.727277\pi\)
0.999819 0.0190242i \(-0.00605594\pi\)
\(398\) −6.36292 + 2.06744i −0.318944 + 0.103631i
\(399\) −6.51390 4.16700i −0.326103 0.208611i
\(400\) 42.4757 + 8.45672i 2.12378 + 0.422836i
\(401\) −11.0235 19.0933i −0.550489 0.953475i −0.998239 0.0593164i \(-0.981108\pi\)
0.447750 0.894159i \(-0.352225\pi\)
\(402\) −4.37248 + 20.5709i −0.218079 + 1.02598i
\(403\) 19.1886 2.01680i 0.955851 0.100464i
\(404\) −31.4803 14.0159i −1.56620 0.697318i
\(405\) −0.479017 2.18416i −0.0238026 0.108532i
\(406\) 31.5428 39.5025i 1.56544 1.96048i
\(407\) 4.96702i 0.246206i
\(408\) 32.6911 + 3.43597i 1.61845 + 0.170106i
\(409\) 18.5199 + 20.5684i 0.915750 + 1.01704i 0.999788 + 0.0205805i \(0.00655143\pi\)
−0.0840386 + 0.996463i \(0.526782\pi\)
\(410\) −3.23525 9.74256i −0.159777 0.481151i
\(411\) −4.23043 + 4.69837i −0.208672 + 0.231754i
\(412\) −20.5966 6.69224i −1.01472 0.329703i
\(413\) 5.48993 0.908126i 0.270142 0.0446860i
\(414\) −6.49993 20.0047i −0.319454 0.983179i
\(415\) −16.0206 17.5633i −0.786421 0.862148i
\(416\) −11.3348 12.5886i −0.555734 0.617205i
\(417\) 6.42189 + 14.4238i 0.314481 + 0.706336i
\(418\) −15.5793 + 8.99470i −0.762007 + 0.439945i
\(419\) −24.5744 17.8543i −1.20054 0.872240i −0.206199 0.978510i \(-0.566109\pi\)
−0.994337 + 0.106270i \(0.966109\pi\)
\(420\) −14.8203 + 23.5002i −0.723156 + 1.14669i
\(421\) 5.25208 3.81586i 0.255971 0.185974i −0.452398 0.891816i \(-0.649431\pi\)
0.708369 + 0.705842i \(0.249431\pi\)
\(422\) −0.587624 + 1.31982i −0.0286051 + 0.0642480i
\(423\) 2.34338 11.0247i 0.113939 0.536041i
\(424\) −14.5367 + 25.1783i −0.705963 + 1.22276i
\(425\) 0.304200 + 23.5550i 0.0147558 + 1.14258i
\(426\) 0.341789 0.0165597
\(427\) −9.16990 33.3079i −0.443762 1.61188i
\(428\) 13.2830 + 18.2825i 0.642060 + 0.883720i
\(429\) 4.35071 + 1.93706i 0.210054 + 0.0935223i
\(430\) −20.1341 27.3393i −0.970954 1.31842i
\(431\) 29.5417 13.1528i 1.42297 0.633549i 0.456363 0.889794i \(-0.349152\pi\)
0.966612 + 0.256245i \(0.0824852\pi\)
\(432\) −7.50140 + 4.33093i −0.360911 + 0.208372i
\(433\) 15.9464 21.9484i 0.766336 1.05477i −0.230325 0.973114i \(-0.573979\pi\)
0.996661 0.0816569i \(-0.0260212\pi\)
\(434\) −50.9867 + 41.8699i −2.44744 + 2.00982i
\(435\) 8.34722 + 14.2446i 0.400219 + 0.682977i
\(436\) −6.06662 + 6.73767i −0.290538 + 0.322676i
\(437\) 17.6550 15.8967i 0.844554 0.760440i
\(438\) −10.7193 + 9.65166i −0.512186 + 0.461174i
\(439\) −13.6095 + 15.1149i −0.649546 + 0.721394i −0.974513 0.224331i \(-0.927980\pi\)
0.324967 + 0.945725i \(0.394647\pi\)
\(440\) 18.7612 + 32.0162i 0.894407 + 1.52631i
\(441\) −4.19172 5.60620i −0.199606 0.266962i
\(442\) 14.3480 19.7484i 0.682466 0.939334i
\(443\) 7.09684 4.09736i 0.337181 0.194672i −0.321844 0.946793i \(-0.604303\pi\)
0.659025 + 0.752121i \(0.270969\pi\)
\(444\) −8.95885 + 3.98874i −0.425168 + 0.189297i
\(445\) 7.15500 + 9.71546i 0.339179 + 0.460557i
\(446\) 58.8515 + 26.2024i 2.78670 + 1.24072i
\(447\) 12.5693 + 17.3001i 0.594507 + 0.818268i
\(448\) 11.6985 + 3.04884i 0.552702 + 0.144044i
\(449\) 29.1862 1.37738 0.688692 0.725054i \(-0.258185\pi\)
0.688692 + 0.725054i \(0.258185\pi\)
\(450\) −7.73960 10.3684i −0.364848 0.488771i
\(451\) 2.10998 3.65460i 0.0993552 0.172088i
\(452\) −15.4604 + 72.7353i −0.727194 + 3.42118i
\(453\) −0.957751 + 2.15114i −0.0449991 + 0.101070i
\(454\) 59.5459 43.2626i 2.79463 2.03042i
\(455\) 5.51763 + 10.4817i 0.258670 + 0.491390i
\(456\) −16.4970 11.9858i −0.772545 0.561287i
\(457\) −15.8833 + 9.17024i −0.742991 + 0.428966i −0.823156 0.567816i \(-0.807789\pi\)
0.0801650 + 0.996782i \(0.474455\pi\)
\(458\) 5.97084 + 13.4107i 0.278999 + 0.626642i
\(459\) −3.15253 3.50124i −0.147148 0.163424i
\(460\) −57.5239 63.0631i −2.68207 2.94033i
\(461\) 4.35107 + 13.3912i 0.202650 + 0.623692i 0.999802 + 0.0199130i \(0.00633892\pi\)
−0.797152 + 0.603779i \(0.793661\pi\)
\(462\) −16.0665 + 2.65766i −0.747481 + 0.123646i
\(463\) 20.6277 + 6.70236i 0.958652 + 0.311485i 0.746226 0.665692i \(-0.231864\pi\)
0.212426 + 0.977177i \(0.431864\pi\)
\(464\) 42.7945 47.5282i 1.98669 2.20644i
\(465\) −6.79082 20.4498i −0.314917 0.948335i
\(466\) 15.6668 + 17.3998i 0.725751 + 0.806028i
\(467\) −4.63086 0.486723i −0.214290 0.0225228i −0.00322517 0.999995i \(-0.501027\pi\)
−0.211065 + 0.977472i \(0.567693\pi\)
\(468\) 9.40279i 0.434644i
\(469\) −21.2601 3.21808i −0.981699 0.148597i
\(470\) −13.9710 63.7032i −0.644436 2.93841i
\(471\) −15.4876 6.89553i −0.713631 0.317729i
\(472\) 14.5935 1.53384i 0.671721 0.0706007i
\(473\) 2.90188 13.6523i 0.133429 0.627733i
\(474\) −13.7733 23.8561i −0.632631 1.09575i
\(475\) 7.14269 12.7489i 0.327729 0.584960i
\(476\) −2.66303 + 58.4783i −0.122060 + 2.68035i
\(477\) 3.96311 1.28769i 0.181458 0.0589593i
\(478\) 5.26554 11.8266i 0.240840 0.540935i
\(479\) 0.997976 + 9.49511i 0.0455987 + 0.433843i 0.993376 + 0.114910i \(0.0366578\pi\)
−0.947777 + 0.318933i \(0.896676\pi\)
\(480\) −11.0207 + 15.3765i −0.503025 + 0.701839i
\(481\) −0.437040 + 4.15816i −0.0199273 + 0.189596i
\(482\) 4.84242i 0.220566i
\(483\) 20.0244 7.84449i 0.911140 0.356937i
\(484\) 7.75278 23.8606i 0.352399 1.08457i
\(485\) −14.6439 + 6.63351i −0.664945 + 0.301212i
\(486\) 2.53115 + 0.538013i 0.114815 + 0.0244048i
\(487\) −2.48736 + 2.23963i −0.112713 + 0.101487i −0.723560 0.690261i \(-0.757496\pi\)
0.610847 + 0.791748i \(0.290829\pi\)
\(488\) −18.9412 89.1112i −0.857427 4.03387i
\(489\) 3.35005 + 10.3104i 0.151494 + 0.466252i
\(490\) −35.4786 19.5407i −1.60276 0.882757i
\(491\) 3.90881 12.0301i 0.176402 0.542909i −0.823293 0.567617i \(-0.807865\pi\)
0.999695 + 0.0247075i \(0.00786546\pi\)
\(492\) 8.28609 + 0.870903i 0.373566 + 0.0392633i
\(493\) 30.1263 + 17.3934i 1.35682 + 0.783360i
\(494\) −13.8337 + 6.15915i −0.622406 + 0.277113i
\(495\) 1.07220 5.20950i 0.0481920 0.234149i
\(496\) −67.5285 + 49.0623i −3.03212 + 2.20296i
\(497\) 0.0206801 + 0.348844i 0.000927627 + 0.0156478i
\(498\) 26.1643 8.50130i 1.17245 0.380952i
\(499\) −7.14203 12.3704i −0.319721 0.553774i 0.660708 0.750643i \(-0.270256\pi\)
−0.980430 + 0.196869i \(0.936923\pi\)
\(500\) −45.9707 25.3669i −2.05587 1.13444i
\(501\) −4.22534 + 7.31851i −0.188774 + 0.326967i
\(502\) 35.8658 + 32.2937i 1.60077 + 1.44134i
\(503\) −0.385441 0.530514i −0.0171859 0.0236544i 0.800338 0.599550i \(-0.204654\pi\)
−0.817524 + 0.575895i \(0.804654\pi\)
\(504\) −10.1595 15.4120i −0.452540 0.686505i
\(505\) 12.2639 + 10.8999i 0.545737 + 0.485040i
\(506\) 5.22975 49.7577i 0.232491 2.21200i
\(507\) −7.78655 4.49557i −0.345813 0.199655i
\(508\) −7.44439 16.7204i −0.330292 0.741847i
\(509\) −7.09187 + 1.50742i −0.314342 + 0.0668154i −0.362381 0.932030i \(-0.618036\pi\)
0.0480393 + 0.998845i \(0.484703\pi\)
\(510\) −24.9756 10.9272i −1.10594 0.483863i
\(511\) −10.4995 10.3565i −0.464469 0.458146i
\(512\) −45.2549 14.7042i −2.00000 0.649840i
\(513\) 0.607661 + 2.85882i 0.0268289 + 0.126220i
\(514\) −16.3279 3.47059i −0.720191 0.153081i
\(515\) 8.38126 + 6.00704i 0.369322 + 0.264702i
\(516\) 26.9545 5.72937i 1.18661 0.252221i
\(517\) 15.7580 21.6891i 0.693037 0.953884i
\(518\) −6.57775 12.6938i −0.289010 0.557732i
\(519\) 3.03607 + 2.20583i 0.133269 + 0.0968252i
\(520\) 12.8890 + 28.4533i 0.565219 + 1.24776i
\(521\) −3.38185 32.1762i −0.148162 1.40966i −0.775711 0.631088i \(-0.782609\pi\)
0.627550 0.778577i \(-0.284058\pi\)
\(522\) −19.0018 + 1.99717i −0.831686 + 0.0874137i
\(523\) 15.8808 + 14.2991i 0.694419 + 0.625258i 0.938817 0.344417i \(-0.111924\pi\)
−0.244398 + 0.969675i \(0.578590\pi\)
\(524\) 14.9884 0.654770
\(525\) 10.1141 8.52670i 0.441416 0.372136i
\(526\) −69.2490 −3.01940
\(527\) −33.7396 30.3793i −1.46972 1.32334i
\(528\) −20.4902 + 2.15360i −0.891720 + 0.0937236i
\(529\) 4.50236 + 42.8371i 0.195755 + 1.86248i
\(530\) 17.8140 16.2493i 0.773789 0.705823i
\(531\) −1.70152 1.23623i −0.0738398 0.0536477i
\(532\) 19.5690 30.5906i 0.848425 1.32627i
\(533\) 2.08794 2.87380i 0.0904388 0.124478i
\(534\) −13.6581 + 2.90312i −0.591044 + 0.125630i
\(535\) −3.39107 10.2118i −0.146609 0.441495i
\(536\) −55.4632 11.7891i −2.39564 0.509210i
\(537\) 3.85626 + 18.1423i 0.166410 + 0.782896i
\(538\) 7.43857 + 2.41694i 0.320700 + 0.104202i
\(539\) −3.68463 16.2373i −0.158708 0.699391i
\(540\) 10.2572 2.24956i 0.441401 0.0968056i
\(541\) −20.5408 + 4.36607i −0.883117 + 0.187712i −0.627080 0.778955i \(-0.715750\pi\)
−0.256037 + 0.966667i \(0.582417\pi\)
\(542\) −8.19008 18.3952i −0.351794 0.790142i
\(543\) −2.95475 1.70593i −0.126800 0.0732083i
\(544\) −4.16654 + 39.6420i −0.178639 + 1.69964i
\(545\) 3.72455 2.18256i 0.159542 0.0934905i
\(546\) −13.6840 + 0.811209i −0.585620 + 0.0347165i
\(547\) −23.7908 32.7453i −1.01722 1.40009i −0.914133 0.405415i \(-0.867127\pi\)
−0.103090 0.994672i \(-0.532873\pi\)
\(548\) −22.0645 19.8669i −0.942547 0.848673i
\(549\) −6.52878 + 11.3082i −0.278642 + 0.482622i
\(550\) −6.78676 30.0178i −0.289389 1.27996i
\(551\) −10.7899 18.6887i −0.459667 0.796166i
\(552\) 53.9367 17.5251i 2.29570 0.745917i
\(553\) 23.5152 15.5011i 0.999968 0.659173i
\(554\) −51.5234 + 37.4340i −2.18902 + 1.59042i
\(555\) 4.64057 0.518059i 0.196981 0.0219904i
\(556\) −67.7370 + 30.1585i −2.87269 + 1.27900i
\(557\) 4.19996 + 2.42485i 0.177958 + 0.102744i 0.586333 0.810070i \(-0.300571\pi\)
−0.408375 + 0.912814i \(0.633904\pi\)
\(558\) 24.7997 + 2.60655i 1.04985 + 0.110344i
\(559\) 3.63057 11.1737i 0.153557 0.472599i
\(560\) −43.3447 27.3352i −1.83165 1.15512i
\(561\) −3.46299 10.6580i −0.146208 0.449981i
\(562\) 9.09758 + 42.8008i 0.383758 + 1.80544i
\(563\) 22.0694 19.8713i 0.930112 0.837477i −0.0568575 0.998382i \(-0.518108\pi\)
0.986970 + 0.160905i \(0.0514414\pi\)
\(564\) 51.7743 + 11.0050i 2.18009 + 0.463393i
\(565\) 17.5048 30.7763i 0.736430 1.29477i
\(566\) 18.5684 57.1476i 0.780487 2.40209i
\(567\) −0.395970 + 2.61595i −0.0166292 + 0.109860i
\(568\) 0.921530i 0.0386665i
\(569\) −3.84370 + 36.5704i −0.161136 + 1.53311i 0.553046 + 0.833151i \(0.313465\pi\)
−0.714182 + 0.699960i \(0.753201\pi\)
\(570\) 10.0285 + 13.6172i 0.420046 + 0.570362i
\(571\) 1.23946 + 11.7927i 0.0518698 + 0.493508i 0.989359 + 0.145494i \(0.0464771\pi\)
−0.937489 + 0.348014i \(0.886856\pi\)
\(572\) −9.09683 + 20.4318i −0.380357 + 0.854297i
\(573\) −22.4923 + 7.30819i −0.939629 + 0.305304i
\(574\) −0.552566 + 12.1340i −0.0230636 + 0.506461i
\(575\) 17.0089 + 36.9124i 0.709322 + 1.53935i
\(576\) −2.28466 3.95714i −0.0951940 0.164881i
\(577\) −1.79624 + 8.45064i −0.0747784 + 0.351805i −0.999590 0.0286198i \(-0.990889\pi\)
0.924812 + 0.380425i \(0.124222\pi\)
\(578\) −13.3751 + 1.40578i −0.556331 + 0.0584727i
\(579\) 17.3674 + 7.73245i 0.721763 + 0.321350i
\(580\) −66.8955 + 39.2002i −2.77768 + 1.62770i
\(581\) 10.2599 + 26.1900i 0.425651 + 1.08654i
\(582\) 18.6044i 0.771176i
\(583\) 9.85743 + 1.03606i 0.408253 + 0.0429091i
\(584\) −26.0228 28.9012i −1.07683 1.19594i
\(585\) 1.35597 4.26681i 0.0560626 0.176411i
\(586\) 15.1539 16.8302i 0.626004 0.695247i
\(587\) 38.7281 + 12.5835i 1.59848 + 0.519377i 0.966731 0.255796i \(-0.0823375\pi\)
0.631749 + 0.775173i \(0.282337\pi\)
\(588\) 26.3278 19.6851i 1.08574 0.811802i
\(589\) 8.70328 + 26.7859i 0.358612 + 1.10370i
\(590\) −11.9198 2.45330i −0.490732 0.101001i
\(591\) −12.9858 14.4222i −0.534164 0.593249i
\(592\) −7.35700 16.5241i −0.302371 0.679136i
\(593\) −16.8302 + 9.71695i −0.691135 + 0.399027i −0.804037 0.594579i \(-0.797319\pi\)
0.112902 + 0.993606i \(0.463985\pi\)
\(594\) 4.97957 + 3.61787i 0.204314 + 0.148443i
\(595\) 9.64157 26.1523i 0.395266 1.07214i
\(596\) −81.2448 + 59.0278i −3.32792 + 2.41787i
\(597\) −1.05160 + 2.36192i −0.0430390 + 0.0966671i
\(598\) 8.75620 41.1947i 0.358068 1.68458i
\(599\) 20.1049 34.8226i 0.821462 1.42281i −0.0831313 0.996539i \(-0.526492\pi\)
0.904593 0.426276i \(-0.140175\pi\)
\(600\) 27.9552 20.8675i 1.14127 0.851911i
\(601\) 1.85473 0.0756560 0.0378280 0.999284i \(-0.487956\pi\)
0.0378280 + 0.999284i \(0.487956\pi\)
\(602\) 10.6634 + 38.7329i 0.434610 + 1.57863i
\(603\) 4.77698 + 6.57495i 0.194534 + 0.267753i
\(604\) −10.1022 4.49779i −0.411052 0.183012i
\(605\) −6.95899 + 9.70946i −0.282923 + 0.394745i
\(606\) −17.3463 + 7.72306i −0.704645 + 0.313728i
\(607\) 15.1124 8.72513i 0.613392 0.354142i −0.160900 0.986971i \(-0.551440\pi\)
0.774292 + 0.632829i \(0.218106\pi\)
\(608\) 14.5343 20.0047i 0.589443 0.811299i
\(609\) −3.18810 19.2732i −0.129188 0.780988i
\(610\) −7.41228 + 75.1902i −0.300114 + 3.04436i
\(611\) 15.1003 16.7706i 0.610892 0.678464i
\(612\) 16.4425 14.8049i 0.664650 0.598454i
\(613\) −14.4839 + 13.0414i −0.585001 + 0.526737i −0.907621 0.419791i \(-0.862103\pi\)
0.322620 + 0.946529i \(0.395437\pi\)
\(614\) −35.4129 + 39.3300i −1.42915 + 1.58723i
\(615\) −3.63448 1.59013i −0.146556 0.0641204i
\(616\) −7.16558 43.3184i −0.288710 1.74535i
\(617\) 19.9305 27.4320i 0.802373 1.10437i −0.190083 0.981768i \(-0.560876\pi\)
0.992456 0.122603i \(-0.0391243\pi\)
\(618\) −10.3345 + 5.96660i −0.415713 + 0.240012i
\(619\) 43.0300 19.1582i 1.72952 0.770033i 0.733624 0.679555i \(-0.237827\pi\)
0.995898 0.0904780i \(-0.0288395\pi\)
\(620\) 96.0361 31.8910i 3.85690 1.28077i
\(621\) −7.42578 3.30617i −0.297986 0.132672i
\(622\) 6.03121 + 8.30125i 0.241829 + 0.332850i
\(623\) −3.78943 13.7644i −0.151820 0.551458i
\(624\) −17.3429 −0.694272
\(625\) 17.2025 + 18.1404i 0.688099 + 0.725617i
\(626\) 26.1898 45.3620i 1.04675 1.81303i
\(627\) −1.44538 + 6.79997i −0.0577228 + 0.271565i
\(628\) 32.3827 72.7328i 1.29221 2.90236i
\(629\) 7.95944 5.78287i 0.317364 0.230578i
\(630\) 4.15873 + 14.7334i 0.165688 + 0.586991i
\(631\) −0.234962 0.170710i −0.00935369 0.00679585i 0.583099 0.812401i \(-0.301840\pi\)
−0.592452 + 0.805606i \(0.701840\pi\)
\(632\) 64.3208 37.1357i 2.55855 1.47718i
\(633\) 0.227083 + 0.510037i 0.00902575 + 0.0202722i
\(634\) −7.63678 8.48151i −0.303295 0.336844i
\(635\) 0.966881 + 8.66094i 0.0383695 + 0.343699i
\(636\) 6.04725 + 18.6115i 0.239789 + 0.737995i
\(637\) −1.65591 13.9173i −0.0656094 0.551425i
\(638\) −43.2221 14.0437i −1.71118 0.555996i
\(639\) 0.0883802 0.0981561i 0.00349627 0.00388300i
\(640\) 9.26332 + 6.63924i 0.366165 + 0.262439i
\(641\) 6.84858 + 7.60611i 0.270502 + 0.300423i 0.863057 0.505107i \(-0.168547\pi\)
−0.592554 + 0.805531i \(0.701880\pi\)
\(642\) 12.3840 + 1.30161i 0.488758 + 0.0513705i
\(643\) 15.4294i 0.608474i −0.952596 0.304237i \(-0.901598\pi\)
0.952596 0.304237i \(-0.0984015\pi\)
\(644\) 36.8393 + 94.0384i 1.45167 + 3.70563i
\(645\) −13.0577 1.28723i −0.514146 0.0506847i
\(646\) 32.5519 + 14.4930i 1.28074 + 0.570221i
\(647\) 16.6825 1.75340i 0.655856 0.0689333i 0.229245 0.973369i \(-0.426374\pi\)
0.426611 + 0.904435i \(0.359707\pi\)
\(648\) −1.45059 + 6.82449i −0.0569845 + 0.268091i
\(649\) −2.50132 4.33242i −0.0981855 0.170062i
\(650\) −3.04035 25.7266i −0.119252 1.00908i
\(651\) −1.15984 + 25.4693i −0.0454578 + 0.998221i
\(652\) −48.4196 + 15.7325i −1.89626 + 0.616131i
\(653\) −7.13652 + 16.0289i −0.279274 + 0.627259i −0.997659 0.0683867i \(-0.978215\pi\)
0.718385 + 0.695645i \(0.244882\pi\)
\(654\) 0.522202 + 4.96842i 0.0204197 + 0.194281i
\(655\) −6.80143 2.16147i −0.265754 0.0844556i
\(656\) −1.60633 + 15.2832i −0.0627167 + 0.596710i
\(657\) 5.57413i 0.217468i
\(658\) −11.5489 + 76.2970i −0.450223 + 2.97437i
\(659\) −2.38937 + 7.35373i −0.0930767 + 0.286461i −0.986748 0.162262i \(-0.948121\pi\)
0.893671 + 0.448723i \(0.148121\pi\)
\(660\) 24.4648 + 5.03528i 0.952292 + 0.195998i
\(661\) −30.9008 6.56816i −1.20190 0.255472i −0.436905 0.899508i \(-0.643925\pi\)
−0.764995 + 0.644036i \(0.777259\pi\)
\(662\) −33.5251 + 30.1861i −1.30299 + 1.17322i
\(663\) −1.96128 9.22707i −0.0761696 0.358350i
\(664\) 22.9212 + 70.5441i 0.889514 + 2.73764i
\(665\) −13.2915 + 11.0594i −0.515423 + 0.428864i
\(666\) −1.66983 + 5.13921i −0.0647046 + 0.199140i
\(667\) 59.6887 + 6.27354i 2.31116 + 0.242912i
\(668\) −34.3692 19.8430i −1.32978 0.767750i
\(669\) 22.7428 10.1257i 0.879286 0.391483i
\(670\) 40.8763 + 23.2493i 1.57919 + 0.898200i
\(671\) −25.1269 + 18.2558i −0.970015 + 0.704757i
\(672\) 18.6890 12.3197i 0.720943 0.475241i
\(673\) 21.3122 6.92476i 0.821525 0.266930i 0.132054 0.991243i \(-0.457843\pi\)
0.689472 + 0.724313i \(0.257843\pi\)
\(674\) −27.8905 48.3078i −1.07430 1.86075i
\(675\) −4.97894 0.458386i −0.191640 0.0176433i
\(676\) 21.1121 36.5672i 0.812003 1.40643i
\(677\) −10.1719 9.15886i −0.390940 0.352004i 0.450099 0.892979i \(-0.351389\pi\)
−0.841039 + 0.540975i \(0.818055\pi\)
\(678\) 24.0839 + 33.1487i 0.924937 + 1.27307i
\(679\) 18.9884 1.12566i 0.728708 0.0431990i
\(680\) 29.4618 67.3391i 1.12981 2.58234i
\(681\) 2.97314 28.2875i 0.113931 1.08398i
\(682\) 51.3668 + 29.6566i 1.96694 + 1.13561i
\(683\) −13.0847 29.3886i −0.500671 1.12452i −0.970354 0.241689i \(-0.922299\pi\)
0.469683 0.882835i \(-0.344368\pi\)
\(684\) −13.4256 + 2.85370i −0.513340 + 0.109114i
\(685\) 7.14743 + 12.1971i 0.273089 + 0.466029i
\(686\) 30.9193 + 36.6168i 1.18051 + 1.39804i
\(687\) 5.39528 + 1.75303i 0.205843 + 0.0668824i
\(688\) 10.5675 + 49.7161i 0.402882 + 1.89541i
\(689\) 8.16102 + 1.73468i 0.310910 + 0.0660860i
\(690\) −47.0329 + 0.303690i −1.79051 + 0.0115613i
\(691\) 1.02322 0.217492i 0.0389252 0.00827380i −0.188408 0.982091i \(-0.560333\pi\)
0.227333 + 0.973817i \(0.426999\pi\)
\(692\) −10.3590 + 14.2580i −0.393791 + 0.542006i
\(693\) −3.39125 + 5.30125i −0.128823 + 0.201378i
\(694\) 37.0191 + 26.8959i 1.40522 + 1.02096i
\(695\) 35.0869 3.91699i 1.33092 0.148580i
\(696\) −5.38476 51.2325i −0.204109 1.94196i
\(697\) −8.31290 + 0.873721i −0.314873 + 0.0330945i
\(698\) 21.9020 + 19.7207i 0.829004 + 0.746438i
\(699\) 9.04806 0.342229
\(700\) 40.0430 + 47.4979i 1.51348 + 1.79525i
\(701\) −12.9841 −0.490404 −0.245202 0.969472i \(-0.578854\pi\)
−0.245202 + 0.969472i \(0.578854\pi\)
\(702\) 3.85033 + 3.46685i 0.145321 + 0.130848i
\(703\) −6.06978 + 0.637960i −0.228926 + 0.0240611i
\(704\) −1.13607 10.8090i −0.0428173 0.407379i
\(705\) −21.9072 12.4602i −0.825071 0.469278i
\(706\) −39.1162 28.4196i −1.47216 1.06959i
\(707\) −8.93202 17.2370i −0.335923 0.648266i
\(708\) 5.80557 7.99068i 0.218187 0.300308i
\(709\) −37.4698 + 7.96444i −1.40721 + 0.299111i −0.848035 0.529941i \(-0.822214\pi\)
−0.559172 + 0.829052i \(0.688881\pi\)
\(710\) 0.231472 0.728367i 0.00868700 0.0273351i
\(711\) −10.4126 2.21327i −0.390504 0.0830041i
\(712\) −7.82738 36.8249i −0.293344 1.38007i
\(713\) −74.4966 24.2054i −2.78992 0.906500i
\(714\) 22.9643 + 22.6517i 0.859417 + 0.847718i
\(715\) 7.07443 7.95971i 0.264569 0.297676i
\(716\) −85.1996 + 18.1097i −3.18406 + 0.676793i
\(717\) −2.03483 4.57031i −0.0759922 0.170681i
\(718\) −4.40234 2.54169i −0.164294 0.0948550i
\(719\) −1.38356 + 13.1637i −0.0515980 + 0.490922i 0.937956 + 0.346756i \(0.112717\pi\)
−0.989553 + 0.144166i \(0.953950\pi\)
\(720\) 4.14919 + 18.9189i 0.154631 + 0.705065i
\(721\) −6.71505 10.1868i −0.250082 0.379375i
\(722\) 15.9066 + 21.8935i 0.591981 + 0.814792i
\(723\) 1.39066 + 1.25216i 0.0517193 + 0.0465683i
\(724\) 8.01136 13.8761i 0.297740 0.515701i
\(725\) 36.0089 8.14132i 1.33734 0.302361i
\(726\) −6.91214 11.9722i −0.256534 0.444329i
\(727\) 25.6014 8.31839i 0.949502 0.308512i 0.206989 0.978343i \(-0.433634\pi\)
0.742513 + 0.669831i \(0.233634\pi\)
\(728\) −2.18718 36.8947i −0.0810622 1.36741i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 13.3086 + 29.3797i 0.492575 + 1.08739i
\(731\) −25.2558 + 11.2446i −0.934118 + 0.415896i
\(732\) −53.1055 30.6605i −1.96283 1.13324i
\(733\) 4.48664 + 0.471565i 0.165718 + 0.0174176i 0.187024 0.982355i \(-0.440116\pi\)
−0.0213061 + 0.999773i \(0.506782\pi\)
\(734\) 17.6419 54.2961i 0.651173 2.00410i
\(735\) −14.7858 + 5.13602i −0.545384 + 0.189445i
\(736\) 21.2514 + 65.4050i 0.783335 + 2.41086i
\(737\) 4.01914 + 18.9086i 0.148047 + 0.696507i
\(738\) 3.41174 3.07195i 0.125588 0.113080i
\(739\) 22.8428 + 4.85538i 0.840285 + 0.178608i 0.607898 0.794015i \(-0.292013\pi\)
0.232387 + 0.972623i \(0.425346\pi\)
\(740\) 2.43291 + 21.7930i 0.0894355 + 0.801128i
\(741\) −1.80832 + 5.56544i −0.0664304 + 0.204452i
\(742\) −26.5638 + 10.4063i −0.975188 + 0.382027i
\(743\) 18.9165i 0.693979i −0.937869 0.346990i \(-0.887204\pi\)
0.937869 0.346990i \(-0.112796\pi\)
\(744\) −7.02778 + 66.8649i −0.257651 + 2.45138i
\(745\) 45.3797 15.0694i 1.66259 0.552100i
\(746\) −2.95641 28.1283i −0.108242 1.02985i
\(747\) 4.32417 9.71223i 0.158213 0.355352i
\(748\) 50.0520 16.2629i 1.83008 0.594630i
\(749\) −0.579180 + 12.7184i −0.0211628 + 0.464720i
\(750\) −27.3370 + 9.47157i −0.998208 + 0.345853i
\(751\) −7.71591 13.3643i −0.281557 0.487672i 0.690211 0.723608i \(-0.257518\pi\)
−0.971769 + 0.235936i \(0.924184\pi\)
\(752\) −20.2980 + 95.4947i −0.740193 + 3.48233i
\(753\) 18.5485 1.94952i 0.675943 0.0710445i
\(754\) −34.9479 15.5598i −1.27273 0.566654i
\(755\) 3.93556 + 3.49784i 0.143230 + 0.127300i
\(756\) −12.2850 1.85955i −0.446802 0.0676313i
\(757\) 32.9124i 1.19622i 0.801414 + 0.598110i \(0.204082\pi\)
−0.801414 + 0.598110i \(0.795918\pi\)
\(758\) 96.4237 + 10.1345i 3.50227 + 0.368103i
\(759\) −12.9373 14.3683i −0.469593 0.521536i
\(760\) −36.7147 + 27.0387i −1.33178 + 0.980796i
\(761\) −5.66716 + 6.29402i −0.205435 + 0.228158i −0.837054 0.547121i \(-0.815724\pi\)
0.631619 + 0.775279i \(0.282391\pi\)
\(762\) −9.59158 3.11649i −0.347466 0.112899i
\(763\) −5.03938 + 0.833597i −0.182438 + 0.0301782i
\(764\) −34.3207 105.628i −1.24168 3.82150i
\(765\) −9.59632 + 4.34702i −0.346956 + 0.157167i
\(766\) −16.2227 18.0171i −0.586150 0.650986i
\(767\) −1.71279 3.84699i −0.0618452 0.138907i
\(768\) −19.3364 + 11.1639i −0.697741 + 0.402841i
\(769\) 8.41745 + 6.11564i 0.303541 + 0.220536i 0.729120 0.684386i \(-0.239930\pi\)
−0.425579 + 0.904921i \(0.639930\pi\)
\(770\) −5.21723 + 36.0383i −0.188016 + 1.29873i
\(771\) −5.21877 + 3.79166i −0.187950 + 0.136553i
\(772\) −36.3131 + 81.5606i −1.30694 + 2.93543i
\(773\) −10.3892 + 48.8771i −0.373672 + 1.75799i 0.242282 + 0.970206i \(0.422104\pi\)
−0.615954 + 0.787782i \(0.711229\pi\)
\(774\) 7.59216 13.1500i 0.272895 0.472667i
\(775\) −48.1783 + 0.622196i −1.73062 + 0.0223500i
\(776\) 50.1611 1.80068
\(777\) −5.34632 1.39335i −0.191798 0.0499861i
\(778\) 11.4276 + 15.7287i 0.409699 + 0.563902i
\(779\) 4.73698 + 2.10904i 0.169720 + 0.0755642i
\(780\) 20.0378 + 6.36792i 0.717467 + 0.228008i
\(781\) 0.287008 0.127784i 0.0102700 0.00457248i
\(782\) −85.8234 + 49.5502i −3.06904 + 1.77191i
\(783\) −4.33995 + 5.97343i −0.155097 + 0.213473i
\(784\) 36.3081 + 48.5602i 1.29672 + 1.73429i
\(785\) −25.1835 + 28.3349i −0.898836 + 1.01131i
\(786\) 5.52628 6.13756i 0.197116 0.218919i
\(787\) −34.4830 + 31.0486i −1.22919 + 1.10676i −0.238423 + 0.971161i \(0.576630\pi\)
−0.990763 + 0.135603i \(0.956703\pi\)
\(788\) 67.7294 60.9838i 2.41276 2.17246i
\(789\) −17.9065 + 19.8872i −0.637487 + 0.708001i
\(790\) −60.1663 + 13.1953i −2.14062 + 0.469469i
\(791\) −32.3757 + 26.5867i −1.15115 + 0.945315i
\(792\) −9.75448 + 13.4259i −0.346610 + 0.477068i
\(793\) −22.6414 + 13.0720i −0.804020 + 0.464201i
\(794\) 39.9465 17.7853i 1.41765 0.631178i
\(795\) −0.0601635 9.31763i −0.00213378 0.330462i
\(796\) −11.0921 4.93850i −0.393148 0.175041i
\(797\) 4.76016 + 6.55180i 0.168614 + 0.232077i 0.884959 0.465669i \(-0.154186\pi\)
−0.716345 + 0.697746i \(0.754186\pi\)
\(798\) −5.31128 19.2922i −0.188017 0.682936i
\(799\) −53.1022 −1.87862
\(800\) 25.3044 + 33.8992i 0.894647 + 1.19852i
\(801\) −2.69800 + 4.67307i −0.0953292 + 0.165115i
\(802\) 11.8616 55.8045i 0.418848 1.97053i
\(803\) −5.39275 + 12.1123i −0.190306 + 0.427434i
\(804\) −30.8773 + 22.4336i −1.08896 + 0.791173i
\(805\) −3.15570 47.9854i −0.111224 1.69126i
\(806\) 40.3925 + 29.3468i 1.42276 + 1.03370i
\(807\) 2.61758 1.51126i 0.0921431 0.0531989i
\(808\) −20.8229 46.7690i −0.732547 1.64533i
\(809\) −19.0876 21.1990i −0.671085 0.745315i 0.307412 0.951577i \(-0.400537\pi\)
−0.978497 + 0.206261i \(0.933870\pi\)
\(810\) 2.86072 5.02964i 0.100516 0.176723i
\(811\) −0.0194947 0.0599985i −0.000684551 0.00210683i 0.950714 0.310070i \(-0.100353\pi\)
−0.951398 + 0.307963i \(0.900353\pi\)
\(812\) 90.5106 14.9720i 3.17630 0.525413i
\(813\) −7.40060 2.40460i −0.259550 0.0843330i
\(814\) −8.60044 + 9.55176i −0.301445 + 0.334789i
\(815\) 24.2407 0.156521i 0.849113 0.00548269i
\(816\) 27.3068 + 30.3273i 0.955931 + 1.06167i
\(817\) 17.0561 + 1.79266i 0.596716 + 0.0627173i
\(818\) 71.6212i 2.50418i
\(819\) −3.30545 + 4.13957i −0.115502 + 0.144648i
\(820\) 7.46758 17.0682i 0.260779 0.596048i
\(821\) 38.1339 + 16.9783i 1.33088 + 0.592548i 0.944111 0.329628i \(-0.106923\pi\)
0.386773 + 0.922175i \(0.373590\pi\)
\(822\) −16.2705 + 1.71010i −0.567501 + 0.0596467i
\(823\) −9.11672 + 42.8908i −0.317789 + 1.49508i 0.471944 + 0.881628i \(0.343552\pi\)
−0.789733 + 0.613450i \(0.789781\pi\)
\(824\) −16.0871 27.8637i −0.560422 0.970679i
\(825\) −10.3755 5.81298i −0.361230 0.202382i
\(826\) 12.1298 + 7.75951i 0.422049 + 0.269988i
\(827\) −12.6910 + 4.12354i −0.441308 + 0.143390i −0.521239 0.853411i \(-0.674530\pi\)
0.0799311 + 0.996800i \(0.474530\pi\)
\(828\) 15.5264 34.8729i 0.539581 1.21192i
\(829\) 1.64422 + 15.6437i 0.0571060 + 0.543327i 0.985252 + 0.171110i \(0.0547355\pi\)
−0.928146 + 0.372217i \(0.878598\pi\)
\(830\) −0.397198 61.5147i −0.0137869 2.13521i
\(831\) −2.57257 + 24.4764i −0.0892416 + 0.849077i
\(832\) 9.14874i 0.317176i
\(833\) −21.7298 + 24.8088i −0.752893 + 0.859575i
\(834\) −12.6254 + 38.8571i −0.437183 + 1.34551i
\(835\) 12.7345 + 13.9608i 0.440696 + 0.483132i
\(836\) −31.9340 6.78778i −1.10446 0.234760i
\(837\) 7.16129 6.44806i 0.247530 0.222877i
\(838\) −16.3425 76.8852i −0.564541 2.65596i
\(839\) −14.4569 44.4938i −0.499108 1.53610i −0.810455 0.585801i \(-0.800780\pi\)
0.311347 0.950296i \(-0.399220\pi\)
\(840\) −39.7240 + 11.2127i −1.37061 + 0.386876i
\(841\) 7.88519 24.2681i 0.271903 0.836831i
\(842\) 16.7071 + 1.75599i 0.575766 + 0.0605155i
\(843\) 14.6441 + 8.45479i 0.504371 + 0.291199i
\(844\) −2.39524 + 1.06643i −0.0824474 + 0.0367080i
\(845\) −14.8536 + 13.5489i −0.510979 + 0.466097i
\(846\) 23.5958 17.1434i 0.811241 0.589401i
\(847\) 11.8011 7.77920i 0.405490 0.267296i
\(848\) −34.3279 + 11.1538i −1.17883 + 0.383023i
\(849\) −11.6104 20.1098i −0.398468 0.690167i
\(850\) −40.2007 + 45.8238i −1.37887 + 1.57174i
\(851\) 8.48708 14.7000i 0.290933 0.503911i
\(852\) 0.460960 + 0.415051i 0.0157922 + 0.0142194i
\(853\) −10.0539 13.8380i −0.344239 0.473804i 0.601435 0.798922i \(-0.294596\pi\)
−0.945673 + 0.325118i \(0.894596\pi\)
\(854\) 40.0388 79.9300i 1.37010 2.73515i
\(855\) 6.50381 + 0.641148i 0.222426 + 0.0219268i
\(856\) −3.50940 + 33.3897i −0.119949 + 1.14124i
\(857\) −16.9560 9.78953i −0.579204 0.334404i 0.181613 0.983370i \(-0.441868\pi\)
−0.760817 + 0.648966i \(0.775202\pi\)
\(858\) 5.01254 + 11.2583i 0.171125 + 0.384354i
\(859\) 14.5818 3.09947i 0.497526 0.105752i 0.0476875 0.998862i \(-0.484815\pi\)
0.449839 + 0.893110i \(0.351482\pi\)
\(860\) 6.04509 61.3215i 0.206136 2.09105i
\(861\) 3.34179 + 3.29630i 0.113888 + 0.112338i
\(862\) 79.5841 + 25.8584i 2.71064 + 0.880742i
\(863\) 4.74756 + 22.3355i 0.161609 + 0.760309i 0.982056 + 0.188588i \(0.0603910\pi\)
−0.820448 + 0.571722i \(0.806276\pi\)
\(864\) −8.27554 1.75902i −0.281540 0.0598431i
\(865\) 6.75686 4.97612i 0.229740 0.169193i
\(866\) 68.6693 14.5961i 2.33348 0.495996i
\(867\) −3.05483 + 4.20462i −0.103748 + 0.142796i
\(868\) −119.609 5.44684i −4.05979 0.184878i
\(869\) −20.4849 14.8831i −0.694901 0.504875i
\(870\) −8.61267 + 41.8462i −0.291997 + 1.41872i
\(871\) 1.70090 + 16.1830i 0.0576330 + 0.548341i
\(872\) −13.3958 + 1.40796i −0.453640 + 0.0476795i
\(873\) −5.34287 4.81074i −0.180829 0.162819i
\(874\) 61.4765 2.07947
\(875\) −11.3211 27.3282i −0.382723 0.923863i
\(876\) −26.1772 −0.884446
\(877\) −9.74490 8.77435i −0.329062 0.296289i 0.487994 0.872847i \(-0.337729\pi\)
−0.817056 + 0.576558i \(0.804395\pi\)
\(878\) −52.3431 + 5.50149i −1.76650 + 0.185666i
\(879\) −0.914819 8.70392i −0.0308561 0.293576i
\(880\) −9.28729 + 45.1240i −0.313074 + 1.52113i
\(881\) −20.7417 15.0697i −0.698805 0.507711i 0.180738 0.983531i \(-0.442151\pi\)
−0.879543 + 0.475820i \(0.842151\pi\)
\(882\) 1.64636 18.0389i 0.0554357 0.607402i
\(883\) −8.77887 + 12.0831i −0.295433 + 0.406628i −0.930769 0.365607i \(-0.880861\pi\)
0.635337 + 0.772235i \(0.280861\pi\)
\(884\) 43.3322 9.21053i 1.45742 0.309784i
\(885\) −3.78679 + 2.78880i −0.127292 + 0.0937444i
\(886\) 20.7421 + 4.40887i 0.696845 + 0.148119i
\(887\) −1.65988 7.80913i −0.0557334 0.262205i 0.941455 0.337138i \(-0.109459\pi\)
−0.997189 + 0.0749332i \(0.976126\pi\)
\(888\) −13.8563 4.50219i −0.464988 0.151084i
\(889\) 2.60048 9.97813i 0.0872173 0.334656i
\(890\) −3.06310 + 31.0721i −0.102675 + 1.04154i
\(891\) 2.32661 0.494537i 0.0779445 0.0165676i
\(892\) 47.5524 + 106.805i 1.59217 + 3.57608i
\(893\) 28.5284 + 16.4709i 0.954665 + 0.551176i
\(894\) −5.78416 + 55.0326i −0.193451 + 1.84057i
\(895\) 41.2736 + 4.06876i 1.37962 + 0.136004i
\(896\) −7.42176 11.2588i −0.247944 0.376132i
\(897\) −9.56624 13.1668i −0.319408 0.439627i
\(898\) 56.1262 + 50.5362i 1.87295 + 1.68642i
\(899\) −35.5757 + 61.6190i −1.18652 + 2.05511i
\(900\) 2.15267 23.3821i 0.0717556 0.779403i
\(901\) −9.81631 17.0024i −0.327029 0.566431i
\(902\) 10.3855 3.37447i 0.345801 0.112357i
\(903\) 13.8808 + 6.95323i 0.461924 + 0.231389i
\(904\) −89.3753 + 64.9350i −2.97258 + 2.15971i
\(905\) −5.63647 + 5.14139i −0.187363 + 0.170905i
\(906\) −5.56652 + 2.47837i −0.184935 + 0.0823384i
\(907\) 41.7662 + 24.1137i 1.38682 + 0.800683i 0.992956 0.118484i \(-0.0378034\pi\)
0.393868 + 0.919167i \(0.371137\pi\)
\(908\) 132.844 + 13.9624i 4.40857 + 0.463359i
\(909\) −2.26749 + 6.97860i −0.0752077 + 0.231466i
\(910\) −7.53857 + 29.7105i −0.249901 + 0.984894i
\(911\) −3.69240 11.3640i −0.122335 0.376507i 0.871071 0.491156i \(-0.163426\pi\)
−0.993406 + 0.114649i \(0.963426\pi\)
\(912\) −5.26348 24.7627i −0.174291 0.819976i
\(913\) 18.7924 16.9208i 0.621938 0.559995i
\(914\) −46.4226 9.86743i −1.53552 0.326385i
\(915\) 19.6767 + 21.5715i 0.650492 + 0.713130i
\(916\) −8.23259 + 25.3373i −0.272013 + 0.837169i
\(917\) 6.59861 + 5.26900i 0.217905 + 0.173998i
\(918\) 12.1917i 0.402385i
\(919\) 2.33494 22.2155i 0.0770226 0.732821i −0.886052 0.463586i \(-0.846562\pi\)
0.963074 0.269235i \(-0.0867709\pi\)
\(920\) −0.818807 126.810i −0.0269953 4.18080i
\(921\) 2.13782 + 20.3400i 0.0704436 + 0.670226i
\(922\) −14.8198 + 33.2857i −0.488063 + 1.09621i
\(923\) 0.251513 0.0817216i 0.00827866 0.00268990i
\(924\) −24.8957 15.9260i −0.819009 0.523927i
\(925\) 2.03876 10.2401i 0.0670340 0.336693i
\(926\) 28.0627 + 48.6060i 0.922197 + 1.59729i
\(927\) −0.958786 + 4.51074i −0.0314907 + 0.148152i
\(928\) 62.1259 6.52969i 2.03938 0.214348i
\(929\) 52.7969 + 23.5067i 1.73221 + 0.771230i 0.995472 + 0.0950530i \(0.0303021\pi\)
0.736739 + 0.676177i \(0.236365\pi\)
\(930\) 22.3500 51.0840i 0.732884 1.67511i
\(931\) 19.3690 6.58819i 0.634794 0.215919i
\(932\) 42.4915i 1.39185i
\(933\) 3.94354 + 0.414482i 0.129106 + 0.0135695i
\(934\) −8.06254 8.95436i −0.263814 0.292996i
\(935\) −25.0579 + 0.161798i −0.819481 + 0.00529135i
\(936\) −9.34732 + 10.3813i −0.305527 + 0.339322i
\(937\) −49.2444 16.0005i −1.60874 0.522712i −0.639495 0.768796i \(-0.720856\pi\)
−0.969249 + 0.246083i \(0.920856\pi\)
\(938\) −35.3117 43.0005i −1.15297 1.40402i
\(939\) −6.25504 19.2510i −0.204126 0.628234i
\(940\) 58.5155 102.880i 1.90857 3.35559i
\(941\) 16.2280 + 18.0230i 0.529018 + 0.587534i 0.947126 0.320863i \(-0.103973\pi\)
−0.418107 + 0.908398i \(0.637306\pi\)
\(942\) −17.8436 40.0773i −0.581375 1.30579i
\(943\) −12.4891 + 7.21060i −0.406702 + 0.234809i
\(944\) 14.7384 + 10.7080i 0.479693 + 0.348517i
\(945\) 5.30654 + 2.61545i 0.172622 + 0.0850806i
\(946\) 29.2195 21.2292i 0.950008 0.690221i
\(947\) 1.52112 3.41648i 0.0494296 0.111021i −0.887143 0.461495i \(-0.847313\pi\)
0.936572 + 0.350475i \(0.113980\pi\)
\(948\) 10.3939 48.8997i 0.337580 1.58819i
\(949\) −5.58030 + 9.66537i −0.181144 + 0.313751i
\(950\) 35.8105 12.1490i 1.16185 0.394166i
\(951\) −4.41048 −0.143019
\(952\) −61.0734 + 61.9162i −1.97940 + 2.00672i
\(953\) 5.33694 + 7.34567i 0.172881 + 0.237950i 0.886661 0.462420i \(-0.153019\pi\)
−0.713781 + 0.700369i \(0.753019\pi\)
\(954\) 9.85085 + 4.38588i 0.318933 + 0.141998i
\(955\) 0.341453 + 52.8815i 0.0110492 + 1.71120i
\(956\) 21.4631 9.55597i 0.694165 0.309062i
\(957\) −15.2096 + 8.78124i −0.491655 + 0.283857i
\(958\) −14.5217 + 19.9874i −0.469176 + 0.645765i
\(959\) −2.72986 16.5029i −0.0881517 0.532907i
\(960\) −9.98010 + 2.18878i −0.322106 + 0.0706426i
\(961\) 41.3934 45.9721i 1.33527 1.48297i
\(962\) −8.04033 + 7.23955i −0.259231 + 0.233412i
\(963\) 3.57607 3.21991i 0.115237 0.103760i
\(964\) −5.88039 + 6.53083i −0.189394 + 0.210344i
\(965\) 28.2400 31.7739i 0.909079 1.02284i
\(966\) 52.0904 + 19.5872i 1.67598 + 0.630206i
\(967\) 1.81264 2.49489i 0.0582906 0.0802302i −0.778877 0.627177i \(-0.784210\pi\)
0.837167 + 0.546947i \(0.184210\pi\)
\(968\) 32.2794 18.6365i 1.03750 0.599000i
\(969\) 12.5795 5.60074i 0.404110 0.179922i
\(970\) −39.6468 12.5996i −1.27298 0.404548i
\(971\) −6.68115 2.97464i −0.214408 0.0954608i 0.296722 0.954964i \(-0.404106\pi\)
−0.511131 + 0.859503i \(0.670773\pi\)
\(972\) 2.76036 + 3.79930i 0.0885384 + 0.121863i
\(973\) −40.4230 10.5350i −1.29590 0.337736i
\(974\) −8.66121 −0.277523
\(975\) −8.17444 5.77928i −0.261792 0.185085i
\(976\) 56.5515 97.9500i 1.81017 3.13530i
\(977\) 1.47443 6.93663i 0.0471711 0.221922i −0.948248 0.317531i \(-0.897146\pi\)
0.995419 + 0.0956084i \(0.0304796\pi\)
\(978\) −11.4103 + 25.6279i −0.364860 + 0.819489i
\(979\) −10.3836 + 7.54415i −0.331862 + 0.241112i
\(980\) −24.1197 69.4373i −0.770477 2.21809i
\(981\) 1.56188 + 1.13477i 0.0498670 + 0.0362305i
\(982\) 28.3470 16.3661i 0.904588 0.522264i
\(983\) −16.8060 37.7470i −0.536029 1.20394i −0.955180 0.296025i \(-0.904339\pi\)
0.419151 0.907917i \(-0.362328\pi\)
\(984\) 8.28258 + 9.19873i 0.264039 + 0.293245i
\(985\) −39.5288 + 17.9060i −1.25949 + 0.570534i
\(986\) 27.8171 + 85.6122i 0.885876 + 2.72645i
\(987\) 18.9249 + 23.0456i 0.602386 + 0.733550i
\(988\) −26.1364 8.49223i −0.831510 0.270174i
\(989\) −31.9157 + 35.4460i −1.01486 + 1.12712i
\(990\) 11.0822 8.16152i 0.352215 0.259390i
\(991\) 15.6503 + 17.3814i 0.497148 + 0.552139i 0.938538 0.345177i \(-0.112181\pi\)
−0.441390 + 0.897316i \(0.645514\pi\)
\(992\) −81.0820 8.52206i −2.57436 0.270576i
\(993\) 17.4334i 0.553233i
\(994\) −0.564258 + 0.706647i −0.0178972 + 0.0224135i
\(995\) 4.32118 + 3.84058i 0.136991 + 0.121755i
\(996\) 45.6106 + 20.3071i 1.44523 + 0.643456i
\(997\) −10.2939 + 1.08193i −0.326011 + 0.0342652i −0.266121 0.963940i \(-0.585742\pi\)
−0.0598909 + 0.998205i \(0.519075\pi\)
\(998\) 7.68502 36.1552i 0.243265 1.14447i
\(999\) 1.04411 + 1.80845i 0.0330342 + 0.0572168i
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 525.2.bo.a.319.38 yes 320
7.2 even 3 inner 525.2.bo.a.394.38 yes 320
25.4 even 10 inner 525.2.bo.a.4.38 320
175.79 even 30 inner 525.2.bo.a.79.38 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.bo.a.4.38 320 25.4 even 10 inner
525.2.bo.a.79.38 yes 320 175.79 even 30 inner
525.2.bo.a.319.38 yes 320 1.1 even 1 trivial
525.2.bo.a.394.38 yes 320 7.2 even 3 inner