Properties

Label 27.3.f.a.5.3
Level $27$
Weight $3$
Character 27.5
Analytic conductor $0.736$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,3,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.735696713773\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 27.5
Dual form 27.3.f.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.374063 - 0.445791i) q^{2} +(-0.428198 - 2.96928i) q^{3} +(0.635786 - 3.60572i) q^{4} +(2.62195 + 7.20376i) q^{5} +(-1.16351 + 1.30159i) q^{6} +(0.231638 + 1.31369i) q^{7} +(-3.86112 + 2.22922i) q^{8} +(-8.63329 + 2.54288i) q^{9} +O(q^{10})\) \(q+(-0.374063 - 0.445791i) q^{2} +(-0.428198 - 2.96928i) q^{3} +(0.635786 - 3.60572i) q^{4} +(2.62195 + 7.20376i) q^{5} +(-1.16351 + 1.30159i) q^{6} +(0.231638 + 1.31369i) q^{7} +(-3.86112 + 2.22922i) q^{8} +(-8.63329 + 2.54288i) q^{9} +(2.23059 - 3.86350i) q^{10} +(0.367624 - 1.01004i) q^{11} +(-10.9787 - 0.343867i) q^{12} +(16.0318 + 13.4523i) q^{13} +(0.498982 - 0.594664i) q^{14} +(20.2673 - 10.8700i) q^{15} +(-11.3241 - 4.12163i) q^{16} +(-12.1867 - 7.03599i) q^{17} +(4.36299 + 2.89745i) q^{18} +(-9.79833 - 16.9712i) q^{19} +(27.6418 - 4.87399i) q^{20} +(3.80152 - 1.25032i) q^{21} +(-0.587780 + 0.213935i) q^{22} +(-1.76488 - 0.311197i) q^{23} +(8.27250 + 10.5102i) q^{24} +(-25.8684 + 21.7062i) q^{25} -12.1788i q^{26} +(11.2473 + 24.5458i) q^{27} +4.88406 q^{28} +(-25.8129 - 30.7626i) q^{29} +(-12.4270 - 4.96893i) q^{30} +(-2.95677 + 16.7687i) q^{31} +(8.49804 + 23.3482i) q^{32} +(-3.15651 - 0.659083i) q^{33} +(1.42201 + 8.06462i) q^{34} +(-8.85613 + 5.11309i) q^{35} +(3.68000 + 32.7460i) q^{36} +(1.80012 - 3.11791i) q^{37} +(-3.90042 + 10.7163i) q^{38} +(33.0788 - 53.3631i) q^{39} +(-26.1824 - 21.9697i) q^{40} +(-3.09265 + 3.68568i) q^{41} +(-1.97939 - 1.22699i) q^{42} +(16.1462 + 5.87675i) q^{43} +(-3.40819 - 1.96772i) q^{44} +(-40.9544 - 55.5248i) q^{45} +(0.521449 + 0.903176i) q^{46} +(45.1184 - 7.95560i) q^{47} +(-7.38935 + 35.3893i) q^{48} +(44.3728 - 16.1504i) q^{49} +(19.3528 + 3.41242i) q^{50} +(-15.6735 + 39.1985i) q^{51} +(58.6979 - 49.2534i) q^{52} +51.2852i q^{53} +(6.73512 - 14.1956i) q^{54} +8.23996 q^{55} +(-3.82288 - 4.55593i) q^{56} +(-46.1967 + 36.3611i) q^{57} +(-4.05804 + 23.0143i) q^{58} +(-32.0502 - 88.0571i) q^{59} +(-26.3084 - 79.9892i) q^{60} +(-3.88855 - 22.0530i) q^{61} +(8.58136 - 4.95445i) q^{62} +(-5.34035 - 10.7524i) q^{63} +(-16.8721 + 29.2233i) q^{64} +(-54.8722 + 150.760i) q^{65} +(0.886919 + 1.65368i) q^{66} +(-14.9624 - 12.5549i) q^{67} +(-33.1179 + 39.4684i) q^{68} +(-0.168312 + 5.37369i) q^{69} +(5.59212 + 2.03537i) q^{70} +(74.9736 + 43.2860i) q^{71} +(27.6655 - 29.0639i) q^{72} +(18.0755 + 31.3076i) q^{73} +(-2.06330 + 0.363815i) q^{74} +(75.5285 + 67.5161i) q^{75} +(-67.4231 + 24.5400i) q^{76} +(1.41203 + 0.248979i) q^{77} +(-36.1624 + 5.21494i) q^{78} +(-22.3922 + 18.7892i) q^{79} -92.3828i q^{80} +(68.0675 - 43.9069i) q^{81} +2.79989 q^{82} +(-76.1905 - 90.8003i) q^{83} +(-2.09134 - 14.5022i) q^{84} +(18.7326 - 106.238i) q^{85} +(-3.41991 - 9.39613i) q^{86} +(-80.2898 + 89.8182i) q^{87} +(0.832156 + 4.71939i) q^{88} +(104.884 - 60.5550i) q^{89} +(-9.43294 + 39.0269i) q^{90} +(-13.9585 + 24.1768i) q^{91} +(-2.24418 + 6.16583i) q^{92} +(51.0571 + 1.59918i) q^{93} +(-20.4237 - 17.1375i) q^{94} +(96.5657 - 115.083i) q^{95} +(65.6885 - 35.2307i) q^{96} +(9.05396 + 3.29537i) q^{97} +(-23.7979 - 13.7397i) q^{98} +(-0.605396 + 9.65478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20} + 132 q^{21} - 42 q^{22} + 120 q^{23} + 144 q^{24} - 15 q^{25} - 90 q^{27} - 12 q^{28} - 168 q^{29} - 243 q^{30} + 39 q^{31} - 360 q^{32} - 207 q^{33} + 54 q^{34} - 252 q^{35} - 360 q^{36} - 3 q^{37} - 84 q^{38} + 15 q^{39} - 33 q^{40} + 228 q^{41} + 486 q^{42} - 96 q^{43} + 639 q^{44} + 477 q^{45} - 3 q^{46} + 399 q^{47} + 453 q^{48} - 78 q^{49} + 303 q^{50} + 36 q^{51} - 9 q^{52} - 54 q^{54} - 12 q^{55} - 393 q^{56} - 192 q^{57} + 129 q^{58} - 474 q^{59} - 846 q^{60} + 138 q^{61} - 900 q^{62} - 585 q^{63} - 51 q^{64} - 411 q^{65} - 423 q^{66} + 354 q^{67} + 99 q^{68} + 99 q^{69} + 489 q^{70} + 315 q^{71} + 720 q^{72} - 66 q^{73} + 321 q^{74} + 255 q^{75} + 258 q^{76} + 201 q^{77} + 180 q^{78} + 30 q^{79} + 36 q^{81} - 12 q^{82} - 33 q^{83} - 588 q^{84} - 261 q^{85} - 258 q^{86} - 279 q^{87} - 642 q^{88} + 72 q^{89} + 288 q^{90} + 96 q^{91} - 3 q^{92} + 591 q^{93} - 861 q^{94} + 681 q^{95} + 270 q^{96} - 582 q^{97} + 882 q^{98} + 513 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.374063 0.445791i −0.187032 0.222895i 0.664378 0.747396i \(-0.268696\pi\)
−0.851410 + 0.524501i \(0.824252\pi\)
\(3\) −0.428198 2.96928i −0.142733 0.989761i
\(4\) 0.635786 3.60572i 0.158947 0.901431i
\(5\) 2.62195 + 7.20376i 0.524391 + 1.44075i 0.865586 + 0.500760i \(0.166946\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(6\) −1.16351 + 1.30159i −0.193918 + 0.216931i
\(7\) 0.231638 + 1.31369i 0.0330912 + 0.187669i 0.996873 0.0790234i \(-0.0251802\pi\)
−0.963782 + 0.266693i \(0.914069\pi\)
\(8\) −3.86112 + 2.22922i −0.482640 + 0.278652i
\(9\) −8.63329 + 2.54288i −0.959255 + 0.282542i
\(10\) 2.23059 3.86350i 0.223059 0.386350i
\(11\) 0.367624 1.01004i 0.0334203 0.0918217i −0.921860 0.387523i \(-0.873331\pi\)
0.955281 + 0.295701i \(0.0955532\pi\)
\(12\) −10.9787 0.343867i −0.914888 0.0286556i
\(13\) 16.0318 + 13.4523i 1.23321 + 1.03479i 0.998024 + 0.0628396i \(0.0200156\pi\)
0.235190 + 0.971949i \(0.424429\pi\)
\(14\) 0.498982 0.594664i 0.0356416 0.0424760i
\(15\) 20.2673 10.8700i 1.35115 0.724664i
\(16\) −11.3241 4.12163i −0.707756 0.257602i
\(17\) −12.1867 7.03599i −0.716864 0.413881i 0.0967335 0.995310i \(-0.469161\pi\)
−0.813597 + 0.581429i \(0.802494\pi\)
\(18\) 4.36299 + 2.89745i 0.242388 + 0.160969i
\(19\) −9.79833 16.9712i −0.515702 0.893221i −0.999834 0.0182265i \(-0.994198\pi\)
0.484132 0.874995i \(-0.339135\pi\)
\(20\) 27.6418 4.87399i 1.38209 0.243699i
\(21\) 3.80152 1.25032i 0.181025 0.0595389i
\(22\) −0.587780 + 0.213935i −0.0267173 + 0.00972430i
\(23\) −1.76488 0.311197i −0.0767341 0.0135303i 0.135149 0.990825i \(-0.456849\pi\)
−0.211883 + 0.977295i \(0.567960\pi\)
\(24\) 8.27250 + 10.5102i 0.344688 + 0.437925i
\(25\) −25.8684 + 21.7062i −1.03474 + 0.868246i
\(26\) 12.1788i 0.468416i
\(27\) 11.2473 + 24.5458i 0.416567 + 0.909105i
\(28\) 4.88406 0.174431
\(29\) −25.8129 30.7626i −0.890099 1.06078i −0.997780 0.0665930i \(-0.978787\pi\)
0.107681 0.994185i \(-0.465657\pi\)
\(30\) −12.4270 4.96893i −0.414232 0.165631i
\(31\) −2.95677 + 16.7687i −0.0953798 + 0.540926i 0.899250 + 0.437434i \(0.144113\pi\)
−0.994630 + 0.103492i \(0.966998\pi\)
\(32\) 8.49804 + 23.3482i 0.265564 + 0.729630i
\(33\) −3.15651 0.659083i −0.0956517 0.0199722i
\(34\) 1.42201 + 8.06462i 0.0418238 + 0.237195i
\(35\) −8.85613 + 5.11309i −0.253032 + 0.146088i
\(36\) 3.68000 + 32.7460i 0.102222 + 0.909611i
\(37\) 1.80012 3.11791i 0.0486520 0.0842678i −0.840674 0.541542i \(-0.817841\pi\)
0.889326 + 0.457274i \(0.151174\pi\)
\(38\) −3.90042 + 10.7163i −0.102643 + 0.282008i
\(39\) 33.0788 53.3631i 0.848174 1.36829i
\(40\) −26.1824 21.9697i −0.654561 0.549241i
\(41\) −3.09265 + 3.68568i −0.0754305 + 0.0898946i −0.802440 0.596733i \(-0.796465\pi\)
0.727009 + 0.686627i \(0.240910\pi\)
\(42\) −1.97939 1.22699i −0.0471283 0.0292139i
\(43\) 16.1462 + 5.87675i 0.375494 + 0.136669i 0.522871 0.852412i \(-0.324861\pi\)
−0.147377 + 0.989080i \(0.547083\pi\)
\(44\) −3.40819 1.96772i −0.0774588 0.0447209i
\(45\) −40.9544 55.5248i −0.910098 1.23389i
\(46\) 0.521449 + 0.903176i 0.0113359 + 0.0196343i
\(47\) 45.1184 7.95560i 0.959966 0.169268i 0.328356 0.944554i \(-0.393505\pi\)
0.631610 + 0.775286i \(0.282394\pi\)
\(48\) −7.38935 + 35.3893i −0.153945 + 0.737278i
\(49\) 44.3728 16.1504i 0.905568 0.329600i
\(50\) 19.3528 + 3.41242i 0.387056 + 0.0682485i
\(51\) −15.6735 + 39.1985i −0.307324 + 0.768598i
\(52\) 58.6979 49.2534i 1.12881 0.947180i
\(53\) 51.2852i 0.967645i 0.875166 + 0.483822i \(0.160752\pi\)
−0.875166 + 0.483822i \(0.839248\pi\)
\(54\) 6.73512 14.1956i 0.124724 0.262882i
\(55\) 8.23996 0.149818
\(56\) −3.82288 4.55593i −0.0682656 0.0813558i
\(57\) −46.1967 + 36.3611i −0.810468 + 0.637913i
\(58\) −4.05804 + 23.0143i −0.0699662 + 0.396798i
\(59\) −32.0502 88.0571i −0.543223 1.49249i −0.842697 0.538389i \(-0.819033\pi\)
0.299473 0.954105i \(-0.403189\pi\)
\(60\) −26.3084 79.9892i −0.438473 1.33315i
\(61\) −3.88855 22.0530i −0.0637467 0.361525i −0.999949 0.0100647i \(-0.996796\pi\)
0.936203 0.351461i \(-0.114315\pi\)
\(62\) 8.58136 4.95445i 0.138409 0.0799105i
\(63\) −5.34035 10.7524i −0.0847675 0.170673i
\(64\) −16.8721 + 29.2233i −0.263627 + 0.456615i
\(65\) −54.8722 + 150.760i −0.844188 + 2.31939i
\(66\) 0.886919 + 1.65368i 0.0134382 + 0.0250558i
\(67\) −14.9624 12.5549i −0.223319 0.187387i 0.524263 0.851556i \(-0.324341\pi\)
−0.747582 + 0.664169i \(0.768785\pi\)
\(68\) −33.1179 + 39.4684i −0.487029 + 0.580418i
\(69\) −0.168312 + 5.37369i −0.00243930 + 0.0778796i
\(70\) 5.59212 + 2.03537i 0.0798875 + 0.0290767i
\(71\) 74.9736 + 43.2860i 1.05597 + 0.609663i 0.924314 0.381633i \(-0.124638\pi\)
0.131653 + 0.991296i \(0.457972\pi\)
\(72\) 27.6655 29.0639i 0.384243 0.403665i
\(73\) 18.0755 + 31.3076i 0.247609 + 0.428871i 0.962862 0.269994i \(-0.0870218\pi\)
−0.715253 + 0.698866i \(0.753689\pi\)
\(74\) −2.06330 + 0.363815i −0.0278824 + 0.00491641i
\(75\) 75.5285 + 67.5161i 1.00705 + 0.900214i
\(76\) −67.4231 + 24.5400i −0.887146 + 0.322895i
\(77\) 1.41203 + 0.248979i 0.0183380 + 0.00323349i
\(78\) −36.1624 + 5.21494i −0.463620 + 0.0668582i
\(79\) −22.3922 + 18.7892i −0.283445 + 0.237839i −0.773414 0.633901i \(-0.781453\pi\)
0.489969 + 0.871740i \(0.337008\pi\)
\(80\) 92.3828i 1.15479i
\(81\) 68.0675 43.9069i 0.840340 0.542060i
\(82\) 2.79989 0.0341450
\(83\) −76.1905 90.8003i −0.917957 1.09398i −0.995287 0.0969733i \(-0.969084\pi\)
0.0773297 0.997006i \(-0.475361\pi\)
\(84\) −2.09134 14.5022i −0.0248970 0.172645i
\(85\) 18.7326 106.238i 0.220384 1.24986i
\(86\) −3.41991 9.39613i −0.0397664 0.109257i
\(87\) −80.2898 + 89.8182i −0.922871 + 1.03239i
\(88\) 0.832156 + 4.71939i 0.00945632 + 0.0536294i
\(89\) 104.884 60.5550i 1.17848 0.680394i 0.222815 0.974861i \(-0.428476\pi\)
0.955662 + 0.294467i \(0.0951422\pi\)
\(90\) −9.43294 + 39.0269i −0.104810 + 0.433632i
\(91\) −13.9585 + 24.1768i −0.153390 + 0.265679i
\(92\) −2.24418 + 6.16583i −0.0243932 + 0.0670199i
\(93\) 51.0571 + 1.59918i 0.549001 + 0.0171955i
\(94\) −20.4237 17.1375i −0.217273 0.182314i
\(95\) 96.5657 115.083i 1.01648 1.21139i
\(96\) 65.6885 35.2307i 0.684255 0.366987i
\(97\) 9.05396 + 3.29537i 0.0933398 + 0.0339729i 0.388268 0.921547i \(-0.373074\pi\)
−0.294928 + 0.955519i \(0.595296\pi\)
\(98\) −23.7979 13.7397i −0.242836 0.140201i
\(99\) −0.605396 + 9.65478i −0.00611511 + 0.0975230i
\(100\) 61.8196 + 107.075i 0.618196 + 1.07075i
\(101\) 3.79771 0.669639i 0.0376011 0.00663009i −0.154816 0.987943i \(-0.549478\pi\)
0.192417 + 0.981313i \(0.438367\pi\)
\(102\) 23.3372 7.67560i 0.228796 0.0752510i
\(103\) −115.073 + 41.8832i −1.11722 + 0.406633i −0.833635 0.552315i \(-0.813744\pi\)
−0.283580 + 0.958948i \(0.591522\pi\)
\(104\) −91.8886 16.2024i −0.883544 0.155793i
\(105\) 18.9744 + 24.1070i 0.180709 + 0.229590i
\(106\) 22.8625 19.1839i 0.215684 0.180980i
\(107\) 80.0804i 0.748415i 0.927345 + 0.374207i \(0.122085\pi\)
−0.927345 + 0.374207i \(0.877915\pi\)
\(108\) 95.6564 24.9487i 0.885707 0.231007i
\(109\) −96.8098 −0.888163 −0.444081 0.895986i \(-0.646470\pi\)
−0.444081 + 0.895986i \(0.646470\pi\)
\(110\) −3.08227 3.67330i −0.0280206 0.0333937i
\(111\) −10.0288 4.01000i −0.0903492 0.0361261i
\(112\) 2.79144 15.8310i 0.0249236 0.141349i
\(113\) 22.1070 + 60.7386i 0.195637 + 0.537509i 0.998259 0.0589789i \(-0.0187845\pi\)
−0.802622 + 0.596488i \(0.796562\pi\)
\(114\) 33.4899 + 6.99274i 0.293771 + 0.0613399i
\(115\) −2.38566 13.5297i −0.0207449 0.117650i
\(116\) −127.333 + 73.5156i −1.09770 + 0.633755i
\(117\) −172.615 75.3704i −1.47534 0.644191i
\(118\) −27.2663 + 47.2266i −0.231070 + 0.400225i
\(119\) 6.42017 17.6393i 0.0539510 0.148229i
\(120\) −54.0229 + 87.1504i −0.450191 + 0.726253i
\(121\) 91.8063 + 77.0347i 0.758730 + 0.636650i
\(122\) −8.37648 + 9.98271i −0.0686597 + 0.0818255i
\(123\) 12.2681 + 7.60476i 0.0997406 + 0.0618273i
\(124\) 58.5834 + 21.3226i 0.472447 + 0.171957i
\(125\) −58.2161 33.6111i −0.465729 0.268889i
\(126\) −2.79570 + 6.40276i −0.0221881 + 0.0508155i
\(127\) −82.7295 143.292i −0.651414 1.12828i −0.982780 0.184779i \(-0.940843\pi\)
0.331366 0.943502i \(-0.392490\pi\)
\(128\) 117.215 20.6682i 0.915744 0.161470i
\(129\) 10.5360 50.4592i 0.0816741 0.391157i
\(130\) 87.7332 31.9323i 0.674871 0.245633i
\(131\) 36.1521 + 6.37458i 0.275970 + 0.0486610i 0.309920 0.950763i \(-0.399698\pi\)
−0.0339502 + 0.999424i \(0.510809\pi\)
\(132\) −4.38334 + 10.9625i −0.0332071 + 0.0830489i
\(133\) 20.0252 16.8031i 0.150565 0.126339i
\(134\) 11.3664i 0.0848241i
\(135\) −147.332 + 145.381i −1.09135 + 1.07690i
\(136\) 62.7390 0.461316
\(137\) 74.9644 + 89.3391i 0.547185 + 0.652110i 0.966783 0.255600i \(-0.0822731\pi\)
−0.419597 + 0.907710i \(0.637829\pi\)
\(138\) 2.45850 1.93507i 0.0178152 0.0140222i
\(139\) −17.1095 + 97.0328i −0.123090 + 0.698078i 0.859334 + 0.511415i \(0.170878\pi\)
−0.982424 + 0.186663i \(0.940233\pi\)
\(140\) 12.8058 + 35.1836i 0.0914699 + 0.251311i
\(141\) −42.9420 130.563i −0.304553 0.925978i
\(142\) −8.74834 49.6143i −0.0616080 0.349396i
\(143\) 19.4810 11.2473i 0.136230 0.0786527i
\(144\) 108.245 + 6.78743i 0.751702 + 0.0471350i
\(145\) 153.926 266.608i 1.06156 1.83867i
\(146\) 7.19529 19.7689i 0.0492828 0.135403i
\(147\) −66.9554 124.840i −0.455479 0.849251i
\(148\) −10.0978 8.47307i −0.0682285 0.0572505i
\(149\) −89.3217 + 106.449i −0.599474 + 0.714426i −0.977397 0.211411i \(-0.932194\pi\)
0.377923 + 0.925837i \(0.376638\pi\)
\(150\) 1.84562 58.9252i 0.0123041 0.392835i
\(151\) −122.547 44.6035i −0.811571 0.295388i −0.0972982 0.995255i \(-0.531020\pi\)
−0.714272 + 0.699868i \(0.753242\pi\)
\(152\) 75.6650 + 43.6852i 0.497796 + 0.287403i
\(153\) 123.103 + 29.7544i 0.804594 + 0.194473i
\(154\) −0.417195 0.722604i −0.00270906 0.00469223i
\(155\) −128.550 + 22.6669i −0.829356 + 0.146238i
\(156\) −171.382 153.201i −1.09860 0.982055i
\(157\) 219.522 79.8994i 1.39823 0.508913i 0.470576 0.882359i \(-0.344046\pi\)
0.927652 + 0.373446i \(0.121824\pi\)
\(158\) 16.7522 + 2.95386i 0.106026 + 0.0186953i
\(159\) 152.280 21.9602i 0.957737 0.138114i
\(160\) −145.913 + 122.436i −0.911957 + 0.765223i
\(161\) 2.39059i 0.0148484i
\(162\) −45.0348 13.9199i −0.277993 0.0859255i
\(163\) 65.8701 0.404111 0.202056 0.979374i \(-0.435238\pi\)
0.202056 + 0.979374i \(0.435238\pi\)
\(164\) 11.3233 + 13.4945i 0.0690443 + 0.0822838i
\(165\) −3.52834 24.4668i −0.0213839 0.148284i
\(166\) −11.9779 + 67.9300i −0.0721560 + 0.409217i
\(167\) 57.3115 + 157.462i 0.343182 + 0.942886i 0.984465 + 0.175581i \(0.0561804\pi\)
−0.641283 + 0.767305i \(0.721597\pi\)
\(168\) −11.8909 + 13.3020i −0.0707791 + 0.0791788i
\(169\) 46.7081 + 264.895i 0.276379 + 1.56742i
\(170\) −54.3671 + 31.3889i −0.319807 + 0.184640i
\(171\) 127.748 + 121.601i 0.747062 + 0.711119i
\(172\) 31.4555 54.4825i 0.182881 0.316759i
\(173\) 90.8802 249.691i 0.525319 1.44330i −0.339206 0.940712i \(-0.610158\pi\)
0.864525 0.502590i \(-0.167620\pi\)
\(174\) 70.0736 + 2.19480i 0.402722 + 0.0126138i
\(175\) −34.5072 28.9550i −0.197184 0.165457i
\(176\) −8.32602 + 9.92256i −0.0473069 + 0.0563782i
\(177\) −247.743 + 132.872i −1.39968 + 0.750689i
\(178\) −66.2283 24.1051i −0.372069 0.135422i
\(179\) −213.546 123.291i −1.19299 0.688776i −0.234010 0.972234i \(-0.575185\pi\)
−0.958985 + 0.283458i \(0.908518\pi\)
\(180\) −226.245 + 112.368i −1.25692 + 0.624268i
\(181\) 0.670719 + 1.16172i 0.00370563 + 0.00641834i 0.867872 0.496787i \(-0.165487\pi\)
−0.864167 + 0.503206i \(0.832154\pi\)
\(182\) 15.9991 2.82108i 0.0879074 0.0155004i
\(183\) −63.8167 + 20.9893i −0.348725 + 0.114695i
\(184\) 7.50815 2.73274i 0.0408052 0.0148519i
\(185\) 27.1805 + 4.79266i 0.146922 + 0.0259062i
\(186\) −18.3857 23.3590i −0.0988478 0.125586i
\(187\) −11.5867 + 9.72242i −0.0619611 + 0.0519916i
\(188\) 167.743i 0.892248i
\(189\) −29.6402 + 20.4612i −0.156827 + 0.108260i
\(190\) −87.4244 −0.460128
\(191\) 29.8515 + 35.5757i 0.156291 + 0.186260i 0.838508 0.544890i \(-0.183428\pi\)
−0.682217 + 0.731150i \(0.738984\pi\)
\(192\) 93.9970 + 37.5847i 0.489568 + 0.195754i
\(193\) −24.7371 + 140.291i −0.128171 + 0.726896i 0.851202 + 0.524838i \(0.175874\pi\)
−0.979374 + 0.202058i \(0.935237\pi\)
\(194\) −1.91770 5.26885i −0.00988508 0.0271590i
\(195\) 471.146 + 98.3760i 2.41613 + 0.504493i
\(196\) −30.0222 170.264i −0.153174 0.868695i
\(197\) −46.8442 + 27.0455i −0.237788 + 0.137287i −0.614160 0.789182i \(-0.710505\pi\)
0.376372 + 0.926469i \(0.377172\pi\)
\(198\) 4.53047 3.34162i 0.0228812 0.0168769i
\(199\) −164.437 + 284.813i −0.826317 + 1.43122i 0.0745915 + 0.997214i \(0.476235\pi\)
−0.900909 + 0.434009i \(0.857099\pi\)
\(200\) 51.4932 141.476i 0.257466 0.707382i
\(201\) −30.8723 + 49.8035i −0.153593 + 0.247779i
\(202\) −1.71910 1.44250i −0.00851041 0.00714108i
\(203\) 34.4331 41.0358i 0.169621 0.202147i
\(204\) 131.374 + 81.4363i 0.643990 + 0.399197i
\(205\) −34.6595 12.6150i −0.169071 0.0615368i
\(206\) 61.7158 + 35.6316i 0.299591 + 0.172969i
\(207\) 16.0281 1.80124i 0.0774304 0.00870164i
\(208\) −126.100 218.412i −0.606250 1.05006i
\(209\) −20.7437 + 3.65767i −0.0992520 + 0.0175008i
\(210\) 3.64904 17.4761i 0.0173764 0.0832197i
\(211\) −89.0532 + 32.4127i −0.422053 + 0.153615i −0.544311 0.838884i \(-0.683209\pi\)
0.122258 + 0.992498i \(0.460987\pi\)
\(212\) 184.920 + 32.6064i 0.872265 + 0.153804i
\(213\) 96.4250 241.153i 0.452700 1.13217i
\(214\) 35.6991 29.9551i 0.166818 0.139977i
\(215\) 131.722i 0.612662i
\(216\) −98.1452 69.7017i −0.454376 0.322693i
\(217\) −22.7137 −0.104671
\(218\) 36.2130 + 43.1569i 0.166114 + 0.197968i
\(219\) 85.2213 67.0770i 0.389138 0.306288i
\(220\) 5.23886 29.7110i 0.0238130 0.135050i
\(221\) −100.724 276.738i −0.455766 1.25221i
\(222\) 1.96377 + 5.97072i 0.00884580 + 0.0268952i
\(223\) −14.1117 80.0312i −0.0632810 0.358884i −0.999962 0.00870098i \(-0.997230\pi\)
0.936681 0.350183i \(-0.113881\pi\)
\(224\) −28.7037 + 16.5721i −0.128141 + 0.0739825i
\(225\) 168.133 253.176i 0.747259 1.12523i
\(226\) 18.8073 32.5752i 0.0832180 0.144138i
\(227\) 57.3885 157.674i 0.252813 0.694597i −0.746752 0.665102i \(-0.768388\pi\)
0.999565 0.0294950i \(-0.00938992\pi\)
\(228\) 101.737 + 189.690i 0.446213 + 0.831975i
\(229\) 56.2458 + 47.1958i 0.245615 + 0.206095i 0.757281 0.653089i \(-0.226527\pi\)
−0.511666 + 0.859184i \(0.670972\pi\)
\(230\) −5.13905 + 6.12448i −0.0223437 + 0.0266282i
\(231\) 0.134661 4.29933i 0.000582948 0.0186118i
\(232\) 168.243 + 61.2354i 0.725185 + 0.263946i
\(233\) −159.041 91.8223i −0.682579 0.394087i 0.118247 0.992984i \(-0.462272\pi\)
−0.800826 + 0.598897i \(0.795606\pi\)
\(234\) 30.9693 + 105.143i 0.132347 + 0.449330i
\(235\) 175.609 + 304.163i 0.747271 + 1.29431i
\(236\) −337.887 + 59.5785i −1.43172 + 0.252451i
\(237\) 65.3789 + 58.4431i 0.275860 + 0.246596i
\(238\) −10.2650 + 3.73615i −0.0431302 + 0.0156981i
\(239\) −8.71524 1.53673i −0.0364655 0.00642984i 0.155386 0.987854i \(-0.450338\pi\)
−0.191851 + 0.981424i \(0.561449\pi\)
\(240\) −274.311 + 39.5581i −1.14296 + 0.164825i
\(241\) −12.1911 + 10.2295i −0.0505853 + 0.0424461i −0.667730 0.744404i \(-0.732734\pi\)
0.617145 + 0.786850i \(0.288289\pi\)
\(242\) 69.7423i 0.288191i
\(243\) −159.518 183.311i −0.656454 0.754366i
\(244\) −81.9894 −0.336022
\(245\) 232.687 + 277.306i 0.949743 + 1.13186i
\(246\) −1.19891 8.31366i −0.00487360 0.0337954i
\(247\) 71.2164 403.888i 0.288325 1.63517i
\(248\) −25.9646 71.3372i −0.104696 0.287650i
\(249\) −236.987 + 265.112i −0.951756 + 1.06471i
\(250\) 6.79298 + 38.5249i 0.0271719 + 0.154100i
\(251\) 228.852 132.128i 0.911762 0.526406i 0.0307645 0.999527i \(-0.490206\pi\)
0.880998 + 0.473121i \(0.156872\pi\)
\(252\) −42.1655 + 12.4196i −0.167324 + 0.0492841i
\(253\) −0.963134 + 1.66820i −0.00380685 + 0.00659366i
\(254\) −32.9321 + 90.4802i −0.129654 + 0.356221i
\(255\) −323.472 10.1316i −1.26852 0.0397317i
\(256\) 50.3387 + 42.2392i 0.196635 + 0.164997i
\(257\) −219.915 + 262.084i −0.855699 + 1.01978i 0.143846 + 0.989600i \(0.454053\pi\)
−0.999544 + 0.0301818i \(0.990391\pi\)
\(258\) −26.4354 + 14.1781i −0.102463 + 0.0549538i
\(259\) 4.51293 + 1.64257i 0.0174244 + 0.00634198i
\(260\) 508.713 + 293.705i 1.95659 + 1.12964i
\(261\) 301.076 + 199.943i 1.15355 + 0.766066i
\(262\) −10.6814 18.5008i −0.0407688 0.0706136i
\(263\) −374.609 + 66.0536i −1.42437 + 0.251154i −0.832117 0.554600i \(-0.812871\pi\)
−0.592250 + 0.805754i \(0.701760\pi\)
\(264\) 13.6569 4.49174i 0.0517306 0.0170142i
\(265\) −369.446 + 134.467i −1.39414 + 0.507424i
\(266\) −14.9813 2.64162i −0.0563209 0.00993089i
\(267\) −224.716 285.502i −0.841634 1.06930i
\(268\) −54.7824 + 45.9679i −0.204412 + 0.171522i
\(269\) 88.9301i 0.330595i 0.986244 + 0.165297i \(0.0528584\pi\)
−0.986244 + 0.165297i \(0.947142\pi\)
\(270\) 119.921 + 11.2979i 0.444152 + 0.0418439i
\(271\) 487.123 1.79750 0.898751 0.438460i \(-0.144476\pi\)
0.898751 + 0.438460i \(0.144476\pi\)
\(272\) 109.003 + 129.905i 0.400748 + 0.477593i
\(273\) 77.7647 + 31.0942i 0.284852 + 0.113898i
\(274\) 11.7851 66.8369i 0.0430115 0.243930i
\(275\) 12.4142 + 34.1078i 0.0451426 + 0.124028i
\(276\) 19.2690 + 4.02341i 0.0698154 + 0.0145776i
\(277\) −15.1883 86.1369i −0.0548312 0.310963i 0.945041 0.326952i \(-0.106022\pi\)
−0.999872 + 0.0159886i \(0.994910\pi\)
\(278\) 49.6564 28.6691i 0.178620 0.103126i
\(279\) −17.1141 152.288i −0.0613410 0.545835i
\(280\) 22.7964 39.4845i 0.0814157 0.141016i
\(281\) −55.1861 + 151.623i −0.196392 + 0.539582i −0.998326 0.0578296i \(-0.981582\pi\)
0.801935 + 0.597412i \(0.203804\pi\)
\(282\) −42.1407 + 67.9819i −0.149435 + 0.241071i
\(283\) −105.120 88.2058i −0.371447 0.311681i 0.437886 0.899030i \(-0.355727\pi\)
−0.809334 + 0.587349i \(0.800172\pi\)
\(284\) 203.745 242.813i 0.717411 0.854977i
\(285\) −383.062 237.453i −1.34408 0.833168i
\(286\) −12.3011 4.47722i −0.0430107 0.0156546i
\(287\) −5.55820 3.20903i −0.0193666 0.0111813i
\(288\) −132.738 179.962i −0.460895 0.624868i
\(289\) −45.4898 78.7907i −0.157404 0.272632i
\(290\) −176.429 + 31.1093i −0.608377 + 0.107273i
\(291\) 5.90801 28.2948i 0.0203024 0.0972332i
\(292\) 124.379 45.2701i 0.425954 0.155035i
\(293\) −382.393 67.4262i −1.30510 0.230124i −0.522492 0.852644i \(-0.674998\pi\)
−0.782604 + 0.622520i \(0.786109\pi\)
\(294\) −30.6070 + 76.5461i −0.104105 + 0.260361i
\(295\) 550.308 461.763i 1.86545 1.56530i
\(296\) 16.0515i 0.0542280i
\(297\) 28.9270 2.33656i 0.0973973 0.00786721i
\(298\) 80.8661 0.271363
\(299\) −24.1079 28.7307i −0.0806285 0.0960893i
\(300\) 291.464 229.409i 0.971547 0.764697i
\(301\) −3.98012 + 22.5724i −0.0132230 + 0.0749913i
\(302\) 25.9565 + 71.3150i 0.0859487 + 0.236142i
\(303\) −3.61452 10.9897i −0.0119291 0.0362698i
\(304\) 41.0081 + 232.569i 0.134895 + 0.765029i
\(305\) 148.669 85.8342i 0.487440 0.281424i
\(306\) −32.7840 66.0082i −0.107137 0.215713i
\(307\) −207.323 + 359.093i −0.675318 + 1.16969i 0.301057 + 0.953606i \(0.402660\pi\)
−0.976376 + 0.216080i \(0.930673\pi\)
\(308\) 1.79550 4.93309i 0.00582954 0.0160165i
\(309\) 173.637 + 323.751i 0.561933 + 1.04774i
\(310\) 58.1906 + 48.8277i 0.187712 + 0.157509i
\(311\) 280.533 334.326i 0.902036 1.07500i −0.0947982 0.995497i \(-0.530221\pi\)
0.996834 0.0795082i \(-0.0253350\pi\)
\(312\) −8.76314 + 279.781i −0.0280870 + 0.896734i
\(313\) 386.486 + 140.669i 1.23478 + 0.449423i 0.875232 0.483703i \(-0.160709\pi\)
0.359548 + 0.933127i \(0.382931\pi\)
\(314\) −117.733 67.9734i −0.374947 0.216476i
\(315\) 63.4556 66.6629i 0.201446 0.211628i
\(316\) 53.5122 + 92.6858i 0.169342 + 0.293310i
\(317\) 402.773 71.0197i 1.27058 0.224037i 0.502602 0.864518i \(-0.332376\pi\)
0.767974 + 0.640481i \(0.221265\pi\)
\(318\) −66.7521 59.6707i −0.209912 0.187644i
\(319\) −40.5608 + 14.7629i −0.127150 + 0.0462788i
\(320\) −254.756 44.9203i −0.796112 0.140376i
\(321\) 237.781 34.2902i 0.740752 0.106823i
\(322\) −1.06570 + 0.894231i −0.00330964 + 0.00277711i
\(323\) 275.764i 0.853757i
\(324\) −115.040 273.348i −0.355061 0.843667i
\(325\) −706.713 −2.17450
\(326\) −24.6396 29.3643i −0.0755815 0.0900745i
\(327\) 41.4537 + 287.456i 0.126770 + 0.879069i
\(328\) 3.72491 21.1250i 0.0113564 0.0644056i
\(329\) 20.9023 + 57.4286i 0.0635329 + 0.174555i
\(330\) −9.58726 + 10.7250i −0.0290523 + 0.0325001i
\(331\) −56.8942 322.663i −0.171886 0.974812i −0.941677 0.336517i \(-0.890751\pi\)
0.769792 0.638295i \(-0.220360\pi\)
\(332\) −375.841 + 216.992i −1.13205 + 0.653591i
\(333\) −7.61253 + 31.4953i −0.0228605 + 0.0945805i
\(334\) 48.7570 84.4496i 0.145979 0.252843i
\(335\) 51.2120 140.704i 0.152872 0.420011i
\(336\) −48.2021 1.50976i −0.143459 0.00449333i
\(337\) −430.977 361.633i −1.27886 1.07309i −0.993400 0.114705i \(-0.963408\pi\)
−0.285464 0.958389i \(-0.592148\pi\)
\(338\) 100.616 119.909i 0.297680 0.354761i
\(339\) 170.884 91.6502i 0.504082 0.270354i
\(340\) −371.155 135.089i −1.09163 0.397321i
\(341\) 15.8500 + 9.15103i 0.0464811 + 0.0268359i
\(342\) 6.42314 102.435i 0.0187811 0.299518i
\(343\) 64.1768 + 111.157i 0.187104 + 0.324074i
\(344\) −75.4431 + 13.3027i −0.219311 + 0.0386705i
\(345\) −39.1521 + 12.8771i −0.113484 + 0.0373249i
\(346\) −145.305 + 52.8867i −0.419957 + 0.152852i
\(347\) 240.215 + 42.3563i 0.692261 + 0.122064i 0.508700 0.860944i \(-0.330126\pi\)
0.183561 + 0.983008i \(0.441237\pi\)
\(348\) 272.812 + 346.608i 0.783944 + 0.996000i
\(349\) −282.886 + 237.369i −0.810561 + 0.680141i −0.950742 0.309985i \(-0.899676\pi\)
0.140181 + 0.990126i \(0.455232\pi\)
\(350\) 26.2140i 0.0748971i
\(351\) −149.883 + 544.815i −0.427017 + 1.55218i
\(352\) 26.7066 0.0758711
\(353\) 60.3702 + 71.9464i 0.171020 + 0.203814i 0.844746 0.535167i \(-0.179751\pi\)
−0.673726 + 0.738982i \(0.735307\pi\)
\(354\) 151.905 + 60.7390i 0.429109 + 0.171579i
\(355\) −115.245 + 653.586i −0.324633 + 1.84109i
\(356\) −151.661 416.684i −0.426013 1.17046i
\(357\) −55.1251 11.5102i −0.154412 0.0322415i
\(358\) 24.9177 + 141.315i 0.0696026 + 0.394736i
\(359\) 89.5202 51.6845i 0.249360 0.143968i −0.370111 0.928987i \(-0.620680\pi\)
0.619471 + 0.785019i \(0.287347\pi\)
\(360\) 281.907 + 123.092i 0.783074 + 0.341921i
\(361\) −11.5145 + 19.9437i −0.0318962 + 0.0552458i
\(362\) 0.266993 0.733557i 0.000737550 0.00202640i
\(363\) 189.427 305.585i 0.521836 0.841832i
\(364\) 78.3002 + 65.7016i 0.215110 + 0.180499i
\(365\) −178.139 + 212.298i −0.488053 + 0.581639i
\(366\) 33.2283 + 20.5976i 0.0907877 + 0.0562776i
\(367\) 85.2083 + 31.0133i 0.232175 + 0.0845048i 0.455488 0.890242i \(-0.349465\pi\)
−0.223313 + 0.974747i \(0.571687\pi\)
\(368\) 18.7031 + 10.7982i 0.0508236 + 0.0293430i
\(369\) 17.3275 39.6838i 0.0469580 0.107544i
\(370\) −8.03070 13.9096i −0.0217046 0.0375935i
\(371\) −67.3726 + 11.8796i −0.181597 + 0.0320205i
\(372\) 38.2276 183.081i 0.102762 0.492154i
\(373\) 406.838 148.077i 1.09072 0.396989i 0.266831 0.963743i \(-0.414023\pi\)
0.823887 + 0.566754i \(0.191801\pi\)
\(374\) 8.66833 + 1.52846i 0.0231774 + 0.00408679i
\(375\) −74.8729 + 187.252i −0.199661 + 0.499340i
\(376\) −156.473 + 131.296i −0.416151 + 0.349192i
\(377\) 840.420i 2.22923i
\(378\) 20.2087 + 5.55958i 0.0534622 + 0.0147079i
\(379\) 333.700 0.880476 0.440238 0.897881i \(-0.354894\pi\)
0.440238 + 0.897881i \(0.354894\pi\)
\(380\) −353.561 421.357i −0.930423 1.10883i
\(381\) −390.049 + 307.005i −1.02375 + 0.805787i
\(382\) 4.69296 26.6151i 0.0122852 0.0696730i
\(383\) 203.470 + 559.030i 0.531254 + 1.45961i 0.857579 + 0.514352i \(0.171967\pi\)
−0.326325 + 0.945258i \(0.605810\pi\)
\(384\) −111.561 339.195i −0.290524 0.883321i
\(385\) 1.90869 + 10.8247i 0.00495764 + 0.0281162i
\(386\) 71.7937 41.4501i 0.185994 0.107384i
\(387\) −154.339 9.67773i −0.398809 0.0250071i
\(388\) 17.6386 30.5509i 0.0454603 0.0787395i
\(389\) 106.062 291.404i 0.272654 0.749111i −0.725491 0.688232i \(-0.758387\pi\)
0.998145 0.0608795i \(-0.0193905\pi\)
\(390\) −132.383 246.832i −0.339444 0.632901i
\(391\) 19.3185 + 16.2102i 0.0494079 + 0.0414582i
\(392\) −135.326 + 161.275i −0.345219 + 0.411416i
\(393\) 3.44771 110.075i 0.00877281 0.280090i
\(394\) 29.5793 + 10.7660i 0.0750744 + 0.0273248i
\(395\) −194.064 112.043i −0.491302 0.283653i
\(396\) 34.4276 + 8.32127i 0.0869383 + 0.0210133i
\(397\) −69.0323 119.567i −0.173885 0.301177i 0.765890 0.642972i \(-0.222299\pi\)
−0.939775 + 0.341794i \(0.888965\pi\)
\(398\) 188.477 33.2336i 0.473561 0.0835015i
\(399\) −58.4679 52.2653i −0.146536 0.130991i
\(400\) 382.401 139.183i 0.956003 0.347956i
\(401\) 266.978 + 47.0754i 0.665780 + 0.117395i 0.496317 0.868142i \(-0.334686\pi\)
0.169463 + 0.985537i \(0.445797\pi\)
\(402\) 33.7501 4.86708i 0.0839556 0.0121072i
\(403\) −272.979 + 229.057i −0.677368 + 0.568379i
\(404\) 14.1192i 0.0349486i
\(405\) 494.765 + 375.220i 1.22164 + 0.926469i
\(406\) −31.1735 −0.0767821
\(407\) −2.48744 2.96441i −0.00611164 0.00728357i
\(408\) −26.8647 186.290i −0.0658448 0.456593i
\(409\) 50.3565 285.586i 0.123121 0.698254i −0.859285 0.511497i \(-0.829091\pi\)
0.982406 0.186757i \(-0.0597976\pi\)
\(410\) 7.34118 + 20.1697i 0.0179053 + 0.0491944i
\(411\) 233.174 260.845i 0.567332 0.634660i
\(412\) 77.8573 + 441.551i 0.188974 + 1.07173i
\(413\) 108.255 62.5013i 0.262120 0.151335i
\(414\) −6.79849 6.47140i −0.0164215 0.0156314i
\(415\) 454.335 786.932i 1.09478 1.89622i
\(416\) −177.847 + 488.630i −0.427517 + 1.17459i
\(417\) 295.444 + 9.25373i 0.708499 + 0.0221912i
\(418\) 9.38999 + 7.87914i 0.0224641 + 0.0188496i
\(419\) −215.521 + 256.848i −0.514371 + 0.613003i −0.959240 0.282592i \(-0.908806\pi\)
0.444870 + 0.895595i \(0.353250\pi\)
\(420\) 98.9867 53.0895i 0.235683 0.126404i
\(421\) −566.754 206.282i −1.34621 0.489980i −0.434447 0.900697i \(-0.643056\pi\)
−0.911763 + 0.410717i \(0.865278\pi\)
\(422\) 47.7608 + 27.5747i 0.113177 + 0.0653429i
\(423\) −369.290 + 183.414i −0.873027 + 0.433602i
\(424\) −114.326 198.018i −0.269636 0.467024i
\(425\) 467.974 82.5165i 1.10112 0.194156i
\(426\) −143.573 + 47.2210i −0.337026 + 0.110847i
\(427\) 28.0700 10.2167i 0.0657378 0.0239266i
\(428\) 288.748 + 50.9140i 0.674644 + 0.118958i
\(429\) −41.7382 53.0284i −0.0972919 0.123609i
\(430\) 58.7206 49.2724i 0.136560 0.114587i
\(431\) 773.546i 1.79477i 0.441247 + 0.897385i \(0.354536\pi\)
−0.441247 + 0.897385i \(0.645464\pi\)
\(432\) −26.1965 324.317i −0.0606400 0.750733i
\(433\) 71.6603 0.165497 0.0827486 0.996570i \(-0.473630\pi\)
0.0827486 + 0.996570i \(0.473630\pi\)
\(434\) 8.49636 + 10.1256i 0.0195769 + 0.0233308i
\(435\) −857.545 342.889i −1.97137 0.788251i
\(436\) −61.5503 + 349.069i −0.141170 + 0.800617i
\(437\) 12.0115 + 33.0014i 0.0274863 + 0.0755181i
\(438\) −61.7805 12.8999i −0.141051 0.0294517i
\(439\) −118.933 674.503i −0.270918 1.53645i −0.751636 0.659579i \(-0.770735\pi\)
0.480717 0.876876i \(-0.340376\pi\)
\(440\) −31.8155 + 18.3687i −0.0723079 + 0.0417470i
\(441\) −342.015 + 252.266i −0.775544 + 0.572031i
\(442\) −85.6900 + 148.419i −0.193869 + 0.335790i
\(443\) −155.729 + 427.863i −0.351534 + 0.965831i 0.630344 + 0.776316i \(0.282914\pi\)
−0.981878 + 0.189515i \(0.939308\pi\)
\(444\) −20.8351 + 33.6114i −0.0469259 + 0.0757014i
\(445\) 711.226 + 596.789i 1.59826 + 1.34110i
\(446\) −30.3985 + 36.2276i −0.0681582 + 0.0812278i
\(447\) 354.326 + 219.640i 0.792675 + 0.491365i
\(448\) −42.2985 15.3954i −0.0944163 0.0343647i
\(449\) −456.689 263.670i −1.01713 0.587238i −0.103856 0.994592i \(-0.533118\pi\)
−0.913270 + 0.407355i \(0.866451\pi\)
\(450\) −175.756 + 19.7515i −0.390569 + 0.0438922i
\(451\) 2.58574 + 4.47864i 0.00573336 + 0.00993046i
\(452\) 233.062 41.0951i 0.515623 0.0909183i
\(453\) −79.9661 + 382.976i −0.176526 + 0.845423i
\(454\) −91.7564 + 33.3966i −0.202107 + 0.0735608i
\(455\) −210.762 37.1631i −0.463214 0.0816770i
\(456\) 97.3142 243.377i 0.213408 0.533721i
\(457\) −112.672 + 94.5433i −0.246548 + 0.206878i −0.757684 0.652622i \(-0.773669\pi\)
0.511136 + 0.859500i \(0.329225\pi\)
\(458\) 42.7281i 0.0932928i
\(459\) 35.6369 378.268i 0.0776404 0.824114i
\(460\) −50.3013 −0.109351
\(461\) −230.109 274.233i −0.499152 0.594866i 0.456368 0.889791i \(-0.349150\pi\)
−0.955521 + 0.294924i \(0.904706\pi\)
\(462\) −1.96697 + 1.54819i −0.00425752 + 0.00335106i
\(463\) 71.1591 403.563i 0.153691 0.871627i −0.806281 0.591533i \(-0.798523\pi\)
0.959972 0.280095i \(-0.0903659\pi\)
\(464\) 165.515 + 454.750i 0.356714 + 0.980064i
\(465\) 122.349 + 371.996i 0.263117 + 0.799992i
\(466\) 18.5578 + 105.246i 0.0398235 + 0.225850i
\(467\) −778.946 + 449.725i −1.66798 + 0.963008i −0.699252 + 0.714876i \(0.746483\pi\)
−0.968726 + 0.248132i \(0.920183\pi\)
\(468\) −381.511 + 574.481i −0.815194 + 1.22752i
\(469\) 13.0274 22.5641i 0.0277769 0.0481110i
\(470\) 69.9044 192.061i 0.148733 0.408640i
\(471\) −331.243 617.610i −0.703276 1.31127i
\(472\) 320.048 + 268.552i 0.678068 + 0.568966i
\(473\) 11.8715 14.1479i 0.0250983 0.0299110i
\(474\) 1.59760 51.0067i 0.00337047 0.107609i
\(475\) 621.847 + 226.334i 1.30915 + 0.476492i
\(476\) −59.5205 34.3642i −0.125043 0.0721937i
\(477\) −130.412 442.760i −0.273401 0.928218i
\(478\) 2.57499 + 4.46001i 0.00538701 + 0.00933057i
\(479\) 822.620 145.050i 1.71737 0.302819i 0.773662 0.633599i \(-0.218423\pi\)
0.943708 + 0.330780i \(0.107312\pi\)
\(480\) 426.026 + 380.831i 0.887554 + 0.793397i
\(481\) 70.8021 25.7699i 0.147198 0.0535756i
\(482\) 9.12045 + 1.60818i 0.0189221 + 0.00333647i
\(483\) −7.09834 + 1.02364i −0.0146963 + 0.00211935i
\(484\) 336.135 282.051i 0.694494 0.582749i
\(485\) 73.8629i 0.152295i
\(486\) −22.0484 + 139.682i −0.0453671 + 0.287411i
\(487\) −601.667 −1.23546 −0.617728 0.786392i \(-0.711947\pi\)
−0.617728 + 0.786392i \(0.711947\pi\)
\(488\) 64.1752 + 76.4810i 0.131506 + 0.156723i
\(489\) −28.2054 195.587i −0.0576798 0.399973i
\(490\) 36.5807 207.460i 0.0746545 0.423387i
\(491\) −146.639 402.888i −0.298655 0.820547i −0.994725 0.102574i \(-0.967292\pi\)
0.696071 0.717973i \(-0.254930\pi\)
\(492\) 35.2205 39.4003i 0.0715865 0.0800820i
\(493\) 98.1282 + 556.513i 0.199043 + 1.12883i
\(494\) −206.689 + 119.332i −0.418399 + 0.241563i
\(495\) −71.1380 + 20.9533i −0.143713 + 0.0423298i
\(496\) 102.597 177.704i 0.206849 0.358274i
\(497\) −39.4975 + 108.519i −0.0794719 + 0.218347i
\(498\) 206.832 + 6.47828i 0.415326 + 0.0130086i
\(499\) −435.651 365.554i −0.873048 0.732574i 0.0916899 0.995788i \(-0.470773\pi\)
−0.964738 + 0.263214i \(0.915218\pi\)
\(500\) −158.205 + 188.542i −0.316411 + 0.377084i
\(501\) 443.009 237.599i 0.884249 0.474249i
\(502\) −144.507 52.5961i −0.287862 0.104773i
\(503\) 178.281 + 102.930i 0.354435 + 0.204633i 0.666637 0.745383i \(-0.267733\pi\)
−0.312202 + 0.950016i \(0.601067\pi\)
\(504\) 44.5892 + 29.6115i 0.0884706 + 0.0587530i
\(505\) 14.7813 + 25.6020i 0.0292700 + 0.0506971i
\(506\) 1.10394 0.194654i 0.00218170 0.000384692i
\(507\) 766.547 252.117i 1.51193 0.497272i
\(508\) −569.269 + 207.197i −1.12061 + 0.407868i
\(509\) 663.268 + 116.952i 1.30308 + 0.229768i 0.781753 0.623589i \(-0.214326\pi\)
0.521327 + 0.853357i \(0.325437\pi\)
\(510\) 116.482 + 147.991i 0.228397 + 0.290178i
\(511\) −36.9414 + 30.9975i −0.0722924 + 0.0606605i
\(512\) 514.334i 1.00456i
\(513\) 306.368 431.388i 0.597208 0.840913i
\(514\) 199.097 0.387347
\(515\) −603.433 719.144i −1.17172 1.39640i
\(516\) −175.243 70.0710i −0.339619 0.135797i
\(517\) 8.55115 48.4960i 0.0165399 0.0938027i
\(518\) −0.955876 2.62625i −0.00184532 0.00506998i
\(519\) −780.319 162.932i −1.50351 0.313934i
\(520\) −124.209 704.425i −0.238864 1.35466i
\(521\) 678.655 391.821i 1.30260 0.752056i 0.321751 0.946824i \(-0.395729\pi\)
0.980849 + 0.194768i \(0.0623954\pi\)
\(522\) −23.4884 209.008i −0.0449969 0.400399i
\(523\) −231.463 + 400.906i −0.442569 + 0.766551i −0.997879 0.0650916i \(-0.979266\pi\)
0.555311 + 0.831643i \(0.312599\pi\)
\(524\) 45.9700 126.301i 0.0877290 0.241033i
\(525\) −71.1996 + 114.860i −0.135618 + 0.218781i
\(526\) 169.573 + 142.289i 0.322383 + 0.270511i
\(527\) 154.018 183.551i 0.292254 0.348294i
\(528\) 33.0281 + 20.4735i 0.0625532 + 0.0387755i
\(529\) −494.079 179.830i −0.933988 0.339944i
\(530\) 198.140 + 114.396i 0.373850 + 0.215842i
\(531\) 500.617 + 678.723i 0.942782 + 1.27820i
\(532\) −47.8556 82.8884i −0.0899542 0.155805i
\(533\) −99.1614 + 17.4848i −0.186044 + 0.0328046i
\(534\) −43.2161 + 206.972i −0.0809291 + 0.387589i
\(535\) −576.880 + 209.967i −1.07828 + 0.392462i
\(536\) 85.7591 + 15.1217i 0.159998 + 0.0282120i
\(537\) −274.646 + 686.872i −0.511444 + 1.27909i
\(538\) 39.6442 33.2654i 0.0736881 0.0618317i
\(539\) 50.7555i 0.0941661i
\(540\) 430.531 + 623.671i 0.797280 + 1.15495i
\(541\) 595.277 1.10033 0.550164 0.835057i \(-0.314565\pi\)
0.550164 + 0.835057i \(0.314565\pi\)
\(542\) −182.215 217.155i −0.336190 0.400655i
\(543\) 3.16228 2.48900i 0.00582371 0.00458380i
\(544\) 60.7145 344.329i 0.111607 0.632957i
\(545\) −253.831 697.394i −0.465744 1.27962i
\(546\) −15.2274 46.2980i −0.0278890 0.0847949i
\(547\) 175.350 + 994.459i 0.320567 + 1.81802i 0.539154 + 0.842207i \(0.318744\pi\)
−0.218588 + 0.975817i \(0.570145\pi\)
\(548\) 369.793 213.500i 0.674805 0.389599i
\(549\) 89.6492 + 180.502i 0.163296 + 0.328784i
\(550\) 10.5612 18.2926i 0.0192022 0.0332593i
\(551\) −269.155 + 739.497i −0.488485 + 1.34210i
\(552\) −11.3293 21.1237i −0.0205240 0.0382675i
\(553\) −29.8701 25.0639i −0.0540146 0.0453236i
\(554\) −32.7177 + 38.9914i −0.0590572 + 0.0703816i
\(555\) 2.59212 82.7588i 0.00467049 0.149115i
\(556\) 338.995 + 123.384i 0.609704 + 0.221914i
\(557\) 53.4658 + 30.8685i 0.0959889 + 0.0554192i 0.547226 0.836985i \(-0.315684\pi\)
−0.451237 + 0.892404i \(0.649017\pi\)
\(558\) −61.4868 + 64.5946i −0.110191 + 0.115761i
\(559\) 179.797 + 311.418i 0.321641 + 0.557099i
\(560\) 121.362 21.3994i 0.216718 0.0382132i
\(561\) 33.8300 + 30.2412i 0.0603031 + 0.0539058i
\(562\) 88.2351 32.1149i 0.157002 0.0571440i
\(563\) −955.335 168.451i −1.69686 0.299203i −0.760267 0.649611i \(-0.774932\pi\)
−0.936597 + 0.350408i \(0.886043\pi\)
\(564\) −498.075 + 71.8270i −0.883112 + 0.127353i
\(565\) −379.582 + 318.507i −0.671827 + 0.563730i
\(566\) 79.8559i 0.141088i
\(567\) 73.4469 + 79.2488i 0.129536 + 0.139769i
\(568\) −385.976 −0.679535
\(569\) −61.7612 73.6041i −0.108543 0.129357i 0.709037 0.705171i \(-0.249130\pi\)
−0.817581 + 0.575814i \(0.804685\pi\)
\(570\) 37.4349 + 259.588i 0.0656753 + 0.455417i
\(571\) −112.283 + 636.787i −0.196642 + 1.11521i 0.713419 + 0.700738i \(0.247146\pi\)
−0.910061 + 0.414475i \(0.863965\pi\)
\(572\) −28.1691 77.3938i −0.0492466 0.135304i
\(573\) 92.8519 103.871i 0.162045 0.181276i
\(574\) 0.648561 + 3.67817i 0.00112990 + 0.00640797i
\(575\) 52.4096 30.2587i 0.0911471 0.0526238i
\(576\) 71.3503 295.197i 0.123872 0.512496i
\(577\) −126.992 + 219.957i −0.220091 + 0.381208i −0.954835 0.297136i \(-0.903969\pi\)
0.734745 + 0.678344i \(0.237302\pi\)
\(578\) −18.1081 + 49.7516i −0.0313289 + 0.0860755i
\(579\) 427.156 + 13.3791i 0.737748 + 0.0231073i
\(580\) −863.450 724.520i −1.48871 1.24917i
\(581\) 101.634 121.123i 0.174930 0.208474i
\(582\) −14.8236 + 7.95032i −0.0254700 + 0.0136603i
\(583\) 51.8000 + 18.8537i 0.0888507 + 0.0323390i
\(584\) −139.583 80.5883i −0.239012 0.137994i
\(585\) 90.3626 1441.09i 0.154466 2.46340i
\(586\) 112.981 + 195.689i 0.192801 + 0.333940i
\(587\) −220.174 + 38.8225i −0.375083 + 0.0661372i −0.358012 0.933717i \(-0.616545\pi\)
−0.0170710 + 0.999854i \(0.505434\pi\)
\(588\) −492.708 + 162.051i −0.837938 + 0.275597i
\(589\) 313.557 114.125i 0.532354 0.193761i
\(590\) −411.700 72.5938i −0.697796 0.123040i
\(591\) 100.364 + 127.513i 0.169821 + 0.215758i
\(592\) −33.2357 + 27.8880i −0.0561413 + 0.0471082i
\(593\) 69.9992i 0.118042i 0.998257 + 0.0590212i \(0.0187980\pi\)
−0.998257 + 0.0590212i \(0.981202\pi\)
\(594\) −11.8621 12.0214i −0.0199699 0.0202380i
\(595\) 143.903 0.241853
\(596\) 327.038 + 389.748i 0.548721 + 0.653940i
\(597\) 916.103 + 366.304i 1.53451 + 0.613574i
\(598\) −3.79001 + 21.4942i −0.00633780 + 0.0359435i
\(599\) 143.261 + 393.606i 0.239167 + 0.657105i 0.999967 + 0.00811910i \(0.00258442\pi\)
−0.760800 + 0.648986i \(0.775193\pi\)
\(600\) −442.133 92.3180i −0.736888 0.153863i
\(601\) −137.993 782.595i −0.229605 1.30216i −0.853683 0.520793i \(-0.825636\pi\)
0.624078 0.781362i \(-0.285475\pi\)
\(602\) 11.5514 6.66919i 0.0191883 0.0110784i
\(603\) 161.100 + 70.3428i 0.267165 + 0.116655i
\(604\) −238.742 + 413.513i −0.395268 + 0.684624i
\(605\) −314.227 + 863.332i −0.519384 + 1.42700i
\(606\) −3.54707 + 5.72218i −0.00585325 + 0.00944254i
\(607\) 251.711 + 211.211i 0.414681 + 0.347959i 0.826135 0.563472i \(-0.190535\pi\)
−0.411454 + 0.911430i \(0.634979\pi\)
\(608\) 312.980 372.995i 0.514770 0.613479i
\(609\) −136.591 84.6703i −0.224288 0.139032i
\(610\) −93.8758 34.1680i −0.153895 0.0560131i
\(611\) 830.349 + 479.402i 1.35900 + 0.784619i
\(612\) 185.553 424.957i 0.303192 0.694375i
\(613\) −367.664 636.812i −0.599778 1.03885i −0.992853 0.119340i \(-0.961922\pi\)
0.393076 0.919506i \(-0.371411\pi\)
\(614\) 237.632 41.9010i 0.387023 0.0682427i
\(615\) −22.6165 + 108.316i −0.0367748 + 0.176123i
\(616\) −6.00704 + 2.18638i −0.00975169 + 0.00354932i
\(617\) −331.915 58.5257i −0.537951 0.0948552i −0.101929 0.994792i \(-0.532502\pi\)
−0.436021 + 0.899936i \(0.643613\pi\)
\(618\) 79.3739 198.509i 0.128437 0.321212i
\(619\) 900.806 755.866i 1.45526 1.22111i 0.526633 0.850093i \(-0.323454\pi\)
0.928627 0.371015i \(-0.120990\pi\)
\(620\) 477.928i 0.770851i
\(621\) −12.2116 46.8207i −0.0196644 0.0753956i
\(622\) −253.977 −0.408323
\(623\) 103.846 + 123.758i 0.166686 + 0.198649i
\(624\) −594.531 + 467.950i −0.952774 + 0.749921i
\(625\) −57.1109 + 323.892i −0.0913775 + 0.518227i
\(626\) −81.8610 224.911i −0.130768 0.359283i
\(627\) 19.7430 + 60.0276i 0.0314881 + 0.0957378i
\(628\) −148.526 842.334i −0.236507 1.34130i
\(629\) −43.8751 + 25.3313i −0.0697537 + 0.0402723i
\(630\) −53.4541 3.35180i −0.0848478 0.00532032i
\(631\) 107.380 185.988i 0.170175 0.294751i −0.768306 0.640082i \(-0.778900\pi\)
0.938481 + 0.345332i \(0.112234\pi\)
\(632\) 44.5734 122.464i 0.0705276 0.193773i
\(633\) 134.375 + 250.545i 0.212283 + 0.395806i
\(634\) −182.322 152.987i −0.287575 0.241304i
\(635\) 815.326 971.668i 1.28398 1.53019i
\(636\) 17.6353 563.042i 0.0277284 0.885287i
\(637\) 928.634 + 337.995i 1.45782 + 0.530605i
\(638\) 21.7535 + 12.5594i 0.0340964 + 0.0196855i
\(639\) −757.341 183.052i −1.18520 0.286466i
\(640\) 456.222 + 790.199i 0.712846 + 1.23469i
\(641\) −979.635 + 172.736i −1.52829 + 0.269479i −0.873685 0.486491i \(-0.838276\pi\)
−0.654606 + 0.755970i \(0.727165\pi\)
\(642\) −104.231 93.1741i −0.162354 0.145131i
\(643\) 797.989 290.444i 1.24104 0.451702i 0.363675 0.931526i \(-0.381522\pi\)
0.877365 + 0.479824i \(0.159300\pi\)
\(644\) −8.61980 1.51990i −0.0133848 0.00236010i
\(645\) 391.121 56.4032i 0.606389 0.0874468i
\(646\) 122.933 103.153i 0.190299 0.159680i
\(647\) 350.755i 0.542125i −0.962562 0.271063i \(-0.912625\pi\)
0.962562 0.271063i \(-0.0873751\pi\)
\(648\) −164.939 + 321.267i −0.254535 + 0.495782i
\(649\) −100.723 −0.155198
\(650\) 264.355 + 315.046i 0.406700 + 0.484687i
\(651\) 9.72596 + 67.4435i 0.0149400 + 0.103600i
\(652\) 41.8793 237.509i 0.0642321 0.364278i
\(653\) 96.2871 + 264.547i 0.147453 + 0.405125i 0.991327 0.131417i \(-0.0419526\pi\)
−0.843874 + 0.536542i \(0.819730\pi\)
\(654\) 112.639 126.006i 0.172231 0.192670i
\(655\) 48.8681 + 277.145i 0.0746078 + 0.423122i
\(656\) 50.2125 28.9902i 0.0765434 0.0441924i
\(657\) −235.662 224.324i −0.358694 0.341437i
\(658\) 17.7824 30.8000i 0.0270249 0.0468085i
\(659\) 34.4733 94.7146i 0.0523115 0.143725i −0.910785 0.412881i \(-0.864523\pi\)
0.963097 + 0.269156i \(0.0867448\pi\)
\(660\) −90.4638 2.83345i −0.137066 0.00429311i
\(661\) −555.119 465.801i −0.839818 0.704691i 0.117705 0.993049i \(-0.462446\pi\)
−0.957523 + 0.288358i \(0.906891\pi\)
\(662\) −122.558 + 146.059i −0.185133 + 0.220633i
\(663\) −778.583 + 417.578i −1.17433 + 0.629830i
\(664\) 496.594 + 180.745i 0.747882 + 0.272207i
\(665\) 173.551 + 100.199i 0.260978 + 0.150676i
\(666\) 16.8879 8.38764i 0.0253572 0.0125940i
\(667\) 35.9835 + 62.3252i 0.0539483 + 0.0934412i
\(668\) 604.202 106.537i 0.904494 0.159487i
\(669\) −231.593 + 76.1707i −0.346178 + 0.113858i
\(670\) −81.8810 + 29.8022i −0.122210 + 0.0444810i
\(671\) −23.7039 4.17964i −0.0353263 0.00622898i
\(672\) 61.4981 + 78.1333i 0.0915150 + 0.116270i
\(673\) 313.428 262.997i 0.465717 0.390783i −0.379512 0.925187i \(-0.623908\pi\)
0.845229 + 0.534404i \(0.179464\pi\)
\(674\) 327.399i 0.485755i
\(675\) −823.745 390.826i −1.22036 0.579001i
\(676\) 984.833 1.45685
\(677\) −217.703 259.448i −0.321570 0.383232i 0.580907 0.813970i \(-0.302698\pi\)
−0.902477 + 0.430738i \(0.858253\pi\)
\(678\) −104.778 41.8955i −0.154540 0.0617928i
\(679\) −2.23184 + 12.6574i −0.00328695 + 0.0186412i
\(680\) 164.499 + 451.956i 0.241910 + 0.664642i
\(681\) −492.751 102.887i −0.723570 0.151083i
\(682\) −1.84947 10.4889i −0.00271183 0.0153796i
\(683\) −269.651 + 155.683i −0.394804 + 0.227940i −0.684239 0.729257i \(-0.739866\pi\)
0.289436 + 0.957197i \(0.406532\pi\)
\(684\) 519.681 383.310i 0.759768 0.560395i
\(685\) −447.024 + 774.268i −0.652590 + 1.13032i
\(686\) 25.5468 70.1893i 0.0372403 0.102317i
\(687\) 116.053 187.219i 0.168928 0.272517i
\(688\) −158.620 133.098i −0.230552 0.193456i
\(689\) −689.901 + 822.192i −1.00131 + 1.19331i
\(690\) 20.3859 + 12.6368i 0.0295447 + 0.0183142i
\(691\) −777.773 283.086i −1.12558 0.409676i −0.288891 0.957362i \(-0.593287\pi\)
−0.836684 + 0.547686i \(0.815509\pi\)
\(692\) −842.537 486.439i −1.21754 0.702947i
\(693\) −12.8236 + 1.44112i −0.0185044 + 0.00207953i
\(694\) −70.9733 122.929i −0.102267 0.177132i
\(695\) −743.861 + 131.163i −1.07030 + 0.188723i
\(696\) 109.784 525.782i 0.157736 0.755434i
\(697\) 63.6215 23.1563i 0.0912791 0.0332229i
\(698\) 211.634 + 37.3168i 0.303201 + 0.0534625i
\(699\) −204.545 + 511.556i −0.292626 + 0.731839i
\(700\) −126.343 + 106.014i −0.180490 + 0.151449i
\(701\) 215.718i 0.307729i 0.988092 + 0.153864i \(0.0491718\pi\)
−0.988092 + 0.153864i \(0.950828\pi\)
\(702\) 298.939 136.979i 0.425839 0.195126i
\(703\) −70.5529 −0.100360
\(704\) 23.3141 + 27.7847i 0.0331166 + 0.0394669i
\(705\) 827.951 651.674i 1.17440 0.924360i
\(706\) 9.49079 53.8250i 0.0134430 0.0762393i
\(707\) 1.75939 + 4.83389i 0.00248853 + 0.00683718i
\(708\) 321.588 + 977.770i 0.454220 + 1.38103i
\(709\) 179.173 + 1016.14i 0.252712 + 1.43320i 0.801878 + 0.597487i \(0.203834\pi\)
−0.549167 + 0.835713i \(0.685055\pi\)
\(710\) 334.472 193.107i 0.471087 0.271982i
\(711\) 145.539 219.154i 0.204696 0.308233i
\(712\) −269.981 + 467.620i −0.379186 + 0.656770i
\(713\) 10.4367 28.6747i 0.0146378 0.0402169i
\(714\) 15.4891 + 28.8798i 0.0216935 + 0.0404479i
\(715\) 132.101 + 110.846i 0.184757 + 0.155030i
\(716\) −580.322 + 691.601i −0.810506 + 0.965924i
\(717\) −0.831146 + 26.5361i −0.00115920 + 0.0370098i
\(718\) −56.5267 20.5740i −0.0787280 0.0286546i
\(719\) 539.953 + 311.742i 0.750978 + 0.433578i 0.826047 0.563601i \(-0.190584\pi\)
−0.0750689 + 0.997178i \(0.523918\pi\)
\(720\) 234.919 + 797.568i 0.326276 + 1.10773i
\(721\) −81.6768 141.468i −0.113283 0.196211i
\(722\) 13.1979 2.32714i 0.0182796 0.00322319i
\(723\) 35.5945 + 31.8184i 0.0492317 + 0.0440089i
\(724\) 4.61527 1.67982i 0.00637469 0.00232020i
\(725\) 1335.47 + 235.480i 1.84203 + 0.324800i
\(726\) −207.085 + 29.8635i −0.285240 + 0.0411343i
\(727\) −575.569 + 482.959i −0.791704 + 0.664318i −0.946167 0.323680i \(-0.895080\pi\)
0.154463 + 0.987999i \(0.450635\pi\)
\(728\) 124.466i 0.170970i
\(729\) −475.997 + 552.149i −0.652945 + 0.757406i
\(730\) 161.276 0.220926
\(731\) −155.420 185.223i −0.212614 0.253383i
\(732\) 35.1077 + 243.450i 0.0479613 + 0.332582i
\(733\) 130.291 738.919i 0.177751 1.00807i −0.757170 0.653218i \(-0.773419\pi\)
0.934921 0.354857i \(-0.115470\pi\)
\(734\) −18.0478 49.5860i −0.0245883 0.0675558i
\(735\) 723.763 809.655i 0.984711 1.10157i
\(736\) −7.73218 43.8514i −0.0105057 0.0595807i
\(737\) −18.1815 + 10.4971i −0.0246696 + 0.0142430i
\(738\) −24.1723 + 7.11979i −0.0327537 + 0.00964741i
\(739\) 676.597 1171.90i 0.915557 1.58579i 0.109474 0.993990i \(-0.465083\pi\)
0.806083 0.591802i \(-0.201583\pi\)
\(740\) 34.5620 94.9583i 0.0467054 0.128322i
\(741\) −1229.75 38.5176i −1.65959 0.0519806i
\(742\) 30.4974 + 25.5904i 0.0411017 + 0.0344884i
\(743\) 545.577 650.194i 0.734290 0.875092i −0.261646 0.965164i \(-0.584265\pi\)
0.995935 + 0.0900717i \(0.0287096\pi\)
\(744\) −200.703 + 107.643i −0.269761 + 0.144681i
\(745\) −1001.03 364.346i −1.34367 0.489056i
\(746\) −218.194 125.975i −0.292486 0.168867i
\(747\) 888.669 + 590.162i 1.18965 + 0.790043i
\(748\) 27.6897 + 47.9599i 0.0370183 + 0.0641175i
\(749\) −105.200 + 18.5497i −0.140455 + 0.0247659i
\(750\) 111.483 36.6666i 0.148644 0.0488888i
\(751\) −757.303 + 275.636i −1.00839 + 0.367025i −0.792816 0.609462i \(-0.791386\pi\)
−0.215577 + 0.976487i \(0.569163\pi\)
\(752\) −543.715 95.8717i −0.723026 0.127489i
\(753\) −490.319 622.951i −0.651155 0.827292i
\(754\) −374.652 + 314.370i −0.496886 + 0.416936i
\(755\) 999.749i 1.32417i
\(756\) 54.9325 + 119.883i 0.0726620 + 0.158576i
\(757\) −171.631 −0.226725 −0.113363 0.993554i \(-0.536162\pi\)
−0.113363 + 0.993554i \(0.536162\pi\)
\(758\) −124.825 148.761i −0.164677 0.196254i
\(759\) 5.36576 + 2.14550i 0.00706951 + 0.00282674i
\(760\) −116.308 + 659.613i −0.153036 + 0.867912i
\(761\) −462.136 1269.71i −0.607275 1.66847i −0.736154 0.676814i \(-0.763360\pi\)
0.128880 0.991660i \(-0.458862\pi\)
\(762\) 282.763 + 59.0413i 0.371080 + 0.0774821i
\(763\) −22.4248 127.178i −0.0293904 0.166681i
\(764\) 147.255 85.0178i 0.192742 0.111280i
\(765\) 108.426 + 964.818i 0.141734 + 1.26120i
\(766\) 173.100 299.818i 0.225979 0.391407i
\(767\) 670.746 1842.86i 0.874506 2.40268i
\(768\) 103.865 167.557i 0.135241 0.218173i
\(769\) 770.979 + 646.928i 1.00257 + 0.841259i 0.987339 0.158625i \(-0.0507060\pi\)
0.0152349 + 0.999884i \(0.495150\pi\)
\(770\) 4.11159 4.90001i 0.00533973 0.00636365i
\(771\) 872.369 + 540.765i 1.13148 + 0.701381i
\(772\) 490.123 + 178.390i 0.634874 + 0.231075i
\(773\) 24.6722 + 14.2445i 0.0319175 + 0.0184276i 0.515874 0.856665i \(-0.327467\pi\)
−0.483956 + 0.875092i \(0.660801\pi\)
\(774\) 53.4183 + 72.4231i 0.0690160 + 0.0935699i
\(775\) −287.497 497.960i −0.370964 0.642528i
\(776\) −42.3045 + 7.45943i −0.0545161 + 0.00961266i
\(777\) 2.94484 14.1035i 0.00379001 0.0181512i
\(778\) −169.579 + 61.7219i −0.217968 + 0.0793340i
\(779\) 92.8532 + 16.3725i 0.119195 + 0.0210174i
\(780\) 654.265 1636.28i 0.838801 2.09779i
\(781\) 71.2827 59.8133i 0.0912710 0.0765855i
\(782\) 14.6756i 0.0187668i
\(783\) 464.768 979.594i 0.593574 1.25108i
\(784\) −569.048 −0.725827
\(785\) 1151.15 + 1371.89i 1.46644 + 1.74763i
\(786\) −50.3603 + 39.6382i −0.0640716 + 0.0504302i
\(787\) 34.7237 196.928i 0.0441216 0.250226i −0.954767 0.297354i \(-0.903896\pi\)
0.998889 + 0.0471280i \(0.0150069\pi\)
\(788\) 67.7357 + 186.102i 0.0859590 + 0.236170i
\(789\) 356.539 + 1084.04i 0.451887 + 1.37394i
\(790\) 22.6445 + 128.423i 0.0286639 + 0.162561i
\(791\) −74.6706 + 43.1111i −0.0944002 + 0.0545020i
\(792\) −19.1851 38.6278i −0.0242236 0.0487725i
\(793\) 234.323 405.859i 0.295489 0.511802i
\(794\) −27.4797 + 75.4997i −0.0346091 + 0.0950878i
\(795\) 557.468 + 1039.41i 0.701217 + 1.30744i
\(796\) 922.411 + 773.995i 1.15881 + 0.972356i
\(797\) −675.871 + 805.471i −0.848018 + 1.01063i 0.151735 + 0.988421i \(0.451514\pi\)
−0.999753 + 0.0222076i \(0.992931\pi\)
\(798\) −1.42873 + 45.6150i −0.00179038 + 0.0571617i
\(799\) −605.819 220.500i −0.758222 0.275970i
\(800\) −726.630 419.520i −0.908287 0.524400i
\(801\) −751.513 + 789.498i −0.938219 + 0.985640i
\(802\) −78.8807 136.625i −0.0983550 0.170356i
\(803\) 38.2669 6.74748i 0.0476549 0.00840284i
\(804\) 159.950 + 142.981i 0.198942 + 0.177837i
\(805\) 17.2212 6.26801i 0.0213928 0.00778635i
\(806\) 204.223 + 36.0100i 0.253378 + 0.0446774i
\(807\) 264.059 38.0797i 0.327210 0.0471867i
\(808\) −13.1706 + 11.0515i −0.0163003 + 0.0136776i
\(809\) 482.349i 0.596229i 0.954530 + 0.298114i \(0.0963577\pi\)
−0.954530 + 0.298114i \(0.903642\pi\)
\(810\) −17.8034 360.918i −0.0219795 0.445577i
\(811\) −1202.48 −1.48272 −0.741358 0.671110i \(-0.765818\pi\)
−0.741358 + 0.671110i \(0.765818\pi\)
\(812\) −126.072 150.246i −0.155261 0.185032i
\(813\) −208.585 1446.41i −0.256562 1.77910i
\(814\) −0.391050 + 2.21775i −0.000480405 + 0.00272451i
\(815\) 172.708 + 474.512i 0.211912 + 0.582224i
\(816\) 339.050 379.287i 0.415503 0.464813i
\(817\) −58.4707 331.604i −0.0715675 0.405880i
\(818\) −146.148 + 84.3786i −0.178665 + 0.103152i
\(819\) 59.0289 244.220i 0.0720743 0.298193i
\(820\) −67.5224 + 116.952i −0.0823444 + 0.142625i
\(821\) 443.863 1219.50i 0.540637 1.48539i −0.305380 0.952231i \(-0.598783\pi\)
0.846016 0.533157i \(-0.178994\pi\)
\(822\) −203.504 6.37403i −0.247572 0.00775430i
\(823\) 810.125 + 679.776i 0.984356 + 0.825973i 0.984741 0.174027i \(-0.0556780\pi\)
−0.000384609 1.00000i \(0.500122\pi\)
\(824\) 350.944 418.239i 0.425903 0.507572i
\(825\) 95.9599 51.4662i 0.116315 0.0623833i
\(826\) −68.3568 24.8799i −0.0827565 0.0301209i
\(827\) −767.759 443.266i −0.928367 0.535993i −0.0420722 0.999115i \(-0.513396\pi\)
−0.886295 + 0.463122i \(0.846729\pi\)
\(828\) 3.69567 58.9381i 0.00446337 0.0711813i
\(829\) −406.625 704.295i −0.490500 0.849572i 0.509440 0.860506i \(-0.329853\pi\)
−0.999940 + 0.0109347i \(0.996519\pi\)
\(830\) −520.757 + 91.8235i −0.627418 + 0.110631i
\(831\) −249.261 + 81.9819i −0.299953 + 0.0986545i
\(832\) −663.610 + 241.534i −0.797608 + 0.290306i
\(833\) −654.391 115.387i −0.785584 0.138520i
\(834\) −106.390 135.168i −0.127565 0.162072i
\(835\) −984.050 + 825.716i −1.17850 + 0.988881i
\(836\) 77.1214i 0.0922505i
\(837\) −444.858 + 116.026i −0.531491 + 0.138621i
\(838\) 195.119 0.232839
\(839\) 960.723 + 1144.94i 1.14508 + 1.36465i 0.920756 + 0.390140i \(0.127573\pi\)
0.224325 + 0.974514i \(0.427982\pi\)
\(840\) −127.002 50.7818i −0.151193 0.0604545i
\(841\) −133.994 + 759.917i −0.159327 + 0.903588i
\(842\) 120.043 + 329.816i 0.142569 + 0.391706i
\(843\) 473.841 + 98.9388i 0.562089 + 0.117365i
\(844\) 60.2525 + 341.709i 0.0713892 + 0.404868i
\(845\) −1785.77 + 1031.02i −2.11334 + 1.22014i
\(846\) 219.902 + 96.0180i 0.259932 + 0.113496i
\(847\) −79.9335 + 138.449i −0.0943725 + 0.163458i
\(848\) 211.379 580.758i 0.249267 0.684856i
\(849\) −216.896 + 349.899i −0.255472 + 0.412131i
\(850\) −211.837 177.752i −0.249220 0.209120i
\(851\) −4.14729 + 4.94255i −0.00487344 + 0.00580793i
\(852\) −808.225 501.004i −0.948621 0.588032i
\(853\) 786.440 + 286.241i 0.921969 + 0.335569i 0.759022 0.651065i \(-0.225678\pi\)
0.162947 + 0.986635i \(0.447900\pi\)
\(854\) −15.0545 8.69169i −0.0176282 0.0101776i
\(855\) −541.039 + 1239.10i −0.632794 + 1.44924i
\(856\) −178.517 309.200i −0.208547 0.361215i
\(857\) 781.650 137.826i 0.912077 0.160824i 0.302131 0.953266i \(-0.402302\pi\)
0.609947 + 0.792443i \(0.291191\pi\)
\(858\) −8.02685 + 38.4425i −0.00935531 + 0.0448048i
\(859\) 925.160 336.731i 1.07702 0.392003i 0.258222 0.966086i \(-0.416863\pi\)
0.818798 + 0.574082i \(0.194641\pi\)
\(860\) 474.954 + 83.7472i 0.552272 + 0.0973805i
\(861\) −7.14851 + 17.8780i −0.00830256 + 0.0207642i
\(862\) 344.840 289.355i 0.400046 0.335679i
\(863\) 217.563i 0.252101i 0.992024 + 0.126050i \(0.0402301\pi\)
−0.992024 + 0.126050i \(0.959770\pi\)
\(864\) −477.520 + 471.195i −0.552686 + 0.545365i
\(865\) 2037.00 2.35491
\(866\) −26.8055 31.9455i −0.0309532 0.0368886i
\(867\) −214.473 + 168.810i −0.247374 + 0.194706i
\(868\) −14.4411 + 81.8994i −0.0166372 + 0.0943541i
\(869\) 10.7460 + 29.5243i 0.0123659 + 0.0339750i
\(870\) 167.919 + 510.548i 0.193010 + 0.586837i
\(871\) −70.9814 402.555i −0.0814941 0.462176i
\(872\) 373.794 215.810i 0.428663 0.247489i
\(873\) −86.5452 5.42676i −0.0991354 0.00621622i
\(874\) 10.2187 17.6992i 0.0116918 0.0202508i
\(875\) 30.6694 84.2634i 0.0350507 0.0963010i
\(876\) −187.679 349.931i −0.214245 0.399465i
\(877\) −237.821 199.556i −0.271176 0.227544i 0.497051 0.867721i \(-0.334416\pi\)
−0.768227 + 0.640178i \(0.778861\pi\)
\(878\) −256.199 + 305.326i −0.291798 + 0.347752i
\(879\) −36.4677 + 1164.31i −0.0414877 + 1.32458i
\(880\) −93.3102 33.9621i −0.106034 0.0385933i
\(881\) 1349.01 + 778.850i 1.53122 + 0.884053i 0.999306 + 0.0372567i \(0.0118619\pi\)
0.531918 + 0.846796i \(0.321471\pi\)
\(882\) 240.393 + 58.1039i 0.272554 + 0.0658774i
\(883\) 412.908 + 715.177i 0.467619 + 0.809940i 0.999315 0.0369949i \(-0.0117785\pi\)
−0.531696 + 0.846935i \(0.678445\pi\)
\(884\) −1061.88 + 187.238i −1.20122 + 0.211808i
\(885\) −1606.75 1436.30i −1.81553 1.62293i
\(886\) 248.990 90.6250i 0.281027 0.102286i
\(887\) 402.913 + 71.0445i 0.454243 + 0.0800953i 0.396089 0.918212i \(-0.370367\pi\)
0.0581543 + 0.998308i \(0.481478\pi\)
\(888\) 47.6614 6.87321i 0.0536727 0.00774010i
\(889\) 169.077 141.872i 0.190188 0.159587i
\(890\) 540.295i 0.607073i
\(891\) −19.3244 84.8920i −0.0216884 0.0952772i
\(892\) −297.542 −0.333568
\(893\) −577.101 687.762i −0.646250 0.770171i
\(894\) −34.6267 240.115i −0.0387323 0.268584i
\(895\) 328.250 1861.60i 0.366760 2.08000i
\(896\) 54.3031 + 149.196i 0.0606061 + 0.166514i
\(897\) −74.9867 + 83.8857i −0.0835972 + 0.0935181i
\(898\) 53.2890 + 302.217i 0.0593419 + 0.336545i
\(899\) 592.171 341.890i 0.658700 0.380301i
\(900\) −805.985 767.208i −0.895539 0.852453i
\(901\) 360.842 624.996i 0.400490 0.693669i
\(902\) 1.02931 2.82799i 0.00114114 0.00313525i
\(903\) 68.7281 + 2.15266i 0.0761108 + 0.00238390i
\(904\) −220.757 185.237i −0.244201 0.204909i
\(905\) −6.61015 + 7.87768i −0.00730404 + 0.00870461i
\(906\) 200.640 107.609i 0.221457 0.118774i
\(907\) −370.613 134.892i −0.408614 0.148723i 0.129532 0.991575i \(-0.458653\pi\)
−0.538145 + 0.842852i \(0.680875\pi\)
\(908\) −532.041 307.174i −0.585948 0.338297i
\(909\) −31.0839 + 15.4383i −0.0341958 + 0.0169839i
\(910\) 62.2714 + 107.857i 0.0684301 + 0.118524i
\(911\) −217.128 + 38.2855i −0.238340 + 0.0420258i −0.291542 0.956558i \(-0.594168\pi\)
0.0532022 + 0.998584i \(0.483057\pi\)
\(912\) 673.003 221.350i 0.737942 0.242709i
\(913\) −119.721 + 43.5749i −0.131129 + 0.0477272i
\(914\) 84.2931 + 14.8631i 0.0922244 + 0.0162617i
\(915\) −318.526 404.687i −0.348116 0.442281i
\(916\) 205.935 172.800i 0.224820 0.188647i
\(917\) 48.9691i 0.0534014i
\(918\) −181.959 + 125.610i −0.198212 + 0.136830i
\(919\) −873.180 −0.950142 −0.475071 0.879948i \(-0.657578\pi\)
−0.475071 + 0.879948i \(0.657578\pi\)
\(920\) 39.3720 + 46.9218i 0.0427957 + 0.0510019i
\(921\) 1155.03 + 461.837i 1.25410 + 0.501452i
\(922\) −36.1755 + 205.161i −0.0392359 + 0.222518i
\(923\) 619.665 + 1702.52i 0.671360 + 1.84455i
\(924\) −15.4166 3.21900i −0.0166846 0.00348377i
\(925\) 21.1115 + 119.729i 0.0228232 + 0.129437i
\(926\) −206.523 + 119.236i −0.223027 + 0.128765i
\(927\) 886.957 654.208i 0.956803 0.705726i
\(928\) 498.891 864.105i 0.537598 0.931147i
\(929\) 13.2277 36.3427i 0.0142386 0.0391202i −0.932370 0.361506i \(-0.882263\pi\)
0.946608 + 0.322386i \(0.104485\pi\)
\(930\) 120.066 193.692i 0.129103 0.208271i
\(931\) −708.871 594.813i −0.761408 0.638897i
\(932\) −432.202 + 515.078i −0.463736 + 0.552659i
\(933\) −1112.83 689.825i −1.19275 0.739362i
\(934\) 491.858 + 179.022i 0.526614 + 0.191672i
\(935\) −100.418 57.9763i −0.107399 0.0620067i
\(936\) 834.502 93.7815i 0.891562 0.100194i
\(937\) 402.676 + 697.456i 0.429750 + 0.744350i 0.996851 0.0792991i \(-0.0252682\pi\)
−0.567100 + 0.823649i \(0.691935\pi\)
\(938\) −14.9319 + 2.63290i −0.0159189 + 0.00280693i
\(939\) 252.195 1207.82i 0.268578 1.28628i
\(940\) 1208.38 439.813i 1.28551 0.467887i
\(941\) 1320.90 + 232.910i 1.40372 + 0.247513i 0.823670 0.567070i \(-0.191923\pi\)
0.580047 + 0.814583i \(0.303034\pi\)
\(942\) −151.419 + 378.690i −0.160742 + 0.402006i
\(943\) 6.60514 5.54237i 0.00700439 0.00587738i
\(944\) 1129.27i 1.19626i
\(945\) −225.113 159.873i −0.238214 0.169178i
\(946\) −10.7477 −0.0113612
\(947\) 379.824 + 452.656i 0.401081 + 0.477990i 0.928349 0.371709i \(-0.121228\pi\)
−0.527268 + 0.849699i \(0.676784\pi\)
\(948\) 252.297 198.581i 0.266136 0.209473i
\(949\) −131.376 + 745.072i −0.138437 + 0.785113i
\(950\) −131.712 361.877i −0.138645 0.380923i
\(951\) −383.344 1165.54i −0.403096 1.22559i
\(952\) 14.5327 + 82.4193i 0.0152655 + 0.0865749i
\(953\) −314.082 + 181.335i −0.329572 + 0.190278i −0.655651 0.755064i \(-0.727606\pi\)
0.326079 + 0.945342i \(0.394272\pi\)
\(954\) −148.596 + 223.757i −0.155761 + 0.234546i
\(955\) −178.009 + 308.321i −0.186397 + 0.322849i
\(956\) −11.0821 + 30.4477i −0.0115921 + 0.0318491i
\(957\) 61.2034 + 114.115i 0.0639534 + 0.119243i
\(958\) −372.374 312.459i −0.388699 0.326157i
\(959\) −99.9989 + 119.174i −0.104274 + 0.124269i
\(960\) −24.2953 + 775.677i −0.0253076 + 0.807997i
\(961\) 630.598 + 229.519i 0.656189 + 0.238833i
\(962\) −37.9724 21.9234i −0.0394724 0.0227894i
\(963\) −203.635 691.357i −0.211459 0.717920i
\(964\) 29.1339 + 50.4614i 0.0302219 + 0.0523458i
\(965\) −1075.48 + 189.636i −1.11449 + 0.196514i
\(966\) 3.11156 + 2.78147i 0.00322107 + 0.00287936i
\(967\) −27.9723 + 10.1811i −0.0289269 + 0.0105285i −0.356443 0.934317i \(-0.616011\pi\)
0.327516 + 0.944846i \(0.393788\pi\)
\(968\) −526.202 92.7836i −0.543597 0.0958509i
\(969\) 818.820 118.081i 0.845016 0.121859i
\(970\) 32.9274 27.6294i 0.0339458 0.0284839i
\(971\) 1095.66i 1.12839i −0.825643 0.564193i \(-0.809188\pi\)
0.825643 0.564193i \(-0.190812\pi\)
\(972\) −762.388 + 458.633i −0.784350 + 0.471844i
\(973\) −131.434 −0.135081
\(974\) 225.061 + 268.218i 0.231069 + 0.275377i
\(975\) 302.613 + 2098.43i 0.310372 + 2.15224i
\(976\) −46.8603 + 265.758i −0.0480126 + 0.272293i
\(977\) −212.328 583.365i −0.217326 0.597099i 0.782342 0.622849i \(-0.214025\pi\)
−0.999668 + 0.0257502i \(0.991803\pi\)
\(978\) −76.6403 + 85.7356i −0.0783643 + 0.0876642i
\(979\) −22.6049 128.199i −0.0230898 0.130949i
\(980\) 1147.83 662.698i 1.17125 0.676222i
\(981\) 835.787 246.176i 0.851975 0.250944i
\(982\) −124.752 + 216.076i −0.127038 + 0.220037i
\(983\) −207.764 + 570.827i −0.211357 + 0.580699i −0.999390 0.0349345i \(-0.988878\pi\)
0.788032 + 0.615634i \(0.211100\pi\)
\(984\) −64.3212 2.01463i −0.0653671 0.00204739i
\(985\) −317.653 266.542i −0.322490 0.270601i
\(986\) 211.382 251.916i 0.214384 0.255492i
\(987\) 161.572 86.6557i 0.163700 0.0877971i
\(988\) −1411.03 513.573i −1.42817 0.519811i
\(989\) −26.6674 15.3964i −0.0269640 0.0155677i
\(990\) 35.9509 + 23.8749i 0.0363140 + 0.0241160i
\(991\) 269.816 + 467.335i 0.272266 + 0.471579i 0.969442 0.245322i \(-0.0788935\pi\)
−0.697176 + 0.716900i \(0.745560\pi\)
\(992\) −416.645 + 73.4658i −0.420005 + 0.0740583i
\(993\) −933.716 + 307.098i −0.940298 + 0.309263i
\(994\) 63.1511 22.9851i 0.0635323 0.0231239i
\(995\) −2482.87 437.798i −2.49535 0.439998i
\(996\) 805.246 + 1023.06i 0.808480 + 1.02717i
\(997\) 508.600 426.766i 0.510130 0.428050i −0.351045 0.936359i \(-0.614174\pi\)
0.861175 + 0.508309i \(0.169729\pi\)
\(998\) 330.950i 0.331613i
\(999\) 96.7782 + 9.11755i 0.0968751 + 0.00912667i
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 27.3.f.a.5.3 30
3.2 odd 2 81.3.f.a.44.3 30
4.3 odd 2 432.3.bc.a.113.2 30
9.2 odd 6 243.3.f.a.53.3 30
9.4 even 3 243.3.f.c.215.3 30
9.5 odd 6 243.3.f.b.215.3 30
9.7 even 3 243.3.f.d.53.3 30
27.2 odd 18 243.3.f.d.188.3 30
27.4 even 9 729.3.b.a.728.13 30
27.7 even 9 243.3.f.b.26.3 30
27.11 odd 18 inner 27.3.f.a.11.3 yes 30
27.16 even 9 81.3.f.a.35.3 30
27.20 odd 18 243.3.f.c.26.3 30
27.23 odd 18 729.3.b.a.728.18 30
27.25 even 9 243.3.f.a.188.3 30
108.11 even 18 432.3.bc.a.65.2 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.3.f.a.5.3 30 1.1 even 1 trivial
27.3.f.a.11.3 yes 30 27.11 odd 18 inner
81.3.f.a.35.3 30 27.16 even 9
81.3.f.a.44.3 30 3.2 odd 2
243.3.f.a.53.3 30 9.2 odd 6
243.3.f.a.188.3 30 27.25 even 9
243.3.f.b.26.3 30 27.7 even 9
243.3.f.b.215.3 30 9.5 odd 6
243.3.f.c.26.3 30 27.20 odd 18
243.3.f.c.215.3 30 9.4 even 3
243.3.f.d.53.3 30 9.7 even 3
243.3.f.d.188.3 30 27.2 odd 18
432.3.bc.a.65.2 30 108.11 even 18
432.3.bc.a.113.2 30 4.3 odd 2
729.3.b.a.728.13 30 27.4 even 9
729.3.b.a.728.18 30 27.23 odd 18