Properties

Label 471.2.s.a.2.7
Level $471$
Weight $2$
Character 471.2
Analytic conductor $3.761$
Analytic rank $0$
Dimension $1200$
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] = [471,2,Mod(2,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(52))
 
chi = DirichletCharacter(H, H._module([26, 47]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.s (of order \(52\), degree \(24\), 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: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(1200\)
Relative dimension: \(50\) over \(\Q(\zeta_{52})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label 2.7
Character \(\chi\) \(=\) 471.2
Dual form 471.2.s.a.236.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.20517 + 0.404112i) q^{2} +(1.03114 + 1.39167i) q^{3} +(2.82943 - 1.07306i) q^{4} +(-0.562752 - 1.80593i) q^{5} +(-2.83623 - 2.65217i) q^{6} +(-2.85622 + 1.28548i) q^{7} +(-1.96860 + 1.19006i) q^{8} +(-0.873498 + 2.87002i) q^{9} +O(q^{10})\) \(q+(-2.20517 + 0.404112i) q^{2} +(1.03114 + 1.39167i) q^{3} +(2.82943 - 1.07306i) q^{4} +(-0.562752 - 1.80593i) q^{5} +(-2.83623 - 2.65217i) q^{6} +(-2.85622 + 1.28548i) q^{7} +(-1.96860 + 1.19006i) q^{8} +(-0.873498 + 2.87002i) q^{9} +(1.97076 + 3.75497i) q^{10} +(0.645800 - 0.445763i) q^{11} +(4.41089 + 2.83116i) q^{12} -6.16163i q^{13} +(5.77897 - 3.98894i) q^{14} +(1.93299 - 2.64534i) q^{15} +(-0.669931 + 0.593507i) q^{16} +(-0.396698 + 0.755845i) q^{17} +(0.766401 - 6.68186i) q^{18} +(-3.57124 - 0.880231i) q^{19} +(-3.53014 - 4.50590i) q^{20} +(-4.73413 - 2.64941i) q^{21} +(-1.24396 + 1.24396i) q^{22} +(0.266137 - 4.39976i) q^{23} +(-3.68607 - 1.51252i) q^{24} +(1.17021 - 0.807738i) q^{25} +(2.48999 + 13.5874i) q^{26} +(-4.89482 + 1.74377i) q^{27} +(-6.70208 + 6.70208i) q^{28} +(-0.986316 - 0.307348i) q^{29} +(-3.19356 + 6.61456i) q^{30} +(-6.41145 - 0.778491i) q^{31} +(4.07480 - 5.20110i) q^{32} +(1.28627 + 0.439096i) q^{33} +(0.569340 - 1.82708i) q^{34} +(3.92884 + 4.43474i) q^{35} +(0.608204 + 9.05783i) q^{36} +(5.53027 - 2.90251i) q^{37} +(8.23090 + 0.497878i) q^{38} +(8.57497 - 6.35351i) q^{39} +(3.25700 + 2.88545i) q^{40} +(-0.0920412 - 1.52162i) q^{41} +(11.5102 + 3.92927i) q^{42} +(-7.51573 - 3.38255i) q^{43} +(1.34891 - 1.95424i) q^{44} +(5.67463 - 0.0376285i) q^{45} +(1.19112 + 9.80976i) q^{46} +(1.50964 - 2.87639i) q^{47} +(-1.51676 - 0.320334i) q^{48} +(1.86368 - 2.10366i) q^{49} +(-2.25409 + 2.25409i) q^{50} +(-1.46094 + 0.227309i) q^{51} +(-6.61181 - 17.4339i) q^{52} +(8.70784 - 5.26407i) q^{53} +(10.0892 - 5.82336i) q^{54} +(-1.16844 - 0.915418i) q^{55} +(4.09295 - 5.92966i) q^{56} +(-2.45746 - 5.87763i) q^{57} +(2.29920 + 0.279173i) q^{58} +(-10.7097 - 6.47422i) q^{59} +(2.63065 - 9.55901i) q^{60} +(8.65364 - 5.23131i) q^{61} +(14.4529 - 0.874241i) q^{62} +(-1.19445 - 9.32027i) q^{63} +(-6.05193 + 11.5310i) q^{64} +(-11.1275 + 3.46747i) q^{65} +(-3.01388 - 0.448485i) q^{66} +(13.8479 + 3.41321i) q^{67} +(-0.311361 + 2.56429i) q^{68} +(6.39744 - 4.16640i) q^{69} +(-10.4559 - 8.19166i) q^{70} +(-1.16964 + 4.74541i) q^{71} +(-1.69592 - 6.68942i) q^{72} +(-3.45689 - 7.68090i) q^{73} +(-11.0222 + 8.63537i) q^{74} +(2.33076 + 0.795657i) q^{75} +(-11.0491 + 1.34161i) q^{76} +(-1.27153 + 2.10336i) q^{77} +(-16.3417 + 17.4758i) q^{78} +(-1.78603 + 9.74607i) q^{79} +(1.44884 + 0.875854i) q^{80} +(-7.47400 - 5.01391i) q^{81} +(0.817873 + 3.31824i) q^{82} +(-7.30548 - 9.32475i) q^{83} +(-16.2379 - 2.41630i) q^{84} +(1.58825 + 0.291058i) q^{85} +(17.9404 + 4.42191i) q^{86} +(-0.589302 - 1.68955i) q^{87} +(-0.740835 + 1.64607i) q^{88} +(-6.41080 - 0.778412i) q^{89} +(-12.4983 + 2.37616i) q^{90} +(7.92066 + 17.5990i) q^{91} +(-3.96820 - 12.7344i) q^{92} +(-5.52770 - 9.72536i) q^{93} +(-2.16664 + 6.95298i) q^{94} +(0.420082 + 6.94478i) q^{95} +(11.4399 + 0.307719i) q^{96} +(-0.0509599 - 0.163536i) q^{97} +(-3.25962 + 5.39207i) q^{98} +(0.715244 + 2.24283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} - 52 q^{10} - 80 q^{12} - 12 q^{15} + 16 q^{16} + 12 q^{18} - 52 q^{19} - 26 q^{21} - 64 q^{22} + 18 q^{24} + 104 q^{25} - 26 q^{27} - 84 q^{28} - 34 q^{30} - 52 q^{31} - 26 q^{33} - 80 q^{34} - 26 q^{36} - 308 q^{37} + 52 q^{39} - 340 q^{40} - 26 q^{42} - 76 q^{43} - 52 q^{45} - 60 q^{46} - 130 q^{48} - 52 q^{49} - 26 q^{51} + 84 q^{52} - 246 q^{54} - 36 q^{55} - 26 q^{57} - 52 q^{58} + 14 q^{60} - 4 q^{61} - 46 q^{63} - 52 q^{64} - 22 q^{66} + 28 q^{67} - 72 q^{69} - 40 q^{70} + 46 q^{72} - 48 q^{73} - 46 q^{75} - 52 q^{76} + 146 q^{78} - 100 q^{79} + 58 q^{81} - 52 q^{82} - 156 q^{84} - 20 q^{85} + 12 q^{87} - 116 q^{88} - 26 q^{90} + 360 q^{91} - 310 q^{93} + 96 q^{94} + 176 q^{96} + 116 q^{97} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(-1\) \(e\left(\frac{47}{52}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20517 + 0.404112i −1.55929 + 0.285750i −0.889547 0.456843i \(-0.848980\pi\)
−0.669742 + 0.742594i \(0.733595\pi\)
\(3\) 1.03114 + 1.39167i 0.595329 + 0.803482i
\(4\) 2.82943 1.07306i 1.41471 0.536531i
\(5\) −0.562752 1.80593i −0.251670 0.807638i −0.990949 0.134239i \(-0.957141\pi\)
0.739279 0.673400i \(-0.235167\pi\)
\(6\) −2.83623 2.65217i −1.15789 1.08275i
\(7\) −2.85622 + 1.28548i −1.07955 + 0.485866i −0.870565 0.492053i \(-0.836247\pi\)
−0.208985 + 0.977919i \(0.567016\pi\)
\(8\) −1.96860 + 1.19006i −0.696004 + 0.420749i
\(9\) −0.873498 + 2.87002i −0.291166 + 0.956673i
\(10\) 1.97076 + 3.75497i 0.623210 + 1.18743i
\(11\) 0.645800 0.445763i 0.194716 0.134403i −0.466718 0.884406i \(-0.654564\pi\)
0.661434 + 0.750004i \(0.269948\pi\)
\(12\) 4.41089 + 2.83116i 1.27331 + 0.817285i
\(13\) 6.16163i 1.70893i −0.519509 0.854465i \(-0.673885\pi\)
0.519509 0.854465i \(-0.326115\pi\)
\(14\) 5.77897 3.98894i 1.54450 1.06609i
\(15\) 1.93299 2.64534i 0.499096 0.683023i
\(16\) −0.669931 + 0.593507i −0.167483 + 0.148377i
\(17\) −0.396698 + 0.755845i −0.0962134 + 0.183319i −0.928806 0.370567i \(-0.879163\pi\)
0.832592 + 0.553886i \(0.186856\pi\)
\(18\) 0.766401 6.68186i 0.180642 1.57493i
\(19\) −3.57124 0.880231i −0.819299 0.201939i −0.192677 0.981262i \(-0.561717\pi\)
−0.626622 + 0.779323i \(0.715563\pi\)
\(20\) −3.53014 4.50590i −0.789364 1.00755i
\(21\) −4.73413 2.64941i −1.03307 0.578149i
\(22\) −1.24396 + 1.24396i −0.265213 + 0.265213i
\(23\) 0.266137 4.39976i 0.0554933 0.917414i −0.858787 0.512332i \(-0.828782\pi\)
0.914281 0.405081i \(-0.132757\pi\)
\(24\) −3.68607 1.51252i −0.752416 0.308742i
\(25\) 1.17021 0.807738i 0.234042 0.161548i
\(26\) 2.48999 + 13.5874i 0.488327 + 2.66472i
\(27\) −4.89482 + 1.74377i −0.942009 + 0.335589i
\(28\) −6.70208 + 6.70208i −1.26657 + 1.26657i
\(29\) −0.986316 0.307348i −0.183154 0.0570732i 0.204554 0.978855i \(-0.434426\pi\)
−0.387708 + 0.921782i \(0.626733\pi\)
\(30\) −3.19356 + 6.61456i −0.583061 + 1.20765i
\(31\) −6.41145 0.778491i −1.15153 0.139821i −0.477573 0.878592i \(-0.658484\pi\)
−0.673957 + 0.738771i \(0.735407\pi\)
\(32\) 4.07480 5.20110i 0.720331 0.919434i
\(33\) 1.28627 + 0.439096i 0.223910 + 0.0764368i
\(34\) 0.569340 1.82708i 0.0976410 0.313341i
\(35\) 3.92884 + 4.43474i 0.664095 + 0.749608i
\(36\) 0.608204 + 9.05783i 0.101367 + 1.50964i
\(37\) 5.53027 2.90251i 0.909171 0.477170i 0.0557812 0.998443i \(-0.482235\pi\)
0.853390 + 0.521273i \(0.174543\pi\)
\(38\) 8.23090 + 0.497878i 1.33523 + 0.0807664i
\(39\) 8.57497 6.35351i 1.37309 1.01738i
\(40\) 3.25700 + 2.88545i 0.514976 + 0.456229i
\(41\) −0.0920412 1.52162i −0.0143744 0.237638i −0.998266 0.0588696i \(-0.981250\pi\)
0.983891 0.178768i \(-0.0572112\pi\)
\(42\) 11.5102 + 3.92927i 1.77607 + 0.606300i
\(43\) −7.51573 3.38255i −1.14614 0.515835i −0.253824 0.967250i \(-0.581688\pi\)
−0.892314 + 0.451416i \(0.850919\pi\)
\(44\) 1.34891 1.95424i 0.203356 0.294613i
\(45\) 5.67463 0.0376285i 0.845923 0.00560932i
\(46\) 1.19112 + 9.80976i 0.175621 + 1.44637i
\(47\) 1.50964 2.87639i 0.220204 0.419564i −0.750144 0.661274i \(-0.770016\pi\)
0.970349 + 0.241710i \(0.0777083\pi\)
\(48\) −1.51676 0.320334i −0.218925 0.0462363i
\(49\) 1.86368 2.10366i 0.266241 0.300523i
\(50\) −2.25409 + 2.25409i −0.318777 + 0.318777i
\(51\) −1.46094 + 0.227309i −0.204572 + 0.0318297i
\(52\) −6.61181 17.4339i −0.916893 2.41765i
\(53\) 8.70784 5.26407i 1.19611 0.723076i 0.228018 0.973657i \(-0.426775\pi\)
0.968096 + 0.250581i \(0.0806216\pi\)
\(54\) 10.0892 5.82336i 1.37297 0.792460i
\(55\) −1.16844 0.915418i −0.157553 0.123435i
\(56\) 4.09295 5.92966i 0.546943 0.792384i
\(57\) −2.45746 5.87763i −0.325498 0.778512i
\(58\) 2.29920 + 0.279173i 0.301899 + 0.0366572i
\(59\) −10.7097 6.47422i −1.39428 0.842871i −0.397089 0.917780i \(-0.629980\pi\)
−0.997190 + 0.0749086i \(0.976134\pi\)
\(60\) 2.63065 9.55901i 0.339616 1.23406i
\(61\) 8.65364 5.23131i 1.10798 0.669800i 0.159682 0.987168i \(-0.448953\pi\)
0.948302 + 0.317368i \(0.102799\pi\)
\(62\) 14.4529 0.874241i 1.83552 0.111029i
\(63\) −1.19445 9.32027i −0.150487 1.17424i
\(64\) −6.05193 + 11.5310i −0.756491 + 1.44137i
\(65\) −11.1275 + 3.46747i −1.38020 + 0.430087i
\(66\) −3.01388 0.448485i −0.370983 0.0552047i
\(67\) 13.8479 + 3.41321i 1.69179 + 0.416990i 0.963378 0.268145i \(-0.0864108\pi\)
0.728416 + 0.685135i \(0.240257\pi\)
\(68\) −0.311361 + 2.56429i −0.0377581 + 0.310966i
\(69\) 6.39744 4.16640i 0.770162 0.501575i
\(70\) −10.4559 8.19166i −1.24972 0.979091i
\(71\) −1.16964 + 4.74541i −0.138810 + 0.563176i 0.859807 + 0.510618i \(0.170583\pi\)
−0.998618 + 0.0525577i \(0.983263\pi\)
\(72\) −1.69592 6.68942i −0.199866 0.788355i
\(73\) −3.45689 7.68090i −0.404598 0.898981i −0.995722 0.0923999i \(-0.970546\pi\)
0.591123 0.806581i \(-0.298685\pi\)
\(74\) −11.0222 + 8.63537i −1.28131 + 1.00384i
\(75\) 2.33076 + 0.795657i 0.269133 + 0.0918745i
\(76\) −11.0491 + 1.34161i −1.26742 + 0.153893i
\(77\) −1.27153 + 2.10336i −0.144904 + 0.239700i
\(78\) −16.3417 + 17.4758i −1.85034 + 1.97875i
\(79\) −1.78603 + 9.74607i −0.200944 + 1.09652i 0.716180 + 0.697916i \(0.245889\pi\)
−0.917124 + 0.398602i \(0.869495\pi\)
\(80\) 1.44884 + 0.875854i 0.161985 + 0.0979235i
\(81\) −7.47400 5.01391i −0.830445 0.557101i
\(82\) 0.817873 + 3.31824i 0.0903189 + 0.366438i
\(83\) −7.30548 9.32475i −0.801880 1.02352i −0.999068 0.0431588i \(-0.986258\pi\)
0.197188 0.980366i \(-0.436819\pi\)
\(84\) −16.2379 2.41630i −1.77170 0.263640i
\(85\) 1.58825 + 0.291058i 0.172270 + 0.0315696i
\(86\) 17.9404 + 4.42191i 1.93456 + 0.476826i
\(87\) −0.589302 1.68955i −0.0631798 0.181138i
\(88\) −0.740835 + 1.64607i −0.0789732 + 0.175471i
\(89\) −6.41080 0.778412i −0.679543 0.0825115i −0.226515 0.974008i \(-0.572733\pi\)
−0.453028 + 0.891496i \(0.649656\pi\)
\(90\) −12.4983 + 2.37616i −1.31744 + 0.250470i
\(91\) 7.92066 + 17.5990i 0.830311 + 1.84488i
\(92\) −3.96820 12.7344i −0.413713 1.32765i
\(93\) −5.52770 9.72536i −0.573196 1.00847i
\(94\) −2.16664 + 6.95298i −0.223472 + 0.717145i
\(95\) 0.420082 + 6.94478i 0.0430995 + 0.712519i
\(96\) 11.4399 + 0.307719i 1.16758 + 0.0314064i
\(97\) −0.0509599 0.163536i −0.00517419 0.0166046i 0.952098 0.305794i \(-0.0989219\pi\)
−0.957272 + 0.289190i \(0.906614\pi\)
\(98\) −3.25962 + 5.39207i −0.329271 + 0.544681i
\(99\) 0.715244 + 2.24283i 0.0718848 + 0.225413i
\(100\) 2.44428 3.54115i 0.244428 0.354115i
\(101\) 6.81945 + 4.70712i 0.678560 + 0.468376i 0.856826 0.515606i \(-0.172433\pi\)
−0.178265 + 0.983982i \(0.557049\pi\)
\(102\) 3.12976 1.09164i 0.309892 0.108088i
\(103\) 3.23029 + 4.12316i 0.318290 + 0.406267i 0.919667 0.392698i \(-0.128458\pi\)
−0.601378 + 0.798965i \(0.705381\pi\)
\(104\) 7.33270 + 12.1298i 0.719030 + 1.18942i
\(105\) −2.12052 + 10.0405i −0.206941 + 0.979852i
\(106\) −17.0750 + 15.1271i −1.65847 + 1.46927i
\(107\) 1.83474 + 1.83474i 0.177371 + 0.177371i 0.790209 0.612838i \(-0.209972\pi\)
−0.612838 + 0.790209i \(0.709972\pi\)
\(108\) −11.9784 + 10.1863i −1.15262 + 0.980179i
\(109\) 0.125899 + 0.331968i 0.0120589 + 0.0317968i 0.940911 0.338655i \(-0.109972\pi\)
−0.928852 + 0.370452i \(0.879203\pi\)
\(110\) 2.94655 + 1.54647i 0.280942 + 0.147450i
\(111\) 9.74183 + 4.70342i 0.924653 + 0.446429i
\(112\) 1.15053 2.55637i 0.108715 0.241554i
\(113\) 9.76307 + 6.73896i 0.918433 + 0.633948i 0.930624 0.365977i \(-0.119265\pi\)
−0.0121911 + 0.999926i \(0.503881\pi\)
\(114\) 7.79433 + 11.9681i 0.730006 + 1.12091i
\(115\) −8.09545 + 1.99535i −0.754904 + 0.186067i
\(116\) −3.12051 + 0.188756i −0.289732 + 0.0175256i
\(117\) 17.6840 + 5.38217i 1.63489 + 0.497582i
\(118\) 26.2329 + 9.94884i 2.41494 + 0.915865i
\(119\) 0.161433 2.66881i 0.0147986 0.244649i
\(120\) −0.657172 + 7.50797i −0.0599913 + 0.685381i
\(121\) −3.68230 + 9.70943i −0.334755 + 0.882676i
\(122\) −16.9687 + 15.0330i −1.53627 + 1.36102i
\(123\) 2.02269 1.69710i 0.182380 0.153022i
\(124\) −18.9761 + 4.67719i −1.70411 + 0.420024i
\(125\) −9.56238 7.49164i −0.855285 0.670073i
\(126\) 6.40040 + 20.0701i 0.570193 + 1.78798i
\(127\) −10.6995 + 1.29915i −0.949426 + 0.115281i −0.580575 0.814207i \(-0.697172\pi\)
−0.368852 + 0.929488i \(0.620249\pi\)
\(128\) 4.75437 15.2573i 0.420231 1.34857i
\(129\) −3.04237 13.9473i −0.267866 1.22799i
\(130\) 23.1368 12.1431i 2.02923 1.06502i
\(131\) −22.1094 + 4.05170i −1.93171 + 0.353999i −0.999959 0.00909634i \(-0.997105\pi\)
−0.931752 + 0.363095i \(0.881720\pi\)
\(132\) 4.11058 0.137851i 0.357780 0.0119984i
\(133\) 11.3318 2.07662i 0.982589 0.180066i
\(134\) −31.9163 1.93058i −2.75715 0.166777i
\(135\) 5.90370 + 7.85841i 0.508110 + 0.676345i
\(136\) −0.118561 1.96005i −0.0101665 0.168073i
\(137\) −8.61461 + 6.74912i −0.735996 + 0.576616i −0.913177 0.407562i \(-0.866379\pi\)
0.177182 + 0.984178i \(0.443302\pi\)
\(138\) −12.4238 + 11.7729i −1.05758 + 1.00218i
\(139\) −11.7462 7.10080i −0.996296 0.602282i −0.0774910 0.996993i \(-0.524691\pi\)
−0.918805 + 0.394711i \(0.870845\pi\)
\(140\) 15.8751 + 8.33191i 1.34169 + 0.704175i
\(141\) 5.55964 0.865031i 0.468206 0.0728488i
\(142\) 0.661572 10.9371i 0.0555179 0.917820i
\(143\) −2.74663 3.97918i −0.229685 0.332756i
\(144\) −1.11819 2.44114i −0.0931827 0.203428i
\(145\) 1.95418i 0.162286i
\(146\) 10.7270 + 15.5407i 0.887770 + 1.28616i
\(147\) 4.84933 + 0.424461i 0.399966 + 0.0350090i
\(148\) 12.5329 14.1468i 1.03020 1.16286i
\(149\) 1.79388 + 2.96743i 0.146960 + 0.243102i 0.920585 0.390542i \(-0.127712\pi\)
−0.773625 + 0.633644i \(0.781559\pi\)
\(150\) −5.46125 0.812670i −0.445909 0.0663542i
\(151\) −6.57812 1.20548i −0.535319 0.0981009i −0.0942068 0.995553i \(-0.530031\pi\)
−0.441113 + 0.897452i \(0.645416\pi\)
\(152\) 8.07785 2.51716i 0.655200 0.204169i
\(153\) −1.82277 1.79876i −0.147363 0.145421i
\(154\) 1.95394 5.15211i 0.157453 0.415169i
\(155\) 2.20215 + 12.0168i 0.176881 + 0.965209i
\(156\) 17.4446 27.1783i 1.39668 2.17600i
\(157\) −6.16621 + 10.9077i −0.492117 + 0.870529i
\(158\) 22.2135i 1.76721i
\(159\) 16.3049 + 6.69045i 1.29306 + 0.530587i
\(160\) −11.6860 4.43190i −0.923856 0.350372i
\(161\) 4.89566 + 12.9088i 0.385832 + 1.01736i
\(162\) 18.5076 + 8.03618i 1.45410 + 0.631382i
\(163\) 1.70465 9.30197i 0.133518 0.728587i −0.846914 0.531730i \(-0.821542\pi\)
0.980432 0.196857i \(-0.0630733\pi\)
\(164\) −1.89322 4.20656i −0.147836 0.328477i
\(165\) 0.0691299 2.57002i 0.00538176 0.200075i
\(166\) 19.8781 + 17.6104i 1.54284 + 1.36683i
\(167\) −12.7023 + 6.66667i −0.982932 + 0.515882i −0.878033 0.478600i \(-0.841144\pi\)
−0.104899 + 0.994483i \(0.533452\pi\)
\(168\) 12.4725 0.418275i 0.962278 0.0322706i
\(169\) −24.9657 −1.92044
\(170\) −3.61998 −0.277640
\(171\) 5.64575 9.48064i 0.431741 0.725003i
\(172\) −24.8949 1.50586i −1.89822 0.114821i
\(173\) −1.60007 1.80611i −0.121651 0.137316i 0.684530 0.728985i \(-0.260008\pi\)
−0.806181 + 0.591669i \(0.798469\pi\)
\(174\) 1.98228 + 3.48759i 0.150276 + 0.264394i
\(175\) −2.30405 + 3.81136i −0.174170 + 0.288112i
\(176\) −0.168078 + 0.681918i −0.0126693 + 0.0514015i
\(177\) −2.03319 21.5802i −0.152824 1.62206i
\(178\) 14.4515 0.874152i 1.08318 0.0655205i
\(179\) 0.752163 + 0.752163i 0.0562193 + 0.0562193i 0.734657 0.678438i \(-0.237343\pi\)
−0.678438 + 0.734657i \(0.737343\pi\)
\(180\) 16.0156 6.19569i 1.19373 0.461799i
\(181\) −0.729320 3.97977i −0.0542099 0.295814i 0.945331 0.326112i \(-0.105739\pi\)
−0.999541 + 0.0302985i \(0.990354\pi\)
\(182\) −24.5784 35.6079i −1.82187 2.63943i
\(183\) 16.2034 + 6.64881i 1.19779 + 0.491494i
\(184\) 4.71205 + 8.97807i 0.347377 + 0.661872i
\(185\) −8.35391 8.35391i −0.614192 0.614192i
\(186\) 16.1197 + 19.2123i 1.18195 + 1.40871i
\(187\) 0.0807406 + 0.664958i 0.00590433 + 0.0486266i
\(188\) 1.18489 9.75847i 0.0864172 0.711710i
\(189\) 11.7391 11.2728i 0.853895 0.819975i
\(190\) −3.73282 15.1446i −0.270807 1.09871i
\(191\) 1.03199 + 0.321582i 0.0746723 + 0.0232688i 0.334612 0.942356i \(-0.391395\pi\)
−0.259939 + 0.965625i \(0.583703\pi\)
\(192\) −22.2877 + 3.46778i −1.60848 + 0.250265i
\(193\) −5.62814 2.13447i −0.405123 0.153643i 0.143622 0.989633i \(-0.454125\pi\)
−0.548745 + 0.835990i \(0.684894\pi\)
\(194\) 0.178462 + 0.340031i 0.0128128 + 0.0244128i
\(195\) −16.2996 11.9104i −1.16724 0.852920i
\(196\) 3.01580 7.95202i 0.215414 0.568001i
\(197\) 16.8449 19.0139i 1.20015 1.35469i 0.281523 0.959554i \(-0.409160\pi\)
0.918624 0.395132i \(-0.129301\pi\)
\(198\) −2.48359 4.65678i −0.176501 0.330943i
\(199\) 1.58082 + 6.41364i 0.112061 + 0.454651i 0.999986 0.00533864i \(-0.00169935\pi\)
−0.887924 + 0.459989i \(0.847853\pi\)
\(200\) −1.34242 + 2.98273i −0.0949232 + 0.210911i
\(201\) 9.52910 + 22.7913i 0.672131 + 1.60757i
\(202\) −16.9402 7.62418i −1.19191 0.536436i
\(203\) 3.21223 0.390035i 0.225454 0.0273751i
\(204\) −3.88971 + 2.21083i −0.272334 + 0.154789i
\(205\) −2.69615 + 1.02252i −0.188308 + 0.0714157i
\(206\) −8.78955 7.78686i −0.612397 0.542536i
\(207\) 12.3949 + 4.60700i 0.861507 + 0.320208i
\(208\) 3.65697 + 4.12787i 0.253565 + 0.286216i
\(209\) −2.69868 + 1.02347i −0.186672 + 0.0707952i
\(210\) 0.618613 22.9979i 0.0426883 1.58701i
\(211\) 14.5973 11.4362i 1.00492 0.787303i 0.0277158 0.999616i \(-0.491177\pi\)
0.977202 + 0.212313i \(0.0680997\pi\)
\(212\) 18.9895 24.2384i 1.30421 1.66470i
\(213\) −7.81011 + 3.26543i −0.535140 + 0.223744i
\(214\) −4.78736 3.30448i −0.327257 0.225889i
\(215\) −1.87918 + 15.4765i −0.128159 + 1.05549i
\(216\) 7.56073 9.25790i 0.514443 0.629920i
\(217\) 19.3133 6.01825i 1.31107 0.408546i
\(218\) −0.411780 0.681168i −0.0278893 0.0461345i
\(219\) 7.12474 12.7309i 0.481445 0.860277i
\(220\) −4.28833 1.33630i −0.289119 0.0900932i
\(221\) 4.65724 + 2.44431i 0.313280 + 0.164422i
\(222\) −23.3831 6.43505i −1.56937 0.431892i
\(223\) 14.7514 6.63906i 0.987826 0.444584i 0.148913 0.988850i \(-0.452423\pi\)
0.838913 + 0.544266i \(0.183192\pi\)
\(224\) −4.95263 + 20.0936i −0.330911 + 1.34256i
\(225\) 1.29605 + 4.06408i 0.0864031 + 0.270939i
\(226\) −24.2525 10.9152i −1.61325 0.726066i
\(227\) −7.92778 + 10.1191i −0.526186 + 0.671626i −0.975053 0.221972i \(-0.928751\pi\)
0.448867 + 0.893598i \(0.351828\pi\)
\(228\) −13.2603 13.9933i −0.878182 0.926732i
\(229\) −1.07850 + 5.88521i −0.0712696 + 0.388905i 0.928573 + 0.371150i \(0.121037\pi\)
−0.999842 + 0.0177551i \(0.994348\pi\)
\(230\) 17.0455 7.67155i 1.12395 0.505847i
\(231\) −4.23831 + 0.399315i −0.278861 + 0.0262730i
\(232\) 2.30742 0.568728i 0.151489 0.0373388i
\(233\) 2.79900 + 23.0518i 0.183369 + 1.51018i 0.736132 + 0.676838i \(0.236650\pi\)
−0.552764 + 0.833338i \(0.686427\pi\)
\(234\) −41.1712 4.72228i −2.69145 0.308705i
\(235\) −6.04412 1.10763i −0.394275 0.0722536i
\(236\) −37.2495 6.82622i −2.42473 0.444349i
\(237\) −15.4050 + 7.56400i −1.00066 + 0.491334i
\(238\) 0.722511 + 5.95041i 0.0468334 + 0.385708i
\(239\) 22.8100 5.62217i 1.47546 0.363668i 0.582138 0.813090i \(-0.302216\pi\)
0.893320 + 0.449422i \(0.148370\pi\)
\(240\) 0.275057 + 2.91944i 0.0177548 + 0.188449i
\(241\) 14.3116 6.44111i 0.921888 0.414908i 0.106824 0.994278i \(-0.465932\pi\)
0.815065 + 0.579370i \(0.196701\pi\)
\(242\) 4.19640 22.8990i 0.269755 1.47200i
\(243\) −0.729038 15.5714i −0.0467678 0.998906i
\(244\) 18.8713 24.0875i 1.20811 1.54204i
\(245\) −4.84787 2.18185i −0.309719 0.139393i
\(246\) −3.77456 + 4.55978i −0.240657 + 0.290721i
\(247\) −5.42366 + 22.0047i −0.345099 + 1.40012i
\(248\) 13.5480 6.09746i 0.860299 0.387189i
\(249\) 5.44401 19.7820i 0.345000 1.25363i
\(250\) 24.1141 + 12.6561i 1.52511 + 0.800440i
\(251\) 23.9309 + 7.45719i 1.51051 + 0.470693i 0.937243 0.348677i \(-0.113369\pi\)
0.573265 + 0.819370i \(0.305677\pi\)
\(252\) −13.3808 25.0893i −0.842913 1.58048i
\(253\) −1.78938 2.96000i −0.112497 0.186094i
\(254\) 23.0692 7.18865i 1.44749 0.451056i
\(255\) 1.23265 + 2.51044i 0.0771917 + 0.157210i
\(256\) −1.17911 + 9.71083i −0.0736943 + 0.606927i
\(257\) 24.8872 + 17.1784i 1.55242 + 1.07156i 0.964990 + 0.262285i \(0.0844762\pi\)
0.587431 + 0.809274i \(0.300139\pi\)
\(258\) 12.3452 + 29.5267i 0.768580 + 1.83825i
\(259\) −12.0646 + 15.3993i −0.749655 + 0.956864i
\(260\) −27.7637 + 21.7515i −1.72183 + 1.34897i
\(261\) 1.74364 2.56228i 0.107929 0.158601i
\(262\) 47.1177 17.8694i 2.91094 1.10397i
\(263\) −15.9301 17.9814i −0.982295 1.10878i −0.994058 0.108851i \(-0.965283\pi\)
0.0117634 0.999931i \(-0.496256\pi\)
\(264\) −3.05469 + 0.666328i −0.188003 + 0.0410097i
\(265\) −14.4069 12.7634i −0.885010 0.784051i
\(266\) −24.1493 + 9.15861i −1.48069 + 0.561551i
\(267\) −5.52714 9.72437i −0.338255 0.595122i
\(268\) 42.8443 5.20224i 2.61713 0.317778i
\(269\) −3.06889 1.38119i −0.187113 0.0842129i 0.314690 0.949194i \(-0.398099\pi\)
−0.501804 + 0.864981i \(0.667330\pi\)
\(270\) −16.1943 14.9434i −0.985556 0.909424i
\(271\) −5.72273 + 12.7154i −0.347631 + 0.772405i 0.652265 + 0.757991i \(0.273819\pi\)
−0.999896 + 0.0144138i \(0.995412\pi\)
\(272\) −0.182839 0.741807i −0.0110862 0.0449787i
\(273\) −16.3247 + 29.1700i −0.988015 + 1.76545i
\(274\) 16.2693 18.3642i 0.982862 1.10942i
\(275\) 0.395662 1.04327i 0.0238593 0.0629118i
\(276\) 13.6303 18.6534i 0.820449 1.12280i
\(277\) −12.7789 24.3481i −0.767809 1.46294i −0.882889 0.469581i \(-0.844405\pi\)
0.115080 0.993356i \(-0.463287\pi\)
\(278\) 28.7718 + 10.9117i 1.72562 + 0.654440i
\(279\) 7.83467 17.7210i 0.469049 1.06093i
\(280\) −13.0119 4.05467i −0.777609 0.242313i
\(281\) −2.94865 11.9631i −0.175902 0.713661i −0.990946 0.134262i \(-0.957134\pi\)
0.815044 0.579399i \(-0.196713\pi\)
\(282\) −11.9104 + 4.15426i −0.709253 + 0.247382i
\(283\) −0.687598 + 5.66288i −0.0408735 + 0.336623i 0.957900 + 0.287103i \(0.0926923\pi\)
−0.998773 + 0.0495201i \(0.984231\pi\)
\(284\) 1.78270 + 14.6819i 0.105784 + 0.871210i
\(285\) −9.23168 + 7.74566i −0.546838 + 0.458813i
\(286\) 7.66482 + 7.66482i 0.453230 + 0.453230i
\(287\) 2.21891 + 4.22778i 0.130978 + 0.249558i
\(288\) 11.3679 + 16.2379i 0.669862 + 0.956828i
\(289\) 9.24317 + 13.3910i 0.543716 + 0.787708i
\(290\) −0.789709 4.30930i −0.0463733 0.253051i
\(291\) 0.175042 0.239548i 0.0102611 0.0140426i
\(292\) −18.0231 18.0231i −1.05472 1.05472i
\(293\) −15.4932 + 0.937167i −0.905124 + 0.0547499i −0.506378 0.862312i \(-0.669016\pi\)
−0.398746 + 0.917062i \(0.630554\pi\)
\(294\) −10.8651 + 1.02366i −0.633667 + 0.0597013i
\(295\) −5.66513 + 22.9843i −0.329837 + 1.33820i
\(296\) −7.43271 + 12.2952i −0.432018 + 0.714645i
\(297\) −2.38376 + 3.30806i −0.138320 + 0.191953i
\(298\) −5.15498 5.81877i −0.298620 0.337072i
\(299\) −27.1097 1.63984i −1.56780 0.0948341i
\(300\) 7.44850 0.249790i 0.430040 0.0144217i
\(301\) 25.8148 1.48794
\(302\) 14.9930 0.862750
\(303\) 0.481040 + 14.3441i 0.0276350 + 0.824049i
\(304\) 2.91491 1.52986i 0.167181 0.0877436i
\(305\) −14.3172 12.6840i −0.819803 0.726282i
\(306\) 4.74643 + 3.22996i 0.271335 + 0.184645i
\(307\) −3.88087 8.62294i −0.221493 0.492137i 0.767326 0.641257i \(-0.221587\pi\)
−0.988819 + 0.149120i \(0.952356\pi\)
\(308\) −1.34066 + 7.31574i −0.0763912 + 0.416853i
\(309\) −2.40720 + 8.74706i −0.136941 + 0.497603i
\(310\) −9.71223 25.6090i −0.551618 1.45450i
\(311\) 9.79517 + 3.71482i 0.555433 + 0.210648i 0.616319 0.787497i \(-0.288623\pi\)
−0.0608856 + 0.998145i \(0.519392\pi\)
\(312\) −9.31960 + 22.7122i −0.527619 + 1.28583i
\(313\) 1.51782i 0.0857922i −0.999080 0.0428961i \(-0.986342\pi\)
0.999080 0.0428961i \(-0.0136584\pi\)
\(314\) 9.18960 26.5452i 0.518599 1.49803i
\(315\) −16.1596 + 7.40210i −0.910491 + 0.417061i
\(316\) 5.40467 + 29.4923i 0.304036 + 1.65907i
\(317\) −5.58529 + 14.7272i −0.313701 + 0.827162i 0.681723 + 0.731610i \(0.261231\pi\)
−0.995424 + 0.0955520i \(0.969538\pi\)
\(318\) −38.6587 8.16458i −2.16787 0.457847i
\(319\) −0.773967 + 0.241178i −0.0433338 + 0.0135034i
\(320\) 24.2299 + 4.44030i 1.35450 + 0.248220i
\(321\) −0.661481 + 4.44524i −0.0369203 + 0.248109i
\(322\) −16.0124 26.4877i −0.892335 1.47610i
\(323\) 2.08202 2.35012i 0.115847 0.130764i
\(324\) −26.5274 6.16644i −1.47374 0.342580i
\(325\) −4.97699 7.21041i −0.276074 0.399962i
\(326\) 21.2013i 1.17423i
\(327\) −0.332171 + 0.517515i −0.0183691 + 0.0286187i
\(328\) 1.99201 + 2.88593i 0.109990 + 0.159349i
\(329\) −0.614338 + 10.1562i −0.0338696 + 0.559930i
\(330\) 0.886131 + 5.69525i 0.0487799 + 0.313513i
\(331\) 28.7882 + 15.1092i 1.58234 + 0.830476i 0.999844 + 0.0176429i \(0.00561619\pi\)
0.582496 + 0.812833i \(0.302076\pi\)
\(332\) −30.6764 18.5445i −1.68358 1.01776i
\(333\) 3.49958 + 18.4073i 0.191776 + 1.00871i
\(334\) 25.3166 19.8343i 1.38526 1.08528i
\(335\) −1.62892 26.9292i −0.0889974 1.47130i
\(336\) 4.74399 1.03482i 0.258806 0.0564541i
\(337\) 7.07387 + 0.427890i 0.385338 + 0.0233087i 0.251912 0.967750i \(-0.418941\pi\)
0.133426 + 0.991059i \(0.457402\pi\)
\(338\) 55.0536 10.0890i 2.99452 0.548767i
\(339\) 0.688681 + 20.5358i 0.0374040 + 1.11535i
\(340\) 4.80616 0.880762i 0.260651 0.0477660i
\(341\) −4.48754 + 2.35524i −0.243014 + 0.127543i
\(342\) −8.61859 + 23.1879i −0.466040 + 1.25386i
\(343\) 3.90393 12.5282i 0.210792 0.676457i
\(344\) 18.8209 2.28527i 1.01475 0.123213i
\(345\) −11.1244 9.20872i −0.598918 0.495781i
\(346\) 4.25829 + 3.33616i 0.228927 + 0.179353i
\(347\) 16.8939 4.16398i 0.906914 0.223534i 0.241844 0.970315i \(-0.422248\pi\)
0.665070 + 0.746781i \(0.268402\pi\)
\(348\) −3.48038 4.14810i −0.186568 0.222361i
\(349\) 5.79549 5.13436i 0.310225 0.274836i −0.493615 0.869680i \(-0.664325\pi\)
0.803841 + 0.594845i \(0.202786\pi\)
\(350\) 3.54060 9.33579i 0.189253 0.499019i
\(351\) 10.7445 + 30.1601i 0.573498 + 1.60983i
\(352\) 0.313046 5.17527i 0.0166854 0.275843i
\(353\) −10.6725 4.04753i −0.568038 0.215428i 0.0538305 0.998550i \(-0.482857\pi\)
−0.621868 + 0.783122i \(0.713626\pi\)
\(354\) 13.2043 + 46.7663i 0.701802 + 2.48560i
\(355\) 9.22811 0.558198i 0.489777 0.0296261i
\(356\) −18.9742 + 4.67672i −1.00563 + 0.247865i
\(357\) 3.88057 2.52726i 0.205381 0.133757i
\(358\) −1.96260 1.35469i −0.103727 0.0715975i
\(359\) 11.6059 25.7873i 0.612536 1.36100i −0.300758 0.953700i \(-0.597240\pi\)
0.913295 0.407299i \(-0.133529\pi\)
\(360\) −11.1263 + 6.82721i −0.586406 + 0.359825i
\(361\) −4.84472 2.54271i −0.254985 0.133827i
\(362\) 3.21655 + 8.48134i 0.169058 + 0.445769i
\(363\) −17.3093 + 4.88724i −0.908503 + 0.256513i
\(364\) 41.2958 + 41.2958i 2.16449 + 2.16449i
\(365\) −11.9258 + 10.5654i −0.624226 + 0.553016i
\(366\) −38.4180 8.11376i −2.00814 0.424113i
\(367\) −2.67644 4.42738i −0.139709 0.231107i 0.778089 0.628154i \(-0.216189\pi\)
−0.917799 + 0.397046i \(0.870035\pi\)
\(368\) 2.43300 + 3.10549i 0.126829 + 0.161885i
\(369\) 4.44748 + 1.06497i 0.231527 + 0.0554403i
\(370\) 21.7977 + 15.0459i 1.13321 + 0.782198i
\(371\) −18.1047 + 26.2291i −0.939947 + 1.36175i
\(372\) −26.0762 21.5857i −1.35199 1.11916i
\(373\) −4.02932 + 6.66532i −0.208631 + 0.345117i −0.942519 0.334153i \(-0.891550\pi\)
0.733888 + 0.679270i \(0.237704\pi\)
\(374\) −0.446764 1.43372i −0.0231016 0.0741357i
\(375\) 0.565749 21.0326i 0.0292152 1.08612i
\(376\) 0.451187 + 7.45901i 0.0232682 + 0.384669i
\(377\) −1.89377 + 6.07732i −0.0975340 + 0.312998i
\(378\) −21.3312 + 29.6023i −1.09716 + 1.52258i
\(379\) −5.18421 16.6367i −0.266295 0.854570i −0.986915 0.161240i \(-0.948451\pi\)
0.720620 0.693330i \(-0.243857\pi\)
\(380\) 8.64076 + 19.1990i 0.443262 + 0.984887i
\(381\) −12.8407 13.5506i −0.657848 0.694216i
\(382\) −2.40567 0.292101i −0.123085 0.0149452i
\(383\) −9.10690 + 20.2347i −0.465341 + 1.03395i 0.518529 + 0.855060i \(0.326480\pi\)
−0.983870 + 0.178885i \(0.942751\pi\)
\(384\) 26.1356 9.11592i 1.33373 0.465195i
\(385\) 4.51409 + 1.11262i 0.230059 + 0.0567045i
\(386\) 13.2736 + 2.43247i 0.675607 + 0.123810i
\(387\) 16.2730 18.6156i 0.827201 0.946285i
\(388\) −0.319672 0.408031i −0.0162289 0.0207146i
\(389\) −5.18323 21.0292i −0.262800 1.06622i −0.942893 0.333096i \(-0.891907\pi\)
0.680093 0.733126i \(-0.261940\pi\)
\(390\) 40.7565 + 19.6775i 2.06379 + 0.996410i
\(391\) 3.21996 + 1.94654i 0.162841 + 0.0984405i
\(392\) −1.16536 + 6.35916i −0.0588595 + 0.321186i
\(393\) −28.4366 26.5912i −1.43444 1.34135i
\(394\) −29.4620 + 48.7361i −1.48428 + 2.45529i
\(395\) 18.6058 2.25916i 0.936162 0.113671i
\(396\) 4.43043 + 5.57843i 0.222637 + 0.280327i
\(397\) −5.21706 + 4.08731i −0.261837 + 0.205136i −0.739048 0.673652i \(-0.764724\pi\)
0.477211 + 0.878788i \(0.341648\pi\)
\(398\) −6.07780 13.5043i −0.304653 0.676911i
\(399\) 14.5746 + 13.6288i 0.729644 + 0.682294i
\(400\) −0.304562 + 1.23566i −0.0152281 + 0.0617829i
\(401\) −30.1435 23.6159i −1.50530 1.17932i −0.933316 0.359057i \(-0.883099\pi\)
−0.571980 0.820267i \(-0.693825\pi\)
\(402\) −30.2235 46.4078i −1.50741 2.31461i
\(403\) −4.79678 + 39.5050i −0.238944 + 1.96788i
\(404\) 24.3462 + 6.00079i 1.21127 + 0.298551i
\(405\) −4.84878 + 16.3191i −0.240938 + 0.810905i
\(406\) −6.92588 + 2.15819i −0.343726 + 0.107109i
\(407\) 2.27762 4.33963i 0.112897 0.215108i
\(408\) 2.60549 2.18608i 0.128991 0.108227i
\(409\) 16.0909 0.973318i 0.795642 0.0481275i 0.342445 0.939538i \(-0.388745\pi\)
0.453197 + 0.891410i \(0.350283\pi\)
\(410\) 5.53226 3.34437i 0.273219 0.165167i
\(411\) −18.2754 5.02942i −0.901460 0.248083i
\(412\) 13.5643 + 8.19989i 0.668264 + 0.403980i
\(413\) 38.9117 + 4.72473i 1.91472 + 0.232489i
\(414\) −29.1946 5.15027i −1.43484 0.253122i
\(415\) −12.7287 + 18.4407i −0.624828 + 0.905220i
\(416\) −32.0473 25.1075i −1.57125 1.23099i
\(417\) −2.22996 23.6687i −0.109202 1.15906i
\(418\) 5.53745 3.34750i 0.270845 0.163732i
\(419\) 7.13183 + 18.8051i 0.348413 + 0.918689i 0.988613 + 0.150481i \(0.0480822\pi\)
−0.640200 + 0.768208i \(0.721149\pi\)
\(420\) 4.77421 + 30.6843i 0.232958 + 1.49724i
\(421\) 15.1102 15.1102i 0.736426 0.736426i −0.235458 0.971884i \(-0.575659\pi\)
0.971884 + 0.235458i \(0.0756591\pi\)
\(422\) −27.5679 + 31.1178i −1.34199 + 1.51479i
\(423\) 6.93661 + 6.84522i 0.337270 + 0.332826i
\(424\) −10.8777 + 20.7257i −0.528266 + 1.00653i
\(425\) 0.146305 + 1.20493i 0.00709681 + 0.0584475i
\(426\) 15.9030 10.3570i 0.770503 0.501797i
\(427\) −17.9920 + 26.0659i −0.870692 + 1.26142i
\(428\) 7.16007 + 3.22249i 0.346095 + 0.155765i
\(429\) 2.70555 7.92550i 0.130625 0.382647i
\(430\) −2.11031 34.8876i −0.101768 1.68243i
\(431\) 17.9240 + 15.8793i 0.863371 + 0.764880i 0.973415 0.229047i \(-0.0735609\pi\)
−0.110045 + 0.993927i \(0.535099\pi\)
\(432\) 2.24425 4.07332i 0.107977 0.195978i
\(433\) −36.2786 2.19445i −1.74344 0.105458i −0.842304 0.539002i \(-0.818801\pi\)
−0.901132 + 0.433544i \(0.857263\pi\)
\(434\) −40.1569 + 21.0760i −1.92759 + 1.01168i
\(435\) −2.71958 + 2.01504i −0.130394 + 0.0966136i
\(436\) 0.712444 + 0.804183i 0.0341199 + 0.0385134i
\(437\) −4.82325 + 15.4783i −0.230727 + 0.740429i
\(438\) −10.5665 + 30.9531i −0.504888 + 1.47899i
\(439\) −9.26693 + 11.8284i −0.442287 + 0.564537i −0.955978 0.293438i \(-0.905201\pi\)
0.513692 + 0.857975i \(0.328278\pi\)
\(440\) 3.38959 + 0.411571i 0.161593 + 0.0196209i
\(441\) 4.40963 + 7.18635i 0.209982 + 0.342207i
\(442\) −11.2578 3.50807i −0.535478 0.166862i
\(443\) 25.0172 25.0172i 1.18860 1.18860i 0.211147 0.977454i \(-0.432280\pi\)
0.977454 0.211147i \(-0.0677198\pi\)
\(444\) 32.6109 + 2.85443i 1.54764 + 0.135465i
\(445\) 2.20193 + 12.0155i 0.104381 + 0.569591i
\(446\) −29.8464 + 20.6015i −1.41327 + 0.975507i
\(447\) −2.27995 + 5.55633i −0.107838 + 0.262805i
\(448\) 2.46279 40.7147i 0.116356 1.92359i
\(449\) 23.9199 23.9199i 1.12885 1.12885i 0.138485 0.990364i \(-0.455777\pi\)
0.990364 0.138485i \(-0.0442234\pi\)
\(450\) −4.50035 8.43824i −0.212148 0.397782i
\(451\) −0.737724 0.941635i −0.0347381 0.0443399i
\(452\) 34.8552 + 8.59105i 1.63945 + 0.404089i
\(453\) −5.10532 10.3976i −0.239869 0.488522i
\(454\) 13.3929 25.5180i 0.628558 1.19762i
\(455\) 27.3253 24.2081i 1.28103 1.13489i
\(456\) 11.8325 + 8.64617i 0.554106 + 0.404894i
\(457\) −15.2358 + 10.5165i −0.712702 + 0.491943i −0.868401 0.495862i \(-0.834852\pi\)
0.155699 + 0.987804i \(0.450237\pi\)
\(458\) 13.4137i 0.626782i
\(459\) 0.623746 4.39148i 0.0291140 0.204977i
\(460\) −20.7644 + 14.3326i −0.968144 + 0.668261i
\(461\) −2.51119 4.78468i −0.116958 0.222845i 0.819939 0.572451i \(-0.194008\pi\)
−0.936897 + 0.349607i \(0.886315\pi\)
\(462\) 9.18483 2.59331i 0.427317 0.120652i
\(463\) −2.22936 + 1.34770i −0.103607 + 0.0626327i −0.568193 0.822896i \(-0.692357\pi\)
0.464586 + 0.885528i \(0.346203\pi\)
\(464\) 0.843177 0.379483i 0.0391435 0.0176171i
\(465\) −14.4526 + 15.4556i −0.670225 + 0.716738i
\(466\) −15.4878 49.7021i −0.717458 2.30240i
\(467\) 24.7453 9.38466i 1.14508 0.434270i 0.292187 0.956361i \(-0.405617\pi\)
0.852890 + 0.522091i \(0.174848\pi\)
\(468\) 55.8110 3.74753i 2.57987 0.173230i
\(469\) −43.9404 + 8.05238i −2.02898 + 0.371824i
\(470\) 13.7759 0.635435
\(471\) −21.5382 + 2.66604i −0.992426 + 0.122844i
\(472\) 28.7877 1.32506
\(473\) −6.36148 + 1.16578i −0.292501 + 0.0536028i
\(474\) 30.9139 22.9052i 1.41992 1.05207i
\(475\) −4.89010 + 1.85457i −0.224373 + 0.0850935i
\(476\) −2.40703 7.72444i −0.110326 0.354049i
\(477\) 7.50170 + 29.5898i 0.343479 + 1.35482i
\(478\) −48.0280 + 21.6156i −2.19675 + 0.988676i
\(479\) 29.3709 17.7553i 1.34199 0.811262i 0.349901 0.936787i \(-0.386215\pi\)
0.992091 + 0.125524i \(0.0400614\pi\)
\(480\) −5.88212 20.8329i −0.268481 0.950888i
\(481\) −17.8842 34.0755i −0.815450 1.55371i
\(482\) −28.9565 + 19.9872i −1.31893 + 0.910392i
\(483\) −12.9167 + 20.1240i −0.587730 + 0.915672i
\(484\) 31.4235i 1.42834i
\(485\) −0.266658 + 0.184060i −0.0121083 + 0.00835775i
\(486\) 7.90024 + 34.0430i 0.358362 + 1.54422i
\(487\) 15.8907 14.0780i 0.720079 0.637934i −0.221331 0.975199i \(-0.571040\pi\)
0.941410 + 0.337265i \(0.109502\pi\)
\(488\) −10.8100 + 20.5967i −0.489344 + 0.932367i
\(489\) 14.7030 7.21933i 0.664894 0.326469i
\(490\) 11.5721 + 2.85226i 0.522773 + 0.128852i
\(491\) 15.6306 + 19.9509i 0.705397 + 0.900373i 0.998446 0.0557246i \(-0.0177469\pi\)
−0.293049 + 0.956097i \(0.594670\pi\)
\(492\) 3.90197 6.97229i 0.175915 0.314335i
\(493\) 0.623577 0.623577i 0.0280845 0.0280845i
\(494\) 3.06774 50.7158i 0.138024 2.28181i
\(495\) 3.64790 2.55384i 0.163961 0.114787i
\(496\) 4.75727 3.28371i 0.213608 0.147443i
\(497\) −2.75939 15.0575i −0.123775 0.675420i
\(498\) −4.01084 + 45.8225i −0.179730 + 2.05336i
\(499\) −14.9920 + 14.9920i −0.671132 + 0.671132i −0.957977 0.286845i \(-0.907394\pi\)
0.286845 + 0.957977i \(0.407394\pi\)
\(500\) −35.0951 10.9361i −1.56950 0.489076i
\(501\) −22.3756 10.8031i −0.999670 0.482648i
\(502\) −55.7853 6.77356i −2.48982 0.302319i
\(503\) 15.4644 19.7389i 0.689525 0.880114i −0.307930 0.951409i \(-0.599636\pi\)
0.997455 + 0.0712951i \(0.0227132\pi\)
\(504\) 13.4431 + 16.9264i 0.598801 + 0.753961i
\(505\) 4.66310 14.9644i 0.207505 0.665908i
\(506\) 5.14206 + 5.80419i 0.228592 + 0.258028i
\(507\) −25.7432 34.7441i −1.14329 1.54304i
\(508\) −28.8794 + 15.1571i −1.28132 + 0.672486i
\(509\) 23.4521 + 1.41859i 1.03950 + 0.0628780i 0.571296 0.820744i \(-0.306441\pi\)
0.468201 + 0.883622i \(0.344902\pi\)
\(510\) −3.73271 5.03782i −0.165287 0.223078i
\(511\) 19.7473 + 17.4946i 0.873569 + 0.773915i
\(512\) 0.605675 + 10.0130i 0.0267673 + 0.442516i
\(513\) 19.0155 1.91885i 0.839555 0.0847192i
\(514\) −61.8225 27.8241i −2.72687 1.22727i
\(515\) 5.62830 8.15400i 0.248013 0.359308i
\(516\) −23.5745 36.1983i −1.03781 1.59354i
\(517\) −0.307260 2.53051i −0.0135133 0.111292i
\(518\) 20.3814 38.8334i 0.895505 1.70624i
\(519\) 0.863608 4.08912i 0.0379082 0.179492i
\(520\) 17.7791 20.0684i 0.779664 0.880058i
\(521\) −18.0039 + 18.0039i −0.788765 + 0.788765i −0.981292 0.192526i \(-0.938332\pi\)
0.192526 + 0.981292i \(0.438332\pi\)
\(522\) −2.80957 + 6.35487i −0.122972 + 0.278145i
\(523\) −6.40141 16.8791i −0.279914 0.738073i −0.999066 0.0432195i \(-0.986239\pi\)
0.719152 0.694853i \(-0.244531\pi\)
\(524\) −58.2094 + 35.1888i −2.54289 + 1.53723i
\(525\) −7.67996 + 0.723572i −0.335181 + 0.0315793i
\(526\) 42.3952 + 33.2145i 1.84852 + 1.44822i
\(527\) 3.13183 4.53724i 0.136425 0.197645i
\(528\) −1.12232 + 0.469244i −0.0488426 + 0.0204212i
\(529\) 3.54524 + 0.430470i 0.154141 + 0.0187161i
\(530\) 36.9275 + 22.3235i 1.60403 + 0.969670i
\(531\) 27.9360 25.0817i 1.21232 1.08845i
\(532\) 29.8341 18.0353i 1.29347 0.781932i
\(533\) −9.37568 + 0.567124i −0.406106 + 0.0245649i
\(534\) 16.1180 + 19.2103i 0.697495 + 0.831311i
\(535\) 2.28092 4.34593i 0.0986129 0.187891i
\(536\) −31.3229 + 9.76061i −1.35294 + 0.421594i
\(537\) −0.271178 + 1.82235i −0.0117022 + 0.0786402i
\(538\) 7.32557 + 1.80559i 0.315828 + 0.0778446i
\(539\) 0.265830 2.18931i 0.0114501 0.0943002i
\(540\) 25.1367 + 15.8998i 1.08171 + 0.684218i
\(541\) −21.5479 16.8817i −0.926417 0.725801i 0.0354349 0.999372i \(-0.488718\pi\)
−0.961852 + 0.273571i \(0.911795\pi\)
\(542\) 7.48115 30.3522i 0.321343 1.30374i
\(543\) 4.78650 5.11868i 0.205408 0.219663i
\(544\) 2.31476 + 5.14319i 0.0992446 + 0.220512i
\(545\) 0.528662 0.414180i 0.0226454 0.0177415i
\(546\) 24.2108 70.9218i 1.03612 3.03517i
\(547\) 27.1149 3.29234i 1.15935 0.140770i 0.481823 0.876269i \(-0.339975\pi\)
0.677526 + 0.735498i \(0.263052\pi\)
\(548\) −17.1322 + 28.3401i −0.731852 + 1.21063i
\(549\) 7.45501 + 29.4056i 0.318172 + 1.25500i
\(550\) −0.450901 + 2.46049i −0.0192265 + 0.104916i
\(551\) 3.25183 + 1.96580i 0.138533 + 0.0837459i
\(552\) −7.63573 + 15.8153i −0.324998 + 0.673143i
\(553\) −7.42708 30.1328i −0.315832 1.28138i
\(554\) 38.0190 + 48.5276i 1.61527 + 2.06174i
\(555\) 3.01184 20.2400i 0.127846 0.859138i
\(556\) −40.8545 7.48687i −1.73262 0.317514i
\(557\) 8.86244 + 2.18440i 0.375514 + 0.0925558i 0.422555 0.906337i \(-0.361133\pi\)
−0.0470417 + 0.998893i \(0.514979\pi\)
\(558\) −10.1155 + 42.2438i −0.428224 + 1.78832i
\(559\) −20.8421 + 46.3092i −0.881525 + 1.95867i
\(560\) −5.26410 0.639178i −0.222449 0.0270102i
\(561\) −0.842149 + 0.798030i −0.0355555 + 0.0336928i
\(562\) 11.3367 + 25.1892i 0.478211 + 1.06254i
\(563\) −4.02119 12.9044i −0.169473 0.543857i 0.830439 0.557109i \(-0.188089\pi\)
−0.999912 + 0.0132516i \(0.995782\pi\)
\(564\) 14.8024 8.41338i 0.623293 0.354267i
\(565\) 6.67594 21.4238i 0.280859 0.901307i
\(566\) −0.772169 12.7655i −0.0324567 0.536573i
\(567\) 27.7927 + 4.71314i 1.16718 + 0.197933i
\(568\) −3.34476 10.7337i −0.140343 0.450377i
\(569\) 16.2127 26.8191i 0.679672 1.12431i −0.305409 0.952221i \(-0.598793\pi\)
0.985081 0.172093i \(-0.0550531\pi\)
\(570\) 17.2273 20.8111i 0.721572 0.871682i
\(571\) −6.90162 + 9.99873i −0.288824 + 0.418434i −0.940358 0.340185i \(-0.889510\pi\)
0.651534 + 0.758619i \(0.274126\pi\)
\(572\) −12.0413 8.31151i −0.503472 0.347522i
\(573\) 0.616593 + 1.76779i 0.0257585 + 0.0738504i
\(574\) −6.60156 8.42627i −0.275544 0.351706i
\(575\) −3.24242 5.36362i −0.135218 0.223678i
\(576\) −27.8078 27.4414i −1.15866 1.14339i
\(577\) 18.9982 16.8309i 0.790905 0.700680i −0.167569 0.985860i \(-0.553592\pi\)
0.958474 + 0.285180i \(0.0920534\pi\)
\(578\) −25.7942 25.7942i −1.07290 1.07290i
\(579\) −2.83292 10.0335i −0.117732 0.416977i
\(580\) 2.09696 + 5.52922i 0.0870714 + 0.229588i
\(581\) 32.8529 + 17.2425i 1.36297 + 0.715340i
\(582\) −0.289192 + 0.598980i −0.0119874 + 0.0248285i
\(583\) 3.27699 7.28117i 0.135719 0.301555i
\(584\) 15.9459 + 11.0067i 0.659847 + 0.455460i
\(585\) −0.231853 34.9650i −0.00958594 1.44562i
\(586\) 33.7864 8.32761i 1.39571 0.344010i
\(587\) −6.72688 + 0.406901i −0.277648 + 0.0167946i −0.198616 0.980077i \(-0.563645\pi\)
−0.0790324 + 0.996872i \(0.525183\pi\)
\(588\) 14.1763 4.00264i 0.584621 0.165066i
\(589\) 22.2116 + 8.42374i 0.915212 + 0.347094i
\(590\) 3.20432 52.9737i 0.131920 2.18089i
\(591\) 43.8306 + 3.83649i 1.80295 + 0.157812i
\(592\) −1.98224 + 5.22674i −0.0814696 + 0.214818i
\(593\) −33.6461 + 29.8078i −1.38168 + 1.22406i −0.435595 + 0.900143i \(0.643462\pi\)
−0.946085 + 0.323919i \(0.895000\pi\)
\(594\) 3.91978 8.25814i 0.160830 0.338835i
\(595\) −4.91054 + 1.21034i −0.201313 + 0.0496191i
\(596\) 8.25989 + 6.47121i 0.338338 + 0.265071i
\(597\) −7.29563 + 8.81335i −0.298590 + 0.360706i
\(598\) 60.4442 7.33925i 2.47175 0.300124i
\(599\) −5.01530 + 16.0947i −0.204920 + 0.657610i 0.793855 + 0.608108i \(0.208071\pi\)
−0.998774 + 0.0495021i \(0.984237\pi\)
\(600\) −5.53520 + 1.20741i −0.225973 + 0.0492923i
\(601\) 12.5017 6.56139i 0.509954 0.267645i −0.190061 0.981772i \(-0.560869\pi\)
0.700016 + 0.714128i \(0.253176\pi\)
\(602\) −56.9260 + 10.4321i −2.32013 + 0.425180i
\(603\) −21.8921 + 36.7624i −0.891516 + 1.49708i
\(604\) −19.9059 + 3.64789i −0.809958 + 0.148430i
\(605\) 19.6068 + 1.18599i 0.797130 + 0.0482175i
\(606\) −6.85741 31.4368i −0.278563 1.27703i
\(607\) −2.97088 49.1145i −0.120584 1.99349i −0.113672 0.993518i \(-0.536261\pi\)
−0.00691255 0.999976i \(-0.502200\pi\)
\(608\) −19.1303 + 14.9876i −0.775835 + 0.607828i
\(609\) 3.85506 + 4.06818i 0.156215 + 0.164851i
\(610\) 36.6977 + 22.1845i 1.48585 + 0.898225i
\(611\) −17.7232 9.30187i −0.717006 0.376314i
\(612\) −7.08759 3.13352i −0.286499 0.126665i
\(613\) −2.56679 + 42.4341i −0.103672 + 1.71390i 0.460017 + 0.887910i \(0.347843\pi\)
−0.563689 + 0.825987i \(0.690618\pi\)
\(614\) 12.0426 + 17.4467i 0.486000 + 0.704093i
\(615\) −4.20312 2.69780i −0.169486 0.108786i
\(616\) 5.65386i 0.227801i
\(617\) −21.6487 31.3635i −0.871542 1.26265i −0.963723 0.266905i \(-0.913999\pi\)
0.0921804 0.995742i \(-0.470616\pi\)
\(618\) 1.77349 20.2615i 0.0713402 0.815038i
\(619\) −15.9314 + 17.9828i −0.640337 + 0.722791i −0.975654 0.219314i \(-0.929618\pi\)
0.335317 + 0.942105i \(0.391156\pi\)
\(620\) 19.1255 + 31.6375i 0.768100 + 1.27059i
\(621\) 6.36948 + 22.0001i 0.255599 + 0.882834i
\(622\) −23.1012 4.23345i −0.926274 0.169746i
\(623\) 19.3113 6.01764i 0.773691 0.241092i
\(624\) −1.97378 + 9.34572i −0.0790146 + 0.374128i
\(625\) −5.62709 + 14.8374i −0.225083 + 0.593496i
\(626\) 0.613369 + 3.34705i 0.0245151 + 0.133775i
\(627\) −4.20706 2.70033i −0.168014 0.107841i
\(628\) −5.74223 + 37.4793i −0.229140 + 1.49559i
\(629\) 5.33145i 0.212579i
\(630\) 32.6434 22.8532i 1.30054 0.910492i
\(631\) 13.2188 + 5.01323i 0.526232 + 0.199573i 0.603391 0.797445i \(-0.293816\pi\)
−0.0771594 + 0.997019i \(0.524585\pi\)
\(632\) −8.08240 21.3115i −0.321501 0.847728i
\(633\) 30.9673 + 8.52224i 1.23084 + 0.338729i
\(634\) 6.36507 34.7331i 0.252789 1.37943i
\(635\) 8.36735 + 18.5915i 0.332048 + 0.737780i
\(636\) 53.3127 + 1.43404i 2.11399 + 0.0568634i
\(637\) −12.9620 11.4833i −0.513573 0.454986i
\(638\) 1.60927 0.844608i 0.0637114 0.0334383i
\(639\) −12.5977 7.50198i −0.498358 0.296774i
\(640\) −30.2292 −1.19492
\(641\) −19.2207 −0.759170 −0.379585 0.925157i \(-0.623933\pi\)
−0.379585 + 0.925157i \(0.623933\pi\)
\(642\) −0.337698 10.0698i −0.0133279 0.397424i
\(643\) 17.9717 + 1.08709i 0.708736 + 0.0428706i 0.410813 0.911720i \(-0.365245\pi\)
0.297922 + 0.954590i \(0.403706\pi\)
\(644\) 27.7039 + 31.2712i 1.09169 + 1.23226i
\(645\) −23.4758 + 13.3432i −0.924360 + 0.525388i
\(646\) −3.64150 + 6.02378i −0.143273 + 0.237002i
\(647\) 1.62375 6.58782i 0.0638363 0.258994i −0.930349 0.366675i \(-0.880496\pi\)
0.994186 + 0.107681i \(0.0343424\pi\)
\(648\) 20.6801 + 0.975862i 0.812392 + 0.0383355i
\(649\) −9.80227 + 0.592928i −0.384773 + 0.0232745i
\(650\) 13.8889 + 13.8889i 0.544768 + 0.544768i
\(651\) 28.2901 + 20.6720i 1.10878 + 0.810201i
\(652\) −5.15840 28.1485i −0.202018 1.10238i
\(653\) 6.28202 + 9.10108i 0.245834 + 0.356153i 0.926404 0.376531i \(-0.122883\pi\)
−0.680570 + 0.732683i \(0.738268\pi\)
\(654\) 0.523358 1.27544i 0.0204649 0.0498738i
\(655\) 19.7592 + 37.6481i 0.772057 + 1.47103i
\(656\) 0.964755 + 0.964755i 0.0376674 + 0.0376674i
\(657\) 25.0639 3.21209i 0.977836 0.125316i
\(658\) −2.74953 22.6444i −0.107188 0.882772i
\(659\) −1.92853 + 15.8829i −0.0751248 + 0.618708i 0.905714 + 0.423889i \(0.139335\pi\)
−0.980839 + 0.194820i \(0.937588\pi\)
\(660\) −2.56219 7.34586i −0.0997329 0.285937i
\(661\) −5.40116 21.9134i −0.210081 0.852331i −0.977457 0.211134i \(-0.932284\pi\)
0.767376 0.641197i \(-0.221562\pi\)
\(662\) −69.5886 21.6847i −2.70464 0.842799i
\(663\) 1.40060 + 9.00178i 0.0543947 + 0.349600i
\(664\) 25.4785 + 9.66273i 0.988758 + 0.374987i
\(665\) −10.1272 19.2958i −0.392717 0.748260i
\(666\) −15.1558 39.1770i −0.587274 1.51808i
\(667\) −1.61475 + 4.25776i −0.0625235 + 0.164861i
\(668\) −28.7865 + 32.4932i −1.11378 + 1.25720i
\(669\) 24.4501 + 13.6833i 0.945297 + 0.529026i
\(670\) 14.4745 + 58.7253i 0.559198 + 2.26875i
\(671\) 3.25659 7.23585i 0.125719 0.279337i
\(672\) −33.0705 + 13.8269i −1.27572 + 0.533384i
\(673\) 25.0779 + 11.2867i 0.966682 + 0.435068i 0.831361 0.555733i \(-0.187562\pi\)
0.135322 + 0.990802i \(0.456793\pi\)
\(674\) −15.7720 + 1.91507i −0.607514 + 0.0737656i
\(675\) −4.31946 + 5.99431i −0.166256 + 0.230721i
\(676\) −70.6388 + 26.7898i −2.71688 + 1.03038i
\(677\) −27.2135 24.1091i −1.04590 0.926588i −0.0485137 0.998823i \(-0.515448\pi\)
−0.997388 + 0.0722348i \(0.976987\pi\)
\(678\) −9.81743 45.0066i −0.377036 1.72847i
\(679\) 0.355775 + 0.401587i 0.0136534 + 0.0154115i
\(680\) −3.47300 + 1.31713i −0.133183 + 0.0505098i
\(681\) −22.2571 0.598685i −0.852893 0.0229417i
\(682\) 8.94399 7.00717i 0.342483 0.268318i
\(683\) 2.51264 3.20715i 0.0961434 0.122718i −0.736717 0.676201i \(-0.763625\pi\)
0.832860 + 0.553483i \(0.186702\pi\)
\(684\) 5.80094 32.8830i 0.221805 1.25731i
\(685\) 17.0363 + 11.7593i 0.650925 + 0.449301i
\(686\) −3.54605 + 29.2043i −0.135389 + 1.11503i
\(687\) −9.30236 + 4.56755i −0.354907 + 0.174263i
\(688\) 7.04259 2.19456i 0.268496 0.0836668i
\(689\) −32.4353 53.6545i −1.23569 2.04407i
\(690\) 28.2526 + 15.8113i 1.07556 + 0.601924i
\(691\) 30.5331 + 9.51450i 1.16153 + 0.361949i 0.816895 0.576787i \(-0.195694\pi\)
0.344639 + 0.938735i \(0.388001\pi\)
\(692\) −6.46535 3.39327i −0.245776 0.128993i
\(693\) −4.92601 5.48659i −0.187124 0.208418i
\(694\) −35.5713 + 16.0093i −1.35027 + 0.607706i
\(695\) −6.21341 + 25.2088i −0.235688 + 0.956224i
\(696\) 3.17076 + 2.62473i 0.120187 + 0.0994901i
\(697\) 1.18662 + 0.534056i 0.0449466 + 0.0202288i
\(698\) −10.7052 + 13.6641i −0.405197 + 0.517196i
\(699\) −29.1944 + 27.6650i −1.10423 + 1.04639i
\(700\) −2.42932 + 13.2564i −0.0918197 + 0.501044i
\(701\) 7.28359 3.27808i 0.275097 0.123811i −0.268168 0.963372i \(-0.586418\pi\)
0.543266 + 0.839561i \(0.317188\pi\)
\(702\) −35.8814 62.1661i −1.35426 2.34631i
\(703\) −22.3048 + 5.49764i −0.841242 + 0.207347i
\(704\) 1.23176 + 10.1444i 0.0464236 + 0.382333i
\(705\) −4.69089 9.55355i −0.176669 0.359807i
\(706\) 25.1702 + 4.61262i 0.947294 + 0.173598i
\(707\) −25.5288 4.67832i −0.960108 0.175946i
\(708\) −28.9096 58.8778i −1.08649 2.21276i
\(709\) −3.69823 30.4576i −0.138890 1.14386i −0.880843 0.473409i \(-0.843023\pi\)
0.741953 0.670452i \(-0.233900\pi\)
\(710\) −20.1240 + 4.96011i −0.755239 + 0.186150i
\(711\) −26.4113 13.6391i −0.990501 0.511507i
\(712\) 13.5466 6.09684i 0.507681 0.228489i
\(713\) −5.13149 + 28.0017i −0.192176 + 1.04867i
\(714\) −7.53601 + 7.14121i −0.282028 + 0.267253i
\(715\) −5.64047 + 7.19953i −0.210942 + 0.269247i
\(716\) 2.93531 + 1.32107i 0.109698 + 0.0493709i
\(717\) 31.3446 + 25.9468i 1.17058 + 0.969002i
\(718\) −15.1720 + 61.5554i −0.566215 + 2.29723i
\(719\) 5.26502 2.36959i 0.196352 0.0883710i −0.309851 0.950785i \(-0.600279\pi\)
0.506203 + 0.862414i \(0.331048\pi\)
\(720\) −3.77927 + 3.39314i −0.140845 + 0.126455i
\(721\) −14.5267 7.62418i −0.541001 0.283939i
\(722\) 11.7110 + 3.64928i 0.435837 + 0.135812i
\(723\) 23.7211 + 13.2753i 0.882198 + 0.493713i
\(724\) −6.33410 10.4779i −0.235405 0.389407i
\(725\) −1.40245 + 0.437022i −0.0520858 + 0.0162306i
\(726\) 36.1949 17.7721i 1.34332 0.659584i
\(727\) 0.485342 3.99715i 0.0180003 0.148246i −0.980938 0.194323i \(-0.937749\pi\)
0.998938 + 0.0460772i \(0.0146720\pi\)
\(728\) −36.5364 25.2193i −1.35413 0.934688i
\(729\) 20.9185 17.0709i 0.774760 0.632255i
\(730\) 22.0289 28.1178i 0.815325 1.04069i
\(731\) 5.53816 4.33887i 0.204836 0.160479i
\(732\) 52.9809 + 1.42511i 1.95823 + 0.0526737i
\(733\) −1.28381 + 0.486884i −0.0474185 + 0.0179835i −0.378200 0.925724i \(-0.623457\pi\)
0.330782 + 0.943707i \(0.392688\pi\)
\(734\) 7.69116 + 8.68153i 0.283886 + 0.320441i
\(735\) −1.96242 8.99644i −0.0723849 0.331839i
\(736\) −21.7992 19.3124i −0.803528 0.711863i
\(737\) 10.4645 3.96865i 0.385464 0.146187i
\(738\) −10.2378 0.551166i −0.376859 0.0202887i
\(739\) −6.55232 + 0.795596i −0.241031 + 0.0292665i −0.240161 0.970733i \(-0.577200\pi\)
−0.000870390 1.00000i \(0.500277\pi\)
\(740\) −32.6011 14.6725i −1.19844 0.539374i
\(741\) −36.2158 + 15.1420i −1.33042 + 0.556254i
\(742\) 29.3243 65.1559i 1.07653 2.39195i
\(743\) −1.47878 5.99966i −0.0542513 0.220106i 0.937559 0.347827i \(-0.113080\pi\)
−0.991810 + 0.127720i \(0.959234\pi\)
\(744\) 22.4556 + 12.5670i 0.823261 + 0.460729i
\(745\) 4.34948 4.90955i 0.159353 0.179872i
\(746\) 6.19180 16.3264i 0.226698 0.597754i
\(747\) 33.1435 12.8217i 1.21266 0.469121i
\(748\) 0.941991 + 1.79481i 0.0344426 + 0.0656249i
\(749\) −7.59897 2.88191i −0.277660 0.105303i
\(750\) 7.25197 + 46.6091i 0.264804 + 1.70192i
\(751\) −25.0460 7.80464i −0.913940 0.284795i −0.195760 0.980652i \(-0.562717\pi\)
−0.718181 + 0.695857i \(0.755025\pi\)
\(752\) 0.695798 + 2.82297i 0.0253732 + 0.102943i
\(753\) 14.2982 + 40.9934i 0.521056 + 1.49388i
\(754\) 1.72016 14.1668i 0.0626446 0.515924i
\(755\) 1.52482 + 12.5580i 0.0554939 + 0.457034i
\(756\) 21.1186 44.4924i 0.768075 1.61817i
\(757\) 9.27346 + 9.27346i 0.337050 + 0.337050i 0.855256 0.518206i \(-0.173400\pi\)
−0.518206 + 0.855256i \(0.673400\pi\)
\(758\) 18.1552 + 34.5917i 0.659425 + 1.25643i
\(759\) 2.27424 5.54241i 0.0825497 0.201177i
\(760\) −9.09165 13.1715i −0.329789 0.477782i
\(761\) 8.88579 + 48.4882i 0.322110 + 1.75769i 0.602796 + 0.797895i \(0.294053\pi\)
−0.280687 + 0.959799i \(0.590562\pi\)
\(762\) 33.7918 + 24.6922i 1.22415 + 0.894504i
\(763\) −0.786333 0.786333i −0.0284672 0.0284672i
\(764\) 3.26502 0.197498i 0.118124 0.00714521i
\(765\) −2.22267 + 4.30407i −0.0803609 + 0.155614i
\(766\) 11.9052 48.3012i 0.430151 1.74519i
\(767\) −39.8918 + 65.9890i −1.44041 + 2.38273i
\(768\) −14.7301 + 8.37230i −0.531527 + 0.302109i
\(769\) 17.4283 + 19.6725i 0.628482 + 0.709410i 0.973371 0.229234i \(-0.0736220\pi\)
−0.344889 + 0.938643i \(0.612084\pi\)
\(770\) −10.4040 0.629323i −0.374932 0.0226792i
\(771\) 1.75553 + 52.3482i 0.0632238 + 1.88527i
\(772\) −18.2149 −0.655567
\(773\) 0.759408 0.0273140 0.0136570 0.999907i \(-0.495653\pi\)
0.0136570 + 0.999907i \(0.495653\pi\)
\(774\) −28.3618 + 47.6267i −1.01944 + 1.71191i
\(775\) −8.13156 + 4.26777i −0.292094 + 0.153303i
\(776\) 0.294937 + 0.261291i 0.0105876 + 0.00937980i
\(777\) −33.8710 0.911084i −1.21511 0.0326849i
\(778\) 19.9281 + 44.2783i 0.714455 + 1.58745i
\(779\) −1.01068 + 5.51510i −0.0362113 + 0.197599i
\(780\) −58.8991 16.2091i −2.10893 0.580379i
\(781\) 1.35998 + 3.58596i 0.0486638 + 0.128316i
\(782\) −7.88718 2.99121i −0.282045 0.106966i
\(783\) 5.36378 0.215493i 0.191686 0.00770109i
\(784\) 2.51542i 0.0898364i
\(785\) 23.1686 + 4.99744i 0.826924 + 0.178366i
\(786\) 73.4533 + 47.1465i 2.61999 + 1.68166i
\(787\) −0.355094 1.93769i −0.0126577 0.0690711i 0.976685 0.214679i \(-0.0688707\pi\)
−0.989342 + 0.145608i \(0.953486\pi\)
\(788\) 27.2583 71.8742i 0.971036 2.56041i
\(789\) 8.59800 40.7109i 0.306097 1.44935i
\(790\) −40.1161 + 12.5007i −1.42727 + 0.444754i
\(791\) −36.5483 6.69773i −1.29951 0.238144i
\(792\) −4.07712 3.56404i −0.144874 0.126643i
\(793\) −32.2334 53.3205i −1.14464 1.89347i
\(794\) 9.85277 11.1215i 0.349662 0.394687i
\(795\) 2.90692 33.2106i 0.103098 1.17786i
\(796\) 11.3550 + 16.4506i 0.402469 + 0.583077i
\(797\) 24.2795i 0.860024i −0.902823 0.430012i \(-0.858509\pi\)
0.902823 0.430012i \(-0.141491\pi\)
\(798\) −37.6471 24.1640i −1.33269 0.855398i
\(799\) 1.57523 + 2.28211i 0.0557276 + 0.0807354i
\(800\) 0.567250 9.37776i 0.0200553 0.331554i
\(801\) 7.83387 17.7192i 0.276796 0.626076i
\(802\) 76.0151 + 39.8958i 2.68418 + 1.40877i
\(803\) −5.65632 3.41937i −0.199607 0.120667i
\(804\) 51.4184 + 54.2610i 1.81339 + 1.91364i
\(805\) 20.5574 16.1057i 0.724554 0.567651i
\(806\) −5.38675 89.0536i −0.189740 3.13678i
\(807\) −1.24229 5.69509i −0.0437306 0.200477i
\(808\) −19.0265 1.15089i −0.669349 0.0404882i
\(809\) −4.38335 + 0.803279i −0.154110 + 0.0282418i −0.256756 0.966476i \(-0.582654\pi\)
0.102646 + 0.994718i \(0.467269\pi\)
\(810\) 4.09761 37.9459i 0.143975 1.33328i
\(811\) −27.5339 + 5.04578i −0.966847 + 0.177181i −0.640406 0.768036i \(-0.721234\pi\)
−0.326441 + 0.945218i \(0.605849\pi\)
\(812\) 8.67024 4.55049i 0.304266 0.159691i
\(813\) −23.5966 + 5.14719i −0.827568 + 0.180520i
\(814\) −3.26883 + 10.4900i −0.114572 + 0.367676i
\(815\) −17.7580 + 2.15622i −0.622037 + 0.0755290i
\(816\) 0.843819 1.01936i 0.0295396 0.0356847i
\(817\) 23.8630 + 18.6955i 0.834862 + 0.654073i
\(818\) −35.0898 + 8.64885i −1.22688 + 0.302400i
\(819\) −57.4281 + 7.35977i −2.00670 + 0.257171i
\(820\) −6.53136 + 5.78628i −0.228085 + 0.202066i
\(821\) 6.80924 17.9545i 0.237644 0.626616i −0.762140 0.647413i \(-0.775851\pi\)
0.999784 + 0.0207966i \(0.00662024\pi\)
\(822\) 42.3328 + 3.70539i 1.47653 + 0.129240i
\(823\) −0.808628 + 13.3682i −0.0281870 + 0.465987i 0.956509 + 0.291704i \(0.0942222\pi\)
−0.984696 + 0.174283i \(0.944239\pi\)
\(824\) −11.2659 4.27260i −0.392467 0.148843i
\(825\) 1.85988 0.525131i 0.0647526 0.0182827i
\(826\) −87.7161 + 5.30585i −3.05203 + 0.184614i
\(827\) −1.87876 + 0.463073i −0.0653309 + 0.0161026i −0.271846 0.962341i \(-0.587634\pi\)
0.206515 + 0.978443i \(0.433788\pi\)
\(828\) 40.0142 0.265334i 1.39059 0.00922100i
\(829\) 24.4715 + 16.8915i 0.849932 + 0.586665i 0.911436 0.411441i \(-0.134975\pi\)
−0.0615046 + 0.998107i \(0.519590\pi\)
\(830\) 20.6168 45.8088i 0.715621 1.59004i
\(831\) 20.7078 42.8904i 0.718344 1.48785i
\(832\) 71.0497 + 37.2898i 2.46321 + 1.29279i
\(833\) 0.850725 + 2.24318i 0.0294759 + 0.0777215i
\(834\) 14.4823 + 51.2924i 0.501480 + 1.77611i
\(835\) 19.1878 + 19.1878i 0.664021 + 0.664021i
\(836\) −6.53748 + 5.79170i −0.226103 + 0.200310i
\(837\) 32.7404 7.36952i 1.13167 0.254728i
\(838\) −23.3263 38.5864i −0.805792 1.33294i
\(839\) −9.29665 11.8663i −0.320956 0.409670i 0.599588 0.800309i \(-0.295331\pi\)
−0.920544 + 0.390639i \(0.872254\pi\)
\(840\) −7.77433 22.2892i −0.268240 0.769051i
\(841\) −22.9882 15.8676i −0.792696 0.547158i
\(842\) −27.2143 + 39.4268i −0.937868 + 1.35874i
\(843\) 13.6083 16.4392i 0.468694 0.566197i
\(844\) 29.0302 48.0218i 0.999260 1.65298i
\(845\) 14.0495 + 45.0865i 0.483318 + 1.55102i
\(846\) −18.0626 12.2917i −0.621006 0.422597i
\(847\) −1.96382 32.4658i −0.0674777 1.11554i
\(848\) −2.70939 + 8.69473i −0.0930407 + 0.298578i
\(849\) −8.58988 + 4.88232i −0.294804 + 0.167561i
\(850\) −0.809552 2.59794i −0.0277674 0.0891087i
\(851\) −11.2985 25.1043i −0.387309 0.860566i
\(852\) −18.5941 + 17.6200i −0.637025 + 0.603652i
\(853\) 9.89138 + 1.20103i 0.338675 + 0.0411225i 0.288107 0.957598i \(-0.406974\pi\)
0.0505672 + 0.998721i \(0.483897\pi\)
\(854\) 29.1418 64.7504i 0.997211 2.21571i
\(855\) −20.2986 4.86060i −0.694196 0.166229i
\(856\) −5.79532 1.42842i −0.198080 0.0488223i
\(857\) −41.6722 7.63672i −1.42350 0.260865i −0.587332 0.809346i \(-0.699822\pi\)
−0.836163 + 0.548481i \(0.815206\pi\)
\(858\) −2.76340 + 18.5704i −0.0943410 + 0.633984i
\(859\) 28.2348 + 36.0390i 0.963358 + 1.22964i 0.973265 + 0.229684i \(0.0737694\pi\)
−0.00990746 + 0.999951i \(0.503154\pi\)
\(860\) 11.2902 + 45.8060i 0.384991 + 1.56197i
\(861\) −3.59567 + 7.44742i −0.122540 + 0.253807i
\(862\) −45.9426 27.7732i −1.56481 0.945961i
\(863\) 3.42366 18.6823i 0.116543 0.635953i −0.872534 0.488553i \(-0.837525\pi\)
0.989077 0.147400i \(-0.0470904\pi\)
\(864\) −10.8759 + 32.5640i −0.370006 + 1.10785i
\(865\) −2.36126 + 3.90601i −0.0802854 + 0.132808i
\(866\) 80.8872 9.82148i 2.74866 0.333747i
\(867\) −9.10492 + 26.6715i −0.309219 + 0.905812i
\(868\) 48.1875 37.7525i 1.63559 1.28140i
\(869\) 3.19102 + 7.09016i 0.108248 + 0.240517i
\(870\) 5.18283 5.54251i 0.175714 0.187909i
\(871\) 21.0309 85.3259i 0.712606 2.89116i
\(872\) −0.642905 0.503684i −0.0217715 0.0170569i
\(873\) 0.513865 0.00340744i 0.0173917 0.000115324i
\(874\) 4.38108 36.0815i 0.148192 1.22047i
\(875\) 36.9426 + 9.10554i 1.24889 + 0.307824i
\(876\) 6.49788 43.6666i 0.219543 1.47536i
\(877\) 44.9576 14.0094i 1.51811 0.473063i 0.578609 0.815605i \(-0.303596\pi\)
0.939502 + 0.342542i \(0.111288\pi\)
\(878\) 15.6552 29.8284i 0.528336 1.00666i
\(879\) −17.2799 20.5951i −0.582837 0.694656i
\(880\) 1.32608 0.0802133i 0.0447023 0.00270399i
\(881\) 19.8625 12.0073i 0.669184 0.404536i −0.141565 0.989929i \(-0.545214\pi\)
0.810750 + 0.585393i \(0.199060\pi\)
\(882\) −12.6281 14.0651i −0.425209 0.473598i
\(883\) −29.2397 17.6760i −0.983993 0.594844i −0.0687016 0.997637i \(-0.521886\pi\)
−0.915291 + 0.402793i \(0.868039\pi\)
\(884\) 15.8002 + 1.91850i 0.531419 + 0.0645260i
\(885\) −37.8282 + 15.8161i −1.27158 + 0.531652i
\(886\) −45.0573 + 65.2768i −1.51373 + 2.19302i
\(887\) −10.1848 7.97930i −0.341973 0.267919i 0.431008 0.902348i \(-0.358158\pi\)
−0.772981 + 0.634429i \(0.781235\pi\)
\(888\) −24.7751 + 2.33420i −0.831397 + 0.0783306i
\(889\) 28.8901 17.4647i 0.968942 0.585746i
\(890\) −9.71124 25.6064i −0.325522 0.858330i
\(891\) −7.06173 + 0.0936568i −0.236577 + 0.00313762i
\(892\) 34.6139 34.6139i 1.15896 1.15896i
\(893\) −7.92319 + 8.94343i −0.265139 + 0.299280i
\(894\) 2.78230 13.1740i 0.0930541 0.440605i
\(895\) 0.935075 1.78164i 0.0312561 0.0595536i
\(896\) 6.03345 + 49.6899i 0.201563 + 1.66002i
\(897\) −25.6718 39.4187i −0.857157 1.31615i
\(898\) −43.0811 + 62.4137i −1.43763 + 2.08277i
\(899\) 6.08444 + 2.73839i 0.202928 + 0.0913303i
\(900\) 8.02808 + 10.1083i 0.267603 + 0.336943i
\(901\) 0.524440 + 8.67003i 0.0174716 + 0.288840i
\(902\) 2.00733 + 1.77834i 0.0668369 + 0.0592123i
\(903\) 26.6187 + 35.9257i 0.885815 + 1.19553i
\(904\) −27.2393 1.64767i −0.905966 0.0548008i
\(905\) −6.77678 + 3.55673i −0.225268 + 0.118230i
\(906\) 15.4599 + 20.8653i 0.513621 + 0.693204i
\(907\) −31.6584 35.7349i −1.05120 1.18656i −0.981985 0.188958i \(-0.939489\pi\)
−0.0692147 0.997602i \(-0.522049\pi\)
\(908\) −11.5727 + 37.1382i −0.384054 + 1.23247i
\(909\) −19.4663 + 15.4603i −0.645656 + 0.512785i
\(910\) −50.4740 + 64.4253i −1.67320 + 2.13568i
\(911\) 16.3706 + 1.98775i 0.542383 + 0.0658572i 0.387143 0.922020i \(-0.373462\pi\)
0.155240 + 0.987877i \(0.450385\pi\)
\(912\) 5.13474 + 2.47909i 0.170028 + 0.0820909i
\(913\) −8.87451 2.76541i −0.293703 0.0915217i
\(914\) 29.3477 29.3477i 0.970736 0.970736i
\(915\) 2.88883 33.0039i 0.0955016 1.09107i
\(916\) 3.26364 + 17.8091i 0.107834 + 0.588429i
\(917\) 57.9411 39.9938i 1.91338 1.32071i
\(918\) 0.399185 + 9.93601i 0.0131751 + 0.327937i
\(919\) 2.74035 45.3035i 0.0903959 1.49442i −0.616640 0.787245i \(-0.711507\pi\)
0.707036 0.707178i \(-0.250032\pi\)
\(920\) 13.5621 13.5621i 0.447129 0.447129i
\(921\) 7.99858 14.2924i 0.263562 0.470949i
\(922\) 7.47115 + 9.53622i 0.246049 + 0.314059i
\(923\) 29.2395 + 7.20688i 0.962428 + 0.237217i
\(924\) −11.5635 + 5.67780i −0.380412 + 0.186786i
\(925\) 4.12711 7.86356i 0.135699 0.258552i
\(926\) 4.37150 3.87281i 0.143656 0.127268i
\(927\) −14.6552 + 5.66942i −0.481340 + 0.186208i
\(928\) −5.61759 + 3.87755i −0.184407 + 0.127287i
\(929\) 0.357528i 0.0117301i 0.999983 + 0.00586506i \(0.00186692\pi\)
−0.999983 + 0.00586506i \(0.998133\pi\)
\(930\) 25.6247 39.9228i 0.840267 1.30912i
\(931\) −8.50737 + 5.87221i −0.278818 + 0.192454i
\(932\) 32.6556 + 62.2200i 1.06967 + 2.03808i
\(933\) 4.93039 + 17.4622i 0.161414 + 0.571685i
\(934\) −50.7751 + 30.6946i −1.66141 + 1.00436i
\(935\) 1.15543 0.520019i 0.0377867 0.0170064i
\(936\) −41.2177 + 10.4497i −1.34724 + 0.341558i
\(937\) 1.72709 + 5.54242i 0.0564215 + 0.181063i 0.978630 0.205631i \(-0.0659247\pi\)
−0.922208 + 0.386694i \(0.873617\pi\)
\(938\) 93.6419 35.5137i 3.05752 1.15956i
\(939\) 2.11230 1.56508i 0.0689324 0.0510746i
\(940\) −18.2900 + 3.35176i −0.596553 + 0.109322i
\(941\) −36.5434 −1.19128 −0.595640 0.803252i \(-0.703101\pi\)
−0.595640 + 0.803252i \(0.703101\pi\)
\(942\) 46.4179 14.5829i 1.51238 0.475136i
\(943\) −6.71927 −0.218810
\(944\) 11.0172 2.01898i 0.358580 0.0657123i
\(945\) −26.9641 14.8563i −0.877143 0.483275i
\(946\) 13.5570 5.14150i 0.440777 0.167165i
\(947\) 1.05525 + 3.38642i 0.0342911 + 0.110044i 0.970280 0.241987i \(-0.0777990\pi\)
−0.935989 + 0.352031i \(0.885491\pi\)
\(948\) −35.4707 + 37.9323i −1.15203 + 1.23198i
\(949\) −47.3269 + 21.3001i −1.53630 + 0.691430i
\(950\) 10.0340 6.06579i 0.325547 0.196800i
\(951\) −26.2546 + 7.41293i −0.851365 + 0.240381i
\(952\) 2.85824 + 5.44592i 0.0926361 + 0.176503i
\(953\) 26.9909 18.6305i 0.874321 0.603500i −0.0441343 0.999026i \(-0.514053\pi\)
0.918455 + 0.395526i \(0.129438\pi\)
\(954\) −28.5001 62.2190i −0.922726 2.01441i
\(955\) 2.04468i 0.0661643i
\(956\) 58.5064 40.3841i 1.89223 1.30611i
\(957\) −1.13371 0.828419i −0.0366476 0.0267790i
\(958\) −57.5927 + 51.0227i −1.86074 + 1.64847i
\(959\) 15.9294 30.3509i 0.514386 0.980081i
\(960\) 18.8050 + 38.2987i 0.606930 + 1.23609i
\(961\) 10.4014 + 2.56372i 0.335530 + 0.0827007i
\(962\) 53.2080 + 67.9150i 1.71550 + 2.18967i
\(963\) −6.86839 + 3.66310i −0.221331 + 0.118042i
\(964\) 33.5818 33.5818i 1.08160 1.08160i
\(965\) −0.687470 + 11.3652i −0.0221304 + 0.365860i
\(966\) 20.3512 49.5965i 0.654788 1.59574i
\(967\) −5.33897 + 3.68522i −0.171690 + 0.118509i −0.650811 0.759240i \(-0.725571\pi\)
0.479121 + 0.877749i \(0.340955\pi\)
\(968\) −4.30582 23.4961i −0.138394 0.755193i
\(969\) 5.41745 + 0.474189i 0.174034 + 0.0152331i
\(970\) 0.513644 0.513644i 0.0164921 0.0164921i
\(971\) −18.4087 5.73639i −0.590764 0.184090i −0.0124761 0.999922i \(-0.503971\pi\)
−0.578288 + 0.815833i \(0.696279\pi\)
\(972\) −18.7718 43.2759i −0.602107 1.38807i
\(973\) 42.6776 + 5.18200i 1.36818 + 0.166127i
\(974\) −29.3527 + 37.4660i −0.940521 + 1.20049i
\(975\) 4.90255 14.3613i 0.157007 0.459929i
\(976\) −2.69252 + 8.64061i −0.0861855 + 0.276579i
\(977\) 18.1464 + 20.4831i 0.580556 + 0.655312i 0.963264 0.268557i \(-0.0865468\pi\)
−0.382708 + 0.923870i \(0.625008\pi\)
\(978\) −29.5052 + 21.8615i −0.943473 + 0.699054i
\(979\) −4.48708 + 2.35500i −0.143408 + 0.0752662i
\(980\) −16.0580 0.971328i −0.512953 0.0310279i
\(981\) −1.06273 + 0.0713586i −0.0339302 + 0.00227831i
\(982\) −42.5304 37.6787i −1.35720 1.20237i
\(983\) 1.59280 + 26.3322i 0.0508026 + 0.839866i 0.930946 + 0.365158i \(0.118985\pi\)
−0.880143 + 0.474709i \(0.842553\pi\)
\(984\) −1.96222 + 5.74802i −0.0625532 + 0.183240i
\(985\) −43.8174 19.7206i −1.39614 0.628351i
\(986\) −1.12310 + 1.62709i −0.0357667 + 0.0518171i
\(987\) −14.7676 + 9.61753i −0.470057 + 0.306129i
\(988\) 8.26648 + 68.0806i 0.262992 + 2.16593i
\(989\) −16.8826 + 32.1672i −0.536837 + 1.02286i
\(990\) −7.01219 + 7.10581i −0.222862 + 0.225837i
\(991\) −14.0629 + 15.8737i −0.446721 + 0.504244i −0.928132 0.372251i \(-0.878586\pi\)
0.481411 + 0.876495i \(0.340124\pi\)
\(992\) −30.1744 + 30.1744i −0.958039 + 0.958039i
\(993\) 8.65762 + 55.6434i 0.274741 + 1.76579i
\(994\) 12.1698 + 32.0892i 0.386003 + 1.01781i
\(995\) 10.6930 6.46414i 0.338991 0.204927i
\(996\) −5.82379 61.8134i −0.184534 1.95863i
\(997\) 35.1454 + 27.5347i 1.11307 + 0.872033i 0.992690 0.120695i \(-0.0385125\pi\)
0.120378 + 0.992728i \(0.461589\pi\)
\(998\) 27.0014 39.1182i 0.854713 1.23827i
\(999\) −22.0084 + 23.8508i −0.696314 + 0.754606i
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 471.2.s.a.2.7 1200
3.2 odd 2 inner 471.2.s.a.2.44 yes 1200
157.79 odd 52 inner 471.2.s.a.236.44 yes 1200
471.236 even 52 inner 471.2.s.a.236.7 yes 1200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.s.a.2.7 1200 1.1 even 1 trivial
471.2.s.a.2.44 yes 1200 3.2 odd 2 inner
471.2.s.a.236.7 yes 1200 471.236 even 52 inner
471.2.s.a.236.44 yes 1200 157.79 odd 52 inner