Properties

Label 252.2.bj.b.103.31
Level $252$
Weight $2$
Character 252.103
Analytic conductor $2.012$
Analytic rank $0$
Dimension $84$
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] = [252,2,Mod(103,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.103");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bj (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 103.31
Character \(\chi\) \(=\) 252.103
Dual form 252.2.bj.b.115.32

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.937998 - 1.05838i) q^{2} +(-1.65520 - 0.510207i) q^{3} +(-0.240318 - 1.98551i) q^{4} +(-3.41753 + 1.97311i) q^{5} +(-2.09257 + 1.27325i) q^{6} +(-0.174185 + 2.64001i) q^{7} +(-2.32683 - 1.60806i) q^{8} +(2.47938 + 1.68899i) q^{9} +O(q^{10})\) \(q+(0.937998 - 1.05838i) q^{2} +(-1.65520 - 0.510207i) q^{3} +(-0.240318 - 1.98551i) q^{4} +(-3.41753 + 1.97311i) q^{5} +(-2.09257 + 1.27325i) q^{6} +(-0.174185 + 2.64001i) q^{7} +(-2.32683 - 1.60806i) q^{8} +(2.47938 + 1.68899i) q^{9} +(-1.11734 + 5.46781i) q^{10} +(-4.23698 - 2.44622i) q^{11} +(-0.615246 + 3.40903i) q^{12} +(-1.13829 - 0.657191i) q^{13} +(2.63074 + 2.66068i) q^{14} +(6.66340 - 1.52225i) q^{15} +(-3.88449 + 0.954307i) q^{16} +(1.67931 - 0.969547i) q^{17} +(4.11324 - 1.03984i) q^{18} +(-1.49477 + 2.58902i) q^{19} +(4.73893 + 6.31137i) q^{20} +(1.63526 - 4.28088i) q^{21} +(-6.56330 + 2.18976i) q^{22} +(-2.92226 + 1.68717i) q^{23} +(3.03093 + 3.84882i) q^{24} +(5.28635 - 9.15623i) q^{25} +(-1.76327 + 0.588292i) q^{26} +(-3.24213 - 4.06061i) q^{27} +(5.28363 - 0.288597i) q^{28} +(-1.32976 - 2.30322i) q^{29} +(4.63914 - 8.48024i) q^{30} -0.886605 q^{31} +(-2.63363 + 5.00639i) q^{32} +(5.76497 + 6.21072i) q^{33} +(0.549040 - 2.68677i) q^{34} +(-4.61376 - 9.36601i) q^{35} +(2.75767 - 5.32872i) q^{36} +(0.237205 - 0.410852i) q^{37} +(1.33806 + 4.01053i) q^{38} +(1.54879 + 1.66854i) q^{39} +(11.1249 + 0.904485i) q^{40} +(-8.79016 - 5.07500i) q^{41} +(-2.99690 - 5.74618i) q^{42} +(2.31047 - 1.33395i) q^{43} +(-3.83877 + 9.00043i) q^{44} +(-11.8059 - 0.880085i) q^{45} +(-0.955417 + 4.67540i) q^{46} -2.46166 q^{47} +(6.91651 + 0.402326i) q^{48} +(-6.93932 - 0.919699i) q^{49} +(-4.73214 - 14.1835i) q^{50} +(-3.27426 + 0.748002i) q^{51} +(-1.03131 + 2.41802i) q^{52} +(6.34427 + 10.9886i) q^{53} +(-7.33877 - 0.377454i) q^{54} +19.3067 q^{55} +(4.65059 - 5.86277i) q^{56} +(3.79508 - 3.52270i) q^{57} +(-3.68499 - 0.753026i) q^{58} +6.99484 q^{59} +(-4.62377 - 12.8644i) q^{60} +2.37140i q^{61} +(-0.831634 + 0.938361i) q^{62} +(-4.89082 + 6.25139i) q^{63} +(2.82830 + 7.48336i) q^{64} +5.18685 q^{65} +(11.9808 - 0.275857i) q^{66} -1.39480i q^{67} +(-2.32861 - 3.10128i) q^{68} +(5.69773 - 1.30164i) q^{69} +(-14.2405 - 3.90221i) q^{70} +2.15535i q^{71} +(-3.05310 - 7.91698i) q^{72} +(3.96915 - 2.29159i) q^{73} +(-0.212337 - 0.636430i) q^{74} +(-13.4215 + 12.4583i) q^{75} +(5.49974 + 2.34569i) q^{76} +(7.19607 - 10.7596i) q^{77} +(3.21871 - 0.0741104i) q^{78} +10.0544i q^{79} +(11.3924 - 10.9259i) q^{80} +(3.29463 + 8.37529i) q^{81} +(-13.6164 + 4.54295i) q^{82} +(-1.29635 - 2.24535i) q^{83} +(-8.89271 - 2.21806i) q^{84} +(-3.82605 + 6.62692i) q^{85} +(0.755397 - 3.69659i) q^{86} +(1.02591 + 4.49075i) q^{87} +(5.92508 + 12.5053i) q^{88} +(-11.6706 - 6.73801i) q^{89} +(-12.0054 + 11.6696i) q^{90} +(1.93326 - 2.89062i) q^{91} +(4.05215 + 5.39671i) q^{92} +(1.46751 + 0.452352i) q^{93} +(-2.30903 + 2.60536i) q^{94} -11.7974i q^{95} +(6.91349 - 6.94289i) q^{96} +(-1.88401 + 1.08773i) q^{97} +(-7.48246 + 6.48173i) q^{98} +(-6.37343 - 13.2213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.937998 1.05838i 0.663265 0.748385i
\(3\) −1.65520 0.510207i −0.955630 0.294568i
\(4\) −0.240318 1.98551i −0.120159 0.992755i
\(5\) −3.41753 + 1.97311i −1.52837 + 0.882403i −0.528936 + 0.848662i \(0.677409\pi\)
−0.999431 + 0.0337413i \(0.989258\pi\)
\(6\) −2.09257 + 1.27325i −0.854287 + 0.519802i
\(7\) −0.174185 + 2.64001i −0.0658356 + 0.997830i
\(8\) −2.32683 1.60806i −0.822660 0.568534i
\(9\) 2.47938 + 1.68899i 0.826459 + 0.562997i
\(10\) −1.11734 + 5.46781i −0.353335 + 1.72907i
\(11\) −4.23698 2.44622i −1.27750 0.737563i −0.301109 0.953590i \(-0.597357\pi\)
−0.976388 + 0.216026i \(0.930690\pi\)
\(12\) −0.615246 + 3.40903i −0.177606 + 0.984102i
\(13\) −1.13829 0.657191i −0.315704 0.182272i 0.333772 0.942654i \(-0.391678\pi\)
−0.649476 + 0.760382i \(0.725012\pi\)
\(14\) 2.63074 + 2.66068i 0.703095 + 0.711096i
\(15\) 6.66340 1.52225i 1.72048 0.393043i
\(16\) −3.88449 + 0.954307i −0.971124 + 0.238577i
\(17\) 1.67931 0.969547i 0.407291 0.235150i −0.282334 0.959316i \(-0.591109\pi\)
0.689625 + 0.724166i \(0.257775\pi\)
\(18\) 4.11324 1.03984i 0.969499 0.245093i
\(19\) −1.49477 + 2.58902i −0.342924 + 0.593962i −0.984974 0.172701i \(-0.944751\pi\)
0.642050 + 0.766662i \(0.278084\pi\)
\(20\) 4.73893 + 6.31137i 1.05966 + 1.41126i
\(21\) 1.63526 4.28088i 0.356844 0.934164i
\(22\) −6.56330 + 2.18976i −1.39930 + 0.466859i
\(23\) −2.92226 + 1.68717i −0.609333 + 0.351798i −0.772704 0.634766i \(-0.781096\pi\)
0.163372 + 0.986565i \(0.447763\pi\)
\(24\) 3.03093 + 3.84882i 0.618686 + 0.785638i
\(25\) 5.28635 9.15623i 1.05727 1.83125i
\(26\) −1.76327 + 0.588292i −0.345805 + 0.115374i
\(27\) −3.24213 4.06061i −0.623949 0.781465i
\(28\) 5.28363 0.288597i 0.998512 0.0545397i
\(29\) −1.32976 2.30322i −0.246931 0.427697i 0.715742 0.698365i \(-0.246089\pi\)
−0.962673 + 0.270668i \(0.912755\pi\)
\(30\) 4.63914 8.48024i 0.846988 1.54827i
\(31\) −0.886605 −0.159239 −0.0796195 0.996825i \(-0.525371\pi\)
−0.0796195 + 0.996825i \(0.525371\pi\)
\(32\) −2.63363 + 5.00639i −0.465565 + 0.885014i
\(33\) 5.76497 + 6.21072i 1.00355 + 1.08115i
\(34\) 0.549040 2.68677i 0.0941596 0.460777i
\(35\) −4.61376 9.36601i −0.779868 1.58314i
\(36\) 2.75767 5.32872i 0.459611 0.888120i
\(37\) 0.237205 0.410852i 0.0389963 0.0675436i −0.845869 0.533391i \(-0.820917\pi\)
0.884865 + 0.465848i \(0.154251\pi\)
\(38\) 1.33806 + 4.01053i 0.217062 + 0.650593i
\(39\) 1.54879 + 1.66854i 0.248005 + 0.267181i
\(40\) 11.1249 + 0.904485i 1.75900 + 0.143012i
\(41\) −8.79016 5.07500i −1.37279 0.792582i −0.381514 0.924363i \(-0.624597\pi\)
−0.991279 + 0.131781i \(0.957930\pi\)
\(42\) −2.99690 5.74618i −0.462432 0.886655i
\(43\) 2.31047 1.33395i 0.352344 0.203426i −0.313373 0.949630i \(-0.601459\pi\)
0.665717 + 0.746204i \(0.268126\pi\)
\(44\) −3.83877 + 9.00043i −0.578717 + 1.35687i
\(45\) −11.8059 0.880085i −1.75992 0.131195i
\(46\) −0.955417 + 4.67540i −0.140869 + 0.689351i
\(47\) −2.46166 −0.359070 −0.179535 0.983752i \(-0.557459\pi\)
−0.179535 + 0.983752i \(0.557459\pi\)
\(48\) 6.91651 + 0.402326i 0.998312 + 0.0580708i
\(49\) −6.93932 0.919699i −0.991331 0.131386i
\(50\) −4.73214 14.1835i −0.669226 2.00585i
\(51\) −3.27426 + 0.748002i −0.458488 + 0.104741i
\(52\) −1.03131 + 2.41802i −0.143017 + 0.335318i
\(53\) 6.34427 + 10.9886i 0.871453 + 1.50940i 0.860494 + 0.509460i \(0.170155\pi\)
0.0109585 + 0.999940i \(0.496512\pi\)
\(54\) −7.33877 0.377454i −0.998680 0.0513650i
\(55\) 19.3067 2.60331
\(56\) 4.65059 5.86277i 0.621461 0.783445i
\(57\) 3.79508 3.52270i 0.502671 0.466594i
\(58\) −3.68499 0.753026i −0.483863 0.0988772i
\(59\) 6.99484 0.910650 0.455325 0.890325i \(-0.349523\pi\)
0.455325 + 0.890325i \(0.349523\pi\)
\(60\) −4.62377 12.8644i −0.596927 1.66079i
\(61\) 2.37140i 0.303626i 0.988409 + 0.151813i \(0.0485112\pi\)
−0.988409 + 0.151813i \(0.951489\pi\)
\(62\) −0.831634 + 0.938361i −0.105618 + 0.119172i
\(63\) −4.89082 + 6.25139i −0.616186 + 0.787601i
\(64\) 2.82830 + 7.48336i 0.353538 + 0.935420i
\(65\) 5.18685 0.643349
\(66\) 11.9808 0.275857i 1.47474 0.0339556i
\(67\) 1.39480i 0.170402i −0.996364 0.0852008i \(-0.972847\pi\)
0.996364 0.0852008i \(-0.0271532\pi\)
\(68\) −2.32861 3.10128i −0.282386 0.376085i
\(69\) 5.69773 1.30164i 0.685925 0.156699i
\(70\) −14.2405 3.90221i −1.70206 0.466403i
\(71\) 2.15535i 0.255793i 0.991788 + 0.127896i \(0.0408225\pi\)
−0.991788 + 0.127896i \(0.959177\pi\)
\(72\) −3.05310 7.91698i −0.359812 0.933025i
\(73\) 3.96915 2.29159i 0.464554 0.268210i −0.249403 0.968400i \(-0.580234\pi\)
0.713957 + 0.700189i \(0.246901\pi\)
\(74\) −0.212337 0.636430i −0.0246837 0.0739835i
\(75\) −13.4215 + 12.4583i −1.54979 + 1.43856i
\(76\) 5.49974 + 2.34569i 0.630864 + 0.269070i
\(77\) 7.19607 10.7596i 0.820068 1.22617i
\(78\) 3.21871 0.0741104i 0.364447 0.00839135i
\(79\) 10.0544i 1.13121i 0.824675 + 0.565607i \(0.191358\pi\)
−0.824675 + 0.565607i \(0.808642\pi\)
\(80\) 11.3924 10.9259i 1.27371 1.22156i
\(81\) 3.29463 + 8.37529i 0.366070 + 0.930587i
\(82\) −13.6164 + 4.54295i −1.50368 + 0.501685i
\(83\) −1.29635 2.24535i −0.142293 0.246459i 0.786067 0.618142i \(-0.212114\pi\)
−0.928360 + 0.371683i \(0.878781\pi\)
\(84\) −8.89271 2.21806i −0.970274 0.242010i
\(85\) −3.82605 + 6.62692i −0.414994 + 0.718790i
\(86\) 0.755397 3.69659i 0.0814566 0.398614i
\(87\) 1.02591 + 4.49075i 0.109989 + 0.481459i
\(88\) 5.92508 + 12.5053i 0.631615 + 1.33306i
\(89\) −11.6706 6.73801i −1.23708 0.714227i −0.268582 0.963257i \(-0.586555\pi\)
−0.968496 + 0.249029i \(0.919888\pi\)
\(90\) −12.0054 + 11.6696i −1.26548 + 1.23008i
\(91\) 1.93326 2.89062i 0.202661 0.303019i
\(92\) 4.05215 + 5.39671i 0.422466 + 0.562646i
\(93\) 1.46751 + 0.452352i 0.152174 + 0.0469067i
\(94\) −2.30903 + 2.60536i −0.238158 + 0.268722i
\(95\) 11.7974i 1.21039i
\(96\) 6.91349 6.94289i 0.705605 0.708605i
\(97\) −1.88401 + 1.08773i −0.191292 + 0.110442i −0.592587 0.805506i \(-0.701893\pi\)
0.401295 + 0.915949i \(0.368560\pi\)
\(98\) −7.48246 + 6.48173i −0.755842 + 0.654754i
\(99\) −6.37343 13.2213i −0.640553 1.32879i
\(100\) −19.4502 8.29569i −1.94502 0.829569i
\(101\) −0.618126 0.356875i −0.0615058 0.0355104i 0.468932 0.883234i \(-0.344639\pi\)
−0.530438 + 0.847724i \(0.677972\pi\)
\(102\) −2.27958 + 4.16702i −0.225712 + 0.412596i
\(103\) 0.582342 + 1.00865i 0.0573798 + 0.0993848i 0.893288 0.449484i \(-0.148392\pi\)
−0.835909 + 0.548869i \(0.815059\pi\)
\(104\) 1.59180 + 3.35961i 0.156089 + 0.329436i
\(105\) 2.85809 + 17.8566i 0.278921 + 1.74263i
\(106\) 17.5810 + 3.59267i 1.70762 + 0.348951i
\(107\) 10.5529 + 6.09270i 1.02018 + 0.589004i 0.914157 0.405360i \(-0.132854\pi\)
0.106027 + 0.994363i \(0.466187\pi\)
\(108\) −7.28324 + 7.41312i −0.700830 + 0.713328i
\(109\) −4.74875 8.22508i −0.454848 0.787820i 0.543832 0.839194i \(-0.316973\pi\)
−0.998679 + 0.0513747i \(0.983640\pi\)
\(110\) 18.1096 20.4337i 1.72669 1.94828i
\(111\) −0.602242 + 0.559018i −0.0571622 + 0.0530596i
\(112\) −1.84276 10.4213i −0.174125 0.984724i
\(113\) −6.24802 + 10.8219i −0.587764 + 1.01804i 0.406761 + 0.913535i \(0.366658\pi\)
−0.994525 + 0.104502i \(0.966675\pi\)
\(114\) −0.168563 7.32091i −0.0157874 0.685666i
\(115\) 6.65794 11.5319i 0.620856 1.07535i
\(116\) −4.25350 + 3.19377i −0.394927 + 0.296534i
\(117\) −1.71226 3.55198i −0.158298 0.328381i
\(118\) 6.56115 7.40317i 0.604003 0.681517i
\(119\) 2.26711 + 4.60227i 0.207825 + 0.421889i
\(120\) −17.9525 7.17311i −1.63883 0.654812i
\(121\) 6.46799 + 11.2029i 0.587999 + 1.01844i
\(122\) 2.50983 + 2.22437i 0.227229 + 0.201385i
\(123\) 11.9602 + 12.8849i 1.07841 + 1.16180i
\(124\) 0.213067 + 1.76036i 0.0191340 + 0.158085i
\(125\) 21.9911i 1.96695i
\(126\) 2.02873 + 11.0401i 0.180734 + 0.983532i
\(127\) 6.01418i 0.533672i −0.963742 0.266836i \(-0.914022\pi\)
0.963742 0.266836i \(-0.0859782\pi\)
\(128\) 10.5732 + 4.02598i 0.934543 + 0.355850i
\(129\) −4.50489 + 1.02914i −0.396633 + 0.0906106i
\(130\) 4.86525 5.48963i 0.426711 0.481473i
\(131\) −0.999291 1.73082i −0.0873085 0.151223i 0.819064 0.573702i \(-0.194493\pi\)
−0.906373 + 0.422479i \(0.861160\pi\)
\(132\) 10.9460 12.9389i 0.952729 1.12619i
\(133\) −6.57467 4.39718i −0.570097 0.381284i
\(134\) −1.47622 1.30832i −0.127526 0.113021i
\(135\) 19.0921 + 7.48018i 1.64319 + 0.643791i
\(136\) −5.46655 0.444445i −0.468753 0.0381109i
\(137\) −5.03081 + 8.71362i −0.429811 + 0.744455i −0.996856 0.0792320i \(-0.974753\pi\)
0.567045 + 0.823687i \(0.308087\pi\)
\(138\) 3.96683 7.25127i 0.337679 0.617269i
\(139\) −8.02010 + 13.8912i −0.680256 + 1.17824i 0.294647 + 0.955606i \(0.404798\pi\)
−0.974903 + 0.222631i \(0.928535\pi\)
\(140\) −17.4875 + 11.4115i −1.47797 + 0.964446i
\(141\) 4.07454 + 1.25596i 0.343138 + 0.105771i
\(142\) 2.28117 + 2.02171i 0.191431 + 0.169658i
\(143\) 3.21527 + 5.56901i 0.268874 + 0.465704i
\(144\) −11.2429 4.19478i −0.936912 0.349565i
\(145\) 9.08903 + 5.24755i 0.754803 + 0.435785i
\(146\) 1.29769 6.35036i 0.107398 0.525560i
\(147\) 11.0167 + 5.06278i 0.908644 + 0.417571i
\(148\) −0.872754 0.372238i −0.0717400 0.0305978i
\(149\) −4.84527 8.39226i −0.396940 0.687521i 0.596406 0.802683i \(-0.296595\pi\)
−0.993347 + 0.115162i \(0.963261\pi\)
\(150\) 0.596134 + 25.8909i 0.0486741 + 2.11398i
\(151\) −14.3307 8.27382i −1.16621 0.673314i −0.213428 0.976959i \(-0.568463\pi\)
−0.952785 + 0.303645i \(0.901796\pi\)
\(152\) 7.64138 3.62054i 0.619797 0.293664i
\(153\) 5.80119 + 0.432456i 0.468998 + 0.0349620i
\(154\) −4.63777 17.7086i −0.373723 1.42700i
\(155\) 3.03000 1.74937i 0.243375 0.140513i
\(156\) 2.94071 3.47612i 0.235445 0.278312i
\(157\) 13.0987i 1.04539i −0.852519 0.522696i \(-0.824926\pi\)
0.852519 0.522696i \(-0.175074\pi\)
\(158\) 10.6414 + 9.43106i 0.846583 + 0.750295i
\(159\) −4.89458 21.4252i −0.388165 1.69913i
\(160\) −0.877652 22.3060i −0.0693845 1.76344i
\(161\) −3.94512 8.00867i −0.310919 0.631172i
\(162\) 11.9546 + 4.36905i 0.939238 + 0.343265i
\(163\) −6.95666 4.01643i −0.544888 0.314591i 0.202170 0.979350i \(-0.435201\pi\)
−0.747057 + 0.664759i \(0.768534\pi\)
\(164\) −7.96403 + 18.6726i −0.621886 + 1.45808i
\(165\) −31.9564 9.85040i −2.48780 0.766853i
\(166\) −3.59240 0.734105i −0.278824 0.0569776i
\(167\) 4.83680 8.37758i 0.374283 0.648277i −0.615937 0.787796i \(-0.711222\pi\)
0.990219 + 0.139519i \(0.0445556\pi\)
\(168\) −10.6889 + 7.33129i −0.824665 + 0.565621i
\(169\) −5.63620 9.76219i −0.433554 0.750937i
\(170\) 3.42494 + 10.2654i 0.262681 + 0.787323i
\(171\) −8.07893 + 3.89450i −0.617811 + 0.297820i
\(172\) −3.20382 4.26689i −0.244289 0.325348i
\(173\) 16.3879i 1.24595i 0.782242 + 0.622974i \(0.214076\pi\)
−0.782242 + 0.622974i \(0.785924\pi\)
\(174\) 5.71520 + 3.12652i 0.433268 + 0.237021i
\(175\) 23.2517 + 15.5509i 1.75767 + 1.17554i
\(176\) 18.7930 + 5.45895i 1.41657 + 0.411484i
\(177\) −11.5779 3.56882i −0.870245 0.268249i
\(178\) −18.0783 + 6.03161i −1.35503 + 0.452088i
\(179\) −16.0572 + 9.27065i −1.20017 + 0.692921i −0.960594 0.277955i \(-0.910343\pi\)
−0.239581 + 0.970876i \(0.577010\pi\)
\(180\) 1.08976 + 23.6523i 0.0812258 + 1.76294i
\(181\) 23.0045i 1.70991i 0.518700 + 0.854956i \(0.326416\pi\)
−0.518700 + 0.854956i \(0.673584\pi\)
\(182\) −1.24596 4.75752i −0.0923570 0.352651i
\(183\) 1.20990 3.92514i 0.0894386 0.290154i
\(184\) 9.51266 + 0.773405i 0.701283 + 0.0570162i
\(185\) 1.87213i 0.137642i
\(186\) 1.85528 1.12887i 0.136036 0.0827728i
\(187\) −9.48691 −0.693751
\(188\) 0.591581 + 4.88764i 0.0431455 + 0.356468i
\(189\) 11.2848 7.85197i 0.820848 0.571147i
\(190\) −12.4861 11.0660i −0.905836 0.802808i
\(191\) 3.94412i 0.285386i −0.989767 0.142693i \(-0.954424\pi\)
0.989767 0.142693i \(-0.0455762\pi\)
\(192\) −0.863340 13.8295i −0.0623062 0.998057i
\(193\) 5.75001 0.413895 0.206947 0.978352i \(-0.433647\pi\)
0.206947 + 0.978352i \(0.433647\pi\)
\(194\) −0.615966 + 3.01427i −0.0442238 + 0.216412i
\(195\) −8.58527 2.64637i −0.614804 0.189510i
\(196\) −0.158427 + 13.9991i −0.0113162 + 0.999936i
\(197\) −16.6012 −1.18279 −0.591393 0.806384i \(-0.701422\pi\)
−0.591393 + 0.806384i \(0.701422\pi\)
\(198\) −19.9714 5.65609i −1.41930 0.401961i
\(199\) −6.23391 10.7974i −0.441910 0.765411i 0.555921 0.831235i \(-0.312366\pi\)
−0.997831 + 0.0658244i \(0.979032\pi\)
\(200\) −27.0242 + 12.8043i −1.91090 + 0.905397i
\(201\) −0.711636 + 2.30867i −0.0501949 + 0.162841i
\(202\) −0.957509 + 0.319461i −0.0673701 + 0.0224772i
\(203\) 6.31215 3.10941i 0.443026 0.218238i
\(204\) 2.27203 + 6.32131i 0.159074 + 0.442580i
\(205\) 40.0542 2.79751
\(206\) 1.61376 + 0.329771i 0.112436 + 0.0229763i
\(207\) −10.0950 0.752541i −0.701650 0.0523052i
\(208\) 5.04883 + 1.46658i 0.350074 + 0.101689i
\(209\) 12.6666 7.31308i 0.876169 0.505856i
\(210\) 21.5799 + 13.7245i 1.48915 + 0.947082i
\(211\) −19.4166 11.2102i −1.33669 0.771739i −0.350376 0.936609i \(-0.613946\pi\)
−0.986315 + 0.164870i \(0.947279\pi\)
\(212\) 20.2933 15.2374i 1.39375 1.04651i
\(213\) 1.09967 3.56754i 0.0753485 0.244444i
\(214\) 16.3469 5.45396i 1.11745 0.372825i
\(215\) −5.26408 + 9.11765i −0.359007 + 0.621819i
\(216\) 1.01420 + 14.6619i 0.0690075 + 0.997616i
\(217\) 0.154433 2.34065i 0.0104836 0.158893i
\(218\) −13.1595 2.68915i −0.891277 0.182132i
\(219\) −7.73893 + 1.76795i −0.522948 + 0.119467i
\(220\) −4.63974 38.3336i −0.312811 2.58445i
\(221\) −2.54871 −0.171445
\(222\) 0.0267493 + 1.16176i 0.00179529 + 0.0779719i
\(223\) −4.48502 7.76829i −0.300339 0.520203i 0.675873 0.737018i \(-0.263767\pi\)
−0.976213 + 0.216815i \(0.930433\pi\)
\(224\) −12.7582 7.82486i −0.852443 0.522820i
\(225\) 28.5716 13.7732i 1.90478 0.918210i
\(226\) 5.59299 + 16.7637i 0.372040 + 1.11510i
\(227\) 3.89688 6.74960i 0.258645 0.447987i −0.707234 0.706980i \(-0.750057\pi\)
0.965879 + 0.258993i \(0.0833906\pi\)
\(228\) −7.90639 6.68860i −0.523613 0.442963i
\(229\) −5.88977 + 3.40046i −0.389207 + 0.224709i −0.681816 0.731523i \(-0.738810\pi\)
0.292610 + 0.956232i \(0.405476\pi\)
\(230\) −5.95993 17.8635i −0.392986 1.17788i
\(231\) −17.4005 + 14.1378i −1.14487 + 0.930197i
\(232\) −0.609571 + 7.49755i −0.0400203 + 0.492238i
\(233\) 8.45700 14.6480i 0.554037 0.959619i −0.443941 0.896056i \(-0.646420\pi\)
0.997978 0.0635635i \(-0.0202466\pi\)
\(234\) −5.36542 1.51954i −0.350749 0.0993355i
\(235\) 8.41279 4.85713i 0.548790 0.316844i
\(236\) −1.68099 13.8883i −0.109423 0.904052i
\(237\) 5.12985 16.6421i 0.333220 1.08102i
\(238\) 6.99747 + 1.91747i 0.453579 + 0.124291i
\(239\) 16.8495 + 9.72804i 1.08990 + 0.629254i 0.933550 0.358447i \(-0.116694\pi\)
0.156351 + 0.987702i \(0.450027\pi\)
\(240\) −24.4312 + 12.2721i −1.57703 + 0.792160i
\(241\) −20.4013 11.7787i −1.31417 0.758734i −0.331382 0.943497i \(-0.607515\pi\)
−0.982783 + 0.184763i \(0.940848\pi\)
\(242\) 17.9238 + 3.66273i 1.15219 + 0.235449i
\(243\) −1.18014 15.5437i −0.0757058 0.997130i
\(244\) 4.70843 0.569889i 0.301426 0.0364834i
\(245\) 25.5300 10.5490i 1.63105 0.673948i
\(246\) 24.8557 0.572300i 1.58474 0.0364885i
\(247\) 3.40296 1.96470i 0.216525 0.125011i
\(248\) 2.06298 + 1.42571i 0.130999 + 0.0905328i
\(249\) 1.00013 + 4.37791i 0.0633807 + 0.277439i
\(250\) 23.2749 + 20.6276i 1.47203 + 1.30461i
\(251\) 4.53190 0.286051 0.143026 0.989719i \(-0.454317\pi\)
0.143026 + 0.989719i \(0.454317\pi\)
\(252\) 13.5875 + 8.20845i 0.855935 + 0.517084i
\(253\) 16.5087 1.03789
\(254\) −6.36526 5.64129i −0.399392 0.353966i
\(255\) 9.71399 9.01680i 0.608313 0.564654i
\(256\) 14.1786 7.41400i 0.886162 0.463375i
\(257\) 20.6842 11.9420i 1.29025 0.744924i 0.311549 0.950230i \(-0.399152\pi\)
0.978698 + 0.205306i \(0.0658189\pi\)
\(258\) −3.13636 + 5.73319i −0.195261 + 0.356933i
\(259\) 1.04334 + 0.697789i 0.0648297 + 0.0433585i
\(260\) −1.24649 10.2985i −0.0773042 0.638688i
\(261\) 0.593127 7.95651i 0.0367136 0.492496i
\(262\) −2.76919 0.565884i −0.171081 0.0349604i
\(263\) 23.5572 + 13.6008i 1.45260 + 0.838660i 0.998628 0.0523561i \(-0.0166731\pi\)
0.453972 + 0.891016i \(0.350006\pi\)
\(264\) −3.42692 23.7217i −0.210912 1.45997i
\(265\) −43.3635 25.0359i −2.66380 1.53794i
\(266\) −10.8209 + 2.83393i −0.663472 + 0.173759i
\(267\) 15.8794 + 17.1072i 0.971801 + 1.04694i
\(268\) −2.76938 + 0.335195i −0.169167 + 0.0204753i
\(269\) 15.8637 9.15891i 0.967227 0.558429i 0.0688372 0.997628i \(-0.478071\pi\)
0.898390 + 0.439199i \(0.144738\pi\)
\(270\) 25.8252 13.1903i 1.57167 0.802734i
\(271\) −0.772505 + 1.33802i −0.0469264 + 0.0812788i −0.888535 0.458810i \(-0.848276\pi\)
0.841608 + 0.540089i \(0.181609\pi\)
\(272\) −5.59801 + 5.36878i −0.339429 + 0.325530i
\(273\) −4.67475 + 3.79819i −0.282929 + 0.229877i
\(274\) 4.50339 + 13.4978i 0.272060 + 0.815435i
\(275\) −44.7963 + 25.8632i −2.70132 + 1.55961i
\(276\) −3.95369 11.0001i −0.237984 0.662127i
\(277\) −0.243046 + 0.420968i −0.0146032 + 0.0252935i −0.873235 0.487300i \(-0.837982\pi\)
0.858631 + 0.512593i \(0.171315\pi\)
\(278\) 7.17929 + 21.5182i 0.430585 + 1.29058i
\(279\) −2.19823 1.49747i −0.131604 0.0896510i
\(280\) −4.32564 + 29.2123i −0.258506 + 1.74577i
\(281\) −13.1672 22.8062i −0.785489 1.36051i −0.928707 0.370815i \(-0.879078\pi\)
0.143218 0.989691i \(-0.454255\pi\)
\(282\) 5.15118 3.13431i 0.306748 0.186645i
\(283\) 17.1770 1.02107 0.510533 0.859858i \(-0.329448\pi\)
0.510533 + 0.859858i \(0.329448\pi\)
\(284\) 4.27947 0.517969i 0.253940 0.0307358i
\(285\) −6.01912 + 19.5271i −0.356542 + 1.15668i
\(286\) 8.91002 + 1.82076i 0.526860 + 0.107664i
\(287\) 14.9292 22.3221i 0.881241 1.31763i
\(288\) −14.9855 + 7.96456i −0.883030 + 0.469316i
\(289\) −6.61996 + 11.4661i −0.389409 + 0.674476i
\(290\) 14.0794 4.69741i 0.826769 0.275841i
\(291\) 3.67337 0.839180i 0.215337 0.0491936i
\(292\) −5.50383 7.33008i −0.322087 0.428960i
\(293\) 21.5170 + 12.4229i 1.25704 + 0.725751i 0.972498 0.232913i \(-0.0748258\pi\)
0.284540 + 0.958664i \(0.408159\pi\)
\(294\) 15.6920 6.91096i 0.915176 0.403055i
\(295\) −23.9051 + 13.8016i −1.39181 + 0.803561i
\(296\) −1.21261 + 0.574543i −0.0704815 + 0.0333946i
\(297\) 3.80369 + 25.1357i 0.220712 + 1.45852i
\(298\) −13.4270 2.74381i −0.777807 0.158944i
\(299\) 4.43516 0.256492
\(300\) 27.9614 + 23.6546i 1.61435 + 1.36570i
\(301\) 3.11920 + 6.33203i 0.179788 + 0.364972i
\(302\) −22.1990 + 7.40641i −1.27741 + 0.426191i
\(303\) 0.841042 + 0.906072i 0.0483166 + 0.0520525i
\(304\) 3.33571 11.4835i 0.191316 0.658624i
\(305\) −4.67903 8.10432i −0.267921 0.464052i
\(306\) 5.89921 5.73419i 0.337235 0.327802i
\(307\) −32.0881 −1.83136 −0.915682 0.401904i \(-0.868348\pi\)
−0.915682 + 0.401904i \(0.868348\pi\)
\(308\) −23.0926 11.7021i −1.31582 0.666791i
\(309\) −0.449274 1.96662i −0.0255583 0.111877i
\(310\) 0.990643 4.84779i 0.0562647 0.275336i
\(311\) −13.0485 −0.739915 −0.369957 0.929049i \(-0.620628\pi\)
−0.369957 + 0.929049i \(0.620628\pi\)
\(312\) −0.920661 6.37297i −0.0521222 0.360798i
\(313\) 13.3212i 0.752960i 0.926425 + 0.376480i \(0.122866\pi\)
−0.926425 + 0.376480i \(0.877134\pi\)
\(314\) −13.8634 12.2866i −0.782355 0.693371i
\(315\) 4.37984 31.0145i 0.246776 1.74747i
\(316\) 19.9632 2.41627i 1.12302 0.135926i
\(317\) −19.6535 −1.10385 −0.551927 0.833893i \(-0.686107\pi\)
−0.551927 + 0.833893i \(0.686107\pi\)
\(318\) −27.2670 14.9165i −1.52906 0.836477i
\(319\) 13.0116i 0.728509i
\(320\) −24.4313 19.9941i −1.36575 1.11770i
\(321\) −14.3586 15.4688i −0.801417 0.863384i
\(322\) −12.1767 3.33670i −0.678581 0.185947i
\(323\) 5.79701i 0.322554i
\(324\) 15.8375 8.55424i 0.879859 0.475236i
\(325\) −12.0348 + 6.94828i −0.667569 + 0.385421i
\(326\) −10.7762 + 3.59536i −0.596840 + 0.199128i
\(327\) 3.66364 + 16.0370i 0.202600 + 0.886848i
\(328\) 12.2923 + 25.9438i 0.678731 + 1.43250i
\(329\) 0.428783 6.49880i 0.0236396 0.358291i
\(330\) −40.4005 + 24.5822i −2.22397 + 1.35321i
\(331\) 14.4064i 0.791847i −0.918283 0.395924i \(-0.870425\pi\)
0.918283 0.395924i \(-0.129575\pi\)
\(332\) −4.14662 + 3.11351i −0.227575 + 0.170876i
\(333\) 1.28205 0.618019i 0.0702557 0.0338672i
\(334\) −4.32972 12.9773i −0.236912 0.710087i
\(335\) 2.75209 + 4.76677i 0.150363 + 0.260436i
\(336\) −2.26690 + 18.1896i −0.123669 + 0.992323i
\(337\) −0.489878 + 0.848494i −0.0266854 + 0.0462204i −0.879060 0.476712i \(-0.841829\pi\)
0.852374 + 0.522932i \(0.175162\pi\)
\(338\) −15.6188 3.19170i −0.849551 0.173605i
\(339\) 15.8631 14.7246i 0.861567 0.799731i
\(340\) 14.0773 + 6.00410i 0.763448 + 0.325618i
\(341\) 3.75652 + 2.16883i 0.203427 + 0.117449i
\(342\) −3.45618 + 12.2036i −0.186889 + 0.659894i
\(343\) 3.63674 18.1597i 0.196365 0.980531i
\(344\) −7.52116 0.611491i −0.405514 0.0329694i
\(345\) −16.9039 + 15.6907i −0.910074 + 0.844757i
\(346\) 17.3445 + 15.3718i 0.932448 + 0.826394i
\(347\) 27.4334i 1.47270i 0.676600 + 0.736351i \(0.263453\pi\)
−0.676600 + 0.736351i \(0.736547\pi\)
\(348\) 8.66987 3.11616i 0.464754 0.167044i
\(349\) 13.0352 7.52589i 0.697760 0.402852i −0.108753 0.994069i \(-0.534686\pi\)
0.806512 + 0.591217i \(0.201352\pi\)
\(350\) 38.2688 10.0224i 2.04555 0.535718i
\(351\) 1.02188 + 6.75285i 0.0545441 + 0.360440i
\(352\) 23.4054 14.7695i 1.24751 0.787219i
\(353\) 16.0275 + 9.25348i 0.853058 + 0.492513i 0.861681 0.507450i \(-0.169412\pi\)
−0.00862373 + 0.999963i \(0.502745\pi\)
\(354\) −14.6372 + 8.90618i −0.777956 + 0.473358i
\(355\) −4.25275 7.36598i −0.225712 0.390945i
\(356\) −10.5737 + 24.7913i −0.560407 + 1.31394i
\(357\) −1.40441 8.77437i −0.0743292 0.464389i
\(358\) −5.24983 + 25.6904i −0.277462 + 1.35778i
\(359\) 5.04854 + 2.91478i 0.266452 + 0.153836i 0.627274 0.778799i \(-0.284171\pi\)
−0.360822 + 0.932635i \(0.617504\pi\)
\(360\) 26.0552 + 21.0324i 1.37323 + 1.10851i
\(361\) 5.03132 + 8.71450i 0.264806 + 0.458658i
\(362\) 24.3474 + 21.5782i 1.27967 + 1.13413i
\(363\) −4.99003 21.8430i −0.261909 1.14646i
\(364\) −6.20395 3.14384i −0.325175 0.164782i
\(365\) −9.04313 + 15.6632i −0.473339 + 0.819848i
\(366\) −3.01938 4.96230i −0.157826 0.259384i
\(367\) −0.903984 + 1.56575i −0.0471876 + 0.0817313i −0.888654 0.458577i \(-0.848359\pi\)
0.841467 + 0.540309i \(0.181693\pi\)
\(368\) 9.74142 9.34252i 0.507806 0.487012i
\(369\) −13.2225 27.4293i −0.688336 1.42791i
\(370\) 1.98142 + 1.75606i 0.103009 + 0.0912930i
\(371\) −30.1151 + 14.8349i −1.56350 + 0.770190i
\(372\) 0.545480 3.02246i 0.0282818 0.156707i
\(373\) 2.97957 + 5.16077i 0.154276 + 0.267214i 0.932795 0.360407i \(-0.117362\pi\)
−0.778519 + 0.627621i \(0.784029\pi\)
\(374\) −8.89870 + 10.0407i −0.460141 + 0.519193i
\(375\) 11.2200 36.3997i 0.579400 1.87967i
\(376\) 5.72787 + 3.95849i 0.295392 + 0.204143i
\(377\) 3.49564i 0.180034i
\(378\) 2.27478 19.3087i 0.117002 0.993132i
\(379\) 16.5311i 0.849146i 0.905394 + 0.424573i \(0.139576\pi\)
−0.905394 + 0.424573i \(0.860424\pi\)
\(380\) −23.4239 + 2.83513i −1.20162 + 0.145439i
\(381\) −3.06848 + 9.95467i −0.157203 + 0.509993i
\(382\) −4.17436 3.69957i −0.213579 0.189287i
\(383\) −1.64900 2.85616i −0.0842601 0.145943i 0.820816 0.571193i \(-0.193519\pi\)
−0.905076 + 0.425250i \(0.860186\pi\)
\(384\) −15.4466 12.0583i −0.788256 0.615347i
\(385\) −3.36293 + 50.9698i −0.171391 + 2.59766i
\(386\) 5.39350 6.08567i 0.274522 0.309753i
\(387\) 7.98157 + 0.594994i 0.405726 + 0.0302453i
\(388\) 2.61246 + 3.47931i 0.132628 + 0.176635i
\(389\) −4.82441 + 8.35612i −0.244607 + 0.423672i −0.962021 0.272975i \(-0.911992\pi\)
0.717414 + 0.696647i \(0.245326\pi\)
\(390\) −10.8538 + 6.60416i −0.549604 + 0.334414i
\(391\) −3.27157 + 5.66653i −0.165451 + 0.286569i
\(392\) 14.6677 + 13.2988i 0.740831 + 0.671691i
\(393\) 0.770949 + 3.37470i 0.0388892 + 0.170231i
\(394\) −15.5719 + 17.5703i −0.784500 + 0.885178i
\(395\) −19.8386 34.3614i −0.998186 1.72891i
\(396\) −24.7194 + 15.8318i −1.24220 + 0.795579i
\(397\) −3.22184 1.86013i −0.161700 0.0933573i 0.416967 0.908922i \(-0.363093\pi\)
−0.578666 + 0.815565i \(0.696427\pi\)
\(398\) −17.2751 3.53017i −0.865925 0.176951i
\(399\) 8.63893 + 10.6327i 0.432488 + 0.532299i
\(400\) −11.7969 + 40.6121i −0.589847 + 2.03061i
\(401\) 11.9860 + 20.7604i 0.598553 + 1.03672i 0.993035 + 0.117821i \(0.0375908\pi\)
−0.394482 + 0.918904i \(0.629076\pi\)
\(402\) 1.77593 + 2.91871i 0.0885752 + 0.145572i
\(403\) 1.00921 + 0.582668i 0.0502724 + 0.0290248i
\(404\) −0.560032 + 1.31306i −0.0278626 + 0.0653271i
\(405\) −27.7849 22.1221i −1.38064 1.09926i
\(406\) 2.62987 9.59725i 0.130518 0.476303i
\(407\) −2.01007 + 1.16051i −0.0996353 + 0.0575245i
\(408\) 8.82148 + 3.52472i 0.436728 + 0.174500i
\(409\) 22.1550i 1.09549i 0.836644 + 0.547747i \(0.184514\pi\)
−0.836644 + 0.547747i \(0.815486\pi\)
\(410\) 37.5708 42.3924i 1.85549 2.09361i
\(411\) 12.7728 11.8560i 0.630033 0.584815i
\(412\) 1.86273 1.39864i 0.0917700 0.0689061i
\(413\) −1.21839 + 18.4665i −0.0599532 + 0.908675i
\(414\) −10.2656 + 9.97840i −0.504524 + 0.490412i
\(415\) 8.86064 + 5.11570i 0.434952 + 0.251120i
\(416\) 6.28799 3.96792i 0.308294 0.194543i
\(417\) 20.3623 18.9008i 0.997144 0.925578i
\(418\) 4.14129 20.2657i 0.202557 0.991228i
\(419\) 17.6835 30.6287i 0.863895 1.49631i −0.00424524 0.999991i \(-0.501351\pi\)
0.868140 0.496319i \(-0.165315\pi\)
\(420\) 34.7676 9.96603i 1.69648 0.486293i
\(421\) −15.4856 26.8219i −0.754723 1.30722i −0.945512 0.325588i \(-0.894438\pi\)
0.190788 0.981631i \(-0.438896\pi\)
\(422\) −30.0773 + 10.0349i −1.46414 + 0.488492i
\(423\) −6.10338 4.15772i −0.296756 0.202155i
\(424\) 2.90825 35.7706i 0.141237 1.73717i
\(425\) 20.5015i 0.994467i
\(426\) −2.74430 4.51021i −0.132962 0.218520i
\(427\) −6.26051 0.413061i −0.302967 0.0199894i
\(428\) 9.56107 22.4170i 0.462152 1.08357i
\(429\) −2.48057 10.8583i −0.119763 0.524242i
\(430\) 4.71220 + 14.1237i 0.227243 + 0.681106i
\(431\) −4.22345 + 2.43841i −0.203437 + 0.117454i −0.598257 0.801304i \(-0.704140\pi\)
0.394821 + 0.918758i \(0.370807\pi\)
\(432\) 16.4691 + 12.6794i 0.792371 + 0.610040i
\(433\) 13.0744i 0.628314i 0.949371 + 0.314157i \(0.101722\pi\)
−0.949371 + 0.314157i \(0.898278\pi\)
\(434\) −2.33243 2.35897i −0.111960 0.113234i
\(435\) −12.3668 13.3230i −0.592944 0.638791i
\(436\) −15.1898 + 11.4053i −0.727458 + 0.546216i
\(437\) 10.0877i 0.482560i
\(438\) −5.38794 + 9.84903i −0.257446 + 0.470605i
\(439\) −1.91733 −0.0915094 −0.0457547 0.998953i \(-0.514569\pi\)
−0.0457547 + 0.998953i \(0.514569\pi\)
\(440\) −44.9234 31.0463i −2.14164 1.48007i
\(441\) −15.6518 14.0007i −0.745325 0.666701i
\(442\) −2.39069 + 2.69749i −0.113713 + 0.128307i
\(443\) 21.2905i 1.01154i −0.862668 0.505770i \(-0.831208\pi\)
0.862668 0.505770i \(-0.168792\pi\)
\(444\) 1.25466 + 1.06141i 0.0595438 + 0.0503725i
\(445\) 53.1794 2.52095
\(446\) −12.4287 2.53980i −0.588516 0.120263i
\(447\) 3.73811 + 16.3630i 0.176806 + 0.773942i
\(448\) −20.2488 + 6.16326i −0.956666 + 0.291187i
\(449\) 5.99969 0.283143 0.141572 0.989928i \(-0.454784\pi\)
0.141572 + 0.989928i \(0.454784\pi\)
\(450\) 12.2230 43.1587i 0.576197 2.03452i
\(451\) 24.8291 + 43.0053i 1.16916 + 2.02504i
\(452\) 22.9885 + 9.80480i 1.08129 + 0.461179i
\(453\) 19.4988 + 21.0064i 0.916133 + 0.986969i
\(454\) −3.48834 10.4555i −0.163716 0.490700i
\(455\) −0.903469 + 13.6933i −0.0423553 + 0.641953i
\(456\) −14.4952 + 2.09403i −0.678801 + 0.0980620i
\(457\) −25.3351 −1.18513 −0.592563 0.805524i \(-0.701884\pi\)
−0.592563 + 0.805524i \(0.701884\pi\)
\(458\) −1.92563 + 9.42321i −0.0899788 + 0.440318i
\(459\) −9.38149 3.67561i −0.437890 0.171563i
\(460\) −24.4967 10.4481i −1.14216 0.487144i
\(461\) −17.3693 + 10.0282i −0.808970 + 0.467059i −0.846598 0.532233i \(-0.821353\pi\)
0.0376278 + 0.999292i \(0.488020\pi\)
\(462\) −1.35861 + 31.6775i −0.0632082 + 1.47377i
\(463\) 33.2880 + 19.2188i 1.54702 + 0.893175i 0.998367 + 0.0571279i \(0.0181943\pi\)
0.548658 + 0.836047i \(0.315139\pi\)
\(464\) 7.36344 + 7.67784i 0.341839 + 0.356435i
\(465\) −5.90780 + 1.34963i −0.273968 + 0.0625877i
\(466\) −7.57039 22.6904i −0.350691 1.05111i
\(467\) 16.3595 28.3355i 0.757028 1.31121i −0.187332 0.982297i \(-0.559984\pi\)
0.944360 0.328914i \(-0.106683\pi\)
\(468\) −6.64100 + 4.25331i −0.306981 + 0.196609i
\(469\) 3.68228 + 0.242952i 0.170032 + 0.0112185i
\(470\) 2.75052 13.4599i 0.126872 0.620858i
\(471\) −6.68306 + 21.6810i −0.307939 + 0.999008i
\(472\) −16.2758 11.2481i −0.749155 0.517736i
\(473\) −13.0526 −0.600158
\(474\) −12.8018 21.0396i −0.588008 0.966381i
\(475\) 15.8038 + 27.3729i 0.725126 + 1.25596i
\(476\) 8.59301 5.60737i 0.393860 0.257013i
\(477\) −2.82979 + 37.9603i −0.129567 + 1.73808i
\(478\) 26.1007 8.70817i 1.19382 0.398302i
\(479\) −18.3983 + 31.8668i −0.840639 + 1.45603i 0.0487157 + 0.998813i \(0.484487\pi\)
−0.889355 + 0.457217i \(0.848846\pi\)
\(480\) −9.92797 + 37.3686i −0.453148 + 1.70564i
\(481\) −0.540016 + 0.311778i −0.0246226 + 0.0142159i
\(482\) −31.6027 + 10.5439i −1.43946 + 0.480259i
\(483\) 2.44389 + 15.2688i 0.111201 + 0.694754i
\(484\) 20.6891 15.5345i 0.940412 0.706114i
\(485\) 4.29243 7.43471i 0.194909 0.337593i
\(486\) −17.5581 13.3310i −0.796450 0.604705i
\(487\) 3.93075 2.26942i 0.178119 0.102837i −0.408289 0.912853i \(-0.633875\pi\)
0.586409 + 0.810015i \(0.300541\pi\)
\(488\) 3.81334 5.51784i 0.172622 0.249781i
\(489\) 9.46546 + 10.1973i 0.428043 + 0.461139i
\(490\) 12.7824 36.9153i 0.577448 1.66766i
\(491\) 10.6660 + 6.15804i 0.481351 + 0.277908i 0.720980 0.692956i \(-0.243692\pi\)
−0.239628 + 0.970865i \(0.577025\pi\)
\(492\) 22.7089 26.8435i 1.02380 1.21020i
\(493\) −4.46616 2.57854i −0.201146 0.116132i
\(494\) 1.11258 5.44449i 0.0500574 0.244959i
\(495\) 47.8685 + 32.6088i 2.15153 + 1.46566i
\(496\) 3.44401 0.846093i 0.154641 0.0379907i
\(497\) −5.69015 0.375429i −0.255238 0.0168403i
\(498\) 5.57159 + 3.04796i 0.249669 + 0.136582i
\(499\) 11.2164 6.47580i 0.502115 0.289896i −0.227471 0.973785i \(-0.573046\pi\)
0.729587 + 0.683888i \(0.239712\pi\)
\(500\) 43.6636 5.28487i 1.95270 0.236346i
\(501\) −12.2802 + 11.3988i −0.548638 + 0.509261i
\(502\) 4.25092 4.79645i 0.189728 0.214076i
\(503\) −20.4872 −0.913480 −0.456740 0.889600i \(-0.650983\pi\)
−0.456740 + 0.889600i \(0.650983\pi\)
\(504\) 21.4327 6.68121i 0.954689 0.297605i
\(505\) 2.81662 0.125338
\(506\) 15.4852 17.4724i 0.688399 0.776744i
\(507\) 4.34831 + 19.0340i 0.193115 + 0.845330i
\(508\) −11.9412 + 1.44532i −0.529806 + 0.0641255i
\(509\) −24.6392 + 14.2255i −1.09211 + 0.630533i −0.934139 0.356910i \(-0.883830\pi\)
−0.157976 + 0.987443i \(0.550497\pi\)
\(510\) −0.431458 18.7388i −0.0191053 0.829768i
\(511\) 5.35846 + 10.8778i 0.237044 + 0.481204i
\(512\) 5.45270 21.9606i 0.240977 0.970531i
\(513\) 15.3593 2.32426i 0.678128 0.102618i
\(514\) 6.76260 33.0933i 0.298286 1.45968i
\(515\) −3.98034 2.29805i −0.175395 0.101264i
\(516\) 3.12597 + 8.69718i 0.137613 + 0.382872i
\(517\) 10.4300 + 6.02176i 0.458710 + 0.264837i
\(518\) 1.71717 0.449716i 0.0754481 0.0197594i
\(519\) 8.36122 27.1252i 0.367017 1.19067i
\(520\) −12.0689 8.34075i −0.529257 0.365766i
\(521\) 32.0751 18.5186i 1.40524 0.811314i 0.410314 0.911944i \(-0.365419\pi\)
0.994924 + 0.100630i \(0.0320858\pi\)
\(522\) −7.86463 8.09095i −0.344225 0.354131i
\(523\) −2.33168 + 4.03859i −0.101957 + 0.176595i −0.912491 0.409097i \(-0.865844\pi\)
0.810534 + 0.585692i \(0.199177\pi\)
\(524\) −3.19642 + 2.40005i −0.139636 + 0.104847i
\(525\) −30.5521 37.6031i −1.33340 1.64113i
\(526\) 36.4914 12.1749i 1.59110 0.530851i
\(527\) −1.48888 + 0.859605i −0.0648566 + 0.0374450i
\(528\) −28.3209 18.6240i −1.23251 0.810504i
\(529\) −5.80694 + 10.0579i −0.252476 + 0.437301i
\(530\) −67.1723 + 22.4112i −2.91778 + 0.973481i
\(531\) 17.3428 + 11.8142i 0.752615 + 0.512693i
\(532\) −7.15063 + 14.1108i −0.310019 + 0.611781i
\(533\) 6.67049 + 11.5536i 0.288931 + 0.500443i
\(534\) 33.0006 0.759835i 1.42808 0.0328813i
\(535\) −48.0864 −2.07895
\(536\) −2.24292 + 3.24546i −0.0968792 + 0.140183i
\(537\) 31.3079 7.15227i 1.35104 0.308643i
\(538\) 5.18656 25.3808i 0.223608 1.09424i
\(539\) 27.1520 + 20.8718i 1.16952 + 0.899014i
\(540\) 10.2638 39.7052i 0.441683 1.70864i
\(541\) 11.6836 20.2366i 0.502318 0.870040i −0.497678 0.867362i \(-0.665814\pi\)
0.999996 0.00267870i \(-0.000852658\pi\)
\(542\) 0.691517 + 2.07266i 0.0297032 + 0.0890284i
\(543\) 11.7371 38.0771i 0.503686 1.63404i
\(544\) 0.431260 + 10.9607i 0.0184901 + 0.469936i
\(545\) 32.4580 + 18.7396i 1.39035 + 0.802718i
\(546\) −0.364998 + 8.51034i −0.0156205 + 0.364209i
\(547\) −21.8092 + 12.5915i −0.932493 + 0.538375i −0.887599 0.460617i \(-0.847628\pi\)
−0.0448939 + 0.998992i \(0.514295\pi\)
\(548\) 18.5100 + 7.89468i 0.790707 + 0.337244i
\(549\) −4.00526 + 5.87959i −0.170940 + 0.250935i
\(550\) −14.6459 + 71.6709i −0.624504 + 3.05606i
\(551\) 7.95077 0.338714
\(552\) −15.3508 6.13357i −0.653372 0.261062i
\(553\) −26.5439 1.75133i −1.12876 0.0744742i
\(554\) 0.217566 + 0.652102i 0.00924348 + 0.0277051i
\(555\) 0.955174 3.09875i 0.0405449 0.131535i
\(556\) 29.5085 + 12.5857i 1.25144 + 0.533751i
\(557\) −3.17042 5.49134i −0.134335 0.232675i 0.791008 0.611806i \(-0.209557\pi\)
−0.925343 + 0.379130i \(0.876223\pi\)
\(558\) −3.64682 + 0.921930i −0.154382 + 0.0390284i
\(559\) −3.50664 −0.148315
\(560\) 26.8602 + 31.9793i 1.13505 + 1.35137i
\(561\) 15.7027 + 4.84029i 0.662970 + 0.204357i
\(562\) −36.4884 7.45638i −1.53917 0.314529i
\(563\) −1.28515 −0.0541628 −0.0270814 0.999633i \(-0.508621\pi\)
−0.0270814 + 0.999633i \(0.508621\pi\)
\(564\) 1.51453 8.39186i 0.0637730 0.353361i
\(565\) 49.3122i 2.07458i
\(566\) 16.1120 18.1797i 0.677237 0.764149i
\(567\) −22.6847 + 7.23900i −0.952669 + 0.304010i
\(568\) 3.46593 5.01514i 0.145427 0.210430i
\(569\) −19.8770 −0.833286 −0.416643 0.909070i \(-0.636793\pi\)
−0.416643 + 0.909070i \(0.636793\pi\)
\(570\) 15.0211 + 24.6869i 0.629163 + 1.03402i
\(571\) 14.3467i 0.600391i −0.953878 0.300196i \(-0.902948\pi\)
0.953878 0.300196i \(-0.0970519\pi\)
\(572\) 10.2846 7.72227i 0.430022 0.322885i
\(573\) −2.01232 + 6.52830i −0.0840657 + 0.272724i
\(574\) −9.62167 36.7388i −0.401601 1.53345i
\(575\) 35.6758i 1.48778i
\(576\) −5.62690 + 23.3311i −0.234454 + 0.972127i
\(577\) 10.9881 6.34398i 0.457440 0.264103i −0.253527 0.967328i \(-0.581591\pi\)
0.710967 + 0.703225i \(0.248257\pi\)
\(578\) 5.92593 + 17.7616i 0.246486 + 0.738784i
\(579\) −9.51742 2.93370i −0.395531 0.121920i
\(580\) 8.23481 19.3074i 0.341932 0.801697i
\(581\) 6.15354 3.03128i 0.255292 0.125759i
\(582\) 2.55745 4.67496i 0.106010 0.193783i
\(583\) 62.0779i 2.57101i
\(584\) −12.9206 1.05048i −0.534657 0.0434690i
\(585\) 12.8602 + 8.76053i 0.531702 + 0.362203i
\(586\) 33.3310 11.1205i 1.37689 0.459382i
\(587\) 12.4489 + 21.5622i 0.513823 + 0.889967i 0.999871 + 0.0160352i \(0.00510440\pi\)
−0.486049 + 0.873932i \(0.661562\pi\)
\(588\) 7.40467 23.0905i 0.305363 0.952236i
\(589\) 1.32527 2.29544i 0.0546068 0.0945818i
\(590\) −7.81565 + 38.2464i −0.321765 + 1.57458i
\(591\) 27.4783 + 8.47004i 1.13031 + 0.348411i
\(592\) −0.529344 + 1.82232i −0.0217559 + 0.0748968i
\(593\) −22.9565 13.2540i −0.942712 0.544275i −0.0519027 0.998652i \(-0.516529\pi\)
−0.890809 + 0.454377i \(0.849862\pi\)
\(594\) 30.1709 + 19.5515i 1.23793 + 0.802208i
\(595\) −16.8287 11.2551i −0.689909 0.461415i
\(596\) −15.4985 + 11.6371i −0.634843 + 0.476676i
\(597\) 4.80943 + 21.0525i 0.196837 + 0.861622i
\(598\) 4.16017 4.69406i 0.170122 0.191955i
\(599\) 24.6495i 1.00715i −0.863951 0.503576i \(-0.832017\pi\)
0.863951 0.503576i \(-0.167983\pi\)
\(600\) 51.2633 7.40567i 2.09281 0.302335i
\(601\) 0.673377 0.388774i 0.0274676 0.0158584i −0.486203 0.873846i \(-0.661619\pi\)
0.513671 + 0.857987i \(0.328285\pi\)
\(602\) 9.62747 + 2.63815i 0.392386 + 0.107523i
\(603\) 2.35580 3.45823i 0.0959356 0.140830i
\(604\) −12.9838 + 30.4420i −0.528304 + 1.23867i
\(605\) −44.2091 25.5241i −1.79736 1.03770i
\(606\) 1.74786 0.0402443i 0.0710020 0.00163481i
\(607\) −21.0843 36.5192i −0.855787 1.48227i −0.875913 0.482469i \(-0.839740\pi\)
0.0201256 0.999797i \(-0.493593\pi\)
\(608\) −9.02497 14.3019i −0.366011 0.580020i
\(609\) −12.0343 + 1.92619i −0.487655 + 0.0780532i
\(610\) −12.9663 2.64967i −0.524992 0.107282i
\(611\) 2.80208 + 1.61778i 0.113360 + 0.0654483i
\(612\) −0.535485 11.6222i −0.0216457 0.469801i
\(613\) 4.18716 + 7.25237i 0.169118 + 0.292921i 0.938110 0.346338i \(-0.112575\pi\)
−0.768992 + 0.639258i \(0.779241\pi\)
\(614\) −30.0986 + 33.9612i −1.21468 + 1.37056i
\(615\) −66.2977 20.4359i −2.67338 0.824057i
\(616\) −34.0461 + 13.4640i −1.37175 + 0.542482i
\(617\) −8.84616 + 15.3220i −0.356133 + 0.616840i −0.987311 0.158797i \(-0.949238\pi\)
0.631178 + 0.775638i \(0.282572\pi\)
\(618\) −2.50285 1.36919i −0.100679 0.0550769i
\(619\) 14.1334 24.4797i 0.568068 0.983922i −0.428689 0.903452i \(-0.641025\pi\)
0.996757 0.0804700i \(-0.0256421\pi\)
\(620\) −4.20156 5.59569i −0.168739 0.224728i
\(621\) 16.3253 + 6.39614i 0.655111 + 0.256668i
\(622\) −12.2395 + 13.8103i −0.490760 + 0.553741i
\(623\) 19.8213 29.6368i 0.794122 1.18737i
\(624\) −7.60858 5.00343i −0.304587 0.200298i
\(625\) −16.9592 29.3743i −0.678369 1.17497i
\(626\) 14.0989 + 12.4953i 0.563504 + 0.499412i
\(627\) −24.6970 + 5.64201i −0.986303 + 0.225320i
\(628\) −26.0076 + 3.14786i −1.03782 + 0.125613i
\(629\) 0.919927i 0.0366799i
\(630\) −28.7167 33.7270i −1.14410 1.34372i
\(631\) 21.2515i 0.846007i −0.906128 0.423004i \(-0.860976\pi\)
0.906128 0.423004i \(-0.139024\pi\)
\(632\) 16.1681 23.3950i 0.643134 0.930604i
\(633\) 26.4188 + 28.4615i 1.05005 + 1.13124i
\(634\) −18.4350 + 20.8008i −0.732147 + 0.826107i
\(635\) 11.8667 + 20.5537i 0.470914 + 0.815647i
\(636\) −41.3637 + 14.8671i −1.64018 + 0.589519i
\(637\) 7.29452 + 5.60734i 0.289020 + 0.222171i
\(638\) 13.7711 + 12.2049i 0.545205 + 0.483195i
\(639\) −3.64036 + 5.34392i −0.144011 + 0.211402i
\(640\) −44.0778 + 7.10311i −1.74233 + 0.280775i
\(641\) 17.2510 29.8796i 0.681373 1.18017i −0.293189 0.956055i \(-0.594716\pi\)
0.974562 0.224119i \(-0.0719503\pi\)
\(642\) −29.8401 + 0.687065i −1.17770 + 0.0271163i
\(643\) −3.50574 + 6.07213i −0.138253 + 0.239461i −0.926835 0.375468i \(-0.877482\pi\)
0.788582 + 0.614929i \(0.210815\pi\)
\(644\) −14.9532 + 9.75771i −0.589239 + 0.384508i
\(645\) 13.3650 12.4058i 0.526246 0.488477i
\(646\) 6.13541 + 5.43758i 0.241394 + 0.213939i
\(647\) 0.330066 + 0.571691i 0.0129762 + 0.0224755i 0.872441 0.488720i \(-0.162536\pi\)
−0.859464 + 0.511196i \(0.829203\pi\)
\(648\) 5.80190 24.7858i 0.227920 0.973680i
\(649\) −29.6370 17.1109i −1.16335 0.671662i
\(650\) −3.93471 + 19.2548i −0.154332 + 0.755235i
\(651\) −1.44983 + 3.79545i −0.0568234 + 0.148755i
\(652\) −6.30285 + 14.7777i −0.246839 + 0.578741i
\(653\) −1.19024 2.06155i −0.0465776 0.0806748i 0.841797 0.539795i \(-0.181498\pi\)
−0.888374 + 0.459120i \(0.848165\pi\)
\(654\) 20.4097 + 11.1652i 0.798081 + 0.436593i
\(655\) 6.83022 + 3.94343i 0.266879 + 0.154083i
\(656\) 38.9884 + 11.3253i 1.52224 + 0.442179i
\(657\) 13.7115 + 1.02214i 0.534937 + 0.0398774i
\(658\) −6.47598 6.54968i −0.252460 0.255333i
\(659\) 4.53599 2.61885i 0.176697 0.102016i −0.409043 0.912515i \(-0.634137\pi\)
0.585740 + 0.810499i \(0.300804\pi\)
\(660\) −11.8784 + 65.8170i −0.462365 + 2.56192i
\(661\) 7.34107i 0.285535i 0.989756 + 0.142767i \(0.0456001\pi\)
−0.989756 + 0.142767i \(0.954400\pi\)
\(662\) −15.2474 13.5132i −0.592606 0.525204i
\(663\) 4.21863 + 1.30037i 0.163838 + 0.0505022i
\(664\) −0.594254 + 7.30915i −0.0230615 + 0.283650i
\(665\) 31.1453 + 2.05493i 1.20776 + 0.0796867i
\(666\) 0.548461 1.93659i 0.0212524 0.0750412i
\(667\) 7.77183 + 4.48707i 0.300926 + 0.173740i
\(668\) −17.7961 7.59023i −0.688553 0.293675i
\(669\) 3.46018 + 15.1464i 0.133778 + 0.585592i
\(670\) 7.62649 + 1.55847i 0.294637 + 0.0602089i
\(671\) 5.80096 10.0476i 0.223943 0.387881i
\(672\) 17.1251 + 19.4610i 0.660614 + 0.750726i
\(673\) 6.21172 + 10.7590i 0.239444 + 0.414730i 0.960555 0.278090i \(-0.0897014\pi\)
−0.721111 + 0.692820i \(0.756368\pi\)
\(674\) 0.438520 + 1.31436i 0.0168912 + 0.0506273i
\(675\) −54.3189 + 8.21988i −2.09074 + 0.316383i
\(676\) −18.0284 + 13.5368i −0.693401 + 0.520645i
\(677\) 29.8294i 1.14644i 0.819403 + 0.573218i \(0.194305\pi\)
−0.819403 + 0.573218i \(0.805695\pi\)
\(678\) −0.704580 30.6008i −0.0270592 1.17522i
\(679\) −2.54346 5.16326i −0.0976089 0.198148i
\(680\) 19.5591 9.26722i 0.750055 0.355382i
\(681\) −9.89382 + 9.18373i −0.379132 + 0.351921i
\(682\) 5.81905 1.94145i 0.222823 0.0743421i
\(683\) −9.32990 + 5.38662i −0.356999 + 0.206113i −0.667763 0.744374i \(-0.732748\pi\)
0.310765 + 0.950487i \(0.399415\pi\)
\(684\) 9.67409 + 15.1049i 0.369898 + 0.577549i
\(685\) 39.7054i 1.51707i
\(686\) −15.8085 20.8828i −0.603572 0.797309i
\(687\) 11.4837 2.62344i 0.438130 0.100091i
\(688\) −7.70202 + 7.38663i −0.293637 + 0.281613i
\(689\) 16.6776i 0.635365i
\(690\) 0.750806 + 32.6085i 0.0285827 + 1.24138i
\(691\) 47.3937 1.80294 0.901471 0.432840i \(-0.142488\pi\)
0.901471 + 0.432840i \(0.142488\pi\)
\(692\) 32.5383 3.93831i 1.23692 0.149712i
\(693\) 36.0146 14.5230i 1.36808 0.551682i
\(694\) 29.0348 + 25.7325i 1.10215 + 0.976791i
\(695\) 63.2982i 2.40104i
\(696\) 4.83426 12.0989i 0.183242 0.458609i
\(697\) −19.6818 −0.745502
\(698\) 4.26180 20.8554i 0.161312 0.789390i
\(699\) −21.4715 + 19.9305i −0.812128 + 0.753840i
\(700\) 25.2886 49.9037i 0.955821 1.88618i
\(701\) −39.5982 −1.49560 −0.747801 0.663923i \(-0.768890\pi\)
−0.747801 + 0.663923i \(0.768890\pi\)
\(702\) 8.10557 + 5.25262i 0.305925 + 0.198247i
\(703\) 0.709135 + 1.22826i 0.0267455 + 0.0463246i
\(704\) 6.32251 38.6255i 0.238288 1.45575i
\(705\) −16.4030 + 3.74726i −0.617773 + 0.141130i
\(706\) 24.8274 8.28336i 0.934392 0.311749i
\(707\) 1.04982 1.56970i 0.0394826 0.0590345i
\(708\) −4.30355 + 23.8456i −0.161737 + 0.896173i
\(709\) 27.4992 1.03276 0.516378 0.856361i \(-0.327280\pi\)
0.516378 + 0.856361i \(0.327280\pi\)
\(710\) −11.7850 2.40827i −0.442285 0.0903807i
\(711\) −16.9819 + 24.9288i −0.636870 + 0.934902i
\(712\) 16.3204 + 34.4452i 0.611632 + 1.29089i
\(713\) 2.59089 1.49585i 0.0970295 0.0560200i
\(714\) −10.6039 6.74395i −0.396841 0.252386i
\(715\) −21.9766 12.6882i −0.821877 0.474511i
\(716\) 22.2658 + 29.6539i 0.832112 + 1.10822i
\(717\) −22.9259 24.6986i −0.856184 0.922385i
\(718\) 7.82045 2.60920i 0.291857 0.0973744i
\(719\) −26.4956 + 45.8917i −0.988118 + 1.71147i −0.360954 + 0.932584i \(0.617549\pi\)
−0.627164 + 0.778887i \(0.715784\pi\)
\(720\) 46.6999 7.84779i 1.74040 0.292470i
\(721\) −2.76427 + 1.36170i −0.102947 + 0.0507123i
\(722\) 13.9426 + 2.84916i 0.518889 + 0.106035i
\(723\) 27.7587 + 29.9050i 1.03236 + 1.11218i
\(724\) 45.6757 5.52840i 1.69752 0.205461i
\(725\) −28.1184 −1.04429
\(726\) −27.7988 15.2074i −1.03171 0.564400i
\(727\) 15.2977 + 26.4963i 0.567359 + 0.982694i 0.996826 + 0.0796118i \(0.0253681\pi\)
−0.429467 + 0.903082i \(0.641299\pi\)
\(728\) −9.14666 + 3.61719i −0.338998 + 0.134062i
\(729\) −5.97715 + 26.3301i −0.221376 + 0.975189i
\(730\) 8.09507 + 24.2631i 0.299612 + 0.898016i
\(731\) 2.58666 4.48023i 0.0956711 0.165707i
\(732\) −8.08415 1.45899i −0.298799 0.0539259i
\(733\) −0.610768 + 0.352627i −0.0225592 + 0.0130246i −0.511237 0.859440i \(-0.670813\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(734\) 0.809212 + 2.42542i 0.0298686 + 0.0895240i
\(735\) −47.6394 + 4.43505i −1.75721 + 0.163589i
\(736\) −0.750461 19.0733i −0.0276624 0.703053i
\(737\) −3.41198 + 5.90973i −0.125682 + 0.217688i
\(738\) −41.4332 11.7343i −1.52518 0.431946i
\(739\) 29.5374 17.0534i 1.08655 0.627321i 0.153896 0.988087i \(-0.450818\pi\)
0.932656 + 0.360766i \(0.117485\pi\)
\(740\) 3.71713 0.449907i 0.136645 0.0165389i
\(741\) −6.63498 + 1.51576i −0.243742 + 0.0556828i
\(742\) −12.5470 + 45.7882i −0.460616 + 1.68094i
\(743\) −32.7970 18.9353i −1.20320 0.694670i −0.241938 0.970292i \(-0.577783\pi\)
−0.961266 + 0.275621i \(0.911116\pi\)
\(744\) −2.68724 3.41239i −0.0985190 0.125104i
\(745\) 33.1178 + 19.1205i 1.21334 + 0.700523i
\(746\) 8.25686 + 1.68729i 0.302305 + 0.0617759i
\(747\) 0.578223 7.75659i 0.0211561 0.283799i
\(748\) 2.27987 + 18.8363i 0.0833605 + 0.688725i
\(749\) −17.9229 + 26.7984i −0.654890 + 0.979194i
\(750\) −28.0002 46.0179i −1.02242 1.68034i
\(751\) 15.6928 9.06026i 0.572639 0.330613i −0.185563 0.982632i \(-0.559411\pi\)
0.758203 + 0.652019i \(0.226078\pi\)
\(752\) 9.56230 2.34918i 0.348701 0.0856657i
\(753\) −7.50120 2.31221i −0.273359 0.0842615i
\(754\) 3.69970 + 3.27890i 0.134735 + 0.119411i
\(755\) 65.3007 2.37654
\(756\) −18.3021 20.5191i −0.665641 0.746272i
\(757\) −30.0755 −1.09311 −0.546555 0.837423i \(-0.684061\pi\)
−0.546555 + 0.837423i \(0.684061\pi\)
\(758\) 17.4961 + 15.5061i 0.635488 + 0.563209i
\(759\) −27.3252 8.42286i −0.991843 0.305731i
\(760\) −18.9709 + 27.4506i −0.688147 + 0.995738i
\(761\) 19.2695 11.1252i 0.698518 0.403290i −0.108277 0.994121i \(-0.534533\pi\)
0.806795 + 0.590831i \(0.201200\pi\)
\(762\) 7.65756 + 12.5851i 0.277404 + 0.455909i
\(763\) 22.5415 11.1041i 0.816056 0.401995i
\(764\) −7.83108 + 0.947842i −0.283318 + 0.0342917i
\(765\) −20.6790 + 9.96847i −0.747652 + 0.360411i
\(766\) −4.56965 0.933806i −0.165108 0.0337398i
\(767\) −7.96214 4.59694i −0.287496 0.165986i
\(768\) −27.2511 + 5.03764i −0.983339 + 0.181780i
\(769\) 9.46235 + 5.46309i 0.341221 + 0.197004i 0.660812 0.750552i \(-0.270212\pi\)
−0.319591 + 0.947556i \(0.603545\pi\)
\(770\) 50.7908 + 51.3689i 1.83037 + 1.85121i
\(771\) −40.3295 + 9.21324i −1.45243 + 0.331807i
\(772\) −1.38183 11.4167i −0.0497332 0.410896i
\(773\) −10.6286 + 6.13643i −0.382284 + 0.220712i −0.678812 0.734312i \(-0.737505\pi\)
0.296527 + 0.955024i \(0.404171\pi\)
\(774\) 8.11642 7.88939i 0.291739 0.283578i
\(775\) −4.68690 + 8.11795i −0.168359 + 0.291605i
\(776\) 6.13290 + 0.498621i 0.220158 + 0.0178995i
\(777\) −1.37091 1.68730i −0.0491812 0.0605314i
\(778\) 4.31863 + 12.9441i 0.154830 + 0.464067i
\(779\) 26.2786 15.1719i 0.941527 0.543591i
\(780\) −3.19119 + 17.6821i −0.114263 + 0.633121i
\(781\) 5.27246 9.13217i 0.188663 0.326775i
\(782\) 2.92859 + 8.77775i 0.104726 + 0.313892i
\(783\) −5.04121 + 12.8670i −0.180158 + 0.459829i
\(784\) 27.8334 3.04968i 0.994051 0.108917i
\(785\) 25.8452 + 44.7653i 0.922456 + 1.59774i
\(786\) 4.29485 + 2.34951i 0.153192 + 0.0838044i
\(787\) −2.27050 −0.0809345 −0.0404672 0.999181i \(-0.512885\pi\)
−0.0404672 + 0.999181i \(0.512885\pi\)
\(788\) 3.98956 + 32.9618i 0.142122 + 1.17422i
\(789\) −32.0527 34.5311i −1.14111 1.22934i
\(790\) −54.9758 11.2343i −1.95595 0.399698i
\(791\) −27.4816 18.3798i −0.977133 0.653512i
\(792\) −6.43074 + 41.0126i −0.228507 + 1.45732i
\(793\) 1.55846 2.69933i 0.0553425 0.0958560i
\(794\) −4.99080 + 1.66512i −0.177117 + 0.0590928i
\(795\) 59.0018 + 63.5638i 2.09258 + 2.25438i
\(796\) −19.9403 + 14.9723i −0.706765 + 0.530679i
\(797\) 4.92030 + 2.84074i 0.174286 + 0.100624i 0.584605 0.811318i \(-0.301249\pi\)
−0.410319 + 0.911942i \(0.634583\pi\)
\(798\) 19.3567 + 0.830182i 0.685218 + 0.0293881i
\(799\) −4.13388 + 2.38669i −0.146246 + 0.0844352i
\(800\) 31.9174 + 50.5797i 1.12845 + 1.78826i
\(801\) −17.5553 36.4175i −0.620287 1.28675i
\(802\) 33.2152 + 6.78750i 1.17287 + 0.239675i
\(803\) −22.4229 −0.791289
\(804\) 4.75490 + 0.858144i 0.167693 + 0.0302644i
\(805\) 29.2846 + 19.5857i 1.03215 + 0.690306i
\(806\) 1.56332 0.521583i 0.0550656 0.0183720i
\(807\) −30.9305 + 7.06606i −1.08881 + 0.248737i
\(808\) 0.864399 + 1.82437i 0.0304095 + 0.0641811i
\(809\) −8.28527 14.3505i −0.291295 0.504537i 0.682821 0.730585i \(-0.260753\pi\)
−0.974116 + 0.226048i \(0.927419\pi\)
\(810\) −49.4757 + 8.65630i −1.73840 + 0.304152i
\(811\) −10.2931 −0.361438 −0.180719 0.983535i \(-0.557842\pi\)
−0.180719 + 0.983535i \(0.557842\pi\)
\(812\) −7.69068 11.7856i −0.269890 0.413593i
\(813\) 1.96132 1.82055i 0.0687864 0.0638495i
\(814\) −0.657181 + 3.21597i −0.0230342 + 0.112720i
\(815\) 31.6995 1.11038
\(816\) 12.0050 6.03026i 0.420259 0.211101i
\(817\) 7.97581i 0.279038i
\(818\) 23.4483 + 20.7814i 0.819851 + 0.726603i
\(819\) 9.67552 3.90168i 0.338090 0.136336i
\(820\) −9.62575 79.5280i −0.336146 2.77724i
\(821\) −0.101592 −0.00354560 −0.00177280 0.999998i \(-0.500564\pi\)
−0.00177280 + 0.999998i \(0.500564\pi\)
\(822\) −0.567317 24.6393i −0.0197875 0.859395i
\(823\) 55.1859i 1.92366i 0.273650 + 0.961829i \(0.411769\pi\)
−0.273650 + 0.961829i \(0.588231\pi\)
\(824\) 0.266948 3.28339i 0.00929959 0.114382i
\(825\) 87.3424 19.9533i 3.04087 0.694685i
\(826\) 18.4016 + 18.6110i 0.640273 + 0.647560i
\(827\) 37.1634i 1.29230i −0.763211 0.646149i \(-0.776378\pi\)
0.763211 0.646149i \(-0.223622\pi\)
\(828\) 0.931829 + 20.2245i 0.0323833 + 0.702851i
\(829\) 33.4823 19.3310i 1.16289 0.671393i 0.210893 0.977509i \(-0.432363\pi\)
0.951994 + 0.306116i \(0.0990295\pi\)
\(830\) 13.7256 4.57938i 0.476422 0.158952i
\(831\) 0.617071 0.572783i 0.0214060 0.0198696i
\(832\) 1.69858 10.3770i 0.0588876 0.359756i
\(833\) −12.5449 + 5.18354i −0.434656 + 0.179599i
\(834\) −0.904414 39.2799i −0.0313173 1.36015i
\(835\) 38.1742i 1.32107i
\(836\) −17.5642 23.3922i −0.607471 0.809037i
\(837\) 2.87449 + 3.60016i 0.0993569 + 0.124440i
\(838\) −15.8296 47.4454i −0.546824 1.63898i
\(839\) 2.58403 + 4.47567i 0.0892106 + 0.154517i 0.907178 0.420748i \(-0.138232\pi\)
−0.817967 + 0.575265i \(0.804899\pi\)
\(840\) 22.0641 46.1453i 0.761285 1.59216i
\(841\) 10.9635 18.9893i 0.378050 0.654802i
\(842\) −42.9131 8.76928i −1.47888 0.302209i
\(843\) 10.1584 + 44.4669i 0.349875 + 1.53152i
\(844\) −17.5917 + 41.2458i −0.605532 + 1.41974i
\(845\) 38.5238 + 22.2417i 1.32526 + 0.765138i
\(846\) −10.1254 + 2.55974i −0.348118 + 0.0880056i
\(847\) −30.7024 + 15.1242i −1.05495 + 0.519673i
\(848\) −35.1308 36.6308i −1.20640 1.25791i
\(849\) −28.4313 8.76381i −0.975761 0.300773i
\(850\) −21.6983 19.2303i −0.744244 0.659595i
\(851\) 1.60082i 0.0548754i
\(852\) −7.34765 1.32607i −0.251726 0.0454304i
\(853\) −30.1332 + 17.3974i −1.03174 + 0.595675i −0.917483 0.397776i \(-0.869782\pi\)
−0.114257 + 0.993451i \(0.536449\pi\)
\(854\) −6.30952 + 6.23852i −0.215907 + 0.213478i
\(855\) 19.9257 29.2502i 0.681445 1.00034i
\(856\) −14.7573 31.1463i −0.504396 1.06456i
\(857\) 37.1025 + 21.4212i 1.26740 + 0.731733i 0.974495 0.224409i \(-0.0720452\pi\)
0.292903 + 0.956142i \(0.405379\pi\)
\(858\) −13.8189 7.55967i −0.471769 0.258083i
\(859\) 15.9716 + 27.6637i 0.544945 + 0.943873i 0.998610 + 0.0527008i \(0.0167830\pi\)
−0.453665 + 0.891172i \(0.649884\pi\)
\(860\) 19.3682 + 8.26074i 0.660451 + 0.281689i
\(861\) −36.0997 + 29.3306i −1.23027 + 0.999586i
\(862\) −1.38084 + 6.75722i −0.0470315 + 0.230152i
\(863\) −30.0490 17.3488i −1.02288 0.590560i −0.107943 0.994157i \(-0.534426\pi\)
−0.914937 + 0.403597i \(0.867760\pi\)
\(864\) 28.8676 5.53722i 0.982096 0.188380i
\(865\) −32.3352 56.0061i −1.09943 1.90427i
\(866\) 13.8376 + 12.2637i 0.470221 + 0.416739i
\(867\) 16.8074 15.6011i 0.570811 0.529843i
\(868\) −4.68449 + 0.255872i −0.159002 + 0.00868485i
\(869\) 24.5954 42.6005i 0.834342 1.44512i
\(870\) −25.7008 + 0.591759i −0.871340 + 0.0200625i
\(871\) −0.916648 + 1.58768i −0.0310594 + 0.0537965i
\(872\) −2.17685 + 26.7747i −0.0737175 + 0.906704i
\(873\) −6.50833 0.485170i −0.220273 0.0164205i
\(874\) −10.6766 9.46225i −0.361141 0.320065i
\(875\) −58.0568 3.83052i −1.96268 0.129495i
\(876\) 5.37009 + 14.9408i 0.181439 + 0.504804i
\(877\) 11.1213 + 19.2627i 0.375540 + 0.650455i 0.990408 0.138175i \(-0.0441238\pi\)
−0.614867 + 0.788631i \(0.710790\pi\)
\(878\) −1.79846 + 2.02926i −0.0606950 + 0.0684842i
\(879\) −29.2767 31.5404i −0.987480 1.06383i
\(880\) −74.9967 + 18.4245i −2.52814 + 0.621090i
\(881\) 20.4228i 0.688061i −0.938958 0.344031i \(-0.888208\pi\)
0.938958 0.344031i \(-0.111792\pi\)
\(882\) −29.4994 + 3.43286i −0.993297 + 0.115590i
\(883\) 11.6027i 0.390461i −0.980757 0.195231i \(-0.937454\pi\)
0.980757 0.195231i \(-0.0625456\pi\)
\(884\) 0.612501 + 5.06049i 0.0206006 + 0.170203i
\(885\) 46.6094 10.6479i 1.56676 0.357925i
\(886\) −22.5333 19.9704i −0.757021 0.670919i
\(887\) −26.5399 45.9684i −0.891123 1.54347i −0.838531 0.544853i \(-0.816585\pi\)
−0.0525911 0.998616i \(-0.516748\pi\)
\(888\) 2.30025 0.332302i 0.0771913 0.0111513i
\(889\) 15.8775 + 1.04758i 0.532514 + 0.0351346i
\(890\) 49.8822 56.2838i 1.67206 1.88664i
\(891\) 6.52854 43.5453i 0.218714 1.45882i
\(892\) −14.3462 + 10.7719i −0.480345 + 0.360670i
\(893\) 3.67962 6.37328i 0.123134 0.213274i
\(894\) 20.8245 + 11.3921i 0.696476 + 0.381009i
\(895\) 36.5841 63.3655i 1.22287 2.11808i
\(896\) −12.4703 + 27.2120i −0.416604 + 0.909088i
\(897\) −7.34108 2.26285i −0.245111 0.0755543i
\(898\) 5.62770 6.34993i 0.187799 0.211900i
\(899\) 1.17898 + 2.04205i 0.0393210 + 0.0681060i
\(900\) −34.2130 53.4193i −1.14043 1.78064i
\(901\) 21.3079 + 12.3021i 0.709870 + 0.409844i
\(902\) 68.8055 + 14.0604i 2.29097 + 0.468159i
\(903\) −1.93226 12.0722i −0.0643014 0.401738i
\(904\) 31.9403 15.1335i 1.06232 0.503334i
\(905\) −45.3905 78.6187i −1.50883 2.61337i
\(906\) 40.5225 0.933026i 1.34627 0.0309977i
\(907\) −47.3583 27.3424i −1.57251 0.907888i −0.995860 0.0908948i \(-0.971027\pi\)
−0.576647 0.816993i \(-0.695639\pi\)
\(908\) −14.3379 6.11525i −0.475819 0.202942i
\(909\) −0.929808 1.92884i −0.0308398 0.0639754i
\(910\) 13.6452 + 13.8005i 0.452335 + 0.457483i
\(911\) 1.27865 0.738229i 0.0423636 0.0244586i −0.478669 0.877996i \(-0.658880\pi\)
0.521032 + 0.853537i \(0.325547\pi\)
\(912\) −11.3802 + 17.3056i −0.376837 + 0.573046i
\(913\) 12.6846i 0.419800i
\(914\) −23.7643 + 26.8141i −0.786053 + 0.886930i
\(915\) 3.60985 + 15.8015i 0.119338 + 0.522383i
\(916\) 8.16706 + 10.8770i 0.269847 + 0.359386i
\(917\) 4.74345 2.33666i 0.156643 0.0771632i
\(918\) −12.6900 + 6.48142i −0.418832 + 0.213919i
\(919\) −16.9505 9.78639i −0.559146 0.322823i 0.193657 0.981069i \(-0.437965\pi\)
−0.752803 + 0.658246i \(0.771299\pi\)
\(920\) −34.0358 + 16.1264i −1.12213 + 0.531672i
\(921\) 53.1122 + 16.3716i 1.75011 + 0.539461i
\(922\) −5.67881 + 27.7897i −0.187022 + 0.915205i
\(923\) 1.41648 2.45341i 0.0466239 0.0807549i
\(924\) 32.2523 + 31.1514i 1.06102 + 1.02481i
\(925\) −2.50790 4.34381i −0.0824592 0.142824i
\(926\) 51.5648 17.2040i 1.69453 0.565358i
\(927\) −0.259747 + 3.48438i −0.00853121 + 0.114442i
\(928\) 15.0329 0.591487i 0.493480 0.0194165i
\(929\) 14.4455i 0.473942i −0.971517 0.236971i \(-0.923845\pi\)
0.971517 0.236971i \(-0.0761546\pi\)
\(930\) −4.11309 + 7.51862i −0.134873 + 0.246545i
\(931\) 12.7538 16.5913i 0.417989 0.543758i
\(932\) −31.1160 13.2713i −1.01924 0.434715i
\(933\) 21.5980 + 6.65746i 0.707085 + 0.217955i
\(934\) −14.6444 43.8932i −0.479180 1.43623i
\(935\) 32.4218 18.7187i 1.06031 0.612168i
\(936\) −1.72766 + 11.0183i −0.0564702 + 0.360143i
\(937\) 31.4809i 1.02844i 0.857659 + 0.514218i \(0.171918\pi\)
−0.857659 + 0.514218i \(0.828082\pi\)
\(938\) 3.71111 3.66935i 0.121172 0.119808i
\(939\) 6.79658 22.0493i 0.221798 0.719552i
\(940\) −11.6656 15.5364i −0.380491 0.506742i
\(941\) 40.3346i 1.31487i 0.753511 + 0.657435i \(0.228359\pi\)
−0.753511 + 0.657435i \(0.771641\pi\)
\(942\) 16.6779 + 27.4099i 0.543397 + 0.893063i
\(943\) 34.2495 1.11532
\(944\) −27.1714 + 6.67523i −0.884354 + 0.217260i
\(945\) −23.0733 + 49.1005i −0.750575 + 1.59724i
\(946\) −12.2433 + 13.8145i −0.398064 + 0.449149i
\(947\) 14.8597i 0.482876i 0.970416 + 0.241438i \(0.0776190\pi\)
−0.970416 + 0.241438i \(0.922381\pi\)
\(948\) −34.2759 6.18596i −1.11323 0.200911i
\(949\) −6.02405 −0.195549
\(950\) 43.7947 + 8.94944i 1.42089 + 0.290358i
\(951\) 32.5306 + 10.0274i 1.05488 + 0.325160i
\(952\) 2.12553 14.3543i 0.0688888 0.465227i
\(953\) −11.8041 −0.382371 −0.191185 0.981554i \(-0.561233\pi\)
−0.191185 + 0.981554i \(0.561233\pi\)
\(954\) 37.5219 + 38.6017i 1.21482 + 1.24978i
\(955\) 7.78219 + 13.4791i 0.251826 + 0.436175i
\(956\) 15.2659 35.7926i 0.493734 1.15761i
\(957\) 6.63860 21.5368i 0.214596 0.696186i
\(958\) 16.4694 + 49.3633i 0.532104 + 1.59486i
\(959\) −22.1278 14.7992i −0.714543 0.477890i
\(960\) 30.2376 + 45.5592i 0.975915 + 1.47042i
\(961\) −30.2139 −0.974643
\(962\) −0.176555 + 0.863987i −0.00569237 + 0.0278561i
\(963\) 15.8740 + 32.9298i 0.511534 + 1.06115i
\(964\) −18.4839 + 43.3377i −0.595327 + 1.39581i
\(965\) −19.6508 + 11.3454i −0.632583 + 0.365222i
\(966\) 18.4525 + 11.7355i 0.593699 + 0.377585i
\(967\) −2.41663 1.39524i −0.0777137 0.0448680i 0.460640 0.887587i \(-0.347620\pi\)
−0.538353 + 0.842719i \(0.680953\pi\)
\(968\) 2.96496 36.4681i 0.0952974 1.17213i
\(969\) 2.95767 9.59521i 0.0950142 0.308242i
\(970\) −3.84242 11.5168i −0.123373 0.369781i
\(971\) −26.2483 + 45.4633i −0.842347 + 1.45899i 0.0455582 + 0.998962i \(0.485493\pi\)
−0.887905 + 0.460026i \(0.847840\pi\)
\(972\) −30.5786 + 6.07861i −0.980809 + 0.194971i
\(973\) −35.2760 23.5928i −1.13090 0.756350i
\(974\) 1.28514 6.28893i 0.0411786 0.201510i
\(975\) 23.4650 5.36057i 0.751482 0.171676i
\(976\) −2.26304 9.21167i −0.0724382 0.294858i
\(977\) −10.2879 −0.329140 −0.164570 0.986365i \(-0.552624\pi\)
−0.164570 + 0.986365i \(0.552624\pi\)
\(978\) 19.6712 0.452927i 0.629015 0.0144830i
\(979\) 32.9653 + 57.0976i 1.05358 + 1.82485i
\(980\) −27.0804 48.1550i −0.865051 1.53825i
\(981\) 2.11813 28.4137i 0.0676266 0.907179i
\(982\) 16.5222 5.51244i 0.527246 0.175909i
\(983\) −16.4524 + 28.4963i −0.524749 + 0.908891i 0.474836 + 0.880074i \(0.342507\pi\)
−0.999585 + 0.0288169i \(0.990826\pi\)
\(984\) −7.10959 49.2138i −0.226646 1.56888i
\(985\) 56.7351 32.7560i 1.80773 1.04369i
\(986\) −6.91832 + 2.30821i −0.220324 + 0.0735084i
\(987\) −4.02546 + 10.5381i −0.128132 + 0.335430i
\(988\) −4.71872 6.28445i −0.150123 0.199935i
\(989\) −4.50120 + 7.79630i −0.143130 + 0.247908i
\(990\) 79.4130 20.0759i 2.52391 0.638054i
\(991\) −48.3716 + 27.9273i −1.53657 + 0.887141i −0.537537 + 0.843240i \(0.680645\pi\)
−0.999036 + 0.0439007i \(0.986021\pi\)
\(992\) 2.33499 4.43869i 0.0741361 0.140929i
\(993\) −7.35024 + 23.8455i −0.233253 + 0.756713i
\(994\) −5.73469 + 5.67016i −0.181893 + 0.179847i
\(995\) 42.6092 + 24.6004i 1.35080 + 0.779885i
\(996\) 8.45202 3.03786i 0.267813 0.0962582i
\(997\) 0.219422 + 0.126684i 0.00694917 + 0.00401211i 0.503471 0.864012i \(-0.332056\pi\)
−0.496521 + 0.868024i \(0.665390\pi\)
\(998\) 3.66715 17.9455i 0.116082 0.568054i
\(999\) −2.43736 + 0.368836i −0.0771147 + 0.0116695i
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 252.2.bj.b.103.31 yes 84
3.2 odd 2 756.2.bj.b.523.12 84
4.3 odd 2 inner 252.2.bj.b.103.32 yes 84
7.3 odd 6 252.2.n.b.31.25 yes 84
9.2 odd 6 756.2.n.b.19.39 84
9.7 even 3 252.2.n.b.187.4 yes 84
12.11 even 2 756.2.bj.b.523.11 84
21.17 even 6 756.2.n.b.199.18 84
28.3 even 6 252.2.n.b.31.4 84
36.7 odd 6 252.2.n.b.187.25 yes 84
36.11 even 6 756.2.n.b.19.18 84
63.38 even 6 756.2.bj.b.451.12 84
63.52 odd 6 inner 252.2.bj.b.115.31 yes 84
84.59 odd 6 756.2.n.b.199.39 84
252.115 even 6 inner 252.2.bj.b.115.32 yes 84
252.227 odd 6 756.2.bj.b.451.11 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.4 84 28.3 even 6
252.2.n.b.31.25 yes 84 7.3 odd 6
252.2.n.b.187.4 yes 84 9.7 even 3
252.2.n.b.187.25 yes 84 36.7 odd 6
252.2.bj.b.103.31 yes 84 1.1 even 1 trivial
252.2.bj.b.103.32 yes 84 4.3 odd 2 inner
252.2.bj.b.115.31 yes 84 63.52 odd 6 inner
252.2.bj.b.115.32 yes 84 252.115 even 6 inner
756.2.n.b.19.18 84 36.11 even 6
756.2.n.b.19.39 84 9.2 odd 6
756.2.n.b.199.18 84 21.17 even 6
756.2.n.b.199.39 84 84.59 odd 6
756.2.bj.b.451.11 84 252.227 odd 6
756.2.bj.b.451.12 84 63.38 even 6
756.2.bj.b.523.11 84 12.11 even 2
756.2.bj.b.523.12 84 3.2 odd 2