Properties

Label 432.2.bg.a.13.8
Level $432$
Weight $2$
Character 432.13
Analytic conductor $3.450$
Analytic rank $0$
Dimension $840$
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] = [432,2,Mod(13,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([0, 27, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.bg (of order \(36\), degree \(12\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(840\)
Relative dimension: \(70\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 13.8
Character \(\chi\) \(=\) 432.13
Dual form 432.2.bg.a.133.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31559 + 0.518866i) q^{2} +(-1.54765 + 0.777673i) q^{3} +(1.46156 - 1.36523i) q^{4} +(-4.10207 + 0.358885i) q^{5} +(1.63257 - 1.82612i) q^{6} +(0.659902 - 1.81306i) q^{7} +(-1.21444 + 2.55443i) q^{8} +(1.79045 - 2.40713i) q^{9} +O(q^{10})\) \(q+(-1.31559 + 0.518866i) q^{2} +(-1.54765 + 0.777673i) q^{3} +(1.46156 - 1.36523i) q^{4} +(-4.10207 + 0.358885i) q^{5} +(1.63257 - 1.82612i) q^{6} +(0.659902 - 1.81306i) q^{7} +(-1.21444 + 2.55443i) q^{8} +(1.79045 - 2.40713i) q^{9} +(5.21044 - 2.60057i) q^{10} +(0.223055 - 2.54953i) q^{11} +(-1.20028 + 3.24951i) q^{12} +(-0.661708 + 0.463333i) q^{13} +(0.0725768 + 2.72765i) q^{14} +(6.06948 - 3.74550i) q^{15} +(0.272296 - 3.99072i) q^{16} +(-0.422494 + 0.731781i) q^{17} +(-1.10652 + 4.09580i) q^{18} +(-1.32857 + 4.95828i) q^{19} +(-5.50545 + 6.12480i) q^{20} +(0.388674 + 3.31918i) q^{21} +(1.02941 + 3.46987i) q^{22} +(1.79779 + 4.93938i) q^{23} +(-0.106986 - 4.89781i) q^{24} +(11.7742 - 2.07610i) q^{25} +(0.630129 - 0.952894i) q^{26} +(-0.899030 + 5.11779i) q^{27} +(-1.51077 - 3.55081i) q^{28} +(4.47569 - 6.39194i) q^{29} +(-6.04154 + 8.07679i) q^{30} +(-6.06802 + 2.20858i) q^{31} +(1.71242 + 5.39144i) q^{32} +(1.63749 + 4.11924i) q^{33} +(0.176133 - 1.18194i) q^{34} +(-2.05628 + 7.67415i) q^{35} +(-0.669445 - 5.96254i) q^{36} +(-0.0658734 - 0.245843i) q^{37} +(-0.824831 - 7.21241i) q^{38} +(0.663772 - 1.23167i) q^{39} +(4.06497 - 10.9143i) q^{40} +(6.33290 + 1.11666i) q^{41} +(-2.23354 - 4.16501i) q^{42} +(-0.865815 + 9.89631i) q^{43} +(-3.15468 - 4.03080i) q^{44} +(-6.48067 + 10.5168i) q^{45} +(-4.92802 - 5.56539i) q^{46} +(2.91666 + 1.06158i) q^{47} +(2.68206 + 6.38800i) q^{48} +(2.51058 + 2.10662i) q^{49} +(-14.4128 + 8.84052i) q^{50} +(0.0847871 - 1.46110i) q^{51} +(-0.334568 + 1.58057i) q^{52} +(-0.319942 + 0.319942i) q^{53} +(-1.47269 - 7.19939i) q^{54} +10.5384i q^{55} +(3.82995 + 3.88753i) q^{56} +(-1.79976 - 8.70688i) q^{57} +(-2.57161 + 10.7315i) q^{58} +(12.8464 - 1.12391i) q^{59} +(3.75743 - 13.7605i) q^{60} +(0.767663 + 1.64626i) q^{61} +(6.83707 - 6.05407i) q^{62} +(-3.18277 - 4.83467i) q^{63} +(-5.05027 - 6.20441i) q^{64} +(2.54809 - 2.13810i) q^{65} +(-4.29159 - 4.56960i) q^{66} +(6.51434 - 4.56139i) q^{67} +(0.381550 + 1.64634i) q^{68} +(-6.62356 - 6.24634i) q^{69} +(-1.27663 - 11.1630i) q^{70} +(-0.00142217 - 0.000821091i) q^{71} +(3.97447 + 7.49690i) q^{72} +(9.80470 - 5.66074i) q^{73} +(0.214222 + 0.289249i) q^{74} +(-16.6078 + 12.3695i) q^{75} +(4.82741 + 9.06061i) q^{76} +(-4.47526 - 2.08685i) q^{77} +(-0.234180 + 1.96478i) q^{78} +(-1.07582 - 6.10127i) q^{79} +(0.315229 + 16.4680i) q^{80} +(-2.58858 - 8.61970i) q^{81} +(-8.91091 + 1.81686i) q^{82} +(-4.75015 + 6.78392i) q^{83} +(5.09951 + 4.32054i) q^{84} +(1.47048 - 3.15345i) q^{85} +(-3.99580 - 13.4687i) q^{86} +(-1.95596 + 13.3731i) q^{87} +(6.24171 + 3.66602i) q^{88} +(-14.7937 + 8.54116i) q^{89} +(3.06910 - 17.1984i) q^{90} +(0.403390 + 1.50547i) q^{91} +(9.37095 + 4.76479i) q^{92} +(7.67362 - 8.13704i) q^{93} +(-4.38795 + 0.116754i) q^{94} +(3.67043 - 20.8160i) q^{95} +(-6.84300 - 7.01237i) q^{96} +(11.8407 - 9.93553i) q^{97} +(-4.39595 - 1.46880i) q^{98} +(-5.73768 - 5.10172i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 30 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} - 54 q^{20} - 12 q^{21} - 12 q^{22} + 18 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 72 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 168 q^{50} + 6 q^{51} - 12 q^{52} - 24 q^{53} + 156 q^{54} - 54 q^{56} + 42 q^{58} - 48 q^{59} - 72 q^{60} - 12 q^{61} + 60 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 198 q^{66} - 12 q^{67} - 66 q^{68} - 12 q^{69} - 54 q^{70} - 144 q^{72} - 96 q^{74} - 96 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 48 q^{83} + 36 q^{84} + 18 q^{85} - 72 q^{86} - 12 q^{88} - 66 q^{90} - 6 q^{91} + 102 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} - 120 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31559 + 0.518866i −0.930263 + 0.366893i
\(3\) −1.54765 + 0.777673i −0.893537 + 0.448990i
\(4\) 1.46156 1.36523i 0.730778 0.682615i
\(5\) −4.10207 + 0.358885i −1.83450 + 0.160498i −0.951255 0.308407i \(-0.900204\pi\)
−0.883249 + 0.468905i \(0.844649\pi\)
\(6\) 1.63257 1.82612i 0.666493 0.745511i
\(7\) 0.659902 1.81306i 0.249419 0.685274i −0.750289 0.661110i \(-0.770085\pi\)
0.999708 0.0241637i \(-0.00769229\pi\)
\(8\) −1.21444 + 2.55443i −0.429369 + 0.903129i
\(9\) 1.79045 2.40713i 0.596817 0.802378i
\(10\) 5.21044 2.60057i 1.64768 0.822373i
\(11\) 0.223055 2.54953i 0.0672535 0.768711i −0.885435 0.464763i \(-0.846140\pi\)
0.952689 0.303948i \(-0.0983049\pi\)
\(12\) −1.20028 + 3.24951i −0.346491 + 0.938053i
\(13\) −0.661708 + 0.463333i −0.183525 + 0.128505i −0.661729 0.749743i \(-0.730177\pi\)
0.478204 + 0.878249i \(0.341288\pi\)
\(14\) 0.0725768 + 2.72765i 0.0193970 + 0.728995i
\(15\) 6.06948 3.74550i 1.56713 0.967084i
\(16\) 0.272296 3.99072i 0.0680741 0.997680i
\(17\) −0.422494 + 0.731781i −0.102470 + 0.177483i −0.912702 0.408627i \(-0.866008\pi\)
0.810232 + 0.586110i \(0.199341\pi\)
\(18\) −1.10652 + 4.09580i −0.260809 + 0.965390i
\(19\) −1.32857 + 4.95828i −0.304794 + 1.13751i 0.628328 + 0.777948i \(0.283740\pi\)
−0.933122 + 0.359559i \(0.882927\pi\)
\(20\) −5.50545 + 6.12480i −1.23106 + 1.36955i
\(21\) 0.388674 + 3.31918i 0.0848156 + 0.724304i
\(22\) 1.02941 + 3.46987i 0.219472 + 0.739778i
\(23\) 1.79779 + 4.93938i 0.374864 + 1.02993i 0.973455 + 0.228876i \(0.0735052\pi\)
−0.598591 + 0.801055i \(0.704273\pi\)
\(24\) −0.106986 4.89781i −0.0218384 0.999762i
\(25\) 11.7742 2.07610i 2.35483 0.415221i
\(26\) 0.630129 0.952894i 0.123578 0.186878i
\(27\) −0.899030 + 5.11779i −0.173018 + 0.984919i
\(28\) −1.51077 3.55081i −0.285508 0.671041i
\(29\) 4.47569 6.39194i 0.831114 1.18695i −0.149062 0.988828i \(-0.547625\pi\)
0.980176 0.198126i \(-0.0634856\pi\)
\(30\) −6.04154 + 8.07679i −1.10303 + 1.47461i
\(31\) −6.06802 + 2.20858i −1.08985 + 0.396672i −0.823564 0.567223i \(-0.808018\pi\)
−0.266283 + 0.963895i \(0.585796\pi\)
\(32\) 1.71242 + 5.39144i 0.302716 + 0.953081i
\(33\) 1.63749 + 4.11924i 0.285050 + 0.717068i
\(34\) 0.176133 1.18194i 0.0302066 0.202701i
\(35\) −2.05628 + 7.67415i −0.347575 + 1.29717i
\(36\) −0.669445 5.96254i −0.111574 0.993756i
\(37\) −0.0658734 0.245843i −0.0108295 0.0404163i 0.960300 0.278971i \(-0.0899932\pi\)
−0.971129 + 0.238554i \(0.923327\pi\)
\(38\) −0.824831 7.21241i −0.133805 1.17001i
\(39\) 0.663772 1.23167i 0.106289 0.197225i
\(40\) 4.06497 10.9143i 0.642728 1.72571i
\(41\) 6.33290 + 1.11666i 0.989033 + 0.174393i 0.644685 0.764449i \(-0.276989\pi\)
0.344349 + 0.938842i \(0.388100\pi\)
\(42\) −2.23354 4.16501i −0.344643 0.642675i
\(43\) −0.865815 + 9.89631i −0.132036 + 1.50917i 0.584369 + 0.811488i \(0.301342\pi\)
−0.716405 + 0.697685i \(0.754214\pi\)
\(44\) −3.15468 4.03080i −0.475586 0.607666i
\(45\) −6.48067 + 10.5168i −0.966082 + 1.56775i
\(46\) −4.92802 5.56539i −0.726597 0.820572i
\(47\) 2.91666 + 1.06158i 0.425439 + 0.154847i 0.545861 0.837876i \(-0.316203\pi\)
−0.120422 + 0.992723i \(0.538425\pi\)
\(48\) 2.68206 + 6.38800i 0.387121 + 0.922029i
\(49\) 2.51058 + 2.10662i 0.358654 + 0.300946i
\(50\) −14.4128 + 8.84052i −2.03827 + 1.25024i
\(51\) 0.0847871 1.46110i 0.0118726 0.204596i
\(52\) −0.334568 + 1.58057i −0.0463962 + 0.219186i
\(53\) −0.319942 + 0.319942i −0.0439474 + 0.0439474i −0.728739 0.684792i \(-0.759893\pi\)
0.684792 + 0.728739i \(0.259893\pi\)
\(54\) −1.47269 7.19939i −0.200408 0.979713i
\(55\) 10.5384i 1.42100i
\(56\) 3.82995 + 3.88753i 0.511798 + 0.519493i
\(57\) −1.79976 8.70688i −0.238384 1.15325i
\(58\) −2.57161 + 10.7315i −0.337669 + 1.40911i
\(59\) 12.8464 1.12391i 1.67245 0.146321i 0.788859 0.614574i \(-0.210672\pi\)
0.883594 + 0.468253i \(0.155116\pi\)
\(60\) 3.75743 13.7605i 0.485082 1.77647i
\(61\) 0.767663 + 1.64626i 0.0982891 + 0.210782i 0.949304 0.314360i \(-0.101790\pi\)
−0.851015 + 0.525142i \(0.824012\pi\)
\(62\) 6.83707 6.05407i 0.868309 0.768867i
\(63\) −3.18277 4.83467i −0.400991 0.609111i
\(64\) −5.05027 6.20441i −0.631284 0.775552i
\(65\) 2.54809 2.13810i 0.316052 0.265199i
\(66\) −4.29159 4.56960i −0.528259 0.562479i
\(67\) 6.51434 4.56139i 0.795853 0.557263i −0.103426 0.994637i \(-0.532981\pi\)
0.899279 + 0.437375i \(0.144092\pi\)
\(68\) 0.381550 + 1.64634i 0.0462698 + 0.199648i
\(69\) −6.62356 6.24634i −0.797383 0.751971i
\(70\) −1.27663 11.1630i −0.152586 1.33423i
\(71\) −0.00142217 0.000821091i −0.000168781 9.74456e-5i 0.499916 0.866074i \(-0.333364\pi\)
−0.500084 + 0.865977i \(0.666698\pi\)
\(72\) 3.97447 + 7.49690i 0.468396 + 0.883519i
\(73\) 9.80470 5.66074i 1.14755 0.662540i 0.199263 0.979946i \(-0.436145\pi\)
0.948290 + 0.317406i \(0.102812\pi\)
\(74\) 0.214222 + 0.289249i 0.0249028 + 0.0336246i
\(75\) −16.6078 + 12.3695i −1.91770 + 1.42831i
\(76\) 4.82741 + 9.06061i 0.553742 + 1.03932i
\(77\) −4.47526 2.08685i −0.510003 0.237818i
\(78\) −0.234180 + 1.96478i −0.0265157 + 0.222468i
\(79\) −1.07582 6.10127i −0.121039 0.686446i −0.983582 0.180462i \(-0.942241\pi\)
0.862543 0.505984i \(-0.168870\pi\)
\(80\) 0.315229 + 16.4680i 0.0352437 + 1.84117i
\(81\) −2.58858 8.61970i −0.287620 0.957745i
\(82\) −8.91091 + 1.81686i −0.984045 + 0.200638i
\(83\) −4.75015 + 6.78392i −0.521397 + 0.744632i −0.990350 0.138591i \(-0.955743\pi\)
0.468953 + 0.883223i \(0.344631\pi\)
\(84\) 5.09951 + 4.32054i 0.556402 + 0.471410i
\(85\) 1.47048 3.15345i 0.159496 0.342039i
\(86\) −3.99580 13.4687i −0.430878 1.45237i
\(87\) −1.95596 + 13.3731i −0.209701 + 1.43375i
\(88\) 6.24171 + 3.66602i 0.665369 + 0.390799i
\(89\) −14.7937 + 8.54116i −1.56813 + 0.905361i −0.571745 + 0.820432i \(0.693733\pi\)
−0.996387 + 0.0849297i \(0.972933\pi\)
\(90\) 3.06910 17.1984i 0.323512 1.81287i
\(91\) 0.403390 + 1.50547i 0.0422868 + 0.157816i
\(92\) 9.37095 + 4.76479i 0.976989 + 0.496764i
\(93\) 7.67362 8.13704i 0.795718 0.843772i
\(94\) −4.38795 + 0.116754i −0.452583 + 0.0120422i
\(95\) 3.67043 20.8160i 0.376578 2.13568i
\(96\) −6.84300 7.01237i −0.698411 0.715697i
\(97\) 11.8407 9.93553i 1.20224 1.00880i 0.202679 0.979245i \(-0.435035\pi\)
0.999563 0.0295553i \(-0.00940912\pi\)
\(98\) −4.39595 1.46880i −0.444058 0.148371i
\(99\) −5.73768 5.10172i −0.576659 0.512742i
\(100\) 14.3743 19.1088i 1.43743 1.91088i
\(101\) 13.0100 6.06666i 1.29454 0.603655i 0.351456 0.936204i \(-0.385687\pi\)
0.943086 + 0.332549i \(0.107909\pi\)
\(102\) 0.646572 + 1.96621i 0.0640201 + 0.194684i
\(103\) −6.55269 + 7.80920i −0.645656 + 0.769463i −0.985252 0.171108i \(-0.945265\pi\)
0.339596 + 0.940571i \(0.389710\pi\)
\(104\) −0.379949 2.25298i −0.0372571 0.220923i
\(105\) −2.78557 13.4760i −0.271844 1.31513i
\(106\) 0.254905 0.586919i 0.0247586 0.0570066i
\(107\) 2.71696 2.71696i 0.262659 0.262659i −0.563475 0.826133i \(-0.690536\pi\)
0.826133 + 0.563475i \(0.190536\pi\)
\(108\) 5.67297 + 8.70732i 0.545882 + 0.837862i
\(109\) −7.44099 7.44099i −0.712717 0.712717i 0.254386 0.967103i \(-0.418127\pi\)
−0.967103 + 0.254386i \(0.918127\pi\)
\(110\) −5.46801 13.8642i −0.521354 1.32190i
\(111\) 0.293135 + 0.329251i 0.0278231 + 0.0312512i
\(112\) −7.05575 3.12717i −0.666705 0.295490i
\(113\) −4.05974 3.40653i −0.381908 0.320459i 0.431543 0.902093i \(-0.357969\pi\)
−0.813451 + 0.581633i \(0.802414\pi\)
\(114\) 6.88545 + 10.5209i 0.644882 + 0.985368i
\(115\) −9.14732 19.6165i −0.852992 1.82925i
\(116\) −2.18500 15.4525i −0.202872 1.43473i
\(117\) −0.0694508 + 2.42239i −0.00642073 + 0.223950i
\(118\) −16.3174 + 8.14414i −1.50214 + 0.749729i
\(119\) 1.04796 + 1.24891i 0.0960665 + 0.114488i
\(120\) 2.19661 + 20.0528i 0.200523 + 1.83056i
\(121\) 4.38256 + 0.772763i 0.398414 + 0.0702512i
\(122\) −1.86412 1.76749i −0.168769 0.160021i
\(123\) −10.6695 + 3.19672i −0.962039 + 0.288239i
\(124\) −5.85353 + 11.5122i −0.525663 + 1.03383i
\(125\) −27.6663 + 7.41315i −2.47455 + 0.663052i
\(126\) 6.69576 + 4.70902i 0.596506 + 0.419513i
\(127\) 6.78143 + 11.7458i 0.601755 + 1.04227i 0.992555 + 0.121795i \(0.0388650\pi\)
−0.390800 + 0.920476i \(0.627802\pi\)
\(128\) 9.86335 + 5.54205i 0.871805 + 0.489853i
\(129\) −6.35611 15.9894i −0.559624 1.40778i
\(130\) −2.24286 + 4.13498i −0.196711 + 0.362662i
\(131\) 5.86573 + 2.73524i 0.512492 + 0.238979i 0.661620 0.749839i \(-0.269869\pi\)
−0.149129 + 0.988818i \(0.547647\pi\)
\(132\) 8.01699 + 3.78496i 0.697789 + 0.329438i
\(133\) 8.11296 + 5.68076i 0.703483 + 0.492584i
\(134\) −6.20346 + 9.38099i −0.535897 + 0.810394i
\(135\) 1.85119 21.3162i 0.159325 1.83461i
\(136\) −1.35619 1.96794i −0.116293 0.168749i
\(137\) 1.90050 0.335109i 0.162371 0.0286303i −0.0918718 0.995771i \(-0.529285\pi\)
0.254242 + 0.967141i \(0.418174\pi\)
\(138\) 11.9549 + 4.78089i 1.01767 + 0.406976i
\(139\) 3.10434 6.65728i 0.263307 0.564663i −0.729557 0.683920i \(-0.760274\pi\)
0.992863 + 0.119257i \(0.0380513\pi\)
\(140\) 7.47161 + 14.0235i 0.631466 + 1.18520i
\(141\) −5.33954 + 0.625256i −0.449670 + 0.0526561i
\(142\) 0.00229703 0.000342304i 0.000192763 2.87255e-5i
\(143\) 1.03368 + 1.79039i 0.0864408 + 0.149720i
\(144\) −9.11866 7.80064i −0.759889 0.650053i
\(145\) −16.0656 + 27.8265i −1.33418 + 2.31086i
\(146\) −9.96180 + 12.5345i −0.824444 + 1.03737i
\(147\) −5.52376 1.30791i −0.455592 0.107875i
\(148\) −0.431910 0.269381i −0.0355028 0.0221430i
\(149\) 4.41180 + 6.30070i 0.361429 + 0.516174i 0.958147 0.286277i \(-0.0924178\pi\)
−0.596718 + 0.802451i \(0.703529\pi\)
\(150\) 15.4309 24.8905i 1.25993 2.03230i
\(151\) −8.22168 9.79822i −0.669071 0.797368i 0.319586 0.947557i \(-0.396456\pi\)
−0.988657 + 0.150190i \(0.952012\pi\)
\(152\) −11.0521 9.41527i −0.896447 0.763679i
\(153\) 1.00504 + 2.32722i 0.0812527 + 0.188144i
\(154\) 6.97041 + 0.423379i 0.561691 + 0.0341168i
\(155\) 24.0988 11.2375i 1.93566 0.902615i
\(156\) −0.711372 2.70636i −0.0569554 0.216682i
\(157\) 0.833825 + 9.53066i 0.0665465 + 0.760630i 0.954015 + 0.299760i \(0.0969067\pi\)
−0.887468 + 0.460869i \(0.847538\pi\)
\(158\) 4.58107 + 7.46856i 0.364451 + 0.594167i
\(159\) 0.246348 0.743968i 0.0195367 0.0590005i
\(160\) −8.95937 21.5015i −0.708300 1.69984i
\(161\) 10.1418 0.799283
\(162\) 7.87798 + 9.99687i 0.618952 + 0.785428i
\(163\) 10.8134 + 10.8134i 0.846968 + 0.846968i 0.989754 0.142785i \(-0.0456059\pi\)
−0.142785 + 0.989754i \(0.545606\pi\)
\(164\) 10.7804 7.01380i 0.841808 0.547686i
\(165\) −8.19542 16.3098i −0.638013 1.26971i
\(166\) 2.72931 11.3896i 0.211836 0.884001i
\(167\) −11.4523 + 13.6484i −0.886209 + 1.05614i 0.111841 + 0.993726i \(0.464325\pi\)
−0.998050 + 0.0624171i \(0.980119\pi\)
\(168\) −8.95065 3.03810i −0.690558 0.234395i
\(169\) −4.22308 + 11.6028i −0.324852 + 0.892525i
\(170\) −0.298329 + 4.91162i −0.0228808 + 0.376704i
\(171\) 9.55651 + 12.0756i 0.730804 + 0.923443i
\(172\) 12.2453 + 15.6461i 0.933695 + 1.19300i
\(173\) 12.9056 + 1.12909i 0.981194 + 0.0858434i 0.566451 0.824095i \(-0.308316\pi\)
0.414743 + 0.909939i \(0.363871\pi\)
\(174\) −4.36561 18.6084i −0.330956 1.41070i
\(175\) 4.00568 22.7174i 0.302801 1.71727i
\(176\) −10.1137 1.58438i −0.762349 0.119427i
\(177\) −19.0077 + 11.7297i −1.42870 + 0.881657i
\(178\) 15.0308 18.9126i 1.12660 1.41756i
\(179\) 8.46944 2.26938i 0.633035 0.169621i 0.0719887 0.997405i \(-0.477065\pi\)
0.561047 + 0.827784i \(0.310399\pi\)
\(180\) 4.88598 + 24.2185i 0.364179 + 1.80514i
\(181\) 16.5414 + 4.43226i 1.22952 + 0.329448i 0.814391 0.580317i \(-0.197071\pi\)
0.415125 + 0.909765i \(0.363738\pi\)
\(182\) −1.31183 1.77128i −0.0972397 0.131296i
\(183\) −2.46832 1.95084i −0.182464 0.144210i
\(184\) −14.8006 1.40625i −1.09112 0.103670i
\(185\) 0.358447 + 0.984825i 0.0263536 + 0.0724058i
\(186\) −5.87331 + 14.6866i −0.430652 + 1.07687i
\(187\) 1.77146 + 1.24039i 0.129542 + 0.0907060i
\(188\) 5.71217 2.43036i 0.416603 0.177252i
\(189\) 8.68561 + 5.00724i 0.631785 + 0.364223i
\(190\) 5.97194 + 29.2898i 0.433250 + 2.12491i
\(191\) 1.37206 + 7.78135i 0.0992789 + 0.563038i 0.993352 + 0.115117i \(0.0367244\pi\)
−0.894073 + 0.447921i \(0.852165\pi\)
\(192\) 12.6411 + 5.67481i 0.912290 + 0.409544i
\(193\) −13.9949 + 5.09371i −1.00737 + 0.366653i −0.792423 0.609972i \(-0.791181\pi\)
−0.214949 + 0.976625i \(0.568958\pi\)
\(194\) −10.4223 + 19.2148i −0.748279 + 1.37954i
\(195\) −2.28081 + 5.29062i −0.163332 + 0.378869i
\(196\) 6.54538 0.348563i 0.467527 0.0248974i
\(197\) −13.8703 3.71653i −0.988216 0.264792i −0.271715 0.962378i \(-0.587591\pi\)
−0.716501 + 0.697586i \(0.754257\pi\)
\(198\) 10.1955 + 3.73469i 0.724566 + 0.265413i
\(199\) −0.526785 0.304139i −0.0373428 0.0215599i 0.481212 0.876604i \(-0.340197\pi\)
−0.518555 + 0.855044i \(0.673530\pi\)
\(200\) −8.99574 + 32.5977i −0.636095 + 2.30500i
\(201\) −6.53466 + 12.1255i −0.460919 + 0.855265i
\(202\) −13.9680 + 14.7317i −0.982788 + 1.03652i
\(203\) −8.63550 12.3328i −0.606093 0.865590i
\(204\) −1.87082 2.25124i −0.130984 0.157618i
\(205\) −26.3788 2.30785i −1.84237 0.161187i
\(206\) 4.56874 13.6737i 0.318319 0.952690i
\(207\) 15.1086 + 4.51619i 1.05012 + 0.313897i
\(208\) 1.66885 + 2.76685i 0.115714 + 0.191847i
\(209\) 12.3449 + 4.49318i 0.853916 + 0.310800i
\(210\) 10.6569 + 16.2836i 0.735397 + 1.12368i
\(211\) 1.67081 + 19.0974i 0.115023 + 1.31472i 0.806031 + 0.591873i \(0.201611\pi\)
−0.691008 + 0.722847i \(0.742833\pi\)
\(212\) −0.0308191 + 0.904407i −0.00211666 + 0.0621149i
\(213\) 0.00283957 0.000164779i 0.000194564 1.12904e-5i
\(214\) −2.16467 + 4.98415i −0.147974 + 0.340710i
\(215\) 40.9061i 2.78977i
\(216\) −11.9812 8.51176i −0.815220 0.579152i
\(217\) 12.4591i 0.845782i
\(218\) 13.6502 + 5.92842i 0.924506 + 0.401523i
\(219\) −10.7720 + 16.3857i −0.727907 + 1.10724i
\(220\) 14.3873 + 15.4025i 0.969993 + 1.03843i
\(221\) −0.0594906 0.679981i −0.00400177 0.0457404i
\(222\) −0.556482 0.281062i −0.0373486 0.0188637i
\(223\) −18.8969 6.87790i −1.26543 0.460578i −0.379841 0.925052i \(-0.624021\pi\)
−0.885587 + 0.464474i \(0.846243\pi\)
\(224\) 10.9051 + 0.453096i 0.728625 + 0.0302738i
\(225\) 16.0836 32.0592i 1.07224 2.13728i
\(226\) 7.10849 + 2.37514i 0.472850 + 0.157992i
\(227\) −12.2847 1.07477i −0.815366 0.0713353i −0.328160 0.944622i \(-0.606428\pi\)
−0.487206 + 0.873287i \(0.661984\pi\)
\(228\) −14.5173 10.2685i −0.961435 0.680049i
\(229\) −9.16724 13.0922i −0.605788 0.865155i 0.392726 0.919656i \(-0.371532\pi\)
−0.998514 + 0.0545005i \(0.982643\pi\)
\(230\) 22.2124 + 21.0610i 1.46465 + 1.38872i
\(231\) 8.54903 0.250575i 0.562485 0.0164866i
\(232\) 10.8924 + 19.1955i 0.715118 + 1.26025i
\(233\) 21.5026 + 12.4146i 1.40868 + 0.813305i 0.995262 0.0972345i \(-0.0309997\pi\)
0.413423 + 0.910539i \(0.364333\pi\)
\(234\) −1.16553 3.22291i −0.0761929 0.210688i
\(235\) −12.3453 3.30793i −0.805322 0.215785i
\(236\) 17.2413 19.1809i 1.12231 1.24857i
\(237\) 6.40978 + 8.60600i 0.416360 + 0.559020i
\(238\) −2.02671 1.09931i −0.131372 0.0712574i
\(239\) −8.30427 + 3.02251i −0.537159 + 0.195510i −0.596332 0.802738i \(-0.703376\pi\)
0.0591732 + 0.998248i \(0.481154\pi\)
\(240\) −13.2945 25.2415i −0.858159 1.62933i
\(241\) 3.34962 + 18.9966i 0.215768 + 1.22368i 0.879569 + 0.475771i \(0.157831\pi\)
−0.663801 + 0.747909i \(0.731058\pi\)
\(242\) −6.16661 + 1.25732i −0.396405 + 0.0808235i
\(243\) 10.7095 + 11.3272i 0.687017 + 0.726642i
\(244\) 3.36950 + 1.35806i 0.215710 + 0.0869411i
\(245\) −11.0546 7.74052i −0.706253 0.494524i
\(246\) 12.3781 9.74163i 0.789196 0.621104i
\(247\) −1.41821 3.89650i −0.0902386 0.247928i
\(248\) 1.72757 18.1825i 0.109701 1.15459i
\(249\) 2.07591 14.1932i 0.131555 0.899458i
\(250\) 32.5510 24.1077i 2.05871 1.52471i
\(251\) −7.85682 2.10523i −0.495918 0.132881i 0.00218687 0.999998i \(-0.499304\pi\)
−0.498105 + 0.867117i \(0.665971\pi\)
\(252\) −11.2522 2.72094i −0.708824 0.171403i
\(253\) 12.9941 3.48175i 0.816930 0.218896i
\(254\) −15.0161 11.9340i −0.942193 0.748805i
\(255\) 0.176565 + 6.02399i 0.0110569 + 0.377237i
\(256\) −15.8517 2.17332i −0.990732 0.135832i
\(257\) 3.15317 17.8825i 0.196689 1.11548i −0.713304 0.700855i \(-0.752802\pi\)
0.909993 0.414624i \(-0.136087\pi\)
\(258\) 16.6584 + 17.7375i 1.03710 + 1.10429i
\(259\) −0.489199 0.0427994i −0.0303974 0.00265943i
\(260\) 0.805179 6.60369i 0.0499351 0.409543i
\(261\) −7.37277 22.2180i −0.456363 1.37526i
\(262\) −9.13612 0.554923i −0.564432 0.0342833i
\(263\) −0.879079 + 2.41525i −0.0542064 + 0.148931i −0.963841 0.266479i \(-0.914140\pi\)
0.909634 + 0.415410i \(0.136362\pi\)
\(264\) −12.5110 0.819716i −0.769996 0.0504501i
\(265\) 1.19760 1.42725i 0.0735681 0.0876750i
\(266\) −13.6209 3.26401i −0.835150 0.200129i
\(267\) 16.2533 24.7234i 0.994686 1.51305i
\(268\) 3.29373 15.5603i 0.201197 0.950497i
\(269\) −20.8872 20.8872i −1.27351 1.27351i −0.944232 0.329281i \(-0.893194\pi\)
−0.329281 0.944232i \(-0.606806\pi\)
\(270\) 8.62483 + 29.0039i 0.524890 + 1.76512i
\(271\) 10.8575 0.659546 0.329773 0.944060i \(-0.393028\pi\)
0.329773 + 0.944060i \(0.393028\pi\)
\(272\) 2.80529 + 1.88532i 0.170096 + 0.114314i
\(273\) −1.79507 2.01624i −0.108643 0.122028i
\(274\) −2.32640 + 1.42697i −0.140543 + 0.0862064i
\(275\) −2.66680 30.4816i −0.160814 1.83811i
\(276\) −18.2084 0.0866985i −1.09602 0.00521864i
\(277\) 1.83990 0.857959i 0.110549 0.0515498i −0.366557 0.930396i \(-0.619464\pi\)
0.477106 + 0.878846i \(0.341686\pi\)
\(278\) −0.629807 + 10.3690i −0.0377733 + 0.621891i
\(279\) −5.54814 + 18.5609i −0.332158 + 1.11121i
\(280\) −17.1059 14.5724i −1.02227 0.870870i
\(281\) 9.35203 + 11.1453i 0.557895 + 0.664874i 0.969100 0.246669i \(-0.0793362\pi\)
−0.411204 + 0.911543i \(0.634892\pi\)
\(282\) 6.70022 3.59308i 0.398992 0.213965i
\(283\) 11.6642 + 16.6582i 0.693366 + 0.990229i 0.999271 + 0.0381670i \(0.0121519\pi\)
−0.305906 + 0.952062i \(0.598959\pi\)
\(284\) −0.00319956 0.000741519i −0.000189859 4.40011e-5i
\(285\) 10.5075 + 35.0704i 0.622412 + 2.07739i
\(286\) −2.28887 1.81908i −0.135344 0.107564i
\(287\) 6.20367 10.7451i 0.366191 0.634262i
\(288\) 16.0439 + 5.53109i 0.945397 + 0.325922i
\(289\) 8.14300 + 14.1041i 0.479000 + 0.829652i
\(290\) 6.69758 44.9442i 0.393295 2.63921i
\(291\) −10.5987 + 24.5849i −0.621306 + 1.44119i
\(292\) 6.60191 21.6592i 0.386347 1.26751i
\(293\) −0.931102 + 1.99675i −0.0543955 + 0.116652i −0.931627 0.363416i \(-0.881610\pi\)
0.877231 + 0.480068i \(0.159388\pi\)
\(294\) 7.94564 1.14541i 0.463399 0.0668019i
\(295\) −52.2934 + 9.22073i −3.04464 + 0.536852i
\(296\) 0.707989 + 0.130292i 0.0411510 + 0.00757307i
\(297\) 12.8474 + 3.43365i 0.745482 + 0.199240i
\(298\) −9.07334 6.00001i −0.525605 0.347571i
\(299\) −3.47818 2.43545i −0.201149 0.140846i
\(300\) −7.38596 + 40.7522i −0.426428 + 2.35283i
\(301\) 17.3713 + 8.10037i 1.00126 + 0.466898i
\(302\) 15.9003 + 8.62449i 0.914961 + 0.496284i
\(303\) −15.4171 + 19.5066i −0.885686 + 1.12062i
\(304\) 19.4253 + 6.65206i 1.11412 + 0.381522i
\(305\) −3.73983 6.47757i −0.214142 0.370904i
\(306\) −2.52973 2.54018i −0.144615 0.145213i
\(307\) −19.6861 + 5.27488i −1.12355 + 0.301053i −0.772318 0.635236i \(-0.780903\pi\)
−0.351229 + 0.936290i \(0.614236\pi\)
\(308\) −9.38988 + 3.05971i −0.535038 + 0.174343i
\(309\) 4.06828 17.1818i 0.231437 0.977436i
\(310\) −25.8734 + 27.2880i −1.46951 + 1.54985i
\(311\) 33.2479 + 5.86250i 1.88531 + 0.332432i 0.992916 0.118816i \(-0.0379099\pi\)
0.892399 + 0.451248i \(0.149021\pi\)
\(312\) 2.34011 + 3.19135i 0.132483 + 0.180675i
\(313\) −14.3312 17.0793i −0.810049 0.965379i 0.189816 0.981820i \(-0.439211\pi\)
−0.999865 + 0.0164408i \(0.994766\pi\)
\(314\) −6.04211 12.1058i −0.340976 0.683170i
\(315\) 14.7910 + 18.6899i 0.833381 + 1.05306i
\(316\) −9.90200 7.44861i −0.557031 0.419017i
\(317\) 8.56789 + 18.3739i 0.481221 + 1.03198i 0.985693 + 0.168553i \(0.0539094\pi\)
−0.504472 + 0.863428i \(0.668313\pi\)
\(318\) 0.0619262 + 1.10658i 0.00347265 + 0.0620539i
\(319\) −15.2981 12.8366i −0.856529 0.718713i
\(320\) 22.9433 + 23.6385i 1.28257 + 1.32143i
\(321\) −2.09200 + 6.31782i −0.116764 + 0.352627i
\(322\) −13.3424 + 5.26222i −0.743544 + 0.293252i
\(323\) −3.06706 3.06706i −0.170656 0.170656i
\(324\) −15.5512 9.06418i −0.863957 0.503565i
\(325\) −6.82913 + 6.82913i −0.378812 + 0.378812i
\(326\) −19.8366 8.61528i −1.09865 0.477156i
\(327\) 17.3027 + 5.72940i 0.956842 + 0.316837i
\(328\) −10.5434 + 14.8209i −0.582160 + 0.818346i
\(329\) 3.84942 4.58756i 0.212225 0.252920i
\(330\) 19.2444 + 17.2046i 1.05937 + 0.947084i
\(331\) 6.96348 3.24712i 0.382747 0.178478i −0.221715 0.975111i \(-0.571166\pi\)
0.604463 + 0.796633i \(0.293388\pi\)
\(332\) 2.31899 + 16.4001i 0.127271 + 0.900074i
\(333\) −0.709720 0.281603i −0.0388924 0.0154318i
\(334\) 7.98493 23.8979i 0.436916 1.30764i
\(335\) −25.0853 + 21.0491i −1.37056 + 1.15003i
\(336\) 13.3518 0.647287i 0.728398 0.0353124i
\(337\) 1.82132 10.3292i 0.0992136 0.562668i −0.894161 0.447746i \(-0.852227\pi\)
0.993374 0.114922i \(-0.0366619\pi\)
\(338\) −0.464460 17.4558i −0.0252633 0.949469i
\(339\) 8.93223 + 2.11497i 0.485132 + 0.114869i
\(340\) −2.15599 6.61648i −0.116925 0.358829i
\(341\) 4.27733 + 15.9632i 0.231630 + 0.864455i
\(342\) −18.8381 10.9280i −1.01865 0.590918i
\(343\) 17.1727 9.91466i 0.927238 0.535341i
\(344\) −24.2280 14.2301i −1.30629 0.767238i
\(345\) 29.4121 + 23.2459i 1.58349 + 1.25152i
\(346\) −17.5643 + 5.21085i −0.944264 + 0.280137i
\(347\) 6.94673 14.8973i 0.372920 0.799729i −0.626868 0.779126i \(-0.715663\pi\)
0.999788 0.0206037i \(-0.00655884\pi\)
\(348\) 15.3986 + 22.2159i 0.825453 + 1.19090i
\(349\) 3.62654 5.17924i 0.194124 0.277238i −0.710276 0.703923i \(-0.751430\pi\)
0.904400 + 0.426685i \(0.140319\pi\)
\(350\) 6.51742 + 31.9651i 0.348371 + 1.70861i
\(351\) −1.77634 3.80303i −0.0948142 0.202991i
\(352\) 14.1276 3.16327i 0.753002 0.168603i
\(353\) −2.81468 15.9628i −0.149810 0.849616i −0.963378 0.268146i \(-0.913589\pi\)
0.813568 0.581470i \(-0.197522\pi\)
\(354\) 18.9202 25.2939i 1.00559 1.34435i
\(355\) 0.00612853 + 0.00285778i 0.000325269 + 0.000151675i
\(356\) −9.96122 + 32.6802i −0.527944 + 1.73205i
\(357\) −2.59313 1.11791i −0.137243 0.0591660i
\(358\) −9.96481 + 7.38007i −0.526656 + 0.390049i
\(359\) 2.67808 1.54619i 0.141344 0.0816049i −0.427660 0.903939i \(-0.640662\pi\)
0.569004 + 0.822335i \(0.307329\pi\)
\(360\) −18.9941 29.3265i −1.00108 1.54564i
\(361\) −6.36497 3.67482i −0.334998 0.193411i
\(362\) −24.0615 + 2.75174i −1.26464 + 0.144628i
\(363\) −7.38363 + 2.21223i −0.387540 + 0.116112i
\(364\) 2.64489 + 1.64961i 0.138630 + 0.0864633i
\(365\) −38.1880 + 26.7395i −1.99885 + 1.39961i
\(366\) 4.25953 + 1.28578i 0.222649 + 0.0672089i
\(367\) 9.49482 7.96710i 0.495625 0.415879i −0.360412 0.932793i \(-0.617364\pi\)
0.856037 + 0.516914i \(0.172919\pi\)
\(368\) 20.2012 5.82949i 1.05306 0.303883i
\(369\) 14.0267 13.2448i 0.730201 0.689498i
\(370\) −0.982562 1.10964i −0.0510809 0.0576875i
\(371\) 0.368945 + 0.791205i 0.0191547 + 0.0410773i
\(372\) 0.106509 22.3690i 0.00552223 1.15978i
\(373\) −14.6676 + 1.28325i −0.759459 + 0.0664441i −0.460305 0.887761i \(-0.652260\pi\)
−0.299154 + 0.954205i \(0.596704\pi\)
\(374\) −2.97410 0.712693i −0.153787 0.0368525i
\(375\) 37.0527 32.9883i 1.91339 1.70351i
\(376\) −6.25384 + 6.16120i −0.322517 + 0.317740i
\(377\) 6.30333i 0.324638i
\(378\) −14.0248 2.08081i −0.721357 0.107025i
\(379\) 13.0497 13.0497i 0.670318 0.670318i −0.287471 0.957789i \(-0.592815\pi\)
0.957789 + 0.287471i \(0.0928145\pi\)
\(380\) −23.0541 35.4348i −1.18265 1.81777i
\(381\) −19.6297 12.9046i −1.00566 0.661125i
\(382\) −5.84254 9.52515i −0.298931 0.487349i
\(383\) −7.75454 6.50683i −0.396238 0.332483i 0.422799 0.906223i \(-0.361048\pi\)
−0.819037 + 0.573740i \(0.805492\pi\)
\(384\) −19.5749 0.906707i −0.998929 0.0462702i
\(385\) 19.1068 + 6.95430i 0.973772 + 0.354424i
\(386\) 15.7685 13.9627i 0.802598 0.710682i
\(387\) 22.2715 + 19.8030i 1.13213 + 1.00664i
\(388\) 3.74158 30.6866i 0.189950 1.55788i
\(389\) −0.106123 + 1.21299i −0.00538066 + 0.0615012i −0.998410 0.0563636i \(-0.982049\pi\)
0.993030 + 0.117865i \(0.0376049\pi\)
\(390\) 0.255495 8.14372i 0.0129375 0.412373i
\(391\) −4.37410 0.771271i −0.221208 0.0390049i
\(392\) −8.43018 + 3.85474i −0.425788 + 0.194694i
\(393\) −11.2052 + 0.328430i −0.565229 + 0.0165671i
\(394\) 20.1760 2.30738i 1.01645 0.116244i
\(395\) 6.60274 + 24.6417i 0.332220 + 1.23986i
\(396\) −15.3510 + 0.376797i −0.771415 + 0.0189348i
\(397\) 7.69753 28.7276i 0.386328 1.44180i −0.449735 0.893162i \(-0.648482\pi\)
0.836063 0.548633i \(-0.184852\pi\)
\(398\) 0.850841 + 0.126792i 0.0426488 + 0.00635552i
\(399\) −16.9738 2.48260i −0.849753 0.124285i
\(400\) −5.07909 47.5527i −0.253954 2.37764i
\(401\) −32.2740 + 11.7468i −1.61169 + 0.586606i −0.981773 0.190057i \(-0.939133\pi\)
−0.629915 + 0.776664i \(0.716910\pi\)
\(402\) 2.30545 19.3428i 0.114985 0.964729i
\(403\) 2.99195 4.27294i 0.149039 0.212850i
\(404\) 10.7325 26.6284i 0.533960 1.32481i
\(405\) 13.7120 + 34.4296i 0.681356 + 1.71082i
\(406\) 17.7598 + 11.7442i 0.881405 + 0.582855i
\(407\) −0.641477 + 0.113110i −0.0317968 + 0.00560664i
\(408\) 3.62933 + 1.99101i 0.179678 + 0.0985695i
\(409\) −5.63079 15.4705i −0.278425 0.764966i −0.997542 0.0700766i \(-0.977676\pi\)
0.719117 0.694889i \(-0.244547\pi\)
\(410\) 35.9011 10.6509i 1.77303 0.526009i
\(411\) −2.68070 + 1.99660i −0.132229 + 0.0984849i
\(412\) 1.08421 + 20.3595i 0.0534153 + 1.00304i
\(413\) 6.43961 24.0330i 0.316873 1.18258i
\(414\) −22.2200 + 1.89786i −1.09205 + 0.0932748i
\(415\) 17.0508 29.5329i 0.836992 1.44971i
\(416\) −3.63115 2.77414i −0.178032 0.136013i
\(417\) 0.372749 + 12.7173i 0.0182536 + 0.622770i
\(418\) −18.5722 + 0.494166i −0.908397 + 0.0241704i
\(419\) −21.9564 + 15.3741i −1.07264 + 0.751072i −0.969868 0.243633i \(-0.921661\pi\)
−0.102774 + 0.994705i \(0.532772\pi\)
\(420\) −22.4691 15.8930i −1.09638 0.775501i
\(421\) −1.75969 + 20.1133i −0.0857618 + 0.980262i 0.824400 + 0.566008i \(0.191513\pi\)
−0.910161 + 0.414254i \(0.864043\pi\)
\(422\) −12.1071 24.2575i −0.589364 1.18083i
\(423\) 7.77750 5.12009i 0.378155 0.248947i
\(424\) −0.428720 1.20582i −0.0208205 0.0585598i
\(425\) −3.45526 + 9.49326i −0.167605 + 0.460491i
\(426\) −0.00382120 + 0.00125657i −0.000185138 + 6.08811e-5i
\(427\) 3.49135 0.305454i 0.168958 0.0147819i
\(428\) 0.261718 7.68028i 0.0126506 0.371240i
\(429\) −2.99212 1.96703i −0.144461 0.0949692i
\(430\) 21.2248 + 53.8157i 1.02355 + 2.59522i
\(431\) 6.38373 0.307493 0.153747 0.988110i \(-0.450866\pi\)
0.153747 + 0.988110i \(0.450866\pi\)
\(432\) 20.1789 + 4.98133i 0.970856 + 0.239664i
\(433\) −3.98243 −0.191383 −0.0956917 0.995411i \(-0.530506\pi\)
−0.0956917 + 0.995411i \(0.530506\pi\)
\(434\) −6.46462 16.3911i −0.310312 0.786800i
\(435\) 3.22409 55.5595i 0.154583 2.66387i
\(436\) −21.0341 0.716770i −1.00735 0.0343270i
\(437\) −26.8793 + 2.35163i −1.28581 + 0.112494i
\(438\) 5.66962 27.1461i 0.270905 1.29709i
\(439\) 6.19053 17.0083i 0.295458 0.811764i −0.699786 0.714352i \(-0.746721\pi\)
0.995244 0.0974116i \(-0.0310563\pi\)
\(440\) −26.9196 12.7982i −1.28334 0.610132i
\(441\) 9.56599 2.27149i 0.455523 0.108166i
\(442\) 0.431084 + 0.863708i 0.0205046 + 0.0410824i
\(443\) 1.54020 17.6045i 0.0731769 0.836416i −0.867572 0.497312i \(-0.834321\pi\)
0.940749 0.339104i \(-0.110124\pi\)
\(444\) 0.877937 + 0.0810235i 0.0416650 + 0.00384521i
\(445\) 57.6197 40.3457i 2.73143 1.91257i
\(446\) 28.4292 0.756440i 1.34616 0.0358185i
\(447\) −11.7278 6.32036i −0.554707 0.298943i
\(448\) −14.5817 + 5.06217i −0.688920 + 0.239165i
\(449\) 4.75838 8.24176i 0.224562 0.388952i −0.731626 0.681706i \(-0.761238\pi\)
0.956188 + 0.292754i \(0.0945716\pi\)
\(450\) −4.52504 + 50.5219i −0.213312 + 2.38163i
\(451\) 4.25954 15.8968i 0.200574 0.748552i
\(452\) −10.5842 + 0.563646i −0.497841 + 0.0265117i
\(453\) 20.3441 + 8.77045i 0.955849 + 0.412072i
\(454\) 16.7193 4.96016i 0.784677 0.232792i
\(455\) −2.19503 6.03079i −0.102905 0.282728i
\(456\) 24.4269 + 5.97661i 1.14389 + 0.279880i
\(457\) 2.94521 0.519320i 0.137771 0.0242928i −0.104337 0.994542i \(-0.533272\pi\)
0.242108 + 0.970249i \(0.422161\pi\)
\(458\) 18.8534 + 12.4674i 0.880962 + 0.582562i
\(459\) −3.36527 2.82013i −0.157077 0.131632i
\(460\) −40.1503 16.1824i −1.87202 0.754509i
\(461\) −5.51386 + 7.87461i −0.256806 + 0.366757i −0.926765 0.375641i \(-0.877423\pi\)
0.669959 + 0.742398i \(0.266312\pi\)
\(462\) −11.1170 + 4.76545i −0.517210 + 0.221709i
\(463\) 5.32601 1.93851i 0.247521 0.0900901i −0.215281 0.976552i \(-0.569067\pi\)
0.462801 + 0.886462i \(0.346844\pi\)
\(464\) −24.2898 19.6017i −1.12762 0.909987i
\(465\) −28.5575 + 36.1327i −1.32432 + 1.67561i
\(466\) −34.7302 5.17549i −1.60884 0.239750i
\(467\) −4.11632 + 15.3623i −0.190480 + 0.710882i 0.802910 + 0.596100i \(0.203284\pi\)
−0.993391 + 0.114782i \(0.963383\pi\)
\(468\) 3.20562 + 3.63528i 0.148180 + 0.168041i
\(469\) −3.97127 14.8210i −0.183376 0.684370i
\(470\) 17.9578 2.05370i 0.828331 0.0947302i
\(471\) −8.70221 14.1017i −0.400977 0.649772i
\(472\) −12.7302 + 34.1801i −0.585954 + 1.57327i
\(473\) 25.0378 + 4.41483i 1.15124 + 0.202994i
\(474\) −12.8980 7.99615i −0.592425 0.367276i
\(475\) −5.34887 + 61.1379i −0.245423 + 2.80520i
\(476\) 3.23671 + 0.394648i 0.148354 + 0.0180887i
\(477\) 0.197303 + 1.34298i 0.00903387 + 0.0614909i
\(478\) 9.35675 8.28519i 0.427968 0.378956i
\(479\) 24.0803 + 8.76453i 1.10026 + 0.400461i 0.827412 0.561596i \(-0.189812\pi\)
0.272847 + 0.962057i \(0.412035\pi\)
\(480\) 30.5871 + 26.3094i 1.39611 + 1.20085i
\(481\) 0.157496 + 0.132155i 0.00718120 + 0.00602575i
\(482\) −14.2634 23.2538i −0.649681 1.05918i
\(483\) −15.6959 + 7.88698i −0.714189 + 0.358870i
\(484\) 7.46036 4.85376i 0.339107 0.220625i
\(485\) −45.0057 + 45.0057i −2.04361 + 2.04361i
\(486\) −19.9667 9.34518i −0.905706 0.423906i
\(487\) 0.321362i 0.0145623i 0.999973 + 0.00728116i \(0.00231769\pi\)
−0.999973 + 0.00728116i \(0.997682\pi\)
\(488\) −5.13754 0.0383364i −0.232565 0.00173541i
\(489\) −25.1446 8.32606i −1.13708 0.376517i
\(490\) 18.5596 + 4.44750i 0.838439 + 0.200917i
\(491\) 2.88903 0.252758i 0.130380 0.0114068i −0.0217788 0.999763i \(-0.506933\pi\)
0.152159 + 0.988356i \(0.451377\pi\)
\(492\) −11.2299 + 19.2385i −0.506281 + 0.867341i
\(493\) 2.78655 + 5.97578i 0.125500 + 0.269136i
\(494\) 3.88754 + 4.39034i 0.174909 + 0.197531i
\(495\) 25.3673 + 18.8685i 1.14018 + 0.848074i
\(496\) 7.16152 + 24.8171i 0.321562 + 1.11432i
\(497\) −0.00242718 + 0.00203665i −0.000108874 + 9.13562e-5i
\(498\) 4.63332 + 19.7496i 0.207624 + 0.884999i
\(499\) −4.28310 + 2.99906i −0.191738 + 0.134256i −0.665504 0.746394i \(-0.731783\pi\)
0.473766 + 0.880651i \(0.342894\pi\)
\(500\) −30.3152 + 48.6055i −1.35573 + 2.17371i
\(501\) 7.11027 30.0291i 0.317663 1.34160i
\(502\) 11.4287 1.30702i 0.510087 0.0583350i
\(503\) 6.24408 + 3.60502i 0.278410 + 0.160740i 0.632703 0.774394i \(-0.281945\pi\)
−0.354293 + 0.935134i \(0.615279\pi\)
\(504\) 16.2151 2.25876i 0.722279 0.100613i
\(505\) −51.1907 + 29.5550i −2.27796 + 1.31518i
\(506\) −15.2883 + 11.3227i −0.679648 + 0.503357i
\(507\) −2.48734 21.2413i −0.110467 0.943359i
\(508\) 25.9472 + 7.90892i 1.15122 + 0.350902i
\(509\) 30.0595 + 14.0170i 1.33236 + 0.621291i 0.952722 0.303843i \(-0.0982698\pi\)
0.379641 + 0.925134i \(0.376048\pi\)
\(510\) −3.35793 7.83348i −0.148692 0.346873i
\(511\) −3.79316 21.5121i −0.167800 0.951639i
\(512\) 21.9820 5.36571i 0.971477 0.237133i
\(513\) −24.1810 11.2570i −1.06762 0.497007i
\(514\) 5.13034 + 25.1621i 0.226289 + 1.10985i
\(515\) 24.0770 34.3856i 1.06096 1.51521i
\(516\) −31.1190 14.6918i −1.36994 0.646771i
\(517\) 3.35710 7.19932i 0.147645 0.316626i
\(518\) 0.665793 0.197522i 0.0292533 0.00867863i
\(519\) −20.8514 + 8.28889i −0.915276 + 0.363842i
\(520\) 2.36714 + 9.10553i 0.103806 + 0.399304i
\(521\) 20.0787 11.5924i 0.879663 0.507874i 0.00911605 0.999958i \(-0.497098\pi\)
0.870547 + 0.492084i \(0.163765\pi\)
\(522\) 21.2277 + 25.4044i 0.929112 + 1.11192i
\(523\) −5.83010 21.7582i −0.254932 0.951420i −0.968128 0.250455i \(-0.919420\pi\)
0.713196 0.700965i \(-0.247247\pi\)
\(524\) 12.3073 4.01037i 0.537648 0.175194i
\(525\) 11.4673 + 38.2737i 0.500473 + 1.67040i
\(526\) −0.0966823 3.63361i −0.00421555 0.158433i
\(527\) 0.947505 5.37357i 0.0412740 0.234076i
\(528\) 16.8846 5.41310i 0.734809 0.235575i
\(529\) −3.54638 + 2.97577i −0.154190 + 0.129381i
\(530\) −0.835005 + 2.49907i −0.0362703 + 0.108553i
\(531\) 20.2954 32.9352i 0.880744 1.42927i
\(532\) 19.6131 2.77331i 0.850335 0.120238i
\(533\) −4.70792 + 2.19534i −0.203923 + 0.0950906i
\(534\) −8.55455 + 40.9592i −0.370192 + 1.77248i
\(535\) −10.1701 + 12.1203i −0.439692 + 0.524005i
\(536\) 3.74050 + 22.1800i 0.161565 + 0.958030i
\(537\) −11.3429 + 10.0987i −0.489482 + 0.435789i
\(538\) 38.3166 + 16.6413i 1.65195 + 0.717458i
\(539\) 5.93089 5.93089i 0.255461 0.255461i
\(540\) −26.3959 33.6821i −1.13590 1.44945i
\(541\) 30.9302 + 30.9302i 1.32979 + 1.32979i 0.905547 + 0.424246i \(0.139461\pi\)
0.424246 + 0.905547i \(0.360539\pi\)
\(542\) −14.2840 + 5.63358i −0.613551 + 0.241983i
\(543\) −29.0472 + 6.00423i −1.24654 + 0.257666i
\(544\) −4.66884 1.02474i −0.200175 0.0439352i
\(545\) 33.1939 + 27.8530i 1.42187 + 1.19309i
\(546\) 3.40774 + 1.72115i 0.145838 + 0.0736583i
\(547\) −2.48007 5.31853i −0.106040 0.227404i 0.846127 0.532981i \(-0.178928\pi\)
−0.952167 + 0.305577i \(0.901151\pi\)
\(548\) 2.32019 3.08440i 0.0991134 0.131759i
\(549\) 5.33722 + 1.09968i 0.227787 + 0.0469330i
\(550\) 19.3243 + 38.7176i 0.823990 + 1.65093i
\(551\) 25.7468 + 30.6838i 1.09685 + 1.30718i
\(552\) 23.9998 9.33366i 1.02150 0.397267i
\(553\) −11.7719 2.07571i −0.500593 0.0882681i
\(554\) −1.97539 + 2.08338i −0.0839262 + 0.0885145i
\(555\) −1.32062 1.24541i −0.0560573 0.0528648i
\(556\) −4.55155 13.9681i −0.193029 0.592381i
\(557\) −9.71109 + 2.60208i −0.411472 + 0.110254i −0.458616 0.888635i \(-0.651655\pi\)
0.0471441 + 0.998888i \(0.484988\pi\)
\(558\) −2.33152 27.2972i −0.0987011 1.15558i
\(559\) −4.01237 6.94962i −0.169705 0.293938i
\(560\) 30.0655 + 10.2957i 1.27050 + 0.435073i
\(561\) −3.70621 0.542073i −0.156476 0.0228863i
\(562\) −18.0864 9.81023i −0.762927 0.413819i
\(563\) 4.24603 + 1.97995i 0.178949 + 0.0834451i 0.510028 0.860158i \(-0.329635\pi\)
−0.331079 + 0.943603i \(0.607413\pi\)
\(564\) −6.95042 + 8.20354i −0.292665 + 0.345431i
\(565\) 17.8759 + 12.5168i 0.752045 + 0.526588i
\(566\) −23.9887 15.8632i −1.00832 0.666782i
\(567\) −17.3363 0.994892i −0.728056 0.0417815i
\(568\) 0.00382456 0.00263568i 0.000160475 0.000110591i
\(569\) −25.5218 + 4.50018i −1.06993 + 0.188657i −0.680758 0.732508i \(-0.738349\pi\)
−0.389171 + 0.921166i \(0.627238\pi\)
\(570\) −32.0204 40.6862i −1.34119 1.70416i
\(571\) −4.30964 + 9.24205i −0.180353 + 0.386768i −0.975612 0.219502i \(-0.929557\pi\)
0.795259 + 0.606269i \(0.207335\pi\)
\(572\) 3.95508 + 1.20554i 0.165370 + 0.0504063i
\(573\) −8.17481 10.9758i −0.341508 0.458520i
\(574\) −2.58624 + 17.3550i −0.107948 + 0.724384i
\(575\) 31.4221 + 54.4247i 1.31039 + 2.26967i
\(576\) −23.9771 + 1.04799i −0.999046 + 0.0436663i
\(577\) −10.5177 + 18.2172i −0.437859 + 0.758393i −0.997524 0.0703252i \(-0.977596\pi\)
0.559666 + 0.828719i \(0.310930\pi\)
\(578\) −18.0310 14.3301i −0.749990 0.596053i
\(579\) 17.6979 18.7667i 0.735500 0.779918i
\(580\) 14.5087 + 62.6032i 0.602441 + 2.59946i
\(581\) 9.16505 + 13.0891i 0.380230 + 0.543025i
\(582\) 1.18726 37.8430i 0.0492134 1.56864i
\(583\) 0.744335 + 0.887064i 0.0308272 + 0.0367384i
\(584\) 2.55279 + 31.9201i 0.105635 + 1.32086i
\(585\) −0.584468 9.96176i −0.0241648 0.411868i
\(586\) 0.188901 3.11003i 0.00780345 0.128474i
\(587\) −5.92211 + 2.76153i −0.244432 + 0.113980i −0.540974 0.841039i \(-0.681944\pi\)
0.296542 + 0.955020i \(0.404166\pi\)
\(588\) −9.85889 + 5.62962i −0.406574 + 0.232161i
\(589\) −2.88898 33.0212i −0.119038 1.36061i
\(590\) 64.0123 39.2639i 2.63535 1.61647i
\(591\) 24.3566 5.03464i 1.00190 0.207098i
\(592\) −0.999028 + 0.195940i −0.0410598 + 0.00805310i
\(593\) −8.27131 −0.339662 −0.169831 0.985473i \(-0.554322\pi\)
−0.169831 + 0.985473i \(0.554322\pi\)
\(594\) −18.6835 + 2.14880i −0.766594 + 0.0881664i
\(595\) −4.74703 4.74703i −0.194609 0.194609i
\(596\) 15.0500 + 3.18572i 0.616472 + 0.130492i
\(597\) 1.05180 + 0.0610354i 0.0430473 + 0.00249801i
\(598\) 5.83954 + 1.39935i 0.238796 + 0.0572235i
\(599\) −11.4922 + 13.6958i −0.469557 + 0.559597i −0.947896 0.318579i \(-0.896795\pi\)
0.478339 + 0.878175i \(0.341239\pi\)
\(600\) −11.4280 57.4455i −0.466547 2.34520i
\(601\) −9.66476 + 26.5537i −0.394234 + 1.08315i 0.570815 + 0.821079i \(0.306627\pi\)
−0.965049 + 0.262070i \(0.915595\pi\)
\(602\) −27.0565 1.64340i −1.10274 0.0669799i
\(603\) 0.683725 23.8478i 0.0278434 0.971159i
\(604\) −25.3933 3.09617i −1.03324 0.125981i
\(605\) −18.2549 1.59710i −0.742167 0.0649312i
\(606\) 10.1612 33.6621i 0.412772 1.36743i
\(607\) −6.35431 + 36.0371i −0.257914 + 1.46270i 0.530568 + 0.847642i \(0.321979\pi\)
−0.788482 + 0.615058i \(0.789133\pi\)
\(608\) −29.0073 + 1.32776i −1.17640 + 0.0538476i
\(609\) 22.9556 + 12.3712i 0.930208 + 0.501308i
\(610\) 8.28107 + 6.58136i 0.335291 + 0.266471i
\(611\) −2.42184 + 0.648931i −0.0979773 + 0.0262529i
\(612\) 4.64611 + 2.02925i 0.187808 + 0.0820275i
\(613\) 7.16072 + 1.91871i 0.289219 + 0.0774960i 0.400512 0.916292i \(-0.368832\pi\)
−0.111293 + 0.993788i \(0.535499\pi\)
\(614\) 23.1619 17.1540i 0.934739 0.692281i
\(615\) 42.6199 16.9423i 1.71860 0.683181i
\(616\) 10.7657 8.89741i 0.433760 0.358487i
\(617\) 8.39124 + 23.0547i 0.337819 + 0.928149i 0.986012 + 0.166673i \(0.0533026\pi\)
−0.648194 + 0.761476i \(0.724475\pi\)
\(618\) 3.56283 + 24.7151i 0.143318 + 0.994186i
\(619\) −5.03248 3.52378i −0.202272 0.141633i 0.468052 0.883701i \(-0.344956\pi\)
−0.670324 + 0.742068i \(0.733845\pi\)
\(620\) 19.8801 49.3246i 0.798403 1.98092i
\(621\) −26.8949 + 4.76004i −1.07926 + 0.191014i
\(622\) −46.7825 + 9.53854i −1.87581 + 0.382461i
\(623\) 5.72328 + 32.4583i 0.229298 + 1.30041i
\(624\) −4.73451 2.98431i −0.189532 0.119468i
\(625\) 54.6546 19.8927i 2.18619 0.795706i
\(626\) 27.7159 + 15.0334i 1.10775 + 0.600855i
\(627\) −22.5999 + 2.64643i −0.902551 + 0.105688i
\(628\) 14.2302 + 12.7912i 0.567848 + 0.510426i
\(629\) 0.207734 + 0.0556623i 0.00828291 + 0.00221940i
\(630\) −29.1565 16.9137i −1.16162 0.673859i
\(631\) 19.7030 + 11.3755i 0.784363 + 0.452852i 0.837974 0.545710i \(-0.183740\pi\)
−0.0536113 + 0.998562i \(0.517073\pi\)
\(632\) 16.8918 + 4.66151i 0.671920 + 0.185425i
\(633\) −17.4374 28.2568i −0.693073 1.12311i
\(634\) −20.8054 19.7269i −0.826289 0.783457i
\(635\) −32.0333 45.7483i −1.27120 1.81547i
\(636\) −0.655635 1.42367i −0.0259976 0.0564523i
\(637\) −2.63734 0.230737i −0.104495 0.00914214i
\(638\) 26.7865 + 8.95009i 1.06049 + 0.354337i
\(639\) −0.00452280 + 0.00195323i −0.000178919 + 7.72687e-5i
\(640\) −42.4491 19.1941i −1.67795 0.758713i
\(641\) 6.15443 + 2.24003i 0.243085 + 0.0884758i 0.460690 0.887561i \(-0.347602\pi\)
−0.217605 + 0.976037i \(0.569824\pi\)
\(642\) −0.525881 9.39714i −0.0207549 0.370875i
\(643\) −0.907362 10.3712i −0.0357829 0.409000i −0.992870 0.119200i \(-0.961967\pi\)
0.957087 0.289800i \(-0.0935886\pi\)
\(644\) 14.8228 13.8458i 0.584099 0.545603i
\(645\) 31.8116 + 63.3084i 1.25258 + 2.49277i
\(646\) 5.62639 + 2.44361i 0.221368 + 0.0961424i
\(647\) 32.7166i 1.28622i 0.765773 + 0.643112i \(0.222357\pi\)
−0.765773 + 0.643112i \(0.777643\pi\)
\(648\) 25.1621 + 3.85575i 0.988462 + 0.151468i
\(649\) 33.0028i 1.29547i
\(650\) 5.44094 12.5277i 0.213411 0.491379i
\(651\) −9.68914 19.2824i −0.379747 0.755738i
\(652\) 30.5671 + 1.04162i 1.19710 + 0.0407931i
\(653\) −0.451383 5.15933i −0.0176640 0.201900i −0.999899 0.0142431i \(-0.995466\pi\)
0.982235 0.187657i \(-0.0600894\pi\)
\(654\) −25.7361 + 1.44024i −1.00636 + 0.0563177i
\(655\) −25.0433 9.11502i −0.978523 0.356153i
\(656\) 6.18071 24.9688i 0.241316 0.974867i
\(657\) 3.92865 33.7365i 0.153271 1.31619i
\(658\) −2.68393 + 8.03268i −0.104631 + 0.313147i
\(659\) −7.80472 0.682824i −0.304029 0.0265991i −0.0658792 0.997828i \(-0.520985\pi\)
−0.238149 + 0.971229i \(0.576541\pi\)
\(660\) −34.2446 12.6490i −1.33297 0.492362i
\(661\) −2.33064 3.32849i −0.0906512 0.129463i 0.771265 0.636514i \(-0.219624\pi\)
−0.861916 + 0.507051i \(0.830736\pi\)
\(662\) −7.47626 + 7.88499i −0.290573 + 0.306459i
\(663\) 0.620873 + 1.00611i 0.0241127 + 0.0390740i
\(664\) −11.5603 20.3726i −0.448627 0.790611i
\(665\) −35.3187 20.3913i −1.36960 0.790739i
\(666\) 1.07982 + 0.00222546i 0.0418420 + 8.62347e-5i
\(667\) 39.6185 + 10.6158i 1.53404 + 0.411044i
\(668\) 1.89491 + 35.5830i 0.0733163 + 1.37675i
\(669\) 34.5945 4.05099i 1.33750 0.156620i
\(670\) 22.0803 40.7078i 0.853038 1.57268i
\(671\) 4.36841 1.58997i 0.168640 0.0613801i
\(672\) −17.2296 + 7.77933i −0.664646 + 0.300094i
\(673\) −4.27667 24.2542i −0.164853 0.934930i −0.949216 0.314627i \(-0.898121\pi\)
0.784362 0.620303i \(-0.212990\pi\)
\(674\) 2.96336 + 14.5340i 0.114145 + 0.559830i
\(675\) 0.0397285 + 62.1242i 0.00152915 + 2.39116i
\(676\) 9.66824 + 22.7237i 0.371855 + 0.873987i
\(677\) 18.5865 + 13.0144i 0.714336 + 0.500183i 0.873350 0.487093i \(-0.161943\pi\)
−0.159014 + 0.987276i \(0.550832\pi\)
\(678\) −12.8485 + 1.85220i −0.493445 + 0.0711332i
\(679\) −10.2001 28.0244i −0.391443 1.07548i
\(680\) 6.26947 + 7.58591i 0.240423 + 0.290906i
\(681\) 19.8483 7.89013i 0.760589 0.302350i
\(682\) −13.9100 18.7817i −0.532640 0.719187i
\(683\) −21.4027 5.73484i −0.818952 0.219438i −0.175064 0.984557i \(-0.556013\pi\)
−0.643888 + 0.765120i \(0.722680\pi\)
\(684\) 30.4533 + 4.60233i 1.16441 + 0.175975i
\(685\) −7.67572 + 2.05670i −0.293274 + 0.0785826i
\(686\) −17.4478 + 21.9539i −0.666162 + 0.838206i
\(687\) 24.3691 + 13.1330i 0.929740 + 0.501055i
\(688\) 39.2577 + 6.14996i 1.49668 + 0.234465i
\(689\) 0.0634684 0.359947i 0.00241795 0.0137129i
\(690\) −50.7557 15.3211i −1.93224 0.583265i
\(691\) 28.3534 + 2.48060i 1.07861 + 0.0943665i 0.612586 0.790404i \(-0.290129\pi\)
0.466028 + 0.884770i \(0.345685\pi\)
\(692\) 20.4037 15.9689i 0.775634 0.607045i
\(693\) −13.0361 + 7.03615i −0.495199 + 0.267281i
\(694\) −1.40935 + 23.2032i −0.0534981 + 0.880781i
\(695\) −10.3450 + 28.4228i −0.392410 + 1.07814i
\(696\) −31.7854 21.2372i −1.20482 0.804995i
\(697\) −3.49277 + 4.16252i −0.132298 + 0.157667i
\(698\) −2.08371 + 8.69544i −0.0788697 + 0.329127i
\(699\) −42.9331 2.49138i −1.62388 0.0942327i
\(700\) −25.1599 38.6714i −0.950954 1.46164i
\(701\) −6.10882 6.10882i −0.230727 0.230727i 0.582269 0.812996i \(-0.302165\pi\)
−0.812996 + 0.582269i \(0.802165\pi\)
\(702\) 4.31020 + 4.08155i 0.162678 + 0.154048i
\(703\) 1.30648 0.0492747
\(704\) −16.9448 + 11.4919i −0.638631 + 0.433116i
\(705\) 21.6788 4.48113i 0.816470 0.168769i
\(706\) 11.9855 + 19.5401i 0.451081 + 0.735402i
\(707\) −2.41393 27.5913i −0.0907852 1.03768i
\(708\) −11.7670 + 43.0934i −0.442233 + 1.61955i
\(709\) 19.3329 9.01509i 0.726063 0.338569i −0.0242011 0.999707i \(-0.507704\pi\)
0.750264 + 0.661138i \(0.229926\pi\)
\(710\) −0.00954544 0.000579785i −0.000358234 2.17589e-5i
\(711\) −16.6128 8.33437i −0.623027 0.312563i
\(712\) −3.85176 48.1623i −0.144351 1.80496i
\(713\) −21.8180 26.0017i −0.817090 0.973770i
\(714\) 3.99154 + 0.125227i 0.149379 + 0.00468652i
\(715\) −4.88278 6.97334i −0.182606 0.260788i
\(716\) 9.28034 14.8796i 0.346823 0.556075i
\(717\) 10.5016 11.1358i 0.392189 0.415874i
\(718\) −2.72099 + 3.42372i −0.101547 + 0.127772i
\(719\) −13.8110 + 23.9214i −0.515065 + 0.892118i 0.484783 + 0.874635i \(0.338899\pi\)
−0.999847 + 0.0174833i \(0.994435\pi\)
\(720\) 40.2050 + 28.7262i 1.49835 + 1.07056i
\(721\) 9.83444 + 17.0338i 0.366254 + 0.634370i
\(722\) 10.2804 + 1.53199i 0.382598 + 0.0570148i
\(723\) −19.9572 26.7952i −0.742216 0.996526i
\(724\) 30.2273 16.1049i 1.12339 0.598532i
\(725\) 39.4272 84.5518i 1.46429 3.14018i
\(726\) 8.56598 6.74150i 0.317913 0.250200i
\(727\) −17.4714 + 3.08068i −0.647978 + 0.114256i −0.487971 0.872860i \(-0.662263\pi\)
−0.160007 + 0.987116i \(0.551152\pi\)
\(728\) −4.33553 0.797872i −0.160685 0.0295711i
\(729\) −25.3835 9.20209i −0.940129 0.340818i
\(730\) 36.3656 54.9928i 1.34595 2.03537i
\(731\) −6.87613 4.81472i −0.254323 0.178079i
\(732\) −6.27094 + 0.518562i −0.231781 + 0.0191666i
\(733\) −23.5433 10.9784i −0.869592 0.405497i −0.0639869 0.997951i \(-0.520382\pi\)
−0.805605 + 0.592454i \(0.798159\pi\)
\(734\) −8.35744 + 15.4080i −0.308479 + 0.568719i
\(735\) 23.1283 + 3.38276i 0.853099 + 0.124775i
\(736\) −23.5518 + 18.1509i −0.868130 + 0.669052i
\(737\) −10.1763 17.6259i −0.374850 0.649259i
\(738\) −11.5811 + 24.7027i −0.426307 + 0.909320i
\(739\) −5.86528 + 1.57160i −0.215758 + 0.0578121i −0.365079 0.930977i \(-0.618958\pi\)
0.149321 + 0.988789i \(0.452291\pi\)
\(740\) 1.86840 + 0.950016i 0.0686839 + 0.0349233i
\(741\) 5.22510 + 4.92752i 0.191949 + 0.181017i
\(742\) −0.895910 0.849469i −0.0328899 0.0311850i
\(743\) 35.6202 + 6.28080i 1.30678 + 0.230420i 0.783313 0.621628i \(-0.213528\pi\)
0.523464 + 0.852048i \(0.324639\pi\)
\(744\) 11.4664 + 29.4837i 0.420378 + 1.08093i
\(745\) −20.3588 24.2626i −0.745887 0.888914i
\(746\) 18.6307 9.29874i 0.682119 0.340451i
\(747\) 7.82489 + 23.5805i 0.286298 + 0.862766i
\(748\) 4.28250 0.605548i 0.156584 0.0221410i
\(749\) −3.13310 6.71896i −0.114481 0.245506i
\(750\) −31.6297 + 62.6244i −1.15495 + 2.28672i
\(751\) 40.8184 + 34.2507i 1.48948 + 1.24983i 0.895275 + 0.445515i \(0.146979\pi\)
0.594209 + 0.804311i \(0.297465\pi\)
\(752\) 5.03066 11.3505i 0.183449 0.413911i
\(753\) 13.7968 2.85188i 0.502783 0.103928i
\(754\) −3.27058 8.29260i −0.119108 0.301999i
\(755\) 37.2424 + 37.2424i 1.35539 + 1.35539i
\(756\) 19.5305 4.53949i 0.710319 0.165100i
\(757\) −1.36227 + 1.36227i −0.0495124 + 0.0495124i −0.731429 0.681917i \(-0.761146\pi\)
0.681917 + 0.731429i \(0.261146\pi\)
\(758\) −10.3970 + 23.9391i −0.377637 + 0.869508i
\(759\) −17.4026 + 15.4937i −0.631675 + 0.562385i
\(760\) 48.7157 + 34.6557i 1.76710 + 1.25709i
\(761\) −2.48671 + 2.96354i −0.0901431 + 0.107428i −0.809230 0.587491i \(-0.800116\pi\)
0.719087 + 0.694920i \(0.244560\pi\)
\(762\) 32.5204 + 6.79207i 1.17809 + 0.246051i
\(763\) −18.4013 + 8.58067i −0.666172 + 0.310641i
\(764\) 12.6287 + 9.49970i 0.456889 + 0.343687i
\(765\) −4.95795 9.18572i −0.179255 0.332110i
\(766\) 13.5780 + 4.53676i 0.490592 + 0.163920i
\(767\) −7.97979 + 6.69584i −0.288134 + 0.241773i
\(768\) 26.2231 8.96391i 0.946243 0.323457i
\(769\) 0.773602 4.38732i 0.0278968 0.158211i −0.967677 0.252192i \(-0.918848\pi\)
0.995574 + 0.0939818i \(0.0299595\pi\)
\(770\) −28.7451 + 0.764843i −1.03590 + 0.0275630i
\(771\) 9.02673 + 30.1280i 0.325090 + 1.08503i
\(772\) −13.5002 + 26.5509i −0.485882 + 0.955589i
\(773\) 9.57568 + 35.7369i 0.344413 + 1.28537i 0.893296 + 0.449469i \(0.148387\pi\)
−0.548883 + 0.835899i \(0.684947\pi\)
\(774\) −39.5753 14.4967i −1.42251 0.521072i
\(775\) −66.8606 + 38.6020i −2.40170 + 1.38662i
\(776\) 10.9998 + 42.3124i 0.394872 + 1.51893i
\(777\) 0.790394 0.314199i 0.0283552 0.0112718i
\(778\) −0.489766 1.65087i −0.0175590 0.0591864i
\(779\) −13.9504 + 29.9168i −0.499825 + 1.07188i
\(780\) 3.88937 + 10.8464i 0.139262 + 0.388362i
\(781\) −0.00241061 + 0.00344271i −8.62586e−5 + 0.000123190i
\(782\) 6.15471 1.25489i 0.220092 0.0448748i
\(783\) 28.6888 + 28.6522i 1.02526 + 1.02394i
\(784\) 9.09057 9.44539i 0.324663 0.337335i
\(785\) −6.84082 38.7962i −0.244159 1.38470i
\(786\) 14.5711 6.24609i 0.519733 0.222791i
\(787\) −19.1320 8.92142i −0.681984 0.318014i 0.0505729 0.998720i \(-0.483895\pi\)
−0.732557 + 0.680706i \(0.761673\pi\)
\(788\) −25.3461 + 13.5042i −0.902918 + 0.481067i
\(789\) −0.517767 4.42160i −0.0184330 0.157413i
\(790\) −21.4723 28.9925i −0.763948 1.03151i
\(791\) −8.85529 + 5.11260i −0.314858 + 0.181783i
\(792\) 20.0001 8.46080i 0.710672 0.300641i
\(793\) −1.27073 0.733658i −0.0451251 0.0260530i
\(794\) 4.77895 + 41.7877i 0.169599 + 1.48299i
\(795\) −0.743539 + 3.14022i −0.0263706 + 0.111372i
\(796\) −1.18515 + 0.274665i −0.0420064 + 0.00973525i
\(797\) 35.2020 24.6487i 1.24692 0.873103i 0.251421 0.967878i \(-0.419102\pi\)
0.995499 + 0.0947751i \(0.0302132\pi\)
\(798\) 23.6187 5.54104i 0.836093 0.196151i
\(799\) −2.00912 + 1.68585i −0.0710774 + 0.0596410i
\(800\) 31.3555 + 59.9246i 1.10858 + 2.11865i
\(801\) −5.92771 + 50.9030i −0.209445 + 1.79857i
\(802\) 36.3644 32.1998i 1.28407 1.13702i
\(803\) −12.2452 26.2600i −0.432125 0.926695i
\(804\) 7.00327 + 26.6434i 0.246986 + 0.939639i
\(805\) −41.6023 + 3.63973i −1.46629 + 0.128284i
\(806\) −1.71909 + 7.17386i −0.0605525 + 0.252688i
\(807\) 48.5694 + 16.0827i 1.70973 + 0.566137i
\(808\) −0.302963 + 40.6008i −0.0106582 + 1.42833i
\(809\) 14.9627i 0.526059i 0.964788 + 0.263030i \(0.0847217\pi\)
−0.964788 + 0.263030i \(0.915278\pi\)
\(810\) −35.9038 38.1806i −1.26153 1.34153i
\(811\) 12.8612 12.8612i 0.451618 0.451618i −0.444274 0.895891i \(-0.646538\pi\)
0.895891 + 0.444274i \(0.146538\pi\)
\(812\) −29.4583 6.23560i −1.03378 0.218827i
\(813\) −16.8036 + 8.44358i −0.589329 + 0.296129i
\(814\) 0.785232 0.481646i 0.0275224 0.0168817i
\(815\) −48.2380 40.4765i −1.68970 1.41783i
\(816\) −5.80777 0.736215i −0.203313 0.0257727i
\(817\) −47.9184 17.4409i −1.67645 0.610179i
\(818\) 15.4349 + 17.4312i 0.539669 + 0.609467i
\(819\) 4.34612 + 1.72446i 0.151866 + 0.0602575i
\(820\) −41.7048 + 32.6401i −1.45640 + 1.13984i
\(821\) −0.121665 + 1.39064i −0.00424614 + 0.0485336i −0.998022 0.0628631i \(-0.979977\pi\)
0.993776 + 0.111397i \(0.0355324\pi\)
\(822\) 2.49074 4.01763i 0.0868746 0.140131i
\(823\) 35.3400 + 6.23140i 1.23188 + 0.217213i 0.751431 0.659812i \(-0.229364\pi\)
0.480445 + 0.877025i \(0.340475\pi\)
\(824\) −11.9902 26.2222i −0.417700 0.913494i
\(825\) 27.8320 + 45.1010i 0.968986 + 1.57022i
\(826\) 3.99798 + 34.9588i 0.139108 + 1.21637i
\(827\) −12.4254 46.3721i −0.432072 1.61252i −0.747977 0.663725i \(-0.768975\pi\)
0.315904 0.948791i \(-0.397692\pi\)
\(828\) 28.2477 14.0260i 0.981675 0.487437i
\(829\) −4.11538 + 15.3588i −0.142933 + 0.533434i 0.856906 + 0.515473i \(0.172384\pi\)
−0.999839 + 0.0179604i \(0.994283\pi\)
\(830\) −7.10830 + 47.7003i −0.246733 + 1.65570i
\(831\) −2.18031 + 2.75866i −0.0756342 + 0.0956969i
\(832\) 6.21651 + 1.76555i 0.215519 + 0.0612095i
\(833\) −2.60229 + 0.947157i −0.0901641 + 0.0328170i
\(834\) −7.08896 16.5374i −0.245471 0.572642i
\(835\) 42.0802 60.0967i 1.45624 2.07973i
\(836\) 24.1770 10.2866i 0.836180 0.355770i
\(837\) −5.84770 33.0404i −0.202126 1.14204i
\(838\) 20.9086 31.6184i 0.722276 1.09224i
\(839\) −31.3495 + 5.52776i −1.08230 + 0.190840i −0.686234 0.727381i \(-0.740738\pi\)
−0.396071 + 0.918220i \(0.629626\pi\)
\(840\) 37.8065 + 9.25026i 1.30445 + 0.319164i
\(841\) −10.9066 29.9656i −0.376089 1.03330i
\(842\) −8.12108 27.3739i −0.279871 0.943367i
\(843\) −23.1411 9.97624i −0.797022 0.343600i
\(844\) 28.5143 + 25.6309i 0.981504 + 0.882253i
\(845\) 13.1593 49.1112i 0.452694 1.68948i
\(846\) −7.57536 + 10.7714i −0.260446 + 0.370329i
\(847\) 4.29313 7.43591i 0.147514 0.255501i
\(848\) 1.18968 + 1.36392i 0.0408537 + 0.0468371i
\(849\) −31.0068 16.7102i −1.06415 0.573492i
\(850\) −0.380014 14.2821i −0.0130344 0.489870i
\(851\) 1.09588 0.767347i 0.0375665 0.0263043i
\(852\) 0.00437515 0.00363583i 0.000149890 0.000124561i
\(853\) 1.74164 19.9071i 0.0596328 0.681606i −0.906270 0.422700i \(-0.861082\pi\)
0.965903 0.258906i \(-0.0833620\pi\)
\(854\) −4.43470 + 2.21340i −0.151752 + 0.0757408i
\(855\) −43.5352 46.1053i −1.48887 1.57677i
\(856\) 3.64072 + 10.2399i 0.124437 + 0.349993i
\(857\) −0.394161 + 1.08295i −0.0134643 + 0.0369928i −0.946243 0.323457i \(-0.895155\pi\)
0.932778 + 0.360450i \(0.117377\pi\)
\(858\) 4.95703 + 1.03530i 0.169230 + 0.0353446i
\(859\) 21.0814 1.84439i 0.719289 0.0629296i 0.278367 0.960475i \(-0.410207\pi\)
0.440922 + 0.897545i \(0.354651\pi\)
\(860\) −55.8462 59.7866i −1.90434 2.03871i
\(861\) −1.24497 + 21.4541i −0.0424284 + 0.731153i
\(862\) −8.39837 + 3.31230i −0.286050 + 0.112817i
\(863\) −53.3148 −1.81486 −0.907428 0.420208i \(-0.861957\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(864\) −29.1318 + 3.91672i −0.991083 + 0.133250i
\(865\) −53.3449 −1.81378
\(866\) 5.23925 2.06635i 0.178037 0.0702173i
\(867\) −23.5709 15.4956i −0.800509 0.526259i
\(868\) 17.0096 + 18.2098i 0.577343 + 0.618079i
\(869\) −15.7953 + 1.38191i −0.535819 + 0.0468781i
\(870\) 24.5863 + 74.7664i 0.833555 + 2.53482i
\(871\) −2.19715 + 6.03661i −0.0744475 + 0.204543i
\(872\) 28.0441 9.97089i 0.949694 0.337657i
\(873\) −2.71596 46.2912i −0.0919213 1.56672i
\(874\) 34.1420 17.0405i 1.15487 0.576404i
\(875\) −4.81648 + 55.0527i −0.162827 + 1.86112i
\(876\) 6.62629 + 38.6550i 0.223882 + 1.30603i
\(877\) 17.8659 12.5099i 0.603289 0.422428i −0.231627 0.972805i \(-0.574405\pi\)
0.834916 + 0.550377i \(0.185516\pi\)
\(878\) 0.680842 + 25.5881i 0.0229773 + 0.863555i
\(879\) −0.111801 3.81437i −0.00377094 0.128656i
\(880\) 42.0558 + 2.86957i 1.41770 + 0.0967331i
\(881\) −5.35638 + 9.27752i −0.180461 + 0.312568i −0.942038 0.335507i \(-0.891092\pi\)
0.761577 + 0.648075i \(0.224426\pi\)
\(882\) −11.4063 + 7.95181i −0.384071 + 0.267751i
\(883\) 3.08521 11.5142i 0.103826 0.387483i −0.894384 0.447301i \(-0.852385\pi\)
0.998209 + 0.0598179i \(0.0190520\pi\)
\(884\) −1.01528 0.912612i −0.0341475 0.0306945i
\(885\) 73.7612 54.9376i 2.47945 1.84671i
\(886\) 7.10811 + 23.9595i 0.238802 + 0.804935i
\(887\) −7.47420 20.5352i −0.250959 0.689505i −0.999647 0.0265815i \(-0.991538\pi\)
0.748688 0.662923i \(-0.230684\pi\)
\(888\) −1.19705 + 0.348937i −0.0401702 + 0.0117096i
\(889\) 25.7710 4.54412i 0.864330 0.152405i
\(890\) −54.8699 + 82.9753i −1.83924 + 2.78134i
\(891\) −22.5535 + 4.67699i −0.755572 + 0.156685i
\(892\) −37.0087 + 15.7461i −1.23914 + 0.527219i
\(893\) −9.13859 + 13.0513i −0.305811 + 0.436744i
\(894\) 18.7084 + 2.22984i 0.625703 + 0.0745770i
\(895\) −33.9278 + 12.3487i −1.13408 + 0.412772i
\(896\) 16.5569 14.2257i 0.553129 0.475247i
\(897\) 7.27700 + 1.06434i 0.242972 + 0.0355372i
\(898\) −1.98372 + 13.3117i −0.0661974 + 0.444218i
\(899\) −13.0414 + 48.6713i −0.434956 + 1.62328i
\(900\) −20.2610 68.8141i −0.675367 2.29380i
\(901\) −0.0989538 0.369301i −0.00329663 0.0123032i
\(902\) 2.64450 + 23.1238i 0.0880524 + 0.769940i
\(903\) −33.1842 + 0.972640i −1.10430 + 0.0323674i
\(904\) 13.6321 6.23332i 0.453396 0.207317i
\(905\) −69.4449 12.2450i −2.30843 0.407038i
\(906\) −31.3152 0.982459i −1.04038 0.0326400i
\(907\) 3.38685 38.7119i 0.112459 1.28541i −0.704912 0.709295i \(-0.749014\pi\)
0.817371 0.576112i \(-0.195431\pi\)
\(908\) −19.4221 + 15.2006i −0.644547 + 0.504451i
\(909\) 8.69048 42.1788i 0.288245 1.39898i
\(910\) 6.01693 + 6.79513i 0.199459 + 0.225256i
\(911\) −39.1871 14.2629i −1.29833 0.472552i −0.401875 0.915694i \(-0.631641\pi\)
−0.896451 + 0.443142i \(0.853864\pi\)
\(912\) −35.2368 + 4.81149i −1.16681 + 0.159324i
\(913\) 16.2362 + 13.6238i 0.537341 + 0.450883i
\(914\) −3.60524 + 2.21138i −0.119251 + 0.0731460i
\(915\) 10.8254 + 7.11666i 0.357876 + 0.235269i
\(916\) −31.2723 6.61957i −1.03326 0.218717i
\(917\) 8.82997 8.82997i 0.291591 0.291591i
\(918\) 5.89058 + 1.96401i 0.194418 + 0.0648221i
\(919\) 10.6068i 0.349887i −0.984579 0.174943i \(-0.944026\pi\)
0.984579 0.174943i \(-0.0559742\pi\)
\(920\) 61.2179 + 0.456809i 2.01829 + 0.0150605i
\(921\) 26.3651 23.4730i 0.868760 0.773463i
\(922\) 3.16812 13.2207i 0.104336 0.435401i
\(923\) 0.00132150 0.000115616i 4.34977e−5 3.80556e-6i
\(924\) 12.1528 12.0376i 0.399798 0.396009i
\(925\) −1.28600 2.75784i −0.0422834 0.0906771i
\(926\) −6.00102 + 5.31377i −0.197206 + 0.174621i
\(927\) 7.06551 + 29.7552i 0.232062 + 0.977288i
\(928\) 42.1260 + 13.1847i 1.38285 + 0.432810i
\(929\) 12.2055 10.2416i 0.400448 0.336016i −0.420219 0.907423i \(-0.638047\pi\)
0.820667 + 0.571407i \(0.193602\pi\)
\(930\) 18.8220 62.3533i 0.617197 2.04465i
\(931\) −13.7807 + 9.64935i −0.451644 + 0.316245i
\(932\) 48.3760 11.2115i 1.58461 0.367244i
\(933\) −56.0152 + 16.7829i −1.83386 + 0.549447i
\(934\) −2.55558 22.3463i −0.0836213 0.731194i
\(935\) −7.71180 4.45241i −0.252203 0.145609i
\(936\) −6.10350 3.11926i −0.199499 0.101956i
\(937\) 0.360122 0.207917i 0.0117647 0.00679235i −0.494106 0.869402i \(-0.664505\pi\)
0.505871 + 0.862609i \(0.331171\pi\)
\(938\) 12.9147 + 17.4378i 0.421679 + 0.569364i
\(939\) 35.4619 + 15.2878i 1.15725 + 0.498898i
\(940\) −22.5595 + 12.0195i −0.735810 + 0.392033i
\(941\) 11.4335 + 5.33155i 0.372723 + 0.173803i 0.599948 0.800039i \(-0.295188\pi\)
−0.227226 + 0.973842i \(0.572966\pi\)
\(942\) 18.7654 + 14.0368i 0.611411 + 0.457343i
\(943\) 5.86959 + 33.2881i 0.191140 + 1.08401i
\(944\) −0.987196 51.5723i −0.0321305 1.67853i
\(945\) −37.4260 17.4229i −1.21747 0.566767i
\(946\) −35.2302 + 7.18313i −1.14543 + 0.233544i
\(947\) −7.02203 + 10.0285i −0.228185 + 0.325883i −0.916876 0.399173i \(-0.869297\pi\)
0.688690 + 0.725056i \(0.258186\pi\)
\(948\) 21.1174 + 3.82733i 0.685862 + 0.124306i
\(949\) −3.86504 + 8.28860i −0.125464 + 0.269059i
\(950\) −24.6854 83.2078i −0.800901 2.69962i
\(951\) −27.5490 21.7734i −0.893337 0.706050i
\(952\) −4.46295 + 1.16022i −0.144645 + 0.0376030i
\(953\) 49.8922 28.8053i 1.61617 0.933095i 0.628268 0.777997i \(-0.283764\pi\)
0.987899 0.155098i \(-0.0495692\pi\)
\(954\) −0.956397 1.66444i −0.0309645 0.0538882i
\(955\) −8.42090 31.4272i −0.272494 1.01696i
\(956\) −8.01075 + 15.7548i −0.259086 + 0.509547i
\(957\) 33.6588 + 7.96971i 1.08804 + 0.257624i
\(958\) −36.2275 + 0.963934i −1.17046 + 0.0311433i
\(959\) 0.646567 3.66687i 0.0208788 0.118409i
\(960\) −53.8912 18.7418i −1.73933 0.604889i
\(961\) 8.19562 6.87694i 0.264375 0.221837i
\(962\) −0.275771 0.0921424i −0.00889122 0.00297079i
\(963\) −1.67551 11.4047i −0.0539925 0.367511i
\(964\) 30.8304 + 23.1916i 0.992981 + 0.746953i
\(965\) 55.5799 25.9173i 1.78918 0.834308i
\(966\) 16.5571 18.5201i 0.532717 0.595875i
\(967\) 28.1828 33.5870i 0.906299 1.08008i −0.0901540 0.995928i \(-0.528736\pi\)
0.996453 0.0841567i \(-0.0268196\pi\)
\(968\) −7.29632 + 10.2565i −0.234513 + 0.329656i
\(969\) 7.13192 + 2.36157i 0.229110 + 0.0758647i
\(970\) 35.8572 82.5611i 1.15131 2.65088i
\(971\) −1.18650 + 1.18650i −0.0380765 + 0.0380765i −0.725889 0.687812i \(-0.758571\pi\)
0.687812 + 0.725889i \(0.258571\pi\)
\(972\) 31.1168 + 1.93442i 0.998073 + 0.0620465i
\(973\) −10.0215 10.0215i −0.321275 0.321275i
\(974\) −0.166744 0.422781i −0.00534282 0.0135468i
\(975\) 5.25828 15.8799i 0.168400 0.508565i
\(976\) 6.77879 2.61526i 0.216984 0.0837123i
\(977\) 46.5426 + 39.0538i 1.48903 + 1.24944i 0.895838 + 0.444381i \(0.146576\pi\)
0.593190 + 0.805062i \(0.297868\pi\)
\(978\) 37.4001 2.09298i 1.19592 0.0669260i
\(979\) 18.4761 + 39.6221i 0.590499 + 1.26633i
\(980\) −26.7245 + 3.77887i −0.853684 + 0.120712i
\(981\) −31.2342 + 4.58873i −0.997230 + 0.146507i
\(982\) −3.66964 + 1.83155i −0.117103 + 0.0584470i
\(983\) −0.431378 0.514096i −0.0137588 0.0163971i 0.759121 0.650949i \(-0.225629\pi\)
−0.772880 + 0.634552i \(0.781185\pi\)
\(984\) 4.79167 31.1368i 0.152753 0.992606i
\(985\) 58.2307 + 10.2676i 1.85538 + 0.327154i
\(986\) −6.76659 6.41583i −0.215492 0.204322i
\(987\) −2.38994 + 10.0935i −0.0760726 + 0.321281i
\(988\) −7.39241 3.75877i −0.235184 0.119583i
\(989\) −50.4381 + 13.5149i −1.60384 + 0.429748i
\(990\) −43.1632 11.6609i −1.37182 0.370609i
\(991\) 1.44716 + 2.50656i 0.0459706 + 0.0796235i 0.888095 0.459660i \(-0.152029\pi\)
−0.842125 + 0.539283i \(0.818695\pi\)
\(992\) −22.2984 28.9333i −0.707974 0.918634i
\(993\) −8.25183 + 10.4407i −0.261864 + 0.331326i
\(994\) 0.00213643 0.00393878i 6.77636e−5 0.000124931i
\(995\) 2.27006 + 1.05855i 0.0719658 + 0.0335582i
\(996\) −16.3429 23.5783i −0.517845 0.747106i
\(997\) −8.19184 5.73599i −0.259438 0.181661i 0.436620 0.899646i \(-0.356175\pi\)
−0.696058 + 0.717986i \(0.745064\pi\)
\(998\) 4.07870 6.16789i 0.129109 0.195241i
\(999\) 1.31739 0.116106i 0.0416805 0.00367343i
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 432.2.bg.a.13.8 840
16.5 even 4 inner 432.2.bg.a.229.70 yes 840
27.25 even 9 inner 432.2.bg.a.349.70 yes 840
432.133 even 36 inner 432.2.bg.a.133.8 yes 840
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.bg.a.13.8 840 1.1 even 1 trivial
432.2.bg.a.133.8 yes 840 432.133 even 36 inner
432.2.bg.a.229.70 yes 840 16.5 even 4 inner
432.2.bg.a.349.70 yes 840 27.25 even 9 inner