Properties

Label 360.2.br.e.77.17
Level $360$
Weight $2$
Character 360.77
Analytic conductor $2.875$
Analytic rank $0$
Dimension $256$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(77,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.br (of order \(12\), degree \(4\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(64\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 77.17
Character \(\chi\) \(=\) 360.77
Dual form 360.2.br.e.173.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.922014 + 1.07233i) q^{2} +(-1.71827 + 0.218017i) q^{3} +(-0.299780 - 1.97741i) q^{4} +(0.420988 - 2.19608i) q^{5} +(1.35049 - 2.04357i) q^{6} +(-0.688838 + 2.57078i) q^{7} +(2.39683 + 1.50173i) q^{8} +(2.90494 - 0.749227i) q^{9} +O(q^{10})\) \(q+(-0.922014 + 1.07233i) q^{2} +(-1.71827 + 0.218017i) q^{3} +(-0.299780 - 1.97741i) q^{4} +(0.420988 - 2.19608i) q^{5} +(1.35049 - 2.04357i) q^{6} +(-0.688838 + 2.57078i) q^{7} +(2.39683 + 1.50173i) q^{8} +(2.90494 - 0.749227i) q^{9} +(1.96676 + 2.47626i) q^{10} +(0.0544515 + 0.0943128i) q^{11} +(0.946212 + 3.33237i) q^{12} +(-4.03491 + 1.08115i) q^{13} +(-2.12160 - 3.10895i) q^{14} +(-0.244590 + 3.86525i) q^{15} +(-3.82026 + 1.18557i) q^{16} +(-0.688778 + 0.688778i) q^{17} +(-1.87497 + 3.80585i) q^{18} -5.72781 q^{19} +(-4.46874 - 0.174124i) q^{20} +(0.623139 - 4.56748i) q^{21} +(-0.151340 - 0.0285678i) q^{22} +(0.0972621 - 0.0260613i) q^{23} +(-4.44582 - 2.05784i) q^{24} +(-4.64554 - 1.84905i) q^{25} +(2.56089 - 5.32358i) q^{26} +(-4.82814 + 1.92070i) q^{27} +(5.28997 + 0.591445i) q^{28} +(3.42010 - 1.97460i) q^{29} +(-3.91931 - 3.82610i) q^{30} +(-4.73047 + 8.19341i) q^{31} +(2.25101 - 5.18969i) q^{32} +(-0.114125 - 0.150184i) q^{33} +(-0.103534 - 1.37366i) q^{34} +(5.35564 + 2.59501i) q^{35} +(-2.35237 - 5.51963i) q^{36} +(-2.63901 + 2.63901i) q^{37} +(5.28112 - 6.14210i) q^{38} +(6.69737 - 2.73739i) q^{39} +(4.30696 - 4.63142i) q^{40} +(-7.31105 - 4.22104i) q^{41} +(4.32330 + 4.87949i) q^{42} +(0.543759 - 2.02933i) q^{43} +(0.170171 - 0.135946i) q^{44} +(-0.422420 - 6.69489i) q^{45} +(-0.0617308 + 0.128326i) q^{46} +(-7.20053 - 1.92938i) q^{47} +(6.30579 - 2.87002i) q^{48} +(-0.0722221 - 0.0416974i) q^{49} +(6.26604 - 3.27670i) q^{50} +(1.03334 - 1.33368i) q^{51} +(3.34746 + 7.65454i) q^{52} +(-9.53682 + 9.53682i) q^{53} +(2.39198 - 6.94827i) q^{54} +(0.230042 - 0.0798754i) q^{55} +(-5.51165 + 5.12727i) q^{56} +(9.84195 - 1.24876i) q^{57} +(-1.03596 + 5.48808i) q^{58} +(7.24384 + 4.18223i) q^{59} +(7.71649 - 0.675071i) q^{60} +(-7.40292 + 4.27408i) q^{61} +(-4.42447 - 12.6271i) q^{62} +(-0.0749338 + 7.98404i) q^{63} +(3.48959 + 7.19880i) q^{64} +(0.675645 + 9.31613i) q^{65} +(0.266271 + 0.0160927i) q^{66} +(0.869122 + 3.24361i) q^{67} +(1.56848 + 1.15551i) q^{68} +(-0.161441 + 0.0659853i) q^{69} +(-7.72068 + 3.35038i) q^{70} -1.84241i q^{71} +(8.08778 + 2.56667i) q^{72} +(10.1414 - 10.1414i) q^{73} +(-0.396683 - 5.26310i) q^{74} +(8.38544 + 2.16436i) q^{75} +(1.71708 + 11.3262i) q^{76} +(-0.279966 + 0.0750166i) q^{77} +(-3.23968 + 9.70570i) q^{78} +(-2.80886 + 1.62169i) q^{79} +(0.995325 + 8.88872i) q^{80} +(7.87732 - 4.35292i) q^{81} +(11.2672 - 3.94800i) q^{82} +(8.99388 + 2.40990i) q^{83} +(-9.21857 + 0.137040i) q^{84} +(1.22265 + 1.80258i) q^{85} +(1.67476 + 2.45416i) q^{86} +(-5.44618 + 4.13854i) q^{87} +(-0.0111216 + 0.307824i) q^{88} -6.68773 q^{89} +(7.56860 + 5.71981i) q^{90} -11.1176i q^{91} +(-0.0806910 - 0.184514i) q^{92} +(6.34194 - 15.1099i) q^{93} +(8.70792 - 5.94243i) q^{94} +(-2.41134 + 12.5787i) q^{95} +(-2.73642 + 9.40808i) q^{96} +(-1.97646 + 7.37624i) q^{97} +(0.111303 - 0.0390002i) q^{98} +(0.228840 + 0.233176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.922014 + 1.07233i −0.651962 + 0.758251i
\(3\) −1.71827 + 0.218017i −0.992046 + 0.125872i
\(4\) −0.299780 1.97741i −0.149890 0.988703i
\(5\) 0.420988 2.19608i 0.188272 0.982117i
\(6\) 1.35049 2.04357i 0.551334 0.834284i
\(7\) −0.688838 + 2.57078i −0.260356 + 0.971663i 0.704676 + 0.709530i \(0.251093\pi\)
−0.965032 + 0.262133i \(0.915574\pi\)
\(8\) 2.39683 + 1.50173i 0.847408 + 0.530943i
\(9\) 2.90494 0.749227i 0.968312 0.249742i
\(10\) 1.96676 + 2.47626i 0.621945 + 0.783061i
\(11\) 0.0544515 + 0.0943128i 0.0164178 + 0.0284364i 0.874118 0.485714i \(-0.161440\pi\)
−0.857700 + 0.514151i \(0.828107\pi\)
\(12\) 0.946212 + 3.33237i 0.273148 + 0.961972i
\(13\) −4.03491 + 1.08115i −1.11908 + 0.299857i −0.770512 0.637426i \(-0.779999\pi\)
−0.348570 + 0.937283i \(0.613333\pi\)
\(14\) −2.12160 3.10895i −0.567022 0.830903i
\(15\) −0.244590 + 3.86525i −0.0631528 + 0.998004i
\(16\) −3.82026 + 1.18557i −0.955066 + 0.296393i
\(17\) −0.688778 + 0.688778i −0.167053 + 0.167053i −0.785683 0.618630i \(-0.787688\pi\)
0.618630 + 0.785683i \(0.287688\pi\)
\(18\) −1.87497 + 3.80585i −0.441936 + 0.897047i
\(19\) −5.72781 −1.31405 −0.657025 0.753869i \(-0.728185\pi\)
−0.657025 + 0.753869i \(0.728185\pi\)
\(20\) −4.46874 0.174124i −0.999242 0.0389353i
\(21\) 0.623139 4.56748i 0.135980 0.996706i
\(22\) −0.151340 0.0285678i −0.0322657 0.00609068i
\(23\) 0.0972621 0.0260613i 0.0202806 0.00543416i −0.248665 0.968590i \(-0.579992\pi\)
0.268945 + 0.963156i \(0.413325\pi\)
\(24\) −4.44582 2.05784i −0.907499 0.420055i
\(25\) −4.64554 1.84905i −0.929108 0.369809i
\(26\) 2.56089 5.32358i 0.502232 1.04404i
\(27\) −4.82814 + 1.92070i −0.929175 + 0.369640i
\(28\) 5.28997 + 0.591445i 0.999710 + 0.111773i
\(29\) 3.42010 1.97460i 0.635097 0.366673i −0.147626 0.989043i \(-0.547163\pi\)
0.782723 + 0.622370i \(0.213830\pi\)
\(30\) −3.91931 3.82610i −0.715564 0.698547i
\(31\) −4.73047 + 8.19341i −0.849617 + 1.47158i 0.0319336 + 0.999490i \(0.489833\pi\)
−0.881551 + 0.472090i \(0.843500\pi\)
\(32\) 2.25101 5.18969i 0.397927 0.917417i
\(33\) −0.114125 0.150184i −0.0198665 0.0261437i
\(34\) −0.103534 1.37366i −0.0177559 0.235581i
\(35\) 5.35564 + 2.59501i 0.905269 + 0.438637i
\(36\) −2.35237 5.51963i −0.392061 0.919939i
\(37\) −2.63901 + 2.63901i −0.433851 + 0.433851i −0.889936 0.456085i \(-0.849251\pi\)
0.456085 + 0.889936i \(0.349251\pi\)
\(38\) 5.28112 6.14210i 0.856711 0.996380i
\(39\) 6.69737 2.73739i 1.07244 0.438334i
\(40\) 4.30696 4.63142i 0.680991 0.732292i
\(41\) −7.31105 4.22104i −1.14179 0.659215i −0.194920 0.980819i \(-0.562445\pi\)
−0.946874 + 0.321604i \(0.895778\pi\)
\(42\) 4.32330 + 4.87949i 0.667100 + 0.752922i
\(43\) 0.543759 2.02933i 0.0829224 0.309471i −0.911990 0.410212i \(-0.865455\pi\)
0.994913 + 0.100741i \(0.0321214\pi\)
\(44\) 0.170171 0.135946i 0.0256543 0.0204946i
\(45\) −0.422420 6.69489i −0.0629706 0.998015i
\(46\) −0.0617308 + 0.128326i −0.00910170 + 0.0189206i
\(47\) −7.20053 1.92938i −1.05031 0.281429i −0.307928 0.951410i \(-0.599636\pi\)
−0.742378 + 0.669981i \(0.766302\pi\)
\(48\) 6.30579 2.87002i 0.910162 0.414252i
\(49\) −0.0722221 0.0416974i −0.0103174 0.00595678i
\(50\) 6.26604 3.27670i 0.886152 0.463395i
\(51\) 1.03334 1.33368i 0.144697 0.186752i
\(52\) 3.34746 + 7.65454i 0.464209 + 1.06149i
\(53\) −9.53682 + 9.53682i −1.30998 + 1.30998i −0.388559 + 0.921424i \(0.627027\pi\)
−0.921424 + 0.388559i \(0.872973\pi\)
\(54\) 2.39198 6.94827i 0.325508 0.945539i
\(55\) 0.230042 0.0798754i 0.0310189 0.0107704i
\(56\) −5.51165 + 5.12727i −0.736525 + 0.685160i
\(57\) 9.84195 1.24876i 1.30360 0.165402i
\(58\) −1.03596 + 5.48808i −0.136029 + 0.720620i
\(59\) 7.24384 + 4.18223i 0.943068 + 0.544481i 0.890921 0.454159i \(-0.150060\pi\)
0.0521473 + 0.998639i \(0.483393\pi\)
\(60\) 7.71649 0.675071i 0.996195 0.0871513i
\(61\) −7.40292 + 4.27408i −0.947847 + 0.547240i −0.892411 0.451223i \(-0.850988\pi\)
−0.0554355 + 0.998462i \(0.517655\pi\)
\(62\) −4.42447 12.6271i −0.561909 1.60364i
\(63\) −0.0749338 + 7.98404i −0.00944077 + 1.00589i
\(64\) 3.48959 + 7.19880i 0.436199 + 0.899850i
\(65\) 0.675645 + 9.31613i 0.0838035 + 1.15552i
\(66\) 0.266271 + 0.0160927i 0.0327757 + 0.00198088i
\(67\) 0.869122 + 3.24361i 0.106180 + 0.396270i 0.998476 0.0551807i \(-0.0175735\pi\)
−0.892296 + 0.451450i \(0.850907\pi\)
\(68\) 1.56848 + 1.15551i 0.190206 + 0.140126i
\(69\) −0.161441 + 0.0659853i −0.0194352 + 0.00794370i
\(70\) −7.72068 + 3.35038i −0.922798 + 0.400446i
\(71\) 1.84241i 0.218654i −0.994006 0.109327i \(-0.965130\pi\)
0.994006 0.109327i \(-0.0348696\pi\)
\(72\) 8.08778 + 2.56667i 0.953154 + 0.302485i
\(73\) 10.1414 10.1414i 1.18696 1.18696i 0.209056 0.977904i \(-0.432961\pi\)
0.977904 0.209056i \(-0.0670393\pi\)
\(74\) −0.396683 5.26310i −0.0461135 0.611823i
\(75\) 8.38544 + 2.16436i 0.968267 + 0.249919i
\(76\) 1.71708 + 11.3262i 0.196963 + 1.29920i
\(77\) −0.279966 + 0.0750166i −0.0319050 + 0.00854893i
\(78\) −3.23968 + 9.70570i −0.366822 + 1.09895i
\(79\) −2.80886 + 1.62169i −0.316021 + 0.182455i −0.649618 0.760261i \(-0.725071\pi\)
0.333597 + 0.942716i \(0.391738\pi\)
\(80\) 0.995325 + 8.88872i 0.111281 + 0.993789i
\(81\) 7.87732 4.35292i 0.875257 0.483657i
\(82\) 11.2672 3.94800i 1.24426 0.435983i
\(83\) 8.99388 + 2.40990i 0.987206 + 0.264521i 0.716077 0.698022i \(-0.245936\pi\)
0.271130 + 0.962543i \(0.412603\pi\)
\(84\) −9.21857 + 0.137040i −1.00583 + 0.0149523i
\(85\) 1.22265 + 1.80258i 0.132614 + 0.195517i
\(86\) 1.67476 + 2.45416i 0.180594 + 0.264639i
\(87\) −5.44618 + 4.13854i −0.583892 + 0.443698i
\(88\) −0.0111216 + 0.307824i −0.00118557 + 0.0328141i
\(89\) −6.68773 −0.708898 −0.354449 0.935075i \(-0.615332\pi\)
−0.354449 + 0.935075i \(0.615332\pi\)
\(90\) 7.56860 + 5.71981i 0.797801 + 0.602921i
\(91\) 11.1176i 1.16544i
\(92\) −0.0806910 0.184514i −0.00841262 0.0192369i
\(93\) 6.34194 15.1099i 0.657628 1.56682i
\(94\) 8.70792 5.94243i 0.898154 0.612915i
\(95\) −2.41134 + 12.5787i −0.247398 + 1.29055i
\(96\) −2.73642 + 9.40808i −0.279285 + 0.960208i
\(97\) −1.97646 + 7.37624i −0.200679 + 0.748944i 0.790045 + 0.613049i \(0.210057\pi\)
−0.990723 + 0.135894i \(0.956609\pi\)
\(98\) 0.111303 0.0390002i 0.0112433 0.00393962i
\(99\) 0.228840 + 0.233176i 0.0229993 + 0.0234351i
\(100\) −2.26368 + 9.74042i −0.226368 + 0.974042i
\(101\) −1.34350 2.32701i −0.133683 0.231546i 0.791410 0.611285i \(-0.209347\pi\)
−0.925094 + 0.379739i \(0.876014\pi\)
\(102\) 0.477381 + 2.33775i 0.0472678 + 0.231472i
\(103\) −1.32955 4.96196i −0.131005 0.488916i 0.868978 0.494851i \(-0.164777\pi\)
−0.999982 + 0.00593496i \(0.998111\pi\)
\(104\) −11.2946 3.46802i −1.10753 0.340067i
\(105\) −9.76822 3.29132i −0.953281 0.321200i
\(106\) −1.43353 19.0197i −0.139236 1.84736i
\(107\) −8.27320 8.27320i −0.799801 0.799801i 0.183263 0.983064i \(-0.441334\pi\)
−0.983064 + 0.183263i \(0.941334\pi\)
\(108\) 5.24539 + 8.97139i 0.504738 + 0.863273i
\(109\) 17.4163 1.66818 0.834090 0.551628i \(-0.185993\pi\)
0.834090 + 0.551628i \(0.185993\pi\)
\(110\) −0.126449 + 0.320327i −0.0120565 + 0.0305420i
\(111\) 3.95920 5.10990i 0.375791 0.485010i
\(112\) −0.416299 10.6377i −0.0393365 1.00517i
\(113\) 11.3221 3.03376i 1.06510 0.285392i 0.316620 0.948553i \(-0.397452\pi\)
0.748477 + 0.663161i \(0.230785\pi\)
\(114\) −7.73534 + 11.7052i −0.724481 + 1.09629i
\(115\) −0.0162865 0.224567i −0.00151873 0.0209410i
\(116\) −4.92985 6.17098i −0.457725 0.572961i
\(117\) −10.9111 + 6.16374i −1.00873 + 0.569838i
\(118\) −11.1637 + 3.91170i −1.02770 + 0.360102i
\(119\) −1.29624 2.24515i −0.118826 0.205813i
\(120\) −6.39082 + 8.89705i −0.583399 + 0.812186i
\(121\) 5.49407 9.51601i 0.499461 0.865092i
\(122\) 2.24238 11.8791i 0.203015 1.07549i
\(123\) 13.4826 + 5.65896i 1.21569 + 0.510252i
\(124\) 17.6198 + 6.89783i 1.58230 + 0.619444i
\(125\) −6.01637 + 9.42355i −0.538121 + 0.842868i
\(126\) −8.49243 7.44175i −0.756566 0.662964i
\(127\) −11.6096 11.6096i −1.03019 1.03019i −0.999530 0.0306566i \(-0.990240\pi\)
−0.0306566 0.999530i \(-0.509760\pi\)
\(128\) −10.9369 2.89540i −0.966698 0.255920i
\(129\) −0.491897 + 3.60550i −0.0433091 + 0.317447i
\(130\) −10.6129 7.86509i −0.930814 0.689814i
\(131\) 6.44369 11.1608i 0.562988 0.975123i −0.434246 0.900794i \(-0.642985\pi\)
0.997234 0.0743288i \(-0.0236814\pi\)
\(132\) −0.262762 + 0.270693i −0.0228705 + 0.0235608i
\(133\) 3.94553 14.7249i 0.342121 1.27681i
\(134\) −4.27956 2.05867i −0.369697 0.177842i
\(135\) 2.18543 + 11.4116i 0.188092 + 0.982151i
\(136\) −2.68525 + 0.616523i −0.230258 + 0.0528664i
\(137\) 13.2225 + 3.54296i 1.12967 + 0.302695i 0.774792 0.632216i \(-0.217854\pi\)
0.354882 + 0.934911i \(0.384521\pi\)
\(138\) 0.0780932 0.233958i 0.00664773 0.0199158i
\(139\) −6.19431 + 10.7289i −0.525394 + 0.910010i 0.474168 + 0.880434i \(0.342749\pi\)
−0.999563 + 0.0295754i \(0.990584\pi\)
\(140\) 3.52587 11.3682i 0.297991 0.960789i
\(141\) 12.7931 + 1.74536i 1.07738 + 0.146986i
\(142\) 1.97567 + 1.69873i 0.165795 + 0.142554i
\(143\) −0.321673 0.321673i −0.0268997 0.0268997i
\(144\) −10.2094 + 6.30626i −0.850780 + 0.525521i
\(145\) −2.89655 8.34210i −0.240545 0.692774i
\(146\) 1.52440 + 20.2254i 0.126160 + 1.67387i
\(147\) 0.133188 + 0.0559020i 0.0109852 + 0.00461072i
\(148\) 6.00952 + 4.42728i 0.493980 + 0.363920i
\(149\) 7.79019 + 4.49767i 0.638198 + 0.368464i 0.783920 0.620862i \(-0.213217\pi\)
−0.145722 + 0.989326i \(0.546551\pi\)
\(150\) −10.0524 + 6.99637i −0.820775 + 0.571251i
\(151\) 2.51689 + 4.35938i 0.204822 + 0.354762i 0.950076 0.312019i \(-0.101005\pi\)
−0.745254 + 0.666780i \(0.767672\pi\)
\(152\) −13.7286 8.60164i −1.11354 0.697685i
\(153\) −1.48481 + 2.51691i −0.120039 + 0.203480i
\(154\) 0.177690 0.369382i 0.0143187 0.0297656i
\(155\) 16.0019 + 13.8378i 1.28530 + 1.11148i
\(156\) −7.42067 12.4228i −0.594129 0.994620i
\(157\) 5.20827 + 19.4375i 0.415665 + 1.55128i 0.783499 + 0.621392i \(0.213433\pi\)
−0.367834 + 0.929891i \(0.619901\pi\)
\(158\) 0.850816 4.50724i 0.0676872 0.358577i
\(159\) 14.3077 18.4661i 1.13467 1.46445i
\(160\) −10.4493 7.12821i −0.826093 0.563534i
\(161\) 0.267991i 0.0211207i
\(162\) −2.59524 + 12.4605i −0.203901 + 0.978991i
\(163\) −17.1770 17.1770i −1.34541 1.34541i −0.890581 0.454825i \(-0.849702\pi\)
−0.454825 0.890581i \(-0.650298\pi\)
\(164\) −6.15500 + 15.7223i −0.480624 + 1.22770i
\(165\) −0.377861 + 0.187401i −0.0294165 + 0.0145892i
\(166\) −10.8767 + 7.42243i −0.844195 + 0.576093i
\(167\) −1.56146 5.82746i −0.120830 0.450942i 0.878827 0.477140i \(-0.158327\pi\)
−0.999657 + 0.0261980i \(0.991660\pi\)
\(168\) 8.35270 10.0117i 0.644425 0.772419i
\(169\) 3.85326 2.22468i 0.296405 0.171129i
\(170\) −3.06026 0.350926i −0.234711 0.0269148i
\(171\) −16.6389 + 4.29143i −1.27241 + 0.328174i
\(172\) −4.17583 0.466878i −0.318404 0.0355991i
\(173\) −13.3028 3.56446i −1.01139 0.271001i −0.285180 0.958474i \(-0.592053\pi\)
−0.726210 + 0.687473i \(0.758720\pi\)
\(174\) 0.583576 9.65589i 0.0442408 0.732011i
\(175\) 7.95351 10.6690i 0.601229 0.806497i
\(176\) −0.319834 0.295744i −0.0241084 0.0222925i
\(177\) −13.3587 5.60695i −1.00410 0.421444i
\(178\) 6.16618 7.17145i 0.462175 0.537523i
\(179\) 13.7083i 1.02461i −0.858805 0.512303i \(-0.828792\pi\)
0.858805 0.512303i \(-0.171208\pi\)
\(180\) −13.1119 + 2.84229i −0.977302 + 0.211852i
\(181\) 11.5140i 0.855827i 0.903820 + 0.427913i \(0.140751\pi\)
−0.903820 + 0.427913i \(0.859249\pi\)
\(182\) 11.9217 + 10.2506i 0.883696 + 0.759823i
\(183\) 11.7884 8.95801i 0.871426 0.662195i
\(184\) 0.272258 + 0.0835973i 0.0200711 + 0.00616287i
\(185\) 4.68449 + 6.90648i 0.344411 + 0.507774i
\(186\) 10.3554 + 20.7321i 0.759293 + 1.52015i
\(187\) −0.102466 0.0274556i −0.00749303 0.00200775i
\(188\) −1.65659 + 14.8168i −0.120819 + 1.08062i
\(189\) −1.61190 13.7351i −0.117249 0.999083i
\(190\) −11.2653 14.1835i −0.817267 1.02898i
\(191\) 6.40397 3.69733i 0.463375 0.267530i −0.250087 0.968223i \(-0.580459\pi\)
0.713462 + 0.700694i \(0.247126\pi\)
\(192\) −7.56554 11.6087i −0.545996 0.837788i
\(193\) −1.83495 6.84812i −0.132082 0.492938i 0.867910 0.496721i \(-0.165463\pi\)
−0.999993 + 0.00378245i \(0.998796\pi\)
\(194\) −6.08743 8.92041i −0.437052 0.640448i
\(195\) −3.19202 15.8604i −0.228585 1.13578i
\(196\) −0.0608020 + 0.155312i −0.00434300 + 0.0110937i
\(197\) −2.76708 2.76708i −0.197146 0.197146i 0.601629 0.798776i \(-0.294519\pi\)
−0.798776 + 0.601629i \(0.794519\pi\)
\(198\) −0.461036 + 0.0304000i −0.0327644 + 0.00216044i
\(199\) 6.88331i 0.487945i 0.969782 + 0.243972i \(0.0784506\pi\)
−0.969782 + 0.243972i \(0.921549\pi\)
\(200\) −8.35779 11.4082i −0.590985 0.806682i
\(201\) −2.20055 5.38392i −0.155215 0.379753i
\(202\) 3.73405 + 0.704863i 0.262727 + 0.0495940i
\(203\) 2.72035 + 10.1525i 0.190931 + 0.712566i
\(204\) −2.94699 1.64353i −0.206331 0.115070i
\(205\) −12.3476 + 14.2786i −0.862394 + 0.997264i
\(206\) 6.54672 + 3.14928i 0.456132 + 0.219421i
\(207\) 0.263015 0.148578i 0.0182808 0.0103269i
\(208\) 14.1326 8.91395i 0.979922 0.618071i
\(209\) −0.311888 0.540206i −0.0215738 0.0373668i
\(210\) 12.5358 7.44011i 0.865053 0.513416i
\(211\) −2.22996 1.28747i −0.153517 0.0886328i 0.421274 0.906933i \(-0.361583\pi\)
−0.574790 + 0.818301i \(0.694916\pi\)
\(212\) 21.7171 + 15.9992i 1.49154 + 1.09883i
\(213\) 0.401677 + 3.16577i 0.0275225 + 0.216915i
\(214\) 16.4996 1.24359i 1.12789 0.0850098i
\(215\) −4.22767 2.04846i −0.288324 0.139704i
\(216\) −14.4566 2.64697i −0.983648 0.180103i
\(217\) −17.8049 17.8049i −1.20868 1.20868i
\(218\) −16.0581 + 18.6760i −1.08759 + 1.26490i
\(219\) −15.2147 + 19.6367i −1.02811 + 1.32692i
\(220\) −0.226908 0.430941i −0.0152981 0.0290541i
\(221\) 2.03448 3.52383i 0.136854 0.237038i
\(222\) 1.82906 + 8.95697i 0.122758 + 0.601152i
\(223\) −14.0398 3.76196i −0.940177 0.251920i −0.243988 0.969778i \(-0.578456\pi\)
−0.696189 + 0.717859i \(0.745122\pi\)
\(224\) 11.7910 + 9.36172i 0.787817 + 0.625506i
\(225\) −14.8804 1.89080i −0.992023 0.126053i
\(226\) −7.18598 + 14.9382i −0.478004 + 0.993676i
\(227\) −4.48454 + 16.7365i −0.297649 + 1.11084i 0.641441 + 0.767172i \(0.278337\pi\)
−0.939091 + 0.343670i \(0.888330\pi\)
\(228\) −5.41972 19.0872i −0.358930 1.26408i
\(229\) 7.39428 12.8073i 0.488628 0.846328i −0.511287 0.859410i \(-0.670831\pi\)
0.999914 + 0.0130823i \(0.00416435\pi\)
\(230\) 0.255826 + 0.189589i 0.0168687 + 0.0125012i
\(231\) 0.464703 0.189936i 0.0305752 0.0124969i
\(232\) 11.1627 + 0.403307i 0.732869 + 0.0264784i
\(233\) −10.0011 10.0011i −0.655196 0.655196i 0.299043 0.954240i \(-0.403333\pi\)
−0.954240 + 0.299043i \(0.903333\pi\)
\(234\) 3.45066 17.3834i 0.225577 1.13639i
\(235\) −7.26841 + 15.0007i −0.474139 + 0.978538i
\(236\) 6.09842 15.5778i 0.396973 1.01403i
\(237\) 4.47283 3.39889i 0.290541 0.220782i
\(238\) 3.60269 + 0.680067i 0.233528 + 0.0440822i
\(239\) −13.0059 + 22.5268i −0.841280 + 1.45714i 0.0475327 + 0.998870i \(0.484864\pi\)
−0.888813 + 0.458270i \(0.848469\pi\)
\(240\) −3.64814 15.0563i −0.235486 0.971878i
\(241\) 9.83165 + 17.0289i 0.633312 + 1.09693i 0.986870 + 0.161516i \(0.0516384\pi\)
−0.353558 + 0.935413i \(0.615028\pi\)
\(242\) 5.13868 + 14.6653i 0.330327 + 0.942724i
\(243\) −12.5864 + 9.19690i −0.807417 + 0.589981i
\(244\) 10.6708 + 13.3573i 0.683130 + 0.855113i
\(245\) −0.121976 + 0.141051i −0.00779273 + 0.00901144i
\(246\) −18.4995 + 9.24019i −1.17948 + 0.589133i
\(247\) 23.1112 6.19262i 1.47053 0.394027i
\(248\) −23.6424 + 12.5343i −1.50130 + 0.795930i
\(249\) −15.9794 2.18005i −1.01265 0.138155i
\(250\) −4.55797 15.1402i −0.288271 0.957549i
\(251\) 12.7535 0.804995 0.402498 0.915421i \(-0.368142\pi\)
0.402498 + 0.915421i \(0.368142\pi\)
\(252\) 15.8102 2.24528i 0.995946 0.141439i
\(253\) 0.00775399 + 0.00775399i 0.000487489 + 0.000487489i
\(254\) 23.1536 1.74510i 1.45278 0.109497i
\(255\) −2.49383 2.83077i −0.156170 0.177270i
\(256\) 13.1888 9.05839i 0.824302 0.566150i
\(257\) 2.06398 + 7.70287i 0.128747 + 0.480492i 0.999946 0.0104398i \(-0.00332314\pi\)
−0.871198 + 0.490932i \(0.836656\pi\)
\(258\) −3.41275 3.85180i −0.212469 0.239803i
\(259\) −4.96646 8.60217i −0.308601 0.534513i
\(260\) 18.2192 4.12881i 1.12991 0.256058i
\(261\) 8.45576 8.29851i 0.523398 0.513665i
\(262\) 6.02687 + 17.2002i 0.372341 + 1.06263i
\(263\) 5.75208 21.4670i 0.354688 1.32371i −0.526188 0.850368i \(-0.676379\pi\)
0.880876 0.473346i \(-0.156954\pi\)
\(264\) −0.0480009 0.531350i −0.00295425 0.0327023i
\(265\) 16.9287 + 24.9585i 1.03992 + 1.53319i
\(266\) 12.1521 + 17.8075i 0.745095 + 1.09185i
\(267\) 11.4914 1.45804i 0.703260 0.0892307i
\(268\) 6.15338 2.69097i 0.375878 0.164377i
\(269\) 7.76468i 0.473421i −0.971580 0.236710i \(-0.923931\pi\)
0.971580 0.236710i \(-0.0760692\pi\)
\(270\) −14.2520 8.17812i −0.867347 0.497705i
\(271\) −8.71891 −0.529636 −0.264818 0.964298i \(-0.585312\pi\)
−0.264818 + 0.964298i \(0.585312\pi\)
\(272\) 1.81472 3.44791i 0.110034 0.209060i
\(273\) 2.42383 + 19.1031i 0.146697 + 1.15617i
\(274\) −15.9905 + 10.9122i −0.966024 + 0.659231i
\(275\) −0.0785679 0.538817i −0.00473782 0.0324919i
\(276\) 0.178877 + 0.299454i 0.0107671 + 0.0180250i
\(277\) 3.04022 + 0.814623i 0.182669 + 0.0489460i 0.348994 0.937125i \(-0.386523\pi\)
−0.166325 + 0.986071i \(0.553190\pi\)
\(278\) −5.79362 16.5345i −0.347479 0.991673i
\(279\) −7.60298 + 27.3455i −0.455179 + 1.63713i
\(280\) 8.93955 + 14.2625i 0.534240 + 0.852350i
\(281\) −19.8081 + 11.4362i −1.18165 + 0.682228i −0.956396 0.292071i \(-0.905655\pi\)
−0.225257 + 0.974299i \(0.572322\pi\)
\(282\) −13.6671 + 12.1092i −0.813861 + 0.721093i
\(283\) 3.52144 0.943567i 0.209328 0.0560892i −0.152631 0.988283i \(-0.548775\pi\)
0.361959 + 0.932194i \(0.382108\pi\)
\(284\) −3.64319 + 0.552317i −0.216184 + 0.0327740i
\(285\) 1.40096 22.1394i 0.0829859 1.31143i
\(286\) 0.641527 0.0483523i 0.0379343 0.00285913i
\(287\) 15.8875 15.8875i 0.937808 0.937808i
\(288\) 2.65080 16.7623i 0.156200 0.987726i
\(289\) 16.0512i 0.944186i
\(290\) 11.6161 + 4.58548i 0.682123 + 0.269269i
\(291\) 1.78795 13.1053i 0.104811 0.768247i
\(292\) −23.0938 17.0135i −1.35146 0.995637i
\(293\) −0.466244 1.74005i −0.0272383 0.101655i 0.950968 0.309288i \(-0.100091\pi\)
−0.978207 + 0.207633i \(0.933424\pi\)
\(294\) −0.182747 + 0.0912791i −0.0106580 + 0.00532350i
\(295\) 12.2341 14.1474i 0.712297 0.823693i
\(296\) −10.2884 + 2.36217i −0.597999 + 0.137299i
\(297\) −0.444047 0.350770i −0.0257662 0.0203537i
\(298\) −12.0057 + 4.20674i −0.695469 + 0.243690i
\(299\) −0.364267 + 0.210310i −0.0210661 + 0.0121625i
\(300\) 1.76604 17.2302i 0.101962 0.994788i
\(301\) 4.84241 + 2.79576i 0.279112 + 0.161145i
\(302\) −6.99531 1.32048i −0.402535 0.0759850i
\(303\) 2.81583 + 3.70554i 0.161765 + 0.212878i
\(304\) 21.8817 6.79073i 1.25500 0.389475i
\(305\) 6.26968 + 18.0567i 0.359001 + 1.03393i
\(306\) −1.32994 3.91283i −0.0760278 0.223681i
\(307\) 23.2586 23.2586i 1.32744 1.32744i 0.419836 0.907600i \(-0.362088\pi\)
0.907600 0.419836i \(-0.137912\pi\)
\(308\) 0.232266 + 0.531117i 0.0132346 + 0.0302632i
\(309\) 3.36633 + 8.23614i 0.191504 + 0.468538i
\(310\) −29.5927 + 4.40066i −1.68075 + 0.249941i
\(311\) −2.07909 1.20036i −0.117894 0.0680664i 0.439893 0.898050i \(-0.355016\pi\)
−0.557788 + 0.829984i \(0.688350\pi\)
\(312\) 20.1633 + 3.49660i 1.14152 + 0.197956i
\(313\) 2.75526 + 0.738270i 0.155737 + 0.0417295i 0.335845 0.941917i \(-0.390978\pi\)
−0.180108 + 0.983647i \(0.557645\pi\)
\(314\) −25.6455 12.3367i −1.44726 0.696200i
\(315\) 17.5021 + 3.52575i 0.986129 + 0.198653i
\(316\) 4.04878 + 5.06810i 0.227762 + 0.285103i
\(317\) −6.01334 + 22.4421i −0.337743 + 1.26047i 0.563122 + 0.826374i \(0.309600\pi\)
−0.900865 + 0.434099i \(0.857067\pi\)
\(318\) 6.60982 + 32.3685i 0.370660 + 1.81514i
\(319\) 0.372460 + 0.215040i 0.0208537 + 0.0120399i
\(320\) 17.2782 4.63282i 0.965882 0.258982i
\(321\) 16.0193 + 12.4119i 0.894112 + 0.692767i
\(322\) −0.287375 0.247092i −0.0160148 0.0137699i
\(323\) 3.94519 3.94519i 0.219516 0.219516i
\(324\) −10.9689 14.2717i −0.609385 0.792874i
\(325\) 20.7434 + 2.43821i 1.15064 + 0.135247i
\(326\) 34.2568 2.58196i 1.89731 0.143001i
\(327\) −29.9260 + 3.79706i −1.65491 + 0.209978i
\(328\) −11.1845 21.0964i −0.617559 1.16485i
\(329\) 9.92000 17.1819i 0.546907 0.947271i
\(330\) 0.147438 0.577978i 0.00811619 0.0318166i
\(331\) −23.6933 + 13.6793i −1.30230 + 0.751883i −0.980798 0.195026i \(-0.937521\pi\)
−0.321501 + 0.946909i \(0.604187\pi\)
\(332\) 2.06917 18.5070i 0.113561 1.01570i
\(333\) −5.68895 + 9.64339i −0.311752 + 0.528454i
\(334\) 7.68864 + 3.69860i 0.420704 + 0.202378i
\(335\) 7.48911 0.543142i 0.409174 0.0296750i
\(336\) 3.03452 + 18.1878i 0.165547 + 0.992224i
\(337\) 0.361233 0.0967920i 0.0196776 0.00527260i −0.248967 0.968512i \(-0.580091\pi\)
0.268644 + 0.963239i \(0.413424\pi\)
\(338\) −1.16717 + 6.18315i −0.0634857 + 0.336319i
\(339\) −18.7931 + 7.68125i −1.02070 + 0.417188i
\(340\) 3.19791 2.95804i 0.173431 0.160422i
\(341\) −1.03032 −0.0557952
\(342\) 10.7395 21.7992i 0.580726 1.17876i
\(343\) −13.0166 + 13.0166i −0.702832 + 0.702832i
\(344\) 4.35082 4.04739i 0.234580 0.218221i
\(345\) 0.0769442 + 0.382317i 0.00414254 + 0.0205833i
\(346\) 16.0876 10.9785i 0.864875 0.590205i
\(347\) 0.163977 0.0439375i 0.00880274 0.00235869i −0.254415 0.967095i \(-0.581883\pi\)
0.263218 + 0.964736i \(0.415216\pi\)
\(348\) 9.81623 + 9.52865i 0.526205 + 0.510789i
\(349\) 2.62257 + 4.54242i 0.140383 + 0.243150i 0.927641 0.373474i \(-0.121833\pi\)
−0.787258 + 0.616624i \(0.788500\pi\)
\(350\) 4.10738 + 18.3657i 0.219549 + 0.981688i
\(351\) 17.4045 12.9698i 0.928984 0.692277i
\(352\) 0.612026 0.0702873i 0.0326211 0.00374633i
\(353\) −7.03634 + 26.2600i −0.374506 + 1.39768i 0.479558 + 0.877510i \(0.340797\pi\)
−0.854065 + 0.520167i \(0.825870\pi\)
\(354\) 18.3294 9.15525i 0.974197 0.486596i
\(355\) −4.04608 0.775633i −0.214744 0.0411663i
\(356\) 2.00485 + 13.2244i 0.106257 + 0.700889i
\(357\) 2.71678 + 3.57519i 0.143787 + 0.189219i
\(358\) 14.6998 + 12.6392i 0.776909 + 0.668005i
\(359\) 25.3530 1.33808 0.669041 0.743225i \(-0.266705\pi\)
0.669041 + 0.743225i \(0.266705\pi\)
\(360\) 9.04147 16.6809i 0.476527 0.879160i
\(361\) 13.8078 0.726726
\(362\) −12.3468 10.6160i −0.648932 0.557967i
\(363\) −7.36567 + 17.5489i −0.386597 + 0.921079i
\(364\) −21.9840 + 3.33283i −1.15227 + 0.174688i
\(365\) −18.0019 26.5407i −0.942263 1.38920i
\(366\) −1.26317 + 20.9005i −0.0660269 + 1.09249i
\(367\) −2.74945 + 10.2611i −0.143520 + 0.535625i 0.856296 + 0.516485i \(0.172760\pi\)
−0.999817 + 0.0191406i \(0.993907\pi\)
\(368\) −0.340669 + 0.214872i −0.0177586 + 0.0112010i
\(369\) −24.4006 6.78421i −1.27025 0.353172i
\(370\) −11.7252 1.34455i −0.609563 0.0699000i
\(371\) −17.9477 31.0864i −0.931799 1.61392i
\(372\) −31.7795 8.01096i −1.64769 0.415349i
\(373\) 0.585374 0.156850i 0.0303095 0.00812141i −0.243632 0.969868i \(-0.578339\pi\)
0.273942 + 0.961746i \(0.411672\pi\)
\(374\) 0.123916 0.0845625i 0.00640756 0.00437262i
\(375\) 8.28328 17.5039i 0.427747 0.903899i
\(376\) −14.3611 15.4377i −0.740615 0.796137i
\(377\) −11.6650 + 11.6650i −0.600776 + 0.600776i
\(378\) 16.2148 + 10.9355i 0.833997 + 0.562461i
\(379\) 15.4427 0.793238 0.396619 0.917983i \(-0.370183\pi\)
0.396619 + 0.917983i \(0.370183\pi\)
\(380\) 25.5961 + 0.997348i 1.31305 + 0.0511629i
\(381\) 22.4796 + 17.4174i 1.15166 + 0.892321i
\(382\) −1.93979 + 10.2762i −0.0992484 + 0.525774i
\(383\) 24.6134 6.59514i 1.25769 0.336996i 0.432385 0.901689i \(-0.357672\pi\)
0.825301 + 0.564693i \(0.191006\pi\)
\(384\) 19.4239 + 2.59066i 0.991223 + 0.132204i
\(385\) 0.0468802 + 0.646408i 0.00238924 + 0.0329440i
\(386\) 9.03528 + 4.34639i 0.459884 + 0.221226i
\(387\) 0.0591517 6.30249i 0.00300685 0.320373i
\(388\) 15.1783 + 1.69701i 0.770562 + 0.0861527i
\(389\) 8.55882 4.94144i 0.433950 0.250541i −0.267078 0.963675i \(-0.586058\pi\)
0.701028 + 0.713134i \(0.252725\pi\)
\(390\) 19.9506 + 11.2006i 1.01024 + 0.567164i
\(391\) −0.0490416 + 0.0849425i −0.00248014 + 0.00429573i
\(392\) −0.110486 0.208400i −0.00558037 0.0105258i
\(393\) −8.63878 + 20.5821i −0.435769 + 1.03823i
\(394\) 5.51851 0.415934i 0.278019 0.0209544i
\(395\) 2.37887 + 6.85119i 0.119694 + 0.344721i
\(396\) 0.392482 0.522411i 0.0197230 0.0262521i
\(397\) 5.36635 5.36635i 0.269329 0.269329i −0.559501 0.828830i \(-0.689007\pi\)
0.828830 + 0.559501i \(0.189007\pi\)
\(398\) −7.38117 6.34651i −0.369985 0.318122i
\(399\) −3.56922 + 26.1617i −0.178684 + 1.30972i
\(400\) 19.9394 + 1.55623i 0.996968 + 0.0778115i
\(401\) −6.90919 3.98902i −0.345029 0.199202i 0.317465 0.948270i \(-0.397168\pi\)
−0.662493 + 0.749068i \(0.730502\pi\)
\(402\) 7.80228 + 2.60434i 0.389142 + 0.129893i
\(403\) 10.2287 38.1740i 0.509527 1.90158i
\(404\) −4.19869 + 3.35424i −0.208893 + 0.166879i
\(405\) −6.24310 19.1317i −0.310222 0.950664i
\(406\) −13.3950 6.44363i −0.664784 0.319792i
\(407\) −0.392591 0.105194i −0.0194600 0.00521430i
\(408\) 4.47958 1.64479i 0.221772 0.0814291i
\(409\) −15.9719 9.22137i −0.789758 0.455967i 0.0501191 0.998743i \(-0.484040\pi\)
−0.839877 + 0.542776i \(0.817373\pi\)
\(410\) −3.92675 26.4058i −0.193928 1.30409i
\(411\) −23.4923 3.20504i −1.15879 0.158093i
\(412\) −9.41323 + 4.11656i −0.463757 + 0.202808i
\(413\) −15.7414 + 15.7414i −0.774585 + 0.774585i
\(414\) −0.0831787 + 0.419029i −0.00408801 + 0.0205942i
\(415\) 9.07865 18.7367i 0.445654 0.919750i
\(416\) −3.47180 + 23.3736i −0.170219 + 1.14599i
\(417\) 8.30445 19.7856i 0.406671 0.968904i
\(418\) 0.866844 + 0.163631i 0.0423987 + 0.00800345i
\(419\) −8.67031 5.00580i −0.423572 0.244550i 0.273032 0.962005i \(-0.411973\pi\)
−0.696604 + 0.717455i \(0.745307\pi\)
\(420\) −3.57995 + 20.3024i −0.174684 + 0.990656i
\(421\) −7.31916 + 4.22572i −0.356714 + 0.205949i −0.667638 0.744486i \(-0.732695\pi\)
0.310924 + 0.950435i \(0.399361\pi\)
\(422\) 3.43664 1.20419i 0.167293 0.0586188i
\(423\) −22.3626 0.209883i −1.08731 0.0102049i
\(424\) −37.1799 + 8.53638i −1.80562 + 0.414563i
\(425\) 4.47333 1.92616i 0.216988 0.0934326i
\(426\) −3.76510 2.48815i −0.182420 0.120551i
\(427\) −5.88829 21.9754i −0.284954 1.06346i
\(428\) −13.8793 + 18.8396i −0.670883 + 0.910647i
\(429\) 0.622853 + 0.482593i 0.0300716 + 0.0232998i
\(430\) 6.09460 2.64474i 0.293907 0.127541i
\(431\) 15.5945i 0.751162i 0.926790 + 0.375581i \(0.122557\pi\)
−0.926790 + 0.375581i \(0.877443\pi\)
\(432\) 16.1676 13.0617i 0.777865 0.628431i
\(433\) −20.6316 + 20.6316i −0.991491 + 0.991491i −0.999964 0.00847358i \(-0.997303\pi\)
0.00847358 + 0.999964i \(0.497303\pi\)
\(434\) 35.5091 2.67634i 1.70449 0.128469i
\(435\) 6.79579 + 13.7025i 0.325833 + 0.656986i
\(436\) −5.22106 34.4391i −0.250043 1.64933i
\(437\) −0.557099 + 0.149274i −0.0266497 + 0.00714075i
\(438\) −7.02883 34.4205i −0.335851 1.64467i
\(439\) −11.8433 + 6.83772i −0.565249 + 0.326347i −0.755250 0.655437i \(-0.772484\pi\)
0.190001 + 0.981784i \(0.439151\pi\)
\(440\) 0.671323 + 0.154014i 0.0320041 + 0.00734233i
\(441\) −0.241041 0.0670177i −0.0114782 0.00319132i
\(442\) 1.90288 + 5.43066i 0.0905109 + 0.258310i
\(443\) −6.68370 1.79089i −0.317552 0.0850879i 0.0965223 0.995331i \(-0.469228\pi\)
−0.414075 + 0.910243i \(0.635895\pi\)
\(444\) −11.2912 6.29710i −0.535858 0.298847i
\(445\) −2.81545 + 14.6868i −0.133465 + 0.696221i
\(446\) 16.9790 11.5867i 0.803978 0.548648i
\(447\) −14.3663 6.02984i −0.679501 0.285202i
\(448\) −20.9103 + 4.01216i −0.987918 + 0.189557i
\(449\) 26.3221 1.24222 0.621108 0.783725i \(-0.286683\pi\)
0.621108 + 0.783725i \(0.286683\pi\)
\(450\) 15.7475 14.2133i 0.742342 0.670021i
\(451\) 0.919368i 0.0432913i
\(452\) −9.39311 21.4790i −0.441815 1.01029i
\(453\) −5.27513 6.94189i −0.247847 0.326159i
\(454\) −13.8123 20.2402i −0.648241 0.949920i
\(455\) −24.4151 4.68037i −1.14460 0.219419i
\(456\) 25.4648 + 11.7869i 1.19250 + 0.551973i
\(457\) 3.89998 14.5549i 0.182434 0.680851i −0.812732 0.582638i \(-0.802021\pi\)
0.995165 0.0982133i \(-0.0313128\pi\)
\(458\) 6.91597 + 19.7376i 0.323162 + 0.922276i
\(459\) 2.00258 4.64845i 0.0934722 0.216971i
\(460\) −0.439178 + 0.0995257i −0.0204768 + 0.00464041i
\(461\) −7.78174 13.4784i −0.362432 0.627750i 0.625929 0.779880i \(-0.284720\pi\)
−0.988361 + 0.152130i \(0.951387\pi\)
\(462\) −0.224788 + 0.673439i −0.0104581 + 0.0313312i
\(463\) 6.56341 + 24.4950i 0.305028 + 1.13838i 0.932922 + 0.360080i \(0.117250\pi\)
−0.627894 + 0.778299i \(0.716083\pi\)
\(464\) −10.7247 + 11.5983i −0.497880 + 0.538436i
\(465\) −30.5126 20.2885i −1.41499 0.940855i
\(466\) 19.9457 1.50332i 0.923967 0.0696400i
\(467\) −20.7735 20.7735i −0.961283 0.961283i 0.0379952 0.999278i \(-0.487903\pi\)
−0.999278 + 0.0379952i \(0.987903\pi\)
\(468\) 15.4591 + 19.7280i 0.714599 + 0.911925i
\(469\) −8.93728 −0.412685
\(470\) −9.38412 21.6250i −0.432857 0.997486i
\(471\) −13.1870 32.2635i −0.607623 1.48662i
\(472\) 11.0817 + 20.9024i 0.510075 + 0.962112i
\(473\) 0.221001 0.0592170i 0.0101616 0.00272280i
\(474\) −0.479278 + 7.93017i −0.0220140 + 0.364245i
\(475\) 26.6088 + 10.5910i 1.22089 + 0.485948i
\(476\) −4.05099 + 3.23624i −0.185677 + 0.148333i
\(477\) −20.5586 + 34.8491i −0.941314 + 1.59563i
\(478\) −12.1646 34.7166i −0.556395 1.58790i
\(479\) −17.4406 30.2080i −0.796881 1.38024i −0.921638 0.388052i \(-0.873148\pi\)
0.124756 0.992187i \(-0.460185\pi\)
\(480\) 19.5089 + 9.97009i 0.890456 + 0.455070i
\(481\) 7.79500 13.5013i 0.355422 0.615608i
\(482\) −27.3255 5.15814i −1.24464 0.234947i
\(483\) −0.0584267 0.460483i −0.00265851 0.0209527i
\(484\) −20.4640 8.01130i −0.930183 0.364150i
\(485\) 15.3667 + 7.44577i 0.697768 + 0.338095i
\(486\) 1.74273 21.9764i 0.0790516 0.996871i
\(487\) 15.3590 + 15.3590i 0.695981 + 0.695981i 0.963541 0.267560i \(-0.0862174\pi\)
−0.267560 + 0.963541i \(0.586217\pi\)
\(488\) −24.1621 0.872972i −1.09377 0.0395176i
\(489\) 33.2597 + 25.7699i 1.50405 + 1.16536i
\(490\) −0.0387903 0.260849i −0.00175237 0.0117840i
\(491\) −5.89878 + 10.2170i −0.266208 + 0.461086i −0.967880 0.251415i \(-0.919104\pi\)
0.701671 + 0.712501i \(0.252438\pi\)
\(492\) 7.14824 28.3571i 0.322268 1.27844i
\(493\) −0.995632 + 3.71575i −0.0448410 + 0.167349i
\(494\) −14.6683 + 30.4925i −0.659958 + 1.37192i
\(495\) 0.608413 0.404387i 0.0273461 0.0181758i
\(496\) 8.35776 36.9093i 0.375274 1.65728i
\(497\) 4.73643 + 1.26912i 0.212458 + 0.0569279i
\(498\) 17.0709 15.1251i 0.764967 0.677771i
\(499\) −13.8498 + 23.9886i −0.620003 + 1.07388i 0.369481 + 0.929238i \(0.379535\pi\)
−0.989484 + 0.144639i \(0.953798\pi\)
\(500\) 20.4378 + 9.07182i 0.914005 + 0.405704i
\(501\) 3.95351 + 9.67275i 0.176630 + 0.432147i
\(502\) −11.7589 + 13.6760i −0.524827 + 0.610389i
\(503\) −2.56078 2.56078i −0.114180 0.114180i 0.647709 0.761888i \(-0.275727\pi\)
−0.761888 + 0.647709i \(0.775727\pi\)
\(504\) −12.1695 + 19.0239i −0.542073 + 0.847390i
\(505\) −5.67590 + 1.97079i −0.252574 + 0.0876991i
\(506\) −0.0154641 + 0.00116554i −0.000687464 + 5.18146e-5i
\(507\) −6.13594 + 4.66269i −0.272507 + 0.207077i
\(508\) −19.4766 + 26.4372i −0.864134 + 1.17296i
\(509\) −21.4007 12.3557i −0.948570 0.547657i −0.0559337 0.998434i \(-0.517814\pi\)
−0.892636 + 0.450777i \(0.851147\pi\)
\(510\) 5.33487 0.0642007i 0.236232 0.00284286i
\(511\) 19.0855 + 33.0570i 0.844292 + 1.46236i
\(512\) −2.44672 + 22.4947i −0.108131 + 0.994137i
\(513\) 27.6546 11.0014i 1.22098 0.485725i
\(514\) −10.1630 4.88889i −0.448272 0.215640i
\(515\) −11.4566 + 0.830880i −0.504838 + 0.0366129i
\(516\) 7.27700 0.108177i 0.320352 0.00476224i
\(517\) −0.210115 0.784160i −0.00924085 0.0344873i
\(518\) 13.8035 + 2.60564i 0.606491 + 0.114485i
\(519\) 23.6349 + 3.22450i 1.03746 + 0.141540i
\(520\) −12.3709 + 23.3438i −0.542502 + 1.02369i
\(521\) 2.80066i 0.122699i −0.998116 0.0613496i \(-0.980460\pi\)
0.998116 0.0613496i \(-0.0195405\pi\)
\(522\) 1.10241 + 16.7187i 0.0482510 + 0.731758i
\(523\) 26.8782 + 26.8782i 1.17530 + 1.17530i 0.980927 + 0.194377i \(0.0622684\pi\)
0.194377 + 0.980927i \(0.437732\pi\)
\(524\) −24.0011 9.39600i −1.04849 0.410466i
\(525\) −11.3403 + 20.0662i −0.494931 + 0.875761i
\(526\) 17.7162 + 25.9610i 0.772465 + 1.13196i
\(527\) −2.38520 8.90168i −0.103901 0.387763i
\(528\) 0.614040 + 0.438440i 0.0267227 + 0.0190806i
\(529\) −19.9098 + 11.4949i −0.865644 + 0.499780i
\(530\) −42.3723 4.85892i −1.84053 0.211058i
\(531\) 24.1764 + 6.72184i 1.04916 + 0.291703i
\(532\) −30.2999 3.38768i −1.31367 0.146875i
\(533\) 34.0630 + 9.12715i 1.47543 + 0.395341i
\(534\) −9.03170 + 13.6669i −0.390840 + 0.591423i
\(535\) −21.6515 + 14.6857i −0.936078 + 0.634918i
\(536\) −2.78789 + 9.07956i −0.120419 + 0.392177i
\(537\) 2.98864 + 23.5546i 0.128970 + 1.01646i
\(538\) 8.32629 + 7.15914i 0.358972 + 0.308653i
\(539\) 0.00908196i 0.000391188i
\(540\) 21.9101 7.74245i 0.942863 0.333182i
\(541\) 1.98608i 0.0853883i 0.999088 + 0.0426942i \(0.0135941\pi\)
−0.999088 + 0.0426942i \(0.986406\pi\)
\(542\) 8.03896 9.34954i 0.345303 0.401597i
\(543\) −2.51024 19.7842i −0.107725 0.849020i
\(544\) 2.02410 + 5.12500i 0.0867825 + 0.219733i
\(545\) 7.33206 38.2476i 0.314071 1.63835i
\(546\) −22.7196 15.0142i −0.972308 0.642547i
\(547\) −0.826578 0.221481i −0.0353419 0.00946984i 0.241105 0.970499i \(-0.422490\pi\)
−0.276447 + 0.961029i \(0.589157\pi\)
\(548\) 3.04203 27.2083i 0.129949 1.16228i
\(549\) −18.3028 + 17.9624i −0.781143 + 0.766617i
\(550\) 0.650230 + 0.412547i 0.0277259 + 0.0175910i
\(551\) −19.5897 + 11.3101i −0.834549 + 0.481827i
\(552\) −0.486040 0.0842861i −0.0206872 0.00358746i
\(553\) −2.23417 8.33803i −0.0950065 0.354569i
\(554\) −3.67667 + 2.50902i −0.156207 + 0.106598i
\(555\) −9.55498 10.8459i −0.405586 0.460384i
\(556\) 23.0722 + 9.03237i 0.978480 + 0.383058i
\(557\) −3.66031 3.66031i −0.155092 0.155092i 0.625296 0.780388i \(-0.284978\pi\)
−0.780388 + 0.625296i \(0.784978\pi\)
\(558\) −22.3134 33.3659i −0.944599 1.41249i
\(559\) 8.77606i 0.371188i
\(560\) −23.5365 3.56413i −0.994600 0.150612i
\(561\) 0.182050 + 0.0248370i 0.00768616 + 0.00104862i
\(562\) 5.99997 31.7852i 0.253094 1.34078i
\(563\) −4.28470 15.9907i −0.180579 0.673929i −0.995534 0.0944047i \(-0.969905\pi\)
0.814955 0.579524i \(-0.196761\pi\)
\(564\) −0.383837 25.8204i −0.0161625 1.08724i
\(565\) −1.89589 26.1415i −0.0797607 1.09978i
\(566\) −2.23500 + 4.64612i −0.0939442 + 0.195291i
\(567\) 5.76418 + 23.2493i 0.242073 + 0.976378i
\(568\) 2.76681 4.41595i 0.116093 0.185289i
\(569\) −13.8463 23.9825i −0.580467 1.00540i −0.995424 0.0955574i \(-0.969537\pi\)
0.414957 0.909841i \(-0.363797\pi\)
\(570\) 22.4490 + 21.9152i 0.940287 + 0.917925i
\(571\) 11.1890 + 6.45999i 0.468246 + 0.270342i 0.715505 0.698607i \(-0.246196\pi\)
−0.247259 + 0.968949i \(0.579530\pi\)
\(572\) −0.539647 + 0.732510i −0.0225638 + 0.0306278i
\(573\) −10.1977 + 7.74921i −0.426015 + 0.323728i
\(574\) 2.38812 + 31.6851i 0.0996784 + 1.32251i
\(575\) −0.500024 0.0587734i −0.0208524 0.00245102i
\(576\) 15.5306 + 18.2976i 0.647108 + 0.762399i
\(577\) 3.81206 + 3.81206i 0.158698 + 0.158698i 0.781990 0.623291i \(-0.214205\pi\)
−0.623291 + 0.781990i \(0.714205\pi\)
\(578\) −17.2121 14.7994i −0.715930 0.615574i
\(579\) 4.64595 + 11.3669i 0.193079 + 0.472392i
\(580\) −15.6274 + 8.22845i −0.648892 + 0.341668i
\(581\) −12.3906 + 21.4612i −0.514051 + 0.890362i
\(582\) 12.4047 + 14.0005i 0.514191 + 0.580341i
\(583\) −1.41874 0.380150i −0.0587582 0.0157442i
\(584\) 39.5369 9.07753i 1.63605 0.375631i
\(585\) 8.94261 + 26.5566i 0.369731 + 1.09798i
\(586\) 2.29579 + 1.10438i 0.0948381 + 0.0456216i
\(587\) 2.74206 10.2335i 0.113177 0.422382i −0.885967 0.463748i \(-0.846504\pi\)
0.999144 + 0.0413660i \(0.0131710\pi\)
\(588\) 0.0706138 0.280125i 0.00291206 0.0115522i
\(589\) 27.0952 46.9303i 1.11644 1.93373i
\(590\) 3.89065 + 26.1631i 0.160176 + 1.07712i
\(591\) 5.35788 + 4.15134i 0.220394 + 0.170763i
\(592\) 6.95299 13.2105i 0.285766 0.542947i
\(593\) −18.1914 18.1914i −0.747032 0.747032i 0.226889 0.973921i \(-0.427145\pi\)
−0.973921 + 0.226889i \(0.927145\pi\)
\(594\) 0.785558 0.152749i 0.0322318 0.00626738i
\(595\) −5.47624 + 1.90146i −0.224504 + 0.0779524i
\(596\) 6.55838 16.7527i 0.268642 0.686217i
\(597\) −1.50068 11.8274i −0.0614187 0.484064i
\(598\) 0.110338 0.584523i 0.00451207 0.0239029i
\(599\) 5.91619 10.2471i 0.241729 0.418687i −0.719478 0.694515i \(-0.755619\pi\)
0.961207 + 0.275829i \(0.0889522\pi\)
\(600\) 16.8482 + 17.7803i 0.687824 + 0.725878i
\(601\) 17.0242 + 29.4868i 0.694431 + 1.20279i 0.970372 + 0.241615i \(0.0776772\pi\)
−0.275941 + 0.961175i \(0.588989\pi\)
\(602\) −7.46275 + 2.61492i −0.304159 + 0.106576i
\(603\) 4.95494 + 8.77130i 0.201781 + 0.357195i
\(604\) 7.86576 6.28377i 0.320053 0.255683i
\(605\) −18.5850 16.0715i −0.755587 0.653401i
\(606\) −6.56979 0.397061i −0.266880 0.0161295i
\(607\) 33.1542 8.88364i 1.34569 0.360576i 0.487146 0.873321i \(-0.338038\pi\)
0.858541 + 0.512745i \(0.171371\pi\)
\(608\) −12.8934 + 29.7256i −0.522896 + 1.20553i
\(609\) −6.88773 16.8517i −0.279105 0.682865i
\(610\) −25.1435 9.92542i −1.01803 0.401868i
\(611\) 31.1394 1.25977
\(612\) 5.42206 + 2.18155i 0.219174 + 0.0881837i
\(613\) −14.1315 14.1315i −0.570766 0.570766i 0.361576 0.932342i \(-0.382239\pi\)
−0.932342 + 0.361576i \(0.882239\pi\)
\(614\) 3.49611 + 46.3855i 0.141091 + 1.87197i
\(615\) 18.1036 27.2266i 0.730007 1.09788i
\(616\) −0.783685 0.240632i −0.0315756 0.00969533i
\(617\) 5.21282 + 19.4545i 0.209860 + 0.783208i 0.987913 + 0.155010i \(0.0495409\pi\)
−0.778053 + 0.628199i \(0.783792\pi\)
\(618\) −11.9357 3.98403i −0.480123 0.160261i
\(619\) −11.4288 19.7952i −0.459362 0.795638i 0.539566 0.841944i \(-0.318589\pi\)
−0.998927 + 0.0463057i \(0.985255\pi\)
\(620\) 22.5659 35.7906i 0.906269 1.43738i
\(621\) −0.419539 + 0.312639i −0.0168355 + 0.0125458i
\(622\) 3.20414 1.12272i 0.128474 0.0450169i
\(623\) 4.60676 17.1927i 0.184566 0.688810i
\(624\) −22.3404 + 18.3978i −0.894330 + 0.736500i
\(625\) 18.1621 + 17.1796i 0.726482 + 0.687185i
\(626\) −3.33206 + 2.27385i −0.133176 + 0.0908814i
\(627\) 0.653684 + 0.860225i 0.0261056 + 0.0343541i
\(628\) 36.8745 16.1258i 1.47145 0.643491i
\(629\) 3.63539i 0.144952i
\(630\) −19.9179 + 15.5172i −0.793548 + 0.618219i
\(631\) −32.3304 −1.28705 −0.643526 0.765424i \(-0.722529\pi\)
−0.643526 + 0.765424i \(0.722529\pi\)
\(632\) −9.16770 0.331228i −0.364672 0.0131755i
\(633\) 4.11237 + 1.72605i 0.163452 + 0.0686044i
\(634\) −18.5209 27.1402i −0.735560 1.07787i
\(635\) −30.3832 + 20.6081i −1.20572 + 0.817809i
\(636\) −40.8041 22.7563i −1.61799 0.902348i
\(637\) 0.336491 + 0.0901624i 0.0133322 + 0.00357236i
\(638\) −0.574006 + 0.201130i −0.0227251 + 0.00796280i
\(639\) −1.38038 5.35209i −0.0546072 0.211725i
\(640\) −10.9629 + 22.7995i −0.433345 + 0.901228i
\(641\) 12.9617 7.48343i 0.511956 0.295578i −0.221681 0.975119i \(-0.571155\pi\)
0.733637 + 0.679541i \(0.237821\pi\)
\(642\) −28.0797 + 5.73402i −1.10822 + 0.226304i
\(643\) 27.6120 7.39862i 1.08891 0.291773i 0.330670 0.943746i \(-0.392725\pi\)
0.758242 + 0.651973i \(0.226059\pi\)
\(644\) 0.529927 0.0803383i 0.0208821 0.00316577i
\(645\) 7.71089 + 2.59812i 0.303616 + 0.102301i
\(646\) 0.593021 + 7.86807i 0.0233321 + 0.309565i
\(647\) −13.1675 + 13.1675i −0.517667 + 0.517667i −0.916865 0.399198i \(-0.869289\pi\)
0.399198 + 0.916865i \(0.369289\pi\)
\(648\) 25.4175 + 1.39643i 0.998494 + 0.0548569i
\(649\) 0.910917i 0.0357566i
\(650\) −21.7403 + 19.9957i −0.852724 + 0.784296i
\(651\) 34.4755 + 26.7119i 1.35120 + 1.04692i
\(652\) −28.8166 + 39.1152i −1.12854 + 1.53187i
\(653\) 5.50631 + 20.5498i 0.215479 + 0.804177i 0.985998 + 0.166760i \(0.0533305\pi\)
−0.770519 + 0.637417i \(0.780003\pi\)
\(654\) 23.5205 35.5915i 0.919725 1.39174i
\(655\) −21.7973 18.8494i −0.851690 0.736508i
\(656\) 32.9345 + 7.45770i 1.28588 + 0.291174i
\(657\) 21.8619 37.0583i 0.852914 1.44578i
\(658\) 9.27832 + 26.4795i 0.361707 + 1.03228i
\(659\) −23.9029 + 13.8004i −0.931126 + 0.537586i −0.887167 0.461448i \(-0.847330\pi\)
−0.0439583 + 0.999033i \(0.513997\pi\)
\(660\) 0.483843 + 0.691006i 0.0188336 + 0.0268974i
\(661\) −21.4371 12.3767i −0.833808 0.481399i 0.0213470 0.999772i \(-0.493205\pi\)
−0.855155 + 0.518373i \(0.826538\pi\)
\(662\) 7.17680 38.0195i 0.278934 1.47767i
\(663\) −2.72755 + 6.49846i −0.105929 + 0.252379i
\(664\) 17.9378 + 19.2825i 0.696121 + 0.748308i
\(665\) −30.6761 14.8637i −1.18957 0.576390i
\(666\) −5.09560 14.9918i −0.197450 0.580919i
\(667\) 0.281186 0.281186i 0.0108876 0.0108876i
\(668\) −11.0552 + 4.83460i −0.427737 + 0.187056i
\(669\) 24.9445 + 3.40316i 0.964409 + 0.131574i
\(670\) −6.32264 + 8.53158i −0.244265 + 0.329604i
\(671\) −0.806201 0.465460i −0.0311230 0.0179689i
\(672\) −22.3011 13.5154i −0.860285 0.521367i
\(673\) −45.4537 12.1793i −1.75211 0.469477i −0.767036 0.641604i \(-0.778269\pi\)
−0.985075 + 0.172127i \(0.944936\pi\)
\(674\) −0.229269 + 0.476604i −0.00883110 + 0.0183581i
\(675\) 25.9808 + 0.00474244i 1.00000 + 0.000182536i
\(676\) −5.55423 6.95255i −0.213624 0.267406i
\(677\) 4.96795 18.5406i 0.190934 0.712574i −0.802348 0.596856i \(-0.796416\pi\)
0.993282 0.115718i \(-0.0369169\pi\)
\(678\) 9.09070 27.2346i 0.349126 1.04594i
\(679\) −17.6012 10.1621i −0.675472 0.389984i
\(680\) 0.223479 + 6.15657i 0.00857001 + 0.236094i
\(681\) 4.05682 29.7357i 0.155458 1.13947i
\(682\) 0.949974 1.10485i 0.0363764 0.0423068i
\(683\) 2.25163 2.25163i 0.0861563 0.0861563i −0.662715 0.748872i \(-0.730596\pi\)
0.748872 + 0.662715i \(0.230596\pi\)
\(684\) 13.4739 + 31.6154i 0.515188 + 1.20885i
\(685\) 13.3471 27.5461i 0.509968 1.05248i
\(686\) −1.95659 25.9596i −0.0747031 0.991144i
\(687\) −9.91320 + 23.6185i −0.378212 + 0.901101i
\(688\) 0.328620 + 8.39726i 0.0125285 + 0.320143i
\(689\) 28.1695 48.7909i 1.07317 1.85879i
\(690\) −0.480913 0.269992i −0.0183081 0.0102784i
\(691\) −16.7659 + 9.67982i −0.637806 + 0.368238i −0.783769 0.621052i \(-0.786705\pi\)
0.145963 + 0.989290i \(0.453372\pi\)
\(692\) −3.06049 + 27.3735i −0.116343 + 1.04058i
\(693\) −0.757078 + 0.427676i −0.0287590 + 0.0162461i
\(694\) −0.104074 + 0.216348i −0.00395058 + 0.00821246i
\(695\) 20.9537 + 18.1199i 0.794819 + 0.687328i
\(696\) −19.2686 + 1.74067i −0.730373 + 0.0659800i
\(697\) 7.94305 2.12833i 0.300864 0.0806164i
\(698\) −7.28901 1.37592i −0.275893 0.0520794i
\(699\) 19.3651 + 15.0043i 0.732456 + 0.567514i
\(700\) −23.4811 12.5290i −0.887504 0.473551i
\(701\) 50.4199 1.90434 0.952168 0.305576i \(-0.0988492\pi\)
0.952168 + 0.305576i \(0.0988492\pi\)
\(702\) −2.13930 + 30.6217i −0.0807429 + 1.15574i
\(703\) 15.1158 15.1158i 0.570102 0.570102i
\(704\) −0.488926 + 0.721099i −0.0184271 + 0.0271775i
\(705\) 9.21871 27.3600i 0.347197 1.03044i
\(706\) −21.6717 31.7573i −0.815626 1.19520i
\(707\) 6.90768 1.85091i 0.259790 0.0696106i
\(708\) −7.08254 + 28.0964i −0.266178 + 1.05593i
\(709\) 10.3220 + 17.8782i 0.387650 + 0.671430i 0.992133 0.125188i \(-0.0399536\pi\)
−0.604483 + 0.796618i \(0.706620\pi\)
\(710\) 4.56228 3.62359i 0.171219 0.135991i
\(711\) −6.94453 + 6.81539i −0.260440 + 0.255597i
\(712\) −16.0294 10.0432i −0.600726 0.376384i
\(713\) −0.246564 + 0.920191i −0.00923391 + 0.0344614i
\(714\) −6.33868 0.383093i −0.237219 0.0143369i
\(715\) −0.841841 + 0.571000i −0.0314831 + 0.0213542i
\(716\) −27.1069 + 4.10947i −1.01303 + 0.153578i
\(717\) 17.4364 41.5428i 0.651175 1.55144i
\(718\) −23.3759 + 27.1868i −0.872379 + 1.01460i
\(719\) 22.4230 0.836238 0.418119 0.908392i \(-0.362690\pi\)
0.418119 + 0.908392i \(0.362690\pi\)
\(720\) 9.55103 + 25.0754i 0.355946 + 0.934507i
\(721\) 13.6719 0.509170
\(722\) −12.7310 + 14.8065i −0.473798 + 0.551041i
\(723\) −20.6061 27.1169i −0.766348 1.00849i
\(724\) 22.7678 3.45165i 0.846158 0.128280i
\(725\) −19.5393 + 2.84914i −0.725673 + 0.105814i
\(726\) −12.0270 24.0788i −0.446363 0.893647i
\(727\) −4.53738 + 16.9337i −0.168282 + 0.628038i 0.829316 + 0.558779i \(0.188730\pi\)
−0.997599 + 0.0692588i \(0.977937\pi\)
\(728\) 16.6957 26.6470i 0.618782 0.987602i
\(729\) 19.6218 18.5468i 0.726733 0.686920i
\(730\) 45.0584 + 5.16695i 1.66769 + 0.191237i
\(731\) 1.02323 + 1.77229i 0.0378456 + 0.0655505i
\(732\) −21.2475 20.6251i −0.785332 0.762325i
\(733\) 2.53605 0.679534i 0.0936713 0.0250992i −0.211679 0.977339i \(-0.567893\pi\)
0.305350 + 0.952240i \(0.401226\pi\)
\(734\) −8.46824 12.4092i −0.312569 0.458032i
\(735\) 0.178836 0.268958i 0.00659646 0.00992066i
\(736\) 0.0836883 0.563425i 0.00308479 0.0207681i
\(737\) −0.258589 + 0.258589i −0.00952524 + 0.00952524i
\(738\) 29.7726 19.9104i 1.09595 0.732912i
\(739\) 2.84381 0.104611 0.0523057 0.998631i \(-0.483343\pi\)
0.0523057 + 0.998631i \(0.483343\pi\)
\(740\) 12.2526 11.3336i 0.450414 0.416630i
\(741\) −38.3613 + 15.6793i −1.40924 + 0.575992i
\(742\) 49.8829 + 9.41621i 1.83126 + 0.345680i
\(743\) 11.6722 3.12756i 0.428212 0.114739i −0.0382747 0.999267i \(-0.512186\pi\)
0.466487 + 0.884528i \(0.345520\pi\)
\(744\) 37.8915 26.6919i 1.38917 0.978571i
\(745\) 13.1568 15.2144i 0.482029 0.557413i
\(746\) −0.371528 + 0.772332i −0.0136026 + 0.0282771i
\(747\) 27.9322 + 0.262156i 1.02199 + 0.00959180i
\(748\) −0.0235737 + 0.210847i −0.000861941 + 0.00770932i
\(749\) 26.9675 15.5697i 0.985370 0.568903i
\(750\) 11.1327 + 25.0213i 0.406507 + 0.913648i
\(751\) 2.95051 5.11043i 0.107666 0.186482i −0.807159 0.590335i \(-0.798996\pi\)
0.914824 + 0.403852i \(0.132329\pi\)
\(752\) 29.7954 1.16602i 1.08653 0.0425203i
\(753\) −21.9141 + 2.78049i −0.798593 + 0.101327i
\(754\) −1.75342 23.2639i −0.0638557 0.847222i
\(755\) 10.6331 3.69205i 0.386980 0.134367i
\(756\) −26.6767 + 7.30489i −0.970221 + 0.265676i
\(757\) −5.52774 + 5.52774i −0.200909 + 0.200909i −0.800389 0.599480i \(-0.795374\pi\)
0.599480 + 0.800389i \(0.295374\pi\)
\(758\) −14.2384 + 16.5596i −0.517161 + 0.601473i
\(759\) −0.0150140 0.0116330i −0.000544973 0.000422250i
\(760\) −24.6695 + 26.5279i −0.894856 + 0.962268i
\(761\) −20.2154 11.6714i −0.732808 0.423087i 0.0866403 0.996240i \(-0.472387\pi\)
−0.819449 + 0.573153i \(0.805720\pi\)
\(762\) −39.4037 + 8.04643i −1.42745 + 0.291492i
\(763\) −11.9970 + 44.7735i −0.434321 + 1.62091i
\(764\) −9.23090 11.5549i −0.333962 0.418040i
\(765\) 4.90225 + 4.32034i 0.177241 + 0.156202i
\(766\) −15.6217 + 32.4745i −0.564436 + 1.17335i
\(767\) −33.7499 9.04325i −1.21864 0.326533i
\(768\) −20.6872 + 18.4402i −0.746484 + 0.665404i
\(769\) −7.20568 4.16020i −0.259843 0.150021i 0.364420 0.931235i \(-0.381267\pi\)
−0.624263 + 0.781214i \(0.714601\pi\)
\(770\) −0.736386 0.545726i −0.0265375 0.0196666i
\(771\) −5.22584 12.7857i −0.188204 0.460465i
\(772\) −12.9914 + 5.68136i −0.467572 + 0.204477i
\(773\) 18.3408 18.3408i 0.659672 0.659672i −0.295630 0.955302i \(-0.595530\pi\)
0.955302 + 0.295630i \(0.0955296\pi\)
\(774\) 6.70380 + 5.87441i 0.240963 + 0.211151i
\(775\) 37.1256 29.3159i 1.33359 1.05306i
\(776\) −15.8144 + 14.7115i −0.567703 + 0.528111i
\(777\) 10.4092 + 13.6981i 0.373427 + 0.491417i
\(778\) −2.59251 + 13.7340i −0.0929459 + 0.492386i
\(779\) 41.8763 + 24.1773i 1.50037 + 0.866241i
\(780\) −30.4055 + 11.0665i −1.08869 + 0.396246i
\(781\) 0.173763 0.100322i 0.00621773 0.00358981i
\(782\) −0.0458693 0.130907i −0.00164028 0.00468122i
\(783\) −12.7201 + 16.1026i −0.454579 + 0.575461i
\(784\) 0.325343 + 0.0736708i 0.0116194 + 0.00263110i
\(785\) 44.8790 3.25481i 1.60180 0.116169i
\(786\) −14.1058 28.2406i −0.503136 1.00731i
\(787\) 5.32908 + 19.8884i 0.189961 + 0.708945i 0.993514 + 0.113711i \(0.0362738\pi\)
−0.803553 + 0.595234i \(0.797060\pi\)
\(788\) −4.64213 + 6.30116i −0.165369 + 0.224469i
\(789\) −5.20346 + 38.1403i −0.185248 + 1.35783i
\(790\) −9.54008 3.76595i −0.339421 0.133987i
\(791\) 31.1964i 1.10922i
\(792\) 0.198322 + 0.902541i 0.00704707 + 0.0320704i
\(793\) 25.2492 25.2492i 0.896625 0.896625i
\(794\) 0.806643 + 10.7023i 0.0286267 + 0.379812i
\(795\) −34.5296 39.1948i −1.22464 1.39010i
\(796\) 13.6111 2.06348i 0.482432 0.0731380i
\(797\) 25.8024 6.91373i 0.913967 0.244897i 0.228962 0.973435i \(-0.426467\pi\)
0.685005 + 0.728539i \(0.259800\pi\)
\(798\) −24.7630 27.9488i −0.876602 0.989377i
\(799\) 6.28849 3.63066i 0.222471 0.128443i
\(800\) −20.0532 + 19.9467i −0.708986 + 0.705222i
\(801\) −19.4274 + 5.01063i −0.686435 + 0.177042i
\(802\) 10.6479 3.73099i 0.375991 0.131746i
\(803\) 1.50868 + 0.404249i 0.0532401 + 0.0142656i
\(804\) −9.98652 + 5.96537i −0.352197 + 0.210383i
\(805\) 0.588530 + 0.112821i 0.0207430 + 0.00397642i
\(806\) 31.5041 + 46.1655i 1.10968 + 1.62611i
\(807\) 1.69283 + 13.3418i 0.0595906 + 0.469655i
\(808\) 0.274407 7.59503i 0.00965362 0.267192i
\(809\) −49.5961 −1.74371 −0.871854 0.489766i \(-0.837082\pi\)
−0.871854 + 0.489766i \(0.837082\pi\)
\(810\) 26.2718 + 10.9451i 0.923095 + 0.384571i
\(811\) 41.7596i 1.46638i 0.680024 + 0.733190i \(0.261969\pi\)
−0.680024 + 0.733190i \(0.738031\pi\)
\(812\) 19.2601 8.42275i 0.675897 0.295581i
\(813\) 14.9815 1.90087i 0.525423 0.0666665i
\(814\) 0.474778 0.323996i 0.0166410 0.0113561i
\(815\) −44.9534 + 30.4908i −1.57465 + 1.06804i
\(816\) −2.36648 + 6.32010i −0.0828434 + 0.221248i
\(817\) −3.11455 + 11.6236i −0.108964 + 0.406660i
\(818\) 24.6146 8.62488i 0.860631 0.301562i
\(819\) −8.32960 32.2959i −0.291060 1.12851i
\(820\) 31.9362 + 20.1358i 1.11526 + 0.703171i
\(821\) −1.86156 3.22432i −0.0649689 0.112529i 0.831711 0.555208i \(-0.187361\pi\)
−0.896680 + 0.442679i \(0.854028\pi\)
\(822\) 25.0971 22.2364i 0.875362 0.775583i
\(823\) 4.20313 + 15.6863i 0.146512 + 0.546790i 0.999683 + 0.0251597i \(0.00800943\pi\)
−0.853171 + 0.521631i \(0.825324\pi\)
\(824\) 4.26483 13.8896i 0.148572 0.483868i
\(825\) 0.252473 + 0.908707i 0.00878997 + 0.0316371i
\(826\) −2.36617 31.3938i −0.0823297 1.09233i
\(827\) 7.78626 + 7.78626i 0.270755 + 0.270755i 0.829404 0.558649i \(-0.188680\pi\)
−0.558649 + 0.829404i \(0.688680\pi\)
\(828\) −0.372645 0.475546i −0.0129503 0.0165264i
\(829\) −49.3670 −1.71459 −0.857293 0.514829i \(-0.827855\pi\)
−0.857293 + 0.514829i \(0.827855\pi\)
\(830\) 11.7213 + 27.0108i 0.406852 + 0.937560i
\(831\) −5.40153 0.736927i −0.187377 0.0255637i
\(832\) −21.8632 25.2737i −0.757969 0.876209i
\(833\) 0.0784653 0.0210247i 0.00271866 0.000728463i
\(834\) 13.5598 + 27.1477i 0.469539 + 0.940048i
\(835\) −13.4549 + 0.975808i −0.465627 + 0.0337692i
\(836\) −0.974709 + 0.778672i −0.0337110 + 0.0269309i
\(837\) 7.10222 48.6447i 0.245489 1.68141i
\(838\) 13.3620 4.68200i 0.461583 0.161737i
\(839\) 1.42565 + 2.46929i 0.0492188 + 0.0852494i 0.889585 0.456769i \(-0.150994\pi\)
−0.840366 + 0.542019i \(0.817660\pi\)
\(840\) −18.4701 22.5580i −0.637279 0.778325i
\(841\) −6.70194 + 11.6081i −0.231101 + 0.400279i
\(842\) 2.21701 11.7447i 0.0764031 0.404750i
\(843\) 31.5425 23.9691i 1.08638 0.825539i
\(844\) −1.87735 + 4.79548i −0.0646209 + 0.165067i
\(845\) −3.26340 9.39864i −0.112264 0.323323i
\(846\) 20.8437 23.7866i 0.716622 0.817800i
\(847\) 20.6790 + 20.6790i 0.710539 + 0.710539i
\(848\) 25.1266 47.7398i 0.862851 1.63939i
\(849\) −5.84509 + 2.38904i −0.200603 + 0.0819917i
\(850\) −2.05899 + 6.57283i −0.0706229 + 0.225446i
\(851\) −0.187900 + 0.325452i −0.00644113 + 0.0111564i
\(852\) 6.13959 1.74331i 0.210339 0.0597249i
\(853\) −2.87650 + 10.7353i −0.0984896 + 0.367568i −0.997525 0.0703069i \(-0.977602\pi\)
0.899036 + 0.437875i \(0.144269\pi\)
\(854\) 28.9940 + 13.9475i 0.992153 + 0.477272i
\(855\) 2.41954 + 38.3471i 0.0827465 + 1.31144i
\(856\) −7.40532 32.2536i −0.253109 1.10241i
\(857\) 39.7451 + 10.6497i 1.35767 + 0.363786i 0.862960 0.505273i \(-0.168608\pi\)
0.494709 + 0.869059i \(0.335275\pi\)
\(858\) −1.09178 + 0.222947i −0.0372727 + 0.00761127i
\(859\) 13.7810 23.8694i 0.470202 0.814413i −0.529218 0.848486i \(-0.677515\pi\)
0.999419 + 0.0340730i \(0.0108479\pi\)
\(860\) −2.78327 + 8.97390i −0.0949089 + 0.306007i
\(861\) −23.8353 + 30.7628i −0.812305 + 1.04839i
\(862\) −16.7225 14.3784i −0.569570 0.489730i
\(863\) 39.7632 + 39.7632i 1.35355 + 1.35355i 0.881650 + 0.471903i \(0.156433\pi\)
0.471903 + 0.881650i \(0.343567\pi\)
\(864\) −0.900334 + 29.3801i −0.0306300 + 0.999531i
\(865\) −13.4282 + 27.7133i −0.456571 + 0.942282i
\(866\) −3.10124 41.1465i −0.105384 1.39821i
\(867\) −3.49943 27.5803i −0.118847 0.936677i
\(868\) −29.8700 + 40.5451i −1.01385 + 1.37619i
\(869\) −0.305893 0.176607i −0.0103767 0.00599100i
\(870\) −20.9594 5.34659i −0.710591 0.181266i
\(871\) −7.01365 12.1480i −0.237649 0.411619i
\(872\) 41.7439 + 26.1547i 1.41363 + 0.885708i
\(873\) −0.215005 + 22.9083i −0.00727681 + 0.775329i
\(874\) 0.353582 0.735026i 0.0119601 0.0248626i
\(875\) −20.0815 21.9580i −0.678880 0.742318i
\(876\) 43.3908 + 24.1989i 1.46604 + 0.817607i
\(877\) 6.58176 + 24.5635i 0.222250 + 0.829449i 0.983488 + 0.180976i \(0.0579256\pi\)
−0.761237 + 0.648474i \(0.775408\pi\)
\(878\) 3.58738 19.0044i 0.121068 0.641366i
\(879\) 1.18050 + 2.88823i 0.0398171 + 0.0974176i
\(880\) −0.784123 + 0.577876i −0.0264328 + 0.0194802i
\(881\) 43.7727i 1.47474i −0.675489 0.737370i \(-0.736068\pi\)
0.675489 0.737370i \(-0.263932\pi\)
\(882\) 0.294109 0.196684i 0.00990315 0.00662271i
\(883\) 26.2906 + 26.2906i 0.884750 + 0.884750i 0.994013 0.109263i \(-0.0348489\pi\)
−0.109263 + 0.994013i \(0.534849\pi\)
\(884\) −7.57794 2.96663i −0.254874 0.0997785i
\(885\) −17.9372 + 26.9764i −0.602951 + 0.906800i
\(886\) 8.08290 5.51590i 0.271550 0.185310i
\(887\) 8.96949 + 33.4746i 0.301166 + 1.12397i 0.936196 + 0.351479i \(0.114321\pi\)
−0.635029 + 0.772488i \(0.719012\pi\)
\(888\) 17.1632 6.30190i 0.575961 0.211478i
\(889\) 37.8429 21.8486i 1.26921 0.732778i
\(890\) −13.1532 16.5605i −0.440896 0.555110i
\(891\) 0.839468 + 0.505909i 0.0281232 + 0.0169486i
\(892\) −3.23007 + 28.8902i −0.108151 + 0.967315i
\(893\) 41.2433 + 11.0511i 1.38015 + 0.369811i
\(894\) 19.7119 9.84577i 0.659264 0.329292i
\(895\) −30.1045 5.77103i −1.00628 0.192904i
\(896\) 14.9772 26.1220i 0.500354 0.872674i
\(897\) 0.580060 0.440787i 0.0193677 0.0147174i
\(898\) −24.2693 + 28.2259i −0.809878 + 0.941912i
\(899\) 37.3631i 1.24613i
\(900\) 0.721946 + 29.9913i 0.0240649 + 0.999710i
\(901\) 13.1375i 0.437674i
\(902\) 0.985865 + 0.847670i 0.0328257 + 0.0282243i
\(903\) −8.93011 3.74816i −0.297175 0.124731i
\(904\) 31.6931 + 9.73142i 1.05410 + 0.323662i
\(905\) 25.2856 + 4.84724i 0.840522 + 0.161128i
\(906\) 12.3077 + 0.743847i 0.408897 + 0.0247127i
\(907\) 25.6494 + 6.87273i 0.851673 + 0.228205i 0.658146 0.752890i \(-0.271341\pi\)
0.193527 + 0.981095i \(0.438007\pi\)
\(908\) 34.4393 + 3.85048i 1.14291 + 0.127783i
\(909\) −5.64625 5.75323i −0.187274 0.190823i
\(910\) 27.5300 21.8657i 0.912610 0.724840i
\(911\) −21.3199 + 12.3090i −0.706359 + 0.407817i −0.809712 0.586828i \(-0.800376\pi\)
0.103352 + 0.994645i \(0.467043\pi\)
\(912\) −36.1184 + 16.4389i −1.19600 + 0.544348i
\(913\) 0.262446 + 0.979461i 0.00868569 + 0.0324154i
\(914\) 12.0118 + 17.6019i 0.397316 + 0.582220i
\(915\) −14.7097 29.6596i −0.486288 0.980515i
\(916\) −27.5418 10.7821i −0.910007 0.356251i
\(917\) 24.2533 + 24.2533i 0.800913 + 0.800913i
\(918\) 3.13827 + 6.43336i 0.103578 + 0.212333i
\(919\) 47.2625i 1.55905i −0.626374 0.779523i \(-0.715462\pi\)
0.626374 0.779523i \(-0.284538\pi\)
\(920\) 0.298204 0.562707i 0.00983148 0.0185519i
\(921\) −34.8938 + 45.0354i −1.14979 + 1.48397i
\(922\) 21.6281 + 4.08266i 0.712285 + 0.134455i
\(923\) 1.99192 + 7.43396i 0.0655650 + 0.244692i
\(924\) −0.514890 0.861967i −0.0169386 0.0283566i
\(925\) 17.1393 7.37998i 0.563537 0.242652i
\(926\) −32.3182 15.5466i −1.06204 0.510893i
\(927\) −7.57990 13.4180i −0.248957 0.440706i
\(928\) −2.54885 22.1941i −0.0836702 0.728558i
\(929\) 22.6123 + 39.1657i 0.741886 + 1.28498i 0.951636 + 0.307229i \(0.0994017\pi\)
−0.209750 + 0.977755i \(0.567265\pi\)
\(930\) 49.8889 14.0133i 1.63592 0.459513i
\(931\) 0.413674 + 0.238835i 0.0135576 + 0.00782750i
\(932\) −16.7782 + 22.7744i −0.549587 + 0.746002i
\(933\) 3.83415 + 1.60928i 0.125524 + 0.0526854i
\(934\) 41.4295 3.12257i 1.35561 0.102174i
\(935\) −0.103432 + 0.213464i −0.00338257 + 0.00698103i
\(936\) −35.4084 1.61217i −1.15736 0.0526955i
\(937\) −31.2670 31.2670i −1.02145 1.02145i −0.999765 0.0216838i \(-0.993097\pi\)
−0.0216838 0.999765i \(-0.506903\pi\)
\(938\) 8.24029 9.58370i 0.269055 0.312919i
\(939\) −4.89525 0.667856i −0.159750 0.0217947i
\(940\) 31.8414 + 9.87568i 1.03855 + 0.322109i
\(941\) −4.43736 + 7.68574i −0.144654 + 0.250548i −0.929244 0.369467i \(-0.879540\pi\)
0.784590 + 0.620015i \(0.212874\pi\)
\(942\) 46.7557 + 15.6067i 1.52338 + 0.508493i
\(943\) −0.821094 0.220011i −0.0267385 0.00716456i
\(944\) −32.6317 7.38915i −1.06207 0.240496i
\(945\) −30.8420 2.24245i −1.00329 0.0729470i
\(946\) −0.140266 + 0.291585i −0.00456043 + 0.00948023i
\(947\) −4.87184 + 18.1820i −0.158314 + 0.590834i 0.840485 + 0.541835i \(0.182270\pi\)
−0.998799 + 0.0489999i \(0.984397\pi\)
\(948\) −8.06186 7.82568i −0.261837 0.254166i
\(949\) −29.9552 + 51.8839i −0.972387 + 1.68422i
\(950\) −35.8907 + 18.7683i −1.16445 + 0.608924i
\(951\) 5.43981 39.8727i 0.176398 1.29296i
\(952\) 0.264754 7.32786i 0.00858074 0.237497i
\(953\) −13.2794 13.2794i −0.430161 0.430161i 0.458522 0.888683i \(-0.348379\pi\)
−0.888683 + 0.458522i \(0.848379\pi\)
\(954\) −18.4144 54.1770i −0.596188 1.75404i
\(955\) −5.42364 15.6202i −0.175505 0.505456i
\(956\) 48.4436 + 18.9648i 1.56678 + 0.613366i
\(957\) −0.686870 0.288295i −0.0222034 0.00931924i
\(958\) 48.4734 + 9.15015i 1.56610 + 0.295628i
\(959\) −18.2163 + 31.5516i −0.588235 + 1.01885i
\(960\) −28.6787 + 11.7274i −0.925601 + 0.378500i
\(961\) −29.2546 50.6705i −0.943698 1.63453i
\(962\) 7.29078 + 20.8072i 0.235064 + 0.670852i
\(963\) −30.2316 17.8346i −0.974201 0.574713i
\(964\) 30.7257 24.5461i 0.989610 0.790576i
\(965\) −15.8115 + 1.14672i −0.508990 + 0.0369141i
\(966\) 0.547659 + 0.361919i 0.0176207 + 0.0116446i
\(967\) −4.00191 + 1.07231i −0.128693 + 0.0344831i −0.322590 0.946539i \(-0.604554\pi\)
0.193898 + 0.981022i \(0.437887\pi\)
\(968\) 27.4589 14.5576i 0.882561 0.467900i
\(969\) −5.91880 + 7.63904i −0.190139 + 0.245401i
\(970\) −22.1527 + 9.61311i −0.711279 + 0.308658i
\(971\) −59.0820 −1.89603 −0.948016 0.318223i \(-0.896914\pi\)
−0.948016 + 0.318223i \(0.896914\pi\)
\(972\) 21.9591 + 22.1313i 0.704340 + 0.709863i
\(973\) −23.3146 23.3146i −0.747433 0.747433i
\(974\) −30.6310 + 2.30868i −0.981482 + 0.0739749i
\(975\) −36.1745 + 0.332910i −1.15851 + 0.0106616i
\(976\) 23.2139 25.1048i 0.743058 0.803585i
\(977\) 10.5980 + 39.5522i 0.339060 + 1.26539i 0.899401 + 0.437125i \(0.144003\pi\)
−0.560341 + 0.828262i \(0.689330\pi\)
\(978\) −58.2997 + 11.9051i −1.86422 + 0.380683i
\(979\) −0.364157 0.630739i −0.0116385 0.0201585i
\(980\) 0.315481 + 0.198911i 0.0100777 + 0.00635397i
\(981\) 50.5933 13.0488i 1.61532 0.416615i
\(982\) −5.51722 15.7456i −0.176061 0.502464i
\(983\) −6.95749 + 25.9657i −0.221909 + 0.828177i 0.761710 + 0.647918i \(0.224360\pi\)
−0.983619 + 0.180259i \(0.942306\pi\)
\(984\) 23.8174 + 33.8109i 0.759270 + 1.07785i
\(985\) −7.24164 + 4.91183i −0.230738 + 0.156504i
\(986\) −3.06652 4.49362i −0.0976579 0.143106i
\(987\) −13.2993 + 31.6860i −0.423322 + 1.00858i
\(988\) −19.1736 43.8438i −0.609993 1.39486i
\(989\) 0.211548i 0.00672685i
\(990\) −0.127330 + 1.02527i −0.00404680 + 0.0325852i
\(991\) −30.3427 −0.963869 −0.481934 0.876207i \(-0.660066\pi\)
−0.481934 + 0.876207i \(0.660066\pi\)
\(992\) 31.8729 + 42.9932i 1.01197 + 1.36503i
\(993\) 37.7292 28.6704i 1.19730 0.909826i
\(994\) −5.72797 + 3.90886i −0.181680 + 0.123982i
\(995\) 15.1163 + 2.89779i 0.479219 + 0.0918661i
\(996\) 0.479435 + 32.2512i 0.0151915 + 1.02192i
\(997\) −16.7638 4.49185i −0.530915 0.142258i −0.0166041 0.999862i \(-0.505285\pi\)
−0.514311 + 0.857604i \(0.671952\pi\)
\(998\) −12.9539 36.9694i −0.410050 1.17025i
\(999\) 7.67275 17.8103i 0.242755 0.563492i
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 360.2.br.e.77.17 256
5.3 odd 4 inner 360.2.br.e.293.49 yes 256
8.5 even 2 inner 360.2.br.e.77.27 yes 256
9.2 odd 6 inner 360.2.br.e.317.5 yes 256
40.13 odd 4 inner 360.2.br.e.293.5 yes 256
45.38 even 12 inner 360.2.br.e.173.27 yes 256
72.29 odd 6 inner 360.2.br.e.317.49 yes 256
360.173 even 12 inner 360.2.br.e.173.17 yes 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.br.e.77.17 256 1.1 even 1 trivial
360.2.br.e.77.27 yes 256 8.5 even 2 inner
360.2.br.e.173.17 yes 256 360.173 even 12 inner
360.2.br.e.173.27 yes 256 45.38 even 12 inner
360.2.br.e.293.5 yes 256 40.13 odd 4 inner
360.2.br.e.293.49 yes 256 5.3 odd 4 inner
360.2.br.e.317.5 yes 256 9.2 odd 6 inner
360.2.br.e.317.49 yes 256 72.29 odd 6 inner