Properties

Label 360.2.bf.b.61.16
Level $360$
Weight $2$
Character 360.61
Analytic conductor $2.875$
Analytic rank $0$
Dimension $92$
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] = [360,2,Mod(61,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(92\)
Relative dimension: \(46\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.16
Character \(\chi\) \(=\) 360.61
Dual form 360.2.bf.b.301.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.705423 - 1.22572i) q^{2} +(1.15336 - 1.29220i) q^{3} +(-1.00476 + 1.72930i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.39747 - 0.502143i) q^{6} +(0.807871 - 1.39927i) q^{7} +(2.82840 + 0.0116626i) q^{8} +(-0.339538 - 2.98072i) q^{9} +O(q^{10})\) \(q+(-0.705423 - 1.22572i) q^{2} +(1.15336 - 1.29220i) q^{3} +(-1.00476 + 1.72930i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.39747 - 0.502143i) q^{6} +(0.807871 - 1.39927i) q^{7} +(2.82840 + 0.0116626i) q^{8} +(-0.339538 - 2.98072i) q^{9} +(1.22377 + 0.708789i) q^{10} +(-4.25826 - 2.45851i) q^{11} +(1.07574 + 3.29284i) q^{12} +(2.37410 - 1.37069i) q^{13} +(-2.28500 - 0.00314063i) q^{14} +(-0.352738 + 1.69575i) q^{15} +(-1.98092 - 3.47504i) q^{16} -2.56736 q^{17} +(-3.41400 + 2.51885i) q^{18} -5.12707i q^{19} +(0.00549781 - 1.99999i) q^{20} +(-0.876372 - 2.65779i) q^{21} +(-0.00955755 + 6.95370i) q^{22} +(-1.57063 - 2.72041i) q^{23} +(3.27723 - 3.64140i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.35482 - 1.94306i) q^{26} +(-4.24329 - 2.99909i) q^{27} +(1.60804 + 2.80298i) q^{28} +(6.66963 + 3.85071i) q^{29} +(2.32734 - 0.763866i) q^{30} +(2.32504 + 4.02708i) q^{31} +(-2.86203 + 4.87943i) q^{32} +(-8.08816 + 2.66697i) q^{33} +(1.81107 + 3.14685i) q^{34} +1.61574i q^{35} +(5.49571 + 2.40774i) q^{36} +6.41455i q^{37} +(-6.28434 + 3.61675i) q^{38} +(0.966989 - 4.64870i) q^{39} +(-2.45530 + 1.40410i) q^{40} +(-4.46182 - 7.72810i) q^{41} +(-2.63948 + 2.94905i) q^{42} +(6.66233 + 3.84650i) q^{43} +(8.53000 - 4.89358i) q^{44} +(1.78441 + 2.41161i) q^{45} +(-2.22650 + 3.84419i) q^{46} +(1.63638 - 2.83430i) q^{47} +(-6.77515 - 1.44822i) q^{48} +(2.19469 + 3.80131i) q^{49} +(-1.41421 - 0.00194377i) q^{50} +(-2.96108 + 3.31753i) q^{51} +(-0.0150716 + 5.48273i) q^{52} +4.51625i q^{53} +(-0.682717 + 7.31669i) q^{54} +4.91701 q^{55} +(2.30131 - 3.94829i) q^{56} +(-6.62518 - 5.91334i) q^{57} +(0.0149698 - 10.8914i) q^{58} +(4.37771 - 2.52747i) q^{59} +(-2.57804 - 2.31381i) q^{60} +(-6.74550 - 3.89452i) q^{61} +(3.29592 - 5.69063i) q^{62} +(-4.44515 - 1.93293i) q^{63} +(7.99973 + 0.0659730i) q^{64} +(-1.37069 + 2.37410i) q^{65} +(8.97452 + 8.03244i) q^{66} +(9.10714 - 5.25801i) q^{67} +(2.57957 - 4.43972i) q^{68} +(-5.32681 - 1.10804i) q^{69} +(1.98044 - 1.13978i) q^{70} -3.72070 q^{71} +(-0.925588 - 8.43465i) q^{72} -5.46178 q^{73} +(7.86241 - 4.52497i) q^{74} +(-0.542396 - 1.64493i) q^{75} +(8.86623 + 5.15147i) q^{76} +(-6.88025 + 3.97231i) q^{77} +(-6.38012 + 2.09404i) q^{78} +(4.40041 - 7.62173i) q^{79} +(3.45305 + 2.01901i) q^{80} +(-8.76943 + 2.02414i) q^{81} +(-6.32499 + 10.9205i) q^{82} +(12.0306 + 6.94585i) q^{83} +(5.47665 + 1.15493i) q^{84} +(2.22340 - 1.28368i) q^{85} +(0.0149534 - 10.8795i) q^{86} +(12.6683 - 4.17722i) q^{87} +(-12.0154 - 7.00331i) q^{88} +10.5539 q^{89} +(1.69719 - 3.88839i) q^{90} -4.42936i q^{91} +(6.28251 + 0.0172701i) q^{92} +(7.88537 + 1.64026i) q^{93} +(-4.62838 - 0.00636150i) q^{94} +(2.56354 + 4.44018i) q^{95} +(3.00424 + 9.32602i) q^{96} +(-4.09768 + 7.09739i) q^{97} +(3.11114 - 5.37159i) q^{98} +(-5.88229 + 13.5274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92 q + 2 q^{2} - 12 q^{6} - 8 q^{7} + 20 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 92 q + 2 q^{2} - 12 q^{6} - 8 q^{7} + 20 q^{8} + 6 q^{9} + 4 q^{10} + 22 q^{12} - 18 q^{14} - 8 q^{16} + 12 q^{17} - 16 q^{18} - 4 q^{20} - 10 q^{22} + 28 q^{23} + 24 q^{24} + 46 q^{25} - 64 q^{26} - 10 q^{30} + 8 q^{31} - 28 q^{32} - 14 q^{33} - 38 q^{36} - 6 q^{38} - 24 q^{39} + 2 q^{40} - 18 q^{41} + 22 q^{42} - 36 q^{44} + 4 q^{46} - 36 q^{47} - 76 q^{48} - 30 q^{49} - 2 q^{50} + 6 q^{52} + 42 q^{54} + 20 q^{55} - 38 q^{56} - 34 q^{57} + 18 q^{58} - 14 q^{60} + 60 q^{62} - 32 q^{63} - 48 q^{64} + 12 q^{65} + 36 q^{66} + 16 q^{68} + 8 q^{70} - 8 q^{71} + 92 q^{72} - 4 q^{73} + 52 q^{74} + 22 q^{76} + 58 q^{78} + 20 q^{79} - 16 q^{80} + 18 q^{81} - 16 q^{82} + 38 q^{84} - 60 q^{86} - 48 q^{87} - 20 q^{88} - 24 q^{89} - 24 q^{90} + 36 q^{92} - 14 q^{94} - 18 q^{95} - 38 q^{96} - 14 q^{97} - 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.705423 1.22572i −0.498809 0.866712i
\(3\) 1.15336 1.29220i 0.665891 0.746049i
\(4\) −1.00476 + 1.72930i −0.502379 + 0.864648i
\(5\) −0.866025 + 0.500000i −0.387298 + 0.223607i
\(6\) −2.39747 0.502143i −0.978762 0.204999i
\(7\) 0.807871 1.39927i 0.305347 0.528876i −0.671992 0.740559i \(-0.734561\pi\)
0.977338 + 0.211683i \(0.0678943\pi\)
\(8\) 2.82840 + 0.0116626i 0.999991 + 0.00412335i
\(9\) −0.339538 2.98072i −0.113179 0.993575i
\(10\) 1.22377 + 0.708789i 0.386991 + 0.224139i
\(11\) −4.25826 2.45851i −1.28391 0.741268i −0.306352 0.951918i \(-0.599108\pi\)
−0.977561 + 0.210651i \(0.932442\pi\)
\(12\) 1.07574 + 3.29284i 0.310541 + 0.950560i
\(13\) 2.37410 1.37069i 0.658458 0.380161i −0.133231 0.991085i \(-0.542535\pi\)
0.791689 + 0.610924i \(0.209202\pi\)
\(14\) −2.28500 0.00314063i −0.610693 0.000839370i
\(15\) −0.352738 + 1.69575i −0.0910766 + 0.437841i
\(16\) −1.98092 3.47504i −0.495231 0.868761i
\(17\) −2.56736 −0.622676 −0.311338 0.950299i \(-0.600777\pi\)
−0.311338 + 0.950299i \(0.600777\pi\)
\(18\) −3.41400 + 2.51885i −0.804688 + 0.593698i
\(19\) 5.12707i 1.17623i −0.808777 0.588116i \(-0.799870\pi\)
0.808777 0.588116i \(-0.200130\pi\)
\(20\) 0.00549781 1.99999i 0.00122935 0.447212i
\(21\) −0.876372 2.65779i −0.191240 0.579977i
\(22\) −0.00955755 + 6.95370i −0.00203768 + 1.48253i
\(23\) −1.57063 2.72041i −0.327499 0.567246i 0.654516 0.756049i \(-0.272873\pi\)
−0.982015 + 0.188803i \(0.939539\pi\)
\(24\) 3.27723 3.64140i 0.668961 0.743297i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −3.35482 1.94306i −0.657934 0.381065i
\(27\) −4.24329 2.99909i −0.816621 0.577175i
\(28\) 1.60804 + 2.80298i 0.303892 + 0.529713i
\(29\) 6.66963 + 3.85071i 1.23852 + 0.715059i 0.968791 0.247878i \(-0.0797331\pi\)
0.269727 + 0.962937i \(0.413066\pi\)
\(30\) 2.32734 0.763866i 0.424912 0.139462i
\(31\) 2.32504 + 4.02708i 0.417589 + 0.723285i 0.995696 0.0926756i \(-0.0295420\pi\)
−0.578108 + 0.815961i \(0.696209\pi\)
\(32\) −2.86203 + 4.87943i −0.505940 + 0.862569i
\(33\) −8.08816 + 2.66697i −1.40797 + 0.464260i
\(34\) 1.81107 + 3.14685i 0.310597 + 0.539681i
\(35\) 1.61574i 0.273110i
\(36\) 5.49571 + 2.40774i 0.915951 + 0.401290i
\(37\) 6.41455i 1.05455i 0.849696 + 0.527273i \(0.176785\pi\)
−0.849696 + 0.527273i \(0.823215\pi\)
\(38\) −6.28434 + 3.61675i −1.01945 + 0.586715i
\(39\) 0.966989 4.64870i 0.154842 0.744387i
\(40\) −2.45530 + 1.40410i −0.388217 + 0.222008i
\(41\) −4.46182 7.72810i −0.696820 1.20693i −0.969563 0.244840i \(-0.921264\pi\)
0.272744 0.962087i \(-0.412069\pi\)
\(42\) −2.63948 + 2.94905i −0.407281 + 0.455048i
\(43\) 6.66233 + 3.84650i 1.01600 + 0.586585i 0.912941 0.408091i \(-0.133805\pi\)
0.103054 + 0.994676i \(0.467139\pi\)
\(44\) 8.53000 4.89358i 1.28595 0.737735i
\(45\) 1.78441 + 2.41161i 0.266004 + 0.359502i
\(46\) −2.22650 + 3.84419i −0.328279 + 0.566795i
\(47\) 1.63638 2.83430i 0.238691 0.413425i −0.721648 0.692260i \(-0.756615\pi\)
0.960339 + 0.278836i \(0.0899484\pi\)
\(48\) −6.77515 1.44822i −0.977909 0.209033i
\(49\) 2.19469 + 3.80131i 0.313527 + 0.543044i
\(50\) −1.41421 0.00194377i −0.200000 0.000274891i
\(51\) −2.96108 + 3.31753i −0.414634 + 0.464547i
\(52\) −0.0150716 + 5.48273i −0.00209005 + 0.760318i
\(53\) 4.51625i 0.620354i 0.950679 + 0.310177i \(0.100388\pi\)
−0.950679 + 0.310177i \(0.899612\pi\)
\(54\) −0.682717 + 7.31669i −0.0929061 + 0.995675i
\(55\) 4.91701 0.663010
\(56\) 2.30131 3.94829i 0.307525 0.527612i
\(57\) −6.62518 5.91334i −0.877527 0.783242i
\(58\) 0.0149698 10.8914i 0.00196563 1.43012i
\(59\) 4.37771 2.52747i 0.569930 0.329049i −0.187192 0.982323i \(-0.559939\pi\)
0.757121 + 0.653274i \(0.226605\pi\)
\(60\) −2.57804 2.31381i −0.332824 0.298711i
\(61\) −6.74550 3.89452i −0.863673 0.498642i 0.00156774 0.999999i \(-0.499501\pi\)
−0.865240 + 0.501357i \(0.832834\pi\)
\(62\) 3.29592 5.69063i 0.418582 0.722710i
\(63\) −4.44515 1.93293i −0.560037 0.243527i
\(64\) 7.99973 + 0.0659730i 0.999966 + 0.00824663i
\(65\) −1.37069 + 2.37410i −0.170013 + 0.294471i
\(66\) 8.97452 + 8.03244i 1.10469 + 0.988726i
\(67\) 9.10714 5.25801i 1.11261 0.642368i 0.173109 0.984903i \(-0.444619\pi\)
0.939505 + 0.342534i \(0.111285\pi\)
\(68\) 2.57957 4.43972i 0.312819 0.538396i
\(69\) −5.32681 1.10804i −0.641272 0.133393i
\(70\) 1.98044 1.13978i 0.236708 0.136230i
\(71\) −3.72070 −0.441566 −0.220783 0.975323i \(-0.570861\pi\)
−0.220783 + 0.975323i \(0.570861\pi\)
\(72\) −0.925588 8.43465i −0.109082 0.994033i
\(73\) −5.46178 −0.639253 −0.319627 0.947544i \(-0.603557\pi\)
−0.319627 + 0.947544i \(0.603557\pi\)
\(74\) 7.86241 4.52497i 0.913987 0.526017i
\(75\) −0.542396 1.64493i −0.0626305 0.189941i
\(76\) 8.86623 + 5.15147i 1.01703 + 0.590914i
\(77\) −6.88025 + 3.97231i −0.784077 + 0.452687i
\(78\) −6.38012 + 2.09404i −0.722406 + 0.237104i
\(79\) 4.40041 7.62173i 0.495084 0.857511i −0.504899 0.863178i \(-0.668470\pi\)
0.999984 + 0.00566670i \(0.00180378\pi\)
\(80\) 3.45305 + 2.01901i 0.386063 + 0.225733i
\(81\) −8.76943 + 2.02414i −0.974381 + 0.224904i
\(82\) −6.32499 + 10.9205i −0.698478 + 1.20597i
\(83\) 12.0306 + 6.94585i 1.32053 + 0.762406i 0.983812 0.179202i \(-0.0573515\pi\)
0.336713 + 0.941607i \(0.390685\pi\)
\(84\) 5.47665 + 1.15493i 0.597551 + 0.126013i
\(85\) 2.22340 1.28368i 0.241161 0.139235i
\(86\) 0.0149534 10.8795i 0.00161247 1.17317i
\(87\) 12.6683 4.17722i 1.35819 0.447845i
\(88\) −12.0154 7.00331i −1.28085 0.746555i
\(89\) 10.5539 1.11871 0.559357 0.828927i \(-0.311048\pi\)
0.559357 + 0.828927i \(0.311048\pi\)
\(90\) 1.69719 3.88839i 0.178899 0.409872i
\(91\) 4.42936i 0.464323i
\(92\) 6.28251 + 0.0172701i 0.654996 + 0.00180053i
\(93\) 7.88537 + 1.64026i 0.817675 + 0.170087i
\(94\) −4.62838 0.00636150i −0.477381 0.000656139i
\(95\) 2.56354 + 4.44018i 0.263013 + 0.455553i
\(96\) 3.00424 + 9.32602i 0.306618 + 0.951833i
\(97\) −4.09768 + 7.09739i −0.416056 + 0.720631i −0.995539 0.0943541i \(-0.969921\pi\)
0.579482 + 0.814985i \(0.303255\pi\)
\(98\) 3.11114 5.37159i 0.314273 0.542613i
\(99\) −5.88229 + 13.5274i −0.591192 + 1.35956i
\(100\) 0.995235 + 1.73479i 0.0995235 + 0.173479i
\(101\) 15.6344 + 9.02650i 1.55568 + 0.898171i 0.997662 + 0.0683401i \(0.0217703\pi\)
0.558015 + 0.829831i \(0.311563\pi\)
\(102\) 6.15516 + 1.28918i 0.609452 + 0.127648i
\(103\) 6.96654 + 12.0664i 0.686433 + 1.18894i 0.972984 + 0.230873i \(0.0741580\pi\)
−0.286551 + 0.958065i \(0.592509\pi\)
\(104\) 6.73091 3.84917i 0.660020 0.377442i
\(105\) 2.08786 + 1.86353i 0.203754 + 0.181862i
\(106\) 5.53563 3.18586i 0.537668 0.309438i
\(107\) 12.3762i 1.19645i −0.801329 0.598225i \(-0.795873\pi\)
0.801329 0.598225i \(-0.204127\pi\)
\(108\) 9.44978 4.32454i 0.909306 0.416129i
\(109\) 14.6333i 1.40161i −0.713351 0.700807i \(-0.752823\pi\)
0.713351 0.700807i \(-0.247177\pi\)
\(110\) −3.46857 6.02686i −0.330715 0.574639i
\(111\) 8.28885 + 7.39826i 0.786743 + 0.702212i
\(112\) −6.46287 0.0355321i −0.610684 0.00335746i
\(113\) 1.61099 + 2.79032i 0.151549 + 0.262491i 0.931797 0.362979i \(-0.118240\pi\)
−0.780248 + 0.625470i \(0.784907\pi\)
\(114\) −2.57452 + 12.2920i −0.241126 + 1.15125i
\(115\) 2.72041 + 1.57063i 0.253680 + 0.146462i
\(116\) −13.3604 + 7.66472i −1.24048 + 0.711652i
\(117\) −4.89174 6.61114i −0.452242 0.611200i
\(118\) −6.18610 3.58289i −0.569477 0.329832i
\(119\) −2.07410 + 3.59244i −0.190132 + 0.329319i
\(120\) −1.01746 + 4.79216i −0.0928812 + 0.437462i
\(121\) 6.58851 + 11.4116i 0.598955 + 1.03742i
\(122\) −0.0151401 + 11.0153i −0.00137072 + 0.997282i
\(123\) −15.1323 3.14771i −1.36443 0.283820i
\(124\) −9.30011 0.0255652i −0.835174 0.00229582i
\(125\) 1.00000i 0.0894427i
\(126\) 0.766484 + 6.81203i 0.0682839 + 0.606864i
\(127\) −1.33329 −0.118310 −0.0591551 0.998249i \(-0.518841\pi\)
−0.0591551 + 0.998249i \(0.518841\pi\)
\(128\) −5.56233 9.85193i −0.491645 0.870796i
\(129\) 12.6545 4.17265i 1.11416 0.367381i
\(130\) 3.87689 + 0.00532861i 0.340026 + 0.000467350i
\(131\) −14.5205 + 8.38341i −1.26866 + 0.732462i −0.974735 0.223366i \(-0.928295\pi\)
−0.293927 + 0.955828i \(0.594962\pi\)
\(132\) 3.51466 16.6665i 0.305912 1.45063i
\(133\) −7.17418 4.14202i −0.622081 0.359158i
\(134\) −12.8692 7.45365i −1.11173 0.643897i
\(135\) 5.17434 + 0.475643i 0.445336 + 0.0409368i
\(136\) −7.26153 0.0299421i −0.622671 0.00256751i
\(137\) 0.391422 0.677963i 0.0334414 0.0579223i −0.848820 0.528681i \(-0.822687\pi\)
0.882262 + 0.470759i \(0.156020\pi\)
\(138\) 2.39950 + 7.31079i 0.204259 + 0.622336i
\(139\) 6.25094 3.60898i 0.530198 0.306110i −0.210899 0.977508i \(-0.567639\pi\)
0.741097 + 0.671398i \(0.234306\pi\)
\(140\) −2.79410 1.62343i −0.236144 0.137205i
\(141\) −1.77513 5.38348i −0.149493 0.453371i
\(142\) 2.62466 + 4.56052i 0.220257 + 0.382710i
\(143\) −13.4794 −1.12720
\(144\) −9.68555 + 7.08450i −0.807129 + 0.590375i
\(145\) −7.70142 −0.639568
\(146\) 3.85286 + 6.69459i 0.318865 + 0.554048i
\(147\) 7.44329 + 1.54830i 0.613912 + 0.127702i
\(148\) −11.0927 6.44507i −0.911810 0.529781i
\(149\) −12.6776 + 7.31940i −1.03859 + 0.599629i −0.919433 0.393247i \(-0.871352\pi\)
−0.119155 + 0.992876i \(0.538018\pi\)
\(150\) −1.63360 + 1.82520i −0.133383 + 0.149027i
\(151\) 9.10259 15.7662i 0.740759 1.28303i −0.211392 0.977401i \(-0.567800\pi\)
0.952150 0.305630i \(-0.0988671\pi\)
\(152\) 0.0597950 14.5014i 0.00485001 1.17622i
\(153\) 0.871717 + 7.65259i 0.0704741 + 0.618675i
\(154\) 9.72241 + 5.63107i 0.783454 + 0.453765i
\(155\) −4.02708 2.32504i −0.323463 0.186751i
\(156\) 7.06738 + 6.34302i 0.565843 + 0.507848i
\(157\) −14.3112 + 8.26260i −1.14216 + 0.659427i −0.946965 0.321337i \(-0.895868\pi\)
−0.195196 + 0.980764i \(0.562534\pi\)
\(158\) −12.4462 0.0171068i −0.990168 0.00136094i
\(159\) 5.83587 + 5.20884i 0.462815 + 0.413088i
\(160\) 0.0388751 5.65672i 0.00307335 0.447203i
\(161\) −5.07548 −0.400004
\(162\) 8.66717 + 9.32095i 0.680957 + 0.732323i
\(163\) 4.70055i 0.368175i −0.982910 0.184088i \(-0.941067\pi\)
0.982910 0.184088i \(-0.0589330\pi\)
\(164\) 17.8472 + 0.0490605i 1.39363 + 0.00383098i
\(165\) 5.67107 6.35374i 0.441492 0.494638i
\(166\) 0.0270023 19.6458i 0.00209578 1.52481i
\(167\) 4.20185 + 7.27782i 0.325149 + 0.563175i 0.981543 0.191244i \(-0.0612521\pi\)
−0.656393 + 0.754419i \(0.727919\pi\)
\(168\) −2.44774 7.52752i −0.188847 0.580761i
\(169\) −2.74242 + 4.75002i −0.210956 + 0.365386i
\(170\) −3.14186 1.81972i −0.240970 0.139566i
\(171\) −15.2824 + 1.74084i −1.16867 + 0.133125i
\(172\) −13.3457 + 7.65633i −1.01760 + 0.583790i
\(173\) 12.4502 + 7.18813i 0.946572 + 0.546504i 0.892014 0.452007i \(-0.149292\pi\)
0.0545575 + 0.998511i \(0.482625\pi\)
\(174\) −14.0566 12.5811i −1.06563 0.953768i
\(175\) −0.807871 1.39927i −0.0610693 0.105775i
\(176\) −0.108131 + 19.6678i −0.00815067 + 1.48251i
\(177\) 1.78307 8.57194i 0.134024 0.644306i
\(178\) −7.44499 12.9361i −0.558025 0.969603i
\(179\) 2.79733i 0.209082i −0.994521 0.104541i \(-0.966663\pi\)
0.994521 0.104541i \(-0.0333373\pi\)
\(180\) −5.96329 + 0.662686i −0.444478 + 0.0493937i
\(181\) 14.9938i 1.11448i −0.830353 0.557238i \(-0.811861\pi\)
0.830353 0.557238i \(-0.188139\pi\)
\(182\) −5.42914 + 3.12457i −0.402434 + 0.231609i
\(183\) −12.8124 + 4.22474i −0.947123 + 0.312302i
\(184\) −4.41065 7.71275i −0.325158 0.568591i
\(185\) −3.20728 5.55516i −0.235804 0.408424i
\(186\) −3.55203 10.8223i −0.260447 0.793529i
\(187\) 10.9325 + 6.31187i 0.799462 + 0.461570i
\(188\) 3.25717 + 5.67757i 0.237553 + 0.414079i
\(189\) −7.62458 + 3.51464i −0.554606 + 0.255653i
\(190\) 3.63402 6.27437i 0.263639 0.455191i
\(191\) 4.03903 6.99580i 0.292254 0.506199i −0.682088 0.731270i \(-0.738928\pi\)
0.974342 + 0.225071i \(0.0722614\pi\)
\(192\) 9.31179 10.2611i 0.672020 0.740533i
\(193\) 5.07408 + 8.78856i 0.365240 + 0.632614i 0.988815 0.149150i \(-0.0476536\pi\)
−0.623575 + 0.781764i \(0.714320\pi\)
\(194\) 11.5900 + 0.0159299i 0.832112 + 0.00114370i
\(195\) 1.48691 + 4.50938i 0.106480 + 0.322924i
\(196\) −8.77872 0.0241319i −0.627051 0.00172371i
\(197\) 16.9545i 1.20796i 0.797000 + 0.603980i \(0.206419\pi\)
−0.797000 + 0.603980i \(0.793581\pi\)
\(198\) 20.7303 2.33256i 1.47324 0.165768i
\(199\) −20.7051 −1.46774 −0.733872 0.679287i \(-0.762289\pi\)
−0.733872 + 0.679287i \(0.762289\pi\)
\(200\) 1.42430 2.44364i 0.100713 0.172791i
\(201\) 3.70940 17.8326i 0.261641 1.25781i
\(202\) 0.0350909 25.5308i 0.00246899 1.79634i
\(203\) 10.7764 6.22176i 0.756355 0.436682i
\(204\) −2.76182 8.45390i −0.193366 0.591891i
\(205\) 7.72810 + 4.46182i 0.539754 + 0.311627i
\(206\) 9.87562 17.0509i 0.688067 1.18799i
\(207\) −7.57552 + 5.60531i −0.526535 + 0.389596i
\(208\) −9.46612 5.53488i −0.656358 0.383775i
\(209\) −12.6049 + 21.8324i −0.871902 + 1.51018i
\(210\) 0.811334 3.87369i 0.0559873 0.267310i
\(211\) −13.8457 + 7.99384i −0.953180 + 0.550319i −0.894067 0.447933i \(-0.852160\pi\)
−0.0591124 + 0.998251i \(0.518827\pi\)
\(212\) −7.80992 4.53773i −0.536388 0.311653i
\(213\) −4.29129 + 4.80787i −0.294034 + 0.329430i
\(214\) −15.1697 + 8.73043i −1.03698 + 0.596800i
\(215\) −7.69299 −0.524658
\(216\) −11.9667 8.53211i −0.814234 0.580537i
\(217\) 7.51332 0.510037
\(218\) −17.9362 + 10.3227i −1.21480 + 0.699138i
\(219\) −6.29938 + 7.05769i −0.425673 + 0.476914i
\(220\) −4.94041 + 8.50297i −0.333082 + 0.573270i
\(221\) −6.09518 + 3.51905i −0.410006 + 0.236717i
\(222\) 3.22102 15.3787i 0.216181 1.03215i
\(223\) −1.14388 + 1.98125i −0.0765996 + 0.132674i −0.901781 0.432194i \(-0.857740\pi\)
0.825181 + 0.564868i \(0.191073\pi\)
\(224\) 4.51551 + 7.94671i 0.301705 + 0.530962i
\(225\) −2.75115 1.19631i −0.183410 0.0797542i
\(226\) 2.28371 3.94297i 0.151910 0.262282i
\(227\) −18.5798 10.7271i −1.23318 0.711980i −0.265492 0.964113i \(-0.585535\pi\)
−0.967693 + 0.252133i \(0.918868\pi\)
\(228\) 16.8826 5.51542i 1.11808 0.365268i
\(229\) −10.8072 + 6.23955i −0.714161 + 0.412321i −0.812600 0.582822i \(-0.801948\pi\)
0.0984391 + 0.995143i \(0.468615\pi\)
\(230\) 0.00610590 4.44241i 0.000402611 0.292924i
\(231\) −2.80237 + 13.4721i −0.184383 + 0.886401i
\(232\) 18.8195 + 10.9691i 1.23556 + 0.720160i
\(233\) 20.8278 1.36448 0.682239 0.731129i \(-0.261006\pi\)
0.682239 + 0.731129i \(0.261006\pi\)
\(234\) −4.65263 + 10.6595i −0.304152 + 0.696836i
\(235\) 3.27276i 0.213492i
\(236\) −0.0277911 + 10.1099i −0.00180905 + 0.658095i
\(237\) −4.77353 14.4768i −0.310074 0.940366i
\(238\) 5.86643 + 0.00806314i 0.380264 + 0.000522656i
\(239\) 11.5517 + 20.0082i 0.747218 + 1.29422i 0.949151 + 0.314821i \(0.101944\pi\)
−0.201933 + 0.979399i \(0.564722\pi\)
\(240\) 6.59156 2.13338i 0.425484 0.137709i
\(241\) 12.5977 21.8199i 0.811492 1.40555i −0.100328 0.994954i \(-0.531989\pi\)
0.911820 0.410591i \(-0.134678\pi\)
\(242\) 9.33973 16.1257i 0.600381 1.03660i
\(243\) −7.49869 + 13.6664i −0.481041 + 0.876698i
\(244\) 13.5124 7.75192i 0.865040 0.496266i
\(245\) −3.80131 2.19469i −0.242857 0.140213i
\(246\) 6.81647 + 20.7684i 0.434602 + 1.32414i
\(247\) −7.02762 12.1722i −0.447157 0.774499i
\(248\) 6.52917 + 11.4173i 0.414603 + 0.725001i
\(249\) 22.8509 7.53480i 1.44812 0.477498i
\(250\) 1.22572 0.705423i 0.0775211 0.0446149i
\(251\) 13.7630i 0.868712i −0.900741 0.434356i \(-0.856976\pi\)
0.900741 0.434356i \(-0.143024\pi\)
\(252\) 7.80892 5.74485i 0.491915 0.361892i
\(253\) 15.4456i 0.971059i
\(254\) 0.940532 + 1.63423i 0.0590142 + 0.102541i
\(255\) 0.905606 4.35361i 0.0567112 0.272633i
\(256\) −8.15187 + 13.7676i −0.509492 + 0.860475i
\(257\) 6.11036 + 10.5834i 0.381154 + 0.660177i 0.991227 0.132167i \(-0.0421936\pi\)
−0.610074 + 0.792345i \(0.708860\pi\)
\(258\) −14.0412 12.5673i −0.874168 0.782405i
\(259\) 8.97572 + 5.18213i 0.557724 + 0.322002i
\(260\) −2.72831 4.75572i −0.169203 0.294937i
\(261\) 9.21331 21.1878i 0.570290 1.31149i
\(262\) 20.5188 + 11.8841i 1.26765 + 0.734205i
\(263\) −8.50732 + 14.7351i −0.524584 + 0.908605i 0.475007 + 0.879982i \(0.342446\pi\)
−0.999590 + 0.0286232i \(0.990888\pi\)
\(264\) −22.9077 + 7.44893i −1.40987 + 0.458450i
\(265\) −2.25812 3.91118i −0.138715 0.240262i
\(266\) −0.0161023 + 11.7154i −0.000987293 + 0.718316i
\(267\) 12.1724 13.6377i 0.744942 0.834616i
\(268\) −0.0578151 + 21.0320i −0.00353162 + 1.28473i
\(269\) 6.36857i 0.388298i −0.980972 0.194149i \(-0.937805\pi\)
0.980972 0.194149i \(-0.0621946\pi\)
\(270\) −3.06709 6.67779i −0.186657 0.406398i
\(271\) −13.2713 −0.806172 −0.403086 0.915162i \(-0.632062\pi\)
−0.403086 + 0.915162i \(0.632062\pi\)
\(272\) 5.08575 + 8.92169i 0.308369 + 0.540957i
\(273\) −5.72360 5.10863i −0.346408 0.309188i
\(274\) −1.10711 0.00152167i −0.0668828 9.19274e-5i
\(275\) −4.25826 + 2.45851i −0.256783 + 0.148254i
\(276\) 7.26828 8.09831i 0.437499 0.487461i
\(277\) 3.63858 + 2.10074i 0.218621 + 0.126221i 0.605312 0.795989i \(-0.293048\pi\)
−0.386690 + 0.922210i \(0.626382\pi\)
\(278\) −8.83314 5.11602i −0.529777 0.306838i
\(279\) 11.2142 8.29764i 0.671375 0.496767i
\(280\) −0.0188438 + 4.56997i −0.00112613 + 0.273108i
\(281\) 5.33562 9.24157i 0.318297 0.551306i −0.661836 0.749649i \(-0.730223\pi\)
0.980133 + 0.198343i \(0.0635559\pi\)
\(282\) −5.34639 + 5.97344i −0.318373 + 0.355713i
\(283\) 8.55828 4.94112i 0.508737 0.293719i −0.223578 0.974686i \(-0.571774\pi\)
0.732314 + 0.680967i \(0.238440\pi\)
\(284\) 3.73840 6.43418i 0.221833 0.381799i
\(285\) 8.69425 + 1.80852i 0.515003 + 0.107127i
\(286\) 9.50867 + 16.5219i 0.562259 + 0.976960i
\(287\) −14.4183 −0.851086
\(288\) 15.5160 + 6.87416i 0.914288 + 0.405064i
\(289\) −10.4087 −0.612274
\(290\) 5.43276 + 9.43975i 0.319023 + 0.554321i
\(291\) 4.44513 + 13.4808i 0.260578 + 0.790260i
\(292\) 5.48777 9.44503i 0.321147 0.552729i
\(293\) 21.7299 12.5458i 1.26948 0.732933i 0.294588 0.955624i \(-0.404818\pi\)
0.974889 + 0.222692i \(0.0714844\pi\)
\(294\) −3.35289 10.2156i −0.195545 0.595784i
\(295\) −2.52747 + 4.37771i −0.147155 + 0.254880i
\(296\) −0.0748103 + 18.1429i −0.00434826 + 1.05454i
\(297\) 10.6957 + 23.2030i 0.620629 + 1.34638i
\(298\) 17.9146 + 10.3758i 1.03776 + 0.601056i
\(299\) −7.45768 4.30570i −0.431289 0.249005i
\(300\) 3.38955 + 0.714797i 0.195696 + 0.0412688i
\(301\) 10.7646 6.21495i 0.620462 0.358224i
\(302\) −25.7460 0.0353867i −1.48152 0.00203628i
\(303\) 29.6960 9.79188i 1.70599 0.562529i
\(304\) −17.8168 + 10.1563i −1.02186 + 0.582507i
\(305\) 7.78903 0.445999
\(306\) 8.76497 6.46679i 0.501060 0.369682i
\(307\) 23.3798i 1.33436i 0.744899 + 0.667178i \(0.232498\pi\)
−0.744899 + 0.667178i \(0.767502\pi\)
\(308\) 0.0436781 15.8892i 0.00248879 0.905371i
\(309\) 23.6270 + 4.91473i 1.34410 + 0.279589i
\(310\) −0.00903867 + 6.57619i −0.000513362 + 0.373502i
\(311\) 0.784497 + 1.35879i 0.0444847 + 0.0770498i 0.887410 0.460980i \(-0.152502\pi\)
−0.842926 + 0.538030i \(0.819169\pi\)
\(312\) 2.78925 13.1371i 0.157910 0.743743i
\(313\) −0.0973273 + 0.168576i −0.00550126 + 0.00952847i −0.868763 0.495228i \(-0.835084\pi\)
0.863262 + 0.504757i \(0.168418\pi\)
\(314\) 20.2231 + 11.7129i 1.14125 + 0.660996i
\(315\) 4.81608 0.548606i 0.271356 0.0309105i
\(316\) 8.75888 + 15.2676i 0.492725 + 0.858869i
\(317\) −16.7835 9.68997i −0.942657 0.544243i −0.0518647 0.998654i \(-0.516516\pi\)
−0.890792 + 0.454411i \(0.849850\pi\)
\(318\) 2.26780 10.8276i 0.127172 0.607179i
\(319\) −18.9340 32.7946i −1.06010 1.83615i
\(320\) −6.96095 + 3.94273i −0.389129 + 0.220405i
\(321\) −15.9924 14.2741i −0.892610 0.796704i
\(322\) 3.58036 + 6.22109i 0.199525 + 0.346688i
\(323\) 13.1630i 0.732412i
\(324\) 5.31081 17.1987i 0.295045 0.955483i
\(325\) 2.74138i 0.152064i
\(326\) −5.76153 + 3.31587i −0.319102 + 0.183649i
\(327\) −18.9091 16.8774i −1.04567 0.933322i
\(328\) −12.5297 21.9102i −0.691837 1.20979i
\(329\) −2.64397 4.57949i −0.145767 0.252476i
\(330\) −11.7884 2.46904i −0.648929 0.135916i
\(331\) −3.19830 1.84654i −0.175794 0.101495i 0.409521 0.912301i \(-0.365696\pi\)
−0.585315 + 0.810806i \(0.699029\pi\)
\(332\) −24.0992 + 13.8255i −1.32262 + 0.758773i
\(333\) 19.1200 2.17798i 1.04777 0.119353i
\(334\) 5.95646 10.2842i 0.325923 0.562728i
\(335\) −5.25801 + 9.10714i −0.287276 + 0.497576i
\(336\) −7.49991 + 8.31032i −0.409154 + 0.453365i
\(337\) 5.84684 + 10.1270i 0.318498 + 0.551654i 0.980175 0.198135i \(-0.0634884\pi\)
−0.661677 + 0.749789i \(0.730155\pi\)
\(338\) 7.75674 + 0.0106613i 0.421911 + 0.000579898i
\(339\) 5.46368 + 1.13652i 0.296746 + 0.0617271i
\(340\) −0.0141149 + 5.13470i −0.000765486 + 0.278468i
\(341\) 22.8645i 1.23818i
\(342\) 12.9143 + 17.5038i 0.698326 + 0.946499i
\(343\) 18.4023 0.993631
\(344\) 18.7989 + 10.9571i 1.01357 + 0.590769i
\(345\) 5.16717 1.70381i 0.278191 0.0917300i
\(346\) 0.0279442 20.3311i 0.00150229 1.09301i
\(347\) 10.8140 6.24349i 0.580529 0.335168i −0.180815 0.983517i \(-0.557873\pi\)
0.761343 + 0.648349i \(0.224540\pi\)
\(348\) −5.50495 + 26.1044i −0.295096 + 1.39934i
\(349\) −6.73105 3.88618i −0.360305 0.208022i 0.308910 0.951091i \(-0.400036\pi\)
−0.669215 + 0.743069i \(0.733369\pi\)
\(350\) −1.14522 + 1.97730i −0.0612147 + 0.105691i
\(351\) −14.1848 1.30392i −0.757129 0.0695979i
\(352\) 24.1834 13.7415i 1.28898 0.732427i
\(353\) 15.4503 26.7607i 0.822338 1.42433i −0.0815994 0.996665i \(-0.526003\pi\)
0.903937 0.427665i \(-0.140664\pi\)
\(354\) −11.7646 + 3.86130i −0.625280 + 0.205226i
\(355\) 3.22222 1.86035i 0.171018 0.0987371i
\(356\) −10.6041 + 18.2509i −0.562018 + 0.967294i
\(357\) 2.24996 + 6.82350i 0.119081 + 0.361138i
\(358\) −3.42873 + 1.97330i −0.181214 + 0.104292i
\(359\) −33.1225 −1.74814 −0.874069 0.485801i \(-0.838528\pi\)
−0.874069 + 0.485801i \(0.838528\pi\)
\(360\) 5.01891 + 6.84183i 0.264520 + 0.360596i
\(361\) −7.28689 −0.383521
\(362\) −18.3781 + 10.5769i −0.965930 + 0.555911i
\(363\) 22.3450 + 4.64804i 1.17281 + 0.243959i
\(364\) 7.65967 + 4.45043i 0.401476 + 0.233266i
\(365\) 4.73004 2.73089i 0.247582 0.142941i
\(366\) 14.2165 + 12.7242i 0.743109 + 0.665104i
\(367\) 1.06456 1.84387i 0.0555696 0.0962493i −0.836902 0.547352i \(-0.815636\pi\)
0.892472 + 0.451103i \(0.148969\pi\)
\(368\) −6.34226 + 10.8470i −0.330613 + 0.565437i
\(369\) −21.5204 + 15.9234i −1.12031 + 0.828942i
\(370\) −4.54657 + 7.84995i −0.236365 + 0.408099i
\(371\) 6.31947 + 3.64855i 0.328090 + 0.189423i
\(372\) −10.7594 + 11.9881i −0.557848 + 0.621553i
\(373\) −27.4841 + 15.8680i −1.42307 + 0.821612i −0.996560 0.0828699i \(-0.973591\pi\)
−0.426513 + 0.904482i \(0.640258\pi\)
\(374\) 0.0245377 17.8527i 0.00126881 0.923139i
\(375\) 1.29220 + 1.15336i 0.0667287 + 0.0595591i
\(376\) 4.66140 7.99745i 0.240393 0.412437i
\(377\) 21.1125 1.08735
\(378\) 9.68650 + 6.86625i 0.498220 + 0.353162i
\(379\) 29.1965i 1.49973i −0.661594 0.749863i \(-0.730120\pi\)
0.661594 0.749863i \(-0.269880\pi\)
\(380\) −10.2541 0.0281877i −0.526025 0.00144600i
\(381\) −1.53776 + 1.72287i −0.0787816 + 0.0882652i
\(382\) −11.4241 0.0157019i −0.584507 0.000803379i
\(383\) −16.3831 28.3764i −0.837139 1.44997i −0.892277 0.451488i \(-0.850893\pi\)
0.0551384 0.998479i \(-0.482440\pi\)
\(384\) −19.1460 4.17517i −0.977038 0.213063i
\(385\) 3.97231 6.88025i 0.202448 0.350650i
\(386\) 7.19290 12.4190i 0.366109 0.632112i
\(387\) 9.20323 21.1646i 0.467826 1.07586i
\(388\) −8.15631 14.2173i −0.414074 0.721772i
\(389\) 12.3493 + 7.12988i 0.626135 + 0.361499i 0.779254 0.626709i \(-0.215598\pi\)
−0.153119 + 0.988208i \(0.548932\pi\)
\(390\) 4.47832 5.00355i 0.226769 0.253365i
\(391\) 4.03238 + 6.98429i 0.203926 + 0.353210i
\(392\) 6.16313 + 10.7772i 0.311285 + 0.544332i
\(393\) −5.91430 + 28.4324i −0.298337 + 1.43422i
\(394\) 20.7814 11.9601i 1.04695 0.602541i
\(395\) 8.80081i 0.442817i
\(396\) −17.4827 23.7640i −0.878538 1.19419i
\(397\) 12.4966i 0.627187i −0.949557 0.313593i \(-0.898467\pi\)
0.949557 0.313593i \(-0.101533\pi\)
\(398\) 14.6058 + 25.3785i 0.732125 + 1.27211i
\(399\) −13.6267 + 4.49323i −0.682188 + 0.224943i
\(400\) −3.99994 0.0219912i −0.199997 0.00109956i
\(401\) 1.15824 + 2.00613i 0.0578397 + 0.100181i 0.893495 0.449072i \(-0.148245\pi\)
−0.835656 + 0.549254i \(0.814912\pi\)
\(402\) −24.4744 + 8.03283i −1.22067 + 0.400641i
\(403\) 11.0397 + 6.37380i 0.549929 + 0.317502i
\(404\) −31.3182 + 17.9670i −1.55814 + 0.893891i
\(405\) 6.58248 6.13767i 0.327086 0.304983i
\(406\) −15.2280 8.81983i −0.755754 0.437721i
\(407\) 15.7702 27.3148i 0.781701 1.35395i
\(408\) −8.41382 + 9.34878i −0.416546 + 0.462834i
\(409\) −13.4362 23.2722i −0.664378 1.15074i −0.979454 0.201670i \(-0.935363\pi\)
0.315076 0.949067i \(-0.397970\pi\)
\(410\) 0.0173455 12.6199i 0.000856634 0.623254i
\(411\) −0.424611 1.28773i −0.0209445 0.0635189i
\(412\) −27.8661 0.0766014i −1.37286 0.00377388i
\(413\) 8.16749i 0.401896i
\(414\) 12.2145 + 5.33132i 0.600308 + 0.262020i
\(415\) −13.8917 −0.681916
\(416\) −0.106571 + 15.5072i −0.00522509 + 0.760303i
\(417\) 2.54605 12.2399i 0.124681 0.599390i
\(418\) 35.6521 + 0.0490023i 1.74380 + 0.00239678i
\(419\) 7.24002 4.18003i 0.353698 0.204208i −0.312615 0.949880i \(-0.601205\pi\)
0.666313 + 0.745672i \(0.267872\pi\)
\(420\) −5.32038 + 1.73813i −0.259608 + 0.0848119i
\(421\) 12.4363 + 7.18011i 0.606109 + 0.349937i 0.771441 0.636301i \(-0.219536\pi\)
−0.165332 + 0.986238i \(0.552870\pi\)
\(422\) 19.5653 + 11.3319i 0.952422 + 0.551628i
\(423\) −9.00387 3.91525i −0.437783 0.190366i
\(424\) −0.0526712 + 12.7738i −0.00255794 + 0.620349i
\(425\) −1.28368 + 2.22340i −0.0622676 + 0.107851i
\(426\) 8.92025 + 1.86832i 0.432188 + 0.0905205i
\(427\) −10.8990 + 6.29254i −0.527439 + 0.304517i
\(428\) 21.4020 + 12.4350i 1.03451 + 0.601071i
\(429\) −15.5465 + 17.4180i −0.750594 + 0.840949i
\(430\) 5.42681 + 9.42942i 0.261704 + 0.454727i
\(431\) 33.6425 1.62050 0.810251 0.586084i \(-0.199331\pi\)
0.810251 + 0.586084i \(0.199331\pi\)
\(432\) −2.01633 + 20.6866i −0.0970108 + 0.995283i
\(433\) 5.37944 0.258519 0.129260 0.991611i \(-0.458740\pi\)
0.129260 + 0.991611i \(0.458740\pi\)
\(434\) −5.30007 9.20919i −0.254411 0.442055i
\(435\) −8.88248 + 9.95174i −0.425883 + 0.477150i
\(436\) 25.3053 + 14.7029i 1.21190 + 0.704141i
\(437\) −13.9478 + 8.05275i −0.667212 + 0.385215i
\(438\) 13.0944 + 2.74259i 0.625677 + 0.131046i
\(439\) −5.78623 + 10.0220i −0.276161 + 0.478326i −0.970427 0.241393i \(-0.922396\pi\)
0.694266 + 0.719718i \(0.255729\pi\)
\(440\) 13.9073 + 0.0573451i 0.663004 + 0.00273382i
\(441\) 10.5855 7.83245i 0.504070 0.372974i
\(442\) 8.61303 + 4.98853i 0.409680 + 0.237280i
\(443\) −16.0282 9.25389i −0.761523 0.439665i 0.0683193 0.997664i \(-0.478236\pi\)
−0.829842 + 0.557998i \(0.811570\pi\)
\(444\) −21.1221 + 6.90042i −1.00241 + 0.327479i
\(445\) −9.13997 + 5.27697i −0.433276 + 0.250152i
\(446\) 3.23537 + 0.00444686i 0.153199 + 0.000210565i
\(447\) −5.16366 + 24.8238i −0.244233 + 1.17412i
\(448\) 6.55507 11.1405i 0.309698 0.526340i
\(449\) 1.08437 0.0511747 0.0255874 0.999673i \(-0.491854\pi\)
0.0255874 + 0.999673i \(0.491854\pi\)
\(450\) 0.474385 + 4.21604i 0.0223627 + 0.198746i
\(451\) 43.8777i 2.06612i
\(452\) −6.44394 0.0177138i −0.303097 0.000833189i
\(453\) −9.87442 29.9463i −0.463941 1.40700i
\(454\) −0.0417019 + 30.3407i −0.00195717 + 1.42396i
\(455\) 2.21468 + 3.83594i 0.103826 + 0.179832i
\(456\) −18.6697 16.8026i −0.874290 0.786853i
\(457\) −3.39008 + 5.87179i −0.158581 + 0.274671i −0.934357 0.356338i \(-0.884025\pi\)
0.775776 + 0.631008i \(0.217359\pi\)
\(458\) 15.2716 + 8.84505i 0.713593 + 0.413302i
\(459\) 10.8940 + 7.69974i 0.508490 + 0.359393i
\(460\) −5.44944 + 3.12630i −0.254082 + 0.145764i
\(461\) 9.41902 + 5.43807i 0.438687 + 0.253276i 0.703041 0.711150i \(-0.251825\pi\)
−0.264353 + 0.964426i \(0.585159\pi\)
\(462\) 18.4899 6.06863i 0.860226 0.282338i
\(463\) 15.0493 + 26.0662i 0.699401 + 1.21140i 0.968674 + 0.248334i \(0.0798830\pi\)
−0.269274 + 0.963064i \(0.586784\pi\)
\(464\) 0.169363 30.8052i 0.00786249 1.43010i
\(465\) −7.64906 + 2.52218i −0.354717 + 0.116963i
\(466\) −14.6924 25.5290i −0.680614 1.18261i
\(467\) 18.4593i 0.854194i 0.904206 + 0.427097i \(0.140464\pi\)
−0.904206 + 0.427097i \(0.859536\pi\)
\(468\) 16.3476 1.81667i 0.755670 0.0839757i
\(469\) 16.9912i 0.784580i
\(470\) 4.01148 2.30868i 0.185036 0.106492i
\(471\) −5.82907 + 28.0226i −0.268589 + 1.29121i
\(472\) 12.4114 7.09766i 0.571281 0.326696i
\(473\) −18.9133 32.7587i −0.869633 1.50625i
\(474\) −14.3770 + 16.0632i −0.660359 + 0.737808i
\(475\) −4.44018 2.56354i −0.203729 0.117623i
\(476\) −4.12843 7.19626i −0.189226 0.329840i
\(477\) 13.4617 1.53344i 0.616368 0.0702113i
\(478\) 16.3755 28.2733i 0.748996 1.29319i
\(479\) 1.73388 3.00316i 0.0792228 0.137218i −0.823692 0.567037i \(-0.808089\pi\)
0.902915 + 0.429820i \(0.141423\pi\)
\(480\) −7.26475 6.57445i −0.331589 0.300081i
\(481\) 8.79235 + 15.2288i 0.400897 + 0.694374i
\(482\) −35.6318 0.0489743i −1.62298 0.00223072i
\(483\) −5.85383 + 6.55851i −0.266359 + 0.298422i
\(484\) −26.3539 0.0724447i −1.19791 0.00329294i
\(485\) 8.19536i 0.372132i
\(486\) 22.0408 0.449302i 0.999792 0.0203808i
\(487\) −6.44561 −0.292078 −0.146039 0.989279i \(-0.546653\pi\)
−0.146039 + 0.989279i \(0.546653\pi\)
\(488\) −19.0336 11.0939i −0.861609 0.502199i
\(489\) −6.07403 5.42141i −0.274677 0.245164i
\(490\) −0.00853194 + 6.20751i −0.000385434 + 0.280427i
\(491\) 8.56812 4.94681i 0.386674 0.223246i −0.294044 0.955792i \(-0.595001\pi\)
0.680718 + 0.732546i \(0.261668\pi\)
\(492\) 20.6476 23.0055i 0.930866 1.03717i
\(493\) −17.1233 9.88616i −0.771196 0.445250i
\(494\) −9.96221 + 17.2004i −0.448221 + 0.773883i
\(495\) −1.66951 14.6563i −0.0750391 0.658750i
\(496\) 9.38856 16.0569i 0.421559 0.720978i
\(497\) −3.00585 + 5.20628i −0.134831 + 0.233533i
\(498\) −25.3551 22.6935i −1.13619 1.01692i
\(499\) 6.29907 3.63677i 0.281985 0.162804i −0.352337 0.935873i \(-0.614613\pi\)
0.634322 + 0.773069i \(0.281279\pi\)
\(500\) −1.72930 1.00476i −0.0773364 0.0449341i
\(501\) 14.2506 + 2.96431i 0.636670 + 0.132436i
\(502\) −16.8695 + 9.70873i −0.752923 + 0.433322i
\(503\) 15.8720 0.707699 0.353849 0.935302i \(-0.384873\pi\)
0.353849 + 0.935302i \(0.384873\pi\)
\(504\) −12.5501 5.51896i −0.559028 0.245834i
\(505\) −18.0530 −0.803348
\(506\) 18.9320 10.8957i 0.841628 0.484373i
\(507\) 2.97496 + 9.02221i 0.132123 + 0.400691i
\(508\) 1.33963 2.30565i 0.0594365 0.102297i
\(509\) −11.4988 + 6.63885i −0.509677 + 0.294262i −0.732701 0.680551i \(-0.761740\pi\)
0.223024 + 0.974813i \(0.428407\pi\)
\(510\) −5.97512 + 1.96112i −0.264583 + 0.0868398i
\(511\) −4.41242 + 7.64253i −0.195194 + 0.338086i
\(512\) 22.6257 + 0.279896i 0.999923 + 0.0123698i
\(513\) −15.3765 + 21.7556i −0.678891 + 0.960535i
\(514\) 8.66191 14.9554i 0.382061 0.659653i
\(515\) −12.0664 6.96654i −0.531709 0.306982i
\(516\) −5.49892 + 26.0758i −0.242077 + 1.14792i
\(517\) −13.9363 + 8.04611i −0.612917 + 0.353868i
\(518\) 0.0201458 14.6573i 0.000885154 0.644003i
\(519\) 23.6480 7.79763i 1.03803 0.342278i
\(520\) −3.90455 + 6.69893i −0.171226 + 0.293768i
\(521\) −12.2090 −0.534886 −0.267443 0.963574i \(-0.586179\pi\)
−0.267443 + 0.963574i \(0.586179\pi\)
\(522\) −32.4695 + 3.65344i −1.42115 + 0.159907i
\(523\) 24.9417i 1.09063i −0.838233 0.545313i \(-0.816411\pi\)
0.838233 0.545313i \(-0.183589\pi\)
\(524\) 0.0921808 33.5335i 0.00402694 1.46492i
\(525\) −2.73990 0.569934i −0.119579 0.0248740i
\(526\) 24.0623 + 0.0330725i 1.04917 + 0.00144203i
\(527\) −5.96920 10.3390i −0.260023 0.450372i
\(528\) 25.2899 + 22.8237i 1.10060 + 0.993272i
\(529\) 6.56623 11.3730i 0.285488 0.494480i
\(530\) −3.20107 + 5.52685i −0.139046 + 0.240071i
\(531\) −9.02010 12.1906i −0.391439 0.529026i
\(532\) 14.3711 8.24456i 0.623066 0.357447i
\(533\) −21.1857 12.2315i −0.917653 0.529807i
\(534\) −25.3027 5.29958i −1.09496 0.229335i
\(535\) 6.18808 + 10.7181i 0.267534 + 0.463383i
\(536\) 25.8200 14.7656i 1.11525 0.637775i
\(537\) −3.61469 3.22631i −0.155985 0.139226i
\(538\) −7.80605 + 4.49253i −0.336543 + 0.193687i
\(539\) 21.5826i 0.929629i
\(540\) −6.02148 + 8.47005i −0.259123 + 0.364493i
\(541\) 11.7941i 0.507070i 0.967326 + 0.253535i \(0.0815933\pi\)
−0.967326 + 0.253535i \(0.918407\pi\)
\(542\) 9.36185 + 16.2668i 0.402126 + 0.698719i
\(543\) −19.3749 17.2931i −0.831455 0.742120i
\(544\) 7.34785 12.5272i 0.315037 0.537101i
\(545\) 7.31664 + 12.6728i 0.313411 + 0.542843i
\(546\) −2.22417 + 10.6193i −0.0951858 + 0.454462i
\(547\) 1.53344 + 0.885334i 0.0655653 + 0.0378542i 0.532424 0.846478i \(-0.321281\pi\)
−0.466859 + 0.884332i \(0.654614\pi\)
\(548\) 0.779114 + 1.35807i 0.0332821 + 0.0580140i
\(549\) −9.31812 + 21.4288i −0.397688 + 0.914559i
\(550\) 6.01730 + 3.48513i 0.256579 + 0.148606i
\(551\) 19.7429 34.1957i 0.841075 1.45678i
\(552\) −15.0534 3.19612i −0.640717 0.136036i
\(553\) −7.10993 12.3148i −0.302345 0.523677i
\(554\) 0.00816670 5.94177i 0.000346970 0.252442i
\(555\) −10.8775 2.26266i −0.461724 0.0960444i
\(556\) −0.0396830 + 14.4359i −0.00168293 + 0.612218i
\(557\) 12.0765i 0.511697i −0.966717 0.255849i \(-0.917645\pi\)
0.966717 0.255849i \(-0.0823548\pi\)
\(558\) −18.0813 7.89205i −0.765441 0.334097i
\(559\) 21.0894 0.891986
\(560\) 5.61478 3.20067i 0.237268 0.135253i
\(561\) 20.7652 6.84707i 0.876708 0.289083i
\(562\) −15.0914 0.0207425i −0.636593 0.000874968i
\(563\) 8.89459 5.13529i 0.374862 0.216427i −0.300718 0.953713i \(-0.597226\pi\)
0.675581 + 0.737286i \(0.263893\pi\)
\(564\) 11.0932 + 2.33936i 0.467108 + 0.0985048i
\(565\) −2.79032 1.61099i −0.117390 0.0677749i
\(566\) −12.0936 7.00443i −0.508332 0.294418i
\(567\) −4.25224 + 13.9061i −0.178577 + 0.584000i
\(568\) −10.5236 0.0433930i −0.441562 0.00182073i
\(569\) −11.7719 + 20.3896i −0.493506 + 0.854777i −0.999972 0.00748293i \(-0.997618\pi\)
0.506466 + 0.862260i \(0.330951\pi\)
\(570\) −3.91640 11.9324i −0.164040 0.499795i
\(571\) −37.7840 + 21.8146i −1.58121 + 0.912912i −0.586527 + 0.809930i \(0.699505\pi\)
−0.994683 + 0.102982i \(0.967162\pi\)
\(572\) 13.5435 23.3098i 0.566283 0.974634i
\(573\) −4.38151 13.2879i −0.183040 0.555109i
\(574\) 10.1710 + 17.6728i 0.424530 + 0.737647i
\(575\) −3.14126 −0.131000
\(576\) −2.51957 23.8674i −0.104982 0.994474i
\(577\) 35.6082 1.48239 0.741195 0.671290i \(-0.234259\pi\)
0.741195 + 0.671290i \(0.234259\pi\)
\(578\) 7.34251 + 12.7581i 0.305408 + 0.530665i
\(579\) 17.2088 + 3.57964i 0.715171 + 0.148765i
\(580\) 7.73806 13.3180i 0.321306 0.553001i
\(581\) 19.4383 11.2227i 0.806436 0.465596i
\(582\) 13.3880 14.9581i 0.554949 0.620035i
\(583\) 11.1032 19.2313i 0.459848 0.796481i
\(584\) −15.4481 0.0636985i −0.639248 0.00263586i
\(585\) 7.54195 + 3.27955i 0.311821 + 0.135593i
\(586\) −30.7064 17.7846i −1.26847 0.734677i
\(587\) −3.82703 2.20954i −0.157959 0.0911974i 0.418937 0.908015i \(-0.362403\pi\)
−0.576896 + 0.816818i \(0.695736\pi\)
\(588\) −10.1562 + 11.3160i −0.418833 + 0.466663i
\(589\) 20.6471 11.9206i 0.850751 0.491181i
\(590\) 7.14877 + 0.00982566i 0.294310 + 0.000404516i
\(591\) 21.9085 + 19.5546i 0.901197 + 0.804369i
\(592\) 22.2909 12.7067i 0.916148 0.522244i
\(593\) 40.3517 1.65705 0.828523 0.559955i \(-0.189182\pi\)
0.828523 + 0.559955i \(0.189182\pi\)
\(594\) 20.8953 29.4779i 0.857345 1.20949i
\(595\) 4.14819i 0.170059i
\(596\) 0.0804813 29.2775i 0.00329664 1.19925i
\(597\) −23.8803 + 26.7550i −0.977357 + 1.09501i
\(598\) −0.0167386 + 12.1783i −0.000684491 + 0.498009i
\(599\) 3.18585 + 5.51806i 0.130170 + 0.225462i 0.923742 0.383015i \(-0.125114\pi\)
−0.793572 + 0.608477i \(0.791781\pi\)
\(600\) −1.51493 4.65886i −0.0618468 0.190197i
\(601\) −19.4131 + 33.6244i −0.791875 + 1.37157i 0.132929 + 0.991126i \(0.457562\pi\)
−0.924804 + 0.380443i \(0.875772\pi\)
\(602\) −15.2114 8.81018i −0.619969 0.359076i
\(603\) −18.7649 25.3606i −0.764166 1.03276i
\(604\) 18.1184 + 31.5822i 0.737229 + 1.28506i
\(605\) −11.4116 6.58851i −0.463949 0.267861i
\(606\) −32.9503 29.4914i −1.33851 1.19801i
\(607\) −8.97333 15.5423i −0.364216 0.630841i 0.624434 0.781078i \(-0.285330\pi\)
−0.988650 + 0.150237i \(0.951996\pi\)
\(608\) 25.0172 + 14.6738i 1.01458 + 0.595102i
\(609\) 4.38930 21.1011i 0.177864 0.855061i
\(610\) −5.49456 9.54714i −0.222468 0.386552i
\(611\) 8.97188i 0.362963i
\(612\) −14.1095 6.18154i −0.570341 0.249874i
\(613\) 34.4046i 1.38959i 0.719208 + 0.694795i \(0.244505\pi\)
−0.719208 + 0.694795i \(0.755495\pi\)
\(614\) 28.6570 16.4926i 1.15650 0.665589i
\(615\) 14.6788 4.84015i 0.591907 0.195174i
\(616\) −19.5065 + 11.1551i −0.785937 + 0.449450i
\(617\) −15.9287 27.5894i −0.641266 1.11071i −0.985150 0.171694i \(-0.945076\pi\)
0.343884 0.939012i \(-0.388257\pi\)
\(618\) −10.6430 32.4270i −0.428124 1.30441i
\(619\) −16.2813 9.40002i −0.654401 0.377819i 0.135739 0.990745i \(-0.456659\pi\)
−0.790140 + 0.612926i \(0.789992\pi\)
\(620\) 8.06691 4.62791i 0.323975 0.185861i
\(621\) −1.49412 + 16.2540i −0.0599569 + 0.652249i
\(622\) 1.11209 1.92009i 0.0445906 0.0769886i
\(623\) 8.52622 14.7678i 0.341596 0.591661i
\(624\) −18.0700 + 5.84839i −0.723377 + 0.234123i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0.275283 0.000378364i 0.0110025 1.51225e-5i
\(627\) 13.6737 + 41.4686i 0.546077 + 1.65610i
\(628\) 0.0908524 33.0503i 0.00362540 1.31885i
\(629\) 16.4685i 0.656641i
\(630\) −4.06981 5.51615i −0.162145 0.219769i
\(631\) −33.2186 −1.32241 −0.661205 0.750205i \(-0.729955\pi\)
−0.661205 + 0.750205i \(0.729955\pi\)
\(632\) 12.5350 21.5060i 0.498616 0.855463i
\(633\) −5.63946 + 27.1111i −0.224149 + 1.07757i
\(634\) −0.0376702 + 27.4074i −0.00149607 + 1.08849i
\(635\) 1.15466 0.666644i 0.0458213 0.0264550i
\(636\) −14.8713 + 4.85833i −0.589684 + 0.192645i
\(637\) 10.4208 + 6.01647i 0.412888 + 0.238381i
\(638\) −26.8404 + 46.3418i −1.06262 + 1.83469i
\(639\) 1.26332 + 11.0904i 0.0499761 + 0.438728i
\(640\) 9.74308 + 5.75086i 0.385129 + 0.227323i
\(641\) −21.4163 + 37.0941i −0.845892 + 1.46513i 0.0389520 + 0.999241i \(0.487598\pi\)
−0.884844 + 0.465887i \(0.845735\pi\)
\(642\) −6.21460 + 29.6715i −0.245271 + 1.17104i
\(643\) −28.3573 + 16.3721i −1.11830 + 0.645653i −0.940967 0.338497i \(-0.890081\pi\)
−0.177336 + 0.984150i \(0.556748\pi\)
\(644\) 5.09962 8.77700i 0.200953 0.345862i
\(645\) −8.87276 + 9.94085i −0.349365 + 0.391421i
\(646\) 16.1342 9.28551i 0.634790 0.365334i
\(647\) −10.5468 −0.414638 −0.207319 0.978273i \(-0.566474\pi\)
−0.207319 + 0.978273i \(0.566474\pi\)
\(648\) −24.8271 + 5.62281i −0.975300 + 0.220885i
\(649\) −24.8552 −0.975653
\(650\) −3.36015 + 1.93383i −0.131796 + 0.0758511i
\(651\) 8.66554 9.70868i 0.339629 0.380513i
\(652\) 8.12863 + 4.72291i 0.318342 + 0.184963i
\(653\) −24.5561 + 14.1775i −0.960956 + 0.554808i −0.896467 0.443110i \(-0.853875\pi\)
−0.0644889 + 0.997918i \(0.520542\pi\)
\(654\) −7.34800 + 35.0828i −0.287330 + 1.37185i
\(655\) 8.38341 14.5205i 0.327567 0.567363i
\(656\) −18.0170 + 30.8138i −0.703445 + 1.20308i
\(657\) 1.85448 + 16.2801i 0.0723503 + 0.635146i
\(658\) −3.74804 + 6.47124i −0.146114 + 0.252275i
\(659\) 2.36264 + 1.36407i 0.0920354 + 0.0531366i 0.545311 0.838234i \(-0.316411\pi\)
−0.453276 + 0.891370i \(0.649745\pi\)
\(660\) 5.28945 + 16.1909i 0.205891 + 0.630231i
\(661\) 20.2542 11.6937i 0.787796 0.454834i −0.0513902 0.998679i \(-0.516365\pi\)
0.839186 + 0.543845i \(0.183032\pi\)
\(662\) −0.00717849 + 5.22279i −0.000279000 + 0.202989i
\(663\) −2.48261 + 11.9349i −0.0964165 + 0.463512i
\(664\) 33.9463 + 19.7860i 1.31737 + 0.767844i
\(665\) 8.28403 0.321241
\(666\) −16.1573 21.8993i −0.626082 0.848580i
\(667\) 24.1922i 0.936726i
\(668\) −16.8074 0.0462020i −0.650296 0.00178761i
\(669\) 1.24087 + 3.76320i 0.0479747 + 0.145494i
\(670\) 14.8719 + 0.0204407i 0.574551 + 0.000789695i
\(671\) 19.1494 + 33.1677i 0.739254 + 1.28043i
\(672\) 15.4767 + 3.33047i 0.597026 + 0.128476i
\(673\) 2.09381 3.62658i 0.0807104 0.139795i −0.822845 0.568266i \(-0.807614\pi\)
0.903555 + 0.428472i \(0.140948\pi\)
\(674\) 8.28836 14.3104i 0.319256 0.551216i
\(675\) −4.71893 + 2.17525i −0.181632 + 0.0837254i
\(676\) −5.45871 9.51508i −0.209951 0.365965i
\(677\) 7.67632 + 4.43192i 0.295025 + 0.170333i 0.640206 0.768203i \(-0.278849\pi\)
−0.345181 + 0.938536i \(0.612182\pi\)
\(678\) −2.46116 7.49864i −0.0945203 0.287984i
\(679\) 6.62080 + 11.4676i 0.254083 + 0.440084i
\(680\) 6.30364 3.60483i 0.241734 0.138239i
\(681\) −35.2906 + 11.6366i −1.35234 + 0.445916i
\(682\) −28.0253 + 16.1291i −1.07315 + 0.617616i
\(683\) 13.8024i 0.528134i 0.964504 + 0.264067i \(0.0850639\pi\)
−0.964504 + 0.264067i \(0.914936\pi\)
\(684\) 12.3447 28.1769i 0.472010 1.07737i
\(685\) 0.782844i 0.0299109i
\(686\) −12.9814 22.5560i −0.495632 0.861192i
\(687\) −4.40185 + 21.1614i −0.167941 + 0.807360i
\(688\) 0.169178 30.7715i 0.00644984 1.17315i
\(689\) 6.19037 + 10.7220i 0.235834 + 0.408477i
\(690\) −5.73343 5.13158i −0.218268 0.195356i
\(691\) −4.84250 2.79582i −0.184217 0.106358i 0.405055 0.914292i \(-0.367252\pi\)
−0.589273 + 0.807934i \(0.700586\pi\)
\(692\) −24.9398 + 14.3078i −0.948071 + 0.543899i
\(693\) 14.1765 + 19.1594i 0.538520 + 0.727804i
\(694\) −15.2812 8.85064i −0.580067 0.335966i
\(695\) −3.60898 + 6.25094i −0.136897 + 0.237112i
\(696\) 35.8799 11.6671i 1.36002 0.442241i
\(697\) 11.4551 + 19.8408i 0.433893 + 0.751525i
\(698\) −0.0151077 + 10.9918i −0.000571834 + 0.416044i
\(699\) 24.0219 26.9137i 0.908593 1.01797i
\(700\) 3.23147 + 0.00888305i 0.122138 + 0.000335748i
\(701\) 44.5221i 1.68158i 0.541363 + 0.840789i \(0.317908\pi\)
−0.541363 + 0.840789i \(0.682092\pi\)
\(702\) 8.40806 + 18.3064i 0.317342 + 0.690929i
\(703\) 32.8879 1.24039
\(704\) −33.9027 19.9483i −1.27776 0.751830i
\(705\) 4.22905 + 3.77466i 0.159275 + 0.142162i
\(706\) −43.7001 0.0600638i −1.64467 0.00226053i
\(707\) 25.2611 14.5845i 0.950042 0.548507i
\(708\) 13.0319 + 11.6962i 0.489767 + 0.439569i
\(709\) 10.1093 + 5.83659i 0.379662 + 0.219198i 0.677671 0.735365i \(-0.262989\pi\)
−0.298009 + 0.954563i \(0.596323\pi\)
\(710\) −4.55328 2.63719i −0.170882 0.0989720i
\(711\) −24.2124 10.5285i −0.908035 0.394851i
\(712\) 29.8508 + 0.123086i 1.11871 + 0.00461285i
\(713\) 7.30355 12.6501i 0.273520 0.473751i
\(714\) 6.77650 7.57127i 0.253604 0.283348i
\(715\) 11.6735 6.73970i 0.436564 0.252050i
\(716\) 4.83740 + 2.81063i 0.180782 + 0.105038i
\(717\) 39.1777 + 8.14946i 1.46312 + 0.304347i
\(718\) 23.3654 + 40.5988i 0.871988 + 1.51513i
\(719\) 29.9132 1.11557 0.557787 0.829984i \(-0.311650\pi\)
0.557787 + 0.829984i \(0.311650\pi\)
\(720\) 4.84568 10.9781i 0.180588 0.409131i
\(721\) 22.5123 0.838401
\(722\) 5.14034 + 8.93166i 0.191304 + 0.332402i
\(723\) −13.6659 41.4449i −0.508241 1.54135i
\(724\) 25.9286 + 15.0651i 0.963630 + 0.559889i
\(725\) 6.66963 3.85071i 0.247704 0.143012i
\(726\) −10.0655 30.6674i −0.373565 1.13817i
\(727\) −6.53600 + 11.3207i −0.242407 + 0.419861i −0.961399 0.275157i \(-0.911270\pi\)
0.718993 + 0.695018i \(0.244603\pi\)
\(728\) 0.0516579 12.5280i 0.00191457 0.464319i
\(729\) 9.01095 + 25.4520i 0.333739 + 0.942666i
\(730\) −6.68397 3.87125i −0.247385 0.143281i
\(731\) −17.1046 9.87534i −0.632636 0.365253i
\(732\) 5.56757 26.4013i 0.205783 0.975821i
\(733\) 0.611885 0.353272i 0.0226005 0.0130484i −0.488657 0.872476i \(-0.662513\pi\)
0.511258 + 0.859427i \(0.329180\pi\)
\(734\) −3.01103 0.00413852i −0.111139 0.000152756i
\(735\) −7.22023 + 2.38078i −0.266322 + 0.0878164i
\(736\) 17.7693 + 0.122117i 0.654983 + 0.00450129i
\(737\) −51.7074 −1.90467
\(738\) 34.6986 + 15.1451i 1.27727 + 0.557499i
\(739\) 50.9622i 1.87467i 0.348423 + 0.937337i \(0.386717\pi\)
−0.348423 + 0.937337i \(0.613283\pi\)
\(740\) 12.8291 + 0.0352660i 0.471605 + 0.00129640i
\(741\) −23.8342 4.95782i −0.875572 0.182130i
\(742\) 0.0141839 10.3196i 0.000520707 0.378846i
\(743\) 21.9712 + 38.0553i 0.806046 + 1.39611i 0.915582 + 0.402130i \(0.131730\pi\)
−0.109536 + 0.993983i \(0.534937\pi\)
\(744\) 22.2839 + 4.73127i 0.816966 + 0.173457i
\(745\) 7.31940 12.6776i 0.268162 0.464470i
\(746\) 38.8375 + 22.4941i 1.42194 + 0.823567i
\(747\) 16.6188 38.2181i 0.608051 1.39833i
\(748\) −21.8996 + 12.5636i −0.800728 + 0.459370i
\(749\) −17.3177 9.99835i −0.632773 0.365332i
\(750\) 0.502143 2.39747i 0.0183357 0.0875432i
\(751\) 19.1191 + 33.1152i 0.697664 + 1.20839i 0.969274 + 0.245983i \(0.0791107\pi\)
−0.271610 + 0.962407i \(0.587556\pi\)
\(752\) −13.0909 0.0719718i −0.477374 0.00262454i
\(753\) −17.7845 15.8736i −0.648102 0.578467i
\(754\) −14.8932 25.8779i −0.542380 0.942419i
\(755\) 18.2052i 0.662555i
\(756\) 1.58299 16.7165i 0.0575728 0.607974i
\(757\) 9.38604i 0.341141i 0.985345 + 0.170571i \(0.0545611\pi\)
−0.985345 + 0.170571i \(0.945439\pi\)
\(758\) −35.7866 + 20.5959i −1.29983 + 0.748077i
\(759\) 19.9588 + 17.8143i 0.724458 + 0.646619i
\(760\) 7.19893 + 12.5885i 0.261133 + 0.456633i
\(761\) −14.5041 25.1219i −0.525774 0.910667i −0.999549 0.0300213i \(-0.990442\pi\)
0.473775 0.880646i \(-0.342891\pi\)
\(762\) 3.19651 + 0.669501i 0.115798 + 0.0242535i
\(763\) −20.4760 11.8218i −0.741280 0.427978i
\(764\) 8.03957 + 14.0138i 0.290861 + 0.507000i
\(765\) −4.58122 6.19148i −0.165635 0.223853i
\(766\) −23.2244 + 40.0984i −0.839131 + 1.44881i
\(767\) 6.92876 12.0010i 0.250183 0.433330i
\(768\) 8.38842 + 26.4128i 0.302691 + 0.953089i
\(769\) −4.53183 7.84936i −0.163422 0.283055i 0.772672 0.634806i \(-0.218920\pi\)
−0.936094 + 0.351751i \(0.885587\pi\)
\(770\) −11.2354 0.0154425i −0.404895 0.000556510i
\(771\) 20.7233 + 4.31071i 0.746332 + 0.155247i
\(772\) −20.2962 0.0557926i −0.730477 0.00200802i
\(773\) 20.3406i 0.731600i −0.930694 0.365800i \(-0.880795\pi\)
0.930694 0.365800i \(-0.119205\pi\)
\(774\) −32.4339 + 3.64944i −1.16581 + 0.131176i
\(775\) 4.65007 0.167036
\(776\) −11.6727 + 20.0265i −0.419024 + 0.718909i
\(777\) 17.0485 5.62153i 0.611613 0.201671i
\(778\) 0.0277177 20.1663i 0.000993728 0.722998i
\(779\) −39.6226 + 22.8761i −1.41963 + 0.819621i
\(780\) −9.29204 1.95953i −0.332709 0.0701623i
\(781\) 15.8437 + 9.14736i 0.566932 + 0.327318i
\(782\) 5.71622 9.86942i 0.204411 0.352930i
\(783\) −16.7525 36.3425i −0.598686 1.29877i
\(784\) 8.86221 15.1567i 0.316508 0.541312i
\(785\) 8.26260 14.3112i 0.294905 0.510790i
\(786\) 39.0221 12.8076i 1.39187 0.456832i
\(787\) 2.52807 1.45958i 0.0901159 0.0520284i −0.454265 0.890867i \(-0.650098\pi\)
0.544381 + 0.838838i \(0.316765\pi\)
\(788\) −29.3194 17.0352i −1.04446 0.606853i
\(789\) 9.22867 + 27.9879i 0.328549 + 0.996397i
\(790\) 10.7873 6.20829i 0.383795 0.220881i
\(791\) 5.20589 0.185100
\(792\) −16.7952 + 38.1925i −0.596793 + 1.35711i
\(793\) −21.3527 −0.758256
\(794\) −15.3173 + 8.81539i −0.543590 + 0.312846i
\(795\) −7.65843 1.59305i −0.271617 0.0564998i
\(796\) 20.8036 35.8052i 0.737364 1.26908i
\(797\) 32.9422 19.0192i 1.16687 0.673694i 0.213931 0.976849i \(-0.431373\pi\)
0.952941 + 0.303155i \(0.0980398\pi\)
\(798\) 15.1200 + 13.5328i 0.535242 + 0.479057i
\(799\) −4.20118 + 7.27666i −0.148627 + 0.257430i
\(800\) 2.79469 + 4.91830i 0.0988073 + 0.173888i
\(801\) −3.58346 31.4584i −0.126615 1.11153i
\(802\) 1.64189 2.83484i 0.0579773 0.100102i
\(803\) 23.2577 + 13.4278i 0.820746 + 0.473858i
\(804\) 27.1107 + 24.3321i 0.956122 + 0.858126i
\(805\) 4.39549 2.53774i 0.154921 0.0894435i
\(806\) 0.0247784 18.0278i 0.000872783 0.635003i
\(807\) −8.22943 7.34523i −0.289690 0.258564i
\(808\) 44.1150 + 25.7129i 1.55196 + 0.904578i
\(809\) 6.51802 0.229161 0.114581 0.993414i \(-0.463448\pi\)
0.114581 + 0.993414i \(0.463448\pi\)
\(810\) −12.1665 3.73859i −0.427486 0.131361i
\(811\) 26.4305i 0.928102i −0.885809 0.464051i \(-0.846396\pi\)
0.885809 0.464051i \(-0.153604\pi\)
\(812\) −0.0684121 + 24.8869i −0.00240079 + 0.873360i
\(813\) −15.3065 + 17.1491i −0.536822 + 0.601444i
\(814\) −44.6049 0.0613074i −1.56340 0.00214882i
\(815\) 2.35027 + 4.07079i 0.0823265 + 0.142594i
\(816\) 17.3942 + 3.71811i 0.608921 + 0.130160i
\(817\) 19.7213 34.1582i 0.689960 1.19505i
\(818\) −19.0469 + 32.8857i −0.665959 + 1.14982i
\(819\) −13.2027 + 1.50394i −0.461340 + 0.0525518i
\(820\) −15.4807 + 8.88113i −0.540609 + 0.310142i
\(821\) 5.77765 + 3.33573i 0.201641 + 0.116418i 0.597421 0.801928i \(-0.296192\pi\)
−0.395779 + 0.918346i \(0.629526\pi\)
\(822\) −1.27886 + 1.42884i −0.0446052 + 0.0498367i
\(823\) 17.3276 + 30.0123i 0.604002 + 1.04616i 0.992208 + 0.124589i \(0.0397613\pi\)
−0.388207 + 0.921572i \(0.626905\pi\)
\(824\) 19.5635 + 34.2099i 0.681525 + 1.19176i
\(825\) −1.73442 + 8.33804i −0.0603847 + 0.290293i
\(826\) −10.0110 + 5.76154i −0.348328 + 0.200469i
\(827\) 24.5697i 0.854371i 0.904164 + 0.427186i \(0.140495\pi\)
−0.904164 + 0.427186i \(0.859505\pi\)
\(828\) −2.08167 18.7323i −0.0723431 0.650992i
\(829\) 43.6041i 1.51443i 0.653163 + 0.757217i \(0.273442\pi\)
−0.653163 + 0.757217i \(0.726558\pi\)
\(830\) 9.79952 + 17.0273i 0.340146 + 0.591025i
\(831\) 6.91114 2.27886i 0.239745 0.0790528i
\(832\) 19.0826 10.8085i 0.661570 0.374718i
\(833\) −5.63455 9.75933i −0.195226 0.338141i
\(834\) −16.7987 + 5.51356i −0.581690 + 0.190919i
\(835\) −7.27782 4.20185i −0.251860 0.145411i
\(836\) −25.0898 43.7340i −0.867748 1.51257i
\(837\) 2.21177 24.0610i 0.0764500 0.831671i
\(838\) −10.2308 5.92552i −0.353417 0.204694i
\(839\) 5.55464 9.62091i 0.191767 0.332151i −0.754069 0.656796i \(-0.771911\pi\)
0.945836 + 0.324645i \(0.105245\pi\)
\(840\) 5.88356 + 5.29516i 0.203002 + 0.182700i
\(841\) 15.1560 + 26.2509i 0.522619 + 0.905203i
\(842\) 0.0279130 20.3084i 0.000961945 0.699874i
\(843\) −5.78804 17.5535i −0.199351 0.604574i
\(844\) 0.0878972 31.9752i 0.00302555 1.10063i
\(845\) 5.48485i 0.188685i
\(846\) 1.55255 + 13.7981i 0.0533778 + 0.474388i
\(847\) 21.2907 0.731556
\(848\) 15.6942 8.94634i 0.538940 0.307219i
\(849\) 3.48585 16.7578i 0.119634 0.575128i
\(850\) 3.63079 + 0.00499036i 0.124535 + 0.000171168i
\(851\) 17.4502 10.0749i 0.598187 0.345363i
\(852\) −4.00252 12.2516i −0.137124 0.419735i
\(853\) 24.7149 + 14.2692i 0.846223 + 0.488567i 0.859375 0.511347i \(-0.170853\pi\)
−0.0131520 + 0.999914i \(0.504187\pi\)
\(854\) 15.4013 + 8.92017i 0.527020 + 0.305242i
\(855\) 12.3645 9.14881i 0.422858 0.312883i
\(856\) 0.144338 35.0048i 0.00493338 1.19644i
\(857\) −12.2373 + 21.1956i −0.418018 + 0.724029i −0.995740 0.0922049i \(-0.970609\pi\)
0.577722 + 0.816234i \(0.303942\pi\)
\(858\) 32.3164 + 6.76858i 1.10326 + 0.231075i
\(859\) 31.5274 18.2023i 1.07570 0.621056i 0.145967 0.989289i \(-0.453371\pi\)
0.929733 + 0.368233i \(0.120037\pi\)
\(860\) 7.72959 13.3035i 0.263577 0.453644i
\(861\) −16.6295 + 18.6313i −0.566730 + 0.634953i
\(862\) −23.7322 41.2361i −0.808321 1.40451i
\(863\) −52.2814 −1.77968 −0.889839 0.456274i \(-0.849184\pi\)
−0.889839 + 0.456274i \(0.849184\pi\)
\(864\) 26.7782 12.1213i 0.911014 0.412376i
\(865\) −14.3763 −0.488808
\(866\) −3.79478 6.59366i −0.128952 0.224062i
\(867\) −12.0049 + 13.4500i −0.407708 + 0.456787i
\(868\) −7.54906 + 12.9927i −0.256232 + 0.441003i
\(869\) −37.4761 + 21.6369i −1.27129 + 0.733980i
\(870\) 18.4639 + 3.86721i 0.625985 + 0.131111i
\(871\) 14.4142 24.9661i 0.488406 0.845945i
\(872\) 0.170662 41.3888i 0.00577935 1.40160i
\(873\) 22.5467 + 9.80422i 0.763089 + 0.331822i
\(874\) 19.7095 + 11.4154i 0.666682 + 0.386132i
\(875\) 1.39927 + 0.807871i 0.0473041 + 0.0273110i
\(876\) −5.87548 17.9848i −0.198514 0.607648i
\(877\) 45.5790 26.3150i 1.53909 0.888596i 0.540201 0.841536i \(-0.318348\pi\)
0.998892 0.0470598i \(-0.0149851\pi\)
\(878\) 16.3659 + 0.0224942i 0.552322 + 0.000759142i
\(879\) 8.85076 42.5491i 0.298529 1.43515i
\(880\) −9.74023 17.0868i −0.328343 0.575997i
\(881\) −23.9641 −0.807371 −0.403686 0.914898i \(-0.632271\pi\)
−0.403686 + 0.914898i \(0.632271\pi\)
\(882\) −17.0676 7.44960i −0.574696 0.250841i
\(883\) 14.2196i 0.478526i −0.970955 0.239263i \(-0.923094\pi\)
0.970955 0.239263i \(-0.0769059\pi\)
\(884\) 0.0386942 14.0762i 0.00130143 0.473432i
\(885\) 2.74178 + 8.31505i 0.0921640 + 0.279507i
\(886\) −0.0359749 + 26.1739i −0.00120860 + 0.879330i
\(887\) 14.3327 + 24.8250i 0.481247 + 0.833543i 0.999768 0.0215209i \(-0.00685085\pi\)
−0.518522 + 0.855064i \(0.673518\pi\)
\(888\) 23.3579 + 21.0219i 0.783841 + 0.705450i
\(889\) −1.07713 + 1.86564i −0.0361256 + 0.0625714i
\(890\) 12.9156 + 7.48052i 0.432932 + 0.250748i
\(891\) 42.3188 + 12.9404i 1.41773 + 0.433519i
\(892\) −2.27685 3.96877i −0.0762346 0.132884i
\(893\) −14.5316 8.38985i −0.486283 0.280756i
\(894\) 34.0695 11.1821i 1.13945 0.373985i
\(895\) 1.39866 + 2.42255i 0.0467521 + 0.0809771i
\(896\) −18.2792 0.175873i −0.610665 0.00587550i
\(897\) −14.1652 + 4.67078i −0.472961 + 0.155953i
\(898\) −0.764942 1.32913i −0.0255264 0.0443538i
\(899\) 35.8122i 1.19440i
\(900\) 4.83302 3.55555i 0.161101 0.118518i
\(901\) 11.5948i 0.386280i
\(902\) 53.7816 30.9523i 1.79073 1.03060i
\(903\) 4.38450 21.0780i 0.145907 0.701433i
\(904\) 4.52399 + 7.91093i 0.150466 + 0.263114i
\(905\) 7.49688 + 12.9850i 0.249205 + 0.431635i
\(906\) −29.7400 + 33.2281i −0.988047 + 1.10393i
\(907\) −26.8939 15.5272i −0.892999 0.515573i −0.0180765 0.999837i \(-0.505754\pi\)
−0.874922 + 0.484264i \(0.839088\pi\)
\(908\) 37.2184 21.3519i 1.23514 0.708587i
\(909\) 21.5971 49.6666i 0.716329 1.64734i
\(910\) 3.13948 5.42053i 0.104073 0.179689i
\(911\) −2.06730 + 3.58066i −0.0684926 + 0.118633i −0.898238 0.439509i \(-0.855152\pi\)
0.829745 + 0.558142i \(0.188486\pi\)
\(912\) −7.42515 + 34.7367i −0.245871 + 1.15025i
\(913\) −34.1528 59.1544i −1.13029 1.95773i
\(914\) 9.58858 + 0.0131791i 0.317162 + 0.000435925i
\(915\) 8.98353 10.0650i 0.296986 0.332737i
\(916\) 0.0686077 24.9581i 0.00226686 0.824638i
\(917\) 27.0909i 0.894619i
\(918\) 1.75278 18.7846i 0.0578504 0.619983i
\(919\) −5.52388 −0.182216 −0.0911080 0.995841i \(-0.529041\pi\)
−0.0911080 + 0.995841i \(0.529041\pi\)
\(920\) 7.67611 + 4.47411i 0.253074 + 0.147507i
\(921\) 30.2113 + 26.9652i 0.995495 + 0.888535i
\(922\) 0.0211407 15.3812i 0.000696233 0.506552i
\(923\) −8.83332 + 5.09992i −0.290752 + 0.167866i
\(924\) −20.4816 18.3823i −0.673794 0.604735i
\(925\) 5.55516 + 3.20728i 0.182653 + 0.105455i
\(926\) 21.3336 36.8338i 0.701065 1.21044i
\(927\) 33.6012 24.8623i 1.10361 0.816586i
\(928\) −37.8779 + 21.5231i −1.24340 + 0.706531i
\(929\) −19.0672 + 33.0253i −0.625573 + 1.08352i 0.362857 + 0.931845i \(0.381801\pi\)
−0.988430 + 0.151680i \(0.951532\pi\)
\(930\) 8.48730 + 7.59637i 0.278309 + 0.249095i
\(931\) 19.4896 11.2523i 0.638746 0.368780i
\(932\) −20.9269 + 36.0175i −0.685485 + 1.17979i
\(933\) 2.66062 + 0.553444i 0.0871049 + 0.0181189i
\(934\) 22.6258 13.0216i 0.740340 0.426080i
\(935\) −12.6237 −0.412841
\(936\) −13.7587 18.7560i −0.449718 0.613060i
\(937\) −44.5566 −1.45560 −0.727800 0.685790i \(-0.759457\pi\)
−0.727800 + 0.685790i \(0.759457\pi\)
\(938\) −20.8264 + 11.9860i −0.680005 + 0.391356i
\(939\) 0.105580 + 0.320194i 0.00344547 + 0.0104491i
\(940\) −5.65957 3.28833i −0.184595 0.107254i
\(941\) 10.4558 6.03667i 0.340850 0.196790i −0.319798 0.947486i \(-0.603615\pi\)
0.660648 + 0.750696i \(0.270282\pi\)
\(942\) 38.4597 12.6230i 1.25309 0.411280i
\(943\) −14.0158 + 24.2760i −0.456416 + 0.790536i
\(944\) −17.4550 10.2060i −0.568112 0.332177i
\(945\) 4.84575 6.85606i 0.157632 0.223028i
\(946\) −26.8111 + 46.2911i −0.871703 + 1.50505i
\(947\) 0.433613 + 0.250347i 0.0140905 + 0.00813517i 0.507029 0.861929i \(-0.330744\pi\)
−0.492938 + 0.870064i \(0.664077\pi\)
\(948\) 29.8308 + 6.29079i 0.968860 + 0.204315i
\(949\) −12.9668 + 7.48640i −0.420921 + 0.243019i
\(950\) −0.00996586 + 7.25077i −0.000323335 + 0.235246i
\(951\) −31.8787 + 10.5116i −1.03374 + 0.340862i
\(952\) −5.90828 + 10.1367i −0.191488 + 0.328532i
\(953\) −1.38585 −0.0448921 −0.0224460 0.999748i \(-0.507145\pi\)
−0.0224460 + 0.999748i \(0.507145\pi\)
\(954\) −11.3757 15.4185i −0.368303 0.499191i
\(955\) 8.07806i 0.261400i
\(956\) −46.2067 0.127018i −1.49443 0.00410806i
\(957\) −64.2147 13.3575i −2.07577 0.431786i
\(958\) −4.90414 0.00674051i −0.158445 0.000217776i
\(959\) −0.632437 1.09541i −0.0204225 0.0353727i
\(960\) −2.93368 + 13.5423i −0.0946842 + 0.437075i
\(961\) 4.68842 8.12058i 0.151239 0.261954i
\(962\) 12.4639 21.5197i 0.401851 0.693822i
\(963\) −36.8899 + 4.20218i −1.18876 + 0.135413i
\(964\) 25.0754 + 43.7090i 0.807625 + 1.40777i
\(965\) −8.78856 5.07408i −0.282914 0.163340i
\(966\) 12.1683 + 2.54861i 0.391508 + 0.0820003i
\(967\) −12.3209 21.3405i −0.396214 0.686263i 0.597041 0.802211i \(-0.296343\pi\)
−0.993255 + 0.115948i \(0.963010\pi\)
\(968\) 18.5019 + 32.3535i 0.594673 + 1.03988i
\(969\) 17.0092 + 15.1817i 0.546415 + 0.487706i
\(970\) −10.0452 + 5.78119i −0.322531 + 0.185623i
\(971\) 43.8577i 1.40746i 0.710467 + 0.703730i \(0.248484\pi\)
−0.710467 + 0.703730i \(0.751516\pi\)
\(972\) −16.0988 26.6988i −0.516370 0.856366i
\(973\) 11.6624i 0.373879i
\(974\) 4.54688 + 7.90048i 0.145691 + 0.253148i
\(975\) −3.54240 3.16179i −0.113447 0.101258i
\(976\) −0.171290 + 31.1557i −0.00548285 + 0.997268i
\(977\) 15.8194 + 27.3999i 0.506106 + 0.876602i 0.999975 + 0.00706520i \(0.00224894\pi\)
−0.493869 + 0.869536i \(0.664418\pi\)
\(978\) −2.36035 + 11.2694i −0.0754755 + 0.360356i
\(979\) −44.9414 25.9469i −1.43633 0.829267i
\(980\) 7.61466 4.36846i 0.243241 0.139545i
\(981\) −43.6178 + 4.96856i −1.39261 + 0.158634i
\(982\) −12.1075 7.01249i −0.386367 0.223778i
\(983\) 3.01501 5.22215i 0.0961638 0.166561i −0.813930 0.580963i \(-0.802676\pi\)
0.910094 + 0.414402i \(0.136009\pi\)
\(984\) −42.7635 9.07948i −1.36325 0.289443i
\(985\) −8.47726 14.6830i −0.270108 0.467841i
\(986\) −0.0384329 + 27.9623i −0.00122395 + 0.890500i
\(987\) −8.96704 1.86526i −0.285424 0.0593719i
\(988\) 28.1104 + 0.0772731i 0.894311 + 0.00245838i
\(989\) 24.1657i 0.768425i
\(990\) −16.7867 + 12.3852i −0.533516 + 0.393628i
\(991\) −43.1103 −1.36944 −0.684722 0.728805i \(-0.740076\pi\)
−0.684722 + 0.728805i \(0.740076\pi\)
\(992\) −26.3042 0.180772i −0.835158 0.00573952i
\(993\) −6.07486 + 2.00311i −0.192780 + 0.0635667i
\(994\) 8.50181 + 0.0116853i 0.269661 + 0.000370637i
\(995\) 17.9311 10.3525i 0.568455 0.328198i
\(996\) −9.92973 + 47.0866i −0.314636 + 1.49200i
\(997\) −8.33653 4.81310i −0.264020 0.152432i 0.362147 0.932121i \(-0.382044\pi\)
−0.626167 + 0.779689i \(0.715377\pi\)
\(998\) −8.90115 5.15540i −0.281761 0.163191i
\(999\) 19.2378 27.2188i 0.608657 0.861164i
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.bf.b.61.16 92
3.2 odd 2 1080.2.bf.b.181.31 92
4.3 odd 2 1440.2.bv.b.241.14 92
8.3 odd 2 1440.2.bv.b.241.33 92
8.5 even 2 inner 360.2.bf.b.61.46 yes 92
9.4 even 3 inner 360.2.bf.b.301.46 yes 92
9.5 odd 6 1080.2.bf.b.901.1 92
12.11 even 2 4320.2.bv.b.721.29 92
24.5 odd 2 1080.2.bf.b.181.1 92
24.11 even 2 4320.2.bv.b.721.20 92
36.23 even 6 4320.2.bv.b.3601.20 92
36.31 odd 6 1440.2.bv.b.1201.33 92
72.5 odd 6 1080.2.bf.b.901.31 92
72.13 even 6 inner 360.2.bf.b.301.16 yes 92
72.59 even 6 4320.2.bv.b.3601.29 92
72.67 odd 6 1440.2.bv.b.1201.14 92
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bf.b.61.16 92 1.1 even 1 trivial
360.2.bf.b.61.46 yes 92 8.5 even 2 inner
360.2.bf.b.301.16 yes 92 72.13 even 6 inner
360.2.bf.b.301.46 yes 92 9.4 even 3 inner
1080.2.bf.b.181.1 92 24.5 odd 2
1080.2.bf.b.181.31 92 3.2 odd 2
1080.2.bf.b.901.1 92 9.5 odd 6
1080.2.bf.b.901.31 92 72.5 odd 6
1440.2.bv.b.241.14 92 4.3 odd 2
1440.2.bv.b.241.33 92 8.3 odd 2
1440.2.bv.b.1201.14 92 72.67 odd 6
1440.2.bv.b.1201.33 92 36.31 odd 6
4320.2.bv.b.721.20 92 24.11 even 2
4320.2.bv.b.721.29 92 12.11 even 2
4320.2.bv.b.3601.20 92 36.23 even 6
4320.2.bv.b.3601.29 92 72.59 even 6