Properties

Label 150.2.l.a.77.3
Level $150$
Weight $2$
Character 150.77
Analytic conductor $1.198$
Analytic rank $0$
Dimension $80$
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] = [150,2,Mod(17,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.l (of order \(20\), degree \(8\), 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: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 77.3
Character \(\chi\) \(=\) 150.77
Dual form 150.2.l.a.113.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.156434 + 0.987688i) q^{2} +(-0.0929751 - 1.72955i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.59953 - 1.56253i) q^{5} +(1.72280 + 0.178731i) q^{6} +(-3.45255 - 3.45255i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.98271 + 0.321611i) q^{9} +O(q^{10})\) \(q+(-0.156434 + 0.987688i) q^{2} +(-0.0929751 - 1.72955i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.59953 - 1.56253i) q^{5} +(1.72280 + 0.178731i) q^{6} +(-3.45255 - 3.45255i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.98271 + 0.321611i) q^{9} +(1.29307 + 1.82427i) q^{10} +(1.48978 + 2.05051i) q^{11} +(-0.446037 + 1.67363i) q^{12} +(3.77229 - 0.597472i) q^{13} +(3.95014 - 2.86994i) q^{14} +(-2.85120 - 2.62120i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.27947 + 2.18050i) q^{17} +(0.148947 - 2.99630i) q^{18} +(0.596005 - 0.193654i) q^{19} +(-2.00409 + 0.991774i) q^{20} +(-5.65036 + 6.29237i) q^{21} +(-2.25832 + 1.15067i) q^{22} +(-0.643277 - 0.101885i) q^{23} +(-1.58325 - 0.702359i) q^{24} +(0.116992 - 4.99863i) q^{25} +3.81931i q^{26} +(0.833561 + 5.12886i) q^{27} +(2.21667 + 4.35046i) q^{28} +(-2.50850 + 7.72038i) q^{29} +(3.03495 - 2.40605i) q^{30} +(0.501043 + 1.54205i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.40795 - 2.76731i) q^{33} +(-2.82311 + 3.88568i) q^{34} +(-10.9172 - 0.127739i) q^{35} +(2.93611 + 0.615838i) q^{36} +(-0.576743 - 3.64141i) q^{37} +(0.0980339 + 0.618961i) q^{38} +(-1.38409 - 6.46882i) q^{39} +(-0.666054 - 2.13457i) q^{40} +(3.69305 - 5.08304i) q^{41} +(-5.33098 - 6.56514i) q^{42} +(-0.951098 + 0.951098i) q^{43} +(-0.783225 - 2.41052i) q^{44} +(-4.26841 + 5.17501i) q^{45} +(0.201261 - 0.619419i) q^{46} +(-1.95031 - 3.82769i) q^{47} +(0.941388 - 1.45389i) q^{48} +16.8402i q^{49} +(4.91879 + 0.897510i) q^{50} +(3.37340 - 7.60430i) q^{51} +(-3.77229 - 0.597472i) q^{52} +(-0.456180 + 0.232435i) q^{53} +(-5.19611 + 0.0209688i) q^{54} +(5.58694 + 0.952020i) q^{55} +(-4.64367 + 1.50882i) q^{56} +(-0.390348 - 1.01282i) q^{57} +(-7.23291 - 3.68535i) q^{58} +(8.96720 + 6.51505i) q^{59} +(1.90166 + 3.37397i) q^{60} +(3.22382 - 2.34224i) q^{61} +(-1.60145 + 0.253644i) q^{62} +(11.4083 + 9.18757i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(5.10032 - 6.84999i) q^{65} +(2.20011 + 3.79890i) q^{66} +(1.95065 - 3.82837i) q^{67} +(-3.39620 - 3.39620i) q^{68} +(-0.116407 + 1.12205i) q^{69} +(1.83399 - 10.7628i) q^{70} +(-0.917028 - 0.297960i) q^{71} +(-1.06757 + 2.80362i) q^{72} +(-1.21191 + 7.65167i) q^{73} +3.68680 q^{74} +(-8.65628 + 0.262405i) q^{75} -0.626677 q^{76} +(1.93594 - 12.2230i) q^{77} +(6.60570 - 0.355101i) q^{78} +(0.139017 + 0.0451693i) q^{79} +(2.21248 - 0.323934i) q^{80} +(8.79313 - 1.91855i) q^{81} +(4.44274 + 4.44274i) q^{82} +(3.59418 - 7.05397i) q^{83} +(7.31826 - 4.23834i) q^{84} +(10.2522 - 3.19903i) q^{85} +(-0.790603 - 1.08817i) q^{86} +(13.5860 + 3.62079i) q^{87} +(2.50336 - 0.396494i) q^{88} +(-8.93519 + 6.49179i) q^{89} +(-4.44357 - 5.02541i) q^{90} +(-15.0868 - 10.9612i) q^{91} +(0.580309 + 0.295682i) q^{92} +(2.62047 - 1.00995i) q^{93} +(4.08566 - 1.32751i) q^{94} +(0.650738 - 1.24103i) q^{95} +(1.28872 + 1.15724i) q^{96} +(-13.5240 + 6.89084i) q^{97} +(-16.6328 - 2.63438i) q^{98} +(-5.10306 - 5.63695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.156434 + 0.987688i −0.110616 + 0.698401i
\(3\) −0.0929751 1.72955i −0.0536792 0.998558i
\(4\) −0.951057 0.309017i −0.475528 0.154508i
\(5\) 1.59953 1.56253i 0.715332 0.698785i
\(6\) 1.72280 + 0.178731i 0.703332 + 0.0729668i
\(7\) −3.45255 3.45255i −1.30494 1.30494i −0.925019 0.379921i \(-0.875951\pi\)
−0.379921 0.925019i \(-0.624049\pi\)
\(8\) 0.453990 0.891007i 0.160510 0.315018i
\(9\) −2.98271 + 0.321611i −0.994237 + 0.107204i
\(10\) 1.29307 + 1.82427i 0.408905 + 0.576885i
\(11\) 1.48978 + 2.05051i 0.449186 + 0.618252i 0.972223 0.234059i \(-0.0752007\pi\)
−0.523036 + 0.852310i \(0.675201\pi\)
\(12\) −0.446037 + 1.67363i −0.128760 + 0.483137i
\(13\) 3.77229 0.597472i 1.04624 0.165709i 0.390431 0.920632i \(-0.372326\pi\)
0.655813 + 0.754923i \(0.272326\pi\)
\(14\) 3.95014 2.86994i 1.05572 0.767025i
\(15\) −2.85120 2.62120i −0.736176 0.676790i
\(16\) 0.809017 + 0.587785i 0.202254 + 0.146946i
\(17\) 4.27947 + 2.18050i 1.03792 + 0.528848i 0.887997 0.459849i \(-0.152096\pi\)
0.149926 + 0.988697i \(0.452096\pi\)
\(18\) 0.148947 2.99630i 0.0351073 0.706235i
\(19\) 0.596005 0.193654i 0.136733 0.0444272i −0.239851 0.970810i \(-0.577099\pi\)
0.376584 + 0.926382i \(0.377099\pi\)
\(20\) −2.00409 + 0.991774i −0.448129 + 0.221767i
\(21\) −5.65036 + 6.29237i −1.23301 + 1.37311i
\(22\) −2.25832 + 1.15067i −0.481475 + 0.245324i
\(23\) −0.643277 0.101885i −0.134133 0.0212445i 0.0890072 0.996031i \(-0.471631\pi\)
−0.223140 + 0.974786i \(0.571631\pi\)
\(24\) −1.58325 0.702359i −0.323180 0.143369i
\(25\) 0.116992 4.99863i 0.0233983 0.999726i
\(26\) 3.81931i 0.749028i
\(27\) 0.833561 + 5.12886i 0.160419 + 0.987049i
\(28\) 2.21667 + 4.35046i 0.418912 + 0.822160i
\(29\) −2.50850 + 7.72038i −0.465817 + 1.43364i 0.392134 + 0.919908i \(0.371737\pi\)
−0.857952 + 0.513731i \(0.828263\pi\)
\(30\) 3.03495 2.40605i 0.554104 0.439283i
\(31\) 0.501043 + 1.54205i 0.0899899 + 0.276960i 0.985916 0.167243i \(-0.0534866\pi\)
−0.895926 + 0.444204i \(0.853487\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 3.40795 2.76731i 0.593249 0.481726i
\(34\) −2.82311 + 3.88568i −0.484159 + 0.666388i
\(35\) −10.9172 0.127739i −1.84534 0.0215919i
\(36\) 2.93611 + 0.615838i 0.489352 + 0.102640i
\(37\) −0.576743 3.64141i −0.0948160 0.598644i −0.988649 0.150244i \(-0.951994\pi\)
0.893833 0.448400i \(-0.148006\pi\)
\(38\) 0.0980339 + 0.618961i 0.0159032 + 0.100409i
\(39\) −1.38409 6.46882i −0.221631 1.03584i
\(40\) −0.666054 2.13457i −0.105312 0.337505i
\(41\) 3.69305 5.08304i 0.576757 0.793838i −0.416578 0.909100i \(-0.636771\pi\)
0.993335 + 0.115262i \(0.0367708\pi\)
\(42\) −5.33098 6.56514i −0.822589 1.01302i
\(43\) −0.951098 + 0.951098i −0.145041 + 0.145041i −0.775899 0.630858i \(-0.782703\pi\)
0.630858 + 0.775899i \(0.282703\pi\)
\(44\) −0.783225 2.41052i −0.118076 0.363399i
\(45\) −4.26841 + 5.17501i −0.636297 + 0.771444i
\(46\) 0.201261 0.619419i 0.0296744 0.0913283i
\(47\) −1.95031 3.82769i −0.284481 0.558326i 0.703904 0.710295i \(-0.251439\pi\)
−0.988385 + 0.151969i \(0.951439\pi\)
\(48\) 0.941388 1.45389i 0.135878 0.209851i
\(49\) 16.8402i 2.40574i
\(50\) 4.91879 + 0.897510i 0.695622 + 0.126927i
\(51\) 3.37340 7.60430i 0.472371 1.06482i
\(52\) −3.77229 0.597472i −0.523122 0.0828544i
\(53\) −0.456180 + 0.232435i −0.0626611 + 0.0319274i −0.485040 0.874492i \(-0.661195\pi\)
0.422379 + 0.906419i \(0.361195\pi\)
\(54\) −5.19611 + 0.0209688i −0.707101 + 0.00285349i
\(55\) 5.58694 + 0.952020i 0.753342 + 0.128370i
\(56\) −4.64367 + 1.50882i −0.620536 + 0.201624i
\(57\) −0.390348 1.01282i −0.0517029 0.134151i
\(58\) −7.23291 3.68535i −0.949728 0.483911i
\(59\) 8.96720 + 6.51505i 1.16743 + 0.848188i 0.990699 0.136071i \(-0.0434476\pi\)
0.176731 + 0.984259i \(0.443448\pi\)
\(60\) 1.90166 + 3.37397i 0.245503 + 0.435578i
\(61\) 3.22382 2.34224i 0.412767 0.299893i −0.361954 0.932196i \(-0.617890\pi\)
0.774721 + 0.632303i \(0.217890\pi\)
\(62\) −1.60145 + 0.253644i −0.203384 + 0.0322128i
\(63\) 11.4083 + 9.18757i 1.43731 + 1.15753i
\(64\) −0.587785 0.809017i −0.0734732 0.101127i
\(65\) 5.10032 6.84999i 0.632617 0.849637i
\(66\) 2.20011 + 3.79890i 0.270815 + 0.467612i
\(67\) 1.95065 3.82837i 0.238310 0.467710i −0.740615 0.671929i \(-0.765466\pi\)
0.978925 + 0.204220i \(0.0654658\pi\)
\(68\) −3.39620 3.39620i −0.411850 0.411850i
\(69\) −0.116407 + 1.12205i −0.0140137 + 0.135080i
\(70\) 1.83399 10.7628i 0.219203 1.28640i
\(71\) −0.917028 0.297960i −0.108831 0.0353614i 0.254095 0.967179i \(-0.418222\pi\)
−0.362926 + 0.931818i \(0.618222\pi\)
\(72\) −1.06757 + 2.80362i −0.125814 + 0.330410i
\(73\) −1.21191 + 7.65167i −0.141843 + 0.895561i 0.809431 + 0.587215i \(0.199776\pi\)
−0.951274 + 0.308346i \(0.900224\pi\)
\(74\) 3.68680 0.428582
\(75\) −8.65628 + 0.262405i −0.999541 + 0.0302999i
\(76\) −0.626677 −0.0718848
\(77\) 1.93594 12.2230i 0.220620 1.39294i
\(78\) 6.60570 0.355101i 0.747948 0.0402072i
\(79\) 0.139017 + 0.0451693i 0.0156406 + 0.00508194i 0.316827 0.948483i \(-0.397383\pi\)
−0.301186 + 0.953565i \(0.597383\pi\)
\(80\) 2.21248 0.323934i 0.247363 0.0362170i
\(81\) 8.79313 1.91855i 0.977015 0.213172i
\(82\) 4.44274 + 4.44274i 0.490619 + 0.490619i
\(83\) 3.59418 7.05397i 0.394512 0.774274i −0.605251 0.796035i \(-0.706927\pi\)
0.999763 + 0.0217608i \(0.00692722\pi\)
\(84\) 7.31826 4.23834i 0.798488 0.462440i
\(85\) 10.2522 3.19903i 1.11201 0.346984i
\(86\) −0.790603 1.08817i −0.0852530 0.117341i
\(87\) 13.5860 + 3.62079i 1.45658 + 0.388189i
\(88\) 2.50336 0.396494i 0.266860 0.0422664i
\(89\) −8.93519 + 6.49179i −0.947128 + 0.688129i −0.950126 0.311867i \(-0.899046\pi\)
0.00299774 + 0.999996i \(0.499046\pi\)
\(90\) −4.44357 5.02541i −0.468393 0.529724i
\(91\) −15.0868 10.9612i −1.58153 1.14905i
\(92\) 0.580309 + 0.295682i 0.0605013 + 0.0308270i
\(93\) 2.62047 1.00995i 0.271731 0.104727i
\(94\) 4.08566 1.32751i 0.421404 0.136922i
\(95\) 0.650738 1.24103i 0.0667643 0.127327i
\(96\) 1.28872 + 1.15724i 0.131530 + 0.118110i
\(97\) −13.5240 + 6.89084i −1.37316 + 0.699659i −0.975935 0.218063i \(-0.930026\pi\)
−0.397223 + 0.917722i \(0.630026\pi\)
\(98\) −16.6328 2.63438i −1.68017 0.266113i
\(99\) −5.10306 5.63695i −0.512877 0.566535i
\(100\) −1.65593 + 4.71783i −0.165593 + 0.471783i
\(101\) 1.94974i 0.194007i 0.995284 + 0.0970033i \(0.0309258\pi\)
−0.995284 + 0.0970033i \(0.969074\pi\)
\(102\) 6.98296 + 4.52145i 0.691416 + 0.447690i
\(103\) −1.56955 3.08042i −0.154653 0.303523i 0.800661 0.599118i \(-0.204482\pi\)
−0.955313 + 0.295595i \(0.904482\pi\)
\(104\) 1.18023 3.63238i 0.115731 0.356184i
\(105\) 0.794093 + 18.8937i 0.0774955 + 1.84384i
\(106\) −0.158211 0.486924i −0.0153668 0.0472943i
\(107\) −7.77089 + 7.77089i −0.751240 + 0.751240i −0.974711 0.223470i \(-0.928261\pi\)
0.223470 + 0.974711i \(0.428261\pi\)
\(108\) 0.792140 5.13542i 0.0762237 0.494156i
\(109\) 10.4733 14.4153i 1.00316 1.38073i 0.0797938 0.996811i \(-0.474574\pi\)
0.923366 0.383920i \(-0.125426\pi\)
\(110\) −1.81429 + 5.36922i −0.172986 + 0.511935i
\(111\) −6.24439 + 1.33607i −0.592692 + 0.126814i
\(112\) −0.763813 4.82253i −0.0721735 0.455686i
\(113\) 2.93571 + 18.5354i 0.276169 + 1.74366i 0.602240 + 0.798315i \(0.294275\pi\)
−0.326071 + 0.945345i \(0.605725\pi\)
\(114\) 1.06141 0.227103i 0.0994104 0.0212701i
\(115\) −1.18814 + 0.842172i −0.110795 + 0.0785330i
\(116\) 4.77146 6.56735i 0.443019 0.609763i
\(117\) −11.0595 + 2.99529i −1.02245 + 0.276915i
\(118\) −7.83762 + 7.83762i −0.721512 + 0.721512i
\(119\) −7.24679 22.3033i −0.664312 2.04454i
\(120\) −3.62992 + 1.35044i −0.331365 + 0.123278i
\(121\) 1.41405 4.35199i 0.128550 0.395636i
\(122\) 1.80909 + 3.55053i 0.163787 + 0.321450i
\(123\) −9.13475 5.91472i −0.823653 0.533313i
\(124\) 1.62141i 0.145607i
\(125\) −7.62339 8.17826i −0.681856 0.731486i
\(126\) −10.8591 + 9.83062i −0.967407 + 0.875781i
\(127\) 2.27911 + 0.360976i 0.202239 + 0.0320315i 0.256732 0.966483i \(-0.417354\pi\)
−0.0544931 + 0.998514i \(0.517354\pi\)
\(128\) 0.891007 0.453990i 0.0787546 0.0401275i
\(129\) 1.73340 + 1.55655i 0.152618 + 0.137046i
\(130\) 5.96779 + 6.10910i 0.523410 + 0.535803i
\(131\) −5.16079 + 1.67684i −0.450901 + 0.146506i −0.525659 0.850695i \(-0.676181\pi\)
0.0747587 + 0.997202i \(0.476181\pi\)
\(132\) −4.09630 + 1.57875i −0.356537 + 0.137412i
\(133\) −2.72633 1.38914i −0.236403 0.120453i
\(134\) 3.47608 + 2.52552i 0.300288 + 0.218172i
\(135\) 9.34731 + 6.90129i 0.804488 + 0.593969i
\(136\) 3.88568 2.82311i 0.333194 0.242080i
\(137\) −4.24769 + 0.672768i −0.362904 + 0.0574784i −0.335224 0.942138i \(-0.608812\pi\)
−0.0276803 + 0.999617i \(0.508812\pi\)
\(138\) −1.09003 0.290502i −0.0927895 0.0247292i
\(139\) 1.72794 + 2.37830i 0.146562 + 0.201725i 0.875986 0.482337i \(-0.160212\pi\)
−0.729424 + 0.684062i \(0.760212\pi\)
\(140\) 10.3434 + 3.49508i 0.874174 + 0.295388i
\(141\) −6.43887 + 3.72904i −0.542251 + 0.314042i
\(142\) 0.437747 0.859126i 0.0367349 0.0720963i
\(143\) 6.84501 + 6.84501i 0.572408 + 0.572408i
\(144\) −2.60210 1.49300i −0.216842 0.124417i
\(145\) 8.05091 + 16.2686i 0.668592 + 1.35103i
\(146\) −7.36789 2.39397i −0.609771 0.198126i
\(147\) 29.1260 1.56572i 2.40227 0.129138i
\(148\) −0.576743 + 3.64141i −0.0474080 + 0.299322i
\(149\) −6.09696 −0.499482 −0.249741 0.968313i \(-0.580346\pi\)
−0.249741 + 0.968313i \(0.580346\pi\)
\(150\) 1.09497 8.59075i 0.0894036 0.701432i
\(151\) 17.4743 1.42203 0.711017 0.703175i \(-0.248235\pi\)
0.711017 + 0.703175i \(0.248235\pi\)
\(152\) 0.0980339 0.618961i 0.00795160 0.0502044i
\(153\) −13.4657 5.12747i −1.08864 0.414531i
\(154\) 11.7697 + 3.82420i 0.948429 + 0.308163i
\(155\) 3.21094 + 1.68366i 0.257909 + 0.135235i
\(156\) −0.682630 + 6.57992i −0.0546542 + 0.526815i
\(157\) −1.62980 1.62980i −0.130072 0.130072i 0.639074 0.769146i \(-0.279318\pi\)
−0.769146 + 0.639074i \(0.779318\pi\)
\(158\) −0.0663602 + 0.130239i −0.00527934 + 0.0103613i
\(159\) 0.444422 + 0.767377i 0.0352450 + 0.0608569i
\(160\) −0.0261619 + 2.23591i −0.00206828 + 0.176765i
\(161\) 1.86918 + 2.57271i 0.147312 + 0.202758i
\(162\) 0.519376 + 8.98500i 0.0408060 + 0.705928i
\(163\) −22.6112 + 3.58126i −1.77105 + 0.280506i −0.954811 0.297213i \(-0.903943\pi\)
−0.816235 + 0.577719i \(0.803943\pi\)
\(164\) −5.08304 + 3.69305i −0.396919 + 0.288378i
\(165\) 1.12712 9.75142i 0.0877464 0.759147i
\(166\) 6.40487 + 4.65341i 0.497114 + 0.361175i
\(167\) 7.89344 + 4.02191i 0.610813 + 0.311225i 0.731895 0.681418i \(-0.238636\pi\)
−0.121082 + 0.992643i \(0.538636\pi\)
\(168\) 3.04133 + 7.89119i 0.234644 + 0.608818i
\(169\) 1.50944 0.490448i 0.116111 0.0377268i
\(170\) 1.55584 + 10.6264i 0.119328 + 0.815011i
\(171\) −1.71543 + 0.769295i −0.131182 + 0.0588295i
\(172\) 1.19845 0.610642i 0.0913812 0.0465610i
\(173\) −16.2880 2.57976i −1.23835 0.196136i −0.497297 0.867580i \(-0.665674\pi\)
−0.741055 + 0.671445i \(0.765674\pi\)
\(174\) −5.70154 + 12.8524i −0.432232 + 0.974335i
\(175\) −17.6619 + 16.8541i −1.33512 + 1.27405i
\(176\) 2.53457i 0.191050i
\(177\) 10.4344 16.1150i 0.784298 1.21128i
\(178\) −5.01410 9.84072i −0.375823 0.737593i
\(179\) −1.95323 + 6.01143i −0.145991 + 0.449315i −0.997137 0.0756142i \(-0.975908\pi\)
0.851146 + 0.524929i \(0.175908\pi\)
\(180\) 5.65866 3.60271i 0.421772 0.268530i
\(181\) −5.79522 17.8358i −0.430755 1.32573i −0.897375 0.441269i \(-0.854528\pi\)
0.466620 0.884458i \(-0.345472\pi\)
\(182\) 13.1863 13.1863i 0.977437 0.977437i
\(183\) −4.35076 5.35799i −0.321618 0.396074i
\(184\) −0.382822 + 0.526909i −0.0282220 + 0.0388443i
\(185\) −6.61234 4.92337i −0.486149 0.361973i
\(186\) 0.587586 + 2.74620i 0.0430839 + 0.201361i
\(187\) 1.90434 + 12.0236i 0.139259 + 0.879250i
\(188\) 0.672030 + 4.24303i 0.0490128 + 0.309455i
\(189\) 14.8297 20.5855i 1.07870 1.49738i
\(190\) 1.12395 + 0.836866i 0.0815402 + 0.0607127i
\(191\) −9.23596 + 12.7122i −0.668290 + 0.919823i −0.999720 0.0236572i \(-0.992469\pi\)
0.331430 + 0.943480i \(0.392469\pi\)
\(192\) −1.34459 + 1.09182i −0.0970373 + 0.0787956i
\(193\) 1.83504 1.83504i 0.132089 0.132089i −0.637971 0.770060i \(-0.720226\pi\)
0.770060 + 0.637971i \(0.220226\pi\)
\(194\) −4.69038 14.4355i −0.336749 1.03641i
\(195\) −12.3216 8.18439i −0.882370 0.586097i
\(196\) 5.20390 16.0159i 0.371707 1.14400i
\(197\) −2.63453 5.17056i −0.187703 0.368387i 0.777909 0.628377i \(-0.216281\pi\)
−0.965611 + 0.259990i \(0.916281\pi\)
\(198\) 6.36584 4.15842i 0.452401 0.295526i
\(199\) 3.86400i 0.273911i −0.990577 0.136956i \(-0.956268\pi\)
0.990577 0.136956i \(-0.0437318\pi\)
\(200\) −4.40070 2.37357i −0.311176 0.167837i
\(201\) −6.80273 3.01781i −0.479827 0.212860i
\(202\) −1.92574 0.305007i −0.135494 0.0214602i
\(203\) 35.3157 17.9942i 2.47868 1.26295i
\(204\) −5.55816 + 6.18968i −0.389149 + 0.433364i
\(205\) −2.03527 13.9010i −0.142150 0.970886i
\(206\) 3.28803 1.06835i 0.229088 0.0744352i
\(207\) 1.95148 + 0.0970088i 0.135637 + 0.00674258i
\(208\) 3.40303 + 1.73393i 0.235958 + 0.120226i
\(209\) 1.28501 + 0.933612i 0.0888858 + 0.0645793i
\(210\) −18.7853 2.17131i −1.29631 0.149835i
\(211\) −8.84519 + 6.42640i −0.608928 + 0.442412i −0.849037 0.528334i \(-0.822817\pi\)
0.240109 + 0.970746i \(0.422817\pi\)
\(212\) 0.505679 0.0800917i 0.0347302 0.00550072i
\(213\) −0.430078 + 1.61375i −0.0294684 + 0.110572i
\(214\) −6.45958 8.89085i −0.441568 0.607766i
\(215\) −0.0351892 + 3.00743i −0.00239989 + 0.205105i
\(216\) 4.94827 + 1.58574i 0.336687 + 0.107896i
\(217\) 3.59413 7.05388i 0.243985 0.478848i
\(218\) 12.5994 + 12.5994i 0.853339 + 0.853339i
\(219\) 13.3467 + 1.38464i 0.901884 + 0.0935654i
\(220\) −5.01930 2.63188i −0.338401 0.177442i
\(221\) 17.4462 + 5.66860i 1.17356 + 0.381311i
\(222\) −0.342781 6.37652i −0.0230059 0.427964i
\(223\) −3.05289 + 19.2752i −0.204437 + 1.29076i 0.645452 + 0.763800i \(0.276669\pi\)
−0.849889 + 0.526962i \(0.823331\pi\)
\(224\) 4.88264 0.326235
\(225\) 1.25866 + 14.9471i 0.0839108 + 0.996473i
\(226\) −18.7664 −1.24832
\(227\) −3.87090 + 24.4399i −0.256921 + 1.62213i 0.435187 + 0.900340i \(0.356682\pi\)
−0.692108 + 0.721794i \(0.743318\pi\)
\(228\) 0.0582654 + 1.08387i 0.00385872 + 0.0717811i
\(229\) 2.89806 + 0.941635i 0.191509 + 0.0622250i 0.403201 0.915111i \(-0.367897\pi\)
−0.211692 + 0.977336i \(0.567897\pi\)
\(230\) −0.645938 1.30526i −0.0425919 0.0860660i
\(231\) −21.3204 2.21187i −1.40278 0.145530i
\(232\) 5.74007 + 5.74007i 0.376854 + 0.376854i
\(233\) 8.40887 16.5033i 0.550883 1.08117i −0.432839 0.901471i \(-0.642488\pi\)
0.983722 0.179698i \(-0.0575120\pi\)
\(234\) −1.22833 11.3919i −0.0802985 0.744712i
\(235\) −9.10046 3.07509i −0.593649 0.200597i
\(236\) −6.51505 8.96720i −0.424094 0.583715i
\(237\) 0.0651976 0.244637i 0.00423504 0.0158909i
\(238\) 23.1624 3.66856i 1.50139 0.237798i
\(239\) 10.8076 7.85218i 0.699086 0.507915i −0.180549 0.983566i \(-0.557787\pi\)
0.879634 + 0.475651i \(0.157787\pi\)
\(240\) −0.765967 3.79648i −0.0494430 0.245062i
\(241\) 4.13071 + 3.00113i 0.266082 + 0.193320i 0.712824 0.701343i \(-0.247416\pi\)
−0.446742 + 0.894663i \(0.647416\pi\)
\(242\) 4.07721 + 2.07744i 0.262093 + 0.133543i
\(243\) −4.13577 15.0298i −0.265310 0.964163i
\(244\) −3.78982 + 1.23139i −0.242618 + 0.0788315i
\(245\) 26.3133 + 26.9363i 1.68109 + 1.72090i
\(246\) 7.27090 8.09702i 0.463575 0.516247i
\(247\) 2.13260 1.08661i 0.135694 0.0691396i
\(248\) 1.60145 + 0.253644i 0.101692 + 0.0161064i
\(249\) −12.5344 5.56048i −0.794335 0.352381i
\(250\) 9.27014 6.25017i 0.586295 0.395295i
\(251\) 10.4406i 0.659004i −0.944155 0.329502i \(-0.893119\pi\)
0.944155 0.329502i \(-0.106881\pi\)
\(252\) −8.01085 12.2633i −0.504636 0.772513i
\(253\) −0.749426 1.47083i −0.0471160 0.0924704i
\(254\) −0.713064 + 2.19459i −0.0447416 + 0.137701i
\(255\) −6.48610 17.4344i −0.406175 1.09178i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 15.7777 15.7777i 0.984185 0.984185i −0.0156919 0.999877i \(-0.504995\pi\)
0.999877 + 0.0156919i \(0.00499509\pi\)
\(258\) −1.80855 + 1.46856i −0.112595 + 0.0914288i
\(259\) −10.5809 + 14.5634i −0.657466 + 0.904924i
\(260\) −6.96745 + 4.93864i −0.432103 + 0.306282i
\(261\) 4.99918 23.8344i 0.309442 1.47531i
\(262\) −0.848873 5.35957i −0.0524435 0.331115i
\(263\) 2.08135 + 13.1411i 0.128342 + 0.810318i 0.964934 + 0.262492i \(0.0845444\pi\)
−0.836592 + 0.547826i \(0.815456\pi\)
\(264\) −0.918508 4.29284i −0.0565303 0.264206i
\(265\) −0.366486 + 1.08458i −0.0225130 + 0.0666254i
\(266\) 1.79853 2.47546i 0.110275 0.151780i
\(267\) 12.0587 + 14.8503i 0.737978 + 0.908824i
\(268\) −3.03821 + 3.03821i −0.185588 + 0.185588i
\(269\) 2.51822 + 7.75028i 0.153539 + 0.472543i 0.998010 0.0630577i \(-0.0200852\pi\)
−0.844471 + 0.535601i \(0.820085\pi\)
\(270\) −8.27857 + 8.15262i −0.503818 + 0.496153i
\(271\) −2.73922 + 8.43044i −0.166396 + 0.512113i −0.999136 0.0415500i \(-0.986770\pi\)
0.832741 + 0.553663i \(0.186770\pi\)
\(272\) 2.18050 + 4.27947i 0.132212 + 0.259481i
\(273\) −17.5553 + 27.1125i −1.06249 + 1.64093i
\(274\) 4.30064i 0.259811i
\(275\) 10.4240 7.20698i 0.628593 0.434597i
\(276\) 0.457444 1.03117i 0.0275349 0.0620689i
\(277\) 12.0346 + 1.90609i 0.723088 + 0.114526i 0.507121 0.861875i \(-0.330710\pi\)
0.215967 + 0.976401i \(0.430710\pi\)
\(278\) −2.61933 + 1.33461i −0.157097 + 0.0800448i
\(279\) −1.99041 4.43835i −0.119162 0.265717i
\(280\) −5.07011 + 9.66927i −0.302997 + 0.577850i
\(281\) 1.89696 0.616361i 0.113163 0.0367690i −0.251888 0.967756i \(-0.581051\pi\)
0.365051 + 0.930987i \(0.381051\pi\)
\(282\) −2.67587 6.94295i −0.159346 0.413446i
\(283\) 1.85853 + 0.946967i 0.110478 + 0.0562913i 0.508356 0.861147i \(-0.330253\pi\)
−0.397878 + 0.917438i \(0.630253\pi\)
\(284\) 0.780070 + 0.566754i 0.0462887 + 0.0336307i
\(285\) −2.20693 1.01010i −0.130727 0.0598332i
\(286\) −7.83153 + 5.68994i −0.463088 + 0.336453i
\(287\) −30.2999 + 4.79903i −1.78854 + 0.283278i
\(288\) 1.88168 2.33651i 0.110879 0.137680i
\(289\) 3.56692 + 4.90945i 0.209819 + 0.288791i
\(290\) −17.3277 + 5.40682i −1.01752 + 0.317499i
\(291\) 13.1755 + 22.7499i 0.772360 + 1.33362i
\(292\) 3.51709 6.90267i 0.205822 0.403948i
\(293\) −14.1457 14.1457i −0.826402 0.826402i 0.160615 0.987017i \(-0.448652\pi\)
−0.987017 + 0.160615i \(0.948652\pi\)
\(294\) −3.00986 + 29.0123i −0.175539 + 1.69203i
\(295\) 24.5233 3.59051i 1.42780 0.209048i
\(296\) −3.50636 1.13928i −0.203803 0.0662196i
\(297\) −9.27495 + 9.35011i −0.538187 + 0.542548i
\(298\) 0.953774 6.02189i 0.0552507 0.348839i
\(299\) −2.48750 −0.143856
\(300\) 8.31370 + 2.42537i 0.479992 + 0.140029i
\(301\) 6.56742 0.378540
\(302\) −2.73358 + 17.2591i −0.157300 + 0.993151i
\(303\) 3.37218 0.181278i 0.193727 0.0104141i
\(304\) 0.596005 + 0.193654i 0.0341832 + 0.0111068i
\(305\) 1.49677 8.78379i 0.0857046 0.502959i
\(306\) 7.17084 12.4978i 0.409930 0.714451i
\(307\) 6.59880 + 6.59880i 0.376613 + 0.376613i 0.869879 0.493266i \(-0.164197\pi\)
−0.493266 + 0.869879i \(0.664197\pi\)
\(308\) −5.61831 + 11.0265i −0.320133 + 0.628296i
\(309\) −5.18183 + 3.00103i −0.294784 + 0.170723i
\(310\) −2.16523 + 2.90802i −0.122977 + 0.165164i
\(311\) 4.60146 + 6.33337i 0.260925 + 0.359133i 0.919300 0.393558i \(-0.128756\pi\)
−0.658375 + 0.752690i \(0.728756\pi\)
\(312\) −6.39213 1.70355i −0.361883 0.0964447i
\(313\) −2.82529 + 0.447482i −0.159695 + 0.0252932i −0.235770 0.971809i \(-0.575761\pi\)
0.0760751 + 0.997102i \(0.475761\pi\)
\(314\) 1.86469 1.35478i 0.105231 0.0764545i
\(315\) 32.6038 3.13007i 1.83702 0.176359i
\(316\) −0.118255 0.0859171i −0.00665235 0.00483322i
\(317\) −22.7876 11.6109i −1.27988 0.652131i −0.324046 0.946041i \(-0.605043\pi\)
−0.955833 + 0.293910i \(0.905043\pi\)
\(318\) −0.827452 + 0.318907i −0.0464012 + 0.0178834i
\(319\) −19.5678 + 6.35798i −1.09559 + 0.355978i
\(320\) −2.20429 0.375614i −0.123224 0.0209975i
\(321\) 14.1627 + 12.7177i 0.790483 + 0.709831i
\(322\) −2.83344 + 1.44371i −0.157901 + 0.0804547i
\(323\) 2.97285 + 0.470853i 0.165414 + 0.0261989i
\(324\) −8.95563 0.892583i −0.497535 0.0495879i
\(325\) −2.54521 18.9262i −0.141183 1.04984i
\(326\) 22.8931i 1.26793i
\(327\) −25.9057 16.7739i −1.43259 0.927597i
\(328\) −2.85242 5.59818i −0.157498 0.309108i
\(329\) −6.48176 + 19.9488i −0.357351 + 1.09981i
\(330\) 9.45504 + 2.63870i 0.520483 + 0.145256i
\(331\) 9.88000 + 30.4075i 0.543054 + 1.67135i 0.725572 + 0.688146i \(0.241575\pi\)
−0.182518 + 0.983203i \(0.558425\pi\)
\(332\) −5.59806 + 5.59806i −0.307234 + 0.307234i
\(333\) 2.89138 + 10.6758i 0.158446 + 0.585030i
\(334\) −5.20720 + 7.16710i −0.284925 + 0.392166i
\(335\) −2.86182 9.17154i −0.156358 0.501095i
\(336\) −8.26980 + 1.76943i −0.451155 + 0.0965303i
\(337\) −2.91531 18.4065i −0.158807 1.00267i −0.930399 0.366549i \(-0.880539\pi\)
0.771592 0.636118i \(-0.219461\pi\)
\(338\) 0.248281 + 1.56758i 0.0135047 + 0.0852653i
\(339\) 31.7850 6.80080i 1.72632 0.369369i
\(340\) −10.7390 0.125655i −0.582404 0.00681458i
\(341\) −2.41555 + 3.32471i −0.130809 + 0.180043i
\(342\) −0.491471 1.81465i −0.0265757 0.0981253i
\(343\) 33.9736 33.9736i 1.83440 1.83440i
\(344\) 0.415645 + 1.27922i 0.0224101 + 0.0689711i
\(345\) 1.56705 + 1.97665i 0.0843671 + 0.106419i
\(346\) 5.09600 15.6839i 0.273963 0.843170i
\(347\) −10.8108 21.2173i −0.580353 1.13901i −0.975420 0.220354i \(-0.929279\pi\)
0.395067 0.918652i \(-0.370721\pi\)
\(348\) −11.8022 7.64189i −0.632665 0.409648i
\(349\) 8.63569i 0.462258i −0.972923 0.231129i \(-0.925758\pi\)
0.972923 0.231129i \(-0.0742419\pi\)
\(350\) −13.8837 20.0810i −0.742112 1.07338i
\(351\) 6.20878 + 18.8495i 0.331400 + 1.00611i
\(352\) −2.50336 0.396494i −0.133430 0.0211332i
\(353\) −25.4664 + 12.9758i −1.35544 + 0.690631i −0.972448 0.233120i \(-0.925106\pi\)
−0.382992 + 0.923751i \(0.625106\pi\)
\(354\) 14.2843 + 12.8269i 0.759202 + 0.681741i
\(355\) −1.93239 + 0.956288i −0.102560 + 0.0507545i
\(356\) 10.5039 3.41294i 0.556708 0.180885i
\(357\) −37.9010 + 14.6074i −2.00594 + 0.773104i
\(358\) −5.63186 2.86958i −0.297653 0.151662i
\(359\) 6.72833 + 4.88842i 0.355108 + 0.258001i 0.751009 0.660292i \(-0.229568\pi\)
−0.395901 + 0.918293i \(0.629568\pi\)
\(360\) 2.67315 + 6.15258i 0.140887 + 0.324270i
\(361\) −15.0536 + 10.9371i −0.792295 + 0.575636i
\(362\) 18.5228 2.93373i 0.973538 0.154193i
\(363\) −7.65848 2.04105i −0.401966 0.107127i
\(364\) 10.9612 + 15.0868i 0.574523 + 0.790763i
\(365\) 10.0175 + 14.1327i 0.524340 + 0.739741i
\(366\) 5.97263 3.45902i 0.312195 0.180806i
\(367\) −7.05620 + 13.8486i −0.368331 + 0.722889i −0.998567 0.0535138i \(-0.982958\pi\)
0.630237 + 0.776403i \(0.282958\pi\)
\(368\) −0.460535 0.460535i −0.0240071 0.0240071i
\(369\) −9.38053 + 16.3490i −0.488331 + 0.851093i
\(370\) 5.89715 5.76074i 0.306578 0.299487i
\(371\) 2.37748 + 0.772489i 0.123432 + 0.0401056i
\(372\) −2.80431 + 0.150751i −0.145397 + 0.00781606i
\(373\) 2.33980 14.7729i 0.121150 0.764912i −0.850060 0.526686i \(-0.823434\pi\)
0.971210 0.238225i \(-0.0765657\pi\)
\(374\) −12.1734 −0.629473
\(375\) −13.4360 + 13.9454i −0.693830 + 0.720139i
\(376\) −4.29592 −0.221545
\(377\) −4.85009 + 30.6223i −0.249792 + 1.57713i
\(378\) 18.0122 + 17.8674i 0.926448 + 0.919001i
\(379\) 5.98428 + 1.94441i 0.307392 + 0.0998776i 0.458651 0.888617i \(-0.348333\pi\)
−0.151259 + 0.988494i \(0.548333\pi\)
\(380\) −1.00239 + 0.979202i −0.0514214 + 0.0502320i
\(381\) 0.412427 3.97541i 0.0211293 0.203667i
\(382\) −11.1109 11.1109i −0.568482 0.568482i
\(383\) −5.34769 + 10.4954i −0.273254 + 0.536292i −0.986327 0.164798i \(-0.947303\pi\)
0.713073 + 0.701090i \(0.247303\pi\)
\(384\) −0.868042 1.49883i −0.0442971 0.0764870i
\(385\) −16.0023 22.5761i −0.815551 1.15058i
\(386\) 1.52538 + 2.09951i 0.0776400 + 0.106862i
\(387\) 2.53097 3.14273i 0.128656 0.159754i
\(388\) 14.9915 2.37442i 0.761078 0.120543i
\(389\) −19.3894 + 14.0872i −0.983082 + 0.714251i −0.958395 0.285444i \(-0.907859\pi\)
−0.0246869 + 0.999695i \(0.507859\pi\)
\(390\) 10.0112 10.8896i 0.506935 0.551417i
\(391\) −2.53072 1.83868i −0.127984 0.0929859i
\(392\) 15.0047 + 7.64527i 0.757851 + 0.386145i
\(393\) 3.38002 + 8.76996i 0.170499 + 0.442386i
\(394\) 5.51903 1.79324i 0.278045 0.0903423i
\(395\) 0.292940 0.144969i 0.0147394 0.00729416i
\(396\) 3.11138 + 6.93799i 0.156353 + 0.348647i
\(397\) −7.12795 + 3.63187i −0.357741 + 0.182278i −0.623619 0.781728i \(-0.714338\pi\)
0.265878 + 0.964007i \(0.414338\pi\)
\(398\) 3.81642 + 0.604462i 0.191300 + 0.0302989i
\(399\) −2.14911 + 4.84450i −0.107590 + 0.242528i
\(400\) 3.03277 3.97521i 0.151638 0.198761i
\(401\) 5.93714i 0.296487i −0.988951 0.148243i \(-0.952638\pi\)
0.988951 0.148243i \(-0.0473619\pi\)
\(402\) 4.04484 6.24689i 0.201738 0.311566i
\(403\) 2.81141 + 5.51770i 0.140046 + 0.274856i
\(404\) 0.602504 1.85432i 0.0299757 0.0922557i
\(405\) 11.0671 16.8083i 0.549928 0.835212i
\(406\) 12.2481 + 37.6958i 0.607864 + 1.87081i
\(407\) 6.60753 6.60753i 0.327523 0.327523i
\(408\) −5.24399 6.45800i −0.259616 0.319719i
\(409\) 12.3971 17.0631i 0.612995 0.843715i −0.383825 0.923406i \(-0.625393\pi\)
0.996820 + 0.0796911i \(0.0253934\pi\)
\(410\) 14.0482 + 0.164375i 0.693792 + 0.00811790i
\(411\) 1.55852 + 7.28405i 0.0768760 + 0.359296i
\(412\) 0.540832 + 3.41468i 0.0266449 + 0.168229i
\(413\) −8.46616 53.4532i −0.416592 2.63026i
\(414\) −0.401093 + 1.91228i −0.0197126 + 0.0939832i
\(415\) −5.27306 16.8991i −0.258844 0.829542i
\(416\) −2.24493 + 3.08989i −0.110067 + 0.151494i
\(417\) 3.95274 3.20968i 0.193567 0.157179i
\(418\) −1.12314 + 1.12314i −0.0549344 + 0.0549344i
\(419\) −11.8698 36.5316i −0.579880 1.78469i −0.618926 0.785450i \(-0.712432\pi\)
0.0390457 0.999237i \(-0.487568\pi\)
\(420\) 5.08325 18.2144i 0.248037 0.888770i
\(421\) −5.24894 + 16.1546i −0.255818 + 0.787326i 0.737850 + 0.674965i \(0.235841\pi\)
−0.993667 + 0.112361i \(0.964159\pi\)
\(422\) −4.96359 9.74160i −0.241624 0.474214i
\(423\) 7.04823 + 10.7897i 0.342697 + 0.524611i
\(424\) 0.511982i 0.0248641i
\(425\) 11.4002 21.1364i 0.552989 1.02526i
\(426\) −1.52660 0.677229i −0.0739642 0.0328119i
\(427\) −19.2171 3.04368i −0.929979 0.147294i
\(428\) 9.79189 4.98922i 0.473309 0.241163i
\(429\) 11.2024 12.4752i 0.540857 0.602310i
\(430\) −2.96490 0.505221i −0.142980 0.0243639i
\(431\) 24.9008 8.09077i 1.19943 0.389719i 0.359879 0.932999i \(-0.382818\pi\)
0.839551 + 0.543280i \(0.182818\pi\)
\(432\) −2.34030 + 4.63929i −0.112598 + 0.223208i
\(433\) 25.3199 + 12.9012i 1.21680 + 0.619990i 0.940078 0.340960i \(-0.110752\pi\)
0.276721 + 0.960950i \(0.410752\pi\)
\(434\) 6.40478 + 4.65335i 0.307440 + 0.223368i
\(435\) 27.3889 15.4371i 1.31320 0.740150i
\(436\) −14.4153 + 10.4733i −0.690366 + 0.501580i
\(437\) −0.403127 + 0.0638490i −0.0192842 + 0.00305431i
\(438\) −3.45547 + 12.9657i −0.165109 + 0.619527i
\(439\) −23.8366 32.8083i −1.13766 1.56585i −0.772628 0.634859i \(-0.781058\pi\)
−0.365032 0.930995i \(-0.618942\pi\)
\(440\) 3.38467 4.54579i 0.161358 0.216712i
\(441\) −5.41598 50.2293i −0.257904 2.39187i
\(442\) −8.32799 + 16.3446i −0.396122 + 0.777434i
\(443\) 4.87049 + 4.87049i 0.231404 + 0.231404i 0.813279 0.581875i \(-0.197681\pi\)
−0.581875 + 0.813279i \(0.697681\pi\)
\(444\) 6.35164 + 0.658947i 0.301435 + 0.0312722i
\(445\) −4.14847 + 24.3453i −0.196656 + 1.15408i
\(446\) −18.5603 6.03061i −0.878856 0.285558i
\(447\) 0.566865 + 10.5450i 0.0268118 + 0.498762i
\(448\) −0.763813 + 4.82253i −0.0360868 + 0.227843i
\(449\) 38.2829 1.80668 0.903340 0.428924i \(-0.141107\pi\)
0.903340 + 0.428924i \(0.141107\pi\)
\(450\) −14.9600 1.09508i −0.705220 0.0516224i
\(451\) 15.9247 0.749863
\(452\) 2.93571 18.5354i 0.138084 0.871830i
\(453\) −1.62467 30.2227i −0.0763337 1.41998i
\(454\) −23.5335 7.64649i −1.10448 0.358868i
\(455\) −41.2590 + 6.04083i −1.93425 + 0.283198i
\(456\) −1.07964 0.112007i −0.0505589 0.00524520i
\(457\) 25.3039 + 25.3039i 1.18366 + 1.18366i 0.978788 + 0.204877i \(0.0656794\pi\)
0.204877 + 0.978788i \(0.434321\pi\)
\(458\) −1.38340 + 2.71507i −0.0646419 + 0.126867i
\(459\) −7.61626 + 23.7664i −0.355497 + 1.10932i
\(460\) 1.39023 0.433798i 0.0648200 0.0202259i
\(461\) 4.06138 + 5.59002i 0.189158 + 0.260353i 0.893054 0.449950i \(-0.148558\pi\)
−0.703896 + 0.710303i \(0.748558\pi\)
\(462\) 5.51988 20.7119i 0.256808 0.963603i
\(463\) 21.7821 3.44995i 1.01230 0.160333i 0.371819 0.928305i \(-0.378734\pi\)
0.640483 + 0.767973i \(0.278734\pi\)
\(464\) −6.56735 + 4.77146i −0.304881 + 0.221509i
\(465\) 2.61345 5.71002i 0.121196 0.264796i
\(466\) 14.9847 + 10.8870i 0.694153 + 0.504332i
\(467\) −4.03552 2.05620i −0.186742 0.0951496i 0.358120 0.933676i \(-0.383418\pi\)
−0.544862 + 0.838526i \(0.683418\pi\)
\(468\) 11.4438 + 0.568876i 0.528990 + 0.0262963i
\(469\) −19.9523 + 6.48290i −0.921313 + 0.299353i
\(470\) 4.46086 8.50737i 0.205764 0.392416i
\(471\) −2.66729 + 2.97036i −0.122902 + 0.136867i
\(472\) 9.87598 5.03206i 0.454579 0.231620i
\(473\) −3.36716 0.533306i −0.154822 0.0245214i
\(474\) 0.231426 + 0.102665i 0.0106297 + 0.00471554i
\(475\) −0.898276 3.00187i −0.0412157 0.137735i
\(476\) 23.4511i 1.07488i
\(477\) 1.28590 0.839999i 0.0588773 0.0384609i
\(478\) 6.06483 + 11.9029i 0.277399 + 0.544426i
\(479\) 11.4075 35.1086i 0.521220 1.60415i −0.250450 0.968129i \(-0.580579\pi\)
0.771671 0.636022i \(-0.219421\pi\)
\(480\) 3.86957 0.162636i 0.176621 0.00742328i
\(481\) −4.35128 13.3919i −0.198401 0.610616i
\(482\) −3.61037 + 3.61037i −0.164448 + 0.164448i
\(483\) 4.27585 3.47205i 0.194558 0.157984i
\(484\) −2.68968 + 3.70203i −0.122258 + 0.168274i
\(485\) −10.8649 + 32.1538i −0.493352 + 1.46003i
\(486\) 15.4918 1.73367i 0.702720 0.0786408i
\(487\) −5.38000 33.9680i −0.243791 1.53923i −0.740941 0.671570i \(-0.765620\pi\)
0.497150 0.867665i \(-0.334380\pi\)
\(488\) −0.623369 3.93579i −0.0282186 0.178165i
\(489\) 8.29627 + 38.7743i 0.375170 + 1.75344i
\(490\) −30.7210 + 21.7755i −1.38783 + 0.983719i
\(491\) −9.76139 + 13.4354i −0.440525 + 0.606331i −0.970329 0.241789i \(-0.922266\pi\)
0.529803 + 0.848120i \(0.322266\pi\)
\(492\) 6.85992 + 8.44803i 0.309269 + 0.380867i
\(493\) −27.5693 + 27.5693i −1.24166 + 1.24166i
\(494\) 0.739624 + 2.27633i 0.0332772 + 0.102417i
\(495\) −16.9704 1.04278i −0.762763 0.0468695i
\(496\) −0.501043 + 1.54205i −0.0224975 + 0.0692401i
\(497\) 2.13736 + 4.19480i 0.0958736 + 0.188163i
\(498\) 7.45283 11.5102i 0.333969 0.515785i
\(499\) 23.6495i 1.05870i −0.848404 0.529349i \(-0.822436\pi\)
0.848404 0.529349i \(-0.177564\pi\)
\(500\) 4.72305 + 10.1337i 0.211221 + 0.453195i
\(501\) 6.22221 14.0261i 0.277988 0.626639i
\(502\) 10.3121 + 1.63327i 0.460249 + 0.0728964i
\(503\) −13.2000 + 6.72572i −0.588557 + 0.299885i −0.722793 0.691065i \(-0.757142\pi\)
0.134236 + 0.990949i \(0.457142\pi\)
\(504\) 13.3655 5.99382i 0.595345 0.266986i
\(505\) 3.04653 + 3.11867i 0.135569 + 0.138779i
\(506\) 1.56996 0.510111i 0.0697932 0.0226772i
\(507\) −0.988597 2.56507i −0.0439051 0.113919i
\(508\) −2.05602 1.04759i −0.0912211 0.0464795i
\(509\) 26.7370 + 19.4255i 1.18510 + 0.861022i 0.992737 0.120303i \(-0.0383865\pi\)
0.192358 + 0.981325i \(0.438386\pi\)
\(510\) 18.2344 3.67891i 0.807431 0.162905i
\(511\) 30.6019 22.2336i 1.35375 0.983557i
\(512\) −0.987688 + 0.156434i −0.0436501 + 0.00691349i
\(513\) 1.49003 + 2.89540i 0.0657864 + 0.127835i
\(514\) 13.1153 + 18.0516i 0.578489 + 0.796222i
\(515\) −7.32381 2.47475i −0.322726 0.109051i
\(516\) −1.16756 2.01601i −0.0513992 0.0887501i
\(517\) 4.94319 9.70155i 0.217401 0.426674i
\(518\) −12.7289 12.7289i −0.559274 0.559274i
\(519\) −2.94746 + 28.4108i −0.129379 + 1.24709i
\(520\) −3.78789 7.65425i −0.166110 0.335661i
\(521\) −10.1727 3.30530i −0.445672 0.144808i 0.0775789 0.996986i \(-0.475281\pi\)
−0.523251 + 0.852179i \(0.675281\pi\)
\(522\) 22.7589 + 8.66616i 0.996132 + 0.379308i
\(523\) 6.12109 38.6470i 0.267656 1.68992i −0.377615 0.925963i \(-0.623256\pi\)
0.645271 0.763953i \(-0.276744\pi\)
\(524\) 5.42638 0.237052
\(525\) 30.7922 + 28.9802i 1.34388 + 1.26480i
\(526\) −13.3050 −0.580124
\(527\) −1.21824 + 7.69168i −0.0530675 + 0.335055i
\(528\) 4.38367 0.235652i 0.190775 0.0102554i
\(529\) −21.4709 6.97631i −0.933516 0.303318i
\(530\) −1.01390 0.531640i −0.0440409 0.0230930i
\(531\) −28.8419 16.5486i −1.25163 0.718147i
\(532\) 2.16363 + 2.16363i 0.0938053 + 0.0938053i
\(533\) 10.8943 21.3812i 0.471883 0.926122i
\(534\) −16.5539 + 9.58709i −0.716356 + 0.414874i
\(535\) −0.287512 + 24.5720i −0.0124302 + 1.06234i
\(536\) −2.52552 3.47608i −0.109086 0.150144i
\(537\) 10.5787 + 2.81930i 0.456504 + 0.121662i
\(538\) −8.04880 + 1.27480i −0.347008 + 0.0549607i
\(539\) −34.5309 + 25.0882i −1.48735 + 1.08062i
\(540\) −6.75720 9.45200i −0.290784 0.406749i
\(541\) 13.6337 + 9.90543i 0.586157 + 0.425868i 0.840938 0.541131i \(-0.182004\pi\)
−0.254782 + 0.966999i \(0.582004\pi\)
\(542\) −7.89814 4.02431i −0.339254 0.172859i
\(543\) −30.3092 + 11.6814i −1.30069 + 0.501298i
\(544\) −4.56788 + 1.48420i −0.195846 + 0.0636344i
\(545\) −5.77194 39.4225i −0.247243 1.68867i
\(546\) −24.0325 21.5805i −1.02850 0.923560i
\(547\) 13.9944 7.13049i 0.598356 0.304878i −0.128455 0.991715i \(-0.541002\pi\)
0.726811 + 0.686838i \(0.241002\pi\)
\(548\) 4.24769 + 0.672768i 0.181452 + 0.0287392i
\(549\) −8.86242 + 8.02304i −0.378239 + 0.342415i
\(550\) 5.48757 + 11.4231i 0.233991 + 0.487083i
\(551\) 5.08717i 0.216721i
\(552\) 0.946910 + 0.613122i 0.0403032 + 0.0260962i
\(553\) −0.324013 0.635911i −0.0137784 0.0270417i
\(554\) −3.76524 + 11.5882i −0.159970 + 0.492337i
\(555\) −7.90045 + 11.8941i −0.335355 + 0.504878i
\(556\) −0.908430 2.79586i −0.0385260 0.118571i
\(557\) 16.7489 16.7489i 0.709672 0.709672i −0.256794 0.966466i \(-0.582666\pi\)
0.966466 + 0.256794i \(0.0826662\pi\)
\(558\) 4.69508 1.27159i 0.198758 0.0538307i
\(559\) −3.01956 + 4.15607i −0.127714 + 0.175783i
\(560\) −8.75709 6.52029i −0.370055 0.275533i
\(561\) 20.6183 4.41156i 0.870507 0.186256i
\(562\) 0.312022 + 1.97003i 0.0131619 + 0.0831007i
\(563\) 7.14192 + 45.0923i 0.300996 + 1.90041i 0.420007 + 0.907521i \(0.362027\pi\)
−0.119011 + 0.992893i \(0.537973\pi\)
\(564\) 7.27606 1.55681i 0.306378 0.0655534i
\(565\) 33.6579 + 25.0607i 1.41600 + 1.05431i
\(566\) −1.22605 + 1.68751i −0.0515345 + 0.0709312i
\(567\) −36.9826 23.7348i −1.55312 0.996769i
\(568\) −0.681806 + 0.681806i −0.0286080 + 0.0286080i
\(569\) −0.701234 2.15818i −0.0293972 0.0904754i 0.935281 0.353905i \(-0.115146\pi\)
−0.964679 + 0.263430i \(0.915146\pi\)
\(570\) 1.34291 2.02175i 0.0562481 0.0846817i
\(571\) −9.62474 + 29.6219i −0.402783 + 1.23964i 0.519950 + 0.854197i \(0.325951\pi\)
−0.922733 + 0.385441i \(0.874049\pi\)
\(572\) −4.39477 8.62521i −0.183754 0.360638i
\(573\) 22.8451 + 14.7922i 0.954370 + 0.617951i
\(574\) 30.6775i 1.28046i
\(575\) −0.584544 + 3.20358i −0.0243772 + 0.133599i
\(576\) 2.01338 + 2.22403i 0.0838909 + 0.0926677i
\(577\) −13.3526 2.11485i −0.555877 0.0880422i −0.127825 0.991797i \(-0.540800\pi\)
−0.428051 + 0.903755i \(0.640800\pi\)
\(578\) −5.40699 + 2.75500i −0.224901 + 0.114593i
\(579\) −3.34441 3.00319i −0.138989 0.124808i
\(580\) −2.62960 17.9602i −0.109188 0.745758i
\(581\) −36.7632 + 11.9451i −1.52520 + 0.495566i
\(582\) −24.5309 + 9.45440i −1.01684 + 0.391897i
\(583\) −1.15622 0.589123i −0.0478857 0.0243990i
\(584\) 6.26750 + 4.55360i 0.259351 + 0.188429i
\(585\) −13.0097 + 22.0719i −0.537887 + 0.912559i
\(586\) 16.1844 11.7587i 0.668573 0.485747i
\(587\) 20.8055 3.29526i 0.858733 0.136010i 0.288487 0.957484i \(-0.406848\pi\)
0.570246 + 0.821474i \(0.306848\pi\)
\(588\) −28.1843 7.51133i −1.16230 0.309762i
\(589\) 0.597248 + 0.822041i 0.0246092 + 0.0338716i
\(590\) −0.289981 + 24.7830i −0.0119383 + 1.02030i
\(591\) −8.69782 + 5.03730i −0.357780 + 0.207207i
\(592\) 1.67377 3.28496i 0.0687917 0.135011i
\(593\) 13.4478 + 13.4478i 0.552235 + 0.552235i 0.927085 0.374851i \(-0.122306\pi\)
−0.374851 + 0.927085i \(0.622306\pi\)
\(594\) −7.78407 10.6234i −0.319384 0.435885i
\(595\) −46.4411 24.3515i −1.90390 0.998314i
\(596\) 5.79855 + 1.88406i 0.237518 + 0.0771743i
\(597\) −6.68299 + 0.359255i −0.273516 + 0.0147033i
\(598\) 0.389131 2.45687i 0.0159127 0.100469i
\(599\) −0.0872460 −0.00356477 −0.00178239 0.999998i \(-0.500567\pi\)
−0.00178239 + 0.999998i \(0.500567\pi\)
\(600\) −3.69606 + 7.83193i −0.150891 + 0.319737i
\(601\) 5.69768 0.232413 0.116207 0.993225i \(-0.462927\pi\)
0.116207 + 0.993225i \(0.462927\pi\)
\(602\) −1.02737 + 6.48656i −0.0418725 + 0.264373i
\(603\) −4.58698 + 12.0463i −0.186796 + 0.490562i
\(604\) −16.6190 5.39984i −0.676218 0.219716i
\(605\) −4.53831 9.17064i −0.184509 0.372840i
\(606\) −0.348480 + 3.35903i −0.0141560 + 0.136451i
\(607\) 29.7432 + 29.7432i 1.20724 + 1.20724i 0.971918 + 0.235320i \(0.0756138\pi\)
0.235320 + 0.971918i \(0.424386\pi\)
\(608\) −0.284505 + 0.558373i −0.0115382 + 0.0226450i
\(609\) −34.4055 59.4074i −1.39418 2.40731i
\(610\) 8.44150 + 2.85243i 0.341787 + 0.115491i
\(611\) −9.64405 13.2739i −0.390157 0.537005i
\(612\) 11.2222 + 9.03764i 0.453629 + 0.365325i
\(613\) −12.4325 + 1.96912i −0.502145 + 0.0795319i −0.402368 0.915478i \(-0.631813\pi\)
−0.0997765 + 0.995010i \(0.531813\pi\)
\(614\) −7.54983 + 5.48528i −0.304687 + 0.221368i
\(615\) −23.8533 + 4.81256i −0.961856 + 0.194061i
\(616\) −10.0119 7.27407i −0.403391 0.293081i
\(617\) 30.8055 + 15.6962i 1.24018 + 0.631904i 0.946099 0.323876i \(-0.104986\pi\)
0.294082 + 0.955780i \(0.404986\pi\)
\(618\) −2.15347 5.58750i −0.0866251 0.224762i
\(619\) 8.55247 2.77887i 0.343753 0.111692i −0.132052 0.991243i \(-0.542157\pi\)
0.475805 + 0.879551i \(0.342157\pi\)
\(620\) −2.53350 2.59349i −0.101748 0.104157i
\(621\) −0.0136569 3.38420i −0.000548031 0.135803i
\(622\) −6.97523 + 3.55406i −0.279681 + 0.142505i
\(623\) 53.2624 + 8.43593i 2.13391 + 0.337979i
\(624\) 2.68253 6.04693i 0.107387 0.242071i
\(625\) −24.9726 1.16960i −0.998905 0.0467839i
\(626\) 2.86051i 0.114329i
\(627\) 1.49526 2.30929i 0.0597149 0.0922242i
\(628\) 1.04640 + 2.05367i 0.0417557 + 0.0819502i
\(629\) 5.47194 16.8409i 0.218180 0.671490i
\(630\) −2.00883 + 32.6921i −0.0800337 + 1.30248i
\(631\) −5.89667 18.1481i −0.234743 0.722463i −0.997155 0.0753725i \(-0.975985\pi\)
0.762413 0.647091i \(-0.224015\pi\)
\(632\) 0.103358 0.103358i 0.00411138 0.00411138i
\(633\) 11.9372 + 14.7007i 0.474461 + 0.584302i
\(634\) 15.0327 20.6907i 0.597024 0.821733i
\(635\) 4.20955 2.98379i 0.167051 0.118408i
\(636\) −0.185538 0.867153i −0.00735708 0.0343848i
\(637\) 10.0615 + 63.5259i 0.398652 + 2.51699i
\(638\) −3.21861 20.3215i −0.127426 0.804537i
\(639\) 2.83106 + 0.593804i 0.111995 + 0.0234905i
\(640\) 0.715817 2.11840i 0.0282952 0.0837370i
\(641\) −5.82328 + 8.01506i −0.230006 + 0.316576i −0.908384 0.418137i \(-0.862683\pi\)
0.678378 + 0.734713i \(0.262683\pi\)
\(642\) −14.7766 + 11.9988i −0.583187 + 0.473556i
\(643\) 14.9895 14.9895i 0.591130 0.591130i −0.346807 0.937937i \(-0.612734\pi\)
0.937937 + 0.346807i \(0.112734\pi\)
\(644\) −0.982687 3.02440i −0.0387233 0.119178i
\(645\) 5.20478 0.218754i 0.204938 0.00861345i
\(646\) −0.930111 + 2.86259i −0.0365947 + 0.112627i
\(647\) 9.58156 + 18.8049i 0.376690 + 0.739296i 0.999056 0.0434301i \(-0.0138286\pi\)
−0.622366 + 0.782726i \(0.713829\pi\)
\(648\) 2.28256 8.70574i 0.0896675 0.341994i
\(649\) 28.0934i 1.10276i
\(650\) 19.0913 + 0.446827i 0.748823 + 0.0175260i
\(651\) −12.5342 5.56040i −0.491255 0.217929i
\(652\) 22.6112 + 3.58126i 0.885523 + 0.140253i
\(653\) −28.9032 + 14.7269i −1.13107 + 0.576309i −0.916355 0.400368i \(-0.868882\pi\)
−0.214715 + 0.976677i \(0.568882\pi\)
\(654\) 20.6199 22.9628i 0.806302 0.897915i
\(655\) −5.63472 + 10.7461i −0.220167 + 0.419883i
\(656\) 5.97547 1.94155i 0.233303 0.0758048i
\(657\) 1.15390 23.2125i 0.0450181 0.905606i
\(658\) −18.6892 9.52264i −0.728582 0.371231i
\(659\) −21.9545 15.9509i −0.855225 0.621357i 0.0713570 0.997451i \(-0.477267\pi\)
−0.926582 + 0.376094i \(0.877267\pi\)
\(660\) −4.08531 + 8.92585i −0.159021 + 0.347438i
\(661\) −20.1069 + 14.6085i −0.782069 + 0.568206i −0.905599 0.424135i \(-0.860578\pi\)
0.123531 + 0.992341i \(0.460578\pi\)
\(662\) −31.5787 + 5.00158i −1.22734 + 0.194392i
\(663\) 8.18209 30.7011i 0.317766 1.19233i
\(664\) −4.65341 6.40487i −0.180587 0.248557i
\(665\) −6.53142 + 2.03802i −0.253278 + 0.0790309i
\(666\) −10.9967 + 1.18572i −0.426112 + 0.0459456i
\(667\) 2.40025 4.71076i 0.0929382 0.182402i
\(668\) −6.26427 6.26427i −0.242372 0.242372i
\(669\) 33.6213 + 3.48802i 1.29988 + 0.134855i
\(670\) 9.50631 1.39184i 0.367261 0.0537715i
\(671\) 9.60557 + 3.12104i 0.370819 + 0.120486i
\(672\) −0.453964 8.44478i −0.0175120 0.325765i
\(673\) 3.13319 19.7822i 0.120775 0.762546i −0.850743 0.525582i \(-0.823848\pi\)
0.971518 0.236964i \(-0.0761524\pi\)
\(674\) 18.6360 0.717830
\(675\) 25.7348 3.56663i 0.990532 0.137280i
\(676\) −1.58712 −0.0610432
\(677\) 3.76633 23.7796i 0.144752 0.913926i −0.803246 0.595648i \(-0.796895\pi\)
0.947997 0.318278i \(-0.103105\pi\)
\(678\) 1.74481 + 32.4575i 0.0670090 + 1.24652i
\(679\) 70.4833 + 22.9014i 2.70490 + 0.878876i
\(680\) 1.80406 10.5871i 0.0691825 0.405998i
\(681\) 42.6300 + 4.42263i 1.63359 + 0.169476i
\(682\) −2.90591 2.90591i −0.111273 0.111273i
\(683\) −5.04753 + 9.90634i −0.193138 + 0.379056i −0.967185 0.254073i \(-0.918230\pi\)
0.774047 + 0.633129i \(0.218230\pi\)
\(684\) 1.86920 0.201546i 0.0714705 0.00770631i
\(685\) −5.74308 + 7.71326i −0.219432 + 0.294708i
\(686\) 28.2407 + 38.8700i 1.07823 + 1.48406i
\(687\) 1.35916 5.09989i 0.0518552 0.194573i
\(688\) −1.32850 + 0.210413i −0.0506484 + 0.00802192i
\(689\) −1.58197 + 1.14937i −0.0602682 + 0.0437874i
\(690\) −2.19745 + 1.23854i −0.0836557 + 0.0471504i
\(691\) −26.5202 19.2681i −1.00888 0.732992i −0.0449036 0.998991i \(-0.514298\pi\)
−0.963973 + 0.265999i \(0.914298\pi\)
\(692\) 14.6936 + 7.48676i 0.558567 + 0.284604i
\(693\) −1.84328 + 37.0804i −0.0700205 + 1.40857i
\(694\) 22.6473 7.35855i 0.859680 0.279327i
\(695\) 6.48005 + 1.10421i 0.245802 + 0.0418850i
\(696\) 9.39408 10.4614i 0.356082 0.396540i
\(697\) 26.8878 13.7000i 1.01845 0.518926i
\(698\) 8.52937 + 1.35092i 0.322841 + 0.0511330i
\(699\) −29.3252 13.0092i −1.10918 0.492053i
\(700\) 22.0057 10.5714i 0.831737 0.399560i
\(701\) 25.1992i 0.951759i 0.879510 + 0.475880i \(0.157870\pi\)
−0.879510 + 0.475880i \(0.842130\pi\)
\(702\) −19.5887 + 3.18363i −0.739328 + 0.120158i
\(703\) −1.04891 2.05861i −0.0395606 0.0776420i
\(704\) 0.783225 2.41052i 0.0295189 0.0908498i
\(705\) −4.47242 + 16.0256i −0.168441 + 0.603561i
\(706\) −8.83221 27.1827i −0.332405 1.02304i
\(707\) 6.73158 6.73158i 0.253167 0.253167i
\(708\) −14.9035 + 12.1019i −0.560109 + 0.454816i
\(709\) 15.3258 21.0942i 0.575574 0.792209i −0.417628 0.908618i \(-0.637138\pi\)
0.993201 + 0.116409i \(0.0371383\pi\)
\(710\) −0.642223 2.05819i −0.0241022 0.0772425i
\(711\) −0.429174 0.0900177i −0.0160953 0.00337593i
\(712\) 1.72774 + 10.9085i 0.0647498 + 0.408814i
\(713\) −0.165197 1.04301i −0.00618669 0.0390612i
\(714\) −8.49850 39.7195i −0.318048 1.48647i
\(715\) 21.6443 + 0.253255i 0.809452 + 0.00947122i
\(716\) 3.71527 5.11362i 0.138846 0.191105i
\(717\) −14.5856 17.9623i −0.544709 0.670813i
\(718\) −5.88078 + 5.88078i −0.219469 + 0.219469i
\(719\) 10.3692 + 31.9130i 0.386705 + 1.19016i 0.935236 + 0.354025i \(0.115187\pi\)
−0.548531 + 0.836130i \(0.684813\pi\)
\(720\) −6.49501 + 1.67776i −0.242055 + 0.0625264i
\(721\) −5.21635 + 16.0543i −0.194267 + 0.597892i
\(722\) −8.44753 16.5792i −0.314384 0.617014i
\(723\) 4.80657 7.42331i 0.178758 0.276076i
\(724\) 18.7537i 0.696976i
\(725\) 38.2979 + 13.4423i 1.42235 + 0.499235i
\(726\) 3.21397 7.24490i 0.119282 0.268883i
\(727\) 39.1616 + 6.20259i 1.45242 + 0.230042i 0.832241 0.554415i \(-0.187058\pi\)
0.620184 + 0.784456i \(0.287058\pi\)
\(728\) −16.6158 + 8.46615i −0.615821 + 0.313777i
\(729\) −25.6104 + 8.55043i −0.948532 + 0.316683i
\(730\) −15.5258 + 7.68332i −0.574636 + 0.284373i
\(731\) −6.14406 + 1.99632i −0.227246 + 0.0738367i
\(732\) 2.48211 + 6.44021i 0.0917414 + 0.238037i
\(733\) −20.5512 10.4714i −0.759077 0.386769i 0.0312046 0.999513i \(-0.490066\pi\)
−0.790281 + 0.612744i \(0.790066\pi\)
\(734\) −12.5742 9.13572i −0.464124 0.337206i
\(735\) 44.1414 48.0146i 1.62818 1.77105i
\(736\) 0.526909 0.382822i 0.0194221 0.0141110i
\(737\) 10.7561 1.70361i 0.396208 0.0627532i
\(738\) −14.6802 11.8226i −0.540387 0.435195i
\(739\) −1.10089 1.51525i −0.0404970 0.0557393i 0.788288 0.615306i \(-0.210968\pi\)
−0.828785 + 0.559567i \(0.810968\pi\)
\(740\) 4.76730 + 6.72573i 0.175250 + 0.247243i
\(741\) −2.07764 3.58742i −0.0763239 0.131787i
\(742\) −1.13490 + 2.22736i −0.0416634 + 0.0817690i
\(743\) −32.5148 32.5148i −1.19285 1.19285i −0.976263 0.216587i \(-0.930507\pi\)
−0.216587 0.976263i \(-0.569493\pi\)
\(744\) 0.289796 2.79337i 0.0106245 0.102410i
\(745\) −9.75227 + 9.52669i −0.357295 + 0.349031i
\(746\) 14.2250 + 4.62198i 0.520814 + 0.169223i
\(747\) −8.45176 + 22.1959i −0.309234 + 0.812105i
\(748\) 1.90434 12.0236i 0.0696297 0.439625i
\(749\) 53.6587 1.96065
\(750\) −11.6719 15.4521i −0.426197 0.564230i
\(751\) −30.1750 −1.10110 −0.550550 0.834802i \(-0.685582\pi\)
−0.550550 + 0.834802i \(0.685582\pi\)
\(752\) 0.672030 4.24303i 0.0245064 0.154727i
\(753\) −18.0576 + 0.970716i −0.658054 + 0.0353748i
\(754\) −29.4865 9.58075i −1.07384 0.348910i
\(755\) 27.9506 27.3041i 1.01723 0.993697i
\(756\) −20.4652 + 14.9954i −0.744311 + 0.545376i
\(757\) −32.7271 32.7271i −1.18949 1.18949i −0.977210 0.212277i \(-0.931912\pi\)
−0.212277 0.977210i \(-0.568088\pi\)
\(758\) −2.85662 + 5.60643i −0.103757 + 0.203635i
\(759\) −2.47421 + 1.43292i −0.0898080 + 0.0520118i
\(760\) −0.810339 1.14323i −0.0293941 0.0414692i
\(761\) −16.4848 22.6894i −0.597574 0.822490i 0.397910 0.917425i \(-0.369736\pi\)
−0.995483 + 0.0949348i \(0.969736\pi\)
\(762\) 3.86195 + 1.02924i 0.139904 + 0.0372855i
\(763\) −85.9289 + 13.6098i −3.11084 + 0.492708i
\(764\) 12.7122 9.23596i 0.459911 0.334145i
\(765\) −29.5506 + 12.8390i −1.06840 + 0.464196i
\(766\) −9.52966 6.92370i −0.344321 0.250164i
\(767\) 37.7194 + 19.2190i 1.36197 + 0.693958i
\(768\) 1.61617 0.622886i 0.0583186 0.0224765i
\(769\) 18.8694 6.13105i 0.680449 0.221091i 0.0516570 0.998665i \(-0.483550\pi\)
0.628792 + 0.777574i \(0.283550\pi\)
\(770\) 24.8014 12.2736i 0.893781 0.442309i
\(771\) −28.7553 25.8214i −1.03560 0.929936i
\(772\) −2.31229 + 1.17817i −0.0832210 + 0.0424032i
\(773\) 17.2870 + 2.73800i 0.621771 + 0.0984789i 0.459369 0.888246i \(-0.348076\pi\)
0.162403 + 0.986725i \(0.448076\pi\)
\(774\) 2.70811 + 2.99144i 0.0973410 + 0.107525i
\(775\) 7.76676 2.32412i 0.278990 0.0834849i
\(776\) 15.1784i 0.544872i
\(777\) 26.1719 + 16.9462i 0.938912 + 0.607942i
\(778\) −10.8806 21.3544i −0.390089 0.765593i
\(779\) 1.21672 3.74469i 0.0435937 0.134167i
\(780\) 9.18945 + 11.5914i 0.329035 + 0.415039i
\(781\) −0.755201 2.32427i −0.0270232 0.0831689i
\(782\) 2.21193 2.21193i 0.0790986 0.0790986i
\(783\) −41.6877 6.43035i −1.48980 0.229802i
\(784\) −9.89840 + 13.6240i −0.353514 + 0.486571i
\(785\) −5.15352 0.0603002i −0.183937 0.00215221i
\(786\) −9.19074 + 1.96648i −0.327823 + 0.0701419i
\(787\) −5.84029 36.8741i −0.208184 1.31442i −0.841386 0.540435i \(-0.818260\pi\)
0.633202 0.773986i \(-0.281740\pi\)
\(788\) 0.907798 + 5.73161i 0.0323390 + 0.204180i
\(789\) 22.5348 4.82161i 0.802260 0.171654i
\(790\) 0.0973578 + 0.312012i 0.00346383 + 0.0111009i
\(791\) 53.8585 74.1299i 1.91499 2.63576i
\(792\) −7.33930 + 1.98774i −0.260791 + 0.0706311i
\(793\) 10.7617 10.7617i 0.382160 0.382160i
\(794\) −2.47210 7.60834i −0.0877315 0.270010i
\(795\) 1.90992 + 0.533018i 0.0677378 + 0.0189042i
\(796\) −1.19404 + 3.67488i −0.0423216 + 0.130253i
\(797\) −9.33967 18.3301i −0.330828 0.649286i 0.664345 0.747426i \(-0.268711\pi\)
−0.995173 + 0.0981399i \(0.968711\pi\)
\(798\) −4.44866 2.88049i −0.157481 0.101968i
\(799\) 20.6331i 0.729947i
\(800\) 3.45184 + 3.61729i 0.122041 + 0.127891i
\(801\) 24.5633 22.2368i 0.867900 0.785699i
\(802\) 5.86405 + 0.928774i 0.207067 + 0.0327961i
\(803\) −17.4953 + 8.91431i −0.617396 + 0.314579i
\(804\) 5.53722 + 4.97227i 0.195283 + 0.175358i
\(805\) 7.00975 + 1.19447i 0.247061 + 0.0420995i
\(806\) −5.88957 + 1.91364i −0.207451 + 0.0674050i
\(807\) 13.1704 5.07598i 0.463620 0.178683i
\(808\) 1.73723 + 0.885165i 0.0611157 + 0.0311400i
\(809\) −35.2216 25.5900i −1.23833 0.899696i −0.240840 0.970565i \(-0.577423\pi\)
−0.997486 + 0.0708691i \(0.977423\pi\)
\(810\) 14.8701 + 13.5602i 0.522482 + 0.476458i
\(811\) 9.88364 7.18088i 0.347062 0.252155i −0.400574 0.916265i \(-0.631189\pi\)
0.747635 + 0.664110i \(0.231189\pi\)
\(812\) −39.1478 + 6.20040i −1.37382 + 0.217591i
\(813\) 14.8356 + 3.95380i 0.520307 + 0.138666i
\(814\) 5.49253 + 7.55982i 0.192513 + 0.264972i
\(815\) −30.5715 + 41.0591i −1.07087 + 1.43824i
\(816\) 7.19884 4.16917i 0.252010 0.145950i
\(817\) −0.382675 + 0.751043i −0.0133881 + 0.0262757i
\(818\) 14.9137 + 14.9137i 0.521444 + 0.521444i
\(819\) 48.5248 + 27.8420i 1.69559 + 0.972879i
\(820\) −2.35998 + 13.8496i −0.0824140 + 0.483647i
\(821\) −9.18310 2.98377i −0.320492 0.104134i 0.144353 0.989526i \(-0.453890\pi\)
−0.464845 + 0.885392i \(0.653890\pi\)
\(822\) −7.43818 + 0.399852i −0.259436 + 0.0139464i
\(823\) −4.59608 + 29.0185i −0.160209 + 1.01152i 0.768267 + 0.640129i \(0.221119\pi\)
−0.928476 + 0.371392i \(0.878881\pi\)
\(824\) −3.45724 −0.120439
\(825\) −13.4340 17.3589i −0.467713 0.604358i
\(826\) 54.1195 1.88306
\(827\) 2.81343 17.7633i 0.0978325 0.617690i −0.889243 0.457435i \(-0.848768\pi\)
0.987076 0.160255i \(-0.0512317\pi\)
\(828\) −1.82599 0.695300i −0.0634574 0.0241634i
\(829\) −16.6482 5.40933i −0.578216 0.187874i 0.00528527 0.999986i \(-0.498318\pi\)
−0.583501 + 0.812112i \(0.698318\pi\)
\(830\) 17.5159 2.56454i 0.607985 0.0890165i
\(831\) 2.17777 20.9917i 0.0755459 0.728193i
\(832\) −2.70066 2.70066i −0.0936285 0.0936285i
\(833\) −36.7199 + 72.0669i −1.27227 + 2.49697i
\(834\) 2.55182 + 4.40618i 0.0883623 + 0.152574i
\(835\) 18.9102 5.90059i 0.654413 0.204198i
\(836\) −0.933612 1.28501i −0.0322897 0.0444429i
\(837\) −7.49131 + 3.85517i −0.258937 + 0.133254i
\(838\) 37.9387 6.00890i 1.31057 0.207574i
\(839\) −24.8896 + 18.0833i −0.859284 + 0.624306i −0.927690 0.373351i \(-0.878209\pi\)
0.0684060 + 0.997658i \(0.478209\pi\)
\(840\) 17.1949 + 7.87002i 0.593281 + 0.271541i
\(841\) −29.8502 21.6874i −1.02932 0.747843i
\(842\) −15.1346 7.71145i −0.521572 0.265754i
\(843\) −1.24240 3.22359i −0.0427905 0.111027i
\(844\) 10.3981 3.37856i 0.357919 0.116295i
\(845\) 1.64806 3.14304i 0.0566950 0.108124i
\(846\) −11.7594 + 5.27358i −0.404297 + 0.181309i
\(847\) −19.9075 + 10.1434i −0.684031 + 0.348531i
\(848\) −0.505679 0.0800917i −0.0173651 0.00275036i
\(849\) 1.46503 3.30247i 0.0502798 0.113340i
\(850\) 19.0928 + 14.5663i 0.654877 + 0.499619i
\(851\) 2.40120i 0.0823120i
\(852\) 0.907705 1.40187i 0.0310975 0.0480272i
\(853\) 18.7621 + 36.8228i 0.642403 + 1.26079i 0.950881 + 0.309556i \(0.100180\pi\)
−0.308478 + 0.951231i \(0.599820\pi\)
\(854\) 6.01242 18.5043i 0.205741 0.633205i
\(855\) −1.54183 + 3.91092i −0.0527296 + 0.133751i
\(856\) 3.39600 + 10.4518i 0.116073 + 0.357236i
\(857\) −9.23819 + 9.23819i −0.315570 + 0.315570i −0.847063 0.531493i \(-0.821631\pi\)
0.531493 + 0.847063i \(0.321631\pi\)
\(858\) 10.5692 + 13.0160i 0.360826 + 0.444360i
\(859\) −31.7094 + 43.6442i −1.08191 + 1.48912i −0.224508 + 0.974472i \(0.572078\pi\)
−0.857401 + 0.514649i \(0.827922\pi\)
\(860\) 0.962813 2.84936i 0.0328317 0.0971624i
\(861\) 11.1173 + 51.9590i 0.378877 + 1.77076i
\(862\) 4.09581 + 25.8599i 0.139504 + 0.880793i
\(863\) −5.91581 37.3509i −0.201376 1.27144i −0.856590 0.515997i \(-0.827422\pi\)
0.655214 0.755443i \(-0.272578\pi\)
\(864\) −4.21607 3.03723i −0.143433 0.103329i
\(865\) −30.0841 + 21.3241i −1.02289 + 0.725040i
\(866\) −16.7032 + 22.9900i −0.567599 + 0.781233i
\(867\) 8.15952 6.62564i 0.277112 0.225019i
\(868\) −5.59799 + 5.59799i −0.190008 + 0.190008i
\(869\) 0.114485 + 0.352348i 0.00388363 + 0.0119526i
\(870\) 10.9624 + 29.4666i 0.371661 + 0.999010i
\(871\) 5.07107 15.6072i 0.171827 0.528828i
\(872\) −8.08931 15.8762i −0.273939 0.537635i
\(873\) 38.1221 24.9029i 1.29024 0.842834i
\(874\) 0.408152i 0.0138059i
\(875\) −1.91574 + 54.5559i −0.0647638 + 1.84433i
\(876\) −12.2655 5.44122i −0.414414 0.183842i
\(877\) −23.3056 3.69125i −0.786976 0.124645i −0.250004 0.968245i \(-0.580432\pi\)
−0.536972 + 0.843600i \(0.680432\pi\)
\(878\) 36.1332 18.4108i 1.21944 0.621334i
\(879\) −23.1506 + 25.7810i −0.780850 + 0.869571i
\(880\) 3.96034 + 4.05412i 0.133503 + 0.136664i
\(881\) −1.56237 + 0.507643i −0.0526374 + 0.0171029i −0.335217 0.942141i \(-0.608810\pi\)
0.282580 + 0.959244i \(0.408810\pi\)
\(882\) 50.4582 + 2.50830i 1.69901 + 0.0844588i
\(883\) 41.1010 + 20.9420i 1.38316 + 0.704755i 0.977827 0.209415i \(-0.0671559\pi\)
0.405332 + 0.914170i \(0.367156\pi\)
\(884\) −14.8406 10.7823i −0.499143 0.362649i
\(885\) −8.49004 42.0805i −0.285390 1.41452i
\(886\) −5.57244 + 4.04861i −0.187210 + 0.136016i
\(887\) −41.9970 + 6.65167i −1.41012 + 0.223341i −0.814612 0.580007i \(-0.803050\pi\)
−0.595510 + 0.803348i \(0.703050\pi\)
\(888\) −1.64445 + 6.17036i −0.0551841 + 0.207064i
\(889\) −6.62246 9.11504i −0.222110 0.305708i
\(890\) −23.3966 7.90584i −0.784257 0.265004i
\(891\) 17.0339 + 15.1722i 0.570655 + 0.508287i
\(892\) 8.85983 17.3884i 0.296649 0.582207i
\(893\) −1.90364 1.90364i −0.0637029 0.0637029i
\(894\) −10.5039 1.08972i −0.351302 0.0364456i
\(895\) 6.26879 + 12.6674i 0.209543 + 0.423426i
\(896\) −4.64367 1.50882i −0.155134 0.0504061i
\(897\) 0.231276 + 4.30226i 0.00772207 + 0.143648i
\(898\) −5.98876 + 37.8116i −0.199848 + 1.26179i
\(899\) −13.1621 −0.438980
\(900\) 3.42185 14.6045i 0.114062 0.486816i
\(901\) −2.45903 −0.0819222
\(902\) −2.49117 + 15.7286i −0.0829468 + 0.523705i
\(903\) −0.610606 11.3587i −0.0203197 0.377994i
\(904\) 17.8479 + 5.79914i 0.593613 + 0.192877i
\(905\) −37.1387 19.4738i −1.23453 0.647329i
\(906\) 30.1047 + 3.12320i 1.00016 + 0.103761i
\(907\) −11.6182 11.6182i −0.385775 0.385775i 0.487403 0.873177i \(-0.337944\pi\)
−0.873177 + 0.487403i \(0.837944\pi\)
\(908\) 11.2338 22.0476i 0.372807 0.731674i
\(909\) −0.627059 5.81552i −0.0207982 0.192889i
\(910\) 0.487876 41.6960i 0.0161729 1.38221i
\(911\) −31.9965 44.0394i −1.06009 1.45909i −0.879720 0.475492i \(-0.842270\pi\)
−0.180371 0.983599i \(-0.557730\pi\)
\(912\) 0.279521 1.04883i 0.00925586 0.0347302i
\(913\) 19.8188 3.13899i 0.655906 0.103885i
\(914\) −28.9507 + 21.0339i −0.957605 + 0.695741i
\(915\) −15.3312 1.77206i −0.506834 0.0585827i
\(916\) −2.46523 1.79110i −0.0814536 0.0591795i
\(917\) 23.6073 + 12.0285i 0.779580 + 0.397216i
\(918\) −22.2823 11.2404i −0.735426 0.370987i
\(919\) 47.1407 15.3170i 1.55503 0.505260i 0.599555 0.800334i \(-0.295344\pi\)
0.955474 + 0.295074i \(0.0953443\pi\)
\(920\) 0.210977 + 1.44098i 0.00695570 + 0.0475076i
\(921\) 10.7994 12.0265i 0.355854 0.396287i
\(922\) −6.15653 + 3.13691i −0.202755 + 0.103309i
\(923\) −3.63731 0.576094i −0.119724 0.0189624i
\(924\) 19.5934 + 8.69197i 0.644575 + 0.285945i
\(925\) −18.2695 + 2.45691i −0.600699 + 0.0807827i
\(926\) 22.0536i 0.724728i
\(927\) 5.67222 + 8.68323i 0.186300 + 0.285195i
\(928\) −3.68535 7.23291i −0.120978 0.237432i
\(929\) −11.6949 + 35.9932i −0.383697 + 1.18090i 0.553723 + 0.832701i \(0.313206\pi\)
−0.937421 + 0.348198i \(0.886794\pi\)
\(930\) 5.23089 + 3.47451i 0.171528 + 0.113934i
\(931\) 3.26116 + 10.0368i 0.106880 + 0.328944i
\(932\) −13.0971 + 13.0971i −0.429010 + 0.429010i
\(933\) 10.5261 8.54733i 0.344609 0.279827i
\(934\) 2.66218 3.66418i 0.0871092 0.119896i
\(935\) 21.8332 + 16.2564i 0.714023 + 0.531642i
\(936\) −2.35208 + 11.2139i −0.0768800 + 0.366538i
\(937\) 4.74297 + 29.9460i 0.154946 + 0.978292i 0.935532 + 0.353243i \(0.114921\pi\)
−0.780586 + 0.625049i \(0.785079\pi\)
\(938\) −3.28186 20.7208i −0.107156 0.676559i
\(939\) 1.03662 + 4.84488i 0.0338290 + 0.158107i
\(940\) 7.70480 + 5.73678i 0.251303 + 0.187113i
\(941\) −18.8958 + 26.0078i −0.615984 + 0.847829i −0.997053 0.0767174i \(-0.975556\pi\)
0.381069 + 0.924547i \(0.375556\pi\)
\(942\) −2.51653 3.09912i −0.0819929 0.100975i
\(943\) −2.89354 + 2.89354i −0.0942265 + 0.0942265i
\(944\) 3.42517 + 10.5416i 0.111480 + 0.343099i
\(945\) −8.44497 56.0991i −0.274715 1.82490i
\(946\) 1.05348 3.24228i 0.0342516 0.105416i
\(947\) −7.77062 15.2507i −0.252511 0.495581i 0.729602 0.683872i \(-0.239705\pi\)
−0.982113 + 0.188291i \(0.939705\pi\)
\(948\) −0.137604 + 0.212516i −0.00446916 + 0.00690220i
\(949\) 29.5884i 0.960480i
\(950\) 3.10543 0.417622i 0.100753 0.0135494i
\(951\) −17.9629 + 40.4919i −0.582488 + 1.31304i
\(952\) −23.1624 3.66856i −0.750697 0.118899i
\(953\) 20.7106 10.5526i 0.670882 0.341831i −0.0851482 0.996368i \(-0.527136\pi\)
0.756030 + 0.654537i \(0.227136\pi\)
\(954\) 0.628499 + 1.40147i 0.0203484 + 0.0453743i
\(955\) 5.09003 + 34.7650i 0.164709 + 1.12497i
\(956\) −12.7051 + 4.12814i −0.410912 + 0.133513i
\(957\) 12.8158 + 33.2525i 0.414275 + 1.07490i
\(958\) 32.8918 + 16.7592i 1.06269 + 0.541466i
\(959\) 16.9881 + 12.3426i 0.548575 + 0.398563i
\(960\) −0.444700 + 3.84737i −0.0143526 + 0.124173i
\(961\) 22.9527 16.6761i 0.740408 0.537938i
\(962\) 13.9077 2.20276i 0.448402 0.0710198i
\(963\) 20.6791 25.6775i 0.666375 0.827447i
\(964\) −3.00113 4.13071i −0.0966600 0.133041i
\(965\) 0.0678938 5.80251i 0.00218558 0.186789i
\(966\) 2.76041 + 4.76635i 0.0888147 + 0.153355i
\(967\) −11.0422 + 21.6716i −0.355094 + 0.696912i −0.997591 0.0693770i \(-0.977899\pi\)
0.642496 + 0.766289i \(0.277899\pi\)
\(968\) −3.23569 3.23569i −0.103999 0.103999i
\(969\) 0.537964 5.18547i 0.0172819 0.166581i
\(970\) −30.0583 15.7611i −0.965114 0.506060i
\(971\) 5.98620 + 1.94504i 0.192106 + 0.0624192i 0.403490 0.914984i \(-0.367797\pi\)
−0.211384 + 0.977403i \(0.567797\pi\)
\(972\) −0.711119 + 15.5722i −0.0228091 + 0.499479i
\(973\) 2.24541 14.1770i 0.0719846 0.454493i
\(974\) 34.3914 1.10197
\(975\) −32.4972 + 6.16175i −1.04074 + 0.197334i
\(976\) 3.98485 0.127552
\(977\) 2.22604 14.0547i 0.0712173 0.449649i −0.926151 0.377152i \(-0.876903\pi\)
0.997369 0.0724964i \(-0.0230966\pi\)
\(978\) −39.5948 + 2.12849i −1.26610 + 0.0680615i
\(979\) −26.6230 8.65033i −0.850874 0.276466i
\(980\) −16.7016 33.7492i −0.533514 1.07808i
\(981\) −26.6027 + 46.3649i −0.849360 + 1.48032i
\(982\) −11.7430 11.7430i −0.374733 0.374733i
\(983\) −7.65935 + 15.0323i −0.244295 + 0.479457i −0.980299 0.197521i \(-0.936711\pi\)
0.736003 + 0.676978i \(0.236711\pi\)
\(984\) −9.41715 + 5.45390i −0.300208 + 0.173864i
\(985\) −12.2932 4.15393i −0.391693 0.132355i
\(986\) −22.9171 31.5427i −0.729830 1.00452i
\(987\) 35.1052 + 9.35581i 1.11741 + 0.297799i
\(988\) −2.36401 + 0.374422i −0.0752090 + 0.0119119i
\(989\) 0.708722 0.514916i 0.0225360 0.0163734i
\(990\) 3.68470 16.5983i 0.117107 0.527530i
\(991\) 24.1908 + 17.5757i 0.768447 + 0.558310i 0.901490 0.432801i \(-0.142475\pi\)
−0.133042 + 0.991110i \(0.542475\pi\)
\(992\) −1.44469 0.736104i −0.0458688 0.0233713i
\(993\) 51.6729 19.9151i 1.63979 0.631988i
\(994\) −4.47751 + 1.45483i −0.142018 + 0.0461445i
\(995\) −6.03761 6.18058i −0.191405 0.195937i
\(996\) 10.2026 + 9.16167i 0.323283 + 0.290299i
\(997\) −12.5490 + 6.39403i −0.397431 + 0.202501i −0.641271 0.767314i \(-0.721593\pi\)
0.243841 + 0.969815i \(0.421593\pi\)
\(998\) 23.3584 + 3.69960i 0.739396 + 0.117109i
\(999\) 18.1955 5.99337i 0.575681 0.189622i
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 150.2.l.a.77.3 80
3.2 odd 2 inner 150.2.l.a.77.7 yes 80
5.2 odd 4 750.2.l.a.593.1 80
5.3 odd 4 750.2.l.c.593.10 80
5.4 even 2 750.2.l.b.407.8 80
15.2 even 4 750.2.l.a.593.8 80
15.8 even 4 750.2.l.c.593.3 80
15.14 odd 2 750.2.l.b.407.4 80
25.9 even 10 750.2.l.a.707.8 80
25.12 odd 20 750.2.l.b.293.4 80
25.13 odd 20 inner 150.2.l.a.113.7 yes 80
25.16 even 5 750.2.l.c.707.3 80
75.38 even 20 inner 150.2.l.a.113.3 yes 80
75.41 odd 10 750.2.l.c.707.10 80
75.59 odd 10 750.2.l.a.707.1 80
75.62 even 20 750.2.l.b.293.8 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.77.3 80 1.1 even 1 trivial
150.2.l.a.77.7 yes 80 3.2 odd 2 inner
150.2.l.a.113.3 yes 80 75.38 even 20 inner
150.2.l.a.113.7 yes 80 25.13 odd 20 inner
750.2.l.a.593.1 80 5.2 odd 4
750.2.l.a.593.8 80 15.2 even 4
750.2.l.a.707.1 80 75.59 odd 10
750.2.l.a.707.8 80 25.9 even 10
750.2.l.b.293.4 80 25.12 odd 20
750.2.l.b.293.8 80 75.62 even 20
750.2.l.b.407.4 80 15.14 odd 2
750.2.l.b.407.8 80 5.4 even 2
750.2.l.c.593.3 80 15.8 even 4
750.2.l.c.593.10 80 5.3 odd 4
750.2.l.c.707.3 80 25.16 even 5
750.2.l.c.707.10 80 75.41 odd 10