Properties

Label 731.2.j.a.509.6
Level $731$
Weight $2$
Character 731.509
Analytic conductor $5.837$
Analytic rank $0$
Dimension $128$
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] = [731,2,Mod(135,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.135");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.j (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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 509.6
Character \(\chi\) \(=\) 731.509
Dual form 731.2.j.a.135.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.51145 q^{2} +(1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(-1.18626 + 0.684888i) q^{5} +(-4.42321 + 2.55374i) q^{6} +(-3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 - 0.983681i) q^{9} +O(q^{10})\) \(q-2.51145 q^{2} +(1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(-1.18626 + 0.684888i) q^{5} +(-4.42321 + 2.55374i) q^{6} +(-3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 - 0.983681i) q^{9} +(2.97923 - 1.72006i) q^{10} -5.71903i q^{11} +(7.58623 - 4.37991i) q^{12} +(-0.967741 + 1.67618i) q^{13} +(9.65264 + 5.57296i) q^{14} +(-1.39284 + 2.41247i) q^{15} +5.93872 q^{16} +(1.23567 - 3.93359i) q^{17} +(-1.42632 + 2.47046i) q^{18} +(3.28388 + 5.68786i) q^{19} +(-5.10967 + 2.95007i) q^{20} -9.02556 q^{21} +14.3631i q^{22} +(-3.56220 + 2.05664i) q^{23} +(-10.2060 + 5.89244i) q^{24} +(-1.56186 + 2.70522i) q^{25} +(2.43043 - 4.20963i) q^{26} +3.79107i q^{27} +(-16.5552 - 9.55815i) q^{28} +(1.60279 + 0.925373i) q^{29} +(3.49805 - 6.05880i) q^{30} +(-7.10692 + 4.10318i) q^{31} -3.32510 q^{32} +(-5.81534 - 10.0725i) q^{33} +(-3.10332 + 9.87901i) q^{34} +6.07912 q^{35} +(2.44628 - 4.23708i) q^{36} +(0.467527 - 0.269927i) q^{37} +(-8.24731 - 14.2848i) q^{38} +3.93615i q^{39} +(6.87420 - 3.96882i) q^{40} +3.51693i q^{41} +22.6672 q^{42} +(4.98908 + 4.25548i) q^{43} -24.6340i q^{44} +1.55587i q^{45} +(8.94629 - 5.16514i) q^{46} -10.7488 q^{47} +(10.4594 - 6.03873i) q^{48} +(6.34810 + 10.9952i) q^{49} +(3.92253 - 6.79401i) q^{50} +(-1.82355 - 8.18439i) q^{51} +(-4.16842 + 7.21992i) q^{52} +(-2.08650 - 3.61392i) q^{53} -9.52108i q^{54} +(3.91689 + 6.78426i) q^{55} +(22.2723 + 12.8589i) q^{56} +(11.5673 + 6.67837i) q^{57} +(-4.02533 - 2.32403i) q^{58} -6.09785 q^{59} +(-5.99949 + 10.3914i) q^{60} +(1.58893 + 0.917368i) q^{61} +(17.8487 - 10.3049i) q^{62} +(-4.36561 + 2.52049i) q^{63} -3.52664 q^{64} -2.65118i q^{65} +(14.6049 + 25.2965i) q^{66} +(-7.10904 - 12.3132i) q^{67} +(5.32249 - 16.9434i) q^{68} +(-4.18255 + 7.24438i) q^{69} -15.2674 q^{70} +(-4.83502 - 2.79150i) q^{71} +(-3.29106 + 5.70028i) q^{72} +(-5.46456 - 3.15496i) q^{73} +(-1.17417 + 0.677908i) q^{74} +6.35264i q^{75} +(14.1449 + 24.4997i) q^{76} +(-12.6906 + 21.9808i) q^{77} -9.88544i q^{78} +(-11.6828 - 6.74508i) q^{79} +(-7.04487 + 4.06736i) q^{80} +(5.55870 + 9.62795i) q^{81} -8.83259i q^{82} +(-4.69845 - 8.13795i) q^{83} -38.8765 q^{84} +(1.22824 + 5.51255i) q^{85} +(-12.5298 - 10.6874i) q^{86} +3.76383 q^{87} +33.1409i q^{88} +(8.13518 + 14.0905i) q^{89} -3.90748i q^{90} +(7.43894 - 4.29487i) q^{91} +(-15.3437 + 8.85871i) q^{92} +(-8.34456 + 14.4532i) q^{93} +26.9951 q^{94} +(-7.79108 - 4.49818i) q^{95} +(-5.85622 + 3.38109i) q^{96} +18.8175i q^{97} +(-15.9429 - 27.6140i) q^{98} +(-5.62570 - 3.24800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9} + 4 q^{13} - 12 q^{15} + 76 q^{16} + 2 q^{17} - 16 q^{18} - 2 q^{19} - 20 q^{21} + 60 q^{25} - 2 q^{26} - 28 q^{30} - 48 q^{32} + 22 q^{33} - 18 q^{34} - 112 q^{35} + 36 q^{36} - 40 q^{38} + 36 q^{42} + 10 q^{43} + 36 q^{47} + 52 q^{49} + 16 q^{50} + 10 q^{51} + 10 q^{52} + 24 q^{55} - 12 q^{59} - 78 q^{60} + 36 q^{64} + 14 q^{66} + 10 q^{67} - q^{68} - 64 q^{70} - 68 q^{72} - 22 q^{76} - 28 q^{77} - 20 q^{81} - 6 q^{83} + 32 q^{84} + 6 q^{85} - 58 q^{86} + 32 q^{87} + 36 q^{89} + 6 q^{93} + 132 q^{94} - 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51145 −1.77586 −0.887931 0.459976i \(-0.847858\pi\)
−0.887931 + 0.459976i \(0.847858\pi\)
\(3\) 1.76122 1.01684i 1.01684 0.587073i 0.103653 0.994614i \(-0.466947\pi\)
0.913187 + 0.407540i \(0.133613\pi\)
\(4\) 4.30737 2.15369
\(5\) −1.18626 + 0.684888i −0.530512 + 0.306291i −0.741225 0.671257i \(-0.765755\pi\)
0.210713 + 0.977548i \(0.432421\pi\)
\(6\) −4.42321 + 2.55374i −1.80577 + 1.04256i
\(7\) −3.84346 2.21902i −1.45269 0.838711i −0.454056 0.890973i \(-0.650024\pi\)
−0.998633 + 0.0522621i \(0.983357\pi\)
\(8\) −5.79485 −2.04879
\(9\) 0.567928 0.983681i 0.189309 0.327894i
\(10\) 2.97923 1.72006i 0.942116 0.543931i
\(11\) 5.71903i 1.72435i −0.506608 0.862176i \(-0.669101\pi\)
0.506608 0.862176i \(-0.330899\pi\)
\(12\) 7.58623 4.37991i 2.18996 1.26437i
\(13\) −0.967741 + 1.67618i −0.268403 + 0.464888i −0.968450 0.249210i \(-0.919829\pi\)
0.700047 + 0.714097i \(0.253163\pi\)
\(14\) 9.65264 + 5.57296i 2.57978 + 1.48944i
\(15\) −1.39284 + 2.41247i −0.359630 + 0.622898i
\(16\) 5.93872 1.48468
\(17\) 1.23567 3.93359i 0.299694 0.954035i
\(18\) −1.42632 + 2.47046i −0.336187 + 0.582294i
\(19\) 3.28388 + 5.68786i 0.753375 + 1.30488i 0.946178 + 0.323646i \(0.104909\pi\)
−0.192803 + 0.981237i \(0.561758\pi\)
\(20\) −5.10967 + 2.95007i −1.14256 + 0.659655i
\(21\) −9.02556 −1.96954
\(22\) 14.3631i 3.06221i
\(23\) −3.56220 + 2.05664i −0.742771 + 0.428839i −0.823076 0.567932i \(-0.807744\pi\)
0.0803052 + 0.996770i \(0.474410\pi\)
\(24\) −10.2060 + 5.89244i −2.08329 + 1.20279i
\(25\) −1.56186 + 2.70522i −0.312372 + 0.541043i
\(26\) 2.43043 4.20963i 0.476647 0.825577i
\(27\) 3.79107i 0.729592i
\(28\) −16.5552 9.55815i −3.12864 1.80632i
\(29\) 1.60279 + 0.925373i 0.297631 + 0.171837i 0.641378 0.767225i \(-0.278363\pi\)
−0.343747 + 0.939062i \(0.611696\pi\)
\(30\) 3.49805 6.05880i 0.638654 1.10618i
\(31\) −7.10692 + 4.10318i −1.27644 + 0.736953i −0.976192 0.216908i \(-0.930403\pi\)
−0.300248 + 0.953861i \(0.597070\pi\)
\(32\) −3.32510 −0.587800
\(33\) −5.81534 10.0725i −1.01232 1.75339i
\(34\) −3.10332 + 9.87901i −0.532215 + 1.69424i
\(35\) 6.07912 1.02756
\(36\) 2.44628 4.23708i 0.407713 0.706180i
\(37\) 0.467527 0.269927i 0.0768610 0.0443757i −0.461077 0.887360i \(-0.652537\pi\)
0.537938 + 0.842984i \(0.319203\pi\)
\(38\) −8.24731 14.2848i −1.33789 2.31729i
\(39\) 3.93615i 0.630289i
\(40\) 6.87420 3.96882i 1.08691 0.627526i
\(41\) 3.51693i 0.549253i 0.961551 + 0.274626i \(0.0885541\pi\)
−0.961551 + 0.274626i \(0.911446\pi\)
\(42\) 22.6672 3.49763
\(43\) 4.98908 + 4.25548i 0.760827 + 0.648955i
\(44\) 24.6340i 3.71372i
\(45\) 1.55587i 0.231935i
\(46\) 8.94629 5.16514i 1.31906 0.761559i
\(47\) −10.7488 −1.56788 −0.783939 0.620838i \(-0.786793\pi\)
−0.783939 + 0.620838i \(0.786793\pi\)
\(48\) 10.4594 6.03873i 1.50968 0.871616i
\(49\) 6.34810 + 10.9952i 0.906872 + 1.57075i
\(50\) 3.92253 6.79401i 0.554729 0.960819i
\(51\) −1.82355 8.18439i −0.255348 1.14604i
\(52\) −4.16842 + 7.21992i −0.578056 + 1.00122i
\(53\) −2.08650 3.61392i −0.286603 0.496411i 0.686394 0.727230i \(-0.259193\pi\)
−0.972997 + 0.230819i \(0.925859\pi\)
\(54\) 9.52108i 1.29566i
\(55\) 3.91689 + 6.78426i 0.528154 + 0.914789i
\(56\) 22.2723 + 12.8589i 2.97626 + 1.71834i
\(57\) 11.5673 + 6.67837i 1.53212 + 0.884572i
\(58\) −4.02533 2.32403i −0.528552 0.305160i
\(59\) −6.09785 −0.793872 −0.396936 0.917846i \(-0.629927\pi\)
−0.396936 + 0.917846i \(0.629927\pi\)
\(60\) −5.99949 + 10.3914i −0.774531 + 1.34153i
\(61\) 1.58893 + 0.917368i 0.203441 + 0.117457i 0.598260 0.801302i \(-0.295859\pi\)
−0.394818 + 0.918759i \(0.629192\pi\)
\(62\) 17.8487 10.3049i 2.26678 1.30873i
\(63\) −4.36561 + 2.52049i −0.550016 + 0.317552i
\(64\) −3.52664 −0.440830
\(65\) 2.65118i 0.328838i
\(66\) 14.6049 + 25.2965i 1.79774 + 3.11378i
\(67\) −7.10904 12.3132i −0.868508 1.50430i −0.863522 0.504312i \(-0.831746\pi\)
−0.00498622 0.999988i \(-0.501587\pi\)
\(68\) 5.32249 16.9434i 0.645447 2.05469i
\(69\) −4.18255 + 7.24438i −0.503519 + 0.872121i
\(70\) −15.2674 −1.82480
\(71\) −4.83502 2.79150i −0.573811 0.331290i 0.184859 0.982765i \(-0.440817\pi\)
−0.758670 + 0.651475i \(0.774151\pi\)
\(72\) −3.29106 + 5.70028i −0.387855 + 0.671785i
\(73\) −5.46456 3.15496i −0.639578 0.369261i 0.144874 0.989450i \(-0.453722\pi\)
−0.784452 + 0.620190i \(0.787056\pi\)
\(74\) −1.17417 + 0.677908i −0.136495 + 0.0788052i
\(75\) 6.35264i 0.733540i
\(76\) 14.1449 + 24.4997i 1.62253 + 2.81031i
\(77\) −12.6906 + 21.9808i −1.44623 + 2.50495i
\(78\) 9.88544i 1.11931i
\(79\) −11.6828 6.74508i −1.31442 0.758880i −0.331595 0.943422i \(-0.607587\pi\)
−0.982825 + 0.184541i \(0.940920\pi\)
\(80\) −7.04487 + 4.06736i −0.787641 + 0.454744i
\(81\) 5.55870 + 9.62795i 0.617633 + 1.06977i
\(82\) 8.83259i 0.975397i
\(83\) −4.69845 8.13795i −0.515722 0.893257i −0.999833 0.0182503i \(-0.994190\pi\)
0.484112 0.875006i \(-0.339143\pi\)
\(84\) −38.8765 −4.24177
\(85\) 1.22824 + 5.51255i 0.133221 + 0.597920i
\(86\) −12.5298 10.6874i −1.35112 1.15245i
\(87\) 3.76383 0.403525
\(88\) 33.1409i 3.53284i
\(89\) 8.13518 + 14.0905i 0.862327 + 1.49359i 0.869677 + 0.493621i \(0.164327\pi\)
−0.00734982 + 0.999973i \(0.502340\pi\)
\(90\) 3.90748i 0.411885i
\(91\) 7.43894 4.29487i 0.779813 0.450225i
\(92\) −15.3437 + 8.85871i −1.59970 + 0.923585i
\(93\) −8.34456 + 14.4532i −0.865291 + 1.49873i
\(94\) 26.9951 2.78434
\(95\) −7.79108 4.49818i −0.799348 0.461504i
\(96\) −5.85622 + 3.38109i −0.597698 + 0.345081i
\(97\) 18.8175i 1.91063i 0.295585 + 0.955316i \(0.404485\pi\)
−0.295585 + 0.955316i \(0.595515\pi\)
\(98\) −15.9429 27.6140i −1.61048 2.78943i
\(99\) −5.62570 3.24800i −0.565404 0.326436i
\(100\) −6.72751 + 11.6524i −0.672751 + 1.16524i
\(101\) −0.223258 + 0.386694i −0.0222150 + 0.0384775i −0.876919 0.480638i \(-0.840405\pi\)
0.854704 + 0.519115i \(0.173739\pi\)
\(102\) 4.57974 + 20.5547i 0.453462 + 2.03522i
\(103\) −1.22446 + 2.12083i −0.120650 + 0.208971i −0.920024 0.391862i \(-0.871831\pi\)
0.799374 + 0.600833i \(0.205164\pi\)
\(104\) 5.60792 9.71319i 0.549901 0.952457i
\(105\) 10.7067 6.18149i 1.04486 0.603252i
\(106\) 5.24014 + 9.07619i 0.508967 + 0.881557i
\(107\) 4.76103i 0.460266i −0.973159 0.230133i \(-0.926084\pi\)
0.973159 0.230133i \(-0.0739161\pi\)
\(108\) 16.3296i 1.57131i
\(109\) 9.19461 5.30851i 0.880684 0.508463i 0.00980034 0.999952i \(-0.496880\pi\)
0.870884 + 0.491489i \(0.163547\pi\)
\(110\) −9.83708 17.0383i −0.937928 1.62454i
\(111\) 0.548945 0.950801i 0.0521036 0.0902460i
\(112\) −22.8252 13.1781i −2.15678 1.24522i
\(113\) 10.9962i 1.03443i −0.855854 0.517217i \(-0.826968\pi\)
0.855854 0.517217i \(-0.173032\pi\)
\(114\) −29.0506 16.7724i −2.72084 1.57088i
\(115\) 2.81713 4.87942i 0.262699 0.455008i
\(116\) 6.90383 + 3.98593i 0.641004 + 0.370084i
\(117\) 1.09921 + 1.90390i 0.101622 + 0.176015i
\(118\) 15.3144 1.40981
\(119\) −13.4780 + 12.3766i −1.23552 + 1.13456i
\(120\) 8.07132 13.9799i 0.736807 1.27619i
\(121\) −21.7073 −1.97339
\(122\) −3.99051 2.30392i −0.361284 0.208587i
\(123\) 3.57616 + 6.19409i 0.322451 + 0.558502i
\(124\) −30.6122 + 17.6739i −2.74905 + 1.58717i
\(125\) 11.1277i 0.995289i
\(126\) 10.9640 6.33008i 0.976752 0.563928i
\(127\) −4.14740 −0.368022 −0.184011 0.982924i \(-0.558908\pi\)
−0.184011 + 0.982924i \(0.558908\pi\)
\(128\) 15.5072 1.37065
\(129\) 13.1140 + 2.42174i 1.15462 + 0.213222i
\(130\) 6.65829i 0.583971i
\(131\) 5.10448i 0.445981i 0.974821 + 0.222990i \(0.0715819\pi\)
−0.974821 + 0.222990i \(0.928418\pi\)
\(132\) −25.0489 43.3859i −2.18022 3.77626i
\(133\) 29.1480i 2.52745i
\(134\) 17.8540 + 30.9240i 1.54235 + 2.67143i
\(135\) −2.59646 4.49720i −0.223468 0.387057i
\(136\) −7.16052 + 22.7946i −0.614010 + 1.95462i
\(137\) −8.15290 −0.696549 −0.348275 0.937393i \(-0.613232\pi\)
−0.348275 + 0.937393i \(0.613232\pi\)
\(138\) 10.5042 18.1939i 0.894181 1.54877i
\(139\) 11.7337 6.77447i 0.995242 0.574603i 0.0884048 0.996085i \(-0.471823\pi\)
0.906837 + 0.421482i \(0.138490\pi\)
\(140\) 26.1850 2.21304
\(141\) −18.9310 + 10.9298i −1.59428 + 0.920459i
\(142\) 12.1429 + 7.01071i 1.01901 + 0.588325i
\(143\) 9.58611 + 5.53454i 0.801630 + 0.462822i
\(144\) 3.37277 5.84181i 0.281064 0.486817i
\(145\) −2.53511 −0.210529
\(146\) 13.7240 + 7.92353i 1.13580 + 0.655756i
\(147\) 22.3608 + 12.9100i 1.84429 + 1.06480i
\(148\) 2.01381 1.16268i 0.165535 0.0955714i
\(149\) 0.586861 + 1.01647i 0.0480775 + 0.0832727i 0.889063 0.457785i \(-0.151357\pi\)
−0.840985 + 0.541058i \(0.818024\pi\)
\(150\) 15.9543i 1.30267i
\(151\) 4.37075 0.355687 0.177843 0.984059i \(-0.443088\pi\)
0.177843 + 0.984059i \(0.443088\pi\)
\(152\) −19.0296 32.9603i −1.54351 2.67343i
\(153\) −3.16762 3.44950i −0.256087 0.278876i
\(154\) 31.8719 55.2038i 2.56831 4.44845i
\(155\) 5.62044 9.73488i 0.451444 0.781924i
\(156\) 16.9545i 1.35744i
\(157\) 4.38370 7.59279i 0.349857 0.605971i −0.636367 0.771387i \(-0.719563\pi\)
0.986224 + 0.165416i \(0.0528967\pi\)
\(158\) 29.3408 + 16.9399i 2.33423 + 1.34767i
\(159\) −7.34957 4.24328i −0.582859 0.336514i
\(160\) 3.94443 2.27732i 0.311835 0.180038i
\(161\) 18.2549 1.43869
\(162\) −13.9604 24.1801i −1.09683 1.89977i
\(163\) −3.58760 2.07130i −0.281003 0.162237i 0.352875 0.935671i \(-0.385204\pi\)
−0.633877 + 0.773434i \(0.718538\pi\)
\(164\) 15.1487i 1.18292i
\(165\) 13.7970 + 7.96571i 1.07410 + 0.620130i
\(166\) 11.7999 + 20.4381i 0.915851 + 1.58630i
\(167\) −2.80154 + 1.61747i −0.216790 + 0.125164i −0.604463 0.796633i \(-0.706612\pi\)
0.387673 + 0.921797i \(0.373279\pi\)
\(168\) 52.3018 4.03517
\(169\) 4.62696 + 8.01412i 0.355920 + 0.616471i
\(170\) −3.08466 13.8445i −0.236583 1.06182i
\(171\) 7.46004 0.570484
\(172\) 21.4898 + 18.3300i 1.63858 + 1.39765i
\(173\) 7.13873i 0.542748i 0.962474 + 0.271374i \(0.0874780\pi\)
−0.962474 + 0.271374i \(0.912522\pi\)
\(174\) −9.45266 −0.716604
\(175\) 12.0059 6.93159i 0.907558 0.523979i
\(176\) 33.9637i 2.56011i
\(177\) −10.7396 + 6.20054i −0.807241 + 0.466061i
\(178\) −20.4311 35.3877i −1.53137 2.65242i
\(179\) 2.57082 4.45279i 0.192152 0.332817i −0.753811 0.657091i \(-0.771787\pi\)
0.945963 + 0.324274i \(0.105120\pi\)
\(180\) 6.70171i 0.499516i
\(181\) 11.0474 + 6.37822i 0.821147 + 0.474089i 0.850812 0.525470i \(-0.176111\pi\)
−0.0296649 + 0.999560i \(0.509444\pi\)
\(182\) −18.6825 + 10.7864i −1.38484 + 0.799538i
\(183\) 3.73127 0.275823
\(184\) 20.6424 11.9179i 1.52178 0.878600i
\(185\) −0.369739 + 0.640407i −0.0271838 + 0.0470837i
\(186\) 20.9569 36.2985i 1.53664 2.66153i
\(187\) −22.4963 7.06683i −1.64509 0.516778i
\(188\) −46.2992 −3.37672
\(189\) 8.41247 14.5708i 0.611917 1.05987i
\(190\) 19.5669 + 11.2970i 1.41953 + 0.819567i
\(191\) 2.78150 + 4.81770i 0.201262 + 0.348597i 0.948935 0.315470i \(-0.102162\pi\)
−0.747673 + 0.664067i \(0.768829\pi\)
\(192\) −6.21118 + 3.58603i −0.448254 + 0.258799i
\(193\) 0.578350i 0.0416306i 0.999783 + 0.0208153i \(0.00662619\pi\)
−0.999783 + 0.0208153i \(0.993374\pi\)
\(194\) 47.2593i 3.39302i
\(195\) −2.69582 4.66930i −0.193052 0.334376i
\(196\) 27.3437 + 47.3606i 1.95312 + 3.38290i
\(197\) −5.49896 3.17483i −0.391785 0.226197i 0.291148 0.956678i \(-0.405963\pi\)
−0.682933 + 0.730481i \(0.739296\pi\)
\(198\) 14.1287 + 8.15718i 1.00408 + 0.579706i
\(199\) 10.0023i 0.709042i 0.935048 + 0.354521i \(0.115356\pi\)
−0.935048 + 0.354521i \(0.884644\pi\)
\(200\) 9.05074 15.6763i 0.639984 1.10848i
\(201\) −25.0412 14.4575i −1.76627 1.01975i
\(202\) 0.560701 0.971163i 0.0394508 0.0683308i
\(203\) −4.10684 7.11326i −0.288244 0.499253i
\(204\) −7.85470 35.2532i −0.549939 2.46822i
\(205\) −2.40870 4.17200i −0.168231 0.291385i
\(206\) 3.07517 5.32635i 0.214257 0.371104i
\(207\) 4.67209i 0.324733i
\(208\) −5.74715 + 9.95435i −0.398493 + 0.690210i
\(209\) 32.5290 18.7806i 2.25008 1.29908i
\(210\) −26.8892 + 15.5245i −1.85553 + 1.07129i
\(211\) 13.1262i 0.903642i −0.892109 0.451821i \(-0.850775\pi\)
0.892109 0.451821i \(-0.149225\pi\)
\(212\) −8.98734 15.5665i −0.617253 1.06911i
\(213\) −11.3540 −0.777966
\(214\) 11.9571i 0.817369i
\(215\) −8.83287 1.63115i −0.602397 0.111244i
\(216\) 21.9687i 1.49478i
\(217\) 36.4202 2.47236
\(218\) −23.0918 + 13.3321i −1.56397 + 0.902961i
\(219\) −12.8324 −0.867132
\(220\) 16.8715 + 29.2223i 1.13748 + 1.97017i
\(221\) 5.39758 + 5.87790i 0.363081 + 0.395390i
\(222\) −1.37865 + 2.38789i −0.0925288 + 0.160265i
\(223\) −13.2886 −0.889872 −0.444936 0.895562i \(-0.646774\pi\)
−0.444936 + 0.895562i \(0.646774\pi\)
\(224\) 12.7799 + 7.37846i 0.853890 + 0.492994i
\(225\) 1.77405 + 3.07274i 0.118270 + 0.204849i
\(226\) 27.6163i 1.83701i
\(227\) 3.39154 1.95811i 0.225105 0.129964i −0.383207 0.923662i \(-0.625180\pi\)
0.608312 + 0.793698i \(0.291847\pi\)
\(228\) 49.8246 + 28.7662i 3.29971 + 1.90509i
\(229\) 2.79328 4.83811i 0.184585 0.319711i −0.758851 0.651264i \(-0.774239\pi\)
0.943437 + 0.331553i \(0.107572\pi\)
\(230\) −7.07508 + 12.2544i −0.466517 + 0.808031i
\(231\) 51.6174i 3.39618i
\(232\) −9.28795 5.36240i −0.609784 0.352059i
\(233\) −9.70656 5.60409i −0.635898 0.367136i 0.147135 0.989116i \(-0.452995\pi\)
−0.783033 + 0.621981i \(0.786328\pi\)
\(234\) −2.76062 4.78154i −0.180467 0.312579i
\(235\) 12.7509 7.36174i 0.831778 0.480227i
\(236\) −26.2657 −1.70975
\(237\) −27.4347 −1.78207
\(238\) 33.8492 31.0832i 2.19412 2.01482i
\(239\) −13.4872 23.3605i −0.872413 1.51106i −0.859493 0.511148i \(-0.829221\pi\)
−0.0129202 0.999917i \(-0.504113\pi\)
\(240\) −8.27171 + 14.3270i −0.533936 + 0.924805i
\(241\) 5.97009 + 3.44683i 0.384567 + 0.222030i 0.679804 0.733394i \(-0.262065\pi\)
−0.295236 + 0.955424i \(0.595398\pi\)
\(242\) 54.5168 3.50447
\(243\) 9.73068 + 5.61801i 0.624223 + 0.360396i
\(244\) 6.84411 + 3.95145i 0.438149 + 0.252965i
\(245\) −15.0610 8.69547i −0.962212 0.555533i
\(246\) −8.98134 15.5561i −0.572629 0.991823i
\(247\) −12.7118 −0.808832
\(248\) 41.1835 23.7773i 2.61516 1.50986i
\(249\) −16.5500 9.55515i −1.04881 0.605533i
\(250\) 27.9466i 1.76750i
\(251\) −12.1298 + 21.0095i −0.765629 + 1.32611i 0.174284 + 0.984695i \(0.444239\pi\)
−0.939913 + 0.341413i \(0.889094\pi\)
\(252\) −18.8043 + 10.8567i −1.18456 + 0.683907i
\(253\) 11.7620 + 20.3723i 0.739469 + 1.28080i
\(254\) 10.4160 0.653556
\(255\) 7.76859 + 8.45989i 0.486488 + 0.529779i
\(256\) −31.8922 −1.99326
\(257\) 1.53014 0.0954475 0.0477237 0.998861i \(-0.484803\pi\)
0.0477237 + 0.998861i \(0.484803\pi\)
\(258\) −32.9351 6.08208i −2.05045 0.378654i
\(259\) −2.39589 −0.148874
\(260\) 11.4196i 0.708214i
\(261\) 1.82054 1.05109i 0.112689 0.0650609i
\(262\) 12.8196i 0.792001i
\(263\) 6.75217 + 11.6951i 0.416357 + 0.721151i 0.995570 0.0940254i \(-0.0299735\pi\)
−0.579213 + 0.815176i \(0.696640\pi\)
\(264\) 33.6990 + 58.3684i 2.07403 + 3.59233i
\(265\) 4.95026 + 2.85804i 0.304092 + 0.175568i
\(266\) 73.2038i 4.48841i
\(267\) 28.6557 + 16.5444i 1.75370 + 1.01250i
\(268\) −30.6213 53.0377i −1.87049 3.23979i
\(269\) 9.71634i 0.592416i −0.955124 0.296208i \(-0.904278\pi\)
0.955124 0.296208i \(-0.0957221\pi\)
\(270\) 6.52087 + 11.2945i 0.396848 + 0.687360i
\(271\) 14.0264 24.2944i 0.852042 1.47578i −0.0273211 0.999627i \(-0.508698\pi\)
0.879363 0.476153i \(-0.157969\pi\)
\(272\) 7.33830 23.3605i 0.444950 1.41644i
\(273\) 8.73440 15.1284i 0.528630 0.915614i
\(274\) 20.4756 1.23698
\(275\) 15.4712 + 8.93231i 0.932950 + 0.538639i
\(276\) −18.0158 + 31.2043i −1.08442 + 1.87828i
\(277\) −19.5223 + 11.2712i −1.17298 + 0.677222i −0.954381 0.298593i \(-0.903483\pi\)
−0.218601 + 0.975814i \(0.570149\pi\)
\(278\) −29.4687 + 17.0137i −1.76741 + 1.02042i
\(279\) 9.32125i 0.558049i
\(280\) −35.2276 −2.10525
\(281\) −7.71795 13.3679i −0.460414 0.797461i 0.538567 0.842582i \(-0.318966\pi\)
−0.998981 + 0.0451218i \(0.985632\pi\)
\(282\) 47.5444 27.4497i 2.83123 1.63461i
\(283\) −25.7997 14.8955i −1.53364 0.885445i −0.999190 0.0402423i \(-0.987187\pi\)
−0.534446 0.845203i \(-0.679480\pi\)
\(284\) −20.8262 12.0240i −1.23581 0.713495i
\(285\) −18.2957 −1.08375
\(286\) −24.0750 13.8997i −1.42359 0.821907i
\(287\) 7.80414 13.5172i 0.460664 0.797894i
\(288\) −1.88842 + 3.27083i −0.111276 + 0.192736i
\(289\) −13.9462 9.72123i −0.820367 0.571837i
\(290\) 6.36679 0.373871
\(291\) 19.1344 + 33.1418i 1.12168 + 1.94281i
\(292\) −23.5379 13.5896i −1.37745 0.795272i
\(293\) −14.1121 −0.824440 −0.412220 0.911084i \(-0.635247\pi\)
−0.412220 + 0.911084i \(0.635247\pi\)
\(294\) −56.1580 32.4228i −3.27520 1.89094i
\(295\) 7.23363 4.17634i 0.421158 0.243156i
\(296\) −2.70925 + 1.56419i −0.157472 + 0.0909165i
\(297\) 21.6813 1.25807
\(298\) −1.47387 2.55282i −0.0853791 0.147881i
\(299\) 7.96117i 0.460407i
\(300\) 27.3632i 1.57982i
\(301\) −9.73229 27.4266i −0.560960 1.58084i
\(302\) −10.9769 −0.631650
\(303\) 0.908071i 0.0521673i
\(304\) 19.5021 + 33.7786i 1.11852 + 1.93734i
\(305\) −2.51318 −0.143904
\(306\) 7.95532 + 8.66324i 0.454776 + 0.495245i
\(307\) 8.07909 + 13.9934i 0.461098 + 0.798646i 0.999016 0.0443517i \(-0.0141222\pi\)
−0.537918 + 0.842997i \(0.680789\pi\)
\(308\) −54.6634 + 94.6797i −3.11473 + 5.39488i
\(309\) 4.98032i 0.283320i
\(310\) −14.1154 + 24.4487i −0.801703 + 1.38859i
\(311\) −15.8950 + 9.17695i −0.901320 + 0.520377i −0.877628 0.479342i \(-0.840875\pi\)
−0.0236918 + 0.999719i \(0.507542\pi\)
\(312\) 22.8094i 1.29133i
\(313\) 2.33614 1.34877i 0.132046 0.0762370i −0.432522 0.901624i \(-0.642376\pi\)
0.564568 + 0.825387i \(0.309043\pi\)
\(314\) −11.0094 + 19.0689i −0.621298 + 1.07612i
\(315\) 3.45250 5.97991i 0.194527 0.336930i
\(316\) −50.3223 29.0536i −2.83085 1.63439i
\(317\) 14.9707i 0.840835i −0.907331 0.420418i \(-0.861884\pi\)
0.907331 0.420418i \(-0.138116\pi\)
\(318\) 18.4581 + 10.6568i 1.03508 + 0.597602i
\(319\) 5.29224 9.16642i 0.296308 0.513221i
\(320\) 4.18351 2.41535i 0.233865 0.135022i
\(321\) −4.84121 8.38521i −0.270210 0.468017i
\(322\) −45.8462 −2.55491
\(323\) 26.4315 5.88914i 1.47069 0.327681i
\(324\) 23.9434 + 41.4712i 1.33019 + 2.30395i
\(325\) −3.02295 5.23590i −0.167683 0.290435i
\(326\) 9.01007 + 5.20197i 0.499022 + 0.288110i
\(327\) 10.7958 18.6989i 0.597010 1.03405i
\(328\) 20.3801i 1.12530i
\(329\) 41.3127 + 23.8519i 2.27764 + 1.31500i
\(330\) −34.6505 20.0055i −1.90745 1.10126i
\(331\) 2.62803 4.55188i 0.144449 0.250194i −0.784718 0.619853i \(-0.787192\pi\)
0.929167 + 0.369659i \(0.120526\pi\)
\(332\) −20.2380 35.0532i −1.11070 1.92380i
\(333\) 0.613196i 0.0336030i
\(334\) 7.03593 4.06219i 0.384989 0.222273i
\(335\) 16.8663 + 9.73779i 0.921507 + 0.532032i
\(336\) −53.6003 −2.92414
\(337\) 19.8729 + 11.4736i 1.08255 + 0.625008i 0.931582 0.363531i \(-0.118429\pi\)
0.150964 + 0.988539i \(0.451762\pi\)
\(338\) −11.6204 20.1271i −0.632064 1.09477i
\(339\) −11.1814 19.3667i −0.607288 1.05185i
\(340\) 5.29049 + 23.7446i 0.286917 + 1.28773i
\(341\) 23.4662 + 40.6447i 1.27077 + 2.20103i
\(342\) −18.7355 −1.01310
\(343\) 25.2800i 1.36499i
\(344\) −28.9110 24.6599i −1.55877 1.32957i
\(345\) 11.4583i 0.616894i
\(346\) 17.9286i 0.963846i
\(347\) 12.0411 6.95194i 0.646401 0.373200i −0.140675 0.990056i \(-0.544927\pi\)
0.787076 + 0.616856i \(0.211594\pi\)
\(348\) 16.2122 0.869066
\(349\) −14.8500 25.7210i −0.794905 1.37682i −0.922900 0.385041i \(-0.874187\pi\)
0.127995 0.991775i \(-0.459146\pi\)
\(350\) −30.1521 + 17.4083i −1.61170 + 0.930514i
\(351\) −6.35451 3.66878i −0.339178 0.195825i
\(352\) 19.0163i 1.01357i
\(353\) 2.32936 4.03456i 0.123979 0.214738i −0.797354 0.603511i \(-0.793768\pi\)
0.921333 + 0.388773i \(0.127101\pi\)
\(354\) 26.9721 15.5723i 1.43355 0.827660i
\(355\) 7.64745 0.405885
\(356\) 35.0413 + 60.6932i 1.85718 + 3.21673i
\(357\) −11.1526 + 35.5028i −0.590259 + 1.87901i
\(358\) −6.45649 + 11.1830i −0.341236 + 0.591038i
\(359\) 1.62902 2.82155i 0.0859766 0.148916i −0.819830 0.572606i \(-0.805932\pi\)
0.905807 + 0.423691i \(0.139266\pi\)
\(360\) 9.01603i 0.475186i
\(361\) −12.0678 + 20.9020i −0.635147 + 1.10011i
\(362\) −27.7450 16.0186i −1.45824 0.841918i
\(363\) −38.2313 + 22.0729i −2.00662 + 1.15853i
\(364\) 32.0423 18.4996i 1.67947 0.969644i
\(365\) 8.64318 0.452405
\(366\) −9.37088 −0.489824
\(367\) −20.2158 + 11.6716i −1.05526 + 0.609253i −0.924117 0.382111i \(-0.875197\pi\)
−0.131141 + 0.991364i \(0.541864\pi\)
\(368\) −21.1549 + 12.2138i −1.10278 + 0.636689i
\(369\) 3.45954 + 1.99737i 0.180096 + 0.103979i
\(370\) 0.928581 1.60835i 0.0482746 0.0836141i
\(371\) 18.5199i 0.961508i
\(372\) −35.9431 + 62.2554i −1.86357 + 3.22779i
\(373\) −1.92466 + 3.33361i −0.0996550 + 0.172608i −0.911542 0.411207i \(-0.865107\pi\)
0.811887 + 0.583815i \(0.198441\pi\)
\(374\) 56.4983 + 17.7480i 2.92146 + 0.917727i
\(375\) −11.3151 19.5983i −0.584307 1.01205i
\(376\) 62.2879 3.21225
\(377\) −3.10218 + 1.79104i −0.159770 + 0.0922434i
\(378\) −21.1275 + 36.5939i −1.08668 + 1.88219i
\(379\) 0.0120364i 0.000618270i −1.00000 0.000309135i \(-0.999902\pi\)
1.00000 0.000309135i \(-9.84007e-5\pi\)
\(380\) −33.5591 19.3754i −1.72155 0.993935i
\(381\) −7.30447 + 4.21724i −0.374220 + 0.216056i
\(382\) −6.98560 12.0994i −0.357414 0.619060i
\(383\) 34.3781 1.75664 0.878320 0.478073i \(-0.158665\pi\)
0.878320 + 0.478073i \(0.158665\pi\)
\(384\) 27.3115 15.7683i 1.39373 0.804673i
\(385\) 34.7667i 1.77187i
\(386\) 1.45250i 0.0739302i
\(387\) 7.01947 2.49085i 0.356820 0.126617i
\(388\) 81.0542i 4.11490i
\(389\) 22.0169 1.11630 0.558150 0.829740i \(-0.311512\pi\)
0.558150 + 0.829740i \(0.311512\pi\)
\(390\) 6.77042 + 11.7267i 0.342833 + 0.593805i
\(391\) 3.68826 + 16.5536i 0.186524 + 0.837150i
\(392\) −36.7863 63.7158i −1.85799 3.21813i
\(393\) 5.19044 + 8.99011i 0.261823 + 0.453491i
\(394\) 13.8104 + 7.97341i 0.695756 + 0.401695i
\(395\) 18.4785 0.929753
\(396\) −24.2320 13.9903i −1.21770 0.703042i
\(397\) 17.7075 10.2234i 0.888715 0.513100i 0.0151930 0.999885i \(-0.495164\pi\)
0.873522 + 0.486785i \(0.161830\pi\)
\(398\) 25.1202i 1.25916i
\(399\) −29.6389 51.3361i −1.48380 2.57002i
\(400\) −9.27544 + 16.0655i −0.463772 + 0.803277i
\(401\) −1.42805 0.824485i −0.0713134 0.0411728i 0.463919 0.885877i \(-0.346443\pi\)
−0.535233 + 0.844705i \(0.679776\pi\)
\(402\) 62.8896 + 36.3093i 3.13665 + 1.81094i
\(403\) 15.8833i 0.791202i
\(404\) −0.961656 + 1.66564i −0.0478442 + 0.0828686i
\(405\) −13.1881 7.61417i −0.655323 0.378351i
\(406\) 10.3141 + 17.8646i 0.511881 + 0.886605i
\(407\) −1.54372 2.67380i −0.0765194 0.132535i
\(408\) 10.5672 + 47.4273i 0.523153 + 2.34800i
\(409\) −30.2220 −1.49438 −0.747191 0.664609i \(-0.768598\pi\)
−0.747191 + 0.664609i \(0.768598\pi\)
\(410\) 6.04933 + 10.4778i 0.298755 + 0.517459i
\(411\) −14.3590 + 8.29020i −0.708280 + 0.408925i
\(412\) −5.27421 + 9.13519i −0.259841 + 0.450059i
\(413\) 23.4368 + 13.5312i 1.15325 + 0.665829i
\(414\) 11.7337i 0.576681i
\(415\) 11.1472 + 6.43582i 0.547193 + 0.315922i
\(416\) 3.21783 5.57345i 0.157767 0.273261i
\(417\) 13.7771 23.8627i 0.674668 1.16856i
\(418\) −81.6950 + 47.1666i −3.99583 + 2.30699i
\(419\) 4.37648i 0.213805i 0.994270 + 0.106902i \(0.0340933\pi\)
−0.994270 + 0.106902i \(0.965907\pi\)
\(420\) 46.1176 26.6260i 2.25031 1.29922i
\(421\) 4.11951 7.13520i 0.200773 0.347749i −0.748005 0.663693i \(-0.768988\pi\)
0.948778 + 0.315945i \(0.102321\pi\)
\(422\) 32.9657i 1.60474i
\(423\) −6.10457 + 10.5734i −0.296814 + 0.514097i
\(424\) 12.0910 + 20.9422i 0.587189 + 1.01704i
\(425\) 8.71127 + 9.48646i 0.422559 + 0.460161i
\(426\) 28.5151 1.38156
\(427\) −4.07132 7.05173i −0.197025 0.341257i
\(428\) 20.5075i 0.991269i
\(429\) 22.5110 1.08684
\(430\) 22.1833 + 4.09655i 1.06977 + 0.197553i
\(431\) 15.6456i 0.753621i 0.926290 + 0.376810i \(0.122979\pi\)
−0.926290 + 0.376810i \(0.877021\pi\)
\(432\) 22.5141i 1.08321i
\(433\) −14.9478 25.8904i −0.718347 1.24421i −0.961654 0.274265i \(-0.911566\pi\)
0.243307 0.969949i \(-0.421768\pi\)
\(434\) −91.4674 −4.39058
\(435\) −4.46488 + 2.57780i −0.214074 + 0.123596i
\(436\) 39.6046 22.8658i 1.89672 1.09507i
\(437\) −23.3957 13.5075i −1.11917 0.646153i
\(438\) 32.2279 1.53991
\(439\) 8.11746 + 4.68662i 0.387425 + 0.223680i 0.681044 0.732242i \(-0.261526\pi\)
−0.293619 + 0.955923i \(0.594860\pi\)
\(440\) −22.6978 39.3138i −1.08208 1.87421i
\(441\) 14.4211 0.686718
\(442\) −13.5557 14.7620i −0.644781 0.702158i
\(443\) 0.638830 1.10649i 0.0303517 0.0525707i −0.850451 0.526055i \(-0.823671\pi\)
0.880802 + 0.473484i \(0.157004\pi\)
\(444\) 2.36451 4.09545i 0.112215 0.194362i
\(445\) −19.3009 11.1434i −0.914949 0.528246i
\(446\) 33.3737 1.58029
\(447\) 2.06718 + 1.19349i 0.0977743 + 0.0564500i
\(448\) 13.5545 + 7.82568i 0.640389 + 0.369729i
\(449\) −18.8811 + 10.9010i −0.891057 + 0.514452i −0.874288 0.485408i \(-0.838671\pi\)
−0.0167686 + 0.999859i \(0.505338\pi\)
\(450\) −4.45543 7.71703i −0.210031 0.363784i
\(451\) 20.1134 0.947105
\(452\) 47.3647i 2.22785i
\(453\) 7.69785 4.44436i 0.361676 0.208814i
\(454\) −8.51768 + 4.91769i −0.399755 + 0.230798i
\(455\) −5.88301 + 10.1897i −0.275800 + 0.477699i
\(456\) −67.0307 38.7002i −3.13900 1.81230i
\(457\) −27.1570 −1.27035 −0.635175 0.772368i \(-0.719072\pi\)
−0.635175 + 0.772368i \(0.719072\pi\)
\(458\) −7.01519 + 12.1507i −0.327798 + 0.567763i
\(459\) 14.9125 + 4.68451i 0.696057 + 0.218654i
\(460\) 12.1344 21.0175i 0.565771 0.979945i
\(461\) −0.901498 1.56144i −0.0419869 0.0727235i 0.844268 0.535921i \(-0.180035\pi\)
−0.886255 + 0.463197i \(0.846702\pi\)
\(462\) 129.635i 6.03115i
\(463\) −14.8320 25.6897i −0.689301 1.19390i −0.972064 0.234714i \(-0.924585\pi\)
0.282764 0.959190i \(-0.408749\pi\)
\(464\) 9.51855 + 5.49553i 0.441887 + 0.255124i
\(465\) 22.8603i 1.06012i
\(466\) 24.3775 + 14.0744i 1.12927 + 0.651983i
\(467\) −10.2978 17.8363i −0.476524 0.825363i 0.523114 0.852262i \(-0.324770\pi\)
−0.999638 + 0.0268992i \(0.991437\pi\)
\(468\) 4.73473 + 8.20079i 0.218863 + 0.379082i
\(469\) 63.1004i 2.91371i
\(470\) −32.0233 + 18.4886i −1.47712 + 0.852817i
\(471\) 17.8301i 0.821567i
\(472\) 35.3361 1.62648
\(473\) 24.3372 28.5327i 1.11903 1.31193i
\(474\) 68.9008 3.16472
\(475\) −20.5158 −0.941332
\(476\) −58.0546 + 53.3106i −2.66093 + 2.44349i
\(477\) −4.73993 −0.217027
\(478\) 33.8724 + 58.6687i 1.54929 + 2.68344i
\(479\) −19.3025 + 11.1443i −0.881952 + 0.509195i −0.871302 0.490748i \(-0.836724\pi\)
−0.0106505 + 0.999943i \(0.503390\pi\)
\(480\) 4.63134 8.02171i 0.211391 0.366139i
\(481\) 1.04488i 0.0476423i
\(482\) −14.9936 8.65654i −0.682939 0.394295i
\(483\) 32.1509 18.5623i 1.46291 0.844614i
\(484\) −93.5015 −4.25007
\(485\) −12.8879 22.3225i −0.585210 1.01361i
\(486\) −24.4381 14.1093i −1.10853 0.640013i
\(487\) 19.8836 + 11.4798i 0.901010 + 0.520198i 0.877528 0.479526i \(-0.159191\pi\)
0.0234821 + 0.999724i \(0.492525\pi\)
\(488\) −9.20760 5.31601i −0.416808 0.240644i
\(489\) −8.42473 −0.380980
\(490\) 37.8249 + 21.8382i 1.70876 + 0.986551i
\(491\) −3.40750 + 5.90197i −0.153778 + 0.266352i −0.932614 0.360877i \(-0.882478\pi\)
0.778835 + 0.627229i \(0.215811\pi\)
\(492\) 15.4039 + 26.6803i 0.694459 + 1.20284i
\(493\) 5.62056 5.16127i 0.253137 0.232452i
\(494\) 31.9250 1.43637
\(495\) 8.89806 0.399938
\(496\) −42.2060 + 24.3677i −1.89511 + 1.09414i
\(497\) 12.3888 + 21.4580i 0.555713 + 0.962523i
\(498\) 41.5645 + 23.9973i 1.86255 + 1.07534i
\(499\) −5.83929 3.37132i −0.261403 0.150921i 0.363572 0.931566i \(-0.381557\pi\)
−0.624974 + 0.780645i \(0.714891\pi\)
\(500\) 47.9310i 2.14354i
\(501\) −3.28942 + 5.69744i −0.146960 + 0.254543i
\(502\) 30.4635 52.7643i 1.35965 2.35499i
\(503\) −13.2162 7.63037i −0.589281 0.340221i 0.175532 0.984474i \(-0.443835\pi\)
−0.764813 + 0.644252i \(0.777169\pi\)
\(504\) 25.2981 14.6059i 1.12687 0.650597i
\(505\) 0.611627i 0.0272170i
\(506\) −29.5396 51.1641i −1.31320 2.27452i
\(507\) 16.2982 + 9.40975i 0.723827 + 0.417902i
\(508\) −17.8644 −0.792604
\(509\) −5.14392 + 8.90953i −0.228000 + 0.394908i −0.957215 0.289376i \(-0.906552\pi\)
0.729215 + 0.684285i \(0.239885\pi\)
\(510\) −19.5104 21.2466i −0.863935 0.940814i
\(511\) 14.0019 + 24.2519i 0.619406 + 1.07284i
\(512\) 49.0812 2.16910
\(513\) −21.5631 + 12.4494i −0.952033 + 0.549656i
\(514\) −3.84287 −0.169502
\(515\) 3.35447i 0.147816i
\(516\) 56.4869 + 10.4313i 2.48670 + 0.459214i
\(517\) 61.4729i 2.70358i
\(518\) 6.01716 0.264379
\(519\) 7.25895 + 12.5729i 0.318633 + 0.551888i
\(520\) 15.3632i 0.673719i
\(521\) −18.6103 + 10.7447i −0.815334 + 0.470733i −0.848805 0.528707i \(-0.822677\pi\)
0.0334709 + 0.999440i \(0.489344\pi\)
\(522\) −4.57220 + 2.63976i −0.200120 + 0.115539i
\(523\) 14.3812 24.9090i 0.628846 1.08919i −0.358937 0.933362i \(-0.616861\pi\)
0.987784 0.155832i \(-0.0498058\pi\)
\(524\) 21.9869i 0.960503i
\(525\) 14.0966 24.4161i 0.615228 1.06561i
\(526\) −16.9577 29.3716i −0.739392 1.28066i
\(527\) 7.35842 + 33.0259i 0.320538 + 1.43863i
\(528\) −34.5357 59.8176i −1.50297 2.60323i
\(529\) −3.04048 + 5.26626i −0.132195 + 0.228968i
\(530\) −12.4323 7.17781i −0.540026 0.311784i
\(531\) −3.46314 + 5.99833i −0.150287 + 0.260306i
\(532\) 125.551i 5.44335i
\(533\) −5.89500 3.40348i −0.255341 0.147421i
\(534\) −71.9672 41.5503i −3.11433 1.79806i
\(535\) 3.26077 + 5.64782i 0.140975 + 0.244176i
\(536\) 41.1958 + 71.3533i 1.77939 + 3.08199i
\(537\) 10.4565i 0.451230i
\(538\) 24.4021i 1.05205i
\(539\) 62.8821 36.3050i 2.70852 1.56377i
\(540\) −11.1839 19.3711i −0.481279 0.833600i
\(541\) 4.91450 + 2.83739i 0.211291 + 0.121989i 0.601911 0.798563i \(-0.294406\pi\)
−0.390620 + 0.920552i \(0.627739\pi\)
\(542\) −35.2265 + 61.0141i −1.51311 + 2.62078i
\(543\) 25.9425 1.11330
\(544\) −4.10872 + 13.0796i −0.176160 + 0.560782i
\(545\) −7.27147 + 12.5946i −0.311476 + 0.539491i
\(546\) −21.9360 + 37.9943i −0.938774 + 1.62600i
\(547\) 23.2117 13.4013i 0.992460 0.572997i 0.0864512 0.996256i \(-0.472447\pi\)
0.906009 + 0.423259i \(0.139114\pi\)
\(548\) −35.1176 −1.50015
\(549\) 1.80479 1.04200i 0.0770267 0.0444714i
\(550\) −38.8552 22.4330i −1.65679 0.956548i
\(551\) 12.1553i 0.517832i
\(552\) 24.2372 41.9801i 1.03161 1.78679i
\(553\) 29.9349 + 51.8488i 1.27296 + 2.20484i
\(554\) 49.0293 28.3071i 2.08305 1.20265i
\(555\) 1.50386i 0.0638354i
\(556\) 50.5416 29.1802i 2.14344 1.23752i
\(557\) −4.61019 −0.195340 −0.0976699 0.995219i \(-0.531139\pi\)
−0.0976699 + 0.995219i \(0.531139\pi\)
\(558\) 23.4098i 0.991018i
\(559\) −11.9611 + 4.24437i −0.505899 + 0.179518i
\(560\) 36.1022 1.52560
\(561\) −46.8068 + 10.4289i −1.97618 + 0.440309i
\(562\) 19.3832 + 33.5727i 0.817632 + 1.41618i
\(563\) 22.1779 0.934688 0.467344 0.884076i \(-0.345211\pi\)
0.467344 + 0.884076i \(0.345211\pi\)
\(564\) −81.5431 + 47.0789i −3.43358 + 1.98238i
\(565\) 7.53115 + 13.0443i 0.316838 + 0.548779i
\(566\) 64.7947 + 37.4093i 2.72353 + 1.57243i
\(567\) 49.3395i 2.07206i
\(568\) 28.0182 + 16.1763i 1.17562 + 0.678744i
\(569\) −20.3358 35.2226i −0.852519 1.47661i −0.878928 0.476955i \(-0.841740\pi\)
0.0264086 0.999651i \(-0.491593\pi\)
\(570\) 45.9488 1.92458
\(571\) −39.4525 + 22.7779i −1.65103 + 0.953225i −0.674386 + 0.738379i \(0.735592\pi\)
−0.976648 + 0.214846i \(0.931075\pi\)
\(572\) 41.2909 + 23.8393i 1.72646 + 0.996773i
\(573\) 9.79767 + 5.65669i 0.409303 + 0.236311i
\(574\) −19.5997 + 33.9477i −0.818076 + 1.41695i
\(575\) 12.8487i 0.535828i
\(576\) −2.00288 + 3.46909i −0.0834532 + 0.144545i
\(577\) −8.81635 + 15.2704i −0.367030 + 0.635714i −0.989100 0.147248i \(-0.952959\pi\)
0.622070 + 0.782962i \(0.286292\pi\)
\(578\) 35.0253 + 24.4144i 1.45686 + 1.01550i
\(579\) 0.588090 + 1.01860i 0.0244402 + 0.0423316i
\(580\) −10.9196 −0.453414
\(581\) 41.7038i 1.73017i
\(582\) −48.0552 83.2340i −1.99195 3.45016i
\(583\) −20.6681 + 11.9328i −0.855987 + 0.494204i
\(584\) 31.6663 + 18.2825i 1.31036 + 0.756537i
\(585\) −2.60791 1.50568i −0.107824 0.0622521i
\(586\) 35.4419 1.46409
\(587\) −15.6017 + 27.0230i −0.643953 + 1.11536i 0.340590 + 0.940212i \(0.389373\pi\)
−0.984542 + 0.175147i \(0.943960\pi\)
\(588\) 96.3163 + 55.6083i 3.97202 + 2.29325i
\(589\) −46.6766 26.9487i −1.92328 1.11040i
\(590\) −18.1669 + 10.4887i −0.747919 + 0.431811i
\(591\) −12.9132 −0.531177
\(592\) 2.77651 1.60302i 0.114114 0.0658838i
\(593\) −11.3200 + 19.6068i −0.464855 + 0.805153i −0.999195 0.0401168i \(-0.987227\pi\)
0.534340 + 0.845270i \(0.320560\pi\)
\(594\) −54.4514 −2.23417
\(595\) 7.51178 23.9127i 0.307953 0.980327i
\(596\) 2.52783 + 4.37833i 0.103544 + 0.179343i
\(597\) 10.1707 + 17.6162i 0.416259 + 0.720982i
\(598\) 19.9941i 0.817619i
\(599\) 0.0513591 + 0.0889565i 0.00209848 + 0.00363467i 0.867073 0.498182i \(-0.165999\pi\)
−0.864974 + 0.501816i \(0.832665\pi\)
\(600\) 36.8126i 1.50287i
\(601\) 16.2904i 0.664500i −0.943191 0.332250i \(-0.892192\pi\)
0.943191 0.332250i \(-0.107808\pi\)
\(602\) 24.4422 + 68.8805i 0.996188 + 2.80736i
\(603\) −16.1497 −0.657667
\(604\) 18.8265 0.766038
\(605\) 25.7505 14.8671i 1.04691 0.604432i
\(606\) 2.28057i 0.0926420i
\(607\) −31.4586 + 18.1626i −1.27686 + 0.737198i −0.976271 0.216554i \(-0.930518\pi\)
−0.300594 + 0.953752i \(0.597185\pi\)
\(608\) −10.9192 18.9127i −0.442833 0.767010i
\(609\) −14.4661 8.35201i −0.586196 0.338440i
\(610\) 6.31171 0.255554
\(611\) 10.4021 18.0169i 0.420823 0.728887i
\(612\) −13.6441 14.8583i −0.551532 0.600611i
\(613\) 28.5802 1.15434 0.577171 0.816623i \(-0.304156\pi\)
0.577171 + 0.816623i \(0.304156\pi\)
\(614\) −20.2902 35.1437i −0.818847 1.41828i
\(615\) −8.48451 4.89853i −0.342128 0.197528i
\(616\) 73.5404 127.376i 2.96303 5.13211i
\(617\) −6.79067 3.92060i −0.273382 0.157837i 0.357042 0.934089i \(-0.383785\pi\)
−0.630424 + 0.776251i \(0.717119\pi\)
\(618\) 12.5078i 0.503138i
\(619\) −31.9910 18.4700i −1.28583 0.742372i −0.307919 0.951413i \(-0.599633\pi\)
−0.977907 + 0.209041i \(0.932966\pi\)
\(620\) 24.2093 41.9318i 0.972270 1.68402i
\(621\) −7.79687 13.5046i −0.312877 0.541920i
\(622\) 39.9194 23.0474i 1.60062 0.924119i
\(623\) 72.2085i 2.89297i
\(624\) 23.3757i 0.935778i
\(625\) −0.188091 0.325782i −0.00752362 0.0130313i
\(626\) −5.86710 + 3.38737i −0.234496 + 0.135386i
\(627\) 38.1938 66.1536i 1.52531 2.64192i
\(628\) 18.8822 32.7050i 0.753483 1.30507i
\(629\) −0.484072 2.17260i −0.0193012 0.0866272i
\(630\) −8.67078 + 15.0182i −0.345452 + 0.598341i
\(631\) −3.32085 + 5.75188i −0.132201 + 0.228979i −0.924525 0.381122i \(-0.875538\pi\)
0.792324 + 0.610101i \(0.208871\pi\)
\(632\) 67.7002 + 39.0867i 2.69297 + 1.55479i
\(633\) −13.3472 23.1180i −0.530504 0.918859i
\(634\) 37.5980i 1.49321i
\(635\) 4.91989 2.84050i 0.195240 0.112722i
\(636\) −31.6573 18.2774i −1.25530 0.724745i
\(637\) −24.5733 −0.973629
\(638\) −13.2912 + 23.0210i −0.526203 + 0.911410i
\(639\) −5.49189 + 3.17074i −0.217256 + 0.125433i
\(640\) −18.3955 + 10.6207i −0.727147 + 0.419819i
\(641\) 25.1134i 0.991919i −0.868346 0.495960i \(-0.834816\pi\)
0.868346 0.495960i \(-0.165184\pi\)
\(642\) 12.1584 + 21.0590i 0.479855 + 0.831134i
\(643\) 3.42114i 0.134916i 0.997722 + 0.0674582i \(0.0214889\pi\)
−0.997722 + 0.0674582i \(0.978511\pi\)
\(644\) 78.6306 3.09848
\(645\) −17.2152 + 6.10880i −0.677849 + 0.240534i
\(646\) −66.3813 + 14.7903i −2.61174 + 0.581916i
\(647\) −13.7238 −0.539537 −0.269769 0.962925i \(-0.586947\pi\)
−0.269769 + 0.962925i \(0.586947\pi\)
\(648\) −32.2118 55.7925i −1.26540 2.19174i
\(649\) 34.8738i 1.36892i
\(650\) 7.59198 + 13.1497i 0.297782 + 0.515773i
\(651\) 64.1439 37.0335i 2.51400 1.45146i
\(652\) −15.4531 8.92187i −0.605192 0.349408i
\(653\) 20.9825i 0.821110i −0.911836 0.410555i \(-0.865335\pi\)
0.911836 0.410555i \(-0.134665\pi\)
\(654\) −27.1131 + 46.9613i −1.06021 + 1.83633i
\(655\) −3.49600 6.05525i −0.136600 0.236598i
\(656\) 20.8861i 0.815465i
\(657\) −6.20695 + 3.58359i −0.242156 + 0.139809i
\(658\) −103.755 59.9028i −4.04478 2.33525i
\(659\) −7.21480 + 12.4964i −0.281049 + 0.486790i −0.971643 0.236452i \(-0.924016\pi\)
0.690595 + 0.723242i \(0.257349\pi\)
\(660\) 59.4289 + 34.3113i 2.31327 + 1.33557i
\(661\) 37.9604 1.47649 0.738245 0.674533i \(-0.235655\pi\)
0.738245 + 0.674533i \(0.235655\pi\)
\(662\) −6.60016 + 11.4318i −0.256522 + 0.444310i
\(663\) 15.4832 + 4.86378i 0.601318 + 0.188894i
\(664\) 27.2268 + 47.1582i 1.05661 + 1.83009i
\(665\) 19.9631 + 34.5771i 0.774137 + 1.34084i
\(666\) 1.54001i 0.0596742i
\(667\) −7.61263 −0.294762
\(668\) −12.0673 + 6.96705i −0.466897 + 0.269563i
\(669\) −23.4042 + 13.5124i −0.904857 + 0.522420i
\(670\) −42.3590 24.4560i −1.63647 0.944816i
\(671\) 5.24646 9.08713i 0.202537 0.350805i
\(672\) 30.0108 1.15769
\(673\) 15.4260 + 8.90621i 0.594629 + 0.343309i 0.766926 0.641736i \(-0.221785\pi\)
−0.172297 + 0.985045i \(0.555119\pi\)
\(674\) −49.9098 28.8154i −1.92245 1.10993i
\(675\) −10.2557 5.92112i −0.394741 0.227904i
\(676\) 19.9300 + 34.5198i 0.766539 + 1.32769i
\(677\) 16.4685i 0.632936i 0.948603 + 0.316468i \(0.102497\pi\)
−0.948603 + 0.316468i \(0.897503\pi\)
\(678\) 28.0814 + 48.6384i 1.07846 + 1.86795i
\(679\) 41.7565 72.3244i 1.60247 2.77556i
\(680\) −7.11747 31.9444i −0.272943 1.22501i
\(681\) 3.98217 6.89731i 0.152597 0.264306i
\(682\) −58.9342 102.077i −2.25671 3.90873i
\(683\) 9.20879 5.31670i 0.352365 0.203438i −0.313362 0.949634i \(-0.601455\pi\)
0.665726 + 0.746196i \(0.268122\pi\)
\(684\) 32.1332 1.22864
\(685\) 9.67146 5.58382i 0.369528 0.213347i
\(686\) 63.4894i 2.42404i
\(687\) 11.3613i 0.433460i
\(688\) 29.6287 + 25.2721i 1.12959 + 0.963491i
\(689\) 8.07677 0.307700
\(690\) 28.7769i 1.09552i
\(691\) 8.97676 5.18273i 0.341492 0.197160i −0.319440 0.947607i \(-0.603495\pi\)
0.660932 + 0.750446i \(0.270161\pi\)
\(692\) 30.7492i 1.16891i
\(693\) 14.4148 + 24.9671i 0.547571 + 0.948421i
\(694\) −30.2407 + 17.4594i −1.14792 + 0.662752i
\(695\) −9.27950 + 16.0726i −0.351992 + 0.609667i
\(696\) −21.8108 −0.826737
\(697\) 13.8342 + 4.34577i 0.524006 + 0.164608i
\(698\) 37.2951 + 64.5971i 1.41164 + 2.44503i
\(699\) −22.7938 −0.862142
\(700\) 51.7138 29.8569i 1.95460 1.12849i
\(701\) 10.6373 18.4243i 0.401765 0.695877i −0.592174 0.805810i \(-0.701730\pi\)
0.993939 + 0.109933i \(0.0350636\pi\)
\(702\) 15.9590 + 9.21394i 0.602334 + 0.347758i
\(703\) 3.07061 + 1.77282i 0.115810 + 0.0668631i
\(704\) 20.1690i 0.760146i
\(705\) 14.9714 25.9313i 0.563857 0.976629i
\(706\) −5.85006 + 10.1326i −0.220170 + 0.381345i
\(707\) 1.71617 0.990828i 0.0645430 0.0372639i
\(708\) −46.2597 + 26.7080i −1.73854 + 1.00375i
\(709\) 45.3238i 1.70217i 0.525027 + 0.851086i \(0.324055\pi\)
−0.525027 + 0.851086i \(0.675945\pi\)
\(710\) −19.2062 −0.720795
\(711\) −13.2700 + 7.66144i −0.497664 + 0.287326i
\(712\) −47.1421 81.6526i −1.76673 3.06006i
\(713\) 16.8775 29.2327i 0.632068 1.09477i
\(714\) 28.0092 89.1635i 1.04822 3.33686i
\(715\) −15.1622 −0.567032
\(716\) 11.0735 19.1798i 0.413836 0.716785i
\(717\) −47.5078 27.4286i −1.77421 1.02434i
\(718\) −4.09121 + 7.08618i −0.152683 + 0.264454i
\(719\) −20.7953 + 12.0062i −0.775534 + 0.447755i −0.834845 0.550485i \(-0.814443\pi\)
0.0593112 + 0.998240i \(0.481110\pi\)
\(720\) 9.23987i 0.344350i
\(721\) 9.41231 5.43420i 0.350533 0.202380i
\(722\) 30.3077 52.4944i 1.12793 1.95364i
\(723\) 14.0195 0.521391
\(724\) 47.5853 + 27.4734i 1.76849 + 1.02104i
\(725\) −5.00667 + 2.89060i −0.185943 + 0.107354i
\(726\) 96.0160 55.4349i 3.56349 2.05738i
\(727\) 25.2064 0.934853 0.467426 0.884032i \(-0.345181\pi\)
0.467426 + 0.884032i \(0.345181\pi\)
\(728\) −43.1075 + 24.8882i −1.59767 + 0.922416i
\(729\) −10.5017 −0.388953
\(730\) −21.7069 −0.803409
\(731\) 22.9042 14.3666i 0.847141 0.531368i
\(732\) 16.0720 0.594037
\(733\) 17.5659 0.648813 0.324406 0.945918i \(-0.394835\pi\)
0.324406 + 0.945918i \(0.394835\pi\)
\(734\) 50.7710 29.3126i 1.87399 1.08195i
\(735\) −35.3676 −1.30455
\(736\) 11.8447 6.83852i 0.436600 0.252071i
\(737\) −70.4197 + 40.6568i −2.59394 + 1.49761i
\(738\) −8.68845 5.01628i −0.319826 0.184652i
\(739\) 31.7737 1.16882 0.584408 0.811460i \(-0.301327\pi\)
0.584408 + 0.811460i \(0.301327\pi\)
\(740\) −1.59260 + 2.75847i −0.0585453 + 0.101403i
\(741\) −22.3883 + 12.9259i −0.822453 + 0.474844i
\(742\) 46.5119i 1.70751i
\(743\) −5.91820 + 3.41688i −0.217118 + 0.125353i −0.604615 0.796518i \(-0.706673\pi\)
0.387497 + 0.921871i \(0.373340\pi\)
\(744\) 48.3555 83.7542i 1.77280 3.07058i
\(745\) −1.39234 0.803867i −0.0510114 0.0294514i
\(746\) 4.83368 8.37218i 0.176974 0.306527i
\(747\) −10.6735 −0.390524
\(748\) −96.9001 30.4395i −3.54302 1.11298i
\(749\) −10.5648 + 18.2988i −0.386030 + 0.668624i
\(750\) 28.4172 + 49.2200i 1.03765 + 1.79726i
\(751\) 24.3491 14.0579i 0.888510 0.512982i 0.0150554 0.999887i \(-0.495208\pi\)
0.873455 + 0.486905i \(0.161874\pi\)
\(752\) −63.8343 −2.32780
\(753\) 49.3365i 1.79792i
\(754\) 7.79096 4.49811i 0.283730 0.163812i
\(755\) −5.18485 + 2.99347i −0.188696 + 0.108944i
\(756\) 36.2356 62.7620i 1.31788 2.28263i
\(757\) −20.6236 + 35.7212i −0.749579 + 1.29831i 0.198446 + 0.980112i \(0.436411\pi\)
−0.948025 + 0.318197i \(0.896923\pi\)
\(758\) 0.0302289i 0.00109796i
\(759\) 41.4308 + 23.9201i 1.50384 + 0.868245i
\(760\) 45.1482 + 26.0663i 1.63770 + 0.945524i
\(761\) −26.9871 + 46.7431i −0.978282 + 1.69443i −0.309635 + 0.950856i \(0.600207\pi\)
−0.668648 + 0.743579i \(0.733127\pi\)
\(762\) 18.3448 10.5914i 0.664562 0.383685i
\(763\) −47.1188 −1.70581
\(764\) 11.9810 + 20.7516i 0.433456 + 0.750768i
\(765\) 6.12015 + 1.92254i 0.221274 + 0.0695096i
\(766\) −86.3389 −3.11955
\(767\) 5.90114 10.2211i 0.213078 0.369061i
\(768\) −56.1691 + 32.4292i −2.02683 + 1.17019i
\(769\) −6.70884 11.6201i −0.241927 0.419030i 0.719336 0.694662i \(-0.244446\pi\)
−0.961263 + 0.275632i \(0.911113\pi\)
\(770\) 87.3147i 3.14660i
\(771\) 2.69491 1.55591i 0.0970548 0.0560346i
\(772\) 2.49117i 0.0896592i
\(773\) −24.1643 −0.869128 −0.434564 0.900641i \(-0.643097\pi\)
−0.434564 + 0.900641i \(0.643097\pi\)
\(774\) −17.6290 + 6.25564i −0.633663 + 0.224854i
\(775\) 25.6343i 0.920813i
\(776\) 109.045i 3.91448i
\(777\) −4.21969 + 2.43624i −0.151381 + 0.0873996i
\(778\) −55.2942 −1.98239
\(779\) −20.0038 + 11.5492i −0.716711 + 0.413793i
\(780\) −11.6119 20.1124i −0.415773 0.720140i
\(781\) −15.9647 + 27.6516i −0.571261 + 0.989453i
\(782\) −9.26288 41.5734i −0.331240 1.48666i
\(783\) −3.50816 + 6.07630i −0.125371 + 0.217149i
\(784\) 37.6996 + 65.2977i 1.34642 + 2.33206i
\(785\) 12.0094i 0.428633i
\(786\) −13.0355 22.5782i −0.464962 0.805338i
\(787\) −0.936636 0.540767i −0.0333875 0.0192763i 0.483213 0.875503i \(-0.339470\pi\)
−0.516601 + 0.856226i \(0.672803\pi\)
\(788\) −23.6861 13.6752i −0.843782 0.487158i
\(789\) 23.7841 + 13.7318i 0.846736 + 0.488863i
\(790\) −46.4078 −1.65111
\(791\) −24.4007 + 42.2633i −0.867591 + 1.50271i
\(792\) 32.6001 + 18.8217i 1.15839 + 0.668799i
\(793\) −3.07534 + 1.77555i −0.109209 + 0.0630516i
\(794\) −44.4715 + 25.6756i −1.57824 + 0.911195i
\(795\) 11.6247 0.412284
\(796\) 43.0835i 1.52705i
\(797\) −2.35135 4.07266i −0.0832892 0.144261i 0.821372 0.570393i \(-0.193209\pi\)
−0.904661 + 0.426132i \(0.859876\pi\)
\(798\) 74.4365 + 128.928i 2.63503 + 4.56400i
\(799\) −13.2820 + 42.2815i −0.469884 + 1.49581i
\(800\) 5.19333 8.99511i 0.183612 0.318025i
\(801\) 18.4808 0.652987
\(802\) 3.58647 + 2.07065i 0.126643 + 0.0731172i
\(803\) −18.0433 + 31.2520i −0.636736 + 1.10286i
\(804\) −107.862 62.2740i −3.80399 2.19623i
\(805\) −21.6550 + 12.5025i −0.763240 + 0.440657i
\(806\) 39.8900i 1.40507i
\(807\) −9.87996 17.1126i −0.347791 0.602392i
\(808\) 1.29375 2.24084i 0.0455139 0.0788323i
\(809\) 10.9139i 0.383713i 0.981423 + 0.191857i \(0.0614509\pi\)
−0.981423 + 0.191857i \(0.938549\pi\)
\(810\) 33.1213 + 19.1226i 1.16376 + 0.671899i
\(811\) 1.01339 0.585080i 0.0355849 0.0205449i −0.482102 0.876115i \(-0.660127\pi\)
0.517687 + 0.855570i \(0.326793\pi\)
\(812\) −17.6897 30.6395i −0.620787 1.07523i
\(813\) 57.0503i 2.00084i
\(814\) 3.87697 + 6.71512i 0.135888 + 0.235365i
\(815\) 5.67444 0.198767
\(816\) −10.8295 48.6048i −0.379110 1.70151i
\(817\) −7.82101 + 42.3516i −0.273623 + 1.48170i
\(818\) 75.9010 2.65382
\(819\) 9.75672i 0.340927i
\(820\) −10.3752 17.9703i −0.362317 0.627552i
\(821\) 43.2389i 1.50905i −0.656272 0.754524i \(-0.727868\pi\)
0.656272 0.754524i \(-0.272132\pi\)
\(822\) 36.0620 20.8204i 1.25781 0.726195i
\(823\) 1.20177 0.693840i 0.0418909 0.0241857i −0.478908 0.877865i \(-0.658967\pi\)
0.520799 + 0.853679i \(0.325634\pi\)
\(824\) 7.09556 12.2899i 0.247186 0.428138i
\(825\) 36.3309 1.26488
\(826\) −58.8603 33.9830i −2.04801 1.18242i
\(827\) −1.72267 + 0.994583i −0.0599030 + 0.0345850i −0.529652 0.848215i \(-0.677678\pi\)
0.469749 + 0.882800i \(0.344344\pi\)
\(828\) 20.1245i 0.699373i
\(829\) 8.47665 + 14.6820i 0.294406 + 0.509927i 0.974847 0.222877i \(-0.0715448\pi\)
−0.680440 + 0.732804i \(0.738211\pi\)
\(830\) −27.9955 16.1632i −0.971739 0.561034i
\(831\) −22.9220 + 39.7021i −0.795157 + 1.37725i
\(832\) 3.41287 5.91127i 0.118320 0.204936i
\(833\) 51.0949 11.3843i 1.77033 0.394444i
\(834\) −34.6005 + 59.9298i −1.19812 + 2.07520i
\(835\) 2.21557 3.83748i 0.0766730 0.132802i
\(836\) 140.115 80.8952i 4.84597 2.79782i
\(837\) −15.5555 26.9428i −0.537675 0.931281i
\(838\) 10.9913i 0.379688i
\(839\) 12.4160i 0.428648i 0.976763 + 0.214324i \(0.0687549\pi\)
−0.976763 + 0.214324i \(0.931245\pi\)
\(840\) −62.0435 + 35.8208i −2.14070 + 1.23594i
\(841\) −12.7874 22.1484i −0.440944 0.763737i
\(842\) −10.3459 + 17.9197i −0.356545 + 0.617554i
\(843\) −27.1860 15.6958i −0.936335 0.540593i
\(844\) 56.5393i 1.94616i
\(845\) −10.9775 6.33789i −0.377639 0.218030i
\(846\) 15.3313 26.5546i 0.527101 0.912966i
\(847\) 83.4311 + 48.1690i 2.86673 + 1.65511i
\(848\) −12.3911 21.4621i −0.425514 0.737012i
\(849\) −60.5853 −2.07928
\(850\) −21.8779 23.8248i −0.750406 0.817183i
\(851\) −1.11028 + 1.92307i −0.0380600 + 0.0659219i
\(852\) −48.9061 −1.67549
\(853\) 24.8955 + 14.3734i 0.852404 + 0.492136i 0.861461 0.507823i \(-0.169550\pi\)
−0.00905718 + 0.999959i \(0.502883\pi\)
\(854\) 10.2249 + 17.7100i 0.349889 + 0.606025i
\(855\) −8.84955 + 5.10929i −0.302648 + 0.174734i
\(856\) 27.5895i 0.942988i
\(857\) −16.0963 + 9.29320i −0.549839 + 0.317450i −0.749057 0.662505i \(-0.769493\pi\)
0.199218 + 0.979955i \(0.436160\pi\)
\(858\) −56.5352 −1.93008
\(859\) 36.4400 1.24332 0.621659 0.783288i \(-0.286459\pi\)
0.621659 + 0.783288i \(0.286459\pi\)
\(860\) −38.0465 7.02598i −1.29737 0.239584i
\(861\) 31.7423i 1.08177i
\(862\) 39.2930i 1.33833i
\(863\) 24.2347 + 41.9758i 0.824960 + 1.42887i 0.901950 + 0.431841i \(0.142136\pi\)
−0.0769892 + 0.997032i \(0.524531\pi\)
\(864\) 12.6057i 0.428854i
\(865\) −4.88923 8.46840i −0.166239 0.287934i
\(866\) 37.5407 + 65.0225i 1.27569 + 2.20955i
\(867\) −34.4473 2.94012i −1.16989 0.0998519i
\(868\) 156.875 5.32470
\(869\) −38.5753 + 66.8144i −1.30858 + 2.26652i
\(870\) 11.2133 6.47401i 0.380167 0.219489i
\(871\) 27.5188 0.932440
\(872\) −53.2814 + 30.7620i −1.80434 + 1.04173i
\(873\) 18.5105 + 10.6870i 0.626484 + 0.361701i
\(874\) 58.7572 + 33.9235i 1.98749 + 1.14748i
\(875\) −24.6925 + 42.7687i −0.834759 + 1.44585i
\(876\) −55.2739 −1.86753
\(877\) 25.3430 + 14.6318i 0.855772 + 0.494080i 0.862594 0.505896i \(-0.168838\pi\)
−0.00682189 + 0.999977i \(0.502171\pi\)
\(878\) −20.3866 11.7702i −0.688014 0.397225i
\(879\) −24.8546 + 14.3498i −0.838324 + 0.484007i
\(880\) 23.2613 + 40.2898i 0.784140 + 1.35817i
\(881\) 52.8264i 1.77977i −0.456187 0.889884i \(-0.650785\pi\)
0.456187 0.889884i \(-0.349215\pi\)
\(882\) −36.2178 −1.21952
\(883\) −8.43591 14.6114i −0.283891 0.491713i 0.688449 0.725285i \(-0.258292\pi\)
−0.972340 + 0.233572i \(0.924959\pi\)
\(884\) 23.2494 + 25.3183i 0.781962 + 0.851546i
\(885\) 8.49334 14.7109i 0.285501 0.494501i
\(886\) −1.60439 + 2.77888i −0.0539005 + 0.0933584i
\(887\) 48.0721i 1.61410i 0.590480 + 0.807052i \(0.298938\pi\)
−0.590480 + 0.807052i \(0.701062\pi\)
\(888\) −3.18106 + 5.50975i −0.106749 + 0.184895i
\(889\) 15.9403 + 9.20316i 0.534622 + 0.308664i
\(890\) 48.4732 + 27.9860i 1.62482 + 0.938092i
\(891\) 55.0625 31.7904i 1.84466 1.06502i
\(892\) −57.2390 −1.91650
\(893\) −35.2979 61.1378i −1.18120 2.04590i
\(894\) −5.19162 2.99738i −0.173634 0.100247i
\(895\) 7.04290i 0.235418i
\(896\) −59.6011 34.4107i −1.99113 1.14958i
\(897\) −8.09524 14.0214i −0.270292 0.468160i
\(898\) 47.4190 27.3774i 1.58239 0.913595i
\(899\) −15.1879 −0.506545
\(900\) 7.64148 + 13.2354i 0.254716 + 0.441181i
\(901\) −16.7939 + 3.74182i −0.559487 + 0.124658i
\(902\) −50.5139 −1.68193
\(903\) −45.0292 38.4081i −1.49848 1.27814i
\(904\) 63.7212i 2.11934i
\(905\) −17.4735 −0.580837
\(906\) −19.3328 + 11.1618i −0.642288 + 0.370825i
\(907\) 39.7575i 1.32013i −0.751211 0.660063i \(-0.770530\pi\)
0.751211 0.660063i \(-0.229470\pi\)
\(908\) 14.6086 8.43430i 0.484805 0.279902i
\(909\) 0.253589 + 0.439229i 0.00841102 + 0.0145683i
\(910\) 14.7749 25.5908i 0.489783 0.848328i
\(911\) 9.10274i 0.301587i −0.988565 0.150794i \(-0.951817\pi\)
0.988565 0.150794i \(-0.0481829\pi\)
\(912\) 68.6949 + 39.6610i 2.27471 + 1.31331i
\(913\) −46.5412 + 26.8706i −1.54029 + 0.889287i
\(914\) 68.2033 2.25597
\(915\) −4.42625 + 2.55550i −0.146327 + 0.0844822i
\(916\) 12.0317 20.8395i 0.397539 0.688558i
\(917\) 11.3270 19.6189i 0.374049 0.647872i
\(918\) −37.4520 11.7649i −1.23610 0.388300i
\(919\) 46.8822 1.54650 0.773251 0.634100i \(-0.218629\pi\)
0.773251 + 0.634100i \(0.218629\pi\)
\(920\) −16.3249 + 28.2755i −0.538215 + 0.932215i
\(921\) 28.4581 + 16.4303i 0.937727 + 0.541397i
\(922\) 2.26407 + 3.92148i 0.0745630 + 0.129147i
\(923\) 9.35809 5.40290i 0.308025 0.177839i
\(924\) 222.336i 7.31431i
\(925\) 1.68635i 0.0554468i
\(926\) 37.2498 + 64.5185i 1.22410 + 2.12021i
\(927\) 1.39081 + 2.40895i 0.0456802 + 0.0791205i
\(928\) −5.32944 3.07695i −0.174947 0.101006i
\(929\) 45.7157 + 26.3940i 1.49988 + 0.865958i 1.00000 0.000134320i \(-4.27555e-5\pi\)
0.499884 + 0.866093i \(0.333376\pi\)
\(930\) 57.4126i 1.88263i
\(931\) −41.6929 + 72.2142i −1.36643 + 2.36672i
\(932\) −41.8098 24.1389i −1.36953 0.790696i
\(933\) −18.6630 + 32.3253i −0.610999 + 1.05828i
\(934\) 25.8623 + 44.7948i 0.846240 + 1.46573i
\(935\) 31.5265 7.02434i 1.03103 0.229721i
\(936\) −6.36979 11.0328i −0.208203 0.360618i
\(937\) 12.1415 21.0297i 0.396645 0.687009i −0.596665 0.802491i \(-0.703508\pi\)
0.993310 + 0.115481i \(0.0368410\pi\)
\(938\) 158.474i 5.17434i
\(939\) 2.74297 4.75096i 0.0895134 0.155042i
\(940\) 54.9229 31.7098i 1.79139 1.03426i
\(941\) −11.7112 + 6.76145i −0.381774 + 0.220417i −0.678590 0.734518i \(-0.737409\pi\)
0.296816 + 0.954935i \(0.404075\pi\)
\(942\) 44.7794i 1.45899i
\(943\) −7.23306 12.5280i −0.235541 0.407969i
\(944\) −36.2134 −1.17865
\(945\) 23.0464i 0.749699i
\(946\) −61.1217 + 71.6584i −1.98724 + 2.32981i
\(947\) 33.5617i 1.09061i −0.838238 0.545304i \(-0.816414\pi\)
0.838238 0.545304i \(-0.183586\pi\)
\(948\) −118.171 −3.83803
\(949\) 10.5766 6.10638i 0.343329 0.198221i
\(950\) 51.5245 1.67168
\(951\) −15.2228 26.3666i −0.493632 0.854995i
\(952\) 78.1028 71.7206i 2.53132 2.32448i
\(953\) 9.75277 16.8923i 0.315923 0.547195i −0.663710 0.747990i \(-0.731019\pi\)
0.979633 + 0.200795i \(0.0643525\pi\)
\(954\) 11.9041 0.385409
\(955\) −6.59917 3.81003i −0.213544 0.123290i
\(956\) −58.0943 100.622i −1.87891 3.25436i
\(957\) 21.5254i 0.695819i
\(958\) 48.4771 27.9883i 1.56623 0.904261i
\(959\) 31.3353 + 18.0915i 1.01187 + 0.584204i
\(960\) 4.91205 8.50792i 0.158536 0.274592i
\(961\) 18.1722 31.4752i 0.586200 1.01533i
\(962\) 2.62416i 0.0846062i
\(963\) −4.68333 2.70392i −0.150918 0.0871327i
\(964\) 25.7154 + 14.8468i 0.828238 + 0.478183i
\(965\) −0.396105 0.686074i −0.0127511 0.0220855i
\(966\) −80.7452 + 46.6183i −2.59794 + 1.49992i
\(967\) 16.0624 0.516532 0.258266 0.966074i \(-0.416849\pi\)
0.258266 + 0.966074i \(0.416849\pi\)
\(968\) 125.791 4.04307
\(969\) 40.5633 37.2487i 1.30308 1.19660i
\(970\) 32.3673 + 56.0618i 1.03925 + 1.80004i
\(971\) 21.9395 38.0003i 0.704071 1.21949i −0.262955 0.964808i \(-0.584697\pi\)
0.967026 0.254678i \(-0.0819696\pi\)
\(972\) 41.9137 + 24.1989i 1.34438 + 0.776179i
\(973\) −60.1308 −1.92770
\(974\) −49.9365 28.8309i −1.60007 0.923800i
\(975\) −10.6481 6.14771i −0.341014 0.196884i
\(976\) 9.43620 + 5.44799i 0.302045 + 0.174386i
\(977\) 3.21030 + 5.56040i 0.102707 + 0.177893i 0.912799 0.408409i \(-0.133916\pi\)
−0.810092 + 0.586302i \(0.800583\pi\)
\(978\) 21.1583 0.676567
\(979\) 80.5842 46.5253i 2.57548 1.48696i
\(980\) −64.8734 37.4547i −2.07230 1.19645i
\(981\) 12.0594i 0.385028i
\(982\) 8.55777 14.8225i 0.273089 0.473005i
\(983\) −3.55603 + 2.05307i −0.113420 + 0.0654828i −0.555637 0.831425i \(-0.687525\pi\)
0.442217 + 0.896908i \(0.354192\pi\)
\(984\) −20.7233 35.8938i −0.660635 1.14425i
\(985\) 8.69760 0.277129
\(986\) −14.1157 + 12.9623i −0.449537 + 0.412803i
\(987\) 97.0142 3.08800
\(988\) −54.7545 −1.74197
\(989\) −26.5241 4.89816i −0.843417 0.155752i
\(990\) −22.3470 −0.710235
\(991\) 61.9572i 1.96814i −0.177794 0.984068i \(-0.556896\pi\)
0.177794 0.984068i \(-0.443104\pi\)
\(992\) 23.6312 13.6435i 0.750291 0.433181i
\(993\) 10.6891i 0.339210i
\(994\) −31.1138 53.8907i −0.986870 1.70931i
\(995\) −6.85043 11.8653i −0.217173 0.376155i
\(996\) −71.2870 41.1576i −2.25882 1.30413i
\(997\) 13.1965i 0.417936i 0.977922 + 0.208968i \(0.0670104\pi\)
−0.977922 + 0.208968i \(0.932990\pi\)
\(998\) 14.6651 + 8.46689i 0.464215 + 0.268015i
\(999\) 1.02331 + 1.77243i 0.0323762 + 0.0560772i
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 731.2.j.a.509.6 yes 128
17.16 even 2 inner 731.2.j.a.509.5 yes 128
43.6 even 3 inner 731.2.j.a.135.5 128
731.135 even 6 inner 731.2.j.a.135.6 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.j.a.135.5 128 43.6 even 3 inner
731.2.j.a.135.6 yes 128 731.135 even 6 inner
731.2.j.a.509.5 yes 128 17.16 even 2 inner
731.2.j.a.509.6 yes 128 1.1 even 1 trivial