Properties

Label 150.2.l.a.53.2
Level $150$
Weight $2$
Character 150.53
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 53.2
Character \(\chi\) \(=\) 150.53
Dual form 150.2.l.a.17.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.891007 + 0.453990i) q^{2} +(-0.873670 - 1.49556i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-2.21391 - 0.314018i) q^{5} +(1.45742 + 0.935916i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-1.47340 + 2.61325i) q^{9} +O(q^{10})\) \(q+(-0.891007 + 0.453990i) q^{2} +(-0.873670 - 1.49556i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-2.21391 - 0.314018i) q^{5} +(1.45742 + 0.935916i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-1.47340 + 2.61325i) q^{9} +(2.11517 - 0.725301i) q^{10} +(0.335657 + 0.109061i) q^{11} +(-1.72346 - 0.172255i) q^{12} +(-1.12512 + 2.20817i) q^{13} +(1.19166 - 3.66754i) q^{14} +(1.46459 + 3.58538i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-3.49819 - 0.554059i) q^{17} +(0.126420 - 2.99734i) q^{18} +(-3.84926 - 5.29805i) q^{19} +(-1.55535 + 1.60651i) q^{20} +(6.46042 + 1.69577i) q^{21} +(-0.348585 + 0.0552105i) q^{22} +(-3.55825 - 6.98347i) q^{23} +(1.61382 - 0.628956i) q^{24} +(4.80279 + 1.39041i) q^{25} -2.47829i q^{26} +(5.19554 - 0.0795559i) q^{27} +(0.603255 + 3.80880i) q^{28} +(5.05137 + 3.67003i) q^{29} +(-2.93269 - 2.52969i) q^{30} +(-3.39184 + 2.46432i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.130145 - 0.597278i) q^{33} +(3.36845 - 1.09448i) q^{34} +(6.89315 - 5.18062i) q^{35} +(1.24812 + 2.72804i) q^{36} +(4.33521 + 2.20890i) q^{37} +(5.83498 + 2.97307i) q^{38} +(4.28544 - 0.246528i) q^{39} +(0.656484 - 2.13753i) q^{40} +(-8.06531 + 2.62058i) q^{41} +(-6.52614 + 1.42202i) q^{42} +(-5.16349 - 5.16349i) q^{43} +(0.285527 - 0.207447i) q^{44} +(4.08259 - 5.32283i) q^{45} +(6.34085 + 4.60690i) q^{46} +(0.668895 + 4.22323i) q^{47} +(-1.15238 + 1.29306i) q^{48} -7.87088i q^{49} +(-4.91055 + 0.941550i) q^{50} +(2.22763 + 5.71582i) q^{51} +(1.12512 + 2.20817i) q^{52} +(4.34698 - 0.688494i) q^{53} +(-4.59315 + 2.42961i) q^{54} +(-0.708866 - 0.346854i) q^{55} +(-2.26666 - 3.11979i) q^{56} +(-4.56057 + 10.3855i) q^{57} +(-6.16696 - 0.976751i) q^{58} +(-0.713107 - 2.19472i) q^{59} +(3.76150 + 0.922555i) q^{60} +(0.0451729 - 0.139028i) q^{61} +(1.90338 - 3.73559i) q^{62} +(-3.10814 - 11.1435i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(3.18432 - 4.53538i) q^{65} +(0.387119 + 0.473094i) q^{66} +(1.18445 - 7.47829i) q^{67} +(-2.50443 + 2.50443i) q^{68} +(-7.33546 + 11.4228i) q^{69} +(-3.78989 + 7.74539i) q^{70} +(-3.62303 + 4.98667i) q^{71} +(-2.35059 - 1.86407i) q^{72} +(-9.30362 + 4.74043i) q^{73} -4.86552 q^{74} +(-2.11660 - 8.39762i) q^{75} -6.54875 q^{76} +(-1.21266 + 0.617880i) q^{77} +(-3.70643 + 2.16521i) q^{78} +(0.803169 - 1.10547i) q^{79} +(0.385487 + 2.20259i) q^{80} +(-4.65817 - 7.70074i) q^{81} +(5.99652 - 5.99652i) q^{82} +(-0.915181 + 5.77823i) q^{83} +(5.16925 - 4.22984i) q^{84} +(7.57069 + 2.32513i) q^{85} +(6.94488 + 2.25653i) q^{86} +(1.07553 - 10.7610i) q^{87} +(-0.160227 + 0.314463i) q^{88} +(-0.633239 + 1.94891i) q^{89} +(-1.22110 + 6.59613i) q^{90} +(-2.95327 - 9.08922i) q^{91} +(-7.74123 - 1.22609i) q^{92} +(6.64888 + 2.91971i) q^{93} +(-2.51330 - 3.45926i) q^{94} +(6.85822 + 12.9381i) q^{95} +(0.439743 - 1.67530i) q^{96} +(6.93926 - 1.09907i) q^{97} +(3.57330 + 7.01300i) q^{98} +(-0.779562 + 0.716464i) 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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 + 0.453990i −0.630037 + 0.321020i
\(3\) −0.873670 1.49556i −0.504413 0.863462i
\(4\) 0.587785 0.809017i 0.293893 0.404508i
\(5\) −2.21391 0.314018i −0.990090 0.140433i
\(6\) 1.45742 + 0.935916i 0.594987 + 0.382086i
\(7\) −2.72680 + 2.72680i −1.03063 + 1.03063i −0.0311178 + 0.999516i \(0.509907\pi\)
−0.999516 + 0.0311178i \(0.990093\pi\)
\(8\) −0.156434 + 0.987688i −0.0553079 + 0.349201i
\(9\) −1.47340 + 2.61325i −0.491134 + 0.871084i
\(10\) 2.11517 0.725301i 0.668875 0.229360i
\(11\) 0.335657 + 0.109061i 0.101204 + 0.0328833i 0.359181 0.933268i \(-0.383056\pi\)
−0.257977 + 0.966151i \(0.583056\pi\)
\(12\) −1.72346 0.172255i −0.497521 0.0497257i
\(13\) −1.12512 + 2.20817i −0.312052 + 0.612437i −0.992760 0.120119i \(-0.961673\pi\)
0.680707 + 0.732555i \(0.261673\pi\)
\(14\) 1.19166 3.66754i 0.318483 0.980191i
\(15\) 1.46459 + 3.58538i 0.378156 + 0.925742i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) −3.49819 0.554059i −0.848436 0.134379i −0.282948 0.959135i \(-0.591312\pi\)
−0.565488 + 0.824756i \(0.691312\pi\)
\(18\) 0.126420 2.99734i 0.0297975 0.706479i
\(19\) −3.84926 5.29805i −0.883080 1.21546i −0.975558 0.219741i \(-0.929479\pi\)
0.0924780 0.995715i \(-0.470521\pi\)
\(20\) −1.55535 + 1.60651i −0.347787 + 0.359228i
\(21\) 6.46042 + 1.69577i 1.40978 + 0.370048i
\(22\) −0.348585 + 0.0552105i −0.0743186 + 0.0117709i
\(23\) −3.55825 6.98347i −0.741947 1.45615i −0.884585 0.466378i \(-0.845559\pi\)
0.142638 0.989775i \(-0.454441\pi\)
\(24\) 1.61382 0.628956i 0.329420 0.128385i
\(25\) 4.80279 + 1.39041i 0.960557 + 0.278083i
\(26\) 2.47829i 0.486033i
\(27\) 5.19554 0.0795559i 0.999883 0.0153105i
\(28\) 0.603255 + 3.80880i 0.114004 + 0.719796i
\(29\) 5.05137 + 3.67003i 0.938015 + 0.681508i 0.947942 0.318443i \(-0.103160\pi\)
−0.00992666 + 0.999951i \(0.503160\pi\)
\(30\) −2.93269 2.52969i −0.535434 0.461856i
\(31\) −3.39184 + 2.46432i −0.609193 + 0.442604i −0.849130 0.528184i \(-0.822873\pi\)
0.239937 + 0.970788i \(0.422873\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.130145 0.597278i −0.0226553 0.103973i
\(34\) 3.36845 1.09448i 0.577684 0.187701i
\(35\) 6.89315 5.18062i 1.16516 0.875685i
\(36\) 1.24812 + 2.72804i 0.208020 + 0.454673i
\(37\) 4.33521 + 2.20890i 0.712704 + 0.363141i 0.772452 0.635073i \(-0.219030\pi\)
−0.0597483 + 0.998213i \(0.519030\pi\)
\(38\) 5.83498 + 2.97307i 0.946558 + 0.482296i
\(39\) 4.28544 0.246528i 0.686219 0.0394761i
\(40\) 0.656484 2.13753i 0.103799 0.337973i
\(41\) −8.06531 + 2.62058i −1.25959 + 0.409265i −0.861348 0.508015i \(-0.830379\pi\)
−0.398241 + 0.917281i \(0.630379\pi\)
\(42\) −6.52614 + 1.42202i −1.00700 + 0.219423i
\(43\) −5.16349 5.16349i −0.787425 0.787425i 0.193647 0.981071i \(-0.437969\pi\)
−0.981071 + 0.193647i \(0.937969\pi\)
\(44\) 0.285527 0.207447i 0.0430448 0.0312738i
\(45\) 4.08259 5.32283i 0.608596 0.793480i
\(46\) 6.34085 + 4.60690i 0.934908 + 0.679250i
\(47\) 0.668895 + 4.22323i 0.0975683 + 0.616022i 0.987218 + 0.159378i \(0.0509488\pi\)
−0.889649 + 0.456644i \(0.849051\pi\)
\(48\) −1.15238 + 1.29306i −0.166332 + 0.186638i
\(49\) 7.87088i 1.12441i
\(50\) −4.91055 + 0.941550i −0.694456 + 0.133155i
\(51\) 2.22763 + 5.71582i 0.311931 + 0.800375i
\(52\) 1.12512 + 2.20817i 0.156026 + 0.306218i
\(53\) 4.34698 0.688494i 0.597103 0.0945719i 0.149435 0.988772i \(-0.452255\pi\)
0.447668 + 0.894200i \(0.352255\pi\)
\(54\) −4.59315 + 2.42961i −0.625048 + 0.330628i
\(55\) −0.708866 0.346854i −0.0955835 0.0467698i
\(56\) −2.26666 3.11979i −0.302896 0.416900i
\(57\) −4.56057 + 10.3855i −0.604063 + 1.37560i
\(58\) −6.16696 0.976751i −0.809762 0.128254i
\(59\) −0.713107 2.19472i −0.0928386 0.285728i 0.893846 0.448375i \(-0.147997\pi\)
−0.986684 + 0.162647i \(0.947997\pi\)
\(60\) 3.76150 + 0.922555i 0.485608 + 0.119101i
\(61\) 0.0451729 0.139028i 0.00578380 0.0178007i −0.948123 0.317904i \(-0.897021\pi\)
0.953907 + 0.300103i \(0.0970211\pi\)
\(62\) 1.90338 3.73559i 0.241729 0.474420i
\(63\) −3.10814 11.1435i −0.391589 1.40395i
\(64\) −0.951057 0.309017i −0.118882 0.0386271i
\(65\) 3.18432 4.53538i 0.394966 0.562545i
\(66\) 0.387119 + 0.473094i 0.0476510 + 0.0582339i
\(67\) 1.18445 7.47829i 0.144703 0.913619i −0.803350 0.595507i \(-0.796951\pi\)
0.948053 0.318112i \(-0.103049\pi\)
\(68\) −2.50443 + 2.50443i −0.303707 + 0.303707i
\(69\) −7.33546 + 11.4228i −0.883085 + 1.37515i
\(70\) −3.78989 + 7.74539i −0.452978 + 0.925752i
\(71\) −3.62303 + 4.98667i −0.429974 + 0.591809i −0.967947 0.251153i \(-0.919190\pi\)
0.537973 + 0.842962i \(0.319190\pi\)
\(72\) −2.35059 1.86407i −0.277019 0.219682i
\(73\) −9.30362 + 4.74043i −1.08891 + 0.554825i −0.903827 0.427898i \(-0.859254\pi\)
−0.185079 + 0.982724i \(0.559254\pi\)
\(74\) −4.86552 −0.565605
\(75\) −2.11660 8.39762i −0.244404 0.969674i
\(76\) −6.54875 −0.751193
\(77\) −1.21266 + 0.617880i −0.138195 + 0.0704139i
\(78\) −3.70643 + 2.16521i −0.419671 + 0.245161i
\(79\) 0.803169 1.10547i 0.0903636 0.124375i −0.761442 0.648234i \(-0.775508\pi\)
0.851805 + 0.523859i \(0.175508\pi\)
\(80\) 0.385487 + 2.20259i 0.0430987 + 0.246257i
\(81\) −4.65817 7.70074i −0.517574 0.855638i
\(82\) 5.99652 5.99652i 0.662205 0.662205i
\(83\) −0.915181 + 5.77823i −0.100454 + 0.634243i 0.885167 + 0.465273i \(0.154044\pi\)
−0.985621 + 0.168969i \(0.945956\pi\)
\(84\) 5.16925 4.22984i 0.564011 0.461513i
\(85\) 7.57069 + 2.32513i 0.821157 + 0.252196i
\(86\) 6.94488 + 2.25653i 0.748886 + 0.243328i
\(87\) 1.07553 10.7610i 0.115309 1.15370i
\(88\) −0.160227 + 0.314463i −0.0170803 + 0.0335219i
\(89\) −0.633239 + 1.94891i −0.0671232 + 0.206584i −0.978992 0.203897i \(-0.934639\pi\)
0.911869 + 0.410481i \(0.134639\pi\)
\(90\) −1.22110 + 6.59613i −0.128715 + 0.695293i
\(91\) −2.95327 9.08922i −0.309587 0.952809i
\(92\) −7.74123 1.22609i −0.807079 0.127829i
\(93\) 6.64888 + 2.91971i 0.689457 + 0.302759i
\(94\) −2.51330 3.45926i −0.259227 0.356795i
\(95\) 6.85822 + 12.9381i 0.703639 + 1.32742i
\(96\) 0.439743 1.67530i 0.0448811 0.170984i
\(97\) 6.93926 1.09907i 0.704575 0.111594i 0.206142 0.978522i \(-0.433909\pi\)
0.498433 + 0.866928i \(0.333909\pi\)
\(98\) 3.57330 + 7.01300i 0.360958 + 0.708420i
\(99\) −0.779562 + 0.716464i −0.0783490 + 0.0720073i
\(100\) 3.94788 3.06827i 0.394788 0.306827i
\(101\) 9.58679i 0.953921i 0.878925 + 0.476961i \(0.158262\pi\)
−0.878925 + 0.476961i \(0.841738\pi\)
\(102\) −4.57976 4.08151i −0.453464 0.404130i
\(103\) 1.04075 + 6.57102i 0.102548 + 0.647462i 0.984401 + 0.175938i \(0.0562959\pi\)
−0.881853 + 0.471524i \(0.843704\pi\)
\(104\) −2.00498 1.45670i −0.196604 0.142841i
\(105\) −13.7703 5.78297i −1.34384 0.564360i
\(106\) −3.56062 + 2.58694i −0.345838 + 0.251266i
\(107\) 10.4337 + 10.4337i 1.00866 + 1.00866i 0.999962 + 0.00870186i \(0.00276992\pi\)
0.00870186 + 0.999962i \(0.497230\pi\)
\(108\) 2.98950 4.25004i 0.287665 0.408961i
\(109\) −10.5722 + 3.43511i −1.01263 + 0.329024i −0.767902 0.640568i \(-0.778699\pi\)
−0.244729 + 0.969592i \(0.578699\pi\)
\(110\) 0.789073 0.0127689i 0.0752351 0.00121747i
\(111\) −0.483998 8.41342i −0.0459391 0.798566i
\(112\) 3.43597 + 1.75071i 0.324668 + 0.165427i
\(113\) 1.56816 + 0.799015i 0.147520 + 0.0751650i 0.526192 0.850366i \(-0.323619\pi\)
−0.378672 + 0.925531i \(0.623619\pi\)
\(114\) −0.651437 11.3240i −0.0610127 1.06059i
\(115\) 5.68471 + 16.5781i 0.530102 + 1.54592i
\(116\) 5.93824 1.92945i 0.551352 0.179145i
\(117\) −4.11276 6.19375i −0.380224 0.572612i
\(118\) 1.63176 + 1.63176i 0.150216 + 0.150216i
\(119\) 11.0497 8.02806i 1.01292 0.735931i
\(120\) −3.77035 + 0.885683i −0.344185 + 0.0808514i
\(121\) −8.79842 6.39242i −0.799856 0.581129i
\(122\) 0.0228680 + 0.144383i 0.00207037 + 0.0130718i
\(123\) 10.9656 + 9.77263i 0.988739 + 0.881169i
\(124\) 4.19255i 0.376502i
\(125\) −10.1963 4.58641i −0.911986 0.410221i
\(126\) 7.82841 + 8.51786i 0.697410 + 0.758831i
\(127\) 2.44874 + 4.80592i 0.217290 + 0.426457i 0.973762 0.227571i \(-0.0730782\pi\)
−0.756471 + 0.654027i \(0.773078\pi\)
\(128\) 0.987688 0.156434i 0.0873001 0.0138270i
\(129\) −3.21113 + 12.2335i −0.282724 + 1.07710i
\(130\) −0.778228 + 5.48671i −0.0682551 + 0.481216i
\(131\) −10.2354 14.0878i −0.894273 1.23086i −0.972259 0.233906i \(-0.924849\pi\)
0.0779865 0.996954i \(-0.475151\pi\)
\(132\) −0.559706 0.245782i −0.0487161 0.0213926i
\(133\) 24.9429 + 3.95056i 2.16282 + 0.342557i
\(134\) 2.33973 + 7.20094i 0.202122 + 0.622066i
\(135\) −11.5274 1.45537i −0.992124 0.125258i
\(136\) 1.09448 3.36845i 0.0938505 0.288842i
\(137\) 8.13848 15.9727i 0.695317 1.36464i −0.225346 0.974279i \(-0.572351\pi\)
0.920663 0.390358i \(-0.127649\pi\)
\(138\) 1.35009 13.5080i 0.114927 1.14988i
\(139\) 17.1405 + 5.56927i 1.45383 + 0.472379i 0.926181 0.377080i \(-0.123072\pi\)
0.527654 + 0.849459i \(0.323072\pi\)
\(140\) −0.139519 8.62177i −0.0117915 0.728673i
\(141\) 5.73171 4.69008i 0.482697 0.394976i
\(142\) 0.964240 6.08797i 0.0809172 0.510891i
\(143\) −0.618480 + 0.618480i −0.0517199 + 0.0517199i
\(144\) 2.94066 + 0.593750i 0.245055 + 0.0494792i
\(145\) −10.0308 9.71134i −0.833014 0.806483i
\(146\) 6.13747 8.44751i 0.507941 0.699121i
\(147\) −11.7714 + 6.87655i −0.970886 + 0.567168i
\(148\) 4.33521 2.20890i 0.356352 0.181570i
\(149\) −4.64891 −0.380854 −0.190427 0.981701i \(-0.560987\pi\)
−0.190427 + 0.981701i \(0.560987\pi\)
\(150\) 5.69834 + 6.52142i 0.465268 + 0.532472i
\(151\) −14.6548 −1.19259 −0.596295 0.802765i \(-0.703361\pi\)
−0.596295 + 0.802765i \(0.703361\pi\)
\(152\) 5.83498 2.97307i 0.473279 0.241148i
\(153\) 6.60214 8.32530i 0.533751 0.673061i
\(154\) 0.799974 1.10107i 0.0644637 0.0887267i
\(155\) 8.28307 4.39067i 0.665312 0.352667i
\(156\) 2.31947 3.61190i 0.185706 0.289183i
\(157\) 3.17235 3.17235i 0.253181 0.253181i −0.569093 0.822273i \(-0.692705\pi\)
0.822273 + 0.569093i \(0.192705\pi\)
\(158\) −0.213757 + 1.34961i −0.0170056 + 0.107369i
\(159\) −4.82751 5.89965i −0.382846 0.467873i
\(160\) −1.34343 1.78751i −0.106207 0.141315i
\(161\) 28.7452 + 9.33987i 2.26544 + 0.736085i
\(162\) 7.64652 + 4.74665i 0.600768 + 0.372932i
\(163\) −4.91227 + 9.64088i −0.384759 + 0.755132i −0.999434 0.0336487i \(-0.989287\pi\)
0.614675 + 0.788781i \(0.289287\pi\)
\(164\) −2.62058 + 8.06531i −0.204633 + 0.629795i
\(165\) 0.100573 + 1.36319i 0.00782959 + 0.106124i
\(166\) −1.80783 5.56392i −0.140315 0.431844i
\(167\) −16.5871 2.62714i −1.28355 0.203295i −0.522866 0.852415i \(-0.675137\pi\)
−0.760686 + 0.649120i \(0.775137\pi\)
\(168\) −2.68553 + 6.11560i −0.207193 + 0.471829i
\(169\) 4.03108 + 5.54830i 0.310083 + 0.426793i
\(170\) −7.80112 + 1.36531i −0.598319 + 0.104715i
\(171\) 19.5166 2.25292i 1.49247 0.172285i
\(172\) −7.21237 + 1.14233i −0.549938 + 0.0871017i
\(173\) −7.90821 15.5207i −0.601250 1.18002i −0.968293 0.249816i \(-0.919630\pi\)
0.367043 0.930204i \(-0.380370\pi\)
\(174\) 3.92710 + 10.0764i 0.297713 + 0.763892i
\(175\) −16.8876 + 9.30485i −1.27658 + 0.703381i
\(176\) 0.352930i 0.0266031i
\(177\) −2.65931 + 2.98395i −0.199886 + 0.224288i
\(178\) −0.320566 2.02397i −0.0240274 0.151703i
\(179\) −5.94519 4.31943i −0.444364 0.322849i 0.343002 0.939334i \(-0.388556\pi\)
−0.787367 + 0.616485i \(0.788556\pi\)
\(180\) −1.90657 6.43156i −0.142107 0.479380i
\(181\) −0.543117 + 0.394597i −0.0403695 + 0.0293302i −0.607787 0.794100i \(-0.707943\pi\)
0.567418 + 0.823430i \(0.307943\pi\)
\(182\) 6.75780 + 6.75780i 0.500922 + 0.500922i
\(183\) −0.247391 + 0.0539056i −0.0182877 + 0.00398482i
\(184\) 7.45412 2.42199i 0.549525 0.178552i
\(185\) −8.90413 6.25164i −0.654644 0.459630i
\(186\) −7.24972 + 0.417054i −0.531575 + 0.0305799i
\(187\) −1.11376 0.567491i −0.0814465 0.0414991i
\(188\) 3.80983 + 1.94121i 0.277861 + 0.141577i
\(189\) −13.9503 + 14.3841i −1.01473 + 1.04629i
\(190\) −11.9845 8.41439i −0.869448 0.610444i
\(191\) −13.4008 + 4.35419i −0.969650 + 0.315058i −0.750675 0.660672i \(-0.770271\pi\)
−0.218975 + 0.975730i \(0.570271\pi\)
\(192\) 0.368756 + 1.69234i 0.0266126 + 0.122134i
\(193\) −2.89340 2.89340i −0.208271 0.208271i 0.595261 0.803532i \(-0.297049\pi\)
−0.803532 + 0.595261i \(0.797049\pi\)
\(194\) −5.68396 + 4.12964i −0.408085 + 0.296491i
\(195\) −9.56499 0.799915i −0.684963 0.0572831i
\(196\) −6.36767 4.62638i −0.454834 0.330456i
\(197\) 3.55739 + 22.4605i 0.253454 + 1.60024i 0.705806 + 0.708405i \(0.250585\pi\)
−0.452353 + 0.891839i \(0.649415\pi\)
\(198\) 0.369327 0.992288i 0.0262470 0.0705188i
\(199\) 6.31867i 0.447919i 0.974598 + 0.223959i \(0.0718983\pi\)
−0.974598 + 0.223959i \(0.928102\pi\)
\(200\) −2.12462 + 4.52615i −0.150233 + 0.320047i
\(201\) −12.2191 + 4.76215i −0.861866 + 0.335896i
\(202\) −4.35231 8.54189i −0.306228 0.601006i
\(203\) −23.7815 + 3.76662i −1.66914 + 0.264365i
\(204\) 5.93357 + 1.55748i 0.415433 + 0.109045i
\(205\) 18.6788 3.26907i 1.30458 0.228321i
\(206\) −3.91049 5.38233i −0.272457 0.375005i
\(207\) 23.4923 + 0.990845i 1.63283 + 0.0688685i
\(208\) 2.44778 + 0.387690i 0.169723 + 0.0268815i
\(209\) −0.714216 2.19813i −0.0494033 0.152048i
\(210\) 14.8948 1.09891i 1.02784 0.0758317i
\(211\) −1.28435 + 3.95283i −0.0884185 + 0.272124i −0.985483 0.169776i \(-0.945696\pi\)
0.897064 + 0.441900i \(0.145696\pi\)
\(212\) 1.99809 3.92147i 0.137229 0.269327i
\(213\) 10.6232 + 1.06175i 0.727889 + 0.0727502i
\(214\) −14.0333 4.55969i −0.959296 0.311694i
\(215\) 9.81007 + 13.0529i 0.669041 + 0.890202i
\(216\) −0.734186 + 5.14402i −0.0499550 + 0.350006i
\(217\) 2.52917 15.9686i 0.171691 1.08402i
\(218\) 7.86037 7.86037i 0.532371 0.532371i
\(219\) 15.2179 + 9.77255i 1.02833 + 0.660368i
\(220\) −0.697272 + 0.369609i −0.0470101 + 0.0249190i
\(221\) 5.15934 7.10123i 0.347055 0.477680i
\(222\) 4.25086 + 7.27668i 0.285299 + 0.488379i
\(223\) 13.6942 6.97753i 0.917030 0.467250i 0.0692509 0.997599i \(-0.477939\pi\)
0.847779 + 0.530349i \(0.177939\pi\)
\(224\) −3.85628 −0.257658
\(225\) −10.7099 + 10.5022i −0.713996 + 0.700150i
\(226\) −1.75998 −0.117072
\(227\) −12.4969 + 6.36747i −0.829445 + 0.422624i −0.816537 0.577293i \(-0.804109\pi\)
−0.0129084 + 0.999917i \(0.504109\pi\)
\(228\) 5.72144 + 9.79405i 0.378912 + 0.648627i
\(229\) 10.1878 14.0224i 0.673232 0.926624i −0.326596 0.945164i \(-0.605902\pi\)
0.999828 + 0.0185396i \(0.00590167\pi\)
\(230\) −12.5914 12.1904i −0.830254 0.803811i
\(231\) 1.98354 + 1.27378i 0.130507 + 0.0838085i
\(232\) −4.41506 + 4.41506i −0.289863 + 0.289863i
\(233\) 0.384884 2.43006i 0.0252146 0.159199i −0.971868 0.235525i \(-0.924319\pi\)
0.997083 + 0.0763263i \(0.0243191\pi\)
\(234\) 6.47640 + 3.65152i 0.423375 + 0.238707i
\(235\) −0.154700 9.55990i −0.0100915 0.623619i
\(236\) −2.19472 0.713107i −0.142864 0.0464193i
\(237\) −2.35500 0.235375i −0.152974 0.0152892i
\(238\) −6.20067 + 12.1695i −0.401930 + 0.788831i
\(239\) −0.751883 + 2.31406i −0.0486352 + 0.149684i −0.972425 0.233217i \(-0.925075\pi\)
0.923790 + 0.382901i \(0.125075\pi\)
\(240\) 2.95732 2.50085i 0.190894 0.161429i
\(241\) 0.500207 + 1.53948i 0.0322212 + 0.0991666i 0.965874 0.259013i \(-0.0833974\pi\)
−0.933653 + 0.358180i \(0.883397\pi\)
\(242\) 10.7415 + 1.70129i 0.690493 + 0.109363i
\(243\) −7.44723 + 13.6945i −0.477740 + 0.878501i
\(244\) −0.0859239 0.118264i −0.00550072 0.00757109i
\(245\) −2.47160 + 17.4254i −0.157905 + 1.11327i
\(246\) −14.2071 3.72918i −0.905814 0.237764i
\(247\) 16.0299 2.53888i 1.01996 0.161545i
\(248\) −1.90338 3.73559i −0.120865 0.237210i
\(249\) 9.44125 3.67955i 0.598315 0.233182i
\(250\) 11.1672 0.542505i 0.706274 0.0343110i
\(251\) 24.7263i 1.56071i −0.625335 0.780357i \(-0.715038\pi\)
0.625335 0.780357i \(-0.284962\pi\)
\(252\) −10.8422 4.03544i −0.682994 0.254209i
\(253\) −0.432724 2.73211i −0.0272052 0.171767i
\(254\) −4.36369 3.17040i −0.273802 0.198929i
\(255\) −3.13691 13.3538i −0.196441 0.836249i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −20.2470 20.2470i −1.26297 1.26297i −0.949646 0.313326i \(-0.898557\pi\)
−0.313326 0.949646i \(-0.601443\pi\)
\(258\) −2.69276 12.3579i −0.167644 0.769372i
\(259\) −17.8445 + 5.79802i −1.10880 + 0.360272i
\(260\) −1.79751 5.24200i −0.111477 0.325095i
\(261\) −17.0334 + 7.79306i −1.05434 + 0.482378i
\(262\) 15.5156 + 7.90558i 0.958555 + 0.488408i
\(263\) −2.68232 1.36671i −0.165399 0.0842750i 0.369331 0.929298i \(-0.379587\pi\)
−0.534730 + 0.845023i \(0.679587\pi\)
\(264\) 0.610284 0.0351078i 0.0375604 0.00216073i
\(265\) −9.84001 + 0.159232i −0.604467 + 0.00978157i
\(266\) −24.0178 + 7.80385i −1.47262 + 0.478485i
\(267\) 3.46795 0.755655i 0.212235 0.0462454i
\(268\) −5.35387 5.35387i −0.327039 0.327039i
\(269\) −10.4918 + 7.62274i −0.639697 + 0.464767i −0.859746 0.510722i \(-0.829378\pi\)
0.220049 + 0.975489i \(0.429378\pi\)
\(270\) 10.9317 3.93661i 0.665285 0.239574i
\(271\) 13.7784 + 10.0106i 0.836981 + 0.608102i 0.921526 0.388317i \(-0.126944\pi\)
−0.0845447 + 0.996420i \(0.526944\pi\)
\(272\) 0.554059 + 3.49819i 0.0335948 + 0.212109i
\(273\) −11.0133 + 12.3578i −0.666555 + 0.747926i
\(274\) 17.9265i 1.08298i
\(275\) 1.46045 + 0.990501i 0.0880682 + 0.0597294i
\(276\) 4.92959 + 12.6487i 0.296726 + 0.761361i
\(277\) −4.82425 9.46812i −0.289861 0.568884i 0.699454 0.714677i \(-0.253427\pi\)
−0.989315 + 0.145793i \(0.953427\pi\)
\(278\) −17.8007 + 2.81935i −1.06761 + 0.169093i
\(279\) −1.44233 12.4947i −0.0863502 0.748036i
\(280\) 4.03851 + 7.61871i 0.241347 + 0.455305i
\(281\) 16.4932 + 22.7009i 0.983902 + 1.35422i 0.934701 + 0.355436i \(0.115668\pi\)
0.0492011 + 0.998789i \(0.484332\pi\)
\(282\) −2.97774 + 6.78104i −0.177322 + 0.403805i
\(283\) −25.3567 4.01611i −1.50730 0.238733i −0.652539 0.757755i \(-0.726296\pi\)
−0.854761 + 0.519022i \(0.826296\pi\)
\(284\) 1.90474 + 5.86218i 0.113025 + 0.347856i
\(285\) 13.3579 21.5605i 0.791256 1.27714i
\(286\) 0.270286 0.831854i 0.0159823 0.0491886i
\(287\) 14.8467 29.1383i 0.876372 1.71998i
\(288\) −2.88970 + 0.805995i −0.170277 + 0.0474937i
\(289\) −4.23760 1.37688i −0.249271 0.0809930i
\(290\) 13.3464 + 4.09898i 0.783726 + 0.240700i
\(291\) −7.70635 9.41786i −0.451754 0.552085i
\(292\) −1.63344 + 10.3131i −0.0955899 + 0.603531i
\(293\) 24.1559 24.1559i 1.41120 1.41120i 0.659495 0.751709i \(-0.270770\pi\)
0.751709 0.659495i \(-0.229230\pi\)
\(294\) 7.36648 11.4711i 0.429622 0.669010i
\(295\) 0.889572 + 5.08283i 0.0517929 + 0.295934i
\(296\) −2.85988 + 3.93629i −0.166227 + 0.228792i
\(297\) 1.75260 + 0.539930i 0.101696 + 0.0313299i
\(298\) 4.14221 2.11056i 0.239952 0.122262i
\(299\) 19.4242 1.12333
\(300\) −8.03792 3.22363i −0.464070 0.186117i
\(301\) 28.1596 1.62309
\(302\) 13.0575 6.65314i 0.751376 0.382845i
\(303\) 14.3376 8.37569i 0.823675 0.481171i
\(304\) −3.84926 + 5.29805i −0.220770 + 0.303864i
\(305\) −0.143666 + 0.293610i −0.00822629 + 0.0168121i
\(306\) −2.10294 + 10.4152i −0.120217 + 0.595398i
\(307\) −12.8970 + 12.8970i −0.736071 + 0.736071i −0.971815 0.235744i \(-0.924247\pi\)
0.235744 + 0.971815i \(0.424247\pi\)
\(308\) −0.212907 + 1.34424i −0.0121315 + 0.0765952i
\(309\) 8.91809 7.29740i 0.507333 0.415135i
\(310\) −5.38694 + 7.67255i −0.305958 + 0.435772i
\(311\) 15.4255 + 5.01205i 0.874699 + 0.284207i 0.711755 0.702428i \(-0.247901\pi\)
0.162945 + 0.986635i \(0.447901\pi\)
\(312\) −0.426897 + 4.27124i −0.0241683 + 0.241812i
\(313\) 2.45198 4.81228i 0.138594 0.272006i −0.811269 0.584674i \(-0.801223\pi\)
0.949863 + 0.312668i \(0.101223\pi\)
\(314\) −1.38637 + 4.26680i −0.0782372 + 0.240789i
\(315\) 3.38188 + 25.6467i 0.190547 + 1.44503i
\(316\) −0.422251 1.29956i −0.0237535 0.0731057i
\(317\) −8.47316 1.34202i −0.475900 0.0753752i −0.0861233 0.996284i \(-0.527448\pi\)
−0.389777 + 0.920909i \(0.627448\pi\)
\(318\) 6.97973 + 3.06499i 0.391404 + 0.171876i
\(319\) 1.29527 + 1.78278i 0.0725210 + 0.0998166i
\(320\) 2.00852 + 0.982784i 0.112279 + 0.0549393i
\(321\) 6.48862 24.7198i 0.362160 1.37973i
\(322\) −29.8523 + 4.72815i −1.66361 + 0.263489i
\(323\) 10.5300 + 20.6663i 0.585905 + 1.14990i
\(324\) −8.96804 0.757846i −0.498224 0.0421025i
\(325\) −8.47399 + 9.04099i −0.470052 + 0.501504i
\(326\) 10.8202i 0.599276i
\(327\) 14.3740 + 12.8102i 0.794884 + 0.708404i
\(328\) −1.32662 8.37596i −0.0732504 0.462485i
\(329\) −13.3399 9.69197i −0.735450 0.534336i
\(330\) −0.708486 1.16895i −0.0390008 0.0643486i
\(331\) 22.9895 16.7029i 1.26362 0.918073i 0.264690 0.964334i \(-0.414731\pi\)
0.998929 + 0.0462607i \(0.0147305\pi\)
\(332\) 4.13675 + 4.13675i 0.227034 + 0.227034i
\(333\) −12.1599 + 8.07440i −0.666360 + 0.442474i
\(334\) 15.9719 5.18960i 0.873946 0.283962i
\(335\) −4.97057 + 16.1843i −0.271571 + 0.884244i
\(336\) −0.383604 6.66824i −0.0209273 0.363783i
\(337\) −4.22871 2.15464i −0.230353 0.117371i 0.335005 0.942216i \(-0.391262\pi\)
−0.565358 + 0.824846i \(0.691262\pi\)
\(338\) −6.11059 3.11350i −0.332372 0.169352i
\(339\) −0.175074 3.04335i −0.00950874 0.165292i
\(340\) 6.33101 4.75814i 0.343347 0.258046i
\(341\) −1.40726 + 0.457245i −0.0762072 + 0.0247612i
\(342\) −16.3666 + 10.8677i −0.885007 + 0.587660i
\(343\) 2.37470 + 2.37470i 0.128222 + 0.128222i
\(344\) 5.90767 4.29217i 0.318520 0.231418i
\(345\) 19.8270 22.9856i 1.06745 1.23750i
\(346\) 14.0925 + 10.2388i 0.757620 + 0.550443i
\(347\) −1.25574 7.92843i −0.0674116 0.425620i −0.998195 0.0600500i \(-0.980874\pi\)
0.930784 0.365570i \(-0.119126\pi\)
\(348\) −8.07367 7.19529i −0.432794 0.385708i
\(349\) 18.9234i 1.01295i −0.862256 0.506474i \(-0.830949\pi\)
0.862256 0.506474i \(-0.169051\pi\)
\(350\) 10.8227 15.9575i 0.578496 0.852964i
\(351\) −5.66994 + 11.5622i −0.302639 + 0.617143i
\(352\) 0.160227 + 0.314463i 0.00854013 + 0.0167609i
\(353\) 4.66620 0.739053i 0.248357 0.0393358i −0.0310149 0.999519i \(-0.509874\pi\)
0.279371 + 0.960183i \(0.409874\pi\)
\(354\) 1.01478 3.86602i 0.0539349 0.205477i
\(355\) 9.58695 9.90233i 0.508823 0.525561i
\(356\) 1.20449 + 1.65784i 0.0638379 + 0.0878654i
\(357\) −21.6602 9.51159i −1.14638 0.503406i
\(358\) 7.25818 + 1.14958i 0.383607 + 0.0607573i
\(359\) −4.67561 14.3900i −0.246769 0.759478i −0.995340 0.0964232i \(-0.969260\pi\)
0.748571 0.663054i \(-0.230740\pi\)
\(360\) 4.61864 + 4.86500i 0.243423 + 0.256408i
\(361\) −7.38121 + 22.7170i −0.388485 + 1.19563i
\(362\) 0.304777 0.598158i 0.0160187 0.0314385i
\(363\) −1.87335 + 18.7434i −0.0983252 + 0.983775i
\(364\) −9.08922 2.95327i −0.476405 0.154793i
\(365\) 22.0859 7.57338i 1.15603 0.396409i
\(366\) 0.195954 0.160343i 0.0102427 0.00838128i
\(367\) −5.73021 + 36.1791i −0.299114 + 1.88853i 0.140078 + 0.990140i \(0.455265\pi\)
−0.439193 + 0.898393i \(0.644735\pi\)
\(368\) −5.54211 + 5.54211i −0.288902 + 0.288902i
\(369\) 5.03522 24.9378i 0.262123 1.29821i
\(370\) 10.7718 + 1.52786i 0.560000 + 0.0794297i
\(371\) −9.97595 + 13.7307i −0.517926 + 0.712864i
\(372\) 6.27021 3.66290i 0.325095 0.189913i
\(373\) −1.97517 + 1.00640i −0.102270 + 0.0521093i −0.504377 0.863483i \(-0.668278\pi\)
0.402107 + 0.915593i \(0.368278\pi\)
\(374\) 1.25001 0.0646363
\(375\) 2.04895 + 19.2562i 0.105807 + 0.994387i
\(376\) −4.27588 −0.220512
\(377\) −13.7875 + 7.02506i −0.710090 + 0.361809i
\(378\) 5.89952 19.1497i 0.303439 0.984952i
\(379\) 4.15559 5.71968i 0.213458 0.293800i −0.688839 0.724914i \(-0.741879\pi\)
0.902297 + 0.431114i \(0.141879\pi\)
\(380\) 14.4983 + 2.05643i 0.743749 + 0.105492i
\(381\) 5.04816 7.86103i 0.258625 0.402733i
\(382\) 9.96347 9.96347i 0.509775 0.509775i
\(383\) −2.17700 + 13.7450i −0.111240 + 0.702339i 0.867532 + 0.497382i \(0.165705\pi\)
−0.978771 + 0.204957i \(0.934295\pi\)
\(384\) −1.09687 1.34048i −0.0559744 0.0684059i
\(385\) 2.87874 0.987133i 0.146714 0.0503090i
\(386\) 3.89161 + 1.26446i 0.198078 + 0.0643593i
\(387\) 21.1014 5.88560i 1.07264 0.299182i
\(388\) 3.18963 6.26000i 0.161929 0.317803i
\(389\) 4.65972 14.3411i 0.236257 0.727125i −0.760695 0.649110i \(-0.775142\pi\)
0.996952 0.0780155i \(-0.0248584\pi\)
\(390\) 8.88562 3.62968i 0.449941 0.183796i
\(391\) 8.57820 + 26.4010i 0.433818 + 1.33515i
\(392\) 7.77397 + 1.23128i 0.392645 + 0.0621888i
\(393\) −12.1268 + 27.6158i −0.611719 + 1.39303i
\(394\) −13.3665 18.3974i −0.673395 0.926849i
\(395\) −2.12528 + 2.19519i −0.106934 + 0.110452i
\(396\) 0.121416 + 1.05181i 0.00610139 + 0.0528552i
\(397\) −13.6256 + 2.15808i −0.683849 + 0.108311i −0.488686 0.872460i \(-0.662524\pi\)
−0.195163 + 0.980771i \(0.562524\pi\)
\(398\) −2.86862 5.62998i −0.143791 0.282205i
\(399\) −15.8835 40.7551i −0.795171 2.04031i
\(400\) −0.161779 4.99738i −0.00808895 0.249869i
\(401\) 15.8196i 0.789991i 0.918683 + 0.394995i \(0.129254\pi\)
−0.918683 + 0.394995i \(0.870746\pi\)
\(402\) 8.72529 9.79044i 0.435178 0.488303i
\(403\) −1.62541 10.2624i −0.0809674 0.511208i
\(404\) 7.75588 + 5.63497i 0.385869 + 0.280350i
\(405\) 7.89459 + 18.5115i 0.392285 + 0.919844i
\(406\) 19.4795 14.1527i 0.966750 0.702385i
\(407\) 1.21424 + 1.21424i 0.0601875 + 0.0601875i
\(408\) −5.99393 + 1.30606i −0.296744 + 0.0646595i
\(409\) −5.65867 + 1.83861i −0.279803 + 0.0909136i −0.445557 0.895254i \(-0.646994\pi\)
0.165754 + 0.986167i \(0.446994\pi\)
\(410\) −15.1588 + 11.3927i −0.748638 + 0.562647i
\(411\) −30.9984 + 1.78324i −1.52904 + 0.0879610i
\(412\) 5.92780 + 3.02037i 0.292042 + 0.148803i
\(413\) 7.92905 + 4.04005i 0.390163 + 0.198798i
\(414\) −21.3816 + 9.78243i −1.05085 + 0.480780i
\(415\) 3.84060 12.5051i 0.188527 0.613850i
\(416\) −2.35699 + 0.765834i −0.115561 + 0.0375481i
\(417\) −6.64591 30.5003i −0.325452 1.49361i
\(418\) 1.63430 + 1.63430i 0.0799363 + 0.0799363i
\(419\) 3.49605 2.54003i 0.170793 0.124088i −0.499105 0.866542i \(-0.666338\pi\)
0.669898 + 0.742453i \(0.266338\pi\)
\(420\) −12.7725 + 7.74124i −0.623233 + 0.377734i
\(421\) −20.2471 14.7103i −0.986781 0.716939i −0.0275674 0.999620i \(-0.508776\pi\)
−0.959214 + 0.282681i \(0.908776\pi\)
\(422\) −0.650182 4.10508i −0.0316503 0.199832i
\(423\) −12.0219 4.47453i −0.584526 0.217559i
\(424\) 4.40116i 0.213739i
\(425\) −16.0307 7.52496i −0.777603 0.365014i
\(426\) −9.94736 + 3.87680i −0.481951 + 0.187831i
\(427\) 0.255924 + 0.502279i 0.0123850 + 0.0243070i
\(428\) 14.5738 2.30827i 0.704452 0.111574i
\(429\) 1.46532 + 0.384627i 0.0707464 + 0.0185700i
\(430\) −14.6667 7.17656i −0.707293 0.346085i
\(431\) −4.11469 5.66339i −0.198198 0.272796i 0.698337 0.715769i \(-0.253924\pi\)
−0.896535 + 0.442973i \(0.853924\pi\)
\(432\) −1.68117 4.91667i −0.0808855 0.236553i
\(433\) −9.74698 1.54377i −0.468410 0.0741889i −0.0822322 0.996613i \(-0.526205\pi\)
−0.386178 + 0.922424i \(0.626205\pi\)
\(434\) 4.99607 + 15.3763i 0.239819 + 0.738087i
\(435\) −5.76028 + 23.4862i −0.276184 + 1.12608i
\(436\) −3.43511 + 10.5722i −0.164512 + 0.506315i
\(437\) −23.3021 + 45.7330i −1.11469 + 2.18770i
\(438\) −17.9959 1.79863i −0.859877 0.0859420i
\(439\) −0.555271 0.180419i −0.0265016 0.00861091i 0.295736 0.955270i \(-0.404435\pi\)
−0.322238 + 0.946659i \(0.604435\pi\)
\(440\) 0.453475 0.645879i 0.0216186 0.0307911i
\(441\) 20.5686 + 11.5970i 0.979456 + 0.552237i
\(442\) −1.37312 + 8.66953i −0.0653126 + 0.412368i
\(443\) −6.33032 + 6.33032i −0.300763 + 0.300763i −0.841312 0.540549i \(-0.818216\pi\)
0.540549 + 0.841312i \(0.318216\pi\)
\(444\) −7.09108 4.55372i −0.336528 0.216110i
\(445\) 2.01393 4.11586i 0.0954692 0.195110i
\(446\) −9.03387 + 12.4341i −0.427766 + 0.588770i
\(447\) 4.06161 + 6.95273i 0.192108 + 0.328853i
\(448\) 3.43597 1.75071i 0.162334 0.0827134i
\(449\) 18.3782 0.867322 0.433661 0.901076i \(-0.357221\pi\)
0.433661 + 0.901076i \(0.357221\pi\)
\(450\) 4.77471 14.2198i 0.225082 0.670327i
\(451\) −2.99298 −0.140934
\(452\) 1.56816 0.799015i 0.0737598 0.0375825i
\(453\) 12.8035 + 21.9171i 0.601559 + 1.02976i
\(454\) 8.24401 11.3469i 0.386911 0.532537i
\(455\) 3.68408 + 21.0501i 0.172713 + 0.986843i
\(456\) −9.54425 6.12908i −0.446950 0.287021i
\(457\) −24.7918 + 24.7918i −1.15971 + 1.15971i −0.175174 + 0.984537i \(0.556049\pi\)
−0.984537 + 0.175174i \(0.943951\pi\)
\(458\) −2.71142 + 17.1192i −0.126696 + 0.799928i
\(459\) −18.2191 2.60034i −0.850394 0.121373i
\(460\) 16.7534 + 5.14534i 0.781130 + 0.239903i
\(461\) −0.133994 0.0435374i −0.00624074 0.00202774i 0.305895 0.952065i \(-0.401044\pi\)
−0.312136 + 0.950038i \(0.601044\pi\)
\(462\) −2.34563 0.234438i −0.109129 0.0109071i
\(463\) −4.02806 + 7.90552i −0.187200 + 0.367401i −0.965464 0.260537i \(-0.916101\pi\)
0.778264 + 0.627937i \(0.216101\pi\)
\(464\) 1.92945 5.93824i 0.0895725 0.275676i
\(465\) −13.8032 8.55183i −0.640107 0.396582i
\(466\) 0.760291 + 2.33993i 0.0352198 + 0.108395i
\(467\) 4.81480 + 0.762590i 0.222803 + 0.0352885i 0.266838 0.963742i \(-0.414021\pi\)
−0.0440349 + 0.999030i \(0.514021\pi\)
\(468\) −7.42827 0.313305i −0.343372 0.0144825i
\(469\) 17.1621 + 23.6216i 0.792470 + 1.09074i
\(470\) 4.47794 + 8.44770i 0.206552 + 0.389663i
\(471\) −7.51602 1.97285i −0.346320 0.0909043i
\(472\) 2.27925 0.360998i 0.104911 0.0166163i
\(473\) −1.17002 2.29630i −0.0537977 0.105584i
\(474\) 2.20518 0.859427i 0.101287 0.0394748i
\(475\) −11.1207 30.7975i −0.510251 1.41308i
\(476\) 13.6581i 0.626020i
\(477\) −4.60564 + 12.3742i −0.210878 + 0.566575i
\(478\) −0.380627 2.40319i −0.0174095 0.109919i
\(479\) 11.5308 + 8.37759i 0.526854 + 0.382782i 0.819180 0.573537i \(-0.194429\pi\)
−0.292326 + 0.956319i \(0.594429\pi\)
\(480\) −1.49963 + 3.57087i −0.0684482 + 0.162987i
\(481\) −9.75526 + 7.08761i −0.444802 + 0.323167i
\(482\) −1.14460 1.14460i −0.0521349 0.0521349i
\(483\) −11.1454 51.1501i −0.507135 2.32741i
\(484\) −10.3432 + 3.36070i −0.470144 + 0.152759i
\(485\) −15.7080 + 0.254189i −0.713265 + 0.0115421i
\(486\) 0.418364 15.5828i 0.0189774 0.706852i
\(487\) −31.0777 15.8349i −1.40827 0.717547i −0.425945 0.904749i \(-0.640058\pi\)
−0.982321 + 0.187202i \(0.940058\pi\)
\(488\) 0.130250 + 0.0663655i 0.00589612 + 0.00300422i
\(489\) 18.7102 1.07634i 0.846106 0.0486739i
\(490\) −5.70876 16.6482i −0.257895 0.752090i
\(491\) 5.09165 1.65438i 0.229783 0.0746610i −0.191862 0.981422i \(-0.561453\pi\)
0.421645 + 0.906761i \(0.361453\pi\)
\(492\) 14.3517 3.12718i 0.647023 0.140984i
\(493\) −15.6372 15.6372i −0.704266 0.704266i
\(494\) −13.1301 + 9.53958i −0.590751 + 0.429206i
\(495\) 1.95086 1.34139i 0.0876848 0.0602909i
\(496\) 3.39184 + 2.46432i 0.152298 + 0.110651i
\(497\) −3.71838 23.4769i −0.166792 1.05308i
\(498\) −6.74174 + 7.56474i −0.302104 + 0.338984i
\(499\) 8.93736i 0.400091i 0.979787 + 0.200046i \(0.0641090\pi\)
−0.979787 + 0.200046i \(0.935891\pi\)
\(500\) −9.70373 + 5.55316i −0.433964 + 0.248345i
\(501\) 10.5626 + 27.1023i 0.471903 + 1.21084i
\(502\) 11.2255 + 22.0313i 0.501020 + 0.983307i
\(503\) −2.88408 + 0.456793i −0.128595 + 0.0203674i −0.220400 0.975410i \(-0.570736\pi\)
0.0918053 + 0.995777i \(0.470736\pi\)
\(504\) 11.4925 1.32665i 0.511917 0.0590936i
\(505\) 3.01043 21.2243i 0.133962 0.944468i
\(506\) 1.62591 + 2.23788i 0.0722807 + 0.0994859i
\(507\) 4.77599 10.8761i 0.212109 0.483025i
\(508\) 5.32741 + 0.843778i 0.236365 + 0.0374366i
\(509\) 3.24395 + 9.98385i 0.143786 + 0.442527i 0.996853 0.0792745i \(-0.0252604\pi\)
−0.853067 + 0.521801i \(0.825260\pi\)
\(510\) 8.85751 + 10.4742i 0.392217 + 0.463806i
\(511\) 12.4429 38.2953i 0.550441 1.69408i
\(512\) 0.453990 0.891007i 0.0200637 0.0393773i
\(513\) −20.4205 27.2200i −0.901586 1.20179i
\(514\) 27.2321 + 8.84825i 1.20116 + 0.390280i
\(515\) −0.240701 14.8745i −0.0106065 0.655447i
\(516\) 8.00965 + 9.78853i 0.352605 + 0.430916i
\(517\) −0.236073 + 1.49051i −0.0103825 + 0.0655524i
\(518\) 13.2673 13.2673i 0.582932 0.582932i
\(519\) −16.3030 + 25.3872i −0.715624 + 1.11437i
\(520\) 3.98141 + 3.85461i 0.174596 + 0.169036i
\(521\) −11.1471 + 15.3427i −0.488364 + 0.672175i −0.980085 0.198578i \(-0.936368\pi\)
0.491722 + 0.870753i \(0.336368\pi\)
\(522\) 11.6389 14.6767i 0.509421 0.642381i
\(523\) 21.7058 11.0596i 0.949127 0.483604i 0.0903250 0.995912i \(-0.471209\pi\)
0.858802 + 0.512308i \(0.171209\pi\)
\(524\) −17.4135 −0.760714
\(525\) 28.6702 + 17.1271i 1.25127 + 0.747487i
\(526\) 3.01044 0.131261
\(527\) 13.2307 6.74137i 0.576338 0.293659i
\(528\) −0.527829 + 0.308344i −0.0229708 + 0.0134190i
\(529\) −22.5886 + 31.0905i −0.982111 + 1.35176i
\(530\) 8.69523 4.60915i 0.377696 0.200209i
\(531\) 6.78604 + 1.37017i 0.294489 + 0.0594605i
\(532\) 17.8571 17.8571i 0.774205 0.774205i
\(533\) 3.28775 20.7580i 0.142408 0.899131i
\(534\) −2.74691 + 2.24771i −0.118870 + 0.0972680i
\(535\) −19.8229 26.3756i −0.857018 1.14032i
\(536\) 7.20094 + 2.33973i 0.311033 + 0.101061i
\(537\) −1.26584 + 12.6651i −0.0546251 + 0.546541i
\(538\) 5.88761 11.5551i 0.253833 0.498175i
\(539\) 0.858409 2.64191i 0.0369743 0.113795i
\(540\) −7.95308 + 8.47045i −0.342246 + 0.364510i
\(541\) 8.94591 + 27.5327i 0.384615 + 1.18372i 0.936759 + 0.349974i \(0.113810\pi\)
−0.552144 + 0.833749i \(0.686190\pi\)
\(542\) −16.8214 2.66425i −0.722542 0.114439i
\(543\) 1.06465 + 0.467516i 0.0456884 + 0.0200630i
\(544\) −2.08182 2.86537i −0.0892571 0.122852i
\(545\) 24.4845 4.28516i 1.04880 0.183556i
\(546\) 4.20261 16.0108i 0.179855 0.685198i
\(547\) 12.9801 2.05584i 0.554988 0.0879014i 0.127360 0.991857i \(-0.459350\pi\)
0.427627 + 0.903955i \(0.359350\pi\)
\(548\) −8.13848 15.9727i −0.347659 0.682319i
\(549\) 0.296757 + 0.322892i 0.0126653 + 0.0137807i
\(550\) −1.75094 0.219514i −0.0746605 0.00936011i
\(551\) 40.8893i 1.74194i
\(552\) −10.1347 9.03207i −0.431360 0.384430i
\(553\) 0.824307 + 5.20447i 0.0350531 + 0.221317i
\(554\) 8.59687 + 6.24599i 0.365246 + 0.265367i
\(555\) −1.57044 + 18.7785i −0.0666614 + 0.797104i
\(556\) 14.5805 10.5934i 0.618353 0.449260i
\(557\) 24.6270 + 24.6270i 1.04348 + 1.04348i 0.999011 + 0.0444707i \(0.0141601\pi\)
0.0444707 + 0.999011i \(0.485840\pi\)
\(558\) 6.95759 + 10.4780i 0.294538 + 0.443570i
\(559\) 17.2114 5.59233i 0.727966 0.236530i
\(560\) −7.05717 4.95488i −0.298220 0.209382i
\(561\) 0.124345 + 2.16150i 0.00524983 + 0.0912587i
\(562\) −25.0016 12.7389i −1.05463 0.537359i
\(563\) 8.71723 + 4.44165i 0.367388 + 0.187193i 0.627931 0.778269i \(-0.283902\pi\)
−0.260544 + 0.965462i \(0.583902\pi\)
\(564\) −0.425343 7.39381i −0.0179102 0.311336i
\(565\) −3.22085 2.26138i −0.135502 0.0951368i
\(566\) 24.4163 7.93332i 1.02629 0.333462i
\(567\) 33.7003 + 8.29649i 1.41528 + 0.348420i
\(568\) −4.35851 4.35851i −0.182879 0.182879i
\(569\) −8.66014 + 6.29196i −0.363052 + 0.263773i −0.754324 0.656502i \(-0.772035\pi\)
0.391272 + 0.920275i \(0.372035\pi\)
\(570\) −2.11373 + 25.2750i −0.0885345 + 1.05865i
\(571\) 12.5798 + 9.13980i 0.526450 + 0.382489i 0.819028 0.573753i \(-0.194513\pi\)
−0.292578 + 0.956242i \(0.594513\pi\)
\(572\) 0.136828 + 0.863895i 0.00572105 + 0.0361213i
\(573\) 18.2199 + 16.2376i 0.761146 + 0.678337i
\(574\) 32.7026i 1.36498i
\(575\) −7.37961 38.4875i −0.307751 1.60504i
\(576\) 2.20883 2.03004i 0.0920345 0.0845852i
\(577\) −6.76199 13.2712i −0.281505 0.552485i 0.706350 0.707863i \(-0.250341\pi\)
−0.987855 + 0.155378i \(0.950341\pi\)
\(578\) 4.40082 0.697022i 0.183050 0.0289923i
\(579\) −1.79938 + 6.85512i −0.0747795 + 0.284889i
\(580\) −13.7526 + 2.40691i −0.571046 + 0.0999417i
\(581\) −13.2606 18.2516i −0.550140 0.757203i
\(582\) 11.1420 + 4.89277i 0.461852 + 0.202812i
\(583\) 1.53418 + 0.242990i 0.0635392 + 0.0100636i
\(584\) −3.22666 9.93064i −0.133520 0.410933i
\(585\) 7.16032 + 15.0039i 0.296043 + 0.620334i
\(586\) −10.5565 + 32.4896i −0.436086 + 1.34213i
\(587\) −11.6079 + 22.7817i −0.479108 + 0.940302i 0.517315 + 0.855795i \(0.326932\pi\)
−0.996423 + 0.0845070i \(0.973068\pi\)
\(588\) −1.35580 + 13.5652i −0.0559121 + 0.559418i
\(589\) 26.1121 + 8.48435i 1.07593 + 0.349592i
\(590\) −3.10017 4.12498i −0.127632 0.169823i
\(591\) 30.4830 24.9433i 1.25390 1.02603i
\(592\) 0.761135 4.80562i 0.0312825 0.197510i
\(593\) 5.46116 5.46116i 0.224263 0.224263i −0.586028 0.810291i \(-0.699309\pi\)
0.810291 + 0.586028i \(0.199309\pi\)
\(594\) −1.80670 + 0.314580i −0.0741297 + 0.0129074i
\(595\) −26.9839 + 14.3036i −1.10623 + 0.586390i
\(596\) −2.73256 + 3.76105i −0.111930 + 0.154058i
\(597\) 9.44996 5.52043i 0.386761 0.225936i
\(598\) −17.3071 + 8.81838i −0.707738 + 0.360611i
\(599\) 20.6409 0.843363 0.421681 0.906744i \(-0.361440\pi\)
0.421681 + 0.906744i \(0.361440\pi\)
\(600\) 8.62534 0.776862i 0.352128 0.0317153i
\(601\) 17.9854 0.733642 0.366821 0.930292i \(-0.380446\pi\)
0.366821 + 0.930292i \(0.380446\pi\)
\(602\) −25.0904 + 12.7842i −1.02261 + 0.521045i
\(603\) 17.7975 + 14.1138i 0.724770 + 0.574758i
\(604\) −8.61387 + 11.8560i −0.350494 + 0.482413i
\(605\) 17.4716 + 16.9151i 0.710320 + 0.687697i
\(606\) −8.97244 + 13.9719i −0.364480 + 0.567571i
\(607\) 5.54524 5.54524i 0.225074 0.225074i −0.585557 0.810631i \(-0.699124\pi\)
0.810631 + 0.585557i \(0.199124\pi\)
\(608\) 1.02445 6.46812i 0.0415469 0.262317i
\(609\) 26.4104 + 32.2759i 1.07020 + 1.30789i
\(610\) −0.00528883 0.326831i −0.000214138 0.0132330i
\(611\) −10.0782 3.27461i −0.407721 0.132477i
\(612\) −2.85467 10.2347i −0.115393 0.413715i
\(613\) −2.13588 + 4.19191i −0.0862676 + 0.169310i −0.930110 0.367282i \(-0.880288\pi\)
0.843842 + 0.536592i \(0.180288\pi\)
\(614\) 5.63620 17.3464i 0.227459 0.700045i
\(615\) −21.2082 25.0791i −0.855195 1.01129i
\(616\) −0.420571 1.29439i −0.0169453 0.0521523i
\(617\) 40.5328 + 6.41977i 1.63179 + 0.258450i 0.904058 0.427410i \(-0.140574\pi\)
0.727733 + 0.685861i \(0.240574\pi\)
\(618\) −4.63313 + 10.5508i −0.186372 + 0.424414i
\(619\) −10.1486 13.9684i −0.407908 0.561438i 0.554798 0.831985i \(-0.312795\pi\)
−0.962707 + 0.270547i \(0.912795\pi\)
\(620\) 1.31654 9.28192i 0.0528733 0.372771i
\(621\) −19.0426 35.9998i −0.764155 1.44462i
\(622\) −16.0196 + 2.53726i −0.642329 + 0.101735i
\(623\) −3.58757 7.04100i −0.143733 0.282092i
\(624\) −1.55874 3.99951i −0.0623994 0.160109i
\(625\) 21.1335 + 13.3557i 0.845340 + 0.534229i
\(626\) 5.40095i 0.215865i
\(627\) −2.66345 + 2.98859i −0.106368 + 0.119353i
\(628\) −0.701824 4.43114i −0.0280058 0.176822i
\(629\) −13.9415 10.1291i −0.555885 0.403874i
\(630\) −14.6566 21.3160i −0.583934 0.849250i
\(631\) −29.4746 + 21.4146i −1.17337 + 0.852501i −0.991408 0.130805i \(-0.958244\pi\)
−0.181959 + 0.983306i \(0.558244\pi\)
\(632\) 0.966214 + 0.966214i 0.0384339 + 0.0384339i
\(633\) 7.03380 1.53264i 0.279569 0.0609171i
\(634\) 8.15891 2.65099i 0.324032 0.105284i
\(635\) −3.91214 11.4088i −0.155249 0.452745i
\(636\) −7.61046 + 0.437806i −0.301774 + 0.0173601i
\(637\) 17.3803 + 8.85568i 0.688631 + 0.350875i
\(638\) −1.96346 1.00043i −0.0777340 0.0396074i
\(639\) −7.69324 16.8152i −0.304340 0.665201i
\(640\) −2.23578 + 0.0361796i −0.0883768 + 0.00143013i
\(641\) −28.1775 + 9.15543i −1.11294 + 0.361618i −0.807071 0.590454i \(-0.798949\pi\)
−0.305874 + 0.952072i \(0.598949\pi\)
\(642\) 5.44117 + 24.9713i 0.214746 + 0.985539i
\(643\) 16.2471 + 16.2471i 0.640721 + 0.640721i 0.950733 0.310012i \(-0.100333\pi\)
−0.310012 + 0.950733i \(0.600333\pi\)
\(644\) 24.4521 17.7655i 0.963547 0.700058i
\(645\) 10.9507 26.0755i 0.431183 1.02672i
\(646\) −18.7646 13.6333i −0.738284 0.536394i
\(647\) −0.280589 1.77157i −0.0110311 0.0696477i 0.981559 0.191161i \(-0.0612253\pi\)
−0.992590 + 0.121513i \(0.961225\pi\)
\(648\) 8.33463 3.39616i 0.327415 0.133414i
\(649\) 0.814444i 0.0319697i
\(650\) 3.44585 11.9027i 0.135157 0.466862i
\(651\) −26.0916 + 10.1687i −1.02261 + 0.398544i
\(652\) 4.91227 + 9.64088i 0.192379 + 0.377566i
\(653\) −26.3159 + 4.16803i −1.02982 + 0.163107i −0.648404 0.761296i \(-0.724563\pi\)
−0.381416 + 0.924404i \(0.624563\pi\)
\(654\) −18.6230 4.88829i −0.728218 0.191147i
\(655\) 18.2364 + 34.4033i 0.712557 + 1.34425i
\(656\) 4.98463 + 6.86076i 0.194617 + 0.267868i
\(657\) 1.32004 31.2973i 0.0514996 1.22102i
\(658\) 16.2860 + 2.57944i 0.634893 + 0.100557i
\(659\) 2.02081 + 6.21940i 0.0787195 + 0.242274i 0.982670 0.185363i \(-0.0593462\pi\)
−0.903951 + 0.427637i \(0.859346\pi\)
\(660\) 1.16196 + 0.719897i 0.0452291 + 0.0280219i
\(661\) 5.97584 18.3917i 0.232433 0.715356i −0.765018 0.644008i \(-0.777270\pi\)
0.997452 0.0713473i \(-0.0227299\pi\)
\(662\) −12.9009 + 25.3194i −0.501407 + 0.984066i
\(663\) −15.1279 1.51198i −0.587518 0.0587206i
\(664\) −5.56392 1.80783i −0.215922 0.0701573i
\(665\) −53.9807 16.5787i −2.09328 0.642894i
\(666\) 7.16887 12.7148i 0.277788 0.492690i
\(667\) 7.65551 48.3350i 0.296422 1.87154i
\(668\) −11.8751 + 11.8751i −0.459461 + 0.459461i
\(669\) −22.3995 14.3844i −0.866015 0.556134i
\(670\) −2.91872 16.6769i −0.112760 0.644286i
\(671\) 0.0303252 0.0417390i 0.00117069 0.00161132i
\(672\) 3.36911 + 5.76730i 0.129966 + 0.222478i
\(673\) 39.1978 19.9723i 1.51096 0.769874i 0.514793 0.857315i \(-0.327869\pi\)
0.996170 + 0.0874407i \(0.0278688\pi\)
\(674\) 4.74599 0.182809
\(675\) 25.0637 + 6.84187i 0.964702 + 0.263344i
\(676\) 6.85808 0.263772
\(677\) 33.3683 17.0020i 1.28245 0.653440i 0.326008 0.945367i \(-0.394296\pi\)
0.956441 + 0.291927i \(0.0942963\pi\)
\(678\) 1.53764 + 2.63216i 0.0590528 + 0.101087i
\(679\) −15.9250 + 21.9189i −0.611147 + 0.841171i
\(680\) −3.48082 + 7.11375i −0.133483 + 0.272800i
\(681\) 20.4411 + 13.1267i 0.783303 + 0.503018i
\(682\) 1.04629 1.04629i 0.0400645 0.0400645i
\(683\) −5.33840 + 33.7054i −0.204268 + 1.28970i 0.645995 + 0.763342i \(0.276443\pi\)
−0.850263 + 0.526358i \(0.823557\pi\)
\(684\) 9.64894 17.1135i 0.368937 0.654352i
\(685\) −23.0336 + 32.8064i −0.880067 + 1.25347i
\(686\) −3.19397 1.03778i −0.121946 0.0396228i
\(687\) −29.8721 2.98562i −1.13969 0.113909i
\(688\) −3.31516 + 6.50638i −0.126389 + 0.248053i
\(689\) −3.37056 + 10.3735i −0.128408 + 0.395199i
\(690\) −7.23074 + 29.4816i −0.275269 + 1.12235i
\(691\) −9.75674 30.0282i −0.371164 1.14232i −0.946030 0.324078i \(-0.894946\pi\)
0.574867 0.818247i \(-0.305054\pi\)
\(692\) −17.2049 2.72498i −0.654031 0.103588i
\(693\) 0.172057 4.07936i 0.00653591 0.154962i
\(694\) 4.71830 + 6.49419i 0.179104 + 0.246516i
\(695\) −36.1986 17.7123i −1.37309 0.671865i
\(696\) 10.4603 + 2.74568i 0.396496 + 0.104075i
\(697\) 29.6659 4.69862i 1.12368 0.177973i
\(698\) 8.59105 + 16.8609i 0.325176 + 0.638194i
\(699\) −3.97056 + 1.54745i −0.150181 + 0.0585301i
\(700\) −2.39851 + 19.1316i −0.0906552 + 0.723107i
\(701\) 41.1349i 1.55364i −0.629720 0.776822i \(-0.716830\pi\)
0.629720 0.776822i \(-0.283170\pi\)
\(702\) −0.197163 12.8761i −0.00744143 0.485976i
\(703\) −4.98448 31.4708i −0.187993 1.18694i
\(704\) −0.285527 0.207447i −0.0107612 0.00781846i
\(705\) −14.1623 + 8.58356i −0.533381 + 0.323275i
\(706\) −3.82209 + 2.77691i −0.143846 + 0.104510i
\(707\) −26.1413 26.1413i −0.983143 0.983143i
\(708\) 0.850963 + 3.90535i 0.0319812 + 0.146772i
\(709\) −48.5191 + 15.7648i −1.82217 + 0.592060i −0.822443 + 0.568848i \(0.807389\pi\)
−0.999731 + 0.0232123i \(0.992611\pi\)
\(710\) −4.04647 + 13.1754i −0.151861 + 0.494465i
\(711\) 1.70547 + 3.72768i 0.0639603 + 0.139799i
\(712\) −1.82585 0.930319i −0.0684268 0.0348652i
\(713\) 29.2785 + 14.9181i 1.09649 + 0.558689i
\(714\) 23.6176 1.35865i 0.883865 0.0508460i
\(715\) 1.56347 1.17505i 0.0584706 0.0439442i
\(716\) −6.98899 + 2.27086i −0.261191 + 0.0848660i
\(717\) 4.11771 0.897235i 0.153779 0.0335079i
\(718\) 10.6989 + 10.6989i 0.399281 + 0.399281i
\(719\) −29.8994 + 21.7232i −1.11506 + 0.810138i −0.983453 0.181164i \(-0.942013\pi\)
−0.131606 + 0.991302i \(0.542013\pi\)
\(720\) −6.32390 2.23793i −0.235678 0.0834026i
\(721\) −20.7558 15.0800i −0.772985 0.561607i
\(722\) −3.73661 23.5920i −0.139062 0.878004i
\(723\) 1.86537 2.09309i 0.0693738 0.0778427i
\(724\) 0.671329i 0.0249497i
\(725\) 19.1578 + 24.6499i 0.711502 + 0.915474i
\(726\) −6.84017 17.5510i −0.253863 0.651379i
\(727\) 8.55075 + 16.7818i 0.317130 + 0.622402i 0.993458 0.114198i \(-0.0364299\pi\)
−0.676328 + 0.736600i \(0.736430\pi\)
\(728\) 9.43931 1.49504i 0.349844 0.0554099i
\(729\) 26.9873 0.826673i 0.999531 0.0306175i
\(730\) −16.2405 + 16.7747i −0.601087 + 0.620861i
\(731\) 15.2020 + 20.9238i 0.562266 + 0.773893i
\(732\) −0.101802 + 0.231828i −0.00376271 + 0.00856862i
\(733\) 34.3095 + 5.43410i 1.26725 + 0.200713i 0.753627 0.657302i \(-0.228302\pi\)
0.513625 + 0.858015i \(0.328302\pi\)
\(734\) −11.3193 34.8373i −0.417804 1.28587i
\(735\) 28.2201 11.5276i 1.04091 0.425203i
\(736\) 2.42199 7.45412i 0.0892758 0.274763i
\(737\) 1.21316 2.38096i 0.0446873 0.0877038i
\(738\) 6.83513 + 24.5057i 0.251605 + 0.902068i
\(739\) 2.70309 + 0.878288i 0.0994348 + 0.0323083i 0.358312 0.933602i \(-0.383352\pi\)
−0.258877 + 0.965910i \(0.583352\pi\)
\(740\) −10.2914 + 3.52897i −0.378319 + 0.129727i
\(741\) −17.8019 21.7555i −0.653968 0.799209i
\(742\) 2.65502 16.7632i 0.0974689 0.615395i
\(743\) −19.3245 + 19.3245i −0.708947 + 0.708947i −0.966314 0.257367i \(-0.917145\pi\)
0.257367 + 0.966314i \(0.417145\pi\)
\(744\) −3.92387 + 6.11028i −0.143856 + 0.224014i
\(745\) 10.2923 + 1.45984i 0.377079 + 0.0534845i
\(746\) 1.30299 1.79341i 0.0477059 0.0656615i
\(747\) −13.7515 10.9053i −0.503142 0.399002i
\(748\) −1.11376 + 0.567491i −0.0407233 + 0.0207495i
\(749\) −56.9012 −2.07913
\(750\) −10.5678 16.2272i −0.385880 0.592534i
\(751\) 13.6596 0.498445 0.249222 0.968446i \(-0.419825\pi\)
0.249222 + 0.968446i \(0.419825\pi\)
\(752\) 3.80983 1.94121i 0.138930 0.0707886i
\(753\) −36.9797 + 21.6027i −1.34762 + 0.787245i
\(754\) 9.09541 12.5188i 0.331235 0.455906i
\(755\) 32.4444 + 4.60187i 1.18077 + 0.167479i
\(756\) 3.43725 + 19.7408i 0.125012 + 0.717966i
\(757\) −11.1659 + 11.1659i −0.405833 + 0.405833i −0.880283 0.474450i \(-0.842647\pi\)
0.474450 + 0.880283i \(0.342647\pi\)
\(758\) −1.10598 + 6.98287i −0.0401710 + 0.253629i
\(759\) −3.70798 + 3.03413i −0.134591 + 0.110132i
\(760\) −13.8517 + 4.74982i −0.502454 + 0.172294i
\(761\) 13.3455 + 4.33621i 0.483774 + 0.157188i 0.540742 0.841188i \(-0.318143\pi\)
−0.0569686 + 0.998376i \(0.518143\pi\)
\(762\) −0.929110 + 9.29604i −0.0336581 + 0.336760i
\(763\) 19.4614 38.1951i 0.704548 1.38275i
\(764\) −4.35419 + 13.4008i −0.157529 + 0.484825i
\(765\) −17.2308 + 16.3583i −0.622982 + 0.591434i
\(766\) −4.30040 13.2353i −0.155380 0.478209i
\(767\) 5.64864 + 0.894657i 0.203961 + 0.0323042i
\(768\) 1.58588 + 0.696404i 0.0572256 + 0.0251293i
\(769\) 13.0082 + 17.9042i 0.469087 + 0.645643i 0.976362 0.216141i \(-0.0693471\pi\)
−0.507275 + 0.861784i \(0.669347\pi\)
\(770\) −2.11683 + 2.18646i −0.0762851 + 0.0787946i
\(771\) −12.5914 + 47.9697i −0.453468 + 1.72759i
\(772\) −4.04150 + 0.640111i −0.145457 + 0.0230381i
\(773\) −19.2486 37.7774i −0.692323 1.35876i −0.922647 0.385646i \(-0.873979\pi\)
0.230324 0.973114i \(-0.426021\pi\)
\(774\) −16.1295 + 14.8239i −0.579762 + 0.532836i
\(775\) −19.7167 + 7.11952i −0.708245 + 0.255741i
\(776\) 7.02576i 0.252210i
\(777\) 24.2615 + 21.6219i 0.870376 + 0.775683i
\(778\) 2.35890 + 14.8935i 0.0845708 + 0.533959i
\(779\) 44.9294 + 32.6431i 1.60976 + 1.16956i
\(780\) −6.26930 + 7.26806i −0.224477 + 0.260238i
\(781\) −1.75995 + 1.27868i −0.0629758 + 0.0457546i
\(782\) −19.6290 19.6290i −0.701932 0.701932i
\(783\) 26.5366 + 18.6660i 0.948340 + 0.667067i
\(784\) −7.48565 + 2.43223i −0.267345 + 0.0868655i
\(785\) −8.01946 + 6.02711i −0.286227 + 0.215117i
\(786\) −1.73221 30.1113i −0.0617860 1.07404i
\(787\) −25.7904 13.1408i −0.919327 0.468420i −0.0707509 0.997494i \(-0.522540\pi\)
−0.848576 + 0.529074i \(0.822540\pi\)
\(788\) 20.2619 + 10.3240i 0.721800 + 0.367776i
\(789\) 0.299464 + 5.20563i 0.0106612 + 0.185325i
\(790\) 0.897041 2.92079i 0.0319153 0.103917i
\(791\) −6.45480 + 2.09729i −0.229506 + 0.0745711i
\(792\) −0.585693 0.882044i −0.0208117 0.0313421i
\(793\) 0.256173 + 0.256173i 0.00909695 + 0.00909695i
\(794\) 11.1607 8.10876i 0.396080 0.287769i
\(795\) 8.83506 + 14.5772i 0.313347 + 0.517001i
\(796\) 5.11191 + 3.71402i 0.181187 + 0.131640i
\(797\) −2.70297 17.0659i −0.0957441 0.604505i −0.988176 0.153323i \(-0.951003\pi\)
0.892432 0.451182i \(-0.148997\pi\)
\(798\) 32.6547 + 29.1021i 1.15597 + 1.03020i
\(799\) 15.1443i 0.535766i
\(800\) 2.41291 + 4.37925i 0.0853093 + 0.154830i
\(801\) −4.15997 4.52634i −0.146985 0.159930i
\(802\) −7.18193 14.0953i −0.253603 0.497723i
\(803\) −3.63982 + 0.576491i −0.128446 + 0.0203439i
\(804\) −3.32952 + 12.6845i −0.117423 + 0.447349i
\(805\) −60.7063 29.7041i −2.13962 1.04693i
\(806\) 6.10729 + 8.40597i 0.215120 + 0.296088i
\(807\) 20.5666 + 9.03137i 0.723980 + 0.317919i
\(808\) −9.46876 1.49970i −0.333110 0.0527594i
\(809\) −14.1884 43.6674i −0.498837 1.53526i −0.810891 0.585198i \(-0.801017\pi\)
0.312054 0.950064i \(-0.398983\pi\)
\(810\) −15.4382 12.9098i −0.542442 0.453604i
\(811\) 14.2314 43.7999i 0.499733 1.53802i −0.309714 0.950830i \(-0.600233\pi\)
0.809448 0.587192i \(-0.199767\pi\)
\(812\) −10.9312 + 21.4536i −0.383609 + 0.752874i
\(813\) 2.93369 29.3525i 0.102889 1.02944i
\(814\) −1.63314 0.530641i −0.0572417 0.0185989i
\(815\) 13.9027 19.8015i 0.486992 0.693616i
\(816\) 4.74769 3.88489i 0.166202 0.135998i
\(817\) −7.48082 + 47.2320i −0.261721 + 1.65244i
\(818\) 4.20720 4.20720i 0.147101 0.147101i
\(819\) 28.1038 + 5.67445i 0.982025 + 0.198281i
\(820\) 8.33437 17.0329i 0.291049 0.594816i
\(821\) −13.3733 + 18.4068i −0.466731 + 0.642400i −0.975888 0.218274i \(-0.929957\pi\)
0.509156 + 0.860674i \(0.329957\pi\)
\(822\) 26.8102 15.6619i 0.935114 0.546271i
\(823\) −33.1249 + 16.8780i −1.15466 + 0.588330i −0.923127 0.384496i \(-0.874375\pi\)
−0.231536 + 0.972826i \(0.574375\pi\)
\(824\) −6.65293 −0.231766
\(825\) 0.205406 3.04956i 0.00715133 0.106172i
\(826\) −8.89898 −0.309635
\(827\) −9.39702 + 4.78802i −0.326766 + 0.166496i −0.609676 0.792651i \(-0.708700\pi\)
0.282910 + 0.959147i \(0.408700\pi\)
\(828\) 14.6100 18.4233i 0.507734 0.640253i
\(829\) 7.78028 10.7086i 0.270220 0.371926i −0.652244 0.758009i \(-0.726172\pi\)
0.922464 + 0.386083i \(0.126172\pi\)
\(830\) 2.25519 + 12.8857i 0.0782789 + 0.447269i
\(831\) −9.94535 + 15.4870i −0.345000 + 0.537237i
\(832\) 1.75242 1.75242i 0.0607541 0.0607541i
\(833\) −4.36093 + 27.5338i −0.151097 + 0.953990i
\(834\) 19.7684 + 24.1588i 0.684524 + 0.836550i
\(835\) 35.8974 + 11.0249i 1.24228 + 0.381533i
\(836\) −2.19813 0.714216i −0.0760239 0.0247017i
\(837\) −17.4264 + 13.0733i −0.602345 + 0.451880i
\(838\) −1.96185 + 3.85035i −0.0677711 + 0.133008i
\(839\) 0.944989 2.90838i 0.0326247 0.100408i −0.933418 0.358790i \(-0.883189\pi\)
0.966043 + 0.258382i \(0.0831893\pi\)
\(840\) 7.86592 12.6961i 0.271400 0.438056i
\(841\) 3.08568 + 9.49674i 0.106403 + 0.327474i
\(842\) 24.7186 + 3.91504i 0.851860 + 0.134921i
\(843\) 19.5410 44.4997i 0.673029 1.53265i
\(844\) 2.44299 + 3.36248i 0.0840910 + 0.115741i
\(845\) −7.18217 13.5493i −0.247074 0.466109i
\(846\) 12.7430 1.47100i 0.438114 0.0505740i
\(847\) 41.4224 6.56066i 1.42329 0.225427i
\(848\) −1.99809 3.92147i −0.0686146 0.134664i
\(849\) 16.1471 + 41.4312i 0.554165 + 1.42192i
\(850\) 17.6997 0.572988i 0.607095 0.0196533i
\(851\) 38.1346i 1.30724i
\(852\) 7.10313 7.97026i 0.243349 0.273057i
\(853\) 5.89808 + 37.2390i 0.201946 + 1.27504i 0.855358 + 0.518037i \(0.173337\pi\)
−0.653412 + 0.757003i \(0.726663\pi\)
\(854\) −0.456059 0.331347i −0.0156060 0.0113384i
\(855\) −43.9155 1.14082i −1.50188 0.0390152i
\(856\) −11.9374 + 8.67305i −0.408013 + 0.296439i
\(857\) 3.57064 + 3.57064i 0.121971 + 0.121971i 0.765457 0.643487i \(-0.222513\pi\)
−0.643487 + 0.765457i \(0.722513\pi\)
\(858\) −1.48023 + 0.322537i −0.0505342 + 0.0110112i
\(859\) 33.5736 10.9087i 1.14552 0.372201i 0.326064 0.945348i \(-0.394278\pi\)
0.819453 + 0.573147i \(0.194278\pi\)
\(860\) 16.3263 0.264194i 0.556721 0.00900893i
\(861\) −56.5491 + 3.25310i −1.92719 + 0.110865i
\(862\) 6.23735 + 3.17809i 0.212445 + 0.108246i
\(863\) 17.9383 + 9.14003i 0.610628 + 0.311130i 0.731819 0.681499i \(-0.238672\pi\)
−0.121191 + 0.992629i \(0.538672\pi\)
\(864\) 3.73006 + 3.61755i 0.126899 + 0.123072i
\(865\) 12.6343 + 36.8448i 0.429578 + 1.25276i
\(866\) 9.38548 3.04953i 0.318932 0.103627i
\(867\) 1.64306 + 7.54053i 0.0558011 + 0.256090i
\(868\) −11.4322 11.4322i −0.388035 0.388035i
\(869\) 0.390153 0.283463i 0.0132350 0.00961581i
\(870\) −5.53006 23.5415i −0.187487 0.798130i
\(871\) 15.1807 + 11.0294i 0.514379 + 0.373718i
\(872\) −1.73896 10.9794i −0.0588887 0.371809i
\(873\) −7.35218 + 19.7534i −0.248834 + 0.668552i
\(874\) 51.3273i 1.73617i
\(875\) 40.3095 15.2971i 1.36271 0.517135i
\(876\) 16.8510 6.56737i 0.569343 0.221891i
\(877\) −19.1482 37.5805i −0.646590 1.26900i −0.948834 0.315774i \(-0.897736\pi\)
0.302244 0.953230i \(-0.402264\pi\)
\(878\) 0.576659 0.0913337i 0.0194613 0.00308236i
\(879\) −57.2309 15.0223i −1.93035 0.506691i
\(880\) −0.110826 + 0.781355i −0.00373596 + 0.0263395i
\(881\) 22.4775 + 30.9376i 0.757285 + 1.04231i 0.997435 + 0.0715779i \(0.0228035\pi\)
−0.240150 + 0.970736i \(0.577197\pi\)
\(882\) −23.5917 0.995035i −0.794372 0.0335046i
\(883\) −13.8121 2.18763i −0.464816 0.0736196i −0.0803657 0.996765i \(-0.525609\pi\)
−0.384450 + 0.923146i \(0.625609\pi\)
\(884\) −2.71243 8.34799i −0.0912288 0.280773i
\(885\) 6.82449 5.77113i 0.229403 0.193994i
\(886\) 2.76645 8.51427i 0.0929408 0.286042i
\(887\) −9.40690 + 18.4621i −0.315853 + 0.619896i −0.993285 0.115689i \(-0.963092\pi\)
0.677433 + 0.735585i \(0.263092\pi\)
\(888\) 8.38555 + 0.838109i 0.281401 + 0.0281251i
\(889\) −19.7820 6.42756i −0.663467 0.215574i
\(890\) 0.0741394 + 4.58156i 0.00248516 + 0.153574i
\(891\) −0.723691 3.09283i −0.0242446 0.103614i
\(892\) 2.40429 15.1801i 0.0805017 0.508268i
\(893\) 19.8002 19.8002i 0.662587 0.662587i
\(894\) −6.77539 4.35099i −0.226603 0.145519i
\(895\) 11.8057 + 11.4297i 0.394622 + 0.382053i
\(896\) −2.26666 + 3.11979i −0.0757239 + 0.104225i
\(897\) −16.9703 29.0500i −0.566622 0.969951i
\(898\) −16.3751 + 8.34354i −0.546445 + 0.278428i
\(899\) −26.1776 −0.873071
\(900\) 2.20135 + 14.8376i 0.0733783 + 0.494586i
\(901\) −15.5880 −0.519312
\(902\) 2.66676 1.35878i 0.0887935 0.0452425i
\(903\) −24.6022 42.1144i −0.818710 1.40148i
\(904\) −1.03449 + 1.42386i −0.0344067 + 0.0473567i
\(905\) 1.32632 0.703054i 0.0440884 0.0233703i
\(906\) −21.3581 13.7157i −0.709576 0.455672i
\(907\) 8.19678 8.19678i 0.272170 0.272170i −0.557803 0.829973i \(-0.688356\pi\)
0.829973 + 0.557803i \(0.188356\pi\)
\(908\) −2.19408 + 13.8529i −0.0728131 + 0.459724i
\(909\) −25.0527 14.1252i −0.830946 0.468503i
\(910\) −12.8391 17.0832i −0.425611 0.566303i
\(911\) −4.38290 1.42409i −0.145212 0.0471822i 0.235509 0.971872i \(-0.424324\pi\)
−0.380721 + 0.924690i \(0.624324\pi\)
\(912\) 11.2865 + 1.12805i 0.373734 + 0.0373536i
\(913\) −0.937368 + 1.83969i −0.0310224 + 0.0608848i
\(914\) 10.8344 33.3449i 0.358371 1.10295i
\(915\) 0.564628 0.0416570i 0.0186660 0.00137714i
\(916\) −5.35607 16.4843i −0.176970 0.544656i
\(917\) 66.3247 + 10.5048i 2.19023 + 0.346899i
\(918\) 17.4138 5.95437i 0.574743 0.196524i
\(919\) 1.33595 + 1.83878i 0.0440689 + 0.0606557i 0.830483 0.557044i \(-0.188065\pi\)
−0.786414 + 0.617700i \(0.788065\pi\)
\(920\) −17.2633 + 3.02134i −0.569154 + 0.0996106i
\(921\) 30.5560 + 8.02053i 1.00685 + 0.264286i
\(922\) 0.139155 0.0220400i 0.00458284 0.000725850i
\(923\) −6.93508 13.6109i −0.228271 0.448007i
\(924\) 2.19640 0.856007i 0.0722564 0.0281606i
\(925\) 17.7498 + 16.6366i 0.583610 + 0.547008i
\(926\) 8.87257i 0.291571i
\(927\) −18.7052 6.96203i −0.614359 0.228663i
\(928\) 0.976751 + 6.16696i 0.0320634 + 0.202440i
\(929\) 12.0105 + 8.72617i 0.394053 + 0.286296i 0.767114 0.641510i \(-0.221692\pi\)
−0.373061 + 0.927807i \(0.621692\pi\)
\(930\) 16.1812 + 1.35322i 0.530602 + 0.0443739i
\(931\) −41.7003 + 30.2970i −1.36667 + 0.992945i
\(932\) −1.73973 1.73973i −0.0569868 0.0569868i
\(933\) −5.98097 27.4486i −0.195808 0.898628i
\(934\) −4.63623 + 1.50640i −0.151702 + 0.0492910i
\(935\) 2.28757 + 1.60612i 0.0748116 + 0.0525256i
\(936\) 6.76087 3.09320i 0.220986 0.101105i
\(937\) 13.2746 + 6.76373i 0.433661 + 0.220961i 0.657173 0.753740i \(-0.271752\pi\)
−0.223512 + 0.974701i \(0.571752\pi\)
\(938\) −26.0155 13.2555i −0.849435 0.432809i
\(939\) −9.33928 + 0.537260i −0.304776 + 0.0175328i
\(940\) −7.82505 5.49401i −0.255225 0.179195i
\(941\) 29.4117 9.55645i 0.958795 0.311531i 0.212511 0.977159i \(-0.431836\pi\)
0.746284 + 0.665627i \(0.231836\pi\)
\(942\) 7.59248 1.65438i 0.247376 0.0539025i
\(943\) 46.9991 + 46.9991i 1.53050 + 1.53050i
\(944\) −1.86694 + 1.35641i −0.0607636 + 0.0441474i
\(945\) 35.4015 27.4645i 1.15161 0.893421i
\(946\) 2.08499 + 1.51484i 0.0677890 + 0.0492516i
\(947\) 1.42242 + 8.98080i 0.0462224 + 0.291837i 0.999961 0.00879948i \(-0.00280100\pi\)
−0.953739 + 0.300636i \(0.902801\pi\)
\(948\) −1.57466 + 1.76688i −0.0511424 + 0.0573857i
\(949\) 25.8775i 0.840021i
\(950\) 23.8903 + 22.3921i 0.775105 + 0.726494i
\(951\) 5.39568 + 13.8446i 0.174967 + 0.448942i
\(952\) 6.20067 + 12.1695i 0.200965 + 0.394416i
\(953\) −18.9081 + 2.99474i −0.612493 + 0.0970093i −0.454971 0.890506i \(-0.650350\pi\)
−0.157522 + 0.987516i \(0.550350\pi\)
\(954\) −1.51410 13.1164i −0.0490209 0.424659i
\(955\) 31.0355 5.43168i 1.00429 0.175765i
\(956\) 1.43017 + 1.96845i 0.0462549 + 0.0636644i
\(957\) 1.53462 3.49471i 0.0496073 0.112968i
\(958\) −14.0773 2.22963i −0.454818 0.0720361i
\(959\) 21.3623 + 65.7463i 0.689823 + 2.12306i
\(960\) −0.284965 3.86249i −0.00919722 0.124661i
\(961\) −4.14780 + 12.7656i −0.133800 + 0.411794i
\(962\) 5.47429 10.7439i 0.176498 0.346397i
\(963\) −42.6389 + 11.8928i −1.37402 + 0.383242i
\(964\) 1.53948 + 0.500207i 0.0495833 + 0.0161106i
\(965\) 5.49714 + 7.31429i 0.176959 + 0.235455i
\(966\) 33.1523 + 40.5151i 1.06666 + 1.30355i
\(967\) −6.88343 + 43.4603i −0.221356 + 1.39759i 0.587330 + 0.809347i \(0.300179\pi\)
−0.808686 + 0.588240i \(0.799821\pi\)
\(968\) 7.69010 7.69010i 0.247169 0.247169i
\(969\) 21.7080 33.8038i 0.697360 1.08593i
\(970\) 13.8806 7.35778i 0.445678 0.236244i
\(971\) −18.1657 + 25.0030i −0.582965 + 0.802383i −0.994017 0.109229i \(-0.965162\pi\)
0.411051 + 0.911612i \(0.365162\pi\)
\(972\) 6.70170 + 14.0743i 0.214957 + 0.451435i
\(973\) −61.9249 + 31.5523i −1.98522 + 1.01152i
\(974\) 34.8793 1.11761
\(975\) 20.9248 + 4.77452i 0.670131 + 0.152907i
\(976\) −0.146183 −0.00467919
\(977\) 42.2813 21.5434i 1.35270 0.689235i 0.380806 0.924655i \(-0.375646\pi\)
0.971894 + 0.235420i \(0.0756465\pi\)
\(978\) −16.1823 + 9.45329i −0.517452 + 0.302283i
\(979\) −0.425102 + 0.585102i −0.0135863 + 0.0186999i
\(980\) 12.6447 + 12.2420i 0.403919 + 0.391055i
\(981\) 6.60027 32.6890i 0.210730 1.04368i
\(982\) −3.78562 + 3.78562i −0.120804 + 0.120804i
\(983\) 5.45227 34.4243i 0.173900 1.09796i −0.734114 0.679026i \(-0.762402\pi\)
0.908015 0.418938i \(-0.137598\pi\)
\(984\) −11.3677 + 9.30186i −0.362390 + 0.296533i
\(985\) −0.822742 50.8426i −0.0262147 1.61998i
\(986\) 21.0320 + 6.83372i 0.669796 + 0.217630i
\(987\) −2.84030 + 28.4181i −0.0904079 + 0.904560i
\(988\) 7.36813 14.4608i 0.234411 0.460058i
\(989\) −17.6860 + 54.4321i −0.562384 + 1.73084i
\(990\) −1.12925 + 2.08086i −0.0358900 + 0.0661341i
\(991\) 1.45449 + 4.47645i 0.0462033 + 0.142199i 0.971497 0.237053i \(-0.0761814\pi\)
−0.925293 + 0.379252i \(0.876181\pi\)
\(992\) −4.14093 0.655859i −0.131475 0.0208235i
\(993\) −45.0654 19.7894i −1.43011 0.627999i
\(994\) 13.9714 + 19.2300i 0.443146 + 0.609938i
\(995\) 1.98418 13.9890i 0.0629027 0.443480i
\(996\) 2.57261 9.80092i 0.0815162 0.310554i
\(997\) −20.4803 + 3.24377i −0.648619 + 0.102731i −0.472070 0.881561i \(-0.656493\pi\)
−0.176548 + 0.984292i \(0.556493\pi\)
\(998\) −4.05748 7.96325i −0.128437 0.252072i
\(999\) 22.6995 + 11.1315i 0.718180 + 0.352186i
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.53.2 yes 80
3.2 odd 2 inner 150.2.l.a.53.8 yes 80
5.2 odd 4 750.2.l.c.257.1 80
5.3 odd 4 750.2.l.a.257.10 80
5.4 even 2 750.2.l.b.743.9 80
15.2 even 4 750.2.l.c.257.6 80
15.8 even 4 750.2.l.a.257.5 80
15.14 odd 2 750.2.l.b.743.3 80
25.6 even 5 750.2.l.c.143.6 80
25.8 odd 20 750.2.l.b.107.3 80
25.17 odd 20 inner 150.2.l.a.17.8 yes 80
25.19 even 10 750.2.l.a.143.5 80
75.8 even 20 750.2.l.b.107.9 80
75.17 even 20 inner 150.2.l.a.17.2 80
75.44 odd 10 750.2.l.a.143.10 80
75.56 odd 10 750.2.l.c.143.1 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.l.a.17.2 80 75.17 even 20 inner
150.2.l.a.17.8 yes 80 25.17 odd 20 inner
150.2.l.a.53.2 yes 80 1.1 even 1 trivial
150.2.l.a.53.8 yes 80 3.2 odd 2 inner
750.2.l.a.143.5 80 25.19 even 10
750.2.l.a.143.10 80 75.44 odd 10
750.2.l.a.257.5 80 15.8 even 4
750.2.l.a.257.10 80 5.3 odd 4
750.2.l.b.107.3 80 25.8 odd 20
750.2.l.b.107.9 80 75.8 even 20
750.2.l.b.743.3 80 15.14 odd 2
750.2.l.b.743.9 80 5.4 even 2
750.2.l.c.143.1 80 75.56 odd 10
750.2.l.c.143.6 80 25.6 even 5
750.2.l.c.257.1 80 5.2 odd 4
750.2.l.c.257.6 80 15.2 even 4