Properties

Label 175.2.s.a.13.2
Level $175$
Weight $2$
Character 175.13
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
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] = [175,2,Mod(13,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([19, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.s (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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 175.13
Dual form 175.2.s.a.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.43824 + 0.386179i) q^{2} +(0.183665 + 0.0935818i) q^{3} +(3.89376 - 1.26516i) q^{4} +(-2.22917 - 0.175511i) q^{5} +(-0.483957 - 0.157247i) q^{6} +(1.07566 + 2.41722i) q^{7} +(-4.60620 + 2.34698i) q^{8} +(-1.73838 - 2.39268i) q^{9} +O(q^{10})\) \(q+(-2.43824 + 0.386179i) q^{2} +(0.183665 + 0.0935818i) q^{3} +(3.89376 - 1.26516i) q^{4} +(-2.22917 - 0.175511i) q^{5} +(-0.483957 - 0.157247i) q^{6} +(1.07566 + 2.41722i) q^{7} +(-4.60620 + 2.34698i) q^{8} +(-1.73838 - 2.39268i) q^{9} +(5.50302 - 0.432920i) q^{10} +(3.57144 + 2.59480i) q^{11} +(0.833541 + 0.132020i) q^{12} +(-0.297223 + 1.87659i) q^{13} +(-3.55620 - 5.47836i) q^{14} +(-0.392995 - 0.240845i) q^{15} +(3.70020 - 2.68836i) q^{16} +(-6.70498 + 3.41636i) q^{17} +(5.16259 + 5.16259i) q^{18} +(-1.89087 + 5.81950i) q^{19} +(-8.90190 + 2.13686i) q^{20} +(-0.0286466 + 0.544620i) q^{21} +(-9.71007 - 4.94753i) q^{22} +(0.763884 + 4.82298i) q^{23} -1.06563 q^{24} +(4.93839 + 0.782488i) q^{25} -4.69036i q^{26} +(-0.192106 - 1.21291i) q^{27} +(7.24654 + 8.05118i) q^{28} +(-1.44631 + 0.469935i) q^{29} +(1.05122 + 0.435471i) q^{30} +(-1.90816 - 0.619999i) q^{31} +(-0.672788 + 0.672788i) q^{32} +(0.413120 + 0.810794i) q^{33} +(15.0290 - 10.9192i) q^{34} +(-1.97359 - 5.57718i) q^{35} +(-9.79595 - 7.11717i) q^{36} +(0.625263 - 3.94776i) q^{37} +(2.36302 - 14.9195i) q^{38} +(-0.230204 + 0.316849i) q^{39} +(10.6799 - 4.42337i) q^{40} +(4.69566 + 6.46303i) q^{41} +(-0.140474 - 1.33898i) q^{42} +(0.773359 + 0.773359i) q^{43} +(17.1891 + 5.58509i) q^{44} +(3.45520 + 5.63878i) q^{45} +(-3.72506 - 11.4646i) q^{46} +(4.03603 - 7.92115i) q^{47} +(0.931177 - 0.147484i) q^{48} +(-4.68590 + 5.20023i) q^{49} +(-12.3432 - 0.000789122i) q^{50} -1.55118 q^{51} +(1.21687 + 7.68303i) q^{52} +(1.12238 - 2.20280i) q^{53} +(0.936802 + 2.88318i) q^{54} +(-7.50592 - 6.41107i) q^{55} +(-10.6279 - 8.60964i) q^{56} +(-0.891884 + 0.891884i) q^{57} +(3.34497 - 1.70435i) q^{58} +(3.46254 - 2.51568i) q^{59} +(-1.83493 - 0.440591i) q^{60} +(3.15174 - 4.33800i) q^{61} +(4.89198 + 0.774813i) q^{62} +(3.91371 - 6.77576i) q^{63} +(-3.99611 + 5.50017i) q^{64} +(0.991924 - 4.13108i) q^{65} +(-1.32040 - 1.81737i) q^{66} +(-2.45898 - 4.82603i) q^{67} +(-21.7854 + 21.7854i) q^{68} +(-0.311044 + 0.957295i) q^{69} +(6.96586 + 12.8363i) q^{70} +(1.20256 + 3.70109i) q^{71} +(13.6229 + 6.94121i) q^{72} +(0.784747 - 0.124292i) q^{73} +9.86703i q^{74} +(0.833781 + 0.605859i) q^{75} +25.0520i q^{76} +(-2.43054 + 11.4241i) q^{77} +(0.438932 - 0.861453i) q^{78} +(-10.4243 + 3.38705i) q^{79} +(-8.72022 + 5.34337i) q^{80} +(-2.66354 + 8.19753i) q^{81} +(-13.9450 - 13.9450i) q^{82} +(-0.370328 - 0.726810i) q^{83} +(0.577488 + 2.15686i) q^{84} +(15.5462 - 6.43885i) q^{85} +(-2.18429 - 1.58698i) q^{86} +(-0.309613 - 0.0490379i) q^{87} +(-22.5407 - 3.57009i) q^{88} +(4.65732 + 3.38374i) q^{89} +(-10.6022 - 12.4144i) q^{90} +(-4.85585 + 1.30013i) q^{91} +(9.07621 + 17.8131i) q^{92} +(-0.292441 - 0.292441i) q^{93} +(-6.78182 + 20.8723i) q^{94} +(5.23645 - 12.6408i) q^{95} +(-0.186528 + 0.0606066i) q^{96} +(1.37761 - 2.70371i) q^{97} +(9.41712 - 14.4890i) q^{98} -13.0560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43824 + 0.386179i −1.72409 + 0.273070i −0.938402 0.345547i \(-0.887694\pi\)
−0.785693 + 0.618616i \(0.787694\pi\)
\(3\) 0.183665 + 0.0935818i 0.106039 + 0.0540295i 0.506205 0.862413i \(-0.331048\pi\)
−0.400167 + 0.916442i \(0.631048\pi\)
\(4\) 3.89376 1.26516i 1.94688 0.632579i
\(5\) −2.22917 0.175511i −0.996915 0.0784910i
\(6\) −0.483957 0.157247i −0.197575 0.0641959i
\(7\) 1.07566 + 2.41722i 0.406562 + 0.913623i
\(8\) −4.60620 + 2.34698i −1.62854 + 0.829781i
\(9\) −1.73838 2.39268i −0.579460 0.797559i
\(10\) 5.50302 0.432920i 1.74021 0.136901i
\(11\) 3.57144 + 2.59480i 1.07683 + 0.782362i 0.977127 0.212656i \(-0.0682113\pi\)
0.0997012 + 0.995017i \(0.468211\pi\)
\(12\) 0.833541 + 0.132020i 0.240623 + 0.0381109i
\(13\) −0.297223 + 1.87659i −0.0824349 + 0.520473i 0.911571 + 0.411143i \(0.134870\pi\)
−0.994006 + 0.109330i \(0.965130\pi\)
\(14\) −3.55620 5.47836i −0.950435 1.46415i
\(15\) −0.392995 0.240845i −0.101471 0.0621858i
\(16\) 3.70020 2.68836i 0.925051 0.672089i
\(17\) −6.70498 + 3.41636i −1.62620 + 0.828589i −0.627445 + 0.778661i \(0.715899\pi\)
−0.998753 + 0.0499278i \(0.984101\pi\)
\(18\) 5.16259 + 5.16259i 1.21683 + 1.21683i
\(19\) −1.89087 + 5.81950i −0.433795 + 1.33508i 0.460521 + 0.887649i \(0.347663\pi\)
−0.894316 + 0.447435i \(0.852337\pi\)
\(20\) −8.90190 + 2.13686i −1.99052 + 0.477815i
\(21\) −0.0286466 + 0.544620i −0.00625119 + 0.118846i
\(22\) −9.71007 4.94753i −2.07019 1.05482i
\(23\) 0.763884 + 4.82298i 0.159281 + 1.00566i 0.929752 + 0.368186i \(0.120021\pi\)
−0.770471 + 0.637475i \(0.779979\pi\)
\(24\) −1.06563 −0.217521
\(25\) 4.93839 + 0.782488i 0.987678 + 0.156498i
\(26\) 4.69036i 0.919856i
\(27\) −0.192106 1.21291i −0.0369709 0.233425i
\(28\) 7.24654 + 8.05118i 1.36947 + 1.52153i
\(29\) −1.44631 + 0.469935i −0.268573 + 0.0872647i −0.440208 0.897896i \(-0.645095\pi\)
0.171635 + 0.985161i \(0.445095\pi\)
\(30\) 1.05122 + 0.435471i 0.191926 + 0.0795057i
\(31\) −1.90816 0.619999i −0.342716 0.111355i 0.132602 0.991169i \(-0.457667\pi\)
−0.475318 + 0.879814i \(0.657667\pi\)
\(32\) −0.672788 + 0.672788i −0.118933 + 0.118933i
\(33\) 0.413120 + 0.810794i 0.0719150 + 0.141141i
\(34\) 15.0290 10.9192i 2.57746 1.87263i
\(35\) −1.97359 5.57718i −0.333597 0.942716i
\(36\) −9.79595 7.11717i −1.63266 1.18620i
\(37\) 0.625263 3.94776i 0.102793 0.649007i −0.881463 0.472254i \(-0.843441\pi\)
0.984255 0.176753i \(-0.0565594\pi\)
\(38\) 2.36302 14.9195i 0.383333 2.42027i
\(39\) −0.230204 + 0.316849i −0.0368622 + 0.0507364i
\(40\) 10.6799 4.42337i 1.68864 0.699396i
\(41\) 4.69566 + 6.46303i 0.733340 + 1.00936i 0.998974 + 0.0452815i \(0.0144185\pi\)
−0.265635 + 0.964074i \(0.585582\pi\)
\(42\) −0.140474 1.33898i −0.0216755 0.206608i
\(43\) 0.773359 + 0.773359i 0.117936 + 0.117936i 0.763612 0.645676i \(-0.223424\pi\)
−0.645676 + 0.763612i \(0.723424\pi\)
\(44\) 17.1891 + 5.58509i 2.59136 + 0.841984i
\(45\) 3.45520 + 5.63878i 0.515071 + 0.840580i
\(46\) −3.72506 11.4646i −0.549231 1.69036i
\(47\) 4.03603 7.92115i 0.588715 1.15542i −0.383982 0.923341i \(-0.625447\pi\)
0.972697 0.232078i \(-0.0745526\pi\)
\(48\) 0.931177 0.147484i 0.134404 0.0212875i
\(49\) −4.68590 + 5.20023i −0.669414 + 0.742889i
\(50\) −12.3432 0.000789122i −1.74559 0.000111599i
\(51\) −1.55118 −0.217208
\(52\) 1.21687 + 7.68303i 0.168750 + 1.06545i
\(53\) 1.12238 2.20280i 0.154171 0.302577i −0.800983 0.598687i \(-0.795689\pi\)
0.955154 + 0.296110i \(0.0956894\pi\)
\(54\) 0.936802 + 2.88318i 0.127483 + 0.392351i
\(55\) −7.50592 6.41107i −1.01210 0.864469i
\(56\) −10.6279 8.60964i −1.42021 1.15051i
\(57\) −0.891884 + 0.891884i −0.118133 + 0.118133i
\(58\) 3.34497 1.70435i 0.439216 0.223792i
\(59\) 3.46254 2.51568i 0.450784 0.327514i −0.339121 0.940743i \(-0.610130\pi\)
0.789905 + 0.613229i \(0.210130\pi\)
\(60\) −1.83493 0.440591i −0.236889 0.0568800i
\(61\) 3.15174 4.33800i 0.403539 0.555424i −0.558089 0.829781i \(-0.688465\pi\)
0.961628 + 0.274357i \(0.0884651\pi\)
\(62\) 4.89198 + 0.774813i 0.621282 + 0.0984014i
\(63\) 3.91371 6.77576i 0.493081 0.853665i
\(64\) −3.99611 + 5.50017i −0.499514 + 0.687521i
\(65\) 0.991924 4.13108i 0.123033 0.512397i
\(66\) −1.32040 1.81737i −0.162530 0.223703i
\(67\) −2.45898 4.82603i −0.300413 0.589593i 0.690619 0.723219i \(-0.257338\pi\)
−0.991032 + 0.133625i \(0.957338\pi\)
\(68\) −21.7854 + 21.7854i −2.64186 + 2.64186i
\(69\) −0.311044 + 0.957295i −0.0374453 + 0.115245i
\(70\) 6.96586 + 12.8363i 0.832580 + 1.53424i
\(71\) 1.20256 + 3.70109i 0.142717 + 0.439239i 0.996710 0.0810457i \(-0.0258260\pi\)
−0.853993 + 0.520284i \(0.825826\pi\)
\(72\) 13.6229 + 6.94121i 1.60547 + 0.818029i
\(73\) 0.784747 0.124292i 0.0918476 0.0145472i −0.110341 0.993894i \(-0.535194\pi\)
0.202189 + 0.979347i \(0.435194\pi\)
\(74\) 9.86703i 1.14702i
\(75\) 0.833781 + 0.605859i 0.0962767 + 0.0699585i
\(76\) 25.0520i 2.87366i
\(77\) −2.43054 + 11.4241i −0.276986 + 1.30189i
\(78\) 0.438932 0.861453i 0.0496993 0.0975404i
\(79\) −10.4243 + 3.38705i −1.17282 + 0.381073i −0.829696 0.558216i \(-0.811486\pi\)
−0.343127 + 0.939289i \(0.611486\pi\)
\(80\) −8.72022 + 5.34337i −0.974950 + 0.597407i
\(81\) −2.66354 + 8.19753i −0.295949 + 0.910837i
\(82\) −13.9450 13.9450i −1.53997 1.53997i
\(83\) −0.370328 0.726810i −0.0406488 0.0797778i 0.869789 0.493424i \(-0.164255\pi\)
−0.910438 + 0.413646i \(0.864255\pi\)
\(84\) 0.577488 + 2.15686i 0.0630091 + 0.235333i
\(85\) 15.5462 6.43885i 1.68622 0.698391i
\(86\) −2.18429 1.58698i −0.235538 0.171128i
\(87\) −0.309613 0.0490379i −0.0331940 0.00525742i
\(88\) −22.5407 3.57009i −2.40284 0.380573i
\(89\) 4.65732 + 3.38374i 0.493675 + 0.358676i 0.806596 0.591103i \(-0.201308\pi\)
−0.312921 + 0.949779i \(0.601308\pi\)
\(90\) −10.6022 12.4144i −1.11757 1.30859i
\(91\) −4.85585 + 1.30013i −0.509031 + 0.136290i
\(92\) 9.07621 + 17.8131i 0.946261 + 1.85714i
\(93\) −0.292441 0.292441i −0.0303247 0.0303247i
\(94\) −6.78182 + 20.8723i −0.699491 + 2.15281i
\(95\) 5.23645 12.6408i 0.537249 1.29692i
\(96\) −0.186528 + 0.0606066i −0.0190374 + 0.00618564i
\(97\) 1.37761 2.70371i 0.139875 0.274520i −0.810433 0.585831i \(-0.800768\pi\)
0.950308 + 0.311311i \(0.100768\pi\)
\(98\) 9.41712 14.4890i 0.951273 1.46361i
\(99\) 13.0560i 1.31218i
\(100\) 20.2189 3.20103i 2.02189 0.320103i
\(101\) 9.05231i 0.900738i −0.892842 0.450369i \(-0.851292\pi\)
0.892842 0.450369i \(-0.148708\pi\)
\(102\) 3.78214 0.599032i 0.374488 0.0593130i
\(103\) 0.197172 + 0.100464i 0.0194279 + 0.00989903i 0.463677 0.886004i \(-0.346530\pi\)
−0.444250 + 0.895903i \(0.646530\pi\)
\(104\) −3.03525 9.34154i −0.297631 0.916013i
\(105\) 0.159445 1.20902i 0.0155602 0.117988i
\(106\) −1.88596 + 5.80438i −0.183180 + 0.563771i
\(107\) −5.28214 + 5.28214i −0.510643 + 0.510643i −0.914724 0.404080i \(-0.867592\pi\)
0.404080 + 0.914724i \(0.367592\pi\)
\(108\) −2.28254 4.47974i −0.219638 0.431063i
\(109\) −4.53859 6.24684i −0.434719 0.598339i 0.534310 0.845289i \(-0.320572\pi\)
−0.969028 + 0.246950i \(0.920572\pi\)
\(110\) 20.7770 + 12.7331i 1.98101 + 1.21405i
\(111\) 0.484277 0.666550i 0.0459655 0.0632661i
\(112\) 10.4785 + 6.05244i 0.990127 + 0.571902i
\(113\) 7.97103 + 1.26249i 0.749851 + 0.118765i 0.519651 0.854379i \(-0.326062\pi\)
0.230200 + 0.973143i \(0.426062\pi\)
\(114\) 1.83020 2.51905i 0.171414 0.235931i
\(115\) −0.856342 10.8853i −0.0798543 1.01506i
\(116\) −5.03704 + 3.65963i −0.467678 + 0.339788i
\(117\) 5.00676 2.55107i 0.462876 0.235847i
\(118\) −7.47099 + 7.47099i −0.687760 + 0.687760i
\(119\) −15.4704 12.5326i −1.41817 1.14886i
\(120\) 2.37547 + 0.187030i 0.216850 + 0.0170734i
\(121\) 2.62298 + 8.07270i 0.238453 + 0.733882i
\(122\) −6.00945 + 11.7942i −0.544070 + 1.06780i
\(123\) 0.257606 + 1.62646i 0.0232275 + 0.146653i
\(124\) −8.21431 −0.737667
\(125\) −10.8712 2.61104i −0.972348 0.233539i
\(126\) −6.92590 + 18.0323i −0.617009 + 1.60645i
\(127\) 11.2355 1.77953i 0.996988 0.157907i 0.363446 0.931615i \(-0.381600\pi\)
0.633542 + 0.773708i \(0.281600\pi\)
\(128\) 8.48333 16.6495i 0.749827 1.47162i
\(129\) 0.0696663 + 0.214411i 0.00613378 + 0.0188778i
\(130\) −0.823211 + 10.4556i −0.0722004 + 0.917018i
\(131\) 4.11189 + 1.33603i 0.359257 + 0.116730i 0.483084 0.875574i \(-0.339517\pi\)
−0.123827 + 0.992304i \(0.539517\pi\)
\(132\) 2.63437 + 2.63437i 0.229293 + 0.229293i
\(133\) −16.1009 + 1.68917i −1.39613 + 0.146470i
\(134\) 7.85930 + 10.8174i 0.678940 + 0.934481i
\(135\) 0.215358 + 2.73750i 0.0185351 + 0.235607i
\(136\) 22.8664 31.4729i 1.96078 2.69878i
\(137\) −2.66715 + 16.8397i −0.227870 + 1.43871i 0.562861 + 0.826551i \(0.309701\pi\)
−0.790731 + 0.612163i \(0.790299\pi\)
\(138\) 0.388712 2.45423i 0.0330894 0.208918i
\(139\) 3.58136 + 2.60201i 0.303767 + 0.220700i 0.729217 0.684282i \(-0.239884\pi\)
−0.425450 + 0.904982i \(0.639884\pi\)
\(140\) −14.7407 19.2193i −1.24582 1.62433i
\(141\) 1.48255 1.07714i 0.124853 0.0907113i
\(142\) −4.36140 8.55974i −0.366001 0.718317i
\(143\) −5.93090 + 5.93090i −0.495966 + 0.495966i
\(144\) −12.8647 4.18000i −1.07206 0.348333i
\(145\) 3.30655 0.793721i 0.274594 0.0659149i
\(146\) −1.86540 + 0.606105i −0.154382 + 0.0501616i
\(147\) −1.34728 + 0.516582i −0.111122 + 0.0426070i
\(148\) −2.55991 16.1627i −0.210424 1.32856i
\(149\) 5.31631i 0.435529i 0.976001 + 0.217764i \(0.0698764\pi\)
−0.976001 + 0.217764i \(0.930124\pi\)
\(150\) −2.26693 1.15524i −0.185094 0.0943249i
\(151\) 12.5100 1.01805 0.509023 0.860753i \(-0.330007\pi\)
0.509023 + 0.860753i \(0.330007\pi\)
\(152\) −4.94850 31.2436i −0.401376 2.53419i
\(153\) 19.8301 + 10.1039i 1.60316 + 0.816853i
\(154\) 1.51450 28.7932i 0.122042 2.32023i
\(155\) 4.14479 + 1.71698i 0.332918 + 0.137912i
\(156\) −0.495495 + 1.52498i −0.0396714 + 0.122096i
\(157\) 4.08176 + 4.08176i 0.325760 + 0.325760i 0.850972 0.525212i \(-0.176014\pi\)
−0.525212 + 0.850972i \(0.676014\pi\)
\(158\) 24.1089 12.2841i 1.91800 0.977268i
\(159\) 0.412283 0.299541i 0.0326962 0.0237552i
\(160\) 1.61784 1.38168i 0.127902 0.109231i
\(161\) −10.8365 + 7.03437i −0.854037 + 0.554386i
\(162\) 3.32863 21.0161i 0.261522 1.65118i
\(163\) −16.9850 2.69015i −1.33036 0.210709i −0.549544 0.835465i \(-0.685199\pi\)
−0.780820 + 0.624756i \(0.785199\pi\)
\(164\) 26.4605 + 19.2247i 2.06622 + 1.50120i
\(165\) −0.778611 1.87990i −0.0606148 0.146350i
\(166\) 1.18363 + 1.62912i 0.0918673 + 0.126445i
\(167\) 14.3079 7.29025i 1.10718 0.564136i 0.197858 0.980231i \(-0.436601\pi\)
0.909321 + 0.416094i \(0.136601\pi\)
\(168\) −1.14626 2.57586i −0.0884357 0.198732i
\(169\) 8.93048 + 2.90169i 0.686960 + 0.223207i
\(170\) −35.4187 + 21.7030i −2.71649 + 1.66455i
\(171\) 17.2112 5.59226i 1.31617 0.427651i
\(172\) 3.98969 + 2.03285i 0.304211 + 0.155003i
\(173\) −10.5652 + 1.67336i −0.803258 + 0.127223i −0.544546 0.838731i \(-0.683298\pi\)
−0.258712 + 0.965955i \(0.583298\pi\)
\(174\) 0.773848 0.0586653
\(175\) 3.42060 + 12.7789i 0.258573 + 0.965992i
\(176\) 20.1908 1.52194
\(177\) 0.871367 0.138011i 0.0654959 0.0103735i
\(178\) −12.6624 6.45181i −0.949086 0.483583i
\(179\) 2.00919 0.652825i 0.150174 0.0487944i −0.232965 0.972485i \(-0.574843\pi\)
0.383139 + 0.923691i \(0.374843\pi\)
\(180\) 20.5877 + 17.5847i 1.53452 + 1.31068i
\(181\) −21.8924 7.11328i −1.62725 0.528726i −0.653614 0.756828i \(-0.726748\pi\)
−0.973637 + 0.228102i \(0.926748\pi\)
\(182\) 11.3376 5.04525i 0.840401 0.373979i
\(183\) 0.984821 0.501791i 0.0728001 0.0370935i
\(184\) −14.8380 20.4228i −1.09387 1.50559i
\(185\) −2.08669 + 8.69048i −0.153417 + 0.638936i
\(186\) 0.825974 + 0.600106i 0.0605634 + 0.0440019i
\(187\) −32.8112 5.19678i −2.39939 0.380026i
\(188\) 5.69381 35.9493i 0.415264 2.62187i
\(189\) 2.72523 1.76905i 0.198231 0.128679i
\(190\) −7.88612 + 32.8434i −0.572119 + 2.38271i
\(191\) 10.5993 7.70086i 0.766940 0.557214i −0.134091 0.990969i \(-0.542812\pi\)
0.901031 + 0.433755i \(0.142812\pi\)
\(192\) −1.24866 + 0.636224i −0.0901142 + 0.0459155i
\(193\) 7.06153 + 7.06153i 0.508300 + 0.508300i 0.914004 0.405704i \(-0.132974\pi\)
−0.405704 + 0.914004i \(0.632974\pi\)
\(194\) −2.31482 + 7.12429i −0.166195 + 0.511494i
\(195\) 0.568775 0.665906i 0.0407308 0.0476866i
\(196\) −11.6667 + 26.1768i −0.833332 + 1.86977i
\(197\) −0.315148 0.160576i −0.0224533 0.0114405i 0.442728 0.896656i \(-0.354011\pi\)
−0.465181 + 0.885216i \(0.654011\pi\)
\(198\) 5.04197 + 31.8337i 0.358317 + 2.26232i
\(199\) −9.51572 −0.674552 −0.337276 0.941406i \(-0.609506\pi\)
−0.337276 + 0.941406i \(0.609506\pi\)
\(200\) −24.5837 + 7.98599i −1.73833 + 0.564695i
\(201\) 1.11649i 0.0787509i
\(202\) 3.49581 + 22.0717i 0.245964 + 1.55296i
\(203\) −2.69168 2.99056i −0.188919 0.209896i
\(204\) −6.03991 + 1.96249i −0.422878 + 0.137401i
\(205\) −9.33310 15.2313i −0.651852 1.06380i
\(206\) −0.519550 0.168812i −0.0361987 0.0117617i
\(207\) 10.2119 10.2119i 0.709776 0.709776i
\(208\) 3.94516 + 7.74282i 0.273548 + 0.536868i
\(209\) −21.8535 + 15.8775i −1.51164 + 1.09827i
\(210\) 0.0781343 + 3.00946i 0.00539178 + 0.207672i
\(211\) 12.8006 + 9.30020i 0.881232 + 0.640252i 0.933577 0.358377i \(-0.116670\pi\)
−0.0523453 + 0.998629i \(0.516670\pi\)
\(212\) 1.58339 9.99714i 0.108748 0.686607i
\(213\) −0.125487 + 0.792296i −0.00859826 + 0.0542873i
\(214\) 10.8393 14.9190i 0.740956 1.01984i
\(215\) −1.58821 1.85968i −0.108315 0.126829i
\(216\) 3.73155 + 5.13604i 0.253900 + 0.349464i
\(217\) −0.553863 5.27935i −0.0375987 0.358386i
\(218\) 13.4786 + 13.4786i 0.912884 + 0.912884i
\(219\) 0.155762 + 0.0506100i 0.0105254 + 0.00341991i
\(220\) −37.3373 15.4670i −2.51728 1.04278i
\(221\) −4.41824 13.5979i −0.297203 0.914697i
\(222\) −0.923374 + 1.81222i −0.0619728 + 0.121629i
\(223\) 14.0460 2.22468i 0.940593 0.148975i 0.332734 0.943021i \(-0.392029\pi\)
0.607859 + 0.794045i \(0.292029\pi\)
\(224\) −2.34997 0.902584i −0.157014 0.0603064i
\(225\) −6.71256 13.1762i −0.447504 0.878415i
\(226\) −19.9228 −1.32525
\(227\) −0.806723 5.09345i −0.0535441 0.338064i −0.999889 0.0149055i \(-0.995255\pi\)
0.946345 0.323159i \(-0.104745\pi\)
\(228\) −2.34441 + 4.60116i −0.155262 + 0.304719i
\(229\) 1.33232 + 4.10046i 0.0880421 + 0.270966i 0.985378 0.170383i \(-0.0545003\pi\)
−0.897336 + 0.441348i \(0.854500\pi\)
\(230\) 6.29164 + 26.2103i 0.414858 + 1.72825i
\(231\) −1.51549 + 1.87074i −0.0997119 + 0.123086i
\(232\) 5.55907 5.55907i 0.364971 0.364971i
\(233\) 10.7294 5.46689i 0.702904 0.358148i −0.0657289 0.997838i \(-0.520937\pi\)
0.768633 + 0.639690i \(0.220937\pi\)
\(234\) −11.2225 + 8.15363i −0.733639 + 0.533020i
\(235\) −10.3872 + 16.9492i −0.677589 + 1.10565i
\(236\) 10.2995 14.1761i 0.670443 0.922786i
\(237\) −2.23154 0.353440i −0.144954 0.0229584i
\(238\) 42.5603 + 24.5830i 2.75878 + 1.59348i
\(239\) −7.68632 + 10.5793i −0.497186 + 0.684318i −0.981693 0.190469i \(-0.938999\pi\)
0.484507 + 0.874788i \(0.338999\pi\)
\(240\) −2.10164 + 0.165335i −0.135660 + 0.0106723i
\(241\) 14.5206 + 19.9860i 0.935357 + 1.28741i 0.957733 + 0.287659i \(0.0928769\pi\)
−0.0223759 + 0.999750i \(0.507123\pi\)
\(242\) −9.51295 18.6702i −0.611516 1.20017i
\(243\) −3.86138 + 3.86138i −0.247708 + 0.247708i
\(244\) 6.78386 20.8786i 0.434292 1.33661i
\(245\) 11.3584 10.7698i 0.725659 0.688054i
\(246\) −1.25621 3.86621i −0.0800929 0.246500i
\(247\) −10.3588 5.27808i −0.659116 0.335836i
\(248\) 10.2445 1.62257i 0.650526 0.103033i
\(249\) 0.168145i 0.0106558i
\(250\) 27.5148 + 2.16812i 1.74019 + 0.137124i
\(251\) 24.7925i 1.56489i −0.622722 0.782443i \(-0.713973\pi\)
0.622722 0.782443i \(-0.286027\pi\)
\(252\) 6.66663 31.3346i 0.419959 1.97390i
\(253\) −9.78649 + 19.2071i −0.615272 + 1.20754i
\(254\) −26.7076 + 8.67782i −1.67578 + 0.544495i
\(255\) 3.45784 + 0.272249i 0.216538 + 0.0170489i
\(256\) −10.0529 + 30.9398i −0.628309 + 1.93374i
\(257\) 13.3266 + 13.3266i 0.831290 + 0.831290i 0.987693 0.156403i \(-0.0499899\pi\)
−0.156403 + 0.987693i \(0.549990\pi\)
\(258\) −0.252664 0.495881i −0.0157302 0.0308722i
\(259\) 10.2152 2.73506i 0.634739 0.169948i
\(260\) −1.36416 17.3404i −0.0846015 1.07540i
\(261\) 3.63864 + 2.64363i 0.225226 + 0.163636i
\(262\) −10.5417 1.66964i −0.651269 0.103151i
\(263\) −18.9224 2.99702i −1.16681 0.184804i −0.457175 0.889377i \(-0.651139\pi\)
−0.709632 + 0.704572i \(0.751139\pi\)
\(264\) −3.80583 2.76510i −0.234233 0.170180i
\(265\) −2.88859 + 4.71341i −0.177445 + 0.289543i
\(266\) 38.6056 10.3364i 2.36706 0.633768i
\(267\) 0.538728 + 1.05731i 0.0329696 + 0.0647065i
\(268\) −15.6804 15.6804i −0.957832 0.957832i
\(269\) 8.47322 26.0779i 0.516621 1.59000i −0.263692 0.964607i \(-0.584940\pi\)
0.780313 0.625389i \(-0.215060\pi\)
\(270\) −1.58226 6.59152i −0.0962933 0.401147i
\(271\) 10.0270 3.25796i 0.609096 0.197907i 0.0118027 0.999930i \(-0.496243\pi\)
0.597293 + 0.802023i \(0.296243\pi\)
\(272\) −15.6254 + 30.6666i −0.947430 + 1.85944i
\(273\) −1.01352 0.215632i −0.0613407 0.0130506i
\(274\) 42.0893i 2.54271i
\(275\) 15.6067 + 15.6087i 0.941122 + 0.941243i
\(276\) 4.12100i 0.248055i
\(277\) −11.5613 + 1.83113i −0.694650 + 0.110022i −0.493768 0.869594i \(-0.664381\pi\)
−0.200882 + 0.979615i \(0.564381\pi\)
\(278\) −9.73705 4.96127i −0.583989 0.297557i
\(279\) 1.83365 + 5.64340i 0.109778 + 0.337862i
\(280\) 22.1802 + 21.0577i 1.32552 + 1.25844i
\(281\) 5.89743 18.1504i 0.351811 1.08276i −0.606024 0.795446i \(-0.707236\pi\)
0.957835 0.287318i \(-0.0927636\pi\)
\(282\) −3.19885 + 3.19885i −0.190488 + 0.190488i
\(283\) −4.75665 9.33546i −0.282754 0.554936i 0.705325 0.708884i \(-0.250801\pi\)
−0.988079 + 0.153948i \(0.950801\pi\)
\(284\) 9.36493 + 12.8897i 0.555707 + 0.764865i
\(285\) 2.14470 1.83163i 0.127041 0.108496i
\(286\) 12.1705 16.7513i 0.719660 0.990527i
\(287\) −10.5716 + 18.3025i −0.624022 + 1.08036i
\(288\) 2.77933 + 0.440202i 0.163773 + 0.0259392i
\(289\) 23.2929 32.0600i 1.37017 1.88588i
\(290\) −7.75564 + 3.21220i −0.455427 + 0.188627i
\(291\) 0.506036 0.367657i 0.0296644 0.0215524i
\(292\) 2.89836 1.47679i 0.169614 0.0864226i
\(293\) 13.9898 13.9898i 0.817291 0.817291i −0.168423 0.985715i \(-0.553868\pi\)
0.985715 + 0.168423i \(0.0538676\pi\)
\(294\) 3.08550 1.77984i 0.179950 0.103802i
\(295\) −8.16011 + 5.00016i −0.475100 + 0.291121i
\(296\) 6.38520 + 19.6516i 0.371132 + 1.14223i
\(297\) 2.46117 4.83031i 0.142811 0.280283i
\(298\) −2.05305 12.9624i −0.118930 0.750893i
\(299\) −9.27781 −0.536549
\(300\) 4.01305 + 1.30420i 0.231693 + 0.0752982i
\(301\) −1.03750 + 2.70125i −0.0598008 + 0.155698i
\(302\) −30.5022 + 4.83108i −1.75521 + 0.277997i
\(303\) 0.847131 1.66259i 0.0486664 0.0955132i
\(304\) 8.64827 + 26.6167i 0.496013 + 1.52657i
\(305\) −7.78714 + 9.11697i −0.445890 + 0.522036i
\(306\) −52.2523 16.9778i −2.98707 0.970557i
\(307\) 21.2978 + 21.2978i 1.21553 + 1.21553i 0.969182 + 0.246347i \(0.0792303\pi\)
0.246347 + 0.969182i \(0.420770\pi\)
\(308\) 4.98933 + 47.5576i 0.284293 + 2.70985i
\(309\) 0.0268119 + 0.0369034i 0.00152528 + 0.00209936i
\(310\) −10.7691 2.58579i −0.611641 0.146863i
\(311\) −15.1640 + 20.8715i −0.859873 + 1.18351i 0.121726 + 0.992564i \(0.461157\pi\)
−0.981600 + 0.190951i \(0.938843\pi\)
\(312\) 0.316730 1.99975i 0.0179313 0.113214i
\(313\) −2.56622 + 16.2025i −0.145052 + 0.915820i 0.802601 + 0.596516i \(0.203449\pi\)
−0.947653 + 0.319303i \(0.896551\pi\)
\(314\) −11.5286 8.37602i −0.650596 0.472686i
\(315\) −9.91355 + 14.4174i −0.558565 + 0.812329i
\(316\) −36.3044 + 26.3767i −2.04228 + 1.48381i
\(317\) 12.5927 + 24.7147i 0.707279 + 1.38811i 0.912368 + 0.409370i \(0.134252\pi\)
−0.205089 + 0.978743i \(0.565748\pi\)
\(318\) −0.889568 + 0.889568i −0.0498845 + 0.0498845i
\(319\) −6.38479 2.07454i −0.357480 0.116152i
\(320\) 9.87334 11.5595i 0.551937 0.646193i
\(321\) −1.46445 + 0.475830i −0.0817378 + 0.0265582i
\(322\) 23.7055 21.3363i 1.32105 1.18903i
\(323\) −7.20325 45.4795i −0.400800 2.53055i
\(324\) 35.2890i 1.96050i
\(325\) −2.93622 + 9.03478i −0.162872 + 0.501159i
\(326\) 42.4523 2.35121
\(327\) −0.248989 1.57205i −0.0137691 0.0869347i
\(328\) −36.7977 18.7494i −2.03182 1.03526i
\(329\) 23.4886 + 1.23548i 1.29497 + 0.0681142i
\(330\) 2.62442 + 4.28297i 0.144470 + 0.235770i
\(331\) 1.21725 3.74631i 0.0669062 0.205916i −0.912014 0.410159i \(-0.865473\pi\)
0.978920 + 0.204243i \(0.0654732\pi\)
\(332\) −2.36150 2.36150i −0.129604 0.129604i
\(333\) −10.5326 + 5.36665i −0.577185 + 0.294091i
\(334\) −32.0708 + 23.3008i −1.75483 + 1.27496i
\(335\) 4.63447 + 11.1896i 0.253208 + 0.611354i
\(336\) 1.35813 + 2.09222i 0.0740923 + 0.114140i
\(337\) −3.60639 + 22.7699i −0.196453 + 1.24035i 0.670480 + 0.741928i \(0.266088\pi\)
−0.866933 + 0.498425i \(0.833912\pi\)
\(338\) −22.8952 3.62624i −1.24533 0.197242i
\(339\) 1.34585 + 0.977817i 0.0730965 + 0.0531077i
\(340\) 52.3868 44.7397i 2.84107 2.42635i
\(341\) −5.20610 7.16558i −0.281926 0.388038i
\(342\) −39.8054 + 20.2819i −2.15243 + 1.09672i
\(343\) −17.6105 5.73316i −0.950879 0.309562i
\(344\) −5.37730 1.74719i −0.289925 0.0942022i
\(345\) 0.861386 2.07938i 0.0463755 0.111950i
\(346\) 25.1143 8.16012i 1.35015 0.438691i
\(347\) 21.0525 + 10.7268i 1.13016 + 0.575844i 0.916089 0.400974i \(-0.131328\pi\)
0.214069 + 0.976819i \(0.431328\pi\)
\(348\) −1.26760 + 0.200768i −0.0679505 + 0.0107623i
\(349\) −9.96173 −0.533239 −0.266620 0.963802i \(-0.585907\pi\)
−0.266620 + 0.963802i \(0.585907\pi\)
\(350\) −13.2752 29.8370i −0.709587 1.59485i
\(351\) 2.33324 0.124539
\(352\) −4.14857 + 0.657069i −0.221120 + 0.0350219i
\(353\) −17.1476 8.73712i −0.912672 0.465030i −0.0664077 0.997793i \(-0.521154\pi\)
−0.846265 + 0.532763i \(0.821154\pi\)
\(354\) −2.07130 + 0.673007i −0.110089 + 0.0357699i
\(355\) −2.03112 8.46142i −0.107801 0.449085i
\(356\) 22.4154 + 7.28322i 1.18802 + 0.386010i
\(357\) −1.66854 3.74953i −0.0883087 0.198446i
\(358\) −4.64677 + 2.36765i −0.245590 + 0.125134i
\(359\) 1.39337 + 1.91781i 0.0735394 + 0.101218i 0.844202 0.536025i \(-0.180075\pi\)
−0.770663 + 0.637243i \(0.780075\pi\)
\(360\) −29.1495 17.8641i −1.53631 0.941520i
\(361\) −14.9198 10.8399i −0.785255 0.570521i
\(362\) 56.1260 + 8.88948i 2.94992 + 0.467221i
\(363\) −0.273709 + 1.72813i −0.0143660 + 0.0907034i
\(364\) −17.2626 + 11.2058i −0.904808 + 0.587344i
\(365\) −1.77115 + 0.139335i −0.0927061 + 0.00729315i
\(366\) −2.20745 + 1.60380i −0.115385 + 0.0838322i
\(367\) −0.381987 + 0.194632i −0.0199396 + 0.0101597i −0.463932 0.885871i \(-0.653562\pi\)
0.443992 + 0.896031i \(0.353562\pi\)
\(368\) 15.7924 + 15.7924i 0.823236 + 0.823236i
\(369\) 7.30108 22.4704i 0.380079 1.16976i
\(370\) 1.73177 21.9953i 0.0900306 1.14348i
\(371\) 6.53194 + 0.343575i 0.339122 + 0.0178375i
\(372\) −1.50868 0.768709i −0.0782213 0.0398557i
\(373\) 3.82756 + 24.1662i 0.198183 + 1.25128i 0.863358 + 0.504592i \(0.168357\pi\)
−0.665174 + 0.746688i \(0.731643\pi\)
\(374\) 82.0084 4.24055
\(375\) −1.75230 1.49690i −0.0904886 0.0772996i
\(376\) 45.9589i 2.37015i
\(377\) −0.451999 2.85381i −0.0232792 0.146979i
\(378\) −5.96160 + 5.36578i −0.306631 + 0.275986i
\(379\) 16.6292 5.40314i 0.854182 0.277541i 0.150986 0.988536i \(-0.451755\pi\)
0.703197 + 0.710995i \(0.251755\pi\)
\(380\) 4.39690 55.8451i 0.225556 2.86479i
\(381\) 2.23009 + 0.724601i 0.114251 + 0.0371224i
\(382\) −22.8698 + 22.8698i −1.17012 + 1.17012i
\(383\) 15.1563 + 29.7460i 0.774453 + 1.51995i 0.852340 + 0.522988i \(0.175183\pi\)
−0.0778868 + 0.996962i \(0.524817\pi\)
\(384\) 3.11617 2.26403i 0.159022 0.115536i
\(385\) 7.42314 25.0396i 0.378318 1.27614i
\(386\) −19.9447 14.4907i −1.01516 0.737556i
\(387\) 0.506005 3.19479i 0.0257217 0.162400i
\(388\) 1.94345 12.2705i 0.0986640 0.622940i
\(389\) −8.93652 + 12.3001i −0.453099 + 0.623638i −0.973060 0.230553i \(-0.925947\pi\)
0.519961 + 0.854190i \(0.325947\pi\)
\(390\) −1.12965 + 1.84329i −0.0572020 + 0.0933385i
\(391\) −21.5989 29.7283i −1.09230 1.50342i
\(392\) 9.37939 34.9510i 0.473731 1.76529i
\(393\) 0.630179 + 0.630179i 0.0317883 + 0.0317883i
\(394\) 0.830416 + 0.269818i 0.0418357 + 0.0135933i
\(395\) 23.8319 5.72074i 1.19911 0.287841i
\(396\) −16.5180 50.8371i −0.830059 2.55466i
\(397\) 10.9935 21.5760i 0.551748 1.08287i −0.431758 0.901990i \(-0.642106\pi\)
0.983506 0.180877i \(-0.0578936\pi\)
\(398\) 23.2016 3.67477i 1.16299 0.184200i
\(399\) −3.11525 1.19651i −0.155957 0.0599006i
\(400\) 20.3767 10.3808i 1.01883 0.519039i
\(401\) −31.4063 −1.56835 −0.784177 0.620537i \(-0.786915\pi\)
−0.784177 + 0.620537i \(0.786915\pi\)
\(402\) 0.431164 + 2.72226i 0.0215045 + 0.135774i
\(403\) 1.73063 3.39656i 0.0862090 0.169195i
\(404\) −11.4526 35.2475i −0.569788 1.75363i
\(405\) 7.37624 17.8062i 0.366528 0.884797i
\(406\) 7.71784 + 6.25223i 0.383030 + 0.310293i
\(407\) 12.4767 12.4767i 0.618448 0.618448i
\(408\) 7.14503 3.64058i 0.353732 0.180235i
\(409\) 17.6612 12.8316i 0.873291 0.634483i −0.0581767 0.998306i \(-0.518529\pi\)
0.931468 + 0.363823i \(0.118529\pi\)
\(410\) 28.6383 + 33.5333i 1.41435 + 1.65609i
\(411\) −2.06575 + 2.84326i −0.101896 + 0.140248i
\(412\) 0.894843 + 0.141729i 0.0440858 + 0.00698250i
\(413\) 9.80547 + 5.66369i 0.482496 + 0.278692i
\(414\) −20.9554 + 28.8427i −1.02990 + 1.41754i
\(415\) 0.697961 + 1.68518i 0.0342616 + 0.0827223i
\(416\) −1.06258 1.46252i −0.0520973 0.0717058i
\(417\) 0.414268 + 0.813047i 0.0202868 + 0.0398151i
\(418\) 47.1526 47.1526i 2.30631 2.30631i
\(419\) −10.8766 + 33.4748i −0.531358 + 1.63535i 0.220033 + 0.975493i \(0.429384\pi\)
−0.751390 + 0.659858i \(0.770616\pi\)
\(420\) −0.908765 4.90936i −0.0443432 0.239552i
\(421\) −3.38146 10.4071i −0.164802 0.507210i 0.834219 0.551433i \(-0.185919\pi\)
−0.999022 + 0.0442233i \(0.985919\pi\)
\(422\) −34.8025 17.7328i −1.69416 0.863218i
\(423\) −25.9689 + 4.11307i −1.26265 + 0.199984i
\(424\) 12.7807i 0.620686i
\(425\) −35.7851 + 11.6248i −1.73583 + 0.563883i
\(426\) 1.98027i 0.0959443i
\(427\) 13.8761 + 2.95223i 0.671512 + 0.142868i
\(428\) −13.8846 + 27.2501i −0.671139 + 1.31718i
\(429\) −1.64432 + 0.534272i −0.0793885 + 0.0257949i
\(430\) 4.59062 + 3.92101i 0.221379 + 0.189088i
\(431\) −4.21755 + 12.9803i −0.203152 + 0.625239i 0.796632 + 0.604465i \(0.206613\pi\)
−0.999784 + 0.0207739i \(0.993387\pi\)
\(432\) −3.97157 3.97157i −0.191082 0.191082i
\(433\) 5.88887 + 11.5575i 0.283001 + 0.555420i 0.988123 0.153666i \(-0.0491078\pi\)
−0.705122 + 0.709086i \(0.749108\pi\)
\(434\) 3.38922 + 12.6584i 0.162688 + 0.607624i
\(435\) 0.681574 + 0.163654i 0.0326790 + 0.00784663i
\(436\) −25.5754 18.5816i −1.22484 0.889899i
\(437\) −29.5117 4.67419i −1.41174 0.223597i
\(438\) −0.399328 0.0632474i −0.0190806 0.00302208i
\(439\) 0.917813 + 0.666831i 0.0438048 + 0.0318261i 0.609472 0.792807i \(-0.291381\pi\)
−0.565667 + 0.824634i \(0.691381\pi\)
\(440\) 49.6204 + 11.9145i 2.36556 + 0.568001i
\(441\) 20.5883 + 2.17187i 0.980397 + 0.103422i
\(442\) 16.0240 + 31.4488i 0.762182 + 1.49587i
\(443\) −13.9503 13.9503i −0.662797 0.662797i 0.293242 0.956038i \(-0.405266\pi\)
−0.956038 + 0.293242i \(0.905266\pi\)
\(444\) 1.04237 3.20807i 0.0494685 0.152248i
\(445\) −9.78807 8.36034i −0.463999 0.396318i
\(446\) −33.3885 + 10.8486i −1.58099 + 0.513695i
\(447\) −0.497509 + 0.976417i −0.0235314 + 0.0461829i
\(448\) −17.5936 3.74314i −0.831219 0.176847i
\(449\) 14.4907i 0.683860i 0.939725 + 0.341930i \(0.111081\pi\)
−0.939725 + 0.341930i \(0.888919\pi\)
\(450\) 21.4552 + 29.5345i 1.01141 + 1.39227i
\(451\) 35.2666i 1.66064i
\(452\) 32.6345 5.16880i 1.53500 0.243120i
\(453\) 2.29763 + 1.17070i 0.107952 + 0.0550044i
\(454\) 3.93397 + 12.1075i 0.184630 + 0.568233i
\(455\) 11.0527 2.04595i 0.518158 0.0959155i
\(456\) 2.01497 6.20143i 0.0943595 0.290409i
\(457\) 4.42308 4.42308i 0.206903 0.206903i −0.596047 0.802950i \(-0.703263\pi\)
0.802950 + 0.596047i \(0.203263\pi\)
\(458\) −4.83202 9.48338i −0.225786 0.443129i
\(459\) 5.43181 + 7.47625i 0.253535 + 0.348961i
\(460\) −17.1060 41.3013i −0.797572 1.92568i
\(461\) −3.16235 + 4.35260i −0.147285 + 0.202721i −0.876285 0.481793i \(-0.839986\pi\)
0.729000 + 0.684514i \(0.239986\pi\)
\(462\) 2.97268 5.14657i 0.138302 0.239440i
\(463\) 24.3710 + 3.85998i 1.13261 + 0.179389i 0.694474 0.719518i \(-0.255637\pi\)
0.438141 + 0.898906i \(0.355637\pi\)
\(464\) −4.08829 + 5.62705i −0.189794 + 0.261229i
\(465\) 0.600573 + 0.703226i 0.0278509 + 0.0326113i
\(466\) −24.0496 + 17.4730i −1.11407 + 0.809422i
\(467\) 7.93600 4.04359i 0.367234 0.187115i −0.260629 0.965439i \(-0.583930\pi\)
0.627863 + 0.778324i \(0.283930\pi\)
\(468\) 16.2676 16.2676i 0.751971 0.751971i
\(469\) 9.02053 11.1351i 0.416530 0.514170i
\(470\) 18.7811 45.3376i 0.866310 2.09127i
\(471\) 0.367696 + 1.13165i 0.0169426 + 0.0521438i
\(472\) −10.0449 + 19.7142i −0.462354 + 0.907420i
\(473\) 0.755290 + 4.76871i 0.0347283 + 0.219266i
\(474\) 5.57751 0.256183
\(475\) −13.8915 + 27.2594i −0.637388 + 1.25075i
\(476\) −76.0937 29.2263i −3.48775 1.33958i
\(477\) −7.22170 + 1.14380i −0.330659 + 0.0523712i
\(478\) 14.6556 28.7632i 0.670330 1.31560i
\(479\) 4.09301 + 12.5970i 0.187014 + 0.575571i 0.999977 0.00674428i \(-0.00214679\pi\)
−0.812963 + 0.582316i \(0.802147\pi\)
\(480\) 0.426440 0.102365i 0.0194642 0.00467229i
\(481\) 7.22249 + 2.34673i 0.329317 + 0.107002i
\(482\) −43.1229 43.1229i −1.96420 1.96420i
\(483\) −2.64857 + 0.277865i −0.120514 + 0.0126433i
\(484\) 20.4265 + 28.1147i 0.928477 + 1.27794i
\(485\) −3.54546 + 5.78524i −0.160991 + 0.262694i
\(486\) 7.92379 10.9062i 0.359430 0.494713i
\(487\) 2.71331 17.1311i 0.122952 0.776286i −0.846749 0.531992i \(-0.821444\pi\)
0.969701 0.244294i \(-0.0785563\pi\)
\(488\) −4.33637 + 27.3788i −0.196298 + 1.23938i
\(489\) −2.86779 2.08357i −0.129686 0.0942222i
\(490\) −23.5353 + 30.6456i −1.06322 + 1.38443i
\(491\) −1.18871 + 0.863649i −0.0536458 + 0.0389759i −0.614285 0.789084i \(-0.710555\pi\)
0.560639 + 0.828060i \(0.310555\pi\)
\(492\) 3.06078 + 6.00712i 0.137991 + 0.270822i
\(493\) 8.09202 8.09202i 0.364446 0.364446i
\(494\) 27.2955 + 8.86886i 1.22808 + 0.399029i
\(495\) −2.29148 + 29.1041i −0.102994 + 1.30813i
\(496\) −8.72735 + 2.83569i −0.391870 + 0.127326i
\(497\) −7.65280 + 6.88797i −0.343275 + 0.308968i
\(498\) 0.0649342 + 0.409978i 0.00290977 + 0.0183716i
\(499\) 18.7450i 0.839142i 0.907722 + 0.419571i \(0.137820\pi\)
−0.907722 + 0.419571i \(0.862180\pi\)
\(500\) −45.6331 + 3.58700i −2.04077 + 0.160416i
\(501\) 3.31009 0.147884
\(502\) 9.57433 + 60.4499i 0.427323 + 2.69801i
\(503\) −26.5174 13.5113i −1.18235 0.602438i −0.251507 0.967856i \(-0.580926\pi\)
−0.930844 + 0.365418i \(0.880926\pi\)
\(504\) −2.12479 + 40.3959i −0.0946457 + 1.79938i
\(505\) −1.58878 + 20.1791i −0.0706998 + 0.897959i
\(506\) 16.4444 50.6108i 0.731044 2.24992i
\(507\) 1.36867 + 1.36867i 0.0607846 + 0.0607846i
\(508\) 41.4969 21.1437i 1.84113 0.938101i
\(509\) 12.1945 8.85982i 0.540512 0.392705i −0.283763 0.958894i \(-0.591583\pi\)
0.824275 + 0.566190i \(0.191583\pi\)
\(510\) −8.53616 + 0.671536i −0.377988 + 0.0297361i
\(511\) 1.14456 + 1.76321i 0.0506325 + 0.0779998i
\(512\) 6.71687 42.4086i 0.296846 1.87421i
\(513\) 7.42178 + 1.17550i 0.327680 + 0.0518994i
\(514\) −37.6399 27.3470i −1.66022 1.20622i
\(515\) −0.421897 0.258558i −0.0185910 0.0113934i
\(516\) 0.542528 + 0.746725i 0.0238834 + 0.0328727i
\(517\) 34.9682 17.8172i 1.53790 0.783600i
\(518\) −23.8508 + 10.6136i −1.04794 + 0.466335i
\(519\) −2.09705 0.681373i −0.0920503 0.0299089i
\(520\) 5.12654 + 21.3566i 0.224814 + 0.936548i
\(521\) −29.0466 + 9.43781i −1.27255 + 0.413478i −0.865952 0.500127i \(-0.833287\pi\)
−0.406603 + 0.913605i \(0.633287\pi\)
\(522\) −9.89278 5.04063i −0.432995 0.220622i
\(523\) 31.3337 4.96277i 1.37013 0.217007i 0.572375 0.819992i \(-0.306022\pi\)
0.797752 + 0.602986i \(0.206022\pi\)
\(524\) 17.7010 0.773271
\(525\) −0.567627 + 2.66713i −0.0247733 + 0.116403i
\(526\) 47.2948 2.06215
\(527\) 14.9123 2.36188i 0.649591 0.102885i
\(528\) 3.70833 + 1.88949i 0.161384 + 0.0822294i
\(529\) −0.803278 + 0.261001i −0.0349251 + 0.0113479i
\(530\) 5.22285 12.6079i 0.226866 0.547654i
\(531\) −12.0384 3.91152i −0.522423 0.169745i
\(532\) −60.5561 + 26.9475i −2.62544 + 1.16832i
\(533\) −13.5241 + 6.89089i −0.585795 + 0.298478i
\(534\) −1.72186 2.36994i −0.0745121 0.102557i
\(535\) 12.7018 10.8477i 0.549149 0.468987i
\(536\) 22.6532 + 16.4585i 0.978467 + 0.710898i
\(537\) 0.430109 + 0.0681226i 0.0185606 + 0.00293971i
\(538\) −10.5890 + 66.8563i −0.456524 + 2.88238i
\(539\) −30.2289 + 6.41330i −1.30205 + 0.276240i
\(540\) 4.30193 + 10.3867i 0.185125 + 0.446973i
\(541\) 27.4655 19.9549i 1.18083 0.857926i 0.188569 0.982060i \(-0.439615\pi\)
0.992266 + 0.124134i \(0.0396151\pi\)
\(542\) −23.1900 + 11.8159i −0.996096 + 0.507536i
\(543\) −3.35519 3.35519i −0.143985 0.143985i
\(544\) 2.21255 6.80952i 0.0948622 0.291956i
\(545\) 9.02091 + 14.7218i 0.386413 + 0.630614i
\(546\) 2.55446 + 0.134363i 0.109321 + 0.00575020i
\(547\) 4.65971 + 2.37424i 0.199235 + 0.101515i 0.550762 0.834663i \(-0.314337\pi\)
−0.351527 + 0.936178i \(0.614337\pi\)
\(548\) 10.9197 + 68.9442i 0.466466 + 2.94515i
\(549\) −15.8584 −0.676818
\(550\) −44.0807 32.0308i −1.87961 1.36580i
\(551\) 9.30539i 0.396423i
\(552\) −0.814018 5.13951i −0.0346469 0.218752i
\(553\) −19.4002 21.5544i −0.824982 0.916588i
\(554\) 27.4820 8.92945i 1.16760 0.379376i
\(555\) −1.19652 + 1.40086i −0.0507895 + 0.0594630i
\(556\) 17.2369 + 5.60061i 0.731008 + 0.237519i
\(557\) −20.1686 + 20.1686i −0.854572 + 0.854572i −0.990692 0.136120i \(-0.956537\pi\)
0.136120 + 0.990692i \(0.456537\pi\)
\(558\) −6.65024 13.0518i −0.281527 0.552528i
\(559\) −1.68114 + 1.22142i −0.0711046 + 0.0516605i
\(560\) −22.2961 15.3310i −0.942183 0.647853i
\(561\) −5.53993 4.02499i −0.233896 0.169935i
\(562\) −7.37003 + 46.5326i −0.310886 + 1.96286i
\(563\) 0.934834 5.90231i 0.0393985 0.248753i −0.960127 0.279565i \(-0.909810\pi\)
0.999525 + 0.0308129i \(0.00980960\pi\)
\(564\) 4.40995 6.06977i 0.185692 0.255584i
\(565\) −17.5472 4.21330i −0.738216 0.177255i
\(566\) 15.2030 + 20.9252i 0.639030 + 0.879550i
\(567\) −22.6803 + 2.37942i −0.952483 + 0.0999262i
\(568\) −14.2256 14.2256i −0.596892 0.596892i
\(569\) 16.1923 + 5.26120i 0.678817 + 0.220561i 0.628077 0.778151i \(-0.283842\pi\)
0.0507396 + 0.998712i \(0.483842\pi\)
\(570\) −4.52195 + 5.29418i −0.189404 + 0.221749i
\(571\) −9.76647 30.0581i −0.408714 1.25789i −0.917754 0.397149i \(-0.870000\pi\)
0.509040 0.860743i \(-0.330000\pi\)
\(572\) −15.5900 + 30.5970i −0.651849 + 1.27932i
\(573\) 2.66738 0.422471i 0.111431 0.0176490i
\(574\) 18.7081 48.7084i 0.780859 2.03305i
\(575\) −0.00156093 + 24.4155i −6.50953e−5 + 1.01820i
\(576\) 20.1069 0.837787
\(577\) 6.61687 + 41.7773i 0.275464 + 1.73921i 0.606043 + 0.795432i \(0.292756\pi\)
−0.330579 + 0.943778i \(0.607244\pi\)
\(578\) −44.4129 + 87.1651i −1.84733 + 3.62559i
\(579\) 0.636122 + 1.95778i 0.0264363 + 0.0813627i
\(580\) 11.8707 7.27387i 0.492905 0.302031i
\(581\) 1.35851 1.67697i 0.0563606 0.0695724i
\(582\) −1.09185 + 1.09185i −0.0452588 + 0.0452588i
\(583\) 9.72432 4.95479i 0.402740 0.205206i
\(584\) −3.32299 + 2.41429i −0.137506 + 0.0999042i
\(585\) −11.6087 + 4.80803i −0.479959 + 0.198788i
\(586\) −28.7078 + 39.5130i −1.18591 + 1.63227i
\(587\) −3.47275 0.550030i −0.143336 0.0227022i 0.0843542 0.996436i \(-0.473117\pi\)
−0.227690 + 0.973734i \(0.573117\pi\)
\(588\) −4.59242 + 3.71597i −0.189388 + 0.153244i
\(589\) 7.21616 9.93219i 0.297337 0.409249i
\(590\) 17.9653 15.3428i 0.739621 0.631655i
\(591\) −0.0428545 0.0589841i −0.00176280 0.00242628i
\(592\) −8.29937 16.2884i −0.341102 0.669450i
\(593\) 6.75921 6.75921i 0.277567 0.277567i −0.554570 0.832137i \(-0.687117\pi\)
0.832137 + 0.554570i \(0.187117\pi\)
\(594\) −4.13555 + 12.7279i −0.169684 + 0.522232i
\(595\) 32.2865 + 30.6524i 1.32362 + 1.25663i
\(596\) 6.72597 + 20.7004i 0.275507 + 0.847922i
\(597\) −1.74770 0.890498i −0.0715287 0.0364457i
\(598\) 22.6215 3.58289i 0.925062 0.146515i
\(599\) 22.1468i 0.904895i −0.891791 0.452448i \(-0.850551\pi\)
0.891791 0.452448i \(-0.149449\pi\)
\(600\) −5.26250 0.833843i −0.214841 0.0340415i
\(601\) 29.6537i 1.20960i −0.796378 0.604800i \(-0.793253\pi\)
0.796378 0.604800i \(-0.206747\pi\)
\(602\) 1.48652 6.98696i 0.0605859 0.284767i
\(603\) −7.27247 + 14.2730i −0.296158 + 0.581243i
\(604\) 48.7107 15.8271i 1.98201 0.643995i
\(605\) −4.43022 18.4558i −0.180114 0.750334i
\(606\) −1.42345 + 4.38093i −0.0578237 + 0.177963i
\(607\) −12.9069 12.9069i −0.523876 0.523876i 0.394864 0.918740i \(-0.370792\pi\)
−0.918740 + 0.394864i \(0.870792\pi\)
\(608\) −2.64313 5.18744i −0.107193 0.210379i
\(609\) −0.214504 0.801152i −0.00869214 0.0324643i
\(610\) 15.4661 25.2366i 0.626204 1.02180i
\(611\) 13.6652 + 9.92833i 0.552834 + 0.401657i
\(612\) 89.9965 + 14.2540i 3.63789 + 0.576186i
\(613\) −26.4801 4.19404i −1.06952 0.169396i −0.403239 0.915095i \(-0.632116\pi\)
−0.666283 + 0.745699i \(0.732116\pi\)
\(614\) −60.1538 43.7043i −2.42761 1.76376i
\(615\) −0.288785 3.67086i −0.0116449 0.148023i
\(616\) −15.6165 58.3260i −0.629205 2.35002i
\(617\) −13.1667 25.8411i −0.530072 1.04032i −0.988447 0.151566i \(-0.951568\pi\)
0.458375 0.888759i \(-0.348432\pi\)
\(618\) −0.0796251 0.0796251i −0.00320299 0.00320299i
\(619\) 3.49027 10.7420i 0.140286 0.431756i −0.856089 0.516829i \(-0.827112\pi\)
0.996375 + 0.0850732i \(0.0271124\pi\)
\(620\) 18.3111 + 1.44170i 0.735391 + 0.0579002i
\(621\) 5.70310 1.85305i 0.228857 0.0743603i
\(622\) 28.9134 56.7457i 1.15932 2.27530i
\(623\) −3.16954 + 14.8975i −0.126985 + 0.596857i
\(624\) 1.79128i 0.0717084i
\(625\) 23.7754 + 7.72846i 0.951017 + 0.309139i
\(626\) 40.4966i 1.61857i
\(627\) −5.49957 + 0.871046i −0.219632 + 0.0347862i
\(628\) 21.0575 + 10.7293i 0.840285 + 0.428146i
\(629\) 9.29458 + 28.6058i 0.370599 + 1.14059i
\(630\) 18.6039 38.9815i 0.741196 1.55306i
\(631\) −4.67999 + 14.4035i −0.186307 + 0.573395i −0.999968 0.00794449i \(-0.997471\pi\)
0.813661 + 0.581339i \(0.197471\pi\)
\(632\) 40.0670 40.0670i 1.59378 1.59378i
\(633\) 1.48069 + 2.90602i 0.0588522 + 0.115504i
\(634\) −40.2484 55.3972i −1.59847 2.20010i
\(635\) −25.3581 + 1.99491i −1.00631 + 0.0791657i
\(636\) 1.22636 1.68794i 0.0486285 0.0669313i
\(637\) −8.36595 10.3392i −0.331471 0.409652i
\(638\) 16.3688 + 2.59256i 0.648047 + 0.102640i
\(639\) 6.76501 9.31123i 0.267620 0.368347i
\(640\) −21.8329 + 35.6256i −0.863023 + 1.40822i
\(641\) −37.9323 + 27.5594i −1.49823 + 1.08853i −0.527156 + 0.849768i \(0.676742\pi\)
−0.971078 + 0.238762i \(0.923258\pi\)
\(642\) 3.38693 1.72573i 0.133671 0.0681090i
\(643\) −16.5448 + 16.5448i −0.652463 + 0.652463i −0.953586 0.301122i \(-0.902639\pi\)
0.301122 + 0.953586i \(0.402639\pi\)
\(644\) −33.2952 + 41.1000i −1.31201 + 1.61957i
\(645\) −0.117667 0.490185i −0.00463311 0.0193010i
\(646\) 35.1265 + 108.108i 1.38203 + 4.25346i
\(647\) 3.81842 7.49408i 0.150118 0.294623i −0.803686 0.595054i \(-0.797131\pi\)
0.953803 + 0.300431i \(0.0971307\pi\)
\(648\) −6.97061 44.0107i −0.273832 1.72890i
\(649\) 18.8939 0.741651
\(650\) 3.67015 23.1628i 0.143955 0.908521i
\(651\) 0.392326 1.02146i 0.0153765 0.0400342i
\(652\) −69.5388 + 11.0139i −2.72335 + 0.431336i
\(653\) 12.4766 24.4867i 0.488246 0.958237i −0.507101 0.861887i \(-0.669283\pi\)
0.995347 0.0963509i \(-0.0307171\pi\)
\(654\) 1.21419 + 3.73688i 0.0474785 + 0.146124i
\(655\) −8.93160 3.69992i −0.348987 0.144568i
\(656\) 34.7498 + 11.2909i 1.35675 + 0.440836i
\(657\) −1.66158 1.66158i −0.0648243 0.0648243i
\(658\) −57.7479 + 6.05840i −2.25125 + 0.236181i
\(659\) −26.2956 36.1928i −1.02433 1.40987i −0.909121 0.416531i \(-0.863246\pi\)
−0.115211 0.993341i \(-0.536754\pi\)
\(660\) −5.41010 6.33483i −0.210588 0.246583i
\(661\) 22.4661 30.9219i 0.873829 1.20272i −0.104263 0.994550i \(-0.533248\pi\)
0.978092 0.208173i \(-0.0667517\pi\)
\(662\) −1.52120 + 9.60448i −0.0591231 + 0.373289i
\(663\) 0.461046 2.91093i 0.0179055 0.113051i
\(664\) 3.41161 + 2.47868i 0.132396 + 0.0961915i
\(665\) 36.1882 0.939551i 1.40332 0.0364342i
\(666\) 23.6086 17.1527i 0.914815 0.664652i
\(667\) −3.37130 6.61655i −0.130537 0.256194i
\(668\) 46.4883 46.4883i 1.79868 1.79868i
\(669\) 2.78795 + 0.905860i 0.107788 + 0.0350226i
\(670\) −15.6211 25.4932i −0.603497 0.984889i
\(671\) 22.5125 7.31475i 0.869085 0.282383i
\(672\) −0.347141 0.385687i −0.0133912 0.0148782i
\(673\) 1.58308 + 9.99517i 0.0610232 + 0.385285i 0.999231 + 0.0392126i \(0.0124850\pi\)
−0.938208 + 0.346073i \(0.887515\pi\)
\(674\) 56.9110i 2.19213i
\(675\) 0.000392552 6.14015i 1.51093e−5 0.236335i
\(676\) 38.4442 1.47862
\(677\) −3.02654 19.1088i −0.116319 0.734412i −0.975050 0.221985i \(-0.928746\pi\)
0.858731 0.512427i \(-0.171254\pi\)
\(678\) −3.65911 1.86441i −0.140527 0.0716023i
\(679\) 8.01730 + 0.421704i 0.307676 + 0.0161835i
\(680\) −56.4969 + 66.1451i −2.16656 + 2.53655i
\(681\) 0.328488 1.01098i 0.0125877 0.0387409i
\(682\) 15.4609 + 15.4609i 0.592028 + 0.592028i
\(683\) 39.0464 19.8951i 1.49407 0.761266i 0.499596 0.866258i \(-0.333482\pi\)
0.994473 + 0.104992i \(0.0334818\pi\)
\(684\) 59.9412 43.5499i 2.29191 1.66517i
\(685\) 8.90109 37.0705i 0.340093 1.41639i
\(686\) 45.1527 + 7.17799i 1.72394 + 0.274057i
\(687\) −0.139028 + 0.877789i −0.00530425 + 0.0334897i
\(688\) 4.94065 + 0.782522i 0.188360 + 0.0298334i
\(689\) 3.80015 + 2.76097i 0.144774 + 0.105185i
\(690\) −1.29725 + 5.40268i −0.0493855 + 0.205676i
\(691\) 26.4300 + 36.3778i 1.00544 + 1.38388i 0.921925 + 0.387369i \(0.126616\pi\)
0.0835193 + 0.996506i \(0.473384\pi\)
\(692\) −39.0213 + 19.8823i −1.48337 + 0.755813i
\(693\) 31.5593 14.0439i 1.19884 0.533483i
\(694\) −55.4735 18.0244i −2.10575 0.684198i
\(695\) −7.52677 6.42889i −0.285507 0.243862i
\(696\) 1.54123 0.500777i 0.0584202 0.0189819i
\(697\) −53.5644 27.2924i −2.02890 1.03377i
\(698\) 24.2891 3.84701i 0.919355 0.145612i
\(699\) 2.48220 0.0938856
\(700\) 29.4863 + 45.4302i 1.11448 + 1.71710i
\(701\) −27.9833 −1.05692 −0.528458 0.848960i \(-0.677230\pi\)
−0.528458 + 0.848960i \(0.677230\pi\)
\(702\) −5.68899 + 0.901048i −0.214717 + 0.0340079i
\(703\) 21.7917 + 11.1034i 0.821888 + 0.418773i
\(704\) −28.5437 + 9.27441i −1.07578 + 0.349542i
\(705\) −3.49391 + 2.14092i −0.131588 + 0.0806315i
\(706\) 45.1839 + 14.6811i 1.70052 + 0.552532i
\(707\) 21.8814 9.73723i 0.822935 0.366206i
\(708\) 3.21829 1.63980i 0.120951 0.0616274i
\(709\) 19.1433 + 26.3484i 0.718940 + 0.989537i 0.999558 + 0.0297170i \(0.00946061\pi\)
−0.280618 + 0.959820i \(0.590539\pi\)
\(710\) 8.21998 + 19.8466i 0.308490 + 0.744829i
\(711\) 26.2255 + 19.0539i 0.983532 + 0.714578i
\(712\) −29.3941 4.65557i −1.10159 0.174475i
\(713\) 1.53263 9.67661i 0.0573973 0.362392i
\(714\) 5.51630 + 8.49790i 0.206442 + 0.318026i
\(715\) 14.2619 12.1800i 0.533365 0.455507i
\(716\) 6.99737 5.08389i 0.261504 0.189994i
\(717\) −2.40173 + 1.22374i −0.0896944 + 0.0457016i
\(718\) −4.13799 4.13799i −0.154429 0.154429i
\(719\) 13.1048 40.3325i 0.488727 1.50415i −0.337782 0.941224i \(-0.609677\pi\)
0.826509 0.562923i \(-0.190323\pi\)
\(720\) 27.9440 + 11.5758i 1.04141 + 0.431406i
\(721\) −0.0307534 + 0.584674i −0.00114531 + 0.0217744i
\(722\) 40.5643 + 20.6685i 1.50965 + 0.769203i
\(723\) 0.796607 + 5.02958i 0.0296261 + 0.187052i
\(724\) −94.2433 −3.50252
\(725\) −7.51017 + 1.18900i −0.278921 + 0.0441584i
\(726\) 4.31930i 0.160304i
\(727\) −0.482868 3.04871i −0.0179086 0.113070i 0.977115 0.212713i \(-0.0682300\pi\)
−0.995023 + 0.0996428i \(0.968230\pi\)
\(728\) 19.3156 17.3852i 0.715885 0.644339i
\(729\) 23.5220 7.64277i 0.871187 0.283066i
\(730\) 4.26467 1.02371i 0.157843 0.0378893i
\(731\) −7.82743 2.54329i −0.289508 0.0940668i
\(732\) 3.19981 3.19981i 0.118268 0.118268i
\(733\) −7.32988 14.3857i −0.270735 0.531348i 0.715109 0.699013i \(-0.246377\pi\)
−0.985844 + 0.167665i \(0.946377\pi\)
\(734\) 0.856213 0.622075i 0.0316034 0.0229612i
\(735\) 3.09398 0.915087i 0.114123 0.0337535i
\(736\) −3.75877 2.73091i −0.138550 0.100663i
\(737\) 3.74047 23.6164i 0.137782 0.869922i
\(738\) −9.12417 + 57.6077i −0.335865 + 2.12057i
\(739\) −2.80874 + 3.86590i −0.103321 + 0.142209i −0.857547 0.514406i \(-0.828012\pi\)
0.754226 + 0.656615i \(0.228012\pi\)
\(740\) 2.86976 + 36.4786i 0.105494 + 1.34098i
\(741\) −1.40862 1.93879i −0.0517468 0.0712233i
\(742\) −16.0591 + 1.68478i −0.589549 + 0.0618503i
\(743\) 4.12484 + 4.12484i 0.151326 + 0.151326i 0.778710 0.627384i \(-0.215874\pi\)
−0.627384 + 0.778710i \(0.715874\pi\)
\(744\) 2.03339 + 0.660689i 0.0745478 + 0.0242220i
\(745\) 0.933071 11.8509i 0.0341851 0.434185i
\(746\) −18.6650 57.4449i −0.683374 2.10321i
\(747\) −1.09525 + 2.14955i −0.0400731 + 0.0786479i
\(748\) −134.334 + 21.2764i −4.91172 + 0.777940i
\(749\) −18.4499 7.08629i −0.674144 0.258927i
\(750\) 4.85061 + 2.97309i 0.177119 + 0.108562i
\(751\) −9.19974 −0.335703 −0.167852 0.985812i \(-0.553683\pi\)
−0.167852 + 0.985812i \(0.553683\pi\)
\(752\) −6.36075 40.1602i −0.231953 1.46449i
\(753\) 2.32012 4.55350i 0.0845500 0.165939i
\(754\) 2.20416 + 6.78372i 0.0802709 + 0.247049i
\(755\) −27.8868 2.19564i −1.01490 0.0799074i
\(756\) 8.37327 10.3361i 0.304533 0.375920i
\(757\) 9.03988 9.03988i 0.328560 0.328560i −0.523479 0.852039i \(-0.675366\pi\)
0.852039 + 0.523479i \(0.175366\pi\)
\(758\) −38.4593 + 19.5960i −1.39690 + 0.711758i
\(759\) −3.59486 + 2.61182i −0.130485 + 0.0948031i
\(760\) 5.54744 + 70.5158i 0.201227 + 2.55788i
\(761\) −23.0673 + 31.7494i −0.836190 + 1.15092i 0.150550 + 0.988602i \(0.451896\pi\)
−0.986739 + 0.162314i \(0.948104\pi\)
\(762\) −5.71732 0.905535i −0.207117 0.0328041i
\(763\) 10.2180 17.6903i 0.369916 0.640431i
\(764\) 31.5284 43.3951i 1.14066 1.56998i
\(765\) −42.4312 26.0037i −1.53410 0.940167i
\(766\) −48.4421 66.6748i −1.75028 2.40906i
\(767\) 3.69176 + 7.24549i 0.133302 + 0.261619i
\(768\) −4.74177 + 4.74177i −0.171104 + 0.171104i
\(769\) 4.04237 12.4411i 0.145771 0.448639i −0.851338 0.524618i \(-0.824208\pi\)
0.997109 + 0.0759792i \(0.0242083\pi\)
\(770\) −8.42961 + 63.9192i −0.303782 + 2.30349i
\(771\) 1.20050 + 3.69475i 0.0432348 + 0.133063i
\(772\) 36.4299 + 18.5619i 1.31114 + 0.668059i
\(773\) 12.3295 1.95280i 0.443461 0.0702372i 0.0692887 0.997597i \(-0.477927\pi\)
0.374172 + 0.927359i \(0.377927\pi\)
\(774\) 7.98507i 0.287017i
\(775\) −8.93810 4.55491i −0.321066 0.163617i
\(776\) 15.6870i 0.563132i
\(777\) 2.13211 + 0.453620i 0.0764892 + 0.0162735i
\(778\) 17.0393 33.4416i 0.610890 1.19894i
\(779\) −46.4905 + 15.1057i −1.66569 + 0.541217i
\(780\) 1.37219 3.31247i 0.0491324 0.118605i
\(781\) −5.30873 + 16.3386i −0.189961 + 0.584641i
\(782\) 64.1436 + 64.1436i 2.29377 + 2.29377i
\(783\) 0.847835 + 1.66397i 0.0302991 + 0.0594654i
\(784\) −3.35873 + 31.8393i −0.119955 + 1.13712i
\(785\) −8.38254 9.81533i −0.299186 0.350324i
\(786\) −1.77989 1.29317i −0.0634865 0.0461257i
\(787\) −45.4672 7.20130i −1.62073 0.256699i −0.720933 0.693005i \(-0.756286\pi\)
−0.899798 + 0.436306i \(0.856286\pi\)
\(788\) −1.43026 0.226531i −0.0509510 0.00806984i
\(789\) −3.19491 2.32124i −0.113742 0.0826384i
\(790\) −55.8987 + 23.1519i −1.98879 + 0.823708i
\(791\) 5.52243 + 20.6257i 0.196355 + 0.733367i
\(792\) 30.6422 + 60.1387i 1.08882 + 2.13694i
\(793\) 7.20389 + 7.20389i 0.255818 + 0.255818i
\(794\) −18.4726 + 56.8528i −0.655568 + 2.01763i
\(795\) −0.971621 + 0.595368i −0.0344599 + 0.0211155i
\(796\) −37.0519 + 12.0389i −1.31327 + 0.426708i
\(797\) 11.5819 22.7307i 0.410251 0.805164i −0.589746 0.807589i \(-0.700772\pi\)
0.999997 + 0.00242539i \(0.000772028\pi\)
\(798\) 8.05778 + 1.71434i 0.285242 + 0.0606871i
\(799\) 66.8997i 2.36674i
\(800\) −3.84894 + 2.79604i −0.136081 + 0.0988551i
\(801\) 17.0257i 0.601573i
\(802\) 76.5760 12.1284i 2.70399 0.428270i
\(803\) 3.12518 + 1.59236i 0.110285 + 0.0561932i
\(804\) −1.41253 4.34733i −0.0498162 0.153318i
\(805\) 25.3910 13.7789i 0.894916 0.485642i
\(806\) −2.90802 + 8.94996i −0.102431 + 0.315249i
\(807\) 3.99664 3.99664i 0.140689 0.140689i
\(808\) 21.2456 + 41.6967i 0.747416 + 1.46689i
\(809\) 19.6228 + 27.0085i 0.689900 + 0.949567i 0.999999 0.00113775i \(-0.000362157\pi\)
−0.310099 + 0.950704i \(0.600362\pi\)
\(810\) −11.1086 + 46.2643i −0.390318 + 1.62556i
\(811\) 0.750387 1.03282i 0.0263497 0.0362672i −0.795639 0.605771i \(-0.792865\pi\)
0.821989 + 0.569504i \(0.192865\pi\)
\(812\) −14.2643 8.23911i −0.500578 0.289136i
\(813\) 2.14649 + 0.339970i 0.0752806 + 0.0119233i
\(814\) −25.6030 + 35.2395i −0.897384 + 1.23514i
\(815\) 37.3902 + 8.97786i 1.30972 + 0.314481i
\(816\) −5.73967 + 4.17011i −0.200929 + 0.145983i
\(817\) −5.96288 + 3.03824i −0.208615 + 0.106295i
\(818\) −38.1070 + 38.1070i −1.33238 + 1.33238i
\(819\) 11.5521 + 9.35835i 0.403663 + 0.327007i
\(820\) −55.6109 47.4992i −1.94202 1.65875i
\(821\) −6.76858 20.8315i −0.236225 0.727026i −0.996957 0.0779591i \(-0.975160\pi\)
0.760732 0.649067i \(-0.224840\pi\)
\(822\) 3.93879 7.73030i 0.137381 0.269625i
\(823\) −4.08930 25.8188i −0.142544 0.899987i −0.950495 0.310738i \(-0.899424\pi\)
0.807951 0.589249i \(-0.200576\pi\)
\(824\) −1.14400 −0.0398532
\(825\) 1.40571 + 4.32728i 0.0489406 + 0.150657i
\(826\) −26.0953 10.0228i −0.907971 0.348736i
\(827\) −12.3593 + 1.95753i −0.429777 + 0.0680699i −0.367575 0.929994i \(-0.619812\pi\)
−0.0622011 + 0.998064i \(0.519812\pi\)
\(828\) 26.8430 52.6823i 0.932858 1.83084i
\(829\) −7.82434 24.0808i −0.271750 0.836362i −0.990061 0.140639i \(-0.955084\pi\)
0.718310 0.695723i \(-0.244916\pi\)
\(830\) −2.35258 3.83933i −0.0816592 0.133265i
\(831\) −2.29476 0.745612i −0.0796042 0.0258650i
\(832\) −9.13385 9.13385i −0.316659 0.316659i
\(833\) 13.6530 50.8761i 0.473050 1.76275i
\(834\) −1.32407 1.82242i −0.0458487 0.0631053i
\(835\) −33.1743 + 13.7400i −1.14804 + 0.475492i
\(836\) −65.0048 + 89.4715i −2.24824 + 3.09444i
\(837\) −0.385434 + 2.43353i −0.0133225 + 0.0841152i
\(838\) 13.5925 85.8198i 0.469546 2.96460i
\(839\) 45.7909 + 33.2690i 1.58088 + 1.14857i 0.915681 + 0.401907i \(0.131652\pi\)
0.665197 + 0.746668i \(0.268348\pi\)
\(840\) 2.10311 + 5.94321i 0.0725642 + 0.205060i
\(841\) −21.5905 + 15.6864i −0.744501 + 0.540911i
\(842\) 12.2638 + 24.0691i 0.422638 + 0.829475i
\(843\) 2.78170 2.78170i 0.0958068 0.0958068i
\(844\) 61.6088 + 20.0179i 2.12066 + 0.689045i
\(845\) −19.3983 8.03575i −0.667321 0.276438i
\(846\) 61.7300 20.0573i 2.12232 0.689584i
\(847\) −16.6920 + 15.0238i −0.573545 + 0.516224i
\(848\) −1.76886 11.1681i −0.0607429 0.383516i
\(849\) 2.15973i 0.0741217i
\(850\) 82.7634 42.1634i 2.83876 1.44619i
\(851\) 19.5176 0.669053
\(852\) 0.513763 + 3.24377i 0.0176012 + 0.111130i
\(853\) 36.9947 + 18.8497i 1.26667 + 0.645402i 0.952666 0.304019i \(-0.0983286\pi\)
0.314007 + 0.949421i \(0.398329\pi\)
\(854\) −34.9734 1.83957i −1.19676 0.0629488i
\(855\) −39.3482 + 9.44534i −1.34568 + 0.323024i
\(856\) 11.9335 36.7276i 0.407880 1.25532i
\(857\) 4.42430 + 4.42430i 0.151131 + 0.151131i 0.778623 0.627492i \(-0.215918\pi\)
−0.627492 + 0.778623i \(0.715918\pi\)
\(858\) 3.80292 1.93768i 0.129829 0.0661514i
\(859\) 0.0963348 0.0699913i 0.00328690 0.00238807i −0.586141 0.810209i \(-0.699353\pi\)
0.589427 + 0.807821i \(0.299353\pi\)
\(860\) −8.53692 5.23180i −0.291106 0.178403i
\(861\) −3.65441 + 2.37221i −0.124542 + 0.0808447i
\(862\) 5.27068 33.2778i 0.179520 1.13345i
\(863\) 31.3863 + 4.97111i 1.06840 + 0.169218i 0.665781 0.746147i \(-0.268099\pi\)
0.402623 + 0.915366i \(0.368099\pi\)
\(864\) 0.945280 + 0.686786i 0.0321591 + 0.0233649i
\(865\) 23.8453 1.87590i 0.810765 0.0637825i
\(866\) −18.8217 25.9059i −0.639589 0.880318i
\(867\) 7.27832 3.70849i 0.247185 0.125947i
\(868\) −8.83582 19.8558i −0.299907 0.673949i
\(869\) −46.0183 14.9523i −1.56107 0.507221i
\(870\) −1.72504 0.135819i −0.0584843 0.00460470i
\(871\) 9.78736 3.18011i 0.331632 0.107754i
\(872\) 35.5669 + 18.1222i 1.20445 + 0.613696i
\(873\) −8.86391 + 1.40391i −0.299998 + 0.0475150i
\(874\) 73.7616 2.49502
\(875\) −5.38226 29.0866i −0.181954 0.983307i
\(876\) 0.670528 0.0226550
\(877\) −28.9141 + 4.57954i −0.976358 + 0.154640i −0.624169 0.781289i \(-0.714563\pi\)
−0.352189 + 0.935929i \(0.614563\pi\)
\(878\) −2.49536 1.27145i −0.0842145 0.0429094i
\(879\) 3.87861 1.26024i 0.130822 0.0425068i
\(880\) −45.0087 3.54371i −1.51724 0.119458i
\(881\) 4.74906 + 1.54306i 0.160000 + 0.0519871i 0.387922 0.921692i \(-0.373193\pi\)
−0.227922 + 0.973679i \(0.573193\pi\)
\(882\) −51.0380 + 2.65525i −1.71854 + 0.0894069i
\(883\) −7.05653 + 3.59548i −0.237471 + 0.120998i −0.568677 0.822561i \(-0.692545\pi\)
0.331206 + 0.943559i \(0.392545\pi\)
\(884\) −34.4071 47.3573i −1.15724 1.59280i
\(885\) −1.96665 + 0.154715i −0.0661081 + 0.00520069i
\(886\) 39.4014 + 28.6268i 1.32371 + 0.961735i
\(887\) 17.9684 + 2.84592i 0.603321 + 0.0955566i 0.450620 0.892716i \(-0.351203\pi\)
0.152701 + 0.988272i \(0.451203\pi\)
\(888\) −0.666299 + 4.20685i −0.0223595 + 0.141173i
\(889\) 16.3871 + 25.2445i 0.549606 + 0.846672i
\(890\) 27.0942 + 16.6046i 0.908201 + 0.556586i
\(891\) −30.7836 + 22.3656i −1.03129 + 0.749276i
\(892\) 51.8773 26.4328i 1.73698 0.885037i
\(893\) 38.4655 + 38.4655i 1.28720 + 1.28720i
\(894\) 0.835975 2.57287i 0.0279592 0.0860495i
\(895\) −4.59340 + 1.10262i −0.153540 + 0.0368566i
\(896\) 49.3706 + 2.59685i 1.64936 + 0.0867548i
\(897\) −1.70400 0.868233i −0.0568950 0.0289895i
\(898\) −5.59602 35.3319i −0.186742 1.17904i
\(899\) 3.05115 0.101762
\(900\) −42.8071 42.8126i −1.42690 1.42709i
\(901\) 18.6042i 0.619794i
\(902\) −13.6192 85.9884i −0.453470 2.86310i
\(903\) −0.443341 + 0.399033i −0.0147535 + 0.0132790i
\(904\) −39.6792 + 12.8925i −1.31971 + 0.428800i
\(905\) 47.5535 + 19.6991i 1.58073 + 0.654819i
\(906\) −6.05428 1.96716i −0.201140 0.0653544i
\(907\) 24.8734 24.8734i 0.825908 0.825908i −0.161040 0.986948i \(-0.551485\pi\)
0.986948 + 0.161040i \(0.0514849\pi\)
\(908\) −9.58521 18.8120i −0.318096 0.624299i
\(909\) −21.6592 + 15.7364i −0.718392 + 0.521942i
\(910\) −26.1590 + 9.25683i −0.867162 + 0.306861i
\(911\) −27.2719 19.8142i −0.903558 0.656473i 0.0358197 0.999358i \(-0.488596\pi\)
−0.939377 + 0.342885i \(0.888596\pi\)
\(912\) −0.902452 + 5.69786i −0.0298832 + 0.188675i
\(913\) 0.563324 3.55669i 0.0186433 0.117709i
\(914\) −9.07642 + 12.4926i −0.300221 + 0.413219i
\(915\) −2.28340 + 0.945731i −0.0754870 + 0.0312649i
\(916\) 10.3755 + 14.2806i 0.342815 + 0.471844i
\(917\) 1.19352 + 11.3764i 0.0394134 + 0.375683i
\(918\) −16.1312 16.1312i −0.532410 0.532410i
\(919\) −13.9765 4.54122i −0.461041 0.149801i 0.0692820 0.997597i \(-0.477929\pi\)
−0.530323 + 0.847796i \(0.677929\pi\)
\(920\) 29.4920 + 48.1301i 0.972323 + 1.58680i
\(921\) 1.91856 + 5.90473i 0.0632188 + 0.194568i
\(922\) 6.02968 11.8339i 0.198577 0.389729i
\(923\) −7.30287 + 1.15666i −0.240377 + 0.0380719i
\(924\) −3.53416 + 9.20156i −0.116265 + 0.302709i
\(925\) 6.17687 19.0063i 0.203094 0.624923i
\(926\) −60.9128 −2.00172
\(927\) −0.102382 0.646414i −0.00336266 0.0212310i
\(928\) 0.656894 1.28923i 0.0215636 0.0423210i
\(929\) −4.05750 12.4877i −0.133122 0.409708i 0.862171 0.506617i \(-0.169104\pi\)
−0.995293 + 0.0969092i \(0.969104\pi\)
\(930\) −1.73591 1.48270i −0.0569228 0.0486198i
\(931\) −21.4023 37.1025i −0.701431 1.21599i
\(932\) 34.8611 34.8611i 1.14191 1.14191i
\(933\) −4.73829 + 2.41428i −0.155125 + 0.0790399i
\(934\) −17.7883 + 12.9240i −0.582051 + 0.422885i
\(935\) 72.2296 + 17.3432i 2.36216 + 0.567184i
\(936\) −17.0749 + 23.5015i −0.558109 + 0.768171i
\(937\) −12.5937 1.99465i −0.411418 0.0651622i −0.0527051 0.998610i \(-0.516784\pi\)
−0.358713 + 0.933448i \(0.616784\pi\)
\(938\) −17.6941 + 30.6335i −0.577732 + 1.00022i
\(939\) −1.98758 + 2.73567i −0.0648623 + 0.0892753i
\(940\) −19.0020 + 79.1377i −0.619776 + 2.58119i
\(941\) 22.2067 + 30.5649i 0.723917 + 0.996386i 0.999385 + 0.0350759i \(0.0111673\pi\)
−0.275468 + 0.961310i \(0.588833\pi\)
\(942\) −1.33355 2.61724i −0.0434495 0.0852744i
\(943\) −27.5841 + 27.5841i −0.898261 + 0.898261i
\(944\) 6.04905 18.6171i 0.196880 0.605933i
\(945\) −6.38549 + 3.46520i −0.207720 + 0.112723i
\(946\) −3.68315 11.3356i −0.119750 0.368552i
\(947\) 14.2973 + 7.28482i 0.464599 + 0.236725i 0.670589 0.741829i \(-0.266042\pi\)
−0.205990 + 0.978554i \(0.566042\pi\)
\(948\) −9.13622 + 1.44703i −0.296731 + 0.0469975i
\(949\) 1.50959i 0.0490034i
\(950\) 23.3439 71.8295i 0.757376 2.33046i
\(951\) 5.71766i 0.185408i
\(952\) 100.673 + 21.4189i 3.26284 + 0.694190i
\(953\) 10.1160 19.8538i 0.327691 0.643129i −0.667111 0.744958i \(-0.732470\pi\)
0.994802 + 0.101829i \(0.0324695\pi\)
\(954\) 17.1665 5.57774i 0.555786 0.180586i
\(955\) −24.9793 + 15.3062i −0.808310 + 0.495297i
\(956\) −16.5442 + 50.9177i −0.535076 + 1.64680i
\(957\) −0.978520 0.978520i −0.0316311 0.0316311i
\(958\) −14.8444 29.1338i −0.479602 0.941272i
\(959\) −43.5743 + 11.6668i −1.40709 + 0.376740i
\(960\) 2.89514 1.19910i 0.0934402 0.0387007i
\(961\) −21.8229 15.8552i −0.703963 0.511459i
\(962\) −18.5164 2.93271i −0.596993 0.0945544i
\(963\) 21.8208 + 3.45608i 0.703166 + 0.111370i
\(964\) 81.8253 + 59.4496i 2.63542 + 1.91474i
\(965\) −14.5020 16.9807i −0.466835 0.546629i
\(966\) 6.35054 1.70032i 0.204325 0.0547070i
\(967\) −18.0398 35.4051i −0.580121 1.13855i −0.975493 0.220030i \(-0.929384\pi\)
0.395372 0.918521i \(-0.370616\pi\)
\(968\) −31.0284 31.0284i −0.997291 0.997291i
\(969\) 2.93307 9.02707i 0.0942239 0.289991i
\(970\) 6.41053 15.4750i 0.205830 0.496872i
\(971\) 27.1538 8.82281i 0.871407 0.283137i 0.161022 0.986951i \(-0.448521\pi\)
0.710385 + 0.703813i \(0.248521\pi\)
\(972\) −10.1500 + 19.9206i −0.325562 + 0.638952i
\(973\) −2.43729 + 11.4558i −0.0781361 + 0.367257i
\(974\) 42.8176i 1.37197i
\(975\) −1.38477 + 1.38459i −0.0443481 + 0.0443424i
\(976\) 24.5245i 0.785010i
\(977\) 48.3318 7.65500i 1.54627 0.244905i 0.675785 0.737099i \(-0.263805\pi\)
0.870486 + 0.492194i \(0.163805\pi\)
\(978\) 7.79698 + 3.97276i 0.249320 + 0.127035i
\(979\) 7.85318 + 24.1696i 0.250989 + 0.772464i
\(980\) 30.6013 56.3050i 0.977522 1.79860i
\(981\) −7.05686 + 21.7188i −0.225308 + 0.693427i
\(982\) 2.56484 2.56484i 0.0818472 0.0818472i
\(983\) −13.5238 26.5420i −0.431344 0.846559i −0.999717 0.0237886i \(-0.992427\pi\)
0.568374 0.822771i \(-0.307573\pi\)
\(984\) −5.00384 6.88719i −0.159517 0.219556i
\(985\) 0.674334 + 0.413262i 0.0214861 + 0.0131676i
\(986\) −16.6053 + 22.8552i −0.528821 + 0.727859i
\(987\) 4.19840 + 2.42502i 0.133637 + 0.0771891i
\(988\) −47.0123 7.44602i −1.49566 0.236890i
\(989\) −3.13913 + 4.32065i −0.0998187 + 0.137389i
\(990\) −5.65223 71.8477i −0.179640 2.28347i
\(991\) 29.6993 21.5778i 0.943431 0.685443i −0.00581317 0.999983i \(-0.501850\pi\)
0.949244 + 0.314540i \(0.101850\pi\)
\(992\) 1.70091 0.866659i 0.0540041 0.0275165i
\(993\) 0.574152 0.574152i 0.0182202 0.0182202i
\(994\) 15.9994 19.7499i 0.507469 0.626428i
\(995\) 21.2122 + 1.67012i 0.672471 + 0.0529462i
\(996\) −0.212731 0.654717i −0.00674062 0.0207455i
\(997\) −19.4930 + 38.2572i −0.617350 + 1.21162i 0.344692 + 0.938716i \(0.387983\pi\)
−0.962042 + 0.272902i \(0.912017\pi\)
\(998\) −7.23893 45.7048i −0.229144 1.44676i
\(999\) −4.90840 −0.155295
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 175.2.s.a.13.2 yes 144
5.2 odd 4 875.2.s.b.832.2 144
5.3 odd 4 875.2.s.a.832.17 144
5.4 even 2 875.2.s.c.293.17 144
7.6 odd 2 inner 175.2.s.a.13.1 144
25.2 odd 20 inner 175.2.s.a.27.1 yes 144
25.11 even 5 875.2.s.b.468.1 144
25.14 even 10 875.2.s.a.468.18 144
25.23 odd 20 875.2.s.c.657.18 144
35.13 even 4 875.2.s.a.832.18 144
35.27 even 4 875.2.s.b.832.1 144
35.34 odd 2 875.2.s.c.293.18 144
175.27 even 20 inner 175.2.s.a.27.2 yes 144
175.48 even 20 875.2.s.c.657.17 144
175.111 odd 10 875.2.s.b.468.2 144
175.139 odd 10 875.2.s.a.468.17 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.s.a.13.1 144 7.6 odd 2 inner
175.2.s.a.13.2 yes 144 1.1 even 1 trivial
175.2.s.a.27.1 yes 144 25.2 odd 20 inner
175.2.s.a.27.2 yes 144 175.27 even 20 inner
875.2.s.a.468.17 144 175.139 odd 10
875.2.s.a.468.18 144 25.14 even 10
875.2.s.a.832.17 144 5.3 odd 4
875.2.s.a.832.18 144 35.13 even 4
875.2.s.b.468.1 144 25.11 even 5
875.2.s.b.468.2 144 175.111 odd 10
875.2.s.b.832.1 144 35.27 even 4
875.2.s.b.832.2 144 5.2 odd 4
875.2.s.c.293.17 144 5.4 even 2
875.2.s.c.293.18 144 35.34 odd 2
875.2.s.c.657.17 144 175.48 even 20
875.2.s.c.657.18 144 25.23 odd 20