Properties

Label 504.2.be.a.139.13
Level $504$
Weight $2$
Character 504.139
Analytic conductor $4.024$
Analytic rank $0$
Dimension $184$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(139,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.be (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(184\)
Relative dimension: \(92\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 139.13
Character \(\chi\) \(=\) 504.139
Dual form 504.2.be.a.475.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28821 + 0.583540i) q^{2} +(-0.476817 + 1.66513i) q^{3} +(1.31896 - 1.50344i) q^{4} +(-0.852648 + 1.47683i) q^{5} +(-0.357427 - 2.42327i) q^{6} +(-1.56588 + 2.13261i) q^{7} +(-0.821782 + 2.70641i) q^{8} +(-2.54529 - 1.58792i) q^{9} +O(q^{10})\) \(q+(-1.28821 + 0.583540i) q^{2} +(-0.476817 + 1.66513i) q^{3} +(1.31896 - 1.50344i) q^{4} +(-0.852648 + 1.47683i) q^{5} +(-0.357427 - 2.42327i) q^{6} +(-1.56588 + 2.13261i) q^{7} +(-0.821782 + 2.70641i) q^{8} +(-2.54529 - 1.58792i) q^{9} +(0.236600 - 2.40002i) q^{10} +(-1.16612 - 2.01978i) q^{11} +(1.87452 + 2.91311i) q^{12} +(0.0781912 - 0.135431i) q^{13} +(0.772723 - 3.66100i) q^{14} +(-2.05255 - 2.12394i) q^{15} +(-0.520672 - 3.96597i) q^{16} +7.04930i q^{17} +(4.20548 + 0.560296i) q^{18} -6.97995i q^{19} +(1.09571 + 3.22979i) q^{20} +(-2.80442 - 3.62426i) q^{21} +(2.68082 + 1.92142i) q^{22} +(-3.56862 - 2.06034i) q^{23} +(-4.11468 - 2.65884i) q^{24} +(1.04598 + 1.81170i) q^{25} +(-0.0216971 + 0.220091i) q^{26} +(3.85773 - 3.48108i) q^{27} +(1.14091 + 5.16704i) q^{28} +(-4.95266 + 2.85942i) q^{29} +(3.88352 + 1.53834i) q^{30} +(-0.0466015 + 0.0807162i) q^{31} +(2.98503 + 4.80516i) q^{32} +(3.91921 - 0.978671i) q^{33} +(-4.11354 - 9.08097i) q^{34} +(-1.81435 - 4.13090i) q^{35} +(-5.74449 + 1.73229i) q^{36} -7.90460i q^{37} +(4.07308 + 8.99164i) q^{38} +(0.188227 + 0.194774i) q^{39} +(-3.29622 - 3.52125i) q^{40} +(1.78316 + 1.02951i) q^{41} +(5.72757 + 3.03231i) q^{42} +(-0.643325 - 1.11427i) q^{43} +(-4.57468 - 0.910820i) q^{44} +(4.51532 - 2.40502i) q^{45} +(5.79942 + 0.571721i) q^{46} +(-1.39077 - 2.40888i) q^{47} +(6.85210 + 1.02406i) q^{48} +(-2.09602 - 6.67882i) q^{49} +(-2.40464 - 1.72347i) q^{50} +(-11.7380 - 3.36123i) q^{51} +(-0.100481 - 0.296184i) q^{52} -8.51500i q^{53} +(-2.93821 + 6.73550i) q^{54} +3.97715 q^{55} +(-4.48490 - 5.99046i) q^{56} +(11.6225 + 3.32816i) q^{57} +(4.71147 - 6.57360i) q^{58} +(-0.873762 - 0.504467i) q^{59} +(-5.90046 + 0.284485i) q^{60} +(2.32246 + 4.02262i) q^{61} +(0.0129314 - 0.131173i) q^{62} +(7.37204 - 2.94161i) q^{63} +(-6.64935 - 4.44817i) q^{64} +(0.133339 + 0.230950i) q^{65} +(-4.47767 + 3.54775i) q^{66} +(-2.78982 + 4.83211i) q^{67} +(10.5982 + 9.29777i) q^{68} +(5.13231 - 4.95979i) q^{69} +(4.74781 + 4.26272i) q^{70} -12.3754i q^{71} +(6.38925 - 5.58368i) q^{72} -0.0440841i q^{73} +(4.61265 + 10.1828i) q^{74} +(-3.51545 + 0.877847i) q^{75} +(-10.4940 - 9.20630i) q^{76} +(6.13340 + 0.675860i) q^{77} +(-0.356134 - 0.141072i) q^{78} +(-10.4431 + 6.02933i) q^{79} +(6.30101 + 2.61263i) q^{80} +(3.95701 + 8.08344i) q^{81} +(-2.89784 - 0.285676i) q^{82} +(-7.66324 + 4.42437i) q^{83} +(-9.14778 - 0.563978i) q^{84} +(-10.4106 - 6.01057i) q^{85} +(1.47896 + 1.06001i) q^{86} +(-2.39978 - 9.61022i) q^{87} +(6.42465 - 1.49618i) q^{88} +10.5874i q^{89} +(-4.41325 + 5.73304i) q^{90} +(0.166383 + 0.378820i) q^{91} +(-7.80448 + 2.64769i) q^{92} +(-0.112182 - 0.116084i) q^{93} +(3.19728 + 2.29157i) q^{94} +(10.3082 + 5.95144i) q^{95} +(-9.42452 + 2.67927i) q^{96} +(-14.8073 + 8.54901i) q^{97} +(6.59747 + 7.38060i) q^{98} +(-0.239136 + 6.99262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28821 + 0.583540i −0.910901 + 0.412625i
\(3\) −0.476817 + 1.66513i −0.275290 + 0.961361i
\(4\) 1.31896 1.50344i 0.659482 0.751721i
\(5\) −0.852648 + 1.47683i −0.381316 + 0.660458i −0.991251 0.131993i \(-0.957862\pi\)
0.609935 + 0.792451i \(0.291196\pi\)
\(6\) −0.357427 2.42327i −0.145919 0.989297i
\(7\) −1.56588 + 2.13261i −0.591848 + 0.806050i
\(8\) −0.821782 + 2.70641i −0.290544 + 0.956862i
\(9\) −2.54529 1.58792i −0.848430 0.529307i
\(10\) 0.236600 2.40002i 0.0748195 0.758952i
\(11\) −1.16612 2.01978i −0.351598 0.608986i 0.634932 0.772568i \(-0.281028\pi\)
−0.986530 + 0.163583i \(0.947695\pi\)
\(12\) 1.87452 + 2.91311i 0.541126 + 0.840942i
\(13\) 0.0781912 0.135431i 0.0216863 0.0375618i −0.854979 0.518663i \(-0.826430\pi\)
0.876665 + 0.481102i \(0.159763\pi\)
\(14\) 0.772723 3.66100i 0.206519 0.978443i
\(15\) −2.05255 2.12394i −0.529966 0.548400i
\(16\) −0.520672 3.96597i −0.130168 0.991492i
\(17\) 7.04930i 1.70971i 0.518870 + 0.854853i \(0.326353\pi\)
−0.518870 + 0.854853i \(0.673647\pi\)
\(18\) 4.20548 + 0.560296i 0.991241 + 0.132063i
\(19\) 6.97995i 1.60131i −0.599125 0.800656i \(-0.704485\pi\)
0.599125 0.800656i \(-0.295515\pi\)
\(20\) 1.09571 + 3.22979i 0.245009 + 0.722203i
\(21\) −2.80442 3.62426i −0.611975 0.790877i
\(22\) 2.68082 + 1.92142i 0.571554 + 0.409648i
\(23\) −3.56862 2.06034i −0.744108 0.429611i 0.0794529 0.996839i \(-0.474683\pi\)
−0.823561 + 0.567228i \(0.808016\pi\)
\(24\) −4.11468 2.65884i −0.839906 0.542733i
\(25\) 1.04598 + 1.81170i 0.209197 + 0.362340i
\(26\) −0.0216971 + 0.220091i −0.00425516 + 0.0431634i
\(27\) 3.85773 3.48108i 0.742420 0.669935i
\(28\) 1.14091 + 5.16704i 0.215611 + 0.976479i
\(29\) −4.95266 + 2.85942i −0.919685 + 0.530981i −0.883535 0.468366i \(-0.844843\pi\)
−0.0361507 + 0.999346i \(0.511510\pi\)
\(30\) 3.88352 + 1.53834i 0.709030 + 0.280861i
\(31\) −0.0466015 + 0.0807162i −0.00836988 + 0.0144971i −0.870180 0.492734i \(-0.835998\pi\)
0.861810 + 0.507231i \(0.169331\pi\)
\(32\) 2.98503 + 4.80516i 0.527684 + 0.849441i
\(33\) 3.91921 0.978671i 0.682247 0.170365i
\(34\) −4.11354 9.08097i −0.705467 1.55737i
\(35\) −1.81435 4.13090i −0.306681 0.698250i
\(36\) −5.74449 + 1.73229i −0.957415 + 0.288714i
\(37\) 7.90460i 1.29951i −0.760145 0.649754i \(-0.774872\pi\)
0.760145 0.649754i \(-0.225128\pi\)
\(38\) 4.07308 + 8.99164i 0.660741 + 1.45864i
\(39\) 0.188227 + 0.194774i 0.0301404 + 0.0311888i
\(40\) −3.29622 3.52125i −0.521178 0.556758i
\(41\) 1.78316 + 1.02951i 0.278482 + 0.160782i 0.632736 0.774367i \(-0.281932\pi\)
−0.354254 + 0.935149i \(0.615265\pi\)
\(42\) 5.72757 + 3.03231i 0.883784 + 0.467895i
\(43\) −0.643325 1.11427i −0.0981061 0.169925i 0.812795 0.582550i \(-0.197945\pi\)
−0.910901 + 0.412626i \(0.864612\pi\)
\(44\) −4.57468 0.910820i −0.689660 0.137311i
\(45\) 4.51532 2.40502i 0.673105 0.358519i
\(46\) 5.79942 + 0.571721i 0.855077 + 0.0842957i
\(47\) −1.39077 2.40888i −0.202864 0.351372i 0.746586 0.665289i \(-0.231692\pi\)
−0.949450 + 0.313918i \(0.898358\pi\)
\(48\) 6.85210 + 1.02406i 0.989016 + 0.147810i
\(49\) −2.09602 6.67882i −0.299432 0.954118i
\(50\) −2.40464 1.72347i −0.340068 0.243736i
\(51\) −11.7380 3.36123i −1.64364 0.470666i
\(52\) −0.100481 0.296184i −0.0139343 0.0410734i
\(53\) 8.51500i 1.16963i −0.811168 0.584813i \(-0.801168\pi\)
0.811168 0.584813i \(-0.198832\pi\)
\(54\) −2.93821 + 6.73550i −0.399840 + 0.916585i
\(55\) 3.97715 0.536279
\(56\) −4.48490 5.99046i −0.599320 0.800509i
\(57\) 11.6225 + 3.32816i 1.53944 + 0.440826i
\(58\) 4.71147 6.57360i 0.618647 0.863156i
\(59\) −0.873762 0.504467i −0.113754 0.0656760i 0.442043 0.896994i \(-0.354254\pi\)
−0.555798 + 0.831318i \(0.687587\pi\)
\(60\) −5.90046 + 0.284485i −0.761746 + 0.0367269i
\(61\) 2.32246 + 4.02262i 0.297361 + 0.515044i 0.975531 0.219861i \(-0.0705602\pi\)
−0.678170 + 0.734905i \(0.737227\pi\)
\(62\) 0.0129314 0.131173i 0.00164229 0.0166590i
\(63\) 7.37204 2.94161i 0.928790 0.370608i
\(64\) −6.64935 4.44817i −0.831168 0.556021i
\(65\) 0.133339 + 0.230950i 0.0165387 + 0.0286458i
\(66\) −4.47767 + 3.54775i −0.551163 + 0.436697i
\(67\) −2.78982 + 4.83211i −0.340831 + 0.590337i −0.984587 0.174894i \(-0.944042\pi\)
0.643756 + 0.765231i \(0.277375\pi\)
\(68\) 10.5982 + 9.29777i 1.28522 + 1.12752i
\(69\) 5.13231 4.95979i 0.617857 0.597089i
\(70\) 4.74781 + 4.26272i 0.567471 + 0.509492i
\(71\) 12.3754i 1.46869i −0.678776 0.734346i \(-0.737489\pi\)
0.678776 0.734346i \(-0.262511\pi\)
\(72\) 6.38925 5.58368i 0.752980 0.658043i
\(73\) 0.0440841i 0.00515966i −0.999997 0.00257983i \(-0.999179\pi\)
0.999997 0.00257983i \(-0.000821186\pi\)
\(74\) 4.61265 + 10.1828i 0.536209 + 1.18372i
\(75\) −3.51545 + 0.877847i −0.405929 + 0.101365i
\(76\) −10.4940 9.20630i −1.20374 1.05604i
\(77\) 6.13340 + 0.675860i 0.698965 + 0.0770214i
\(78\) −0.356134 0.141072i −0.0403242 0.0159732i
\(79\) −10.4431 + 6.02933i −1.17494 + 0.678352i −0.954839 0.297125i \(-0.903972\pi\)
−0.220102 + 0.975477i \(0.570639\pi\)
\(80\) 6.30101 + 2.61263i 0.704474 + 0.292101i
\(81\) 3.95701 + 8.08344i 0.439668 + 0.898160i
\(82\) −2.89784 0.285676i −0.320013 0.0315477i
\(83\) −7.66324 + 4.42437i −0.841150 + 0.485638i −0.857655 0.514226i \(-0.828079\pi\)
0.0165050 + 0.999864i \(0.494746\pi\)
\(84\) −9.14778 0.563978i −0.998105 0.0615350i
\(85\) −10.4106 6.01057i −1.12919 0.651938i
\(86\) 1.47896 + 1.06001i 0.159480 + 0.114304i
\(87\) −2.39978 9.61022i −0.257283 1.03032i
\(88\) 6.42465 1.49618i 0.684870 0.159494i
\(89\) 10.5874i 1.12226i 0.827728 + 0.561130i \(0.189633\pi\)
−0.827728 + 0.561130i \(0.810367\pi\)
\(90\) −4.41325 + 5.73304i −0.465198 + 0.604316i
\(91\) 0.166383 + 0.378820i 0.0174417 + 0.0397111i
\(92\) −7.80448 + 2.64769i −0.813673 + 0.276041i
\(93\) −0.112182 0.116084i −0.0116328 0.0120374i
\(94\) 3.19728 + 2.29157i 0.329774 + 0.236358i
\(95\) 10.3082 + 5.95144i 1.05760 + 0.610605i
\(96\) −9.42452 + 2.67927i −0.961886 + 0.273452i
\(97\) −14.8073 + 8.54901i −1.50346 + 0.868020i −0.503463 + 0.864017i \(0.667941\pi\)
−0.999992 + 0.00400382i \(0.998726\pi\)
\(98\) 6.59747 + 7.38060i 0.666446 + 0.745554i
\(99\) −0.239136 + 6.99262i −0.0240340 + 0.702785i
\(100\) 4.10340 + 0.816987i 0.410340 + 0.0816987i
\(101\) 0.125401 + 0.217200i 0.0124778 + 0.0216122i 0.872197 0.489155i \(-0.162695\pi\)
−0.859719 + 0.510767i \(0.829361\pi\)
\(102\) 17.0824 2.51961i 1.69141 0.249479i
\(103\) −6.28035 + 10.8779i −0.618821 + 1.07183i 0.370880 + 0.928681i \(0.379056\pi\)
−0.989701 + 0.143148i \(0.954277\pi\)
\(104\) 0.302276 + 0.322912i 0.0296406 + 0.0316642i
\(105\) 7.74359 1.05144i 0.755697 0.102610i
\(106\) 4.96884 + 10.9691i 0.482616 + 1.06541i
\(107\) −7.30166 −0.705878 −0.352939 0.935646i \(-0.614818\pi\)
−0.352939 + 0.935646i \(0.614818\pi\)
\(108\) −0.145403 10.3913i −0.0139914 0.999902i
\(109\) 16.6158i 1.59151i 0.605620 + 0.795754i \(0.292925\pi\)
−0.605620 + 0.795754i \(0.707075\pi\)
\(110\) −5.12340 + 2.32083i −0.488497 + 0.221282i
\(111\) 13.1622 + 3.76905i 1.24930 + 0.357742i
\(112\) 9.27316 + 5.09985i 0.876231 + 0.481891i
\(113\) −1.52197 + 2.63613i −0.143175 + 0.247986i −0.928691 0.370856i \(-0.879064\pi\)
0.785516 + 0.618842i \(0.212398\pi\)
\(114\) −16.9143 + 2.49482i −1.58417 + 0.233662i
\(115\) 6.08555 3.51349i 0.567480 0.327635i
\(116\) −2.23341 + 11.2175i −0.207366 + 1.04152i
\(117\) −0.414073 + 0.220550i −0.0382811 + 0.0203899i
\(118\) 1.41996 + 0.139984i 0.130718 + 0.0128866i
\(119\) −15.0334 11.0384i −1.37811 1.01189i
\(120\) 7.43502 3.80963i 0.678721 0.347770i
\(121\) 2.78033 4.81568i 0.252758 0.437789i
\(122\) −5.33918 3.82673i −0.483386 0.346456i
\(123\) −2.56450 + 2.47830i −0.231233 + 0.223460i
\(124\) 0.0598864 + 0.176524i 0.00537796 + 0.0158524i
\(125\) −12.0939 −1.08171
\(126\) −7.78018 + 8.09128i −0.693114 + 0.720828i
\(127\) 1.67707i 0.148816i −0.997228 0.0744080i \(-0.976293\pi\)
0.997228 0.0744080i \(-0.0237067\pi\)
\(128\) 11.1614 + 1.85001i 0.986540 + 0.163519i
\(129\) 2.16215 0.539914i 0.190367 0.0475367i
\(130\) −0.306537 0.219703i −0.0268851 0.0192692i
\(131\) −9.30712 5.37347i −0.813167 0.469482i 0.0348874 0.999391i \(-0.488893\pi\)
−0.848054 + 0.529909i \(0.822226\pi\)
\(132\) 3.69792 7.18313i 0.321862 0.625211i
\(133\) 14.8855 + 10.9298i 1.29074 + 0.947733i
\(134\) 0.774143 7.85274i 0.0668758 0.678373i
\(135\) 1.85168 + 8.66534i 0.159367 + 0.745794i
\(136\) −19.0783 5.79299i −1.63595 0.496745i
\(137\) 3.32113 + 5.75236i 0.283743 + 0.491457i 0.972304 0.233721i \(-0.0750904\pi\)
−0.688560 + 0.725179i \(0.741757\pi\)
\(138\) −3.71725 + 9.38415i −0.316433 + 0.798832i
\(139\) 15.1113 + 8.72452i 1.28172 + 0.740004i 0.977163 0.212489i \(-0.0681570\pi\)
0.304561 + 0.952493i \(0.401490\pi\)
\(140\) −8.60363 2.72074i −0.727139 0.229944i
\(141\) 4.67423 1.16721i 0.393642 0.0982967i
\(142\) 7.22154 + 15.9421i 0.606018 + 1.33783i
\(143\) −0.364721 −0.0304995
\(144\) −4.97238 + 10.9213i −0.414365 + 0.910111i
\(145\) 9.75230i 0.809885i
\(146\) 0.0257248 + 0.0567896i 0.00212900 + 0.00469994i
\(147\) 12.1205 0.305568i 0.999682 0.0252028i
\(148\) −11.8841 10.4259i −0.976867 0.857002i
\(149\) 10.4500 + 6.03333i 0.856100 + 0.494270i 0.862704 0.505709i \(-0.168769\pi\)
−0.00660430 + 0.999978i \(0.502102\pi\)
\(150\) 4.01637 3.18225i 0.327936 0.259830i
\(151\) 14.4824 8.36144i 1.17856 0.680444i 0.222882 0.974845i \(-0.428454\pi\)
0.955682 + 0.294401i \(0.0951202\pi\)
\(152\) 18.8906 + 5.73600i 1.53223 + 0.465251i
\(153\) 11.1937 17.9425i 0.904960 1.45057i
\(154\) −8.29548 + 2.70843i −0.668469 + 0.218251i
\(155\) −0.0794693 0.137645i −0.00638313 0.0110559i
\(156\) 0.541096 0.0260884i 0.0433223 0.00208875i
\(157\) −9.11409 + 15.7861i −0.727384 + 1.25987i 0.230602 + 0.973048i \(0.425931\pi\)
−0.957985 + 0.286817i \(0.907403\pi\)
\(158\) 9.93454 13.8610i 0.790350 1.10272i
\(159\) 14.1785 + 4.06010i 1.12443 + 0.321987i
\(160\) −9.64158 + 0.311275i −0.762234 + 0.0246084i
\(161\) 9.98194 4.38420i 0.786687 0.345524i
\(162\) −9.81447 8.10409i −0.771097 0.636717i
\(163\) −12.4195 −0.972772 −0.486386 0.873744i \(-0.661685\pi\)
−0.486386 + 0.873744i \(0.661685\pi\)
\(164\) 3.89972 1.32299i 0.304517 0.103308i
\(165\) −1.89637 + 6.62246i −0.147633 + 0.515558i
\(166\) 7.29006 10.1713i 0.565818 0.789448i
\(167\) −10.5236 + 18.2274i −0.814341 + 1.41048i 0.0954600 + 0.995433i \(0.469568\pi\)
−0.909800 + 0.415046i \(0.863766\pi\)
\(168\) 12.1134 4.61157i 0.934566 0.355790i
\(169\) 6.48777 + 11.2372i 0.499059 + 0.864396i
\(170\) 16.9184 + 1.66786i 1.29759 + 0.127919i
\(171\) −11.0836 + 17.7660i −0.847586 + 1.35860i
\(172\) −2.52376 0.502482i −0.192435 0.0383139i
\(173\) −11.2627 19.5075i −0.856286 1.48313i −0.875447 0.483315i \(-0.839433\pi\)
0.0191605 0.999816i \(-0.493901\pi\)
\(174\) 8.69936 + 10.9796i 0.659497 + 0.832361i
\(175\) −5.50153 0.606233i −0.415876 0.0458269i
\(176\) −7.40320 + 5.67643i −0.558038 + 0.427877i
\(177\) 1.25663 1.21439i 0.0944538 0.0912789i
\(178\) −6.17815 13.6387i −0.463072 1.02227i
\(179\) −5.77555 −0.431685 −0.215842 0.976428i \(-0.569250\pi\)
−0.215842 + 0.976428i \(0.569250\pi\)
\(180\) 2.33974 9.96066i 0.174394 0.742424i
\(181\) −11.0397 −0.820572 −0.410286 0.911957i \(-0.634571\pi\)
−0.410286 + 0.911957i \(0.634571\pi\)
\(182\) −0.435393 0.390908i −0.0322734 0.0289760i
\(183\) −7.80557 + 1.94914i −0.577004 + 0.144084i
\(184\) 8.50876 7.96500i 0.627274 0.587188i
\(185\) 11.6737 + 6.73984i 0.858270 + 0.495523i
\(186\) 0.212254 + 0.0840780i 0.0155632 + 0.00616490i
\(187\) 14.2380 8.22032i 1.04119 0.601129i
\(188\) −5.45599 1.08629i −0.397919 0.0792256i
\(189\) 1.38303 + 13.6780i 0.100601 + 0.994927i
\(190\) −16.7520 1.65146i −1.21532 0.119809i
\(191\) −6.92192 + 3.99637i −0.500852 + 0.289167i −0.729065 0.684444i \(-0.760045\pi\)
0.228213 + 0.973611i \(0.426712\pi\)
\(192\) 10.5773 8.95104i 0.763349 0.645986i
\(193\) 10.8021 18.7097i 0.777549 1.34676i −0.155801 0.987788i \(-0.549796\pi\)
0.933350 0.358967i \(-0.116871\pi\)
\(194\) 14.0862 19.6536i 1.01133 1.41104i
\(195\) −0.448139 + 0.111905i −0.0320919 + 0.00801371i
\(196\) −12.8058 5.65787i −0.914700 0.404134i
\(197\) 13.1532i 0.937127i −0.883430 0.468564i \(-0.844772\pi\)
0.883430 0.468564i \(-0.155228\pi\)
\(198\) −3.77242 9.14751i −0.268094 0.650085i
\(199\) −15.2510 −1.08111 −0.540557 0.841307i \(-0.681787\pi\)
−0.540557 + 0.841307i \(0.681787\pi\)
\(200\) −5.76278 + 1.34204i −0.407490 + 0.0948969i
\(201\) −6.71584 6.94944i −0.473699 0.490176i
\(202\) −0.288287 0.206623i −0.0202838 0.0145380i
\(203\) 1.65726 15.0396i 0.116317 1.05557i
\(204\) −20.5354 + 13.2140i −1.43776 + 0.925166i
\(205\) −3.04081 + 1.75561i −0.212379 + 0.122617i
\(206\) 1.74272 17.6778i 0.121421 1.23167i
\(207\) 5.81151 + 10.9109i 0.403928 + 0.758357i
\(208\) −0.577827 0.239588i −0.0400651 0.0166125i
\(209\) −14.0980 + 8.13946i −0.975176 + 0.563018i
\(210\) −9.36180 + 5.87316i −0.646026 + 0.405286i
\(211\) −1.82227 + 3.15626i −0.125450 + 0.217286i −0.921909 0.387407i \(-0.873371\pi\)
0.796459 + 0.604693i \(0.206704\pi\)
\(212\) −12.8018 11.2310i −0.879231 0.771346i
\(213\) 20.6066 + 5.90081i 1.41194 + 0.404317i
\(214\) 9.40606 4.26081i 0.642985 0.291263i
\(215\) 2.19412 0.149638
\(216\) 6.25104 + 13.3013i 0.425329 + 0.905039i
\(217\) −0.0991634 0.225775i −0.00673165 0.0153266i
\(218\) −9.69599 21.4047i −0.656696 1.44971i
\(219\) 0.0734056 + 0.0210201i 0.00496029 + 0.00142040i
\(220\) 5.24572 5.97942i 0.353666 0.403132i
\(221\) 0.954694 + 0.551193i 0.0642197 + 0.0370772i
\(222\) −19.1550 + 2.82532i −1.28560 + 0.189623i
\(223\) 7.00685 + 12.1362i 0.469213 + 0.812701i 0.999381 0.0351919i \(-0.0112042\pi\)
−0.530167 + 0.847893i \(0.677871\pi\)
\(224\) −14.9217 1.15841i −0.997000 0.0773998i
\(225\) 0.214500 6.27224i 0.0143000 0.418149i
\(226\) 0.422329 4.28401i 0.0280929 0.284968i
\(227\) 7.37007 4.25511i 0.489169 0.282422i −0.235061 0.971981i \(-0.575529\pi\)
0.724230 + 0.689559i \(0.242196\pi\)
\(228\) 20.3334 13.0840i 1.34661 0.866511i
\(229\) 7.85630 13.6075i 0.519159 0.899209i −0.480593 0.876944i \(-0.659579\pi\)
0.999752 0.0222657i \(-0.00708798\pi\)
\(230\) −5.78919 + 8.07727i −0.381728 + 0.532599i
\(231\) −4.04990 + 9.89062i −0.266464 + 0.650755i
\(232\) −3.66876 15.7538i −0.240866 1.03428i
\(233\) −24.2284 −1.58726 −0.793629 0.608402i \(-0.791811\pi\)
−0.793629 + 0.608402i \(0.791811\pi\)
\(234\) 0.404713 0.525743i 0.0264569 0.0343689i
\(235\) 4.74334 0.309422
\(236\) −1.91090 + 0.648277i −0.124389 + 0.0421993i
\(237\) −5.06014 20.2640i −0.328691 1.31629i
\(238\) 25.8075 + 5.44715i 1.67285 + 0.353087i
\(239\) 8.62438 + 4.97929i 0.557864 + 0.322083i 0.752288 0.658834i \(-0.228950\pi\)
−0.194423 + 0.980918i \(0.562284\pi\)
\(240\) −7.35478 + 9.24622i −0.474749 + 0.596841i
\(241\) −11.7613 + 6.79039i −0.757612 + 0.437408i −0.828438 0.560081i \(-0.810770\pi\)
0.0708256 + 0.997489i \(0.477437\pi\)
\(242\) −0.771511 + 7.82604i −0.0495946 + 0.503077i
\(243\) −15.3467 + 2.73460i −0.984493 + 0.175425i
\(244\) 9.11102 + 1.81401i 0.583273 + 0.116130i
\(245\) 11.6506 + 2.59921i 0.744333 + 0.166058i
\(246\) 1.85743 4.68905i 0.118425 0.298963i
\(247\) −0.945303 0.545771i −0.0601482 0.0347266i
\(248\) −0.180155 0.192454i −0.0114399 0.0122208i
\(249\) −3.71318 14.8699i −0.235313 0.942340i
\(250\) 15.5795 7.05727i 0.985332 0.446341i
\(251\) 22.8277i 1.44087i −0.693522 0.720436i \(-0.743942\pi\)
0.693522 0.720436i \(-0.256058\pi\)
\(252\) 5.30091 14.9633i 0.333926 0.942599i
\(253\) 9.61042i 0.604202i
\(254\) 0.978637 + 2.16042i 0.0614051 + 0.135557i
\(255\) 14.9723 14.4690i 0.937602 0.906086i
\(256\) −15.4578 + 4.12994i −0.966113 + 0.258121i
\(257\) 18.5995 + 10.7384i 1.16021 + 0.669846i 0.951354 0.308101i \(-0.0996934\pi\)
0.208854 + 0.977947i \(0.433027\pi\)
\(258\) −2.47024 + 1.95722i −0.153790 + 0.121851i
\(259\) 16.8574 + 12.3777i 1.04747 + 0.769111i
\(260\) 0.523089 + 0.104147i 0.0324406 + 0.00645893i
\(261\) 17.1465 + 0.586380i 1.06134 + 0.0362960i
\(262\) 15.1251 + 1.49108i 0.934435 + 0.0921190i
\(263\) 14.9826 8.65021i 0.923867 0.533395i 0.0390002 0.999239i \(-0.487583\pi\)
0.884867 + 0.465844i \(0.154249\pi\)
\(264\) −0.572049 + 11.4113i −0.0352072 + 0.702314i
\(265\) 12.5752 + 7.26029i 0.772488 + 0.445996i
\(266\) −25.5536 5.39357i −1.56679 0.330701i
\(267\) −17.6293 5.04824i −1.07890 0.308947i
\(268\) 3.58513 + 10.5677i 0.218996 + 0.645526i
\(269\) 7.73853 0.471826 0.235913 0.971774i \(-0.424192\pi\)
0.235913 + 0.971774i \(0.424192\pi\)
\(270\) −7.44192 10.0822i −0.452901 0.613585i
\(271\) 7.52766 0.457273 0.228637 0.973512i \(-0.426573\pi\)
0.228637 + 0.973512i \(0.426573\pi\)
\(272\) 27.9573 3.67037i 1.69516 0.222549i
\(273\) −0.710118 + 0.0964209i −0.0429783 + 0.00583566i
\(274\) −7.63504 5.47223i −0.461249 0.330590i
\(275\) 2.43948 4.22531i 0.147106 0.254796i
\(276\) −0.687432 14.2579i −0.0413785 0.858225i
\(277\) −12.2577 + 7.07701i −0.736496 + 0.425216i −0.820794 0.571224i \(-0.806469\pi\)
0.0842977 + 0.996441i \(0.473135\pi\)
\(278\) −24.5576 2.42095i −1.47287 0.145199i
\(279\) 0.246785 0.131447i 0.0147747 0.00786950i
\(280\) 12.6709 1.51568i 0.757233 0.0905791i
\(281\) −2.71235 4.69792i −0.161805 0.280255i 0.773711 0.633539i \(-0.218398\pi\)
−0.935516 + 0.353284i \(0.885065\pi\)
\(282\) −5.34028 + 4.23121i −0.318009 + 0.251965i
\(283\) −1.40185 0.809356i −0.0833311 0.0481112i 0.457755 0.889078i \(-0.348654\pi\)
−0.541087 + 0.840967i \(0.681987\pi\)
\(284\) −18.6057 16.3227i −1.10405 0.968575i
\(285\) −14.8250 + 14.3267i −0.878159 + 0.848641i
\(286\) 0.469836 0.212829i 0.0277820 0.0125848i
\(287\) −4.98775 + 2.19069i −0.294417 + 0.129312i
\(288\) 0.0324396 16.9705i 0.00191152 0.999998i
\(289\) −32.6926 −1.92309
\(290\) 5.69085 + 12.5630i 0.334178 + 0.737725i
\(291\) −7.17480 28.7324i −0.420594 1.68432i
\(292\) −0.0662779 0.0581453i −0.00387862 0.00340270i
\(293\) 3.86639 6.69678i 0.225877 0.391230i −0.730705 0.682693i \(-0.760809\pi\)
0.956582 + 0.291463i \(0.0941419\pi\)
\(294\) −15.4354 + 7.46643i −0.900212 + 0.435451i
\(295\) 1.49002 0.860265i 0.0867525 0.0500866i
\(296\) 21.3931 + 6.49586i 1.24345 + 0.377564i
\(297\) −11.5296 3.73239i −0.669014 0.216575i
\(298\) −16.9825 1.67418i −0.983770 0.0969826i
\(299\) −0.558069 + 0.322201i −0.0322739 + 0.0186334i
\(300\) −3.31696 + 6.44312i −0.191505 + 0.371994i
\(301\) 3.38367 + 0.372859i 0.195032 + 0.0214912i
\(302\) −13.7772 + 19.2223i −0.792787 + 1.10612i
\(303\) −0.421459 + 0.105243i −0.0242122 + 0.00604606i
\(304\) −27.6823 + 3.63427i −1.58769 + 0.208440i
\(305\) −7.92097 −0.453553
\(306\) −3.94970 + 29.6457i −0.225789 + 1.69473i
\(307\) 19.2532i 1.09884i 0.835547 + 0.549419i \(0.185151\pi\)
−0.835547 + 0.549419i \(0.814849\pi\)
\(308\) 9.10584 8.32977i 0.518853 0.474632i
\(309\) −15.1185 15.6443i −0.860059 0.889975i
\(310\) 0.182694 + 0.130942i 0.0103763 + 0.00743700i
\(311\) −9.34520 + 16.1864i −0.529918 + 0.917844i 0.469473 + 0.882947i \(0.344444\pi\)
−0.999391 + 0.0348976i \(0.988889\pi\)
\(312\) −0.681821 + 0.349358i −0.0386005 + 0.0197785i
\(313\) −6.13100 + 3.53974i −0.346545 + 0.200078i −0.663162 0.748476i \(-0.730786\pi\)
0.316618 + 0.948553i \(0.397453\pi\)
\(314\) 2.52906 25.6542i 0.142723 1.44775i
\(315\) −1.94150 + 13.3954i −0.109391 + 0.754745i
\(316\) −4.70932 + 23.6530i −0.264920 + 1.33059i
\(317\) −6.89036 + 3.97815i −0.387001 + 0.223435i −0.680860 0.732414i \(-0.738394\pi\)
0.293859 + 0.955849i \(0.405060\pi\)
\(318\) −20.6342 + 3.04349i −1.15711 + 0.170671i
\(319\) 11.5508 + 6.66884i 0.646719 + 0.373383i
\(320\) 12.2387 6.02723i 0.684166 0.336932i
\(321\) 3.48156 12.1582i 0.194321 0.678604i
\(322\) −10.3005 + 11.4726i −0.574022 + 0.639344i
\(323\) 49.2038 2.73777
\(324\) 17.3721 + 4.71263i 0.965119 + 0.261813i
\(325\) 0.327147 0.0181468
\(326\) 15.9989 7.24728i 0.886099 0.401390i
\(327\) −27.6675 7.92271i −1.53001 0.438127i
\(328\) −4.25164 + 3.97993i −0.234757 + 0.219755i
\(329\) 7.31498 + 0.806063i 0.403288 + 0.0444397i
\(330\) −1.42154 9.63772i −0.0782533 0.530539i
\(331\) −0.952118 1.64912i −0.0523332 0.0906437i 0.838672 0.544637i \(-0.183332\pi\)
−0.891005 + 0.453993i \(0.849999\pi\)
\(332\) −3.45575 + 17.3568i −0.189659 + 0.952579i
\(333\) −12.5519 + 20.1195i −0.687839 + 1.10254i
\(334\) 2.92018 29.6216i 0.159785 1.62082i
\(335\) −4.75747 8.24018i −0.259928 0.450209i
\(336\) −12.9135 + 13.0093i −0.704489 + 0.709715i
\(337\) 1.89149 3.27615i 0.103036 0.178463i −0.809898 0.586570i \(-0.800478\pi\)
0.912934 + 0.408107i \(0.133811\pi\)
\(338\) −14.9149 10.6899i −0.811265 0.581455i
\(339\) −3.66378 3.79122i −0.198989 0.205911i
\(340\) −22.7677 + 7.72402i −1.23475 + 0.418894i
\(341\) 0.217372 0.0117713
\(342\) 3.91084 29.3541i 0.211474 1.58729i
\(343\) 17.5254 + 5.98826i 0.946284 + 0.323335i
\(344\) 3.54435 0.825415i 0.191099 0.0445034i
\(345\) 2.94871 + 11.8085i 0.158753 + 0.635748i
\(346\) 25.8921 + 18.5576i 1.39197 + 0.997661i
\(347\) 4.25153 7.36387i 0.228234 0.395313i −0.729051 0.684460i \(-0.760038\pi\)
0.957285 + 0.289147i \(0.0933715\pi\)
\(348\) −17.6136 9.06760i −0.944189 0.486074i
\(349\) −2.15354 3.73004i −0.115276 0.199665i 0.802614 0.596499i \(-0.203442\pi\)
−0.917890 + 0.396834i \(0.870109\pi\)
\(350\) 7.44088 2.42941i 0.397732 0.129857i
\(351\) −0.169806 0.794646i −0.00906360 0.0424151i
\(352\) 6.22445 11.6325i 0.331764 0.620014i
\(353\) 31.4501 18.1577i 1.67392 0.966437i 0.708507 0.705703i \(-0.249369\pi\)
0.965411 0.260734i \(-0.0839644\pi\)
\(354\) −0.910154 + 2.29767i −0.0483742 + 0.122120i
\(355\) 18.2764 + 10.5519i 0.970009 + 0.560035i
\(356\) 15.9175 + 13.9644i 0.843625 + 0.740109i
\(357\) 25.5485 19.7692i 1.35217 1.04630i
\(358\) 7.44011 3.37026i 0.393222 0.178124i
\(359\) 10.4504i 0.551551i 0.961222 + 0.275776i \(0.0889347\pi\)
−0.961222 + 0.275776i \(0.911065\pi\)
\(360\) 2.79837 + 14.1967i 0.147487 + 0.748234i
\(361\) −29.7198 −1.56420
\(362\) 14.2214 6.44208i 0.747460 0.338588i
\(363\) 6.69300 + 6.92581i 0.351292 + 0.363511i
\(364\) 0.788987 + 0.249503i 0.0413542 + 0.0130775i
\(365\) 0.0651047 + 0.0375882i 0.00340774 + 0.00196746i
\(366\) 8.91780 7.06575i 0.466141 0.369333i
\(367\) −7.96003 13.7872i −0.415510 0.719685i 0.579972 0.814637i \(-0.303064\pi\)
−0.995482 + 0.0949517i \(0.969730\pi\)
\(368\) −6.31317 + 15.2258i −0.329097 + 0.793699i
\(369\) −2.90388 5.45191i −0.151170 0.283815i
\(370\) −18.9712 1.87023i −0.986264 0.0972285i
\(371\) 18.1591 + 13.3335i 0.942776 + 0.692240i
\(372\) −0.322490 + 0.0155486i −0.0167203 + 0.000806156i
\(373\) 16.7190 + 9.65271i 0.865676 + 0.499798i 0.865909 0.500202i \(-0.166741\pi\)
−0.000232989 1.00000i \(0.500074\pi\)
\(374\) −13.5446 + 18.8979i −0.700377 + 0.977189i
\(375\) 5.76658 20.1379i 0.297785 1.03992i
\(376\) 7.66234 1.78442i 0.395155 0.0920244i
\(377\) 0.894325i 0.0460601i
\(378\) −9.76328 16.8130i −0.502169 0.864770i
\(379\) 31.8440 1.63572 0.817858 0.575420i \(-0.195161\pi\)
0.817858 + 0.575420i \(0.195161\pi\)
\(380\) 22.5438 7.64804i 1.15647 0.392336i
\(381\) 2.79253 + 0.799656i 0.143066 + 0.0409676i
\(382\) 6.58483 9.18737i 0.336909 0.470067i
\(383\) 16.2991 28.2309i 0.832847 1.44253i −0.0629252 0.998018i \(-0.520043\pi\)
0.895772 0.444514i \(-0.146624\pi\)
\(384\) −8.40246 + 17.7031i −0.428786 + 0.903406i
\(385\) −6.22775 + 8.48170i −0.317396 + 0.432268i
\(386\) −2.99745 + 30.4055i −0.152566 + 1.54760i
\(387\) −0.131926 + 3.85769i −0.00670620 + 0.196098i
\(388\) −6.67737 + 33.5378i −0.338992 + 1.70262i
\(389\) −28.0956 + 16.2210i −1.42450 + 0.822438i −0.996680 0.0814235i \(-0.974053\pi\)
−0.427825 + 0.903862i \(0.640720\pi\)
\(390\) 0.511995 0.405664i 0.0259259 0.0205416i
\(391\) 14.5240 25.1563i 0.734509 1.27221i
\(392\) 19.7981 0.184170i 0.999957 0.00930200i
\(393\) 13.3853 12.9354i 0.675199 0.652503i
\(394\) 7.67542 + 16.9441i 0.386682 + 0.853630i
\(395\) 20.5636i 1.03467i
\(396\) 10.1976 + 9.58254i 0.512448 + 0.481541i
\(397\) 26.2431 1.31710 0.658551 0.752536i \(-0.271170\pi\)
0.658551 + 0.752536i \(0.271170\pi\)
\(398\) 19.6465 8.89956i 0.984789 0.446095i
\(399\) −25.2971 + 19.5747i −1.26644 + 0.979962i
\(400\) 6.64052 5.09164i 0.332026 0.254582i
\(401\) −3.97077 + 6.87757i −0.198291 + 0.343450i −0.947974 0.318347i \(-0.896872\pi\)
0.749684 + 0.661796i \(0.230206\pi\)
\(402\) 12.7067 + 5.03337i 0.633752 + 0.251042i
\(403\) 0.00728765 + 0.0126226i 0.000363024 + 0.000628776i
\(404\) 0.491947 + 0.0979467i 0.0244753 + 0.00487303i
\(405\) −15.3118 1.04850i −0.760849 0.0521004i
\(406\) 6.64129 + 20.3412i 0.329602 + 1.00952i
\(407\) −15.9655 + 9.21770i −0.791382 + 0.456904i
\(408\) 18.7429 29.0056i 0.927913 1.43599i
\(409\) −23.5890 13.6191i −1.16640 0.673422i −0.213572 0.976927i \(-0.568510\pi\)
−0.952830 + 0.303505i \(0.901843\pi\)
\(410\) 2.89273 4.03603i 0.142862 0.199325i
\(411\) −11.1620 + 2.78727i −0.550580 + 0.137486i
\(412\) 8.07071 + 23.7897i 0.397615 + 1.17203i
\(413\) 2.44404 1.07346i 0.120263 0.0528213i
\(414\) −13.8534 10.6642i −0.680855 0.524117i
\(415\) 15.0897i 0.740726i
\(416\) 0.884171 0.0285451i 0.0433501 0.00139954i
\(417\) −21.7328 + 21.0022i −1.06426 + 1.02848i
\(418\) 13.4114 18.7120i 0.655973 0.915235i
\(419\) −28.2258 16.2962i −1.37892 0.796121i −0.386892 0.922125i \(-0.626451\pi\)
−0.992030 + 0.126004i \(0.959785\pi\)
\(420\) 8.63273 13.0288i 0.421234 0.635742i
\(421\) 15.4585 8.92495i 0.753400 0.434975i −0.0735214 0.997294i \(-0.523424\pi\)
0.826921 + 0.562318i \(0.190090\pi\)
\(422\) 0.505658 5.12929i 0.0246151 0.249690i
\(423\) −0.285204 + 8.33974i −0.0138671 + 0.405492i
\(424\) 23.0451 + 6.99748i 1.11917 + 0.339827i
\(425\) −12.7712 + 7.37346i −0.619494 + 0.357665i
\(426\) −29.9890 + 4.42331i −1.45297 + 0.214310i
\(427\) −12.2154 1.34606i −0.591144 0.0651402i
\(428\) −9.63062 + 10.9776i −0.465514 + 0.530623i
\(429\) 0.173905 0.607306i 0.00839622 0.0293210i
\(430\) −2.82648 + 1.28035i −0.136305 + 0.0617442i
\(431\) 27.7446i 1.33641i −0.743976 0.668206i \(-0.767062\pi\)
0.743976 0.668206i \(-0.232938\pi\)
\(432\) −15.8145 13.4871i −0.760874 0.648899i
\(433\) 26.4586i 1.27152i 0.771888 + 0.635759i \(0.219313\pi\)
−0.771888 + 0.635759i \(0.780687\pi\)
\(434\) 0.259492 + 0.232979i 0.0124560 + 0.0111834i
\(435\) 16.2388 + 4.65007i 0.778592 + 0.222954i
\(436\) 24.9809 + 21.9157i 1.19637 + 1.04957i
\(437\) −14.3811 + 24.9088i −0.687941 + 1.19155i
\(438\) −0.106828 + 0.0157569i −0.00510443 + 0.000752892i
\(439\) −1.94216 3.36393i −0.0926944 0.160551i 0.815950 0.578123i \(-0.196215\pi\)
−0.908644 + 0.417572i \(0.862881\pi\)
\(440\) −3.26835 + 10.7638i −0.155813 + 0.513145i
\(441\) −5.27045 + 20.3279i −0.250974 + 0.967994i
\(442\) −1.55149 0.152950i −0.0737968 0.00727507i
\(443\) 3.33597 + 5.77807i 0.158497 + 0.274525i 0.934327 0.356417i \(-0.116002\pi\)
−0.775830 + 0.630942i \(0.782669\pi\)
\(444\) 23.0269 14.8173i 1.09281 0.703198i
\(445\) −15.6357 9.02730i −0.741205 0.427935i
\(446\) −16.1082 11.5452i −0.762747 0.546681i
\(447\) −15.0290 + 14.5238i −0.710848 + 0.686954i
\(448\) 19.8983 7.21514i 0.940106 0.340883i
\(449\) −6.68442 −0.315457 −0.157729 0.987483i \(-0.550417\pi\)
−0.157729 + 0.987483i \(0.550417\pi\)
\(450\) 3.38378 + 8.20512i 0.159513 + 0.386793i
\(451\) 4.80211i 0.226122i
\(452\) 1.95584 + 5.76515i 0.0919951 + 0.271170i
\(453\) 7.01738 + 28.1020i 0.329705 + 1.32035i
\(454\) −7.01116 + 9.78220i −0.329050 + 0.459101i
\(455\) −0.701319 0.0772808i −0.0328783 0.00362298i
\(456\) −18.5586 + 28.7203i −0.869084 + 1.34495i
\(457\) 3.61752 + 6.26573i 0.169221 + 0.293099i 0.938146 0.346240i \(-0.112542\pi\)
−0.768925 + 0.639338i \(0.779208\pi\)
\(458\) −2.18003 + 22.1138i −0.101866 + 1.03331i
\(459\) 24.5392 + 27.1943i 1.14539 + 1.26932i
\(460\) 2.74428 13.7834i 0.127953 0.642656i
\(461\) 13.4965 + 23.3766i 0.628595 + 1.08876i 0.987834 + 0.155513i \(0.0497029\pi\)
−0.359239 + 0.933246i \(0.616964\pi\)
\(462\) −0.554448 15.1045i −0.0257953 0.702723i
\(463\) −7.82602 4.51835i −0.363706 0.209986i 0.306999 0.951710i \(-0.400675\pi\)
−0.670705 + 0.741724i \(0.734008\pi\)
\(464\) 13.9191 + 18.1533i 0.646177 + 0.842744i
\(465\) 0.267088 0.0666950i 0.0123859 0.00309291i
\(466\) 31.2113 14.1383i 1.44583 0.654942i
\(467\) 6.39572i 0.295959i 0.988990 + 0.147979i \(0.0472769\pi\)
−0.988990 + 0.147979i \(0.952723\pi\)
\(468\) −0.214563 + 0.913432i −0.00991819 + 0.0422234i
\(469\) −5.93646 13.5161i −0.274120 0.624116i
\(470\) −6.11041 + 2.76793i −0.281852 + 0.127675i
\(471\) −21.9400 22.7032i −1.01094 1.04611i
\(472\) 2.08334 1.95020i 0.0958934 0.0897653i
\(473\) −1.50039 + 2.59875i −0.0689878 + 0.119490i
\(474\) 18.3433 + 23.1514i 0.842538 + 1.06338i
\(475\) 12.6456 7.30092i 0.580219 0.334989i
\(476\) −36.4240 + 8.04260i −1.66949 + 0.368632i
\(477\) −13.5211 + 21.6731i −0.619091 + 0.992345i
\(478\) −14.0156 1.38169i −0.641059 0.0631972i
\(479\) 9.46833 + 16.3996i 0.432619 + 0.749319i 0.997098 0.0761291i \(-0.0242561\pi\)
−0.564479 + 0.825448i \(0.690923\pi\)
\(480\) 4.07896 16.2029i 0.186178 0.739557i
\(481\) −1.07053 0.618070i −0.0488119 0.0281816i
\(482\) 11.1886 15.6106i 0.509625 0.711045i
\(483\) 2.54070 + 18.7116i 0.115606 + 0.851409i
\(484\) −3.57293 10.5318i −0.162406 0.478717i
\(485\) 29.1572i 1.32396i
\(486\) 18.1740 12.4782i 0.824391 0.566021i
\(487\) 19.0394i 0.862757i 0.902171 + 0.431379i \(0.141973\pi\)
−0.902171 + 0.431379i \(0.858027\pi\)
\(488\) −12.7954 + 2.97982i −0.579222 + 0.134890i
\(489\) 5.92184 20.6801i 0.267795 0.935185i
\(490\) −16.5252 + 3.45029i −0.746533 + 0.155868i
\(491\) −7.97064 + 13.8055i −0.359710 + 0.623036i −0.987912 0.155014i \(-0.950458\pi\)
0.628202 + 0.778050i \(0.283791\pi\)
\(492\) 0.343494 + 7.12435i 0.0154859 + 0.321191i
\(493\) −20.1569 34.9128i −0.907821 1.57239i
\(494\) 1.53623 + 0.151445i 0.0691181 + 0.00681384i
\(495\) −10.1230 6.31541i −0.454996 0.283856i
\(496\) 0.344382 + 0.142793i 0.0154632 + 0.00641161i
\(497\) 26.3919 + 19.3784i 1.18384 + 0.869242i
\(498\) 13.4605 + 16.9887i 0.603180 + 0.761283i
\(499\) −10.7917 + 18.6918i −0.483103 + 0.836759i −0.999812 0.0194021i \(-0.993824\pi\)
0.516709 + 0.856161i \(0.327157\pi\)
\(500\) −15.9514 + 18.1825i −0.713369 + 0.813145i
\(501\) −25.3331 26.2143i −1.13180 1.17117i
\(502\) 13.3209 + 29.4068i 0.594539 + 1.31249i
\(503\) 8.82443 0.393462 0.196731 0.980457i \(-0.436967\pi\)
0.196731 + 0.980457i \(0.436967\pi\)
\(504\) 1.90299 + 22.3691i 0.0847661 + 0.996401i
\(505\) −0.427690 −0.0190320
\(506\) −5.60806 12.3802i −0.249309 0.550368i
\(507\) −21.8048 + 5.44489i −0.968383 + 0.241816i
\(508\) −2.52138 2.21199i −0.111868 0.0981414i
\(509\) 0.491418 0.851161i 0.0217817 0.0377270i −0.854929 0.518745i \(-0.826399\pi\)
0.876711 + 0.481018i \(0.159733\pi\)
\(510\) −10.8442 + 27.3761i −0.480189 + 1.21223i
\(511\) 0.0940141 + 0.0690306i 0.00415894 + 0.00305373i
\(512\) 17.5029 14.3405i 0.773526 0.633765i
\(513\) −24.2978 26.9268i −1.07277 1.18885i
\(514\) −30.2264 2.97980i −1.33323 0.131433i
\(515\) −10.7098 18.5500i −0.471932 0.817410i
\(516\) 2.04007 3.96279i 0.0898090 0.174452i
\(517\) −3.24360 + 5.61808i −0.142653 + 0.247083i
\(518\) −28.9387 6.10806i −1.27149 0.268373i
\(519\) 37.8528 9.45226i 1.66155 0.414908i
\(520\) −0.734622 + 0.171080i −0.0322153 + 0.00750235i
\(521\) 7.98737i 0.349933i 0.984574 + 0.174967i \(0.0559817\pi\)
−0.984574 + 0.174967i \(0.944018\pi\)
\(522\) −22.4304 + 9.25027i −0.981753 + 0.404873i
\(523\) 21.0125i 0.918811i 0.888227 + 0.459405i \(0.151937\pi\)
−0.888227 + 0.459405i \(0.848063\pi\)
\(524\) −20.3544 + 6.90530i −0.889188 + 0.301660i
\(525\) 3.63268 8.87168i 0.158543 0.387192i
\(526\) −14.2530 + 19.8862i −0.621459 + 0.867080i
\(527\) −0.568992 0.328508i −0.0247857 0.0143100i
\(528\) −5.92200 15.0339i −0.257722 0.654266i
\(529\) −3.00998 5.21344i −0.130869 0.226671i
\(530\) −20.4361 2.01465i −0.887689 0.0875107i
\(531\) 1.42293 + 2.67148i 0.0617497 + 0.115932i
\(532\) 36.0657 7.96349i 1.56365 0.345261i
\(533\) 0.278854 0.160997i 0.0120785 0.00697354i
\(534\) 25.6561 3.78421i 1.11025 0.163759i
\(535\) 6.22574 10.7833i 0.269162 0.466203i
\(536\) −10.7851 11.5214i −0.465844 0.497647i
\(537\) 2.75388 9.61702i 0.118839 0.415005i
\(538\) −9.96884 + 4.51574i −0.429787 + 0.194687i
\(539\) −11.0455 + 12.0218i −0.475764 + 0.517816i
\(540\) 15.4701 + 8.64537i 0.665728 + 0.372038i
\(541\) 1.44275i 0.0620286i −0.999519 0.0310143i \(-0.990126\pi\)
0.999519 0.0310143i \(-0.00987375\pi\)
\(542\) −9.69720 + 4.39269i −0.416530 + 0.188682i
\(543\) 5.26390 18.3824i 0.225896 0.788866i
\(544\) −33.8730 + 21.0424i −1.45229 + 0.902185i
\(545\) −24.5387 14.1674i −1.05112 0.606867i
\(546\) 0.858514 0.538592i 0.0367410 0.0230496i
\(547\) −14.8099 25.6514i −0.633224 1.09678i −0.986888 0.161404i \(-0.948398\pi\)
0.353664 0.935372i \(-0.384936\pi\)
\(548\) 13.0288 + 2.59403i 0.556562 + 0.110812i
\(549\) 0.476267 13.9266i 0.0203266 0.594374i
\(550\) −0.676929 + 6.86662i −0.0288643 + 0.292793i
\(551\) 19.9586 + 34.5693i 0.850265 + 1.47270i
\(552\) 9.20561 + 17.9660i 0.391817 + 0.764684i
\(553\) 3.49448 31.7122i 0.148601 1.34854i
\(554\) 11.6608 16.2695i 0.495421 0.691227i
\(555\) −16.7889 + 16.2246i −0.712650 + 0.688695i
\(556\) 33.0481 11.2116i 1.40155 0.475480i
\(557\) 34.7745i 1.47344i 0.676197 + 0.736721i \(0.263627\pi\)
−0.676197 + 0.736721i \(0.736373\pi\)
\(558\) −0.241207 + 0.313340i −0.0102111 + 0.0132647i
\(559\) −0.201209 −0.00851025
\(560\) −15.4383 + 9.34650i −0.652389 + 0.394962i
\(561\) 6.89894 + 27.6277i 0.291274 + 1.16644i
\(562\) 6.23549 + 4.46914i 0.263028 + 0.188519i
\(563\) 28.6370 + 16.5336i 1.20691 + 0.696809i 0.962082 0.272759i \(-0.0879361\pi\)
0.244825 + 0.969567i \(0.421269\pi\)
\(564\) 4.41031 8.56694i 0.185708 0.360733i
\(565\) −2.59541 4.49538i −0.109190 0.189122i
\(566\) 2.27816 + 0.224587i 0.0957582 + 0.00944010i
\(567\) −23.4350 4.21897i −0.984178 0.177180i
\(568\) 33.4930 + 10.1699i 1.40533 + 0.426719i
\(569\) −10.5456 18.2655i −0.442095 0.765731i 0.555750 0.831350i \(-0.312431\pi\)
−0.997845 + 0.0656186i \(0.979098\pi\)
\(570\) 10.7375 27.1068i 0.449746 1.13538i
\(571\) −12.1276 + 21.0056i −0.507523 + 0.879055i 0.492439 + 0.870347i \(0.336105\pi\)
−0.999962 + 0.00870832i \(0.997228\pi\)
\(572\) −0.481053 + 0.548336i −0.0201138 + 0.0229271i
\(573\) −3.35397 13.4314i −0.140114 0.561105i
\(574\) 5.14691 5.73261i 0.214828 0.239275i
\(575\) 8.62034i 0.359493i
\(576\) 9.86119 + 21.8805i 0.410883 + 0.911688i
\(577\) 36.7196i 1.52866i −0.644826 0.764329i \(-0.723070\pi\)
0.644826 0.764329i \(-0.276930\pi\)
\(578\) 42.1149 19.0774i 1.75175 0.793517i
\(579\) 26.0034 + 26.9079i 1.08067 + 1.11825i
\(580\) −14.6620 12.8629i −0.608807 0.534104i
\(581\) 2.56428 23.2707i 0.106384 0.965433i
\(582\) 26.0091 + 32.8265i 1.07811 + 1.36070i
\(583\) −17.1984 + 9.92950i −0.712285 + 0.411238i
\(584\) 0.119310 + 0.0362276i 0.00493708 + 0.00149911i
\(585\) 0.0273438 0.799567i 0.00113053 0.0330580i
\(586\) −1.07288 + 10.8830i −0.0443202 + 0.449575i
\(587\) −32.4043 + 18.7087i −1.33747 + 0.772189i −0.986432 0.164172i \(-0.947505\pi\)
−0.351038 + 0.936361i \(0.614171\pi\)
\(588\) 15.5271 18.6255i 0.640327 0.768103i
\(589\) 0.563395 + 0.325276i 0.0232143 + 0.0134028i
\(590\) −1.41746 + 1.97769i −0.0583560 + 0.0814201i
\(591\) 21.9018 + 6.27167i 0.900918 + 0.257982i
\(592\) −31.3494 + 4.11571i −1.28845 + 0.169154i
\(593\) 13.4184i 0.551026i −0.961297 0.275513i \(-0.911152\pi\)
0.961297 0.275513i \(-0.0888477\pi\)
\(594\) 17.0305 1.91986i 0.698770 0.0787729i
\(595\) 29.1200 12.7899i 1.19380 0.524334i
\(596\) 22.8540 7.75327i 0.936135 0.317586i
\(597\) 7.27194 25.3948i 0.297621 1.03934i
\(598\) 0.530892 0.740717i 0.0217098 0.0302902i
\(599\) −8.15665 4.70925i −0.333272 0.192415i 0.324021 0.946050i \(-0.394965\pi\)
−0.657293 + 0.753635i \(0.728298\pi\)
\(600\) 0.513116 10.2357i 0.0209479 0.417869i
\(601\) 18.4529 10.6538i 0.752710 0.434577i −0.0739624 0.997261i \(-0.523564\pi\)
0.826672 + 0.562684i \(0.190231\pi\)
\(602\) −4.57646 + 1.49419i −0.186522 + 0.0608985i
\(603\) 14.7739 7.86911i 0.601641 0.320455i
\(604\) 6.53087 32.8019i 0.265737 1.33469i
\(605\) 4.74129 + 8.21216i 0.192761 + 0.333872i
\(606\) 0.481514 0.381513i 0.0195602 0.0154979i
\(607\) −16.3125 + 28.2540i −0.662103 + 1.14680i 0.317960 + 0.948104i \(0.397002\pi\)
−0.980062 + 0.198691i \(0.936331\pi\)
\(608\) 33.5398 20.8354i 1.36022 0.844987i
\(609\) 24.2526 + 9.93069i 0.982765 + 0.402412i
\(610\) 10.2039 4.62220i 0.413142 0.187147i
\(611\) −0.434983 −0.0175975
\(612\) −12.2114 40.4946i −0.493617 1.63690i
\(613\) 43.3004i 1.74889i −0.485129 0.874443i \(-0.661227\pi\)
0.485129 0.874443i \(-0.338773\pi\)
\(614\) −11.2350 24.8021i −0.453408 1.00093i
\(615\) −1.47341 5.90044i −0.0594135 0.237929i
\(616\) −6.86947 + 16.0441i −0.276779 + 0.646435i
\(617\) −9.24430 + 16.0116i −0.372162 + 0.644603i −0.989898 0.141783i \(-0.954717\pi\)
0.617736 + 0.786385i \(0.288050\pi\)
\(618\) 28.6048 + 11.3309i 1.15065 + 0.455797i
\(619\) 3.89488 2.24871i 0.156549 0.0903833i −0.419679 0.907672i \(-0.637857\pi\)
0.576228 + 0.817289i \(0.304524\pi\)
\(620\) −0.311758 0.0620711i −0.0125205 0.00249284i
\(621\) −20.9390 + 4.47441i −0.840252 + 0.179552i
\(622\) 2.59319 26.3047i 0.103977 1.05472i
\(623\) −22.5787 16.5786i −0.904597 0.664207i
\(624\) 0.674463 0.847915i 0.0270001 0.0339438i
\(625\) 5.08191 8.80213i 0.203276 0.352085i
\(626\) 5.83243 8.13760i 0.233111 0.325244i
\(627\) −6.83108 27.3559i −0.272807 1.09249i
\(628\) 11.7123 + 34.5237i 0.467371 + 1.37765i
\(629\) 55.7219 2.22178
\(630\) −5.31568 18.3890i −0.211782 0.732635i
\(631\) 7.16821i 0.285362i −0.989769 0.142681i \(-0.954428\pi\)
0.989769 0.142681i \(-0.0455723\pi\)
\(632\) −7.73590 33.2181i −0.307717 1.32135i
\(633\) −4.38668 4.53927i −0.174355 0.180420i
\(634\) 6.55482 9.14549i 0.260325 0.363214i
\(635\) 2.47675 + 1.42995i 0.0982866 + 0.0567458i
\(636\) 24.8051 15.9615i 0.983586 0.632915i
\(637\) −1.06841 0.238358i −0.0423320 0.00944409i
\(638\) −18.7713 1.85053i −0.743164 0.0732631i
\(639\) −19.6512 + 31.4990i −0.777389 + 1.24608i
\(640\) −12.2489 + 14.9061i −0.484181 + 0.589216i
\(641\) −3.94787 6.83792i −0.155932 0.270081i 0.777466 0.628925i \(-0.216505\pi\)
−0.933398 + 0.358843i \(0.883171\pi\)
\(642\) 2.60981 + 17.6939i 0.103001 + 0.698323i
\(643\) −1.91190 1.10384i −0.0753981 0.0435311i 0.461827 0.886970i \(-0.347194\pi\)
−0.537225 + 0.843439i \(0.680527\pi\)
\(644\) 6.57441 20.7899i 0.259068 0.819235i
\(645\) −1.04619 + 3.65348i −0.0411938 + 0.143856i
\(646\) −63.3847 + 28.7124i −2.49384 + 1.12967i
\(647\) 15.2484 0.599477 0.299739 0.954021i \(-0.403101\pi\)
0.299739 + 0.954021i \(0.403101\pi\)
\(648\) −25.1289 + 4.06648i −0.987158 + 0.159746i
\(649\) 2.35307i 0.0923662i
\(650\) −0.421433 + 0.190903i −0.0165300 + 0.00748784i
\(651\) 0.423226 0.0574663i 0.0165875 0.00225228i
\(652\) −16.3809 + 18.6720i −0.641525 + 0.731253i
\(653\) 19.3833 + 11.1909i 0.758526 + 0.437935i 0.828766 0.559595i \(-0.189043\pi\)
−0.0702401 + 0.997530i \(0.522377\pi\)
\(654\) 40.2647 5.93895i 1.57447 0.232231i
\(655\) 15.8714 9.16335i 0.620147 0.358042i
\(656\) 3.15455 7.60798i 0.123164 0.297042i
\(657\) −0.0700021 + 0.112207i −0.00273104 + 0.00437761i
\(658\) −9.89359 + 3.23020i −0.385692 + 0.125926i
\(659\) −0.155016 0.268496i −0.00603858 0.0104591i 0.862990 0.505220i \(-0.168589\pi\)
−0.869029 + 0.494761i \(0.835255\pi\)
\(660\) 7.45524 + 11.5859i 0.290195 + 0.450979i
\(661\) 12.5267 21.6969i 0.487232 0.843911i −0.512660 0.858592i \(-0.671340\pi\)
0.999892 + 0.0146804i \(0.00467310\pi\)
\(662\) 2.18885 + 1.56881i 0.0850722 + 0.0609735i
\(663\) −1.37302 + 1.32687i −0.0533237 + 0.0515313i
\(664\) −5.67667 24.3758i −0.220298 0.945963i
\(665\) −28.8335 + 12.6641i −1.11812 + 0.491092i
\(666\) 4.42892 33.2426i 0.171617 1.28813i
\(667\) 23.5655 0.912461
\(668\) 13.5236 + 39.8629i 0.523244 + 1.54234i
\(669\) −23.5493 + 5.88053i −0.910469 + 0.227354i
\(670\) 10.9371 + 7.83890i 0.422536 + 0.302843i
\(671\) 5.41653 9.38171i 0.209103 0.362177i
\(672\) 9.04384 24.2942i 0.348874 0.937170i
\(673\) 2.40246 + 4.16118i 0.0926080 + 0.160402i 0.908608 0.417650i \(-0.137146\pi\)
−0.816000 + 0.578052i \(0.803813\pi\)
\(674\) −0.524866 + 5.32412i −0.0202171 + 0.205078i
\(675\) 10.3418 + 3.34788i 0.398056 + 0.128860i
\(676\) 25.4515 + 5.06740i 0.978905 + 0.194900i
\(677\) −19.1231 33.1221i −0.734959 1.27299i −0.954741 0.297437i \(-0.903868\pi\)
0.219782 0.975549i \(-0.429465\pi\)
\(678\) 6.93205 + 2.74592i 0.266224 + 0.105456i
\(679\) 4.95484 44.9649i 0.190149 1.72560i
\(680\) 24.8223 23.2360i 0.951893 0.891061i
\(681\) 3.57112 + 14.3010i 0.136846 + 0.548016i
\(682\) −0.280020 + 0.126845i −0.0107225 + 0.00485714i
\(683\) 5.79588 0.221773 0.110887 0.993833i \(-0.464631\pi\)
0.110887 + 0.993833i \(0.464631\pi\)
\(684\) 12.0913 + 40.0963i 0.462322 + 1.53312i
\(685\) −11.3270 −0.432783
\(686\) −26.0708 + 2.51266i −0.995388 + 0.0959338i
\(687\) 18.9122 + 19.5700i 0.721545 + 0.746643i
\(688\) −4.08420 + 3.13158i −0.155709 + 0.119390i
\(689\) −1.15320 0.665798i −0.0439332 0.0253649i
\(690\) −10.6893 13.4911i −0.406934 0.513598i
\(691\) −1.16532 + 0.672797i −0.0443308 + 0.0255944i −0.522002 0.852945i \(-0.674815\pi\)
0.477671 + 0.878539i \(0.341481\pi\)
\(692\) −44.1835 8.79694i −1.67961 0.334410i
\(693\) −14.5381 11.4596i −0.552255 0.435315i
\(694\) −1.17975 + 11.9671i −0.0447827 + 0.454266i
\(695\) −25.7692 + 14.8779i −0.977483 + 0.564350i
\(696\) 27.9813 + 1.40271i 1.06063 + 0.0531696i
\(697\) −7.25730 + 12.5700i −0.274890 + 0.476123i
\(698\) 4.95084 + 3.54840i 0.187392 + 0.134309i
\(699\) 11.5525 40.3434i 0.436957 1.52593i
\(700\) −8.16775 + 7.47163i −0.308712 + 0.282401i
\(701\) 28.9430i 1.09316i 0.837407 + 0.546580i \(0.184071\pi\)
−0.837407 + 0.546580i \(0.815929\pi\)
\(702\) 0.682454 + 0.924581i 0.0257576 + 0.0348961i
\(703\) −55.1737 −2.08092
\(704\) −1.23037 + 18.6173i −0.0463714 + 0.701665i
\(705\) −2.26171 + 7.89826i −0.0851808 + 0.297466i
\(706\) −29.9185 + 41.7433i −1.12600 + 1.57103i
\(707\) −0.659566 0.0726799i −0.0248055 0.00273341i
\(708\) −0.168315 3.49099i −0.00632567 0.131200i
\(709\) 11.9231 6.88378i 0.447780 0.258526i −0.259112 0.965847i \(-0.583430\pi\)
0.706892 + 0.707321i \(0.250097\pi\)
\(710\) −29.7012 2.92802i −1.11467 0.109887i
\(711\) 36.1548 + 1.23643i 1.35591 + 0.0463698i
\(712\) −28.6538 8.70051i −1.07385 0.326066i
\(713\) 0.332606 0.192030i 0.0124562 0.00719158i
\(714\) −21.3756 + 40.3754i −0.799963 + 1.51101i
\(715\) 0.310978 0.538630i 0.0116299 0.0201436i
\(716\) −7.61774 + 8.68320i −0.284688 + 0.324506i
\(717\) −12.4034 + 11.9865i −0.463213 + 0.447643i
\(718\) −6.09823 13.4623i −0.227584 0.502409i
\(719\) 35.9954 1.34240 0.671202 0.741275i \(-0.265778\pi\)
0.671202 + 0.741275i \(0.265778\pi\)
\(720\) −11.8892 16.6554i −0.443086 0.620710i
\(721\) −13.3640 30.4270i −0.497700 1.13316i
\(722\) 38.2853 17.3427i 1.42483 0.645427i
\(723\) −5.69887 22.8218i −0.211943 0.848753i
\(724\) −14.5609 + 16.5975i −0.541152 + 0.616841i
\(725\) −10.3608 5.98181i −0.384791 0.222159i
\(726\) −12.6635 5.01625i −0.469985 0.186171i
\(727\) −13.0085 22.5313i −0.482457 0.835640i 0.517340 0.855780i \(-0.326922\pi\)
−0.999797 + 0.0201397i \(0.993589\pi\)
\(728\) −1.16197 + 0.138994i −0.0430656 + 0.00515145i
\(729\) 2.76413 26.8581i 0.102375 0.994746i
\(730\) −0.105803 0.0104303i −0.00391593 0.000386043i
\(731\) 7.85483 4.53499i 0.290521 0.167733i
\(732\) −7.36484 + 14.3061i −0.272212 + 0.528767i
\(733\) 4.82860 8.36339i 0.178349 0.308909i −0.762966 0.646438i \(-0.776258\pi\)
0.941315 + 0.337529i \(0.109591\pi\)
\(734\) 18.2995 + 13.1158i 0.675449 + 0.484112i
\(735\) −9.88325 + 18.1605i −0.364549 + 0.669858i
\(736\) −0.752166 23.2980i −0.0277252 0.858775i
\(737\) 13.0131 0.479342
\(738\) 6.92221 + 5.32867i 0.254810 + 0.196151i
\(739\) 15.3510 0.564696 0.282348 0.959312i \(-0.408887\pi\)
0.282348 + 0.959312i \(0.408887\pi\)
\(740\) 25.5302 8.66119i 0.938508 0.318392i
\(741\) 1.35951 1.31382i 0.0499430 0.0482642i
\(742\) −31.1734 6.57973i −1.14441 0.241550i
\(743\) 25.3821 + 14.6543i 0.931178 + 0.537616i 0.887184 0.461416i \(-0.152658\pi\)
0.0439942 + 0.999032i \(0.485992\pi\)
\(744\) 0.406361 0.208216i 0.0148979 0.00763355i
\(745\) −17.8204 + 10.2886i −0.652889 + 0.376945i
\(746\) −27.1703 2.67852i −0.994774 0.0980674i
\(747\) 26.5307 + 0.907305i 0.970709 + 0.0331966i
\(748\) 6.42064 32.2483i 0.234762 1.17912i
\(749\) 11.4335 15.5716i 0.417772 0.568973i
\(750\) 4.32269 + 29.3068i 0.157842 + 1.07013i
\(751\) 20.0404 + 11.5703i 0.731283 + 0.422207i 0.818891 0.573948i \(-0.194589\pi\)
−0.0876082 + 0.996155i \(0.527922\pi\)
\(752\) −8.82941 + 6.76998i −0.321976 + 0.246876i
\(753\) 38.0110 + 10.8846i 1.38520 + 0.396658i
\(754\) −0.521874 1.15208i −0.0190055 0.0419562i
\(755\) 28.5174i 1.03786i
\(756\) 22.3882 + 15.9614i 0.814252 + 0.580512i
\(757\) 34.9114i 1.26888i 0.772974 + 0.634438i \(0.218768\pi\)
−0.772974 + 0.634438i \(0.781232\pi\)
\(758\) −41.0217 + 18.5822i −1.48998 + 0.674937i
\(759\) −16.0026 4.58241i −0.580856 0.166331i
\(760\) −24.5782 + 23.0075i −0.891543 + 0.834568i
\(761\) −24.0170 13.8662i −0.870617 0.502651i −0.00306388 0.999995i \(-0.500975\pi\)
−0.867553 + 0.497344i \(0.834309\pi\)
\(762\) −4.06400 + 0.599430i −0.147223 + 0.0217151i
\(763\) −35.4350 26.0184i −1.28283 0.941931i
\(764\) −3.12144 + 15.6778i −0.112930 + 0.567202i
\(765\) 16.9537 + 31.8299i 0.612963 + 1.15081i
\(766\) −4.52282 + 45.8785i −0.163416 + 1.65766i
\(767\) −0.136641 + 0.0788897i −0.00493382 + 0.00284854i
\(768\) 0.493675 27.7084i 0.0178139 0.999841i
\(769\) 22.2777 + 12.8621i 0.803356 + 0.463818i 0.844643 0.535330i \(-0.179813\pi\)
−0.0412873 + 0.999147i \(0.513146\pi\)
\(770\) 3.07324 14.5603i 0.110752 0.524718i
\(771\) −26.7495 + 25.8503i −0.963358 + 0.930976i
\(772\) −13.8814 40.9177i −0.499604 1.47266i
\(773\) 2.62966 0.0945822 0.0472911 0.998881i \(-0.484941\pi\)
0.0472911 + 0.998881i \(0.484941\pi\)
\(774\) −2.08117 5.04650i −0.0748061 0.181393i
\(775\) −0.194978 −0.00700381
\(776\) −10.9688 47.1002i −0.393756 1.69080i
\(777\) −28.6483 + 22.1678i −1.02775 + 0.795266i
\(778\) 26.7274 37.2910i 0.958224 1.33695i
\(779\) 7.18591 12.4464i 0.257462 0.445937i
\(780\) −0.422836 + 0.821350i −0.0151399 + 0.0294090i
\(781\) −24.9956 + 14.4312i −0.894412 + 0.516389i
\(782\) −4.03023 + 40.8818i −0.144121 + 1.46193i
\(783\) −9.15213 + 28.2715i −0.327071 + 1.01034i
\(784\) −25.3967 + 11.7902i −0.907023 + 0.421080i
\(785\) −15.5422 26.9199i −0.554725 0.960813i
\(786\) −9.69476 + 24.4743i −0.345801 + 0.872970i
\(787\) −39.9887 23.0875i −1.42544 0.822980i −0.428687 0.903453i \(-0.641024\pi\)
−0.996757 + 0.0804729i \(0.974357\pi\)
\(788\) −19.7751 17.3486i −0.704458 0.618018i
\(789\) 7.25973 + 29.0725i 0.258453 + 1.03501i
\(790\) 11.9997 + 26.4902i 0.426928 + 0.942478i
\(791\) −3.23860 7.37363i −0.115151 0.262176i
\(792\) −18.7284 6.39361i −0.665485 0.227187i
\(793\) 0.726384 0.0257947
\(794\) −33.8066 + 15.3139i −1.19975 + 0.543469i
\(795\) −18.0854 + 17.4775i −0.641422 + 0.619862i
\(796\) −20.1155 + 22.9290i −0.712975 + 0.812696i
\(797\) −11.9083 + 20.6257i −0.421812 + 0.730600i −0.996117 0.0880418i \(-0.971939\pi\)
0.574305 + 0.818642i \(0.305272\pi\)
\(798\) 21.1654 39.9782i 0.749246 1.41521i
\(799\) 16.9809 9.80394i 0.600742 0.346839i
\(800\) −5.58320 + 10.4341i −0.197396 + 0.368901i
\(801\) 16.8119 26.9479i 0.594020 0.952159i
\(802\) 1.10184 11.1768i 0.0389074 0.394668i
\(803\) −0.0890401 + 0.0514073i −0.00314216 + 0.00181413i
\(804\) −19.3060 + 0.930822i −0.680871 + 0.0328276i
\(805\) −2.03635 + 18.4798i −0.0717720 + 0.651327i
\(806\) −0.0167538 0.0120079i −0.000590127 0.000422960i
\(807\) −3.68986 + 12.8856i −0.129889 + 0.453596i
\(808\) −0.690886 + 0.160895i −0.0243053 + 0.00566026i
\(809\) 35.3210 1.24182 0.620910 0.783882i \(-0.286763\pi\)
0.620910 + 0.783882i \(0.286763\pi\)
\(810\) 20.3366 7.58435i 0.714556 0.266487i
\(811\) 33.1297i 1.16334i 0.813424 + 0.581671i \(0.197601\pi\)
−0.813424 + 0.581671i \(0.802399\pi\)
\(812\) −20.4253 22.3283i −0.716786 0.783568i
\(813\) −3.58932 + 12.5345i −0.125883 + 0.439604i
\(814\) 15.1880 21.1908i 0.532340 0.742739i
\(815\) 10.5895 18.3415i 0.370933 0.642475i
\(816\) −7.21888 + 48.3025i −0.252711 + 1.69093i
\(817\) −7.77756 + 4.49038i −0.272103 + 0.157098i
\(818\) 38.3349 + 3.77915i 1.34035 + 0.132135i
\(819\) 0.178043 1.22841i 0.00622134 0.0429241i
\(820\) −1.37126 + 6.88727i −0.0478863 + 0.240514i
\(821\) 17.5369 10.1250i 0.612043 0.353363i −0.161721 0.986836i \(-0.551705\pi\)
0.773765 + 0.633473i \(0.218371\pi\)
\(822\) 12.7525 10.1040i 0.444794 0.352419i
\(823\) −9.88368 5.70635i −0.344524 0.198911i 0.317747 0.948176i \(-0.397074\pi\)
−0.662271 + 0.749265i \(0.730407\pi\)
\(824\) −24.2790 25.9365i −0.845798 0.903539i
\(825\) 5.87249 + 6.07675i 0.204454 + 0.211565i
\(826\) −2.52203 + 2.80903i −0.0877526 + 0.0977386i
\(827\) −33.7568 −1.17384 −0.586919 0.809645i \(-0.699659\pi\)
−0.586919 + 0.809645i \(0.699659\pi\)
\(828\) 24.0690 + 5.65375i 0.836455 + 0.196482i
\(829\) −20.1138 −0.698583 −0.349291 0.937014i \(-0.613578\pi\)
−0.349291 + 0.937014i \(0.613578\pi\)
\(830\) 8.80545 + 19.4387i 0.305642 + 0.674728i
\(831\) −5.93942 23.7851i −0.206036 0.825097i
\(832\) −1.12234 + 0.552721i −0.0389101 + 0.0191622i
\(833\) 47.0810 14.7755i 1.63126 0.511941i
\(834\) 15.7407 39.7372i 0.545055 1.37599i
\(835\) −17.9458 31.0831i −0.621041 1.07568i
\(836\) −6.35748 + 31.9311i −0.219878 + 1.10436i
\(837\) 0.101204 + 0.473605i 0.00349811 + 0.0163702i
\(838\) 45.8702 + 4.52200i 1.58456 + 0.156210i
\(839\) 2.60470 + 4.51147i 0.0899242 + 0.155753i 0.907479 0.420098i \(-0.138004\pi\)
−0.817555 + 0.575851i \(0.804671\pi\)
\(840\) −3.51792 + 21.8214i −0.121380 + 0.752910i
\(841\) 1.85254 3.20870i 0.0638808 0.110645i
\(842\) −14.7057 + 20.5178i −0.506791 + 0.707091i
\(843\) 9.11593 2.27635i 0.313969 0.0784017i
\(844\) 2.34175 + 6.90267i 0.0806063 + 0.237600i
\(845\) −22.1271 −0.761197
\(846\) −4.49916 10.9097i −0.154684 0.375085i
\(847\) 5.91628 + 13.4701i 0.203286 + 0.462840i
\(848\) −33.7702 + 4.43352i −1.15967 + 0.152248i
\(849\) 2.01610 1.94834i 0.0691925 0.0668667i
\(850\) 12.1493 16.9511i 0.416716 0.581416i
\(851\) −16.2862 + 28.2085i −0.558283 + 0.966975i
\(852\) 36.0509 23.1979i 1.23508 0.794747i
\(853\) 8.76786 + 15.1864i 0.300206 + 0.519972i 0.976182 0.216951i \(-0.0696113\pi\)
−0.675977 + 0.736923i \(0.736278\pi\)
\(854\) 16.5214 5.39416i 0.565352 0.184584i
\(855\) −16.7869 31.5168i −0.574101 1.07785i
\(856\) 6.00037 19.7613i 0.205089 0.675428i
\(857\) 3.62766 2.09443i 0.123918 0.0715444i −0.436759 0.899578i \(-0.643874\pi\)
0.560678 + 0.828034i \(0.310541\pi\)
\(858\) 0.130361 + 0.883817i 0.00445045 + 0.0301730i
\(859\) −27.1230 15.6595i −0.925426 0.534295i −0.0400638 0.999197i \(-0.512756\pi\)
−0.885362 + 0.464902i \(0.846089\pi\)
\(860\) 2.89396 3.29873i 0.0986832 0.112486i
\(861\) −1.26953 9.34979i −0.0432654 0.318640i
\(862\) 16.1901 + 35.7409i 0.551437 + 1.21734i
\(863\) 10.5571i 0.359368i 0.983724 + 0.179684i \(0.0575075\pi\)
−0.983724 + 0.179684i \(0.942492\pi\)
\(864\) 28.2426 + 8.14586i 0.960833 + 0.277128i
\(865\) 38.4124 1.30606
\(866\) −15.4396 34.0842i −0.524660 1.15823i
\(867\) 15.5884 54.4373i 0.529410 1.84879i
\(868\) −0.470232 0.148702i −0.0159607 0.00504728i
\(869\) 24.3558 + 14.0618i 0.826214 + 0.477015i
\(870\) −23.6325 + 3.48574i −0.801216 + 0.118178i
\(871\) 0.436279 + 0.755657i 0.0147827 + 0.0256045i
\(872\) −44.9693 13.6546i −1.52285 0.462403i
\(873\) 51.2641 + 1.75314i 1.73503 + 0.0593349i
\(874\) 3.99059 40.4797i 0.134984 1.36924i
\(875\) 18.9376 25.7915i 0.640209 0.871913i
\(876\) 0.128422 0.0826364i 0.00433897 0.00279202i
\(877\) 36.2637 + 20.9368i 1.22454 + 0.706987i 0.965882 0.258983i \(-0.0833873\pi\)
0.258655 + 0.965970i \(0.416721\pi\)
\(878\) 4.46490 + 3.20011i 0.150683 + 0.107998i
\(879\) 9.30743 + 9.63117i 0.313932 + 0.324851i
\(880\) −2.07079 15.7733i −0.0698064 0.531717i
\(881\) 18.8874i 0.636333i 0.948035 + 0.318166i \(0.103067\pi\)
−0.948035 + 0.318166i \(0.896933\pi\)
\(882\) −5.07267 29.2621i −0.170806 0.985305i
\(883\) −13.2644 −0.446381 −0.223190 0.974775i \(-0.571647\pi\)
−0.223190 + 0.974775i \(0.571647\pi\)
\(884\) 2.08789 0.708323i 0.0702234 0.0238235i
\(885\) 0.721982 + 2.89127i 0.0242691 + 0.0971888i
\(886\) −7.66916 5.49669i −0.257651 0.184665i
\(887\) −15.4053 + 26.6828i −0.517260 + 0.895920i 0.482539 + 0.875874i \(0.339714\pi\)
−0.999799 + 0.0200457i \(0.993619\pi\)
\(888\) −21.0170 + 32.5249i −0.705285 + 1.09146i
\(889\) 3.57653 + 2.62609i 0.119953 + 0.0880764i
\(890\) 25.4099 + 2.50497i 0.851741 + 0.0839668i
\(891\) 11.7124 17.4185i 0.392380 0.583543i
\(892\) 27.4879 + 5.47284i 0.920362 + 0.183244i
\(893\) −16.8139 + 9.70750i −0.562655 + 0.324849i
\(894\) 10.8853 27.4797i 0.364058 0.919060i
\(895\) 4.92451 8.52950i 0.164608 0.285110i
\(896\) −21.4228 + 20.9060i −0.715686 + 0.698422i
\(897\) −0.270409 1.08289i −0.00902869 0.0361565i
\(898\) 8.61092 3.90062i 0.287350 0.130165i
\(899\) 0.533013i 0.0177770i
\(900\) −9.14703 8.59534i −0.304901 0.286511i
\(901\) 60.0248 1.99972
\(902\) 2.80222 + 6.18612i 0.0933037 + 0.205975i
\(903\) −2.23425 + 5.45646i −0.0743512 + 0.181580i
\(904\) −5.88372 6.28540i −0.195690 0.209049i
\(905\) 9.41295 16.3037i 0.312897 0.541953i
\(906\) −25.4384 32.1063i −0.845136 1.06666i
\(907\) −10.5936 18.3487i −0.351756 0.609260i 0.634801 0.772676i \(-0.281082\pi\)
−0.986557 + 0.163416i \(0.947749\pi\)
\(908\) 3.32354 16.6928i 0.110296 0.553970i
\(909\) 0.0257159 0.751965i 0.000852942 0.0249411i
\(910\) 0.948541 0.309693i 0.0314438 0.0102662i
\(911\) 11.6648 6.73469i 0.386473 0.223130i −0.294158 0.955757i \(-0.595039\pi\)
0.680631 + 0.732627i \(0.261706\pi\)
\(912\) 7.14787 47.8274i 0.236690 1.58372i
\(913\) 17.8725 + 10.3187i 0.591493 + 0.341499i
\(914\) −8.31643 5.96060i −0.275083 0.197159i
\(915\) 3.77685 13.1894i 0.124859 0.436029i
\(916\) −10.0959 29.7593i −0.333579 0.983274i
\(917\) 26.0334 11.4342i 0.859697 0.377591i
\(918\) −47.4805 20.7123i −1.56709 0.683608i
\(919\) 6.58757i 0.217304i 0.994080 + 0.108652i \(0.0346534\pi\)
−0.994080 + 0.108652i \(0.965347\pi\)
\(920\) 4.50797 + 19.3573i 0.148623 + 0.638192i
\(921\) −32.0590 9.18025i −1.05638 0.302499i
\(922\) −31.0275 22.2382i −1.02184 0.732377i
\(923\) −1.67602 0.967648i −0.0551667 0.0318505i
\(924\) 9.52829 + 19.1341i 0.313458 + 0.629467i
\(925\) 14.3207 8.26809i 0.470863 0.271853i
\(926\) 12.7182 + 1.25379i 0.417945 + 0.0412021i
\(927\) 33.2585 17.7147i 1.09235 0.581826i
\(928\) −28.5238 15.2629i −0.936340 0.501028i
\(929\) −48.4355 + 27.9643i −1.58912 + 0.917478i −0.595666 + 0.803232i \(0.703112\pi\)
−0.993453 + 0.114246i \(0.963555\pi\)
\(930\) −0.305147 + 0.241774i −0.0100061 + 0.00792807i
\(931\) −46.6179 + 14.6302i −1.52784 + 0.479484i
\(932\) −31.9564 + 36.4260i −1.04677 + 1.19317i
\(933\) −22.4964 23.2789i −0.736499 0.762116i
\(934\) −3.73216 8.23902i −0.122120 0.269589i
\(935\) 28.0361i 0.916880i
\(936\) −0.256622 1.30190i −0.00838794 0.0425538i
\(937\) 8.83248i 0.288545i 0.989538 + 0.144272i \(0.0460841\pi\)
−0.989538 + 0.144272i \(0.953916\pi\)
\(938\) 15.5346 + 13.9474i 0.507222 + 0.455399i
\(939\) −2.97074 11.8967i −0.0969465 0.388234i
\(940\) 6.25629 7.13134i 0.204058 0.232599i
\(941\) −1.40988 + 2.44199i −0.0459609 + 0.0796066i −0.888091 0.459668i \(-0.847968\pi\)
0.842130 + 0.539275i \(0.181302\pi\)
\(942\) 41.5116 + 16.4436i 1.35252 + 0.535760i
\(943\) −4.24227 7.34783i −0.138147 0.239278i
\(944\) −1.54576 + 3.72798i −0.0503101 + 0.121335i
\(945\) −21.3793 9.62000i −0.695468 0.312939i
\(946\) 0.416340 4.22326i 0.0135364 0.137310i
\(947\) −1.25684 2.17690i −0.0408417 0.0707399i 0.844882 0.534953i \(-0.179671\pi\)
−0.885724 + 0.464213i \(0.846337\pi\)
\(948\) −37.1398 19.1198i −1.20625 0.620982i
\(949\) −0.00597036 0.00344699i −0.000193806 0.000111894i
\(950\) −12.0298 + 16.7843i −0.390297 + 0.544555i
\(951\) −3.33868 13.3702i −0.108264 0.433558i
\(952\) 42.2286 31.6154i 1.36864 1.02466i
\(953\) 58.5707 1.89729 0.948646 0.316339i \(-0.102454\pi\)
0.948646 + 0.316339i \(0.102454\pi\)
\(954\) 4.77092 35.8097i 0.154464 1.15938i
\(955\) 13.6300i 0.441056i
\(956\) 18.8613 6.39875i 0.610018 0.206950i
\(957\) −16.6121 + 16.0537i −0.536992 + 0.518942i
\(958\) −21.7670 15.6010i −0.703261 0.504046i
\(959\) −17.4680 1.92486i −0.564072 0.0621571i
\(960\) 4.20047 + 23.2529i 0.135569 + 0.750485i
\(961\) 15.4957 + 26.8393i 0.499860 + 0.865783i
\(962\) 1.73973 + 0.171507i 0.0560912 + 0.00552962i
\(963\) 18.5848 + 11.5945i 0.598888 + 0.373626i
\(964\) −5.30377 + 26.6387i −0.170823 + 0.857975i
\(965\) 18.4207 + 31.9056i 0.592983 + 1.02708i
\(966\) −14.1919 22.6219i −0.456618 0.727848i
\(967\) 50.3787 + 29.0861i 1.62007 + 0.935347i 0.986900 + 0.161334i \(0.0515797\pi\)
0.633169 + 0.774013i \(0.281754\pi\)
\(968\) 10.7484 + 11.4822i 0.345466 + 0.369051i
\(969\) −23.4612 + 81.9305i −0.753683 + 2.63199i
\(970\) 17.0144 + 37.5605i 0.546298 + 1.20600i
\(971\) 5.11576i 0.164172i −0.996625 0.0820862i \(-0.973842\pi\)
0.996625 0.0820862i \(-0.0261583\pi\)
\(972\) −16.1305 + 26.6797i −0.517385 + 0.855753i
\(973\) −42.2685 + 18.5649i −1.35507 + 0.595164i
\(974\) −11.1102 24.5267i −0.355995 0.785887i
\(975\) −0.155989 + 0.544741i −0.00499565 + 0.0174457i
\(976\) 14.7444 11.3053i 0.471955 0.361873i
\(977\) −8.42764 + 14.5971i −0.269624 + 0.467003i −0.968765 0.247981i \(-0.920233\pi\)
0.699141 + 0.714984i \(0.253566\pi\)
\(978\) 4.43907 + 30.0959i 0.141946 + 0.962360i
\(979\) 21.3841 12.3461i 0.683440 0.394584i
\(980\) 19.2745 14.0878i 0.615703 0.450018i
\(981\) 26.3846 42.2921i 0.842396 1.35028i
\(982\) 2.21176 22.4356i 0.0705801 0.715949i
\(983\) 17.7243 + 30.6994i 0.565318 + 0.979160i 0.997020 + 0.0771436i \(0.0245800\pi\)
−0.431702 + 0.902016i \(0.642087\pi\)
\(984\) −4.59983 8.97721i −0.146637 0.286183i
\(985\) 19.4250 + 11.2151i 0.618933 + 0.357341i
\(986\) 46.3393 + 33.2126i 1.47574 + 1.05770i
\(987\) −4.83010 + 11.7960i −0.153744 + 0.375471i
\(988\) −2.06735 + 0.701356i −0.0657713 + 0.0223131i
\(989\) 5.30188i 0.168590i
\(990\) 16.7258 + 2.22838i 0.531582 + 0.0708227i
\(991\) 58.5071i 1.85854i −0.369404 0.929269i \(-0.620438\pi\)
0.369404 0.929269i \(-0.379562\pi\)
\(992\) −0.526961 + 0.0170127i −0.0167310 + 0.000540155i
\(993\) 3.19998 0.799070i 0.101548 0.0253577i
\(994\) −45.3064 9.56277i −1.43703 0.303312i
\(995\) 13.0037 22.5231i 0.412246 0.714031i
\(996\) −27.2535 14.0303i −0.863561 0.444566i
\(997\) 2.99279 + 5.18367i 0.0947827 + 0.164168i 0.909518 0.415665i \(-0.136451\pi\)
−0.814735 + 0.579833i \(0.803118\pi\)
\(998\) 2.99457 30.3763i 0.0947916 0.961545i
\(999\) −27.5166 30.4938i −0.870585 0.964781i
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 504.2.be.a.139.13 184
7.6 odd 2 inner 504.2.be.a.139.14 yes 184
8.3 odd 2 inner 504.2.be.a.139.75 yes 184
9.7 even 3 inner 504.2.be.a.475.76 yes 184
56.27 even 2 inner 504.2.be.a.139.76 yes 184
63.34 odd 6 inner 504.2.be.a.475.75 yes 184
72.43 odd 6 inner 504.2.be.a.475.14 yes 184
504.475 even 6 inner 504.2.be.a.475.13 yes 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.be.a.139.13 184 1.1 even 1 trivial
504.2.be.a.139.14 yes 184 7.6 odd 2 inner
504.2.be.a.139.75 yes 184 8.3 odd 2 inner
504.2.be.a.139.76 yes 184 56.27 even 2 inner
504.2.be.a.475.13 yes 184 504.475 even 6 inner
504.2.be.a.475.14 yes 184 72.43 odd 6 inner
504.2.be.a.475.75 yes 184 63.34 odd 6 inner
504.2.be.a.475.76 yes 184 9.7 even 3 inner