Properties

Label 231.2.y.b.4.1
Level $231$
Weight $2$
Character 231.4
Analytic conductor $1.845$
Analytic rank $0$
Dimension $64$
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] = [231,2,Mod(4,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.y (of order \(15\), 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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 4.1
Character \(\chi\) \(=\) 231.4
Dual form 231.2.y.b.58.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.266544 + 2.53600i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-4.40395 - 0.936088i) q^{4} +(-2.83093 - 1.26041i) q^{5} +(-2.06297 + 1.49883i) q^{6} +(-2.61901 - 0.375200i) q^{7} +(1.97180 - 6.06857i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(-0.266544 + 2.53600i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-4.40395 - 0.936088i) q^{4} +(-2.83093 - 1.26041i) q^{5} +(-2.06297 + 1.49883i) q^{6} +(-2.61901 - 0.375200i) q^{7} +(1.97180 - 6.06857i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(3.95097 - 6.84328i) q^{10} +(2.24626 + 2.44014i) q^{11} +(-2.25117 - 3.89914i) q^{12} +(-2.46901 - 1.79384i) q^{13} +(1.64959 - 6.54180i) q^{14} +(-0.957594 - 2.94717i) q^{15} +(6.63815 + 2.95549i) q^{16} +(0.741373 + 7.05370i) q^{17} +(-2.49424 - 0.530168i) q^{18} +(-6.37455 + 1.35495i) q^{19} +(11.2874 + 8.20079i) q^{20} +(-1.47363 - 2.19736i) q^{21} +(-6.78693 + 5.04612i) q^{22} +(-0.779405 - 1.34997i) q^{23} +(5.82922 - 2.59534i) q^{24} +(3.07987 + 3.42055i) q^{25} +(5.20727 - 5.78326i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(11.1828 + 4.10399i) q^{28} +(1.45432 + 4.47592i) q^{29} +(7.72926 - 1.64291i) q^{30} +(-2.98307 + 1.32815i) q^{31} +(-2.88361 + 4.99456i) q^{32} +(-0.310336 + 3.30207i) q^{33} -18.0858 q^{34} +(6.94133 + 4.36320i) q^{35} +(1.39130 - 4.28198i) q^{36} +(4.65214 - 5.16673i) q^{37} +(-1.73706 - 16.5270i) q^{38} +(-0.319006 - 3.03514i) q^{39} +(-13.2309 + 14.6944i) q^{40} +(-0.724748 + 2.23054i) q^{41} +(5.96530 - 3.15144i) q^{42} +4.80759 q^{43} +(-7.60824 - 12.8490i) q^{44} +(1.54942 - 2.68367i) q^{45} +(3.63127 - 1.61674i) q^{46} +(-1.56680 + 0.333033i) q^{47} +(2.24543 + 6.91072i) q^{48} +(6.71845 + 1.96531i) q^{49} +(-9.49543 + 6.89883i) q^{50} +(-4.74584 + 5.27079i) q^{51} +(9.19419 + 10.2112i) q^{52} +(-4.86180 + 2.16461i) q^{53} +(-1.27498 - 2.20834i) q^{54} +(-3.28343 - 9.73909i) q^{55} +(-7.44109 + 15.1539i) q^{56} +(-5.27234 - 3.83058i) q^{57} +(-11.7386 + 2.49511i) q^{58} +(-5.67070 - 1.20535i) q^{59} +(1.45838 + 13.8756i) q^{60} +(1.00640 + 0.448077i) q^{61} +(-2.57306 - 7.91908i) q^{62} +(0.646906 - 2.56545i) q^{63} +(-0.140386 - 0.101996i) q^{64} +(4.72861 + 8.19020i) q^{65} +(-8.29134 - 1.66716i) q^{66} +(-0.148356 + 0.256960i) q^{67} +(3.33791 - 31.7581i) q^{68} +(0.481699 - 1.48252i) q^{69} +(-12.9152 + 16.4402i) q^{70} +(-6.72342 + 4.88485i) q^{71} +(5.82922 + 2.59534i) q^{72} +(2.97938 + 0.633287i) q^{73} +(11.8628 + 13.1750i) q^{74} +(-0.481124 + 4.57759i) q^{75} +29.3416 q^{76} +(-4.96745 - 7.23356i) q^{77} +7.78215 q^{78} +(-1.64680 + 15.6683i) q^{79} +(-15.0670 - 16.7336i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-5.46348 - 2.43250i) q^{82} +(8.60152 - 6.24937i) q^{83} +(4.43288 + 11.0565i) q^{84} +(6.79178 - 20.9030i) q^{85} +(-1.28143 + 12.1920i) q^{86} +(-2.35313 + 4.07575i) q^{87} +(19.2374 - 8.82015i) q^{88} +(1.06044 + 1.83674i) q^{89} +(6.39280 + 4.64464i) q^{90} +(5.79331 + 5.62446i) q^{91} +(2.16877 + 6.67479i) q^{92} +(-2.98307 - 1.32815i) q^{93} +(-0.426951 - 4.06216i) q^{94} +(19.7537 + 4.19878i) q^{95} +(-5.64120 + 1.19907i) q^{96} +(-9.39758 - 6.82775i) q^{97} +(-6.77478 + 16.5141i) q^{98} +(-2.66157 + 1.97889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.266544 + 2.53600i −0.188475 + 1.79322i 0.336068 + 0.941838i \(0.390903\pi\)
−0.524543 + 0.851384i \(0.675764\pi\)
\(3\) 0.669131 + 0.743145i 0.386323 + 0.429055i
\(4\) −4.40395 0.936088i −2.20197 0.468044i
\(5\) −2.83093 1.26041i −1.26603 0.563673i −0.339753 0.940515i \(-0.610343\pi\)
−0.926278 + 0.376842i \(0.877010\pi\)
\(6\) −2.06297 + 1.49883i −0.842203 + 0.611896i
\(7\) −2.61901 0.375200i −0.989894 0.141812i
\(8\) 1.97180 6.06857i 0.697136 2.14557i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) 3.95097 6.84328i 1.24941 2.16404i
\(11\) 2.24626 + 2.44014i 0.677274 + 0.735731i
\(12\) −2.25117 3.89914i −0.649856 1.12558i
\(13\) −2.46901 1.79384i −0.684780 0.497521i 0.190160 0.981753i \(-0.439099\pi\)
−0.874940 + 0.484232i \(0.839099\pi\)
\(14\) 1.64959 6.54180i 0.440871 1.74837i
\(15\) −0.957594 2.94717i −0.247250 0.760956i
\(16\) 6.63815 + 2.95549i 1.65954 + 0.738874i
\(17\) 0.741373 + 7.05370i 0.179809 + 1.71077i 0.597239 + 0.802063i \(0.296264\pi\)
−0.417430 + 0.908709i \(0.637069\pi\)
\(18\) −2.49424 0.530168i −0.587899 0.124962i
\(19\) −6.37455 + 1.35495i −1.46242 + 0.310848i −0.869308 0.494270i \(-0.835435\pi\)
−0.593115 + 0.805118i \(0.702102\pi\)
\(20\) 11.2874 + 8.20079i 2.52394 + 1.83375i
\(21\) −1.47363 2.19736i −0.321573 0.479504i
\(22\) −6.78693 + 5.04612i −1.44698 + 1.07584i
\(23\) −0.779405 1.34997i −0.162517 0.281488i 0.773254 0.634097i \(-0.218628\pi\)
−0.935771 + 0.352609i \(0.885295\pi\)
\(24\) 5.82922 2.59534i 1.18988 0.529771i
\(25\) 3.07987 + 3.42055i 0.615975 + 0.684109i
\(26\) 5.20727 5.78326i 1.02123 1.13419i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 11.1828 + 4.10399i 2.11335 + 0.775581i
\(29\) 1.45432 + 4.47592i 0.270060 + 0.831158i 0.990484 + 0.137625i \(0.0439469\pi\)
−0.720425 + 0.693533i \(0.756053\pi\)
\(30\) 7.72926 1.64291i 1.41116 0.299952i
\(31\) −2.98307 + 1.32815i −0.535776 + 0.238543i −0.656744 0.754114i \(-0.728067\pi\)
0.120968 + 0.992656i \(0.461400\pi\)
\(32\) −2.88361 + 4.99456i −0.509756 + 0.882923i
\(33\) −0.310336 + 3.30207i −0.0540225 + 0.574817i
\(34\) −18.0858 −3.10168
\(35\) 6.94133 + 4.36320i 1.17330 + 0.737515i
\(36\) 1.39130 4.28198i 0.231883 0.713663i
\(37\) 4.65214 5.16673i 0.764807 0.849405i −0.227426 0.973795i \(-0.573031\pi\)
0.992233 + 0.124391i \(0.0396976\pi\)
\(38\) −1.73706 16.5270i −0.281788 2.68104i
\(39\) −0.319006 3.03514i −0.0510819 0.486012i
\(40\) −13.2309 + 14.6944i −2.09199 + 2.32339i
\(41\) −0.724748 + 2.23054i −0.113187 + 0.348352i −0.991564 0.129614i \(-0.958626\pi\)
0.878378 + 0.477967i \(0.158626\pi\)
\(42\) 5.96530 3.15144i 0.920466 0.486278i
\(43\) 4.80759 0.733150 0.366575 0.930388i \(-0.380530\pi\)
0.366575 + 0.930388i \(0.380530\pi\)
\(44\) −7.60824 12.8490i −1.14699 1.93705i
\(45\) 1.54942 2.68367i 0.230974 0.400058i
\(46\) 3.63127 1.61674i 0.535401 0.238376i
\(47\) −1.56680 + 0.333033i −0.228541 + 0.0485779i −0.320758 0.947161i \(-0.603938\pi\)
0.0922176 + 0.995739i \(0.470604\pi\)
\(48\) 2.24543 + 6.91072i 0.324100 + 0.997476i
\(49\) 6.71845 + 1.96531i 0.959779 + 0.280758i
\(50\) −9.49543 + 6.89883i −1.34286 + 0.975642i
\(51\) −4.74584 + 5.27079i −0.664551 + 0.738058i
\(52\) 9.19419 + 10.2112i 1.27501 + 1.41604i
\(53\) −4.86180 + 2.16461i −0.667820 + 0.297333i −0.712504 0.701669i \(-0.752439\pi\)
0.0446834 + 0.999001i \(0.485772\pi\)
\(54\) −1.27498 2.20834i −0.173503 0.300517i
\(55\) −3.28343 9.73909i −0.442738 1.31322i
\(56\) −7.44109 + 15.1539i −0.994358 + 2.02502i
\(57\) −5.27234 3.83058i −0.698338 0.507372i
\(58\) −11.7386 + 2.49511i −1.54135 + 0.327624i
\(59\) −5.67070 1.20535i −0.738263 0.156923i −0.176593 0.984284i \(-0.556508\pi\)
−0.561670 + 0.827361i \(0.689841\pi\)
\(60\) 1.45838 + 13.8756i 0.188276 + 1.79133i
\(61\) 1.00640 + 0.448077i 0.128856 + 0.0573704i 0.470152 0.882586i \(-0.344199\pi\)
−0.341296 + 0.939956i \(0.610866\pi\)
\(62\) −2.57306 7.91908i −0.326780 1.00572i
\(63\) 0.646906 2.56545i 0.0815025 0.323216i
\(64\) −0.140386 0.101996i −0.0175482 0.0127495i
\(65\) 4.72861 + 8.19020i 0.586512 + 1.01587i
\(66\) −8.29134 1.66716i −1.02059 0.205213i
\(67\) −0.148356 + 0.256960i −0.0181246 + 0.0313927i −0.874945 0.484222i \(-0.839103\pi\)
0.856821 + 0.515614i \(0.172436\pi\)
\(68\) 3.33791 31.7581i 0.404781 3.85124i
\(69\) 0.481699 1.48252i 0.0579897 0.178474i
\(70\) −12.9152 + 16.4402i −1.54367 + 1.96498i
\(71\) −6.72342 + 4.88485i −0.797924 + 0.579725i −0.910304 0.413940i \(-0.864152\pi\)
0.112381 + 0.993665i \(0.464152\pi\)
\(72\) 5.82922 + 2.59534i 0.686980 + 0.305863i
\(73\) 2.97938 + 0.633287i 0.348710 + 0.0741207i 0.378937 0.925422i \(-0.376290\pi\)
−0.0302268 + 0.999543i \(0.509623\pi\)
\(74\) 11.8628 + 13.1750i 1.37902 + 1.53156i
\(75\) −0.481124 + 4.57759i −0.0555554 + 0.528574i
\(76\) 29.3416 3.36571
\(77\) −4.96745 7.23356i −0.566094 0.824341i
\(78\) 7.78215 0.881155
\(79\) −1.64680 + 15.6683i −0.185279 + 1.76282i 0.368005 + 0.929824i \(0.380041\pi\)
−0.553285 + 0.832992i \(0.686626\pi\)
\(80\) −15.0670 16.7336i −1.68454 1.87087i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) −5.46348 2.43250i −0.603340 0.268624i
\(83\) 8.60152 6.24937i 0.944139 0.685957i −0.00527445 0.999986i \(-0.501679\pi\)
0.949413 + 0.314029i \(0.101679\pi\)
\(84\) 4.43288 + 11.0565i 0.483667 + 1.20637i
\(85\) 6.79178 20.9030i 0.736672 2.26724i
\(86\) −1.28143 + 12.1920i −0.138181 + 1.31470i
\(87\) −2.35313 + 4.07575i −0.252282 + 0.436966i
\(88\) 19.2374 8.82015i 2.05071 0.940231i
\(89\) 1.06044 + 1.83674i 0.112407 + 0.194695i 0.916740 0.399484i \(-0.130811\pi\)
−0.804333 + 0.594178i \(0.797477\pi\)
\(90\) 6.39280 + 4.64464i 0.673861 + 0.489588i
\(91\) 5.79331 + 5.62446i 0.607304 + 0.589603i
\(92\) 2.16877 + 6.67479i 0.226110 + 0.695895i
\(93\) −2.98307 1.32815i −0.309330 0.137723i
\(94\) −0.426951 4.06216i −0.0440366 0.418980i
\(95\) 19.7537 + 4.19878i 2.02669 + 0.430786i
\(96\) −5.64120 + 1.19907i −0.575752 + 0.122380i
\(97\) −9.39758 6.82775i −0.954180 0.693252i −0.00238834 0.999997i \(-0.500760\pi\)
−0.951792 + 0.306745i \(0.900760\pi\)
\(98\) −6.77478 + 16.5141i −0.684356 + 1.66818i
\(99\) −2.66157 + 1.97889i −0.267498 + 0.198886i
\(100\) −10.3617 17.9469i −1.03617 1.79469i
\(101\) −0.0192069 + 0.00855147i −0.00191116 + 0.000850904i −0.407692 0.913120i \(-0.633666\pi\)
0.405781 + 0.913970i \(0.367000\pi\)
\(102\) −12.1017 13.4403i −1.19825 1.33079i
\(103\) 6.48177 7.19873i 0.638667 0.709312i −0.333723 0.942671i \(-0.608305\pi\)
0.972391 + 0.233359i \(0.0749717\pi\)
\(104\) −15.7544 + 11.4463i −1.54485 + 1.12240i
\(105\) 1.40217 + 8.07796i 0.136838 + 0.788329i
\(106\) −4.19357 12.9065i −0.407316 1.25359i
\(107\) −13.5545 + 2.88111i −1.31037 + 0.278527i −0.809563 0.587033i \(-0.800296\pi\)
−0.500805 + 0.865560i \(0.666963\pi\)
\(108\) 4.11309 1.83127i 0.395782 0.176214i
\(109\) 5.21036 9.02461i 0.499062 0.864401i −0.500937 0.865484i \(-0.667011\pi\)
0.999999 + 0.00108239i \(0.000344537\pi\)
\(110\) 25.5735 5.73088i 2.43834 0.546418i
\(111\) 6.95252 0.659904
\(112\) −16.2765 10.2311i −1.53798 0.966749i
\(113\) 1.90279 5.85617i 0.178999 0.550902i −0.820794 0.571224i \(-0.806469\pi\)
0.999794 + 0.0203212i \(0.00646889\pi\)
\(114\) 11.1196 12.3496i 1.04145 1.15665i
\(115\) 0.504925 + 4.80404i 0.0470845 + 0.447979i
\(116\) −2.21487 21.0731i −0.205646 1.95659i
\(117\) 2.04209 2.26798i 0.188792 0.209674i
\(118\) 4.56825 14.0596i 0.420541 1.29429i
\(119\) 0.704879 18.7519i 0.0646162 1.71898i
\(120\) −19.7733 −1.80505
\(121\) −0.908596 + 10.9624i −0.0825996 + 0.996583i
\(122\) −1.40457 + 2.43279i −0.127164 + 0.220255i
\(123\) −2.14257 + 0.953933i −0.193189 + 0.0860132i
\(124\) 14.3806 3.05668i 1.29141 0.274498i
\(125\) 0.380356 + 1.17062i 0.0340201 + 0.104703i
\(126\) 6.33354 + 2.32436i 0.564237 + 0.207070i
\(127\) −8.10566 + 5.88911i −0.719261 + 0.522574i −0.886148 0.463402i \(-0.846629\pi\)
0.166887 + 0.985976i \(0.446629\pi\)
\(128\) −7.42197 + 8.24294i −0.656016 + 0.728580i
\(129\) 3.21690 + 3.57273i 0.283233 + 0.314562i
\(130\) −22.0307 + 9.80871i −1.93222 + 0.860281i
\(131\) 1.15372 + 1.99830i 0.100801 + 0.174592i 0.912015 0.410157i \(-0.134526\pi\)
−0.811214 + 0.584749i \(0.801193\pi\)
\(132\) 4.45773 14.2517i 0.387996 1.24045i
\(133\) 17.2034 1.15691i 1.49172 0.100317i
\(134\) −0.612108 0.444722i −0.0528781 0.0384182i
\(135\) 3.03112 0.644285i 0.260877 0.0554512i
\(136\) 44.2677 + 9.40939i 3.79593 + 0.806849i
\(137\) −0.492016 4.68122i −0.0420358 0.399944i −0.995228 0.0975782i \(-0.968890\pi\)
0.953192 0.302365i \(-0.0977763\pi\)
\(138\) 3.63127 + 1.61674i 0.309114 + 0.137626i
\(139\) 4.48081 + 13.7905i 0.380057 + 1.16970i 0.940003 + 0.341166i \(0.110822\pi\)
−0.559946 + 0.828529i \(0.689178\pi\)
\(140\) −26.4849 25.7130i −2.23839 2.17314i
\(141\) −1.29588 0.941515i −0.109133 0.0792898i
\(142\) −10.5959 18.3526i −0.889188 1.54012i
\(143\) −1.16882 10.0542i −0.0977416 0.840772i
\(144\) −3.63318 + 6.29285i −0.302765 + 0.524404i
\(145\) 1.52444 14.5041i 0.126598 1.20450i
\(146\) −2.40015 + 7.38691i −0.198638 + 0.611345i
\(147\) 3.03501 + 6.30783i 0.250324 + 0.520261i
\(148\) −25.3243 + 18.3992i −2.08165 + 1.51240i
\(149\) 15.6261 + 6.95718i 1.28014 + 0.569954i 0.930281 0.366849i \(-0.119563\pi\)
0.349857 + 0.936803i \(0.386230\pi\)
\(150\) −11.4805 2.44026i −0.937380 0.199246i
\(151\) −4.20320 4.66812i −0.342051 0.379886i 0.547435 0.836848i \(-0.315604\pi\)
−0.889486 + 0.456962i \(0.848938\pi\)
\(152\) −4.34671 + 41.3561i −0.352564 + 3.35443i
\(153\) −7.09255 −0.573399
\(154\) 19.6684 10.6694i 1.58492 0.859764i
\(155\) 10.1189 0.812768
\(156\) −1.43627 + 13.6652i −0.114994 + 1.09409i
\(157\) −6.65685 7.39318i −0.531274 0.590040i 0.416439 0.909164i \(-0.363278\pi\)
−0.947713 + 0.319124i \(0.896611\pi\)
\(158\) −39.2957 8.35256i −3.12620 0.664494i
\(159\) −4.86180 2.16461i −0.385566 0.171665i
\(160\) 14.4585 10.5047i 1.14305 0.830471i
\(161\) 1.53476 + 3.82802i 0.120956 + 0.301690i
\(162\) 0.787983 2.42516i 0.0619098 0.190539i
\(163\) 0.361962 3.44384i 0.0283511 0.269742i −0.971159 0.238434i \(-0.923366\pi\)
0.999510 0.0313083i \(-0.00996738\pi\)
\(164\) 5.27974 9.14478i 0.412278 0.714087i
\(165\) 5.04051 8.95679i 0.392403 0.697285i
\(166\) 13.5557 + 23.4792i 1.05213 + 1.82234i
\(167\) 12.9916 + 9.43895i 1.00532 + 0.730408i 0.963222 0.268706i \(-0.0865959\pi\)
0.0420978 + 0.999113i \(0.486596\pi\)
\(168\) −16.2406 + 4.61010i −1.25299 + 0.355677i
\(169\) −1.13908 3.50573i −0.0876215 0.269671i
\(170\) 51.1996 + 22.7955i 3.92683 + 1.74834i
\(171\) −0.681208 6.48126i −0.0520933 0.495635i
\(172\) −21.1724 4.50033i −1.61438 0.343147i
\(173\) −1.93413 + 0.411111i −0.147049 + 0.0312562i −0.280848 0.959752i \(-0.590616\pi\)
0.133799 + 0.991008i \(0.457282\pi\)
\(174\) −9.70887 7.05391i −0.736028 0.534755i
\(175\) −6.78284 10.1140i −0.512735 0.764548i
\(176\) 7.69921 + 22.8369i 0.580350 + 1.72139i
\(177\) −2.89869 5.02069i −0.217879 0.377378i
\(178\) −4.94064 + 2.19971i −0.370316 + 0.164875i
\(179\) 11.4963 + 12.7680i 0.859276 + 0.954322i 0.999358 0.0358173i \(-0.0114035\pi\)
−0.140083 + 0.990140i \(0.544737\pi\)
\(180\) −9.33572 + 10.3684i −0.695843 + 0.772812i
\(181\) −6.37993 + 4.63529i −0.474217 + 0.344539i −0.799082 0.601222i \(-0.794681\pi\)
0.324866 + 0.945760i \(0.394681\pi\)
\(182\) −15.8078 + 13.1927i −1.17175 + 0.977906i
\(183\) 0.340425 + 1.04772i 0.0251650 + 0.0774498i
\(184\) −9.72922 + 2.06801i −0.717248 + 0.152456i
\(185\) −19.6821 + 8.76303i −1.44706 + 0.644271i
\(186\) 4.16331 7.21106i 0.305268 0.528740i
\(187\) −15.5467 + 17.6535i −1.13689 + 1.29095i
\(188\) 7.21184 0.525978
\(189\) 2.33936 1.23587i 0.170164 0.0898966i
\(190\) −15.9133 + 48.9762i −1.15448 + 3.55311i
\(191\) −7.66979 + 8.51817i −0.554967 + 0.616353i −0.953717 0.300707i \(-0.902777\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(192\) −0.0181385 0.172576i −0.00130903 0.0124546i
\(193\) 0.514673 + 4.89679i 0.0370470 + 0.352479i 0.997305 + 0.0733652i \(0.0233739\pi\)
−0.960258 + 0.279113i \(0.909959\pi\)
\(194\) 19.8200 22.0124i 1.42299 1.58040i
\(195\) −2.92244 + 8.99436i −0.209281 + 0.644099i
\(196\) −27.7480 14.9442i −1.98200 1.06744i
\(197\) −2.21650 −0.157919 −0.0789595 0.996878i \(-0.525160\pi\)
−0.0789595 + 0.996878i \(0.525160\pi\)
\(198\) −4.30905 7.27721i −0.306231 0.517169i
\(199\) −4.28549 + 7.42268i −0.303790 + 0.526180i −0.976991 0.213280i \(-0.931585\pi\)
0.673201 + 0.739459i \(0.264919\pi\)
\(200\) 26.8307 11.9458i 1.89722 0.844697i
\(201\) −0.290228 + 0.0616900i −0.0204711 + 0.00435127i
\(202\) −0.0165670 0.0509881i −0.00116565 0.00358751i
\(203\) −2.12951 12.2682i −0.149462 0.861056i
\(204\) 25.8344 18.7698i 1.80877 1.31415i
\(205\) 4.86311 5.40103i 0.339655 0.377225i
\(206\) 16.5283 + 18.3565i 1.15158 + 1.27896i
\(207\) 1.42404 0.634025i 0.0989779 0.0440678i
\(208\) −11.0880 19.2049i −0.768812 1.33162i
\(209\) −17.6252 12.5112i −1.21916 0.865420i
\(210\) −20.8595 + 1.40277i −1.43944 + 0.0968005i
\(211\) −14.9628 10.8711i −1.03008 0.748399i −0.0617573 0.998091i \(-0.519670\pi\)
−0.968325 + 0.249692i \(0.919670\pi\)
\(212\) 23.4374 4.98178i 1.60969 0.342150i
\(213\) −8.12900 1.72787i −0.556990 0.118392i
\(214\) −3.69360 35.1423i −0.252489 2.40228i
\(215\) −13.6099 6.05954i −0.928190 0.413257i
\(216\) 1.97180 + 6.06857i 0.134164 + 0.412914i
\(217\) 8.31102 2.35919i 0.564189 0.160152i
\(218\) 21.4976 + 15.6189i 1.45600 + 1.05785i
\(219\) 1.52297 + 2.63787i 0.102913 + 0.178250i
\(220\) 5.34342 + 45.9640i 0.360253 + 3.09889i
\(221\) 10.8227 18.7455i 0.728016 1.26096i
\(222\) −1.85315 + 17.6316i −0.124376 + 1.18335i
\(223\) −0.585549 + 1.80213i −0.0392112 + 0.120680i −0.968746 0.248055i \(-0.920209\pi\)
0.929535 + 0.368734i \(0.120209\pi\)
\(224\) 9.42618 11.9989i 0.629813 0.801710i
\(225\) −3.72374 + 2.70546i −0.248250 + 0.180364i
\(226\) 14.3441 + 6.38639i 0.954153 + 0.424816i
\(227\) −12.4306 2.64221i −0.825050 0.175370i −0.224008 0.974587i \(-0.571914\pi\)
−0.601042 + 0.799218i \(0.705248\pi\)
\(228\) 19.6333 + 21.8050i 1.30025 + 1.44407i
\(229\) 1.21918 11.5997i 0.0805657 0.766531i −0.877422 0.479720i \(-0.840738\pi\)
0.957987 0.286811i \(-0.0925951\pi\)
\(230\) −12.3176 −0.812200
\(231\) 2.05171 8.53173i 0.134993 0.561347i
\(232\) 30.0301 1.97157
\(233\) 2.38460 22.6880i 0.156221 1.48634i −0.582778 0.812632i \(-0.698034\pi\)
0.738998 0.673707i \(-0.235299\pi\)
\(234\) 5.20727 + 5.78326i 0.340410 + 0.378064i
\(235\) 4.85525 + 1.03202i 0.316722 + 0.0673213i
\(236\) 23.8452 + 10.6166i 1.55219 + 0.691079i
\(237\) −12.7457 + 9.26030i −0.827922 + 0.601521i
\(238\) 47.3669 + 6.78578i 3.07034 + 0.439857i
\(239\) −7.26303 + 22.3533i −0.469807 + 1.44592i 0.383029 + 0.923736i \(0.374881\pi\)
−0.852836 + 0.522180i \(0.825119\pi\)
\(240\) 2.35370 22.3939i 0.151930 1.44552i
\(241\) 8.79167 15.2276i 0.566321 0.980897i −0.430604 0.902541i \(-0.641700\pi\)
0.996925 0.0783560i \(-0.0249671\pi\)
\(242\) −27.5585 5.22616i −1.77153 0.335951i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −4.01269 2.91539i −0.256886 0.186639i
\(245\) −16.5424 14.0317i −1.05685 0.896449i
\(246\) −1.84808 5.68782i −0.117829 0.362642i
\(247\) 18.1694 + 8.08953i 1.15609 + 0.514725i
\(248\) 2.17795 + 20.7218i 0.138300 + 1.31584i
\(249\) 10.3997 + 2.21053i 0.659056 + 0.140087i
\(250\) −3.07006 + 0.652562i −0.194168 + 0.0412716i
\(251\) −8.14907 5.92065i −0.514365 0.373708i 0.300112 0.953904i \(-0.402976\pi\)
−0.814477 + 0.580196i \(0.802976\pi\)
\(252\) −5.25042 + 10.6925i −0.330746 + 0.673566i
\(253\) 1.54337 4.93425i 0.0970308 0.310214i
\(254\) −12.7743 22.1257i −0.801528 1.38829i
\(255\) 20.0785 8.93953i 1.25736 0.559815i
\(256\) −19.1580 21.2771i −1.19738 1.32982i
\(257\) 2.80591 3.11628i 0.175028 0.194388i −0.649248 0.760577i \(-0.724916\pi\)
0.824276 + 0.566189i \(0.191583\pi\)
\(258\) −9.91790 + 7.20577i −0.617461 + 0.448612i
\(259\) −14.1226 + 11.7862i −0.877534 + 0.732361i
\(260\) −13.1578 40.4956i −0.816014 2.51143i
\(261\) −4.60342 + 0.978488i −0.284945 + 0.0605669i
\(262\) −5.37520 + 2.39319i −0.332081 + 0.147852i
\(263\) −10.6282 + 18.4086i −0.655363 + 1.13512i 0.326439 + 0.945218i \(0.394151\pi\)
−0.981803 + 0.189905i \(0.939182\pi\)
\(264\) 19.4270 + 8.39432i 1.19565 + 0.516635i
\(265\) 16.4917 1.01308
\(266\) −1.65155 + 43.9362i −0.101263 + 2.69390i
\(267\) −0.655391 + 2.01709i −0.0401093 + 0.123444i
\(268\) 0.893891 0.992766i 0.0546031 0.0606428i
\(269\) 0.353750 + 3.36571i 0.0215685 + 0.205211i 0.999999 0.00136533i \(-0.000434597\pi\)
−0.978431 + 0.206576i \(0.933768\pi\)
\(270\) 0.825977 + 7.85865i 0.0502674 + 0.478262i
\(271\) 6.43346 7.14508i 0.390805 0.434033i −0.515349 0.856980i \(-0.672338\pi\)
0.906154 + 0.422947i \(0.139005\pi\)
\(272\) −15.9258 + 49.0146i −0.965644 + 2.97195i
\(273\) −0.303303 + 8.06877i −0.0183568 + 0.488344i
\(274\) 12.0027 0.725110
\(275\) −1.42841 + 15.1988i −0.0861365 + 0.916521i
\(276\) −3.50914 + 6.07802i −0.211226 + 0.365854i
\(277\) 27.0588 12.0474i 1.62581 0.723856i 0.627317 0.778764i \(-0.284153\pi\)
0.998491 + 0.0549076i \(0.0174864\pi\)
\(278\) −36.1670 + 7.68754i −2.16915 + 0.461068i
\(279\) −1.00906 3.10556i −0.0604107 0.185925i
\(280\) 40.1653 33.5207i 2.40034 2.00324i
\(281\) −18.9501 + 13.7680i −1.13047 + 0.821333i −0.985763 0.168142i \(-0.946223\pi\)
−0.144705 + 0.989475i \(0.546223\pi\)
\(282\) 2.73309 3.03540i 0.162753 0.180756i
\(283\) 8.32968 + 9.25104i 0.495148 + 0.549918i 0.937981 0.346687i \(-0.112693\pi\)
−0.442833 + 0.896604i \(0.646027\pi\)
\(284\) 34.1823 15.2189i 2.02834 0.903077i
\(285\) 10.0975 + 17.4894i 0.598125 + 1.03598i
\(286\) 25.8089 0.284244i 1.52611 0.0168077i
\(287\) 2.73502 5.56990i 0.161443 0.328781i
\(288\) −4.66578 3.38989i −0.274934 0.199751i
\(289\) −32.5765 + 6.92434i −1.91626 + 0.407314i
\(290\) 36.3760 + 7.73195i 2.13607 + 0.454036i
\(291\) −1.21421 11.5524i −0.0711781 0.677215i
\(292\) −12.5282 5.57793i −0.733160 0.326424i
\(293\) −5.55538 17.0977i −0.324548 0.998857i −0.971644 0.236449i \(-0.924017\pi\)
0.647096 0.762409i \(-0.275983\pi\)
\(294\) −16.8056 + 6.01548i −0.980123 + 0.350830i
\(295\) 14.5341 + 10.5597i 0.846210 + 0.614807i
\(296\) −22.1816 38.4196i −1.28928 2.23310i
\(297\) −3.25155 0.653796i −0.188674 0.0379371i
\(298\) −21.8084 + 37.7733i −1.26333 + 2.18815i
\(299\) −0.497271 + 4.73121i −0.0287579 + 0.273613i
\(300\) 6.40387 19.7091i 0.369727 1.13790i
\(301\) −12.5911 1.80381i −0.725741 0.103970i
\(302\) 12.9587 9.41504i 0.745689 0.541775i
\(303\) −0.0192069 0.00855147i −0.00110341 0.000491269i
\(304\) −46.3198 9.84557i −2.65662 0.564682i
\(305\) −2.28428 2.53695i −0.130798 0.145265i
\(306\) 1.89048 17.9867i 0.108071 1.02823i
\(307\) 7.51127 0.428691 0.214345 0.976758i \(-0.431238\pi\)
0.214345 + 0.976758i \(0.431238\pi\)
\(308\) 15.1052 + 36.5062i 0.860696 + 2.08013i
\(309\) 9.68685 0.551066
\(310\) −2.69713 + 25.6615i −0.153187 + 1.45747i
\(311\) 0.711026 + 0.789675i 0.0403186 + 0.0447783i 0.762967 0.646438i \(-0.223742\pi\)
−0.722648 + 0.691216i \(0.757075\pi\)
\(312\) −19.0480 4.04878i −1.07838 0.229217i
\(313\) 0.781524 + 0.347957i 0.0441743 + 0.0196677i 0.428705 0.903445i \(-0.358970\pi\)
−0.384531 + 0.923112i \(0.625637\pi\)
\(314\) 20.5234 14.9111i 1.15820 0.841485i
\(315\) −5.06486 + 6.44723i −0.285373 + 0.363260i
\(316\) 21.9193 67.4606i 1.23306 3.79496i
\(317\) 3.34496 31.8252i 0.187872 1.78748i −0.342302 0.939590i \(-0.611207\pi\)
0.530174 0.847889i \(-0.322127\pi\)
\(318\) 6.78535 11.7526i 0.380503 0.659051i
\(319\) −7.65512 + 13.6028i −0.428604 + 0.761613i
\(320\) 0.268865 + 0.465688i 0.0150300 + 0.0260328i
\(321\) −11.2108 8.14516i −0.625728 0.454618i
\(322\) −10.1169 + 2.87182i −0.563795 + 0.160040i
\(323\) −14.2833 43.9596i −0.794747 2.44598i
\(324\) 4.11309 + 1.83127i 0.228505 + 0.101737i
\(325\) −1.46832 13.9702i −0.0814479 0.774925i
\(326\) 8.63709 + 1.83587i 0.478364 + 0.101679i
\(327\) 10.1930 2.16659i 0.563675 0.119813i
\(328\) 12.1072 + 8.79637i 0.668506 + 0.485698i
\(329\) 4.22841 0.284356i 0.233120 0.0156770i
\(330\) 21.3709 + 15.1701i 1.17643 + 0.835087i
\(331\) −4.65386 8.06072i −0.255799 0.443057i 0.709313 0.704894i \(-0.249005\pi\)
−0.965112 + 0.261836i \(0.915672\pi\)
\(332\) −43.7306 + 19.4701i −2.40003 + 1.06856i
\(333\) 4.65214 + 5.16673i 0.254936 + 0.283135i
\(334\) −27.4000 + 30.4308i −1.49926 + 1.66510i
\(335\) 0.743862 0.540447i 0.0406415 0.0295278i
\(336\) −3.28790 18.9417i −0.179370 1.03336i
\(337\) 0.365236 + 1.12408i 0.0198957 + 0.0612326i 0.960511 0.278241i \(-0.0897512\pi\)
−0.940616 + 0.339473i \(0.889751\pi\)
\(338\) 9.19414 1.95427i 0.500095 0.106299i
\(339\) 5.62520 2.50450i 0.305519 0.136026i
\(340\) −49.4777 + 85.6978i −2.68330 + 4.64762i
\(341\) −9.94164 4.29575i −0.538370 0.232628i
\(342\) 16.6181 0.898601
\(343\) −16.8583 7.66792i −0.910264 0.414029i
\(344\) 9.47960 29.1752i 0.511106 1.57302i
\(345\) −3.23224 + 3.58976i −0.174018 + 0.193266i
\(346\) −0.527047 5.01452i −0.0283342 0.269582i
\(347\) 2.82052 + 26.8355i 0.151414 + 1.44060i 0.761446 + 0.648228i \(0.224490\pi\)
−0.610033 + 0.792376i \(0.708844\pi\)
\(348\) 14.1783 15.7466i 0.760039 0.844108i
\(349\) −10.5292 + 32.4056i −0.563616 + 1.73463i 0.108412 + 0.994106i \(0.465423\pi\)
−0.672028 + 0.740526i \(0.734577\pi\)
\(350\) 27.4571 14.5054i 1.46764 0.775348i
\(351\) 3.05186 0.162896
\(352\) −18.6648 + 4.18268i −0.994838 + 0.222938i
\(353\) −14.0749 + 24.3785i −0.749133 + 1.29754i 0.199106 + 0.979978i \(0.436196\pi\)
−0.948239 + 0.317559i \(0.897137\pi\)
\(354\) 13.5051 6.01285i 0.717787 0.319579i
\(355\) 25.1905 5.35440i 1.33697 0.284182i
\(356\) −2.95079 9.08160i −0.156392 0.481324i
\(357\) 14.4070 12.0236i 0.762500 0.636358i
\(358\) −35.4438 + 25.7514i −1.87326 + 1.36101i
\(359\) −16.4335 + 18.2513i −0.867330 + 0.963267i −0.999609 0.0279453i \(-0.991104\pi\)
0.132280 + 0.991212i \(0.457770\pi\)
\(360\) −13.2309 14.6944i −0.697331 0.774464i
\(361\) 21.4417 9.54645i 1.12851 0.502445i
\(362\) −10.0546 17.4150i −0.528456 0.915313i
\(363\) −8.75463 + 6.66007i −0.459499 + 0.349563i
\(364\) −20.2485 30.1929i −1.06131 1.58254i
\(365\) −7.63622 5.54804i −0.399698 0.290398i
\(366\) −2.74776 + 0.584054i −0.143628 + 0.0305290i
\(367\) −28.5462 6.06768i −1.49010 0.316731i −0.610337 0.792142i \(-0.708966\pi\)
−0.879764 + 0.475412i \(0.842299\pi\)
\(368\) −1.18398 11.2648i −0.0617193 0.587220i
\(369\) −2.14257 0.953933i −0.111538 0.0496598i
\(370\) −16.9769 52.2495i −0.882586 2.71632i
\(371\) 13.5453 3.84500i 0.703236 0.199623i
\(372\) 11.8940 + 8.64152i 0.616677 + 0.448042i
\(373\) −2.22979 3.86211i −0.115454 0.199972i 0.802507 0.596643i \(-0.203499\pi\)
−0.917961 + 0.396670i \(0.870166\pi\)
\(374\) −40.6254 44.1319i −2.10069 2.28200i
\(375\) −0.615429 + 1.06595i −0.0317806 + 0.0550457i
\(376\) −1.06837 + 10.1649i −0.0550972 + 0.524215i
\(377\) 4.43837 13.6599i 0.228588 0.703521i
\(378\) 2.51063 + 6.26204i 0.129133 + 0.322084i
\(379\) 17.9144 13.0156i 0.920200 0.668564i −0.0233739 0.999727i \(-0.507441\pi\)
0.943574 + 0.331162i \(0.107441\pi\)
\(380\) −83.0639 36.9824i −4.26109 1.89716i
\(381\) −9.80021 2.08310i −0.502080 0.106720i
\(382\) −19.5577 21.7210i −1.00066 1.11135i
\(383\) −3.59683 + 34.2215i −0.183789 + 1.74864i 0.382068 + 0.924134i \(0.375212\pi\)
−0.565857 + 0.824504i \(0.691455\pi\)
\(384\) −11.0920 −0.566035
\(385\) 4.94525 + 26.7387i 0.252033 + 1.36273i
\(386\) −12.5554 −0.639055
\(387\) −0.502530 + 4.78125i −0.0255450 + 0.243045i
\(388\) 34.9951 + 38.8660i 1.77661 + 1.97312i
\(389\) 12.4308 + 2.64224i 0.630265 + 0.133967i 0.511959 0.859010i \(-0.328920\pi\)
0.118307 + 0.992977i \(0.462253\pi\)
\(390\) −22.0307 9.80871i −1.11557 0.496683i
\(391\) 8.94444 6.49852i 0.452340 0.328644i
\(392\) 25.1740 36.8962i 1.27148 1.86354i
\(393\) −0.713037 + 2.19450i −0.0359680 + 0.110698i
\(394\) 0.590795 5.62104i 0.0297638 0.283184i
\(395\) 24.4104 42.2801i 1.22822 2.12734i
\(396\) 13.5739 6.22348i 0.682112 0.312742i
\(397\) 15.1184 + 26.1858i 0.758769 + 1.31423i 0.943479 + 0.331434i \(0.107532\pi\)
−0.184709 + 0.982793i \(0.559134\pi\)
\(398\) −17.6816 12.8465i −0.886300 0.643935i
\(399\) 12.3711 + 12.0105i 0.619329 + 0.601277i
\(400\) 10.3353 + 31.8087i 0.516763 + 1.59043i
\(401\) 11.6945 + 5.20673i 0.583996 + 0.260012i 0.677398 0.735617i \(-0.263108\pi\)
−0.0934022 + 0.995628i \(0.529774\pi\)
\(402\) −0.0790870 0.752462i −0.00394450 0.0375294i
\(403\) 9.74772 + 2.07194i 0.485568 + 0.103211i
\(404\) 0.0925913 0.0196809i 0.00460659 0.000979160i
\(405\) 2.50701 + 1.82145i 0.124574 + 0.0905087i
\(406\) 31.6796 2.13042i 1.57223 0.105731i
\(407\) 23.0575 0.253942i 1.14292 0.0125874i
\(408\) 22.6283 + 39.1934i 1.12027 + 1.94036i
\(409\) −8.78566 + 3.91163i −0.434423 + 0.193417i −0.612284 0.790638i \(-0.709749\pi\)
0.177861 + 0.984056i \(0.443082\pi\)
\(410\) 12.4008 + 13.7725i 0.612431 + 0.680173i
\(411\) 3.14960 3.49799i 0.155358 0.172543i
\(412\) −35.2840 + 25.6353i −1.73832 + 1.26296i
\(413\) 14.3994 + 5.28446i 0.708548 + 0.260031i
\(414\) 1.22832 + 3.78037i 0.0603685 + 0.185795i
\(415\) −32.2271 + 6.85007i −1.58196 + 0.336257i
\(416\) 16.0791 7.15888i 0.788343 0.350993i
\(417\) −7.25010 + 12.5575i −0.355039 + 0.614945i
\(418\) 36.4264 41.3627i 1.78167 2.02312i
\(419\) 31.6704 1.54720 0.773600 0.633675i \(-0.218454\pi\)
0.773600 + 0.633675i \(0.218454\pi\)
\(420\) 1.38659 36.8875i 0.0676589 1.79993i
\(421\) −3.02343 + 9.30517i −0.147353 + 0.453506i −0.997306 0.0733524i \(-0.976630\pi\)
0.849953 + 0.526858i \(0.176630\pi\)
\(422\) 31.5574 35.0480i 1.53619 1.70611i
\(423\) −0.167434 1.59303i −0.00814091 0.0774555i
\(424\) 3.54962 + 33.7724i 0.172385 + 1.64013i
\(425\) −21.8442 + 24.2604i −1.05960 + 1.17680i
\(426\) 6.54862 20.1546i 0.317282 0.976493i
\(427\) −2.46765 1.55112i −0.119418 0.0750640i
\(428\) 62.3905 3.01576
\(429\) 6.68961 7.59615i 0.322977 0.366746i
\(430\) 18.9946 32.8997i 0.916002 1.58656i
\(431\) −19.5798 + 8.71748i −0.943125 + 0.419906i −0.819922 0.572475i \(-0.805983\pi\)
−0.123203 + 0.992381i \(0.539317\pi\)
\(432\) −7.10757 + 1.51076i −0.341963 + 0.0726865i
\(433\) 10.2200 + 31.4541i 0.491144 + 1.51159i 0.822881 + 0.568214i \(0.192366\pi\)
−0.331736 + 0.943372i \(0.607634\pi\)
\(434\) 3.76765 + 21.7056i 0.180853 + 1.04190i
\(435\) 11.7987 8.57223i 0.565703 0.411007i
\(436\) −31.3940 + 34.8666i −1.50350 + 1.66981i
\(437\) 6.79751 + 7.54940i 0.325169 + 0.361137i
\(438\) −7.09556 + 3.15915i −0.339039 + 0.150950i
\(439\) −3.57043 6.18417i −0.170407 0.295154i 0.768155 0.640264i \(-0.221175\pi\)
−0.938562 + 0.345110i \(0.887842\pi\)
\(440\) −65.5767 + 0.722223i −3.12624 + 0.0344306i
\(441\) −2.65681 + 6.47622i −0.126515 + 0.308391i
\(442\) 44.6539 + 32.4430i 2.12397 + 1.54315i
\(443\) 21.5292 4.57616i 1.02288 0.217420i 0.334213 0.942497i \(-0.391529\pi\)
0.688667 + 0.725077i \(0.258196\pi\)
\(444\) −30.6185 6.50817i −1.45309 0.308864i
\(445\) −0.686992 6.53629i −0.0325665 0.309850i
\(446\) −4.41413 1.96530i −0.209015 0.0930596i
\(447\) 5.28569 + 16.2677i 0.250005 + 0.769436i
\(448\) 0.329403 + 0.319802i 0.0155628 + 0.0151092i
\(449\) 8.06904 + 5.86250i 0.380802 + 0.276669i 0.761676 0.647958i \(-0.224377\pi\)
−0.380874 + 0.924627i \(0.624377\pi\)
\(450\) −5.86850 10.1645i −0.276644 0.479161i
\(451\) −7.07082 + 3.24190i −0.332952 + 0.152655i
\(452\) −13.8617 + 24.0091i −0.651998 + 1.12929i
\(453\) 0.656604 6.24717i 0.0308499 0.293518i
\(454\) 10.0140 30.8198i 0.469978 1.44644i
\(455\) −9.31134 23.2244i −0.436522 1.08878i
\(456\) −33.6421 + 24.4424i −1.57544 + 1.14462i
\(457\) 28.5999 + 12.7335i 1.33785 + 0.595647i 0.945935 0.324356i \(-0.105148\pi\)
0.391910 + 0.920003i \(0.371814\pi\)
\(458\) 29.0919 + 6.18368i 1.35938 + 0.288944i
\(459\) −4.74584 5.27079i −0.221517 0.246019i
\(460\) 2.27334 21.6294i 0.105995 1.00848i
\(461\) 17.8709 0.832329 0.416165 0.909289i \(-0.363374\pi\)
0.416165 + 0.909289i \(0.363374\pi\)
\(462\) 21.0896 + 7.47722i 0.981177 + 0.347872i
\(463\) 7.52215 0.349584 0.174792 0.984605i \(-0.444075\pi\)
0.174792 + 0.984605i \(0.444075\pi\)
\(464\) −3.57460 + 34.0101i −0.165947 + 1.57888i
\(465\) 6.77085 + 7.51980i 0.313991 + 0.348722i
\(466\) 56.9011 + 12.0947i 2.63589 + 0.560276i
\(467\) −16.9002 7.52444i −0.782046 0.348189i −0.0234285 0.999726i \(-0.507458\pi\)
−0.758618 + 0.651536i \(0.774125\pi\)
\(468\) −11.1163 + 8.07647i −0.513851 + 0.373335i
\(469\) 0.484958 0.617319i 0.0223933 0.0285052i
\(470\) −3.91133 + 12.0378i −0.180416 + 0.555264i
\(471\) 1.03990 9.89400i 0.0479161 0.455892i
\(472\) −18.4962 + 32.0364i −0.851357 + 1.47459i
\(473\) 10.7991 + 11.7312i 0.496544 + 0.539401i
\(474\) −20.0868 34.7914i −0.922618 1.59802i
\(475\) −24.2675 17.6314i −1.11347 0.808983i
\(476\) −20.6577 + 81.9225i −0.946843 + 3.75491i
\(477\) −1.64456 5.06143i −0.0752992 0.231747i
\(478\) −54.7521 24.3772i −2.50430 1.11499i
\(479\) 0.665282 + 6.32974i 0.0303975 + 0.289213i 0.999151 + 0.0411889i \(0.0131146\pi\)
−0.968754 + 0.248024i \(0.920219\pi\)
\(480\) 17.4812 + 3.71574i 0.797902 + 0.169599i
\(481\) −20.7545 + 4.41150i −0.946322 + 0.201147i
\(482\) 36.2738 + 26.3545i 1.65223 + 1.20041i
\(483\) −1.81782 + 3.70200i −0.0827135 + 0.168447i
\(484\) 14.2632 47.4274i 0.648327 2.15579i
\(485\) 17.9981 + 31.1737i 0.817253 + 1.41552i
\(486\) 2.32951 1.03717i 0.105669 0.0470468i
\(487\) −4.71554 5.23714i −0.213682 0.237317i 0.626770 0.779205i \(-0.284377\pi\)
−0.840451 + 0.541887i \(0.817710\pi\)
\(488\) 4.70361 5.22388i 0.212922 0.236474i
\(489\) 2.80147 2.03539i 0.126687 0.0920434i
\(490\) 39.9935 38.2114i 1.80672 1.72621i
\(491\) −1.84399 5.67521i −0.0832180 0.256119i 0.900786 0.434262i \(-0.142991\pi\)
−0.984005 + 0.178143i \(0.942991\pi\)
\(492\) 10.3287 2.19544i 0.465655 0.0989780i
\(493\) −30.4936 + 13.5766i −1.37336 + 0.611461i
\(494\) −25.3580 + 43.9213i −1.14091 + 1.97611i
\(495\) 10.0290 2.24743i 0.450768 0.101015i
\(496\) −23.7274 −1.06539
\(497\) 19.4415 10.2709i 0.872072 0.460711i
\(498\) −8.37788 + 25.7845i −0.375422 + 1.15543i
\(499\) 23.6185 26.2310i 1.05731 1.17426i 0.0730849 0.997326i \(-0.476716\pi\)
0.984223 0.176933i \(-0.0566177\pi\)
\(500\) −0.579270 5.51138i −0.0259057 0.246476i
\(501\) 1.67857 + 15.9705i 0.0749930 + 0.713511i
\(502\) 17.1868 19.0879i 0.767086 0.851936i
\(503\) 10.9822 33.7999i 0.489674 1.50706i −0.335421 0.942068i \(-0.608879\pi\)
0.825095 0.564993i \(-0.191121\pi\)
\(504\) −14.2930 8.98434i −0.636662 0.400194i
\(505\) 0.0651518 0.00289922
\(506\) 12.1019 + 5.22918i 0.537994 + 0.232465i
\(507\) 1.84307 3.19229i 0.0818536 0.141775i
\(508\) 41.2096 18.3477i 1.82838 0.814048i
\(509\) 20.1770 4.28874i 0.894328 0.190095i 0.262250 0.965000i \(-0.415536\pi\)
0.632078 + 0.774905i \(0.282202\pi\)
\(510\) 17.3188 + 53.3019i 0.766890 + 2.36025i
\(511\) −7.56543 2.77645i −0.334675 0.122823i
\(512\) 41.1181 29.8740i 1.81718 1.32026i
\(513\) 4.36070 4.84305i 0.192530 0.213826i
\(514\) 7.15499 + 7.94642i 0.315593 + 0.350501i
\(515\) −27.4228 + 12.2094i −1.20839 + 0.538011i
\(516\) −10.8227 18.7454i −0.476442 0.825222i
\(517\) −4.33209 3.07513i −0.190525 0.135244i
\(518\) −26.1256 38.9564i −1.14789 1.71165i
\(519\) −1.59970 1.16225i −0.0702189 0.0510170i
\(520\) 59.0267 12.5465i 2.58849 0.550201i
\(521\) 34.3592 + 7.30328i 1.50531 + 0.319963i 0.885443 0.464748i \(-0.153855\pi\)
0.619862 + 0.784711i \(0.287188\pi\)
\(522\) −1.25443 11.9351i −0.0549048 0.522384i
\(523\) −20.8712 9.29245i −0.912633 0.406330i −0.103955 0.994582i \(-0.533150\pi\)
−0.808678 + 0.588252i \(0.799816\pi\)
\(524\) −3.21033 9.88039i −0.140244 0.431627i
\(525\) 2.97758 11.8082i 0.129952 0.515354i
\(526\) −43.8513 31.8598i −1.91201 1.38915i
\(527\) −11.5799 20.0570i −0.504430 0.873698i
\(528\) −11.8193 + 21.0025i −0.514370 + 0.914015i
\(529\) 10.2851 17.8142i 0.447176 0.774532i
\(530\) −4.39578 + 41.8230i −0.190940 + 1.81668i
\(531\) 1.79149 5.51365i 0.0777441 0.239272i
\(532\) −76.8459 11.0089i −3.33169 0.477298i
\(533\) 5.79065 4.20715i 0.250821 0.182232i
\(534\) −4.94064 2.19971i −0.213802 0.0951909i
\(535\) 42.0034 + 8.92809i 1.81596 + 0.385995i
\(536\) 1.26685 + 1.40698i 0.0547198 + 0.0607725i
\(537\) −1.79590 + 17.0869i −0.0774989 + 0.737353i
\(538\) −8.62972 −0.372053
\(539\) 10.2958 + 20.8086i 0.443471 + 0.896289i
\(540\) −13.9520 −0.600399
\(541\) −2.53705 + 24.1385i −0.109077 + 1.03779i 0.793884 + 0.608070i \(0.208056\pi\)
−0.902960 + 0.429724i \(0.858611\pi\)
\(542\) 16.4051 + 18.2197i 0.704660 + 0.782604i
\(543\) −7.71370 1.63960i −0.331027 0.0703619i
\(544\) −37.3680 16.6373i −1.60214 0.713318i
\(545\) −26.1249 + 18.9809i −1.11907 + 0.813050i
\(546\) −20.3815 2.91986i −0.872250 0.124958i
\(547\) −11.8808 + 36.5654i −0.507987 + 1.56342i 0.287703 + 0.957720i \(0.407108\pi\)
−0.795690 + 0.605704i \(0.792892\pi\)
\(548\) −2.21522 + 21.0764i −0.0946296 + 0.900340i
\(549\) −0.550820 + 0.954048i −0.0235084 + 0.0407178i
\(550\) −38.1634 7.67360i −1.62729 0.327203i
\(551\) −15.3353 26.5615i −0.653305 1.13156i
\(552\) −8.04695 5.84645i −0.342501 0.248842i
\(553\) 10.1917 40.4175i 0.433396 1.71873i
\(554\) 23.3397 + 71.8324i 0.991611 + 3.05186i
\(555\) −19.6821 8.76303i −0.835458 0.371970i
\(556\) −6.82411 64.9271i −0.289407 2.75352i
\(557\) −38.0115 8.07960i −1.61060 0.342344i −0.687285 0.726388i \(-0.741198\pi\)
−0.923315 + 0.384044i \(0.874531\pi\)
\(558\) 8.14466 1.73120i 0.344791 0.0732875i
\(559\) −11.8700 8.62404i −0.502046 0.364758i
\(560\) 33.1822 + 49.4786i 1.40220 + 2.09085i
\(561\) −23.5219 + 0.259057i −0.993095 + 0.0109374i
\(562\) −29.8647 51.7272i −1.25977 2.18198i
\(563\) −9.73670 + 4.33506i −0.410353 + 0.182701i −0.601522 0.798856i \(-0.705439\pi\)
0.191169 + 0.981557i \(0.438772\pi\)
\(564\) 4.82566 + 5.35944i 0.203197 + 0.225673i
\(565\) −12.7678 + 14.1801i −0.537147 + 0.596562i
\(566\) −25.6809 + 18.6582i −1.07945 + 0.784264i
\(567\) 2.48377 + 0.911524i 0.104309 + 0.0382804i
\(568\) 16.3869 + 50.4336i 0.687577 + 2.11614i
\(569\) 1.05651 0.224567i 0.0442910 0.00941434i −0.185713 0.982604i \(-0.559459\pi\)
0.230004 + 0.973190i \(0.426126\pi\)
\(570\) −47.0445 + 20.9456i −1.97048 + 0.877314i
\(571\) 6.09434 10.5557i 0.255040 0.441743i −0.709866 0.704337i \(-0.751245\pi\)
0.964906 + 0.262594i \(0.0845779\pi\)
\(572\) −4.26417 + 45.3722i −0.178294 + 1.89711i
\(573\) −11.4623 −0.478845
\(574\) 13.3962 + 8.42064i 0.559149 + 0.351471i
\(575\) 2.21716 6.82373i 0.0924621 0.284569i
\(576\) 0.116112 0.128955i 0.00483800 0.00537314i
\(577\) 4.80817 + 45.7467i 0.200167 + 1.90446i 0.387021 + 0.922071i \(0.373504\pi\)
−0.186855 + 0.982388i \(0.559829\pi\)
\(578\) −8.87706 84.4595i −0.369237 3.51305i
\(579\) −3.29464 + 3.65907i −0.136921 + 0.152066i
\(580\) −20.2906 + 62.4482i −0.842523 + 2.59302i
\(581\) −24.8722 + 13.1399i −1.03187 + 0.545134i
\(582\) 29.6206 1.22781
\(583\) −16.2029 7.00120i −0.671054 0.289960i
\(584\) 9.71790 16.8319i 0.402129 0.696509i
\(585\) −8.63961 + 3.84660i −0.357204 + 0.159037i
\(586\) 44.8405 9.53114i 1.85234 0.393728i
\(587\) 7.03808 + 21.6610i 0.290492 + 0.894044i 0.984698 + 0.174267i \(0.0557557\pi\)
−0.694206 + 0.719776i \(0.744244\pi\)
\(588\) −7.46136 30.6204i −0.307701 1.26276i
\(589\) 17.2162 12.5083i 0.709380 0.515395i
\(590\) −30.6533 + 34.0439i −1.26198 + 1.40157i
\(591\) −1.48313 1.64718i −0.0610077 0.0677559i
\(592\) 46.1518 20.5481i 1.89683 0.844523i
\(593\) 3.36377 + 5.82622i 0.138134 + 0.239254i 0.926790 0.375580i \(-0.122556\pi\)
−0.788657 + 0.614834i \(0.789223\pi\)
\(594\) 2.52471 8.07165i 0.103590 0.331184i
\(595\) −25.6305 + 52.1968i −1.05075 + 2.13986i
\(596\) −62.3039 45.2664i −2.55207 1.85419i
\(597\) −8.38368 + 1.78201i −0.343121 + 0.0729326i
\(598\) −11.8658 2.52216i −0.485229 0.103139i
\(599\) 2.68566 + 25.5524i 0.109733 + 1.04404i 0.901370 + 0.433050i \(0.142563\pi\)
−0.791637 + 0.610992i \(0.790771\pi\)
\(600\) 26.8307 + 11.9458i 1.09536 + 0.487686i
\(601\) 9.16323 + 28.2015i 0.373776 + 1.15036i 0.944301 + 0.329084i \(0.106740\pi\)
−0.570525 + 0.821280i \(0.693260\pi\)
\(602\) 7.93054 31.4503i 0.323225 1.28182i
\(603\) −0.240045 0.174403i −0.00977540 0.00710224i
\(604\) 14.1409 + 24.4927i 0.575385 + 0.996596i
\(605\) 16.3893 29.8886i 0.666320 1.21514i
\(606\) 0.0268060 0.0464294i 0.00108892 0.00188607i
\(607\) −3.91480 + 37.2468i −0.158897 + 1.51180i 0.566840 + 0.823828i \(0.308166\pi\)
−0.725736 + 0.687973i \(0.758501\pi\)
\(608\) 11.6143 35.7453i 0.471024 1.44966i
\(609\) 7.69210 9.79153i 0.311700 0.396773i
\(610\) 7.04257 5.11672i 0.285145 0.207170i
\(611\) 4.46584 + 1.98832i 0.180669 + 0.0804389i
\(612\) 31.2352 + 6.63925i 1.26261 + 0.268376i
\(613\) −28.7089 31.8845i −1.15954 1.28780i −0.950791 0.309834i \(-0.899726\pi\)
−0.208753 0.977969i \(-0.566940\pi\)
\(614\) −2.00209 + 19.0486i −0.0807976 + 0.768738i
\(615\) 7.26781 0.293066
\(616\) −53.6922 + 15.8822i −2.16332 + 0.639913i
\(617\) −33.7625 −1.35923 −0.679613 0.733571i \(-0.737852\pi\)
−0.679613 + 0.733571i \(0.737852\pi\)
\(618\) −2.58197 + 24.5658i −0.103862 + 0.988183i
\(619\) −2.07356 2.30292i −0.0833433 0.0925621i 0.700031 0.714113i \(-0.253170\pi\)
−0.783374 + 0.621551i \(0.786503\pi\)
\(620\) −44.5630 9.47217i −1.78969 0.380411i
\(621\) 1.42404 + 0.634025i 0.0571449 + 0.0254426i
\(622\) −2.19213 + 1.59268i −0.0878966 + 0.0638606i
\(623\) −2.08817 5.20833i −0.0836608 0.208668i
\(624\) 6.85274 21.0906i 0.274329 0.844298i
\(625\) 2.80431 26.6813i 0.112173 1.06725i
\(626\) −1.09073 + 1.88920i −0.0435943 + 0.0755075i
\(627\) −2.49590 21.4697i −0.0996768 0.857419i
\(628\) 22.3957 + 38.7906i 0.893688 + 1.54791i
\(629\) 39.8935 + 28.9843i 1.59066 + 1.15568i
\(630\) −15.0002 14.5630i −0.597621 0.580202i
\(631\) −3.11731 9.59410i −0.124098 0.381935i 0.869637 0.493691i \(-0.164353\pi\)
−0.993736 + 0.111756i \(0.964353\pi\)
\(632\) 91.8368 + 40.8884i 3.65307 + 1.62645i
\(633\) −1.93326 18.3937i −0.0768402 0.731085i
\(634\) 79.8170 + 16.9656i 3.16994 + 0.673791i
\(635\) 30.3693 6.45518i 1.20517 0.256166i
\(636\) 19.3849 + 14.0839i 0.768660 + 0.558464i
\(637\) −13.0625 16.9042i −0.517554 0.669768i
\(638\) −32.4564 23.0391i −1.28496 0.912128i
\(639\) −4.15530 7.19720i −0.164381 0.284717i
\(640\) 31.4006 13.9804i 1.24122 0.552625i
\(641\) −3.04453 3.38130i −0.120252 0.133553i 0.680013 0.733200i \(-0.261974\pi\)
−0.800265 + 0.599647i \(0.795308\pi\)
\(642\) 23.6443 26.2596i 0.933166 1.03639i
\(643\) 6.55022 4.75901i 0.258315 0.187677i −0.451089 0.892479i \(-0.648964\pi\)
0.709404 + 0.704802i \(0.248964\pi\)
\(644\) −3.17566 18.2951i −0.125138 0.720927i
\(645\) −4.60372 14.1688i −0.181271 0.557895i
\(646\) 115.289 24.5054i 4.53597 0.964151i
\(647\) 44.7441 19.9213i 1.75907 0.783188i 0.769587 0.638542i \(-0.220462\pi\)
0.989483 0.144646i \(-0.0462044\pi\)
\(648\) −3.19044 + 5.52600i −0.125332 + 0.217082i
\(649\) −9.79668 16.5448i −0.384553 0.649442i
\(650\) 35.8197 1.40496
\(651\) 7.31438 + 4.59769i 0.286673 + 0.180198i
\(652\) −4.81780 + 14.8277i −0.188680 + 0.580696i
\(653\) −6.97460 + 7.74608i −0.272937 + 0.303127i −0.863994 0.503503i \(-0.832044\pi\)
0.591056 + 0.806630i \(0.298711\pi\)
\(654\) 2.77758 + 26.4270i 0.108612 + 1.03338i
\(655\) −0.747418 7.11120i −0.0292040 0.277858i
\(656\) −11.4033 + 12.6647i −0.445226 + 0.494473i
\(657\) −0.941249 + 2.89687i −0.0367216 + 0.113017i
\(658\) −0.405934 + 10.7990i −0.0158250 + 0.420991i
\(659\) −11.6399 −0.453427 −0.226713 0.973962i \(-0.572798\pi\)
−0.226713 + 0.973962i \(0.572798\pi\)
\(660\) −30.5825 + 34.7269i −1.19042 + 1.35174i
\(661\) 4.28380 7.41976i 0.166620 0.288595i −0.770609 0.637308i \(-0.780048\pi\)
0.937230 + 0.348713i \(0.113381\pi\)
\(662\) 21.6824 9.65364i 0.842712 0.375199i
\(663\) 21.1725 4.50035i 0.822271 0.174779i
\(664\) −20.9643 64.5214i −0.813572 2.50392i
\(665\) −50.1598 18.4082i −1.94511 0.713841i
\(666\) −14.3428 + 10.4207i −0.555773 + 0.403793i
\(667\) 4.90886 5.45184i 0.190072 0.211096i
\(668\) −48.3787 53.7299i −1.87183 2.07887i
\(669\) −1.73105 + 0.770715i −0.0669264 + 0.0297976i
\(670\) 1.17230 + 2.03049i 0.0452899 + 0.0784445i
\(671\) 1.16726 + 3.46226i 0.0450617 + 0.133659i
\(672\) 15.2243 1.02381i 0.587289 0.0394944i
\(673\) 1.53843 + 1.11773i 0.0593020 + 0.0430854i 0.617041 0.786931i \(-0.288331\pi\)
−0.557739 + 0.830016i \(0.688331\pi\)
\(674\) −2.94802 + 0.626621i −0.113553 + 0.0241365i
\(675\) −4.50222 0.956976i −0.173290 0.0368340i
\(676\) 1.73478 + 16.5053i 0.0667223 + 0.634820i
\(677\) −12.0578 5.36848i −0.463419 0.206327i 0.161727 0.986836i \(-0.448294\pi\)
−0.625145 + 0.780508i \(0.714960\pi\)
\(678\) 4.85204 + 14.9331i 0.186342 + 0.573500i
\(679\) 22.0506 + 21.4079i 0.846225 + 0.821561i
\(680\) −113.459 82.4329i −4.35096 3.16116i
\(681\) −6.35417 11.0057i −0.243492 0.421741i
\(682\) 13.5439 24.0670i 0.518623 0.921573i
\(683\) 9.17303 15.8882i 0.350996 0.607943i −0.635428 0.772160i \(-0.719176\pi\)
0.986424 + 0.164217i \(0.0525096\pi\)
\(684\) −3.06703 + 29.1808i −0.117271 + 1.11576i
\(685\) −4.50740 + 13.8723i −0.172219 + 0.530035i
\(686\) 23.9393 40.7088i 0.914008 1.55427i
\(687\) 9.43606 6.85570i 0.360008 0.261561i
\(688\) 31.9135 + 14.2088i 1.21669 + 0.541705i
\(689\) 15.8868 + 3.37684i 0.605239 + 0.128648i
\(690\) −8.24210 9.15378i −0.313771 0.348478i
\(691\) 1.83377 17.4472i 0.0697600 0.663722i −0.902639 0.430398i \(-0.858373\pi\)
0.972399 0.233324i \(-0.0749602\pi\)
\(692\) 8.90263 0.338427
\(693\) 7.71318 4.18413i 0.292999 0.158942i
\(694\) −68.8066 −2.61186
\(695\) 4.69686 44.6876i 0.178162 1.69510i
\(696\) 20.0941 + 22.3167i 0.761663 + 0.845913i
\(697\) −16.2709 3.45848i −0.616304 0.130999i
\(698\) −79.3740 35.3396i −3.00435 1.33762i
\(699\) 18.4561 13.4091i 0.698073 0.507179i
\(700\) 20.4037 + 50.8910i 0.771186 + 1.92350i
\(701\) 1.45326 4.47267i 0.0548888 0.168930i −0.919854 0.392261i \(-0.871693\pi\)
0.974743 + 0.223331i \(0.0716930\pi\)
\(702\) −0.813456 + 7.73952i −0.0307019 + 0.292109i
\(703\) −22.6547 + 39.2390i −0.854436 + 1.47993i
\(704\) −0.0664582 0.571672i −0.00250474 0.0215457i
\(705\) 2.48186 + 4.29871i 0.0934723 + 0.161899i
\(706\) −58.0723 42.1920i −2.18558 1.58792i
\(707\) 0.0535117 0.0151900i 0.00201251 0.000571278i
\(708\) 8.06590 + 24.8243i 0.303135 + 0.932954i
\(709\) 1.74099 + 0.775140i 0.0653843 + 0.0291110i 0.439168 0.898405i \(-0.355273\pi\)
−0.373784 + 0.927516i \(0.621940\pi\)
\(710\) 6.86438 + 65.3102i 0.257615 + 2.45105i
\(711\) −15.4103 3.27556i −0.577931 0.122843i
\(712\) 13.2374 2.81370i 0.496093 0.105448i
\(713\) 4.11798 + 2.99189i 0.154220 + 0.112047i
\(714\) 26.6518 + 39.7410i 0.997419 + 1.48727i
\(715\) −9.36354 + 29.9358i −0.350177 + 1.11954i
\(716\) −38.6773 66.9910i −1.44544 2.50357i
\(717\) −21.4717 + 9.55980i −0.801874 + 0.357017i
\(718\) −41.9050 46.5402i −1.56388 1.73687i
\(719\) −19.7930 + 21.9824i −0.738155 + 0.819804i −0.988952 0.148235i \(-0.952641\pi\)
0.250797 + 0.968040i \(0.419307\pi\)
\(720\) 18.2169 13.2353i 0.678902 0.493251i
\(721\) −19.6768 + 16.4216i −0.732802 + 0.611573i
\(722\) 18.4946 + 56.9206i 0.688299 + 2.11837i
\(723\) 17.1991 3.65578i 0.639641 0.135960i
\(724\) 32.4360 14.4414i 1.20547 0.536711i
\(725\) −10.8310 + 18.7598i −0.402253 + 0.696723i
\(726\) −14.5564 23.9769i −0.540240 0.889867i
\(727\) −21.5880 −0.800654 −0.400327 0.916372i \(-0.631103\pi\)
−0.400327 + 0.916372i \(0.631103\pi\)
\(728\) 45.5557 24.0669i 1.68841 0.891977i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 16.1052 17.8867i 0.596081 0.662015i
\(731\) 3.56422 + 33.9113i 0.131827 + 1.25425i
\(732\) −0.518456 4.93278i −0.0191627 0.182321i
\(733\) 6.54669 7.27084i 0.241808 0.268555i −0.610009 0.792394i \(-0.708834\pi\)
0.851817 + 0.523840i \(0.175501\pi\)
\(734\) 22.9965 70.7759i 0.848815 2.61238i
\(735\) −0.641455 21.6824i −0.0236604 0.799767i
\(736\) 8.99001 0.331376
\(737\) −0.960267 + 0.215191i −0.0353719 + 0.00792665i
\(738\) 2.99026 5.17929i 0.110073 0.190652i
\(739\) −5.56276 + 2.47670i −0.204629 + 0.0911068i −0.506492 0.862244i \(-0.669058\pi\)
0.301863 + 0.953351i \(0.402391\pi\)
\(740\) 94.8819 20.1678i 3.48793 0.741382i
\(741\) 6.14600 + 18.9154i 0.225779 + 0.694876i
\(742\) 6.14051 + 35.3757i 0.225425 + 1.29868i
\(743\) 16.4179 11.9283i 0.602313 0.437606i −0.244386 0.969678i \(-0.578586\pi\)
0.846699 + 0.532072i \(0.178586\pi\)
\(744\) −13.9420 + 15.4842i −0.511138 + 0.567677i
\(745\) −35.4674 39.3906i −1.29943 1.44316i
\(746\) 10.3886 4.62532i 0.380355 0.169345i
\(747\) 5.31603 + 9.20763i 0.194503 + 0.336890i
\(748\) 84.9922 63.1921i 3.10762 2.31053i
\(749\) 36.5805 2.45999i 1.33662 0.0898862i
\(750\) −2.53922 1.84485i −0.0927193 0.0673645i
\(751\) −22.3840 + 4.75787i −0.816804 + 0.173617i −0.597324 0.802000i \(-0.703769\pi\)
−0.219480 + 0.975617i \(0.570436\pi\)
\(752\) −11.3849 2.41994i −0.415165 0.0882460i
\(753\) −1.05289 10.0176i −0.0383696 0.365063i
\(754\) 33.4585 + 14.8967i 1.21849 + 0.542505i
\(755\) 6.01520 + 18.5129i 0.218916 + 0.673753i
\(756\) −11.4593 + 3.25288i −0.416771 + 0.118306i
\(757\) 35.8965 + 26.0803i 1.30468 + 0.947906i 0.999990 0.00454467i \(-0.00144662\pi\)
0.304692 + 0.952451i \(0.401447\pi\)
\(758\) 28.2325 + 48.9001i 1.02545 + 1.77613i
\(759\) 4.69958 2.15471i 0.170584 0.0782110i
\(760\) 64.4310 111.598i 2.33716 4.04807i
\(761\) 3.65740 34.7978i 0.132581 1.26142i −0.702656 0.711530i \(-0.748003\pi\)
0.835237 0.549891i \(-0.185331\pi\)
\(762\) 7.89492 24.2981i 0.286003 0.880226i
\(763\) −17.0320 + 21.6806i −0.616601 + 0.784892i
\(764\) 41.7511 30.3340i 1.51050 1.09744i
\(765\) 20.0785 + 8.93953i 0.725940 + 0.323209i
\(766\) −85.8270 18.2431i −3.10106 0.659150i
\(767\) 11.8388 + 13.1483i 0.427475 + 0.474759i
\(768\) 2.99278 28.4744i 0.107993 1.02748i
\(769\) 1.66567 0.0600656 0.0300328 0.999549i \(-0.490439\pi\)
0.0300328 + 0.999549i \(0.490439\pi\)
\(770\) −69.1275 + 5.41408i −2.49118 + 0.195110i
\(771\) 4.19337 0.151021
\(772\) 2.31723 22.0470i 0.0833990 0.793488i
\(773\) 0.706391 + 0.784527i 0.0254071 + 0.0282175i 0.755714 0.654901i \(-0.227290\pi\)
−0.730307 + 0.683119i \(0.760623\pi\)
\(774\) −11.9913 2.54883i −0.431018 0.0916158i
\(775\) −13.7305 6.11321i −0.493214 0.219593i
\(776\) −59.9648 + 43.5670i −2.15261 + 1.56396i
\(777\) −18.2087 2.60858i −0.653234 0.0935824i
\(778\) −10.0141 + 30.8201i −0.359022 + 1.10496i
\(779\) 1.59766 15.2007i 0.0572421 0.544622i
\(780\) 21.2898 36.8750i 0.762297 1.32034i
\(781\) −27.0223 5.43345i −0.966935 0.194424i
\(782\) 14.0961 + 24.4152i 0.504077 + 0.873087i
\(783\) −3.80745 2.76627i −0.136067 0.0988585i
\(784\) 38.7896 + 32.9023i 1.38534 + 1.17508i
\(785\) 9.52662 + 29.3199i 0.340020 + 1.04647i
\(786\) −5.37520 2.39319i −0.191727 0.0853624i
\(787\) −4.65130 44.2541i −0.165801 1.57749i −0.688669 0.725076i \(-0.741805\pi\)
0.522868 0.852414i \(-0.324862\pi\)
\(788\) 9.76134 + 2.07484i 0.347733 + 0.0739130i
\(789\) −20.7919 + 4.41946i −0.740212 + 0.157337i
\(790\) 100.716 + 73.1743i 3.58331 + 2.60342i
\(791\) −7.18065 + 14.6235i −0.255315 + 0.519951i
\(792\) 6.76098 + 20.0539i 0.240241 + 0.712586i
\(793\) −1.68103 2.91162i −0.0596950 0.103395i
\(794\) −70.4368 + 31.3605i −2.49971 + 1.11294i
\(795\) 11.0351 + 12.2557i 0.391375 + 0.434666i
\(796\) 25.8213 28.6775i 0.915213 1.01645i
\(797\) 6.09615 4.42911i 0.215937 0.156887i −0.474559 0.880224i \(-0.657392\pi\)
0.690496 + 0.723336i \(0.257392\pi\)
\(798\) −33.7561 + 28.1717i −1.19495 + 0.997268i
\(799\) −3.51069 10.8048i −0.124199 0.382247i
\(800\) −25.9653 + 5.51910i −0.918012 + 0.195130i
\(801\) −1.93753 + 0.862644i −0.0684592 + 0.0304800i
\(802\) −16.3214 + 28.2694i −0.576327 + 0.998228i
\(803\) 5.14717 + 8.69265i 0.181640 + 0.306757i
\(804\) 1.33590 0.0471135
\(805\) 0.480070 12.7713i 0.0169202 0.450129i
\(806\) −7.85264 + 24.1679i −0.276597 + 0.851279i
\(807\) −2.26450 + 2.51498i −0.0797142 + 0.0885316i
\(808\) 0.0140231 + 0.133420i 0.000493329 + 0.00469372i
\(809\) −0.522040 4.96688i −0.0183540 0.174626i 0.981505 0.191438i \(-0.0613151\pi\)
−0.999859 + 0.0168118i \(0.994648\pi\)
\(810\) −5.28743 + 5.87228i −0.185781 + 0.206331i
\(811\) −1.17982 + 3.63110i −0.0414290 + 0.127505i −0.969632 0.244569i \(-0.921353\pi\)
0.928203 + 0.372075i \(0.121353\pi\)
\(812\) −2.10585 + 56.0218i −0.0739007 + 1.96598i
\(813\) 9.61465 0.337201
\(814\) −5.50185 + 58.5415i −0.192840 + 2.05188i
\(815\) −5.36534 + 9.29305i −0.187940 + 0.325521i
\(816\) −47.0814 + 20.9620i −1.64818 + 0.733816i
\(817\) −30.6462 + 6.51406i −1.07218 + 0.227898i
\(818\) −7.57811 23.3230i −0.264963 0.815471i
\(819\) −6.19921 + 5.17366i −0.216618 + 0.180782i
\(820\) −26.4727 + 19.2336i −0.924468 + 0.671666i
\(821\) −3.83810 + 4.26264i −0.133951 + 0.148767i −0.806388 0.591387i \(-0.798581\pi\)
0.672437 + 0.740154i \(0.265247\pi\)
\(822\) 8.03138 + 8.91975i 0.280127 + 0.311112i
\(823\) 14.1979 6.32131i 0.494908 0.220347i −0.144077 0.989566i \(-0.546021\pi\)
0.638985 + 0.769219i \(0.279355\pi\)
\(824\) −30.9053 53.5295i −1.07664 1.86479i
\(825\) −12.2507 + 9.10846i −0.426514 + 0.317116i
\(826\) −17.2395 + 35.1083i −0.599838 + 1.22157i
\(827\) −31.9408 23.2064i −1.11069 0.806965i −0.127919 0.991785i \(-0.540830\pi\)
−0.982772 + 0.184820i \(0.940830\pi\)
\(828\) −6.86492 + 1.45918i −0.238573 + 0.0507102i
\(829\) 37.9542 + 8.06741i 1.31820 + 0.280193i 0.812726 0.582647i \(-0.197983\pi\)
0.505478 + 0.862839i \(0.331316\pi\)
\(830\) −8.78184 83.5536i −0.304822 2.90019i
\(831\) 27.0588 + 12.0474i 0.938661 + 0.417919i
\(832\) 0.163649 + 0.503659i 0.00567350 + 0.0174612i
\(833\) −8.88179 + 48.8469i −0.307736 + 1.69245i
\(834\) −29.9134 21.7334i −1.03582 0.752565i
\(835\) −24.8813 43.0958i −0.861055 1.49139i
\(836\) 65.9089 + 71.5976i 2.27951 + 2.47626i
\(837\) 1.63269 2.82790i 0.0564340 0.0977466i
\(838\) −8.44156 + 80.3160i −0.291609 + 2.77447i
\(839\) 0.173527 0.534062i 0.00599082 0.0184379i −0.948016 0.318221i \(-0.896914\pi\)
0.954007 + 0.299784i \(0.0969145\pi\)
\(840\) 51.7865 + 7.41894i 1.78681 + 0.255978i
\(841\) 5.54263 4.02696i 0.191125 0.138861i
\(842\) −22.7920 10.1477i −0.785465 0.349711i
\(843\) −22.9117 4.87004i −0.789122 0.167733i
\(844\) 55.7191 + 61.8824i 1.91793 + 2.13008i
\(845\) −1.19400 + 11.3602i −0.0410750 + 0.390802i
\(846\) 4.08454 0.140429
\(847\) 6.49272 28.3698i 0.223092 0.974797i
\(848\) −38.6709 −1.32796
\(849\) −1.30122 + 12.3803i −0.0446579 + 0.424891i
\(850\) −55.7019 61.8632i −1.91056 2.12189i
\(851\) −10.6008 2.25328i −0.363392 0.0772413i
\(852\) 34.1823 + 15.2189i 1.17107 + 0.521392i
\(853\) 35.2322 25.5977i 1.20633 0.876447i 0.211434 0.977392i \(-0.432187\pi\)
0.994892 + 0.100945i \(0.0321867\pi\)
\(854\) 4.59138 5.84452i 0.157114 0.199995i
\(855\) −6.24060 + 19.2066i −0.213424 + 0.656852i
\(856\) −9.24263 + 87.9378i −0.315907 + 3.00565i
\(857\) −18.1727 + 31.4760i −0.620766 + 1.07520i 0.368577 + 0.929597i \(0.379845\pi\)
−0.989343 + 0.145601i \(0.953488\pi\)
\(858\) 17.4808 + 18.9896i 0.596783 + 0.648293i
\(859\) 12.5605 + 21.7554i 0.428559 + 0.742285i 0.996745 0.0806142i \(-0.0256882\pi\)
−0.568187 + 0.822900i \(0.692355\pi\)
\(860\) 54.2652 + 39.4260i 1.85043 + 1.34442i
\(861\) 5.96933 1.69447i 0.203434 0.0577474i
\(862\) −16.8886 51.9779i −0.575230 1.77037i
\(863\) −22.8705 10.1826i −0.778520 0.346619i −0.0212948 0.999773i \(-0.506779\pi\)
−0.757225 + 0.653154i \(0.773446\pi\)
\(864\) −0.602839 5.73563i −0.0205090 0.195130i
\(865\) 5.99354 + 1.27397i 0.203787 + 0.0433162i
\(866\) −82.4916 + 17.5341i −2.80318 + 0.595834i
\(867\) −26.9437 19.5757i −0.915056 0.664827i
\(868\) −38.8097 + 2.60991i −1.31729 + 0.0885860i
\(869\) −41.9319 + 31.1766i −1.42244 + 1.05759i
\(870\) 18.5943 + 32.2063i 0.630406 + 1.09190i
\(871\) 0.827238 0.368310i 0.0280299 0.0124797i
\(872\) −44.4928 49.4142i −1.50671 1.67338i
\(873\) 7.77266 8.63241i 0.263065 0.292163i
\(874\) −20.9571 + 15.2262i −0.708884 + 0.515035i
\(875\) −0.556943 3.20857i −0.0188281 0.108469i
\(876\) −4.23782 13.0427i −0.143183 0.440671i
\(877\) 43.2419 9.19135i 1.46017 0.310370i 0.591722 0.806142i \(-0.298448\pi\)
0.868453 + 0.495772i \(0.165115\pi\)
\(878\) 16.6347 7.40625i 0.561394 0.249949i
\(879\) 8.98879 15.5690i 0.303184 0.525130i
\(880\) 6.98791 74.3537i 0.235562 2.50646i
\(881\) −23.3263 −0.785884 −0.392942 0.919563i \(-0.628543\pi\)
−0.392942 + 0.919563i \(0.628543\pi\)
\(882\) −15.7155 8.46386i −0.529169 0.284993i
\(883\) 14.5052 44.6424i 0.488139 1.50234i −0.339243 0.940699i \(-0.610171\pi\)
0.827382 0.561639i \(-0.189829\pi\)
\(884\) −65.2103 + 72.4233i −2.19326 + 2.43586i
\(885\) 1.87787 + 17.8668i 0.0631240 + 0.600585i
\(886\) 5.86667 + 55.8177i 0.197095 + 1.87523i
\(887\) 18.3530 20.3830i 0.616232 0.684395i −0.351555 0.936167i \(-0.614347\pi\)
0.967786 + 0.251773i \(0.0810135\pi\)
\(888\) 13.7090 42.1919i 0.460043 1.41587i
\(889\) 23.4384 12.3824i 0.786099 0.415292i
\(890\) 16.7591 0.561768
\(891\) −1.68984 2.85384i −0.0566119 0.0956074i
\(892\) 4.26568 7.38838i 0.142826 0.247381i
\(893\) 9.53639 4.24587i 0.319123 0.142083i
\(894\) −42.6637 + 9.06846i −1.42689 + 0.303295i
\(895\) −16.4524 50.6353i −0.549943 1.69255i
\(896\) 22.5310 18.8036i 0.752708 0.628185i
\(897\) −3.84872 + 2.79626i −0.128505 + 0.0933643i
\(898\) −17.0181 + 18.9005i −0.567900 + 0.630717i
\(899\) −10.2830 11.4205i −0.342958 0.380894i
\(900\) 18.9317 8.42895i 0.631057 0.280965i
\(901\) −18.8729 32.6889i −0.628749 1.08903i
\(902\) −6.33678 18.7957i −0.210992 0.625829i
\(903\) −7.08462 10.5640i −0.235761 0.351548i
\(904\) −31.7867 23.0944i −1.05721 0.768108i
\(905\) 23.9035 5.08085i 0.794580 0.168893i
\(906\) 15.6678 + 3.33029i 0.520528 + 0.110642i
\(907\) 4.08168 + 38.8346i 0.135530 + 1.28948i 0.824985 + 0.565154i \(0.191183\pi\)
−0.689455 + 0.724328i \(0.742150\pi\)
\(908\) 52.2705 + 23.2723i 1.73466 + 0.772320i
\(909\) −0.00649696 0.0199956i −0.000215491 0.000663212i
\(910\) 61.3789 17.4232i 2.03469 0.577574i
\(911\) 21.6383 + 15.7212i 0.716910 + 0.520865i 0.885395 0.464839i \(-0.153888\pi\)
−0.168486 + 0.985704i \(0.553888\pi\)
\(912\) −23.6773 41.0103i −0.784034 1.35799i
\(913\) 34.5706 + 6.95120i 1.14412 + 0.230051i
\(914\) −39.9152 + 69.1352i −1.32028 + 2.28679i
\(915\) 0.356840 3.39510i 0.0117968 0.112239i
\(916\) −16.2276 + 49.9433i −0.536174 + 1.65017i
\(917\) −2.27184 5.66644i −0.0750228 0.187122i
\(918\) 14.6317 10.6306i 0.482918 0.350860i
\(919\) −25.2946 11.2619i −0.834392 0.371495i −0.0553499 0.998467i \(-0.517627\pi\)
−0.779042 + 0.626972i \(0.784294\pi\)
\(920\) 30.1493 + 6.40843i 0.993993 + 0.211280i
\(921\) 5.02602 + 5.58196i 0.165613 + 0.183932i
\(922\) −4.76338 + 45.3205i −0.156873 + 1.49255i
\(923\) 25.3628 0.834828
\(924\) −17.0221 + 35.6527i −0.559985 + 1.17289i
\(925\) 32.0010 1.05219
\(926\) −2.00499 + 19.0762i −0.0658880 + 0.626882i
\(927\) 6.48177 + 7.19873i 0.212889 + 0.236437i
\(928\) −26.5490 5.64316i −0.871513 0.185246i
\(929\) 21.0857 + 9.38794i 0.691798 + 0.308008i 0.722353 0.691525i \(-0.243061\pi\)
−0.0305549 + 0.999533i \(0.509727\pi\)
\(930\) −20.8749 + 15.1665i −0.684516 + 0.497330i
\(931\) −45.4900 3.42476i −1.49088 0.112242i
\(932\) −31.7396 + 97.6845i −1.03967 + 3.19976i
\(933\) −0.111073 + 1.05679i −0.00363637 + 0.0345978i
\(934\) 23.5866 40.8532i 0.771777 1.33676i
\(935\) 66.2623 30.3806i 2.16701 0.993553i
\(936\) −9.73678 16.8646i −0.318256 0.551236i
\(937\) 34.4432 + 25.0245i 1.12521 + 0.817514i 0.984991 0.172606i \(-0.0552188\pi\)
0.140221 + 0.990120i \(0.455219\pi\)
\(938\) 1.43626 + 1.39440i 0.0468955 + 0.0455286i
\(939\) 0.264359 + 0.813614i 0.00862704 + 0.0265513i
\(940\) −20.4162 9.08989i −0.665904 0.296479i
\(941\) −4.31420 41.0469i −0.140639 1.33809i −0.806154 0.591706i \(-0.798455\pi\)
0.665515 0.746385i \(-0.268212\pi\)
\(942\) 24.8140 + 5.27438i 0.808484 + 0.171849i
\(943\) 3.57604 0.760111i 0.116452 0.0247526i
\(944\) −34.0806 24.7610i −1.10923 0.805902i
\(945\) −8.18028 + 0.550114i −0.266105 + 0.0178952i
\(946\) −32.6288 + 24.2597i −1.06085 + 0.788749i
\(947\) 0.553573 + 0.958817i 0.0179887 + 0.0311574i 0.874880 0.484340i \(-0.160940\pi\)
−0.856891 + 0.515498i \(0.827607\pi\)
\(948\) 64.7999 28.8508i 2.10460 0.937029i
\(949\) −6.22010 6.90813i −0.201913 0.224247i
\(950\) 51.1815 56.8428i 1.66055 1.84422i
\(951\) 25.8889 18.8094i 0.839506 0.609937i
\(952\) −112.407 41.2526i −3.64314 1.33700i
\(953\) −9.89852 30.4645i −0.320644 0.986842i −0.973368 0.229246i \(-0.926374\pi\)
0.652724 0.757596i \(-0.273626\pi\)
\(954\) 13.2741 2.82151i 0.429766 0.0913496i
\(955\) 32.4490 14.4472i 1.05003 0.467502i
\(956\) 52.9107 91.6440i 1.71125 2.96398i
\(957\) −15.2312 + 3.41322i −0.492353 + 0.110334i
\(958\) −16.2295 −0.524352
\(959\) −0.467797 + 12.4448i −0.0151059 + 0.401863i
\(960\) −0.166168 + 0.511412i −0.00536305 + 0.0165058i
\(961\) −13.6083 + 15.1136i −0.438978 + 0.487534i
\(962\) −5.65557 53.8091i −0.182343 1.73488i
\(963\) −1.44849 13.7815i −0.0466769 0.444101i
\(964\) −52.9724 + 58.8319i −1.70613 + 1.89485i
\(965\) 4.71496 14.5112i 0.151780 0.467131i
\(966\) −8.90373 5.59672i −0.286473 0.180072i
\(967\) 11.0182 0.354323 0.177161 0.984182i \(-0.443309\pi\)
0.177161 + 0.984182i \(0.443309\pi\)
\(968\) 64.7346 + 27.1296i 2.08065 + 0.871977i
\(969\) 23.1109 40.0293i 0.742431 1.28593i
\(970\) −83.8537 + 37.3341i −2.69238 + 1.19873i
\(971\) −1.03983 + 0.221022i −0.0333696 + 0.00709293i −0.224566 0.974459i \(-0.572097\pi\)
0.191197 + 0.981552i \(0.438763\pi\)
\(972\) 1.39130 + 4.28198i 0.0446259 + 0.137344i
\(973\) −6.56109 37.7987i −0.210339 1.21177i
\(974\) 14.5383 10.5627i 0.465837 0.338450i
\(975\) 9.39935 10.4390i 0.301020 0.334317i
\(976\) 5.35633 + 5.94881i 0.171452 + 0.190417i
\(977\) 2.38529 1.06200i 0.0763120 0.0339763i −0.368226 0.929736i \(-0.620035\pi\)
0.444538 + 0.895760i \(0.353368\pi\)
\(978\) 4.41503 + 7.64705i 0.141177 + 0.244526i
\(979\) −2.09988 + 6.71345i −0.0671124 + 0.214563i
\(980\) 59.7169 + 77.2798i 1.90759 + 2.46861i
\(981\) 8.43055 + 6.12515i 0.269167 + 0.195561i
\(982\) 14.8838 3.16366i 0.474962 0.100956i
\(983\) 17.8777 + 3.80002i 0.570210 + 0.121202i 0.483989 0.875074i \(-0.339187\pi\)
0.0862212 + 0.996276i \(0.472521\pi\)
\(984\) 1.56430 + 14.8833i 0.0498680 + 0.474462i
\(985\) 6.27475 + 2.79370i 0.199930 + 0.0890146i
\(986\) −26.3024 80.9506i −0.837640 2.57799i
\(987\) 3.04068 + 2.95205i 0.0967859 + 0.0939649i
\(988\) −72.4446 52.6341i −2.30477 1.67451i
\(989\) −3.74706 6.49010i −0.119150 0.206373i
\(990\) 3.02633 + 26.0324i 0.0961831 + 0.827365i
\(991\) −22.3144 + 38.6497i −0.708841 + 1.22775i 0.256447 + 0.966558i \(0.417448\pi\)
−0.965287 + 0.261190i \(0.915885\pi\)
\(992\) 1.96850 18.7290i 0.0624999 0.594647i
\(993\) 2.87624 8.85216i 0.0912748 0.280915i
\(994\) 20.8649 + 52.0413i 0.661794 + 1.65065i
\(995\) 21.4875 15.6116i 0.681201 0.494921i
\(996\) −43.7306 19.4701i −1.38566 0.616934i
\(997\) 30.4719 + 6.47700i 0.965054 + 0.205129i 0.663380 0.748282i \(-0.269121\pi\)
0.301674 + 0.953411i \(0.402455\pi\)
\(998\) 60.2263 + 66.8881i 1.90643 + 2.11731i
\(999\) −0.726736 + 6.91443i −0.0229929 + 0.218763i
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 231.2.y.b.4.1 64
3.2 odd 2 693.2.by.c.235.8 64
7.2 even 3 inner 231.2.y.b.37.8 yes 64
11.3 even 5 inner 231.2.y.b.25.8 yes 64
21.2 odd 6 693.2.by.c.37.1 64
33.14 odd 10 693.2.by.c.487.1 64
77.58 even 15 inner 231.2.y.b.58.1 yes 64
231.212 odd 30 693.2.by.c.289.8 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.y.b.4.1 64 1.1 even 1 trivial
231.2.y.b.25.8 yes 64 11.3 even 5 inner
231.2.y.b.37.8 yes 64 7.2 even 3 inner
231.2.y.b.58.1 yes 64 77.58 even 15 inner
693.2.by.c.37.1 64 21.2 odd 6
693.2.by.c.235.8 64 3.2 odd 2
693.2.by.c.289.8 64 231.212 odd 30
693.2.by.c.487.1 64 33.14 odd 10