Properties

Label 164.2.o.b.11.3
Level $164$
Weight $2$
Character 164.11
Analytic conductor $1.310$
Analytic rank $0$
Dimension $288$
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] = [164,2,Mod(7,164)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(164, base_ring=CyclotomicField(40))
 
chi = DirichletCharacter(H, H._module([20, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("164.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 164 = 2^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 164.o (of order \(40\), degree \(16\), 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: \(1.30954659315\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{40})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label 11.3
Character \(\chi\) \(=\) 164.11
Dual form 164.2.o.b.15.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23657 + 0.686220i) q^{2} +(-0.869335 + 2.09876i) q^{3} +(1.05820 - 1.69712i) q^{4} +(1.95666 - 3.84017i) q^{5} +(-0.365220 - 3.19182i) q^{6} +(-0.861690 - 3.58920i) q^{7} +(-0.143945 + 2.82476i) q^{8} +(-1.52773 - 1.52773i) q^{9} +O(q^{10})\) \(q+(-1.23657 + 0.686220i) q^{2} +(-0.869335 + 2.09876i) q^{3} +(1.05820 - 1.69712i) q^{4} +(1.95666 - 3.84017i) q^{5} +(-0.365220 - 3.19182i) q^{6} +(-0.861690 - 3.58920i) q^{7} +(-0.143945 + 2.82476i) q^{8} +(-1.52773 - 1.52773i) q^{9} +(0.215653 + 6.09133i) q^{10} +(1.33744 - 1.56594i) q^{11} +(2.64191 + 3.69628i) q^{12} +(-0.539305 - 0.880065i) q^{13} +(3.52852 + 3.84698i) q^{14} +(6.35859 + 7.44496i) q^{15} +(-1.76041 - 3.59179i) q^{16} +(0.209993 + 2.66821i) q^{17} +(2.93751 + 0.840784i) q^{18} +(-0.0153290 - 0.00939360i) q^{19} +(-4.44666 - 7.38436i) q^{20} +(8.28196 + 1.31173i) q^{21} +(-0.579255 + 2.85417i) q^{22} +(3.82860 + 2.78164i) q^{23} +(-5.80336 - 2.75777i) q^{24} +(-7.97942 - 10.9827i) q^{25} +(1.27081 + 0.718179i) q^{26} +(-1.76183 + 0.729773i) q^{27} +(-7.00313 - 2.33571i) q^{28} +(-0.347443 + 4.41468i) q^{29} +(-12.9717 - 4.84280i) q^{30} +(2.93653 - 9.03770i) q^{31} +(4.64163 + 3.23346i) q^{32} +(2.12385 + 4.16829i) q^{33} +(-2.09065 - 3.15532i) q^{34} +(-15.4691 - 3.71381i) q^{35} +(-4.20939 + 0.976089i) q^{36} +(1.09296 + 3.36379i) q^{37} +(0.0254014 + 0.00109678i) q^{38} +(2.31588 - 0.366800i) q^{39} +(10.5659 + 6.07988i) q^{40} +(6.09681 + 1.95675i) q^{41} +(-11.1413 + 4.06120i) q^{42} +(0.739649 + 4.66996i) q^{43} +(-1.24230 - 3.92687i) q^{44} +(-8.85600 + 2.87749i) q^{45} +(-6.64314 - 0.812425i) q^{46} +(-0.161108 + 0.671065i) q^{47} +(9.06869 - 0.572214i) q^{48} +(-5.90277 + 3.00761i) q^{49} +(17.4037 + 8.10526i) q^{50} +(-5.78248 - 1.87884i) q^{51} +(-2.06427 - 0.0160249i) q^{52} +(0.621948 + 0.0489484i) q^{53} +(1.67784 - 2.11142i) q^{54} +(-3.39655 - 8.20000i) q^{55} +(10.2627 - 1.91742i) q^{56} +(0.0330409 - 0.0240056i) q^{57} +(-2.59981 - 5.69748i) q^{58} +(1.67985 - 2.31211i) q^{59} +(19.3636 - 2.91300i) q^{60} +(-0.0314575 + 0.198615i) q^{61} +(2.57064 + 13.1908i) q^{62} +(-4.16690 + 6.79976i) q^{63} +(-7.95856 - 0.813219i) q^{64} +(-4.43483 + 0.349029i) q^{65} +(-5.48665 - 3.69695i) q^{66} +(-7.84431 + 6.69967i) q^{67} +(4.75048 + 2.46713i) q^{68} +(-9.16633 + 5.61713i) q^{69} +(21.6772 - 6.02286i) q^{70} +(-1.54140 - 1.31648i) q^{71} +(4.53539 - 4.09557i) q^{72} +(3.34006 - 3.34006i) q^{73} +(-3.65982 - 3.40954i) q^{74} +(29.9869 - 7.19922i) q^{75} +(-0.0321632 + 0.0160747i) q^{76} +(-6.77292 - 3.45098i) q^{77} +(-2.61204 + 2.04278i) q^{78} +(1.95198 + 0.808536i) q^{79} +(-17.2376 - 0.267646i) q^{80} -10.8137i q^{81} +(-8.88189 + 1.76410i) q^{82} +14.8802i q^{83} +(10.9902 - 12.6674i) q^{84} +(10.6572 + 4.41438i) q^{85} +(-4.11925 - 5.26716i) q^{86} +(-8.96332 - 4.56704i) q^{87} +(4.23089 + 4.00336i) q^{88} +(3.06418 - 0.735646i) q^{89} +(8.97646 - 9.63538i) q^{90} +(-2.69401 + 2.69401i) q^{91} +(8.77220 - 3.55404i) q^{92} +(16.4151 + 14.0199i) q^{93} +(-0.261277 - 0.940374i) q^{94} +(-0.0660666 + 0.0404856i) q^{95} +(-10.8214 + 6.93070i) q^{96} +(-2.16349 + 1.84779i) q^{97} +(5.23530 - 7.76972i) q^{98} +(-4.43558 + 0.349088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(129\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{40}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23657 + 0.686220i −0.874386 + 0.485231i
\(3\) −0.869335 + 2.09876i −0.501911 + 1.21172i 0.446531 + 0.894768i \(0.352659\pi\)
−0.948442 + 0.316952i \(0.897341\pi\)
\(4\) 1.05820 1.69712i 0.529102 0.848558i
\(5\) 1.95666 3.84017i 0.875046 1.71737i 0.199723 0.979852i \(-0.435996\pi\)
0.675323 0.737522i \(-0.264004\pi\)
\(6\) −0.365220 3.19182i −0.149100 1.30305i
\(7\) −0.861690 3.58920i −0.325688 1.35659i −0.859565 0.511026i \(-0.829265\pi\)
0.533877 0.845562i \(-0.320735\pi\)
\(8\) −0.143945 + 2.82476i −0.0508921 + 0.998704i
\(9\) −1.52773 1.52773i −0.509244 0.509244i
\(10\) 0.215653 + 6.09133i 0.0681955 + 1.92625i
\(11\) 1.33744 1.56594i 0.403253 0.472149i −0.521206 0.853431i \(-0.674518\pi\)
0.924459 + 0.381283i \(0.124518\pi\)
\(12\) 2.64191 + 3.69628i 0.762653 + 1.06702i
\(13\) −0.539305 0.880065i −0.149576 0.244086i 0.769073 0.639162i \(-0.220718\pi\)
−0.918649 + 0.395075i \(0.870718\pi\)
\(14\) 3.52852 + 3.84698i 0.943036 + 1.02815i
\(15\) 6.35859 + 7.44496i 1.64178 + 1.92228i
\(16\) −1.76041 3.59179i −0.440103 0.897947i
\(17\) 0.209993 + 2.66821i 0.0509307 + 0.647136i 0.968412 + 0.249356i \(0.0802190\pi\)
−0.917481 + 0.397779i \(0.869781\pi\)
\(18\) 2.93751 + 0.840784i 0.692377 + 0.198175i
\(19\) −0.0153290 0.00939360i −0.00351670 0.00215504i 0.520739 0.853716i \(-0.325656\pi\)
−0.524256 + 0.851561i \(0.675656\pi\)
\(20\) −4.44666 7.38436i −0.994304 1.65119i
\(21\) 8.28196 + 1.31173i 1.80727 + 0.286244i
\(22\) −0.579255 + 2.85417i −0.123498 + 0.608511i
\(23\) 3.82860 + 2.78164i 0.798318 + 0.580012i 0.910420 0.413685i \(-0.135758\pi\)
−0.112103 + 0.993697i \(0.535758\pi\)
\(24\) −5.80336 2.75777i −1.18461 0.562927i
\(25\) −7.97942 10.9827i −1.59588 2.19655i
\(26\) 1.27081 + 0.718179i 0.249225 + 0.140846i
\(27\) −1.76183 + 0.729773i −0.339064 + 0.140445i
\(28\) −7.00313 2.33571i −1.32347 0.441408i
\(29\) −0.347443 + 4.41468i −0.0645186 + 0.819786i 0.876494 + 0.481414i \(0.159876\pi\)
−0.941012 + 0.338373i \(0.890124\pi\)
\(30\) −12.9717 4.84280i −2.36830 0.884171i
\(31\) 2.93653 9.03770i 0.527416 1.62322i −0.232072 0.972699i \(-0.574551\pi\)
0.759488 0.650521i \(-0.225449\pi\)
\(32\) 4.64163 + 3.23346i 0.820532 + 0.571601i
\(33\) 2.12385 + 4.16829i 0.369715 + 0.725606i
\(34\) −2.09065 3.15532i −0.358543 0.541133i
\(35\) −15.4691 3.71381i −2.61476 0.627749i
\(36\) −4.20939 + 0.976089i −0.701565 + 0.162681i
\(37\) 1.09296 + 3.36379i 0.179682 + 0.553003i 0.999816 0.0191673i \(-0.00610151\pi\)
−0.820135 + 0.572171i \(0.806102\pi\)
\(38\) 0.0254014 + 0.00109678i 0.00412065 + 0.000177922i
\(39\) 2.31588 0.366800i 0.370838 0.0587350i
\(40\) 10.5659 + 6.07988i 1.67062 + 0.961313i
\(41\) 6.09681 + 1.95675i 0.952162 + 0.305593i
\(42\) −11.1413 + 4.06120i −1.71915 + 0.626657i
\(43\) 0.739649 + 4.66996i 0.112795 + 0.712162i 0.977666 + 0.210166i \(0.0674006\pi\)
−0.864870 + 0.501995i \(0.832599\pi\)
\(44\) −1.24230 3.92687i −0.187284 0.591998i
\(45\) −8.85600 + 2.87749i −1.32017 + 0.428951i
\(46\) −6.64314 0.812425i −0.979477 0.119786i
\(47\) −0.161108 + 0.671065i −0.0235001 + 0.0978849i −0.982887 0.184207i \(-0.941028\pi\)
0.959387 + 0.282092i \(0.0910283\pi\)
\(48\) 9.06869 0.572214i 1.30895 0.0825919i
\(49\) −5.90277 + 3.00761i −0.843253 + 0.429659i
\(50\) 17.4037 + 8.10526i 2.46125 + 1.14626i
\(51\) −5.78248 1.87884i −0.809710 0.263091i
\(52\) −2.06427 0.0160249i −0.286262 0.00222225i
\(53\) 0.621948 + 0.0489484i 0.0854312 + 0.00672358i 0.121103 0.992640i \(-0.461357\pi\)
−0.0356715 + 0.999364i \(0.511357\pi\)
\(54\) 1.67784 2.11142i 0.228324 0.287327i
\(55\) −3.39655 8.20000i −0.457991 1.10569i
\(56\) 10.2627 1.91742i 1.37141 0.256226i
\(57\) 0.0330409 0.0240056i 0.00437638 0.00317962i
\(58\) −2.59981 5.69748i −0.341372 0.748116i
\(59\) 1.67985 2.31211i 0.218697 0.301011i −0.685545 0.728030i \(-0.740436\pi\)
0.904243 + 0.427019i \(0.140436\pi\)
\(60\) 19.3636 2.91300i 2.49984 0.376067i
\(61\) −0.0314575 + 0.198615i −0.00402771 + 0.0254300i −0.989620 0.143707i \(-0.954098\pi\)
0.985593 + 0.169136i \(0.0540979\pi\)
\(62\) 2.57064 + 13.1908i 0.326471 + 1.67524i
\(63\) −4.16690 + 6.79976i −0.524980 + 0.856689i
\(64\) −7.95856 0.813219i −0.994820 0.101652i
\(65\) −4.43483 + 0.349029i −0.550073 + 0.0432917i
\(66\) −5.48665 3.69695i −0.675360 0.455063i
\(67\) −7.84431 + 6.69967i −0.958335 + 0.818495i −0.983448 0.181189i \(-0.942005\pi\)
0.0251134 + 0.999685i \(0.492005\pi\)
\(68\) 4.75048 + 2.46713i 0.576080 + 0.299183i
\(69\) −9.16633 + 5.61713i −1.10350 + 0.676223i
\(70\) 21.6772 6.02286i 2.59092 0.719869i
\(71\) −1.54140 1.31648i −0.182931 0.156238i 0.553267 0.833004i \(-0.313381\pi\)
−0.736198 + 0.676766i \(0.763381\pi\)
\(72\) 4.53539 4.09557i 0.534501 0.482668i
\(73\) 3.34006 3.34006i 0.390924 0.390924i −0.484093 0.875017i \(-0.660850\pi\)
0.875017 + 0.484093i \(0.160850\pi\)
\(74\) −3.65982 3.40954i −0.425446 0.396351i
\(75\) 29.9869 7.19922i 3.46259 0.831294i
\(76\) −0.0321632 + 0.0160747i −0.00368937 + 0.00184389i
\(77\) −6.77292 3.45098i −0.771846 0.393275i
\(78\) −2.61204 + 2.04278i −0.295755 + 0.231299i
\(79\) 1.95198 + 0.808536i 0.219615 + 0.0909674i 0.489778 0.871847i \(-0.337078\pi\)
−0.270164 + 0.962814i \(0.587078\pi\)
\(80\) −17.2376 0.267646i −1.92722 0.0299238i
\(81\) 10.8137i 1.20152i
\(82\) −8.88189 + 1.76410i −0.980840 + 0.194813i
\(83\) 14.8802i 1.63332i 0.577121 + 0.816658i \(0.304176\pi\)
−0.577121 + 0.816658i \(0.695824\pi\)
\(84\) 10.9902 12.6674i 1.19913 1.38212i
\(85\) 10.6572 + 4.41438i 1.15594 + 0.478806i
\(86\) −4.11925 5.26716i −0.444190 0.567973i
\(87\) −8.96332 4.56704i −0.960969 0.489638i
\(88\) 4.23089 + 4.00336i 0.451014 + 0.426759i
\(89\) 3.06418 0.735646i 0.324803 0.0779783i −0.0677650 0.997701i \(-0.521587\pi\)
0.392568 + 0.919723i \(0.371587\pi\)
\(90\) 8.97646 9.63538i 0.946202 1.01566i
\(91\) −2.69401 + 2.69401i −0.282409 + 0.282409i
\(92\) 8.77220 3.55404i 0.914565 0.370534i
\(93\) 16.4151 + 14.0199i 1.70217 + 1.45379i
\(94\) −0.261277 0.940374i −0.0269486 0.0969922i
\(95\) −0.0660666 + 0.0404856i −0.00677829 + 0.00415374i
\(96\) −10.8214 + 6.93070i −1.10445 + 0.707362i
\(97\) −2.16349 + 1.84779i −0.219669 + 0.187615i −0.752472 0.658624i \(-0.771139\pi\)
0.532803 + 0.846239i \(0.321139\pi\)
\(98\) 5.23530 7.76972i 0.528845 0.784861i
\(99\) −4.43558 + 0.349088i −0.445793 + 0.0350847i
\(100\) −27.0828 + 1.92005i −2.70828 + 0.192005i
\(101\) −7.24965 + 11.8304i −0.721367 + 1.17716i 0.256217 + 0.966619i \(0.417524\pi\)
−0.977584 + 0.210545i \(0.932476\pi\)
\(102\) 8.43974 1.64474i 0.835659 0.162854i
\(103\) −0.480440 + 3.03338i −0.0473391 + 0.298888i −0.999987 0.00518966i \(-0.998348\pi\)
0.952647 + 0.304077i \(0.0983481\pi\)
\(104\) 2.56360 1.39673i 0.251382 0.136960i
\(105\) 21.2423 29.2375i 2.07303 2.85329i
\(106\) −0.802671 + 0.366265i −0.0779623 + 0.0355748i
\(107\) 9.75028 7.08399i 0.942595 0.684835i −0.00644893 0.999979i \(-0.502053\pi\)
0.949044 + 0.315144i \(0.102053\pi\)
\(108\) −0.625862 + 3.76227i −0.0602236 + 0.362025i
\(109\) 4.33962 + 10.4768i 0.415660 + 1.00349i 0.983590 + 0.180416i \(0.0577443\pi\)
−0.567930 + 0.823077i \(0.692256\pi\)
\(110\) 9.82708 + 7.80908i 0.936975 + 0.744567i
\(111\) −8.00993 0.630396i −0.760269 0.0598345i
\(112\) −11.3747 + 9.41347i −1.07481 + 0.889489i
\(113\) −4.46010 1.44917i −0.419571 0.136327i 0.0916200 0.995794i \(-0.470795\pi\)
−0.511191 + 0.859467i \(0.670795\pi\)
\(114\) −0.0243842 + 0.0523579i −0.00228379 + 0.00490377i
\(115\) 18.1732 9.25972i 1.69466 0.863473i
\(116\) 7.12457 + 5.26129i 0.661500 + 0.488498i
\(117\) −0.520591 + 2.16842i −0.0481286 + 0.200470i
\(118\) −0.490628 + 4.01183i −0.0451660 + 0.369319i
\(119\) 9.39578 3.05287i 0.861309 0.279856i
\(120\) −21.9455 + 16.8899i −2.00334 + 1.54183i
\(121\) 1.05735 + 6.67587i 0.0961231 + 0.606898i
\(122\) −0.0973940 0.267187i −0.00881764 0.0241900i
\(123\) −9.40692 + 11.0947i −0.848194 + 1.00037i
\(124\) −12.2306 14.5474i −1.09834 1.30639i
\(125\) −36.5043 + 5.78171i −3.26504 + 0.517132i
\(126\) 0.486522 11.2678i 0.0433428 1.00381i
\(127\) −1.87165 5.76034i −0.166082 0.511148i 0.833032 0.553224i \(-0.186603\pi\)
−0.999114 + 0.0420763i \(0.986603\pi\)
\(128\) 10.3994 4.45572i 0.919182 0.393834i
\(129\) −10.4441 2.50741i −0.919554 0.220765i
\(130\) 5.24446 3.47487i 0.459970 0.304766i
\(131\) 5.91575 + 11.6103i 0.516862 + 1.01440i 0.990989 + 0.133942i \(0.0427635\pi\)
−0.474128 + 0.880456i \(0.657236\pi\)
\(132\) 9.32154 + 0.806477i 0.811336 + 0.0701948i
\(133\) −0.0205067 + 0.0631130i −0.00177815 + 0.00547259i
\(134\) 5.10257 13.6675i 0.440795 1.18069i
\(135\) −0.644853 + 8.19363i −0.0555001 + 0.705195i
\(136\) −7.56728 + 0.209104i −0.648889 + 0.0179306i
\(137\) −1.69788 + 0.703284i −0.145059 + 0.0600856i −0.454032 0.890985i \(-0.650015\pi\)
0.308973 + 0.951071i \(0.400015\pi\)
\(138\) 7.48020 13.2361i 0.636757 1.12673i
\(139\) −3.30464 4.54845i −0.280296 0.385794i 0.645536 0.763730i \(-0.276634\pi\)
−0.925832 + 0.377936i \(0.876634\pi\)
\(140\) −22.6723 + 22.3230i −1.91616 + 1.88664i
\(141\) −1.26835 0.921509i −0.106814 0.0776050i
\(142\) 2.80945 + 0.570179i 0.235764 + 0.0478484i
\(143\) −2.09942 0.332515i −0.175562 0.0278063i
\(144\) −2.79785 + 8.17673i −0.233155 + 0.681394i
\(145\) 16.2733 + 9.97229i 1.35142 + 0.828153i
\(146\) −1.83819 + 6.42223i −0.152130 + 0.531507i
\(147\) −1.18077 15.0031i −0.0973885 1.23744i
\(148\) 6.86532 + 1.70469i 0.564326 + 0.140125i
\(149\) −11.8134 13.8318i −0.967794 1.13314i −0.991061 0.133412i \(-0.957407\pi\)
0.0232661 0.999729i \(-0.492593\pi\)
\(150\) −32.1406 + 29.4800i −2.62427 + 2.40703i
\(151\) 4.79935 + 7.83183i 0.390566 + 0.637345i 0.986132 0.165960i \(-0.0530724\pi\)
−0.595567 + 0.803306i \(0.703072\pi\)
\(152\) 0.0287412 0.0419485i 0.00233122 0.00340247i
\(153\) 3.75549 4.39712i 0.303614 0.355486i
\(154\) 10.7433 0.380348i 0.865721 0.0306494i
\(155\) −28.9605 28.9605i −2.32616 2.32616i
\(156\) 1.82817 4.31847i 0.146371 0.345754i
\(157\) −4.03242 16.7962i −0.321822 1.34049i −0.865381 0.501114i \(-0.832924\pi\)
0.543559 0.839371i \(-0.317076\pi\)
\(158\) −2.96859 + 0.339677i −0.236168 + 0.0270233i
\(159\) −0.643412 + 1.26277i −0.0510259 + 0.100144i
\(160\) 21.4991 11.4978i 1.69966 0.908983i
\(161\) 6.68478 16.1385i 0.526835 1.27189i
\(162\) 7.42057 + 13.3719i 0.583015 + 1.05059i
\(163\) −2.59627 −0.203356 −0.101678 0.994817i \(-0.532421\pi\)
−0.101678 + 0.994817i \(0.532421\pi\)
\(164\) 9.77250 8.27637i 0.763104 0.646276i
\(165\) 20.1626 1.56966
\(166\) −10.2111 18.4004i −0.792536 1.42815i
\(167\) 4.97935 12.0212i 0.385314 0.930230i −0.605605 0.795766i \(-0.707069\pi\)
0.990918 0.134464i \(-0.0429313\pi\)
\(168\) −4.89748 + 23.2057i −0.377849 + 1.79036i
\(169\) 5.41821 10.6338i 0.416785 0.817988i
\(170\) −16.2077 + 1.85454i −1.24307 + 0.142237i
\(171\) 0.00906764 + 0.0377694i 0.000693420 + 0.00288830i
\(172\) 8.70816 + 3.68649i 0.663991 + 0.281093i
\(173\) −7.17636 7.17636i −0.545608 0.545608i 0.379559 0.925167i \(-0.376076\pi\)
−0.925167 + 0.379559i \(0.876076\pi\)
\(174\) 14.2178 0.503355i 1.07785 0.0381593i
\(175\) −32.5434 + 38.1034i −2.46005 + 2.88035i
\(176\) −7.97897 2.04710i −0.601437 0.154306i
\(177\) 3.39222 + 5.53560i 0.254975 + 0.416081i
\(178\) −3.28426 + 3.01238i −0.246166 + 0.225788i
\(179\) 7.96834 + 9.32973i 0.595582 + 0.697337i 0.973548 0.228483i \(-0.0733765\pi\)
−0.377966 + 0.925819i \(0.623376\pi\)
\(180\) −4.48801 + 18.0746i −0.334517 + 1.34720i
\(181\) 0.995377 + 12.6475i 0.0739858 + 0.940079i 0.916144 + 0.400849i \(0.131285\pi\)
−0.842158 + 0.539230i \(0.818715\pi\)
\(182\) 1.48264 5.18002i 0.109901 0.383968i
\(183\) −0.389497 0.238684i −0.0287925 0.0176440i
\(184\) −8.40857 + 10.4145i −0.619888 + 0.767765i
\(185\) 15.0561 + 2.38465i 1.10694 + 0.175323i
\(186\) −29.9192 6.07211i −2.19378 0.445229i
\(187\) 4.45911 + 3.23973i 0.326082 + 0.236913i
\(188\) 0.968390 + 0.983543i 0.0706271 + 0.0717323i
\(189\) 4.13745 + 5.69471i 0.300955 + 0.414229i
\(190\) 0.0539138 0.0953995i 0.00391132 0.00692101i
\(191\) 4.76911 1.97543i 0.345081 0.142937i −0.203410 0.979094i \(-0.565203\pi\)
0.548491 + 0.836157i \(0.315203\pi\)
\(192\) 8.62541 15.9962i 0.622485 1.15442i
\(193\) −0.784454 + 9.96743i −0.0564662 + 0.717471i 0.901903 + 0.431939i \(0.142170\pi\)
−0.958369 + 0.285532i \(0.907830\pi\)
\(194\) 1.40731 3.76955i 0.101039 0.270638i
\(195\) 3.12283 9.61107i 0.223630 0.688263i
\(196\) −1.14206 + 13.2004i −0.0815759 + 0.942883i
\(197\) 3.54985 + 6.96697i 0.252916 + 0.496376i 0.982201 0.187835i \(-0.0601469\pi\)
−0.729284 + 0.684211i \(0.760147\pi\)
\(198\) 5.24535 3.47546i 0.372771 0.246990i
\(199\) 15.1589 + 3.63932i 1.07458 + 0.257985i 0.731863 0.681452i \(-0.238651\pi\)
0.342721 + 0.939437i \(0.388651\pi\)
\(200\) 32.1722 20.9591i 2.27492 1.48203i
\(201\) −7.24168 22.2876i −0.510788 1.57205i
\(202\) 0.846460 19.6039i 0.0595567 1.37933i
\(203\) 16.1446 2.55705i 1.13313 0.179469i
\(204\) −9.30766 + 7.82535i −0.651667 + 0.547884i
\(205\) 19.4436 19.5841i 1.35800 1.36781i
\(206\) −1.48747 4.08067i −0.103637 0.284313i
\(207\) −1.59947 10.0987i −0.111171 0.701906i
\(208\) −2.21161 + 3.48634i −0.153348 + 0.241735i
\(209\) −0.0352114 + 0.0114409i −0.00243562 + 0.000791381i
\(210\) −6.20417 + 50.7310i −0.428129 + 3.50077i
\(211\) −5.98663 + 24.9361i −0.412137 + 1.71667i 0.250835 + 0.968030i \(0.419295\pi\)
−0.662972 + 0.748644i \(0.730705\pi\)
\(212\) 0.741219 1.00372i 0.0509071 0.0689359i
\(213\) 4.10298 2.09057i 0.281132 0.143244i
\(214\) −7.19571 + 15.4507i −0.491888 + 1.05619i
\(215\) 19.3807 + 6.29716i 1.32175 + 0.429463i
\(216\) −1.80783 5.08179i −0.123007 0.345772i
\(217\) −34.9685 2.75208i −2.37381 0.186823i
\(218\) −12.5556 9.97730i −0.850373 0.675748i
\(219\) 4.10635 + 9.91361i 0.277482 + 0.669900i
\(220\) −17.5106 2.91292i −1.18056 0.196389i
\(221\) 2.23495 1.62378i 0.150339 0.109228i
\(222\) 10.3374 4.71705i 0.693802 0.316588i
\(223\) 10.7018 14.7298i 0.716646 0.986379i −0.282982 0.959125i \(-0.591324\pi\)
0.999629 0.0272536i \(-0.00867617\pi\)
\(224\) 7.60589 19.4460i 0.508190 1.29929i
\(225\) −4.58825 + 28.9691i −0.305883 + 1.93127i
\(226\) 6.50967 1.26861i 0.433017 0.0843865i
\(227\) 6.60481 10.7781i 0.438376 0.715365i −0.554800 0.831983i \(-0.687205\pi\)
0.993177 + 0.116618i \(0.0372054\pi\)
\(228\) −0.00577635 0.0814771i −0.000382548 0.00539595i
\(229\) 21.5728 1.69781i 1.42557 0.112195i 0.657930 0.753079i \(-0.271432\pi\)
0.767638 + 0.640884i \(0.221432\pi\)
\(230\) −16.1182 + 23.9211i −1.06280 + 1.57731i
\(231\) 13.1307 11.2147i 0.863937 0.737872i
\(232\) −12.4204 1.61692i −0.815441 0.106156i
\(233\) 6.67617 4.09116i 0.437371 0.268021i −0.286335 0.958129i \(-0.592437\pi\)
0.723706 + 0.690108i \(0.242437\pi\)
\(234\) −0.844265 3.03863i −0.0551913 0.198642i
\(235\) 2.26177 + 1.93173i 0.147541 + 0.126012i
\(236\) −2.14630 5.29758i −0.139712 0.344843i
\(237\) −3.39384 + 3.39384i −0.220454 + 0.220454i
\(238\) −9.52358 + 10.2227i −0.617322 + 0.662637i
\(239\) −21.1671 + 5.08178i −1.36919 + 0.328713i −0.850376 0.526176i \(-0.823625\pi\)
−0.518811 + 0.854889i \(0.673625\pi\)
\(240\) 15.5470 35.9449i 1.00355 2.32023i
\(241\) −1.98558 1.01171i −0.127903 0.0651697i 0.388868 0.921293i \(-0.372866\pi\)
−0.516771 + 0.856124i \(0.672866\pi\)
\(242\) −5.88861 7.52960i −0.378534 0.484021i
\(243\) 17.4099 + 7.21140i 1.11684 + 0.462612i
\(244\) 0.303784 + 0.263562i 0.0194478 + 0.0168728i
\(245\) 28.5525i 1.82415i
\(246\) 4.01891 20.1746i 0.256236 1.28628i
\(247\) 0.0185565i 0.00118072i
\(248\) 25.1067 + 9.59592i 1.59427 + 0.609342i
\(249\) −31.2300 12.9359i −1.97912 0.819779i
\(250\) 41.1725 32.1994i 2.60398 2.03647i
\(251\) −14.4328 7.35387i −0.910989 0.464172i −0.0653104 0.997865i \(-0.520804\pi\)
−0.845678 + 0.533693i \(0.820804\pi\)
\(252\) 7.13056 + 14.2672i 0.449183 + 0.898752i
\(253\) 9.47639 2.27508i 0.595776 0.143033i
\(254\) 6.26729 + 5.83870i 0.393245 + 0.366352i
\(255\) −18.5294 + 18.5294i −1.16036 + 1.16036i
\(256\) −9.80190 + 12.6461i −0.612619 + 0.790378i
\(257\) −8.49992 7.25961i −0.530210 0.452842i 0.343595 0.939118i \(-0.388355\pi\)
−0.873806 + 0.486275i \(0.838355\pi\)
\(258\) 14.6355 4.06638i 0.911167 0.253162i
\(259\) 11.1315 6.82139i 0.691678 0.423861i
\(260\) −4.10061 + 7.89577i −0.254309 + 0.489675i
\(261\) 7.27525 6.21365i 0.450327 0.384616i
\(262\) −15.2825 10.2974i −0.944154 0.636178i
\(263\) −12.1068 + 0.952827i −0.746538 + 0.0587538i −0.446021 0.895023i \(-0.647159\pi\)
−0.300517 + 0.953776i \(0.597159\pi\)
\(264\) −12.0801 + 5.39937i −0.743482 + 0.332308i
\(265\) 1.40491 2.29261i 0.0863031 0.140834i
\(266\) −0.0179515 0.0921156i −0.00110068 0.00564797i
\(267\) −1.11986 + 7.07051i −0.0685343 + 0.432708i
\(268\) 3.06925 + 20.4023i 0.187485 + 1.24627i
\(269\) −9.90223 + 13.6293i −0.603750 + 0.830990i −0.996045 0.0888492i \(-0.971681\pi\)
0.392295 + 0.919839i \(0.371681\pi\)
\(270\) −4.82523 10.5745i −0.293654 0.643543i
\(271\) 22.1685 16.1064i 1.34664 0.978394i 0.347472 0.937690i \(-0.387040\pi\)
0.999171 0.0407033i \(-0.0129598\pi\)
\(272\) 9.21397 5.45139i 0.558679 0.330539i
\(273\) −3.31209 7.99609i −0.200457 0.483945i
\(274\) 1.61693 2.03478i 0.0976825 0.122925i
\(275\) −27.8703 2.19344i −1.68064 0.132269i
\(276\) −0.166907 + 21.5004i −0.0100466 + 1.29417i
\(277\) −26.0020 8.44858i −1.56231 0.507626i −0.604887 0.796311i \(-0.706782\pi\)
−0.957424 + 0.288685i \(0.906782\pi\)
\(278\) 7.20765 + 3.35676i 0.432286 + 0.201325i
\(279\) −18.2934 + 9.32096i −1.09520 + 0.558031i
\(280\) 12.7173 43.1621i 0.760006 2.57943i
\(281\) −6.04359 + 25.1734i −0.360530 + 1.50172i 0.437566 + 0.899186i \(0.355841\pi\)
−0.798096 + 0.602530i \(0.794159\pi\)
\(282\) 2.20076 + 0.269142i 0.131053 + 0.0160272i
\(283\) 17.7644 5.77200i 1.05598 0.343110i 0.270970 0.962588i \(-0.412656\pi\)
0.785014 + 0.619478i \(0.212656\pi\)
\(284\) −3.86534 + 1.22284i −0.229366 + 0.0725619i
\(285\) −0.0275357 0.173853i −0.00163107 0.0102982i
\(286\) 2.82425 1.02948i 0.167001 0.0608747i
\(287\) 1.76960 23.5688i 0.104456 1.39122i
\(288\) −2.15130 12.0310i −0.126766 0.708935i
\(289\) 9.71546 1.53878i 0.571498 0.0905164i
\(290\) −26.9662 1.16435i −1.58351 0.0683730i
\(291\) −1.99728 6.14699i −0.117083 0.360343i
\(292\) −2.13401 9.20293i −0.124883 0.538561i
\(293\) 17.7956 + 4.27234i 1.03963 + 0.249593i 0.717102 0.696968i \(-0.245468\pi\)
0.322526 + 0.946561i \(0.395468\pi\)
\(294\) 11.7556 + 17.7421i 0.685598 + 1.03474i
\(295\) −5.59200 10.9749i −0.325579 0.638984i
\(296\) −9.65923 + 2.60315i −0.561431 + 0.151305i
\(297\) −1.21356 + 3.73494i −0.0704177 + 0.216723i
\(298\) 24.0998 + 8.99729i 1.39606 + 0.521199i
\(299\) 0.383243 4.86956i 0.0221635 0.281614i
\(300\) 19.5143 58.5095i 1.12666 3.37805i
\(301\) 16.1240 6.67880i 0.929375 0.384960i
\(302\) −11.3091 6.39118i −0.650765 0.367771i
\(303\) −18.5267 25.4998i −1.06433 1.46493i
\(304\) −0.00675455 + 0.0715950i −0.000387400 + 0.00410625i
\(305\) 0.701161 + 0.509423i 0.0401484 + 0.0291695i
\(306\) −1.62653 + 8.01444i −0.0929827 + 0.458155i
\(307\) −14.9585 2.36919i −0.853726 0.135217i −0.285793 0.958291i \(-0.592257\pi\)
−0.567933 + 0.823075i \(0.692257\pi\)
\(308\) −13.0238 + 7.84261i −0.742102 + 0.446874i
\(309\) −5.94867 3.64535i −0.338408 0.207377i
\(310\) 55.6849 + 15.9384i 3.16269 + 0.905238i
\(311\) 2.44109 + 31.0170i 0.138422 + 1.75881i 0.538773 + 0.842451i \(0.318888\pi\)
−0.400351 + 0.916362i \(0.631112\pi\)
\(312\) 0.702763 + 6.59461i 0.0397861 + 0.373347i
\(313\) −3.67861 4.30710i −0.207928 0.243452i 0.646636 0.762799i \(-0.276175\pi\)
−0.854564 + 0.519347i \(0.826175\pi\)
\(314\) 16.5123 + 18.0026i 0.931842 + 1.01594i
\(315\) 17.9590 + 29.3064i 1.01187 + 1.65123i
\(316\) 3.43777 2.45714i 0.193390 0.138225i
\(317\) 4.23405 4.95743i 0.237808 0.278437i −0.628649 0.777689i \(-0.716392\pi\)
0.866457 + 0.499252i \(0.166392\pi\)
\(318\) −0.0709135 2.00302i −0.00397663 0.112324i
\(319\) 6.44845 + 6.44845i 0.361044 + 0.361044i
\(320\) −18.6951 + 28.9710i −1.04509 + 1.61953i
\(321\) 6.39134 + 26.6219i 0.356730 + 1.48589i
\(322\) 2.80837 + 24.5436i 0.156504 + 1.36776i
\(323\) 0.0218451 0.0428734i 0.00121549 0.00238554i
\(324\) −18.3521 11.4431i −1.01956 0.635727i
\(325\) −5.36218 + 12.9454i −0.297440 + 0.718084i
\(326\) 3.21047 1.78161i 0.177811 0.0986744i
\(327\) −25.7608 −1.42458
\(328\) −6.40495 + 16.9404i −0.353654 + 0.935376i
\(329\) 2.54741 0.140443
\(330\) −24.9324 + 13.8360i −1.37248 + 0.761645i
\(331\) −0.0384810 + 0.0929014i −0.00211511 + 0.00510633i −0.924934 0.380129i \(-0.875880\pi\)
0.922818 + 0.385235i \(0.125880\pi\)
\(332\) 25.2535 + 15.7463i 1.38596 + 0.864191i
\(333\) 3.46921 6.80872i 0.190112 0.373115i
\(334\) 2.09189 + 18.2820i 0.114463 + 1.00035i
\(335\) 10.3792 + 43.2324i 0.567076 + 2.36204i
\(336\) −9.86819 32.0562i −0.538354 1.74881i
\(337\) 2.95470 + 2.95470i 0.160953 + 0.160953i 0.782989 0.622036i \(-0.213694\pi\)
−0.622036 + 0.782989i \(0.713694\pi\)
\(338\) 0.597167 + 16.8676i 0.0324816 + 0.917474i
\(339\) 6.91879 8.10086i 0.375777 0.439979i
\(340\) 18.7692 13.4153i 1.01791 0.727546i
\(341\) −10.2251 16.6858i −0.553719 0.903587i
\(342\) −0.0371309 0.0404821i −0.00200781 0.00218902i
\(343\) −0.899350 1.05300i −0.0485603 0.0568568i
\(344\) −13.2980 + 1.41712i −0.716979 + 0.0764057i
\(345\) 3.63531 + 46.1910i 0.195719 + 2.48684i
\(346\) 13.7986 + 3.94950i 0.741818 + 0.212326i
\(347\) 9.42708 + 5.77692i 0.506072 + 0.310121i 0.751996 0.659168i \(-0.229091\pi\)
−0.245924 + 0.969289i \(0.579091\pi\)
\(348\) −17.2358 + 10.3789i −0.923937 + 0.556370i
\(349\) −2.82487 0.447415i −0.151212 0.0239496i 0.0803696 0.996765i \(-0.474390\pi\)
−0.231581 + 0.972816i \(0.574390\pi\)
\(350\) 14.0948 69.4494i 0.753398 3.71223i
\(351\) 1.59241 + 1.15695i 0.0849965 + 0.0617536i
\(352\) 11.2713 2.94395i 0.600762 0.156913i
\(353\) 12.1777 + 16.7612i 0.648154 + 0.892108i 0.999017 0.0443190i \(-0.0141118\pi\)
−0.350863 + 0.936427i \(0.614112\pi\)
\(354\) −7.99335 4.51734i −0.424842 0.240094i
\(355\) −8.07152 + 3.34333i −0.428392 + 0.177446i
\(356\) 1.99405 5.97874i 0.105685 0.316873i
\(357\) −1.76083 + 22.3735i −0.0931929 + 1.18413i
\(358\) −16.2556 6.06881i −0.859138 0.320747i
\(359\) −0.367344 + 1.13057i −0.0193877 + 0.0596691i −0.960282 0.279030i \(-0.909987\pi\)
0.940895 + 0.338699i \(0.109987\pi\)
\(360\) −6.85345 25.4303i −0.361208 1.34029i
\(361\) −8.62567 16.9288i −0.453983 0.890991i
\(362\) −9.90980 14.9564i −0.520848 0.786091i
\(363\) −14.9303 3.58444i −0.783635 0.188134i
\(364\) 1.72124 + 7.42287i 0.0902176 + 0.389064i
\(365\) −6.29101 19.3617i −0.329287 1.01344i
\(366\) 0.645430 + 0.0278685i 0.0337372 + 0.00145671i
\(367\) −19.4772 + 3.08489i −1.01670 + 0.161030i −0.642475 0.766306i \(-0.722092\pi\)
−0.374229 + 0.927336i \(0.622092\pi\)
\(368\) 3.25115 18.6483i 0.169478 0.972112i
\(369\) −6.32491 12.3037i −0.329262 0.640504i
\(370\) −20.2542 + 7.38300i −1.05297 + 0.383824i
\(371\) −0.360241 2.27447i −0.0187028 0.118085i
\(372\) 41.1639 13.0226i 2.13425 0.675188i
\(373\) −20.4999 + 6.66083i −1.06145 + 0.344885i −0.787151 0.616761i \(-0.788445\pi\)
−0.274295 + 0.961646i \(0.588445\pi\)
\(374\) −7.73716 0.946219i −0.400079 0.0489278i
\(375\) 19.6000 81.6399i 1.01214 4.21587i
\(376\) −1.87241 0.551689i −0.0965621 0.0284512i
\(377\) 4.07259 2.07509i 0.209749 0.106872i
\(378\) −9.02406 4.20269i −0.464148 0.216163i
\(379\) −36.2712 11.7852i −1.86313 0.605367i −0.993807 0.111117i \(-0.964557\pi\)
−0.869320 0.494250i \(-0.835443\pi\)
\(380\) −0.00120299 + 0.154965i −6.17120e−5 + 0.00794952i
\(381\) 13.7167 + 1.07953i 0.702726 + 0.0553058i
\(382\) −4.54175 + 5.71541i −0.232376 + 0.292426i
\(383\) −7.78364 18.7914i −0.397725 0.960194i −0.988204 0.153141i \(-0.951061\pi\)
0.590479 0.807053i \(-0.298939\pi\)
\(384\) 0.310977 + 25.6993i 0.0158695 + 1.31146i
\(385\) −26.5046 + 19.2568i −1.35080 + 0.981415i
\(386\) −5.86982 12.8637i −0.298766 0.654746i
\(387\) 6.00446 8.26443i 0.305224 0.420104i
\(388\) 0.846510 + 5.62703i 0.0429751 + 0.285669i
\(389\) −1.98100 + 12.5075i −0.100441 + 0.634157i 0.885189 + 0.465232i \(0.154029\pi\)
−0.985629 + 0.168924i \(0.945971\pi\)
\(390\) 2.73372 + 14.0277i 0.138428 + 0.710320i
\(391\) −6.61801 + 10.7996i −0.334687 + 0.546160i
\(392\) −7.64612 17.1069i −0.386187 0.864027i
\(393\) −29.5100 + 2.32249i −1.48858 + 0.117154i
\(394\) −9.17051 6.17916i −0.462004 0.311302i
\(395\) 6.92427 5.91389i 0.348398 0.297560i
\(396\) −4.10131 + 7.89711i −0.206098 + 0.396845i
\(397\) 32.5139 19.9245i 1.63183 0.999984i 0.664214 0.747542i \(-0.268766\pi\)
0.967612 0.252442i \(-0.0812338\pi\)
\(398\) −21.2424 + 5.90205i −1.06478 + 0.295843i
\(399\) −0.114632 0.0979049i −0.00573877 0.00490138i
\(400\) −25.4006 + 47.9945i −1.27003 + 2.39973i
\(401\) −10.5966 + 10.5966i −0.529168 + 0.529168i −0.920324 0.391156i \(-0.872075\pi\)
0.391156 + 0.920324i \(0.372075\pi\)
\(402\) 24.2490 + 22.5907i 1.20943 + 1.12672i
\(403\) −9.53745 + 2.28974i −0.475094 + 0.114060i
\(404\) 12.4059 + 24.8224i 0.617216 + 1.23496i
\(405\) −41.5264 21.1587i −2.06346 1.05139i
\(406\) −18.2092 + 14.2407i −0.903705 + 0.706753i
\(407\) 6.72926 + 2.78735i 0.333557 + 0.138164i
\(408\) 6.13964 16.0637i 0.303958 0.795271i
\(409\) 16.6196i 0.821786i 0.911683 + 0.410893i \(0.134783\pi\)
−0.911683 + 0.410893i \(0.865217\pi\)
\(410\) −10.6044 + 37.5597i −0.523714 + 1.85494i
\(411\) 4.17483i 0.205929i
\(412\) 4.63959 + 4.02529i 0.228576 + 0.198312i
\(413\) −9.74613 4.03698i −0.479576 0.198647i
\(414\) 8.90777 + 11.3901i 0.437793 + 0.559793i
\(415\) 57.1425 + 29.1156i 2.80502 + 1.42923i
\(416\) 0.342407 5.82876i 0.0167879 0.285778i
\(417\) 12.4189 2.98152i 0.608158 0.146006i
\(418\) 0.0356903 0.0383102i 0.00174567 0.00187381i
\(419\) 6.18450 6.18450i 0.302132 0.302132i −0.539715 0.841848i \(-0.681468\pi\)
0.841848 + 0.539715i \(0.181468\pi\)
\(420\) −27.1408 66.9898i −1.32433 3.26877i
\(421\) 0.481574 + 0.411303i 0.0234705 + 0.0200457i 0.661106 0.750293i \(-0.270087\pi\)
−0.637635 + 0.770338i \(0.720087\pi\)
\(422\) −9.70879 34.9434i −0.472617 1.70102i
\(423\) 1.27134 0.779077i 0.0618146 0.0378800i
\(424\) −0.227794 + 1.74981i −0.0110626 + 0.0849783i
\(425\) 27.6286 23.5971i 1.34018 1.14463i
\(426\) −3.63902 + 5.40068i −0.176311 + 0.261664i
\(427\) 0.739973 0.0582371i 0.0358098 0.00281829i
\(428\) −1.70459 24.0437i −0.0823943 1.16219i
\(429\) 2.52296 4.11710i 0.121810 0.198776i
\(430\) −28.2867 + 5.51253i −1.36411 + 0.265838i
\(431\) −2.67940 + 16.9171i −0.129062 + 0.814868i 0.835205 + 0.549938i \(0.185349\pi\)
−0.964268 + 0.264930i \(0.914651\pi\)
\(432\) 5.72273 + 5.04341i 0.275335 + 0.242651i
\(433\) 13.8259 19.0297i 0.664429 0.914508i −0.335189 0.942151i \(-0.608800\pi\)
0.999618 + 0.0276428i \(0.00880009\pi\)
\(434\) 45.1294 20.5929i 2.16628 0.988493i
\(435\) −35.0764 + 25.4845i −1.68178 + 1.22189i
\(436\) 22.3725 + 3.72171i 1.07145 + 0.178237i
\(437\) −0.0325588 0.0786039i −0.00155750 0.00376013i
\(438\) −11.8807 9.44100i −0.567682 0.451108i
\(439\) −6.02938 0.474523i −0.287767 0.0226477i −0.0662458 0.997803i \(-0.521102\pi\)
−0.221521 + 0.975156i \(0.571102\pi\)
\(440\) 23.6520 8.41410i 1.12756 0.401127i
\(441\) 13.6127 + 4.42303i 0.648223 + 0.210620i
\(442\) −1.64939 + 3.54159i −0.0784535 + 0.168456i
\(443\) 4.92060 2.50717i 0.233785 0.119119i −0.333174 0.942865i \(-0.608120\pi\)
0.566959 + 0.823746i \(0.308120\pi\)
\(444\) −9.54599 + 12.9267i −0.453033 + 0.613474i
\(445\) 3.17057 13.2064i 0.150300 0.626043i
\(446\) −3.12565 + 25.5582i −0.148004 + 1.21021i
\(447\) 39.2994 12.7691i 1.85880 0.603960i
\(448\) 3.93901 + 29.2656i 0.186101 + 1.38267i
\(449\) −0.894540 5.64791i −0.0422160 0.266541i 0.957548 0.288274i \(-0.0930815\pi\)
−0.999764 + 0.0217333i \(0.993082\pi\)
\(450\) −14.2055 38.9708i −0.669653 1.83710i
\(451\) 11.2183 6.93021i 0.528248 0.326331i
\(452\) −7.17911 + 6.03579i −0.337677 + 0.283900i
\(453\) −20.6094 + 3.26421i −0.968313 + 0.153366i
\(454\) −0.771168 + 17.8602i −0.0361927 + 0.838219i
\(455\) 5.07418 + 15.6167i 0.237881 + 0.732124i
\(456\) 0.0630541 + 0.0967882i 0.00295278 + 0.00453252i
\(457\) −23.9165 5.74184i −1.11877 0.268592i −0.368434 0.929654i \(-0.620106\pi\)
−0.750331 + 0.661062i \(0.770106\pi\)
\(458\) −25.5111 + 16.9031i −1.19206 + 0.789831i
\(459\) −2.31716 4.54768i −0.108156 0.212267i
\(460\) 3.51614 40.6408i 0.163941 1.89488i
\(461\) 6.26359 19.2773i 0.291724 0.897835i −0.692578 0.721343i \(-0.743525\pi\)
0.984302 0.176492i \(-0.0564750\pi\)
\(462\) −8.54128 + 22.8783i −0.397376 + 1.06439i
\(463\) −0.163110 + 2.07251i −0.00758036 + 0.0963176i −0.999544 0.0302087i \(-0.990383\pi\)
0.991963 + 0.126526i \(0.0403828\pi\)
\(464\) 16.4683 6.52372i 0.764520 0.302856i
\(465\) 85.9575 35.6048i 3.98618 1.65113i
\(466\) −5.44811 + 9.64033i −0.252379 + 0.446580i
\(467\) 11.4598 + 15.7730i 0.530295 + 0.729889i 0.987175 0.159639i \(-0.0510332\pi\)
−0.456880 + 0.889528i \(0.651033\pi\)
\(468\) 3.12916 + 3.17813i 0.144646 + 0.146909i
\(469\) 30.8058 + 22.3817i 1.42248 + 1.03349i
\(470\) −4.12242 0.836648i −0.190153 0.0385917i
\(471\) 38.7568 + 6.13847i 1.78582 + 0.282846i
\(472\) 6.28936 + 5.07798i 0.289491 + 0.233733i
\(473\) 8.30211 + 5.08754i 0.381731 + 0.233925i
\(474\) 1.86780 6.52565i 0.0857907 0.299733i
\(475\) 0.0191489 + 0.243309i 0.000878610 + 0.0111638i
\(476\) 4.76156 19.1763i 0.218246 0.878944i
\(477\) −0.875390 1.02495i −0.0400814 0.0469292i
\(478\) 22.6874 20.8093i 1.03770 0.951794i
\(479\) −2.86815 4.68039i −0.131049 0.213852i 0.780385 0.625300i \(-0.215023\pi\)
−0.911433 + 0.411447i \(0.865023\pi\)
\(480\) 5.44123 + 55.1170i 0.248357 + 2.51574i
\(481\) 2.37091 2.77598i 0.108104 0.126574i
\(482\) 3.14956 0.111505i 0.143459 0.00507891i
\(483\) 28.0595 + 28.0595i 1.27675 + 1.27675i
\(484\) 12.4486 + 5.26998i 0.565847 + 0.239544i
\(485\) 2.86262 + 11.9237i 0.129985 + 0.541425i
\(486\) −26.4771 + 3.02961i −1.20103 + 0.137426i
\(487\) −11.9778 + 23.5078i −0.542767 + 1.06524i 0.442905 + 0.896569i \(0.353948\pi\)
−0.985672 + 0.168672i \(0.946052\pi\)
\(488\) −0.556511 0.117449i −0.0251921 0.00531668i
\(489\) 2.25703 5.44895i 0.102066 0.246410i
\(490\) −19.5933 35.3071i −0.885136 1.59501i
\(491\) −27.9739 −1.26244 −0.631222 0.775602i \(-0.717446\pi\)
−0.631222 + 0.775602i \(0.717446\pi\)
\(492\) 8.87453 + 27.7051i 0.400095 + 1.24904i
\(493\) −11.8523 −0.533799
\(494\) −0.0127338 0.0229464i −0.000572923 0.00103241i
\(495\) −7.33838 + 17.7164i −0.329836 + 0.796294i
\(496\) −37.6310 + 5.36269i −1.68968 + 0.240792i
\(497\) −3.39690 + 6.66680i −0.152372 + 0.299047i
\(498\) 47.4949 5.43455i 2.12830 0.243528i
\(499\) −5.06177 21.0838i −0.226596 0.943839i −0.963471 0.267811i \(-0.913700\pi\)
0.736876 0.676028i \(-0.236300\pi\)
\(500\) −28.8167 + 68.0702i −1.28872 + 3.04419i
\(501\) 20.9009 + 20.9009i 0.933785 + 0.933785i
\(502\) 22.8935 0.810504i 1.02179 0.0361746i
\(503\) 9.01031 10.5497i 0.401750 0.470389i −0.522244 0.852796i \(-0.674905\pi\)
0.923994 + 0.382408i \(0.124905\pi\)
\(504\) −18.6079 12.7493i −0.828862 0.567898i
\(505\) 31.2454 + 50.9879i 1.39040 + 2.26893i
\(506\) −10.1570 + 9.31619i −0.451534 + 0.414155i
\(507\) 17.6076 + 20.6159i 0.781983 + 0.915584i
\(508\) −11.7566 2.91921i −0.521613 0.129519i
\(509\) −3.06441 38.9371i −0.135828 1.72586i −0.567113 0.823640i \(-0.691940\pi\)
0.431285 0.902216i \(-0.358060\pi\)
\(510\) 10.1976 35.6282i 0.451559 1.57764i
\(511\) −14.8662 9.11003i −0.657643 0.403004i
\(512\) 3.44274 22.3640i 0.152149 0.988358i
\(513\) 0.0338622 + 0.00536324i 0.00149505 + 0.000236793i
\(514\) 15.4924 + 3.14420i 0.683342 + 0.138685i
\(515\) 10.7086 + 7.78026i 0.471878 + 0.342839i
\(516\) −15.3074 + 15.0715i −0.673870 + 0.663488i
\(517\) 0.835375 + 1.14979i 0.0367397 + 0.0505679i
\(518\) −9.08389 + 16.0738i −0.399123 + 0.706241i
\(519\) 21.3001 8.82280i 0.934971 0.387278i
\(520\) −0.347553 12.5776i −0.0152412 0.551564i
\(521\) 2.64879 33.6561i 0.116046 1.47450i −0.613026 0.790063i \(-0.710048\pi\)
0.729072 0.684437i \(-0.239952\pi\)
\(522\) −4.73241 + 12.6760i −0.207132 + 0.554815i
\(523\) −5.22103 + 16.0687i −0.228300 + 0.702634i 0.769640 + 0.638478i \(0.220436\pi\)
−0.997940 + 0.0641564i \(0.979564\pi\)
\(524\) 25.9641 + 2.24635i 1.13425 + 0.0981324i
\(525\) −51.6788 101.425i −2.25545 4.42657i
\(526\) 14.3171 9.48618i 0.624253 0.413617i
\(527\) 24.7311 + 5.93742i 1.07730 + 0.258638i
\(528\) 11.2328 14.9663i 0.488844 0.651326i
\(529\) −0.186750 0.574758i −0.00811957 0.0249895i
\(530\) −0.164036 + 3.79905i −0.00712526 + 0.165020i
\(531\) −6.09864 + 0.965930i −0.264659 + 0.0419178i
\(532\) 0.0854099 + 0.101589i 0.00370299 + 0.00440442i
\(533\) −1.56597 6.42088i −0.0678298 0.278119i
\(534\) −3.46715 9.51164i −0.150038 0.411609i
\(535\) −8.12570 51.3037i −0.351305 2.21805i
\(536\) −17.7958 23.1227i −0.768663 0.998748i
\(537\) −26.5080 + 8.61298i −1.14391 + 0.371677i
\(538\) 2.89212 23.6486i 0.124688 1.01956i
\(539\) −3.18486 + 13.2659i −0.137182 + 0.571402i
\(540\) 13.2232 + 9.76491i 0.569034 + 0.420215i
\(541\) 11.0564 5.63350i 0.475351 0.242203i −0.199865 0.979823i \(-0.564050\pi\)
0.675216 + 0.737620i \(0.264050\pi\)
\(542\) −16.3604 + 35.1292i −0.702739 + 1.50893i
\(543\) −27.4093 8.90583i −1.17625 0.382186i
\(544\) −7.65285 + 13.0638i −0.328113 + 0.560107i
\(545\) 48.7237 + 3.83464i 2.08709 + 0.164258i
\(546\) 9.58270 + 7.61489i 0.410102 + 0.325887i
\(547\) 3.31752 + 8.00921i 0.141847 + 0.342449i 0.978798 0.204829i \(-0.0656639\pi\)
−0.836951 + 0.547278i \(0.815664\pi\)
\(548\) −0.603144 + 3.62571i −0.0257651 + 0.154883i
\(549\) 0.351488 0.255371i 0.0150012 0.0108990i
\(550\) 35.9687 16.4128i 1.53371 0.699845i
\(551\) 0.0467957 0.0644088i 0.00199356 0.00274391i
\(552\) −14.5476 26.7012i −0.619188 1.13648i
\(553\) 1.21999 7.70274i 0.0518794 0.327554i
\(554\) 37.9509 7.39589i 1.61238 0.314221i
\(555\) −18.0936 + 29.5260i −0.768029 + 1.25331i
\(556\) −11.2162 + 0.795179i −0.475674 + 0.0337231i
\(557\) −29.4053 + 2.31424i −1.24594 + 0.0980577i −0.684224 0.729272i \(-0.739859\pi\)
−0.561717 + 0.827330i \(0.689859\pi\)
\(558\) 16.2248 24.0793i 0.686852 1.01936i
\(559\) 3.71097 3.16947i 0.156957 0.134054i
\(560\) 13.8928 + 62.0997i 0.587079 + 2.62419i
\(561\) −10.6759 + 6.54218i −0.450736 + 0.276211i
\(562\) −9.80116 35.2758i −0.413437 1.48802i
\(563\) −11.4193 9.75297i −0.481264 0.411039i 0.375440 0.926847i \(-0.377492\pi\)
−0.856704 + 0.515808i \(0.827492\pi\)
\(564\) −2.90608 + 1.17739i −0.122368 + 0.0495771i
\(565\) −14.2920 + 14.2920i −0.601268 + 0.601268i
\(566\) −18.0060 + 19.3278i −0.756850 + 0.812407i
\(567\) −38.8124 + 9.31804i −1.62997 + 0.391321i
\(568\) 3.94063 4.16460i 0.165345 0.174743i
\(569\) −3.00933 1.53333i −0.126158 0.0642806i 0.389773 0.920911i \(-0.372554\pi\)
−0.515930 + 0.856631i \(0.672554\pi\)
\(570\) 0.153352 + 0.196086i 0.00642319 + 0.00821315i
\(571\) −20.7785 8.60672i −0.869552 0.360180i −0.0971160 0.995273i \(-0.530962\pi\)
−0.772436 + 0.635093i \(0.780962\pi\)
\(572\) −2.78593 + 3.21109i −0.116485 + 0.134262i
\(573\) 11.7265i 0.489883i
\(574\) 13.9851 + 30.3587i 0.583729 + 1.26715i
\(575\) 64.2443i 2.67917i
\(576\) 10.9162 + 13.4009i 0.454840 + 0.558372i
\(577\) −22.6018 9.36197i −0.940925 0.389744i −0.141112 0.989994i \(-0.545068\pi\)
−0.799813 + 0.600250i \(0.795068\pi\)
\(578\) −10.9579 + 8.56975i −0.455788 + 0.356455i
\(579\) −20.2373 10.3114i −0.841034 0.428528i
\(580\) 34.1446 17.0650i 1.41778 0.708584i
\(581\) 53.4080 12.8221i 2.21574 0.531952i
\(582\) 6.68796 + 6.23060i 0.277225 + 0.258267i
\(583\) 0.908468 0.908468i 0.0376249 0.0376249i
\(584\) 8.95408 + 9.91565i 0.370523 + 0.410313i
\(585\) 7.30846 + 6.24201i 0.302168 + 0.258075i
\(586\) −24.9372 + 6.92864i −1.03015 + 0.286219i
\(587\) −20.3249 + 12.4551i −0.838900 + 0.514079i −0.874352 0.485293i \(-0.838713\pi\)
0.0354515 + 0.999371i \(0.488713\pi\)
\(588\) −26.7116 13.8725i −1.10157 0.572090i
\(589\) −0.129910 + 0.110954i −0.00535287 + 0.00457178i
\(590\) 14.4461 + 9.73389i 0.594736 + 0.400738i
\(591\) −17.7080 + 1.39365i −0.728410 + 0.0573271i
\(592\) 10.1580 9.84734i 0.417489 0.404723i
\(593\) 2.34482 3.82639i 0.0962900 0.157131i −0.800868 0.598841i \(-0.795628\pi\)
0.897158 + 0.441710i \(0.145628\pi\)
\(594\) −1.06235 5.45128i −0.0435887 0.223669i
\(595\) 6.66082 42.0548i 0.273067 1.72408i
\(596\) −35.9751 + 5.41197i −1.47360 + 0.221683i
\(597\) −20.8162 + 28.6511i −0.851951 + 1.17261i
\(598\) 2.86769 + 6.28454i 0.117268 + 0.256994i
\(599\) −17.9450 + 13.0378i −0.733213 + 0.532710i −0.890578 0.454830i \(-0.849700\pi\)
0.157365 + 0.987540i \(0.449700\pi\)
\(600\) 16.0196 + 85.7422i 0.653998 + 3.50041i
\(601\) −8.78650 21.2125i −0.358409 0.865275i −0.995524 0.0945069i \(-0.969873\pi\)
0.637115 0.770768i \(-0.280127\pi\)
\(602\) −15.3554 + 19.3234i −0.625838 + 0.787565i
\(603\) 22.2193 + 1.74870i 0.904840 + 0.0712125i
\(604\) 18.3702 + 0.142608i 0.747474 + 0.00580262i
\(605\) 27.7054 + 9.00201i 1.12638 + 0.365984i
\(606\) 40.4080 + 18.8189i 1.64146 + 0.764465i
\(607\) 15.7435 8.02169i 0.639007 0.325590i −0.104295 0.994546i \(-0.533259\pi\)
0.743302 + 0.668956i \(0.233259\pi\)
\(608\) −0.0407775 0.0931672i −0.00165374 0.00377843i
\(609\) −8.66840 + 36.1065i −0.351261 + 1.46311i
\(610\) −1.21661 0.148786i −0.0492591 0.00602416i
\(611\) 0.677467 0.220123i 0.0274074 0.00890520i
\(612\) −3.48835 11.0266i −0.141008 0.445722i
\(613\) −5.42815 34.2720i −0.219241 1.38423i −0.814251 0.580513i \(-0.802852\pi\)
0.595010 0.803718i \(-0.297148\pi\)
\(614\) 20.1230 7.33515i 0.812098 0.296023i
\(615\) 24.1992 + 57.8327i 0.975808 + 2.33204i
\(616\) 10.7231 18.6351i 0.432047 0.750831i
\(617\) −33.1851 + 5.25601i −1.33598 + 0.211599i −0.783223 0.621741i \(-0.786426\pi\)
−0.552761 + 0.833340i \(0.686426\pi\)
\(618\) 9.85745 + 0.425626i 0.396525 + 0.0171212i
\(619\) −7.14784 21.9988i −0.287296 0.884206i −0.985701 0.168503i \(-0.946107\pi\)
0.698405 0.715702i \(-0.253893\pi\)
\(620\) −79.7954 + 18.5032i −3.20466 + 0.743108i
\(621\) −8.77529 2.10676i −0.352140 0.0845414i
\(622\) −24.3031 36.6795i −0.974464 1.47071i
\(623\) −5.28075 10.3641i −0.211569 0.415227i
\(624\) −5.39437 7.67244i −0.215948 0.307143i
\(625\) −28.2486 + 86.9404i −1.12995 + 3.47762i
\(626\) 7.50448 + 2.80169i 0.299939 + 0.111978i
\(627\) 0.00659883 0.0838461i 0.000263532 0.00334849i
\(628\) −32.7723 10.9303i −1.30776 0.436168i
\(629\) −8.74577 + 3.62262i −0.348717 + 0.144443i
\(630\) −42.3182 23.9156i −1.68600 0.952819i
\(631\) 21.1924 + 29.1688i 0.843656 + 1.16119i 0.985225 + 0.171265i \(0.0547853\pi\)
−0.141569 + 0.989928i \(0.545215\pi\)
\(632\) −2.56490 + 5.39749i −0.102026 + 0.214701i
\(633\) −47.1306 34.2424i −1.87327 1.36101i
\(634\) −1.83380 + 9.03569i −0.0728294 + 0.358853i
\(635\) −25.7829 4.08360i −1.02316 0.162053i
\(636\) 1.46220 + 2.42821i 0.0579801 + 0.0962848i
\(637\) 5.83029 + 3.57281i 0.231004 + 0.141560i
\(638\) −12.3990 3.54889i −0.490881 0.140502i
\(639\) 0.343618 + 4.36609i 0.0135933 + 0.172720i
\(640\) 3.23730 48.6536i 0.127965 1.92320i
\(641\) 24.3122 + 28.4659i 0.960273 + 1.12433i 0.992176 + 0.124844i \(0.0398430\pi\)
−0.0319038 + 0.999491i \(0.510157\pi\)
\(642\) −26.1718 28.5339i −1.03292 1.12614i
\(643\) −3.97213 6.48193i −0.156646 0.255623i 0.764683 0.644406i \(-0.222895\pi\)
−0.921329 + 0.388784i \(0.872895\pi\)
\(644\) −20.3151 28.4227i −0.800525 1.12001i
\(645\) −30.0645 + 35.2010i −1.18379 + 1.38604i
\(646\) 0.00240765 + 0.0680065i 9.47278e−5 + 0.00267568i
\(647\) 7.27507 + 7.27507i 0.286012 + 0.286012i 0.835501 0.549489i \(-0.185177\pi\)
−0.549489 + 0.835501i \(0.685177\pi\)
\(648\) 30.5461 + 1.55657i 1.19996 + 0.0611480i
\(649\) −1.37393 5.72285i −0.0539316 0.224641i
\(650\) −2.25273 19.6876i −0.0883592 0.772210i
\(651\) 36.1753 70.9980i 1.41782 2.78263i
\(652\) −2.74738 + 4.40617i −0.107596 + 0.172559i
\(653\) −16.1999 + 39.1099i −0.633949 + 1.53049i 0.200668 + 0.979659i \(0.435689\pi\)
−0.834618 + 0.550830i \(0.814311\pi\)
\(654\) 31.8550 17.6776i 1.24563 0.691248i
\(655\) 56.1607 2.19438
\(656\) −3.70467 25.3432i −0.144643 0.989484i
\(657\) −10.2054 −0.398152
\(658\) −3.15005 + 1.74808i −0.122802 + 0.0681474i
\(659\) 9.96689 24.0622i 0.388255 0.937330i −0.602055 0.798455i \(-0.705651\pi\)
0.990310 0.138876i \(-0.0443488\pi\)
\(660\) 21.3361 34.2183i 0.830507 1.33194i
\(661\) 11.5705 22.7084i 0.450040 0.883254i −0.548839 0.835928i \(-0.684930\pi\)
0.998879 0.0473260i \(-0.0150700\pi\)
\(662\) −0.0161664 0.141285i −0.000628326 0.00549122i
\(663\) 1.46502 + 6.10223i 0.0568965 + 0.236991i
\(664\) −42.0331 2.14193i −1.63120 0.0831230i
\(665\) 0.202240 + 0.202240i 0.00784252 + 0.00784252i
\(666\) 0.382359 + 10.8001i 0.0148161 + 0.418495i
\(667\) −13.6103 + 15.9356i −0.526992 + 0.617028i
\(668\) −15.1322 21.1714i −0.585484 0.819147i
\(669\) 21.6108 + 35.2656i 0.835522 + 1.36345i
\(670\) −42.5016 46.3375i −1.64198 1.79017i
\(671\) 0.268946 + 0.314895i 0.0103825 + 0.0121564i
\(672\) 34.2003 + 32.8680i 1.31931 + 1.26791i
\(673\) 0.826021 + 10.4956i 0.0318408 + 0.404575i 0.992099 + 0.125461i \(0.0400409\pi\)
−0.960258 + 0.279114i \(0.909959\pi\)
\(674\) −5.68126 1.62611i −0.218834 0.0626355i
\(675\) 22.0733 + 13.5265i 0.849600 + 0.520636i
\(676\) −12.3133 20.4481i −0.473588 0.786465i
\(677\) 16.2895 + 2.58000i 0.626056 + 0.0991576i 0.461398 0.887193i \(-0.347348\pi\)
0.164658 + 0.986351i \(0.447348\pi\)
\(678\) −2.99658 + 14.7651i −0.115083 + 0.567050i
\(679\) 8.49634 + 6.17295i 0.326060 + 0.236896i
\(680\) −14.0036 + 29.4688i −0.537014 + 1.13008i
\(681\) 16.8788 + 23.2317i 0.646796 + 0.890239i
\(682\) 24.0941 + 13.6165i 0.922612 + 0.521402i
\(683\) −22.5799 + 9.35290i −0.863996 + 0.357879i −0.770269 0.637719i \(-0.779878\pi\)
−0.0937270 + 0.995598i \(0.529878\pi\)
\(684\) 0.0736945 + 0.0245789i 0.00281778 + 0.000939798i
\(685\) −0.621446 + 7.89622i −0.0237442 + 0.301699i
\(686\) 1.83470 + 0.684958i 0.0700492 + 0.0261518i
\(687\) −15.1907 + 46.7520i −0.579560 + 1.78370i
\(688\) 15.4714 10.8777i 0.589842 0.414709i
\(689\) −0.292342 0.573753i −0.0111373 0.0218582i
\(690\) −36.1925 54.6238i −1.37783 2.07949i
\(691\) −40.3328 9.68306i −1.53433 0.368361i −0.623729 0.781640i \(-0.714383\pi\)
−0.910604 + 0.413280i \(0.864383\pi\)
\(692\) −19.7732 + 4.58507i −0.751663 + 0.174298i
\(693\) 5.07504 + 15.6194i 0.192785 + 0.593331i
\(694\) −15.6215 0.674505i −0.592983 0.0256039i
\(695\) −23.9329 + 3.79059i −0.907825 + 0.143785i
\(696\) 14.1910 24.6618i 0.537909 0.934805i
\(697\) −3.94073 + 16.6785i −0.149266 + 0.631742i
\(698\) 3.80017 1.38522i 0.143839 0.0524315i
\(699\) 2.78254 + 17.5683i 0.105245 + 0.664493i
\(700\) 30.2284 + 95.5511i 1.14253 + 3.61149i
\(701\) 25.4960 8.28415i 0.962970 0.312888i 0.214995 0.976615i \(-0.431026\pi\)
0.747975 + 0.663727i \(0.231026\pi\)
\(702\) −2.76305 0.337908i −0.104284 0.0127535i
\(703\) 0.0148441 0.0618302i 0.000559856 0.00233197i
\(704\) −11.9175 + 11.3750i −0.449159 + 0.428711i
\(705\) −6.02047 + 3.06758i −0.226744 + 0.115532i
\(706\) −26.5604 12.3698i −0.999615 0.465542i
\(707\) 48.7084 + 15.8263i 1.83187 + 0.595210i
\(708\) 12.9842 + 0.100796i 0.487976 + 0.00378815i
\(709\) −3.01604 0.237368i −0.113270 0.00891453i 0.0216975 0.999765i \(-0.493093\pi\)
−0.134967 + 0.990850i \(0.543093\pi\)
\(710\) 7.68673 9.67310i 0.288478 0.363025i
\(711\) −1.74687 4.21732i −0.0655128 0.158162i
\(712\) 1.63695 + 8.76149i 0.0613473 + 0.328351i
\(713\) 36.3824 26.4334i 1.36253 0.989937i
\(714\) −13.1757 28.8746i −0.493089 1.08061i
\(715\) −5.38476 + 7.41149i −0.201379 + 0.277174i
\(716\) 24.2658 3.65046i 0.906854 0.136424i
\(717\) 7.73589 48.8425i 0.288902 1.82406i
\(718\) −0.321573 1.65010i −0.0120010 0.0615813i
\(719\) 25.6223 41.8119i 0.955552 1.55932i 0.132629 0.991166i \(-0.457658\pi\)
0.822923 0.568153i \(-0.192342\pi\)
\(720\) 25.9255 + 26.7433i 0.966188 + 0.996665i
\(721\) 11.3014 0.889438i 0.420885 0.0331244i
\(722\) 22.2831 + 15.0146i 0.829293 + 0.558784i
\(723\) 3.84946 3.28775i 0.143163 0.122273i
\(724\) 22.5175 + 11.6943i 0.836858 + 0.434616i
\(725\) 51.2577 31.4108i 1.90366 1.16657i
\(726\) 20.9220 5.81304i 0.776488 0.215742i
\(727\) −7.19476 6.14491i −0.266839 0.227902i 0.505954 0.862561i \(-0.331141\pi\)
−0.772793 + 0.634659i \(0.781141\pi\)
\(728\) −7.22216 7.99773i −0.267671 0.296416i
\(729\) −7.33071 + 7.33071i −0.271508 + 0.271508i
\(730\) 21.0657 + 19.6251i 0.779676 + 0.726357i
\(731\) −12.3051 + 2.95419i −0.455121 + 0.109265i
\(732\) −0.817242 + 0.408446i −0.0302061 + 0.0150966i
\(733\) −12.3525 6.29391i −0.456250 0.232471i 0.210733 0.977544i \(-0.432415\pi\)
−0.666983 + 0.745073i \(0.732415\pi\)
\(734\) 21.9680 17.1804i 0.810855 0.634139i
\(735\) −59.9249 24.8217i −2.21036 0.915562i
\(736\) 8.77660 + 25.2910i 0.323510 + 0.932237i
\(737\) 21.2441i 0.782537i
\(738\) 16.2642 + 10.8741i 0.598694 + 0.400280i
\(739\) 23.1456i 0.851425i 0.904859 + 0.425712i \(0.139976\pi\)
−0.904859 + 0.425712i \(0.860024\pi\)
\(740\) 19.9794 23.0285i 0.734457 0.846543i
\(741\) −0.0389456 0.0161318i −0.00143070 0.000592617i
\(742\) 2.00625 + 2.56534i 0.0736518 + 0.0941765i
\(743\) 1.48566 + 0.756984i 0.0545038 + 0.0277711i 0.481030 0.876704i \(-0.340263\pi\)
−0.426526 + 0.904475i \(0.640263\pi\)
\(744\) −41.9656 + 44.3508i −1.53854 + 1.62598i
\(745\) −76.2312 + 18.3015i −2.79289 + 0.670514i
\(746\) 20.7788 22.3040i 0.760765 0.816609i
\(747\) 22.7330 22.7330i 0.831757 0.831757i
\(748\) 10.2168 4.13933i 0.373565 0.151349i
\(749\) −33.8276 28.8915i −1.23603 1.05567i
\(750\) 31.7862 + 114.403i 1.16067 + 4.17742i
\(751\) −19.8253 + 12.1490i −0.723436 + 0.443322i −0.834868 0.550450i \(-0.814456\pi\)
0.111432 + 0.993772i \(0.464456\pi\)
\(752\) 2.69394 0.602683i 0.0982379 0.0219776i
\(753\) 27.9809 23.8980i 1.01968 0.870890i
\(754\) −3.61207 + 5.36068i −0.131544 + 0.195224i
\(755\) 39.4663 3.10606i 1.43632 0.113041i
\(756\) 14.0428 0.995573i 0.510733 0.0362086i
\(757\) 8.84942 14.4409i 0.321638 0.524865i −0.650430 0.759566i \(-0.725411\pi\)
0.972068 + 0.234701i \(0.0754112\pi\)
\(758\) 52.9391 10.3168i 1.92283 0.374723i
\(759\) −3.46331 + 21.8665i −0.125710 + 0.793703i
\(760\) −0.104852 0.192450i −0.00380340 0.00698090i
\(761\) −31.6751 + 43.5970i −1.14822 + 1.58039i −0.400619 + 0.916245i \(0.631205\pi\)
−0.747602 + 0.664147i \(0.768795\pi\)
\(762\) −17.7024 + 8.07775i −0.641290 + 0.292626i
\(763\) 33.8638 24.6035i 1.22595 0.890705i
\(764\) 1.69415 10.1841i 0.0612922 0.368449i
\(765\) −9.53743 23.0254i −0.344827 0.832485i
\(766\) 22.5200 + 17.8955i 0.813681 + 0.646591i
\(767\) −2.94076 0.231443i −0.106185 0.00835691i
\(768\) −18.0199 31.5655i −0.650237 1.13902i
\(769\) 20.9032 + 6.79188i 0.753790 + 0.244921i 0.660611 0.750728i \(-0.270297\pi\)
0.0931789 + 0.995649i \(0.470297\pi\)
\(770\) 19.5604 42.0003i 0.704909 1.51359i
\(771\) 22.6255 11.5283i 0.814836 0.415180i
\(772\) 16.0858 + 11.8789i 0.578940 + 0.427530i
\(773\) −10.0460 + 41.8447i −0.361330 + 1.50505i 0.435136 + 0.900365i \(0.356700\pi\)
−0.796466 + 0.604683i \(0.793300\pi\)
\(774\) −1.75371 + 14.3399i −0.0630356 + 0.515438i
\(775\) −122.690 + 39.8645i −4.40717 + 1.43198i
\(776\) −4.90815 6.37731i −0.176192 0.228932i
\(777\) 4.63947 + 29.2924i 0.166440 + 1.05086i
\(778\) −6.13328 16.8258i −0.219889 0.603234i
\(779\) −0.0750769 0.0872659i −0.00268991 0.00312663i
\(780\) −13.0065 15.4703i −0.465708 0.553925i
\(781\) −4.12307 + 0.653030i −0.147535 + 0.0233672i
\(782\) 0.772711 17.8959i 0.0276321 0.639955i
\(783\) −2.60958 8.03147i −0.0932588 0.287021i
\(784\) 21.1940 + 15.9069i 0.756930 + 0.568103i
\(785\) −72.3904 17.3794i −2.58372 0.620297i
\(786\) 34.8974 23.1223i 1.24475 0.824745i
\(787\) 17.0371 + 33.4371i 0.607305 + 1.19190i 0.966023 + 0.258457i \(0.0832142\pi\)
−0.358717 + 0.933446i \(0.616786\pi\)
\(788\) 15.5802 + 1.34796i 0.555023 + 0.0480192i
\(789\) 8.52512 26.2376i 0.303502 0.934084i
\(790\) −4.50411 + 12.0645i −0.160249 + 0.429236i
\(791\) −1.35815 + 17.2569i −0.0482902 + 0.613585i
\(792\) −0.347612 12.5797i −0.0123518 0.447001i
\(793\) 0.191759 0.0794291i 0.00680956 0.00282061i
\(794\) −26.5330 + 46.9498i −0.941622 + 1.66619i
\(795\) 3.59030 + 4.94162i 0.127335 + 0.175261i
\(796\) 22.2175 21.8752i 0.787479 0.775347i
\(797\) 40.2404 + 29.2364i 1.42539 + 1.03560i 0.990852 + 0.134950i \(0.0430874\pi\)
0.434535 + 0.900655i \(0.356913\pi\)
\(798\) 0.208935 + 0.0424034i 0.00739620 + 0.00150106i
\(799\) −1.82437 0.288952i −0.0645417 0.0102224i
\(800\) −1.52525 76.7789i −0.0539257 2.71454i
\(801\) −5.80512 3.55738i −0.205114 0.125694i
\(802\) 5.83181 20.3750i 0.205928 0.719466i
\(803\) −0.763206 9.69745i −0.0269330 0.342216i
\(804\) −45.4878 11.2948i −1.60423 0.398338i
\(805\) −48.8946 57.2483i −1.72331 2.01774i
\(806\) 10.2224 9.37621i 0.360070 0.330263i
\(807\) −19.9962 32.6308i −0.703899 1.14866i
\(808\) −32.3744 22.1815i −1.13893 0.780341i
\(809\) 30.6215 35.8532i 1.07660 1.26053i 0.112878 0.993609i \(-0.463993\pi\)
0.963718 0.266923i \(-0.0860069\pi\)
\(810\) 65.8697 2.33200i 2.31443 0.0819383i
\(811\) 13.5831 + 13.5831i 0.476968 + 0.476968i 0.904161 0.427193i \(-0.140497\pi\)
−0.427193 + 0.904161i \(0.640497\pi\)
\(812\) 12.7446 30.1051i 0.447248 1.05648i
\(813\) 14.5316 + 60.5283i 0.509644 + 2.12282i
\(814\) −10.2339 + 1.17100i −0.358699 + 0.0410437i
\(815\) −5.08002 + 9.97011i −0.177945 + 0.349238i
\(816\) 3.43114 + 24.0770i 0.120114 + 0.842864i
\(817\) 0.0325297 0.0785335i 0.00113807 0.00274754i
\(818\) −11.4047 20.5513i −0.398756 0.718559i
\(819\) 8.23146 0.287630
\(820\) −12.6611 53.7221i −0.442146 1.87606i
\(821\) 14.1767 0.494770 0.247385 0.968917i \(-0.420429\pi\)
0.247385 + 0.968917i \(0.420429\pi\)
\(822\) 2.86485 + 5.16246i 0.0999231 + 0.180061i
\(823\) 14.4702 34.9342i 0.504400 1.21773i −0.442665 0.896687i \(-0.645967\pi\)
0.947065 0.321042i \(-0.104033\pi\)
\(824\) −8.49941 1.79377i −0.296091 0.0624888i
\(825\) 28.8321 56.5862i 1.00381 1.97008i
\(826\) 14.8220 1.69599i 0.515724 0.0590111i
\(827\) 2.50888 + 10.4502i 0.0872422 + 0.363390i 0.998865 0.0476388i \(-0.0151696\pi\)
−0.911622 + 0.411029i \(0.865170\pi\)
\(828\) −18.8312 7.97195i −0.654429 0.277044i
\(829\) −19.3019 19.3019i −0.670382 0.670382i 0.287422 0.957804i \(-0.407202\pi\)
−0.957804 + 0.287422i \(0.907202\pi\)
\(830\) −90.6404 + 3.20897i −3.14617 + 0.111385i
\(831\) 40.3360 47.2274i 1.39924 1.63830i
\(832\) 3.57640 + 7.44262i 0.123989 + 0.258027i
\(833\) −9.26448 15.1183i −0.320995 0.523817i
\(834\) −13.3109 + 12.2090i −0.460919 + 0.422763i
\(835\) −36.4206 42.6430i −1.26039 1.47572i
\(836\) −0.0178443 + 0.0718645i −0.000617158 + 0.00248549i
\(837\) 1.42181 + 18.0659i 0.0491451 + 0.624448i
\(838\) −3.40363 + 11.8915i −0.117576 + 0.410784i
\(839\) −43.6140 26.7267i −1.50572 0.922709i −0.998131 0.0611117i \(-0.980535\pi\)
−0.507593 0.861597i \(-0.669465\pi\)
\(840\) 79.5312 + 64.2129i 2.74409 + 2.21556i
\(841\) 9.27424 + 1.46889i 0.319801 + 0.0506515i
\(842\) −0.877744 0.178139i −0.0302491 0.00613906i
\(843\) −47.5790 34.5681i −1.63871 1.19059i
\(844\) 35.9844 + 36.5475i 1.23864 + 1.25802i
\(845\) −30.2341 41.6137i −1.04008 1.43155i
\(846\) −1.03748 + 1.83580i −0.0356692 + 0.0631161i
\(847\) 23.0499 9.54759i 0.792004 0.328059i
\(848\) −0.919073 2.32008i −0.0315611 0.0796717i
\(849\) −3.32916 + 42.3010i −0.114257 + 1.45177i
\(850\) −17.9719 + 48.1387i −0.616430 + 1.65114i
\(851\) −5.17233 + 15.9188i −0.177305 + 0.545690i
\(852\) 0.793841 9.17549i 0.0271965 0.314347i
\(853\) 2.41421 + 4.73816i 0.0826611 + 0.162232i 0.928637 0.370989i \(-0.120981\pi\)
−0.845976 + 0.533221i \(0.820981\pi\)
\(854\) −0.875064 + 0.579799i −0.0299441 + 0.0198403i
\(855\) 0.162783 + 0.0390808i 0.00556707 + 0.00133653i
\(856\) 18.6071 + 28.5619i 0.635977 + 0.976226i
\(857\) −4.07561 12.5434i −0.139220 0.428476i 0.857002 0.515313i \(-0.172324\pi\)
−0.996223 + 0.0868366i \(0.972324\pi\)
\(858\) −0.294578 + 6.82239i −0.0100567 + 0.232913i
\(859\) 45.4393 7.19688i 1.55037 0.245554i 0.678244 0.734837i \(-0.262741\pi\)
0.872125 + 0.489283i \(0.162741\pi\)
\(860\) 31.1957 26.2276i 1.06376 0.894353i
\(861\) 47.9268 + 24.2031i 1.63334 + 0.824840i
\(862\) −8.29559 22.7578i −0.282549 0.775134i
\(863\) −0.293954 1.85595i −0.0100063 0.0631773i 0.982180 0.187943i \(-0.0601820\pi\)
−0.992186 + 0.124766i \(0.960182\pi\)
\(864\) −10.5374 2.30947i −0.358491 0.0785698i
\(865\) −41.6001 + 13.5167i −1.41445 + 0.459581i
\(866\) −4.03808 + 33.0191i −0.137220 + 1.12203i
\(867\) −5.21647 + 21.7281i −0.177160 + 0.737926i
\(868\) −41.6743 + 56.4333i −1.41452 + 1.91547i
\(869\) 3.87677 1.97531i 0.131510 0.0670079i
\(870\) 25.8864 55.5834i 0.877631 1.88446i
\(871\) 10.1266 + 3.29034i 0.343127 + 0.111489i
\(872\) −30.2190 + 10.7503i −1.02335 + 0.364052i
\(873\) 6.12816 + 0.482296i 0.207407 + 0.0163233i
\(874\) 0.0942008 + 0.0748566i 0.00318639 + 0.00253206i
\(875\) 52.2070 + 126.039i 1.76492 + 4.26089i
\(876\) 21.1699 + 3.52166i 0.715265 + 0.118986i
\(877\) 7.56470 5.49608i 0.255442 0.185589i −0.452693 0.891666i \(-0.649537\pi\)
0.708135 + 0.706077i \(0.249537\pi\)
\(878\) 7.78137 3.55071i 0.262609 0.119831i
\(879\) −24.4369 + 33.6345i −0.824237 + 1.13446i
\(880\) −23.4734 + 26.6351i −0.791287 + 0.897868i
\(881\) −4.87723 + 30.7936i −0.164318 + 1.03746i 0.758345 + 0.651854i \(0.226009\pi\)
−0.922662 + 0.385609i \(0.873991\pi\)
\(882\) −19.8682 + 3.87192i −0.668997 + 0.130374i
\(883\) 10.4586 17.0670i 0.351961 0.574349i −0.626843 0.779145i \(-0.715653\pi\)
0.978805 + 0.204797i \(0.0656533\pi\)
\(884\) −0.390723 5.51126i −0.0131414 0.185364i
\(885\) 27.8950 2.19539i 0.937681 0.0737971i
\(886\) −4.36419 + 6.47691i −0.146618 + 0.217596i
\(887\) −22.5997 + 19.3020i −0.758825 + 0.648098i −0.942240 0.334938i \(-0.891285\pi\)
0.183415 + 0.983036i \(0.441285\pi\)
\(888\) 2.93371 22.5354i 0.0984487 0.756239i
\(889\) −19.0622 + 11.6813i −0.639327 + 0.391780i
\(890\) 5.14186 + 18.5063i 0.172356 + 0.620333i
\(891\) −16.9336 14.4626i −0.567296 0.484517i
\(892\) −13.6735 33.7493i −0.457821 1.13001i
\(893\) 0.00877334 0.00877334i 0.000293589 0.000293589i
\(894\) −39.8339 + 42.7580i −1.33225 + 1.43004i
\(895\) 51.4191 12.3446i 1.71875 0.412635i
\(896\) −24.9535 33.4859i −0.833637 1.11868i
\(897\) 9.88688 + 5.03762i 0.330113 + 0.168201i
\(898\) 4.98187 + 6.37017i 0.166247 + 0.212575i
\(899\) 38.8783 + 16.1039i 1.29667 + 0.537096i
\(900\) 44.3086 + 38.4420i 1.47695 + 1.28140i
\(901\) 1.66977i 0.0556280i
\(902\) −9.11650 + 16.2679i −0.303546 + 0.541661i
\(903\) 39.6466i 1.31936i
\(904\) 4.73558 12.3901i 0.157503 0.412089i
\(905\) 50.5160 + 20.9244i 1.67921 + 0.695551i
\(906\) 23.2450 18.1790i 0.772262 0.603957i
\(907\) 22.8468 + 11.6410i 0.758614 + 0.386533i 0.790106 0.612971i \(-0.210026\pi\)
−0.0314913 + 0.999504i \(0.510026\pi\)
\(908\) −11.3024 22.6145i −0.375083 0.750489i
\(909\) 29.1491 6.99809i 0.966816 0.232112i
\(910\) −16.9911 15.8291i −0.563249 0.524731i
\(911\) −10.0980 + 10.0980i −0.334562 + 0.334562i −0.854316 0.519754i \(-0.826024\pi\)
0.519754 + 0.854316i \(0.326024\pi\)
\(912\) −0.144389 0.0764162i −0.00478119 0.00253039i
\(913\) 23.3015 + 19.9014i 0.771168 + 0.658640i
\(914\) 33.5145 9.31180i 1.10856 0.308007i
\(915\) −1.67870 + 1.02871i −0.0554962 + 0.0340081i
\(916\) 19.9470 38.4081i 0.659067 1.26904i
\(917\) 36.5742 31.2373i 1.20779 1.03155i
\(918\) 5.98603 + 4.03343i 0.197568 + 0.133123i
\(919\) −47.5244 + 3.74025i −1.56769 + 0.123380i −0.832322 0.554293i \(-0.812989\pi\)
−0.735364 + 0.677672i \(0.762989\pi\)
\(920\) 23.5406 + 52.6679i 0.776109 + 1.73641i
\(921\) 17.9763 29.3347i 0.592339 0.966610i
\(922\) 5.48315 + 28.1360i 0.180578 + 0.926608i
\(923\) −0.327305 + 2.06652i −0.0107734 + 0.0680204i
\(924\) −5.13767 34.1518i −0.169017 1.12351i
\(925\) 28.2224 38.8448i 0.927946 1.27721i
\(926\) −1.22050 2.67473i −0.0401081 0.0878970i
\(927\) 5.36817 3.90020i 0.176314 0.128099i
\(928\) −15.8874 + 19.3679i −0.521530 + 0.635782i
\(929\) −12.5384 30.2704i −0.411372 0.993140i −0.984770 0.173863i \(-0.944375\pi\)
0.573398 0.819277i \(-0.305625\pi\)
\(930\) −81.8596 + 103.014i −2.68428 + 3.37795i
\(931\) 0.118736 + 0.00934470i 0.00389140 + 0.000306260i
\(932\) 0.121565 15.6595i 0.00398198 0.512945i
\(933\) −67.2194 21.8409i −2.20066 0.715039i
\(934\) −24.9946 11.6405i −0.817848 0.380889i
\(935\) 21.1661 10.7846i 0.692204 0.352696i
\(936\) −6.05032 1.78268i −0.197761 0.0582686i
\(937\) 2.72851 11.3651i 0.0891365 0.371280i −0.909916 0.414792i \(-0.863854\pi\)
0.999053 + 0.0435113i \(0.0138545\pi\)
\(938\) −53.4523 6.53697i −1.74528 0.213440i
\(939\) 12.2375 3.97621i 0.399357 0.129759i
\(940\) 5.67178 1.79432i 0.184993 0.0585242i
\(941\) 3.90593 + 24.6611i 0.127330 + 0.803928i 0.965858 + 0.259071i \(0.0834163\pi\)
−0.838529 + 0.544858i \(0.816584\pi\)
\(942\) −52.1378 + 19.0051i −1.69874 + 0.619218i
\(943\) 17.8993 + 24.4507i 0.582880 + 0.796225i
\(944\) −11.2618 1.96339i −0.366542 0.0639029i
\(945\) 29.9642 4.74586i 0.974736 0.154383i
\(946\) −13.7573 0.594014i −0.447288 0.0193131i
\(947\) −15.9068 48.9561i −0.516902 1.59086i −0.779795 0.626035i \(-0.784677\pi\)
0.262893 0.964825i \(-0.415323\pi\)
\(948\) 2.16837 + 9.35113i 0.0704255 + 0.303711i
\(949\) −4.74078 1.13816i −0.153892 0.0369462i
\(950\) −0.190643 0.287728i −0.00618526 0.00933514i
\(951\) 6.72366 + 13.1959i 0.218030 + 0.427907i
\(952\) 7.27117 + 26.9803i 0.235660 + 0.874436i
\(953\) 11.1507 34.3183i 0.361207 1.11168i −0.591116 0.806587i \(-0.701312\pi\)
0.952322 0.305093i \(-0.0986877\pi\)
\(954\) 1.78582 + 0.666711i 0.0578181 + 0.0215856i
\(955\) 1.74556 22.1794i 0.0564849 0.717709i
\(956\) −13.7747 + 41.3006i −0.445507 + 1.33576i
\(957\) −19.1396 + 7.92788i −0.618696 + 0.256272i
\(958\) 6.75844 + 3.81944i 0.218355 + 0.123401i
\(959\) 3.98727 + 5.48800i 0.128756 + 0.177217i
\(960\) −44.5509 64.4221i −1.43787 2.07921i
\(961\) −47.9774 34.8576i −1.54766 1.12444i
\(962\) −1.02686 + 5.05966i −0.0331073 + 0.163130i
\(963\) −25.7183 4.07337i −0.828759 0.131263i
\(964\) −3.81813 + 2.29918i −0.122974 + 0.0740515i
\(965\) 36.7417 + 22.5153i 1.18276 + 0.724794i
\(966\) −53.9525 15.4425i −1.73589 0.496854i
\(967\) −3.06057 38.8882i −0.0984212 1.25056i −0.825657 0.564173i \(-0.809195\pi\)
0.727236 0.686388i \(-0.240805\pi\)
\(968\) −19.0100 + 2.02582i −0.611003 + 0.0651123i
\(969\) 0.0709904 + 0.0831190i 0.00228054 + 0.00267017i
\(970\) −11.7221 12.7800i −0.376373 0.410342i
\(971\) −5.17664 8.44750i −0.166126 0.271093i 0.758734 0.651401i \(-0.225818\pi\)
−0.924860 + 0.380307i \(0.875818\pi\)
\(972\) 30.6618 21.9154i 0.983476 0.702938i
\(973\) −13.4777 + 15.7804i −0.432075 + 0.505895i
\(974\) −1.32013 37.2885i −0.0422998 1.19480i
\(975\) −22.5079 22.5079i −0.720828 0.720828i
\(976\) 0.768760 0.236655i 0.0246074 0.00757513i
\(977\) 4.59519 + 19.1403i 0.147013 + 0.612354i 0.996414 + 0.0846062i \(0.0269632\pi\)
−0.849401 + 0.527747i \(0.823037\pi\)
\(978\) 0.948209 + 8.28682i 0.0303204 + 0.264983i
\(979\) 2.94618 5.78221i 0.0941604 0.184800i
\(980\) 48.4570 + 30.2144i 1.54790 + 0.965163i
\(981\) 9.37592 22.6355i 0.299350 0.722695i
\(982\) 34.5917 19.1963i 1.10386 0.612577i
\(983\) −18.4369 −0.588047 −0.294024 0.955798i \(-0.594994\pi\)
−0.294024 + 0.955798i \(0.594994\pi\)
\(984\) −29.9858 28.1693i −0.955911 0.898006i
\(985\) 33.7002 1.07378
\(986\) 14.6561 8.13326i 0.466746 0.259016i
\(987\) −2.21455 + 5.34640i −0.0704900 + 0.170178i
\(988\) 0.0314925 + 0.0196365i 0.00100191 + 0.000624721i
\(989\) −10.1583 + 19.9368i −0.323016 + 0.633954i
\(990\) −3.08296 26.9433i −0.0979828 0.856315i
\(991\) 7.14384 + 29.7562i 0.226931 + 0.945237i 0.963251 + 0.268603i \(0.0865621\pi\)
−0.736319 + 0.676634i \(0.763438\pi\)
\(992\) 42.8534 32.4545i 1.36060 1.03043i
\(993\) −0.161525 0.161525i −0.00512584 0.00512584i
\(994\) −0.374389 10.5750i −0.0118749 0.335418i
\(995\) 43.6364 51.0917i 1.38337 1.61971i
\(996\) −55.0015 + 39.3122i −1.74279 + 1.24565i
\(997\) 0.578235 + 0.943594i 0.0183129 + 0.0298839i 0.861666 0.507476i \(-0.169422\pi\)
−0.843353 + 0.537360i \(0.819422\pi\)
\(998\) 20.7273 + 22.5980i 0.656112 + 0.715328i
\(999\) −4.38041 5.12880i −0.138590 0.162268i
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 164.2.o.b.11.3 yes 288
4.3 odd 2 inner 164.2.o.b.11.1 288
41.15 odd 40 inner 164.2.o.b.15.1 yes 288
164.15 even 40 inner 164.2.o.b.15.3 yes 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
164.2.o.b.11.1 288 4.3 odd 2 inner
164.2.o.b.11.3 yes 288 1.1 even 1 trivial
164.2.o.b.15.1 yes 288 41.15 odd 40 inner
164.2.o.b.15.3 yes 288 164.15 even 40 inner