Properties

Label 96.2.o.a.35.9
Level $96$
Weight $2$
Character 96.35
Analytic conductor $0.767$
Analytic rank $0$
Dimension $56$
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] = [96,2,Mod(11,96)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(96, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("96.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 96.o (of order \(8\), degree \(4\), 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: \(0.766563859404\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 35.9
Character \(\chi\) \(=\) 96.35
Dual form 96.2.o.a.11.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.478581 - 1.33077i) q^{2} +(0.0499748 - 1.73133i) q^{3} +(-1.54192 - 1.27377i) q^{4} +(-1.06973 + 0.443098i) q^{5} +(-2.28009 - 0.895086i) q^{6} +(2.37247 + 2.37247i) q^{7} +(-2.43303 + 1.44235i) q^{8} +(-2.99501 - 0.173046i) q^{9} +O(q^{10})\) \(q+(0.478581 - 1.33077i) q^{2} +(0.0499748 - 1.73133i) q^{3} +(-1.54192 - 1.27377i) q^{4} +(-1.06973 + 0.443098i) q^{5} +(-2.28009 - 0.895086i) q^{6} +(2.37247 + 2.37247i) q^{7} +(-2.43303 + 1.44235i) q^{8} +(-2.99501 - 0.173046i) q^{9} +(0.0777099 + 1.63563i) q^{10} +(5.50127 - 2.27870i) q^{11} +(-2.28237 + 2.60592i) q^{12} +(0.346353 - 0.836171i) q^{13} +(4.29263 - 2.02180i) q^{14} +(0.713689 + 1.87421i) q^{15} +(0.755041 + 3.92809i) q^{16} -0.685064 q^{17} +(-1.66364 + 3.90286i) q^{18} +(-3.35074 - 1.38792i) q^{19} +(2.21385 + 0.679368i) q^{20} +(4.22609 - 3.98896i) q^{21} +(-0.399635 - 8.41149i) q^{22} +(2.05133 + 2.05133i) q^{23} +(2.37559 + 4.28446i) q^{24} +(-2.58754 + 2.58754i) q^{25} +(-0.946997 - 0.861094i) q^{26} +(-0.449274 + 5.17669i) q^{27} +(-0.636189 - 6.68012i) q^{28} +(-1.98869 + 4.80112i) q^{29} +(2.83570 - 0.0528009i) q^{30} +6.36503i q^{31} +(5.58875 + 0.875120i) q^{32} +(-3.67025 - 9.63838i) q^{33} +(-0.327858 + 0.911666i) q^{34} +(-3.58914 - 1.48667i) q^{35} +(4.39764 + 4.08176i) q^{36} +(0.112738 + 0.272172i) q^{37} +(-3.45061 + 3.79484i) q^{38} +(-1.43038 - 0.641440i) q^{39} +(1.96359 - 2.62100i) q^{40} +(-3.26585 + 3.26585i) q^{41} +(-3.28588 - 7.53300i) q^{42} +(-0.993018 - 2.39736i) q^{43} +(-11.3850 - 3.49375i) q^{44} +(3.28053 - 1.14197i) q^{45} +(3.71159 - 1.74813i) q^{46} -11.7975i q^{47} +(6.83856 - 1.11092i) q^{48} +4.25719i q^{49} +(2.20508 + 4.68178i) q^{50} +(-0.0342360 + 1.18607i) q^{51} +(-1.59914 + 0.848137i) q^{52} +(-1.56192 - 3.77080i) q^{53} +(6.67400 + 3.07535i) q^{54} +(-4.87520 + 4.87520i) q^{55} +(-9.19420 - 2.35035i) q^{56} +(-2.57040 + 5.73187i) q^{57} +(5.43746 + 4.94422i) q^{58} +(-2.20815 - 5.33094i) q^{59} +(1.28685 - 3.79895i) q^{60} +(-1.53549 - 0.636020i) q^{61} +(8.47042 + 3.04618i) q^{62} +(-6.69500 - 7.51609i) q^{63} +(3.83926 - 7.01855i) q^{64} +1.04795i q^{65} +(-14.5830 + 0.271537i) q^{66} +(4.69605 - 11.3373i) q^{67} +(1.05631 + 0.872611i) q^{68} +(3.65405 - 3.44902i) q^{69} +(-3.69612 + 4.06485i) q^{70} +(-7.99150 + 7.99150i) q^{71} +(7.53653 - 3.89882i) q^{72} +(-2.34760 - 2.34760i) q^{73} +(0.416154 - 0.0197717i) q^{74} +(4.35057 + 4.60920i) q^{75} +(3.39869 + 6.40812i) q^{76} +(18.4577 + 7.64543i) q^{77} +(-1.53816 + 1.59653i) q^{78} +8.91043 q^{79} +(-2.54822 - 3.86746i) q^{80} +(8.94011 + 1.03655i) q^{81} +(2.78314 + 5.90908i) q^{82} +(-3.06920 + 7.40970i) q^{83} +(-11.5973 + 0.767615i) q^{84} +(0.732836 - 0.303551i) q^{85} +(-3.66558 + 0.174154i) q^{86} +(8.21294 + 3.68301i) q^{87} +(-10.0981 + 13.4789i) q^{88} +(-1.99332 - 1.99332i) q^{89} +(0.0502980 - 4.91218i) q^{90} +(2.80550 - 1.16208i) q^{91} +(-0.550075 - 5.77591i) q^{92} +(11.0200 + 0.318091i) q^{93} +(-15.6997 - 5.64603i) q^{94} +4.19938 q^{95} +(1.79442 - 9.63224i) q^{96} +8.66510 q^{97} +(5.66537 + 2.03741i) q^{98} +(-16.8706 + 5.87274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} - 16 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 24 q^{22} + 16 q^{24} - 8 q^{25} - 28 q^{27} - 8 q^{28} + 44 q^{30} - 8 q^{33} - 24 q^{34} + 48 q^{36} - 8 q^{37} - 28 q^{39} + 24 q^{40} + 56 q^{42} - 8 q^{43} - 4 q^{45} + 24 q^{46} + 48 q^{48} - 16 q^{51} + 48 q^{52} + 40 q^{54} + 24 q^{55} - 4 q^{57} + 96 q^{58} + 8 q^{60} - 40 q^{61} + 40 q^{64} - 28 q^{66} + 56 q^{67} - 4 q^{69} + 40 q^{70} - 64 q^{72} - 8 q^{73} + 16 q^{75} + 48 q^{76} - 92 q^{78} + 16 q^{79} - 48 q^{82} - 136 q^{84} - 48 q^{85} + 52 q^{87} - 48 q^{88} - 136 q^{90} + 40 q^{91} + 8 q^{93} - 64 q^{94} - 104 q^{96} - 16 q^{97} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.478581 1.33077i 0.338408 0.941000i
\(3\) 0.0499748 1.73133i 0.0288530 0.999584i
\(4\) −1.54192 1.27377i −0.770961 0.636883i
\(5\) −1.06973 + 0.443098i −0.478400 + 0.198160i −0.608834 0.793297i \(-0.708363\pi\)
0.130435 + 0.991457i \(0.458363\pi\)
\(6\) −2.28009 0.895086i −0.930844 0.365417i
\(7\) 2.37247 + 2.37247i 0.896708 + 0.896708i 0.995143 0.0984354i \(-0.0313838\pi\)
−0.0984354 + 0.995143i \(0.531384\pi\)
\(8\) −2.43303 + 1.44235i −0.860206 + 0.509948i
\(9\) −2.99501 0.173046i −0.998335 0.0576820i
\(10\) 0.0777099 + 1.63563i 0.0245740 + 0.517232i
\(11\) 5.50127 2.27870i 1.65869 0.687054i 0.660718 0.750635i \(-0.270252\pi\)
0.997977 + 0.0635809i \(0.0202521\pi\)
\(12\) −2.28237 + 2.60592i −0.658862 + 0.752264i
\(13\) 0.346353 0.836171i 0.0960612 0.231912i −0.868543 0.495613i \(-0.834943\pi\)
0.964604 + 0.263701i \(0.0849433\pi\)
\(14\) 4.29263 2.02180i 1.14725 0.540349i
\(15\) 0.713689 + 1.87421i 0.184274 + 0.483918i
\(16\) 0.755041 + 3.92809i 0.188760 + 0.982023i
\(17\) −0.685064 −0.166152 −0.0830762 0.996543i \(-0.526474\pi\)
−0.0830762 + 0.996543i \(0.526474\pi\)
\(18\) −1.66364 + 3.90286i −0.392123 + 0.919913i
\(19\) −3.35074 1.38792i −0.768712 0.318411i −0.0363614 0.999339i \(-0.511577\pi\)
−0.732351 + 0.680928i \(0.761577\pi\)
\(20\) 2.21385 + 0.679368i 0.495032 + 0.151911i
\(21\) 4.22609 3.98896i 0.922207 0.870462i
\(22\) −0.399635 8.41149i −0.0852024 1.79333i
\(23\) 2.05133 + 2.05133i 0.427732 + 0.427732i 0.887855 0.460123i \(-0.152195\pi\)
−0.460123 + 0.887855i \(0.652195\pi\)
\(24\) 2.37559 + 4.28446i 0.484916 + 0.874561i
\(25\) −2.58754 + 2.58754i −0.517508 + 0.517508i
\(26\) −0.946997 0.861094i −0.185721 0.168874i
\(27\) −0.449274 + 5.17669i −0.0864629 + 0.996255i
\(28\) −0.636189 6.68012i −0.120228 1.26242i
\(29\) −1.98869 + 4.80112i −0.369291 + 0.891546i 0.624576 + 0.780964i \(0.285272\pi\)
−0.993867 + 0.110582i \(0.964728\pi\)
\(30\) 2.83570 0.0528009i 0.517726 0.00964009i
\(31\) 6.36503i 1.14319i 0.820535 + 0.571596i \(0.193676\pi\)
−0.820535 + 0.571596i \(0.806324\pi\)
\(32\) 5.58875 + 0.875120i 0.987961 + 0.154701i
\(33\) −3.67025 9.63838i −0.638909 1.67783i
\(34\) −0.327858 + 0.911666i −0.0562273 + 0.156349i
\(35\) −3.58914 1.48667i −0.606676 0.251293i
\(36\) 4.39764 + 4.08176i 0.732940 + 0.680293i
\(37\) 0.112738 + 0.272172i 0.0185339 + 0.0447449i 0.932876 0.360199i \(-0.117291\pi\)
−0.914342 + 0.404944i \(0.867291\pi\)
\(38\) −3.45061 + 3.79484i −0.559763 + 0.615605i
\(39\) −1.43038 0.641440i −0.229044 0.102713i
\(40\) 1.96359 2.62100i 0.310471 0.414417i
\(41\) −3.26585 + 3.26585i −0.510040 + 0.510040i −0.914539 0.404499i \(-0.867446\pi\)
0.404499 + 0.914539i \(0.367446\pi\)
\(42\) −3.28588 7.53300i −0.507022 1.16237i
\(43\) −0.993018 2.39736i −0.151434 0.365594i 0.829898 0.557915i \(-0.188398\pi\)
−0.981332 + 0.192321i \(0.938398\pi\)
\(44\) −11.3850 3.49375i −1.71636 0.526703i
\(45\) 3.28053 1.14197i 0.489033 0.170235i
\(46\) 3.71159 1.74813i 0.547244 0.257748i
\(47\) 11.7975i 1.72084i −0.509589 0.860418i \(-0.670203\pi\)
0.509589 0.860418i \(-0.329797\pi\)
\(48\) 6.83856 1.11092i 0.987061 0.160347i
\(49\) 4.25719i 0.608171i
\(50\) 2.20508 + 4.68178i 0.311846 + 0.662103i
\(51\) −0.0342360 + 1.18607i −0.00479399 + 0.166083i
\(52\) −1.59914 + 0.848137i −0.221760 + 0.117615i
\(53\) −1.56192 3.77080i −0.214546 0.517959i 0.779566 0.626320i \(-0.215440\pi\)
−0.994112 + 0.108361i \(0.965440\pi\)
\(54\) 6.67400 + 3.07535i 0.908216 + 0.418502i
\(55\) −4.87520 + 4.87520i −0.657372 + 0.657372i
\(56\) −9.19420 2.35035i −1.22863 0.314079i
\(57\) −2.57040 + 5.73187i −0.340458 + 0.759205i
\(58\) 5.43746 + 4.94422i 0.713974 + 0.649208i
\(59\) −2.20815 5.33094i −0.287476 0.694029i 0.712495 0.701678i \(-0.247565\pi\)
−0.999971 + 0.00764882i \(0.997565\pi\)
\(60\) 1.28685 3.79895i 0.166131 0.490442i
\(61\) −1.53549 0.636020i −0.196599 0.0814341i 0.282212 0.959352i \(-0.408932\pi\)
−0.478811 + 0.877918i \(0.658932\pi\)
\(62\) 8.47042 + 3.04618i 1.07574 + 0.386865i
\(63\) −6.69500 7.51609i −0.843491 0.946939i
\(64\) 3.83926 7.01855i 0.479907 0.877319i
\(65\) 1.04795i 0.129982i
\(66\) −14.5830 + 0.271537i −1.79505 + 0.0334239i
\(67\) 4.69605 11.3373i 0.573714 1.38507i −0.324657 0.945832i \(-0.605249\pi\)
0.898371 0.439237i \(-0.144751\pi\)
\(68\) 1.05631 + 0.872611i 0.128097 + 0.105820i
\(69\) 3.65405 3.44902i 0.439895 0.415213i
\(70\) −3.69612 + 4.06485i −0.441771 + 0.485842i
\(71\) −7.99150 + 7.99150i −0.948416 + 0.948416i −0.998733 0.0503173i \(-0.983977\pi\)
0.0503173 + 0.998733i \(0.483977\pi\)
\(72\) 7.53653 3.89882i 0.888188 0.459480i
\(73\) −2.34760 2.34760i −0.274766 0.274766i 0.556250 0.831015i \(-0.312240\pi\)
−0.831015 + 0.556250i \(0.812240\pi\)
\(74\) 0.416154 0.0197717i 0.0483769 0.00229842i
\(75\) 4.35057 + 4.60920i 0.502361 + 0.532224i
\(76\) 3.39869 + 6.40812i 0.389856 + 0.735062i
\(77\) 18.4577 + 7.64543i 2.10345 + 0.871278i
\(78\) −1.53816 + 1.59653i −0.174163 + 0.180772i
\(79\) 8.91043 1.00250 0.501251 0.865302i \(-0.332873\pi\)
0.501251 + 0.865302i \(0.332873\pi\)
\(80\) −2.54822 3.86746i −0.284900 0.432395i
\(81\) 8.94011 + 1.03655i 0.993346 + 0.115172i
\(82\) 2.78314 + 5.90908i 0.307346 + 0.652549i
\(83\) −3.06920 + 7.40970i −0.336888 + 0.813320i 0.661123 + 0.750278i \(0.270080\pi\)
−0.998011 + 0.0630420i \(0.979920\pi\)
\(84\) −11.5973 + 0.767615i −1.26537 + 0.0837537i
\(85\) 0.732836 0.303551i 0.0794872 0.0329247i
\(86\) −3.66558 + 0.174154i −0.395270 + 0.0187795i
\(87\) 8.21294 + 3.68301i 0.880520 + 0.394861i
\(88\) −10.0981 + 13.4789i −1.07646 + 1.43685i
\(89\) −1.99332 1.99332i −0.211291 0.211291i 0.593525 0.804816i \(-0.297736\pi\)
−0.804816 + 0.593525i \(0.797736\pi\)
\(90\) 0.0502980 4.91218i 0.00530187 0.517789i
\(91\) 2.80550 1.16208i 0.294096 0.121819i
\(92\) −0.550075 5.77591i −0.0573493 0.602180i
\(93\) 11.0200 + 0.318091i 1.14272 + 0.0329845i
\(94\) −15.6997 5.64603i −1.61931 0.582344i
\(95\) 4.19938 0.430848
\(96\) 1.79442 9.63224i 0.183142 0.983086i
\(97\) 8.66510 0.879807 0.439904 0.898045i \(-0.355013\pi\)
0.439904 + 0.898045i \(0.355013\pi\)
\(98\) 5.66537 + 2.03741i 0.572288 + 0.205810i
\(99\) −16.8706 + 5.87274i −1.69556 + 0.590233i
\(100\) 7.28570 0.693862i 0.728570 0.0693862i
\(101\) −15.6920 + 6.49983i −1.56141 + 0.646758i −0.985334 0.170637i \(-0.945417\pi\)
−0.576077 + 0.817395i \(0.695417\pi\)
\(102\) 1.56201 + 0.613191i 0.154662 + 0.0607150i
\(103\) −5.39788 5.39788i −0.531869 0.531869i 0.389259 0.921128i \(-0.372731\pi\)
−0.921128 + 0.389259i \(0.872731\pi\)
\(104\) 0.363363 + 2.53399i 0.0356307 + 0.248478i
\(105\) −2.75329 + 6.13969i −0.268693 + 0.599173i
\(106\) −5.76559 + 0.273927i −0.560004 + 0.0266061i
\(107\) 0.0169596 0.00702491i 0.00163955 0.000679124i −0.381864 0.924219i \(-0.624718\pi\)
0.383503 + 0.923540i \(0.374718\pi\)
\(108\) 7.28664 7.40978i 0.701157 0.713007i
\(109\) −4.94357 + 11.9348i −0.473508 + 1.14315i 0.489094 + 0.872231i \(0.337328\pi\)
−0.962602 + 0.270919i \(0.912672\pi\)
\(110\) 4.15462 + 8.82097i 0.396127 + 0.841047i
\(111\) 0.476854 0.181584i 0.0452610 0.0172352i
\(112\) −7.52796 + 11.1106i −0.711325 + 1.04985i
\(113\) 10.4984 0.987609 0.493804 0.869573i \(-0.335606\pi\)
0.493804 + 0.869573i \(0.335606\pi\)
\(114\) 6.39768 + 6.16379i 0.599198 + 0.577292i
\(115\) −3.10332 1.28544i −0.289386 0.119868i
\(116\) 9.18191 4.86983i 0.852519 0.452152i
\(117\) −1.18203 + 2.44440i −0.109278 + 0.225985i
\(118\) −8.15105 + 0.387261i −0.750365 + 0.0356503i
\(119\) −1.62529 1.62529i −0.148990 0.148990i
\(120\) −4.43969 3.53061i −0.405286 0.322299i
\(121\) 17.2933 17.2933i 1.57212 1.57212i
\(122\) −1.58125 + 1.73900i −0.143160 + 0.157442i
\(123\) 5.49105 + 5.81747i 0.495112 + 0.524544i
\(124\) 8.10756 9.81437i 0.728080 0.881357i
\(125\) 3.83694 9.26318i 0.343186 0.828524i
\(126\) −13.2063 + 5.31248i −1.17651 + 0.473273i
\(127\) 0.793212i 0.0703862i −0.999381 0.0351931i \(-0.988795\pi\)
0.999381 0.0351931i \(-0.0112046\pi\)
\(128\) −7.50272 8.46813i −0.663153 0.748484i
\(129\) −4.20024 + 1.59943i −0.369811 + 0.140822i
\(130\) 1.39458 + 0.501528i 0.122313 + 0.0439869i
\(131\) 9.39267 + 3.89057i 0.820641 + 0.339921i 0.753191 0.657802i \(-0.228514\pi\)
0.0674502 + 0.997723i \(0.478514\pi\)
\(132\) −6.61780 + 19.5367i −0.576006 + 1.70045i
\(133\) −4.65672 11.2423i −0.403789 0.974832i
\(134\) −12.8399 11.6752i −1.10920 1.00858i
\(135\) −1.81318 5.73676i −0.156054 0.493741i
\(136\) 1.66678 0.988102i 0.142925 0.0847290i
\(137\) 2.95969 2.95969i 0.252863 0.252863i −0.569280 0.822144i \(-0.692778\pi\)
0.822144 + 0.569280i \(0.192778\pi\)
\(138\) −2.84111 6.51334i −0.241851 0.554453i
\(139\) −1.91155 4.61488i −0.162135 0.391429i 0.821844 0.569713i \(-0.192946\pi\)
−0.983979 + 0.178284i \(0.942946\pi\)
\(140\) 3.64050 + 6.86406i 0.307679 + 0.580119i
\(141\) −20.4253 0.589576i −1.72012 0.0496512i
\(142\) 6.81030 + 14.4595i 0.571508 + 1.21341i
\(143\) 5.38924i 0.450671i
\(144\) −1.58161 11.8953i −0.131801 0.991276i
\(145\) 6.01711i 0.499694i
\(146\) −4.24764 + 2.00061i −0.351537 + 0.165572i
\(147\) 7.37061 + 0.212753i 0.607917 + 0.0175475i
\(148\) 0.172852 0.563270i 0.0142083 0.0463005i
\(149\) −5.53451 13.3615i −0.453405 1.09462i −0.971019 0.239002i \(-0.923180\pi\)
0.517614 0.855614i \(-0.326820\pi\)
\(150\) 8.21590 3.58376i 0.670825 0.292613i
\(151\) 2.96063 2.96063i 0.240932 0.240932i −0.576303 0.817236i \(-0.695505\pi\)
0.817236 + 0.576303i \(0.195505\pi\)
\(152\) 10.1543 1.45608i 0.823623 0.118104i
\(153\) 2.05177 + 0.118548i 0.165876 + 0.00958400i
\(154\) 19.0078 20.9041i 1.53170 1.68450i
\(155\) −2.82033 6.80889i −0.226535 0.546903i
\(156\) 1.38849 + 2.81102i 0.111168 + 0.225062i
\(157\) −16.1213 6.67768i −1.28662 0.532937i −0.368646 0.929570i \(-0.620178\pi\)
−0.917977 + 0.396633i \(0.870178\pi\)
\(158\) 4.26436 11.8578i 0.339254 0.943354i
\(159\) −6.60656 + 2.51575i −0.523934 + 0.199512i
\(160\) −6.36624 + 1.54022i −0.503296 + 0.121765i
\(161\) 9.73343i 0.767102i
\(162\) 5.65797 11.4012i 0.444532 0.895763i
\(163\) −4.62172 + 11.1578i −0.362001 + 0.873949i 0.633006 + 0.774147i \(0.281821\pi\)
−0.995007 + 0.0998018i \(0.968179\pi\)
\(164\) 9.19561 0.875755i 0.718057 0.0683849i
\(165\) 8.19695 + 8.68422i 0.638131 + 0.676066i
\(166\) 8.39177 + 7.63054i 0.651328 + 0.592245i
\(167\) −1.28603 + 1.28603i −0.0995157 + 0.0995157i −0.755112 0.655596i \(-0.772417\pi\)
0.655596 + 0.755112i \(0.272417\pi\)
\(168\) −4.52872 + 15.8007i −0.349398 + 1.21905i
\(169\) 8.61317 + 8.61317i 0.662551 + 0.662551i
\(170\) −0.0532362 1.12051i −0.00408303 0.0859394i
\(171\) 9.79530 + 4.73666i 0.749065 + 0.362222i
\(172\) −1.52252 + 4.96141i −0.116091 + 0.378304i
\(173\) 0.0565964 + 0.0234430i 0.00430295 + 0.00178234i 0.384834 0.922986i \(-0.374259\pi\)
−0.380531 + 0.924768i \(0.624259\pi\)
\(174\) 8.83182 9.16695i 0.669538 0.694945i
\(175\) −12.2777 −0.928107
\(176\) 13.1046 + 19.8890i 0.987798 + 1.49919i
\(177\) −9.33996 + 3.55662i −0.702034 + 0.267332i
\(178\) −3.60662 + 1.69869i −0.270327 + 0.127322i
\(179\) 1.17461 2.83576i 0.0877946 0.211955i −0.873884 0.486135i \(-0.838406\pi\)
0.961678 + 0.274180i \(0.0884064\pi\)
\(180\) −6.51293 2.41781i −0.485445 0.180213i
\(181\) −20.8334 + 8.62949i −1.54854 + 0.641425i −0.983051 0.183334i \(-0.941311\pi\)
−0.565485 + 0.824758i \(0.691311\pi\)
\(182\) −0.203803 4.28964i −0.0151069 0.317969i
\(183\) −1.17790 + 2.62665i −0.0870726 + 0.194168i
\(184\) −7.94968 2.03221i −0.586058 0.149817i
\(185\) −0.241198 0.241198i −0.0177333 0.0177333i
\(186\) 5.69725 14.5129i 0.417743 1.06413i
\(187\) −3.76872 + 1.56105i −0.275596 + 0.114156i
\(188\) −15.0272 + 18.1907i −1.09597 + 1.32670i
\(189\) −13.3474 + 11.2156i −0.970882 + 0.815818i
\(190\) 2.00974 5.58843i 0.145802 0.405427i
\(191\) 23.0566 1.66832 0.834158 0.551525i \(-0.185954\pi\)
0.834158 + 0.551525i \(0.185954\pi\)
\(192\) −11.9596 6.99777i −0.863107 0.505021i
\(193\) 7.52832 0.541900 0.270950 0.962593i \(-0.412662\pi\)
0.270950 + 0.962593i \(0.412662\pi\)
\(194\) 4.14695 11.5313i 0.297734 0.827898i
\(195\) 1.81435 + 0.0523711i 0.129928 + 0.00375037i
\(196\) 5.42267 6.56426i 0.387333 0.468876i
\(197\) 2.14750 0.889524i 0.153003 0.0633760i −0.304868 0.952395i \(-0.598612\pi\)
0.457871 + 0.889019i \(0.348612\pi\)
\(198\) −0.258665 + 25.2616i −0.0183825 + 1.79526i
\(199\) 7.46994 + 7.46994i 0.529530 + 0.529530i 0.920432 0.390902i \(-0.127837\pi\)
−0.390902 + 0.920432i \(0.627837\pi\)
\(200\) 2.56342 10.0277i 0.181261 0.709065i
\(201\) −19.3939 8.69699i −1.36794 0.613439i
\(202\) 1.13993 + 23.9932i 0.0802053 + 1.68816i
\(203\) −16.1086 + 6.67240i −1.13060 + 0.468311i
\(204\) 1.56357 1.78522i 0.109472 0.124990i
\(205\) 2.04650 4.94068i 0.142934 0.345072i
\(206\) −9.76668 + 4.60004i −0.680477 + 0.320500i
\(207\) −5.78877 6.49872i −0.402348 0.451692i
\(208\) 3.54607 + 0.729165i 0.245876 + 0.0505585i
\(209\) −21.5960 −1.49382
\(210\) 6.85288 + 6.60234i 0.472894 + 0.455605i
\(211\) 15.9819 + 6.61994i 1.10024 + 0.455735i 0.857567 0.514372i \(-0.171975\pi\)
0.242676 + 0.970107i \(0.421975\pi\)
\(212\) −2.39477 + 7.80380i −0.164473 + 0.535967i
\(213\) 13.4365 + 14.2353i 0.920657 + 0.975386i
\(214\) −0.00123202 0.0259314i −8.42191e−5 0.00177264i
\(215\) 2.12453 + 2.12453i 0.144892 + 0.144892i
\(216\) −6.37350 13.2431i −0.433662 0.901076i
\(217\) −15.1008 + 15.1008i −1.02511 + 1.02511i
\(218\) 13.5167 + 12.2906i 0.915465 + 0.832422i
\(219\) −4.18179 + 3.94715i −0.282579 + 0.266723i
\(220\) 13.7270 1.30731i 0.925477 0.0881389i
\(221\) −0.237274 + 0.572831i −0.0159608 + 0.0385328i
\(222\) −0.0134341 0.721488i −0.000901641 0.0484231i
\(223\) 18.2244i 1.22040i −0.792248 0.610199i \(-0.791090\pi\)
0.792248 0.610199i \(-0.208910\pi\)
\(224\) 11.1829 + 15.3353i 0.747191 + 1.02463i
\(225\) 8.19746 7.30193i 0.546497 0.486795i
\(226\) 5.02434 13.9710i 0.334214 0.929339i
\(227\) 10.8455 + 4.49234i 0.719840 + 0.298167i 0.712369 0.701805i \(-0.247622\pi\)
0.00747022 + 0.999972i \(0.497622\pi\)
\(228\) 11.2644 5.56400i 0.746004 0.368485i
\(229\) 5.20986 + 12.5777i 0.344277 + 0.831159i 0.997273 + 0.0737978i \(0.0235119\pi\)
−0.652996 + 0.757362i \(0.726488\pi\)
\(230\) −3.19582 + 3.51463i −0.210726 + 0.231748i
\(231\) 14.1592 31.5743i 0.931606 2.07744i
\(232\) −2.08636 14.5497i −0.136976 0.955232i
\(233\) 11.7233 11.7233i 0.768016 0.768016i −0.209741 0.977757i \(-0.567262\pi\)
0.977757 + 0.209741i \(0.0672620\pi\)
\(234\) 2.68725 + 2.74285i 0.175671 + 0.179306i
\(235\) 5.22743 + 12.6201i 0.341000 + 0.823247i
\(236\) −3.38558 + 11.0325i −0.220382 + 0.718157i
\(237\) 0.445297 15.4269i 0.0289252 1.00208i
\(238\) −2.94073 + 1.38506i −0.190619 + 0.0897803i
\(239\) 21.5949i 1.39685i 0.715681 + 0.698427i \(0.246117\pi\)
−0.715681 + 0.698427i \(0.753883\pi\)
\(240\) −6.82319 + 4.21854i −0.440435 + 0.272306i
\(241\) 14.6095i 0.941078i −0.882379 0.470539i \(-0.844059\pi\)
0.882379 0.470539i \(-0.155941\pi\)
\(242\) −14.7372 31.2897i −0.947345 2.01138i
\(243\) 2.24138 15.4265i 0.143785 0.989609i
\(244\) 1.55746 + 2.93655i 0.0997063 + 0.187993i
\(245\) −1.88636 4.55406i −0.120515 0.290949i
\(246\) 10.3697 4.52322i 0.661145 0.288390i
\(247\) −2.32108 + 2.32108i −0.147687 + 0.147687i
\(248\) −9.18060 15.4863i −0.582968 0.983381i
\(249\) 12.6752 + 5.68409i 0.803261 + 0.360215i
\(250\) −10.4909 9.53928i −0.663504 0.603317i
\(251\) 1.08581 + 2.62137i 0.0685355 + 0.165459i 0.954436 0.298416i \(-0.0964584\pi\)
−0.885900 + 0.463876i \(0.846458\pi\)
\(252\) 0.749422 + 20.1171i 0.0472092 + 1.26726i
\(253\) 15.9593 + 6.61055i 1.00335 + 0.415602i
\(254\) −1.05559 0.379616i −0.0662334 0.0238192i
\(255\) −0.488923 1.28395i −0.0306175 0.0804041i
\(256\) −14.8598 + 5.93174i −0.928739 + 0.370734i
\(257\) 1.35436i 0.0844827i 0.999107 + 0.0422414i \(0.0134498\pi\)
−0.999107 + 0.0422414i \(0.986550\pi\)
\(258\) 0.118331 + 6.35503i 0.00736697 + 0.395647i
\(259\) −0.378254 + 0.913186i −0.0235036 + 0.0567426i
\(260\) 1.33484 1.61586i 0.0827834 0.100211i
\(261\) 6.78695 14.0353i 0.420102 0.868760i
\(262\) 9.67262 10.6376i 0.597576 0.657191i
\(263\) −3.52372 + 3.52372i −0.217282 + 0.217282i −0.807352 0.590070i \(-0.799100\pi\)
0.590070 + 0.807352i \(0.299100\pi\)
\(264\) 22.8318 + 18.1567i 1.40520 + 1.11747i
\(265\) 3.34167 + 3.34167i 0.205277 + 0.205277i
\(266\) −17.1896 + 0.816688i −1.05396 + 0.0500743i
\(267\) −3.55070 + 3.35147i −0.217299 + 0.205107i
\(268\) −21.6820 + 11.4995i −1.32444 + 0.702444i
\(269\) −16.4741 6.82380i −1.00444 0.416055i −0.181020 0.983479i \(-0.557940\pi\)
−0.823425 + 0.567425i \(0.807940\pi\)
\(270\) −8.50208 0.332568i −0.517420 0.0202394i
\(271\) −8.50293 −0.516516 −0.258258 0.966076i \(-0.583149\pi\)
−0.258258 + 0.966076i \(0.583149\pi\)
\(272\) −0.517252 2.69100i −0.0313630 0.163166i
\(273\) −1.87173 4.91532i −0.113282 0.297489i
\(274\) −2.52223 5.35513i −0.152374 0.323515i
\(275\) −8.33852 + 20.1310i −0.502832 + 1.21394i
\(276\) −10.0275 + 0.663711i −0.603584 + 0.0399507i
\(277\) 20.2028 8.36828i 1.21387 0.502801i 0.318414 0.947952i \(-0.396850\pi\)
0.895456 + 0.445150i \(0.146850\pi\)
\(278\) −7.05619 + 0.335244i −0.423202 + 0.0201066i
\(279\) 1.10144 19.0633i 0.0659416 1.14129i
\(280\) 10.8768 1.55968i 0.650012 0.0932089i
\(281\) −10.3342 10.3342i −0.616487 0.616487i 0.328142 0.944629i \(-0.393578\pi\)
−0.944629 + 0.328142i \(0.893578\pi\)
\(282\) −10.5597 + 26.8993i −0.628823 + 1.60183i
\(283\) 8.67342 3.59265i 0.515581 0.213561i −0.109694 0.993965i \(-0.534987\pi\)
0.625275 + 0.780405i \(0.284987\pi\)
\(284\) 22.5015 2.14296i 1.33522 0.127161i
\(285\) 0.209864 7.27052i 0.0124312 0.430668i
\(286\) −7.17186 2.57918i −0.424081 0.152510i
\(287\) −15.4962 −0.914714
\(288\) −16.5869 3.58810i −0.977393 0.211431i
\(289\) −16.5307 −0.972393
\(290\) −8.00741 2.87967i −0.470212 0.169100i
\(291\) 0.433037 15.0021i 0.0253851 0.879441i
\(292\) 0.629521 + 6.61010i 0.0368399 + 0.386827i
\(293\) 11.3816 4.71442i 0.664922 0.275420i −0.0245862 0.999698i \(-0.507827\pi\)
0.689508 + 0.724278i \(0.257827\pi\)
\(294\) 3.81056 9.70680i 0.222236 0.566112i
\(295\) 4.72426 + 4.72426i 0.275057 + 0.275057i
\(296\) −0.666861 0.499597i −0.0387605 0.0290385i
\(297\) 9.32455 + 29.5021i 0.541065 + 1.71189i
\(298\) −20.4298 + 0.970634i −1.18347 + 0.0562273i
\(299\) 2.42575 1.00478i 0.140285 0.0581078i
\(300\) −0.837202 12.6486i −0.0483359 0.730269i
\(301\) 3.33175 8.04355i 0.192039 0.463623i
\(302\) −2.52303 5.35683i −0.145184 0.308251i
\(303\) 10.4692 + 27.4928i 0.601437 + 1.57942i
\(304\) 2.92194 14.2099i 0.167585 0.814996i
\(305\) 1.92438 0.110190
\(306\) 1.13970 2.67371i 0.0651522 0.152846i
\(307\) −12.6145 5.22511i −0.719950 0.298213i −0.00753514 0.999972i \(-0.502399\pi\)
−0.712415 + 0.701759i \(0.752399\pi\)
\(308\) −18.7218 35.2995i −1.06678 2.01137i
\(309\) −9.61527 + 9.07575i −0.546994 + 0.516302i
\(310\) −10.4108 + 0.494626i −0.591297 + 0.0280928i
\(311\) −18.8020 18.8020i −1.06617 1.06617i −0.997650 0.0685162i \(-0.978174\pi\)
−0.0685162 0.997650i \(-0.521826\pi\)
\(312\) 4.40533 0.502466i 0.249403 0.0284465i
\(313\) 4.30835 4.30835i 0.243522 0.243522i −0.574783 0.818306i \(-0.694914\pi\)
0.818306 + 0.574783i \(0.194914\pi\)
\(314\) −16.6018 + 18.2581i −0.936896 + 1.03036i
\(315\) 10.4922 + 5.07368i 0.591171 + 0.285869i
\(316\) −13.7392 11.3498i −0.772889 0.638476i
\(317\) 0.543402 1.31189i 0.0305205 0.0736830i −0.907884 0.419221i \(-0.862303\pi\)
0.938405 + 0.345538i \(0.112303\pi\)
\(318\) 0.186123 + 9.99583i 0.0104372 + 0.560538i
\(319\) 30.9439i 1.73252i
\(320\) −0.997073 + 9.20915i −0.0557381 + 0.514807i
\(321\) −0.0113149 0.0297138i −0.000631535 0.00165846i
\(322\) 12.9530 + 4.65823i 0.721842 + 0.259593i
\(323\) 2.29547 + 0.950815i 0.127723 + 0.0529047i
\(324\) −12.4646 12.9859i −0.692479 0.721438i
\(325\) 1.26742 + 3.05983i 0.0703040 + 0.169729i
\(326\) 12.6367 + 11.4904i 0.699881 + 0.636394i
\(327\) 20.4161 + 9.15540i 1.12901 + 0.506295i
\(328\) 3.23541 12.6564i 0.178646 0.698833i
\(329\) 27.9891 27.9891i 1.54309 1.54309i
\(330\) 15.4796 6.75219i 0.852126 0.371696i
\(331\) −5.18815 12.5253i −0.285167 0.688453i 0.714774 0.699356i \(-0.246530\pi\)
−0.999941 + 0.0109024i \(0.996530\pi\)
\(332\) 14.1707 7.51573i 0.777717 0.412479i
\(333\) −0.290551 0.834667i −0.0159221 0.0457395i
\(334\) 1.09594 + 2.32688i 0.0599673 + 0.127321i
\(335\) 14.2087i 0.776303i
\(336\) 18.8599 + 13.5886i 1.02889 + 0.741320i
\(337\) 19.9878i 1.08881i 0.838824 + 0.544403i \(0.183244\pi\)
−0.838824 + 0.544403i \(0.816756\pi\)
\(338\) 15.5843 7.34009i 0.847673 0.399248i
\(339\) 0.524657 18.1762i 0.0284955 0.987197i
\(340\) −1.51663 0.465411i −0.0822507 0.0252404i
\(341\) 14.5040 + 35.0157i 0.785435 + 1.89621i
\(342\) 10.9913 10.7685i 0.594340 0.582292i
\(343\) 6.50721 6.50721i 0.351357 0.351357i
\(344\) 5.87387 + 4.40056i 0.316698 + 0.237262i
\(345\) −2.38060 + 5.30863i −0.128167 + 0.285807i
\(346\) 0.0582833 0.0640977i 0.00313333 0.00344591i
\(347\) −5.84634 14.1143i −0.313848 0.757696i −0.999555 0.0298187i \(-0.990507\pi\)
0.685707 0.727877i \(-0.259493\pi\)
\(348\) −7.97241 16.1403i −0.427366 0.865210i
\(349\) 7.90170 + 3.27299i 0.422969 + 0.175199i 0.584007 0.811749i \(-0.301484\pi\)
−0.161038 + 0.986948i \(0.551484\pi\)
\(350\) −5.87587 + 16.3389i −0.314078 + 0.873348i
\(351\) 4.17299 + 2.16864i 0.222738 + 0.115753i
\(352\) 32.7394 7.92082i 1.74501 0.422181i
\(353\) 28.4566i 1.51459i 0.653072 + 0.757296i \(0.273480\pi\)
−0.653072 + 0.757296i \(0.726520\pi\)
\(354\) 0.263129 + 14.1315i 0.0139852 + 0.751081i
\(355\) 5.00776 12.0898i 0.265784 0.641659i
\(356\) 0.534518 + 5.61255i 0.0283294 + 0.297465i
\(357\) −2.89514 + 2.73269i −0.153227 + 0.144629i
\(358\) −3.21161 2.92028i −0.169739 0.154342i
\(359\) −3.48589 + 3.48589i −0.183978 + 0.183978i −0.793087 0.609109i \(-0.791527\pi\)
0.609109 + 0.793087i \(0.291527\pi\)
\(360\) −6.33452 + 7.51012i −0.333858 + 0.395818i
\(361\) −4.13391 4.13391i −0.217574 0.217574i
\(362\) 1.51343 + 31.8545i 0.0795439 + 1.67423i
\(363\) −29.0762 30.8046i −1.52610 1.61682i
\(364\) −5.80607 1.78172i −0.304321 0.0933875i
\(365\) 3.55152 + 1.47109i 0.185895 + 0.0770003i
\(366\) 2.93176 + 2.82458i 0.153246 + 0.147643i
\(367\) 7.37411 0.384925 0.192463 0.981304i \(-0.438353\pi\)
0.192463 + 0.981304i \(0.438353\pi\)
\(368\) −6.50898 + 9.60666i −0.339304 + 0.500782i
\(369\) 10.3464 9.21609i 0.538611 0.479771i
\(370\) −0.436413 + 0.205548i −0.0226881 + 0.0106859i
\(371\) 5.24050 12.6517i 0.272073 0.656843i
\(372\) −16.5867 14.5273i −0.859982 0.753207i
\(373\) −7.72861 + 3.20130i −0.400172 + 0.165757i −0.573687 0.819074i \(-0.694488\pi\)
0.173515 + 0.984831i \(0.444488\pi\)
\(374\) 0.273775 + 5.76241i 0.0141566 + 0.297967i
\(375\) −15.8459 7.10593i −0.818277 0.366948i
\(376\) 17.0160 + 28.7035i 0.877536 + 1.48027i
\(377\) 3.32577 + 3.32577i 0.171286 + 0.171286i
\(378\) 8.53767 + 23.1300i 0.439131 + 1.18968i
\(379\) −22.6759 + 9.39268i −1.16478 + 0.482470i −0.879465 0.475963i \(-0.842100\pi\)
−0.285319 + 0.958433i \(0.592100\pi\)
\(380\) −6.47512 5.34903i −0.332166 0.274399i
\(381\) −1.37331 0.0396406i −0.0703569 0.00203085i
\(382\) 11.0344 30.6831i 0.564571 1.56989i
\(383\) −11.3729 −0.581129 −0.290565 0.956855i \(-0.593843\pi\)
−0.290565 + 0.956855i \(0.593843\pi\)
\(384\) −15.0361 + 12.5665i −0.767306 + 0.641281i
\(385\) −23.1325 −1.17894
\(386\) 3.60291 10.0185i 0.183383 0.509928i
\(387\) 2.55924 + 7.35194i 0.130094 + 0.373720i
\(388\) −13.3609 11.0373i −0.678297 0.560334i
\(389\) 11.2635 4.66550i 0.571083 0.236550i −0.0784059 0.996922i \(-0.524983\pi\)
0.649489 + 0.760371i \(0.274983\pi\)
\(390\) 0.938005 2.38942i 0.0474977 0.120993i
\(391\) −1.40529 1.40529i −0.0710687 0.0710687i
\(392\) −6.14036 10.3579i −0.310135 0.523152i
\(393\) 7.20526 16.0674i 0.363457 0.810492i
\(394\) −0.156003 3.28355i −0.00785933 0.165423i
\(395\) −9.53179 + 3.94820i −0.479596 + 0.198655i
\(396\) 33.4937 + 12.4339i 1.68312 + 0.624829i
\(397\) 3.65241 8.81769i 0.183309 0.442547i −0.805336 0.592819i \(-0.798015\pi\)
0.988645 + 0.150272i \(0.0480149\pi\)
\(398\) 13.5158 6.36583i 0.677484 0.319090i
\(399\) −19.6969 + 7.50048i −0.986076 + 0.375494i
\(400\) −12.1178 8.21040i −0.605890 0.410520i
\(401\) 5.46170 0.272744 0.136372 0.990658i \(-0.456456\pi\)
0.136372 + 0.990658i \(0.456456\pi\)
\(402\) −20.8553 + 21.6467i −1.04017 + 1.07964i
\(403\) 5.32225 + 2.20455i 0.265120 + 0.109816i
\(404\) 32.4751 + 9.96569i 1.61570 + 0.495811i
\(405\) −10.0228 + 2.85252i −0.498038 + 0.141743i
\(406\) 1.17020 + 24.6302i 0.0580758 + 1.22238i
\(407\) 1.24040 + 1.24040i 0.0614843 + 0.0614843i
\(408\) −1.62743 2.93513i −0.0805699 0.145310i
\(409\) −21.6474 + 21.6474i −1.07039 + 1.07039i −0.0730670 + 0.997327i \(0.523279\pi\)
−0.997327 + 0.0730670i \(0.976721\pi\)
\(410\) −5.59552 5.08794i −0.276343 0.251276i
\(411\) −4.97629 5.27211i −0.245462 0.260054i
\(412\) 1.44747 + 15.1987i 0.0713117 + 0.748788i
\(413\) 7.40871 17.8862i 0.364559 0.880123i
\(414\) −11.4187 + 4.59339i −0.561200 + 0.225753i
\(415\) 9.28636i 0.455849i
\(416\) 2.66743 4.37005i 0.130782 0.214260i
\(417\) −8.08541 + 3.07889i −0.395944 + 0.150774i
\(418\) −10.3354 + 28.7393i −0.505521 + 1.40569i
\(419\) 16.1057 + 6.67119i 0.786814 + 0.325909i 0.739662 0.672979i \(-0.234986\pi\)
0.0471519 + 0.998888i \(0.484986\pi\)
\(420\) 12.0659 5.95988i 0.588755 0.290812i
\(421\) 11.0865 + 26.7651i 0.540321 + 1.30445i 0.924497 + 0.381190i \(0.124486\pi\)
−0.384176 + 0.923260i \(0.625514\pi\)
\(422\) 16.4583 18.1002i 0.801177 0.881104i
\(423\) −2.04150 + 35.3334i −0.0992612 + 1.71797i
\(424\) 9.23900 + 6.92164i 0.448686 + 0.336144i
\(425\) 1.77263 1.77263i 0.0859852 0.0859852i
\(426\) 25.3744 11.0683i 1.22939 0.536259i
\(427\) −2.13396 5.15183i −0.103270 0.249315i
\(428\) −0.0350985 0.0107708i −0.00169655 0.000520624i
\(429\) −9.33055 0.269326i −0.450483 0.0130032i
\(430\) 3.84403 1.81051i 0.185376 0.0873106i
\(431\) 20.4774i 0.986361i −0.869927 0.493180i \(-0.835834\pi\)
0.869927 0.493180i \(-0.164166\pi\)
\(432\) −20.6738 + 2.14382i −0.994666 + 0.103145i
\(433\) 14.6756i 0.705262i 0.935762 + 0.352631i \(0.114713\pi\)
−0.935762 + 0.352631i \(0.885287\pi\)
\(434\) 12.8688 + 27.3227i 0.617723 + 1.31153i
\(435\) −10.4176 0.300704i −0.499486 0.0144177i
\(436\) 22.8248 12.1056i 1.09311 0.579754i
\(437\) −4.02639 9.72056i −0.192608 0.464997i
\(438\) 3.25144 + 7.45405i 0.155360 + 0.356168i
\(439\) 4.86825 4.86825i 0.232349 0.232349i −0.581324 0.813672i \(-0.697465\pi\)
0.813672 + 0.581324i \(0.197465\pi\)
\(440\) 4.82976 18.8933i 0.230250 0.900701i
\(441\) 0.736690 12.7503i 0.0350805 0.607158i
\(442\) 0.648754 + 0.589904i 0.0308581 + 0.0280589i
\(443\) −6.00738 14.5031i −0.285419 0.689063i 0.714525 0.699610i \(-0.246643\pi\)
−0.999944 + 0.0105468i \(0.996643\pi\)
\(444\) −0.966567 0.327412i −0.0458713 0.0155383i
\(445\) 3.01555 + 1.24908i 0.142951 + 0.0592122i
\(446\) −24.2526 8.72186i −1.14839 0.412992i
\(447\) −23.4097 + 8.91432i −1.10724 + 0.421633i
\(448\) 25.7598 7.54278i 1.21704 0.356363i
\(449\) 1.76611i 0.0833480i 0.999131 + 0.0416740i \(0.0132691\pi\)
−0.999131 + 0.0416740i \(0.986731\pi\)
\(450\) −5.79408 14.4035i −0.273135 0.678989i
\(451\) −10.5244 + 25.4082i −0.495576 + 1.19643i
\(452\) −16.1877 13.3725i −0.761407 0.628991i
\(453\) −4.97787 5.27378i −0.233881 0.247784i
\(454\) 11.1687 12.2829i 0.524175 0.576467i
\(455\) −2.48622 + 2.48622i −0.116556 + 0.116556i
\(456\) −2.01350 17.6532i −0.0942908 0.826688i
\(457\) −22.3579 22.3579i −1.04586 1.04586i −0.998897 0.0469601i \(-0.985047\pi\)
−0.0469601 0.998897i \(-0.514953\pi\)
\(458\) 19.2315 0.913698i 0.898627 0.0426943i
\(459\) 0.307782 3.54637i 0.0143660 0.165530i
\(460\) 3.14773 + 5.93495i 0.146764 + 0.276718i
\(461\) 0.811938 + 0.336316i 0.0378157 + 0.0156638i 0.401511 0.915854i \(-0.368485\pi\)
−0.363695 + 0.931518i \(0.618485\pi\)
\(462\) −35.2420 33.9535i −1.63960 1.57966i
\(463\) 14.0009 0.650678 0.325339 0.945597i \(-0.394522\pi\)
0.325339 + 0.945597i \(0.394522\pi\)
\(464\) −20.3608 4.18671i −0.945226 0.194363i
\(465\) −11.9294 + 4.54265i −0.553211 + 0.210661i
\(466\) −9.99049 21.2115i −0.462800 0.982606i
\(467\) 5.94695 14.3572i 0.275192 0.664373i −0.724498 0.689277i \(-0.757928\pi\)
0.999690 + 0.0249045i \(0.00792818\pi\)
\(468\) 4.93619 2.26345i 0.228175 0.104628i
\(469\) 38.0385 15.7561i 1.75646 0.727548i
\(470\) 19.2963 0.916779i 0.890072 0.0422878i
\(471\) −12.3669 + 27.5776i −0.569838 + 1.27071i
\(472\) 13.0616 + 9.78540i 0.601207 + 0.450410i
\(473\) −10.9257 10.9257i −0.502365 0.502365i
\(474\) −20.3166 7.97560i −0.933173 0.366332i
\(475\) 12.2615 5.07887i 0.562595 0.233034i
\(476\) 0.435830 + 4.57631i 0.0199763 + 0.209755i
\(477\) 4.02543 + 11.5639i 0.184312 + 0.529473i
\(478\) 28.7379 + 10.3349i 1.31444 + 0.472706i
\(479\) 34.4708 1.57501 0.787505 0.616309i \(-0.211373\pi\)
0.787505 + 0.616309i \(0.211373\pi\)
\(480\) 2.34848 + 11.0990i 0.107193 + 0.506599i
\(481\) 0.266630 0.0121573
\(482\) −19.4419 6.99181i −0.885554 0.318468i
\(483\) 16.8518 + 0.486427i 0.766782 + 0.0221332i
\(484\) −48.6925 + 4.63729i −2.21329 + 0.210786i
\(485\) −9.26935 + 3.83949i −0.420899 + 0.174342i
\(486\) −19.4565 10.3656i −0.882564 0.470193i
\(487\) −13.6710 13.6710i −0.619490 0.619490i 0.325911 0.945401i \(-0.394329\pi\)
−0.945401 + 0.325911i \(0.894329\pi\)
\(488\) 4.65325 0.667256i 0.210643 0.0302052i
\(489\) 19.0869 + 8.55934i 0.863140 + 0.387067i
\(490\) −6.96321 + 0.330826i −0.314566 + 0.0149452i
\(491\) −16.0034 + 6.62882i −0.722223 + 0.299154i −0.713352 0.700806i \(-0.752824\pi\)
−0.00887095 + 0.999961i \(0.502824\pi\)
\(492\) −1.05667 15.9644i −0.0476384 0.719731i
\(493\) 1.36238 3.28908i 0.0613585 0.148133i
\(494\) 1.97801 + 4.19966i 0.0889948 + 0.188951i
\(495\) 15.4449 13.7576i 0.694196 0.618359i
\(496\) −25.0024 + 4.80586i −1.12264 + 0.215789i
\(497\) −37.9191 −1.70090
\(498\) 13.6304 14.1476i 0.610791 0.633969i
\(499\) −6.36166 2.63509i −0.284787 0.117963i 0.235717 0.971822i \(-0.424256\pi\)
−0.520504 + 0.853859i \(0.674256\pi\)
\(500\) −17.7154 + 9.39574i −0.792256 + 0.420190i
\(501\) 2.16227 + 2.29080i 0.0966029 + 0.102346i
\(502\) 4.00810 0.190427i 0.178890 0.00849918i
\(503\) 16.8510 + 16.8510i 0.751350 + 0.751350i 0.974731 0.223381i \(-0.0717095\pi\)
−0.223381 + 0.974731i \(0.571709\pi\)
\(504\) 27.1300 + 8.63034i 1.20846 + 0.384426i
\(505\) 13.9062 13.9062i 0.618817 0.618817i
\(506\) 16.4350 18.0745i 0.730623 0.803511i
\(507\) 15.3427 14.4818i 0.681392 0.643159i
\(508\) −1.01037 + 1.22307i −0.0448277 + 0.0542650i
\(509\) −6.71610 + 16.2141i −0.297686 + 0.718678i 0.702291 + 0.711890i \(0.252161\pi\)
−0.999977 + 0.00678764i \(0.997839\pi\)
\(510\) −1.94264 + 0.0361720i −0.0860215 + 0.00160172i
\(511\) 11.1392i 0.492769i
\(512\) 0.782187 + 22.6139i 0.0345681 + 0.999402i
\(513\) 8.69024 16.7222i 0.383684 0.738302i
\(514\) 1.80235 + 0.648171i 0.0794982 + 0.0285896i
\(515\) 8.16609 + 3.38250i 0.359841 + 0.149051i
\(516\) 8.51375 + 2.88392i 0.374797 + 0.126958i
\(517\) −26.8828 64.9009i −1.18231 2.85434i
\(518\) 1.03422 + 0.940404i 0.0454410 + 0.0413190i
\(519\) 0.0434160 0.0968155i 0.00190575 0.00424973i
\(520\) −1.51151 2.54969i −0.0662841 0.111811i
\(521\) −18.2126 + 18.2126i −0.797908 + 0.797908i −0.982765 0.184858i \(-0.940818\pi\)
0.184858 + 0.982765i \(0.440818\pi\)
\(522\) −15.4297 15.7489i −0.675337 0.689311i
\(523\) −0.472480 1.14067i −0.0206601 0.0498779i 0.913213 0.407483i \(-0.133593\pi\)
−0.933873 + 0.357605i \(0.883593\pi\)
\(524\) −9.52708 17.9630i −0.416192 0.784718i
\(525\) −0.613576 + 21.2567i −0.0267787 + 0.927721i
\(526\) 3.00289 + 6.37565i 0.130932 + 0.277992i
\(527\) 4.36045i 0.189944i
\(528\) 35.0893 21.6945i 1.52706 0.944131i
\(529\) 14.5841i 0.634090i
\(530\) 6.04627 2.84775i 0.262633 0.123698i
\(531\) 5.69091 + 16.3483i 0.246965 + 0.709455i
\(532\) −7.13978 + 23.2663i −0.309549 + 1.00872i
\(533\) 1.59967 + 3.86195i 0.0692895 + 0.167280i
\(534\) 2.76075 + 6.32913i 0.119470 + 0.273888i
\(535\) −0.0150296 + 0.0150296i −0.000649785 + 0.000649785i
\(536\) 4.92668 + 34.3573i 0.212800 + 1.48401i
\(537\) −4.85094 2.17536i −0.209333 0.0938735i
\(538\) −16.9651 + 18.6576i −0.731419 + 0.804386i
\(539\) 9.70087 + 23.4200i 0.417846 + 1.00877i
\(540\) −4.51150 + 11.1552i −0.194144 + 0.480043i
\(541\) 14.2297 + 5.89412i 0.611781 + 0.253408i 0.666990 0.745067i \(-0.267582\pi\)
−0.0552087 + 0.998475i \(0.517582\pi\)
\(542\) −4.06934 + 11.3155i −0.174793 + 0.486042i
\(543\) 13.8993 + 36.5008i 0.596478 + 1.56640i
\(544\) −3.82865 0.599513i −0.164152 0.0257039i
\(545\) 14.9576i 0.640713i
\(546\) −7.43696 + 0.138477i −0.318272 + 0.00592625i
\(547\) −6.24323 + 15.0725i −0.266941 + 0.644453i −0.999336 0.0364266i \(-0.988402\pi\)
0.732395 + 0.680880i \(0.238402\pi\)
\(548\) −8.33356 + 0.793657i −0.355992 + 0.0339033i
\(549\) 4.48874 + 2.17059i 0.191575 + 0.0926387i
\(550\) 22.7991 + 20.7310i 0.972158 + 0.883972i
\(551\) 13.3272 13.3272i 0.567756 0.567756i
\(552\) −3.91571 + 13.6620i −0.166664 + 0.581492i
\(553\) 21.1397 + 21.1397i 0.898952 + 0.898952i
\(554\) −1.46762 30.8903i −0.0623531 1.31240i
\(555\) −0.429648 + 0.405540i −0.0182375 + 0.0172142i
\(556\) −2.93082 + 9.55064i −0.124295 + 0.405038i
\(557\) 7.09223 + 2.93770i 0.300507 + 0.124474i 0.527842 0.849342i \(-0.323001\pi\)
−0.227335 + 0.973817i \(0.573001\pi\)
\(558\) −24.8418 10.5891i −1.05164 0.448272i
\(559\) −2.34854 −0.0993325
\(560\) 3.12983 15.2210i 0.132260 0.643204i
\(561\) 2.51436 + 6.60291i 0.106156 + 0.278775i
\(562\) −18.6982 + 8.80674i −0.788738 + 0.371490i
\(563\) 0.517007 1.24817i 0.0217892 0.0526039i −0.912610 0.408830i \(-0.865937\pi\)
0.934400 + 0.356226i \(0.115937\pi\)
\(564\) 30.7432 + 26.9261i 1.29452 + 1.13379i
\(565\) −11.2305 + 4.65183i −0.472471 + 0.195704i
\(566\) −0.630073 13.2617i −0.0264839 0.557432i
\(567\) 18.7509 + 23.6693i 0.787465 + 0.994016i
\(568\) 7.91701 30.9701i 0.332190 1.29948i
\(569\) 4.40004 + 4.40004i 0.184459 + 0.184459i 0.793296 0.608836i \(-0.208363\pi\)
−0.608836 + 0.793296i \(0.708363\pi\)
\(570\) −9.57498 3.75881i −0.401052 0.157439i
\(571\) 23.9135 9.90528i 1.00075 0.414523i 0.178676 0.983908i \(-0.442819\pi\)
0.822071 + 0.569385i \(0.192819\pi\)
\(572\) −6.86463 + 8.30978i −0.287024 + 0.347449i
\(573\) 1.15225 39.9186i 0.0481359 1.66762i
\(574\) −7.41620 + 20.6220i −0.309546 + 0.860745i
\(575\) −10.6158 −0.442709
\(576\) −12.7131 + 20.3562i −0.529714 + 0.848177i
\(577\) −7.45244 −0.310249 −0.155124 0.987895i \(-0.549578\pi\)
−0.155124 + 0.987895i \(0.549578\pi\)
\(578\) −7.91127 + 21.9986i −0.329065 + 0.915022i
\(579\) 0.376226 13.0340i 0.0156354 0.541675i
\(580\) −7.66439 + 9.27791i −0.318246 + 0.385244i
\(581\) −24.8608 + 10.2977i −1.03140 + 0.427220i
\(582\) −19.7572 7.75601i −0.818963 0.321497i
\(583\) −17.1850 17.1850i −0.711732 0.711732i
\(584\) 9.09783 + 2.32572i 0.376471 + 0.0962389i
\(585\) 0.181343 3.13861i 0.00749762 0.129766i
\(586\) −0.826808 17.4026i −0.0341551 0.718895i
\(587\) 39.1257 16.2064i 1.61489 0.668910i 0.621472 0.783436i \(-0.286535\pi\)
0.993420 + 0.114526i \(0.0365349\pi\)
\(588\) −11.0939 9.71647i −0.457505 0.400701i
\(589\) 8.83416 21.3275i 0.364005 0.878786i
\(590\) 8.54786 4.02598i 0.351910 0.165747i
\(591\) −1.43274 3.76249i −0.0589350 0.154768i
\(592\) −0.983997 + 0.648345i −0.0404420 + 0.0266468i
\(593\) 42.7694 1.75633 0.878164 0.478359i \(-0.158768\pi\)
0.878164 + 0.478359i \(0.158768\pi\)
\(594\) 43.7232 + 1.71028i 1.79399 + 0.0701736i
\(595\) 2.45879 + 1.01847i 0.100801 + 0.0417530i
\(596\) −8.48563 + 27.6520i −0.347585 + 1.13267i
\(597\) 13.3062 12.5596i 0.544588 0.514031i
\(598\) −0.176216 3.70899i −0.00720603 0.151672i
\(599\) −21.3145 21.3145i −0.870885 0.870885i 0.121684 0.992569i \(-0.461171\pi\)
−0.992569 + 0.121684i \(0.961171\pi\)
\(600\) −17.2331 4.93926i −0.703540 0.201644i
\(601\) −4.26621 + 4.26621i −0.174022 + 0.174022i −0.788744 0.614722i \(-0.789268\pi\)
0.614722 + 0.788744i \(0.289268\pi\)
\(602\) −9.10964 8.28329i −0.371281 0.337602i
\(603\) −16.0266 + 33.1426i −0.652652 + 1.34967i
\(604\) −8.33620 + 0.793908i −0.339195 + 0.0323036i
\(605\) −10.8366 + 26.1618i −0.440570 + 1.06363i
\(606\) 41.5971 0.774540i 1.68977 0.0314635i
\(607\) 30.5562i 1.24024i −0.784508 0.620118i \(-0.787085\pi\)
0.784508 0.620118i \(-0.212915\pi\)
\(608\) −17.5118 10.6890i −0.710199 0.433498i
\(609\) 10.7471 + 28.2228i 0.435495 + 1.14364i
\(610\) 0.920973 2.56092i 0.0372891 0.103689i
\(611\) −9.86469 4.08609i −0.399083 0.165305i
\(612\) −3.01267 2.79627i −0.121780 0.113032i
\(613\) 13.4587 + 32.4921i 0.543590 + 1.31234i 0.922174 + 0.386775i \(0.126411\pi\)
−0.378584 + 0.925567i \(0.623589\pi\)
\(614\) −12.9905 + 14.2865i −0.524255 + 0.576555i
\(615\) −8.45168 3.79007i −0.340804 0.152830i
\(616\) −55.9355 + 8.02091i −2.25371 + 0.323172i
\(617\) −32.1395 + 32.1395i −1.29389 + 1.29389i −0.361524 + 0.932363i \(0.617743\pi\)
−0.932363 + 0.361524i \(0.882257\pi\)
\(618\) 7.47610 + 17.1392i 0.300733 + 0.689441i
\(619\) 14.9456 + 36.0820i 0.600716 + 1.45026i 0.872846 + 0.487996i \(0.162272\pi\)
−0.272129 + 0.962261i \(0.587728\pi\)
\(620\) −4.32420 + 14.0912i −0.173664 + 0.565917i
\(621\) −11.5407 + 9.69750i −0.463113 + 0.389147i
\(622\) −34.0196 + 16.0230i −1.36406 + 0.642463i
\(623\) 9.45815i 0.378933i
\(624\) 1.43964 6.10298i 0.0576317 0.244315i
\(625\) 6.68739i 0.267496i
\(626\) −3.67155 7.79533i −0.146745 0.311564i
\(627\) −1.07925 + 37.3897i −0.0431013 + 1.49320i
\(628\) 16.3520 + 30.8313i 0.652517 + 1.23030i
\(629\) −0.0772324 0.186456i −0.00307946 0.00743447i
\(630\) 11.7733 11.5346i 0.469060 0.459551i
\(631\) 20.5960 20.5960i 0.819912 0.819912i −0.166183 0.986095i \(-0.553144\pi\)
0.986095 + 0.166183i \(0.0531442\pi\)
\(632\) −21.6793 + 12.8520i −0.862358 + 0.511223i
\(633\) 12.2600 27.3392i 0.487291 1.08664i
\(634\) −1.48577 1.35099i −0.0590073 0.0536547i
\(635\) 0.351471 + 0.848526i 0.0139477 + 0.0336727i
\(636\) 13.3913 + 4.53612i 0.530998 + 0.179869i
\(637\) 3.55974 + 1.47449i 0.141042 + 0.0584216i
\(638\) 41.1793 + 14.8091i 1.63031 + 0.586300i
\(639\) 25.3175 22.5517i 1.00154 0.892130i
\(640\) 11.7781 + 5.73420i 0.465571 + 0.226664i
\(641\) 12.6916i 0.501289i 0.968079 + 0.250645i \(0.0806426\pi\)
−0.968079 + 0.250645i \(0.919357\pi\)
\(642\) −0.0449575 0.000837110i −0.00177433 3.30381e-5i
\(643\) 0.974363 2.35232i 0.0384251 0.0927665i −0.903502 0.428584i \(-0.859013\pi\)
0.941927 + 0.335818i \(0.109013\pi\)
\(644\) 12.3981 15.0082i 0.488554 0.591405i
\(645\) 3.78444 3.57209i 0.149012 0.140651i
\(646\) 2.36389 2.59971i 0.0930059 0.102284i
\(647\) 22.3823 22.3823i 0.879941 0.879941i −0.113587 0.993528i \(-0.536234\pi\)
0.993528 + 0.113587i \(0.0362341\pi\)
\(648\) −23.2466 + 10.3728i −0.913213 + 0.407483i
\(649\) −24.2952 24.2952i −0.953670 0.953670i
\(650\) 4.67851 0.222279i 0.183506 0.00871849i
\(651\) 25.3898 + 26.8992i 0.995106 + 1.05426i
\(652\) 21.3388 11.3175i 0.835692 0.443227i
\(653\) −2.02663 0.839459i −0.0793083 0.0328506i 0.342677 0.939453i \(-0.388666\pi\)
−0.421985 + 0.906603i \(0.638666\pi\)
\(654\) 21.9545 22.7876i 0.858489 0.891066i
\(655\) −11.7716 −0.459953
\(656\) −15.2944 10.3627i −0.597146 0.404596i
\(657\) 6.62483 + 7.43731i 0.258459 + 0.290157i
\(658\) −23.8521 50.6422i −0.929852 1.97424i
\(659\) 4.65284 11.2330i 0.181249 0.437574i −0.806975 0.590585i \(-0.798897\pi\)
0.988224 + 0.153011i \(0.0488971\pi\)
\(660\) −1.57738 23.8314i −0.0613994 0.927635i
\(661\) −22.0472 + 9.13226i −0.857538 + 0.355204i −0.767744 0.640757i \(-0.778621\pi\)
−0.0897938 + 0.995960i \(0.528621\pi\)
\(662\) −19.1513 + 0.909890i −0.744337 + 0.0353639i
\(663\) 0.979901 + 0.439427i 0.0380562 + 0.0170659i
\(664\) −3.21993 22.4549i −0.124957 0.871417i
\(665\) 9.96289 + 9.96289i 0.386344 + 0.386344i
\(666\) −1.24981 0.0127973i −0.0484290 0.000495886i
\(667\) −13.9282 + 5.76923i −0.539300 + 0.223386i
\(668\) 3.62105 0.344855i 0.140102 0.0133428i
\(669\) −31.5525 0.910763i −1.21989 0.0352121i
\(670\) 18.9085 + 6.80000i 0.730501 + 0.262707i
\(671\) −9.89643 −0.382048
\(672\) 27.1094 18.5950i 1.04577 0.717317i
\(673\) 1.77155 0.0682883 0.0341441 0.999417i \(-0.489129\pi\)
0.0341441 + 0.999417i \(0.489129\pi\)
\(674\) 26.5993 + 9.56579i 1.02457 + 0.368461i
\(675\) −12.2324 14.5574i −0.470825 0.560315i
\(676\) −2.30967 24.2520i −0.0888333 0.932768i
\(677\) −31.1005 + 12.8822i −1.19529 + 0.495105i −0.889474 0.456986i \(-0.848929\pi\)
−0.305815 + 0.952091i \(0.598929\pi\)
\(678\) −23.9374 9.39699i −0.919309 0.360889i
\(679\) 20.5577 + 20.5577i 0.788930 + 0.788930i
\(680\) −1.34519 + 1.79555i −0.0515855 + 0.0688563i
\(681\) 8.31973 18.5526i 0.318813 0.710937i
\(682\) 53.5394 2.54369i 2.05013 0.0974028i
\(683\) −2.51740 + 1.04274i −0.0963256 + 0.0398994i −0.430326 0.902674i \(-0.641601\pi\)
0.334000 + 0.942573i \(0.391601\pi\)
\(684\) −9.07018 19.7805i −0.346807 0.756326i
\(685\) −1.85465 + 4.47752i −0.0708624 + 0.171077i
\(686\) −5.54541 11.7739i −0.211725 0.449528i
\(687\) 22.0365 8.39142i 0.840747 0.320153i
\(688\) 8.66727 5.71077i 0.330437 0.217721i
\(689\) −3.69401 −0.140731
\(690\) 5.92528 + 5.70865i 0.225571 + 0.217325i
\(691\) 36.0335 + 14.9256i 1.37078 + 0.567795i 0.942000 0.335614i \(-0.108944\pi\)
0.428779 + 0.903409i \(0.358944\pi\)
\(692\) −0.0574063 0.108238i −0.00218226 0.00411459i
\(693\) −53.9579 26.0921i −2.04969 0.991158i
\(694\) −21.5809 + 1.02532i −0.819200 + 0.0389207i
\(695\) 4.08969 + 4.08969i 0.155131 + 0.155131i
\(696\) −25.2945 + 2.88505i −0.958786 + 0.109358i
\(697\) 2.23732 2.23732i 0.0847444 0.0847444i
\(698\) 8.13722 8.94899i 0.307998 0.338724i
\(699\) −19.7110 20.8827i −0.745537 0.789856i
\(700\) 18.9312 + 15.6389i 0.715534 + 0.591095i
\(701\) 1.39440 3.36638i 0.0526658 0.127147i −0.895357 0.445350i \(-0.853079\pi\)
0.948023 + 0.318203i \(0.103079\pi\)
\(702\) 4.88308 4.51545i 0.184300 0.170425i
\(703\) 1.06845i 0.0402973i
\(704\) 5.12760 47.3595i 0.193254 1.78493i
\(705\) 22.1109 8.41972i 0.832743 0.317105i
\(706\) 37.8693 + 13.6188i 1.42523 + 0.512550i
\(707\) −52.6494 21.8081i −1.98008 0.820177i
\(708\) 18.9318 + 6.41290i 0.711500 + 0.241012i
\(709\) 9.10175 + 21.9736i 0.341824 + 0.825235i 0.997531 + 0.0702205i \(0.0223703\pi\)
−0.655708 + 0.755015i \(0.727630\pi\)
\(710\) −13.6922 12.4501i −0.513858 0.467245i
\(711\) −26.6868 1.54191i −1.00083 0.0578263i
\(712\) 7.72485 + 1.97474i 0.289501 + 0.0740064i
\(713\) −13.0568 + 13.0568i −0.488980 + 0.488980i
\(714\) 2.25104 + 5.16059i 0.0842430 + 0.193130i
\(715\) 2.38796 + 5.76505i 0.0893047 + 0.215601i
\(716\) −5.42325 + 2.87634i −0.202677 + 0.107494i
\(717\) 37.3878 + 1.07920i 1.39627 + 0.0403034i
\(718\) 2.97065 + 6.30721i 0.110864 + 0.235383i
\(719\) 19.5450i 0.728907i 0.931222 + 0.364453i \(0.118744\pi\)
−0.931222 + 0.364453i \(0.881256\pi\)
\(720\) 6.96270 + 12.0240i 0.259484 + 0.448108i
\(721\) 25.6126i 0.953863i
\(722\) −7.47971 + 3.52289i −0.278366 + 0.131109i
\(723\) −25.2938 0.730106i −0.940686 0.0271529i
\(724\) 43.1154 + 13.2309i 1.60237 + 0.491723i
\(725\) −7.27728 17.5689i −0.270271 0.652493i
\(726\) −54.9093 + 23.9513i −2.03787 + 0.888917i
\(727\) −20.8914 + 20.8914i −0.774821 + 0.774821i −0.978945 0.204124i \(-0.934565\pi\)
0.204124 + 0.978945i \(0.434565\pi\)
\(728\) −5.14974 + 6.87388i −0.190862 + 0.254763i
\(729\) −26.5963 4.65151i −0.985048 0.172278i
\(730\) 3.65738 4.02224i 0.135366 0.148870i
\(731\) 0.680281 + 1.64234i 0.0251611 + 0.0607443i
\(732\) 5.16196 2.54973i 0.190792 0.0942406i
\(733\) −9.09957 3.76916i −0.336100 0.139217i 0.208249 0.978076i \(-0.433223\pi\)
−0.544350 + 0.838859i \(0.683223\pi\)
\(734\) 3.52911 9.81328i 0.130262 0.362215i
\(735\) −7.97886 + 3.03831i −0.294305 + 0.112070i
\(736\) 9.66922 + 13.2595i 0.356412 + 0.488753i
\(737\) 73.0703i 2.69158i
\(738\) −7.31297 18.1793i −0.269194 0.669191i
\(739\) 8.03797 19.4054i 0.295682 0.713839i −0.704311 0.709892i \(-0.748744\pi\)
0.999992 0.00394665i \(-0.00125626\pi\)
\(740\) 0.0646786 + 0.679139i 0.00237763 + 0.0249656i
\(741\) 3.90256 + 4.13455i 0.143364 + 0.151886i
\(742\) −14.3286 13.0288i −0.526018 0.478302i
\(743\) −14.8827 + 14.8827i −0.545995 + 0.545995i −0.925280 0.379285i \(-0.876170\pi\)
0.379285 + 0.925280i \(0.376170\pi\)
\(744\) −27.2707 + 15.1207i −0.999792 + 0.554352i
\(745\) 11.8409 + 11.8409i 0.433817 + 0.433817i
\(746\) 0.561438 + 11.8171i 0.0205557 + 0.432655i
\(747\) 10.4745 21.6610i 0.383241 0.792533i
\(748\) 7.79949 + 2.39344i 0.285177 + 0.0875130i
\(749\) 0.0569026 + 0.0235698i 0.00207917 + 0.000861222i
\(750\) −17.0399 + 17.6865i −0.622210 + 0.645820i
\(751\) −47.9945 −1.75135 −0.875673 0.482905i \(-0.839582\pi\)
−0.875673 + 0.482905i \(0.839582\pi\)
\(752\) 46.3415 8.90756i 1.68990 0.324825i
\(753\) 4.59272 1.74889i 0.167368 0.0637330i
\(754\) 6.01750 2.83420i 0.219144 0.103216i
\(755\) −1.85523 + 4.47893i −0.0675189 + 0.163005i
\(756\) 34.8668 0.292149i 1.26809 0.0106253i
\(757\) −4.61422 + 1.91127i −0.167707 + 0.0694663i −0.464957 0.885333i \(-0.653930\pi\)
0.297251 + 0.954799i \(0.403930\pi\)
\(758\) 1.64727 + 34.6717i 0.0598317 + 1.25933i
\(759\) 12.2426 27.3004i 0.444379 0.990943i
\(760\) −10.2172 + 6.05698i −0.370617 + 0.219710i
\(761\) 35.4112 + 35.4112i 1.28365 + 1.28365i 0.938573 + 0.345081i \(0.112149\pi\)
0.345081 + 0.938573i \(0.387851\pi\)
\(762\) −0.709993 + 1.80860i −0.0257203 + 0.0655185i
\(763\) −40.0435 + 16.5865i −1.44967 + 0.600473i
\(764\) −35.5515 29.3687i −1.28621 1.06252i
\(765\) −2.24738 + 0.782322i −0.0812541 + 0.0282849i
\(766\) −5.44286 + 15.1348i −0.196659 + 0.546842i
\(767\) −5.22237 −0.188569
\(768\) 9.52719 + 26.0237i 0.343783 + 0.939049i
\(769\) 49.1306 1.77169 0.885847 0.463978i \(-0.153578\pi\)
0.885847 + 0.463978i \(0.153578\pi\)
\(770\) −11.0708 + 30.7842i −0.398963 + 1.10938i
\(771\) 2.34485 + 0.0676840i 0.0844476 + 0.00243758i
\(772\) −11.6081 9.58931i −0.417784 0.345127i
\(773\) 48.9331 20.2688i 1.76000 0.729017i 0.763467 0.645847i \(-0.223496\pi\)
0.996535 0.0831696i \(-0.0265043\pi\)
\(774\) 11.0086 + 0.112722i 0.395695 + 0.00405170i
\(775\) −16.4698 16.4698i −0.591611 0.591611i
\(776\) −21.0824 + 12.4981i −0.756815 + 0.448656i
\(777\) 1.56212 + 0.700519i 0.0560408 + 0.0251310i
\(778\) −0.818228 17.2220i −0.0293349 0.617439i
\(779\) 15.4757 6.41026i 0.554476 0.229672i
\(780\) −2.73087 2.39180i −0.0977808 0.0856403i
\(781\) −25.7531 + 62.1736i −0.921520 + 2.22474i
\(782\) −2.54267 + 1.19758i −0.0909259 + 0.0428254i
\(783\) −23.9605 12.4519i −0.856277 0.444993i
\(784\) −16.7227 + 3.21436i −0.597238 + 0.114798i
\(785\) 20.2044 0.721126
\(786\) −17.9338 17.2781i −0.639676 0.616290i
\(787\) −44.3943 18.3887i −1.58249 0.655487i −0.593681 0.804701i \(-0.702326\pi\)
−0.988805 + 0.149214i \(0.952326\pi\)
\(788\) −4.44432 1.36384i −0.158322 0.0485847i
\(789\) 5.92462 + 6.27681i 0.210922 + 0.223460i
\(790\) 0.692429 + 14.5742i 0.0246355 + 0.518527i
\(791\) 24.9072 + 24.9072i 0.885597 + 0.885597i
\(792\) 32.5762 38.6219i 1.15754 1.37237i
\(793\) −1.06364 + 1.06364i −0.0377711 + 0.0377711i
\(794\) −9.98639 9.08051i −0.354404 0.322255i
\(795\) 5.95253 5.61854i 0.211115 0.199269i
\(796\) −2.00310 21.0330i −0.0709981 0.745495i
\(797\) 10.5848 25.5539i 0.374931 0.905164i −0.617968 0.786203i \(-0.712044\pi\)
0.992899 0.118961i \(-0.0379562\pi\)
\(798\) 0.554909 + 29.8017i 0.0196435 + 1.05497i
\(799\) 8.08201i 0.285921i
\(800\) −16.7255 + 12.1967i −0.591337 + 0.431219i
\(801\) 5.62505 + 6.31492i 0.198752 + 0.223127i
\(802\) 2.61386 7.26829i 0.0922987 0.256652i
\(803\) −18.2642 7.56530i −0.644531 0.266974i
\(804\) 18.8259 + 38.1133i 0.663938 + 1.34415i
\(805\) −4.31287 10.4122i −0.152009 0.366981i
\(806\) 5.48089 6.02767i 0.193056 0.212315i
\(807\) −12.6375 + 28.1811i −0.444863 + 0.992022i
\(808\) 28.8040 38.4476i 1.01332 1.35258i
\(809\) −26.4258 + 26.4258i −0.929083 + 0.929083i −0.997647 0.0685638i \(-0.978158\pi\)
0.0685638 + 0.997647i \(0.478158\pi\)
\(810\) −1.00067 + 14.7033i −0.0351601 + 0.516621i
\(811\) 10.2190 + 24.6709i 0.358838 + 0.866311i 0.995464 + 0.0951387i \(0.0303295\pi\)
−0.636626 + 0.771173i \(0.719671\pi\)
\(812\) 33.3373 + 10.2303i 1.16991 + 0.359012i
\(813\) −0.424933 + 14.7214i −0.0149030 + 0.516301i
\(814\) 2.24432 1.05706i 0.0786634 0.0370499i
\(815\) 13.9838i 0.489831i
\(816\) −4.68485 + 0.761051i −0.164003 + 0.0266421i
\(817\) 9.41115i 0.329254i
\(818\) 18.4478 + 39.1678i 0.645011 + 1.36947i
\(819\) −8.60358 + 2.99494i −0.300633 + 0.104652i
\(820\) −9.44881 + 5.01138i −0.329967 + 0.175005i
\(821\) −15.9273 38.4519i −0.555866 1.34198i −0.913013 0.407932i \(-0.866250\pi\)
0.357146 0.934048i \(-0.383750\pi\)
\(822\) −9.39755 + 4.09919i −0.327777 + 0.142976i
\(823\) −27.1818 + 27.1818i −0.947499 + 0.947499i −0.998689 0.0511904i \(-0.983698\pi\)
0.0511904 + 0.998689i \(0.483698\pi\)
\(824\) 20.9188 + 5.34757i 0.728742 + 0.186291i
\(825\) 34.4366 + 15.4428i 1.19893 + 0.537648i
\(826\) −20.2569 18.4193i −0.704826 0.640890i
\(827\) 12.6297 + 30.4907i 0.439176 + 1.06027i 0.976234 + 0.216720i \(0.0695358\pi\)
−0.537058 + 0.843546i \(0.680464\pi\)
\(828\) 0.647981 + 17.3941i 0.0225189 + 0.604485i
\(829\) −34.6568 14.3553i −1.20368 0.498581i −0.311494 0.950248i \(-0.600829\pi\)
−0.892187 + 0.451667i \(0.850829\pi\)
\(830\) −12.3580 4.44427i −0.428954 0.154263i
\(831\) −13.4786 35.3960i −0.467568 1.22787i
\(832\) −4.53897 5.64118i −0.157361 0.195573i
\(833\) 2.91645i 0.101049i
\(834\) 0.227786 + 12.2334i 0.00788757 + 0.423606i
\(835\) 0.805870 1.94554i 0.0278883 0.0673282i
\(836\) 33.2993 + 27.5082i 1.15168 + 0.951391i
\(837\) −32.9498 2.85964i −1.13891 0.0988438i
\(838\) 16.5857 18.2403i 0.572944 0.630101i
\(839\) 5.13731 5.13731i 0.177360 0.177360i −0.612844 0.790204i \(-0.709975\pi\)
0.790204 + 0.612844i \(0.209975\pi\)
\(840\) −2.15676 18.9093i −0.0744153 0.652431i
\(841\) 1.41020 + 1.41020i 0.0486277 + 0.0486277i
\(842\) 40.9240 1.94433i 1.41034 0.0670059i
\(843\) −18.4084 + 17.3755i −0.634018 + 0.598443i
\(844\) −16.2107 30.5647i −0.557994 1.05208i
\(845\) −13.0303 5.39732i −0.448255 0.185673i
\(846\) 46.0438 + 19.6267i 1.58302 + 0.674779i
\(847\) 82.0555 2.81946
\(848\) 13.6327 8.98247i 0.468150 0.308459i
\(849\) −5.78660 15.1961i −0.198596 0.521528i
\(850\) −1.51062 3.20732i −0.0518140 0.110010i
\(851\) −0.327054 + 0.789578i −0.0112113 + 0.0270664i
\(852\) −2.58566 39.0647i −0.0885833 1.33833i
\(853\) 27.7734 11.5041i 0.950943 0.393893i 0.147358 0.989083i \(-0.452923\pi\)
0.803585 + 0.595190i \(0.202923\pi\)
\(854\) −7.87720 + 0.374250i −0.269552 + 0.0128066i
\(855\) −12.5772 0.726686i −0.430130 0.0248521i
\(856\) −0.0311309 + 0.0415535i −0.00106403 + 0.00142027i
\(857\) 23.9037 + 23.9037i 0.816536 + 0.816536i 0.985604 0.169069i \(-0.0540760\pi\)
−0.169069 + 0.985604i \(0.554076\pi\)
\(858\) −4.82383 + 12.2880i −0.164683 + 0.419504i
\(859\) 36.4970 15.1176i 1.24526 0.515805i 0.339907 0.940459i \(-0.389604\pi\)
0.905356 + 0.424654i \(0.139604\pi\)
\(860\) −0.569704 5.98201i −0.0194267 0.203985i
\(861\) −0.774422 + 26.8291i −0.0263922 + 0.914333i
\(862\) −27.2508 9.80008i −0.928165 0.333792i
\(863\) −48.7809 −1.66052 −0.830260 0.557377i \(-0.811808\pi\)
−0.830260 + 0.557377i \(0.811808\pi\)
\(864\) −7.04111 + 28.5381i −0.239543 + 0.970886i
\(865\) −0.0709307 −0.00241172
\(866\) 19.5298 + 7.02344i 0.663651 + 0.238666i
\(867\) −0.826119 + 28.6201i −0.0280565 + 0.971989i
\(868\) 42.5192 4.04936i 1.44319 0.137444i
\(869\) 49.0187 20.3042i 1.66284 0.688773i
\(870\) −5.38583 + 13.7196i −0.182597 + 0.465137i
\(871\) −7.85341 7.85341i −0.266103 0.266103i
\(872\) −5.18636 36.1682i −0.175632 1.22481i
\(873\) −25.9520 1.49946i −0.878342 0.0507490i
\(874\) −14.8628 + 0.706141i −0.502742 + 0.0238856i
\(875\) 31.0796 12.8736i 1.05068 0.435207i
\(876\) 11.4757 0.759569i 0.387729 0.0256635i
\(877\) −8.45430 + 20.4105i −0.285481 + 0.689213i −0.999945 0.0104591i \(-0.996671\pi\)
0.714464 + 0.699672i \(0.246671\pi\)
\(878\) −4.14869 8.80839i −0.140012 0.297269i
\(879\) −7.59343 19.9410i −0.256120 0.672592i
\(880\) −22.8312 15.4693i −0.769641 0.521469i
\(881\) 25.8223 0.869976 0.434988 0.900436i \(-0.356753\pi\)
0.434988 + 0.900436i \(0.356753\pi\)
\(882\) −16.6152 7.08242i −0.559464 0.238478i
\(883\) 33.3809 + 13.8268i 1.12336 + 0.465310i 0.865518 0.500878i \(-0.166990\pi\)
0.257839 + 0.966188i \(0.416990\pi\)
\(884\) 1.09551 0.581028i 0.0368460 0.0195421i
\(885\) 8.41534 7.94315i 0.282879 0.267006i
\(886\) −22.1754 + 1.05356i −0.744996 + 0.0353952i
\(887\) 34.6997 + 34.6997i 1.16510 + 1.16510i 0.983343 + 0.181760i \(0.0581796\pi\)
0.181760 + 0.983343i \(0.441820\pi\)
\(888\) −0.898293 + 1.12959i −0.0301447 + 0.0379066i
\(889\) 1.88187 1.88187i 0.0631158 0.0631158i
\(890\) 3.10543 3.41523i 0.104094 0.114479i
\(891\) 51.5439 14.6695i 1.72679 0.491447i
\(892\) −23.2137 + 28.1006i −0.777251 + 0.940879i
\(893\) −16.3739 + 39.5302i −0.547933 + 1.32283i
\(894\) 0.659509 + 35.4193i 0.0220573 + 1.18460i
\(895\) 3.55398i 0.118796i
\(896\) 2.29040 37.8903i 0.0765170 1.26583i
\(897\) −1.61838 4.24999i −0.0540360 0.141903i
\(898\) 2.35030 + 0.845227i 0.0784304 + 0.0282056i
\(899\) −30.5593 12.6581i −1.01921 0.422170i
\(900\) −21.9408 + 0.817360i −0.731359 + 0.0272453i
\(901\) 1.07001 + 2.58324i 0.0356473 + 0.0860602i
\(902\) 28.7758 + 26.1655i 0.958129 + 0.871216i
\(903\) −13.7595 6.17033i −0.457889 0.205336i
\(904\) −25.5430 + 15.1424i −0.849546 + 0.503629i
\(905\) 18.4625 18.4625i 0.613715 0.613715i
\(906\) −9.40052 + 4.10049i −0.312311 + 0.136230i
\(907\) −7.42403 17.9232i −0.246511 0.595130i 0.751392 0.659856i \(-0.229383\pi\)
−0.997903 + 0.0647258i \(0.979383\pi\)
\(908\) −11.0007 20.7414i −0.365070 0.688329i
\(909\) 48.1224 16.7516i 1.59612 0.555616i
\(910\) 2.11875 + 4.49846i 0.0702357 + 0.149123i
\(911\) 37.5930i 1.24551i −0.782416 0.622756i \(-0.786013\pi\)
0.782416 0.622756i \(-0.213987\pi\)
\(912\) −24.4561 5.76898i −0.809822 0.191030i
\(913\) 47.7565i 1.58051i
\(914\) −40.4533 + 19.0532i −1.33808 + 0.630225i
\(915\) 0.0961708 3.33174i 0.00317931 0.110144i
\(916\) 7.98788 26.0300i 0.263927 0.860056i
\(917\) 13.0535 + 31.5140i 0.431066 + 1.04069i
\(918\) −4.57212 2.10681i −0.150902 0.0695351i
\(919\) 28.3220 28.3220i 0.934258 0.934258i −0.0637109 0.997968i \(-0.520294\pi\)
0.997968 + 0.0637109i \(0.0202936\pi\)
\(920\) 9.40451 1.34857i 0.310058 0.0444609i
\(921\) −9.67681 + 21.5788i −0.318862 + 0.711046i
\(922\) 0.836138 0.919552i 0.0275368 0.0302838i
\(923\) 3.91438 + 9.45014i 0.128843 + 0.311055i
\(924\) −62.0506 + 30.6496i −2.04132 + 1.00830i
\(925\) −0.995970 0.412544i −0.0327473 0.0135644i
\(926\) 6.70057 18.6321i 0.220194 0.612288i
\(927\) 15.2326 + 17.1008i 0.500304 + 0.561663i
\(928\) −15.3159 + 25.0920i −0.502768 + 0.823684i
\(929\) 14.6297i 0.479986i −0.970775 0.239993i \(-0.922855\pi\)
0.970775 0.239993i \(-0.0771452\pi\)
\(930\) 0.336079 + 18.0493i 0.0110205 + 0.591861i
\(931\) 5.90865 14.2647i 0.193648 0.467508i
\(932\) −33.0090 + 3.14365i −1.08125 + 0.102974i
\(933\) −33.4922 + 31.6129i −1.09648 + 1.03496i
\(934\) −16.2601 14.7851i −0.532047 0.483785i
\(935\) 3.33983 3.33983i 0.109224 0.109224i
\(936\) −0.649778 7.65220i −0.0212387 0.250120i
\(937\) 5.60824 + 5.60824i 0.183213 + 0.183213i 0.792754 0.609541i \(-0.208646\pi\)
−0.609541 + 0.792754i \(0.708646\pi\)
\(938\) −2.76328 58.1612i −0.0902241 1.89903i
\(939\) −7.24386 7.67448i −0.236395 0.250447i
\(940\) 8.01481 26.1178i 0.261414 0.851868i
\(941\) 10.5273 + 4.36054i 0.343180 + 0.142150i 0.547615 0.836730i \(-0.315536\pi\)
−0.204435 + 0.978880i \(0.565536\pi\)
\(942\) 30.7810 + 29.6557i 1.00290 + 0.966235i
\(943\) −13.3987 −0.436321
\(944\) 19.2732 12.6989i 0.627288 0.413313i
\(945\) 9.30855 17.9120i 0.302807 0.582676i
\(946\) −19.7685 + 9.31083i −0.642729 + 0.302721i
\(947\) −22.3491 + 53.9555i −0.726248 + 1.75332i −0.0715370 + 0.997438i \(0.522790\pi\)
−0.654711 + 0.755879i \(0.727210\pi\)
\(948\) −20.3369 + 23.2199i −0.660511 + 0.754146i
\(949\) −2.77609 + 1.14990i −0.0901158 + 0.0373272i
\(950\) −0.890724 18.7479i −0.0288989 0.608262i
\(951\) −2.24416 1.00637i −0.0727718 0.0326338i
\(952\) 6.29862 + 1.61014i 0.204139 + 0.0521850i
\(953\) −32.8805 32.8805i −1.06510 1.06510i −0.997728 0.0673750i \(-0.978538\pi\)
−0.0673750 0.997728i \(-0.521462\pi\)
\(954\) 17.3154 + 0.177300i 0.560606 + 0.00574030i
\(955\) −24.6644 + 10.2163i −0.798122 + 0.330593i
\(956\) 27.5068 33.2976i 0.889633 1.07692i
\(957\) 53.5741 + 1.54642i 1.73180 + 0.0499885i
\(958\) 16.4970 45.8728i 0.532995 1.48208i
\(959\) 14.0435 0.453489
\(960\) 15.8943 + 2.18649i 0.512985 + 0.0705686i
\(961\) −9.51359 −0.306890
\(962\) 0.127604 0.354824i 0.00411411 0.0114400i
\(963\) −0.0520098 + 0.0181049i −0.00167599 + 0.000583421i
\(964\) −18.6090 + 22.5266i −0.599357 + 0.725534i
\(965\) −8.05330 + 3.33578i −0.259245 + 0.107383i
\(966\) 8.71226 22.1931i 0.280312 0.714052i
\(967\) 14.6204 + 14.6204i 0.470160 + 0.470160i 0.901966 0.431807i \(-0.142124\pi\)
−0.431807 + 0.901966i \(0.642124\pi\)
\(968\) −17.1321 + 67.0180i −0.550647 + 2.15404i
\(969\) 1.76089 3.92670i 0.0565679 0.126144i
\(970\) 0.673364 + 14.1729i 0.0216204 + 0.455065i
\(971\) −39.9825 + 16.5613i −1.28310 + 0.531477i −0.916921 0.399068i \(-0.869334\pi\)
−0.366178 + 0.930545i \(0.619334\pi\)
\(972\) −23.1058 + 20.9314i −0.741118 + 0.671375i
\(973\) 6.41357 15.4837i 0.205610 0.496386i
\(974\) −24.7356 + 11.6503i −0.792580 + 0.373300i
\(975\) 5.36091 2.04141i 0.171687 0.0653775i
\(976\) 1.33899 6.51176i 0.0428600 0.208436i
\(977\) −14.1567 −0.452912 −0.226456 0.974021i \(-0.572714\pi\)
−0.226456 + 0.974021i \(0.572714\pi\)
\(978\) 20.5252 21.3040i 0.656323 0.681228i
\(979\) −15.5079 6.42359i −0.495635 0.205299i
\(980\) −2.89220 + 9.42478i −0.0923880 + 0.301064i
\(981\) 16.8713 34.8894i 0.538659 1.11393i
\(982\) 1.16255 + 24.4693i 0.0370985 + 0.780847i
\(983\) −27.5590 27.5590i −0.878995 0.878995i 0.114436 0.993431i \(-0.463494\pi\)
−0.993431 + 0.114436i \(0.963494\pi\)
\(984\) −21.7507 6.23406i −0.693387 0.198735i
\(985\) −1.90311 + 1.90311i −0.0606381 + 0.0606381i
\(986\) −3.72501 3.38711i −0.118628 0.107868i
\(987\) −47.0595 49.8570i −1.49792 1.58697i
\(988\) 6.53543 0.622410i 0.207920 0.0198015i
\(989\) 2.88077 6.95478i 0.0916030 0.221149i
\(990\) −10.9167 27.1378i −0.346954 0.862496i
\(991\) 14.9042i 0.473446i −0.971577 0.236723i \(-0.923927\pi\)
0.971577 0.236723i \(-0.0760734\pi\)
\(992\) −5.57016 + 35.5726i −0.176853 + 1.12943i
\(993\) −21.9447 + 8.35645i −0.696395 + 0.265184i
\(994\) −18.1474 + 50.4618i −0.575599 + 1.60055i
\(995\) −11.3008 4.68093i −0.358258 0.148395i
\(996\) −12.3040 24.9097i −0.389868 0.789294i
\(997\) −4.66402 11.2599i −0.147711 0.356606i 0.832655 0.553792i \(-0.186820\pi\)
−0.980366 + 0.197186i \(0.936820\pi\)
\(998\) −6.55127 + 7.20484i −0.207377 + 0.228065i
\(999\) −1.45960 + 0.461327i −0.0461798 + 0.0145958i
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 96.2.o.a.35.9 yes 56
3.2 odd 2 inner 96.2.o.a.35.6 yes 56
4.3 odd 2 384.2.o.a.47.7 56
8.3 odd 2 768.2.o.a.95.8 56
8.5 even 2 768.2.o.b.95.7 56
12.11 even 2 384.2.o.a.47.4 56
24.5 odd 2 768.2.o.b.95.4 56
24.11 even 2 768.2.o.a.95.11 56
32.5 even 8 768.2.o.a.671.11 56
32.11 odd 8 inner 96.2.o.a.11.6 56
32.21 even 8 384.2.o.a.335.4 56
32.27 odd 8 768.2.o.b.671.4 56
96.5 odd 8 768.2.o.a.671.8 56
96.11 even 8 inner 96.2.o.a.11.9 yes 56
96.53 odd 8 384.2.o.a.335.7 56
96.59 even 8 768.2.o.b.671.7 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.2.o.a.11.6 56 32.11 odd 8 inner
96.2.o.a.11.9 yes 56 96.11 even 8 inner
96.2.o.a.35.6 yes 56 3.2 odd 2 inner
96.2.o.a.35.9 yes 56 1.1 even 1 trivial
384.2.o.a.47.4 56 12.11 even 2
384.2.o.a.47.7 56 4.3 odd 2
384.2.o.a.335.4 56 32.21 even 8
384.2.o.a.335.7 56 96.53 odd 8
768.2.o.a.95.8 56 8.3 odd 2
768.2.o.a.95.11 56 24.11 even 2
768.2.o.a.671.8 56 96.5 odd 8
768.2.o.a.671.11 56 32.5 even 8
768.2.o.b.95.4 56 24.5 odd 2
768.2.o.b.95.7 56 8.5 even 2
768.2.o.b.671.4 56 32.27 odd 8
768.2.o.b.671.7 56 96.59 even 8