Properties

Label 177.2.f.a.155.3
Level $177$
Weight $2$
Character 177.155
Analytic conductor $1.413$
Analytic rank $0$
Dimension $504$
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] = [177,2,Mod(2,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([29, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.f (of order \(58\), degree \(28\), 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: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(504\)
Relative dimension: \(18\) over \(\Q(\zeta_{58})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label 155.3
Character \(\chi\) \(=\) 177.155
Dual form 177.2.f.a.8.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.317307 - 1.93549i) q^{2} +(1.61303 - 0.630969i) q^{3} +(-1.75012 + 0.589685i) q^{4} +(2.92507 + 1.98325i) q^{5} +(-1.73306 - 2.92180i) q^{6} +(-2.73852 - 0.602794i) q^{7} +(-0.140747 - 0.265477i) q^{8} +(2.20376 - 2.03555i) q^{9} +O(q^{10})\) \(q+(-0.317307 - 1.93549i) q^{2} +(1.61303 - 0.630969i) q^{3} +(-1.75012 + 0.589685i) q^{4} +(2.92507 + 1.98325i) q^{5} +(-1.73306 - 2.92180i) q^{6} +(-2.73852 - 0.602794i) q^{7} +(-0.140747 - 0.265477i) q^{8} +(2.20376 - 2.03555i) q^{9} +(2.91041 - 6.29074i) q^{10} +(2.01160 + 1.52918i) q^{11} +(-2.45094 + 2.05546i) q^{12} +(-2.03098 + 3.37551i) q^{13} +(-0.297748 + 5.49164i) q^{14} +(5.96961 + 1.35342i) q^{15} +(-3.40961 + 2.59192i) q^{16} +(-1.04883 - 4.76487i) q^{17} +(-4.63905 - 3.61945i) q^{18} +(-5.48029 - 0.596018i) q^{19} +(-6.28873 - 1.74606i) q^{20} +(-4.79767 + 0.755593i) q^{21} +(2.32141 - 4.37865i) q^{22} +(-5.39194 + 6.34788i) q^{23} +(-0.394538 - 0.339417i) q^{24} +(2.77209 + 6.95741i) q^{25} +(7.17771 + 2.85986i) q^{26} +(2.27037 - 4.67391i) q^{27} +(5.14821 - 0.559901i) q^{28} +(4.96592 + 0.814121i) q^{29} +(0.725325 - 11.9836i) q^{30} +(-0.0516452 - 0.474870i) q^{31} +(5.66223 + 5.36355i) q^{32} +(4.20965 + 1.19736i) q^{33} +(-8.88956 + 3.54192i) q^{34} +(-6.81488 - 7.19438i) q^{35} +(-2.65651 + 4.86198i) q^{36} +(4.35883 + 2.31091i) q^{37} +(0.585351 + 10.7962i) q^{38} +(-1.14619 + 6.72630i) q^{39} +(0.114812 - 1.05568i) q^{40} +(5.04670 - 4.28671i) q^{41} +(2.98478 + 9.04608i) q^{42} +(-1.09884 - 1.44550i) q^{43} +(-4.42229 - 1.49004i) q^{44} +(10.4831 - 1.58353i) q^{45} +(13.9971 + 8.42180i) q^{46} +(-2.14776 - 3.16771i) q^{47} +(-3.86440 + 6.33222i) q^{48} +(0.783101 + 0.362301i) q^{49} +(12.5864 - 7.57298i) q^{50} +(-4.69828 - 7.02413i) q^{51} +(1.56397 - 7.10520i) q^{52} +(-2.23874 - 4.83896i) q^{53} +(-9.76670 - 2.91121i) q^{54} +(2.85134 + 8.46247i) q^{55} +(0.225411 + 0.811856i) q^{56} +(-9.21597 + 2.49650i) q^{57} -9.86981i q^{58} +(7.29534 + 2.40374i) q^{59} +(-11.2456 + 1.15154i) q^{60} +(10.4904 - 1.71981i) q^{61} +(-0.902718 + 0.250638i) q^{62} +(-7.26205 + 4.24598i) q^{63} +(3.77737 - 5.57120i) q^{64} +(-12.6352 + 5.84569i) q^{65} +(0.981728 - 8.52765i) q^{66} +(-2.77767 + 1.47262i) q^{67} +(4.64536 + 7.72064i) q^{68} +(-4.69207 + 13.6415i) q^{69} +(-11.7622 + 15.4729i) q^{70} +(-2.09285 + 1.41899i) q^{71} +(-0.850564 - 0.298550i) q^{72} +(-4.66322 - 0.252832i) q^{73} +(3.08964 - 9.16973i) q^{74} +(8.86138 + 9.47344i) q^{75} +(9.94265 - 2.18854i) q^{76} +(-4.58703 - 5.40027i) q^{77} +(13.3824 + 0.0841429i) q^{78} +(0.406217 - 1.46306i) q^{79} +(-15.1138 + 0.819446i) q^{80} +(0.713091 - 8.97171i) q^{81} +(-9.89822 - 8.40762i) q^{82} +(-0.830942 + 0.787110i) q^{83} +(7.95095 - 4.15150i) q^{84} +(6.38203 - 16.0177i) q^{85} +(-2.44908 + 2.58546i) q^{86} +(8.52388 - 1.82014i) q^{87} +(0.122835 - 0.749262i) q^{88} +(-1.85800 + 11.3333i) q^{89} +(-6.39128 - 19.7875i) q^{90} +(7.59661 - 8.01965i) q^{91} +(5.69331 - 14.2891i) q^{92} +(-0.382934 - 0.733395i) q^{93} +(-5.44957 + 5.16211i) q^{94} +(-14.8482 - 12.6122i) q^{95} +(12.5176 + 5.07890i) q^{96} +(-11.0444 + 0.598809i) q^{97} +(0.452746 - 1.63064i) q^{98} +(7.54580 - 0.724770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 504 q - 27 q^{3} - 70 q^{4} - 29 q^{6} - 58 q^{7} - 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 504 q - 27 q^{3} - 70 q^{4} - 29 q^{6} - 58 q^{7} - 19 q^{9} - 58 q^{10} - 15 q^{12} - 58 q^{13} - 38 q^{15} - 66 q^{16} - 29 q^{18} - 66 q^{19} - 24 q^{21} - 62 q^{22} - 29 q^{24} - 20 q^{25} - 54 q^{27} - 26 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 13 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} - q^{45} - 46 q^{46} + 147 q^{48} - 48 q^{49} + 59 q^{51} - 58 q^{52} + 174 q^{54} - 58 q^{55} + 83 q^{57} + 250 q^{60} - 58 q^{61} + 82 q^{63} + 10 q^{64} + 226 q^{66} - 58 q^{67} + 87 q^{69} - 58 q^{70} + 145 q^{72} - 58 q^{73} - 28 q^{75} - 150 q^{76} - 13 q^{78} - 30 q^{79} + 13 q^{81} - 58 q^{82} - 69 q^{84} - 86 q^{85} - 36 q^{87} + 22 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 162 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{55}{58}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.317307 1.93549i −0.224370 1.36860i −0.823214 0.567731i \(-0.807821\pi\)
0.598844 0.800866i \(-0.295627\pi\)
\(3\) 1.61303 0.630969i 0.931286 0.364290i
\(4\) −1.75012 + 0.589685i −0.875062 + 0.294843i
\(5\) 2.92507 + 1.98325i 1.30813 + 0.886936i 0.997966 0.0637465i \(-0.0203049\pi\)
0.310166 + 0.950682i \(0.399615\pi\)
\(6\) −1.73306 2.92180i −0.707519 1.19282i
\(7\) −2.73852 0.602794i −1.03506 0.227835i −0.335226 0.942138i \(-0.608813\pi\)
−0.699837 + 0.714303i \(0.746744\pi\)
\(8\) −0.140747 0.265477i −0.0497616 0.0938604i
\(9\) 2.20376 2.03555i 0.734586 0.678516i
\(10\) 2.91041 6.29074i 0.920352 1.98931i
\(11\) 2.01160 + 1.52918i 0.606521 + 0.461065i 0.862805 0.505536i \(-0.168705\pi\)
−0.256285 + 0.966601i \(0.582498\pi\)
\(12\) −2.45094 + 2.05546i −0.707524 + 0.593359i
\(13\) −2.03098 + 3.37551i −0.563292 + 0.936199i 0.436050 + 0.899923i \(0.356377\pi\)
−0.999342 + 0.0362761i \(0.988450\pi\)
\(14\) −0.297748 + 5.49164i −0.0795766 + 1.46770i
\(15\) 5.96961 + 1.35342i 1.54135 + 0.349451i
\(16\) −3.40961 + 2.59192i −0.852403 + 0.647980i
\(17\) −1.04883 4.76487i −0.254378 1.15565i −0.914530 0.404519i \(-0.867439\pi\)
0.660151 0.751133i \(-0.270492\pi\)
\(18\) −4.63905 3.61945i −1.09343 0.853113i
\(19\) −5.48029 0.596018i −1.25727 0.136736i −0.544874 0.838518i \(-0.683422\pi\)
−0.712392 + 0.701782i \(0.752388\pi\)
\(20\) −6.28873 1.74606i −1.40620 0.390430i
\(21\) −4.79767 + 0.755593i −1.04694 + 0.164884i
\(22\) 2.32141 4.37865i 0.494927 0.933531i
\(23\) −5.39194 + 6.34788i −1.12430 + 1.32362i −0.184133 + 0.982901i \(0.558948\pi\)
−0.940164 + 0.340723i \(0.889328\pi\)
\(24\) −0.394538 0.339417i −0.0805347 0.0692832i
\(25\) 2.77209 + 6.95741i 0.554417 + 1.39148i
\(26\) 7.17771 + 2.85986i 1.40766 + 0.560865i
\(27\) 2.27037 4.67391i 0.436933 0.899494i
\(28\) 5.14821 0.559901i 0.972920 0.105811i
\(29\) 4.96592 + 0.814121i 0.922148 + 0.151179i 0.604112 0.796900i \(-0.293528\pi\)
0.318037 + 0.948078i \(0.396976\pi\)
\(30\) 0.725325 11.9836i 0.132426 2.18789i
\(31\) −0.0516452 0.474870i −0.00927576 0.0852892i 0.988585 0.150664i \(-0.0481412\pi\)
−0.997861 + 0.0653749i \(0.979176\pi\)
\(32\) 5.66223 + 5.36355i 1.00095 + 0.948151i
\(33\) 4.20965 + 1.19736i 0.732805 + 0.208434i
\(34\) −8.88956 + 3.54192i −1.52455 + 0.607435i
\(35\) −6.81488 7.19438i −1.15192 1.21607i
\(36\) −2.65651 + 4.86198i −0.442752 + 0.810331i
\(37\) 4.35883 + 2.31091i 0.716587 + 0.379911i 0.786457 0.617646i \(-0.211913\pi\)
−0.0698691 + 0.997556i \(0.522258\pi\)
\(38\) 0.585351 + 10.7962i 0.0949564 + 1.75137i
\(39\) −1.14619 + 6.72630i −0.183538 + 1.07707i
\(40\) 0.114812 1.05568i 0.0181533 0.166917i
\(41\) 5.04670 4.28671i 0.788162 0.669471i −0.160050 0.987109i \(-0.551166\pi\)
0.948212 + 0.317638i \(0.102890\pi\)
\(42\) 2.98478 + 9.04608i 0.460561 + 1.39584i
\(43\) −1.09884 1.44550i −0.167571 0.220437i 0.704641 0.709564i \(-0.251108\pi\)
−0.872212 + 0.489128i \(0.837315\pi\)
\(44\) −4.42229 1.49004i −0.666685 0.224632i
\(45\) 10.4831 1.58353i 1.56274 0.236058i
\(46\) 13.9971 + 8.42180i 2.06377 + 1.24173i
\(47\) −2.14776 3.16771i −0.313283 0.462058i 0.638151 0.769912i \(-0.279700\pi\)
−0.951434 + 0.307853i \(0.900389\pi\)
\(48\) −3.86440 + 6.33222i −0.557778 + 0.913977i
\(49\) 0.783101 + 0.362301i 0.111872 + 0.0517573i
\(50\) 12.5864 7.57298i 1.77998 1.07098i
\(51\) −4.69828 7.02413i −0.657891 0.983574i
\(52\) 1.56397 7.10520i 0.216884 0.985314i
\(53\) −2.23874 4.83896i −0.307515 0.664682i 0.690779 0.723066i \(-0.257268\pi\)
−0.998294 + 0.0583832i \(0.981405\pi\)
\(54\) −9.76670 2.91121i −1.32908 0.396165i
\(55\) 2.85134 + 8.46247i 0.384474 + 1.14108i
\(56\) 0.225411 + 0.811856i 0.0301218 + 0.108489i
\(57\) −9.21597 + 2.49650i −1.22068 + 0.330669i
\(58\) 9.86981i 1.29597i
\(59\) 7.29534 + 2.40374i 0.949773 + 0.312940i
\(60\) −11.2456 + 1.15154i −1.45181 + 0.148663i
\(61\) 10.4904 1.71981i 1.34316 0.220199i 0.553039 0.833156i \(-0.313468\pi\)
0.790117 + 0.612957i \(0.210020\pi\)
\(62\) −0.902718 + 0.250638i −0.114645 + 0.0318311i
\(63\) −7.26205 + 4.24598i −0.914932 + 0.534943i
\(64\) 3.77737 5.57120i 0.472171 0.696400i
\(65\) −12.6352 + 5.84569i −1.56721 + 0.725068i
\(66\) 0.981728 8.52765i 0.120842 1.04968i
\(67\) −2.77767 + 1.47262i −0.339346 + 0.179910i −0.629363 0.777112i \(-0.716684\pi\)
0.290017 + 0.957022i \(0.406339\pi\)
\(68\) 4.64536 + 7.72064i 0.563332 + 0.936265i
\(69\) −4.69207 + 13.6415i −0.564858 + 1.64224i
\(70\) −11.7622 + 15.4729i −1.40586 + 1.84937i
\(71\) −2.09285 + 1.41899i −0.248376 + 0.168403i −0.679022 0.734118i \(-0.737596\pi\)
0.430646 + 0.902521i \(0.358286\pi\)
\(72\) −0.850564 0.298550i −0.100240 0.0351845i
\(73\) −4.66322 0.252832i −0.545788 0.0295918i −0.220816 0.975315i \(-0.570872\pi\)
−0.324972 + 0.945724i \(0.605355\pi\)
\(74\) 3.08964 9.16973i 0.359164 1.06596i
\(75\) 8.86138 + 9.47344i 1.02322 + 1.09390i
\(76\) 9.94265 2.18854i 1.14050 0.251043i
\(77\) −4.58703 5.40027i −0.522741 0.615418i
\(78\) 13.3824 + 0.0841429i 1.51525 + 0.00952730i
\(79\) 0.406217 1.46306i 0.0457030 0.164607i −0.937177 0.348854i \(-0.886571\pi\)
0.982880 + 0.184247i \(0.0589846\pi\)
\(80\) −15.1138 + 0.819446i −1.68977 + 0.0916169i
\(81\) 0.713091 8.97171i 0.0792323 0.996856i
\(82\) −9.89822 8.40762i −1.09308 0.928467i
\(83\) −0.830942 + 0.787110i −0.0912077 + 0.0863965i −0.731945 0.681364i \(-0.761387\pi\)
0.640738 + 0.767760i \(0.278629\pi\)
\(84\) 7.95095 4.15150i 0.867520 0.452965i
\(85\) 6.38203 16.0177i 0.692229 1.73736i
\(86\) −2.44908 + 2.58546i −0.264091 + 0.278797i
\(87\) 8.52388 1.82014i 0.913856 0.195139i
\(88\) 0.122835 0.749262i 0.0130943 0.0798716i
\(89\) −1.85800 + 11.3333i −0.196948 + 1.20133i 0.684487 + 0.729025i \(0.260026\pi\)
−0.881435 + 0.472305i \(0.843422\pi\)
\(90\) −6.39128 19.7875i −0.673700 2.08579i
\(91\) 7.59661 8.01965i 0.796341 0.840687i
\(92\) 5.69331 14.2891i 0.593568 1.48974i
\(93\) −0.382934 0.733395i −0.0397084 0.0760495i
\(94\) −5.44957 + 5.16211i −0.562080 + 0.532430i
\(95\) −14.8482 12.6122i −1.52339 1.29398i
\(96\) 12.5176 + 5.07890i 1.27757 + 0.518363i
\(97\) −11.0444 + 0.598809i −1.12139 + 0.0607999i −0.605492 0.795852i \(-0.707024\pi\)
−0.515896 + 0.856651i \(0.672541\pi\)
\(98\) 0.452746 1.63064i 0.0457342 0.164720i
\(99\) 7.54580 0.724770i 0.758381 0.0728422i
\(100\) −8.95418 10.5417i −0.895418 1.05417i
\(101\) −3.38838 + 0.745839i −0.337156 + 0.0742137i −0.380322 0.924854i \(-0.624187\pi\)
0.0431655 + 0.999068i \(0.486256\pi\)
\(102\) −12.1043 + 11.3223i −1.19851 + 1.12107i
\(103\) 1.52377 4.52239i 0.150142 0.445604i −0.846019 0.533153i \(-0.821007\pi\)
0.996160 + 0.0875489i \(0.0279034\pi\)
\(104\) 1.18198 + 0.0640849i 0.115902 + 0.00628404i
\(105\) −15.5321 7.30481i −1.51577 0.712876i
\(106\) −8.65538 + 5.86849i −0.840685 + 0.569999i
\(107\) 7.36764 9.69196i 0.712256 0.936957i −0.287527 0.957773i \(-0.592833\pi\)
0.999783 + 0.0208154i \(0.00662624\pi\)
\(108\) −1.21729 + 9.51872i −0.117134 + 0.915939i
\(109\) 2.27824 + 3.78647i 0.218216 + 0.362678i 0.946557 0.322537i \(-0.104536\pi\)
−0.728341 + 0.685215i \(0.759708\pi\)
\(110\) 15.4743 8.20393i 1.47541 0.782214i
\(111\) 8.48905 + 0.977284i 0.805745 + 0.0927597i
\(112\) 10.8997 5.04273i 1.02992 0.476493i
\(113\) 2.50884 3.70026i 0.236012 0.348091i −0.691177 0.722685i \(-0.742908\pi\)
0.927189 + 0.374594i \(0.122218\pi\)
\(114\) 7.75623 + 17.0452i 0.726438 + 1.59643i
\(115\) −28.3612 + 7.87446i −2.64470 + 0.734297i
\(116\) −9.17105 + 1.50352i −0.851511 + 0.139598i
\(117\) 2.39523 + 11.5730i 0.221439 + 1.06992i
\(118\) 2.33755 14.8828i 0.215189 1.37007i
\(119\) 13.6809i 1.25413i
\(120\) −0.480904 1.77529i −0.0439003 0.162061i
\(121\) −1.23466 4.44685i −0.112242 0.404259i
\(122\) −6.65734 19.7583i −0.602728 1.78883i
\(123\) 5.43572 10.0989i 0.490122 0.910588i
\(124\) 0.370409 + 0.800627i 0.0332637 + 0.0718984i
\(125\) −1.89117 + 8.59167i −0.169151 + 0.768463i
\(126\) 10.5223 + 12.7083i 0.937404 + 1.13215i
\(127\) −14.8793 + 8.95260i −1.32033 + 0.794415i −0.988831 0.149041i \(-0.952381\pi\)
−0.331497 + 0.943456i \(0.607554\pi\)
\(128\) 2.17526 + 1.00638i 0.192268 + 0.0889526i
\(129\) −2.68453 1.63831i −0.236360 0.144245i
\(130\) 15.3235 + 22.6005i 1.34396 + 1.98219i
\(131\) 13.0645 + 7.86064i 1.14145 + 0.686788i 0.955272 0.295729i \(-0.0955624\pi\)
0.186178 + 0.982516i \(0.440390\pi\)
\(132\) −8.07347 + 0.386836i −0.702705 + 0.0336698i
\(133\) 14.6486 + 4.93569i 1.27020 + 0.427979i
\(134\) 3.73162 + 4.90886i 0.322363 + 0.424061i
\(135\) 15.9105 9.16882i 1.36936 0.789127i
\(136\) −1.11735 + 0.949083i −0.0958117 + 0.0813832i
\(137\) 0.408724 3.75816i 0.0349197 0.321081i −0.963630 0.267241i \(-0.913888\pi\)
0.998550 0.0538407i \(-0.0171463\pi\)
\(138\) 27.8918 + 4.75289i 2.37430 + 0.404593i
\(139\) 0.313579 + 5.78363i 0.0265974 + 0.490561i 0.981238 + 0.192800i \(0.0617569\pi\)
−0.954641 + 0.297761i \(0.903760\pi\)
\(140\) 16.1693 + 8.57242i 1.36656 + 0.724502i
\(141\) −5.46314 3.75446i −0.460079 0.316182i
\(142\) 3.41052 + 3.60044i 0.286204 + 0.302142i
\(143\) −9.24728 + 3.68445i −0.773297 + 0.308110i
\(144\) −2.23798 + 12.6524i −0.186498 + 1.05437i
\(145\) 12.9111 + 12.2300i 1.07221 + 1.01565i
\(146\) 0.990318 + 9.10582i 0.0819593 + 0.753603i
\(147\) 1.49177 + 0.0902918i 0.123039 + 0.00744714i
\(148\) −8.99120 1.47403i −0.739072 0.121165i
\(149\) −2.81878 + 0.306561i −0.230924 + 0.0251145i −0.222849 0.974853i \(-0.571536\pi\)
−0.00807447 + 0.999967i \(0.502570\pi\)
\(150\) 15.5240 20.1571i 1.26753 1.64582i
\(151\) −12.8488 5.11941i −1.04562 0.416612i −0.216850 0.976205i \(-0.569578\pi\)
−0.828768 + 0.559593i \(0.810957\pi\)
\(152\) 0.613107 + 1.53878i 0.0497295 + 0.124812i
\(153\) −12.0105 8.36569i −0.970991 0.676326i
\(154\) −8.99666 + 10.5917i −0.724971 + 0.853502i
\(155\) 0.790719 1.49145i 0.0635121 0.119797i
\(156\) −1.96042 12.4478i −0.156959 0.996618i
\(157\) −1.16061 0.322242i −0.0926268 0.0257177i 0.220906 0.975295i \(-0.429099\pi\)
−0.313533 + 0.949577i \(0.601512\pi\)
\(158\) −2.96064 0.321989i −0.235536 0.0256160i
\(159\) −6.66440 6.39283i −0.528521 0.506985i
\(160\) 5.92519 + 26.9184i 0.468427 + 2.12809i
\(161\) 18.5924 14.1336i 1.46529 1.11388i
\(162\) −17.5909 + 1.46661i −1.38207 + 0.115228i
\(163\) 0.783382 14.4486i 0.0613592 1.13170i −0.792048 0.610459i \(-0.790985\pi\)
0.853407 0.521245i \(-0.174532\pi\)
\(164\) −6.30454 + 10.4782i −0.492302 + 0.818212i
\(165\) 9.93886 + 11.8511i 0.773739 + 0.922610i
\(166\) 1.78711 + 1.35852i 0.138706 + 0.105442i
\(167\) 4.86358 10.5125i 0.376355 0.813478i −0.623152 0.782100i \(-0.714148\pi\)
0.999508 0.0313779i \(-0.00998953\pi\)
\(168\) 0.875851 + 1.16732i 0.0675734 + 0.0900611i
\(169\) −1.17990 2.22553i −0.0907616 0.171195i
\(170\) −33.0271 7.26982i −2.53306 0.557570i
\(171\) −13.2905 + 9.84192i −1.01635 + 0.752630i
\(172\) 2.77549 + 1.88183i 0.211630 + 0.143488i
\(173\) −13.2431 + 4.46213i −1.00686 + 0.339250i −0.773948 0.633249i \(-0.781721\pi\)
−0.232909 + 0.972499i \(0.574824\pi\)
\(174\) −6.22754 15.9203i −0.472109 1.20692i
\(175\) −3.39753 20.7240i −0.256829 1.56659i
\(176\) −10.8223 −0.815761
\(177\) 13.2843 0.725817i 0.998511 0.0545557i
\(178\) 22.5251 1.68833
\(179\) −3.59827 21.9485i −0.268948 1.64051i −0.683118 0.730308i \(-0.739377\pi\)
0.414170 0.910199i \(-0.364072\pi\)
\(180\) −17.4130 + 8.95313i −1.29789 + 0.667327i
\(181\) 13.4277 4.52433i 0.998077 0.336291i 0.227597 0.973755i \(-0.426913\pi\)
0.770480 + 0.637464i \(0.220017\pi\)
\(182\) −17.9324 12.1585i −1.32924 0.901245i
\(183\) 15.8362 9.39321i 1.17064 0.694366i
\(184\) 2.44412 + 0.537991i 0.180183 + 0.0396612i
\(185\) 8.16680 + 15.4042i 0.600435 + 1.13254i
\(186\) −1.29797 + 0.973875i −0.0951717 + 0.0714080i
\(187\) 5.17652 11.1889i 0.378545 0.818211i
\(188\) 5.62680 + 4.27738i 0.410377 + 0.311960i
\(189\) −9.03485 + 11.4310i −0.657189 + 0.831485i
\(190\) −19.6993 + 32.7405i −1.42914 + 2.37524i
\(191\) 0.830614 15.3198i 0.0601011 1.10850i −0.800537 0.599283i \(-0.795452\pi\)
0.860638 0.509217i \(-0.170065\pi\)
\(192\) 2.57777 11.3699i 0.186035 0.820555i
\(193\) −14.6765 + 11.1568i −1.05644 + 0.803083i −0.980988 0.194067i \(-0.937832\pi\)
−0.0754494 + 0.997150i \(0.524039\pi\)
\(194\) 4.66345 + 21.1863i 0.334816 + 1.52109i
\(195\) −16.6926 + 17.4017i −1.19538 + 1.24616i
\(196\) −1.58417 0.172289i −0.113155 0.0123063i
\(197\) 26.1430 + 7.25858i 1.86261 + 0.517152i 0.999935 + 0.0114000i \(0.00362880\pi\)
0.862679 + 0.505752i \(0.168785\pi\)
\(198\) −3.79712 14.3748i −0.269850 1.02157i
\(199\) 7.20346 13.5872i 0.510640 0.963169i −0.485403 0.874291i \(-0.661327\pi\)
0.996043 0.0888780i \(-0.0283281\pi\)
\(200\) 1.45687 1.71516i 0.103016 0.121280i
\(201\) −3.55129 + 4.12801i −0.250489 + 0.291168i
\(202\) 2.51872 + 6.32151i 0.177216 + 0.444780i
\(203\) −13.1085 5.22291i −0.920038 0.366577i
\(204\) 12.3646 + 9.52258i 0.865695 + 0.666714i
\(205\) 23.2636 2.53007i 1.62480 0.176707i
\(206\) −9.23654 1.51425i −0.643540 0.105503i
\(207\) 1.03889 + 24.9647i 0.0722080 + 1.73517i
\(208\) −1.82421 16.7733i −0.126486 1.16302i
\(209\) −10.1127 9.57930i −0.699513 0.662614i
\(210\) −9.20993 + 32.3800i −0.635546 + 2.23443i
\(211\) −12.1728 + 4.85010i −0.838012 + 0.333895i −0.749356 0.662168i \(-0.769637\pi\)
−0.0886566 + 0.996062i \(0.528257\pi\)
\(212\) 6.77154 + 7.14863i 0.465071 + 0.490970i
\(213\) −2.48051 + 3.60940i −0.169961 + 0.247312i
\(214\) −21.0965 11.1846i −1.44213 0.764566i
\(215\) −0.347403 6.40746i −0.0236927 0.436985i
\(216\) −1.56037 + 0.0551083i −0.106169 + 0.00374964i
\(217\) −0.144817 + 1.33157i −0.00983083 + 0.0903930i
\(218\) 6.60577 5.61099i 0.447399 0.380024i
\(219\) −7.68145 + 2.53452i −0.519065 + 0.171267i
\(220\) −9.98039 13.1290i −0.672878 0.885155i
\(221\) 18.2140 + 6.13702i 1.22521 + 0.412821i
\(222\) −0.802115 16.7406i −0.0538345 1.12355i
\(223\) 20.4891 + 12.3279i 1.37205 + 0.825535i 0.994924 0.100626i \(-0.0320847\pi\)
0.377126 + 0.926162i \(0.376912\pi\)
\(224\) −12.2730 18.1014i −0.820026 1.20945i
\(225\) 20.2711 + 9.68973i 1.35141 + 0.645982i
\(226\) −7.95788 3.68171i −0.529350 0.244904i
\(227\) 9.31905 5.60708i 0.618527 0.372155i −0.171539 0.985177i \(-0.554874\pi\)
0.790066 + 0.613022i \(0.210046\pi\)
\(228\) 14.6569 9.80370i 0.970679 0.649266i
\(229\) −4.66292 + 21.1838i −0.308134 + 1.39987i 0.527021 + 0.849853i \(0.323309\pi\)
−0.835155 + 0.550015i \(0.814622\pi\)
\(230\) 24.2401 + 52.3942i 1.59835 + 3.45477i
\(231\) −10.8064 5.81654i −0.711011 0.382701i
\(232\) −0.482809 1.43292i −0.0316979 0.0940761i
\(233\) −1.36198 4.90543i −0.0892266 0.321365i 0.905444 0.424465i \(-0.139538\pi\)
−0.994671 + 0.103100i \(0.967124\pi\)
\(234\) 21.6393 8.30813i 1.41461 0.543119i
\(235\) 13.5253i 0.882296i
\(236\) −14.1852 + 0.0951123i −0.923378 + 0.00619128i
\(237\) −0.267904 2.61628i −0.0174023 0.169946i
\(238\) 26.4793 4.34106i 1.71640 0.281389i
\(239\) −5.75444 + 1.59771i −0.372224 + 0.103347i −0.448602 0.893731i \(-0.648078\pi\)
0.0763785 + 0.997079i \(0.475664\pi\)
\(240\) −23.8620 + 10.8581i −1.54029 + 0.700889i
\(241\) −0.251706 + 0.371239i −0.0162138 + 0.0239136i −0.835710 0.549172i \(-0.814943\pi\)
0.819496 + 0.573085i \(0.194254\pi\)
\(242\) −8.21506 + 3.80069i −0.528084 + 0.244318i
\(243\) −4.51063 14.9216i −0.289357 0.957221i
\(244\) −17.3453 + 9.19590i −1.11042 + 0.588707i
\(245\) 1.57209 + 2.61284i 0.100437 + 0.166928i
\(246\) −21.2711 7.31632i −1.35620 0.466471i
\(247\) 13.1422 17.2883i 0.836219 1.10003i
\(248\) −0.118798 + 0.0805473i −0.00754370 + 0.00511476i
\(249\) −0.843696 + 1.79393i −0.0534670 + 0.113686i
\(250\) 17.2292 + 0.934138i 1.08967 + 0.0590801i
\(251\) −4.78916 + 14.2137i −0.302289 + 0.897161i 0.683614 + 0.729844i \(0.260407\pi\)
−0.985903 + 0.167318i \(0.946489\pi\)
\(252\) 10.2057 11.7133i 0.642898 0.737869i
\(253\) −20.5535 + 4.52416i −1.29219 + 0.284432i
\(254\) 22.0490 + 25.9581i 1.38348 + 1.62875i
\(255\) 0.187772 29.8639i 0.0117588 1.87015i
\(256\) 4.85910 17.5009i 0.303694 1.09381i
\(257\) 8.52521 0.462223i 0.531788 0.0288327i 0.213710 0.976897i \(-0.431445\pi\)
0.318078 + 0.948065i \(0.396963\pi\)
\(258\) −2.31910 + 5.71572i −0.144381 + 0.355845i
\(259\) −10.5437 8.95594i −0.655156 0.556495i
\(260\) 18.6661 17.6815i 1.15762 1.09656i
\(261\) 12.6009 8.31424i 0.779974 0.514639i
\(262\) 11.0687 27.7804i 0.683828 1.71628i
\(263\) −10.4865 + 11.0704i −0.646624 + 0.682632i −0.964071 0.265644i \(-0.914416\pi\)
0.317448 + 0.948276i \(0.397174\pi\)
\(264\) −0.274624 1.28609i −0.0169019 0.0791534i
\(265\) 3.04838 18.5943i 0.187260 1.14224i
\(266\) 4.90486 29.9183i 0.300736 1.83441i
\(267\) 4.15395 + 19.4534i 0.254217 + 1.19053i
\(268\) 3.99287 4.21522i 0.243903 0.257486i
\(269\) −5.50159 + 13.8080i −0.335438 + 0.841886i 0.660414 + 0.750901i \(0.270381\pi\)
−0.995852 + 0.0909845i \(0.970999\pi\)
\(270\) −22.7947 27.8853i −1.38724 1.69704i
\(271\) −9.97089 + 9.44493i −0.605689 + 0.573739i −0.927854 0.372945i \(-0.878348\pi\)
0.322165 + 0.946684i \(0.395589\pi\)
\(272\) 15.9263 + 13.5279i 0.965672 + 0.820249i
\(273\) 7.19345 17.7292i 0.435367 1.07302i
\(274\) −7.40356 + 0.401409i −0.447266 + 0.0242500i
\(275\) −5.06280 + 18.2346i −0.305298 + 1.09959i
\(276\) 0.167509 26.6411i 0.0100828 1.60361i
\(277\) −14.7747 17.3941i −0.887724 1.04511i −0.998684 0.0512844i \(-0.983669\pi\)
0.110960 0.993825i \(-0.464607\pi\)
\(278\) 11.0946 2.44211i 0.665412 0.146468i
\(279\) −1.08043 0.941372i −0.0646839 0.0563585i
\(280\) −0.950770 + 2.82179i −0.0568194 + 0.168634i
\(281\) −21.3154 1.15568i −1.27157 0.0689424i −0.594037 0.804437i \(-0.702467\pi\)
−0.677530 + 0.735495i \(0.736950\pi\)
\(282\) −5.53321 + 11.7652i −0.329498 + 0.700605i
\(283\) 14.8764 10.0865i 0.884313 0.599579i −0.0322456 0.999480i \(-0.510266\pi\)
0.916558 + 0.399901i \(0.130956\pi\)
\(284\) 2.82600 3.71753i 0.167692 0.220595i
\(285\) −31.9085 10.9751i −1.89010 0.650110i
\(286\) 10.0654 + 16.7289i 0.595182 + 0.989201i
\(287\) −16.4045 + 8.69711i −0.968326 + 0.513374i
\(288\) 23.3960 + 0.294220i 1.37862 + 0.0173371i
\(289\) −6.17520 + 2.85695i −0.363247 + 0.168056i
\(290\) 19.5743 28.8699i 1.14944 1.69530i
\(291\) −17.4371 + 7.93456i −1.02218 + 0.465132i
\(292\) 8.31030 2.30734i 0.486323 0.135027i
\(293\) 17.4739 2.86470i 1.02084 0.167358i 0.371958 0.928249i \(-0.378686\pi\)
0.648879 + 0.760892i \(0.275238\pi\)
\(294\) −0.298590 2.91595i −0.0174141 0.170062i
\(295\) 16.5722 + 21.4996i 0.964870 + 1.25176i
\(296\) 1.48242i 0.0861642i
\(297\) 11.7143 5.93024i 0.679734 0.344108i
\(298\) 1.48776 + 5.35844i 0.0861839 + 0.310406i
\(299\) −10.4764 31.0930i −0.605868 1.79815i
\(300\) −21.0949 11.3543i −1.21791 0.655539i
\(301\) 2.13786 + 4.62090i 0.123224 + 0.266344i
\(302\) −5.83156 + 26.4930i −0.335569 + 1.52450i
\(303\) −4.99497 + 3.34102i −0.286954 + 0.191937i
\(304\) 20.2305 12.1723i 1.16030 0.698129i
\(305\) 34.0959 + 15.7745i 1.95233 + 0.903243i
\(306\) −12.3807 + 25.9007i −0.707756 + 1.48064i
\(307\) 15.6892 + 23.1398i 0.895428 + 1.32066i 0.946748 + 0.321975i \(0.104347\pi\)
−0.0513203 + 0.998682i \(0.516343\pi\)
\(308\) 11.2123 + 6.74623i 0.638882 + 0.384402i
\(309\) −0.395593 8.25622i −0.0225045 0.469680i
\(310\) −3.13759 1.05718i −0.178203 0.0600437i
\(311\) 1.19138 + 1.56724i 0.0675570 + 0.0888698i 0.828631 0.559796i \(-0.189120\pi\)
−0.761073 + 0.648666i \(0.775327\pi\)
\(312\) 1.94700 0.642419i 0.110227 0.0363698i
\(313\) 19.6652 16.7038i 1.11154 0.944154i 0.112768 0.993621i \(-0.464028\pi\)
0.998776 + 0.0494678i \(0.0157525\pi\)
\(314\) −0.255425 + 2.34860i −0.0144145 + 0.132539i
\(315\) −29.6628 1.98266i −1.67131 0.111710i
\(316\) 0.151816 + 2.80008i 0.00854031 + 0.157517i
\(317\) −0.414060 0.219521i −0.0232559 0.0123295i 0.456740 0.889600i \(-0.349017\pi\)
−0.479996 + 0.877271i \(0.659362\pi\)
\(318\) −10.2586 + 14.9274i −0.575273 + 0.837084i
\(319\) 8.74452 + 9.23147i 0.489599 + 0.516863i
\(320\) 22.0982 8.80471i 1.23533 0.492199i
\(321\) 5.76892 20.2822i 0.321990 1.13204i
\(322\) −33.2548 31.5007i −1.85322 1.75546i
\(323\) 2.90794 + 26.7380i 0.161802 + 1.48774i
\(324\) 4.04249 + 16.1221i 0.224583 + 0.895672i
\(325\) −29.1149 4.77314i −1.61500 0.264766i
\(326\) −28.2137 + 3.06843i −1.56261 + 0.169944i
\(327\) 6.06403 + 4.67021i 0.335342 + 0.258263i
\(328\) −1.84833 0.736443i −0.102057 0.0406633i
\(329\) 3.97221 + 9.96950i 0.218995 + 0.549636i
\(330\) 19.7841 22.9970i 1.08908 1.26594i
\(331\) −0.648888 + 0.763930i −0.0356661 + 0.0419894i −0.779706 0.626146i \(-0.784631\pi\)
0.744040 + 0.668135i \(0.232907\pi\)
\(332\) 0.990104 1.86753i 0.0543390 0.102494i
\(333\) 14.3098 3.77993i 0.784170 0.207139i
\(334\) −21.8900 6.07772i −1.19777 0.332558i
\(335\) −11.0455 1.20127i −0.603478 0.0656322i
\(336\) 14.3998 15.0115i 0.785571 0.818942i
\(337\) 5.38470 + 24.4629i 0.293323 + 1.33258i 0.860695 + 0.509120i \(0.170029\pi\)
−0.567372 + 0.823462i \(0.692040\pi\)
\(338\) −3.93309 + 2.98986i −0.213932 + 0.162627i
\(339\) 1.71209 7.55164i 0.0929881 0.410149i
\(340\) −1.72395 + 31.7963i −0.0934942 + 1.72440i
\(341\) 0.622272 1.03422i 0.0336979 0.0560064i
\(342\) 23.2661 + 22.6006i 1.25809 + 1.22210i
\(343\) 13.7000 + 10.4145i 0.739731 + 0.562329i
\(344\) −0.229089 + 0.495167i −0.0123516 + 0.0266976i
\(345\) −40.7791 + 30.5968i −2.19547 + 1.64728i
\(346\) 12.8385 + 24.2161i 0.690205 + 1.30186i
\(347\) −16.2990 3.58769i −0.874978 0.192597i −0.245294 0.969449i \(-0.578885\pi\)
−0.629684 + 0.776852i \(0.716816\pi\)
\(348\) −13.8445 + 8.21187i −0.742146 + 0.440203i
\(349\) −3.03224 2.05591i −0.162312 0.110050i 0.477327 0.878726i \(-0.341606\pi\)
−0.639639 + 0.768675i \(0.720916\pi\)
\(350\) −39.0330 + 13.1518i −2.08640 + 0.702991i
\(351\) 11.1658 + 17.1563i 0.595985 + 0.915734i
\(352\) 3.18832 + 19.4479i 0.169938 + 1.03658i
\(353\) −19.3622 −1.03054 −0.515272 0.857026i \(-0.672309\pi\)
−0.515272 + 0.857026i \(0.672309\pi\)
\(354\) −5.62002 25.4813i −0.298701 1.35432i
\(355\) −8.93596 −0.474272
\(356\) −3.43136 20.9304i −0.181862 1.10931i
\(357\) 8.63224 + 22.0678i 0.456866 + 1.16795i
\(358\) −41.3393 + 13.9288i −2.18485 + 0.736161i
\(359\) 2.50053 + 1.69540i 0.131973 + 0.0894798i 0.625387 0.780315i \(-0.284941\pi\)
−0.493414 + 0.869794i \(0.664251\pi\)
\(360\) −1.89586 2.56016i −0.0999208 0.134932i
\(361\) 11.1226 + 2.44826i 0.585399 + 0.128856i
\(362\) −13.0175 24.5536i −0.684185 1.29051i
\(363\) −4.79738 6.39389i −0.251797 0.335592i
\(364\) −8.56594 + 18.5150i −0.448977 + 0.970449i
\(365\) −13.1388 9.98787i −0.687717 0.522789i
\(366\) −23.2054 27.6702i −1.21296 1.44635i
\(367\) 5.84796 9.71938i 0.305261 0.507348i −0.665816 0.746116i \(-0.731916\pi\)
0.971076 + 0.238769i \(0.0767438\pi\)
\(368\) 1.93122 35.6193i 0.100672 1.85678i
\(369\) 2.39591 19.7197i 0.124726 1.02656i
\(370\) 27.2233 20.6946i 1.41527 1.07586i
\(371\) 3.21394 + 14.6011i 0.166860 + 0.758051i
\(372\) 1.10265 + 1.05772i 0.0571699 + 0.0548403i
\(373\) −27.8641 3.03041i −1.44275 0.156909i −0.646980 0.762507i \(-0.723968\pi\)
−0.795770 + 0.605598i \(0.792934\pi\)
\(374\) −23.2985 6.46879i −1.20474 0.334493i
\(375\) 2.37055 + 15.0519i 0.122415 + 0.777278i
\(376\) −0.538664 + 1.01603i −0.0277795 + 0.0523977i
\(377\) −12.8338 + 15.1091i −0.660972 + 0.778156i
\(378\) 24.9914 + 13.8597i 1.28542 + 0.712866i
\(379\) 5.12241 + 12.8563i 0.263120 + 0.660382i 0.999876 0.0157772i \(-0.00502225\pi\)
−0.736755 + 0.676160i \(0.763643\pi\)
\(380\) 33.4234 + 13.3171i 1.71458 + 0.683153i
\(381\) −18.3521 + 23.8293i −0.940205 + 1.22081i
\(382\) −29.9148 + 3.25343i −1.53057 + 0.166460i
\(383\) 14.9859 + 2.45681i 0.765741 + 0.125537i 0.531980 0.846757i \(-0.321448\pi\)
0.233762 + 0.972294i \(0.424896\pi\)
\(384\) 4.14377 + 0.250808i 0.211461 + 0.0127990i
\(385\) −2.70732 24.8934i −0.137978 1.26869i
\(386\) 26.2508 + 24.8661i 1.33613 + 1.26565i
\(387\) −5.36396 0.948788i −0.272665 0.0482296i
\(388\) 18.9759 7.56070i 0.963357 0.383837i
\(389\) −6.61731 6.98581i −0.335511 0.354195i 0.536308 0.844022i \(-0.319818\pi\)
−0.871819 + 0.489827i \(0.837060\pi\)
\(390\) 38.9775 + 26.7867i 1.97370 + 1.35640i
\(391\) 35.9021 + 19.0341i 1.81565 + 0.962594i
\(392\) −0.0140365 0.258888i −0.000708952 0.0130758i
\(393\) 26.0333 + 4.43620i 1.31321 + 0.223777i
\(394\) 5.75352 52.9027i 0.289858 2.66520i
\(395\) 4.08983 3.47393i 0.205782 0.174793i
\(396\) −12.7787 + 5.71808i −0.642154 + 0.287345i
\(397\) −0.374817 0.493063i −0.0188115 0.0247461i 0.786591 0.617474i \(-0.211844\pi\)
−0.805403 + 0.592728i \(0.798051\pi\)
\(398\) −28.5835 9.63090i −1.43276 0.482754i
\(399\) 26.7430 1.28138i 1.33882 0.0641491i
\(400\) −27.4848 16.5371i −1.37424 0.826853i
\(401\) 14.8142 + 21.8493i 0.739785 + 1.09110i 0.992342 + 0.123520i \(0.0394183\pi\)
−0.252557 + 0.967582i \(0.581271\pi\)
\(402\) 9.11657 + 5.56363i 0.454693 + 0.277488i
\(403\) 1.70782 + 0.790122i 0.0850726 + 0.0393588i
\(404\) 5.49027 3.30339i 0.273151 0.164350i
\(405\) 19.8790 24.8287i 0.987794 1.23375i
\(406\) −5.94946 + 27.0287i −0.295267 + 1.34141i
\(407\) 5.23444 + 11.3141i 0.259462 + 0.560817i
\(408\) −1.20348 + 2.23591i −0.0595810 + 0.110694i
\(409\) 2.00352 + 5.94622i 0.0990675 + 0.294022i 0.985714 0.168425i \(-0.0538681\pi\)
−0.886647 + 0.462447i \(0.846972\pi\)
\(410\) −12.2786 44.2236i −0.606397 2.18405i
\(411\) −1.71199 6.31993i −0.0844464 0.311739i
\(412\) 8.81329i 0.434200i
\(413\) −18.5295 10.9803i −0.911776 0.540304i
\(414\) 47.9893 9.93225i 2.35855 0.488143i
\(415\) −3.99160 + 0.654390i −0.195940 + 0.0321227i
\(416\) −29.6046 + 8.21968i −1.45149 + 0.403003i
\(417\) 4.15510 + 9.13133i 0.203476 + 0.447163i
\(418\) −15.3318 + 22.6127i −0.749902 + 1.10602i
\(419\) 5.65987 2.61854i 0.276503 0.127924i −0.276737 0.960946i \(-0.589253\pi\)
0.553240 + 0.833022i \(0.313391\pi\)
\(420\) 31.4906 + 3.62528i 1.53658 + 0.176896i
\(421\) 33.0926 17.5446i 1.61283 0.855071i 0.615054 0.788485i \(-0.289134\pi\)
0.997781 0.0665861i \(-0.0212107\pi\)
\(422\) 13.2498 + 22.0214i 0.644992 + 1.07199i
\(423\) −11.1812 2.60900i −0.543647 0.126854i
\(424\) −0.969538 + 1.27541i −0.0470849 + 0.0619392i
\(425\) 30.2438 20.5058i 1.46704 0.994676i
\(426\) 7.77304 + 3.65570i 0.376605 + 0.177119i
\(427\) −29.7648 1.61380i −1.44042 0.0780973i
\(428\) −7.17907 + 21.3067i −0.347013 + 1.02990i
\(429\) −12.5914 + 11.7779i −0.607919 + 0.568642i
\(430\) −12.2913 + 2.70553i −0.592741 + 0.130472i
\(431\) 5.96317 + 7.02039i 0.287236 + 0.338160i 0.886789 0.462175i \(-0.152931\pi\)
−0.599553 + 0.800335i \(0.704655\pi\)
\(432\) 4.37333 + 21.8208i 0.210412 + 1.04986i
\(433\) −10.7421 + 38.6894i −0.516231 + 1.85929i −0.00476849 + 0.999989i \(0.501518\pi\)
−0.511462 + 0.859306i \(0.670896\pi\)
\(434\) 2.62319 0.142225i 0.125917 0.00682704i
\(435\) 28.5428 + 11.5810i 1.36852 + 0.555264i
\(436\) −6.22004 5.28335i −0.297886 0.253026i
\(437\) 33.3328 31.5745i 1.59453 1.51042i
\(438\) 7.34291 + 14.0631i 0.350858 + 0.671963i
\(439\) −13.7886 + 34.6068i −0.658095 + 1.65169i 0.0963631 + 0.995346i \(0.469279\pi\)
−0.754458 + 0.656348i \(0.772100\pi\)
\(440\) 1.84528 1.94803i 0.0879701 0.0928689i
\(441\) 2.46325 0.795616i 0.117297 0.0378865i
\(442\) 6.09869 37.2004i 0.290085 1.76944i
\(443\) 3.06155 18.6746i 0.145459 0.887258i −0.808758 0.588141i \(-0.799860\pi\)
0.954217 0.299116i \(-0.0966919\pi\)
\(444\) −15.4332 + 3.29550i −0.732426 + 0.156398i
\(445\) −27.9116 + 29.4659i −1.32314 + 1.39682i
\(446\) 17.3591 43.5681i 0.821978 2.06301i
\(447\) −4.35336 + 2.27306i −0.205907 + 0.107512i
\(448\) −13.7027 + 12.9799i −0.647391 + 0.613241i
\(449\) 0.293431 + 0.249243i 0.0138479 + 0.0117625i 0.654284 0.756249i \(-0.272970\pi\)
−0.640436 + 0.768012i \(0.721246\pi\)
\(450\) 12.3222 42.3092i 0.580873 1.99447i
\(451\) 16.7071 0.905832i 0.786706 0.0426540i
\(452\) −2.20879 + 7.95534i −0.103893 + 0.374188i
\(453\) −23.9557 0.150624i −1.12554 0.00707691i
\(454\) −13.8094 16.2577i −0.648109 0.763013i
\(455\) 38.1256 8.39208i 1.78736 0.393427i
\(456\) 1.95988 + 2.09526i 0.0917800 + 0.0981193i
\(457\) −5.28931 + 15.6981i −0.247423 + 0.734326i 0.749923 + 0.661525i \(0.230090\pi\)
−0.997346 + 0.0728014i \(0.976806\pi\)
\(458\) 42.4806 + 2.30323i 1.98499 + 0.107623i
\(459\) −24.6518 5.91589i −1.15065 0.276130i
\(460\) 44.9922 30.5055i 2.09777 1.42233i
\(461\) −4.15597 + 5.46708i −0.193563 + 0.254627i −0.882628 0.470072i \(-0.844228\pi\)
0.689066 + 0.724699i \(0.258021\pi\)
\(462\) −7.82889 + 22.7614i −0.364233 + 1.05895i
\(463\) 1.33356 + 2.21639i 0.0619757 + 0.103004i 0.886296 0.463120i \(-0.153270\pi\)
−0.824320 + 0.566124i \(0.808442\pi\)
\(464\) −19.0420 + 10.0954i −0.884003 + 0.468669i
\(465\) 0.334396 2.90469i 0.0155072 0.134702i
\(466\) −9.06223 + 4.19263i −0.419799 + 0.194220i
\(467\) −2.74519 + 4.04885i −0.127032 + 0.187358i −0.885887 0.463902i \(-0.846449\pi\)
0.758854 + 0.651260i \(0.225759\pi\)
\(468\) −11.0164 18.8417i −0.509231 0.870957i
\(469\) 8.49438 2.35845i 0.392234 0.108903i
\(470\) −26.1781 + 4.29169i −1.20751 + 0.197961i
\(471\) −2.07543 + 0.212522i −0.0956307 + 0.00979248i
\(472\) −0.388660 2.27507i −0.0178895 0.104719i
\(473\) 4.58809i 0.210961i
\(474\) −4.97877 + 1.34869i −0.228682 + 0.0619474i
\(475\) −11.0451 39.7809i −0.506784 1.82527i
\(476\) −8.06744 23.9433i −0.369771 1.09744i
\(477\) −14.7836 6.10683i −0.676894 0.279612i
\(478\) 4.91828 + 10.6307i 0.224957 + 0.486236i
\(479\) −0.894506 + 4.06378i −0.0408710 + 0.185679i −0.992633 0.121157i \(-0.961339\pi\)
0.951762 + 0.306836i \(0.0992704\pi\)
\(480\) 26.5422 + 39.6817i 1.21148 + 1.81121i
\(481\) −16.6532 + 10.0199i −0.759320 + 0.456868i
\(482\) 0.798397 + 0.369378i 0.0363660 + 0.0168247i
\(483\) 21.0723 34.5291i 0.958824 1.57113i
\(484\) 4.78305 + 7.05448i 0.217412 + 0.320658i
\(485\) −33.4932 20.1522i −1.52085 0.915065i
\(486\) −27.4493 + 13.4650i −1.24513 + 0.610785i
\(487\) 15.6833 + 5.28432i 0.710678 + 0.239455i 0.651344 0.758783i \(-0.274206\pi\)
0.0593345 + 0.998238i \(0.481102\pi\)
\(488\) −1.93306 2.54290i −0.0875056 0.115112i
\(489\) −7.85301 23.8004i −0.355125 1.07629i
\(490\) 4.55829 3.87184i 0.205922 0.174912i
\(491\) −1.72957 + 15.9031i −0.0780543 + 0.717697i 0.888086 + 0.459678i \(0.152035\pi\)
−0.966140 + 0.258019i \(0.916930\pi\)
\(492\) −3.55801 + 20.8797i −0.160407 + 0.941330i
\(493\) −1.32921 24.5159i −0.0598647 1.10414i
\(494\) −37.6314 19.9509i −1.69312 0.897634i
\(495\) 23.5094 + 12.8452i 1.05667 + 0.577348i
\(496\) 1.40692 + 1.48526i 0.0631724 + 0.0666903i
\(497\) 6.58668 2.62437i 0.295453 0.117719i
\(498\) 3.73985 + 1.06373i 0.167587 + 0.0476671i
\(499\) −2.94016 2.78507i −0.131620 0.124677i 0.619058 0.785345i \(-0.287514\pi\)
−0.750678 + 0.660668i \(0.770273\pi\)
\(500\) −1.75660 16.1517i −0.0785576 0.722325i
\(501\) 1.21209 20.0257i 0.0541522 0.894683i
\(502\) 29.0301 + 4.75924i 1.29568 + 0.212415i
\(503\) 28.9410 3.14752i 1.29042 0.140341i 0.562953 0.826489i \(-0.309665\pi\)
0.727462 + 0.686148i \(0.240700\pi\)
\(504\) 2.14932 + 1.33030i 0.0957385 + 0.0592563i
\(505\) −11.3904 4.53837i −0.506868 0.201955i
\(506\) 15.2782 + 38.3455i 0.679200 + 1.70466i
\(507\) −3.30746 2.84537i −0.146889 0.126367i
\(508\) 20.7615 24.4423i 0.921141 1.08445i
\(509\) −17.1125 + 32.2776i −0.758497 + 1.43068i 0.139292 + 0.990251i \(0.455517\pi\)
−0.897789 + 0.440426i \(0.854827\pi\)
\(510\) −57.8609 + 9.11261i −2.56212 + 0.403513i
\(511\) 12.6179 + 3.50334i 0.558183 + 0.154979i
\(512\) −30.6492 3.33330i −1.35451 0.147312i
\(513\) −15.2280 + 24.2612i −0.672333 + 1.07116i
\(514\) −3.59974 16.3538i −0.158778 0.721334i
\(515\) 13.4262 10.2063i 0.591628 0.449744i
\(516\) 5.66434 + 1.28421i 0.249359 + 0.0565342i
\(517\) 0.523560 9.65649i 0.0230261 0.424692i
\(518\) −13.9885 + 23.2491i −0.614620 + 1.02151i
\(519\) −18.5462 + 15.5536i −0.814086 + 0.682726i
\(520\) 3.33027 + 2.53161i 0.146042 + 0.111018i
\(521\) 7.14695 15.4479i 0.313113 0.676783i −0.685574 0.728003i \(-0.740449\pi\)
0.998687 + 0.0512194i \(0.0163108\pi\)
\(522\) −20.0905 21.7507i −0.879336 0.952000i
\(523\) −13.3743 25.2266i −0.584817 1.10308i −0.982623 0.185612i \(-0.940573\pi\)
0.397806 0.917470i \(-0.369772\pi\)
\(524\) −27.4998 6.05316i −1.20133 0.264433i
\(525\) −18.5565 31.2848i −0.809873 1.36538i
\(526\) 24.7541 + 16.7837i 1.07933 + 0.731805i
\(527\) −2.20853 + 0.744140i −0.0962050 + 0.0324152i
\(528\) −17.4567 + 6.82853i −0.759707 + 0.297174i
\(529\) −7.50160 45.7577i −0.326157 1.98947i
\(530\) −36.9563 −1.60528
\(531\) 20.9701 9.55276i 0.910025 0.414554i
\(532\) −28.5474 −1.23769
\(533\) 4.22009 + 25.7414i 0.182792 + 1.11498i
\(534\) 36.3337 14.2126i 1.57231 0.615040i
\(535\) 40.7724 13.7378i 1.76275 0.593938i
\(536\) 0.781897 + 0.530139i 0.0337728 + 0.0228985i
\(537\) −19.6529 33.1333i −0.848087 1.42981i
\(538\) 28.4708 + 6.26690i 1.22746 + 0.270185i
\(539\) 1.02126 + 1.92631i 0.0439889 + 0.0829719i
\(540\) −22.4387 + 25.4288i −0.965606 + 1.09428i
\(541\) −6.46735 + 13.9790i −0.278053 + 0.601002i −0.995410 0.0957040i \(-0.969490\pi\)
0.717357 + 0.696706i \(0.245352\pi\)
\(542\) 21.4444 + 16.3016i 0.921115 + 0.700214i
\(543\) 18.8047 15.7704i 0.806987 0.676772i
\(544\) 19.6179 32.6053i 0.841112 1.39794i
\(545\) −0.845484 + 15.5940i −0.0362165 + 0.667975i
\(546\) −36.5972 8.29723i −1.56621 0.355089i
\(547\) −17.1765 + 13.0572i −0.734413 + 0.558286i −0.904156 0.427202i \(-0.859499\pi\)
0.169743 + 0.985488i \(0.445706\pi\)
\(548\) 1.50081 + 6.81826i 0.0641115 + 0.291262i
\(549\) 19.6175 25.1437i 0.837254 1.07311i
\(550\) 36.8992 + 4.01303i 1.57339 + 0.171116i
\(551\) −26.7295 7.42140i −1.13871 0.316162i
\(552\) 4.28190 0.674364i 0.182250 0.0287028i
\(553\) −1.99436 + 3.76176i −0.0848088 + 0.159966i
\(554\) −28.9779 + 34.1155i −1.23115 + 1.44943i
\(555\) 22.8929 + 19.6945i 0.971750 + 0.835986i
\(556\) −3.95932 9.93715i −0.167913 0.421429i
\(557\) 24.3716 + 9.71054i 1.03266 + 0.411449i 0.824030 0.566546i \(-0.191721\pi\)
0.208628 + 0.977995i \(0.433100\pi\)
\(558\) −1.47918 + 2.38987i −0.0626189 + 0.101171i
\(559\) 7.11102 0.773370i 0.300764 0.0327101i
\(560\) 41.8834 + 6.86643i 1.76990 + 0.290160i
\(561\) 1.29008 21.3143i 0.0544672 0.899889i
\(562\) 4.52670 + 41.6223i 0.190947 + 1.75573i
\(563\) −10.7173 10.1520i −0.451682 0.427856i 0.427738 0.903903i \(-0.359311\pi\)
−0.879420 + 0.476047i \(0.842069\pi\)
\(564\) 11.7751 + 3.34923i 0.495822 + 0.141028i
\(565\) 14.6771 5.84788i 0.617469 0.246022i
\(566\) −24.2427 25.5927i −1.01899 1.07574i
\(567\) −7.36090 + 24.1393i −0.309129 + 1.01376i
\(568\) 0.671273 + 0.355886i 0.0281660 + 0.0149327i
\(569\) −1.69608 31.2824i −0.0711035 1.31143i −0.788618 0.614883i \(-0.789203\pi\)
0.717515 0.696543i \(-0.245280\pi\)
\(570\) −11.1174 + 65.2411i −0.465657 + 2.73265i
\(571\) −0.0898877 + 0.826504i −0.00376168 + 0.0345881i −0.995868 0.0908086i \(-0.971055\pi\)
0.992107 + 0.125397i \(0.0400204\pi\)
\(572\) 14.0112 11.9012i 0.585839 0.497616i
\(573\) −8.32649 25.2354i −0.347844 1.05422i
\(574\) 22.0384 + 28.9910i 0.919865 + 1.21006i
\(575\) −59.1117 19.9171i −2.46513 0.830599i
\(576\) −3.01605 19.9666i −0.125669 0.831942i
\(577\) −28.5757 17.1934i −1.18962 0.715771i −0.223712 0.974655i \(-0.571818\pi\)
−0.965908 + 0.258884i \(0.916645\pi\)
\(578\) 7.48903 + 11.0455i 0.311503 + 0.459432i
\(579\) −16.6341 + 27.2567i −0.691290 + 1.13275i
\(580\) −29.8078 13.7906i −1.23770 0.572623i
\(581\) 2.75001 1.65463i 0.114090 0.0686456i
\(582\) 20.8902 + 31.2317i 0.865926 + 1.29459i
\(583\) 2.89618 13.1575i 0.119948 0.544928i
\(584\) 0.589213 + 1.27356i 0.0243818 + 0.0527004i
\(585\) −15.9458 + 38.6021i −0.659279 + 1.59600i
\(586\) −11.0892 32.9116i −0.458091 1.35956i
\(587\) 12.0287 + 43.3234i 0.496477 + 1.78815i 0.607489 + 0.794328i \(0.292177\pi\)
−0.111012 + 0.993819i \(0.535409\pi\)
\(588\) −2.66402 + 0.721653i −0.109863 + 0.0297605i
\(589\) 2.63321i 0.108499i
\(590\) 36.3537 38.8973i 1.49666 1.60137i
\(591\) 46.7495 4.78710i 1.92302 0.196915i
\(592\) −20.8516 + 3.41845i −0.856996 + 0.140497i
\(593\) −15.8554 + 4.40224i −0.651105 + 0.180778i −0.577349 0.816498i \(-0.695913\pi\)
−0.0737567 + 0.997276i \(0.523499\pi\)
\(594\) −15.1949 20.7912i −0.623456 0.853074i
\(595\) −27.1327 + 40.0177i −1.11233 + 1.64057i
\(596\) 4.75244 2.19871i 0.194668 0.0900628i
\(597\) 3.04635 26.4617i 0.124679 1.08301i
\(598\) −56.8558 + 30.1430i −2.32501 + 1.23264i
\(599\) 6.18311 + 10.2764i 0.252635 + 0.419883i 0.957057 0.289898i \(-0.0936215\pi\)
−0.704422 + 0.709781i \(0.748794\pi\)
\(600\) 1.26777 3.68586i 0.0517565 0.150474i
\(601\) 0.716451 0.942475i 0.0292246 0.0384443i −0.781249 0.624220i \(-0.785417\pi\)
0.810473 + 0.585776i \(0.199210\pi\)
\(602\) 8.26534 5.60404i 0.336870 0.228404i
\(603\) −3.12370 + 8.89938i −0.127207 + 0.362411i
\(604\) 25.5058 + 1.38288i 1.03781 + 0.0562687i
\(605\) 5.20773 15.4560i 0.211725 0.628376i
\(606\) 8.05145 + 8.60757i 0.327068 + 0.349659i
\(607\) 4.27809 0.941680i 0.173643 0.0382216i −0.127298 0.991865i \(-0.540630\pi\)
0.300941 + 0.953643i \(0.402699\pi\)
\(608\) −27.8339 32.7686i −1.12881 1.32894i
\(609\) −24.4400 0.153669i −0.990358 0.00622697i
\(610\) 19.7124 70.9976i 0.798131 2.87461i
\(611\) 15.0547 0.816243i 0.609048 0.0330216i
\(612\) 25.9530 + 7.55857i 1.04909 + 0.305537i
\(613\) 19.2013 + 16.3098i 0.775534 + 0.658745i 0.945103 0.326774i \(-0.105962\pi\)
−0.169568 + 0.985518i \(0.554237\pi\)
\(614\) 39.8085 37.7086i 1.60654 1.52180i
\(615\) 35.9285 18.7597i 1.44878 0.756463i
\(616\) −0.788038 + 1.97783i −0.0317509 + 0.0796888i
\(617\) 10.1877 10.7550i 0.410141 0.432981i −0.487895 0.872902i \(-0.662235\pi\)
0.898036 + 0.439921i \(0.144994\pi\)
\(618\) −15.8543 + 3.38542i −0.637753 + 0.136182i
\(619\) −3.74739 + 22.8580i −0.150620 + 0.918742i 0.798077 + 0.602556i \(0.205851\pi\)
−0.948697 + 0.316187i \(0.897597\pi\)
\(620\) −0.504368 + 3.07651i −0.0202559 + 0.123555i
\(621\) 17.4277 + 39.6135i 0.699351 + 1.58963i
\(622\) 2.65533 2.80320i 0.106469 0.112398i
\(623\) 11.9198 29.9165i 0.477558 1.19858i
\(624\) −13.5260 25.9049i −0.541472 1.03703i
\(625\) 4.61486 4.37143i 0.184594 0.174857i
\(626\) −38.5699 32.7616i −1.54156 1.30942i
\(627\) −22.3564 9.07091i −0.892830 0.362257i
\(628\) 2.22123 0.120432i 0.0886368 0.00480575i
\(629\) 6.43951 23.1930i 0.256760 0.924767i
\(630\) 5.57483 + 58.0412i 0.222106 + 2.31242i
\(631\) −17.8274 20.9880i −0.709696 0.835519i 0.282622 0.959231i \(-0.408796\pi\)
−0.992318 + 0.123713i \(0.960520\pi\)
\(632\) −0.445584 + 0.0980804i −0.0177244 + 0.00390143i
\(633\) −16.5749 + 15.5041i −0.658794 + 0.616231i
\(634\) −0.293496 + 0.871064i −0.0116562 + 0.0345944i
\(635\) −61.2784 3.32242i −2.43176 0.131846i
\(636\) 15.4333 + 7.25835i 0.611969 + 0.287812i
\(637\) −2.81341 + 1.90754i −0.111471 + 0.0755795i
\(638\) 15.0927 19.8541i 0.597526 0.786032i
\(639\) −1.72372 + 7.38721i −0.0681893 + 0.292234i
\(640\) 4.36689 + 7.25783i 0.172617 + 0.286891i
\(641\) 26.9370 14.2811i 1.06395 0.564069i 0.157991 0.987441i \(-0.449498\pi\)
0.905956 + 0.423371i \(0.139153\pi\)
\(642\) −41.0865 4.72999i −1.62155 0.186678i
\(643\) 6.39730 2.95970i 0.252285 0.116719i −0.289671 0.957126i \(-0.593546\pi\)
0.541956 + 0.840407i \(0.317684\pi\)
\(644\) −24.2046 + 35.6991i −0.953796 + 1.40674i
\(645\) −4.60328 10.1163i −0.181254 0.398327i
\(646\) 50.8284 14.1124i 1.99982 0.555247i
\(647\) 25.2336 4.13684i 0.992036 0.162636i 0.356158 0.934426i \(-0.384086\pi\)
0.635878 + 0.771790i \(0.280638\pi\)
\(648\) −2.48215 + 1.07343i −0.0975081 + 0.0421684i
\(649\) 10.9996 + 15.9913i 0.431771 + 0.627712i
\(650\) 57.8661i 2.26969i
\(651\) 0.606585 + 2.23925i 0.0237740 + 0.0877630i
\(652\) 7.14913 + 25.7488i 0.279981 + 1.00840i
\(653\) 0.984127 + 2.92078i 0.0385119 + 0.114299i 0.965184 0.261571i \(-0.0842405\pi\)
−0.926672 + 0.375870i \(0.877344\pi\)
\(654\) 7.11497 13.2187i 0.278217 0.516894i
\(655\) 22.6250 + 48.9031i 0.884031 + 1.91080i
\(656\) −6.09650 + 27.6967i −0.238028 + 1.08137i
\(657\) −10.7912 + 8.93502i −0.421007 + 0.348588i
\(658\) 18.0354 10.8516i 0.703094 0.423038i
\(659\) −6.29956 2.91449i −0.245396 0.113532i 0.293336 0.956009i \(-0.405234\pi\)
−0.538732 + 0.842477i \(0.681097\pi\)
\(660\) −24.3827 14.8802i −0.949094 0.579210i
\(661\) −3.54891 5.23424i −0.138036 0.203588i 0.752387 0.658721i \(-0.228902\pi\)
−0.890424 + 0.455133i \(0.849592\pi\)
\(662\) 1.68447 + 1.01351i 0.0654689 + 0.0393913i
\(663\) 33.2521 1.59326i 1.29141 0.0618771i
\(664\) 0.325913 + 0.109813i 0.0126479 + 0.00426156i
\(665\) 33.0596 + 43.4891i 1.28199 + 1.68644i
\(666\) −11.8566 26.4970i −0.459434 1.02674i
\(667\) −31.9439 + 27.1334i −1.23687 + 1.05061i
\(668\) −2.31283 + 21.2661i −0.0894859 + 0.822809i
\(669\) 40.8281 + 6.95731i 1.57851 + 0.268985i
\(670\) 1.17977 + 21.7595i 0.0455784 + 0.840643i
\(671\) 23.7324 + 12.5821i 0.916177 + 0.485726i
\(672\) −31.2182 21.4542i −1.20427 0.827614i
\(673\) −34.4657 36.3850i −1.32856 1.40254i −0.852134 0.523324i \(-0.824692\pi\)
−0.476423 0.879216i \(-0.658067\pi\)
\(674\) 45.6391 18.1843i 1.75795 0.700433i
\(675\) 38.8120 + 2.83941i 1.49387 + 0.109289i
\(676\) 3.37733 + 3.19918i 0.129897 + 0.123045i
\(677\) 4.81215 + 44.2470i 0.184946 + 1.70055i 0.607586 + 0.794254i \(0.292138\pi\)
−0.422640 + 0.906298i \(0.638897\pi\)
\(678\) −15.1594 0.917546i −0.582192 0.0352381i
\(679\) 30.6062 + 5.01764i 1.17456 + 0.192559i
\(680\) −5.15059 + 0.560160i −0.197516 + 0.0214812i
\(681\) 11.4940 14.9244i 0.440453 0.571906i
\(682\) −2.19918 0.876233i −0.0842109 0.0335527i
\(683\) −3.77406 9.47217i −0.144410 0.362443i 0.838924 0.544248i \(-0.183185\pi\)
−0.983334 + 0.181806i \(0.941806\pi\)
\(684\) 17.4563 25.0618i 0.667459 0.958260i
\(685\) 8.64891 10.1823i 0.330458 0.389045i
\(686\) 15.8100 29.8208i 0.603628 1.13856i
\(687\) 5.84490 + 37.1124i 0.222997 + 1.41593i
\(688\) 7.49324 + 2.08049i 0.285677 + 0.0793178i
\(689\) 20.8808 + 2.27092i 0.795495 + 0.0865153i
\(690\) 72.1593 + 69.2189i 2.74706 + 2.63512i
\(691\) −5.37851 24.4348i −0.204608 0.929543i −0.961242 0.275705i \(-0.911089\pi\)
0.756634 0.653838i \(-0.226842\pi\)
\(692\) 20.5459 15.6186i 0.781037 0.593729i
\(693\) −21.1012 2.56376i −0.801568 0.0973893i
\(694\) −1.77213 + 32.6850i −0.0672691 + 1.24070i
\(695\) −10.5531 + 17.5394i −0.400303 + 0.665309i
\(696\) −1.68292 2.00672i −0.0637908 0.0760645i
\(697\) −25.7187 19.5509i −0.974166 0.740542i
\(698\) −3.01704 + 6.52122i −0.114197 + 0.246832i
\(699\) −5.29210 7.05325i −0.200166 0.266778i
\(700\) 18.1667 + 34.2661i 0.686638 + 1.29514i
\(701\) −31.0515 6.83496i −1.17280 0.258153i −0.414494 0.910052i \(-0.636042\pi\)
−0.758306 + 0.651899i \(0.773973\pi\)
\(702\) 29.6628 27.0550i 1.11955 1.02113i
\(703\) −22.5103 15.2624i −0.848993 0.575632i
\(704\) 16.1179 5.43076i 0.607467 0.204680i
\(705\) −8.53406 21.8168i −0.321411 0.821669i
\(706\) 6.14376 + 37.4753i 0.231223 + 1.41040i
\(707\) 9.72873 0.365887
\(708\) −22.8212 + 9.10384i −0.857673 + 0.342143i
\(709\) −9.07304 −0.340745 −0.170373 0.985380i \(-0.554497\pi\)
−0.170373 + 0.985380i \(0.554497\pi\)
\(710\) 2.83544 + 17.2954i 0.106412 + 0.649087i
\(711\) −2.08293 4.05111i −0.0781159 0.151928i
\(712\) 3.27025 1.10188i 0.122558 0.0412945i
\(713\) 3.29289 + 2.23263i 0.123320 + 0.0836127i
\(714\) 39.9729 23.7099i 1.49595 0.887319i
\(715\) −34.3562 7.56236i −1.28485 0.282816i
\(716\) 19.2401 + 36.2907i 0.719037 + 1.35625i
\(717\) −8.27400 + 6.20804i −0.308998 + 0.231843i
\(718\) 2.48799 5.37771i 0.0928511 0.200694i
\(719\) −4.26859 3.24490i −0.159191 0.121014i 0.522546 0.852611i \(-0.324982\pi\)
−0.681738 + 0.731597i \(0.738775\pi\)
\(720\) −31.6391 + 32.5707i −1.17912 + 1.21384i
\(721\) −6.89895 + 11.4661i −0.256930 + 0.427021i
\(722\) 1.20931 22.3045i 0.0450060 0.830086i
\(723\) −0.171771 + 0.757640i −0.00638822 + 0.0281770i
\(724\) −20.8323 + 15.8363i −0.774226 + 0.588551i
\(725\) 8.10178 + 36.8068i 0.300893 + 1.36697i
\(726\) −10.8531 + 11.3141i −0.402795 + 0.419905i
\(727\) 6.99812 + 0.761091i 0.259546 + 0.0282273i 0.236967 0.971518i \(-0.423847\pi\)
0.0225790 + 0.999745i \(0.492812\pi\)
\(728\) −3.19824 0.887986i −0.118535 0.0329109i
\(729\) −16.6909 21.2230i −0.618180 0.786037i
\(730\) −15.1624 + 28.5992i −0.561184 + 1.05851i
\(731\) −5.73513 + 6.75191i −0.212121 + 0.249729i
\(732\) −22.1762 + 25.7776i −0.819658 + 0.952769i
\(733\) −17.1166 42.9595i −0.632217 1.58674i −0.799387 0.600817i \(-0.794842\pi\)
0.167170 0.985928i \(-0.446537\pi\)
\(734\) −20.6673 8.23462i −0.762846 0.303945i
\(735\) 4.18446 + 3.22266i 0.154346 + 0.118870i
\(736\) −64.5776 + 7.02324i −2.38036 + 0.258880i
\(737\) −7.83946 1.28521i −0.288770 0.0473415i
\(738\) −38.9274 + 1.61994i −1.43294 + 0.0596308i
\(739\) 0.894006 + 8.22025i 0.0328865 + 0.302387i 0.999017 + 0.0443321i \(0.0141160\pi\)
−0.966130 + 0.258055i \(0.916919\pi\)
\(740\) −23.3765 22.1434i −0.859339 0.814009i
\(741\) 10.2905 36.1789i 0.378030 1.32907i
\(742\) 27.2404 10.8536i 1.00003 0.398447i
\(743\) −4.91795 5.19182i −0.180422 0.190469i 0.629511 0.776992i \(-0.283255\pi\)
−0.809933 + 0.586522i \(0.800497\pi\)
\(744\) −0.140803 + 0.204883i −0.00516209 + 0.00751139i
\(745\) −8.85313 4.69363i −0.324354 0.171961i
\(746\) 2.97617 + 54.8923i 0.108965 + 2.00975i
\(747\) −0.228994 + 3.42602i −0.00837846 + 0.125352i
\(748\) −2.46164 + 22.6344i −0.0900066 + 0.827597i
\(749\) −26.0187 + 22.1005i −0.950701 + 0.807533i
\(750\) 28.3806 9.36426i 1.03631 0.341935i
\(751\) −17.1770 22.5960i −0.626798 0.824538i 0.367629 0.929973i \(-0.380170\pi\)
−0.994426 + 0.105435i \(0.966377\pi\)
\(752\) 15.5335 + 5.23384i 0.566448 + 0.190859i
\(753\) 1.24333 + 25.9490i 0.0453096 + 0.945634i
\(754\) 33.3157 + 20.0454i 1.21328 + 0.730009i
\(755\) −27.4305 40.4570i −0.998298 1.47238i
\(756\) 9.07140 25.3334i 0.329924 0.921368i
\(757\) 31.9694 + 14.7906i 1.16195 + 0.537574i 0.903557 0.428467i \(-0.140946\pi\)
0.258389 + 0.966041i \(0.416808\pi\)
\(758\) 23.2578 13.9937i 0.844761 0.508276i
\(759\) −30.2989 + 20.2662i −1.09978 + 0.735617i
\(760\) −1.25840 + 5.71699i −0.0456471 + 0.207377i
\(761\) 2.99057 + 6.46401i 0.108408 + 0.234320i 0.954186 0.299216i \(-0.0967250\pi\)
−0.845777 + 0.533536i \(0.820863\pi\)
\(762\) 51.9445 + 27.9590i 1.88175 + 1.01285i
\(763\) −3.95656 11.7426i −0.143237 0.425112i
\(764\) 7.58017 + 27.3013i 0.274241 + 0.987726i
\(765\) −18.5403 48.2900i −0.670327 1.74593i
\(766\) 29.7845i 1.07616i
\(767\) −22.9305 + 19.7436i −0.827974 + 0.712899i
\(768\) −3.20463 31.2955i −0.115637 1.12928i
\(769\) 1.63749 0.268452i 0.0590493 0.00968063i −0.132185 0.991225i \(-0.542199\pi\)
0.191234 + 0.981544i \(0.438751\pi\)
\(770\) −47.3218 + 13.1388i −1.70536 + 0.473491i
\(771\) 13.4598 6.12472i 0.484743 0.220576i
\(772\) 19.1067 28.1803i 0.687665 1.01423i
\(773\) −9.79829 + 4.53317i −0.352420 + 0.163047i −0.588109 0.808782i \(-0.700127\pi\)
0.235689 + 0.971829i \(0.424265\pi\)
\(774\) −0.134345 + 10.6829i −0.00482894 + 0.383990i
\(775\) 3.16070 1.67570i 0.113536 0.0601928i
\(776\) 1.71344 + 2.84775i 0.0615088 + 0.102228i
\(777\) −22.6583 7.79346i −0.812863 0.279589i
\(778\) −11.4212 + 15.0244i −0.409471 + 0.538650i
\(779\) −30.2123 + 20.4845i −1.08247 + 0.733933i
\(780\) 18.9526 40.2986i 0.678613 1.44292i
\(781\) −6.37988 0.345907i −0.228290 0.0123775i
\(782\) 25.4482 75.5277i 0.910027 2.70086i
\(783\) 15.0796 21.3619i 0.538901 0.763412i
\(784\) −3.60913 + 0.794429i −0.128897 + 0.0283725i
\(785\) −2.75578 3.24436i −0.0983582 0.115796i
\(786\) 0.325664 51.7947i 0.0116161 1.84746i
\(787\) −1.33765 + 4.81778i −0.0476821 + 0.171735i −0.983557 0.180596i \(-0.942197\pi\)
0.935875 + 0.352332i \(0.114611\pi\)
\(788\) −50.0338 + 2.71275i −1.78238 + 0.0966379i
\(789\) −9.92994 + 24.4736i −0.353515 + 0.871284i
\(790\) −8.02149 6.81352i −0.285392 0.242414i
\(791\) −9.10100 + 8.62092i −0.323594 + 0.306525i
\(792\) −1.25446 1.90123i −0.0445753 0.0675572i
\(793\) −15.5005 + 38.9033i −0.550438 + 1.38150i
\(794\) −0.835386 + 0.881906i −0.0296467 + 0.0312977i
\(795\) −6.81528 31.9167i −0.241713 1.13197i
\(796\) −4.59479 + 28.0270i −0.162858 + 0.993391i
\(797\) 2.06031 12.5673i 0.0729798 0.445157i −0.924908 0.380192i \(-0.875858\pi\)
0.997888 0.0649653i \(-0.0206937\pi\)
\(798\) −10.9658 51.3541i −0.388186 1.81792i
\(799\) −12.8411 + 13.5562i −0.454286 + 0.479584i
\(800\) −21.6202 + 54.2627i −0.764391 + 1.91848i
\(801\) 18.9749 + 28.7579i 0.670446 + 1.01611i
\(802\) 37.5884 35.6056i 1.32729 1.25728i
\(803\) −8.99390 7.63949i −0.317388 0.269592i
\(804\) 3.78096 9.31868i 0.133344 0.328644i
\(805\) 82.4145 4.46838i 2.90473 0.157490i
\(806\) 0.987368 3.55618i 0.0347785 0.125261i
\(807\) −0.161868 + 25.7440i −0.00569802 + 0.906233i
\(808\) 0.674908 + 0.794563i 0.0237432 + 0.0279526i
\(809\) 31.6003 6.95576i 1.11101 0.244551i 0.378696 0.925521i \(-0.376372\pi\)
0.732312 + 0.680970i \(0.238441\pi\)
\(810\) −54.3633 30.5972i −1.91013 1.07508i
\(811\) −2.24786 + 6.67142i −0.0789332 + 0.234265i −0.979853 0.199720i \(-0.935997\pi\)
0.900920 + 0.433986i \(0.142893\pi\)
\(812\) 26.0214 + 1.41084i 0.913173 + 0.0495108i
\(813\) −10.1239 + 21.5263i −0.355062 + 0.754961i
\(814\) 20.2373 13.7212i 0.709317 0.480929i
\(815\) 30.9467 40.7096i 1.08401 1.42600i
\(816\) 34.2253 + 11.7720i 1.19813 + 0.412102i
\(817\) 5.16042 + 8.57669i 0.180540 + 0.300060i
\(818\) 10.8731 5.76456i 0.380170 0.201553i
\(819\) 0.416716 33.1366i 0.0145612 1.15789i
\(820\) −39.2222 + 18.1461i −1.36970 + 0.633690i
\(821\) 0.655352 0.966573i 0.0228720 0.0337336i −0.816081 0.577937i \(-0.803858\pi\)
0.838953 + 0.544204i \(0.183168\pi\)
\(822\) −11.6889 + 5.31890i −0.407698 + 0.185518i
\(823\) −26.5014 + 7.35807i −0.923780 + 0.256486i −0.696677 0.717385i \(-0.745339\pi\)
−0.227103 + 0.973871i \(0.572925\pi\)
\(824\) −1.41506 + 0.231987i −0.0492959 + 0.00808166i
\(825\) 3.33897 + 32.6074i 0.116248 + 1.13524i
\(826\) −15.3727 + 39.3477i −0.534883 + 1.36908i
\(827\) 14.9144i 0.518626i −0.965793 0.259313i \(-0.916504\pi\)
0.965793 0.259313i \(-0.0834962\pi\)
\(828\) −16.5395 43.0788i −0.574788 1.49709i
\(829\) −2.51270 9.04993i −0.0872697 0.314317i 0.907012 0.421104i \(-0.138357\pi\)
−0.994282 + 0.106787i \(0.965944\pi\)
\(830\) 2.53313 + 7.51805i 0.0879261 + 0.260955i
\(831\) −34.8072 18.7349i −1.20745 0.649906i
\(832\) 11.1339 + 24.0656i 0.385999 + 0.834323i
\(833\) 0.904981 4.11137i 0.0313557 0.142451i
\(834\) 16.3551 10.9396i 0.566332 0.378807i
\(835\) 35.0751 21.1040i 1.21383 0.730335i
\(836\) 23.3473 + 10.8016i 0.807484 + 0.373582i
\(837\) −2.33675 0.836745i −0.0807700 0.0289221i
\(838\) −6.86406 10.1237i −0.237115 0.349719i
\(839\) 37.5493 + 22.5927i 1.29635 + 0.779986i 0.985370 0.170432i \(-0.0545162\pi\)
0.310977 + 0.950417i \(0.399344\pi\)
\(840\) 0.246834 + 5.15154i 0.00851657 + 0.177745i
\(841\) −3.48436 1.17402i −0.120150 0.0404834i
\(842\) −44.4579 58.4833i −1.53212 2.01547i
\(843\) −35.1116 + 11.5852i −1.20931 + 0.399014i
\(844\) 18.4439 15.6664i 0.634866 0.539260i
\(845\) 0.962481 8.84987i 0.0331104 0.304445i
\(846\) −1.50181 + 22.4689i −0.0516334 + 0.772496i
\(847\) 0.700612 + 12.9220i 0.0240733 + 0.444006i
\(848\) 20.1754 + 10.6963i 0.692828 + 0.367314i
\(849\) 17.6320 25.6564i 0.605127 0.880525i
\(850\) −49.2852 52.0298i −1.69047 1.78461i
\(851\) −38.1719 + 15.2091i −1.30852 + 0.521360i
\(852\) 2.21278 7.77962i 0.0758086 0.266526i
\(853\) 5.72117 + 5.41938i 0.195889 + 0.185556i 0.779357 0.626580i \(-0.215546\pi\)
−0.583468 + 0.812136i \(0.698305\pi\)
\(854\) 6.32109 + 58.1215i 0.216303 + 1.98888i
\(855\) −58.3945 + 2.43005i −1.99705 + 0.0831060i
\(856\) −3.60997 0.591825i −0.123386 0.0202281i
\(857\) −43.2873 + 4.70778i −1.47867 + 0.160815i −0.811614 0.584195i \(-0.801410\pi\)
−0.667054 + 0.745009i \(0.732445\pi\)
\(858\) 26.7913 + 20.6333i 0.914641 + 0.704409i
\(859\) 44.4772 + 17.7214i 1.51754 + 0.604645i 0.972322 0.233647i \(-0.0750659\pi\)
0.545222 + 0.838291i \(0.316445\pi\)
\(860\) 4.38638 + 11.0090i 0.149574 + 0.375404i
\(861\) −20.9734 + 24.3794i −0.714771 + 0.830849i
\(862\) 11.6957 13.7693i 0.398358 0.468983i
\(863\) −11.5205 + 21.7301i −0.392164 + 0.739700i −0.998456 0.0555421i \(-0.982311\pi\)
0.606292 + 0.795242i \(0.292656\pi\)
\(864\) 37.9241 14.2875i 1.29020 0.486072i
\(865\) −47.5867 13.2124i −1.61800 0.449234i
\(866\) 78.2914 + 8.51471i 2.66045 + 0.289341i
\(867\) −8.15816 + 8.50472i −0.277066 + 0.288836i
\(868\) −0.531761 2.41581i −0.0180491 0.0819980i
\(869\) 3.05443 2.32192i 0.103615 0.0787657i
\(870\) 13.3580 58.9189i 0.452878 1.99754i
\(871\) 0.670514 12.3669i 0.0227195 0.419037i
\(872\) 0.684566 1.13776i 0.0231823 0.0385293i
\(873\) −23.1202 + 23.8010i −0.782502 + 0.805542i
\(874\) −71.6889 54.4965i −2.42491 1.84337i
\(875\) 10.3580 22.3885i 0.350165 0.756869i
\(876\) 11.9489 8.96536i 0.403717 0.302911i
\(877\) −14.0547 26.5100i −0.474595 0.895180i −0.999043 0.0437382i \(-0.986073\pi\)
0.524448 0.851442i \(-0.324272\pi\)
\(878\) 71.3564 + 15.7067i 2.40816 + 0.530076i
\(879\) 26.3785 15.6464i 0.889724 0.527739i
\(880\) −31.6560 21.4633i −1.06712 0.723528i
\(881\) 35.6847 12.0236i 1.20225 0.405084i 0.354283 0.935138i \(-0.384725\pi\)
0.847964 + 0.530054i \(0.177828\pi\)
\(882\) −2.32151 4.51513i −0.0781693 0.152032i
\(883\) 9.39999 + 57.3374i 0.316335 + 1.92956i 0.365600 + 0.930772i \(0.380864\pi\)
−0.0492648 + 0.998786i \(0.515688\pi\)
\(884\) −35.4957 −1.19385
\(885\) 40.2971 + 24.2230i 1.35457 + 0.814249i
\(886\) −37.1159 −1.24693
\(887\) −0.566484 3.45540i −0.0190207 0.116021i 0.975610 0.219513i \(-0.0704467\pi\)
−0.994630 + 0.103492i \(0.966998\pi\)
\(888\) −0.935363 2.39120i −0.0313887 0.0802435i
\(889\) 46.1439 15.5477i 1.54762 0.521453i
\(890\) 65.8875 + 44.6728i 2.20855 + 1.49744i
\(891\) 15.1538 16.9571i 0.507671 0.568083i
\(892\) −43.1280 9.49319i −1.44403 0.317856i
\(893\) 9.88235 + 18.6401i 0.330700 + 0.623767i
\(894\) 5.78083 + 7.70462i 0.193340 + 0.257681i
\(895\) 33.0041 71.3372i 1.10321 2.38454i
\(896\) −5.35036 4.06724i −0.178743 0.135877i
\(897\) −36.5175 43.5437i −1.21928 1.45388i
\(898\) 0.389298 0.647019i 0.0129911 0.0215913i
\(899\) 0.130136 2.40021i 0.00434027 0.0800516i
\(900\) −41.1909 5.00463i −1.37303 0.166821i
\(901\) −20.7090 + 15.7426i −0.689916 + 0.524461i
\(902\) −7.05451 32.0489i −0.234889 1.06711i
\(903\) 6.36408 + 6.10475i 0.211783 + 0.203153i
\(904\) −1.33545 0.145239i −0.0444163 0.00483056i
\(905\) 48.2500 + 13.3966i 1.60389 + 0.445317i
\(906\) 7.30978 + 46.4137i 0.242851 + 1.54199i
\(907\) 5.95865 11.2392i 0.197854 0.373192i −0.764656 0.644439i \(-0.777091\pi\)
0.962510 + 0.271247i \(0.0874359\pi\)
\(908\) −13.0031 + 15.3084i −0.431522 + 0.508027i
\(909\) −5.94897 + 8.54085i −0.197315 + 0.283282i
\(910\) −28.3403 71.1288i −0.939472 2.35790i
\(911\) −40.5608 16.1609i −1.34384 0.535435i −0.416323 0.909217i \(-0.636682\pi\)
−0.927517 + 0.373782i \(0.878061\pi\)
\(912\) 24.9522 32.3991i 0.826249 1.07284i
\(913\) −2.87516 + 0.312692i −0.0951538 + 0.0103486i
\(914\) 32.0618 + 5.25627i 1.06051 + 0.173862i
\(915\) 64.9511 + 3.93127i 2.14722 + 0.129964i
\(916\) −4.33112 39.8240i −0.143104 1.31582i
\(917\) −31.0390 29.4017i −1.02500 0.970930i
\(918\) −3.62794 + 49.5904i −0.119740 + 1.63673i
\(919\) 9.67537 3.85502i 0.319161 0.127165i −0.205056 0.978750i \(-0.565738\pi\)
0.524217 + 0.851585i \(0.324358\pi\)
\(920\) 6.08226 + 6.42096i 0.200526 + 0.211693i
\(921\) 39.9076 + 27.4259i 1.31500 + 0.903714i
\(922\) 11.9002 + 6.30908i 0.391912 + 0.207779i
\(923\) −0.539278 9.94639i −0.0177505 0.327390i
\(924\) 22.3425 + 3.80728i 0.735015 + 0.125250i
\(925\) −3.99487 + 36.7322i −0.131351 + 1.20775i
\(926\) 3.86665 3.28436i 0.127066 0.107931i
\(927\) −5.84752 13.0680i −0.192058 0.429208i
\(928\) 23.7516 + 31.2447i 0.779685 + 1.02566i
\(929\) 2.75605 + 0.928621i 0.0904230 + 0.0304671i 0.364149 0.931341i \(-0.381360\pi\)
−0.273726 + 0.961808i \(0.588256\pi\)
\(930\) −5.72809 + 0.274459i −0.187832 + 0.00899985i
\(931\) −4.07568 2.45226i −0.133575 0.0803695i
\(932\) 5.27630 + 7.78196i 0.172831 + 0.254907i
\(933\) 2.91061 + 1.77628i 0.0952892 + 0.0581528i
\(934\) 8.70757 + 4.02855i 0.284920 + 0.131818i
\(935\) 37.3320 22.4619i 1.22089 0.734584i
\(936\) 2.73524 2.26474i 0.0894040 0.0740254i
\(937\) 3.56885 16.2134i 0.116589 0.529670i −0.881732 0.471751i \(-0.843622\pi\)
0.998321 0.0579195i \(-0.0184467\pi\)
\(938\) −7.26008 15.6924i −0.237050 0.512376i
\(939\) 21.1811 39.3519i 0.691219 1.28420i
\(940\) 7.97569 + 23.6710i 0.260138 + 0.772063i
\(941\) −8.57622 30.8888i −0.279577 1.00694i −0.961338 0.275370i \(-0.911200\pi\)
0.681761 0.731575i \(-0.261214\pi\)
\(942\) 1.06988 + 3.94953i 0.0348586 + 0.128683i
\(943\) 55.1495i 1.79591i
\(944\) −31.1046 + 10.7131i −1.01237 + 0.348682i
\(945\) −49.0982 + 15.5182i −1.59716 + 0.504808i
\(946\) −8.88019 + 1.45583i −0.288720 + 0.0473332i
\(947\) 12.6753 3.51929i 0.411893 0.114362i −0.0553995 0.998464i \(-0.517643\pi\)
0.467293 + 0.884103i \(0.345229\pi\)
\(948\) 2.01165 + 4.42083i 0.0653353 + 0.143582i
\(949\) 10.3243 15.2272i 0.335142 0.494297i
\(950\) −73.4907 + 34.0004i −2.38435 + 1.10312i
\(951\) −0.806404 0.0928355i −0.0261494 0.00301040i
\(952\) 3.63198 1.92555i 0.117713 0.0624075i
\(953\) 13.8601 + 23.0357i 0.448973 + 0.746198i 0.995850 0.0910147i \(-0.0290110\pi\)
−0.546877 + 0.837213i \(0.684183\pi\)
\(954\) −7.12876 + 30.5512i −0.230802 + 0.989131i
\(955\) 32.8125 43.1641i 1.06179 1.39676i
\(956\) 9.12884 6.18950i 0.295248 0.200183i
\(957\) 19.9300 + 9.37316i 0.644244 + 0.302991i
\(958\) 8.14923 + 0.441839i 0.263290 + 0.0142752i
\(959\) −3.38469 + 10.0454i −0.109297 + 0.324383i
\(960\) 30.0896 28.1456i 0.971138 0.908394i
\(961\) 30.0524 6.61503i 0.969432 0.213388i
\(962\) 24.6775 + 29.0527i 0.795636 + 0.936695i
\(963\) −3.49197 36.3559i −0.112527 1.17155i
\(964\) 0.221603 0.798142i 0.00713736 0.0257064i
\(965\) −65.0565 + 3.52726i −2.09424 + 0.113547i
\(966\) −73.5171 29.8289i −2.36537 0.959728i
\(967\) 15.6803 + 13.3190i 0.504245 + 0.428309i 0.863062 0.505099i \(-0.168544\pi\)
−0.358817 + 0.933408i \(0.616820\pi\)
\(968\) −1.00676 + 0.953657i −0.0323586 + 0.0306517i
\(969\) 21.5615 + 41.2945i 0.692654 + 1.32657i
\(970\) −28.3767 + 71.2202i −0.911121 + 2.28674i
\(971\) −25.4664 + 26.8845i −0.817255 + 0.862765i −0.992561 0.121749i \(-0.961150\pi\)
0.175306 + 0.984514i \(0.443908\pi\)
\(972\) 16.6932 + 23.4548i 0.535435 + 0.752313i
\(973\) 2.62759 16.0276i 0.0842367 0.513821i
\(974\) 5.25131 32.0316i 0.168263 1.02636i
\(975\) −49.9750 + 10.6713i −1.60048 + 0.341756i
\(976\) −31.3105 + 33.0541i −1.00223 + 1.05804i
\(977\) 6.93235 17.3989i 0.221786 0.556640i −0.775412 0.631456i \(-0.782458\pi\)
0.997197 + 0.0748160i \(0.0238370\pi\)
\(978\) −43.5736 + 22.7514i −1.39333 + 0.727511i
\(979\) −21.0682 + 19.9569i −0.673344 + 0.637825i
\(980\) −4.29211 3.64575i −0.137107 0.116459i
\(981\) 12.7282 + 3.70699i 0.406381 + 0.118355i
\(982\) 31.3291 1.69861i 0.999751 0.0542049i
\(983\) −3.06566 + 11.0415i −0.0977794 + 0.352170i −0.996214 0.0869384i \(-0.972292\pi\)
0.898434 + 0.439108i \(0.144705\pi\)
\(984\) −3.44609 0.0216676i −0.109857 0.000690739i
\(985\) 62.0747 + 73.0800i 1.97786 + 2.32852i
\(986\) −47.0284 + 10.3517i −1.49769 + 0.329666i
\(987\) 12.6978 + 13.5748i 0.404174 + 0.432091i
\(988\) −12.8059 + 38.0064i −0.407409 + 1.20915i
\(989\) 15.1007 + 0.818738i 0.480175 + 0.0260343i
\(990\) 17.4020 49.5781i 0.553072 1.57569i
\(991\) −19.9213 + 13.5070i −0.632822 + 0.429064i −0.834973 0.550290i \(-0.814517\pi\)
0.202152 + 0.979354i \(0.435207\pi\)
\(992\) 2.25456 2.96583i 0.0715824 0.0941651i
\(993\) −0.564662 + 1.64167i −0.0179190 + 0.0520969i
\(994\) −7.16944 11.9157i −0.227401 0.377943i
\(995\) 48.0174 25.4572i 1.52225 0.807048i
\(996\) 0.418716 3.63712i 0.0132675 0.115247i
\(997\) −25.2278 + 11.6716i −0.798974 + 0.369645i −0.776512 0.630103i \(-0.783013\pi\)
−0.0224624 + 0.999748i \(0.507151\pi\)
\(998\) −4.45753 + 6.57437i −0.141101 + 0.208108i
\(999\) 20.6971 15.1262i 0.654828 0.478571i
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 177.2.f.a.155.3 yes 504
3.2 odd 2 inner 177.2.f.a.155.16 yes 504
59.8 odd 58 inner 177.2.f.a.8.16 yes 504
177.8 even 58 inner 177.2.f.a.8.3 504
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.f.a.8.3 504 177.8 even 58 inner
177.2.f.a.8.16 yes 504 59.8 odd 58 inner
177.2.f.a.155.3 yes 504 1.1 even 1 trivial
177.2.f.a.155.16 yes 504 3.2 odd 2 inner