Properties

Label 547.2.h.a.13.2
Level $547$
Weight $2$
Character 547.13
Analytic conductor $4.368$
Analytic rank $0$
Dimension $540$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [547,2,Mod(13,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([22]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("547.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.h (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.36781699056\)
Analytic rank: \(0\)
Dimension: \(540\)
Relative dimension: \(45\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 547.13
Dual form 547.2.h.a.505.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.198483 + 2.64858i) q^{2} +(-1.46769 + 1.84043i) q^{3} +(-4.99791 - 0.753313i) q^{4} +(1.33165 - 1.23559i) q^{5} +(-4.58320 - 4.25259i) q^{6} +(-1.49769 + 0.225741i) q^{7} +(1.80518 - 7.90900i) q^{8} +(-0.565489 - 2.47757i) q^{9} +O(q^{10})\) \(q+(-0.198483 + 2.64858i) q^{2} +(-1.46769 + 1.84043i) q^{3} +(-4.99791 - 0.753313i) q^{4} +(1.33165 - 1.23559i) q^{5} +(-4.58320 - 4.25259i) q^{6} +(-1.49769 + 0.225741i) q^{7} +(1.80518 - 7.90900i) q^{8} +(-0.565489 - 2.47757i) q^{9} +(3.00825 + 3.77223i) q^{10} +(2.79702 - 4.84459i) q^{11} +(8.72180 - 8.09265i) q^{12} +(0.365334 - 0.249080i) q^{13} +(-0.300625 - 4.01156i) q^{14} +(0.319564 + 4.26428i) q^{15} +(10.9297 + 3.37136i) q^{16} +(-6.48257 - 1.99961i) q^{17} +(6.67428 - 1.00599i) q^{18} +(-0.224076 - 2.99008i) q^{19} +(-7.58627 + 5.17223i) q^{20} +(1.78269 - 3.08771i) q^{21} +(12.2761 + 8.36970i) q^{22} +(-0.289476 - 3.86278i) q^{23} +(11.9065 + 14.9303i) q^{24} +(-0.127042 + 1.69525i) q^{25} +(0.587196 + 1.01705i) q^{26} +(-0.972877 - 0.468513i) q^{27} +7.65539 q^{28} +(-1.26282 + 5.53278i) q^{29} -11.3577 q^{30} +(3.36920 - 4.22484i) q^{31} +(-5.17109 + 13.1757i) q^{32} +(4.81094 + 12.2581i) q^{33} +(6.58280 - 16.7727i) q^{34} +(-1.71549 + 2.15115i) q^{35} +(0.959876 + 12.8087i) q^{36} +(-6.43854 - 1.98603i) q^{37} +7.96394 q^{38} +(-0.0777831 + 1.03794i) q^{39} +(-7.36844 - 12.7625i) q^{40} +(2.07558 - 3.59501i) q^{41} +(7.82421 + 5.33446i) q^{42} +(-7.52267 + 1.13386i) q^{43} +(-17.6287 + 22.1057i) q^{44} +(-3.81431 - 2.60055i) q^{45} +10.2883 q^{46} +(-3.92461 - 6.79762i) q^{47} +(-22.2461 + 15.1671i) q^{48} +(-4.49688 + 1.38710i) q^{49} +(-4.46480 - 0.672960i) q^{50} +(13.1945 - 8.99589i) q^{51} +(-2.01354 + 0.969670i) q^{52} +(-1.53158 + 1.04421i) q^{53} +(1.43399 - 2.48375i) q^{54} +(-2.26127 - 9.90729i) q^{55} +(-0.918217 + 12.2528i) q^{56} +(5.83190 + 3.97612i) q^{57} +(-14.4034 - 4.44285i) q^{58} +(-0.690824 + 1.19654i) q^{59} +(1.61519 - 21.5532i) q^{60} +(-0.655073 - 0.202063i) q^{61} +(10.5211 + 9.76214i) q^{62} +(1.40622 + 3.58299i) q^{63} +(-13.2603 - 6.38581i) q^{64} +(0.178736 - 0.783093i) q^{65} +(-33.4213 + 10.3091i) q^{66} +(10.8193 + 3.33731i) q^{67} +(30.8930 + 14.8773i) q^{68} +(7.53403 + 5.13661i) q^{69} +(-5.35699 - 4.97056i) q^{70} +(15.5824 + 4.80654i) q^{71} -20.6159 q^{72} +(0.168670 - 2.25075i) q^{73} +(6.53809 - 16.6588i) q^{74} +(-2.93353 - 2.72192i) q^{75} +(-1.13256 + 15.1130i) q^{76} +(-3.09546 + 7.88711i) q^{77} +(-2.73363 - 0.412029i) q^{78} +(-8.66189 - 10.8617i) q^{79} +(18.7202 - 9.01516i) q^{80} +(9.15900 - 4.41074i) q^{81} +(9.10971 + 6.21089i) q^{82} +(0.103491 - 0.179252i) q^{83} +(-11.2357 + 14.0892i) q^{84} +(-11.1032 + 5.34704i) q^{85} +(-1.50999 - 20.1494i) q^{86} +(-8.32925 - 10.4445i) q^{87} +(-33.2667 - 30.8670i) q^{88} +(1.89945 - 8.32202i) q^{89} +(7.64483 - 9.58632i) q^{90} +(-0.490931 + 0.455517i) q^{91} +(-1.46311 + 19.5239i) q^{92} +(2.83057 + 12.4015i) q^{93} +(18.7830 - 9.04542i) q^{94} +(-3.99292 - 3.70489i) q^{95} +(-16.6594 - 28.8549i) q^{96} +(1.17674 + 15.7025i) q^{97} +(-2.78130 - 12.1857i) q^{98} +(-13.5845 - 4.19026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 540 q - 13 q^{2} - 10 q^{3} + 33 q^{4} - 15 q^{5} + 10 q^{6} - 2 q^{7} - 26 q^{8} - 96 q^{9} - 4 q^{10} - 8 q^{11} - 18 q^{12} - 11 q^{13} + 5 q^{14} - 7 q^{15} + 53 q^{16} - 10 q^{17} - 59 q^{18} - 12 q^{19} - 18 q^{20} + 20 q^{21} + 70 q^{22} - 15 q^{23} - 46 q^{24} + 26 q^{25} - 39 q^{26} - q^{27} - 56 q^{28} - 40 q^{29} - 100 q^{30} + 59 q^{31} - 5 q^{32} - 15 q^{33} - 8 q^{34} + 36 q^{35} + 43 q^{36} - 32 q^{37} - 108 q^{38} + 34 q^{39} - 27 q^{40} + 39 q^{41} + 46 q^{42} - 16 q^{43} - 110 q^{44} - 103 q^{45} + 12 q^{46} - 60 q^{47} + 42 q^{48} + 57 q^{49} - 168 q^{50} + 57 q^{51} - 46 q^{52} - 30 q^{53} + 113 q^{54} + 38 q^{55} + 64 q^{56} + 22 q^{57} - 88 q^{58} + 55 q^{59} + 9 q^{60} + 26 q^{61} - 32 q^{62} + 6 q^{63} - 50 q^{64} + 73 q^{65} + 72 q^{66} - 104 q^{67} - 181 q^{68} - 125 q^{69} - 50 q^{70} + 39 q^{71} - 434 q^{72} + 46 q^{73} - 178 q^{74} + 248 q^{75} - 126 q^{76} - 52 q^{77} - 82 q^{78} + 86 q^{79} + 208 q^{80} - 4 q^{81} + 177 q^{82} + 39 q^{83} + 124 q^{84} - 12 q^{85} + 2 q^{86} + 162 q^{87} - 34 q^{88} + 63 q^{89} + 121 q^{90} + 21 q^{91} + q^{92} - 57 q^{93} + 67 q^{94} - 143 q^{95} + 489 q^{96} + 119 q^{97} - 10 q^{98} - 120 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/547\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{21}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.198483 + 2.64858i −0.140349 + 1.87283i 0.272674 + 0.962107i \(0.412092\pi\)
−0.413023 + 0.910721i \(0.635527\pi\)
\(3\) −1.46769 + 1.84043i −0.847372 + 1.06257i 0.149896 + 0.988702i \(0.452106\pi\)
−0.997268 + 0.0738688i \(0.976465\pi\)
\(4\) −4.99791 0.753313i −2.49895 0.376657i
\(5\) 1.33165 1.23559i 0.595533 0.552574i −0.323764 0.946138i \(-0.604948\pi\)
0.919297 + 0.393564i \(0.128758\pi\)
\(6\) −4.58320 4.25259i −1.87108 1.73611i
\(7\) −1.49769 + 0.225741i −0.566075 + 0.0853221i −0.425844 0.904797i \(-0.640023\pi\)
−0.140231 + 0.990119i \(0.544785\pi\)
\(8\) 1.80518 7.90900i 0.638226 2.79625i
\(9\) −0.565489 2.47757i −0.188496 0.825857i
\(10\) 3.00825 + 3.77223i 0.951294 + 1.19288i
\(11\) 2.79702 4.84459i 0.843334 1.46070i −0.0437260 0.999044i \(-0.513923\pi\)
0.887060 0.461654i \(-0.152744\pi\)
\(12\) 8.72180 8.09265i 2.51777 2.33615i
\(13\) 0.365334 0.249080i 0.101325 0.0690825i −0.511597 0.859225i \(-0.670946\pi\)
0.612923 + 0.790143i \(0.289994\pi\)
\(14\) −0.300625 4.01156i −0.0803455 1.07214i
\(15\) 0.319564 + 4.26428i 0.0825110 + 1.10103i
\(16\) 10.9297 + 3.37136i 2.73242 + 0.842840i
\(17\) −6.48257 1.99961i −1.57225 0.484976i −0.618556 0.785740i \(-0.712282\pi\)
−0.953699 + 0.300764i \(0.902758\pi\)
\(18\) 6.67428 1.00599i 1.57314 0.237113i
\(19\) −0.224076 2.99008i −0.0514065 0.685972i −0.962066 0.272815i \(-0.912045\pi\)
0.910660 0.413157i \(-0.135574\pi\)
\(20\) −7.58627 + 5.17223i −1.69634 + 1.15655i
\(21\) 1.78269 3.08771i 0.389015 0.673794i
\(22\) 12.2761 + 8.36970i 2.61727 + 1.78443i
\(23\) −0.289476 3.86278i −0.0603598 0.805446i −0.942446 0.334358i \(-0.891481\pi\)
0.882086 0.471088i \(-0.156139\pi\)
\(24\) 11.9065 + 14.9303i 2.43040 + 3.04763i
\(25\) −0.127042 + 1.69525i −0.0254083 + 0.339051i
\(26\) 0.587196 + 1.01705i 0.115159 + 0.199461i
\(27\) −0.972877 0.468513i −0.187230 0.0901653i
\(28\) 7.65539 1.44673
\(29\) −1.26282 + 5.53278i −0.234500 + 1.02741i 0.711358 + 0.702830i \(0.248081\pi\)
−0.945858 + 0.324582i \(0.894776\pi\)
\(30\) −11.3577 −2.07362
\(31\) 3.36920 4.22484i 0.605126 0.758803i −0.381041 0.924558i \(-0.624434\pi\)
0.986167 + 0.165754i \(0.0530059\pi\)
\(32\) −5.17109 + 13.1757i −0.914127 + 2.32916i
\(33\) 4.81094 + 12.2581i 0.837477 + 2.13386i
\(34\) 6.58280 16.7727i 1.12894 2.87650i
\(35\) −1.71549 + 2.15115i −0.289970 + 0.363611i
\(36\) 0.959876 + 12.8087i 0.159979 + 2.13478i
\(37\) −6.43854 1.98603i −1.05849 0.326501i −0.283827 0.958875i \(-0.591604\pi\)
−0.774663 + 0.632374i \(0.782080\pi\)
\(38\) 7.96394 1.29192
\(39\) −0.0777831 + 1.03794i −0.0124553 + 0.166204i
\(40\) −7.36844 12.7625i −1.16505 2.01793i
\(41\) 2.07558 3.59501i 0.324152 0.561447i −0.657189 0.753726i \(-0.728255\pi\)
0.981340 + 0.192279i \(0.0615879\pi\)
\(42\) 7.82421 + 5.33446i 1.20730 + 0.823125i
\(43\) −7.52267 + 1.13386i −1.14720 + 0.172912i −0.695002 0.719007i \(-0.744597\pi\)
−0.452194 + 0.891919i \(0.649359\pi\)
\(44\) −17.6287 + 22.1057i −2.65763 + 3.33257i
\(45\) −3.81431 2.60055i −0.568603 0.387667i
\(46\) 10.2883 1.51693
\(47\) −3.92461 6.79762i −0.572463 0.991535i −0.996312 0.0858024i \(-0.972655\pi\)
0.423849 0.905733i \(-0.360679\pi\)
\(48\) −22.2461 + 15.1671i −3.21095 + 2.18919i
\(49\) −4.49688 + 1.38710i −0.642412 + 0.198158i
\(50\) −4.46480 0.672960i −0.631417 0.0951709i
\(51\) 13.1945 8.99589i 1.84761 1.25968i
\(52\) −2.01354 + 0.969670i −0.279228 + 0.134469i
\(53\) −1.53158 + 1.04421i −0.210378 + 0.143434i −0.663925 0.747799i \(-0.731111\pi\)
0.453547 + 0.891232i \(0.350158\pi\)
\(54\) 1.43399 2.48375i 0.195142 0.337995i
\(55\) −2.26127 9.90729i −0.304910 1.33590i
\(56\) −0.918217 + 12.2528i −0.122702 + 1.63734i
\(57\) 5.83190 + 3.97612i 0.772454 + 0.526650i
\(58\) −14.4034 4.44285i −1.89125 0.583374i
\(59\) −0.690824 + 1.19654i −0.0899376 + 0.155777i −0.907485 0.420085i \(-0.862000\pi\)
0.817547 + 0.575862i \(0.195333\pi\)
\(60\) 1.61519 21.5532i 0.208520 2.78251i
\(61\) −0.655073 0.202063i −0.0838736 0.0258716i 0.252534 0.967588i \(-0.418736\pi\)
−0.336408 + 0.941716i \(0.609212\pi\)
\(62\) 10.5211 + 9.76214i 1.33618 + 1.23979i
\(63\) 1.40622 + 3.58299i 0.177167 + 0.451414i
\(64\) −13.2603 6.38581i −1.65753 0.798226i
\(65\) 0.178736 0.783093i 0.0221695 0.0971308i
\(66\) −33.4213 + 10.3091i −4.11388 + 1.26896i
\(67\) 10.8193 + 3.33731i 1.32179 + 0.407717i 0.873784 0.486315i \(-0.161659\pi\)
0.448003 + 0.894032i \(0.352135\pi\)
\(68\) 30.8930 + 14.8773i 3.74632 + 1.80413i
\(69\) 7.53403 + 5.13661i 0.906990 + 0.618375i
\(70\) −5.35699 4.97056i −0.640283 0.594096i
\(71\) 15.5824 + 4.80654i 1.84929 + 0.570432i 0.999028 + 0.0440784i \(0.0140351\pi\)
0.850266 + 0.526353i \(0.176441\pi\)
\(72\) −20.6159 −2.42961
\(73\) 0.168670 2.25075i 0.0197413 0.263430i −0.978596 0.205790i \(-0.934024\pi\)
0.998337 0.0576396i \(-0.0183574\pi\)
\(74\) 6.53809 16.6588i 0.760038 1.93655i
\(75\) −2.93353 2.72192i −0.338735 0.314300i
\(76\) −1.13256 + 15.1130i −0.129913 + 1.73357i
\(77\) −3.09546 + 7.88711i −0.352761 + 0.898820i
\(78\) −2.73363 0.412029i −0.309523 0.0466531i
\(79\) −8.66189 10.8617i −0.974538 1.22203i −0.975039 0.222033i \(-0.928731\pi\)
0.000500771 1.00000i \(-0.499841\pi\)
\(80\) 18.7202 9.01516i 2.09298 1.00793i
\(81\) 9.15900 4.41074i 1.01767 0.490083i
\(82\) 9.10971 + 6.21089i 1.00600 + 0.685878i
\(83\) 0.103491 0.179252i 0.0113596 0.0196754i −0.860290 0.509805i \(-0.829717\pi\)
0.871649 + 0.490130i \(0.163051\pi\)
\(84\) −11.2357 + 14.0892i −1.22592 + 1.53726i
\(85\) −11.1032 + 5.34704i −1.20432 + 0.579968i
\(86\) −1.50999 20.1494i −0.162827 2.17277i
\(87\) −8.32925 10.4445i −0.892989 1.11977i
\(88\) −33.2667 30.8670i −3.54624 3.29043i
\(89\) 1.89945 8.32202i 0.201341 0.882132i −0.768781 0.639513i \(-0.779136\pi\)
0.970121 0.242620i \(-0.0780067\pi\)
\(90\) 7.64483 9.58632i 0.805836 1.01049i
\(91\) −0.490931 + 0.455517i −0.0514635 + 0.0477512i
\(92\) −1.46311 + 19.5239i −0.152540 + 2.03551i
\(93\) 2.83057 + 12.4015i 0.293516 + 1.28598i
\(94\) 18.7830 9.04542i 1.93732 0.932964i
\(95\) −3.99292 3.70489i −0.409665 0.380113i
\(96\) −16.6594 28.8549i −1.70029 2.94499i
\(97\) 1.17674 + 15.7025i 0.119480 + 1.59434i 0.658850 + 0.752275i \(0.271043\pi\)
−0.539370 + 0.842069i \(0.681338\pi\)
\(98\) −2.78130 12.1857i −0.280953 1.23094i
\(99\) −13.5845 4.19026i −1.36529 0.421137i
\(100\) 1.91200 8.37702i 0.191200 0.837702i
\(101\) 2.67073 + 11.7012i 0.265748 + 1.16432i 0.914907 + 0.403664i \(0.132264\pi\)
−0.649160 + 0.760652i \(0.724879\pi\)
\(102\) 21.2074 + 36.7323i 2.09985 + 3.63704i
\(103\) 11.5486 5.56153i 1.13792 0.547994i 0.232537 0.972588i \(-0.425297\pi\)
0.905384 + 0.424594i \(0.139583\pi\)
\(104\) −1.31048 3.33906i −0.128504 0.327422i
\(105\) −1.44123 6.31445i −0.140650 0.616227i
\(106\) −2.46168 4.26376i −0.239100 0.414133i
\(107\) −17.0913 −1.65228 −0.826138 0.563468i \(-0.809467\pi\)
−0.826138 + 0.563468i \(0.809467\pi\)
\(108\) 4.50941 + 3.07446i 0.433918 + 0.295840i
\(109\) 1.93138 1.79206i 0.184993 0.171648i −0.582240 0.813017i \(-0.697824\pi\)
0.767233 + 0.641369i \(0.221633\pi\)
\(110\) 26.6891 4.02273i 2.54470 0.383552i
\(111\) 13.1049 8.93479i 1.24386 0.848053i
\(112\) −17.1304 2.58199i −1.61867 0.243975i
\(113\) −6.54337 4.46119i −0.615548 0.419674i 0.215005 0.976613i \(-0.431023\pi\)
−0.830553 + 0.556939i \(0.811976\pi\)
\(114\) −11.6886 + 14.6570i −1.09474 + 1.37276i
\(115\) −5.15831 4.78621i −0.481015 0.446317i
\(116\) 10.4794 26.7010i 0.972986 2.47913i
\(117\) −0.823707 0.764288i −0.0761517 0.0706585i
\(118\) −3.03202 2.06719i −0.279120 0.190301i
\(119\) 10.1603 + 1.53142i 0.931394 + 0.140385i
\(120\) 34.3030 + 5.17035i 3.13142 + 0.471986i
\(121\) −10.1467 17.5746i −0.922425 1.59769i
\(122\) 0.665202 1.69491i 0.0602245 0.153450i
\(123\) 3.57004 + 9.09633i 0.321900 + 0.820188i
\(124\) −20.0216 + 18.5773i −1.79799 + 1.66829i
\(125\) 7.58859 + 9.51579i 0.678744 + 0.851118i
\(126\) −9.76893 + 3.01332i −0.870286 + 0.268448i
\(127\) 0.166285 + 2.21891i 0.0147554 + 0.196897i 0.999710 + 0.0240834i \(0.00766672\pi\)
−0.984955 + 0.172813i \(0.944714\pi\)
\(128\) 5.39112 9.33770i 0.476512 0.825343i
\(129\) 8.95417 15.5091i 0.788371 1.36550i
\(130\) 2.03861 + 0.628827i 0.178798 + 0.0551518i
\(131\) −3.60027 15.7738i −0.314557 1.37816i −0.846953 0.531668i \(-0.821565\pi\)
0.532396 0.846495i \(-0.321292\pi\)
\(132\) −14.8104 64.8888i −1.28908 5.64785i
\(133\) 1.01058 + 4.42765i 0.0876285 + 0.383926i
\(134\) −10.9866 + 27.9933i −0.949096 + 2.41826i
\(135\) −1.87443 + 0.578184i −0.161325 + 0.0497621i
\(136\) −27.5171 + 47.6610i −2.35957 + 4.08690i
\(137\) 0.110593 0.0166692i 0.00944859 0.00142415i −0.144316 0.989532i \(-0.546098\pi\)
0.153765 + 0.988107i \(0.450860\pi\)
\(138\) −15.1001 + 18.9349i −1.28541 + 1.61185i
\(139\) −0.699492 1.78228i −0.0593301 0.151171i 0.898135 0.439720i \(-0.144922\pi\)
−0.957465 + 0.288549i \(0.906827\pi\)
\(140\) 10.1943 9.45895i 0.861578 0.799427i
\(141\) 18.2706 + 2.75386i 1.53867 + 0.231916i
\(142\) −15.8234 + 40.3173i −1.32787 + 3.38335i
\(143\) −0.184844 2.46658i −0.0154575 0.206265i
\(144\) 2.17216 28.9855i 0.181014 2.41546i
\(145\) 5.15463 + 8.92808i 0.428069 + 0.741437i
\(146\) 5.92780 + 0.893472i 0.490588 + 0.0739442i
\(147\) 4.04717 10.3120i 0.333805 0.850521i
\(148\) 30.6831 + 14.7762i 2.52214 + 1.21460i
\(149\) 19.1368 9.21582i 1.56775 0.754989i 0.569976 0.821661i \(-0.306952\pi\)
0.997775 + 0.0666719i \(0.0212381\pi\)
\(150\) 7.79147 7.22943i 0.636171 0.590280i
\(151\) −16.2260 7.81404i −1.32045 0.635897i −0.364992 0.931011i \(-0.618928\pi\)
−0.955462 + 0.295113i \(0.904643\pi\)
\(152\) −24.0530 3.62541i −1.95096 0.294060i
\(153\) −1.28835 + 17.1918i −0.104157 + 1.38987i
\(154\) −20.2752 9.76403i −1.63382 0.786808i
\(155\) −0.733583 9.78898i −0.0589228 0.786270i
\(156\) 1.17065 5.12895i 0.0937269 0.410645i
\(157\) 4.23887 2.89001i 0.338299 0.230648i −0.382240 0.924063i \(-0.624847\pi\)
0.720538 + 0.693415i \(0.243895\pi\)
\(158\) 30.4872 20.7858i 2.42543 1.65363i
\(159\) 0.326088 4.35134i 0.0258604 0.345083i
\(160\) 9.39373 + 23.9348i 0.742640 + 1.89222i
\(161\) 1.30553 + 5.71992i 0.102891 + 0.450793i
\(162\) 9.86428 + 25.1338i 0.775011 + 1.97470i
\(163\) −5.53796 14.1105i −0.433767 1.10522i −0.965982 0.258610i \(-0.916736\pi\)
0.532215 0.846609i \(-0.321360\pi\)
\(164\) −13.0817 + 16.4040i −1.02151 + 1.28094i
\(165\) 21.5525 + 10.3791i 1.67786 + 0.808014i
\(166\) 0.454220 + 0.309682i 0.0352543 + 0.0240360i
\(167\) −0.0488804 0.0612941i −0.00378248 0.00474308i 0.779937 0.625858i \(-0.215251\pi\)
−0.783719 + 0.621115i \(0.786680\pi\)
\(168\) −21.2026 19.6732i −1.63582 1.51782i
\(169\) −4.67801 + 11.9194i −0.359847 + 0.916874i
\(170\) −11.9582 30.4691i −0.917155 2.33687i
\(171\) −7.28143 + 2.24602i −0.556825 + 0.171758i
\(172\) 38.4518 2.93192
\(173\) −3.65349 4.58133i −0.277770 0.348312i 0.623303 0.781980i \(-0.285790\pi\)
−0.901073 + 0.433668i \(0.857219\pi\)
\(174\) 29.3164 19.9876i 2.22247 1.51525i
\(175\) −0.192419 2.56765i −0.0145455 0.194096i
\(176\) 46.9034 43.5200i 3.53548 3.28044i
\(177\) −1.18823 3.02756i −0.0893129 0.227566i
\(178\) 21.6645 + 6.68262i 1.62382 + 0.500883i
\(179\) −1.21676 + 5.33096i −0.0909446 + 0.398454i −0.999827 0.0185981i \(-0.994080\pi\)
0.908882 + 0.417052i \(0.136937\pi\)
\(180\) 17.1045 + 15.8707i 1.27489 + 1.18293i
\(181\) −7.85333 13.6024i −0.583734 1.01106i −0.995032 0.0995557i \(-0.968258\pi\)
0.411298 0.911501i \(-0.365075\pi\)
\(182\) −1.10903 1.39068i −0.0822069 0.103084i
\(183\) 1.33333 0.909048i 0.0985624 0.0671987i
\(184\) −31.0733 4.68354i −2.29075 0.345275i
\(185\) −11.0278 + 5.31072i −0.810782 + 0.390452i
\(186\) −33.4082 + 5.03548i −2.44961 + 0.369219i
\(187\) −27.8192 + 25.8124i −2.03434 + 1.88759i
\(188\) 14.4941 + 36.9303i 1.05709 + 2.69342i
\(189\) 1.56283 + 0.482071i 0.113679 + 0.0350655i
\(190\) 10.6052 9.84020i 0.769383 0.713883i
\(191\) −8.19014 + 20.8681i −0.592618 + 1.50997i 0.248233 + 0.968700i \(0.420150\pi\)
−0.840851 + 0.541266i \(0.817945\pi\)
\(192\) 31.2146 15.0322i 2.25272 1.08485i
\(193\) −19.8560 + 6.12478i −1.42927 + 0.440871i −0.910310 0.413928i \(-0.864157\pi\)
−0.518959 + 0.854799i \(0.673680\pi\)
\(194\) −41.8228 −3.00270
\(195\) 1.17890 + 1.47829i 0.0844225 + 0.105862i
\(196\) 23.5199 3.54506i 1.67999 0.253218i
\(197\) −3.48088 −0.248002 −0.124001 0.992282i \(-0.539573\pi\)
−0.124001 + 0.992282i \(0.539573\pi\)
\(198\) 13.7945 35.1479i 0.980334 2.49785i
\(199\) −3.31937 5.74932i −0.235304 0.407559i 0.724057 0.689740i \(-0.242275\pi\)
−0.959361 + 0.282182i \(0.908942\pi\)
\(200\) 13.1784 + 4.06501i 0.931855 + 0.287439i
\(201\) −22.0215 + 15.0140i −1.55327 + 1.05900i
\(202\) −31.5217 + 4.75113i −2.21786 + 0.334289i
\(203\) 0.642344 8.57149i 0.0450837 0.601600i
\(204\) −72.7218 + 35.0210i −5.09155 + 2.45196i
\(205\) −1.67802 7.35189i −0.117198 0.513478i
\(206\) 12.4379 + 31.6913i 0.866591 + 2.20804i
\(207\) −9.40662 + 2.90156i −0.653805 + 0.201672i
\(208\) 4.83272 1.49070i 0.335089 0.103361i
\(209\) −15.1125 7.27778i −1.04535 0.503414i
\(210\) 17.0104 2.56390i 1.17383 0.176926i
\(211\) 14.7929 13.7258i 1.01838 0.944921i 0.0198902 0.999802i \(-0.493668\pi\)
0.998493 + 0.0548807i \(0.0174779\pi\)
\(212\) 8.44130 4.06512i 0.579751 0.279193i
\(213\) −31.7163 + 21.6238i −2.17316 + 1.48164i
\(214\) 3.39234 45.2676i 0.231895 3.09443i
\(215\) −8.61660 + 10.8049i −0.587647 + 0.736886i
\(216\) −5.46168 + 6.84873i −0.371620 + 0.465997i
\(217\) −4.09231 + 7.08808i −0.277804 + 0.481170i
\(218\) 4.36306 + 5.47110i 0.295504 + 0.370550i
\(219\) 3.89478 + 3.61382i 0.263185 + 0.244200i
\(220\) 3.83835 + 51.2192i 0.258781 + 3.45320i
\(221\) −2.86637 + 0.884157i −0.192813 + 0.0594749i
\(222\) 21.0634 + 36.4828i 1.41368 + 2.44857i
\(223\) 5.33469 1.64553i 0.357237 0.110193i −0.110941 0.993827i \(-0.535387\pi\)
0.468179 + 0.883634i \(0.344910\pi\)
\(224\) 4.77041 20.9005i 0.318736 1.39647i
\(225\) 4.27195 0.643893i 0.284797 0.0429262i
\(226\) 13.1146 16.4451i 0.872368 1.09391i
\(227\) 3.79034 1.16916i 0.251574 0.0776002i −0.166404 0.986058i \(-0.553215\pi\)
0.417977 + 0.908458i \(0.362739\pi\)
\(228\) −26.1520 24.2655i −1.73196 1.60702i
\(229\) −24.1734 3.64355i −1.59742 0.240772i −0.710843 0.703351i \(-0.751686\pi\)
−0.886578 + 0.462578i \(0.846924\pi\)
\(230\) 13.7005 12.7122i 0.903384 0.838218i
\(231\) −9.97246 17.2728i −0.656140 1.13647i
\(232\) 41.4791 + 19.9753i 2.72324 + 1.31144i
\(233\) 5.71469 + 9.89813i 0.374381 + 0.648448i 0.990234 0.139414i \(-0.0445217\pi\)
−0.615853 + 0.787861i \(0.711188\pi\)
\(234\) 2.18777 2.02995i 0.143019 0.132702i
\(235\) −13.6253 4.20285i −0.888818 0.274164i
\(236\) 4.35404 5.45980i 0.283424 0.355403i
\(237\) 32.7031 2.12429
\(238\) −6.07274 + 26.6064i −0.393637 + 1.72464i
\(239\) −7.87342 + 13.6372i −0.509289 + 0.882115i 0.490653 + 0.871355i \(0.336758\pi\)
−0.999942 + 0.0107598i \(0.996575\pi\)
\(240\) −10.8837 + 47.6846i −0.702539 + 3.07802i
\(241\) −16.6055 2.50288i −1.06965 0.161225i −0.409467 0.912325i \(-0.634285\pi\)
−0.660188 + 0.751100i \(0.729523\pi\)
\(242\) 48.5615 23.3860i 3.12165 1.50331i
\(243\) −4.60410 + 20.1719i −0.295353 + 1.29403i
\(244\) 3.12178 + 1.50337i 0.199851 + 0.0962434i
\(245\) −4.27439 + 7.40346i −0.273081 + 0.472990i
\(246\) −24.8009 + 7.65007i −1.58125 + 0.487751i
\(247\) −0.826634 1.03657i −0.0525974 0.0659551i
\(248\) −27.3322 34.2735i −1.73560 2.17637i
\(249\) 0.178007 + 0.453553i 0.0112807 + 0.0287428i
\(250\) −26.7095 + 18.2102i −1.68926 + 1.15172i
\(251\) −1.94190 + 3.36348i −0.122572 + 0.212301i −0.920781 0.390079i \(-0.872448\pi\)
0.798209 + 0.602380i \(0.205781\pi\)
\(252\) −4.32904 18.9668i −0.272704 1.19479i
\(253\) −19.5232 9.40190i −1.22742 0.591092i
\(254\) −5.90997 −0.370825
\(255\) 6.45530 28.2825i 0.404246 1.77112i
\(256\) −0.659253 0.449471i −0.0412033 0.0280919i
\(257\) 19.3977 9.34145i 1.21000 0.582704i 0.283488 0.958976i \(-0.408508\pi\)
0.926509 + 0.376272i \(0.122794\pi\)
\(258\) 39.2997 + 26.7941i 2.44670 + 1.66813i
\(259\) 10.0913 + 1.52102i 0.627043 + 0.0945115i
\(260\) −1.48322 + 3.77918i −0.0919854 + 0.234375i
\(261\) 14.4220 0.892697
\(262\) 42.4927 6.40475i 2.62521 0.395687i
\(263\) −0.480778 0.231530i −0.0296460 0.0142768i 0.419002 0.907985i \(-0.362380\pi\)
−0.448648 + 0.893709i \(0.648094\pi\)
\(264\) 105.634 15.9217i 6.50130 0.979913i
\(265\) −0.749309 + 3.28294i −0.0460297 + 0.201669i
\(266\) −11.9275 + 1.79779i −0.731325 + 0.110229i
\(267\) 12.5283 + 15.7099i 0.766717 + 0.961433i
\(268\) −51.5598 24.8299i −3.14951 1.51673i
\(269\) 2.09708 0.646865i 0.127861 0.0394400i −0.230164 0.973152i \(-0.573926\pi\)
0.358026 + 0.933712i \(0.383450\pi\)
\(270\) −1.15932 5.07932i −0.0705541 0.309118i
\(271\) 4.40698 + 4.08908i 0.267705 + 0.248394i 0.802590 0.596531i \(-0.203455\pi\)
−0.534885 + 0.844925i \(0.679645\pi\)
\(272\) −64.1110 43.7102i −3.88730 2.65032i
\(273\) −0.117811 1.57208i −0.00713025 0.0951466i
\(274\) 0.0221988 + 0.296222i 0.00134108 + 0.0178955i
\(275\) 7.85746 + 5.35713i 0.473823 + 0.323047i
\(276\) −33.7849 31.3478i −2.03361 1.88691i
\(277\) −2.35492 10.3176i −0.141493 0.619922i −0.995089 0.0989860i \(-0.968440\pi\)
0.853596 0.520936i \(-0.174417\pi\)
\(278\) 4.85933 1.49891i 0.291444 0.0898984i
\(279\) −12.3726 5.95832i −0.740727 0.356715i
\(280\) 13.9167 + 17.4510i 0.831681 + 1.04289i
\(281\) 27.4341 4.13503i 1.63658 0.246675i 0.734617 0.678481i \(-0.237362\pi\)
0.901966 + 0.431806i \(0.142124\pi\)
\(282\) −10.9202 + 47.8446i −0.650290 + 2.84910i
\(283\) 22.8472 3.44367i 1.35813 0.204705i 0.570723 0.821143i \(-0.306663\pi\)
0.787403 + 0.616438i \(0.211425\pi\)
\(284\) −74.2587 35.7611i −4.40644 2.12203i
\(285\) 12.6789 1.91104i 0.751036 0.113200i
\(286\) 6.56961 0.388469
\(287\) −2.29705 + 5.85278i −0.135590 + 0.345478i
\(288\) 35.5679 + 5.36100i 2.09586 + 0.315900i
\(289\) 23.9793 + 16.3488i 1.41054 + 0.961693i
\(290\) −24.6698 + 11.8804i −1.44866 + 0.697639i
\(291\) −30.6263 20.8807i −1.79535 1.22405i
\(292\) −2.53851 + 11.1220i −0.148555 + 0.650863i
\(293\) −0.582406 −0.0340245 −0.0170123 0.999855i \(-0.505415\pi\)
−0.0170123 + 0.999855i \(0.505415\pi\)
\(294\) 26.5089 + 12.7660i 1.54603 + 0.744529i
\(295\) 0.558502 + 2.44696i 0.0325172 + 0.142467i
\(296\) −27.3302 + 47.3373i −1.58854 + 2.75142i
\(297\) −4.99091 + 3.40274i −0.289602 + 0.197447i
\(298\) 20.6105 + 52.5146i 1.19393 + 3.04209i
\(299\) −1.06790 1.33910i −0.0617582 0.0774423i
\(300\) 12.6111 + 15.8138i 0.728100 + 0.913008i
\(301\) 11.0107 3.39635i 0.634646 0.195762i
\(302\) 23.9167 41.4249i 1.37625 2.38374i
\(303\) −25.4551 12.2585i −1.46236 0.704233i
\(304\) 7.63157 33.4361i 0.437700 1.91769i
\(305\) −1.12200 + 0.540326i −0.0642455 + 0.0309390i
\(306\) −45.2781 6.82457i −2.58837 0.390135i
\(307\) −1.29541 + 5.67555i −0.0739328 + 0.323921i −0.998347 0.0574686i \(-0.981697\pi\)
0.924415 + 0.381389i \(0.124554\pi\)
\(308\) 21.4123 37.0872i 1.22008 2.11324i
\(309\) −6.71424 + 29.4170i −0.381960 + 1.67348i
\(310\) 26.0725 1.48082
\(311\) 6.43214 8.06565i 0.364733 0.457361i −0.565273 0.824904i \(-0.691229\pi\)
0.930007 + 0.367542i \(0.119801\pi\)
\(312\) 8.06868 + 2.48886i 0.456799 + 0.140904i
\(313\) −8.48390 + 7.87191i −0.479538 + 0.444947i −0.882529 0.470257i \(-0.844161\pi\)
0.402991 + 0.915204i \(0.367971\pi\)
\(314\) 6.81308 + 11.8006i 0.384484 + 0.665946i
\(315\) 6.29971 + 3.03378i 0.354949 + 0.170934i
\(316\) 35.1091 + 60.8107i 1.97504 + 3.42087i
\(317\) −3.93278 + 3.64908i −0.220887 + 0.204953i −0.782852 0.622208i \(-0.786236\pi\)
0.561965 + 0.827161i \(0.310045\pi\)
\(318\) 11.4601 + 1.72734i 0.642652 + 0.0968642i
\(319\) 23.2719 + 21.5932i 1.30298 + 1.20899i
\(320\) −25.5483 + 7.88062i −1.42820 + 0.440540i
\(321\) 25.0847 31.4552i 1.40009 1.75566i
\(322\) −15.4088 + 2.32250i −0.858698 + 0.129428i
\(323\) −4.52641 + 19.8315i −0.251856 + 1.10345i
\(324\) −49.0985 + 15.1449i −2.72769 + 0.841382i
\(325\) 0.375842 + 0.650977i 0.0208480 + 0.0361097i
\(326\) 38.4719 11.8670i 2.13076 0.657253i
\(327\) 0.463483 + 6.18475i 0.0256307 + 0.342017i
\(328\) −24.6862 22.9054i −1.36307 1.26474i
\(329\) 7.41237 + 9.29481i 0.408657 + 0.512440i
\(330\) −31.7678 + 55.0234i −1.74876 + 3.02894i
\(331\) −2.73083 + 3.42435i −0.150100 + 0.188219i −0.851197 0.524847i \(-0.824123\pi\)
0.701097 + 0.713066i \(0.252694\pi\)
\(332\) −0.652271 + 0.817921i −0.0357980 + 0.0448893i
\(333\) −1.27960 + 17.0750i −0.0701214 + 0.935705i
\(334\) 0.172044 0.117298i 0.00941384 0.00641825i
\(335\) 18.5311 8.92411i 1.01246 0.487576i
\(336\) 29.8940 27.7376i 1.63085 1.51321i
\(337\) −34.0841 + 5.13735i −1.85668 + 0.279849i −0.979669 0.200622i \(-0.935704\pi\)
−0.877010 + 0.480472i \(0.840466\pi\)
\(338\) −30.6409 14.7559i −1.66664 0.802613i
\(339\) 17.8141 5.49493i 0.967531 0.298444i
\(340\) 59.5210 18.3598i 3.22798 0.995699i
\(341\) −11.0439 28.1393i −0.598059 1.52383i
\(342\) −4.50352 19.7312i −0.243523 1.06694i
\(343\) 15.9741 7.69274i 0.862523 0.415369i
\(344\) −4.61206 + 61.5436i −0.248665 + 3.31821i
\(345\) 16.3795 2.46881i 0.881841 0.132916i
\(346\) 12.8592 8.76723i 0.691313 0.471329i
\(347\) 18.4421 + 5.68864i 0.990025 + 0.305382i 0.747136 0.664672i \(-0.231428\pi\)
0.242890 + 0.970054i \(0.421905\pi\)
\(348\) 33.7608 + 58.4754i 1.80977 + 3.13461i
\(349\) −7.69699 + 19.6116i −0.412010 + 1.04979i 0.562769 + 0.826614i \(0.309736\pi\)
−0.974779 + 0.223171i \(0.928359\pi\)
\(350\) 6.83881 0.365550
\(351\) −0.472122 + 0.0711610i −0.0252000 + 0.00379829i
\(352\) 49.3672 + 61.9045i 2.63128 + 3.29952i
\(353\) −14.7508 −0.785104 −0.392552 0.919730i \(-0.628408\pi\)
−0.392552 + 0.919730i \(0.628408\pi\)
\(354\) 8.25458 2.54620i 0.438726 0.135329i
\(355\) 26.6893 12.8529i 1.41652 0.682161i
\(356\) −15.7623 + 40.1618i −0.835402 + 2.12857i
\(357\) −17.7307 + 16.4516i −0.938406 + 0.870713i
\(358\) −13.8779 4.28078i −0.733472 0.226246i
\(359\) 9.23942 + 23.5417i 0.487638 + 1.24248i 0.937062 + 0.349163i \(0.113534\pi\)
−0.449424 + 0.893318i \(0.648371\pi\)
\(360\) −27.4532 + 25.4729i −1.44691 + 1.34254i
\(361\) 9.89740 1.49179i 0.520916 0.0785154i
\(362\) 37.5857 18.1003i 1.97546 0.951332i
\(363\) 47.2368 + 7.11981i 2.47929 + 0.373693i
\(364\) 2.79677 1.90681i 0.146591 0.0999439i
\(365\) −2.55640 3.20562i −0.133808 0.167790i
\(366\) 2.14304 + 3.71185i 0.112018 + 0.194022i
\(367\) 0.528890 + 0.490738i 0.0276078 + 0.0256163i 0.693856 0.720114i \(-0.255910\pi\)
−0.666248 + 0.745730i \(0.732101\pi\)
\(368\) 9.85895 43.1949i 0.513933 2.25169i
\(369\) −10.0806 3.10946i −0.524776 0.161872i
\(370\) −11.8770 30.2622i −0.617457 1.57325i
\(371\) 2.05811 1.90965i 0.106852 0.0991441i
\(372\) −4.80467 64.1139i −0.249111 3.32415i
\(373\) 22.2034 15.1380i 1.14965 0.783816i 0.170179 0.985413i \(-0.445565\pi\)
0.979469 + 0.201597i \(0.0646131\pi\)
\(374\) −62.8446 78.8046i −3.24962 4.07489i
\(375\) −28.6508 −1.47952
\(376\) −60.8470 + 18.7688i −3.13794 + 0.967927i
\(377\) 0.916757 + 2.33586i 0.0472154 + 0.120303i
\(378\) −1.58700 + 4.04360i −0.0816264 + 0.207981i
\(379\) −23.8178 22.0996i −1.22344 1.13518i −0.986518 0.163653i \(-0.947672\pi\)
−0.236918 0.971530i \(-0.576137\pi\)
\(380\) 17.1653 + 21.5246i 0.880561 + 1.10419i
\(381\) −4.32780 2.95065i −0.221720 0.151166i
\(382\) −53.6453 25.8342i −2.74473 1.32179i
\(383\) 20.7442 26.0124i 1.05998 1.32917i 0.118181 0.992992i \(-0.462294\pi\)
0.941798 0.336179i \(-0.109135\pi\)
\(384\) 9.27284 + 23.6268i 0.473203 + 1.20570i
\(385\) 5.62318 + 14.3276i 0.286584 + 0.730204i
\(386\) −12.2809 53.8059i −0.625079 2.73865i
\(387\) 7.06321 + 17.9968i 0.359043 + 0.914827i
\(388\) 5.94765 79.3659i 0.301946 4.02919i
\(389\) −11.4569 + 7.81120i −0.580889 + 0.396044i −0.817812 0.575485i \(-0.804813\pi\)
0.236923 + 0.971528i \(0.423861\pi\)
\(390\) −4.14935 + 2.82898i −0.210111 + 0.143251i
\(391\) −5.84751 + 25.6196i −0.295721 + 1.29564i
\(392\) 2.85294 + 38.0698i 0.144095 + 1.92281i
\(393\) 34.3146 + 16.5250i 1.73094 + 0.833578i
\(394\) 0.690897 9.21938i 0.0348069 0.464465i
\(395\) −24.9552 3.76140i −1.25563 0.189256i
\(396\) 64.7374 + 31.1759i 3.25318 + 1.56665i
\(397\) 26.6356 24.7142i 1.33680 1.24037i 0.389106 0.921193i \(-0.372784\pi\)
0.947695 0.319177i \(-0.103407\pi\)
\(398\) 15.8864 7.65047i 0.796312 0.383483i
\(399\) −9.63198 4.63852i −0.482202 0.232216i
\(400\) −7.10383 + 18.1003i −0.355192 + 0.905014i
\(401\) 27.3196 + 4.11777i 1.36428 + 0.205631i 0.790038 0.613057i \(-0.210061\pi\)
0.574237 + 0.818689i \(0.305299\pi\)
\(402\) −35.3948 61.3056i −1.76533 3.05764i
\(403\) 0.178557 2.38268i 0.00889456 0.118690i
\(404\) −4.53337 60.4936i −0.225543 3.00967i
\(405\) 6.74673 17.1904i 0.335248 0.854197i
\(406\) 22.5748 + 3.40260i 1.12037 + 0.168868i
\(407\) −27.6302 + 25.6371i −1.36958 + 1.27078i
\(408\) −47.3300 120.595i −2.34318 5.97033i
\(409\) 5.17302 6.48676i 0.255789 0.320750i −0.637311 0.770606i \(-0.719953\pi\)
0.893101 + 0.449857i \(0.148525\pi\)
\(410\) 19.8051 2.98514i 0.978105 0.147426i
\(411\) −0.131638 + 0.228003i −0.00649321 + 0.0112466i
\(412\) −61.9085 + 19.0963i −3.05002 + 0.940805i
\(413\) 0.764534 1.94800i 0.0376203 0.0958549i
\(414\) −5.81794 25.4901i −0.285936 1.25277i
\(415\) −0.0836681 0.366574i −0.00410710 0.0179944i
\(416\) 1.39264 + 6.10155i 0.0682798 + 0.299153i
\(417\) 4.30679 + 1.32847i 0.210904 + 0.0650553i
\(418\) 22.2753 38.5820i 1.08952 1.88711i
\(419\) −11.7711 + 20.3881i −0.575055 + 0.996024i 0.420981 + 0.907070i \(0.361686\pi\)
−0.996036 + 0.0889548i \(0.971647\pi\)
\(420\) 2.44638 + 32.6447i 0.119371 + 1.59290i
\(421\) −26.9429 + 8.31080i −1.31312 + 0.405043i −0.870722 0.491776i \(-0.836348\pi\)
−0.442397 + 0.896819i \(0.645872\pi\)
\(422\) 33.4176 + 41.9044i 1.62675 + 2.03987i
\(423\) −14.6223 + 13.5675i −0.710959 + 0.659673i
\(424\) 5.49390 + 13.9982i 0.266807 + 0.679814i
\(425\) 4.21340 10.7356i 0.204380 0.520752i
\(426\) −50.9771 88.2950i −2.46985 4.27791i
\(427\) 1.02671 + 0.154752i 0.0496862 + 0.00748898i
\(428\) 85.4206 + 12.8751i 4.12896 + 0.622341i
\(429\) 4.81084 + 3.27998i 0.232270 + 0.158359i
\(430\) −26.9073 24.9663i −1.29759 1.20398i
\(431\) −7.66729 + 19.5359i −0.369320 + 0.941012i 0.618552 + 0.785744i \(0.287720\pi\)
−0.987872 + 0.155269i \(0.950376\pi\)
\(432\) −9.05370 8.40061i −0.435596 0.404174i
\(433\) 20.6593 25.9059i 0.992822 1.24496i 0.0233571 0.999727i \(-0.492565\pi\)
0.969464 0.245232i \(-0.0788641\pi\)
\(434\) −17.9611 12.2457i −0.862159 0.587810i
\(435\) −23.9969 3.61695i −1.15056 0.173419i
\(436\) −11.0028 + 7.50161i −0.526940 + 0.359262i
\(437\) −11.4852 + 1.73111i −0.549410 + 0.0828103i
\(438\) −10.3445 + 9.59833i −0.494281 + 0.458626i
\(439\) 8.89623 + 6.06535i 0.424594 + 0.289483i 0.756704 0.653757i \(-0.226808\pi\)
−0.332110 + 0.943241i \(0.607761\pi\)
\(440\) −82.4387 −3.93011
\(441\) 5.97958 + 10.3569i 0.284742 + 0.493188i
\(442\) −1.77283 7.76729i −0.0843251 0.369452i
\(443\) −2.77834 7.07909i −0.132003 0.336338i 0.849556 0.527499i \(-0.176870\pi\)
−0.981559 + 0.191161i \(0.938775\pi\)
\(444\) −72.2279 + 34.7831i −3.42778 + 1.65073i
\(445\) −7.75323 13.4290i −0.367538 0.636595i
\(446\) 3.29947 + 14.4559i 0.156235 + 0.684509i
\(447\) −11.1259 + 48.7459i −0.526239 + 2.30560i
\(448\) 21.3014 + 6.57060i 1.00639 + 0.310432i
\(449\) 0.261188 + 1.14434i 0.0123262 + 0.0540048i 0.980717 0.195433i \(-0.0626113\pi\)
−0.968391 + 0.249438i \(0.919754\pi\)
\(450\) 0.857489 + 11.4424i 0.0404224 + 0.539400i
\(451\) −11.6109 20.1107i −0.546736 0.946975i
\(452\) 29.3425 + 27.2258i 1.38015 + 1.28060i
\(453\) 38.1959 18.3942i 1.79460 0.864234i
\(454\) 2.34430 + 10.2711i 0.110024 + 0.482045i
\(455\) −0.0909154 + 1.21318i −0.00426218 + 0.0568749i
\(456\) 41.9747 38.9469i 1.96565 1.82385i
\(457\) −6.24116 + 7.82617i −0.291949 + 0.366093i −0.906076 0.423114i \(-0.860937\pi\)
0.614127 + 0.789207i \(0.289508\pi\)
\(458\) 14.4482 63.3019i 0.675122 2.95790i
\(459\) 5.36990 + 4.98254i 0.250646 + 0.232565i
\(460\) 22.1752 + 27.8069i 1.03393 + 1.29650i
\(461\) −1.51371 20.1990i −0.0705005 0.940763i −0.914543 0.404488i \(-0.867450\pi\)
0.844043 0.536276i \(-0.180169\pi\)
\(462\) 47.7277 22.9845i 2.22050 1.06933i
\(463\) −12.5421 + 15.7272i −0.582879 + 0.730907i −0.982601 0.185730i \(-0.940535\pi\)
0.399722 + 0.916636i \(0.369107\pi\)
\(464\) −32.4552 + 56.2141i −1.50670 + 2.60967i
\(465\) 19.0926 + 13.0171i 0.885397 + 0.603653i
\(466\) −27.3502 + 13.1712i −1.26697 + 0.610143i
\(467\) 18.5946 8.95468i 0.860455 0.414373i 0.0490071 0.998798i \(-0.484394\pi\)
0.811447 + 0.584425i \(0.198680\pi\)
\(468\) 3.54106 + 4.44035i 0.163686 + 0.205255i
\(469\) −16.9574 2.55591i −0.783018 0.118021i
\(470\) 13.8360 35.2535i 0.638206 1.62612i
\(471\) −0.902496 + 12.0430i −0.0415848 + 0.554911i
\(472\) 8.21639 + 7.62369i 0.378190 + 0.350909i
\(473\) −15.5480 + 39.6157i −0.714898 + 1.82153i
\(474\) −6.49102 + 86.6166i −0.298142 + 3.97843i
\(475\) 5.09742 0.233886
\(476\) −49.6266 15.3078i −2.27463 0.701631i
\(477\) 3.45320 + 3.20410i 0.158111 + 0.146706i
\(478\) −34.5564 23.5601i −1.58057 1.07761i
\(479\) −14.4133 6.94107i −0.658560 0.317146i 0.0745884 0.997214i \(-0.476236\pi\)
−0.733148 + 0.680069i \(0.761950\pi\)
\(480\) −57.8374 17.8405i −2.63990 0.814303i
\(481\) −2.84690 + 0.878152i −0.129807 + 0.0400403i
\(482\) 9.92498 43.4842i 0.452071 1.98065i
\(483\) −12.4432 5.99233i −0.566186 0.272661i
\(484\) 37.4730 + 95.4796i 1.70332 + 4.33998i
\(485\) 20.9689 + 19.4563i 0.952147 + 0.883464i
\(486\) −52.5129 16.1981i −2.38203 0.734760i
\(487\) 0.114242 1.52446i 0.00517682 0.0690798i −0.994017 0.109225i \(-0.965163\pi\)
0.999194 + 0.0401453i \(0.0127821\pi\)
\(488\) −2.78064 + 4.81621i −0.125874 + 0.218020i
\(489\) 34.0973 + 10.5176i 1.54193 + 0.475624i
\(490\) −18.7602 12.7905i −0.847501 0.577817i
\(491\) −0.986545 + 13.1645i −0.0445221 + 0.594107i 0.929671 + 0.368391i \(0.120091\pi\)
−0.974193 + 0.225716i \(0.927528\pi\)
\(492\) −10.9904 48.1519i −0.495484 2.17086i
\(493\) 19.2497 33.3415i 0.866964 1.50163i
\(494\) 2.90950 1.98366i 0.130905 0.0892492i
\(495\) −23.2673 + 11.2049i −1.04579 + 0.503624i
\(496\) 51.0677 34.8173i 2.29301 1.56335i
\(497\) −24.4227 3.68114i −1.09551 0.165122i
\(498\) −1.23660 + 0.381441i −0.0554135 + 0.0170928i
\(499\) 11.2849 7.69389i 0.505180 0.344426i −0.283761 0.958895i \(-0.591582\pi\)
0.788941 + 0.614469i \(0.210630\pi\)
\(500\) −30.7587 53.2756i −1.37557 2.38256i
\(501\) 0.184549 0.00824503
\(502\) −8.52299 5.81088i −0.380400 0.259352i
\(503\) −5.06184 + 6.34735i −0.225696 + 0.283014i −0.881767 0.471685i \(-0.843646\pi\)
0.656071 + 0.754699i \(0.272217\pi\)
\(504\) 30.8763 4.65385i 1.37534 0.207299i
\(505\) 18.0145 + 12.2820i 0.801633 + 0.546544i
\(506\) 28.7767 49.8427i 1.27928 2.21578i
\(507\) −15.0708 26.1035i −0.669320 1.15930i
\(508\) 0.840462 11.2152i 0.0372895 0.497594i
\(509\) 20.5969 0.912943 0.456471 0.889738i \(-0.349113\pi\)
0.456471 + 0.889738i \(0.349113\pi\)
\(510\) 73.6271 + 22.7110i 3.26026 + 1.00566i
\(511\) 0.255470 + 3.40901i 0.0113013 + 0.150806i
\(512\) 14.7665 18.5167i 0.652595 0.818329i
\(513\) −1.18289 + 3.01396i −0.0522260 + 0.133070i
\(514\) 20.8914 + 53.2305i 0.921482 + 2.34790i
\(515\) 8.50699 21.6754i 0.374863 0.955134i
\(516\) −56.4353 + 70.7676i −2.48443 + 3.11537i
\(517\) −43.9089 −1.93111
\(518\) −6.03149 + 26.4257i −0.265008 + 1.16108i
\(519\) 13.7938 0.605480
\(520\) −5.87083 2.82724i −0.257453 0.123983i
\(521\) 2.78752 + 4.82813i 0.122124 + 0.211524i 0.920605 0.390495i \(-0.127696\pi\)
−0.798481 + 0.602020i \(0.794363\pi\)
\(522\) −2.86252 + 38.1977i −0.125289 + 1.67187i
\(523\) −11.5650 14.5020i −0.505700 0.634128i 0.461804 0.886982i \(-0.347202\pi\)
−0.967504 + 0.252854i \(0.918631\pi\)
\(524\) 6.11119 + 81.5481i 0.266968 + 3.56245i
\(525\) 5.00798 + 3.41438i 0.218566 + 0.149016i
\(526\) 0.708653 1.22742i 0.0308987 0.0535182i
\(527\) −30.2891 + 20.6508i −1.31941 + 0.899561i
\(528\) 11.2556 + 150.196i 0.489839 + 6.53645i
\(529\) 7.90582 1.19161i 0.343731 0.0518092i
\(530\) −8.54639 2.63621i −0.371231 0.114510i
\(531\) 3.35517 + 1.03493i 0.145602 + 0.0449123i
\(532\) −1.71539 22.8902i −0.0743714 0.992418i
\(533\) −0.137167 1.83037i −0.00594137 0.0792820i
\(534\) −44.0957 + 30.0639i −1.90821 + 1.30099i
\(535\) −22.7597 + 21.1179i −0.983986 + 0.913005i
\(536\) 45.9255 79.5453i 1.98368 3.43583i
\(537\) −8.02541 10.0635i −0.346322 0.434274i
\(538\) 1.29704 + 5.68268i 0.0559192 + 0.244998i
\(539\) −5.85793 + 25.6653i −0.252319 + 1.10548i
\(540\) 9.80376 1.47768i 0.421887 0.0635892i
\(541\) 12.0261 + 11.1586i 0.517043 + 0.479746i 0.894993 0.446080i \(-0.147180\pi\)
−0.377950 + 0.925826i \(0.623371\pi\)
\(542\) −11.7050 + 10.8606i −0.502771 + 0.466504i
\(543\) 36.5604 + 5.51060i 1.56896 + 0.236482i
\(544\) 59.8682 75.0724i 2.56683 3.21870i
\(545\) 0.357672 4.77280i 0.0153210 0.204444i
\(546\) 4.18716 0.179194
\(547\) 16.7347 16.3386i 0.715523 0.698589i
\(548\) −0.565290 −0.0241480
\(549\) −0.130189 + 1.73725i −0.00555634 + 0.0741442i
\(550\) −15.7483 + 19.7478i −0.671512 + 0.842049i
\(551\) 16.8264 + 2.53618i 0.716831 + 0.108045i
\(552\) 54.2257 50.3141i 2.30800 2.14151i
\(553\) 15.4248 + 14.3121i 0.655928 + 0.608613i
\(554\) 27.7943 4.18931i 1.18087 0.177987i
\(555\) 6.41145 28.0904i 0.272151 1.19237i
\(556\) 2.15338 + 9.43458i 0.0913238 + 0.400116i
\(557\) −15.4934 19.4281i −0.656477 0.823196i 0.336477 0.941692i \(-0.390764\pi\)
−0.992955 + 0.118495i \(0.962193\pi\)
\(558\) 18.2368 31.5871i 0.772026 1.33719i
\(559\) −2.46587 + 2.28799i −0.104295 + 0.0967716i
\(560\) −26.0020 + 17.7279i −1.09878 + 0.749139i
\(561\) −6.67591 89.0838i −0.281857 3.76112i
\(562\) 5.50673 + 73.4822i 0.232287 + 3.09966i
\(563\) 12.3398 + 3.80632i 0.520060 + 0.160417i 0.543662 0.839304i \(-0.317037\pi\)
−0.0236023 + 0.999721i \(0.507514\pi\)
\(564\) −89.2404 27.5270i −3.75770 1.15910i
\(565\) −14.2257 + 2.14418i −0.598481 + 0.0902064i
\(566\) 4.58602 + 61.1962i 0.192765 + 2.57227i
\(567\) −12.7217 + 8.67351i −0.534261 + 0.364253i
\(568\) 66.1440 114.565i 2.77534 4.80703i
\(569\) 20.3856 + 13.8987i 0.854611 + 0.582664i 0.909441 0.415832i \(-0.136510\pi\)
−0.0548309 + 0.998496i \(0.517462\pi\)
\(570\) 2.54499 + 33.9605i 0.106598 + 1.42245i
\(571\) −28.2223 35.3897i −1.18107 1.48101i −0.841354 0.540484i \(-0.818241\pi\)
−0.339714 0.940529i \(-0.610330\pi\)
\(572\) −0.934269 + 12.4670i −0.0390638 + 0.521270i
\(573\) −26.3857 45.7013i −1.10228 1.90920i
\(574\) −15.0456 7.24558i −0.627991 0.302425i
\(575\) 6.58517 0.274621
\(576\) −8.32275 + 36.4643i −0.346781 + 1.51935i
\(577\) 43.3976 1.80667 0.903333 0.428941i \(-0.141113\pi\)
0.903333 + 0.428941i \(0.141113\pi\)
\(578\) −48.0605 + 60.2660i −1.99905 + 2.50673i
\(579\) 17.8703 45.5329i 0.742666 1.89228i
\(580\) −19.0367 48.5048i −0.790457 2.01405i
\(581\) −0.114533 + 0.291826i −0.00475164 + 0.0121070i
\(582\) 61.3829 76.9717i 2.54440 3.19058i
\(583\) 0.774917 + 10.3405i 0.0320938 + 0.428262i
\(584\) −17.4967 5.39701i −0.724017 0.223330i
\(585\) −2.04124 −0.0843949
\(586\) 0.115598 1.54255i 0.00477530 0.0637220i
\(587\) 6.65055 + 11.5191i 0.274498 + 0.475444i 0.970008 0.243072i \(-0.0781551\pi\)
−0.695511 + 0.718516i \(0.744822\pi\)
\(588\) −27.9955 + 48.4897i −1.15452 + 1.99968i
\(589\) −13.3876 9.12749i −0.551625 0.376092i
\(590\) −6.59181 + 0.993555i −0.271380 + 0.0409040i
\(591\) 5.10885 6.40630i 0.210150 0.263520i
\(592\) −63.6756 43.4133i −2.61705 1.78427i
\(593\) −3.01001 −0.123606 −0.0618031 0.998088i \(-0.519685\pi\)
−0.0618031 + 0.998088i \(0.519685\pi\)
\(594\) −8.02182 13.8942i −0.329139 0.570086i
\(595\) 15.4222 10.5147i 0.632249 0.431060i
\(596\) −102.587 + 31.6438i −4.20211 + 1.29618i
\(597\) 15.4530 + 2.32917i 0.632450 + 0.0953265i
\(598\) 3.75868 2.56262i 0.153704 0.104793i
\(599\) −9.01303 + 4.34045i −0.368262 + 0.177346i −0.608857 0.793280i \(-0.708372\pi\)
0.240595 + 0.970626i \(0.422657\pi\)
\(600\) −26.8232 + 18.2877i −1.09505 + 0.746594i
\(601\) −3.71042 + 6.42664i −0.151351 + 0.262148i −0.931724 0.363166i \(-0.881696\pi\)
0.780373 + 0.625314i \(0.215029\pi\)
\(602\) 6.81006 + 29.8368i 0.277557 + 1.21606i
\(603\) 2.15023 28.6928i 0.0875640 1.16846i
\(604\) 75.2097 + 51.2771i 3.06024 + 2.08644i
\(605\) −35.2269 10.8660i −1.43218 0.441768i
\(606\) 37.5200 64.9866i 1.52415 2.63990i
\(607\) 1.65585 22.0958i 0.0672089 0.896841i −0.857089 0.515169i \(-0.827729\pi\)
0.924298 0.381672i \(-0.124652\pi\)
\(608\) 40.5552 + 12.5096i 1.64473 + 0.507332i
\(609\) 14.8324 + 13.7625i 0.601040 + 0.557684i
\(610\) −1.20840 3.07895i −0.0489266 0.124663i
\(611\) −3.12695 1.50586i −0.126503 0.0609205i
\(612\) 19.3898 84.9524i 0.783787 3.43400i
\(613\) −0.0463443 + 0.0142953i −0.00187183 + 0.000577383i −0.295691 0.955284i \(-0.595550\pi\)
0.293819 + 0.955861i \(0.405074\pi\)
\(614\) −14.7750 4.55749i −0.596271 0.183925i
\(615\) 15.9934 + 7.70203i 0.644917 + 0.310576i
\(616\) 56.7913 + 38.7196i 2.28819 + 1.56006i
\(617\) 16.2241 + 15.0538i 0.653159 + 0.606043i 0.935524 0.353264i \(-0.114928\pi\)
−0.282365 + 0.959307i \(0.591119\pi\)
\(618\) −76.5806 23.6220i −3.08052 0.950215i
\(619\) 27.0395 1.08681 0.543405 0.839470i \(-0.317135\pi\)
0.543405 + 0.839470i \(0.317135\pi\)
\(620\) −3.70779 + 49.4770i −0.148908 + 1.98704i
\(621\) −1.52814 + 3.89363i −0.0613221 + 0.156246i
\(622\) 20.0858 + 18.6369i 0.805369 + 0.747273i
\(623\) −0.966169 + 12.8926i −0.0387087 + 0.516532i
\(624\) −4.34942 + 11.0821i −0.174116 + 0.443641i
\(625\) 13.4579 + 2.02846i 0.538317 + 0.0811382i
\(626\) −19.1654 24.0327i −0.766005 0.960540i
\(627\) 35.5746 17.1318i 1.42071 0.684180i
\(628\) −23.3626 + 11.2508i −0.932268 + 0.448956i
\(629\) 37.7671 + 25.7491i 1.50587 + 1.02669i
\(630\) −9.28560 + 16.0831i −0.369947 + 0.640767i
\(631\) −6.52520 + 8.18234i −0.259764 + 0.325734i −0.894562 0.446945i \(-0.852512\pi\)
0.634797 + 0.772679i \(0.281084\pi\)
\(632\) −101.541 + 48.8996i −4.03909 + 1.94512i
\(633\) 3.54992 + 47.3704i 0.141097 + 1.88280i
\(634\) −8.88429 11.1405i −0.352840 0.442448i
\(635\) 2.96311 + 2.74936i 0.117587 + 0.109105i
\(636\) −4.90767 + 21.5019i −0.194602 + 0.852607i
\(637\) −1.29736 + 1.62684i −0.0514034 + 0.0644578i
\(638\) −61.8103 + 57.3515i −2.44709 + 2.27057i
\(639\) 3.09685 41.3246i 0.122510 1.63478i
\(640\) −4.35849 19.0958i −0.172285 0.754828i
\(641\) 9.24777 4.45349i 0.365265 0.175902i −0.242244 0.970215i \(-0.577883\pi\)
0.607509 + 0.794313i \(0.292169\pi\)
\(642\) 78.3327 + 72.6821i 3.09155 + 2.86854i
\(643\) 1.05011 + 1.81884i 0.0414123 + 0.0717282i 0.885989 0.463707i \(-0.153481\pi\)
−0.844576 + 0.535435i \(0.820148\pi\)
\(644\) −2.21605 29.5711i −0.0873245 1.16526i
\(645\) −7.23907 31.7164i −0.285038 1.24883i
\(646\) −51.6268 15.9248i −2.03123 0.626552i
\(647\) −10.5538 + 46.2393i −0.414914 + 1.81786i 0.145155 + 0.989409i \(0.453632\pi\)
−0.560068 + 0.828446i \(0.689225\pi\)
\(648\) −18.3509 80.4007i −0.720893 3.15844i
\(649\) 3.86450 + 6.69351i 0.151695 + 0.262743i
\(650\) −1.79876 + 0.866238i −0.0705533 + 0.0339767i
\(651\) −7.03885 17.9347i −0.275874 0.702916i
\(652\) 17.0486 + 74.6947i 0.667674 + 2.92527i
\(653\) 5.65040 + 9.78679i 0.221117 + 0.382986i 0.955148 0.296130i \(-0.0956963\pi\)
−0.734030 + 0.679117i \(0.762363\pi\)
\(654\) −16.4728 −0.644137
\(655\) −24.2843 16.5568i −0.948867 0.646926i
\(656\) 34.8055 32.2948i 1.35893 1.26090i
\(657\) −5.67176 + 0.854881i −0.221277 + 0.0333521i
\(658\) −26.0893 + 17.7874i −1.01707 + 0.693424i
\(659\) −15.0450 2.26767i −0.586069 0.0883358i −0.150687 0.988581i \(-0.548149\pi\)
−0.435382 + 0.900246i \(0.643387\pi\)
\(660\) −99.8986 68.1097i −3.88855 2.65117i
\(661\) −21.6083 + 27.0959i −0.840465 + 1.05391i 0.157331 + 0.987546i \(0.449711\pi\)
−0.997796 + 0.0663636i \(0.978860\pi\)
\(662\) −8.52764 7.91249i −0.331436 0.307528i
\(663\) 2.57972 6.57301i 0.100188 0.255274i
\(664\) −1.23088 1.14209i −0.0477674 0.0443217i
\(665\) 6.81652 + 4.64742i 0.264333 + 0.180219i
\(666\) −44.9705 6.77822i −1.74257 0.262651i
\(667\) 21.7375 + 3.27640i 0.841679 + 0.126863i
\(668\) 0.198126 + 0.343165i 0.00766573 + 0.0132774i
\(669\) −4.80119 + 12.2332i −0.185625 + 0.472964i
\(670\) 19.9581 + 50.8524i 0.771048 + 1.96460i
\(671\) −2.81117 + 2.60838i −0.108524 + 0.100696i
\(672\) 31.4644 + 39.4551i 1.21376 + 1.52201i
\(673\) −26.0171 + 8.02523i −1.00289 + 0.309350i −0.752355 0.658758i \(-0.771082\pi\)
−0.250533 + 0.968108i \(0.580606\pi\)
\(674\) −6.84154 91.2941i −0.263526 3.51652i
\(675\) 0.917844 1.58975i 0.0353278 0.0611896i
\(676\) 32.3592 56.0479i 1.24459 2.15569i
\(677\) −17.5686 5.41918i −0.675215 0.208276i −0.0618614 0.998085i \(-0.519704\pi\)
−0.613353 + 0.789809i \(0.710180\pi\)
\(678\) 11.0179 + 48.2728i 0.423142 + 1.85391i
\(679\) −5.30708 23.2518i −0.203667 0.892324i
\(680\) 22.2464 + 97.4679i 0.853111 + 3.73772i
\(681\) −3.41128 + 8.69181i −0.130721 + 0.333071i
\(682\) 76.7212 23.6654i 2.93781 0.906194i
\(683\) −1.01724 + 1.76191i −0.0389235 + 0.0674175i −0.884831 0.465912i \(-0.845726\pi\)
0.845907 + 0.533330i \(0.179060\pi\)
\(684\) 38.0838 5.74022i 1.45617 0.219483i
\(685\) 0.126675 0.158845i 0.00484000 0.00606917i
\(686\) 17.2042 + 43.8357i 0.656860 + 1.67365i
\(687\) 42.1847 39.1417i 1.60945 1.49335i
\(688\) −86.0430 12.9689i −3.28036 0.494435i
\(689\) −0.299445 + 0.762972i −0.0114079 + 0.0290669i
\(690\) 3.28778 + 43.8723i 0.125164 + 1.67019i
\(691\) −0.0493475 + 0.658496i −0.00187727 + 0.0250504i −0.998064 0.0621990i \(-0.980189\pi\)
0.996187 + 0.0872494i \(0.0278077\pi\)
\(692\) 14.8086 + 25.6493i 0.562939 + 0.975039i
\(693\) 21.2913 + 3.20915i 0.808790 + 0.121906i
\(694\) −18.7273 + 47.7163i −0.710878 + 1.81129i
\(695\) −3.13365 1.50909i −0.118866 0.0572429i
\(696\) −97.6416 + 47.0217i −3.70110 + 1.78235i
\(697\) −20.6437 + 19.1546i −0.781937 + 0.725532i
\(698\) −50.4152 24.2787i −1.90824 0.918961i
\(699\) −26.6042 4.00993i −1.00626 0.151670i
\(700\) −0.972554 + 12.9778i −0.0367591 + 0.490516i
\(701\) −37.2117 17.9202i −1.40547 0.676837i −0.431205 0.902254i \(-0.641911\pi\)
−0.974262 + 0.225417i \(0.927626\pi\)
\(702\) −0.0947669 1.26458i −0.00357675 0.0477284i
\(703\) −4.49567 + 19.6968i −0.169557 + 0.742879i
\(704\) −68.0259 + 46.3793i −2.56382 + 1.74798i
\(705\) 27.7328 18.9079i 1.04448 0.712113i
\(706\) 2.92778 39.0685i 0.110189 1.47036i
\(707\) −6.64139 16.9220i −0.249775 0.636416i
\(708\) 3.65796 + 16.0266i 0.137475 + 0.602316i
\(709\) 7.31238 + 18.6316i 0.274622 + 0.699726i 0.999936 + 0.0113074i \(0.00359934\pi\)
−0.725314 + 0.688418i \(0.758305\pi\)
\(710\) 28.7445 + 73.2398i 1.07876 + 2.74864i
\(711\) −22.0123 + 27.6026i −0.825527 + 1.03518i
\(712\) −62.3900 30.0454i −2.33816 1.12600i
\(713\) −17.2949 11.7915i −0.647700 0.441595i
\(714\) −40.0542 50.2264i −1.49899 1.87968i
\(715\) −3.29383 3.05623i −0.123182 0.114297i
\(716\) 10.0971 25.7270i 0.377347 0.961464i
\(717\) −13.5424 34.5056i −0.505752 1.28864i
\(718\) −64.1858 + 19.7987i −2.39539 + 0.738880i
\(719\) −31.3015 −1.16735 −0.583674 0.811988i \(-0.698385\pi\)
−0.583674 + 0.811988i \(0.698385\pi\)
\(720\) −32.9217 41.2825i −1.22692 1.53851i
\(721\) −16.0409 + 10.9365i −0.597393 + 0.407295i
\(722\) 1.98666 + 26.5101i 0.0739358 + 0.986605i
\(723\) 28.9781 26.8878i 1.07771 0.999967i
\(724\) 29.0034 + 73.8994i 1.07790 + 2.74645i
\(725\) −9.21904 2.84370i −0.342387 0.105612i
\(726\) −28.2331 + 123.697i −1.04783 + 4.59084i
\(727\) −34.1385 31.6759i −1.26613 1.17479i −0.975992 0.217808i \(-0.930109\pi\)
−0.290135 0.956986i \(-0.593700\pi\)
\(728\) 2.71647 + 4.70506i 0.100679 + 0.174381i
\(729\) −11.3527 14.2359i −0.420472 0.527255i
\(730\) 8.99774 6.13456i 0.333021 0.227050i
\(731\) 51.0336 + 7.69207i 1.88754 + 0.284502i
\(732\) −7.34865 + 3.53892i −0.271614 + 0.130802i
\(733\) 6.58194 0.992068i 0.243110 0.0366429i −0.0263571 0.999653i \(-0.508391\pi\)
0.269467 + 0.963010i \(0.413153\pi\)
\(734\) −1.40473 + 1.30340i −0.0518497 + 0.0481095i
\(735\) −7.35204 18.7327i −0.271184 0.690966i
\(736\) 52.3918 + 16.1607i 1.93119 + 0.595692i
\(737\) 46.4297 43.0805i 1.71026 1.58689i
\(738\) 10.2365 26.0821i 0.376810 0.960096i
\(739\) 37.9772 18.2889i 1.39702 0.672767i 0.424462 0.905446i \(-0.360463\pi\)
0.972554 + 0.232678i \(0.0747490\pi\)
\(740\) 59.1167 18.2351i 2.17317 0.670335i
\(741\) 3.12097 0.114652
\(742\) 4.64936 + 5.83011i 0.170683 + 0.214030i
\(743\) 52.3758 7.89438i 1.92148 0.289617i 0.925468 0.378826i \(-0.123672\pi\)
0.996013 + 0.0892089i \(0.0284339\pi\)
\(744\) 103.193 3.78325
\(745\) 14.0966 35.9176i 0.516461 1.31592i
\(746\) 35.6872 + 61.8120i 1.30660 + 2.26310i
\(747\) −0.502631 0.155041i −0.0183903 0.00567266i
\(748\) 158.482 108.052i 5.79469 3.95076i
\(749\) 25.5975 3.85820i 0.935312 0.140976i
\(750\) 5.68671 75.8839i 0.207649 2.77089i
\(751\) −43.4421 + 20.9206i −1.58523 + 0.763405i −0.998910 0.0466777i \(-0.985137\pi\)
−0.586316 + 0.810082i \(0.699422\pi\)
\(752\) −19.9775 87.5271i −0.728504 3.19178i
\(753\) −3.34012 8.51048i −0.121721 0.310139i
\(754\) −6.36866 + 1.96447i −0.231933 + 0.0715418i
\(755\) −31.2624 + 9.64317i −1.13776 + 0.350951i
\(756\) −7.44775 3.58665i −0.270872 0.130445i
\(757\) −36.2909 + 5.46997i −1.31902 + 0.198810i −0.770559 0.637369i \(-0.780023\pi\)
−0.548457 + 0.836179i \(0.684785\pi\)
\(758\) 63.2600 58.6967i 2.29771 2.13196i
\(759\) 45.9576 22.1320i 1.66816 0.803341i
\(760\) −36.5099 + 24.8920i −1.32435 + 0.902928i
\(761\) −2.19342 + 29.2691i −0.0795113 + 1.06100i 0.804627 + 0.593780i \(0.202365\pi\)
−0.884139 + 0.467225i \(0.845254\pi\)
\(762\) 8.67401 10.8769i 0.314226 0.394027i
\(763\) −2.48808 + 3.11995i −0.0900744 + 0.112950i
\(764\) 56.6538 98.1273i 2.04966 3.55012i
\(765\) 19.5264 + 24.4854i 0.705980 + 0.885270i
\(766\) 64.7785 + 60.1056i 2.34054 + 2.17170i
\(767\) 0.0456538 + 0.609208i 0.00164846 + 0.0219972i
\(768\) 1.79480 0.553622i 0.0647642 0.0199771i
\(769\) −13.4940 23.3724i −0.486608 0.842829i 0.513274 0.858225i \(-0.328433\pi\)
−0.999881 + 0.0153957i \(0.995099\pi\)
\(770\) −39.0640 + 12.0496i −1.40777 + 0.434239i
\(771\) −11.2776 + 49.4104i −0.406153 + 1.77947i
\(772\) 103.853 15.6532i 3.73773 0.563373i
\(773\) −14.0720 + 17.6458i −0.506135 + 0.634674i −0.967601 0.252484i \(-0.918752\pi\)
0.461466 + 0.887158i \(0.347324\pi\)
\(774\) −49.0677 + 15.1354i −1.76370 + 0.544031i
\(775\) 6.73415 + 6.24837i 0.241898 + 0.224448i
\(776\) 126.315 + 19.0389i 4.53444 + 0.683457i
\(777\) −17.6102 + 16.3399i −0.631763 + 0.586191i
\(778\) −18.4146 31.8949i −0.660194 1.14349i
\(779\) −11.2145 5.40061i −0.401800 0.193497i
\(780\) −4.77840 8.27643i −0.171094 0.296344i
\(781\) 66.8701 62.0464i 2.39280 2.22019i
\(782\) −66.6949 20.5726i −2.38500 0.735676i
\(783\) 3.82075 4.79107i 0.136542 0.171219i
\(784\) −53.8259 −1.92235
\(785\) 2.07382 9.08602i 0.0740180 0.324294i
\(786\) −50.5787 + 87.6049i −1.80408 + 3.12476i
\(787\) 2.52999 11.0846i 0.0901845 0.395124i −0.909609 0.415466i \(-0.863618\pi\)
0.999793 + 0.0203421i \(0.00647553\pi\)
\(788\) 17.3971 + 2.62219i 0.619746 + 0.0934117i
\(789\) 1.13175 0.545021i 0.0402913 0.0194033i
\(790\) 14.9156 65.3493i 0.530671 2.32502i
\(791\) 10.8070 + 5.20440i 0.384254 + 0.185047i
\(792\) −57.6631 + 99.8755i −2.04897 + 3.54892i
\(793\) −0.289651 + 0.0893454i −0.0102858 + 0.00317275i
\(794\) 60.1708 + 75.4518i 2.13538 + 2.67768i
\(795\) −4.94225 6.19738i −0.175284 0.219799i
\(796\) 12.2589 + 31.2351i 0.434504 + 1.10710i
\(797\) 31.8961 21.7464i 1.12982 0.770298i 0.153826 0.988098i \(-0.450840\pi\)
0.975993 + 0.217800i \(0.0698880\pi\)
\(798\) 14.1973 24.5904i 0.502577 0.870490i
\(799\) 11.8490 + 51.9138i 0.419187 + 1.83658i
\(800\) −21.6792 10.4402i −0.766477 0.369116i
\(801\) −21.6925 −0.766467
\(802\) −16.3287 + 71.5408i −0.576587 + 2.52619i
\(803\) −10.4322 7.11253i −0.368143 0.250996i
\(804\) 121.371 58.4494i 4.28044 2.06135i
\(805\) 8.80602 + 6.00384i 0.310371 + 0.211608i
\(806\) 6.27527 + 0.945844i 0.221037 + 0.0333159i
\(807\) −1.88736 + 4.80893i −0.0664384 + 0.169282i
\(808\) 97.3661 3.42533
\(809\) 27.6351 4.16532i 0.971598 0.146445i 0.355983 0.934492i \(-0.384146\pi\)
0.615614 + 0.788048i \(0.288908\pi\)
\(810\) 44.1910 + 21.2812i 1.55271 + 0.747747i
\(811\) 17.9159 2.70039i 0.629113 0.0948235i 0.173256 0.984877i \(-0.444571\pi\)
0.455857 + 0.890053i \(0.349333\pi\)
\(812\) −9.66739 + 42.3556i −0.339259 + 1.48639i
\(813\) −13.9937 + 2.10922i −0.490782 + 0.0739735i
\(814\) −62.4177 78.2694i −2.18774 2.74334i
\(815\) −24.8095 11.9476i −0.869038 0.418507i
\(816\) 174.540 53.8386i 6.11014 1.88473i
\(817\) 5.07598 + 22.2393i 0.177586 + 0.778056i
\(818\) 16.1539 + 14.9887i 0.564809 + 0.524066i
\(819\) 1.40619 + 0.958725i 0.0491363 + 0.0335006i
\(820\) 2.84832 + 38.0081i 0.0994675 + 1.32730i
\(821\) 1.60751 + 21.4508i 0.0561026 + 0.748638i 0.952335 + 0.305053i \(0.0986743\pi\)
−0.896233 + 0.443584i \(0.853707\pi\)
\(822\) −0.577756 0.393908i −0.0201516 0.0137391i
\(823\) −10.6783 9.90797i −0.372220 0.345370i 0.471776 0.881718i \(-0.343613\pi\)
−0.843997 + 0.536348i \(0.819803\pi\)
\(824\) −23.1388 101.378i −0.806078 3.53166i
\(825\) −21.3917 + 6.59847i −0.744764 + 0.229729i
\(826\) 5.00769 + 2.41157i 0.174240 + 0.0839094i
\(827\) −22.2131 27.8543i −0.772424 0.968589i 0.227563 0.973763i \(-0.426924\pi\)
−0.999987 + 0.00517443i \(0.998353\pi\)
\(828\) 49.1992 7.41558i 1.70979 0.257709i
\(829\) 2.01776 8.84038i 0.0700797 0.307039i −0.927725 0.373264i \(-0.878238\pi\)
0.997805 + 0.0662253i \(0.0210956\pi\)
\(830\) 0.987506 0.148843i 0.0342768 0.00516640i
\(831\) 22.4450 + 10.8089i 0.778608 + 0.374958i
\(832\) −6.43501 + 0.969921i −0.223094 + 0.0336260i
\(833\) 31.9250 1.10614
\(834\) −4.37337 + 11.1432i −0.151438 + 0.385857i
\(835\) −0.140826 0.0212262i −0.00487350 0.000734562i
\(836\) 70.0482 + 47.7581i 2.42267 + 1.65175i
\(837\) −5.25720 + 2.53174i −0.181716 + 0.0875096i
\(838\) −51.6631 35.2233i −1.78467 1.21677i
\(839\) 8.84881 38.7692i 0.305495 1.33846i −0.556207 0.831044i \(-0.687744\pi\)
0.861701 0.507416i \(-0.169399\pi\)
\(840\) −52.5426 −1.81289
\(841\) −2.88887 1.39120i −0.0996161 0.0479726i
\(842\) −16.6641 73.0100i −0.574281 2.51609i
\(843\) −32.6546 + 56.5595i −1.12469 + 1.94801i
\(844\) −84.2732 + 57.4565i −2.90080 + 1.97773i
\(845\) 8.49801 + 21.6526i 0.292340 + 0.744871i
\(846\) −33.0322 41.4211i −1.13567 1.42409i
\(847\) 19.1639 + 24.0308i 0.658480 + 0.825708i
\(848\) −20.2601 + 6.24940i −0.695733 + 0.214605i
\(849\) −27.1949 + 47.1029i −0.933325 + 1.61657i
\(850\) 27.5977 + 13.2904i 0.946594 + 0.455855i
\(851\) −5.80779 + 25.4456i −0.199089 + 0.872264i
\(852\) 174.804 84.1814i 5.98870 2.88401i
\(853\) 39.8023 + 5.99924i 1.36281 + 0.205410i 0.789409 0.613868i \(-0.210387\pi\)
0.573397 + 0.819278i \(0.305625\pi\)
\(854\) −0.613659 + 2.68861i −0.0209990 + 0.0920025i
\(855\) −6.92116 + 11.9878i −0.236699 + 0.409974i
\(856\) −30.8528 + 135.175i −1.05453 + 4.62018i
\(857\) −18.8239 −0.643013 −0.321506 0.946907i \(-0.604189\pi\)
−0.321506 + 0.946907i \(0.604189\pi\)
\(858\) −9.64215 + 12.0909i −0.329178 + 0.412776i
\(859\) 7.17145 + 2.21210i 0.244687 + 0.0754759i 0.414673 0.909971i \(-0.363896\pi\)
−0.169986 + 0.985446i \(0.554372\pi\)
\(860\) 51.2044 47.5108i 1.74606 1.62010i
\(861\) −7.40025 12.8176i −0.252200 0.436823i
\(862\) −50.2206 24.1850i −1.71052 0.823743i
\(863\) 16.9120 + 29.2924i 0.575691 + 0.997126i 0.995966 + 0.0897296i \(0.0286003\pi\)
−0.420275 + 0.907397i \(0.638066\pi\)
\(864\) 11.2038 10.3956i 0.381162 0.353666i
\(865\) −10.5258 1.58652i −0.357889 0.0539431i
\(866\) 64.5133 + 59.8596i 2.19225 + 2.03411i
\(867\) −65.2829 + 20.1371i −2.21712 + 0.683892i
\(868\) 25.7925 32.3428i 0.875455 1.09779i
\(869\) −76.8478 + 11.5829i −2.60688 + 0.392924i
\(870\) 14.3428 62.8397i 0.486265 2.13047i
\(871\) 4.78391 1.47564i 0.162097 0.0500002i
\(872\) −10.6869 18.5103i −0.361904 0.626836i
\(873\) 38.2385 11.7950i 1.29418 0.399201i
\(874\) −2.30537 30.7630i −0.0779802 1.04057i
\(875\) −13.5135 12.5387i −0.456839 0.423885i
\(876\) −16.7434 20.9955i −0.565707 0.709374i
\(877\) 23.9398 41.4649i 0.808388 1.40017i −0.105591 0.994410i \(-0.533674\pi\)
0.913980 0.405760i \(-0.132993\pi\)
\(878\) −17.8303 + 22.3585i −0.601744 + 0.754563i
\(879\) 0.854791 1.07187i 0.0288314 0.0361534i
\(880\) 8.68603 115.907i 0.292806 3.90723i
\(881\) −2.88149 + 1.96457i −0.0970800 + 0.0661880i −0.610887 0.791718i \(-0.709187\pi\)
0.513807 + 0.857906i \(0.328235\pi\)
\(882\) −28.6180 + 13.7817i −0.963619 + 0.464054i
\(883\) −1.05391 + 0.977886i −0.0354669 + 0.0329085i −0.697707 0.716383i \(-0.745796\pi\)
0.662240 + 0.749292i \(0.269606\pi\)
\(884\) 14.9919 2.25966i 0.504232 0.0760007i
\(885\) −5.32315 2.56349i −0.178936 0.0861709i
\(886\) 19.3010 5.95356i 0.648429 0.200014i
\(887\) −14.0311 + 4.32803i −0.471119 + 0.145321i −0.521219 0.853423i \(-0.674522\pi\)
0.0500994 + 0.998744i \(0.484046\pi\)
\(888\) −47.0085 119.776i −1.57750 4.01941i
\(889\) −0.749944 3.28572i −0.0251523 0.110199i
\(890\) 37.1066 17.8696i 1.24382 0.598990i
\(891\) 4.24972 56.7085i 0.142371 1.89981i
\(892\) −27.9019 + 4.20553i −0.934224 + 0.140812i
\(893\) −19.4460 + 13.2581i −0.650737 + 0.443665i
\(894\) −126.899 39.1432i −4.24414 1.30914i
\(895\) 4.96660 + 8.60240i 0.166015 + 0.287547i
\(896\) −5.96635 + 15.2020i −0.199322 + 0.507863i
\(897\) 4.03187 0.134620
\(898\) −3.08272 + 0.464645i −0.102872 + 0.0155054i
\(899\) 19.1204 + 23.9762i 0.637702 + 0.799653i
\(900\) −21.8359 −0.727862
\(901\) 12.0166 3.70663i 0.400330 0.123486i
\(902\) 55.5692 26.7607i 1.85025 0.891035i
\(903\) −9.90957 + 25.2492i −0.329770 + 0.840240i
\(904\) −47.0955 + 43.6982i −1.56637 + 1.45338i
\(905\) −27.2649 8.41012i −0.906317 0.279562i
\(906\) 41.1372 + 104.816i 1.36669 + 3.48227i
\(907\) 25.6311 23.7822i 0.851068 0.789675i −0.128306 0.991735i \(-0.540954\pi\)
0.979373 + 0.202059i \(0.0647633\pi\)
\(908\) −19.8245 + 2.98806i −0.657899 + 0.0991623i
\(909\) 27.4804 13.2338i 0.911466 0.438939i
\(910\) −3.19516 0.481593i −0.105919 0.0159647i
\(911\) −8.24887 + 5.62398i −0.273297 + 0.186331i −0.692211 0.721695i \(-0.743363\pi\)
0.418914 + 0.908026i \(0.362411\pi\)
\(912\) 50.3358 + 63.1192i 1.66679 + 2.09008i
\(913\) −0.578933 1.00274i −0.0191599 0.0331859i
\(914\) −19.4894 18.0836i −0.644654 0.598151i
\(915\) 0.652317 2.85799i 0.0215649 0.0944822i
\(916\) 118.071 + 36.4202i 3.90119 + 1.20336i
\(917\) 8.95289 + 22.8116i 0.295651 + 0.753305i
\(918\) −14.2625 + 13.2337i −0.470732 + 0.436776i
\(919\) 1.45623 + 19.4320i 0.0480365 + 0.641003i 0.968314 + 0.249736i \(0.0803439\pi\)
−0.920277 + 0.391267i \(0.872037\pi\)
\(920\) −47.1658 + 32.1571i −1.55501 + 1.06019i
\(921\) −8.54417 10.7141i −0.281540 0.353040i
\(922\) 53.7992 1.77178
\(923\) 6.89001 2.12529i 0.226787 0.0699546i
\(924\) 36.8296 + 93.8403i 1.21160 + 3.08712i
\(925\) 4.18479 10.6627i 0.137595 0.350586i
\(926\) −39.1654 36.3402i −1.28706 1.19421i
\(927\) −20.3097 25.4676i −0.667058 0.836464i
\(928\) −66.3682 45.2491i −2.17864 1.48537i
\(929\) −30.4802 14.6785i −1.00002 0.481586i −0.139077 0.990282i \(-0.544413\pi\)
−0.860946 + 0.508696i \(0.830128\pi\)
\(930\) −38.2663 + 47.9845i −1.25480 + 1.57347i
\(931\) 5.15520 + 13.1352i 0.168955 + 0.430490i
\(932\) −21.1051 53.7748i −0.691320 1.76145i
\(933\) 5.40384 + 23.6758i 0.176914 + 0.775110i
\(934\) 20.0264 + 51.0265i 0.655285 + 1.66964i
\(935\) −5.15183 + 68.7464i −0.168483 + 2.24825i
\(936\) −7.53169 + 5.13502i −0.246181 + 0.167843i
\(937\) 4.93207 3.36263i 0.161124 0.109852i −0.480074 0.877228i \(-0.659390\pi\)
0.641198 + 0.767376i \(0.278438\pi\)
\(938\) 10.1353 44.4056i 0.330929 1.44989i
\(939\) −2.03592 27.1675i −0.0664399 0.886579i
\(940\) 64.9320 + 31.2696i 2.11785 + 1.01990i
\(941\) −0.989393 + 13.2025i −0.0322533 + 0.430390i 0.957581 + 0.288164i \(0.0930449\pi\)
−0.989834 + 0.142226i \(0.954574\pi\)
\(942\) −31.7176 4.78066i −1.03342 0.155762i
\(943\) −14.4876 6.97685i −0.471781 0.227198i
\(944\) −11.5845 + 10.7488i −0.377042 + 0.349844i
\(945\) 2.67680 1.28908i 0.0870762 0.0419337i
\(946\) −101.839 49.0431i −3.31108 1.59453i
\(947\) −9.50886 + 24.2282i −0.308997 + 0.787310i 0.689043 + 0.724721i \(0.258031\pi\)
−0.998039 + 0.0625896i \(0.980064\pi\)
\(948\) −163.447 24.6356i −5.30851 0.800129i
\(949\) −0.498996 0.864286i −0.0161981 0.0280559i
\(950\) −1.01175 + 13.5009i −0.0328256 + 0.438027i
\(951\) −0.943768 12.5937i −0.0306038 0.408379i
\(952\) 30.4531 77.5933i 0.986992 2.51481i
\(953\) 13.9982 + 2.10989i 0.453446 + 0.0683460i 0.371795 0.928315i \(-0.378742\pi\)
0.0816515 + 0.996661i \(0.473981\pi\)
\(954\) −9.17171 + 8.51011i −0.296945 + 0.275525i
\(955\) 14.8781 + 37.9088i 0.481445 + 1.22670i
\(956\) 49.6237 62.2261i 1.60494 2.01254i
\(957\) −73.8966 + 11.1381i −2.38874 + 0.360044i
\(958\) 21.2448 36.7970i 0.686388 1.18886i
\(959\) −0.161871 + 0.0499307i −0.00522710 + 0.00161235i
\(960\) 22.9934 58.5862i 0.742108 1.89086i
\(961\) 0.400370 + 1.75414i 0.0129152 + 0.0565851i
\(962\) −1.76079 7.71453i −0.0567702 0.248727i
\(963\) 9.66493 + 42.3448i 0.311448 + 1.36454i
\(964\) 81.1073 + 25.0183i 2.61229 + 0.805785i
\(965\) −18.8736 + 32.6901i −0.607564 + 1.05233i
\(966\) 18.3409 31.7674i 0.590110 1.02210i
\(967\) 3.02733 + 40.3969i 0.0973524 + 1.29908i 0.805323 + 0.592836i \(0.201992\pi\)
−0.707971 + 0.706242i \(0.750389\pi\)
\(968\) −157.314 + 48.5248i −5.05625 + 1.55965i
\(969\) −29.8550 37.4370i −0.959082 1.20265i
\(970\) −55.6934 + 51.6759i −1.78821 + 1.65921i
\(971\) −13.3854 34.1054i −0.429558 1.09450i −0.967803 0.251708i \(-0.919008\pi\)
0.538245 0.842788i \(-0.319087\pi\)
\(972\) 38.2066 97.3487i 1.22548 3.12246i
\(973\) 1.44996 + 2.51140i 0.0464835 + 0.0805118i
\(974\) 4.01497 + 0.605160i 0.128648 + 0.0193906i
\(975\) −1.74970 0.263724i −0.0560351 0.00844593i
\(976\) −6.47851 4.41697i −0.207372 0.141384i
\(977\) 36.8698 + 34.2102i 1.17957 + 1.09448i 0.993719 + 0.111902i \(0.0356944\pi\)
0.185850 + 0.982578i \(0.440496\pi\)
\(978\) −34.6245 + 88.2219i −1.10717 + 2.82102i
\(979\) −35.0039 32.4789i −1.11873 1.03803i
\(980\) 26.9401 33.7818i 0.860571 1.07912i
\(981\) −5.53213 3.77174i −0.176627 0.120422i
\(982\) −34.6715 5.22588i −1.10641 0.166765i
\(983\) 23.5588 16.0621i 0.751410 0.512303i −0.126008 0.992029i \(-0.540216\pi\)
0.877418 + 0.479726i \(0.159264\pi\)
\(984\) 78.3874 11.8150i 2.49890 0.376648i
\(985\) −4.63532 + 4.30095i −0.147694 + 0.137040i
\(986\) 84.4868 + 57.6022i 2.69061 + 1.83443i
\(987\) −27.9855 −0.890788
\(988\) 3.35058 + 5.80337i 0.106596 + 0.184630i
\(989\) 6.55749 + 28.7302i 0.208516 + 0.913568i
\(990\) −25.0590 63.8492i −0.796426 2.02926i
\(991\) −37.9383 + 18.2701i −1.20515 + 0.580369i −0.925139 0.379628i \(-0.876052\pi\)
−0.280009 + 0.959997i \(0.590338\pi\)
\(992\) 38.2429 + 66.2386i 1.21421 + 2.10308i
\(993\) −2.29425 10.0518i −0.0728060 0.318984i
\(994\) 14.5973 63.9549i 0.462998 2.02853i
\(995\) −11.5241 3.55471i −0.365338 0.112692i
\(996\) −0.547992 2.40091i −0.0173638 0.0760758i
\(997\) −1.81415 24.2082i −0.0574548 0.766681i −0.949306 0.314352i \(-0.898213\pi\)
0.891852 0.452328i \(-0.149406\pi\)
\(998\) 18.1380 + 31.4160i 0.574149 + 0.994455i
\(999\) 5.33343 + 4.94870i 0.168742 + 0.156570i
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 547.2.h.a.13.2 540
547.505 even 21 inner 547.2.h.a.505.2 yes 540
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.h.a.13.2 540 1.1 even 1 trivial
547.2.h.a.505.2 yes 540 547.505 even 21 inner