Properties

Label 270.2.r.a.23.13
Level $270$
Weight $2$
Character 270.23
Analytic conductor $2.156$
Analytic rank $0$
Dimension $216$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [270,2,Mod(23,270)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(270, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([22, 27]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("270.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 270.r (of order \(36\), 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: \(2.15596085457\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 23.13
Character \(\chi\) \(=\) 270.23
Dual form 270.2.r.a.47.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.422618 + 0.906308i) q^{2} +(-0.572880 - 1.63457i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(-2.22872 + 0.181179i) q^{5} +(1.23931 - 1.21000i) q^{6} +(0.347359 - 3.97033i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.34362 + 1.87282i) q^{9} +(-1.10610 - 1.94333i) q^{10} +(-1.35885 + 0.239602i) q^{11} +(1.62039 + 0.611828i) q^{12} +(-6.29127 - 2.93367i) q^{13} +(3.74514 - 1.36312i) q^{14} +(1.57294 + 3.53919i) q^{15} +(-0.173648 - 0.984808i) q^{16} +(3.88494 - 1.04097i) q^{17} +(-2.68781 - 1.33255i) q^{18} +(3.21964 - 1.85886i) q^{19} +(1.29380 - 1.82375i) q^{20} +(-6.68877 + 1.70674i) q^{21} +(-0.791429 - 1.13028i) q^{22} +(-0.493571 + 0.0431819i) q^{23} +(0.130302 + 1.72714i) q^{24} +(4.93435 - 0.807592i) q^{25} -6.94165i q^{26} +(4.40386 + 2.75790i) q^{27} +(2.81817 + 2.81817i) q^{28} +(-5.74999 - 2.09283i) q^{29} +(-2.54285 + 2.92129i) q^{30} +(-1.18093 - 0.990920i) q^{31} +(0.819152 - 0.573576i) q^{32} +(1.17011 + 2.08387i) q^{33} +(2.58528 + 3.08102i) q^{34} +(-0.0548245 + 8.91168i) q^{35} +(0.0717843 - 2.99914i) q^{36} +(-0.520493 - 1.94251i) q^{37} +(3.04538 + 2.13240i) q^{38} +(-1.19113 + 11.9641i) q^{39} +(2.19967 + 0.401829i) q^{40} +(2.87157 + 7.88959i) q^{41} +(-4.37363 - 5.34078i) q^{42} +(-0.771633 + 1.10201i) q^{43} +(0.689907 - 1.19495i) q^{44} +(4.88394 - 4.59860i) q^{45} +(-0.247728 - 0.429078i) q^{46} +(8.00145 + 0.700036i) q^{47} +(-1.51025 + 0.848016i) q^{48} +(-8.74923 - 1.54272i) q^{49} +(2.81727 + 4.13074i) q^{50} +(-3.92714 - 5.75385i) q^{51} +(6.29127 - 2.93367i) q^{52} +(2.13282 - 2.13282i) q^{53} +(-0.638352 + 5.15679i) q^{54} +(2.98508 - 0.780201i) q^{55} +(-1.36312 + 3.74514i) q^{56} +(-4.88290 - 4.19782i) q^{57} +(-0.533307 - 6.09573i) q^{58} +(-0.447387 + 2.53726i) q^{59} +(-3.72224 - 1.07001i) q^{60} +(6.83565 - 5.73579i) q^{61} +(0.398995 - 1.48907i) q^{62} +(6.62164 + 9.95548i) q^{63} +(0.866025 + 0.500000i) q^{64} +(14.5530 + 5.39846i) q^{65} +(-1.39412 + 1.94116i) q^{66} +(-1.77666 + 3.81006i) q^{67} +(-1.69977 + 3.64516i) q^{68} +(0.353341 + 0.782037i) q^{69} +(-8.09989 + 3.71655i) q^{70} +(-10.9974 - 6.34938i) q^{71} +(2.74848 - 1.20243i) q^{72} +(2.06099 - 7.69172i) q^{73} +(1.54054 - 1.29267i) q^{74} +(-4.14685 - 7.60287i) q^{75} +(-0.645576 + 3.66124i) q^{76} +(0.479291 + 5.47832i) q^{77} +(-11.3466 + 3.97673i) q^{78} +(-1.30184 + 3.57678i) q^{79} +(0.565439 + 2.16340i) q^{80} +(1.98508 - 8.77835i) q^{81} +(-5.93681 + 5.93681i) q^{82} +(-1.01524 + 0.473413i) q^{83} +(2.99202 - 6.22097i) q^{84} +(-8.46983 + 3.02389i) q^{85} +(-1.32486 - 0.233609i) q^{86} +(-0.126809 + 10.5977i) q^{87} +(1.37456 + 0.120259i) q^{88} +(-3.93997 - 6.82423i) q^{89} +(6.23179 + 2.48290i) q^{90} +(-13.8330 + 23.9594i) q^{91} +(0.284182 - 0.405854i) q^{92} +(-0.943192 + 2.49799i) q^{93} +(2.74711 + 7.54763i) q^{94} +(-6.83889 + 4.72621i) q^{95} +(-1.40682 - 1.01037i) q^{96} +(-8.52287 - 5.96778i) q^{97} +(-2.29940 - 8.58148i) q^{98} +(2.73590 - 3.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(217\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.422618 + 0.906308i 0.298836 + 0.640856i
\(3\) −0.572880 1.63457i −0.330752 0.943718i
\(4\) −0.642788 + 0.766044i −0.321394 + 0.383022i
\(5\) −2.22872 + 0.181179i −0.996712 + 0.0810256i
\(6\) 1.23931 1.21000i 0.505947 0.493982i
\(7\) 0.347359 3.97033i 0.131289 1.50064i −0.589657 0.807654i \(-0.700737\pi\)
0.720946 0.692991i \(-0.243707\pi\)
\(8\) −0.965926 0.258819i −0.341506 0.0915064i
\(9\) −2.34362 + 1.87282i −0.781206 + 0.624274i
\(10\) −1.10610 1.94333i −0.349779 0.614536i
\(11\) −1.35885 + 0.239602i −0.409709 + 0.0722428i −0.374704 0.927144i \(-0.622256\pi\)
−0.0350050 + 0.999387i \(0.511145\pi\)
\(12\) 1.62039 + 0.611828i 0.467767 + 0.176619i
\(13\) −6.29127 2.93367i −1.74488 0.813653i −0.986891 0.161390i \(-0.948402\pi\)
−0.757993 0.652263i \(-0.773820\pi\)
\(14\) 3.74514 1.36312i 1.00093 0.364309i
\(15\) 1.57294 + 3.53919i 0.406130 + 0.913815i
\(16\) −0.173648 0.984808i −0.0434120 0.246202i
\(17\) 3.88494 1.04097i 0.942237 0.252472i 0.245172 0.969480i \(-0.421156\pi\)
0.697065 + 0.717008i \(0.254489\pi\)
\(18\) −2.68781 1.33255i −0.633522 0.314085i
\(19\) 3.21964 1.85886i 0.738637 0.426452i −0.0829365 0.996555i \(-0.526430\pi\)
0.821574 + 0.570103i \(0.193097\pi\)
\(20\) 1.29380 1.82375i 0.289302 0.407804i
\(21\) −6.68877 + 1.70674i −1.45961 + 0.372442i
\(22\) −0.791429 1.13028i −0.168733 0.240976i
\(23\) −0.493571 + 0.0431819i −0.102917 + 0.00900405i −0.138498 0.990363i \(-0.544227\pi\)
0.0355810 + 0.999367i \(0.488672\pi\)
\(24\) 0.130302 + 1.72714i 0.0265979 + 0.352551i
\(25\) 4.93435 0.807592i 0.986870 0.161518i
\(26\) 6.94165i 1.36137i
\(27\) 4.40386 + 2.75790i 0.847524 + 0.530758i
\(28\) 2.81817 + 2.81817i 0.532585 + 0.532585i
\(29\) −5.74999 2.09283i −1.06775 0.388628i −0.252413 0.967620i \(-0.581224\pi\)
−0.815333 + 0.578992i \(0.803446\pi\)
\(30\) −2.54285 + 2.92129i −0.464258 + 0.533352i
\(31\) −1.18093 0.990920i −0.212102 0.177974i 0.530547 0.847655i \(-0.321986\pi\)
−0.742649 + 0.669681i \(0.766431\pi\)
\(32\) 0.819152 0.573576i 0.144807 0.101395i
\(33\) 1.17011 + 2.08387i 0.203689 + 0.362755i
\(34\) 2.58528 + 3.08102i 0.443373 + 0.528391i
\(35\) −0.0548245 + 8.91168i −0.00926704 + 1.50635i
\(36\) 0.0717843 2.99914i 0.0119640 0.499857i
\(37\) −0.520493 1.94251i −0.0855685 0.319346i 0.909853 0.414931i \(-0.136194\pi\)
−0.995421 + 0.0955853i \(0.969528\pi\)
\(38\) 3.04538 + 2.13240i 0.494026 + 0.345921i
\(39\) −1.19113 + 11.9641i −0.190734 + 1.91579i
\(40\) 2.19967 + 0.401829i 0.347798 + 0.0635347i
\(41\) 2.87157 + 7.88959i 0.448465 + 1.23215i 0.933793 + 0.357814i \(0.116478\pi\)
−0.485328 + 0.874332i \(0.661300\pi\)
\(42\) −4.37363 5.34078i −0.674866 0.824101i
\(43\) −0.771633 + 1.10201i −0.117673 + 0.168054i −0.873667 0.486524i \(-0.838265\pi\)
0.755995 + 0.654578i \(0.227154\pi\)
\(44\) 0.689907 1.19495i 0.104007 0.180146i
\(45\) 4.88394 4.59860i 0.728055 0.685519i
\(46\) −0.247728 0.429078i −0.0365255 0.0632641i
\(47\) 8.00145 + 0.700036i 1.16713 + 0.102111i 0.654202 0.756320i \(-0.273005\pi\)
0.512930 + 0.858431i \(0.328560\pi\)
\(48\) −1.51025 + 0.848016i −0.217986 + 0.122401i
\(49\) −8.74923 1.54272i −1.24989 0.220389i
\(50\) 2.81727 + 4.13074i 0.398423 + 0.584174i
\(51\) −3.92714 5.75385i −0.549909 0.805700i
\(52\) 6.29127 2.93367i 0.872442 0.406826i
\(53\) 2.13282 2.13282i 0.292965 0.292965i −0.545285 0.838251i \(-0.683579\pi\)
0.838251 + 0.545285i \(0.183579\pi\)
\(54\) −0.638352 + 5.15679i −0.0868687 + 0.701751i
\(55\) 2.98508 0.780201i 0.402509 0.105202i
\(56\) −1.36312 + 3.74514i −0.182155 + 0.500466i
\(57\) −4.88290 4.19782i −0.646757 0.556015i
\(58\) −0.533307 6.09573i −0.0700266 0.800408i
\(59\) −0.447387 + 2.53726i −0.0582449 + 0.330323i −0.999982 0.00602718i \(-0.998081\pi\)
0.941737 + 0.336350i \(0.109193\pi\)
\(60\) −3.72224 1.07001i −0.480539 0.138138i
\(61\) 6.83565 5.73579i 0.875215 0.734393i −0.0899743 0.995944i \(-0.528678\pi\)
0.965190 + 0.261551i \(0.0842340\pi\)
\(62\) 0.398995 1.48907i 0.0506724 0.189112i
\(63\) 6.62164 + 9.95548i 0.834249 + 1.25427i
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) 14.5530 + 5.39846i 1.80507 + 0.669597i
\(66\) −1.39412 + 1.94116i −0.171604 + 0.238940i
\(67\) −1.77666 + 3.81006i −0.217054 + 0.465473i −0.984442 0.175710i \(-0.943778\pi\)
0.767388 + 0.641182i \(0.221556\pi\)
\(68\) −1.69977 + 3.64516i −0.206127 + 0.442041i
\(69\) 0.353341 + 0.782037i 0.0425372 + 0.0941462i
\(70\) −8.09989 + 3.71655i −0.968122 + 0.444213i
\(71\) −10.9974 6.34938i −1.30516 0.753532i −0.323873 0.946101i \(-0.604985\pi\)
−0.981284 + 0.192568i \(0.938318\pi\)
\(72\) 2.74848 1.20243i 0.323912 0.141708i
\(73\) 2.06099 7.69172i 0.241221 0.900248i −0.734025 0.679123i \(-0.762360\pi\)
0.975245 0.221125i \(-0.0709729\pi\)
\(74\) 1.54054 1.29267i 0.179084 0.150269i
\(75\) −4.14685 7.60287i −0.478837 0.877904i
\(76\) −0.645576 + 3.66124i −0.0740527 + 0.419974i
\(77\) 0.479291 + 5.47832i 0.0546203 + 0.624313i
\(78\) −11.3466 + 3.97673i −1.28475 + 0.450276i
\(79\) −1.30184 + 3.57678i −0.146469 + 0.402420i −0.991132 0.132878i \(-0.957578\pi\)
0.844664 + 0.535297i \(0.179800\pi\)
\(80\) 0.565439 + 2.16340i 0.0632180 + 0.241875i
\(81\) 1.98508 8.77835i 0.220565 0.975372i
\(82\) −5.93681 + 5.93681i −0.655611 + 0.655611i
\(83\) −1.01524 + 0.473413i −0.111437 + 0.0519639i −0.477537 0.878611i \(-0.658470\pi\)
0.366100 + 0.930575i \(0.380693\pi\)
\(84\) 2.99202 6.22097i 0.326456 0.678763i
\(85\) −8.46983 + 3.02389i −0.918682 + 0.327987i
\(86\) −1.32486 0.233609i −0.142864 0.0251907i
\(87\) −0.126809 + 10.5977i −0.0135954 + 1.13619i
\(88\) 1.37456 + 0.120259i 0.146529 + 0.0128196i
\(89\) −3.93997 6.82423i −0.417636 0.723367i 0.578065 0.815991i \(-0.303808\pi\)
−0.995701 + 0.0926237i \(0.970475\pi\)
\(90\) 6.23179 + 2.48290i 0.656888 + 0.261721i
\(91\) −13.8330 + 23.9594i −1.45009 + 2.51163i
\(92\) 0.284182 0.405854i 0.0296280 0.0423132i
\(93\) −0.943192 + 2.49799i −0.0978045 + 0.259030i
\(94\) 2.74711 + 7.54763i 0.283343 + 0.778478i
\(95\) −6.83889 + 4.72621i −0.701655 + 0.484899i
\(96\) −1.40682 1.01037i −0.143583 0.103120i
\(97\) −8.52287 5.96778i −0.865366 0.605936i 0.0543491 0.998522i \(-0.482692\pi\)
−0.919715 + 0.392586i \(0.871581\pi\)
\(98\) −2.29940 8.58148i −0.232274 0.866860i
\(99\) 2.73590 3.10642i 0.274968 0.312207i
\(100\) −2.55309 + 4.29904i −0.255309 + 0.429904i
\(101\) 8.81667 + 10.5073i 0.877291 + 1.04552i 0.998600 + 0.0529004i \(0.0168466\pi\)
−0.121308 + 0.992615i \(0.538709\pi\)
\(102\) 3.55508 5.99088i 0.352005 0.593185i
\(103\) 15.4719 10.8335i 1.52449 1.06746i 0.552194 0.833716i \(-0.313791\pi\)
0.972298 0.233745i \(-0.0750982\pi\)
\(104\) 5.31761 + 4.46200i 0.521434 + 0.437535i
\(105\) 14.5981 5.01571i 1.42463 0.489483i
\(106\) 2.83436 + 1.03162i 0.275297 + 0.100200i
\(107\) −9.84993 9.84993i −0.952229 0.952229i 0.0466807 0.998910i \(-0.485136\pi\)
−0.998910 + 0.0466807i \(0.985136\pi\)
\(108\) −4.94342 + 1.60081i −0.475681 + 0.154038i
\(109\) 15.5323i 1.48772i −0.668334 0.743861i \(-0.732992\pi\)
0.668334 0.743861i \(-0.267008\pi\)
\(110\) 1.96865 + 2.37568i 0.187704 + 0.226512i
\(111\) −2.87698 + 1.96360i −0.273070 + 0.186377i
\(112\) −3.97033 + 0.347359i −0.375161 + 0.0328223i
\(113\) −6.50804 9.29445i −0.612225 0.874348i 0.386628 0.922236i \(-0.373640\pi\)
−0.998853 + 0.0478879i \(0.984751\pi\)
\(114\) 1.74091 6.19949i 0.163051 0.580635i
\(115\) 1.09221 0.185665i 0.101849 0.0173133i
\(116\) 5.29922 3.05951i 0.492020 0.284068i
\(117\) 20.2386 4.90703i 1.87105 0.453655i
\(118\) −2.48861 + 0.666822i −0.229095 + 0.0613859i
\(119\) −2.78352 15.7861i −0.255165 1.44711i
\(120\) −0.603329 3.82570i −0.0550761 0.349237i
\(121\) −8.54755 + 3.11105i −0.777050 + 0.282823i
\(122\) 8.08726 + 3.77115i 0.732186 + 0.341424i
\(123\) 11.2510 9.21356i 1.01447 0.830759i
\(124\) 1.51818 0.267696i 0.136336 0.0240398i
\(125\) −10.8509 + 2.69389i −0.970538 + 0.240949i
\(126\) −6.22430 + 10.2086i −0.554505 + 0.909456i
\(127\) 14.0644 + 3.76854i 1.24801 + 0.334404i 0.821568 0.570110i \(-0.193100\pi\)
0.426444 + 0.904514i \(0.359766\pi\)
\(128\) −0.0871557 + 0.996195i −0.00770355 + 0.0880520i
\(129\) 2.24335 + 0.629968i 0.197516 + 0.0554656i
\(130\) 1.25768 + 15.4710i 0.110306 + 1.35689i
\(131\) 13.5155 16.1071i 1.18085 1.40728i 0.287586 0.957755i \(-0.407147\pi\)
0.893266 0.449529i \(-0.148408\pi\)
\(132\) −2.34847 0.443134i −0.204408 0.0385699i
\(133\) −6.26193 13.4288i −0.542978 1.16442i
\(134\) −4.20394 −0.363165
\(135\) −10.3146 5.34868i −0.887742 0.460341i
\(136\) −4.02199 −0.344883
\(137\) 0.0907604 + 0.194636i 0.00775418 + 0.0166289i 0.910147 0.414286i \(-0.135969\pi\)
−0.902393 + 0.430915i \(0.858191\pi\)
\(138\) −0.559438 + 0.650739i −0.0476225 + 0.0553945i
\(139\) 5.37083 6.40070i 0.455548 0.542901i −0.488563 0.872528i \(-0.662479\pi\)
0.944111 + 0.329628i \(0.106923\pi\)
\(140\) −6.79150 5.77031i −0.573987 0.487681i
\(141\) −3.43961 13.4799i −0.289668 1.13522i
\(142\) 1.10677 12.6504i 0.0928780 1.06160i
\(143\) 9.25182 + 2.47902i 0.773676 + 0.207306i
\(144\) 2.25133 + 1.98280i 0.187611 + 0.165233i
\(145\) 13.1943 + 3.62254i 1.09572 + 0.300835i
\(146\) 7.84208 1.38277i 0.649015 0.114439i
\(147\) 2.49057 + 15.1850i 0.205419 + 1.25244i
\(148\) 1.82261 + 0.849898i 0.149818 + 0.0698612i
\(149\) −6.83147 + 2.48645i −0.559655 + 0.203698i −0.606331 0.795212i \(-0.707359\pi\)
0.0466758 + 0.998910i \(0.485137\pi\)
\(150\) 5.13800 6.97144i 0.419516 0.569215i
\(151\) 2.77651 + 15.7463i 0.225949 + 1.28142i 0.860863 + 0.508837i \(0.169924\pi\)
−0.634914 + 0.772583i \(0.718965\pi\)
\(152\) −3.59105 + 0.962218i −0.291272 + 0.0780462i
\(153\) −7.15527 + 9.71543i −0.578470 + 0.785446i
\(154\) −4.76249 + 2.74963i −0.383772 + 0.221571i
\(155\) 2.81150 + 1.99452i 0.225825 + 0.160204i
\(156\) −8.39941 8.60286i −0.672491 0.688780i
\(157\) −7.89740 11.2787i −0.630281 0.900135i 0.369293 0.929313i \(-0.379600\pi\)
−0.999574 + 0.0291784i \(0.990711\pi\)
\(158\) −3.79185 + 0.331744i −0.301663 + 0.0263921i
\(159\) −4.70808 2.26439i −0.373375 0.179578i
\(160\) −1.72174 + 1.42675i −0.136115 + 0.112795i
\(161\) 1.97464i 0.155624i
\(162\) 8.79482 1.91079i 0.690986 0.150126i
\(163\) 13.9177 + 13.9177i 1.09012 + 1.09012i 0.995515 + 0.0946021i \(0.0301579\pi\)
0.0946021 + 0.995515i \(0.469842\pi\)
\(164\) −7.88959 2.87157i −0.616073 0.224232i
\(165\) −2.98539 4.43236i −0.232412 0.345059i
\(166\) −0.858116 0.720045i −0.0666027 0.0558863i
\(167\) −6.51381 + 4.56102i −0.504053 + 0.352942i −0.797781 0.602947i \(-0.793993\pi\)
0.293728 + 0.955889i \(0.405104\pi\)
\(168\) 6.90259 + 0.0825947i 0.532547 + 0.00637232i
\(169\) 22.6174 + 26.9544i 1.73980 + 2.07341i
\(170\) −6.32008 6.39832i −0.484728 0.490729i
\(171\) −4.06430 + 10.3863i −0.310805 + 0.794259i
\(172\) −0.348189 1.29946i −0.0265492 0.0990829i
\(173\) −17.2309 12.0652i −1.31004 0.917298i −0.310590 0.950544i \(-0.600527\pi\)
−0.999447 + 0.0332458i \(0.989416\pi\)
\(174\) −9.65835 + 4.36385i −0.732198 + 0.330822i
\(175\) −1.49242 19.8715i −0.112816 1.50215i
\(176\) 0.471924 + 1.29660i 0.0355726 + 0.0977350i
\(177\) 4.40362 0.722260i 0.330996 0.0542884i
\(178\) 4.51975 6.45487i 0.338770 0.483813i
\(179\) −5.88150 + 10.1870i −0.439604 + 0.761416i −0.997659 0.0683880i \(-0.978214\pi\)
0.558055 + 0.829804i \(0.311548\pi\)
\(180\) 0.383394 + 6.69724i 0.0285765 + 0.499183i
\(181\) 5.53321 + 9.58380i 0.411280 + 0.712358i 0.995030 0.0995756i \(-0.0317485\pi\)
−0.583750 + 0.811933i \(0.698415\pi\)
\(182\) −27.5606 2.41124i −2.04293 0.178733i
\(183\) −13.2915 7.88741i −0.982539 0.583054i
\(184\) 0.487929 + 0.0860351i 0.0359706 + 0.00634259i
\(185\) 1.51197 + 4.23499i 0.111162 + 0.311363i
\(186\) −2.66256 + 0.200874i −0.195228 + 0.0147288i
\(187\) −5.02965 + 2.34536i −0.367804 + 0.171510i
\(188\) −5.67949 + 5.67949i −0.414220 + 0.414220i
\(189\) 12.4795 16.5268i 0.907750 1.20215i
\(190\) −7.17364 4.20075i −0.520430 0.304755i
\(191\) 5.91305 16.2460i 0.427853 1.17552i −0.519260 0.854617i \(-0.673792\pi\)
0.947113 0.320901i \(-0.103986\pi\)
\(192\) 0.321155 1.70202i 0.0231774 0.122832i
\(193\) 0.135785 + 1.55203i 0.00977402 + 0.111718i 0.999514 0.0311598i \(-0.00992008\pi\)
−0.989740 + 0.142877i \(0.954365\pi\)
\(194\) 1.80672 10.2464i 0.129715 0.735651i
\(195\) 0.487049 26.8805i 0.0348783 1.92495i
\(196\) 6.80569 5.71065i 0.486121 0.407904i
\(197\) −1.53697 + 5.73604i −0.109504 + 0.408676i −0.998817 0.0486235i \(-0.984517\pi\)
0.889313 + 0.457299i \(0.151183\pi\)
\(198\) 3.97162 + 1.16673i 0.282250 + 0.0829162i
\(199\) 1.77045 + 1.02217i 0.125504 + 0.0724599i 0.561438 0.827519i \(-0.310248\pi\)
−0.435934 + 0.899979i \(0.643582\pi\)
\(200\) −4.97523 0.497029i −0.351802 0.0351453i
\(201\) 7.24561 + 0.721363i 0.511066 + 0.0508810i
\(202\) −5.79676 + 12.4312i −0.407859 + 0.874656i
\(203\) −10.3065 + 22.1024i −0.723376 + 1.55129i
\(204\) 6.93202 + 0.690142i 0.485338 + 0.0483196i
\(205\) −7.82935 17.0634i −0.546825 1.19176i
\(206\) 16.3572 + 9.44385i 1.13966 + 0.657984i
\(207\) 1.07587 1.02557i 0.0747781 0.0712822i
\(208\) −1.79663 + 6.70511i −0.124574 + 0.464916i
\(209\) −3.92963 + 3.29735i −0.271818 + 0.228083i
\(210\) 10.7152 + 11.1107i 0.739420 + 0.766710i
\(211\) −1.44626 + 8.20212i −0.0995643 + 0.564657i 0.893688 + 0.448688i \(0.148109\pi\)
−0.993253 + 0.115969i \(0.963003\pi\)
\(212\) 0.262885 + 3.00478i 0.0180550 + 0.206369i
\(213\) −4.07827 + 21.6135i −0.279438 + 1.48093i
\(214\) 4.76431 13.0898i 0.325682 0.894803i
\(215\) 1.52009 2.59586i 0.103669 0.177036i
\(216\) −3.54001 3.80373i −0.240867 0.258811i
\(217\) −4.34449 + 4.34449i −0.294923 + 0.294923i
\(218\) 14.0770 6.56422i 0.953416 0.444585i
\(219\) −13.7533 + 1.03761i −0.929364 + 0.0701149i
\(220\) −1.32111 + 2.78821i −0.0890690 + 0.187981i
\(221\) −27.4951 4.84812i −1.84952 0.326120i
\(222\) −2.99549 1.77757i −0.201044 0.119303i
\(223\) −11.2247 0.982038i −0.751664 0.0657621i −0.295117 0.955461i \(-0.595359\pi\)
−0.456547 + 0.889699i \(0.650914\pi\)
\(224\) −1.99275 3.45154i −0.133146 0.230616i
\(225\) −10.0517 + 11.1338i −0.670117 + 0.742256i
\(226\) 5.67321 9.82629i 0.377376 0.653635i
\(227\) −1.03065 + 1.47192i −0.0684066 + 0.0976948i −0.851898 0.523708i \(-0.824548\pi\)
0.783491 + 0.621403i \(0.213437\pi\)
\(228\) 6.35439 1.04222i 0.420830 0.0690224i
\(229\) 3.83749 + 10.5434i 0.253588 + 0.696728i 0.999528 + 0.0307150i \(0.00977844\pi\)
−0.745940 + 0.666013i \(0.767999\pi\)
\(230\) 0.629856 + 0.911410i 0.0415315 + 0.0600966i
\(231\) 8.68011 3.92185i 0.571109 0.258039i
\(232\) 5.01240 + 3.50972i 0.329080 + 0.230424i
\(233\) 2.08560 + 7.78355i 0.136632 + 0.509917i 0.999986 + 0.00531842i \(0.00169291\pi\)
−0.863354 + 0.504599i \(0.831640\pi\)
\(234\) 13.0005 + 16.2686i 0.849867 + 1.06351i
\(235\) −17.9598 0.110488i −1.17157 0.00720747i
\(236\) −1.65608 1.97364i −0.107802 0.128473i
\(237\) 6.59229 + 0.0788818i 0.428215 + 0.00512392i
\(238\) 13.1307 9.19422i 0.851137 0.595973i
\(239\) 7.43783 + 6.24108i 0.481113 + 0.403702i 0.850829 0.525443i \(-0.176100\pi\)
−0.369715 + 0.929145i \(0.620545\pi\)
\(240\) 3.21229 2.16361i 0.207352 0.139661i
\(241\) 6.66292 + 2.42510i 0.429196 + 0.156215i 0.547580 0.836753i \(-0.315549\pi\)
−0.118384 + 0.992968i \(0.537771\pi\)
\(242\) −6.43192 6.43192i −0.413460 0.413460i
\(243\) −15.4860 + 1.78419i −0.993428 + 0.114456i
\(244\) 8.92331i 0.571256i
\(245\) 19.7791 + 1.85312i 1.26364 + 0.118392i
\(246\) 13.1052 + 6.30304i 0.835557 + 0.401867i
\(247\) −25.7089 + 2.24924i −1.63582 + 0.143116i
\(248\) 0.884224 + 1.26280i 0.0561483 + 0.0801880i
\(249\) 1.35543 + 1.38827i 0.0858972 + 0.0879777i
\(250\) −7.02730 8.69580i −0.444446 0.549971i
\(251\) 4.18510 2.41627i 0.264161 0.152513i −0.362070 0.932151i \(-0.617930\pi\)
0.626231 + 0.779637i \(0.284597\pi\)
\(252\) −11.8827 1.32679i −0.748537 0.0835797i
\(253\) 0.660344 0.176939i 0.0415155 0.0111240i
\(254\) 2.52841 + 14.3393i 0.158646 + 0.899728i
\(255\) 9.79495 + 12.1122i 0.613383 + 0.758494i
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −4.31999 2.01444i −0.269473 0.125657i 0.283185 0.959065i \(-0.408609\pi\)
−0.552659 + 0.833408i \(0.686387\pi\)
\(258\) 0.377137 + 2.29941i 0.0234796 + 0.143155i
\(259\) −7.89319 + 1.39178i −0.490459 + 0.0864812i
\(260\) −13.4899 + 7.67815i −0.836610 + 0.476179i
\(261\) 17.3953 5.86392i 1.07674 0.362968i
\(262\) 20.3099 + 5.44201i 1.25475 + 0.336209i
\(263\) 0.698450 7.98332i 0.0430683 0.492273i −0.943775 0.330590i \(-0.892752\pi\)
0.986843 0.161683i \(-0.0516921\pi\)
\(264\) −0.590889 2.31571i −0.0363667 0.142522i
\(265\) −4.36703 + 5.13987i −0.268264 + 0.315740i
\(266\) 9.52418 11.3505i 0.583965 0.695942i
\(267\) −8.89753 + 10.3496i −0.544520 + 0.633386i
\(268\) −1.77666 3.81006i −0.108527 0.232736i
\(269\) −2.04232 −0.124522 −0.0622611 0.998060i \(-0.519831\pi\)
−0.0622611 + 0.998060i \(0.519831\pi\)
\(270\) 0.488403 11.6087i 0.0297233 0.706482i
\(271\) 20.6542 1.25465 0.627326 0.778757i \(-0.284149\pi\)
0.627326 + 0.778757i \(0.284149\pi\)
\(272\) −1.69977 3.64516i −0.103063 0.221020i
\(273\) 47.0878 + 8.88505i 2.84989 + 0.537747i
\(274\) −0.138043 + 0.164514i −0.00833951 + 0.00993864i
\(275\) −6.51155 + 2.27968i −0.392661 + 0.137470i
\(276\) −0.826198 0.232009i −0.0497313 0.0139653i
\(277\) −1.57950 + 18.0538i −0.0949032 + 1.08475i 0.788152 + 0.615480i \(0.211038\pi\)
−0.883056 + 0.469268i \(0.844518\pi\)
\(278\) 8.07082 + 2.16257i 0.484055 + 0.129702i
\(279\) 4.62347 + 0.110662i 0.276800 + 0.00662519i
\(280\) 2.35947 8.59383i 0.141005 0.513580i
\(281\) 18.1038 3.19219i 1.07998 0.190430i 0.394776 0.918778i \(-0.370822\pi\)
0.685208 + 0.728347i \(0.259711\pi\)
\(282\) 10.7633 8.81422i 0.640947 0.524879i
\(283\) 22.8469 + 10.6537i 1.35811 + 0.633295i 0.958947 0.283586i \(-0.0915242\pi\)
0.399159 + 0.916882i \(0.369302\pi\)
\(284\) 11.9329 4.34323i 0.708089 0.257723i
\(285\) 11.6432 + 8.47107i 0.689681 + 0.501783i
\(286\) 1.66323 + 9.43267i 0.0983491 + 0.557766i
\(287\) 32.3217 8.66059i 1.90789 0.511218i
\(288\) −0.845573 + 2.87837i −0.0498259 + 0.169609i
\(289\) −0.713261 + 0.411802i −0.0419566 + 0.0242236i
\(290\) 2.29301 + 13.4890i 0.134650 + 0.792103i
\(291\) −4.87215 + 17.3500i −0.285610 + 1.01708i
\(292\) 4.56742 + 6.52295i 0.267288 + 0.381727i
\(293\) −12.5077 + 1.09429i −0.730711 + 0.0639289i −0.446438 0.894815i \(-0.647308\pi\)
−0.284273 + 0.958743i \(0.591752\pi\)
\(294\) −12.7097 + 8.67468i −0.741246 + 0.505917i
\(295\) 0.537402 5.73589i 0.0312887 0.333956i
\(296\) 2.01103i 0.116889i
\(297\) −6.64500 2.69240i −0.385582 0.156229i
\(298\) −5.14059 5.14059i −0.297786 0.297786i
\(299\) 3.23187 + 1.17630i 0.186904 + 0.0680274i
\(300\) 8.48968 + 1.71036i 0.490152 + 0.0987475i
\(301\) 4.10730 + 3.44643i 0.236741 + 0.198649i
\(302\) −13.0976 + 9.17106i −0.753684 + 0.527735i
\(303\) 12.1240 20.4309i 0.696505 1.17372i
\(304\) −2.38971 2.84794i −0.137059 0.163341i
\(305\) −14.1955 + 14.0219i −0.812833 + 0.802893i
\(306\) −11.8291 2.37896i −0.676226 0.135996i
\(307\) −0.631788 2.35787i −0.0360581 0.134571i 0.945550 0.325476i \(-0.105524\pi\)
−0.981609 + 0.190905i \(0.938858\pi\)
\(308\) −4.50472 3.15424i −0.256680 0.179730i
\(309\) −26.5717 19.0835i −1.51161 1.08562i
\(310\) −0.619458 + 3.39100i −0.0351829 + 0.192596i
\(311\) −0.679124 1.86588i −0.0385096 0.105804i 0.918948 0.394380i \(-0.129041\pi\)
−0.957457 + 0.288576i \(0.906818\pi\)
\(312\) 4.24709 11.2482i 0.240444 0.636803i
\(313\) −10.5165 + 15.0191i −0.594429 + 0.848932i −0.997813 0.0660983i \(-0.978945\pi\)
0.403384 + 0.915031i \(0.367834\pi\)
\(314\) 6.88435 11.9240i 0.388506 0.672912i
\(315\) −16.5615 20.9882i −0.933134 1.18255i
\(316\) −1.90317 3.29638i −0.107062 0.185436i
\(317\) 2.27739 + 0.199246i 0.127911 + 0.0111907i 0.150931 0.988544i \(-0.451773\pi\)
−0.0230205 + 0.999735i \(0.507328\pi\)
\(318\) 0.0625084 5.22394i 0.00350530 0.292944i
\(319\) 8.31483 + 1.46613i 0.465541 + 0.0820875i
\(320\) −2.02071 0.957452i −0.112961 0.0535232i
\(321\) −10.4575 + 21.7432i −0.583683 + 1.21359i
\(322\) −1.78963 + 0.834520i −0.0997323 + 0.0465060i
\(323\) 10.5731 10.5731i 0.588304 0.588304i
\(324\) 5.44862 + 7.16328i 0.302701 + 0.397960i
\(325\) −33.4125 9.39495i −1.85339 0.521138i
\(326\) −6.73184 + 18.4956i −0.372842 + 1.02438i
\(327\) −25.3885 + 8.89813i −1.40399 + 0.492068i
\(328\) −0.731753 8.36397i −0.0404043 0.461823i
\(329\) 5.55875 31.5253i 0.306464 1.73804i
\(330\) 2.75540 4.57887i 0.151680 0.252059i
\(331\) −3.07159 + 2.57737i −0.168830 + 0.141665i −0.723288 0.690547i \(-0.757370\pi\)
0.554458 + 0.832212i \(0.312926\pi\)
\(332\) 0.289927 1.08202i 0.0159118 0.0593836i
\(333\) 4.85780 + 3.57770i 0.266206 + 0.196057i
\(334\) −6.88654 3.97594i −0.376815 0.217554i
\(335\) 3.26937 8.81343i 0.178625 0.481529i
\(336\) 2.84231 + 6.29078i 0.155060 + 0.343190i
\(337\) 10.3495 22.1947i 0.563775 1.20902i −0.393361 0.919384i \(-0.628688\pi\)
0.957137 0.289636i \(-0.0935343\pi\)
\(338\) −14.8704 + 31.8897i −0.808845 + 1.73457i
\(339\) −11.4641 + 15.9624i −0.622643 + 0.866960i
\(340\) 3.12787 8.43199i 0.169633 0.457289i
\(341\) 1.84214 + 1.06356i 0.0997574 + 0.0575950i
\(342\) −11.1308 + 0.705926i −0.601885 + 0.0381721i
\(343\) −1.94359 + 7.25359i −0.104944 + 0.391657i
\(344\) 1.03056 0.864743i 0.0555641 0.0466238i
\(345\) −0.929185 1.67892i −0.0500256 0.0903900i
\(346\) 3.65269 20.7154i 0.196370 1.11367i
\(347\) −0.127861 1.46146i −0.00686396 0.0784554i 0.991990 0.126316i \(-0.0403153\pi\)
−0.998854 + 0.0478605i \(0.984760\pi\)
\(348\) −8.03678 6.90920i −0.430817 0.370372i
\(349\) 1.32197 3.63209i 0.0707637 0.194422i −0.899269 0.437396i \(-0.855901\pi\)
0.970033 + 0.242974i \(0.0781231\pi\)
\(350\) 17.3790 9.75066i 0.928946 0.521195i
\(351\) −19.6151 30.2701i −1.04698 1.61570i
\(352\) −0.975676 + 0.975676i −0.0520037 + 0.0520037i
\(353\) 1.52716 0.712125i 0.0812824 0.0379026i −0.381552 0.924347i \(-0.624610\pi\)
0.462834 + 0.886445i \(0.346832\pi\)
\(354\) 2.51564 + 3.68579i 0.133705 + 0.195898i
\(355\) 25.6606 + 12.1585i 1.36192 + 0.645304i
\(356\) 7.76023 + 1.36834i 0.411291 + 0.0725217i
\(357\) −24.2088 + 13.5934i −1.28127 + 0.719438i
\(358\) −11.7182 1.02521i −0.619328 0.0541842i
\(359\) −1.44240 2.49831i −0.0761271 0.131856i 0.825449 0.564477i \(-0.190922\pi\)
−0.901576 + 0.432621i \(0.857589\pi\)
\(360\) −5.90773 + 3.17785i −0.311365 + 0.167487i
\(361\) −2.58926 + 4.48473i −0.136277 + 0.236038i
\(362\) −6.34743 + 9.06508i −0.333614 + 0.476450i
\(363\) 9.98194 + 12.1893i 0.523916 + 0.639771i
\(364\) −9.46230 25.9975i −0.495959 1.36264i
\(365\) −3.19979 + 17.5161i −0.167484 + 0.916833i
\(366\) 1.53117 15.3796i 0.0800356 0.803904i
\(367\) 19.5523 + 13.6907i 1.02062 + 0.714647i 0.958987 0.283452i \(-0.0914796\pi\)
0.0616352 + 0.998099i \(0.480368\pi\)
\(368\) 0.128234 + 0.478574i 0.00668464 + 0.0249474i
\(369\) −21.5057 13.1122i −1.11954 0.682595i
\(370\) −3.19922 + 3.16010i −0.166319 + 0.164286i
\(371\) −7.72715 9.20885i −0.401173 0.478100i
\(372\) −1.30730 2.32820i −0.0677803 0.120712i
\(373\) −19.7533 + 13.8314i −1.02279 + 0.716162i −0.959464 0.281831i \(-0.909058\pi\)
−0.0633211 + 0.997993i \(0.520169\pi\)
\(374\) −4.25124 3.56721i −0.219826 0.184456i
\(375\) 10.6196 + 16.1933i 0.548396 + 0.836219i
\(376\) −7.54763 2.74711i −0.389239 0.141671i
\(377\) 30.0351 + 30.0351i 1.54689 + 1.54689i
\(378\) 20.2524 + 4.32573i 1.04167 + 0.222491i
\(379\) 26.5732i 1.36497i −0.730898 0.682487i \(-0.760899\pi\)
0.730898 0.682487i \(-0.239101\pi\)
\(380\) 0.775466 8.27684i 0.0397806 0.424593i
\(381\) −1.89727 25.1481i −0.0972001 1.28838i
\(382\) 17.2228 1.50680i 0.881196 0.0770946i
\(383\) −10.6186 15.1649i −0.542585 0.774892i 0.450438 0.892808i \(-0.351268\pi\)
−0.993024 + 0.117915i \(0.962379\pi\)
\(384\) 1.67828 0.428238i 0.0856442 0.0218534i
\(385\) −2.06076 12.1228i −0.105026 0.617835i
\(386\) −1.34923 + 0.778980i −0.0686741 + 0.0396490i
\(387\) −0.255447 4.02781i −0.0129851 0.204745i
\(388\) 10.0500 2.69288i 0.510210 0.136710i
\(389\) 1.17271 + 6.65076i 0.0594586 + 0.337207i 0.999997 0.00248101i \(-0.000789730\pi\)
−0.940538 + 0.339688i \(0.889679\pi\)
\(390\) 24.5678 10.9188i 1.24404 0.552893i
\(391\) −1.87255 + 0.681551i −0.0946987 + 0.0344675i
\(392\) 8.05182 + 3.75462i 0.406678 + 0.189637i
\(393\) −34.0709 12.8645i −1.71865 0.648928i
\(394\) −5.84817 + 1.03119i −0.294626 + 0.0519506i
\(395\) 2.25340 8.20750i 0.113381 0.412964i
\(396\) 0.621057 + 4.09259i 0.0312093 + 0.205660i
\(397\) −20.9576 5.61558i −1.05183 0.281838i −0.308824 0.951119i \(-0.599935\pi\)
−0.743009 + 0.669281i \(0.766602\pi\)
\(398\) −0.178176 + 2.03657i −0.00893118 + 0.102084i
\(399\) −18.3629 + 17.9286i −0.919293 + 0.897553i
\(400\) −1.65216 4.71915i −0.0826082 0.235957i
\(401\) 12.7195 15.1585i 0.635183 0.756982i −0.348418 0.937339i \(-0.613281\pi\)
0.983601 + 0.180358i \(0.0577255\pi\)
\(402\) 2.40835 + 6.87161i 0.120118 + 0.342725i
\(403\) 4.52253 + 9.69860i 0.225283 + 0.483122i
\(404\) −13.7163 −0.682412
\(405\) −2.83374 + 19.9241i −0.140810 + 0.990037i
\(406\) −24.3873 −1.21032
\(407\) 1.17270 + 2.51487i 0.0581287 + 0.124657i
\(408\) 2.30412 + 6.57421i 0.114071 + 0.325472i
\(409\) 10.1988 12.1545i 0.504300 0.601002i −0.452494 0.891767i \(-0.649466\pi\)
0.956794 + 0.290766i \(0.0939101\pi\)
\(410\) 12.1558 14.3071i 0.600334 0.706577i
\(411\) 0.266151 0.259857i 0.0131283 0.0128178i
\(412\) −1.64617 + 18.8158i −0.0811011 + 0.926990i
\(413\) 9.91836 + 2.65762i 0.488051 + 0.130773i
\(414\) 1.38417 + 0.541644i 0.0680281 + 0.0266203i
\(415\) 2.17690 1.23904i 0.106860 0.0608222i
\(416\) −6.83619 + 1.20540i −0.335172 + 0.0590998i
\(417\) −13.5392 5.11214i −0.663018 0.250343i
\(418\) −4.64915 2.16794i −0.227397 0.106037i
\(419\) 29.3155 10.6700i 1.43216 0.521262i 0.494607 0.869117i \(-0.335312\pi\)
0.937548 + 0.347855i \(0.113090\pi\)
\(420\) −5.54125 + 14.4069i −0.270385 + 0.702983i
\(421\) −5.28257 29.9590i −0.257457 1.46011i −0.789687 0.613511i \(-0.789757\pi\)
0.532230 0.846600i \(-0.321354\pi\)
\(422\) −8.04486 + 2.15561i −0.391618 + 0.104934i
\(423\) −20.0634 + 13.3447i −0.975515 + 0.648840i
\(424\) −2.61216 + 1.50813i −0.126858 + 0.0732413i
\(425\) 18.3290 8.27395i 0.889086 0.401345i
\(426\) −21.3120 + 5.43809i −1.03257 + 0.263476i
\(427\) −20.3986 29.1322i −0.987156 1.40981i
\(428\) 13.8769 1.21407i 0.670765 0.0586844i
\(429\) −1.24806 16.5429i −0.0602569 0.798698i
\(430\) 2.99507 + 0.280611i 0.144435 + 0.0135323i
\(431\) 31.2636i 1.50592i 0.658069 + 0.752958i \(0.271373\pi\)
−0.658069 + 0.752958i \(0.728627\pi\)
\(432\) 1.95128 4.81586i 0.0938808 0.231703i
\(433\) 13.7999 + 13.7999i 0.663181 + 0.663181i 0.956129 0.292948i \(-0.0946361\pi\)
−0.292948 + 0.956129i \(0.594636\pi\)
\(434\) −5.77350 2.10138i −0.277137 0.100870i
\(435\) −1.63745 23.6422i −0.0785099 1.13356i
\(436\) 11.8984 + 9.98396i 0.569831 + 0.478145i
\(437\) −1.50885 + 1.05651i −0.0721783 + 0.0505398i
\(438\) −6.75280 12.0262i −0.322661 0.574636i
\(439\) 4.44322 + 5.29522i 0.212063 + 0.252727i 0.861582 0.507618i \(-0.169474\pi\)
−0.649519 + 0.760346i \(0.725030\pi\)
\(440\) −3.08530 0.0189807i −0.147086 0.000904871i
\(441\) 23.3941 12.7702i 1.11400 0.608104i
\(442\) −7.22603 26.9679i −0.343707 1.28273i
\(443\) 1.21988 + 0.854169i 0.0579583 + 0.0405828i 0.602197 0.798348i \(-0.294292\pi\)
−0.544238 + 0.838931i \(0.683181\pi\)
\(444\) 0.345077 3.46607i 0.0163766 0.164492i
\(445\) 10.0175 + 14.4954i 0.474874 + 0.687149i
\(446\) −3.85375 10.5881i −0.182480 0.501361i
\(447\) 7.97788 + 9.74205i 0.377341 + 0.460783i
\(448\) 2.28599 3.26473i 0.108003 0.154244i
\(449\) −12.5295 + 21.7017i −0.591304 + 1.02417i 0.402754 + 0.915308i \(0.368053\pi\)
−0.994057 + 0.108859i \(0.965280\pi\)
\(450\) −14.3387 4.40462i −0.675935 0.207636i
\(451\) −5.79241 10.0327i −0.272754 0.472424i
\(452\) 11.3032 + 0.988906i 0.531660 + 0.0465142i
\(453\) 24.1478 13.5591i 1.13456 0.637064i
\(454\) −1.76958 0.312025i −0.0830507 0.0146441i
\(455\) 26.4888 55.9049i 1.24181 2.62086i
\(456\) 3.63005 + 5.31857i 0.169993 + 0.249065i
\(457\) −24.5331 + 11.4400i −1.14761 + 0.535139i −0.900933 0.433958i \(-0.857117\pi\)
−0.246677 + 0.969098i \(0.579339\pi\)
\(458\) −7.93379 + 7.93379i −0.370721 + 0.370721i
\(459\) 19.9796 + 6.13000i 0.932569 + 0.286124i
\(460\) −0.559829 + 0.956022i −0.0261022 + 0.0445747i
\(461\) −3.95298 + 10.8607i −0.184109 + 0.505835i −0.997071 0.0764818i \(-0.975631\pi\)
0.812962 + 0.582316i \(0.197854\pi\)
\(462\) 7.22278 + 6.20940i 0.336034 + 0.288888i
\(463\) −0.819693 9.36914i −0.0380944 0.435421i −0.991161 0.132661i \(-0.957648\pi\)
0.953067 0.302759i \(-0.0979078\pi\)
\(464\) −1.06256 + 6.02605i −0.0493279 + 0.279752i
\(465\) 1.64952 5.73820i 0.0764949 0.266103i
\(466\) −6.17288 + 5.17966i −0.285953 + 0.239943i
\(467\) 2.20035 8.21181i 0.101820 0.379997i −0.896145 0.443761i \(-0.853644\pi\)
0.997965 + 0.0637641i \(0.0203105\pi\)
\(468\) −9.25009 + 18.6578i −0.427586 + 0.862457i
\(469\) 14.5101 + 8.37739i 0.670012 + 0.386832i
\(470\) −7.49000 16.3238i −0.345488 0.752961i
\(471\) −13.9115 + 19.3701i −0.641006 + 0.892529i
\(472\) 1.08883 2.33501i 0.0501177 0.107478i
\(473\) 0.784492 1.68235i 0.0360710 0.0773544i
\(474\) 2.71453 + 6.00798i 0.124683 + 0.275956i
\(475\) 14.3856 11.7724i 0.660059 0.540156i
\(476\) 13.8821 + 8.01482i 0.636284 + 0.367358i
\(477\) −1.00412 + 8.99290i −0.0459757 + 0.411757i
\(478\) −2.51298 + 9.37856i −0.114941 + 0.428965i
\(479\) −13.1222 + 11.0108i −0.599566 + 0.503096i −0.891306 0.453402i \(-0.850210\pi\)
0.291740 + 0.956498i \(0.405766\pi\)
\(480\) 3.31847 + 1.99694i 0.151467 + 0.0911473i
\(481\) −2.42410 + 13.7478i −0.110530 + 0.626845i
\(482\) 0.617981 + 7.06355i 0.0281482 + 0.321736i
\(483\) 3.22768 1.13123i 0.146865 0.0514729i
\(484\) 3.11105 8.54755i 0.141412 0.388525i
\(485\) 20.0763 + 11.7563i 0.911617 + 0.533827i
\(486\) −8.16170 13.2811i −0.370222 0.602441i
\(487\) 24.7608 24.7608i 1.12202 1.12202i 0.130583 0.991437i \(-0.458315\pi\)
0.991437 0.130583i \(-0.0416847\pi\)
\(488\) −8.08726 + 3.77115i −0.366093 + 0.170712i
\(489\) 14.7762 30.7225i 0.668204 1.38932i
\(490\) 6.67949 + 18.7091i 0.301749 + 0.845190i
\(491\) 24.8545 + 4.38251i 1.12167 + 0.197780i 0.703572 0.710624i \(-0.251587\pi\)
0.418094 + 0.908404i \(0.362698\pi\)
\(492\) −0.173996 + 14.5411i −0.00784432 + 0.655564i
\(493\) −24.5169 2.14496i −1.10419 0.0966039i
\(494\) −12.9036 22.3496i −0.580559 1.00556i
\(495\) −5.53472 + 7.41902i −0.248767 + 0.333460i
\(496\) −0.770799 + 1.33506i −0.0346099 + 0.0599461i
\(497\) −29.0292 + 41.4580i −1.30214 + 1.85965i
\(498\) −0.685364 + 1.81515i −0.0307119 + 0.0813387i
\(499\) −5.42986 14.9184i −0.243074 0.667840i −0.999899 0.0142224i \(-0.995473\pi\)
0.756825 0.653618i \(-0.226750\pi\)
\(500\) 4.91121 10.0439i 0.219636 0.449177i
\(501\) 11.1869 + 8.03434i 0.499794 + 0.358948i
\(502\) 3.95858 + 2.77183i 0.176680 + 0.123713i
\(503\) −3.89277 14.5280i −0.173570 0.647771i −0.996791 0.0800503i \(-0.974492\pi\)
0.823221 0.567721i \(-0.192175\pi\)
\(504\) −3.81935 11.3301i −0.170127 0.504681i
\(505\) −21.5536 21.8204i −0.959120 0.970995i
\(506\) 0.439434 + 0.523697i 0.0195352 + 0.0232812i
\(507\) 31.1017 52.4113i 1.38127 2.32767i
\(508\) −11.9273 + 8.35157i −0.529187 + 0.370541i
\(509\) 33.2789 + 27.9243i 1.47506 + 1.23772i 0.911274 + 0.411801i \(0.135100\pi\)
0.563786 + 0.825921i \(0.309344\pi\)
\(510\) −6.83784 + 13.9961i −0.302785 + 0.619756i
\(511\) −29.8228 10.8546i −1.31928 0.480180i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 19.3054 + 0.693277i 0.852355 + 0.0306089i
\(514\) 4.76658i 0.210245i
\(515\) −32.5197 + 26.9481i −1.43299 + 1.18747i
\(516\) −1.92458 + 1.31357i −0.0847251 + 0.0578269i
\(517\) −11.0405 + 0.965921i −0.485562 + 0.0424811i
\(518\) −4.59719 6.56547i −0.201989 0.288470i
\(519\) −9.85012 + 35.0769i −0.432372 + 1.53970i
\(520\) −12.6599 8.98110i −0.555172 0.393847i
\(521\) 5.78678 3.34100i 0.253523 0.146372i −0.367853 0.929884i \(-0.619907\pi\)
0.621376 + 0.783512i \(0.286574\pi\)
\(522\) 12.6661 + 13.2873i 0.554379 + 0.581568i
\(523\) 3.75281 1.00556i 0.164099 0.0439702i −0.175834 0.984420i \(-0.556262\pi\)
0.339933 + 0.940450i \(0.389596\pi\)
\(524\) 3.65118 + 20.7069i 0.159503 + 0.904585i
\(525\) −31.6264 + 13.8235i −1.38029 + 0.603305i
\(526\) 7.53052 2.74089i 0.328346 0.119508i
\(527\) −5.61937 2.62035i −0.244784 0.114144i
\(528\) 1.84903 1.51419i 0.0804685 0.0658966i
\(529\) −22.4088 + 3.95128i −0.974297 + 0.171795i
\(530\) −6.50389 1.78567i −0.282511 0.0775644i
\(531\) −3.70333 6.78424i −0.160711 0.294411i
\(532\) 14.3121 + 3.83492i 0.620509 + 0.166265i
\(533\) 5.07957 58.0597i 0.220021 2.51485i
\(534\) −13.1402 3.68997i −0.568632 0.159680i
\(535\) 23.7373 + 20.1681i 1.02625 + 0.871943i
\(536\) 2.70224 3.22040i 0.116719 0.139100i
\(537\) 20.0208 + 3.77774i 0.863961 + 0.163022i
\(538\) −0.863121 1.85097i −0.0372118 0.0798009i
\(539\) 12.2585 0.528013
\(540\) 10.7274 4.46340i 0.461636 0.192074i
\(541\) 20.8588 0.896788 0.448394 0.893836i \(-0.351996\pi\)
0.448394 + 0.893836i \(0.351996\pi\)
\(542\) 8.72883 + 18.7190i 0.374935 + 0.804051i
\(543\) 12.4955 14.5348i 0.536233 0.623746i
\(544\) 2.58528 3.08102i 0.110843 0.132098i
\(545\) 2.81412 + 34.6170i 0.120544 + 1.48283i
\(546\) 11.8476 + 46.4311i 0.507030 + 1.98707i
\(547\) 2.61574 29.8981i 0.111841 1.27835i −0.708186 0.706026i \(-0.750486\pi\)
0.820027 0.572324i \(-0.193958\pi\)
\(548\) −0.207440 0.0555833i −0.00886139 0.00237440i
\(549\) −5.27804 + 26.2444i −0.225261 + 1.12009i
\(550\) −4.81799 4.93803i −0.205440 0.210558i
\(551\) −22.4032 + 3.95029i −0.954408 + 0.168288i
\(552\) −0.138895 0.846841i −0.00591175 0.0360440i
\(553\) 13.7488 + 6.41118i 0.584659 + 0.272631i
\(554\) −17.0298 + 6.19835i −0.723528 + 0.263343i
\(555\) 6.05620 4.89756i 0.257071 0.207890i
\(556\) 1.45092 + 8.22858i 0.0615328 + 0.348970i
\(557\) 17.6438 4.72765i 0.747594 0.200317i 0.135143 0.990826i \(-0.456851\pi\)
0.612451 + 0.790509i \(0.290184\pi\)
\(558\) 1.85367 + 4.23705i 0.0784720 + 0.179369i
\(559\) 8.08746 4.66930i 0.342063 0.197490i
\(560\) 8.78581 1.49350i 0.371268 0.0631121i
\(561\) 6.71503 + 6.87768i 0.283509 + 0.290376i
\(562\) 10.5441 + 15.0586i 0.444777 + 0.635207i
\(563\) 24.3545 2.13074i 1.02642 0.0898001i 0.438510 0.898727i \(-0.355507\pi\)
0.587910 + 0.808926i \(0.299951\pi\)
\(564\) 12.5372 + 6.02984i 0.527910 + 0.253902i
\(565\) 16.1885 + 19.5356i 0.681057 + 0.821867i
\(566\) 25.2087i 1.05960i
\(567\) −34.1634 10.9307i −1.43473 0.459046i
\(568\) 8.97938 + 8.97938i 0.376766 + 0.376766i
\(569\) 6.28696 + 2.28827i 0.263563 + 0.0959291i 0.470422 0.882442i \(-0.344102\pi\)
−0.206859 + 0.978371i \(0.566324\pi\)
\(570\) −2.75678 + 14.1323i −0.115469 + 0.591938i
\(571\) 18.3978 + 15.4376i 0.769924 + 0.646043i 0.940690 0.339269i \(-0.110180\pi\)
−0.170765 + 0.985312i \(0.554624\pi\)
\(572\) −7.84599 + 5.49382i −0.328057 + 0.229708i
\(573\) −29.9426 0.358286i −1.25087 0.0149676i
\(574\) 21.5089 + 25.6333i 0.897765 + 1.06991i
\(575\) −2.40058 + 0.611679i −0.100111 + 0.0255088i
\(576\) −2.96604 + 0.450102i −0.123585 + 0.0187542i
\(577\) −0.846255 3.15827i −0.0352301 0.131480i 0.946071 0.323959i \(-0.105014\pi\)
−0.981301 + 0.192479i \(0.938347\pi\)
\(578\) −0.674656 0.472399i −0.0280620 0.0196492i
\(579\) 2.45911 1.11108i 0.102197 0.0461748i
\(580\) −11.2561 + 7.77888i −0.467386 + 0.323000i
\(581\) 1.52696 + 4.19528i 0.0633488 + 0.174049i
\(582\) −17.7835 + 2.91677i −0.737150 + 0.120904i
\(583\) −2.38716 + 3.40921i −0.0988660 + 0.141195i
\(584\) −3.98153 + 6.89621i −0.164757 + 0.285367i
\(585\) −44.2169 + 14.6032i −1.82815 + 0.603766i
\(586\) −6.27776 10.8734i −0.259332 0.449176i
\(587\) −12.5047 1.09402i −0.516124 0.0451550i −0.173882 0.984767i \(-0.555631\pi\)
−0.342243 + 0.939612i \(0.611187\pi\)
\(588\) −13.2333 7.85284i −0.545732 0.323846i
\(589\) −5.64417 0.995219i −0.232564 0.0410073i
\(590\) 5.42560 1.93704i 0.223368 0.0797467i
\(591\) 10.2564 0.773786i 0.421893 0.0318293i
\(592\) −1.82261 + 0.849898i −0.0749089 + 0.0349306i
\(593\) −14.2960 + 14.2960i −0.587065 + 0.587065i −0.936835 0.349771i \(-0.886259\pi\)
0.349771 + 0.936835i \(0.386259\pi\)
\(594\) −0.368153 7.16027i −0.0151055 0.293789i
\(595\) 9.06377 + 34.6784i 0.371579 + 1.42168i
\(596\) 2.48645 6.83147i 0.101849 0.279828i
\(597\) 0.656551 3.47951i 0.0268709 0.142407i
\(598\) 0.299753 + 3.42620i 0.0122578 + 0.140108i
\(599\) −1.75900 + 9.97576i −0.0718706 + 0.407599i 0.927554 + 0.373689i \(0.121907\pi\)
−0.999425 + 0.0339101i \(0.989204\pi\)
\(600\) 2.03778 + 8.41709i 0.0831922 + 0.343626i
\(601\) 19.0179 15.9580i 0.775758 0.650939i −0.166418 0.986055i \(-0.553220\pi\)
0.942177 + 0.335117i \(0.108776\pi\)
\(602\) −1.38771 + 5.17900i −0.0565588 + 0.211080i
\(603\) −2.97175 12.2567i −0.121019 0.499131i
\(604\) −13.8471 7.99463i −0.563431 0.325297i
\(605\) 18.4864 8.48229i 0.751579 0.344854i
\(606\) 23.6405 + 2.35361i 0.960328 + 0.0956090i
\(607\) 8.72581 18.7126i 0.354170 0.759519i −0.645823 0.763488i \(-0.723485\pi\)
0.999992 + 0.00396842i \(0.00126319\pi\)
\(608\) 1.57118 3.36940i 0.0637197 0.136647i
\(609\) 42.0323 + 4.18468i 1.70323 + 0.169572i
\(610\) −18.7075 6.93959i −0.757443 0.280976i
\(611\) −48.2856 27.8777i −1.95343 1.12781i
\(612\) −2.84313 11.7262i −0.114927 0.474004i
\(613\) 4.31596 16.1074i 0.174320 0.650570i −0.822347 0.568987i \(-0.807336\pi\)
0.996666 0.0815837i \(-0.0259978\pi\)
\(614\) 1.86995 1.56907i 0.0754649 0.0633226i
\(615\) −23.4060 + 22.5729i −0.943819 + 0.910225i
\(616\) 0.954935 5.41570i 0.0384754 0.218205i
\(617\) −3.76852 43.0744i −0.151715 1.73411i −0.566388 0.824139i \(-0.691659\pi\)
0.414673 0.909971i \(-0.363896\pi\)
\(618\) 6.06588 32.1472i 0.244005 1.29315i
\(619\) −3.88899 + 10.6849i −0.156312 + 0.429462i −0.992985 0.118239i \(-0.962275\pi\)
0.836674 + 0.547702i \(0.184497\pi\)
\(620\) −3.33508 + 0.871679i −0.133940 + 0.0350075i
\(621\) −2.29271 1.17105i −0.0920033 0.0469927i
\(622\) 1.40405 1.40405i 0.0562973 0.0562973i
\(623\) −28.4630 + 13.2725i −1.14035 + 0.531753i
\(624\) 11.9892 0.904513i 0.479953 0.0362095i
\(625\) 23.6956 7.96988i 0.947824 0.318795i
\(626\) −18.0564 3.18384i −0.721681 0.127252i
\(627\) 7.64095 + 4.53426i 0.305150 + 0.181081i
\(628\) 13.7163 + 1.20002i 0.547340 + 0.0478860i
\(629\) −4.04417 7.00471i −0.161252 0.279296i
\(630\) 12.0226 23.8798i 0.478993 0.951395i
\(631\) 5.21919 9.03991i 0.207773 0.359873i −0.743240 0.669025i \(-0.766712\pi\)
0.951013 + 0.309152i \(0.100045\pi\)
\(632\) 2.18322 3.11797i 0.0868440 0.124026i
\(633\) 14.2354 2.33483i 0.565808 0.0928011i
\(634\) 0.781888 + 2.14822i 0.0310527 + 0.0853167i
\(635\) −32.0283 5.85084i −1.27100 0.232183i
\(636\) 4.76092 2.15108i 0.188783 0.0852960i
\(637\) 50.5179 + 35.3730i 2.00159 + 1.40153i
\(638\) 2.18524 + 8.15541i 0.0865143 + 0.322876i
\(639\) 37.6650 5.71573i 1.49001 0.226111i
\(640\) 0.0137560 2.23603i 0.000543754 0.0883867i
\(641\) −7.45071 8.87941i −0.294285 0.350715i 0.598561 0.801077i \(-0.295739\pi\)
−0.892846 + 0.450362i \(0.851295\pi\)
\(642\) −24.1256 0.288681i −0.952161 0.0113933i
\(643\) 0.975543 0.683083i 0.0384717 0.0269382i −0.554182 0.832395i \(-0.686969\pi\)
0.592654 + 0.805457i \(0.298080\pi\)
\(644\) −1.51266 1.26928i −0.0596073 0.0500164i
\(645\) −5.11394 0.997572i −0.201361 0.0392794i
\(646\) 14.0509 + 5.11411i 0.552825 + 0.201212i
\(647\) −35.5625 35.5625i −1.39811 1.39811i −0.805472 0.592634i \(-0.798088\pi\)
−0.592634 0.805472i \(-0.701912\pi\)
\(648\) −4.18945 + 7.96546i −0.164577 + 0.312913i
\(649\) 3.55496i 0.139544i
\(650\) −5.60602 34.2525i −0.219886 1.34349i
\(651\) 9.59023 + 4.61249i 0.375871 + 0.180778i
\(652\) −19.6077 + 1.71545i −0.767896 + 0.0671822i
\(653\) −11.0851 15.8312i −0.433794 0.619523i 0.541429 0.840747i \(-0.317884\pi\)
−0.975223 + 0.221224i \(0.928995\pi\)
\(654\) −18.7941 19.2493i −0.734908 0.752708i
\(655\) −27.2039 + 38.3469i −1.06294 + 1.49834i
\(656\) 7.27108 4.19796i 0.283888 0.163903i
\(657\) 9.57504 + 21.8863i 0.373558 + 0.853867i
\(658\) 30.9208 8.28521i 1.20542 0.322991i
\(659\) 2.19147 + 12.4284i 0.0853676 + 0.484144i 0.997277 + 0.0737513i \(0.0234971\pi\)
−0.911909 + 0.410392i \(0.865392\pi\)
\(660\) 5.31435 + 0.562128i 0.206861 + 0.0218808i
\(661\) −20.0840 + 7.30999i −0.781179 + 0.284326i −0.701664 0.712508i \(-0.747559\pi\)
−0.0795146 + 0.996834i \(0.525337\pi\)
\(662\) −3.63400 1.69456i −0.141239 0.0658610i
\(663\) 7.82679 + 47.7199i 0.303967 + 1.85329i
\(664\) 1.10317 0.194519i 0.0428114 0.00754881i
\(665\) 16.3891 + 28.7943i 0.635541 + 1.11660i
\(666\) −1.18950 + 5.91467i −0.0460923 + 0.229189i
\(667\) 2.92840 + 0.784663i 0.113388 + 0.0303823i
\(668\) 0.693053 7.92163i 0.0268150 0.306497i
\(669\) 4.82522 + 18.9102i 0.186554 + 0.731110i
\(670\) 9.36938 0.761664i 0.361971 0.0294256i
\(671\) −7.91433 + 9.43193i −0.305529 + 0.364116i
\(672\) −4.50017 + 5.23460i −0.173598 + 0.201929i
\(673\) 11.8117 + 25.3302i 0.455307 + 0.976409i 0.991231 + 0.132142i \(0.0421856\pi\)
−0.535924 + 0.844266i \(0.680037\pi\)
\(674\) 24.4891 0.943285
\(675\) 23.9574 + 10.0519i 0.922123 + 0.386898i
\(676\) −35.1864 −1.35332
\(677\) −15.9845 34.2788i −0.614333 1.31744i −0.929646 0.368453i \(-0.879887\pi\)
0.315313 0.948988i \(-0.397890\pi\)
\(678\) −19.3118 3.64396i −0.741665 0.139945i
\(679\) −26.6546 + 31.7657i −1.02291 + 1.21905i
\(680\) 8.96387 0.728699i 0.343749 0.0279443i
\(681\) 2.99639 + 0.841432i 0.114822 + 0.0322438i
\(682\) −0.185391 + 2.11902i −0.00709897 + 0.0811416i
\(683\) 17.3808 + 4.65718i 0.665059 + 0.178202i 0.575528 0.817782i \(-0.304796\pi\)
0.0895311 + 0.995984i \(0.471463\pi\)
\(684\) −5.34387 9.78960i −0.204328 0.374315i
\(685\) −0.237543 0.417345i −0.00907606 0.0159459i
\(686\) −7.39538 + 1.30401i −0.282357 + 0.0497872i
\(687\) 15.0355 12.3127i 0.573640 0.469760i
\(688\) 1.21926 + 0.568549i 0.0464837 + 0.0216757i
\(689\) −19.6751 + 7.16116i −0.749562 + 0.272818i
\(690\) 1.12893 1.55167i 0.0429776 0.0590711i
\(691\) 3.48622 + 19.7713i 0.132622 + 0.752137i 0.976486 + 0.215580i \(0.0691642\pi\)
−0.843864 + 0.536557i \(0.819725\pi\)
\(692\) 20.3182 5.44426i 0.772383 0.206960i
\(693\) −11.3832 11.9415i −0.432412 0.453619i
\(694\) 1.27050 0.733522i 0.0482274 0.0278441i
\(695\) −10.8104 + 15.2384i −0.410061 + 0.578027i
\(696\) 2.86537 10.2038i 0.108612 0.386772i
\(697\) 19.3687 + 27.6614i 0.733642 + 1.04775i
\(698\) 3.85049 0.336874i 0.145743 0.0127509i
\(699\) 11.5279 7.86808i 0.436027 0.297598i
\(700\) 16.1818 + 11.6299i 0.611614 + 0.439569i
\(701\) 13.6300i 0.514800i 0.966305 + 0.257400i \(0.0828657\pi\)
−0.966305 + 0.257400i \(0.917134\pi\)
\(702\) 19.1443 30.5700i 0.722557 1.15379i
\(703\) −5.28665 5.28665i −0.199390 0.199390i
\(704\) −1.29660 0.471924i −0.0488675 0.0177863i
\(705\) 10.1082 + 29.4198i 0.380697 + 1.10801i
\(706\) 1.29081 + 1.08312i 0.0485802 + 0.0407637i
\(707\) 44.7800 31.3553i 1.68413 1.17924i
\(708\) −2.27731 + 3.83763i −0.0855865 + 0.144227i
\(709\) 7.94365 + 9.46687i 0.298330 + 0.355536i 0.894298 0.447473i \(-0.147676\pi\)
−0.595968 + 0.803008i \(0.703231\pi\)
\(710\) −0.174684 + 28.3947i −0.00655578 + 1.06564i
\(711\) −3.64765 10.8207i −0.136798 0.405809i
\(712\) 2.03948 + 7.61144i 0.0764327 + 0.285251i
\(713\) 0.625664 + 0.438095i 0.0234313 + 0.0164068i
\(714\) −22.5509 16.1958i −0.843946 0.606114i
\(715\) −21.0688 3.84879i −0.787929 0.143937i
\(716\) −4.02318 11.0536i −0.150353 0.413092i
\(717\) 5.94048 15.7330i 0.221851 0.587561i
\(718\) 1.65466 2.36309i 0.0617512 0.0881899i
\(719\) 13.8540 23.9958i 0.516666 0.894891i −0.483147 0.875539i \(-0.660506\pi\)
0.999813 0.0193519i \(-0.00616029\pi\)
\(720\) −5.37682 4.01121i −0.200382 0.149489i
\(721\) −37.6385 65.1917i −1.40173 2.42787i
\(722\) −5.15881 0.451338i −0.191991 0.0167970i
\(723\) 0.146943 12.2803i 0.00546486 0.456709i
\(724\) −10.8983 1.92166i −0.405032 0.0714180i
\(725\) −30.0626 5.68308i −1.11650 0.211064i
\(726\) −6.82869 + 14.1981i −0.253436 + 0.526942i
\(727\) −16.8057 + 7.83664i −0.623290 + 0.290645i −0.708492 0.705719i \(-0.750624\pi\)
0.0852018 + 0.996364i \(0.472846\pi\)
\(728\) 19.5628 19.5628i 0.725044 0.725044i
\(729\) 11.7880 + 24.2908i 0.436593 + 0.899659i
\(730\) −17.2272 + 4.50262i −0.637609 + 0.166649i
\(731\) −1.85060 + 5.08447i −0.0684468 + 0.188056i
\(732\) 14.5857 5.11198i 0.539105 0.188944i
\(733\) −4.35514 49.7795i −0.160861 1.83865i −0.464160 0.885751i \(-0.653644\pi\)
0.303299 0.952895i \(-0.401912\pi\)
\(734\) −4.14480 + 23.5063i −0.152987 + 0.867634i
\(735\) −8.30197 33.3918i −0.306223 1.23167i
\(736\) −0.379542 + 0.318473i −0.0139901 + 0.0117391i
\(737\) 1.50132 5.60300i 0.0553018 0.206389i
\(738\) 2.79503 25.0322i 0.102887 0.921448i
\(739\) −25.8007 14.8961i −0.949095 0.547960i −0.0562951 0.998414i \(-0.517929\pi\)
−0.892800 + 0.450454i \(0.851262\pi\)
\(740\) −4.21607 1.56396i −0.154986 0.0574924i
\(741\) 18.4047 + 40.7344i 0.676112 + 1.49642i
\(742\) 5.08042 10.8950i 0.186508 0.399968i
\(743\) −10.8490 + 23.2658i −0.398011 + 0.853538i 0.600533 + 0.799600i \(0.294955\pi\)
−0.998544 + 0.0539380i \(0.982823\pi\)
\(744\) 1.55758 2.16876i 0.0571037 0.0795105i
\(745\) 14.7749 6.77931i 0.541311 0.248375i
\(746\) −20.8836 12.0571i −0.764602 0.441443i
\(747\) 1.49271 3.01086i 0.0546154 0.110162i
\(748\) 1.43634 5.36050i 0.0525179 0.195999i
\(749\) −42.5290 + 35.6861i −1.55398 + 1.30394i
\(750\) −10.1881 + 16.4682i −0.372016 + 0.601335i
\(751\) 3.03368 17.2049i 0.110701 0.627814i −0.878089 0.478498i \(-0.841182\pi\)
0.988789 0.149317i \(-0.0477073\pi\)
\(752\) −0.700036 8.00145i −0.0255277 0.291783i
\(753\) −6.34711 5.45659i −0.231301 0.198849i
\(754\) −14.5277 + 39.9144i −0.529066 + 1.45360i
\(755\) −9.04095 34.5911i −0.329034 1.25890i
\(756\) 4.63861 + 20.1831i 0.168705 + 0.734051i
\(757\) 0.867061 0.867061i 0.0315139 0.0315139i −0.691174 0.722688i \(-0.742906\pi\)
0.722688 + 0.691174i \(0.242906\pi\)
\(758\) 24.0835 11.2303i 0.874752 0.407903i
\(759\) −0.667516 0.978012i −0.0242293 0.0354996i
\(760\) 7.82909 2.79513i 0.283991 0.101390i
\(761\) −21.0273 3.70768i −0.762239 0.134403i −0.221002 0.975273i \(-0.570933\pi\)
−0.541237 + 0.840870i \(0.682044\pi\)
\(762\) 21.9901 12.3476i 0.796617 0.447305i
\(763\) −61.6683 5.39528i −2.23254 0.195322i
\(764\) 8.64430 + 14.9724i 0.312740 + 0.541681i
\(765\) 14.1868 22.9493i 0.512926 0.829734i
\(766\) 9.25649 16.0327i 0.334450 0.579285i
\(767\) 10.2581 14.6501i 0.370399 0.528984i
\(768\) 1.09739 + 1.34005i 0.0395985 + 0.0483550i
\(769\) 6.04624 + 16.6119i 0.218033 + 0.599041i 0.999696 0.0246605i \(-0.00785048\pi\)
−0.781663 + 0.623701i \(0.785628\pi\)
\(770\) 10.1161 6.99100i 0.364558 0.251938i
\(771\) −0.817908 + 8.21534i −0.0294562 + 0.295868i
\(772\) −1.27621 0.893609i −0.0459316 0.0321617i
\(773\) 9.71674 + 36.2634i 0.349487 + 1.30430i 0.887282 + 0.461227i \(0.152591\pi\)
−0.537795 + 0.843075i \(0.680743\pi\)
\(774\) 3.54248 1.93374i 0.127332 0.0695068i
\(775\) −6.62739 3.93583i −0.238063 0.141379i
\(776\) 6.68788 + 7.97031i 0.240081 + 0.286117i
\(777\) 6.79681 + 12.1046i 0.243834 + 0.434251i
\(778\) −5.53202 + 3.87356i −0.198333 + 0.138874i
\(779\) 23.9111 + 20.0638i 0.856704 + 0.718860i
\(780\) 20.2786 + 17.6515i 0.726089 + 0.632026i
\(781\) 16.4652 + 5.99285i 0.589172 + 0.214441i
\(782\) −1.40907 1.40907i −0.0503881 0.0503881i
\(783\) −19.5504 25.0744i −0.698673 0.896086i
\(784\) 8.88420i 0.317293i
\(785\) 19.6445 + 23.7061i 0.701143 + 0.846106i
\(786\) −2.73978 36.3155i −0.0977247 1.29533i
\(787\) 1.93066 0.168911i 0.0688205 0.00602102i −0.0526935 0.998611i \(-0.516781\pi\)
0.121514 + 0.992590i \(0.461225\pi\)
\(788\) −3.40612 4.86444i −0.121338 0.173288i
\(789\) −13.4494 + 3.43182i −0.478811 + 0.122176i
\(790\) 8.39085 1.42637i 0.298533 0.0507478i
\(791\) −39.1627 + 22.6106i −1.39246 + 0.803940i
\(792\) −3.44668 + 2.29247i −0.122472 + 0.0814594i
\(793\) −59.8318 + 16.0319i −2.12469 + 0.569309i
\(794\) −3.76763 21.3673i −0.133708 0.758297i
\(795\) 10.9032 + 4.19367i 0.386698 + 0.148734i
\(796\) −1.92106 + 0.699207i −0.0680900 + 0.0247827i
\(797\) 44.4514 + 20.7280i 1.57455 + 0.734225i 0.996642 0.0818766i \(-0.0260913\pi\)
0.577908 + 0.816102i \(0.303869\pi\)
\(798\) −24.0093 9.06545i −0.849920 0.320913i
\(799\) 31.8139 5.60965i 1.12549 0.198455i
\(800\) 3.57877 3.49177i 0.126528 0.123453i
\(801\) 22.0143 + 8.61452i 0.777839 + 0.304379i
\(802\) 19.1138 + 5.12153i 0.674932 + 0.180848i
\(803\) −0.957628 + 10.9457i −0.0337939 + 0.386267i
\(804\) −5.20998 + 5.08678i −0.183742 + 0.179397i
\(805\) −0.357763 4.40091i −0.0126095 0.155112i
\(806\) −6.87861 + 8.19761i −0.242289 + 0.288749i
\(807\) 1.17000 + 3.33830i 0.0411860 + 0.117514i
\(808\) −5.79676 12.4312i −0.203929 0.437328i
\(809\) −7.77851 −0.273478 −0.136739 0.990607i \(-0.543662\pi\)
−0.136739 + 0.990607i \(0.543662\pi\)
\(810\) −19.2550 + 5.85205i −0.676550 + 0.205620i
\(811\) −23.3881 −0.821267 −0.410634 0.911800i \(-0.634692\pi\)
−0.410634 + 0.911800i \(0.634692\pi\)
\(812\) −10.3065 22.1024i −0.361688 0.775643i
\(813\) −11.8324 33.7606i −0.414979 1.18404i
\(814\) −1.78364 + 2.12566i −0.0625165 + 0.0745043i
\(815\) −33.5402 28.4970i −1.17486 0.998206i
\(816\) −4.98450 + 4.86662i −0.174492 + 0.170366i
\(817\) −0.435906 + 4.98243i −0.0152504 + 0.174313i
\(818\) 15.3259 + 4.10657i 0.535859 + 0.143583i
\(819\) −12.4525 82.0583i −0.435125 2.86735i
\(820\) 18.1039 + 4.97050i 0.632216 + 0.173577i
\(821\) −1.35556 + 0.239021i −0.0473093 + 0.00834190i −0.197253 0.980353i \(-0.563202\pi\)
0.149943 + 0.988695i \(0.452091\pi\)
\(822\) 0.347991 + 0.131395i 0.0121376 + 0.00458291i
\(823\) 9.75163 + 4.54726i 0.339920 + 0.158507i 0.585081 0.810975i \(-0.301063\pi\)
−0.245160 + 0.969483i \(0.578841\pi\)
\(824\) −17.7486 + 6.45998i −0.618303 + 0.225044i
\(825\) 7.45663 + 9.33758i 0.259606 + 0.325093i
\(826\) 1.78306 + 10.1122i 0.0620406 + 0.351850i
\(827\) 20.8152 5.57741i 0.723815 0.193946i 0.121942 0.992537i \(-0.461088\pi\)
0.601873 + 0.798592i \(0.294421\pi\)
\(828\) 0.0940779 + 1.48339i 0.00326943 + 0.0515513i
\(829\) 33.7715 19.4980i 1.17293 0.677192i 0.218563 0.975823i \(-0.429863\pi\)
0.954369 + 0.298631i \(0.0965298\pi\)
\(830\) 2.04295 + 1.44930i 0.0709120 + 0.0503060i
\(831\) 30.4150 7.76086i 1.05509 0.269221i
\(832\) −3.98156 5.68626i −0.138036 0.197136i
\(833\) −35.5962 + 3.11426i −1.23333 + 0.107903i
\(834\) −1.08874 14.4312i −0.0377002 0.499711i
\(835\) 13.6911 11.3454i 0.473799 0.392623i
\(836\) 5.12977i 0.177417i
\(837\) −2.46781 7.62076i −0.0852999 0.263412i
\(838\) 22.0595 + 22.0595i 0.762034 + 0.762034i
\(839\) −13.7227 4.99464i −0.473759 0.172434i 0.0940957 0.995563i \(-0.470004\pi\)
−0.567854 + 0.823129i \(0.692226\pi\)
\(840\) −15.3989 + 1.06652i −0.531312 + 0.0367985i
\(841\) 6.46718 + 5.42661i 0.223006 + 0.187124i
\(842\) 24.9195 17.4488i 0.858784 0.601327i
\(843\) −15.5892 27.7632i −0.536920 0.956215i
\(844\) −5.35355 6.38012i −0.184277 0.219613i
\(845\) −55.2913 55.9759i −1.90208 1.92563i
\(846\) −20.5735 12.5439i −0.707333 0.431268i
\(847\) 9.38285 + 35.0173i 0.322398 + 1.20321i
\(848\) −2.47078 1.73006i −0.0848468 0.0594104i
\(849\) 4.32563 43.4480i 0.148455 1.49113i
\(850\) 15.2449 + 13.1150i 0.522896 + 0.449840i
\(851\) 0.340781 + 0.936289i 0.0116818 + 0.0320956i
\(852\) −13.9354 17.0170i −0.477420 0.582993i
\(853\) −4.31796 + 6.16668i −0.147844 + 0.211143i −0.886243 0.463221i \(-0.846693\pi\)
0.738399 + 0.674365i \(0.235582\pi\)
\(854\) 17.7819 30.7992i 0.608485 1.05393i
\(855\) 7.17639 23.8844i 0.245427 0.816830i
\(856\) 6.96496 + 12.0637i 0.238057 + 0.412327i
\(857\) −14.8296 1.29742i −0.506568 0.0443190i −0.168992 0.985617i \(-0.554051\pi\)
−0.337576 + 0.941298i \(0.609607\pi\)
\(858\) 14.4655 8.12246i 0.493844 0.277296i
\(859\) 4.25194 + 0.749731i 0.145074 + 0.0255805i 0.245714 0.969342i \(-0.420978\pi\)
−0.100639 + 0.994923i \(0.532089\pi\)
\(860\) 1.01145 + 2.83304i 0.0344902 + 0.0966060i
\(861\) −32.6728 47.8706i −1.11349 1.63142i
\(862\) −28.3345 + 13.2126i −0.965075 + 0.450022i
\(863\) −8.34154 + 8.34154i −0.283949 + 0.283949i −0.834682 0.550733i \(-0.814348\pi\)
0.550733 + 0.834682i \(0.314348\pi\)
\(864\) 5.18930 0.266814i 0.176543 0.00907719i
\(865\) 40.5886 + 23.7680i 1.38005 + 0.808135i
\(866\) −6.67487 + 18.3390i −0.226821 + 0.623186i
\(867\) 1.08173 + 0.929961i 0.0367375 + 0.0315831i
\(868\) −0.535488 6.12065i −0.0181756 0.207749i
\(869\) 0.912007 5.17225i 0.0309377 0.175456i
\(870\) 20.7351 11.4757i 0.702985 0.389061i
\(871\) 22.3549 18.7580i 0.757466 0.635590i
\(872\) −4.02005 + 15.0030i −0.136136 + 0.508067i
\(873\) 31.1509 1.97562i 1.05430 0.0668646i
\(874\) −1.59519 0.920986i −0.0539582 0.0311528i
\(875\) 6.92648 + 44.0176i 0.234158 + 1.48807i
\(876\) 8.04562 11.2026i 0.271836 0.378502i
\(877\) −6.00372 + 12.8750i −0.202731 + 0.434759i −0.981218 0.192903i \(-0.938210\pi\)
0.778487 + 0.627661i \(0.215988\pi\)
\(878\) −2.92131 + 6.26478i −0.0985896 + 0.211426i
\(879\) 8.95412 + 19.8179i 0.302015 + 0.668440i
\(880\) −1.28670 2.80425i −0.0433747 0.0945314i
\(881\) 17.1342 + 9.89241i 0.577264 + 0.333284i 0.760045 0.649870i \(-0.225177\pi\)
−0.182781 + 0.983154i \(0.558510\pi\)
\(882\) 21.4605 + 15.8053i 0.722612 + 0.532193i
\(883\) −8.82448 + 32.9334i −0.296967 + 1.10830i 0.642675 + 0.766139i \(0.277825\pi\)
−0.939642 + 0.342158i \(0.888842\pi\)
\(884\) 21.3874 17.9461i 0.719335 0.603594i
\(885\) −9.68356 + 2.40756i −0.325509 + 0.0809291i
\(886\) −0.258597 + 1.46657i −0.00868773 + 0.0492705i
\(887\) 3.43553 + 39.2682i 0.115354 + 1.31850i 0.804533 + 0.593908i \(0.202416\pi\)
−0.689180 + 0.724591i \(0.742029\pi\)
\(888\) 3.28716 1.15208i 0.110310 0.0386612i
\(889\) 19.8477 54.5312i 0.665672 1.82892i
\(890\) −8.90375 + 15.2050i −0.298454 + 0.509671i
\(891\) −0.594124 + 12.4041i −0.0199039 + 0.415553i
\(892\) 7.96741 7.96741i 0.266769 0.266769i
\(893\) 27.0631 12.6197i 0.905632 0.422303i
\(894\) −5.45770 + 11.3476i −0.182533 + 0.379520i
\(895\) 11.2625 23.7696i 0.376464 0.794531i
\(896\) 3.92495 + 0.692075i 0.131123 + 0.0231206i
\(897\) 0.0712751 5.95659i 0.00237981 0.198885i
\(898\) −24.9636 2.18404i −0.833047 0.0728822i
\(899\) 4.71653 + 8.16926i 0.157305 + 0.272460i
\(900\) −2.06787 14.8568i −0.0689291 0.495226i
\(901\) 6.06569 10.5061i 0.202077 0.350008i
\(902\) 6.64478 9.48973i 0.221247 0.315973i
\(903\) 3.28043 8.68804i 0.109166 0.289120i
\(904\) 3.88071 + 10.6622i 0.129070 + 0.354618i
\(905\) −14.0683 20.3571i −0.467647 0.676691i
\(906\) 22.4941 + 16.1550i 0.747316 + 0.536715i
\(907\) −26.0320 18.2278i −0.864378 0.605244i 0.0550582 0.998483i \(-0.482466\pi\)
−0.919436 + 0.393239i \(0.871354\pi\)
\(908\) −0.465067 1.73566i −0.0154338 0.0575997i
\(909\) −40.3412 8.11304i −1.33803 0.269093i
\(910\) 61.8617 + 0.380573i 2.05070 + 0.0126159i
\(911\) 22.3307 + 26.6127i 0.739850 + 0.881719i 0.996397 0.0848128i \(-0.0270292\pi\)
−0.256547 + 0.966532i \(0.582585\pi\)
\(912\) −3.28614 + 5.53767i −0.108815 + 0.183370i
\(913\) 1.26613 0.886552i 0.0419027 0.0293406i
\(914\) −20.7363 17.3998i −0.685895 0.575534i
\(915\) 31.0521 + 15.1706i 1.02655 + 0.501526i
\(916\) −10.5434 3.83749i −0.348364 0.126794i
\(917\) −59.2558 59.2558i −1.95680 1.95680i
\(918\) 2.88809 + 20.6983i 0.0953212 + 0.683147i
\(919\) 42.9427i 1.41655i 0.705937 + 0.708275i \(0.250526\pi\)
−0.705937 + 0.708275i \(0.749474\pi\)
\(920\) −1.10304 0.103345i −0.0363663 0.00340720i
\(921\) −3.49215 + 2.38347i −0.115070 + 0.0785381i
\(922\) −11.5138 + 1.00732i −0.379186 + 0.0331744i
\(923\) 50.5609 + 72.2085i 1.66423 + 2.37677i
\(924\) −2.57515 + 9.17027i −0.0847163 + 0.301680i
\(925\) −4.13705 9.16466i −0.136025 0.301332i
\(926\) 8.14491 4.70246i 0.267658 0.154533i
\(927\) −15.9709 + 54.3658i −0.524554 + 1.78561i
\(928\) −5.91051 + 1.58372i −0.194022 + 0.0519881i
\(929\) −6.54454 37.1159i −0.214719 1.21773i −0.881393 0.472385i \(-0.843393\pi\)
0.666673 0.745350i \(-0.267718\pi\)
\(930\) 5.89769 0.930090i 0.193393 0.0304989i
\(931\) −31.0371 + 11.2966i −1.01720 + 0.370231i
\(932\) −7.30314 3.40551i −0.239222 0.111551i
\(933\) −2.66085 + 2.17900i −0.0871122 + 0.0713372i
\(934\) 8.37233 1.47627i 0.273951 0.0483050i
\(935\) 10.7847 6.13841i 0.352698 0.200748i
\(936\) −20.8190 0.498301i −0.680489 0.0162875i
\(937\) −34.0800 9.13172i −1.11335 0.298320i −0.345158 0.938545i \(-0.612175\pi\)
−0.768188 + 0.640224i \(0.778841\pi\)
\(938\) −1.46028 + 16.6910i −0.0476797 + 0.544981i
\(939\) 30.5745 + 8.58579i 0.997761 + 0.280187i
\(940\) 11.6290 13.6870i 0.379295 0.446420i
\(941\) −4.79884 + 5.71903i −0.156438 + 0.186435i −0.838570 0.544793i \(-0.816608\pi\)
0.682133 + 0.731228i \(0.261053\pi\)
\(942\) −23.4345 4.42188i −0.763539 0.144073i
\(943\) −1.75801 3.77007i −0.0572488 0.122770i
\(944\) 2.57640 0.0838547
\(945\) −24.8189 + 39.0946i −0.807360 + 1.27175i
\(946\) 1.85627 0.0603524
\(947\) 19.4134 + 41.6322i 0.630851 + 1.35286i 0.918611 + 0.395162i \(0.129312\pi\)
−0.287760 + 0.957703i \(0.592911\pi\)
\(948\) −4.29787 + 4.99929i −0.139588 + 0.162369i
\(949\) −35.5312 + 42.3444i −1.15339 + 1.37456i
\(950\) 16.7491 + 8.06258i 0.543412 + 0.261584i
\(951\) −0.978989 3.83669i −0.0317459 0.124413i
\(952\) −1.39707 + 15.9686i −0.0452794 + 0.517546i
\(953\) 54.0330 + 14.4781i 1.75030 + 0.468992i 0.984690 0.174312i \(-0.0557701\pi\)
0.765611 + 0.643304i \(0.222437\pi\)
\(954\) −8.57470 + 2.89052i −0.277616 + 0.0935840i
\(955\) −10.2351 + 37.2790i −0.331199 + 1.20632i
\(956\) −9.56189 + 1.68602i −0.309254 + 0.0545298i
\(957\) −2.36691 14.4311i −0.0765115 0.466490i
\(958\) −15.5248 7.23935i −0.501584 0.233893i
\(959\) 0.804297 0.292740i 0.0259721 0.00945308i
\(960\) −0.407394 + 3.85150i −0.0131486 + 0.124307i
\(961\) −4.97041 28.1886i −0.160336 0.909310i
\(962\) −13.4842 + 3.61308i −0.434748 + 0.116490i
\(963\) 41.5316 + 4.63732i 1.33834 + 0.149435i
\(964\) −6.14058 + 3.54527i −0.197775 + 0.114185i
\(965\) −0.583821 3.43443i −0.0187939 0.110558i
\(966\) 2.38932 + 2.44720i 0.0768752 + 0.0787372i
\(967\) 14.3690 + 20.5211i 0.462076 + 0.659914i 0.980797 0.195030i \(-0.0624805\pi\)
−0.518721 + 0.854944i \(0.673592\pi\)
\(968\) 9.06150 0.792778i 0.291248 0.0254809i
\(969\) −23.3396 11.2253i −0.749776 0.360610i
\(970\) −2.17023 + 23.1637i −0.0696820 + 0.743742i
\(971\) 23.4434i 0.752336i −0.926551 0.376168i \(-0.877242\pi\)
0.926551 0.376168i \(-0.122758\pi\)
\(972\) 8.58745 13.0098i 0.275443 0.417290i
\(973\) −23.5473 23.5473i −0.754892 0.754892i
\(974\) 32.9053 + 11.9766i 1.05435 + 0.383753i
\(975\) 3.78468 + 59.9972i 0.121207 + 1.92145i
\(976\) −6.83565 5.73579i −0.218804 0.183598i
\(977\) −27.4981 + 19.2543i −0.879741 + 0.616001i −0.923736 0.383031i \(-0.874880\pi\)
0.0439949 + 0.999032i \(0.485991\pi\)
\(978\) 34.0888 + 0.407898i 1.09004 + 0.0130431i
\(979\) 6.98894 + 8.32909i 0.223368 + 0.266199i
\(980\) −14.1333 + 13.9605i −0.451472 + 0.445951i
\(981\) 29.0892 + 36.4017i 0.928746 + 1.16222i
\(982\) 6.53205 + 24.3779i 0.208446 + 0.777931i
\(983\) −11.1543 7.81033i −0.355767 0.249111i 0.382006 0.924160i \(-0.375234\pi\)
−0.737773 + 0.675049i \(0.764122\pi\)
\(984\) −13.2523 + 5.98765i −0.422467 + 0.190879i
\(985\) 2.38621 13.0625i 0.0760311 0.416205i
\(986\) −8.41732 23.1264i −0.268062 0.736495i
\(987\) −54.7146 + 8.97403i −1.74159 + 0.285647i
\(988\) 14.8024 21.1400i 0.470926 0.672552i
\(989\) 0.333269 0.577239i 0.0105973 0.0183551i
\(990\) −9.06299 1.88075i −0.288041 0.0597741i
\(991\) 16.5679 + 28.6964i 0.526296 + 0.911571i 0.999531 + 0.0306346i \(0.00975283\pi\)
−0.473235 + 0.880936i \(0.656914\pi\)
\(992\) −1.53573 0.134359i −0.0487595 0.00426590i
\(993\) 5.97254 + 3.54420i 0.189533 + 0.112472i
\(994\) −49.8420 8.78849i −1.58089 0.278754i
\(995\) −4.13104 1.95736i −0.130963 0.0620526i
\(996\) −1.93473 + 0.145964i −0.0613043 + 0.00462503i
\(997\) −7.54880 + 3.52006i −0.239073 + 0.111481i −0.538463 0.842649i \(-0.680995\pi\)
0.299390 + 0.954131i \(0.403217\pi\)
\(998\) 11.2259 11.2259i 0.355350 0.355350i
\(999\) 3.06505 9.98999i 0.0969740 0.316069i
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 270.2.r.a.23.13 216
3.2 odd 2 810.2.s.a.503.9 216
5.2 odd 4 inner 270.2.r.a.77.1 yes 216
15.2 even 4 810.2.s.a.17.18 216
27.7 even 9 810.2.s.a.143.18 216
27.20 odd 18 inner 270.2.r.a.263.1 yes 216
135.7 odd 36 810.2.s.a.467.9 216
135.47 even 36 inner 270.2.r.a.47.13 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.2.r.a.23.13 216 1.1 even 1 trivial
270.2.r.a.47.13 yes 216 135.47 even 36 inner
270.2.r.a.77.1 yes 216 5.2 odd 4 inner
270.2.r.a.263.1 yes 216 27.20 odd 18 inner
810.2.s.a.17.18 216 15.2 even 4
810.2.s.a.143.18 216 27.7 even 9
810.2.s.a.467.9 216 135.7 odd 36
810.2.s.a.503.9 216 3.2 odd 2