Properties

Label 27.3.f.a.14.5
Level $27$
Weight $3$
Character 27.14
Analytic conductor $0.736$
Analytic rank $0$
Dimension $30$
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] = [27,3,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.735696713773\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 14.5
Character \(\chi\) \(=\) 27.14
Dual form 27.3.f.a.2.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.58003 - 0.454929i) q^{2} +(-2.92175 + 0.680712i) q^{3} +(2.69082 - 0.979377i) q^{4} +(0.519123 - 0.618667i) q^{5} +(-7.22853 + 3.08544i) q^{6} +(-5.56035 - 2.02380i) q^{7} +(-2.57852 + 1.48871i) q^{8} +(8.07326 - 3.97774i) q^{9} +O(q^{10})\) \(q+(2.58003 - 0.454929i) q^{2} +(-2.92175 + 0.680712i) q^{3} +(2.69082 - 0.979377i) q^{4} +(0.519123 - 0.618667i) q^{5} +(-7.22853 + 3.08544i) q^{6} +(-5.56035 - 2.02380i) q^{7} +(-2.57852 + 1.48871i) q^{8} +(8.07326 - 3.97774i) q^{9} +(1.05790 - 1.83234i) q^{10} +(12.1979 + 14.5368i) q^{11} +(-7.19523 + 4.69317i) q^{12} +(3.42641 - 19.4321i) q^{13} +(-15.2665 - 2.69190i) q^{14} +(-1.09562 + 2.16096i) q^{15} +(-14.7497 + 12.3765i) q^{16} +(4.04738 + 2.33676i) q^{17} +(19.0197 - 13.9354i) q^{18} +(-4.96228 - 8.59492i) q^{19} +(0.790957 - 2.17314i) q^{20} +(17.6236 + 2.12805i) q^{21} +(38.0840 + 31.9563i) q^{22} +(-4.36717 - 11.9987i) q^{23} +(6.52041 - 6.10486i) q^{24} +(4.22794 + 23.9779i) q^{25} -51.6943i q^{26} +(-20.8804 + 17.1175i) q^{27} -16.9439 q^{28} +(-5.94796 + 1.04879i) q^{29} +(-1.84363 + 6.07378i) q^{30} +(-34.4136 + 12.5255i) q^{31} +(-24.7688 + 29.5183i) q^{32} +(-45.5345 - 34.1698i) q^{33} +(11.5054 + 4.18763i) q^{34} +(-4.13856 + 2.38940i) q^{35} +(17.8280 - 18.6101i) q^{36} +(9.43563 - 16.3430i) q^{37} +(-16.7129 - 19.9177i) q^{38} +(3.21657 + 59.1083i) q^{39} +(-0.417554 + 2.36807i) q^{40} +(21.6826 + 3.82322i) q^{41} +(46.4374 - 2.52704i) q^{42} +(26.6242 - 22.3404i) q^{43} +(47.0593 + 27.1697i) q^{44} +(1.73012 - 7.05960i) q^{45} +(-16.7260 - 28.9703i) q^{46} +(-9.90463 + 27.2128i) q^{47} +(34.6701 - 46.2012i) q^{48} +(-10.7145 - 8.99053i) q^{49} +(21.8164 + 59.9402i) q^{50} +(-13.4161 - 4.07232i) q^{51} +(-9.81156 - 55.6441i) q^{52} -19.9708i q^{53} +(-46.0847 + 53.6628i) q^{54} +15.3257 q^{55} +(17.3503 - 3.05933i) q^{56} +(20.3492 + 21.7343i) q^{57} +(-14.8688 + 5.41180i) q^{58} +(38.4471 - 45.8195i) q^{59} +(-0.831700 + 6.88778i) q^{60} +(13.9494 + 5.07718i) q^{61} +(-83.0898 + 47.9719i) q^{62} +(-52.9403 + 5.77895i) q^{63} +(-11.9669 + 20.7272i) q^{64} +(-10.2433 - 12.2075i) q^{65} +(-133.025 - 67.4441i) q^{66} +(10.1402 - 57.5078i) q^{67} +(13.1793 + 2.32387i) q^{68} +(20.9275 + 32.0845i) q^{69} +(-9.59061 + 8.04747i) q^{70} +(72.4603 + 41.8350i) q^{71} +(-14.8954 + 22.2754i) q^{72} +(57.2344 + 99.1330i) q^{73} +(16.9093 - 46.4579i) q^{74} +(-28.6750 - 67.1793i) q^{75} +(-21.7703 - 18.2674i) q^{76} +(-38.4046 - 105.516i) q^{77} +(35.1889 + 151.038i) q^{78} +(4.96527 + 28.1594i) q^{79} +15.5501i q^{80} +(49.3551 - 64.2267i) q^{81} +57.6809 q^{82} +(-22.9583 + 4.04818i) q^{83} +(49.5060 - 11.5339i) q^{84} +(3.54676 - 1.29092i) q^{85} +(58.5279 - 69.7509i) q^{86} +(16.6645 - 7.11314i) q^{87} +(-53.0935 - 19.3244i) q^{88} +(-121.389 + 70.0840i) q^{89} +(1.25215 - 19.0010i) q^{90} +(-58.3788 + 101.115i) q^{91} +(-23.5025 - 28.0092i) q^{92} +(92.0217 - 60.0222i) q^{93} +(-13.1744 + 74.7156i) q^{94} +(-7.89343 - 1.39182i) q^{95} +(52.2749 - 103.106i) q^{96} +(50.5839 - 42.4449i) q^{97} +(-31.7338 - 18.3215i) q^{98} +(156.300 + 68.8398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 15 q^{5} - 18 q^{6} - 6 q^{7} - 9 q^{8} - 3 q^{10} - 6 q^{11} - 15 q^{12} - 6 q^{13} - 15 q^{14} - 9 q^{15} - 18 q^{16} - 9 q^{17} + 63 q^{18} - 3 q^{19} + 213 q^{20} + 132 q^{21} - 42 q^{22} + 120 q^{23} + 144 q^{24} - 15 q^{25} - 90 q^{27} - 12 q^{28} - 168 q^{29} - 243 q^{30} + 39 q^{31} - 360 q^{32} - 207 q^{33} + 54 q^{34} - 252 q^{35} - 360 q^{36} - 3 q^{37} - 84 q^{38} + 15 q^{39} - 33 q^{40} + 228 q^{41} + 486 q^{42} - 96 q^{43} + 639 q^{44} + 477 q^{45} - 3 q^{46} + 399 q^{47} + 453 q^{48} - 78 q^{49} + 303 q^{50} + 36 q^{51} - 9 q^{52} - 54 q^{54} - 12 q^{55} - 393 q^{56} - 192 q^{57} + 129 q^{58} - 474 q^{59} - 846 q^{60} + 138 q^{61} - 900 q^{62} - 585 q^{63} - 51 q^{64} - 411 q^{65} - 423 q^{66} + 354 q^{67} + 99 q^{68} + 99 q^{69} + 489 q^{70} + 315 q^{71} + 720 q^{72} - 66 q^{73} + 321 q^{74} + 255 q^{75} + 258 q^{76} + 201 q^{77} + 180 q^{78} + 30 q^{79} + 36 q^{81} - 12 q^{82} - 33 q^{83} - 588 q^{84} - 261 q^{85} - 258 q^{86} - 279 q^{87} - 642 q^{88} + 72 q^{89} + 288 q^{90} + 96 q^{91} - 3 q^{92} + 591 q^{93} - 861 q^{94} + 681 q^{95} + 270 q^{96} - 582 q^{97} + 882 q^{98} + 513 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58003 0.454929i 1.29001 0.227464i 0.513787 0.857918i \(-0.328242\pi\)
0.776227 + 0.630453i \(0.217131\pi\)
\(3\) −2.92175 + 0.680712i −0.973917 + 0.226904i
\(4\) 2.69082 0.979377i 0.672704 0.244844i
\(5\) 0.519123 0.618667i 0.103825 0.123733i −0.711630 0.702555i \(-0.752043\pi\)
0.815454 + 0.578821i \(0.196487\pi\)
\(6\) −7.22853 + 3.08544i −1.20475 + 0.514241i
\(7\) −5.56035 2.02380i −0.794335 0.289114i −0.0871982 0.996191i \(-0.527791\pi\)
−0.707137 + 0.707077i \(0.750014\pi\)
\(8\) −2.57852 + 1.48871i −0.322315 + 0.186088i
\(9\) 8.07326 3.97774i 0.897029 0.441971i
\(10\) 1.05790 1.83234i 0.105790 0.183234i
\(11\) 12.1979 + 14.5368i 1.10890 + 1.32153i 0.942021 + 0.335553i \(0.108923\pi\)
0.166875 + 0.985978i \(0.446632\pi\)
\(12\) −7.19523 + 4.69317i −0.599602 + 0.391097i
\(13\) 3.42641 19.4321i 0.263570 1.49478i −0.509506 0.860467i \(-0.670172\pi\)
0.773076 0.634313i \(-0.218717\pi\)
\(14\) −15.2665 2.69190i −1.09047 0.192279i
\(15\) −1.09562 + 2.16096i −0.0730410 + 0.144064i
\(16\) −14.7497 + 12.3765i −0.921856 + 0.773529i
\(17\) 4.04738 + 2.33676i 0.238081 + 0.137456i 0.614294 0.789077i \(-0.289441\pi\)
−0.376213 + 0.926533i \(0.622774\pi\)
\(18\) 19.0197 13.9354i 1.05665 0.774191i
\(19\) −4.96228 8.59492i −0.261173 0.452364i 0.705381 0.708828i \(-0.250776\pi\)
−0.966554 + 0.256464i \(0.917443\pi\)
\(20\) 0.790957 2.17314i 0.0395479 0.108657i
\(21\) 17.6236 + 2.12805i 0.839218 + 0.101336i
\(22\) 38.0840 + 31.9563i 1.73109 + 1.45256i
\(23\) −4.36717 11.9987i −0.189877 0.521683i 0.807826 0.589421i \(-0.200644\pi\)
−0.997703 + 0.0677380i \(0.978422\pi\)
\(24\) 6.52041 6.10486i 0.271684 0.254369i
\(25\) 4.22794 + 23.9779i 0.169118 + 0.959115i
\(26\) 51.6943i 1.98824i
\(27\) −20.8804 + 17.1175i −0.773347 + 0.633983i
\(28\) −16.9439 −0.605141
\(29\) −5.94796 + 1.04879i −0.205102 + 0.0361650i −0.275255 0.961371i \(-0.588762\pi\)
0.0701531 + 0.997536i \(0.477651\pi\)
\(30\) −1.84363 + 6.07378i −0.0614545 + 0.202459i
\(31\) −34.4136 + 12.5255i −1.11012 + 0.404049i −0.831036 0.556219i \(-0.812252\pi\)
−0.279080 + 0.960268i \(0.590029\pi\)
\(32\) −24.7688 + 29.5183i −0.774026 + 0.922448i
\(33\) −45.5345 34.1698i −1.37983 1.03545i
\(34\) 11.5054 + 4.18763i 0.338394 + 0.123165i
\(35\) −4.13856 + 2.38940i −0.118245 + 0.0682686i
\(36\) 17.8280 18.6101i 0.495221 0.516949i
\(37\) 9.43563 16.3430i 0.255017 0.441702i −0.709883 0.704319i \(-0.751252\pi\)
0.964900 + 0.262617i \(0.0845856\pi\)
\(38\) −16.7129 19.9177i −0.439813 0.524149i
\(39\) 3.21657 + 59.1083i 0.0824761 + 1.51560i
\(40\) −0.417554 + 2.36807i −0.0104388 + 0.0592017i
\(41\) 21.6826 + 3.82322i 0.528843 + 0.0932493i 0.431693 0.902021i \(-0.357916\pi\)
0.0971497 + 0.995270i \(0.469027\pi\)
\(42\) 46.4374 2.52704i 1.10565 0.0601677i
\(43\) 26.6242 22.3404i 0.619168 0.519543i −0.278374 0.960473i \(-0.589796\pi\)
0.897542 + 0.440929i \(0.145351\pi\)
\(44\) 47.0593 + 27.1697i 1.06953 + 0.617493i
\(45\) 1.73012 7.05960i 0.0384471 0.156880i
\(46\) −16.7260 28.9703i −0.363608 0.629788i
\(47\) −9.90463 + 27.2128i −0.210737 + 0.578995i −0.999356 0.0358875i \(-0.988574\pi\)
0.788619 + 0.614882i \(0.210796\pi\)
\(48\) 34.6701 46.2012i 0.722294 0.962526i
\(49\) −10.7145 8.99053i −0.218663 0.183480i
\(50\) 21.8164 + 59.9402i 0.436329 + 1.19880i
\(51\) −13.4161 4.07232i −0.263061 0.0798494i
\(52\) −9.81156 55.6441i −0.188684 1.07008i
\(53\) 19.9708i 0.376808i −0.982092 0.188404i \(-0.939669\pi\)
0.982092 0.188404i \(-0.0603314\pi\)
\(54\) −46.0847 + 53.6628i −0.853420 + 0.993756i
\(55\) 15.3257 0.278648
\(56\) 17.3503 3.05933i 0.309827 0.0546308i
\(57\) 20.3492 + 21.7343i 0.357004 + 0.381304i
\(58\) −14.8688 + 5.41180i −0.256358 + 0.0933068i
\(59\) 38.4471 45.8195i 0.651646 0.776601i −0.334516 0.942390i \(-0.608573\pi\)
0.986161 + 0.165789i \(0.0530172\pi\)
\(60\) −0.831700 + 6.88778i −0.0138617 + 0.114796i
\(61\) 13.9494 + 5.07718i 0.228679 + 0.0832325i 0.453819 0.891094i \(-0.350061\pi\)
−0.225139 + 0.974327i \(0.572284\pi\)
\(62\) −83.0898 + 47.9719i −1.34016 + 0.773741i
\(63\) −52.9403 + 5.77895i −0.840322 + 0.0917293i
\(64\) −11.9669 + 20.7272i −0.186982 + 0.323863i
\(65\) −10.2433 12.2075i −0.157589 0.187807i
\(66\) −133.025 67.4441i −2.01553 1.02188i
\(67\) 10.1402 57.5078i 0.151346 0.858325i −0.810705 0.585455i \(-0.800916\pi\)
0.962051 0.272870i \(-0.0879729\pi\)
\(68\) 13.1793 + 2.32387i 0.193814 + 0.0341746i
\(69\) 20.9275 + 32.0845i 0.303296 + 0.464992i
\(70\) −9.59061 + 8.04747i −0.137009 + 0.114964i
\(71\) 72.4603 + 41.8350i 1.02057 + 0.589225i 0.914268 0.405109i \(-0.132767\pi\)
0.106299 + 0.994334i \(0.466100\pi\)
\(72\) −14.8954 + 22.2754i −0.206880 + 0.309381i
\(73\) 57.2344 + 99.1330i 0.784033 + 1.35799i 0.929575 + 0.368634i \(0.120174\pi\)
−0.145541 + 0.989352i \(0.546492\pi\)
\(74\) 16.9093 46.4579i 0.228504 0.627810i
\(75\) −28.6750 67.1793i −0.382334 0.895725i
\(76\) −21.7703 18.2674i −0.286451 0.240361i
\(77\) −38.4046 105.516i −0.498762 1.37034i
\(78\) 35.1889 + 151.038i 0.451140 + 1.93638i
\(79\) 4.96527 + 28.1594i 0.0628515 + 0.356449i 0.999972 + 0.00744337i \(0.00236932\pi\)
−0.937121 + 0.349005i \(0.886520\pi\)
\(80\) 15.5501i 0.194376i
\(81\) 49.3551 64.2267i 0.609323 0.792922i
\(82\) 57.6809 0.703426
\(83\) −22.9583 + 4.04818i −0.276607 + 0.0487732i −0.310231 0.950661i \(-0.600406\pi\)
0.0336240 + 0.999435i \(0.489295\pi\)
\(84\) 49.5060 11.5339i 0.589357 0.137309i
\(85\) 3.54676 1.29092i 0.0417266 0.0151872i
\(86\) 58.5279 69.7509i 0.680557 0.811057i
\(87\) 16.6645 7.11314i 0.191546 0.0817602i
\(88\) −53.0935 19.3244i −0.603335 0.219596i
\(89\) −121.389 + 70.0840i −1.36392 + 0.787461i −0.990143 0.140057i \(-0.955271\pi\)
−0.373779 + 0.927518i \(0.621938\pi\)
\(90\) 1.25215 19.0010i 0.0139128 0.211123i
\(91\) −58.3788 + 101.115i −0.641525 + 1.11115i
\(92\) −23.5025 28.0092i −0.255462 0.304448i
\(93\) 92.0217 60.0222i 0.989481 0.645400i
\(94\) −13.1744 + 74.7156i −0.140153 + 0.794847i
\(95\) −7.89343 1.39182i −0.0830887 0.0146508i
\(96\) 52.2749 103.106i 0.544530 1.07402i
\(97\) 50.5839 42.4449i 0.521483 0.437576i −0.343665 0.939092i \(-0.611669\pi\)
0.865149 + 0.501516i \(0.167224\pi\)
\(98\) −31.7338 18.3215i −0.323814 0.186954i
\(99\) 156.300 + 68.8398i 1.57879 + 0.695352i
\(100\) 34.8600 + 60.3793i 0.348600 + 0.603793i
\(101\) −7.92206 + 21.7657i −0.0784363 + 0.215502i −0.972713 0.232013i \(-0.925469\pi\)
0.894276 + 0.447515i \(0.147691\pi\)
\(102\) −36.4665 4.40334i −0.357515 0.0431700i
\(103\) −130.500 109.502i −1.26699 1.06313i −0.994901 0.100858i \(-0.967841\pi\)
−0.272088 0.962272i \(-0.587714\pi\)
\(104\) 20.0937 + 55.2070i 0.193209 + 0.530837i
\(105\) 10.4654 9.79840i 0.0996701 0.0933181i
\(106\) −9.08529 51.5253i −0.0857103 0.486087i
\(107\) 2.15337i 0.0201249i −0.999949 0.0100625i \(-0.996797\pi\)
0.999949 0.0100625i \(-0.00320304\pi\)
\(108\) −39.4207 + 66.5099i −0.365007 + 0.615833i
\(109\) −46.2958 −0.424732 −0.212366 0.977190i \(-0.568117\pi\)
−0.212366 + 0.977190i \(0.568117\pi\)
\(110\) 39.5406 6.97208i 0.359460 0.0633825i
\(111\) −16.4437 + 54.1731i −0.148141 + 0.488046i
\(112\) 107.061 38.9670i 0.955901 0.347919i
\(113\) −78.6830 + 93.7708i −0.696310 + 0.829830i −0.992103 0.125422i \(-0.959972\pi\)
0.295794 + 0.955252i \(0.404416\pi\)
\(114\) 62.3891 + 46.8178i 0.547273 + 0.410682i
\(115\) −9.69030 3.52698i −0.0842635 0.0306694i
\(116\) −14.9777 + 8.64739i −0.129118 + 0.0745465i
\(117\) −49.6337 170.510i −0.424220 1.45735i
\(118\) 78.3500 135.706i 0.663983 1.15005i
\(119\) −17.7757 21.1843i −0.149376 0.178019i
\(120\) −0.391982 7.20313i −0.00326651 0.0600261i
\(121\) −41.5206 + 235.475i −0.343145 + 1.94607i
\(122\) 38.2997 + 6.75327i 0.313932 + 0.0553547i
\(123\) −65.9536 + 3.58908i −0.536208 + 0.0291795i
\(124\) −80.3335 + 67.4078i −0.647851 + 0.543611i
\(125\) 34.5145 + 19.9269i 0.276116 + 0.159415i
\(126\) −133.958 + 38.9939i −1.06316 + 0.309475i
\(127\) −55.7242 96.5172i −0.438773 0.759978i 0.558822 0.829288i \(-0.311254\pi\)
−0.997595 + 0.0693101i \(0.977920\pi\)
\(128\) 31.2715 85.9176i 0.244308 0.671231i
\(129\) −62.5820 + 83.3964i −0.485131 + 0.646484i
\(130\) −31.9815 26.8357i −0.246012 0.206428i
\(131\) 1.28028 + 3.51755i 0.00977316 + 0.0268515i 0.944483 0.328559i \(-0.106563\pi\)
−0.934710 + 0.355411i \(0.884341\pi\)
\(132\) −155.990 47.3492i −1.18174 0.358706i
\(133\) 10.1976 + 57.8334i 0.0766736 + 0.434838i
\(134\) 152.985i 1.14168i
\(135\) −0.249431 + 21.8041i −0.00184764 + 0.161512i
\(136\) −13.9150 −0.102316
\(137\) −191.020 + 33.6820i −1.39431 + 0.245854i −0.819802 0.572648i \(-0.805916\pi\)
−0.574504 + 0.818501i \(0.694805\pi\)
\(138\) 68.5896 + 73.2583i 0.497026 + 0.530857i
\(139\) 138.533 50.4220i 0.996642 0.362748i 0.208353 0.978054i \(-0.433190\pi\)
0.788289 + 0.615306i \(0.210967\pi\)
\(140\) −8.79599 + 10.4827i −0.0628285 + 0.0748761i
\(141\) 10.4148 86.2511i 0.0738640 0.611710i
\(142\) 205.982 + 74.9712i 1.45057 + 0.527966i
\(143\) 324.277 187.221i 2.26767 1.30924i
\(144\) −69.8478 + 158.589i −0.485054 + 1.10131i
\(145\) −2.43888 + 4.22426i −0.0168198 + 0.0291328i
\(146\) 192.765 + 229.728i 1.32031 + 1.57348i
\(147\) 37.4251 + 18.9746i 0.254592 + 0.129079i
\(148\) 9.38360 53.2170i 0.0634027 0.359575i
\(149\) 75.3342 + 13.2835i 0.505599 + 0.0891507i 0.420629 0.907233i \(-0.361809\pi\)
0.0849698 + 0.996384i \(0.472921\pi\)
\(150\) −104.544 160.280i −0.696961 1.06853i
\(151\) 148.499 124.606i 0.983438 0.825202i −0.00116684 0.999999i \(-0.500371\pi\)
0.984604 + 0.174797i \(0.0559270\pi\)
\(152\) 25.5907 + 14.7748i 0.168360 + 0.0972024i
\(153\) 41.9706 + 2.76581i 0.274317 + 0.0180772i
\(154\) −147.087 254.763i −0.955112 1.65430i
\(155\) −10.1158 + 27.7928i −0.0652630 + 0.179309i
\(156\) 66.5445 + 155.899i 0.426567 + 0.999355i
\(157\) 137.746 + 115.582i 0.877361 + 0.736193i 0.965635 0.259903i \(-0.0836906\pi\)
−0.0882738 + 0.996096i \(0.528135\pi\)
\(158\) 25.6211 + 70.3933i 0.162159 + 0.445527i
\(159\) 13.5944 + 58.3497i 0.0854992 + 0.366980i
\(160\) 5.40395 + 30.6473i 0.0337747 + 0.191546i
\(161\) 75.5552i 0.469287i
\(162\) 98.1191 188.160i 0.605674 1.16148i
\(163\) −91.8649 −0.563588 −0.281794 0.959475i \(-0.590930\pi\)
−0.281794 + 0.959475i \(0.590930\pi\)
\(164\) 62.0882 10.9478i 0.378586 0.0667550i
\(165\) −44.7777 + 10.4324i −0.271380 + 0.0632264i
\(166\) −57.3916 + 20.8888i −0.345732 + 0.125836i
\(167\) −119.775 + 142.742i −0.717216 + 0.854744i −0.994357 0.106085i \(-0.966169\pi\)
0.277141 + 0.960829i \(0.410613\pi\)
\(168\) −48.6107 + 20.7491i −0.289350 + 0.123507i
\(169\) −207.060 75.3636i −1.22521 0.445939i
\(170\) 8.56347 4.94412i 0.0503734 0.0290831i
\(171\) −74.2502 49.6504i −0.434212 0.290353i
\(172\) 49.7612 86.1890i 0.289309 0.501099i
\(173\) −104.602 124.659i −0.604633 0.720574i 0.373714 0.927544i \(-0.378084\pi\)
−0.978347 + 0.206970i \(0.933640\pi\)
\(174\) 39.7590 25.9333i 0.228500 0.149042i
\(175\) 25.0176 141.882i 0.142958 0.810753i
\(176\) −359.829 63.4476i −2.04448 0.360498i
\(177\) −81.1430 + 160.044i −0.458435 + 0.904206i
\(178\) −281.304 + 236.042i −1.58036 + 1.32608i
\(179\) −131.530 75.9388i −0.734803 0.424239i 0.0853735 0.996349i \(-0.472792\pi\)
−0.820177 + 0.572110i \(0.806125\pi\)
\(180\) −2.25857 20.6905i −0.0125476 0.114947i
\(181\) 2.78080 + 4.81648i 0.0153635 + 0.0266104i 0.873605 0.486636i \(-0.161776\pi\)
−0.858241 + 0.513246i \(0.828443\pi\)
\(182\) −104.619 + 287.438i −0.574829 + 1.57933i
\(183\) −44.2129 5.33871i −0.241601 0.0291733i
\(184\) 29.1234 + 24.4374i 0.158279 + 0.132812i
\(185\) −5.21261 14.3215i −0.0281763 0.0774137i
\(186\) 210.113 196.722i 1.12964 1.05765i
\(187\) 15.4003 + 87.3395i 0.0823546 + 0.467056i
\(188\) 82.9249i 0.441090i
\(189\) 150.745 52.9217i 0.797590 0.280009i
\(190\) −20.9985 −0.110518
\(191\) 372.156 65.6211i 1.94846 0.343566i 0.948847 0.315737i \(-0.102252\pi\)
0.999613 0.0278287i \(-0.00885930\pi\)
\(192\) 20.8549 68.7057i 0.108619 0.357842i
\(193\) −21.9199 + 7.97819i −0.113575 + 0.0413378i −0.398182 0.917306i \(-0.630359\pi\)
0.284608 + 0.958644i \(0.408137\pi\)
\(194\) 111.198 132.521i 0.573188 0.683099i
\(195\) 38.2381 + 28.6945i 0.196093 + 0.147151i
\(196\) −37.6359 13.6983i −0.192020 0.0698895i
\(197\) −48.3057 + 27.8893i −0.245207 + 0.141570i −0.617567 0.786518i \(-0.711882\pi\)
0.372361 + 0.928088i \(0.378548\pi\)
\(198\) 434.576 + 106.503i 2.19483 + 0.537895i
\(199\) −11.0228 + 19.0921i −0.0553910 + 0.0959400i −0.892391 0.451262i \(-0.850974\pi\)
0.837000 + 0.547202i \(0.184307\pi\)
\(200\) −46.5979 55.5332i −0.232989 0.277666i
\(201\) 9.51916 + 174.926i 0.0473590 + 0.870278i
\(202\) −10.5373 + 59.7601i −0.0521649 + 0.295842i
\(203\) 35.1953 + 6.20587i 0.173376 + 0.0305708i
\(204\) −40.0886 + 2.18155i −0.196513 + 0.0106939i
\(205\) 13.6212 11.4296i 0.0664450 0.0557540i
\(206\) −386.509 223.151i −1.87626 1.08326i
\(207\) −82.9851 79.4972i −0.400894 0.384045i
\(208\) 189.963 + 329.025i 0.913282 + 1.58185i
\(209\) 64.4138 176.975i 0.308200 0.846773i
\(210\) 22.5434 30.0412i 0.107349 0.143053i
\(211\) 128.818 + 108.091i 0.610512 + 0.512280i 0.894805 0.446457i \(-0.147315\pi\)
−0.284293 + 0.958737i \(0.591759\pi\)
\(212\) −19.5590 53.7378i −0.0922593 0.253480i
\(213\) −240.189 72.9068i −1.12765 0.342285i
\(214\) −0.979628 5.55575i −0.00457770 0.0259614i
\(215\) 28.0689i 0.130553i
\(216\) 28.3574 75.2226i 0.131284 0.348253i
\(217\) 216.701 0.998621
\(218\) −119.444 + 21.0613i −0.547910 + 0.0966113i
\(219\) −234.706 250.682i −1.07172 1.14467i
\(220\) 41.2385 15.0096i 0.187448 0.0682254i
\(221\) 59.2761 70.6426i 0.268218 0.319650i
\(222\) −17.7803 + 147.249i −0.0800915 + 0.663283i
\(223\) −10.4645 3.80878i −0.0469262 0.0170797i 0.318450 0.947940i \(-0.396838\pi\)
−0.365377 + 0.930860i \(0.619060\pi\)
\(224\) 197.463 114.005i 0.881529 0.508951i
\(225\) 129.511 + 176.762i 0.575605 + 0.785609i
\(226\) −160.345 + 277.726i −0.709493 + 1.22888i
\(227\) 155.762 + 185.630i 0.686175 + 0.817752i 0.990887 0.134693i \(-0.0430047\pi\)
−0.304712 + 0.952445i \(0.598560\pi\)
\(228\) 76.0421 + 38.5536i 0.333518 + 0.169095i
\(229\) 34.4423 195.332i 0.150403 0.852978i −0.812466 0.583009i \(-0.801875\pi\)
0.962869 0.269969i \(-0.0870136\pi\)
\(230\) −26.6058 4.69132i −0.115677 0.0203970i
\(231\) 184.035 + 282.149i 0.796687 + 1.22142i
\(232\) 13.7756 11.5591i 0.0593775 0.0498237i
\(233\) 90.0701 + 52.0020i 0.386567 + 0.223184i 0.680672 0.732589i \(-0.261688\pi\)
−0.294105 + 0.955773i \(0.595021\pi\)
\(234\) −205.626 417.341i −0.878745 1.78351i
\(235\) 11.6939 + 20.2544i 0.0497613 + 0.0861891i
\(236\) 58.5796 160.946i 0.248218 0.681975i
\(237\) −33.6757 78.8949i −0.142092 0.332890i
\(238\) −55.4991 46.5693i −0.233190 0.195669i
\(239\) −114.970 315.876i −0.481044 1.32166i −0.908599 0.417669i \(-0.862847\pi\)
0.427555 0.903989i \(-0.359375\pi\)
\(240\) −10.5851 45.4334i −0.0441046 0.189306i
\(241\) −16.0293 90.9066i −0.0665115 0.377206i −0.999835 0.0181689i \(-0.994216\pi\)
0.933323 0.359037i \(-0.116895\pi\)
\(242\) 626.421i 2.58852i
\(243\) −100.484 + 221.251i −0.413513 + 0.910498i
\(244\) 42.5079 0.174213
\(245\) −11.1243 + 1.96151i −0.0454053 + 0.00800617i
\(246\) −168.529 + 39.2641i −0.685078 + 0.159610i
\(247\) −184.021 + 66.9780i −0.745023 + 0.271166i
\(248\) 70.0892 83.5291i 0.282618 0.336811i
\(249\) 64.3229 27.4558i 0.258325 0.110264i
\(250\) 98.1136 + 35.7104i 0.392454 + 0.142842i
\(251\) −140.368 + 81.0414i −0.559234 + 0.322874i −0.752838 0.658206i \(-0.771316\pi\)
0.193604 + 0.981080i \(0.437982\pi\)
\(252\) −136.793 + 67.3986i −0.542829 + 0.267455i
\(253\) 121.153 209.843i 0.478866 0.829420i
\(254\) −187.678 223.667i −0.738892 0.880577i
\(255\) −9.48401 + 6.18606i −0.0371922 + 0.0242590i
\(256\) 58.2190 330.177i 0.227418 1.28975i
\(257\) 327.025 + 57.6633i 1.27247 + 0.224371i 0.768780 0.639513i \(-0.220864\pi\)
0.503691 + 0.863884i \(0.331975\pi\)
\(258\) −123.524 + 243.635i −0.478775 + 0.944323i
\(259\) −85.5403 + 71.7768i −0.330271 + 0.277131i
\(260\) −39.5186 22.8161i −0.151995 0.0877541i
\(261\) −43.8477 + 32.1266i −0.167999 + 0.123090i
\(262\) 4.90340 + 8.49294i 0.0187153 + 0.0324158i
\(263\) −97.3777 + 267.543i −0.370257 + 1.01727i 0.605005 + 0.796222i \(0.293171\pi\)
−0.975262 + 0.221052i \(0.929051\pi\)
\(264\) 168.280 + 20.3199i 0.637426 + 0.0769692i
\(265\) −12.3553 10.3673i −0.0466237 0.0391219i
\(266\) 52.6201 + 144.573i 0.197820 + 0.543506i
\(267\) 306.962 287.399i 1.14967 1.07640i
\(268\) −29.0365 164.674i −0.108345 0.614455i
\(269\) 123.107i 0.457646i 0.973468 + 0.228823i \(0.0734877\pi\)
−0.973468 + 0.228823i \(0.926512\pi\)
\(270\) 9.27577 + 56.3687i 0.0343547 + 0.208773i
\(271\) −345.130 −1.27354 −0.636772 0.771052i \(-0.719731\pi\)
−0.636772 + 0.771052i \(0.719731\pi\)
\(272\) −88.6183 + 15.6258i −0.325803 + 0.0574478i
\(273\) 101.738 335.172i 0.372667 1.22774i
\(274\) −477.514 + 173.801i −1.74275 + 0.634310i
\(275\) −296.991 + 353.940i −1.07997 + 1.28705i
\(276\) 87.7347 + 65.8375i 0.317879 + 0.238542i
\(277\) −147.517 53.6918i −0.532553 0.193833i 0.0617250 0.998093i \(-0.480340\pi\)
−0.594278 + 0.804260i \(0.702562\pi\)
\(278\) 334.481 193.113i 1.20317 0.694650i
\(279\) −228.007 + 238.010i −0.817228 + 0.853083i
\(280\) 7.11424 12.3222i 0.0254080 0.0440079i
\(281\) 21.6740 + 25.8301i 0.0771318 + 0.0919222i 0.803230 0.595669i \(-0.203113\pi\)
−0.726098 + 0.687591i \(0.758668\pi\)
\(282\) −12.3675 227.268i −0.0438565 0.805916i
\(283\) 17.8594 101.285i 0.0631073 0.357899i −0.936859 0.349707i \(-0.886281\pi\)
0.999966 0.00819227i \(-0.00260771\pi\)
\(284\) 235.950 + 41.6043i 0.830809 + 0.146494i
\(285\) 24.0101 1.30659i 0.0842459 0.00458451i
\(286\) 751.471 630.559i 2.62752 2.20475i
\(287\) −112.825 65.1396i −0.393119 0.226967i
\(288\) −82.5490 + 336.833i −0.286628 + 1.16956i
\(289\) −133.579 231.366i −0.462212 0.800574i
\(290\) −4.37063 + 12.0082i −0.0150711 + 0.0414076i
\(291\) −118.901 + 158.447i −0.408594 + 0.544490i
\(292\) 251.096 + 210.695i 0.859918 + 0.721557i
\(293\) 162.927 + 447.638i 0.556064 + 1.52777i 0.825297 + 0.564699i \(0.191008\pi\)
−0.269233 + 0.963075i \(0.586770\pi\)
\(294\) 105.190 + 31.9293i 0.357788 + 0.108603i
\(295\) −8.38821 47.5719i −0.0284346 0.161261i
\(296\) 56.1876i 0.189823i
\(297\) −503.531 94.7373i −1.69539 0.318981i
\(298\) 200.407 0.672508
\(299\) −248.124 + 43.7510i −0.829847 + 0.146324i
\(300\) −142.953 152.684i −0.476511 0.508946i
\(301\) −193.252 + 70.3381i −0.642034 + 0.233681i
\(302\) 326.445 389.042i 1.08094 1.28822i
\(303\) 8.33014 68.9866i 0.0274922 0.227678i
\(304\) 179.567 + 65.3570i 0.590680 + 0.214990i
\(305\) 10.3826 5.99438i 0.0340412 0.0196537i
\(306\) 109.543 11.9577i 0.357985 0.0390776i
\(307\) 16.6781 28.8873i 0.0543260 0.0940954i −0.837584 0.546309i \(-0.816032\pi\)
0.891910 + 0.452214i \(0.149366\pi\)
\(308\) −206.680 246.311i −0.671038 0.799712i
\(309\) 455.828 + 231.106i 1.47517 + 0.747916i
\(310\) −13.4552 + 76.3083i −0.0434039 + 0.246156i
\(311\) 211.519 + 37.2966i 0.680126 + 0.119925i 0.503030 0.864269i \(-0.332218\pi\)
0.177096 + 0.984194i \(0.443330\pi\)
\(312\) −96.2889 147.623i −0.308618 0.473151i
\(313\) −234.192 + 196.511i −0.748218 + 0.627830i −0.935031 0.354566i \(-0.884629\pi\)
0.186813 + 0.982396i \(0.440184\pi\)
\(314\) 407.970 + 235.541i 1.29927 + 0.750132i
\(315\) −23.9073 + 35.7524i −0.0758962 + 0.113500i
\(316\) 40.9393 + 70.9090i 0.129555 + 0.224396i
\(317\) 202.382 556.041i 0.638430 1.75407i −0.0181701 0.999835i \(-0.505784\pi\)
0.656601 0.754238i \(-0.271994\pi\)
\(318\) 61.6188 + 144.360i 0.193770 + 0.453961i
\(319\) −87.7984 73.6716i −0.275230 0.230945i
\(320\) 6.61096 + 18.1635i 0.0206593 + 0.0567608i
\(321\) 1.46582 + 6.29160i 0.00456643 + 0.0196000i
\(322\) 34.3722 + 194.935i 0.106746 + 0.605387i
\(323\) 46.3825i 0.143599i
\(324\) 69.9035 221.160i 0.215752 0.682592i
\(325\) 480.428 1.47824
\(326\) −237.014 + 41.7920i −0.727037 + 0.128196i
\(327\) 135.265 31.5141i 0.413653 0.0963733i
\(328\) −61.6005 + 22.4208i −0.187806 + 0.0683559i
\(329\) 110.146 131.267i 0.334791 0.398989i
\(330\) −110.782 + 47.2865i −0.335703 + 0.143292i
\(331\) 497.363 + 181.025i 1.50261 + 0.546905i 0.956734 0.290963i \(-0.0939756\pi\)
0.545874 + 0.837867i \(0.316198\pi\)
\(332\) −57.8120 + 33.3778i −0.174133 + 0.100536i
\(333\) 11.1681 169.474i 0.0335379 0.508930i
\(334\) −244.085 + 422.768i −0.730795 + 1.26577i
\(335\) −30.3142 36.1270i −0.0904900 0.107842i
\(336\) −286.280 + 186.729i −0.852024 + 0.555742i
\(337\) −89.2378 + 506.093i −0.264801 + 1.50176i 0.504802 + 0.863235i \(0.331566\pi\)
−0.769602 + 0.638524i \(0.779545\pi\)
\(338\) −568.505 100.243i −1.68197 0.296576i
\(339\) 166.061 327.535i 0.489856 0.966181i
\(340\) 8.27939 6.94724i 0.0243512 0.0204330i
\(341\) −601.854 347.480i −1.76497 1.01900i
\(342\) −214.155 94.3209i −0.626184 0.275792i
\(343\) 186.353 + 322.772i 0.543302 + 0.941027i
\(344\) −35.3927 + 97.2407i −0.102886 + 0.282676i
\(345\) 30.7135 + 3.70866i 0.0890247 + 0.0107497i
\(346\) −326.586 274.038i −0.943891 0.792018i
\(347\) −93.5499 257.026i −0.269596 0.740710i −0.998430 0.0560187i \(-0.982159\pi\)
0.728833 0.684691i \(-0.240063\pi\)
\(348\) 37.8748 35.4610i 0.108836 0.101900i
\(349\) −43.3413 245.801i −0.124187 0.704301i −0.981787 0.189984i \(-0.939157\pi\)
0.857600 0.514317i \(-0.171955\pi\)
\(350\) 377.440i 1.07840i
\(351\) 261.086 + 464.402i 0.743834 + 1.32308i
\(352\) −731.230 −2.07736
\(353\) 69.1294 12.1894i 0.195834 0.0345308i −0.0748707 0.997193i \(-0.523854\pi\)
0.270705 + 0.962662i \(0.412743\pi\)
\(354\) −136.542 + 449.834i −0.385713 + 1.27072i
\(355\) 63.4977 23.1113i 0.178867 0.0651022i
\(356\) −257.997 + 307.469i −0.724711 + 0.863677i
\(357\) 66.3566 + 49.7950i 0.185873 + 0.139482i
\(358\) −373.897 136.088i −1.04441 0.380133i
\(359\) −113.033 + 65.2597i −0.314855 + 0.181782i −0.649097 0.760706i \(-0.724853\pi\)
0.334242 + 0.942487i \(0.391520\pi\)
\(360\) 6.04853 + 20.7789i 0.0168015 + 0.0577193i
\(361\) 131.252 227.334i 0.363578 0.629735i
\(362\) 9.36569 + 11.1616i 0.0258721 + 0.0308332i
\(363\) −38.9777 716.262i −0.107377 1.97317i
\(364\) −58.0569 + 329.257i −0.159497 + 0.904552i
\(365\) 91.0420 + 16.0532i 0.249430 + 0.0439813i
\(366\) −116.499 + 6.33968i −0.318304 + 0.0173215i
\(367\) −309.570 + 259.760i −0.843516 + 0.707794i −0.958352 0.285591i \(-0.907810\pi\)
0.114836 + 0.993384i \(0.463366\pi\)
\(368\) 212.916 + 122.927i 0.578576 + 0.334041i
\(369\) 190.257 55.3818i 0.515601 0.150086i
\(370\) −19.9640 34.5786i −0.0539567 0.0934557i
\(371\) −40.4169 + 111.045i −0.108941 + 0.299312i
\(372\) 188.829 251.633i 0.507605 0.676432i
\(373\) 147.121 + 123.449i 0.394427 + 0.330963i 0.818335 0.574742i \(-0.194898\pi\)
−0.423908 + 0.905705i \(0.639342\pi\)
\(374\) 79.4665 + 218.332i 0.212477 + 0.583776i
\(375\) −114.407 34.7271i −0.305086 0.0926057i
\(376\) −14.9726 84.9136i −0.0398207 0.225834i
\(377\) 119.175i 0.316115i
\(378\) 364.850 205.118i 0.965211 0.542639i
\(379\) 220.367 0.581442 0.290721 0.956808i \(-0.406105\pi\)
0.290721 + 0.956808i \(0.406105\pi\)
\(380\) −22.6029 + 3.98550i −0.0594813 + 0.0104882i
\(381\) 228.513 + 244.067i 0.599771 + 0.640596i
\(382\) 930.320 338.609i 2.43539 0.886410i
\(383\) 31.9732 38.1042i 0.0834810 0.0994888i −0.722687 0.691175i \(-0.757093\pi\)
0.806168 + 0.591687i \(0.201538\pi\)
\(384\) −32.8823 + 272.317i −0.0856309 + 0.709158i
\(385\) −85.2159 31.0161i −0.221340 0.0805612i
\(386\) −52.9245 + 30.5559i −0.137110 + 0.0791605i
\(387\) 126.080 286.264i 0.325788 0.739700i
\(388\) 94.5424 163.752i 0.243666 0.422042i
\(389\) 334.415 + 398.540i 0.859678 + 1.02452i 0.999410 + 0.0343355i \(0.0109315\pi\)
−0.139732 + 0.990189i \(0.544624\pi\)
\(390\) 111.709 + 56.6370i 0.286434 + 0.145223i
\(391\) 10.3624 58.7683i 0.0265024 0.150303i
\(392\) 41.0118 + 7.23148i 0.104622 + 0.0184477i
\(393\) −6.13511 9.40590i −0.0156110 0.0239336i
\(394\) −111.942 + 93.9309i −0.284118 + 0.238403i
\(395\) 19.9989 + 11.5464i 0.0506301 + 0.0292313i
\(396\) 487.996 + 32.1584i 1.23231 + 0.0812080i
\(397\) −236.091 408.922i −0.594688 1.03003i −0.993591 0.113037i \(-0.963942\pi\)
0.398903 0.916993i \(-0.369391\pi\)
\(398\) −19.7536 + 54.2727i −0.0496323 + 0.136364i
\(399\) −69.1627 162.033i −0.173340 0.406098i
\(400\) −359.122 301.339i −0.897805 0.753348i
\(401\) −197.351 542.218i −0.492148 1.35216i −0.898711 0.438542i \(-0.855495\pi\)
0.406563 0.913623i \(-0.366727\pi\)
\(402\) 104.139 + 446.983i 0.259051 + 1.11190i
\(403\) 125.483 + 711.648i 0.311371 + 1.76587i
\(404\) 66.3262i 0.164174i
\(405\) −14.1135 63.8760i −0.0348482 0.157718i
\(406\) 93.6280 0.230611
\(407\) 352.670 62.1852i 0.866511 0.152789i
\(408\) 40.6561 9.47209i 0.0996473 0.0232159i
\(409\) 544.458 198.167i 1.33119 0.484515i 0.424166 0.905584i \(-0.360567\pi\)
0.907028 + 0.421069i \(0.138345\pi\)
\(410\) 29.9435 35.6853i 0.0730329 0.0870373i
\(411\) 535.185 228.440i 1.30215 0.555815i
\(412\) −458.396 166.842i −1.11261 0.404957i
\(413\) −306.509 + 176.963i −0.742151 + 0.428481i
\(414\) −250.269 167.353i −0.604516 0.404234i
\(415\) −9.41374 + 16.3051i −0.0226837 + 0.0392893i
\(416\) 488.737 + 582.454i 1.17485 + 1.40013i
\(417\) −370.437 + 241.622i −0.888338 + 0.579428i
\(418\) 85.6783 485.906i 0.204972 1.16245i
\(419\) −698.951 123.244i −1.66814 0.294138i −0.741742 0.670685i \(-0.766000\pi\)
−0.926398 + 0.376547i \(0.877111\pi\)
\(420\) 18.5640 36.6153i 0.0442001 0.0871792i
\(421\) −312.697 + 262.384i −0.742747 + 0.623239i −0.933574 0.358385i \(-0.883328\pi\)
0.190827 + 0.981624i \(0.438883\pi\)
\(422\) 381.528 + 220.275i 0.904094 + 0.521979i
\(423\) 28.2826 + 259.094i 0.0668619 + 0.612515i
\(424\) 29.7307 + 51.4951i 0.0701196 + 0.121451i
\(425\) −38.9183 + 106.927i −0.0915725 + 0.251593i
\(426\) −652.861 78.8330i −1.53254 0.185054i
\(427\) −67.2885 56.4618i −0.157584 0.132229i
\(428\) −2.10896 5.79432i −0.00492748 0.0135381i
\(429\) −820.013 + 767.753i −1.91145 + 1.78963i
\(430\) −12.7694 72.4186i −0.0296962 0.168415i
\(431\) 607.828i 1.41027i −0.709071 0.705137i \(-0.750885\pi\)
0.709071 0.705137i \(-0.249115\pi\)
\(432\) 96.1245 510.903i 0.222510 1.18265i
\(433\) −80.5066 −0.185928 −0.0929638 0.995669i \(-0.529634\pi\)
−0.0929638 + 0.995669i \(0.529634\pi\)
\(434\) 559.094 98.5834i 1.28823 0.227151i
\(435\) 4.25029 14.0024i 0.00977077 0.0321894i
\(436\) −124.573 + 45.3410i −0.285719 + 0.103993i
\(437\) −81.4568 + 97.0764i −0.186400 + 0.222143i
\(438\) −719.590 539.992i −1.64290 1.23286i
\(439\) −37.2491 13.5576i −0.0848500 0.0308829i 0.299246 0.954176i \(-0.403265\pi\)
−0.384096 + 0.923293i \(0.625487\pi\)
\(440\) −39.5175 + 22.8154i −0.0898124 + 0.0518532i
\(441\) −122.263 29.9634i −0.277240 0.0679443i
\(442\) 120.797 209.226i 0.273296 0.473363i
\(443\) −314.490 374.794i −0.709909 0.846036i 0.283700 0.958913i \(-0.408438\pi\)
−0.993609 + 0.112877i \(0.963993\pi\)
\(444\) 8.80892 + 161.874i 0.0198399 + 0.364582i
\(445\) −19.6572 + 111.482i −0.0441735 + 0.250521i
\(446\) −28.7315 5.06614i −0.0644204 0.0113591i
\(447\) −229.150 + 12.4699i −0.512640 + 0.0278969i
\(448\) 108.488 91.0319i 0.242160 0.203196i
\(449\) 334.763 + 193.275i 0.745574 + 0.430457i 0.824093 0.566455i \(-0.191686\pi\)
−0.0785183 + 0.996913i \(0.525019\pi\)
\(450\) 414.556 + 397.133i 0.921236 + 0.882517i
\(451\) 208.903 + 361.831i 0.463200 + 0.802286i
\(452\) −119.885 + 329.380i −0.265232 + 0.728718i
\(453\) −349.057 + 465.151i −0.770545 + 1.02682i
\(454\) 486.318 + 408.069i 1.07119 + 0.898831i
\(455\) 32.2508 + 88.6082i 0.0708808 + 0.194743i
\(456\) −84.8269 25.7483i −0.186024 0.0564657i
\(457\) −83.9707 476.221i −0.183743 1.04206i −0.927559 0.373676i \(-0.878097\pi\)
0.743816 0.668384i \(-0.233014\pi\)
\(458\) 519.631i 1.13457i
\(459\) −124.510 + 20.4888i −0.271264 + 0.0446380i
\(460\) −29.5291 −0.0641937
\(461\) 324.900 57.2886i 0.704771 0.124270i 0.190235 0.981739i \(-0.439075\pi\)
0.514537 + 0.857468i \(0.327964\pi\)
\(462\) 603.172 + 644.229i 1.30557 + 1.39444i
\(463\) 504.528 183.633i 1.08969 0.396616i 0.266186 0.963922i \(-0.414237\pi\)
0.823507 + 0.567306i \(0.192014\pi\)
\(464\) 74.7503 89.0840i 0.161100 0.191991i
\(465\) 10.6368 88.0897i 0.0228749 0.189440i
\(466\) 256.041 + 93.1911i 0.549443 + 0.199981i
\(467\) 150.586 86.9408i 0.322454 0.186169i −0.330032 0.943970i \(-0.607060\pi\)
0.652486 + 0.757801i \(0.273726\pi\)
\(468\) −300.549 410.202i −0.642199 0.876499i
\(469\) −172.767 + 299.241i −0.368373 + 0.638041i
\(470\) 39.3849 + 46.9371i 0.0837977 + 0.0998663i
\(471\) −481.137 243.938i −1.02152 0.517915i
\(472\) −30.9247 + 175.383i −0.0655184 + 0.371574i
\(473\) 649.516 + 114.527i 1.37318 + 0.242130i
\(474\) −122.776 188.231i −0.259021 0.397112i
\(475\) 185.108 155.324i 0.389700 0.326997i
\(476\) −68.5785 39.5938i −0.144073 0.0831803i
\(477\) −79.4387 161.230i −0.166538 0.338008i
\(478\) −440.326 762.667i −0.921184 1.59554i
\(479\) −223.306 + 613.528i −0.466192 + 1.28085i 0.454564 + 0.890714i \(0.349795\pi\)
−0.920756 + 0.390138i \(0.872427\pi\)
\(480\) −36.6510 85.8653i −0.0763562 0.178886i
\(481\) −285.249 239.352i −0.593033 0.497614i
\(482\) −82.7120 227.249i −0.171602 0.471472i
\(483\) −51.4313 220.754i −0.106483 0.457047i
\(484\) 118.894 + 674.284i 0.245650 + 1.39315i
\(485\) 53.3287i 0.109956i
\(486\) −158.597 + 616.547i −0.326331 + 1.26862i
\(487\) −294.728 −0.605192 −0.302596 0.953119i \(-0.597853\pi\)
−0.302596 + 0.953119i \(0.597853\pi\)
\(488\) −43.5273 + 7.67504i −0.0891953 + 0.0157275i
\(489\) 268.406 62.5335i 0.548888 0.127880i
\(490\) −27.8086 + 10.1215i −0.0567523 + 0.0206562i
\(491\) −409.156 + 487.613i −0.833312 + 0.993103i 0.166663 + 0.986014i \(0.446701\pi\)
−0.999975 + 0.00708859i \(0.997744\pi\)
\(492\) −173.954 + 74.2510i −0.353565 + 0.150917i
\(493\) −26.5244 9.65409i −0.0538020 0.0195823i
\(494\) −444.308 + 256.521i −0.899409 + 0.519274i
\(495\) 123.728 60.9615i 0.249956 0.123155i
\(496\) 352.568 610.666i 0.710823 1.23118i
\(497\) −318.239 379.262i −0.640319 0.763103i
\(498\) 153.465 100.099i 0.308162 0.201002i
\(499\) −70.1195 + 397.667i −0.140520 + 0.796929i 0.830336 + 0.557264i \(0.188149\pi\)
−0.970856 + 0.239665i \(0.922962\pi\)
\(500\) 112.388 + 19.8171i 0.224776 + 0.0396341i
\(501\) 252.786 498.590i 0.504564 0.995189i
\(502\) −325.285 + 272.946i −0.647978 + 0.543718i
\(503\) 260.231 + 150.244i 0.517357 + 0.298696i 0.735853 0.677142i \(-0.236782\pi\)
−0.218496 + 0.975838i \(0.570115\pi\)
\(504\) 127.904 93.7137i 0.253778 0.185940i
\(505\) 9.35318 + 16.2002i 0.0185212 + 0.0320796i
\(506\) 217.115 596.518i 0.429081 1.17889i
\(507\) 656.278 + 79.2457i 1.29443 + 0.156303i
\(508\) −244.470 205.135i −0.481241 0.403809i
\(509\) 201.902 + 554.722i 0.396665 + 1.08983i 0.963898 + 0.266270i \(0.0857914\pi\)
−0.567234 + 0.823557i \(0.691986\pi\)
\(510\) −21.6548 + 20.2748i −0.0424604 + 0.0397544i
\(511\) −117.618 667.045i −0.230172 1.30537i
\(512\) 512.624i 1.00122i
\(513\) 250.738 + 94.5231i 0.488768 + 0.184256i
\(514\) 869.966 1.69254
\(515\) −135.491 + 23.8907i −0.263089 + 0.0463898i
\(516\) −86.7201 + 285.696i −0.168062 + 0.553674i
\(517\) −516.403 + 187.955i −0.998845 + 0.363550i
\(518\) −188.043 + 224.101i −0.363018 + 0.432627i
\(519\) 390.477 + 293.020i 0.752364 + 0.564586i
\(520\) 44.5859 + 16.2279i 0.0857421 + 0.0312076i
\(521\) 56.9434 32.8763i 0.109296 0.0631022i −0.444355 0.895851i \(-0.646567\pi\)
0.553652 + 0.832748i \(0.313234\pi\)
\(522\) −98.5129 + 102.835i −0.188722 + 0.197002i
\(523\) 0.475172 0.823023i 0.000908551 0.00157366i −0.865571 0.500787i \(-0.833044\pi\)
0.866479 + 0.499213i \(0.166377\pi\)
\(524\) 6.89002 + 8.21121i 0.0131489 + 0.0156702i
\(525\) 23.4854 + 431.573i 0.0447342 + 0.822044i
\(526\) −129.524 + 734.568i −0.246244 + 1.39652i
\(527\) −168.554 29.7206i −0.319837 0.0563958i
\(528\) 1094.52 59.5619i 2.07296 0.112807i
\(529\) 280.341 235.234i 0.529945 0.444676i
\(530\) −36.5934 21.1272i −0.0690441 0.0398626i
\(531\) 128.136 522.845i 0.241310 0.984642i
\(532\) 84.0806 + 145.632i 0.158046 + 0.273744i
\(533\) 148.587 408.239i 0.278774 0.765926i
\(534\) 661.224 881.144i 1.23825 1.65008i
\(535\) −1.33222 1.11786i −0.00249013 0.00208946i
\(536\) 59.4656 + 163.380i 0.110943 + 0.304814i
\(537\) 435.990 + 132.340i 0.811899 + 0.246444i
\(538\) 56.0048 + 317.619i 0.104098 + 0.590370i
\(539\) 265.420i 0.492431i
\(540\) 20.6833 + 58.9152i 0.0383024 + 0.109102i
\(541\) −823.790 −1.52272 −0.761359 0.648331i \(-0.775467\pi\)
−0.761359 + 0.648331i \(0.775467\pi\)
\(542\) −890.446 + 157.010i −1.64289 + 0.289686i
\(543\) −11.4034 12.1796i −0.0210008 0.0224303i
\(544\) −169.226 + 61.5932i −0.311077 + 0.113223i
\(545\) −24.0332 + 28.6417i −0.0440976 + 0.0525535i
\(546\) 110.008 911.038i 0.201480 1.66857i
\(547\) 682.001 + 248.228i 1.24680 + 0.453799i 0.879320 0.476232i \(-0.157998\pi\)
0.367482 + 0.930031i \(0.380220\pi\)
\(548\) −481.012 + 277.713i −0.877760 + 0.506775i
\(549\) 132.813 14.4979i 0.241918 0.0264077i
\(550\) −605.227 + 1048.28i −1.10041 + 1.90597i
\(551\) 38.5297 + 45.9179i 0.0699268 + 0.0833355i
\(552\) −101.726 51.5755i −0.184287 0.0934338i
\(553\) 29.3805 166.625i 0.0531292 0.301311i
\(554\) −405.024 71.4167i −0.731091 0.128911i
\(555\) 24.9788 + 38.2957i 0.0450068 + 0.0690012i
\(556\) 323.385 271.353i 0.581628 0.488044i
\(557\) 669.336 + 386.441i 1.20168 + 0.693790i 0.960929 0.276796i \(-0.0892728\pi\)
0.240752 + 0.970587i \(0.422606\pi\)
\(558\) −479.986 + 717.800i −0.860190 + 1.28638i
\(559\) −342.896 593.913i −0.613409 1.06246i
\(560\) 31.4702 86.4637i 0.0561968 0.154399i
\(561\) −104.449 244.701i −0.186183 0.436187i
\(562\) 67.6705 + 56.7823i 0.120410 + 0.101036i
\(563\) 53.7401 + 147.650i 0.0954531 + 0.262255i 0.978225 0.207546i \(-0.0665478\pi\)
−0.882772 + 0.469801i \(0.844326\pi\)
\(564\) −56.4480 242.286i −0.100085 0.429585i
\(565\) 17.1667 + 97.3572i 0.0303835 + 0.172314i
\(566\) 269.444i 0.476050i
\(567\) −404.414 + 257.238i −0.713252 + 0.453682i
\(568\) −249.120 −0.438592
\(569\) −1090.01 + 192.198i −1.91566 + 0.337783i −0.998196 0.0600323i \(-0.980880\pi\)
−0.917466 + 0.397815i \(0.869769\pi\)
\(570\) 61.3523 14.2939i 0.107636 0.0250770i
\(571\) −222.438 + 80.9607i −0.389558 + 0.141788i −0.529371 0.848390i \(-0.677572\pi\)
0.139813 + 0.990178i \(0.455350\pi\)
\(572\) 689.209 821.368i 1.20491 1.43596i
\(573\) −1042.68 + 445.059i −1.81968 + 0.776718i
\(574\) −320.726 116.735i −0.558756 0.203371i
\(575\) 269.239 155.445i 0.468242 0.270340i
\(576\) −14.1641 + 214.937i −0.0245905 + 0.373155i
\(577\) 213.678 370.101i 0.370326 0.641423i −0.619290 0.785162i \(-0.712579\pi\)
0.989616 + 0.143740i \(0.0459128\pi\)
\(578\) −449.893 536.162i −0.778362 0.927615i
\(579\) 58.6136 38.2314i 0.101233 0.0660301i
\(580\) −2.42543 + 13.7553i −0.00418177 + 0.0237160i
\(581\) 135.849 + 23.9539i 0.233819 + 0.0412287i
\(582\) −234.686 + 462.888i −0.403240 + 0.795340i
\(583\) 290.312 243.601i 0.497963 0.417841i
\(584\) −295.160 170.411i −0.505411 0.291799i
\(585\) −131.255 57.8090i −0.224368 0.0988189i
\(586\) 623.999 + 1080.80i 1.06484 + 1.84437i
\(587\) −35.0782 + 96.3766i −0.0597585 + 0.164185i −0.965979 0.258620i \(-0.916732\pi\)
0.906221 + 0.422805i \(0.138954\pi\)
\(588\) 119.287 + 14.4040i 0.202870 + 0.0244965i
\(589\) 278.426 + 233.627i 0.472709 + 0.396650i
\(590\) −43.2836 118.921i −0.0733621 0.201561i
\(591\) 122.153 114.368i 0.206688 0.193516i
\(592\) 63.0957 + 357.834i 0.106581 + 0.604449i
\(593\) 707.734i 1.19348i 0.802435 + 0.596740i \(0.203538\pi\)
−0.802435 + 0.596740i \(0.796462\pi\)
\(594\) −1342.22 15.3545i −2.25963 0.0258494i
\(595\) −22.3338 −0.0375358
\(596\) 215.720 38.0373i 0.361946 0.0638209i
\(597\) 19.2097 63.2856i 0.0321771 0.106006i
\(598\) −620.264 + 225.758i −1.03723 + 0.377521i
\(599\) 692.971 825.851i 1.15688 1.37872i 0.244360 0.969685i \(-0.421422\pi\)
0.912520 0.409032i \(-0.134133\pi\)
\(600\) 173.949 + 130.534i 0.289916 + 0.217557i
\(601\) −136.612 49.7226i −0.227307 0.0827331i 0.225856 0.974161i \(-0.427482\pi\)
−0.453163 + 0.891428i \(0.649704\pi\)
\(602\) −466.598 + 269.390i −0.775079 + 0.447492i
\(603\) −146.887 504.610i −0.243593 0.836833i
\(604\) 277.548 480.727i 0.459517 0.795906i
\(605\) 124.126 + 147.928i 0.205167 + 0.244509i
\(606\) −9.89198 181.777i −0.0163234 0.299962i
\(607\) 123.075 697.992i 0.202759 1.14990i −0.698168 0.715934i \(-0.746001\pi\)
0.900927 0.433970i \(-0.142888\pi\)
\(608\) 376.618 + 66.4079i 0.619437 + 0.109223i
\(609\) −107.056 + 5.82581i −0.175790 + 0.00956619i
\(610\) 24.0603 20.1890i 0.0394431 0.0330967i
\(611\) 494.865 + 285.710i 0.809926 + 0.467611i
\(612\) 115.644 33.6627i 0.188961 0.0550045i
\(613\) 335.095 + 580.401i 0.546647 + 0.946821i 0.998501 + 0.0547290i \(0.0174295\pi\)
−0.451854 + 0.892092i \(0.649237\pi\)
\(614\) 29.8883 82.1174i 0.0486780 0.133742i
\(615\) −32.0176 + 42.6665i −0.0520611 + 0.0693764i
\(616\) 256.109 + 214.901i 0.415762 + 0.348866i
\(617\) −158.123 434.438i −0.256276 0.704114i −0.999389 0.0349474i \(-0.988874\pi\)
0.743113 0.669166i \(-0.233349\pi\)
\(618\) 1281.19 + 388.891i 2.07312 + 0.629273i
\(619\) −132.113 749.252i −0.213430 1.21042i −0.883610 0.468224i \(-0.844894\pi\)
0.670180 0.742199i \(-0.266217\pi\)
\(620\) 84.6926i 0.136601i
\(621\) 296.576 + 175.782i 0.477579 + 0.283063i
\(622\) 562.693 0.904651
\(623\) 816.801 144.024i 1.31108 0.231178i
\(624\) −778.995 832.019i −1.24839 1.33336i
\(625\) −541.740 + 197.177i −0.866784 + 0.315484i
\(626\) −514.824 + 613.544i −0.822403 + 0.980102i
\(627\) −67.7318 + 560.926i −0.108025 + 0.894618i
\(628\) 483.847 + 176.106i 0.770457 + 0.280424i
\(629\) 76.3791 44.0975i 0.121429 0.0701073i
\(630\) −45.4167 + 103.118i −0.0720900 + 0.163680i
\(631\) −524.586 + 908.610i −0.831357 + 1.43995i 0.0656051 + 0.997846i \(0.479102\pi\)
−0.896962 + 0.442107i \(0.854231\pi\)
\(632\) −54.7242 65.2178i −0.0865889 0.103193i
\(633\) −449.953 228.127i −0.710826 0.360391i
\(634\) 269.193 1526.67i 0.424595 2.40800i
\(635\) −88.6397 15.6296i −0.139590 0.0246135i
\(636\) 93.7264 + 143.694i 0.147369 + 0.225935i
\(637\) −211.418 + 177.400i −0.331896 + 0.278494i
\(638\) −260.038 150.133i −0.407583 0.235318i
\(639\) 751.400 + 49.5164i 1.17590 + 0.0774905i
\(640\) −36.9207 63.9484i −0.0576885 0.0999194i
\(641\) 167.123 459.168i 0.260723 0.716330i −0.738396 0.674367i \(-0.764417\pi\)
0.999119 0.0419631i \(-0.0133612\pi\)
\(642\) 6.64409 + 15.5657i 0.0103491 + 0.0242456i
\(643\) 112.264 + 94.2007i 0.174594 + 0.146502i 0.725897 0.687803i \(-0.241425\pi\)
−0.551303 + 0.834305i \(0.685869\pi\)
\(644\) 73.9971 + 203.305i 0.114902 + 0.315692i
\(645\) 19.1068 + 82.0104i 0.0296230 + 0.127148i
\(646\) −21.1007 119.668i −0.0326637 0.185245i
\(647\) 265.958i 0.411064i 0.978650 + 0.205532i \(0.0658925\pi\)
−0.978650 + 0.205532i \(0.934108\pi\)
\(648\) −31.6483 + 239.085i −0.0488400 + 0.368958i
\(649\) 1135.04 1.74891
\(650\) 1239.52 218.560i 1.90695 0.336247i
\(651\) −633.146 + 147.511i −0.972574 + 0.226591i
\(652\) −247.192 + 89.9704i −0.379128 + 0.137991i
\(653\) 41.9175 49.9553i 0.0641921 0.0765012i −0.732993 0.680236i \(-0.761877\pi\)
0.797185 + 0.603735i \(0.206322\pi\)
\(654\) 334.650 142.843i 0.511697 0.218414i
\(655\) 2.84082 + 1.03397i 0.00433713 + 0.00157858i
\(656\) −367.129 + 211.962i −0.559648 + 0.323113i
\(657\) 856.394 + 572.663i 1.30349 + 0.871633i
\(658\) 224.464 388.782i 0.341130 0.590854i
\(659\) 24.8265 + 29.5871i 0.0376730 + 0.0448969i 0.784552 0.620063i \(-0.212893\pi\)
−0.746879 + 0.664960i \(0.768449\pi\)
\(660\) −110.272 + 71.9259i −0.167078 + 0.108979i
\(661\) 172.296 977.141i 0.260660 1.47828i −0.520454 0.853889i \(-0.674237\pi\)
0.781115 0.624388i \(-0.214651\pi\)
\(662\) 1365.57 + 240.786i 2.06279 + 0.363725i
\(663\) −125.103 + 246.750i −0.188692 + 0.372172i
\(664\) 53.1719 44.6166i 0.0800782 0.0671936i
\(665\) 41.0734 + 23.7138i 0.0617645 + 0.0356598i
\(666\) −48.2844 442.328i −0.0724990 0.664156i
\(667\) 38.5598 + 66.7876i 0.0578109 + 0.100131i
\(668\) −182.494 + 501.399i −0.273195 + 0.750597i
\(669\) 33.1674 + 4.00497i 0.0495776 + 0.00598651i
\(670\) −94.6466 79.4179i −0.141264 0.118534i
\(671\) 96.3471 + 264.712i 0.143587 + 0.394503i
\(672\) −499.332 + 467.510i −0.743053 + 0.695699i
\(673\) −185.898 1054.28i −0.276223 1.56654i −0.735049 0.678014i \(-0.762841\pi\)
0.458826 0.888526i \(-0.348270\pi\)
\(674\) 1346.33i 1.99752i
\(675\) −498.723 428.295i −0.738849 0.634511i
\(676\) −630.970 −0.933387
\(677\) −1123.05 + 198.024i −1.65886 + 0.292502i −0.923048 0.384684i \(-0.874310\pi\)
−0.735812 + 0.677186i \(0.763199\pi\)
\(678\) 279.438 920.597i 0.412150 1.35781i
\(679\) −367.164 + 133.637i −0.540742 + 0.196814i
\(680\) −7.22359 + 8.60874i −0.0106229 + 0.0126599i
\(681\) −581.458 436.335i −0.853829 0.640727i
\(682\) −1710.88 622.709i −2.50862 0.913063i
\(683\) −753.443 + 435.001i −1.10314 + 0.636897i −0.937043 0.349213i \(-0.886449\pi\)
−0.166095 + 0.986110i \(0.553116\pi\)
\(684\) −248.420 60.8812i −0.363187 0.0890076i
\(685\) −78.3250 + 135.663i −0.114343 + 0.198048i
\(686\) 627.633 + 747.984i 0.914917 + 1.09036i
\(687\) 32.3330 + 594.157i 0.0470640 + 0.864857i
\(688\) −116.204 + 659.027i −0.168901 + 0.957888i
\(689\) −388.076 68.4282i −0.563245 0.0993153i
\(690\) 80.9289 4.40401i 0.117288 0.00638262i
\(691\) −7.01355 + 5.88507i −0.0101499 + 0.00851674i −0.647848 0.761769i \(-0.724331\pi\)
0.637699 + 0.770286i \(0.279887\pi\)
\(692\) −403.552 232.991i −0.583168 0.336692i
\(693\) −729.766 699.094i −1.05305 1.00879i
\(694\) −358.290 620.577i −0.516268 0.894203i
\(695\) 40.7214 111.881i 0.0585919 0.160980i
\(696\) −32.3804 + 43.1500i −0.0465236 + 0.0619971i
\(697\) 78.8236 + 66.1409i 0.113090 + 0.0948936i
\(698\) −223.644 614.456i −0.320407 0.880310i
\(699\) −298.561 90.6251i −0.427125 0.129650i
\(700\) −71.6380 406.280i −0.102340 0.580399i
\(701\) 141.002i 0.201144i −0.994930 0.100572i \(-0.967933\pi\)
0.994930 0.100572i \(-0.0320673\pi\)
\(702\) 884.878 + 1079.40i 1.26051 + 1.53760i
\(703\) −187.289 −0.266414
\(704\) −447.278 + 78.8672i −0.635338 + 0.112027i
\(705\) −47.9541 51.2183i −0.0680200 0.0726500i
\(706\) 172.810 62.8979i 0.244774 0.0890905i
\(707\) 88.0988 104.992i 0.124609 0.148504i
\(708\) −61.5971 + 510.120i −0.0870015 + 0.720508i
\(709\) 659.284 + 239.960i 0.929878 + 0.338448i 0.762161 0.647387i \(-0.224138\pi\)
0.167717 + 0.985835i \(0.446360\pi\)
\(710\) 153.312 88.5147i 0.215932 0.124669i
\(711\) 152.097 + 207.588i 0.213920 + 0.291966i
\(712\) 208.669 361.426i 0.293075 0.507620i
\(713\) 300.580 + 358.218i 0.421571 + 0.502409i
\(714\) 193.855 + 98.2850i 0.271506 + 0.137654i
\(715\) 52.5120 297.810i 0.0734433 0.416518i
\(716\) −428.295 75.5200i −0.598178 0.105475i
\(717\) 550.933 + 844.651i 0.768387 + 1.17803i
\(718\) −261.940 + 219.794i −0.364819 + 0.306120i
\(719\) −327.929 189.330i −0.456091 0.263324i 0.254308 0.967123i \(-0.418152\pi\)
−0.710399 + 0.703799i \(0.751485\pi\)
\(720\) 61.8541 + 125.540i 0.0859085 + 0.174361i
\(721\) 504.014 + 872.977i 0.699048 + 1.21079i
\(722\) 235.212 646.239i 0.325778 0.895068i
\(723\) 108.715 + 254.695i 0.150366 + 0.352275i
\(724\) 12.1998 + 10.2368i 0.0168505 + 0.0141393i
\(725\) −50.2953 138.185i −0.0693728 0.190600i
\(726\) −426.412 1830.25i −0.587344 2.52100i
\(727\) 205.791 + 1167.10i 0.283068 + 1.60536i 0.712106 + 0.702072i \(0.247742\pi\)
−0.429037 + 0.903287i \(0.641147\pi\)
\(728\) 347.636i 0.477522i
\(729\) 142.980 714.841i 0.196131 0.980578i
\(730\) 242.194 0.331773
\(731\) 159.962 28.2057i 0.218827 0.0385850i
\(732\) −124.197 + 28.9356i −0.169669 + 0.0395295i
\(733\) 583.010 212.198i 0.795375 0.289493i 0.0878065 0.996138i \(-0.472014\pi\)
0.707569 + 0.706645i \(0.249792\pi\)
\(734\) −680.528 + 811.022i −0.927150 + 1.10493i
\(735\) 31.1672 13.3035i 0.0424043 0.0181000i
\(736\) 462.352 + 168.282i 0.628195 + 0.228644i
\(737\) 959.669 554.065i 1.30213 0.751785i
\(738\) 465.673 229.440i 0.630993 0.310894i
\(739\) −359.270 + 622.274i −0.486157 + 0.842049i −0.999873 0.0159112i \(-0.994935\pi\)
0.513716 + 0.857960i \(0.328268\pi\)
\(740\) −28.0524 33.4315i −0.0379086 0.0451777i
\(741\) 492.070 320.958i 0.664062 0.433142i
\(742\) −53.7595 + 304.885i −0.0724521 + 0.410896i
\(743\) −196.466 34.6423i −0.264423 0.0466249i 0.0398647 0.999205i \(-0.487307\pi\)
−0.304288 + 0.952580i \(0.598418\pi\)
\(744\) −147.924 + 291.762i −0.198823 + 0.392153i
\(745\) 47.3258 39.7110i 0.0635245 0.0533034i
\(746\) 435.738 + 251.573i 0.584099 + 0.337230i
\(747\) −169.246 + 124.004i −0.226568 + 0.166003i
\(748\) 126.978 + 219.932i 0.169756 + 0.294027i
\(749\) −4.35799 + 11.9735i −0.00581841 + 0.0159859i
\(750\) −310.972 37.5499i −0.414630 0.0500666i
\(751\) −351.265 294.747i −0.467730 0.392472i 0.378236 0.925709i \(-0.376531\pi\)
−0.845966 + 0.533237i \(0.820975\pi\)
\(752\) −190.707 523.964i −0.253600 0.696761i
\(753\) 354.954 332.333i 0.471386 0.441345i
\(754\) 54.2162 + 307.475i 0.0719048 + 0.407792i
\(755\) 156.557i 0.207360i
\(756\) 353.796 290.039i 0.467984 0.383649i
\(757\) −687.585 −0.908303 −0.454152 0.890924i \(-0.650058\pi\)
−0.454152 + 0.890924i \(0.650058\pi\)
\(758\) 568.552 100.251i 0.750069 0.132257i
\(759\) −211.136 + 695.581i −0.278177 + 0.916443i
\(760\) 22.4254 8.16216i 0.0295071 0.0107397i
\(761\) 501.129 597.223i 0.658514 0.784787i −0.328657 0.944449i \(-0.606596\pi\)
0.987172 + 0.159663i \(0.0510406\pi\)
\(762\) 700.602 + 525.743i 0.919426 + 0.689951i
\(763\) 257.420 + 93.6934i 0.337379 + 0.122796i
\(764\) 937.135 541.055i 1.22662 0.708188i
\(765\) 23.4990 24.5300i 0.0307177 0.0320654i
\(766\) 65.1571 112.855i 0.0850615 0.147331i
\(767\) −758.635 904.106i −0.989093 1.17876i
\(768\) 54.6535 + 1004.32i 0.0711635 + 1.30771i
\(769\) −211.116 + 1197.30i −0.274533 + 1.55695i 0.465908 + 0.884833i \(0.345728\pi\)
−0.740441 + 0.672122i \(0.765383\pi\)
\(770\) −233.970 41.2552i −0.303857 0.0535781i
\(771\) −994.738 + 54.1319i −1.29019 + 0.0702099i
\(772\) −51.1688 + 42.9357i −0.0662808 + 0.0556162i
\(773\) −985.144 568.773i −1.27444 0.735800i −0.298622 0.954371i \(-0.596527\pi\)
−0.975821 + 0.218572i \(0.929860\pi\)
\(774\) 195.060 795.926i 0.252016 1.02833i
\(775\) −445.834 772.207i −0.575270 0.996397i
\(776\) −67.2433 + 184.750i −0.0866538 + 0.238079i
\(777\) 201.068 267.942i 0.258775 0.344842i
\(778\) 1044.11 + 876.110i 1.34204 + 1.12611i
\(779\) −74.7347 205.332i −0.0959367 0.263584i
\(780\) 130.995 + 39.7621i 0.167942 + 0.0509770i
\(781\) 275.712 + 1563.64i 0.353024 + 2.00210i
\(782\) 156.338i 0.199921i
\(783\) 106.243 123.713i 0.135687 0.157999i
\(784\) 269.306 0.343503
\(785\) 143.014 25.2172i 0.182183 0.0321238i
\(786\) −20.1078 21.4765i −0.0255824 0.0273237i
\(787\) 169.933 61.8505i 0.215925 0.0785902i −0.231793 0.972765i \(-0.574459\pi\)
0.447718 + 0.894175i \(0.352237\pi\)
\(788\) −102.668 + 122.355i −0.130289 + 0.155272i
\(789\) 102.394 847.980i 0.129777 1.07475i
\(790\) 56.8505 + 20.6919i 0.0719627 + 0.0261923i
\(791\) 627.278 362.159i 0.793019 0.457850i
\(792\) −505.505 + 55.1808i −0.638264 + 0.0696727i
\(793\) 146.457 253.671i 0.184687 0.319888i
\(794\) −795.152 947.625i −1.00145 1.19348i
\(795\) 43.1562 + 21.8803i 0.0542845 + 0.0275224i
\(796\) −10.9620 + 62.1688i −0.0137714 + 0.0781015i
\(797\) −1158.07 204.200i −1.45304 0.256210i −0.609291 0.792947i \(-0.708546\pi\)
−0.843750 + 0.536736i \(0.819657\pi\)
\(798\) −252.155 386.586i −0.315984 0.484444i
\(799\) −103.677 + 86.9956i −0.129759 + 0.108881i
\(800\) −812.508 469.102i −1.01564 0.586377i
\(801\) −701.230 + 1048.66i −0.875443 + 1.30919i
\(802\) −755.842 1309.16i −0.942447 1.63237i
\(803\) −742.942 + 2041.22i −0.925209 + 2.54199i
\(804\) 196.933 + 461.371i 0.244941 + 0.573844i
\(805\) 46.7435 + 39.2225i 0.0580665 + 0.0487236i
\(806\) 647.498 + 1778.99i 0.803347 + 2.20718i
\(807\) −83.8002 359.687i −0.103842 0.445709i
\(808\) −11.9756 67.9168i −0.0148212 0.0840555i
\(809\) 304.680i 0.376613i −0.982110 0.188306i \(-0.939700\pi\)
0.982110 0.188306i \(-0.0602998\pi\)
\(810\) −65.4723 158.381i −0.0808301 0.195532i
\(811\) 483.057 0.595631 0.297816 0.954623i \(-0.403742\pi\)
0.297816 + 0.954623i \(0.403742\pi\)
\(812\) 100.782 17.7706i 0.124116 0.0218849i
\(813\) 1008.38 234.934i 1.24033 0.288972i
\(814\) 881.608 320.879i 1.08306 0.394200i
\(815\) −47.6892 + 56.8338i −0.0585143 + 0.0697347i
\(816\) 248.284 105.978i 0.304270 0.129875i
\(817\) −324.130 117.974i −0.396732 0.144399i
\(818\) 1314.57 758.966i 1.60705 0.927831i
\(819\) −69.0979 + 1048.54i −0.0843686 + 1.28027i
\(820\) 25.4584 44.0952i 0.0310468 0.0537746i
\(821\) 614.221 + 732.000i 0.748138 + 0.891596i 0.997036 0.0769335i \(-0.0245129\pi\)
−0.248898 + 0.968530i \(0.580068\pi\)
\(822\) 1276.87 832.852i 1.55337 1.01320i
\(823\) −81.7368 + 463.552i −0.0993157 + 0.563247i 0.894024 + 0.448020i \(0.147871\pi\)
−0.993339 + 0.115227i \(0.963240\pi\)
\(824\) 499.513 + 88.0777i 0.606205 + 0.106890i
\(825\) 626.802 1236.29i 0.759760 1.49853i
\(826\) −710.295 + 596.009i −0.859922 + 0.721560i
\(827\) 25.6736 + 14.8227i 0.0310443 + 0.0179234i 0.515442 0.856925i \(-0.327628\pi\)
−0.484398 + 0.874848i \(0.660961\pi\)
\(828\) −301.155 132.639i −0.363714 0.160192i
\(829\) −391.655 678.367i −0.472443 0.818296i 0.527059 0.849828i \(-0.323295\pi\)
−0.999503 + 0.0315327i \(0.989961\pi\)
\(830\) −16.8701 + 46.3501i −0.0203254 + 0.0558435i
\(831\) 467.557 + 56.4576i 0.562644 + 0.0679393i
\(832\) 361.771 + 303.562i 0.434820 + 0.364858i
\(833\) −22.3570 61.4252i −0.0268391 0.0737398i
\(834\) −845.817 + 791.913i −1.01417 + 0.949536i
\(835\) 26.1320 + 148.202i 0.0312958 + 0.177487i
\(836\) 539.294i 0.645089i
\(837\) 504.163 850.614i 0.602345 1.01626i
\(838\) −1859.38 −2.21883
\(839\) −138.056 + 24.3429i −0.164548 + 0.0290142i −0.255315 0.966858i \(-0.582179\pi\)
0.0907673 + 0.995872i \(0.471068\pi\)
\(840\) −12.3982 + 40.8452i −0.0147597 + 0.0486253i
\(841\) −756.003 + 275.163i −0.898934 + 0.327185i
\(842\) −687.400 + 819.212i −0.816390 + 0.972936i
\(843\) −80.9091 60.7154i −0.0959775 0.0720230i
\(844\) 452.488 + 164.692i 0.536123 + 0.195133i
\(845\) −154.115 + 88.9781i −0.182384 + 0.105300i
\(846\) 190.839 + 655.603i 0.225578 + 0.774944i
\(847\) 707.423 1225.29i 0.835210 1.44663i
\(848\) 247.168 + 294.563i 0.291472 + 0.347362i
\(849\) 16.7656 + 308.088i 0.0197475 + 0.362883i
\(850\) −51.7661 + 293.580i −0.0609013 + 0.345389i
\(851\) −237.302 41.8427i −0.278850 0.0491688i
\(852\) −717.707 + 39.0563i −0.842379 + 0.0458408i
\(853\) 818.007 686.389i 0.958977 0.804677i −0.0218097 0.999762i \(-0.506943\pi\)
0.980786 + 0.195085i \(0.0624983\pi\)
\(854\) −199.292 115.062i −0.233364 0.134732i
\(855\) −69.2620 + 20.1615i −0.0810082 + 0.0235806i
\(856\) 3.20573 + 5.55249i 0.00374502 + 0.00648656i
\(857\) 104.143 286.129i 0.121520 0.333873i −0.863986 0.503516i \(-0.832039\pi\)
0.985506 + 0.169643i \(0.0542616\pi\)
\(858\) −1766.38 + 2353.87i −2.05872 + 2.74344i
\(859\) −397.291 333.367i −0.462504 0.388087i 0.381547 0.924349i \(-0.375391\pi\)
−0.844051 + 0.536262i \(0.819836\pi\)
\(860\) −27.4901 75.5283i −0.0319652 0.0878236i
\(861\) 373.988 + 113.520i 0.434365 + 0.131847i
\(862\) −276.519 1568.21i −0.320787 1.81927i
\(863\) 1526.04i 1.76830i 0.467202 + 0.884151i \(0.345262\pi\)
−0.467202 + 0.884151i \(0.654738\pi\)
\(864\) 11.9011 1040.34i 0.0137744 1.20409i
\(865\) −131.424 −0.151935
\(866\) −207.709 + 36.6248i −0.239849 + 0.0422919i
\(867\) 547.779 + 585.065i 0.631809 + 0.674815i
\(868\) 583.102 212.232i 0.671776 0.244507i
\(869\) −348.784 + 415.664i −0.401362 + 0.478325i
\(870\) 4.59577 38.0602i 0.00528249 0.0437473i
\(871\) −1082.75 394.090i −1.24312 0.452457i
\(872\) 119.374 68.9208i 0.136897 0.0790377i
\(873\) 239.542 543.879i 0.274390 0.623000i
\(874\) −165.998 + 287.517i −0.189929 + 0.328967i
\(875\) −151.584 180.651i −0.173239 0.206458i
\(876\) −877.063 444.673i −1.00121 0.507618i
\(877\) 37.8081 214.421i 0.0431108 0.244493i −0.955636 0.294552i \(-0.904830\pi\)
0.998746 + 0.0500585i \(0.0159408\pi\)
\(878\) −102.272 18.0332i −0.116482 0.0205390i
\(879\) −780.744 1196.98i −0.888218 1.36175i
\(880\) −226.049 + 189.677i −0.256873 + 0.215542i
\(881\) −569.630 328.876i −0.646572 0.373299i 0.140570 0.990071i \(-0.455107\pi\)
−0.787142 + 0.616772i \(0.788440\pi\)
\(882\) −329.073 21.6856i −0.373099 0.0245868i
\(883\) 262.788 + 455.162i 0.297608 + 0.515473i 0.975588 0.219608i \(-0.0704777\pi\)
−0.677980 + 0.735080i \(0.737144\pi\)
\(884\) 90.3156 248.140i 0.102167 0.280701i
\(885\) 56.8910 + 133.283i 0.0642836 + 0.150603i
\(886\) −981.897 823.909i −1.10824 0.929920i
\(887\) 309.283 + 849.749i 0.348685 + 0.958003i 0.982785 + 0.184752i \(0.0591483\pi\)
−0.634101 + 0.773251i \(0.718630\pi\)
\(888\) −38.2475 164.166i −0.0430715 0.184872i
\(889\) 114.514 + 649.444i 0.128813 + 0.730533i
\(890\) 296.569i 0.333223i
\(891\) 1535.68 65.9603i 1.72355 0.0740295i
\(892\) −31.8884 −0.0357493
\(893\) 283.041 49.9078i 0.316955 0.0558878i
\(894\) −585.541 + 136.420i −0.654967 + 0.152595i
\(895\) −115.261 + 41.9516i −0.128783 + 0.0468733i
\(896\) −347.760 + 414.445i −0.388125 + 0.462550i
\(897\) 695.176 296.731i 0.775001 0.330803i
\(898\) 951.624 + 346.363i 1.05972 + 0.385705i
\(899\) 191.554 110.594i 0.213075 0.123019i
\(900\) 521.607 + 348.794i 0.579564 + 0.387549i
\(901\) 46.6669 80.8294i 0.0517946 0.0897108i
\(902\) 703.584 + 838.498i 0.780026 + 0.929599i
\(903\) 516.755 337.059i 0.572265 0.373266i
\(904\) 63.2883 358.926i 0.0700091 0.397042i
\(905\) 4.42338 + 0.779960i 0.00488771 + 0.000861835i
\(906\) −688.966 + 1358.90i −0.760448 + 1.49989i
\(907\) −427.504 + 358.719i −0.471339 + 0.395500i −0.847283 0.531142i \(-0.821763\pi\)
0.375944 + 0.926642i \(0.377319\pi\)
\(908\) 600.928 + 346.946i 0.661815 + 0.382099i
\(909\) 22.6214 + 207.232i 0.0248860 + 0.227978i
\(910\) 123.518 + 213.940i 0.135734 + 0.235099i
\(911\) 424.323 1165.82i 0.465777 1.27971i −0.455302 0.890337i \(-0.650469\pi\)
0.921079 0.389375i \(-0.127309\pi\)
\(912\) −569.139 68.7236i −0.624056 0.0753548i
\(913\) −338.890 284.363i −0.371183 0.311460i
\(914\) −433.293 1190.46i −0.474063 1.30248i
\(915\) −26.2548 + 24.5816i −0.0286938 + 0.0268652i
\(916\) −98.6258 559.335i −0.107670 0.610627i
\(917\) 22.1498i 0.0241547i
\(918\) −311.919 + 109.505i −0.339781 + 0.119287i
\(919\) 796.922 0.867162 0.433581 0.901115i \(-0.357250\pi\)
0.433581 + 0.901115i \(0.357250\pi\)
\(920\) 30.2373 5.33164i 0.0328666 0.00579527i
\(921\) −29.0653 + 95.7544i −0.0315584 + 0.103968i
\(922\) 812.188 295.612i 0.880898 0.320621i
\(923\) 1061.22 1264.72i 1.14975 1.37022i
\(924\) 771.534 + 578.971i 0.834993 + 0.626592i
\(925\) 431.763 + 157.149i 0.466771 + 0.169891i
\(926\) 1218.16 703.303i 1.31550 0.759506i
\(927\) −1489.13 364.947i −1.60640 0.393686i
\(928\) 116.366 201.551i 0.125394 0.217189i
\(929\) 681.108 + 811.713i 0.733163 + 0.873750i 0.995839 0.0911345i \(-0.0290493\pi\)
−0.262676 + 0.964884i \(0.584605\pi\)
\(930\) −12.6312 232.113i −0.0135819 0.249584i
\(931\) −24.1046 + 136.704i −0.0258910 + 0.146835i
\(932\) 293.292 + 51.7152i 0.314691 + 0.0554884i
\(933\) −643.395 + 35.0124i −0.689598 + 0.0375267i
\(934\) 348.964 292.816i 0.373623 0.313507i
\(935\) 62.0287 + 35.8123i 0.0663409 + 0.0383019i
\(936\) 381.821 + 365.773i 0.407929 + 0.390783i
\(937\) 322.950 + 559.366i 0.344664 + 0.596975i 0.985293 0.170876i \(-0.0546596\pi\)
−0.640629 + 0.767851i \(0.721326\pi\)
\(938\) −309.611 + 850.648i −0.330075 + 0.906874i
\(939\) 550.484 733.573i 0.586245 0.781228i
\(940\) 51.3029 + 43.0483i 0.0545776 + 0.0457960i
\(941\) 164.806 + 452.801i 0.175139 + 0.481191i 0.995940 0.0900242i \(-0.0286944\pi\)
−0.820800 + 0.571215i \(0.806472\pi\)
\(942\) −1352.32 410.483i −1.43559 0.435757i
\(943\) −48.8178 276.859i −0.0517686 0.293594i
\(944\) 1151.66i 1.21998i
\(945\) 45.5141 120.734i 0.0481631 0.127760i
\(946\) 1727.87 1.82650
\(947\) 1580.88 278.751i 1.66935 0.294352i 0.742519 0.669825i \(-0.233631\pi\)
0.926833 + 0.375473i \(0.122520\pi\)
\(948\) −167.883 179.311i −0.177092 0.189146i
\(949\) 2122.47 772.518i 2.23654 0.814033i
\(950\) 406.922 484.950i 0.428339 0.510474i
\(951\) −212.807 + 1762.38i −0.223772 + 1.85318i
\(952\) 77.3721 + 28.1611i 0.0812732 + 0.0295810i
\(953\) −1484.70 + 857.192i −1.55792 + 0.899466i −0.560466 + 0.828177i \(0.689378\pi\)
−0.997456 + 0.0712890i \(0.977289\pi\)
\(954\) −278.302 379.838i −0.291721 0.398153i
\(955\) 152.597 264.306i 0.159788 0.276760i
\(956\) −618.724 737.367i −0.647201 0.771304i
\(957\) 306.674 + 155.485i 0.320454 + 0.162471i
\(958\) −297.024 + 1684.51i −0.310046 + 1.75836i
\(959\) 1130.30 + 199.303i 1.17863 + 0.207824i
\(960\) −31.6797 48.5690i −0.0329997 0.0505927i
\(961\) 291.238 244.378i 0.303057 0.254295i
\(962\) −844.839 487.768i −0.878211 0.507035i
\(963\) −8.56554 17.3847i −0.00889464 0.0180526i
\(964\) −132.164 228.914i −0.137099 0.237463i
\(965\) −6.44328 + 17.7028i −0.00667698 + 0.0183448i
\(966\) −233.122 546.153i −0.241327 0.565376i
\(967\) −312.147 261.922i −0.322799 0.270861i 0.466959 0.884279i \(-0.345350\pi\)
−0.789758 + 0.613418i \(0.789794\pi\)
\(968\) −243.492 668.988i −0.251541 0.691103i
\(969\) 31.5731 + 135.518i 0.0325832 + 0.139854i
\(970\) −24.2608 137.590i −0.0250111 0.141845i
\(971\) 794.804i 0.818542i −0.912413 0.409271i \(-0.865783\pi\)
0.912413 0.409271i \(-0.134217\pi\)
\(972\) −53.6947 + 693.758i −0.0552414 + 0.713742i
\(973\) −872.337 −0.896543
\(974\) −760.408 + 134.080i −0.780706 + 0.137660i
\(975\) −1403.69 + 327.033i −1.43968 + 0.335418i
\(976\) −268.588 + 97.7579i −0.275192 + 0.100162i
\(977\) 282.343 336.483i 0.288989 0.344404i −0.601944 0.798538i \(-0.705607\pi\)
0.890933 + 0.454134i \(0.150051\pi\)
\(978\) 664.048 283.444i 0.678985 0.289820i
\(979\) −2499.49 909.739i −2.55310 0.929253i
\(980\) −28.0124 + 16.1729i −0.0285840 + 0.0165030i
\(981\) −373.758 + 184.153i −0.380997 + 0.187719i
\(982\) −833.805 + 1444.19i −0.849089 + 1.47067i
\(983\) 169.427 + 201.915i 0.172357 + 0.205407i 0.845307 0.534281i \(-0.179418\pi\)
−0.672950 + 0.739688i \(0.734973\pi\)
\(984\) 164.719 107.440i 0.167398 0.109187i
\(985\) −7.82242 + 44.3631i −0.00794154 + 0.0450387i
\(986\) −72.8257 12.8411i −0.0738597 0.0130235i
\(987\) −232.465 + 458.508i −0.235527 + 0.464548i
\(988\) −429.569 + 360.451i −0.434786 + 0.364829i
\(989\) −384.328 221.892i −0.388603 0.224360i
\(990\) 291.489 213.570i 0.294433 0.215727i
\(991\) 152.474 + 264.093i 0.153859 + 0.266491i 0.932643 0.360801i \(-0.117497\pi\)
−0.778784 + 0.627292i \(0.784163\pi\)
\(992\) 482.652 1326.08i 0.486544 1.33677i
\(993\) −1576.40 190.350i −1.58751 0.191692i
\(994\) −993.602 833.731i −0.999600 0.838764i
\(995\) 6.08943 + 16.7306i 0.00612003 + 0.0168147i
\(996\) 146.192 136.875i 0.146779 0.137425i
\(997\) 260.718 + 1478.61i 0.261503 + 1.48305i 0.778812 + 0.627257i \(0.215822\pi\)
−0.517310 + 0.855798i \(0.673067\pi\)
\(998\) 1057.89i 1.06001i
\(999\) 82.7323 + 502.762i 0.0828151 + 0.503266i
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 27.3.f.a.14.5 yes 30
3.2 odd 2 81.3.f.a.71.1 30
4.3 odd 2 432.3.bc.a.257.5 30
9.2 odd 6 243.3.f.a.134.5 30
9.4 even 3 243.3.f.c.53.1 30
9.5 odd 6 243.3.f.b.53.5 30
9.7 even 3 243.3.f.d.134.1 30
27.2 odd 18 inner 27.3.f.a.2.5 30
27.5 odd 18 729.3.b.a.728.25 30
27.7 even 9 243.3.f.a.107.5 30
27.11 odd 18 243.3.f.c.188.1 30
27.16 even 9 243.3.f.b.188.5 30
27.20 odd 18 243.3.f.d.107.1 30
27.22 even 9 729.3.b.a.728.6 30
27.25 even 9 81.3.f.a.8.1 30
108.83 even 18 432.3.bc.a.353.5 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.3.f.a.2.5 30 27.2 odd 18 inner
27.3.f.a.14.5 yes 30 1.1 even 1 trivial
81.3.f.a.8.1 30 27.25 even 9
81.3.f.a.71.1 30 3.2 odd 2
243.3.f.a.107.5 30 27.7 even 9
243.3.f.a.134.5 30 9.2 odd 6
243.3.f.b.53.5 30 9.5 odd 6
243.3.f.b.188.5 30 27.16 even 9
243.3.f.c.53.1 30 9.4 even 3
243.3.f.c.188.1 30 27.11 odd 18
243.3.f.d.107.1 30 27.20 odd 18
243.3.f.d.134.1 30 9.7 even 3
432.3.bc.a.257.5 30 4.3 odd 2
432.3.bc.a.353.5 30 108.83 even 18
729.3.b.a.728.6 30 27.22 even 9
729.3.b.a.728.25 30 27.5 odd 18