Properties

Label 27.2.e.a.7.2
Level $27$
Weight $2$
Character 27.7
Analytic conductor $0.216$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,2,Mod(4,27)]
 
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([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 27.e (of order \(9\), 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: \(0.215596085457\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.2
Root \(0.500000 + 0.0126039i\) of defining polynomial
Character \(\chi\) \(=\) 27.7
Dual form 27.2.e.a.4.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.753189 - 0.274138i) q^{2} +(-1.68842 + 0.386327i) q^{3} +(-1.03995 + 0.872619i) q^{4} +(-0.477505 - 2.70806i) q^{5} +(-1.16579 + 0.753837i) q^{6} +(1.82076 + 1.52780i) q^{7} +(-1.34559 + 2.33062i) q^{8} +(2.70150 - 1.30456i) q^{9} +(-1.10204 - 1.90878i) q^{10} +(-0.0434396 + 0.246358i) q^{11} +(1.41875 - 1.87510i) q^{12} +(-2.45446 - 0.893351i) q^{13} +(1.79020 + 0.651581i) q^{14} +(1.85243 + 4.38787i) q^{15} +(0.0969067 - 0.549585i) q^{16} +(0.146688 + 0.254072i) q^{17} +(1.67711 - 1.72317i) q^{18} +(1.39237 - 2.41166i) q^{19} +(2.85969 + 2.39956i) q^{20} +(-3.66443 - 1.87615i) q^{21} +(0.0348180 + 0.197463i) q^{22} +(-5.12472 + 4.30015i) q^{23} +(1.37153 - 4.45490i) q^{24} +(-2.40714 + 0.876128i) q^{25} -2.09357 q^{26} +(-4.05728 + 3.24631i) q^{27} -3.22668 q^{28} +(0.333645 - 0.121437i) q^{29} +(2.59811 + 2.79707i) q^{30} +(2.11847 - 1.77761i) q^{31} +(-1.01231 - 5.74108i) q^{32} +(-0.0218307 - 0.432738i) q^{33} +(0.180135 + 0.151151i) q^{34} +(3.26796 - 5.66027i) q^{35} +(-1.67103 + 3.71406i) q^{36} +(3.49619 + 6.05558i) q^{37} +(0.387591 - 2.19814i) q^{38} +(4.48928 + 0.560124i) q^{39} +(6.95400 + 2.53105i) q^{40} +(9.13156 + 3.32362i) q^{41} +(-3.27434 - 0.408537i) q^{42} +(0.0452712 - 0.256746i) q^{43} +(-0.169802 - 0.294106i) q^{44} +(-4.82282 - 6.69291i) q^{45} +(-2.68104 + 4.64370i) q^{46} +(-8.75249 - 7.34421i) q^{47} +(0.0487006 + 0.965367i) q^{48} +(-0.234540 - 1.33014i) q^{49} +(-1.57285 + 1.31978i) q^{50} +(-0.345826 - 0.372309i) q^{51} +(3.33207 - 1.21277i) q^{52} +5.43137 q^{53} +(-2.16596 + 3.55734i) q^{54} +0.687897 q^{55} +(-6.01071 + 2.18772i) q^{56} +(-1.41922 + 4.60980i) q^{57} +(0.218007 - 0.182930i) q^{58} +(1.03788 + 5.88612i) q^{59} +(-5.75536 - 2.94669i) q^{60} +(-9.07515 - 7.61495i) q^{61} +(1.10830 - 1.91963i) q^{62} +(6.91190 + 1.75206i) q^{63} +(-1.77824 - 3.08001i) q^{64} +(-1.24723 + 7.07342i) q^{65} +(-0.135073 - 0.319949i) q^{66} +(-1.70113 - 0.619160i) q^{67} +(-0.374256 - 0.136218i) q^{68} +(6.99139 - 9.24026i) q^{69} +(0.909693 - 5.15912i) q^{70} +(0.185255 + 0.320871i) q^{71} +(-0.594663 + 8.05158i) q^{72} +(-2.51339 + 4.35333i) q^{73} +(4.29336 + 3.60255i) q^{74} +(3.72579 - 2.40921i) q^{75} +(0.656467 + 3.72301i) q^{76} +(-0.455479 + 0.382193i) q^{77} +(3.53483 - 0.808804i) q^{78} +(-0.754406 + 0.274581i) q^{79} -1.53459 q^{80} +(5.59624 - 7.04855i) q^{81} +7.78892 q^{82} +(2.58947 - 0.942488i) q^{83} +(5.44798 - 1.24655i) q^{84} +(0.617998 - 0.518562i) q^{85} +(-0.0362861 - 0.205789i) q^{86} +(-0.516417 + 0.333932i) q^{87} +(-0.515717 - 0.432738i) q^{88} +(-5.22533 + 9.05054i) q^{89} +(-5.46728 - 3.71891i) q^{90} +(-3.10412 - 5.37650i) q^{91} +(1.57704 - 8.94385i) q^{92} +(-2.89012 + 3.81976i) q^{93} +(-8.60560 - 3.13218i) q^{94} +(-7.19580 - 2.61906i) q^{95} +(3.92713 + 9.30225i) q^{96} +(-2.57600 + 14.6092i) q^{97} +(-0.541296 - 0.937552i) q^{98} +(0.204037 + 0.722208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23}+ \cdots - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.753189 0.274138i 0.532585 0.193845i −0.0617072 0.998094i \(-0.519654\pi\)
0.594292 + 0.804249i \(0.297432\pi\)
\(3\) −1.68842 + 0.386327i −0.974808 + 0.223046i
\(4\) −1.03995 + 0.872619i −0.519974 + 0.436310i
\(5\) −0.477505 2.70806i −0.213547 1.21108i −0.883411 0.468600i \(-0.844759\pi\)
0.669864 0.742484i \(-0.266352\pi\)
\(6\) −1.16579 + 0.753837i −0.475932 + 0.307753i
\(7\) 1.82076 + 1.52780i 0.688183 + 0.577454i 0.918385 0.395689i \(-0.129494\pi\)
−0.230202 + 0.973143i \(0.573939\pi\)
\(8\) −1.34559 + 2.33062i −0.475736 + 0.823999i
\(9\) 2.70150 1.30456i 0.900501 0.434854i
\(10\) −1.10204 1.90878i −0.348494 0.603610i
\(11\) −0.0434396 + 0.246358i −0.0130975 + 0.0742798i −0.990656 0.136385i \(-0.956452\pi\)
0.977558 + 0.210665i \(0.0675628\pi\)
\(12\) 1.41875 1.87510i 0.409557 0.541296i
\(13\) −2.45446 0.893351i −0.680745 0.247771i −0.0215777 0.999767i \(-0.506869\pi\)
−0.659167 + 0.751996i \(0.729091\pi\)
\(14\) 1.79020 + 0.651581i 0.478452 + 0.174142i
\(15\) 1.85243 + 4.38787i 0.478294 + 1.13294i
\(16\) 0.0969067 0.549585i 0.0242267 0.137396i
\(17\) 0.146688 + 0.254072i 0.0355772 + 0.0616215i 0.883266 0.468873i \(-0.155340\pi\)
−0.847689 + 0.530494i \(0.822006\pi\)
\(18\) 1.67711 1.72317i 0.395299 0.406154i
\(19\) 1.39237 2.41166i 0.319432 0.553273i −0.660937 0.750441i \(-0.729841\pi\)
0.980370 + 0.197168i \(0.0631745\pi\)
\(20\) 2.85969 + 2.39956i 0.639446 + 0.536559i
\(21\) −3.66443 1.87615i −0.799645 0.409410i
\(22\) 0.0348180 + 0.197463i 0.00742323 + 0.0420992i
\(23\) −5.12472 + 4.30015i −1.06858 + 0.896643i −0.994923 0.100641i \(-0.967911\pi\)
−0.0736543 + 0.997284i \(0.523466\pi\)
\(24\) 1.37153 4.45490i 0.279962 0.909352i
\(25\) −2.40714 + 0.876128i −0.481428 + 0.175226i
\(26\) −2.09357 −0.410584
\(27\) −4.05728 + 3.24631i −0.780823 + 0.624752i
\(28\) −3.22668 −0.609786
\(29\) 0.333645 0.121437i 0.0619562 0.0225502i −0.310856 0.950457i \(-0.600616\pi\)
0.372812 + 0.927907i \(0.378394\pi\)
\(30\) 2.59811 + 2.79707i 0.474348 + 0.510673i
\(31\) 2.11847 1.77761i 0.380488 0.319268i −0.432406 0.901679i \(-0.642335\pi\)
0.812894 + 0.582411i \(0.197891\pi\)
\(32\) −1.01231 5.74108i −0.178952 1.01489i
\(33\) −0.0218307 0.432738i −0.00380023 0.0753299i
\(34\) 0.180135 + 0.151151i 0.0308929 + 0.0259222i
\(35\) 3.26796 5.66027i 0.552386 0.956760i
\(36\) −1.67103 + 3.71406i −0.278506 + 0.619010i
\(37\) 3.49619 + 6.05558i 0.574770 + 0.995531i 0.996067 + 0.0886080i \(0.0282418\pi\)
−0.421297 + 0.906923i \(0.638425\pi\)
\(38\) 0.387591 2.19814i 0.0628756 0.356585i
\(39\) 4.48928 + 0.560124i 0.718860 + 0.0896917i
\(40\) 6.95400 + 2.53105i 1.09952 + 0.400194i
\(41\) 9.13156 + 3.32362i 1.42611 + 0.519062i 0.935814 0.352494i \(-0.114666\pi\)
0.490296 + 0.871556i \(0.336888\pi\)
\(42\) −3.27434 0.408537i −0.505241 0.0630386i
\(43\) 0.0452712 0.256746i 0.00690379 0.0391534i −0.981161 0.193191i \(-0.938116\pi\)
0.988065 + 0.154037i \(0.0492276\pi\)
\(44\) −0.169802 0.294106i −0.0255986 0.0443381i
\(45\) −4.82282 6.69291i −0.718943 0.997720i
\(46\) −2.68104 + 4.64370i −0.395298 + 0.684677i
\(47\) −8.75249 7.34421i −1.27668 1.07126i −0.993692 0.112140i \(-0.964230\pi\)
−0.282989 0.959123i \(-0.591326\pi\)
\(48\) 0.0487006 + 0.965367i 0.00702933 + 0.139339i
\(49\) −0.234540 1.33014i −0.0335057 0.190020i
\(50\) −1.57285 + 1.31978i −0.222435 + 0.186645i
\(51\) −0.345826 0.372309i −0.0484253 0.0521337i
\(52\) 3.33207 1.21277i 0.462074 0.168181i
\(53\) 5.43137 0.746056 0.373028 0.927820i \(-0.378320\pi\)
0.373028 + 0.927820i \(0.378320\pi\)
\(54\) −2.16596 + 3.55734i −0.294750 + 0.484092i
\(55\) 0.687897 0.0927560
\(56\) −6.01071 + 2.18772i −0.803215 + 0.292346i
\(57\) −1.41922 + 4.60980i −0.187980 + 0.610583i
\(58\) 0.218007 0.182930i 0.0286257 0.0240198i
\(59\) 1.03788 + 5.88612i 0.135121 + 0.766308i 0.974776 + 0.223188i \(0.0716462\pi\)
−0.839655 + 0.543121i \(0.817243\pi\)
\(60\) −5.75536 2.94669i −0.743014 0.380416i
\(61\) −9.07515 7.61495i −1.16195 0.974995i −0.162023 0.986787i \(-0.551802\pi\)
−0.999930 + 0.0117924i \(0.996246\pi\)
\(62\) 1.10830 1.91963i 0.140754 0.243793i
\(63\) 6.91190 + 1.75206i 0.870817 + 0.220739i
\(64\) −1.77824 3.08001i −0.222281 0.385001i
\(65\) −1.24723 + 7.07342i −0.154700 + 0.877350i
\(66\) −0.135073 0.319949i −0.0166263 0.0393829i
\(67\) −1.70113 0.619160i −0.207826 0.0756424i 0.236010 0.971751i \(-0.424160\pi\)
−0.443835 + 0.896108i \(0.646383\pi\)
\(68\) −0.374256 0.136218i −0.0453852 0.0165189i
\(69\) 6.99139 9.24026i 0.841665 1.11240i
\(70\) 0.909693 5.15912i 0.108729 0.616633i
\(71\) 0.185255 + 0.320871i 0.0219857 + 0.0380804i 0.876809 0.480839i \(-0.159668\pi\)
−0.854823 + 0.518919i \(0.826334\pi\)
\(72\) −0.594663 + 8.05158i −0.0700817 + 0.948888i
\(73\) −2.51339 + 4.35333i −0.294171 + 0.509518i −0.974792 0.223117i \(-0.928377\pi\)
0.680621 + 0.732636i \(0.261710\pi\)
\(74\) 4.29336 + 3.60255i 0.499093 + 0.418789i
\(75\) 3.72579 2.40921i 0.430217 0.278192i
\(76\) 0.656467 + 3.72301i 0.0753019 + 0.427059i
\(77\) −0.455479 + 0.382193i −0.0519067 + 0.0435549i
\(78\) 3.53483 0.808804i 0.400240 0.0915790i
\(79\) −0.754406 + 0.274581i −0.0848773 + 0.0308928i −0.384110 0.923287i \(-0.625492\pi\)
0.299233 + 0.954180i \(0.403269\pi\)
\(80\) −1.53459 −0.171572
\(81\) 5.59624 7.04855i 0.621804 0.783173i
\(82\) 7.78892 0.860143
\(83\) 2.58947 0.942488i 0.284231 0.103452i −0.195971 0.980610i \(-0.562786\pi\)
0.480201 + 0.877158i \(0.340564\pi\)
\(84\) 5.44798 1.24655i 0.594424 0.136010i
\(85\) 0.617998 0.518562i 0.0670313 0.0562460i
\(86\) −0.0362861 0.205789i −0.00391283 0.0221908i
\(87\) −0.516417 + 0.333932i −0.0553657 + 0.0358012i
\(88\) −0.515717 0.432738i −0.0549756 0.0461300i
\(89\) −5.22533 + 9.05054i −0.553884 + 0.959356i 0.444105 + 0.895975i \(0.353522\pi\)
−0.997989 + 0.0633809i \(0.979812\pi\)
\(90\) −5.46728 3.71891i −0.576302 0.392007i
\(91\) −3.10412 5.37650i −0.325401 0.563611i
\(92\) 1.57704 8.94385i 0.164418 0.932461i
\(93\) −2.89012 + 3.81976i −0.299692 + 0.396091i
\(94\) −8.60560 3.13218i −0.887600 0.323060i
\(95\) −7.19580 2.61906i −0.738273 0.268709i
\(96\) 3.92713 + 9.30225i 0.400811 + 0.949407i
\(97\) −2.57600 + 14.6092i −0.261553 + 1.48334i 0.517120 + 0.855913i \(0.327004\pi\)
−0.778673 + 0.627430i \(0.784107\pi\)
\(98\) −0.541296 0.937552i −0.0546791 0.0947070i
\(99\) 0.204037 + 0.722208i 0.0205065 + 0.0725846i
\(100\) 1.73877 3.01164i 0.173877 0.301164i
\(101\) 3.06826 + 2.57457i 0.305303 + 0.256180i 0.782548 0.622591i \(-0.213920\pi\)
−0.477244 + 0.878771i \(0.658364\pi\)
\(102\) −0.362537 0.185615i −0.0358965 0.0183786i
\(103\) −1.02789 5.82943i −0.101281 0.574391i −0.992641 0.121095i \(-0.961359\pi\)
0.891360 0.453296i \(-0.149752\pi\)
\(104\) 5.38475 4.51834i 0.528018 0.443060i
\(105\) −3.33096 + 10.8194i −0.325069 + 1.05586i
\(106\) 4.09085 1.48895i 0.397338 0.144619i
\(107\) −0.258978 −0.0250364 −0.0125182 0.999922i \(-0.503985\pi\)
−0.0125182 + 0.999922i \(0.503985\pi\)
\(108\) 1.38656 6.91645i 0.133422 0.665535i
\(109\) −8.55787 −0.819695 −0.409848 0.912154i \(-0.634418\pi\)
−0.409848 + 0.912154i \(0.634418\pi\)
\(110\) 0.518117 0.188579i 0.0494005 0.0179803i
\(111\) −8.24246 8.87367i −0.782340 0.842251i
\(112\) 1.01610 0.852609i 0.0960124 0.0805640i
\(113\) −0.541640 3.07179i −0.0509532 0.288970i 0.948675 0.316254i \(-0.102425\pi\)
−0.999628 + 0.0272843i \(0.991314\pi\)
\(114\) 0.194784 + 3.86111i 0.0182432 + 0.361626i
\(115\) 14.0922 + 11.8247i 1.31410 + 1.10266i
\(116\) −0.241005 + 0.417432i −0.0223767 + 0.0387576i
\(117\) −7.79617 + 0.788606i −0.720756 + 0.0729066i
\(118\) 2.39533 + 4.14884i 0.220508 + 0.381932i
\(119\) −0.121086 + 0.686714i −0.0111000 + 0.0629510i
\(120\) −12.7191 1.58695i −1.16109 0.144868i
\(121\) 10.2778 + 3.74082i 0.934347 + 0.340074i
\(122\) −8.92285 3.24765i −0.807837 0.294029i
\(123\) −16.7019 2.08388i −1.50596 0.187897i
\(124\) −0.651922 + 3.69724i −0.0585444 + 0.332022i
\(125\) −3.35257 5.80682i −0.299863 0.519378i
\(126\) 5.68627 0.575183i 0.506573 0.0512414i
\(127\) 9.22726 15.9821i 0.818787 1.41818i −0.0877893 0.996139i \(-0.527980\pi\)
0.906576 0.422042i \(-0.138686\pi\)
\(128\) 6.74783 + 5.66210i 0.596430 + 0.500464i
\(129\) 0.0227511 + 0.450983i 0.00200312 + 0.0397069i
\(130\) 0.999692 + 5.66954i 0.0876788 + 0.497251i
\(131\) 10.8973 9.14396i 0.952105 0.798911i −0.0275454 0.999621i \(-0.508769\pi\)
0.979651 + 0.200709i \(0.0643246\pi\)
\(132\) 0.400318 + 0.430974i 0.0348432 + 0.0375115i
\(133\) 6.21971 2.26379i 0.539317 0.196295i
\(134\) −1.45101 −0.125348
\(135\) 10.7286 + 9.43724i 0.923369 + 0.812228i
\(136\) −0.789527 −0.0677014
\(137\) 18.4984 6.73287i 1.58042 0.575228i 0.605128 0.796128i \(-0.293122\pi\)
0.975296 + 0.220900i \(0.0708995\pi\)
\(138\) 2.73273 8.87627i 0.232626 0.755598i
\(139\) −13.7206 + 11.5129i −1.16377 + 0.976515i −0.999950 0.00997617i \(-0.996824\pi\)
−0.163815 + 0.986491i \(0.552380\pi\)
\(140\) 1.54076 + 8.73806i 0.130218 + 0.738501i
\(141\) 17.6151 + 9.01876i 1.48346 + 0.759517i
\(142\) 0.227495 + 0.190891i 0.0190910 + 0.0160192i
\(143\) 0.326705 0.565870i 0.0273205 0.0473205i
\(144\) −0.455174 1.61113i −0.0379312 0.134261i
\(145\) −0.488175 0.845544i −0.0405408 0.0702186i
\(146\) −0.699647 + 3.96789i −0.0579032 + 0.328385i
\(147\) 0.909870 + 2.15522i 0.0750449 + 0.177760i
\(148\) −8.92007 3.24664i −0.733225 0.266872i
\(149\) −15.3071 5.57132i −1.25401 0.456421i −0.372252 0.928132i \(-0.621414\pi\)
−0.881753 + 0.471711i \(0.843637\pi\)
\(150\) 2.14576 2.83597i 0.175201 0.231556i
\(151\) 2.47880 14.0580i 0.201722 1.14402i −0.700793 0.713365i \(-0.747170\pi\)
0.902515 0.430659i \(-0.141719\pi\)
\(152\) 3.74711 + 6.49019i 0.303931 + 0.526424i
\(153\) 0.727731 + 0.495012i 0.0588336 + 0.0400193i
\(154\) −0.238288 + 0.412728i −0.0192018 + 0.0332585i
\(155\) −5.82546 4.88814i −0.467912 0.392625i
\(156\) −5.15739 + 3.33493i −0.412922 + 0.267008i
\(157\) 0.132555 + 0.751757i 0.0105790 + 0.0599968i 0.989640 0.143569i \(-0.0458580\pi\)
−0.979061 + 0.203566i \(0.934747\pi\)
\(158\) −0.492937 + 0.413623i −0.0392159 + 0.0329061i
\(159\) −9.17041 + 2.09828i −0.727261 + 0.166405i
\(160\) −15.0638 + 5.48279i −1.19090 + 0.433452i
\(161\) −15.9006 −1.25315
\(162\) 2.28275 6.84304i 0.179349 0.537640i
\(163\) 5.12834 0.401682 0.200841 0.979624i \(-0.435632\pi\)
0.200841 + 0.979624i \(0.435632\pi\)
\(164\) −12.3966 + 4.51199i −0.968011 + 0.352327i
\(165\) −1.16146 + 0.265753i −0.0904193 + 0.0206889i
\(166\) 1.69198 1.41974i 0.131323 0.110193i
\(167\) 1.54566 + 8.76590i 0.119607 + 0.678325i 0.984366 + 0.176137i \(0.0563603\pi\)
−0.864759 + 0.502188i \(0.832529\pi\)
\(168\) 9.30341 6.01588i 0.717774 0.464135i
\(169\) −4.73227 3.97085i −0.364021 0.305450i
\(170\) 0.323312 0.559992i 0.0247969 0.0429495i
\(171\) 0.615340 8.33154i 0.0470562 0.637129i
\(172\) 0.176962 + 0.306507i 0.0134932 + 0.0233709i
\(173\) −1.18276 + 6.70776i −0.0899235 + 0.509982i 0.906262 + 0.422717i \(0.138924\pi\)
−0.996185 + 0.0872644i \(0.972188\pi\)
\(174\) −0.297416 + 0.393083i −0.0225470 + 0.0297996i
\(175\) −5.72137 2.08241i −0.432495 0.157415i
\(176\) 0.131185 + 0.0477476i 0.00988847 + 0.00359911i
\(177\) −4.02635 9.53727i −0.302639 0.716865i
\(178\) −1.45456 + 8.24923i −0.109024 + 0.618306i
\(179\) 9.17382 + 15.8895i 0.685684 + 1.18764i 0.973221 + 0.229870i \(0.0738301\pi\)
−0.287538 + 0.957769i \(0.592837\pi\)
\(180\) 10.8558 + 2.75179i 0.809146 + 0.205106i
\(181\) −5.66282 + 9.80830i −0.420914 + 0.729045i −0.996029 0.0890276i \(-0.971624\pi\)
0.575115 + 0.818073i \(0.304957\pi\)
\(182\) −3.81190 3.19856i −0.282557 0.237093i
\(183\) 18.2645 + 9.35124i 1.35015 + 0.691264i
\(184\) −3.12628 17.7300i −0.230472 1.30707i
\(185\) 14.7295 12.3595i 1.08293 0.908687i
\(186\) −1.12966 + 3.66930i −0.0828310 + 0.269046i
\(187\) −0.0689648 + 0.0251011i −0.00504321 + 0.00183558i
\(188\) 15.5108 1.13124
\(189\) −12.3470 0.287957i −0.898115 0.0209458i
\(190\) −6.13778 −0.445281
\(191\) −6.44480 + 2.34571i −0.466329 + 0.169730i −0.564489 0.825441i \(-0.690927\pi\)
0.0981596 + 0.995171i \(0.468704\pi\)
\(192\) 4.19231 + 4.51336i 0.302554 + 0.325724i
\(193\) 15.6371 13.1211i 1.12558 0.944477i 0.126711 0.991940i \(-0.459558\pi\)
0.998873 + 0.0474627i \(0.0151135\pi\)
\(194\) 2.06474 + 11.7097i 0.148239 + 0.840707i
\(195\) −0.626800 12.4247i −0.0448861 0.889753i
\(196\) 1.40462 + 1.17861i 0.100330 + 0.0841866i
\(197\) −1.51786 + 2.62902i −0.108143 + 0.187310i −0.915018 0.403413i \(-0.867824\pi\)
0.806875 + 0.590723i \(0.201157\pi\)
\(198\) 0.351663 + 0.488024i 0.0249916 + 0.0346824i
\(199\) 1.13124 + 1.95936i 0.0801912 + 0.138895i 0.903332 0.428942i \(-0.141114\pi\)
−0.823141 + 0.567837i \(0.807780\pi\)
\(200\) 1.19709 6.78904i 0.0846471 0.480058i
\(201\) 3.11141 + 0.388209i 0.219462 + 0.0273821i
\(202\) 3.01677 + 1.09801i 0.212259 + 0.0772560i
\(203\) 0.793018 + 0.288635i 0.0556589 + 0.0202582i
\(204\) 0.684525 + 0.0854077i 0.0479263 + 0.00597974i
\(205\) 4.64020 26.3159i 0.324086 1.83798i
\(206\) −2.37226 4.10888i −0.165283 0.286279i
\(207\) −8.23463 + 18.3024i −0.572346 + 1.27210i
\(208\) −0.728826 + 1.26236i −0.0505350 + 0.0875292i
\(209\) 0.533649 + 0.447784i 0.0369132 + 0.0309739i
\(210\) 0.457167 + 9.06219i 0.0315476 + 0.625351i
\(211\) 4.41601 + 25.0445i 0.304011 + 1.72413i 0.628124 + 0.778113i \(0.283823\pi\)
−0.324113 + 0.946018i \(0.605066\pi\)
\(212\) −5.64834 + 4.73952i −0.387929 + 0.325511i
\(213\) −0.436749 0.470195i −0.0299255 0.0322172i
\(214\) −0.195060 + 0.0709959i −0.0133340 + 0.00485318i
\(215\) −0.716901 −0.0488923
\(216\) −2.10650 13.8242i −0.143329 0.940615i
\(217\) 6.57305 0.446208
\(218\) −6.44569 + 2.34604i −0.436557 + 0.158894i
\(219\) 2.56185 8.32122i 0.173114 0.562296i
\(220\) −0.715377 + 0.600272i −0.0482307 + 0.0404703i
\(221\) −0.133066 0.754654i −0.00895097 0.0507635i
\(222\) −8.64074 4.42398i −0.579929 0.296918i
\(223\) −2.93497 2.46274i −0.196540 0.164917i 0.539206 0.842174i \(-0.318724\pi\)
−0.735747 + 0.677257i \(0.763169\pi\)
\(224\) 6.92805 11.9997i 0.462900 0.801766i
\(225\) −5.35994 + 5.50713i −0.357329 + 0.367142i
\(226\) −1.25005 2.16515i −0.0831523 0.144024i
\(227\) 0.436897 2.47777i 0.0289979 0.164455i −0.966870 0.255269i \(-0.917836\pi\)
0.995868 + 0.0908142i \(0.0289469\pi\)
\(228\) −2.54669 6.03238i −0.168659 0.399504i
\(229\) 14.9783 + 5.45167i 0.989797 + 0.360257i 0.785642 0.618682i \(-0.212333\pi\)
0.204155 + 0.978939i \(0.434555\pi\)
\(230\) 13.8557 + 5.04305i 0.913615 + 0.332529i
\(231\) 0.621388 0.821264i 0.0408843 0.0540352i
\(232\) −0.165924 + 0.941003i −0.0108935 + 0.0617799i
\(233\) −14.0641 24.3598i −0.921372 1.59586i −0.797295 0.603590i \(-0.793736\pi\)
−0.124077 0.992273i \(-0.539597\pi\)
\(234\) −5.65580 + 2.73120i −0.369731 + 0.178544i
\(235\) −15.7092 + 27.2092i −1.02476 + 1.77493i
\(236\) −6.21569 5.21558i −0.404607 0.339505i
\(237\) 1.16767 0.755055i 0.0758485 0.0490461i
\(238\) 0.0970539 + 0.550420i 0.00629107 + 0.0356784i
\(239\) −11.2653 + 9.45270i −0.728691 + 0.611444i −0.929774 0.368130i \(-0.879998\pi\)
0.201083 + 0.979574i \(0.435554\pi\)
\(240\) 2.59102 0.592852i 0.167250 0.0382684i
\(241\) −7.93378 + 2.88766i −0.511059 + 0.186010i −0.584662 0.811277i \(-0.698773\pi\)
0.0736022 + 0.997288i \(0.476550\pi\)
\(242\) 8.76664 0.563541
\(243\) −6.72574 + 14.0629i −0.431456 + 0.902134i
\(244\) 16.0826 1.02958
\(245\) −3.49012 + 1.27030i −0.222975 + 0.0811564i
\(246\) −13.1509 + 3.00907i −0.838474 + 0.191851i
\(247\) −5.57198 + 4.67545i −0.354537 + 0.297492i
\(248\) 1.29235 + 7.32927i 0.0820642 + 0.465409i
\(249\) −4.00799 + 2.59169i −0.253996 + 0.164242i
\(250\) −4.11699 3.45457i −0.260381 0.218486i
\(251\) 11.6102 20.1095i 0.732832 1.26930i −0.222835 0.974856i \(-0.571531\pi\)
0.955668 0.294447i \(-0.0951354\pi\)
\(252\) −8.71689 + 4.20940i −0.549112 + 0.265168i
\(253\) −0.836762 1.44931i −0.0526067 0.0911176i
\(254\) 2.56857 14.5671i 0.161166 0.914020i
\(255\) −0.843104 + 1.11430i −0.0527972 + 0.0697801i
\(256\) 13.3186 + 4.84758i 0.832413 + 0.302973i
\(257\) −6.45118 2.34804i −0.402413 0.146466i 0.132881 0.991132i \(-0.457577\pi\)
−0.535294 + 0.844666i \(0.679799\pi\)
\(258\) 0.140768 + 0.333439i 0.00876382 + 0.0207590i
\(259\) −2.88598 + 16.3672i −0.179326 + 1.01701i
\(260\) −4.87534 8.44434i −0.302356 0.523696i
\(261\) 0.742920 0.763321i 0.0459856 0.0472484i
\(262\) 5.70105 9.87451i 0.352212 0.610049i
\(263\) 2.56850 + 2.15523i 0.158381 + 0.132897i 0.718534 0.695492i \(-0.244813\pi\)
−0.560154 + 0.828389i \(0.689258\pi\)
\(264\) 1.03792 + 0.531406i 0.0638797 + 0.0327058i
\(265\) −2.59351 14.7085i −0.159318 0.903536i
\(266\) 4.06402 3.41012i 0.249181 0.209088i
\(267\) 5.32607 17.2998i 0.325950 1.05873i
\(268\) 2.30937 0.840543i 0.141067 0.0513444i
\(269\) 12.7416 0.776869 0.388434 0.921476i \(-0.373016\pi\)
0.388434 + 0.921476i \(0.373016\pi\)
\(270\) 10.6678 + 4.16691i 0.649219 + 0.253590i
\(271\) −23.5566 −1.43096 −0.715481 0.698632i \(-0.753792\pi\)
−0.715481 + 0.698632i \(0.753792\pi\)
\(272\) 0.153849 0.0559965i 0.00932848 0.00339529i
\(273\) 7.31814 + 7.87857i 0.442914 + 0.476833i
\(274\) 12.0871 10.1422i 0.730206 0.612715i
\(275\) −0.111276 0.631078i −0.00671020 0.0380554i
\(276\) 0.792545 + 15.7102i 0.0477056 + 0.945643i
\(277\) 3.20300 + 2.68763i 0.192450 + 0.161484i 0.733921 0.679235i \(-0.237688\pi\)
−0.541472 + 0.840719i \(0.682133\pi\)
\(278\) −7.17806 + 12.4328i −0.430511 + 0.745667i
\(279\) 3.40406 7.56589i 0.203795 0.452958i
\(280\) 8.79463 + 15.2327i 0.525580 + 0.910331i
\(281\) −3.75705 + 21.3073i −0.224127 + 1.27109i 0.640220 + 0.768192i \(0.278843\pi\)
−0.864347 + 0.502896i \(0.832268\pi\)
\(282\) 15.7399 + 1.96386i 0.937297 + 0.116946i
\(283\) −4.91209 1.78785i −0.291993 0.106277i 0.191870 0.981420i \(-0.438545\pi\)
−0.483864 + 0.875143i \(0.660767\pi\)
\(284\) −0.472654 0.172032i −0.0280468 0.0102082i
\(285\) 13.1613 + 1.64213i 0.779609 + 0.0972713i
\(286\) 0.0909441 0.515770i 0.00537764 0.0304981i
\(287\) 11.5486 + 20.0027i 0.681690 + 1.18072i
\(288\) −10.2243 14.1889i −0.602475 0.836090i
\(289\) 8.45697 14.6479i 0.497469 0.861641i
\(290\) −0.599484 0.503027i −0.0352029 0.0295388i
\(291\) −1.29457 25.6617i −0.0758893 1.50431i
\(292\) −1.18500 6.72047i −0.0693468 0.393285i
\(293\) −4.70517 + 3.94811i −0.274879 + 0.230651i −0.769797 0.638289i \(-0.779643\pi\)
0.494918 + 0.868940i \(0.335198\pi\)
\(294\) 1.27613 + 1.37386i 0.0744257 + 0.0801252i
\(295\) 15.4444 5.62131i 0.899208 0.327285i
\(296\) −18.8177 −1.09376
\(297\) −0.623508 1.14056i −0.0361796 0.0661821i
\(298\) −13.0564 −0.756339
\(299\) 16.4200 5.97638i 0.949591 0.345623i
\(300\) −1.77230 + 5.75665i −0.102324 + 0.332360i
\(301\) 0.474684 0.398307i 0.0273603 0.0229580i
\(302\) −1.98683 11.2679i −0.114329 0.648393i
\(303\) −6.17513 3.16160i −0.354752 0.181629i
\(304\) −1.19048 0.998934i −0.0682789 0.0572928i
\(305\) −16.2884 + 28.2123i −0.932669 + 1.61543i
\(306\) 0.683821 + 0.173338i 0.0390914 + 0.00990909i
\(307\) −9.50194 16.4578i −0.542304 0.939298i −0.998771 0.0495580i \(-0.984219\pi\)
0.456467 0.889740i \(-0.349115\pi\)
\(308\) 0.140166 0.794920i 0.00798669 0.0452948i
\(309\) 3.98757 + 9.44541i 0.226845 + 0.537331i
\(310\) −5.72769 2.08471i −0.325311 0.118404i
\(311\) 20.2475 + 7.36948i 1.14813 + 0.417885i 0.844843 0.535015i \(-0.179694\pi\)
0.303286 + 0.952900i \(0.401916\pi\)
\(312\) −7.34615 + 9.70912i −0.415894 + 0.549671i
\(313\) −0.662228 + 3.75568i −0.0374313 + 0.212284i −0.997787 0.0664949i \(-0.978818\pi\)
0.960355 + 0.278778i \(0.0899295\pi\)
\(314\) 0.305925 + 0.529877i 0.0172643 + 0.0299027i
\(315\) 1.44423 19.5545i 0.0813731 1.10177i
\(316\) 0.544937 0.943859i 0.0306551 0.0530962i
\(317\) 3.25913 + 2.73473i 0.183051 + 0.153598i 0.729709 0.683758i \(-0.239656\pi\)
−0.546658 + 0.837356i \(0.684100\pi\)
\(318\) −6.33183 + 4.09437i −0.355072 + 0.229601i
\(319\) 0.0154235 + 0.0874713i 0.000863553 + 0.00489745i
\(320\) −7.49175 + 6.28632i −0.418801 + 0.351416i
\(321\) 0.437264 0.100050i 0.0244057 0.00558426i
\(322\) −11.9762 + 4.35898i −0.667407 + 0.242916i
\(323\) 0.816980 0.0454580
\(324\) 0.330912 + 12.2135i 0.0183840 + 0.678528i
\(325\) 6.69092 0.371146
\(326\) 3.86261 1.40587i 0.213930 0.0778642i
\(327\) 14.4493 3.30614i 0.799046 0.182830i
\(328\) −20.0334 + 16.8100i −1.10616 + 0.928178i
\(329\) −4.71570 26.7441i −0.259985 1.47445i
\(330\) −0.801944 + 0.518562i −0.0441455 + 0.0285459i
\(331\) −10.9497 9.18787i −0.601849 0.505011i 0.290191 0.956969i \(-0.406281\pi\)
−0.892039 + 0.451958i \(0.850726\pi\)
\(332\) −1.87047 + 3.23976i −0.102656 + 0.177805i
\(333\) 17.3448 + 11.7982i 0.950491 + 0.646536i
\(334\) 3.56725 + 6.17865i 0.195191 + 0.338081i
\(335\) −0.864428 + 4.90242i −0.0472288 + 0.267848i
\(336\) −1.38621 + 1.83211i −0.0756242 + 0.0999496i
\(337\) −33.5644 12.2164i −1.82837 0.665472i −0.993333 0.115278i \(-0.963224\pi\)
−0.835037 0.550194i \(-0.814554\pi\)
\(338\) −4.65286 1.69350i −0.253082 0.0921143i
\(339\) 2.10123 + 4.97721i 0.114123 + 0.270325i
\(340\) −0.190178 + 1.07855i −0.0103139 + 0.0584928i
\(341\) 0.345903 + 0.599121i 0.0187317 + 0.0324442i
\(342\) −1.82053 6.44391i −0.0984429 0.348447i
\(343\) 9.92407 17.1890i 0.535849 0.928118i
\(344\) 0.537461 + 0.450983i 0.0289780 + 0.0243154i
\(345\) −28.3616 14.5209i −1.52694 0.781778i
\(346\) 0.948013 + 5.37645i 0.0509655 + 0.289040i
\(347\) −14.8931 + 12.4968i −0.799502 + 0.670862i −0.948078 0.318039i \(-0.896976\pi\)
0.148575 + 0.988901i \(0.452531\pi\)
\(348\) 0.245651 0.797906i 0.0131683 0.0427723i
\(349\) 7.53700 2.74324i 0.403446 0.146842i −0.132323 0.991207i \(-0.542244\pi\)
0.535770 + 0.844364i \(0.320022\pi\)
\(350\) −4.88014 −0.260855
\(351\) 12.8585 4.34336i 0.686337 0.231832i
\(352\) 1.45834 0.0777296
\(353\) −8.22589 + 2.99398i −0.437820 + 0.159354i −0.551520 0.834162i \(-0.685952\pi\)
0.113700 + 0.993515i \(0.463730\pi\)
\(354\) −5.64713 6.07959i −0.300142 0.323127i
\(355\) 0.780479 0.654900i 0.0414235 0.0347585i
\(356\) −2.46361 13.9718i −0.130571 0.740505i
\(357\) −0.0608521 1.20624i −0.00322063 0.0638409i
\(358\) 11.2656 + 9.45292i 0.595403 + 0.499602i
\(359\) 4.13896 7.16888i 0.218446 0.378359i −0.735887 0.677104i \(-0.763235\pi\)
0.954333 + 0.298745i \(0.0965680\pi\)
\(360\) 22.0882 2.23428i 1.16415 0.117757i
\(361\) 5.62260 + 9.73862i 0.295926 + 0.512559i
\(362\) −1.57635 + 8.93990i −0.0828509 + 0.469871i
\(363\) −18.7984 2.34547i −0.986661 0.123105i
\(364\) 7.91977 + 2.88256i 0.415108 + 0.151087i
\(365\) 12.9892 + 4.72770i 0.679888 + 0.247459i
\(366\) 16.3201 + 2.03625i 0.853068 + 0.106437i
\(367\) −2.56997 + 14.5750i −0.134151 + 0.760809i 0.841296 + 0.540575i \(0.181793\pi\)
−0.975447 + 0.220234i \(0.929318\pi\)
\(368\) 1.86668 + 3.23318i 0.0973074 + 0.168541i
\(369\) 29.0048 2.93392i 1.50993 0.152734i
\(370\) 7.70585 13.3469i 0.400608 0.693874i
\(371\) 9.88922 + 8.29804i 0.513423 + 0.430813i
\(372\) −0.327625 6.49433i −0.0169865 0.336715i
\(373\) 4.43383 + 25.1455i 0.229575 + 1.30198i 0.853743 + 0.520694i \(0.174327\pi\)
−0.624168 + 0.781290i \(0.714562\pi\)
\(374\) −0.0450623 + 0.0378118i −0.00233012 + 0.00195520i
\(375\) 7.90387 + 8.50915i 0.408154 + 0.439411i
\(376\) 28.8938 10.5165i 1.49008 0.542346i
\(377\) −0.927403 −0.0477637
\(378\) −9.37859 + 3.16791i −0.482383 + 0.162940i
\(379\) 20.1244 1.03372 0.516861 0.856070i \(-0.327101\pi\)
0.516861 + 0.856070i \(0.327101\pi\)
\(380\) 9.76869 3.55551i 0.501123 0.182394i
\(381\) −9.40516 + 30.5492i −0.481841 + 1.56508i
\(382\) −4.21110 + 3.53353i −0.215459 + 0.180791i
\(383\) −4.14346 23.4987i −0.211721 1.20073i −0.886507 0.462716i \(-0.846875\pi\)
0.674785 0.738014i \(-0.264236\pi\)
\(384\) −13.5806 6.95312i −0.693031 0.354825i
\(385\) 1.25250 + 1.05097i 0.0638331 + 0.0535623i
\(386\) 8.18070 14.1694i 0.416387 0.721203i
\(387\) −0.212640 0.752659i −0.0108091 0.0382598i
\(388\) −10.0694 17.4407i −0.511196 0.885418i
\(389\) 6.59400 37.3964i 0.334329 1.89607i −0.0994307 0.995044i \(-0.531702\pi\)
0.433760 0.901029i \(-0.357187\pi\)
\(390\) −3.87819 9.18633i −0.196380 0.465168i
\(391\) −1.84428 0.671264i −0.0932694 0.0339473i
\(392\) 3.41565 + 1.24320i 0.172516 + 0.0627908i
\(393\) −14.8667 + 19.6487i −0.749926 + 0.991148i
\(394\) −0.422524 + 2.39625i −0.0212864 + 0.120721i
\(395\) 1.10382 + 1.91187i 0.0555390 + 0.0961964i
\(396\) −0.842400 0.573011i −0.0423322 0.0287949i
\(397\) −10.1747 + 17.6230i −0.510651 + 0.884474i 0.489272 + 0.872131i \(0.337262\pi\)
−0.999924 + 0.0123433i \(0.996071\pi\)
\(398\) 1.38917 + 1.16565i 0.0696328 + 0.0584289i
\(399\) −9.62690 + 6.22506i −0.481948 + 0.311643i
\(400\) 0.248239 + 1.40783i 0.0124119 + 0.0703916i
\(401\) 5.32015 4.46414i 0.265676 0.222928i −0.500212 0.865903i \(-0.666744\pi\)
0.765887 + 0.642975i \(0.222300\pi\)
\(402\) 2.44990 0.560563i 0.122190 0.0279583i
\(403\) −6.78773 + 2.47053i −0.338121 + 0.123066i
\(404\) −5.43745 −0.270523
\(405\) −21.7602 11.7893i −1.08127 0.585813i
\(406\) 0.676418 0.0335701
\(407\) −1.64372 + 0.598264i −0.0814760 + 0.0296548i
\(408\) 1.33305 0.305015i 0.0659958 0.0151005i
\(409\) −8.35444 + 7.01021i −0.413101 + 0.346633i −0.825531 0.564356i \(-0.809124\pi\)
0.412431 + 0.910989i \(0.364680\pi\)
\(410\) −3.71925 21.0929i −0.183681 1.04170i
\(411\) −28.6319 + 18.5143i −1.41231 + 0.913244i
\(412\) 6.15582 + 5.16535i 0.303276 + 0.254478i
\(413\) −7.10308 + 12.3029i −0.349520 + 0.605386i
\(414\) −1.18485 + 16.0426i −0.0582322 + 0.788449i
\(415\) −3.78880 6.56240i −0.185985 0.322135i
\(416\) −2.64413 + 14.9956i −0.129639 + 0.735220i
\(417\) 18.7183 24.7393i 0.916640 1.21149i
\(418\) 0.524693 + 0.190973i 0.0256636 + 0.00934078i
\(419\) 9.46194 + 3.44386i 0.462246 + 0.168244i 0.562637 0.826704i \(-0.309787\pi\)
−0.100391 + 0.994948i \(0.532009\pi\)
\(420\) −5.97719 14.1583i −0.291657 0.690852i
\(421\) −0.539623 + 3.06035i −0.0262996 + 0.149152i −0.995130 0.0985733i \(-0.968572\pi\)
0.968830 + 0.247726i \(0.0796832\pi\)
\(422\) 10.1917 + 17.6526i 0.496126 + 0.859315i
\(423\) −33.2258 8.42224i −1.61550 0.409504i
\(424\) −7.30837 + 12.6585i −0.354926 + 0.614750i
\(425\) −0.575699 0.483069i −0.0279255 0.0234323i
\(426\) −0.457853 0.234416i −0.0221830 0.0113575i
\(427\) −4.88955 27.7300i −0.236622 1.34195i
\(428\) 0.269324 0.225990i 0.0130183 0.0109236i
\(429\) −0.333004 + 1.08164i −0.0160776 + 0.0522221i
\(430\) −0.539962 + 0.196530i −0.0260393 + 0.00947753i
\(431\) −28.0701 −1.35209 −0.676044 0.736862i \(-0.736307\pi\)
−0.676044 + 0.736862i \(0.736307\pi\)
\(432\) 1.39095 + 2.54441i 0.0669219 + 0.122418i
\(433\) 19.5251 0.938317 0.469158 0.883114i \(-0.344557\pi\)
0.469158 + 0.883114i \(0.344557\pi\)
\(434\) 4.95075 1.80193i 0.237644 0.0864952i
\(435\) 1.15090 + 1.23904i 0.0551814 + 0.0594072i
\(436\) 8.89973 7.46776i 0.426220 0.357641i
\(437\) 3.23498 + 18.3465i 0.154750 + 0.877631i
\(438\) −0.351609 6.96975i −0.0168005 0.333028i
\(439\) 11.2069 + 9.40371i 0.534876 + 0.448815i 0.869781 0.493437i \(-0.164260\pi\)
−0.334905 + 0.942252i \(0.608704\pi\)
\(440\) −0.925624 + 1.60323i −0.0441274 + 0.0764309i
\(441\) −2.36886 3.28741i −0.112803 0.156543i
\(442\) −0.307103 0.531918i −0.0146074 0.0253008i
\(443\) 3.18748 18.0771i 0.151442 0.858868i −0.810526 0.585703i \(-0.800818\pi\)
0.961967 0.273165i \(-0.0880704\pi\)
\(444\) 16.3151 + 2.03562i 0.774278 + 0.0966062i
\(445\) 27.0046 + 9.82886i 1.28014 + 0.465933i
\(446\) −2.88572 1.05032i −0.136643 0.0497339i
\(447\) 27.9971 + 3.49318i 1.32422 + 0.165222i
\(448\) 1.46788 8.32476i 0.0693508 0.393308i
\(449\) −6.92969 12.0026i −0.327032 0.566437i 0.654889 0.755725i \(-0.272715\pi\)
−0.981922 + 0.189288i \(0.939382\pi\)
\(450\) −2.52733 + 5.61727i −0.119140 + 0.264801i
\(451\) −1.21547 + 2.10526i −0.0572344 + 0.0991328i
\(452\) 3.24378 + 2.72185i 0.152575 + 0.128025i
\(453\) 1.24573 + 24.6934i 0.0585294 + 1.16020i
\(454\) −0.350185 1.98600i −0.0164350 0.0932075i
\(455\) −13.0777 + 10.9735i −0.613091 + 0.514445i
\(456\) −8.83402 9.51053i −0.413691 0.445372i
\(457\) −16.5838 + 6.03602i −0.775758 + 0.282353i −0.699403 0.714728i \(-0.746551\pi\)
−0.0763555 + 0.997081i \(0.524328\pi\)
\(458\) 12.7760 0.596985
\(459\) −1.41995 0.554644i −0.0662776 0.0258886i
\(460\) −24.9736 −1.16440
\(461\) −24.0919 + 8.76872i −1.12207 + 0.408400i −0.835407 0.549631i \(-0.814768\pi\)
−0.286663 + 0.958032i \(0.592546\pi\)
\(462\) 0.242882 0.788913i 0.0112999 0.0367036i
\(463\) 14.0549 11.7935i 0.653189 0.548090i −0.254848 0.966981i \(-0.582025\pi\)
0.908037 + 0.418891i \(0.137581\pi\)
\(464\) −0.0344074 0.195134i −0.00159732 0.00905888i
\(465\) 11.7242 + 6.00268i 0.543698 + 0.278368i
\(466\) −17.2709 14.4920i −0.800059 0.671329i
\(467\) 8.13092 14.0832i 0.376254 0.651692i −0.614260 0.789104i \(-0.710545\pi\)
0.990514 + 0.137412i \(0.0438786\pi\)
\(468\) 7.41945 7.62319i 0.342964 0.352382i
\(469\) −2.15139 3.72632i −0.0993421 0.172066i
\(470\) −4.37294 + 24.8002i −0.201709 + 1.14395i
\(471\) −0.514232 1.21807i −0.0236946 0.0561257i
\(472\) −15.1149 5.50137i −0.695719 0.253221i
\(473\) 0.0612849 + 0.0223059i 0.00281788 + 0.00102563i
\(474\) 0.672489 0.888803i 0.0308884 0.0408241i
\(475\) −1.23872 + 7.02510i −0.0568362 + 0.322334i
\(476\) −0.473317 0.819809i −0.0216944 0.0375759i
\(477\) 14.6729 7.08555i 0.671824 0.324425i
\(478\) −5.89354 + 10.2079i −0.269564 + 0.466899i
\(479\) −7.25575 6.08830i −0.331524 0.278181i 0.461797 0.886986i \(-0.347205\pi\)
−0.793320 + 0.608804i \(0.791649\pi\)
\(480\) 23.3159 15.0768i 1.06422 0.688158i
\(481\) −3.17151 17.9865i −0.144608 0.820114i
\(482\) −5.18401 + 4.34990i −0.236125 + 0.198133i
\(483\) 26.8469 6.14284i 1.22158 0.279509i
\(484\) −13.9527 + 5.07836i −0.634213 + 0.230835i
\(485\) 40.7928 1.85231
\(486\) −1.21058 + 12.4358i −0.0549129 + 0.564099i
\(487\) −0.467564 −0.0211874 −0.0105937 0.999944i \(-0.503372\pi\)
−0.0105937 + 0.999944i \(0.503372\pi\)
\(488\) 29.9590 10.9042i 1.35618 0.493608i
\(489\) −8.65877 + 1.98121i −0.391563 + 0.0895936i
\(490\) −2.28048 + 1.91355i −0.103022 + 0.0864453i
\(491\) 4.34936 + 24.6665i 0.196284 + 1.11318i 0.910578 + 0.413337i \(0.135637\pi\)
−0.714294 + 0.699846i \(0.753252\pi\)
\(492\) 19.1875 12.4073i 0.865040 0.559363i
\(493\) 0.0797954 + 0.0669563i 0.00359380 + 0.00301556i
\(494\) −2.91504 + 5.04899i −0.131154 + 0.227165i
\(495\) 1.85836 0.897404i 0.0835269 0.0403353i
\(496\) −0.771653 1.33654i −0.0346482 0.0600125i
\(497\) −0.152922 + 0.867261i −0.00685947 + 0.0389020i
\(498\) −2.30829 + 3.05078i −0.103437 + 0.136709i
\(499\) 13.1878 + 4.79996i 0.590367 + 0.214876i 0.619891 0.784688i \(-0.287177\pi\)
−0.0295240 + 0.999564i \(0.509399\pi\)
\(500\) 8.55364 + 3.11327i 0.382530 + 0.139230i
\(501\) −5.99623 14.2034i −0.267892 0.634559i
\(502\) 3.23191 18.3291i 0.144247 0.818068i
\(503\) −14.1558 24.5186i −0.631176 1.09323i −0.987312 0.158794i \(-0.949239\pi\)
0.356136 0.934434i \(-0.384094\pi\)
\(504\) −13.3839 + 13.7515i −0.596168 + 0.612539i
\(505\) 5.50701 9.53842i 0.245059 0.424454i
\(506\) −1.02755 0.862218i −0.0456803 0.0383303i
\(507\) 9.52410 + 4.87624i 0.422980 + 0.216562i
\(508\) 4.35041 + 24.6724i 0.193018 + 1.09466i
\(509\) −21.9759 + 18.4399i −0.974063 + 0.817336i −0.983183 0.182622i \(-0.941541\pi\)
0.00912008 + 0.999958i \(0.497097\pi\)
\(510\) −0.329545 + 1.07040i −0.0145925 + 0.0473983i
\(511\) −11.2273 + 4.08640i −0.496666 + 0.180772i
\(512\) −6.25700 −0.276523
\(513\) 2.17975 + 14.3048i 0.0962382 + 0.631574i
\(514\) −5.50264 −0.242711
\(515\) −15.2957 + 5.56716i −0.674007 + 0.245319i
\(516\) −0.417197 0.449146i −0.0183661 0.0197725i
\(517\) 2.18951 1.83722i 0.0962946 0.0808008i
\(518\) 2.31319 + 13.1188i 0.101636 + 0.576406i
\(519\) −0.594397 11.7824i −0.0260911 0.517191i
\(520\) −14.8072 12.4247i −0.649339 0.544860i
\(521\) 12.4548 21.5724i 0.545655 0.945102i −0.452910 0.891556i \(-0.649614\pi\)
0.998565 0.0535462i \(-0.0170525\pi\)
\(522\) 0.350304 0.778588i 0.0153324 0.0340779i
\(523\) 12.9324 + 22.3995i 0.565494 + 0.979464i 0.997004 + 0.0773554i \(0.0246476\pi\)
−0.431510 + 0.902108i \(0.642019\pi\)
\(524\) −3.35347 + 19.0185i −0.146497 + 0.830826i
\(525\) 10.4646 + 1.30566i 0.456711 + 0.0569835i
\(526\) 2.52540 + 0.919169i 0.110113 + 0.0400777i
\(527\) 0.762395 + 0.277489i 0.0332104 + 0.0120876i
\(528\) −0.239942 0.0299374i −0.0104421 0.00130286i
\(529\) 3.77754 21.4235i 0.164241 0.931456i
\(530\) −5.98556 10.3673i −0.259996 0.450327i
\(531\) 10.4827 + 14.5474i 0.454908 + 0.631303i
\(532\) −4.49274 + 7.78166i −0.194785 + 0.337378i
\(533\) −19.4439 16.3154i −0.842209 0.706698i
\(534\) −0.730992 14.4901i −0.0316331 0.627047i
\(535\) 0.123663 + 0.701330i 0.00534644 + 0.0303212i
\(536\) 3.73204 3.13155i 0.161200 0.135262i
\(537\) −21.6278 23.2841i −0.933308 1.00478i
\(538\) 9.59683 3.49296i 0.413749 0.150592i
\(539\) 0.337880 0.0145535
\(540\) −19.3923 0.452267i −0.834511 0.0194625i
\(541\) −21.9158 −0.942232 −0.471116 0.882071i \(-0.656149\pi\)
−0.471116 + 0.882071i \(0.656149\pi\)
\(542\) −17.7426 + 6.45777i −0.762109 + 0.277385i
\(543\) 5.77200 18.7482i 0.247700 0.804562i
\(544\) 1.31015 1.09935i 0.0561723 0.0471342i
\(545\) 4.08643 + 23.1753i 0.175043 + 0.992720i
\(546\) 7.67176 + 3.92787i 0.328321 + 0.168097i
\(547\) −7.64210 6.41248i −0.326752 0.274178i 0.464623 0.885509i \(-0.346190\pi\)
−0.791375 + 0.611331i \(0.790634\pi\)
\(548\) −13.3621 + 23.1439i −0.570802 + 0.988658i
\(549\) −34.4507 8.73273i −1.47032 0.372704i
\(550\) −0.256815 0.444816i −0.0109506 0.0189670i
\(551\) 0.171694 0.973722i 0.00731439 0.0414820i
\(552\) 12.1280 + 28.7278i 0.516203 + 1.22274i
\(553\) −1.79310 0.652634i −0.0762502 0.0277528i
\(554\) 3.14925 + 1.14623i 0.133799 + 0.0486987i
\(555\) −20.0947 + 26.5583i −0.852971 + 1.12734i
\(556\) 4.22227 23.9457i 0.179064 1.01552i
\(557\) 9.26650 + 16.0500i 0.392634 + 0.680062i 0.992796 0.119816i \(-0.0382305\pi\)
−0.600162 + 0.799879i \(0.704897\pi\)
\(558\) 0.489797 6.63172i 0.0207348 0.280743i
\(559\) −0.340480 + 0.589729i −0.0144008 + 0.0249429i
\(560\) −2.79411 2.34454i −0.118073 0.0990749i
\(561\) 0.106744 0.0690241i 0.00450674 0.00291420i
\(562\) 3.01138 + 17.0784i 0.127027 + 0.720408i
\(563\) 33.4632 28.0789i 1.41031 1.18339i 0.454005 0.890999i \(-0.349995\pi\)
0.956300 0.292388i \(-0.0944498\pi\)
\(564\) −26.1887 + 5.99225i −1.10274 + 0.252319i
\(565\) −8.05997 + 2.93359i −0.339086 + 0.123417i
\(566\) −4.18985 −0.176113
\(567\) 20.9582 4.28380i 0.880161 0.179903i
\(568\) −0.997105 −0.0418376
\(569\) −12.7485 + 4.64008i −0.534446 + 0.194522i −0.595122 0.803635i \(-0.702896\pi\)
0.0606766 + 0.998157i \(0.480674\pi\)
\(570\) 10.3631 2.37119i 0.434064 0.0993182i
\(571\) 18.1926 15.2654i 0.761335 0.638836i −0.177139 0.984186i \(-0.556684\pi\)
0.938474 + 0.345350i \(0.112240\pi\)
\(572\) 0.154033 + 0.873565i 0.00644044 + 0.0365256i
\(573\) 9.97529 6.45034i 0.416724 0.269467i
\(574\) 14.1818 + 11.8999i 0.591935 + 0.496693i
\(575\) 8.56844 14.8410i 0.357329 0.618911i
\(576\) −8.82200 6.00083i −0.367583 0.250034i
\(577\) 4.05951 + 7.03128i 0.169000 + 0.292716i 0.938068 0.346450i \(-0.112613\pi\)
−0.769069 + 0.639166i \(0.779280\pi\)
\(578\) 2.35414 13.3510i 0.0979194 0.555329i
\(579\) −21.3329 + 28.1949i −0.886566 + 1.17174i
\(580\) 1.24551 + 0.453330i 0.0517172 + 0.0188235i
\(581\) 6.15473 + 2.24014i 0.255341 + 0.0929366i
\(582\) −8.00990 18.9732i −0.332021 0.786464i
\(583\) −0.235937 + 1.33806i −0.00977150 + 0.0554169i
\(584\) −6.76397 11.7155i −0.279895 0.484793i
\(585\) 5.85830 + 20.7360i 0.242211 + 0.857326i
\(586\) −2.46156 + 4.26354i −0.101686 + 0.176125i
\(587\) −2.82823 2.37317i −0.116734 0.0979511i 0.582552 0.812793i \(-0.302054\pi\)
−0.699286 + 0.714842i \(0.746499\pi\)
\(588\) −2.82691 1.44735i −0.116580 0.0596877i
\(589\) −1.33729 7.58412i −0.0551019 0.312498i
\(590\) 10.0915 8.46781i 0.415462 0.348614i
\(591\) 1.54713 5.02527i 0.0636403 0.206712i
\(592\) 3.66686 1.33463i 0.150707 0.0548529i
\(593\) 29.4590 1.20974 0.604869 0.796325i \(-0.293226\pi\)
0.604869 + 0.796325i \(0.293226\pi\)
\(594\) −0.782291 0.688131i −0.0320978 0.0282344i
\(595\) 1.91749 0.0786093
\(596\) 20.7802 7.56338i 0.851190 0.309808i
\(597\) −2.66695 2.87119i −0.109151 0.117510i
\(598\) 10.7290 9.00268i 0.438740 0.368147i
\(599\) −3.79862 21.5431i −0.155207 0.880225i −0.958596 0.284770i \(-0.908083\pi\)
0.803388 0.595455i \(-0.203028\pi\)
\(600\) 0.601600 + 11.9252i 0.0245602 + 0.486844i
\(601\) 27.9764 + 23.4750i 1.14118 + 0.957566i 0.999477 0.0323424i \(-0.0102967\pi\)
0.141706 + 0.989909i \(0.454741\pi\)
\(602\) 0.248335 0.430130i 0.0101214 0.0175308i
\(603\) −5.40333 + 0.546563i −0.220041 + 0.0222578i
\(604\) 9.68946 + 16.7826i 0.394258 + 0.682876i
\(605\) 5.22267 29.6192i 0.212332 1.20419i
\(606\) −5.51775 0.688447i −0.224143 0.0279662i
\(607\) 6.18395 + 2.25077i 0.250999 + 0.0913561i 0.464456 0.885596i \(-0.346250\pi\)
−0.213457 + 0.976953i \(0.568472\pi\)
\(608\) −15.2550 5.55238i −0.618674 0.225179i
\(609\) −1.45045 0.180972i −0.0587753 0.00733335i
\(610\) −4.53415 + 25.7144i −0.183582 + 1.04115i
\(611\) 14.9217 + 25.8451i 0.603667 + 1.04558i
\(612\) −1.18876 + 0.120247i −0.0480527 + 0.00486068i
\(613\) 3.57434 6.19093i 0.144366 0.250049i −0.784770 0.619787i \(-0.787219\pi\)
0.929136 + 0.369737i \(0.120552\pi\)
\(614\) −11.6685 9.79101i −0.470901 0.395133i
\(615\) 2.33194 + 46.2249i 0.0940330 + 1.86397i
\(616\) −0.277860 1.57582i −0.0111953 0.0634917i
\(617\) 12.6684 10.6301i 0.510012 0.427951i −0.351121 0.936330i \(-0.614200\pi\)
0.861133 + 0.508379i \(0.169755\pi\)
\(618\) 5.59274 + 6.02103i 0.224973 + 0.242202i
\(619\) 1.40893 0.512808i 0.0566296 0.0206115i −0.313550 0.949572i \(-0.601518\pi\)
0.370180 + 0.928960i \(0.379296\pi\)
\(620\) 10.3236 0.414608
\(621\) 6.83279 34.0833i 0.274190 1.36772i
\(622\) 17.2704 0.692481
\(623\) −23.3415 + 8.49561i −0.935157 + 0.340369i
\(624\) 0.742878 2.41296i 0.0297389 0.0965958i
\(625\) −23.9360 + 20.0847i −0.957439 + 0.803387i
\(626\) 0.530793 + 3.01028i 0.0212148 + 0.120315i
\(627\) −1.07401 0.549884i −0.0428919 0.0219602i
\(628\) −0.793848 0.666118i −0.0316780 0.0265810i
\(629\) −1.02570 + 1.77657i −0.0408974 + 0.0708363i
\(630\) −4.27286 15.1241i −0.170235 0.602560i
\(631\) 17.9456 + 31.0827i 0.714404 + 1.23738i 0.963189 + 0.268826i \(0.0866356\pi\)
−0.248785 + 0.968559i \(0.580031\pi\)
\(632\) 0.375172 2.12771i 0.0149235 0.0846356i
\(633\) −17.1314 40.5795i −0.680913 1.61289i
\(634\) 3.20443 + 1.16632i 0.127264 + 0.0463204i
\(635\) −47.6866 17.3565i −1.89238 0.688772i
\(636\) 7.70574 10.1844i 0.305553 0.403837i
\(637\) −0.612614 + 3.47431i −0.0242727 + 0.137657i
\(638\) 0.0355961 + 0.0616542i 0.00140926 + 0.00244091i
\(639\) 0.919063 + 0.625157i 0.0363576 + 0.0247308i
\(640\) 12.1112 20.9772i 0.478738 0.829198i
\(641\) 30.0504 + 25.2152i 1.18692 + 0.995942i 0.999908 + 0.0135840i \(0.00432406\pi\)
0.187010 + 0.982358i \(0.440120\pi\)
\(642\) 0.301914 0.195227i 0.0119156 0.00770501i
\(643\) −1.80915 10.2602i −0.0713461 0.404624i −0.999476 0.0323674i \(-0.989695\pi\)
0.928130 0.372256i \(-0.121416\pi\)
\(644\) 16.5358 13.8752i 0.651603 0.546760i
\(645\) 1.21043 0.276958i 0.0476606 0.0109052i
\(646\) 0.615340 0.223965i 0.0242102 0.00881180i
\(647\) −39.1517 −1.53921 −0.769606 0.638519i \(-0.779547\pi\)
−0.769606 + 0.638519i \(0.779547\pi\)
\(648\) 8.89730 + 22.5271i 0.349519 + 0.884950i
\(649\) −1.49518 −0.0586910
\(650\) 5.03953 1.83424i 0.197667 0.0719448i
\(651\) −11.0981 + 2.53935i −0.434967 + 0.0995248i
\(652\) −5.33320 + 4.47509i −0.208864 + 0.175258i
\(653\) 5.71474 + 32.4099i 0.223635 + 1.26830i 0.865277 + 0.501294i \(0.167142\pi\)
−0.641642 + 0.767004i \(0.721747\pi\)
\(654\) 9.97668 6.45124i 0.390119 0.252263i
\(655\) −29.9660 25.1444i −1.17087 0.982474i
\(656\) 2.71152 4.69649i 0.105867 0.183367i
\(657\) −1.11076 + 15.0394i −0.0433349 + 0.586743i
\(658\) −10.8834 18.8506i −0.424279 0.734873i
\(659\) −3.74532 + 21.2407i −0.145897 + 0.827422i 0.820746 + 0.571293i \(0.193558\pi\)
−0.966643 + 0.256128i \(0.917553\pi\)
\(660\) 0.975953 1.28988i 0.0379889 0.0502085i
\(661\) −24.7105 8.99389i −0.961127 0.349822i −0.186652 0.982426i \(-0.559764\pi\)
−0.774475 + 0.632604i \(0.781986\pi\)
\(662\) −10.7659 3.91848i −0.418430 0.152296i
\(663\) 0.516213 + 1.22276i 0.0200481 + 0.0474882i
\(664\) −1.28776 + 7.30326i −0.0499749 + 0.283422i
\(665\) −9.10043 15.7624i −0.352900 0.611240i
\(666\) 16.2983 + 4.13136i 0.631545 + 0.160087i
\(667\) −1.18764 + 2.05705i −0.0459855 + 0.0796493i
\(668\) −9.25670 7.76729i −0.358152 0.300526i
\(669\) 5.90688 + 3.02427i 0.228373 + 0.116925i
\(670\) 0.692862 + 3.92942i 0.0267676 + 0.151807i
\(671\) 2.27023 1.90495i 0.0876412 0.0735397i
\(672\) −7.06161 + 22.9370i −0.272408 + 0.884815i
\(673\) −10.8272 + 3.94080i −0.417360 + 0.151907i −0.542160 0.840275i \(-0.682393\pi\)
0.124800 + 0.992182i \(0.460171\pi\)
\(674\) −28.6293 −1.10276
\(675\) 6.92226 11.3690i 0.266438 0.437593i
\(676\) 8.38635 0.322552
\(677\) 31.8791 11.6030i 1.22521 0.445941i 0.353257 0.935526i \(-0.385074\pi\)
0.871955 + 0.489585i \(0.162852\pi\)
\(678\) 2.94707 + 3.17275i 0.113181 + 0.121849i
\(679\) −27.0103 + 22.6643i −1.03656 + 0.869776i
\(680\) 0.377003 + 2.13809i 0.0144574 + 0.0819920i
\(681\) 0.219563 + 4.35229i 0.00841369 + 0.166780i
\(682\) 0.424772 + 0.356426i 0.0162654 + 0.0136483i
\(683\) −18.3777 + 31.8310i −0.703201 + 1.21798i 0.264135 + 0.964486i \(0.414913\pi\)
−0.967337 + 0.253495i \(0.918420\pi\)
\(684\) 6.63034 + 9.20132i 0.253518 + 0.351821i
\(685\) −27.0661 46.8799i −1.03414 1.79119i
\(686\) 2.76254 15.6671i 0.105474 0.598174i
\(687\) −27.3958 3.41816i −1.04522 0.130411i
\(688\) −0.136717 0.0497608i −0.00521227 0.00189711i
\(689\) −13.3311 4.85212i −0.507874 0.184851i
\(690\) −25.3424 3.16195i −0.964769 0.120374i
\(691\) 2.32309 13.1749i 0.0883744 0.501196i −0.908203 0.418530i \(-0.862545\pi\)
0.996577 0.0826660i \(-0.0263435\pi\)
\(692\) −4.62331 8.00781i −0.175752 0.304411i
\(693\) −0.731885 + 1.62670i −0.0278020 + 0.0617930i
\(694\) −7.79146 + 13.4952i −0.295760 + 0.512271i
\(695\) 37.7294 + 31.6588i 1.43116 + 1.20089i
\(696\) −0.0833854 1.65291i −0.00316072 0.0626532i
\(697\) 0.495057 + 2.80761i 0.0187516 + 0.106346i
\(698\) 4.92475 4.13236i 0.186405 0.156412i
\(699\) 33.1570 + 35.6961i 1.25411 + 1.35015i
\(700\) 7.76708 2.82699i 0.293568 0.106850i
\(701\) 5.00452 0.189018 0.0945091 0.995524i \(-0.469872\pi\)
0.0945091 + 0.995524i \(0.469872\pi\)
\(702\) 8.49421 6.79639i 0.320593 0.256513i
\(703\) 19.4720 0.734400
\(704\) 0.836033 0.304291i 0.0315092 0.0114684i
\(705\) 16.0121 52.0094i 0.603050 1.95879i
\(706\) −5.37489 + 4.51007i −0.202287 + 0.169739i
\(707\) 1.65313 + 9.37537i 0.0621724 + 0.352597i
\(708\) 12.5096 + 6.40479i 0.470139 + 0.240707i
\(709\) 13.1330 + 11.0199i 0.493218 + 0.413859i 0.855178 0.518334i \(-0.173448\pi\)
−0.361960 + 0.932194i \(0.617892\pi\)
\(710\) 0.408315 0.707223i 0.0153238 0.0265416i
\(711\) −1.67982 + 1.72595i −0.0629982 + 0.0647282i
\(712\) −14.0623 24.3566i −0.527006 0.912800i
\(713\) −3.21258 + 18.2195i −0.120312 + 0.682324i
\(714\) −0.376509 0.891844i −0.0140905 0.0333764i
\(715\) −1.68842 0.614533i −0.0631432 0.0229822i
\(716\) −23.4058 8.51902i −0.874716 0.318371i
\(717\) 15.3687 20.3122i 0.573954 0.758572i
\(718\) 1.15215 6.53417i 0.0429979 0.243853i
\(719\) 21.6760 + 37.5439i 0.808377 + 1.40015i 0.913987 + 0.405742i \(0.132987\pi\)
−0.105610 + 0.994408i \(0.533680\pi\)
\(720\) −4.14569 + 2.00196i −0.154501 + 0.0746087i
\(721\) 7.03467 12.1844i 0.261985 0.453771i
\(722\) 6.90461 + 5.79365i 0.256963 + 0.215617i
\(723\) 12.2799 7.94060i 0.456696 0.295314i
\(724\) −2.66987 15.1416i −0.0992251 0.562733i
\(725\) −0.696735 + 0.584630i −0.0258761 + 0.0217126i
\(726\) −14.8017 + 3.38679i −0.549344 + 0.125695i
\(727\) 34.1521 12.4303i 1.26663 0.461016i 0.380642 0.924722i \(-0.375703\pi\)
0.885989 + 0.463706i \(0.153481\pi\)
\(728\) 16.7075 0.619220
\(729\) 5.92298 26.3423i 0.219370 0.975642i
\(730\) 11.0794 0.410067
\(731\) 0.0718726 0.0261595i 0.00265830 0.000967544i
\(732\) −27.1542 + 6.21315i −1.00365 + 0.229645i
\(733\) 2.96889 2.49119i 0.109658 0.0920143i −0.586310 0.810087i \(-0.699420\pi\)
0.695968 + 0.718073i \(0.254975\pi\)
\(734\) 2.05990 + 11.6823i 0.0760322 + 0.431200i
\(735\) 5.40202 3.49312i 0.199257 0.128846i
\(736\) 29.8753 + 25.0683i 1.10122 + 0.924031i
\(737\) 0.226432 0.392191i 0.00834071 0.0144465i
\(738\) 21.0418 10.1611i 0.774559 0.374036i
\(739\) −13.2241 22.9048i −0.486456 0.842567i 0.513422 0.858136i \(-0.328377\pi\)
−0.999879 + 0.0155689i \(0.995044\pi\)
\(740\) −4.53273 + 25.7064i −0.166627 + 0.944986i
\(741\) 7.60158 10.0467i 0.279251 0.369075i
\(742\) 9.72326 + 3.53898i 0.356952 + 0.129920i
\(743\) 12.6514 + 4.60474i 0.464136 + 0.168932i 0.563494 0.826120i \(-0.309457\pi\)
−0.0993584 + 0.995052i \(0.531679\pi\)
\(744\) −5.01352 11.8756i −0.183805 0.435381i
\(745\) −7.77830 + 44.1129i −0.284975 + 1.61617i
\(746\) 10.2329 + 17.7238i 0.374651 + 0.648915i
\(747\) 5.76591 5.92425i 0.210964 0.216757i
\(748\) 0.0498160 0.0862839i 0.00182145 0.00315485i
\(749\) −0.471538 0.395667i −0.0172296 0.0144574i
\(750\) 8.28579 + 4.24224i 0.302554 + 0.154905i
\(751\) 0.654359 + 3.71106i 0.0238779 + 0.135418i 0.994416 0.105528i \(-0.0336533\pi\)
−0.970538 + 0.240946i \(0.922542\pi\)
\(752\) −4.88444 + 4.09854i −0.178117 + 0.149458i
\(753\) −11.8341 + 38.4386i −0.431258 + 1.40078i
\(754\) −0.698510 + 0.254237i −0.0254382 + 0.00925876i
\(755\) −39.2536 −1.42859
\(756\) 13.0915 10.4748i 0.476135 0.380965i
\(757\) −33.7073 −1.22511 −0.612556 0.790427i \(-0.709859\pi\)
−0.612556 + 0.790427i \(0.709859\pi\)
\(758\) 15.1575 5.51687i 0.550544 0.200382i
\(759\) 1.97271 + 2.12378i 0.0716049 + 0.0770884i
\(760\) 15.7866 13.2465i 0.572640 0.480502i
\(761\) −1.67665 9.50874i −0.0607784 0.344692i −0.999999 0.00137744i \(-0.999562\pi\)
0.939221 0.343314i \(-0.111550\pi\)
\(762\) 1.29084 + 25.5876i 0.0467621 + 0.926941i
\(763\) −15.5818 13.0747i −0.564100 0.473336i
\(764\) 4.65533 8.06327i 0.168424 0.291719i
\(765\) 0.993028 2.20711i 0.0359030 0.0797984i
\(766\) −9.56272 16.5631i −0.345515 0.598450i
\(767\) 2.71093 15.3745i 0.0978861 0.555139i
\(768\) −24.3601 3.03939i −0.879019 0.109675i
\(769\) −36.3764 13.2399i −1.31177 0.477445i −0.410957 0.911655i \(-0.634805\pi\)
−0.900812 + 0.434210i \(0.857027\pi\)
\(770\) 1.23148 + 0.448221i 0.0443793 + 0.0161528i
\(771\) 11.7994 + 1.47220i 0.424944 + 0.0530200i
\(772\) −4.81205 + 27.2905i −0.173189 + 0.982206i
\(773\) −12.1519 21.0478i −0.437075 0.757036i 0.560387 0.828231i \(-0.310652\pi\)
−0.997462 + 0.0711944i \(0.977319\pi\)
\(774\) −0.366491 0.508601i −0.0131732 0.0182813i
\(775\) −3.54205 + 6.13500i −0.127234 + 0.220376i
\(776\) −30.5824 25.6617i −1.09784 0.921200i
\(777\) −1.45036 28.7496i −0.0520312 1.03139i
\(778\) −5.28527 29.9742i −0.189486 1.07463i
\(779\) 20.7300 17.3945i 0.742728 0.623223i
\(780\) 11.4939 + 12.3741i 0.411547 + 0.443064i
\(781\) −0.0870967 + 0.0317006i −0.00311656 + 0.00113434i
\(782\) −1.57311 −0.0562544
\(783\) −0.959467 + 1.57581i −0.0342886 + 0.0563150i
\(784\) −0.753755 −0.0269198
\(785\) 1.97251 0.717936i 0.0704020 0.0256242i
\(786\) −5.81096 + 18.8748i −0.207270 + 0.673240i
\(787\) 16.0414 13.4604i 0.571816 0.479810i −0.310432 0.950596i \(-0.600474\pi\)
0.882248 + 0.470785i \(0.156029\pi\)
\(788\) −0.715633 4.05856i −0.0254934 0.144580i
\(789\) −5.16932 2.64664i −0.184033 0.0942229i
\(790\) 1.35550 + 1.13740i 0.0482264 + 0.0404668i
\(791\) 3.70688 6.42051i 0.131802 0.228287i
\(792\) −1.95774 0.496258i −0.0695654 0.0176338i
\(793\) 15.4718 + 26.7979i 0.549419 + 0.951621i
\(794\) −2.83229 + 16.0627i −0.100514 + 0.570045i
\(795\) 10.0612 + 23.8321i 0.356834 + 0.845239i
\(796\) −2.88620 1.05049i −0.102299 0.0372337i
\(797\) −11.2169 4.08261i −0.397322 0.144614i 0.135628 0.990760i \(-0.456695\pi\)
−0.532951 + 0.846146i \(0.678917\pi\)
\(798\) −5.54435 + 7.32775i −0.196268 + 0.259400i
\(799\) 0.582068 3.30107i 0.0205921 0.116783i
\(800\) 7.46668 + 12.9327i 0.263987 + 0.457239i
\(801\) −2.30926 + 31.2668i −0.0815939 + 1.10476i
\(802\) 2.78329 4.82080i 0.0982814 0.170228i
\(803\) −0.963297 0.808303i −0.0339940 0.0285244i
\(804\) −3.57446 + 2.31136i −0.126062 + 0.0815154i
\(805\) 7.59263 + 43.0600i 0.267605 + 1.51766i
\(806\) −4.43518 + 3.72155i −0.156222 + 0.131086i
\(807\) −21.5131 + 4.92242i −0.757298 + 0.173277i
\(808\) −10.1290 + 3.68664i −0.356336 + 0.129696i
\(809\) 8.60808 0.302644 0.151322 0.988485i \(-0.451647\pi\)
0.151322 + 0.988485i \(0.451647\pi\)
\(810\) −19.6214 2.91424i −0.689426 0.102396i
\(811\) 1.53770 0.0539958 0.0269979 0.999635i \(-0.491405\pi\)
0.0269979 + 0.999635i \(0.491405\pi\)
\(812\) −1.07656 + 0.391837i −0.0377800 + 0.0137508i
\(813\) 39.7734 9.10055i 1.39491 0.319170i
\(814\) −1.07402 + 0.901211i −0.0376444 + 0.0315874i
\(815\) −2.44881 13.8879i −0.0857779 0.486471i
\(816\) −0.238129 + 0.153982i −0.00833617 + 0.00539043i
\(817\) −0.556149 0.466665i −0.0194572 0.0163265i
\(818\) −4.37071 + 7.57029i −0.152818 + 0.264689i
\(819\) −15.3998 10.4751i −0.538112 0.366030i
\(820\) 18.1382 + 31.4163i 0.633413 + 1.09710i
\(821\) 5.03168 28.5361i 0.175607 0.995915i −0.761835 0.647772i \(-0.775701\pi\)
0.937441 0.348144i \(-0.113188\pi\)
\(822\) −16.4898 + 21.7939i −0.575147 + 0.760149i
\(823\) 10.5779 + 3.85004i 0.368722 + 0.134204i 0.519734 0.854328i \(-0.326031\pi\)
−0.151012 + 0.988532i \(0.548253\pi\)
\(824\) 14.9693 + 5.44838i 0.521481 + 0.189803i
\(825\) 0.431683 + 1.02253i 0.0150293 + 0.0356001i
\(826\) −1.97727 + 11.2136i −0.0687979 + 0.390172i
\(827\) −15.4640 26.7844i −0.537734 0.931383i −0.999026 0.0441346i \(-0.985947\pi\)
0.461291 0.887249i \(-0.347386\pi\)
\(828\) −7.40742 26.2192i −0.257426 0.911180i
\(829\) 4.91762 8.51757i 0.170796 0.295827i −0.767902 0.640567i \(-0.778699\pi\)
0.938698 + 0.344739i \(0.112033\pi\)
\(830\) −4.65269 3.90407i −0.161497 0.135512i
\(831\) −6.44630 3.30044i −0.223620 0.114491i
\(832\) 1.61310 + 9.14836i 0.0559243 + 0.317162i
\(833\) 0.303547 0.254706i 0.0105173 0.00882505i
\(834\) 7.31644 23.7648i 0.253348 0.822906i
\(835\) 23.0006 8.37152i 0.795967 0.289708i
\(836\) −0.945711 −0.0327081
\(837\) −2.82456 + 14.0894i −0.0976310 + 0.487003i
\(838\) 8.07072 0.278798
\(839\) 12.3506 4.49524i 0.426389 0.155193i −0.119907 0.992785i \(-0.538260\pi\)
0.546296 + 0.837592i \(0.316037\pi\)
\(840\) −20.7338 22.3216i −0.715385 0.770169i
\(841\) −22.1187 + 18.5598i −0.762714 + 0.639993i
\(842\) 0.432522 + 2.45296i 0.0149057 + 0.0845344i
\(843\) −1.88811 37.4271i −0.0650301 1.28906i
\(844\) −26.4467 22.1914i −0.910333 0.763860i
\(845\) −8.49363 + 14.7114i −0.292190 + 0.506088i
\(846\) −27.3342 + 2.76494i −0.939769 + 0.0950604i
\(847\) 12.9982 + 22.5136i 0.446624 + 0.773575i
\(848\) 0.526336 2.98500i 0.0180745 0.102505i
\(849\) 8.98435 + 1.12097i 0.308342 + 0.0384717i
\(850\) −0.566038 0.206021i −0.0194149 0.00706646i
\(851\) −43.9569 15.9990i −1.50682 0.548438i
\(852\) 0.864497 + 0.107863i 0.0296172 + 0.00369531i
\(853\) 2.68153 15.2077i 0.0918139 0.520703i −0.903863 0.427821i \(-0.859281\pi\)
0.995677 0.0928812i \(-0.0296077\pi\)
\(854\) −11.2846 19.5455i −0.386151 0.668834i
\(855\) −22.8562 + 2.31197i −0.781665 + 0.0790678i
\(856\) 0.348478 0.603581i 0.0119107 0.0206300i
\(857\) 16.8398 + 14.1302i 0.575235 + 0.482680i 0.883378 0.468660i \(-0.155263\pi\)
−0.308143 + 0.951340i \(0.599708\pi\)
\(858\) 0.0457041 + 0.905968i 0.00156031 + 0.0309293i
\(859\) 3.39772 + 19.2694i 0.115929 + 0.657464i 0.986286 + 0.165044i \(0.0527765\pi\)
−0.870358 + 0.492420i \(0.836112\pi\)
\(860\) 0.745540 0.625582i 0.0254227 0.0213322i
\(861\) −27.2264 29.3114i −0.927873 0.998929i
\(862\) −21.1421 + 7.69508i −0.720101 + 0.262095i
\(863\) 21.8676 0.744383 0.372191 0.928156i \(-0.378607\pi\)
0.372191 + 0.928156i \(0.378607\pi\)
\(864\) 22.7445 + 20.0069i 0.773784 + 0.680648i
\(865\) 18.7298 0.636833
\(866\) 14.7061 5.35258i 0.499733 0.181888i
\(867\) −8.62001 + 27.9989i −0.292751 + 0.950893i
\(868\) −6.83563 + 5.73577i −0.232016 + 0.194685i
\(869\) −0.0348743 0.197782i −0.00118303 0.00670929i
\(870\) 1.20651 + 0.617723i 0.0409046 + 0.0209428i
\(871\) 3.62223 + 3.03941i 0.122734 + 0.102986i
\(872\) 11.5153 19.9452i 0.389959 0.675428i
\(873\) 12.0996 + 42.8275i 0.409508 + 1.44949i
\(874\) 7.46602 + 12.9315i 0.252542 + 0.437416i
\(875\) 2.76743 15.6949i 0.0935563 0.530584i
\(876\) 4.59707 + 10.8891i 0.155321 + 0.367910i
\(877\) 36.7419 + 13.3729i 1.24068 + 0.451572i 0.877244 0.480045i \(-0.159380\pi\)
0.363441 + 0.931617i \(0.381602\pi\)
\(878\) 11.0188 + 4.01053i 0.371868 + 0.135349i
\(879\) 6.41903 8.48379i 0.216509 0.286151i
\(880\) 0.0666619 0.378058i 0.00224717 0.0127443i
\(881\) 3.65254 + 6.32639i 0.123057 + 0.213141i 0.920972 0.389629i \(-0.127397\pi\)
−0.797915 + 0.602771i \(0.794063\pi\)
\(882\) −2.68541 1.82665i −0.0904223 0.0615063i
\(883\) 1.74646 3.02496i 0.0587732 0.101798i −0.835142 0.550035i \(-0.814614\pi\)
0.893915 + 0.448237i \(0.147948\pi\)
\(884\) 0.796907 + 0.668684i 0.0268029 + 0.0224903i
\(885\) −23.9049 + 15.4577i −0.803556 + 0.519605i
\(886\) −2.55485 14.4893i −0.0858318 0.486776i
\(887\) 21.7720 18.2688i 0.731031 0.613408i −0.199381 0.979922i \(-0.563893\pi\)
0.930413 + 0.366514i \(0.119449\pi\)
\(888\) 31.7721 7.26978i 1.06620 0.243958i
\(889\) 41.2181 15.0021i 1.38241 0.503156i
\(890\) 23.0340 0.772102
\(891\) 1.49337 + 1.68487i 0.0500298 + 0.0564452i
\(892\) 5.20125 0.174151
\(893\) −29.8985 + 10.8821i −1.00051 + 0.364157i
\(894\) 22.0447 5.04405i 0.737286 0.168698i
\(895\) 38.6493 32.4306i 1.29190 1.08404i
\(896\) 3.63563 + 20.6187i 0.121458 + 0.688821i
\(897\) −25.4149 + 16.4341i −0.848579 + 0.548718i
\(898\) −8.50974 7.14052i −0.283974 0.238282i
\(899\) 0.490949 0.850349i 0.0163741 0.0283607i
\(900\) 0.768427 10.4043i 0.0256142 0.346810i
\(901\) 0.796719 + 1.37996i 0.0265426 + 0.0459731i
\(902\) −0.338348 + 1.91887i −0.0112658 + 0.0638913i
\(903\) −0.647588 + 0.855892i −0.0215504 + 0.0284823i
\(904\) 7.88800 + 2.87100i 0.262351 + 0.0954880i
\(905\) 29.2655 + 10.6518i 0.972819 + 0.354077i
\(906\) 7.70767 + 18.2573i 0.256070 + 0.606558i
\(907\) 9.22362 52.3097i 0.306265 1.73692i −0.311224 0.950337i \(-0.600739\pi\)
0.617489 0.786579i \(-0.288150\pi\)
\(908\) 1.70780 + 2.95799i 0.0566753 + 0.0981644i
\(909\) 11.6476 + 2.95249i 0.386327 + 0.0979279i
\(910\) −6.84171 + 11.8502i −0.226801 + 0.392830i
\(911\) −6.18649 5.19108i −0.204968 0.171988i 0.534526 0.845152i \(-0.320490\pi\)
−0.739493 + 0.673164i \(0.764935\pi\)
\(912\) 2.39595 + 1.22670i 0.0793377 + 0.0406201i
\(913\) 0.119704 + 0.678878i 0.00396164 + 0.0224676i
\(914\) −10.8360 + 9.09252i −0.358424 + 0.300754i
\(915\) 16.6024 53.9267i 0.548858 1.78276i
\(916\) −20.3339 + 7.40094i −0.671852 + 0.244534i
\(917\) 33.8116 1.11656
\(918\) −1.22154 0.0284888i −0.0403168 0.000940269i
\(919\) −47.9961 −1.58325 −0.791623 0.611009i \(-0.790764\pi\)
−0.791623 + 0.611009i \(0.790764\pi\)
\(920\) −46.5212 + 16.9323i −1.53376 + 0.558242i
\(921\) 22.4013 + 24.1168i 0.738149 + 0.794677i
\(922\) −15.7419 + 13.2090i −0.518431 + 0.435016i
\(923\) −0.168051 0.953063i −0.00553146 0.0313705i
\(924\) 0.0704406 + 1.39631i 0.00231732 + 0.0459351i
\(925\) −13.7213 11.5135i −0.451153 0.378562i
\(926\) 7.35298 12.7357i 0.241634 0.418522i
\(927\) −10.3817 14.4073i −0.340979 0.473197i
\(928\) −1.03493 1.79255i −0.0339732 0.0588433i
\(929\) −5.03474 + 28.5534i −0.165185 + 0.936808i 0.783689 + 0.621153i \(0.213335\pi\)
−0.948874 + 0.315655i \(0.897776\pi\)
\(930\) 10.4761 + 1.30710i 0.343525 + 0.0428614i
\(931\) −3.53442 1.28642i −0.115836 0.0421608i
\(932\) 35.8828 + 13.0603i 1.17538 + 0.427803i
\(933\) −37.0332 4.62061i −1.21241 0.151272i
\(934\) 2.26338 12.8363i 0.0740602 0.420016i
\(935\) 0.100907 + 0.174775i 0.00330000 + 0.00571576i
\(936\) 8.65246 19.2311i 0.282815 0.628587i
\(937\) −2.51425 + 4.35481i −0.0821369 + 0.142265i −0.904168 0.427178i \(-0.859508\pi\)
0.822031 + 0.569443i \(0.192841\pi\)
\(938\) −2.64193 2.21685i −0.0862622 0.0723826i
\(939\) −0.332803 6.59699i −0.0108606 0.215285i
\(940\) −7.40649 42.0043i −0.241573 1.37003i
\(941\) −42.7767 + 35.8939i −1.39448 + 1.17011i −0.430995 + 0.902354i \(0.641837\pi\)
−0.963487 + 0.267755i \(0.913718\pi\)
\(942\) −0.721234 0.776466i −0.0234991 0.0252986i
\(943\) −61.0887 + 22.2345i −1.98932 + 0.724054i
\(944\) 3.33551 0.108561
\(945\) 5.11596 + 33.5741i 0.166422 + 1.09216i
\(946\) 0.0522740 0.00169957
\(947\) −39.9645 + 14.5459i −1.29867 + 0.472678i −0.896564 0.442914i \(-0.853945\pi\)
−0.402109 + 0.915592i \(0.631723\pi\)
\(948\) −0.555443 + 1.80415i −0.0180400 + 0.0585961i
\(949\) 10.0581 8.43973i 0.326499 0.273965i
\(950\) 0.992864 + 5.63081i 0.0322127 + 0.182688i
\(951\) −6.55926 3.35828i −0.212699 0.108900i
\(952\) −1.43754 1.20624i −0.0465909 0.0390944i
\(953\) −10.9074 + 18.8922i −0.353325 + 0.611977i −0.986830 0.161762i \(-0.948282\pi\)
0.633505 + 0.773739i \(0.281616\pi\)
\(954\) 9.10901 9.35916i 0.294915 0.303014i
\(955\) 9.42977 + 16.3328i 0.305140 + 0.528518i
\(956\) 3.46670 19.6606i 0.112121 0.635870i
\(957\) −0.0598339 0.141729i −0.00193415 0.00458146i
\(958\) −7.13399 2.59656i −0.230489 0.0838910i
\(959\) 43.9676 + 16.0029i 1.41979 + 0.516761i
\(960\) 10.2206 13.5082i 0.329869 0.435975i
\(961\) −4.05507 + 22.9974i −0.130809 + 0.741852i
\(962\) −7.31954 12.6778i −0.235991 0.408749i
\(963\) −0.699631 + 0.337853i −0.0225453 + 0.0108872i
\(964\) 5.73088 9.92618i 0.184579 0.319701i
\(965\) −42.9996 36.0809i −1.38421 1.16149i
\(966\) 18.5368 11.9865i 0.596412 0.385659i
\(967\) 0.803746 + 4.55827i 0.0258467 + 0.146584i 0.995000 0.0998746i \(-0.0318442\pi\)
−0.969153 + 0.246459i \(0.920733\pi\)
\(968\) −22.5481 + 18.9201i −0.724724 + 0.608115i
\(969\) −1.37940 + 0.315621i −0.0443128 + 0.0101392i
\(970\) 30.7247 11.1829i 0.986511 0.359060i
\(971\) −21.6509 −0.694809 −0.347405 0.937715i \(-0.612937\pi\)
−0.347405 + 0.937715i \(0.612937\pi\)
\(972\) −5.27712 20.4937i −0.169264 0.657334i
\(973\) −42.5714 −1.36478
\(974\) −0.352164 + 0.128177i −0.0112841 + 0.00410707i
\(975\) −11.2971 + 2.58488i −0.361796 + 0.0827825i
\(976\) −5.06451 + 4.24963i −0.162111 + 0.136027i
\(977\) −3.83499 21.7493i −0.122692 0.695822i −0.982652 0.185460i \(-0.940623\pi\)
0.859960 0.510362i \(-0.170489\pi\)
\(978\) −5.97856 + 3.86593i −0.191173 + 0.123619i
\(979\) −2.00269 1.68046i −0.0640063 0.0537076i
\(980\) 2.52105 4.36659i 0.0805320 0.139485i
\(981\) −23.1191 + 11.1643i −0.738137 + 0.356448i
\(982\) 10.0379 + 17.3862i 0.320323 + 0.554815i
\(983\) −2.40729 + 13.6524i −0.0767807 + 0.435445i 0.922049 + 0.387074i \(0.126514\pi\)
−0.998829 + 0.0483713i \(0.984597\pi\)
\(984\) 27.3306 36.1217i 0.871266 1.15152i
\(985\) 7.84434 + 2.85511i 0.249941 + 0.0909712i
\(986\) 0.0784563 + 0.0285558i 0.00249856 + 0.000909401i
\(987\) 18.2940 + 43.3334i 0.582305 + 1.37932i
\(988\) 1.71468 9.72444i 0.0545513 0.309376i
\(989\) 0.872042 + 1.51042i 0.0277293 + 0.0480286i
\(990\) 1.15368 1.18536i 0.0366664 0.0376733i
\(991\) −17.4112 + 30.1570i −0.553084 + 0.957970i 0.444966 + 0.895548i \(0.353216\pi\)
−0.998050 + 0.0624224i \(0.980117\pi\)
\(992\) −12.3499 10.3628i −0.392111 0.329020i
\(993\) 22.0371 + 11.2828i 0.699328 + 0.358049i
\(994\) 0.122571 + 0.695133i 0.00388771 + 0.0220483i
\(995\) 4.76590 3.99906i 0.151089 0.126779i
\(996\) 1.90653 6.19267i 0.0604109 0.196222i
\(997\) 23.2572 8.46492i 0.736562 0.268087i 0.0536221 0.998561i \(-0.482923\pi\)
0.682940 + 0.730475i \(0.260701\pi\)
\(998\) 11.2488 0.356073
\(999\) −33.8433 13.2195i −1.07075 0.418245i
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 27.2.e.a.7.2 yes 12
3.2 odd 2 81.2.e.a.19.1 12
4.3 odd 2 432.2.u.c.385.2 12
5.2 odd 4 675.2.u.b.574.3 24
5.3 odd 4 675.2.u.b.574.2 24
5.4 even 2 675.2.l.c.601.1 12
9.2 odd 6 243.2.e.a.136.2 12
9.4 even 3 243.2.e.c.217.1 12
9.5 odd 6 243.2.e.b.217.2 12
9.7 even 3 243.2.e.d.136.1 12
27.2 odd 18 729.2.a.d.1.4 6
27.4 even 9 inner 27.2.e.a.4.2 12
27.5 odd 18 243.2.e.b.28.2 12
27.7 even 9 729.2.c.e.487.4 12
27.11 odd 18 729.2.c.b.244.3 12
27.13 even 9 243.2.e.d.109.1 12
27.14 odd 18 243.2.e.a.109.2 12
27.16 even 9 729.2.c.e.244.4 12
27.20 odd 18 729.2.c.b.487.3 12
27.22 even 9 243.2.e.c.28.1 12
27.23 odd 18 81.2.e.a.64.1 12
27.25 even 9 729.2.a.a.1.3 6
108.31 odd 18 432.2.u.c.193.2 12
135.4 even 18 675.2.l.c.301.1 12
135.58 odd 36 675.2.u.b.274.3 24
135.112 odd 36 675.2.u.b.274.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.4.2 12 27.4 even 9 inner
27.2.e.a.7.2 yes 12 1.1 even 1 trivial
81.2.e.a.19.1 12 3.2 odd 2
81.2.e.a.64.1 12 27.23 odd 18
243.2.e.a.109.2 12 27.14 odd 18
243.2.e.a.136.2 12 9.2 odd 6
243.2.e.b.28.2 12 27.5 odd 18
243.2.e.b.217.2 12 9.5 odd 6
243.2.e.c.28.1 12 27.22 even 9
243.2.e.c.217.1 12 9.4 even 3
243.2.e.d.109.1 12 27.13 even 9
243.2.e.d.136.1 12 9.7 even 3
432.2.u.c.193.2 12 108.31 odd 18
432.2.u.c.385.2 12 4.3 odd 2
675.2.l.c.301.1 12 135.4 even 18
675.2.l.c.601.1 12 5.4 even 2
675.2.u.b.274.2 24 135.112 odd 36
675.2.u.b.274.3 24 135.58 odd 36
675.2.u.b.574.2 24 5.3 odd 4
675.2.u.b.574.3 24 5.2 odd 4
729.2.a.a.1.3 6 27.25 even 9
729.2.a.d.1.4 6 27.2 odd 18
729.2.c.b.244.3 12 27.11 odd 18
729.2.c.b.487.3 12 27.20 odd 18
729.2.c.e.244.4 12 27.16 even 9
729.2.c.e.487.4 12 27.7 even 9