Properties

Label 27.2.e.a.13.1
Level $27$
Weight $2$
Character 27.13
Analytic conductor $0.216$
Analytic rank $0$
Dimension $12$
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] = [27,2,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: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) 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 13.1
Root \(0.500000 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 27.13
Dual form 27.2.e.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.417037 - 2.36514i) q^{2} +(-0.210069 + 1.71926i) q^{3} +(-3.54056 + 1.28866i) q^{4} +(0.0713060 + 0.0598329i) q^{5} +(4.15390 - 0.220155i) q^{6} +(0.544891 + 0.198324i) q^{7} +(2.12277 + 3.67675i) q^{8} +(-2.91174 - 0.722330i) q^{9} +O(q^{10})\) \(q+(-0.417037 - 2.36514i) q^{2} +(-0.210069 + 1.71926i) q^{3} +(-3.54056 + 1.28866i) q^{4} +(0.0713060 + 0.0598329i) q^{5} +(4.15390 - 0.220155i) q^{6} +(0.544891 + 0.198324i) q^{7} +(2.12277 + 3.67675i) q^{8} +(-2.91174 - 0.722330i) q^{9} +(0.111776 - 0.193601i) q^{10} +(-2.36944 + 1.98820i) q^{11} +(-1.47178 - 6.35787i) q^{12} +(0.729623 - 4.13790i) q^{13} +(0.241824 - 1.37145i) q^{14} +(-0.117848 + 0.110025i) q^{15} +(2.03816 - 1.71022i) q^{16} +(0.995493 - 1.72424i) q^{17} +(-0.494102 + 7.18790i) q^{18} +(1.92271 + 3.33023i) q^{19} +(-0.329567 - 0.119953i) q^{20} +(-0.455437 + 0.895151i) q^{21} +(5.69050 + 4.77489i) q^{22} +(4.18428 - 1.52295i) q^{23} +(-6.76724 + 2.87724i) q^{24} +(-0.866736 - 4.91551i) q^{25} -10.0910 q^{26} +(1.85354 - 4.85432i) q^{27} -2.18479 q^{28} +(1.11126 + 6.30229i) q^{29} +(0.309371 + 0.232841i) q^{30} +(-1.55754 + 0.566898i) q^{31} +(1.60967 + 1.35067i) q^{32} +(-2.92049 - 4.49135i) q^{33} +(-4.49323 - 1.63540i) q^{34} +(0.0269877 + 0.0467441i) q^{35} +(11.2400 - 1.19479i) q^{36} +(-2.01505 + 3.49016i) q^{37} +(7.07461 - 5.93630i) q^{38} +(6.96087 + 2.12366i) q^{39} +(-0.0686240 + 0.389186i) q^{40} +(-0.190345 + 1.07950i) q^{41} +(2.30709 + 0.703859i) q^{42} +(-5.28657 + 4.43596i) q^{43} +(5.82704 - 10.0927i) q^{44} +(-0.164406 - 0.225724i) q^{45} +(-5.34699 - 9.26126i) q^{46} +(-3.37650 - 1.22894i) q^{47} +(2.51217 + 3.86340i) q^{48} +(-5.10474 - 4.28338i) q^{49} +(-11.2644 + 4.09990i) q^{50} +(2.75531 + 2.07373i) q^{51} +(2.74906 + 15.5907i) q^{52} +5.40034 q^{53} +(-12.2541 - 2.35945i) q^{54} -0.287915 q^{55} +(0.427492 + 2.42443i) q^{56} +(-6.12946 + 2.60607i) q^{57} +(14.4423 - 5.25657i) q^{58} +(-7.87850 - 6.61085i) q^{59} +(0.275462 - 0.541415i) q^{60} +(12.4005 + 4.51341i) q^{61} +(1.99034 + 3.44738i) q^{62} +(-1.44333 - 0.971060i) q^{63} +(5.18386 - 8.97871i) q^{64} +(0.299609 - 0.251402i) q^{65} +(-9.40470 + 8.78041i) q^{66} +(-1.53458 + 8.70304i) q^{67} +(-1.30264 + 7.38764i) q^{68} +(1.73937 + 7.51381i) q^{69} +(0.0993013 - 0.0833237i) q^{70} +(-0.572473 + 0.991553i) q^{71} +(-3.52514 - 12.2391i) q^{72} +(-0.0977361 - 0.169284i) q^{73} +(9.09506 + 3.31033i) q^{74} +(8.63313 - 0.457552i) q^{75} +(-11.0990 - 9.31317i) q^{76} +(-1.68539 + 0.613433i) q^{77} +(2.11980 - 17.3491i) q^{78} +(-1.25166 - 7.09849i) q^{79} +0.247661 q^{80} +(7.95648 + 4.20647i) q^{81} +2.63255 q^{82} +(-2.58744 - 14.6741i) q^{83} +(0.458958 - 3.75624i) q^{84} +(0.174151 - 0.0633858i) q^{85} +(12.6963 + 10.6535i) q^{86} +(-11.0687 + 0.586638i) q^{87} +(-12.3399 - 4.49135i) q^{88} +(0.776563 + 1.34505i) q^{89} +(-0.465305 + 0.482977i) q^{90} +(1.21821 - 2.11000i) q^{91} +(-12.8521 + 10.7842i) q^{92} +(-0.647457 - 2.79691i) q^{93} +(-1.49850 + 8.49839i) q^{94} +(-0.0621565 + 0.352507i) q^{95} +(-2.66030 + 2.48371i) q^{96} +(4.05661 - 3.40390i) q^{97} +(-8.00191 + 13.8597i) q^{98} +(8.33533 - 4.07760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.417037 2.36514i −0.294890 1.67240i −0.667650 0.744475i \(-0.732700\pi\)
0.372760 0.927928i \(-0.378411\pi\)
\(3\) −0.210069 + 1.71926i −0.121284 + 0.992618i
\(4\) −3.54056 + 1.28866i −1.77028 + 0.644329i
\(5\) 0.0713060 + 0.0598329i 0.0318890 + 0.0267581i 0.658593 0.752499i \(-0.271152\pi\)
−0.626704 + 0.779258i \(0.715596\pi\)
\(6\) 4.15390 0.220155i 1.69582 0.0898778i
\(7\) 0.544891 + 0.198324i 0.205950 + 0.0749595i 0.442935 0.896554i \(-0.353937\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(8\) 2.12277 + 3.67675i 0.750514 + 1.29993i
\(9\) −2.91174 0.722330i −0.970581 0.240777i
\(10\) 0.111776 0.193601i 0.0353465 0.0612220i
\(11\) −2.36944 + 1.98820i −0.714413 + 0.599464i −0.925834 0.377932i \(-0.876635\pi\)
0.211421 + 0.977395i \(0.432191\pi\)
\(12\) −1.47178 6.35787i −0.424867 1.83536i
\(13\) 0.729623 4.13790i 0.202361 1.14765i −0.699178 0.714948i \(-0.746450\pi\)
0.901539 0.432699i \(-0.142439\pi\)
\(14\) 0.241824 1.37145i 0.0646301 0.366536i
\(15\) −0.117848 + 0.110025i −0.0304282 + 0.0284083i
\(16\) 2.03816 1.71022i 0.509540 0.427555i
\(17\) 0.995493 1.72424i 0.241443 0.418191i −0.719683 0.694303i \(-0.755713\pi\)
0.961125 + 0.276112i \(0.0890461\pi\)
\(18\) −0.494102 + 7.18790i −0.116461 + 1.69420i
\(19\) 1.92271 + 3.33023i 0.441100 + 0.764008i 0.997771 0.0667249i \(-0.0212550\pi\)
−0.556671 + 0.830733i \(0.687922\pi\)
\(20\) −0.329567 0.119953i −0.0736935 0.0268222i
\(21\) −0.455437 + 0.895151i −0.0993845 + 0.195338i
\(22\) 5.69050 + 4.77489i 1.21322 + 1.01801i
\(23\) 4.18428 1.52295i 0.872482 0.317558i 0.133310 0.991074i \(-0.457439\pi\)
0.739172 + 0.673517i \(0.235217\pi\)
\(24\) −6.76724 + 2.87724i −1.38136 + 0.587314i
\(25\) −0.866736 4.91551i −0.173347 0.983101i
\(26\) −10.0910 −1.97900
\(27\) 1.85354 4.85432i 0.356715 0.934213i
\(28\) −2.18479 −0.412887
\(29\) 1.11126 + 6.30229i 0.206356 + 1.17031i 0.895291 + 0.445482i \(0.146968\pi\)
−0.688935 + 0.724823i \(0.741921\pi\)
\(30\) 0.309371 + 0.232841i 0.0564831 + 0.0425108i
\(31\) −1.55754 + 0.566898i −0.279743 + 0.101818i −0.478081 0.878316i \(-0.658668\pi\)
0.198339 + 0.980134i \(0.436445\pi\)
\(32\) 1.60967 + 1.35067i 0.284552 + 0.238767i
\(33\) −2.92049 4.49135i −0.508392 0.781844i
\(34\) −4.49323 1.63540i −0.770582 0.280469i
\(35\) 0.0269877 + 0.0467441i 0.00456176 + 0.00790120i
\(36\) 11.2400 1.19479i 1.87334 0.199132i
\(37\) −2.01505 + 3.49016i −0.331272 + 0.573779i −0.982761 0.184878i \(-0.940811\pi\)
0.651490 + 0.758657i \(0.274144\pi\)
\(38\) 7.07461 5.93630i 1.14765 0.962996i
\(39\) 6.96087 + 2.12366i 1.11463 + 0.340058i
\(40\) −0.0686240 + 0.389186i −0.0108504 + 0.0615358i
\(41\) −0.190345 + 1.07950i −0.0297270 + 0.168590i −0.996057 0.0887159i \(-0.971724\pi\)
0.966330 + 0.257306i \(0.0828348\pi\)
\(42\) 2.30709 + 0.703859i 0.355991 + 0.108608i
\(43\) −5.28657 + 4.43596i −0.806194 + 0.676477i −0.949696 0.313173i \(-0.898608\pi\)
0.143502 + 0.989650i \(0.454164\pi\)
\(44\) 5.82704 10.0927i 0.878459 1.52154i
\(45\) −0.164406 0.225724i −0.0245082 0.0336490i
\(46\) −5.34699 9.26126i −0.788370 1.36550i
\(47\) −3.37650 1.22894i −0.492513 0.179260i 0.0838106 0.996482i \(-0.473291\pi\)
−0.576323 + 0.817222i \(0.695513\pi\)
\(48\) 2.51217 + 3.86340i 0.362600 + 0.557634i
\(49\) −5.10474 4.28338i −0.729248 0.611912i
\(50\) −11.2644 + 4.09990i −1.59302 + 0.579813i
\(51\) 2.75531 + 2.07373i 0.385821 + 0.290380i
\(52\) 2.74906 + 15.5907i 0.381226 + 2.16204i
\(53\) 5.40034 0.741793 0.370897 0.928674i \(-0.379050\pi\)
0.370897 + 0.928674i \(0.379050\pi\)
\(54\) −12.2541 2.35945i −1.66757 0.321081i
\(55\) −0.287915 −0.0388224
\(56\) 0.427492 + 2.42443i 0.0571260 + 0.323978i
\(57\) −6.12946 + 2.60607i −0.811866 + 0.345182i
\(58\) 14.4423 5.25657i 1.89637 0.690222i
\(59\) −7.87850 6.61085i −1.02569 0.860659i −0.0353615 0.999375i \(-0.511258\pi\)
−0.990332 + 0.138715i \(0.955703\pi\)
\(60\) 0.275462 0.541415i 0.0355620 0.0698964i
\(61\) 12.4005 + 4.51341i 1.58772 + 0.577883i 0.976864 0.213860i \(-0.0686036\pi\)
0.610855 + 0.791742i \(0.290826\pi\)
\(62\) 1.99034 + 3.44738i 0.252774 + 0.437817i
\(63\) −1.44333 0.971060i −0.181842 0.122342i
\(64\) 5.18386 8.97871i 0.647982 1.12234i
\(65\) 0.299609 0.251402i 0.0371619 0.0311825i
\(66\) −9.40470 + 8.78041i −1.15764 + 1.08079i
\(67\) −1.53458 + 8.70304i −0.187479 + 1.06324i 0.735250 + 0.677796i \(0.237065\pi\)
−0.922729 + 0.385449i \(0.874046\pi\)
\(68\) −1.30264 + 7.38764i −0.157968 + 0.895883i
\(69\) 1.73937 + 7.51381i 0.209396 + 0.904556i
\(70\) 0.0993013 0.0833237i 0.0118688 0.00995909i
\(71\) −0.572473 + 0.991553i −0.0679401 + 0.117676i −0.897994 0.440007i \(-0.854976\pi\)
0.830054 + 0.557683i \(0.188309\pi\)
\(72\) −3.52514 12.2391i −0.415442 1.44239i
\(73\) −0.0977361 0.169284i −0.0114391 0.0198132i 0.860249 0.509874i \(-0.170308\pi\)
−0.871688 + 0.490061i \(0.836975\pi\)
\(74\) 9.09506 + 3.31033i 1.05728 + 0.384818i
\(75\) 8.63313 0.457552i 0.996868 0.0528336i
\(76\) −11.0990 9.31317i −1.27314 1.06829i
\(77\) −1.68539 + 0.613433i −0.192069 + 0.0699072i
\(78\) 2.11980 17.3491i 0.240020 1.96439i
\(79\) −1.25166 7.09849i −0.140822 0.798642i −0.970627 0.240589i \(-0.922659\pi\)
0.829805 0.558054i \(-0.188452\pi\)
\(80\) 0.247661 0.0276893
\(81\) 7.95648 + 4.20647i 0.884053 + 0.467386i
\(82\) 2.63255 0.290717
\(83\) −2.58744 14.6741i −0.284008 1.61069i −0.708808 0.705402i \(-0.750767\pi\)
0.424800 0.905287i \(-0.360344\pi\)
\(84\) 0.458958 3.75624i 0.0500764 0.409839i
\(85\) 0.174151 0.0633858i 0.0188893 0.00687516i
\(86\) 12.6963 + 10.6535i 1.36908 + 1.14879i
\(87\) −11.0687 + 0.586638i −1.18669 + 0.0628942i
\(88\) −12.3399 4.49135i −1.31544 0.478780i
\(89\) 0.776563 + 1.34505i 0.0823155 + 0.142575i 0.904244 0.427016i \(-0.140435\pi\)
−0.821929 + 0.569590i \(0.807102\pi\)
\(90\) −0.465305 + 0.482977i −0.0490475 + 0.0509103i
\(91\) 1.21821 2.11000i 0.127703 0.221189i
\(92\) −12.8521 + 10.7842i −1.33993 + 1.12433i
\(93\) −0.647457 2.79691i −0.0671381 0.290026i
\(94\) −1.49850 + 8.49839i −0.154558 + 0.876542i
\(95\) −0.0621565 + 0.352507i −0.00637712 + 0.0361665i
\(96\) −2.66030 + 2.48371i −0.271516 + 0.253492i
\(97\) 4.05661 3.40390i 0.411887 0.345614i −0.413180 0.910649i \(-0.635582\pi\)
0.825067 + 0.565035i \(0.191137\pi\)
\(98\) −8.00191 + 13.8597i −0.808315 + 1.40004i
\(99\) 8.33533 4.07760i 0.837732 0.409814i
\(100\) 9.40314 + 16.2867i 0.940314 + 1.62867i
\(101\) 6.83061 + 2.48614i 0.679671 + 0.247380i 0.658706 0.752400i \(-0.271104\pi\)
0.0209647 + 0.999780i \(0.493326\pi\)
\(102\) 3.75558 7.38150i 0.371858 0.730878i
\(103\) 4.90374 + 4.11472i 0.483179 + 0.405436i 0.851574 0.524234i \(-0.175648\pi\)
−0.368395 + 0.929669i \(0.620093\pi\)
\(104\) 16.7629 6.10118i 1.64373 0.598270i
\(105\) −0.0860348 + 0.0365796i −0.00839614 + 0.00356980i
\(106\) −2.25214 12.7725i −0.218747 1.24058i
\(107\) −5.54365 −0.535925 −0.267963 0.963429i \(-0.586350\pi\)
−0.267963 + 0.963429i \(0.586350\pi\)
\(108\) −0.307026 + 19.5756i −0.0295436 + 1.88366i
\(109\) −6.23137 −0.596857 −0.298428 0.954432i \(-0.596462\pi\)
−0.298428 + 0.954432i \(0.596462\pi\)
\(110\) 0.120071 + 0.680957i 0.0114483 + 0.0649267i
\(111\) −5.57722 4.19758i −0.529366 0.398416i
\(112\) 1.44975 0.527668i 0.136989 0.0498599i
\(113\) −9.07301 7.61316i −0.853517 0.716186i 0.107044 0.994254i \(-0.465861\pi\)
−0.960561 + 0.278068i \(0.910306\pi\)
\(114\) 8.71992 + 13.4102i 0.816695 + 1.25598i
\(115\) 0.389487 + 0.141762i 0.0363198 + 0.0132193i
\(116\) −12.0560 20.8816i −1.11937 1.93881i
\(117\) −5.11340 + 11.5215i −0.472734 + 1.06516i
\(118\) −12.3499 + 21.3907i −1.13690 + 1.96917i
\(119\) 0.884395 0.742096i 0.0810724 0.0680278i
\(120\) −0.654698 0.199739i −0.0597655 0.0182336i
\(121\) −0.248809 + 1.41107i −0.0226190 + 0.128279i
\(122\) 5.50336 31.2111i 0.498250 2.82572i
\(123\) −1.81597 0.554025i −0.163740 0.0499547i
\(124\) 4.78403 4.01427i 0.429618 0.360492i
\(125\) 0.465014 0.805428i 0.0415921 0.0720396i
\(126\) −1.69477 + 3.81863i −0.150982 + 0.340191i
\(127\) −5.76469 9.98473i −0.511533 0.886002i −0.999911 0.0133693i \(-0.995744\pi\)
0.488377 0.872633i \(-0.337589\pi\)
\(128\) −19.4486 7.07872i −1.71903 0.625676i
\(129\) −6.51604 10.0209i −0.573705 0.882288i
\(130\) −0.719547 0.603772i −0.0631085 0.0529543i
\(131\) 8.46830 3.08221i 0.739879 0.269294i 0.0555383 0.998457i \(-0.482312\pi\)
0.684340 + 0.729163i \(0.260090\pi\)
\(132\) 16.1280 + 12.1384i 1.40376 + 1.05651i
\(133\) 0.387203 + 2.19594i 0.0335747 + 0.190412i
\(134\) 21.2238 1.83346
\(135\) 0.422616 0.235239i 0.0363730 0.0202462i
\(136\) 8.45283 0.724824
\(137\) 2.00047 + 11.3452i 0.170911 + 0.969287i 0.942758 + 0.333478i \(0.108222\pi\)
−0.771846 + 0.635809i \(0.780667\pi\)
\(138\) 17.0458 7.24738i 1.45103 0.616938i
\(139\) −1.60108 + 0.582746i −0.135802 + 0.0494279i −0.409027 0.912522i \(-0.634132\pi\)
0.273225 + 0.961950i \(0.411910\pi\)
\(140\) −0.155789 0.130722i −0.0131666 0.0110481i
\(141\) 2.82218 5.54693i 0.237670 0.467136i
\(142\) 2.58390 + 0.940462i 0.216836 + 0.0789219i
\(143\) 6.49816 + 11.2551i 0.543403 + 0.941202i
\(144\) −7.16994 + 3.50750i −0.597495 + 0.292291i
\(145\) −0.297844 + 0.515881i −0.0247346 + 0.0428416i
\(146\) −0.359620 + 0.301757i −0.0297623 + 0.0249736i
\(147\) 8.43662 7.87659i 0.695840 0.649650i
\(148\) 2.63677 14.9538i 0.216741 1.22920i
\(149\) −3.75996 + 21.3238i −0.308028 + 1.74691i 0.300869 + 0.953666i \(0.402723\pi\)
−0.608897 + 0.793249i \(0.708388\pi\)
\(150\) −4.68251 20.2277i −0.382325 1.65159i
\(151\) −3.63222 + 3.04779i −0.295586 + 0.248026i −0.778504 0.627640i \(-0.784021\pi\)
0.482918 + 0.875665i \(0.339577\pi\)
\(152\) −8.16296 + 14.1387i −0.662104 + 1.14680i
\(153\) −4.14409 + 4.30148i −0.335030 + 0.347754i
\(154\) 2.15373 + 3.73036i 0.173552 + 0.300601i
\(155\) −0.144981 0.0527688i −0.0116452 0.00423849i
\(156\) −27.3821 + 1.45124i −2.19232 + 0.116192i
\(157\) −0.160261 0.134475i −0.0127902 0.0107323i 0.636370 0.771384i \(-0.280435\pi\)
−0.649160 + 0.760652i \(0.724880\pi\)
\(158\) −16.2669 + 5.92067i −1.29412 + 0.471023i
\(159\) −1.13444 + 9.28461i −0.0899673 + 0.736317i
\(160\) 0.0339644 + 0.192622i 0.00268513 + 0.0152281i
\(161\) 2.58202 0.203491
\(162\) 6.63073 20.5724i 0.520960 1.61632i
\(163\) 5.62384 0.440493 0.220247 0.975444i \(-0.429314\pi\)
0.220247 + 0.975444i \(0.429314\pi\)
\(164\) −0.717181 4.06733i −0.0560024 0.317605i
\(165\) 0.0604821 0.495002i 0.00470852 0.0385358i
\(166\) −33.6271 + 12.2393i −2.60997 + 0.949951i
\(167\) 12.7780 + 10.7220i 0.988791 + 0.829695i 0.985392 0.170300i \(-0.0544736\pi\)
0.00339914 + 0.999994i \(0.498918\pi\)
\(168\) −4.25804 + 0.225674i −0.328515 + 0.0174111i
\(169\) −4.37386 1.59195i −0.336451 0.122458i
\(170\) −0.222544 0.385457i −0.0170683 0.0295632i
\(171\) −3.19291 11.0856i −0.244168 0.847738i
\(172\) 13.0010 22.5183i 0.991315 1.71701i
\(173\) 14.5565 12.2143i 1.10671 0.928639i 0.108851 0.994058i \(-0.465283\pi\)
0.997858 + 0.0654187i \(0.0208383\pi\)
\(174\) 6.00355 + 25.9344i 0.455128 + 1.96608i
\(175\) 0.502587 2.85031i 0.0379920 0.215463i
\(176\) −1.42905 + 8.10453i −0.107718 + 0.610902i
\(177\) 13.0208 12.1565i 0.978706 0.913738i
\(178\) 2.85736 2.39761i 0.214168 0.179709i
\(179\) −8.11761 + 14.0601i −0.606739 + 1.05090i 0.385035 + 0.922902i \(0.374189\pi\)
−0.991774 + 0.128001i \(0.959144\pi\)
\(180\) 0.872970 + 0.587328i 0.0650673 + 0.0437768i
\(181\) 1.49579 + 2.59078i 0.111181 + 0.192571i 0.916247 0.400614i \(-0.131203\pi\)
−0.805066 + 0.593186i \(0.797870\pi\)
\(182\) −5.49848 2.00128i −0.407575 0.148345i
\(183\) −10.3647 + 20.3716i −0.766181 + 1.50591i
\(184\) 14.4818 + 12.1517i 1.06761 + 0.895833i
\(185\) −0.352512 + 0.128304i −0.0259172 + 0.00943308i
\(186\) −6.34506 + 2.69774i −0.465242 + 0.197808i
\(187\) 1.06938 + 6.06473i 0.0782005 + 0.443497i
\(188\) 13.5384 0.987388
\(189\) 1.97271 2.27747i 0.143493 0.165662i
\(190\) 0.859649 0.0623655
\(191\) −0.391371 2.21958i −0.0283186 0.160603i 0.967369 0.253371i \(-0.0815395\pi\)
−0.995688 + 0.0927685i \(0.970428\pi\)
\(192\) 14.3478 + 10.7986i 1.03546 + 0.779320i
\(193\) 0.827186 0.301071i 0.0595422 0.0216716i −0.312077 0.950057i \(-0.601025\pi\)
0.371620 + 0.928385i \(0.378803\pi\)
\(194\) −9.74245 8.17489i −0.699467 0.586923i
\(195\) 0.369287 + 0.567919i 0.0264452 + 0.0406695i
\(196\) 23.5934 + 8.58731i 1.68525 + 0.613379i
\(197\) −10.1383 17.5600i −0.722322 1.25110i −0.960067 0.279771i \(-0.909741\pi\)
0.237744 0.971328i \(-0.423592\pi\)
\(198\) −13.1202 18.0137i −0.932413 1.28018i
\(199\) 9.50472 16.4627i 0.673772 1.16701i −0.303054 0.952973i \(-0.598006\pi\)
0.976826 0.214034i \(-0.0686603\pi\)
\(200\) 16.2332 13.6213i 1.14786 0.963170i
\(201\) −14.6405 4.46659i −1.03266 0.315049i
\(202\) 3.03144 17.1921i 0.213291 1.20963i
\(203\) −0.644379 + 3.65445i −0.0452265 + 0.256492i
\(204\) −12.4277 3.79150i −0.870110 0.265458i
\(205\) −0.0781625 + 0.0655862i −0.00545911 + 0.00458074i
\(206\) 7.68684 13.3140i 0.535567 0.927630i
\(207\) −13.2836 + 1.41202i −0.923275 + 0.0981420i
\(208\) −5.58963 9.68152i −0.387571 0.671293i
\(209\) −11.1769 4.06806i −0.773123 0.281394i
\(210\) 0.122395 + 0.188229i 0.00844608 + 0.0129890i
\(211\) 12.3977 + 10.4029i 0.853494 + 0.716166i 0.960556 0.278086i \(-0.0897000\pi\)
−0.107062 + 0.994252i \(0.534144\pi\)
\(212\) −19.1202 + 6.95919i −1.31318 + 0.477959i
\(213\) −1.58448 1.19253i −0.108567 0.0817107i
\(214\) 2.31191 + 13.1115i 0.158039 + 0.896283i
\(215\) −0.642380 −0.0438100
\(216\) 21.7828 3.48960i 1.48213 0.237437i
\(217\) −0.961120 −0.0652451
\(218\) 2.59871 + 14.7380i 0.176007 + 0.998186i
\(219\) 0.311575 0.132473i 0.0210543 0.00895168i
\(220\) 1.01938 0.371024i 0.0687265 0.0250144i
\(221\) −6.40842 5.37730i −0.431077 0.361716i
\(222\) −7.60193 + 14.9414i −0.510208 + 1.00280i
\(223\) −20.1633 7.33883i −1.35023 0.491444i −0.437212 0.899359i \(-0.644034\pi\)
−0.913020 + 0.407914i \(0.866256\pi\)
\(224\) 0.609223 + 1.05520i 0.0407054 + 0.0705038i
\(225\) −1.02690 + 14.9388i −0.0684602 + 0.995917i
\(226\) −14.2224 + 24.6339i −0.946058 + 1.63862i
\(227\) −14.6424 + 12.2864i −0.971848 + 0.815477i −0.982840 0.184462i \(-0.940946\pi\)
0.0109918 + 0.999940i \(0.496501\pi\)
\(228\) 18.3434 17.1257i 1.21482 1.13418i
\(229\) 3.90190 22.1288i 0.257845 1.46231i −0.530818 0.847486i \(-0.678115\pi\)
0.788663 0.614826i \(-0.210774\pi\)
\(230\) 0.172855 0.980309i 0.0113977 0.0646397i
\(231\) −0.700605 3.02650i −0.0460964 0.199129i
\(232\) −20.8130 + 17.4642i −1.36644 + 1.14658i
\(233\) 8.84074 15.3126i 0.579176 1.00316i −0.416398 0.909182i \(-0.636708\pi\)
0.995574 0.0939796i \(-0.0299589\pi\)
\(234\) 29.3823 + 7.28901i 1.92078 + 0.476497i
\(235\) −0.167233 0.289657i −0.0109091 0.0188951i
\(236\) 36.4134 + 13.2534i 2.37031 + 0.862723i
\(237\) 12.4671 0.660752i 0.809826 0.0429204i
\(238\) −2.12398 1.78223i −0.137677 0.115525i
\(239\) 14.4904 5.27406i 0.937303 0.341151i 0.172203 0.985061i \(-0.444912\pi\)
0.765100 + 0.643911i \(0.222689\pi\)
\(240\) −0.0520259 + 0.425794i −0.00335826 + 0.0274849i
\(241\) 2.28373 + 12.9516i 0.147108 + 0.834289i 0.965651 + 0.259844i \(0.0836711\pi\)
−0.818543 + 0.574445i \(0.805218\pi\)
\(242\) 3.44113 0.221204
\(243\) −8.90345 + 12.7956i −0.571157 + 0.820841i
\(244\) −49.7209 −3.18305
\(245\) −0.107711 0.610862i −0.00688143 0.0390265i
\(246\) −0.553018 + 4.52605i −0.0352592 + 0.288571i
\(247\) 15.1830 5.52617i 0.966073 0.351622i
\(248\) −5.39065 4.52329i −0.342307 0.287229i
\(249\) 25.7722 1.36591i 1.63324 0.0865612i
\(250\) −2.09887 0.763927i −0.132744 0.0483150i
\(251\) −8.70830 15.0832i −0.549663 0.952045i −0.998297 0.0583292i \(-0.981423\pi\)
0.448634 0.893716i \(-0.351911\pi\)
\(252\) 6.36155 + 1.57814i 0.400740 + 0.0994135i
\(253\) −6.88646 + 11.9277i −0.432948 + 0.749889i
\(254\) −21.2112 + 17.7983i −1.33091 + 1.11676i
\(255\) 0.0723932 + 0.312727i 0.00453344 + 0.0195837i
\(256\) −5.03066 + 28.5303i −0.314416 + 1.78314i
\(257\) 1.94270 11.0176i 0.121182 0.687260i −0.862320 0.506364i \(-0.830989\pi\)
0.983502 0.180896i \(-0.0578997\pi\)
\(258\) −20.9833 + 19.5904i −1.30636 + 1.21964i
\(259\) −1.79017 + 1.50213i −0.111236 + 0.0933377i
\(260\) −0.736812 + 1.27620i −0.0456952 + 0.0791463i
\(261\) 1.31662 19.1533i 0.0814965 1.18556i
\(262\) −10.8214 18.7433i −0.668550 1.15796i
\(263\) 19.4619 + 7.08354i 1.20007 + 0.436790i 0.863249 0.504779i \(-0.168426\pi\)
0.336821 + 0.941569i \(0.390648\pi\)
\(264\) 10.3141 20.2720i 0.634786 1.24766i
\(265\) 0.385077 + 0.323118i 0.0236551 + 0.0198490i
\(266\) 5.03221 1.83157i 0.308544 0.112301i
\(267\) −2.47562 + 1.05256i −0.151506 + 0.0644159i
\(268\) −5.78197 32.7912i −0.353190 2.00304i
\(269\) −28.2449 −1.72212 −0.861060 0.508504i \(-0.830199\pi\)
−0.861060 + 0.508504i \(0.830199\pi\)
\(270\) −0.732619 0.901441i −0.0445858 0.0548600i
\(271\) 17.2626 1.04863 0.524316 0.851524i \(-0.324321\pi\)
0.524316 + 0.851524i \(0.324321\pi\)
\(272\) −0.919863 5.21680i −0.0557749 0.316315i
\(273\) 3.37175 + 2.53767i 0.204067 + 0.153587i
\(274\) 25.9987 9.46275i 1.57064 0.571666i
\(275\) 11.8267 + 9.92375i 0.713175 + 0.598425i
\(276\) −15.8411 24.3616i −0.953520 1.46640i
\(277\) −4.85725 1.76789i −0.291844 0.106222i 0.191949 0.981405i \(-0.438519\pi\)
−0.483793 + 0.875182i \(0.660741\pi\)
\(278\) 2.04598 + 3.54375i 0.122710 + 0.212540i
\(279\) 4.94464 0.525604i 0.296028 0.0314671i
\(280\) −0.114578 + 0.198454i −0.00684733 + 0.0118599i
\(281\) −2.52522 + 2.11891i −0.150642 + 0.126404i −0.714994 0.699131i \(-0.753571\pi\)
0.564352 + 0.825534i \(0.309126\pi\)
\(282\) −14.2962 4.36156i −0.851326 0.259727i
\(283\) −1.58553 + 8.99200i −0.0942501 + 0.534519i 0.900724 + 0.434391i \(0.143036\pi\)
−0.994975 + 0.100128i \(0.968075\pi\)
\(284\) 0.749103 4.24837i 0.0444511 0.252095i
\(285\) −0.592996 0.180914i −0.0351260 0.0107164i
\(286\) 23.9099 20.0628i 1.41382 1.18634i
\(287\) −0.317809 + 0.550462i −0.0187597 + 0.0324927i
\(288\) −3.71130 5.09551i −0.218691 0.300256i
\(289\) 6.51799 + 11.2895i 0.383411 + 0.664087i
\(290\) 1.34434 + 0.489300i 0.0789424 + 0.0287327i
\(291\) 5.00004 + 7.68945i 0.293108 + 0.450764i
\(292\) 0.564189 + 0.473411i 0.0330167 + 0.0277043i
\(293\) 2.65598 0.966697i 0.155164 0.0564750i −0.263271 0.964722i \(-0.584801\pi\)
0.418434 + 0.908247i \(0.362579\pi\)
\(294\) −22.1476 16.6689i −1.29167 0.972151i
\(295\) −0.166239 0.942787i −0.00967880 0.0548912i
\(296\) −17.1100 −0.994496
\(297\) 5.25947 + 15.1872i 0.305185 + 0.881251i
\(298\) 52.0017 3.01238
\(299\) −3.24888 18.4253i −0.187887 1.06556i
\(300\) −29.9765 + 12.7451i −1.73069 + 0.735841i
\(301\) −3.76036 + 1.36866i −0.216744 + 0.0788882i
\(302\) 8.72321 + 7.31964i 0.501964 + 0.421198i
\(303\) −5.70923 + 11.2214i −0.327987 + 0.644650i
\(304\) 9.61423 + 3.49929i 0.551414 + 0.200698i
\(305\) 0.614179 + 1.06379i 0.0351678 + 0.0609124i
\(306\) 11.9018 + 8.00746i 0.680382 + 0.457756i
\(307\) −3.14723 + 5.45116i −0.179622 + 0.311114i −0.941751 0.336311i \(-0.890821\pi\)
0.762129 + 0.647425i \(0.224154\pi\)
\(308\) 5.17673 4.34380i 0.294972 0.247511i
\(309\) −8.10442 + 7.56644i −0.461045 + 0.430440i
\(310\) −0.0643429 + 0.364907i −0.00365443 + 0.0207253i
\(311\) −1.28029 + 7.26088i −0.0725985 + 0.411727i 0.926751 + 0.375675i \(0.122589\pi\)
−0.999350 + 0.0360515i \(0.988522\pi\)
\(312\) 6.96818 + 30.1015i 0.394496 + 1.70416i
\(313\) −3.27159 + 2.74519i −0.184921 + 0.155167i −0.730549 0.682860i \(-0.760736\pi\)
0.545628 + 0.838028i \(0.316291\pi\)
\(314\) −0.251217 + 0.435120i −0.0141770 + 0.0245552i
\(315\) −0.0448167 0.155601i −0.00252513 0.00876712i
\(316\) 13.5791 + 23.5197i 0.763883 + 1.32308i
\(317\) −15.1738 5.52279i −0.852243 0.310191i −0.121288 0.992617i \(-0.538703\pi\)
−0.730954 + 0.682426i \(0.760925\pi\)
\(318\) 22.4325 1.18891i 1.25795 0.0666708i
\(319\) −15.1632 12.7235i −0.848979 0.712378i
\(320\) 0.906862 0.330071i 0.0506951 0.0184515i
\(321\) 1.16455 9.53101i 0.0649989 0.531969i
\(322\) −1.07680 6.10682i −0.0600075 0.340320i
\(323\) 7.65618 0.426001
\(324\) −33.5911 4.64009i −1.86617 0.257783i
\(325\) −20.9723 −1.16333
\(326\) −2.34535 13.3012i −0.129897 0.736683i
\(327\) 1.30902 10.7134i 0.0723890 0.592451i
\(328\) −4.37313 + 1.59169i −0.241465 + 0.0878862i
\(329\) −1.59610 1.33928i −0.0879956 0.0738371i
\(330\) −1.19597 + 0.0633858i −0.0658359 + 0.00348928i
\(331\) −18.0686 6.57644i −0.993142 0.361474i −0.206206 0.978509i \(-0.566112\pi\)
−0.786936 + 0.617035i \(0.788334\pi\)
\(332\) 28.0708 + 48.6201i 1.54059 + 2.66838i
\(333\) 8.38834 8.70693i 0.459678 0.477137i
\(334\) 20.0301 34.6932i 1.09600 1.89833i
\(335\) −0.630152 + 0.528761i −0.0344289 + 0.0288893i
\(336\) 0.602651 + 2.60336i 0.0328773 + 0.142025i
\(337\) −5.11615 + 29.0152i −0.278695 + 1.58056i 0.448281 + 0.893893i \(0.352036\pi\)
−0.726976 + 0.686663i \(0.759075\pi\)
\(338\) −1.94112 + 11.0087i −0.105583 + 0.598792i
\(339\) 14.9950 13.9996i 0.814417 0.760355i
\(340\) −0.534910 + 0.448843i −0.0290096 + 0.0243419i
\(341\) 2.56339 4.43993i 0.138815 0.240435i
\(342\) −24.8874 + 12.1748i −1.34576 + 0.658337i
\(343\) −3.96154 6.86159i −0.213903 0.370491i
\(344\) −27.5321 10.0209i −1.48443 0.540289i
\(345\) −0.325545 + 0.639851i −0.0175268 + 0.0344484i
\(346\) −34.9592 29.3342i −1.87942 1.57702i
\(347\) −10.7097 + 3.89801i −0.574927 + 0.209256i −0.613087 0.790015i \(-0.710073\pi\)
0.0381600 + 0.999272i \(0.487850\pi\)
\(348\) 38.4336 16.3408i 2.06025 0.875961i
\(349\) 4.89021 + 27.7338i 0.261767 + 1.48456i 0.778085 + 0.628158i \(0.216191\pi\)
−0.516318 + 0.856397i \(0.672698\pi\)
\(350\) −6.95097 −0.371545
\(351\) −18.7343 11.2116i −0.999962 0.598431i
\(352\) −6.49941 −0.346419
\(353\) 4.97573 + 28.2188i 0.264831 + 1.50193i 0.769515 + 0.638629i \(0.220498\pi\)
−0.504683 + 0.863305i \(0.668391\pi\)
\(354\) −34.1819 25.7263i −1.81675 1.36734i
\(355\) −0.100148 + 0.0364510i −0.00531532 + 0.00193462i
\(356\) −4.48277 3.76149i −0.237586 0.199359i
\(357\) 1.09007 + 1.67640i 0.0576929 + 0.0887245i
\(358\) 36.6394 + 13.3357i 1.93645 + 0.704812i
\(359\) 15.5161 + 26.8747i 0.818909 + 1.41839i 0.906486 + 0.422235i \(0.138754\pi\)
−0.0875770 + 0.996158i \(0.527912\pi\)
\(360\) 0.480936 1.08364i 0.0253476 0.0571129i
\(361\) 2.10636 3.64833i 0.110861 0.192017i
\(362\) 5.50376 4.61820i 0.289271 0.242727i
\(363\) −2.37373 0.724191i −0.124589 0.0380102i
\(364\) −1.59408 + 9.04045i −0.0835523 + 0.473848i
\(365\) 0.00315957 0.0179188i 0.000165379 0.000937912i
\(366\) 52.5040 + 16.0182i 2.74443 + 0.837286i
\(367\) 18.4802 15.5067i 0.964660 0.809446i −0.0170450 0.999855i \(-0.505426\pi\)
0.981705 + 0.190409i \(0.0609814\pi\)
\(368\) 5.92365 10.2601i 0.308791 0.534843i
\(369\) 1.33399 3.00574i 0.0694449 0.156473i
\(370\) 0.450466 + 0.780230i 0.0234186 + 0.0405622i
\(371\) 2.94260 + 1.07102i 0.152772 + 0.0556045i
\(372\) 5.89662 + 9.06828i 0.305726 + 0.470169i
\(373\) −9.64114 8.08988i −0.499199 0.418878i 0.358110 0.933679i \(-0.383421\pi\)
−0.857309 + 0.514801i \(0.827866\pi\)
\(374\) 13.8979 5.05843i 0.718645 0.261565i
\(375\) 1.28706 + 0.968677i 0.0664634 + 0.0500223i
\(376\) −2.64902 15.0233i −0.136613 0.774769i
\(377\) 26.8890 1.38486
\(378\) −6.20922 3.71593i −0.319368 0.191127i
\(379\) −7.70522 −0.395790 −0.197895 0.980223i \(-0.563411\pi\)
−0.197895 + 0.980223i \(0.563411\pi\)
\(380\) −0.234192 1.32817i −0.0120138 0.0681337i
\(381\) 18.3774 7.81354i 0.941502 0.400300i
\(382\) −5.08638 + 1.85129i −0.260242 + 0.0947203i
\(383\) −13.6828 11.4812i −0.699159 0.586664i 0.222376 0.974961i \(-0.428619\pi\)
−0.921534 + 0.388297i \(0.873063\pi\)
\(384\) 16.2557 31.9503i 0.829548 1.63046i
\(385\) −0.156882 0.0571005i −0.00799546 0.00291011i
\(386\) −1.05704 1.83085i −0.0538020 0.0931878i
\(387\) 18.5973 9.09771i 0.945356 0.462463i
\(388\) −9.97622 + 17.2793i −0.506466 + 0.877224i
\(389\) 20.9808 17.6050i 1.06377 0.892607i 0.0692941 0.997596i \(-0.477925\pi\)
0.994473 + 0.104989i \(0.0334809\pi\)
\(390\) 1.18920 1.11026i 0.0602174 0.0562201i
\(391\) 1.53948 8.73081i 0.0778547 0.441536i
\(392\) 4.91274 27.8615i 0.248131 1.40722i
\(393\) 3.52020 + 15.2067i 0.177571 + 0.767078i
\(394\) −37.3038 + 31.3016i −1.87934 + 1.57695i
\(395\) 0.335472 0.581055i 0.0168794 0.0292361i
\(396\) −24.2571 + 25.1784i −1.21896 + 1.26526i
\(397\) −2.10799 3.65115i −0.105797 0.183246i 0.808266 0.588817i \(-0.200406\pi\)
−0.914064 + 0.405571i \(0.867073\pi\)
\(398\) −42.9002 15.6144i −2.15039 0.782680i
\(399\) −3.85673 + 0.204405i −0.193078 + 0.0102331i
\(400\) −10.1731 8.53628i −0.508657 0.426814i
\(401\) −14.2575 + 5.18930i −0.711985 + 0.259141i −0.672519 0.740080i \(-0.734788\pi\)
−0.0394656 + 0.999221i \(0.512566\pi\)
\(402\) −4.45848 + 36.4894i −0.222369 + 1.81993i
\(403\) 1.20935 + 6.85857i 0.0602420 + 0.341650i
\(404\) −27.3880 −1.36260
\(405\) 0.315660 + 0.776006i 0.0156853 + 0.0385600i
\(406\) 8.91200 0.442295
\(407\) −2.16460 12.2760i −0.107295 0.608501i
\(408\) −1.77568 + 14.5326i −0.0879093 + 0.719473i
\(409\) −4.42559 + 1.61078i −0.218831 + 0.0796481i −0.449109 0.893477i \(-0.648259\pi\)
0.230278 + 0.973125i \(0.426036\pi\)
\(410\) 0.187717 + 0.157513i 0.00927067 + 0.00777902i
\(411\) −19.9257 + 1.05605i −0.982860 + 0.0520912i
\(412\) −22.6644 8.24918i −1.11660 0.406408i
\(413\) −2.98184 5.16469i −0.146727 0.254138i
\(414\) 8.87937 + 30.8287i 0.436397 + 1.51515i
\(415\) 0.693492 1.20116i 0.0340422 0.0589628i
\(416\) 6.76339 5.67516i 0.331602 0.278248i
\(417\) −0.665556 2.87510i −0.0325924 0.140794i
\(418\) −4.96033 + 28.1314i −0.242618 + 1.37595i
\(419\) 3.43669 19.4905i 0.167894 0.952171i −0.778137 0.628094i \(-0.783835\pi\)
0.946031 0.324077i \(-0.105054\pi\)
\(420\) 0.257473 0.240382i 0.0125634 0.0117294i
\(421\) 21.5915 18.1174i 1.05231 0.882989i 0.0589715 0.998260i \(-0.481218\pi\)
0.993334 + 0.115270i \(0.0367734\pi\)
\(422\) 19.4340 33.6607i 0.946032 1.63858i
\(423\) 8.94379 + 6.01731i 0.434862 + 0.292572i
\(424\) 11.4637 + 19.8557i 0.556726 + 0.964278i
\(425\) −9.33836 3.39889i −0.452977 0.164870i
\(426\) −2.15970 + 4.24484i −0.104638 + 0.205663i
\(427\) 5.86180 + 4.91863i 0.283672 + 0.238029i
\(428\) 19.6276 7.14387i 0.948737 0.345312i
\(429\) −20.7156 + 8.80769i −1.00016 + 0.425239i
\(430\) 0.267896 + 1.51932i 0.0129191 + 0.0732679i
\(431\) −5.19681 −0.250321 −0.125161 0.992136i \(-0.539945\pi\)
−0.125161 + 0.992136i \(0.539945\pi\)
\(432\) −4.52413 13.0638i −0.217667 0.628534i
\(433\) 25.3285 1.21721 0.608605 0.793473i \(-0.291730\pi\)
0.608605 + 0.793473i \(0.291730\pi\)
\(434\) 0.400823 + 2.27318i 0.0192401 + 0.109116i
\(435\) −0.824368 0.620444i −0.0395254 0.0297480i
\(436\) 22.0625 8.03011i 1.05660 0.384572i
\(437\) 13.1169 + 11.0064i 0.627469 + 0.526509i
\(438\) −0.443254 0.681671i −0.0211795 0.0325715i
\(439\) 14.7167 + 5.35646i 0.702392 + 0.255650i 0.668432 0.743773i \(-0.266966\pi\)
0.0339602 + 0.999423i \(0.489188\pi\)
\(440\) −0.611178 1.05859i −0.0291368 0.0504664i
\(441\) 11.7697 + 16.1594i 0.560460 + 0.769496i
\(442\) −10.0455 + 17.3993i −0.477815 + 0.827600i
\(443\) −13.9833 + 11.7333i −0.664365 + 0.557468i −0.911391 0.411541i \(-0.864991\pi\)
0.247027 + 0.969009i \(0.420546\pi\)
\(444\) 25.1557 + 7.67464i 1.19384 + 0.364222i
\(445\) −0.0251044 + 0.142374i −0.00119006 + 0.00674917i
\(446\) −8.94849 + 50.7494i −0.423723 + 2.40305i
\(447\) −35.8714 10.9439i −1.69666 0.517626i
\(448\) 4.60534 3.86434i 0.217582 0.182573i
\(449\) −14.3608 + 24.8737i −0.677729 + 1.17386i 0.297934 + 0.954586i \(0.403702\pi\)
−0.975663 + 0.219274i \(0.929631\pi\)
\(450\) 35.7604 3.80125i 1.68576 0.179193i
\(451\) −1.69525 2.93626i −0.0798262 0.138263i
\(452\) 41.9343 + 15.2628i 1.97242 + 0.717904i
\(453\) −4.47694 6.88499i −0.210345 0.323485i
\(454\) 35.1654 + 29.5073i 1.65039 + 1.38485i
\(455\) 0.213113 0.0775669i 0.00999091 0.00363639i
\(456\) −22.5933 17.0044i −1.05803 0.796304i
\(457\) −6.14505 34.8503i −0.287453 1.63023i −0.696389 0.717665i \(-0.745211\pi\)
0.408936 0.912563i \(-0.365900\pi\)
\(458\) −53.9648 −2.52161
\(459\) −6.52484 8.02840i −0.304553 0.374734i
\(460\) −1.56168 −0.0728139
\(461\) 0.395350 + 2.24214i 0.0184133 + 0.104427i 0.992629 0.121190i \(-0.0386712\pi\)
−0.974216 + 0.225617i \(0.927560\pi\)
\(462\) −6.86591 + 2.91919i −0.319431 + 0.135813i
\(463\) −17.2664 + 6.28446i −0.802438 + 0.292064i −0.710496 0.703701i \(-0.751530\pi\)
−0.0919417 + 0.995764i \(0.529307\pi\)
\(464\) 13.0432 + 10.9446i 0.605517 + 0.508089i
\(465\) 0.121180 0.238176i 0.00561957 0.0110451i
\(466\) −39.9033 14.5236i −1.84848 0.672793i
\(467\) −2.32935 4.03455i −0.107789 0.186697i 0.807085 0.590435i \(-0.201044\pi\)
−0.914874 + 0.403738i \(0.867711\pi\)
\(468\) 3.25707 47.3819i 0.150558 2.19023i
\(469\) −2.56220 + 4.43786i −0.118312 + 0.204922i
\(470\) −0.615335 + 0.516327i −0.0283833 + 0.0238164i
\(471\) 0.264864 0.247282i 0.0122043 0.0113941i
\(472\) 7.58218 43.0007i 0.348998 1.97927i
\(473\) 3.70665 21.0215i 0.170432 0.966568i
\(474\) −6.76202 29.2109i −0.310590 1.34170i
\(475\) 14.7033 12.3375i 0.674634 0.566085i
\(476\) −2.17495 + 3.76712i −0.0996885 + 0.172666i
\(477\) −15.7244 3.90082i −0.719970 0.178606i
\(478\) −18.5169 32.0722i −0.846942 1.46695i
\(479\) 13.3210 + 4.84844i 0.608651 + 0.221531i 0.627913 0.778283i \(-0.283909\pi\)
−0.0192617 + 0.999814i \(0.506132\pi\)
\(480\) −0.338303 + 0.0179299i −0.0154413 + 0.000818385i
\(481\) 12.9717 + 10.8846i 0.591460 + 0.496294i
\(482\) 29.6800 10.8026i 1.35189 0.492047i
\(483\) −0.542402 + 4.43917i −0.0246802 + 0.201989i
\(484\) −0.937459 5.31660i −0.0426118 0.241663i
\(485\) 0.492926 0.0223826
\(486\) 33.9765 + 15.7216i 1.54121 + 0.713147i
\(487\) −21.4338 −0.971258 −0.485629 0.874165i \(-0.661409\pi\)
−0.485629 + 0.874165i \(0.661409\pi\)
\(488\) 9.72875 + 55.1745i 0.440400 + 2.49763i
\(489\) −1.18140 + 9.66888i −0.0534246 + 0.437242i
\(490\) −1.39985 + 0.509504i −0.0632389 + 0.0230171i
\(491\) −10.7919 9.05550i −0.487033 0.408669i 0.365929 0.930643i \(-0.380751\pi\)
−0.852961 + 0.521974i \(0.825196\pi\)
\(492\) 7.14348 0.378601i 0.322053 0.0170687i
\(493\) 11.9729 + 4.35779i 0.539234 + 0.196265i
\(494\) −19.4020 33.6053i −0.872938 1.51197i
\(495\) 0.838333 + 0.207969i 0.0376803 + 0.00934753i
\(496\) −2.20500 + 3.81917i −0.0990073 + 0.171486i
\(497\) −0.508585 + 0.426753i −0.0228131 + 0.0191425i
\(498\) −13.9785 60.3850i −0.626392 2.70592i
\(499\) 2.58898 14.6828i 0.115899 0.657294i −0.870403 0.492340i \(-0.836142\pi\)
0.986301 0.164953i \(-0.0527473\pi\)
\(500\) −0.608488 + 3.45091i −0.0272124 + 0.154329i
\(501\) −21.1182 + 19.7164i −0.943494 + 0.880864i
\(502\) −32.0422 + 26.8866i −1.43011 + 1.20001i
\(503\) 7.93153 13.7378i 0.353650 0.612539i −0.633236 0.773958i \(-0.718274\pi\)
0.986886 + 0.161420i \(0.0516072\pi\)
\(504\) 0.506490 7.36810i 0.0225608 0.328201i
\(505\) 0.338311 + 0.585972i 0.0150546 + 0.0260754i
\(506\) 31.0826 + 11.3131i 1.38179 + 0.502930i
\(507\) 3.65580 7.18540i 0.162360 0.319115i
\(508\) 33.2771 + 27.9228i 1.47643 + 1.23888i
\(509\) −31.8807 + 11.6036i −1.41309 + 0.514321i −0.932034 0.362371i \(-0.881967\pi\)
−0.481052 + 0.876692i \(0.659745\pi\)
\(510\) 0.709452 0.301639i 0.0314151 0.0133568i
\(511\) −0.0196825 0.111625i −0.000870700 0.00493799i
\(512\) 28.1824 1.24550
\(513\) 19.7298 3.16072i 0.871093 0.139549i
\(514\) −26.8683 −1.18511
\(515\) 0.103470 + 0.586809i 0.00455945 + 0.0258579i
\(516\) 35.9839 + 27.0825i 1.58410 + 1.19224i
\(517\) 10.4438 3.80123i 0.459317 0.167178i
\(518\) 4.29930 + 3.60754i 0.188900 + 0.158506i
\(519\) 17.9418 + 27.5923i 0.787558 + 1.21117i
\(520\) 1.56034 + 0.567919i 0.0684256 + 0.0249049i
\(521\) 21.3899 + 37.0484i 0.937108 + 1.62312i 0.770831 + 0.637040i \(0.219841\pi\)
0.166277 + 0.986079i \(0.446825\pi\)
\(522\) −45.8493 + 4.87367i −2.00677 + 0.213315i
\(523\) 1.38893 2.40569i 0.0607335 0.105193i −0.834060 0.551674i \(-0.813989\pi\)
0.894793 + 0.446480i \(0.147323\pi\)
\(524\) −26.0106 + 21.8255i −1.13628 + 0.953451i
\(525\) 4.79486 + 1.46284i 0.209265 + 0.0638437i
\(526\) 8.63721 48.9840i 0.376600 2.13581i
\(527\) −0.573049 + 3.24992i −0.0249624 + 0.141569i
\(528\) −13.6336 4.15942i −0.593327 0.181016i
\(529\) −2.43023 + 2.03920i −0.105662 + 0.0886609i
\(530\) 0.603626 1.04551i 0.0262198 0.0454141i
\(531\) 18.1650 + 24.9400i 0.788292 + 1.08230i
\(532\) −4.20073 7.27587i −0.182125 0.315449i
\(533\) 4.32799 + 1.57526i 0.187466 + 0.0682321i
\(534\) 3.52188 + 5.41622i 0.152407 + 0.234383i
\(535\) −0.395296 0.331693i −0.0170901 0.0143403i
\(536\) −35.2565 + 12.8323i −1.52285 + 0.554271i
\(537\) −22.4678 16.9099i −0.969557 0.729717i
\(538\) 11.7792 + 66.8029i 0.507835 + 2.88008i
\(539\) 20.6116 0.887803
\(540\) −1.19316 + 1.37749i −0.0513452 + 0.0592776i
\(541\) −3.59390 −0.154514 −0.0772570 0.997011i \(-0.524616\pi\)
−0.0772570 + 0.997011i \(0.524616\pi\)
\(542\) −7.19917 40.8285i −0.309231 1.75373i
\(543\) −4.76846 + 2.02741i −0.204634 + 0.0870047i
\(544\) 3.93130 1.43088i 0.168553 0.0613483i
\(545\) −0.444334 0.372841i −0.0190332 0.0159707i
\(546\) 4.59580 9.03294i 0.196682 0.386574i
\(547\) 37.1985 + 13.5392i 1.59049 + 0.578892i 0.977452 0.211158i \(-0.0677235\pi\)
0.613042 + 0.790051i \(0.289946\pi\)
\(548\) −21.7029 37.5905i −0.927101 1.60579i
\(549\) −32.8468 22.0991i −1.40187 0.943167i
\(550\) 18.5389 32.1102i 0.790499 1.36919i
\(551\) −18.8514 + 15.8182i −0.803099 + 0.673880i
\(552\) −23.9341 + 22.3453i −1.01870 + 0.951081i
\(553\) 0.725786 4.11614i 0.0308636 0.175036i
\(554\) −2.15566 + 12.2253i −0.0915850 + 0.519405i
\(555\) −0.146536 0.633013i −0.00622011 0.0268699i
\(556\) 4.91776 4.12649i 0.208560 0.175002i
\(557\) 5.71731 9.90267i 0.242250 0.419590i −0.719105 0.694902i \(-0.755448\pi\)
0.961355 + 0.275312i \(0.0887812\pi\)
\(558\) −3.30522 11.4756i −0.139921 0.485799i
\(559\) 14.4983 + 25.1119i 0.613214 + 1.06212i
\(560\) 0.134948 + 0.0491171i 0.00570260 + 0.00207558i
\(561\) −10.6515 + 0.564526i −0.449707 + 0.0238343i
\(562\) 6.06462 + 5.08882i 0.255821 + 0.214659i
\(563\) −13.6357 + 4.96298i −0.574676 + 0.209165i −0.612976 0.790101i \(-0.710028\pi\)
0.0383005 + 0.999266i \(0.487806\pi\)
\(564\) −2.84400 + 23.2761i −0.119754 + 0.980099i
\(565\) −0.191443 1.08573i −0.00805408 0.0456770i
\(566\) 21.9285 0.921725
\(567\) 3.50117 + 3.87003i 0.147035 + 0.162526i
\(568\) −4.86093 −0.203960
\(569\) −0.225601 1.27945i −0.00945767 0.0536371i 0.979714 0.200402i \(-0.0642249\pi\)
−0.989171 + 0.146765i \(0.953114\pi\)
\(570\) −0.180586 + 1.47796i −0.00756391 + 0.0619051i
\(571\) −15.0890 + 5.49193i −0.631453 + 0.229830i −0.637864 0.770149i \(-0.720182\pi\)
0.00641065 + 0.999979i \(0.497959\pi\)
\(572\) −37.5111 31.4756i −1.56842 1.31606i
\(573\) 3.89825 0.206606i 0.162852 0.00863108i
\(574\) 1.43445 + 0.522099i 0.0598730 + 0.0217920i
\(575\) −11.1127 19.2478i −0.463434 0.802691i
\(576\) −21.5796 + 22.3992i −0.899152 + 0.933301i
\(577\) 4.23017 7.32686i 0.176104 0.305021i −0.764439 0.644696i \(-0.776984\pi\)
0.940543 + 0.339675i \(0.110317\pi\)
\(578\) 23.9829 20.1241i 0.997558 0.837050i
\(579\) 0.343854 + 1.48540i 0.0142901 + 0.0617310i
\(580\) 0.389740 2.21033i 0.0161831 0.0917788i
\(581\) 1.50035 8.50893i 0.0622452 0.353010i
\(582\) 16.1014 15.0326i 0.667424 0.623120i
\(583\) −12.7958 + 10.7369i −0.529947 + 0.444678i
\(584\) 0.414943 0.718703i 0.0171705 0.0297401i
\(585\) −1.05398 + 0.515601i −0.0435767 + 0.0213175i
\(586\) −3.39401 5.87860i −0.140205 0.242843i
\(587\) 17.2764 + 6.28811i 0.713075 + 0.259538i 0.672983 0.739658i \(-0.265013\pi\)
0.0400919 + 0.999196i \(0.487235\pi\)
\(588\) −19.7201 + 38.7594i −0.813244 + 1.59841i
\(589\) −4.88260 4.09699i −0.201184 0.168814i
\(590\) −2.16049 + 0.786354i −0.0889460 + 0.0323737i
\(591\) 32.3200 13.7416i 1.32947 0.565252i
\(592\) 1.86196 + 10.5597i 0.0765260 + 0.434001i
\(593\) 13.5128 0.554905 0.277452 0.960739i \(-0.410510\pi\)
0.277452 + 0.960739i \(0.410510\pi\)
\(594\) 33.7264 18.7730i 1.38381 0.770265i
\(595\) 0.107464 0.00440561
\(596\) −14.1667 80.3435i −0.580292 3.29100i
\(597\) 26.3070 + 19.7994i 1.07667 + 0.810337i
\(598\) −42.2234 + 15.3681i −1.72664 + 0.628447i
\(599\) 8.44772 + 7.08848i 0.345165 + 0.289627i 0.798845 0.601537i \(-0.205445\pi\)
−0.453680 + 0.891164i \(0.649889\pi\)
\(600\) 20.0085 + 30.7706i 0.816843 + 1.25620i
\(601\) −24.2421 8.82341i −0.988856 0.359914i −0.203579 0.979058i \(-0.565257\pi\)
−0.785277 + 0.619144i \(0.787480\pi\)
\(602\) 4.80528 + 8.32298i 0.195848 + 0.339219i
\(603\) 10.7548 24.2325i 0.437968 0.986824i
\(604\) 8.93252 15.4716i 0.363459 0.629529i
\(605\) −0.102170 + 0.0857306i −0.00415379 + 0.00348545i
\(606\) 28.9210 + 8.82338i 1.17484 + 0.358425i
\(607\) −2.56823 + 14.5652i −0.104241 + 0.591182i 0.887279 + 0.461233i \(0.152593\pi\)
−0.991521 + 0.129950i \(0.958518\pi\)
\(608\) −1.40312 + 7.95752i −0.0569042 + 0.322720i
\(609\) −6.14761 1.87555i −0.249114 0.0760009i
\(610\) 2.25987 1.89626i 0.0914995 0.0767772i
\(611\) −7.54882 + 13.0749i −0.305393 + 0.528956i
\(612\) 9.12926 20.5700i 0.369029 0.831492i
\(613\) −18.1370 31.4141i −0.732545 1.26880i −0.955792 0.294043i \(-0.904999\pi\)
0.223248 0.974762i \(-0.428334\pi\)
\(614\) 14.2053 + 5.17029i 0.573277 + 0.208656i
\(615\) −0.0963404 0.148160i −0.00388482 0.00597438i
\(616\) −5.83316 4.89460i −0.235025 0.197209i
\(617\) 37.9387 13.8086i 1.52736 0.555912i 0.564383 0.825513i \(-0.309114\pi\)
0.962972 + 0.269601i \(0.0868918\pi\)
\(618\) 21.2755 + 16.0126i 0.855826 + 0.644120i
\(619\) −1.19701 6.78858i −0.0481119 0.272856i 0.951256 0.308402i \(-0.0997941\pi\)
−0.999368 + 0.0355458i \(0.988683\pi\)
\(620\) 0.581315 0.0233462
\(621\) 0.362848 23.1347i 0.0145606 0.928362i
\(622\) 17.7069 0.709981
\(623\) 0.156387 + 0.886916i 0.00626552 + 0.0355335i
\(624\) 17.8193 7.57626i 0.713343 0.303293i
\(625\) −23.3703 + 8.50608i −0.934810 + 0.340243i
\(626\) 7.85711 + 6.59290i 0.314033 + 0.263505i
\(627\) 9.34200 18.3615i 0.373083 0.733287i
\(628\) 0.740705 + 0.269595i 0.0295574 + 0.0107580i
\(629\) 4.01193 + 6.94887i 0.159966 + 0.277070i
\(630\) −0.349327 + 0.170889i −0.0139175 + 0.00680837i
\(631\) −14.9095 + 25.8241i −0.593539 + 1.02804i 0.400212 + 0.916423i \(0.368936\pi\)
−0.993751 + 0.111617i \(0.964397\pi\)
\(632\) 23.4424 19.6705i 0.932489 0.782451i
\(633\) −20.4897 + 19.1296i −0.814394 + 0.760334i
\(634\) −6.73414 + 38.1912i −0.267447 + 1.51677i
\(635\) 0.186358 1.05689i 0.00739540 0.0419414i
\(636\) −7.94811 34.3346i −0.315163 1.36146i
\(637\) −21.4487 + 17.9976i −0.849830 + 0.713092i
\(638\) −23.7691 + 41.1693i −0.941028 + 1.62991i
\(639\) 2.38312 2.47363i 0.0942749 0.0978554i
\(640\) −0.963264 1.66842i −0.0380763 0.0659502i
\(641\) −40.2947 14.6661i −1.59155 0.579275i −0.613872 0.789406i \(-0.710389\pi\)
−0.977673 + 0.210131i \(0.932611\pi\)
\(642\) −23.0278 + 1.22046i −0.908834 + 0.0481678i
\(643\) −20.9998 17.6209i −0.828150 0.694901i 0.126715 0.991939i \(-0.459557\pi\)
−0.954866 + 0.297038i \(0.904001\pi\)
\(644\) −9.14178 + 3.32734i −0.360237 + 0.131115i
\(645\) 0.134944 1.10442i 0.00531343 0.0434865i
\(646\) −3.19291 18.1079i −0.125623 0.712446i
\(647\) −16.1623 −0.635407 −0.317703 0.948190i \(-0.602912\pi\)
−0.317703 + 0.948190i \(0.602912\pi\)
\(648\) 1.42365 + 38.1834i 0.0559261 + 1.49999i
\(649\) 31.8113 1.24870
\(650\) 8.74621 + 49.6022i 0.343055 + 1.94556i
\(651\) 0.201902 1.65242i 0.00791316 0.0647634i
\(652\) −19.9116 + 7.24721i −0.779797 + 0.283823i
\(653\) 24.7021 + 20.7275i 0.966668 + 0.811130i 0.982025 0.188752i \(-0.0604441\pi\)
−0.0153573 + 0.999882i \(0.504889\pi\)
\(654\) −25.8845 + 1.37187i −1.01216 + 0.0536442i
\(655\) 0.788258 + 0.286903i 0.0307998 + 0.0112102i
\(656\) 1.45823 + 2.52573i 0.0569344 + 0.0986133i
\(657\) 0.162303 + 0.563508i 0.00633206 + 0.0219846i
\(658\) −2.50195 + 4.33351i −0.0975363 + 0.168938i
\(659\) 21.3103 17.8814i 0.830130 0.696562i −0.125191 0.992133i \(-0.539954\pi\)
0.955321 + 0.295571i \(0.0955098\pi\)
\(660\) 0.423748 + 1.83052i 0.0164944 + 0.0712530i
\(661\) 5.34639 30.3209i 0.207950 1.17934i −0.684779 0.728751i \(-0.740101\pi\)
0.892729 0.450594i \(-0.148788\pi\)
\(662\) −8.01889 + 45.4774i −0.311663 + 1.76753i
\(663\) 10.5912 9.88816i 0.411329 0.384024i
\(664\) 48.4604 40.6631i 1.88063 1.57803i
\(665\) −0.103779 + 0.179751i −0.00402439 + 0.00697044i
\(666\) −24.0913 16.2085i −0.933519 0.628065i
\(667\) 14.2479 + 24.6781i 0.551682 + 0.955540i
\(668\) −59.0583 21.4955i −2.28503 0.831684i
\(669\) 16.8531 33.1243i 0.651577 1.28066i
\(670\) 1.51339 + 1.26988i 0.0584673 + 0.0490598i
\(671\) −38.3557 + 13.9603i −1.48071 + 0.538933i
\(672\) −1.94216 + 0.825749i −0.0749203 + 0.0318540i
\(673\) −4.53753 25.7336i −0.174909 0.991959i −0.938249 0.345961i \(-0.887553\pi\)
0.763340 0.645997i \(-0.223558\pi\)
\(674\) 70.7584 2.72551
\(675\) −25.4679 4.90369i −0.980262 0.188743i
\(676\) 17.5374 0.674515
\(677\) 3.15944 + 17.9181i 0.121427 + 0.688648i 0.983366 + 0.181635i \(0.0581391\pi\)
−0.861939 + 0.507012i \(0.830750\pi\)
\(678\) −39.3645 29.6269i −1.51178 1.13781i
\(679\) 2.88549 1.05023i 0.110735 0.0403042i
\(680\) 0.602738 + 0.505757i 0.0231139 + 0.0193949i
\(681\) −18.0477 27.7551i −0.691588 1.06358i
\(682\) −11.5701 4.21116i −0.443040 0.161253i
\(683\) −11.7486 20.3491i −0.449546 0.778636i 0.548811 0.835947i \(-0.315081\pi\)
−0.998356 + 0.0573104i \(0.981748\pi\)
\(684\) 25.5903 + 35.1347i 0.978468 + 1.34341i
\(685\) −0.536171 + 0.928676i −0.0204860 + 0.0354829i
\(686\) −14.5765 + 12.2311i −0.556533 + 0.466987i
\(687\) 37.2256 + 11.3570i 1.42024 + 0.433296i
\(688\) −3.18841 + 18.0824i −0.121557 + 0.689384i
\(689\) 3.94021 22.3460i 0.150110 0.851317i
\(690\) 1.64910 + 0.503116i 0.0627801 + 0.0191533i
\(691\) −34.1180 + 28.6284i −1.29791 + 1.08908i −0.307409 + 0.951577i \(0.599462\pi\)
−0.990502 + 0.137499i \(0.956094\pi\)
\(692\) −35.7980 + 62.0039i −1.36084 + 2.35704i
\(693\) 5.35054 0.568750i 0.203250 0.0216050i
\(694\) 13.6857 + 23.7043i 0.519501 + 0.899802i
\(695\) −0.149034 0.0542440i −0.00565318 0.00205759i
\(696\) −25.6534 39.4517i −0.972388 1.49541i
\(697\) 1.67184 + 1.40284i 0.0633254 + 0.0531363i
\(698\) 63.5547 23.1320i 2.40558 0.875560i
\(699\) 24.4692 + 18.4163i 0.925512 + 0.696567i
\(700\) 1.89364 + 10.7394i 0.0715728 + 0.405910i
\(701\) −25.2567 −0.953934 −0.476967 0.878921i \(-0.658264\pi\)
−0.476967 + 0.878921i \(0.658264\pi\)
\(702\) −18.7041 + 48.9848i −0.705939 + 1.84881i
\(703\) −15.4974 −0.584496
\(704\) 5.56859 + 31.5810i 0.209874 + 1.19025i
\(705\) 0.533127 0.226670i 0.0200787 0.00853690i
\(706\) 64.6662 23.5366i 2.43374 0.885810i
\(707\) 3.22888 + 2.70935i 0.121434 + 0.101896i
\(708\) −30.4355 + 59.8202i −1.14383 + 2.24818i
\(709\) 14.7382 + 5.36425i 0.553503 + 0.201459i 0.603602 0.797286i \(-0.293731\pi\)
−0.0500991 + 0.998744i \(0.515954\pi\)
\(710\) 0.127977 + 0.221663i 0.00480289 + 0.00831886i
\(711\) −1.48295 + 21.5731i −0.0556150 + 0.809053i
\(712\) −3.29694 + 5.71046i −0.123558 + 0.214009i
\(713\) −5.65382 + 4.74412i −0.211737 + 0.177669i
\(714\) 3.51031 3.27730i 0.131370 0.122650i
\(715\) −0.210069 + 1.19136i −0.00785615 + 0.0445544i
\(716\) 10.6222 60.2415i 0.396970 2.25133i
\(717\) 6.02352 + 26.0207i 0.224953 + 0.971760i
\(718\) 57.0915 47.9055i 2.13064 1.78782i
\(719\) 26.5804 46.0385i 0.991280 1.71695i 0.381523 0.924359i \(-0.375400\pi\)
0.609757 0.792588i \(-0.291267\pi\)
\(720\) −0.721124 0.178893i −0.0268747 0.00666693i
\(721\) 1.85595 + 3.21461i 0.0691194 + 0.119718i
\(722\) −9.50721 3.46034i −0.353822 0.128781i
\(723\) −22.7471 + 1.20558i −0.845972 + 0.0448361i
\(724\) −8.63457 7.24526i −0.320901 0.269268i
\(725\) 30.0158 10.9248i 1.11476 0.405738i
\(726\) −0.722875 + 5.91621i −0.0268284 + 0.219571i
\(727\) 0.0814709 + 0.462044i 0.00302159 + 0.0171363i 0.986281 0.165073i \(-0.0527861\pi\)
−0.983260 + 0.182210i \(0.941675\pi\)
\(728\) 10.3440 0.383372
\(729\) −20.1288 17.9954i −0.745509 0.666495i
\(730\) −0.0436980 −0.00161734
\(731\) 2.38593 + 13.5313i 0.0882469 + 0.500473i
\(732\) 10.4448 85.4834i 0.386052 3.15956i
\(733\) 43.6076 15.8719i 1.61068 0.586241i 0.629109 0.777317i \(-0.283420\pi\)
0.981575 + 0.191075i \(0.0611975\pi\)
\(734\) −44.3825 37.2413i −1.63819 1.37460i
\(735\) 1.07286 0.0568611i 0.0395731 0.00209735i
\(736\) 8.79230 + 3.20014i 0.324088 + 0.117959i
\(737\) −13.6672 23.6724i −0.503439 0.871983i
\(738\) −7.66531 1.90157i −0.282164 0.0699977i
\(739\) −12.9047 + 22.3515i −0.474706 + 0.822214i −0.999580 0.0289653i \(-0.990779\pi\)
0.524875 + 0.851179i \(0.324112\pi\)
\(740\) 1.08275 0.908534i 0.0398026 0.0333984i
\(741\) 6.31146 + 27.2645i 0.231857 + 1.00159i
\(742\) 1.30593 7.40629i 0.0479422 0.271894i
\(743\) 6.02726 34.1823i 0.221119 1.25403i −0.648848 0.760918i \(-0.724749\pi\)
0.869967 0.493110i \(-0.164140\pi\)
\(744\) 8.90915 8.31775i 0.326625 0.304944i
\(745\) −1.54397 + 1.29555i −0.0565668 + 0.0474652i
\(746\) −15.1129 + 26.1764i −0.553324 + 0.958385i
\(747\) −3.06557 + 44.5961i −0.112163 + 1.63169i
\(748\) −11.6015 20.0945i −0.424195 0.734727i
\(749\) −3.02069 1.09944i −0.110374 0.0401727i
\(750\) 1.75430 3.44804i 0.0640581 0.125905i
\(751\) 18.3742 + 15.4178i 0.670485 + 0.562604i 0.913209 0.407492i \(-0.133596\pi\)
−0.242724 + 0.970095i \(0.578041\pi\)
\(752\) −8.98361 + 3.26977i −0.327599 + 0.119236i
\(753\) 27.7614 11.8034i 1.01168 0.430138i
\(754\) −11.2137 63.5962i −0.408380 2.31604i
\(755\) −0.441357 −0.0160626
\(756\) −4.04961 + 10.6057i −0.147283 + 0.385725i
\(757\) −8.78780 −0.319398 −0.159699 0.987166i \(-0.551052\pi\)
−0.159699 + 0.987166i \(0.551052\pi\)
\(758\) 3.21336 + 18.2239i 0.116715 + 0.661921i
\(759\) −19.0603 14.3453i −0.691843 0.520701i
\(760\) −1.42803 + 0.519759i −0.0517999 + 0.0188536i
\(761\) 10.5361 + 8.84082i 0.381933 + 0.320479i 0.813461 0.581620i \(-0.197581\pi\)
−0.431528 + 0.902100i \(0.642025\pi\)
\(762\) −26.1441 40.2065i −0.947102 1.45653i
\(763\) −3.39542 1.23583i −0.122922 0.0447401i
\(764\) 4.24595 + 7.35420i 0.153613 + 0.266066i
\(765\) −0.552869 + 0.0587687i −0.0199890 + 0.00212479i
\(766\) −21.4484 + 37.1498i −0.774963 + 1.34228i
\(767\) −33.1034 + 27.7770i −1.19529 + 1.00297i
\(768\) −47.9943 14.6424i −1.73185 0.528361i
\(769\) −5.44525 + 30.8815i −0.196361 + 1.11362i 0.714107 + 0.700036i \(0.246833\pi\)
−0.910468 + 0.413580i \(0.864278\pi\)
\(770\) −0.0696246 + 0.394861i −0.00250910 + 0.0142298i
\(771\) 18.5341 + 5.65448i 0.667489 + 0.203641i
\(772\) −2.54072 + 2.13192i −0.0914426 + 0.0767295i
\(773\) −14.0607 + 24.3539i −0.505729 + 0.875948i 0.494249 + 0.869320i \(0.335443\pi\)
−0.999978 + 0.00662776i \(0.997890\pi\)
\(774\) −29.2731 40.1911i −1.05220 1.44464i
\(775\) 4.13657 + 7.16475i 0.148590 + 0.257365i
\(776\) 21.1266 + 7.68945i 0.758400 + 0.276035i
\(777\) −2.20650 3.39332i −0.0791576 0.121735i
\(778\) −50.3879 42.2804i −1.80649 1.51583i
\(779\) −3.96098 + 1.44168i −0.141917 + 0.0516535i
\(780\) −2.03934 1.53486i −0.0730200 0.0549570i
\(781\) −0.614960 3.48761i −0.0220050 0.124797i
\(782\) −21.2916 −0.761385
\(783\) 32.6531 + 6.28714i 1.16693 + 0.224684i
\(784\) −17.7298 −0.633207
\(785\) −0.00338155 0.0191777i −0.000120693 0.000684483i
\(786\) 34.4979 14.6675i 1.23050 0.523173i
\(787\) 34.0170 12.3812i 1.21258 0.441342i 0.344979 0.938610i \(-0.387886\pi\)
0.867597 + 0.497269i \(0.165664\pi\)
\(788\) 58.5240 + 49.1075i 2.08483 + 1.74938i
\(789\) −16.2668 + 31.9721i −0.579114 + 1.13824i
\(790\) −1.51418 0.551116i −0.0538721 0.0196078i
\(791\) −3.43393 5.94775i −0.122097 0.211478i
\(792\) 32.6863 + 21.9911i 1.16146 + 0.781421i
\(793\) 27.7237 48.0189i 0.984498 1.70520i
\(794\) −7.75636 + 6.50836i −0.275263 + 0.230973i
\(795\) −0.636417 + 0.594171i −0.0225714 + 0.0210731i
\(796\) −12.4373 + 70.5354i −0.440828 + 2.50006i
\(797\) −5.14000 + 29.1504i −0.182068 + 1.03256i 0.747596 + 0.664153i \(0.231208\pi\)
−0.929665 + 0.368407i \(0.879903\pi\)
\(798\) 2.09185 + 9.03645i 0.0740506 + 0.319887i
\(799\) −5.48028 + 4.59850i −0.193878 + 0.162683i
\(800\) 5.24407 9.08300i 0.185406 0.321133i
\(801\) −1.28958 4.47736i −0.0455652 0.158200i
\(802\) 18.2193 + 31.5568i 0.643346 + 1.11431i
\(803\) 0.568149 + 0.206789i 0.0200495 + 0.00729744i
\(804\) 57.5913 3.05231i 2.03109 0.107647i
\(805\) 0.184113 + 0.154489i 0.00648914 + 0.00544504i
\(806\) 15.7171 5.72055i 0.553611 0.201498i
\(807\) 5.93338 48.5604i 0.208865 1.70941i
\(808\) 5.35892 + 30.3920i 0.188526 + 1.06919i
\(809\) −5.75943 −0.202491 −0.101245 0.994861i \(-0.532283\pi\)
−0.101245 + 0.994861i \(0.532283\pi\)
\(810\) 1.70372 1.07020i 0.0598625 0.0376030i
\(811\) 12.4896 0.438569 0.219284 0.975661i \(-0.429628\pi\)
0.219284 + 0.975661i \(0.429628\pi\)
\(812\) −2.42788 13.7692i −0.0852019 0.483204i
\(813\) −3.62635 + 29.6791i −0.127182 + 1.04089i
\(814\) −28.1318 + 10.2391i −0.986018 + 0.358881i
\(815\) 0.401014 + 0.336491i 0.0140469 + 0.0117868i
\(816\) 9.16230 0.485598i 0.320744 0.0169993i
\(817\) −24.9373 9.07644i −0.872446 0.317544i
\(818\) 5.65535 + 9.79536i 0.197735 + 0.342487i
\(819\) −5.07123 + 5.26384i −0.177203 + 0.183933i
\(820\) 0.192221 0.332936i 0.00671265 0.0116266i
\(821\) 32.9911 27.6828i 1.15140 0.966136i 0.151644 0.988435i \(-0.451543\pi\)
0.999751 + 0.0222995i \(0.00709873\pi\)
\(822\) 10.8074 + 46.6865i 0.376953 + 1.62838i
\(823\) 1.78581 10.1279i 0.0622496 0.353035i −0.937734 0.347353i \(-0.887080\pi\)
0.999984 0.00568141i \(-0.00180846\pi\)
\(824\) −4.71930 + 26.7645i −0.164404 + 0.932384i
\(825\) −19.5460 + 18.2485i −0.680504 + 0.635331i
\(826\) −10.9717 + 9.20632i −0.381753 + 0.320329i
\(827\) −3.04731 + 5.27810i −0.105965 + 0.183538i −0.914132 0.405416i \(-0.867127\pi\)
0.808167 + 0.588954i \(0.200460\pi\)
\(828\) 45.2118 22.1174i 1.57122 0.768632i
\(829\) 16.8489 + 29.1832i 0.585188 + 1.01358i 0.994852 + 0.101339i \(0.0323126\pi\)
−0.409664 + 0.912236i \(0.634354\pi\)
\(830\) −3.13013 1.13927i −0.108648 0.0395447i
\(831\) 4.05984 7.97952i 0.140834 0.276806i
\(832\) −33.3707 28.0014i −1.15692 0.970772i
\(833\) −12.4673 + 4.53774i −0.431967 + 0.157223i
\(834\) −6.52244 + 2.77315i −0.225853 + 0.0960264i
\(835\) 0.269620 + 1.52909i 0.00933057 + 0.0529163i
\(836\) 44.8148 1.54995
\(837\) −0.135065 + 8.61156i −0.00466853 + 0.297659i
\(838\) −47.5308 −1.64192
\(839\) −7.33250 41.5847i −0.253146 1.43566i −0.800787 0.598950i \(-0.795585\pi\)
0.547641 0.836714i \(-0.315526\pi\)
\(840\) −0.317126 0.238679i −0.0109419 0.00823520i
\(841\) −11.2328 + 4.08841i −0.387339 + 0.140980i
\(842\) −51.8546 43.5112i −1.78703 1.49949i
\(843\) −3.11250 4.78664i −0.107200 0.164861i
\(844\) −57.3007 20.8557i −1.97237 0.717884i
\(845\) −0.216631 0.375216i −0.00745234 0.0129078i
\(846\) 10.5019 23.6627i 0.361062 0.813541i
\(847\) −0.415423 + 0.719533i −0.0142741 + 0.0247235i
\(848\) 11.0068 9.23576i 0.377973 0.317157i
\(849\) −15.1266 4.61489i −0.519142 0.158383i
\(850\) −4.14438 + 23.5040i −0.142151 + 0.806179i
\(851\) −3.11616 + 17.6726i −0.106821 + 0.605810i
\(852\) 7.14672 + 2.18036i 0.244842 + 0.0746979i
\(853\) −27.3705 + 22.9665i −0.937147 + 0.786359i −0.977086 0.212843i \(-0.931728\pi\)
0.0399399 + 0.999202i \(0.487283\pi\)
\(854\) 9.18865 15.9152i 0.314429 0.544607i
\(855\) 0.435610 0.981512i 0.0148975 0.0335670i
\(856\) −11.7679 20.3826i −0.402219 0.696664i
\(857\) −7.43170 2.70492i −0.253862 0.0923983i 0.211954 0.977280i \(-0.432017\pi\)
−0.465817 + 0.884881i \(0.654239\pi\)
\(858\) 29.4706 + 45.3221i 1.00611 + 1.54727i
\(859\) −34.2569 28.7449i −1.16883 0.980764i −0.168841 0.985643i \(-0.554002\pi\)
−0.999988 + 0.00487963i \(0.998447\pi\)
\(860\) 2.27438 0.827808i 0.0775559 0.0282280i
\(861\) −0.879627 0.662033i −0.0299776 0.0225620i
\(862\) 2.16726 + 12.2911i 0.0738172 + 0.418638i
\(863\) −22.9170 −0.780103 −0.390052 0.920793i \(-0.627543\pi\)
−0.390052 + 0.920793i \(0.627543\pi\)
\(864\) 9.54017 5.31030i 0.324563 0.180660i
\(865\) 1.76878 0.0601405
\(866\) −10.5629 59.9053i −0.358943 2.03567i
\(867\) −20.7788 + 8.83457i −0.705686 + 0.300038i
\(868\) 3.40290 1.23856i 0.115502 0.0420393i
\(869\) 17.0789 + 14.3309i 0.579362 + 0.486143i
\(870\) −1.12364 + 2.20849i −0.0380950 + 0.0748748i
\(871\) 34.8926 + 12.6999i 1.18229 + 0.430319i
\(872\) −13.2278 22.9112i −0.447950 0.775871i
\(873\) −14.2706 + 6.98108i −0.482985 + 0.236274i
\(874\) 20.5614 35.6134i 0.695501 1.20464i
\(875\) 0.413118 0.346647i 0.0139659 0.0117188i
\(876\) −0.932438 + 0.870542i −0.0315041 + 0.0294129i
\(877\) −3.84416 + 21.8013i −0.129808 + 0.736178i 0.848527 + 0.529152i \(0.177490\pi\)
−0.978335 + 0.207026i \(0.933621\pi\)
\(878\) 6.53132 37.0409i 0.220421 1.25007i
\(879\) 1.10407 + 4.76940i 0.0372393 + 0.160868i
\(880\) −0.586817 + 0.492398i −0.0197816 + 0.0165987i
\(881\) −4.93202 + 8.54251i −0.166164 + 0.287804i −0.937068 0.349147i \(-0.886471\pi\)
0.770904 + 0.636951i \(0.219805\pi\)
\(882\) 33.3108 34.5759i 1.12163 1.16423i
\(883\) −23.7865 41.1995i −0.800481 1.38647i −0.919300 0.393558i \(-0.871244\pi\)
0.118819 0.992916i \(-0.462089\pi\)
\(884\) 29.6189 + 10.7804i 0.996191 + 0.362584i
\(885\) 1.65582 0.0877578i 0.0556598 0.00294995i
\(886\) 33.5825 + 28.1791i 1.12823 + 0.946694i
\(887\) −12.5517 + 4.56846i −0.421446 + 0.153394i −0.544033 0.839064i \(-0.683103\pi\)
0.122587 + 0.992458i \(0.460881\pi\)
\(888\) 3.59428 29.4165i 0.120616 0.987155i
\(889\) −1.16091 6.58387i −0.0389358 0.220816i
\(890\) 0.347203 0.0116383
\(891\) −27.2157 + 5.85205i −0.911760 + 0.196051i
\(892\) 80.8465 2.70694
\(893\) −2.39936 13.6074i −0.0802914 0.455355i
\(894\) −10.9240 + 89.4048i −0.365352 + 2.99014i
\(895\) −1.42009 + 0.516871i −0.0474684 + 0.0172771i
\(896\) −9.19350 7.71427i −0.307133 0.257716i
\(897\) 32.3605 1.71509i 1.08048 0.0572652i
\(898\) 64.8186 + 23.5920i 2.16302 + 0.787276i
\(899\) −5.30359 9.18609i −0.176885 0.306373i
\(900\) −15.6151 54.2149i −0.520505 1.80716i
\(901\) 5.37600 9.31150i 0.179100 0.310211i
\(902\) −6.23767 + 5.23403i −0.207692 + 0.174274i
\(903\) −1.56315 6.75257i −0.0520184 0.224712i
\(904\) 8.73176 49.5203i 0.290414 1.64702i
\(905\) −0.0483552 + 0.274236i −0.00160738 + 0.00911591i
\(906\) −14.4169 + 13.4599i −0.478969 + 0.447174i
\(907\) 28.3135 23.7578i 0.940134 0.788866i −0.0374746 0.999298i \(-0.511931\pi\)
0.977609 + 0.210431i \(0.0674869\pi\)
\(908\) 36.0092 62.3697i 1.19501 2.06981i
\(909\) −18.0932 12.1729i −0.600112 0.403751i
\(910\) −0.272332 0.471694i −0.00902773 0.0156365i
\(911\) 45.4916 + 16.5576i 1.50720 + 0.548577i 0.957914 0.287056i \(-0.0926766\pi\)
0.549288 + 0.835633i \(0.314899\pi\)
\(912\) −8.03587 + 15.7943i −0.266094 + 0.523002i
\(913\) 35.3057 + 29.6250i 1.16845 + 0.980445i
\(914\) −79.8629 + 29.0677i −2.64163 + 0.961475i
\(915\) −1.95796 + 0.832467i −0.0647280 + 0.0275205i
\(916\) 14.7015 + 83.3765i 0.485752 + 2.75484i
\(917\) 5.22558 0.172564
\(918\) −16.2671 + 18.7803i −0.536896 + 0.619841i
\(919\) 8.93459 0.294725 0.147363 0.989083i \(-0.452922\pi\)
0.147363 + 0.989083i \(0.452922\pi\)
\(920\) 0.305570 + 1.73297i 0.0100744 + 0.0571345i
\(921\) −8.71086 6.55604i −0.287032 0.216029i
\(922\) 5.13809 1.87011i 0.169214 0.0615889i
\(923\) 3.68526 + 3.09230i 0.121302 + 0.101784i
\(924\) 6.38066 + 9.81267i 0.209908 + 0.322813i
\(925\) 18.9024 + 6.87992i 0.621508 + 0.226211i
\(926\) 22.0643 + 38.2165i 0.725079 + 1.25587i
\(927\) −11.3062 15.5231i −0.371345 0.509846i
\(928\) −6.72355 + 11.6455i −0.220711 + 0.382283i
\(929\) −4.78330 + 4.01366i −0.156935 + 0.131684i −0.717874 0.696173i \(-0.754885\pi\)
0.560939 + 0.827857i \(0.310440\pi\)
\(930\) −0.613855 0.187278i −0.0201291 0.00614109i
\(931\) 4.44973 25.2357i 0.145834 0.827066i
\(932\) −11.5684 + 65.6079i −0.378937 + 2.14906i
\(933\) −12.2144 3.72644i −0.399882 0.121998i
\(934\) −8.57084 + 7.19179i −0.280446 + 0.235322i
\(935\) −0.286617 + 0.496435i −0.00937338 + 0.0162352i
\(936\) −53.2162 + 5.65676i −1.73943 + 0.184897i
\(937\) −22.9212 39.7006i −0.748802 1.29696i −0.948397 0.317085i \(-0.897296\pi\)
0.199595 0.979878i \(-0.436037\pi\)
\(938\) 11.5647 + 4.20920i 0.377600 + 0.137435i
\(939\) −4.03244 6.20140i −0.131594 0.202375i
\(940\) 0.965368 + 0.810040i 0.0314868 + 0.0264206i
\(941\) 4.09014 1.48869i 0.133335 0.0485298i −0.274491 0.961590i \(-0.588509\pi\)
0.407826 + 0.913060i \(0.366287\pi\)
\(942\) −0.695313 0.523313i −0.0226545 0.0170505i
\(943\) 0.847573 + 4.80683i 0.0276008 + 0.156532i
\(944\) −27.3637 −0.890612
\(945\) 0.276934 0.0443647i 0.00900865 0.00144318i
\(946\) −51.2644 −1.66675
\(947\) 0.350202 + 1.98610i 0.0113800 + 0.0645395i 0.989969 0.141285i \(-0.0451235\pi\)
−0.978589 + 0.205825i \(0.934012\pi\)
\(948\) −43.2891 + 18.4053i −1.40596 + 0.597776i
\(949\) −0.771790 + 0.280909i −0.0250534 + 0.00911868i
\(950\) −35.3118 29.6301i −1.14566 0.961327i
\(951\) 12.6827 24.9275i 0.411264 0.808331i
\(952\) 4.60587 + 1.67640i 0.149277 + 0.0543325i
\(953\) 17.8644 + 30.9420i 0.578684 + 1.00231i 0.995631 + 0.0933786i \(0.0297667\pi\)
−0.416947 + 0.908931i \(0.636900\pi\)
\(954\) −2.66832 + 38.8171i −0.0863900 + 1.25675i
\(955\) 0.104896 0.181686i 0.00339437 0.00587922i
\(956\) −44.5075 + 37.3462i −1.43948 + 1.20786i
\(957\) 25.0604 23.3968i 0.810086 0.756312i
\(958\) 5.91188 33.5279i 0.191004 1.08324i
\(959\) −1.15999 + 6.57865i −0.0374581 + 0.212436i
\(960\) 0.376975 + 1.62847i 0.0121668 + 0.0525588i
\(961\) −21.6428 + 18.1605i −0.698155 + 0.585822i
\(962\) 20.3338 35.2191i 0.655587 1.13551i
\(963\) 16.1417 + 4.00434i 0.520159 + 0.129038i
\(964\) −24.7759 42.9131i −0.797978 1.38214i
\(965\) 0.0769973 + 0.0280247i 0.00247863 + 0.000902148i
\(966\) 10.7254 0.568443i 0.345085 0.0182894i
\(967\) −0.531112 0.445656i −0.0170794 0.0143313i 0.634208 0.773163i \(-0.281326\pi\)
−0.651287 + 0.758831i \(0.725771\pi\)
\(968\) −5.71631 + 2.08057i −0.183729 + 0.0668719i
\(969\) −1.60833 + 13.1630i −0.0516670 + 0.422857i
\(970\) −0.205569 1.16584i −0.00660041 0.0374328i
\(971\) 47.4942 1.52416 0.762081 0.647482i \(-0.224178\pi\)
0.762081 + 0.647482i \(0.224178\pi\)
\(972\) 15.0340 56.7772i 0.482216 1.82113i
\(973\) −0.987988 −0.0316734
\(974\) 8.93869 + 50.6938i 0.286414 + 1.62434i
\(975\) 4.40563 36.0569i 0.141093 1.15474i
\(976\) 32.9931 12.0085i 1.05608 0.384383i
\(977\) −9.65470 8.10126i −0.308881 0.259182i 0.475148 0.879906i \(-0.342394\pi\)
−0.784029 + 0.620724i \(0.786839\pi\)
\(978\) 23.3609 1.23812i 0.746999 0.0395906i
\(979\) −4.51423 1.64305i −0.144276 0.0525120i
\(980\) 1.16855 + 2.02399i 0.0373280 + 0.0646540i
\(981\) 18.1441 + 4.50110i 0.579298 + 0.143709i
\(982\) −16.9168 + 29.3008i −0.539838 + 0.935027i
\(983\) 8.84400 7.42100i 0.282080 0.236693i −0.490759 0.871295i \(-0.663280\pi\)
0.772839 + 0.634602i \(0.218836\pi\)
\(984\) −1.81787 7.85292i −0.0579517 0.250342i
\(985\) 0.327745 1.85874i 0.0104428 0.0592243i
\(986\) 5.31361 30.1350i 0.169220 0.959693i
\(987\) 2.63787 2.46277i 0.0839644 0.0783908i
\(988\) −46.6351 + 39.1315i −1.48366 + 1.24494i
\(989\) −15.3647 + 26.6125i −0.488569 + 0.846227i
\(990\) 0.142259 2.06950i 0.00452130 0.0657731i
\(991\) −9.34676 16.1891i −0.296910 0.514263i 0.678518 0.734584i \(-0.262623\pi\)
−0.975427 + 0.220322i \(0.929289\pi\)
\(992\) −3.27281 1.19121i −0.103912 0.0378209i
\(993\) 15.1023 29.6832i 0.479257 0.941969i
\(994\) 1.22143 + 1.02490i 0.0387413 + 0.0325079i
\(995\) 1.66275 0.605192i 0.0527128 0.0191859i
\(996\) −89.4877 + 38.0476i −2.83553 + 1.20558i
\(997\) 0.583250 + 3.30778i 0.0184717 + 0.104758i 0.992650 0.121023i \(-0.0386175\pi\)
−0.974178 + 0.225782i \(0.927506\pi\)
\(998\) −35.8066 −1.13344
\(999\) 13.2074 + 16.2508i 0.417863 + 0.514154i
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.13.1 12
3.2 odd 2 81.2.e.a.10.2 12
4.3 odd 2 432.2.u.c.337.1 12
5.2 odd 4 675.2.u.b.499.4 24
5.3 odd 4 675.2.u.b.499.1 24
5.4 even 2 675.2.l.c.526.2 12
9.2 odd 6 243.2.e.b.109.2 12
9.4 even 3 243.2.e.d.190.2 12
9.5 odd 6 243.2.e.a.190.1 12
9.7 even 3 243.2.e.c.109.1 12
27.2 odd 18 81.2.e.a.73.2 12
27.4 even 9 729.2.c.e.487.6 12
27.5 odd 18 729.2.a.d.1.6 6
27.7 even 9 243.2.e.c.136.1 12
27.11 odd 18 243.2.e.a.55.1 12
27.13 even 9 729.2.c.e.244.6 12
27.14 odd 18 729.2.c.b.244.1 12
27.16 even 9 243.2.e.d.55.2 12
27.20 odd 18 243.2.e.b.136.2 12
27.22 even 9 729.2.a.a.1.1 6
27.23 odd 18 729.2.c.b.487.1 12
27.25 even 9 inner 27.2.e.a.25.1 yes 12
108.79 odd 18 432.2.u.c.241.1 12
135.52 odd 36 675.2.u.b.349.1 24
135.79 even 18 675.2.l.c.376.2 12
135.133 odd 36 675.2.u.b.349.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.1 12 1.1 even 1 trivial
27.2.e.a.25.1 yes 12 27.25 even 9 inner
81.2.e.a.10.2 12 3.2 odd 2
81.2.e.a.73.2 12 27.2 odd 18
243.2.e.a.55.1 12 27.11 odd 18
243.2.e.a.190.1 12 9.5 odd 6
243.2.e.b.109.2 12 9.2 odd 6
243.2.e.b.136.2 12 27.20 odd 18
243.2.e.c.109.1 12 9.7 even 3
243.2.e.c.136.1 12 27.7 even 9
243.2.e.d.55.2 12 27.16 even 9
243.2.e.d.190.2 12 9.4 even 3
432.2.u.c.241.1 12 108.79 odd 18
432.2.u.c.337.1 12 4.3 odd 2
675.2.l.c.376.2 12 135.79 even 18
675.2.l.c.526.2 12 5.4 even 2
675.2.u.b.349.1 24 135.52 odd 36
675.2.u.b.349.4 24 135.133 odd 36
675.2.u.b.499.1 24 5.3 odd 4
675.2.u.b.499.4 24 5.2 odd 4
729.2.a.a.1.1 6 27.22 even 9
729.2.a.d.1.6 6 27.5 odd 18
729.2.c.b.244.1 12 27.14 odd 18
729.2.c.b.487.1 12 27.23 odd 18
729.2.c.e.244.6 12 27.13 even 9
729.2.c.e.487.6 12 27.4 even 9