Properties

Label 273.2.i.d.235.1
Level $273$
Weight $2$
Character 273.235
Analytic conductor $2.180$
Analytic rank $0$
Dimension $8$
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] = [273,2,Mod(79,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4868829729.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} - x^{6} + 5x^{5} - 8x^{4} + 15x^{3} - 9x^{2} - 54x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(-1.70103 + 0.326320i\) of defining polynomial
Character \(\chi\) \(=\) 273.235
Dual form 273.2.i.d.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13312 - 1.96262i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.56792 + 2.71571i) q^{4} +(-1.63312 - 2.82864i) q^{5} +2.26624 q^{6} +(-0.133118 + 2.64240i) q^{7} +2.57406 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.13312 - 1.96262i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.56792 + 2.71571i) q^{4} +(-1.63312 - 2.82864i) q^{5} +2.26624 q^{6} +(-0.133118 + 2.64240i) q^{7} +2.57406 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.70103 + 6.41038i) q^{10} +(-1.06520 + 1.84499i) q^{11} +(-1.56792 - 2.71571i) q^{12} -1.00000 q^{13} +(5.33686 - 2.73289i) q^{14} +3.26624 q^{15} +(0.219115 + 0.379518i) q^{16} +(-1.72183 + 2.98229i) q^{17} +(-1.13312 + 1.96262i) q^{18} +(0.635830 + 1.10129i) q^{19} +10.2424 q^{20} +(-2.22183 - 1.43648i) q^{21} +4.82801 q^{22} +(4.48806 + 7.77355i) q^{23} +(-1.28703 + 2.22920i) q^{24} +(-2.83415 + 4.90890i) q^{25} +(1.13312 + 1.96262i) q^{26} +1.00000 q^{27} +(-6.96727 - 4.50457i) q^{28} -8.53790 q^{29} +(-3.70103 - 6.41038i) q^{30} +(1.78703 - 3.09523i) q^{31} +(3.07063 - 5.31848i) q^{32} +(-1.06520 - 1.84499i) q^{33} +7.80413 q^{34} +(7.69181 - 3.93881i) q^{35} +3.13583 q^{36} +(0.890499 + 1.54239i) q^{37} +(1.44094 - 2.49578i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-4.20375 - 7.28110i) q^{40} +2.95841 q^{41} +(-0.301678 + 5.98831i) q^{42} -11.7803 q^{43} +(-3.34030 - 5.78556i) q^{44} +(-1.63312 + 2.82864i) q^{45} +(10.1710 - 17.6167i) q^{46} +(-3.61233 - 6.25673i) q^{47} -0.438230 q^{48} +(-6.96456 - 0.703505i) q^{49} +12.8457 q^{50} +(-1.72183 - 2.98229i) q^{51} +(1.56792 - 2.71571i) q^{52} +(-5.60310 + 9.70485i) q^{53} +(-1.13312 - 1.96262i) q^{54} +6.95841 q^{55} +(-0.342655 + 6.80170i) q^{56} -1.27166 q^{57} +(9.67445 + 16.7566i) q^{58} +(-2.97921 + 5.16014i) q^{59} +(-5.12118 + 8.87015i) q^{60} +(-1.45559 - 2.52116i) q^{61} -8.09967 q^{62} +(2.35495 - 1.20592i) q^{63} -13.0411 q^{64} +(1.63312 + 2.82864i) q^{65} +(-2.41400 + 4.18118i) q^{66} +(-3.20103 + 5.54435i) q^{67} +(-5.39936 - 9.35196i) q^{68} -8.97613 q^{69} +(-16.4461 - 10.6330i) q^{70} +4.23007 q^{71} +(-1.28703 - 2.22920i) q^{72} +(0.479207 - 0.830011i) q^{73} +(2.01808 - 3.49542i) q^{74} +(-2.83415 - 4.90890i) q^{75} -3.98771 q^{76} +(-4.73339 - 3.06030i) q^{77} -2.26624 q^{78} +(-1.65662 - 2.86936i) q^{79} +(0.715682 - 1.23960i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.35223 - 5.80624i) q^{82} -10.4779 q^{83} +(7.38471 - 3.78155i) q^{84} +11.2478 q^{85} +(13.3484 + 23.1202i) q^{86} +(4.26895 - 7.39404i) q^{87} +(-2.74190 + 4.74911i) q^{88} +(-7.54712 - 13.0720i) q^{89} +7.40207 q^{90} +(0.133118 - 2.64240i) q^{91} -28.1476 q^{92} +(1.78703 + 3.09523i) q^{93} +(-8.18639 + 14.1792i) q^{94} +(2.07677 - 3.59707i) q^{95} +(3.07063 + 5.31848i) q^{96} +3.78100 q^{97} +(6.51096 + 14.4659i) q^{98} +2.13041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 4 q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 9 q^{7} - 12 q^{8} - 4 q^{9} - 14 q^{10} - 4 q^{11} - 7 q^{12} - 8 q^{13} + 16 q^{14} + 6 q^{15} - 9 q^{16} - 2 q^{17} + q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21} + 40 q^{22} + 4 q^{23} + 6 q^{24} + 3 q^{25} - q^{26} + 8 q^{27} - 20 q^{28} - 26 q^{29} - 14 q^{30} - 2 q^{31} + 18 q^{32} - 4 q^{33} + 13 q^{35} + 14 q^{36} + 5 q^{37} - 11 q^{38} + 4 q^{39} - 17 q^{40} + 16 q^{41} - 17 q^{42} + 32 q^{43} + 26 q^{44} - 3 q^{45} + 29 q^{46} - 15 q^{47} + 18 q^{48} - 21 q^{49} + 48 q^{50} - 2 q^{51} + 7 q^{52} + 2 q^{53} + q^{54} + 48 q^{55} - 35 q^{56} + 12 q^{57} - q^{58} - 20 q^{59} + q^{60} - 20 q^{61} - 44 q^{62} - 3 q^{63} + 40 q^{64} + 3 q^{65} - 20 q^{66} - 10 q^{67} - 13 q^{68} - 8 q^{69} - 31 q^{70} + 4 q^{71} + 6 q^{72} + 21 q^{74} + 3 q^{75} - 86 q^{76} + 3 q^{77} + 2 q^{78} - 6 q^{79} + 21 q^{80} - 4 q^{81} - 6 q^{82} + 32 q^{83} - 2 q^{84} + 4 q^{85} + 51 q^{86} + 13 q^{87} - 39 q^{88} - 51 q^{89} + 28 q^{90} - 9 q^{91} - 8 q^{92} - 2 q^{93} - 19 q^{94} - 17 q^{95} + 18 q^{96} + 26 q^{97} + 33 q^{98} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13312 1.96262i −0.801236 1.38778i −0.918803 0.394716i \(-0.870843\pi\)
0.117567 0.993065i \(-0.462490\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −1.56792 + 2.71571i −0.783958 + 1.35785i
\(5\) −1.63312 2.82864i −0.730353 1.26501i −0.956732 0.290969i \(-0.906022\pi\)
0.226380 0.974039i \(-0.427311\pi\)
\(6\) 2.26624 0.925187
\(7\) −0.133118 + 2.64240i −0.0503141 + 0.998733i
\(8\) 2.57406 0.910068
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −3.70103 + 6.41038i −1.17037 + 2.02714i
\(11\) −1.06520 + 1.84499i −0.321171 + 0.556284i −0.980730 0.195368i \(-0.937410\pi\)
0.659559 + 0.751653i \(0.270743\pi\)
\(12\) −1.56792 2.71571i −0.452618 0.783958i
\(13\) −1.00000 −0.277350
\(14\) 5.33686 2.73289i 1.42634 0.730396i
\(15\) 3.26624 0.843339
\(16\) 0.219115 + 0.379518i 0.0547788 + 0.0948796i
\(17\) −1.72183 + 2.98229i −0.417604 + 0.723312i −0.995698 0.0926586i \(-0.970463\pi\)
0.578094 + 0.815970i \(0.303797\pi\)
\(18\) −1.13312 + 1.96262i −0.267079 + 0.462594i
\(19\) 0.635830 + 1.10129i 0.145869 + 0.252653i 0.929697 0.368325i \(-0.120069\pi\)
−0.783828 + 0.620979i \(0.786735\pi\)
\(20\) 10.2424 2.29026
\(21\) −2.22183 1.43648i −0.484842 0.313467i
\(22\) 4.82801 1.02933
\(23\) 4.48806 + 7.77355i 0.935826 + 1.62090i 0.773154 + 0.634218i \(0.218678\pi\)
0.162671 + 0.986680i \(0.447989\pi\)
\(24\) −1.28703 + 2.22920i −0.262714 + 0.455034i
\(25\) −2.83415 + 4.90890i −0.566830 + 0.981779i
\(26\) 1.13312 + 1.96262i 0.222223 + 0.384901i
\(27\) 1.00000 0.192450
\(28\) −6.96727 4.50457i −1.31669 0.851284i
\(29\) −8.53790 −1.58545 −0.792724 0.609581i \(-0.791338\pi\)
−0.792724 + 0.609581i \(0.791338\pi\)
\(30\) −3.70103 6.41038i −0.675713 1.17037i
\(31\) 1.78703 3.09523i 0.320960 0.555919i −0.659726 0.751506i \(-0.729328\pi\)
0.980686 + 0.195587i \(0.0626611\pi\)
\(32\) 3.07063 5.31848i 0.542815 0.940184i
\(33\) −1.06520 1.84499i −0.185428 0.321171i
\(34\) 7.80413 1.33840
\(35\) 7.69181 3.93881i 1.30015 0.665780i
\(36\) 3.13583 0.522638
\(37\) 0.890499 + 1.54239i 0.146397 + 0.253567i 0.929893 0.367829i \(-0.119899\pi\)
−0.783496 + 0.621397i \(0.786566\pi\)
\(38\) 1.44094 2.49578i 0.233752 0.404870i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) −4.20375 7.28110i −0.664670 1.15124i
\(41\) 2.95841 0.462027 0.231013 0.972951i \(-0.425796\pi\)
0.231013 + 0.972951i \(0.425796\pi\)
\(42\) −0.301678 + 5.98831i −0.0465499 + 0.924016i
\(43\) −11.7803 −1.79647 −0.898236 0.439512i \(-0.855151\pi\)
−0.898236 + 0.439512i \(0.855151\pi\)
\(44\) −3.34030 5.78556i −0.503569 0.872207i
\(45\) −1.63312 + 2.82864i −0.243451 + 0.421669i
\(46\) 10.1710 17.6167i 1.49963 2.59744i
\(47\) −3.61233 6.25673i −0.526912 0.912638i −0.999508 0.0313590i \(-0.990016\pi\)
0.472596 0.881279i \(-0.343317\pi\)
\(48\) −0.438230 −0.0632531
\(49\) −6.96456 0.703505i −0.994937 0.100501i
\(50\) 12.8457 1.81666
\(51\) −1.72183 2.98229i −0.241104 0.417604i
\(52\) 1.56792 2.71571i 0.217431 0.376601i
\(53\) −5.60310 + 9.70485i −0.769645 + 1.33306i 0.168110 + 0.985768i \(0.446233\pi\)
−0.937755 + 0.347296i \(0.887100\pi\)
\(54\) −1.13312 1.96262i −0.154198 0.267079i
\(55\) 6.95841 0.938272
\(56\) −0.342655 + 6.80170i −0.0457892 + 0.908915i
\(57\) −1.27166 −0.168435
\(58\) 9.67445 + 16.7566i 1.27032 + 2.20025i
\(59\) −2.97921 + 5.16014i −0.387860 + 0.671793i −0.992161 0.124963i \(-0.960119\pi\)
0.604302 + 0.796756i \(0.293452\pi\)
\(60\) −5.12118 + 8.87015i −0.661142 + 1.14513i
\(61\) −1.45559 2.52116i −0.186369 0.322801i 0.757668 0.652640i \(-0.226339\pi\)
−0.944037 + 0.329839i \(0.893005\pi\)
\(62\) −8.09967 −1.02866
\(63\) 2.35495 1.20592i 0.296695 0.151931i
\(64\) −13.0411 −1.63013
\(65\) 1.63312 + 2.82864i 0.202563 + 0.350850i
\(66\) −2.41400 + 4.18118i −0.297143 + 0.514667i
\(67\) −3.20103 + 5.54435i −0.391068 + 0.677350i −0.992591 0.121506i \(-0.961228\pi\)
0.601522 + 0.798856i \(0.294561\pi\)
\(68\) −5.39936 9.35196i −0.654768 1.13409i
\(69\) −8.97613 −1.08060
\(70\) −16.4461 10.6330i −1.96569 1.27088i
\(71\) 4.23007 0.502017 0.251009 0.967985i \(-0.419238\pi\)
0.251009 + 0.967985i \(0.419238\pi\)
\(72\) −1.28703 2.22920i −0.151678 0.262714i
\(73\) 0.479207 0.830011i 0.0560869 0.0971454i −0.836619 0.547786i \(-0.815471\pi\)
0.892706 + 0.450640i \(0.148804\pi\)
\(74\) 2.01808 3.49542i 0.234597 0.406334i
\(75\) −2.83415 4.90890i −0.327260 0.566830i
\(76\) −3.98771 −0.457422
\(77\) −4.73339 3.06030i −0.539420 0.348753i
\(78\) −2.26624 −0.256601
\(79\) −1.65662 2.86936i −0.186385 0.322828i 0.757658 0.652652i \(-0.226344\pi\)
−0.944042 + 0.329825i \(0.893010\pi\)
\(80\) 0.715682 1.23960i 0.0800156 0.138591i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.35223 5.80624i −0.370192 0.641192i
\(83\) −10.4779 −1.15009 −0.575047 0.818120i \(-0.695016\pi\)
−0.575047 + 0.818120i \(0.695016\pi\)
\(84\) 7.38471 3.78155i 0.805738 0.412601i
\(85\) 11.2478 1.21999
\(86\) 13.3484 + 23.1202i 1.43940 + 2.49311i
\(87\) 4.26895 7.39404i 0.457679 0.792724i
\(88\) −2.74190 + 4.74911i −0.292287 + 0.506256i
\(89\) −7.54712 13.0720i −0.799993 1.38563i −0.919620 0.392810i \(-0.871503\pi\)
0.119626 0.992819i \(-0.461830\pi\)
\(90\) 7.40207 0.780246
\(91\) 0.133118 2.64240i 0.0139546 0.276999i
\(92\) −28.1476 −2.93459
\(93\) 1.78703 + 3.09523i 0.185306 + 0.320960i
\(94\) −8.18639 + 14.1792i −0.844361 + 1.46248i
\(95\) 2.07677 3.59707i 0.213072 0.369052i
\(96\) 3.07063 + 5.31848i 0.313395 + 0.542815i
\(97\) 3.78100 0.383902 0.191951 0.981404i \(-0.438519\pi\)
0.191951 + 0.981404i \(0.438519\pi\)
\(98\) 6.51096 + 14.4659i 0.657706 + 1.46128i
\(99\) 2.13041 0.214114
\(100\) −8.88742 15.3935i −0.888742 1.53935i
\(101\) 4.85777 8.41390i 0.483366 0.837215i −0.516451 0.856316i \(-0.672747\pi\)
0.999818 + 0.0191018i \(0.00608066\pi\)
\(102\) −3.90207 + 6.75858i −0.386362 + 0.669199i
\(103\) 6.24816 + 10.8221i 0.615649 + 1.06634i 0.990270 + 0.139157i \(0.0444394\pi\)
−0.374621 + 0.927178i \(0.622227\pi\)
\(104\) −2.57406 −0.252407
\(105\) −0.434797 + 8.63071i −0.0424318 + 0.842271i
\(106\) 25.3959 2.46667
\(107\) 6.44648 + 11.1656i 0.623204 + 1.07942i 0.988885 + 0.148681i \(0.0475029\pi\)
−0.365681 + 0.930740i \(0.619164\pi\)
\(108\) −1.56792 + 2.71571i −0.150873 + 0.261319i
\(109\) 3.68295 6.37906i 0.352763 0.611003i −0.633970 0.773358i \(-0.718576\pi\)
0.986732 + 0.162355i \(0.0519089\pi\)
\(110\) −7.88471 13.6567i −0.751777 1.30212i
\(111\) −1.78100 −0.169045
\(112\) −1.03201 + 0.528469i −0.0975156 + 0.0499356i
\(113\) 12.7333 1.19784 0.598922 0.800808i \(-0.295596\pi\)
0.598922 + 0.800808i \(0.295596\pi\)
\(114\) 1.44094 + 2.49578i 0.134957 + 0.233752i
\(115\) 14.6591 25.3903i 1.36697 2.36765i
\(116\) 13.3867 23.1864i 1.24292 2.15281i
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) 13.5032 1.24307
\(119\) −7.65120 4.94675i −0.701384 0.453468i
\(120\) 8.40749 0.767495
\(121\) 3.23068 + 5.59571i 0.293698 + 0.508701i
\(122\) −3.29871 + 5.71353i −0.298651 + 0.517279i
\(123\) −1.47921 + 2.56206i −0.133376 + 0.231013i
\(124\) 5.60382 + 9.70611i 0.503238 + 0.871634i
\(125\) 2.18284 0.195239
\(126\) −5.03519 3.25541i −0.448570 0.290015i
\(127\) 10.5972 0.940349 0.470175 0.882573i \(-0.344191\pi\)
0.470175 + 0.882573i \(0.344191\pi\)
\(128\) 8.63583 + 14.9577i 0.763307 + 1.32209i
\(129\) 5.89013 10.2020i 0.518597 0.898236i
\(130\) 3.70103 6.41038i 0.324602 0.562227i
\(131\) −8.64198 14.9683i −0.755053 1.30779i −0.945348 0.326063i \(-0.894278\pi\)
0.190295 0.981727i \(-0.439055\pi\)
\(132\) 6.68059 0.581471
\(133\) −2.99469 + 1.53352i −0.259673 + 0.132973i
\(134\) 14.5086 1.25335
\(135\) −1.63312 2.82864i −0.140556 0.243451i
\(136\) −4.43208 + 7.67660i −0.380048 + 0.658263i
\(137\) −8.06755 + 13.9734i −0.689257 + 1.19383i 0.282822 + 0.959173i \(0.408730\pi\)
−0.972079 + 0.234656i \(0.924604\pi\)
\(138\) 10.1710 + 17.6167i 0.865814 + 1.49963i
\(139\) 1.31325 0.111388 0.0556940 0.998448i \(-0.482263\pi\)
0.0556940 + 0.998448i \(0.482263\pi\)
\(140\) −1.36345 + 27.0644i −0.115232 + 2.28736i
\(141\) 7.22465 0.608425
\(142\) −4.79318 8.30202i −0.402234 0.696690i
\(143\) 1.06520 1.84499i 0.0890768 0.154286i
\(144\) 0.219115 0.379518i 0.0182596 0.0316265i
\(145\) 13.9434 + 24.1507i 1.15794 + 2.00560i
\(146\) −2.17199 −0.179755
\(147\) 4.09153 5.67973i 0.337464 0.468456i
\(148\) −5.58491 −0.459076
\(149\) −2.82801 4.89825i −0.231679 0.401280i 0.726623 0.687036i \(-0.241089\pi\)
−0.958302 + 0.285756i \(0.907755\pi\)
\(150\) −6.42286 + 11.1247i −0.524424 + 0.908330i
\(151\) 4.19181 7.26043i 0.341125 0.590845i −0.643517 0.765432i \(-0.722526\pi\)
0.984642 + 0.174587i \(0.0558589\pi\)
\(152\) 1.63666 + 2.83479i 0.132751 + 0.229932i
\(153\) 3.44365 0.278403
\(154\) −0.642697 + 12.7575i −0.0517900 + 1.02803i
\(155\) −11.6737 −0.937656
\(156\) 1.56792 + 2.71571i 0.125534 + 0.217431i
\(157\) 1.24544 2.15717i 0.0993972 0.172161i −0.812038 0.583604i \(-0.801642\pi\)
0.911435 + 0.411443i \(0.134975\pi\)
\(158\) −3.75430 + 6.50264i −0.298676 + 0.517322i
\(159\) −5.60310 9.70485i −0.444355 0.769645i
\(160\) −20.0588 −1.58579
\(161\) −21.1383 + 10.8245i −1.66593 + 0.853087i
\(162\) 2.26624 0.178052
\(163\) −5.64209 9.77238i −0.441922 0.765432i 0.555910 0.831243i \(-0.312370\pi\)
−0.997832 + 0.0658106i \(0.979037\pi\)
\(164\) −4.63854 + 8.03419i −0.362209 + 0.627365i
\(165\) −3.47921 + 6.02616i −0.270856 + 0.469136i
\(166\) 11.8727 + 20.5640i 0.921497 + 1.59608i
\(167\) 3.27166 0.253169 0.126584 0.991956i \(-0.459599\pi\)
0.126584 + 0.991956i \(0.459599\pi\)
\(168\) −5.71912 3.69760i −0.441239 0.285276i
\(169\) 1.00000 0.0769231
\(170\) −12.7451 22.0751i −0.977503 1.69308i
\(171\) 0.635830 1.10129i 0.0486231 0.0842177i
\(172\) 18.4704 31.9918i 1.40836 2.43935i
\(173\) 9.90207 + 17.1509i 0.752840 + 1.30396i 0.946441 + 0.322877i \(0.104650\pi\)
−0.193601 + 0.981080i \(0.562017\pi\)
\(174\) −19.3489 −1.46684
\(175\) −12.5940 8.14243i −0.952016 0.615510i
\(176\) −0.933608 −0.0703734
\(177\) −2.97921 5.16014i −0.223931 0.387860i
\(178\) −17.1036 + 29.6242i −1.28197 + 2.22043i
\(179\) 1.52362 2.63898i 0.113881 0.197247i −0.803451 0.595371i \(-0.797005\pi\)
0.917332 + 0.398124i \(0.130339\pi\)
\(180\) −5.12118 8.87015i −0.381710 0.661142i
\(181\) 10.7931 0.802242 0.401121 0.916025i \(-0.368621\pi\)
0.401121 + 0.916025i \(0.368621\pi\)
\(182\) −5.33686 + 2.73289i −0.395595 + 0.202575i
\(183\) 2.91118 0.215201
\(184\) 11.5525 + 20.0096i 0.851665 + 1.47513i
\(185\) 2.90858 5.03781i 0.213843 0.370387i
\(186\) 4.04983 7.01452i 0.296948 0.514329i
\(187\) −3.66819 6.35349i −0.268245 0.464613i
\(188\) 22.6553 1.65231
\(189\) −0.133118 + 2.64240i −0.00968295 + 0.192206i
\(190\) −9.41291 −0.682885
\(191\) 9.07135 + 15.7120i 0.656380 + 1.13688i 0.981546 + 0.191226i \(0.0612464\pi\)
−0.325166 + 0.945657i \(0.605420\pi\)
\(192\) 6.52054 11.2939i 0.470579 0.815067i
\(193\) −3.90195 + 6.75838i −0.280869 + 0.486479i −0.971599 0.236634i \(-0.923956\pi\)
0.690730 + 0.723113i \(0.257289\pi\)
\(194\) −4.28432 7.42066i −0.307596 0.532772i
\(195\) −3.26624 −0.233900
\(196\) 12.8304 17.8107i 0.916454 1.27219i
\(197\) −5.12476 −0.365124 −0.182562 0.983194i \(-0.558439\pi\)
−0.182562 + 0.983194i \(0.558439\pi\)
\(198\) −2.41400 4.18118i −0.171556 0.297143i
\(199\) −4.52904 + 7.84453i −0.321055 + 0.556084i −0.980706 0.195488i \(-0.937371\pi\)
0.659651 + 0.751572i \(0.270704\pi\)
\(200\) −7.29528 + 12.6358i −0.515854 + 0.893485i
\(201\) −3.20103 5.54435i −0.225783 0.391068i
\(202\) −22.0177 −1.54916
\(203\) 1.13655 22.5605i 0.0797703 1.58344i
\(204\) 10.7987 0.756061
\(205\) −4.83144 8.36830i −0.337442 0.584467i
\(206\) 14.1598 24.5255i 0.986560 1.70877i
\(207\) 4.48806 7.77355i 0.311942 0.540299i
\(208\) −0.219115 0.379518i −0.0151929 0.0263149i
\(209\) −2.70915 −0.187396
\(210\) 17.4315 8.92627i 1.20289 0.615971i
\(211\) −5.28960 −0.364151 −0.182075 0.983285i \(-0.558282\pi\)
−0.182075 + 0.983285i \(0.558282\pi\)
\(212\) −17.5704 30.4328i −1.20674 2.09013i
\(213\) −2.11504 + 3.66335i −0.144920 + 0.251009i
\(214\) 14.6092 25.3040i 0.998667 1.72974i
\(215\) 19.2386 + 33.3222i 1.31206 + 2.27255i
\(216\) 2.57406 0.175143
\(217\) 7.94094 + 5.13408i 0.539066 + 0.348524i
\(218\) −16.6929 −1.13058
\(219\) 0.479207 + 0.830011i 0.0323818 + 0.0560869i
\(220\) −10.9102 + 18.8970i −0.735566 + 1.27404i
\(221\) 1.72183 2.98229i 0.115823 0.200611i
\(222\) 2.01808 + 3.49542i 0.135445 + 0.234597i
\(223\) −23.5197 −1.57499 −0.787497 0.616319i \(-0.788623\pi\)
−0.787497 + 0.616319i \(0.788623\pi\)
\(224\) 13.6448 + 8.82181i 0.911682 + 0.589432i
\(225\) 5.66830 0.377887
\(226\) −14.4283 24.9905i −0.959755 1.66234i
\(227\) −5.40207 + 9.35665i −0.358548 + 0.621023i −0.987718 0.156244i \(-0.950061\pi\)
0.629171 + 0.777267i \(0.283395\pi\)
\(228\) 1.99385 3.45346i 0.132046 0.228711i
\(229\) 14.9342 + 25.8667i 0.986878 + 1.70932i 0.633275 + 0.773927i \(0.281710\pi\)
0.353603 + 0.935395i \(0.384956\pi\)
\(230\) −66.4419 −4.38105
\(231\) 5.01699 2.56909i 0.330094 0.169034i
\(232\) −21.9771 −1.44286
\(233\) −5.47330 9.48004i −0.358568 0.621058i 0.629154 0.777281i \(-0.283402\pi\)
−0.987722 + 0.156223i \(0.950068\pi\)
\(234\) 1.13312 1.96262i 0.0740743 0.128300i
\(235\) −11.7987 + 20.4360i −0.769663 + 1.33310i
\(236\) −9.34229 16.1813i −0.608131 1.05331i
\(237\) 3.31325 0.215218
\(238\) −1.03887 + 20.6216i −0.0673402 + 1.33670i
\(239\) 30.2945 1.95959 0.979795 0.200007i \(-0.0640964\pi\)
0.979795 + 0.200007i \(0.0640964\pi\)
\(240\) 0.715682 + 1.23960i 0.0461970 + 0.0800156i
\(241\) −11.9048 + 20.6197i −0.766854 + 1.32823i 0.172406 + 0.985026i \(0.444846\pi\)
−0.939261 + 0.343205i \(0.888488\pi\)
\(242\) 7.32149 12.6812i 0.470643 0.815178i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 9.12896 0.584422
\(245\) 9.38399 + 20.8492i 0.599521 + 1.33200i
\(246\) 6.70447 0.427461
\(247\) −0.635830 1.10129i −0.0404569 0.0700734i
\(248\) 4.59992 7.96730i 0.292095 0.505924i
\(249\) 5.23893 9.07409i 0.332004 0.575047i
\(250\) −2.47342 4.28408i −0.156433 0.270949i
\(251\) 20.5084 1.29448 0.647239 0.762287i \(-0.275924\pi\)
0.647239 + 0.762287i \(0.275924\pi\)
\(252\) −0.417437 + 8.28612i −0.0262961 + 0.521976i
\(253\) −19.1228 −1.20224
\(254\) −12.0079 20.7983i −0.753441 1.30500i
\(255\) −5.62389 + 9.74087i −0.352182 + 0.609997i
\(256\) 6.52976 11.3099i 0.408110 0.706868i
\(257\) −1.34598 2.33130i −0.0839597 0.145422i 0.820988 0.570946i \(-0.193423\pi\)
−0.904947 + 0.425523i \(0.860090\pi\)
\(258\) −26.6969 −1.66207
\(259\) −4.19415 + 2.14773i −0.260612 + 0.133454i
\(260\) −10.2424 −0.635204
\(261\) 4.26895 + 7.39404i 0.264241 + 0.457679i
\(262\) −19.5848 + 33.9218i −1.20995 + 2.09570i
\(263\) 1.33415 2.31082i 0.0822673 0.142491i −0.821956 0.569551i \(-0.807117\pi\)
0.904224 + 0.427060i \(0.140451\pi\)
\(264\) −2.74190 4.74911i −0.168752 0.292287i
\(265\) 36.6021 2.24845
\(266\) 6.40304 + 4.13978i 0.392596 + 0.253826i
\(267\) 15.0942 0.923753
\(268\) −10.0379 17.3861i −0.613162 1.06203i
\(269\) −0.449557 + 0.778656i −0.0274100 + 0.0474755i −0.879405 0.476074i \(-0.842059\pi\)
0.851995 + 0.523550i \(0.175393\pi\)
\(270\) −3.70103 + 6.41038i −0.225238 + 0.390123i
\(271\) −11.0287 19.1022i −0.669944 1.16038i −0.977919 0.208983i \(-0.932985\pi\)
0.307975 0.951394i \(-0.400349\pi\)
\(272\) −1.50911 −0.0915034
\(273\) 2.22183 + 1.43648i 0.134471 + 0.0869400i
\(274\) 36.5659 2.20903
\(275\) −6.03790 10.4579i −0.364099 0.630638i
\(276\) 14.0738 24.3765i 0.847143 1.46730i
\(277\) −4.83415 + 8.37300i −0.290456 + 0.503085i −0.973918 0.226902i \(-0.927140\pi\)
0.683462 + 0.729986i \(0.260474\pi\)
\(278\) −1.48806 2.57740i −0.0892481 0.154582i
\(279\) −3.57406 −0.213973
\(280\) 19.7992 10.1387i 1.18323 0.605905i
\(281\) −27.1538 −1.61986 −0.809929 0.586528i \(-0.800494\pi\)
−0.809929 + 0.586528i \(0.800494\pi\)
\(282\) −8.18639 14.1792i −0.487492 0.844361i
\(283\) 13.7949 23.8935i 0.820022 1.42032i −0.0856426 0.996326i \(-0.527294\pi\)
0.905665 0.423994i \(-0.139372\pi\)
\(284\) −6.63240 + 11.4876i −0.393560 + 0.681666i
\(285\) 2.07677 + 3.59707i 0.123017 + 0.213072i
\(286\) −4.82801 −0.285486
\(287\) −0.393820 + 7.81731i −0.0232464 + 0.461441i
\(288\) −6.14125 −0.361877
\(289\) 2.57063 + 4.45246i 0.151213 + 0.261909i
\(290\) 31.5990 54.7311i 1.85556 3.21392i
\(291\) −1.89050 + 3.27444i −0.110823 + 0.191951i
\(292\) 1.50271 + 2.60277i 0.0879395 + 0.152316i
\(293\) 0.331470 0.0193647 0.00968236 0.999953i \(-0.496918\pi\)
0.00968236 + 0.999953i \(0.496918\pi\)
\(294\) −15.7833 1.59431i −0.920503 0.0929819i
\(295\) 19.4616 1.13310
\(296\) 2.29220 + 3.97020i 0.133231 + 0.230763i
\(297\) −1.06520 + 1.84499i −0.0618094 + 0.107057i
\(298\) −6.40893 + 11.1006i −0.371260 + 0.643040i
\(299\) −4.48806 7.77355i −0.259551 0.449556i
\(300\) 17.7748 1.02623
\(301\) 1.56817 31.1282i 0.0903878 1.79420i
\(302\) −18.9993 −1.09328
\(303\) 4.85777 + 8.41390i 0.279072 + 0.483366i
\(304\) −0.278640 + 0.482618i −0.0159811 + 0.0276801i
\(305\) −4.75430 + 8.23469i −0.272230 + 0.471517i
\(306\) −3.90207 6.75858i −0.223066 0.386362i
\(307\) 2.21236 0.126266 0.0631331 0.998005i \(-0.479891\pi\)
0.0631331 + 0.998005i \(0.479891\pi\)
\(308\) 15.7324 8.05624i 0.896439 0.459047i
\(309\) −12.4963 −0.710890
\(310\) 13.2277 + 22.9111i 0.751284 + 1.30126i
\(311\) 4.35162 7.53723i 0.246758 0.427397i −0.715866 0.698237i \(-0.753968\pi\)
0.962624 + 0.270840i \(0.0873014\pi\)
\(312\) 1.28703 2.22920i 0.0728637 0.126204i
\(313\) −17.2034 29.7971i −0.972392 1.68423i −0.688285 0.725441i \(-0.741636\pi\)
−0.284107 0.958792i \(-0.591697\pi\)
\(314\) −5.64494 −0.318563
\(315\) −7.25701 4.69190i −0.408886 0.264358i
\(316\) 10.3898 0.584471
\(317\) 4.74164 + 8.21277i 0.266317 + 0.461275i 0.967908 0.251305i \(-0.0808598\pi\)
−0.701591 + 0.712580i \(0.747526\pi\)
\(318\) −12.6980 + 21.9935i −0.712066 + 1.23333i
\(319\) 9.09460 15.7523i 0.509200 0.881960i
\(320\) 21.2976 + 36.8886i 1.19057 + 2.06213i
\(321\) −12.8930 −0.719615
\(322\) 45.1965 + 29.2210i 2.51870 + 1.62842i
\(323\) −4.37916 −0.243663
\(324\) −1.56792 2.71571i −0.0871064 0.150873i
\(325\) 2.83415 4.90890i 0.157210 0.272297i
\(326\) −12.7863 + 22.1465i −0.708168 + 1.22658i
\(327\) 3.68295 + 6.37906i 0.203668 + 0.352763i
\(328\) 7.61514 0.420475
\(329\) 17.0137 8.71232i 0.937993 0.480326i
\(330\) 15.7694 0.868078
\(331\) 4.06188 + 7.03539i 0.223261 + 0.386700i 0.955796 0.294029i \(-0.0949964\pi\)
−0.732535 + 0.680729i \(0.761663\pi\)
\(332\) 16.4284 28.4548i 0.901625 1.56166i
\(333\) 0.890499 1.54239i 0.0487990 0.0845224i
\(334\) −3.70718 6.42102i −0.202848 0.351343i
\(335\) 20.9107 1.14247
\(336\) 0.0583365 1.15798i 0.00318252 0.0631729i
\(337\) −31.5558 −1.71896 −0.859478 0.511173i \(-0.829211\pi\)
−0.859478 + 0.511173i \(0.829211\pi\)
\(338\) −1.13312 1.96262i −0.0616335 0.106752i
\(339\) −6.36663 + 11.0273i −0.345788 + 0.598922i
\(340\) −17.6356 + 30.5457i −0.956423 + 1.65657i
\(341\) 3.80710 + 6.59409i 0.206166 + 0.357090i
\(342\) −2.88188 −0.155834
\(343\) 2.78605 18.3095i 0.150433 0.988620i
\(344\) −30.3231 −1.63491
\(345\) 14.6591 + 25.3903i 0.789218 + 1.36697i
\(346\) 22.4404 38.8680i 1.20641 2.08955i
\(347\) 1.27546 2.20916i 0.0684704 0.118594i −0.829758 0.558124i \(-0.811521\pi\)
0.898228 + 0.439529i \(0.144855\pi\)
\(348\) 13.3867 + 23.1864i 0.717602 + 1.24292i
\(349\) −7.54309 −0.403773 −0.201886 0.979409i \(-0.564707\pi\)
−0.201886 + 0.979409i \(0.564707\pi\)
\(350\) −1.71000 + 33.9435i −0.0914035 + 1.81436i
\(351\) −1.00000 −0.0533761
\(352\) 6.54168 + 11.3305i 0.348673 + 0.603919i
\(353\) −1.28334 + 2.22281i −0.0683053 + 0.118308i −0.898155 0.439678i \(-0.855093\pi\)
0.829850 + 0.557986i \(0.188426\pi\)
\(354\) −6.75159 + 11.6941i −0.358843 + 0.621534i
\(355\) −6.90821 11.9654i −0.366650 0.635056i
\(356\) 47.3330 2.50864
\(357\) 8.10961 4.15276i 0.429206 0.219787i
\(358\) −6.90576 −0.364981
\(359\) 14.8495 + 25.7201i 0.783728 + 1.35746i 0.929756 + 0.368176i \(0.120018\pi\)
−0.146028 + 0.989280i \(0.546649\pi\)
\(360\) −4.20375 + 7.28110i −0.221557 + 0.383748i
\(361\) 8.69144 15.0540i 0.457444 0.792317i
\(362\) −12.2298 21.1827i −0.642785 1.11334i
\(363\) −6.46137 −0.339134
\(364\) 6.96727 + 4.50457i 0.365184 + 0.236104i
\(365\) −3.13041 −0.163853
\(366\) −3.29871 5.71353i −0.172426 0.298651i
\(367\) 1.49187 2.58399i 0.0778747 0.134883i −0.824458 0.565923i \(-0.808520\pi\)
0.902333 + 0.431040i \(0.141853\pi\)
\(368\) −1.96680 + 3.40660i −0.102527 + 0.177582i
\(369\) −1.47921 2.56206i −0.0770044 0.133376i
\(370\) −13.1831 −0.685355
\(371\) −24.8982 16.0975i −1.29265 0.835742i
\(372\) −11.2076 −0.581089
\(373\) −17.4579 30.2380i −0.903936 1.56566i −0.822339 0.568998i \(-0.807331\pi\)
−0.0815967 0.996665i \(-0.526002\pi\)
\(374\) −8.31299 + 14.3985i −0.429855 + 0.744530i
\(375\) −1.09142 + 1.89039i −0.0563607 + 0.0976195i
\(376\) −9.29834 16.1052i −0.479525 0.830562i
\(377\) 8.53790 0.439724
\(378\) 5.33686 2.73289i 0.274499 0.140565i
\(379\) −13.1172 −0.673783 −0.336891 0.941543i \(-0.609376\pi\)
−0.336891 + 0.941543i \(0.609376\pi\)
\(380\) 6.51240 + 11.2798i 0.334079 + 0.578642i
\(381\) −5.29860 + 9.17744i −0.271455 + 0.470175i
\(382\) 20.5578 35.6072i 1.05183 1.82182i
\(383\) 8.66548 + 15.0091i 0.442785 + 0.766927i 0.997895 0.0648505i \(-0.0206570\pi\)
−0.555110 + 0.831777i \(0.687324\pi\)
\(384\) −17.2717 −0.881391
\(385\) −0.926294 + 18.3869i −0.0472083 + 0.937084i
\(386\) 17.6855 0.900169
\(387\) 5.89013 + 10.2020i 0.299412 + 0.518597i
\(388\) −5.92828 + 10.2681i −0.300963 + 0.521283i
\(389\) 10.1952 17.6587i 0.516919 0.895330i −0.482888 0.875682i \(-0.660412\pi\)
0.999807 0.0196482i \(-0.00625461\pi\)
\(390\) 3.70103 + 6.41038i 0.187409 + 0.324602i
\(391\) −30.9107 −1.56322
\(392\) −17.9272 1.81086i −0.905460 0.0914624i
\(393\) 17.2840 0.871860
\(394\) 5.80696 + 10.0579i 0.292550 + 0.506712i
\(395\) −5.41092 + 9.37199i −0.272253 + 0.471556i
\(396\) −3.34030 + 5.78556i −0.167856 + 0.290736i
\(397\) −5.17644 8.96585i −0.259798 0.449983i 0.706390 0.707823i \(-0.250323\pi\)
−0.966188 + 0.257840i \(0.916989\pi\)
\(398\) 20.5278 1.02896
\(399\) 0.169281 3.36024i 0.00847467 0.168222i
\(400\) −2.48402 −0.124201
\(401\) −0.809925 1.40283i −0.0404457 0.0700541i 0.845094 0.534618i \(-0.179544\pi\)
−0.885540 + 0.464564i \(0.846211\pi\)
\(402\) −7.25430 + 12.5648i −0.361812 + 0.626676i
\(403\) −1.78703 + 3.09523i −0.0890183 + 0.154184i
\(404\) 15.2331 + 26.3846i 0.757877 + 1.31268i
\(405\) 3.26624 0.162301
\(406\) −45.5656 + 23.3331i −2.26138 + 1.15800i
\(407\) −3.79425 −0.188074
\(408\) −4.43208 7.67660i −0.219421 0.380048i
\(409\) −5.12758 + 8.88123i −0.253543 + 0.439149i −0.964499 0.264088i \(-0.914929\pi\)
0.710956 + 0.703236i \(0.248262\pi\)
\(410\) −10.9492 + 18.9646i −0.540742 + 0.936592i
\(411\) −8.06755 13.9734i −0.397943 0.689257i
\(412\) −39.1863 −1.93057
\(413\) −13.2386 8.55917i −0.651427 0.421169i
\(414\) −20.3420 −0.999756
\(415\) 17.1116 + 29.6381i 0.839975 + 1.45488i
\(416\) −3.07063 + 5.31848i −0.150550 + 0.260760i
\(417\) −0.656623 + 1.13730i −0.0321550 + 0.0556940i
\(418\) 3.06979 + 5.31704i 0.150148 + 0.260065i
\(419\) −34.2709 −1.67424 −0.837122 0.547016i \(-0.815764\pi\)
−0.837122 + 0.547016i \(0.815764\pi\)
\(420\) −22.7568 14.7130i −1.11042 0.717921i
\(421\) 22.8979 1.11597 0.557987 0.829850i \(-0.311574\pi\)
0.557987 + 0.829850i \(0.311574\pi\)
\(422\) 5.99374 + 10.3815i 0.291771 + 0.505362i
\(423\) −3.61233 + 6.25673i −0.175637 + 0.304213i
\(424\) −14.4227 + 24.9809i −0.700429 + 1.21318i
\(425\) −9.75984 16.9045i −0.473422 0.819990i
\(426\) 9.58635 0.464460
\(427\) 6.85567 3.51064i 0.331769 0.169892i
\(428\) −40.4301 −1.95426
\(429\) 1.06520 + 1.84499i 0.0514285 + 0.0890768i
\(430\) 43.5991 75.5159i 2.10254 3.64170i
\(431\) −2.05869 + 3.56576i −0.0991636 + 0.171756i −0.911339 0.411657i \(-0.864950\pi\)
0.812175 + 0.583414i \(0.198283\pi\)
\(432\) 0.219115 + 0.379518i 0.0105422 + 0.0182596i
\(433\) 25.2549 1.21367 0.606836 0.794827i \(-0.292438\pi\)
0.606836 + 0.794827i \(0.292438\pi\)
\(434\) 1.07822 21.4026i 0.0517560 1.02736i
\(435\) −27.8868 −1.33707
\(436\) 11.5491 + 20.0036i 0.553102 + 0.958001i
\(437\) −5.70729 + 9.88532i −0.273017 + 0.472879i
\(438\) 1.08600 1.88100i 0.0518909 0.0898777i
\(439\) −0.819150 1.41881i −0.0390959 0.0677161i 0.845815 0.533476i \(-0.179114\pi\)
−0.884911 + 0.465760i \(0.845781\pi\)
\(440\) 17.9114 0.853891
\(441\) 2.87303 + 6.38324i 0.136811 + 0.303964i
\(442\) −7.80413 −0.371205
\(443\) 14.5940 + 25.2775i 0.693381 + 1.20097i 0.970723 + 0.240200i \(0.0772132\pi\)
−0.277342 + 0.960771i \(0.589454\pi\)
\(444\) 2.79245 4.83667i 0.132524 0.229538i
\(445\) −24.6507 + 42.6962i −1.16855 + 2.02400i
\(446\) 26.6506 + 46.1602i 1.26194 + 2.18575i
\(447\) 5.65601 0.267520
\(448\) 1.73601 34.4597i 0.0820187 1.62807i
\(449\) −8.63336 −0.407433 −0.203717 0.979030i \(-0.565302\pi\)
−0.203717 + 0.979030i \(0.565302\pi\)
\(450\) −6.42286 11.1247i −0.302777 0.524424i
\(451\) −3.15131 + 5.45823i −0.148390 + 0.257018i
\(452\) −19.9647 + 34.5798i −0.939058 + 1.62650i
\(453\) 4.19181 + 7.26043i 0.196948 + 0.341125i
\(454\) 24.4847 1.14913
\(455\) −7.69181 + 3.93881i −0.360598 + 0.184654i
\(456\) −3.27333 −0.153288
\(457\) −3.72736 6.45598i −0.174359 0.301998i 0.765580 0.643340i \(-0.222452\pi\)
−0.939939 + 0.341342i \(0.889119\pi\)
\(458\) 33.8444 58.6202i 1.58144 2.73914i
\(459\) −1.72183 + 2.98229i −0.0803680 + 0.139201i
\(460\) 45.9684 + 79.6196i 2.14329 + 3.71228i
\(461\) 13.8405 0.644617 0.322309 0.946635i \(-0.395541\pi\)
0.322309 + 0.946635i \(0.395541\pi\)
\(462\) −10.7270 6.93536i −0.499065 0.322662i
\(463\) 23.3893 1.08699 0.543496 0.839412i \(-0.317100\pi\)
0.543496 + 0.839412i \(0.317100\pi\)
\(464\) −1.87078 3.24029i −0.0868488 0.150427i
\(465\) 5.83686 10.1097i 0.270678 0.468828i
\(466\) −12.4038 + 21.4840i −0.574595 + 0.995228i
\(467\) 13.0768 + 22.6496i 0.605121 + 1.04810i 0.992032 + 0.125983i \(0.0402085\pi\)
−0.386912 + 0.922117i \(0.626458\pi\)
\(468\) −3.13583 −0.144954
\(469\) −14.2243 9.19647i −0.656816 0.424653i
\(470\) 53.4774 2.46673
\(471\) 1.24544 + 2.15717i 0.0573870 + 0.0993972i
\(472\) −7.66866 + 13.2825i −0.352979 + 0.611377i
\(473\) 12.5484 21.7344i 0.576975 0.999350i
\(474\) −3.75430 6.50264i −0.172441 0.298676i
\(475\) −7.20816 −0.330733
\(476\) 25.4304 13.0223i 1.16560 0.596878i
\(477\) 11.2062 0.513097
\(478\) −34.3273 59.4566i −1.57009 2.71948i
\(479\) −7.45559 + 12.9135i −0.340655 + 0.590031i −0.984554 0.175079i \(-0.943982\pi\)
0.643900 + 0.765110i \(0.277315\pi\)
\(480\) 10.0294 17.3714i 0.457777 0.792893i
\(481\) −0.890499 1.54239i −0.0406033 0.0703269i
\(482\) 53.9581 2.45772
\(483\) 1.19489 23.7185i 0.0543693 1.07923i
\(484\) −20.2617 −0.920988
\(485\) −6.17482 10.6951i −0.280384 0.485639i
\(486\) −1.13312 + 1.96262i −0.0513993 + 0.0890262i
\(487\) 1.65970 2.87469i 0.0752083 0.130265i −0.825969 0.563716i \(-0.809371\pi\)
0.901177 + 0.433452i \(0.142704\pi\)
\(488\) −3.74678 6.48960i −0.169609 0.293771i
\(489\) 11.2842 0.510288
\(490\) 30.2858 42.0418i 1.36817 1.89925i
\(491\) 20.7495 0.936413 0.468206 0.883619i \(-0.344900\pi\)
0.468206 + 0.883619i \(0.344900\pi\)
\(492\) −4.63854 8.03419i −0.209122 0.362209i
\(493\) 14.7008 25.4625i 0.662090 1.14677i
\(494\) −1.44094 + 2.49578i −0.0648310 + 0.112291i
\(495\) −3.47921 6.02616i −0.156379 0.270856i
\(496\) 1.56626 0.0703272
\(497\) −0.563101 + 11.1775i −0.0252585 + 0.501382i
\(498\) −23.7453 −1.06405
\(499\) −12.4855 21.6255i −0.558926 0.968089i −0.997586 0.0694355i \(-0.977880\pi\)
0.438660 0.898653i \(-0.355453\pi\)
\(500\) −3.42251 + 5.92796i −0.153059 + 0.265106i
\(501\) −1.63583 + 2.83334i −0.0730835 + 0.126584i
\(502\) −23.2384 40.2501i −1.03718 1.79645i
\(503\) −9.50934 −0.424000 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(504\) 6.06177 3.10410i 0.270013 0.138268i
\(505\) −31.7333 −1.41211
\(506\) 21.6684 + 37.5308i 0.963278 + 1.66845i
\(507\) −0.500000 + 0.866025i −0.0222058 + 0.0384615i
\(508\) −16.6155 + 28.7789i −0.737194 + 1.27686i
\(509\) −4.64457 8.04464i −0.205867 0.356572i 0.744542 0.667576i \(-0.232668\pi\)
−0.950409 + 0.311004i \(0.899335\pi\)
\(510\) 25.4902 1.12872
\(511\) 2.12943 + 1.37675i 0.0942004 + 0.0609037i
\(512\) 4.94734 0.218644
\(513\) 0.635830 + 1.10129i 0.0280726 + 0.0486231i
\(514\) −3.05030 + 5.28327i −0.134543 + 0.233035i
\(515\) 20.4080 35.3476i 0.899282 1.55760i
\(516\) 18.4704 + 31.9918i 0.813116 + 1.40836i
\(517\) 15.3914 0.676915
\(518\) 8.96765 + 5.79788i 0.394016 + 0.254744i
\(519\) −19.8041 −0.869305
\(520\) 4.20375 + 7.28110i 0.184346 + 0.319297i
\(521\) −5.85434 + 10.1400i −0.256483 + 0.444242i −0.965297 0.261153i \(-0.915897\pi\)
0.708814 + 0.705395i \(0.249230\pi\)
\(522\) 9.67445 16.7566i 0.423439 0.733418i
\(523\) 14.4198 + 24.9758i 0.630533 + 1.09212i 0.987443 + 0.157976i \(0.0504970\pi\)
−0.356910 + 0.934139i \(0.616170\pi\)
\(524\) 54.1995 2.36772
\(525\) 13.3485 6.83550i 0.582578 0.298326i
\(526\) −6.04701 −0.263662
\(527\) 6.15391 + 10.6589i 0.268069 + 0.464308i
\(528\) 0.466804 0.808528i 0.0203150 0.0351867i
\(529\) −28.7854 + 49.8578i −1.25154 + 2.16773i
\(530\) −41.4745 71.8360i −1.80154 3.12036i
\(531\) 5.95841 0.258573
\(532\) 0.530838 10.5371i 0.0230147 0.456842i
\(533\) −2.95841 −0.128143
\(534\) −17.1036 29.6242i −0.740144 1.28197i
\(535\) 21.0557 36.4696i 0.910318 1.57672i
\(536\) −8.23965 + 14.2715i −0.355899 + 0.616435i
\(537\) 1.52362 + 2.63898i 0.0657489 + 0.113881i
\(538\) 2.03761 0.0878475
\(539\) 8.71663 12.1001i 0.375452 0.521190i
\(540\) 10.2424 0.440761
\(541\) −2.10125 3.63948i −0.0903400 0.156473i 0.817314 0.576192i \(-0.195462\pi\)
−0.907654 + 0.419719i \(0.862129\pi\)
\(542\) −24.9936 + 43.2902i −1.07357 + 1.85947i
\(543\) −5.39653 + 9.34707i −0.231587 + 0.401121i
\(544\) 10.5742 + 18.3150i 0.453364 + 0.785249i
\(545\) −24.0588 −1.03057
\(546\) 0.301678 5.98831i 0.0129106 0.256276i
\(547\) 26.1238 1.11697 0.558486 0.829514i \(-0.311383\pi\)
0.558486 + 0.829514i \(0.311383\pi\)
\(548\) −25.2985 43.8182i −1.08070 1.87182i
\(549\) −1.45559 + 2.52116i −0.0621230 + 0.107600i
\(550\) −13.6833 + 23.7002i −0.583458 + 1.01058i
\(551\) −5.42865 9.40270i −0.231268 0.400568i
\(552\) −23.1051 −0.983418
\(553\) 7.80251 3.99550i 0.331797 0.169906i
\(554\) 21.9107 0.930895
\(555\) 2.90858 + 5.03781i 0.123462 + 0.213843i
\(556\) −2.05906 + 3.56639i −0.0873235 + 0.151249i
\(557\) 19.0885 33.0622i 0.808804 1.40089i −0.104889 0.994484i \(-0.533449\pi\)
0.913693 0.406405i \(-0.133218\pi\)
\(558\) 4.04983 + 7.01452i 0.171443 + 0.296948i
\(559\) 11.7803 0.498252
\(560\) 3.18024 + 2.05613i 0.134390 + 0.0868874i
\(561\) 7.33638 0.309742
\(562\) 30.7684 + 53.2925i 1.29789 + 2.24801i
\(563\) 13.7658 23.8430i 0.580157 1.00486i −0.415303 0.909683i \(-0.636324\pi\)
0.995460 0.0951789i \(-0.0303423\pi\)
\(564\) −11.3276 + 19.6200i −0.476980 + 0.826153i
\(565\) −20.7949 36.0178i −0.874848 1.51528i
\(566\) −62.5251 −2.62812
\(567\) −2.22183 1.43648i −0.0933079 0.0603267i
\(568\) 10.8885 0.456870
\(569\) −10.7777 18.6675i −0.451824 0.782583i 0.546675 0.837345i \(-0.315893\pi\)
−0.998499 + 0.0547621i \(0.982560\pi\)
\(570\) 4.70646 8.15182i 0.197132 0.341442i
\(571\) −9.16017 + 15.8659i −0.383341 + 0.663966i −0.991538 0.129820i \(-0.958560\pi\)
0.608196 + 0.793787i \(0.291893\pi\)
\(572\) 3.34030 + 5.78556i 0.139665 + 0.241907i
\(573\) −18.1427 −0.757922
\(574\) 15.7887 8.08503i 0.659006 0.337462i
\(575\) −50.8794 −2.12182
\(576\) 6.52054 + 11.2939i 0.271689 + 0.470579i
\(577\) −6.10310 + 10.5709i −0.254075 + 0.440072i −0.964644 0.263556i \(-0.915104\pi\)
0.710569 + 0.703628i \(0.248438\pi\)
\(578\) 5.82565 10.0903i 0.242315 0.419702i
\(579\) −3.90195 6.75838i −0.162160 0.280869i
\(580\) −87.4483 −3.63109
\(581\) 1.39480 27.6867i 0.0578659 1.14864i
\(582\) 8.56864 0.355181
\(583\) −11.9369 20.6753i −0.494375 0.856283i
\(584\) 1.23351 2.13650i 0.0510429 0.0884089i
\(585\) 1.63312 2.82864i 0.0675211 0.116950i
\(586\) −0.375595 0.650550i −0.0155157 0.0268740i
\(587\) 13.9272 0.574836 0.287418 0.957805i \(-0.407203\pi\)
0.287418 + 0.957805i \(0.407203\pi\)
\(588\) 9.00932 + 20.0167i 0.371538 + 0.825477i
\(589\) 4.54499 0.187273
\(590\) −22.0523 38.1957i −0.907878 1.57249i
\(591\) 2.56238 4.43817i 0.105402 0.182562i
\(592\) −0.390243 + 0.675921i −0.0160389 + 0.0277802i
\(593\) −11.0999 19.2256i −0.455819 0.789501i 0.542916 0.839787i \(-0.317320\pi\)
−0.998735 + 0.0502859i \(0.983987\pi\)
\(594\) 4.82801 0.198096
\(595\) −1.49729 + 29.7212i −0.0613828 + 1.21845i
\(596\) 17.7363 0.726507
\(597\) −4.52904 7.84453i −0.185361 0.321055i
\(598\) −10.1710 + 17.6167i −0.415924 + 0.720401i
\(599\) −11.9406 + 20.6817i −0.487879 + 0.845031i −0.999903 0.0139405i \(-0.995562\pi\)
0.512024 + 0.858971i \(0.328896\pi\)
\(600\) −7.29528 12.6358i −0.297828 0.515854i
\(601\) 40.0534 1.63381 0.816905 0.576772i \(-0.195688\pi\)
0.816905 + 0.576772i \(0.195688\pi\)
\(602\) −62.8696 + 32.1942i −2.56238 + 1.31214i
\(603\) 6.40207 0.260712
\(604\) 13.1448 + 22.7675i 0.534854 + 0.926395i
\(605\) 10.5522 18.2769i 0.429007 0.743062i
\(606\) 11.0089 19.0679i 0.447204 0.774580i
\(607\) 9.76515 + 16.9137i 0.396355 + 0.686507i 0.993273 0.115795i \(-0.0369416\pi\)
−0.596918 + 0.802302i \(0.703608\pi\)
\(608\) 7.80959 0.316721
\(609\) 18.9697 + 12.2646i 0.768692 + 0.496985i
\(610\) 21.5487 0.872483
\(611\) 3.61233 + 6.25673i 0.146139 + 0.253120i
\(612\) −5.39936 + 9.35196i −0.218256 + 0.378030i
\(613\) −8.96124 + 15.5213i −0.361941 + 0.626900i −0.988280 0.152650i \(-0.951219\pi\)
0.626339 + 0.779551i \(0.284552\pi\)
\(614\) −2.50687 4.34202i −0.101169 0.175230i
\(615\) 9.66288 0.389645
\(616\) −12.1840 7.87739i −0.490909 0.317389i
\(617\) −23.8703 −0.960982 −0.480491 0.877000i \(-0.659542\pi\)
−0.480491 + 0.877000i \(0.659542\pi\)
\(618\) 14.1598 + 24.5255i 0.569591 + 0.986560i
\(619\) −22.3244 + 38.6670i −0.897294 + 1.55416i −0.0663545 + 0.997796i \(0.521137\pi\)
−0.830940 + 0.556363i \(0.812197\pi\)
\(620\) 18.3034 31.7024i 0.735083 1.27320i
\(621\) 4.48806 + 7.77355i 0.180100 + 0.311942i
\(622\) −19.7236 −0.790845
\(623\) 35.5461 18.2024i 1.42413 0.729263i
\(624\) 0.438230 0.0175432
\(625\) 10.6059 + 18.3700i 0.424237 + 0.734800i
\(626\) −38.9869 + 67.5273i −1.55823 + 2.69894i
\(627\) 1.35458 2.34620i 0.0540966 0.0936980i
\(628\) 3.90550 + 6.76453i 0.155846 + 0.269934i
\(629\) −6.13314 −0.244544
\(630\) −0.985352 + 19.5592i −0.0392574 + 0.779258i
\(631\) 10.5992 0.421946 0.210973 0.977492i \(-0.432337\pi\)
0.210973 + 0.977492i \(0.432337\pi\)
\(632\) −4.26425 7.38589i −0.169623 0.293795i
\(633\) 2.64480 4.58093i 0.105121 0.182075i
\(634\) 10.7457 18.6121i 0.426766 0.739180i
\(635\) −17.3065 29.9757i −0.686787 1.18955i
\(636\) 35.1407 1.39342
\(637\) 6.96456 + 0.703505i 0.275946 + 0.0278739i
\(638\) −41.2210 −1.63196
\(639\) −2.11504 3.66335i −0.0836696 0.144920i
\(640\) 28.2067 48.8554i 1.11497 1.93118i
\(641\) 0.760092 1.31652i 0.0300218 0.0519993i −0.850624 0.525774i \(-0.823776\pi\)
0.880646 + 0.473775i \(0.157109\pi\)
\(642\) 14.6092 + 25.3040i 0.576581 + 0.998667i
\(643\) 6.86343 0.270667 0.135334 0.990800i \(-0.456789\pi\)
0.135334 + 0.990800i \(0.456789\pi\)
\(644\) 3.74697 74.3773i 0.147651 2.93087i
\(645\) −38.4771 −1.51504
\(646\) 4.96210 + 8.59461i 0.195231 + 0.338151i
\(647\) −22.1345 + 38.3381i −0.870196 + 1.50722i −0.00840308 + 0.999965i \(0.502675\pi\)
−0.861793 + 0.507260i \(0.830659\pi\)
\(648\) −1.28703 + 2.22920i −0.0505593 + 0.0875713i
\(649\) −6.34692 10.9932i −0.249139 0.431521i
\(650\) −12.8457 −0.503851
\(651\) −8.41672 + 4.31002i −0.329877 + 0.168923i
\(652\) 35.3853 1.38579
\(653\) 3.88127 + 6.72256i 0.151886 + 0.263074i 0.931921 0.362662i \(-0.118132\pi\)
−0.780035 + 0.625736i \(0.784799\pi\)
\(654\) 8.34644 14.4565i 0.326372 0.565292i
\(655\) −28.2267 + 48.8901i −1.10291 + 1.91030i
\(656\) 0.648233 + 1.12277i 0.0253092 + 0.0438369i
\(657\) −0.958414 −0.0373913
\(658\) −36.3775 23.5192i −1.41814 0.916875i
\(659\) −3.76377 −0.146616 −0.0733078 0.997309i \(-0.523356\pi\)
−0.0733078 + 0.997309i \(0.523356\pi\)
\(660\) −10.9102 18.8970i −0.424679 0.735566i
\(661\) −15.5918 + 27.0057i −0.606450 + 1.05040i 0.385371 + 0.922762i \(0.374074\pi\)
−0.991821 + 0.127640i \(0.959260\pi\)
\(662\) 9.20519 15.9439i 0.357770 0.619676i
\(663\) 1.72183 + 2.98229i 0.0668702 + 0.115823i
\(664\) −26.9706 −1.04666
\(665\) 9.22845 + 5.96650i 0.357864 + 0.231371i
\(666\) −4.03616 −0.156398
\(667\) −38.3186 66.3698i −1.48370 2.56985i
\(668\) −5.12969 + 8.88488i −0.198473 + 0.343766i
\(669\) 11.7598 20.3686i 0.454662 0.787497i
\(670\) −23.6943 41.0397i −0.915389 1.58550i
\(671\) 6.20200 0.239425
\(672\) −14.4623 + 7.40584i −0.557896 + 0.285686i
\(673\) −29.1587 −1.12398 −0.561992 0.827142i \(-0.689965\pi\)
−0.561992 + 0.827142i \(0.689965\pi\)
\(674\) 35.7565 + 61.9321i 1.37729 + 2.38553i
\(675\) −2.83415 + 4.90890i −0.109087 + 0.188943i
\(676\) −1.56792 + 2.71571i −0.0603044 + 0.104450i
\(677\) 10.3784 + 17.9760i 0.398876 + 0.690874i 0.993588 0.113065i \(-0.0360670\pi\)
−0.594711 + 0.803939i \(0.702734\pi\)
\(678\) 28.8566 1.10823
\(679\) −0.503321 + 9.99091i −0.0193157 + 0.383416i
\(680\) 28.9525 1.11028
\(681\) −5.40207 9.35665i −0.207008 0.358548i
\(682\) 8.62779 14.9438i 0.330375 0.572227i
\(683\) 12.9259 22.3884i 0.494597 0.856667i −0.505384 0.862895i \(-0.668649\pi\)
0.999981 + 0.00622790i \(0.00198241\pi\)
\(684\) 1.99385 + 3.45346i 0.0762370 + 0.132046i
\(685\) 52.7010 2.01360
\(686\) −39.0915 + 15.2789i −1.49252 + 0.583350i
\(687\) −29.8683 −1.13955
\(688\) −2.58123 4.47082i −0.0984085 0.170449i
\(689\) 5.60310 9.70485i 0.213461 0.369726i
\(690\) 33.2209 57.5404i 1.26470 2.19052i
\(691\) 1.02988 + 1.78380i 0.0391783 + 0.0678588i 0.884950 0.465687i \(-0.154193\pi\)
−0.845771 + 0.533546i \(0.820859\pi\)
\(692\) −62.1024 −2.36078
\(693\) −0.283597 + 5.62939i −0.0107729 + 0.213843i
\(694\) −5.78100 −0.219444
\(695\) −2.14469 3.71471i −0.0813526 0.140907i
\(696\) 10.9885 19.0327i 0.416519 0.721432i
\(697\) −5.09388 + 8.82285i −0.192944 + 0.334189i
\(698\) 8.54722 + 14.8042i 0.323517 + 0.560348i
\(699\) 10.9466 0.414039
\(700\) 41.8588 21.4350i 1.58211 0.810166i
\(701\) 2.70966 0.102343 0.0511713 0.998690i \(-0.483705\pi\)
0.0511713 + 0.998690i \(0.483705\pi\)
\(702\) 1.13312 + 1.96262i 0.0427668 + 0.0740743i
\(703\) −1.13241 + 1.96139i −0.0427097 + 0.0739754i
\(704\) 13.8914 24.0606i 0.523552 0.906818i
\(705\) −11.7987 20.4360i −0.444365 0.769663i
\(706\) 5.81671 0.218915
\(707\) 21.5862 + 13.9562i 0.811834 + 0.524878i
\(708\) 18.6846 0.702209
\(709\) −3.98094 6.89519i −0.149507 0.258954i 0.781538 0.623857i \(-0.214435\pi\)
−0.931045 + 0.364903i \(0.881102\pi\)
\(710\) −15.6556 + 27.1164i −0.587546 + 1.01766i
\(711\) −1.65662 + 2.86936i −0.0621282 + 0.107609i
\(712\) −19.4267 33.6481i −0.728048 1.26102i
\(713\) 32.0812 1.20145
\(714\) −17.3394 11.2105i −0.648912 0.419543i
\(715\) −6.95841 −0.260230
\(716\) 4.77781 + 8.27540i 0.178555 + 0.309266i
\(717\) −15.1473 + 26.2358i −0.565685 + 0.979795i
\(718\) 33.6525 58.2879i 1.25590 2.17529i
\(719\) −4.49334 7.78270i −0.167573 0.290246i 0.769993 0.638053i \(-0.220260\pi\)
−0.937566 + 0.347807i \(0.886926\pi\)
\(720\) −1.43136 −0.0533438
\(721\) −29.4281 + 15.0695i −1.09596 + 0.561218i
\(722\) −39.3937 −1.46608
\(723\) −11.9048 20.6197i −0.442743 0.766854i
\(724\) −16.9226 + 29.3108i −0.628924 + 1.08933i
\(725\) 24.1977 41.9116i 0.898680 1.55656i
\(726\) 7.32149 + 12.6812i 0.271726 + 0.470643i
\(727\) −12.1319 −0.449945 −0.224973 0.974365i \(-0.572229\pi\)
−0.224973 + 0.974365i \(0.572229\pi\)
\(728\) 0.342655 6.80170i 0.0126996 0.252088i
\(729\) 1.00000 0.0370370
\(730\) 3.54712 + 6.14380i 0.131285 + 0.227392i
\(731\) 20.2836 35.1322i 0.750215 1.29941i
\(732\) −4.56448 + 7.90591i −0.168708 + 0.292211i
\(733\) −0.780629 1.35209i −0.0288332 0.0499406i 0.851249 0.524762i \(-0.175846\pi\)
−0.880082 + 0.474822i \(0.842513\pi\)
\(734\) −6.76184 −0.249584
\(735\) −22.7479 2.29781i −0.839069 0.0847561i
\(736\) 55.1247 2.03192
\(737\) −6.81950 11.8117i −0.251200 0.435091i
\(738\) −3.35223 + 5.80624i −0.123397 + 0.213731i
\(739\) 17.3246 30.0070i 0.637294 1.10383i −0.348730 0.937223i \(-0.613387\pi\)
0.986024 0.166603i \(-0.0532797\pi\)
\(740\) 9.12081 + 15.7977i 0.335288 + 0.580735i
\(741\) 1.27166 0.0467156
\(742\) −3.38066 + 67.1062i −0.124108 + 2.46354i
\(743\) −5.28770 −0.193987 −0.0969935 0.995285i \(-0.530923\pi\)
−0.0969935 + 0.995285i \(0.530923\pi\)
\(744\) 4.59992 + 7.96730i 0.168641 + 0.292095i
\(745\) −9.23694 + 15.9989i −0.338415 + 0.586153i
\(746\) −39.5637 + 68.5264i −1.44853 + 2.50893i
\(747\) 5.23893 + 9.07409i 0.191682 + 0.332004i
\(748\) 23.0056 0.841170
\(749\) −30.3622 + 15.5478i −1.10941 + 0.568105i
\(750\) 4.94683 0.180633
\(751\) 17.2297 + 29.8427i 0.628721 + 1.08898i 0.987809 + 0.155673i \(0.0497545\pi\)
−0.359088 + 0.933304i \(0.616912\pi\)
\(752\) 1.58303 2.74189i 0.0577271 0.0999863i
\(753\) −10.2542 + 17.7608i −0.373683 + 0.647239i
\(754\) −9.67445 16.7566i −0.352323 0.610241i
\(755\) −27.3829 −0.996565
\(756\) −6.96727 4.50457i −0.253397 0.163830i
\(757\) 19.7567 0.718069 0.359034 0.933324i \(-0.383106\pi\)
0.359034 + 0.933324i \(0.383106\pi\)
\(758\) 14.8633 + 25.7440i 0.539859 + 0.935063i
\(759\) 9.56140 16.5608i 0.347057 0.601120i
\(760\) 5.34573 9.25908i 0.193910 0.335862i
\(761\) 7.94858 + 13.7673i 0.288136 + 0.499066i 0.973365 0.229262i \(-0.0736312\pi\)
−0.685229 + 0.728328i \(0.740298\pi\)
\(762\) 24.0158 0.869999
\(763\) 16.3658 + 10.5810i 0.592480 + 0.383058i
\(764\) −56.8924 −2.05830
\(765\) −5.62389 9.74087i −0.203332 0.352182i
\(766\) 19.6380 34.0141i 0.709551 1.22898i
\(767\) 2.97921 5.16014i 0.107573 0.186322i
\(768\) 6.52976 + 11.3099i 0.235623 + 0.408110i
\(769\) −29.1892 −1.05259 −0.526295 0.850302i \(-0.676419\pi\)
−0.526295 + 0.850302i \(0.676419\pi\)
\(770\) 37.1361 19.0166i 1.33829 0.685310i
\(771\) 2.69195 0.0969483
\(772\) −12.2359 21.1931i −0.440378 0.762758i
\(773\) −19.9770 + 34.6011i −0.718521 + 1.24452i 0.243064 + 0.970010i \(0.421847\pi\)
−0.961586 + 0.274505i \(0.911486\pi\)
\(774\) 13.3484 23.1202i 0.479799 0.831037i
\(775\) 10.1294 + 17.5447i 0.363860 + 0.630224i
\(776\) 9.73252 0.349377
\(777\) 0.237084 4.70611i 0.00850533 0.168831i
\(778\) −46.2097 −1.65670
\(779\) 1.88105 + 3.25807i 0.0673956 + 0.116733i
\(780\) 5.12118 8.87015i 0.183368 0.317602i
\(781\) −4.50589 + 7.80443i −0.161233 + 0.279264i
\(782\) 35.0254 + 60.6659i 1.25251 + 2.16941i
\(783\) −8.53790 −0.305120
\(784\) −1.25905 2.79733i −0.0449659 0.0999045i
\(785\) −8.13583 −0.290380
\(786\) −19.5848 33.9218i −0.698565 1.20995i
\(787\) −16.6801 + 28.8908i −0.594581 + 1.02984i 0.399025 + 0.916940i \(0.369349\pi\)
−0.993606 + 0.112905i \(0.963985\pi\)
\(788\) 8.03519 13.9173i 0.286242 0.495785i
\(789\) 1.33415 + 2.31082i 0.0474971 + 0.0822673i
\(790\) 24.5249 0.872556
\(791\) −1.69503 + 33.6463i −0.0602684 + 1.19633i
\(792\) 5.48380 0.194858
\(793\) 1.45559 + 2.52116i 0.0516895 + 0.0895288i
\(794\) −11.7310 + 20.3188i −0.416319 + 0.721086i
\(795\) −18.3011 + 31.6984i −0.649072 + 1.12422i
\(796\) −14.2023 24.5991i −0.503387 0.871892i
\(797\) 1.65037 0.0584589 0.0292295 0.999573i \(-0.490695\pi\)
0.0292295 + 0.999573i \(0.490695\pi\)
\(798\) −6.78668 + 3.47531i −0.240246 + 0.123025i
\(799\) 24.8792 0.880163
\(800\) 17.4052 + 30.1468i 0.615368 + 1.06585i
\(801\) −7.54712 + 13.0720i −0.266664 + 0.461876i
\(802\) −1.83548 + 3.17915i −0.0648132 + 0.112260i
\(803\) 1.02091 + 1.76826i 0.0360270 + 0.0624006i
\(804\) 20.0758 0.708019
\(805\) 65.1399 + 42.1151i 2.29588 + 1.48436i
\(806\) 8.09967 0.285299
\(807\) −0.449557 0.778656i −0.0158252 0.0274100i
\(808\) 12.5042 21.6579i 0.439896 0.761922i
\(809\) −11.5637 + 20.0290i −0.406560 + 0.704182i −0.994502 0.104721i \(-0.966605\pi\)
0.587942 + 0.808903i \(0.299938\pi\)
\(810\) −3.70103 6.41038i −0.130041 0.225238i
\(811\) −43.9914 −1.54475 −0.772373 0.635169i \(-0.780930\pi\)
−0.772373 + 0.635169i \(0.780930\pi\)
\(812\) 59.4858 + 38.4596i 2.08754 + 1.34967i
\(813\) 22.0573 0.773585
\(814\) 4.29933 + 7.44667i 0.150692 + 0.261006i
\(815\) −18.4284 + 31.9189i −0.645519 + 1.11807i
\(816\) 0.754556 1.30693i 0.0264147 0.0457517i
\(817\) −7.49024 12.9735i −0.262050 0.453885i
\(818\) 23.2406 0.812590
\(819\) −2.35495 + 1.20592i −0.0822884 + 0.0421381i
\(820\) 30.3012 1.05816
\(821\) 7.98474 + 13.8300i 0.278669 + 0.482670i 0.971054 0.238859i \(-0.0767733\pi\)
−0.692385 + 0.721528i \(0.743440\pi\)
\(822\) −18.2830 + 31.6670i −0.637692 + 1.10451i
\(823\) −9.84326 + 17.0490i −0.343115 + 0.594292i −0.985009 0.172501i \(-0.944815\pi\)
0.641895 + 0.766793i \(0.278149\pi\)
\(824\) 16.0831 + 27.8568i 0.560282 + 0.970437i
\(825\) 12.0758 0.420425
\(826\) −1.79752 + 35.6808i −0.0625438 + 1.24149i
\(827\) −8.49580 −0.295428 −0.147714 0.989030i \(-0.547192\pi\)
−0.147714 + 0.989030i \(0.547192\pi\)
\(828\) 14.0738 + 24.3765i 0.489099 + 0.847143i
\(829\) 9.58661 16.6045i 0.332957 0.576698i −0.650134 0.759820i \(-0.725287\pi\)
0.983090 + 0.183122i \(0.0586204\pi\)
\(830\) 38.7789 67.1671i 1.34604 2.33140i
\(831\) −4.83415 8.37300i −0.167695 0.290456i
\(832\) 13.0411 0.452118
\(833\) 14.0898 19.5590i 0.488183 0.677680i
\(834\) 2.97613 0.103055
\(835\) −5.34301 9.25436i −0.184902 0.320260i
\(836\) 4.24772 7.35727i 0.146911 0.254457i
\(837\) 1.78703 3.09523i 0.0617688 0.106987i
\(838\) 38.8330 + 67.2608i 1.34146 + 2.32348i
\(839\) 24.1587 0.834050 0.417025 0.908895i \(-0.363073\pi\)
0.417025 + 0.908895i \(0.363073\pi\)
\(840\) −1.11919 + 22.2160i −0.0386158 + 0.766523i
\(841\) 43.8957 1.51364
\(842\) −25.9460 44.9398i −0.894158 1.54873i
\(843\) 13.5769 23.5159i 0.467613 0.809929i
\(844\) 8.29364 14.3650i 0.285479 0.494464i
\(845\) −1.63312 2.82864i −0.0561810 0.0973083i
\(846\) 16.3728 0.562907
\(847\) −15.2162 + 7.79187i −0.522834 + 0.267732i
\(848\) −4.91089 −0.168641
\(849\) 13.7949 + 23.8935i 0.473440 + 0.820022i
\(850\) −22.1181 + 38.3097i −0.758645 + 1.31401i
\(851\) −7.99323 + 13.8447i −0.274004 + 0.474590i
\(852\) −6.63240 11.4876i −0.227222 0.393560i
\(853\) 4.75591 0.162839 0.0814196 0.996680i \(-0.474055\pi\)
0.0814196 + 0.996680i \(0.474055\pi\)
\(854\) −14.6583 9.47709i −0.501598 0.324299i
\(855\) −4.15354 −0.142048
\(856\) 16.5936 + 28.7410i 0.567158 + 0.982347i
\(857\) 11.1127 19.2477i 0.379602 0.657490i −0.611402 0.791320i \(-0.709394\pi\)
0.991004 + 0.133830i \(0.0427276\pi\)
\(858\) 2.41400 4.18118i 0.0824127 0.142743i
\(859\) −12.3227 21.3435i −0.420445 0.728232i 0.575538 0.817775i \(-0.304793\pi\)
−0.995983 + 0.0895430i \(0.971459\pi\)
\(860\) −120.658 −4.11439
\(861\) −6.57308 4.24971i −0.224010 0.144830i
\(862\) 9.33096 0.317814
\(863\) −7.77543 13.4674i −0.264679 0.458437i 0.702801 0.711387i \(-0.251933\pi\)
−0.967479 + 0.252950i \(0.918599\pi\)
\(864\) 3.07063 5.31848i 0.104465 0.180938i
\(865\) 32.3425 56.0188i 1.09968 1.90470i
\(866\) −28.6168 49.5657i −0.972437 1.68431i
\(867\) −5.14125 −0.174606
\(868\) −26.3934 + 13.5155i −0.895850 + 0.458745i
\(869\) 7.05856 0.239445
\(870\) 31.5990 + 54.7311i 1.07131 + 1.85556i
\(871\) 3.20103 5.54435i 0.108463 0.187863i
\(872\) 9.48014 16.4201i 0.321038 0.556054i
\(873\) −1.89050 3.27444i −0.0639837 0.110823i
\(874\) 25.8681 0.875003
\(875\) −0.290576 + 5.76794i −0.00982327 + 0.194992i
\(876\) −3.00542 −0.101544
\(877\) −10.1085 17.5085i −0.341341 0.591219i 0.643341 0.765579i \(-0.277548\pi\)
−0.984682 + 0.174360i \(0.944214\pi\)
\(878\) −1.85639 + 3.21536i −0.0626501 + 0.108513i
\(879\) −0.165735 + 0.287062i −0.00559011 + 0.00968236i
\(880\) 1.52469 + 2.64085i 0.0513974 + 0.0890229i
\(881\) −16.1927 −0.545545 −0.272772 0.962079i \(-0.587941\pi\)
−0.272772 + 0.962079i \(0.587941\pi\)
\(882\) 9.27238 12.8716i 0.312217 0.433410i
\(883\) 37.3295 1.25624 0.628118 0.778118i \(-0.283825\pi\)
0.628118 + 0.778118i \(0.283825\pi\)
\(884\) 5.39936 + 9.35196i 0.181600 + 0.314540i
\(885\) −9.73080 + 16.8542i −0.327097 + 0.566549i
\(886\) 33.0734 57.2849i 1.11112 1.92452i
\(887\) 20.3137 + 35.1844i 0.682068 + 1.18138i 0.974349 + 0.225043i \(0.0722524\pi\)
−0.292281 + 0.956332i \(0.594414\pi\)
\(888\) −4.58440 −0.153842
\(889\) −1.41068 + 28.0020i −0.0473128 + 0.939158i
\(890\) 111.729 3.74515
\(891\) −1.06520 1.84499i −0.0356857 0.0618094i
\(892\) 36.8768 63.8726i 1.23473 2.13861i
\(893\) 4.59365 7.95644i 0.153721 0.266252i
\(894\) −6.40893 11.1006i −0.214347 0.371260i
\(895\) −9.95299 −0.332692
\(896\) −40.6738 + 20.8282i −1.35882 + 0.695820i
\(897\) 8.97613 0.299704
\(898\) 9.78262 + 16.9440i 0.326450 + 0.565428i
\(899\) −15.2575 + 26.4267i −0.508865 + 0.881381i
\(900\) −8.88742 + 15.3935i −0.296247 + 0.513115i
\(901\) −19.2951 33.4202i −0.642814 1.11339i
\(902\) 14.2832 0.475580
\(903\) 26.1737 + 16.9222i 0.871006 + 0.563134i
\(904\) 32.7762 1.09012
\(905\) −17.6263 30.5297i −0.585920 1.01484i
\(906\) 9.49963 16.4538i 0.315604 0.546642i
\(907\) −4.42854 + 7.67045i −0.147047 + 0.254693i −0.930135 0.367218i \(-0.880310\pi\)
0.783088 + 0.621911i \(0.213644\pi\)
\(908\) −16.9400 29.3409i −0.562172 0.973711i
\(909\) −9.71554 −0.322244
\(910\) 16.4461 + 10.6330i 0.545183 + 0.352479i
\(911\) 4.01325 0.132965 0.0664825 0.997788i \(-0.478822\pi\)
0.0664825 + 0.997788i \(0.478822\pi\)
\(912\) −0.278640 0.482618i −0.00922669 0.0159811i
\(913\) 11.1611 19.3315i 0.369377 0.639780i
\(914\) −8.44709 + 14.6308i −0.279405 + 0.483943i
\(915\) −4.75430 8.23469i −0.157172 0.272230i
\(916\) −93.6621 −3.09468
\(917\) 40.7028 20.8430i 1.34412 0.688296i
\(918\) 7.80413 0.257575
\(919\) 17.1415 + 29.6899i 0.565446 + 0.979381i 0.997008 + 0.0772976i \(0.0246292\pi\)
−0.431562 + 0.902083i \(0.642038\pi\)
\(920\) 37.7333 65.3561i 1.24403 2.15473i
\(921\) −1.10618 + 1.91596i −0.0364499 + 0.0631331i
\(922\) −15.6830 27.1637i −0.516491 0.894588i
\(923\) −4.23007 −0.139235
\(924\) −0.889311 + 17.6528i −0.0292562 + 0.580735i
\(925\) −10.0952 −0.331929
\(926\) −26.5028 45.9042i −0.870936 1.50851i
\(927\) 6.24816 10.8221i 0.205216 0.355445i
\(928\) −26.2167 + 45.4086i −0.860605 + 1.49061i
\(929\) 2.60864 + 4.51829i 0.0855866 + 0.148240i 0.905641 0.424045i \(-0.139390\pi\)
−0.820054 + 0.572286i \(0.806057\pi\)
\(930\) −26.4554 −0.867508
\(931\) −3.65351 8.11731i −0.119739 0.266034i
\(932\) 34.3267 1.12441
\(933\) 4.35162 + 7.53723i 0.142466 + 0.246758i
\(934\) 29.6351 51.3294i 0.969689 1.67955i
\(935\) −11.9812 + 20.7520i −0.391827 + 0.678663i
\(936\) 1.28703 + 2.22920i 0.0420679 + 0.0728637i
\(937\) 12.6090 0.411919 0.205960 0.978560i \(-0.433968\pi\)
0.205960 + 0.978560i \(0.433968\pi\)
\(938\) −1.93136 + 38.3375i −0.0630612 + 1.25176i
\(939\) 34.4068 1.12282
\(940\) −36.9988 64.0837i −1.20677 2.09018i
\(941\) −4.91020 + 8.50472i −0.160068 + 0.277246i −0.934893 0.354930i \(-0.884505\pi\)
0.774825 + 0.632176i \(0.217838\pi\)
\(942\) 2.82247 4.88866i 0.0919611 0.159281i
\(943\) 13.2775 + 22.9974i 0.432377 + 0.748898i
\(944\) −2.61116 −0.0849859
\(945\) 7.69181 3.93881i 0.250215 0.128129i
\(946\) −56.8752 −1.84917
\(947\) 14.9545 + 25.9020i 0.485956 + 0.841700i 0.999870 0.0161415i \(-0.00513821\pi\)
−0.513914 + 0.857842i \(0.671805\pi\)
\(948\) −5.19489 + 8.99781i −0.168722 + 0.292235i
\(949\) −0.479207 + 0.830011i −0.0155557 + 0.0269433i
\(950\) 8.16769 + 14.1469i 0.264995 + 0.458985i
\(951\) −9.48328 −0.307517
\(952\) −19.6946 12.7332i −0.638307 0.412687i
\(953\) −40.0603 −1.29768 −0.648840 0.760925i \(-0.724746\pi\)
−0.648840 + 0.760925i \(0.724746\pi\)
\(954\) −12.6980 21.9935i −0.411111 0.712066i
\(955\) 29.6292 51.3192i 0.958778 1.66065i
\(956\) −47.4992 + 82.2711i −1.53623 + 2.66084i
\(957\) 9.09460 + 15.7523i 0.293987 + 0.509200i
\(958\) 33.7923 1.09178
\(959\) −35.8494 23.1778i −1.15764 0.748450i
\(960\) −42.5952 −1.37476
\(961\) 9.11305 + 15.7843i 0.293969 + 0.509170i
\(962\) −2.01808 + 3.49542i −0.0650656 + 0.112697i
\(963\) 6.44648 11.1656i 0.207735 0.359807i
\(964\) −37.3314 64.6598i −1.20236 2.08255i
\(965\) 25.4894 0.820533
\(966\) −47.9044 + 24.5308i −1.54130 + 0.789265i
\(967\) −20.8069 −0.669104 −0.334552 0.942377i \(-0.608585\pi\)
−0.334552 + 0.942377i \(0.608585\pi\)
\(968\) 8.31597 + 14.4037i 0.267285 + 0.462952i
\(969\) 2.18958 3.79246i 0.0703394 0.121831i
\(970\) −13.9936 + 24.2376i −0.449307 + 0.778223i
\(971\) 5.61948 + 9.73323i 0.180338 + 0.312354i 0.941996 0.335625i \(-0.108948\pi\)
−0.761658 + 0.647979i \(0.775614\pi\)
\(972\) 3.13583 0.100582
\(973\) −0.174817 + 3.47012i −0.00560439 + 0.111247i
\(974\) −7.52256 −0.241038
\(975\) 2.83415 + 4.90890i 0.0907655 + 0.157210i
\(976\) 0.637883 1.10485i 0.0204181 0.0353653i
\(977\) 17.3199 29.9989i 0.554112 0.959750i −0.443860 0.896096i \(-0.646391\pi\)
0.997972 0.0636538i \(-0.0202753\pi\)
\(978\) −12.7863 22.1465i −0.408861 0.708168i
\(979\) 32.1569 1.02774
\(980\) −71.3335 7.20555i −2.27867 0.230173i
\(981\) −7.36590 −0.235175
\(982\) −23.5117 40.7234i −0.750287 1.29954i
\(983\) 23.4095 40.5464i 0.746646 1.29323i −0.202776 0.979225i \(-0.564996\pi\)
0.949422 0.314004i \(-0.101670\pi\)
\(984\) −3.80757 + 6.59490i −0.121381 + 0.210238i
\(985\) 8.36934 + 14.4961i 0.266669 + 0.461885i
\(986\) −66.6309 −2.12196
\(987\) −0.961735 + 19.0904i −0.0306124 + 0.607655i
\(988\) 3.98771 0.126866
\(989\) −52.8706 91.5745i −1.68119 2.91190i
\(990\) −7.88471 + 13.6567i −0.250592 + 0.434039i
\(991\) 7.67373 13.2913i 0.243764 0.422212i −0.718019 0.696023i \(-0.754951\pi\)
0.961783 + 0.273811i \(0.0882844\pi\)
\(992\) −10.9746 19.0086i −0.348444 0.603523i
\(993\) −8.12377 −0.257800
\(994\) 22.5753 11.5603i 0.716046 0.366672i
\(995\) 29.5858 0.937934
\(996\) 16.4284 + 28.4548i 0.520554 + 0.901625i
\(997\) −25.5823 + 44.3098i −0.810199 + 1.40331i 0.102526 + 0.994730i \(0.467308\pi\)
−0.912725 + 0.408575i \(0.866026\pi\)
\(998\) −28.2950 + 49.0084i −0.895663 + 1.55133i
\(999\) 0.890499 + 1.54239i 0.0281741 + 0.0487990i
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 273.2.i.d.235.1 yes 8
3.2 odd 2 819.2.j.f.235.4 8
7.2 even 3 inner 273.2.i.d.79.1 8
7.3 odd 6 1911.2.a.q.1.4 4
7.4 even 3 1911.2.a.r.1.4 4
21.2 odd 6 819.2.j.f.352.4 8
21.11 odd 6 5733.2.a.bj.1.1 4
21.17 even 6 5733.2.a.bk.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.i.d.79.1 8 7.2 even 3 inner
273.2.i.d.235.1 yes 8 1.1 even 1 trivial
819.2.j.f.235.4 8 3.2 odd 2
819.2.j.f.352.4 8 21.2 odd 6
1911.2.a.q.1.4 4 7.3 odd 6
1911.2.a.r.1.4 4 7.4 even 3
5733.2.a.bj.1.1 4 21.11 odd 6
5733.2.a.bk.1.1 4 21.17 even 6