Properties

Label 165.2.k.b.122.2
Level $165$
Weight $2$
Character 165.122
Analytic conductor $1.318$
Analytic rank $0$
Dimension $4$
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] = [165,2,Mod(23,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.k (of order \(4\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 122.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 165.122
Dual form 165.2.k.b.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.70711 - 1.70711i) q^{2} +(-1.41421 + 1.00000i) q^{3} -3.82843i q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.707107 + 4.12132i) q^{6} +(-0.585786 - 0.585786i) q^{7} +(-3.12132 - 3.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(1.70711 - 1.70711i) q^{2} +(-1.41421 + 1.00000i) q^{3} -3.82843i q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.707107 + 4.12132i) q^{6} +(-0.585786 - 0.585786i) q^{7} +(-3.12132 - 3.12132i) q^{8} +(1.00000 - 2.82843i) q^{9} +(1.70711 - 5.12132i) q^{10} +1.00000i q^{11} +(3.82843 + 5.41421i) q^{12} +(-2.00000 + 2.00000i) q^{13} -2.00000 q^{14} +(-1.82843 + 3.41421i) q^{15} -3.00000 q^{16} +(-2.82843 + 2.82843i) q^{17} +(-3.12132 - 6.53553i) q^{18} +2.82843i q^{19} +(-3.82843 - 7.65685i) q^{20} +(1.41421 + 0.242641i) q^{21} +(1.70711 + 1.70711i) q^{22} +(5.24264 + 5.24264i) q^{23} +(7.53553 + 1.29289i) q^{24} +(3.00000 - 4.00000i) q^{25} +6.82843i q^{26} +(1.41421 + 5.00000i) q^{27} +(-2.24264 + 2.24264i) q^{28} +4.82843 q^{29} +(2.70711 + 8.94975i) q^{30} -8.82843 q^{31} +(1.12132 - 1.12132i) q^{32} +(-1.00000 - 1.41421i) q^{33} +9.65685i q^{34} +(-1.75736 - 0.585786i) q^{35} +(-10.8284 - 3.82843i) q^{36} +(-5.82843 - 5.82843i) q^{37} +(4.82843 + 4.82843i) q^{38} +(0.828427 - 4.82843i) q^{39} +(-9.36396 - 3.12132i) q^{40} -3.65685i q^{41} +(2.82843 - 2.00000i) q^{42} +(-8.24264 + 8.24264i) q^{43} +3.82843 q^{44} +(-0.828427 - 6.65685i) q^{45} +17.8995 q^{46} +(-1.24264 + 1.24264i) q^{47} +(4.24264 - 3.00000i) q^{48} -6.31371i q^{49} +(-1.70711 - 11.9497i) q^{50} +(1.17157 - 6.82843i) q^{51} +(7.65685 + 7.65685i) q^{52} +(-1.00000 - 1.00000i) q^{53} +(10.9497 + 6.12132i) q^{54} +(1.00000 + 2.00000i) q^{55} +3.65685i q^{56} +(-2.82843 - 4.00000i) q^{57} +(8.24264 - 8.24264i) q^{58} +4.00000 q^{59} +(13.0711 + 7.00000i) q^{60} +10.4853 q^{61} +(-15.0711 + 15.0711i) q^{62} +(-2.24264 + 1.07107i) q^{63} -9.82843i q^{64} +(-2.00000 + 6.00000i) q^{65} +(-4.12132 - 0.707107i) q^{66} +(-3.58579 - 3.58579i) q^{67} +(10.8284 + 10.8284i) q^{68} +(-12.6569 - 2.17157i) q^{69} +(-4.00000 + 2.00000i) q^{70} -14.4853i q^{71} +(-11.9497 + 5.70711i) q^{72} -19.8995 q^{74} +(-0.242641 + 8.65685i) q^{75} +10.8284 q^{76} +(0.585786 - 0.585786i) q^{77} +(-6.82843 - 9.65685i) q^{78} +5.17157i q^{79} +(-6.00000 + 3.00000i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(-6.24264 - 6.24264i) q^{82} +(-5.07107 - 5.07107i) q^{83} +(0.928932 - 5.41421i) q^{84} +(-2.82843 + 8.48528i) q^{85} +28.1421i q^{86} +(-6.82843 + 4.82843i) q^{87} +(3.12132 - 3.12132i) q^{88} -1.65685 q^{89} +(-12.7782 - 9.94975i) q^{90} +2.34315 q^{91} +(20.0711 - 20.0711i) q^{92} +(12.4853 - 8.82843i) q^{93} +4.24264i q^{94} +(2.82843 + 5.65685i) q^{95} +(-0.464466 + 2.70711i) q^{96} +(-0.656854 - 0.656854i) q^{97} +(-10.7782 - 10.7782i) q^{98} +(2.82843 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 8 q^{5} - 8 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 8 q^{5} - 8 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 8 q^{14} + 4 q^{15} - 12 q^{16} - 4 q^{18} - 4 q^{20} + 4 q^{22} + 4 q^{23} + 16 q^{24} + 12 q^{25} + 8 q^{28} + 8 q^{29} + 8 q^{30} - 24 q^{31} - 4 q^{32} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 12 q^{37} + 8 q^{38} - 8 q^{39} - 12 q^{40} - 16 q^{43} + 4 q^{44} + 8 q^{45} + 32 q^{46} + 12 q^{47} - 4 q^{50} + 16 q^{51} + 8 q^{52} - 4 q^{53} + 24 q^{54} + 4 q^{55} + 16 q^{58} + 16 q^{59} + 24 q^{60} + 8 q^{61} - 32 q^{62} + 8 q^{63} - 8 q^{65} - 8 q^{66} - 20 q^{67} + 32 q^{68} - 28 q^{69} - 16 q^{70} - 28 q^{72} - 40 q^{74} + 16 q^{75} + 32 q^{76} + 8 q^{77} - 16 q^{78} - 24 q^{80} - 28 q^{81} - 8 q^{82} + 8 q^{83} + 32 q^{84} - 16 q^{87} + 4 q^{88} + 16 q^{89} - 20 q^{90} + 32 q^{91} + 52 q^{92} + 16 q^{93} - 16 q^{96} + 20 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.70711 1.70711i 1.20711 1.20711i 0.235147 0.971960i \(-0.424443\pi\)
0.971960 0.235147i \(-0.0755571\pi\)
\(3\) −1.41421 + 1.00000i −0.816497 + 0.577350i
\(4\) 3.82843i 1.91421i
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) −0.707107 + 4.12132i −0.288675 + 1.68252i
\(7\) −0.585786 0.585786i −0.221406 0.221406i 0.587684 0.809091i \(-0.300040\pi\)
−0.809091 + 0.587684i \(0.800040\pi\)
\(8\) −3.12132 3.12132i −1.10355 1.10355i
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 1.70711 5.12132i 0.539835 1.61950i
\(11\) 1.00000i 0.301511i
\(12\) 3.82843 + 5.41421i 1.10517 + 1.56295i
\(13\) −2.00000 + 2.00000i −0.554700 + 0.554700i −0.927794 0.373094i \(-0.878297\pi\)
0.373094 + 0.927794i \(0.378297\pi\)
\(14\) −2.00000 −0.534522
\(15\) −1.82843 + 3.41421i −0.472098 + 0.881546i
\(16\) −3.00000 −0.750000
\(17\) −2.82843 + 2.82843i −0.685994 + 0.685994i −0.961344 0.275350i \(-0.911206\pi\)
0.275350 + 0.961344i \(0.411206\pi\)
\(18\) −3.12132 6.53553i −0.735702 1.54044i
\(19\) 2.82843i 0.648886i 0.945905 + 0.324443i \(0.105177\pi\)
−0.945905 + 0.324443i \(0.894823\pi\)
\(20\) −3.82843 7.65685i −0.856062 1.71212i
\(21\) 1.41421 + 0.242641i 0.308607 + 0.0529485i
\(22\) 1.70711 + 1.70711i 0.363956 + 0.363956i
\(23\) 5.24264 + 5.24264i 1.09317 + 1.09317i 0.995189 + 0.0979775i \(0.0312373\pi\)
0.0979775 + 0.995189i \(0.468763\pi\)
\(24\) 7.53553 + 1.29289i 1.53818 + 0.263911i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 6.82843i 1.33916i
\(27\) 1.41421 + 5.00000i 0.272166 + 0.962250i
\(28\) −2.24264 + 2.24264i −0.423819 + 0.423819i
\(29\) 4.82843 0.896616 0.448308 0.893879i \(-0.352027\pi\)
0.448308 + 0.893879i \(0.352027\pi\)
\(30\) 2.70711 + 8.94975i 0.494248 + 1.63399i
\(31\) −8.82843 −1.58563 −0.792816 0.609461i \(-0.791386\pi\)
−0.792816 + 0.609461i \(0.791386\pi\)
\(32\) 1.12132 1.12132i 0.198223 0.198223i
\(33\) −1.00000 1.41421i −0.174078 0.246183i
\(34\) 9.65685i 1.65614i
\(35\) −1.75736 0.585786i −0.297048 0.0990160i
\(36\) −10.8284 3.82843i −1.80474 0.638071i
\(37\) −5.82843 5.82843i −0.958188 0.958188i 0.0409727 0.999160i \(-0.486954\pi\)
−0.999160 + 0.0409727i \(0.986954\pi\)
\(38\) 4.82843 + 4.82843i 0.783274 + 0.783274i
\(39\) 0.828427 4.82843i 0.132655 0.773167i
\(40\) −9.36396 3.12132i −1.48057 0.493524i
\(41\) 3.65685i 0.571105i −0.958363 0.285552i \(-0.907823\pi\)
0.958363 0.285552i \(-0.0921770\pi\)
\(42\) 2.82843 2.00000i 0.436436 0.308607i
\(43\) −8.24264 + 8.24264i −1.25699 + 1.25699i −0.304469 + 0.952522i \(0.598479\pi\)
−0.952522 + 0.304469i \(0.901521\pi\)
\(44\) 3.82843 0.577157
\(45\) −0.828427 6.65685i −0.123495 0.992345i
\(46\) 17.8995 2.63914
\(47\) −1.24264 + 1.24264i −0.181258 + 0.181258i −0.791904 0.610646i \(-0.790910\pi\)
0.610646 + 0.791904i \(0.290910\pi\)
\(48\) 4.24264 3.00000i 0.612372 0.433013i
\(49\) 6.31371i 0.901958i
\(50\) −1.70711 11.9497i −0.241421 1.68995i
\(51\) 1.17157 6.82843i 0.164053 0.956171i
\(52\) 7.65685 + 7.65685i 1.06181 + 1.06181i
\(53\) −1.00000 1.00000i −0.137361 0.137361i 0.635083 0.772444i \(-0.280966\pi\)
−0.772444 + 0.635083i \(0.780966\pi\)
\(54\) 10.9497 + 6.12132i 1.49007 + 0.833006i
\(55\) 1.00000 + 2.00000i 0.134840 + 0.269680i
\(56\) 3.65685i 0.488668i
\(57\) −2.82843 4.00000i −0.374634 0.529813i
\(58\) 8.24264 8.24264i 1.08231 1.08231i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 13.0711 + 7.00000i 1.68747 + 0.903696i
\(61\) 10.4853 1.34250 0.671251 0.741230i \(-0.265757\pi\)
0.671251 + 0.741230i \(0.265757\pi\)
\(62\) −15.0711 + 15.0711i −1.91403 + 1.91403i
\(63\) −2.24264 + 1.07107i −0.282546 + 0.134942i
\(64\) 9.82843i 1.22855i
\(65\) −2.00000 + 6.00000i −0.248069 + 0.744208i
\(66\) −4.12132 0.707107i −0.507299 0.0870388i
\(67\) −3.58579 3.58579i −0.438074 0.438074i 0.453290 0.891363i \(-0.350250\pi\)
−0.891363 + 0.453290i \(0.850250\pi\)
\(68\) 10.8284 + 10.8284i 1.31314 + 1.31314i
\(69\) −12.6569 2.17157i −1.52371 0.261427i
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 14.4853i 1.71909i −0.511063 0.859543i \(-0.670748\pi\)
0.511063 0.859543i \(-0.329252\pi\)
\(72\) −11.9497 + 5.70711i −1.40829 + 0.672589i
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) −19.8995 −2.31327
\(75\) −0.242641 + 8.65685i −0.0280177 + 0.999607i
\(76\) 10.8284 1.24211
\(77\) 0.585786 0.585786i 0.0667566 0.0667566i
\(78\) −6.82843 9.65685i −0.773167 1.09342i
\(79\) 5.17157i 0.581847i 0.956746 + 0.290924i \(0.0939626\pi\)
−0.956746 + 0.290924i \(0.906037\pi\)
\(80\) −6.00000 + 3.00000i −0.670820 + 0.335410i
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) −6.24264 6.24264i −0.689384 0.689384i
\(83\) −5.07107 5.07107i −0.556622 0.556622i 0.371722 0.928344i \(-0.378767\pi\)
−0.928344 + 0.371722i \(0.878767\pi\)
\(84\) 0.928932 5.41421i 0.101355 0.590739i
\(85\) −2.82843 + 8.48528i −0.306786 + 0.920358i
\(86\) 28.1421i 3.03464i
\(87\) −6.82843 + 4.82843i −0.732084 + 0.517662i
\(88\) 3.12132 3.12132i 0.332734 0.332734i
\(89\) −1.65685 −0.175626 −0.0878131 0.996137i \(-0.527988\pi\)
−0.0878131 + 0.996137i \(0.527988\pi\)
\(90\) −12.7782 9.94975i −1.34694 1.04880i
\(91\) 2.34315 0.245628
\(92\) 20.0711 20.0711i 2.09255 2.09255i
\(93\) 12.4853 8.82843i 1.29466 0.915465i
\(94\) 4.24264i 0.437595i
\(95\) 2.82843 + 5.65685i 0.290191 + 0.580381i
\(96\) −0.464466 + 2.70711i −0.0474044 + 0.276293i
\(97\) −0.656854 0.656854i −0.0666934 0.0666934i 0.672973 0.739667i \(-0.265017\pi\)
−0.739667 + 0.672973i \(0.765017\pi\)
\(98\) −10.7782 10.7782i −1.08876 1.08876i
\(99\) 2.82843 + 1.00000i 0.284268 + 0.100504i
\(100\) −15.3137 11.4853i −1.53137 1.14853i
\(101\) 12.8284i 1.27648i 0.769839 + 0.638238i \(0.220336\pi\)
−0.769839 + 0.638238i \(0.779664\pi\)
\(102\) −9.65685 13.6569i −0.956171 1.35223i
\(103\) −3.58579 + 3.58579i −0.353318 + 0.353318i −0.861343 0.508025i \(-0.830376\pi\)
0.508025 + 0.861343i \(0.330376\pi\)
\(104\) 12.4853 1.22428
\(105\) 3.07107 0.928932i 0.299706 0.0906545i
\(106\) −3.41421 −0.331618
\(107\) 8.24264 8.24264i 0.796846 0.796846i −0.185751 0.982597i \(-0.559472\pi\)
0.982597 + 0.185751i \(0.0594717\pi\)
\(108\) 19.1421 5.41421i 1.84195 0.520983i
\(109\) 8.82843i 0.845610i 0.906221 + 0.422805i \(0.138954\pi\)
−0.906221 + 0.422805i \(0.861046\pi\)
\(110\) 5.12132 + 1.70711i 0.488299 + 0.162766i
\(111\) 14.0711 + 2.41421i 1.33557 + 0.229147i
\(112\) 1.75736 + 1.75736i 0.166055 + 0.166055i
\(113\) 0.171573 + 0.171573i 0.0161402 + 0.0161402i 0.715131 0.698991i \(-0.246367\pi\)
−0.698991 + 0.715131i \(0.746367\pi\)
\(114\) −11.6569 2.00000i −1.09176 0.187317i
\(115\) 15.7279 + 5.24264i 1.46664 + 0.488879i
\(116\) 18.4853i 1.71632i
\(117\) 3.65685 + 7.65685i 0.338076 + 0.707876i
\(118\) 6.82843 6.82843i 0.628608 0.628608i
\(119\) 3.31371 0.303767
\(120\) 16.3640 4.94975i 1.49382 0.451848i
\(121\) −1.00000 −0.0909091
\(122\) 17.8995 17.8995i 1.62054 1.62054i
\(123\) 3.65685 + 5.17157i 0.329727 + 0.466305i
\(124\) 33.7990i 3.03524i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) −2.00000 + 5.65685i −0.178174 + 0.503953i
\(127\) −1.41421 1.41421i −0.125491 0.125491i 0.641572 0.767063i \(-0.278283\pi\)
−0.767063 + 0.641572i \(0.778283\pi\)
\(128\) −14.5355 14.5355i −1.28477 1.28477i
\(129\) 3.41421 19.8995i 0.300605 1.75205i
\(130\) 6.82843 + 13.6569i 0.598893 + 1.19779i
\(131\) 1.17157i 0.102361i −0.998689 0.0511804i \(-0.983702\pi\)
0.998689 0.0511804i \(-0.0162983\pi\)
\(132\) −5.41421 + 3.82843i −0.471247 + 0.333222i
\(133\) 1.65685 1.65685i 0.143667 0.143667i
\(134\) −12.2426 −1.05760
\(135\) 7.82843 + 8.58579i 0.673764 + 0.738947i
\(136\) 17.6569 1.51406
\(137\) −5.82843 + 5.82843i −0.497956 + 0.497956i −0.910801 0.412845i \(-0.864535\pi\)
0.412845 + 0.910801i \(0.364535\pi\)
\(138\) −25.3137 + 17.8995i −2.15485 + 1.52371i
\(139\) 6.34315i 0.538019i −0.963138 0.269009i \(-0.913304\pi\)
0.963138 0.269009i \(-0.0866962\pi\)
\(140\) −2.24264 + 6.72792i −0.189538 + 0.568613i
\(141\) 0.514719 3.00000i 0.0433471 0.252646i
\(142\) −24.7279 24.7279i −2.07512 2.07512i
\(143\) −2.00000 2.00000i −0.167248 0.167248i
\(144\) −3.00000 + 8.48528i −0.250000 + 0.707107i
\(145\) 9.65685 4.82843i 0.801958 0.400979i
\(146\) 0 0
\(147\) 6.31371 + 8.92893i 0.520746 + 0.736446i
\(148\) −22.3137 + 22.3137i −1.83418 + 1.83418i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 14.3640 + 15.1924i 1.17281 + 1.24045i
\(151\) −18.1421 −1.47639 −0.738193 0.674590i \(-0.764321\pi\)
−0.738193 + 0.674590i \(0.764321\pi\)
\(152\) 8.82843 8.82843i 0.716080 0.716080i
\(153\) 5.17157 + 10.8284i 0.418097 + 0.875426i
\(154\) 2.00000i 0.161165i
\(155\) −17.6569 + 8.82843i −1.41823 + 0.709116i
\(156\) −18.4853 3.17157i −1.48001 0.253929i
\(157\) 7.48528 + 7.48528i 0.597390 + 0.597390i 0.939617 0.342227i \(-0.111181\pi\)
−0.342227 + 0.939617i \(0.611181\pi\)
\(158\) 8.82843 + 8.82843i 0.702352 + 0.702352i
\(159\) 2.41421 + 0.414214i 0.191460 + 0.0328493i
\(160\) 1.12132 3.36396i 0.0886482 0.265944i
\(161\) 6.14214i 0.484068i
\(162\) −21.6066 + 2.29289i −1.69757 + 0.180147i
\(163\) 6.41421 6.41421i 0.502400 0.502400i −0.409783 0.912183i \(-0.634396\pi\)
0.912183 + 0.409783i \(0.134396\pi\)
\(164\) −14.0000 −1.09322
\(165\) −3.41421 1.82843i −0.265796 0.142343i
\(166\) −17.3137 −1.34380
\(167\) 10.7279 10.7279i 0.830152 0.830152i −0.157386 0.987537i \(-0.550307\pi\)
0.987537 + 0.157386i \(0.0503066\pi\)
\(168\) −3.65685 5.17157i −0.282132 0.398996i
\(169\) 5.00000i 0.384615i
\(170\) 9.65685 + 19.3137i 0.740647 + 1.48129i
\(171\) 8.00000 + 2.82843i 0.611775 + 0.216295i
\(172\) 31.5563 + 31.5563i 2.40615 + 2.40615i
\(173\) 8.48528 + 8.48528i 0.645124 + 0.645124i 0.951811 0.306687i \(-0.0992203\pi\)
−0.306687 + 0.951811i \(0.599220\pi\)
\(174\) −3.41421 + 19.8995i −0.258831 + 1.50858i
\(175\) −4.10051 + 0.585786i −0.309969 + 0.0442813i
\(176\) 3.00000i 0.226134i
\(177\) −5.65685 + 4.00000i −0.425195 + 0.300658i
\(178\) −2.82843 + 2.82843i −0.212000 + 0.212000i
\(179\) 4.14214 0.309598 0.154799 0.987946i \(-0.450527\pi\)
0.154799 + 0.987946i \(0.450527\pi\)
\(180\) −25.4853 + 3.17157i −1.89956 + 0.236395i
\(181\) −5.65685 −0.420471 −0.210235 0.977651i \(-0.567423\pi\)
−0.210235 + 0.977651i \(0.567423\pi\)
\(182\) 4.00000 4.00000i 0.296500 0.296500i
\(183\) −14.8284 + 10.4853i −1.09615 + 0.775094i
\(184\) 32.7279i 2.41273i
\(185\) −17.4853 5.82843i −1.28554 0.428514i
\(186\) 6.24264 36.3848i 0.457733 2.66786i
\(187\) −2.82843 2.82843i −0.206835 0.206835i
\(188\) 4.75736 + 4.75736i 0.346966 + 0.346966i
\(189\) 2.10051 3.75736i 0.152789 0.273308i
\(190\) 14.4853 + 4.82843i 1.05087 + 0.350291i
\(191\) 11.3137i 0.818631i 0.912393 + 0.409316i \(0.134232\pi\)
−0.912393 + 0.409316i \(0.865768\pi\)
\(192\) 9.82843 + 13.8995i 0.709306 + 1.00311i
\(193\) 8.00000 8.00000i 0.575853 0.575853i −0.357905 0.933758i \(-0.616509\pi\)
0.933758 + 0.357905i \(0.116509\pi\)
\(194\) −2.24264 −0.161012
\(195\) −3.17157 10.4853i −0.227121 0.750867i
\(196\) −24.1716 −1.72654
\(197\) −14.1421 + 14.1421i −1.00759 + 1.00759i −0.00761443 + 0.999971i \(0.502424\pi\)
−0.999971 + 0.00761443i \(0.997576\pi\)
\(198\) 6.53553 3.12132i 0.464460 0.221823i
\(199\) 2.48528i 0.176177i 0.996113 + 0.0880885i \(0.0280758\pi\)
−0.996113 + 0.0880885i \(0.971924\pi\)
\(200\) −21.8492 + 3.12132i −1.54497 + 0.220711i
\(201\) 8.65685 + 1.48528i 0.610607 + 0.104764i
\(202\) 21.8995 + 21.8995i 1.54084 + 1.54084i
\(203\) −2.82843 2.82843i −0.198517 0.198517i
\(204\) −26.1421 4.48528i −1.83032 0.314033i
\(205\) −3.65685 7.31371i −0.255406 0.510812i
\(206\) 12.2426i 0.852985i
\(207\) 20.0711 9.58579i 1.39504 0.666258i
\(208\) 6.00000 6.00000i 0.416025 0.416025i
\(209\) −2.82843 −0.195646
\(210\) 3.65685 6.82843i 0.252347 0.471206i
\(211\) 12.4853 0.859522 0.429761 0.902943i \(-0.358598\pi\)
0.429761 + 0.902943i \(0.358598\pi\)
\(212\) −3.82843 + 3.82843i −0.262937 + 0.262937i
\(213\) 14.4853 + 20.4853i 0.992515 + 1.40363i
\(214\) 28.1421i 1.92376i
\(215\) −8.24264 + 24.7279i −0.562143 + 1.68643i
\(216\) 11.1924 20.0208i 0.761546 1.36224i
\(217\) 5.17157 + 5.17157i 0.351069 + 0.351069i
\(218\) 15.0711 + 15.0711i 1.02074 + 1.02074i
\(219\) 0 0
\(220\) 7.65685 3.82843i 0.516225 0.258113i
\(221\) 11.3137i 0.761042i
\(222\) 28.1421 19.8995i 1.88878 1.33557i
\(223\) 14.5563 14.5563i 0.974765 0.974765i −0.0249241 0.999689i \(-0.507934\pi\)
0.999689 + 0.0249241i \(0.00793441\pi\)
\(224\) −1.31371 −0.0877758
\(225\) −8.31371 12.4853i −0.554247 0.832352i
\(226\) 0.585786 0.0389659
\(227\) −1.75736 + 1.75736i −0.116640 + 0.116640i −0.763018 0.646378i \(-0.776283\pi\)
0.646378 + 0.763018i \(0.276283\pi\)
\(228\) −15.3137 + 10.8284i −1.01418 + 0.717130i
\(229\) 1.65685i 0.109488i 0.998500 + 0.0547440i \(0.0174343\pi\)
−0.998500 + 0.0547440i \(0.982566\pi\)
\(230\) 35.7990 17.8995i 2.36052 1.18026i
\(231\) −0.242641 + 1.41421i −0.0159646 + 0.0930484i
\(232\) −15.0711 15.0711i −0.989464 0.989464i
\(233\) −8.34315 8.34315i −0.546578 0.546578i 0.378872 0.925449i \(-0.376312\pi\)
−0.925449 + 0.378872i \(0.876312\pi\)
\(234\) 19.3137 + 6.82843i 1.26258 + 0.446388i
\(235\) −1.24264 + 3.72792i −0.0810609 + 0.243183i
\(236\) 15.3137i 0.996838i
\(237\) −5.17157 7.31371i −0.335930 0.475076i
\(238\) 5.65685 5.65685i 0.366679 0.366679i
\(239\) −15.7990 −1.02195 −0.510976 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(240\) 5.48528 10.2426i 0.354073 0.661160i
\(241\) −28.1421 −1.81279 −0.906397 0.422427i \(-0.861178\pi\)
−0.906397 + 0.422427i \(0.861178\pi\)
\(242\) −1.70711 + 1.70711i −0.109737 + 0.109737i
\(243\) 15.5563 + 1.00000i 0.997940 + 0.0641500i
\(244\) 40.1421i 2.56984i
\(245\) −6.31371 12.6274i −0.403368 0.806736i
\(246\) 15.0711 + 2.58579i 0.960896 + 0.164864i
\(247\) −5.65685 5.65685i −0.359937 0.359937i
\(248\) 27.5563 + 27.5563i 1.74983 + 1.74983i
\(249\) 12.2426 + 2.10051i 0.775846 + 0.133114i
\(250\) −15.3640 22.1924i −0.971702 1.40357i
\(251\) 12.1421i 0.766405i −0.923664 0.383202i \(-0.874821\pi\)
0.923664 0.383202i \(-0.125179\pi\)
\(252\) 4.10051 + 8.58579i 0.258308 + 0.540854i
\(253\) −5.24264 + 5.24264i −0.329602 + 0.329602i
\(254\) −4.82843 −0.302962
\(255\) −4.48528 14.8284i −0.280879 0.928592i
\(256\) −29.9706 −1.87316
\(257\) −3.82843 + 3.82843i −0.238811 + 0.238811i −0.816358 0.577547i \(-0.804010\pi\)
0.577547 + 0.816358i \(0.304010\pi\)
\(258\) −28.1421 39.7990i −1.75205 2.47778i
\(259\) 6.82843i 0.424298i
\(260\) 22.9706 + 7.65685i 1.42457 + 0.474858i
\(261\) 4.82843 13.6569i 0.298872 0.845338i
\(262\) −2.00000 2.00000i −0.123560 0.123560i
\(263\) 10.2426 + 10.2426i 0.631588 + 0.631588i 0.948466 0.316878i \(-0.102635\pi\)
−0.316878 + 0.948466i \(0.602635\pi\)
\(264\) −1.29289 + 7.53553i −0.0795721 + 0.463780i
\(265\) −3.00000 1.00000i −0.184289 0.0614295i
\(266\) 5.65685i 0.346844i
\(267\) 2.34315 1.65685i 0.143398 0.101398i
\(268\) −13.7279 + 13.7279i −0.838566 + 0.838566i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 28.0208 + 1.29289i 1.70529 + 0.0786830i
\(271\) −8.48528 −0.515444 −0.257722 0.966219i \(-0.582972\pi\)
−0.257722 + 0.966219i \(0.582972\pi\)
\(272\) 8.48528 8.48528i 0.514496 0.514496i
\(273\) −3.31371 + 2.34315i −0.200555 + 0.141814i
\(274\) 19.8995i 1.20217i
\(275\) 4.00000 + 3.00000i 0.241209 + 0.180907i
\(276\) −8.31371 + 48.4558i −0.500426 + 2.91670i
\(277\) −1.51472 1.51472i −0.0910106 0.0910106i 0.660136 0.751146i \(-0.270499\pi\)
−0.751146 + 0.660136i \(0.770499\pi\)
\(278\) −10.8284 10.8284i −0.649446 0.649446i
\(279\) −8.82843 + 24.9706i −0.528544 + 1.49495i
\(280\) 3.65685 + 7.31371i 0.218539 + 0.437078i
\(281\) 16.6274i 0.991909i 0.868349 + 0.495954i \(0.165182\pi\)
−0.868349 + 0.495954i \(0.834818\pi\)
\(282\) −4.24264 6.00000i −0.252646 0.357295i
\(283\) −0.928932 + 0.928932i −0.0552193 + 0.0552193i −0.734177 0.678958i \(-0.762432\pi\)
0.678958 + 0.734177i \(0.262432\pi\)
\(284\) −55.4558 −3.29070
\(285\) −9.65685 5.17157i −0.572023 0.306338i
\(286\) −6.82843 −0.403773
\(287\) −2.14214 + 2.14214i −0.126446 + 0.126446i
\(288\) −2.05025 4.29289i −0.120812 0.252961i
\(289\) 1.00000i 0.0588235i
\(290\) 8.24264 24.7279i 0.484025 1.45207i
\(291\) 1.58579 + 0.272078i 0.0929604 + 0.0159495i
\(292\) 0 0
\(293\) −7.65685 7.65685i −0.447318 0.447318i 0.447144 0.894462i \(-0.352441\pi\)
−0.894462 + 0.447144i \(0.852441\pi\)
\(294\) 26.0208 + 4.46447i 1.51756 + 0.260373i
\(295\) 8.00000 4.00000i 0.465778 0.232889i
\(296\) 36.3848i 2.11482i
\(297\) −5.00000 + 1.41421i −0.290129 + 0.0820610i
\(298\) 17.0711 17.0711i 0.988900 0.988900i
\(299\) −20.9706 −1.21276
\(300\) 33.1421 + 0.928932i 1.91346 + 0.0536319i
\(301\) 9.65685 0.556612
\(302\) −30.9706 + 30.9706i −1.78216 + 1.78216i
\(303\) −12.8284 18.1421i −0.736974 1.04224i
\(304\) 8.48528i 0.486664i
\(305\) 20.9706 10.4853i 1.20077 0.600385i
\(306\) 27.3137 + 9.65685i 1.56142 + 0.552046i
\(307\) 7.89949 + 7.89949i 0.450848 + 0.450848i 0.895636 0.444788i \(-0.146721\pi\)
−0.444788 + 0.895636i \(0.646721\pi\)
\(308\) −2.24264 2.24264i −0.127786 0.127786i
\(309\) 1.48528 8.65685i 0.0844947 0.492471i
\(310\) −15.0711 + 45.2132i −0.855979 + 2.56794i
\(311\) 0.142136i 0.00805977i 0.999992 + 0.00402989i \(0.00128276\pi\)
−0.999992 + 0.00402989i \(0.998717\pi\)
\(312\) −17.6569 + 12.4853i −0.999623 + 0.706840i
\(313\) 1.34315 1.34315i 0.0759191 0.0759191i −0.668128 0.744047i \(-0.732904\pi\)
0.744047 + 0.668128i \(0.232904\pi\)
\(314\) 25.5563 1.44223
\(315\) −3.41421 + 4.38478i −0.192369 + 0.247054i
\(316\) 19.7990 1.11378
\(317\) 20.3137 20.3137i 1.14093 1.14093i 0.152651 0.988280i \(-0.451219\pi\)
0.988280 0.152651i \(-0.0487812\pi\)
\(318\) 4.82843 3.41421i 0.270765 0.191460i
\(319\) 4.82843i 0.270340i
\(320\) −9.82843 19.6569i −0.549426 1.09885i
\(321\) −3.41421 + 19.8995i −0.190563 + 1.11068i
\(322\) −10.4853 10.4853i −0.584322 0.584322i
\(323\) −8.00000 8.00000i −0.445132 0.445132i
\(324\) −21.6569 + 26.7990i −1.20316 + 1.48883i
\(325\) 2.00000 + 14.0000i 0.110940 + 0.776580i
\(326\) 21.8995i 1.21290i
\(327\) −8.82843 12.4853i −0.488213 0.690438i
\(328\) −11.4142 + 11.4142i −0.630245 + 0.630245i
\(329\) 1.45584 0.0802633
\(330\) −8.94975 + 2.70711i −0.492667 + 0.149021i
\(331\) 10.4853 0.576323 0.288162 0.957582i \(-0.406956\pi\)
0.288162 + 0.957582i \(0.406956\pi\)
\(332\) −19.4142 + 19.4142i −1.06549 + 1.06549i
\(333\) −22.3137 + 10.6569i −1.22278 + 0.583992i
\(334\) 36.6274i 2.00416i
\(335\) −10.7574 3.58579i −0.587737 0.195912i
\(336\) −4.24264 0.727922i −0.231455 0.0397114i
\(337\) −5.17157 5.17157i −0.281714 0.281714i 0.552079 0.833792i \(-0.313835\pi\)
−0.833792 + 0.552079i \(0.813835\pi\)
\(338\) 8.53553 + 8.53553i 0.464272 + 0.464272i
\(339\) −0.414214 0.0710678i −0.0224970 0.00385987i
\(340\) 32.4853 + 10.8284i 1.76176 + 0.587254i
\(341\) 8.82843i 0.478086i
\(342\) 18.4853 8.82843i 0.999570 0.477387i
\(343\) −7.79899 + 7.79899i −0.421106 + 0.421106i
\(344\) 51.4558 2.77431
\(345\) −27.4853 + 8.31371i −1.47976 + 0.447595i
\(346\) 28.9706 1.55747
\(347\) 17.8995 17.8995i 0.960895 0.960895i −0.0383684 0.999264i \(-0.512216\pi\)
0.999264 + 0.0383684i \(0.0122160\pi\)
\(348\) 18.4853 + 26.1421i 0.990915 + 1.40137i
\(349\) 30.0000i 1.60586i 0.596071 + 0.802932i \(0.296728\pi\)
−0.596071 + 0.802932i \(0.703272\pi\)
\(350\) −6.00000 + 8.00000i −0.320713 + 0.427618i
\(351\) −12.8284 7.17157i −0.684731 0.382790i
\(352\) 1.12132 + 1.12132i 0.0597666 + 0.0597666i
\(353\) −2.17157 2.17157i −0.115581 0.115581i 0.646951 0.762532i \(-0.276044\pi\)
−0.762532 + 0.646951i \(0.776044\pi\)
\(354\) −2.82843 + 16.4853i −0.150329 + 0.876183i
\(355\) −14.4853 28.9706i −0.768799 1.53760i
\(356\) 6.34315i 0.336186i
\(357\) −4.68629 + 3.31371i −0.248025 + 0.175380i
\(358\) 7.07107 7.07107i 0.373718 0.373718i
\(359\) −6.14214 −0.324170 −0.162085 0.986777i \(-0.551822\pi\)
−0.162085 + 0.986777i \(0.551822\pi\)
\(360\) −18.1924 + 23.3640i −0.958823 + 1.23139i
\(361\) 11.0000 0.578947
\(362\) −9.65685 + 9.65685i −0.507553 + 0.507553i
\(363\) 1.41421 1.00000i 0.0742270 0.0524864i
\(364\) 8.97056i 0.470185i
\(365\) 0 0
\(366\) −7.41421 + 43.2132i −0.387547 + 2.25879i
\(367\) −20.8995 20.8995i −1.09094 1.09094i −0.995428 0.0955170i \(-0.969550\pi\)
−0.0955170 0.995428i \(-0.530450\pi\)
\(368\) −15.7279 15.7279i −0.819875 0.819875i
\(369\) −10.3431 3.65685i −0.538443 0.190368i
\(370\) −39.7990 + 19.8995i −2.06905 + 1.03453i
\(371\) 1.17157i 0.0608250i
\(372\) −33.7990 47.7990i −1.75240 2.47826i
\(373\) 20.4853 20.4853i 1.06069 1.06069i 0.0626522 0.998035i \(-0.480044\pi\)
0.998035 0.0626522i \(-0.0199559\pi\)
\(374\) −9.65685 −0.499344
\(375\) 8.17157 + 17.5563i 0.421978 + 0.906606i
\(376\) 7.75736 0.400055
\(377\) −9.65685 + 9.65685i −0.497353 + 0.497353i
\(378\) −2.82843 10.0000i −0.145479 0.514344i
\(379\) 0.142136i 0.00730102i 0.999993 + 0.00365051i \(0.00116200\pi\)
−0.999993 + 0.00365051i \(0.998838\pi\)
\(380\) 21.6569 10.8284i 1.11097 0.555487i
\(381\) 3.41421 + 0.585786i 0.174915 + 0.0300107i
\(382\) 19.3137 + 19.3137i 0.988175 + 0.988175i
\(383\) −8.07107 8.07107i −0.412412 0.412412i 0.470166 0.882578i \(-0.344194\pi\)
−0.882578 + 0.470166i \(0.844194\pi\)
\(384\) 35.0919 + 6.02082i 1.79078 + 0.307248i
\(385\) 0.585786 1.75736i 0.0298544 0.0895633i
\(386\) 27.3137i 1.39023i
\(387\) 15.0711 + 31.5563i 0.766105 + 1.60410i
\(388\) −2.51472 + 2.51472i −0.127665 + 0.127665i
\(389\) −5.31371 −0.269416 −0.134708 0.990885i \(-0.543010\pi\)
−0.134708 + 0.990885i \(0.543010\pi\)
\(390\) −23.3137 12.4853i −1.18054 0.632217i
\(391\) −29.6569 −1.49981
\(392\) −19.7071 + 19.7071i −0.995359 + 0.995359i
\(393\) 1.17157 + 1.65685i 0.0590980 + 0.0835772i
\(394\) 48.2843i 2.43253i
\(395\) 5.17157 + 10.3431i 0.260210 + 0.520420i
\(396\) 3.82843 10.8284i 0.192386 0.544149i
\(397\) 11.8284 + 11.8284i 0.593652 + 0.593652i 0.938616 0.344964i \(-0.112109\pi\)
−0.344964 + 0.938616i \(0.612109\pi\)
\(398\) 4.24264 + 4.24264i 0.212664 + 0.212664i
\(399\) −0.686292 + 4.00000i −0.0343575 + 0.200250i
\(400\) −9.00000 + 12.0000i −0.450000 + 0.600000i
\(401\) 24.3431i 1.21564i −0.794075 0.607819i \(-0.792044\pi\)
0.794075 0.607819i \(-0.207956\pi\)
\(402\) 17.3137 12.2426i 0.863529 0.610607i
\(403\) 17.6569 17.6569i 0.879551 0.879551i
\(404\) 49.1127 2.44345
\(405\) −19.6569 4.31371i −0.976757 0.214350i
\(406\) −9.65685 −0.479262
\(407\) 5.82843 5.82843i 0.288904 0.288904i
\(408\) −24.9706 + 17.6569i −1.23623 + 0.874145i
\(409\) 1.51472i 0.0748980i 0.999299 + 0.0374490i \(0.0119232\pi\)
−0.999299 + 0.0374490i \(0.988077\pi\)
\(410\) −18.7279 6.24264i −0.924906 0.308302i
\(411\) 2.41421 14.0711i 0.119084 0.694075i
\(412\) 13.7279 + 13.7279i 0.676326 + 0.676326i
\(413\) −2.34315 2.34315i −0.115299 0.115299i
\(414\) 17.8995 50.6274i 0.879712 2.48820i
\(415\) −15.2132 5.07107i −0.746787 0.248929i
\(416\) 4.48528i 0.219909i
\(417\) 6.34315 + 8.97056i 0.310625 + 0.439290i
\(418\) −4.82843 + 4.82843i −0.236166 + 0.236166i
\(419\) 35.4558 1.73213 0.866066 0.499930i \(-0.166641\pi\)
0.866066 + 0.499930i \(0.166641\pi\)
\(420\) −3.55635 11.7574i −0.173532 0.573700i
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) 21.3137 21.3137i 1.03754 1.03754i
\(423\) 2.27208 + 4.75736i 0.110472 + 0.231311i
\(424\) 6.24264i 0.303169i
\(425\) 2.82843 + 19.7990i 0.137199 + 0.960392i
\(426\) 59.6985 + 10.2426i 2.89240 + 0.496258i
\(427\) −6.14214 6.14214i −0.297239 0.297239i
\(428\) −31.5563 31.5563i −1.52533 1.52533i
\(429\) 4.82843 + 0.828427i 0.233119 + 0.0399968i
\(430\) 28.1421 + 56.2843i 1.35713 + 2.71427i
\(431\) 17.6569i 0.850501i 0.905076 + 0.425250i \(0.139814\pi\)
−0.905076 + 0.425250i \(0.860186\pi\)
\(432\) −4.24264 15.0000i −0.204124 0.721688i
\(433\) 22.3137 22.3137i 1.07233 1.07233i 0.0751567 0.997172i \(-0.476054\pi\)
0.997172 0.0751567i \(-0.0239457\pi\)
\(434\) 17.6569 0.847556
\(435\) −8.82843 + 16.4853i −0.423291 + 0.790409i
\(436\) 33.7990 1.61868
\(437\) −14.8284 + 14.8284i −0.709340 + 0.709340i
\(438\) 0 0
\(439\) 15.3137i 0.730883i −0.930834 0.365442i \(-0.880918\pi\)
0.930834 0.365442i \(-0.119082\pi\)
\(440\) 3.12132 9.36396i 0.148803 0.446409i
\(441\) −17.8579 6.31371i −0.850374 0.300653i
\(442\) −19.3137 19.3137i −0.918659 0.918659i
\(443\) 29.2426 + 29.2426i 1.38936 + 1.38936i 0.826664 + 0.562696i \(0.190236\pi\)
0.562696 + 0.826664i \(0.309764\pi\)
\(444\) 9.24264 53.8701i 0.438636 2.55656i
\(445\) −3.31371 + 1.65685i −0.157085 + 0.0785424i
\(446\) 49.6985i 2.35329i
\(447\) −14.1421 + 10.0000i −0.668900 + 0.472984i
\(448\) −5.75736 + 5.75736i −0.272010 + 0.272010i
\(449\) 36.9706 1.74475 0.872374 0.488838i \(-0.162579\pi\)
0.872374 + 0.488838i \(0.162579\pi\)
\(450\) −35.5061 7.12132i −1.67377 0.335702i
\(451\) 3.65685 0.172195
\(452\) 0.656854 0.656854i 0.0308958 0.0308958i
\(453\) 25.6569 18.1421i 1.20546 0.852392i
\(454\) 6.00000i 0.281594i
\(455\) 4.68629 2.34315i 0.219697 0.109848i
\(456\) −3.65685 + 21.3137i −0.171248 + 0.998106i
\(457\) 10.4853 + 10.4853i 0.490481 + 0.490481i 0.908458 0.417977i \(-0.137261\pi\)
−0.417977 + 0.908458i \(0.637261\pi\)
\(458\) 2.82843 + 2.82843i 0.132164 + 0.132164i
\(459\) −18.1421 10.1421i −0.846802 0.473394i
\(460\) 20.0711 60.2132i 0.935818 2.80746i
\(461\) 30.4853i 1.41984i 0.704282 + 0.709921i \(0.251269\pi\)
−0.704282 + 0.709921i \(0.748731\pi\)
\(462\) 2.00000 + 2.82843i 0.0930484 + 0.131590i
\(463\) −13.7279 + 13.7279i −0.637991 + 0.637991i −0.950059 0.312069i \(-0.898978\pi\)
0.312069 + 0.950059i \(0.398978\pi\)
\(464\) −14.4853 −0.672462
\(465\) 16.1421 30.1421i 0.748574 1.39781i
\(466\) −28.4853 −1.31956
\(467\) −2.41421 + 2.41421i −0.111716 + 0.111716i −0.760755 0.649039i \(-0.775171\pi\)
0.649039 + 0.760755i \(0.275171\pi\)
\(468\) 29.3137 14.0000i 1.35503 0.647150i
\(469\) 4.20101i 0.193985i
\(470\) 4.24264 + 8.48528i 0.195698 + 0.391397i
\(471\) −18.0711 3.10051i −0.832671 0.142864i
\(472\) −12.4853 12.4853i −0.574682 0.574682i
\(473\) −8.24264 8.24264i −0.378997 0.378997i
\(474\) −21.3137 3.65685i −0.978971 0.167965i
\(475\) 11.3137 + 8.48528i 0.519109 + 0.389331i
\(476\) 12.6863i 0.581475i
\(477\) −3.82843 + 1.82843i −0.175292 + 0.0837179i
\(478\) −26.9706 + 26.9706i −1.23360 + 1.23360i
\(479\) 1.85786 0.0848880 0.0424440 0.999099i \(-0.486486\pi\)
0.0424440 + 0.999099i \(0.486486\pi\)
\(480\) 1.77817 + 5.87868i 0.0811622 + 0.268324i
\(481\) 23.3137 1.06301
\(482\) −48.0416 + 48.0416i −2.18824 + 2.18824i
\(483\) 6.14214 + 8.68629i 0.279477 + 0.395240i
\(484\) 3.82843i 0.174019i
\(485\) −1.97056 0.656854i −0.0894786 0.0298262i
\(486\) 28.2635 24.8492i 1.28206 1.12718i
\(487\) −13.7279 13.7279i −0.622072 0.622072i 0.323989 0.946061i \(-0.394976\pi\)
−0.946061 + 0.323989i \(0.894976\pi\)
\(488\) −32.7279 32.7279i −1.48152 1.48152i
\(489\) −2.65685 + 15.4853i −0.120147 + 0.700269i
\(490\) −32.3345 10.7782i −1.46072 0.486908i
\(491\) 20.0000i 0.902587i 0.892375 + 0.451294i \(0.149037\pi\)
−0.892375 + 0.451294i \(0.850963\pi\)
\(492\) 19.7990 14.0000i 0.892607 0.631169i
\(493\) −13.6569 + 13.6569i −0.615074 + 0.615074i
\(494\) −19.3137 −0.868965
\(495\) 6.65685 0.828427i 0.299203 0.0372350i
\(496\) 26.4853 1.18922
\(497\) −8.48528 + 8.48528i −0.380617 + 0.380617i
\(498\) 24.4853 17.3137i 1.09721 0.775846i
\(499\) 19.1716i 0.858237i −0.903248 0.429119i \(-0.858824\pi\)
0.903248 0.429119i \(-0.141176\pi\)
\(500\) −42.1127 7.65685i −1.88334 0.342425i
\(501\) −4.44365 + 25.8995i −0.198528 + 1.15710i
\(502\) −20.7279 20.7279i −0.925132 0.925132i
\(503\) −15.0711 15.0711i −0.671986 0.671986i 0.286188 0.958174i \(-0.407612\pi\)
−0.958174 + 0.286188i \(0.907612\pi\)
\(504\) 10.3431 + 3.65685i 0.460720 + 0.162889i
\(505\) 12.8284 + 25.6569i 0.570858 + 1.14172i
\(506\) 17.8995i 0.795730i
\(507\) −5.00000 7.07107i −0.222058 0.314037i
\(508\) −5.41421 + 5.41421i −0.240217 + 0.240217i
\(509\) −24.3431 −1.07899 −0.539495 0.841988i \(-0.681385\pi\)
−0.539495 + 0.841988i \(0.681385\pi\)
\(510\) −32.9706 17.6569i −1.45996 0.781859i
\(511\) 0 0
\(512\) −22.0919 + 22.0919i −0.976333 + 0.976333i
\(513\) −14.1421 + 4.00000i −0.624391 + 0.176604i
\(514\) 13.0711i 0.576540i
\(515\) −3.58579 + 10.7574i −0.158009 + 0.474026i
\(516\) −76.1838 13.0711i −3.35380 0.575422i
\(517\) −1.24264 1.24264i −0.0546513 0.0546513i
\(518\) 11.6569 + 11.6569i 0.512173 + 0.512173i
\(519\) −20.4853 3.51472i −0.899204 0.154279i
\(520\) 24.9706 12.4853i 1.09503 0.547516i
\(521\) 16.3431i 0.716006i 0.933720 + 0.358003i \(0.116542\pi\)
−0.933720 + 0.358003i \(0.883458\pi\)
\(522\) −15.0711 31.5563i −0.659643 1.38118i
\(523\) 15.2132 15.2132i 0.665227 0.665227i −0.291380 0.956607i \(-0.594115\pi\)
0.956607 + 0.291380i \(0.0941145\pi\)
\(524\) −4.48528 −0.195940
\(525\) 5.21320 4.92893i 0.227523 0.215116i
\(526\) 34.9706 1.52479
\(527\) 24.9706 24.9706i 1.08773 1.08773i
\(528\) 3.00000 + 4.24264i 0.130558 + 0.184637i
\(529\) 31.9706i 1.39002i
\(530\) −6.82843 + 3.41421i −0.296608 + 0.148304i
\(531\) 4.00000 11.3137i 0.173585 0.490973i
\(532\) −6.34315 6.34315i −0.275010 0.275010i
\(533\) 7.31371 + 7.31371i 0.316792 + 0.316792i
\(534\) 1.17157 6.82843i 0.0506989 0.295495i
\(535\) 8.24264 24.7279i 0.356360 1.06908i
\(536\) 22.3848i 0.966875i
\(537\) −5.85786 + 4.14214i −0.252786 + 0.178746i
\(538\) 23.8995 23.8995i 1.03038 1.03038i
\(539\) 6.31371 0.271951
\(540\) 32.8701 29.9706i 1.41450 1.28973i
\(541\) −33.3137 −1.43227 −0.716134 0.697963i \(-0.754090\pi\)
−0.716134 + 0.697963i \(0.754090\pi\)
\(542\) −14.4853 + 14.4853i −0.622196 + 0.622196i
\(543\) 8.00000 5.65685i 0.343313 0.242759i
\(544\) 6.34315i 0.271960i
\(545\) 8.82843 + 17.6569i 0.378168 + 0.756337i
\(546\) −1.65685 + 9.65685i −0.0709068 + 0.413275i
\(547\) 21.8995 + 21.8995i 0.936355 + 0.936355i 0.998092 0.0617376i \(-0.0196642\pi\)
−0.0617376 + 0.998092i \(0.519664\pi\)
\(548\) 22.3137 + 22.3137i 0.953194 + 0.953194i
\(549\) 10.4853 29.6569i 0.447501 1.26572i
\(550\) 11.9497 1.70711i 0.509539 0.0727913i
\(551\) 13.6569i 0.581802i
\(552\) 32.7279 + 46.2843i 1.39299 + 1.96999i
\(553\) 3.02944 3.02944i 0.128825 0.128825i
\(554\) −5.17157 −0.219719
\(555\) 30.5563 9.24264i 1.29704 0.392328i
\(556\) −24.2843 −1.02988
\(557\) 24.9706 24.9706i 1.05804 1.05804i 0.0598280 0.998209i \(-0.480945\pi\)
0.998209 0.0598280i \(-0.0190552\pi\)
\(558\) 27.5563 + 57.6985i 1.16655 + 2.44257i
\(559\) 32.9706i 1.39451i
\(560\) 5.27208 + 1.75736i 0.222786 + 0.0742620i
\(561\) 6.82843 + 1.17157i 0.288296 + 0.0494638i
\(562\) 28.3848 + 28.3848i 1.19734 + 1.19734i
\(563\) −9.89949 9.89949i −0.417214 0.417214i 0.467028 0.884242i \(-0.345325\pi\)
−0.884242 + 0.467028i \(0.845325\pi\)
\(564\) −11.4853 1.97056i −0.483618 0.0829757i
\(565\) 0.514719 + 0.171573i 0.0216544 + 0.00721813i
\(566\) 3.17157i 0.133311i
\(567\) 0.786797 + 7.41421i 0.0330423 + 0.311368i
\(568\) −45.2132 + 45.2132i −1.89710 + 1.89710i
\(569\) 39.6569 1.66250 0.831251 0.555897i \(-0.187625\pi\)
0.831251 + 0.555897i \(0.187625\pi\)
\(570\) −25.3137 + 7.65685i −1.06027 + 0.320710i
\(571\) 18.3431 0.767637 0.383818 0.923409i \(-0.374609\pi\)
0.383818 + 0.923409i \(0.374609\pi\)
\(572\) −7.65685 + 7.65685i −0.320149 + 0.320149i
\(573\) −11.3137 16.0000i −0.472637 0.668410i
\(574\) 7.31371i 0.305268i
\(575\) 36.6985 5.24264i 1.53043 0.218633i
\(576\) −27.7990 9.82843i −1.15829 0.409518i
\(577\) 17.0000 + 17.0000i 0.707719 + 0.707719i 0.966055 0.258336i \(-0.0831741\pi\)
−0.258336 + 0.966055i \(0.583174\pi\)
\(578\) 1.70711 + 1.70711i 0.0710063 + 0.0710063i
\(579\) −3.31371 + 19.3137i −0.137713 + 0.802650i
\(580\) −18.4853 36.9706i −0.767560 1.53512i
\(581\) 5.94113i 0.246479i
\(582\) 3.17157 2.24264i 0.131466 0.0929604i
\(583\) 1.00000 1.00000i 0.0414158 0.0414158i
\(584\) 0 0
\(585\) 14.9706 + 11.6569i 0.618957 + 0.481952i
\(586\) −26.1421 −1.07992
\(587\) −2.41421 + 2.41421i −0.0996453 + 0.0996453i −0.755172 0.655527i \(-0.772447\pi\)
0.655527 + 0.755172i \(0.272447\pi\)
\(588\) 34.1838 24.1716i 1.40971 0.996819i
\(589\) 24.9706i 1.02889i
\(590\) 6.82843 20.4853i 0.281122 0.843366i
\(591\) 5.85786 34.1421i 0.240960 1.40442i
\(592\) 17.4853 + 17.4853i 0.718641 + 0.718641i
\(593\) −34.1421 34.1421i −1.40205 1.40205i −0.793568 0.608481i \(-0.791779\pi\)
−0.608481 0.793568i \(-0.708221\pi\)
\(594\) −6.12132 + 10.9497i −0.251161 + 0.449274i
\(595\) 6.62742 3.31371i 0.271698 0.135849i
\(596\) 38.2843i 1.56818i
\(597\) −2.48528 3.51472i −0.101716 0.143848i
\(598\) −35.7990 + 35.7990i −1.46393 + 1.46393i
\(599\) −47.4558 −1.93899 −0.969497 0.245105i \(-0.921178\pi\)
−0.969497 + 0.245105i \(0.921178\pi\)
\(600\) 27.7782 26.2635i 1.13404 1.07220i
\(601\) 23.4558 0.956784 0.478392 0.878146i \(-0.341220\pi\)
0.478392 + 0.878146i \(0.341220\pi\)
\(602\) 16.4853 16.4853i 0.671890 0.671890i
\(603\) −13.7279 + 6.55635i −0.559044 + 0.266995i
\(604\) 69.4558i 2.82612i
\(605\) −2.00000 + 1.00000i −0.0813116 + 0.0406558i
\(606\) −52.8701 9.07107i −2.14770 0.368487i
\(607\) −2.10051 2.10051i −0.0852569 0.0852569i 0.663192 0.748449i \(-0.269201\pi\)
−0.748449 + 0.663192i \(0.769201\pi\)
\(608\) 3.17157 + 3.17157i 0.128624 + 0.128624i
\(609\) 6.82843 + 1.17157i 0.276702 + 0.0474745i
\(610\) 17.8995 53.6985i 0.724729 2.17419i
\(611\) 4.97056i 0.201087i
\(612\) 41.4558 19.7990i 1.67575 0.800327i
\(613\) −16.0000 + 16.0000i −0.646234 + 0.646234i −0.952081 0.305847i \(-0.901060\pi\)
0.305847 + 0.952081i \(0.401060\pi\)
\(614\) 26.9706 1.08844
\(615\) 12.4853 + 6.68629i 0.503455 + 0.269617i
\(616\) −3.65685 −0.147339
\(617\) −24.1716 + 24.1716i −0.973111 + 0.973111i −0.999648 0.0265370i \(-0.991552\pi\)
0.0265370 + 0.999648i \(0.491552\pi\)
\(618\) −12.2426 17.3137i −0.492471 0.696459i
\(619\) 23.3137i 0.937057i 0.883448 + 0.468529i \(0.155216\pi\)
−0.883448 + 0.468529i \(0.844784\pi\)
\(620\) 33.7990 + 67.5980i 1.35740 + 2.71480i
\(621\) −18.7990 + 33.6274i −0.754377 + 1.34942i
\(622\) 0.242641 + 0.242641i 0.00972901 + 0.00972901i
\(623\) 0.970563 + 0.970563i 0.0388848 + 0.0388848i
\(624\) −2.48528 + 14.4853i −0.0994909 + 0.579875i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 4.58579i 0.183285i
\(627\) 4.00000 2.82843i 0.159745 0.112956i
\(628\) 28.6569 28.6569i 1.14353 1.14353i
\(629\) 32.9706 1.31462
\(630\) 1.65685 + 13.3137i 0.0660107 + 0.530431i
\(631\) 16.9706 0.675587 0.337794 0.941220i \(-0.390319\pi\)
0.337794 + 0.941220i \(0.390319\pi\)
\(632\) 16.1421 16.1421i 0.642100 0.642100i
\(633\) −17.6569 + 12.4853i −0.701797 + 0.496245i
\(634\) 69.3553i 2.75445i
\(635\) −4.24264 1.41421i −0.168364 0.0561214i
\(636\) 1.58579 9.24264i 0.0628805 0.366495i
\(637\) 12.6274 + 12.6274i 0.500316 + 0.500316i
\(638\) 8.24264 + 8.24264i 0.326329 + 0.326329i
\(639\) −40.9706 14.4853i −1.62077 0.573029i
\(640\) −43.6066 14.5355i −1.72370 0.574567i
\(641\) 12.6274i 0.498753i −0.968407 0.249376i \(-0.919774\pi\)
0.968407 0.249376i \(-0.0802257\pi\)
\(642\) 28.1421 + 39.7990i 1.11068 + 1.57074i
\(643\) −0.757359 + 0.757359i −0.0298673 + 0.0298673i −0.721883 0.692015i \(-0.756723\pi\)
0.692015 + 0.721883i \(0.256723\pi\)
\(644\) −23.5147 −0.926610
\(645\) −13.0711 43.2132i −0.514673 1.70152i
\(646\) −27.3137 −1.07464
\(647\) 13.7279 13.7279i 0.539700 0.539700i −0.383741 0.923441i \(-0.625364\pi\)
0.923441 + 0.383741i \(0.125364\pi\)
\(648\) 4.19239 + 39.5061i 0.164693 + 1.55195i
\(649\) 4.00000i 0.157014i
\(650\) 27.3137 + 20.4853i 1.07133 + 0.803499i
\(651\) −12.4853 2.14214i −0.489337 0.0839569i
\(652\) −24.5563 24.5563i −0.961701 0.961701i
\(653\) 2.65685 + 2.65685i 0.103971 + 0.103971i 0.757179 0.653208i \(-0.226577\pi\)
−0.653208 + 0.757179i \(0.726577\pi\)
\(654\) −36.3848 6.24264i −1.42276 0.244107i
\(655\) −1.17157 2.34315i −0.0457771 0.0915543i
\(656\) 10.9706i 0.428329i
\(657\) 0 0
\(658\) 2.48528 2.48528i 0.0968864 0.0968864i
\(659\) −8.97056 −0.349444 −0.174722 0.984618i \(-0.555903\pi\)
−0.174722 + 0.984618i \(0.555903\pi\)
\(660\) −7.00000 + 13.0711i −0.272475 + 0.508791i
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 17.8995 17.8995i 0.695684 0.695684i
\(663\) 11.3137 + 16.0000i 0.439388 + 0.621389i
\(664\) 31.6569i 1.22852i
\(665\) 1.65685 4.97056i 0.0642501 0.192750i
\(666\) −19.8995 + 56.2843i −0.771090 + 2.18097i
\(667\) 25.3137 + 25.3137i 0.980151 + 0.980151i
\(668\) −41.0711 41.0711i −1.58909 1.58909i
\(669\) −6.02944 + 35.1421i −0.233112 + 1.35867i
\(670\) −24.4853 + 12.2426i −0.945949 + 0.472974i
\(671\) 10.4853i 0.404780i
\(672\) 1.85786 1.31371i 0.0716687 0.0506774i
\(673\) −33.6569 + 33.6569i −1.29738 + 1.29738i −0.367257 + 0.930120i \(0.619703\pi\)
−0.930120 + 0.367257i \(0.880297\pi\)
\(674\) −17.6569 −0.680117
\(675\) 24.2426 + 9.34315i 0.933100 + 0.359618i
\(676\) 19.1421 0.736236
\(677\) −8.34315 + 8.34315i −0.320653 + 0.320653i −0.849018 0.528365i \(-0.822805\pi\)
0.528365 + 0.849018i \(0.322805\pi\)
\(678\) −0.828427 + 0.585786i −0.0318156 + 0.0224970i
\(679\) 0.769553i 0.0295327i
\(680\) 35.3137 17.6569i 1.35422 0.677109i
\(681\) 0.727922 4.24264i 0.0278940 0.162578i
\(682\) −15.0711 15.0711i −0.577101 0.577101i
\(683\) 17.7279 + 17.7279i 0.678340 + 0.678340i 0.959624 0.281284i \(-0.0907604\pi\)
−0.281284 + 0.959624i \(0.590760\pi\)
\(684\) 10.8284 30.6274i 0.414035 1.17107i
\(685\) −5.82843 + 17.4853i −0.222693 + 0.668078i
\(686\) 26.6274i 1.01664i
\(687\) −1.65685 2.34315i −0.0632129 0.0893966i
\(688\) 24.7279 24.7279i 0.942743 0.942743i
\(689\) 4.00000 0.152388
\(690\) −32.7279 + 61.1127i −1.24593 + 2.32652i
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 32.4853 32.4853i 1.23491 1.23491i
\(693\) −1.07107 2.24264i −0.0406865 0.0851909i
\(694\) 61.1127i 2.31981i
\(695\) −6.34315 12.6863i −0.240609 0.481218i
\(696\) 36.3848 + 6.24264i 1.37916 + 0.236627i
\(697\) 10.3431 + 10.3431i 0.391775 + 0.391775i
\(698\) 51.2132 + 51.2132i 1.93845 + 1.93845i
\(699\) 20.1421 + 3.45584i 0.761846 + 0.130712i
\(700\) 2.24264 + 15.6985i 0.0847639 + 0.593347i
\(701\) 21.3137i 0.805008i 0.915418 + 0.402504i \(0.131860\pi\)
−0.915418 + 0.402504i \(0.868140\pi\)
\(702\) −34.1421 + 9.65685i −1.28861 + 0.364474i
\(703\) 16.4853 16.4853i 0.621754 0.621754i
\(704\) 9.82843 0.370423
\(705\) −1.97056 6.51472i −0.0742157 0.245358i
\(706\) −7.41421 −0.279038
\(707\) 7.51472 7.51472i 0.282620 0.282620i
\(708\) 15.3137 + 21.6569i 0.575524 + 0.813914i
\(709\) 6.68629i 0.251109i −0.992087 0.125554i \(-0.959929\pi\)
0.992087 0.125554i \(-0.0400710\pi\)
\(710\) −74.1838 24.7279i −2.78407 0.928022i
\(711\) 14.6274 + 5.17157i 0.548571 + 0.193949i
\(712\) 5.17157 + 5.17157i 0.193813 + 0.193813i
\(713\) −46.2843 46.2843i −1.73336 1.73336i
\(714\) −2.34315 + 13.6569i −0.0876900 + 0.511095i
\(715\) −6.00000 2.00000i −0.224387 0.0747958i
\(716\) 15.8579i 0.592636i
\(717\) 22.3431 15.7990i 0.834420 0.590024i
\(718\) −10.4853 + 10.4853i −0.391307 + 0.391307i
\(719\) −50.7696 −1.89338 −0.946692 0.322139i \(-0.895598\pi\)
−0.946692 + 0.322139i \(0.895598\pi\)
\(720\) 2.48528 + 19.9706i 0.0926210 + 0.744259i
\(721\) 4.20101 0.156454
\(722\) 18.7782 18.7782i 0.698851 0.698851i
\(723\) 39.7990 28.1421i 1.48014 1.04662i
\(724\) 21.6569i 0.804871i
\(725\) 14.4853 19.3137i 0.537970 0.717293i
\(726\) 0.707107 4.12132i 0.0262432 0.152957i
\(727\) −22.2132 22.2132i −0.823842 0.823842i 0.162815 0.986657i \(-0.447943\pi\)
−0.986657 + 0.162815i \(0.947943\pi\)
\(728\) −7.31371 7.31371i −0.271064 0.271064i
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) 0 0
\(731\) 46.6274i 1.72458i
\(732\) 40.1421 + 56.7696i 1.48370 + 2.09826i
\(733\) −35.7990 + 35.7990i −1.32227 + 1.32227i −0.410328 + 0.911938i \(0.634586\pi\)
−0.911938 + 0.410328i \(0.865414\pi\)
\(734\) −71.3553 −2.63377
\(735\) 21.5563 + 11.5442i 0.795118 + 0.425813i
\(736\) 11.7574 0.433382
\(737\) 3.58579 3.58579i 0.132084 0.132084i
\(738\) −23.8995 + 11.4142i −0.879753 + 0.420163i
\(739\) 30.6274i 1.12665i −0.826236 0.563324i \(-0.809522\pi\)
0.826236 0.563324i \(-0.190478\pi\)
\(740\) −22.3137 + 66.9411i −0.820268 + 2.46080i
\(741\) 13.6569 + 2.34315i 0.501697 + 0.0860776i
\(742\) 2.00000 + 2.00000i 0.0734223 + 0.0734223i
\(743\) −22.0416 22.0416i −0.808629 0.808629i 0.175797 0.984426i \(-0.443750\pi\)
−0.984426 + 0.175797i \(0.943750\pi\)
\(744\) −66.5269 11.4142i −2.43899 0.418465i
\(745\) 20.0000 10.0000i 0.732743 0.366372i
\(746\) 69.9411i 2.56073i
\(747\) −19.4142 + 9.27208i −0.710329 + 0.339248i
\(748\) −10.8284 + 10.8284i −0.395927 + 0.395927i
\(749\) −9.65685 −0.352854
\(750\) 43.9203 + 16.0208i 1.60374 + 0.584997i
\(751\) −1.37258 −0.0500863 −0.0250431 0.999686i \(-0.507972\pi\)
−0.0250431 + 0.999686i \(0.507972\pi\)
\(752\) 3.72792 3.72792i 0.135943 0.135943i
\(753\) 12.1421 + 17.1716i 0.442484 + 0.625767i
\(754\) 32.9706i 1.20072i
\(755\) −36.2843 + 18.1421i −1.32052 + 0.660260i
\(756\) −14.3848 8.04163i −0.523169 0.292471i
\(757\) 5.82843 + 5.82843i 0.211838 + 0.211838i 0.805048 0.593210i \(-0.202140\pi\)
−0.593210 + 0.805048i \(0.702140\pi\)
\(758\) 0.242641 + 0.242641i 0.00881311 + 0.00881311i
\(759\) 2.17157 12.6569i 0.0788231 0.459415i
\(760\) 8.82843 26.4853i 0.320241 0.960722i
\(761\) 18.4853i 0.670091i −0.942202 0.335045i \(-0.891248\pi\)
0.942202 0.335045i \(-0.108752\pi\)
\(762\) 6.82843 4.82843i 0.247368 0.174915i
\(763\) 5.17157 5.17157i 0.187224 0.187224i
\(764\) 43.3137 1.56703
\(765\) 21.1716 + 16.4853i 0.765460 + 0.596027i
\(766\) −27.5563 −0.995651
\(767\) −8.00000 + 8.00000i −0.288863 + 0.288863i
\(768\) 42.3848 29.9706i 1.52943 1.08147i
\(769\) 7.37258i 0.265862i −0.991125 0.132931i \(-0.957561\pi\)
0.991125 0.132931i \(-0.0424389\pi\)
\(770\) −2.00000 4.00000i −0.0720750 0.144150i
\(771\) 1.58579 9.24264i 0.0571107 0.332866i
\(772\) −30.6274 30.6274i −1.10230 1.10230i
\(773\) 0.656854 + 0.656854i 0.0236254 + 0.0236254i 0.718821 0.695195i \(-0.244682\pi\)
−0.695195 + 0.718821i \(0.744682\pi\)
\(774\) 79.5980 + 28.1421i 2.86109 + 1.01155i
\(775\) −26.4853 + 35.3137i −0.951379 + 1.26851i
\(776\) 4.10051i 0.147200i
\(777\) −6.82843 9.65685i −0.244968 0.346438i
\(778\) −9.07107 + 9.07107i −0.325214 + 0.325214i
\(779\) 10.3431 0.370582
\(780\) −40.1421 + 12.1421i −1.43732 + 0.434758i
\(781\) 14.4853 0.518324
\(782\) −50.6274 + 50.6274i −1.81043 + 1.81043i
\(783\) 6.82843 + 24.1421i 0.244028 + 0.862770i
\(784\) 18.9411i 0.676469i
\(785\) 22.4558 + 7.48528i 0.801483 + 0.267161i
\(786\) 4.82843 + 0.828427i 0.172224 + 0.0295490i
\(787\) −31.4142 31.4142i −1.11980 1.11980i −0.991771 0.128025i \(-0.959136\pi\)
−0.128025 0.991771i \(-0.540864\pi\)
\(788\) 54.1421 + 54.1421i 1.92873 + 1.92873i
\(789\) −24.7279 4.24264i −0.880337 0.151042i
\(790\) 26.4853 + 8.82843i 0.942304 + 0.314101i
\(791\) 0.201010i 0.00714710i
\(792\) −5.70711 11.9497i −0.202793 0.424616i
\(793\) −20.9706 + 20.9706i −0.744687 + 0.744687i
\(794\) 40.3848 1.43320
\(795\) 5.24264 1.58579i 0.185937 0.0562420i
\(796\) 9.51472 0.337240
\(797\) 7.97056 7.97056i 0.282332 0.282332i −0.551707 0.834038i \(-0.686023\pi\)
0.834038 + 0.551707i \(0.186023\pi\)
\(798\) 5.65685 + 8.00000i 0.200250 + 0.283197i
\(799\) 7.02944i 0.248684i
\(800\) −1.12132 7.84924i −0.0396447 0.277513i
\(801\) −1.65685 + 4.68629i −0.0585421 + 0.165582i
\(802\) −41.5563 41.5563i −1.46741 1.46741i
\(803\) 0 0
\(804\) 5.68629 33.1421i 0.200540 1.16883i
\(805\) −6.14214 12.2843i −0.216482 0.432964i
\(806\) 60.2843i 2.12342i
\(807\) −19.7990 + 14.0000i −0.696957 + 0.492823i
\(808\) 40.0416 40.0416i 1.40866 1.40866i
\(809\) 44.1421 1.55195 0.775977 0.630761i \(-0.217257\pi\)
0.775977 + 0.630761i \(0.217257\pi\)
\(810\) −40.9203 + 26.1924i −1.43779 + 0.920307i
\(811\) −30.3431 −1.06549 −0.532746 0.846275i \(-0.678840\pi\)
−0.532746 + 0.846275i \(0.678840\pi\)
\(812\) −10.8284 + 10.8284i −0.380003 + 0.380003i
\(813\) 12.0000 8.48528i 0.420858 0.297592i
\(814\) 19.8995i 0.697477i
\(815\) 6.41421 19.2426i 0.224680 0.674040i
\(816\) −3.51472 + 20.4853i −0.123040 + 0.717128i
\(817\) −23.3137 23.3137i −0.815643 0.815643i
\(818\) 2.58579 + 2.58579i 0.0904099 + 0.0904099i
\(819\) 2.34315 6.62742i 0.0818761 0.231581i
\(820\) −28.0000 + 14.0000i −0.977802 + 0.488901i
\(821\) 11.6569i 0.406827i 0.979093 + 0.203414i \(0.0652036\pi\)
−0.979093 + 0.203414i \(0.934796\pi\)
\(822\) −19.8995 28.1421i −0.694075 0.981570i
\(823\) −15.5858 + 15.5858i −0.543286 + 0.543286i −0.924491 0.381204i \(-0.875509\pi\)
0.381204 + 0.924491i \(0.375509\pi\)
\(824\) 22.3848 0.779811
\(825\) −8.65685 0.242641i −0.301393 0.00844766i
\(826\) −8.00000 −0.278356
\(827\) −20.0416 + 20.0416i −0.696916 + 0.696916i −0.963744 0.266828i \(-0.914024\pi\)
0.266828 + 0.963744i \(0.414024\pi\)
\(828\) −36.6985 76.8406i −1.27536 2.67040i
\(829\) 22.9706i 0.797801i −0.916994 0.398900i \(-0.869392\pi\)
0.916994 0.398900i \(-0.130608\pi\)
\(830\) −34.6274 + 17.3137i −1.20194 + 0.600968i
\(831\) 3.65685 + 0.627417i 0.126855 + 0.0217649i
\(832\) 19.6569 + 19.6569i 0.681479 + 0.681479i
\(833\) 17.8579 + 17.8579i 0.618738 + 0.618738i
\(834\) 26.1421 + 4.48528i 0.905228 + 0.155313i
\(835\) 10.7279 32.1838i 0.371255 1.11377i
\(836\) 10.8284i 0.374509i
\(837\) −12.4853 44.1421i −0.431554 1.52578i
\(838\) 60.5269 60.5269i 2.09087 2.09087i
\(839\) 10.3431 0.357085 0.178543 0.983932i \(-0.442862\pi\)
0.178543 + 0.983932i \(0.442862\pi\)
\(840\) −12.4853 6.68629i −0.430783 0.230699i
\(841\) −5.68629 −0.196079
\(842\) −6.82843 + 6.82843i −0.235323 + 0.235323i
\(843\) −16.6274 23.5147i −0.572679 0.809890i
\(844\) 47.7990i 1.64531i
\(845\) 5.00000 + 10.0000i 0.172005 + 0.344010i
\(846\) 12.0000 + 4.24264i 0.412568 + 0.145865i
\(847\) 0.585786 + 0.585786i 0.0201279 + 0.0201279i
\(848\) 3.00000 + 3.00000i 0.103020 + 0.103020i
\(849\) 0.384776 2.24264i 0.0132055 0.0769672i
\(850\) 38.6274 + 28.9706i 1.32491 + 0.993682i
\(851\) 61.1127i 2.09492i
\(852\) 78.4264 55.4558i 2.68684 1.89989i
\(853\) −10.1421 + 10.1421i −0.347260 + 0.347260i −0.859088 0.511828i \(-0.828969\pi\)
0.511828 + 0.859088i \(0.328969\pi\)
\(854\) −20.9706 −0.717598
\(855\) 18.8284 2.34315i 0.643919 0.0801339i
\(856\) −51.4558 −1.75872
\(857\) −0.485281 + 0.485281i −0.0165769 + 0.0165769i −0.715347 0.698770i \(-0.753731\pi\)
0.698770 + 0.715347i \(0.253731\pi\)
\(858\) 9.65685 6.82843i 0.329680 0.233119i
\(859\) 36.0000i 1.22830i 0.789188 + 0.614152i \(0.210502\pi\)
−0.789188 + 0.614152i \(0.789498\pi\)
\(860\) 94.6690 + 31.5563i 3.22819 + 1.07606i
\(861\) 0.887302 5.17157i 0.0302392 0.176247i
\(862\) 30.1421 + 30.1421i 1.02665 + 1.02665i
\(863\) 18.5563 + 18.5563i 0.631665 + 0.631665i 0.948486 0.316820i \(-0.102615\pi\)
−0.316820 + 0.948486i \(0.602615\pi\)
\(864\) 7.19239 + 4.02082i 0.244690 + 0.136791i
\(865\) 25.4558 + 8.48528i 0.865525 + 0.288508i
\(866\) 76.1838i 2.58883i
\(867\) −1.00000 1.41421i −0.0339618 0.0480292i
\(868\) 19.7990 19.7990i 0.672022 0.672022i
\(869\) −5.17157 −0.175434
\(870\) 13.0711 + 43.2132i 0.443151 + 1.46506i
\(871\) 14.3431 0.485999
\(872\) 27.5563 27.5563i 0.933176 0.933176i
\(873\) −2.51472 + 1.20101i −0.0851103 + 0.0406480i
\(874\) 50.6274i 1.71250i
\(875\) −7.61522 + 5.27208i −0.257442 + 0.178229i
\(876\) 0 0
\(877\) −38.6274 38.6274i −1.30436 1.30436i −0.925425 0.378930i \(-0.876292\pi\)
−0.378930 0.925425i \(-0.623708\pi\)
\(878\) −26.1421 26.1421i −0.882254 0.882254i
\(879\) 18.4853 + 3.17157i 0.623493 + 0.106974i
\(880\) −3.00000 6.00000i −0.101130 0.202260i
\(881\) 20.9706i 0.706516i 0.935526 + 0.353258i \(0.114926\pi\)
−0.935526 + 0.353258i \(0.885074\pi\)
\(882\) −41.2635 + 19.7071i −1.38941 + 0.663573i
\(883\) −6.41421 + 6.41421i −0.215855 + 0.215855i −0.806749 0.590894i \(-0.798775\pi\)
0.590894 + 0.806749i \(0.298775\pi\)
\(884\) −43.3137 −1.45680
\(885\) −7.31371 + 13.6569i −0.245848 + 0.459070i
\(886\) 99.8406 3.35421
\(887\) 18.2426 18.2426i 0.612528 0.612528i −0.331076 0.943604i \(-0.607412\pi\)
0.943604 + 0.331076i \(0.107412\pi\)
\(888\) −36.3848 51.4558i −1.22099 1.72675i
\(889\) 1.65685i 0.0555691i
\(890\) −2.82843 + 8.48528i −0.0948091 + 0.284427i
\(891\) 5.65685 7.00000i 0.189512 0.234509i
\(892\) −55.7279 55.7279i −1.86591 1.86591i
\(893\) −3.51472 3.51472i −0.117616 0.117616i
\(894\) −7.07107 + 41.2132i −0.236492 + 1.37838i
\(895\) 8.28427 4.14214i 0.276913 0.138456i
\(896\) 17.0294i 0.568914i
\(897\) 29.6569 20.9706i 0.990214 0.700187i
\(898\) 63.1127 63.1127i 2.10610 2.10610i
\(899\) −42.6274 −1.42170
\(900\) −47.7990 + 31.8284i −1.59330 + 1.06095i
\(901\) 5.65685 0.188457
\(902\) 6.24264 6.24264i 0.207857 0.207857i
\(903\) −13.6569 + 9.65685i −0.454472 + 0.321360i
\(904\) 1.07107i 0.0356232i
\(905\) −11.3137 + 5.65685i −0.376080 + 0.188040i
\(906\) 12.8284 74.7696i 0.426196 2.48405i
\(907\) −19.0416 19.0416i −0.632267 0.632267i 0.316369 0.948636i \(-0.397536\pi\)
−0.948636 + 0.316369i \(0.897536\pi\)
\(908\) 6.72792 + 6.72792i 0.223274 + 0.223274i
\(909\) 36.2843 + 12.8284i 1.20347 + 0.425492i
\(910\) 4.00000 12.0000i 0.132599 0.397796i
\(911\) 56.0000i 1.85536i 0.373373 + 0.927681i \(0.378201\pi\)
−0.373373 + 0.927681i \(0.621799\pi\)
\(912\) 8.48528 + 12.0000i 0.280976 + 0.397360i
\(913\) 5.07107 5.07107i 0.167828 0.167828i
\(914\) 35.7990 1.18413
\(915\) −19.1716 + 35.7990i −0.633793 + 1.18348i
\(916\) 6.34315 0.209583
\(917\) −0.686292 + 0.686292i −0.0226633 + 0.0226633i
\(918\) −48.2843 + 13.6569i −1.59362 + 0.450743i
\(919\) 30.6274i 1.01031i 0.863030 + 0.505153i \(0.168564\pi\)
−0.863030 + 0.505153i \(0.831436\pi\)
\(920\) −32.7279 65.4558i −1.07901 2.15802i
\(921\) −19.0711 3.27208i −0.628413 0.107819i
\(922\) 52.0416 + 52.0416i 1.71390 + 1.71390i
\(923\) 28.9706 + 28.9706i 0.953578 + 0.953578i
\(924\) 5.41421 + 0.928932i 0.178115 + 0.0305596i
\(925\) −40.7990 + 5.82843i −1.34146 + 0.191638i
\(926\) 46.8701i 1.54025i
\(927\) 6.55635 + 13.7279i 0.215339 + 0.450884i
\(928\) 5.41421 5.41421i 0.177730 0.177730i
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) −23.8995 79.0122i −0.783695 2.59091i
\(931\) 17.8579 0.585268
\(932\) −31.9411 + 31.9411i −1.04627 + 1.04627i
\(933\) −0.142136 0.201010i −0.00465331 0.00658078i
\(934\) 8.24264i 0.269707i
\(935\) −8.48528 2.82843i −0.277498 0.0924995i
\(936\) 12.4853 35.3137i 0.408094 1.15426i
\(937\) 22.9706 + 22.9706i 0.750416 + 0.750416i 0.974557 0.224141i \(-0.0719577\pi\)
−0.224141 + 0.974557i \(0.571958\pi\)
\(938\) 7.17157 + 7.17157i 0.234160 + 0.234160i
\(939\) −0.556349 + 3.24264i −0.0181558 + 0.105820i
\(940\) 14.2721 + 4.75736i 0.465504 + 0.155168i
\(941\) 25.1127i 0.818651i 0.912389 + 0.409325i \(0.134236\pi\)
−0.912389 + 0.409325i \(0.865764\pi\)
\(942\) −36.1421 + 25.5563i −1.17757 + 0.832671i
\(943\) 19.1716 19.1716i 0.624312 0.624312i
\(944\) −12.0000 −0.390567
\(945\) 0.443651 9.61522i 0.0144320 0.312783i
\(946\) −28.1421 −0.914980
\(947\) 8.75736 8.75736i 0.284576 0.284576i −0.550355 0.834931i \(-0.685508\pi\)
0.834931 + 0.550355i \(0.185508\pi\)
\(948\) −28.0000 + 19.7990i −0.909398 + 0.643041i
\(949\) 0 0
\(950\) 33.7990 4.82843i 1.09658 0.156655i
\(951\) −8.41421 + 49.0416i −0.272850 + 1.59028i
\(952\) −10.3431 10.3431i −0.335223 0.335223i
\(953\) 33.7990 + 33.7990i 1.09486 + 1.09486i 0.995002 + 0.0998546i \(0.0318378\pi\)
0.0998546 + 0.995002i \(0.468162\pi\)
\(954\) −3.41421 + 9.65685i −0.110539 + 0.312652i
\(955\) 11.3137 + 22.6274i 0.366103 + 0.732206i
\(956\) 60.4853i 1.95623i
\(957\) −4.82843 6.82843i −0.156081 0.220732i
\(958\) 3.17157 3.17157i 0.102469 0.102469i
\(959\) 6.82843 0.220501
\(960\) 33.5563 + 17.9706i 1.08303 + 0.579997i
\(961\) 46.9411 1.51423
\(962\) 39.7990 39.7990i 1.28317 1.28317i
\(963\) −15.0711 31.5563i −0.485658 1.01689i
\(964\) 107.740i 3.47008i
\(965\) 8.00000 24.0000i 0.257529 0.772587i
\(966\) 25.3137 + 4.34315i 0.814455 + 0.139738i
\(967\) 1.61522 + 1.61522i 0.0519421 + 0.0519421i 0.732601 0.680659i \(-0.238306\pi\)
−0.680659 + 0.732601i \(0.738306\pi\)
\(968\) 3.12132 + 3.12132i 0.100323 + 0.100323i
\(969\) 19.3137 + 3.31371i 0.620446 + 0.106452i
\(970\) −4.48528 + 2.24264i −0.144014 + 0.0720069i
\(971\) 20.0000i 0.641831i 0.947108 + 0.320915i \(0.103990\pi\)
−0.947108 + 0.320915i \(0.896010\pi\)
\(972\) 3.82843 59.5563i 0.122797 1.91027i
\(973\) −3.71573 + 3.71573i −0.119121 + 0.119121i
\(974\) −46.8701 −1.50181
\(975\) −16.8284 17.7990i −0.538941 0.570024i
\(976\) −31.4558 −1.00688
\(977\) −24.1127 + 24.1127i −0.771434 + 0.771434i −0.978357 0.206924i \(-0.933655\pi\)
0.206924 + 0.978357i \(0.433655\pi\)
\(978\) 21.8995 + 30.9706i 0.700269 + 0.990329i
\(979\) 1.65685i 0.0529533i
\(980\) −48.3431 + 24.1716i −1.54427 + 0.772133i
\(981\) 24.9706 + 8.82843i 0.797249 + 0.281870i
\(982\) 34.1421 + 34.1421i 1.08952 + 1.08952i
\(983\) 1.72792 + 1.72792i 0.0551122 + 0.0551122i 0.734126 0.679014i \(-0.237592\pi\)
−0.679014 + 0.734126i \(0.737592\pi\)
\(984\) 4.72792 27.5563i 0.150721 0.878464i
\(985\) −14.1421 + 42.4264i −0.450606 + 1.35182i
\(986\) 46.6274i 1.48492i
\(987\) −2.05887 + 1.45584i −0.0655347 + 0.0463400i
\(988\) −21.6569 + 21.6569i −0.688996 + 0.688996i
\(989\) −86.4264 −2.74820
\(990\) 9.94975 12.7782i 0.316224 0.406117i
\(991\) 19.1716 0.609005 0.304503 0.952512i \(-0.401510\pi\)
0.304503 + 0.952512i \(0.401510\pi\)
\(992\) −9.89949 + 9.89949i −0.314309 + 0.314309i
\(993\) −14.8284 + 10.4853i −0.470566 + 0.332740i
\(994\) 28.9706i 0.918890i
\(995\) 2.48528 + 4.97056i 0.0787887 + 0.157577i
\(996\) 8.04163 46.8701i 0.254809 1.48513i
\(997\) −36.7696 36.7696i −1.16450 1.16450i −0.983479 0.181025i \(-0.942059\pi\)
−0.181025 0.983479i \(-0.557941\pi\)
\(998\) −32.7279 32.7279i −1.03598 1.03598i
\(999\) 20.8995 37.3848i 0.661231 1.18280i
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 165.2.k.b.122.2 yes 4
3.2 odd 2 165.2.k.a.122.1 yes 4
5.2 odd 4 825.2.k.f.518.2 4
5.3 odd 4 165.2.k.a.23.1 4
5.4 even 2 825.2.k.c.782.1 4
15.2 even 4 825.2.k.c.518.1 4
15.8 even 4 inner 165.2.k.b.23.2 yes 4
15.14 odd 2 825.2.k.f.782.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.k.a.23.1 4 5.3 odd 4
165.2.k.a.122.1 yes 4 3.2 odd 2
165.2.k.b.23.2 yes 4 15.8 even 4 inner
165.2.k.b.122.2 yes 4 1.1 even 1 trivial
825.2.k.c.518.1 4 15.2 even 4
825.2.k.c.782.1 4 5.4 even 2
825.2.k.f.518.2 4 5.2 odd 4
825.2.k.f.782.2 4 15.14 odd 2