Properties

Label 1110.2.i.a.121.1
Level $1110$
Weight $2$
Character 1110.121
Analytic conductor $8.863$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(121,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1110.121
Dual form 1110.2.i.a.211.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +3.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.500000 + 0.866025i) q^{13} -4.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +(2.00000 - 3.46410i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{26} +1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} -3.00000 q^{29} +(0.500000 + 0.866025i) q^{30} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(-2.00000 + 3.46410i) q^{35} +1.00000 q^{36} +(5.50000 + 2.59808i) q^{37} +2.00000 q^{38} +(0.500000 - 0.866025i) q^{39} +(0.500000 + 0.866025i) q^{40} +(2.00000 + 3.46410i) q^{42} +8.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} -1.00000 q^{45} -9.00000 q^{47} +1.00000 q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +3.00000 q^{51} +(0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{55} +(2.00000 + 3.46410i) q^{56} +(-1.00000 + 1.73205i) q^{57} +(1.50000 - 2.59808i) q^{58} +(-1.50000 + 2.59808i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(2.00000 - 3.46410i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +3.00000 q^{66} +(6.50000 + 11.2583i) q^{67} +3.00000 q^{68} +(-2.00000 - 3.46410i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.00000 q^{73} +(-5.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(6.00000 + 10.3923i) q^{77} +(0.500000 + 0.866025i) q^{78} +(8.00000 + 13.8564i) q^{79} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{83} -4.00000 q^{84} -3.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(1.50000 + 2.59808i) q^{87} +3.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-2.00000 + 3.46410i) q^{91} +(2.00000 + 3.46410i) q^{93} +(4.50000 - 7.79423i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +(-4.50000 - 7.79423i) q^{98} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} - 2 q^{10} + 6 q^{11} - q^{12} + q^{13} - 8 q^{14} + q^{15} - q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + q^{20} + 4 q^{21} - 3 q^{22} - q^{24} - q^{25} - 2 q^{26} + 2 q^{27} + 4 q^{28} - 6 q^{29} + q^{30} - 8 q^{31} - q^{32} - 3 q^{33} - 3 q^{34} - 4 q^{35} + 2 q^{36} + 11 q^{37} + 4 q^{38} + q^{39} + q^{40} + 4 q^{42} + 16 q^{43} - 3 q^{44} - 2 q^{45} - 18 q^{47} + 2 q^{48} - 9 q^{49} - q^{50} + 6 q^{51} + q^{52} - q^{54} + 3 q^{55} + 4 q^{56} - 2 q^{57} + 3 q^{58} - 3 q^{59} - 2 q^{60} + 10 q^{61} + 4 q^{62} - 8 q^{63} + 2 q^{64} - q^{65} + 6 q^{66} + 13 q^{67} + 6 q^{68} - 4 q^{70} - 6 q^{71} - q^{72} - 8 q^{73} - 10 q^{74} + 2 q^{75} - 2 q^{76} + 12 q^{77} + q^{78} + 16 q^{79} - 2 q^{80} - q^{81} - 12 q^{83} - 8 q^{84} - 6 q^{85} - 8 q^{86} + 3 q^{87} + 6 q^{88} + 6 q^{89} + q^{90} - 4 q^{91} + 4 q^{93} + 9 q^{94} + 2 q^{95} - q^{96} + 4 q^{97} - 9 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 1.00000 0.408248
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.00000 −0.316228
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 2.00000 3.46410i 0.436436 0.755929i
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.00000 −0.196116
\(27\) 1.00000 0.192450
\(28\) 2.00000 3.46410i 0.377964 0.654654i
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) −2.00000 + 3.46410i −0.338062 + 0.585540i
\(36\) 1.00000 0.166667
\(37\) 5.50000 + 2.59808i 0.904194 + 0.427121i
\(38\) 2.00000 0.324443
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 2.00000 + 3.46410i 0.308607 + 0.534522i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 1.00000 0.144338
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 3.00000 0.420084
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) 2.00000 + 3.46410i 0.267261 + 0.462910i
\(57\) −1.00000 + 1.73205i −0.132453 + 0.229416i
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) −1.00000 −0.129099
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) 3.00000 0.369274
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) −2.00000 3.46410i −0.239046 0.414039i
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −5.00000 + 3.46410i −0.581238 + 0.402694i
\(75\) 1.00000 0.115470
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) 6.00000 + 10.3923i 0.683763 + 1.18431i
\(78\) 0.500000 + 0.866025i 0.0566139 + 0.0980581i
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) −1.00000 −0.111803
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) −4.00000 −0.436436
\(85\) −3.00000 −0.325396
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) 3.00000 0.319801
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0.500000 0.866025i 0.0527046 0.0912871i
\(91\) −2.00000 + 3.46410i −0.209657 + 0.363137i
\(92\) 0 0
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −4.50000 7.79423i −0.454569 0.787336i
\(99\) −1.50000 + 2.59808i −0.150756 + 0.261116i
\(100\) 1.00000 0.100000
\(101\) −9.00000 −0.895533 −0.447767 0.894150i \(-0.647781\pi\)
−0.447767 + 0.894150i \(0.647781\pi\)
\(102\) −1.50000 + 2.59808i −0.148522 + 0.257248i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0.500000 + 0.866025i 0.0490290 + 0.0849208i
\(105\) 4.00000 0.390360
\(106\) 0 0
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) −3.00000 −0.286039
\(111\) −0.500000 6.06218i −0.0474579 0.575396i
\(112\) −4.00000 −0.377964
\(113\) 4.50000 7.79423i 0.423324 0.733219i −0.572938 0.819599i \(-0.694196\pi\)
0.996262 + 0.0863794i \(0.0275297\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 0 0
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) −1.00000 −0.0924500
\(118\) −1.50000 2.59808i −0.138086 0.239172i
\(119\) −12.0000 −1.10004
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) −2.00000 −0.181818
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) 2.00000 3.46410i 0.178174 0.308607i
\(127\) 2.00000 3.46410i 0.177471 0.307389i −0.763542 0.645758i \(-0.776542\pi\)
0.941014 + 0.338368i \(0.109875\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i \(-0.875170\pi\)
0.793028 + 0.609185i \(0.208503\pi\)
\(132\) −1.50000 + 2.59808i −0.130558 + 0.226134i
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) −13.0000 −1.12303
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) 0 0
\(139\) −10.0000 + 17.3205i −0.848189 + 1.46911i 0.0346338 + 0.999400i \(0.488974\pi\)
−0.882823 + 0.469706i \(0.844360\pi\)
\(140\) 4.00000 0.338062
\(141\) 4.50000 + 7.79423i 0.378968 + 0.656392i
\(142\) 6.00000 0.503509
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −1.50000 2.59808i −0.124568 0.215758i
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) 9.00000 0.742307
\(148\) −0.500000 6.06218i −0.0410997 0.498308i
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) −12.0000 −0.966988
\(155\) −2.00000 3.46410i −0.160644 0.278243i
\(156\) −1.00000 −0.0800641
\(157\) 9.50000 16.4545i 0.758183 1.31321i −0.185594 0.982627i \(-0.559421\pi\)
0.943777 0.330584i \(-0.107246\pi\)
\(158\) −16.0000 −1.27289
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −5.50000 + 9.52628i −0.430793 + 0.746156i −0.996942 0.0781474i \(-0.975100\pi\)
0.566149 + 0.824303i \(0.308433\pi\)
\(164\) 0 0
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) −4.50000 7.79423i −0.348220 0.603136i 0.637713 0.770274i \(-0.279881\pi\)
−0.985933 + 0.167139i \(0.946547\pi\)
\(168\) 2.00000 3.46410i 0.154303 0.267261i
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 1.50000 2.59808i 0.115045 0.199263i
\(171\) 2.00000 0.152944
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 6.00000 10.3923i 0.456172 0.790112i −0.542583 0.840002i \(-0.682554\pi\)
0.998755 + 0.0498898i \(0.0158870\pi\)
\(174\) −3.00000 −0.227429
\(175\) −4.00000 −0.302372
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) 3.00000 0.225494
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −13.0000 22.5167i −0.966282 1.67365i −0.706129 0.708083i \(-0.749560\pi\)
−0.260153 0.965567i \(-0.583773\pi\)
\(182\) −2.00000 3.46410i −0.148250 0.256776i
\(183\) 5.00000 8.66025i 0.369611 0.640184i
\(184\) 0 0
\(185\) 0.500000 + 6.06218i 0.0367607 + 0.445700i
\(186\) −4.00000 −0.293294
\(187\) −4.50000 + 7.79423i −0.329073 + 0.569970i
\(188\) 4.50000 + 7.79423i 0.328196 + 0.568453i
\(189\) 2.00000 + 3.46410i 0.145479 + 0.251976i
\(190\) 1.00000 + 1.73205i 0.0725476 + 0.125656i
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 1.00000 0.0716115
\(196\) 9.00000 0.642857
\(197\) 3.00000 5.19615i 0.213741 0.370211i −0.739141 0.673550i \(-0.764768\pi\)
0.952882 + 0.303340i \(0.0981018\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 6.50000 11.2583i 0.458475 0.794101i
\(202\) 4.50000 7.79423i 0.316619 0.548400i
\(203\) −6.00000 10.3923i −0.421117 0.729397i
\(204\) −1.50000 2.59808i −0.105021 0.181902i
\(205\) 0 0
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −3.00000 5.19615i −0.207514 0.359425i
\(210\) −2.00000 + 3.46410i −0.138013 + 0.239046i
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) 0 0
\(215\) 4.00000 + 6.92820i 0.272798 + 0.472500i
\(216\) 1.00000 0.0680414
\(217\) −8.00000 13.8564i −0.543075 0.940634i
\(218\) 2.00000 + 3.46410i 0.135457 + 0.234619i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) −3.00000 −0.201802
\(222\) 5.50000 + 2.59808i 0.369136 + 0.174371i
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 2.00000 3.46410i 0.133631 0.231455i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) 4.50000 + 7.79423i 0.299336 + 0.518464i
\(227\) 12.0000 + 20.7846i 0.796468 + 1.37952i 0.921903 + 0.387421i \(0.126634\pi\)
−0.125435 + 0.992102i \(0.540033\pi\)
\(228\) 2.00000 0.132453
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 6.00000 10.3923i 0.394771 0.683763i
\(232\) −3.00000 −0.196960
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) −4.50000 7.79423i −0.293548 0.508439i
\(236\) 3.00000 0.195283
\(237\) 8.00000 13.8564i 0.519656 0.900070i
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 5.00000 8.66025i 0.320092 0.554416i
\(245\) −9.00000 −0.574989
\(246\) 0 0
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) −4.00000 −0.254000
\(249\) 12.0000 0.760469
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 2.00000 + 3.46410i 0.125988 + 0.218218i
\(253\) 0 0
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) 1.50000 + 2.59808i 0.0939336 + 0.162698i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 8.00000 0.498058
\(259\) 2.00000 + 24.2487i 0.124274 + 1.50674i
\(260\) 1.00000 0.0620174
\(261\) 1.50000 2.59808i 0.0928477 0.160817i
\(262\) −1.50000 2.59808i −0.0926703 0.160510i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) 0 0
\(266\) 4.00000 + 6.92820i 0.245256 + 0.424795i
\(267\) −6.00000 −0.367194
\(268\) 6.50000 11.2583i 0.397051 0.687712i
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i \(-0.765137\pi\)
0.952531 + 0.304443i \(0.0984703\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 4.00000 0.242091
\(274\) −4.50000 + 7.79423i −0.271855 + 0.470867i
\(275\) −1.50000 + 2.59808i −0.0904534 + 0.156670i
\(276\) 0 0
\(277\) −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i \(-0.996047\pi\)
0.489207 0.872167i \(-0.337286\pi\)
\(278\) −10.0000 17.3205i −0.599760 1.03882i
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) −2.00000 + 3.46410i −0.119523 + 0.207020i
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) −9.00000 −0.535942
\(283\) 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i \(0.0243478\pi\)
−0.432360 + 0.901701i \(0.642319\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) −2.00000 −0.118470
\(286\) −3.00000 −0.177394
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 3.00000 0.176166
\(291\) −1.00000 1.73205i −0.0586210 0.101535i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) −4.50000 + 7.79423i −0.262445 + 0.454569i
\(295\) −3.00000 −0.174667
\(296\) 5.50000 + 2.59808i 0.319681 + 0.151010i
\(297\) 3.00000 0.174078
\(298\) 7.50000 12.9904i 0.434463 0.752513i
\(299\) 0 0
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 16.0000 + 27.7128i 0.922225 + 1.59734i
\(302\) 8.00000 0.460348
\(303\) 4.50000 + 7.79423i 0.258518 + 0.447767i
\(304\) 2.00000 0.114708
\(305\) −5.00000 + 8.66025i −0.286299 + 0.495885i
\(306\) 3.00000 0.171499
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 6.00000 10.3923i 0.341882 0.592157i
\(309\) −7.00000 12.1244i −0.398216 0.689730i
\(310\) 4.00000 0.227185
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0.500000 0.866025i 0.0283069 0.0490290i
\(313\) −7.00000 + 12.1244i −0.395663 + 0.685309i −0.993186 0.116543i \(-0.962819\pi\)
0.597522 + 0.801852i \(0.296152\pi\)
\(314\) 9.50000 + 16.4545i 0.536116 + 0.928580i
\(315\) −2.00000 3.46410i −0.112687 0.195180i
\(316\) 8.00000 13.8564i 0.450035 0.779484i
\(317\) 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) 0 0
\(319\) −9.00000 −0.503903
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −1.00000 −0.0554700
\(326\) −5.50000 9.52628i −0.304617 0.527612i
\(327\) −4.00000 −0.221201
\(328\) 0 0
\(329\) −18.0000 31.1769i −0.992372 1.71884i
\(330\) 1.50000 + 2.59808i 0.0825723 + 0.143019i
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 12.0000 0.658586
\(333\) −5.00000 + 3.46410i −0.273998 + 0.189832i
\(334\) 9.00000 0.492458
\(335\) −6.50000 + 11.2583i −0.355133 + 0.615108i
\(336\) 2.00000 + 3.46410i 0.109109 + 0.188982i
\(337\) −10.0000 17.3205i −0.544735 0.943508i −0.998624 0.0524499i \(-0.983297\pi\)
0.453889 0.891058i \(-0.350036\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) −9.00000 −0.488813
\(340\) 1.50000 + 2.59808i 0.0813489 + 0.140900i
\(341\) −12.0000 −0.649836
\(342\) −1.00000 + 1.73205i −0.0540738 + 0.0936586i
\(343\) −8.00000 −0.431959
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 6.00000 + 10.3923i 0.322562 + 0.558694i
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 14.0000 24.2487i 0.749403 1.29800i −0.198706 0.980059i \(-0.563674\pi\)
0.948109 0.317945i \(-0.102993\pi\)
\(350\) 2.00000 3.46410i 0.106904 0.185164i
\(351\) 0.500000 + 0.866025i 0.0266880 + 0.0462250i
\(352\) −1.50000 2.59808i −0.0799503 0.138478i
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) −1.50000 + 2.59808i −0.0797241 + 0.138086i
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) −6.00000 −0.317999
\(357\) 6.00000 + 10.3923i 0.317554 + 0.550019i
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 26.0000 1.36653
\(363\) 1.00000 + 1.73205i 0.0524864 + 0.0909091i
\(364\) 4.00000 0.209657
\(365\) −2.00000 3.46410i −0.104685 0.181319i
\(366\) 5.00000 + 8.66025i 0.261354 + 0.452679i
\(367\) −10.0000 17.3205i −0.521996 0.904123i −0.999673 0.0255875i \(-0.991854\pi\)
0.477677 0.878536i \(-0.341479\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −5.50000 2.59808i −0.285931 0.135068i
\(371\) 0 0
\(372\) 2.00000 3.46410i 0.103695 0.179605i
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) −4.50000 7.79423i −0.232689 0.403030i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) −9.00000 −0.464140
\(377\) −1.50000 2.59808i −0.0772539 0.133808i
\(378\) −4.00000 −0.205738
\(379\) 8.00000 13.8564i 0.410932 0.711756i −0.584060 0.811711i \(-0.698537\pi\)
0.994992 + 0.0999550i \(0.0318699\pi\)
\(380\) −2.00000 −0.102598
\(381\) −4.00000 −0.204926
\(382\) −12.0000 + 20.7846i −0.613973 + 1.06343i
\(383\) 4.50000 + 7.79423i 0.229939 + 0.398266i 0.957790 0.287469i \(-0.0928139\pi\)
−0.727851 + 0.685736i \(0.759481\pi\)
\(384\) 1.00000 0.0510310
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) −4.00000 + 6.92820i −0.203595 + 0.352636i
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) −1.00000 1.73205i −0.0507673 0.0879316i
\(389\) −15.0000 25.9808i −0.760530 1.31728i −0.942578 0.333987i \(-0.891606\pi\)
0.182047 0.983290i \(-0.441728\pi\)
\(390\) −0.500000 + 0.866025i −0.0253185 + 0.0438529i
\(391\) 0 0
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) 3.00000 0.151330
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) −8.00000 + 13.8564i −0.402524 + 0.697191i
\(396\) 3.00000 0.150756
\(397\) −25.0000 −1.25471 −0.627357 0.778732i \(-0.715863\pi\)
−0.627357 + 0.778732i \(0.715863\pi\)
\(398\) 3.50000 6.06218i 0.175439 0.303870i
\(399\) −8.00000 −0.400501
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 6.50000 + 11.2583i 0.324191 + 0.561514i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 4.50000 + 7.79423i 0.223883 + 0.387777i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 12.0000 0.595550
\(407\) 16.5000 + 7.79423i 0.817875 + 0.386346i
\(408\) 3.00000 0.148522
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 0 0
\(411\) −4.50000 7.79423i −0.221969 0.384461i
\(412\) −7.00000 12.1244i −0.344865 0.597324i
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 20.0000 0.979404
\(418\) 6.00000 0.293470
\(419\) 18.0000 31.1769i 0.879358 1.52309i 0.0273103 0.999627i \(-0.491306\pi\)
0.852047 0.523465i \(-0.175361\pi\)
\(420\) −2.00000 3.46410i −0.0975900 0.169031i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 0 0
\(425\) −1.50000 2.59808i −0.0727607 0.126025i
\(426\) −3.00000 5.19615i −0.145350 0.251754i
\(427\) −20.0000 + 34.6410i −0.967868 + 1.67640i
\(428\) 0 0
\(429\) 1.50000 2.59808i 0.0724207 0.125436i
\(430\) −8.00000 −0.385794
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 16.0000 0.768025
\(435\) −1.50000 + 2.59808i −0.0719195 + 0.124568i
\(436\) −4.00000 −0.191565
\(437\) 0 0
\(438\) −4.00000 −0.191127
\(439\) 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 1.50000 + 2.59808i 0.0715097 + 0.123858i
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) 1.50000 2.59808i 0.0713477 0.123578i
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) −5.00000 + 3.46410i −0.237289 + 0.164399i
\(445\) 6.00000 0.284427
\(446\) −10.0000 + 17.3205i −0.473514 + 0.820150i
\(447\) 7.50000 + 12.9904i 0.354738 + 0.614424i
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) 18.0000 + 31.1769i 0.849473 + 1.47133i 0.881680 + 0.471848i \(0.156413\pi\)
−0.0322072 + 0.999481i \(0.510254\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −9.00000 −0.423324
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) −24.0000 −1.12638
\(455\) −4.00000 −0.187523
\(456\) −1.00000 + 1.73205i −0.0468293 + 0.0811107i
\(457\) −4.00000 6.92820i −0.187112 0.324088i 0.757174 0.653213i \(-0.226579\pi\)
−0.944286 + 0.329125i \(0.893246\pi\)
\(458\) 14.0000 0.654177
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) 0 0
\(461\) 7.50000 12.9904i 0.349310 0.605022i −0.636817 0.771015i \(-0.719749\pi\)
0.986127 + 0.165992i \(0.0530827\pi\)
\(462\) 6.00000 + 10.3923i 0.279145 + 0.483494i
\(463\) 11.0000 + 19.0526i 0.511213 + 0.885448i 0.999916 + 0.0129968i \(0.00413714\pi\)
−0.488702 + 0.872451i \(0.662530\pi\)
\(464\) 1.50000 2.59808i 0.0696358 0.120613i
\(465\) −2.00000 + 3.46410i −0.0927478 + 0.160644i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0.500000 + 0.866025i 0.0231125 + 0.0400320i
\(469\) −26.0000 + 45.0333i −1.20057 + 2.07945i
\(470\) 9.00000 0.415139
\(471\) −19.0000 −0.875474
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) 24.0000 1.10352
\(474\) 8.00000 + 13.8564i 0.367452 + 0.636446i
\(475\) 2.00000 0.0917663
\(476\) 6.00000 + 10.3923i 0.275010 + 0.476331i
\(477\) 0 0
\(478\) 0 0
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 0.500000 + 6.06218i 0.0227980 + 0.276412i
\(482\) 5.00000 0.227744
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 11.0000 0.497437
\(490\) 4.50000 7.79423i 0.203289 0.352107i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) 4.50000 7.79423i 0.202670 0.351034i
\(494\) 1.00000 + 1.73205i 0.0449921 + 0.0779287i
\(495\) −3.00000 −0.134840
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) 12.0000 20.7846i 0.538274 0.932317i
\(498\) −6.00000 + 10.3923i −0.268866 + 0.465690i
\(499\) 11.0000 + 19.0526i 0.492428 + 0.852910i 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) −4.50000 + 7.79423i −0.201045 + 0.348220i
\(502\) −4.50000 + 7.79423i −0.200845 + 0.347873i
\(503\) 10.5000 18.1865i 0.468172 0.810897i −0.531167 0.847267i \(-0.678246\pi\)
0.999338 + 0.0363700i \(0.0115795\pi\)
\(504\) −4.00000 −0.178174
\(505\) −4.50000 7.79423i −0.200247 0.346839i
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) −4.00000 −0.177471
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) −3.00000 −0.132842
\(511\) −8.00000 13.8564i −0.353899 0.612971i
\(512\) 1.00000 0.0441942
\(513\) −1.00000 1.73205i −0.0441511 0.0764719i
\(514\) −1.50000 2.59808i −0.0661622 0.114596i
\(515\) 7.00000 + 12.1244i 0.308457 + 0.534263i
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) −27.0000 −1.18746
\(518\) −22.0000 10.3923i −0.966625 0.456612i
\(519\) −12.0000 −0.526742
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) 3.00000 0.131056
\(525\) 2.00000 + 3.46410i 0.0872872 + 0.151186i
\(526\) 0 0
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 3.00000 0.130558
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) −1.50000 2.59808i −0.0650945 0.112747i
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 3.00000 5.19615i 0.129823 0.224860i
\(535\) 0 0
\(536\) 6.50000 + 11.2583i 0.280757 + 0.486286i
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 3.00000 5.19615i 0.129339 0.224022i
\(539\) −13.5000 + 23.3827i −0.581486 + 1.00716i
\(540\) 0.500000 0.866025i 0.0215166 0.0372678i
\(541\) 26.0000 1.11783 0.558914 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) 3.50000 + 6.06218i 0.150338 + 0.260393i
\(543\) −13.0000 + 22.5167i −0.557883 + 0.966282i
\(544\) 3.00000 0.128624
\(545\) 4.00000 0.171341
\(546\) −2.00000 + 3.46410i −0.0855921 + 0.148250i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) −10.0000 −0.426790
\(550\) −1.50000 2.59808i −0.0639602 0.110782i
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 0 0
\(553\) −32.0000 + 55.4256i −1.36078 + 2.35694i
\(554\) 17.0000 0.722261
\(555\) 5.00000 3.46410i 0.212238 0.147043i
\(556\) 20.0000 0.848189
\(557\) −3.00000 + 5.19615i −0.127114 + 0.220168i −0.922557 0.385860i \(-0.873905\pi\)
0.795443 + 0.606028i \(0.207238\pi\)
\(558\) 2.00000 + 3.46410i 0.0846668 + 0.146647i
\(559\) 4.00000 + 6.92820i 0.169182 + 0.293032i
\(560\) −2.00000 3.46410i −0.0845154 0.146385i
\(561\) 9.00000 0.379980
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) −42.0000 −1.77009 −0.885044 0.465506i \(-0.845872\pi\)
−0.885044 + 0.465506i \(0.845872\pi\)
\(564\) 4.50000 7.79423i 0.189484 0.328196i
\(565\) 9.00000 0.378633
\(566\) −19.0000 −0.798630
\(567\) 2.00000 3.46410i 0.0839921 0.145479i
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 1.00000 1.73205i 0.0418854 0.0725476i
\(571\) −1.00000 + 1.73205i −0.0418487 + 0.0724841i −0.886191 0.463320i \(-0.846658\pi\)
0.844342 + 0.535804i \(0.179991\pi\)
\(572\) 1.50000 2.59808i 0.0627182 0.108631i
\(573\) −12.0000 20.7846i −0.501307 0.868290i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) −8.00000 −0.332756
\(579\) −4.00000 6.92820i −0.166234 0.287926i
\(580\) −1.50000 + 2.59808i −0.0622841 + 0.107879i
\(581\) −48.0000 −1.99138
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) −4.00000 −0.165521
\(585\) −0.500000 0.866025i −0.0206725 0.0358057i
\(586\) −6.00000 −0.247858
\(587\) −12.0000 20.7846i −0.495293 0.857873i 0.504692 0.863299i \(-0.331606\pi\)
−0.999985 + 0.00542667i \(0.998273\pi\)
\(588\) −4.50000 7.79423i −0.185577 0.321429i
\(589\) 4.00000 + 6.92820i 0.164817 + 0.285472i
\(590\) 1.50000 2.59808i 0.0617540 0.106961i
\(591\) −6.00000 −0.246807
\(592\) −5.00000 + 3.46410i −0.205499 + 0.142374i
\(593\) 39.0000 1.60154 0.800769 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) −6.00000 10.3923i −0.245976 0.426043i
\(596\) 7.50000 + 12.9904i 0.307212 + 0.532107i
\(597\) 3.50000 + 6.06218i 0.143245 + 0.248108i
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 1.00000 0.0408248
\(601\) 21.5000 37.2391i 0.877003 1.51901i 0.0223900 0.999749i \(-0.492872\pi\)
0.854613 0.519265i \(-0.173794\pi\)
\(602\) −32.0000 −1.30422
\(603\) −13.0000 −0.529401
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) −9.00000 −0.365600
\(607\) 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i \(-0.686012\pi\)
0.998154 + 0.0607380i \(0.0193454\pi\)
\(608\) −1.00000 + 1.73205i −0.0405554 + 0.0702439i
\(609\) −6.00000 + 10.3923i −0.243132 + 0.421117i
\(610\) −5.00000 8.66025i −0.202444 0.350643i
\(611\) −4.50000 7.79423i −0.182051 0.315321i
\(612\) −1.50000 + 2.59808i −0.0606339 + 0.105021i
\(613\) −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 0 0
\(616\) 6.00000 + 10.3923i 0.241747 + 0.418718i
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 14.0000 0.563163
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) 0 0
\(622\) 3.00000 + 5.19615i 0.120289 + 0.208347i
\(623\) 24.0000 0.961540
\(624\) 0.500000 + 0.866025i 0.0200160 + 0.0346688i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −7.00000 12.1244i −0.279776 0.484587i
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) −19.0000 −0.758183
\(629\) −15.0000 + 10.3923i −0.598089 + 0.414368i
\(630\) 4.00000 0.159364
\(631\) 18.5000 32.0429i 0.736473 1.27561i −0.217601 0.976038i \(-0.569823\pi\)
0.954074 0.299571i \(-0.0968437\pi\)
\(632\) 8.00000 + 13.8564i 0.318223 + 0.551178i
\(633\) −4.00000 6.92820i −0.158986 0.275371i
\(634\) 12.0000 + 20.7846i 0.476581 + 0.825462i
\(635\) 4.00000 0.158735
\(636\) 0 0
\(637\) −9.00000 −0.356593
\(638\) 4.50000 7.79423i 0.178157 0.308576i
\(639\) 6.00000 0.237356
\(640\) −1.00000 −0.0395285
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 0 0
\(643\) −25.0000 −0.985904 −0.492952 0.870057i \(-0.664082\pi\)
−0.492952 + 0.870057i \(0.664082\pi\)
\(644\) 0 0
\(645\) 4.00000 6.92820i 0.157500 0.272798i
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) 1.50000 + 2.59808i 0.0589711 + 0.102141i 0.894004 0.448059i \(-0.147885\pi\)
−0.835033 + 0.550200i \(0.814551\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −4.50000 + 7.79423i −0.176640 + 0.305950i
\(650\) 0.500000 0.866025i 0.0196116 0.0339683i
\(651\) −8.00000 + 13.8564i −0.313545 + 0.543075i
\(652\) 11.0000 0.430793
\(653\) 24.0000 + 41.5692i 0.939193 + 1.62673i 0.766982 + 0.641669i \(0.221758\pi\)
0.172211 + 0.985060i \(0.444909\pi\)
\(654\) 2.00000 3.46410i 0.0782062 0.135457i
\(655\) −3.00000 −0.117220
\(656\) 0 0
\(657\) 2.00000 3.46410i 0.0780274 0.135147i
\(658\) 36.0000 1.40343
\(659\) 13.5000 + 23.3827i 0.525885 + 0.910860i 0.999545 + 0.0301523i \(0.00959924\pi\)
−0.473660 + 0.880708i \(0.657067\pi\)
\(660\) −3.00000 −0.116775
\(661\) 2.00000 + 3.46410i 0.0777910 + 0.134738i 0.902297 0.431116i \(-0.141880\pi\)
−0.824506 + 0.565854i \(0.808547\pi\)
\(662\) 5.00000 + 8.66025i 0.194331 + 0.336590i
\(663\) 1.50000 + 2.59808i 0.0582552 + 0.100901i
\(664\) −6.00000 + 10.3923i −0.232845 + 0.403300i
\(665\) 8.00000 0.310227
\(666\) −0.500000 6.06218i −0.0193746 0.234905i
\(667\) 0 0
\(668\) −4.50000 + 7.79423i −0.174110 + 0.301568i
\(669\) −10.0000 17.3205i −0.386622 0.669650i
\(670\) −6.50000 11.2583i −0.251117 0.434947i
\(671\) 15.0000 + 25.9808i 0.579069 + 1.00298i
\(672\) −4.00000 −0.154303
\(673\) −4.00000 6.92820i −0.154189 0.267063i 0.778575 0.627552i \(-0.215943\pi\)
−0.932763 + 0.360489i \(0.882610\pi\)
\(674\) 20.0000 0.770371
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −12.0000 −0.461538
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 4.50000 7.79423i 0.172821 0.299336i
\(679\) 4.00000 + 6.92820i 0.153506 + 0.265880i
\(680\) −3.00000 −0.115045
\(681\) 12.0000 20.7846i 0.459841 0.796468i
\(682\) 6.00000 10.3923i 0.229752 0.397942i
\(683\) −9.00000 + 15.5885i −0.344375 + 0.596476i −0.985240 0.171178i \(-0.945243\pi\)
0.640865 + 0.767654i \(0.278576\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) 4.50000 + 7.79423i 0.171936 + 0.297802i
\(686\) 4.00000 6.92820i 0.152721 0.264520i
\(687\) −7.00000 + 12.1244i −0.267067 + 0.462573i
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 0 0
\(690\) 0 0
\(691\) 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i \(-0.772417\pi\)
0.945319 + 0.326146i \(0.105750\pi\)
\(692\) −12.0000 −0.456172
\(693\) −12.0000 −0.455842
\(694\) −3.00000 + 5.19615i −0.113878 + 0.197243i
\(695\) −20.0000 −0.758643
\(696\) 1.50000 + 2.59808i 0.0568574 + 0.0984798i
\(697\) 0 0
\(698\) 14.0000 + 24.2487i 0.529908 + 0.917827i
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) 2.00000 + 3.46410i 0.0755929 + 0.130931i
\(701\) 1.50000 2.59808i 0.0566542 0.0981280i −0.836307 0.548261i \(-0.815290\pi\)
0.892962 + 0.450133i \(0.148623\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −1.00000 12.1244i −0.0377157 0.457279i
\(704\) 3.00000 0.113067
\(705\) −4.50000 + 7.79423i −0.169480 + 0.293548i
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) −18.0000 31.1769i −0.676960 1.17253i
\(708\) −1.50000 2.59808i −0.0563735 0.0976417i
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 3.00000 + 5.19615i 0.112588 + 0.195008i
\(711\) −16.0000 −0.600047
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 0 0
\(714\) −12.0000 −0.449089
\(715\) −1.50000 + 2.59808i −0.0560968 + 0.0971625i
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) −24.0000 + 41.5692i −0.895049 + 1.55027i −0.0613050 + 0.998119i \(0.519526\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(720\) 0.500000 0.866025i 0.0186339 0.0322749i
\(721\) 28.0000 + 48.4974i 1.04277 + 1.80614i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) −2.50000 + 4.33013i −0.0929760 + 0.161039i
\(724\) −13.0000 + 22.5167i −0.483141 + 0.836825i
\(725\) 1.50000 2.59808i 0.0557086 0.0964901i
\(726\) −2.00000 −0.0742270
\(727\) 2.00000 + 3.46410i 0.0741759 + 0.128476i 0.900728 0.434384i \(-0.143034\pi\)
−0.826552 + 0.562861i \(0.809701\pi\)
\(728\) −2.00000 + 3.46410i −0.0741249 + 0.128388i
\(729\) 1.00000 0.0370370
\(730\) 4.00000 0.148047
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) −10.0000 −0.369611
\(733\) −2.50000 4.33013i −0.0923396 0.159937i 0.816156 0.577832i \(-0.196101\pi\)
−0.908495 + 0.417895i \(0.862768\pi\)
\(734\) 20.0000 0.738213
\(735\) 4.50000 + 7.79423i 0.165985 + 0.287494i
\(736\) 0 0
\(737\) 19.5000 + 33.7750i 0.718292 + 1.24412i
\(738\) 0 0
\(739\) 38.0000 1.39785 0.698926 0.715194i \(-0.253662\pi\)
0.698926 + 0.715194i \(0.253662\pi\)
\(740\) 5.00000 3.46410i 0.183804 0.127343i
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 25.5000 + 44.1673i 0.935504 + 1.62034i 0.773732 + 0.633513i \(0.218388\pi\)
0.161772 + 0.986828i \(0.448279\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) −7.50000 12.9904i −0.274779 0.475931i
\(746\) −22.0000 −0.805477
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −43.0000 −1.56909 −0.784546 0.620070i \(-0.787104\pi\)
−0.784546 + 0.620070i \(0.787104\pi\)
\(752\) 4.50000 7.79423i 0.164098 0.284226i
\(753\) −4.50000 7.79423i −0.163989 0.284037i
\(754\) 3.00000 0.109254
\(755\) 4.00000 6.92820i 0.145575 0.252143i
\(756\) 2.00000 3.46410i 0.0727393 0.125988i
\(757\) 11.0000 19.0526i 0.399802 0.692477i −0.593899 0.804539i \(-0.702412\pi\)
0.993701 + 0.112062i \(0.0357456\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) 0 0
\(760\) 1.00000 1.73205i 0.0362738 0.0628281i
\(761\) 3.00000 5.19615i 0.108750 0.188360i −0.806514 0.591215i \(-0.798649\pi\)
0.915264 + 0.402854i \(0.131982\pi\)
\(762\) 2.00000 3.46410i 0.0724524 0.125491i
\(763\) 16.0000 0.579239
\(764\) −12.0000 20.7846i −0.434145 0.751961i
\(765\) 1.50000 2.59808i 0.0542326 0.0939336i
\(766\) −9.00000 −0.325183
\(767\) −3.00000 −0.108324
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −13.0000 −0.468792 −0.234396 0.972141i \(-0.575311\pi\)
−0.234396 + 0.972141i \(0.575311\pi\)
\(770\) −6.00000 10.3923i −0.216225 0.374513i
\(771\) 3.00000 0.108042
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) −6.00000 10.3923i −0.215805 0.373785i 0.737716 0.675111i \(-0.235904\pi\)
−0.953521 + 0.301326i \(0.902571\pi\)
\(774\) −4.00000 6.92820i