Properties

Label 1078.2.e.n.177.1
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
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] = [1078,2,Mod(67,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not 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: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.n.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61803 - 2.80252i) q^{5} +3.23607 q^{6} +1.00000 q^{8} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.61803 - 2.80252i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.61803 - 2.80252i) q^{5} +3.23607 q^{6} +1.00000 q^{8} +(-3.73607 + 6.47106i) q^{9} +(1.61803 + 2.80252i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.61803 + 2.80252i) q^{12} -1.23607 q^{13} -10.4721 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.23607 - 5.60503i) q^{17} +(-3.73607 - 6.47106i) q^{18} +(-1.38197 + 2.39364i) q^{19} -3.23607 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-1.61803 - 2.80252i) q^{24} +(-2.73607 - 4.73901i) q^{25} +(0.618034 - 1.07047i) q^{26} +14.4721 q^{27} -4.47214 q^{29} +(5.23607 - 9.06914i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.61803 + 2.80252i) q^{33} +6.47214 q^{34} +7.47214 q^{36} +(5.47214 - 9.47802i) q^{37} +(-1.38197 - 2.39364i) q^{38} +(2.00000 + 3.46410i) q^{39} +(1.61803 - 2.80252i) q^{40} -6.47214 q^{41} -1.52786 q^{43} +(-0.500000 + 0.866025i) q^{44} +(12.0902 + 20.9408i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(-1.00000 + 1.73205i) q^{47} +3.23607 q^{48} +5.47214 q^{50} +(-10.4721 + 18.1383i) q^{51} +(0.618034 + 1.07047i) q^{52} +(0.236068 + 0.408882i) q^{53} +(-7.23607 + 12.5332i) q^{54} -3.23607 q^{55} +8.94427 q^{57} +(2.23607 - 3.87298i) q^{58} +(3.61803 + 6.26662i) q^{59} +(5.23607 + 9.06914i) q^{60} +(-2.61803 + 4.53457i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-1.61803 - 2.80252i) q^{66} +(7.70820 + 13.3510i) q^{67} +(-3.23607 + 5.60503i) q^{68} +12.9443 q^{69} -2.47214 q^{71} +(-3.73607 + 6.47106i) q^{72} +(-2.47214 - 4.28187i) q^{73} +(5.47214 + 9.47802i) q^{74} +(-8.85410 + 15.3358i) q^{75} +2.76393 q^{76} -4.00000 q^{78} +(1.61803 + 2.80252i) q^{80} +(-12.2082 - 21.1452i) q^{81} +(3.23607 - 5.60503i) q^{82} -10.1803 q^{83} -20.9443 q^{85} +(0.763932 - 1.32317i) q^{86} +(7.23607 + 12.5332i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(5.00000 - 8.66025i) q^{89} -24.1803 q^{90} +4.00000 q^{92} +(3.23607 - 5.60503i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(4.47214 + 7.74597i) q^{95} +(-1.61803 + 2.80252i) q^{96} -3.52786 q^{97} +7.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{8} - 6 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 24 q^{15} - 2 q^{16} - 4 q^{17} - 6 q^{18} - 10 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 40 q^{27} + 12 q^{30} + 4 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 12 q^{36} + 4 q^{37} - 10 q^{38} + 8 q^{39} + 2 q^{40} - 8 q^{41} - 24 q^{43} - 2 q^{44} + 26 q^{45} - 8 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} - 24 q^{51} - 2 q^{52} - 8 q^{53} - 20 q^{54} - 4 q^{55} + 10 q^{59} + 12 q^{60} - 6 q^{61} - 8 q^{62} + 4 q^{64} - 8 q^{65} - 2 q^{66} + 4 q^{67} - 4 q^{68} + 16 q^{69} + 8 q^{71} - 6 q^{72} + 8 q^{73} + 4 q^{74} - 22 q^{75} + 20 q^{76} - 16 q^{78} + 2 q^{80} - 22 q^{81} + 4 q^{82} + 4 q^{83} - 48 q^{85} + 12 q^{86} + 20 q^{87} - 2 q^{88} + 20 q^{89} - 52 q^{90} + 16 q^{92} + 4 q^{93} - 4 q^{94} - 2 q^{96} - 32 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −1.61803 2.80252i −0.934172 1.61803i −0.776103 0.630606i \(-0.782806\pi\)
−0.158069 0.987428i \(-0.550527\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.61803 2.80252i 0.723607 1.25332i −0.235938 0.971768i \(-0.575816\pi\)
0.959545 0.281556i \(-0.0908504\pi\)
\(6\) 3.23607 1.32112
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −3.73607 + 6.47106i −1.24536 + 2.15702i
\(10\) 1.61803 + 2.80252i 0.511667 + 0.886234i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −1.61803 + 2.80252i −0.467086 + 0.809017i
\(13\) −1.23607 −0.342824 −0.171412 0.985199i \(-0.554833\pi\)
−0.171412 + 0.985199i \(0.554833\pi\)
\(14\) 0 0
\(15\) −10.4721 −2.70389
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.23607 5.60503i −0.784862 1.35942i −0.929082 0.369875i \(-0.879401\pi\)
0.144220 0.989546i \(-0.453933\pi\)
\(18\) −3.73607 6.47106i −0.880600 1.52524i
\(19\) −1.38197 + 2.39364i −0.317045 + 0.549138i −0.979870 0.199636i \(-0.936024\pi\)
0.662825 + 0.748774i \(0.269357\pi\)
\(20\) −3.23607 −0.723607
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) −1.61803 2.80252i −0.330280 0.572061i
\(25\) −2.73607 4.73901i −0.547214 0.947802i
\(26\) 0.618034 1.07047i 0.121206 0.209936i
\(27\) 14.4721 2.78516
\(28\) 0 0
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 5.23607 9.06914i 0.955971 1.65579i
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.61803 + 2.80252i −0.281664 + 0.487856i
\(34\) 6.47214 1.10996
\(35\) 0 0
\(36\) 7.47214 1.24536
\(37\) 5.47214 9.47802i 0.899614 1.55818i 0.0716249 0.997432i \(-0.477182\pi\)
0.827989 0.560745i \(-0.189485\pi\)
\(38\) −1.38197 2.39364i −0.224184 0.388299i
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) 1.61803 2.80252i 0.255834 0.443117i
\(41\) −6.47214 −1.01078 −0.505389 0.862892i \(-0.668651\pi\)
−0.505389 + 0.862892i \(0.668651\pi\)
\(42\) 0 0
\(43\) −1.52786 −0.232997 −0.116499 0.993191i \(-0.537167\pi\)
−0.116499 + 0.993191i \(0.537167\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 12.0902 + 20.9408i 1.80230 + 3.12167i
\(46\) −2.00000 3.46410i −0.294884 0.510754i
\(47\) −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) 3.23607 0.467086
\(49\) 0 0
\(50\) 5.47214 0.773877
\(51\) −10.4721 + 18.1383i −1.46639 + 2.53987i
\(52\) 0.618034 + 1.07047i 0.0857059 + 0.148447i
\(53\) 0.236068 + 0.408882i 0.0324264 + 0.0561642i 0.881783 0.471655i \(-0.156343\pi\)
−0.849357 + 0.527819i \(0.823010\pi\)
\(54\) −7.23607 + 12.5332i −0.984704 + 1.70556i
\(55\) −3.23607 −0.436351
\(56\) 0 0
\(57\) 8.94427 1.18470
\(58\) 2.23607 3.87298i 0.293610 0.508548i
\(59\) 3.61803 + 6.26662i 0.471028 + 0.815844i 0.999451 0.0331370i \(-0.0105498\pi\)
−0.528423 + 0.848981i \(0.677216\pi\)
\(60\) 5.23607 + 9.06914i 0.675973 + 1.17082i
\(61\) −2.61803 + 4.53457i −0.335205 + 0.580592i −0.983524 0.180777i \(-0.942139\pi\)
0.648319 + 0.761369i \(0.275472\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) −1.61803 2.80252i −0.199166 0.344966i
\(67\) 7.70820 + 13.3510i 0.941707 + 1.63108i 0.762214 + 0.647325i \(0.224112\pi\)
0.179493 + 0.983759i \(0.442554\pi\)
\(68\) −3.23607 + 5.60503i −0.392431 + 0.679710i
\(69\) 12.9443 1.55831
\(70\) 0 0
\(71\) −2.47214 −0.293389 −0.146694 0.989182i \(-0.546863\pi\)
−0.146694 + 0.989182i \(0.546863\pi\)
\(72\) −3.73607 + 6.47106i −0.440300 + 0.762622i
\(73\) −2.47214 4.28187i −0.289342 0.501154i 0.684311 0.729190i \(-0.260103\pi\)
−0.973653 + 0.228036i \(0.926770\pi\)
\(74\) 5.47214 + 9.47802i 0.636123 + 1.10180i
\(75\) −8.85410 + 15.3358i −1.02238 + 1.77082i
\(76\) 2.76393 0.317045
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 1.61803 + 2.80252i 0.180902 + 0.313331i
\(81\) −12.2082 21.1452i −1.35647 2.34947i
\(82\) 3.23607 5.60503i 0.357364 0.618972i
\(83\) −10.1803 −1.11744 −0.558719 0.829357i \(-0.688707\pi\)
−0.558719 + 0.829357i \(0.688707\pi\)
\(84\) 0 0
\(85\) −20.9443 −2.27173
\(86\) 0.763932 1.32317i 0.0823769 0.142681i
\(87\) 7.23607 + 12.5332i 0.775788 + 1.34370i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) −24.1803 −2.54883
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 3.23607 5.60503i 0.335565 0.581215i
\(94\) −1.00000 1.73205i −0.103142 0.178647i
\(95\) 4.47214 + 7.74597i 0.458831 + 0.794719i
\(96\) −1.61803 + 2.80252i −0.165140 + 0.286031i
\(97\) −3.52786 −0.358200 −0.179100 0.983831i \(-0.557319\pi\)
−0.179100 + 0.983831i \(0.557319\pi\)
\(98\) 0 0
\(99\) 7.47214 0.750978
\(100\) −2.73607 + 4.73901i −0.273607 + 0.473901i
\(101\) −7.09017 12.2805i −0.705498 1.22196i −0.966511 0.256624i \(-0.917390\pi\)
0.261013 0.965335i \(-0.415943\pi\)
\(102\) −10.4721 18.1383i −1.03690 1.79596i
\(103\) 1.47214 2.54981i 0.145054 0.251241i −0.784339 0.620332i \(-0.786998\pi\)
0.929393 + 0.369092i \(0.120331\pi\)
\(104\) −1.23607 −0.121206
\(105\) 0 0
\(106\) −0.472136 −0.0458579
\(107\) 3.23607 5.60503i 0.312842 0.541859i −0.666134 0.745832i \(-0.732052\pi\)
0.978977 + 0.203973i \(0.0653855\pi\)
\(108\) −7.23607 12.5332i −0.696291 1.20601i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 1.61803 2.80252i 0.154273 0.267210i
\(111\) −35.4164 −3.36158
\(112\) 0 0
\(113\) 8.47214 0.796992 0.398496 0.917170i \(-0.369532\pi\)
0.398496 + 0.917170i \(0.369532\pi\)
\(114\) −4.47214 + 7.74597i −0.418854 + 0.725476i
\(115\) 6.47214 + 11.2101i 0.603530 + 1.04534i
\(116\) 2.23607 + 3.87298i 0.207614 + 0.359597i
\(117\) 4.61803 7.99867i 0.426937 0.739477i
\(118\) −7.23607 −0.666134
\(119\) 0 0
\(120\) −10.4721 −0.955971
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −2.61803 4.53457i −0.237026 0.410540i
\(123\) 10.4721 + 18.1383i 0.944241 + 1.63547i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −1.52786 −0.136656
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 2.47214 + 4.28187i 0.217659 + 0.376997i
\(130\) −2.00000 3.46410i −0.175412 0.303822i
\(131\) 4.61803 7.99867i 0.403480 0.698847i −0.590664 0.806918i \(-0.701134\pi\)
0.994143 + 0.108071i \(0.0344673\pi\)
\(132\) 3.23607 0.281664
\(133\) 0 0
\(134\) −15.4164 −1.33177
\(135\) 23.4164 40.5584i 2.01536 3.49071i
\(136\) −3.23607 5.60503i −0.277491 0.480628i
\(137\) −7.94427 13.7599i −0.678725 1.17559i −0.975365 0.220597i \(-0.929200\pi\)
0.296640 0.954989i \(-0.404134\pi\)
\(138\) −6.47214 + 11.2101i −0.550945 + 0.954264i
\(139\) 8.29180 0.703301 0.351650 0.936131i \(-0.385621\pi\)
0.351650 + 0.936131i \(0.385621\pi\)
\(140\) 0 0
\(141\) 6.47214 0.545052
\(142\) 1.23607 2.14093i 0.103729 0.179663i
\(143\) 0.618034 + 1.07047i 0.0516826 + 0.0895169i
\(144\) −3.73607 6.47106i −0.311339 0.539255i
\(145\) −7.23607 + 12.5332i −0.600923 + 1.04083i
\(146\) 4.94427 0.409191
\(147\) 0 0
\(148\) −10.9443 −0.899614
\(149\) −11.1803 + 19.3649i −0.915929 + 1.58644i −0.110394 + 0.993888i \(0.535211\pi\)
−0.805535 + 0.592548i \(0.798122\pi\)
\(150\) −8.85410 15.3358i −0.722934 1.25216i
\(151\) −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i \(-0.329040\pi\)
−0.999909 + 0.0134886i \(0.995706\pi\)
\(152\) −1.38197 + 2.39364i −0.112092 + 0.194149i
\(153\) 48.3607 3.90973
\(154\) 0 0
\(155\) 6.47214 0.519854
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 9.32624 + 16.1535i 0.744315 + 1.28919i 0.950514 + 0.310681i \(0.100557\pi\)
−0.206199 + 0.978510i \(0.566110\pi\)
\(158\) 0 0
\(159\) 0.763932 1.32317i 0.0605838 0.104934i
\(160\) −3.23607 −0.255834
\(161\) 0 0
\(162\) 24.4164 1.91833
\(163\) −3.70820 + 6.42280i −0.290449 + 0.503072i −0.973916 0.226909i \(-0.927138\pi\)
0.683467 + 0.729981i \(0.260471\pi\)
\(164\) 3.23607 + 5.60503i 0.252694 + 0.437680i
\(165\) 5.23607 + 9.06914i 0.407627 + 0.706031i
\(166\) 5.09017 8.81643i 0.395074 0.684288i
\(167\) 15.4164 1.19296 0.596479 0.802629i \(-0.296566\pi\)
0.596479 + 0.802629i \(0.296566\pi\)
\(168\) 0 0
\(169\) −11.4721 −0.882472
\(170\) 10.4721 18.1383i 0.803176 1.39114i
\(171\) −10.3262 17.8856i −0.789667 1.36774i
\(172\) 0.763932 + 1.32317i 0.0582493 + 0.100891i
\(173\) 0.618034 1.07047i 0.0469883 0.0813860i −0.841575 0.540141i \(-0.818371\pi\)
0.888563 + 0.458755i \(0.151704\pi\)
\(174\) −14.4721 −1.09713
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 11.7082 20.2792i 0.880042 1.52428i
\(178\) 5.00000 + 8.66025i 0.374766 + 0.649113i
\(179\) −4.47214 7.74597i −0.334263 0.578961i 0.649080 0.760720i \(-0.275154\pi\)
−0.983343 + 0.181760i \(0.941821\pi\)
\(180\) 12.0902 20.9408i 0.901148 1.56083i
\(181\) −4.76393 −0.354100 −0.177050 0.984202i \(-0.556655\pi\)
−0.177050 + 0.984202i \(0.556655\pi\)
\(182\) 0 0
\(183\) 16.9443 1.25256
\(184\) −2.00000 + 3.46410i −0.147442 + 0.255377i
\(185\) −17.7082 30.6715i −1.30193 2.25501i
\(186\) 3.23607 + 5.60503i 0.237280 + 0.410981i
\(187\) −3.23607 + 5.60503i −0.236645 + 0.409881i
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) −8.94427 −0.648886
\(191\) −3.23607 + 5.60503i −0.234154 + 0.405566i −0.959026 0.283317i \(-0.908565\pi\)
0.724873 + 0.688883i \(0.241899\pi\)
\(192\) −1.61803 2.80252i −0.116772 0.202254i
\(193\) −1.47214 2.54981i −0.105967 0.183540i 0.808166 0.588955i \(-0.200460\pi\)
−0.914133 + 0.405415i \(0.867127\pi\)
\(194\) 1.76393 3.05522i 0.126643 0.219352i
\(195\) 12.9443 0.926959
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −3.73607 + 6.47106i −0.265511 + 0.459878i
\(199\) 0.527864 + 0.914287i 0.0374193 + 0.0648121i 0.884129 0.467244i \(-0.154753\pi\)
−0.846709 + 0.532056i \(0.821420\pi\)
\(200\) −2.73607 4.73901i −0.193469 0.335099i
\(201\) 24.9443 43.2047i 1.75943 3.04743i
\(202\) 14.1803 0.997725
\(203\) 0 0
\(204\) 20.9443 1.46639
\(205\) −10.4721 + 18.1383i −0.731406 + 1.26683i
\(206\) 1.47214 + 2.54981i 0.102569 + 0.177654i
\(207\) −14.9443 25.8842i −1.03870 1.79908i
\(208\) 0.618034 1.07047i 0.0428529 0.0742235i
\(209\) 2.76393 0.191185
\(210\) 0 0
\(211\) −22.4721 −1.54705 −0.773523 0.633768i \(-0.781507\pi\)
−0.773523 + 0.633768i \(0.781507\pi\)
\(212\) 0.236068 0.408882i 0.0162132 0.0280821i
\(213\) 4.00000 + 6.92820i 0.274075 + 0.474713i
\(214\) 3.23607 + 5.60503i 0.221213 + 0.383152i
\(215\) −2.47214 + 4.28187i −0.168598 + 0.292021i
\(216\) 14.4721 0.984704
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) −8.00000 + 13.8564i −0.540590 + 0.936329i
\(220\) 1.61803 + 2.80252i 0.109088 + 0.188946i
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) 17.7082 30.6715i 1.18850 2.05854i
\(223\) −8.47214 −0.567336 −0.283668 0.958923i \(-0.591551\pi\)
−0.283668 + 0.958923i \(0.591551\pi\)
\(224\) 0 0
\(225\) 40.8885 2.72590
\(226\) −4.23607 + 7.33708i −0.281779 + 0.488056i
\(227\) −7.38197 12.7859i −0.489958 0.848633i 0.509975 0.860189i \(-0.329655\pi\)
−0.999933 + 0.0115566i \(0.996321\pi\)
\(228\) −4.47214 7.74597i −0.296174 0.512989i
\(229\) 6.38197 11.0539i 0.421732 0.730462i −0.574377 0.818591i \(-0.694756\pi\)
0.996109 + 0.0881294i \(0.0280889\pi\)
\(230\) −12.9443 −0.853520
\(231\) 0 0
\(232\) −4.47214 −0.293610
\(233\) −1.47214 + 2.54981i −0.0964428 + 0.167044i −0.910210 0.414147i \(-0.864080\pi\)
0.813767 + 0.581191i \(0.197413\pi\)
\(234\) 4.61803 + 7.99867i 0.301890 + 0.522889i
\(235\) 3.23607 + 5.60503i 0.211098 + 0.365632i
\(236\) 3.61803 6.26662i 0.235514 0.407922i
\(237\) 0 0
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 5.23607 9.06914i 0.337987 0.585410i
\(241\) −5.70820 9.88690i −0.367698 0.636871i 0.621507 0.783408i \(-0.286521\pi\)
−0.989205 + 0.146537i \(0.953187\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) −17.7984 + 30.8277i −1.14177 + 1.97760i
\(244\) 5.23607 0.335205
\(245\) 0 0
\(246\) −20.9443 −1.33536
\(247\) 1.70820 2.95870i 0.108690 0.188257i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 16.4721 + 28.5306i 1.04388 + 1.80805i
\(250\) 0.763932 1.32317i 0.0483153 0.0836846i
\(251\) −24.7639 −1.56309 −0.781543 0.623852i \(-0.785567\pi\)
−0.781543 + 0.623852i \(0.785567\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 6.00000 10.3923i 0.376473 0.652071i
\(255\) 33.8885 + 58.6967i 2.12218 + 3.67573i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.47214 + 9.47802i −0.341342 + 0.591222i −0.984682 0.174358i \(-0.944215\pi\)
0.643340 + 0.765581i \(0.277548\pi\)
\(258\) −4.94427 −0.307817
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) 16.7082 28.9395i 1.03421 1.79131i
\(262\) 4.61803 + 7.99867i 0.285303 + 0.494159i
\(263\) −6.47214 11.2101i −0.399089 0.691242i 0.594525 0.804077i \(-0.297340\pi\)
−0.993614 + 0.112835i \(0.964007\pi\)
\(264\) −1.61803 + 2.80252i −0.0995831 + 0.172483i
\(265\) 1.52786 0.0938559
\(266\) 0 0
\(267\) −32.3607 −1.98044
\(268\) 7.70820 13.3510i 0.470853 0.815542i
\(269\) −13.6180 23.5871i −0.830306 1.43813i −0.897796 0.440413i \(-0.854832\pi\)
0.0674893 0.997720i \(-0.478501\pi\)
\(270\) 23.4164 + 40.5584i 1.42508 + 2.46831i
\(271\) −8.47214 + 14.6742i −0.514646 + 0.891392i 0.485210 + 0.874398i \(0.338743\pi\)
−0.999856 + 0.0169947i \(0.994590\pi\)
\(272\) 6.47214 0.392431
\(273\) 0 0
\(274\) 15.8885 0.959862
\(275\) −2.73607 + 4.73901i −0.164991 + 0.285773i
\(276\) −6.47214 11.2101i −0.389577 0.674767i
\(277\) −6.23607 10.8012i −0.374689 0.648980i 0.615591 0.788065i \(-0.288917\pi\)
−0.990280 + 0.139085i \(0.955584\pi\)
\(278\) −4.14590 + 7.18091i −0.248654 + 0.430682i
\(279\) −14.9443 −0.894690
\(280\) 0 0
\(281\) −24.8328 −1.48140 −0.740701 0.671835i \(-0.765506\pi\)
−0.740701 + 0.671835i \(0.765506\pi\)
\(282\) −3.23607 + 5.60503i −0.192705 + 0.333775i
\(283\) −8.32624 14.4215i −0.494943 0.857267i 0.505040 0.863096i \(-0.331478\pi\)
−0.999983 + 0.00582897i \(0.998145\pi\)
\(284\) 1.23607 + 2.14093i 0.0733471 + 0.127041i
\(285\) 14.4721 25.0665i 0.857255 1.48481i
\(286\) −1.23607 −0.0730902
\(287\) 0 0
\(288\) 7.47214 0.440300
\(289\) −12.4443 + 21.5541i −0.732016 + 1.26789i
\(290\) −7.23607 12.5332i −0.424917 0.735977i
\(291\) 5.70820 + 9.88690i 0.334621 + 0.579580i
\(292\) −2.47214 + 4.28187i −0.144671 + 0.250577i
\(293\) −4.65248 −0.271801 −0.135900 0.990723i \(-0.543393\pi\)
−0.135900 + 0.990723i \(0.543393\pi\)
\(294\) 0 0
\(295\) 23.4164 1.36336
\(296\) 5.47214 9.47802i 0.318061 0.550899i
\(297\) −7.23607 12.5332i −0.419879 0.727252i
\(298\) −11.1803 19.3649i −0.647660 1.12178i
\(299\) 2.47214 4.28187i 0.142967 0.247627i
\(300\) 17.7082 1.02238
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) −22.9443 + 39.7406i −1.31811 + 2.28304i
\(304\) −1.38197 2.39364i −0.0792612 0.137284i
\(305\) 8.47214 + 14.6742i 0.485113 + 0.840241i
\(306\) −24.1803 + 41.8816i −1.38230 + 2.39421i
\(307\) −32.0689 −1.83027 −0.915134 0.403150i \(-0.867915\pi\)
−0.915134 + 0.403150i \(0.867915\pi\)
\(308\) 0 0
\(309\) −9.52786 −0.542021
\(310\) −3.23607 + 5.60503i −0.183796 + 0.318345i
\(311\) 2.70820 + 4.69075i 0.153568 + 0.265988i 0.932537 0.361075i \(-0.117590\pi\)
−0.778969 + 0.627063i \(0.784257\pi\)
\(312\) 2.00000 + 3.46410i 0.113228 + 0.196116i
\(313\) 14.2361 24.6576i 0.804670 1.39373i −0.111843 0.993726i \(-0.535675\pi\)
0.916514 0.400004i \(-0.130991\pi\)
\(314\) −18.6525 −1.05262
\(315\) 0 0
\(316\) 0 0
\(317\) 6.52786 11.3066i 0.366641 0.635041i −0.622397 0.782702i \(-0.713841\pi\)
0.989038 + 0.147660i \(0.0471743\pi\)
\(318\) 0.763932 + 1.32317i 0.0428392 + 0.0741996i
\(319\) 2.23607 + 3.87298i 0.125196 + 0.216845i
\(320\) 1.61803 2.80252i 0.0904508 0.156665i
\(321\) −20.9443 −1.16900
\(322\) 0 0
\(323\) 17.8885 0.995345
\(324\) −12.2082 + 21.1452i −0.678234 + 1.17473i
\(325\) 3.38197 + 5.85774i 0.187598 + 0.324929i
\(326\) −3.70820 6.42280i −0.205378 0.355726i
\(327\) 16.1803 28.0252i 0.894775 1.54980i
\(328\) −6.47214 −0.357364
\(329\) 0 0
\(330\) −10.4721 −0.576472
\(331\) −0.472136 + 0.817763i −0.0259509 + 0.0449483i −0.878709 0.477357i \(-0.841595\pi\)
0.852758 + 0.522306i \(0.174928\pi\)
\(332\) 5.09017 + 8.81643i 0.279359 + 0.483865i
\(333\) 40.8885 + 70.8210i 2.24068 + 3.88097i
\(334\) −7.70820 + 13.3510i −0.421774 + 0.730534i
\(335\) 49.8885 2.72570
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 5.73607 9.93516i 0.312001 0.540402i
\(339\) −13.7082 23.7433i −0.744527 1.28956i
\(340\) 10.4721 + 18.1383i 0.567931 + 0.983686i
\(341\) 1.00000 1.73205i 0.0541530 0.0937958i
\(342\) 20.6525 1.11676
\(343\) 0 0
\(344\) −1.52786 −0.0823769
\(345\) 20.9443 36.2765i 1.12760 1.95306i
\(346\) 0.618034 + 1.07047i 0.0332257 + 0.0575486i
\(347\) 3.23607 + 5.60503i 0.173721 + 0.300894i 0.939718 0.341950i \(-0.111087\pi\)
−0.765997 + 0.642844i \(0.777754\pi\)
\(348\) 7.23607 12.5332i 0.387894 0.671852i
\(349\) −8.29180 −0.443850 −0.221925 0.975064i \(-0.571234\pi\)
−0.221925 + 0.975064i \(0.571234\pi\)
\(350\) 0 0
\(351\) −17.8885 −0.954820
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −17.4721 30.2626i −0.929948 1.61072i −0.783404 0.621513i \(-0.786518\pi\)
−0.146544 0.989204i \(-0.546815\pi\)
\(354\) 11.7082 + 20.2792i 0.622284 + 1.07783i
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 8.94427 0.472719
\(359\) 13.4164 23.2379i 0.708091 1.22645i −0.257473 0.966285i \(-0.582890\pi\)
0.965564 0.260164i \(-0.0837767\pi\)
\(360\) 12.0902 + 20.9408i 0.637208 + 1.10368i
\(361\) 5.68034 + 9.83864i 0.298965 + 0.517823i
\(362\) 2.38197 4.12569i 0.125193 0.216841i
\(363\) 3.23607 0.169850
\(364\) 0 0
\(365\) −16.0000 −0.837478
\(366\) −8.47214 + 14.6742i −0.442846 + 0.767031i
\(367\) 10.7082 + 18.5472i 0.558964 + 0.968154i 0.997583 + 0.0694807i \(0.0221342\pi\)
−0.438620 + 0.898673i \(0.644532\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 24.1803 41.8816i 1.25878 2.18027i
\(370\) 35.4164 1.84121
\(371\) 0 0
\(372\) −6.47214 −0.335565
\(373\) 3.00000 5.19615i 0.155334 0.269047i −0.777847 0.628454i \(-0.783688\pi\)
0.933181 + 0.359408i \(0.117021\pi\)
\(374\) −3.23607 5.60503i −0.167333 0.289829i
\(375\) 2.47214 + 4.28187i 0.127661 + 0.221115i
\(376\) −1.00000 + 1.73205i −0.0515711 + 0.0893237i
\(377\) 5.52786 0.284699
\(378\) 0 0
\(379\) 5.52786 0.283947 0.141974 0.989870i \(-0.454655\pi\)
0.141974 + 0.989870i \(0.454655\pi\)
\(380\) 4.47214 7.74597i 0.229416 0.397360i
\(381\) 19.4164 + 33.6302i 0.994733 + 1.72293i
\(382\) −3.23607 5.60503i −0.165572 0.286778i
\(383\) 5.94427 10.2958i 0.303738 0.526090i −0.673241 0.739423i \(-0.735099\pi\)
0.976980 + 0.213333i \(0.0684319\pi\)
\(384\) 3.23607 0.165140
\(385\) 0 0
\(386\) 2.94427 0.149859
\(387\) 5.70820 9.88690i 0.290164 0.502579i
\(388\) 1.76393 + 3.05522i 0.0895501 + 0.155105i
\(389\) −3.29180 5.70156i −0.166901 0.289080i 0.770428 0.637527i \(-0.220043\pi\)
−0.937329 + 0.348447i \(0.886709\pi\)
\(390\) −6.47214 + 11.2101i −0.327729 + 0.567644i
\(391\) 25.8885 1.30924
\(392\) 0 0
\(393\) −29.8885 −1.50768
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 0 0
\(396\) −3.73607 6.47106i −0.187744 0.325183i
\(397\) −5.14590 + 8.91296i −0.258265 + 0.447328i −0.965777 0.259373i \(-0.916484\pi\)
0.707512 + 0.706701i \(0.249818\pi\)
\(398\) −1.05573 −0.0529189
\(399\) 0 0
\(400\) 5.47214 0.273607
\(401\) 15.1803 26.2931i 0.758070 1.31302i −0.185764 0.982594i \(-0.559476\pi\)
0.943834 0.330421i \(-0.107191\pi\)
\(402\) 24.9443 + 43.2047i 1.24411 + 2.15486i
\(403\) −1.23607 2.14093i −0.0615729 0.106647i
\(404\) −7.09017 + 12.2805i −0.352749 + 0.610979i
\(405\) −79.0132 −3.92620
\(406\) 0 0
\(407\) −10.9443 −0.542487
\(408\) −10.4721 + 18.1383i −0.518448 + 0.897978i
\(409\) −11.7082 20.2792i −0.578933 1.00274i −0.995602 0.0936836i \(-0.970136\pi\)
0.416669 0.909058i \(-0.363198\pi\)
\(410\) −10.4721 18.1383i −0.517182 0.895785i
\(411\) −25.7082 + 44.5279i −1.26809 + 2.19640i
\(412\) −2.94427 −0.145054
\(413\) 0 0
\(414\) 29.8885 1.46894
\(415\) −16.4721 + 28.5306i −0.808585 + 1.40051i
\(416\) 0.618034 + 1.07047i 0.0303016 + 0.0524839i
\(417\) −13.4164 23.2379i −0.657004 1.13796i
\(418\) −1.38197 + 2.39364i −0.0675942 + 0.117077i
\(419\) −12.7639 −0.623559 −0.311779 0.950155i \(-0.600925\pi\)
−0.311779 + 0.950155i \(0.600925\pi\)
\(420\) 0 0
\(421\) 7.52786 0.366886 0.183443 0.983030i \(-0.441276\pi\)
0.183443 + 0.983030i \(0.441276\pi\)
\(422\) 11.2361 19.4614i 0.546963 0.947368i
\(423\) −7.47214 12.9421i −0.363308 0.629267i
\(424\) 0.236068 + 0.408882i 0.0114645 + 0.0198571i
\(425\) −17.7082 + 30.6715i −0.858974 + 1.48779i
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) −6.47214 −0.312842
\(429\) 2.00000 3.46410i 0.0965609 0.167248i
\(430\) −2.47214 4.28187i −0.119217 0.206490i
\(431\) −20.4721 35.4588i −0.986108 1.70799i −0.636905 0.770942i \(-0.719786\pi\)
−0.349203 0.937047i \(-0.613548\pi\)
\(432\) −7.23607 + 12.5332i −0.348145 + 0.603006i
\(433\) −19.5279 −0.938449 −0.469225 0.883079i \(-0.655467\pi\)
−0.469225 + 0.883079i \(0.655467\pi\)
\(434\) 0 0
\(435\) 46.8328 2.24546
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) −5.52786 9.57454i −0.264434 0.458012i
\(438\) −8.00000 13.8564i −0.382255 0.662085i
\(439\) −4.47214 + 7.74597i −0.213443 + 0.369695i −0.952790 0.303630i \(-0.901801\pi\)
0.739347 + 0.673325i \(0.235135\pi\)
\(440\) −3.23607 −0.154273
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) 3.52786 6.11044i 0.167614 0.290316i −0.769967 0.638084i \(-0.779727\pi\)
0.937580 + 0.347768i \(0.113060\pi\)
\(444\) 17.7082 + 30.6715i 0.840394 + 1.45561i
\(445\) −16.1803 28.0252i −0.767022 1.32852i
\(446\) 4.23607 7.33708i 0.200584 0.347421i
\(447\) 72.3607 3.42254
\(448\) 0 0
\(449\) 1.05573 0.0498229 0.0249114 0.999690i \(-0.492070\pi\)
0.0249114 + 0.999690i \(0.492070\pi\)
\(450\) −20.4443 + 35.4105i −0.963752 + 1.66927i
\(451\) 3.23607 + 5.60503i 0.152380 + 0.263931i
\(452\) −4.23607 7.33708i −0.199248 0.345107i
\(453\) −19.4164 + 33.6302i −0.912262 + 1.58008i
\(454\) 14.7639 0.692906
\(455\) 0 0
\(456\) 8.94427 0.418854
\(457\) −4.52786 + 7.84249i −0.211805 + 0.366856i −0.952279 0.305228i \(-0.901267\pi\)
0.740475 + 0.672084i \(0.234601\pi\)
\(458\) 6.38197 + 11.0539i 0.298210 + 0.516514i
\(459\) −46.8328 81.1168i −2.18597 3.78621i
\(460\) 6.47214 11.2101i 0.301765 0.522672i
\(461\) −29.2361 −1.36166 −0.680830 0.732442i \(-0.738381\pi\)
−0.680830 + 0.732442i \(0.738381\pi\)
\(462\) 0 0
\(463\) −21.5279 −1.00048 −0.500242 0.865885i \(-0.666756\pi\)
−0.500242 + 0.865885i \(0.666756\pi\)
\(464\) 2.23607 3.87298i 0.103807 0.179799i
\(465\) −10.4721 18.1383i −0.485634 0.841142i
\(466\) −1.47214 2.54981i −0.0681954 0.118118i
\(467\) 6.56231 11.3662i 0.303667 0.525967i −0.673296 0.739373i \(-0.735122\pi\)
0.976964 + 0.213405i \(0.0684555\pi\)
\(468\) −9.23607 −0.426937
\(469\) 0 0
\(470\) −6.47214 −0.298537
\(471\) 30.1803 52.2739i 1.39064 2.40865i
\(472\) 3.61803 + 6.26662i 0.166534 + 0.288445i
\(473\) 0.763932 + 1.32317i 0.0351256 + 0.0608394i
\(474\) 0 0
\(475\) 15.1246 0.693965
\(476\) 0 0
\(477\) −3.52786 −0.161530
\(478\) −10.0000 + 17.3205i −0.457389 + 0.792222i
\(479\) −16.1803 28.0252i −0.739299 1.28050i −0.952812 0.303562i \(-0.901824\pi\)
0.213513 0.976940i \(-0.431509\pi\)
\(480\) 5.23607 + 9.06914i 0.238993 + 0.413948i
\(481\) −6.76393 + 11.7155i −0.308409 + 0.534180i
\(482\) 11.4164 0.520003
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −5.70820 + 9.88690i −0.259196 + 0.448941i
\(486\) −17.7984 30.8277i −0.807351 1.39837i
\(487\) 0.472136 + 0.817763i 0.0213945 + 0.0370564i 0.876524 0.481357i \(-0.159856\pi\)
−0.855130 + 0.518414i \(0.826523\pi\)
\(488\) −2.61803 + 4.53457i −0.118513 + 0.205270i
\(489\) 24.0000 1.08532
\(490\) 0 0
\(491\) 0.944272 0.0426144 0.0213072 0.999773i \(-0.493217\pi\)
0.0213072 + 0.999773i \(0.493217\pi\)
\(492\) 10.4721 18.1383i 0.472120 0.817736i
\(493\) 14.4721 + 25.0665i 0.651792 + 1.12894i
\(494\) 1.70820 + 2.95870i 0.0768557 + 0.133118i
\(495\) 12.0902 20.9408i 0.543413 0.941218i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −32.9443 −1.47627
\(499\) −6.18034 + 10.7047i −0.276670 + 0.479207i −0.970555 0.240879i \(-0.922564\pi\)
0.693885 + 0.720086i \(0.255898\pi\)
\(500\) 0.763932 + 1.32317i 0.0341641 + 0.0591739i
\(501\) −24.9443 43.2047i −1.11443 1.93025i
\(502\) 12.3820 21.4462i 0.552634 0.957190i
\(503\) −4.00000 −0.178351 −0.0891756 0.996016i \(-0.528423\pi\)
−0.0891756 + 0.996016i \(0.528423\pi\)
\(504\) 0 0
\(505\) −45.8885 −2.04201
\(506\) −2.00000 + 3.46410i −0.0889108 + 0.153998i
\(507\) 18.5623 + 32.1509i 0.824381 + 1.42787i
\(508\) 6.00000 + 10.3923i 0.266207 + 0.461084i
\(509\) −17.0344 + 29.5045i −0.755038 + 1.30776i 0.190317 + 0.981723i \(0.439048\pi\)
−0.945355 + 0.326042i \(0.894285\pi\)
\(510\) −67.7771 −3.00122
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −20.0000 + 34.6410i −0.883022 + 1.52944i
\(514\) −5.47214 9.47802i −0.241366 0.418057i
\(515\) −4.76393 8.25137i −0.209924 0.363599i
\(516\) 2.47214 4.28187i 0.108830 0.188499i
\(517\) 2.00000 0.0879599
\(518\) 0 0
\(519\) −4.00000 −0.175581
\(520\) −2.00000 + 3.46410i −0.0877058 + 0.151911i
\(521\) 17.1803 + 29.7572i 0.752684 + 1.30369i 0.946517 + 0.322653i \(0.104575\pi\)
−0.193833 + 0.981035i \(0.562092\pi\)
\(522\) 16.7082 + 28.9395i 0.731298 + 1.26665i
\(523\) −13.8541 + 23.9960i −0.605798 + 1.04927i 0.386127 + 0.922446i \(0.373813\pi\)
−0.991925 + 0.126827i \(0.959521\pi\)
\(524\) −9.23607 −0.403480
\(525\) 0 0
\(526\) 12.9443 0.564397
\(527\) 6.47214 11.2101i 0.281931 0.488318i
\(528\) −1.61803 2.80252i −0.0704159 0.121964i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −0.763932 + 1.32317i −0.0331831 + 0.0574748i
\(531\) −54.0689 −2.34639
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 16.1803 28.0252i 0.700192 1.21277i
\(535\) −10.4721 18.1383i −0.452750 0.784186i
\(536\) 7.70820 + 13.3510i 0.332944 + 0.576675i
\(537\) −14.4721 + 25.0665i −0.624519 + 1.08170i
\(538\) 27.2361 1.17423
\(539\) 0 0
\(540\) −46.8328 −2.01536
\(541\) 4.52786 7.84249i 0.194668 0.337175i −0.752124 0.659022i \(-0.770970\pi\)
0.946792 + 0.321847i \(0.104304\pi\)
\(542\) −8.47214 14.6742i −0.363909 0.630310i
\(543\) 7.70820 + 13.3510i 0.330791 + 0.572946i
\(544\) −3.23607 + 5.60503i −0.138745 + 0.240314i
\(545\) 32.3607 1.38618
\(546\) 0 0
\(547\) 16.9443 0.724485 0.362242 0.932084i \(-0.382011\pi\)
0.362242 + 0.932084i \(0.382011\pi\)
\(548\) −7.94427 + 13.7599i −0.339362 + 0.587793i
\(549\) −19.5623 33.8829i −0.834899 1.44609i
\(550\) −2.73607 4.73901i −0.116666 0.202072i
\(551\) 6.18034 10.7047i 0.263291 0.456034i
\(552\) 12.9443 0.550945
\(553\) 0 0
\(554\) 12.4721 0.529890
\(555\) −57.3050 + 99.2551i −2.43246 + 4.21314i
\(556\) −4.14590 7.18091i −0.175825 0.304538i
\(557\) 14.4164 + 24.9700i 0.610843 + 1.05801i 0.991099 + 0.133129i \(0.0425026\pi\)
−0.380256 + 0.924881i \(0.624164\pi\)
\(558\) 7.47214 12.9421i 0.316321 0.547884i
\(559\) 1.88854 0.0798769
\(560\) 0 0
\(561\) 20.9443 0.884268
\(562\) 12.4164 21.5058i 0.523755 0.907169i
\(563\) 13.3820 + 23.1782i 0.563983 + 0.976847i 0.997144 + 0.0755300i \(0.0240648\pi\)
−0.433161 + 0.901317i \(0.642602\pi\)
\(564\) −3.23607 5.60503i −0.136263 0.236015i
\(565\) 13.7082 23.7433i 0.576708 0.998888i
\(566\) 16.6525 0.699956
\(567\) 0 0
\(568\) −2.47214 −0.103729
\(569\) −8.41641 + 14.5776i −0.352834 + 0.611127i −0.986745 0.162280i \(-0.948115\pi\)
0.633911 + 0.773406i \(0.281449\pi\)
\(570\) 14.4721 + 25.0665i 0.606171 + 1.04992i
\(571\) 22.9443 + 39.7406i 0.960188 + 1.66309i 0.722022 + 0.691870i \(0.243213\pi\)
0.238165 + 0.971225i \(0.423454\pi\)
\(572\) 0.618034 1.07047i 0.0258413 0.0447584i
\(573\) 20.9443 0.874960
\(574\) 0 0
\(575\) 21.8885 0.912815
\(576\) −3.73607 + 6.47106i −0.155669 + 0.269627i
\(577\) 4.52786 + 7.84249i 0.188497 + 0.326487i 0.944749 0.327793i \(-0.106305\pi\)
−0.756252 + 0.654280i \(0.772972\pi\)
\(578\) −12.4443 21.5541i −0.517613 0.896533i
\(579\) −4.76393 + 8.25137i −0.197982 + 0.342915i
\(580\) 14.4721 0.600923
\(581\) 0 0
\(582\) −11.4164 −0.473225
\(583\) 0.236068 0.408882i 0.00977694 0.0169342i
\(584\) −2.47214 4.28187i −0.102298 0.177185i
\(585\) −14.9443 25.8842i −0.617870 1.07018i
\(586\) 2.32624 4.02916i 0.0960960 0.166443i
\(587\) 28.1803 1.16313 0.581564 0.813501i \(-0.302441\pi\)
0.581564 + 0.813501i \(0.302441\pi\)
\(588\) 0 0
\(589\) −5.52786 −0.227772
\(590\) −11.7082 + 20.2792i −0.482019 + 0.834882i
\(591\) −29.1246 50.4453i −1.19803 2.07504i
\(592\) 5.47214 + 9.47802i 0.224903 + 0.389544i
\(593\) 12.0000 20.7846i 0.492781 0.853522i −0.507184 0.861838i \(-0.669314\pi\)
0.999965 + 0.00831589i \(0.00264706\pi\)
\(594\) 14.4721 0.593799
\(595\) 0 0
\(596\) 22.3607 0.915929
\(597\) 1.70820 2.95870i 0.0699121 0.121091i
\(598\) 2.47214 + 4.28187i 0.101093 + 0.175098i
\(599\) −6.18034 10.7047i −0.252522 0.437381i 0.711698 0.702486i \(-0.247927\pi\)
−0.964219 + 0.265105i \(0.914593\pi\)
\(600\) −8.85410 + 15.3358i −0.361467 + 0.626080i
\(601\) −18.8328 −0.768207 −0.384103 0.923290i \(-0.625489\pi\)
−0.384103 + 0.923290i \(0.625489\pi\)
\(602\) 0 0
\(603\) −115.193 −4.69104
\(604\) −6.00000 + 10.3923i −0.244137 + 0.422857i
\(605\) 1.61803 + 2.80252i 0.0657824 + 0.113939i
\(606\) −22.9443 39.7406i −0.932047 1.61435i
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 2.76393 0.112092
\(609\) 0 0
\(610\) −16.9443 −0.686054
\(611\) 1.23607 2.14093i 0.0500060 0.0866129i
\(612\) −24.1803 41.8816i −0.977432 1.69296i
\(613\) −9.76393 16.9116i −0.394362 0.683054i 0.598658 0.801005i \(-0.295701\pi\)
−0.993019 + 0.117951i \(0.962368\pi\)
\(614\) 16.0344 27.7725i 0.647097 1.12081i
\(615\) 67.7771 2.73304
\(616\) 0 0
\(617\) −5.41641 −0.218056 −0.109028 0.994039i \(-0.534774\pi\)
−0.109028 + 0.994039i \(0.534774\pi\)
\(618\) 4.76393 8.25137i 0.191633 0.331919i
\(619\) −24.2705 42.0378i −0.975514 1.68964i −0.678228 0.734852i \(-0.737252\pi\)
−0.297286 0.954788i \(-0.596082\pi\)
\(620\) −3.23607 5.60503i −0.129964 0.225104i
\(621\) −28.9443 + 50.1329i −1.16149 + 2.01177i
\(622\) −5.41641 −0.217178
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 11.2082 19.4132i 0.448328 0.776527i
\(626\) 14.2361 + 24.6576i 0.568988 + 0.985516i
\(627\) −4.47214 7.74597i −0.178600 0.309344i
\(628\) 9.32624 16.1535i 0.372157 0.644596i
\(629\) −70.8328 −2.82429
\(630\) 0 0
\(631\) −4.58359 −0.182470 −0.0912350 0.995829i \(-0.529081\pi\)
−0.0912350 + 0.995829i \(0.529081\pi\)
\(632\) 0 0
\(633\) 36.3607 + 62.9785i 1.44521 + 2.50317i
\(634\) 6.52786 + 11.3066i 0.259255 + 0.449042i
\(635\) −19.4164 + 33.6302i −0.770517 + 1.33457i
\(636\) −1.52786 −0.0605838
\(637\) 0 0
\(638\) −4.47214 −0.177054
\(639\) 9.23607 15.9973i 0.365373 0.632845i
\(640\) 1.61803 + 2.80252i 0.0639584 + 0.110779i
\(641\) −18.2361 31.5858i −0.720281 1.24756i −0.960887 0.276941i \(-0.910679\pi\)
0.240606 0.970623i \(-0.422654\pi\)
\(642\) 10.4721 18.1383i 0.413302 0.715860i
\(643\) 23.2361 0.916341 0.458171 0.888864i \(-0.348505\pi\)
0.458171 + 0.888864i \(0.348505\pi\)
\(644\) 0 0
\(645\) 16.0000 0.629999
\(646\) −8.94427 + 15.4919i −0.351908 + 0.609522i
\(647\) 12.4164 + 21.5058i 0.488139 + 0.845482i 0.999907 0.0136418i \(-0.00434244\pi\)
−0.511768 + 0.859124i \(0.671009\pi\)
\(648\) −12.2082 21.1452i −0.479584 0.830663i
\(649\) 3.61803 6.26662i 0.142020 0.245986i
\(650\) −6.76393 −0.265303
\(651\) 0 0
\(652\) 7.41641 0.290449
\(653\) −0.819660 + 1.41969i −0.0320758 + 0.0555569i −0.881618 0.471964i \(-0.843545\pi\)
0.849542 + 0.527521i \(0.176878\pi\)
\(654\) 16.1803 + 28.0252i 0.632701 + 1.09587i
\(655\) −14.9443 25.8842i −0.583921 1.01138i
\(656\) 3.23607 5.60503i 0.126347 0.218840i
\(657\) 36.9443 1.44133
\(658\) 0 0
\(659\) 43.4164 1.69126 0.845632 0.533767i \(-0.179224\pi\)
0.845632 + 0.533767i \(0.179224\pi\)
\(660\) 5.23607 9.06914i 0.203814 0.353016i
\(661\) 18.5623 + 32.1509i 0.721990 + 1.25052i 0.960201 + 0.279310i \(0.0901057\pi\)
−0.238211 + 0.971213i \(0.576561\pi\)
\(662\) −0.472136 0.817763i −0.0183501 0.0317833i
\(663\) 12.9443 22.4201i 0.502714 0.870726i
\(664\) −10.1803 −0.395074
\(665\) 0 0
\(666\) −81.7771 −3.16880
\(667\) 8.94427 15.4919i 0.346324 0.599850i
\(668\) −7.70820 13.3510i −0.298239 0.516566i
\(669\) 13.7082 + 23.7433i 0.529990 + 0.917969i
\(670\) −24.9443 + 43.2047i −0.963681 + 1.66914i
\(671\) 5.23607 0.202136
\(672\) 0 0
\(673\) 31.8885 1.22921 0.614607 0.788834i \(-0.289315\pi\)
0.614607 + 0.788834i \(0.289315\pi\)
\(674\) −9.00000 + 15.5885i −0.346667 + 0.600445i
\(675\) −39.5967 68.5836i −1.52408 2.63978i
\(676\) 5.73607 + 9.93516i 0.220618 + 0.382122i
\(677\) 16.0344 27.7725i 0.616254 1.06738i −0.373910 0.927465i \(-0.621983\pi\)
0.990163 0.139917i \(-0.0446837\pi\)
\(678\) 27.4164 1.05292
\(679\) 0 0
\(680\) −20.9443 −0.803176
\(681\) −23.8885 + 41.3762i −0.915411 + 1.58554i
\(682\) 1.00000 + 1.73205i 0.0382920 + 0.0663237i
\(683\) −7.52786 13.0386i −0.288046 0.498910i 0.685297 0.728263i \(-0.259672\pi\)
−0.973343 + 0.229353i \(0.926339\pi\)
\(684\) −10.3262 + 17.8856i −0.394834 + 0.683872i
\(685\) −51.4164 −1.96452
\(686\) 0 0
\(687\) −41.3050 −1.57588
\(688\) 0.763932 1.32317i 0.0291246 0.0504453i
\(689\) −0.291796 0.505406i −0.0111165 0.0192544i
\(690\) 20.9443 + 36.2765i 0.797335 + 1.38102i
\(691\) −9.32624 + 16.1535i −0.354787 + 0.614509i −0.987081 0.160219i \(-0.948780\pi\)
0.632295 + 0.774728i \(0.282113\pi\)
\(692\) −1.23607 −0.0469883
\(693\) 0 0
\(694\) −6.47214 −0.245679
\(695\) 13.4164 23.2379i 0.508913 0.881464i
\(696\) 7.23607 + 12.5332i 0.274282 + 0.475071i
\(697\) 20.9443 + 36.2765i 0.793321 + 1.37407i
\(698\) 4.14590 7.18091i 0.156925 0.271801i
\(699\) 9.52786 0.360377
\(700\) 0 0
\(701\) 46.7214 1.76464 0.882321 0.470649i \(-0.155980\pi\)
0.882321 + 0.470649i \(0.155980\pi\)
\(702\) 8.94427 15.4919i 0.337580 0.584705i
\(703\) 15.1246 + 26.1966i 0.570436 + 0.988023i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 10.4721 18.1383i 0.394403 0.683127i
\(706\) 34.9443 1.31515
\(707\) 0 0
\(708\) −23.4164 −0.880042
\(709\) 2.23607 3.87298i 0.0839773 0.145453i −0.820978 0.570960i \(-0.806571\pi\)
0.904955 + 0.425507i \(0.139904\pi\)
\(710\) −4.00000 6.92820i −0.150117 0.260011i
\(711\) 0 0
\(712\) 5.00000 8.66025i 0.187383 0.324557i
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) −4.47214 + 7.74597i −0.167132 + 0.289480i
\(717\) −32.3607 56.0503i −1.20853 2.09324i
\(718\) 13.4164 + 23.2379i 0.500696 + 0.867231i
\(719\) −18.4164 + 31.8982i −0.686816 + 1.18960i 0.286046 + 0.958216i \(0.407659\pi\)
−0.972862 + 0.231385i \(0.925674\pi\)
\(720\) −24.1803 −0.901148
\(721\) 0 0
\(722\) −11.3607 −0.422801
\(723\) −18.4721 + 31.9947i −0.686986 + 1.18989i
\(724\) 2.38197 + 4.12569i 0.0885251 + 0.153330i
\(725\) 12.2361 + 21.1935i 0.454436 + 0.787107i
\(726\) −1.61803 + 2.80252i −0.0600509 + 0.104011i
\(727\) −18.0000 −0.667583 −0.333792 0.942647i \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 8.00000 13.8564i 0.296093 0.512849i
\(731\) 4.94427 + 8.56373i 0.182871 + 0.316741i
\(732\) −8.47214 14.6742i −0.313139 0.542373i
\(733\) 4.43769 7.68631i 0.163910 0.283900i −0.772358 0.635188i \(-0.780923\pi\)
0.936268 + 0.351287i \(0.114256\pi\)
\(734\) −21.4164 −0.790494
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 7.70820 13.3510i 0.283935 0.491790i
\(738\) 24.1803 + 41.8816i 0.890091 + 1.54168i
\(739\) −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i \(-0.286575\pi\)
−0.989230 + 0.146369i \(0.953241\pi\)
\(740\) −17.7082 + 30.6715i −0.650967 + 1.12751i
\(741\) −11.0557 −0.406142
\(742\) 0 0
\(743\) −13.8885 −0.509521 −0.254761 0.967004i \(-0.581997\pi\)
−0.254761 + 0.967004i \(0.581997\pi\)
\(744\) 3.23607 5.60503i 0.118640 0.205491i
\(745\) 36.1803 + 62.6662i 1.32555 + 2.29591i
\(746\) 3.00000 + 5.19615i 0.109838 + 0.190245i
\(747\) 38.0344 65.8776i 1.39161 2.41033i
\(748\) 6.47214 0.236645
\(749\) 0 0
\(750\) −4.94427 −0.180539
\(751\) −0.472136 + 0.817763i −0.0172285 + 0.0298406i −0.874511 0.485005i \(-0.838818\pi\)
0.857283 + 0.514846i \(0.172151\pi\)
\(752\) −1.00000 1.73205i −0.0364662 0.0631614i
\(753\) 40.0689 + 69.4013i 1.46019 + 2.52913i
\(754\) −2.76393 + 4.78727i −0.100656 + 0.174342i
\(755\) −38.8328 −1.41327
\(756\) 0 0
\(757\) 39.3050 1.42856 0.714281 0.699859i \(-0.246754\pi\)
0.714281 + 0.699859i \(0.246754\pi\)
\(758\) −2.76393 + 4.78727i −0.100391 + 0.173882i
\(759\) −6.47214 11.2101i −0.234924 0.406900i
\(760\) 4.47214 + 7.74597i 0.162221 + 0.280976i
\(761\) 7.70820 13.3510i 0.279422 0.483973i −0.691819 0.722071i \(-0.743190\pi\)
0.971241 + 0.238097i \(0.0765238\pi\)
\(762\) −38.8328 −1.40676
\(763\) 0 0
\(764\) 6.47214 0.234154
\(765\) 78.2492 135.532i 2.82911 4.90016i
\(766\) 5.94427 + 10.2958i 0.214775 + 0.372002i
\(767\) −4.47214 7.74597i −0.161479 0.279691i
\(768\) −1.61803 + 2.80252i −0.0583858 + 0.101127i
\(769\) 16.5836 0.598020 0.299010 0.954250i \(-0.403344\pi\)
0.299010 + 0.954250i \(0.403344\pi\)
\(770\) 0 0
\(771\) 35.4164 1.27549
\(772\) −1.47214 + 2.54981i −0.0529833 + 0.0917698i
\(773\) 1.14590 + 1.98475i 0.0412151 + 0.0713866i 0.885897 0.463882i \(-0.153544\pi\)
−0.844682 + 0.535268i \(0.820210\pi\)
\(774\) 5.70820 + 9.88690i 0.205177 + 0.355377i
\(775\) 5.47214 9.47802i 0.196565 0.340460i
\(776\) −3.52786