Properties

Label 930.2.i.g.211.1
Level $930$
Weight $2$
Character 930.211
Analytic conductor $7.426$
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] = [930,2,Mod(211,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.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: \(7.42608738798\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 930.211
Dual form 930.2.i.g.811.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{20} +(2.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +3.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +2.00000 q^{29} +1.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} +3.00000 q^{33} +(-1.50000 - 2.59808i) q^{34} -4.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 - 0.866025i) q^{37} +2.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(1.00000 - 1.73205i) q^{41} +(2.00000 - 3.46410i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +3.00000 q^{46} -1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.50000 - 2.59808i) q^{51} +(1.00000 - 1.73205i) q^{52} +(-2.00000 + 3.46410i) q^{53} -1.00000 q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.00000 - 3.46410i) q^{56} +2.00000 q^{58} +(2.00000 + 3.46410i) q^{59} +1.00000 q^{60} +6.00000 q^{61} +(2.00000 + 5.19615i) q^{62} +4.00000 q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +3.00000 q^{66} +(-5.50000 + 9.52628i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{75} -12.0000 q^{77} +2.00000 q^{78} +(6.50000 + 11.2583i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(2.00000 - 3.46410i) q^{84} -3.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(1.00000 + 1.73205i) q^{87} +(1.50000 - 2.59808i) q^{88} -8.00000 q^{89} +(0.500000 + 0.866025i) q^{90} -8.00000 q^{91} +3.00000 q^{92} +(-3.50000 + 4.33013i) q^{93} -1.00000 q^{94} +(0.500000 + 0.866025i) q^{96} +14.0000 q^{97} +(-4.50000 + 7.79423i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 2 q^{16} - 3 q^{17} - q^{18} + q^{20} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} - q^{25} + 2 q^{26} - 2 q^{27} - 4 q^{28} + 4 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} + 6 q^{33} - 3 q^{34} - 8 q^{35} - q^{36} - q^{37} + 4 q^{39} + q^{40} + 2 q^{41} + 4 q^{42} + q^{43} + 3 q^{44} + q^{45} + 6 q^{46} - 2 q^{47} + q^{48} - 9 q^{49} - q^{50} + 3 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 3 q^{55} - 4 q^{56} + 4 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 6 q^{66} - 11 q^{67} - 3 q^{68} + 3 q^{69} - 8 q^{70} - 6 q^{71} - q^{72} + 14 q^{73} - q^{74} + q^{75} - 24 q^{77} + 4 q^{78} + 13 q^{79} + q^{80} - q^{81} + 2 q^{82} - 12 q^{83} + 4 q^{84} - 6 q^{85} + q^{86} + 2 q^{87} + 3 q^{88} - 16 q^{89} + q^{90} - 16 q^{91} + 6 q^{92} - 7 q^{93} - 2 q^{94} + q^{96} + 28 q^{97} - 9 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 1.00000 0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −2.00000 3.46410i −0.755929 1.30931i −0.944911 0.327327i \(-0.893852\pi\)
0.188982 0.981981i \(-0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) −2.00000 3.46410i −0.534522 0.925820i
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 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
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) −1.00000 −0.192450
\(28\) −2.00000 3.46410i −0.377964 0.654654i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 1.00000 0.182574
\(31\) 2.00000 + 5.19615i 0.359211 + 0.933257i
\(32\) 1.00000 0.176777
\(33\) 3.00000 0.522233
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) −4.00000 −0.676123
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −0.500000 0.866025i −0.0821995 0.142374i 0.821995 0.569495i \(-0.192861\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 1.00000 1.73205i 0.156174 0.270501i −0.777312 0.629115i \(-0.783417\pi\)
0.933486 + 0.358614i \(0.116751\pi\)
\(42\) 2.00000 3.46410i 0.308607 0.534522i
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 3.00000 0.442326
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) 1.50000 2.59808i 0.210042 0.363803i
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) −2.00000 + 3.46410i −0.274721 + 0.475831i −0.970065 0.242846i \(-0.921919\pi\)
0.695344 + 0.718677i \(0.255252\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) −2.00000 3.46410i −0.267261 0.462910i
\(57\) 0 0
\(58\) 2.00000 0.262613
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 1.00000 0.129099
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 2.00000 + 5.19615i 0.254000 + 0.659912i
\(63\) 4.00000 0.503953
\(64\) 1.00000 0.125000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 3.00000 0.369274
\(67\) −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i \(0.401202\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) −4.00000 −0.478091
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) −12.0000 −1.36753
\(78\) 2.00000 0.226455
\(79\) 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i \(0.0944227\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 2.00000 3.46410i 0.218218 0.377964i
\(85\) −3.00000 −0.325396
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) 1.00000 + 1.73205i 0.107211 + 0.185695i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) −8.00000 −0.838628
\(92\) 3.00000 0.312772
\(93\) −3.50000 + 4.33013i −0.362933 + 0.449013i
\(94\) −1.00000 −0.103142
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −4.50000 + 7.79423i −0.454569 + 0.787336i
\(99\) 1.50000 + 2.59808i 0.150756 + 0.261116i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) 3.00000 5.19615i 0.295599 0.511992i −0.679525 0.733652i \(-0.737814\pi\)
0.975124 + 0.221660i \(0.0711475\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) −2.00000 3.46410i −0.195180 0.338062i
\(106\) −2.00000 + 3.46410i −0.194257 + 0.336463i
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) 0.500000 0.866025i 0.0474579 0.0821995i
\(112\) −2.00000 3.46410i −0.188982 0.327327i
\(113\) 0.500000 0.866025i 0.0470360 0.0814688i −0.841549 0.540181i \(-0.818356\pi\)
0.888585 + 0.458712i \(0.151689\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) 2.00000 0.185695
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 2.00000 + 3.46410i 0.184115 + 0.318896i
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) 1.00000 0.0912871
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 6.00000 0.543214
\(123\) 2.00000 0.180334
\(124\) 2.00000 + 5.19615i 0.179605 + 0.466628i
\(125\) −1.00000 −0.0894427
\(126\) 4.00000 0.356348
\(127\) −3.00000 5.19615i −0.266207 0.461084i 0.701672 0.712500i \(-0.252437\pi\)
−0.967879 + 0.251416i \(0.919104\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.500000 + 0.866025i −0.0440225 + 0.0762493i
\(130\) −1.00000 1.73205i −0.0877058 0.151911i
\(131\) −10.5000 18.1865i −0.917389 1.58896i −0.803365 0.595487i \(-0.796959\pi\)
−0.114024 0.993478i \(-0.536374\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) −5.50000 + 9.52628i −0.475128 + 0.822945i
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 1.50000 + 2.59808i 0.127688 + 0.221163i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) −4.00000 −0.338062
\(141\) −0.500000 0.866025i −0.0421076 0.0729325i
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 1.00000 1.73205i 0.0830455 0.143839i
\(146\) 7.00000 12.1244i 0.579324 1.00342i
\(147\) −9.00000 −0.742307
\(148\) −0.500000 0.866025i −0.0410997 0.0711868i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −23.0000 −1.87171 −0.935857 0.352381i \(-0.885372\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) −12.0000 −0.966988
\(155\) 5.50000 + 0.866025i 0.441771 + 0.0695608i
\(156\) 2.00000 0.160128
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 6.50000 + 11.2583i 0.517112 + 0.895665i
\(159\) −4.00000 −0.317221
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −6.00000 10.3923i −0.472866 0.819028i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 3.00000 0.234978 0.117489 0.993074i \(-0.462515\pi\)
0.117489 + 0.993074i \(0.462515\pi\)
\(164\) 1.00000 1.73205i 0.0780869 0.135250i
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) −8.00000 13.8564i −0.619059 1.07224i −0.989658 0.143448i \(-0.954181\pi\)
0.370599 0.928793i \(-0.379152\pi\)
\(168\) 2.00000 3.46410i 0.154303 0.267261i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) −3.00000 −0.230089
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) −11.0000 + 19.0526i −0.836315 + 1.44854i 0.0566411 + 0.998395i \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 1.00000 + 1.73205i 0.0758098 + 0.131306i
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −2.00000 + 3.46410i −0.150329 + 0.260378i
\(178\) −8.00000 −0.599625
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −6.00000 + 10.3923i −0.445976 + 0.772454i −0.998120 0.0612954i \(-0.980477\pi\)
0.552143 + 0.833749i \(0.313810\pi\)
\(182\) −8.00000 −0.592999
\(183\) 3.00000 + 5.19615i 0.221766 + 0.384111i
\(184\) 3.00000 0.221163
\(185\) −1.00000 −0.0735215
\(186\) −3.50000 + 4.33013i −0.256632 + 0.317500i
\(187\) −9.00000 −0.658145
\(188\) −1.00000 −0.0729325
\(189\) 2.00000 + 3.46410i 0.145479 + 0.251976i
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 1.00000 + 1.73205i 0.0719816 + 0.124676i 0.899770 0.436365i \(-0.143734\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 14.0000 1.00514
\(195\) 1.00000 1.73205i 0.0716115 0.124035i
\(196\) −4.50000 + 7.79423i −0.321429 + 0.556731i
\(197\) 4.00000 6.92820i 0.284988 0.493614i −0.687618 0.726073i \(-0.741344\pi\)
0.972606 + 0.232458i \(0.0746770\pi\)
\(198\) 1.50000 + 2.59808i 0.106600 + 0.184637i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −11.0000 −0.775880
\(202\) −3.00000 −0.211079
\(203\) −4.00000 6.92820i −0.280745 0.486265i
\(204\) 1.50000 2.59808i 0.105021 0.181902i
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 3.00000 5.19615i 0.209020 0.362033i
\(207\) −1.50000 + 2.59808i −0.104257 + 0.180579i
\(208\) 1.00000 1.73205i 0.0693375 0.120096i
\(209\) 0 0
\(210\) −2.00000 3.46410i −0.138013 0.239046i
\(211\) 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i \(-0.0778659\pi\)
−0.694857 + 0.719148i \(0.744533\pi\)
\(212\) −2.00000 + 3.46410i −0.137361 + 0.237915i
\(213\) −6.00000 −0.411113
\(214\) −4.00000 6.92820i −0.273434 0.473602i
\(215\) 1.00000 0.0681994
\(216\) −1.00000 −0.0680414
\(217\) 14.0000 17.3205i 0.950382 1.17579i
\(218\) 12.0000 0.812743
\(219\) 14.0000 0.946032
\(220\) −1.50000 2.59808i −0.101130 0.175162i
\(221\) −6.00000 −0.403604
\(222\) 0.500000 0.866025i 0.0335578 0.0581238i
\(223\) 13.0000 + 22.5167i 0.870544 + 1.50783i 0.861435 + 0.507869i \(0.169566\pi\)
0.00910984 + 0.999959i \(0.497100\pi\)
\(224\) −2.00000 3.46410i −0.133631 0.231455i
\(225\) 1.00000 0.0666667
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i \(0.209391\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) −6.00000 10.3923i −0.394771 0.683763i
\(232\) 2.00000 0.131306
\(233\) −11.0000 −0.720634 −0.360317 0.932830i \(-0.617331\pi\)
−0.360317 + 0.932830i \(0.617331\pi\)
\(234\) 1.00000 + 1.73205i 0.0653720 + 0.113228i
\(235\) −0.500000 + 0.866025i −0.0326164 + 0.0564933i
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) −6.50000 + 11.2583i −0.422220 + 0.731307i
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) −3.00000 + 5.19615i −0.194054 + 0.336111i −0.946590 0.322440i \(-0.895497\pi\)
0.752536 + 0.658551i \(0.228830\pi\)
\(240\) 1.00000 0.0645497
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 6.00000 0.384111
\(245\) 4.50000 + 7.79423i 0.287494 + 0.497955i
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) 2.00000 + 5.19615i 0.127000 + 0.329956i
\(249\) −12.0000 −0.760469
\(250\) −1.00000 −0.0632456
\(251\) −4.50000 7.79423i −0.284037 0.491967i 0.688338 0.725390i \(-0.258341\pi\)
−0.972375 + 0.233423i \(0.925007\pi\)
\(252\) 4.00000 0.251976
\(253\) 4.50000 7.79423i 0.282913 0.490019i
\(254\) −3.00000 5.19615i −0.188237 0.326036i
\(255\) −1.50000 2.59808i −0.0939336 0.162698i
\(256\) 1.00000 0.0625000
\(257\) 6.50000 11.2583i 0.405459 0.702275i −0.588916 0.808194i \(-0.700445\pi\)
0.994375 + 0.105919i \(0.0337784\pi\)
\(258\) −0.500000 + 0.866025i −0.0311286 + 0.0539164i
\(259\) −2.00000 + 3.46410i −0.124274 + 0.215249i
\(260\) −1.00000 1.73205i −0.0620174 0.107417i
\(261\) −1.00000 + 1.73205i −0.0618984 + 0.107211i
\(262\) −10.5000 18.1865i −0.648692 1.12357i
\(263\) −23.0000 −1.41824 −0.709120 0.705087i \(-0.750908\pi\)
−0.709120 + 0.705087i \(0.750908\pi\)
\(264\) 3.00000 0.184637
\(265\) 2.00000 + 3.46410i 0.122859 + 0.212798i
\(266\) 0 0
\(267\) −4.00000 6.92820i −0.244796 0.423999i
\(268\) −5.50000 + 9.52628i −0.335966 + 0.581910i
\(269\) −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i \(0.387814\pi\)
−0.985389 + 0.170321i \(0.945520\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) −4.00000 6.92820i −0.242091 0.419314i
\(274\) 1.50000 2.59808i 0.0906183 0.156956i
\(275\) −3.00000 −0.180907
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) 19.0000 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(278\) −14.0000 −0.839664
\(279\) −5.50000 0.866025i −0.329276 0.0518476i
\(280\) −4.00000 −0.239046
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) −0.500000 0.866025i −0.0297746 0.0515711i
\(283\) 11.0000 0.653882 0.326941 0.945045i \(-0.393982\pi\)
0.326941 + 0.945045i \(0.393982\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) −3.00000 5.19615i −0.177394 0.307255i
\(287\) −8.00000 −0.472225
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 1.00000 1.73205i 0.0587220 0.101710i
\(291\) 7.00000 + 12.1244i 0.410347 + 0.710742i
\(292\) 7.00000 12.1244i 0.409644 0.709524i
\(293\) 6.00000 + 10.3923i 0.350524 + 0.607125i 0.986341 0.164714i \(-0.0526703\pi\)
−0.635818 + 0.771839i \(0.719337\pi\)
\(294\) −9.00000 −0.524891
\(295\) 4.00000 0.232889
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) −1.50000 + 2.59808i −0.0870388 + 0.150756i
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) 2.00000 3.46410i 0.115278 0.199667i
\(302\) −23.0000 −1.32350
\(303\) −1.50000 2.59808i −0.0861727 0.149256i
\(304\) 0 0
\(305\) 3.00000 5.19615i 0.171780 0.297531i
\(306\) 3.00000 0.171499
\(307\) −8.00000 13.8564i −0.456584 0.790827i 0.542194 0.840254i \(-0.317594\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) −12.0000 −0.683763
\(309\) 6.00000 0.341328
\(310\) 5.50000 + 0.866025i 0.312379 + 0.0491869i
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 2.00000 0.113228
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) 18.0000 1.01580
\(315\) 2.00000 3.46410i 0.112687 0.195180i
\(316\) 6.50000 + 11.2583i 0.365654 + 0.633331i
\(317\) −4.00000 6.92820i −0.224662 0.389127i 0.731556 0.681782i \(-0.238795\pi\)
−0.956218 + 0.292655i \(0.905461\pi\)
\(318\) −4.00000 −0.224309
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 4.00000 6.92820i 0.223258 0.386695i
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −2.00000 −0.110940
\(326\) 3.00000 0.166155
\(327\) 6.00000 + 10.3923i 0.331801 + 0.574696i
\(328\) 1.00000 1.73205i 0.0552158 0.0956365i
\(329\) 2.00000 + 3.46410i 0.110264 + 0.190982i
\(330\) 1.50000 2.59808i 0.0825723 0.143019i
\(331\) −12.0000 + 20.7846i −0.659580 + 1.14243i 0.321145 + 0.947030i \(0.395932\pi\)
−0.980725 + 0.195395i \(0.937401\pi\)
\(332\) −6.00000 + 10.3923i −0.329293 + 0.570352i
\(333\) 1.00000 0.0547997
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) 5.50000 + 9.52628i 0.300497 + 0.520476i
\(336\) 2.00000 3.46410i 0.109109 0.188982i
\(337\) 16.0000 0.871576 0.435788 0.900049i \(-0.356470\pi\)
0.435788 + 0.900049i \(0.356470\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 1.00000 0.0543125
\(340\) −3.00000 −0.162698
\(341\) 16.5000 + 2.59808i 0.893525 + 0.140694i
\(342\) 0 0
\(343\) 8.00000 0.431959
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 3.00000 0.161515
\(346\) −11.0000 + 19.0526i −0.591364 + 1.02427i
\(347\) −13.0000 22.5167i −0.697877 1.20876i −0.969201 0.246270i \(-0.920795\pi\)
0.271325 0.962488i \(-0.412538\pi\)
\(348\) 1.00000 + 1.73205i 0.0536056 + 0.0928477i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −2.00000 + 3.46410i −0.106904 + 0.185164i
\(351\) −1.00000 + 1.73205i −0.0533761 + 0.0924500i
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −8.50000 14.7224i −0.452409 0.783596i 0.546126 0.837703i \(-0.316102\pi\)
−0.998535 + 0.0541072i \(0.982769\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) −8.00000 −0.423999
\(357\) −12.0000 −0.635107
\(358\) 4.50000 + 7.79423i 0.237832 + 0.411938i
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) −6.00000 + 10.3923i −0.315353 + 0.546207i
\(363\) −1.00000 + 1.73205i −0.0524864 + 0.0909091i
\(364\) −8.00000 −0.419314
\(365\) −7.00000 12.1244i −0.366397 0.634618i
\(366\) 3.00000 + 5.19615i 0.156813 + 0.271607i
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 3.00000 0.156386
\(369\) 1.00000 + 1.73205i 0.0520579 + 0.0901670i
\(370\) −1.00000 −0.0519875
\(371\) 16.0000 0.830679
\(372\) −3.50000 + 4.33013i −0.181467 + 0.224507i
\(373\) 3.00000 0.155334 0.0776671 0.996979i \(-0.475253\pi\)
0.0776671 + 0.996979i \(0.475253\pi\)
\(374\) −9.00000 −0.465379
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) −1.00000 −0.0515711
\(377\) 2.00000 3.46410i 0.103005 0.178410i
\(378\) 2.00000 + 3.46410i 0.102869 + 0.178174i
\(379\) 11.0000 + 19.0526i 0.565032 + 0.978664i 0.997047 + 0.0767976i \(0.0244695\pi\)
−0.432015 + 0.901867i \(0.642197\pi\)
\(380\) 0 0
\(381\) 3.00000 5.19615i 0.153695 0.266207i
\(382\) −5.00000 + 8.66025i −0.255822 + 0.443097i
\(383\) −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i \(-0.958522\pi\)
0.608290 + 0.793715i \(0.291856\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) 1.00000 + 1.73205i 0.0508987 + 0.0881591i
\(387\) −1.00000 −0.0508329
\(388\) 14.0000 0.710742
\(389\) −9.50000 16.4545i −0.481669 0.834275i 0.518110 0.855314i \(-0.326636\pi\)
−0.999779 + 0.0210389i \(0.993303\pi\)
\(390\) 1.00000 1.73205i 0.0506370 0.0877058i
\(391\) −4.50000 7.79423i −0.227575 0.394171i
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) 10.5000 18.1865i 0.529655 0.917389i
\(394\) 4.00000 6.92820i 0.201517 0.349038i
\(395\) 13.0000 0.654101
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −10.5000 18.1865i −0.526980 0.912756i −0.999506 0.0314391i \(-0.989991\pi\)
0.472526 0.881317i \(-0.343342\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 10.0000 0.499376 0.249688 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) −11.0000 −0.548630
\(403\) 11.0000 + 1.73205i 0.547949 + 0.0862796i
\(404\) −3.00000 −0.149256
\(405\) −1.00000 −0.0496904
\(406\) −4.00000 6.92820i −0.198517 0.343841i
\(407\) −3.00000 −0.148704
\(408\) 1.50000 2.59808i 0.0742611 0.128624i
\(409\) −1.50000 2.59808i −0.0741702 0.128467i 0.826555 0.562856i \(-0.190297\pi\)
−0.900725 + 0.434389i \(0.856964\pi\)
\(410\) −1.00000 1.73205i −0.0493865 0.0855399i
\(411\) 3.00000 0.147979
\(412\) 3.00000 5.19615i 0.147799 0.255996i
\(413\) 8.00000 13.8564i 0.393654 0.681829i
\(414\) −1.50000 + 2.59808i −0.0737210 + 0.127688i
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) −7.00000 12.1244i −0.342791 0.593732i
\(418\) 0 0
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) −2.00000 3.46410i −0.0975900 0.169031i
\(421\) −3.00000 + 5.19615i −0.146211 + 0.253245i −0.929824 0.368004i \(-0.880041\pi\)
0.783613 + 0.621249i \(0.213375\pi\)
\(422\) 4.00000 + 6.92820i 0.194717 + 0.337260i
\(423\) 0.500000 0.866025i 0.0243108 0.0421076i
\(424\) −2.00000 + 3.46410i −0.0971286 + 0.168232i
\(425\) −1.50000 + 2.59808i −0.0727607 + 0.126025i
\(426\) −6.00000 −0.290701
\(427\) −12.0000 20.7846i −0.580721 1.00584i
\(428\) −4.00000 6.92820i −0.193347 0.334887i
\(429\) 3.00000 5.19615i 0.144841 0.250873i
\(430\) 1.00000 0.0482243
\(431\) 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 14.0000 17.3205i 0.672022 0.831411i
\(435\) 2.00000 0.0958927
\(436\) 12.0000 0.574696
\(437\) 0 0
\(438\) 14.0000 0.668946
\(439\) 13.5000 23.3827i 0.644320 1.11599i −0.340138 0.940375i \(-0.610474\pi\)
0.984458 0.175619i \(-0.0561928\pi\)
\(440\) −1.50000 2.59808i −0.0715097 0.123858i
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) −6.00000 −0.285391
\(443\) 9.00000 15.5885i 0.427603 0.740630i −0.569057 0.822298i \(-0.692691\pi\)
0.996660 + 0.0816684i \(0.0260248\pi\)
\(444\) 0.500000 0.866025i 0.0237289 0.0410997i
\(445\) −4.00000 + 6.92820i −0.189618 + 0.328428i
\(446\) 13.0000 + 22.5167i 0.615568 + 1.06619i
\(447\) −3.00000 + 5.19615i −0.141895 + 0.245770i
\(448\) −2.00000 3.46410i −0.0944911 0.163663i
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 1.00000 0.0471405
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) 0.500000 0.866025i 0.0235180 0.0407344i
\(453\) −11.5000 19.9186i −0.540317 0.935857i
\(454\) 0 0
\(455\) −4.00000 + 6.92820i −0.187523 + 0.324799i
\(456\) 0 0
\(457\) −4.00000 −0.187112 −0.0935561 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) 14.0000 + 24.2487i 0.654177 + 1.13307i
\(459\) 1.50000 + 2.59808i 0.0700140 + 0.121268i
\(460\) 1.50000 2.59808i 0.0699379 0.121136i
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) −6.00000 10.3923i −0.279145 0.483494i
\(463\) −12.0000 −0.557687 −0.278844 0.960337i \(-0.589951\pi\)
−0.278844 + 0.960337i \(0.589951\pi\)
\(464\) 2.00000 0.0928477
\(465\) 2.00000 + 5.19615i 0.0927478 + 0.240966i
\(466\) −11.0000 −0.509565
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 1.00000 + 1.73205i 0.0462250 + 0.0800641i
\(469\) 44.0000 2.03173
\(470\) −0.500000 + 0.866025i −0.0230633 + 0.0399468i
\(471\) 9.00000 + 15.5885i 0.414698 + 0.718278i
\(472\) 2.00000 + 3.46410i 0.0920575 + 0.159448i
\(473\) 3.00000 0.137940
\(474\) −6.50000 + 11.2583i −0.298555 + 0.517112i
\(475\) 0 0
\(476\) −6.00000 + 10.3923i −0.275010 + 0.476331i
\(477\) −2.00000 3.46410i −0.0915737 0.158610i
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 1.00000 0.0456435
\(481\) −2.00000 −0.0911922
\(482\) −5.00000 8.66025i −0.227744 0.394464i
\(483\) 6.00000 10.3923i 0.273009 0.472866i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 7.00000 12.1244i 0.317854 0.550539i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −2.00000 + 3.46410i −0.0906287 + 0.156973i −0.907776 0.419456i \(-0.862221\pi\)
0.817147 + 0.576429i \(0.195554\pi\)
\(488\) 6.00000 0.271607
\(489\) 1.50000 + 2.59808i 0.0678323 + 0.117489i
\(490\) 4.50000 + 7.79423i 0.203289 + 0.352107i
\(491\) 7.50000 12.9904i 0.338470 0.586248i −0.645675 0.763612i \(-0.723424\pi\)
0.984145 + 0.177365i \(0.0567572\pi\)
\(492\) 2.00000 0.0901670
\(493\) −3.00000 5.19615i −0.135113 0.234023i
\(494\) 0 0
\(495\) 3.00000 0.134840
\(496\) 2.00000 + 5.19615i 0.0898027 + 0.233314i
\(497\) 24.0000 1.07655
\(498\) −12.0000 −0.537733
\(499\) −4.00000 6.92820i −0.179065 0.310149i 0.762496 0.646993i \(-0.223974\pi\)
−0.941560 + 0.336844i \(0.890640\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 8.00000 13.8564i 0.357414 0.619059i
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) −8.00000 13.8564i −0.356702 0.617827i 0.630705 0.776022i \(-0.282766\pi\)
−0.987408 + 0.158196i \(0.949432\pi\)
\(504\) 4.00000 0.178174
\(505\) −1.50000 + 2.59808i −0.0667491 + 0.115613i
\(506\) 4.50000 7.79423i 0.200049 0.346496i
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) −3.00000 5.19615i −0.133103 0.230542i
\(509\) 20.5000 35.5070i 0.908647 1.57382i 0.0927004 0.995694i \(-0.470450\pi\)
0.815946 0.578128i \(-0.196217\pi\)
\(510\) −1.50000 2.59808i −0.0664211 0.115045i
\(511\) −56.0000 −2.47729
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.50000 11.2583i 0.286703 0.496584i
\(515\) −3.00000 5.19615i −0.132196 0.228970i
\(516\) −0.500000 + 0.866025i −0.0220113 + 0.0381246i
\(517\) −1.50000 + 2.59808i −0.0659699 + 0.114263i
\(518\) −2.00000 + 3.46410i −0.0878750 + 0.152204i
\(519\) −22.0000 −0.965693
\(520\) −1.00000 1.73205i −0.0438529 0.0759555i
\(521\) −12.0000 20.7846i −0.525730 0.910590i −0.999551 0.0299693i \(-0.990459\pi\)
0.473821 0.880621i \(-0.342874\pi\)
\(522\) −1.00000 + 1.73205i −0.0437688 + 0.0758098i
\(523\) 27.0000 1.18063 0.590314 0.807174i \(-0.299004\pi\)
0.590314 + 0.807174i \(0.299004\pi\)
\(524\) −10.5000 18.1865i −0.458695 0.794482i
\(525\) −4.00000 −0.174574
\(526\) −23.0000 −1.00285
\(527\) 10.5000 12.9904i 0.457387 0.565870i
\(528\) 3.00000 0.130558
\(529\) −14.0000 −0.608696
\(530\) 2.00000 + 3.46410i 0.0868744 + 0.150471i
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −2.00000 3.46410i −0.0866296 0.150047i
\(534\) −4.00000 6.92820i −0.173097 0.299813i
\(535\) −8.00000 −0.345870
\(536\) −5.50000 + 9.52628i −0.237564 + 0.411473i
\(537\) −4.50000 + 7.79423i −0.194189 + 0.336346i
\(538\) −10.5000 + 18.1865i −0.452687 + 0.784077i
\(539\) 13.5000 + 23.3827i 0.581486 + 1.00716i
\(540\) −0.500000 + 0.866025i −0.0215166 + 0.0372678i
\(541\) 3.00000 + 5.19615i 0.128980 + 0.223400i 0.923282 0.384124i \(-0.125496\pi\)
−0.794302 + 0.607524i \(0.792163\pi\)
\(542\) 20.0000 0.859074
\(543\) −12.0000 −0.514969
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 6.00000 10.3923i 0.257012 0.445157i
\(546\) −4.00000 6.92820i −0.171184 0.296500i
\(547\) 7.50000 12.9904i 0.320677 0.555429i −0.659951 0.751309i \(-0.729423\pi\)
0.980628 + 0.195880i \(0.0627563\pi\)
\(548\) 1.50000 2.59808i 0.0640768 0.110984i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) −3.00000 −0.127920
\(551\) 0 0
\(552\) 1.50000 + 2.59808i 0.0638442 + 0.110581i
\(553\) 26.0000 45.0333i 1.10563 1.91501i
\(554\) 19.0000 0.807233
\(555\) −0.500000 0.866025i −0.0212238 0.0367607i
\(556\) −14.0000 −0.593732
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) −5.50000 0.866025i −0.232834 0.0366618i
\(559\) 2.00000 0.0845910
\(560\) −4.00000 −0.169031
\(561\) −4.50000 7.79423i −0.189990 0.329073i
\(562\) 30.0000 1.26547
\(563\) 7.00000 12.1244i 0.295015 0.510981i −0.679974 0.733237i \(-0.738009\pi\)
0.974988 + 0.222256i \(0.0713421\pi\)
\(564\) −0.500000 0.866025i −0.0210538 0.0364662i
\(565\) −0.500000 0.866025i −0.0210352 0.0364340i
\(566\) 11.0000 0.462364
\(567\) −2.00000 + 3.46410i −0.0839921 + 0.145479i
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −3.00000 5.19615i −0.125436 0.217262i
\(573\) −10.0000 −0.417756
\(574\) −8.00000 −0.333914
\(575\) −1.50000 2.59808i −0.0625543 0.108347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −12.0000 20.7846i −0.499567 0.865275i 0.500433 0.865775i \(-0.333174\pi\)
−1.00000 0.000500448i \(0.999841\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) −1.00000 + 1.73205i −0.0415586 + 0.0719816i
\(580\) 1.00000 1.73205i 0.0415227 0.0719195i
\(581\) 48.0000 1.99138
\(582\) 7.00000 + 12.1244i 0.290159 + 0.502571i
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) 7.00000 12.1244i 0.289662 0.501709i
\(585\) 2.00000 0.0826898
\(586\) 6.00000 + 10.3923i 0.247858 + 0.429302i
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) −9.00000 −0.371154
\(589\) 0 0
\(590\) 4.00000 0.164677
\(591\) 8.00000 0.329076
\(592\) −0.500000 0.866025i −0.0205499 0.0355934i
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 6.00000 + 10.3923i 0.245976 + 0.426043i
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 0 0
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) −9.00000 + 15.5885i −0.367730 + 0.636927i −0.989210 0.146503i \(-0.953198\pi\)
0.621480 + 0.783430i \(0.286532\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) 9.50000 + 16.4545i 0.387513 + 0.671192i 0.992114 0.125336i \(-0.0400009\pi\)
−0.604601 + 0.796528i \(0.706668\pi\)
\(602\) 2.00000 3.46410i 0.0815139 0.141186i
\(603\) −5.50000 9.52628i −0.223977 0.387940i
\(604\) −23.0000 −0.935857
\(605\) 2.00000 0.0813116
\(606\) −1.50000 2.59808i −0.0609333 0.105540i
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 0 0
\(609\) 4.00000 6.92820i 0.162088 0.280745i
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) −1.00000 + 1.73205i −0.0404557 + 0.0700713i
\(612\) 3.00000 0.121268
\(613\) 1.00000 + 1.73205i 0.0403896 + 0.0699569i 0.885514 0.464614i \(-0.153807\pi\)
−0.845124 + 0.534570i \(0.820473\pi\)
\(614\) −8.00000 13.8564i −0.322854 0.559199i
\(615\) 1.00000 1.73205i 0.0403239 0.0698430i
\(616\) −12.0000 −0.483494
\(617\) 21.5000 + 37.2391i 0.865557 + 1.49919i 0.866493 + 0.499190i \(0.166369\pi\)
−0.000935233 1.00000i \(0.500298\pi\)
\(618\) 6.00000 0.241355
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 5.50000 + 0.866025i 0.220885 + 0.0347804i
\(621\) −3.00000 −0.120386
\(622\) 18.0000 0.721734
\(623\) 16.0000 + 27.7128i 0.641026 + 1.11029i
\(624\) 2.00000 0.0800641
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −7.00000 12.1244i −0.279776 0.484587i
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) −1.50000 + 2.59808i −0.0598089 + 0.103592i
\(630\) 2.00000 3.46410i 0.0796819 0.138013i
\(631\) −6.50000 + 11.2583i −0.258761 + 0.448187i −0.965910 0.258877i \(-0.916648\pi\)
0.707149 + 0.707064i \(0.249981\pi\)
\(632\) 6.50000 + 11.2583i 0.258556 + 0.447832i
\(633\) −4.00000 + 6.92820i −0.158986 + 0.275371i
\(634\) −4.00000 6.92820i −0.158860 0.275154i
\(635\) −6.00000 −0.238103
\(636\) −4.00000 −0.158610
\(637\) 9.00000 + 15.5885i 0.356593 + 0.617637i
\(638\) 3.00000 5.19615i 0.118771 0.205718i
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −2.00000 + 3.46410i −0.0789953 + 0.136824i −0.902817 0.430026i \(-0.858505\pi\)
0.823821 + 0.566849i \(0.191838\pi\)
\(642\) 4.00000 6.92820i 0.157867 0.273434i
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) −6.00000 10.3923i −0.236433 0.409514i
\(645\) 0.500000 + 0.866025i 0.0196875 + 0.0340997i
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 12.0000 0.471041
\(650\) −2.00000 −0.0784465
\(651\) 22.0000 + 3.46410i 0.862248 + 0.135769i
\(652\) 3.00000 0.117489
\(653\) −4.00000 −0.156532 −0.0782660 0.996933i \(-0.524938\pi\)
−0.0782660 + 0.996933i \(0.524938\pi\)
\(654\) 6.00000 + 10.3923i 0.234619 + 0.406371i
\(655\) −21.0000 −0.820538
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 7.00000 + 12.1244i 0.273096 + 0.473016i
\(658\) 2.00000 + 3.46410i 0.0779681 + 0.135045i
\(659\) 9.00000 0.350590 0.175295 0.984516i \(-0.443912\pi\)
0.175295 + 0.984516i \(0.443912\pi\)
\(660\) 1.50000 2.59808i 0.0583874 0.101130i
\(661\) 21.0000 36.3731i 0.816805 1.41475i −0.0912190 0.995831i \(-0.529076\pi\)
0.908024 0.418917i \(-0.137590\pi\)
\(662\) −12.0000 + 20.7846i −0.466393 + 0.807817i
\(663\) −3.00000 5.19615i −0.116510 0.201802i
\(664\) −6.00000 + 10.3923i −0.232845 + 0.403300i
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 6.00000 0.232321
\(668\) −8.00000 13.8564i −0.309529 0.536120i
\(669\) −13.0000 + 22.5167i −0.502609 + 0.870544i
\(670\) 5.50000 + 9.52628i 0.212484 + 0.368032i
\(671\) 9.00000 15.5885i 0.347441 0.601786i
\(672\) 2.00000 3.46410i 0.0771517 0.133631i
\(673\) −17.0000 + 29.4449i −0.655302 + 1.13502i 0.326516 + 0.945192i \(0.394125\pi\)
−0.981818 + 0.189824i \(0.939208\pi\)
\(674\) 16.0000 0.616297
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 17.0000 29.4449i 0.653363 1.13166i −0.328938 0.944351i \(-0.606691\pi\)
0.982301 0.187307i \(-0.0599758\pi\)
\(678\) 1.00000 0.0384048
\(679\) −28.0000 48.4974i −1.07454 1.86116i
\(680\) −3.00000 −0.115045
\(681\) 0 0
\(682\) 16.5000 + 2.59808i 0.631818 + 0.0994855i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −1.50000 2.59808i −0.0573121 0.0992674i
\(686\) 8.00000 0.305441
\(687\) −14.0000 + 24.2487i −0.534133 + 0.925146i
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) 4.00000 + 6.92820i 0.152388 + 0.263944i
\(690\) 3.00000 0.114208
\(691\) −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i \(0.566655\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(692\) −11.0000 + 19.0526i −0.418157 + 0.724270i
\(693\) 6.00000 10.3923i 0.227921 0.394771i
\(694\) −13.0000 22.5167i −0.493473 0.854721i
\(695\) −7.00000 + 12.1244i −0.265525 + 0.459903i
\(696\) 1.00000 + 1.73205i 0.0379049 + 0.0656532i
\(697\) −6.00000 −0.227266
\(698\) 14.0000 0.529908
\(699\) −5.50000 9.52628i −0.208029 0.360317i
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) −13.5000 23.3827i −0.509888 0.883152i −0.999934 0.0114555i \(-0.996354\pi\)
0.490046 0.871696i \(-0.336980\pi\)
\(702\) −1.00000 + 1.73205i −0.0377426 + 0.0653720i
\(703\) 0 0
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) −1.00000 −0.0376622
\(706\) −8.50000 14.7224i −0.319902 0.554086i
\(707\) 6.00000 + 10.3923i 0.225653 + 0.390843i
\(708\) −2.00000 + 3.46410i −0.0751646 + 0.130189i
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 3.00000 + 5.19615i 0.112588 + 0.195008i
\(711\) −13.0000 −0.487538
\(712\) −8.00000 −0.299813
\(713\) 6.00000 + 15.5885i 0.224702 + 0.583792i
\(714\) −12.0000 −0.449089
\(715\) −6.00000 −0.224387
\(716\) 4.50000 + 7.79423i 0.168173 + 0.291284i
\(717\) −6.00000 −0.224074
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) 14.0000 + 24.2487i 0.522112 + 0.904324i 0.999669 + 0.0257237i \(0.00818900\pi\)
−0.477557 + 0.878601i \(0.658478\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −24.0000 −0.893807
\(722\) 9.50000 16.4545i 0.353553 0.612372i
\(723\) 5.00000 8.66025i 0.185952 0.322078i
\(724\) −6.00000 + 10.3923i −0.222988 + 0.386227i
\(725\) −1.00000 1.73205i −0.0371391 0.0643268i
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) −22.0000 38.1051i −0.815935 1.41324i −0.908655 0.417548i \(-0.862889\pi\)
0.0927199 0.995692i \(-0.470444\pi\)
\(728\) −8.00000 −0.296500
\(729\) 1.00000 0.0370370
\(730\) −7.00000 12.1244i −0.259082 0.448743i
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 3.00000 + 5.19615i 0.110883 + 0.192055i
\(733\) 6.50000 11.2583i 0.240083 0.415836i −0.720655 0.693294i \(-0.756159\pi\)
0.960738 + 0.277458i \(0.0894920\pi\)
\(734\) 0 0
\(735\) −4.50000 + 7.79423i −0.165985 + 0.287494i
\(736\) 3.00000 0.110581
\(737\) 16.5000 + 28.5788i 0.607785 + 1.05272i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) 5.00000 8.66025i 0.183928 0.318573i −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) −1.00000 −0.0367607
\(741\) 0 0
\(742\) 16.0000 0.587378
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) −3.50000 + 4.33013i −0.128316 + 0.158750i
\(745\) 6.00000 0.219823
\(746\) 3.00000 0.109838
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) −9.00000 −0.329073
\(749\) −16.0000 + 27.7128i −0.584627 + 1.01260i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 20.5000 + 35.5070i 0.748056 + 1.29567i 0.948753 + 0.316017i \(0.102346\pi\)
−0.200698 + 0.979653i \(0.564321\pi\)
\(752\) −1.00000 −0.0364662
\(753\) 4.50000 7.79423i 0.163989 0.284037i
\(754\) 2.00000 3.46410i 0.0728357 0.126155i
\(755\) −11.5000 + 19.9186i −0.418528 + 0.724912i
\(756\) 2.00000 + 3.46410i 0.0727393 + 0.125988i
\(757\) −13.5000 + 23.3827i −0.490666 + 0.849858i −0.999942 0.0107448i \(-0.996580\pi\)
0.509276 + 0.860603i \(0.329913\pi\)
\(758\) 11.0000 + 19.0526i 0.399538 + 0.692020i
\(759\) 9.00000 0.326679
\(760\) 0 0
\(761\) −14.0000 24.2487i −0.507500 0.879015i −0.999962 0.00868155i \(-0.997237\pi\)
0.492463 0.870334i \(-0.336097\pi\)
\(762\) 3.00000 5.19615i 0.108679 0.188237i
\(763\) −24.0000 41.5692i −0.868858 1.50491i
\(764\) −5.00000 + 8.66025i −0.180894 + 0.313317i
\(765\) 1.50000 2.59808i 0.0542326 0.0939336i
\(766\) −7.50000 + 12.9904i −0.270986 + 0.469362i
\(767\) 8.00000 0.288863
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −15.0000 25.9808i −0.540914 0.936890i −0.998852 0.0479061i \(-0.984745\pi\)
0.457938 0.888984i \(-0.348588\pi\)
\(770\) −6.00000 + 10.3923i −0.216225 + 0.374513i
\(771\) 13.0000 0.468184
\(772\) 1.00000 + 1.73205i 0.0359908 + 0.0623379i
\(773\) −10.0000 −0.359675 −0.179838