Properties

Label 546.2.i.f.79.1
Level $546$
Weight $2$
Character 546.79
Analytic conductor $4.360$
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] = [546,2,Mod(79,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.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: \(4.35983195036\)
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 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.79
Dual form 546.2.i.f.235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.500000 + 2.59808i) 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 q^{13} +(2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +1.00000 q^{20} +(-2.50000 + 0.866025i) q^{21} +3.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +2.00000 q^{34} +(-2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(4.00000 - 6.92820i) q^{37} +(-0.500000 - 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} -4.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{46} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(0.500000 - 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(3.50000 + 6.06218i) q^{59} +(0.500000 + 0.866025i) q^{60} +(2.00000 - 3.46410i) q^{61} -5.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(1.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{69} +(-2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(-7.50000 + 2.59808i) q^{77} -1.00000 q^{78} +(6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} -3.00000 q^{83} +(2.00000 + 1.73205i) q^{84} -2.00000 q^{85} +(4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(4.00000 - 6.92820i) q^{89} -1.00000 q^{90} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(-0.500000 + 0.866025i) q^{96} -15.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + 2 q^{20} - 5 q^{21} + 6 q^{22} - 6 q^{23} - q^{24} + 4 q^{25} - q^{26} - 2 q^{27} + 5 q^{28} + 18 q^{29} - q^{30} - 5 q^{31} + q^{32} - 3 q^{33} + 4 q^{34} - 4 q^{35} + 2 q^{36} + 8 q^{37} - q^{39} + q^{40} - 8 q^{41} - q^{42} + 3 q^{44} - q^{45} + 6 q^{46} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 2 q^{51} + q^{52} - q^{53} - q^{54} - 6 q^{55} + q^{56} + 9 q^{58} + 7 q^{59} + q^{60} + 4 q^{61} - 10 q^{62} - 4 q^{63} + 2 q^{64} + q^{65} + 3 q^{66} + 4 q^{67} + 2 q^{68} - 12 q^{69} - 5 q^{70} + 12 q^{71} + q^{72} - 6 q^{73} - 8 q^{74} - 4 q^{75} - 15 q^{77} - 2 q^{78} + 13 q^{79} - q^{80} - q^{81} - 4 q^{82} - 6 q^{83} + 4 q^{84} - 4 q^{85} + 9 q^{87} - 3 q^{88} + 8 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 5 q^{93} - q^{96} - 30 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) −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 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −1.00000 −0.277350
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.50000 + 0.866025i −0.545545 + 0.188982i
\(22\) 3.00000 0.639602
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) −1.00000 −0.192450
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 2.00000 0.342997
\(35\) −2.00000 1.73205i −0.338062 0.292770i
\(36\) 1.00000 0.166667
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 0 0
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) −0.500000 + 2.59808i −0.0771517 + 0.400892i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 4.00000 0.565685
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i \(-0.188546\pi\)
−0.898321 + 0.439340i \(0.855212\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −3.00000 −0.404520
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) −5.00000 −0.635001
\(63\) −2.00000 1.73205i −0.251976 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) 1.50000 + 2.59808i 0.184637 + 0.319801i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) −6.00000 −0.722315
\(70\) −2.50000 + 0.866025i −0.298807 + 0.103510i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −3.00000 5.19615i −0.351123 0.608164i 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) 0 0
\(77\) −7.50000 + 2.59808i −0.854704 + 0.296078i
\(78\) −1.00000 −0.113228
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.00000 + 3.46410i −0.220863 + 0.382546i
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 2.00000 + 1.73205i 0.218218 + 0.188982i
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 4.50000 + 7.79423i 0.482451 + 0.835629i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 4.00000 6.92820i 0.423999 0.734388i −0.572327 0.820025i \(-0.693959\pi\)
0.996326 + 0.0856373i \(0.0272926\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0.500000 2.59808i 0.0524142 0.272352i
\(92\) 6.00000 0.625543
\(93\) 2.50000 4.33013i 0.259238 0.449013i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −15.0000 −1.52302 −0.761510 0.648154i \(-0.775541\pi\)
−0.761510 + 0.648154i \(0.775541\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) −3.00000 −0.301511
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 1.00000 + 1.73205i 0.0990148 + 0.171499i
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0.500000 2.59808i 0.0487950 0.253546i
\(106\) −1.00000 −0.0971286
\(107\) −8.50000 + 14.7224i −0.821726 + 1.42327i 0.0826699 + 0.996577i \(0.473655\pi\)
−0.904396 + 0.426694i \(0.859678\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) 8.00000 0.759326
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) −3.00000 5.19615i −0.279751 0.484544i
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) 7.00000 0.644402
\(119\) −5.00000 + 1.73205i −0.458349 + 0.158777i
\(120\) 1.00000 0.0912871
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −2.00000 3.46410i −0.181071 0.313625i
\(123\) −2.00000 3.46410i −0.180334 0.312348i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −9.00000 −0.804984
\(126\) −2.50000 + 0.866025i −0.222718 + 0.0771517i
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) −3.00000 + 5.19615i −0.255377 + 0.442326i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) −0.500000 + 2.59808i −0.0422577 + 0.219578i
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) −1.50000 2.59808i −0.125436 0.217262i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) −6.00000 −0.496564
\(147\) −1.00000 6.92820i −0.0824786 0.571429i
\(148\) −8.00000 −0.657596
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) 5.50000 + 9.52628i 0.447584 + 0.775238i 0.998228 0.0595022i \(-0.0189513\pi\)
−0.550645 + 0.834740i \(0.685618\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) 5.00000 0.401610
\(156\) −0.500000 + 0.866025i −0.0400320 + 0.0693375i
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) −6.50000 11.2583i −0.517112 0.895665i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) −1.00000 −0.0790569
\(161\) −12.0000 10.3923i −0.945732 0.819028i
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) −1.50000 + 2.59808i −0.116423 + 0.201650i
\(167\) −4.00000 −0.309529 −0.154765 0.987951i \(-0.549462\pi\)
−0.154765 + 0.987951i \(0.549462\pi\)
\(168\) 2.50000 0.866025i 0.192879 0.0668153i
\(169\) 1.00000 0.0769231
\(170\) −1.00000 + 1.73205i −0.0766965 + 0.132842i
\(171\) 0 0
\(172\) 0 0
\(173\) 7.00000 12.1244i 0.532200 0.921798i −0.467093 0.884208i \(-0.654699\pi\)
0.999293 0.0375896i \(-0.0119679\pi\)
\(174\) 9.00000 0.682288
\(175\) −10.0000 + 3.46410i −0.755929 + 0.261861i
\(176\) −3.00000 −0.226134
\(177\) −3.50000 + 6.06218i −0.263076 + 0.455661i
\(178\) −4.00000 6.92820i −0.299813 0.519291i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) −2.00000 1.73205i −0.148250 0.128388i
\(183\) 4.00000 0.295689
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 4.00000 + 6.92820i 0.294086 + 0.509372i
\(186\) −2.50000 4.33013i −0.183309 0.317500i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 0 0
\(189\) 0.500000 2.59808i 0.0363696 0.188982i
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −9.50000 16.4545i −0.683825 1.18442i −0.973805 0.227387i \(-0.926982\pi\)
0.289980 0.957033i \(-0.406351\pi\)
\(194\) −7.50000 + 12.9904i −0.538469 + 0.932655i
\(195\) 1.00000 0.0716115
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 12.0000 + 20.7846i 0.850657 + 1.47338i 0.880616 + 0.473831i \(0.157129\pi\)
−0.0299585 + 0.999551i \(0.509538\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) −2.00000 + 3.46410i −0.141069 + 0.244339i
\(202\) 2.00000 0.140720
\(203\) −4.50000 + 23.3827i −0.315838 + 1.64114i
\(204\) 2.00000 0.140028
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) 0 0
\(210\) −2.00000 1.73205i −0.138013 0.119523i
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) 8.50000 + 14.7224i 0.581048 + 1.00640i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 12.5000 4.33013i 0.848555 0.293948i
\(218\) −16.0000 −1.08366
\(219\) 3.00000 5.19615i 0.202721 0.351123i
\(220\) 1.50000 + 2.59808i 0.101130 + 0.175162i
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 4.00000 6.92820i 0.268462 0.464991i
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) −4.00000 −0.266667
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) 6.50000 + 11.2583i 0.431420 + 0.747242i 0.996996 0.0774548i \(-0.0246793\pi\)
−0.565576 + 0.824696i \(0.691346\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) −6.00000 −0.395628
\(231\) −6.00000 5.19615i −0.394771 0.341882i
\(232\) −9.00000 −0.590879
\(233\) 7.00000 12.1244i 0.458585 0.794293i −0.540301 0.841472i \(-0.681690\pi\)
0.998886 + 0.0471787i \(0.0150230\pi\)
\(234\) −0.500000 0.866025i −0.0326860 0.0566139i
\(235\) 0 0
\(236\) 3.50000 6.06218i 0.227831 0.394614i
\(237\) 13.0000 0.844441
\(238\) −1.00000 + 5.19615i −0.0648204 + 0.336817i
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 13.5000 + 23.3827i 0.869611 + 1.50621i 0.862394 + 0.506237i \(0.168964\pi\)
0.00721719 + 0.999974i \(0.497703\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −4.00000 −0.256074
\(245\) 5.50000 4.33013i 0.351382 0.276642i
\(246\) −4.00000 −0.255031
\(247\) 0 0
\(248\) 2.50000 + 4.33013i 0.158750 + 0.274963i
\(249\) −1.50000 2.59808i −0.0950586 0.164646i
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) 23.0000 1.45175 0.725874 0.687828i \(-0.241436\pi\)
0.725874 + 0.687828i \(0.241436\pi\)
\(252\) −0.500000 + 2.59808i −0.0314970 + 0.163663i
\(253\) −18.0000 −1.13165
\(254\) 2.50000 4.33013i 0.156864 0.271696i
\(255\) −1.00000 1.73205i −0.0626224 0.108465i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.0000 22.5167i 0.810918 1.40455i −0.101305 0.994855i \(-0.532302\pi\)
0.912222 0.409695i \(-0.134365\pi\)
\(258\) 0 0
\(259\) 16.0000 + 13.8564i 0.994192 + 0.860995i
\(260\) −1.00000 −0.0620174
\(261\) −4.50000 + 7.79423i −0.278543 + 0.482451i
\(262\) 7.50000 + 12.9904i 0.463352 + 0.802548i
\(263\) 13.0000 + 22.5167i 0.801614 + 1.38844i 0.918553 + 0.395298i \(0.129359\pi\)
−0.116939 + 0.993139i \(0.537308\pi\)
\(264\) 1.50000 2.59808i 0.0923186 0.159901i
\(265\) 1.00000 0.0614295
\(266\) 0 0
\(267\) 8.00000 0.489592
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −4.50000 + 7.79423i −0.273356 + 0.473466i −0.969719 0.244224i \(-0.921467\pi\)
0.696363 + 0.717689i \(0.254800\pi\)
\(272\) −2.00000 −0.121268
\(273\) 2.50000 0.866025i 0.151307 0.0524142i
\(274\) 12.0000 0.724947
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) 5.00000 0.299342
\(280\) 2.00000 + 1.73205i 0.119523 + 0.103510i
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) 2.00000 10.3923i 0.118056 0.613438i
\(288\) −1.00000 −0.0589256
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 4.50000 + 7.79423i 0.264249 + 0.457693i
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) 15.0000 0.876309 0.438155 0.898900i \(-0.355632\pi\)
0.438155 + 0.898900i \(0.355632\pi\)
\(294\) −6.50000 2.59808i −0.379088 0.151523i
\(295\) −7.00000 −0.407556
\(296\) −4.00000 + 6.92820i −0.232495 + 0.402694i
\(297\) −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
\(300\) 4.00000 0.230940
\(301\) 0 0
\(302\) 11.0000 0.632979
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 0 0
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) −1.00000 + 1.73205i −0.0571662 + 0.0990148i
\(307\) −18.0000 −1.02731 −0.513657 0.857996i \(-0.671710\pi\)
−0.513657 + 0.857996i \(0.671710\pi\)
\(308\) 6.00000 + 5.19615i 0.341882 + 0.296078i
\(309\) 16.0000 0.910208
\(310\) 2.50000 4.33013i 0.141990 0.245935i
\(311\) −1.00000 1.73205i −0.0567048 0.0982156i 0.836280 0.548303i \(-0.184726\pi\)
−0.892984 + 0.450088i \(0.851393\pi\)
\(312\) 0.500000 + 0.866025i 0.0283069 + 0.0490290i
\(313\) −6.50000 + 11.2583i −0.367402 + 0.636358i −0.989158 0.146852i \(-0.953086\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 14.0000 0.790066
\(315\) 2.50000 0.866025i 0.140859 0.0487950i
\(316\) −13.0000 −0.731307
\(317\) −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i \(-0.860182\pi\)
0.820822 + 0.571184i \(0.193516\pi\)
\(318\) −0.500000 0.866025i −0.0280386 0.0485643i
\(319\) 13.5000 + 23.3827i 0.755855 + 1.30918i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −17.0000 −0.948847
\(322\) −15.0000 + 5.19615i −0.835917 + 0.289570i
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) 8.00000 13.8564i 0.442401 0.766261i
\(328\) 4.00000 0.220863
\(329\) 0 0
\(330\) −3.00000 −0.165145
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 1.50000 + 2.59808i 0.0823232 + 0.142588i
\(333\) 4.00000 + 6.92820i 0.219199 + 0.379663i
\(334\) −2.00000 + 3.46410i −0.109435 + 0.189547i
\(335\) −4.00000 −0.218543
\(336\) 0.500000 2.59808i 0.0272772 0.141737i
\(337\) 1.00000 0.0544735 0.0272367 0.999629i \(-0.491329\pi\)
0.0272367 + 0.999629i \(0.491329\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) 6.00000 + 10.3923i 0.325875 + 0.564433i
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 7.50000 12.9904i 0.406148 0.703469i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 3.00000 5.19615i 0.161515 0.279751i
\(346\) −7.00000 12.1244i −0.376322 0.651809i
\(347\) 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i \(0.104031\pi\)
−0.195507 + 0.980702i \(0.562635\pi\)
\(348\) 4.50000 7.79423i 0.241225 0.417815i
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) −2.00000 + 10.3923i −0.106904 + 0.555492i
\(351\) 1.00000 0.0533761
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 3.50000 + 6.06218i 0.186023 + 0.322201i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) −8.00000 −0.423999
\(357\) −4.00000 3.46410i −0.211702 0.183340i
\(358\) −12.0000 −0.634220
\(359\) 1.00000 1.73205i 0.0527780 0.0914141i −0.838429 0.545010i \(-0.816526\pi\)
0.891207 + 0.453596i \(0.149859\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) −4.00000 + 6.92820i −0.210235 + 0.364138i
\(363\) 2.00000 0.104973
\(364\) −2.50000 + 0.866025i −0.131036 + 0.0453921i
\(365\) 6.00000 0.314054
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) 1.50000 + 2.59808i 0.0782994 + 0.135618i 0.902516 0.430656i \(-0.141718\pi\)
−0.824217 + 0.566274i \(0.808384\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 2.00000 3.46410i 0.104116 0.180334i
\(370\) 8.00000 0.415900
\(371\) 2.50000 0.866025i 0.129794 0.0449618i
\(372\) −5.00000 −0.259238
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) 0 0
\(377\) −9.00000 −0.463524
\(378\) −2.00000 1.73205i −0.102869 0.0890871i
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 0 0
\(381\) 2.50000 + 4.33013i 0.128079 + 0.221839i
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) 13.0000 22.5167i 0.664269 1.15055i −0.315214 0.949021i \(-0.602076\pi\)
0.979483 0.201527i \(-0.0645904\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.50000 7.79423i 0.0764471 0.397231i
\(386\) −19.0000 −0.967075
\(387\) 0 0
\(388\) 7.50000 + 12.9904i 0.380755 + 0.659487i
\(389\) −17.0000 29.4449i −0.861934 1.49291i −0.870059 0.492947i \(-0.835920\pi\)
0.00812520 0.999967i \(-0.497414\pi\)
\(390\) 0.500000 0.866025i 0.0253185 0.0438529i
\(391\) −12.0000 −0.606866
\(392\) 6.50000 + 2.59808i 0.328300 + 0.131223i
\(393\) −15.0000 −0.756650
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) 6.50000 + 11.2583i 0.327050 + 0.566468i
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −17.0000 + 29.4449i −0.853206 + 1.47780i 0.0250943 + 0.999685i \(0.492011\pi\)
−0.878300 + 0.478110i \(0.841322\pi\)
\(398\) 24.0000 1.20301
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i \(-0.881200\pi\)
0.781345 + 0.624099i \(0.214534\pi\)
\(402\) 2.00000 + 3.46410i 0.0997509 + 0.172774i
\(403\) 2.50000 + 4.33013i 0.124534 + 0.215699i
\(404\) 1.00000 1.73205i 0.0497519 0.0861727i
\(405\) 1.00000 0.0496904
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) 24.0000 1.18964
\(408\) 1.00000 1.73205i 0.0495074 0.0857493i
\(409\) 5.50000 + 9.52628i 0.271957 + 0.471044i 0.969363 0.245633i \(-0.0789957\pi\)
−0.697406 + 0.716677i \(0.745662\pi\)
\(410\) −2.00000 3.46410i −0.0987730 0.171080i
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) −16.0000 −0.788263
\(413\) −17.5000 + 6.06218i −0.861119 + 0.298300i
\(414\) −6.00000 −0.294884
\(415\) 1.50000 2.59808i 0.0736321 0.127535i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 2.00000 + 3.46410i 0.0979404 + 0.169638i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −2.50000 + 0.866025i −0.121988 + 0.0422577i
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) −4.00000 + 6.92820i −0.194029 + 0.336067i
\(426\) 6.00000 0.290701
\(427\) 8.00000 + 6.92820i 0.387147 + 0.335279i
\(428\) 17.0000 0.821726
\(429\) 1.50000 2.59808i 0.0724207 0.125436i
\(430\) 0 0
\(431\) −13.0000 22.5167i −0.626188 1.08459i −0.988310 0.152459i \(-0.951281\pi\)
0.362122 0.932131i \(-0.382052\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 2.50000 12.9904i 0.120004 0.623558i
\(435\) −9.00000 −0.431517
\(436\) −8.00000 + 13.8564i −0.383131 + 0.663602i
\(437\) 0 0
\(438\) −3.00000 5.19615i −0.143346 0.248282i
\(439\) 14.5000 25.1147i 0.692047 1.19866i −0.279119 0.960257i \(-0.590042\pi\)
0.971166 0.238404i \(-0.0766244\pi\)
\(440\) 3.00000 0.143019
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) −2.00000 −0.0951303
\(443\) −19.5000 + 33.7750i −0.926473 + 1.60470i −0.137298 + 0.990530i \(0.543842\pi\)
−0.789175 + 0.614168i \(0.789492\pi\)
\(444\) −4.00000 6.92820i −0.189832 0.328798i
\(445\) 4.00000 + 6.92820i 0.189618 + 0.328428i
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 6.00000 0.283790
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) −2.00000 + 3.46410i −0.0942809 + 0.163299i
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) −5.50000 + 9.52628i −0.258413 + 0.447584i
\(454\) 13.0000 0.610120
\(455\) 2.00000 + 1.73205i 0.0937614 + 0.0811998i
\(456\) 0 0
\(457\) −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i \(-0.840779\pi\)
0.854094 + 0.520119i \(0.174112\pi\)
\(458\) −7.00000 12.1244i −0.327089 0.566534i
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) −26.0000 −1.21094 −0.605470 0.795868i \(-0.707015\pi\)
−0.605470 + 0.795868i \(0.707015\pi\)
\(462\) −7.50000 + 2.59808i −0.348932 + 0.120873i
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 2.50000 + 4.33013i 0.115935 + 0.200805i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −10.0000 + 3.46410i −0.461757 + 0.159957i
\(470\) 0 0
\(471\) −7.00000 + 12.1244i −0.322543 + 0.558661i
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 0 0
\(474\) 6.50000 11.2583i 0.298555 0.517112i
\(475\) 0 0
\(476\) 4.00000 + 3.46410i 0.183340 + 0.158777i
\(477\) 1.00000 0.0457869
\(478\) 11.0000 19.0526i 0.503128 0.871444i
\(479\) −15.0000 25.9808i −0.685367 1.18709i −0.973321 0.229447i \(-0.926308\pi\)
0.287954 0.957644i \(-0.407025\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) 27.0000 1.22982
\(483\) 3.00000 15.5885i 0.136505 0.709299i
\(484\) −2.00000 −0.0909091
\(485\) 7.50000 12.9904i 0.340557 0.589863i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 4.50000 + 7.79423i 0.203914 + 0.353190i 0.949786 0.312899i \(-0.101300\pi\)
−0.745872 + 0.666089i \(0.767967\pi\)
\(488\) −2.00000 + 3.46410i −0.0905357 + 0.156813i
\(489\) 4.00000 0.180886
\(490\) −1.00000 6.92820i −0.0451754 0.312984i
\(491\) −29.0000 −1.30875 −0.654376 0.756169i \(-0.727069\pi\)
−0.654376 + 0.756169i \(0.727069\pi\)
\(492\) −2.00000 + 3.46410i −0.0901670 + 0.156174i
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) 1.50000 2.59808i 0.0674200 0.116775i
\(496\) 5.00000 0.224507
\(497\) −3.00000 + 15.5885i −0.134568 + 0.699238i
\(498\) −3.00000 −0.134433
\(499\) −8.00000 + 13.8564i −0.358129 + 0.620298i −0.987648 0.156687i \(-0.949919\pi\)
0.629519 + 0.776985i \(0.283252\pi\)
\(500\) 4.50000 + 7.79423i 0.201246 + 0.348569i
\(501\) −2.00000 3.46410i −0.0893534 0.154765i
\(502\) 11.5000 19.9186i 0.513270 0.889010i
\(503\) −26.0000 −1.15928 −0.579641 0.814872i \(-0.696807\pi\)
−0.579641 + 0.814872i \(0.696807\pi\)
\(504\) 2.00000 + 1.73205i 0.0890871 + 0.0771517i
\(505\) −2.00000 −0.0889988
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) 0.500000 + 0.866025i 0.0222058 + 0.0384615i
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) 10.5000 18.1865i 0.465404 0.806104i −0.533815 0.845601i \(-0.679242\pi\)
0.999220 + 0.0394971i \(0.0125756\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 15.0000 5.19615i 0.663561 0.229864i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −13.0000 22.5167i −0.573405 0.993167i
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 0 0
\(517\) 0 0
\(518\) 20.0000 6.92820i 0.878750 0.304408i
\(519\) 14.0000 0.614532
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) −14.0000 24.2487i −0.613351 1.06236i −0.990671 0.136272i \(-0.956488\pi\)
0.377320 0.926083i \(-0.376846\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) 6.00000 10.3923i 0.262362 0.454424i −0.704507 0.709697i \(-0.748832\pi\)
0.966869 + 0.255273i \(0.0821653\pi\)
\(524\) 15.0000 0.655278
\(525\) −8.00000 6.92820i −0.349149 0.302372i
\(526\) 26.0000 1.13365
\(527\) 5.00000 8.66025i 0.217803 0.377247i
\(528\) −1.50000 2.59808i −0.0652791 0.113067i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0.500000 0.866025i 0.0217186 0.0376177i
\(531\) −7.00000 −0.303774
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 4.00000 6.92820i 0.173097 0.299813i
\(535\) −8.50000 14.7224i −0.367487 0.636506i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 6.00000 10.3923i 0.258919 0.448461i
\(538\) 3.00000 0.129339
\(539\) −3.00000 20.7846i −0.129219 0.895257i
\(540\) −1.00000 −0.0430331
\(541\) 16.0000 27.7128i 0.687894 1.19147i −0.284624 0.958639i \(-0.591869\pi\)
0.972518 0.232828i \(-0.0747978\pi\)
\(542\) 4.50000 + 7.79423i 0.193292 + 0.334791i
\(543\) −4.00000 6.92820i −0.171656 0.297318i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) 16.0000 0.685365
\(546\) 0.500000 2.59808i 0.0213980 0.111187i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) 2.00000 + 3.46410i 0.0853579 + 0.147844i
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) 26.0000 + 22.5167i 1.10563 + 0.957506i
\(554\) 22.0000 0.934690
\(555\) −4.00000 + 6.92820i −0.169791 + 0.294086i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) −8.50000 14.7224i −0.360157 0.623809i 0.627830 0.778351i \(-0.283943\pi\)
−0.987986 + 0.154541i \(0.950610\pi\)
\(558\) 2.50000 4.33013i 0.105833 0.183309i
\(559\) 0 0
\(560\) 2.50000 0.866025i 0.105644 0.0365963i
\(561\) −6.00000 −0.253320
\(562\) 0 0
\(563\) −1.50000 2.59808i −0.0632175 0.109496i 0.832684 0.553748i \(-0.186803\pi\)
−0.895902 + 0.444252i \(0.853470\pi\)
\(564\) 0 0
\(565\) −6.00000 + 10.3923i −0.252422 + 0.437208i
\(566\) −14.0000 −0.588464
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) −6.00000 −0.251754
\(569\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −1.50000 + 2.59808i −0.0627182 + 0.108631i
\(573\) 6.00000 0.250654
\(574\) −8.00000 6.92820i −0.333914 0.289178i
\(575\) −24.0000 −1.00087
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 1.50000 + 2.59808i 0.0624458 + 0.108159i 0.895558 0.444945i \(-0.146777\pi\)
−0.833112 + 0.553104i \(0.813443\pi\)
\(578\) −6.50000 11.2583i −0.270364 0.468285i
\(579\) 9.50000 16.4545i 0.394807 0.683825i
\(580\) 9.00000 0.373705
\(581\) 1.50000 7.79423i 0.0622305 0.323359i
\(582\) −15.0000 −0.621770
\(583\) 1.50000 2.59808i 0.0621237 0.107601i
\(584\) 3.00000 + 5.19615i 0.124141 + 0.215018i
\(585\) 0.500000 + 0.866025i 0.0206725 + 0.0358057i
\(586\) 7.50000 12.9904i 0.309822 0.536628i
\(587\) −9.00000 −0.371470 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(588\) −5.50000 + 4.33013i −0.226816 + 0.178571i
\(589\) 0 0
\(590\) −3.50000 + 6.06218i −0.144093 + 0.249576i
\(591\) −11.0000 19.0526i −0.452480 0.783718i
\(592\) 4.00000 + 6.92820i 0.164399 + 0.284747i
\(593\) 20.0000 34.6410i 0.821302 1.42254i −0.0834118 0.996515i \(-0.526582\pi\)
0.904713 0.426021i \(-0.140085\pi\)
\(594\) −3.00000 −0.123091
\(595\) 1.00000 5.19615i 0.0409960 0.213021i
\(596\) −6.00000 −0.245770
\(597\) −12.0000 + 20.7846i −0.491127 + 0.850657i
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −9.00000 15.5885i −0.367730 0.636927i 0.621480 0.783430i \(-0.286532\pi\)
−0.989210 + 0.146503i \(0.953198\pi\)
\(600\) 2.00000 3.46410i 0.0816497 0.141421i
\(601\) 19.0000 0.775026 0.387513 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 5.50000 9.52628i 0.223792 0.387619i
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) 1.00000 + 1.73205i 0.0406222 + 0.0703598i
\(607\) −0.500000 + 0.866025i −0.0202944 + 0.0351509i −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) 0 0
\(609\) −22.5000 + 7.79423i −0.911746 + 0.315838i
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) 1.00000 + 1.73205i 0.0404226 + 0.0700140i
\(613\) 14.0000 + 24.2487i 0.565455 + 0.979396i 0.997007 + 0.0773084i \(0.0246326\pi\)
−0.431553 + 0.902088i \(0.642034\pi\)
\(614\) −9.00000 + 15.5885i −0.363210 + 0.629099i
\(615\) 4.00000 0.161296
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) 4.00000 0.161034 0.0805170 0.996753i \(-0.474343\pi\)
0.0805170 + 0.996753i \(0.474343\pi\)
\(618\) 8.00000 13.8564i 0.321807 0.557386i
\(619\) −16.0000 27.7128i −0.643094 1.11387i −0.984738 0.174042i \(-0.944317\pi\)
0.341644 0.939829i \(-0.389016\pi\)
\(620\) −2.50000 4.33013i −0.100402 0.173902i
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) −2.00000 −0.0801927
\(623\) 16.0000 + 13.8564i 0.641026 + 0.555145i
\(624\) 1.00000 0.0400320
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 6.50000 + 11.2583i 0.259792 + 0.449973i
\(627\) 0 0
\(628\) 7.00000 12.1244i 0.279330 0.483814i
\(629\) 16.0000 0.637962
\(630\) 0.500000 2.59808i 0.0199205 0.103510i
\(631\) −13.0000 −0.517522 −0.258761 0.965941i \(-0.583314\pi\)
−0.258761 + 0.965941i \(0.583314\pi\)
\(632\) −6.50000 + 11.2583i −0.258556 + 0.447832i
\(633\) 10.0000 + 17.3205i 0.397464 + 0.688428i
\(634\) 1.50000 + 2.59808i 0.0595726 + 0.103183i
\(635\) −2.50000 + 4.33013i −0.0992095 + 0.171836i
\(636\) −1.00000 −0.0396526
\(637\) 6.50000 + 2.59808i 0.257539 + 0.102940i
\(638\) 27.0000 1.06894
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i \(-0.242826\pi\)
−0.959848 + 0.280521i \(0.909493\pi\)
\(642\) −8.50000 + 14.7224i −0.335468 + 0.581048i
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) −3.00000 + 15.5885i −0.118217 + 0.614271i
\(645\) 0 0
\(646\) 0 0
\(647\) −18.0000 31.1769i −0.707653 1.22569i −0.965726 0.259565i \(-0.916421\pi\)
0.258073 0.966126i \(-0.416913\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −10.5000 + 18.1865i −0.412161 + 0.713884i
\(650\) −4.00000 −0.156893
\(651\) 10.0000 + 8.66025i 0.391931 + 0.339422i
\(652\) −4.00000 −0.156652
\(653\) −19.5000 + 33.7750i −0.763094 + 1.32172i 0.178154 + 0.984003i \(0.442987\pi\)
−0.941248 + 0.337715i \(0.890346\pi\)
\(654\) −8.00000 13.8564i −0.312825 0.541828i
\(655\) −7.50000 12.9904i −0.293049 0.507576i
\(656\) 2.00000 3.46410i 0.0780869 0.135250i
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) −1.50000 + 2.59808i −0.0583874 + 0.101130i
\(661\) −13.0000 22.5167i −0.505641 0.875797i −0.999979 0.00652642i \(-0.997923\pi\)
0.494337 0.869270i \(-0.335411\pi\)
\(662\) 4.00000 + 6.92820i 0.155464 + 0.269272i
\(663\) 1.00000 1.73205i 0.0388368 0.0672673i
\(664\) 3.00000 0.116423
\(665\) 0 0
\(666\) 8.00000 0.309994
\(667\) −27.0000 + 46.7654i −1.04544 + 1.81076i
\(668\) 2.00000 + 3.46410i 0.0773823 + 0.134030i
\(669\) −0.500000 0.866025i −0.0193311 0.0334825i
\(670\) −2.00000 + 3.46410i −0.0772667 + 0.133830i
\(671\) 12.0000 0.463255
\(672\) −2.00000 1.73205i −0.0771517 0.0668153i
\(673\) 17.0000 0.655302 0.327651 0.944799i \(-0.393743\pi\)
0.327651 + 0.944799i \(0.393743\pi\)
\(674\) 0.500000 0.866025i 0.0192593 0.0333581i
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) −15.5000 + 26.8468i −0.595713 + 1.03181i 0.397732 + 0.917501i \(0.369797\pi\)
−0.993446 + 0.114304i \(0.963536\pi\)
\(678\) 12.0000 0.460857
\(679\) 7.50000 38.9711i 0.287824 1.49558i
\(680\) 2.00000 0.0766965
\(681\) −6.50000 + 11.2583i −0.249081 + 0.431420i
\(682\) −7.50000 12.9904i −0.287190 0.497427i
\(683\) 20.5000 + 35.5070i 0.784411 + 1.35864i 0.929350 + 0.369199i \(0.120368\pi\)
−0.144940 + 0.989440i \(0.546299\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 14.0000 0.534133
\(688\) 0 0
\(689\) 0.500000 + 0.866025i 0.0190485 + 0.0329929i
\(690\) −3.00000 5.19615i −0.114208 0.197814i
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −14.0000 −0.532200
\(693\) 1.50000 7.79423i 0.0569803 0.296078i
\(694\) 28.0000 1.06287
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) −4.50000 7.79423i −0.170572 0.295439i
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) −17.0000 + 29.4449i −0.643459 + 1.11450i
\(699\) 14.0000 0.529529
\(700\) 8.00000 + 6.92820i 0.302372 + 0.261861i
\(701\) −39.0000 −1.47301 −0.736505 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) 0.500000 0.866025i 0.0188713 0.0326860i
\(703\) 0 0
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) −5.00000 + 1.73205i −0.188044 + 0.0651405i
\(708\) 7.00000 0.263076
\(709\) 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i \(-0.670978\pi\)
0.999908 + 0.0135434i \(0.00431112\pi\)
\(710\) 3.00000 + 5.19615i 0.112588 + 0.195008i
\(711\) 6.50000 + 11.2583i 0.243769 + 0.422220i
\(712\) −4.00000 + 6.92820i −0.149906 + 0.259645i
\(713\) 30.0000 1.12351
\(714\) −5.00000 + 1.73205i −0.187120 + 0.0648204i
\(715\) 3.00000 0.112194
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 11.0000 + 19.0526i 0.410803 + 0.711531i
\(718\) −1.00000 1.73205i −0.0373197 0.0646396i
\(719\) −1.00000 + 1.73205i −0.0372937 + 0.0645946i −0.884070 0.467355i \(-0.845207\pi\)
0.846776 + 0.531949i \(0.178540\pi\)
\(720\) 1.00000 0.0372678
\(721\) 32.0000 + 27.7128i 1.19174 + 1.03208i
\(722\) 19.0000 0.707107
\(723\) −13.5000 + 23.3827i −0.502070 + 0.869611i
\(724\) 4.00000 + 6.92820i 0.148659 + 0.257485i
\(725\) 18.0000 + 31.1769i 0.668503 + 1.15788i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) −9.00000 −0.333792 −0.166896 0.985975i \(-0.553374\pi\)
−0.166896 + 0.985975i \(0.553374\pi\)
\(728\) −0.500000 + 2.59808i −0.0185312 + 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) −2.00000 3.46410i −0.0739221 0.128037i
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) 3.00000 0.110732
\(735\) 6.50000 + 2.59808i 0.239756 + 0.0958315i
\(736\) −6.00000 −0.221163
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) −2.00000 3.46410i −0.0736210 0.127515i
\(739\) 9.00000 + 15.5885i 0.331070 + 0.573431i 0.982722 0.185088i \(-0.0592569\pi\)
−0.651652 + 0.758518i \(0.725924\pi\)
\(740\) 4.00000 6.92820i 0.147043 0.254686i
\(741\) 0 0
\(742\) 0.500000 2.59808i 0.0183556 0.0953784i
\(743\) −20.0000 −0.733729 −0.366864 0.930274i \(-0.619569\pi\)
−0.366864 + 0.930274i \(0.619569\pi\)
\(744\) −2.50000 + 4.33013i −0.0916544 + 0.158750i
\(745\) 3.00000 + 5.19615i 0.109911 + 0.190372i
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 1.50000 2.59808i 0.0548821 0.0950586i
\(748\) 6.00000 0.219382
\(749\) −34.0000 29.4449i −1.24233 1.07589i
\(750\) −9.00000 −0.328634
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 0 0
\(753\) 11.5000 + 19.9186i 0.419083 + 0.725874i
\(754\) −4.50000 + 7.79423i −0.163880 + 0.283849i
\(755\) −11.0000 −0.400331
\(756\) −2.50000 + 0.866025i −0.0909241 + 0.0314970i
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −12.0000 + 20.7846i −0.435860 + 0.754931i
\(759\) −9.00000 15.5885i −0.326679 0.565825i
\(760\) 0 0
\(761\) 16.0000 27.7128i 0.580000 1.00459i −0.415479 0.909603i \(-0.636386\pi\)
0.995479 0.0949859i \(-0.0302806\pi\)
\(762\) 5.00000 0.181131
\(763\) 40.0000 13.8564i 1.44810 0.501636i
\(764\) −6.00000 −0.217072
\(765\) 1.00000 1.73205i 0.0361551 0.0626224i
\(766\) −13.0000 22.5167i −0.469709 0.813560i
\(767\) −3.50000 6.06218i −0.126378 0.218893i
\(768\) 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 5.19615i −0.216225 0.187256i
\(771\) 26.0000 0.936367
\(772\) −9.50000 + 16.4545i −0.341912 + 0.592210i
\(773\) −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i \(-0.271596\pi\)