Properties

Label 169.2.c.a.22.2
Level $169$
Weight $2$
Character 169.22
Analytic conductor $1.349$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(22,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.c (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: \(1.34947179416\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.22
Dual form 169.2.c.a.146.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.73205 q^{5} +(1.73205 + 3.00000i) q^{6} +1.73205 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.73205 q^{5} +(1.73205 + 3.00000i) q^{6} +1.73205 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +2.00000 q^{12} +(-1.73205 + 3.00000i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-1.50000 - 2.59808i) q^{17} -1.73205 q^{18} +(-1.73205 - 3.00000i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(-3.00000 + 5.19615i) q^{23} +(-1.73205 + 3.00000i) q^{24} -2.00000 q^{25} -4.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +(3.00000 + 5.19615i) q^{30} -3.46410 q^{31} +(-2.59808 - 4.50000i) q^{32} -5.19615 q^{34} +(-0.500000 + 0.866025i) q^{36} +(4.33013 - 7.50000i) q^{37} -6.00000 q^{38} +3.00000 q^{40} +(2.59808 - 4.50000i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-0.866025 - 1.50000i) q^{45} +(5.19615 + 9.00000i) q^{46} -3.46410 q^{47} +(5.00000 + 8.66025i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-1.73205 + 3.00000i) q^{50} +6.00000 q^{51} -3.00000 q^{53} +(-3.46410 + 6.00000i) q^{54} +6.92820 q^{57} +(2.59808 + 4.50000i) q^{58} +(-3.46410 - 6.00000i) q^{59} +3.46410 q^{60} +(-0.500000 - 0.866025i) q^{61} +(-3.00000 + 5.19615i) q^{62} +1.00000 q^{64} +(-1.73205 + 3.00000i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-6.00000 - 10.3923i) q^{69} +(1.73205 + 3.00000i) q^{71} +(-0.866025 - 1.50000i) q^{72} +1.73205 q^{73} +(-7.50000 - 12.9904i) q^{74} +(2.00000 - 3.46410i) q^{75} +(-1.73205 + 3.00000i) q^{76} +4.00000 q^{79} +(4.33013 - 7.50000i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-4.50000 - 7.79423i) q^{82} -13.8564 q^{83} +(-2.59808 - 4.50000i) q^{85} +13.8564 q^{86} +(-3.00000 - 5.19615i) q^{87} +(-3.46410 + 6.00000i) q^{89} -3.00000 q^{90} +6.00000 q^{92} +(3.46410 - 6.00000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 - 5.19615i) q^{95} +10.3923 q^{96} +(3.46410 + 6.00000i) q^{97} +(-6.06218 - 10.5000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 2 q^{4} - 2 q^{9} + 6 q^{10} + 8 q^{12} + 10 q^{16} - 6 q^{17} - 12 q^{23} - 8 q^{25} - 16 q^{27} - 6 q^{29} + 12 q^{30} - 2 q^{36} - 24 q^{38} + 12 q^{40} + 16 q^{43} + 20 q^{48} + 14 q^{49} + 24 q^{51} - 12 q^{53} - 2 q^{61} - 12 q^{62} + 4 q^{64} - 6 q^{68} - 24 q^{69} - 30 q^{74} + 8 q^{75} + 16 q^{79} + 22 q^{81} - 18 q^{82} - 12 q^{87} - 12 q^{90} + 24 q^{92} - 12 q^{94} - 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 1.50000i 0.612372 1.06066i −0.378467 0.925615i \(-0.623549\pi\)
0.990839 0.135045i \(-0.0431180\pi\)
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.73205 0.774597 0.387298 0.921954i \(-0.373408\pi\)
0.387298 + 0.921954i \(0.373408\pi\)
\(6\) 1.73205 + 3.00000i 0.707107 + 1.22474i
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 1.73205 0.612372
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 2.00000 0.577350
\(13\) 0 0
\(14\) 0 0
\(15\) −1.73205 + 3.00000i −0.447214 + 0.774597i
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) −1.73205 −0.408248
\(19\) −1.73205 3.00000i −0.397360 0.688247i 0.596040 0.802955i \(-0.296740\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) −0.866025 1.50000i −0.193649 0.335410i
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) −1.73205 + 3.00000i −0.353553 + 0.612372i
\(25\) −2.00000 −0.400000
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 3.00000 + 5.19615i 0.547723 + 0.948683i
\(31\) −3.46410 −0.622171 −0.311086 0.950382i \(-0.600693\pi\)
−0.311086 + 0.950382i \(0.600693\pi\)
\(32\) −2.59808 4.50000i −0.459279 0.795495i
\(33\) 0 0
\(34\) −5.19615 −0.891133
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 4.33013 7.50000i 0.711868 1.23299i −0.252286 0.967653i \(-0.581183\pi\)
0.964155 0.265340i \(-0.0854841\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 2.59808 4.50000i 0.405751 0.702782i −0.588657 0.808383i \(-0.700343\pi\)
0.994409 + 0.105601i \(0.0336766\pi\)
\(42\) 0 0
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) −0.866025 1.50000i −0.129099 0.223607i
\(46\) 5.19615 + 9.00000i 0.766131 + 1.32698i
\(47\) −3.46410 −0.505291 −0.252646 0.967559i \(-0.581301\pi\)
−0.252646 + 0.967559i \(0.581301\pi\)
\(48\) 5.00000 + 8.66025i 0.721688 + 1.25000i
\(49\) 3.50000 6.06218i 0.500000 0.866025i
\(50\) −1.73205 + 3.00000i −0.244949 + 0.424264i
\(51\) 6.00000 0.840168
\(52\) 0 0
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) −3.46410 + 6.00000i −0.471405 + 0.816497i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.92820 0.917663
\(58\) 2.59808 + 4.50000i 0.341144 + 0.590879i
\(59\) −3.46410 6.00000i −0.450988 0.781133i 0.547460 0.836832i \(-0.315595\pi\)
−0.998448 + 0.0556984i \(0.982261\pi\)
\(60\) 3.46410 0.447214
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −3.00000 + 5.19615i −0.381000 + 0.659912i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.73205 + 3.00000i −0.211604 + 0.366508i −0.952217 0.305424i \(-0.901202\pi\)
0.740613 + 0.671932i \(0.234535\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) −6.00000 10.3923i −0.722315 1.25109i
\(70\) 0 0
\(71\) 1.73205 + 3.00000i 0.205557 + 0.356034i 0.950310 0.311305i \(-0.100766\pi\)
−0.744753 + 0.667340i \(0.767433\pi\)
\(72\) −0.866025 1.50000i −0.102062 0.176777i
\(73\) 1.73205 0.202721 0.101361 0.994850i \(-0.467680\pi\)
0.101361 + 0.994850i \(0.467680\pi\)
\(74\) −7.50000 12.9904i −0.871857 1.51010i
\(75\) 2.00000 3.46410i 0.230940 0.400000i
\(76\) −1.73205 + 3.00000i −0.198680 + 0.344124i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 4.33013 7.50000i 0.484123 0.838525i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) −4.50000 7.79423i −0.496942 0.860729i
\(83\) −13.8564 −1.52094 −0.760469 0.649374i \(-0.775031\pi\)
−0.760469 + 0.649374i \(0.775031\pi\)
\(84\) 0 0
\(85\) −2.59808 4.50000i −0.281801 0.488094i
\(86\) 13.8564 1.49417
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) −3.46410 + 6.00000i −0.367194 + 0.635999i −0.989126 0.147073i \(-0.953015\pi\)
0.621932 + 0.783072i \(0.286348\pi\)
\(90\) −3.00000 −0.316228
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 3.46410 6.00000i 0.359211 0.622171i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 10.3923 1.06066
\(97\) 3.46410 + 6.00000i 0.351726 + 0.609208i 0.986552 0.163448i \(-0.0522615\pi\)
−0.634826 + 0.772655i \(0.718928\pi\)
\(98\) −6.06218 10.5000i −0.612372 1.06066i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 5.19615 9.00000i 0.514496 0.891133i
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.59808 + 4.50000i −0.252347 + 0.437079i
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 13.8564 1.32720 0.663602 0.748086i \(-0.269027\pi\)
0.663602 + 0.748086i \(0.269027\pi\)
\(110\) 0 0
\(111\) 8.66025 + 15.0000i 0.821995 + 1.42374i
\(112\) 0 0
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) 6.00000 10.3923i 0.561951 0.973329i
\(115\) −5.19615 + 9.00000i −0.484544 + 0.839254i
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) −1.73205 −0.156813
\(123\) 5.19615 + 9.00000i 0.468521 + 0.811503i
\(124\) 1.73205 + 3.00000i 0.155543 + 0.269408i
\(125\) −12.1244 −1.08444
\(126\) 0 0
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) 6.06218 10.5000i 0.535826 0.928078i
\(129\) −16.0000 −1.40872
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.00000 + 5.19615i 0.259161 + 0.448879i
\(135\) −6.92820 −0.596285
\(136\) −2.59808 4.50000i −0.222783 0.385872i
\(137\) 7.79423 + 13.5000i 0.665906 + 1.15338i 0.979039 + 0.203674i \(0.0652881\pi\)
−0.313133 + 0.949709i \(0.601379\pi\)
\(138\) −20.7846 −1.76930
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) 3.46410 6.00000i 0.291730 0.505291i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) −2.59808 + 4.50000i −0.215758 + 0.373705i
\(146\) 1.50000 2.59808i 0.124141 0.215018i
\(147\) 7.00000 + 12.1244i 0.577350 + 1.00000i
\(148\) −8.66025 −0.711868
\(149\) −9.52628 16.5000i −0.780423 1.35173i −0.931695 0.363241i \(-0.881670\pi\)
0.151272 0.988492i \(-0.451663\pi\)
\(150\) −3.46410 6.00000i −0.282843 0.489898i
\(151\) 17.3205 1.40952 0.704761 0.709444i \(-0.251054\pi\)
0.704761 + 0.709444i \(0.251054\pi\)
\(152\) −3.00000 5.19615i −0.243332 0.421464i
\(153\) −1.50000 + 2.59808i −0.121268 + 0.210042i
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 3.46410 6.00000i 0.275589 0.477334i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) −4.50000 7.79423i −0.355756 0.616188i
\(161\) 0 0
\(162\) −9.52628 16.5000i −0.748455 1.29636i
\(163\) −10.3923 18.0000i −0.813988 1.40987i −0.910052 0.414494i \(-0.863959\pi\)
0.0960641 0.995375i \(-0.469375\pi\)
\(164\) −5.19615 −0.405751
\(165\) 0 0
\(166\) −12.0000 + 20.7846i −0.931381 + 1.61320i
\(167\) −6.92820 + 12.0000i −0.536120 + 0.928588i 0.462988 + 0.886365i \(0.346777\pi\)
−0.999108 + 0.0422232i \(0.986556\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −9.00000 −0.690268
\(171\) −1.73205 + 3.00000i −0.132453 + 0.229416i
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) −10.3923 −0.787839
\(175\) 0 0
\(176\) 0 0
\(177\) 13.8564 1.04151
\(178\) 6.00000 + 10.3923i 0.449719 + 0.778936i
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) −0.866025 + 1.50000i −0.0645497 + 0.111803i
\(181\) −11.0000 −0.817624 −0.408812 0.912619i \(-0.634057\pi\)
−0.408812 + 0.912619i \(0.634057\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) −5.19615 + 9.00000i −0.383065 + 0.663489i
\(185\) 7.50000 12.9904i 0.551411 0.955072i
\(186\) −6.00000 10.3923i −0.439941 0.762001i
\(187\) 0 0
\(188\) 1.73205 + 3.00000i 0.126323 + 0.218797i
\(189\) 0 0
\(190\) −10.3923 −0.753937
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) −1.00000 + 1.73205i −0.0721688 + 0.125000i
\(193\) −2.59808 + 4.50000i −0.187014 + 0.323917i −0.944253 0.329220i \(-0.893214\pi\)
0.757240 + 0.653137i \(0.226548\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −6.92820 + 12.0000i −0.493614 + 0.854965i −0.999973 0.00735824i \(-0.997658\pi\)
0.506359 + 0.862323i \(0.330991\pi\)
\(198\) 0 0
\(199\) −1.00000 1.73205i −0.0708881 0.122782i 0.828403 0.560133i \(-0.189250\pi\)
−0.899291 + 0.437351i \(0.855917\pi\)
\(200\) −3.46410 −0.244949
\(201\) −3.46410 6.00000i −0.244339 0.423207i
\(202\) 2.59808 + 4.50000i 0.182800 + 0.316619i
\(203\) 0 0
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 8.66025 15.0000i 0.603388 1.04510i
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 + 8.66025i −0.344214 + 0.596196i −0.985211 0.171347i \(-0.945188\pi\)
0.640996 + 0.767544i \(0.278521\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) −6.92820 −0.474713
\(214\) 5.19615 + 9.00000i 0.355202 + 0.615227i
\(215\) 6.92820 + 12.0000i 0.472500 + 0.818393i
\(216\) −6.92820 −0.471405
\(217\) 0 0
\(218\) 12.0000 20.7846i 0.812743 1.40771i
\(219\) −1.73205 + 3.00000i −0.117041 + 0.202721i
\(220\) 0 0
\(221\) 0 0
\(222\) 30.0000 2.01347
\(223\) 5.19615 9.00000i 0.347960 0.602685i −0.637927 0.770097i \(-0.720208\pi\)
0.985887 + 0.167412i \(0.0535411\pi\)
\(224\) 0 0
\(225\) 1.00000 + 1.73205i 0.0666667 + 0.115470i
\(226\) 25.9808 1.72821
\(227\) 12.1244 + 21.0000i 0.804722 + 1.39382i 0.916479 + 0.400083i \(0.131019\pi\)
−0.111757 + 0.993736i \(0.535648\pi\)
\(228\) −3.46410 6.00000i −0.229416 0.397360i
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 9.00000 + 15.5885i 0.593442 + 1.02787i
\(231\) 0 0
\(232\) −2.59808 + 4.50000i −0.170572 + 0.295439i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −3.46410 + 6.00000i −0.225494 + 0.390567i
\(237\) −4.00000 + 6.92820i −0.259828 + 0.450035i
\(238\) 0 0
\(239\) 20.7846 1.34444 0.672222 0.740349i \(-0.265340\pi\)
0.672222 + 0.740349i \(0.265340\pi\)
\(240\) 8.66025 + 15.0000i 0.559017 + 0.968246i
\(241\) 0.866025 + 1.50000i 0.0557856 + 0.0966235i 0.892570 0.450910i \(-0.148900\pi\)
−0.836784 + 0.547533i \(0.815567\pi\)
\(242\) 19.0526 1.22474
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) −0.500000 + 0.866025i −0.0320092 + 0.0554416i
\(245\) 6.06218 10.5000i 0.387298 0.670820i
\(246\) 18.0000 1.14764
\(247\) 0 0
\(248\) −6.00000 −0.381000
\(249\) 13.8564 24.0000i 0.878114 1.52094i
\(250\) −10.5000 + 18.1865i −0.664078 + 1.15022i
\(251\) −9.00000 15.5885i −0.568075 0.983935i −0.996756 0.0804789i \(-0.974355\pi\)
0.428681 0.903456i \(-0.358978\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.73205 + 3.00000i 0.108679 + 0.188237i
\(255\) 10.3923 0.650791
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) −13.8564 + 24.0000i −0.862662 + 1.49417i
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 15.5885 27.0000i 0.963058 1.66807i
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) −5.19615 −0.319197
\(266\) 0 0
\(267\) −6.92820 12.0000i −0.423999 0.734388i
\(268\) 3.46410 0.211604
\(269\) 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) −6.00000 + 10.3923i −0.365148 + 0.632456i
\(271\) 10.3923 18.0000i 0.631288 1.09342i −0.356001 0.934485i \(-0.615860\pi\)
0.987289 0.158937i \(-0.0508066\pi\)
\(272\) −15.0000 −0.909509
\(273\) 0 0
\(274\) 27.0000 1.63113
\(275\) 0 0
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i \(-0.234109\pi\)
−0.951807 + 0.306699i \(0.900776\pi\)
\(278\) 6.92820 0.415526
\(279\) 1.73205 + 3.00000i 0.103695 + 0.179605i
\(280\) 0 0
\(281\) −22.5167 −1.34323 −0.671616 0.740900i \(-0.734399\pi\)
−0.671616 + 0.740900i \(0.734399\pi\)
\(282\) −6.00000 10.3923i −0.357295 0.618853i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 1.73205 3.00000i 0.102778 0.178017i
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) 0 0
\(288\) −2.59808 + 4.50000i −0.153093 + 0.265165i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 4.50000 + 7.79423i 0.264249 + 0.457693i
\(291\) −13.8564 −0.812277
\(292\) −0.866025 1.50000i −0.0506803 0.0877809i
\(293\) −2.59808 4.50000i −0.151781 0.262893i 0.780101 0.625653i \(-0.215168\pi\)
−0.931882 + 0.362761i \(0.881834\pi\)
\(294\) 24.2487 1.41421
\(295\) −6.00000 10.3923i −0.349334 0.605063i
\(296\) 7.50000 12.9904i 0.435929 0.755051i
\(297\) 0 0
\(298\) −33.0000 −1.91164
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) 15.0000 25.9808i 0.863153 1.49502i
\(303\) −3.00000 5.19615i −0.172345 0.298511i
\(304\) −17.3205 −0.993399
\(305\) −0.866025 1.50000i −0.0495885 0.0858898i
\(306\) 2.59808 + 4.50000i 0.148522 + 0.257248i
\(307\) −17.3205 −0.988534 −0.494267 0.869310i \(-0.664563\pi\)
−0.494267 + 0.869310i \(0.664563\pi\)
\(308\) 0 0
\(309\) −10.0000 + 17.3205i −0.568880 + 0.985329i
\(310\) −5.19615 + 9.00000i −0.295122 + 0.511166i
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) −11.2583 + 19.5000i −0.635344 + 1.10045i
\(315\) 0 0
\(316\) −2.00000 3.46410i −0.112509 0.194871i
\(317\) 5.19615 0.291845 0.145922 0.989296i \(-0.453385\pi\)
0.145922 + 0.989296i \(0.453385\pi\)
\(318\) −5.19615 9.00000i −0.291386 0.504695i
\(319\) 0 0
\(320\) 1.73205 0.0968246
\(321\) −6.00000 10.3923i −0.334887 0.580042i
\(322\) 0 0
\(323\) −5.19615 + 9.00000i −0.289122 + 0.500773i
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −36.0000 −1.99386
\(327\) −13.8564 + 24.0000i −0.766261 + 1.32720i
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.8564 24.0000i −0.761617 1.31916i −0.942017 0.335566i \(-0.891072\pi\)
0.180400 0.983593i \(-0.442261\pi\)
\(332\) 6.92820 + 12.0000i 0.380235 + 0.658586i
\(333\) −8.66025 −0.474579
\(334\) 12.0000 + 20.7846i 0.656611 + 1.13728i
\(335\) −3.00000 + 5.19615i −0.163908 + 0.283896i
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) −30.0000 −1.62938
\(340\) −2.59808 + 4.50000i −0.140900 + 0.244047i
\(341\) 0 0
\(342\) 3.00000 + 5.19615i 0.162221 + 0.280976i
\(343\) 0 0
\(344\) 6.92820 + 12.0000i 0.373544 + 0.646997i
\(345\) −10.3923 18.0000i −0.559503 0.969087i
\(346\) 10.3923 0.558694
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) −3.00000 + 5.19615i −0.160817 + 0.278543i
\(349\) 6.92820 12.0000i 0.370858 0.642345i −0.618840 0.785517i \(-0.712397\pi\)
0.989698 + 0.143172i \(0.0457302\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −16.4545 + 28.5000i −0.875784 + 1.51690i −0.0198582 + 0.999803i \(0.506321\pi\)
−0.855926 + 0.517099i \(0.827012\pi\)
\(354\) 12.0000 20.7846i 0.637793 1.10469i
\(355\) 3.00000 + 5.19615i 0.159223 + 0.275783i
\(356\) 6.92820 0.367194
\(357\) 0 0
\(358\) 0 0
\(359\) −6.92820 −0.365657 −0.182828 0.983145i \(-0.558525\pi\)
−0.182828 + 0.983145i \(0.558525\pi\)
\(360\) −1.50000 2.59808i −0.0790569 0.136931i
\(361\) 3.50000 6.06218i 0.184211 0.319062i
\(362\) −9.52628 + 16.5000i −0.500690 + 0.867221i
\(363\) −22.0000 −1.15470
\(364\) 0 0
\(365\) 3.00000 0.157027
\(366\) 1.73205 3.00000i 0.0905357 0.156813i
\(367\) 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i \(-0.638648\pi\)
0.996129 0.0879086i \(-0.0280183\pi\)
\(368\) 15.0000 + 25.9808i 0.781929 + 1.35434i
\(369\) −5.19615 −0.270501
\(370\) −12.9904 22.5000i −0.675338 1.16972i
\(371\) 0 0
\(372\) −6.92820 −0.359211
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) 0 0
\(375\) 12.1244 21.0000i 0.626099 1.08444i
\(376\) −6.00000 −0.309426
\(377\) 0 0
\(378\) 0 0
\(379\) 12.1244 21.0000i 0.622786 1.07870i −0.366178 0.930545i \(-0.619334\pi\)
0.988964 0.148153i \(-0.0473327\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) −2.00000 3.46410i −0.102463 0.177471i
\(382\) −31.1769 −1.59515
\(383\) −10.3923 18.0000i −0.531022 0.919757i −0.999345 0.0361995i \(-0.988475\pi\)
0.468323 0.883558i \(-0.344859\pi\)
\(384\) 12.1244 + 21.0000i 0.618718 + 1.07165i
\(385\) 0 0
\(386\) 4.50000 + 7.79423i 0.229044 + 0.396716i
\(387\) 4.00000 6.92820i 0.203331 0.352180i
\(388\) 3.46410 6.00000i 0.175863 0.304604i
\(389\) 9.00000 0.456318 0.228159 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 6.06218 10.5000i 0.306186 0.530330i
\(393\) −18.0000 + 31.1769i −0.907980 + 1.57267i
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) 6.92820 0.348596
\(396\) 0 0
\(397\) 6.92820 + 12.0000i 0.347717 + 0.602263i 0.985843 0.167668i \(-0.0536238\pi\)
−0.638127 + 0.769931i \(0.720290\pi\)
\(398\) −3.46410 −0.173640
\(399\) 0 0
\(400\) −5.00000 + 8.66025i −0.250000 + 0.433013i
\(401\) −0.866025 + 1.50000i −0.0432472 + 0.0749064i −0.886839 0.462079i \(-0.847104\pi\)
0.843592 + 0.536985i \(0.180437\pi\)
\(402\) −12.0000 −0.598506
\(403\) 0 0
\(404\) 3.00000 0.149256
\(405\) 9.52628 16.5000i 0.473365 0.819892i
\(406\) 0 0
\(407\) 0 0
\(408\) 10.3923 0.514496
\(409\) 7.79423 + 13.5000i 0.385400 + 0.667532i 0.991825 0.127609i \(-0.0407302\pi\)
−0.606425 + 0.795141i \(0.707397\pi\)
\(410\) −7.79423 13.5000i −0.384930 0.666717i
\(411\) −31.1769 −1.53784
\(412\) −5.00000 8.66025i −0.246332 0.426660i
\(413\) 0 0
\(414\) 5.19615 9.00000i 0.255377 0.442326i
\(415\) −24.0000 −1.17811
\(416\) 0 0
\(417\) −8.00000 −0.391762
\(418\) 0 0
\(419\) −9.00000 + 15.5885i −0.439679 + 0.761546i −0.997665 0.0683046i \(-0.978241\pi\)
0.557986 + 0.829851i \(0.311574\pi\)
\(420\) 0 0
\(421\) −15.5885 −0.759735 −0.379867 0.925041i \(-0.624030\pi\)
−0.379867 + 0.925041i \(0.624030\pi\)
\(422\) 8.66025 + 15.0000i 0.421575 + 0.730189i
\(423\) 1.73205 + 3.00000i 0.0842152 + 0.145865i
\(424\) −5.19615 −0.252347
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) −6.00000 + 10.3923i −0.290701 + 0.503509i
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 24.0000 1.15738
\(431\) 3.46410 6.00000i 0.166860 0.289010i −0.770454 0.637495i \(-0.779971\pi\)
0.937314 + 0.348485i \(0.113304\pi\)
\(432\) −10.0000 + 17.3205i −0.481125 + 0.833333i
\(433\) −8.50000 14.7224i −0.408484 0.707515i 0.586236 0.810140i \(-0.300609\pi\)
−0.994720 + 0.102625i \(0.967276\pi\)
\(434\) 0 0
\(435\) −5.19615 9.00000i −0.249136 0.431517i
\(436\) −6.92820 12.0000i −0.331801 0.574696i
\(437\) 20.7846 0.994263
\(438\) 3.00000 + 5.19615i 0.143346 + 0.248282i
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) 8.66025 15.0000i 0.410997 0.711868i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −9.00000 15.5885i −0.426162 0.738135i
\(447\) 38.1051 1.80231
\(448\) 0 0
\(449\) 3.46410 + 6.00000i 0.163481 + 0.283158i 0.936115 0.351694i \(-0.114394\pi\)
−0.772634 + 0.634852i \(0.781061\pi\)
\(450\) 3.46410 0.163299
\(451\) 0 0
\(452\) 7.50000 12.9904i 0.352770 0.611016i
\(453\) −17.3205 + 30.0000i −0.813788 + 1.40952i
\(454\) 42.0000 1.97116
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −0.866025 + 1.50000i −0.0405110 + 0.0701670i −0.885570 0.464506i \(-0.846232\pi\)
0.845059 + 0.534673i \(0.179565\pi\)
\(458\) 0 0
\(459\) 6.00000 + 10.3923i 0.280056 + 0.485071i
\(460\) 10.3923 0.484544
\(461\) 11.2583 + 19.5000i 0.524353 + 0.908206i 0.999598 + 0.0283522i \(0.00902599\pi\)
−0.475245 + 0.879853i \(0.657641\pi\)
\(462\) 0 0
\(463\) 13.8564 0.643962 0.321981 0.946746i \(-0.395651\pi\)
0.321981 + 0.946746i \(0.395651\pi\)
\(464\) 7.50000 + 12.9904i 0.348179 + 0.603063i
\(465\) 6.00000 10.3923i 0.278243 0.481932i
\(466\) −5.19615 + 9.00000i −0.240707 + 0.416917i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −5.19615 + 9.00000i −0.239681 + 0.415139i
\(471\) 13.0000 22.5167i 0.599008 1.03751i
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) 0 0
\(474\) 6.92820 + 12.0000i 0.318223 + 0.551178i
\(475\) 3.46410 + 6.00000i 0.158944 + 0.275299i
\(476\) 0 0
\(477\) 1.50000 + 2.59808i 0.0686803 + 0.118958i
\(478\) 18.0000 31.1769i 0.823301 1.42600i
\(479\) 12.1244 21.0000i 0.553976 0.959514i −0.444006 0.896024i \(-0.646443\pi\)
0.997982 0.0634909i \(-0.0202234\pi\)
\(480\) 18.0000 0.821584
\(481\) 0 0
\(482\) 3.00000 0.136646
\(483\) 0 0
\(484\) 5.50000 9.52628i 0.250000 0.433013i
\(485\) 6.00000 + 10.3923i 0.272446 + 0.471890i
\(486\) 17.3205 0.785674
\(487\) −3.46410 6.00000i −0.156973 0.271886i 0.776802 0.629744i \(-0.216840\pi\)
−0.933776 + 0.357858i \(0.883507\pi\)
\(488\) −0.866025 1.50000i −0.0392031 0.0679018i
\(489\) 41.5692 1.87983
\(490\) −10.5000 18.1865i −0.474342 0.821584i
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 5.19615 9.00000i 0.234261 0.405751i
\(493\) 9.00000 0.405340
\(494\) 0 0
\(495\) 0 0
\(496\) −8.66025 + 15.0000i −0.388857 + 0.673520i
\(497\) 0 0
\(498\) −24.0000 41.5692i −1.07547 1.86276i
\(499\) −31.1769 −1.39567 −0.697835 0.716258i \(-0.745853\pi\)
−0.697835 + 0.716258i \(0.745853\pi\)
\(500\) 6.06218 + 10.5000i 0.271109 + 0.469574i
\(501\) −13.8564 24.0000i −0.619059 1.07224i
\(502\) −31.1769 −1.39149
\(503\) −18.0000 31.1769i −0.802580 1.39011i −0.917912 0.396783i \(-0.870127\pi\)
0.115332 0.993327i \(-0.463207\pi\)
\(504\) 0 0
\(505\) −2.59808 + 4.50000i −0.115613 + 0.200247i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) −9.52628 + 16.5000i −0.422245 + 0.731350i −0.996159 0.0875661i \(-0.972091\pi\)
0.573914 + 0.818916i \(0.305424\pi\)
\(510\) 9.00000 15.5885i 0.398527 0.690268i
\(511\) 0 0
\(512\) −8.66025 −0.382733
\(513\) 6.92820 + 12.0000i 0.305888 + 0.529813i
\(514\) −2.59808 4.50000i −0.114596 0.198486i
\(515\) 17.3205 0.763233
\(516\) 8.00000 + 13.8564i 0.352180 + 0.609994i
\(517\) 0 0
\(518\) 0 0
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) 9.00000 0.394297 0.197149 0.980374i \(-0.436832\pi\)
0.197149 + 0.980374i \(0.436832\pi\)
\(522\) 2.59808 4.50000i 0.113715 0.196960i
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) −9.00000 15.5885i −0.393167 0.680985i
\(525\) 0 0
\(526\) 10.3923 + 18.0000i 0.453126 + 0.784837i
\(527\) 5.19615 + 9.00000i 0.226348 + 0.392046i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) −3.46410 + 6.00000i −0.150329 + 0.260378i
\(532\) 0 0
\(533\) 0 0
\(534\) −24.0000 −1.03858
\(535\) −5.19615 + 9.00000i −0.224649 + 0.389104i
\(536\) −3.00000 + 5.19615i −0.129580 + 0.224440i
\(537\) 0 0
\(538\) 10.3923 0.448044
\(539\) 0 0
\(540\) 3.46410 + 6.00000i 0.149071 + 0.258199i
\(541\) 29.4449 1.26593 0.632967 0.774179i \(-0.281837\pi\)
0.632967 + 0.774179i \(0.281837\pi\)
\(542\) −18.0000 31.1769i −0.773166 1.33916i
\(543\) 11.0000 19.0526i 0.472055 0.817624i
\(544\) −7.79423 + 13.5000i −0.334175 + 0.578808i
\(545\) 24.0000 1.02805
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 7.79423 13.5000i 0.332953 0.576691i
\(549\) −0.500000 + 0.866025i −0.0213395 + 0.0369611i
\(550\) 0 0
\(551\) 10.3923 0.442727
\(552\) −10.3923 18.0000i −0.442326 0.766131i
\(553\) 0 0
\(554\) −12.1244 −0.515115
\(555\) 15.0000 + 25.9808i 0.636715 + 1.10282i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −7.79423 + 13.5000i −0.330252 + 0.572013i −0.982561 0.185940i \(-0.940467\pi\)
0.652309 + 0.757953i \(0.273800\pi\)
\(558\) 6.00000 0.254000
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −19.5000 + 33.7750i −0.822558 + 1.42471i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) −6.92820 −0.291730
\(565\) 12.9904 + 22.5000i 0.546509 + 0.946582i
\(566\) −3.46410 6.00000i −0.145607 0.252199i
\(567\) 0 0
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 10.3923 18.0000i 0.435286 0.753937i
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) 36.0000 1.50392
\(574\) 0 0
\(575\) 6.00000 10.3923i 0.250217 0.433389i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 19.0526 0.793168 0.396584 0.917998i \(-0.370195\pi\)
0.396584 + 0.917998i \(0.370195\pi\)
\(578\) −6.92820 12.0000i −0.288175 0.499134i
\(579\) −5.19615 9.00000i −0.215945 0.374027i
\(580\) 5.19615 0.215758
\(581\) 0 0
\(582\) −12.0000 + 20.7846i −0.497416 + 0.861550i
\(583\) 0 0
\(584\) 3.00000 0.124141
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) 10.3923 18.0000i 0.428936 0.742940i −0.567843 0.823137i \(-0.692222\pi\)
0.996779 + 0.0801976i \(0.0255551\pi\)
\(588\) 7.00000 12.1244i 0.288675 0.500000i
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) −20.7846 −0.855689
\(591\) −13.8564 24.0000i −0.569976 0.987228i
\(592\) −21.6506 37.5000i −0.889836 1.54124i
\(593\) −25.9808 −1.06690 −0.533451 0.845831i \(-0.679105\pi\)
−0.533451 + 0.845831i \(0.679105\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.52628 + 16.5000i −0.390212 + 0.675866i
\(597\) 4.00000 0.163709
\(598\) 0 0
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 3.46410 6.00000i 0.141421 0.244949i
\(601\) −12.5000 + 21.6506i −0.509886 + 0.883148i 0.490049 + 0.871695i \(0.336979\pi\)
−0.999934 + 0.0114528i \(0.996354\pi\)
\(602\) 0 0
\(603\) 3.46410 0.141069
\(604\) −8.66025 15.0000i −0.352381 0.610341i
\(605\) 9.52628 + 16.5000i 0.387298 + 0.670820i
\(606\) −10.3923 −0.422159
\(607\) 17.0000 + 29.4449i 0.690009 + 1.19513i 0.971834 + 0.235665i \(0.0757267\pi\)
−0.281826 + 0.959466i \(0.590940\pi\)
\(608\) −9.00000 + 15.5885i −0.364998 + 0.632195i
\(609\) 0 0
\(610\) −3.00000 −0.121466
\(611\) 0 0
\(612\) 3.00000 0.121268
\(613\) 6.06218 10.5000i 0.244849 0.424091i −0.717240 0.696826i \(-0.754595\pi\)
0.962089 + 0.272735i \(0.0879283\pi\)
\(614\) −15.0000 + 25.9808i −0.605351 + 1.04850i
\(615\) 9.00000 + 15.5885i 0.362915 + 0.628587i
\(616\) 0 0
\(617\) −11.2583 19.5000i −0.453243 0.785040i 0.545342 0.838214i \(-0.316400\pi\)
−0.998585 + 0.0531732i \(0.983066\pi\)
\(618\) 17.3205 + 30.0000i 0.696733 + 1.20678i
\(619\) −20.7846 −0.835404 −0.417702 0.908584i \(-0.637164\pi\)
−0.417702 + 0.908584i \(0.637164\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) 12.0000 20.7846i 0.481543 0.834058i
\(622\) 25.9808 45.0000i 1.04173 1.80434i
\(623\) 0 0
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 8.66025 15.0000i 0.346133 0.599521i
\(627\) 0 0
\(628\) 6.50000 + 11.2583i 0.259378 + 0.449256i
\(629\) −25.9808 −1.03592
\(630\) 0 0
\(631\) 24.2487 + 42.0000i 0.965326 + 1.67199i 0.708737 + 0.705473i \(0.249265\pi\)
0.256589 + 0.966521i \(0.417401\pi\)
\(632\) 6.92820 0.275589
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 4.50000 7.79423i 0.178718 0.309548i
\(635\) −1.73205 + 3.00000i −0.0687343 + 0.119051i
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 1.73205 3.00000i 0.0685189 0.118678i
\(640\) 10.5000 18.1865i 0.415049 0.718886i
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) −20.7846 −0.820303
\(643\) 6.92820 + 12.0000i 0.273222 + 0.473234i 0.969685 0.244359i \(-0.0785774\pi\)
−0.696463 + 0.717592i \(0.745244\pi\)
\(644\) 0 0
\(645\) −27.7128 −1.09119
\(646\) 9.00000 + 15.5885i 0.354100 + 0.613320i
\(647\) 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i \(-0.718214\pi\)
0.986916 + 0.161233i \(0.0515470\pi\)
\(648\) 9.52628 16.5000i 0.374228 0.648181i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −10.3923 + 18.0000i −0.406994 + 0.704934i
\(653\) 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i \(-0.633644\pi\)
0.994623 0.103558i \(-0.0330227\pi\)
\(654\) 24.0000 + 41.5692i 0.938474 + 1.62549i
\(655\) 31.1769 1.21818
\(656\) −12.9904 22.5000i −0.507189 0.878477i
\(657\) −0.866025 1.50000i −0.0337869 0.0585206i
\(658\) 0 0
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) −23.3827 + 40.5000i −0.909481 + 1.57527i −0.0946945 + 0.995506i \(0.530187\pi\)
−0.814787 + 0.579761i \(0.803146\pi\)
\(662\) −48.0000 −1.86557
\(663\) 0 0
\(664\) −24.0000 −0.931381
\(665\) 0 0
\(666\) −7.50000 + 12.9904i −0.290619 + 0.503367i
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 13.8564 0.536120
\(669\) 10.3923 + 18.0000i 0.401790 + 0.695920i
\(670\) 5.19615 + 9.00000i 0.200745 + 0.347700i
\(671\) 0 0
\(672\) 0 0
\(673\) −9.50000 + 16.4545i −0.366198 + 0.634274i −0.988968 0.148132i \(-0.952674\pi\)
0.622770 + 0.782405i \(0.286007\pi\)
\(674\) 19.9186 34.5000i 0.767235 1.32889i
\(675\) 8.00000 0.307920
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −25.9808 + 45.0000i −0.997785 + 1.72821i
\(679\) 0 0
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) −48.4974 −1.85843
\(682\) 0 0
\(683\) −12.1244 21.0000i −0.463926 0.803543i 0.535227 0.844708i \(-0.320226\pi\)
−0.999152 + 0.0411658i \(0.986893\pi\)
\(684\) 3.46410 0.132453
\(685\) 13.5000 + 23.3827i 0.515808 + 0.893407i
\(686\) 0 0
\(687\) 0 0
\(688\) 40.0000 1.52499
\(689\) 0 0
\(690\) −36.0000 −1.37050
\(691\) −6.92820 + 12.0000i −0.263561 + 0.456502i −0.967186 0.254071i \(-0.918230\pi\)
0.703624 + 0.710572i \(0.251564\pi\)
\(692\) 3.00000 5.19615i 0.114043 0.197528i
\(693\) 0 0
\(694\) 51.9615 1.97243
\(695\) 3.46410 + 6.00000i 0.131401 + 0.227593i
\(696\) −5.19615 9.00000i −0.196960 0.341144i
\(697\) −15.5885 −0.590455
\(698\) −12.0000 20.7846i −0.454207 0.786709i
\(699\) 6.00000 10.3923i 0.226941 0.393073i
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −30.0000 −1.13147
\(704\) 0 0
\(705\) 6.00000 10.3923i 0.225973 0.391397i
\(706\) 28.5000 + 49.3634i 1.07261 + 1.85782i
\(707\) 0 0
\(708\) −6.92820 12.0000i −0.260378 0.450988i
\(709\) 2.59808 + 4.50000i 0.0975728 + 0.169001i 0.910679 0.413114i \(-0.135559\pi\)
−0.813107 + 0.582115i \(0.802225\pi\)
\(710\) 10.3923 0.390016
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −6.00000 + 10.3923i −0.224860 + 0.389468i
\(713\) 10.3923 18.0000i 0.389195 0.674105i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −20.7846 + 36.0000i −0.776215 + 1.34444i
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −24.0000 41.5692i −0.895049 1.55027i −0.833744 0.552151i \(-0.813807\pi\)
−0.0613050 0.998119i \(-0.519526\pi\)
\(720\) −8.66025 −0.322749
\(721\) 0 0
\(722\) −6.06218 10.5000i −0.225611 0.390770i
\(723\) −3.46410 −0.128831
\(724\) 5.50000 + 9.52628i 0.204406 + 0.354041i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) −19.0526 + 33.0000i −0.707107 + 1.22474i
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 2.59808 4.50000i 0.0961591 0.166552i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −1.00000 1.73205i −0.0369611 0.0640184i
\(733\) −12.1244 −0.447823 −0.223912 0.974609i \(-0.571883\pi\)
−0.223912 + 0.974609i \(0.571883\pi\)
\(734\) −19.0526 33.0000i −0.703243 1.21805i
\(735\) 12.1244 + 21.0000i 0.447214 + 0.774597i
\(736\) 31.1769 1.14920
\(737\) 0 0
\(738\) −4.50000 + 7.79423i −0.165647 + 0.286910i
\(739\) −10.3923 + 18.0000i −0.382287 + 0.662141i −0.991389 0.130951i \(-0.958197\pi\)
0.609102 + 0.793092i \(0.291530\pi\)
\(740\) −15.0000 −0.551411
\(741\) 0 0
\(742\) 0 0
\(743\) 17.3205 30.0000i 0.635428 1.10059i −0.350997 0.936377i \(-0.614157\pi\)
0.986424 0.164216i \(-0.0525096\pi\)
\(744\) 6.00000 10.3923i 0.219971 0.381000i
\(745\) −16.5000 28.5788i −0.604513 1.04705i
\(746\) −32.9090 −1.20488
\(747\) 6.92820 + 12.0000i 0.253490 + 0.439057i
\(748\) 0 0
\(749\) 0 0
\(750\) −21.0000 36.3731i −0.766812 1.32816i
\(751\) −8.00000 + 13.8564i −0.291924 + 0.505627i −0.974265 0.225407i \(-0.927629\pi\)
0.682341 + 0.731034i \(0.260962\pi\)
\(752\) −8.66025 + 15.0000i −0.315807 + 0.546994i
\(753\) 36.0000 1.31191
\(754\) 0 0
\(755\) 30.0000 1.09181
\(756\) 0 0
\(757\) 13.0000 22.5167i 0.472493 0.818382i −0.527011 0.849858i \(-0.676688\pi\)
0.999505 + 0.0314762i \(0.0100208\pi\)
\(758\) −21.0000 36.3731i −0.762754 1.32113i
\(759\) 0 0
\(760\) −5.19615 9.00000i −0.188484 0.326464i
\(761\) −17.3205 30.0000i −0.627868 1.08750i −0.987979 0.154590i \(-0.950594\pi\)
0.360111 0.932910i \(-0.382739\pi\)
\(762\) −6.92820 −0.250982
\(763\) 0 0
\(764\) −9.00000 + 15.5885i −0.325609 + 0.563971i
\(765\) −2.59808 + 4.50000i −0.0939336 + 0.162698i
\(766\) −36.0000 −1.30073
\(767\) 0 0
\(768\) 38.0000 1.37121
\(769\) −3.46410 + 6.00000i −0.124919 + 0.216366i −0.921701 0.387901i \(-0.873200\pi\)
0.796782 + 0.604266i \(0.206534\pi\)
\(770\) 0 0
\(771\) 3.00000 + 5.19615i 0.108042 + 0.187135i
\(772\) 5.19615 0.187014
\(773\) −17.3205 30.0000i −0.622975 1.07903i −0.988929 0.148392i \(-0.952590\pi\)
0.365953 0.930633i \(-0.380743\pi\)
\(774\) −6.92820 12.0000i −0.249029 0.431331i
\(775\) 6.92820 0.248868
\(776\) 6.00000 + 10.3923i 0.215387 + 0.373062i
\(777\) 0 0
\(778\) 7.79423 13.5000i 0.279437 0.483998i
\(779\) −18.0000 −0.644917
\(780\) 0 0
\(781\) 0 0
\(782\)