Properties

Label 169.2.e.a.23.1
Level $169$
Weight $2$
Character 169.23
Analytic conductor $1.349$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(23,169)]
 
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([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), 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: \(2\)
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: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.2.e.a.147.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(-3.00000 - 1.73205i) q^{6} +1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(-3.00000 - 1.73205i) q^{6} +1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} -2.00000 q^{12} +(-3.00000 + 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +1.73205i q^{18} +(3.00000 + 1.73205i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(3.00000 + 5.19615i) q^{23} +(3.00000 - 1.73205i) q^{24} +2.00000 q^{25} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(-3.00000 + 5.19615i) q^{30} +3.46410i q^{31} +(4.50000 + 2.59808i) q^{32} -5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(-7.50000 + 4.33013i) q^{37} +6.00000 q^{38} +3.00000 q^{40} +(4.50000 - 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(1.50000 + 0.866025i) q^{45} +(9.00000 + 5.19615i) q^{46} -3.46410i q^{47} +(5.00000 - 8.66025i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(3.00000 - 1.73205i) q^{50} -6.00000 q^{51} -3.00000 q^{53} +(-6.00000 + 3.46410i) q^{54} -6.92820i q^{57} +(-4.50000 - 2.59808i) q^{58} +(-6.00000 - 3.46410i) q^{59} +3.46410i q^{60} +(-0.500000 + 0.866025i) q^{61} +(3.00000 + 5.19615i) q^{62} -1.00000 q^{64} +(-3.00000 + 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +(-3.00000 - 1.73205i) q^{71} +(-1.50000 - 0.866025i) q^{72} +1.73205i q^{73} +(-7.50000 + 12.9904i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(3.00000 - 1.73205i) q^{76} +4.00000 q^{79} +(7.50000 - 4.33013i) q^{80} +(5.50000 + 9.52628i) q^{81} +(4.50000 - 7.79423i) q^{82} +13.8564i q^{83} +(-4.50000 - 2.59808i) q^{85} +13.8564i q^{86} +(-3.00000 + 5.19615i) q^{87} +(6.00000 - 3.46410i) q^{89} +3.00000 q^{90} +6.00000 q^{92} +(6.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} -10.3923i q^{96} +(-6.00000 - 3.46410i) q^{97} +(-10.5000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} - 2 q^{3} + q^{4} - 6 q^{6} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} - 2 q^{3} + q^{4} - 6 q^{6} - q^{9} - 3 q^{10} - 4 q^{12} - 6 q^{15} + 5 q^{16} + 3 q^{17} + 6 q^{19} - 3 q^{20} + 6 q^{23} + 6 q^{24} + 4 q^{25} - 8 q^{27} - 3 q^{29} - 6 q^{30} + 9 q^{32} + q^{36} - 15 q^{37} + 12 q^{38} + 6 q^{40} + 9 q^{41} - 8 q^{43} + 3 q^{45} + 18 q^{46} + 10 q^{48} - 7 q^{49} + 6 q^{50} - 12 q^{51} - 6 q^{53} - 12 q^{54} - 9 q^{58} - 12 q^{59} - q^{61} + 6 q^{62} - 2 q^{64} - 6 q^{67} - 3 q^{68} + 12 q^{69} - 6 q^{71} - 3 q^{72} - 15 q^{74} - 4 q^{75} + 6 q^{76} + 8 q^{79} + 15 q^{80} + 11 q^{81} + 9 q^{82} - 9 q^{85} - 6 q^{87} + 12 q^{89} + 6 q^{90} + 12 q^{92} + 12 q^{93} - 6 q^{94} + 6 q^{95} - 12 q^{97} - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) −3.00000 1.73205i −1.22474 0.707107i
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.73205i 0.612372i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) −2.00000 −0.577350
\(13\) 0 0
\(14\) 0 0
\(15\) −3.00000 + 1.73205i −0.774597 + 0.447214i
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 1.73205i 0.408248i
\(19\) 3.00000 + 1.73205i 0.688247 + 0.397360i 0.802955 0.596040i \(-0.203260\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −1.50000 0.866025i −0.335410 0.193649i
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 3.00000 1.73205i 0.612372 0.353553i
\(25\) 2.00000 0.400000
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) −3.00000 + 5.19615i −0.547723 + 0.948683i
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 4.50000 + 2.59808i 0.795495 + 0.459279i
\(33\) 0 0
\(34\) 5.19615i 0.891133i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −7.50000 + 4.33013i −1.23299 + 0.711868i −0.967653 0.252286i \(-0.918817\pi\)
−0.265340 + 0.964155i \(0.585484\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 4.50000 2.59808i 0.702782 0.405751i −0.105601 0.994409i \(-0.533677\pi\)
0.808383 + 0.588657i \(0.200343\pi\)
\(42\) 0 0
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 0 0
\(45\) 1.50000 + 0.866025i 0.223607 + 0.129099i
\(46\) 9.00000 + 5.19615i 1.32698 + 0.766131i
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) 5.00000 8.66025i 0.721688 1.25000i
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 3.00000 1.73205i 0.424264 0.244949i
\(51\) −6.00000 −0.840168
\(52\) 0 0
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) −6.00000 + 3.46410i −0.816497 + 0.471405i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.92820i 0.917663i
\(58\) −4.50000 2.59808i −0.590879 0.341144i
\(59\) −6.00000 3.46410i −0.781133 0.450988i 0.0556984 0.998448i \(-0.482261\pi\)
−0.836832 + 0.547460i \(0.815595\pi\)
\(60\) 3.46410i 0.447214i
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 3.00000 + 5.19615i 0.381000 + 0.659912i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −3.00000 + 1.73205i −0.366508 + 0.211604i −0.671932 0.740613i \(-0.734535\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 6.00000 10.3923i 0.722315 1.25109i
\(70\) 0 0
\(71\) −3.00000 1.73205i −0.356034 0.205557i 0.311305 0.950310i \(-0.399234\pi\)
−0.667340 + 0.744753i \(0.732567\pi\)
\(72\) −1.50000 0.866025i −0.176777 0.102062i
\(73\) 1.73205i 0.202721i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) −7.50000 + 12.9904i −0.871857 + 1.51010i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 3.00000 1.73205i 0.344124 0.198680i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 7.50000 4.33013i 0.838525 0.484123i
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 13.8564i 1.52094i 0.649374 + 0.760469i \(0.275031\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(84\) 0 0
\(85\) −4.50000 2.59808i −0.488094 0.281801i
\(86\) 13.8564i 1.49417i
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0 0
\(89\) 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i \(-0.546985\pi\)
0.783072 + 0.621932i \(0.213652\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 6.00000 3.46410i 0.622171 0.359211i
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 10.3923i 1.06066i
\(97\) −6.00000 3.46410i −0.609208 0.351726i 0.163448 0.986552i \(-0.447739\pi\)
−0.772655 + 0.634826i \(0.781072\pi\)
\(98\) −10.5000 6.06218i −1.06066 0.612372i
\(99\) 0 0
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i \(-0.118979\pi\)
−0.781697 + 0.623658i \(0.785646\pi\)
\(102\) −9.00000 + 5.19615i −0.891133 + 0.514496i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −4.50000 + 2.59808i −0.437079 + 0.252347i
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) 13.8564i 1.32720i −0.748086 0.663602i \(-0.769027\pi\)
0.748086 0.663602i \(-0.230973\pi\)
\(110\) 0 0
\(111\) 15.0000 + 8.66025i 1.42374 + 0.821995i
\(112\) 0 0
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) −6.00000 10.3923i −0.561951 0.973329i
\(115\) 9.00000 5.19615i 0.839254 0.484544i
\(116\) −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
\(122\) 1.73205i 0.156813i
\(123\) −9.00000 5.19615i −0.811503 0.468521i
\(124\) 3.00000 + 1.73205i 0.269408 + 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) −10.5000 + 6.06218i −0.928078 + 0.535826i
\(129\) 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
\(135\) 6.92820i 0.596285i
\(136\) 4.50000 + 2.59808i 0.385872 + 0.222783i
\(137\) 13.5000 + 7.79423i 1.15338 + 0.665906i 0.949709 0.313133i \(-0.101379\pi\)
0.203674 + 0.979039i \(0.434712\pi\)
\(138\) 20.7846i 1.76930i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 0 0
\(141\) −6.00000 + 3.46410i −0.505291 + 0.291730i
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) −5.00000 −0.416667
\(145\) −4.50000 + 2.59808i −0.373705 + 0.215758i
\(146\) 1.50000 + 2.59808i 0.124141 + 0.215018i
\(147\) −7.00000 + 12.1244i −0.577350 + 1.00000i
\(148\) 8.66025i 0.711868i
\(149\) 16.5000 + 9.52628i 1.35173 + 0.780423i 0.988492 0.151272i \(-0.0483370\pi\)
0.363241 + 0.931695i \(0.381670\pi\)
\(150\) −6.00000 3.46410i −0.489898 0.282843i
\(151\) 17.3205i 1.40952i 0.709444 + 0.704761i \(0.248946\pi\)
−0.709444 + 0.704761i \(0.751054\pi\)
\(152\) −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 \(0.673605\pi\)
\(158\) 6.00000 3.46410i 0.477334 0.275589i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 0 0
\(162\) 16.5000 + 9.52628i 1.29636 + 0.748455i
\(163\) −18.0000 10.3923i −1.40987 0.813988i −0.414494 0.910052i \(-0.636041\pi\)
−0.995375 + 0.0960641i \(0.969375\pi\)
\(164\) 5.19615i 0.405751i
\(165\) 0 0
\(166\) 12.0000 + 20.7846i 0.931381 + 1.61320i
\(167\) 12.0000 6.92820i 0.928588 0.536120i 0.0422232 0.999108i \(-0.486556\pi\)
0.886365 + 0.462988i \(0.153223\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −9.00000 −0.690268
\(171\) −3.00000 + 1.73205i −0.229416 + 0.132453i
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 0 0
\(176\) 0 0
\(177\) 13.8564i 1.04151i
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 1.50000 0.866025i 0.111803 0.0645497i
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) −9.00000 + 5.19615i −0.663489 + 0.383065i
\(185\) 7.50000 + 12.9904i 0.551411 + 0.955072i
\(186\) 6.00000 10.3923i 0.439941 0.762001i
\(187\) 0 0
\(188\) −3.00000 1.73205i −0.218797 0.126323i
\(189\) 0 0
\(190\) 10.3923i 0.753937i
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 1.00000 + 1.73205i 0.0721688 + 0.125000i
\(193\) 4.50000 2.59808i 0.323917 0.187014i −0.329220 0.944253i \(-0.606786\pi\)
0.653137 + 0.757240i \(0.273452\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −12.0000 + 6.92820i −0.854965 + 0.493614i −0.862323 0.506359i \(-0.830991\pi\)
0.00735824 + 0.999973i \(0.497658\pi\)
\(198\) 0 0
\(199\) 1.00000 1.73205i 0.0708881 0.122782i −0.828403 0.560133i \(-0.810750\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(200\) 3.46410i 0.244949i
\(201\) 6.00000 + 3.46410i 0.423207 + 0.244339i
\(202\) 4.50000 + 2.59808i 0.316619 + 0.182800i
\(203\) 0 0
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) −15.0000 + 8.66025i −1.04510 + 0.603388i
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 8.66025i −0.344214 0.596196i 0.640996 0.767544i \(-0.278521\pi\)
−0.985211 + 0.171347i \(0.945188\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 6.92820i 0.474713i
\(214\) −9.00000 5.19615i −0.615227 0.355202i
\(215\) 12.0000 + 6.92820i 0.818393 + 0.472500i
\(216\) 6.92820i 0.471405i
\(217\) 0 0
\(218\) −12.0000 20.7846i −0.812743 1.40771i
\(219\) 3.00000 1.73205i 0.202721 0.117041i
\(220\) 0 0
\(221\) 0 0
\(222\) 30.0000 2.01347
\(223\) 9.00000 5.19615i 0.602685 0.347960i −0.167412 0.985887i \(-0.553541\pi\)
0.770097 + 0.637927i \(0.220208\pi\)
\(224\) 0 0
\(225\) −1.00000 + 1.73205i −0.0666667 + 0.115470i
\(226\) 25.9808i 1.72821i
\(227\) −21.0000 12.1244i −1.39382 0.804722i −0.400083 0.916479i \(-0.631019\pi\)
−0.993736 + 0.111757i \(0.964352\pi\)
\(228\) −6.00000 3.46410i −0.397360 0.229416i
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 9.00000 15.5885i 0.593442 1.02787i
\(231\) 0 0
\(232\) 4.50000 2.59808i 0.295439 0.170572i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −6.00000 + 3.46410i −0.390567 + 0.225494i
\(237\) −4.00000 6.92820i −0.259828 0.450035i
\(238\) 0 0
\(239\) 20.7846i 1.34444i −0.740349 0.672222i \(-0.765340\pi\)
0.740349 0.672222i \(-0.234660\pi\)
\(240\) −15.0000 8.66025i −0.968246 0.559017i
\(241\) 1.50000 + 0.866025i 0.0966235 + 0.0557856i 0.547533 0.836784i \(-0.315567\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 19.0526i 1.22474i
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) −10.5000 + 6.06218i −0.670820 + 0.387298i
\(246\) −18.0000 −1.14764
\(247\) 0 0
\(248\) −6.00000 −0.381000
\(249\) 24.0000 13.8564i 1.52094 0.878114i
\(250\) −10.5000 18.1865i −0.664078 1.15022i
\(251\) 9.00000 15.5885i 0.568075 0.983935i −0.428681 0.903456i \(-0.641022\pi\)
0.996756 0.0804789i \(-0.0256450\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 3.00000 + 1.73205i 0.188237 + 0.108679i
\(255\) 10.3923i 0.650791i
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 24.0000 13.8564i 1.49417 0.862662i
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 27.0000 15.5885i 1.66807 0.963058i
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 0 0
\(265\) 5.19615i 0.319197i
\(266\) 0 0
\(267\) −12.0000 6.92820i −0.734388 0.423999i
\(268\) 3.46410i 0.211604i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 6.00000 + 10.3923i 0.365148 + 0.632456i
\(271\) −18.0000 + 10.3923i −1.09342 + 0.631288i −0.934485 0.356001i \(-0.884140\pi\)
−0.158937 + 0.987289i \(0.550807\pi\)
\(272\) 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 \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 6.92820i 0.415526i
\(279\) −3.00000 1.73205i −0.179605 0.103695i
\(280\) 0 0
\(281\) 22.5167i 1.34323i −0.740900 0.671616i \(-0.765601\pi\)
0.740900 0.671616i \(-0.234399\pi\)
\(282\) −6.00000 + 10.3923i −0.357295 + 0.618853i
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) −3.00000 + 1.73205i −0.178017 + 0.102778i
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 0 0
\(288\) −4.50000 + 2.59808i −0.265165 + 0.153093i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −4.50000 + 7.79423i −0.264249 + 0.457693i
\(291\) 13.8564i 0.812277i
\(292\) 1.50000 + 0.866025i 0.0877809 + 0.0506803i
\(293\) −4.50000 2.59808i −0.262893 0.151781i 0.362761 0.931882i \(-0.381834\pi\)
−0.625653 + 0.780101i \(0.715168\pi\)
\(294\) 24.2487i 1.41421i
\(295\) −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
\(304\) 17.3205i 0.993399i
\(305\) 1.50000 + 0.866025i 0.0858898 + 0.0495885i
\(306\) 4.50000 + 2.59808i 0.257248 + 0.148522i
\(307\) 17.3205i 0.988534i −0.869310 0.494267i \(-0.835437\pi\)
0.869310 0.494267i \(-0.164563\pi\)
\(308\) 0 0
\(309\) 10.0000 + 17.3205i 0.568880 + 0.985329i
\(310\) 9.00000 5.19615i 0.511166 0.295122i
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) −19.5000 + 11.2583i −1.10045 + 0.635344i
\(315\) 0 0
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) 5.19615i 0.291845i −0.989296 0.145922i \(-0.953385\pi\)
0.989296 0.145922i \(-0.0466150\pi\)
\(318\) 9.00000 + 5.19615i 0.504695 + 0.291386i
\(319\) 0 0
\(320\) 1.73205i 0.0968246i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) 0 0
\(323\) 9.00000 5.19615i 0.500773 0.289122i
\(324\) 11.0000 0.611111
\(325\) 0 0
\(326\) −36.0000 −1.99386
\(327\) −24.0000 + 13.8564i −1.32720 + 0.766261i
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) 24.0000 + 13.8564i 1.31916 + 0.761617i 0.983593 0.180400i \(-0.0577391\pi\)
0.335566 + 0.942017i \(0.391072\pi\)
\(332\) 12.0000 + 6.92820i 0.658586 + 0.380235i
\(333\) 8.66025i 0.474579i
\(334\) 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 \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) 0 0
\(339\) −30.0000 −1.62938
\(340\) −4.50000 + 2.59808i −0.244047 + 0.140900i
\(341\) 0 0
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 0 0
\(344\) −12.0000 6.92820i −0.646997 0.373544i
\(345\) −18.0000 10.3923i −0.969087 0.559503i
\(346\) 10.3923i 0.558694i
\(347\) 15.0000 25.9808i 0.805242 1.39472i −0.110885 0.993833i \(-0.535369\pi\)
0.916127 0.400887i \(-0.131298\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −12.0000 + 6.92820i −0.642345 + 0.370858i −0.785517 0.618840i \(-0.787603\pi\)
0.143172 + 0.989698i \(0.454270\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −28.5000 + 16.4545i −1.51690 + 0.875784i −0.517099 + 0.855926i \(0.672988\pi\)
−0.999803 + 0.0198582i \(0.993679\pi\)
\(354\) 12.0000 + 20.7846i 0.637793 + 1.10469i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) 0 0
\(359\) 6.92820i 0.365657i −0.983145 0.182828i \(-0.941475\pi\)
0.983145 0.182828i \(-0.0585252\pi\)
\(360\) −1.50000 + 2.59808i −0.0790569 + 0.136931i
\(361\) −3.50000 6.06218i −0.184211 0.319062i
\(362\) 16.5000 9.52628i 0.867221 0.500690i
\(363\) 22.0000 1.15470
\(364\) 0 0
\(365\) 3.00000 0.157027
\(366\) 3.00000 1.73205i 0.156813 0.0905357i
\(367\) 11.0000 + 19.0526i 0.574195 + 0.994535i 0.996129 + 0.0879086i \(0.0280183\pi\)
−0.421933 + 0.906627i \(0.638648\pi\)
\(368\) −15.0000 + 25.9808i −0.781929 + 1.35434i
\(369\) 5.19615i 0.270501i
\(370\) 22.5000 + 12.9904i 1.16972 + 0.675338i
\(371\) 0 0
\(372\) 6.92820i 0.359211i
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 0 0
\(375\) −21.0000 + 12.1244i −1.08444 + 0.626099i
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) 0 0
\(379\) 21.0000 12.1244i 1.07870 0.622786i 0.148153 0.988964i \(-0.452667\pi\)
0.930545 + 0.366178i \(0.119334\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 2.00000 3.46410i 0.102463 0.177471i
\(382\) 31.1769i 1.59515i
\(383\) 18.0000 + 10.3923i 0.919757 + 0.531022i 0.883558 0.468323i \(-0.155141\pi\)
0.0361995 + 0.999345i \(0.488475\pi\)
\(384\) 21.0000 + 12.1244i 1.07165 + 0.618718i
\(385\) 0 0
\(386\) 4.50000 7.79423i 0.229044 0.396716i
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −6.00000 + 3.46410i −0.304604 + 0.175863i
\(389\) −9.00000 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 10.5000 6.06218i 0.530330 0.306186i
\(393\) −18.0000 31.1769i −0.907980 1.57267i
\(394\) −12.0000 + 20.7846i −0.604551 + 1.04711i
\(395\) 6.92820i 0.348596i
\(396\) 0 0
\(397\) 12.0000 + 6.92820i 0.602263 + 0.347717i 0.769931 0.638127i \(-0.220290\pi\)
−0.167668 + 0.985843i \(0.553624\pi\)
\(398\) 3.46410i 0.173640i
\(399\) 0 0
\(400\) 5.00000 + 8.66025i 0.250000 + 0.433013i
\(401\) 1.50000 0.866025i 0.0749064 0.0432472i −0.462079 0.886839i \(-0.652896\pi\)
0.536985 + 0.843592i \(0.319563\pi\)
\(402\) 12.0000 0.598506
\(403\) 0 0
\(404\) 3.00000 0.149256
\(405\) 16.5000 9.52628i 0.819892 0.473365i
\(406\) 0 0
\(407\) 0 0
\(408\) 10.3923i 0.514496i
\(409\) −13.5000 7.79423i −0.667532 0.385400i 0.127609 0.991825i \(-0.459270\pi\)
−0.795141 + 0.606425i \(0.792603\pi\)
\(410\) −13.5000 7.79423i −0.666717 0.384930i
\(411\) 31.1769i 1.53784i
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) 0 0
\(414\) −9.00000 + 5.19615i −0.442326 + 0.255377i
\(415\) 24.0000 1.17811
\(416\) 0 0
\(417\) −8.00000 −0.391762
\(418\) 0 0
\(419\) −9.00000 15.5885i −0.439679 0.761546i 0.557986 0.829851i \(-0.311574\pi\)
−0.997665 + 0.0683046i \(0.978241\pi\)
\(420\) 0 0
\(421\) 15.5885i 0.759735i 0.925041 + 0.379867i \(0.124030\pi\)
−0.925041 + 0.379867i \(0.875970\pi\)
\(422\) −15.0000 8.66025i −0.730189 0.421575i
\(423\) 3.00000 + 1.73205i 0.145865 + 0.0842152i
\(424\) 5.19615i 0.252347i
\(425\) 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
\(431\) 6.00000 3.46410i 0.289010 0.166860i −0.348485 0.937314i \(-0.613304\pi\)
0.637495 + 0.770454i \(0.279971\pi\)
\(432\) −10.0000 17.3205i −0.481125 0.833333i
\(433\) 8.50000 14.7224i 0.408484 0.707515i −0.586236 0.810140i \(-0.699391\pi\)
0.994720 + 0.102625i \(0.0327243\pi\)
\(434\) 0 0
\(435\) 9.00000 + 5.19615i 0.431517 + 0.249136i
\(436\) −12.0000 6.92820i −0.574696 0.331801i
\(437\) 20.7846i 0.994263i
\(438\) 3.00000 5.19615i 0.143346 0.248282i
\(439\) 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 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 \(0.592016\pi\)
\(444\) 15.0000 8.66025i 0.711868 0.410997i
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) 9.00000 15.5885i 0.426162 0.738135i
\(447\) 38.1051i 1.80231i
\(448\) 0 0
\(449\) 6.00000 + 3.46410i 0.283158 + 0.163481i 0.634852 0.772634i \(-0.281061\pi\)
−0.351694 + 0.936115i \(0.614394\pi\)
\(450\) 3.46410i 0.163299i
\(451\) 0 0
\(452\) −7.50000 12.9904i −0.352770 0.611016i
\(453\) 30.0000 17.3205i 1.40952 0.813788i
\(454\) −42.0000 −1.97116
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −1.50000 + 0.866025i −0.0701670 + 0.0405110i −0.534673 0.845059i \(-0.679565\pi\)
0.464506 + 0.885570i \(0.346232\pi\)
\(458\) 0 0
\(459\) −6.00000 + 10.3923i −0.280056 + 0.485071i
\(460\) 10.3923i 0.484544i
\(461\) −19.5000 11.2583i −0.908206 0.524353i −0.0283522 0.999598i \(-0.509026\pi\)
−0.879853 + 0.475245i \(0.842359\pi\)
\(462\) 0 0
\(463\) 13.8564i 0.643962i 0.946746 + 0.321981i \(0.104349\pi\)
−0.946746 + 0.321981i \(0.895651\pi\)
\(464\) 7.50000 12.9904i 0.348179 0.603063i
\(465\) −6.00000 10.3923i −0.278243 0.481932i
\(466\) 9.00000 5.19615i 0.416917 0.240707i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.00000 + 5.19615i −0.415139 + 0.239681i
\(471\) 13.0000 + 22.5167i 0.599008 + 1.03751i
\(472\) 6.00000 10.3923i 0.276172 0.478345i
\(473\) 0 0
\(474\) −12.0000 6.92820i −0.551178 0.318223i
\(475\) 6.00000 + 3.46410i 0.275299 + 0.158944i
\(476\) 0 0
\(477\) 1.50000 2.59808i 0.0686803 0.118958i
\(478\) −18.0000 31.1769i −0.823301 1.42600i
\(479\) −21.0000 + 12.1244i −0.959514 + 0.553976i −0.896024 0.444006i \(-0.853557\pi\)
−0.0634909 + 0.997982i \(0.520223\pi\)
\(480\) −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
\(486\) 17.3205i 0.785674i
\(487\) 6.00000 + 3.46410i 0.271886 + 0.156973i 0.629744 0.776802i \(-0.283160\pi\)
−0.357858 + 0.933776i \(0.616493\pi\)
\(488\) −1.50000 0.866025i −0.0679018 0.0392031i
\(489\) 41.5692i 1.87983i
\(490\) −10.5000 + 18.1865i −0.474342 + 0.821584i
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) −9.00000 + 5.19615i −0.405751 + 0.234261i
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) 0 0
\(496\) −15.0000 + 8.66025i −0.673520 + 0.388857i
\(497\) 0 0
\(498\) 24.0000 41.5692i 1.07547 1.86276i
\(499\) 31.1769i 1.39567i 0.716258 + 0.697835i \(0.245853\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) −10.5000 6.06218i −0.469574 0.271109i
\(501\) −24.0000 13.8564i −1.07224 0.619059i
\(502\) 31.1769i 1.39149i
\(503\) −18.0000 + 31.1769i −0.802580 + 1.39011i 0.115332 + 0.993327i \(0.463207\pi\)
−0.917912 + 0.396783i \(0.870127\pi\)
\(504\) 0 0
\(505\) 4.50000 2.59808i 0.200247 0.115613i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) −16.5000 + 9.52628i −0.731350 + 0.422245i −0.818916 0.573914i \(-0.805424\pi\)
0.0875661 + 0.996159i \(0.472091\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) −12.0000 6.92820i −0.529813 0.305888i
\(514\) −4.50000 2.59808i −0.198486 0.114596i
\(515\) 17.3205i 0.763233i
\(516\) 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 \(0.436832\pi\)
\(522\) 4.50000 2.59808i 0.196960 0.113715i
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) 9.00000 15.5885i 0.393167 0.680985i
\(525\) 0 0
\(526\) −18.0000 10.3923i −0.784837 0.453126i
\(527\) 9.00000 + 5.19615i 0.392046 + 0.226348i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) 6.00000 3.46410i 0.260378 0.150329i
\(532\) 0 0
\(533\) 0 0
\(534\) −24.0000 −1.03858
\(535\) −9.00000 + 5.19615i −0.389104 + 0.224649i
\(536\) −3.00000 5.19615i −0.129580 0.224440i
\(537\) 0 0
\(538\) 10.3923i 0.448044i
\(539\) 0 0
\(540\) 6.00000 + 3.46410i 0.258199 + 0.149071i
\(541\) 29.4449i 1.26593i 0.774179 + 0.632967i \(0.218163\pi\)
−0.774179 + 0.632967i \(0.781837\pi\)
\(542\) −18.0000 + 31.1769i −0.773166 + 1.33916i
\(543\) −11.0000 19.0526i −0.472055 0.817624i
\(544\) 13.5000 7.79423i 0.578808 0.334175i
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 13.5000 7.79423i 0.576691 0.332953i
\(549\) −0.500000 0.866025i −0.0213395 0.0369611i
\(550\) 0 0
\(551\) 10.3923i 0.442727i
\(552\) 18.0000 + 10.3923i 0.766131 + 0.442326i
\(553\) 0 0
\(554\) 12.1244i 0.515115i
\(555\) 15.0000 25.9808i 0.636715 1.10282i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 13.5000 7.79423i 0.572013 0.330252i −0.185940 0.982561i \(-0.559533\pi\)
0.757953 + 0.652309i \(0.226200\pi\)
\(558\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 6.92820i 0.291730i
\(565\) −22.5000 12.9904i −0.946582 0.546509i
\(566\) −6.00000 3.46410i −0.252199 0.145607i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i \(0.176036\pi\)
0.0294311 + 0.999567i \(0.490630\pi\)
\(570\) −18.0000 + 10.3923i −0.753937 + 0.435286i
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 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
\(577\) 19.0526i 0.793168i −0.917998 0.396584i \(-0.870195\pi\)
0.917998 0.396584i \(-0.129805\pi\)
\(578\) 12.0000 + 6.92820i 0.499134 + 0.288175i
\(579\) −9.00000 5.19615i −0.374027 0.215945i
\(580\) 5.19615i 0.215758i
\(581\) 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
\(587\) 18.0000 10.3923i 0.742940 0.428936i −0.0801976 0.996779i \(-0.525555\pi\)
0.823137 + 0.567843i \(0.192222\pi\)
\(588\) 7.00000 + 12.1244i 0.288675 + 0.500000i
\(589\) −6.00000 + 10.3923i −0.247226 + 0.428207i
\(590\) 20.7846i 0.855689i
\(591\) 24.0000 + 13.8564i 0.987228 + 0.569976i
\(592\) −37.5000 21.6506i −1.54124 0.889836i
\(593\) 25.9808i 1.06690i −0.845831 0.533451i \(-0.820895\pi\)
0.845831 0.533451i \(-0.179105\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.5000 9.52628i 0.675866 0.390212i
\(597\) −4.00000 −0.163709
\(598\) 0 0
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 6.00000 3.46410i 0.244949 0.141421i
\(601\) −12.5000 21.6506i −0.509886 0.883148i −0.999934 0.0114528i \(-0.996354\pi\)
0.490049 0.871695i \(-0.336979\pi\)
\(602\) 0 0
\(603\) 3.46410i 0.141069i
\(604\) 15.0000 + 8.66025i 0.610341 + 0.352381i
\(605\) 16.5000 + 9.52628i 0.670820 + 0.387298i
\(606\) 10.3923i 0.422159i
\(607\) 17.0000 29.4449i 0.690009 1.19513i −0.281826 0.959466i \(-0.590940\pi\)
0.971834 0.235665i \(-0.0757267\pi\)
\(608\) 9.00000 + 15.5885i 0.364998 + 0.632195i
\(609\) 0 0
\(610\) 3.00000 0.121466
\(611\) 0 0
\(612\) 3.00000 0.121268
\(613\) 10.5000 6.06218i 0.424091 0.244849i −0.272735 0.962089i \(-0.587928\pi\)
0.696826 + 0.717240i \(0.254595\pi\)
\(614\) −15.0000 25.9808i −0.605351 1.04850i
\(615\) −9.00000 + 15.5885i −0.362915 + 0.628587i
\(616\) 0 0
\(617\) 19.5000 + 11.2583i 0.785040 + 0.453243i 0.838214 0.545342i \(-0.183600\pi\)
−0.0531732 + 0.998585i \(0.516934\pi\)
\(618\) 30.0000 + 17.3205i 1.20678 + 0.696733i
\(619\) 20.7846i 0.835404i −0.908584 0.417702i \(-0.862836\pi\)
0.908584 0.417702i \(-0.137164\pi\)
\(620\) 3.00000 5.19615i 0.120483 0.208683i
\(621\) −12.0000 20.7846i −0.481543 0.834058i
\(622\) −45.0000 + 25.9808i −1.80434 + 1.04173i
\(623\) 0 0
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 15.0000 8.66025i 0.599521 0.346133i
\(627\) 0 0
\(628\) −6.50000 + 11.2583i −0.259378 + 0.449256i
\(629\) 25.9808i 1.03592i
\(630\) 0 0
\(631\) 42.0000 + 24.2487i 1.67199 + 0.965326i 0.966521 + 0.256589i \(0.0825987\pi\)
0.705473 + 0.708737i \(0.250735\pi\)
\(632\) 6.92820i 0.275589i
\(633\) −10.0000 + 17.3205i −0.397464 + 0.688428i
\(634\) −4.50000 7.79423i −0.178718 0.309548i
\(635\) 3.00000 1.73205i 0.119051 0.0687343i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 3.00000 1.73205i 0.118678 0.0685189i
\(640\) 10.5000 + 18.1865i 0.415049 + 0.718886i
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 20.7846i 0.820303i
\(643\) −12.0000 6.92820i −0.473234 0.273222i 0.244359 0.969685i \(-0.421423\pi\)
−0.717592 + 0.696463i \(0.754756\pi\)
\(644\) 0 0
\(645\) 27.7128i 1.09119i
\(646\) 9.00000 15.5885i 0.354100 0.613320i
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) −16.5000 + 9.52628i −0.648181 + 0.374228i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −18.0000 + 10.3923i −0.704934 + 0.406994i
\(653\) 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) −24.0000 + 41.5692i −0.938474 + 1.62549i
\(655\) 31.1769i 1.21818i
\(656\) 22.5000 + 12.9904i 0.878477 + 0.507189i
\(657\) −1.50000 0.866025i −0.0585206 0.0337869i
\(658\) 0 0
\(659\) 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i \(-0.758241\pi\)
0.958902 + 0.283738i \(0.0915745\pi\)
\(660\) 0 0
\(661\) 40.5000 23.3827i 1.57527 0.909481i 0.579761 0.814787i \(-0.303146\pi\)
0.995506 0.0946945i \(-0.0301874\pi\)
\(662\) 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
\(668\) 13.8564i 0.536120i
\(669\) −18.0000 10.3923i −0.695920 0.401790i
\(670\) 9.00000 + 5.19615i 0.347700 + 0.200745i
\(671\) 0 0
\(672\) 0 0
\(673\) 9.50000 + 16.4545i 0.366198 + 0.634274i 0.988968 0.148132i \(-0.0473259\pi\)
−0.622770 + 0.782405i \(0.713993\pi\)
\(674\) −34.5000 + 19.9186i −1.32889 + 0.767235i
\(675\) −8.00000 −0.307920
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −45.0000 + 25.9808i −1.72821 + 0.997785i
\(679\) 0 0
\(680\) 4.50000 7.79423i 0.172567 0.298895i
\(681\) 48.4974i 1.85843i
\(682\) 0 0
\(683\) −21.0000 12.1244i −0.803543 0.463926i 0.0411658 0.999152i \(-0.486893\pi\)
−0.844708 + 0.535227i \(0.820226\pi\)
\(684\) 3.46410i 0.132453i
\(685\) 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
\(691\) −12.0000 + 6.92820i −0.456502 + 0.263561i −0.710572 0.703624i \(-0.751564\pi\)
0.254071 + 0.967186i \(0.418230\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 0 0
\(694\) 51.9615i 1.97243i
\(695\) −6.00000 3.46410i −0.227593 0.131401i
\(696\) −9.00000 5.19615i −0.341144 0.196960i
\(697\) 15.5885i 0.590455i
\(698\) −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 \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 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
\(708\) 12.0000 + 6.92820i 0.450988 + 0.260378i
\(709\) 4.50000 + 2.59808i 0.169001 + 0.0975728i 0.582115 0.813107i \(-0.302225\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 10.3923i 0.390016i
\(711\) −2.00000 + 3.46410i −0.0750059 + 0.129914i
\(712\) 6.00000 + 10.3923i 0.224860 + 0.389468i
\(713\) −18.0000 + 10.3923i −0.674105 + 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −36.0000 + 20.7846i −1.34444 + 0.776215i
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 8.66025i 0.322749i
\(721\) 0 0
\(722\) −10.5000 6.06218i −0.390770 0.225611i
\(723\) 3.46410i 0.128831i
\(724\) 5.50000 9.52628i 0.204406 0.354041i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 33.0000 19.0526i 1.22474 0.707107i
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 4.50000 2.59808i 0.166552 0.0961591i
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 1.00000 1.73205i 0.0369611 0.0640184i
\(733\) 12.1244i 0.447823i 0.974609 + 0.223912i \(0.0718827\pi\)
−0.974609 + 0.223912i \(0.928117\pi\)
\(734\) 33.0000 + 19.0526i 1.21805 + 0.703243i
\(735\) 21.0000 + 12.1244i 0.774597 + 0.447214i
\(736\) 31.1769i 1.14920i
\(737\) 0 0
\(738\) 4.50000 + 7.79423i 0.165647 + 0.286910i
\(739\) 18.0000 10.3923i 0.662141 0.382287i −0.130951 0.991389i \(-0.541803\pi\)
0.793092 + 0.609102i \(0.208470\pi\)
\(740\) 15.0000 0.551411
\(741\) 0 0
\(742\) 0 0
\(743\) 30.0000 17.3205i 1.10059 0.635428i 0.164216 0.986424i \(-0.447490\pi\)
0.936377 + 0.350997i \(0.114157\pi\)
\(744\) 6.00000 + 10.3923i 0.219971 + 0.381000i
\(745\) 16.5000 28.5788i 0.604513 1.04705i
\(746\) 32.9090i 1.20488i
\(747\) −12.0000 6.92820i −0.439057 0.253490i
\(748\) 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 \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 15.0000 8.66025i 0.546994 0.315807i
\(753\) −36.0000 −1.31191
\(754\) 0 0
\(755\) 30.0000 1.09181
\(756\) 0 0
\(757\) 13.0000 + 22.5167i 0.472493 + 0.818382i 0.999505 0.0314762i \(-0.0100208\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 21.0000 36.3731i 0.762754 1.32113i
\(759\) 0 0
\(760\) 9.00000 + 5.19615i 0.326464 + 0.188484i
\(761\) −30.0000 17.3205i −1.08750 0.627868i −0.154590 0.987979i \(-0.549406\pi\)
−0.932910 + 0.360111i \(0.882739\pi\)
\(762\) 6.92820i 0.250982i
\(763\) 0 0
\(764\) 9.00000 + 15.5885i 0.325609 + 0.563971i
\(765\) 4.50000 2.59808i 0.162698 0.0939336i
\(766\) 36.0000 1.30073
\(767\) 0 0
\(768\) 38.0000 1.37121
\(769\) −6.00000 + 3.46410i −0.216366 + 0.124919i −0.604266 0.796782i \(-0.706534\pi\)
0.387901 + 0.921701i \(0.373200\pi\)
\(770\) 0 0
\(771\) −3.00000 + 5.19615i −0.108042 + 0.187135i
\(772\) 5.19615i 0.187014i
\(773\) 30.0000 + 17.3205i 1.07903 + 0.622975i 0.930633 0.365953i \(-0.119257\pi\)
0.148392 + 0.988929i \(0.452590\pi\)
\(774\) −12.0000 6.92820i −0.431331 0.249029i
\(775\) 6.92820i 0.248868i
\(776\) 6.00000 10.3923i 0.215387 0.373062i
\(777\) 0 0
\(778\) −13.5000 + 7.79423i −0.483998 + 0.279437i
\(779\)