Properties

Label 169.2.c.a.146.1
Level $169$
Weight $2$
Character 169.146
Analytic conductor $1.349$
Analytic rank $0$
Dimension $4$
CM no
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 146.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.2.c.a.22.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 1.50000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-1.73205 + 3.00000i) q^{6} -1.73205 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 1.50000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-1.73205 + 3.00000i) q^{6} -1.73205 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{10} +2.00000 q^{12} +(1.73205 + 3.00000i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.73205 q^{18} +(1.73205 - 3.00000i) q^{19} +(0.866025 - 1.50000i) q^{20} +(-3.00000 - 5.19615i) q^{23} +(1.73205 + 3.00000i) q^{24} -2.00000 q^{25} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(3.00000 - 5.19615i) q^{30} +3.46410 q^{31} +(2.59808 - 4.50000i) q^{32} +5.19615 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-4.33013 - 7.50000i) q^{37} -6.00000 q^{38} +3.00000 q^{40} +(-2.59808 - 4.50000i) q^{41} +(4.00000 - 6.92820i) q^{43} +(0.866025 - 1.50000i) q^{45} +(-5.19615 + 9.00000i) q^{46} +3.46410 q^{47} +(5.00000 - 8.66025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(1.73205 + 3.00000i) q^{50} +6.00000 q^{51} -3.00000 q^{53} +(3.46410 + 6.00000i) q^{54} -6.92820 q^{57} +(-2.59808 + 4.50000i) q^{58} +(3.46410 - 6.00000i) q^{59} -3.46410 q^{60} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 - 5.19615i) q^{62} +1.00000 q^{64} +(1.73205 + 3.00000i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-6.00000 + 10.3923i) q^{69} +(-1.73205 + 3.00000i) q^{71} +(0.866025 - 1.50000i) q^{72} -1.73205 q^{73} +(-7.50000 + 12.9904i) q^{74} +(2.00000 + 3.46410i) q^{75} +(1.73205 + 3.00000i) q^{76} +4.00000 q^{79} +(-4.33013 - 7.50000i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-4.50000 + 7.79423i) q^{82} +13.8564 q^{83} +(2.59808 - 4.50000i) q^{85} -13.8564 q^{86} +(-3.00000 + 5.19615i) q^{87} +(3.46410 + 6.00000i) q^{89} -3.00000 q^{90} +6.00000 q^{92} +(-3.46410 - 6.00000i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} -10.3923 q^{96} +(-3.46410 + 6.00000i) q^{97} +(6.06218 - 10.5000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 1.50000i −0.612372 1.06066i −0.990839 0.135045i \(-0.956882\pi\)
0.378467 0.925615i \(-0.376451\pi\)
\(3\) −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
\(5\) −1.73205 −0.774597 −0.387298 0.921954i \(-0.626592\pi\)
−0.387298 + 0.921954i \(0.626592\pi\)
\(6\) −1.73205 + 3.00000i −0.707107 + 1.22474i
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 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 −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 1.73205 0.408248
\(19\) 1.73205 3.00000i 0.397360 0.688247i −0.596040 0.802955i \(-0.703260\pi\)
0.993399 + 0.114708i \(0.0365932\pi\)
\(20\) 0.866025 1.50000i 0.193649 0.335410i
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 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 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 3.00000 5.19615i 0.547723 0.948683i
\(31\) 3.46410 0.622171 0.311086 0.950382i \(-0.399307\pi\)
0.311086 + 0.950382i \(0.399307\pi\)
\(32\) 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 −0.964155 0.265340i \(-0.914516\pi\)
0.252286 0.967653i \(-0.418817\pi\)
\(38\) −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 \(-0.299657\pi\)
−0.994409 + 0.105601i \(0.966323\pi\)
\(42\) 0 0
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) 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 \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) 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 \(-0.684405\pi\)
0.998448 + 0.0556984i \(0.0177385\pi\)
\(60\) −3.46410 −0.447214
\(61\) −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
\(67\) 1.73205 + 3.00000i 0.211604 + 0.366508i 0.952217 0.305424i \(-0.0987981\pi\)
−0.740613 + 0.671932i \(0.765465\pi\)
\(68\) −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 \(-0.899234\pi\)
0.744753 + 0.667340i \(0.232567\pi\)
\(72\) 0.866025 1.50000i 0.102062 0.176777i
\(73\) −1.73205 −0.202721 −0.101361 0.994850i \(-0.532320\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(74\) −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 \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 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 \(-0.0469852\pi\)
−0.621932 + 0.783072i \(0.713652\pi\)
\(90\) −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 \(-0.947739\pi\)
0.634826 + 0.772655i \(0.281072\pi\)
\(98\) 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 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) −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 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) −13.8564 −1.32720 −0.663602 0.748086i \(-0.730973\pi\)
−0.663602 + 0.748086i \(0.730973\pi\)
\(110\) 0 0
\(111\) −8.66025 + 15.0000i −0.821995 + 1.42374i
\(112\) 0 0
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) 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 0.818241 0.574875i \(-0.194949\pi\)
−0.906977 + 0.421180i \(0.861616\pi\)
\(128\) −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 0.313133 + 0.949709i \(0.398621\pi\)
−0.979039 + 0.203674i \(0.934712\pi\)
\(138\) 20.7846 1.76930
\(139\) 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
\(141\) −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 −0.151272 0.988492i \(-0.548337\pi\)
0.931695 0.363241i \(-0.118330\pi\)
\(150\) 3.46410 6.00000i 0.282843 0.489898i
\(151\) −17.3205 −1.40952 −0.704761 0.709444i \(-0.748946\pi\)
−0.704761 + 0.709444i \(0.748946\pi\)
\(152\) −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 −0.0960641 0.995375i \(-0.530625\pi\)
0.910052 0.414494i \(-0.136041\pi\)
\(164\) 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 0.999108 + 0.0422232i \(0.0134441\pi\)
−0.462988 + 0.886365i \(0.653223\pi\)
\(168\) 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 −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 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 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) −1.00000 1.73205i −0.0721688 0.125000i
\(193\) 2.59808 + 4.50000i 0.187014 + 0.323917i 0.944253 0.329220i \(-0.106786\pi\)
−0.757240 + 0.653137i \(0.773452\pi\)
\(194\) 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 \(-0.00234222\pi\)
−0.506359 + 0.862323i \(0.669009\pi\)
\(198\) 0 0
\(199\) −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i \(-0.855917\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(200\) 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 0.640996 0.767544i \(-0.278521\pi\)
−0.985211 + 0.171347i \(0.945188\pi\)
\(212\) 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 \(-0.279792\pi\)
−0.985887 + 0.167412i \(0.946459\pi\)
\(224\) 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 0.111757 + 0.993736i \(0.464352\pi\)
−0.916479 + 0.400083i \(0.868981\pi\)
\(228\) 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 \(-0.734660\pi\)
−0.672222 + 0.740349i \(0.734660\pi\)
\(240\) −8.66025 + 15.0000i −0.559017 + 0.968246i
\(241\) −0.866025 + 1.50000i −0.0557856 + 0.0966235i −0.892570 0.450910i \(-0.851100\pi\)
0.836784 + 0.547533i \(0.184433\pi\)
\(242\) −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 0.428681 + 0.903456i \(0.358978\pi\)
−0.996756 + 0.0804789i \(0.974355\pi\)
\(252\) 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 0.909010 0.416775i \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) 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 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 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 −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) −6.00000 10.3923i −0.365148 0.632456i
\(271\) −10.3923 18.0000i −0.631288 1.09342i −0.987289 0.158937i \(-0.949193\pi\)
0.356001 0.934485i \(-0.384140\pi\)
\(272\) −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 −0.951807 0.306699i \(-0.900776\pi\)
0.741512 + 0.670940i \(0.234109\pi\)
\(278\) −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 \(-0.265601\pi\)
0.671616 + 0.740900i \(0.265601\pi\)
\(282\) −6.00000 + 10.3923i −0.357295 + 0.618853i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) −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 \(-0.784832\pi\)
0.931882 + 0.362761i \(0.118166\pi\)
\(294\) −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 \(-0.335437\pi\)
0.494267 + 0.869310i \(0.335437\pi\)
\(308\) 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 \(-0.546615\pi\)
−0.145922 + 0.989296i \(0.546615\pi\)
\(318\) 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 −0.180400 0.983593i \(-0.557739\pi\)
0.942017 0.335566i \(-0.108928\pi\)
\(332\) −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 −0.110885 0.993833i \(-0.535369\pi\)
0.916127 0.400887i \(-0.131298\pi\)
\(348\) −3.00000 5.19615i −0.160817 0.278543i
\(349\) −6.92820 12.0000i −0.370858 0.642345i 0.618840 0.785517i \(-0.287603\pi\)
−0.989698 + 0.143172i \(0.954270\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.4545 + 28.5000i 0.875784 + 1.51690i 0.855926 + 0.517099i \(0.172988\pi\)
0.0198582 + 0.999803i \(0.493679\pi\)
\(354\) 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 \(-0.441475\pi\)
0.182828 + 0.983145i \(0.441475\pi\)
\(360\) −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 0.996129 + 0.0879086i \(0.0280183\pi\)
−0.421933 + 0.906627i \(0.638648\pi\)
\(368\) 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 −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 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 −0.988964 0.148153i \(-0.952667\pi\)
0.366178 0.930545i \(-0.380666\pi\)
\(380\) −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 −0.468323 0.883558i \(-0.655141\pi\)
0.999345 0.0361995i \(-0.0115252\pi\)
\(384\) −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 \(-0.946376\pi\)
0.638127 + 0.769931i \(0.279710\pi\)
\(398\) 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 \(-0.152896\pi\)
−0.843592 + 0.536985i \(0.819563\pi\)
\(402\) −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 \(-0.959270\pi\)
0.606425 + 0.795141i \(0.292603\pi\)
\(410\) 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 0.557986 0.829851i \(-0.311574\pi\)
−0.997665 + 0.0683046i \(0.978241\pi\)
\(420\) 0 0
\(421\) 15.5885 0.759735 0.379867 0.925041i \(-0.375970\pi\)
0.379867 + 0.925041i \(0.375970\pi\)
\(422\) −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 \(-0.220029\pi\)
−0.937314 + 0.348485i \(0.886696\pi\)
\(432\) −10.0000 17.3205i −0.481125 0.833333i
\(433\) −8.50000 + 14.7224i −0.408484 + 0.707515i −0.994720 0.102625i \(-0.967276\pi\)
0.586236 + 0.810140i \(0.300609\pi\)
\(434\) 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 −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 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 \(-0.885606\pi\)
0.772634 + 0.634852i \(0.218939\pi\)
\(450\) −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 \(-0.153768\pi\)
−0.845059 + 0.534673i \(0.820435\pi\)
\(458\) 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 0.475245 + 0.879853i \(0.342359\pi\)
−0.999598 + 0.0283522i \(0.990974\pi\)
\(462\) 0 0
\(463\) −13.8564 −0.643962 −0.321981 0.946746i \(-0.604349\pi\)
−0.321981 + 0.946746i \(0.604349\pi\)
\(464\) 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 −0.997982 0.0634909i \(-0.979777\pi\)
0.444006 0.896024i \(-0.353557\pi\)
\(480\) 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 \(-0.783160\pi\)
0.933776 + 0.357858i \(0.116493\pi\)
\(488\) 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 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) −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 \(-0.254147\pi\)
0.697835 + 0.716258i \(0.254147\pi\)
\(500\) −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 0.115332 + 0.993327i \(0.463207\pi\)
−0.917912 + 0.396783i \(0.870127\pi\)
\(504\) 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 \(-0.0279089\pi\)
−0.573914 + 0.818916i \(0.694576\pi\)
\(510\) 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 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) −9.00000 + 15.5885i −0.393167 + 0.680985i
\(525\) 0 0
\(526\) −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 \(-0.718163\pi\)
−0.632967 + 0.774179i \(0.718163\pi\)
\(542\) −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 \(-0.0595329\pi\)
−0.652309 + 0.757953i \(0.726200\pi\)
\(558\) 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 \(0.166667\pi\)
\(564\) 6.92820 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 −0.850935 0.525271i \(-0.823964\pi\)
−0.0294311 0.999567i \(-0.509370\pi\)
\(570\) −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 \(-0.629805\pi\)
−0.396584 + 0.917998i \(0.629805\pi\)
\(578\) 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 \(-0.307778\pi\)
−0.996779 + 0.0801976i \(0.974445\pi\)
\(588\) 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 \(-0.320895\pi\)
0.533451 + 0.845831i \(0.320895\pi\)
\(594\) 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 −0.999934 0.0114528i \(-0.996354\pi\)
0.490049 0.871695i \(-0.336979\pi\)
\(602\) 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 −0.281826 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
\(613\) −6.06218 10.5000i −0.244849 0.424091i 0.717240 0.696826i \(-0.245405\pi\)
−0.962089 + 0.272735i \(0.912072\pi\)
\(614\) −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 \(-0.683600\pi\)
0.998585 + 0.0531732i \(0.0169335\pi\)
\(618\) −17.3205 + 30.0000i −0.696733 + 1.20678i
\(619\) 20.7846 0.835404 0.417702 0.908584i \(-0.362836\pi\)
0.417702 + 0.908584i \(0.362836\pi\)
\(620\) 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 −0.256589 + 0.966521i \(0.582599\pi\)
−0.708737 + 0.705473i \(0.750735\pi\)
\(632\) −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 −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 20.7846 0.820303
\(643\) −6.92820 + 12.0000i −0.273222 + 0.473234i −0.969685 0.244359i \(-0.921423\pi\)
0.696463 + 0.717592i \(0.254756\pi\)
\(644\) 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 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) −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 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) 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 −0.725175 0.688565i \(-0.758241\pi\)
0.958902 + 0.283738i \(0.0915745\pi\)
\(660\) 0 0
\(661\) 23.3827 + 40.5000i 0.909481 + 1.57527i 0.814787 + 0.579761i \(0.196854\pi\)
0.0946945 + 0.995506i \(0.469813\pi\)
\(662\) −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 0.622770 0.782405i \(-0.286007\pi\)
−0.988968 + 0.148132i \(0.952674\pi\)
\(674\) −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 \(-0.679774\pi\)
0.999152 + 0.0411658i \(0.0131072\pi\)
\(684\) −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 \(-0.0817696\pi\)
−0.703624 + 0.710572i \(0.748436\pi\)
\(692\) 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 \(-0.864441\pi\)
0.813107 + 0.582115i \(0.197775\pi\)
\(710\) −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 −0.0613050 + 0.998119i \(0.519526\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(720\) 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 \(-0.428117\pi\)
0.223912 + 0.974609i \(0.428117\pi\)
\(734\) 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 \(-0.0418032\pi\)
−0.609102 + 0.793092i \(0.708470\pi\)
\(740\) −15.0000 −0.551411
\(741\) 0 0
\(742\) 0 0
\(743\) −17.3205 30.0000i −0.635428 1.10059i −0.986424 0.164216i \(-0.947490\pi\)
0.350997 0.936377i \(-0.385843\pi\)
\(744\) 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 0.682341 0.731034i \(-0.260962\pi\)
−0.974265 + 0.225407i \(0.927629\pi\)
\(752\) 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 0.999505 0.0314762i \(-0.0100208\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) −21.0000 + 36.3731i −0.762754 + 1.32113i
\(759\) 0 0
\(760\) 5.19615 9.00000i 0.188484 0.326464i
\(761\) 17.3205 30.0000i 0.627868 1.08750i −0.360111 0.932910i \(-0.617261\pi\)
0.987979 0.154590i \(-0.0494055\pi\)
\(762\) 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 \(-0.126800\pi\)
−0.796782 + 0.604266i \(0.793466\pi\)
\(770\) 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 −0.365953 0.930633i \(-0.619257\pi\)
0.988929 0.148392i \(-0.0474097\pi\)
\(774\) 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
\(782\) −15.5885