Properties

Label 1078.2.e.o.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1078,2,Mod(67,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (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: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.o.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.41421 + 2.44949i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.82843 q^{6} +1.00000 q^{8} +(-2.50000 - 4.33013i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.41421 + 2.44949i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.82843 q^{6} +1.00000 q^{8} +(-2.50000 - 4.33013i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-1.41421 - 2.44949i) q^{12} +4.24264 q^{13} +(-0.500000 - 0.866025i) q^{16} +(1.41421 - 2.44949i) q^{17} +(-2.50000 + 4.33013i) q^{18} +(2.12132 + 3.67423i) q^{19} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(-1.41421 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-2.12132 - 3.67423i) q^{26} +5.65685 q^{27} -4.00000 q^{29} +(3.53553 - 6.12372i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.41421 + 2.44949i) q^{33} -2.82843 q^{34} +5.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(2.12132 - 3.67423i) q^{38} +(-6.00000 + 10.3923i) q^{39} +2.82843 q^{41} +10.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(6.36396 + 11.0227i) q^{47} +2.82843 q^{48} -5.00000 q^{50} +(4.00000 + 6.92820i) q^{51} +(-2.12132 + 3.67423i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-2.82843 - 4.89898i) q^{54} -12.0000 q^{57} +(2.00000 + 3.46410i) q^{58} +(-5.65685 + 9.79796i) q^{59} +(4.94975 + 8.57321i) q^{61} -7.07107 q^{62} +1.00000 q^{64} +(1.41421 - 2.44949i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(1.41421 + 2.44949i) q^{68} +16.9706 q^{69} +16.0000 q^{71} +(-2.50000 - 4.33013i) q^{72} +(4.24264 - 7.34847i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(7.07107 + 12.2474i) q^{75} -4.24264 q^{76} +12.0000 q^{78} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.41421 - 2.44949i) q^{82} -12.7279 q^{83} +(-5.00000 - 8.66025i) q^{86} +(5.65685 - 9.79796i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-3.53553 - 6.12372i) q^{89} +6.00000 q^{92} +(10.0000 + 17.3205i) q^{93} +(6.36396 - 11.0227i) q^{94} +(-1.41421 - 2.44949i) q^{96} -7.07107 q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 10 q^{9} + 2 q^{11} - 2 q^{16} - 10 q^{18} - 4 q^{22} - 12 q^{23} + 10 q^{25} - 16 q^{29} - 2 q^{32} + 20 q^{36} - 4 q^{37} - 24 q^{39} + 40 q^{43} + 2 q^{44} - 12 q^{46} - 20 q^{50} + 16 q^{51} - 4 q^{53} - 48 q^{57} + 8 q^{58} + 4 q^{64} - 16 q^{67} + 64 q^{71} - 10 q^{72} - 4 q^{74} + 48 q^{78} + 16 q^{79} - 2 q^{81} - 20 q^{86} + 2 q^{88} + 24 q^{92} + 40 q^{93} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.41421 + 2.44949i −0.816497 + 1.41421i 0.0917517 + 0.995782i \(0.470753\pi\)
−0.908248 + 0.418432i \(0.862580\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 2.82843 1.15470
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.50000 4.33013i −0.833333 1.44338i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) −1.41421 2.44949i −0.408248 0.707107i
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.41421 2.44949i 0.342997 0.594089i −0.641991 0.766712i \(-0.721891\pi\)
0.984988 + 0.172624i \(0.0552245\pi\)
\(18\) −2.50000 + 4.33013i −0.589256 + 1.02062i
\(19\) 2.12132 + 3.67423i 0.486664 + 0.842927i 0.999882 0.0153309i \(-0.00488018\pi\)
−0.513218 + 0.858258i \(0.671547\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) −1.41421 + 2.44949i −0.288675 + 0.500000i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −2.12132 3.67423i −0.416025 0.720577i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 3.53553 6.12372i 0.635001 1.09985i −0.351514 0.936182i \(-0.614333\pi\)
0.986515 0.163671i \(-0.0523335\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 1.41421 + 2.44949i 0.246183 + 0.426401i
\(34\) −2.82843 −0.485071
\(35\) 0 0
\(36\) 5.00000 0.833333
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 2.12132 3.67423i 0.344124 0.596040i
\(39\) −6.00000 + 10.3923i −0.960769 + 1.66410i
\(40\) 0 0
\(41\) 2.82843 0.441726 0.220863 0.975305i \(-0.429113\pi\)
0.220863 + 0.975305i \(0.429113\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 6.36396 + 11.0227i 0.928279 + 1.60783i 0.786201 + 0.617971i \(0.212045\pi\)
0.142078 + 0.989855i \(0.454621\pi\)
\(48\) 2.82843 0.408248
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) 4.00000 + 6.92820i 0.560112 + 0.970143i
\(52\) −2.12132 + 3.67423i −0.294174 + 0.509525i
\(53\) −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i \(-0.877195\pi\)
0.789136 + 0.614218i \(0.210529\pi\)
\(54\) −2.82843 4.89898i −0.384900 0.666667i
\(55\) 0 0
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) 2.00000 + 3.46410i 0.262613 + 0.454859i
\(59\) −5.65685 + 9.79796i −0.736460 + 1.27559i 0.217620 + 0.976034i \(0.430171\pi\)
−0.954080 + 0.299552i \(0.903163\pi\)
\(60\) 0 0
\(61\) 4.94975 + 8.57321i 0.633750 + 1.09769i 0.986778 + 0.162075i \(0.0518186\pi\)
−0.353028 + 0.935613i \(0.614848\pi\)
\(62\) −7.07107 −0.898027
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.41421 2.44949i 0.174078 0.301511i
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 1.41421 + 2.44949i 0.171499 + 0.297044i
\(69\) 16.9706 2.04302
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) −2.50000 4.33013i −0.294628 0.510310i
\(73\) 4.24264 7.34847i 0.496564 0.860073i −0.503429 0.864037i \(-0.667928\pi\)
0.999992 + 0.00396356i \(0.00126164\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 7.07107 + 12.2474i 0.816497 + 1.41421i
\(76\) −4.24264 −0.486664
\(77\) 0 0
\(78\) 12.0000 1.35873
\(79\) 4.00000 + 6.92820i 0.450035 + 0.779484i 0.998388 0.0567635i \(-0.0180781\pi\)
−0.548352 + 0.836247i \(0.684745\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.41421 2.44949i −0.156174 0.270501i
\(83\) −12.7279 −1.39707 −0.698535 0.715575i \(-0.746165\pi\)
−0.698535 + 0.715575i \(0.746165\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 5.65685 9.79796i 0.606478 1.05045i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) −3.53553 6.12372i −0.374766 0.649113i 0.615526 0.788116i \(-0.288944\pi\)
−0.990292 + 0.139003i \(0.955610\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 10.0000 + 17.3205i 1.03695 + 1.79605i
\(94\) 6.36396 11.0227i 0.656392 1.13691i
\(95\) 0 0
\(96\) −1.41421 2.44949i −0.144338 0.250000i
\(97\) −7.07107 −0.717958 −0.358979 0.933346i \(-0.616875\pi\)
−0.358979 + 0.933346i \(0.616875\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 0.707107 1.22474i 0.0703598 0.121867i −0.828699 0.559694i \(-0.810919\pi\)
0.899059 + 0.437828i \(0.144252\pi\)
\(102\) 4.00000 6.92820i 0.396059 0.685994i
\(103\) 0.707107 + 1.22474i 0.0696733 + 0.120678i 0.898757 0.438446i \(-0.144471\pi\)
−0.829084 + 0.559124i \(0.811138\pi\)
\(104\) 4.24264 0.416025
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 7.00000 + 12.1244i 0.676716 + 1.17211i 0.975964 + 0.217931i \(0.0699306\pi\)
−0.299249 + 0.954175i \(0.596736\pi\)
\(108\) −2.82843 + 4.89898i −0.272166 + 0.471405i
\(109\) 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i \(-0.599422\pi\)
0.977769 0.209687i \(-0.0672444\pi\)
\(110\) 0 0
\(111\) 5.65685 0.536925
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 6.00000 + 10.3923i 0.561951 + 0.973329i
\(115\) 0 0
\(116\) 2.00000 3.46410i 0.185695 0.321634i
\(117\) −10.6066 18.3712i −0.980581 1.69842i
\(118\) 11.3137 1.04151
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 4.94975 8.57321i 0.448129 0.776182i
\(123\) −4.00000 + 6.92820i −0.360668 + 0.624695i
\(124\) 3.53553 + 6.12372i 0.317500 + 0.549927i
\(125\) 0 0
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −14.1421 + 24.4949i −1.24515 + 2.15666i
\(130\) 0 0
\(131\) −3.53553 6.12372i −0.308901 0.535032i 0.669221 0.743063i \(-0.266628\pi\)
−0.978122 + 0.208031i \(0.933295\pi\)
\(132\) −2.82843 −0.246183
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 1.41421 2.44949i 0.121268 0.210042i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) −8.48528 14.6969i −0.722315 1.25109i
\(139\) 18.3848 1.55938 0.779688 0.626168i \(-0.215378\pi\)
0.779688 + 0.626168i \(0.215378\pi\)
\(140\) 0 0
\(141\) −36.0000 −3.03175
\(142\) −8.00000 13.8564i −0.671345 1.16280i
\(143\) 2.12132 3.67423i 0.177394 0.307255i
\(144\) −2.50000 + 4.33013i −0.208333 + 0.360844i
\(145\) 0 0
\(146\) −8.48528 −0.702247
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −4.00000 6.92820i −0.327693 0.567581i 0.654361 0.756182i \(-0.272938\pi\)
−0.982054 + 0.188602i \(0.939604\pi\)
\(150\) 7.07107 12.2474i 0.577350 1.00000i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 2.12132 + 3.67423i 0.172062 + 0.298020i
\(153\) −14.1421 −1.14332
\(154\) 0 0
\(155\) 0 0
\(156\) −6.00000 10.3923i −0.480384 0.832050i
\(157\) −4.24264 + 7.34847i −0.338600 + 0.586472i −0.984170 0.177229i \(-0.943287\pi\)
0.645570 + 0.763701i \(0.276620\pi\)
\(158\) 4.00000 6.92820i 0.318223 0.551178i
\(159\) −2.82843 4.89898i −0.224309 0.388514i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) −1.41421 + 2.44949i −0.110432 + 0.191273i
\(165\) 0 0
\(166\) 6.36396 + 11.0227i 0.493939 + 0.855528i
\(167\) −14.1421 −1.09435 −0.547176 0.837018i \(-0.684297\pi\)
−0.547176 + 0.837018i \(0.684297\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 10.6066 18.3712i 0.811107 1.40488i
\(172\) −5.00000 + 8.66025i −0.381246 + 0.660338i
\(173\) −3.53553 6.12372i −0.268802 0.465578i 0.699751 0.714387i \(-0.253294\pi\)
−0.968553 + 0.248809i \(0.919961\pi\)
\(174\) −11.3137 −0.857690
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −16.0000 27.7128i −1.20263 2.08302i
\(178\) −3.53553 + 6.12372i −0.264999 + 0.458993i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 11.3137 0.840941 0.420471 0.907306i \(-0.361865\pi\)
0.420471 + 0.907306i \(0.361865\pi\)
\(182\) 0 0
\(183\) −28.0000 −2.06982
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 0 0
\(186\) 10.0000 17.3205i 0.733236 1.27000i
\(187\) −1.41421 2.44949i −0.103418 0.179124i
\(188\) −12.7279 −0.928279
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) −1.41421 + 2.44949i −0.102062 + 0.176777i
\(193\) −3.00000 + 5.19615i −0.215945 + 0.374027i −0.953564 0.301189i \(-0.902616\pi\)
0.737620 + 0.675216i \(0.235950\pi\)
\(194\) 3.53553 + 6.12372i 0.253837 + 0.439658i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 2.50000 + 4.33013i 0.177667 + 0.307729i
\(199\) −4.94975 + 8.57321i −0.350878 + 0.607739i −0.986404 0.164341i \(-0.947450\pi\)
0.635525 + 0.772080i \(0.280784\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) −11.3137 19.5959i −0.798007 1.38219i
\(202\) −1.41421 −0.0995037
\(203\) 0 0
\(204\) −8.00000 −0.560112
\(205\) 0 0
\(206\) 0.707107 1.22474i 0.0492665 0.0853320i
\(207\) −15.0000 + 25.9808i −1.04257 + 1.80579i
\(208\) −2.12132 3.67423i −0.147087 0.254762i
\(209\) 4.24264 0.293470
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) −1.00000 1.73205i −0.0686803 0.118958i
\(213\) −22.6274 + 39.1918i −1.55041 + 2.68538i
\(214\) 7.00000 12.1244i 0.478510 0.828804i
\(215\) 0 0
\(216\) 5.65685 0.384900
\(217\) 0 0
\(218\) −14.0000 −0.948200
\(219\) 12.0000 + 20.7846i 0.810885 + 1.40449i
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) −2.82843 4.89898i −0.189832 0.328798i
\(223\) 21.2132 1.42054 0.710271 0.703929i \(-0.248573\pi\)
0.710271 + 0.703929i \(0.248573\pi\)
\(224\) 0 0
\(225\) −25.0000 −1.66667
\(226\) −8.00000 13.8564i −0.532152 0.921714i
\(227\) 3.53553 6.12372i 0.234662 0.406446i −0.724513 0.689261i \(-0.757935\pi\)
0.959174 + 0.282816i \(0.0912685\pi\)
\(228\) 6.00000 10.3923i 0.397360 0.688247i
\(229\) 11.3137 + 19.5959i 0.747631 + 1.29493i 0.948955 + 0.315410i \(0.102142\pi\)
−0.201325 + 0.979525i \(0.564525\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) −13.0000 22.5167i −0.851658 1.47512i −0.879711 0.475509i \(-0.842264\pi\)
0.0280525 0.999606i \(-0.491069\pi\)
\(234\) −10.6066 + 18.3712i −0.693375 + 1.20096i
\(235\) 0 0
\(236\) −5.65685 9.79796i −0.368230 0.637793i
\(237\) −22.6274 −1.46981
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 4.24264 7.34847i 0.273293 0.473357i −0.696410 0.717644i \(-0.745221\pi\)
0.969703 + 0.244287i \(0.0785540\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 7.07107 + 12.2474i 0.453609 + 0.785674i
\(244\) −9.89949 −0.633750
\(245\) 0 0
\(246\) 8.00000 0.510061
\(247\) 9.00000 + 15.5885i 0.572656 + 0.991870i
\(248\) 3.53553 6.12372i 0.224507 0.388857i
\(249\) 18.0000 31.1769i 1.14070 1.97576i
\(250\) 0 0
\(251\) −5.65685 −0.357057 −0.178529 0.983935i \(-0.557134\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 10.0000 + 17.3205i 0.627456 + 1.08679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.53553 6.12372i −0.220541 0.381987i 0.734432 0.678683i \(-0.237449\pi\)
−0.954972 + 0.296695i \(0.904115\pi\)
\(258\) 28.2843 1.76090
\(259\) 0 0
\(260\) 0 0
\(261\) 10.0000 + 17.3205i 0.618984 + 1.07211i
\(262\) −3.53553 + 6.12372i −0.218426 + 0.378325i
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 1.41421 + 2.44949i 0.0870388 + 0.150756i
\(265\) 0 0
\(266\) 0 0
\(267\) 20.0000 1.22398
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) −5.65685 + 9.79796i −0.344904 + 0.597392i −0.985336 0.170623i \(-0.945422\pi\)
0.640432 + 0.768015i \(0.278755\pi\)
\(270\) 0 0
\(271\) −4.24264 7.34847i −0.257722 0.446388i 0.707909 0.706303i \(-0.249639\pi\)
−0.965631 + 0.259916i \(0.916305\pi\)
\(272\) −2.82843 −0.171499
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −2.50000 4.33013i −0.150756 0.261116i
\(276\) −8.48528 + 14.6969i −0.510754 + 0.884652i
\(277\) 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) −9.19239 15.9217i −0.551323 0.954919i
\(279\) −35.3553 −2.11667
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 18.0000 + 31.1769i 1.07188 + 1.85656i
\(283\) −3.53553 + 6.12372i −0.210166 + 0.364018i −0.951766 0.306824i \(-0.900734\pi\)
0.741601 + 0.670842i \(0.234067\pi\)
\(284\) −8.00000 + 13.8564i −0.474713 + 0.822226i
\(285\) 0 0
\(286\) −4.24264 −0.250873
\(287\) 0 0
\(288\) 5.00000 0.294628
\(289\) 4.50000 + 7.79423i 0.264706 + 0.458484i
\(290\) 0 0
\(291\) 10.0000 17.3205i 0.586210 1.01535i
\(292\) 4.24264 + 7.34847i 0.248282 + 0.430037i
\(293\) −21.2132 −1.23929 −0.619644 0.784883i \(-0.712723\pi\)
−0.619644 + 0.784883i \(0.712723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 2.82843 4.89898i 0.164122 0.284268i
\(298\) −4.00000 + 6.92820i −0.231714 + 0.401340i
\(299\) −12.7279 22.0454i −0.736075 1.27492i
\(300\) −14.1421 −0.816497
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) 2.00000 + 3.46410i 0.114897 + 0.199007i
\(304\) 2.12132 3.67423i 0.121666 0.210732i
\(305\) 0 0
\(306\) 7.07107 + 12.2474i 0.404226 + 0.700140i
\(307\) 21.2132 1.21070 0.605351 0.795959i \(-0.293033\pi\)
0.605351 + 0.795959i \(0.293033\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 0.707107 1.22474i 0.0400963 0.0694489i −0.845281 0.534322i \(-0.820567\pi\)
0.885377 + 0.464873i \(0.153900\pi\)
\(312\) −6.00000 + 10.3923i −0.339683 + 0.588348i
\(313\) 14.8492 + 25.7196i 0.839329 + 1.45376i 0.890457 + 0.455068i \(0.150385\pi\)
−0.0511279 + 0.998692i \(0.516282\pi\)
\(314\) 8.48528 0.478852
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) −2.82843 + 4.89898i −0.158610 + 0.274721i
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) 0 0
\(321\) −39.5980 −2.21014
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 10.6066 18.3712i 0.588348 1.01905i
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 19.7990 + 34.2929i 1.09489 + 1.89640i
\(328\) 2.82843 0.156174
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 6.36396 11.0227i 0.349268 0.604949i
\(333\) −5.00000 + 8.66025i −0.273998 + 0.474579i
\(334\) 7.07107 + 12.2474i 0.386912 + 0.670151i
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −2.50000 4.33013i −0.135982 0.235528i
\(339\) −22.6274 + 39.1918i −1.22895 + 2.12861i
\(340\) 0 0
\(341\) −3.53553 6.12372i −0.191460 0.331618i
\(342\) −21.2132 −1.14708
\(343\) 0 0
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −3.53553 + 6.12372i −0.190071 + 0.329213i
\(347\) −13.0000 + 22.5167i −0.697877 + 1.20876i 0.271325 + 0.962488i \(0.412538\pi\)
−0.969201 + 0.246270i \(0.920795\pi\)
\(348\) 5.65685 + 9.79796i 0.303239 + 0.525226i
\(349\) −26.8701 −1.43832 −0.719161 0.694844i \(-0.755473\pi\)
−0.719161 + 0.694844i \(0.755473\pi\)
\(350\) 0 0
\(351\) 24.0000 1.28103
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −7.77817 + 13.4722i −0.413990 + 0.717053i −0.995322 0.0966144i \(-0.969199\pi\)
0.581331 + 0.813667i \(0.302532\pi\)
\(354\) −16.0000 + 27.7128i −0.850390 + 1.47292i
\(355\) 0 0
\(356\) 7.07107 0.374766
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −6.00000 10.3923i −0.316668 0.548485i 0.663123 0.748511i \(-0.269231\pi\)
−0.979791 + 0.200026i \(0.935897\pi\)
\(360\) 0 0
\(361\) 0.500000 0.866025i 0.0263158 0.0455803i
\(362\) −5.65685 9.79796i −0.297318 0.514969i
\(363\) 2.82843 0.148454
\(364\) 0 0
\(365\) 0 0
\(366\) 14.0000 + 24.2487i 0.731792 + 1.26750i
\(367\) 10.6066 18.3712i 0.553660 0.958967i −0.444346 0.895855i \(-0.646564\pi\)
0.998006 0.0631123i \(-0.0201026\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) −7.07107 12.2474i −0.368105 0.637577i
\(370\) 0 0
\(371\) 0 0
\(372\) −20.0000 −1.03695
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) −1.41421 + 2.44949i −0.0731272 + 0.126660i
\(375\) 0 0
\(376\) 6.36396 + 11.0227i 0.328196 + 0.568453i
\(377\) −16.9706 −0.874028
\(378\) 0 0
\(379\) 24.0000 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) 0 0
\(381\) 28.2843 48.9898i 1.44905 2.50982i
\(382\) −5.00000 + 8.66025i −0.255822 + 0.443097i
\(383\) 7.77817 + 13.4722i 0.397446 + 0.688397i 0.993410 0.114614i \(-0.0365632\pi\)
−0.595964 + 0.803011i \(0.703230\pi\)
\(384\) 2.82843 0.144338
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) −25.0000 43.3013i −1.27082 2.20113i
\(388\) 3.53553 6.12372i 0.179490 0.310885i
\(389\) 15.0000 25.9808i 0.760530 1.31728i −0.182047 0.983290i \(-0.558272\pi\)
0.942578 0.333987i \(-0.108394\pi\)
\(390\) 0 0
\(391\) −16.9706 −0.858238
\(392\) 0 0
\(393\) 20.0000 1.00887
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) −12.7279 22.0454i −0.638796 1.10643i −0.985697 0.168526i \(-0.946099\pi\)
0.346901 0.937902i \(-0.387234\pi\)
\(398\) 9.89949 0.496217
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) −11.3137 + 19.5959i −0.564276 + 0.977356i
\(403\) 15.0000 25.9808i 0.747203 1.29419i
\(404\) 0.707107 + 1.22474i 0.0351799 + 0.0609333i
\(405\) 0 0
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) 4.00000 + 6.92820i 0.198030 + 0.342997i
\(409\) −14.1421 + 24.4949i −0.699284 + 1.21119i 0.269432 + 0.963020i \(0.413164\pi\)
−0.968715 + 0.248175i \(0.920169\pi\)
\(410\) 0 0
\(411\) 8.48528 + 14.6969i 0.418548 + 0.724947i
\(412\) −1.41421 −0.0696733
\(413\) 0 0
\(414\) 30.0000 1.47442
\(415\) 0 0
\(416\) −2.12132 + 3.67423i −0.104006 + 0.180144i
\(417\) −26.0000 + 45.0333i −1.27323 + 2.20529i
\(418\) −2.12132 3.67423i −0.103757 0.179713i
\(419\) 14.1421 0.690889 0.345444 0.938439i \(-0.387728\pi\)
0.345444 + 0.938439i \(0.387728\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −13.0000 22.5167i −0.632830 1.09609i
\(423\) 31.8198 55.1135i 1.54713 2.67971i
\(424\) −1.00000 + 1.73205i −0.0485643 + 0.0841158i
\(425\) −7.07107 12.2474i −0.342997 0.594089i
\(426\) 45.2548 2.19260
\(427\) 0 0
\(428\) −14.0000 −0.676716
\(429\) 6.00000 + 10.3923i 0.289683 + 0.501745i
\(430\) 0 0
\(431\) −4.00000 + 6.92820i −0.192673 + 0.333720i −0.946135 0.323772i \(-0.895049\pi\)
0.753462 + 0.657491i \(0.228382\pi\)
\(432\) −2.82843 4.89898i −0.136083 0.235702i
\(433\) 29.6985 1.42722 0.713609 0.700544i \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) 12.7279 22.0454i 0.608859 1.05457i
\(438\) 12.0000 20.7846i 0.573382 0.993127i
\(439\) −12.7279 22.0454i −0.607471 1.05217i −0.991656 0.128914i \(-0.958851\pi\)
0.384185 0.923256i \(-0.374482\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) −2.82843 + 4.89898i −0.134231 + 0.232495i
\(445\) 0 0
\(446\) −10.6066 18.3712i −0.502237 0.869900i
\(447\) 22.6274 1.07024
\(448\) 0 0
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 12.5000 + 21.6506i 0.589256 + 1.02062i
\(451\) 1.41421 2.44949i 0.0665927 0.115342i
\(452\) −8.00000 + 13.8564i −0.376288 + 0.651751i
\(453\) 11.3137 + 19.5959i 0.531564 + 0.920697i
\(454\) −7.07107 −0.331862
\(455\) 0 0
\(456\) −12.0000 −0.561951
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) 11.3137 19.5959i 0.528655 0.915657i
\(459\) 8.00000 13.8564i 0.373408 0.646762i
\(460\) 0 0
\(461\) 1.41421 0.0658665 0.0329332 0.999458i \(-0.489515\pi\)
0.0329332 + 0.999458i \(0.489515\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) 0 0
\(466\) −13.0000 + 22.5167i −0.602213 + 1.04306i
\(467\) −12.7279 22.0454i −0.588978 1.02014i −0.994367 0.105995i \(-0.966197\pi\)
0.405389 0.914144i \(-0.367136\pi\)
\(468\) 21.2132 0.980581
\(469\) 0 0
\(470\) 0 0
\(471\) −12.0000 20.7846i −0.552931 0.957704i
\(472\) −5.65685 + 9.79796i −0.260378 + 0.450988i
\(473\) 5.00000 8.66025i 0.229900 0.398199i
\(474\) 11.3137 + 19.5959i 0.519656 + 0.900070i
\(475\) 21.2132 0.973329
\(476\) 0 0
\(477\) 10.0000 0.457869
\(478\) 0 0
\(479\) 14.1421 24.4949i 0.646171 1.11920i −0.337859 0.941197i \(-0.609703\pi\)
0.984030 0.178004i \(-0.0569639\pi\)
\(480\) 0 0
\(481\) −4.24264 7.34847i −0.193448 0.335061i
\(482\) −8.48528 −0.386494
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 7.07107 12.2474i 0.320750 0.555556i
\(487\) −19.0000 + 32.9090i −0.860972 + 1.49125i 0.0100195 + 0.999950i \(0.496811\pi\)
−0.870992 + 0.491298i \(0.836523\pi\)
\(488\) 4.94975 + 8.57321i 0.224065 + 0.388091i
\(489\) −11.3137 −0.511624
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −4.00000 6.92820i −0.180334 0.312348i
\(493\) −5.65685 + 9.79796i −0.254772 + 0.441278i
\(494\) 9.00000 15.5885i 0.404929 0.701358i
\(495\) 0 0
\(496\) −7.07107 −0.317500
\(497\) 0 0
\(498\) −36.0000 −1.61320
\(499\) −18.0000 31.1769i −0.805791 1.39567i −0.915756 0.401735i \(-0.868407\pi\)
0.109965 0.993935i \(-0.464926\pi\)
\(500\) 0 0
\(501\) 20.0000 34.6410i 0.893534 1.54765i
\(502\) 2.82843 + 4.89898i 0.126239 + 0.218652i
\(503\) 19.7990 0.882793 0.441397 0.897312i \(-0.354483\pi\)
0.441397 + 0.897312i \(0.354483\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) −7.07107 + 12.2474i −0.314037 + 0.543928i
\(508\) 10.0000 17.3205i 0.443678 0.768473i
\(509\) −8.48528 14.6969i −0.376103 0.651430i 0.614388 0.789004i \(-0.289403\pi\)
−0.990492 + 0.137574i \(0.956070\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 12.0000 + 20.7846i 0.529813 + 0.917663i
\(514\) −3.53553 + 6.12372i −0.155946 + 0.270106i
\(515\) 0 0
\(516\) −14.1421 24.4949i −0.622573 1.07833i
\(517\) 12.7279 0.559773
\(518\) 0 0
\(519\) 20.0000 0.877903
\(520\) 0 0
\(521\) 0.707107 1.22474i 0.0309789 0.0536570i −0.850120 0.526589i \(-0.823471\pi\)
0.881099 + 0.472931i \(0.156804\pi\)
\(522\) 10.0000 17.3205i 0.437688 0.758098i
\(523\) −2.12132 3.67423i −0.0927589 0.160663i 0.815912 0.578176i \(-0.196235\pi\)
−0.908671 + 0.417513i \(0.862902\pi\)
\(524\) 7.07107 0.308901
\(525\) 0 0
\(526\) 4.00000 0.174408
\(527\) −10.0000 17.3205i −0.435607 0.754493i
\(528\) 1.41421 2.44949i 0.0615457 0.106600i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 56.5685 2.45487
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) −10.0000 17.3205i −0.432742 0.749532i
\(535\) 0 0
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 16.9706 + 29.3939i 0.732334 + 1.26844i
\(538\) 11.3137 0.487769
\(539\) 0 0
\(540\) 0 0
\(541\) 15.0000 + 25.9808i 0.644900 + 1.11700i 0.984325 + 0.176367i \(0.0564345\pi\)
−0.339424 + 0.940633i \(0.610232\pi\)
\(542\) −4.24264 + 7.34847i −0.182237 + 0.315644i
\(543\) −16.0000 + 27.7128i −0.686626 + 1.18927i
\(544\) 1.41421 + 2.44949i 0.0606339 + 0.105021i
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 24.7487 42.8661i 1.05625 1.82948i
\(550\) −2.50000 + 4.33013i −0.106600 + 0.184637i
\(551\) −8.48528 14.6969i −0.361485 0.626111i
\(552\) 16.9706 0.722315
\(553\) 0 0
\(554\) −8.00000 −0.339887
\(555\) 0 0
\(556\) −9.19239 + 15.9217i −0.389844 + 0.675230i
\(557\) 3.00000 5.19615i 0.127114 0.220168i −0.795443 0.606028i \(-0.792762\pi\)
0.922557 + 0.385860i \(0.126095\pi\)
\(558\) 17.6777 + 30.6186i 0.748355 + 1.29619i
\(559\) 42.4264 1.79445
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) −11.0000 19.0526i −0.464007 0.803684i
\(563\) −20.5061 + 35.5176i −0.864229 + 1.49689i 0.00358183 + 0.999994i \(0.498860\pi\)
−0.867811 + 0.496895i \(0.834473\pi\)
\(564\) 18.0000 31.1769i 0.757937 1.31278i
\(565\) 0 0
\(566\) 7.07107 0.297219
\(567\) 0 0
\(568\) 16.0000 0.671345
\(569\) −21.0000 36.3731i −0.880366 1.52484i −0.850935 0.525271i \(-0.823964\pi\)
−0.0294311 0.999567i \(-0.509370\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 2.12132 + 3.67423i 0.0886969 + 0.153627i
\(573\) 28.2843 1.18159
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) −2.50000 4.33013i −0.104167 0.180422i
\(577\) 4.94975 8.57321i 0.206061 0.356908i −0.744409 0.667723i \(-0.767269\pi\)
0.950470 + 0.310816i \(0.100602\pi\)
\(578\) 4.50000 7.79423i 0.187175 0.324197i
\(579\) −8.48528 14.6969i −0.352636 0.610784i
\(580\) 0 0
\(581\) 0 0
\(582\) −20.0000 −0.829027
\(583\) 1.00000 + 1.73205i 0.0414158 + 0.0717342i
\(584\) 4.24264 7.34847i 0.175562 0.304082i
\(585\) 0 0
\(586\) 10.6066 + 18.3712i 0.438155 + 0.758906i
\(587\) 5.65685 0.233483 0.116742 0.993162i \(-0.462755\pi\)
0.116742 + 0.993162i \(0.462755\pi\)
\(588\) 0 0
\(589\) 30.0000 1.23613
\(590\) 0 0
\(591\) 2.82843 4.89898i 0.116346 0.201517i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −4.24264 7.34847i −0.174224 0.301765i 0.765668 0.643236i \(-0.222408\pi\)
−0.939893 + 0.341470i \(0.889075\pi\)
\(594\) −5.65685 −0.232104
\(595\) 0 0
\(596\) 8.00000 0.327693
\(597\) −14.0000 24.2487i −0.572982 0.992434i
\(598\) −12.7279 + 22.0454i −0.520483 + 0.901504i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 7.07107 + 12.2474i 0.288675 + 0.500000i
\(601\) 11.3137 0.461496 0.230748 0.973014i \(-0.425883\pi\)
0.230748 + 0.973014i \(0.425883\pi\)
\(602\) 0 0
\(603\) 40.0000 1.62893
\(604\) 4.00000 + 6.92820i 0.162758 + 0.281905i
\(605\) 0 0
\(606\) 2.00000 3.46410i 0.0812444 0.140720i
\(607\) 8.48528 + 14.6969i 0.344407 + 0.596530i 0.985246 0.171145i \(-0.0547467\pi\)
−0.640839 + 0.767675i \(0.721413\pi\)
\(608\) −4.24264 −0.172062
\(609\) 0 0
\(610\) 0 0
\(611\) 27.0000 + 46.7654i 1.09230 + 1.89192i
\(612\) 7.07107 12.2474i 0.285831 0.495074i
\(613\) 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i \(-0.728603\pi\)
0.981129 + 0.193352i \(0.0619359\pi\)
\(614\) −10.6066 18.3712i −0.428048 0.741400i
\(615\) 0 0
\(616\) 0 0
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) 2.00000 + 3.46410i 0.0804518 + 0.139347i
\(619\) 7.07107 12.2474i 0.284210 0.492267i −0.688207 0.725514i \(-0.741602\pi\)
0.972417 + 0.233248i \(0.0749353\pi\)
\(620\) 0 0
\(621\) −16.9706 29.3939i −0.681005 1.17954i
\(622\) −1.41421 −0.0567048
\(623\) 0 0
\(624\) 12.0000 0.480384
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 14.8492 25.7196i 0.593495 1.02796i
\(627\) −6.00000 + 10.3923i −0.239617 + 0.415029i
\(628\) −4.24264 7.34847i −0.169300 0.293236i
\(629\) −5.65685 −0.225554
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 4.00000 + 6.92820i 0.159111 + 0.275589i
\(633\) −36.7696 + 63.6867i −1.46146 + 2.53132i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 0 0
\(636\) 5.65685 0.224309
\(637\) 0 0
\(638\) 4.00000 0.158362
\(639\) −40.0000 69.2820i −1.58238 2.74075i
\(640\) 0 0
\(641\) −22.0000 + 38.1051i −0.868948 + 1.50506i −0.00587459 + 0.999983i \(0.501870\pi\)
−0.863073 + 0.505079i \(0.831463\pi\)
\(642\) 19.7990 + 34.2929i 0.781404 + 1.35343i
\(643\) −33.9411 −1.33851 −0.669254 0.743034i \(-0.733386\pi\)
−0.669254 + 0.743034i \(0.733386\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) −16.2635 + 28.1691i −0.639382 + 1.10744i 0.346186 + 0.938166i \(0.387477\pi\)
−0.985569 + 0.169277i \(0.945857\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 5.65685 + 9.79796i 0.222051 + 0.384604i
\(650\) −21.2132 −0.832050
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) 19.7990 34.2929i 0.774202 1.34096i
\(655\) 0 0
\(656\) −1.41421 2.44949i −0.0552158 0.0956365i
\(657\) −42.4264 −1.65521
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) 8.48528 14.6969i 0.330039 0.571645i −0.652480 0.757806i \(-0.726271\pi\)
0.982519 + 0.186161i \(0.0596047\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) 16.9706 + 29.3939i 0.659082 + 1.14156i
\(664\) −12.7279 −0.493939
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 12.0000 + 20.7846i 0.464642 + 0.804783i
\(668\) 7.07107 12.2474i 0.273588 0.473868i
\(669\) −30.0000 + 51.9615i −1.15987 + 2.00895i
\(670\) 0 0
\(671\) 9.89949 0.382166
\(672\) 0 0
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 11.0000 + 19.0526i 0.423704 + 0.733877i
\(675\) 14.1421 24.4949i 0.544331 0.942809i
\(676\) −2.50000 + 4.33013i −0.0961538 + 0.166543i
\(677\) −4.94975 8.57321i −0.190234 0.329495i 0.755094 0.655617i \(-0.227591\pi\)
−0.945328 + 0.326122i \(0.894258\pi\)
\(678\) 45.2548 1.73800
\(679\) 0 0
\(680\) 0 0
\(681\) 10.0000 + 17.3205i 0.383201 + 0.663723i
\(682\) −3.53553 + 6.12372i −0.135383 + 0.234490i
\(683\) −16.0000 + 27.7128i −0.612223 + 1.06040i 0.378642 + 0.925543i \(0.376391\pi\)
−0.990865 + 0.134858i \(0.956942\pi\)
\(684\) 10.6066 + 18.3712i 0.405554 + 0.702439i
\(685\) 0 0
\(686\) 0 0
\(687\) −64.0000 −2.44175
\(688\) −5.00000 8.66025i −0.190623 0.330169i
\(689\) −4.24264 + 7.34847i −0.161632 + 0.279954i
\(690\) 0 0
\(691\) −19.7990 34.2929i −0.753189 1.30456i −0.946270 0.323379i \(-0.895181\pi\)
0.193081 0.981183i \(-0.438152\pi\)
\(692\) 7.07107 0.268802
\(693\) 0 0
\(694\) 26.0000 0.986947
\(695\) 0 0
\(696\) 5.65685 9.79796i 0.214423 0.371391i
\(697\) 4.00000 6.92820i 0.151511 0.262424i
\(698\) 13.4350 + 23.2702i 0.508523 + 0.880788i
\(699\) 73.5391 2.78150
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) −12.0000 20.7846i −0.452911 0.784465i
\(703\) 4.24264 7.34847i 0.160014 0.277153i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) 15.5563 0.585471
\(707\) 0 0
\(708\) 32.0000 1.20263
\(709\) 19.0000 + 32.9090i 0.713560 + 1.23592i 0.963512 + 0.267664i \(0.0862517\pi\)
−0.249952 + 0.968258i \(0.580415\pi\)
\(710\) 0 0
\(711\) 20.0000 34.6410i 0.750059 1.29914i
\(712\) −3.53553 6.12372i −0.132500 0.229496i
\(713\) −42.4264 −1.58888
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) −16.2635 28.1691i −0.606525 1.05053i −0.991809 0.127733i \(-0.959230\pi\)
0.385284 0.922798i \(-0.374103\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.00000 −0.0372161
\(723\) 12.0000 + 20.7846i 0.446285 + 0.772988i
\(724\) −5.65685 + 9.79796i −0.210235 + 0.364138i
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) −1.41421 2.44949i −0.0524864 0.0909091i
\(727\) −46.6690 −1.73086 −0.865430 0.501031i \(-0.832954\pi\)
−0.865430 + 0.501031i \(0.832954\pi\)
\(728\) 0 0
\(729\) −43.0000 −1.59259
\(730\) 0 0
\(731\) 14.1421 24.4949i 0.523066 0.905977i
\(732\) 14.0000 24.2487i 0.517455 0.896258i
\(733\) −3.53553 6.12372i −0.130588 0.226185i 0.793315 0.608811i \(-0.208353\pi\)
−0.923903 + 0.382626i \(0.875020\pi\)
\(734\) −21.2132 −0.782994
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 4.00000 + 6.92820i 0.147342 + 0.255204i
\(738\) −7.07107 + 12.2474i −0.260290 + 0.450835i
\(739\) 6.00000 10.3923i 0.220714 0.382287i −0.734311 0.678813i \(-0.762495\pi\)
0.955025 + 0.296526i \(0.0958281\pi\)
\(740\) 0 0
\(741\) −50.9117 −1.87029
\(742\) 0 0
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 10.0000 + 17.3205i 0.366618 + 0.635001i
\(745\) 0 0
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 31.8198 + 55.1135i 1.16423 + 2.01650i
\(748\) 2.82843 0.103418
\(749\) 0 0
\(750\) 0 0
\(751\) 1.00000 + 1.73205i 0.0364905 + 0.0632034i 0.883694 0.468065i \(-0.155049\pi\)
−0.847203 + 0.531269i \(0.821715\pi\)
\(752\) 6.36396 11.0227i 0.232070 0.401957i
\(753\) 8.00000 13.8564i 0.291536 0.504956i
\(754\) 8.48528 + 14.6969i 0.309016 + 0.535231i
\(755\) 0 0
\(756\) 0 0
\(757\) 46.0000 1.67190 0.835949 0.548807i \(-0.184918\pi\)
0.835949 + 0.548807i \(0.184918\pi\)
\(758\) −12.0000 20.7846i −0.435860 0.754931i
\(759\) 8.48528 14.6969i 0.307996 0.533465i
\(760\) 0 0
\(761\) 16.9706 + 29.3939i 0.615182 + 1.06553i 0.990352 + 0.138571i \(0.0442510\pi\)
−0.375170 + 0.926956i \(0.622416\pi\)
\(762\) −56.5685 −2.04926
\(763\) 0 0
\(764\) 10.0000 0.361787
\(765\) 0 0
\(766\) 7.77817 13.4722i 0.281037 0.486770i
\(767\) −24.0000 + 41.5692i −0.866590 + 1.50098i
\(768\) −1.41421 2.44949i −0.0510310 0.0883883i
\(769\) 5.65685 0.203991 0.101996 0.994785i \(-0.467477\pi\)
0.101996 + 0.994785i \(0.467477\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) −3.00000 5.19615i −0.107972 0.187014i
\(773\) 24.0416 41.6413i 0.864717 1.49773i −0.00261021 0.999997i \(-0.500831\pi\)
0.867328 0.497738i \(-0.165836\pi\)
\(774\) −25.0000 + 43.3013i −0.898606 + 1.55643i
\(775\) −17.6777 30.6186i −0.635001 1.09985i
\(776\) −7.07107 −0.253837
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) 8.00000 13.8564i 0.286263 0.495821i
\(782\) 8.48528 + 14.6969i 0.303433 + 0.525561i
\(783\) −22.6274