Properties

Label 784.2.i.l.177.1
Level $784$
Weight $2$
Character 784.177
Analytic conductor $6.260$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(177,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.177");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.i (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: \(6.26027151847\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 196)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 784.177
Dual form 784.2.i.l.753.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41421 - 2.44949i) q^{3} +(-0.707107 + 1.22474i) q^{5} +(-2.50000 + 4.33013i) q^{9} +O(q^{10})\) \(q+(-1.41421 - 2.44949i) q^{3} +(-0.707107 + 1.22474i) q^{5} +(-2.50000 + 4.33013i) q^{9} +(2.00000 + 3.46410i) q^{11} +4.24264 q^{13} +4.00000 q^{15} +(-0.707107 - 1.22474i) q^{17} +(1.41421 - 2.44949i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(1.50000 + 2.59808i) q^{25} +5.65685 q^{27} +8.00000 q^{29} +(5.65685 - 9.79796i) q^{33} +(4.00000 - 6.92820i) q^{37} +(-6.00000 - 10.3923i) q^{39} -7.07107 q^{41} +4.00000 q^{43} +(-3.53553 - 6.12372i) q^{45} +(2.82843 - 4.89898i) q^{47} +(-2.00000 + 3.46410i) q^{51} +(-5.00000 - 8.66025i) q^{53} -5.65685 q^{55} -8.00000 q^{57} +(7.07107 + 12.2474i) q^{59} +(3.53553 - 6.12372i) q^{61} +(-3.00000 + 5.19615i) q^{65} +11.3137 q^{69} +(3.53553 + 6.12372i) q^{73} +(4.24264 - 7.34847i) q^{75} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.1421 q^{83} +2.00000 q^{85} +(-11.3137 - 19.5959i) q^{87} +(-3.53553 + 6.12372i) q^{89} +(2.00000 + 3.46410i) q^{95} -1.41421 q^{97} -20.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 10 q^{9} + 8 q^{11} + 16 q^{15} - 8 q^{23} + 6 q^{25} + 32 q^{29} + 16 q^{37} - 24 q^{39} + 16 q^{43} - 8 q^{51} - 20 q^{53} - 32 q^{57} - 12 q^{65} + 16 q^{79} - 2 q^{81} + 8 q^{85} + 8 q^{95} - 80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −1.41421 2.44949i −0.816497 1.41421i −0.908248 0.418432i \(-0.862580\pi\)
0.0917517 0.995782i \(-0.470753\pi\)
\(4\) 0 0
\(5\) −0.707107 + 1.22474i −0.316228 + 0.547723i −0.979698 0.200480i \(-0.935750\pi\)
0.663470 + 0.748203i \(0.269083\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.50000 + 4.33013i −0.833333 + 1.44338i
\(10\) 0 0
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0 0
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) 0 0
\(17\) −0.707107 1.22474i −0.171499 0.297044i 0.767445 0.641114i \(-0.221528\pi\)
−0.938944 + 0.344070i \(0.888194\pi\)
\(18\) 0 0
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 1.50000 + 2.59808i 0.300000 + 0.519615i
\(26\) 0 0
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) 5.65685 9.79796i 0.984732 1.70561i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 0 0
\(39\) −6.00000 10.3923i −0.960769 1.66410i
\(40\) 0 0
\(41\) −7.07107 −1.10432 −0.552158 0.833740i \(-0.686195\pi\)
−0.552158 + 0.833740i \(0.686195\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −3.53553 6.12372i −0.527046 0.912871i
\(46\) 0 0
\(47\) 2.82843 4.89898i 0.412568 0.714590i −0.582601 0.812758i \(-0.697965\pi\)
0.995170 + 0.0981685i \(0.0312984\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) −5.00000 8.66025i −0.686803 1.18958i −0.972867 0.231367i \(-0.925680\pi\)
0.286064 0.958211i \(-0.407653\pi\)
\(54\) 0 0
\(55\) −5.65685 −0.762770
\(56\) 0 0
\(57\) −8.00000 −1.05963
\(58\) 0 0
\(59\) 7.07107 + 12.2474i 0.920575 + 1.59448i 0.798528 + 0.601958i \(0.205612\pi\)
0.122047 + 0.992524i \(0.461054\pi\)
\(60\) 0 0
\(61\) 3.53553 6.12372i 0.452679 0.784063i −0.545873 0.837868i \(-0.683802\pi\)
0.998551 + 0.0538056i \(0.0171351\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) 11.3137 1.36201
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 3.53553 + 6.12372i 0.413803 + 0.716728i 0.995302 0.0968194i \(-0.0308669\pi\)
−0.581499 + 0.813547i \(0.697534\pi\)
\(74\) 0 0
\(75\) 4.24264 7.34847i 0.489898 0.848528i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 14.1421 1.55230 0.776151 0.630548i \(-0.217170\pi\)
0.776151 + 0.630548i \(0.217170\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 0 0
\(87\) −11.3137 19.5959i −1.21296 2.10090i
\(88\) 0 0
\(89\) −3.53553 + 6.12372i −0.374766 + 0.649113i −0.990292 0.139003i \(-0.955610\pi\)
0.615526 + 0.788116i \(0.288944\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) 0 0
\(97\) −1.41421 −0.143592 −0.0717958 0.997419i \(-0.522873\pi\)
−0.0717958 + 0.997419i \(0.522873\pi\)
\(98\) 0 0
\(99\) −20.0000 −2.01008
\(100\) 0 0
\(101\) 6.36396 + 11.0227i 0.633238 + 1.09680i 0.986886 + 0.161421i \(0.0516078\pi\)
−0.353648 + 0.935379i \(0.615059\pi\)
\(102\) 0 0
\(103\) −5.65685 + 9.79796i −0.557386 + 0.965422i 0.440327 + 0.897837i \(0.354862\pi\)
−0.997714 + 0.0675842i \(0.978471\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) 0 0
\(109\) 4.00000 + 6.92820i 0.383131 + 0.663602i 0.991508 0.130046i \(-0.0415126\pi\)
−0.608377 + 0.793648i \(0.708179\pi\)
\(110\) 0 0
\(111\) −22.6274 −2.14770
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −2.82843 4.89898i −0.263752 0.456832i
\(116\) 0 0
\(117\) −10.6066 + 18.3712i −0.980581 + 1.69842i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 10.0000 + 17.3205i 0.901670 + 1.56174i
\(124\) 0 0
\(125\) −11.3137 −1.01193
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) −5.65685 9.79796i −0.498058 0.862662i
\(130\) 0 0
\(131\) −4.24264 + 7.34847i −0.370681 + 0.642039i −0.989671 0.143361i \(-0.954209\pi\)
0.618989 + 0.785399i \(0.287542\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −4.00000 + 6.92820i −0.344265 + 0.596285i
\(136\) 0 0
\(137\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(138\) 0 0
\(139\) −2.82843 −0.239904 −0.119952 0.992780i \(-0.538274\pi\)
−0.119952 + 0.992780i \(0.538274\pi\)
\(140\) 0 0
\(141\) −16.0000 −1.34744
\(142\) 0 0
\(143\) 8.48528 + 14.6969i 0.709575 + 1.22902i
\(144\) 0 0
\(145\) −5.65685 + 9.79796i −0.469776 + 0.813676i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) 0 0
\(151\) −2.00000 3.46410i −0.162758 0.281905i 0.773099 0.634285i \(-0.218706\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0 0
\(153\) 7.07107 0.571662
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3.53553 6.12372i −0.282166 0.488726i 0.689752 0.724046i \(-0.257720\pi\)
−0.971918 + 0.235320i \(0.924386\pi\)
\(158\) 0 0
\(159\) −14.1421 + 24.4949i −1.12154 + 1.94257i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 8.00000 + 13.8564i 0.622799 + 1.07872i
\(166\) 0 0
\(167\) 5.65685 0.437741 0.218870 0.975754i \(-0.429763\pi\)
0.218870 + 0.975754i \(0.429763\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 7.07107 + 12.2474i 0.540738 + 0.936586i
\(172\) 0 0
\(173\) 2.12132 3.67423i 0.161281 0.279347i −0.774047 0.633128i \(-0.781771\pi\)
0.935328 + 0.353781i \(0.115104\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 20.0000 34.6410i 1.50329 2.60378i
\(178\) 0 0
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) −21.2132 −1.57676 −0.788382 0.615185i \(-0.789081\pi\)
−0.788382 + 0.615185i \(0.789081\pi\)
\(182\) 0 0
\(183\) −20.0000 −1.47844
\(184\) 0 0
\(185\) 5.65685 + 9.79796i 0.415900 + 0.720360i
\(186\) 0 0
\(187\) 2.82843 4.89898i 0.206835 0.358249i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 + 13.8564i −0.578860 + 1.00261i 0.416751 + 0.909021i \(0.363169\pi\)
−0.995610 + 0.0935936i \(0.970165\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) 0 0
\(195\) 16.9706 1.21529
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 5.00000 8.66025i 0.349215 0.604858i
\(206\) 0 0
\(207\) −10.0000 17.3205i −0.695048 1.20386i
\(208\) 0 0
\(209\) 11.3137 0.782586
\(210\) 0 0
\(211\) −24.0000 −1.65223 −0.826114 0.563503i \(-0.809453\pi\)
−0.826114 + 0.563503i \(0.809453\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.82843 + 4.89898i −0.192897 + 0.334108i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.0000 17.3205i 0.675737 1.17041i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) −16.9706 −1.13643 −0.568216 0.822879i \(-0.692366\pi\)
−0.568216 + 0.822879i \(0.692366\pi\)
\(224\) 0 0
\(225\) −15.0000 −1.00000
\(226\) 0 0
\(227\) 4.24264 + 7.34847i 0.281594 + 0.487735i 0.971778 0.235899i \(-0.0758036\pi\)
−0.690184 + 0.723634i \(0.742470\pi\)
\(228\) 0 0
\(229\) 10.6066 18.3712i 0.700904 1.21400i −0.267246 0.963628i \(-0.586113\pi\)
0.968149 0.250373i \(-0.0805532\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) 0 0
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) 0 0
\(237\) −22.6274 −1.46981
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −6.36396 11.0227i −0.409939 0.710035i 0.584944 0.811074i \(-0.301117\pi\)
−0.994882 + 0.101039i \(0.967783\pi\)
\(242\) 0 0
\(243\) 7.07107 12.2474i 0.453609 0.785674i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.00000 10.3923i 0.381771 0.661247i
\(248\) 0 0
\(249\) −20.0000 34.6410i −1.26745 2.19529i
\(250\) 0 0
\(251\) −19.7990 −1.24970 −0.624851 0.780744i \(-0.714840\pi\)
−0.624851 + 0.780744i \(0.714840\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) 0 0
\(255\) −2.82843 4.89898i −0.177123 0.306786i
\(256\) 0 0
\(257\) −10.6066 + 18.3712i −0.661622 + 1.14596i 0.318568 + 0.947900i \(0.396798\pi\)
−0.980189 + 0.198062i \(0.936535\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −20.0000 + 34.6410i −1.23797 + 2.14423i
\(262\) 0 0
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 14.1421 0.868744
\(266\) 0 0
\(267\) 20.0000 1.22398
\(268\) 0 0
\(269\) 9.19239 + 15.9217i 0.560470 + 0.970762i 0.997455 + 0.0712937i \(0.0227127\pi\)
−0.436986 + 0.899469i \(0.643954\pi\)
\(270\) 0 0
\(271\) 14.1421 24.4949i 0.859074 1.48796i −0.0137402 0.999906i \(-0.504374\pi\)
0.872814 0.488053i \(-0.162293\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 0 0
\(277\) −11.0000 19.0526i −0.660926 1.14476i −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 0 0
\(283\) −1.41421 2.44949i −0.0840663 0.145607i 0.820927 0.571034i \(-0.193457\pi\)
−0.904993 + 0.425427i \(0.860124\pi\)
\(284\) 0 0
\(285\) 5.65685 9.79796i 0.335083 0.580381i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.50000 12.9904i 0.441176 0.764140i
\(290\) 0 0
\(291\) 2.00000 + 3.46410i 0.117242 + 0.203069i
\(292\) 0 0
\(293\) 32.5269 1.90024 0.950121 0.311881i \(-0.100959\pi\)
0.950121 + 0.311881i \(0.100959\pi\)
\(294\) 0 0
\(295\) −20.0000 −1.16445
\(296\) 0 0
\(297\) 11.3137 + 19.5959i 0.656488 + 1.13707i
\(298\) 0 0
\(299\) −8.48528 + 14.6969i −0.490716 + 0.849946i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 18.0000 31.1769i 1.03407 1.79107i
\(304\) 0 0
\(305\) 5.00000 + 8.66025i 0.286299 + 0.495885i
\(306\) 0 0
\(307\) 19.7990 1.12999 0.564994 0.825095i \(-0.308878\pi\)
0.564994 + 0.825095i \(0.308878\pi\)
\(308\) 0 0
\(309\) 32.0000 1.82042
\(310\) 0 0
\(311\) −11.3137 19.5959i −0.641542 1.11118i −0.985089 0.172047i \(-0.944962\pi\)
0.343547 0.939135i \(-0.388371\pi\)
\(312\) 0 0
\(313\) −2.12132 + 3.67423i −0.119904 + 0.207680i −0.919730 0.392553i \(-0.871592\pi\)
0.799825 + 0.600233i \(0.204925\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00000 1.73205i 0.0561656 0.0972817i −0.836576 0.547852i \(-0.815446\pi\)
0.892741 + 0.450570i \(0.148779\pi\)
\(318\) 0 0
\(319\) 16.0000 + 27.7128i 0.895828 + 1.55162i
\(320\) 0 0
\(321\) −22.6274 −1.26294
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 0 0
\(325\) 6.36396 + 11.0227i 0.353009 + 0.611430i
\(326\) 0 0
\(327\) 11.3137 19.5959i 0.625650 1.08366i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 0 0
\(333\) 20.0000 + 34.6410i 1.09599 + 1.89832i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) −8.48528 14.6969i −0.460857 0.798228i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −8.00000 + 13.8564i −0.430706 + 0.746004i
\(346\) 0 0
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −4.24264 −0.227103 −0.113552 0.993532i \(-0.536223\pi\)
−0.113552 + 0.993532i \(0.536223\pi\)
\(350\) 0 0
\(351\) 24.0000 1.28103
\(352\) 0 0
\(353\) −4.94975 8.57321i −0.263448 0.456306i 0.703707 0.710490i \(-0.251527\pi\)
−0.967156 + 0.254184i \(0.918193\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) 0 0
\(363\) 14.1421 0.742270
\(364\) 0 0
\(365\) −10.0000 −0.523424
\(366\) 0 0
\(367\) 2.82843 + 4.89898i 0.147643 + 0.255725i 0.930356 0.366658i \(-0.119498\pi\)
−0.782713 + 0.622383i \(0.786165\pi\)
\(368\) 0 0
\(369\) 17.6777 30.6186i 0.920263 1.59394i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 0 0
\(375\) 16.0000 + 27.7128i 0.826236 + 1.43108i
\(376\) 0 0
\(377\) 33.9411 1.74806
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) −28.2843 48.9898i −1.44905 2.50982i
\(382\) 0 0
\(383\) −2.82843 + 4.89898i −0.144526 + 0.250326i −0.929196 0.369587i \(-0.879499\pi\)
0.784670 + 0.619914i \(0.212832\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −10.0000 + 17.3205i −0.508329 + 0.880451i
\(388\) 0 0
\(389\) −4.00000 6.92820i −0.202808 0.351274i 0.746624 0.665246i \(-0.231673\pi\)
−0.949432 + 0.313972i \(0.898340\pi\)
\(390\) 0 0
\(391\) 5.65685 0.286079
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 0 0
\(395\) 5.65685 + 9.79796i 0.284627 + 0.492989i
\(396\) 0 0
\(397\) −7.77817 + 13.4722i −0.390375 + 0.676150i −0.992499 0.122253i \(-0.960988\pi\)
0.602124 + 0.798403i \(0.294321\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.41421 0.0702728
\(406\) 0 0
\(407\) 32.0000 1.58618
\(408\) 0 0
\(409\) −19.0919 33.0681i −0.944033 1.63511i −0.757676 0.652631i \(-0.773665\pi\)
−0.186357 0.982482i \(-0.559668\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −10.0000 + 17.3205i −0.490881 + 0.850230i
\(416\) 0 0
\(417\) 4.00000 + 6.92820i 0.195881 + 0.339276i
\(418\) 0 0
\(419\) −14.1421 −0.690889 −0.345444 0.938439i \(-0.612272\pi\)
−0.345444 + 0.938439i \(0.612272\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 0 0
\(423\) 14.1421 + 24.4949i 0.687614 + 1.19098i
\(424\) 0 0
\(425\) 2.12132 3.67423i 0.102899 0.178227i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 24.0000 41.5692i 1.15873 2.00698i
\(430\) 0 0
\(431\) −18.0000 31.1769i −0.867029 1.50174i −0.865018 0.501741i \(-0.832693\pi\)
−0.00201168 0.999998i \(-0.500640\pi\)
\(432\) 0 0
\(433\) −21.2132 −1.01944 −0.509721 0.860340i \(-0.670251\pi\)
−0.509721 + 0.860340i \(0.670251\pi\)
\(434\) 0 0
\(435\) 32.0000 1.53428
\(436\) 0 0
\(437\) 5.65685 + 9.79796i 0.270604 + 0.468700i
\(438\) 0 0
\(439\) −8.48528 + 14.6969i −0.404980 + 0.701447i −0.994319 0.106439i \(-0.966055\pi\)
0.589339 + 0.807886i \(0.299388\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −8.00000 + 13.8564i −0.380091 + 0.658338i −0.991075 0.133306i \(-0.957441\pi\)
0.610984 + 0.791643i \(0.290774\pi\)
\(444\) 0 0
\(445\) −5.00000 8.66025i −0.237023 0.410535i
\(446\) 0 0
\(447\) 28.2843 1.33780
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −14.1421 24.4949i −0.665927 1.15342i
\(452\) 0 0
\(453\) −5.65685 + 9.79796i −0.265782 + 0.460348i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.0000 + 25.9808i −0.701670 + 1.21533i 0.266209 + 0.963915i \(0.414229\pi\)
−0.967880 + 0.251414i \(0.919105\pi\)
\(458\) 0 0
\(459\) −4.00000 6.92820i −0.186704 0.323381i
\(460\) 0 0
\(461\) 7.07107 0.329332 0.164666 0.986349i \(-0.447345\pi\)
0.164666 + 0.986349i \(0.447345\pi\)
\(462\) 0 0
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.89949 + 17.1464i −0.458094 + 0.793442i −0.998860 0.0477308i \(-0.984801\pi\)
0.540766 + 0.841173i \(0.318134\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −10.0000 + 17.3205i −0.460776 + 0.798087i
\(472\) 0 0
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) 8.48528 0.389331
\(476\) 0 0
\(477\) 50.0000 2.28934
\(478\) 0 0
\(479\) −5.65685 9.79796i −0.258468 0.447680i 0.707364 0.706850i \(-0.249884\pi\)
−0.965832 + 0.259170i \(0.916551\pi\)
\(480\) 0 0
\(481\) 16.9706 29.3939i 0.773791 1.34025i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) −6.00000 10.3923i −0.271886 0.470920i 0.697459 0.716625i \(-0.254314\pi\)
−0.969345 + 0.245705i \(0.920981\pi\)
\(488\) 0 0
\(489\) −11.3137 −0.511624
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) −5.65685 9.79796i −0.254772 0.441278i
\(494\) 0 0
\(495\) 14.1421 24.4949i 0.635642 1.10096i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) 0 0
\(501\) −8.00000 13.8564i −0.357414 0.619059i
\(502\) 0 0
\(503\) 39.5980 1.76559 0.882793 0.469762i \(-0.155660\pi\)
0.882793 + 0.469762i \(0.155660\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −7.07107 12.2474i −0.314037 0.543928i
\(508\) 0 0
\(509\) 9.19239 15.9217i 0.407445 0.705716i −0.587157 0.809473i \(-0.699753\pi\)
0.994603 + 0.103757i \(0.0330863\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 8.00000 13.8564i 0.353209 0.611775i
\(514\) 0 0
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) 22.6274 0.995153
\(518\) 0 0
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) 20.5061 + 35.5176i 0.898388 + 1.55605i 0.829554 + 0.558426i \(0.188595\pi\)
0.0688342 + 0.997628i \(0.478072\pi\)
\(522\) 0 0
\(523\) 21.2132 36.7423i 0.927589 1.60663i 0.140244 0.990117i \(-0.455211\pi\)
0.787344 0.616514i \(-0.211456\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −70.7107 −3.06858
\(532\) 0 0
\(533\) −30.0000 −1.29944
\(534\) 0 0
\(535\) 5.65685 + 9.79796i 0.244567 + 0.423603i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7.00000 12.1244i 0.300954 0.521267i −0.675399 0.737453i \(-0.736028\pi\)
0.976352 + 0.216186i \(0.0693618\pi\)
\(542\) 0 0
\(543\) 30.0000 + 51.9615i 1.28742 + 2.22988i
\(544\) 0 0
\(545\) −11.3137 −0.484626
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) 17.6777 + 30.6186i 0.754465 + 1.30677i
\(550\) 0 0
\(551\) 11.3137 19.5959i 0.481980 0.834814i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 16.0000 27.7128i 0.679162 1.17634i
\(556\) 0 0
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 0 0
\(559\) 16.9706 0.717778
\(560\) 0 0
\(561\) −16.0000 −0.675521
\(562\) 0 0
\(563\) 7.07107 + 12.2474i 0.298010 + 0.516168i 0.975681 0.219197i \(-0.0703438\pi\)
−0.677671 + 0.735366i \(0.737010\pi\)
\(564\) 0 0
\(565\) −4.24264 + 7.34847i −0.178489 + 0.309152i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −20.0000 + 34.6410i −0.838444 + 1.45223i 0.0527519 + 0.998608i \(0.483201\pi\)
−0.891196 + 0.453619i \(0.850133\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 0 0
\(573\) 45.2548 1.89055
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −6.36396 11.0227i −0.264935 0.458881i 0.702611 0.711574i \(-0.252017\pi\)
−0.967547 + 0.252693i \(0.918684\pi\)
\(578\) 0 0
\(579\) 14.1421 24.4949i 0.587727 1.01797i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 20.0000 34.6410i 0.828315 1.43468i
\(584\) 0 0
\(585\) −15.0000 25.9808i −0.620174 1.07417i
\(586\) 0 0
\(587\) −25.4558 −1.05068 −0.525338 0.850894i \(-0.676061\pi\)
−0.525338 + 0.850894i \(0.676061\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 14.1421 + 24.4949i 0.581730 + 1.00759i
\(592\) 0 0
\(593\) 4.94975 8.57321i 0.203262 0.352060i −0.746316 0.665592i \(-0.768179\pi\)
0.949578 + 0.313532i \(0.101512\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.00000 + 6.92820i 0.163436 + 0.283079i 0.936099 0.351738i \(-0.114409\pi\)
−0.772663 + 0.634816i \(0.781076\pi\)
\(600\) 0 0
\(601\) −29.6985 −1.21143 −0.605713 0.795683i \(-0.707112\pi\)
−0.605713 + 0.795683i \(0.707112\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.53553 6.12372i −0.143740 0.248965i
\(606\) 0 0
\(607\) −16.9706 + 29.3939i −0.688814 + 1.19306i 0.283408 + 0.958999i \(0.408535\pi\)
−0.972222 + 0.234061i \(0.924798\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 20.7846i 0.485468 0.840855i
\(612\) 0 0
\(613\) −12.0000 20.7846i −0.484675 0.839482i 0.515170 0.857088i \(-0.327729\pi\)
−0.999845 + 0.0176058i \(0.994396\pi\)
\(614\) 0 0
\(615\) −28.2843 −1.14053
\(616\) 0 0
\(617\) −8.00000 −0.322068 −0.161034 0.986949i \(-0.551483\pi\)
−0.161034 + 0.986949i \(0.551483\pi\)
\(618\) 0 0
\(619\) −15.5563 26.9444i −0.625262 1.08299i −0.988490 0.151286i \(-0.951659\pi\)
0.363228 0.931700i \(-0.381675\pi\)
\(620\) 0 0
\(621\) −11.3137 + 19.5959i −0.454003 + 0.786357i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.0200000 0.0346410i
\(626\) 0 0
\(627\) −16.0000 27.7128i −0.638978 1.10674i
\(628\) 0 0
\(629\) −11.3137 −0.451107
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 33.9411 + 58.7878i 1.34904 + 2.33660i
\(634\) 0 0
\(635\) −14.1421 + 24.4949i −0.561214 + 0.972050i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.00000 6.92820i −0.157991 0.273648i 0.776153 0.630544i \(-0.217168\pi\)
−0.934144 + 0.356897i \(0.883835\pi\)
\(642\) 0 0
\(643\) −2.82843 −0.111542 −0.0557711 0.998444i \(-0.517762\pi\)
−0.0557711 + 0.998444i \(0.517762\pi\)
\(644\) 0 0
\(645\) 16.0000 0.629999
\(646\) 0 0
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0 0
\(649\) −28.2843 + 48.9898i −1.11025 + 1.92302i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12.0000 20.7846i 0.469596 0.813365i −0.529799 0.848123i \(-0.677733\pi\)
0.999396 + 0.0347583i \(0.0110661\pi\)
\(654\) 0 0
\(655\) −6.00000 10.3923i −0.234439 0.406061i
\(656\) 0 0
\(657\) −35.3553 −1.37934
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 10.6066 + 18.3712i 0.412549 + 0.714556i 0.995168 0.0981898i \(-0.0313052\pi\)
−0.582619 + 0.812746i \(0.697972\pi\)
\(662\) 0 0
\(663\) −8.48528 + 14.6969i −0.329541 + 0.570782i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −16.0000 + 27.7128i −0.619522 + 1.07304i
\(668\) 0 0
\(669\) 24.0000 + 41.5692i 0.927894 + 1.60716i
\(670\) 0 0
\(671\) 28.2843 1.09190
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 8.48528 + 14.6969i 0.326599 + 0.565685i
\(676\) 0 0
\(677\) −6.36396 + 11.0227i −0.244587 + 0.423637i −0.962015 0.272995i \(-0.911986\pi\)
0.717428 + 0.696632i \(0.245319\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 20.7846i 0.459841 0.796468i
\(682\) 0 0
\(683\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −60.0000 −2.28914
\(688\) 0 0
\(689\) −21.2132 36.7423i −0.808159 1.39977i
\(690\) 0 0
\(691\) −21.2132 + 36.7423i −0.806988 + 1.39774i 0.107952 + 0.994156i \(0.465571\pi\)
−0.914941 + 0.403589i \(0.867763\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 0 0
\(697\) 5.00000 + 8.66025i 0.189389 + 0.328031i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 24.0000 0.906467 0.453234 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) 0 0
\(703\) −11.3137 19.5959i −0.426705 0.739074i
\(704\) 0 0
\(705\) 11.3137 19.5959i 0.426099 0.738025i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 4.00000 6.92820i 0.150223 0.260194i −0.781086 0.624423i \(-0.785334\pi\)
0.931309 + 0.364229i \(0.118667\pi\)
\(710\) 0 0
\(711\) 20.0000 + 34.6410i 0.750059 + 1.29914i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −24.0000 −0.897549
\(716\) 0 0
\(717\) −16.9706 29.3939i −0.633777 1.09773i
\(718\) 0 0
\(719\) 19.7990 34.2929i 0.738378 1.27891i −0.214848 0.976648i \(-0.568926\pi\)
0.953225 0.302260i \(-0.0977411\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −18.0000 + 31.1769i −0.669427 + 1.15948i
\(724\) 0 0
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) −28.2843 −1.04901 −0.524503 0.851409i \(-0.675749\pi\)
−0.524503 + 0.851409i \(0.675749\pi\)
\(728\) 0 0
\(729\) −43.0000 −1.59259
\(730\) 0 0
\(731\) −2.82843 4.89898i −0.104613 0.181195i
\(732\) 0 0
\(733\) 19.0919 33.0681i 0.705175 1.22140i −0.261454 0.965216i \(-0.584202\pi\)
0.966628 0.256183i \(-0.0824648\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −6.00000 10.3923i −0.220714 0.382287i 0.734311 0.678813i \(-0.237505\pi\)
−0.955025 + 0.296526i \(0.904172\pi\)
\(740\) 0 0
\(741\) −33.9411 −1.24686
\(742\) 0 0
\(743\) 20.0000 0.733729 0.366864 0.930274i \(-0.380431\pi\)
0.366864 + 0.930274i \(0.380431\pi\)
\(744\) 0 0
\(745\) −7.07107 12.2474i −0.259064 0.448712i
\(746\) 0 0
\(747\) −35.3553 + 61.2372i −1.29358 + 2.24055i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) 0 0
\(753\) 28.0000 + 48.4974i 1.02038 + 1.76734i
\(754\) 0 0
\(755\) 5.65685 0.205874
\(756\) 0 0
\(757\) −40.0000 −1.45382 −0.726912 0.686730i \(-0.759045\pi\)
−0.726912 + 0.686730i \(0.759045\pi\)
\(758\) 0 0
\(759\) 22.6274 + 39.1918i 0.821323 + 1.42257i
\(760\) 0 0
\(761\) −20.5061 + 35.5176i −0.743345 + 1.28751i 0.207618 + 0.978210i \(0.433429\pi\)
−0.950964 + 0.309302i \(0.899905\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −5.00000 + 8.66025i −0.180775 + 0.313112i
\(766\) 0 0
\(767\) 30.0000 + 51.9615i 1.08324 + 1.87622i
\(768\) 0 0
\(769\) 46.6690 1.68293 0.841464 0.540312i \(-0.181694\pi\)
0.841464 + 0.540312i \(0.181694\pi\)
\(770\) 0 0
\(771\) 60.0000 2.16085
\(772\) 0 0
\(773\) −12.0208 20.8207i −0.432359 0.748867i 0.564717 0.825284i \(-0.308985\pi\)
−0.997076 + 0.0764173i \(0.975652\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.0000 + 17.3205i −0.358287 + 0.620572i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 45.2548 1.61728
\(784\) 0 0
\(785\) 10.0000 0.356915
\(786\) 0 0
\(787\) 24.0416 + 41.6413i 0.856992 + 1.48435i 0.874785 + 0.484511i \(0.161003\pi\)
−0.0177934 + 0.999842i \(0.505664\pi\)
\(788\) 0 0
\(789\) −33.9411 + 58.7878i −1.20834 + 2.09290i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 15.0000 25.9808i 0.532666 0.922604i
\(794\) 0 0
\(795\) −20.0000