Properties

Label 700.2.r.a.249.2
Level $700$
Weight $2$
Character 700.249
Analytic conductor $5.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 249.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.249
Dual form 700.2.r.a.149.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{3} +(0.866025 + 2.50000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{3} +(0.866025 + 2.50000i) q^{7} +(-1.00000 - 1.73205i) q^{9} +(-3.00000 + 5.19615i) q^{11} -2.00000i q^{13} +(5.19615 + 3.00000i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(-2.59808 + 1.50000i) q^{23} -5.00000i q^{27} -3.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-5.19615 + 3.00000i) q^{33} +(6.92820 - 4.00000i) q^{37} +(1.00000 - 1.73205i) q^{39} -3.00000 q^{41} -5.00000i q^{43} +(-5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(10.3923 + 6.00000i) q^{53} +8.00000i q^{57} +(0.500000 + 0.866025i) q^{61} +(3.46410 - 4.00000i) q^{63} +(6.06218 + 3.50000i) q^{67} -3.00000 q^{69} +(-8.66025 - 5.00000i) q^{73} +(-15.5885 - 3.00000i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} -3.00000i q^{83} +(-2.59808 - 1.50000i) q^{87} +(-1.50000 - 2.59808i) q^{89} +(5.00000 - 1.73205i) q^{91} +(-1.73205 + 1.00000i) q^{93} -10.0000i q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{9} - 12 q^{11} + 16 q^{19} - 2 q^{21} - 12 q^{29} - 4 q^{31} + 4 q^{39} - 12 q^{41} - 22 q^{49} + 12 q^{51} + 2 q^{61} - 12 q^{69} - 8 q^{79} - 2 q^{81} - 6 q^{89} + 20 q^{91} + 48 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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 0
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i 0.728714 0.684819i \(-0.240119\pi\)
−0.228714 + 0.973494i \(0.573452\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.866025 + 2.50000i 0.327327 + 0.944911i
\(8\) 0 0
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.19615 + 3.00000i 1.26025 + 0.727607i 0.973123 0.230285i \(-0.0739659\pi\)
0.287129 + 0.957892i \(0.407299\pi\)
\(18\) 0 0
\(19\) 4.00000 + 6.92820i 0.917663 + 1.58944i 0.802955 + 0.596040i \(0.203260\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 0 0
\(23\) −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i \(-0.767924\pi\)
0.204046 + 0.978961i \(0.434591\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 0 0
\(33\) −5.19615 + 3.00000i −0.904534 + 0.522233i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.92820 4.00000i 1.13899 0.657596i 0.192809 0.981236i \(-0.438240\pi\)
0.946180 + 0.323640i \(0.104907\pi\)
\(38\) 0 0
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) 5.00000i 0.762493i −0.924473 0.381246i \(-0.875495\pi\)
0.924473 0.381246i \(-0.124505\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 0 0
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0 0
\(53\) 10.3923 + 6.00000i 1.42749 + 0.824163i 0.996922 0.0783936i \(-0.0249791\pi\)
0.430570 + 0.902557i \(0.358312\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.00000i 1.05963i
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 3.46410 4.00000i 0.436436 0.503953i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.06218 + 3.50000i 0.740613 + 0.427593i 0.822292 0.569066i \(-0.192695\pi\)
−0.0816792 + 0.996659i \(0.526028\pi\)
\(68\) 0 0
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −8.66025 5.00000i −1.01361 0.585206i −0.101361 0.994850i \(-0.532320\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −15.5885 3.00000i −1.77647 0.341882i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 3.00000i 0.329293i −0.986353 0.164646i \(-0.947352\pi\)
0.986353 0.164646i \(-0.0526483\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.59808 1.50000i −0.278543 0.160817i
\(88\) 0 0
\(89\) −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) 0 0
\(91\) 5.00000 1.73205i 0.524142 0.181568i
\(92\) 0 0
\(93\) −1.73205 + 1.00000i −0.179605 + 0.103695i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 0 0
\(99\) 12.0000 1.20605
\(100\) 0 0
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 0 0
\(103\) 6.06218 3.50000i 0.597324 0.344865i −0.170664 0.985329i \(-0.554591\pi\)
0.767988 + 0.640464i \(0.221258\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) 0 0
\(109\) 8.50000 14.7224i 0.814152 1.41015i −0.0957826 0.995402i \(-0.530535\pi\)
0.909935 0.414751i \(-0.136131\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) 0 0
\(113\) 12.0000i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.46410 + 2.00000i −0.320256 + 0.184900i
\(118\) 0 0
\(119\) −3.00000 + 15.5885i −0.275010 + 1.42899i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) 0 0
\(123\) −2.59808 1.50000i −0.234261 0.135250i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 0 0
\(129\) 2.50000 4.33013i 0.220113 0.381246i
\(130\) 0 0
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 0 0
\(133\) −13.8564 + 16.0000i −1.20150 + 1.38738i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.3923 + 6.00000i 0.869048 + 0.501745i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.92820 + 1.00000i −0.571429 + 0.0824786i
\(148\) 0 0
\(149\) −7.50000 12.9904i −0.614424 1.06421i −0.990485 0.137619i \(-0.956055\pi\)
0.376061 0.926595i \(-0.377278\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 0 0
\(153\) 12.0000i 0.970143i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.1244 7.00000i −0.967629 0.558661i −0.0691164 0.997609i \(-0.522018\pi\)
−0.898513 + 0.438948i \(0.855351\pi\)
\(158\) 0 0
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) −6.00000 5.19615i −0.472866 0.409514i
\(162\) 0 0
\(163\) 13.8564 8.00000i 1.08532 0.626608i 0.152992 0.988227i \(-0.451109\pi\)
0.932326 + 0.361619i \(0.117776\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.0000i 1.62503i −0.582941 0.812514i \(-0.698098\pi\)
0.582941 0.812514i \(-0.301902\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) 8.00000 13.8564i 0.611775 1.05963i
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) 0 0
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) 0 0
\(183\) 1.00000i 0.0739221i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −31.1769 + 18.0000i −2.27988 + 1.31629i
\(188\) 0 0
\(189\) 12.5000 4.33013i 0.909241 0.314970i
\(190\) 0 0
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0 0
\(193\) 1.73205 + 1.00000i 0.124676 + 0.0719816i 0.561041 0.827788i \(-0.310401\pi\)
−0.436365 + 0.899770i \(0.643734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i \(-0.582534\pi\)
0.965272 0.261245i \(-0.0841331\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 0 0
\(203\) −2.59808 7.50000i −0.182349 0.526397i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 5.19615 + 3.00000i 0.361158 + 0.208514i
\(208\) 0 0
\(209\) −48.0000 −3.32023
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5.19615 1.00000i −0.352738 0.0678844i
\(218\) 0 0
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.3923 + 6.00000i 0.689761 + 0.398234i 0.803523 0.595274i \(-0.202957\pi\)
−0.113761 + 0.993508i \(0.536290\pi\)
\(228\) 0 0
\(229\) 1.00000 + 1.73205i 0.0660819 + 0.114457i 0.897173 0.441679i \(-0.145617\pi\)
−0.831092 + 0.556136i \(0.812283\pi\)
\(230\) 0 0
\(231\) −12.0000 10.3923i −0.789542 0.683763i
\(232\) 0 0
\(233\) −5.19615 + 3.00000i −0.340411 + 0.196537i −0.660454 0.750867i \(-0.729636\pi\)
0.320043 + 0.947403i \(0.396303\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 4.00000i 0.259828i
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) 0 0
\(243\) −13.8564 + 8.00000i −0.888889 + 0.513200i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 13.8564 8.00000i 0.881662 0.509028i
\(248\) 0 0
\(249\) 1.50000 2.59808i 0.0950586 0.164646i
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 18.0000i 1.13165i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −20.7846 + 12.0000i −1.29651 + 0.748539i −0.979799 0.199983i \(-0.935911\pi\)
−0.316709 + 0.948523i \(0.602578\pi\)
\(258\) 0 0
\(259\) 16.0000 + 13.8564i 0.994192 + 0.860995i
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 0 0
\(263\) −2.59808 1.50000i −0.160204 0.0924940i 0.417755 0.908560i \(-0.362817\pi\)
−0.577959 + 0.816066i \(0.696151\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.00000i 0.183597i
\(268\) 0 0
\(269\) −7.50000 + 12.9904i −0.457283 + 0.792038i −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) 5.19615 + 1.00000i 0.314485 + 0.0605228i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 19.0526 + 11.0000i 1.14476 + 0.660926i 0.947604 0.319447i \(-0.103497\pi\)
0.197153 + 0.980373i \(0.436830\pi\)
\(278\) 0 0
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 17.3205 + 10.0000i 1.02960 + 0.594438i 0.916869 0.399188i \(-0.130708\pi\)
0.112728 + 0.993626i \(0.464041\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.59808 7.50000i −0.153360 0.442711i
\(288\) 0 0
\(289\) 9.50000 + 16.4545i 0.558824 + 0.967911i
\(290\) 0 0
\(291\) 5.00000 8.66025i 0.293105 0.507673i
\(292\) 0 0
\(293\) 12.0000i 0.701047i 0.936554 + 0.350524i \(0.113996\pi\)
−0.936554 + 0.350524i \(0.886004\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 25.9808 + 15.0000i 1.50756 + 0.870388i
\(298\) 0 0
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 12.5000 4.33013i 0.720488 0.249584i
\(302\) 0 0
\(303\) 2.59808 1.50000i 0.149256 0.0861727i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 19.0000i 1.08439i −0.840254 0.542194i \(-0.817594\pi\)
0.840254 0.542194i \(-0.182406\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 3.46410 2.00000i 0.195803 0.113047i −0.398894 0.916997i \(-0.630606\pi\)
0.594696 + 0.803951i \(0.297272\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 48.0000i 2.67079i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 14.7224 8.50000i 0.814152 0.470051i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 11.0000 + 19.0526i 0.604615 + 1.04722i 0.992112 + 0.125353i \(0.0400062\pi\)
−0.387498 + 0.921871i \(0.626660\pi\)
\(332\) 0 0
\(333\) −13.8564 8.00000i −0.759326 0.438397i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 20.0000i 1.08947i 0.838608 + 0.544735i \(0.183370\pi\)
−0.838608 + 0.544735i \(0.816630\pi\)
\(338\) 0 0
\(339\) −6.00000 + 10.3923i −0.325875 + 0.564433i
\(340\) 0 0
\(341\) −6.00000 10.3923i −0.324918 0.562775i
\(342\) 0 0
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.3827 + 13.5000i 1.25525 + 0.724718i 0.972147 0.234372i \(-0.0753034\pi\)
0.283101 + 0.959090i \(0.408637\pi\)
\(348\) 0 0
\(349\) 1.00000 0.0535288 0.0267644 0.999642i \(-0.491480\pi\)
0.0267644 + 0.999642i \(0.491480\pi\)
\(350\) 0 0
\(351\) −10.0000 −0.533761
\(352\) 0 0
\(353\) −10.3923 6.00000i −0.553127 0.319348i 0.197256 0.980352i \(-0.436797\pi\)
−0.750382 + 0.661004i \(0.770130\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −10.3923 + 12.0000i −0.550019 + 0.635107i
\(358\) 0 0
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 0 0
\(361\) −22.5000 + 38.9711i −1.18421 + 2.05111i
\(362\) 0 0
\(363\) 25.0000i 1.31216i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.33013 2.50000i −0.226031 0.130499i 0.382709 0.923869i \(-0.374991\pi\)
−0.608740 + 0.793370i \(0.708325\pi\)
\(368\) 0 0
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 0 0
\(371\) −6.00000 + 31.1769i −0.311504 + 1.61862i
\(372\) 0 0
\(373\) 13.8564 8.00000i 0.717458 0.414224i −0.0963587 0.995347i \(-0.530720\pi\)
0.813816 + 0.581122i \(0.197386\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) −2.59808 + 1.50000i −0.132755 + 0.0766464i −0.564907 0.825155i \(-0.691088\pi\)
0.432151 + 0.901801i \(0.357755\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.66025 + 5.00000i −0.440225 + 0.254164i
\(388\) 0 0
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 12.0000i 0.605320i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 22.5167 13.0000i 1.13008 0.652451i 0.186124 0.982526i \(-0.440407\pi\)
0.943955 + 0.330075i \(0.107074\pi\)
\(398\) 0 0
\(399\) −20.0000 + 6.92820i −1.00125 + 0.346844i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 3.46410 + 2.00000i 0.172559 + 0.0996271i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 48.0000i 2.37927i
\(408\) 0 0
\(409\) 5.50000 9.52628i 0.271957 0.471044i −0.697406 0.716677i \(-0.745662\pi\)
0.969363 + 0.245633i \(0.0789957\pi\)
\(410\) 0 0
\(411\) 6.00000 + 10.3923i 0.295958 + 0.512615i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.73205 1.00000i −0.0848189 0.0489702i
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) 23.0000 1.12095 0.560476 0.828171i \(-0.310618\pi\)
0.560476 + 0.828171i \(0.310618\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.73205 + 2.00000i −0.0838198 + 0.0967868i
\(428\) 0 0
\(429\) 6.00000 + 10.3923i 0.289683 + 0.501745i
\(430\) 0 0
\(431\) −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) 0 0
\(433\) 28.0000i 1.34559i 0.739827 + 0.672797i \(0.234907\pi\)
−0.739827 + 0.672797i \(0.765093\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −20.7846 12.0000i −0.994263 0.574038i
\(438\) 0 0
\(439\) −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
\(441\) 13.0000 + 5.19615i 0.619048 + 0.247436i
\(442\) 0 0
\(443\) −7.79423 + 4.50000i −0.370315 + 0.213801i −0.673596 0.739100i \(-0.735251\pi\)
0.303281 + 0.952901i \(0.401918\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.0000i 0.709476i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 0 0
\(453\) 8.66025 5.00000i 0.406894 0.234920i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.46410 + 2.00000i −0.162044 + 0.0935561i −0.578829 0.815449i \(-0.696490\pi\)
0.416785 + 0.909005i \(0.363157\pi\)
\(458\) 0 0
\(459\) 15.0000 25.9808i 0.700140 1.21268i
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) 29.0000i 1.34774i −0.738848 0.673872i \(-0.764630\pi\)
0.738848 0.673872i \(-0.235370\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.5788 16.5000i 1.32247 0.763529i 0.338349 0.941021i \(-0.390132\pi\)
0.984122 + 0.177492i \(0.0567983\pi\)
\(468\) 0 0
\(469\) −3.50000 + 18.1865i −0.161615 + 0.839776i
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 0 0
\(473\) 25.9808 + 15.0000i 1.19460 + 0.689701i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 24.0000i 1.09888i
\(478\) 0 0
\(479\) −15.0000 + 25.9808i −0.685367 + 1.18709i 0.287954 + 0.957644i \(0.407025\pi\)
−0.973321 + 0.229447i \(0.926308\pi\)
\(480\) 0 0
\(481\) −8.00000 13.8564i −0.364769 0.631798i
\(482\) 0 0
\(483\) −2.59808 7.50000i −0.118217 0.341262i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6.92820 4.00000i −0.313947 0.181257i 0.334744 0.942309i \(-0.391350\pi\)
−0.648691 + 0.761052i \(0.724683\pi\)
\(488\) 0 0
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) 0 0
\(493\) −15.5885 9.00000i −0.702069 0.405340i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.00000 + 1.73205i 0.0447661 + 0.0775372i 0.887540 0.460730i \(-0.152412\pi\)
−0.842774 + 0.538267i \(0.819079\pi\)
\(500\) 0 0
\(501\) 10.5000 18.1865i 0.469105 0.812514i
\(502\) 0 0
\(503\) 9.00000i 0.401290i 0.979664 + 0.200645i \(0.0643038\pi\)
−0.979664 + 0.200645i \(0.935696\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 7.79423 + 4.50000i 0.346154 + 0.199852i
\(508\) 0 0
\(509\) 19.5000 + 33.7750i 0.864322 + 1.49705i 0.867719 + 0.497056i \(0.165586\pi\)
−0.00339621 + 0.999994i \(0.501081\pi\)
\(510\) 0 0
\(511\) 5.00000 25.9808i 0.221187 1.14932i
\(512\) 0 0
\(513\) 34.6410 20.0000i 1.52944 0.883022i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15.0000 + 25.9808i −0.657162 + 1.13824i 0.324185 + 0.945994i \(0.394910\pi\)
−0.981347 + 0.192244i \(0.938423\pi\)
\(522\) 0 0
\(523\) −38.1051 + 22.0000i −1.66622 + 0.961993i −0.696573 + 0.717486i \(0.745293\pi\)
−0.969648 + 0.244507i \(0.921374\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.3923 + 6.00000i −0.452696 + 0.261364i
\(528\) 0 0
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −5.19615 + 3.00000i −0.224231 + 0.129460i
\(538\) 0 0
\(539\) −6.00000 41.5692i −0.258438 1.79051i
\(540\) 0 0
\(541\) −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i \(-0.285749\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 0 0
\(543\) 14.7224 + 8.50000i 0.631800 + 0.364770i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 19.0000i 0.812381i −0.913788 0.406191i \(-0.866857\pi\)
0.913788 0.406191i \(-0.133143\pi\)
\(548\) 0 0
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 0 0
\(553\) 6.92820 8.00000i 0.294617 0.340195i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −25.9808 15.0000i −1.10084 0.635570i −0.164399 0.986394i \(-0.552568\pi\)
−0.936442 + 0.350824i \(0.885902\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) −36.0000 −1.51992
\(562\) 0 0
\(563\) −7.79423 4.50000i −0.328488 0.189652i 0.326682 0.945134i \(-0.394069\pi\)
−0.655169 + 0.755482i \(0.727403\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.59808 0.500000i −0.109109 0.0209980i
\(568\) 0 0
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) 8.00000 13.8564i 0.334790 0.579873i −0.648655 0.761083i \(-0.724668\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) 0 0
\(573\) 18.0000i 0.751961i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8.66025 + 5.00000i 0.360531 + 0.208153i 0.669314 0.742980i \(-0.266588\pi\)
−0.308783 + 0.951133i \(0.599922\pi\)
\(578\) 0 0
\(579\) 1.00000 + 1.73205i 0.0415586 + 0.0719816i
\(580\) 0 0
\(581\) 7.50000 2.59808i 0.311152 0.107786i
\(582\) 0 0
\(583\) −62.3538 + 36.0000i −2.58243 + 1.49097i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) 0 0
\(593\) 10.3923 6.00000i 0.426761 0.246390i −0.271205 0.962522i \(-0.587422\pi\)
0.697966 + 0.716131i \(0.254089\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 17.3205 10.0000i 0.708881 0.409273i
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 14.0000i 0.570124i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −37.2391 + 21.5000i −1.51149 + 0.872658i −0.511578 + 0.859237i \(0.670939\pi\)
−0.999910 + 0.0134214i \(0.995728\pi\)
\(608\) 0 0
\(609\) 1.50000 7.79423i 0.0607831 0.315838i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.73205 + 1.00000i 0.0699569 + 0.0403896i 0.534570 0.845124i \(-0.320473\pi\)
−0.464614 + 0.885514i \(0.653807\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) 7.00000 12.1244i 0.281354 0.487319i −0.690365 0.723462i \(-0.742550\pi\)
0.971718 + 0.236143i \(0.0758832\pi\)
\(620\) 0 0
\(621\) 7.50000 + 12.9904i 0.300965 + 0.521286i
\(622\) 0 0
\(623\) 5.19615 6.00000i 0.208179 0.240385i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −41.5692 24.0000i −1.66011 0.958468i
\(628\) 0 0
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) 0 0
\(633\) −3.46410 2.00000i −0.137686 0.0794929i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 8.66025 + 11.0000i 0.343132 + 0.435836i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19.5000 33.7750i 0.770204 1.33403i −0.167247 0.985915i \(-0.553488\pi\)
0.937451 0.348117i \(-0.113179\pi\)
\(642\) 0 0
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.1865 10.5000i −0.714986 0.412798i 0.0979182 0.995194i \(-0.468782\pi\)
−0.812905 + 0.582397i \(0.802115\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −4.00000 3.46410i −0.156772 0.135769i
\(652\) 0 0
\(653\) 36.3731 21.0000i 1.42339 0.821794i 0.426801 0.904345i \(-0.359640\pi\)
0.996587 + 0.0825519i \(0.0263070\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 20.0000i 0.780274i
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 12.5000 21.6506i 0.486194 0.842112i −0.513680 0.857982i \(-0.671718\pi\)
0.999874 + 0.0158695i \(0.00505163\pi\)
\(662\) 0 0
\(663\) 10.3923 6.00000i 0.403604 0.233021i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.79423 4.50000i 0.301794 0.174241i
\(668\) 0 0
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) 0 0
\(673\) 32.0000i 1.23351i −0.787155 0.616755i \(-0.788447\pi\)
0.787155 0.616755i \(-0.211553\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.5885 + 9.00000i −0.599113 + 0.345898i −0.768693 0.639618i \(-0.779092\pi\)
0.169580 + 0.985517i \(0.445759\pi\)
\(678\) 0 0
\(679\) 25.0000 8.66025i 0.959412 0.332350i
\(680\) 0 0
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 0 0
\(683\) −12.9904 7.50000i −0.497063 0.286980i 0.230437 0.973087i \(-0.425985\pi\)
−0.727500 + 0.686108i \(0.759318\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.00000i 0.0763048i
\(688\) 0 0
\(689\) 12.0000 20.7846i 0.457164 0.791831i
\(690\) 0 0
\(691\) −7.00000 12.1244i −0.266293 0.461232i 0.701609 0.712562i \(-0.252465\pi\)
−0.967901 + 0.251330i \(0.919132\pi\)
\(692\) 0 0
\(693\) 10.3923 + 30.0000i 0.394771 + 1.13961i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −15.5885 9.00000i −0.590455 0.340899i
\(698\) 0 0
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) 0 0
\(703\) 55.4256 + 32.0000i 2.09042 + 1.20690i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 7.79423 + 1.50000i 0.293132 + 0.0564133i
\(708\) 0 0
\(709\) −0.500000 0.866025i −0.0187779 0.0325243i 0.856484 0.516174i \(-0.172644\pi\)
−0.875262 + 0.483650i \(0.839311\pi\)
\(710\) 0 0
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) 0 0
\(713\) 6.00000i 0.224702i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −5.19615 3.00000i −0.194054 0.112037i
\(718\) 0 0
\(719\) −15.0000 25.9808i −0.559406 0.968919i −0.997546 0.0700124i \(-0.977696\pi\)
0.438141 0.898906i \(-0.355637\pi\)
\(720\) 0 0
\(721\) 14.0000 + 12.1244i 0.521387 + 0.451535i
\(722\) 0 0
\(723\) −22.5167 + 13.0000i −0.837404 + 0.483475i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 23.0000i 0.853023i 0.904482 + 0.426511i \(0.140258\pi\)
−0.904482 + 0.426511i \(0.859742\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 15.0000 25.9808i 0.554795 0.960933i
\(732\) 0 0
\(733\) −1.73205 + 1.00000i −0.0639748 + 0.0369358i −0.531646 0.846967i \(-0.678426\pi\)
0.467671 + 0.883902i \(0.345093\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −36.3731 + 21.0000i −1.33982 + 0.773545i
\(738\) 0 0
\(739\) −23.0000 + 39.8372i −0.846069 + 1.46543i 0.0386212 + 0.999254i \(0.487703\pi\)
−0.884690 + 0.466180i \(0.845630\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 39.0000i 1.43077i 0.698730 + 0.715386i \(0.253749\pi\)
−0.698730 + 0.715386i \(0.746251\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.19615 + 3.00000i −0.190117 + 0.109764i
\(748\) 0 0
\(749\) −6.00000 5.19615i −0.219235 0.189863i
\(750\) 0 0
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 0 0
\(753\) −15.5885 9.00000i −0.568075 0.327978i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 0 0
\(759\) 9.00000 15.5885i 0.326679 0.565825i
\(760\) 0 0
\(761\) −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i \(-0.983671\pi\)
0.454935 0.890525i \(-0.349663\pi\)
\(762\) 0 0
\(763\) 44.1673 + 8.50000i 1.59896 + 0.307721i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −24.0000 −0.864339
\(772\) 0 0
\(773\) −36.3731 21.0000i −1.30825 0.755318i −0.326445 0.945216i \(-0.605851\pi\)
−0.981804 + 0.189899i \(0.939184\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.92820 + 20.0000i 0.248548 + 0.717496i
\(778\) 0 0
\(779\) −12.0000 20.7846i −0.429945 0.744686i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 15.0000i 0.536056i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 26.8468 + 15.5000i 0.956985 + 0.552515i 0.895244 0.445577i \(-0.147001\pi\)
0.0617409 + 0.998092i \(0.480335\pi\)
\(788\) 0 0
\(789\) −1.50000 2.59808i −0.0534014 0.0924940i
\(790\) 0 0
\(791\) −30.0000 + 10.3923i −1.06668 + 0.369508i
\(792\) 0 0
\(793\) 1.73205 1.00000i 0.0615069 0.0355110i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.0000i 0.425062i −0.977154 0.212531i \(-0.931829\pi\)
0.977154 0.212531i \(-0.0681706\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0