Properties

Label 1755.2.i.d.1171.1
Level $1755$
Weight $2$
Character 1755.1171
Analytic conductor $14.014$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0137455547\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1171.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1755.1171
Dual form 1755.2.i.d.586.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +(-0.500000 + 0.866025i) q^{13} +(-2.00000 - 3.46410i) q^{16} +3.00000 q^{17} +2.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +8.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +4.00000 q^{35} +8.00000 q^{37} +(-6.00000 + 10.3923i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-4.50000 + 7.79423i) q^{49} +(1.00000 + 1.73205i) q^{52} +3.00000 q^{53} +(3.00000 - 5.19615i) q^{59} +(-5.50000 - 9.52628i) q^{61} -8.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(2.00000 - 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{71} +8.00000 q^{73} +(2.00000 - 3.46410i) q^{76} +(3.50000 + 6.06218i) q^{79} -4.00000 q^{80} +(3.00000 + 5.19615i) q^{83} +(1.50000 - 2.59808i) q^{85} +18.0000 q^{89} -4.00000 q^{91} +(-3.00000 - 5.19615i) q^{92} +(1.00000 - 1.73205i) q^{95} +(-7.00000 - 12.1244i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} + q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} + q^{5} + 4 q^{7} - q^{13} - 4 q^{16} + 6 q^{17} + 4 q^{19} - 2 q^{20} + 3 q^{23} - q^{25} + 16 q^{28} + 6 q^{29} + 4 q^{31} + 8 q^{35} + 16 q^{37} - 12 q^{41} + q^{43} - 9 q^{49} + 2 q^{52} + 6 q^{53} + 6 q^{59} - 11 q^{61} - 16 q^{64} + q^{65} + 4 q^{67} + 6 q^{68} - 12 q^{71} + 16 q^{73} + 4 q^{76} + 7 q^{79} - 8 q^{80} + 6 q^{83} + 3 q^{85} + 36 q^{89} - 8 q^{91} - 6 q^{92} + 2 q^{95} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −1.00000 1.73205i −0.223607 0.387298i
\(21\) 0 0
\(22\) 0 0
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 8.00000 1.51186
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.00000 + 10.3923i −0.937043 + 1.62301i −0.166092 + 0.986110i \(0.553115\pi\)
−0.770950 + 0.636895i \(0.780218\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i \(-0.917971\pi\)
0.262776 0.964857i \(-0.415362\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.50000 + 6.06218i 0.393781 + 0.682048i 0.992945 0.118578i \(-0.0378336\pi\)
−0.599164 + 0.800626i \(0.704500\pi\)
\(80\) −4.00000 −0.447214
\(81\) 0 0
\(82\) 0 0
\(83\) 3.00000 + 5.19615i 0.329293 + 0.570352i 0.982372 0.186938i \(-0.0598564\pi\)
−0.653079 + 0.757290i \(0.726523\pi\)
\(84\) 0 0
\(85\) 1.50000 2.59808i 0.162698 0.281801i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) −3.00000 5.19615i −0.312772 0.541736i
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) −7.00000 12.1244i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 8.00000 13.8564i 0.755929 1.30931i
\(113\) 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i \(-0.788267\pi\)
0.927914 + 0.372794i \(0.121600\pi\)
\(114\) 0 0
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 12.0000 1.11417
\(117\) 0 0
\(118\) 0 0
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10.5000 + 18.1865i −0.917389 + 1.58896i −0.114024 + 0.993478i \(0.536374\pi\)
−0.803365 + 0.595487i \(0.796959\pi\)
\(132\) 0 0
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 4.00000 6.92820i 0.338062 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 6.00000 0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 8.00000 13.8564i 0.657596 1.13899i
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i \(0.186277\pi\)
0.0615699 + 0.998103i \(0.480389\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 3.46410i −0.160644 0.278243i
\(156\) 0 0
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 12.0000 + 20.7846i 0.937043 + 1.62301i
\(165\) 0 0
\(166\) 0 0
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 0 0
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) 7.50000 + 12.9904i 0.570214 + 0.987640i 0.996544 + 0.0830722i \(0.0264732\pi\)
−0.426329 + 0.904568i \(0.640193\pi\)
\(174\) 0 0
\(175\) 2.00000 3.46410i 0.151186 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.00000 6.92820i 0.294086 0.509372i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 0 0
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 9.00000 + 15.5885i 0.642857 + 1.11346i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −12.0000 + 20.7846i −0.842235 + 1.45879i
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 0 0
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −2.50000 + 4.33013i −0.172107 + 0.298098i −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000 0.0681994
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.50000 + 2.59808i −0.100901 + 0.174766i
\(222\) 0 0
\(223\) 11.0000 + 19.0526i 0.736614 + 1.27585i 0.954011 + 0.299770i \(0.0969101\pi\)
−0.217397 + 0.976083i \(0.569757\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) −1.00000 + 1.73205i −0.0660819 + 0.114457i −0.897173 0.441679i \(-0.854383\pi\)
0.831092 + 0.556136i \(0.187717\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −27.0000 −1.76883 −0.884414 0.466702i \(-0.845442\pi\)
−0.884414 + 0.466702i \(0.845442\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) −9.00000 + 15.5885i −0.582162 + 1.00833i 0.413061 + 0.910703i \(0.364460\pi\)
−0.995223 + 0.0976302i \(0.968874\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −22.0000 −1.40841
\(245\) 4.50000 + 7.79423i 0.287494 + 0.497955i
\(246\) 0 0
\(247\) −1.00000 + 1.73205i −0.0636285 + 0.110208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 0 0
\(259\) 16.0000 + 27.7128i 0.994192 + 1.72199i
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) 0 0
\(263\) −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i \(-0.196151\pi\)
−0.908560 + 0.417755i \(0.862817\pi\)
\(264\) 0 0
\(265\) 1.50000 2.59808i 0.0921443 0.159599i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) −6.00000 10.3923i −0.363803 0.630126i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 10.3923i −0.357930 0.619953i 0.629685 0.776851i \(-0.283184\pi\)
−0.987615 + 0.156898i \(0.949851\pi\)
\(282\) 0 0
\(283\) 6.50000 11.2583i 0.386385 0.669238i −0.605575 0.795788i \(-0.707057\pi\)
0.991960 + 0.126550i \(0.0403903\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) 0 0
\(287\) −48.0000 −2.83335
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 8.00000 13.8564i 0.468165 0.810885i
\(293\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(294\) 0 0
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.50000 + 2.59808i 0.0867472 + 0.150251i
\(300\) 0 0
\(301\) −2.00000 + 3.46410i −0.115278 + 0.199667i
\(302\) 0 0
\(303\) 0 0
\(304\) −4.00000 6.92820i −0.229416 0.397360i
\(305\) −11.0000 −0.629858
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −4.00000 + 6.92820i −0.223607 + 0.387298i
\(321\) 0 0
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) 0 0
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) 0 0
\(337\) −2.50000 + 4.33013i −0.136184 + 0.235877i −0.926049 0.377403i \(-0.876817\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 0 0
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.50000 12.9904i 0.402621 0.697360i −0.591420 0.806363i \(-0.701433\pi\)
0.994041 + 0.109003i \(0.0347659\pi\)
\(348\) 0 0
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 18.0000 31.1769i 0.953998 1.65237i
\(357\) 0 0
\(358\) 0 0
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) −4.00000 + 6.92820i −0.209657 + 0.363137i
\(365\) 4.00000 6.92820i 0.209370 0.362639i
\(366\) 0 0
\(367\) −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) −12.0000 −0.625543
\(369\) 0 0
\(370\) 0 0
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) 0 0
\(373\) −17.5000 + 30.3109i −0.906116 + 1.56944i −0.0867031 + 0.996234i \(0.527633\pi\)
−0.819413 + 0.573204i \(0.805700\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) 0 0
\(382\) 0 0
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −28.0000 −1.42148
\(389\) −4.50000 7.79423i −0.228159 0.395183i 0.729103 0.684403i \(-0.239937\pi\)
−0.957263 + 0.289220i \(0.906604\pi\)
\(390\) 0 0
\(391\) 4.50000 7.79423i 0.227575 0.394171i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.00000 0.352208
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) −30.0000 −1.49256
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −16.0000 + 27.7128i −0.791149 + 1.37031i 0.134107 + 0.990967i \(0.457183\pi\)
−0.925256 + 0.379344i \(0.876150\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) 24.0000 1.18096
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.50000 12.9904i 0.366399 0.634622i −0.622601 0.782540i \(-0.713924\pi\)
0.989000 + 0.147918i \(0.0472572\pi\)
\(420\) 0 0
\(421\) −1.00000 1.73205i −0.0487370 0.0844150i 0.840628 0.541613i \(-0.182186\pi\)
−0.889365 + 0.457198i \(0.848853\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.50000 2.59808i −0.0727607 0.126025i
\(426\) 0 0
\(427\) 22.0000 38.1051i 1.06465 1.84404i
\(428\) 3.00000 5.19615i 0.145010 0.251166i
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −37.0000 −1.77811 −0.889053 0.457804i \(-0.848636\pi\)
−0.889053 + 0.457804i \(0.848636\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.0000 + 17.3205i −0.478913 + 0.829502i
\(437\) 3.00000 5.19615i 0.143509 0.248566i
\(438\) 0 0
\(439\) 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.50000 + 7.79423i 0.213801 + 0.370315i 0.952901 0.303281i \(-0.0980821\pi\)
−0.739100 + 0.673596i \(0.764749\pi\)
\(444\) 0 0
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 0 0
\(447\) 0 0
\(448\) −16.0000 27.7128i −0.755929 1.30931i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 0 0
\(454\) 0 0
\(455\) −2.00000 + 3.46410i −0.0937614 + 0.162400i
\(456\) 0 0
\(457\) −4.00000 6.92820i −0.187112 0.324088i 0.757174 0.653213i \(-0.226579\pi\)
−0.944286 + 0.329125i \(0.893246\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −6.00000 −0.279751
\(461\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(462\) 0 0
\(463\) −13.0000 + 22.5167i −0.604161 + 1.04644i 0.388022 + 0.921650i \(0.373158\pi\)
−0.992183 + 0.124788i \(0.960175\pi\)
\(464\) 12.0000 20.7846i 0.557086 0.964901i
\(465\) 0 0
\(466\) 0 0
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.00000 1.73205i −0.0458831 0.0794719i
\(476\) 24.0000 1.10004
\(477\) 0 0
\(478\) 0 0
\(479\) 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i \(-0.122897\pi\)
−0.789314 + 0.613990i \(0.789564\pi\)
\(480\) 0 0
\(481\) −4.00000 + 6.92820i −0.182384 + 0.315899i
\(482\) 0 0
\(483\) 0 0
\(484\) −11.0000 19.0526i −0.500000 0.866025i
\(485\) −14.0000 −0.635707
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −18.0000 + 31.1769i −0.812329 + 1.40699i 0.0989017 + 0.995097i \(0.468467\pi\)
−0.911230 + 0.411897i \(0.864866\pi\)
\(492\) 0 0
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) −16.0000 −0.718421
\(497\) −12.0000 20.7846i −0.538274 0.932317i
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −1.00000 + 1.73205i −0.0447214 + 0.0774597i
\(501\) 0 0
\(502\) 0 0
\(503\) 33.0000 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 0 0
\(508\) −16.0000 + 27.7128i −0.709885 + 1.22956i
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) 0 0
\(511\) 16.0000 + 27.7128i 0.707798 + 1.22594i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 21.0000 + 36.3731i 0.917389 + 1.58896i
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 16.0000 0.693688
\(533\) −6.00000 10.3923i −0.259889 0.450141i
\(534\) 0 0
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.00000 + 8.66025i −0.214176 + 0.370965i
\(546\) 0 0
\(547\) 20.0000 + 34.6410i 0.855138 + 1.48114i 0.876517 + 0.481371i \(0.159861\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) 12.0000 0.512615
\(549\) 0 0
\(550\) 0 0
\(551\) 6.00000 + 10.3923i 0.255609 + 0.442727i
\(552\) 0 0
\(553\) −14.0000 + 24.2487i −0.595341 + 1.03116i
\(554\) 0 0
\(555\) 0 0
\(556\) 5.00000 + 8.66025i 0.212047 + 0.367277i
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) −8.00000 13.8564i −0.338062 0.585540i
\(561\) 0 0
\(562\) 0 0
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 0 0
\(565\) −1.50000 2.59808i −0.0631055 0.109302i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i \(0.176036\pi\)
0.0294311 + 0.999567i \(0.490630\pi\)
\(570\) 0 0
\(571\) 14.0000 24.2487i 0.585882 1.01478i −0.408883 0.912587i \(-0.634082\pi\)
0.994765 0.102190i \(-0.0325850\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.00000 −0.125109
\(576\) 0 0
\(577\) −28.0000 −1.16566 −0.582828 0.812596i \(-0.698054\pi\)
−0.582828 + 0.812596i \(0.698054\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 6.00000 10.3923i 0.249136 0.431517i
\(581\) −12.0000 + 20.7846i −0.497844 + 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i \(-0.0455206\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(588\) 0 0
\(589\) 4.00000 6.92820i 0.164817 0.285472i
\(590\) 0 0
\(591\) 0 0
\(592\) −16.0000 27.7128i −0.657596 1.13899i
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) −18.0000 31.1769i −0.737309 1.27706i
\(597\) 0 0
\(598\) 0 0
\(599\) −16.5000 + 28.5788i −0.674172 + 1.16770i 0.302539 + 0.953137i \(0.402166\pi\)
−0.976710 + 0.214563i \(0.931167\pi\)
\(600\) 0 0
\(601\) −14.5000 25.1147i −0.591467 1.02445i −0.994035 0.109061i \(-0.965216\pi\)
0.402568 0.915390i \(-0.368118\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 44.0000 1.79033
\(605\) −5.50000 9.52628i −0.223607 0.387298i
\(606\) 0 0
\(607\) 3.50000 6.06218i 0.142061 0.246056i −0.786212 0.617957i \(-0.787961\pi\)
0.928272 + 0.371901i \(0.121294\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i \(-0.794795\pi\)
0.920074 + 0.391745i \(0.128129\pi\)
\(618\) 0 0
\(619\) 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i \(-0.102258\pi\)
−0.747873 + 0.663842i \(0.768925\pi\)
\(620\) −8.00000 −0.321288
\(621\) 0 0
\(622\) 0 0
\(623\) 36.0000 + 62.3538i 1.44231 + 2.49815i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) −13.0000 22.5167i −0.518756 0.898513i
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) −4.50000 7.79423i −0.178296 0.308819i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21.0000 36.3731i −0.829450 1.43665i −0.898470 0.439034i \(-0.855321\pi\)
0.0690201 0.997615i \(-0.478013\pi\)
\(642\) 0 0
\(643\) 11.0000 19.0526i 0.433798 0.751360i −0.563399 0.826185i \(-0.690507\pi\)
0.997197 + 0.0748254i \(0.0238399\pi\)
\(644\) 12.0000 20.7846i 0.472866 0.819028i
\(645\) 0 0
\(646\) 0 0
\(647\) −9.00000 −0.353827 −0.176913 0.984226i \(-0.556611\pi\)
−0.176913 + 0.984226i \(0.556611\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −16.0000 + 27.7128i −0.626608 + 1.08532i
\(653\) 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i \(-0.633644\pi\)
0.994623 0.103558i \(-0.0330227\pi\)
\(654\) 0 0
\(655\) 10.5000 + 18.1865i 0.410269 + 0.710607i
\(656\) 48.0000 1.87409
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) 18.0000 0.696963
\(668\) −12.0000 20.7846i −0.464294 0.804181i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 3.50000 + 6.06218i 0.134915 + 0.233680i 0.925565 0.378589i \(-0.123591\pi\)
−0.790650 + 0.612268i \(0.790257\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −2.00000 −0.0769231
\(677\) 21.0000 + 36.3731i 0.807096 + 1.39793i 0.914867 + 0.403755i \(0.132295\pi\)
−0.107772 + 0.994176i \(0.534372\pi\)
\(678\) 0 0
\(679\) 28.0000 48.4974i 1.07454 1.86116i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −1.50000 + 2.59808i −0.0571454 + 0.0989788i
\(690\) 0 0
\(691\) −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) 30.0000 1.14043
\(693\) 0 0
\(694\) 0 0
\(695\) 2.50000 + 4.33013i 0.0948304 + 0.164251i
\(696\) 0 0
\(697\) −18.0000 + 31.1769i −0.681799 + 1.18091i
\(698\) 0 0
\(699\) 0 0
\(700\) −4.00000 6.92820i −0.151186 0.261861i
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 0 0
\(703\) 16.0000 0.603451
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30.0000 51.9615i 1.12827 1.95421i
\(708\) 0 0
\(709\) −1.00000 1.73205i −0.0375558 0.0650485i 0.846637 0.532172i \(-0.178624\pi\)
−0.884192 + 0.467123i \(0.845291\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.00000 10.3923i −0.224702 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) −9.00000 + 15.5885i −0.336346 + 0.582568i
\(717\) 0 0
\(718\) 0 0
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) 0 0
\(723\) 0 0
\(724\) −25.0000 + 43.3013i −0.929118 + 1.60928i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 0 0
\(727\) 15.5000 + 26.8468i 0.574863 + 0.995692i 0.996056 + 0.0887213i \(0.0282781\pi\)
−0.421193 + 0.906971i \(0.638389\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.50000 + 2.59808i 0.0554795 + 0.0960933i
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) −8.00000 13.8564i −0.294086 0.509372i
\(741\) 0 0
\(742\) 0 0
\(743\) 21.0000 36.3731i 0.770415 1.33440i −0.166920 0.985970i \(-0.553382\pi\)
0.937336 0.348428i \(-0.113284\pi\)
\(744\) 0 0
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.00000 + 10.3923i 0.219235 + 0.379727i
\(750\) 0 0
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 22.0000 0.800662
\(756\) 0 0
\(757\) −19.0000 −0.690567 −0.345283 0.938498i \(-0.612217\pi\)
−0.345283 + 0.938498i \(0.612217\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) 0 0
\(763\) −20.0000 34.6410i −0.724049 1.25409i
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) 0 0
\(767\) 3.00000 + 5.19615i 0.108324 + 0.187622i
\(768\) 0 0
\(769\) −16.0000 + 27.7128i −0.576975 + 0.999350i 0.418849 + 0.908056i \(0.362434\pi\)
−0.995824 + 0.0912938i \(0.970900\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.0000 + 20.7846i −0.429945 + 0.744686i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 36.0000 1.28571
\(785\) −6.50000 11.2583i −0.231995 0.401827i
\(786\) 0 0
\(787\) 23.0000 39.8372i 0.819861 1.42004i −0.0859225 0.996302i \(-0.527384\pi\)
0.905784 0.423740i \(-0.139283\pi\)
\(788\) −12.0000 + 20.7846i −0.427482 + 0.740421i
\(789\) 0 0
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) 11.0000 0.390621
\(794\) 0 0
\(795\) 0 0
\(796\) −7.00000 + 12.1244i −0.248108 + 0.429736i
\(797\) 27.0000 46.7654i 0.956389 1.65651i 0.225232 0.974305i \(-0.427686\pi\)
0.731157 0.682209i \(-0.238981\pi\)
\(798\) 0 0