Properties

Label 51.2.d.b.16.2
Level $51$
Weight $2$
Character 51.16
Analytic conductor $0.407$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 51 = 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 51.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.407237050309\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 16.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 51.16
Dual form 51.2.d.b.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -4.00000i q^{7} -3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{6} -4.00000i q^{7} -3.00000 q^{8} -1.00000 q^{9} +4.00000i q^{11} -1.00000i q^{12} +2.00000 q^{13} -4.00000i q^{14} -1.00000 q^{16} +(1.00000 + 4.00000i) q^{17} -1.00000 q^{18} -4.00000 q^{19} +4.00000 q^{21} +4.00000i q^{22} -4.00000i q^{23} -3.00000i q^{24} +5.00000 q^{25} +2.00000 q^{26} -1.00000i q^{27} +4.00000i q^{28} -4.00000i q^{31} +5.00000 q^{32} -4.00000 q^{33} +(1.00000 + 4.00000i) q^{34} +1.00000 q^{36} +8.00000i q^{37} -4.00000 q^{38} +2.00000i q^{39} -8.00000i q^{41} +4.00000 q^{42} -4.00000 q^{43} -4.00000i q^{44} -4.00000i q^{46} -8.00000 q^{47} -1.00000i q^{48} -9.00000 q^{49} +5.00000 q^{50} +(-4.00000 + 1.00000i) q^{51} -2.00000 q^{52} +6.00000 q^{53} -1.00000i q^{54} +12.0000i q^{56} -4.00000i q^{57} -12.0000 q^{59} -8.00000i q^{61} -4.00000i q^{62} +4.00000i q^{63} +7.00000 q^{64} -4.00000 q^{66} +12.0000 q^{67} +(-1.00000 - 4.00000i) q^{68} +4.00000 q^{69} +12.0000i q^{71} +3.00000 q^{72} +8.00000i q^{74} +5.00000i q^{75} +4.00000 q^{76} +16.0000 q^{77} +2.00000i q^{78} -4.00000i q^{79} +1.00000 q^{81} -8.00000i q^{82} +12.0000 q^{83} -4.00000 q^{84} -4.00000 q^{86} -12.0000i q^{88} -10.0000 q^{89} -8.00000i q^{91} +4.00000i q^{92} +4.00000 q^{93} -8.00000 q^{94} +5.00000i q^{96} +16.0000i q^{97} -9.00000 q^{98} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{4} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{4} - 6q^{8} - 2q^{9} + 4q^{13} - 2q^{16} + 2q^{17} - 2q^{18} - 8q^{19} + 8q^{21} + 10q^{25} + 4q^{26} + 10q^{32} - 8q^{33} + 2q^{34} + 2q^{36} - 8q^{38} + 8q^{42} - 8q^{43} - 16q^{47} - 18q^{49} + 10q^{50} - 8q^{51} - 4q^{52} + 12q^{53} - 24q^{59} + 14q^{64} - 8q^{66} + 24q^{67} - 2q^{68} + 8q^{69} + 6q^{72} + 8q^{76} + 32q^{77} + 2q^{81} + 24q^{83} - 8q^{84} - 8q^{86} - 20q^{89} + 8q^{93} - 16q^{94} - 18q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/51\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(37\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 4.00000i 1.51186i −0.654654 0.755929i \(-0.727186\pi\)
0.654654 0.755929i \(-0.272814\pi\)
\(8\) −3.00000 −1.06066
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 4.00000i 1.20605i 0.797724 + 0.603023i \(0.206037\pi\)
−0.797724 + 0.603023i \(0.793963\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 4.00000i 1.06904i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 1.00000 + 4.00000i 0.242536 + 0.970143i
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 4.00000 0.872872
\(22\) 4.00000i 0.852803i
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 3.00000i 0.612372i
\(25\) 5.00000 1.00000
\(26\) 2.00000 0.392232
\(27\) 1.00000i 0.192450i
\(28\) 4.00000i 0.755929i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 4.00000i 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) 5.00000 0.883883
\(33\) −4.00000 −0.696311
\(34\) 1.00000 + 4.00000i 0.171499 + 0.685994i
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 8.00000i 1.31519i 0.753371 + 0.657596i \(0.228427\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(38\) −4.00000 −0.648886
\(39\) 2.00000i 0.320256i
\(40\) 0 0
\(41\) 8.00000i 1.24939i −0.780869 0.624695i \(-0.785223\pi\)
0.780869 0.624695i \(-0.214777\pi\)
\(42\) 4.00000 0.617213
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 4.00000i 0.603023i
\(45\) 0 0
\(46\) 4.00000i 0.589768i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −9.00000 −1.28571
\(50\) 5.00000 0.707107
\(51\) −4.00000 + 1.00000i −0.560112 + 0.140028i
\(52\) −2.00000 −0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0 0
\(56\) 12.0000i 1.60357i
\(57\) 4.00000i 0.529813i
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) 8.00000i 1.02430i −0.858898 0.512148i \(-0.828850\pi\)
0.858898 0.512148i \(-0.171150\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 4.00000i 0.503953i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −1.00000 4.00000i −0.121268 0.485071i
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 3.00000 0.353553
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 8.00000i 0.929981i
\(75\) 5.00000i 0.577350i
\(76\) 4.00000 0.458831
\(77\) 16.0000 1.82337
\(78\) 2.00000i 0.226455i
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 8.00000i 0.883452i
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −4.00000 −0.436436
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 12.0000i 1.27920i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 8.00000i 0.838628i
\(92\) 4.00000i 0.417029i
\(93\) 4.00000 0.414781
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 5.00000i 0.510310i
\(97\) 16.0000i 1.62455i 0.583272 + 0.812277i \(0.301772\pi\)
−0.583272 + 0.812277i \(0.698228\pi\)
\(98\) −9.00000 −0.909137
\(99\) 4.00000i 0.402015i
\(100\) −5.00000 −0.500000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −4.00000 + 1.00000i −0.396059 + 0.0990148i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 8.00000i 0.766261i 0.923694 + 0.383131i \(0.125154\pi\)
−0.923694 + 0.383131i \(0.874846\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 4.00000i 0.377964i
\(113\) 8.00000i 0.752577i −0.926503 0.376288i \(-0.877200\pi\)
0.926503 0.376288i \(-0.122800\pi\)
\(114\) 4.00000i 0.374634i
\(115\) 0 0
\(116\) 0 0
\(117\) −2.00000 −0.184900
\(118\) −12.0000 −1.10469
\(119\) 16.0000 4.00000i 1.46672 0.366679i
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) 8.00000i 0.724286i
\(123\) 8.00000 0.721336
\(124\) 4.00000i 0.359211i
\(125\) 0 0
\(126\) 4.00000i 0.356348i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −3.00000 −0.265165
\(129\) 4.00000i 0.352180i
\(130\) 0 0
\(131\) 4.00000i 0.349482i 0.984614 + 0.174741i \(0.0559088\pi\)
−0.984614 + 0.174741i \(0.944091\pi\)
\(132\) 4.00000 0.348155
\(133\) 16.0000i 1.38738i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) −3.00000 12.0000i −0.257248 1.02899i
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 4.00000 0.340503
\(139\) 4.00000i 0.339276i 0.985506 + 0.169638i \(0.0542598\pi\)
−0.985506 + 0.169638i \(0.945740\pi\)
\(140\) 0 0
\(141\) 8.00000i 0.673722i
\(142\) 12.0000i 1.00702i
\(143\) 8.00000i 0.668994i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 0 0
\(147\) 9.00000i 0.742307i
\(148\) 8.00000i 0.657596i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 5.00000i 0.408248i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 12.0000 0.973329
\(153\) −1.00000 4.00000i −0.0808452 0.323381i
\(154\) 16.0000 1.28932
\(155\) 0 0
\(156\) 2.00000i 0.160128i
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 4.00000i 0.318223i
\(159\) 6.00000i 0.475831i
\(160\) 0 0
\(161\) −16.0000 −1.26098
\(162\) 1.00000 0.0785674
\(163\) 20.0000i 1.56652i 0.621694 + 0.783260i \(0.286445\pi\)
−0.621694 + 0.783260i \(0.713555\pi\)
\(164\) 8.00000i 0.624695i
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) −12.0000 −0.925820
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 4.00000 0.304997
\(173\) 16.0000i 1.21646i −0.793762 0.608229i \(-0.791880\pi\)
0.793762 0.608229i \(-0.208120\pi\)
\(174\) 0 0
\(175\) 20.0000i 1.51186i
\(176\) 4.00000i 0.301511i
\(177\) 12.0000i 0.901975i
\(178\) −10.0000 −0.749532
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 0 0
\(181\) 8.00000i 0.594635i −0.954779 0.297318i \(-0.903908\pi\)
0.954779 0.297318i \(-0.0960920\pi\)
\(182\) 8.00000i 0.592999i
\(183\) 8.00000 0.591377
\(184\) 12.0000i 0.884652i
\(185\) 0 0
\(186\) 4.00000 0.293294
\(187\) −16.0000 + 4.00000i −1.17004 + 0.292509i
\(188\) 8.00000 0.583460
\(189\) −4.00000 −0.290957
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 7.00000i 0.505181i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 16.0000i 1.14873i
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 16.0000i 1.13995i 0.821661 + 0.569976i \(0.193048\pi\)
−0.821661 + 0.569976i \(0.806952\pi\)
\(198\) 4.00000i 0.284268i
\(199\) 20.0000i 1.41776i −0.705328 0.708881i \(-0.749200\pi\)
0.705328 0.708881i \(-0.250800\pi\)
\(200\) −15.0000 −1.06066
\(201\) 12.0000i 0.846415i
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) 4.00000 1.00000i 0.280056 0.0700140i
\(205\) 0 0
\(206\) 0 0
\(207\) 4.00000i 0.278019i
\(208\) −2.00000 −0.138675
\(209\) 16.0000i 1.10674i
\(210\) 0 0
\(211\) 4.00000i 0.275371i 0.990476 + 0.137686i \(0.0439664\pi\)
−0.990476 + 0.137686i \(0.956034\pi\)
\(212\) −6.00000 −0.412082
\(213\) −12.0000 −0.822226
\(214\) 12.0000i 0.820303i
\(215\) 0 0
\(216\) 3.00000i 0.204124i
\(217\) −16.0000 −1.08615
\(218\) 8.00000i 0.541828i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.00000 + 8.00000i 0.134535 + 0.538138i
\(222\) −8.00000 −0.536925
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 20.0000i 1.33631i
\(225\) −5.00000 −0.333333
\(226\) 8.00000i 0.532152i
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 4.00000i 0.264906i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 16.0000i 1.05272i
\(232\) 0 0
\(233\) 8.00000i 0.524097i 0.965055 + 0.262049i \(0.0843981\pi\)
−0.965055 + 0.262049i \(0.915602\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 12.0000 0.781133
\(237\) 4.00000 0.259828
\(238\) 16.0000 4.00000i 1.03713 0.259281i
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) 16.0000i 1.03065i −0.856995 0.515325i \(-0.827671\pi\)
0.856995 0.515325i \(-0.172329\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000i 0.0641500i
\(244\) 8.00000i 0.512148i
\(245\) 0 0
\(246\) 8.00000 0.510061
\(247\) −8.00000 −0.509028
\(248\) 12.0000i 0.762001i
\(249\) 12.0000i 0.760469i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 16.0000 1.00591
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 32.0000 1.98838
\(260\) 0 0
\(261\) 0 0
\(262\) 4.00000i 0.247121i
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 12.0000 0.738549
\(265\) 0 0
\(266\) 16.0000i 0.981023i
\(267\) 10.0000i 0.611990i
\(268\) −12.0000 −0.733017
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −1.00000 4.00000i −0.0606339 0.242536i
\(273\) 8.00000 0.484182
\(274\) −10.0000 −0.604122
\(275\) 20.0000i 1.20605i
\(276\) −4.00000 −0.240772
\(277\) 8.00000i 0.480673i −0.970690 0.240337i \(-0.922742\pi\)
0.970690 0.240337i \(-0.0772579\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 4.00000i 0.239474i
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 12.0000i 0.712069i
\(285\) 0 0
\(286\) 8.00000i 0.473050i
\(287\) −32.0000 −1.88890
\(288\) −5.00000 −0.294628
\(289\) −15.0000 + 8.00000i −0.882353 + 0.470588i
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) 0 0
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 9.00000i 0.524891i
\(295\) 0 0
\(296\) 24.0000i 1.39497i
\(297\) 4.00000 0.232104
\(298\) 6.00000 0.347571
\(299\) 8.00000i 0.462652i
\(300\) 5.00000i 0.288675i
\(301\) 16.0000i 0.922225i
\(302\) 0 0
\(303\) 6.00000i 0.344691i
\(304\) 4.00000 0.229416
\(305\) 0 0
\(306\) −1.00000 4.00000i −0.0571662 0.228665i
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) −16.0000 −0.911685
\(309\) 0 0
\(310\) 0 0
\(311\) 12.0000i 0.680458i 0.940343 + 0.340229i \(0.110505\pi\)
−0.940343 + 0.340229i \(0.889495\pi\)
\(312\) 6.00000i 0.339683i
\(313\) 16.0000i 0.904373i −0.891923 0.452187i \(-0.850644\pi\)
0.891923 0.452187i \(-0.149356\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 4.00000i 0.225018i
\(317\) 32.0000i 1.79730i −0.438667 0.898650i \(-0.644549\pi\)
0.438667 0.898650i \(-0.355451\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 0 0
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) −16.0000 −0.891645
\(323\) −4.00000 16.0000i −0.222566 0.890264i
\(324\) −1.00000 −0.0555556
\(325\) 10.0000 0.554700
\(326\) 20.0000i 1.10770i
\(327\) −8.00000 −0.442401
\(328\) 24.0000i 1.32518i
\(329\) 32.0000i 1.76422i
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) −12.0000 −0.658586
\(333\) 8.00000i 0.438397i
\(334\) 12.0000i 0.656611i
\(335\) 0 0
\(336\) −4.00000 −0.218218
\(337\) 16.0000i 0.871576i −0.900049 0.435788i \(-0.856470\pi\)
0.900049 0.435788i \(-0.143530\pi\)
\(338\) −9.00000 −0.489535
\(339\) 8.00000 0.434500
\(340\) 0 0
\(341\) 16.0000 0.866449
\(342\) 4.00000 0.216295
\(343\) 8.00000i 0.431959i
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 16.0000i 0.860165i
\(347\) 4.00000i 0.214731i 0.994220 + 0.107366i \(0.0342415\pi\)
−0.994220 + 0.107366i \(0.965758\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 20.0000i 1.06904i
\(351\) 2.00000i 0.106752i
\(352\) 20.0000i 1.06600i
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 12.0000i 0.637793i
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 4.00000 + 16.0000i 0.211702 + 0.846810i
\(358\) 4.00000 0.211407
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 8.00000i 0.420471i
\(363\) 5.00000i 0.262432i
\(364\) 8.00000i 0.419314i
\(365\) 0 0
\(366\) 8.00000 0.418167
\(367\) 12.0000i 0.626395i 0.949688 + 0.313197i \(0.101400\pi\)
−0.949688 + 0.313197i \(0.898600\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 8.00000i 0.416463i
\(370\) 0 0
\(371\) 24.0000i 1.24602i
\(372\) −4.00000 −0.207390
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) −16.0000 + 4.00000i −0.827340 + 0.206835i
\(375\) 0 0
\(376\) 24.0000 1.23771
\(377\) 0 0
\(378\) −4.00000 −0.205738
\(379\) 20.0000i 1.02733i 0.857991 + 0.513665i \(0.171713\pi\)
−0.857991 + 0.513665i \(0.828287\pi\)
\(380\) 0 0
\(381\) 8.00000i 0.409852i
\(382\) −8.00000 −0.409316
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 3.00000i 0.153093i
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000 0.203331
\(388\) 16.0000i 0.812277i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 16.0000 4.00000i 0.809155 0.202289i
\(392\) 27.0000 1.36371
\(393\) −4.00000 −0.201773
\(394\) 16.0000i 0.806068i
\(395\) 0 0
\(396\) 4.00000i 0.201008i
\(397\) 8.00000i 0.401508i −0.979642 0.200754i \(-0.935661\pi\)
0.979642 0.200754i \(-0.0643393\pi\)
\(398\) 20.0000i 1.00251i
\(399\) −16.0000 −0.801002
\(400\) −5.00000 −0.250000
\(401\) 24.0000i 1.19850i −0.800561 0.599251i \(-0.795465\pi\)
0.800561 0.599251i \(-0.204535\pi\)
\(402\) 12.0000i 0.598506i
\(403\) 8.00000i 0.398508i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) −32.0000 −1.58618
\(408\) 12.0000 3.00000i 0.594089 0.148522i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 10.0000i 0.493264i
\(412\) 0 0
\(413\) 48.0000i 2.36193i
\(414\) 4.00000i 0.196589i
\(415\) 0 0
\(416\) 10.0000 0.490290
\(417\) −4.00000 −0.195881
\(418\) 16.0000i 0.782586i
\(419\) 4.00000i 0.195413i 0.995215 + 0.0977064i \(0.0311506\pi\)
−0.995215 + 0.0977064i \(0.968849\pi\)
\(420\) 0 0
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 8.00000 0.388973
\(424\) −18.0000 −0.874157
\(425\) 5.00000 + 20.0000i 0.242536 + 0.970143i
\(426\) −12.0000 −0.581402
\(427\) −32.0000 −1.54859
\(428\) 12.0000i 0.580042i
\(429\) −8.00000 −0.386244
\(430\) 0 0
\(431\) 20.0000i 0.963366i −0.876346 0.481683i \(-0.840026\pi\)
0.876346 0.481683i \(-0.159974\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) 8.00000i 0.383131i
\(437\) 16.0000i 0.765384i
\(438\) 0 0
\(439\) 36.0000i 1.71819i −0.511819 0.859093i \(-0.671028\pi\)
0.511819 0.859093i \(-0.328972\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 2.00000 + 8.00000i 0.0951303 + 0.380521i
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 8.00000 0.379663
\(445\) 0 0
\(446\) 16.0000 0.757622
\(447\) 6.00000i 0.283790i
\(448\) 28.0000i 1.32288i
\(449\) 8.00000i 0.377543i 0.982021 + 0.188772i \(0.0604506\pi\)
−0.982021 + 0.188772i \(0.939549\pi\)
\(450\) −5.00000 −0.235702
\(451\) 32.0000 1.50682
\(452\) 8.00000i 0.376288i
\(453\) 0 0
\(454\) 12.0000i 0.563188i
\(455\) 0 0
\(456\) 12.0000i 0.561951i
\(457\) 38.0000 1.77757 0.888783 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) 10.0000 0.467269
\(459\) 4.00000 1.00000i 0.186704 0.0466760i
\(460\) 0 0
\(461\) −34.0000 −1.58354 −0.791769 0.610821i \(-0.790840\pi\)
−0.791769 + 0.610821i \(0.790840\pi\)
\(462\) 16.0000i 0.744387i
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 8.00000i 0.370593i
\(467\) 4.00000 0.185098 0.0925490 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) 2.00000 0.0924500
\(469\) 48.0000i 2.21643i
\(470\) 0 0
\(471\) 2.00000i 0.0921551i
\(472\) 36.0000 1.65703
\(473\) 16.0000i 0.735681i
\(474\) 4.00000 0.183726
\(475\) −20.0000 −0.917663
\(476\) −16.0000 + 4.00000i −0.733359 + 0.183340i
\(477\) −6.00000 −0.274721
\(478\) −8.00000 −0.365911
\(479\) 12.0000i 0.548294i 0.961688 + 0.274147i \(0.0883955\pi\)
−0.961688 + 0.274147i \(0.911605\pi\)
\(480\) 0 0
\(481\) 16.0000i 0.729537i
\(482\) 16.0000i 0.728780i
\(483\) 16.0000i 0.728025i
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 4.00000i 0.181257i −0.995885 0.0906287i \(-0.971112\pi\)
0.995885 0.0906287i \(-0.0288876\pi\)
\(488\) 24.0000i 1.08643i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) −8.00000 −0.360668
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) 4.00000i 0.179605i
\(497\) 48.0000 2.15309
\(498\) 12.0000i 0.537733i
\(499\) 36.0000i 1.61158i 0.592200 + 0.805791i \(0.298259\pi\)
−0.592200 + 0.805791i \(0.701741\pi\)
\(500\) 0 0
\(501\) −12.0000 −0.536120
\(502\) 12.0000 0.535586
\(503\) 12.0000i 0.535054i 0.963550 + 0.267527i \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 12.0000i 0.534522i
\(505\) 0 0
\(506\) 16.0000 0.711287
\(507\) 9.00000i 0.399704i
\(508\) −8.00000 −0.354943
\(509\) −18.0000 −0.797836 −0.398918 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −11.0000 −0.486136
\(513\) 4.00000i 0.176604i
\(514\) −2.00000 −0.0882162
\(515\) 0 0
\(516\) 4.00000i 0.176090i
\(517\) 32.0000i 1.40736i
\(518\) 32.0000 1.40600
\(519\) 16.0000 0.702322
\(520\) 0 0
\(521\) 24.0000i 1.05146i 0.850652 + 0.525730i \(0.176208\pi\)
−0.850652 + 0.525730i \(0.823792\pi\)
\(522\) 0 0
\(523\) −12.0000 −0.524723 −0.262362 0.964970i \(-0.584501\pi\)
−0.262362 + 0.964970i \(0.584501\pi\)
\(524\) 4.00000i 0.174741i
\(525\) 20.0000 0.872872
\(526\) 24.0000 1.04645
\(527\) 16.0000 4.00000i 0.696971 0.174243i
\(528\) 4.00000 0.174078
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 16.0000i 0.693688i
\(533\) 16.0000i 0.693037i
\(534\) 10.0000i 0.432742i
\(535\) 0 0
\(536\) −36.0000 −1.55496
\(537\) 4.00000i 0.172613i
\(538\) 0 0
\(539\) 36.0000i 1.55063i
\(540\) 0 0
\(541\) 40.0000i 1.71973i 0.510518 + 0.859867i \(0.329454\pi\)
−0.510518 + 0.859867i \(0.670546\pi\)
\(542\) 0 0
\(543\) 8.00000 0.343313
\(544\) 5.00000 + 20.0000i 0.214373 + 0.857493i
\(545\) 0 0
\(546\) 8.00000 0.342368
\(547\) 36.0000i 1.53925i 0.638497 + 0.769624i \(0.279557\pi\)
−0.638497 + 0.769624i \(0.720443\pi\)
\(548\) 10.0000 0.427179
\(549\) 8.00000i 0.341432i
\(550\) 20.0000i 0.852803i
\(551\) 0 0
\(552\) −12.0000 −0.510754
\(553\) −16.0000 −0.680389
\(554\) 8.00000i 0.339887i
\(555\) 0 0
\(556\) 4.00000i 0.169638i
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −4.00000 16.0000i −0.168880 0.675521i
\(562\) 10.0000 0.421825
\(563\) 44.0000 1.85438 0.927189 0.374593i \(-0.122217\pi\)
0.927189 + 0.374593i \(0.122217\pi\)
\(564\) 8.00000i 0.336861i
\(565\) 0 0
\(566\) 4.00000i 0.168133i
\(567\) 4.00000i 0.167984i
\(568\) 36.0000i 1.51053i
\(569\) 26.0000 1.08998 0.544988 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) 0 0
\(571\) 20.0000i 0.836974i 0.908223 + 0.418487i \(0.137439\pi\)
−0.908223 + 0.418487i \(0.862561\pi\)
\(572\) 8.00000i 0.334497i
\(573\) 8.00000i 0.334205i
\(574\) −32.0000 −1.33565
\(575\) 20.0000i 0.834058i
\(576\) −7.00000 −0.291667
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) −15.0000 + 8.00000i −0.623918 + 0.332756i
\(579\) 0 0
\(580\) 0 0
\(581\) 48.0000i 1.99138i
\(582\) −16.0000 −0.663221
\(583\) 24.0000i 0.993978i
\(584\) 0 0
\(585\) 0 0
\(586\) −10.0000 −0.413096
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 9.00000i 0.371154i
\(589\) 16.0000i 0.659269i
\(590\) 0 0
\(591\) −16.0000 −0.658152
\(592\) 8.00000i 0.328798i
\(593\) −46.0000 −1.88899 −0.944497 0.328521i \(-0.893450\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 20.0000 0.818546
\(598\) 8.00000i 0.327144i
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 15.0000i 0.612372i
\(601\) 16.0000i 0.652654i 0.945257 + 0.326327i \(0.105811\pi\)
−0.945257 + 0.326327i \(0.894189\pi\)
\(602\) 16.0000i 0.652111i
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) 0 0
\(606\) 6.00000i 0.243733i
\(607\) 4.00000i 0.162355i −0.996700 0.0811775i \(-0.974132\pi\)
0.996700 0.0811775i \(-0.0258681\pi\)
\(608\) −20.0000 −0.811107
\(609\) 0 0
\(610\) 0 0
\(611\) −16.0000 −0.647291
\(612\) 1.00000 + 4.00000i 0.0404226 + 0.161690i
\(613\) 6.00000 0.242338 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) −48.0000 −1.93398
\(617\) 24.0000i 0.966204i −0.875564 0.483102i \(-0.839510\pi\)
0.875564 0.483102i \(-0.160490\pi\)
\(618\) 0 0
\(619\) 36.0000i 1.44696i 0.690344 + 0.723481i \(0.257459\pi\)
−0.690344 + 0.723481i \(0.742541\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 12.0000i 0.481156i
\(623\) 40.0000i 1.60257i
\(624\) 2.00000i 0.0800641i
\(625\) 25.0000 1.00000
\(626\) 16.0000i 0.639489i
\(627\) 16.0000 0.638978
\(628\) 2.00000 0.0798087
\(629\) −32.0000 + 8.00000i −1.27592 + 0.318981i
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 12.0000i 0.477334i
\(633\) −4.00000 −0.158986
\(634\) 32.0000i 1.27088i
\(635\) 0 0
\(636\) 6.00000i 0.237915i
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) 12.0000i 0.474713i
\(640\) 0 0
\(641\) 8.00000i 0.315981i 0.987441 + 0.157991i \(0.0505015\pi\)
−0.987441 + 0.157991i \(0.949498\pi\)
\(642\) 12.0000 0.473602
\(643\) 4.00000i 0.157745i 0.996885 + 0.0788723i \(0.0251319\pi\)
−0.996885 + 0.0788723i \(0.974868\pi\)
\(644\) 16.0000 0.630488
\(645\) 0 0
\(646\) −4.00000 16.0000i −0.157378 0.629512i
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) −3.00000 −0.117851
\(649\) 48.0000i 1.88416i
\(650\) 10.0000 0.392232
\(651\) 16.0000i 0.627089i
\(652\) 20.0000i 0.783260i
\(653\) 32.0000i 1.25226i −0.779720 0.626128i \(-0.784639\pi\)
0.779720 0.626128i \(-0.215361\pi\)
\(654\) −8.00000 −0.312825
\(655\) 0 0
\(656\) 8.00000i 0.312348i
\(657\) 0 0
\(658\) 32.0000i 1.24749i
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) −42.0000 −1.63361 −0.816805 0.576913i \(-0.804257\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) −20.0000 −0.777322
\(663\) −8.00000 + 2.00000i −0.310694 + 0.0776736i
\(664\) −36.0000 −1.39707
\(665\) 0 0
\(666\) 8.00000i 0.309994i
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 16.0000i 0.618596i
\(670\) 0 0
\(671\) 32.0000 1.23535
\(672\) 20.0000 0.771517
\(673\) 32.0000i 1.23351i 0.787155 + 0.616755i \(0.211553\pi\)
−0.787155 + 0.616755i \(0.788447\pi\)
\(674\) 16.0000i 0.616297i
\(675\) 5.00000i 0.192450i
\(676\) 9.00000 0.346154
\(677\) 48.0000i 1.84479i 0.386248 + 0.922395i \(0.373771\pi\)
−0.386248 + 0.922395i \(0.626229\pi\)
\(678\) 8.00000 0.307238
\(679\) 64.0000 2.45609
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 16.0000 0.612672
\(683\) 12.0000i 0.459167i −0.973289 0.229584i \(-0.926264\pi\)
0.973289 0.229584i \(-0.0737364\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) 8.00000i 0.305441i
\(687\) 10.0000i 0.381524i
\(688\) 4.00000 0.152499
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 20.0000i 0.760836i 0.924815 + 0.380418i \(0.124220\pi\)
−0.924815 + 0.380418i \(0.875780\pi\)
\(692\) 16.0000i 0.608229i
\(693\) −16.0000 −0.607790
\(694\) 4.00000i 0.151838i
\(695\) 0 0
\(696\) 0 0
\(697\) 32.0000 8.00000i 1.21209 0.303022i
\(698\) −2.00000 −0.0757011
\(699\) −8.00000 −0.302588
\(700\) 20.0000i 0.755929i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 2.00000i 0.0754851i
\(703\) 32.0000i 1.20690i
\(704\) 28.0000i 1.05529i
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 24.0000i 0.902613i
\(708\) 12.0000i 0.450988i
\(709\) 40.0000i 1.50223i −0.660171 0.751116i \(-0.729516\pi\)
0.660171 0.751116i \(-0.270484\pi\)
\(710\) 0 0
\(711\) 4.00000i 0.150012i
\(712\) 30.0000 1.12430
\(713\) −16.0000 −0.599205
\(714\) 4.00000 + 16.0000i 0.149696 + 0.598785i
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) 8.00000i 0.298765i
\(718\) 32.0000 1.19423
\(719\) 36.0000i 1.34257i −0.741198 0.671287i \(-0.765742\pi\)
0.741198 0.671287i \(-0.234258\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) 16.0000 0.595046
\(724\) 8.00000i 0.297318i
\(725\) 0 0
\(726\) 5.00000i 0.185567i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 24.0000i 0.889499i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −4.00000 16.0000i −0.147945 0.591781i
\(732\) −8.00000 −0.295689
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 12.0000i 0.442928i
\(735\) 0 0
\(736\) 20.0000i 0.737210i
\(737\) 48.0000i 1.76810i
\(738\) 8.00000i 0.294484i
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 0 0
\(741\) 8.00000i 0.293887i
\(742\) 24.0000i 0.881068i
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) −12.0000 −0.439941
\(745\) 0 0
\(746\) 26.0000 0.951928
\(747\) −12.0000 −0.439057
\(748\) 16.0000 4.00000i 0.585018 0.146254i
\(749\) −48.0000 −1.75388
\(750\) 0 0
\(751\) 20.0000i 0.729810i −0.931045 0.364905i \(-0.881101\pi\)
0.931045 0.364905i \(-0.118899\pi\)
\(752\) 8.00000 0.291730
\(753\) 12.0000i 0.437304i
\(754\) 0 0
\(755\) 0 0
\(756\) 4.00000 0.145479
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 20.0000i 0.726433i
\(759\) 16.0000i 0.580763i
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 8.00000i 0.289809i
\(763\) 32.0000 1.15848
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) −24.0000 −0.866590
\(768\) 17.0000i 0.613435i
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) 2.00000i 0.0720282i
\(772\) 0 0
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 4.00000 0.143777
\(775\) 20.0000i 0.718421i
\(776\) 48.0000i 1.72310i
\(777\) 32.0000i 1.14799i
\(778\) −6.00000 −0.215110
\(779\) 32.0000i 1.14652i
\(780\) 0 0
\(781\) −48.0000 −1.71758
\(782\) 16.0000 4.00000i 0.572159 0.143040i
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 0 0
\(786\) −4.00000 −0.142675
\(787\) 12.0000i 0.427754i −0.976861 0.213877i \(-0.931391\pi\)
0.976861 0.213877i \(-0.0686091\pi\)
\(788\) 16.0000i 0.569976i
\(789\) 24.0000i 0.854423i
\(790\) 0 0
\(791\) −32.0000 −1.13779
\(792\) 12.0000i 0.426401i
\(793\) 16.0000i 0.568177i
\(794\) 8.00000i 0.283909i
\(795\) 0 0
\(796\) 20.0000i 0.708881i
\(797\) −18.0000 −0.637593 −0.318796