Properties

Label 1280.2.o.o.383.1
Level $1280$
Weight $2$
Character 1280.383
Analytic conductor $10.221$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1280.o (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.2208514587\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 383.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1280.383
Dual form 1280.2.o.o.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.00000 + 2.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{7} +5.00000i q^{9} +O(q^{10})\) \(q+(2.00000 + 2.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{7} +5.00000i q^{9} +(1.00000 - 1.00000i) q^{13} +(-6.00000 + 2.00000i) q^{15} +(-5.00000 + 5.00000i) q^{17} +4.00000i q^{19} -8.00000i q^{21} +(-2.00000 + 2.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} -4.00000 q^{29} +4.00000i q^{31} +(6.00000 - 2.00000i) q^{35} +(-1.00000 - 1.00000i) q^{37} +4.00000 q^{39} +(6.00000 + 6.00000i) q^{43} +(-10.0000 - 5.00000i) q^{45} +(-2.00000 - 2.00000i) q^{47} +1.00000i q^{49} -20.0000 q^{51} +(-7.00000 + 7.00000i) q^{53} +(-8.00000 + 8.00000i) q^{57} -4.00000i q^{59} -4.00000i q^{61} +(10.0000 - 10.0000i) q^{63} +(1.00000 + 3.00000i) q^{65} +(10.0000 - 10.0000i) q^{67} -8.00000 q^{69} +12.0000i q^{71} +(3.00000 + 3.00000i) q^{73} +(2.00000 - 14.0000i) q^{75} +16.0000 q^{79} -1.00000 q^{81} +(-2.00000 - 2.00000i) q^{83} +(-5.00000 - 15.0000i) q^{85} +(-8.00000 - 8.00000i) q^{87} -4.00000 q^{91} +(-8.00000 + 8.00000i) q^{93} +(-8.00000 - 4.00000i) q^{95} +(-3.00000 + 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{3} - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 2q + 4q^{3} - 2q^{5} - 4q^{7} + 2q^{13} - 12q^{15} - 10q^{17} - 4q^{23} - 6q^{25} - 8q^{27} - 8q^{29} + 12q^{35} - 2q^{37} + 8q^{39} + 12q^{43} - 20q^{45} - 4q^{47} - 40q^{51} - 14q^{53} - 16q^{57} + 20q^{63} + 2q^{65} + 20q^{67} - 16q^{69} + 6q^{73} + 4q^{75} + 32q^{79} - 2q^{81} - 4q^{83} - 10q^{85} - 16q^{87} - 8q^{91} - 16q^{93} - 16q^{95} - 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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
\(3\) 2.00000 + 2.00000i 1.15470 + 1.15470i 0.985599 + 0.169102i \(0.0540867\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) 0 0
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) −2.00000 2.00000i −0.755929 0.755929i 0.219650 0.975579i \(-0.429509\pi\)
−0.975579 + 0.219650i \(0.929509\pi\)
\(8\) 0 0
\(9\) 5.00000i 1.66667i
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i \(-0.687167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) −6.00000 + 2.00000i −1.54919 + 0.516398i
\(16\) 0 0
\(17\) −5.00000 + 5.00000i −1.21268 + 1.21268i −0.242536 + 0.970143i \(0.577979\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 0 0
\(21\) 8.00000i 1.74574i
\(22\) 0 0
\(23\) −2.00000 + 2.00000i −0.417029 + 0.417029i −0.884178 0.467150i \(-0.845281\pi\)
0.467150 + 0.884178i \(0.345281\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) −4.00000 + 4.00000i −0.769800 + 0.769800i
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 4.00000i 0.718421i 0.933257 + 0.359211i \(0.116954\pi\)
−0.933257 + 0.359211i \(0.883046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.00000 2.00000i 1.01419 0.338062i
\(36\) 0 0
\(37\) −1.00000 1.00000i −0.164399 0.164399i 0.620113 0.784512i \(-0.287087\pi\)
−0.784512 + 0.620113i \(0.787087\pi\)
\(38\) 0 0
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 6.00000 + 6.00000i 0.914991 + 0.914991i 0.996660 0.0816682i \(-0.0260248\pi\)
−0.0816682 + 0.996660i \(0.526025\pi\)
\(44\) 0 0
\(45\) −10.0000 5.00000i −1.49071 0.745356i
\(46\) 0 0
\(47\) −2.00000 2.00000i −0.291730 0.291730i 0.546033 0.837763i \(-0.316137\pi\)
−0.837763 + 0.546033i \(0.816137\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −20.0000 −2.80056
\(52\) 0 0
\(53\) −7.00000 + 7.00000i −0.961524 + 0.961524i −0.999287 0.0377628i \(-0.987977\pi\)
0.0377628 + 0.999287i \(0.487977\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −8.00000 + 8.00000i −1.05963 + 1.05963i
\(58\) 0 0
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) 0 0
\(61\) 4.00000i 0.512148i −0.966657 0.256074i \(-0.917571\pi\)
0.966657 0.256074i \(-0.0824290\pi\)
\(62\) 0 0
\(63\) 10.0000 10.0000i 1.25988 1.25988i
\(64\) 0 0
\(65\) 1.00000 + 3.00000i 0.124035 + 0.372104i
\(66\) 0 0
\(67\) 10.0000 10.0000i 1.22169 1.22169i 0.254665 0.967029i \(-0.418035\pi\)
0.967029 0.254665i \(-0.0819652\pi\)
\(68\) 0 0
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 0 0
\(73\) 3.00000 + 3.00000i 0.351123 + 0.351123i 0.860527 0.509404i \(-0.170134\pi\)
−0.509404 + 0.860527i \(0.670134\pi\)
\(74\) 0 0
\(75\) 2.00000 14.0000i 0.230940 1.61658i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −2.00000 2.00000i −0.219529 0.219529i 0.588771 0.808300i \(-0.299612\pi\)
−0.808300 + 0.588771i \(0.799612\pi\)
\(84\) 0 0
\(85\) −5.00000 15.0000i −0.542326 1.62698i
\(86\) 0 0
\(87\) −8.00000 8.00000i −0.857690 0.857690i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) −8.00000 + 8.00000i −0.829561 + 0.829561i
\(94\) 0 0
\(95\) −8.00000 4.00000i −0.820783 0.410391i
\(96\) 0 0
\(97\) −3.00000 + 3.00000i −0.304604 + 0.304604i −0.842812 0.538208i \(-0.819101\pi\)
0.538208 + 0.842812i \(0.319101\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.00000i 0.597022i 0.954406 + 0.298511i \(0.0964900\pi\)
−0.954406 + 0.298511i \(0.903510\pi\)
\(102\) 0 0
\(103\) 6.00000 6.00000i 0.591198 0.591198i −0.346757 0.937955i \(-0.612717\pi\)
0.937955 + 0.346757i \(0.112717\pi\)
\(104\) 0 0
\(105\) 16.0000 + 8.00000i 1.56144 + 0.780720i
\(106\) 0 0
\(107\) 6.00000 6.00000i 0.580042 0.580042i −0.354873 0.934915i \(-0.615476\pi\)
0.934915 + 0.354873i \(0.115476\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 4.00000i 0.379663i
\(112\) 0 0
\(113\) −9.00000 9.00000i −0.846649 0.846649i 0.143065 0.989713i \(-0.454304\pi\)
−0.989713 + 0.143065i \(0.954304\pi\)
\(114\) 0 0
\(115\) −2.00000 6.00000i −0.186501 0.559503i
\(116\) 0 0
\(117\) 5.00000 + 5.00000i 0.462250 + 0.462250i
\(118\) 0 0
\(119\) 20.0000 1.83340
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 10.0000 + 10.0000i 0.887357 + 0.887357i 0.994268 0.106912i \(-0.0340963\pi\)
−0.106912 + 0.994268i \(0.534096\pi\)
\(128\) 0 0
\(129\) 24.0000i 2.11308i
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 0 0
\(133\) 8.00000 8.00000i 0.693688 0.693688i
\(134\) 0 0
\(135\) −4.00000 12.0000i −0.344265 1.03280i
\(136\) 0 0
\(137\) −1.00000 + 1.00000i −0.0854358 + 0.0854358i −0.748533 0.663097i \(-0.769242\pi\)
0.663097 + 0.748533i \(0.269242\pi\)
\(138\) 0 0
\(139\) 12.0000i 1.01783i 0.860818 + 0.508913i \(0.169953\pi\)
−0.860818 + 0.508913i \(0.830047\pi\)
\(140\) 0 0
\(141\) 8.00000i 0.673722i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.00000 8.00000i 0.332182 0.664364i
\(146\) 0 0
\(147\) −2.00000 + 2.00000i −0.164957 + 0.164957i
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) 12.0000i 0.976546i 0.872691 + 0.488273i \(0.162373\pi\)
−0.872691 + 0.488273i \(0.837627\pi\)
\(152\) 0 0
\(153\) −25.0000 25.0000i −2.02113 2.02113i
\(154\) 0 0
\(155\) −8.00000 4.00000i −0.642575 0.321288i
\(156\) 0 0
\(157\) −9.00000 9.00000i −0.718278 0.718278i 0.249974 0.968252i \(-0.419578\pi\)
−0.968252 + 0.249974i \(0.919578\pi\)
\(158\) 0 0
\(159\) −28.0000 −2.22054
\(160\) 0 0
\(161\) 8.00000 0.630488
\(162\) 0 0
\(163\) 2.00000 + 2.00000i 0.156652 + 0.156652i 0.781081 0.624429i \(-0.214668\pi\)
−0.624429 + 0.781081i \(0.714668\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 + 2.00000i 0.154765 + 0.154765i 0.780242 0.625478i \(-0.215096\pi\)
−0.625478 + 0.780242i \(0.715096\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) −20.0000 −1.52944
\(172\) 0 0
\(173\) −13.0000 + 13.0000i −0.988372 + 0.988372i −0.999933 0.0115615i \(-0.996320\pi\)
0.0115615 + 0.999933i \(0.496320\pi\)
\(174\) 0 0
\(175\) −2.00000 + 14.0000i −0.151186 + 1.05830i
\(176\) 0 0
\(177\) 8.00000 8.00000i 0.601317 0.601317i
\(178\) 0 0
\(179\) 12.0000i 0.896922i 0.893802 + 0.448461i \(0.148028\pi\)
−0.893802 + 0.448461i \(0.851972\pi\)
\(180\) 0 0
\(181\) 10.0000i 0.743294i 0.928374 + 0.371647i \(0.121207\pi\)
−0.928374 + 0.371647i \(0.878793\pi\)
\(182\) 0 0
\(183\) 8.00000 8.00000i 0.591377 0.591377i
\(184\) 0 0
\(185\) 3.00000 1.00000i 0.220564 0.0735215i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 16.0000 1.16383
\(190\) 0 0
\(191\) 20.0000i 1.44715i 0.690246 + 0.723575i \(0.257502\pi\)
−0.690246 + 0.723575i \(0.742498\pi\)
\(192\) 0 0
\(193\) −5.00000 5.00000i −0.359908 0.359908i 0.503871 0.863779i \(-0.331909\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 0 0
\(195\) −4.00000 + 8.00000i −0.286446 + 0.572892i
\(196\) 0 0
\(197\) −5.00000 5.00000i −0.356235 0.356235i 0.506188 0.862423i \(-0.331054\pi\)
−0.862423 + 0.506188i \(0.831054\pi\)
\(198\) 0 0
\(199\) −24.0000 −1.70131 −0.850657 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 0 0
\(201\) 40.0000 2.82138
\(202\) 0 0
\(203\) 8.00000 + 8.00000i 0.561490 + 0.561490i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −10.0000 10.0000i −0.695048 0.695048i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 0 0
\(213\) −24.0000 + 24.0000i −1.64445 + 1.64445i
\(214\) 0 0
\(215\) −18.0000 + 6.00000i −1.22759 + 0.409197i
\(216\) 0 0
\(217\) 8.00000 8.00000i 0.543075 0.543075i
\(218\) 0 0
\(219\) 12.0000i 0.810885i
\(220\) 0 0
\(221\) 10.0000i 0.672673i
\(222\) 0 0
\(223\) −10.0000 + 10.0000i −0.669650 + 0.669650i −0.957635 0.287985i \(-0.907015\pi\)
0.287985 + 0.957635i \(0.407015\pi\)
\(224\) 0 0
\(225\) 20.0000 15.0000i 1.33333 1.00000i
\(226\) 0 0
\(227\) −10.0000 + 10.0000i −0.663723 + 0.663723i −0.956256 0.292532i \(-0.905502\pi\)
0.292532 + 0.956256i \(0.405502\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.00000 + 5.00000i 0.327561 + 0.327561i 0.851658 0.524097i \(-0.175597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 0 0
\(235\) 6.00000 2.00000i 0.391397 0.130466i
\(236\) 0 0
\(237\) 32.0000 + 32.0000i 2.07862 + 2.07862i
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −16.0000 −1.03065 −0.515325 0.856995i \(-0.672329\pi\)
−0.515325 + 0.856995i \(0.672329\pi\)
\(242\) 0 0
\(243\) 10.0000 + 10.0000i 0.641500 + 0.641500i
\(244\) 0 0
\(245\) −2.00000 1.00000i −0.127775 0.0638877i
\(246\) 0 0
\(247\) 4.00000 + 4.00000i 0.254514 + 0.254514i
\(248\) 0 0
\(249\) 8.00000i 0.506979i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 20.0000 40.0000i 1.25245 2.50490i
\(256\) 0 0
\(257\) 7.00000 7.00000i 0.436648 0.436648i −0.454234 0.890882i \(-0.650087\pi\)
0.890882 + 0.454234i \(0.150087\pi\)
\(258\) 0 0
\(259\) 4.00000i 0.248548i
\(260\) 0 0
\(261\) 20.0000i 1.23797i
\(262\) 0 0
\(263\) −6.00000 + 6.00000i −0.369976 + 0.369976i −0.867468 0.497492i \(-0.834254\pi\)
0.497492 + 0.867468i \(0.334254\pi\)
\(264\) 0 0
\(265\) −7.00000 21.0000i −0.430007 1.29002i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) 20.0000i 1.21491i −0.794353 0.607457i \(-0.792190\pi\)
0.794353 0.607457i \(-0.207810\pi\)
\(272\) 0 0
\(273\) −8.00000 8.00000i −0.484182 0.484182i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 9.00000 + 9.00000i 0.540758 + 0.540758i 0.923751 0.382993i \(-0.125107\pi\)
−0.382993 + 0.923751i \(0.625107\pi\)
\(278\) 0 0
\(279\) −20.0000 −1.19737
\(280\) 0 0
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 0 0
\(283\) −6.00000 6.00000i −0.356663 0.356663i 0.505918 0.862581i \(-0.331154\pi\)
−0.862581 + 0.505918i \(0.831154\pi\)
\(284\) 0 0
\(285\) −8.00000 24.0000i −0.473879 1.42164i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 33.0000i 1.94118i
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) 0 0
\(293\) −5.00000 + 5.00000i −0.292103 + 0.292103i −0.837911 0.545807i \(-0.816223\pi\)
0.545807 + 0.837911i \(0.316223\pi\)
\(294\) 0 0
\(295\) 8.00000 + 4.00000i 0.465778 + 0.232889i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.00000i 0.231326i
\(300\) 0 0
\(301\) 24.0000i 1.38334i
\(302\) 0 0
\(303\) −12.0000 + 12.0000i −0.689382 + 0.689382i
\(304\) 0 0
\(305\) 8.00000 + 4.00000i 0.458079 + 0.229039i
\(306\) 0 0
\(307\) 10.0000 10.0000i 0.570730 0.570730i −0.361602 0.932332i \(-0.617770\pi\)
0.932332 + 0.361602i \(0.117770\pi\)
\(308\) 0 0
\(309\) 24.0000 1.36531
\(310\) 0 0
\(311\) 28.0000i 1.58773i −0.608091 0.793867i \(-0.708065\pi\)
0.608091 0.793867i \(-0.291935\pi\)
\(312\) 0 0
\(313\) −15.0000 15.0000i −0.847850 0.847850i 0.142014 0.989865i \(-0.454642\pi\)
−0.989865 + 0.142014i \(0.954642\pi\)
\(314\) 0 0
\(315\) 10.0000 + 30.0000i 0.563436 + 1.69031i
\(316\) 0 0
\(317\) 11.0000 + 11.0000i 0.617822 + 0.617822i 0.944972 0.327151i \(-0.106088\pi\)
−0.327151 + 0.944972i \(0.606088\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) −20.0000 20.0000i −1.11283 1.11283i
\(324\) 0 0
\(325\) −7.00000 1.00000i −0.388290 0.0554700i
\(326\) 0 0
\(327\) 20.0000 + 20.0000i 1.10600 + 1.10600i
\(328\) 0 0
\(329\) 8.00000i 0.441054i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 5.00000 5.00000i 0.273998 0.273998i
\(334\) 0 0
\(335\) 10.0000 + 30.0000i 0.546358 + 1.63908i
\(336\) 0 0
\(337\) −23.0000 + 23.0000i −1.25289 + 1.25289i −0.298471 + 0.954419i \(0.596477\pi\)
−0.954419 + 0.298471i \(0.903523\pi\)
\(338\) 0 0
\(339\) 36.0000i 1.95525i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 0 0
\(345\) 8.00000 16.0000i 0.430706 0.861411i
\(346\) 0 0
\(347\) 18.0000 18.0000i 0.966291 0.966291i −0.0331594 0.999450i \(-0.510557\pi\)
0.999450 + 0.0331594i \(0.0105569\pi\)
\(348\) 0 0
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 0 0
\(351\) 8.00000i 0.427008i
\(352\) 0 0
\(353\) 9.00000 + 9.00000i 0.479022 + 0.479022i 0.904819 0.425797i \(-0.140006\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) 0 0
\(355\) −24.0000 12.0000i −1.27379 0.636894i
\(356\) 0 0
\(357\) 40.0000 + 40.0000i 2.11702 + 2.11702i
\(358\) 0 0
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 0 0
\(363\) −22.0000 22.0000i −1.15470 1.15470i
\(364\) 0 0
\(365\) −9.00000 + 3.00000i −0.471082 + 0.157027i
\(366\) 0 0
\(367\) −22.0000 22.0000i −1.14839 1.14839i −0.986869 0.161521i \(-0.948360\pi\)
−0.161521 0.986869i \(-0.551640\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 28.0000 1.45369
\(372\) 0 0
\(373\) 21.0000 21.0000i 1.08734 1.08734i 0.0915371 0.995802i \(-0.470822\pi\)
0.995802 0.0915371i \(-0.0291780\pi\)
\(374\) 0 0
\(375\) 26.0000 + 18.0000i 1.34263 + 0.929516i
\(376\) 0 0
\(377\) −4.00000 + 4.00000i −0.206010 + 0.206010i
\(378\) 0 0
\(379\) 28.0000i 1.43826i −0.694874 0.719132i \(-0.744540\pi\)
0.694874 0.719132i \(-0.255460\pi\)
\(380\) 0 0
\(381\) 40.0000i 2.04926i
\(382\) 0 0
\(383\) 22.0000 22.0000i 1.12415 1.12415i 0.133036 0.991111i \(-0.457527\pi\)
0.991111 0.133036i \(-0.0424727\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −30.0000 + 30.0000i −1.52499 + 1.52499i
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 20.0000i 1.01144i
\(392\) 0 0
\(393\) 16.0000 + 16.0000i 0.807093 + 0.807093i
\(394\) 0 0
\(395\) −16.0000 + 32.0000i −0.805047 + 1.61009i
\(396\) 0 0
\(397\) 13.0000 + 13.0000i 0.652451 + 0.652451i 0.953583 0.301131i \(-0.0973643\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 0 0
\(399\) 32.0000 1.60200
\(400\) 0 0
\(401\) 34.0000 1.69788 0.848939 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) 0 0
\(403\) 4.00000 + 4.00000i 0.199254 + 0.199254i
\(404\) 0 0
\(405\) 1.00000 2.00000i 0.0496904 0.0993808i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 2.00000i 0.0988936i 0.998777 + 0.0494468i \(0.0157458\pi\)
−0.998777 + 0.0494468i \(0.984254\pi\)
\(410\) 0 0
\(411\) −4.00000 −0.197305
\(412\) 0 0
\(413\) −8.00000 + 8.00000i −0.393654 + 0.393654i
\(414\) 0 0
\(415\) 6.00000 2.00000i 0.294528 0.0981761i
\(416\) 0 0
\(417\) −24.0000 + 24.0000i −1.17529 + 1.17529i
\(418\) 0 0
\(419\) 12.0000i 0.586238i −0.956076 0.293119i \(-0.905307\pi\)
0.956076 0.293119i \(-0.0946933\pi\)
\(420\) 0 0
\(421\) 20.0000i 0.974740i −0.873195 0.487370i \(-0.837956\pi\)
0.873195 0.487370i \(-0.162044\pi\)
\(422\) 0 0
\(423\) 10.0000 10.0000i 0.486217 0.486217i
\(424\) 0 0
\(425\) 35.0000 + 5.00000i 1.69775 + 0.242536i
\(426\) 0 0
\(427\) −8.00000 + 8.00000i −0.387147 + 0.387147i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.00000i 0.192673i −0.995349 0.0963366i \(-0.969287\pi\)
0.995349 0.0963366i \(-0.0307125\pi\)
\(432\) 0 0
\(433\) −19.0000 19.0000i −0.913082 0.913082i 0.0834318 0.996513i \(-0.473412\pi\)
−0.996513 + 0.0834318i \(0.973412\pi\)
\(434\) 0 0
\(435\) 24.0000 8.00000i 1.15071 0.383571i
\(436\) 0 0
\(437\) −8.00000 8.00000i −0.382692 0.382692i
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) −5.00000 −0.238095
\(442\) 0 0
\(443\) −22.0000 22.0000i −1.04525 1.04525i −0.998926 0.0463251i \(-0.985249\pi\)
−0.0463251 0.998926i \(-0.514751\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 36.0000 + 36.0000i 1.70274 + 1.70274i
\(448\) 0 0
\(449\) 26.0000i 1.22702i 0.789689 + 0.613508i \(0.210242\pi\)
−0.789689 + 0.613508i \(0.789758\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −24.0000 + 24.0000i −1.12762 + 1.12762i
\(454\) 0 0
\(455\) 4.00000 8.00000i 0.187523 0.375046i
\(456\) 0 0
\(457\) −15.0000 + 15.0000i −0.701670 + 0.701670i −0.964769 0.263099i \(-0.915256\pi\)
0.263099 + 0.964769i \(0.415256\pi\)
\(458\) 0 0
\(459\) 40.0000i 1.86704i
\(460\) 0 0
\(461\) 14.0000i 0.652045i −0.945362 0.326023i \(-0.894291\pi\)
0.945362 0.326023i \(-0.105709\pi\)
\(462\) 0 0
\(463\) −22.0000 + 22.0000i −1.02243 + 1.02243i −0.0226840 + 0.999743i \(0.507221\pi\)
−0.999743 + 0.0226840i \(0.992779\pi\)
\(464\) 0 0
\(465\) −8.00000 24.0000i −0.370991 1.11297i
\(466\) 0 0
\(467\) −2.00000 + 2.00000i −0.0925490 + 0.0925490i −0.751865 0.659317i \(-0.770846\pi\)
0.659317 + 0.751865i \(0.270846\pi\)
\(468\) 0 0
\(469\) −40.0000 −1.84703
\(470\) 0 0
\(471\) 36.0000i 1.65879i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 16.0000 12.0000i 0.734130 0.550598i
\(476\) 0 0
\(477\) −35.0000 35.0000i −1.60254 1.60254i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 0 0
\(483\) 16.0000 + 16.0000i 0.728025 + 0.728025i
\(484\) 0 0
\(485\) −3.00000 9.00000i −0.136223 0.408669i
\(486\) 0 0
\(487\) 6.00000 + 6.00000i 0.271886 + 0.271886i 0.829859 0.557973i \(-0.188421\pi\)
−0.557973 + 0.829859i \(0.688421\pi\)
\(488\) 0 0
\(489\) 8.00000i 0.361773i
\(490\) 0 0
\(491\) 16.0000 0.722070 0.361035 0.932552i \(-0.382424\pi\)
0.361035 + 0.932552i \(0.382424\pi\)
\(492\) 0 0
\(493\) 20.0000 20.0000i 0.900755 0.900755i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 24.0000i 1.07655 1.07655i
\(498\) 0 0
\(499\) 4.00000i 0.179065i 0.995984 + 0.0895323i \(0.0285372\pi\)
−0.995984 + 0.0895323i \(0.971463\pi\)
\(500\) 0 0
\(501\) 8.00000i 0.357414i
\(502\) 0 0
\(503\) −10.0000 + 10.0000i −0.445878 + 0.445878i −0.893982 0.448104i \(-0.852100\pi\)
0.448104 + 0.893982i \(0.352100\pi\)
\(504\) 0 0
\(505\) −12.0000 6.00000i −0.533993 0.266996i
\(506\) 0 0
\(507\) −22.0000 + 22.0000i −0.977054 + 0.977054i
\(508\) 0 0
\(509\) 36.0000 1.59567 0.797836 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) 12.0000i 0.530849i
\(512\) 0 0
\(513\) −16.0000 16.0000i −0.706417 0.706417i
\(514\) 0 0
\(515\) 6.00000 + 18.0000i 0.264392 + 0.793175i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −52.0000 −2.28255
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −14.0000 14.0000i −0.612177 0.612177i 0.331336 0.943513i \(-0.392501\pi\)
−0.943513 + 0.331336i \(0.892501\pi\)
\(524\) 0 0
\(525\) −32.0000 + 24.0000i −1.39659 + 1.04745i
\(526\) 0 0
\(527\) −20.0000 20.0000i −0.871214 0.871214i
\(528\) 0 0
\(529\) 15.0000i 0.652174i
\(530\) 0 0
\(531\) 20.0000 0.867926
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 6.00000 + 18.0000i 0.259403 + 0.778208i
\(536\) 0 0
\(537\) −24.0000 + 24.0000i −1.03568 + 1.03568i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 30.0000i 1.28980i −0.764267 0.644900i \(-0.776899\pi\)
0.764267 0.644900i \(-0.223101\pi\)
\(542\) 0 0
\(543\) −20.0000 + 20.0000i −0.858282 + 0.858282i
\(544\) 0 0
\(545\) −10.0000 + 20.0000i −0.428353 + 0.856706i
\(546\) 0 0
\(547\) 6.00000 6.00000i 0.256541 0.256541i −0.567104 0.823646i \(-0.691936\pi\)
0.823646 + 0.567104i \(0.191936\pi\)
\(548\) 0 0
\(549\) 20.0000 0.853579
\(550\) 0 0
\(551\) 16.0000i 0.681623i
\(552\) 0 0
\(553\) −32.0000 32.0000i −1.36078 1.36078i
\(554\) 0 0
\(555\) 8.00000 + 4.00000i 0.339581 + 0.169791i
\(556\) 0 0
\(557\) −15.0000 15.0000i −0.635570 0.635570i 0.313889 0.949460i \(-0.398368\pi\)
−0.949460 + 0.313889i \(0.898368\pi\)
\(558\) 0 0
\(559\) 12.0000 0.507546
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.00000 6.00000i −0.252870 0.252870i 0.569276 0.822146i \(-0.307223\pi\)
−0.822146 + 0.569276i \(0.807223\pi\)
\(564\) 0 0
\(565\) 27.0000 9.00000i 1.13590 0.378633i
\(566\) 0 0
\(567\) 2.00000 + 2.00000i 0.0839921 + 0.0839921i
\(568\) 0 0
\(569\) 2.00000i 0.0838444i −0.999121 0.0419222i \(-0.986652\pi\)
0.999121 0.0419222i \(-0.0133482\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) −40.0000 + 40.0000i −1.67102 + 1.67102i
\(574\) 0 0
\(575\) 14.0000 + 2.00000i 0.583840 + 0.0834058i
\(576\) 0 0
\(577\) 15.0000 15.0000i 0.624458 0.624458i −0.322210 0.946668i \(-0.604426\pi\)
0.946668 + 0.322210i \(0.104426\pi\)
\(578\) 0 0
\(579\) 20.0000i 0.831172i
\(580\) 0 0
\(581\) 8.00000i 0.331896i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −15.0000 + 5.00000i −0.620174 + 0.206725i
\(586\) 0 0
\(587\) −14.0000 + 14.0000i −0.577842 + 0.577842i −0.934308 0.356466i \(-0.883981\pi\)
0.356466 + 0.934308i \(0.383981\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) 20.0000i 0.822690i
\(592\) 0 0
\(593\) 1.00000 + 1.00000i 0.0410651 + 0.0410651i 0.727341 0.686276i \(-0.240756\pi\)
−0.686276 + 0.727341i \(0.740756\pi\)
\(594\) 0 0
\(595\) −20.0000 + 40.0000i −0.819920 + 1.63984i
\(596\) 0 0
\(597\) −48.0000 48.0000i −1.96451 1.96451i
\(598\) 0 0
\(599\) 8.00000 0.326871 0.163436 0.986554i \(-0.447742\pi\)
0.163436 + 0.986554i \(0.447742\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) 50.0000 + 50.0000i 2.03616 + 2.03616i
\(604\) 0 0
\(605\) 11.0000 22.0000i 0.447214 0.894427i
\(606\) 0 0
\(607\) −18.0000 18.0000i −0.730597 0.730597i 0.240141 0.970738i \(-0.422806\pi\)
−0.970738 + 0.240141i \(0.922806\pi\)
\(608\) 0 0
\(609\) 32.0000i 1.29671i
\(610\) 0 0
\(611\) −4.00000 −0.161823
\(612\) 0 0
\(613\) −9.00000 + 9.00000i −0.363507 + 0.363507i −0.865102 0.501596i \(-0.832747\pi\)
0.501596 + 0.865102i \(0.332747\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29.0000 29.0000i 1.16750 1.16750i 0.184701 0.982795i \(-0.440868\pi\)
0.982795 0.184701i \(-0.0591318\pi\)
\(618\) 0 0
\(619\) 28.0000i 1.12542i 0.826656 + 0.562708i \(0.190240\pi\)
−0.826656 + 0.562708i \(0.809760\pi\)
\(620\) 0 0
\(621\) 16.0000i 0.642058i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 4.00000i 0.159237i 0.996825 + 0.0796187i \(0.0253703\pi\)
−0.996825 + 0.0796187i \(0.974630\pi\)
\(632\) 0 0
\(633\) 32.0000 + 32.0000i 1.27189 + 1.27189i
\(634\) 0 0
\(635\) −30.0000 + 10.0000i −1.19051 + 0.396838i
\(636\) 0 0
\(637\) 1.00000 + 1.00000i 0.0396214 + 0.0396214i
\(638\) 0 0
\(639\) −60.0000 −2.37356
\(640\) 0 0
\(641\) −48.0000 −1.89589 −0.947943 0.318440i \(-0.896841\pi\)
−0.947943 + 0.318440i \(0.896841\pi\)
\(642\) 0 0
\(643\) −10.0000 10.0000i −0.394362 0.394362i 0.481877 0.876239i \(-0.339955\pi\)
−0.876239 + 0.481877i \(0.839955\pi\)
\(644\) 0 0
\(645\) −48.0000 24.0000i −1.89000 0.944999i
\(646\) 0 0
\(647\) −10.0000 10.0000i −0.393141 0.393141i 0.482665 0.875805i \(-0.339669\pi\)
−0.875805 + 0.482665i \(0.839669\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 32.0000 1.25418
\(652\) 0 0
\(653\) −1.00000 + 1.00000i −0.0391330 + 0.0391330i −0.726403 0.687270i \(-0.758809\pi\)
0.687270 + 0.726403i \(0.258809\pi\)
\(654\) 0 0
\(655\) −8.00000 + 16.0000i −0.312586 + 0.625172i
\(656\) 0 0
\(657\) −15.0000 + 15.0000i −0.585206 + 0.585206i
\(658\) 0 0
\(659\) 20.0000i 0.779089i 0.921008 + 0.389545i \(0.127368\pi\)
−0.921008 + 0.389545i \(0.872632\pi\)
\(660\) 0 0
\(661\) 12.0000i 0.466746i −0.972387 0.233373i \(-0.925024\pi\)
0.972387 0.233373i \(-0.0749763\pi\)
\(662\) 0 0
\(663\) −20.0000 + 20.0000i −0.776736 + 0.776736i
\(664\) 0 0
\(665\) 8.00000 + 24.0000i 0.310227 + 0.930680i
\(666\) 0 0
\(667\) 8.00000 8.00000i 0.309761 0.309761i
\(668\) 0 0
\(669\) −40.0000 −1.54649
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 5.00000 + 5.00000i 0.192736 + 0.192736i 0.796877 0.604141i \(-0.206484\pi\)
−0.604141 + 0.796877i \(0.706484\pi\)
\(674\) 0 0
\(675\) 28.0000 + 4.00000i 1.07772 + 0.153960i
\(676\) 0 0
\(677\) 3.00000 + 3.00000i 0.115299 + 0.115299i 0.762402 0.647103i \(-0.224020\pi\)
−0.647103 + 0.762402i \(0.724020\pi\)
\(678\) 0 0
\(679\) 12.0000 0.460518
\(680\) 0 0
\(681\) −40.0000 −1.53280
\(682\) 0 0
\(683\) 22.0000 + 22.0000i 0.841807 + 0.841807i 0.989094 0.147287i \(-0.0470541\pi\)
−0.147287 + 0.989094i \(0.547054\pi\)
\(684\) 0 0
\(685\) −1.00000 3.00000i −0.0382080 0.114624i
\(686\) 0 0
\(687\) 40.0000 + 40.0000i 1.52610 + 1.52610i
\(688\) 0 0
\(689\) 14.0000i 0.533358i
\(690\) 0 0
\(691\) −32.0000 −1.21734 −0.608669 0.793424i \(-0.708296\pi\)
−0.608669 + 0.793424i \(0.708296\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.0000 12.0000i −0.910372 0.455186i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 20.0000i 0.756469i
\(700\) 0 0
\(701\) 20.0000i 0.755390i 0.925930 + 0.377695i \(0.123283\pi\)
−0.925930 + 0.377695i \(0.876717\pi\)
\(702\) 0 0
\(703\) 4.00000 4.00000i 0.150863 0.150863i
\(704\) 0 0
\(705\) 16.0000 + 8.00000i 0.602595 + 0.301297i
\(706\) 0 0
\(707\) 12.0000 12.0000i 0.451306 0.451306i
\(708\) 0 0
\(709\) 12.0000 0.450669 0.225335 0.974281i \(-0.427652\pi\)
0.225335 + 0.974281i \(0.427652\pi\)
\(710\) 0 0
\(711\) 80.0000i 3.00023i
\(712\) 0 0
\(713\) −8.00000 8.00000i −0.299602 0.299602i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 16.0000 + 16.0000i 0.597531 + 0.597531i
\(718\) 0 0
\(719\) 8.00000 0.298350 0.149175 0.988811i \(-0.452338\pi\)
0.149175 + 0.988811i \(0.452338\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 0 0
\(723\) −32.0000 32.0000i −1.19009 1.19009i
\(724\) 0 0
\(725\) 12.0000 + 16.0000i 0.445669 + 0.594225i
\(726\) 0 0
\(727\) −18.0000 18.0000i −0.667583 0.667583i 0.289573 0.957156i \(-0.406487\pi\)
−0.957156 + 0.289573i \(0.906487\pi\)
\(728\) 0 0
\(729\) 43.0000i 1.59259i
\(730\) 0 0
\(731\) −60.0000 −2.21918
\(732\) 0 0
\(733\) −21.0000 + 21.0000i −0.775653 + 0.775653i −0.979088 0.203436i \(-0.934789\pi\)
0.203436 + 0.979088i \(0.434789\pi\)
\(734\) 0 0
\(735\) −2.00000 6.00000i −0.0737711 0.221313i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 44.0000i 1.61857i 0.587419 + 0.809283i \(0.300144\pi\)
−0.587419 + 0.809283i \(0.699856\pi\)
\(740\) 0 0
\(741\) 16.0000i 0.587775i
\(742\) 0 0
\(743\) −30.0000 + 30.0000i −1.10059 + 1.10059i −0.106254 + 0.994339i \(0.533886\pi\)
−0.994339 + 0.106254i \(0.966114\pi\)
\(744\) 0 0
\(745\) −18.0000 + 36.0000i −0.659469 + 1.31894i
\(746\) 0 0
\(747\) 10.0000 10.0000i 0.365881 0.365881i
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 44.0000i 1.60558i −0.596260 0.802791i \(-0.703347\pi\)
0.596260 0.802791i \(-0.296653\pi\)
\(752\) 0 0
\(753\) 48.0000 + 48.0000i 1.74922 + 1.74922i
\(754\) 0 0
\(755\) −24.0000 12.0000i −0.873449 0.436725i
\(756\) 0 0
\(757\) 1.00000 + 1.00000i 0.0363456 + 0.0363456i 0.725046 0.688700i \(-0.241818\pi\)
−0.688700 + 0.725046i \(0.741818\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 0 0
\(763\) −20.0000 20.0000i −0.724049 0.724049i
\(764\) 0 0
\(765\) 75.0000 25.0000i 2.71163 0.903877i
\(766\) 0 0
\(767\) −4.00000 4.00000i −0.144432 0.144432i
\(768\) 0 0
\(769\) 40.0000i 1.44244i −0.692708 0.721218i \(-0.743582\pi\)
0.692708 0.721218i \(-0.256418\pi\)
\(770\) 0 0
\(771\) 28.0000 1.00840
\(772\) 0 0
\(773\) −1.00000 + 1.00000i −0.0359675 + 0.0359675i −0.724862 0.688894i \(-0.758096\pi\)
0.688894 + 0.724862i \(0.258096\pi\)
\(774\) 0 0
\(775\) 16.0000 12.0000i 0.574737 0.431053i
\(776\) 0 0
\(777\) −8.00000 + 8.00000i −0.286998 + 0.286998i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 16.0000 16.0000i 0.571793 0.571793i
\(784\) 0 0
\(785\) 27.0000 9.00000i 0.963671 0.321224i
\(786\) 0 0
\(787\) −30.0000 + 30.0000i −1.06938 + 1.06938i −0.0719783 + 0.997406i \(0.522931\pi\)
−0.997406 + 0.0719783i \(0.977069\pi\)
\(788\) 0 0
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) 36.0000i 1.28001i
\(792\) 0 0
\(793\) −4.00000 4.00000i −0.142044 0.142044i
\(794\) 0 0
\(795\) 28.0000 56.0000i 0.993058 1.98612i
\(796\) 0 0
\(797\) −29.0000 29.0000i −1.02723 1.02723i −0.999619 0.0276140i \(-0.991209\pi\)
−0.0276140 0.999619i \(-0.508791\pi\)
\(798\) 0