Properties

Label 1280.2.n.c.767.1
Level $1280$
Weight $2$
Character 1280.767
Analytic conductor $10.221$
Analytic rank $1$
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.n (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.2208514587\)
Analytic rank: \(1\)
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: no (minimal twist has level 320)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 767.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1280.767
Dual form 1280.2.n.c.1023.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{3} +(-2.00000 + 1.00000i) q^{5} +(1.00000 - 1.00000i) q^{7} -1.00000i q^{9} +4.00000i q^{11} +(3.00000 - 3.00000i) q^{13} +(3.00000 + 1.00000i) q^{15} +(-3.00000 - 3.00000i) q^{17} -6.00000 q^{19} -2.00000 q^{21} +(3.00000 + 3.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +2.00000i q^{29} -6.00000i q^{31} +(4.00000 - 4.00000i) q^{33} +(-1.00000 + 3.00000i) q^{35} +(3.00000 + 3.00000i) q^{37} -6.00000 q^{39} -6.00000 q^{41} +(-3.00000 - 3.00000i) q^{43} +(1.00000 + 2.00000i) q^{45} +(-9.00000 + 9.00000i) q^{47} +5.00000i q^{49} +6.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-4.00000 - 8.00000i) q^{55} +(6.00000 + 6.00000i) q^{57} -10.0000 q^{59} -12.0000 q^{61} +(-1.00000 - 1.00000i) q^{63} +(-3.00000 + 9.00000i) q^{65} +(-9.00000 + 9.00000i) q^{67} -6.00000i q^{69} +6.00000i q^{71} +(-5.00000 + 5.00000i) q^{73} +(-7.00000 + 1.00000i) q^{75} +(4.00000 + 4.00000i) q^{77} +5.00000 q^{81} +(3.00000 + 3.00000i) q^{83} +(9.00000 + 3.00000i) q^{85} +(2.00000 - 2.00000i) q^{87} -6.00000i q^{91} +(-6.00000 + 6.00000i) q^{93} +(12.0000 - 6.00000i) q^{95} +(-7.00000 - 7.00000i) q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - 4q^{5} + 2q^{7} + O(q^{10}) \) \( 2q - 2q^{3} - 4q^{5} + 2q^{7} + 6q^{13} + 6q^{15} - 6q^{17} - 12q^{19} - 4q^{21} + 6q^{23} + 6q^{25} - 8q^{27} + 8q^{33} - 2q^{35} + 6q^{37} - 12q^{39} - 12q^{41} - 6q^{43} + 2q^{45} - 18q^{47} + 10q^{53} - 8q^{55} + 12q^{57} - 20q^{59} - 24q^{61} - 2q^{63} - 6q^{65} - 18q^{67} - 10q^{73} - 14q^{75} + 8q^{77} + 10q^{81} + 6q^{83} + 18q^{85} + 4q^{87} - 12q^{93} + 24q^{95} - 14q^{97} + 8q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −1.00000 1.00000i −0.577350 0.577350i 0.356822 0.934172i \(-0.383860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 0 0
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 0 0
\(7\) 1.00000 1.00000i 0.377964 0.377964i −0.492403 0.870367i \(-0.663881\pi\)
0.870367 + 0.492403i \(0.163881\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 4.00000i 1.20605i 0.797724 + 0.603023i \(0.206037\pi\)
−0.797724 + 0.603023i \(0.793963\pi\)
\(12\) 0 0
\(13\) 3.00000 3.00000i 0.832050 0.832050i −0.155747 0.987797i \(-0.549778\pi\)
0.987797 + 0.155747i \(0.0497784\pi\)
\(14\) 0 0
\(15\) 3.00000 + 1.00000i 0.774597 + 0.258199i
\(16\) 0 0
\(17\) −3.00000 3.00000i −0.727607 0.727607i 0.242536 0.970143i \(-0.422021\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 3.00000 + 3.00000i 0.625543 + 0.625543i 0.946943 0.321400i \(-0.104153\pi\)
−0.321400 + 0.946943i \(0.604153\pi\)
\(24\) 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
\(29\) 2.00000i 0.371391i 0.982607 + 0.185695i \(0.0594537\pi\)
−0.982607 + 0.185695i \(0.940546\pi\)
\(30\) 0 0
\(31\) 6.00000i 1.07763i −0.842424 0.538816i \(-0.818872\pi\)
0.842424 0.538816i \(-0.181128\pi\)
\(32\) 0 0
\(33\) 4.00000 4.00000i 0.696311 0.696311i
\(34\) 0 0
\(35\) −1.00000 + 3.00000i −0.169031 + 0.507093i
\(36\) 0 0
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −3.00000 3.00000i −0.457496 0.457496i 0.440337 0.897833i \(-0.354859\pi\)
−0.897833 + 0.440337i \(0.854859\pi\)
\(44\) 0 0
\(45\) 1.00000 + 2.00000i 0.149071 + 0.298142i
\(46\) 0 0
\(47\) −9.00000 + 9.00000i −1.31278 + 1.31278i −0.393431 + 0.919354i \(0.628712\pi\)
−0.919354 + 0.393431i \(0.871288\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 6.00000i 0.840168i
\(52\) 0 0
\(53\) 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i \(-0.588586\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 0 0
\(55\) −4.00000 8.00000i −0.539360 1.07872i
\(56\) 0 0
\(57\) 6.00000 + 6.00000i 0.794719 + 0.794719i
\(58\) 0 0
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) −12.0000 −1.53644 −0.768221 0.640184i \(-0.778858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) 0 0
\(63\) −1.00000 1.00000i −0.125988 0.125988i
\(64\) 0 0
\(65\) −3.00000 + 9.00000i −0.372104 + 1.11631i
\(66\) 0 0
\(67\) −9.00000 + 9.00000i −1.09952 + 1.09952i −0.105059 + 0.994466i \(0.533503\pi\)
−0.994466 + 0.105059i \(0.966497\pi\)
\(68\) 0 0
\(69\) 6.00000i 0.722315i
\(70\) 0 0
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 0 0
\(73\) −5.00000 + 5.00000i −0.585206 + 0.585206i −0.936329 0.351123i \(-0.885800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 0 0
\(75\) −7.00000 + 1.00000i −0.808290 + 0.115470i
\(76\) 0 0
\(77\) 4.00000 + 4.00000i 0.455842 + 0.455842i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 3.00000 + 3.00000i 0.329293 + 0.329293i 0.852318 0.523025i \(-0.175196\pi\)
−0.523025 + 0.852318i \(0.675196\pi\)
\(84\) 0 0
\(85\) 9.00000 + 3.00000i 0.976187 + 0.325396i
\(86\) 0 0
\(87\) 2.00000 2.00000i 0.214423 0.214423i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 6.00000i 0.628971i
\(92\) 0 0
\(93\) −6.00000 + 6.00000i −0.622171 + 0.622171i
\(94\) 0 0
\(95\) 12.0000 6.00000i 1.23117 0.615587i
\(96\) 0 0
\(97\) −7.00000 7.00000i −0.710742 0.710742i 0.255948 0.966691i \(-0.417612\pi\)
−0.966691 + 0.255948i \(0.917612\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 0 0
\(103\) 11.0000 + 11.0000i 1.08386 + 1.08386i 0.996145 + 0.0877167i \(0.0279570\pi\)
0.0877167 + 0.996145i \(0.472043\pi\)
\(104\) 0 0
\(105\) 4.00000 2.00000i 0.390360 0.195180i
\(106\) 0 0
\(107\) −3.00000 + 3.00000i −0.290021 + 0.290021i −0.837088 0.547068i \(-0.815744\pi\)
0.547068 + 0.837088i \(0.315744\pi\)
\(108\) 0 0
\(109\) 18.0000i 1.72409i −0.506834 0.862044i \(-0.669184\pi\)
0.506834 0.862044i \(-0.330816\pi\)
\(110\) 0 0
\(111\) 6.00000i 0.569495i
\(112\) 0 0
\(113\) −3.00000 + 3.00000i −0.282216 + 0.282216i −0.833992 0.551776i \(-0.813950\pi\)
0.551776 + 0.833992i \(0.313950\pi\)
\(114\) 0 0
\(115\) −9.00000 3.00000i −0.839254 0.279751i
\(116\) 0 0
\(117\) −3.00000 3.00000i −0.277350 0.277350i
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) 0 0
\(123\) 6.00000 + 6.00000i 0.541002 + 0.541002i
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) −5.00000 + 5.00000i −0.443678 + 0.443678i −0.893246 0.449568i \(-0.851578\pi\)
0.449568 + 0.893246i \(0.351578\pi\)
\(128\) 0 0
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) 4.00000i 0.349482i −0.984614 0.174741i \(-0.944091\pi\)
0.984614 0.174741i \(-0.0559088\pi\)
\(132\) 0 0
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 0 0
\(135\) 4.00000 12.0000i 0.344265 1.03280i
\(136\) 0 0
\(137\) 3.00000 + 3.00000i 0.256307 + 0.256307i 0.823550 0.567243i \(-0.191990\pi\)
−0.567243 + 0.823550i \(0.691990\pi\)
\(138\) 0 0
\(139\) 6.00000 0.508913 0.254457 0.967084i \(-0.418103\pi\)
0.254457 + 0.967084i \(0.418103\pi\)
\(140\) 0 0
\(141\) 18.0000 1.51587
\(142\) 0 0
\(143\) 12.0000 + 12.0000i 1.00349 + 1.00349i
\(144\) 0 0
\(145\) −2.00000 4.00000i −0.166091 0.332182i
\(146\) 0 0
\(147\) 5.00000 5.00000i 0.412393 0.412393i
\(148\) 0 0
\(149\) 2.00000i 0.163846i 0.996639 + 0.0819232i \(0.0261062\pi\)
−0.996639 + 0.0819232i \(0.973894\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i −0.913475 0.406894i \(-0.866612\pi\)
0.913475 0.406894i \(-0.133388\pi\)
\(152\) 0 0
\(153\) −3.00000 + 3.00000i −0.242536 + 0.242536i
\(154\) 0 0
\(155\) 6.00000 + 12.0000i 0.481932 + 0.963863i
\(156\) 0 0
\(157\) −3.00000 3.00000i −0.239426 0.239426i 0.577186 0.816612i \(-0.304151\pi\)
−0.816612 + 0.577186i \(0.804151\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) −9.00000 9.00000i −0.704934 0.704934i 0.260531 0.965465i \(-0.416102\pi\)
−0.965465 + 0.260531i \(0.916102\pi\)
\(164\) 0 0
\(165\) −4.00000 + 12.0000i −0.311400 + 0.934199i
\(166\) 0 0
\(167\) −3.00000 + 3.00000i −0.232147 + 0.232147i −0.813588 0.581441i \(-0.802489\pi\)
0.581441 + 0.813588i \(0.302489\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 6.00000i 0.458831i
\(172\) 0 0
\(173\) 15.0000 15.0000i 1.14043 1.14043i 0.152057 0.988372i \(-0.451410\pi\)
0.988372 0.152057i \(-0.0485898\pi\)
\(174\) 0 0
\(175\) −1.00000 7.00000i −0.0755929 0.529150i
\(176\) 0 0
\(177\) 10.0000 + 10.0000i 0.751646 + 0.751646i
\(178\) 0 0
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 12.0000 + 12.0000i 0.887066 + 0.887066i
\(184\) 0 0
\(185\) −9.00000 3.00000i −0.661693 0.220564i
\(186\) 0 0
\(187\) 12.0000 12.0000i 0.877527 0.877527i
\(188\) 0 0
\(189\) 8.00000i 0.581914i
\(190\) 0 0
\(191\) 6.00000i 0.434145i −0.976156 0.217072i \(-0.930349\pi\)
0.976156 0.217072i \(-0.0696508\pi\)
\(192\) 0 0
\(193\) 5.00000 5.00000i 0.359908 0.359908i −0.503871 0.863779i \(-0.668091\pi\)
0.863779 + 0.503871i \(0.168091\pi\)
\(194\) 0 0
\(195\) 12.0000 6.00000i 0.859338 0.429669i
\(196\) 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
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 18.0000 1.26962
\(202\) 0 0
\(203\) 2.00000 + 2.00000i 0.140372 + 0.140372i
\(204\) 0 0
\(205\) 12.0000 6.00000i 0.838116 0.419058i
\(206\) 0 0
\(207\) 3.00000 3.00000i 0.208514 0.208514i
\(208\) 0 0
\(209\) 24.0000i 1.66011i
\(210\) 0 0
\(211\) 12.0000i 0.826114i −0.910705 0.413057i \(-0.864461\pi\)
0.910705 0.413057i \(-0.135539\pi\)
\(212\) 0 0
\(213\) 6.00000 6.00000i 0.411113 0.411113i
\(214\) 0 0
\(215\) 9.00000 + 3.00000i 0.613795 + 0.204598i
\(216\) 0 0
\(217\) −6.00000 6.00000i −0.407307 0.407307i
\(218\) 0 0
\(219\) 10.0000 0.675737
\(220\) 0 0
\(221\) −18.0000 −1.21081
\(222\) 0 0
\(223\) 13.0000 + 13.0000i 0.870544 + 0.870544i 0.992532 0.121987i \(-0.0389267\pi\)
−0.121987 + 0.992532i \(0.538927\pi\)
\(224\) 0 0
\(225\) −4.00000 3.00000i −0.266667 0.200000i
\(226\) 0 0
\(227\) 11.0000 11.0000i 0.730096 0.730096i −0.240543 0.970639i \(-0.577325\pi\)
0.970639 + 0.240543i \(0.0773255\pi\)
\(228\) 0 0
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) 15.0000 15.0000i 0.982683 0.982683i −0.0171699 0.999853i \(-0.505466\pi\)
0.999853 + 0.0171699i \(0.00546562\pi\)
\(234\) 0 0
\(235\) 9.00000 27.0000i 0.587095 1.76129i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) 7.00000 + 7.00000i 0.449050 + 0.449050i
\(244\) 0 0
\(245\) −5.00000 10.0000i −0.319438 0.638877i
\(246\) 0 0
\(247\) −18.0000 + 18.0000i −1.14531 + 1.14531i
\(248\) 0 0
\(249\) 6.00000i 0.380235i
\(250\) 0 0
\(251\) 4.00000i 0.252478i −0.992000 0.126239i \(-0.959709\pi\)
0.992000 0.126239i \(-0.0402906\pi\)
\(252\) 0 0
\(253\) −12.0000 + 12.0000i −0.754434 + 0.754434i
\(254\) 0 0
\(255\) −6.00000 12.0000i −0.375735 0.751469i
\(256\) 0 0
\(257\) −3.00000 3.00000i −0.187135 0.187135i 0.607321 0.794456i \(-0.292244\pi\)
−0.794456 + 0.607321i \(0.792244\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 0 0
\(263\) −9.00000 9.00000i −0.554964 0.554964i 0.372906 0.927869i \(-0.378362\pi\)
−0.927869 + 0.372906i \(0.878362\pi\)
\(264\) 0 0
\(265\) −5.00000 + 15.0000i −0.307148 + 0.921443i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 14.0000i 0.853595i 0.904347 + 0.426798i \(0.140358\pi\)
−0.904347 + 0.426798i \(0.859642\pi\)
\(270\) 0 0
\(271\) 2.00000i 0.121491i 0.998153 + 0.0607457i \(0.0193479\pi\)
−0.998153 + 0.0607457i \(0.980652\pi\)
\(272\) 0 0
\(273\) −6.00000 + 6.00000i −0.363137 + 0.363137i
\(274\) 0 0
\(275\) 16.0000 + 12.0000i 0.964836 + 0.723627i
\(276\) 0 0
\(277\) 15.0000 + 15.0000i 0.901263 + 0.901263i 0.995545 0.0942828i \(-0.0300558\pi\)
−0.0942828 + 0.995545i \(0.530056\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −15.0000 15.0000i −0.891657 0.891657i 0.103022 0.994679i \(-0.467149\pi\)
−0.994679 + 0.103022i \(0.967149\pi\)
\(284\) 0 0
\(285\) −18.0000 6.00000i −1.06623 0.355409i
\(286\) 0 0
\(287\) −6.00000 + 6.00000i −0.354169 + 0.354169i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 14.0000i 0.820695i
\(292\) 0 0
\(293\) 1.00000 1.00000i 0.0584206 0.0584206i −0.677293 0.735714i \(-0.736847\pi\)
0.735714 + 0.677293i \(0.236847\pi\)
\(294\) 0 0
\(295\) 20.0000 10.0000i 1.16445 0.582223i
\(296\) 0 0
\(297\) −16.0000 16.0000i −0.928414 0.928414i
\(298\) 0 0
\(299\) 18.0000 1.04097
\(300\) 0 0
\(301\) −6.00000 −0.345834
\(302\) 0 0
\(303\) 8.00000 + 8.00000i 0.459588 + 0.459588i
\(304\) 0 0
\(305\) 24.0000 12.0000i 1.37424 0.687118i
\(306\) 0 0
\(307\) 15.0000 15.0000i 0.856095 0.856095i −0.134780 0.990876i \(-0.543033\pi\)
0.990876 + 0.134780i \(0.0430329\pi\)
\(308\) 0 0
\(309\) 22.0000i 1.25154i
\(310\) 0 0
\(311\) 18.0000i 1.02069i −0.859971 0.510343i \(-0.829518\pi\)
0.859971 0.510343i \(-0.170482\pi\)
\(312\) 0 0
\(313\) −1.00000 + 1.00000i −0.0565233 + 0.0565233i −0.734803 0.678280i \(-0.762726\pi\)
0.678280 + 0.734803i \(0.262726\pi\)
\(314\) 0 0
\(315\) 3.00000 + 1.00000i 0.169031 + 0.0563436i
\(316\) 0 0
\(317\) −3.00000 3.00000i −0.168497 0.168497i 0.617822 0.786318i \(-0.288015\pi\)
−0.786318 + 0.617822i \(0.788015\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) 18.0000 + 18.0000i 1.00155 + 1.00155i
\(324\) 0 0
\(325\) −3.00000 21.0000i −0.166410 1.16487i
\(326\) 0 0
\(327\) −18.0000 + 18.0000i −0.995402 + 0.995402i
\(328\) 0 0
\(329\) 18.0000i 0.992372i
\(330\) 0 0
\(331\) 12.0000i 0.659580i −0.944054 0.329790i \(-0.893022\pi\)
0.944054 0.329790i \(-0.106978\pi\)
\(332\) 0 0
\(333\) 3.00000 3.00000i 0.164399 0.164399i
\(334\) 0 0
\(335\) 9.00000 27.0000i 0.491723 1.47517i
\(336\) 0 0
\(337\) 25.0000 + 25.0000i 1.36184 + 1.36184i 0.871576 + 0.490261i \(0.163099\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) 0 0
\(345\) 6.00000 + 12.0000i 0.323029 + 0.646058i
\(346\) 0 0
\(347\) 17.0000 17.0000i 0.912608 0.912608i −0.0838690 0.996477i \(-0.526728\pi\)
0.996477 + 0.0838690i \(0.0267277\pi\)
\(348\) 0 0
\(349\) 18.0000i 0.963518i 0.876304 + 0.481759i \(0.160002\pi\)
−0.876304 + 0.481759i \(0.839998\pi\)
\(350\) 0 0
\(351\) 24.0000i 1.28103i
\(352\) 0 0
\(353\) −15.0000 + 15.0000i −0.798369 + 0.798369i −0.982838 0.184469i \(-0.940943\pi\)
0.184469 + 0.982838i \(0.440943\pi\)
\(354\) 0 0
\(355\) −6.00000 12.0000i −0.318447 0.636894i
\(356\) 0 0
\(357\) 6.00000 + 6.00000i 0.317554 + 0.317554i
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 0 0
\(363\) 5.00000 + 5.00000i 0.262432 + 0.262432i
\(364\) 0 0
\(365\) 5.00000 15.0000i 0.261712 0.785136i
\(366\) 0 0
\(367\) 11.0000 11.0000i 0.574195 0.574195i −0.359103 0.933298i \(-0.616917\pi\)
0.933298 + 0.359103i \(0.116917\pi\)
\(368\) 0 0
\(369\) 6.00000i 0.312348i
\(370\) 0 0
\(371\) 10.0000i 0.519174i
\(372\) 0 0
\(373\) −3.00000 + 3.00000i −0.155334 + 0.155334i −0.780496 0.625161i \(-0.785033\pi\)
0.625161 + 0.780496i \(0.285033\pi\)
\(374\) 0 0
\(375\) 13.0000 9.00000i 0.671317 0.464758i
\(376\) 0 0
\(377\) 6.00000 + 6.00000i 0.309016 + 0.309016i
\(378\) 0 0
\(379\) −18.0000 −0.924598 −0.462299 0.886724i \(-0.652975\pi\)
−0.462299 + 0.886724i \(0.652975\pi\)
\(380\) 0 0
\(381\) 10.0000 0.512316
\(382\) 0 0
\(383\) 21.0000 + 21.0000i 1.07305 + 1.07305i 0.997113 + 0.0759373i \(0.0241949\pi\)
0.0759373 + 0.997113i \(0.475805\pi\)
\(384\) 0 0
\(385\) −12.0000 4.00000i −0.611577 0.203859i
\(386\) 0 0
\(387\) −3.00000 + 3.00000i −0.152499 + 0.152499i
\(388\) 0 0
\(389\) 26.0000i 1.31825i 0.752032 + 0.659126i \(0.229074\pi\)
−0.752032 + 0.659126i \(0.770926\pi\)
\(390\) 0 0
\(391\) 18.0000i 0.910299i
\(392\) 0 0
\(393\) −4.00000 + 4.00000i −0.201773 + 0.201773i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 9.00000 + 9.00000i 0.451697 + 0.451697i 0.895918 0.444220i \(-0.146519\pi\)
−0.444220 + 0.895918i \(0.646519\pi\)
\(398\) 0 0
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) −18.0000 18.0000i −0.896644 0.896644i
\(404\) 0 0
\(405\) −10.0000 + 5.00000i −0.496904 + 0.248452i
\(406\) 0 0
\(407\) −12.0000 + 12.0000i −0.594818 + 0.594818i
\(408\) 0 0
\(409\) 12.0000i 0.593362i 0.954977 + 0.296681i \(0.0958798\pi\)
−0.954977 + 0.296681i \(0.904120\pi\)
\(410\) 0 0
\(411\) 6.00000i 0.295958i
\(412\) 0 0
\(413\) −10.0000 + 10.0000i −0.492068 + 0.492068i
\(414\) 0 0
\(415\) −9.00000 3.00000i −0.441793 0.147264i
\(416\) 0 0
\(417\) −6.00000 6.00000i −0.293821 0.293821i
\(418\) 0 0
\(419\) 10.0000 0.488532 0.244266 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) 0 0
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) 0 0
\(423\) 9.00000 + 9.00000i 0.437595 + 0.437595i
\(424\) 0 0
\(425\) −21.0000 + 3.00000i −1.01865 + 0.145521i
\(426\) 0 0
\(427\) −12.0000 + 12.0000i −0.580721 + 0.580721i
\(428\) 0 0
\(429\) 24.0000i 1.15873i
\(430\) 0 0
\(431\) 30.0000i 1.44505i −0.691345 0.722525i \(-0.742982\pi\)
0.691345 0.722525i \(-0.257018\pi\)
\(432\) 0 0
\(433\) −7.00000 + 7.00000i −0.336399 + 0.336399i −0.855010 0.518611i \(-0.826449\pi\)
0.518611 + 0.855010i \(0.326449\pi\)
\(434\) 0 0
\(435\) −2.00000 + 6.00000i −0.0958927 + 0.287678i
\(436\) 0 0
\(437\) −18.0000 18.0000i −0.861057 0.861057i
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) 25.0000 + 25.0000i 1.18779 + 1.18779i 0.977678 + 0.210108i \(0.0673814\pi\)
0.210108 + 0.977678i \(0.432619\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.00000 2.00000i 0.0945968 0.0945968i
\(448\) 0 0
\(449\) 12.0000i 0.566315i 0.959073 + 0.283158i \(0.0913819\pi\)
−0.959073 + 0.283158i \(0.908618\pi\)
\(450\) 0 0
\(451\) 24.0000i 1.13012i
\(452\) 0 0
\(453\) −10.0000 + 10.0000i −0.469841 + 0.469841i
\(454\) 0 0
\(455\) 6.00000 + 12.0000i 0.281284 + 0.562569i
\(456\) 0 0
\(457\) −17.0000 17.0000i −0.795226 0.795226i 0.187112 0.982339i \(-0.440087\pi\)
−0.982339 + 0.187112i \(0.940087\pi\)
\(458\) 0 0
\(459\) 24.0000 1.12022
\(460\) 0 0
\(461\) 40.0000 1.86299 0.931493 0.363760i \(-0.118507\pi\)
0.931493 + 0.363760i \(0.118507\pi\)
\(462\) 0 0
\(463\) 1.00000 + 1.00000i 0.0464739 + 0.0464739i 0.729962 0.683488i \(-0.239538\pi\)
−0.683488 + 0.729962i \(0.739538\pi\)
\(464\) 0 0
\(465\) 6.00000 18.0000i 0.278243 0.834730i
\(466\) 0 0
\(467\) −21.0000 + 21.0000i −0.971764 + 0.971764i −0.999612 0.0278481i \(-0.991135\pi\)
0.0278481 + 0.999612i \(0.491135\pi\)
\(468\) 0 0
\(469\) 18.0000i 0.831163i
\(470\) 0 0
\(471\) 6.00000i 0.276465i
\(472\) 0 0
\(473\) 12.0000 12.0000i 0.551761 0.551761i
\(474\) 0 0
\(475\) −18.0000 + 24.0000i −0.825897 + 1.10120i
\(476\) 0 0
\(477\) −5.00000 5.00000i −0.228934 0.228934i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 18.0000 0.820729
\(482\) 0 0
\(483\) −6.00000 6.00000i −0.273009 0.273009i
\(484\) 0 0
\(485\) 21.0000 + 7.00000i 0.953561 + 0.317854i
\(486\) 0 0
\(487\) 1.00000 1.00000i 0.0453143 0.0453143i −0.684087 0.729401i \(-0.739799\pi\)
0.729401 + 0.684087i \(0.239799\pi\)
\(488\) 0 0
\(489\) 18.0000i 0.813988i
\(490\) 0 0
\(491\) 20.0000i 0.902587i 0.892375 + 0.451294i \(0.149037\pi\)
−0.892375 + 0.451294i \(0.850963\pi\)
\(492\) 0 0
\(493\) 6.00000 6.00000i 0.270226 0.270226i
\(494\) 0 0
\(495\) −8.00000 + 4.00000i −0.359573 + 0.179787i
\(496\) 0 0
\(497\) 6.00000 + 6.00000i 0.269137 + 0.269137i
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 0 0
\(501\) 6.00000 0.268060
\(502\) 0 0
\(503\) −21.0000 21.0000i −0.936344 0.936344i 0.0617480 0.998092i \(-0.480332\pi\)
−0.998092 + 0.0617480i \(0.980332\pi\)
\(504\) 0 0
\(505\) 16.0000 8.00000i 0.711991 0.355995i
\(506\) 0 0
\(507\) −5.00000 + 5.00000i −0.222058 + 0.222058i
\(508\) 0 0
\(509\) 14.0000i 0.620539i −0.950649 0.310270i \(-0.899581\pi\)
0.950649 0.310270i \(-0.100419\pi\)
\(510\) 0 0
\(511\) 10.0000i 0.442374i
\(512\) 0 0
\(513\) 24.0000 24.0000i 1.05963 1.05963i
\(514\) 0 0
\(515\) −33.0000 11.0000i −1.45415 0.484718i
\(516\) 0 0
\(517\) −36.0000 36.0000i −1.58328 1.58328i
\(518\) 0 0
\(519\) −30.0000 −1.31685
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) −15.0000 15.0000i −0.655904 0.655904i 0.298504 0.954408i \(-0.403512\pi\)
−0.954408 + 0.298504i \(0.903512\pi\)
\(524\) 0 0
\(525\) −6.00000 + 8.00000i −0.261861 + 0.349149i
\(526\) 0 0
\(527\) −18.0000 + 18.0000i −0.784092 + 0.784092i
\(528\) 0 0
\(529\) 5.00000i 0.217391i
\(530\) 0 0
\(531\) 10.0000i 0.433963i
\(532\) 0 0
\(533\) −18.0000 + 18.0000i −0.779667 + 0.779667i
\(534\) 0 0
\(535\) 3.00000 9.00000i 0.129701 0.389104i
\(536\) 0 0
\(537\) −2.00000 2.00000i −0.0863064 0.0863064i
\(538\) 0 0
\(539\) −20.0000 −0.861461
\(540\) 0 0
\(541\) 24.0000 1.03184 0.515920 0.856637i \(-0.327450\pi\)
0.515920 + 0.856637i \(0.327450\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.0000 + 36.0000i 0.771035 + 1.54207i
\(546\) 0 0
\(547\) 3.00000 3.00000i 0.128271 0.128271i −0.640057 0.768328i \(-0.721089\pi\)
0.768328 + 0.640057i \(0.221089\pi\)
\(548\) 0 0
\(549\) 12.0000i 0.512148i
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.00000 + 12.0000i 0.254686 + 0.509372i
\(556\) 0 0
\(557\) −31.0000 31.0000i −1.31351 1.31351i −0.918808 0.394704i \(-0.870847\pi\)
−0.394704 0.918808i \(-0.629153\pi\)
\(558\) 0 0
\(559\) −18.0000 −0.761319
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 0 0
\(563\) −1.00000 1.00000i −0.0421450 0.0421450i 0.685720 0.727865i \(-0.259487\pi\)
−0.727865 + 0.685720i \(0.759487\pi\)
\(564\) 0 0
\(565\) 3.00000 9.00000i 0.126211 0.378633i
\(566\) 0 0
\(567\) 5.00000 5.00000i 0.209980 0.209980i
\(568\) 0 0
\(569\) 12.0000i 0.503066i −0.967849 0.251533i \(-0.919065\pi\)
0.967849 0.251533i \(-0.0809347\pi\)
\(570\) 0 0
\(571\) 12.0000i 0.502184i −0.967963 0.251092i \(-0.919210\pi\)
0.967963 0.251092i \(-0.0807897\pi\)
\(572\) 0 0
\(573\) −6.00000 + 6.00000i −0.250654 + 0.250654i
\(574\) 0 0
\(575\) 21.0000 3.00000i 0.875761 0.125109i
\(576\) 0 0
\(577\) −19.0000 19.0000i −0.790980 0.790980i 0.190673 0.981654i \(-0.438933\pi\)
−0.981654 + 0.190673i \(0.938933\pi\)
\(578\) 0 0
\(579\) −10.0000 −0.415586
\(580\) 0 0
\(581\) 6.00000 0.248922
\(582\) 0 0
\(583\) 20.0000 + 20.0000i 0.828315 + 0.828315i
\(584\) 0 0
\(585\) 9.00000 + 3.00000i 0.372104 + 0.124035i
\(586\) 0 0
\(587\) −15.0000 + 15.0000i −0.619116 + 0.619116i −0.945305 0.326188i \(-0.894236\pi\)
0.326188 + 0.945305i \(0.394236\pi\)
\(588\) 0 0
\(589\) 36.0000i 1.48335i
\(590\) 0 0
\(591\) 10.0000i 0.411345i
\(592\) 0 0
\(593\) −15.0000 + 15.0000i −0.615976 + 0.615976i −0.944497 0.328521i \(-0.893450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) 0 0
\(595\) 12.0000 6.00000i 0.491952 0.245976i
\(596\) 0 0
\(597\) 16.0000 + 16.0000i 0.654836 + 0.654836i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 9.00000 + 9.00000i 0.366508 + 0.366508i
\(604\) 0 0
\(605\) 10.0000 5.00000i 0.406558 0.203279i
\(606\) 0 0
\(607\) 7.00000 7.00000i 0.284121 0.284121i −0.550629 0.834750i \(-0.685612\pi\)
0.834750 + 0.550629i \(0.185612\pi\)
\(608\) 0 0
\(609\) 4.00000i 0.162088i
\(610\) 0 0
\(611\) 54.0000i 2.18461i
\(612\) 0 0
\(613\) 9.00000 9.00000i 0.363507 0.363507i −0.501596 0.865102i \(-0.667253\pi\)
0.865102 + 0.501596i \(0.167253\pi\)
\(614\) 0 0
\(615\) −18.0000 6.00000i −0.725830 0.241943i
\(616\) 0 0
\(617\) 15.0000 + 15.0000i 0.603877 + 0.603877i 0.941339 0.337462i \(-0.109568\pi\)
−0.337462 + 0.941339i \(0.609568\pi\)
\(618\) 0 0
\(619\) −42.0000 −1.68812 −0.844061 0.536247i \(-0.819842\pi\)
−0.844061 + 0.536247i \(0.819842\pi\)
\(620\) 0 0
\(621\) −24.0000 −0.963087
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) −24.0000 + 24.0000i −0.958468 + 0.958468i
\(628\) 0 0
\(629\) 18.0000i 0.717707i
\(630\) 0 0
\(631\) 30.0000i 1.19428i 0.802137 + 0.597141i \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) 0 0
\(633\) −12.0000 + 12.0000i −0.476957 + 0.476957i
\(634\) 0 0
\(635\) 5.00000 15.0000i 0.198419 0.595257i
\(636\) 0 0
\(637\) 15.0000 + 15.0000i 0.594322 + 0.594322i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) 3.00000 + 3.00000i 0.118308 + 0.118308i 0.763782 0.645474i \(-0.223340\pi\)
−0.645474 + 0.763782i \(0.723340\pi\)
\(644\) 0 0
\(645\) −6.00000 12.0000i −0.236250 0.472500i
\(646\) 0 0
\(647\) 9.00000 9.00000i 0.353827 0.353827i −0.507705 0.861531i \(-0.669506\pi\)
0.861531 + 0.507705i \(0.169506\pi\)
\(648\) 0 0
\(649\) 40.0000i 1.57014i
\(650\) 0 0
\(651\) 12.0000i 0.470317i
\(652\) 0 0
\(653\) −33.0000 + 33.0000i −1.29139 + 1.29139i −0.357462 + 0.933928i \(0.616358\pi\)
−0.933928 + 0.357462i \(0.883642\pi\)
\(654\) 0 0
\(655\) 4.00000 + 8.00000i 0.156293 + 0.312586i
\(656\) 0 0
\(657\) 5.00000 + 5.00000i 0.195069 + 0.195069i
\(658\) 0 0
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 0 0
\(661\) 12.0000 0.466746 0.233373 0.972387i \(-0.425024\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 0 0
\(663\) 18.0000 + 18.0000i 0.699062 + 0.699062i
\(664\) 0 0
\(665\) 6.00000 18.0000i 0.232670 0.698010i
\(666\) 0 0
\(667\) −6.00000 + 6.00000i −0.232321 + 0.232321i
\(668\) 0 0
\(669\) 26.0000i 1.00522i
\(670\) 0 0
\(671\) 48.0000i 1.85302i
\(672\) 0 0
\(673\) 25.0000 25.0000i 0.963679 0.963679i −0.0356839 0.999363i \(-0.511361\pi\)
0.999363 + 0.0356839i \(0.0113610\pi\)
\(674\) 0 0
\(675\) 4.00000 + 28.0000i 0.153960 + 1.07772i
\(676\) 0 0
\(677\) 27.0000 + 27.0000i 1.03769 + 1.03769i 0.999261 + 0.0384331i \(0.0122367\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) −14.0000 −0.537271
\(680\) 0 0
\(681\) −22.0000 −0.843042
\(682\) 0 0
\(683\) −27.0000 27.0000i −1.03313 1.03313i −0.999432 0.0336941i \(-0.989273\pi\)
−0.0336941 0.999432i \(-0.510727\pi\)
\(684\) 0 0
\(685\) −9.00000 3.00000i −0.343872 0.114624i
\(686\) 0 0
\(687\) 6.00000 6.00000i 0.228914 0.228914i
\(688\) 0 0
\(689\) 30.0000i 1.14291i
\(690\) 0 0
\(691\) 12.0000i 0.456502i −0.973602 0.228251i \(-0.926699\pi\)
0.973602 0.228251i \(-0.0733006\pi\)
\(692\) 0 0
\(693\) 4.00000 4.00000i 0.151947 0.151947i
\(694\) 0 0
\(695\) −12.0000 + 6.00000i −0.455186 + 0.227593i
\(696\) 0 0
\(697\) 18.0000 + 18.0000i 0.681799 + 0.681799i
\(698\) 0 0
\(699\) −30.0000 −1.13470
\(700\) 0 0
\(701\) −20.0000 −0.755390 −0.377695 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 0 0
\(703\) −18.0000 18.0000i −0.678883 0.678883i
\(704\) 0 0
\(705\) −36.0000 + 18.0000i −1.35584 + 0.677919i
\(706\) 0 0
\(707\) −8.00000 + 8.00000i −0.300871 + 0.300871i
\(708\) 0 0
\(709\) 42.0000i 1.57734i −0.614815 0.788672i \(-0.710769\pi\)
0.614815 0.788672i \(-0.289231\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 18.0000 18.0000i 0.674105 0.674105i
\(714\) 0 0
\(715\) −36.0000 12.0000i −1.34632 0.448775i
\(716\) 0 0
\(717\) 24.0000 + 24.0000i 0.896296 + 0.896296i
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 22.0000 0.819323
\(722\) 0 0
\(723\) 18.0000 + 18.0000i 0.669427 + 0.669427i
\(724\) 0 0
\(725\) 8.00000 + 6.00000i 0.297113 + 0.222834i
\(726\) 0 0
\(727\) 25.0000 25.0000i 0.927199 0.927199i −0.0703254 0.997524i \(-0.522404\pi\)
0.997524 + 0.0703254i \(0.0224038\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 18.0000i 0.665754i
\(732\) 0 0
\(733\) 15.0000 15.0000i 0.554038 0.554038i −0.373566 0.927604i \(-0.621865\pi\)
0.927604 + 0.373566i \(0.121865\pi\)
\(734\) 0 0
\(735\) −5.00000 + 15.0000i −0.184428 + 0.553283i
\(736\) 0 0
\(737\) −36.0000 36.0000i −1.32608 1.32608i
\(738\) 0 0
\(739\) −30.0000 −1.10357 −0.551784 0.833987i \(-0.686053\pi\)
−0.551784 + 0.833987i \(0.686053\pi\)
\(740\) 0 0
\(741\) 36.0000 1.32249
\(742\) 0 0
\(743\) −9.00000 9.00000i −0.330178 0.330178i 0.522476 0.852654i \(-0.325008\pi\)
−0.852654 + 0.522476i \(0.825008\pi\)
\(744\) 0 0
\(745\) −2.00000 4.00000i −0.0732743 0.146549i
\(746\) 0 0
\(747\) 3.00000 3.00000i 0.109764 0.109764i
\(748\) 0 0
\(749\) 6.00000i 0.219235i
\(750\) 0 0
\(751\) 42.0000i 1.53260i 0.642482 + 0.766301i \(0.277905\pi\)
−0.642482 + 0.766301i \(0.722095\pi\)
\(752\) 0 0
\(753\) −4.00000 + 4.00000i −0.145768 + 0.145768i
\(754\) 0 0
\(755\) 10.0000 + 20.0000i 0.363937 + 0.727875i
\(756\) 0 0
\(757\) −9.00000 9.00000i −0.327111 0.327111i 0.524376 0.851487i \(-0.324299\pi\)
−0.851487 + 0.524376i \(0.824299\pi\)
\(758\) 0 0
\(759\) 24.0000 0.871145
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 0 0
\(763\) −18.0000 18.0000i −0.651644 0.651644i
\(764\) 0 0
\(765\) 3.00000 9.00000i 0.108465 0.325396i
\(766\) 0 0
\(767\) −30.0000 + 30.0000i −1.08324 + 1.08324i
\(768\) 0 0
\(769\) 40.0000i 1.44244i 0.692708 + 0.721218i \(0.256418\pi\)
−0.692708 + 0.721218i \(0.743582\pi\)
\(770\) 0 0
\(771\) 6.00000i 0.216085i
\(772\) 0 0
\(773\) 9.00000 9.00000i 0.323708 0.323708i −0.526480 0.850188i \(-0.676489\pi\)
0.850188 + 0.526480i \(0.176489\pi\)
\(774\) 0 0
\(775\) −24.0000 18.0000i −0.862105 0.646579i
\(776\) 0 0
\(777\) −6.00000 6.00000i −0.215249 0.215249i
\(778\) 0 0
\(779\) 36.0000 1.28983
\(780\) 0 0
\(781\) −24.0000 −0.858788
\(782\) 0 0
\(783\) −8.00000 8.00000i −0.285897 0.285897i
\(784\) 0 0
\(785\) 9.00000 + 3.00000i 0.321224 + 0.107075i
\(786\) 0 0
\(787\) 15.0000 15.0000i 0.534692 0.534692i −0.387273 0.921965i \(-0.626583\pi\)
0.921965 + 0.387273i \(0.126583\pi\)
\(788\) 0 0
\(789\) 18.0000i 0.640817i
\(790\) 0 0
\(791\) 6.00000i 0.213335i
\(792\) 0 0
\(793\) −36.0000 + 36.0000i −1.27840 + 1.27840i
\(794\) 0 0
\(795\) 20.0000 10.0000i 0.709327 0.354663i
\(796\) 0 0