Properties

Label 1280.2.n.c.1023.1
Level $1280$
Weight $2$
Character 1280.1023
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 1023.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1280.1023
Dual form 1280.2.n.c.767.1

$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i \(-0.883860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 0 0
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) 1.00000 + 1.00000i 0.377964 + 0.377964i 0.870367 0.492403i \(-0.163881\pi\)
−0.492403 + 0.870367i \(0.663881\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 4.00000i 1.20605i −0.797724 0.603023i \(-0.793963\pi\)
0.797724 0.603023i \(-0.206037\pi\)
\(12\) 0 0
\(13\) 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i \(-0.0497784\pi\)
−0.155747 + 0.987797i \(0.549778\pi\)
\(14\) 0 0
\(15\) 3.00000 1.00000i 0.774597 0.258199i
\(16\) 0 0
\(17\) −3.00000 + 3.00000i −0.727607 + 0.727607i −0.970143 0.242536i \(-0.922021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 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 −0.321400 0.946943i \(-0.604153\pi\)
0.946943 + 0.321400i \(0.104153\pi\)
\(24\) 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 \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) 0 0
\(31\) 6.00000i 1.07763i 0.842424 + 0.538816i \(0.181128\pi\)
−0.842424 + 0.538816i \(0.818872\pi\)
\(32\) 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 −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 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 −0.897833 0.440337i \(-0.854859\pi\)
0.440337 + 0.897833i \(0.354859\pi\)
\(44\) 0 0
\(45\) 1.00000 2.00000i 0.149071 0.298142i
\(46\) 0 0
\(47\) −9.00000 9.00000i −1.31278 1.31278i −0.919354 0.393431i \(-0.871288\pi\)
−0.393431 0.919354i \(-0.628712\pi\)
\(48\) 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 0.961524 0.274721i \(-0.0885855\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 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 −0.994466 0.105059i \(-0.966497\pi\)
−0.105059 0.994466i \(-0.533503\pi\)
\(68\) 0 0
\(69\) 6.00000i 0.722315i
\(70\) 0 0
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 0 0
\(73\) −5.00000 5.00000i −0.585206 0.585206i 0.351123 0.936329i \(-0.385800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 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 −0.523025 0.852318i \(-0.675196\pi\)
0.852318 + 0.523025i \(0.175196\pi\)
\(84\) 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 −0.966691 0.255948i \(-0.917612\pi\)
0.255948 + 0.966691i \(0.417612\pi\)
\(98\) 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 0.0877167 0.996145i \(-0.472043\pi\)
0.996145 0.0877167i \(-0.0279570\pi\)
\(104\) 0 0
\(105\) 4.00000 + 2.00000i 0.390360 + 0.195180i
\(106\) 0 0
\(107\) −3.00000 3.00000i −0.290021 0.290021i 0.547068 0.837088i \(-0.315744\pi\)
−0.837088 + 0.547068i \(0.815744\pi\)
\(108\) 0 0
\(109\) 18.0000i 1.72409i 0.506834 + 0.862044i \(0.330816\pi\)
−0.506834 + 0.862044i \(0.669184\pi\)
\(110\) 0 0
\(111\) 6.00000i 0.569495i
\(112\) 0 0
\(113\) −3.00000 3.00000i −0.282216 0.282216i 0.551776 0.833992i \(-0.313950\pi\)
−0.833992 + 0.551776i \(0.813950\pi\)
\(114\) 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 0.449568 0.893246i \(-0.351578\pi\)
−0.893246 + 0.449568i \(0.851578\pi\)
\(128\) 0 0
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) 4.00000i 0.349482i 0.984614 + 0.174741i \(0.0559088\pi\)
−0.984614 + 0.174741i \(0.944091\pi\)
\(132\) 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 −0.567243 0.823550i \(-0.691990\pi\)
0.823550 + 0.567243i \(0.191990\pi\)
\(138\) 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 \(-0.973894\pi\)
0.996639 0.0819232i \(-0.0261062\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 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 −0.816612 0.577186i \(-0.804151\pi\)
0.577186 + 0.816612i \(0.304151\pi\)
\(158\) 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 −0.965465 0.260531i \(-0.916102\pi\)
0.260531 + 0.965465i \(0.416102\pi\)
\(164\) 0 0
\(165\) −4.00000 12.0000i −0.311400 0.934199i
\(166\) 0 0
\(167\) −3.00000 3.00000i −0.232147 0.232147i 0.581441 0.813588i \(-0.302489\pi\)
−0.813588 + 0.581441i \(0.802489\pi\)
\(168\) 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 0.988372 + 0.152057i \(0.0485898\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 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 \(0.0696508\pi\)
−0.976156 + 0.217072i \(0.930349\pi\)
\(192\) 0 0
\(193\) 5.00000 + 5.00000i 0.359908 + 0.359908i 0.863779 0.503871i \(-0.168091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 0 0
\(195\) 12.0000 + 6.00000i 0.859338 + 0.429669i
\(196\) 0 0
\(197\) −5.00000 + 5.00000i −0.356235 + 0.356235i −0.862423 0.506188i \(-0.831054\pi\)
0.506188 + 0.862423i \(0.331054\pi\)
\(198\) 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 \(0.135539\pi\)
−0.910705 + 0.413057i \(0.864461\pi\)
\(212\) 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 −0.121987 0.992532i \(-0.538927\pi\)
0.992532 + 0.121987i \(0.0389267\pi\)
\(224\) 0 0
\(225\) −4.00000 + 3.00000i −0.266667 + 0.200000i
\(226\) 0 0
\(227\) 11.0000 + 11.0000i 0.730096 + 0.730096i 0.970639 0.240543i \(-0.0773255\pi\)
−0.240543 + 0.970639i \(0.577325\pi\)
\(228\) 0 0
\(229\) 6.00000i 0.396491i −0.980152 0.198246i \(-0.936476\pi\)
0.980152 0.198246i \(-0.0635244\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) 15.0000 + 15.0000i 0.982683 + 0.982683i 0.999853 0.0171699i \(-0.00546562\pi\)
−0.0171699 + 0.999853i \(0.505466\pi\)
\(234\) 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 \(0.0402906\pi\)
−0.992000 + 0.126239i \(0.959709\pi\)
\(252\) 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 −0.794456 0.607321i \(-0.792244\pi\)
0.607321 + 0.794456i \(0.292244\pi\)
\(258\) 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 −0.927869 0.372906i \(-0.878362\pi\)
0.372906 + 0.927869i \(0.378362\pi\)
\(264\) 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 \(-0.859642\pi\)
0.904347 0.426798i \(-0.140358\pi\)
\(270\) 0 0
\(271\) 2.00000i 0.121491i −0.998153 0.0607457i \(-0.980652\pi\)
0.998153 0.0607457i \(-0.0193479\pi\)
\(272\) 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 −0.0942828 0.995545i \(-0.530056\pi\)
0.995545 + 0.0942828i \(0.0300558\pi\)
\(278\) 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 −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) 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 0.735714 0.677293i \(-0.236847\pi\)
−0.677293 + 0.735714i \(0.736847\pi\)
\(294\) 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 0.990876 0.134780i \(-0.0430329\pi\)
−0.134780 + 0.990876i \(0.543033\pi\)
\(308\) 0 0
\(309\) 22.0000i 1.25154i
\(310\) 0 0
\(311\) 18.0000i 1.02069i 0.859971 + 0.510343i \(0.170482\pi\)
−0.859971 + 0.510343i \(0.829518\pi\)
\(312\) 0 0
\(313\) −1.00000 1.00000i −0.0565233 0.0565233i 0.678280 0.734803i \(-0.262726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 0 0
\(315\) 3.00000 1.00000i 0.169031 0.0563436i
\(316\) 0 0
\(317\) −3.00000 + 3.00000i −0.168497 + 0.168497i −0.786318 0.617822i \(-0.788015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) 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 \(0.106978\pi\)
−0.944054 + 0.329790i \(0.893022\pi\)
\(332\) 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 0.490261 0.871576i \(-0.336901\pi\)
0.871576 0.490261i \(-0.163099\pi\)
\(338\) 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 0.996477 0.0838690i \(-0.0267277\pi\)
−0.0838690 + 0.996477i \(0.526728\pi\)
\(348\) 0 0
\(349\) 18.0000i 0.963518i −0.876304 0.481759i \(-0.839998\pi\)
0.876304 0.481759i \(-0.160002\pi\)
\(350\) 0 0
\(351\) 24.0000i 1.28103i
\(352\) 0 0
\(353\) −15.0000 15.0000i −0.798369 0.798369i 0.184469 0.982838i \(-0.440943\pi\)
−0.982838 + 0.184469i \(0.940943\pi\)
\(354\) 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 0.933298 0.359103i \(-0.116917\pi\)
−0.359103 + 0.933298i \(0.616917\pi\)
\(368\) 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 0.625161 0.780496i \(-0.285033\pi\)
−0.780496 + 0.625161i \(0.785033\pi\)
\(374\) 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 0.0759373 0.997113i \(-0.475805\pi\)
0.997113 0.0759373i \(-0.0241949\pi\)
\(384\) 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 \(-0.770926\pi\)
0.752032 0.659126i \(-0.229074\pi\)
\(390\) 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 −0.444220 0.895918i \(-0.646519\pi\)
0.895918 + 0.444220i \(0.146519\pi\)
\(398\) 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 \(-0.904120\pi\)
0.954977 0.296681i \(-0.0958798\pi\)
\(410\) 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 \(0.257018\pi\)
−0.691345 + 0.722525i \(0.742982\pi\)
\(432\) 0 0
\(433\) −7.00000 7.00000i −0.336399 0.336399i 0.518611 0.855010i \(-0.326449\pi\)
−0.855010 + 0.518611i \(0.826449\pi\)
\(434\) 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 0.210108 0.977678i \(-0.432619\pi\)
0.977678 0.210108i \(-0.0673814\pi\)
\(444\) 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 \(-0.908618\pi\)
0.959073 0.283158i \(-0.0913819\pi\)
\(450\) 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 −0.982339 0.187112i \(-0.940087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 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 −0.683488 0.729962i \(-0.739538\pi\)
0.729962 + 0.683488i \(0.239538\pi\)
\(464\) 0 0
\(465\) 6.00000 + 18.0000i 0.278243 + 0.834730i
\(466\) 0 0
\(467\) −21.0000 21.0000i −0.971764 0.971764i 0.0278481 0.999612i \(-0.491135\pi\)
−0.999612 + 0.0278481i \(0.991135\pi\)
\(468\) 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 0.729401 0.684087i \(-0.239799\pi\)
−0.684087 + 0.729401i \(0.739799\pi\)
\(488\) 0 0
\(489\) 18.0000i 0.813988i
\(490\) 0 0
\(491\) 20.0000i 0.902587i −0.892375 0.451294i \(-0.850963\pi\)
0.892375 0.451294i \(-0.149037\pi\)
\(492\) 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 −0.998092 0.0617480i \(-0.980332\pi\)
0.0617480 + 0.998092i \(0.480332\pi\)
\(504\) 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 \(0.100419\pi\)
−0.950649 + 0.310270i \(0.899581\pi\)
\(510\) 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 −0.954408 0.298504i \(-0.903512\pi\)
0.298504 + 0.954408i \(0.403512\pi\)
\(524\) 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 0.768328 0.640057i \(-0.221089\pi\)
−0.640057 + 0.768328i \(0.721089\pi\)
\(548\) 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 −0.394704 + 0.918808i \(0.629153\pi\)
−0.918808 + 0.394704i \(0.870847\pi\)
\(558\) 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 −0.727865 0.685720i \(-0.759487\pi\)
0.685720 + 0.727865i \(0.259487\pi\)
\(564\) 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 \(0.0809347\pi\)
−0.967849 + 0.251533i \(0.919065\pi\)
\(570\) 0 0
\(571\) 12.0000i 0.502184i 0.967963 + 0.251092i \(0.0807897\pi\)
−0.967963 + 0.251092i \(0.919210\pi\)
\(572\) 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 −0.981654 0.190673i \(-0.938933\pi\)
0.190673 + 0.981654i \(0.438933\pi\)
\(578\) 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 0.326188 0.945305i \(-0.394236\pi\)
−0.945305 + 0.326188i \(0.894236\pi\)
\(588\) 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 0.328521 0.944497i \(-0.393450\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) 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 0.834750 0.550629i \(-0.185612\pi\)
−0.550629 + 0.834750i \(0.685612\pi\)
\(608\) 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 0.865102 0.501596i \(-0.167253\pi\)
−0.501596 + 0.865102i \(0.667253\pi\)
\(614\) 0 0
\(615\) −18.0000 + 6.00000i −0.725830 + 0.241943i
\(616\) 0 0
\(617\) 15.0000 15.0000i 0.603877 0.603877i −0.337462 0.941339i \(-0.609568\pi\)
0.941339 + 0.337462i \(0.109568\pi\)
\(618\) 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 \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 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 −0.645474 0.763782i \(-0.723340\pi\)
0.763782 + 0.645474i \(0.223340\pi\)
\(644\) 0 0
\(645\) −6.00000 + 12.0000i −0.236250 + 0.472500i
\(646\) 0 0
\(647\) 9.00000 + 9.00000i 0.353827 + 0.353827i 0.861531 0.507705i \(-0.169506\pi\)
−0.507705 + 0.861531i \(0.669506\pi\)
\(648\) 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 −0.933928 0.357462i \(-0.883642\pi\)
−0.357462 0.933928i \(-0.616358\pi\)
\(654\) 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 0.999363 0.0356839i \(-0.0113610\pi\)
−0.0356839 + 0.999363i \(0.511361\pi\)
\(674\) 0 0
\(675\) 4.00000 28.0000i 0.153960 1.07772i
\(676\) 0 0
\(677\) 27.0000 27.0000i 1.03769 1.03769i 0.0384331 0.999261i \(-0.487763\pi\)
0.999261 0.0384331i \(-0.0122367\pi\)
\(678\) 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 −0.0336941 + 0.999432i \(0.510727\pi\)
−0.999432 + 0.0336941i \(0.989273\pi\)
\(684\) 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 \(0.0733006\pi\)
−0.973602 + 0.228251i \(0.926699\pi\)
\(692\) 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 \(0.289231\pi\)
−0.614815 + 0.788672i \(0.710769\pi\)
\(710\) 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 0.997524 0.0703254i \(-0.0224038\pi\)
−0.0703254 + 0.997524i \(0.522404\pi\)
\(728\) 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 0.927604 0.373566i \(-0.121865\pi\)
−0.373566 + 0.927604i \(0.621865\pi\)
\(734\) 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 −0.852654 0.522476i \(-0.825008\pi\)
0.522476 + 0.852654i \(0.325008\pi\)
\(744\) 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 \(-0.722095\pi\)
0.642482 0.766301i \(-0.277905\pi\)
\(752\) 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 −0.851487 0.524376i \(-0.824299\pi\)
0.524376 + 0.851487i \(0.324299\pi\)
\(758\) 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 \(-0.743582\pi\)
0.692708 0.721218i \(-0.256418\pi\)
\(770\) 0 0
\(771\) 6.00000i 0.216085i
\(772\) 0 0
\(773\) 9.00000 + 9.00000i 0.323708 + 0.323708i 0.850188 0.526480i \(-0.176489\pi\)
−0.526480 + 0.850188i \(0.676489\pi\)
\(774\) 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 0.921965 0.387273i \(-0.126583\pi\)
−0.387273 + 0.921965i \(0.626583\pi\)
\(788\) 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