Properties

Label 320.2.n.a.63.1
Level $320$
Weight $2$
Character 320.63
Analytic conductor $2.555$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.n (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 160)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 63.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 320.63
Dual form 320.2.n.a.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 + 2.00000i) q^{3} +(2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} -5.00000i q^{9} +O(q^{10})\) \(q+(-2.00000 + 2.00000i) q^{3} +(2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} -5.00000i q^{9} +(1.00000 + 1.00000i) q^{13} +(-6.00000 + 2.00000i) q^{15} +(-5.00000 + 5.00000i) q^{17} -4.00000 q^{19} -8.00000 q^{21} +(2.00000 - 2.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -4.00000i q^{29} +4.00000i q^{31} +(2.00000 + 6.00000i) q^{35} +(-1.00000 + 1.00000i) q^{37} -4.00000 q^{39} +(6.00000 - 6.00000i) q^{43} +(5.00000 - 10.0000i) q^{45} +(-2.00000 - 2.00000i) q^{47} +1.00000i q^{49} -20.0000i q^{51} +(7.00000 + 7.00000i) q^{53} +(8.00000 - 8.00000i) q^{57} -4.00000 q^{59} +4.00000 q^{61} +(10.0000 - 10.0000i) q^{63} +(1.00000 + 3.00000i) q^{65} +(10.0000 + 10.0000i) q^{67} +8.00000i q^{69} -12.0000i q^{71} +(-3.00000 - 3.00000i) q^{73} +(-14.0000 - 2.00000i) q^{75} +16.0000 q^{79} -1.00000 q^{81} +(2.00000 - 2.00000i) q^{83} +(-15.0000 + 5.00000i) q^{85} +(8.00000 + 8.00000i) q^{87} +4.00000i q^{91} +(-8.00000 - 8.00000i) q^{93} +(-8.00000 - 4.00000i) q^{95} +(-3.00000 + 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{3} + 4q^{5} + 4q^{7} + O(q^{10}) \) \( 2q - 4q^{3} + 4q^{5} + 4q^{7} + 2q^{13} - 12q^{15} - 10q^{17} - 8q^{19} - 16q^{21} + 4q^{23} + 6q^{25} + 8q^{27} + 4q^{35} - 2q^{37} - 8q^{39} + 12q^{43} + 10q^{45} - 4q^{47} + 14q^{53} + 16q^{57} - 8q^{59} + 8q^{61} + 20q^{63} + 2q^{65} + 20q^{67} - 6q^{73} - 28q^{75} + 32q^{79} - 2q^{81} + 4q^{83} - 30q^{85} + 16q^{87} - 16q^{93} - 16q^{95} - 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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 −0.169102 + 0.985599i \(0.554087\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(4\) 0 0
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) 0 0
\(7\) 2.00000 + 2.00000i 0.755929 + 0.755929i 0.975579 0.219650i \(-0.0704915\pi\)
−0.219650 + 0.975579i \(0.570491\pi\)
\(8\) 0 0
\(9\) 5.00000i 1.66667i
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.00000i 0.277350 + 0.277350i 0.832050 0.554700i \(-0.187167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 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
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −8.00000 −1.74574
\(22\) 0 0
\(23\) 2.00000 2.00000i 0.417029 0.417029i −0.467150 0.884178i \(-0.654719\pi\)
0.884178 + 0.467150i \(0.154719\pi\)
\(24\) 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
\(29\) 4.00000i 0.742781i −0.928477 0.371391i \(-0.878881\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 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
\(35\) 2.00000 + 6.00000i 0.338062 + 1.01419i
\(36\) 0 0
\(37\) −1.00000 + 1.00000i −0.164399 + 0.164399i −0.784512 0.620113i \(-0.787087\pi\)
0.620113 + 0.784512i \(0.287087\pi\)
\(38\) 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 −0.0816682 0.996660i \(-0.526025\pi\)
0.996660 + 0.0816682i \(0.0260248\pi\)
\(44\) 0 0
\(45\) 5.00000 10.0000i 0.745356 1.49071i
\(46\) 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
\(51\) 20.0000i 2.80056i
\(52\) 0 0
\(53\) 7.00000 + 7.00000i 0.961524 + 0.961524i 0.999287 0.0377628i \(-0.0120231\pi\)
−0.0377628 + 0.999287i \(0.512023\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.00000 8.00000i 1.05963 1.05963i
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 4.00000 0.512148 0.256074 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) 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 0.967029 + 0.254665i \(0.0819652\pi\)
0.254665 + 0.967029i \(0.418035\pi\)
\(68\) 0 0
\(69\) 8.00000i 0.963087i
\(70\) 0 0
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) 0 0
\(73\) −3.00000 3.00000i −0.351123 0.351123i 0.509404 0.860527i \(-0.329866\pi\)
−0.860527 + 0.509404i \(0.829866\pi\)
\(74\) 0 0
\(75\) −14.0000 2.00000i −1.61658 0.230940i
\(76\) 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 \(-0.700388\pi\)
0.808300 + 0.588771i \(0.200388\pi\)
\(84\) 0 0
\(85\) −15.0000 + 5.00000i −1.62698 + 0.542326i
\(86\) 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
\(91\) 4.00000i 0.419314i
\(92\) 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
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −6.00000 + 6.00000i −0.591198 + 0.591198i −0.937955 0.346757i \(-0.887283\pi\)
0.346757 + 0.937955i \(0.387283\pi\)
\(104\) 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 \(-0.384524\pi\)
−0.934915 + 0.354873i \(0.884524\pi\)
\(108\) 0 0
\(109\) 10.0000i 0.957826i 0.877862 + 0.478913i \(0.158969\pi\)
−0.877862 + 0.478913i \(0.841031\pi\)
\(110\) 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
\(115\) 6.00000 2.00000i 0.559503 0.186501i
\(116\) 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
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 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
\(131\) 8.00000i 0.698963i 0.936943 + 0.349482i \(0.113642\pi\)
−0.936943 + 0.349482i \(0.886358\pi\)
\(132\) 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 −0.663097 0.748533i \(-0.730758\pi\)
0.748533 + 0.663097i \(0.230758\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 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
\(149\) 18.0000i 1.47462i −0.675556 0.737309i \(-0.736096\pi\)
0.675556 0.737309i \(-0.263904\pi\)
\(150\) 0 0
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) 0 0
\(153\) 25.0000 + 25.0000i 2.02113 + 2.02113i
\(154\) 0 0
\(155\) −4.00000 + 8.00000i −0.321288 + 0.642575i
\(156\) 0 0
\(157\) 9.00000 9.00000i 0.718278 0.718278i −0.249974 0.968252i \(-0.580422\pi\)
0.968252 + 0.249974i \(0.0804222\pi\)
\(158\) 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 \(-0.785332\pi\)
0.624429 + 0.781081i \(0.285332\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 2.00000i −0.154765 0.154765i 0.625478 0.780242i \(-0.284904\pi\)
−0.780242 + 0.625478i \(0.784904\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) 20.0000i 1.52944i
\(172\) 0 0
\(173\) −13.0000 13.0000i −0.988372 0.988372i 0.0115615 0.999933i \(-0.496320\pi\)
−0.999933 + 0.0115615i \(0.996320\pi\)
\(174\) 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
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 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
\(189\) 16.0000i 1.16383i
\(190\) 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
\(195\) −8.00000 4.00000i −0.572892 0.286446i
\(196\) 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
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 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
\(211\) 16.0000i 1.10149i 0.834675 + 0.550743i \(0.185655\pi\)
−0.834675 + 0.550743i \(0.814345\pi\)
\(212\) 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
\(219\) 12.0000 0.810885
\(220\) 0 0
\(221\) −10.0000 −0.672673
\(222\) 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 0.292532 0.956256i \(-0.405502\pi\)
−0.956256 + 0.292532i \(0.905502\pi\)
\(228\) 0 0
\(229\) 20.0000i 1.32164i −0.750546 0.660819i \(-0.770209\pi\)
0.750546 0.660819i \(-0.229791\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.00000 5.00000i −0.327561 0.327561i 0.524097 0.851658i \(-0.324403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) −2.00000 6.00000i −0.130466 0.391397i
\(236\) 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
\(245\) −1.00000 + 2.00000i −0.0638877 + 0.127775i
\(246\) 0 0
\(247\) −4.00000 4.00000i −0.254514 0.254514i
\(248\) 0 0
\(249\) 8.00000i 0.506979i
\(250\) 0 0
\(251\) 24.0000i 1.51487i −0.652913 0.757433i \(-0.726453\pi\)
0.652913 0.757433i \(-0.273547\pi\)
\(252\) 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
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) −20.0000 −1.23797
\(262\) 0 0
\(263\) 6.00000 6.00000i 0.369976 0.369976i −0.497492 0.867468i \(-0.665746\pi\)
0.867468 + 0.497492i \(0.165746\pi\)
\(264\) 0 0
\(265\) 7.00000 + 21.0000i 0.430007 + 1.29002i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.0000i 0.609711i −0.952399 0.304855i \(-0.901392\pi\)
0.952399 0.304855i \(-0.0986081\pi\)
\(270\) 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 −0.382993 0.923751i \(-0.625107\pi\)
0.923751 + 0.382993i \(0.125107\pi\)
\(278\) 0 0
\(279\) 20.0000 1.19737
\(280\) 0 0
\(281\) 8.00000 0.477240 0.238620 0.971113i \(-0.423305\pi\)
0.238620 + 0.971113i \(0.423305\pi\)
\(282\) 0 0
\(283\) −6.00000 + 6.00000i −0.356663 + 0.356663i −0.862581 0.505918i \(-0.831154\pi\)
0.505918 + 0.862581i \(0.331154\pi\)
\(284\) 0 0
\(285\) 24.0000 8.00000i 1.42164 0.473879i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 33.0000i 1.94118i
\(290\) 0 0
\(291\) 12.0000i 0.703452i
\(292\) 0 0
\(293\) 5.00000 + 5.00000i 0.292103 + 0.292103i 0.837911 0.545807i \(-0.183777\pi\)
−0.545807 + 0.837911i \(0.683777\pi\)
\(294\) 0 0
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.00000 0.231326
\(300\) 0 0
\(301\) 24.0000 1.38334
\(302\) 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 0.932332 0.361602i \(-0.117770\pi\)
−0.361602 + 0.932332i \(0.617770\pi\)
\(308\) 0 0
\(309\) 24.0000i 1.36531i
\(310\) 0 0
\(311\) 28.0000i 1.58773i 0.608091 + 0.793867i \(0.291935\pi\)
−0.608091 + 0.793867i \(0.708065\pi\)
\(312\) 0 0
\(313\) 15.0000 + 15.0000i 0.847850 + 0.847850i 0.989865 0.142014i \(-0.0453579\pi\)
−0.142014 + 0.989865i \(0.545358\pi\)
\(314\) 0 0
\(315\) 30.0000 10.0000i 1.69031 0.563436i
\(316\) 0 0
\(317\) −11.0000 + 11.0000i −0.617822 + 0.617822i −0.944972 0.327151i \(-0.893912\pi\)
0.327151 + 0.944972i \(0.393912\pi\)
\(318\) 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
\(325\) −1.00000 + 7.00000i −0.0554700 + 0.388290i
\(326\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 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
\(339\) 36.0000 1.95525
\(340\) 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 \(-0.489443\pi\)
−0.999450 + 0.0331594i \(0.989443\pi\)
\(348\) 0 0
\(349\) 20.0000i 1.07058i 0.844670 + 0.535288i \(0.179797\pi\)
−0.844670 + 0.535288i \(0.820203\pi\)
\(350\) 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
\(355\) 12.0000 24.0000i 0.636894 1.27379i
\(356\) 0 0
\(357\) 40.0000 40.0000i 2.11702 2.11702i
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −22.0000 + 22.0000i −1.15470 + 1.15470i
\(364\) 0 0
\(365\) −3.00000 9.00000i −0.157027 0.471082i
\(366\) 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
\(371\) 28.0000i 1.45369i
\(372\) 0 0
\(373\) −21.0000 21.0000i −1.08734 1.08734i −0.995802 0.0915371i \(-0.970822\pi\)
−0.0915371 0.995802i \(-0.529178\pi\)
\(374\) 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
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) −40.0000 −2.04926
\(382\) 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
\(389\) 18.0000i 0.912636i 0.889817 + 0.456318i \(0.150832\pi\)
−0.889817 + 0.456318i \(0.849168\pi\)
\(390\) 0 0
\(391\) 20.0000i 1.01144i
\(392\) 0 0
\(393\) −16.0000 16.0000i −0.807093 0.807093i
\(394\) 0 0
\(395\) 32.0000 + 16.0000i 1.61009 + 0.805047i
\(396\) 0 0
\(397\) −13.0000 + 13.0000i −0.652451 + 0.652451i −0.953583 0.301131i \(-0.902636\pi\)
0.301131 + 0.953583i \(0.402636\pi\)
\(398\) 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
\(405\) −2.00000 1.00000i −0.0993808 0.0496904i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 2.00000i 0.0988936i −0.998777 0.0494468i \(-0.984254\pi\)
0.998777 0.0494468i \(-0.0157458\pi\)
\(410\) 0 0
\(411\) 4.00000i 0.197305i
\(412\) 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
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 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
\(435\) 8.00000 + 24.0000i 0.383571 + 1.15071i
\(436\) 0 0
\(437\) −8.00000 + 8.00000i −0.382692 + 0.382692i
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −22.0000 + 22.0000i −1.04525 + 1.04525i −0.0463251 + 0.998926i \(0.514751\pi\)
−0.998926 + 0.0463251i \(0.985249\pi\)
\(444\) 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 −0.263099 0.964769i \(-0.584744\pi\)
0.964769 + 0.263099i \(0.0847444\pi\)
\(458\) 0 0
\(459\) −40.0000 −1.86704
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 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 0.659317 0.751865i \(-0.270846\pi\)
−0.751865 + 0.659317i \(0.770846\pi\)
\(468\) 0 0
\(469\) 40.0000i 1.84703i
\(470\) 0 0
\(471\) 36.0000i 1.65879i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −12.0000 16.0000i −0.550598 0.734130i
\(476\) 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
\(485\) −9.00000 + 3.00000i −0.408669 + 0.136223i
\(486\) 0 0
\(487\) −6.00000 6.00000i −0.271886 0.271886i 0.557973 0.829859i \(-0.311579\pi\)
−0.829859 + 0.557973i \(0.811579\pi\)
\(488\) 0 0
\(489\) 8.00000i 0.361773i
\(490\) 0 0
\(491\) 16.0000i 0.722070i −0.932552 0.361035i \(-0.882424\pi\)
0.932552 0.361035i \(-0.117576\pi\)
\(492\) 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
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 8.00000 0.357414
\(502\) 0 0
\(503\) 10.0000 10.0000i 0.445878 0.445878i −0.448104 0.893982i \(-0.647900\pi\)
0.893982 + 0.448104i \(0.147900\pi\)
\(504\) 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
\(509\) 36.0000i 1.59567i 0.602875 + 0.797836i \(0.294022\pi\)
−0.602875 + 0.797836i \(0.705978\pi\)
\(510\) 0 0
\(511\) 12.0000i 0.530849i
\(512\) 0 0
\(513\) −16.0000 16.0000i −0.706417 0.706417i
\(514\) 0 0
\(515\) −18.0000 + 6.00000i −0.793175 + 0.264392i
\(516\) 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 \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −14.0000 + 14.0000i −0.612177 + 0.612177i −0.943513 0.331336i \(-0.892501\pi\)
0.331336 + 0.943513i \(0.392501\pi\)
\(524\) 0 0
\(525\) −24.0000 32.0000i −1.04745 1.39659i
\(526\) 0 0
\(527\) −20.0000 20.0000i −0.871214 0.871214i
\(528\) 0 0
\(529\) 15.0000i 0.652174i
\(530\) 0 0
\(531\) 20.0000i 0.867926i
\(532\) 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
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 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 0.823646 0.567104i \(-0.191936\pi\)
−0.567104 + 0.823646i \(0.691936\pi\)
\(548\) 0 0
\(549\) 20.0000i 0.853579i
\(550\) 0 0
\(551\) 16.0000i 0.681623i
\(552\) 0 0
\(553\) 32.0000 + 32.0000i 1.36078 + 1.36078i
\(554\) 0 0
\(555\) 4.00000 8.00000i 0.169791 0.339581i
\(556\) 0 0
\(557\) 15.0000 15.0000i 0.635570 0.635570i −0.313889 0.949460i \(-0.601632\pi\)
0.949460 + 0.313889i \(0.101632\pi\)
\(558\) 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 \(-0.692777\pi\)
0.822146 + 0.569276i \(0.192777\pi\)
\(564\) 0 0
\(565\) −9.00000 27.0000i −0.378633 1.13590i
\(566\) 0 0
\(567\) −2.00000 2.00000i −0.0839921 0.0839921i
\(568\) 0 0
\(569\) 2.00000i 0.0838444i 0.999121 + 0.0419222i \(0.0133482\pi\)
−0.999121 + 0.0419222i \(0.986652\pi\)
\(570\) 0 0
\(571\) 16.0000i 0.669579i −0.942293 0.334790i \(-0.891335\pi\)
0.942293 0.334790i \(-0.108665\pi\)
\(572\) 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
\(579\) 20.0000 0.831172
\(580\) 0 0
\(581\) 8.00000 0.331896
\(582\) 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 \(-0.116019\pi\)
−0.356466 + 0.934308i \(0.616019\pi\)
\(588\) 0 0
\(589\) 16.0000i 0.659269i
\(590\) 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
\(595\) −40.0000 20.0000i −1.63984 0.819920i
\(596\) 0 0
\(597\) −48.0000 + 48.0000i −1.96451 + 1.96451i
\(598\) 0 0
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) 50.0000 50.0000i 2.03616 2.03616i
\(604\) 0 0
\(605\) 22.0000 + 11.0000i 0.894427 + 0.447214i
\(606\) 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
\(611\) 4.00000i 0.161823i
\(612\) 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
\(615\) 0 0
\(616\) 0 0
\(617\) −29.0000 + 29.0000i −1.16750 + 1.16750i −0.184701 + 0.982795i \(0.559132\pi\)
−0.982795 + 0.184701i \(0.940868\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 16.0000 0.642058
\(622\) 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
\(629\) 10.0000i 0.398726i
\(630\) 0 0
\(631\) 4.00000i 0.159237i −0.996825 0.0796187i \(-0.974630\pi\)
0.996825 0.0796187i \(-0.0253703\pi\)
\(632\) 0 0
\(633\) −32.0000 32.0000i −1.27189 1.27189i
\(634\) 0 0
\(635\) 10.0000 + 30.0000i 0.396838 + 1.19051i
\(636\) 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 \(-0.660045\pi\)
0.876239 + 0.481877i \(0.160045\pi\)
\(644\) 0 0
\(645\) −24.0000 + 48.0000i −0.944999 + 1.89000i
\(646\) 0 0
\(647\) 10.0000 + 10.0000i 0.393141 + 0.393141i 0.875805 0.482665i \(-0.160331\pi\)
−0.482665 + 0.875805i \(0.660331\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 32.0000i 1.25418i
\(652\) 0 0
\(653\) −1.00000 1.00000i −0.0391330 0.0391330i 0.687270 0.726403i \(-0.258809\pi\)
−0.726403 + 0.687270i \(0.758809\pi\)
\(654\) 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
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 0 0
\(661\) −12.0000 −0.466746 −0.233373 0.972387i \(-0.574976\pi\)
−0.233373 + 0.972387i \(0.574976\pi\)
\(662\) 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
\(669\) 40.0000i 1.54649i
\(670\) 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
\(675\) −4.00000 + 28.0000i −0.153960 + 1.07772i
\(676\) 0 0
\(677\) 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i \(-0.724020\pi\)
0.762402 + 0.647103i \(0.224020\pi\)
\(678\) 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 −0.147287 0.989094i \(-0.547054\pi\)
0.989094 + 0.147287i \(0.0470541\pi\)
\(684\) 0 0
\(685\) 3.00000 1.00000i 0.114624 0.0382080i
\(686\) 0 0
\(687\) 40.0000 + 40.0000i 1.52610 + 1.52610i
\(688\) 0 0
\(689\) 14.0000i 0.533358i
\(690\) 0 0
\(691\) 32.0000i 1.21734i −0.793424 0.608669i \(-0.791704\pi\)
0.793424 0.608669i \(-0.208296\pi\)
\(692\) 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
\(699\) 20.0000 0.756469
\(700\) 0 0
\(701\) −20.0000 −0.755390 −0.377695 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 0 0
\(703\) 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
\(709\) 12.0000i 0.450669i −0.974281 0.225335i \(-0.927652\pi\)
0.974281 0.225335i \(-0.0723476\pi\)
\(710\) 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
\(725\) 16.0000 12.0000i 0.594225 0.445669i
\(726\) 0 0
\(727\) 18.0000 + 18.0000i 0.667583 + 0.667583i 0.957156 0.289573i \(-0.0935133\pi\)
−0.289573 + 0.957156i \(0.593513\pi\)
\(728\) 0 0
\(729\) 43.0000i 1.59259i
\(730\) 0 0
\(731\) 60.0000i 2.21918i
\(732\) 0 0
\(733\) −21.0000 21.0000i −0.775653 0.775653i 0.203436 0.979088i \(-0.434789\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(734\) 0 0
\(735\) −2.00000 6.00000i −0.0737711 0.221313i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −44.0000 −1.61857 −0.809283 0.587419i \(-0.800144\pi\)
−0.809283 + 0.587419i \(0.800144\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 30.0000 30.0000i 1.10059 1.10059i 0.106254 0.994339i \(-0.466114\pi\)
0.994339 0.106254i \(-0.0338857\pi\)
\(744\) 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
\(749\) 24.0000i 0.876941i
\(750\) 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
\(755\) 12.0000 24.0000i 0.436725 0.873449i
\(756\) 0 0
\(757\) 1.00000 1.00000i 0.0363456 0.0363456i −0.688700 0.725046i \(-0.741818\pi\)
0.725046 + 0.688700i \(0.241818\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 0 0
\(763\) −20.0000 + 20.0000i −0.724049 + 0.724049i
\(764\) 0 0
\(765\) 25.0000 + 75.0000i 0.903877 + 2.71163i
\(766\) 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
\(771\) 28.0000i 1.00840i
\(772\) 0 0
\(773\) 1.00000 + 1.00000i 0.0359675 + 0.0359675i 0.724862 0.688894i \(-0.241904\pi\)
−0.688894 + 0.724862i \(0.741904\pi\)
\(774\) 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 −0.997406 0.0719783i \(-0.977069\pi\)
−0.0719783 0.997406i \(-0.522931\pi\)
\(788\) 0 0
\(789\) 24.0000i 0.854423i
\(790\) 0 0
\(791\) 36.0000i 1.28001i
\(792\) 0 0
\(793\) 4.00000 + 4.00000i 0.142044 + 0.142044i
\(794\) 0 0
\(795\) −56.0000 28.0000i −1.98612 0.993058i
\(796\) 0 0
\(797\) 29.0000 29.0000i 1.02723 1.02723i 0.0276140