Properties

Label 1260.2.s.f.541.1
Level $1260$
Weight $2$
Character 1260.541
Analytic conductor $10.061$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(-1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 1260.541
Dual form 1260.2.s.f.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(-1.32288 + 2.29129i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(-1.32288 + 2.29129i) q^{7} +(-0.822876 - 1.42526i) q^{11} -2.64575 q^{13} +(-0.822876 - 1.42526i) q^{17} +(-4.14575 + 7.18065i) q^{19} +(0.822876 - 1.42526i) q^{23} +(-0.500000 - 0.866025i) q^{25} -7.64575 q^{29} +(2.14575 + 3.71655i) q^{31} +(1.32288 + 2.29129i) q^{35} +(-0.322876 + 0.559237i) q^{37} -4.93725 q^{41} -5.93725 q^{43} +(3.00000 - 5.19615i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(1.64575 + 2.85052i) q^{53} -1.64575 q^{55} +(5.46863 + 9.47194i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-1.32288 + 2.29129i) q^{65} +(-0.322876 - 0.559237i) q^{67} -13.6458 q^{71} +(-6.61438 - 11.4564i) q^{73} +4.35425 q^{77} +(-1.14575 + 1.98450i) q^{79} +10.9373 q^{83} -1.64575 q^{85} +(-7.11438 + 12.3225i) q^{89} +(3.50000 - 6.06218i) q^{91} +(4.14575 + 7.18065i) q^{95} +8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{5} + 2 q^{11} + 2 q^{17} - 6 q^{19} - 2 q^{23} - 2 q^{25} - 20 q^{29} - 2 q^{31} + 4 q^{37} + 12 q^{41} + 8 q^{43} + 12 q^{47} - 14 q^{49} - 4 q^{53} + 4 q^{55} + 6 q^{59} - 16 q^{61} + 4 q^{67} - 44 q^{71} + 28 q^{77} + 6 q^{79} + 12 q^{83} + 4 q^{85} - 2 q^{89} + 14 q^{91} + 6 q^{95} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −1.32288 + 2.29129i −0.500000 + 0.866025i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.822876 1.42526i −0.248106 0.429733i 0.714894 0.699233i \(-0.246475\pi\)
−0.963000 + 0.269500i \(0.913142\pi\)
\(12\) 0 0
\(13\) −2.64575 −0.733799 −0.366900 0.930261i \(-0.619581\pi\)
−0.366900 + 0.930261i \(0.619581\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.822876 1.42526i −0.199577 0.345677i 0.748815 0.662780i \(-0.230623\pi\)
−0.948391 + 0.317103i \(0.897290\pi\)
\(18\) 0 0
\(19\) −4.14575 + 7.18065i −0.951101 + 1.64735i −0.208051 + 0.978118i \(0.566712\pi\)
−0.743049 + 0.669237i \(0.766621\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.822876 1.42526i 0.171581 0.297188i −0.767391 0.641179i \(-0.778446\pi\)
0.938973 + 0.343991i \(0.111779\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7.64575 −1.41978 −0.709890 0.704312i \(-0.751255\pi\)
−0.709890 + 0.704312i \(0.751255\pi\)
\(30\) 0 0
\(31\) 2.14575 + 3.71655i 0.385388 + 0.667512i 0.991823 0.127621i \(-0.0407342\pi\)
−0.606435 + 0.795133i \(0.707401\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.32288 + 2.29129i 0.223607 + 0.387298i
\(36\) 0 0
\(37\) −0.322876 + 0.559237i −0.0530804 + 0.0919380i −0.891345 0.453326i \(-0.850237\pi\)
0.838264 + 0.545264i \(0.183571\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.93725 −0.771070 −0.385535 0.922693i \(-0.625983\pi\)
−0.385535 + 0.922693i \(0.625983\pi\)
\(42\) 0 0
\(43\) −5.93725 −0.905423 −0.452711 0.891657i \(-0.649543\pi\)
−0.452711 + 0.891657i \(0.649543\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.64575 + 2.85052i 0.226061 + 0.391550i 0.956637 0.291282i \(-0.0940817\pi\)
−0.730576 + 0.682831i \(0.760748\pi\)
\(54\) 0 0
\(55\) −1.64575 −0.221913
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.46863 + 9.47194i 0.711955 + 1.23314i 0.964122 + 0.265458i \(0.0855232\pi\)
−0.252168 + 0.967684i \(0.581144\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.32288 + 2.29129i −0.164083 + 0.284199i
\(66\) 0 0
\(67\) −0.322876 0.559237i −0.0394455 0.0683217i 0.845629 0.533772i \(-0.179226\pi\)
−0.885074 + 0.465450i \(0.845892\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −13.6458 −1.61945 −0.809726 0.586808i \(-0.800384\pi\)
−0.809726 + 0.586808i \(0.800384\pi\)
\(72\) 0 0
\(73\) −6.61438 11.4564i −0.774154 1.34087i −0.935269 0.353939i \(-0.884842\pi\)
0.161114 0.986936i \(-0.448491\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.35425 0.496213
\(78\) 0 0
\(79\) −1.14575 + 1.98450i −0.128907 + 0.223274i −0.923253 0.384192i \(-0.874480\pi\)
0.794346 + 0.607465i \(0.207814\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.9373 1.20052 0.600260 0.799805i \(-0.295064\pi\)
0.600260 + 0.799805i \(0.295064\pi\)
\(84\) 0 0
\(85\) −1.64575 −0.178507
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.11438 + 12.3225i −0.754123 + 1.30618i 0.191687 + 0.981456i \(0.438604\pi\)
−0.945809 + 0.324722i \(0.894729\pi\)
\(90\) 0 0
\(91\) 3.50000 6.06218i 0.366900 0.635489i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.14575 + 7.18065i 0.425345 + 0.736719i
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.46863 4.27579i −0.245638 0.425457i 0.716673 0.697409i \(-0.245664\pi\)
−0.962311 + 0.271953i \(0.912331\pi\)
\(102\) 0 0
\(103\) −4.67712 + 8.10102i −0.460851 + 0.798217i −0.999004 0.0446304i \(-0.985789\pi\)
0.538153 + 0.842847i \(0.319122\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.46863 + 14.6681i −0.818693 + 1.41802i 0.0879524 + 0.996125i \(0.471968\pi\)
−0.906645 + 0.421893i \(0.861366\pi\)
\(108\) 0 0
\(109\) 6.50000 + 11.2583i 0.622587 + 1.07835i 0.989002 + 0.147901i \(0.0472517\pi\)
−0.366415 + 0.930451i \(0.619415\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −0.822876 1.42526i −0.0767336 0.132906i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.35425 0.399153
\(120\) 0 0
\(121\) 4.14575 7.18065i 0.376886 0.652787i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −2.06275 −0.183039 −0.0915196 0.995803i \(-0.529172\pi\)
−0.0915196 + 0.995803i \(0.529172\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.6458 18.4390i 0.930124 1.61102i 0.147017 0.989134i \(-0.453033\pi\)
0.783107 0.621887i \(-0.213634\pi\)
\(132\) 0 0
\(133\) −10.9686 18.9982i −0.951101 1.64735i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.1144 17.5186i −0.864130 1.49672i −0.867909 0.496724i \(-0.834536\pi\)
0.00377913 0.999993i \(-0.498797\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.17712 + 3.77089i 0.182060 + 0.315338i
\(144\) 0 0
\(145\) −3.82288 + 6.62141i −0.317473 + 0.549879i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.29150 + 5.70105i −0.269650 + 0.467048i −0.968772 0.247955i \(-0.920241\pi\)
0.699121 + 0.715003i \(0.253575\pi\)
\(150\) 0 0
\(151\) 2.29150 + 3.96900i 0.186480 + 0.322993i 0.944074 0.329733i \(-0.106959\pi\)
−0.757594 + 0.652726i \(0.773625\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.29150 0.344702
\(156\) 0 0
\(157\) 0.645751 + 1.11847i 0.0515366 + 0.0892639i 0.890643 0.454704i \(-0.150255\pi\)
−0.839106 + 0.543968i \(0.816921\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.17712 + 3.77089i 0.171581 + 0.297188i
\(162\) 0 0
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.6458 −1.52023 −0.760117 0.649786i \(-0.774858\pi\)
−0.760117 + 0.649786i \(0.774858\pi\)
\(168\) 0 0
\(169\) −6.00000 −0.461538
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.93725 8.55157i 0.375372 0.650164i −0.615010 0.788519i \(-0.710848\pi\)
0.990383 + 0.138355i \(0.0441815\pi\)
\(174\) 0 0
\(175\) 2.64575 0.200000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.291503 + 0.504897i 0.0217879 + 0.0377378i 0.876714 0.481012i \(-0.159731\pi\)
−0.854926 + 0.518750i \(0.826397\pi\)
\(180\) 0 0
\(181\) −4.29150 −0.318985 −0.159492 0.987199i \(-0.550986\pi\)
−0.159492 + 0.987199i \(0.550986\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.322876 + 0.559237i 0.0237383 + 0.0411159i
\(186\) 0 0
\(187\) −1.35425 + 2.34563i −0.0990325 + 0.171529i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.58301 16.5983i 0.693402 1.20101i −0.277315 0.960779i \(-0.589444\pi\)
0.970716 0.240228i \(-0.0772223\pi\)
\(192\) 0 0
\(193\) 4.03137 + 6.98254i 0.290185 + 0.502614i 0.973853 0.227178i \(-0.0729500\pi\)
−0.683669 + 0.729793i \(0.739617\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.93725 0.351765 0.175882 0.984411i \(-0.443722\pi\)
0.175882 + 0.984411i \(0.443722\pi\)
\(198\) 0 0
\(199\) 11.5830 + 20.0624i 0.821097 + 1.42218i 0.904866 + 0.425697i \(0.139971\pi\)
−0.0837682 + 0.996485i \(0.526696\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.1144 17.5186i 0.709890 1.22957i
\(204\) 0 0
\(205\) −2.46863 + 4.27579i −0.172416 + 0.298634i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 13.6458 0.943896
\(210\) 0 0
\(211\) 8.58301 0.590878 0.295439 0.955362i \(-0.404534\pi\)
0.295439 + 0.955362i \(0.404534\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.96863 + 5.14181i −0.202459 + 0.350669i
\(216\) 0 0
\(217\) −11.3542 −0.770777
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.17712 + 3.77089i 0.146449 + 0.253658i
\(222\) 0 0
\(223\) 17.8745 1.19697 0.598483 0.801136i \(-0.295770\pi\)
0.598483 + 0.801136i \(0.295770\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.82288 + 17.0137i 0.651967 + 1.12924i 0.982645 + 0.185497i \(0.0593893\pi\)
−0.330678 + 0.943744i \(0.607277\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.6458 18.4390i 0.697426 1.20798i −0.271930 0.962317i \(-0.587662\pi\)
0.969356 0.245661i \(-0.0790049\pi\)
\(234\) 0 0
\(235\) −3.00000 5.19615i −0.195698 0.338960i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 6.35425 + 11.0059i 0.409313 + 0.708951i 0.994813 0.101721i \(-0.0324350\pi\)
−0.585500 + 0.810673i \(0.699102\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −7.00000 −0.447214
\(246\) 0 0
\(247\) 10.9686 18.9982i 0.697917 1.20883i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.9373 0.690353 0.345177 0.938538i \(-0.387819\pi\)
0.345177 + 0.938538i \(0.387819\pi\)
\(252\) 0 0
\(253\) −2.70850 −0.170282
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.76013 4.78068i 0.172172 0.298211i −0.767007 0.641639i \(-0.778255\pi\)
0.939179 + 0.343428i \(0.111588\pi\)
\(258\) 0 0
\(259\) −0.854249 1.47960i −0.0530804 0.0919380i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.2288 24.6449i −0.877383 1.51967i −0.854203 0.519940i \(-0.825954\pi\)
−0.0231800 0.999731i \(-0.507379\pi\)
\(264\) 0 0
\(265\) 3.29150 0.202195
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.9373 + 24.1400i 0.849769 + 1.47184i 0.881414 + 0.472345i \(0.156592\pi\)
−0.0316446 + 0.999499i \(0.510074\pi\)
\(270\) 0 0
\(271\) −3.70850 + 6.42331i −0.225275 + 0.390188i −0.956402 0.292054i \(-0.905661\pi\)
0.731127 + 0.682242i \(0.238995\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.822876 + 1.42526i −0.0496213 + 0.0859466i
\(276\) 0 0
\(277\) 10.3229 + 17.8797i 0.620241 + 1.07429i 0.989441 + 0.144939i \(0.0462987\pi\)
−0.369199 + 0.929350i \(0.620368\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) 7.32288 + 12.6836i 0.435300 + 0.753961i 0.997320 0.0731621i \(-0.0233091\pi\)
−0.562020 + 0.827123i \(0.689976\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.53137 11.3127i 0.385535 0.667766i
\(288\) 0 0
\(289\) 7.14575 12.3768i 0.420338 0.728047i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 10.9373 0.636792
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.17712 + 3.77089i −0.125906 + 0.218076i
\(300\) 0 0
\(301\) 7.85425 13.6040i 0.452711 0.784119i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.00000 + 6.92820i 0.229039 + 0.396708i
\(306\) 0 0
\(307\) 27.9373 1.59446 0.797232 0.603674i \(-0.206297\pi\)
0.797232 + 0.603674i \(0.206297\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6.82288 + 11.8176i 0.386890 + 0.670113i 0.992029 0.126007i \(-0.0402161\pi\)
−0.605140 + 0.796119i \(0.706883\pi\)
\(312\) 0 0
\(313\) 10.6144 18.3846i 0.599960 1.03916i −0.392866 0.919596i \(-0.628516\pi\)
0.992826 0.119566i \(-0.0381502\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.7601 20.3691i 0.660515 1.14404i −0.319966 0.947429i \(-0.603671\pi\)
0.980481 0.196616i \(-0.0629952\pi\)
\(318\) 0 0
\(319\) 6.29150 + 10.8972i 0.352257 + 0.610126i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 13.6458 0.759270
\(324\) 0 0
\(325\) 1.32288 + 2.29129i 0.0733799 + 0.127098i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.93725 + 13.7477i 0.437595 + 0.757937i
\(330\) 0 0
\(331\) 10.0830 17.4643i 0.554212 0.959923i −0.443752 0.896149i \(-0.646353\pi\)
0.997964 0.0637740i \(-0.0203137\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.645751 −0.0352812
\(336\) 0 0
\(337\) −33.2288 −1.81009 −0.905043 0.425320i \(-0.860161\pi\)
−0.905043 + 0.425320i \(0.860161\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.53137 6.11652i 0.191235 0.331228i
\(342\) 0 0
\(343\) 18.5203 1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.58301 + 11.4021i 0.353394 + 0.612097i 0.986842 0.161689i \(-0.0516941\pi\)
−0.633448 + 0.773786i \(0.718361\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −18.0516 31.2663i −0.960791 1.66414i −0.720520 0.693434i \(-0.756097\pi\)
−0.240271 0.970706i \(-0.577236\pi\)
\(354\) 0 0
\(355\) −6.82288 + 11.8176i −0.362121 + 0.627211i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.4059 + 18.0235i −0.549201 + 0.951245i 0.449128 + 0.893467i \(0.351735\pi\)
−0.998329 + 0.0577773i \(0.981599\pi\)
\(360\) 0 0
\(361\) −24.8745 43.0839i −1.30918 2.26757i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −13.2288 −0.692425
\(366\) 0 0
\(367\) −3.61438 6.26029i −0.188669 0.326784i 0.756138 0.654413i \(-0.227084\pi\)
−0.944807 + 0.327628i \(0.893751\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.70850 −0.452123
\(372\) 0 0
\(373\) −0.0313730 + 0.0543397i −0.00162443 + 0.00281360i −0.866836 0.498593i \(-0.833850\pi\)
0.865212 + 0.501406i \(0.167184\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 20.2288 1.04183
\(378\) 0 0
\(379\) −15.7085 −0.806891 −0.403446 0.915004i \(-0.632188\pi\)
−0.403446 + 0.915004i \(0.632188\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −13.6458 + 23.6351i −0.697265 + 1.20770i 0.272146 + 0.962256i \(0.412267\pi\)
−0.969411 + 0.245443i \(0.921067\pi\)
\(384\) 0 0
\(385\) 2.17712 3.77089i 0.110957 0.192182i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.239870 0.415468i −0.0121619 0.0210651i 0.859880 0.510496i \(-0.170538\pi\)
−0.872042 + 0.489430i \(0.837205\pi\)
\(390\) 0 0
\(391\) −2.70850 −0.136975
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.14575 + 1.98450i 0.0576490 + 0.0998510i
\(396\) 0 0
\(397\) 5.67712 9.83307i 0.284927 0.493508i −0.687665 0.726028i \(-0.741364\pi\)
0.972591 + 0.232521i \(0.0746974\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.35425 7.54178i 0.217441 0.376619i −0.736584 0.676346i \(-0.763562\pi\)
0.954025 + 0.299727i \(0.0968958\pi\)
\(402\) 0 0
\(403\) −5.67712 9.83307i −0.282798 0.489820i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.06275 0.0526784
\(408\) 0 0
\(409\) −3.08301 5.33992i −0.152445 0.264042i 0.779681 0.626177i \(-0.215381\pi\)
−0.932126 + 0.362135i \(0.882048\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −28.9373 −1.42391
\(414\) 0 0
\(415\) 5.46863 9.47194i 0.268444 0.464959i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.2915 −1.04016 −0.520079 0.854118i \(-0.674097\pi\)
−0.520079 + 0.854118i \(0.674097\pi\)
\(420\) 0 0
\(421\) −19.5830 −0.954417 −0.477209 0.878790i \(-0.658351\pi\)
−0.477209 + 0.878790i \(0.658351\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.822876 + 1.42526i −0.0399153 + 0.0691354i
\(426\) 0 0
\(427\) −10.5830 18.3303i −0.512148 0.887066i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 19.9373 + 34.5323i 0.960344 + 1.66336i 0.721636 + 0.692273i \(0.243390\pi\)
0.238708 + 0.971091i \(0.423276\pi\)
\(432\) 0 0
\(433\) 3.35425 0.161195 0.0805975 0.996747i \(-0.474317\pi\)
0.0805975 + 0.996747i \(0.474317\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.82288 + 11.8176i 0.326382 + 0.565311i
\(438\) 0 0
\(439\) −2.64575 + 4.58258i −0.126275 + 0.218714i −0.922231 0.386640i \(-0.873635\pi\)
0.795956 + 0.605355i \(0.206969\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.93725 8.55157i 0.234576 0.406298i −0.724573 0.689198i \(-0.757963\pi\)
0.959149 + 0.282900i \(0.0912965\pi\)
\(444\) 0 0
\(445\) 7.11438 + 12.3225i 0.337254 + 0.584141i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12.5830 0.593829 0.296914 0.954904i \(-0.404042\pi\)
0.296914 + 0.954904i \(0.404042\pi\)
\(450\) 0 0
\(451\) 4.06275 + 7.03688i 0.191307 + 0.331354i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.50000 6.06218i −0.164083 0.284199i
\(456\) 0 0
\(457\) 7.32288 12.6836i 0.342550 0.593313i −0.642356 0.766407i \(-0.722043\pi\)
0.984905 + 0.173093i \(0.0553762\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19.6458 0.914994 0.457497 0.889211i \(-0.348746\pi\)
0.457497 + 0.889211i \(0.348746\pi\)
\(462\) 0 0
\(463\) 10.5203 0.488918 0.244459 0.969660i \(-0.421390\pi\)
0.244459 + 0.969660i \(0.421390\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.8745 + 32.6916i −0.873408 + 1.51279i −0.0149591 + 0.999888i \(0.504762\pi\)
−0.858449 + 0.512899i \(0.828572\pi\)
\(468\) 0 0
\(469\) 1.70850 0.0788911
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.88562 + 8.46215i 0.224641 + 0.389090i
\(474\) 0 0
\(475\) 8.29150 0.380440
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.29150 5.70105i −0.150393 0.260488i 0.780979 0.624557i \(-0.214720\pi\)
−0.931372 + 0.364069i \(0.881387\pi\)
\(480\) 0 0
\(481\) 0.854249 1.47960i 0.0389504 0.0674641i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.00000 6.92820i 0.181631 0.314594i
\(486\) 0 0
\(487\) 1.32288 + 2.29129i 0.0599452 + 0.103828i 0.894441 0.447187i \(-0.147574\pi\)
−0.834495 + 0.551015i \(0.814241\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.12549 −0.0959221 −0.0479611 0.998849i \(-0.515272\pi\)
−0.0479611 + 0.998849i \(0.515272\pi\)
\(492\) 0 0
\(493\) 6.29150 + 10.8972i 0.283355 + 0.490785i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 18.0516 31.2663i 0.809726 1.40249i
\(498\) 0 0
\(499\) −13.7288 + 23.7789i −0.614584 + 1.06449i 0.375874 + 0.926671i \(0.377343\pi\)
−0.990457 + 0.137819i \(0.955991\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.4575 −1.00133 −0.500666 0.865641i \(-0.666911\pi\)
−0.500666 + 0.865641i \(0.666911\pi\)
\(504\) 0 0
\(505\) −4.93725 −0.219705
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −13.9373 + 24.1400i −0.617758 + 1.06999i 0.372136 + 0.928178i \(0.378626\pi\)
−0.989894 + 0.141810i \(0.954708\pi\)
\(510\) 0 0
\(511\) 35.0000 1.54831
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.67712 + 8.10102i 0.206099 + 0.356973i
\(516\) 0 0
\(517\) −9.87451 −0.434280
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.06275 1.84073i −0.0465598 0.0806439i 0.841806 0.539780i \(-0.181492\pi\)
−0.888366 + 0.459136i \(0.848159\pi\)
\(522\) 0 0
\(523\) −15.6144 + 27.0449i −0.682769 + 1.18259i 0.291363 + 0.956612i \(0.405891\pi\)
−0.974132 + 0.225978i \(0.927442\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.53137 6.11652i 0.153829 0.266440i
\(528\) 0 0
\(529\) 10.1458 + 17.5730i 0.441120 + 0.764042i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13.0627 0.565810
\(534\) 0 0
\(535\) 8.46863 + 14.6681i 0.366131 + 0.634157i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.76013 + 9.97684i −0.248106 + 0.429733i
\(540\) 0 0
\(541\) −18.3745 + 31.8256i −0.789982 + 1.36829i 0.135996 + 0.990709i \(0.456577\pi\)
−0.925977 + 0.377579i \(0.876757\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13.0000 0.556859
\(546\) 0 0
\(547\) −43.2915 −1.85101 −0.925505 0.378734i \(-0.876359\pi\)
−0.925505 + 0.378734i \(0.876359\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 31.6974 54.9015i 1.35035 2.33888i
\(552\) 0 0
\(553\) −3.03137 5.25049i −0.128907 0.223274i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.00000 15.5885i −0.381342 0.660504i 0.609912 0.792469i \(-0.291205\pi\)
−0.991254 + 0.131965i \(0.957871\pi\)
\(558\) 0 0
\(559\) 15.7085 0.664399
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −18.2915 31.6818i −0.770895 1.33523i −0.937073 0.349133i \(-0.886476\pi\)
0.166178 0.986096i \(-0.446857\pi\)
\(564\) 0 0
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.88562 + 3.26599i −0.0790494 + 0.136918i −0.902840 0.429977i \(-0.858522\pi\)
0.823791 + 0.566894i \(0.191855\pi\)
\(570\) 0 0
\(571\) −22.1458 38.3576i −0.926771 1.60521i −0.788688 0.614793i \(-0.789239\pi\)
−0.138083 0.990421i \(-0.544094\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.64575 −0.0686326
\(576\) 0 0
\(577\) 21.2601 + 36.8236i 0.885071 + 1.53299i 0.845633 + 0.533766i \(0.179224\pi\)
0.0394383 + 0.999222i \(0.487443\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −14.4686 + 25.0604i −0.600260 + 1.03968i
\(582\) 0 0
\(583\) 2.70850 4.69126i 0.112174 0.194292i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.9373 −0.699075 −0.349538 0.936922i \(-0.613661\pi\)
−0.349538 + 0.936922i \(0.613661\pi\)
\(588\) 0 0
\(589\) −35.5830 −1.46617
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.5314 + 21.7050i −0.514602 + 0.891316i 0.485255 + 0.874373i \(0.338727\pi\)
−0.999856 + 0.0169436i \(0.994606\pi\)
\(594\) 0 0
\(595\) 2.17712 3.77089i 0.0892534 0.154591i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.06275 + 1.84073i 0.0434226 + 0.0752102i 0.886920 0.461923i \(-0.152840\pi\)
−0.843497 + 0.537133i \(0.819507\pi\)
\(600\) 0 0
\(601\) −37.5830 −1.53304 −0.766521 0.642219i \(-0.778014\pi\)
−0.766521 + 0.642219i \(0.778014\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.14575 7.18065i −0.168549 0.291935i
\(606\) 0 0
\(607\) 8.38562 14.5243i 0.340362 0.589524i −0.644138 0.764909i \(-0.722784\pi\)
0.984500 + 0.175385i \(0.0561171\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.93725 + 13.7477i −0.321107 + 0.556174i
\(612\) 0 0
\(613\) 20.5830 + 35.6508i 0.831340 + 1.43992i 0.896976 + 0.442079i \(0.145759\pi\)
−0.0656363 + 0.997844i \(0.520908\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.29150 −0.374062 −0.187031 0.982354i \(-0.559886\pi\)
−0.187031 + 0.982354i \(0.559886\pi\)
\(618\) 0 0
\(619\) 9.50000 + 16.4545i 0.381837 + 0.661361i 0.991325 0.131434i \(-0.0419582\pi\)
−0.609488 + 0.792796i \(0.708625\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −18.8229 32.6022i −0.754123 1.30618i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.06275 0.0423745
\(630\) 0 0
\(631\) −35.7490 −1.42315 −0.711573 0.702612i \(-0.752017\pi\)
−0.711573 + 0.702612i \(0.752017\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.03137 + 1.78639i −0.0409288 + 0.0708907i
\(636\) 0 0
\(637\) 9.26013 + 16.0390i 0.366900 + 0.635489i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.05163 10.4817i −0.239025 0.414004i 0.721410 0.692509i \(-0.243494\pi\)
−0.960435 + 0.278505i \(0.910161\pi\)
\(642\) 0 0
\(643\) −21.8118 −0.860172 −0.430086 0.902788i \(-0.641517\pi\)
−0.430086 + 0.902788i \(0.641517\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 11.4686 + 19.8642i 0.450878 + 0.780944i 0.998441 0.0558207i \(-0.0177775\pi\)
−0.547563 + 0.836765i \(0.684444\pi\)
\(648\) 0 0
\(649\) 9.00000 15.5885i 0.353281 0.611900i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14.1771 24.5555i 0.554794 0.960931i −0.443126 0.896459i \(-0.646131\pi\)
0.997920 0.0644715i \(-0.0205362\pi\)
\(654\) 0 0
\(655\) −10.6458 18.4390i −0.415964 0.720471i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 20.4373 + 35.3984i 0.794917 + 1.37684i 0.922892 + 0.385059i \(0.125819\pi\)
−0.127975 + 0.991777i \(0.540848\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −21.9373 −0.850690
\(666\) 0 0
\(667\) −6.29150 + 10.8972i −0.243608 + 0.421941i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 13.1660 0.508268
\(672\) 0 0
\(673\) −5.35425 −0.206391 −0.103196 0.994661i \(-0.532907\pi\)
−0.103196 + 0.994661i \(0.532907\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −11.1771 + 19.3593i −0.429572 + 0.744040i −0.996835 0.0794963i \(-0.974669\pi\)
0.567263 + 0.823536i \(0.308002\pi\)
\(678\) 0 0
\(679\) −10.5830 + 18.3303i −0.406138 + 0.703452i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.46863 + 4.27579i 0.0944594 + 0.163608i 0.909383 0.415960i \(-0.136554\pi\)
−0.814923 + 0.579569i \(0.803221\pi\)
\(684\) 0 0
\(685\) −20.2288 −0.772901
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.35425 7.54178i −0.165884 0.287319i
\(690\) 0 0
\(691\) −11.7915 + 20.4235i −0.448570 + 0.776946i −0.998293 0.0584009i \(-0.981400\pi\)
0.549723 + 0.835347i \(0.314733\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.50000 4.33013i 0.0948304 0.164251i
\(696\) 0 0
\(697\) 4.06275 + 7.03688i 0.153887 + 0.266541i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −34.9373 −1.31956 −0.659781 0.751458i \(-0.729351\pi\)
−0.659781 + 0.751458i \(0.729351\pi\)
\(702\) 0 0
\(703\) −2.67712 4.63692i −0.100970 0.174885i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.0627 0.491275
\(708\) 0 0
\(709\) 11.2915 19.5575i 0.424061 0.734496i −0.572271 0.820065i \(-0.693937\pi\)
0.996332 + 0.0855689i \(0.0272708\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.06275 0.264502
\(714\) 0 0
\(715\) 4.35425 0.162840
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −7.35425 + 12.7379i −0.274267 + 0.475045i −0.969950 0.243304i \(-0.921769\pi\)
0.695683 + 0.718349i \(0.255102\pi\)
\(720\) 0 0
\(721\) −12.3745 21.4333i −0.460851 0.798217i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.82288 + 6.62141i 0.141978 + 0.245913i
\(726\) 0 0
\(727\) −33.8118 −1.25401 −0.627004 0.779016i \(-0.715719\pi\)
−0.627004 + 0.779016i \(0.715719\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.88562 + 8.46215i 0.180701 + 0.312984i
\(732\) 0 0
\(733\) −3.61438 + 6.26029i −0.133500 + 0.231229i −0.925023 0.379910i \(-0.875955\pi\)
0.791523 + 0.611139i \(0.209288\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.531373 + 0.920365i −0.0195734 + 0.0339021i
\(738\) 0 0
\(739\) −14.5000 25.1147i −0.533391 0.923861i −0.999239 0.0389959i \(-0.987584\pi\)
0.465848 0.884865i \(-0.345749\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.0627 0.479226 0.239613 0.970869i \(-0.422979\pi\)
0.239613 + 0.970869i \(0.422979\pi\)
\(744\) 0 0
\(745\) 3.29150 + 5.70105i 0.120591 + 0.208870i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −22.4059 38.8081i −0.818693 1.41802i
\(750\) 0 0
\(751\) −12.0830 + 20.9284i −0.440915 + 0.763687i −0.997758 0.0669307i \(-0.978679\pi\)
0.556843 + 0.830618i \(0.312013\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.58301 0.166793
\(756\) 0 0
\(757\) −8.83399 −0.321077 −0.160538 0.987030i \(-0.551323\pi\)
−0.160538 + 0.987030i \(0.551323\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.05163 + 10.4817i −0.219371 + 0.379963i −0.954616 0.297839i \(-0.903734\pi\)
0.735244 + 0.677802i \(0.237067\pi\)
\(762\) 0 0
\(763\) −34.3948 −1.24517
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14.4686 25.0604i −0.522432 0.904878i
\(768\) 0 0
\(769\) −3.70850 −0.133732 −0.0668659 0.997762i \(-0.521300\pi\)
−0.0668659 + 0.997762i \(0.521300\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.6974 + 23.7246i 0.492661 + 0.853313i 0.999964 0.00845413i \(-0.00269106\pi\)
−0.507304 + 0.861767i \(0.669358\pi\)
\(774\) 0 0
\(775\) 2.14575 3.71655i 0.0770777 0.133502i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.4686 35.4527i 0.733365 1.27022i
\(780\) 0 0
\(781\) 11.2288 + 19.4488i 0.401796 + 0.695932i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.29150 0.0460957
\(786\) 0 0
\(787\) −2.93725 5.08747i −0.104702 0.181349i 0.808915 0.587926i \(-0.200055\pi\)
−0.913616 + 0.406577i \(0.866722\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.93725 13.7477i 0.282216 0.488813i
\(792\) 0 0
\(793\) 10.5830 18.3303i 0.375814 0.650928i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.93725 −0.174887 −0.0874433 0.996170i \(-0.527870\pi\)
−0.0874433 + 0.996170i \(0.527870\pi\)
\(798\) 0 0
\(799\) −9.87451 −0.349335
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −10.8856 + 18.8544i −0.38