Properties

Label 3024.2.q.e.2881.1
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.e.2305.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-2.00000 - 3.46410i) q^{11} +(-1.50000 - 2.59808i) q^{13} +(3.50000 - 6.06218i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{29} +3.00000 q^{31} +(4.00000 - 3.46410i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-4.50000 - 7.79423i) q^{41} +(2.50000 - 4.33013i) q^{43} +3.00000 q^{47} +(5.50000 + 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{53} -8.00000 q^{55} -7.00000 q^{59} +3.00000 q^{61} -6.00000 q^{65} -13.0000 q^{67} -8.00000 q^{71} +(-3.50000 + 6.06218i) q^{73} +(-2.00000 - 10.3923i) q^{77} +9.00000 q^{79} +(-0.500000 + 0.866025i) q^{83} +(-7.00000 - 12.1244i) q^{85} +(7.50000 + 12.9904i) q^{89} +(-1.50000 - 7.79423i) q^{91} +10.0000 q^{95} +(8.50000 - 14.7224i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} + 5q^{7} + O(q^{10}) \) \( 2q + 2q^{5} + 5q^{7} - 4q^{11} - 3q^{13} + 7q^{17} + 5q^{19} - 4q^{23} + q^{25} - q^{29} + 6q^{31} + 8q^{35} - 11q^{37} - 9q^{41} + 5q^{43} + 6q^{47} + 11q^{49} + 3q^{53} - 16q^{55} - 14q^{59} + 6q^{61} - 12q^{65} - 26q^{67} - 16q^{71} - 7q^{73} - 4q^{77} + 18q^{79} - q^{83} - 14q^{85} + 15q^{89} - 3q^{91} + 20q^{95} + 17q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.50000 6.06218i 0.848875 1.47029i −0.0333386 0.999444i \(-0.510614\pi\)
0.882213 0.470850i \(-0.156053\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.500000 + 0.866025i −0.0928477 + 0.160817i −0.908708 0.417432i \(-0.862930\pi\)
0.815861 + 0.578249i \(0.196264\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 3.46410i 0.676123 0.585540i
\(36\) 0 0
\(37\) −5.50000 9.52628i −0.904194 1.56611i −0.821995 0.569495i \(-0.807139\pi\)
−0.0821995 0.996616i \(-0.526194\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i \(-0.918608\pi\)
0.264704 0.964330i \(-0.414726\pi\)
\(42\) 0 0
\(43\) 2.50000 4.33013i 0.381246 0.660338i −0.609994 0.792406i \(-0.708828\pi\)
0.991241 + 0.132068i \(0.0421616\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.00000 −0.911322 −0.455661 0.890153i \(-0.650597\pi\)
−0.455661 + 0.890153i \(0.650597\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) −13.0000 −1.58820 −0.794101 0.607785i \(-0.792058\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −3.50000 + 6.06218i −0.409644 + 0.709524i −0.994850 0.101361i \(-0.967680\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 10.3923i −0.227921 1.18431i
\(78\) 0 0
\(79\) 9.00000 1.01258 0.506290 0.862364i \(-0.331017\pi\)
0.506290 + 0.862364i \(0.331017\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.500000 + 0.866025i −0.0548821 + 0.0950586i −0.892161 0.451717i \(-0.850812\pi\)
0.837279 + 0.546776i \(0.184145\pi\)
\(84\) 0 0
\(85\) −7.00000 12.1244i −0.759257 1.31507i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.50000 + 12.9904i 0.794998 + 1.37698i 0.922840 + 0.385183i \(0.125862\pi\)
−0.127842 + 0.991795i \(0.540805\pi\)
\(90\) 0 0
\(91\) −1.50000 7.79423i −0.157243 0.817057i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.0000 1.02598
\(96\) 0 0
\(97\) 8.50000 14.7224i 0.863044 1.49484i −0.00593185 0.999982i \(-0.501888\pi\)
0.868976 0.494854i \(-0.164778\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 0 0
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i \(-0.942150\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.500000 0.866025i −0.0470360 0.0814688i 0.841549 0.540181i \(-0.181644\pi\)
−0.888585 + 0.458712i \(0.848311\pi\)
\(114\) 0 0
\(115\) 4.00000 + 6.92820i 0.373002 + 0.646058i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.0000 12.1244i 1.28338 1.11144i
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) 2.50000 + 12.9904i 0.216777 + 1.12641i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.00000 + 12.1244i 0.598050 + 1.03585i 0.993109 + 0.117198i \(0.0373911\pi\)
−0.395058 + 0.918656i \(0.629276\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −6.00000 + 10.3923i −0.501745 + 0.869048i
\(144\) 0 0
\(145\) 1.00000 + 1.73205i 0.0830455 + 0.143839i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.00000 5.19615i 0.240966 0.417365i
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −8.00000 + 6.92820i −0.630488 + 0.546019i
\(162\) 0 0
\(163\) −9.50000 16.4545i −0.744097 1.28881i −0.950615 0.310372i \(-0.899546\pi\)
0.206518 0.978443i \(-0.433787\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.5000 19.9186i −0.889897 1.54135i −0.839996 0.542592i \(-0.817443\pi\)
−0.0499004 0.998754i \(-0.515890\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.00000 0.0760286 0.0380143 0.999277i \(-0.487897\pi\)
0.0380143 + 0.999277i \(0.487897\pi\)
\(174\) 0 0
\(175\) 0.500000 + 2.59808i 0.0377964 + 0.196396i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.5000 18.1865i 0.784807 1.35933i −0.144308 0.989533i \(-0.546095\pi\)
0.929114 0.369792i \(-0.120571\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −22.0000 −1.61747
\(186\) 0 0
\(187\) −28.0000 −2.04756
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) −1.00000 −0.0719816 −0.0359908 0.999352i \(-0.511459\pi\)
−0.0359908 + 0.999352i \(0.511459\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 26.0000 1.85242 0.926212 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) 0 0
\(199\) −6.50000 + 11.2583i −0.460773 + 0.798082i −0.999000 0.0447181i \(-0.985761\pi\)
0.538227 + 0.842800i \(0.319094\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.00000 + 1.73205i −0.140372 + 0.121566i
\(204\) 0 0
\(205\) −18.0000 −1.25717
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 10.0000 17.3205i 0.691714 1.19808i
\(210\) 0 0
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 0 0
\(217\) 7.50000 + 2.59808i 0.509133 + 0.176369i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −21.0000 −1.41261
\(222\) 0 0
\(223\) −3.50000 + 6.06218i −0.234377 + 0.405953i −0.959092 0.283096i \(-0.908638\pi\)
0.724714 + 0.689050i \(0.241972\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −14.5000 25.1147i −0.949927 1.64532i −0.745573 0.666424i \(-0.767824\pi\)
−0.204354 0.978897i \(-0.565509\pi\)
\(234\) 0 0
\(235\) 3.00000 5.19615i 0.195698 0.338960i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 10.5000 + 18.1865i 0.679189 + 1.17639i 0.975226 + 0.221213i \(0.0710015\pi\)
−0.296037 + 0.955176i \(0.595665\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 13.0000 5.19615i 0.830540 0.331970i
\(246\) 0 0
\(247\) 7.50000 12.9904i 0.477214 0.826558i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 0 0
\(259\) −5.50000 28.5788i −0.341753 1.77580i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) −3.00000 5.19615i −0.184289 0.319197i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.500000 + 0.866025i −0.0304855 + 0.0528025i −0.880866 0.473366i \(-0.843039\pi\)
0.850380 + 0.526169i \(0.176372\pi\)
\(270\) 0 0
\(271\) −1.50000 2.59808i −0.0911185 0.157822i 0.816864 0.576831i \(-0.195711\pi\)
−0.907982 + 0.419009i \(0.862378\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.00000 3.46410i 0.120605 0.208893i
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.50000 + 14.7224i −0.507067 + 0.878267i 0.492899 + 0.870087i \(0.335937\pi\)
−0.999967 + 0.00818015i \(0.997396\pi\)
\(282\) 0 0
\(283\) −1.00000 −0.0594438 −0.0297219 0.999558i \(-0.509462\pi\)
−0.0297219 + 0.999558i \(0.509462\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.50000 23.3827i −0.265627 1.38024i
\(288\) 0 0
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 13.5000 + 23.3827i 0.788678 + 1.36603i 0.926777 + 0.375613i \(0.122568\pi\)
−0.138098 + 0.990419i \(0.544099\pi\)
\(294\) 0 0
\(295\) −7.00000 + 12.1244i −0.407556 + 0.705907i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 12.0000 0.693978
\(300\) 0 0
\(301\) 10.0000 8.66025i 0.576390 0.499169i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.00000 5.19615i 0.171780 0.297531i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −31.0000 −1.75785 −0.878924 0.476961i \(-0.841738\pi\)
−0.878924 + 0.476961i \(0.841738\pi\)
\(312\) 0 0
\(313\) −17.0000 −0.960897 −0.480448 0.877023i \(-0.659526\pi\)
−0.480448 + 0.877023i \(0.659526\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 0.505490 0.252745 0.967533i \(-0.418667\pi\)
0.252745 + 0.967533i \(0.418667\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 35.0000 1.94745
\(324\) 0 0
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.50000 + 2.59808i 0.413488 + 0.143237i
\(330\) 0 0
\(331\) 25.0000 1.37412 0.687062 0.726599i \(-0.258900\pi\)
0.687062 + 0.726599i \(0.258900\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.0000 + 22.5167i −0.710266 + 1.23022i
\(336\) 0 0
\(337\) −1.50000 2.59808i −0.0817102 0.141526i 0.822274 0.569091i \(-0.192705\pi\)
−0.903985 + 0.427565i \(0.859372\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.00000 10.3923i −0.324918 0.562775i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.0000 −0.805242 −0.402621 0.915367i \(-0.631901\pi\)
−0.402621 + 0.915367i \(0.631901\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) −8.00000 + 13.8564i −0.424596 + 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.5000 + 26.8468i 0.818059 + 1.41692i 0.907111 + 0.420892i \(0.138283\pi\)
−0.0890519 + 0.996027i \(0.528384\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.00000 + 12.1244i 0.366397 + 0.634618i
\(366\) 0 0
\(367\) 16.0000 + 27.7128i 0.835193 + 1.44660i 0.893873 + 0.448320i \(0.147978\pi\)
−0.0586798 + 0.998277i \(0.518689\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.00000 5.19615i 0.311504 0.269771i
\(372\) 0 0
\(373\) −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i \(0.359552\pi\)
−0.996610 + 0.0822766i \(0.973781\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.00000 0.154508
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.00000 + 13.8564i −0.408781 + 0.708029i −0.994753 0.102302i \(-0.967379\pi\)
0.585973 + 0.810331i \(0.300713\pi\)
\(384\) 0 0
\(385\) −20.0000 6.92820i −1.01929 0.353094i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13.0000 + 22.5167i 0.659126 + 1.14164i 0.980842 + 0.194804i \(0.0624070\pi\)
−0.321716 + 0.946836i \(0.604260\pi\)
\(390\) 0 0
\(391\) 14.0000 + 24.2487i 0.708010 + 1.22631i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.00000 15.5885i 0.452839 0.784340i
\(396\) 0 0
\(397\) 10.5000 + 18.1865i 0.526980 + 0.912756i 0.999506 + 0.0314391i \(0.0100090\pi\)
−0.472526 + 0.881317i \(0.656658\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i \(-0.563837\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(402\) 0 0
\(403\) −4.50000 7.79423i −0.224161 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −22.0000 + 38.1051i −1.09050 + 1.88880i
\(408\) 0 0
\(409\) 23.0000 1.13728 0.568638 0.822588i \(-0.307470\pi\)
0.568638 + 0.822588i \(0.307470\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −17.5000 6.06218i −0.861119 0.298300i
\(414\) 0 0
\(415\) 1.00000 + 1.73205i 0.0490881 + 0.0850230i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) 0 0
\(421\) 4.50000 7.79423i 0.219317 0.379867i −0.735283 0.677761i \(-0.762951\pi\)
0.954599 + 0.297893i \(0.0962839\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 7.00000 0.339550
\(426\) 0 0
\(427\) 7.50000 + 2.59808i 0.362950 + 0.125730i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −19.5000 + 33.7750i −0.939282 + 1.62688i −0.172468 + 0.985015i \(0.555174\pi\)
−0.766814 + 0.641869i \(0.778159\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −20.0000 −0.956730
\(438\) 0 0
\(439\) 21.0000 1.00228 0.501138 0.865368i \(-0.332915\pi\)
0.501138 + 0.865368i \(0.332915\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −29.0000 −1.37783 −0.688916 0.724841i \(-0.741913\pi\)
−0.688916 + 0.724841i \(0.741913\pi\)
\(444\) 0 0
\(445\) 30.0000 1.42214
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) −18.0000 + 31.1769i −0.847587 + 1.46806i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15.0000 5.19615i −0.703211 0.243599i
\(456\) 0 0
\(457\) 31.0000 1.45012 0.725059 0.688686i \(-0.241812\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.5000 19.9186i 0.535608 0.927701i −0.463525 0.886084i \(-0.653416\pi\)
0.999134 0.0416172i \(-0.0132510\pi\)
\(462\) 0 0
\(463\) −2.50000 4.33013i −0.116185 0.201238i 0.802068 0.597233i \(-0.203733\pi\)
−0.918253 + 0.395995i \(0.870400\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.50000 14.7224i −0.393333 0.681273i 0.599554 0.800334i \(-0.295345\pi\)
−0.992887 + 0.119062i \(0.962011\pi\)
\(468\) 0 0
\(469\) −32.5000 11.2583i −1.50071 0.519861i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −20.0000 −0.919601
\(474\) 0 0
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.00000 + 6.92820i 0.182765 + 0.316558i 0.942821 0.333300i \(-0.108162\pi\)
−0.760056 + 0.649857i \(0.774829\pi\)
\(480\) 0 0
\(481\) −16.5000 + 28.5788i −0.752335 + 1.30308i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.0000 29.4449i −0.771930 1.33702i
\(486\) 0 0
\(487\) −0.500000 + 0.866025i −0.0226572 + 0.0392434i −0.877132 0.480250i \(-0.840546\pi\)
0.854475 + 0.519493i \(0.173879\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 3.50000 + 6.06218i 0.157632 + 0.273027i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −20.0000 6.92820i −0.897123 0.310772i
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 0 0
\(511\) −14.0000 + 12.1244i −0.619324 + 0.536350i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) −6.00000 10.3923i −0.263880 0.457053i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50000 2.59808i 0.0657162 0.113824i −0.831295 0.555831i \(-0.812400\pi\)
0.897011 + 0.442007i \(0.145733\pi\)
\(522\) 0 0
\(523\) 14.5000 + 25.1147i 0.634041 + 1.09819i 0.986718 + 0.162446i \(0.0519382\pi\)
−0.352677 + 0.935745i \(0.614728\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.5000 18.1865i 0.457387 0.792218i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13.5000 + 23.3827i −0.584750 + 1.01282i
\(534\) 0 0
\(535\) 6.00000 0.259403
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.00000 27.7128i 0.172292 1.19368i
\(540\) 0 0
\(541\) 16.5000 + 28.5788i 0.709390 + 1.22870i 0.965084 + 0.261942i \(0.0843630\pi\)
−0.255693 + 0.966758i \(0.582304\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.00000 + 12.1244i 0.299847 + 0.519350i
\(546\) 0 0
\(547\) 16.5000 28.5788i 0.705489 1.22194i −0.261026 0.965332i \(-0.584061\pi\)
0.966515 0.256611i \(-0.0826059\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) 0 0
\(553\) 22.5000 + 7.79423i 0.956797 + 0.331444i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.50000 9.52628i 0.233042 0.403641i −0.725660 0.688054i \(-0.758465\pi\)
0.958702 + 0.284413i \(0.0917985\pi\)
\(558\) 0 0
\(559\) −15.0000 −0.634432
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 13.0000 0.547885 0.273942 0.961746i \(-0.411672\pi\)
0.273942 + 0.961746i \(0.411672\pi\)
\(564\) 0 0
\(565\) −2.00000 −0.0841406
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −27.0000 −1.13190 −0.565949 0.824440i \(-0.691490\pi\)
−0.565949 + 0.824440i \(0.691490\pi\)
\(570\) 0 0
\(571\) 3.00000 0.125546 0.0627730 0.998028i \(-0.480006\pi\)
0.0627730 + 0.998028i \(0.480006\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −3.50000 + 6.06218i −0.145707 + 0.252372i −0.929636 0.368478i \(-0.879879\pi\)
0.783930 + 0.620850i \(0.213212\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 + 1.73205i −0.0829740 + 0.0718576i
\(582\) 0 0
\(583\) −12.0000 −0.496989
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.5000 + 32.0429i −0.763577 + 1.32255i 0.177419 + 0.984135i \(0.443225\pi\)
−0.940996 + 0.338418i \(0.890108\pi\)
\(588\) 0 0
\(589\) 7.50000 + 12.9904i 0.309032 + 0.535259i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13.5000 + 23.3827i 0.554379 + 0.960212i 0.997952 + 0.0639736i \(0.0203773\pi\)
−0.443573 + 0.896238i \(0.646289\pi\)
\(594\) 0 0
\(595\) −7.00000 36.3731i −0.286972 1.49115i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.00000 −0.122577 −0.0612883 0.998120i \(-0.519521\pi\)
−0.0612883 + 0.998120i \(0.519521\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) −24.0000 + 41.5692i −0.974130 + 1.68724i −0.291353 + 0.956616i \(0.594105\pi\)
−0.682777 + 0.730627i \(0.739228\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.50000 7.79423i −0.182051 0.315321i
\(612\) 0 0
\(613\) 4.50000 7.79423i 0.181753 0.314806i −0.760724 0.649075i \(-0.775156\pi\)
0.942478 + 0.334269i \(0.108489\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.5000 + 37.2391i 0.865557 + 1.49919i 0.866493 + 0.499190i \(0.166369\pi\)
−0.000935233 1.00000i \(0.500298\pi\)
\(618\) 0 0
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.50000 + 38.9711i 0.300481 + 1.56135i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −77.0000 −3.07019
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 20.7846i 0.118864 0.823516i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 0 0
\(643\) −6.50000 11.2583i −0.256335 0.443985i 0.708922 0.705287i \(-0.249182\pi\)
−0.965257 + 0.261301i \(0.915848\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.50000 + 2.59808i −0.0589711 + 0.102141i −0.894004 0.448059i \(-0.852115\pi\)
0.835033 + 0.550200i \(0.185449\pi\)
\(648\) 0 0
\(649\) 14.0000 + 24.2487i 0.549548 + 0.951845i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 0 0
\(655\) −4.00000 6.92820i −0.156293 0.270707i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12.5000 + 21.6506i −0.486931 + 0.843389i −0.999887 0.0150258i \(-0.995217\pi\)
0.512956 + 0.858415i \(0.328550\pi\)
\(660\) 0 0
\(661\) −17.0000 −0.661223 −0.330612 0.943767i \(-0.607255\pi\)
−0.330612 + 0.943767i \(0.607255\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 25.0000 + 8.66025i 0.969458 + 0.335830i
\(666\) 0 0
\(667\) −2.00000 3.46410i −0.0774403 0.134131i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) 12.5000 21.6506i 0.481840 0.834571i −0.517943 0.855415i \(-0.673302\pi\)
0.999783 + 0.0208444i \(0.00663546\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −27.0000 −1.03769 −0.518847 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(678\) 0 0
\(679\) 34.0000 29.4449i 1.30480 1.12999i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) 28.0000 1.06983
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.00000 −0.342873
\(690\) 0 0
\(691\) −11.0000 −0.418460 −0.209230 0.977866i \(-0.567096\pi\)
−0.209230 + 0.977866i \(0.567096\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.0000 −0.379322
\(696\) 0 0
\(697\) −63.0000 −2.38630
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 27.5000 47.6314i 1.03718 1.79645i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.00000 + 5.19615i 0.0376089 + 0.195421i
\(708\) 0 0
\(709\) −25.0000 −0.938895 −0.469447 0.882960i \(-0.655547\pi\)
−0.469447 + 0.882960i \(0.655547\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.00000 + 10.3923i −0.224702 + 0.389195i
\(714\) 0 0
\(715\) 12.0000 + 20.7846i 0.448775 + 0.777300i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 0 0
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.00000 −0.0371391
\(726\) 0 0
\(727\) −23.5000 + 40.7032i −0.871567 + 1.50960i −0.0111912 + 0.999937i \(0.503562\pi\)
−0.860376 + 0.509661i \(0.829771\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −17.5000 30.3109i −0.647261 1.12109i
\(732\) 0 0
\(733\) −15.0000 + 25.9808i −0.554038 + 0.959621i 0.443940 + 0.896056i \(0.353580\pi\)
−0.997978 + 0.0635649i \(0.979753\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 26.0000 + 45.0333i 0.957722 + 1.65882i
\(738\) 0 0
\(739\) −10.5000 + 18.1865i −0.386249 + 0.669002i −0.991942 0.126696i \(-0.959563\pi\)
0.605693 + 0.795699i \(0.292896\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) 6.00000 + 10.3923i 0.219823 + 0.380745i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.50000 + 7.79423i 0.0548088 + 0.284795i
\(750\) 0 0
\(751\) −12.0000 + 20.7846i −0.437886 + 0.758441i −0.997526 0.0702946i \(-0.977606\pi\)
0.559640 + 0.828736i \(0.310939\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.00000 + 1.73205i −0.0362500 + 0.0627868i −0.883581 0.468278i \(-0.844875\pi\)
0.847331 + 0.531065i \(0.178208\pi\)
\(762\) 0 0
\(763\) −14.0000 + 12.1244i −0.506834 + 0.438931i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10.5000 + 18.1865i 0.379133 + 0.656678i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11.5000 19.9186i 0.413626 0.716422i −0.581657 0.813434i \(-0.697595\pi\)
0.995283 + 0.0970125i \(0.0309287\pi\)
\(774\) 0 0
\(775\) 1.50000 + 2.59808i 0.0538816 + 0.0933257i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22.5000 38.9711i 0.806146 1.39629i
\(780\) 0 0
\(781\) 16.0000 + 27.7128i 0.572525 + 0.991642i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −13.0000 + 22.5167i −0.463990 + 0.803654i
\(786\) 0 0
\(787\) −21.0000 −0.748569 −0.374285 0.927314i \(-0.622112\pi\)
−0.374285 + 0.927314i \(0.622112\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.500000 2.59808i −0.0177780 0.0923770i
\(792\) 0 0
\(793\) −4.50000 7.79423i −0.159800 0.276781i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.50000 + 12.9904i 0.265664 + 0.460143i 0.967737 0.251961i \(-0.0810756\pi\)
−0.702074 + 0.712104i \(0.747742\pi\)
\(798\) 0 0
\(799\) 10.5000 18.1865i 0.371463 0.643393i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 28.0000 0.988099
\(804\) 0 0
\(805\) 4.00000 + 20.7846i 0.140981 + 0.732561i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.500000 + 0.866025i −0.0175791 + 0.0304478i −0.874681 0.484699i \(-0.838929\pi\)
0.857102 + 0.515147i \(0.172263\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −38.0000 −1.33108
\(816\) 0 0