Properties

Label 3024.2.q.e.2305.1
Level $3024$
Weight $2$
Character 3024.2305
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 2305.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.e.2881.1

$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 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 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) −1.50000 + 2.59808i −0.416025 + 0.720577i −0.995535 0.0943882i \(-0.969911\pi\)
0.579510 + 0.814965i \(0.303244\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.50000 + 6.06218i 0.848875 + 1.47029i 0.882213 + 0.470850i \(0.156053\pi\)
−0.0333386 + 0.999444i \(0.510614\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 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 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 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 −0.0821995 + 0.996616i \(0.526194\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 0 0
\(43\) 2.50000 + 4.33013i 0.381246 + 0.660338i 0.991241 0.132068i \(-0.0421616\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 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 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 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 0.585206 0.810885i \(-0.301014\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 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 0.837279 0.546776i \(-0.184145\pi\)
−0.892161 + 0.451717i \(0.850812\pi\)
\(84\) 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 −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 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 0.868976 + 0.494854i \(0.164778\pi\)
−0.00593185 + 0.999982i \(0.501888\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) −3.50000 6.06218i −0.335239 0.580651i 0.648292 0.761392i \(-0.275484\pi\)
−0.983531 + 0.180741i \(0.942150\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.500000 + 0.866025i −0.0470360 + 0.0814688i −0.888585 0.458712i \(-0.848311\pi\)
0.841549 + 0.540181i \(0.181644\pi\)
\(114\) 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 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) 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 −0.395058 0.918656i \(-0.629276\pi\)
0.993109 0.117198i \(-0.0373911\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 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 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 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 0.206518 + 0.978443i \(0.433787\pi\)
−0.950615 + 0.310372i \(0.899546\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.5000 + 19.9186i −0.889897 + 1.54135i −0.0499004 + 0.998754i \(0.515890\pi\)
−0.839996 + 0.542592i \(0.817443\pi\)
\(168\) 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 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) 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 0.538227 0.842800i \(-0.319094\pi\)
−0.999000 + 0.0447181i \(0.985761\pi\)
\(200\) 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 −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 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 0.724714 0.689050i \(-0.241972\pi\)
−0.959092 + 0.283096i \(0.908638\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −14.5000 + 25.1147i −0.949927 + 1.64532i −0.204354 + 0.978897i \(0.565509\pi\)
−0.745573 + 0.666424i \(0.767824\pi\)
\(234\) 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 −0.296037 0.955176i \(-0.595665\pi\)
0.975226 0.221213i \(-0.0710015\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 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 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 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 0.850380 0.526169i \(-0.176372\pi\)
−0.880866 + 0.473366i \(0.843039\pi\)
\(270\) 0 0
\(271\) −1.50000 + 2.59808i −0.0911185 + 0.157822i −0.907982 0.419009i \(-0.862378\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(272\) 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 −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.50000 14.7224i −0.507067 0.878267i −0.999967 0.00818015i \(-0.997396\pi\)
0.492899 0.870087i \(-0.335937\pi\)
\(282\) 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 −0.138098 0.990419i \(-0.544099\pi\)
0.926777 0.375613i \(-0.122568\pi\)
\(294\) 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 −0.903985 0.427565i \(-0.859372\pi\)
0.822274 + 0.569091i \(0.192705\pi\)
\(338\) 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 0.925147 0.379610i \(-0.123942\pi\)
−0.791325 + 0.611396i \(0.790608\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 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 −0.0890519 0.996027i \(-0.528384\pi\)
0.907111 0.420892i \(-0.138283\pi\)
\(360\) 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 −0.0586798 0.998277i \(-0.518689\pi\)
0.893873 0.448320i \(-0.147978\pi\)
\(368\) 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 −0.996610 0.0822766i \(-0.973781\pi\)
0.427051 0.904227i \(-0.359552\pi\)
\(374\) 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 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) 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 −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) 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 −0.472526 0.881317i \(-0.656658\pi\)
0.999506 0.0314391i \(-0.0100090\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) 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 −0.989000 0.147918i \(-0.952743\pi\)
0.622601 + 0.782540i \(0.286076\pi\)
\(420\) 0 0
\(421\) 4.50000 + 7.79423i 0.219317 + 0.379867i 0.954599 0.297893i \(-0.0962839\pi\)
−0.735283 + 0.677761i \(0.762951\pi\)
\(422\) 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 −0.766814 0.641869i \(-0.778159\pi\)
−0.172468 0.985015i \(-0.555174\pi\)
\(432\) 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 0.999134 + 0.0416172i \(0.0132510\pi\)
−0.463525 + 0.886084i \(0.653416\pi\)
\(462\) 0 0
\(463\) −2.50000 + 4.33013i −0.116185 + 0.201238i −0.918253 0.395995i \(-0.870400\pi\)
0.802068 + 0.597233i \(0.203733\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.50000 + 14.7224i −0.393333 + 0.681273i −0.992887 0.119062i \(-0.962011\pi\)
0.599554 + 0.800334i \(0.295345\pi\)
\(468\) 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 −0.760056 0.649857i \(-0.774829\pi\)
0.942821 + 0.333300i \(0.108162\pi\)
\(480\) 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 0.854475 0.519493i \(-0.173879\pi\)
−0.877132 + 0.480250i \(0.840546\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.50000 7.79423i 0.203082 0.351749i −0.746438 0.665455i \(-0.768237\pi\)
0.949520 + 0.313707i \(0.101571\pi\)
\(492\) 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 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 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 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 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 0.897011 0.442007i \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) 0 0
\(523\) 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i \(-0.614728\pi\)
0.986718 0.162446i \(-0.0519382\pi\)
\(524\) 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 −0.255693 0.966758i \(-0.582304\pi\)
0.965084 0.261942i \(-0.0843630\pi\)
\(542\) 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 0.966515 + 0.256611i \(0.0826059\pi\)
−0.261026 + 0.965332i \(0.584061\pi\)
\(548\) 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 0.958702 0.284413i \(-0.0917985\pi\)
−0.725660 + 0.688054i \(0.758465\pi\)
\(558\) 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 0.783930 0.620850i \(-0.213212\pi\)
−0.929636 + 0.368478i \(0.879879\pi\)
\(578\) 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 −0.940996 0.338418i \(-0.890108\pi\)
0.177419 0.984135i \(-0.443225\pi\)
\(588\) 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 −0.443573 0.896238i \(-0.646289\pi\)
0.997952 0.0639736i \(-0.0203773\pi\)
\(594\) 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 −0.963405 0.268049i \(-0.913621\pi\)
0.249565 0.968358i \(-0.419712\pi\)
\(602\) 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 −0.682777 0.730627i \(-0.739228\pi\)
−0.291353 0.956616i \(-0.594105\pi\)
\(608\) 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 0.942478 0.334269i \(-0.108489\pi\)
−0.760724 + 0.649075i \(0.775156\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.5000 37.2391i 0.865557 1.49919i −0.000935233 1.00000i \(-0.500298\pi\)
0.866493 0.499190i \(-0.166369\pi\)
\(618\) 0 0
\(619\) −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i \(-0.964995\pi\)
0.592025 + 0.805919i \(0.298329\pi\)
\(620\) 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 −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 0 0
\(643\) −6.50000 + 11.2583i −0.256335 + 0.443985i −0.965257 0.261301i \(-0.915848\pi\)
0.708922 + 0.705287i \(0.249182\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.50000 2.59808i −0.0589711 0.102141i 0.835033 0.550200i \(-0.185449\pi\)
−0.894004 + 0.448059i \(0.852115\pi\)
\(648\) 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 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 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 0.512956 0.858415i \(-0.328550\pi\)
−0.999887 + 0.0150258i \(0.995217\pi\)
\(660\) 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 0.999783 0.0208444i \(-0.00663546\pi\)
−0.517943 + 0.855415i \(0.673302\pi\)
\(674\) 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 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) 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 −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 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 −0.860376 0.509661i \(-0.829771\pi\)
−0.0111912 0.999937i \(-0.503562\pi\)
\(728\) 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 −0.997978 0.0635649i \(-0.979753\pi\)
0.443940 0.896056i \(-0.353580\pi\)
\(734\) 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 0.605693 0.795699i \(-0.292896\pi\)
−0.991942 + 0.126696i \(0.959563\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.50000 7.79423i 0.165089 0.285943i −0.771598 0.636111i \(-0.780542\pi\)
0.936687 + 0.350168i \(0.113876\pi\)
\(744\) 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 0.559640 0.828736i \(-0.310939\pi\)
−0.997526 + 0.0702946i \(0.977606\pi\)
\(752\) 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 0.847331 0.531065i \(-0.178208\pi\)
−0.883581 + 0.468278i \(0.844875\pi\)
\(762\) 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 −0.817423 0.576038i \(-0.804598\pi\)
0.907575 + 0.419890i \(0.137931\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11.5000 + 19.9186i 0.413626 + 0.716422i 0.995283 0.0970125i \(-0.0309287\pi\)
−0.581657 + 0.813434i \(0.697595\pi\)
\(774\) 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 −0.702074 0.712104i \(-0.747742\pi\)
0.967737 + 0.251961i \(0.0810756\pi\)
\(798\) 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 0.857102 0.515147i \(-0.172263\pi\)
−0.874681 + 0.484699i \(0.838929\pi\)
\(810\) 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