Properties

Label 3024.2.q.d.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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
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.d.2881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +(4.50000 + 7.79423i) q^{29} -4.00000 q^{31} +(-2.50000 - 0.866025i) q^{35} +(-2.50000 + 4.33013i) q^{37} +(3.50000 - 6.06218i) q^{41} +(1.50000 + 2.59808i) q^{43} +8.00000 q^{47} +(1.00000 - 6.92820i) q^{49} +(4.50000 + 7.79423i) q^{53} +3.00000 q^{55} -4.00000 q^{59} +2.00000 q^{61} -1.00000 q^{65} -12.0000 q^{67} +8.00000 q^{71} +(6.50000 + 11.2583i) q^{73} +(1.50000 + 7.79423i) q^{77} -8.00000 q^{79} +(6.50000 + 11.2583i) q^{83} +(-1.50000 + 2.59808i) q^{85} +(-4.50000 + 7.79423i) q^{89} +(-0.500000 - 2.59808i) q^{91} +5.00000 q^{95} +(8.50000 + 14.7224i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{5} - 4q^{7} + O(q^{10}) \) \( 2q + q^{5} - 4q^{7} + 3q^{11} - q^{13} + 3q^{17} + 5q^{19} - q^{23} + 4q^{25} + 9q^{29} - 8q^{31} - 5q^{35} - 5q^{37} + 7q^{41} + 3q^{43} + 16q^{47} + 2q^{49} + 9q^{53} + 6q^{55} - 8q^{59} + 4q^{61} - 2q^{65} - 24q^{67} + 16q^{71} + 13q^{73} + 3q^{77} - 16q^{79} + 13q^{83} - 3q^{85} - 9q^{89} - q^{91} + 10q^{95} + 17q^{97} + O(q^{100}) \)

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
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 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
\(23\) −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.50000 0.866025i −0.422577 0.146385i
\(36\) 0 0
\(37\) −2.50000 + 4.33013i −0.410997 + 0.711868i −0.994999 0.0998840i \(-0.968153\pi\)
0.584002 + 0.811752i \(0.301486\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.50000 6.06218i 0.546608 0.946753i −0.451896 0.892071i \(-0.649252\pi\)
0.998504 0.0546823i \(-0.0174146\pi\)
\(42\) 0 0
\(43\) 1.50000 + 2.59808i 0.228748 + 0.396203i 0.957437 0.288641i \(-0.0932035\pi\)
−0.728689 + 0.684844i \(0.759870\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 6.50000 + 11.2583i 0.760767 + 1.31769i 0.942455 + 0.334332i \(0.108511\pi\)
−0.181688 + 0.983356i \(0.558156\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.50000 + 11.2583i 0.713468 + 1.23576i 0.963548 + 0.267537i \(0.0862098\pi\)
−0.250080 + 0.968225i \(0.580457\pi\)
\(84\) 0 0
\(85\) −1.50000 + 2.59808i −0.162698 + 0.281801i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.50000 + 7.79423i −0.476999 + 0.826187i −0.999653 0.0263586i \(-0.991609\pi\)
0.522654 + 0.852545i \(0.324942\pi\)
\(90\) 0 0
\(91\) −0.500000 2.59808i −0.0524142 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.00000 0.512989
\(96\) 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
\(101\) −3.50000 + 6.06218i −0.348263 + 0.603209i −0.985941 0.167094i \(-0.946562\pi\)
0.637678 + 0.770303i \(0.279895\pi\)
\(102\) 0 0
\(103\) 4.50000 + 7.79423i 0.443398 + 0.767988i 0.997939 0.0641683i \(-0.0204394\pi\)
−0.554541 + 0.832156i \(0.687106\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.50000 6.06218i 0.338358 0.586053i −0.645766 0.763535i \(-0.723462\pi\)
0.984124 + 0.177482i \(0.0567953\pi\)
\(108\) 0 0
\(109\) −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i \(-0.243636\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(110\) 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
\(115\) 0.500000 0.866025i 0.0466252 0.0807573i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.50000 2.59808i −0.687524 0.238165i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 2.50000 + 12.9904i 0.216777 + 1.12641i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.50000 9.52628i 0.469897 0.813885i −0.529511 0.848303i \(-0.677624\pi\)
0.999408 + 0.0344182i \(0.0109578\pi\)
\(138\) 0 0
\(139\) 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i \(-0.765320\pi\)
0.952355 + 0.304991i \(0.0986536\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 0 0
\(145\) −4.50000 + 7.79423i −0.373705 + 0.647275i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.50000 12.9904i −0.614424 1.06421i −0.990485 0.137619i \(-0.956055\pi\)
0.376061 0.926595i \(-0.377278\pi\)
\(150\) 0 0
\(151\) −8.50000 + 14.7224i −0.691720 + 1.19809i 0.279554 + 0.960130i \(0.409814\pi\)
−0.971274 + 0.237964i \(0.923520\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 3.46410i −0.160644 0.278243i
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.50000 + 0.866025i 0.197028 + 0.0682524i
\(162\) 0 0
\(163\) 8.50000 14.7224i 0.665771 1.15315i −0.313304 0.949653i \(-0.601436\pi\)
0.979076 0.203497i \(-0.0652307\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.500000 0.866025i 0.0386912 0.0670151i −0.846031 0.533133i \(-0.821014\pi\)
0.884723 + 0.466118i \(0.154348\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 2.00000 + 10.3923i 0.151186 + 0.785584i
\(176\) 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
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.00000 −0.367607
\(186\) 0 0
\(187\) 9.00000 0.658145
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) −18.0000 −1.29567 −0.647834 0.761781i \(-0.724325\pi\)
−0.647834 + 0.761781i \(0.724325\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) 10.5000 + 18.1865i 0.744325 + 1.28921i 0.950509 + 0.310696i \(0.100562\pi\)
−0.206184 + 0.978513i \(0.566105\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −22.5000 7.79423i −1.57919 0.547048i
\(204\) 0 0
\(205\) 7.00000 0.488901
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.50000 12.9904i −0.518786 0.898563i
\(210\) 0 0
\(211\) −13.5000 + 23.3827i −0.929378 + 1.60973i −0.145014 + 0.989430i \(0.546323\pi\)
−0.784364 + 0.620301i \(0.787010\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.50000 + 2.59808i −0.102299 + 0.177187i
\(216\) 0 0
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 6.50000 + 11.2583i 0.435272 + 0.753914i 0.997318 0.0731927i \(-0.0233188\pi\)
−0.562046 + 0.827106i \(0.689985\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.50000 12.9904i 0.497792 0.862202i −0.502204 0.864749i \(-0.667477\pi\)
0.999997 + 0.00254715i \(0.000810783\pi\)
\(228\) 0 0
\(229\) −10.5000 18.1865i −0.693860 1.20180i −0.970564 0.240845i \(-0.922576\pi\)
0.276704 0.960955i \(-0.410758\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.50000 7.79423i 0.291081 0.504167i −0.682985 0.730433i \(-0.739318\pi\)
0.974066 + 0.226266i \(0.0726518\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.50000 2.59808i 0.415270 0.165985i
\(246\) 0 0
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.50000 14.7224i −0.530215 0.918360i −0.999379 0.0352486i \(-0.988778\pi\)
0.469163 0.883112i \(-0.344556\pi\)
\(258\) 0 0
\(259\) −2.50000 12.9904i −0.155342 0.807183i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −5.50000 + 9.52628i −0.339145 + 0.587416i −0.984272 0.176659i \(-0.943471\pi\)
0.645128 + 0.764075i \(0.276804\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3.50000 6.06218i −0.213399 0.369618i 0.739377 0.673291i \(-0.235120\pi\)
−0.952776 + 0.303674i \(0.901787\pi\)
\(270\) 0 0
\(271\) 15.5000 26.8468i 0.941558 1.63083i 0.179057 0.983839i \(-0.442695\pi\)
0.762501 0.646988i \(-0.223971\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) 9.50000 16.4545i 0.570800 0.988654i −0.425684 0.904872i \(-0.639967\pi\)
0.996484 0.0837823i \(-0.0267000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.5000 + 23.3827i 0.805342 + 1.39489i 0.916060 + 0.401042i \(0.131352\pi\)
−0.110717 + 0.993852i \(0.535315\pi\)
\(282\) 0 0
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.50000 + 18.1865i 0.206598 + 1.07352i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.500000 0.866025i 0.0292103 0.0505937i −0.851051 0.525084i \(-0.824034\pi\)
0.880261 + 0.474490i \(0.157367\pi\)
\(294\) 0 0
\(295\) −2.00000 3.46410i −0.116445 0.201688i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.00000 0.0578315
\(300\) 0 0
\(301\) −7.50000 2.59808i −0.432293 0.149751i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.00000 + 1.73205i 0.0572598 + 0.0991769i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 0 0
\(319\) 27.0000 1.51171
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.0000 0.834622
\(324\) 0 0
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −16.0000 + 13.8564i −0.882109 + 0.763928i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.00000 10.3923i −0.327815 0.567792i
\(336\) 0 0
\(337\) −7.50000 + 12.9904i −0.408551 + 0.707631i −0.994728 0.102552i \(-0.967299\pi\)
0.586177 + 0.810183i \(0.300632\pi\)
\(338\) 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
\(347\) −28.0000 −1.50312 −0.751559 0.659665i \(-0.770698\pi\)
−0.751559 + 0.659665i \(0.770698\pi\)
\(348\) 0 0
\(349\) −8.50000 14.7224i −0.454995 0.788074i 0.543693 0.839284i \(-0.317025\pi\)
−0.998688 + 0.0512103i \(0.983692\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.5000 26.8468i 0.824982 1.42891i −0.0769515 0.997035i \(-0.524519\pi\)
0.901933 0.431875i \(-0.142148\pi\)
\(354\) 0 0
\(355\) 4.00000 + 6.92820i 0.212298 + 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.5000 + 23.3827i −0.712503 + 1.23409i 0.251412 + 0.967880i \(0.419105\pi\)
−0.963915 + 0.266211i \(0.914228\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.50000 + 11.2583i −0.340226 + 0.589288i
\(366\) 0 0
\(367\) 5.50000 9.52628i 0.287098 0.497268i −0.686018 0.727585i \(-0.740643\pi\)
0.973116 + 0.230317i \(0.0739762\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −22.5000 7.79423i −1.16814 0.404656i
\(372\) 0 0
\(373\) −6.50000 11.2583i −0.336557 0.582934i 0.647225 0.762299i \(-0.275929\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.00000 −0.463524
\(378\) 0 0
\(379\) −32.0000 −1.64373 −0.821865 0.569683i \(-0.807066\pi\)
−0.821865 + 0.569683i \(0.807066\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 17.5000 + 30.3109i 0.894208 + 1.54881i 0.834781 + 0.550581i \(0.185594\pi\)
0.0594268 + 0.998233i \(0.481073\pi\)
\(384\) 0 0
\(385\) −6.00000 + 5.19615i −0.305788 + 0.264820i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 18.5000 32.0429i 0.937987 1.62464i 0.168769 0.985656i \(-0.446021\pi\)
0.769218 0.638986i \(-0.220646\pi\)
\(390\) 0 0
\(391\) 1.50000 2.59808i 0.0758583 0.131390i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 6.92820i −0.201262 0.348596i
\(396\) 0 0
\(397\) −12.5000 + 21.6506i −0.627357 + 1.08661i 0.360723 + 0.932673i \(0.382530\pi\)
−0.988080 + 0.153941i \(0.950803\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.50000 11.2583i −0.324595 0.562214i 0.656836 0.754034i \(-0.271895\pi\)
−0.981430 + 0.191820i \(0.938561\pi\)
\(402\) 0 0
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 7.50000 + 12.9904i 0.371761 + 0.643909i
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.00000 6.92820i 0.393654 0.340915i
\(414\) 0 0
\(415\) −6.50000 + 11.2583i −0.319072 + 0.552650i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.5000 + 18.1865i −0.512959 + 0.888470i 0.486928 + 0.873442i \(0.338117\pi\)
−0.999887 + 0.0150285i \(0.995216\pi\)
\(420\) 0 0
\(421\) 1.50000 + 2.59808i 0.0731055 + 0.126622i 0.900261 0.435351i \(-0.143376\pi\)
−0.827155 + 0.561973i \(0.810042\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) −4.00000 + 3.46410i −0.193574 + 0.167640i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i \(-0.0490126\pi\)
−0.626907 + 0.779094i \(0.715679\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.00000 −0.239182
\(438\) 0 0
\(439\) −24.0000 −1.14546 −0.572729 0.819745i \(-0.694115\pi\)
−0.572729 + 0.819745i \(0.694115\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.0000 0.760183 0.380091 0.924949i \(-0.375893\pi\)
0.380091 + 0.924949i \(0.375893\pi\)
\(444\) 0 0
\(445\) −9.00000 −0.426641
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) −10.5000 18.1865i −0.494426 0.856370i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.00000 1.73205i 0.0937614 0.0811998i
\(456\) 0 0
\(457\) −26.0000 −1.21623 −0.608114 0.793849i \(-0.708074\pi\)
−0.608114 + 0.793849i \(0.708074\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −13.5000 23.3827i −0.628758 1.08904i −0.987801 0.155719i \(-0.950230\pi\)
0.359044 0.933321i \(-0.383103\pi\)
\(462\) 0 0
\(463\) −0.500000 + 0.866025i −0.0232370 + 0.0402476i −0.877410 0.479741i \(-0.840731\pi\)
0.854173 + 0.519989i \(0.174064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.50000 + 11.2583i −0.300784 + 0.520973i −0.976314 0.216359i \(-0.930582\pi\)
0.675530 + 0.737333i \(0.263915\pi\)
\(468\) 0 0
\(469\) 24.0000 20.7846i 1.10822 0.959744i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.00000 0.413820
\(474\) 0 0
\(475\) −10.0000 17.3205i −0.458831 0.794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10.5000 18.1865i 0.479757 0.830964i −0.519973 0.854183i \(-0.674058\pi\)
0.999730 + 0.0232187i \(0.00739140\pi\)
\(480\) 0 0
\(481\) −2.50000 4.33013i −0.113990 0.197437i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.50000 + 14.7224i −0.385965 + 0.668511i
\(486\) 0 0
\(487\) 18.5000 + 32.0429i 0.838315 + 1.45200i 0.891303 + 0.453409i \(0.149792\pi\)
−0.0529875 + 0.998595i \(0.516874\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.50000 + 7.79423i −0.203082 + 0.351749i −0.949520 0.313707i \(-0.898429\pi\)
0.746438 + 0.665455i \(0.231763\pi\)
\(492\) 0 0
\(493\) −13.5000 + 23.3827i −0.608009 + 1.05310i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.0000 + 13.8564i −0.717698 + 0.621545i
\(498\) 0 0
\(499\) −14.5000 25.1147i −0.649109 1.12429i −0.983336 0.181797i \(-0.941809\pi\)
0.334227 0.942493i \(-0.391525\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) 0 0
\(505\) −7.00000 −0.311496
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16.5000 + 28.5788i 0.731350 + 1.26673i 0.956306 + 0.292366i \(0.0944425\pi\)
−0.224957 + 0.974369i \(0.572224\pi\)
\(510\) 0 0
\(511\) −32.5000 11.2583i −1.43772 0.498039i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.50000 + 7.79423i −0.198294 + 0.343455i
\(516\) 0 0
\(517\) 12.0000 20.7846i 0.527759 0.914106i
\(518\) 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
\(523\) 16.5000 28.5788i 0.721495 1.24967i −0.238906 0.971043i \(-0.576789\pi\)
0.960401 0.278623i \(-0.0898779\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.50000 + 6.06218i 0.151602 + 0.262582i
\(534\) 0 0
\(535\) 7.00000 0.302636
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) 5.50000 9.52628i 0.236463 0.409567i −0.723234 0.690604i \(-0.757345\pi\)
0.959697 + 0.281037i \(0.0906783\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.50000 4.33013i 0.107088 0.185482i
\(546\) 0 0
\(547\) −2.50000 4.33013i −0.106892 0.185143i 0.807617 0.589707i \(-0.200757\pi\)
−0.914510 + 0.404564i \(0.867423\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 45.0000 1.91706
\(552\) 0 0
\(553\) 16.0000 13.8564i 0.680389 0.589234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.5000 33.7750i −0.826242 1.43109i −0.900967 0.433888i \(-0.857141\pi\)
0.0747252 0.997204i \(-0.476192\pi\)
\(558\) 0 0
\(559\) −3.00000 −0.126886
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −1.00000 −0.0420703
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 42.0000 1.76073 0.880366 0.474295i \(-0.157297\pi\)
0.880366 + 0.474295i \(0.157297\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −1.50000 2.59808i −0.0624458 0.108159i 0.833112 0.553104i \(-0.186557\pi\)
−0.895558 + 0.444945i \(0.853223\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −32.5000 11.2583i −1.34833 0.467074i
\(582\) 0 0
\(583\) 27.0000 1.11823
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.50000 12.9904i −0.309558 0.536170i 0.668708 0.743525i \(-0.266848\pi\)
−0.978266 + 0.207355i \(0.933514\pi\)
\(588\) 0 0
\(589\) −10.0000 + 17.3205i −0.412043 + 0.713679i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10.5000 + 18.1865i −0.431183 + 0.746831i −0.996976 0.0777165i \(-0.975237\pi\)
0.565792 + 0.824548i \(0.308570\pi\)
\(594\) 0 0
\(595\) −1.50000 7.79423i −0.0614940 0.319532i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −11.5000 19.9186i −0.469095 0.812496i 0.530281 0.847822i \(-0.322086\pi\)
−0.999376 + 0.0353259i \(0.988753\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −11.5000 19.9186i −0.466771 0.808470i 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) 0 0
\(613\) −2.50000 4.33013i −0.100974 0.174892i 0.811112 0.584891i \(-0.198863\pi\)
−0.912086 + 0.409998i \(0.865529\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 2.59808i 0.0603877 0.104595i −0.834251 0.551385i \(-0.814100\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(618\) 0 0
\(619\) 10.5000 18.1865i 0.422031 0.730978i −0.574107 0.818780i \(-0.694651\pi\)
0.996138 + 0.0878015i \(0.0279841\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.50000 23.3827i −0.180289 0.936808i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) 5.50000 + 4.33013i 0.217918 + 0.171566i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i \(-0.864816\pi\)
0.812421 + 0.583071i \(0.198149\pi\)
\(642\) 0 0
\(643\) 18.5000 32.0429i 0.729569 1.26365i −0.227497 0.973779i \(-0.573054\pi\)
0.957066 0.289871i \(-0.0936125\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.5000 35.5070i −0.805938 1.39593i −0.915656 0.401963i \(-0.868328\pi\)
0.109718 0.993963i \(-0.465005\pi\)
\(648\) 0 0
\(649\) −6.00000 + 10.3923i −0.235521 + 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) 0 0
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i \(-0.261040\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.0000 + 8.66025i −0.387783 + 0.335830i
\(666\) 0 0
\(667\) 4.50000 7.79423i 0.174241 0.301794i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.00000 5.19615i 0.115814 0.200595i
\(672\) 0 0
\(673\) −17.5000 30.3109i −0.674575 1.16840i −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −38.0000 −1.46046 −0.730229 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(678\) 0 0
\(679\) −42.5000 14.7224i −1.63100 0.564995i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −15.5000 26.8468i −0.593091 1.02726i −0.993813 0.111064i \(-0.964574\pi\)
0.400722 0.916200i \(-0.368759\pi\)
\(684\) 0 0
\(685\) 11.0000 0.420288
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −9.00000 −0.342873
\(690\) 0 0
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.00000 0.189661
\(696\) 0 0
\(697\) 21.0000 0.795432
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 12.5000 + 21.6506i 0.471446 + 0.816569i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.50000 18.1865i −0.131631 0.683975i
\(708\) 0 0
\(709\) −18.0000 −0.676004 −0.338002 0.941145i \(-0.609751\pi\)
−0.338002 + 0.941145i \(0.609751\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.00000 + 3.46410i 0.0749006 + 0.129732i
\(714\) 0 0
\(715\) −1.50000 + 2.59808i −0.0560968 + 0.0971625i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.50000 + 16.4545i −0.354290 + 0.613649i −0.986996 0.160743i \(-0.948611\pi\)
0.632706 + 0.774392i \(0.281944\pi\)
\(720\) 0 0
\(721\) −22.5000 7.79423i −0.837944 0.290272i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 36.0000 1.33701
\(726\) 0 0
\(727\) 8.50000 + 14.7224i 0.315248 + 0.546025i 0.979490 0.201492i \(-0.0645791\pi\)
−0.664243 + 0.747517i \(0.731246\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.50000 + 7.79423i −0.166439 + 0.288280i
\(732\) 0 0
\(733\) 21.5000 + 37.2391i 0.794121 + 1.37546i 0.923396 + 0.383849i \(0.125402\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.0000 + 31.1769i −0.663039 + 1.14842i
\(738\) 0 0
\(739\) −8.50000 14.7224i −0.312678 0.541573i 0.666264 0.745716i \(-0.267893\pi\)
−0.978941 + 0.204143i \(0.934559\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.500000 0.866025i 0.0183432 0.0317714i −0.856708 0.515802i \(-0.827494\pi\)
0.875051 + 0.484030i \(0.160828\pi\)
\(744\) 0 0
\(745\) 7.50000 12.9904i 0.274779 0.475931i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.50000 + 18.1865i 0.127887 + 0.664521i
\(750\) 0 0
\(751\) −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i \(-0.254907\pi\)
−0.969801 + 0.243898i \(0.921574\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −17.0000 −0.618693
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i \(-0.863060\pi\)
0.0932544 0.995642i \(-0.470273\pi\)
\(762\) 0 0
\(763\) 12.5000 + 4.33013i 0.452530 + 0.156761i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.00000 3.46410i 0.0722158 0.125081i
\(768\) 0 0
\(769\) 20.5000 35.5070i 0.739249 1.28042i −0.213585 0.976924i \(-0.568514\pi\)
0.952834 0.303492i \(-0.0981526\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.50000 6.06218i −0.125886 0.218041i 0.796193 0.605043i \(-0.206844\pi\)
−0.922079 + 0.387002i \(0.873511\pi\)
\(774\) 0 0
\(775\) −8.00000 + 13.8564i −0.287368 + 0.497737i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −17.5000 30.3109i −0.627003 1.08600i
\(780\) 0 0
\(781\) 12.0000 20.7846i 0.429394 0.743732i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.00000 + 12.1244i 0.249841 + 0.432737i
\(786\) 0 0
\(787\) −20.0000 −0.712923 −0.356462 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.500000 2.59808i −0.0177780 0.0923770i
\(792\) 0 0
\(793\) −1.00000 + 1.73205i −0.0355110 + 0.0615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −19.5000 + 33.7750i −0.690725 + 1.19637i 0.280875 + 0.959744i \(0.409375\pi\)
−0.971601 + 0.236627i \(0.923958\pi\)
\(798\) 0 0
\(799\) 12.0000 + 20.7846i 0.424529 + 0.735307i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 39.0000 1.37628
\(804\) 0 0
\(805\) 0.500000 + 2.59808i 0.0176227 + 0.0915702i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.5000 + 47.6314i 0.966849 + 1.67463i 0.704564 + 0.709640i \(0.251142\pi\)
0.262284 + 0.964991i \(0.415524\pi\)
\(810\) 0 0
\(811\) 4.00000 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 17.0000 0.595484
\(816\) 0 0