Properties

Label 1344.2.bl.f.1279.1
Level $1344$
Weight $2$
Character 1344.1279
Analytic conductor $10.732$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.bl (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 336)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1279.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1344.1279
Dual form 1344.2.bl.f.703.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 + 0.866025i) q^{11} -1.73205i q^{15} +(3.00000 - 1.73205i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(2.50000 - 0.866025i) q^{21} +(-1.00000 - 1.73205i) q^{25} -1.00000 q^{27} -9.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-1.50000 - 0.866025i) q^{33} +(-3.00000 + 3.46410i) q^{35} +(5.00000 - 8.66025i) q^{37} -10.3923i q^{41} -3.46410i q^{43} +(1.50000 - 0.866025i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(3.00000 + 1.73205i) q^{51} +(-4.50000 - 7.79423i) q^{53} +3.00000 q^{55} -2.00000 q^{57} +(-4.50000 - 7.79423i) q^{59} +(2.00000 + 1.73205i) q^{63} +(12.0000 - 6.92820i) q^{67} +13.8564i q^{71} +(-6.00000 + 3.46410i) q^{73} +(1.00000 - 1.73205i) q^{75} +(1.50000 + 4.33013i) q^{77} +(4.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.00000 q^{83} -6.00000 q^{85} +(-4.50000 - 7.79423i) q^{87} +(-3.00000 - 1.73205i) q^{89} +(2.50000 - 4.33013i) q^{93} +(3.00000 - 1.73205i) q^{95} -19.0526i q^{97} -1.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 3q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - 3q^{5} + q^{7} - q^{9} - 3q^{11} + 6q^{17} - 2q^{19} + 5q^{21} - 2q^{25} - 2q^{27} - 18q^{29} - 5q^{31} - 3q^{33} - 6q^{35} + 10q^{37} + 3q^{45} - 12q^{47} - 13q^{49} + 6q^{51} - 9q^{53} + 6q^{55} - 4q^{57} - 9q^{59} + 4q^{63} + 24q^{67} - 12q^{73} + 2q^{75} + 3q^{77} + 9q^{79} - q^{81} - 6q^{83} - 12q^{85} - 9q^{87} - 6q^{89} + 5q^{93} + 6q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i \(-0.459925\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) 0 0
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.50000 + 0.866025i −0.452267 + 0.261116i −0.708787 0.705422i \(-0.750757\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 1.73205i 0.447214i
\(16\) 0 0
\(17\) 3.00000 1.73205i 0.727607 0.420084i −0.0899392 0.995947i \(-0.528667\pi\)
0.817546 + 0.575863i \(0.195334\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 0 0
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0 0
\(33\) −1.50000 0.866025i −0.261116 0.150756i
\(34\) 0 0
\(35\) −3.00000 + 3.46410i −0.507093 + 0.585540i
\(36\) 0 0
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.3923i 1.62301i −0.584349 0.811503i \(-0.698650\pi\)
0.584349 0.811503i \(-0.301350\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i −0.964486 0.264135i \(-0.914913\pi\)
0.964486 0.264135i \(-0.0850865\pi\)
\(44\) 0 0
\(45\) 1.50000 0.866025i 0.223607 0.129099i
\(46\) 0 0
\(47\) −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 3.00000 + 1.73205i 0.420084 + 0.242536i
\(52\) 0 0
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 2.00000 + 1.73205i 0.251976 + 0.218218i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 12.0000 6.92820i 1.46603 0.846415i 0.466755 0.884387i \(-0.345423\pi\)
0.999279 + 0.0379722i \(0.0120898\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.8564i 1.64445i 0.569160 + 0.822226i \(0.307268\pi\)
−0.569160 + 0.822226i \(0.692732\pi\)
\(72\) 0 0
\(73\) −6.00000 + 3.46410i −0.702247 + 0.405442i −0.808184 0.588930i \(-0.799549\pi\)
0.105937 + 0.994373i \(0.466216\pi\)
\(74\) 0 0
\(75\) 1.00000 1.73205i 0.115470 0.200000i
\(76\) 0 0
\(77\) 1.50000 + 4.33013i 0.170941 + 0.493464i
\(78\) 0 0
\(79\) 4.50000 + 2.59808i 0.506290 + 0.292306i 0.731307 0.682048i \(-0.238911\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 0 0
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) 0 0
\(89\) −3.00000 1.73205i −0.317999 0.183597i 0.332501 0.943103i \(-0.392107\pi\)
−0.650500 + 0.759506i \(0.725441\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.50000 4.33013i 0.259238 0.449013i
\(94\) 0 0
\(95\) 3.00000 1.73205i 0.307794 0.177705i
\(96\) 0 0
\(97\) 19.0526i 1.93449i −0.253837 0.967247i \(-0.581693\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) 0 0
\(99\) 1.73205i 0.174078i
\(100\) 0 0
\(101\) 12.0000 6.92820i 1.19404 0.689382i 0.234823 0.972038i \(-0.424549\pi\)
0.959221 + 0.282656i \(0.0912155\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 0 0
\(105\) −4.50000 0.866025i −0.439155 0.0845154i
\(106\) 0 0
\(107\) 10.5000 + 6.06218i 1.01507 + 0.586053i 0.912673 0.408690i \(-0.134014\pi\)
0.102400 + 0.994743i \(0.467348\pi\)
\(108\) 0 0
\(109\) −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i \(-0.228023\pi\)
−0.945769 + 0.324840i \(0.894690\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.00000 8.66025i −0.275010 0.793884i
\(120\) 0 0
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) 0 0
\(123\) 9.00000 5.19615i 0.811503 0.468521i
\(124\) 0 0
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 5.19615i 0.461084i 0.973062 + 0.230542i \(0.0740499\pi\)
−0.973062 + 0.230542i \(0.925950\pi\)
\(128\) 0 0
\(129\) 3.00000 1.73205i 0.264135 0.152499i
\(130\) 0 0
\(131\) −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 0 0
\(133\) 4.00000 + 3.46410i 0.346844 + 0.300376i
\(134\) 0 0
\(135\) 1.50000 + 0.866025i 0.129099 + 0.0745356i
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 13.5000 + 7.79423i 1.12111 + 0.647275i
\(146\) 0 0
\(147\) −1.00000 6.92820i −0.0824786 0.571429i
\(148\) 0 0
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 4.50000 2.59808i 0.366205 0.211428i −0.305594 0.952162i \(-0.598855\pi\)
0.671799 + 0.740733i \(0.265522\pi\)
\(152\) 0 0
\(153\) 3.46410i 0.280056i
\(154\) 0 0
\(155\) 8.66025i 0.695608i
\(156\) 0 0
\(157\) −6.00000 + 3.46410i −0.478852 + 0.276465i −0.719938 0.694038i \(-0.755830\pi\)
0.241086 + 0.970504i \(0.422496\pi\)
\(158\) 0 0
\(159\) 4.50000 7.79423i 0.356873 0.618123i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.0000 + 6.92820i 0.939913 + 0.542659i 0.889933 0.456091i \(-0.150751\pi\)
0.0499796 + 0.998750i \(0.484084\pi\)
\(164\) 0 0
\(165\) 1.50000 + 2.59808i 0.116775 + 0.202260i
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) 0 0
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) −5.00000 + 1.73205i −0.377964 + 0.130931i
\(176\) 0 0
\(177\) 4.50000 7.79423i 0.338241 0.585850i
\(178\) 0 0
\(179\) −21.0000 + 12.1244i −1.56961 + 0.906217i −0.573400 + 0.819275i \(0.694376\pi\)
−0.996213 + 0.0869415i \(0.972291\pi\)
\(180\) 0 0
\(181\) 10.3923i 0.772454i −0.922404 0.386227i \(-0.873778\pi\)
0.922404 0.386227i \(-0.126222\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −15.0000 + 8.66025i −1.10282 + 0.636715i
\(186\) 0 0
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 0 0
\(189\) −0.500000 + 2.59808i −0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −12.0000 6.92820i −0.868290 0.501307i −0.00151007 0.999999i \(-0.500481\pi\)
−0.866779 + 0.498692i \(0.833814\pi\)
\(192\) 0 0
\(193\) 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i \(-0.109072\pi\)
−0.761911 + 0.647682i \(0.775738\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 0 0
\(201\) 12.0000 + 6.92820i 0.846415 + 0.488678i
\(202\) 0 0
\(203\) −4.50000 + 23.3827i −0.315838 + 1.64114i
\(204\) 0 0
\(205\) −9.00000 + 15.5885i −0.628587 + 1.08875i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.46410i 0.239617i
\(210\) 0 0
\(211\) 6.92820i 0.476957i 0.971148 + 0.238479i \(0.0766487\pi\)
−0.971148 + 0.238479i \(0.923351\pi\)
\(212\) 0 0
\(213\) −12.0000 + 6.92820i −0.822226 + 0.474713i
\(214\) 0 0
\(215\) −3.00000 + 5.19615i −0.204598 + 0.354375i
\(216\) 0 0
\(217\) −12.5000 + 4.33013i −0.848555 + 0.293948i
\(218\) 0 0
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 0 0
\(225\) 2.00000 0.133333
\(226\) 0 0
\(227\) −10.5000 18.1865i −0.696909 1.20708i −0.969533 0.244962i \(-0.921225\pi\)
0.272623 0.962121i \(-0.412109\pi\)
\(228\) 0 0
\(229\) 3.00000 + 1.73205i 0.198246 + 0.114457i 0.595837 0.803105i \(-0.296820\pi\)
−0.397591 + 0.917563i \(0.630154\pi\)
\(230\) 0 0
\(231\) −3.00000 + 3.46410i −0.197386 + 0.227921i
\(232\) 0 0
\(233\) −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 0 0
\(235\) 18.0000 10.3923i 1.17419 0.677919i
\(236\) 0 0
\(237\) 5.19615i 0.337526i
\(238\) 0 0
\(239\) 6.92820i 0.448148i 0.974572 + 0.224074i \(0.0719358\pi\)
−0.974572 + 0.224074i \(0.928064\pi\)
\(240\) 0 0
\(241\) 19.5000 11.2583i 1.25611 0.725213i 0.283790 0.958886i \(-0.408408\pi\)
0.972315 + 0.233674i \(0.0750747\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 7.50000 + 9.52628i 0.479157 + 0.608612i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −1.50000 2.59808i −0.0950586 0.164646i
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −3.00000 5.19615i −0.187867 0.325396i
\(256\) 0 0
\(257\) −9.00000 5.19615i −0.561405 0.324127i 0.192304 0.981335i \(-0.438404\pi\)
−0.753709 + 0.657208i \(0.771737\pi\)
\(258\) 0 0
\(259\) −20.0000 17.3205i −1.24274 1.07624i
\(260\) 0 0
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) 0 0
\(263\) 15.0000 8.66025i 0.924940 0.534014i 0.0397320 0.999210i \(-0.487350\pi\)
0.885208 + 0.465196i \(0.154016\pi\)
\(264\) 0 0
\(265\) 15.5885i 0.957591i
\(266\) 0 0
\(267\) 3.46410i 0.212000i
\(268\) 0 0
\(269\) 13.5000 7.79423i 0.823110 0.475223i −0.0283781 0.999597i \(-0.509034\pi\)
0.851488 + 0.524375i \(0.175701\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.00000 + 1.73205i 0.180907 + 0.104447i
\(276\) 0 0
\(277\) 14.0000 + 24.2487i 0.841178 + 1.45696i 0.888899 + 0.458103i \(0.151471\pi\)
−0.0477206 + 0.998861i \(0.515196\pi\)
\(278\) 0 0
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 0 0
\(285\) 3.00000 + 1.73205i 0.177705 + 0.102598i
\(286\) 0 0
\(287\) −27.0000 5.19615i −1.59376 0.306719i
\(288\) 0 0
\(289\) −2.50000 + 4.33013i −0.147059 + 0.254713i
\(290\) 0 0
\(291\) 16.5000 9.52628i 0.967247 0.558440i
\(292\) 0 0
\(293\) 5.19615i 0.303562i −0.988414 0.151781i \(-0.951499\pi\)
0.988414 0.151781i \(-0.0485009\pi\)
\(294\) 0 0
\(295\) 15.5885i 0.907595i
\(296\) 0 0
\(297\) 1.50000 0.866025i 0.0870388 0.0502519i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −9.00000 1.73205i −0.518751 0.0998337i
\(302\) 0 0
\(303\) 12.0000 + 6.92820i 0.689382 + 0.398015i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) 0 0
\(313\) −4.50000 2.59808i −0.254355 0.146852i 0.367402 0.930062i \(-0.380247\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) −1.50000 4.33013i −0.0845154 0.243975i
\(316\) 0 0
\(317\) −10.5000 + 18.1865i −0.589739 + 1.02146i 0.404528 + 0.914526i \(0.367436\pi\)
−0.994266 + 0.106932i \(0.965897\pi\)
\(318\) 0 0
\(319\) 13.5000 7.79423i 0.755855 0.436393i
\(320\) 0 0
\(321\) 12.1244i 0.676716i
\(322\) 0 0
\(323\) 6.92820i 0.385496i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 2.00000 3.46410i 0.110600 0.191565i
\(328\) 0 0
\(329\) 24.0000 + 20.7846i 1.32316 + 1.14589i
\(330\) 0 0
\(331\) −12.0000 6.92820i −0.659580 0.380808i 0.132537 0.991178i \(-0.457688\pi\)
−0.792117 + 0.610370i \(0.791021\pi\)
\(332\) 0 0
\(333\) 5.00000 + 8.66025i 0.273998 + 0.474579i
\(334\) 0 0
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) −1.00000 −0.0544735 −0.0272367 0.999629i \(-0.508671\pi\)
−0.0272367 + 0.999629i \(0.508671\pi\)
\(338\) 0 0
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) 7.50000 + 4.33013i 0.406148 + 0.234490i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.0000 8.66025i 0.805242 0.464907i −0.0400587 0.999197i \(-0.512754\pi\)
0.845301 + 0.534291i \(0.179421\pi\)
\(348\) 0 0
\(349\) 6.92820i 0.370858i 0.982658 + 0.185429i \(0.0593675\pi\)
−0.982658 + 0.185429i \(0.940632\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.00000 3.46410i 0.319348 0.184376i −0.331754 0.943366i \(-0.607640\pi\)
0.651102 + 0.758990i \(0.274307\pi\)
\(354\) 0 0
\(355\) 12.0000 20.7846i 0.636894 1.10313i
\(356\) 0 0
\(357\) 6.00000 6.92820i 0.317554 0.366679i
\(358\) 0 0
\(359\) 24.0000 + 13.8564i 1.26667 + 0.731313i 0.974357 0.225009i \(-0.0722411\pi\)
0.292315 + 0.956322i \(0.405574\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) −8.00000 −0.419891
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 0 0
\(367\) −9.50000 16.4545i −0.495896 0.858917i 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) 0 0
\(369\) 9.00000 + 5.19615i 0.468521 + 0.270501i
\(370\) 0 0
\(371\) −22.5000 + 7.79423i −1.16814 + 0.404656i
\(372\) 0 0
\(373\) 1.00000 1.73205i 0.0517780 0.0896822i −0.838975 0.544170i \(-0.816844\pi\)
0.890753 + 0.454488i \(0.150178\pi\)
\(374\) 0 0
\(375\) −10.5000 + 6.06218i −0.542218 + 0.313050i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 24.2487i 1.24557i 0.782392 + 0.622786i \(0.213999\pi\)
−0.782392 + 0.622786i \(0.786001\pi\)
\(380\) 0 0
\(381\) −4.50000 + 2.59808i −0.230542 + 0.133103i
\(382\) 0 0
\(383\) −9.00000 + 15.5885i −0.459879 + 0.796533i −0.998954 0.0457244i \(-0.985440\pi\)
0.539076 + 0.842257i \(0.318774\pi\)
\(384\) 0 0
\(385\) 1.50000 7.79423i 0.0764471 0.397231i
\(386\) 0 0
\(387\) 3.00000 + 1.73205i 0.152499 + 0.0880451i
\(388\) 0 0
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −9.00000 −0.453990
\(394\) 0 0
\(395\) −4.50000 7.79423i −0.226420 0.392170i
\(396\) 0 0
\(397\) 18.0000 + 10.3923i 0.903394 + 0.521575i 0.878300 0.478110i \(-0.158678\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) 0 0
\(399\) −1.00000 + 5.19615i −0.0500626 + 0.260133i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.73205i 0.0860663i
\(406\) 0 0
\(407\) 17.3205i 0.858546i
\(408\) 0 0
\(409\) −19.5000 + 11.2583i −0.964213 + 0.556689i −0.897467 0.441081i \(-0.854595\pi\)
−0.0667458 + 0.997770i \(0.521262\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) 0 0
\(413\) −22.5000 + 7.79423i −1.10715 + 0.383529i
\(414\) 0 0
\(415\) 4.50000 + 2.59808i 0.220896 + 0.127535i
\(416\) 0 0
\(417\) −7.00000 12.1244i −0.342791 0.593732i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 0 0
\(423\) −6.00000 10.3923i −0.291730 0.505291i
\(424\) 0 0
\(425\) −6.00000 3.46410i −0.291043 0.168034i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.0000 19.0526i 1.58955 0.917729i 0.596174 0.802855i \(-0.296687\pi\)
0.993380 0.114874i \(-0.0366465\pi\)
\(432\) 0 0
\(433\) 34.6410i 1.66474i 0.554220 + 0.832370i \(0.313017\pi\)
−0.554220 + 0.832370i \(0.686983\pi\)
\(434\) 0 0
\(435\) 15.5885i 0.747409i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 14.5000 25.1147i 0.692047 1.19866i −0.279119 0.960257i \(-0.590042\pi\)
0.971166 0.238404i \(-0.0766244\pi\)
\(440\) 0 0
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 0 0
\(443\) −10.5000 6.06218i −0.498870 0.288023i 0.229377 0.973338i \(-0.426331\pi\)
−0.728247 + 0.685315i \(0.759665\pi\)
\(444\) 0 0
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) 0 0
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 0 0
\(453\) 4.50000 + 2.59808i 0.211428 + 0.122068i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 15.5000 26.8468i 0.725059 1.25584i −0.233890 0.972263i \(-0.575146\pi\)
0.958950 0.283577i \(-0.0915211\pi\)
\(458\) 0 0
\(459\) −3.00000 + 1.73205i −0.140028 + 0.0808452i
\(460\) 0 0
\(461\) 6.92820i 0.322679i 0.986899 + 0.161339i \(0.0515813\pi\)
−0.986899 + 0.161339i \(0.948419\pi\)
\(462\) 0 0
\(463\) 38.1051i 1.77090i −0.464739 0.885448i \(-0.653852\pi\)
0.464739 0.885448i \(-0.346148\pi\)
\(464\) 0 0
\(465\) −7.50000 + 4.33013i −0.347804 + 0.200805i
\(466\) 0 0
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 0 0
\(469\) −12.0000 34.6410i −0.554109 1.59957i
\(470\) 0 0
\(471\) −6.00000 3.46410i −0.276465 0.159617i
\(472\) 0 0
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) 0 0
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.5000 + 28.5788i −0.749226 + 1.29770i
\(486\) 0 0
\(487\) −7.50000 + 4.33013i −0.339857 + 0.196217i −0.660209 0.751082i \(-0.729532\pi\)
0.320352 + 0.947299i \(0.396199\pi\)
\(488\) 0 0
\(489\) 13.8564i 0.626608i
\(490\) 0 0
\(491\) 25.9808i 1.17250i 0.810132 + 0.586248i \(0.199395\pi\)
−0.810132 + 0.586248i \(0.800605\pi\)
\(492\) 0 0
\(493\) −27.0000 + 15.5885i −1.21602 + 0.702069i
\(494\) 0 0
\(495\) −1.50000 + 2.59808i −0.0674200 + 0.116775i
\(496\) 0 0
\(497\) 36.0000 + 6.92820i 1.61482 + 0.310772i
\(498\) 0 0
\(499\) −3.00000 1.73205i −0.134298 0.0775372i 0.431346 0.902187i \(-0.358039\pi\)
−0.565644 + 0.824650i \(0.691372\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) −24.0000 −1.06799
\(506\) 0 0
\(507\) 6.50000 + 11.2583i 0.288675 + 0.500000i
\(508\) 0 0
\(509\) −28.5000 16.4545i −1.26324 0.729332i −0.289540 0.957166i \(-0.593502\pi\)
−0.973700 + 0.227834i \(0.926836\pi\)
\(510\) 0 0
\(511\) 6.00000 + 17.3205i 0.265424 + 0.766214i
\(512\) 0 0
\(513\) 1.00000 1.73205i 0.0441511 0.0764719i
\(514\) 0 0
\(515\) −6.00000 + 3.46410i −0.264392 + 0.152647i
\(516\) 0 0
\(517\) 20.7846i 0.914106i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 33.0000 19.0526i 1.44576 0.834708i 0.447532 0.894268i \(-0.352303\pi\)
0.998225 + 0.0595604i \(0.0189699\pi\)
\(522\) 0 0
\(523\) −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i \(0.376373\pi\)
−0.990873 + 0.134801i \(0.956961\pi\)
\(524\) 0 0
\(525\) −4.00000 3.46410i −0.174574 0.151186i
\(526\) 0 0
\(527\) −15.0000 8.66025i −0.653410 0.377247i
\(528\) 0 0
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 0 0
\(531\) 9.00000 0.390567
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −10.5000 18.1865i −0.453955 0.786272i
\(536\) 0 0
\(537\) −21.0000 12.1244i −0.906217 0.523205i
\(538\) 0 0
\(539\) 12.0000 1.73205i 0.516877 0.0746047i
\(540\) 0 0
\(541\) 11.0000 19.0526i 0.472927 0.819133i −0.526593 0.850118i \(-0.676531\pi\)
0.999520 + 0.0309841i \(0.00986412\pi\)
\(542\) 0 0
\(543\) 9.00000 5.19615i 0.386227 0.222988i
\(544\) 0 0
\(545\) 6.92820i 0.296772i
\(546\) 0 0
\(547\) 10.3923i 0.444343i 0.975008 + 0.222171i \(0.0713145\pi\)
−0.975008 + 0.222171i \(0.928686\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.00000 15.5885i 0.383413 0.664091i
\(552\) 0 0
\(553\) 9.00000 10.3923i 0.382719 0.441926i
\(554\) 0 0
\(555\) −15.0000 8.66025i −0.636715 0.367607i
\(556\) 0 0
\(557\) −13.5000 23.3827i −0.572013 0.990756i −0.996359 0.0852559i \(-0.972829\pi\)
0.424346 0.905500i \(-0.360504\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) 0 0
\(563\) −22.5000 38.9711i −0.948262 1.64244i −0.749085 0.662474i \(-0.769506\pi\)
−0.199177 0.979963i \(-0.563827\pi\)
\(564\) 0 0
\(565\) −9.00000 5.19615i −0.378633 0.218604i
\(566\) 0 0
\(567\) −2.50000 + 0.866025i −0.104990 + 0.0363696i
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 18.0000 10.3923i 0.753277 0.434904i −0.0736000 0.997288i \(-0.523449\pi\)
0.826877 + 0.562383i \(0.190115\pi\)
\(572\) 0 0
\(573\) 13.8564i 0.578860i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.50000 + 0.866025i −0.0624458 + 0.0360531i −0.530898 0.847436i \(-0.678145\pi\)
0.468452 + 0.883489i \(0.344812\pi\)
\(578\) 0 0
\(579\) −2.50000 + 4.33013i −0.103896 + 0.179954i
\(580\) 0 0
\(581\) −1.50000 + 7.79423i −0.0622305 + 0.323359i
\(582\) 0 0
\(583\) 13.5000 + 7.79423i 0.559113 + 0.322804i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 33.0000 1.36206 0.681028 0.732257i \(-0.261533\pi\)
0.681028 + 0.732257i \(0.261533\pi\)
\(588\) 0 0
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) 3.00000 + 5.19615i 0.123404 + 0.213741i
\(592\) 0 0
\(593\) −24.0000 13.8564i −0.985562 0.569014i −0.0816172 0.996664i \(-0.526008\pi\)
−0.903945 + 0.427649i \(0.859342\pi\)
\(594\) 0 0
\(595\) −3.00000 + 15.5885i −0.122988 + 0.639064i
\(596\) 0 0
\(597\) 8.00000 13.8564i 0.327418 0.567105i
\(598\) 0 0
\(599\) 24.0000 13.8564i 0.980613 0.566157i 0.0781581 0.996941i \(-0.475096\pi\)
0.902455 + 0.430784i \(0.141763\pi\)
\(600\) 0 0
\(601\) 15.5885i 0.635866i −0.948113 0.317933i \(-0.897011\pi\)
0.948113 0.317933i \(-0.102989\pi\)
\(602\) 0 0
\(603\) 13.8564i 0.564276i
\(604\) 0 0
\(605\) 12.0000 6.92820i 0.487869 0.281672i
\(606\) 0 0
\(607\) −9.50000 + 16.4545i −0.385593 + 0.667867i −0.991851 0.127401i \(-0.959336\pi\)
0.606258 + 0.795268i \(0.292670\pi\)
\(608\) 0 0
\(609\) −22.5000 + 7.79423i −0.911746 + 0.315838i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −2.00000 3.46410i −0.0807792 0.139914i 0.822806 0.568323i \(-0.192408\pi\)
−0.903585 + 0.428409i \(0.859074\pi\)
\(614\) 0 0
\(615\) −18.0000 −0.725830
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 0 0
\(619\) −14.0000 24.2487i −0.562708 0.974638i −0.997259 0.0739910i \(-0.976426\pi\)
0.434551 0.900647i \(-0.356907\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 + 6.92820i −0.240385 + 0.277573i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 0 0
\(627\) 3.00000 1.73205i 0.119808 0.0691714i
\(628\) 0 0
\(629\) 34.6410i 1.38123i
\(630\) 0 0
\(631\) 32.9090i 1.31009i 0.755592 + 0.655043i \(0.227349\pi\)
−0.755592 + 0.655043i \(0.772651\pi\)
\(632\) 0 0
\(633\) −6.00000 + 3.46410i −0.238479 + 0.137686i
\(634\) 0 0
\(635\) 4.50000 7.79423i 0.178577 0.309305i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −12.0000 6.92820i −0.474713 0.274075i
\(640\) 0 0
\(641\) −18.0000 31.1769i −0.710957 1.23141i −0.964498 0.264089i \(-0.914929\pi\)
0.253541 0.967325i \(-0.418405\pi\)
\(642\) 0 0
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0 0
\(649\) 13.5000 + 7.79423i 0.529921 + 0.305950i
\(650\) 0 0
\(651\) −10.0000 8.66025i −0.391931 0.339422i
\(652\) 0 0
\(653\) −13.5000 + 23.3827i −0.528296 + 0.915035i 0.471160 + 0.882048i \(0.343835\pi\)
−0.999456 + 0.0329874i \(0.989498\pi\)
\(654\) 0 0
\(655\) 13.5000 7.79423i 0.527489 0.304546i
\(656\) 0 0
\(657\) 6.92820i 0.270295i
\(658\) 0 0
\(659\) 10.3923i 0.404827i −0.979300 0.202413i \(-0.935122\pi\)
0.979300 0.202413i \(-0.0648785\pi\)
\(660\) 0 0
\(661\) −3.00000 + 1.73205i −0.116686 + 0.0673690i −0.557207 0.830373i \(-0.688127\pi\)
0.440521 + 0.897742i \(0.354794\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.00000 8.66025i −0.116335 0.335830i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 9.50000 + 16.4545i 0.367291 + 0.636167i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −35.0000 −1.34915 −0.674575 0.738206i \(-0.735673\pi\)
−0.674575 + 0.738206i \(0.735673\pi\)
\(674\) 0 0
\(675\) 1.00000 + 1.73205i 0.0384900 + 0.0666667i
\(676\) 0 0
\(677\) −25.5000 14.7224i −0.980045 0.565829i −0.0777610 0.996972i \(-0.524777\pi\)
−0.902284 + 0.431143i \(0.858110\pi\)
\(678\) 0 0
\(679\) −49.5000 9.52628i −1.89964 0.365585i
\(680\) 0 0
\(681\) 10.5000 18.1865i 0.402361 0.696909i
\(682\) 0 0
\(683\) 22.5000 12.9904i 0.860939 0.497063i −0.00338791 0.999994i \(-0.501078\pi\)
0.864326 + 0.502931i \(0.167745\pi\)
\(684\) 0 0
\(685\) 20.7846i 0.794139i
\(686\) 0 0
\(687\) 3.46410i 0.132164i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −11.0000 + 19.0526i −0.418460 + 0.724793i −0.995785 0.0917209i \(-0.970763\pi\)
0.577325 + 0.816514i \(0.304097\pi\)
\(692\) 0 0
\(693\) −4.50000 0.866025i −0.170941 0.0328976i
\(694\) 0 0
\(695\) 21.0000 + 12.1244i 0.796575 + 0.459903i
\(696\) 0 0
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) 0 0
\(699\) −18.0000 −0.680823
\(700\) 0 0
\(701\) 45.0000 1.69963 0.849813 0.527084i \(-0.176715\pi\)
0.849813 + 0.527084i \(0.176715\pi\)
\(702\) 0 0
\(703\) 10.0000 + 17.3205i 0.377157 + 0.653255i
\(704\) 0 0
\(705\) 18.0000 + 10.3923i 0.677919 + 0.391397i
\(706\) 0 0
\(707\) −12.0000 34.6410i −0.451306 1.30281i
\(708\) 0 0
\(709\) −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) 0 0
\(711\) −4.50000 + 2.59808i −0.168763 + 0.0974355i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.00000 + 3.46410i −0.224074 + 0.129369i
\(718\) 0 0
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 0 0
\(721\) −8.00000 6.92820i −0.297936 0.258020i
\(722\) 0 0
\(723\) 19.5000 + 11.2583i 0.725213 + 0.418702i
\(724\) 0 0
\(725\) 9.00000 + 15.5885i 0.334252 + 0.578941i
\(726\) 0 0
\(727\) −37.0000 −1.37225 −0.686127 0.727482i \(-0.740691\pi\)
−0.686127 + 0.727482i \(0.740691\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −6.00000 10.3923i −0.221918 0.384373i
\(732\) 0 0
\(733\) 9.00000 + 5.19615i 0.332423 + 0.191924i 0.656916 0.753964i \(-0.271861\pi\)
−0.324494 + 0.945888i \(0.605194\pi\)
\(734\) 0 0
\(735\) −4.50000 + 11.2583i −0.165985 + 0.415270i
\(736\) 0 0
\(737\) −12.0000 + 20.7846i −0.442026 + 0.765611i
\(738\) 0 0
\(739\) −9.00000 + 5.19615i −0.331070 + 0.191144i −0.656316 0.754486i \(-0.727886\pi\)
0.325246 + 0.945629i \(0.394553\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.8564i 0.508342i −0.967159 0.254171i \(-0.918197\pi\)
0.967159 0.254171i \(-0.0818026\pi\)
\(744\) 0 0
\(745\) −9.00000 + 5.19615i −0.329734 + 0.190372i
\(746\) 0 0
\(747\) 1.50000 2.59808i 0.0548821 0.0950586i
\(748\) 0 0
\(749\) 21.0000 24.2487i 0.767323 0.886029i
\(750\) 0 0
\(751\) 4.50000 + 2.59808i 0.164207 + 0.0948051i 0.579852 0.814722i \(-0.303111\pi\)
−0.415644 + 0.909527i \(0.636444\pi\)
\(752\) 0 0
\(753\) 7.50000 + 12.9904i 0.273315 + 0.473396i
\(754\) 0 0
\(755\) −9.00000 −0.327544
\(756\) 0 0
\(757\) 4.00000 0.145382 0.0726912 0.997354i \(-0.476841\pi\)
0.0726912 + 0.997354i \(0.476841\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 24.2487i −1.52250 0.879015i −0.999646 0.0265919i \(-0.991535\pi\)
−0.522852 0.852423i \(-0.675132\pi\)
\(762\) 0 0
\(763\) −10.0000 + 3.46410i −0.362024 + 0.125409i
\(764\) 0 0
\(765\) 3.00000 5.19615i 0.108465 0.187867i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 19.0526i 0.687053i 0.939143 + 0.343526i \(0.111621\pi\)
−0.939143 + 0.343526i \(0.888379\pi\)
\(770\) 0 0
\(771\) 10.3923i 0.374270i
\(772\) 0 0
\(773\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) −5.00000 + 8.66025i −0.179605 + 0.311086i
\(776\) 0 0
\(777\) 5.00000 25.9808i 0.179374 0.932055i
\(778\) 0 0
\(779\) 18.0000 + 10.3923i 0.644917 + 0.372343i
\(780\) 0 0
\(781\) −12.0000 20.7846i −0.429394 0.743732i
\(782\) 0 0
\(783\) 9.00000 0.321634
\(784\) 0 0
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) −14.0000 24.2487i −0.499046 0.864373i 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) 0 0
\(789\) 15.0000 + 8.66025i 0.534014 + 0.308313i
\(790\) 0 0
\(791\) 3.00000 15.5885i 0.106668 0.554262i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −13.5000 + 7.79423i −0.478796 + 0.276433i
\(796\) 0 0
\(797\) 5.19615i 0.184057i −0.995756 0.0920286i \(-0.970665\pi\)
0.995756 0.0920286i \(-0.0293351\pi\)