Properties

Label 2352.2.bl.h.31.1
Level $2352$
Weight $2$
Character 2352.31
Analytic conductor $18.781$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bl (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
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 31.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2352.31
Dual form 2352.2.bl.h.607.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 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 \(-0.249243\pi\)
−0.256520 + 0.966539i \(0.582576\pi\)
\(12\) 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 \(-0.471333\pi\)
−0.817546 + 0.575863i \(0.804666\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 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 \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0 0
\(33\) 1.50000 0.866025i 0.261116 0.150756i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 8.66025i −0.821995 1.42374i −0.904194 0.427121i \(-0.859528\pi\)
0.0821995 0.996616i \(-0.473806\pi\)
\(38\) 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 0.856560 + 0.516047i \(0.172597\pi\)
0.0186297 + 0.999826i \(0.494070\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.00000 + 1.73205i −0.420084 + 0.242536i
\(52\) 0 0
\(53\) 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) 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 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.0000 6.92820i −1.46603 0.846415i −0.466755 0.884387i \(-0.654577\pi\)
−0.999279 + 0.0379722i \(0.987910\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.8564i 1.64445i −0.569160 0.822226i \(-0.692732\pi\)
0.569160 0.822226i \(-0.307268\pi\)
\(72\) 0 0
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) 0 0
\(75\) 1.00000 + 1.73205i 0.115470 + 0.200000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.50000 2.59808i 0.506290 0.292306i −0.225018 0.974355i \(-0.572244\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 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 \(-0.607893\pi\)
0.650500 + 0.759506i \(0.274559\pi\)
\(90\) 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 0.959221 0.282656i \(-0.0912155\pi\)
0.234823 + 0.972038i \(0.424549\pi\)
\(102\) 0 0
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.5000 + 6.06218i −1.01507 + 0.586053i −0.912673 0.408690i \(-0.865986\pi\)
−0.102400 + 0.994743i \(0.532652\pi\)
\(108\) 0 0
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 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
\(119\) 0 0
\(120\) 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 \(-0.925950\pi\)
0.973062 0.230542i \(-0.0740499\pi\)
\(128\) 0 0
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) 0 0
\(131\) −4.50000 7.79423i −0.393167 0.680985i 0.599699 0.800226i \(-0.295287\pi\)
−0.992865 + 0.119241i \(0.961954\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.50000 0.866025i 0.129099 0.0745356i
\(136\) 0 0
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 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
\(147\) 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
\(151\) 4.50000 + 2.59808i 0.366205 + 0.211428i 0.671799 0.740733i \(-0.265522\pi\)
−0.305594 + 0.952162i \(0.598855\pi\)
\(152\) 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 0.241086 0.970504i \(-0.422496\pi\)
−0.719938 + 0.694038i \(0.755830\pi\)
\(158\) 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 \(-0.849249\pi\)
−0.0499796 + 0.998750i \(0.515916\pi\)
\(164\) 0 0
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.50000 + 7.79423i 0.338241 + 0.585850i
\(178\) 0 0
\(179\) 21.0000 + 12.1244i 1.56961 + 0.906217i 0.996213 + 0.0869415i \(0.0277093\pi\)
0.573400 + 0.819275i \(0.305624\pi\)
\(180\) 0 0
\(181\) 10.3923i 0.772454i 0.922404 + 0.386227i \(0.126222\pi\)
−0.922404 + 0.386227i \(0.873778\pi\)
\(182\) 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 0
\(190\) 0 0
\(191\) −12.0000 + 6.92820i −0.868290 + 0.501307i −0.866779 0.498692i \(-0.833814\pi\)
−0.00151007 + 0.999999i \(0.500481\pi\)
\(192\) 0 0
\(193\) 2.50000 4.33013i 0.179954 0.311689i −0.761911 0.647682i \(-0.775738\pi\)
0.941865 + 0.335993i \(0.109072\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 0 0
\(201\) −12.0000 + 6.92820i −0.846415 + 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) 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
\(217\) 0 0
\(218\) 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 \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 0 0
\(225\) 2.00000 0.133333
\(226\) 0 0
\(227\) −10.5000 + 18.1865i −0.696909 + 1.20708i 0.272623 + 0.962121i \(0.412109\pi\)
−0.969533 + 0.244962i \(0.921225\pi\)
\(228\) 0 0
\(229\) 3.00000 1.73205i 0.198246 0.114457i −0.397591 0.917563i \(-0.630154\pi\)
0.595837 + 0.803105i \(0.296820\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 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 \(-0.928064\pi\)
0.974572 0.224074i \(-0.0719358\pi\)
\(240\) 0 0
\(241\) −19.5000 11.2583i −1.25611 0.725213i −0.283790 0.958886i \(-0.591592\pi\)
−0.972315 + 0.233674i \(0.924925\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 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 \(-0.561596\pi\)
0.753709 + 0.657208i \(0.228263\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −4.50000 7.79423i −0.278543 0.482451i
\(262\) 0 0
\(263\) 15.0000 + 8.66025i 0.924940 + 0.534014i 0.885208 0.465196i \(-0.154016\pi\)
0.0397320 + 0.999210i \(0.487350\pi\)
\(264\) 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 0.851488 0.524375i \(-0.175701\pi\)
−0.0283781 + 0.999597i \(0.509034\pi\)
\(270\) 0 0
\(271\) 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i \(-0.0582339\pi\)
−0.649211 + 0.760609i \(0.724901\pi\)
\(272\) 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 0.0477206 + 0.998861i \(0.484804\pi\)
−0.888899 + 0.458103i \(0.848529\pi\)
\(278\) 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 −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 0 0
\(285\) 3.00000 1.73205i 0.177705 0.102598i
\(286\) 0 0
\(287\) 0 0
\(288\) 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 \(0.0485009\pi\)
−0.988414 + 0.151781i \(0.951499\pi\)
\(294\) 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
\(301\) 0 0
\(302\) 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 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) 0 0
\(313\) 4.50000 2.59808i 0.254355 0.146852i −0.367402 0.930062i \(-0.619753\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.5000 + 18.1865i 0.589739 + 1.02146i 0.994266 + 0.106932i \(0.0341026\pi\)
−0.404528 + 0.914526i \(0.632564\pi\)
\(318\) 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
\(329\) 0 0
\(330\) 0 0
\(331\) 12.0000 6.92820i 0.659580 0.380808i −0.132537 0.991178i \(-0.542312\pi\)
0.792117 + 0.610370i \(0.208979\pi\)
\(332\) 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
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.0000 8.66025i −0.805242 0.464907i 0.0400587 0.999197i \(-0.487246\pi\)
−0.845301 + 0.534291i \(0.820579\pi\)
\(348\) 0 0
\(349\) 6.92820i 0.370858i −0.982658 0.185429i \(-0.940632\pi\)
0.982658 0.185429i \(-0.0593675\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.00000 3.46410i −0.319348 0.184376i 0.331754 0.943366i \(-0.392360\pi\)
−0.651102 + 0.758990i \(0.725693\pi\)
\(354\) 0 0
\(355\) 12.0000 + 20.7846i 0.636894 + 1.10313i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 24.0000 13.8564i 1.26667 0.731313i 0.292315 0.956322i \(-0.405574\pi\)
0.974357 + 0.225009i \(0.0722411\pi\)
\(360\) 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 \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) 0 0
\(369\) −9.00000 + 5.19615i −0.468521 + 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) 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 \(-0.0145596\pi\)
−0.539076 + 0.842257i \(0.681226\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 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 \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 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 0.0250943 0.999685i \(-0.492011\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 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 \(-0.145405\pi\)
0.0667458 + 0.997770i \(0.478738\pi\)
\(410\) 0 0
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) 0 0
\(413\) 0 0
\(414\) 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 \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 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 0.993380 + 0.114874i \(0.0366465\pi\)
0.596174 + 0.802855i \(0.296687\pi\)
\(432\) 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 −0.971166 0.238404i \(-0.923376\pi\)
0.279119 0.960257i \(-0.409958\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.5000 6.06218i 0.498870 0.288023i −0.229377 0.973338i \(-0.573669\pi\)
0.728247 + 0.685315i \(0.240335\pi\)
\(444\) 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 0.958950 + 0.283577i \(0.0915211\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 3.00000 + 1.73205i 0.140028 + 0.0808452i
\(460\) 0 0
\(461\) 6.92820i 0.322679i −0.986899 0.161339i \(-0.948419\pi\)
0.986899 0.161339i \(-0.0515813\pi\)
\(462\) 0 0
\(463\) 38.1051i 1.77090i 0.464739 + 0.885448i \(0.346148\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 0 0
\(465\) 7.50000 + 4.33013i 0.347804 + 0.200805i
\(466\) 0 0
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 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 \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 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 0.320352 0.947299i \(-0.396199\pi\)
−0.660209 + 0.751082i \(0.729532\pi\)
\(488\) 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
\(497\) 0 0
\(498\) 0 0
\(499\) 3.00000 1.73205i 0.134298 0.0775372i −0.431346 0.902187i \(-0.641961\pi\)
0.565644 + 0.824650i \(0.308628\pi\)
\(500\) 0 0
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 0 0
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 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 −0.973700 0.227834i \(-0.926836\pi\)
−0.289540 + 0.957166i \(0.593502\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 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 \(-0.647697\pi\)
−0.998225 + 0.0595604i \(0.981030\pi\)
\(522\) 0 0
\(523\) −14.0000 24.2487i −0.612177 1.06032i −0.990873 0.134801i \(-0.956961\pi\)
0.378695 0.925521i \(-0.376373\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(539\) 0 0
\(540\) 0 0
\(541\) −11.0000 19.0526i −0.472927 0.819133i 0.526593 0.850118i \(-0.323469\pi\)
−0.999520 + 0.0309841i \(0.990136\pi\)
\(542\) 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
\(553\) 0 0
\(554\) 0 0
\(555\) 15.0000 8.66025i 0.636715 0.367607i
\(556\) 0 0
\(557\) 13.5000 23.3827i 0.572013 0.990756i −0.424346 0.905500i \(-0.639496\pi\)
0.996359 0.0852559i \(-0.0271708\pi\)
\(558\) 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 −0.199177 + 0.979963i \(0.563827\pi\)
−0.749085 + 0.662474i \(0.769506\pi\)
\(564\) 0 0
\(565\) −9.00000 + 5.19615i −0.378633 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) −18.0000 10.3923i −0.753277 0.434904i 0.0736000 0.997288i \(-0.476551\pi\)
−0.826877 + 0.562383i \(0.809885\pi\)
\(572\) 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 \(-0.321855\pi\)
−0.468452 + 0.883489i \(0.655188\pi\)
\(578\) 0 0
\(579\) −2.50000 4.33013i −0.103896 0.179954i
\(580\) 0 0
\(581\) 0 0
\(582\) 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 \(-0.473992\pi\)
0.903945 + 0.427649i \(0.140658\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.00000 13.8564i −0.327418 0.567105i
\(598\) 0 0
\(599\) 24.0000 + 13.8564i 0.980613 + 0.566157i 0.902455 0.430784i \(-0.141763\pi\)
0.0781581 + 0.996941i \(0.475096\pi\)
\(600\) 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 \(-0.0406635\pi\)
−0.606258 + 0.795268i \(0.707330\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 2.00000 3.46410i 0.0807792 0.139914i −0.822806 0.568323i \(-0.807592\pi\)
0.903585 + 0.428409i \(0.140926\pi\)
\(614\) 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 0.434551 + 0.900647i \(0.356907\pi\)
−0.997259 + 0.0739910i \(0.976426\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 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 \(-0.772651\pi\)
0.755592 0.655043i \(-0.227349\pi\)
\(632\) 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 0.253541 + 0.967325i \(0.418405\pi\)
−0.964498 + 0.264089i \(0.914929\pi\)
\(642\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0 0
\(649\) −13.5000 + 7.79423i −0.529921 + 0.305950i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.5000 + 23.3827i 0.528296 + 0.915035i 0.999456 + 0.0329874i \(0.0105021\pi\)
−0.471160 + 0.882048i \(0.656165\pi\)
\(654\) 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 0.440521 0.897742i \(-0.354794\pi\)
−0.557207 + 0.830373i \(0.688127\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 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 −0.902284 0.431143i \(-0.858110\pi\)
−0.0777610 + 0.996972i \(0.524777\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 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 \(-0.498922\pi\)
−0.864326 + 0.502931i \(0.832255\pi\)
\(684\) 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 0.577325 0.816514i \(-0.304097\pi\)
−0.995785 + 0.0917209i \(0.970763\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 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 \(-0.823285\pi\)
−0.849813 + 0.527084i \(0.823285\pi\)
\(702\) 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
\(707\) 0 0
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 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 \(-0.0577130\pi\)
−0.647965 + 0.761670i \(0.724380\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 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 \(-0.259309\pi\)
0.686127 + 0.727482i \(0.259309\pi\)
\(728\) 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 −0.324494 0.945888i \(-0.605194\pi\)
0.656916 + 0.753964i \(0.271861\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 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 \(-0.272114\pi\)
−0.325246 + 0.945629i \(0.605447\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.8564i 0.508342i 0.967159 + 0.254171i \(0.0818026\pi\)
−0.967159 + 0.254171i \(0.918197\pi\)
\(744\) 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
\(749\) 0 0
\(750\) 0 0
\(751\) 4.50000 2.59808i 0.164207 0.0948051i −0.415644 0.909527i \(-0.636444\pi\)
0.579852 + 0.814722i \(0.303111\pi\)
\(752\) 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 \(-0.523159\pi\)
−0.0726912 + 0.997354i \(0.523159\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.0000 24.2487i 1.52250 0.879015i 0.522852 0.852423i \(-0.324868\pi\)
0.999646 0.0265919i \(-0.00846546\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(774\) 0 0
\(775\) 5.00000 + 8.66025i 0.179605 + 0.311086i
\(776\) 0 0
\(777\) 0 0
\(778\) 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 −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) 0 0
\(789\) 15.0000 8.66025i 0.534014 0.308313i
\(790\) 0 0
\(791\) 0 0
\(792\) 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 \(0.0293351\pi\)
−0.995756 + 0.0920286i \(0.970665\pi\)
\(798\) 0 0
\(799\) 41.5692i 1.47061i
\(800\) 0 0
\(801\) −3.00000