Properties

Label 336.2.bl.a.31.1
Level $336$
Weight $2$
Character 336.31
Analytic conductor $2.683$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bl (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(1\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.31
Dual form 336.2.bl.a.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} +5.19615i q^{13} -3.46410i q^{15} +(-6.00000 - 3.46410i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(2.00000 + 1.73205i) q^{21} +(3.50000 - 6.06218i) q^{25} +1.00000 q^{27} +(-2.50000 + 4.33013i) q^{31} +(3.00000 - 1.73205i) q^{33} +(3.00000 + 8.66025i) q^{35} +(-0.500000 - 0.866025i) q^{37} +(-4.50000 - 2.59808i) q^{39} +10.3923i q^{41} +1.73205i q^{43} +(3.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(6.00000 - 3.46410i) q^{51} +12.0000 q^{55} +7.00000 q^{57} +(-2.50000 + 0.866025i) q^{63} +(-9.00000 - 15.5885i) q^{65} +(1.50000 + 0.866025i) q^{67} -3.46410i q^{71} +(7.50000 + 4.33013i) q^{73} +(3.50000 + 6.06218i) q^{75} +(-6.00000 + 6.92820i) q^{77} +(-13.5000 + 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} -6.00000 q^{83} +24.0000 q^{85} +(6.00000 - 3.46410i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-2.50000 - 4.33013i) q^{93} +(21.0000 + 12.1244i) q^{95} -6.92820i q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 6q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - 6q^{5} + q^{7} - q^{9} - 6q^{11} - 12q^{17} - 7q^{19} + 4q^{21} + 7q^{25} + 2q^{27} - 5q^{31} + 6q^{33} + 6q^{35} - q^{37} - 9q^{39} + 6q^{45} + 6q^{47} - 13q^{49} + 12q^{51} + 24q^{55} + 14q^{57} - 5q^{63} - 18q^{65} + 3q^{67} + 15q^{73} + 7q^{75} - 12q^{77} - 27q^{79} - q^{81} - 12q^{83} + 48q^{85} + 12q^{89} + 27q^{91} - 5q^{93} + 42q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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
\(5\) −3.00000 + 1.73205i −1.34164 + 0.774597i −0.987048 0.160424i \(-0.948714\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(6\) 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
\(11\) −3.00000 1.73205i −0.904534 0.522233i −0.0258656 0.999665i \(-0.508234\pi\)
−0.878668 + 0.477432i \(0.841568\pi\)
\(12\) 0 0
\(13\) 5.19615i 1.44115i 0.693375 + 0.720577i \(0.256123\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 0 0
\(17\) −6.00000 3.46410i −1.45521 0.840168i −0.456444 0.889752i \(-0.650877\pi\)
−0.998770 + 0.0495842i \(0.984210\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(1.53659\pi\)
\(20\) 0 0
\(21\) 2.00000 + 1.73205i 0.436436 + 0.377964i
\(22\) 0 0
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) 3.50000 6.06218i 0.700000 1.21244i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 0 0
\(33\) 3.00000 1.73205i 0.522233 0.301511i
\(34\) 0 0
\(35\) 3.00000 + 8.66025i 0.507093 + 1.46385i
\(36\) 0 0
\(37\) −0.500000 0.866025i −0.0821995 0.142374i 0.821995 0.569495i \(-0.192861\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 0 0
\(39\) −4.50000 2.59808i −0.720577 0.416025i
\(40\) 0 0
\(41\) 10.3923i 1.62301i 0.584349 + 0.811503i \(0.301350\pi\)
−0.584349 + 0.811503i \(0.698650\pi\)
\(42\) 0 0
\(43\) 1.73205i 0.264135i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 0 0
\(45\) 3.00000 + 1.73205i 0.447214 + 0.258199i
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 6.00000 3.46410i 0.840168 0.485071i
\(52\) 0 0
\(53\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) 0 0
\(55\) 12.0000 1.61808
\(56\) 0 0
\(57\) 7.00000 0.927173
\(58\) 0 0
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) −2.50000 + 0.866025i −0.314970 + 0.109109i
\(64\) 0 0
\(65\) −9.00000 15.5885i −1.11631 1.93351i
\(66\) 0 0
\(67\) 1.50000 + 0.866025i 0.183254 + 0.105802i 0.588821 0.808264i \(-0.299592\pi\)
−0.405567 + 0.914066i \(0.632926\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.46410i 0.411113i −0.978645 0.205557i \(-0.934100\pi\)
0.978645 0.205557i \(-0.0659005\pi\)
\(72\) 0 0
\(73\) 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i \(-0.164160\pi\)
0.00787336 + 0.999969i \(0.497494\pi\)
\(74\) 0 0
\(75\) 3.50000 + 6.06218i 0.404145 + 0.700000i
\(76\) 0 0
\(77\) −6.00000 + 6.92820i −0.683763 + 0.789542i
\(78\) 0 0
\(79\) −13.5000 + 7.79423i −1.51887 + 0.876919i −0.519115 + 0.854704i \(0.673739\pi\)
−0.999753 + 0.0222151i \(0.992928\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 24.0000 2.60317
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i \(-0.546985\pi\)
0.783072 + 0.621932i \(0.213652\pi\)
\(90\) 0 0
\(91\) 13.5000 + 2.59808i 1.41518 + 0.272352i
\(92\) 0 0
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) 0 0
\(95\) 21.0000 + 12.1244i 2.15455 + 1.24393i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 0 0
\(99\) 3.46410i 0.348155i
\(100\) 0 0
\(101\) −3.00000 1.73205i −0.298511 0.172345i 0.343263 0.939239i \(-0.388468\pi\)
−0.641774 + 0.766894i \(0.721801\pi\)
\(102\) 0 0
\(103\) −2.50000 4.33013i −0.246332 0.426660i 0.716173 0.697923i \(-0.245892\pi\)
−0.962505 + 0.271263i \(0.912559\pi\)
\(104\) 0 0
\(105\) −9.00000 1.73205i −0.878310 0.169031i
\(106\) 0 0
\(107\) −6.00000 + 3.46410i −0.580042 + 0.334887i −0.761150 0.648576i \(-0.775365\pi\)
0.181108 + 0.983463i \(0.442032\pi\)
\(108\) 0 0
\(109\) −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i \(-0.910303\pi\)
0.721102 + 0.692829i \(0.243636\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 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
\(117\) 4.50000 2.59808i 0.416025 0.240192i
\(118\) 0 0
\(119\) −12.0000 + 13.8564i −1.10004 + 1.27021i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) −9.00000 5.19615i −0.811503 0.468521i
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 15.5885i 1.38325i −0.722256 0.691626i \(-0.756895\pi\)
0.722256 0.691626i \(-0.243105\pi\)
\(128\) 0 0
\(129\) −1.50000 0.866025i −0.132068 0.0762493i
\(130\) 0 0
\(131\) −9.00000 15.5885i −0.786334 1.36197i −0.928199 0.372084i \(-0.878643\pi\)
0.141865 0.989886i \(1.54531\pi\)
\(132\) 0 0
\(133\) −17.5000 + 6.06218i −1.51744 + 0.525657i
\(134\) 0 0
\(135\) −3.00000 + 1.73205i −0.258199 + 0.149071i
\(136\) 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
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 9.00000 15.5885i 0.752618 1.30357i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.50000 4.33013i 0.453632 0.357143i
\(148\) 0 0
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) −9.00000 5.19615i −0.732410 0.422857i 0.0868934 0.996218i \(-0.472306\pi\)
−0.819303 + 0.573361i \(0.805639\pi\)
\(152\) 0 0
\(153\) 6.92820i 0.560112i
\(154\) 0 0
\(155\) 17.3205i 1.39122i
\(156\) 0 0
\(157\) −12.0000 6.92820i −0.957704 0.552931i −0.0622385 0.998061i \(-0.519824\pi\)
−0.895466 + 0.445130i \(0.853157\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3.00000 + 1.73205i −0.234978 + 0.135665i −0.612866 0.790186i \(-0.709984\pi\)
0.377888 + 0.925851i \(0.376650\pi\)
\(164\) 0 0
\(165\) −6.00000 + 10.3923i −0.467099 + 0.809040i
\(166\) 0 0
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) −14.0000 −1.07692
\(170\) 0 0
\(171\) −3.50000 + 6.06218i −0.267652 + 0.463586i
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) −14.0000 12.1244i −1.05830 0.916515i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −15.0000 8.66025i −1.12115 0.647298i −0.179458 0.983766i \(-0.557434\pi\)
−0.941695 + 0.336468i \(0.890768\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i 0.815086 + 0.579340i \(0.196690\pi\)
−0.815086 + 0.579340i \(0.803310\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 + 1.73205i 0.220564 + 0.127343i
\(186\) 0 0
\(187\) 12.0000 + 20.7846i 0.877527 + 1.51992i
\(188\) 0 0
\(189\) 0.500000 2.59808i 0.0363696 0.188982i
\(190\) 0 0
\(191\) −3.00000 + 1.73205i −0.217072 + 0.125327i −0.604594 0.796534i \(-0.706665\pi\)
0.387522 + 0.921861i \(0.373331\pi\)
\(192\) 0 0
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) 0 0
\(195\) 18.0000 1.28901
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 0 0
\(201\) −1.50000 + 0.866025i −0.105802 + 0.0610847i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −18.0000 31.1769i −1.25717 2.17749i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 24.2487i 1.67732i
\(210\) 0 0
\(211\) 17.3205i 1.19239i 0.802839 + 0.596196i \(0.203322\pi\)
−0.802839 + 0.596196i \(0.796678\pi\)
\(212\) 0 0
\(213\) 3.00000 + 1.73205i 0.205557 + 0.118678i
\(214\) 0 0
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) 10.0000 + 8.66025i 0.678844 + 0.587896i
\(218\) 0 0
\(219\) −7.50000 + 4.33013i −0.506803 + 0.292603i
\(220\) 0 0
\(221\) 18.0000 31.1769i 1.21081 2.09719i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) −7.00000 −0.466667
\(226\) 0 0
\(227\) 15.0000 25.9808i 0.995585 1.72440i 0.416503 0.909134i \(-0.363255\pi\)
0.579082 0.815270i \(-0.303411\pi\)
\(228\) 0 0
\(229\) 1.50000 0.866025i 0.0991228 0.0572286i −0.449619 0.893220i \(-0.648440\pi\)
0.548742 + 0.835992i \(0.315107\pi\)
\(230\) 0 0
\(231\) −3.00000 8.66025i −0.197386 0.569803i
\(232\) 0 0
\(233\) 9.00000 + 15.5885i 0.589610 + 1.02123i 0.994283 + 0.106773i \(0.0340517\pi\)
−0.404674 + 0.914461i \(0.632615\pi\)
\(234\) 0 0
\(235\) −18.0000 10.3923i −1.17419 0.677919i
\(236\) 0 0
\(237\) 15.5885i 1.01258i
\(238\) 0 0
\(239\) 17.3205i 1.12037i −0.828367 0.560185i \(-0.810730\pi\)
0.828367 0.560185i \(-0.189270\pi\)
\(240\) 0 0
\(241\) −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i \(-0.480586\pi\)
−0.833939 + 0.551856i \(0.813920\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 24.0000 3.46410i 1.53330 0.221313i
\(246\) 0 0
\(247\) 31.5000 18.1865i 2.00430 1.15718i
\(248\) 0 0
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −12.0000 + 20.7846i −0.751469 + 1.30158i
\(256\) 0 0
\(257\) −9.00000 + 5.19615i −0.561405 + 0.324127i −0.753709 0.657208i \(-0.771737\pi\)
0.192304 + 0.981335i \(0.438404\pi\)
\(258\) 0 0
\(259\) −2.50000 + 0.866025i −0.155342 + 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.0000 + 13.8564i 1.47990 + 0.854423i 0.999741 0.0227570i \(-0.00724440\pi\)
0.480162 + 0.877180i \(0.340578\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.92820i 0.423999i
\(268\) 0 0
\(269\) −27.0000 15.5885i −1.64622 0.950445i −0.978556 0.205982i \(-0.933961\pi\)
−0.667663 0.744463i \(-0.732705\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) −9.00000 + 10.3923i −0.544705 + 0.628971i
\(274\) 0 0
\(275\) −21.0000 + 12.1244i −1.26635 + 0.731126i
\(276\) 0 0
\(277\) 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i \(-0.662714\pi\)
0.999923 0.0124177i \(-0.00395278\pi\)
\(278\) 0 0
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i \(-0.785854\pi\)
0.930714 + 0.365748i \(0.119187\pi\)
\(284\) 0 0
\(285\) −21.0000 + 12.1244i −1.24393 + 0.718185i
\(286\) 0 0
\(287\) 27.0000 + 5.19615i 1.59376 + 0.306719i
\(288\) 0 0
\(289\) 15.5000 + 26.8468i 0.911765 + 1.57922i
\(290\) 0 0
\(291\) 6.00000 + 3.46410i 0.351726 + 0.203069i
\(292\) 0 0
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.00000 1.73205i −0.174078 0.100504i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 4.50000 + 0.866025i 0.259376 + 0.0499169i
\(302\) 0 0
\(303\) 3.00000 1.73205i 0.172345 0.0995037i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 25.0000 1.42683 0.713413 0.700744i \(-0.247149\pi\)
0.713413 + 0.700744i \(0.247149\pi\)
\(308\) 0 0
\(309\) 5.00000 0.284440
\(310\) 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
\(313\) 13.5000 7.79423i 0.763065 0.440556i −0.0673300 0.997731i \(-0.521448\pi\)
0.830395 + 0.557175i \(0.188115\pi\)
\(314\) 0 0
\(315\) 6.00000 6.92820i 0.338062 0.390360i
\(316\) 0 0
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 6.92820i 0.386695i
\(322\) 0 0
\(323\) 48.4974i 2.69847i
\(324\) 0 0
\(325\) 31.5000 + 18.1865i 1.74731 + 1.00881i
\(326\) 0 0
\(327\) −2.50000 4.33013i −0.138250 0.239457i
\(328\) 0 0
\(329\) 15.0000 5.19615i 0.826977 0.286473i
\(330\) 0 0
\(331\) 7.50000 4.33013i 0.412237 0.238005i −0.279513 0.960142i \(-0.590173\pi\)
0.691751 + 0.722137i \(0.256840\pi\)
\(332\) 0 0
\(333\) −0.500000 + 0.866025i −0.0273998 + 0.0474579i
\(334\) 0 0
\(335\) −6.00000 −0.327815
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 0 0
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) 15.0000 8.66025i 0.812296 0.468979i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 30.0000 + 17.3205i 1.61048 + 0.929814i 0.989258 + 0.146183i \(0.0466988\pi\)
0.621227 + 0.783631i \(0.286635\pi\)
\(348\) 0 0
\(349\) 13.8564i 0.741716i −0.928689 0.370858i \(-0.879064\pi\)
0.928689 0.370858i \(-0.120936\pi\)
\(350\) 0 0
\(351\) 5.19615i 0.277350i
\(352\) 0 0
\(353\) 15.0000 + 8.66025i 0.798369 + 0.460939i 0.842901 0.538069i \(-0.180846\pi\)
−0.0445312 + 0.999008i \(0.514179\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 0 0
\(357\) −6.00000 17.3205i −0.317554 0.916698i
\(358\) 0 0
\(359\) 6.00000 3.46410i 0.316668 0.182828i −0.333238 0.942843i \(-0.608141\pi\)
0.649906 + 0.760014i \(0.274808\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −30.0000 −1.57027
\(366\) 0 0
\(367\) −18.5000 + 32.0429i −0.965692 + 1.67263i −0.257948 + 0.966159i \(0.583046\pi\)
−0.707744 + 0.706469i \(0.750287\pi\)
\(368\) 0 0
\(369\) 9.00000 5.19615i 0.468521 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) −6.00000 3.46410i −0.309839 0.178885i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 12.1244i 0.622786i −0.950281 0.311393i \(-0.899204\pi\)
0.950281 0.311393i \(-0.100796\pi\)
\(380\) 0 0
\(381\) 13.5000 + 7.79423i 0.691626 + 0.399310i
\(382\) 0 0
\(383\) −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i \(-0.795052\pi\)
−0.119974 0.992777i \(1.46172\pi\)
\(384\) 0 0
\(385\) 6.00000 31.1769i 0.305788 1.58892i
\(386\) 0 0
\(387\) 1.50000 0.866025i 0.0762493 0.0440225i
\(388\) 0 0
\(389\) −15.0000 + 25.9808i −0.760530 + 1.31728i 0.182047 + 0.983290i \(0.441728\pi\)
−0.942578 + 0.333987i \(0.891606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) 0 0
\(395\) 27.0000 46.7654i 1.35852 2.35302i
\(396\) 0 0
\(397\) 4.50000 2.59808i 0.225849 0.130394i −0.382807 0.923828i \(-0.625043\pi\)
0.608655 + 0.793435i \(0.291709\pi\)
\(398\) 0 0
\(399\) 3.50000 18.1865i 0.175219 0.910465i
\(400\) 0 0
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) −22.5000 12.9904i −1.12080 0.647097i
\(404\) 0 0
\(405\) 3.46410i 0.172133i
\(406\) 0 0
\(407\) 3.46410i 0.171709i
\(408\) 0 0
\(409\) 16.5000 + 9.52628i 0.815872 + 0.471044i 0.848991 0.528407i \(-0.177211\pi\)
−0.0331186 + 0.999451i \(0.510544\pi\)
\(410\) 0 0
\(411\) 6.00000 + 10.3923i 0.295958 + 0.512615i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 18.0000 10.3923i 0.883585 0.510138i
\(416\) 0 0
\(417\) −2.50000 + 4.33013i −0.122426 + 0.212047i
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −29.0000 −1.41337 −0.706687 0.707527i \(-0.749811\pi\)
−0.706687 + 0.707527i \(0.749811\pi\)
\(422\) 0 0
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 0 0
\(425\) −42.0000 + 24.2487i −2.03730 + 1.17624i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 9.00000 + 15.5885i 0.434524 + 0.752618i
\(430\) 0 0
\(431\) 15.0000 + 8.66025i 0.722525 + 0.417150i 0.815681 0.578502i \(-0.196362\pi\)
−0.0931566 + 0.995651i \(0.529696\pi\)
\(432\) 0 0
\(433\) 29.4449i 1.41503i −0.706698 0.707515i \(-0.749816\pi\)
0.706698 0.707515i \(-0.250184\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) 6.00000 3.46410i 0.285069 0.164584i −0.350647 0.936508i \(-0.614038\pi\)
0.635716 + 0.771923i \(0.280705\pi\)
\(444\) 0 0
\(445\) −12.0000 + 20.7846i −0.568855 + 0.985285i
\(446\) 0 0
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 18.0000 31.1769i 0.847587 1.46806i
\(452\) 0 0
\(453\) 9.00000 5.19615i 0.422857 0.244137i
\(454\) 0 0
\(455\) −45.0000 + 15.5885i −2.10963 + 0.730798i
\(456\) 0 0
\(457\) −2.50000 4.33013i −0.116945 0.202555i 0.801611 0.597847i \(-0.203977\pi\)
−0.918556 + 0.395292i \(0.870643\pi\)
\(458\) 0 0
\(459\) −6.00000 3.46410i −0.280056 0.161690i
\(460\) 0 0
\(461\) 13.8564i 0.645357i −0.946509 0.322679i \(-0.895417\pi\)
0.946509 0.322679i \(-0.104583\pi\)
\(462\) 0 0
\(463\) 12.1244i 0.563467i 0.959493 + 0.281733i \(0.0909093\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(464\) 0 0
\(465\) 15.0000 + 8.66025i 0.695608 + 0.401610i
\(466\) 0 0
\(467\) 3.00000 + 5.19615i 0.138823 + 0.240449i 0.927052 0.374934i \(-0.122335\pi\)
−0.788228 + 0.615383i \(0.789001\pi\)
\(468\) 0 0
\(469\) 3.00000 3.46410i 0.138527 0.159957i
\(470\) 0 0
\(471\) 12.0000 6.92820i 0.552931 0.319235i
\(472\) 0 0
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) 0 0
\(475\) −49.0000 −2.24827
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) 4.50000 2.59808i 0.205182 0.118462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.0000 + 20.7846i 0.544892 + 0.943781i
\(486\) 0 0
\(487\) 10.5000 + 6.06218i 0.475800 + 0.274703i 0.718665 0.695357i \(-0.244754\pi\)
−0.242864 + 0.970060i \(0.578087\pi\)
\(488\) 0 0
\(489\) 3.46410i 0.156652i
\(490\) 0 0
\(491\) 20.7846i 0.937996i −0.883199 0.468998i \(-0.844615\pi\)
0.883199 0.468998i \(-0.155385\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −6.00000 10.3923i −0.269680 0.467099i
\(496\) 0 0
\(497\) −9.00000 1.73205i −0.403705 0.0776931i
\(498\) 0 0
\(499\) −10.5000 + 6.06218i −0.470045 + 0.271380i −0.716258 0.697835i \(-0.754147\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) 0 0
\(501\) −3.00000 + 5.19615i −0.134030 + 0.232147i
\(502\) 0 0
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) 7.00000 12.1244i 0.310881 0.538462i
\(508\) 0 0
\(509\) −3.00000 + 1.73205i −0.132973 + 0.0767718i −0.565011 0.825084i \(-0.691128\pi\)
0.432038 + 0.901855i \(0.357795\pi\)
\(510\) 0 0
\(511\) 15.0000 17.3205i 0.663561 0.766214i
\(512\) 0 0
\(513\) −3.50000 6.06218i −0.154529 0.267652i
\(514\) 0 0
\(515\) 15.0000 + 8.66025i 0.660979 + 0.381616i
\(516\) 0 0
\(517\) 20.7846i 0.914106i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.0000 6.92820i −0.525730 0.303530i 0.213546 0.976933i \(-0.431499\pi\)
−0.739276 + 0.673403i \(0.764832\pi\)
\(522\) 0 0
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) 0 0
\(525\) 17.5000 6.06218i 0.763763 0.264575i
\(526\) 0 0
\(527\) 30.0000 17.3205i 1.30682 0.754493i
\(528\) 0 0
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −54.0000 −2.33900
\(534\) 0 0
\(535\) 12.0000 20.7846i 0.518805 0.898597i
\(536\) 0 0
\(537\) 15.0000 8.66025i 0.647298 0.373718i
\(538\) 0 0
\(539\) 15.0000 + 19.0526i 0.646096 + 0.820652i
\(540\) 0 0
\(541\) 20.5000 + 35.5070i 0.881364 + 1.52657i 0.849825 + 0.527064i \(0.176707\pi\)
0.0315385 + 0.999503i \(0.489959\pi\)
\(542\) 0 0
\(543\) −13.5000 7.79423i −0.579340 0.334482i
\(544\) 0 0
\(545\) 17.3205i 0.741929i
\(546\) 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
\(551\) 0 0
\(552\) 0 0
\(553\) 13.5000 + 38.9711i 0.574078 + 1.65722i
\(554\) 0 0
\(555\) −3.00000 + 1.73205i −0.127343 + 0.0735215i
\(556\) 0 0
\(557\) −9.00000 + 15.5885i −0.381342 + 0.660504i −0.991254 0.131965i \(-0.957871\pi\)
0.609912 + 0.792469i \(0.291205\pi\)
\(558\) 0 0
\(559\) −9.00000 −0.380659
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 0 0
\(563\) −9.00000 + 15.5885i −0.379305 + 0.656975i −0.990961 0.134148i \(-0.957170\pi\)
0.611656 + 0.791123i \(0.290503\pi\)
\(564\) 0 0
\(565\) −18.0000 + 10.3923i −0.757266 + 0.437208i
\(566\) 0 0
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 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
\(571\) −22.5000 12.9904i −0.941596 0.543631i −0.0511355 0.998692i \(-0.516284\pi\)
−0.890460 + 0.455061i \(0.849617\pi\)
\(572\) 0 0
\(573\) 3.46410i 0.144715i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.50000 0.866025i −0.0624458 0.0360531i 0.468452 0.883489i \(-0.344812\pi\)
−0.530898 + 0.847436i \(0.678145\pi\)
\(578\) 0 0
\(579\) −6.50000 11.2583i −0.270131 0.467880i
\(580\) 0 0
\(581\) −3.00000 + 15.5885i −0.124461 + 0.646718i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 35.0000 1.44215
\(590\) 0 0
\(591\) −6.00000 + 10.3923i −0.246807 + 0.427482i
\(592\) 0 0
\(593\) −33.0000 + 19.0526i −1.35515 + 0.782395i −0.988965 0.148148i \(-0.952669\pi\)
−0.366182 + 0.930543i \(0.619335\pi\)
\(594\) 0 0
\(595\) 12.0000 62.3538i 0.491952 2.55626i
\(596\) 0 0
\(597\) −8.00000 13.8564i −0.327418 0.567105i
\(598\) 0 0
\(599\) 6.00000 + 3.46410i 0.245153 + 0.141539i 0.617543 0.786537i \(-0.288128\pi\)
−0.372390 + 0.928076i \(0.621461\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i −0.848067 0.529889i \(-0.822234\pi\)
0.848067 0.529889i \(-0.177766\pi\)
\(602\) 0 0
\(603\) 1.73205i 0.0705346i
\(604\) 0 0
\(605\) −3.00000 1.73205i −0.121967 0.0704179i
\(606\) 0 0
\(607\) −18.5000 32.0429i −0.750892 1.30058i −0.947391 0.320079i \(-0.896291\pi\)
0.196499 0.980504i \(1.56296\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −27.0000 + 15.5885i −1.09230 + 0.630641i
\(612\) 0 0
\(613\) 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) 0 0
\(615\) 36.0000 1.45166
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 17.3205i −0.240385 0.693932i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) −21.0000 12.1244i −0.838659 0.484200i
\(628\) 0 0
\(629\) 6.92820i 0.276246i
\(630\) 0 0
\(631\) 3.46410i 0.137904i 0.997620 + 0.0689519i \(0.0219655\pi\)
−0.997620 + 0.0689519i \(0.978035\pi\)
\(632\) 0 0
\(633\) −15.0000 8.66025i −0.596196 0.344214i
\(634\) 0 0
\(635\) 27.0000 + 46.7654i 1.07146 + 1.85583i
\(636\) 0 0
\(637\) 13.5000 33.7750i 0.534889 1.33821i
\(638\) 0 0
\(639\) −3.00000 + 1.73205i −0.118678 + 0.0685189i
\(640\) 0 0
\(641\) 18.0000 31.1769i 0.710957 1.23141i −0.253541 0.967325i \(-0.581595\pi\)
0.964498 0.264089i \(-0.0850714\pi\)
\(642\) 0 0
\(643\) 43.0000 1.69575 0.847877 0.530193i \(-0.177880\pi\)
0.847877 + 0.530193i \(0.177880\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i \(-0.718214\pi\)
0.986916 + 0.161233i \(0.0515470\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −12.5000 + 4.33013i −0.489914 + 0.169711i
\(652\) 0 0
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) 54.0000 + 31.1769i 2.10995 + 1.21818i
\(656\) 0 0
\(657\) 8.66025i 0.337869i
\(658\) 0 0
\(659\) 20.7846i 0.809653i 0.914393 + 0.404827i \(0.132668\pi\)
−0.914393 + 0.404827i \(0.867332\pi\)
\(660\) 0 0
\(661\) 16.5000 + 9.52628i 0.641776 + 0.370529i 0.785298 0.619118i \(-0.212510\pi\)
−0.143523 + 0.989647i \(0.545843\pi\)
\(662\) 0 0
\(663\) 18.0000 + 31.1769i 0.699062 + 1.21081i
\(664\) 0 0
\(665\) 42.0000 48.4974i 1.62869 1.88065i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) 0 0
\(675\) 3.50000 6.06218i 0.134715 0.233333i
\(676\) 0 0
\(677\) 30.0000 17.3205i 1.15299 0.665681i 0.203379 0.979100i \(-0.434808\pi\)
0.949615 + 0.313419i \(0.101474\pi\)
\(678\) 0 0
\(679\) −18.0000 3.46410i −0.690777 0.132940i
\(680\) 0 0
\(681\) 15.0000 + 25.9808i 0.574801 + 0.995585i
\(682\) 0 0
\(683\) −36.0000 20.7846i −1.37750 0.795301i −0.385643 0.922648i \(-0.626021\pi\)
−0.991858 + 0.127347i \(0.959354\pi\)
\(684\) 0 0
\(685\) 41.5692i 1.58828i
\(686\) 0 0
\(687\) 1.73205i 0.0660819i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 6.50000 + 11.2583i 0.247272 + 0.428287i 0.962768 0.270330i \(-0.0871327\pi\)
−0.715496 + 0.698617i \(0.753799\pi\)
\(692\) 0 0
\(693\) 9.00000 + 1.73205i 0.341882 + 0.0657952i
\(694\) 0 0
\(695\) −15.0000 + 8.66025i −0.568982 + 0.328502i
\(696\) 0 0
\(697\) 36.0000 62.3538i 1.36360 2.36182i
\(698\) 0 0
\(699\) −18.0000 −0.680823
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) 0 0
\(705\) 18.0000 10.3923i 0.677919 0.391397i
\(706\) 0 0
\(707\) −6.00000 + 6.92820i −0.225653 + 0.260562i
\(708\) 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
\(711\) 13.5000 + 7.79423i 0.506290 + 0.292306i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 62.3538i 2.33190i
\(716\) 0 0
\(717\) 15.0000 + 8.66025i 0.560185 + 0.323423i
\(718\) 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
\(721\) −12.5000 + 4.33013i −0.465524 + 0.161262i
\(722\) 0 0
\(723\) 12.0000 6.92820i 0.446285 0.257663i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.00000 −0.0370879 −0.0185440 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 6.00000 10.3923i 0.221918 0.384373i
\(732\) 0 0
\(733\) −31.5000 + 18.1865i −1.16348 + 0.671735i −0.952135 0.305677i \(-0.901117\pi\)
−0.211344 + 0.977412i \(0.567784\pi\)
\(734\) 0 0
\(735\) −9.00000 + 22.5167i −0.331970 + 0.830540i
\(736\) 0 0
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 0 0
\(739\) 31.5000 + 18.1865i 1.15875 + 0.669002i 0.951003 0.309181i \(-0.100055\pi\)
0.207743 + 0.978183i \(0.433388\pi\)
\(740\) 0 0
\(741\) 36.3731i 1.33620i
\(742\) 0 0
\(743\) 3.46410i 0.127086i 0.997979 + 0.0635428i \(0.0202399\pi\)
−0.997979 + 0.0635428i \(0.979760\pi\)
\(744\) 0 0
\(745\) −36.0000 20.7846i −1.31894 0.761489i
\(746\) 0 0
\(747\) 3.00000 + 5.19615i 0.109764 + 0.190117i
\(748\) 0 0
\(749\) 6.00000 + 17.3205i 0.219235 + 0.632878i
\(750\) 0 0
\(751\) −40.5000 + 23.3827i −1.47787 + 0.853246i −0.999687 0.0250161i \(-0.992036\pi\)
−0.478179 + 0.878262i \(0.658703\pi\)
\(752\) 0 0
\(753\) 12.0000 20.7846i 0.437304 0.757433i
\(754\) 0 0
\(755\) 36.0000 1.31017
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 30.0000 17.3205i 1.08750 0.627868i 0.154590 0.987979i \(-0.450594\pi\)
0.932910 + 0.360111i \(0.117261\pi\)
\(762\) 0 0
\(763\) 10.0000 + 8.66025i 0.362024 + 0.313522i
\(764\) 0 0
\(765\) −12.0000 20.7846i −0.433861 0.751469i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 29.4449i 1.06181i −0.847432 0.530904i \(-0.821852\pi\)
0.847432 0.530904i \(-0.178148\pi\)
\(770\) 0 0
\(771\) 10.3923i 0.374270i
\(772\) 0 0
\(773\) −27.0000 15.5885i −0.971123 0.560678i −0.0715442 0.997437i \(-0.522793\pi\)
−0.899578 + 0.436760i \(0.856126\pi\)
\(774\) 0 0
\(775\) 17.5000 + 30.3109i 0.628619 + 1.08880i
\(776\) 0 0
\(777\) 0.500000 2.59808i 0.0179374 0.0932055i
\(778\) 0 0
\(779\) 63.0000 36.3731i 2.25721 1.30320i
\(780\) 0 0
\(781\) −6.00000 + 10.3923i −0.214697 + 0.371866i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 48.0000 1.71319
\(786\) 0 0
\(787\) −4.00000 + 6.92820i −0.142585 + 0.246964i −0.928469 0.371409i \(-0.878875\pi\)
0.785885 + 0.618373i \(0.212208\pi\)
\(788\) 0 0
\(789\) −24.0000 + 13.8564i −0.854423 + 0.493301i
\(790\) 0 0
\(791\) 3.00000 15.5885i 0.106668 0.554262i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 41.5692i 1.47246i 0.676733