Properties

Label 56.2.i.b.9.1
Level $56$
Weight $2$
Character 56.9
Analytic conductor $0.447$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 56.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.447162251319\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 56.9
Dual form 56.2.i.b.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -6.00000 q^{13} +1.00000 q^{15} +(2.50000 + 4.33013i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-2.50000 - 0.866025i) q^{21} +(3.50000 - 6.06218i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{27} +2.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(1.50000 - 2.59808i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-3.00000 - 5.19615i) q^{39} -2.00000 q^{41} -4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(-2.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-2.50000 + 4.33013i) q^{51} +(0.500000 + 0.866025i) q^{53} -3.00000 q^{55} -1.00000 q^{57} +(-7.50000 - 12.9904i) q^{59} +(2.50000 - 4.33013i) q^{61} +(1.00000 + 5.19615i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(4.50000 + 7.79423i) q^{67} +7.00000 q^{69} +(-3.50000 - 6.06218i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(7.50000 + 2.59808i) q^{77} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +5.00000 q^{85} +(1.00000 + 1.73205i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(12.0000 - 10.3923i) q^{91} +(-2.50000 + 4.33013i) q^{93} +(0.500000 + 0.866025i) q^{95} -2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + q^{5} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} + q^{5} - 4q^{7} + 2q^{9} - 3q^{11} - 12q^{13} + 2q^{15} + 5q^{17} - q^{19} - 5q^{21} + 7q^{23} + 4q^{25} + 10q^{27} + 4q^{29} + 5q^{31} + 3q^{33} + q^{35} - 3q^{37} - 6q^{39} - 4q^{41} - 8q^{43} - 2q^{45} - 5q^{47} + 2q^{49} - 5q^{51} + q^{53} - 6q^{55} - 2q^{57} - 15q^{59} + 5q^{61} + 2q^{63} - 6q^{65} + 9q^{67} + 14q^{69} - 7q^{73} - 4q^{75} + 15q^{77} - q^{79} - q^{81} + 24q^{83} + 10q^{85} + 2q^{87} - 7q^{89} + 24q^{91} - 5q^{93} + q^{95} - 4q^{97} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i \(0.0406959\pi\)
−0.385499 + 0.922708i \(0.625971\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) 0 0
\(23\) 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i \(-0.572946\pi\)
0.956967 0.290196i \(-0.0937204\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 2.50000 + 4.33013i 0.449013 + 0.777714i 0.998322 0.0579057i \(-0.0184423\pi\)
−0.549309 + 0.835619i \(0.685109\pi\)
\(32\) 0 0
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 0 0
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 0 0
\(39\) −3.00000 5.19615i −0.480384 0.832050i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 0 0
\(47\) −2.50000 + 4.33013i −0.364662 + 0.631614i −0.988722 0.149763i \(-0.952149\pi\)
0.624059 + 0.781377i \(0.285482\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) −2.50000 + 4.33013i −0.350070 + 0.606339i
\(52\) 0 0
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 0 0
\(63\) 1.00000 + 5.19615i 0.125988 + 0.654654i
\(64\) 0 0
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) 4.50000 + 7.79423i 0.549762 + 0.952217i 0.998290 + 0.0584478i \(0.0186151\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(68\) 0 0
\(69\) 7.00000 0.842701
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −3.50000 6.06218i −0.409644 0.709524i 0.585206 0.810885i \(-0.301014\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 0 0
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) 0 0
\(77\) 7.50000 + 2.59808i 0.854704 + 0.296078i
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 5.00000 0.542326
\(86\) 0 0
\(87\) 1.00000 + 1.73205i 0.107211 + 0.185695i
\(88\) 0 0
\(89\) −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i \(-0.954318\pi\)
0.618720 + 0.785611i \(0.287651\pi\)
\(90\) 0 0
\(91\) 12.0000 10.3923i 1.25794 1.08941i
\(92\) 0 0
\(93\) −2.50000 + 4.33013i −0.259238 + 0.449013i
\(94\) 0 0
\(95\) 0.500000 + 0.866025i 0.0512989 + 0.0888523i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) 7.50000 12.9904i 0.738997 1.27998i −0.213950 0.976845i \(-0.568633\pi\)
0.952947 0.303136i \(-0.0980336\pi\)
\(104\) 0 0
\(105\) −2.00000 + 1.73205i −0.195180 + 0.169031i
\(106\) 0 0
\(107\) −4.50000 + 7.79423i −0.435031 + 0.753497i −0.997298 0.0734594i \(-0.976596\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(108\) 0 0
\(109\) 2.50000 + 4.33013i 0.239457 + 0.414751i 0.960558 0.278078i \(-0.0896974\pi\)
−0.721102 + 0.692829i \(0.756364\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) −3.50000 6.06218i −0.326377 0.565301i
\(116\) 0 0
\(117\) −6.00000 + 10.3923i −0.554700 + 0.960769i
\(118\) 0 0
\(119\) −12.5000 4.33013i −1.14587 0.396942i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) −1.00000 1.73205i −0.0901670 0.156174i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0 0
\(131\) −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i \(-0.903426\pi\)
0.735901 + 0.677089i \(0.236759\pi\)
\(132\) 0 0
\(133\) −0.500000 2.59808i −0.0433555 0.225282i
\(134\) 0 0
\(135\) 2.50000 4.33013i 0.215166 0.372678i
\(136\) 0 0
\(137\) −5.50000 9.52628i −0.469897 0.813885i 0.529511 0.848303i \(-0.322376\pi\)
−0.999408 + 0.0344182i \(0.989042\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) −5.00000 −0.421076
\(142\) 0 0
\(143\) 9.00000 + 15.5885i 0.752618 + 1.30357i
\(144\) 0 0
\(145\) 1.00000 1.73205i 0.0830455 0.143839i
\(146\) 0 0
\(147\) 6.50000 2.59808i 0.536111 0.214286i
\(148\) 0 0
\(149\) 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i \(-0.588141\pi\)
0.969724 0.244202i \(-0.0785259\pi\)
\(150\) 0 0
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) 0 0
\(153\) 10.0000 0.808452
\(154\) 0 0
\(155\) 5.00000 0.401610
\(156\) 0 0
\(157\) 4.50000 + 7.79423i 0.359139 + 0.622047i 0.987817 0.155618i \(-0.0497370\pi\)
−0.628678 + 0.777666i \(0.716404\pi\)
\(158\) 0 0
\(159\) −0.500000 + 0.866025i −0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) 3.50000 + 18.1865i 0.275839 + 1.43330i
\(162\) 0 0
\(163\) −6.50000 + 11.2583i −0.509119 + 0.881820i 0.490825 + 0.871258i \(0.336695\pi\)
−0.999944 + 0.0105623i \(0.996638\pi\)
\(164\) 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
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 0 0
\(173\) 6.50000 11.2583i 0.494186 0.855955i −0.505792 0.862656i \(-0.668800\pi\)
0.999978 + 0.00670064i \(0.00213290\pi\)
\(174\) 0 0
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) 0 0
\(177\) 7.50000 12.9904i 0.563735 0.976417i
\(178\) 0 0
\(179\) 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i \(-0.00518305\pi\)
−0.514035 + 0.857769i \(0.671850\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 5.00000 0.369611
\(184\) 0 0
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) 7.50000 12.9904i 0.548454 0.949951i
\(188\) 0 0
\(189\) −10.0000 + 8.66025i −0.727393 + 0.629941i
\(190\) 0 0
\(191\) 5.50000 9.52628i 0.397966 0.689297i −0.595509 0.803349i \(-0.703050\pi\)
0.993475 + 0.114051i \(0.0363829\pi\)
\(192\) 0 0
\(193\) −1.50000 2.59808i −0.107972 0.187014i 0.806976 0.590584i \(-0.201102\pi\)
−0.914949 + 0.403570i \(0.867769\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 6.50000 + 11.2583i 0.460773 + 0.798082i 0.999000 0.0447181i \(-0.0142390\pi\)
−0.538227 + 0.842800i \(0.680906\pi\)
\(200\) 0 0
\(201\) −4.50000 + 7.79423i −0.317406 + 0.549762i
\(202\) 0 0
\(203\) −4.00000 + 3.46410i −0.280745 + 0.243132i
\(204\) 0 0
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) 0 0
\(207\) −7.00000 12.1244i −0.486534 0.842701i
\(208\) 0 0
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) 0 0
\(217\) −12.5000 4.33013i −0.848555 0.293948i
\(218\) 0 0
\(219\) 3.50000 6.06218i 0.236508 0.409644i
\(220\) 0 0
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 0 0
\(227\) −5.50000 9.52628i −0.365048 0.632281i 0.623736 0.781635i \(-0.285614\pi\)
−0.988784 + 0.149354i \(0.952281\pi\)
\(228\) 0 0
\(229\) −11.5000 + 19.9186i −0.759941 + 1.31626i 0.182939 + 0.983124i \(0.441439\pi\)
−0.942880 + 0.333133i \(0.891894\pi\)
\(230\) 0 0
\(231\) 1.50000 + 7.79423i 0.0986928 + 0.512823i
\(232\) 0 0
\(233\) −5.50000 + 9.52628i −0.360317 + 0.624087i −0.988013 0.154371i \(-0.950665\pi\)
0.627696 + 0.778459i \(0.283998\pi\)
\(234\) 0 0
\(235\) 2.50000 + 4.33013i 0.163082 + 0.282466i
\(236\) 0 0
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 8.50000 + 14.7224i 0.547533 + 0.948355i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) 0 0
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) 0 0
\(247\) 3.00000 5.19615i 0.190885 0.330623i
\(248\) 0 0
\(249\) 6.00000 + 10.3923i 0.380235 + 0.658586i
\(250\) 0 0
\(251\) 16.0000 1.00991 0.504956 0.863145i \(-0.331509\pi\)
0.504956 + 0.863145i \(0.331509\pi\)
\(252\) 0 0
\(253\) −21.0000 −1.32026
\(254\) 0 0
\(255\) 2.50000 + 4.33013i 0.156556 + 0.271163i
\(256\) 0 0
\(257\) 10.5000 18.1865i 0.654972 1.13444i −0.326929 0.945049i \(-0.606014\pi\)
0.981901 0.189396i \(-0.0606529\pi\)
\(258\) 0 0
\(259\) −1.50000 7.79423i −0.0932055 0.484310i
\(260\) 0 0
\(261\) 2.00000 3.46410i 0.123797 0.214423i
\(262\) 0 0
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 0 0
\(265\) 1.00000 0.0614295
\(266\) 0 0
\(267\) −7.00000 −0.428393
\(268\) 0 0
\(269\) 4.50000 + 7.79423i 0.274370 + 0.475223i 0.969976 0.243201i \(-0.0781974\pi\)
−0.695606 + 0.718423i \(0.744864\pi\)
\(270\) 0 0
\(271\) 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i \(-0.765137\pi\)
0.952531 + 0.304443i \(0.0984703\pi\)
\(272\) 0 0
\(273\) 15.0000 + 5.19615i 0.907841 + 0.314485i
\(274\) 0 0
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 0 0
\(277\) 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i \(0.00395278\pi\)
−0.489207 + 0.872167i \(0.662714\pi\)
\(278\) 0 0
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 0 0
\(285\) −0.500000 + 0.866025i −0.0296174 + 0.0512989i
\(286\) 0 0
\(287\) 4.00000 3.46410i 0.236113 0.204479i
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) −1.00000 1.73205i −0.0586210 0.101535i
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −15.0000 −0.873334
\(296\) 0 0
\(297\) −7.50000 12.9904i −0.435194 0.753778i
\(298\) 0 0
\(299\) −21.0000 + 36.3731i −1.21446 + 2.10351i
\(300\) 0 0
\(301\) 8.00000 6.92820i 0.461112 0.399335i
\(302\) 0 0
\(303\) 1.50000 2.59808i 0.0861727 0.149256i
\(304\) 0 0
\(305\) −2.50000 4.33013i −0.143150 0.247942i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) −7.50000 12.9904i −0.425286 0.736617i 0.571161 0.820838i \(-0.306493\pi\)
−0.996447 + 0.0842210i \(0.973160\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 0 0
\(315\) 5.00000 + 1.73205i 0.281718 + 0.0975900i
\(316\) 0 0
\(317\) −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i \(-0.860182\pi\)
0.820822 + 0.571184i \(0.193516\pi\)
\(318\) 0 0
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) −5.00000 −0.278207
\(324\) 0 0
\(325\) −12.0000 20.7846i −0.665640 1.15292i
\(326\) 0 0
\(327\) −2.50000 + 4.33013i −0.138250 + 0.239457i
\(328\) 0 0
\(329\) −2.50000 12.9904i −0.137829 0.716183i
\(330\) 0 0
\(331\) −14.5000 + 25.1147i −0.796992 + 1.38043i 0.124574 + 0.992210i \(0.460243\pi\)
−0.921567 + 0.388221i \(0.873090\pi\)
\(332\) 0 0
\(333\) 3.00000 + 5.19615i 0.164399 + 0.284747i
\(334\) 0 0
\(335\) 9.00000 0.491723
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 0 0
\(339\) −9.00000 15.5885i −0.488813 0.846649i
\(340\) 0 0
\(341\) 7.50000 12.9904i 0.406148 0.703469i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 3.50000 6.06218i 0.188434 0.326377i
\(346\) 0 0
\(347\) −7.50000 12.9904i −0.402621 0.697360i 0.591420 0.806363i \(-0.298567\pi\)
−0.994041 + 0.109003i \(0.965234\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) −30.0000 −1.60128
\(352\) 0 0
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.50000 12.9904i −0.132314 0.687524i
\(358\) 0 0
\(359\) −10.5000 + 18.1865i −0.554169 + 0.959849i 0.443799 + 0.896126i \(0.353630\pi\)
−0.997968 + 0.0637221i \(0.979703\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) −7.00000 −0.366397
\(366\) 0 0
\(367\) −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i \(-0.961716\pi\)
0.392481 0.919760i \(-0.371617\pi\)
\(368\) 0 0
\(369\) −2.00000 + 3.46410i −0.104116 + 0.180334i
\(370\) 0 0
\(371\) −2.50000 0.866025i −0.129794 0.0449618i
\(372\) 0 0
\(373\) −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i \(-0.925254\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(374\) 0 0
\(375\) 4.50000 + 7.79423i 0.232379 + 0.402492i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 24.0000 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) 0 0
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 0 0
\(383\) 1.50000 2.59808i 0.0766464 0.132755i −0.825155 0.564907i \(-0.808912\pi\)
0.901801 + 0.432151i \(0.142245\pi\)
\(384\) 0 0
\(385\) 6.00000 5.19615i 0.305788 0.264820i
\(386\) 0 0
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 0 0
\(389\) 14.5000 + 25.1147i 0.735179 + 1.27337i 0.954645 + 0.297747i \(0.0962353\pi\)
−0.219465 + 0.975620i \(0.570431\pi\)
\(390\) 0 0
\(391\) 35.0000 1.77003
\(392\) 0 0
\(393\) −5.00000 −0.252217
\(394\) 0 0
\(395\) 0.500000 + 0.866025i 0.0251577 + 0.0435745i
\(396\) 0 0
\(397\) 8.50000 14.7224i 0.426603 0.738898i −0.569966 0.821668i \(-0.693044\pi\)
0.996569 + 0.0827707i \(0.0263769\pi\)
\(398\) 0 0
\(399\) 2.00000 1.73205i 0.100125 0.0867110i
\(400\) 0 0
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) −15.0000 25.9808i −0.747203 1.29419i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 9.00000 0.446113
\(408\) 0 0
\(409\) −13.5000 23.3827i −0.667532 1.15620i −0.978592 0.205809i \(-0.934017\pi\)
0.311060 0.950390i \(-0.399316\pi\)
\(410\) 0 0
\(411\) 5.50000 9.52628i 0.271295 0.469897i
\(412\) 0 0
\(413\) 37.5000 + 12.9904i 1.84525 + 0.639215i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 5.00000 + 8.66025i 0.243108 + 0.421076i
\(424\) 0 0
\(425\) −10.0000 + 17.3205i −0.485071 + 0.840168i
\(426\) 0 0
\(427\) 2.50000 + 12.9904i 0.120983 + 0.628649i
\(428\) 0 0
\(429\) −9.00000 + 15.5885i −0.434524 + 0.752618i
\(430\) 0 0
\(431\) −1.50000 2.59808i −0.0722525 0.125145i 0.827636 0.561266i \(-0.189685\pi\)
−0.899888 + 0.436121i \(0.856352\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 2.00000 0.0958927
\(436\) 0 0
\(437\) 3.50000 + 6.06218i 0.167428 + 0.289993i
\(438\) 0 0
\(439\) −10.5000 + 18.1865i −0.501138 + 0.867996i 0.498861 + 0.866682i \(0.333752\pi\)
−0.999999 + 0.00131415i \(0.999582\pi\)
\(440\) 0 0
\(441\) −11.0000 8.66025i −0.523810 0.412393i
\(442\) 0 0
\(443\) 15.5000 26.8468i 0.736427 1.27553i −0.217667 0.976023i \(-0.569845\pi\)
0.954094 0.299506i \(-0.0968220\pi\)
\(444\) 0 0
\(445\) 3.50000 + 6.06218i 0.165916 + 0.287375i
\(446\) 0 0
\(447\) 17.0000 0.804072
\(448\) 0 0
\(449\) −26.0000 −1.22702 −0.613508 0.789689i \(-0.710242\pi\)
−0.613508 + 0.789689i \(0.710242\pi\)
\(450\) 0 0
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) 0 0
\(453\) −2.50000 + 4.33013i −0.117460 + 0.203447i
\(454\) 0 0
\(455\) −3.00000 15.5885i −0.140642 0.730798i
\(456\) 0 0
\(457\) 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i \(-0.703172\pi\)
0.993431 + 0.114433i \(0.0365053\pi\)
\(458\) 0 0
\(459\) 12.5000 + 21.6506i 0.583450 + 1.01057i
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 2.50000 + 4.33013i 0.115935 + 0.200805i
\(466\) 0 0
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 0 0
\(469\) −22.5000 7.79423i −1.03895 0.359904i
\(470\) 0 0
\(471\) −4.50000 + 7.79423i −0.207349 + 0.359139i
\(472\) 0 0
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) −15.5000 26.8468i −0.708213 1.22666i −0.965519 0.260331i \(-0.916168\pi\)
0.257306 0.966330i \(-0.417165\pi\)
\(480\) 0 0
\(481\) 9.00000 15.5885i 0.410365 0.710772i
\(482\) 0 0
\(483\) −14.0000 + 12.1244i −0.637022 + 0.551677i
\(484\) 0 0
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) −3.50000 6.06218i −0.158600 0.274703i 0.775764 0.631023i \(-0.217365\pi\)
−0.934364 + 0.356320i \(0.884031\pi\)
\(488\) 0 0
\(489\) −13.0000 −0.587880
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 5.00000 + 8.66025i 0.225189 + 0.390038i
\(494\) 0 0
\(495\) −3.00000 + 5.19615i −0.134840 + 0.233550i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 17.5000 30.3109i 0.783408 1.35690i −0.146538 0.989205i \(-0.546813\pi\)
0.929946 0.367697i \(-0.119854\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) −32.0000 −1.42681 −0.713405 0.700752i \(-0.752848\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(504\) 0 0
\(505\) −3.00000 −0.133498
\(506\) 0 0
\(507\) 11.5000 + 19.9186i 0.510733 + 0.884615i
\(508\) 0 0
\(509\) 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i \(-0.769415\pi\)
0.948353 + 0.317217i \(0.102748\pi\)
\(510\) 0 0
\(511\) 17.5000 + 6.06218i 0.774154 + 0.268175i
\(512\) 0 0
\(513\) −2.50000 + 4.33013i −0.110378 + 0.191180i
\(514\) 0 0
\(515\) −7.50000 12.9904i −0.330489 0.572425i
\(516\) 0 0
\(517\) 15.0000 0.659699
\(518\) 0 0
\(519\) 13.0000 0.570637
\(520\) 0 0
\(521\) 16.5000 + 28.5788i 0.722878 + 1.25206i 0.959841 + 0.280543i \(0.0905145\pi\)
−0.236963 + 0.971519i \(0.576152\pi\)
\(522\) 0 0
\(523\) 3.50000 6.06218i 0.153044 0.265081i −0.779301 0.626650i \(-0.784426\pi\)
0.932345 + 0.361569i \(0.117759\pi\)
\(524\) 0 0
\(525\) −2.00000 10.3923i −0.0872872 0.453557i
\(526\) 0 0
\(527\) −12.5000 + 21.6506i −0.544509 + 0.943116i
\(528\) 0 0
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) 0 0
\(531\) −30.0000 −1.30189
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 4.50000 + 7.79423i 0.194552 + 0.336974i
\(536\) 0 0
\(537\) −6.50000 + 11.2583i −0.280496 + 0.485833i
\(538\) 0 0
\(539\) −19.5000 + 7.79423i −0.839924 + 0.335721i
\(540\) 0 0
\(541\) 20.5000 35.5070i 0.881364 1.52657i 0.0315385 0.999503i \(-0.489959\pi\)
0.849825 0.527064i \(-0.176707\pi\)
\(542\) 0 0
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) 0 0
\(545\) 5.00000 0.214176
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 0 0
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) 0 0
\(551\) −1.00000 + 1.73205i −0.0426014 + 0.0737878i
\(552\) 0 0
\(553\) −0.500000 2.59808i −0.0212622 0.110481i
\(554\) 0 0
\(555\) −1.50000 + 2.59808i −0.0636715 + 0.110282i
\(556\) 0 0
\(557\) 2.50000 + 4.33013i 0.105928 + 0.183473i 0.914117 0.405450i \(-0.132885\pi\)
−0.808189 + 0.588924i \(0.799552\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 15.0000 0.633300
\(562\) 0 0
\(563\) 20.5000 + 35.5070i 0.863972 + 1.49644i 0.868064 + 0.496452i \(0.165364\pi\)
−0.00409232 + 0.999992i \(0.501303\pi\)
\(564\) 0 0
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) 0 0
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) 0 0
\(569\) 16.5000 28.5788i 0.691716 1.19809i −0.279559 0.960128i \(-0.590188\pi\)
0.971275 0.237959i \(-0.0764783\pi\)
\(570\) 0 0
\(571\) 6.50000 + 11.2583i 0.272017 + 0.471146i 0.969378 0.245573i \(-0.0789761\pi\)
−0.697362 + 0.716720i \(0.745643\pi\)
\(572\) 0 0
\(573\) 11.0000 0.459532
\(574\) 0 0
\(575\) 28.0000 1.16768
\(576\) 0 0
\(577\) 16.5000 + 28.5788i 0.686904 + 1.18975i 0.972834 + 0.231502i \(0.0743641\pi\)
−0.285930 + 0.958250i \(0.592303\pi\)
\(578\) 0 0
\(579\) 1.50000 2.59808i 0.0623379 0.107972i
\(580\) 0 0
\(581\) −24.0000 + 20.7846i −0.995688 + 0.862291i
\(582\) 0 0
\(583\) 1.50000 2.59808i 0.0621237 0.107601i
\(584\) 0 0
\(585\) 6.00000 + 10.3923i 0.248069 + 0.429669i
\(586\) 0 0
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 0 0
\(589\) −5.00000 −0.206021
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 0 0
\(593\) 22.5000 38.9711i 0.923964 1.60035i 0.130746 0.991416i \(-0.458263\pi\)
0.793219 0.608937i \(-0.208404\pi\)
\(594\) 0 0
\(595\) −10.0000 + 8.66025i −0.409960 + 0.355036i
\(596\) 0 0
\(597\) −6.50000 + 11.2583i −0.266027 + 0.460773i
\(598\) 0 0
\(599\) 8.50000 + 14.7224i 0.347301 + 0.601542i 0.985769 0.168106i \(-0.0537650\pi\)
−0.638468 + 0.769648i \(0.720432\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 18.0000 0.733017
\(604\) 0 0
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) 0 0
\(607\) −6.50000 + 11.2583i −0.263827 + 0.456962i −0.967256 0.253804i \(-0.918318\pi\)
0.703429 + 0.710766i \(0.251651\pi\)
\(608\) 0 0
\(609\) −5.00000 1.73205i −0.202610 0.0701862i
\(610\) 0 0
\(611\) 15.0000 25.9808i 0.606835 1.05107i
\(612\) 0 0
\(613\) −21.5000 37.2391i −0.868377 1.50407i −0.863655 0.504084i \(-0.831830\pi\)
−0.00472215 0.999989i \(-0.501503\pi\)
\(614\) 0 0
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) 4.50000 + 7.79423i 0.180870 + 0.313276i 0.942177 0.335115i \(-0.108775\pi\)
−0.761307 + 0.648392i \(0.775442\pi\)
\(620\) 0 0
\(621\) 17.5000 30.3109i 0.702251 1.21633i
\(622\) 0 0
\(623\) −3.50000 18.1865i −0.140225 0.728628i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) 1.50000 + 2.59808i 0.0599042 + 0.103757i
\(628\) 0 0
\(629\) −15.0000 −0.598089
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) 0 0
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) 0 0
\(637\) −6.00000 + 41.5692i −0.237729 + 1.64703i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.50000 + 14.7224i 0.335730 + 0.581501i 0.983625 0.180229i \(-0.0576838\pi\)
−0.647895 + 0.761730i \(0.724350\pi\)
\(642\) 0 0
\(643\) −44.0000 −1.73519 −0.867595 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) −7.50000 12.9904i −0.294855 0.510705i 0.680096 0.733123i \(-0.261938\pi\)
−0.974951 + 0.222419i \(0.928605\pi\)
\(648\) 0 0
\(649\) −22.5000 + 38.9711i −0.883202 + 1.52975i
\(650\) 0 0
\(651\) −2.50000 12.9904i −0.0979827 0.509133i
\(652\) 0 0
\(653\) −17.5000 + 30.3109i −0.684828 + 1.18616i 0.288663 + 0.957431i \(0.406789\pi\)
−0.973491 + 0.228726i \(0.926544\pi\)
\(654\) 0 0
\(655\) 2.50000 + 4.33013i 0.0976831 + 0.169192i
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) 44.0000 1.71400 0.856998 0.515319i \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(660\) 0 0
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) 0 0
\(663\) 15.0000 25.9808i 0.582552 1.00901i
\(664\) 0 0
\(665\) −2.50000 0.866025i −0.0969458 0.0335830i
\(666\) 0 0
\(667\) 7.00000 12.1244i 0.271041 0.469457i
\(668\) 0 0
\(669\) −12.0000 20.7846i −0.463947 0.803579i
\(670\) 0 0
\(671\) −15.0000 −0.579069
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) 10.0000 + 17.3205i 0.384900 + 0.666667i
\(676\) 0 0
\(677\) −19.5000 + 33.7750i −0.749446 + 1.29808i 0.198643 + 0.980072i \(0.436347\pi\)
−0.948089 + 0.318006i \(0.896987\pi\)
\(678\) 0 0
\(679\) 4.00000 3.46410i 0.153506 0.132940i
\(680\) 0 0
\(681\) 5.50000 9.52628i 0.210760 0.365048i
\(682\) 0 0
\(683\) −13.5000 23.3827i −0.516563 0.894714i −0.999815 0.0192323i \(-0.993878\pi\)
0.483252 0.875481i \(-0.339456\pi\)
\(684\) 0 0
\(685\) −11.0000 −0.420288
\(686\) 0 0
\(687\) −23.0000 −0.877505
\(688\) 0 0
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) −2.50000 + 4.33013i −0.0951045 + 0.164726i −0.909652 0.415371i \(-0.863652\pi\)
0.814548 + 0.580097i \(0.196985\pi\)
\(692\) 0 0
\(693\) 12.0000 10.3923i 0.455842 0.394771i
\(694\) 0 0
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 0 0
\(697\) −5.00000 8.66025i −0.189389 0.328031i
\(698\) 0 0
\(699\) −11.0000 −0.416058
\(700\) 0 0
\(701\) −50.0000 −1.88847 −0.944237 0.329267i \(-0.893198\pi\)
−0.944237 + 0.329267i \(0.893198\pi\)
\(702\) 0 0
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) 0 0
\(705\) −2.50000 + 4.33013i −0.0941554 + 0.163082i
\(706\) 0 0
\(707\) 7.50000 + 2.59808i 0.282067 + 0.0977107i
\(708\) 0 0
\(709\) 14.5000 25.1147i 0.544559 0.943204i −0.454076 0.890963i \(-0.650030\pi\)
0.998635 0.0522406i \(-0.0166363\pi\)
\(710\) 0 0
\(711\) 1.00000 + 1.73205i 0.0375029 + 0.0649570i
\(712\) 0 0
\(713\) 35.0000 1.31076
\(714\) 0 0
\(715\) 18.0000 0.673162
\(716\) 0 0
\(717\) 10.0000 + 17.3205i 0.373457 + 0.646846i
\(718\) 0 0
\(719\) 19.5000 33.7750i 0.727227 1.25959i −0.230823 0.972996i \(-0.574142\pi\)
0.958051 0.286599i \(-0.0925247\pi\)
\(720\) 0 0
\(721\) 7.50000 + 38.9711i 0.279315 + 1.45136i
\(722\) 0 0
\(723\) −8.50000 + 14.7224i −0.316118 + 0.547533i
\(724\) 0 0
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −10.0000 17.3205i −0.369863 0.640622i
\(732\) 0 0
\(733\) −9.50000 + 16.4545i −0.350891 + 0.607760i −0.986406 0.164328i \(-0.947454\pi\)
0.635515 + 0.772088i \(0.280788\pi\)
\(734\) 0 0
\(735\) 1.00000 6.92820i 0.0368856 0.255551i
\(736\) 0 0
\(737\) 13.5000 23.3827i 0.497279 0.861312i
\(738\) 0 0
\(739\) 2.50000 + 4.33013i 0.0919640 + 0.159286i 0.908337 0.418238i \(-0.137352\pi\)
−0.816373 + 0.577524i \(0.804019\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −8.50000 14.7224i −0.311416 0.539388i
\(746\) 0 0
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) 0 0
\(749\) −4.50000 23.3827i −0.164426 0.854385i
\(750\) 0 0
\(751\) −26.5000 + 45.8993i −0.966999 + 1.67489i −0.262852 + 0.964836i \(0.584663\pi\)
−0.704146 + 0.710055i \(0.748670\pi\)
\(752\) 0 0
\(753\) 8.00000 + 13.8564i 0.291536 + 0.504956i
\(754\) 0 0
\(755\) 5.00000 0.181969
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) −10.5000 18.1865i −0.381126 0.660129i
\(760\) 0 0
\(761\) −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i \(-0.850650\pi\)
0.837557 + 0.546350i \(0.183983\pi\)
\(762\) 0 0
\(763\) −12.5000 4.33013i −0.452530 0.156761i
\(764\) 0 0
\(765\) 5.00000 8.66025i 0.180775 0.313112i
\(766\) 0 0
\(767\) 45.0000 + 77.9423i 1.62486 + 2.81433i
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) 21.0000 0.756297
\(772\) 0 0
\(773\) −9.50000 16.4545i −0.341691 0.591827i 0.643056 0.765819i \(-0.277666\pi\)
−0.984747 + 0.173993i \(0.944333\pi\)
\(774\) 0 0
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) 0 0
\(777\) 6.00000 5.19615i 0.215249 0.186411i
\(778\) 0 0
\(779\) 1.00000 1.73205i 0.0358287 0.0620572i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 10.0000 0.357371
\(784\) 0 0
\(785\) 9.00000 0.321224
\(786\) 0 0
\(787\) 8.50000 + 14.7224i 0.302992 + 0.524798i 0.976812 0.214097i \(-0.0686810\pi\)
−0.673820 + 0.738896i \(0.735348\pi\)
\(788\) 0 0
\(789\) −4.50000 + 7.79423i −0.160204 + 0.277482i
\(790\) 0 0
\(791\) 36.0000 31.1769i 1.28001 1.10852i
\(792\) 0 0
\(793\) −15.0000 + 25.9808i −0.532666 + 0.922604i
\(794\) 0 0
\(795\) 0.500000 + 0.866025i 0.0177332 + 0.0307148i
\(796\) 0 0
\(797\) 18.0000