Properties

Label 1400.2.bh.a.849.2
Level $1400$
Weight $2$
Character 1400.849
Analytic conductor $11.179$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 849.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1400.849
Dual form 1400.2.bh.a.249.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{3} +(-1.73205 - 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{3} +(-1.73205 - 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +6.00000i q^{13} +(-4.33013 + 2.50000i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-2.50000 - 0.866025i) q^{21} +(-6.06218 - 3.50000i) q^{23} +5.00000i q^{27} -2.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(-2.59808 - 1.50000i) q^{33} +(-2.59808 - 1.50000i) q^{37} +(3.00000 + 5.19615i) q^{39} -2.00000 q^{41} +4.00000i q^{43} +(-4.33013 - 2.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-2.50000 + 4.33013i) q^{51} +(0.866025 - 0.500000i) q^{53} -1.00000i q^{57} +(7.50000 + 12.9904i) q^{59} +(2.50000 - 4.33013i) q^{61} +(5.19615 - 1.00000i) q^{63} +(-7.79423 + 4.50000i) q^{67} -7.00000 q^{69} +(-6.06218 + 3.50000i) q^{73} +(-2.59808 + 7.50000i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000i q^{83} +(-1.73205 + 1.00000i) q^{87} +(3.50000 - 6.06218i) q^{89} +(12.0000 - 10.3923i) q^{91} +(4.33013 + 2.50000i) q^{93} -2.00000i q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} - 6q^{11} + 2q^{19} - 10q^{21} - 8q^{29} + 10q^{31} + 12q^{39} - 8q^{41} - 4q^{49} - 10q^{51} + 30q^{59} + 10q^{61} - 28q^{69} + 2q^{79} - 2q^{81} + 14q^{89} + 48q^{91} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) 0.866025 0.500000i 0.500000 0.288675i −0.228714 0.973494i \(-0.573452\pi\)
0.728714 + 0.684819i \(0.240119\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) 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
\(13\) 6.00000i 1.66410i 0.554700 + 0.832050i \(0.312833\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.33013 + 2.50000i −1.05021 + 0.606339i −0.922708 0.385499i \(-0.874029\pi\)
−0.127502 + 0.991838i \(0.540696\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) 0 0
\(23\) −6.06218 3.50000i −1.26405 0.729800i −0.290196 0.956967i \(-0.593720\pi\)
−0.973856 + 0.227167i \(0.927054\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 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
\(33\) −2.59808 1.50000i −0.452267 0.261116i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.59808 1.50000i −0.427121 0.246598i 0.270998 0.962580i \(-0.412646\pi\)
−0.698119 + 0.715981i \(0.745980\pi\)
\(38\) 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
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.33013 2.50000i −0.631614 0.364662i 0.149763 0.988722i \(-0.452149\pi\)
−0.781377 + 0.624059i \(0.785482\pi\)
\(48\) 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
\(53\) 0.866025 0.500000i 0.118958 0.0686803i −0.439340 0.898321i \(-0.644788\pi\)
0.558298 + 0.829640i \(0.311454\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 0 0
\(59\) 7.50000 + 12.9904i 0.976417 + 1.69120i 0.675178 + 0.737655i \(0.264067\pi\)
0.301239 + 0.953549i \(0.402600\pi\)
\(60\) 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
\(63\) 5.19615 1.00000i 0.654654 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.79423 + 4.50000i −0.952217 + 0.549762i −0.893769 0.448528i \(-0.851948\pi\)
−0.0584478 + 0.998290i \(0.518615\pi\)
\(68\) 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
\(73\) −6.06218 + 3.50000i −0.709524 + 0.409644i −0.810885 0.585206i \(-0.801014\pi\)
0.101361 + 0.994850i \(0.467680\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.59808 + 7.50000i −0.296078 + 0.854704i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.73205 + 1.00000i −0.185695 + 0.107211i
\(88\) 0 0
\(89\) 3.50000 6.06218i 0.370999 0.642590i −0.618720 0.785611i \(-0.712349\pi\)
0.989720 + 0.143022i \(0.0456819\pi\)
\(90\) 0 0
\(91\) 12.0000 10.3923i 1.25794 1.08941i
\(92\) 0 0
\(93\) 4.33013 + 2.50000i 0.449013 + 0.259238i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 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
\(103\) −12.9904 7.50000i −1.27998 0.738997i −0.303136 0.952947i \(-0.598034\pi\)
−0.976845 + 0.213950i \(0.931367\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.79423 4.50000i −0.753497 0.435031i 0.0734594 0.997298i \(-0.476596\pi\)
−0.826956 + 0.562267i \(0.809929\pi\)
\(108\) 0 0
\(109\) −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i \(-0.243636\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 0 0
\(113\) 18.0000i 1.69330i 0.532152 + 0.846649i \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −10.3923 6.00000i −0.960769 0.554700i
\(118\) 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
\(123\) −1.73205 + 1.00000i −0.156174 + 0.0901670i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 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
\(133\) −2.59808 + 0.500000i −0.225282 + 0.0433555i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.52628 5.50000i 0.813885 0.469897i −0.0344182 0.999408i \(-0.510958\pi\)
0.848303 + 0.529511i \(0.177624\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) −5.00000 −0.421076
\(142\) 0 0
\(143\) 15.5885 9.00000i 1.30357 0.752618i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 0 0
\(149\) −8.50000 + 14.7224i −0.696347 + 1.20611i 0.273377 + 0.961907i \(0.411859\pi\)
−0.969724 + 0.244202i \(0.921474\pi\)
\(150\) 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
\(153\) 10.0000i 0.808452i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.79423 + 4.50000i −0.622047 + 0.359139i −0.777666 0.628678i \(-0.783596\pi\)
0.155618 + 0.987817i \(0.450263\pi\)
\(158\) 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
\(163\) 11.2583 + 6.50000i 0.881820 + 0.509119i 0.871258 0.490825i \(-0.163305\pi\)
0.0105623 + 0.999944i \(0.496638\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 0 0
\(173\) −11.2583 6.50000i −0.855955 0.494186i 0.00670064 0.999978i \(-0.497867\pi\)
−0.862656 + 0.505792i \(0.831200\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.9904 + 7.50000i 0.976417 + 0.563735i
\(178\) 0 0
\(179\) −6.50000 11.2583i −0.485833 0.841487i 0.514035 0.857769i \(-0.328150\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 5.00000i 0.369611i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 12.9904 + 7.50000i 0.949951 + 0.548454i
\(188\) 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
\(193\) −2.59808 + 1.50000i −0.187014 + 0.107972i −0.590584 0.806976i \(-0.701102\pi\)
0.403570 + 0.914949i \(0.367769\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000i 0.427482i −0.976890 0.213741i \(-0.931435\pi\)
0.976890 0.213741i \(-0.0685649\pi\)
\(198\) 0 0
\(199\) −6.50000 11.2583i −0.460773 0.798082i 0.538227 0.842800i \(-0.319094\pi\)
−0.999000 + 0.0447181i \(0.985761\pi\)
\(200\) 0 0
\(201\) −4.50000 + 7.79423i −0.317406 + 0.549762i
\(202\) 0 0
\(203\) 3.46410 + 4.00000i 0.243132 + 0.280745i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 12.1244 7.00000i 0.842701 0.486534i
\(208\) 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
\(215\) 0 0
\(216\) 0 0
\(217\) 4.33013 12.5000i 0.293948 0.848555i
\(218\) 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
\(223\) 24.0000i 1.60716i 0.595198 + 0.803579i \(0.297074\pi\)
−0.595198 + 0.803579i \(0.702926\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.52628 5.50000i 0.632281 0.365048i −0.149354 0.988784i \(-0.547719\pi\)
0.781635 + 0.623736i \(0.214386\pi\)
\(228\) 0 0
\(229\) 11.5000 19.9186i 0.759941 1.31626i −0.182939 0.983124i \(-0.558561\pi\)
0.942880 0.333133i \(-0.108106\pi\)
\(230\) 0 0
\(231\) 1.50000 + 7.79423i 0.0986928 + 0.512823i
\(232\) 0 0
\(233\) 9.52628 + 5.50000i 0.624087 + 0.360317i 0.778459 0.627696i \(-0.216002\pi\)
−0.154371 + 0.988013i \(0.549335\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.00000i 0.0649570i
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 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
\(243\) −13.8564 8.00000i −0.888889 0.513200i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.19615 + 3.00000i 0.330623 + 0.190885i
\(248\) 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
\(253\) 21.0000i 1.32026i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.1865 + 10.5000i 1.13444 + 0.654972i 0.945049 0.326929i \(-0.106014\pi\)
0.189396 + 0.981901i \(0.439347\pi\)
\(258\) 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
\(263\) 7.79423 4.50000i 0.480613 0.277482i −0.240059 0.970758i \(-0.577167\pi\)
0.720672 + 0.693276i \(0.243833\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.00000i 0.428393i
\(268\) 0 0
\(269\) −4.50000 7.79423i −0.274370 0.475223i 0.695606 0.718423i \(-0.255136\pi\)
−0.969976 + 0.243201i \(0.921803\pi\)
\(270\) 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
\(273\) 5.19615 15.0000i 0.314485 0.907841i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −14.7224 + 8.50000i −0.884585 + 0.510716i −0.872167 0.489207i \(-0.837286\pi\)
−0.0124177 + 0.999923i \(0.503953\pi\)
\(278\) 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
\(283\) 11.2583 6.50000i 0.669238 0.386385i −0.126550 0.991960i \(-0.540390\pi\)
0.795788 + 0.605575i \(0.207057\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.46410 + 4.00000i 0.204479 + 0.236113i
\(288\) 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
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 12.9904 7.50000i 0.753778 0.435194i
\(298\) 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
\(303\) −2.59808 1.50000i −0.149256 0.0861727i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 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
\(313\) −0.866025 0.500000i −0.0489506 0.0282617i 0.475325 0.879810i \(-0.342331\pi\)
−0.524276 + 0.851549i \(0.675664\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.59808 1.50000i −0.145922 0.0842484i 0.425261 0.905071i \(-0.360182\pi\)
−0.571184 + 0.820822i \(0.693516\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 5.00000i 0.278207i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.33013 2.50000i −0.239457 0.138250i
\(328\) 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
\(333\) 5.19615 3.00000i 0.284747 0.164399i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 10.0000i 0.544735i −0.962193 0.272367i \(-0.912193\pi\)
0.962193 0.272367i \(-0.0878066\pi\)
\(338\) 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
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.9904 7.50000i 0.697360 0.402621i −0.109003 0.994041i \(-0.534766\pi\)
0.806363 + 0.591420i \(0.201433\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −30.0000 −1.60128
\(352\) 0 0
\(353\) −2.59808 + 1.50000i −0.138282 + 0.0798369i −0.567545 0.823343i \(-0.692107\pi\)
0.429263 + 0.903179i \(0.358773\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 12.9904 2.50000i 0.687524 0.132314i
\(358\) 0 0
\(359\) 10.5000 18.1865i 0.554169 0.959849i −0.443799 0.896126i \(-0.646370\pi\)
0.997968 0.0637221i \(-0.0202971\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 2.00000i 0.104973i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 19.9186 11.5000i 1.03974 0.600295i 0.119982 0.992776i \(-0.461716\pi\)
0.919760 + 0.392481i \(0.128383\pi\)
\(368\) 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
\(373\) 9.52628 + 5.50000i 0.493252 + 0.284779i 0.725923 0.687776i \(-0.241413\pi\)
−0.232671 + 0.972556i \(0.574746\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 0 0
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 0 0
\(383\) −2.59808 1.50000i −0.132755 0.0766464i 0.432151 0.901801i \(-0.357755\pi\)
−0.564907 + 0.825155i \(0.691088\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.92820 4.00000i −0.352180 0.203331i
\(388\) 0 0
\(389\) −14.5000 25.1147i −0.735179 1.27337i −0.954645 0.297747i \(-0.903765\pi\)
0.219465 0.975620i \(-0.429569\pi\)
\(390\) 0 0
\(391\) 35.0000 1.77003
\(392\) 0 0
\(393\) 5.00000i 0.252217i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 14.7224 + 8.50000i 0.738898 + 0.426603i 0.821668 0.569966i \(-0.193044\pi\)
−0.0827707 + 0.996569i \(0.526377\pi\)
\(398\) 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
\(403\) −25.9808 + 15.0000i −1.29419 + 0.747203i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.00000i 0.446113i
\(408\) 0 0
\(409\) 13.5000 + 23.3827i 0.667532 + 1.15620i 0.978592 + 0.205809i \(0.0659826\pi\)
−0.311060 + 0.950390i \(0.600684\pi\)
\(410\) 0 0
\(411\) 5.50000 9.52628i 0.271295 0.469897i
\(412\) 0 0
\(413\) 12.9904 37.5000i 0.639215 1.84525i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 10.3923 6.00000i 0.508913 0.293821i
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 8.66025 5.00000i 0.421076 0.243108i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −12.9904 + 2.50000i −0.628649 + 0.120983i
\(428\) 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
\(433\) 2.00000i 0.0961139i 0.998845 + 0.0480569i \(0.0153029\pi\)
−0.998845 + 0.0480569i \(0.984697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.06218 + 3.50000i −0.289993 + 0.167428i
\(438\) 0 0
\(439\) 10.5000 18.1865i 0.501138 0.867996i −0.498861 0.866682i \(-0.666248\pi\)
0.999999 0.00131415i \(-0.000418308\pi\)
\(440\) 0 0
\(441\) −11.0000 8.66025i −0.523810 0.412393i
\(442\) 0 0
\(443\) −26.8468 15.5000i −1.27553 0.736427i −0.299506 0.954094i \(-0.596822\pi\)
−0.976023 + 0.217667i \(0.930155\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 17.0000i 0.804072i
\(448\) 0 0
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) 0 0
\(453\) 4.33013 + 2.50000i 0.203447 + 0.117460i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.7224 + 8.50000i 0.688686 + 0.397613i 0.803120 0.595818i \(-0.203172\pi\)
−0.114433 + 0.993431i \(0.536505\pi\)
\(458\) 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
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.59808 + 1.50000i 0.120225 + 0.0694117i 0.558906 0.829231i \(-0.311221\pi\)
−0.438682 + 0.898642i \(0.644554\pi\)
\(468\) 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
\(473\) 10.3923 6.00000i 0.477839 0.275880i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 2.00000i 0.0915737i
\(478\) 0 0
\(479\) 15.5000 + 26.8468i 0.708213 + 1.22666i 0.965519 + 0.260331i \(0.0838317\pi\)
−0.257306 + 0.966330i \(0.582835\pi\)
\(480\) 0 0
\(481\) 9.00000 15.5885i 0.410365 0.710772i
\(482\) 0 0
\(483\) 12.1244 + 14.0000i 0.551677 + 0.637022i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.06218 3.50000i 0.274703 0.158600i −0.356320 0.934364i \(-0.615969\pi\)
0.631023 + 0.775764i \(0.282635\pi\)
\(488\) 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
\(493\) 8.66025 5.00000i 0.390038 0.225189i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −17.5000 + 30.3109i −0.783408 + 1.35690i 0.146538 + 0.989205i \(0.453187\pi\)
−0.929946 + 0.367697i \(0.880146\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 32.0000i 1.42681i 0.700752 + 0.713405i \(0.252848\pi\)
−0.700752 + 0.713405i \(0.747152\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −19.9186 + 11.5000i −0.884615 + 0.510733i
\(508\) 0 0
\(509\) −4.50000 + 7.79423i −0.199459 + 0.345473i −0.948353 0.317217i \(-0.897252\pi\)
0.748894 + 0.662690i \(0.230585\pi\)
\(510\) 0 0
\(511\) 17.5000 + 6.06218i 0.774154 + 0.268175i
\(512\) 0 0
\(513\) 4.33013 + 2.50000i 0.191180 + 0.110378i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 15.0000i 0.659699i
\(518\) 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
\(523\) −6.06218 3.50000i −0.265081 0.153044i 0.361569 0.932345i \(-0.382241\pi\)
−0.626650 + 0.779301i \(0.715574\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.6506 12.5000i −0.943116 0.544509i
\(528\) 0 0
\(529\) 13.0000 + 22.5167i 0.565217 + 0.978985i
\(530\) 0 0
\(531\) −30.0000 −1.30189
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −11.2583 6.50000i −0.485833 0.280496i
\(538\) 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
\(543\) −8.66025 + 5.00000i −0.371647 + 0.214571i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000i 0.342055i −0.985266 0.171028i \(-0.945291\pi\)
0.985266 0.171028i \(-0.0547087\pi\)
\(548\) 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
\(553\) −2.59808 + 0.500000i −0.110481 + 0.0212622i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.33013 + 2.50000i −0.183473 + 0.105928i −0.588924 0.808189i \(-0.700448\pi\)
0.405450 + 0.914117i \(0.367115\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 15.0000 0.633300
\(562\) 0 0
\(563\) 35.5070 20.5000i 1.49644 0.863972i 0.496452 0.868064i \(-0.334636\pi\)
0.999992 + 0.00409232i \(0.00130263\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.866025 + 2.50000i −0.0363696 + 0.104990i
\(568\) 0 0
\(569\) −16.5000 + 28.5788i −0.691716 + 1.19809i 0.279559 + 0.960128i \(0.409812\pi\)
−0.971275 + 0.237959i \(0.923522\pi\)
\(570\) 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
\(573\) 11.0000i 0.459532i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −28.5788 + 16.5000i −1.18975 + 0.686904i −0.958250 0.285930i \(-0.907697\pi\)
−0.231502 + 0.972834i \(0.574364\pi\)
\(578\) 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
\(583\) −2.59808 1.50000i −0.107601 0.0621237i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.0000i 0.825488i −0.910847 0.412744i \(-0.864570\pi\)
0.910847 0.412744i \(-0.135430\pi\)
\(588\) 0 0
\(589\) 5.00000 0.206021
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 0 0
\(593\) −38.9711 22.5000i −1.60035 0.923964i −0.991416 0.130746i \(-0.958263\pi\)
−0.608937 0.793219i \(-0.708404\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −11.2583 6.50000i −0.460773 0.266027i
\(598\) 0 0
\(599\) −8.50000 14.7224i −0.347301 0.601542i 0.638468 0.769648i \(-0.279568\pi\)
−0.985769 + 0.168106i \(0.946235\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 18.0000i 0.733017i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −11.2583 6.50000i −0.456962 0.263827i 0.253804 0.967256i \(-0.418318\pi\)
−0.710766 + 0.703429i \(0.751651\pi\)
\(608\) 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
\(613\) −37.2391 + 21.5000i −1.50407 + 0.868377i −0.504084 + 0.863655i \(0.668170\pi\)
−0.999989 + 0.00472215i \(0.998497\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 30.0000i 1.20775i 0.797077 + 0.603877i \(0.206378\pi\)
−0.797077 + 0.603877i \(0.793622\pi\)
\(618\) 0 0
\(619\) −4.50000 7.79423i −0.180870 0.313276i 0.761307 0.648392i \(-0.224558\pi\)
−0.942177 + 0.335115i \(0.891225\pi\)
\(620\) 0 0
\(621\) 17.5000 30.3109i 0.702251 1.21633i
\(622\) 0 0
\(623\) −18.1865 + 3.50000i −0.728628 + 0.140225i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.59808 + 1.50000i −0.103757 + 0.0599042i
\(628\) 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
\(633\) −3.46410 + 2.00000i −0.137686 + 0.0794929i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −41.5692 6.00000i −1.64703 0.237729i
\(638\) 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
\(643\) 44.0000i 1.73519i 0.497271 + 0.867595i \(0.334335\pi\)
−0.497271 + 0.867595i \(0.665665\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.9904 7.50000i 0.510705 0.294855i −0.222419 0.974951i \(-0.571395\pi\)
0.733123 + 0.680096i \(0.238062\pi\)
\(648\) 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
\(653\) 30.3109 + 17.5000i 1.18616 + 0.684828i 0.957431 0.288663i \(-0.0932107\pi\)
0.228726 + 0.973491i \(0.426544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.0000i 0.546192i
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 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
\(663\) −25.9808 15.0000i −1.00901 0.582552i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.1244 + 7.00000i 0.469457 + 0.271041i
\(668\) 0 0
\(669\) 12.0000 + 20.7846i 0.463947 + 0.803579i
\(670\) 0 0
\(671\) −15.0000 −0.579069
\(672\) 0 0
\(673\) 26.0000i 1.00223i 0.865382 + 0.501113i \(0.167076\pi\)
−0.865382 + 0.501113i \(0.832924\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33.7750 19.5000i −1.29808 0.749446i −0.318006 0.948089i \(-0.603013\pi\)
−0.980072 + 0.198643i \(0.936347\pi\)
\(678\) 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
\(683\) −23.3827 + 13.5000i −0.894714 + 0.516563i −0.875481 0.483252i \(-0.839456\pi\)
−0.0192323 + 0.999815i \(0.506122\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 23.0000i 0.877505i
\(688\) 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
\(693\) −10.3923 12.0000i −0.394771 0.455842i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 8.66025 5.00000i 0.328031 0.189389i
\(698\) 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
\(703\) −2.59808 + 1.50000i −0.0979883 + 0.0565736i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.59808 + 7.50000i −0.0977107 + 0.282067i
\(708\) 0 0
\(709\) −14.5000 + 25.1147i −0.544559 + 0.943204i 0.454076 + 0.890963i \(0.349970\pi\)
−0.998635 + 0.0522406i \(0.983364\pi\)
\(710\) 0 0
\(711\) 1.00000 + 1.73205i 0.0375029 + 0.0649570i
\(712\) 0 0
\(713\) 35.0000i 1.31076i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −17.3205 + 10.0000i −0.646846 + 0.373457i
\(718\) 0 0
\(719\) −19.5000 + 33.7750i −0.727227 + 1.25959i 0.230823 + 0.972996i \(0.425858\pi\)
−0.958051 + 0.286599i \(0.907475\pi\)
\(720\) 0 0
\(721\) 7.50000 + 38.9711i 0.279315 + 1.45136i
\(722\) 0 0
\(723\) 14.7224 + 8.50000i 0.547533 + 0.316118i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 32.0000i 1.18681i 0.804902 + 0.593407i \(0.202218\pi\)
−0.804902 + 0.593407i \(0.797782\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) −10.0000 17.3205i −0.369863 0.640622i
\(732\) 0 0
\(733\) 16.4545 + 9.50000i 0.607760 + 0.350891i 0.772088 0.635515i \(-0.219212\pi\)
−0.164328 + 0.986406i \(0.552546\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 23.3827 + 13.5000i 0.861312 + 0.497279i
\(738\) 0 0
\(739\) −2.50000 4.33013i −0.0919640 0.159286i 0.816373 0.577524i \(-0.195981\pi\)
−0.908337 + 0.418238i \(0.862648\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 20.7846 + 12.0000i 0.760469 + 0.439057i
\(748\) 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
\(753\) 13.8564 8.00000i 0.504956 0.291536i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000i 0.363456i 0.983349 + 0.181728i \(0.0581691\pi\)
−0.983349 + 0.181728i \(0.941831\pi\)
\(758\) 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
\(763\) −4.33013 + 12.5000i −0.156761 + 0.452530i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −77.9423 + 45.0000i −2.81433 + 1.62486i
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 21.0000 0.756297
\(772\) 0 0
\(773\) −16.4545 + 9.50000i −0.591827 + 0.341691i −0.765819 0.643056i \(-0.777666\pi\)
0.173993 + 0.984747i \(0.444333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 5.19615 + 6.00000i 0.186411 + 0.215249i
\(778\) 0 0
\(779\) −1.00000 + 1.73205i −0.0358287 + 0.0620572i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 10.0000i 0.357371i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −14.7224 + 8.50000i −0.524798 + 0.302992i −0.738896 0.673820i \(-0.764652\pi\)
0.214097 + 0.976812i \(0.431319\pi\)
\(788\) 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
\(793\) 25.9808 + 15.0000i 0.922604 + 0.532666i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.0000i 0.637593i 0.947823 + 0.318796i \(0.103279\pi\)
−0.947823 + 0.318796i \(0.896721\pi\)
\(798\) 0 0
\(799\) 25.0000 0.884436
\(800\) 0 0