Properties

Label 1960.2.q.p.361.2
Level $1960$
Weight $2$
Character 1960.361
Analytic conductor $15.651$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.p.961.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +(0.500000 - 0.866025i) q^{11} +2.41421 q^{13} +0.414214 q^{15} +(0.207107 - 0.358719i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.12132 + 1.94218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.41421 q^{27} +1.00000 q^{29} +(-0.878680 + 1.52192i) q^{31} +(-0.207107 - 0.358719i) q^{33} +(3.94975 + 6.84116i) q^{37} +(0.500000 - 0.866025i) q^{39} +7.41421 q^{41} -0.343146 q^{43} +(-1.41421 + 2.44949i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-0.0857864 - 0.148586i) q^{51} +(-4.70711 + 8.15295i) q^{53} +1.00000 q^{55} -0.828427 q^{57} +(-5.12132 + 8.87039i) q^{59} +(0.585786 + 1.01461i) q^{61} +(1.20711 + 2.09077i) q^{65} +(-0.707107 + 1.22474i) q^{67} +0.928932 q^{69} +14.4853 q^{71} +(2.58579 - 4.47871i) q^{73} +(0.207107 + 0.358719i) q^{75} +(7.32843 + 12.6932i) q^{79} +(-3.74264 + 6.48244i) q^{81} +11.3137 q^{83} +0.414214 q^{85} +(0.207107 - 0.358719i) q^{87} +(0.828427 + 1.43488i) q^{89} +(0.363961 + 0.630399i) q^{93} +(1.00000 - 1.73205i) q^{95} -0.0710678 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{5} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{5} + 2q^{11} + 4q^{13} - 4q^{15} - 2q^{17} - 4q^{19} - 4q^{23} - 2q^{25} + 4q^{27} + 4q^{29} - 12q^{31} + 2q^{33} - 4q^{37} + 2q^{39} + 24q^{41} - 24q^{43} - 18q^{47} - 6q^{51} - 16q^{53} + 4q^{55} + 8q^{57} - 12q^{59} + 8q^{61} + 2q^{65} + 32q^{69} + 24q^{71} + 16q^{73} - 2q^{75} + 18q^{79} + 2q^{81} - 4q^{85} - 2q^{87} - 8q^{89} - 24q^{93} + 4q^{95} + 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.207107 0.358719i 0.119573 0.207107i −0.800025 0.599966i \(-0.795181\pi\)
0.919599 + 0.392859i \(0.128514\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.41421 + 2.44949i 0.471405 + 0.816497i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) 2.41421 0.669582 0.334791 0.942292i \(-0.391334\pi\)
0.334791 + 0.942292i \(0.391334\pi\)
\(14\) 0 0
\(15\) 0.414214 0.106949
\(16\) 0 0
\(17\) 0.207107 0.358719i 0.0502308 0.0870023i −0.839817 0.542870i \(-0.817338\pi\)
0.890048 + 0.455868i \(0.150671\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.12132 + 1.94218i 0.233811 + 0.404973i 0.958927 0.283654i \(-0.0915468\pi\)
−0.725115 + 0.688628i \(0.758213\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 2.41421 0.464616
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) −0.878680 + 1.52192i −0.157816 + 0.273345i −0.934081 0.357062i \(-0.883778\pi\)
0.776265 + 0.630407i \(0.217112\pi\)
\(32\) 0 0
\(33\) −0.207107 0.358719i −0.0360527 0.0624450i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.94975 + 6.84116i 0.649334 + 1.12468i 0.983282 + 0.182089i \(0.0582858\pi\)
−0.333948 + 0.942592i \(0.608381\pi\)
\(38\) 0 0
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) 7.41421 1.15791 0.578953 0.815361i \(-0.303462\pi\)
0.578953 + 0.815361i \(0.303462\pi\)
\(42\) 0 0
\(43\) −0.343146 −0.0523292 −0.0261646 0.999658i \(-0.508329\pi\)
−0.0261646 + 0.999658i \(0.508329\pi\)
\(44\) 0 0
\(45\) −1.41421 + 2.44949i −0.210819 + 0.365148i
\(46\) 0 0
\(47\) −5.20711 9.01897i −0.759535 1.31555i −0.943088 0.332543i \(-0.892093\pi\)
0.183554 0.983010i \(-0.441240\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.0857864 0.148586i −0.0120125 0.0208063i
\(52\) 0 0
\(53\) −4.70711 + 8.15295i −0.646571 + 1.11989i 0.337365 + 0.941374i \(0.390464\pi\)
−0.983936 + 0.178520i \(0.942869\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −0.828427 −0.109728
\(58\) 0 0
\(59\) −5.12132 + 8.87039i −0.666739 + 1.15483i 0.312072 + 0.950059i \(0.398977\pi\)
−0.978811 + 0.204767i \(0.934356\pi\)
\(60\) 0 0
\(61\) 0.585786 + 1.01461i 0.0750023 + 0.129908i 0.901087 0.433638i \(-0.142770\pi\)
−0.826085 + 0.563546i \(0.809437\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.20711 + 2.09077i 0.149723 + 0.259328i
\(66\) 0 0
\(67\) −0.707107 + 1.22474i −0.0863868 + 0.149626i −0.905981 0.423318i \(-0.860865\pi\)
0.819594 + 0.572944i \(0.194199\pi\)
\(68\) 0 0
\(69\) 0.928932 0.111830
\(70\) 0 0
\(71\) 14.4853 1.71909 0.859543 0.511063i \(-0.170748\pi\)
0.859543 + 0.511063i \(0.170748\pi\)
\(72\) 0 0
\(73\) 2.58579 4.47871i 0.302643 0.524194i −0.674090 0.738649i \(-0.735464\pi\)
0.976734 + 0.214455i \(0.0687975\pi\)
\(74\) 0 0
\(75\) 0.207107 + 0.358719i 0.0239146 + 0.0414214i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 7.32843 + 12.6932i 0.824512 + 1.42810i 0.902291 + 0.431127i \(0.141884\pi\)
−0.0777789 + 0.996971i \(0.524783\pi\)
\(80\) 0 0
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) 0 0
\(83\) 11.3137 1.24184 0.620920 0.783874i \(-0.286759\pi\)
0.620920 + 0.783874i \(0.286759\pi\)
\(84\) 0 0
\(85\) 0.414214 0.0449278
\(86\) 0 0
\(87\) 0.207107 0.358719i 0.0222042 0.0384588i
\(88\) 0 0
\(89\) 0.828427 + 1.43488i 0.0878131 + 0.152097i 0.906586 0.422020i \(-0.138679\pi\)
−0.818773 + 0.574117i \(0.805346\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.363961 + 0.630399i 0.0377410 + 0.0653693i
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) −0.0710678 −0.00721584 −0.00360792 0.999993i \(-0.501148\pi\)
−0.00360792 + 0.999993i \(0.501148\pi\)
\(98\) 0 0
\(99\) 2.82843 0.284268
\(100\) 0 0
\(101\) 3.24264 5.61642i 0.322655 0.558855i −0.658380 0.752686i \(-0.728758\pi\)
0.981035 + 0.193831i \(0.0620914\pi\)
\(102\) 0 0
\(103\) −7.62132 13.2005i −0.750951 1.30069i −0.947362 0.320164i \(-0.896262\pi\)
0.196411 0.980522i \(-0.437071\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.24264 2.15232i −0.120131 0.208072i 0.799688 0.600415i \(-0.204998\pi\)
−0.919819 + 0.392343i \(0.871665\pi\)
\(108\) 0 0
\(109\) −2.15685 + 3.73578i −0.206589 + 0.357823i −0.950638 0.310302i \(-0.899570\pi\)
0.744049 + 0.668125i \(0.232903\pi\)
\(110\) 0 0
\(111\) 3.27208 0.310572
\(112\) 0 0
\(113\) 5.07107 0.477046 0.238523 0.971137i \(-0.423337\pi\)
0.238523 + 0.971137i \(0.423337\pi\)
\(114\) 0 0
\(115\) −1.12132 + 1.94218i −0.104564 + 0.181110i
\(116\) 0 0
\(117\) 3.41421 + 5.91359i 0.315644 + 0.546712i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 1.53553 2.65962i 0.138454 0.239810i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 12.2426 1.08636 0.543179 0.839617i \(-0.317220\pi\)
0.543179 + 0.839617i \(0.317220\pi\)
\(128\) 0 0
\(129\) −0.0710678 + 0.123093i −0.00625717 + 0.0108377i
\(130\) 0 0
\(131\) −5.87868 10.1822i −0.513623 0.889620i −0.999875 0.0158021i \(-0.994970\pi\)
0.486253 0.873818i \(-0.338364\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.20711 + 2.09077i 0.103891 + 0.179945i
\(136\) 0 0
\(137\) −1.65685 + 2.86976i −0.141555 + 0.245180i −0.928082 0.372375i \(-0.878543\pi\)
0.786528 + 0.617555i \(0.211877\pi\)
\(138\) 0 0
\(139\) −1.41421 −0.119952 −0.0599760 0.998200i \(-0.519102\pi\)
−0.0599760 + 0.998200i \(0.519102\pi\)
\(140\) 0 0
\(141\) −4.31371 −0.363280
\(142\) 0 0
\(143\) 1.20711 2.09077i 0.100943 0.174839i
\(144\) 0 0
\(145\) 0.500000 + 0.866025i 0.0415227 + 0.0719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.41421 + 12.8418i 0.607396 + 1.05204i 0.991668 + 0.128821i \(0.0411192\pi\)
−0.384272 + 0.923220i \(0.625547\pi\)
\(150\) 0 0
\(151\) −2.32843 + 4.03295i −0.189485 + 0.328197i −0.945079 0.326843i \(-0.894015\pi\)
0.755594 + 0.655040i \(0.227348\pi\)
\(152\) 0 0
\(153\) 1.17157 0.0947161
\(154\) 0 0
\(155\) −1.75736 −0.141154
\(156\) 0 0
\(157\) 3.24264 5.61642i 0.258791 0.448239i −0.707127 0.707086i \(-0.750009\pi\)
0.965918 + 0.258847i \(0.0833426\pi\)
\(158\) 0 0
\(159\) 1.94975 + 3.37706i 0.154625 + 0.267818i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −8.53553 14.7840i −0.668555 1.15797i −0.978308 0.207154i \(-0.933580\pi\)
0.309754 0.950817i \(-0.399753\pi\)
\(164\) 0 0
\(165\) 0.207107 0.358719i 0.0161232 0.0279263i
\(166\) 0 0
\(167\) 10.4142 0.805876 0.402938 0.915227i \(-0.367989\pi\)
0.402938 + 0.915227i \(0.367989\pi\)
\(168\) 0 0
\(169\) −7.17157 −0.551659
\(170\) 0 0
\(171\) 2.82843 4.89898i 0.216295 0.374634i
\(172\) 0 0
\(173\) −5.86396 10.1567i −0.445829 0.772198i 0.552281 0.833658i \(-0.313758\pi\)
−0.998110 + 0.0614602i \(0.980424\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.12132 + 3.67423i 0.159448 + 0.276172i
\(178\) 0 0
\(179\) 12.0711 20.9077i 0.902234 1.56272i 0.0776462 0.996981i \(-0.475260\pi\)
0.824588 0.565734i \(-0.191407\pi\)
\(180\) 0 0
\(181\) 5.55635 0.413000 0.206500 0.978447i \(-0.433793\pi\)
0.206500 + 0.978447i \(0.433793\pi\)
\(182\) 0 0
\(183\) 0.485281 0.0358730
\(184\) 0 0
\(185\) −3.94975 + 6.84116i −0.290391 + 0.502972i
\(186\) 0 0
\(187\) −0.207107 0.358719i −0.0151451 0.0262322i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.08579 7.07679i −0.295637 0.512059i 0.679496 0.733679i \(-0.262199\pi\)
−0.975133 + 0.221621i \(0.928865\pi\)
\(192\) 0 0
\(193\) −11.6569 + 20.1903i −0.839079 + 1.45333i 0.0515871 + 0.998668i \(0.483572\pi\)
−0.890666 + 0.454658i \(0.849761\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) −3.75736 −0.267701 −0.133850 0.991002i \(-0.542734\pi\)
−0.133850 + 0.991002i \(0.542734\pi\)
\(198\) 0 0
\(199\) −12.1924 + 21.1178i −0.864295 + 1.49700i 0.00344954 + 0.999994i \(0.498902\pi\)
−0.867745 + 0.497010i \(0.834431\pi\)
\(200\) 0 0
\(201\) 0.292893 + 0.507306i 0.0206591 + 0.0357826i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.70711 + 6.42090i 0.258916 + 0.448455i
\(206\) 0 0
\(207\) −3.17157 + 5.49333i −0.220440 + 0.381813i
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −11.1421 −0.767056 −0.383528 0.923529i \(-0.625291\pi\)
−0.383528 + 0.923529i \(0.625291\pi\)
\(212\) 0 0
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) −0.171573 0.297173i −0.0117012 0.0202670i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.07107 1.85514i −0.0723761 0.125359i
\(220\) 0 0
\(221\) 0.500000 0.866025i 0.0336336 0.0582552i
\(222\) 0 0
\(223\) 19.3848 1.29810 0.649050 0.760745i \(-0.275166\pi\)
0.649050 + 0.760745i \(0.275166\pi\)
\(224\) 0 0
\(225\) −2.82843 −0.188562
\(226\) 0 0
\(227\) −2.20711 + 3.82282i −0.146491 + 0.253730i −0.929928 0.367741i \(-0.880131\pi\)
0.783437 + 0.621471i \(0.213465\pi\)
\(228\) 0 0
\(229\) 11.9497 + 20.6976i 0.789662 + 1.36773i 0.926174 + 0.377096i \(0.123077\pi\)
−0.136513 + 0.990638i \(0.543589\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −10.2426 17.7408i −0.671018 1.16224i −0.977616 0.210398i \(-0.932524\pi\)
0.306598 0.951839i \(-0.400809\pi\)
\(234\) 0 0
\(235\) 5.20711 9.01897i 0.339674 0.588333i
\(236\) 0 0
\(237\) 6.07107 0.394358
\(238\) 0 0
\(239\) 6.65685 0.430596 0.215298 0.976548i \(-0.430928\pi\)
0.215298 + 0.976548i \(0.430928\pi\)
\(240\) 0 0
\(241\) 13.1924 22.8499i 0.849796 1.47189i −0.0315933 0.999501i \(-0.510058\pi\)
0.881390 0.472390i \(-0.156609\pi\)
\(242\) 0 0
\(243\) 5.17157 + 8.95743i 0.331757 + 0.574619i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.41421 4.18154i −0.153613 0.266065i
\(248\) 0 0
\(249\) 2.34315 4.05845i 0.148491 0.257194i
\(250\) 0 0
\(251\) −23.5563 −1.48686 −0.743432 0.668812i \(-0.766803\pi\)
−0.743432 + 0.668812i \(0.766803\pi\)
\(252\) 0 0
\(253\) 2.24264 0.140994
\(254\) 0 0
\(255\) 0.0857864 0.148586i 0.00537216 0.00930485i
\(256\) 0 0
\(257\) 3.24264 + 5.61642i 0.202270 + 0.350343i 0.949260 0.314494i \(-0.101835\pi\)
−0.746989 + 0.664836i \(0.768501\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.41421 + 2.44949i 0.0875376 + 0.151620i
\(262\) 0 0
\(263\) 7.48528 12.9649i 0.461562 0.799449i −0.537477 0.843279i \(-0.680622\pi\)
0.999039 + 0.0438293i \(0.0139558\pi\)
\(264\) 0 0
\(265\) −9.41421 −0.578311
\(266\) 0 0
\(267\) 0.686292 0.0420004
\(268\) 0 0
\(269\) −10.7071 + 18.5453i −0.652824 + 1.13072i 0.329611 + 0.944117i \(0.393082\pi\)
−0.982435 + 0.186607i \(0.940251\pi\)
\(270\) 0 0
\(271\) −6.82843 11.8272i −0.414797 0.718450i 0.580610 0.814182i \(-0.302814\pi\)
−0.995407 + 0.0957318i \(0.969481\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) −0.535534 + 0.927572i −0.0321771 + 0.0557324i −0.881666 0.471875i \(-0.843577\pi\)
0.849488 + 0.527607i \(0.176911\pi\)
\(278\) 0 0
\(279\) −4.97056 −0.297580
\(280\) 0 0
\(281\) −4.31371 −0.257334 −0.128667 0.991688i \(-0.541070\pi\)
−0.128667 + 0.991688i \(0.541070\pi\)
\(282\) 0 0
\(283\) 11.5208 19.9546i 0.684841 1.18618i −0.288645 0.957436i \(-0.593205\pi\)
0.973487 0.228744i \(-0.0734619\pi\)
\(284\) 0 0
\(285\) −0.414214 0.717439i −0.0245359 0.0424974i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.41421 + 14.5738i 0.494954 + 0.857285i
\(290\) 0 0
\(291\) −0.0147186 + 0.0254934i −0.000862821 + 0.00149445i
\(292\) 0 0
\(293\) −15.5858 −0.910531 −0.455266 0.890356i \(-0.650456\pi\)
−0.455266 + 0.890356i \(0.650456\pi\)
\(294\) 0 0
\(295\) −10.2426 −0.596350
\(296\) 0 0
\(297\) 1.20711 2.09077i 0.0700434 0.121319i
\(298\) 0 0
\(299\) 2.70711 + 4.68885i 0.156556 + 0.271163i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1.34315 2.32640i −0.0771617 0.133648i
\(304\) 0 0
\(305\) −0.585786 + 1.01461i −0.0335420 + 0.0580965i
\(306\) 0 0
\(307\) −26.0711 −1.48795 −0.743977 0.668205i \(-0.767063\pi\)
−0.743977 + 0.668205i \(0.767063\pi\)
\(308\) 0 0
\(309\) −6.31371 −0.359174
\(310\) 0 0
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) −0.863961 1.49642i −0.0488340 0.0845829i 0.840575 0.541695i \(-0.182217\pi\)
−0.889409 + 0.457112i \(0.848884\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.8284 20.4874i −0.664351 1.15069i −0.979461 0.201634i \(-0.935375\pi\)
0.315110 0.949055i \(-0.397958\pi\)
\(318\) 0 0
\(319\) 0.500000 0.866025i 0.0279946 0.0484881i
\(320\) 0 0
\(321\) −1.02944 −0.0574576
\(322\) 0 0
\(323\) −0.828427 −0.0460949
\(324\) 0 0
\(325\) −1.20711 + 2.09077i −0.0669582 + 0.115975i
\(326\) 0 0
\(327\) 0.893398 + 1.54741i 0.0494050 + 0.0855720i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −13.2426 22.9369i −0.727881 1.26073i −0.957777 0.287512i \(-0.907172\pi\)
0.229896 0.973215i \(-0.426162\pi\)
\(332\) 0 0
\(333\) −11.1716 + 19.3497i −0.612198 + 1.06036i
\(334\) 0 0
\(335\) −1.41421 −0.0772667
\(336\) 0 0
\(337\) 1.07107 0.0583448 0.0291724 0.999574i \(-0.490713\pi\)
0.0291724 + 0.999574i \(0.490713\pi\)
\(338\) 0 0
\(339\) 1.05025 1.81909i 0.0570419 0.0987994i
\(340\) 0 0
\(341\) 0.878680 + 1.52192i 0.0475832 + 0.0824165i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.464466 + 0.804479i 0.0250060 + 0.0433117i
\(346\) 0 0
\(347\) 12.4350 21.5381i 0.667547 1.15623i −0.311041 0.950397i \(-0.600678\pi\)
0.978588 0.205829i \(-0.0659892\pi\)
\(348\) 0 0
\(349\) −29.3137 −1.56913 −0.784563 0.620049i \(-0.787113\pi\)
−0.784563 + 0.620049i \(0.787113\pi\)
\(350\) 0 0
\(351\) 5.82843 0.311098
\(352\) 0 0
\(353\) 6.10660 10.5769i 0.325022 0.562954i −0.656495 0.754330i \(-0.727962\pi\)
0.981517 + 0.191376i \(0.0612951\pi\)
\(354\) 0 0
\(355\) 7.24264 + 12.5446i 0.384399 + 0.665799i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.17157 + 15.8856i 0.484057 + 0.838411i 0.999832 0.0183125i \(-0.00582936\pi\)
−0.515775 + 0.856724i \(0.672496\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0 0
\(363\) 4.14214 0.217406
\(364\) 0 0
\(365\) 5.17157 0.270692
\(366\) 0 0
\(367\) −1.37868 + 2.38794i −0.0719665 + 0.124650i −0.899763 0.436379i \(-0.856261\pi\)
0.827797 + 0.561028i \(0.189594\pi\)
\(368\) 0 0
\(369\) 10.4853 + 18.1610i 0.545842 + 0.945426i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −8.58579 14.8710i −0.444555 0.769992i 0.553466 0.832872i \(-0.313305\pi\)
−0.998021 + 0.0628797i \(0.979972\pi\)
\(374\) 0 0
\(375\) −0.207107 + 0.358719i −0.0106949 + 0.0185242i
\(376\) 0 0
\(377\) 2.41421 0.124338
\(378\) 0 0
\(379\) −16.6274 −0.854093 −0.427047 0.904230i \(-0.640446\pi\)
−0.427047 + 0.904230i \(0.640446\pi\)
\(380\) 0 0
\(381\) 2.53553 4.39167i 0.129899 0.224992i
\(382\) 0 0
\(383\) −8.58579 14.8710i −0.438713 0.759874i 0.558877 0.829250i \(-0.311232\pi\)
−0.997591 + 0.0693768i \(0.977899\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.485281 0.840532i −0.0246682 0.0427266i
\(388\) 0 0
\(389\) 14.3995 24.9407i 0.730083 1.26454i −0.226764 0.973950i \(-0.572815\pi\)
0.956847 0.290592i \(-0.0938521\pi\)
\(390\) 0 0
\(391\) 0.928932 0.0469781
\(392\) 0 0
\(393\) −4.87006 −0.245662
\(394\) 0 0
\(395\) −7.32843 + 12.6932i −0.368733 + 0.638665i
\(396\) 0 0
\(397\) 4.20711 + 7.28692i 0.211149 + 0.365720i 0.952074 0.305867i \(-0.0989463\pi\)
−0.740926 + 0.671587i \(0.765613\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.2279 22.9114i −0.660571 1.14414i −0.980466 0.196689i \(-0.936981\pi\)
0.319895 0.947453i \(-0.396352\pi\)
\(402\) 0 0
\(403\) −2.12132 + 3.67423i −0.105670 + 0.183027i
\(404\) 0 0
\(405\) −7.48528 −0.371947
\(406\) 0 0
\(407\) 7.89949 0.391563
\(408\) 0 0
\(409\) −14.5563 + 25.2123i −0.719765 + 1.24667i 0.241328 + 0.970444i \(0.422417\pi\)
−0.961093 + 0.276226i \(0.910916\pi\)
\(410\) 0 0
\(411\) 0.686292 + 1.18869i 0.0338523 + 0.0586338i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 5.65685 + 9.79796i 0.277684 + 0.480963i
\(416\) 0 0
\(417\) −0.292893 + 0.507306i −0.0143430 + 0.0248429i
\(418\) 0 0
\(419\) −31.4142 −1.53468 −0.767342 0.641238i \(-0.778421\pi\)
−0.767342 + 0.641238i \(0.778421\pi\)
\(420\) 0 0
\(421\) −3.68629 −0.179659 −0.0898294 0.995957i \(-0.528632\pi\)
−0.0898294 + 0.995957i \(0.528632\pi\)
\(422\) 0 0
\(423\) 14.7279 25.5095i 0.716096 1.24031i
\(424\) 0 0
\(425\) 0.207107 + 0.358719i 0.0100462 + 0.0174005i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.500000 0.866025i −0.0241402 0.0418121i
\(430\) 0 0
\(431\) −5.67157 + 9.82345i −0.273190 + 0.473179i −0.969677 0.244391i \(-0.921412\pi\)
0.696487 + 0.717570i \(0.254745\pi\)
\(432\) 0 0
\(433\) −26.9706 −1.29612 −0.648061 0.761588i \(-0.724420\pi\)
−0.648061 + 0.761588i \(0.724420\pi\)
\(434\) 0 0
\(435\) 0.414214 0.0198600
\(436\) 0 0
\(437\) 2.24264 3.88437i 0.107280 0.185815i
\(438\) 0 0
\(439\) 6.12132 + 10.6024i 0.292155 + 0.506027i 0.974319 0.225172i \(-0.0722945\pi\)
−0.682164 + 0.731199i \(0.738961\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −19.3848 33.5754i −0.920999 1.59522i −0.797873 0.602825i \(-0.794042\pi\)
−0.123125 0.992391i \(-0.539292\pi\)
\(444\) 0 0
\(445\) −0.828427 + 1.43488i −0.0392712 + 0.0680197i
\(446\) 0 0
\(447\) 6.14214 0.290513
\(448\) 0 0
\(449\) −10.5147 −0.496220 −0.248110 0.968732i \(-0.579809\pi\)
−0.248110 + 0.968732i \(0.579809\pi\)
\(450\) 0 0
\(451\) 3.70711 6.42090i 0.174561 0.302348i
\(452\) 0 0
\(453\) 0.964466 + 1.67050i 0.0453146 + 0.0784871i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.53553 16.5160i −0.446053 0.772587i 0.552071 0.833797i \(-0.313838\pi\)
−0.998125 + 0.0612095i \(0.980504\pi\)
\(458\) 0 0
\(459\) 0.500000 0.866025i 0.0233380 0.0404226i
\(460\) 0 0
\(461\) 24.2843 1.13103 0.565516 0.824738i \(-0.308677\pi\)
0.565516 + 0.824738i \(0.308677\pi\)
\(462\) 0 0
\(463\) −25.4558 −1.18303 −0.591517 0.806293i \(-0.701471\pi\)
−0.591517 + 0.806293i \(0.701471\pi\)
\(464\) 0 0
\(465\) −0.363961 + 0.630399i −0.0168783 + 0.0292341i
\(466\) 0 0
\(467\) −2.79289 4.83743i −0.129240 0.223850i 0.794143 0.607732i \(-0.207920\pi\)
−0.923382 + 0.383882i \(0.874587\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.34315 2.32640i −0.0618889 0.107195i
\(472\) 0 0
\(473\) −0.171573 + 0.297173i −0.00788893 + 0.0136640i
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) −26.6274 −1.21919
\(478\) 0 0
\(479\) −12.2635 + 21.2409i −0.560332 + 0.970523i 0.437136 + 0.899396i \(0.355993\pi\)
−0.997467 + 0.0711272i \(0.977340\pi\)
\(480\) 0 0
\(481\) 9.53553 + 16.5160i 0.434783 + 0.753066i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.0355339 0.0615465i −0.00161351 0.00279468i
\(486\) 0 0
\(487\) −13.3640 + 23.1471i −0.605579 + 1.04889i 0.386381 + 0.922339i \(0.373725\pi\)
−0.991960 + 0.126554i \(0.959608\pi\)
\(488\) 0 0
\(489\) −7.07107 −0.319765
\(490\) 0 0
\(491\) 5.48528 0.247547 0.123774 0.992310i \(-0.460500\pi\)
0.123774 + 0.992310i \(0.460500\pi\)
\(492\) 0 0
\(493\) 0.207107 0.358719i 0.00932762 0.0161559i
\(494\) 0 0
\(495\) 1.41421 + 2.44949i 0.0635642 + 0.110096i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −6.39949 11.0843i −0.286481 0.496199i 0.686486 0.727143i \(-0.259152\pi\)
−0.972967 + 0.230943i \(0.925819\pi\)
\(500\) 0 0
\(501\) 2.15685 3.73578i 0.0963611 0.166902i
\(502\) 0 0
\(503\) 31.0416 1.38408 0.692039 0.721860i \(-0.256713\pi\)
0.692039 + 0.721860i \(0.256713\pi\)
\(504\) 0 0
\(505\) 6.48528 0.288591
\(506\) 0 0
\(507\) −1.48528 + 2.57258i −0.0659637 + 0.114252i
\(508\) 0 0
\(509\) −3.87868 6.71807i −0.171919 0.297773i 0.767171 0.641442i \(-0.221664\pi\)
−0.939091 + 0.343669i \(0.888330\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.41421 4.18154i −0.106590 0.184620i
\(514\) 0 0
\(515\) 7.62132 13.2005i 0.335836 0.581684i
\(516\) 0 0
\(517\) −10.4142 −0.458017
\(518\) 0 0
\(519\) −4.85786 −0.213237
\(520\) 0 0
\(521\) −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i \(-0.875291\pi\)
0.792797 + 0.609486i \(0.208624\pi\)
\(522\) 0 0
\(523\) 16.2426 + 28.1331i 0.710241 + 1.23017i 0.964767 + 0.263108i \(0.0847474\pi\)
−0.254525 + 0.967066i \(0.581919\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.363961 + 0.630399i 0.0158544 + 0.0274606i
\(528\) 0 0
\(529\) 8.98528 15.5630i 0.390664 0.676651i
\(530\) 0 0
\(531\) −28.9706 −1.25722
\(532\) 0 0
\(533\) 17.8995 0.775313
\(534\) 0 0
\(535\) 1.24264 2.15232i 0.0537240 0.0930528i
\(536\) 0 0
\(537\) −5.00000 8.66025i −0.215766 0.373718i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −5.15685 8.93193i −0.221710 0.384014i 0.733617 0.679563i \(-0.237831\pi\)
−0.955327 + 0.295549i \(0.904497\pi\)
\(542\) 0 0
\(543\) 1.15076 1.99317i 0.0493837 0.0855351i
\(544\) 0 0
\(545\) −4.31371 −0.184779
\(546\) 0 0
\(547\) −27.1127 −1.15926 −0.579628 0.814881i \(-0.696802\pi\)
−0.579628 + 0.814881i \(0.696802\pi\)
\(548\) 0 0
\(549\) −1.65685 + 2.86976i −0.0707128 + 0.122478i
\(550\) 0 0
\(551\) −1.00000 1.73205i −0.0426014 0.0737878i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.63604 + 2.83370i 0.0694460 + 0.120284i
\(556\) 0 0
\(557\) 13.0711 22.6398i 0.553839 0.959277i −0.444154 0.895950i \(-0.646496\pi\)
0.997993 0.0633267i \(-0.0201710\pi\)
\(558\) 0 0
\(559\) −0.828427 −0.0350387
\(560\) 0 0
\(561\) −0.171573 −0.00724381
\(562\) 0 0
\(563\) 19.9706 34.5900i 0.841659 1.45780i −0.0468326 0.998903i \(-0.514913\pi\)
0.888491 0.458893i \(-0.151754\pi\)
\(564\) 0 0
\(565\) 2.53553 + 4.39167i 0.106671 + 0.184759i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.92893 + 5.07306i 0.122787 + 0.212674i 0.920866 0.389880i \(-0.127483\pi\)
−0.798079 + 0.602553i \(0.794150\pi\)
\(570\) 0 0
\(571\) −13.7279 + 23.7775i −0.574496 + 0.995056i 0.421601 + 0.906782i \(0.361468\pi\)
−0.996096 + 0.0882740i \(0.971865\pi\)
\(572\) 0 0
\(573\) −3.38478 −0.141401
\(574\) 0 0
\(575\) −2.24264 −0.0935246
\(576\) 0 0
\(577\) 16.7929 29.0861i 0.699097 1.21087i −0.269683 0.962949i \(-0.586919\pi\)
0.968780 0.247923i \(-0.0797479\pi\)
\(578\) 0 0
\(579\) 4.82843 + 8.36308i 0.200663 + 0.347558i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.70711 + 8.15295i 0.194948 + 0.337661i
\(584\) 0 0
\(585\) −3.41421 + 5.91359i −0.141160 + 0.244497i
\(586\) 0 0
\(587\) −42.1421 −1.73939 −0.869696 0.493588i \(-0.835685\pi\)
−0.869696 + 0.493588i \(0.835685\pi\)
\(588\) 0 0
\(589\) 3.51472 0.144821
\(590\) 0 0
\(591\) −0.778175 + 1.34784i −0.0320098 + 0.0554426i
\(592\) 0 0
\(593\) −20.2782 35.1228i −0.832725 1.44232i −0.895869 0.444317i \(-0.853446\pi\)
0.0631447 0.998004i \(-0.479887\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.05025 + 8.74729i 0.206693 + 0.358003i
\(598\) 0 0
\(599\) 6.84315 11.8527i 0.279603 0.484287i −0.691683 0.722201i \(-0.743130\pi\)
0.971286 + 0.237914i \(0.0764637\pi\)
\(600\) 0 0
\(601\) 38.2843 1.56165 0.780824 0.624751i \(-0.214800\pi\)
0.780824 + 0.624751i \(0.214800\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) −5.00000 + 8.66025i −0.203279 + 0.352089i
\(606\) 0 0
\(607\) −2.96447 5.13461i −0.120324 0.208407i 0.799571 0.600571i \(-0.205060\pi\)
−0.919895 + 0.392164i \(0.871727\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.5711 21.7737i −0.508571 0.880871i
\(612\) 0 0
\(613\) −3.34315 + 5.79050i −0.135028 + 0.233876i −0.925608 0.378483i \(-0.876446\pi\)
0.790580 + 0.612359i \(0.209779\pi\)
\(614\) 0 0
\(615\) 3.07107 0.123837
\(616\) 0 0
\(617\) −8.58579 −0.345651 −0.172825 0.984952i \(-0.555290\pi\)
−0.172825 + 0.984952i \(0.555290\pi\)
\(618\) 0 0
\(619\) 0.464466 0.804479i 0.0186685 0.0323347i −0.856540 0.516080i \(-0.827391\pi\)
0.875209 + 0.483745i \(0.160724\pi\)
\(620\) 0 0
\(621\) 2.70711 + 4.68885i 0.108632 + 0.188157i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −0.414214 + 0.717439i −0.0165421 + 0.0286518i
\(628\) 0 0
\(629\) 3.27208 0.130466
\(630\) 0 0
\(631\) 7.62742 0.303643 0.151821 0.988408i \(-0.451486\pi\)
0.151821 + 0.988408i \(0.451486\pi\)
\(632\) 0 0
\(633\) −2.30761 + 3.99690i −0.0917193 + 0.158863i
\(634\) 0 0
\(635\) 6.12132 + 10.6024i 0.242917 + 0.420745i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 20.4853 + 35.4815i 0.810385 + 1.40363i
\(640\) 0 0
\(641\) 12.1421 21.0308i 0.479586 0.830666i −0.520140 0.854081i \(-0.674120\pi\)
0.999726 + 0.0234143i \(0.00745369\pi\)
\(642\) 0 0
\(643\) 12.2132 0.481642 0.240821 0.970570i \(-0.422583\pi\)
0.240821 + 0.970570i \(0.422583\pi\)
\(644\) 0 0
\(645\) −0.142136 −0.00559658
\(646\) 0 0
\(647\) 5.07107 8.78335i 0.199364 0.345309i −0.748958 0.662617i \(-0.769446\pi\)
0.948322 + 0.317308i \(0.102779\pi\)
\(648\) 0 0
\(649\) 5.12132 + 8.87039i 0.201029 + 0.348193i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17.1421 29.6910i −0.670824 1.16190i −0.977671 0.210142i \(-0.932607\pi\)
0.306847 0.951759i \(-0.400726\pi\)
\(654\) 0 0
\(655\) 5.87868 10.1822i 0.229699 0.397850i
\(656\) 0 0
\(657\) 14.6274 0.570670
\(658\) 0 0
\(659\) 0.514719 0.0200506 0.0100253 0.999950i \(-0.496809\pi\)
0.0100253 + 0.999950i \(0.496809\pi\)
\(660\) 0 0
\(661\) 12.5858 21.7992i 0.489530 0.847891i −0.510397 0.859939i \(-0.670502\pi\)
0.999927 + 0.0120474i \(0.00383490\pi\)
\(662\) 0 0
\(663\) −0.207107 0.358719i −0.00804336 0.0139315i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.12132 + 1.94218i 0.0434177 + 0.0752017i
\(668\) 0 0
\(669\) 4.01472 6.95370i 0.155218 0.268845i
\(670\) 0 0
\(671\) 1.17157 0.0452281
\(672\) 0 0
\(673\) 45.1716 1.74124 0.870618 0.491959i \(-0.163719\pi\)
0.870618 + 0.491959i \(0.163719\pi\)
\(674\) 0 0
\(675\) −1.20711 + 2.09077i −0.0464616 + 0.0804738i
\(676\) 0 0
\(677\) −10.9645 18.9910i −0.421399 0.729884i 0.574678 0.818380i \(-0.305127\pi\)
−0.996077 + 0.0884958i \(0.971794\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.914214 + 1.58346i 0.0350327 + 0.0606785i
\(682\) 0 0
\(683\) 9.41421 16.3059i 0.360225 0.623928i −0.627773 0.778397i \(-0.716033\pi\)
0.987998 + 0.154469i \(0.0493666\pi\)
\(684\) 0 0
\(685\) −3.31371 −0.126610
\(686\) 0 0
\(687\) 9.89949 0.377689
\(688\) 0 0
\(689\) −11.3640 + 19.6830i −0.432932 + 0.749861i
\(690\) 0 0
\(691\) 9.07107 + 15.7116i 0.345080 + 0.597696i 0.985368 0.170439i \(-0.0545186\pi\)
−0.640289 + 0.768134i \(0.721185\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.707107 1.22474i −0.0268221 0.0464572i
\(696\) 0 0
\(697\) 1.53553 2.65962i 0.0581625 0.100740i
\(698\) 0 0
\(699\) −8.48528 −0.320943
\(700\) 0 0
\(701\) −8.85786 −0.334557 −0.167278 0.985910i \(-0.553498\pi\)
−0.167278 + 0.985910i \(0.553498\pi\)
\(702\) 0 0
\(703\) 7.89949 13.6823i 0.297935 0.516039i
\(704\) 0 0
\(705\) −2.15685 3.73578i −0.0812318 0.140698i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 16.3284 + 28.2817i 0.613227 + 1.06214i 0.990693 + 0.136117i \(0.0434622\pi\)
−0.377466 + 0.926024i \(0.623204\pi\)
\(710\) 0 0
\(711\) −20.7279 + 35.9018i −0.777358 + 1.34642i
\(712\) 0 0
\(713\) −3.94113 −0.147596
\(714\) 0 0
\(715\) 2.41421 0.0902865
\(716\) 0 0
\(717\) 1.37868 2.38794i 0.0514877 0.0891794i
\(718\) 0 0
\(719\) 4.84924 + 8.39913i 0.180846 + 0.313235i 0.942169 0.335138i \(-0.108783\pi\)
−0.761323 + 0.648373i \(0.775450\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −5.46447 9.46473i −0.203226 0.351997i
\(724\) 0 0
\(725\) −0.500000 + 0.866025i −0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) 18.6863 0.693036 0.346518 0.938043i \(-0.387364\pi\)
0.346518 + 0.938043i \(0.387364\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) −0.0710678 + 0.123093i −0.00262854 + 0.00455276i
\(732\) 0 0
\(733\) −16.3492 28.3177i −0.603873 1.04594i −0.992228 0.124429i \(-0.960290\pi\)
0.388355 0.921510i \(-0.373043\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.707107 + 1.22474i 0.0260466 + 0.0451141i
\(738\) 0 0
\(739\) −17.3995 + 30.1368i −0.640051 + 1.10860i 0.345370 + 0.938467i \(0.387753\pi\)
−0.985421 + 0.170134i \(0.945580\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 13.8995 0.509923 0.254962 0.966951i \(-0.417937\pi\)
0.254962 + 0.966951i \(0.417937\pi\)
\(744\) 0 0
\(745\) −7.41421 + 12.8418i −0.271636 + 0.470487i
\(746\) 0 0
\(747\) 16.0000 + 27.7128i 0.585409 + 1.01396i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 9.81371 + 16.9978i 0.358107 + 0.620260i 0.987645 0.156710i \(-0.0500889\pi\)
−0.629537 + 0.776970i \(0.716756\pi\)
\(752\) 0 0
\(753\) −4.87868 + 8.45012i −0.177789 + 0.307940i
\(754\) 0 0
\(755\) −4.65685 −0.169480
\(756\) 0 0
\(757\) 36.7696 1.33641 0.668206 0.743976i \(-0.267062\pi\)
0.668206 + 0.743976i \(0.267062\pi\)
\(758\) 0 0
\(759\) 0.464466 0.804479i 0.0168591 0.0292007i
\(760\) 0 0
\(761\) −17.7782 30.7927i −0.644458 1.11623i −0.984426 0.175798i \(-0.943750\pi\)
0.339968 0.940437i \(-0.389584\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.585786 + 1.01461i 0.0211792 + 0.0366834i
\(766\) 0 0
\(767\) −12.3640 + 21.4150i −0.446437 + 0.773251i
\(768\) 0 0
\(769\) −1.51472 −0.0546222 −0.0273111 0.999627i \(-0.508694\pi\)
−0.0273111 + 0.999627i \(0.508694\pi\)
\(770\) 0 0
\(771\) 2.68629 0.0967444
\(772\) 0 0
\(773\) −7.69239 + 13.3236i −0.276676 + 0.479217i −0.970557 0.240873i \(-0.922566\pi\)
0.693881 + 0.720090i \(0.255900\pi\)
\(774\) 0 0
\(775\) −0.878680 1.52192i −0.0315631 0.0546689i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.41421 12.8418i −0.265642 0.460105i
\(780\) 0 0
\(781\) 7.24264 12.5446i 0.259162 0.448882i
\(782\) 0 0
\(783\) 2.41421 0.0862770
\(784\) 0 0
\(785\) 6.48528 0.231470
\(786\) 0 0
\(787\) −22.4203 + 38.8331i −0.799198 + 1.38425i 0.120941 + 0.992660i \(0.461409\pi\)
−0.920139 + 0.391591i \(0.871925\pi\)
\(788\) 0 0
\(789\) −3.10051 5.37023i −0.110381 0.191185i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.41421 + 2.44949i 0.0502202 + 0.0869839i
\(794\) 0 0
\(795\) −1.94975 + 3.37706i −0.0691504 + 0.119772i
\(796\) 0 0
\(797\) 50.0711 1.77361 0.886804 0.462146i \(-0.152920\pi\)
0.886804 + 0.462146i \(0.152920\pi\)
\(798\) 0 0
\(799\) −4.31371 −0.152608
\(800\) 0