Properties

Label 2016.2.s.v.865.2
Level $2016$
Weight $2$
Character 2016.865
Analytic conductor $16.098$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.0978410475\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 672)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.2
Root \(0.500000 - 1.51496i\) of defining polynomial
Character \(\chi\) \(=\) 2016.865
Dual form 2016.2.s.v.289.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.227452 + 0.393958i) q^{5} +(-2.16908 + 1.51496i) q^{7} +O(q^{10})\) \(q+(0.227452 + 0.393958i) q^{5} +(-2.16908 + 1.51496i) q^{7} +(2.89653 - 5.01694i) q^{11} -5.88325 q^{13} +(1.45490 - 2.51997i) q^{17} +(2.94163 + 5.09505i) q^{19} +(1.45490 + 2.51997i) q^{23} +(2.39653 - 4.15091i) q^{25} -3.54510 q^{29} +(-2.16908 + 3.75696i) q^{31} +(-1.09019 - 0.509947i) q^{35} +(-3.85144 - 6.67088i) q^{37} -9.58612 q^{41} -10.7931 q^{43} +(-2.45490 - 4.25202i) q^{47} +(2.40981 - 6.57212i) q^{49} +(6.56561 - 11.3720i) q^{53} +2.63529 q^{55} +(0.896531 - 1.55284i) q^{59} +(-2.33816 - 4.04981i) q^{61} +(-1.33816 - 2.31776i) q^{65} +(3.94163 - 6.82710i) q^{67} -0.909808 q^{71} +(-2.60347 + 4.50934i) q^{73} +(1.31764 + 15.2703i) q^{77} +(-1.37602 - 2.38333i) q^{79} +9.97345 q^{83} +1.32368 q^{85} +(-2.45490 - 4.25202i) q^{89} +(12.7612 - 8.91288i) q^{91} +(-1.33816 + 2.31776i) q^{95} -5.79306 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{7} + O(q^{10}) \) \( 6q + 3q^{7} - 6q^{13} + 6q^{17} + 3q^{19} + 6q^{23} - 3q^{25} - 24q^{29} + 3q^{31} - 12q^{35} - 3q^{37} + 12q^{41} - 30q^{43} - 12q^{47} + 9q^{49} + 6q^{53} + 24q^{55} - 12q^{59} + 18q^{61} + 24q^{65} + 9q^{67} - 33q^{73} + 12q^{77} - 27q^{79} + 36q^{83} + 72q^{85} - 12q^{89} + 51q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1765\) \(1793\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0
\(4\) 0 0
\(5\) 0.227452 + 0.393958i 0.101720 + 0.176184i 0.912393 0.409315i \(-0.134232\pi\)
−0.810674 + 0.585498i \(0.800899\pi\)
\(6\) 0 0
\(7\) −2.16908 + 1.51496i −0.819835 + 0.572600i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.89653 5.01694i 0.873337 1.51266i 0.0148132 0.999890i \(-0.495285\pi\)
0.858524 0.512774i \(-0.171382\pi\)
\(12\) 0 0
\(13\) −5.88325 −1.63172 −0.815861 0.578249i \(-0.803736\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.45490 2.51997i 0.352866 0.611182i −0.633884 0.773428i \(-0.718540\pi\)
0.986750 + 0.162246i \(0.0518738\pi\)
\(18\) 0 0
\(19\) 2.94163 + 5.09505i 0.674856 + 1.16888i 0.976511 + 0.215467i \(0.0691274\pi\)
−0.301656 + 0.953417i \(0.597539\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.45490 + 2.51997i 0.303368 + 0.525450i 0.976897 0.213712i \(-0.0685554\pi\)
−0.673528 + 0.739161i \(0.735222\pi\)
\(24\) 0 0
\(25\) 2.39653 4.15091i 0.479306 0.830183i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.54510 −0.658308 −0.329154 0.944276i \(-0.606763\pi\)
−0.329154 + 0.944276i \(0.606763\pi\)
\(30\) 0 0
\(31\) −2.16908 + 3.75696i −0.389578 + 0.674769i −0.992393 0.123112i \(-0.960713\pi\)
0.602815 + 0.797881i \(0.294046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.09019 0.509947i −0.184276 0.0861968i
\(36\) 0 0
\(37\) −3.85144 6.67088i −0.633172 1.09669i −0.986899 0.161338i \(-0.948419\pi\)
0.353727 0.935349i \(-0.384914\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.58612 −1.49710 −0.748551 0.663078i \(-0.769250\pi\)
−0.748551 + 0.663078i \(0.769250\pi\)
\(42\) 0 0
\(43\) −10.7931 −1.64593 −0.822963 0.568095i \(-0.807681\pi\)
−0.822963 + 0.568095i \(0.807681\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.45490 4.25202i −0.358085 0.620221i 0.629556 0.776955i \(-0.283237\pi\)
−0.987641 + 0.156734i \(0.949903\pi\)
\(48\) 0 0
\(49\) 2.40981 6.57212i 0.344258 0.938875i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.56561 11.3720i 0.901856 1.56206i 0.0767730 0.997049i \(-0.475538\pi\)
0.825083 0.565012i \(-0.191128\pi\)
\(54\) 0 0
\(55\) 2.63529 0.355342
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.896531 1.55284i 0.116718 0.202162i −0.801747 0.597664i \(-0.796096\pi\)
0.918465 + 0.395501i \(0.129429\pi\)
\(60\) 0 0
\(61\) −2.33816 4.04981i −0.299370 0.518525i 0.676622 0.736331i \(-0.263443\pi\)
−0.975992 + 0.217806i \(0.930110\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.33816 2.31776i −0.165978 0.287482i
\(66\) 0 0
\(67\) 3.94163 6.82710i 0.481546 0.834063i −0.518229 0.855242i \(-0.673409\pi\)
0.999776 + 0.0211789i \(0.00674196\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.909808 −0.107974 −0.0539872 0.998542i \(-0.517193\pi\)
−0.0539872 + 0.998542i \(0.517193\pi\)
\(72\) 0 0
\(73\) −2.60347 + 4.50934i −0.304713 + 0.527778i −0.977197 0.212333i \(-0.931894\pi\)
0.672484 + 0.740111i \(0.265227\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.31764 + 15.2703i 0.150159 + 1.74021i
\(78\) 0 0
\(79\) −1.37602 2.38333i −0.154814 0.268146i 0.778177 0.628045i \(-0.216144\pi\)
−0.932991 + 0.359899i \(0.882811\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.97345 1.09473 0.547364 0.836895i \(-0.315631\pi\)
0.547364 + 0.836895i \(0.315631\pi\)
\(84\) 0 0
\(85\) 1.32368 0.143574
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.45490 4.25202i −0.260219 0.450713i 0.706081 0.708131i \(-0.250462\pi\)
−0.966300 + 0.257418i \(0.917128\pi\)
\(90\) 0 0
\(91\) 12.7612 8.91288i 1.33774 0.934324i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.33816 + 2.31776i −0.137292 + 0.237797i
\(96\) 0 0
\(97\) −5.79306 −0.588196 −0.294098 0.955775i \(-0.595019\pi\)
−0.294098 + 0.955775i \(0.595019\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.33816 14.4421i 0.829678 1.43704i −0.0686134 0.997643i \(-0.521858\pi\)
0.898291 0.439401i \(-0.144809\pi\)
\(102\) 0 0
\(103\) −0.396531 0.686812i −0.0390714 0.0676736i 0.845828 0.533455i \(-0.179107\pi\)
−0.884900 + 0.465781i \(0.845773\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.98672 10.3693i −0.578758 1.00244i −0.995622 0.0934699i \(-0.970204\pi\)
0.416864 0.908969i \(-0.363129\pi\)
\(108\) 0 0
\(109\) 2.30634 3.99470i 0.220907 0.382623i −0.734176 0.678959i \(-0.762432\pi\)
0.955084 + 0.296336i \(0.0957649\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 0 0
\(115\) −0.661842 + 1.14634i −0.0617171 + 0.106897i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.661842 + 7.67013i 0.0606709 + 0.703119i
\(120\) 0 0
\(121\) −11.2798 19.5372i −1.02544 1.77611i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 4.45490 0.398459
\(126\) 0 0
\(127\) 1.24797 0.110739 0.0553696 0.998466i \(-0.482366\pi\)
0.0553696 + 0.998466i \(0.482366\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.89653 + 5.01694i 0.253071 + 0.438332i 0.964370 0.264558i \(-0.0852260\pi\)
−0.711299 + 0.702890i \(0.751893\pi\)
\(132\) 0 0
\(133\) −14.0994 6.59512i −1.22257 0.571870i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.54510 + 2.67618i −0.132006 + 0.228642i −0.924450 0.381303i \(-0.875475\pi\)
0.792443 + 0.609945i \(0.208809\pi\)
\(138\) 0 0
\(139\) 5.70287 0.483711 0.241856 0.970312i \(-0.422244\pi\)
0.241856 + 0.970312i \(0.422244\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −17.0410 + 29.5159i −1.42504 + 2.46825i
\(144\) 0 0
\(145\) −0.806339 1.39662i −0.0669628 0.115983i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.54510 + 2.67618i 0.126579 + 0.219242i 0.922349 0.386357i \(-0.126267\pi\)
−0.795770 + 0.605599i \(0.792934\pi\)
\(150\) 0 0
\(151\) −0.862740 + 1.49431i −0.0702088 + 0.121605i −0.898993 0.437964i \(-0.855700\pi\)
0.828784 + 0.559569i \(0.189033\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.97345 −0.158511
\(156\) 0 0
\(157\) 2.79306 4.83773i 0.222911 0.386093i −0.732780 0.680466i \(-0.761778\pi\)
0.955691 + 0.294373i \(0.0951109\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.97345 3.26189i −0.549585 0.257073i
\(162\) 0 0
\(163\) −4.42835 7.67013i −0.346855 0.600771i 0.638834 0.769345i \(-0.279417\pi\)
−0.985689 + 0.168574i \(0.946084\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −17.4057 −1.34690 −0.673448 0.739234i \(-0.735188\pi\)
−0.673448 + 0.739234i \(0.735188\pi\)
\(168\) 0 0
\(169\) 21.6127 1.66251
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.33816 14.4421i −0.633938 1.09801i −0.986739 0.162315i \(-0.948104\pi\)
0.352801 0.935699i \(-0.385229\pi\)
\(174\) 0 0
\(175\) 1.09019 + 12.6343i 0.0824108 + 0.955064i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.09019 + 5.35237i −0.230972 + 0.400055i −0.958094 0.286453i \(-0.907524\pi\)
0.727123 + 0.686508i \(0.240857\pi\)
\(180\) 0 0
\(181\) −3.20694 −0.238370 −0.119185 0.992872i \(-0.538028\pi\)
−0.119185 + 0.992872i \(0.538028\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.75203 3.03461i 0.128812 0.223109i
\(186\) 0 0
\(187\) −8.42835 14.5983i −0.616342 1.06754i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.6763 + 18.4919i 0.772511 + 1.33803i 0.936183 + 0.351514i \(0.114333\pi\)
−0.163672 + 0.986515i \(0.552334\pi\)
\(192\) 0 0
\(193\) −8.20287 + 14.2078i −0.590456 + 1.02270i 0.403716 + 0.914885i \(0.367719\pi\)
−0.994171 + 0.107814i \(0.965615\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −24.6763 −1.75811 −0.879057 0.476716i \(-0.841827\pi\)
−0.879057 + 0.476716i \(0.841827\pi\)
\(198\) 0 0
\(199\) −6.90981 + 11.9681i −0.489823 + 0.848399i −0.999931 0.0117114i \(-0.996272\pi\)
0.510108 + 0.860110i \(0.329605\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.68959 5.37067i 0.539704 0.376947i
\(204\) 0 0
\(205\) −2.18038 3.77654i −0.152285 0.263765i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 34.0821 2.35751
\(210\) 0 0
\(211\) 11.5861 0.797622 0.398811 0.917033i \(-0.369423\pi\)
0.398811 + 0.917033i \(0.369423\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.45490 4.25202i −0.167423 0.289985i
\(216\) 0 0
\(217\) −0.986723 11.4352i −0.0669831 0.776272i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −8.55957 + 14.8256i −0.575779 + 0.997279i
\(222\) 0 0
\(223\) 20.4549 1.36976 0.684881 0.728655i \(-0.259854\pi\)
0.684881 + 0.728655i \(0.259854\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.86998 15.3633i 0.588721 1.01969i −0.405679 0.914016i \(-0.632965\pi\)
0.994400 0.105679i \(-0.0337017\pi\)
\(228\) 0 0
\(229\) 12.0994 + 20.9568i 0.799551 + 1.38486i 0.919909 + 0.392132i \(0.128262\pi\)
−0.120358 + 0.992731i \(0.538404\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.3382 + 19.6383i 0.742787 + 1.28655i 0.951221 + 0.308509i \(0.0998300\pi\)
−0.208434 + 0.978036i \(0.566837\pi\)
\(234\) 0 0
\(235\) 1.11675 1.93426i 0.0728485 0.126177i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.90981 −0.188220 −0.0941099 0.995562i \(-0.530001\pi\)
−0.0941099 + 0.995562i \(0.530001\pi\)
\(240\) 0 0
\(241\) −10.8700 + 18.8274i −0.700197 + 1.21278i 0.268200 + 0.963363i \(0.413571\pi\)
−0.968397 + 0.249413i \(0.919762\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.13726 0.545479i 0.200432 0.0348494i
\(246\) 0 0
\(247\) −17.3063 29.9755i −1.10118 1.90729i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.02655 0.506632 0.253316 0.967384i \(-0.418479\pi\)
0.253316 + 0.967384i \(0.418479\pi\)
\(252\) 0 0
\(253\) 16.8567 1.05977
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.45490 11.1802i −0.402646 0.697403i 0.591398 0.806379i \(-0.298576\pi\)
−0.994044 + 0.108976i \(0.965243\pi\)
\(258\) 0 0
\(259\) 18.4602 + 8.63491i 1.14706 + 0.536547i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.45490 7.71612i 0.274701 0.475796i −0.695359 0.718663i \(-0.744754\pi\)
0.970060 + 0.242867i \(0.0780877\pi\)
\(264\) 0 0
\(265\) 5.97345 0.366946
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3.02051 + 5.23168i −0.184164 + 0.318981i −0.943295 0.331957i \(-0.892291\pi\)
0.759130 + 0.650938i \(0.225624\pi\)
\(270\) 0 0
\(271\) −6.68236 11.5742i −0.405924 0.703081i 0.588504 0.808494i \(-0.299717\pi\)
−0.994429 + 0.105413i \(0.966384\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13.8833 24.0465i −0.837192 1.45006i
\(276\) 0 0
\(277\) −2.39653 + 4.15091i −0.143994 + 0.249404i −0.928997 0.370087i \(-0.879328\pi\)
0.785003 + 0.619491i \(0.212661\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.32368 −0.436894 −0.218447 0.975849i \(-0.570099\pi\)
−0.218447 + 0.975849i \(0.570099\pi\)
\(282\) 0 0
\(283\) −6.60347 + 11.4375i −0.392535 + 0.679891i −0.992783 0.119923i \(-0.961735\pi\)
0.600248 + 0.799814i \(0.295069\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.7931 14.5226i 1.22738 0.857240i
\(288\) 0 0
\(289\) 4.26651 + 7.38981i 0.250971 + 0.434695i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.54510 −0.440789 −0.220395 0.975411i \(-0.570735\pi\)
−0.220395 + 0.975411i \(0.570735\pi\)
\(294\) 0 0
\(295\) 0.815671 0.0474902
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.55957 14.8256i −0.495013 0.857387i
\(300\) 0 0
\(301\) 23.4110 16.3510i 1.34939 0.942458i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.06364 1.84227i 0.0609037 0.105488i
\(306\) 0 0
\(307\) −23.1086 −1.31888 −0.659439 0.751758i \(-0.729206\pi\)
−0.659439 + 0.751758i \(0.729206\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.70287 6.41356i 0.209971 0.363680i −0.741734 0.670694i \(-0.765997\pi\)
0.951705 + 0.307014i \(0.0993299\pi\)
\(312\) 0 0
\(313\) −7.29306 12.6320i −0.412228 0.714000i 0.582905 0.812540i \(-0.301916\pi\)
−0.995133 + 0.0985402i \(0.968583\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.682356 + 1.18188i 0.0383249 + 0.0663807i 0.884552 0.466442i \(-0.154464\pi\)
−0.846227 + 0.532823i \(0.821131\pi\)
\(318\) 0 0
\(319\) −10.2685 + 17.7855i −0.574925 + 0.995799i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 17.1191 0.952534
\(324\) 0 0
\(325\) −14.0994 + 24.4209i −0.782094 + 1.35463i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11.7665 + 5.50389i 0.648709 + 0.303439i
\(330\) 0 0
\(331\) 5.48672 + 9.50328i 0.301578 + 0.522348i 0.976493 0.215547i \(-0.0691534\pi\)
−0.674916 + 0.737895i \(0.735820\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.58612 0.195931
\(336\) 0 0
\(337\) −22.1722 −1.20780 −0.603900 0.797060i \(-0.706387\pi\)
−0.603900 + 0.797060i \(0.706387\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 12.5656 + 21.7643i 0.680466 + 1.17860i
\(342\) 0 0
\(343\) 4.72942 + 17.9062i 0.255365 + 0.966845i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.116746 + 0.202210i −0.00626725 + 0.0108552i −0.869142 0.494563i \(-0.835328\pi\)
0.862875 + 0.505418i \(0.168662\pi\)
\(348\) 0 0
\(349\) 7.35263 0.393577 0.196789 0.980446i \(-0.436949\pi\)
0.196789 + 0.980446i \(0.436949\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.58612 16.6037i 0.510218 0.883723i −0.489712 0.871884i \(-0.662898\pi\)
0.999930 0.0118391i \(-0.00376859\pi\)
\(354\) 0 0
\(355\) −0.206938 0.358427i −0.0109831 0.0190233i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.4694 18.1335i −0.552553 0.957049i −0.998089 0.0617857i \(-0.980320\pi\)
0.445537 0.895264i \(-0.353013\pi\)
\(360\) 0 0
\(361\) −7.80634 + 13.5210i −0.410860 + 0.711630i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.36866 −0.123981
\(366\) 0 0
\(367\) −12.5072 + 21.6632i −0.652872 + 1.13081i 0.329550 + 0.944138i \(0.393103\pi\)
−0.982423 + 0.186670i \(0.940230\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.98672 + 34.6133i 0.155063 + 1.79703i
\(372\) 0 0
\(373\) 10.1630 + 17.6029i 0.526222 + 0.911444i 0.999533 + 0.0305483i \(0.00972533\pi\)
−0.473311 + 0.880895i \(0.656941\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 20.8567 1.07417
\(378\) 0 0
\(379\) −20.7931 −1.06807 −0.534034 0.845463i \(-0.679325\pi\)
−0.534034 + 0.845463i \(0.679325\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.5861 + 21.7998i 0.643121 + 1.11392i 0.984732 + 0.174077i \(0.0556941\pi\)
−0.341611 + 0.939841i \(0.610973\pi\)
\(384\) 0 0
\(385\) −5.71615 + 3.99235i −0.291322 + 0.203469i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.2214 21.1681i 0.619650 1.07327i −0.369899 0.929072i \(-0.620608\pi\)
0.989549 0.144194i \(-0.0460589\pi\)
\(390\) 0 0
\(391\) 8.46698 0.428194
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.625956 1.08419i 0.0314952 0.0545514i
\(396\) 0 0
\(397\) 4.39653 + 7.61502i 0.220656 + 0.382187i 0.955007 0.296583i \(-0.0958470\pi\)
−0.734352 + 0.678769i \(0.762514\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.5596 + 28.6820i 0.826945 + 1.43231i 0.900423 + 0.435015i \(0.143257\pi\)
−0.0734778 + 0.997297i \(0.523410\pi\)
\(402\) 0 0
\(403\) 12.7612 22.1031i 0.635683 1.10103i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −44.6232 −2.21189
\(408\) 0 0
\(409\) 3.47345 6.01618i 0.171751 0.297481i −0.767281 0.641311i \(-0.778391\pi\)
0.939032 + 0.343830i \(0.111724\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.407836 + 4.72643i 0.0200683 + 0.232573i
\(414\) 0 0
\(415\) 2.26848 + 3.92912i 0.111355 + 0.192873i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 29.2254 1.42775 0.713876 0.700272i \(-0.246938\pi\)
0.713876 + 0.700272i \(0.246938\pi\)
\(420\) 0 0
\(421\) 33.2359 1.61982 0.809909 0.586556i \(-0.199516\pi\)
0.809909 + 0.586556i \(0.199516\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.97345 12.0784i −0.338262 0.585887i
\(426\) 0 0
\(427\) 11.2069 + 5.24215i 0.542342 + 0.253685i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.09019 5.35237i 0.148849 0.257815i −0.781953 0.623337i \(-0.785776\pi\)
0.930802 + 0.365523i \(0.119110\pi\)
\(432\) 0 0
\(433\) 16.6127 0.798354 0.399177 0.916874i \(-0.369296\pi\)
0.399177 + 0.916874i \(0.369296\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −8.55957 + 14.8256i −0.409460 + 0.709205i
\(438\) 0 0
\(439\) 13.8136 + 23.9258i 0.659286 + 1.14192i 0.980801 + 0.195012i \(0.0624747\pi\)
−0.321515 + 0.946905i \(0.604192\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.0133 17.3435i −0.475745 0.824015i 0.523869 0.851799i \(-0.324488\pi\)
−0.999614 + 0.0277842i \(0.991155\pi\)
\(444\) 0 0
\(445\) 1.11675 1.93426i 0.0529388 0.0916927i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −15.0371 −0.709644 −0.354822 0.934934i \(-0.615459\pi\)
−0.354822 + 0.934934i \(0.615459\pi\)
\(450\) 0 0
\(451\) −27.7665 + 48.0930i −1.30747 + 2.26461i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.41388 + 3.00015i 0.300687 + 0.140649i
\(456\) 0 0
\(457\) 21.0596 + 36.4762i 0.985125 + 1.70629i 0.641379 + 0.767224i \(0.278363\pi\)
0.343746 + 0.939063i \(0.388304\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −20.9098 −0.973867 −0.486933 0.873439i \(-0.661885\pi\)
−0.486933 + 0.873439i \(0.661885\pi\)
\(462\) 0 0
\(463\) −38.1457 −1.77278 −0.886390 0.462939i \(-0.846795\pi\)
−0.886390 + 0.462939i \(0.846795\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.76651 + 9.98789i 0.266842 + 0.462184i 0.968045 0.250778i \(-0.0806864\pi\)
−0.701202 + 0.712962i \(0.747353\pi\)
\(468\) 0 0
\(469\) 1.79306 + 20.7799i 0.0827959 + 0.959527i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −31.2624 + 54.1481i −1.43745 + 2.48973i
\(474\) 0 0
\(475\) 28.1988 1.29385
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.66184 + 6.34250i −0.167314 + 0.289796i −0.937475 0.348054i \(-0.886843\pi\)
0.770161 + 0.637850i \(0.220176\pi\)
\(480\) 0 0
\(481\) 22.6590 + 39.2465i 1.03316 + 1.78949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.31764 2.28223i −0.0598311 0.103631i
\(486\) 0 0
\(487\) 13.0258 22.5613i 0.590254 1.02235i −0.403943 0.914784i \(-0.632361\pi\)
0.994198 0.107567i \(-0.0343059\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.37919 −0.333018 −0.166509 0.986040i \(-0.553249\pi\)
−0.166509 + 0.986040i \(0.553249\pi\)
\(492\) 0 0
\(493\) −5.15777 + 8.93353i −0.232294 + 0.402346i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.97345 1.37832i 0.0885211 0.0618261i
\(498\) 0 0
\(499\) −0.175119 0.303315i −0.00783940 0.0135782i 0.862079 0.506774i \(-0.169162\pi\)
−0.869918 + 0.493196i \(0.835829\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14.9098 0.664795 0.332398 0.943139i \(-0.392142\pi\)
0.332398 + 0.943139i \(0.392142\pi\)
\(504\) 0 0
\(505\) 7.58612 0.337578
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.44886 + 14.6339i 0.374489 + 0.648635i 0.990250 0.139298i \(-0.0444847\pi\)
−0.615761 + 0.787933i \(0.711151\pi\)
\(510\) 0 0
\(511\) −1.18433 13.7253i −0.0523916 0.607170i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.180384 0.312434i 0.00794865 0.0137675i
\(516\) 0 0
\(517\) −28.4428 −1.25091
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.79306 6.56978i 0.166177 0.287827i −0.770896 0.636962i \(-0.780191\pi\)
0.937073 + 0.349134i \(0.113524\pi\)
\(522\) 0 0
\(523\) −21.2572 36.8185i −0.929511 1.60996i −0.784140 0.620584i \(-0.786896\pi\)
−0.145371 0.989377i \(-0.546438\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.31160 + 10.9320i 0.274938 + 0.476206i
\(528\) 0 0
\(529\) 7.26651 12.5860i 0.315935 0.547216i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 56.3976 2.44285
\(534\) 0 0
\(535\) 2.72338 4.71704i 0.117742 0.203935i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −25.9919 31.1262i −1.11955 1.34070i
\(540\) 0 0
\(541\) −7.03182 12.1795i −0.302322 0.523636i 0.674340 0.738421i \(-0.264428\pi\)
−0.976661 + 0.214785i \(0.931095\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.09833 0.0898824
\(546\) 0 0
\(547\) 4.49593 0.192232 0.0961161 0.995370i \(-0.469358\pi\)
0.0961161 + 0.995370i \(0.469358\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.4283 18.0624i −0.444263 0.769485i
\(552\) 0 0
\(553\) 6.59533 + 3.08503i 0.280462 + 0.131189i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.9303 27.5921i 0.674989 1.16912i −0.301483 0.953472i \(-0.597482\pi\)
0.976472 0.215644i \(-0.0691852\pi\)
\(558\) 0 0
\(559\) 63.4983 2.68569
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −23.0688 + 39.9563i −0.972233 + 1.68396i −0.283454 + 0.958986i \(0.591480\pi\)
−0.688779 + 0.724972i \(0.741853\pi\)
\(564\) 0 0
\(565\) −1.81962 3.15167i −0.0765518 0.132592i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.31160 14.3961i −0.348441 0.603517i 0.637532 0.770424i \(-0.279955\pi\)
−0.985973 + 0.166907i \(0.946622\pi\)
\(570\) 0 0
\(571\) 18.2532 31.6155i 0.763874 1.32307i −0.176966 0.984217i \(-0.556628\pi\)
0.940840 0.338852i \(-0.110038\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.9469 0.581626
\(576\) 0 0
\(577\) 7.59019 13.1466i 0.315984 0.547300i −0.663662 0.748032i \(-0.730999\pi\)
0.979646 + 0.200732i \(0.0643321\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −21.6332 + 15.1093i −0.897496 + 0.626841i
\(582\) 0 0
\(583\) −38.0350 65.8785i −1.57525 2.72841i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.20694 0.338737 0.169368 0.985553i \(-0.445827\pi\)
0.169368 + 0.985553i \(0.445827\pi\)
\(588\) 0 0
\(589\) −25.5225 −1.05164
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.77859 4.81266i −0.114103 0.197632i 0.803318 0.595550i \(-0.203066\pi\)
−0.917421 + 0.397918i \(0.869733\pi\)
\(594\) 0 0
\(595\) −2.87117 + 2.00532i −0.117707 + 0.0822103i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 17.7931 30.8185i 0.727005 1.25921i −0.231139 0.972921i \(-0.574245\pi\)
0.958143 0.286288i \(-0.0924216\pi\)
\(600\) 0 0
\(601\) 1.18038 0.0481489 0.0240744 0.999710i \(-0.492336\pi\)
0.0240744 + 0.999710i \(0.492336\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.13122 8.88753i 0.208614 0.361330i
\(606\) 0 0
\(607\) 6.16908 + 10.6852i 0.250395 + 0.433697i 0.963635 0.267223i \(-0.0861061\pi\)
−0.713239 + 0.700920i \(0.752773\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 14.4428 + 25.0157i 0.584294 + 1.01203i
\(612\) 0 0
\(613\) 10.5451 18.2646i 0.425912 0.737702i −0.570593 0.821233i \(-0.693287\pi\)
0.996505 + 0.0835312i \(0.0266198\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.3526 −0.618074 −0.309037 0.951050i \(-0.600007\pi\)
−0.309037 + 0.951050i \(0.600007\pi\)
\(618\) 0 0
\(619\) −9.21615 + 15.9628i −0.370428 + 0.641601i −0.989631 0.143630i \(-0.954122\pi\)
0.619203 + 0.785231i \(0.287456\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.7665 + 5.50389i 0.471415 + 0.220509i
\(624\) 0 0
\(625\) −10.9694 18.9995i −0.438775 0.759981i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −22.4139 −0.893700
\(630\) 0 0
\(631\) 5.91375 0.235423 0.117711 0.993048i \(-0.462444\pi\)
0.117711 + 0.993048i \(0.462444\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.283853 + 0.491647i 0.0112643 + 0.0195104i
\(636\) 0 0
\(637\) −14.1775 + 38.6655i −0.561734 + 1.53198i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.0821 39.9793i 0.911686 1.57909i 0.100005 0.994987i \(-0.468114\pi\)
0.811681 0.584100i \(-0.198553\pi\)
\(642\) 0 0
\(643\) 31.0555 1.22471 0.612355 0.790583i \(-0.290222\pi\)
0.612355 + 0.790583i \(0.290222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.51854 + 14.7545i −0.334898 + 0.580061i −0.983465 0.181097i \(-0.942035\pi\)
0.648567 + 0.761158i \(0.275369\pi\)
\(648\) 0 0
\(649\) −5.19366 8.99568i −0.203869 0.353111i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.06968 7.04889i −0.159259 0.275844i 0.775343 0.631541i \(-0.217577\pi\)
−0.934602 + 0.355696i \(0.884244\pi\)
\(654\) 0 0
\(655\) −1.31764 + 2.28223i −0.0514846 + 0.0891740i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −41.1191 −1.60177 −0.800887 0.598815i \(-0.795638\pi\)
−0.800887 + 0.598815i \(0.795638\pi\)
\(660\) 0 0
\(661\) 6.67105 11.5546i 0.259474 0.449422i −0.706627 0.707586i \(-0.749784\pi\)
0.966101 + 0.258164i \(0.0831175\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.608734 7.05465i −0.0236057 0.273568i
\(666\) 0 0
\(667\) −5.15777 8.93353i −0.199710 0.345908i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −27.0902 −1.04581
\(672\) 0 0
\(673\) 9.75837 0.376158 0.188079 0.982154i \(-0.439774\pi\)
0.188079 + 0.982154i \(0.439774\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16.2275 + 28.1068i 0.623672 + 1.08023i 0.988796 + 0.149272i \(0.0476931\pi\)
−0.365124 + 0.930959i \(0.618974\pi\)
\(678\) 0 0
\(679\) 12.5656 8.77624i 0.482224 0.336801i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.4827 + 32.0129i −0.707219 + 1.22494i 0.258666 + 0.965967i \(0.416717\pi\)
−0.965885 + 0.258973i \(0.916616\pi\)
\(684\) 0 0
\(685\) −1.40574 −0.0537106
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −38.6272 + 66.9042i −1.47158 + 2.54885i
\(690\) 0 0
\(691\) 7.12596 + 12.3425i 0.271084 + 0.469531i 0.969140 0.246512i \(-0.0792845\pi\)
−0.698056 + 0.716044i \(0.745951\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.29713 + 2.24669i 0.0492029 + 0.0852220i
\(696\) 0 0
\(697\) −13.9469 + 24.1567i −0.528276 + 0.915001i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 51.3937 1.94111 0.970556 0.240876i \(-0.0774347\pi\)
0.970556 + 0.240876i \(0.0774347\pi\)
\(702\) 0 0
\(703\) 22.6590 39.2465i 0.854599 1.48021i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.79306 + 43.9580i 0.142653 + 1.65321i
\(708\) 0 0
\(709\) −12.5861 21.7998i −0.472682 0.818709i 0.526829 0.849971i \(-0.323381\pi\)
−0.999511 + 0.0312621i \(0.990047\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −12.6232 −0.472743
\(714\) 0 0
\(715\) −15.5041 −0.579819
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4.09019 7.08442i −0.152538 0.264204i 0.779622 0.626251i \(-0.215411\pi\)
−0.932160 + 0.362047i \(0.882078\pi\)
\(720\) 0 0
\(721\) 1.90060 + 0.889022i 0.0707820 + 0.0331089i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.49593 + 14.7154i −0.315531 + 0.546516i
\(726\) 0 0
\(727\) −26.9614 −0.999942 −0.499971 0.866042i \(-0.666656\pi\)
−0.499971 + 0.866042i \(0.666656\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −15.7029 + 27.1982i −0.580792 + 1.00596i
\(732\) 0 0
\(733\) 10.7347 + 18.5930i 0.396495 + 0.686749i 0.993291 0.115644i \(-0.0368931\pi\)
−0.596796 + 0.802393i \(0.703560\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −22.8341 39.5498i −0.841105 1.45684i
\(738\) 0 0
\(739\) −0.671052 + 1.16230i −0.0246850 + 0.0427557i −0.878104 0.478470i \(-0.841192\pi\)
0.853419 + 0.521226i \(0.174525\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 26.9919 0.990236 0.495118 0.868826i \(-0.335125\pi\)
0.495118 + 0.868826i \(0.335125\pi\)
\(744\) 0 0
\(745\) −0.702870 + 1.21741i −0.0257512 + 0.0446024i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 28.6947 + 13.4222i 1.04848 + 0.490437i
\(750\) 0 0
\(751\) −6.44360 11.1606i −0.235130 0.407258i 0.724180 0.689611i \(-0.242218\pi\)
−0.959311 + 0.282353i \(0.908885\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.784928 −0.0285664
\(756\) 0 0
\(757\) −26.3897 −0.959151 −0.479575 0.877501i \(-0.659209\pi\)
−0.479575 + 0.877501i \(0.659209\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.2214 + 26.3643i 0.551776 + 0.955704i 0.998147 + 0.0608556i \(0.0193829\pi\)
−0.446371 + 0.894848i \(0.647284\pi\)
\(762\) 0 0
\(763\) 1.04916 + 12.1588i 0.0379823 + 0.440179i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.27452 + 9.13574i −0.190452 + 0.329872i
\(768\) 0 0
\(769\) 42.1191 1.51886 0.759428 0.650592i \(-0.225479\pi\)
0.759428 + 0.650592i \(0.225479\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 19.0145 32.9340i 0.683903 1.18455i −0.289877 0.957064i \(-0.593614\pi\)
0.973780 0.227491i \(-0.0730522\pi\)
\(774\) 0 0
\(775\) 10.3965 + 18.0073i 0.373454 + 0.646842i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −28.1988 48.8418i −1.01033 1.74994i
\(780\) 0 0
\(781\) −2.63529 + 4.56445i −0.0942980 + 0.163329i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.54115 0.0906976
\(786\) 0 0
\(787\) −15.7931 + 27.3544i −0.562962 + 0.975079i 0.434274 + 0.900781i \(0.357005\pi\)
−0.997236 + 0.0742978i \(0.976328\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 17.3526 12.1197i 0.616989 0.430925i
\(792\) 0 0
\(793\) 13.7560 + 23.8261i 0.488489 + 0.846088i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −45.2133 −1.60154 −0.800768 0.598974i \(-0.795575\pi\)
−0.800768 + 0.598974i \(0.795575\pi\)
\(798\) 0 0
\(799\) −14.2866 −0.505424
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15.0821 + 26.1229i 0.532234 + 0.921857i
\(804\) 0